LMFDB - Embedded newform 29.8.e.a.4.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,8,Mod(4,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("29.4");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	29.e (of order $14$, degree $6$, 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:	$9.05916573904$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			4.15
Character	$\chi$	$=$	29.4
Dual form			29.8.e.a.22.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(17.9566 + 4.09849i) q^{2} +(26.3233 + 54.6609i) q^{3} +(190.320 + 91.6531i) q^{4} +(30.2961 - 132.736i) q^{5} +(248.651 + 1089.41i) q^{6} +(459.975 - 221.512i) q^{7} +(1198.65 + 955.891i) q^{8} +(-931.324 + 1167.84i) q^{9} +O(q^{10})$	\(q+(17.9566 + 4.09849i) q^{2} +(26.3233 + 54.6609i) q^{3} +(190.320 + 91.6531i) q^{4} +(30.2961 - 132.736i) q^{5} +(248.651 + 1089.41i) q^{6} +(459.975 - 221.512i) q^{7} +(1198.65 + 955.891i) q^{8} +(-931.324 + 1167.84i) q^{9} +(1088.03 - 2259.33i) q^{10} +(-4318.10 + 3443.57i) q^{11} +12815.7i q^{12} +(-2853.18 - 3577.78i) q^{13} +(9167.47 - 2092.41i) q^{14} +(8052.97 - 1838.04i) q^{15} +(747.744 + 937.641i) q^{16} +752.320i q^{17} +(-21509.9 + 17153.5i) q^{18} +(18928.8 - 39306.1i) q^{19} +(17931.6 - 22485.5i) q^{20} +(24216.1 + 19311.7i) q^{21} +(-91652.1 + 44137.3i) q^{22} +(4143.38 + 18153.3i) q^{23} +(-20697.4 + 90681.4i) q^{24} +(53687.2 + 25854.4i) q^{25} +(-36570.1 - 75938.7i) q^{26} +(41005.6 + 9359.26i) q^{27} +107844. q^{28} +(128165. - 28697.7i) q^{29} +152137. q^{30} +(-271537. - 61976.6i) q^{31} +(-75561.6 - 156905. i) q^{32} +(-301895. - 145385. i) q^{33} +(-3083.37 + 13509.1i) q^{34} +(-15467.2 - 67766.2i) q^{35} +(-284286. + 136905. i) q^{36} +(-199573. - 159154. i) q^{37} +(500994. - 628227. i) q^{38} +(120459. - 250137. i) q^{39} +(163196. - 130144. i) q^{40} +270766. i q^{41} +(355691. + 446023. i) q^{42} +(173542. - 39609.8i) q^{43} +(-1.13743e6 + 259612. i) q^{44} +(126799. + 159001. i) q^{45} +342954. i q^{46} +(-143643. + 114551. i) q^{47} +(-31569.2 + 65554.2i) q^{48} +(-350962. + 440092. i) q^{49} +(858078. + 684294. i) q^{50} +(-41122.5 + 19803.5i) q^{51} +(-215102. - 942425. i) q^{52} +(-327225. + 1.43367e6i) q^{53} +(697964. + 336122. i) q^{54} +(326264. + 677495. i) q^{55} +(763090. + 174170. i) q^{56} +2.64678e6 q^{57} +(2.41903e6 + 9969.81i) q^{58} -1.74886e6 q^{59} +(1.70110e6 + 388265. i) q^{60} +(1.24019e6 + 2.57527e6i) q^{61} +(-4.62189e6 - 2.22578e6i) q^{62} +(-169694. + 743478. i) q^{63} +(-747917. - 3.27684e6i) q^{64} +(-561341. + 270328. i) q^{65} +(-4.82517e6 - 3.84794e6i) q^{66} +(-865257. + 1.08500e6i) q^{67} +(-68952.4 + 143181. i) q^{68} +(-883209. + 704336. i) q^{69} -1.28025e6i q^{70} +(-2.34765e6 - 2.94386e6i) q^{71} +(-2.23266e6 + 509591. i) q^{72} +(5.10639e6 - 1.16550e6i) q^{73} +(-2.93136e6 - 3.67581e6i) q^{74} +3.61516e6i q^{75} +(7.20506e6 - 5.74584e6i) q^{76} +(-1.22342e6 + 2.54047e6i) q^{77} +(3.18823e6 - 3.99791e6i) q^{78} +(-4.43239e6 - 3.53471e6i) q^{79} +(147113. - 70845.7i) q^{80} +(1.29474e6 + 5.67265e6i) q^{81} +(-1.10973e6 + 4.86205e6i) q^{82} +(4.39466e6 + 2.11636e6i) q^{83} +(2.83882e6 + 5.89487e6i) q^{84} +(99860.0 + 22792.4i) q^{85} +3.27857e6 q^{86} +(4.94237e6 + 6.25021e6i) q^{87} -8.46757e6 q^{88} +(5.56990e6 + 1.27129e6i) q^{89} +(1.62523e6 + 3.37482e6i) q^{90} +(-2.10491e6 - 1.01367e6i) q^{91} +(-875242. + 3.83469e6i) q^{92} +(-3.76006e6 - 1.64739e7i) q^{93} +(-3.04883e6 + 1.46824e6i) q^{94} +(-4.64387e6 - 3.70336e6i) q^{95} +(6.58755e6 - 8.26052e6i) q^{96} +(-881024. + 1.82947e6i) q^{97} +(-8.10581e6 + 6.46417e6i) q^{98} -8.24995e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 7 q^{2} - 7 q^{3} + 709 q^{4} + 191 q^{5} + 1801 q^{6} - 667 q^{7} + 9086 q^{8} + 9103 q^{9}+O(q^{10}) $ 96 * q - 7 * q^2 - 7 * q^3 + 709 * q^4 + 191 * q^5 + 1801 * q^6 - 667 * q^7 + 9086 * q^8 + 9103 * q^9	\( 96 q - 7 q^{2} - 7 q^{3} + 709 q^{4} + 191 q^{5} + 1801 q^{6} - 667 q^{7} + 9086 q^{8} + 9103 q^{9} - 7 q^{10} + 4207 q^{11} + 377 q^{13} - 7 q^{14} - 74473 q^{15} - 125851 q^{16} - 194880 q^{18} - 7 q^{19} + 162901 q^{20} + 86933 q^{21} + 252614 q^{22} + 238675 q^{23} - 490819 q^{24} - 107349 q^{25} + 367017 q^{26} + 75593 q^{27} + 1397540 q^{28} + 379863 q^{29} - 175646 q^{30} - 143885 q^{31} + 473172 q^{32} - 1419437 q^{33} - 2314463 q^{34} - 1018325 q^{35} + 1720462 q^{36} + 662991 q^{37} - 2763860 q^{38} + 42189 q^{39} + 580601 q^{40} - 3296492 q^{42} - 1587425 q^{43} + 2344398 q^{44} + 6508254 q^{45} + 526673 q^{47} + 6175806 q^{48} - 1391517 q^{49} - 4194526 q^{50} - 68204 q^{51} - 7720808 q^{52} + 1762640 q^{53} - 2032428 q^{54} + 2655709 q^{55} + 17091081 q^{56} + 4906842 q^{57} + 13231229 q^{58} - 8638324 q^{59} - 9957136 q^{60} + 2797697 q^{61} - 884069 q^{62} - 20232301 q^{63} - 17528026 q^{64} - 7454088 q^{65} - 17541475 q^{66} - 4890949 q^{67} + 22029140 q^{68} + 13204429 q^{69} - 1091301 q^{71} + 25137595 q^{72} + 14363636 q^{73} + 3185328 q^{74} - 41019881 q^{76} - 25204627 q^{77} - 15753743 q^{78} + 31186057 q^{79} + 24146022 q^{80} - 29435757 q^{81} - 51438506 q^{82} - 8367235 q^{83} + 78906093 q^{84} + 41540198 q^{85} + 65794492 q^{86} + 11089375 q^{87} + 39260390 q^{88} + 6628699 q^{89} + 32127214 q^{90} + 24315293 q^{91} - 39469980 q^{92} - 31050649 q^{93} - 102445588 q^{94} - 75684679 q^{95} - 95069050 q^{96} + 38131380 q^{97} + 19581828 q^{98}+O(q^{100}) \) 96 * q - 7 * q^2 - 7 * q^3 + 709 * q^4 + 191 * q^5 + 1801 * q^6 - 667 * q^7 + 9086 * q^8 + 9103 * q^9 - 7 * q^10 + 4207 * q^11 + 377 * q^13 - 7 * q^14 - 74473 * q^15 - 125851 * q^16 - 194880 * q^18 - 7 * q^19 + 162901 * q^20 + 86933 * q^21 + 252614 * q^22 + 238675 * q^23 - 490819 * q^24 - 107349 * q^25 + 367017 * q^26 + 75593 * q^27 + 1397540 * q^28 + 379863 * q^29 - 175646 * q^30 - 143885 * q^31 + 473172 * q^32 - 