LMFDB - Embedded newform 32.9.h.a.11.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [32,9,Mod(3,32)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(32, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("32.3");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 32 = 2^{5} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	32.h (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.0361155220$
Analytic rank:	$0$
Dimension:	$124$
Relative dimension:	$31$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			11.13
Character	$\chi$	$=$	32.11
Dual form			32.9.h.a.3.13

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.39384 + 15.0634i) q^{2} +(3.10339 + 7.49224i) q^{3} +(-197.813 - 162.499i) q^{4} +(88.9809 - 214.819i) q^{5} +(-129.598 + 6.33566i) q^{6} +(-1135.75 + 1135.75i) q^{7} +(3514.77 - 2103.24i) q^{8} +(4592.82 - 4592.82i) q^{9} +O(q^{10})$	\(q+(-5.39384 + 15.0634i) q^{2} +(3.10339 + 7.49224i) q^{3} +(-197.813 - 162.499i) q^{4} +(88.9809 - 214.819i) q^{5} +(-129.598 + 6.33566i) q^{6} +(-1135.75 + 1135.75i) q^{7} +(3514.77 - 2103.24i) q^{8} +(4592.82 - 4592.82i) q^{9} +(2755.96 + 2499.06i) q^{10} +(6740.21 - 16272.3i) q^{11} +(603.593 - 1986.36i) q^{12} +(20108.1 + 48545.2i) q^{13} +(-10982.2 - 23234.3i) q^{14} +1885.62 q^{15} +(12723.9 + 64288.9i) q^{16} -36792.0i q^{17} +(44410.7 + 93956.6i) q^{18} +(-34824.1 + 14424.6i) q^{19} +(-52509.5 + 28034.6i) q^{20} +(-12033.9 - 4984.62i) q^{21} +(208761. + 189301. i) q^{22} +(358200. + 358200. i) q^{23} +(26665.7 + 19806.3i) q^{24} +(237984. + 237984. i) q^{25} +(-839716. + 41051.3i) q^{26} +(97820.4 + 40518.5i) q^{27} +(409223. - 40107.4i) q^{28} +(455103. - 188510. i) q^{29} +(-10170.7 + 28403.8i) q^{30} -1.59181e6i q^{31} +(-1.03704e6 - 155098. i) q^{32} +142833. q^{33} +(554213. + 198450. i) q^{34} +(142920. + 345040. i) q^{35} +(-1.65485e6 + 162189. i) q^{36} +(308866. - 745668. i) q^{37} +(-29448.3 - 602374. i) q^{38} +(-301309. + 301309. i) q^{39} +(-139069. - 942187. i) q^{40} +(2.70399e6 - 2.70399e6i) q^{41} +(139995. - 154386. i) q^{42} +(518225. - 1.25111e6i) q^{43} +(-3.97754e6 + 2.12359e6i) q^{44} +(-577952. - 1.39530e6i) q^{45} +(-7.32779e6 + 3.46364e6i) q^{46} +584083. q^{47} +(-442181. + 294844. i) q^{48} +3.18496e6i q^{49} +(-4.86850e6 + 2.30120e6i) q^{50} +(275655. - 114180. i) q^{51} +(3.91092e6 - 1.28704e7i) q^{52} +(5.98108e6 + 2.47744e6i) q^{53} +(-1.13798e6 + 1.25496e6i) q^{54} +(-2.89585e6 - 2.89585e6i) q^{55} +(-1.60313e6 + 6.38064e6i) q^{56} +(-216145. - 216145. i) q^{57} +(384849. + 7.87219e6i) q^{58} +(-8.77638e6 - 3.63530e6i) q^{59} +(-372999. - 306411. i) q^{60} +(1.95565e7 - 8.10055e6i) q^{61} +(2.39781e7 + 8.58597e6i) q^{62} +1.04326e7i q^{63} +(7.92995e6 - 1.47848e7i) q^{64} +1.22177e7 q^{65} +(-770420. + 2.15156e6i) q^{66} +(728387. + 1.75848e6i) q^{67} +(-5.97868e6 + 7.27794e6i) q^{68} +(-1.57209e6 + 3.79535e6i) q^{69} +(-5.96836e6 + 291776. i) q^{70} +(-1.02024e7 + 1.02024e7i) q^{71} +(6.48288e6 - 2.58025e7i) q^{72} +(-1.36169e7 + 1.36169e7i) q^{73} +(9.56633e6 + 8.67459e6i) q^{74} +(-1.04448e6 + 2.52159e6i) q^{75} +(9.23265e6 + 2.80552e6i) q^{76} +(1.08260e7 + 2.61364e7i) q^{77} +(-2.91353e6 - 6.16396e6i) q^{78} -4.65357e7 q^{79} +(1.49427e7 + 2.98715e6i) q^{80} -4.17566e7i q^{81} +(2.61465e7 + 5.53163e7i) q^{82} +(-6.00110e7 + 2.48574e7i) q^{83} +(1.57047e6 + 2.94153e6i) q^{84} +(-7.90362e6 - 3.27379e6i) q^{85} +(1.60507e7 + 1.45545e7i) q^{86} +(2.82472e6 + 2.82472e6i) q^{87} +(-1.05344e7 - 7.13696e7i) q^{88} +(4.92785e7 + 4.92785e7i) q^{89} +(2.41354e7 - 1.17991e6i) q^{90} +(-7.79727e7 - 3.22974e7i) q^{91} +(-1.26494e7 - 1.29064e8i) q^{92} +(1.19262e7 - 4.94000e6i) q^{93} +(-3.15045e6 + 8.79828e6i) q^{94} +8.76439e6i q^{95} +(-2.05631e6 - 8.25110e6i) q^{96} -5.51041e7 q^{97} +(-4.79764e7 - 1.71792e7i) q^{98} +(-4.37792e7 - 1.05692e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 124 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 124 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 124 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 34996 q^{10} - 4 q^{11} - 45364 q^{12} - 4 q^{13} + 145580 q^{14} - 8 q^{15} - 278384 q^{16} - 131224 q^{18} - 4 q^{19} + 689996 q^{20} - 4 q^{21} + 6048 q^{22} + 845564 q^{23} - 310832 q^{24} - 4 q^{25} + 1682096 q^{26} - 51076 q^{27} - 1807624 q^{28} - 4 q^{29} - 3968188 q^{30} + 2420456 q^{32} - 8 q^{33} + 4139280 q^{34} - 2415748 q^{35} - 2364816 q^{36} - 4 q^{37} - 4553644 q^{38} + 7650044 q^{39} - 14971800 q^{40} - 4 q^{41} + 17019656 q^{42} - 1859716 q^{43} + 13377860 q^{44} - 26248 q^{45} + 11790684 q^{46} - 8 q^{47} - 21819984 q^{48} - 49149676 q^{50} - 27697792 q^{51} - 33503196 q^{52} - 5358724 q^{53} + 82403296 q^{54} + 46326780 q^{55} + 87708200 q^{56} - 4 q^{57} - 37235424 q^{58} - 44938756 q^{59} - 167711176 q^{60} + 48952060 q^{61} + 23721528 q^{62} + 27135128 q^{64} - 8 q^{65} + 226680332 q^{66} + 93380476 q^{67} - 491760 q^{68} - 17273092 q^{69} - 167238952 q^{70} - 79832068 q^{71} - 184202092 q^{72} - 4 q^{73} + 28015148 q^{74} - 27399560 q^{75} + 201789948 q^{76} - 94964356 q^{77} + 473461108 q^{78} + 144406520 q^{79} - 447998920 q^{80} - 231632004 q^{82} - 140384644 q^{83} + 263072 q^{84} + 1562496 q^{85} + 268005440 q^{86} - 149712644 q^{87} + 220344096 q^{88} - 4 q^{89} + 51924392 q^{90} + 350400764 q^{91} - 622977496 q^{92} + 26240 q^{93} - 100742552 q^{94} + 101686144 q^{96} - 8 q^{97} + 721239576 q^{98} - 630043272 q^{99}+O(q^{100}) \) 124 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 34996 * q^10 - 4 * q^11 - 45364 * q^12 - 4 * q^13 + 145580 * q^14 - 8 * q^15 - 278384 * q^16 - 131224 * q^18 - 4 * q^19 + 689996 * q^20 - 4 * q^21 + 6048 * q^22 + 845564 * q^23 - 310832 * q^24 - 4 * q^25 + 1682096 * q^26 - 51076 * q^27 - 1807624 * q^28 - 4 * q^29 - 3968188 * q^30 + 2420456 * q^32 - 8 * q^33 + 4139280 * q^34 - 2415748 * q^35 - 2364816 * q^36 - 4 * q^37 - 4553644 * q^38 + 7650044 * q^39 - 14971800 * q^40 - 4 * q^41 + 17019656 * q^42 - 1859716 * q^43 + 13377860 * q^44 - 26248 * q^45 + 11790684 * q^46 - 8 * q^47 - 21819984 * q^48 - 49149676 * q^50 - 27697792 * q^51 - 33503196 * q^52 - 5358724 * q^53 + 82403296 * q^54 + 46326780 * q^55 + 87708200 * q^56 - 4 * q^57 - 37235424 * q^58 - 44938756 * q^59 - 167711176 * q^60 + 48952060 * q^61 + 23721528 * q^62 + 27135128 * q^64 - 8 * q^65 + 226680332 * q^66 + 93380476 * q^67 - 491760 * q^68 - 17273092 * q^69 - 167238952 * q^70 - 79832068 * q^71 - 184202092 * q^72 - 4 * q^73 + 28015148 * q^74 - 27399560 * q^75 + 201789948 * q^76 - 94964356 * q^77 + 473461108 * q^78 + 144406520 * q^79 - 447998920 * q^80 - 231632004 * q^82 - 140384644 * q^83 + 263072 * q^84 + 1562496 * q^85 + 268005440 * q^86 - 149712644 * q^87 + 220344096 * q^88 - 4 * q^89 + 51924392 * q^90 + 350400764 * q^91 - 622977496 * q^92 + 26240 * q^93 - 100742552 * q^94 + 101686144 * q^96 - 8 * q^97 + 721239576 * q^98 - 630043272 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/32\mathbb{Z}\right)^\times$.

$n$	$5$	$31$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−5.39384	+	15.0634i	−0.337115	+	0.941463i
$2$	−5.39384	+	15.0634i	−0.337115	+	0.941463i
$3$	3.10339	+	7.49224i	0.0383134	+	0.0924968i	0.941878	−	0.335955i	$-0.109059\pi$
$3$	3.10339	+	7.49224i	0.0383134	+	0.0924968i	−0.903565	+	0.428452i	$0.859059\pi$
$4$	−197.813	−	162.499i	−0.772707	−	0.634763i
$5$	88.9809	−	214.819i	0.142369	−	0.343710i	−0.836570	−	0.547860i	$-0.815443\pi$
$5$	88.9809	−	214.819i	0.142369	−	0.343710i	0.978940	+	0.204149i	$0.0654428\pi$
$6$	−129.598	+	6.33566i	−0.0999983	+	0.00488863i
$7$	−1135.75	+	1135.75i	−0.473031	+	0.473031i	−0.902894	−	0.429863i	$-0.858562\pi$
$7$	−1135.75	+	1135.75i	−0.473031	+	0.473031i	0.429863	+	0.902894i	$0.358562\pi$
$8$	3514.77	−	2103.24i	0.858097	−	0.513487i
$9$	4592.82	−	4592.82i	0.700019	−	0.700019i
$10$	2755.96	+	2499.06i	0.275596	+	0.249906i
$11$	6740.21	−	16272.3i	0.460365	−	1.11142i	−0.507882	−	0.861426i	$-0.669572\pi$
$11$	6740.21	−	16272.3i	0.460365	−	1.11142i	0.968248	−	0.249993i	$-0.0804284\pi$
$12$	603.593	−	1986.36i	0.0291085	−	0.0957928i
$13$	20108.1	+	48545.2i	0.704040	+	1.69970i	0.714382	+	0.699756i	$0.246708\pi$
$13$	20108.1	+	48545.2i	0.704040	+	1.69970i	−0.0103421	+	0.999947i	$0.503292\pi$
$14$	−10982.2	−	23234.3i	−0.285875	−	0.604807i
$15$	1885.62			0.0372467
$16$	12723.9	+	64288.9i	0.194152	+	0.980971i
$17$		−	36792.0i		−	0.440512i	−0.975442	−	0.220256i	$-0.929311\pi$
$17$		−	36792.0i		−	0.440512i	0.975442	−	0.220256i	$-0.0706893\pi$
$18$	44410.7	+	93956.6i	0.423055	+	0.895029i
$19$	−34824.1	+	14424.6i	−0.267218	+	0.110685i	−0.512269	−	0.858825i	$-0.671195\pi$
$19$	−34824.1	+	14424.6i	−0.267218	+	0.110685i	0.245052	+	0.969510i	$0.421195\pi$
$20$	−52509.5	+	28034.6i	−0.328184	+	0.175216i
$21$	−12033.9	−	4984.62i	−0.0618772	−	0.0256304i
$22$	208761.	+	189301.i	0.891165	+	0.808093i
$23$	358200.	+	358200.i	1.28001	+	1.28001i	0.940658	+	0.339355i	$0.110209\pi$
$23$	358200.	+	358200.i	1.28001	+	1.28001i	0.339355	+	0.940658i	$0.389791\pi$
$24$	26665.7	+	19806.3i	0.0803725	+	0.0596978i
$25$	237984.	+	237984.i	0.609239	+	0.609239i
$26$	−839716.	+	41051.3i	−1.83755	+	0.0898325i
$27$	97820.4	+	40518.5i	0.184066	+	0.0762428i
$28$	409223.	−	40107.4i	0.665776	−	0.0652517i
$29$	455103.	−	188510.i	0.643454	−	0.266527i	−0.0370033	−	0.999315i	$-0.511781\pi$
$29$	455103.	−	188510.i	0.643454	−	0.266527i	0.680457	+	0.732788i	$0.261781\pi$
$30$	−10170.7	+	28403.8i	−0.0125564	+	0.0350664i
$31$		−	1.59181e6i		−	1.72363i	−0.507221	−	0.861816i	$-0.669327\pi$
$31$		−	1.59181e6i		−	1.72363i	0.507221	−	0.861816i	$-0.330673\pi$
$32$	−1.03704e6	−	155098.i	−0.989000	−	0.147913i
$33$	142833.			0.120441
$34$	554213.	+	198450.i	0.414726	+	0.148503i
$35$	142920.	+	345040.i	0.0952404	+	0.229931i
$36$	−1.65485e6	+	162189.i	−0.985256	+	0.0965634i
$37$	308866.	−	745668.i	0.164802	−	0.397868i	−0.819807	−	0.572640i	$-0.805919\pi$
$37$	308866.	−	745668.i	0.164802	−	0.397868i	0.984609	+	0.174773i	$0.0559191\pi$
$38$	−29448.3	−	602374.i	−0.0141230	−	0.288890i
$39$	−301309.	+	301309.i	−0.130243	+	0.130243i
$40$	−139069.	−	942187.i	−0.0543240	−	0.368042i
$41$	2.70399e6	−	2.70399e6i	0.956908	−	0.956908i	−0.0422013	−	0.999109i	$-0.513437\pi$
$41$	2.70399e6	−	2.70399e6i	0.956908	−	0.956908i	0.999109	+	0.0422013i	$0.0134371\pi$
$42$	139995.	−	154386.i	0.0449898	−	0.0496148i
$43$	518225.	−	1.25111e6i	0.151581	−	0.365949i	−0.829789	−	0.558077i	$-0.811539\pi$
$43$	518225.	−	1.25111e6i	0.151581	−	0.365949i	0.981370	+	0.192129i	$0.0615392\pi$
$44$	−3.97754e6	+	2.12359e6i	−1.06122	+	0.566579i
$45$	−577952.	−	1.39530e6i	−0.140942	−	0.340265i
$46$	−7.32779e6	+	3.46364e6i	−1.63660	+	0.773574i
$47$	584083.			0.119697			0.0598484	−	0.998207i	$-0.480938\pi$
$47$	584083.			0.119697			0.0598484	+	0.998207i	$0.480938\pi$
$48$	−442181.	+	294844.i	−0.0832981	+	0.0555428i
$49$			3.18496e6i			0.552484i
$50$	−4.86850e6	+	2.30120e6i	−0.778960	+	0.368193i
$51$	275655.	−	114180.i	0.0407460	−	0.0168775i
$52$	3.91092e6	−	1.28704e7i	0.534892	−	1.76027i
$53$	5.98108e6	+	2.47744e6i	0.758012	+	0.313979i	0.728006	−	0.685571i	$-0.240447\pi$
$53$	5.98108e6	+	2.47744e6i	0.758012	+	0.313979i	0.0300062	+	0.999550i	$0.490447\pi$
$54$	−1.13798e6	+	1.25496e6i	−0.133831	+	0.147589i
$55$	−2.89585e6	−	2.89585e6i	−0.316464	−	0.316464i
$56$	−1.60313e6	+	6.38064e6i	−0.163011	+	0.648802i
$57$	−216145.	−	216145.i	−0.0204761	−	0.0204761i
$58$	384849.	+	7.87219e6i	0.0340078	+	0.695639i
$59$	−8.77638e6	−	3.63530e6i	−0.724281	−	0.300007i	−0.0100817	−	0.999949i	$-0.503209\pi$
$59$	−8.77638e6	−	3.63530e6i	−0.724281	−	0.300007i	−0.714200	+	0.699942i	$0.753209\pi$
$60$	−372999.	−	306411.i	−0.0287808	−	0.0236429i
$61$	1.95565e7	−	8.10055e6i	1.41244	−	0.585053i	0.459493	−	0.888181i	$-0.348031\pi$
$61$	1.95565e7	−	8.10055e6i	1.41244	−	0.585053i	0.952950	+	0.303129i	$0.0980312\pi$
$62$	2.39781e7	+	8.58597e6i	1.62274	+	0.581062i
$63$			1.04326e7i			0.662261i
$64$	7.92995e6	−	1.47848e7i	0.472662	−	0.881244i
$65$	1.22177e7			0.684439
$66$	−770420.	+	2.15156e6i	−0.0406024	+	0.113391i
$67$	728387.	+	1.75848e6i	0.0361462	+	0.0872647i	0.940922	−	0.338624i	$-0.109961\pi$
$67$	728387.	+	1.75848e6i	0.0361462	+	0.0872647i	−0.904776	+	0.425889i	$0.859961\pi$
$68$	−5.97868e6	+	7.27794e6i	−0.279621	+	0.340387i
$69$	−1.57209e6	+	3.79535e6i	−0.0693554	+	0.167439i
$70$	−5.96836e6	+	291776.i	−0.248578	+	0.0121523i
$71$	−1.02024e7	+	1.02024e7i	−0.401485	+	0.401485i	−0.878756	−	0.477271i	$-0.841626\pi$
$71$	−1.02024e7	+	1.02024e7i	−0.401485	+	0.401485i	0.477271	+	0.878756i	$0.341626\pi$
$72$	6.48288e6	−	2.58025e7i	0.241234	−	0.960135i
$73$	−1.36169e7	+	1.36169e7i	−0.479500	+	0.479500i	−0.904972	−	0.425472i	$-0.860108\pi$
$73$	−1.36169e7	+	1.36169e7i	−0.479500	+	0.479500i	0.425472	+	0.904972i	$0.360108\pi$
$74$	9.56633e6	+	8.67459e6i	0.319021	+	0.289282i
$75$	−1.04448e6	+	2.52159e6i	−0.0330106	+	0.0796947i
$76$	9.23265e6	+	2.80552e6i	0.276740	+	0.0840927i
$77$	1.08260e7	+	2.61364e7i	0.307969	+	0.743502i
$78$	−2.91353e6	−	6.16396e6i	−0.0787120	−	0.166526i
$79$	−4.65357e7			−1.19475			−0.597376	−	0.801961i	$-0.703790\pi$
$79$	−4.65357e7			−1.19475			−0.597376	+	0.801961i	$0.703790\pi$
$80$	1.49427e7	+	2.98715e6i	0.364811	+	0.0729284i
$81$		−	4.17566e7i		−	0.970030i
$82$	2.61465e7	+	5.53163e7i	0.578306	+	1.22348i
$83$	−6.00110e7	+	2.48574e7i	−1.26450	+	0.523773i	−0.911288	−	0.411771i	$-0.864910\pi$
$83$	−6.00110e7	+	2.48574e7i	−1.26450	+	0.523773i	−0.353212	+	0.935543i	$0.614910\pi$
$84$	1.57047e6	+	2.94153e6i	0.0315437	+	0.0590822i
$85$	−7.90362e6	−	3.27379e6i	−0.151409	−	0.0627155i
$86$	1.60507e7	+	1.45545e7i	0.293427	+	0.266075i
$87$	2.82472e6	+	2.82472e6i	0.0493058	+	0.0493058i
$88$	−1.05344e7	−	7.13696e7i	−0.175662	−	1.19010i
$89$	4.92785e7	+	4.92785e7i	0.785411	+	0.785411i	0.980738	−	0.195327i	$-0.0625768\pi$
$89$	4.92785e7	+	4.92785e7i	0.785411	+	0.785411i	−0.195327	+	0.980738i	$0.562577\pi$
$90$	2.41354e7	−	1.17991e6i	0.367861	−	0.0179837i
$91$	−7.79727e7	−	3.22974e7i	−1.13704	−	0.470979i
$92$	−1.26494e7	−	1.29064e8i	−0.176570	−	1.80158i
$93$	1.19262e7	−	4.94000e6i	0.159430	−	0.0660382i
$94$	−3.15045e6	+	8.79828e6i	−0.0403516	+	0.112690i
$95$			8.76439e6i			0.107604i
$96$	−2.05631e6	−	8.25110e6i	−0.0242105	−	0.0971464i
$97$	−5.51041e7			−0.622439			−0.311220	−	0.950338i	$-0.600737\pi$
$97$	−5.51041e7			−0.622439			−0.311220	+	0.950338i	$0.600737\pi$
$98$	−4.79764e7	−	1.71792e7i	−0.520143	−	0.186251i
$99$	−4.37792e7	−	1.05692e8i	−0.455751	−	1.10028i
$100$	−8.40408e6	−	8.57486e7i	−0.0840408	−	0.857486i
$101$	4.42459e7	−	1.06819e8i	0.425195	−	1.02651i	−0.555597	−	0.831452i	$-0.687510\pi$
$101$	4.42459e7	−	1.06819e8i	0.425195	−	1.02651i	0.980792	−	0.195059i	$-0.0624898\pi$
$102$	233102.	+	4.76817e6i	0.00215350	+	0.0440505i
$103$	−4.21448e7	+	4.21448e7i	−0.374451	+	0.374451i	−0.869095	−	0.494645i	$-0.835298\pi$
$103$	−4.21448e7	+	4.21448e7i	−0.374451	+	0.374451i	0.494645	+	0.869095i	$0.335298\pi$
$104$	1.72778e8	+	1.28333e8i	1.47691	+	1.09699i
$105$	−2.14158e6	+	2.14158e6i	−0.0176189	+	0.0176189i
$106$	−6.95798e7	+	7.67326e7i	−0.551137	+	0.607794i
$107$	−2.21903e7	+	5.35721e7i	−0.169289	+	0.408699i	−0.985641	−	0.168856i	$-0.945993\pi$
$107$	−2.21903e7	+	5.35721e7i	−0.169289	+	0.408699i	0.816352	+	0.577554i	$0.195993\pi$
$108$	−1.27659e7	−	2.39108e7i	−0.0938333	−	0.175752i
$109$	−2.74189e7	−	6.61950e7i	−0.194242	−	0.468942i	0.796510	−	0.604625i	$-0.206677\pi$
$109$	−2.74189e7	−	6.61950e7i	−0.194242	−	0.468942i	−0.990752	+	0.135683i	$0.956677\pi$
$110$	5.92411e7	−	2.80016e7i	0.404625	−	0.191255i
$111$	6.54525e6			0.0431156
$112$	−8.74671e7	−	5.85648e7i	−0.555869	−	0.372190i
$113$			1.58631e8i			0.972914i	0.873704	+	0.486457i	$0.161711\pi$
$113$			1.58631e8i			0.972914i	−0.873704	+	0.486457i	$0.838289\pi$
$114$	4.42174e6	−	2.09003e6i	0.0261802	−	0.0123747i
$115$	1.08821e8	−	4.50752e7i	0.622188	−	0.257719i
$116$	−1.20658e8	−	3.66642e7i	−0.666383	−	0.202493i
$117$	3.15313e8	+	1.30607e8i	1.68267	+	0.696983i
$118$	1.02098e8	−	1.12594e8i	0.526612	−	0.580748i
$119$	4.17864e7	+	4.17864e7i	0.208376	+	0.208376i
$120$	6.62750e6	−	3.96591e6i	0.0319613	−	0.0191257i
$121$	−6.77826e7	−	6.77826e7i	−0.316211	−	0.316211i
$122$	1.65375e7	+	3.38280e8i	0.0746503	+	1.52699i
$123$	2.86505e7	+	1.18674e7i	0.125173	+	0.0518485i
$124$	−2.58668e8	+	3.14881e8i	−1.09410	+	1.33186i
$125$	1.56213e8	−	6.47056e7i	0.639849	−	0.265034i
$126$	−1.57150e8	−	5.62716e7i	−0.623495	−	0.223258i
$127$			2.56623e8i			0.986463i	0.869898	+	0.493232i	$0.164184\pi$
$127$			2.56623e8i			0.986463i	−0.869898	+	0.493232i	$0.835816\pi$
$128$	1.79937e8	+	1.99199e8i	0.670318	+	0.742074i
$129$	1.09818e7			0.0396566
$130$	−6.59001e7	+	1.84040e8i	−0.230735	+	0.644374i
$131$	−3.58496e7	−	8.65485e7i	−0.121730	−	0.293883i	0.851254	−	0.524754i	$-0.175843\pi$
$131$	−3.58496e7	−	8.65485e7i	−0.121730	−	0.293883i	−0.972984	+	0.230871i	$0.925843\pi$
$132$	−2.82543e7	−	2.32103e7i	−0.0930655	−	0.0764514i
$133$	2.31686e7	−	5.59341e7i	0.0740447	−	0.178760i
$134$	−3.04176e7	+	1.48703e6i	−0.0943420	+	0.00461211i
$135$	1.74083e7	−	1.74083e7i	0.0524109	−	0.0524109i
$136$	−7.73826e7	−	1.29315e8i	−0.226197	−	0.378002i
$137$	−7.17793e7	+	7.17793e7i	−0.203759	+	0.203759i	−0.801608	−	0.597849i	$-0.796022\pi$
$137$	−7.17793e7	+	7.17793e7i	−0.203759	+	0.203759i	0.597849	+	0.801608i	$0.296022\pi$
$138$	−4.86914e7	−	4.41525e7i	−0.134257	−	0.121742i
$139$	1.68437e8	−	4.06644e8i	0.451211	−	1.08932i	−0.520651	−	0.853769i	$-0.674311\pi$
$139$	1.68437e8	−	4.06644e8i	0.451211	−	1.08932i	0.971862	−	0.235550i	$-0.0756891\pi$
$140$	2.77973e7	−	9.14777e7i	0.0723585	−	0.238124i
$141$	1.81263e6	+	4.37609e6i	0.00458600	+	0.0110716i
$142$	−9.86530e7	−	2.08713e8i	−0.242637	−	0.513330i
$143$	9.25475e8			2.21320
$144$	3.53707e8	+	2.36829e8i	0.822609	+	0.550789i
$145$		−	1.14538e8i		−	0.259107i
$146$	−1.31670e8	−	2.78565e8i	−0.289785	−	0.613078i
$147$	−2.38625e7	+	9.88416e6i	−0.0511030	+	0.0211675i
$148$	−1.82268e8	+	9.73123e7i	−0.379895	+	0.202825i
$149$	−5.42928e8	−	2.24888e8i	−1.10153	−	0.456269i	−0.243518	−	0.969896i	$-0.578302\pi$
$149$	−5.42928e8	−	2.24888e8i	−1.10153	−	0.456269i	−0.858014	+	0.513627i	$0.828302\pi$
$150$	−3.23500e7	−	2.93344e7i	−0.0639013	−	0.0579446i
$151$	3.23382e8	+	3.23382e8i	0.622025	+	0.622025i	0.946049	−	0.324024i	$-0.105036\pi$
$151$	3.23382e8	+	3.23382e8i	0.622025	+	0.622025i	−0.324024	+	0.946049i	$0.605036\pi$
$152$	−9.20601e7	+	1.23943e8i	−0.172463	+	0.232192i
$153$	−1.68979e8	−	1.68979e8i	−0.308367	−	0.308367i
$154$	−4.52097e8	+	2.21017e7i	−0.803801	+	0.0392955i
$155$	−3.41951e8	−	1.41641e8i	−0.592430	−	0.245392i
$156$	1.08565e8	−	1.06403e7i	0.183313	−	0.0179662i
$157$	7.13763e8	−	2.95650e8i	1.17478	−	0.486609i	0.292008	−	0.956416i	$-0.405677\pi$
$157$	7.13763e8	−	2.95650e8i	1.17478	−	0.486609i	0.882769	+	0.469807i	$0.155677\pi$
$158$	2.51006e8	−	7.00986e8i	0.402769	−	1.12482i
$159$			5.25001e7i			0.0821433i
$160$	−1.25595e8	+	2.08975e8i	−0.191643	+	0.318871i
$161$	−8.13649e8			−1.21097
$162$	6.28997e8	+	2.25228e8i	0.913248	+	0.327012i
$163$	−2.84750e8	−	6.87447e8i	−0.403379	−	0.973842i	−0.986840	−	0.161701i	$-0.948302\pi$
$163$	−2.84750e8	−	6.87447e8i	−0.403379	−	0.973842i	0.583461	−	0.812141i	$-0.301698\pi$
$164$	−9.74282e8	+	9.54878e7i	−1.34682	+	0.132000i
$165$	1.27094e7	−	3.06833e7i	0.0171471	−	0.0413968i
$166$	−5.07471e7	−	1.03805e9i	−0.0668312	−	1.36705i
$167$	−1.64220e8	+	1.64220e8i	−0.211135	+	0.211135i	−0.804749	−	0.593615i	$-0.797700\pi$
$167$	−1.64220e8	+	1.64220e8i	−0.211135	+	0.211135i	0.593615	+	0.804749i	$0.297700\pi$
$168$	−5.27804e7	+	7.79053e6i	−0.0662576	+	0.00977980i
$169$	−1.37549e9	+	1.37549e9i	−1.68621	+	1.68621i
$170$	9.19453e7	−	1.01397e8i	0.110086	−	0.121403i
$171$	−9.36913e7	+	2.26191e8i	−0.109576	+	0.264539i
$172$	−3.05815e8	+	1.63274e8i	−0.349418	+	0.186553i
$173$	1.38065e8	+	3.33318e8i	0.154134	+	0.372113i	0.982018	−	0.188787i	$-0.0604554\pi$
$173$	1.38065e8	+	3.33318e8i	0.154134	+	0.372113i	−0.827884	+	0.560899i	$0.810455\pi$
$174$	−5.77860e7	+	2.73138e7i	−0.0630414	+	0.0297979i
$175$	−5.40579e8			−0.576378
$176$	1.13189e9	+	2.26273e8i	1.17965	+	0.235821i
$177$		−	7.70365e7i		−	0.0784880i
$178$	−1.00810e9	+	4.76502e8i	−1.00421	+	0.474662i
$179$	1.70876e9	−	7.07791e8i	1.66444	−	0.689435i	0.666039	−	0.745917i	$-0.267989\pi$
$179$	1.70876e9	−	7.07791e8i	1.66444	−	0.689435i	0.998404	+	0.0564825i	$0.0179885\pi$
$180$	−1.12409e8	+	3.69925e8i	−0.107080	+	0.352390i
$181$	−1.58125e8	−	6.54975e7i	−0.147328	−	0.0610254i	0.307801	−	0.951451i	$-0.400407\pi$
$181$	−1.58125e8	−	6.54975e7i	−0.147328	−	0.0610254i	−0.455129	+	0.890425i	$0.650407\pi$
$182$	9.07081e8	−	1.00033e9i	0.826724	−	0.911711i
$183$	1.21382e8	+	1.21382e8i	0.108231	+	0.108231i
$184$	2.01237e9	+	5.05608e8i	1.75565	+	0.441105i
$185$	−1.32700e8	−	1.32700e8i	−0.113288	−	0.113288i
$186$	1.00852e7	+	2.06295e8i	0.00842620	+	0.172360i
$187$	−5.98691e8	−	2.47986e8i	−0.489594	−	0.202796i
$188$	−1.15539e8	−	9.49130e7i	−0.0924906	−	0.0759792i