1419437 * q^33 - 2314463 * q^34 - 1018325 * q^35 + 1720462 * q^36 + 662991 * q^37 - 2763860 * q^38 + 42189 * q^39 + 580601 * q^40 - 3296492 * q^42 - 1587425 * q^43 + 2344398 * q^44 + 6508254 * q^45 + 526673 * q^47 + 6175806 * q^48 - 1391517 * q^49 - 4194526 * q^50 - 68204 * q^51 - 7720808 * q^52 + 1762640 * q^53 - 2032428 * q^54 + 2655709 * q^55 + 17091081 * q^56 + 4906842 * q^57 + 13231229 * q^58 - 8638324 * q^59 - 9957136 * q^60 + 2797697 * q^61 - 884069 * q^62 - 20232301 * q^63 - 17528026 * q^64 - 7454088 * q^65 - 17541475 * q^66 - 4890949 * q^67 + 22029140 * q^68 + 13204429 * q^69 - 1091301 * q^71 + 25137595 * q^72 + 14363636 * q^73 + 3185328 * q^74 - 41019881 * q^76 - 25204627 * q^77 - 15753743 * q^78 + 31186057 * q^79 + 24146022 * q^80 - 29435757 * q^81 - 51438506 * q^82 - 8367235 * q^83 + 78906093 * q^84 + 41540198 * q^85 + 65794492 * q^86 + 11089375 * q^87 + 39260390 * q^88 + 6628699 * q^89 + 32127214 * q^90 + 24315293 * q^91 - 39469980 * q^92 - 31050649 * q^93 - 102445588 * q^94 - 75684679 * q^95 - 95069050 * q^96 + 38131380 * q^97 + 19581828 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{14}\right)$

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 $

$2$	17.9566	+	4.09849i	1.58716	+	0.362259i	0.922838	−	0.385189i	$-0.125864\pi$
$2$	17.9566	+	4.09849i	1.58716	+	0.362259i	0.664321	+	0.747448i	$0.268721\pi$
$3$	26.3233	+	54.6609i	0.562880	+	1.16883i	0.967153	+	0.254194i	$0.0818102\pi$
$3$	26.3233	+	54.6609i	0.562880	+	1.16883i	−0.404273	+	0.914638i	$0.632475\pi$
$4$	190.320	+	91.6531i	1.48687	+	0.716040i
$5$	30.2961	−	132.736i	0.108391	−	0.474891i	−0.891375	−	0.453266i	$-0.850259\pi$
$5$	30.2961	−	132.736i	0.108391	−	0.474891i	0.999766	−	0.0216251i	$-0.00688403\pi$
$6$	248.651	+	1089.41i	0.469960	+	2.05903i
$7$	459.975	−	221.512i	0.506863	−	0.244092i	−0.162933	−	0.986637i	$-0.552096\pi$
$7$	459.975	−	221.512i	0.506863	−	0.244092i	0.669797	+	0.742545i	$0.266381\pi$
$8$	1198.65	+	955.891i	0.827708	+	0.660075i
$9$	−931.324	+	1167.84i	−0.425846	+	0.533993i
$10$	1088.03	−	2259.33i	0.344067	−	0.714462i
$11$	−4318.10	+	3443.57i	−0.978179	+	0.780072i	−0.975517	−	0.219925i	$-0.929419\pi$
$11$	−4318.10	+	3443.57i	−0.978179	+	0.780072i	−0.00266235	+	0.999996i	$0.500847\pi$
$12$			12815.7i			2.14095i
$13$	−2853.18	−	3577.78i	−0.360187	−	0.451660i	0.568412	−	0.822744i	$-0.307558\pi$
$13$	−2853.18	−	3577.78i	−0.360187	−	0.451660i	−0.928600	+	0.371083i	$0.878986\pi$
$14$	9167.47	−	2092.41i	0.892897	−	0.203798i
$15$	8052.97	−	1838.04i	0.616079	−	0.140616i
$16$	747.744	+	937.641i	0.0456387	+	0.0572291i
$17$			752.320i			0.0371391i	0.999828	+	0.0185695i	$0.00591121\pi$
$17$			752.320i			0.0371391i	−0.999828	+	0.0185695i	$0.994089\pi$
$18$	−21509.9	+	17153.5i	−0.869328	+	0.693266i
$19$	18928.8	−	39306.1i	0.633120	−	1.31469i	−0.299592	−	0.954067i	$-0.596851\pi$
$19$	18928.8	−	39306.1i	0.633120	−	1.31469i	0.932713	−	0.360620i	$-0.117435\pi$
$20$	17931.6	−	22485.5i	0.501204	−	0.628490i
$21$	24216.1	+	19311.7i	0.570606	+	0.455043i
$22$	−91652.1	+	44137.3i	−1.83511	+	0.883744i
$23$	4143.38	+	18153.3i	0.0710079	+	0.311106i	0.997942	−	0.0641172i	$-0.0204232\pi$
$23$	4143.38	+	18153.3i	0.0710079	+	0.311106i	−0.926934	+	0.375223i	$0.877566\pi$
$24$	−20697.4	+	90681.4i	−0.305617	+	1.33900i
$25$	53687.2	+	25854.4i	0.687196	+	0.330936i
$26$	−36570.1	−	75938.7i	−0.408056	−	0.847337i
$27$	41005.6	+	9359.26i	0.400931	+	0.0915099i
$28$	107844.			0.928421
$29$	128165.	−	28697.7i	0.975837	−	0.218501i
$29$	128165.	−	28697.7i	0.975837	−	0.218501i
$30$	152137.			1.02875
$31$	−271537.	−	61976.6i	−1.63705	−	0.373647i	−0.697645	−	0.716443i	$-0.745769\pi$
$31$	−271537.	−	61976.6i	−1.63705	−	0.373647i	−0.939410	+	0.342796i	$0.888626\pi$
$32$	−75561.6	−	156905.i	−0.407639	−	0.846472i
$33$	−301895.	−	145385.i	−1.46237	−	0.704241i
$34$	−3083.37	+	13509.1i	−0.0134540	+	0.0589456i
$35$	−15467.2	−	67766.2i	−0.0609780	−	0.267162i
$36$	−284286.	+	136905.i	−1.01554	+	0.489058i
$37$	−199573.	−	159154.i	−0.647731	−	0.516548i	0.243615	−	0.969872i	$-0.421667\pi$
$37$	−199573.	−	159154.i	−0.647731	−	0.516548i	−0.891346	+	0.453324i	$0.850238\pi$
$38$	500994.	−	628227.i	1.48112	−	1.85726i
$39$	120459.	−	250137.i	0.325173	−	0.675229i
$40$	163196.	−	130144.i	0.403180	−	0.321525i
$41$			270766.i			0.613551i	0.951782	+	0.306775i	$0.0992500\pi$
$41$			270766.i			0.613551i	−0.951782	+	0.306775i	$0.900750\pi$
$42$	355691.	+	446023.i	0.740799	+	0.928933i
$43$	173542.	−	39609.8i	0.332862	−	0.0759736i	−0.0528235	−	0.998604i	$-0.516822\pi$
$43$	173542.	−	39609.8i	0.332862	−	0.0759736i	0.385686	+	0.922630i	$0.373965\pi$
$44$	−1.13743e6	+	259612.i	−2.01299	+	0.459452i
$45$	126799.	+	159001.i	0.207431	+	0.260110i
$46$			342954.i			0.519498i
$47$	−143643.	+	114551.i	−0.201809	+	0.160937i	−0.719180	−	0.694824i	$-0.755482\pi$
$47$	−143643.	+	114551.i	−0.201809	+	0.160937i	0.517371	+	0.855761i	$0.326911\pi$
$48$	−31569.2	+	65554.2i	−0.0412021	+	0.0855571i
$49$	−350962.	+	440092.i	−0.426161	+	0.534389i
$50$	858078.	+	684294.i	0.970805	+	0.774191i
$51$	−41122.5	+	19803.5i	−0.0434094	+	0.0209049i
$52$	−215102.	−	942425.i	−0.212145	−	0.929469i
$53$	−327225.	+	1.43367e6i	−0.301912	+	1.32276i	0.565324	+	0.824869i	$0.308751\pi$
$53$	−327225.	+	1.43367e6i	−0.301912	+	1.32276i	−0.867237	+	0.497896i	$0.834106\pi$
$54$	697964.	+	336122.i	0.603191	+	0.290482i
$55$	326264.	+	677495.i	0.264424	+	0.549081i
$56$	763090.	+	174170.i	0.580654	+	0.132530i
$57$	2.64678e6			1.89302
$58$	2.41903e6	+	9969.81i	1.62796	+	0.00670948i
$59$	−1.74886e6			−1.10860			−0.554298	−	0.832318i	$-0.687013\pi$
$59$	−1.74886e6			−1.10860			−0.554298	+	0.832318i	$0.687013\pi$
$60$	1.70110e6	+	388265.i	1.01672	+	0.232059i
$61$	1.24019e6	+	2.57527e6i	0.699572	+	1.45268i	0.882869	+	0.469619i	$0.155609\pi$
$61$	1.24019e6	+	2.57527e6i	0.699572	+	1.45268i	−0.183297	+	0.983058i	$0.558677\pi$