$189$	−1.57118e8	+	6.50804e7i	−0.123134	+	0.0510039i
$190$	−1.32022e8	−	4.72737e7i	−0.101305	−	0.0362748i
$191$			2.09625e9i			1.57511i	0.616246	+	0.787554i	$0.288653\pi$
$191$			2.09625e9i			1.57511i	−0.616246	+	0.787554i	$0.711347\pi$
$192$	1.35381e8	+	1.35301e7i	0.0996215	+	0.00995623i
$193$	−2.34406e9			−1.68942			−0.844712	−	0.535221i	$-0.820228\pi$
$193$	−2.34406e9			−1.68942			−0.844712	+	0.535221i	$0.820228\pi$
$194$	2.97223e8	−	8.30056e8i	0.209834	−	0.586004i
$195$	3.79161e7	+	9.15376e7i	0.0262232	+	0.0633084i
$196$	5.17554e8	−	6.30026e8i	0.350696	−	0.426908i
$197$	3.43772e8	−	8.29939e8i	0.228247	−	0.551038i	−0.767717	−	0.640789i	$-0.778607\pi$
$197$	3.43772e8	−	8.29939e8i	0.228247	−	0.551038i	0.995964	+	0.0897514i	$0.0286073\pi$
$198$	1.82823e9	−	8.93767e7i	1.18951	−	0.0581518i
$199$	2.59396e8	−	2.59396e8i	0.165406	−	0.165406i	−0.619551	−	0.784957i	$-0.712685\pi$
$199$	2.59396e8	−	2.59396e8i	0.165406	−	0.165406i	0.784957	+	0.619551i	$0.212685\pi$
$200$	1.33700e9	+	3.35920e8i	0.835623	+	0.209950i
$201$	−1.09145e7	+	1.09145e7i	−0.00668682	+	0.00668682i
$202$	1.37041e9	+	1.24266e9i	0.823083	+	0.746357i
$203$	−3.02782e8	+	7.30981e8i	−0.178298	+	0.430449i
$204$	−7.30822e7	−	2.22074e7i	−0.0421979	−	0.0128226i
$205$	−3.40265e8	−	8.21472e8i	−0.192665	−	0.465133i
$206$	−4.07522e8	−	8.62166e8i	−0.226299	−	0.478765i
$207$	3.29030e9			1.79207
$208$	−2.86507e9	+	1.91041e9i	−1.53067	+	1.02064i
$209$			6.63893e8i			0.347947i
$210$	−2.07082e7	−	4.38109e7i	−0.0106479	−	0.0225271i
$211$	−2.02968e9	+	8.40723e8i	−1.02400	+	0.424153i	−0.830542	−	0.556956i	$-0.811969\pi$
$211$	−2.02968e9	+	8.40723e8i	−1.02400	+	0.424153i	−0.193455	+	0.981109i	$0.561969\pi$
$212$	−7.80552e8	−	1.46199e9i	−0.386419	−	0.723772i
$213$	−1.08101e8	−	4.47769e7i	−0.0525183	−	0.0217538i
$214$	−6.87287e8	−	6.23220e8i	−0.327705	−	0.297157i
$215$	−2.22649e8	−	2.22649e8i	−0.104200	−	0.104200i
$216$	4.29036e8	−	6.33269e7i	0.197097	−	0.0290920i
$217$	1.80789e9	+	1.80789e9i	0.815331	+	0.815331i
$218$	1.14502e9	−	5.59765e7i	0.506974	−	0.0247845i
$219$	−1.44280e8	−	5.97627e7i	−0.0627234	−	0.0259809i
$220$	1.02263e8	+	1.04341e9i	0.0436543	+	0.445414i
$221$	1.78608e9	−	7.39817e8i	0.748740	−	0.310138i
$222$	−3.53040e7	+	9.85938e7i	−0.0145349	+	0.0405918i
$223$			4.11891e8i			0.166557i	0.996526	+	0.0832785i	$0.0265391\pi$
$223$			4.11891e8i			0.166557i	−0.996526	+	0.0832785i	$0.973461\pi$
$224$	1.35397e9	−	1.00166e9i	0.537795	−	0.397860i
$225$	2.18604e9			0.852958
$226$	−2.38953e9	−	8.55631e8i	−0.915963	−	0.327984i
$227$	−1.56457e9	−	3.77719e9i	−0.589237	−	1.42254i	−0.884233	−	0.467046i	$-0.845318\pi$
$227$	−1.56457e9	−	3.77719e9i	−0.589237	−	1.42254i	0.294996	−	0.955499i	$-0.404682\pi$
$228$	7.63288e6	+	7.78798e7i	0.00282455	+	0.0288194i
$229$	−1.35454e9	+	3.27015e9i	−0.492549	+	1.18912i	0.460869	+	0.887468i	$0.347538\pi$
$229$	−1.35454e9	+	3.27015e9i	−0.492549	+	1.18912i	−0.953418	+	0.301651i	$0.902462\pi$
$230$	9.20225e7	+	1.88235e9i	0.0328838	+	0.672649i
$231$	−1.62223e8	+	1.62223e8i	−0.0569722	+	0.0569722i
$232$	1.20310e9	−	1.61976e9i	0.415288	−	0.559112i
$233$	−1.16352e9	+	1.16352e9i	−0.394775	+	0.394775i	−0.876386	−	0.481610i	$-0.840052\pi$
$233$	−1.16352e9	+	1.16352e9i	−0.394775	+	0.394775i	0.481610	+	0.876386i	$0.340052\pi$
$234$	−3.66813e9	+	4.04521e9i	−1.22344	+	1.34920i
$235$	5.19722e7	−	1.25472e8i	0.0170412	−	0.0411410i
$236$	1.14535e9	+	2.14526e9i	0.369224	+	0.691565i
$237$	−1.44418e8	−	3.48656e8i	−0.0457750	−	0.110511i
$238$	−8.54835e8	+	4.04057e8i	−0.266425	+	0.125932i
$239$	−3.67499e9			−1.12633			−0.563164	−	0.826345i	$-0.690416\pi$
$239$	−3.67499e9			−1.12633			−0.563164	+	0.826345i	$0.690416\pi$
$240$	2.39925e7	+	1.21224e8i	0.00723153	+	0.0365380i
$241$		−	6.24262e9i		−	1.85054i	−0.379309	−	0.925270i	$-0.623838\pi$
$241$		−	6.24262e9i		−	1.85054i	0.379309	−	0.925270i	$-0.376162\pi$
$242$	1.38665e9	−	6.55429e8i	0.404300	−	0.191102i
$243$	9.54650e8	−	3.95429e8i	0.273791	−	0.113408i
$244$	−5.18485e9	−	1.57552e9i	−1.46277	−	0.444492i
$245$	6.84190e8	+	2.83401e8i	0.189894	+	0.0786568i
$246$	−3.33300e8	+	3.67563e8i	−0.0910112	+	0.100367i
$247$	−1.40049e9	−	1.40049e9i	−0.376264	−	0.376264i
$248$	−3.34796e9	−	5.59484e9i	−0.885063	−	1.47904i
$249$	−3.72475e8	−	3.72475e8i	−0.0968946	−	0.0968946i
$250$	1.32099e8	+	2.70211e9i	0.0338172	+	0.691741i
$251$	1.40143e9	+	5.80490e8i	0.353082	+	0.146251i	0.552173	−	0.833730i	$-0.313799\pi$
$251$	1.40143e9	+	5.80490e8i	0.353082	+	0.146251i	−0.199091	+	0.979981i	$0.563799\pi$
$252$	1.69529e9	−	2.06370e9i	0.420379	−	0.511734i
$253$	8.24308e9	−	3.41440e9i	2.01191	−	0.833358i
$254$	−3.86562e9	−	1.38418e9i	−0.928719	−	0.332552i
$255$		−	6.93756e7i		−	0.0164076i
$256$	−3.97117e9	+	1.63602e9i	−0.924610	+	0.380915i
$257$	9.44379e8			0.216478			0.108239	−	0.994125i	$-0.465479\pi$
$257$	9.44379e8			0.216478			0.108239	+	0.994125i	$0.465479\pi$
$258$	−5.92342e7	+	1.65424e8i	−0.0133688	+	0.0373353i
$259$	4.96097e8	+	1.19768e9i	0.110247	+	0.266160i
$260$	−2.41681e9	−	1.98536e9i	−0.528871	−	0.434456i
$261$	1.22442e9	−	2.95600e9i	0.263856	−	0.637004i
$262$	1.49708e9	−	7.31881e7i	0.317717	−	0.0155323i
$263$	−1.61368e9	+	1.61368e9i	−0.337282	+	0.337282i	−0.855343	−	0.518061i	$-0.826654\pi$
$263$	−1.61368e9	+	1.61368e9i	−0.337282	+	0.337282i	0.518061	+	0.855343i	$0.326654\pi$
$264$	5.02026e8	−	3.00413e8i	0.103350	−	0.0618448i
$265$	1.06440e9	−	1.06440e9i	0.215836	−	0.215836i
$266$	7.17590e8	+	6.50698e8i	0.143334	+	0.129973i
$267$	−2.16276e8	+	5.22136e8i	−0.0425562	+	0.102740i
$268$	1.41668e8	−	4.66213e8i	0.0274620	−	0.0903744i
$269$	2.28303e9	+	5.51172e9i	0.436016	+	1.05264i	0.977312	+	0.211804i	$0.0679338\pi$
$269$	2.28303e9	+	5.51172e9i	0.436016	+	1.05264i	−0.541296	+	0.840832i	$0.682066\pi$
$270$	1.68331e8	+	3.56126e8i	0.0316744	+	0.0670114i
$271$	6.56238e9			1.21670			0.608351	−	0.793668i	$-0.291831\pi$
$271$	6.56238e9			1.21670			0.608351	+	0.793668i	$0.291831\pi$
$272$	2.36532e9	−	4.68139e8i	0.432130	−	0.0855263i
$273$		−	6.84422e8i		−	0.123218i
$274$	−6.94075e8	−	1.46841e9i	−0.123141	−	0.260522i
$275$	5.47661e9	−	2.26849e9i	0.957593	−	0.396648i
$276$	9.27722e8	−	4.95307e8i	0.159875	−	0.0853568i
$277$	−7.61638e9	−	3.15481e9i	−1.29369	−	0.535863i	−0.373606	−	0.927588i	$-0.621879\pi$
$277$	−7.61638e9	−	3.15481e9i	−1.29369	−	0.535863i	−0.920083	+	0.391724i	$0.871879\pi$
$278$	5.21692e9	+	4.73062e9i	0.873444	+	0.792024i
$279$	−7.31090e9	−	7.31090e9i	−1.20657	−	1.20657i
$280$	1.22803e9	+	9.12138e8i	0.199792	+	0.148398i
$281$	7.60218e9	+	7.60218e9i	1.21931	+	1.21931i	0.967875	+	0.251430i	$0.0809010\pi$
$281$	7.60218e9	+	7.60218e9i	1.21931	+	1.21931i	0.251430	+	0.967875i	$0.419099\pi$
$282$	−7.56959e7	+	3.70055e6i	−0.0119695	+	0.000585154i
$283$	−8.42494e9	−	3.48973e9i	−1.31347	−	0.544058i	−0.387577	−	0.921837i	$-0.626688\pi$
$283$	−8.42494e9	−	3.48973e9i	−1.31347	−	0.544058i	−0.925896	+	0.377779i	$0.876688\pi$
$284$	3.67605e9	−	3.60284e8i	0.565078	−	0.0553824i
$285$	−6.56649e7	+	2.71993e7i	−0.00995300	+	0.00412267i
$286$	−4.99186e9	+	1.39408e10i	−0.746102	+	2.08365i
$287$			6.14210e9i			0.905294i
$288$	−5.47529e9	+	4.05061e9i	−0.795861	+	0.588777i
$289$	5.62210e9			0.805949
$290$	1.72534e9	+	6.17802e8i	0.243940	+	0.0873489i
$291$	−1.71009e8	−	4.12853e8i	−0.0238478	−	0.0575736i
$292$	4.90635e9	−	4.80864e8i	0.674881	−	0.0661441i
$293$	−1.48624e9	+	3.58810e9i	−0.201660	+	0.486849i	−0.992064	−	0.125737i	$-0.959871\pi$
$293$	−1.48624e9	+	3.58810e9i	−0.201660	+	0.486849i	0.790404	+	0.612586i	$0.209871\pi$
$294$	−2.01788e7	−	4.12764e8i	−0.00270089	−	0.0552475i
$295$	−1.56186e9	+	1.56186e9i	−0.206231	+	0.206231i
$296$	−4.82730e8	−	3.27047e9i	−0.0628836	−	0.426033i
$297$	1.31866e9	−	1.31866e9i	0.169475	−	0.169475i
$298$	6.31605e9	−	6.96534e9i	0.800904	−	0.883237i
$299$	−1.01862e10	+	2.45916e10i	−1.27446	+	3.07682i
$300$	6.16368e8	−	3.29076e8i	0.0760948	−	0.0406267i
$301$	8.32367e8	+	2.00951e9i	0.101402	+	0.244807i
$302$	−6.61551e9	+	3.12697e9i	−0.795308	+	0.375920i
$303$	9.37626e8			0.111240
$304$	−1.37044e9	−	2.05527e9i	−0.160460	−	0.240643i
$305$		−	4.92189e9i		−	0.568765i
$306$	3.45685e9	−	1.63396e9i	0.394271	−	0.186361i
$307$	1.00385e10	−	4.15809e9i	1.13010	−	0.468101i	0.262283	−	0.964991i	$-0.415525\pi$
$307$	1.00385e10	−	4.15809e9i	1.13010	−	0.468101i	0.867814	+	0.496890i	$0.165525\pi$
$308$	2.10561e9	−	6.92934e9i	0.233978	−	0.769997i
$309$	−4.46550e8	−	1.84967e8i	−0.0489820	−	0.0202890i
$310$	3.97802e9	−	4.38696e9i	0.430745	−	0.475026i
$311$	−8.88510e9	−	8.88510e9i	−0.949775	−	0.949775i	0.0490222	−	0.998798i	$-0.484389\pi$
$311$	−8.88510e9	−	8.88510e9i	−0.949775	−	0.949775i	−0.998798	+	0.0490222i	$0.984389\pi$
$312$	−4.25305e8	+	1.69276e9i	−0.0448830	+	0.178639i
$313$	6.02359e8	+	6.02359e8i	0.0627593	+	0.0627593i	0.737790	−	0.675031i	$-0.235870\pi$
$313$	6.02359e8	+	6.02359e8i	0.0627593	+	0.0627593i	−0.675031	+	0.737790i	$0.735870\pi$
$314$	6.03580e8	+	1.23464e10i	0.0620892	+	1.27005i
$315$	2.24111e9	+	9.28300e8i	0.227626	+	0.0942857i
$316$	9.20536e9	+	7.56202e9i	0.923193	+	0.758384i
$317$	−5.68499e9	+	2.35480e9i	−0.562980	+	0.233194i	−0.645978	−	0.763356i	$-0.723550\pi$
$317$	−5.68499e9	+	2.35480e9i	−0.562980	+	0.233194i	0.0829985	+	0.996550i	$0.473550\pi$
$318$	−7.90832e8	−	2.83177e8i	−0.0773349	−	0.0276917i
$319$		−	8.67616e9i		−	0.837847i
$320$	−2.47044e9	−	3.01907e9i	−0.235600	−	0.287921i
$321$	−4.70240e8			−0.0442893
$322$	4.38869e9	−	1.22563e10i	0.408237	−	1.14009i
$323$	5.30711e8	+	1.28125e9i	0.0487582	+	0.117713i
$324$	−6.78542e9	+	8.26000e9i	−0.615739	+	0.749549i
$325$	−6.76758e9	+	1.63384e10i	−0.606597	+	1.46445i
$326$	1.18912e10	−	5.81326e8i	1.05282	−	0.0514694i
$327$	4.10857e8	−	4.10857e8i	0.0359335	−	0.0359335i
$328$	3.81675e9	−	1.51911e10i	0.329760	−	1.31248i
$329$	−6.63370e8	+	6.63370e8i	−0.0566203	+	0.0566203i
$330$	3.93643e8	+	3.56948e8i	0.0331930	+	0.0300988i
$331$	−3.43776e8	+	8.29950e8i	−0.0286394	+	0.0691417i	−0.937552	−	0.347845i	$-0.886914\pi$
$331$	−3.43776e8	+	8.29950e8i	−0.0286394	+	0.0691417i	0.908913	+	0.416986i	$0.136914\pi$
$332$	1.59103e10	+	4.83464e9i	1.30956	+	0.397935i
$333$	−2.00616e9	−	4.84329e9i	−0.163150	−	0.393880i
$334$	−1.58794e9	−	3.35949e9i	−0.127599	−	0.269953i
$335$	4.42568e8			0.0351399
$336$	1.67337e8	−	8.37074e8i	0.0131291	−	0.0656760i
$337$		−	1.29734e10i		−	1.00585i	−0.864330	−	0.502925i	$-0.832257\pi$
$337$		−	1.29734e10i		−	1.00585i	0.864330	−	0.502925i	$-0.167743\pi$
$338$	−1.33004e10	−	2.81388e10i	−1.01906	−	2.15595i
$339$	−1.18850e9	+	4.92294e8i	−0.0899914	+	0.0372757i
$340$	1.03145e9	+	1.93193e9i	0.0771850	+	0.144569i
$341$	−2.59024e10	−	1.07291e10i	−1.91568	−	0.793500i
$342$	−2.90185e9	−	2.63135e9i	−0.212115	−	0.192342i
$343$	−1.01647e10	−	1.01647e10i	−0.734373	−	0.734373i
$344$	−8.09940e8	−	5.48730e9i	−0.0578388	−	0.391854i
$345$	6.75428e8	+	6.75428e8i	0.0476763	+	0.0476763i
$346$	−5.76561e9	+	2.81864e8i	−0.402292	+	0.0196669i
$347$	1.00971e10	+	4.18237e9i	0.696434	+	0.288473i	0.702678	−	0.711508i	$-0.251987\pi$
$347$	1.00971e10	+	4.18237e9i	0.696434	+	0.288473i	−0.00624364	+	0.999981i	$0.501987\pi$
$348$	−9.97511e7	−	1.01778e9i	−0.00680144	−	0.0693965i
$349$	3.47157e9	−	1.43797e9i	0.234005	−	0.0969279i	−0.262600	−	0.964905i	$-0.584580\pi$
$349$	3.47157e9	−	1.43797e9i	0.234005	−	0.0969279i	0.496605	+	0.867977i	$0.334580\pi$
$350$	2.91580e9	−	8.14297e9i	0.194306	−	0.542638i
$351$			5.56346e9i			0.366536i
$352$	−9.51368e9	+	1.58297e10i	−0.619695	+	1.03110i
$353$	−7.49630e9			−0.482779			−0.241389	−	0.970428i	$-0.577603\pi$
$353$	−7.49630e9			−0.482779			−0.241389	+	0.970428i	$0.577603\pi$
$354$	1.16043e9	+	4.15522e8i	0.0738936	+	0.0264595i
$355$	1.28385e9	+	3.09949e9i	0.0808353	+	0.195154i
$356$	−1.74020e9	−	1.77556e10i	−0.108343	−	1.10544i
$357$	−1.83394e8	+	4.42753e8i	−0.0112905	+	0.0272577i
$358$	1.44498e9	+	2.95575e10i	0.0879689	+	1.79943i
$359$	1.56368e9	−	1.56368e9i	0.0941389	−	0.0941389i	−0.658469	−	0.752608i	$-0.728796\pi$
$359$	1.56368e9	−	1.56368e9i	0.0941389	−	0.0941389i	0.752608	+	0.658469i	$0.228796\pi$
$360$	−4.96602e9	−	3.68858e9i	−0.295664	−	0.219608i
$361$	−1.10045e10	+	1.10045e10i	−0.647953	+	0.647953i
$362$	1.83952e9	−	2.02862e9i	0.107120	−	0.118132i
$363$	2.97488e8	−	7.18199e8i	0.0171334	−	0.0413636i
$364$	1.01757e10	+	1.90594e10i	0.579642	+	1.08568i
$365$	1.71353e9	+	4.13683e9i	0.0965428	+	0.233075i
$366$	−2.48315e9	+	1.17372e9i	−0.138382	+	0.0654092i
$367$	2.12322e10			1.17039			0.585194	−	0.810893i	$-0.301018\pi$
$367$	2.12322e10			1.17039			0.585194	+	0.810893i	$0.301018\pi$
$368$	−1.84706e10	+	2.75860e10i	−1.00714	+	1.50417i
$369$		−	2.48379e10i		−	1.33971i
$370$	2.71469e9	−	1.28316e9i	0.144848	−	0.0684657i
$371$	−9.60674e9	+	3.97924e9i	−0.507085	+	0.210041i
$372$	−3.16191e9	−	9.60806e8i	−0.165112	−	0.0501723i
$373$	−3.95674e9	−	1.63894e9i	−0.204410	−	0.0846694i	0.278130	−	0.960544i	$-0.410286\pi$
$373$	−3.95674e9	−	1.63894e9i	−0.204410	−	0.0846694i	−0.482540	+	0.875874i	$0.660286\pi$
$374$	6.96475e9	−	7.68073e9i	0.355975	−	0.392569i
$375$	9.69579e8	+	9.69579e8i	0.0490296	+	0.0490296i
$376$	2.05291e9	−	1.22847e9i	0.102712	−	0.0614628i
$377$	1.83025e10	+	1.83025e10i	0.906034	+	0.906034i
$378$	−1.32864e8	−	2.71777e9i	−0.00650788	−	0.133121i
$379$	2.38713e10	+	9.88784e9i	1.15696	+	0.479231i	0.876863	−	0.480740i	$-0.159632\pi$
$379$	2.38713e10	+	9.88784e9i	1.15696	+	0.479231i	0.280102	+	0.959970i	$0.409632\pi$
$380$	1.42421e9	−	1.73371e9i	0.0683029	−	0.0831461i
$381$	−1.92268e9	+	7.96401e8i	−0.0912446	+	0.0377948i
$382$	−3.15767e10	−	1.13069e10i	−1.48291	−	0.530992i
$383$		−	4.53330e9i		−	0.210678i	−0.994436	−	0.105339i	$-0.966407\pi$
$383$		−	4.53330e9i		−	0.210678i	0.994436	−	0.105339i	$-0.0335928\pi$
$384$	−9.34033e8	+	1.96632e9i	−0.0429573	+	0.0904336i
$385$	6.57790e9			0.299395
$386$	1.26435e10	−	3.53095e10i	0.569530	−	1.59053i
$387$	−3.36599e9	−	8.12622e9i	−0.150061	−	0.362280i
$388$	1.09003e10	+	8.95438e9i	0.480963	+	0.395101i
$389$	−1.31707e10	+	3.17970e10i	−0.575191	+	1.38863i	0.321894	+	0.946776i	$0.395681\pi$
$389$	−1.31707e10	+	3.17970e10i	−0.575191	+	1.38863i	−0.897085	+	0.441858i	$0.854319\pi$
$390$	−1.58338e9	+	7.74070e7i	−0.0684428	+	0.00334597i
$391$	1.31789e10	−	1.31789e10i	0.563861	−	0.563861i
$392$	6.69875e9	+	1.11944e10i	0.283693	+	0.474085i
$393$	5.37187e8	−	5.37187e8i	0.0225193	−	0.0225193i
$394$	1.06475e10	+	9.65494e9i	0.441836	+	0.400650i
$395$	−4.14079e9	+	9.99674e9i	−0.170096	+	0.410648i
$396$	−8.51484e9	+	2.80214e10i	−0.346255	+	1.13949i
$397$	−3.36681e8	−	8.12819e8i	−0.0135537	−	0.0327214i	0.916958	−	0.398984i	$-0.130637\pi$
$397$	−3.36681e8	−	8.12819e8i	−0.0135537	−	0.0327214i	−0.930511	+	0.366263i	$0.880637\pi$
$398$	2.50825e9	+	5.30653e9i	0.0999627	+	0.211484i
$399$	4.90973e8			0.0193716
$400$	−1.22716e10	+	1.83278e10i	−0.479361	+	0.715931i
$401$		−	1.39089e10i		−	0.537918i	−0.963152	−	0.268959i	$-0.913320\pi$
$401$		−	1.39089e10i		−	0.537918i	0.963152	−	0.268959i	$-0.0866795\pi$
$402$	−1.05539e8	−	2.23281e8i	−0.00404117	−	0.00854962i
$403$	7.72747e10	−	3.20082e10i	2.92966	−	1.21351i
$404$	−2.61105e10	+	1.39403e10i	−0.980142	+	0.523294i
$405$	−8.97011e9	−	3.71554e9i	−0.333409	−	0.138103i
$406$	−9.37791e9	−	8.50373e9i	−0.345145	−	0.312972i
$407$	−1.00519e10	−	1.00519e10i	−0.366329	−	0.366329i
$408$	7.28713e8	−	9.81084e8i	0.0262976	−	0.0354051i
$409$	9.94619e8	+	9.94619e8i	0.0355438	+	0.0355438i	0.724655	−	0.689112i	$-0.241999\pi$
$409$	9.94619e8	+	9.94619e8i	0.0355438	+	0.0355438i	−0.689112	+	0.724655i	$0.741999\pi$
$410$	1.42095e10	−	6.94662e8i	0.502856	−	0.0245832i
$411$	−7.60546e8	−	3.15028e8i	−0.0266537	−	0.0110403i
$412$	1.51853e10	−	1.48829e9i	0.527028	−	0.0516532i
$413$	1.40965e10	−	5.83897e9i	0.484520	−	0.200695i
$414$	−1.77474e10	+	4.95632e10i	−0.604133	+	1.68717i
$415$			1.51033e10i			0.509191i
$416$	−1.33236e10	−	5.34621e10i	−0.444887	−	1.78514i
$417$	3.56940e9			0.118046
$418$	−1.00005e10	−	3.58093e9i	−0.327579	−	0.117298i
$419$	1.31884e10	+	3.18396e10i	0.427893	+	1.03303i	0.979954	+	0.199222i	$0.0638416\pi$
$419$	1.31884e10	+	3.18396e10i	0.427893	+	1.03303i	−0.552061	+	0.833804i	$0.686158\pi$
$420$	7.71639e8	−	7.56271e7i	0.0247980	−	0.00243041i
$421$	1.16351e10	−	2.80896e10i	0.370375	−	0.894165i	−0.623311	−	0.781974i	$-0.714213\pi$
$421$	1.16351e10	−	2.80896e10i	0.370375	−	0.894165i	0.993687	−	0.112191i	$-0.0357869\pi$
$422$	−1.71636e9	−	3.51087e10i	−0.0541202	−	1.10704i
$423$	2.68259e9	−	2.68259e9i	0.0837901	−	0.0837901i
$424$	2.62328e10	−	3.87203e9i	0.811672	−	0.119805i
$425$	8.75591e9	−	8.75591e9i	0.268377	−	0.268377i
$426$	1.25757e9	−	1.38685e9i	0.0381851	−	0.0421106i
$427$	−1.30110e10	+	3.14114e10i	−0.391381	+	0.944877i
$428$	1.30949e10	−	6.99134e9i	0.390237	−	0.208346i
$429$	2.87211e9	+	6.93388e9i	0.0847952	+	0.204714i
$430$	4.55479e9	−	2.15292e9i	0.133228	−	0.0629730i
$431$	2.49717e10			0.723668			0.361834	−	0.932242i	$-0.382151\pi$
$431$	2.49717e10			0.723668			0.361834	+	0.932242i	$0.382151\pi$
$432$	−1.36023e9	+	6.80433e9i	−0.0390552	+	0.195367i
$433$			5.43314e9i			0.154561i	0.997009	+	0.0772805i	$0.0246237\pi$
$433$			5.43314e9i			0.154561i	−0.997009	+	0.0772805i	$0.975376\pi$
$434$	−3.69845e10	+	1.74816e10i	−1.04246	+	0.492744i
$435$	8.58149e8	−	3.55457e8i	0.0239666	−	0.00992728i
$436$	−5.33283e9	+	1.75498e10i	−0.147575	+	0.485652i
$437$	−1.76409e10	−	7.30710e9i	−0.483721	−	0.200364i
$438$	1.67845e9	−	1.85100e9i	0.0456051	−	0.0502933i
$439$	−1.13713e10	−	1.13713e10i	−0.306162	−	0.306162i	0.537257	−	0.843419i	$-0.319461\pi$
$439$	−1.13713e10	−	1.13713e10i	−0.306162	−	0.306162i	−0.843419	+	0.537257i	$0.819461\pi$
$440$	−1.62689e10	−	4.08755e9i	−0.434058	−	0.109057i
$441$	1.46280e10	+	1.46280e10i	0.386749	+	0.386749i
$442$	1.51036e9	+	3.08949e10i	0.0395723	+	0.809463i
$443$	−6.02552e10	−	2.49585e10i	−1.56451	−	0.648043i	−0.578648	−	0.815577i	$-0.696419\pi$
$443$	−6.02552e10	−	2.49585e10i	−1.56451	−	0.648043i	−0.985866	+	0.167534i	$0.946419\pi$
$444$	−1.29474e9	−	1.06360e9i	−0.0333157	−	0.0273682i
$445$	1.49708e10	−	6.20110e9i	0.381772	−	0.158135i
$446$	−6.20449e9	−	2.22168e9i	−0.156807	−	0.0561489i
$447$		−	4.76566e9i		−	0.119369i
$448$	7.78539e9	+	2.57982e10i	0.193272	+	0.640439i
$449$	−3.97397e10			−0.977775			−0.488887	−	0.872347i	$-0.662597\pi$
$449$	−3.97397e10			−0.977775			−0.488887	+	0.872347i	$0.662597\pi$
$450$	−1.17911e10	+	3.29292e10i	−0.287545	+	0.803029i
$451$	−2.57747e10	−	6.22256e10i	−0.622999	−	1.50405i
$452$	2.57774e10	−	3.13793e10i	0.617570	−	0.751777i
$453$	−1.41928e9	+	3.42643e9i	−0.0337034	+	0.0813672i
$454$	6.53365e10	−	3.19411e9i	1.53791	−	0.0751842i
$455$	−1.38762e10	+	1.38762e10i	−0.323761	+	0.323761i
$456$	−1.21431e9	−	3.05094e8i	−0.0280846	−	0.00705626i
$457$	−2.43829e10	+	2.43829e10i	−0.559012	+	0.559012i	−0.929026	−	0.370014i	$-0.879353\pi$
$457$	−2.43829e10	+	2.43829e10i	−0.559012	+	0.559012i	0.370014	+	0.929026i	$0.379353\pi$
$458$	−4.19534e10	−	3.80426e10i	−0.953466	−	0.864587i
$459$	1.49076e9	−	3.59901e9i	0.0335859	−	0.0810835i
$460$	−2.88509e10	−	8.76690e9i	−0.644360	−	0.195801i
$461$	7.28674e9	+	1.75917e10i	0.161335	+	0.389498i	0.983788	−	0.179336i	$-0.0573949\pi$
$461$	7.28674e9	+	1.75917e10i	0.161335	+	0.389498i	−0.822453	+	0.568834i	$0.807395\pi$
$462$	−1.56862e9	−	3.31863e9i	−0.0344311	−	0.0728435i
$463$	3.24730e9			0.0706641			0.0353320	−	0.999376i	$-0.488751\pi$
$463$	3.24730e9			0.0706641			0.0353320	+	0.999376i	$0.488751\pi$
$464$	1.79098e10	+	2.68595e10i	0.386384	+	0.579463i
$465$		−	3.00154e9i		−	0.0641997i
$466$	−1.12507e10	−	2.38024e10i	−0.238582	−	0.504751i
$467$	−5.17010e10	+	2.14153e10i	−1.08700	+	0.450252i	−0.852961	−	0.521974i	$-0.825196\pi$
$467$	−5.17010e10	+	2.14153e10i	−1.08700	+	0.450252i	−0.234043	+	0.972226i	$0.575196\pi$
$468$	−4.11494e10	−	7.70738e10i	−0.857788	−	1.60666i
$469$	−2.82445e9	−	1.16993e9i	−0.0583772	−	0.0241806i
$470$	1.60971e9	+	1.45965e9i	0.0329880	+	0.0299129i
$471$	4.43017e9	+	4.43017e9i	0.0900195	+	0.0900195i
$472$	−3.84928e10	+	5.68165e9i	−0.775554	+	0.114474i
$473$	−1.68654e10	−	1.68654e10i	−0.336940	−	0.336940i
$474$	6.03093e9	−	2.94834e8i	0.119473	−	0.00584070i
$475$	−1.17204e10	−	4.85475e9i	−0.230233	−	0.0953658i
$476$	−1.47563e9	−	1.50562e10i	−0.0287442	−	0.293283i
$477$	3.88485e10	−	1.60916e10i	0.750414	−	0.310832i
$478$	1.98223e10	−	5.53580e10i	0.379702	−	1.06040i
$479$			6.20703e10i			1.17908i	0.807741	+	0.589538i	$0.200690\pi$
$479$			6.20703e10i			1.17908i	−0.807741	+	0.589538i	$0.799310\pi$
$480$	−1.95546e9	−	2.92456e8i	−0.0368370	−	0.00550929i
$481$	4.24093e10			0.792284
$482$	9.40351e10	+	3.36717e10i	1.74222	+	0.623845i
$483$	−2.52507e9	−	6.09605e9i	−0.0463964	−	0.112011i
$484$	2.39365e9	+	2.44229e10i	0.0436194	+	0.445057i
$485$	−4.90321e9	+	1.18374e10i	−0.0886163	+	0.213939i
$486$	8.07281e8	+	1.65132e10i	0.0144704	+	0.295996i
$487$	−4.26003e10	+	4.26003e10i	−0.757349	+	0.757349i	−0.975839	−	0.218490i	$-0.929887\pi$
$487$	−4.26003e10	+	4.26003e10i	−0.757349	+	0.757349i	0.218490	+	0.975839i	$0.429887\pi$
$488$	5.16989e10	−	6.96035e10i	0.911596	−	1.22730i