$62$	−4.62189e6	−	2.22578e6i	−2.46291	−	1.18607i
$63$	−169694.	+	743478.i	−0.0855016	+	0.374607i
$64$	−747917.	−	3.27684e6i	−0.356635	−	1.56252i
$65$	−561341.	+	270328.i	−0.253530	+	0.122094i
$66$	−4.82517e6	−	3.84794e6i	−2.06590	−	1.64750i
$67$	−865257.	+	1.08500e6i	−0.351466	+	0.440724i	−0.925867	−	0.377850i	$-0.876664\pi$
$67$	−865257.	+	1.08500e6i	−0.351466	+	0.440724i	0.574401	+	0.818574i	$0.305235\pi$
$68$	−68952.4	+	143181.i	−0.0265931	+	0.0552211i
$69$	−883209.	+	704336.i	−0.323662	+	0.258112i
$70$		−	1.28025e6i		−	0.446118i
$71$	−2.34765e6	−	2.94386e6i	−0.778447	−	0.976142i	−1.00000		0.000993536i	$-0.999684\pi$
$71$	−2.34765e6	−	2.94386e6i	−0.778447	−	0.976142i	0.221552	−	0.975149i	$-0.428888\pi$
$72$	−2.23266e6	+	509591.i	−0.704952	+	0.160901i
$73$	5.10639e6	−	1.16550e6i	1.53633	−	0.350657i	0.631139	−	0.775669i	$-0.282588\pi$
$73$	5.10639e6	−	1.16550e6i	1.53633	−	0.350657i	0.905187	+	0.425013i	$0.139730\pi$
$74$	−2.93136e6	−	3.67581e6i	−0.840928	−	1.05449i
$75$			3.61516e6i			0.989494i
$76$	7.20506e6	−	5.74584e6i	1.88274	−	1.50143i
$77$	−1.22342e6	+	2.54047e6i	−0.305393	+	0.634156i
$78$	3.18823e6	−	3.99791e6i	0.760709	−	0.953899i
$79$	−4.43239e6	−	3.53471e6i	−1.01145	−	0.806602i	−0.0302367	−	0.999543i	$-0.509626\pi$
$79$	−4.43239e6	−	3.53471e6i	−1.01145	−	0.806602i	−0.981210	+	0.192941i	$0.938198\pi$
$80$	147113.	−	70845.7i	0.0321244	−	0.0154703i
$81$	1.29474e6	+	5.67265e6i	0.270699	+	1.18601i
$82$	−1.10973e6	+	4.86205e6i	−0.222264	+	0.973802i
$83$	4.39466e6	+	2.11636e6i	0.843630	+	0.406271i	0.805209	−	0.592991i	$-0.202053\pi$
$83$	4.39466e6	+	2.11636e6i	0.843630	+	0.406271i	0.0384207	+	0.999262i	$0.487767\pi$
$84$	2.83882e6	+	5.89487e6i	0.522589	+	1.08517i
$85$	99860.0	+	22792.4i	0.0176370	+	0.00402553i
$86$	3.27857e6			0.555827
$87$	4.94237e6	+	6.25021e6i	0.804670	+	1.01760i
$88$	−8.46757e6			−1.32455
$89$	5.56990e6	+	1.27129e6i	0.837495	+	0.191153i	0.619697	−	0.784841i	$-0.287256\pi$
$89$	5.56990e6	+	1.27129e6i	0.837495	+	0.191153i	0.217798	+	0.975994i	$0.430113\pi$
$90$	1.62523e6	+	3.37482e6i	0.234999	+	0.487980i
$91$	−2.10491e6	−	1.01367e6i	−0.292812	−	0.141011i
$92$	−875242.	+	3.83469e6i	−0.117185	+	0.513420i
$93$	−3.76006e6	−	1.64739e7i	−0.484735	−	2.12376i
$94$	−3.04883e6	+	1.46824e6i	−0.378604	+	0.182326i
$95$	−4.64387e6	−	3.70336e6i	−0.555709	−	0.443163i
$96$	6.58755e6	−	8.26052e6i	0.759932	−	0.952924i
$97$	−881024.	+	1.82947e6i	−0.0980137	+	0.203528i	−0.944210	−	0.329343i	$-0.893173\pi$
$97$	−881024.	+	1.82947e6i	−0.0980137	+	0.203528i	0.846196	+	0.532871i	$0.178887\pi$
$98$	−8.10581e6	+	6.46417e6i	−0.869972	+	0.693779i
$99$		−	8.24995e6i		−	0.854531i
$100$	7.84809e6	+	9.84120e6i	0.784809	+	0.984120i
$101$	−1.44399e7	+	3.29582e6i	−1.39457	+	0.318301i	−0.852805	−	0.522230i	$-0.825100\pi$
$101$	−1.44399e7	+	3.29582e6i	−1.39457	+	0.318301i	−0.541764	+	0.840531i	$0.682243\pi$
$102$	−819586.	+	187065.i	−0.0764705	+	0.0174539i
$103$	−6.09622e6	−	7.64442e6i	−0.549706	−	0.689309i	0.426912	−	0.904293i	$-0.359601\pi$
$103$	−6.09622e6	−	7.64442e6i	−0.549706	−	0.689309i	−0.976618	+	0.214984i	$0.931030\pi$
$104$		−	7.01584e6i		−	0.611593i
$105$	3.29701e6	−	2.62928e6i	0.277944	−	0.221653i
$106$	−1.17517e7	+	2.44027e7i	−0.958366	+	1.99007i
$107$	7.20377e6	−	9.03324e6i	0.568482	−	0.712854i	−0.411619	−	0.911356i	$-0.635036\pi$
$107$	7.20377e6	−	9.03324e6i	0.568482	−	0.712854i	0.980100	+	0.198503i	$0.0636078\pi$
$108$	6.94636e6	+	5.53954e6i	0.530609	+	0.423146i
$109$	−8.48411e6	+	4.08573e6i	−0.627499	+	0.302188i	−0.720475	−	0.693481i	$-0.756076\pi$
$109$	−8.48411e6	+	4.08573e6i	−0.627499	+	0.302188i	0.0929759	+	0.995668i	$0.470362\pi$
$110$	3.08191e6	+	1.35027e7i	0.220773	+	0.967269i
$111$	3.44608e6	−	1.50983e7i	0.239163	−	1.04784i
$112$	551642.	+	265657.i	0.0371017	+	0.0178673i
$113$	−632602.	−	1.31361e6i	−0.0412435	−	0.0856431i	0.879329	−	0.476215i	$-0.157992\pi$
$113$	−632602.	−	1.31361e6i	−0.0412435	−	0.0856431i	−0.920572	+	0.390572i	$0.872277\pi$
$114$	4.75272e7	+	1.08478e7i	3.00452	+	0.685763i
$115$	2.53513e6			0.155438
$116$	2.70226e7	+	6.28501e6i	1.60740	+	0.373855i
$117$	6.83553e6			0.394568
$118$	−3.14037e7	−	7.16769e6i	−1.75952	−	0.401599i
$119$	166648.	+	346048.i	0.00906537	+	0.0188244i
$120$	1.14096e7	+	5.49460e6i	0.602751	+	0.290269i
$121$	2.45152e6	−	1.07408e7i	0.125801	−	0.551172i
$122$	1.17149e7	+	5.13262e7i	0.584087	+	2.55905i
$123$	−1.48003e7	+	7.12745e6i	−0.717138	+	0.345355i
$124$	−4.59985e7	−	3.66826e7i	−2.16655	−	1.72776i
$125$	1.16902e7	−	1.46590e7i	0.535348	−	0.671306i
$126$	−6.09427e6	+	1.26549e7i	−0.271409	+	0.563587i
$127$	−2.12339e7	+	1.69335e7i	−0.919849	+	0.733555i	−0.964121	−	0.265464i	$-0.914475\pi$
$127$	−2.12339e7	+	1.69335e7i	−0.919849	+	0.733555i	0.0442716	+	0.999020i	$0.485903\pi$
$128$		−	3.96150e7i		−	1.66965i
$129$	6.73330e6	+	8.44329e6i	0.276162	+	0.346296i
$130$	−1.11877e7	+	2.55353e6i	−0.446622	+	0.101939i
$131$	3.41229e7	−	7.78833e6i	1.32616	−	0.302688i	0.499953	−	0.866052i	$-0.333350\pi$
$131$	3.41229e7	−	7.78833e6i	1.32616	−	0.302688i	0.826208	+	0.563365i	$0.190493\pi$
$132$	−4.41316e7	−	5.53393e7i	−1.67009	−	2.09423i
$133$		−	2.22728e7i		−	0.820906i
$134$	−1.99840e7	+	1.59367e7i	−0.717489	+	0.572178i
$135$	2.48462e6	−	5.15937e6i	0.0869145	−	0.180480i
$136$	−719136.	+	901768.i	−0.0245146	+	0.0307403i
$137$	1.29860e7	+	1.03560e7i	0.431472	+	0.344088i	0.815020	−	0.579434i	$-0.196726\pi$
$137$	1.29860e7	+	1.03560e7i	0.431472	+	0.344088i	−0.383547	+	0.923521i	$0.625298\pi$
$138$	−1.87462e7	+	9.02769e6i	−0.607206	+	0.292415i
$139$	9.69907e6	+	4.24944e7i	0.306322	+	1.34208i	0.860400	+	0.509620i	$0.170214\pi$
$139$	9.69907e6	+	4.24944e7i	0.306322	+	1.34208i	−0.554078	+	0.832465i	$0.686929\pi$
$140$	3.26727e6	−	1.43149e7i	0.100632	−	0.440899i
$141$	−1.00426e7	−	4.83627e6i	−0.301703	−	0.145293i