$489$	4.26682e9	−	4.26682e9i	0.0746224	−	0.0746224i
$490$	−7.95939e9	+	8.77761e9i	−0.138069	+	0.152262i
$491$	1.65632e10	−	3.99872e10i	0.284983	−	0.688010i	−0.714955	−	0.699171i	$-0.753553\pi$
$491$	1.65632e10	−	3.99872e10i	0.284983	−	0.688010i	0.999938	+	0.0111609i	$0.00355271\pi$
$492$	−3.73899e9	−	7.00322e9i	−0.0638108	−	0.119519i
$493$	−6.93565e9	−	1.67441e10i	−0.117409	−	0.283449i
$494$	2.86502e10	−	1.35422e10i	0.481083	−	0.227395i
$495$	−2.66002e10			−0.443062
$496$	1.02336e11	−	2.02541e10i	1.69083	−	0.334646i
$497$		−	2.31747e10i		−	0.379830i
$498$	7.61981e9	−	3.60167e9i	0.123887	−	0.0585581i
$499$	−4.80053e10	+	1.98845e10i	−0.774261	+	0.320709i	−0.734597	−	0.678504i	$-0.762629\pi$
$499$	−4.80053e10	+	1.98845e10i	−0.774261	+	0.320709i	−0.0396640	+	0.999213i	$0.512629\pi$
$500$	−4.14156e10	−	1.25849e10i	−0.662650	−	0.201359i
$501$	−1.74001e9	−	7.20737e8i	−0.0276186	−	0.0114400i
$502$	−1.63032e10	+	1.79792e10i	−0.256720	+	0.283110i
$503$	1.83189e10	+	1.83189e10i	0.286173	+	0.286173i	0.835565	−	0.549392i	$-0.185141\pi$
$503$	1.83189e10	+	1.83189e10i	0.286173	+	0.286173i	−0.549392	+	0.835565i	$0.685141\pi$
$504$	2.19422e10	+	3.66681e10i	0.340063	+	0.568284i
$505$	−1.90097e10	−	1.90097e10i	−0.292288	−	0.292288i
$506$	6.97060e9	+	1.42586e11i	0.106333	+	2.17507i
$507$	−1.45742e10	−	6.03683e9i	−0.220573	−	0.0913645i
$508$	4.17011e10	−	5.07634e10i	0.626170	−	0.762247i
$509$	5.68833e10	−	2.35618e10i	0.847449	−	0.351025i	0.0836625	−	0.996494i	$-0.473338\pi$
$509$	5.68833e10	−	2.35618e10i	0.847449	−	0.351025i	0.763786	+	0.645469i	$0.223338\pi$
$510$	1.04503e9	+	3.74201e8i	0.0154472	+	0.00553126i
$511$		−	3.09308e10i		−	0.453636i
$512$	−3.22415e9	−	6.86438e10i	−0.0469176	−	0.998899i
$513$	−3.99097e9			−0.0576248
$514$	−5.09383e9	+	1.42256e10i	−0.0729780	+	0.203806i
$515$	5.30341e9	+	1.28036e10i	0.0753922	+	0.182013i
$516$	−2.17235e9	−	1.78454e9i	−0.0306430	−	0.0251726i
$517$	3.93684e9	−	9.50437e9i	0.0551043	−	0.133033i
$518$	−2.07171e10	+	1.01280e9i	−0.287746	+	0.0140671i
$519$	−2.06883e9	+	2.06883e9i	−0.0285138	+	0.0285138i
$520$	4.29422e10	−	2.56967e10i	0.587315	−	0.351451i
$521$	−5.43949e10	+	5.43949e10i	−0.738256	+	0.738256i	−0.972240	−	0.233984i	$-0.924824\pi$
$521$	−5.43949e10	+	5.43949e10i	−0.738256	+	0.738256i	0.233984	+	0.972240i	$0.424824\pi$
$522$	3.79232e10	+	3.43881e10i	0.510766	+	0.463154i
$523$	−5.44855e7	+	1.31540e8i	−0.000728239	+	0.00175812i	−0.924243	−	0.381804i	$-0.875303\pi$
$523$	−5.44855e7	+	1.31540e8i	−0.000728239	+	0.00175812i	0.923515	+	0.383562i	$0.125303\pi$
$524$	−6.97257e9	+	2.29460e10i	−0.0924842	+	0.304355i
$525$	−1.67763e9	−	4.05015e9i	−0.0220830	−	0.0533131i
$526$	−1.56036e10	−	3.30114e10i	−0.203836	−	0.431242i
$527$	−5.85659e10			−0.759281
$528$	1.81740e9	+	9.18261e9i	0.0233838	+	0.118149i
$529$			1.78304e11i			2.27687i
$530$	1.02923e10	+	2.17748e10i	0.130440	+	0.275963i
$531$	−5.70047e10	+	2.36121e10i	−0.717022	+	0.297000i
$532$	−1.36723e10	+	7.29959e9i	−0.170685	+	0.0911281i
$533$	1.85638e11	+	7.68938e10i	2.30016	+	0.952757i
$534$	−6.69860e9	−	6.07417e9i	−0.0823794	−	0.0747003i
$535$	9.53378e9	+	9.53378e9i	0.116372	+	0.116372i
$536$	6.25863e9	+	4.64868e9i	0.0758263	+	0.0563210i
$537$	1.06059e10	+	1.06059e10i	0.127541	+	0.127541i
$538$	−9.53397e10	+	4.66088e9i	−1.13801	+	0.0556338i
$539$	5.18266e10	+	2.14673e10i	0.614042	+	0.254344i
$540$	−6.27242e9	+	6.14750e8i	−0.0737667	+	0.00722976i
$541$	−4.63351e10	+	1.91926e10i	−0.540905	+	0.224050i	−0.636372	−	0.771382i	$-0.719566\pi$
$541$	−4.63351e10	+	1.91926e10i	−0.540905	+	0.224050i	0.0954668	+	0.995433i	$0.469566\pi$
$542$	−3.53965e10	+	9.88519e10i	−0.410169	+	1.14548i
$543$		−	1.38797e9i		−	0.0159655i
$544$	−5.70638e9	+	3.81549e10i	−0.0651576	+	0.435667i
$545$	−1.66597e10			−0.188834
$546$	1.03097e10	+	3.69166e9i	0.116005	+	0.0415385i
$547$	−4.30001e10	−	1.03811e11i	−0.480308	−	1.15957i	−0.959463	−	0.281836i	$-0.909057\pi$
$547$	−4.30001e10	−	1.03811e11i	−0.480308	−	1.15957i	0.479154	−	0.877731i	$-0.340943\pi$
$548$	2.58629e10	−	2.53479e9i	0.286785	−	0.0281073i
$549$	5.26150e10	−	1.27024e11i	0.579189	−	1.39828i
$550$	4.63119e9	+	9.47323e10i	0.0506106	+	1.03525i
$551$	−1.31294e10	+	1.31294e10i	−0.142442	+	0.142442i
$552$	2.45703e9	+	1.66463e10i	0.0264640	+	0.179292i
$553$	5.28528e10	−	5.28528e10i	0.565154	−	0.565154i
$554$	8.86037e10	−	9.77122e10i	0.940617	−	1.03731i
$555$	5.82402e8	−	1.40604e9i	0.00613834	−	0.0148193i
$556$	−9.93985e10	+	5.30685e10i	−1.04011	+	0.555313i
$557$	−2.18150e10	−	5.26662e10i	−0.226639	−	0.547156i	0.769125	−	0.639098i	$-0.220692\pi$
$557$	−2.18150e10	−	5.26662e10i	−0.226639	−	0.547156i	−0.995764	+	0.0919427i	$0.970692\pi$
$558$	1.49561e11	−	7.06933e10i	1.54270	−	0.729192i
$559$	7.11557e10			0.728723
$560$	−2.03637e10	+	1.35784e10i	−0.207064	+	0.138070i
$561$		−	5.25513e9i		−	0.0530557i
$562$	−1.55520e11	+	7.35098e10i	−1.55898	+	0.736886i
$563$	7.57182e10	−	3.13635e10i	0.753645	−	0.312170i	0.0274173	−	0.999624i	$-0.491272\pi$
$563$	7.57182e10	−	3.13635e10i	0.753645	−	0.312170i	0.726228	+	0.687454i	$0.241272\pi$
$564$	3.52548e8	−	1.16020e9i	0.00348419	−	0.0114661i
$565$	3.40770e10	+	1.41151e10i	0.334401	+	0.138513i
$566$	9.80100e10	−	1.08085e11i	0.955003	−	1.05318i
$567$	4.74249e10	+	4.74249e10i	0.458854	+	0.458854i
$568$	−1.44009e10	+	5.73173e10i	−0.138356	+	0.550671i
$569$	−2.98582e9	−	2.98582e9i	−0.0284849	−	0.0284849i	0.692721	−	0.721206i	$-0.256412\pi$
$569$	−2.98582e9	−	2.98582e9i	−0.0284849	−	0.0284849i	−0.721206	+	0.692721i	$0.756412\pi$
$570$	−5.55282e7	−	1.13585e9i	−0.000526035	−	0.0107602i
$571$	−9.61056e10	−	3.98082e10i	−0.904074	−	0.374480i	−0.118289	−	0.992979i	$-0.537741\pi$
$571$	−9.61056e10	−	3.98082e10i	−0.904074	−	0.374480i	−0.785785	+	0.618499i	$0.787741\pi$
$572$	−1.83071e11	−	1.50389e11i	−1.71015	−	1.40486i
$573$	−1.57056e10	+	6.50548e9i	−0.145692	+	0.0603478i
$574$	−9.25210e10	−	3.31295e10i	−0.852301	−	0.305188i
$575$			1.70492e11i			1.55967i
$576$	−3.14832e10	−	1.04325e11i	−0.286015	−	0.947760i
$577$	−1.27180e11			−1.14740			−0.573699	−	0.819066i	$-0.694492\pi$
$577$	−1.27180e11			−1.14740			−0.573699	+	0.819066i	$0.694492\pi$
$578$	−3.03247e10	+	8.46881e10i	−0.271698	+	0.758772i
$579$	−7.27451e9	−	1.75622e10i	−0.0647276	−	0.156266i
$580$	−1.86124e10	+	2.26572e10i	−0.164472	+	0.200214i
$581$	3.99256e10	−	9.63890e10i	0.350386	−	0.845908i
$582$	7.14137e9	−	3.49121e8i	0.0622429	−	0.00304287i
$583$	8.06274e10	−	8.06274e10i	0.697925	−	0.697925i
$584$	−1.92206e10	+	7.65001e10i	−0.165240	+	0.657674i
$585$	5.61136e10	−	5.61136e10i	0.479120	−	0.479120i
$586$	−4.60325e10	−	4.17415e10i	−0.390368	−	0.353979i
$587$	3.83444e10	−	9.25715e10i	0.322960	−	0.779695i	−0.676119	−	0.736792i	$-0.736339\pi$
$587$	3.83444e10	−	9.25715e10i	0.322960	−	0.779695i	0.999079	−	0.0429027i	$-0.0136605\pi$
$588$	6.32648e9	+	1.92242e9i	0.0529240	+	0.0160820i
$589$	2.29612e10	+	5.54333e10i	0.190781	+	0.460585i
$590$	−1.51025e10	−	3.19514e10i	−0.124635	−	0.263683i
$591$	7.28496e9			0.0597141
$592$	5.18682e10	+	1.03688e10i	0.422293	+	0.0844195i
$593$		−	1.00251e11i		−	0.810719i	−0.914157	−	0.405360i	$-0.867146\pi$
$593$		−	1.00251e11i		−	0.810719i	0.914157	−	0.405360i	$-0.132854\pi$
$594$	1.27509e10	+	2.69762e10i	0.102422	+	0.216688i
$595$	1.26947e10	−	5.25832e9i	0.101287	−	0.0419545i
$596$	7.08540e10	+	1.32711e11i	0.561538	+	1.05177i
$597$	2.74846e9	+	1.13845e9i	0.0216368	+	0.00896224i
$598$	−3.15491e11	−	2.86082e11i	−2.46708	−	2.23710i
$599$	7.13509e10	+	7.13509e10i	0.554233	+	0.554233i	0.927660	−	0.373427i	$-0.121817\pi$
$599$	7.13509e10	+	7.13509e10i	0.554233	+	0.554233i	−0.373427	+	0.927660i	$0.621817\pi$
$600$	1.63243e9	+	1.10596e10i	0.0125959	+	0.0853363i
$601$	−1.09865e11	−	1.09865e11i	−0.842095	−	0.842095i	0.147036	−	0.989131i	$-0.453027\pi$
$601$	−1.09865e11	−	1.09865e11i	−0.842095	−	0.842095i	−0.989131	+	0.147036i	$0.953027\pi$
$602$	−3.47597e10	+	1.69930e9i	−0.264661	+	0.0129385i
$603$	1.14218e10	+	4.73105e9i	0.0863900	+	0.0357839i
$604$	−1.14198e10	−	1.16519e11i	−0.0858046	−	0.875482i
$605$	−2.05923e10	+	8.52963e9i	−0.153704	+	0.0636662i
$606$	−5.05741e9	+	1.41239e10i	−0.0375005	+	0.104728i
$607$		−	2.42537e11i		−	1.78658i	−0.449478	−	0.893291i	$-0.648390\pi$
$607$		−	2.42537e11i		−	1.78658i	0.449478	−	0.893291i	$-0.351610\pi$
$608$	3.83513e10	−	9.55777e9i	0.280650	−	0.0699427i
$609$	−6.41633e9			−0.0466463
$610$	7.41405e10	+	2.65479e10i	0.535471	+	0.191739i
$611$	1.17448e10	+	2.83544e10i	0.0842714	+	0.203449i
$612$	5.96728e9	+	6.08853e10i	0.0425373	+	0.434017i
$613$	−3.32280e10	+	8.02195e10i	−0.235322	+	0.568117i	−0.996788	−	0.0800876i	$-0.974480\pi$
$613$	−3.32280e10	+	8.02195e10i	−0.235322	+	0.568117i	0.761466	+	0.648205i	$0.224480\pi$
$614$	8.48887e9	+	1.73642e11i	0.0597278	+	1.22175i
$615$	5.09869e9	−	5.09869e9i	0.0356417	−	0.0356417i
$616$	9.30222e10	+	6.90934e10i	0.646046	+	0.479859i
$617$	−4.69250e10	+	4.69250e10i	−0.323790	+	0.323790i	−0.850219	−	0.526429i	$-0.823531\pi$
$617$	−4.69250e10	+	4.69250e10i	−0.323790	+	0.323790i	0.526429	+	0.850219i	$0.323531\pi$
$618$	5.19486e9	−	5.72889e9i	0.0356139	−	0.0392750i
$619$	7.26227e10	−	1.75327e11i	0.494664	−	1.19422i	−0.457658	−	0.889128i	$-0.651312\pi$
$619$	7.26227e10	−	1.75327e11i	0.494664	−	1.19422i	0.952322	−	0.305095i	$-0.0986884\pi$
$620$	4.46258e10	+	8.35851e10i	0.302009	+	0.565669i
$621$	2.05255e10	+	4.95530e10i	0.138016	+	0.333199i
$622$	1.81765e11	−	8.59152e10i	1.21436	−	0.573995i
$623$	−1.11936e11			−0.743047
$624$	−2.32047e10	−	1.55370e10i	−0.153051	−	0.102478i
$625$			9.21538e10i			0.603939i
$626$	−1.23226e10	+	5.82456e9i	−0.0802427	+	0.0379285i
$627$	−4.97404e9	+	2.06032e9i	−0.0321840	+	0.0133310i
$628$	−1.89235e11	−	5.75026e10i	−1.21664	−	0.369699i
$629$	−2.74346e10	−	1.13638e10i	−0.175266	−	0.0725974i
$630$	−2.60716e10	+	2.87517e10i	−0.165503	+	0.182516i
$631$	1.70168e11	+	1.70168e11i	1.07340	+	1.07340i	0.997084	+	0.0763132i	$0.0243149\pi$
$631$	1.70168e11	+	1.70168e11i	1.07340	+	1.07340i	0.0763132	+	0.997084i	$0.475685\pi$
$632$	−1.63562e11	+	9.78759e10i	−1.02521	+	0.613490i
$633$	−1.25978e10	−	1.25978e10i	−0.0784656	−	0.0784656i
$634$	−4.80740e9	−	9.83368e10i	−0.0297545	−	0.608638i
$635$	5.51275e10	+	2.28346e10i	0.339057	+	0.140442i
$636$	8.53124e9	−	1.03852e10i	0.0521415	−	0.0634727i
$637$	−1.54615e11	+	6.40434e10i	−0.939058	+	0.388971i
$638$	1.30693e11	+	4.67978e10i	0.788803	+	0.282451i
$639$			9.37158e10i			0.562095i
$640$	5.88027e10	−	2.09290e10i	0.350491	−	0.124746i
$641$	2.85301e11			1.68994			0.844970	−	0.534813i	$-0.179618\pi$
$641$	2.85301e11			1.68994			0.844970	+	0.534813i	$0.179618\pi$
$642$	2.53640e9	−	7.08341e9i	0.0149306	−	0.0416968i
$643$	1.25298e11	+	3.02495e11i	0.732992	+	1.76960i	0.632360	+	0.774675i	$0.282086\pi$
$643$	1.25298e11	+	3.02495e11i	0.732992	+	1.76960i	0.100632	+	0.994924i	$0.467914\pi$
$644$	1.60950e11	+	1.32217e11i	0.935726	+	0.768680i
$645$	9.77173e8	−	2.35910e9i	0.00564589	−	0.0136304i
$646$	−2.21626e10	+	1.08346e9i	−0.127259	+	0.00622134i
$647$	3.61425e10	−	3.61425e10i	0.206253	−	0.206253i	−0.596419	−	0.802673i	$-0.703410\pi$
$647$	3.61425e10	−	3.61425e10i	0.206253	−	0.206253i	0.802673	+	0.596419i	$0.203410\pi$
$648$	−8.78243e10	−	1.46765e11i	−0.498098	−	0.832380i
$649$	−1.18309e11	+	1.18309e11i	−0.666868	+	0.666868i
$650$	−2.09609e11	−	1.90070e11i	−1.17424	−	1.06478i
$651$	−7.93457e9	+	1.91558e10i	−0.0441773	+	0.106654i
$652$	−5.53824e10	+	1.82257e11i	−0.306465	+	1.00854i
$653$	−8.55476e10	−	2.06530e11i	−0.470495	−	1.13588i	−0.963945	−	0.266102i	$-0.914264\pi$
$653$	−8.55476e10	−	2.06530e11i	−0.470495	−	1.13588i	0.493450	−	0.869774i	$-0.335736\pi$
$654$	3.97282e9	+	8.40501e9i	0.0217164	+	0.0459439i
$655$	−2.17822e10			−0.118341
$656$	2.08242e11	+	1.39431e11i	1.12448	+	0.752914i
$657$			1.25080e11i			0.671318i
$658$	−6.41451e9	−	1.35707e10i	−0.0342184	−	0.0723935i
$659$	−2.37063e11	+	9.81948e10i	−1.25696	+	0.520651i	−0.908976	−	0.416848i	$-0.863135\pi$
$659$	−2.37063e11	+	9.81948e10i	−1.25696	+	0.520651i	−0.347987	+	0.937499i	$0.613135\pi$
$660$	−7.50011e9	+	4.00428e9i	−0.0395268	+	0.0211032i
$661$	−1.90650e11	−	7.89697e10i	−0.998689	−	0.413671i	−0.177373	−	0.984144i	$-0.556760\pi$
$661$	−1.90650e11	−	7.89697e10i	−0.998689	−	0.413671i	−0.821316	+	0.570473i	$0.806760\pi$
$662$	−1.06476e10	−	9.65506e9i	−0.0554396	−	0.0502717i
$663$	1.10858e10	+	1.10858e10i	0.0573735	+	0.0573735i
$664$	−1.58644e11	+	2.13586e11i	−0.816113	+	1.09875i
$665$	−9.95413e9	−	9.95413e9i	−0.0508999	−	0.0508999i
$666$	8.37774e10	−	4.09563e9i	0.425824	−	0.0208173i
$667$	2.30542e11	+	9.54937e10i	1.16479	+	0.482471i
$668$	5.91705e10	−	5.79921e9i	0.297166	−	0.0291248i
$669$	−3.08599e9	+	1.27826e9i	−0.0154060	+	0.00638137i
$670$	−2.38714e9	+	6.66658e9i	−0.0118462	+	0.0330829i
$671$		−	3.72828e11i		−	1.83915i
$672$	1.17066e10	+	7.03571e9i	0.0574055	+	0.0345009i
$673$	−2.80493e11			−1.36729			−0.683646	−	0.729814i	$-0.739607\pi$
$673$	−2.80493e11			−1.36729			−0.683646	+	0.729814i	$0.739607\pi$
$674$	1.95423e11	+	6.99762e10i	0.946970	+	0.339087i
$675$	1.36369e10	+	3.29225e10i	0.0656903	+	0.158591i
$676$	4.95607e11	−	4.85737e10i	2.37329	−	0.232602i
$677$	−1.53243e10	+	3.69962e10i	−0.0729502	+	0.176117i	−0.956148	−	0.292882i	$-0.905386\pi$
$677$	−1.53243e10	+	3.69962e10i	−0.0729502	+	0.176117i	0.883198	+	0.469000i	$0.155386\pi$
$678$	−1.00503e9	−	2.05582e10i	−0.00475622	−	0.0972898i
$679$	6.25843e10	−	6.25843e10i	0.294433	−	0.294433i
$680$	−3.46650e10	+	5.11664e9i	−0.162127	+	0.0239304i
$681$	2.34442e10	−	2.34442e10i	0.109005	−	0.109005i
$682$	3.01331e11	−	3.32307e11i	1.39285	−	1.53604i
$683$	6.32293e10	−	1.52649e11i	0.290560	−	0.701474i	−0.709435	−	0.704771i	$-0.751050\pi$
$683$	6.32293e10	−	1.52649e11i	0.290560	−	0.701474i	0.999995	+	0.00329737i	$0.00104959\pi$
$684$	5.52892e10	−	2.95187e10i	0.252590	−	0.134857i
$685$	9.03256e9	+	2.18065e10i	0.0410250	+	0.0990431i
$686$	2.07941e11	−	9.82880e10i	0.938953	−	0.443817i
$687$	−2.87044e10			−0.128861
$688$	8.70261e10	+	1.73971e10i	0.388415	+	0.0776469i
$689$			3.40169e11i			1.50945i
$690$	−1.38174e10	+	6.53110e9i	−0.0609579	+	0.0288131i
$691$	−1.12525e11	+	4.66095e10i	−0.493558	+	0.204438i	−0.615558	−	0.788092i	$-0.711069\pi$
$691$	−1.12525e11	+	4.66095e10i	−0.493558	+	0.204438i	0.122000	+	0.992530i	$0.461069\pi$
$692$	2.68530e10	−	8.83701e10i	0.117103	−	0.385373i
$693$	1.69762e11	+	7.03177e10i	0.736050	+	0.304882i
$694$	−1.17463e11	+	1.29538e11i	−0.506365	+	0.558419i
$695$	−7.23671e10	−	7.23671e10i	−0.310172	−	0.310172i
$696$	1.58693e10	+	3.98716e9i	0.0676271	+	0.0169913i
$697$	−9.94854e10	−	9.94854e10i	−0.421530	−	0.421530i
$698$	2.93567e9	+	6.00499e10i	0.0123676	+	0.252983i
$699$	−1.23282e10	−	5.10652e9i	−0.0516406	−	0.0213903i
$700$	1.06934e11	+	8.78437e10i	0.445371	+	0.365863i
$701$	−3.17095e11	+	1.31345e11i	−1.31316	+	0.543928i	−0.925804	−	0.378004i	$-0.876611\pi$
$701$	−3.17095e11	+	1.31345e11i	−1.31316	+	0.543928i	−0.387353	+	0.921931i	$0.626611\pi$
$702$	−8.38047e10	−	3.00084e10i	−0.345080	−	0.123565i
$703$			3.04225e10i			0.124559i
$704$	−1.87133e11	−	2.28691e11i	−0.761835	−	0.931020i
$705$	1.10136e9			0.00445832
$706$	4.04339e10	−	1.12920e11i	0.162752	−	0.454519i
$707$	7.10673e10	+	1.71572e11i	0.284441	+	0.686701i
$708$	−1.25184e10	+	1.52388e10i	−0.0498213	+	0.0606482i
$709$	−7.23432e10	+	1.74652e11i	−0.286294	+	0.691176i	−0.999957	−	0.00931429i	$-0.997035\pi$
$709$	−7.23432e10	+	1.74652e11i	−0.286294	+	0.691176i	0.713662	+	0.700490i	$0.247035\pi$
$710$	−5.36138e10	+	2.62102e9i	−0.210981	+	0.0103142i
$711$	−2.13730e11	+	2.13730e11i	−0.836349	+	0.836349i
$712$	2.76847e11	+	6.95577e10i	1.07726	+	0.270661i
$713$	5.70187e11	−	5.70187e11i	2.20627	−	2.20627i
$714$	−5.68017e9	−	5.15069e9i	−0.0218559	−	0.0198186i
$715$	8.23496e10	−	1.98809e11i	0.315092	−	0.760699i
$716$	−4.53030e11	−	1.37662e11i	−1.72375	−	0.523796i
$717$	−1.14049e10	−	2.75339e10i	−0.0431535	−	0.104182i
$718$	1.51201e10	+	3.19885e10i	0.0568927	+	0.120364i
$719$	−1.84126e11			−0.688969			−0.344484	−	0.938792i	$-0.611946\pi$
$719$	−1.84126e11			−0.688969			−0.344484	+	0.938792i	$0.611946\pi$
$720$	8.23485e10	−	5.49096e10i	0.306426	−	0.204324i
$721$		−	9.57316e10i		−	0.354254i
$722$	−1.06409e11	−	2.25123e11i	−0.391589	−	0.828458i
$723$	4.67712e10	−	1.93733e10i	0.171169	−	0.0709005i
$724$	2.06359e10	+	3.86514e10i	0.0751049	+	0.140673i
$725$	1.53170e11	+	6.34449e10i	0.554396	+	0.229638i
$726$	9.21393e9	+	8.35503e9i	0.0331664	+	0.0300747i
$727$	6.26856e10	+	6.26856e10i	0.224404	+	0.224404i	0.810350	−	0.585946i	$-0.199277\pi$
$727$	6.26856e10	+	6.26856e10i	0.224404	+	0.224404i	−0.585946	+	0.810350i	$0.699277\pi$
$728$	−3.41985e11	+	5.04780e10i	−1.21754	+	0.179712i
$729$	−1.87797e11	−	1.87797e11i	−0.664935	−	0.664935i
$730$	−7.15572e10	+	3.49823e9i	−0.251978	+	0.0123185i
$731$	−4.60307e10	−	1.90665e10i	−0.161205	−	0.0667732i
$732$	−4.28646e9	−	4.37356e10i	−0.0149298	−	0.152332i
$733$	−5.16331e11	+	2.13871e11i	−1.78859	+	0.740860i	−0.798234	+	0.602347i	$0.794232\pi$
$733$	−5.16331e11	+	2.13871e11i	−1.78859	+	0.740860i	−0.990361	+	0.138513i	$0.955768\pi$
$734$	−1.14523e11	+	3.19829e11i	−0.394555	+	1.10188i
$735$			6.00561e9i			0.0205782i
$736$	−3.15912e11	−	4.27025e11i	−1.07660	−	1.45526i
$737$	3.35240e10			0.113628
$738$	3.74144e11	+	1.33972e11i	1.26129	+	0.451636i
$739$	−2.34594e10	−	5.66359e10i	−0.0786572	−	0.189895i	0.879659	−	0.475605i	$-0.157771\pi$
$739$	−2.34594e10	−	5.66359e10i	−0.0786572	−	0.189895i	−0.958316	+	0.285710i	$0.907771\pi$
$740$	4.68614e9	+	4.78136e10i	0.0156274	+	0.159450i
$741$	6.14655e9	−	1.48391e10i	0.0203872	−	0.0492192i
$742$	−8.12375e9	−	1.66174e11i	−0.0268004	−	0.548210i
$743$	−2.23511e9	+	2.23511e9i	−0.00733405	+	0.00733405i	−0.710764	−	0.703430i	$-0.751651\pi$
$743$	−2.23511e9	+	2.23511e9i	−0.00733405	+	0.00733405i	0.703430	+	0.710764i	$0.251651\pi$
$744$	3.15278e10	−	4.24467e10i	0.102897	−	0.138533i
$745$	−9.66204e10	+	9.66204e10i	−0.313649	+	0.313649i
$746$	4.60300e10	−	5.07619e10i	0.148623	−	0.163901i
$747$	−1.61455e11	+	3.89786e11i	−0.518523	+	1.25182i
$748$	7.81312e10	+	1.46342e11i	0.249585	+	0.467478i
$749$	−3.56418e10	−	8.60468e10i	−0.113248	−	0.273406i
$750$	−1.98349e10	+	9.37542e9i	−0.0626882	+	0.0296310i
$751$	−4.27545e11			−1.34407			−0.672036	−	0.740519i	$-0.734580\pi$
$751$	−4.27545e11			−1.34407			−0.672036	+	0.740519i	$0.734580\pi$
$752$	7.43183e9	+	3.75501e10i	0.0232394	+	0.117419i
$753$			1.23013e10i			0.0382623i
$754$	−3.74419e11	+	1.76977e11i	−1.15844	+	0.547561i
$755$	9.82434e10	−	4.06937e10i	0.302354	−	0.125239i
$756$	4.16555e10	+	1.26578e10i	0.127522	+	0.0387500i
$757$	3.02543e11	+	1.25317e11i	0.921305	+	0.381617i	0.792373	−	0.610037i	$-0.208845\pi$
$757$	3.02543e11	+	1.25317e11i	0.921305	+	0.381617i	0.128931	+	0.991654i	$0.458845\pi$
$758$	−2.77703e11	+	3.06251e11i	−0.841208	+	0.927684i
$759$	5.11629e10	+	5.11629e10i	0.154166	+	0.154166i
$760$	1.84336e10	+	3.08048e10i	0.0552531	+	0.0923345i
$761$	−2.09140e11	−	2.09140e11i	−0.623590	−	0.623590i	0.322857	−	0.946448i	$-0.395357\pi$
$761$	−2.09140e11	−	2.09140e11i	−0.623590	−	0.623590i	−0.946448	+	0.322857i	$0.895357\pi$
$762$	−1.62588e9	−	3.32578e10i	−0.00482245	−	0.0986447i
$763$	1.06322e11	+	4.40399e10i	0.313706	+	0.129941i
$764$	3.40640e11	−	4.14666e11i	0.999820	−	1.21710i
$765$	−5.13359e10	+	2.12640e10i	−0.149891	+	0.0620868i
$766$	6.82870e10	+	2.44519e10i	0.198346	+	0.0710228i
$767$		−	4.99150e11i		−	1.44228i
$768$	−2.45815e10	−	2.46758e10i	−0.0706584	−	0.0709293i
$769$	4.71714e11			1.34888			0.674441	−	0.738329i	$-0.264385\pi$
$769$	4.71714e11			1.34888			0.674441	+	0.738329i	$0.264385\pi$
$770$	−3.54801e10	+	9.90856e10i	−0.100930	+	0.281869i
$771$	2.93077e9	+	7.07551e9i	0.00829401	+	0.0200235i
$772$	4.63685e11	+	3.80907e11i	1.30543	+	1.07238i
$773$	2.22944e11	−	5.38236e11i	0.624423	−	1.50749i	−0.222038	−	0.975038i	$-0.571271\pi$
$773$	2.22944e11	−	5.38236e11i	0.624423	−	1.50749i	0.846460	−	0.532452i	$-0.178729\pi$
$774$	1.40564e11	−	6.87178e9i	0.391662	−	0.0191472i
$775$	3.78825e11	−	3.78825e11i	1.05010	−	1.05010i
$776$	−1.93678e11	+	1.15897e11i	−0.534113	+	0.319614i
$777$	−7.43375e9	+	7.43375e9i	−0.0203950	+	0.0203950i
$778$	−4.07930e11	−	3.69904e11i	−1.11344	−	1.00965i
$779$	−5.51601e10	+	1.33168e11i	−0.149787	+	0.361618i
$780$	7.37450e9	−	2.42687e10i	0.0199230	−	0.0655643i
$781$	9.72503e10	+	2.34783e11i	0.261389	+	0.631048i
$782$	1.27434e11	+	2.69604e11i	0.340769	+	0.720941i
$783$	5.21565e10			0.138759
$784$	−2.04758e11	+	4.05252e10i	−0.541971	+	0.107266i
$785$		−	1.79637e11i		−	0.473061i
$786$	5.19437e9	+	1.09894e10i	0.0136095	+	0.0287927i
$787$	−1.94685e11	+	8.06412e10i	−0.507497	+	0.210212i	−0.621715	−	0.783243i	$-0.713564\pi$
$787$	−1.94685e11	+	8.06412e10i	−0.507497	+	0.210212i	0.114218	+	0.993456i	$0.463564\pi$
$788$	−2.02867e11	+	1.08310e11i	−0.526147	+	0.280908i
$789$	−1.70979e10	−	7.08218e9i	−0.0441199	−	0.0182751i
$790$	−1.28250e11	−	1.16295e11i	−0.329269	−	0.298575i
$791$	−1.80165e11	−	1.80165e11i	−0.460218	−	0.460218i