$142$	−3.00906e7	−	6.24837e7i	−0.881904	−	1.83129i
$143$	2.46407e7	+	5.62407e6i	0.704655	+	0.160833i
$144$	−1.79141e6			−0.0499950
$145$	73697.1	−	1.78816e7i	0.00200753	−	0.487100i
$146$	9.64704e7			2.56542
$147$	−3.32943e7	−	7.59920e6i	−0.864488	−	0.197314i
$148$	−2.33956e7	−	4.85815e7i	−0.593224	−	1.23184i
$149$	3.66992e7	+	1.76734e7i	0.908877	+	0.437692i	0.829087	−	0.559120i	$-0.188861\pi$
$149$	3.66992e7	+	1.76734e7i	0.908877	+	0.437692i	0.0797898	+	0.996812i	$0.474575\pi$
$150$	−1.48167e7	+	6.49162e7i	−0.358453	+	1.57048i
$151$	5.81187e6	+	2.54634e7i	0.137371	+	0.601863i	0.996007	+	0.0892767i	$0.0284555\pi$
$151$	5.81187e6	+	2.54634e7i	0.137371	+	0.601863i	−0.858635	+	0.512587i	$0.828687\pi$
$152$	6.02614e7	−	2.90204e7i	1.39183	−	0.670271i
$153$	−878592.	−	700654.i	−0.0198320	−	0.0158155i
$154$	−3.23807e7	+	4.06041e7i	−0.714436	+	0.895874i
$155$	−1.64531e7	+	3.41651e7i	−0.354883	+	0.736923i
$156$	4.58516e7	−	3.65654e7i	0.966982	−	0.771142i
$157$		−	7.92206e7i		−	1.63376i	−0.576805	−	0.816882i	$-0.695701\pi$
$157$		−	7.92206e7i		−	1.63376i	0.576805	−	0.816882i	$-0.304299\pi$
$158$	−6.51039e7	−	8.16377e7i	−1.31313	−	1.64661i
$159$	−8.69791e7	+	1.98524e7i	−1.71603	+	0.391673i
$160$	−2.31162e7	+	5.27612e6i	−0.446166	+	0.101835i
$161$	5.92703e6	+	7.43226e6i	0.111930	+	0.140356i
$162$			1.07168e8i			1.98045i
$163$	4.98367e6	−	3.97434e6i	0.0901348	−	0.0718801i	−0.577386	−	0.816472i	$-0.695927\pi$
$163$	4.98367e6	−	3.97434e6i	0.0901348	−	0.0718801i	0.667520	+	0.744591i	$0.267356\pi$
$164$	−2.48165e7	+	5.15321e7i	−0.439327	+	0.912272i
$165$	−2.84441e7	+	3.56678e7i	−0.492945	+	0.618134i
$166$	7.02395e7	+	5.60141e7i	1.19180	+	0.950428i
$167$	3.73623e7	−	1.79927e7i	0.620764	−	0.298944i	−0.0969427	−	0.995290i	$-0.530906\pi$
$167$	3.73623e7	−	1.79927e7i	0.620764	−	0.298944i	0.717706	+	0.696346i	$0.245192\pi$
$168$	1.05667e7	+	4.62959e7i	0.171933	+	0.753286i
$169$	9.30301e6	−	4.07591e7i	0.148259	−	0.649564i
$170$	1.69974e6	+	818550.i	0.0265345	+	0.0127783i
$171$	2.82745e7	+	5.87127e7i	0.432423	+	0.897936i
$172$	3.66588e7	+	8.36713e6i	0.549324	+	0.125380i
$173$	6.80887e7			0.999801			0.499901	−	0.866083i	$-0.333370\pi$
$173$	6.80887e7			0.999801			0.499901	+	0.866083i	$0.333370\pi$
$174$	6.31320e7	+	1.32489e8i	0.908505	+	1.90659i
$175$	3.04218e7			0.429093
$176$	−6.45767e6	−	1.47392e6i	−0.0892856	−	0.0203789i
$177$	−4.60358e7	−	9.55943e7i	−0.624007	−	1.29576i
$178$	9.48063e7	+	4.56563e7i	1.25999	+	0.606779i
$179$	−8.52659e6	+	3.73574e7i	−0.111119	+	0.486846i	0.888490	+	0.458896i	$0.151755\pi$
$179$	−8.52659e6	+	3.73574e7i	−0.111119	+	0.486846i	−0.999609	+	0.0279497i	$0.991102\pi$
$180$	9.55945e6	+	4.18827e7i	0.122174	+	0.535279i
$181$	−5.04985e7	+	2.43188e7i	−0.633000	+	0.304837i	−0.722731	−	0.691129i	$-0.757113\pi$
$181$	−5.04985e7	+	2.43188e7i	−0.633000	+	0.304837i	0.0897313	+	0.995966i	$0.471399\pi$
$182$	−3.36427e7	−	2.68291e7i	−0.413657	−	0.329881i
$183$	−1.08121e8	+	1.35579e8i	−1.30416	+	1.63536i
$184$	−1.23861e7	+	2.57201e7i	−0.146580	+	0.304376i
$185$	−2.71717e7	+	2.16687e7i	−0.315512	+	0.251613i
$186$		−	3.11226e8i		−	3.54635i
$187$	−2.59067e6	−	3.24859e6i	−0.0289712	−	0.0363287i
$188$	−3.78370e7	+	8.63604e6i	−0.415302	+	0.0947900i
$189$	2.09347e7	−	4.77821e6i	0.225554	−	0.0514813i
$190$	−6.82102e7	−	8.55328e7i	−0.721459	−	0.904681i
$191$		−	3.97549e7i		−	0.412833i	−0.978464	−	0.206416i	$-0.933820\pi$
$191$		−	3.97549e7i		−	0.412833i	0.978464	−	0.206416i	$-0.0661801\pi$
$192$	1.59427e8	−	1.27139e8i	1.62558	−	1.29636i
$193$	2.95529e7	−	6.13672e7i	0.295903	−	0.614448i	−0.699019	−	0.715103i	$-0.746380\pi$
$193$	2.95529e7	−	6.13672e7i	0.295903	−	0.614448i	0.994921	+	0.100655i	$0.0320938\pi$
$194$	−2.33183e7	+	2.92402e7i	−0.229293	+	0.287524i
$195$	−2.95527e7	−	2.35675e7i	−0.285414	−	0.227610i
$196$	−1.07131e8	+	5.15914e7i	−1.01629	+	0.489420i
$197$	−3.85873e7	−	1.69062e8i	−0.359594	−	1.57548i	−0.754207	−	0.656637i	$-0.771979\pi$
$197$	−3.85873e7	−	1.69062e8i	−0.359594	−	1.57548i	0.394613	−	0.918847i	$-0.370879\pi$
$198$	3.38123e7	−	1.48141e8i	0.309561	−	1.35628i
$199$	1.73800e8	+	8.36978e7i	1.56338	+	0.752884i	0.997436	−	0.0715597i	$-0.0227977\pi$
$199$	1.73800e8	+	8.36978e7i	1.56338	+	0.752884i	0.565944	+	0.824444i	$0.308512\pi$
$200$	3.96381e7	+	8.23094e7i	0.350355	+	0.727520i
$201$	−8.20834e7	−	1.87350e7i	−0.712966	−	0.162730i
$202$	−2.72800e8			−2.32871
$203$	5.25959e7	−	4.15903e7i	0.441281	−	0.348944i
$204$	−9.64147e6			−0.0795129
$205$	3.59404e7	+	8.20316e6i	0.291370	+	0.0665032i
$206$	−7.81371e7	−	1.62253e8i	−0.622762	−	1.29318i
$207$	−2.50591e7	−	1.20678e7i	−0.196367	−	0.0945654i
$208$	1.22122e6	−	5.35053e6i	0.00940965	−	0.0412264i
$209$	5.36168e7	+	2.34911e8i	0.406246	+	1.77988i
$210$	6.99793e7	−	3.37003e7i	0.521438	−	0.251111i
$211$	−1.52935e8	−	1.21961e8i	−1.12077	−	0.893786i	−0.125615	−	0.992079i	$-0.540090\pi$
$211$	−1.52935e8	−	1.21961e8i	−1.12077	−	0.893786i	−0.995158	+	0.0982927i	$0.968662\pi$
$212$	−1.93677e8	+	2.42864e8i	−1.39606	+	1.75060i
$213$	9.91161e7	−	2.05817e8i	0.702774	−	1.45933i
$214$	1.66378e8	−	1.32682e8i	1.16051	−	0.925474i
$215$		−	2.42353e7i		−	0.166308i
$216$	4.02049e7	+	5.04153e7i	0.271451	+	0.340388i
$217$	−1.38629e8	+	3.16411e7i	−0.920967	+	0.210205i
$218$	−1.69091e8	+	3.85940e7i	−1.10541	+	0.252303i
$219$	1.98124e8	+	2.48440e8i	1.27463	+	1.59833i
$220$			1.58844e8i			1.00575i
$221$	2.69163e6	−	2.14651e6i	0.0167743	−	0.0133770i
$222$	1.23760e8	−	2.56990e8i	0.759181	−	1.57646i
$223$	−6.93362e7	+	8.69448e7i	−0.418690	+	0.525021i	−0.945788	−	0.324783i	$-0.894709\pi$
$223$	−6.93362e7	+	8.69448e7i	−0.418690	+	0.525021i	0.527098	+	0.849804i	$0.323280\pi$
$224$	−6.95128e7	−	5.54346e7i	−0.413235	−	0.329544i
$225$	−8.01940e7	+	3.86194e7i	−0.469357	+	0.226030i
$226$	−5.97559e6	−	2.61808e7i	−0.0344351	−	0.150870i