$792$	−3.76171e11	−	2.79406e11i	−0.956058	−	0.710125i
$793$	7.86486e11	+	7.86486e11i	1.98883	+	1.98883i
$794$	1.40598e10	−	6.87345e8i	0.0353752	−	0.00172939i
$795$	1.12780e10	+	4.67151e9i	0.0282335	+	0.0116947i
$796$	−9.34635e10	+	9.16021e9i	−0.232804	+	0.0228167i
$797$	2.74350e11	−	1.13639e11i	0.679941	−	0.281641i	−0.0158614	−	0.999874i	$-0.505049\pi$
$797$	2.74350e11	−	1.13639e11i	0.679941	−	0.281641i	0.695802	+	0.718234i	$0.255049\pi$
$798$	−2.64823e9	+	7.39572e9i	−0.00653046	+	0.0182377i
$799$		−	2.14896e10i		−	0.0527279i
$800$	−2.09889e11	−	2.83710e11i	−0.512423	−	0.692652i
$801$	4.52655e11			1.09961
$802$	2.09516e11	+	7.50225e10i	0.506430	+	0.181340i
$803$	1.29798e11	+	3.13360e11i	0.312180	+	0.753670i
$804$	3.93263e9	−	3.85431e8i	0.00941150	−	0.000922406i
$805$	−7.23993e10	+	1.74787e11i	−0.172405	+	0.416223i
$806$	6.53459e10	+	1.33667e12i	0.154838	+	3.16726i
$807$	−3.42100e10	+	3.42100e10i	−0.0806601	+	0.0806601i
$808$	−6.91525e10	−	4.68504e11i	−0.162242	−	1.09918i
$809$	4.69409e11	−	4.69409e11i	1.09587	−	1.09587i	0.100977	−	0.994889i	$-0.467803\pi$
$809$	4.69409e11	−	4.69409e11i	1.09587	−	1.09587i	0.994889	−	0.100977i	$-0.0321968\pi$
$810$	1.04352e11	−	1.15079e11i	0.242416	−	0.267336i
$811$	1.31291e11	−	3.16966e11i	0.303496	−	0.732704i	−0.696391	−	0.717663i	$-0.745212\pi$
$811$	1.31291e11	−	3.16966e11i	0.303496	−	0.732704i	0.999887	−	0.0150414i	$-0.00478800\pi$
$812$	1.78678e11	−	9.53956e10i	0.411005	−	0.219434i
$813$	2.03656e10	+	4.91669e10i	0.0466160	+	0.112541i
$814$	2.05635e11	−	9.71977e10i	0.468380	−	0.221390i
$815$	−1.73014e11			−0.392148
$816$	1.08479e10	+	1.62687e10i	0.0244673	+	0.0366938i
$817$			5.10438e10i			0.114566i
$818$	−2.03472e10	+	9.61754e9i	−0.0454455	+	0.0214808i
$819$	−5.06451e11	+	2.09779e11i	−1.12565	+	0.466258i
$820$	−6.61799e10	+	2.17791e11i	−0.146376	+	0.481708i
$821$	−3.12050e11	−	1.29256e11i	−0.686834	−	0.284496i	0.0118462	−	0.999930i	$-0.496229\pi$
$821$	−3.12050e11	−	1.29256e11i	−0.686834	−	0.284496i	−0.698681	+	0.715434i	$0.746229\pi$
$822$	8.84767e9	−	9.75721e9i	0.0193795	−	0.0213717i
$823$	−2.18029e11	−	2.18029e11i	−0.475242	−	0.475242i	0.428364	−	0.903606i	$-0.359090\pi$
$823$	−2.18029e11	−	2.18029e11i	−0.475242	−	0.475242i	−0.903606	+	0.428364i	$0.859090\pi$
$824$	−5.94883e10	+	2.36770e11i	−0.129040	+	0.513591i
$825$	3.39921e10	+	3.39921e10i	0.0733773	+	0.0733773i
$826$	1.19204e10	+	2.43836e11i	0.0256078	+	0.523815i
$827$	3.42756e11	+	1.41974e11i	0.732763	+	0.303520i	0.717687	−	0.696366i	$-0.245201\pi$
$827$	3.42756e11	+	1.41974e11i	0.732763	+	0.303520i	0.0150762	+	0.999886i	$0.495201\pi$
$828$	−6.50864e11	−	5.34672e11i	−1.38474	−	1.13754i
$829$	2.46512e11	−	1.02108e11i	0.521938	−	0.216194i	−0.106130	−	0.994352i	$-0.533846\pi$
$829$	2.46512e11	−	1.02108e11i	0.521938	−	0.216194i	0.628068	+	0.778158i	$0.283846\pi$
$830$	−2.27508e11	−	8.14650e10i	−0.479384	−	0.171656i
$831$		−	6.68543e10i		−	0.140193i
$832$	8.77188e11	+	8.76667e10i	1.83063	+	0.182954i
$833$	1.17181e11			0.243376
$834$	−1.92528e10	+	5.37674e10i	−0.0397951	+	0.111136i
$835$	2.06651e10	+	4.98900e10i	0.0425101	+	0.102628i
$836$	1.07882e11	−	1.31327e11i	0.220864	−	0.268861i
$837$	6.44978e10	−	1.55712e11i	0.131414	−	0.317263i
$838$	−5.50749e11	+	2.69245e10i	−1.11681	+	0.0545974i
$839$	−1.63023e11	+	1.63023e11i	−0.329005	+	0.329005i	−0.852208	−	0.523203i	$-0.824737\pi$
$839$	−1.63023e11	+	1.63023e11i	−0.329005	+	0.329005i	0.523203	+	0.852208i	$0.324737\pi$
$840$	−3.02289e9	+	1.20314e10i	−0.00607163	+	0.0241657i
$841$	−1.82145e11	+	1.82145e11i	−0.364111	+	0.364111i
$842$	3.60368e11	+	3.26775e11i	0.716964	+	0.650131i
$843$	−3.33648e10	+	8.05498e10i	−0.0660661	+	0.159498i
$844$	5.38115e11	+	1.63516e11i	1.06049	+	0.322249i
$845$	1.73089e11	+	4.17875e11i	0.339503	+	0.819632i
$846$	2.59395e10	+	5.48784e10i	0.0506384	+	0.107132i
$847$	1.53968e11			0.299155
$848$	−8.31694e10	+	4.16040e11i	−0.160835	+	0.804548i
$849$		−	7.39516e10i		−	0.142337i
$850$	8.46660e10	+	1.79122e11i	0.162193	+	0.343141i
$851$	3.77734e11	−	1.56463e11i	0.720225	−	0.298327i
$852$	1.41076e10	+	2.64238e10i	0.0267728	+	0.0501460i
$853$	1.78042e11	+	7.37475e10i	0.336300	+	0.139300i	0.544442	−	0.838799i	$-0.316742\pi$
$853$	1.78042e11	+	7.37475e10i	0.336300	+	0.139300i	−0.208142	+	0.978099i	$0.566742\pi$
$854$	−4.02983e11	−	3.65418e11i	−0.757627	−	0.687003i
$855$	4.02533e10	+	4.02533e10i	0.0753247	+	0.0753247i
$856$	3.46815e10	+	2.34965e11i	0.0645955	+	0.437631i
$857$	−4.35430e11	−	4.35430e11i	−0.807225	−	0.807225i	0.176988	−	0.984213i	$-0.443365\pi$
$857$	−4.35430e11	−	4.35430e11i	−0.807225	−	0.807225i	−0.984213	+	0.176988i	$0.943365\pi$
$858$	−1.19940e11	+	5.86350e9i	−0.221316	+	0.0108195i
$859$	9.53532e10	+	3.94966e10i	0.175131	+	0.0725416i	0.468526	−	0.883450i	$-0.344785\pi$
$859$	9.53532e10	+	3.94966e10i	0.175131	+	0.0725416i	−0.293395	+	0.955991i	$0.594785\pi$
$860$	7.86255e9	+	8.02231e10i	0.0143737	+	0.146658i
$861$	−4.60181e10	+	1.90613e10i	−0.0837367	+	0.0346849i
$862$	−1.34694e11	+	3.76160e11i	−0.243959	+	0.681307i
$863$			7.56010e11i			1.36296i	0.731835	+	0.681482i	$0.238664\pi$
$863$			7.56010e11i			1.36296i	−0.731835	+	0.681482i	$0.761336\pi$
$864$	−9.51595e10	−	5.71912e10i	−0.170764	−	0.102630i
$865$	8.38882e10			0.149843
$866$	−8.18417e10	−	2.93055e10i	−0.145513	−	0.0521048i
$867$	1.74476e10	+	4.21221e10i	0.0308787	+	0.0745477i
$868$	−6.38433e10	−	6.51406e11i	−0.112470	−	1.14755i
$869$	−3.13660e11	+	7.57242e11i	−0.550022	+	1.32787i
$870$	7.25677e8	+	1.48439e10i	0.00126668	+	0.0259103i
$871$	−7.07194e10	+	7.07194e10i	−0.122876	+	0.122876i
$872$	−2.35595e11	−	1.74991e11i	−0.407474	−	0.302657i
$873$	−2.53083e11	+	2.53083e11i	−0.435719	+	0.435719i
$874$	2.05222e11	−	2.26319e11i	0.351705	−	0.387860i
$875$	−1.03929e11	+	2.50908e11i	−0.177299	+	0.428037i
$876$	1.88291e10	+	3.52673e10i	0.0319751	+	0.0598901i
$877$	−2.67186e11	−	6.45043e11i	−0.451663	−	1.09041i	−0.971690	−	0.236261i	$-0.924078\pi$
$877$	−2.67186e11	−	6.45043e11i	−0.451663	−	1.09041i	0.520026	−	0.854150i	$-0.325922\pi$
$878$	2.32625e11	−	1.09955e11i	0.391452	−	0.185028i
$879$	−3.14953e10			−0.0527582
$880$	1.49324e11	−	2.23018e11i	0.249000	−	0.371885i
$881$		−	3.58562e11i		−	0.595197i	−0.954691	−	0.297598i	$-0.903814\pi$
$881$		−	3.58562e11i		−	0.595197i	0.954691	−	0.297598i	$-0.0961857\pi$
$882$	−2.99248e11	+	1.41446e11i	−0.494489	+	0.233731i
$883$	4.01806e9	−	1.66433e9i	0.00660958	−	0.00273778i	−0.379376	−	0.925243i	$-0.623861\pi$
$883$	4.01806e9	−	1.66433e9i	0.00660958	−	0.00273778i	0.385986	+	0.922505i	$0.373861\pi$
$884$	−4.73529e11	−	1.43891e11i	−0.775421	−	0.235626i
$885$	−1.65489e10	−	6.85477e9i	−0.0269771	−	0.0111743i
$886$	7.00967e11	−	7.73027e11i	1.13753	−	1.25447i
$887$	−3.15335e10	−	3.15335e10i	−0.0509422	−	0.0509422i	0.681177	−	0.732119i	$-0.261469\pi$
$887$	−3.15335e10	−	3.15335e10i	−0.0509422	−	0.0509422i	−0.732119	+	0.681177i	$0.761469\pi$
$888$	2.30050e10	−	1.37663e10i	0.0369974	−	0.0221393i
$889$	−2.91459e11	−	2.91459e11i	−0.466627	−	0.466627i
$890$	1.26598e10	+	2.58959e11i	0.0201774	+	0.412735i
$891$	−6.79476e11	−	2.81448e11i	−1.07811	−	0.446568i
$892$	6.69320e10	−	8.14774e10i	0.105724	−	0.128700i
$893$	−2.03402e10	+	8.42517e9i	−0.0319852	+	0.0132487i
$894$	7.17871e10	+	2.57052e10i	0.112382	+	0.0402412i
$895$		−	4.30054e11i		−	0.670240i
$896$	−4.30603e11	−	2.18769e10i	−0.668105	−	0.0339432i
$897$	−2.15858e11			−0.333425
$898$	2.14349e11	−	5.98615e11i	0.329623	−	0.920539i
$899$	−3.00072e11	−	7.24437e11i	−0.459395	−	1.10908i
$900$	−4.32427e11	−	3.55230e11i	−0.659087	−	0.541426i
$901$	9.11502e10	−	2.20056e11i	0.138312	−	0.333914i
$902$	1.07636e12	−	5.26199e10i	1.62603	−	0.0794921i
$903$	−1.24726e10	+	1.24726e10i	−0.0187588	+	0.0187588i
$904$	3.33640e11	+	5.57551e11i	0.499579	+	0.834855i
$905$	−2.81402e10	+	2.81402e10i	−0.0419501	+	0.0419501i
$906$	−4.39585e10	−	3.98608e10i	−0.0652424	−	0.0591607i
$907$	6.49605e10	−	1.56829e11i	0.0959887	−	0.231737i	−0.868591	−	0.495531i	$-0.834974\pi$
$907$	6.49605e10	−	1.56829e11i	0.0959887	−	0.231737i	0.964579	+	0.263793i	$0.0849737\pi$
$908$	−3.04300e11	+	1.00142e12i	−0.447671	+	1.47324i
$909$	−2.87388e11	−	6.93815e11i	−0.420933	−	1.01622i
$910$	−1.34177e11	−	2.83868e11i	−0.195664	−	0.413953i
$911$	−5.03249e11			−0.730650			−0.365325	−	0.930880i	$-0.619042\pi$
$911$	−5.03249e11			−0.730650			−0.365325	+	0.930880i	$0.619042\pi$
$912$	1.11455e10	−	1.66460e10i	0.0161110	−	0.0240619i
$913$			1.14406e12i			1.64652i
$914$	−2.35772e11	−	4.98808e11i	−0.337838	−	0.714740i
$915$	3.68760e10	−	1.52745e10i	0.0526089	−	0.0217913i
$916$	7.99342e11	−	4.26766e11i	1.13540	−	0.606188i
$917$	1.39013e11	+	5.75812e10i	0.196598	+	0.0814335i
$918$	4.61725e10	+	4.18684e10i	0.0650148	+	0.0589543i
$919$	−6.50045e10	−	6.50045e10i	−0.0911342	−	0.0911342i	0.660070	−	0.751204i	$-0.270527\pi$
$919$	−6.50045e10	−	6.50045e10i	−0.0911342	−	0.0911342i	−0.751204	+	0.660070i	$0.770527\pi$
$920$	2.87677e11	−	3.87306e11i	0.401563	−	0.540634i
$921$	6.23067e10	+	6.23067e10i	0.0865957	+	0.0865957i
$922$	−3.04295e11	+	1.48761e10i	−0.421086	+	0.0205857i
$923$	−7.00429e11	−	2.90127e11i	−0.965067	−	0.399744i
$924$	5.84508e10	−	5.72867e9i	0.0801867	−	0.00785897i
$925$	2.50962e11	−	1.03952e11i	0.342800	−	0.141993i
$926$	−1.75154e10	+	4.89154e10i	−0.0238219	+	0.0665276i
$927$			3.87127e11i			0.524246i
$928$	−5.01198e11	+	1.24907e11i	−0.675799	+	0.168420i
$929$	−8.78802e11			−1.17985			−0.589927	−	0.807457i	$-0.700843\pi$
$929$	−8.78802e11			−1.17985			−0.589927	+	0.807457i	$0.700843\pi$
$930$	4.52135e10	+	1.61898e10i	0.0604416	+	0.0216427i
$931$	−4.59418e10	−	1.10913e11i	−0.0611518	−	0.147634i
$932$	4.19231e11	−	4.10881e10i	0.555635	−	0.0544569i
$933$	3.89954e10	−	9.41432e10i	0.0514620	−	0.124240i
$934$	−4.37199e10	−	8.94304e11i	−0.0574503	−	1.17516i
$935$	−1.06544e11	+	1.06544e11i	−0.139406	+	0.139406i
$936$	1.38295e12	−	2.04127e11i	1.80178	−	0.265948i
$937$	−1.93881e11	+	1.93881e11i	−0.251523	+	0.251523i	−0.821595	−	0.570072i	$-0.806915\pi$
$937$	−1.93881e11	+	1.93881e11i	−0.251523	+	0.251523i	0.570072	+	0.821595i	$0.306915\pi$
$938$	3.28578e10	−	3.62355e10i	0.0424450	−	0.0468083i
$939$	−2.64366e9	+	6.38237e9i	−0.00340051	+	0.00820956i
$940$	−3.06699e10	+	1.63745e10i	−0.0392827	+	0.0209729i
$941$	3.11462e11	+	7.51936e11i	0.397234	+	0.959009i	0.988319	+	0.152399i	$0.0486999\pi$
$941$	3.11462e11	+	7.51936e11i	0.397234	+	0.959009i	−0.591085	+	0.806609i	$0.701300\pi$
$942$	−9.06291e10	+	4.28378e10i	−0.115097	+	0.0544031i
$943$	1.93714e12			2.44971