$227$	−3.86058e7	+	1.69143e8i	−0.219060	+	0.959763i	0.739115	+	0.673579i	$0.235244\pi$
$227$	−3.86058e7	+	1.69143e8i	−0.219060	+	0.959763i	−0.958175	+	0.286184i	$0.907613\pi$
$228$	5.03734e8	+	2.42585e8i	2.81468	+	1.35548i
$229$	4.22762e7	+	8.77875e7i	0.232633	+	0.483068i	0.984306	−	0.176468i	$-0.0564671\pi$
$229$	4.22762e7	+	8.77875e7i	0.232633	+	0.483068i	−0.751673	+	0.659536i	$0.770753\pi$
$230$	4.55224e7	+	1.03902e7i	0.246705	+	0.0563088i
$231$	−1.71069e8			−0.913122
$232$	1.81057e8	+	8.81135e7i	0.951935	+	0.463271i
$233$	2.95105e8			1.52838			0.764189	−	0.644992i	$-0.223139\pi$
$233$	2.95105e8			1.52838			0.764189	+	0.644992i	$0.223139\pi$
$234$	1.22743e8	+	2.80153e7i	0.626241	+	0.142936i
$235$	1.08533e7	+	2.25370e7i	0.0545535	+	0.113281i
$236$	−3.32843e8	−	1.60289e8i	−1.64834	−	0.793799i
$237$	7.65354e7	−	3.35324e8i	0.373459	−	1.63623i
$238$	1.57416e6	+	6.89687e6i	0.00756887	+	0.0331614i
$239$	−994815.	+	479078.i	−0.00471357	+	0.00226993i	−0.436239	−	0.899831i	$-0.643690\pi$
$239$	−994815.	+	479078.i	−0.00471357	+	0.00226993i	0.431525	+	0.902101i	$0.357976\pi$
$240$	7.74498e6	+	6.17641e6i	0.0361644	+	0.0288401i
$241$	1.78744e8	−	2.24138e8i	0.822567	−	1.03147i	−0.176322	−	0.984333i	$-0.556420\pi$
$241$	1.78744e8	−	2.24138e8i	0.822567	−	1.03147i	0.998889	−	0.0471338i	$-0.0150087\pi$
$242$	8.80420e7	−	1.82821e8i	0.399334	−	0.829225i
$243$	−2.04073e8	+	1.62743e8i	−0.912353	+	0.727578i
$244$			6.03792e8i			2.66087i
$245$	4.77833e7	+	5.99184e7i	0.207584	+	0.260303i
$246$	−2.94976e8	+	6.73263e7i	−1.26332	+	0.288344i
$247$	−1.94636e8	+	4.44244e7i	−0.821834	+	0.187578i
$248$	−2.66235e8	−	3.33848e8i	−1.10837	−	1.38985i
$249$			2.95925e8i			1.21474i
$250$	2.69997e8	−	2.15315e8i	1.09287	−	0.871534i
$251$	5.23561e7	−	1.08719e8i	0.208982	−	0.433956i	−0.769960	−	0.638092i	$-0.779724\pi$
$251$	5.23561e7	−	1.08719e8i	0.208982	−	0.433956i	0.978943	+	0.204136i	$0.0654384\pi$
$252$	−1.00438e8	+	1.25945e8i	−0.395364	+	0.495770i
$253$	−8.04037e7	−	6.41199e7i	−0.312144	−	0.248926i
$254$	−4.50691e8	+	2.17041e8i	−1.72568	+	0.831045i
$255$	1.38279e6	+	6.05840e6i	0.00522235	+	0.0228806i
$256$	6.66282e7	−	2.91917e8i	0.248209	−	1.08748i
$257$	2.16900e8	+	1.04454e8i	0.797066	+	0.383847i	0.787661	−	0.616109i	$-0.211292\pi$
$257$	2.16900e8	+	1.04454e8i	0.797066	+	0.383847i	0.00940507	+	0.999956i	$0.497006\pi$
$258$	8.63028e7	+	1.79210e8i	0.312864	+	0.649669i
$259$	−1.27053e8	−	2.89990e7i	−0.454396	−	0.103713i
$260$	−1.31611e8			−0.464391
$261$	−8.58490e7	+	1.76404e8i	−0.298878	+	0.614138i
$262$	6.44654e8			2.21448
$263$	1.20937e8	+	2.76031e7i	0.409934	+	0.0935648i	0.422515	−	0.906356i	$-0.361147\pi$
$263$	1.20937e8	+	2.76031e7i	0.409934	+	0.0935648i	−0.0125804	+	0.999921i	$0.504005\pi$
$264$	−2.22894e8	−	4.62845e8i	−0.745565	−	1.54818i
$265$	1.80386e8	+	8.68691e7i	0.595445	+	0.286751i
$266$	9.12847e7	−	3.99944e8i	0.297380	−	1.30291i
$267$	7.71280e7	+	3.37920e8i	0.247984	+	1.08649i
$268$	−2.64119e8	+	1.27193e8i	−0.838161	+	0.403637i
$269$	−1.53608e8	−	1.22498e8i	−0.481151	−	0.383705i	0.352663	−	0.935750i	$-0.385276\pi$
$269$	−1.53608e8	−	1.22498e8i	−0.481151	−	0.383705i	−0.833814	+	0.552045i	$0.813848\pi$
$270$	6.57611e7	−	8.24618e7i	0.203327	−	0.254965i
$271$	1.61224e8	−	3.34785e8i	0.492081	−	1.02182i	−0.496063	−	0.868287i	$-0.665221\pi$
$271$	1.61224e8	−	3.34785e8i	0.492081	−	1.02182i	0.988144	−	0.153530i	$-0.0490643\pi$
$272$	−705406.	+	562543.i	−0.00212544	+	0.00169498i
$273$		−	1.41740e8i		−	0.421621i
$274$	1.90741e8	+	2.39182e8i	0.560167	+	0.702427i
$275$	−3.20858e8	+	7.32338e7i	−0.930355	+	0.212347i
$276$	−2.32647e8	+	5.31001e7i	−0.666062	+	0.152024i
$277$	−2.07873e8	−	2.60664e8i	−0.587650	−	0.736889i	0.395747	−	0.918360i	$-0.370486\pi$
$277$	−2.07873e8	−	2.60664e8i	−0.587650	−	0.736889i	−0.983396	+	0.181470i	$0.941914\pi$
$278$			8.02809e8i			2.24107i
$279$	3.25268e8	−	2.59393e8i	0.896658	−	0.715061i
$280$	4.62373e7	−	9.60128e7i	0.125875	−	0.261382i
$281$	−3.38149e8	+	4.24025e8i	−0.909150	+	1.14004i	0.0805313	+	0.996752i	$0.474338\pi$
$281$	−3.38149e8	+	4.24025e8i	−0.909150	+	1.14004i	−0.989681	+	0.143286i	$0.954233\pi$
$282$	−1.60510e8	−	1.28003e8i	−0.426217	−	0.339897i
$283$	−3.45214e8	+	1.66246e8i	−0.905389	+	0.436012i	−0.827832	−	0.560976i	$-0.810426\pi$
$283$	−3.45214e8	+	1.66246e8i	−0.905389	+	0.436012i	−0.0775567	+	0.996988i	$0.524712\pi$
$284$	−1.76990e8	−	7.75444e8i	−0.458495	−	2.00880i
$285$	8.01871e7	−	3.51323e8i	0.205186	−	0.898978i
$286$	4.19414e8	+	2.01979e8i	1.06014	+	0.510535i
$287$	5.99779e7	+	1.24545e8i	0.149763	+	0.310986i
$288$	2.53613e8	+	5.78855e7i	0.625602	+	0.142790i
$289$	4.09773e8			0.998621
$290$	7.46108e7	−	3.20791e8i	0.179642	−	0.772377i
$291$	−1.23192e8			−0.293060
$292$	1.07867e9	+	2.46199e8i	2.53541	+	0.578690i
$293$	6.83137e7	+	1.41855e8i	0.158661	+	0.329464i	0.965112	−	0.261838i	$-0.0843285\pi$
$293$	6.83137e7	+	1.41855e8i	0.158661	+	0.329464i	−0.806450	+	0.591302i	$0.798614\pi$
$294$	−5.66709e8	−	2.72912e8i	−1.30060	−	0.626337i
$295$	−5.29838e7	+	2.32137e8i	−0.120162	+	0.526462i
$296$	−8.70838e7	−	3.81539e8i	−0.195172	−	0.855102i
$297$	−2.09296e8	+	1.00791e8i	−0.463567	+	0.223242i
$298$	5.86561e8	+	4.67767e8i	1.28397	+	1.02393i
$299$	5.31268e7	−	6.66188e7i	0.114938	−	0.144128i
$300$	−3.31341e8	+	6.88036e8i	−0.708517	+	1.47125i
$301$	7.10508e7	−	5.66611e7i	0.150171	−	0.119757i
$302$			4.81058e8i			1.00502i
$303$	−5.60258e8	−	7.02542e8i	−1.15702	−	1.45085i
$304$	5.10090e7	−	1.16425e7i	0.104133	−	0.0237677i
$305$	3.79404e8	−	8.65966e7i	0.765690	−	0.174764i
$306$	−1.29049e7	−	1.61823e7i	−0.0257473	−	0.0322861i
$307$		−	7.11608e8i		−	1.40364i	−0.712353	−	0.701821i	$-0.752371\pi$
$307$		−	7.11608e8i		−	1.40364i	0.712353	−	0.701821i	$-0.247629\pi$
$308$	−4.65683e8	+	3.71370e8i	−0.908162	+	0.724235i
$309$	2.57378e8	−	5.34451e8i	0.496269	−	1.03051i
$310$	−4.35467e8	+	5.46058e8i	−0.830213	+	1.04105i
$311$	3.68654e8	+	2.93992e8i	0.694956	+	0.554209i	0.906005	−	0.423266i	$-0.139117\pi$
$311$	3.68654e8	+	2.93992e8i	0.694956	+	0.554209i	−0.211049	+	0.977475i	$0.567688\pi$
$312$	3.83492e8	−	1.84680e8i	0.714850	−	0.344254i
$313$	−1.07619e8	−	4.71512e8i	−0.198374	−	0.869135i	−0.971904	−	0.235376i	$-0.924368\pi$
$313$	−1.07619e8	−	4.71512e8i	−0.198374	−	0.869135i	0.773530	−	0.633760i	$-0.218489\pi$
$314$	3.24685e8	−	1.42254e9i	0.591845	−	2.59304i
$315$	9.35452e7	+	4.50490e7i	0.168630	+	0.0812079i
$316$	−5.19604e8	−	1.07897e9i	−0.926333	−	1.92355i
$317$	−3.25657e8	−	7.43292e7i	−0.574187	−	0.131054i	−0.0744395	−	0.997226i	$-0.523717\pi$
$317$	−3.25657e8	−	7.43292e7i	−0.574187	−	0.131054i	−0.499748	+	0.866171i	$0.666574\pi$
$318$	−1.64322e9			−2.86550
$319$	−4.54608e8	+	5.65265e8i	−0.784097	+	0.974956i
$320$	−4.57614e8			−0.780682
$321$	6.83392e8	+	1.55980e8i	1.15319	+	0.263209i
$322$	7.59685e7	+	1.57750e8i	0.126805	+	0.263314i
$323$	2.95708e7	+	1.42405e7i	0.0488263	+	0.0235135i
$324$	−2.73500e8	+	1.19828e9i	−0.446735	+	1.95728i
$325$	−6.06781e7	−	2.65848e8i	−0.0980484	−	0.429578i
$326$	1.05779e8	−	5.09404e7i	0.169097	−	0.0814330i
$327$	−4.46659e8	−	3.56199e8i	−0.706414	−	0.563346i
$328$	−2.58823e8	+	3.24553e8i	−0.404990	+	0.507841i
$329$	−4.06975e7	+	8.45092e7i	−0.0630060	+	0.130833i
$330$	−6.56945e8	+	5.23896e8i	−1.00631	+	0.802502i
$331$		−	7.48461e8i		−	1.13441i	−0.823576	−	0.567207i	$-0.808024\pi$
$331$		−	7.48461e8i		−	1.13441i	0.823576	−	0.567207i	$-0.191976\pi$
$332$	6.42419e8	+	8.05569e8i	0.963464	+	1.20815i
$333$	3.71733e8	−	8.48457e7i	0.551667	−	0.125914i
$334$	7.44645e8	−	1.69960e8i	1.09355	−	0.249595i
$335$	1.17804e8	+	1.47722e8i	0.171200	+	0.214679i
$336$			3.71462e7i			0.0534228i
$337$	−6.20578e8	+	4.94895e8i	−0.883267	+	0.704382i	−0.956125	−	0.292960i	$-0.905360\pi$
$337$	−6.20578e8	+	4.94895e8i	−0.883267	+	0.704382i	0.0728575	+	0.997342i	$0.476788\pi$
$338$	3.34102e8	−	6.93769e8i	0.470620	−	0.977252i
$339$	5.51510e7	−	6.91572e7i	0.0768873	−	0.0964136i
$340$	1.69163e7	+	1.34903e7i	0.0233416	+	0.0186143i
$341$	1.38595e9	−	6.67436e8i	1.89280	−	0.911527i
$342$	2.67083e8	+	1.17017e9i	0.361039	+	1.58182i
$343$	−1.57506e8	+	6.90078e8i	−0.210750	+	0.923355i
$344$	2.45878e8	+	1.18409e8i	0.325661	+	0.156830i
$345$	6.67329e7	+	1.38572e8i	0.0874930	+	0.181681i
$346$	1.22265e9	+	2.79061e8i	1.58684	+	0.362187i
$347$	9.92955e8			1.27578			0.637891	−	0.770127i	$-0.279807\pi$
$347$	9.92955e8			1.27578			0.637891	+	0.770127i	$0.279807\pi$
$348$	3.67779e8	+	1.64252e9i	0.467800	+	2.08922i
$349$	7.61047e8			0.958346			0.479173	−	0.877720i	$-0.340937\pi$
$349$	7.61047e8			0.958346			0.479173	+	0.877720i	$0.340937\pi$
$350$	5.46274e8	+	1.24683e8i	0.681039	+	0.155443i
$351$	−8.35111e7	−	1.73413e8i	−0.103079	−	0.214045i
$352$	8.66597e8	+	4.17331e8i	1.05905	+	0.510013i
$353$	−2.12713e8	+	9.31958e8i	−0.257385	+	1.12768i	0.666650	+	0.745371i	$0.267728\pi$
$353$	−2.12713e8	+	9.31958e8i	−0.257385	+	1.12768i	−0.924035	+	0.382307i	$0.875130\pi$
$354$	−4.34857e8	−	1.90523e9i	−0.520996	−	2.28263i
$355$	−4.61881e8	+	2.22430e8i	−0.547938	+	0.263873i
$356$	9.43543e8	+	7.52450e8i	1.10837	+	0.883899i
$357$	−1.45286e7	+	1.82182e7i	−0.0168999	+	0.0211918i
$358$	−3.06218e8	+	6.35868e8i	−0.352728	+	0.732447i
$359$	−3.42666e8	+	2.73267e8i	−0.390877	+	0.311714i	−0.799134	−	0.601153i	$-0.794708\pi$
$359$	−3.42666e8	+	2.73267e8i	−0.390877	+	0.311714i	0.408257	+	0.912867i	$0.366137\pi$
$360$			3.11793e8i			0.352215i
$361$	−6.29351e8	−	7.89181e8i	−0.704073	−	0.882879i
$362$	−1.00645e9	+	2.29717e8i	−1.11510	+	0.254514i
$363$	6.51633e8	−	1.48731e8i	0.715039	−	0.163203i
$364$	−3.07700e8	−	3.85844e8i	−0.334405	−	0.419331i
$365$		−	7.13112e8i		−	0.767596i
$366$	−2.49716e9	+	1.99142e9i	−2.66233	+	2.12314i
$367$	−4.92675e8	+	1.02305e9i	−0.520271	+	1.08035i	0.460943	+	0.887430i	$0.347511\pi$
$367$	−4.92675e8	+	1.02305e9i	−0.520271	+	1.08035i	−0.981214	+	0.192924i	$0.938203\pi$
$368$	−1.39231e7	+	1.74590e7i	−0.0145636	+	0.0182622i
$369$	−3.16212e8	−	2.52171e8i	−0.327632	−	0.261278i
$370$	−5.76722e8	+	2.77735e8i	−0.591917	+	0.285052i
$371$	1.67059e8	+	7.31934e8i	0.169849	+	0.744155i
$372$	7.94270e8	−	3.47993e9i	0.799959	−	3.50485i
$373$	−1.25170e9	−	6.02789e8i	−1.24888	−	0.601429i	−0.311669	−	0.950191i	$-0.600888\pi$
$373$	−1.25170e9	−	6.02789e8i	−1.24888	−	0.601429i	−0.937212	+	0.348761i	$0.886602\pi$
$374$	−3.32054e7	−	6.89517e7i	−0.0328214	−	0.0681544i
$375$	1.10900e9	+	2.53122e8i	1.08598	+	0.247868i
$376$	−2.81676e8			−0.273270
$377$	−4.68353e8	−	3.76667e8i	−0.450172	−	0.362045i
$378$	3.95501e8			0.376640
$379$	−1.77874e9	−	4.05985e8i	−1.67832	−	0.383065i	−0.725886	−	0.687815i	$-0.758570\pi$
$379$	−1.77874e9	−	4.05985e8i	−1.67832	−	0.383065i	−0.952432	+	0.304750i	$0.901427\pi$
$380$	−5.44395e8	−	1.13045e9i	−0.508946	−	1.05684i
$381$	−1.48454e9	−	7.14919e8i	−1.37517	−	0.662246i
$382$	1.62935e8	−	7.13865e8i	0.149552	−	0.655231i
$383$	−2.55813e8	−	1.12079e9i	−0.232663	−	1.01936i	−0.947421	−	0.319990i	$-0.896320\pi$
$383$	−2.55813e8	−	1.12079e9i	−0.232663	−	1.01936i	0.714758	−	0.699372i	$-0.246537\pi$
$384$	2.16539e9	−	1.04280e9i	1.95154	−	0.939811i
$385$	3.00146e8	+	2.39359e8i	0.268053	+	0.213765i
$386$	7.82183e8	−	9.80827e8i	0.692234	−	0.868034i
$387$	−1.15366e8	+	2.39559e8i	−0.101178	+	0.210099i
$388$	−3.35353e8	+	2.67435e8i	−0.291468	+	0.232438i
$389$			1.64977e8i			0.142102i	0.997473	+	0.0710509i	$0.0226353\pi$
$389$			1.64977e8i			0.142102i	−0.997473	+	0.0710509i	$0.977365\pi$
$390$	−4.34076e8	−	5.44314e8i	−0.370544	−	0.464648i
$391$	−1.36571e7	+	3.11714e6i	−0.0115542	+	0.00263717i
$392$	−8.41360e8	+	1.92035e8i	−0.705473	+	0.161020i
$393$	1.32394e9	+	1.66017e9i	1.10026	+	1.37968i
$394$		−	3.19394e9i		−	2.63081i
$395$	−6.03468e8	+	4.81250e8i	−0.492680	+	0.392899i