$944$	1.22039e11	−	6.10479e11i	0.153678	−	0.768746i
$945$			3.95428e10i			0.0495839i
$946$	3.45020e11	−	1.63081e11i	0.430804	−	0.203629i
$947$	7.80398e10	−	3.23251e10i	0.0970323	−	0.0401921i	−0.333639	−	0.942701i	$-0.608277\pi$
$947$	7.80398e10	−	3.23251e10i	0.0970323	−	0.0401921i	0.430672	+	0.902509i	$0.358277\pi$
$948$	−2.80886e10	+	9.24366e10i	−0.0347774	+	0.114449i
$949$	−9.34848e11	−	3.87227e11i	−1.15259	−	0.477420i
$950$	1.36347e11	−	1.50364e11i	0.167399	−	0.184607i
$951$	−3.52854e10	−	3.52854e10i	−0.0431393	−	0.0431393i
$952$	2.34756e11	+	5.89825e10i	0.285805	+	0.0718084i
$953$	5.35508e11	+	5.35508e11i	0.649223	+	0.649223i	0.952805	−	0.303582i	$-0.0981827\pi$
$953$	5.35508e11	+	5.35508e11i	0.649223	+	0.649223i	−0.303582	+	0.952805i	$0.598183\pi$
$954$	3.28515e10	+	6.71987e11i	0.0396608	+	0.811274i
$955$	4.50315e11	+	1.86526e11i	0.541381	+	0.224247i
$956$	7.26962e11	+	5.97184e11i	0.870322	+	0.714952i
$957$	6.50039e10	−	2.69255e10i	0.0774982	−	0.0321008i
$958$	−9.34990e11	−	3.34797e11i	−1.11006	−	0.397484i
$959$		−	1.63046e11i		−	0.192768i
$960$	1.49528e10	−	2.78785e10i	0.0176051	−	0.0328235i
$961$	−1.68097e12			−1.97091
$962$	−2.28749e11	+	6.38829e11i	−0.267091	+	0.745906i
$963$	1.44131e11	+	3.47963e11i	0.167592	+	0.404602i
$964$	−1.01442e12	+	1.23487e12i	−1.17465	+	1.42993i
$965$	−2.08576e11	+	5.03547e11i	−0.240522	+	0.580672i
$966$	1.05447e11	−	5.15501e9i	0.121095	−	0.00591999i
$967$	−2.69766e11	+	2.69766e11i	−0.308518	+	0.308518i	−0.844335	−	0.535816i	$-0.820004\pi$
$967$	−2.69766e11	+	2.69766e11i	−0.308518	+	0.308518i	0.535816	+	0.844335i	$0.320004\pi$
$968$	−3.80803e11	−	9.56767e10i	−0.433710	−	0.108969i
$969$	−7.95242e9	+	7.95242e9i	−0.00901995	+	0.00901995i
$970$	−1.51865e11	−	1.37708e11i	−0.171542	−	0.155551i
$971$	−3.57835e10	+	8.63889e10i	−0.0402537	+	0.0971810i	−0.942728	−	0.333563i	$-0.891749\pi$
$971$	−3.57835e10	+	8.63889e10i	−0.0402537	+	0.0971810i	0.902474	+	0.430744i	$0.141749\pi$
$972$	−2.53099e11	−	7.69090e10i	−0.283547	−	0.0861613i
$973$	2.70542e11	+	6.53147e11i	0.301845	+	0.728718i
$974$	−4.11926e11	−	8.71484e11i	−0.457703	−	0.968331i
$975$	−1.43413e11			−0.158698
$976$	7.69611e11	+	1.15419e12i	0.848149	+	1.27198i
$977$		−	1.52574e12i		−	1.67456i	−0.546771	−	0.837282i	$-0.684143\pi$
$977$		−	1.52574e12i		−	1.67456i	0.546771	−	0.837282i	$-0.315857\pi$
$978$	4.12584e10	+	8.72875e10i	0.0450979	+	0.0954106i
$979$	1.13402e12	−	4.69727e11i	1.23450	−	0.511346i
$980$	−8.92892e10	−	1.67241e11i	−0.0968043	−	0.181317i
$981$	−4.29952e11	−	1.78092e11i	−0.464242	−	0.192295i
$982$	5.13004e11	+	4.65183e11i	0.551664	+	0.500240i
$983$	1.00978e12	+	1.00978e12i	1.08147	+	1.08147i	0.996373	+	0.0850967i	$0.0271199\pi$
$983$	1.00978e12	+	1.00978e12i	1.08147	+	1.08147i	0.0850967	+	0.996373i	$0.472880\pi$
$984$	1.25660e11	−	1.85477e10i	0.134034	−	0.0197838i
$985$	−1.47697e11	−	1.47697e11i	−0.156902	−	0.156902i
$986$	2.89634e11	−	1.41594e10i	0.306437	−	0.0149808i
$987$	−7.02882e9	−	2.91143e9i	−0.00740651	−	0.00306788i
$988$	4.94565e10	+	5.04614e11i	0.0519033	+	0.529580i
$989$	6.33774e11	−	2.62518e11i	0.662444	−	0.274393i
$990$	1.43477e11	−	4.00690e11i	0.149363	−	0.417127i
$991$			1.39019e12i			1.44138i	0.693257	+	0.720691i	$0.256175\pi$
$991$			1.39019e12i			1.44138i	−0.693257	+	0.720691i	$0.743825\pi$
$992$	−2.46887e11	+	1.65077e12i	−0.254948	+	1.70467i
$993$	−7.28505e9			−0.00749265
$994$	3.49090e11	+	1.25001e11i	0.357596	+	0.128046i
$995$	−3.26419e10	−	7.88044e10i	−0.0333029	−	0.0804004i
$996$	1.31534e10	+	1.34207e11i	0.0133660	+	0.136376i
$997$	1.03607e11	−	2.50130e11i	0.104860	−	0.253154i	−0.862738	−	0.505652i	$-0.831252\pi$
$997$	1.03607e11	−	2.50130e11i	0.104860	−	0.253154i	0.967598	+	0.252498i	$0.0812520\pi$
$998$	−4.05948e10	−	8.30378e11i	−0.0409212	−	0.837054i
$999$	6.04268e10	−	6.04268e10i	0.0606691	−	0.0606691i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.9.h.a.11.13	yes	124
32.3	odd	8	inner	32.9.h.a.3.13	✓	124

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.9.h.a.3.13	✓	124	32.3	odd	8	inner
32.9.h.a.11.13	yes	124	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	32.h (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.39384 + 15.0634i) q^{2} +(3.10339 + 7.49224i) q^{3} +(-197.813 - 162.499i) q^{4} +(88.9809 - 214.819i) q^{5} +(-129.598 + 6.33566i) q^{6} +(-1135.75 + 1135.75i) q^{7} +(3514.77 - 2103.24i) q^{8} +(4592.82 - 4592.82i) q^{9} +O(q^{10})\)	\(q+(-5.39384 + 15.0634i) q^{2} +(3.10339 + 7.49224i) q^{3} +(-197.813 - 162.499i) q^{4} +(88.9809 - 214.819i) q^{5} +(-129.598 + 6.33566i) q^{6} +(-1135.75 + 1135.75i) q^{7} +(3514.77 - 2103.24i) q^{8} +(4592.82 - 4592.82i) q^{9} +(2755.96 + 2499.06i) q^{10} +(6740.21 - 16272.3i) q^{11} +(603.593 - 1986.36i) q^{12} +(20108.1 + 48545.2i) q^{13} +(-10982.2 - 23234.3i) q^{14} +1885.62 q^{15} +(12723.9 + 64288.9i) q^{16} -36792.0i q^{17} +(44410.7 + 93956.6i) q^{18} +(-34824.1 + 14424.6i) q^{19} +(-52509.5 + 28034.6i) q^{20} +(-12033.9 - 4984.62i) q^{21} +(208761. + 189301. i) q^{22} +(358200. + 358200. i) q^{23} +(26665.7 + 19806.3i) q^{24} +(237984. + 237984. i) q^{25} +(-839716. + 41051.3i) q^{26} +(97820.4 + 40518.5i) q^{27} +(409223. - 40107.4i) q^{28} +(455103. - 188510. i) q^{29} +(-10170.7 + 28403.8i) q^{30} -1.59181e6i q^{31} +(-1.03704e6 - 155098. i) q^{32} +142833. q^{33} +(554213. + 198450. i) q^{34} +(142920. + 345040. i) q^{35} +(-1.65485e6 + 162189. i) q^{36} +(308866. - 745668. i) q^{37} +(-29448.3 - 602374. i) q^{38} +(-301309. + 301309. i) q^{39} +(-139069. - 942187. i) q^{40} +(2.70399e6 - 2.70399e6i) q^{41} +(139995. - 154386. i) q^{42} +(518225. - 1.25111e6i) q^{43} +(-3.97754e6 + 2.12359e6i) q^{44} +(-577952. - 1.39530e6i) q^{45} +(-7.32779e6 + 3.46364e6i) q^{46} +584083. q^{47} +(-442181. + 294844. i) q^{48} +3.18496e6i q^{49} +(-4.86850e6 + 2.30120e6i) q^{50} +(275655. - 114180. i) q^{51} +(3.91092e6 - 1.28704e7i) q^{52} +(5.98108e6 + 2.47744e6i) q^{53} +(-1.13798e6 + 1.25496e6i) q^{54} +(-2.89585e6 - 2.89585e6i) q^{55} +(-1.60313e6 + 6.38064e6i) q^{56} +(-216145. - 216145. i) q^{57} +(384849. + 7.87219e6i) q^{58} +(-8.77638e6 - 3.63530e6i) q^{59} +(-372999. - 306411. i) q^{60} +(1.95565e7 - 8.10055e6i) q^{61} +(2.39781e7 + 8.58597e6i) q^{62} +1.04326e7i q^{63} +(7.92995e6 - 1.47848e7i) q^{64} +1.22177e7 q^{65} +(-770420. + 2.15156e6i) q^{66} +(728387. + 1.75848e6i) q^{67} +(-5.97868e6 + 7.27794e6i) q^{68} +(-1.57209e6 + 3.79535e6i) q^{69} +(-5.96836e6 + 291776. i) q^{70} +(-1.02024e7 + 1.02024e7i) q^{71} +(6.48288e6 - 2.58025e7i) q^{72} +(-1.36169e7 + 1.36169e7i) q^{73} +(9.56633e6 + 8.67459e6i) q^{74} +(-1.04448e6 + 2.52159e6i) q^{75} +(9.23265e6 + 2.80552e6i) q^{76} +(1.08260e7 + 2.61364e7i) q^{77} +(-2.91353e6 - 6.16396e6i) q^{78} -4.65357e7 q^{79} +(1.49427e7 + 2.98715e6i) q^{80} -4.17566e7i q^{81} +(2.61465e7 + 5.53163e7i) q^{82} +(-6.00110e7 + 2.48574e7i) q^{83} +(1.57047e6 + 2.94153e6i) q^{84} +(-7.90362e6 - 3.27379e6i) q^{85} +(1.60507e7 + 1.45545e7i) q^{86} +(2.82472e6 + 2.82472e6i) q^{87} +(-1.05344e7 - 7.13696e7i) q^{88} +(4.92785e7 + 4.92785e7i) q^{89} +(2.41354e7 - 1.17991e6i) q^{90} +(-7.79727e7 - 3.22974e7i) q^{91} +(-1.26494e7 - 1.29064e8i) q^{92} +(1.19262e7 - 4.94000e6i) q^{93} +(-3.15045e6 + 8.79828e6i) q^{94} +8.76439e6i q^{95} +(-2.05631e6 - 8.25110e6i) q^{96} -5.51041e7 q^{97} +(-4.79764e7 - 1.71792e7i) q^{98} +(-4.37792e7 - 1.05692e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 124 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 124 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 124 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 34996 q^{10} - 4 q^{11} - 45364 q^{12} - 4 q^{13} + 145580 q^{14} - 8 q^{15} - 278384 q^{16} - 131224 q^{18} - 4 q^{19} + 689996 q^{20} - 4 q^{21} + 6048 q^{22} + 845564 q^{23} - 310832 q^{24} - 4 q^{25} + 1682096 q^{26} - 51076 q^{27} - 1807624 q^{28} - 4 q^{29} - 3968188 q^{30} + 2420456 q^{32} - 8 q^{33} + 4139280 q^{34} - 2415748 q^{35} - 2364816 q^{36} - 4 q^{37} - 4553644 q^{38} + 7650044 q^{39} - 14971800 q^{40} - 4 q^{41} + 17019656 q^{42} - 1859716 q^{43} + 13377860 q^{44} - 26248 q^{45} + 11790684 q^{46} - 8 q^{47} - 21819984 q^{48} - 49149676 q^{50} - 27697792 q^{51} - 33503196 q^{52} - 5358724 q^{53} + 82403296 q^{54} + 46326780 q^{55} + 87708200 q^{56} - 4 q^{57} - 37235424 q^{58} - 44938756 q^{59} - 167711176 q^{60} + 48952060 q^{61} + 23721528 q^{62} + 27135128 q^{64} - 8 q^{65} + 226680332 q^{66} + 93380476 q^{67} - 491760 q^{68} - 17273092 q^{69} - 167238952 q^{70} - 79832068 q^{71} - 184202092 q^{72} - 4 q^{73} + 28015148 q^{74} - 27399560 q^{75} + 201789948 q^{76} - 94964356 q^{77} + 473461108 q^{78} + 144406520 q^{79} - 447998920 q^{80} - 231632004 q^{82} - 140384644 q^{83} + 263072 q^{84} + 1562496 q^{85} + 268005440 q^{86} - 149712644 q^{87} + 220344096 q^{88} - 4 q^{89} + 51924392 q^{90} + 350400764 q^{91} - 622977496 q^{92} + 26240 q^{93} - 100742552 q^{94} + 101686144 q^{96} - 8 q^{97} + 721239576 q^{98} - 630043272 q^{99}+O(q^{100}) \) 124 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 34996 * q^10 - 4 * q^11 - 45364 * q^12 - 4 * q^13 + 145580 * q^14 - 8 * q^15 - 278384 * q^16 - 131224 * q^18 - 4 * q^19 + 689996 * q^20 - 4 * q^21 + 6048 * q^22 + 845564 * q^23 - 310832 * q^24 - 4 * q^25 + 1682096 * q^26 - 51076 * q^27 - 1807624 * q^28 - 4 * q^29 - 3968188 * q^30 + 2420456 * q^32 - 8 * q^33 + 4139280 * q^34 - 2415748 * q^35 - 2364816 * q^36 - 4 * q^37 - 4553644 * q^38 + 7650044 * q^39 - 14971800 * q^40 - 4 * q^41 + 17019656 * q^42 - 1859716 * q^43 + 13377860 * q^44 - 26248 * q^45 + 11790684 * q^46 - 8 * q^47 - 21819984 * q^48 - 49149676 * q^50 - 27697792 * q^51 - 33503196 * q^52 - 5358724 * q^53 + 82403296 * q^54 + 46326780 * q^55 + 87708200 * q^56 - 4 * q^57 - 37235424 * q^58 - 44938756 * q^59 - 167711176 * q^60 + 48952060 * q^61 + 23721528 * q^62 + 27135128 * q^64 - 8 * q^65 + 226680332 * q^66 + 93380476 * q^67 - 491760 * q^68 - 17273092 * q^69 - 167238952 * q^70 - 79832068 * q^71 - 184202092 * q^72 - 4 * q^73 + 28015148 * q^74 - 27399560 * q^75 + 201789948 * q^76 - 94964356 * q^77 + 473461108 * q^78 + 144406520 * q^79 - 447998920 * q^80 - 231632004 * q^82 - 140384644 * q^83 + 263072 * q^84 + 1562496 * q^85 + 268005440 * q^86 - 149712644 * q^87 + 220344096 * q^88 - 4 * q^89 + 51924392 * q^90 + 350400764 * q^91 - 622977496 * q^92 + 26240 * q^93 - 100742552 * q^94 + 101686144 * q^96 - 8 * q^97 + 721239576 * q^98 - 630043272 * q^99

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