$396$	7.56133e8	−	1.57013e9i	0.611879	−	1.27058i
$397$	−3.56261e8	+	4.46737e8i	−0.285760	+	0.358332i	−0.903906	−	0.427732i	$-0.859313\pi$
$397$	−3.56261e8	+	4.46737e8i	−0.285760	+	0.358332i	0.618146	+	0.786064i	$0.287884\pi$
$398$	2.77784e9	+	2.21525e9i	2.20859	+	1.76129i
$399$	1.21745e9	−	5.86293e8i	0.959502	−	0.462072i
$400$	1.59021e7	+	6.96718e7i	0.0124235	+	0.0544311i
$401$	−2.04061e8	+	8.94051e8i	−0.158036	+	0.692400i	0.832371	+	0.554218i	$0.186983\pi$
$401$	−2.04061e8	+	8.94051e8i	−0.158036	+	0.692400i	−0.990407	+	0.138181i	$0.955874\pi$
$402$	−1.39716e9	−	6.72835e8i	−1.07264	−	0.516556i
$403$	5.53007e8	+	1.14833e9i	0.420884	+	0.873976i
$404$	−3.05027e9	−	6.96205e8i	−2.30146	−	0.525294i
$405$	7.92191e8			0.592566
$406$	1.11490e9	−	5.31259e8i	0.826791	−	0.393972i
$407$	1.40983e9			1.03654
$408$	−6.82214e7	−	1.55711e7i	−0.0497291	−	0.0113503i
$409$	−3.26927e8	−	6.78871e8i	−0.236276	−	0.490632i	0.748790	−	0.662807i	$-0.230635\pi$
$409$	−3.26927e8	−	6.78871e8i	−0.236276	−	0.490632i	−0.985066	+	0.172175i	$0.944921\pi$
$410$	6.11749e8	+	2.94603e8i	0.438359	+	0.211102i
$411$	−2.24233e8	+	9.82429e8i	−0.159314	+	0.697999i
$412$	−4.59596e8	−	2.01362e9i	−0.323769	−	1.41853i
$413$	−8.04432e8	+	3.87394e8i	−0.561907	+	0.270600i
$414$	−4.00517e8	−	3.19402e8i	−0.277408	−	0.221226i
$415$	4.14058e8	−	5.19212e8i	0.284376	−	0.356596i
$416$	−3.45781e8	+	7.18022e8i	−0.235491	+	0.489003i
$417$	−2.06747e9	+	1.64875e9i	−1.39625	+	1.11347i
$418$			4.43796e9i			2.97212i
$419$	8.32172e8	+	1.04351e9i	0.552668	+	0.693024i	0.977183	−	0.212397i	$-0.0681270\pi$
$419$	8.32172e8	+	1.04351e9i	0.552668	+	0.693024i	−0.424516	+	0.905421i	$0.639556\pi$
$420$	8.68468e8	−	1.98222e8i	0.571980	−	0.130551i
$421$	−1.55121e9	+	3.54054e8i	−1.01317	+	0.231250i	−0.696709	−	0.717354i	$-0.745353\pi$
$421$	−1.55121e9	+	3.54054e8i	−1.01317	+	0.231250i	−0.316465	+	0.948604i	$0.602496\pi$
$422$	−2.24634e9	−	2.81682e9i	−1.45506	−	1.82459i
$423$		−	2.74436e8i		−	0.176299i
$424$	−1.76266e9	+	1.40567e9i	−1.12302	+	0.895578i
$425$	−1.94508e7	+	4.03899e7i	−0.0122907	+	0.0255218i
$426$	2.62333e9	−	3.28955e9i	1.64407	−	2.06159i
$427$	1.14091e9	+	9.09844e8i	0.709174	+	0.565548i
$428$	2.19894e9	−	1.05896e9i	1.35569	−	0.652867i
$429$	3.41207e8	+	1.49493e9i	0.208650	+	0.914153i
$430$	9.93280e7	−	4.35184e8i	0.0602465	−	0.263957i
$431$	8.23657e8	+	3.96652e8i	0.495537	+	0.238638i	0.664923	−	0.746912i	$-0.268464\pi$
$431$	8.23657e8	+	3.96652e8i	0.495537	+	0.238638i	−0.169386	+	0.985550i	$0.554179\pi$
$432$	2.18861e7	+	4.54469e7i	0.0130609	+	0.0271213i
$433$	2.02601e9	+	4.62423e8i	1.19932	+	0.273736i	0.775108	−	0.631829i	$-0.217695\pi$
$433$	2.02601e9	+	4.62423e8i	1.19932	+	0.273736i	0.424208	+	0.905565i	$0.360552\pi$
$434$	−2.61899e9			−1.53787
$435$	9.79363e8	−	4.66674e8i	0.570468	−	0.271832i
$436$	−1.98916e9			−1.14939
$437$	7.91966e8	+	1.80761e8i	0.453964	+	0.103614i
$438$	2.53942e9	+	5.27315e9i	1.44403	+	2.99855i
$439$	8.07667e8	+	3.88952e8i	0.455624	+	0.219417i	0.647597	−	0.761983i	$-0.275774\pi$
$439$	8.07667e8	+	3.88952e8i	0.455624	+	0.219417i	−0.191973	+	0.981400i	$0.561488\pi$
$440$	−2.56535e8	+	1.12395e9i	−0.143569	+	0.629018i
$441$	−1.87100e8	−	8.19737e8i	−0.103881	−	0.455134i
$442$	5.71302e7	−	2.75124e7i	0.0314693	−	0.0151548i
$443$	−9.37589e8	−	7.47702e8i	−0.512388	−	0.408616i	0.332871	−	0.942972i	$-0.391983\pi$
$443$	−9.37589e8	−	7.47702e8i	−0.512388	−	0.408616i	−0.845259	+	0.534356i	$0.820554\pi$
$444$	2.03966e9	−	2.55765e9i	1.10590	−	1.38676i
$445$	3.37493e8	−	7.00811e8i	0.181553	−	0.377000i
$446$	−1.60139e9	+	1.27706e9i	−0.854721	+	0.681618i
$447$			2.47123e9i			1.30869i
$448$	−1.06988e9	−	1.34159e9i	−0.562164	−	0.704931i
$449$	7.87890e7	−	1.79831e7i	0.0410775	−	0.00937566i	−0.201933	−	0.979399i	$-0.564722\pi$
$449$	7.87890e7	−	1.79831e7i	0.0410775	−	0.00937566i	0.243010	+	0.970024i	$0.421865\pi$
$450$	−1.59830e9	+	3.64801e8i	−0.826826	+	0.188718i
$451$	−9.32402e8	−	1.16919e9i	−0.478614	−	0.600163i
$452$		−	3.07986e8i		−	0.156872i
$453$	−1.23887e9	+	9.87964e8i	−0.626154	+	0.499341i
$454$	−1.38646e9	+	2.87902e9i	−0.695365	+	1.44394i
$455$	−1.98322e8	+	2.48688e8i	−0.0987030	+	0.123770i
$456$	3.17256e9	+	2.53003e9i	1.56687	+	1.24954i
$457$	1.86802e9	−	8.99590e8i	0.915533	−	0.440898i	0.0840590	−	0.996461i	$-0.473212\pi$
$457$	1.86802e9	−	8.99590e8i	0.915533	−	0.440898i	0.831474	+	0.555563i	$0.187497\pi$
$458$	3.99344e8	+	1.74964e9i	0.194231	+	0.850980i
$459$	−7.04115e6	+	3.08493e7i	−0.00339860	+	0.0148902i
$460$	4.82485e8	+	2.32352e8i	0.231117	+	0.111300i
$461$	−1.12500e9	−	2.33609e9i	−0.534809	−	1.11054i	−0.976924	−	0.213585i	$-0.931486\pi$
$461$	−1.12500e9	−	2.33609e9i	−0.534809	−	1.11054i	0.442115	−	0.896958i	$-0.354228\pi$
$462$	−3.07182e9	−	7.01123e8i	−1.44927	−	0.330786i
$463$	−1.30435e9			−0.610748			−0.305374	−	0.952232i	$-0.598781\pi$
$463$	−1.30435e9			−0.610748			−0.305374	+	0.952232i	$0.598781\pi$
$464$	1.22743e8	+	9.87145e7i	0.0570405	+	0.0458742i
$465$	−2.30059e9			−1.06110
$466$	5.29910e9	+	1.20948e9i	2.42578	+	0.553668i
$467$	1.28479e8	+	2.66789e8i	0.0583744	+	0.121216i	0.928115	−	0.372293i	$-0.121428\pi$
$467$	1.28479e8	+	2.66789e8i	0.0583744	+	0.121216i	−0.869741	+	0.493509i	$0.835714\pi$
$468$	1.30094e9	+	6.26497e8i	0.586672	+	0.282526i
$469$	−1.57656e8	+	6.90736e8i	−0.0705677	+	0.309177i
$470$	1.02520e8	+	4.49171e8i	0.0455478	+	0.199558i
$471$	4.33027e9	−	2.08535e9i	1.90960	−	0.919613i
$472$	−2.09627e9	−	1.67172e9i	−0.917594	−	0.731757i
$473$	−6.12972e8	+	7.68643e8i	−0.266334	+	0.333972i
$474$	2.74864e9	−	5.70761e9i	1.18548	−	2.46167i
$475$	2.03247e9	−	1.62084e9i	0.870155	−	0.693926i
$476$			8.11335e7i			0.0344807i
$477$	−1.36955e9	−	1.71736e9i	−0.577780	−	0.724513i
$478$	−1.98270e7	+	4.52539e6i	−0.00830348	+	0.00189522i
$479$	−2.23215e9	+	5.09474e8i	−0.928003	+	0.211811i	−0.659704	−	0.751525i	$-0.729318\pi$
$479$	−2.23215e9	+	5.09474e8i	−0.928003	+	0.211811i	−0.268298	+	0.963336i	$0.586461\pi$
$480$	−8.96892e8	−	1.12467e9i	−0.370165	−	0.464173i
$481$			1.16812e9i			0.478608i
$482$	4.12826e9	−	3.29218e9i	1.67920	−	1.33912i
$483$	−2.50235e8	+	5.19618e8i	−0.101049	+	0.209831i
$484$	1.45100e9	−	1.81949e9i	0.581712	−	0.729444i
$485$	2.16145e8	+	1.72369e8i	0.0860296	+	0.0686064i
$486$	−4.33146e9	+	2.08592e9i	−1.71162	+	0.824273i
$487$	−7.90499e8	−	3.46340e9i	−0.310134	−	1.35879i	−0.854287	−	0.519801i	$-0.826006\pi$
$487$	−7.90499e8	−	3.46340e9i	−0.310134	−	1.35879i	0.544153	−	0.838986i	$-0.316851\pi$
$488$	−9.75132e8	+	4.27233e9i	−0.379834	+	1.66416i
$489$	3.48428e8	+	1.67794e8i	0.134751	+	0.0648926i
$490$	6.12453e8	+	1.27177e9i	0.235173	+	0.488341i
$491$	−4.70624e9	−	1.07417e9i	−1.79427	−	0.409531i	−0.810036	−	0.586380i	$-0.800553\pi$
$491$	−4.70624e9	−	1.07417e9i	−1.79427	−	0.409531i	−0.984238	+	0.176848i	$0.943410\pi$
$492$	−3.47004e9			−1.31358
$493$	2.15898e7	+	9.64212e7i	0.00811493	+	0.0362417i
$494$	−3.67709e9			−1.37233
$495$	−1.09507e9	−	2.49942e8i	−0.405809	−	0.0926233i
$496$	−1.44928e8	−	3.00947e8i	−0.0533295	−	0.110740i
$497$	−1.73196e9	−	8.34068e8i	−0.632835	−	0.304757i
$498$	−1.21285e9	+	5.31383e9i	−0.440051	+	1.92799i
$499$	−1.06353e9	−	4.65963e9i	−0.383175	−	1.67880i	−0.687462	−	0.726220i	$-0.741275\pi$
$499$	−1.06353e9	−	4.65963e9i	−0.383175	−	1.67880i	0.304287	−	0.952581i	$-0.401582\pi$
$500$	3.56842e9	−	1.71846e9i	1.27668	−	0.614815i
$501$	1.96700e9	+	1.56863e9i	0.698831	+	0.557299i
$502$	1.38572e9	−	1.73764e9i	0.488892	−	0.613051i
$503$	1.56997e9	−	3.26008e9i	0.550052	−	1.14219i	−0.421819	−	0.906680i	$-0.638608\pi$
$503$	1.56997e9	−	3.26008e9i	0.550052	−	1.14219i	0.971871	−	0.235515i	$-0.0756776\pi$
$504$	−9.14087e8	+	7.28960e8i	−0.318039	+	0.253628i
$505$			2.01655e9i			0.696769i
$506$	−1.18099e9	−	1.48091e9i	−0.405246	−	0.508162i
$507$	2.47282e9	−	5.64404e8i	0.842683	−	0.192337i
$508$	−5.59323e9	+	1.27662e9i	−1.89295	+	0.432054i
$509$	1.84754e9	+	2.31674e9i	0.620984	+	0.778689i	0.988483	−	0.151335i	$-0.0483571\pi$
$509$	1.84754e9	+	2.31674e9i	0.620984	+	0.778689i	−0.367499	+	0.930024i	$0.619786\pi$
$510$			1.14456e8i			0.0382070i
$511$	2.09063e9	−	1.66723e9i	0.693115	−	0.552740i
$512$	1.92734e8	−	4.00217e8i	0.0634621	−	0.131780i
$513$	1.14406e9	−	1.43461e9i	0.374145	−	0.469163i
$514$	3.46670e9	+	2.76460e9i	1.12602	+	0.897970i
$515$	−1.19938e9	+	5.77592e8i	−0.386930	+	0.186336i
$516$	5.07625e8	+	2.22405e9i	0.162656	+	0.712641i
$517$	2.25798e8	−	9.89287e8i	0.0718627	−	0.314851i
$518$	−2.16259e9	−	1.04145e9i	−0.683628	−	0.329218i
$519$	1.79232e9	+	3.72179e9i	0.562768	+	1.16860i
$520$	−9.31255e8	−	2.12553e8i	−0.290440	−	0.0662911i
$521$	2.51807e9			0.780073			0.390036	−	0.920800i	$-0.372462\pi$
$521$	2.51807e9			0.780073			0.390036	+	0.920800i	$0.372462\pi$
$522$	−2.26455e9	+	2.81577e9i	−0.696843	+	0.866463i
$523$	−5.30017e9			−1.62007			−0.810035	−	0.586381i	$-0.800552\pi$
$523$	−5.30017e9			−1.62007			−0.810035	+	0.586381i	$0.800552\pi$
$524$	7.20809e9	+	1.64520e9i	2.18857	+	0.499527i
$525$	8.00802e8	+	1.66288e9i	0.241528	+	0.501538i
$526$	2.05849e9	+	9.91318e8i	0.616736	+	0.297005i
$527$	4.66262e7	−	2.04283e8i	0.0138769	−	0.0607987i
$528$	−8.94213e7	−	3.91780e8i	−0.0264376	−	0.115831i
$529$	2.75527e9	−	1.32687e9i	0.809224	−	0.389702i
$530$	2.88309e9	+	2.29919e9i	0.841187	+	0.670824i
$531$	1.62876e9	−	2.04240e9i	0.472091	−	0.591983i
$532$	2.04137e9	−	4.23895e9i	0.587802	−	1.22058i
$533$	9.68741e8	−	7.72545e8i	0.277116	−	0.220993i
$534$			6.38402e9i			1.81426i
$535$	−9.80790e8	−	1.22987e9i	−0.276910	−	0.347234i
$536$	−2.07428e9	+	4.73441e8i	−0.581823	+	0.132797i
$537$	−2.26644e9	+	5.17300e8i	−0.631588	+	0.144156i
$538$	−2.25623e9	−	2.82922e9i	−0.624663	−	0.783302i
$539$		−	3.10892e9i		−	0.855164i
$540$	9.45745e8	−	7.54206e8i	0.258461	−	0.206116i
$541$	1.65258e8	−	3.43163e8i	0.0448718	−	0.0931772i	−0.877328	−	0.479892i	$-0.840676\pi$
$541$	1.65258e8	−	3.43163e8i	0.0448718	−	0.0931772i	0.922199	+	0.386715i	$0.126390\pi$
$542$	4.26715e9	−	5.35084e9i	1.15117	−	1.44352i
$543$	−2.65857e9	−	2.12014e9i	−0.712606	−	0.568284i
$544$	1.18043e8	−	5.68465e7i	0.0314372	−	0.0151394i
$545$	2.85288e8	+	1.24993e9i	0.0754911	+	0.330748i
$546$	5.80918e8	−	2.54517e9i	0.152736	−	0.669179i
$547$	1.15262e9	+	5.55074e8i	0.301114	+	0.145009i	0.578340	−	0.815796i	$-0.303701\pi$
$547$	1.15262e9	+	5.55074e8i	0.301114	+	0.145009i	−0.277226	+	0.960805i	$0.589415\pi$
$548$	1.52233e9	+	3.16115e9i	0.395164	+	0.820566i
$549$	−4.16253e9	−	9.50070e8i	−1.07363	−	0.245049i
$550$	−6.06168e9			−1.55355
$551$	1.29802e9	−	5.58089e9i	0.330561	−	1.42126i
$552$	−1.73193e9			−0.438271
$553$	−2.82177e9	−	6.44050e8i	−0.709551	−	0.161950i
$554$	−2.66437e9	−	5.53262e9i	−0.665749	−	1.38244i
$555$	−1.89968e9	−	9.14838e8i	−0.471688	−	0.227153i
$556$	−2.04882e9	+	8.97647e9i	−0.505524	+	2.21485i
$557$	9.63053e8	+	4.21941e9i	0.236133	+	1.03457i	0.944446	+	0.328668i	$0.106600\pi$
$557$	9.63053e8	+	4.21941e9i	0.236133	+	1.03457i	−0.708312	+	0.705899i	$0.750543\pi$
$558$	6.90384e9	−	3.32471e9i	1.68217	−	0.810093i
$559$	−6.36862e8	−	5.07880e8i	−0.154207	−	0.122976i
$560$	5.19749e7	−	6.51744e7i	0.0125065	−	0.0156826i
$561$	1.09376e8	−	2.27122e8i	0.0261549	−	0.0543111i
$562$	−7.80988e9	+	6.22817e9i	−1.85595	+	1.48007i
$563$			2.40249e9i			0.567390i	0.958915	+	0.283695i	$0.0915603\pi$
$563$			2.40249e9i			0.567390i	−0.958915	+	0.283695i	$0.908440\pi$
$564$	−1.46805e9	−	1.84087e9i	−0.344559	−	0.432063i
$565$	−1.93529e8	+	4.41717e7i	−0.0451416	+	0.0103033i
$566$	−6.88024e9	+	1.57037e9i	−1.59495	+	0.364036i
$567$	1.85211e9	+	2.32247e9i	0.426703	+	0.535069i
$568$		−	5.77276e9i		−	1.32179i
$569$	−4.84248e9	+	3.86175e9i	−1.10198	+	0.878801i	−0.993333	−	0.115279i	$-0.963224\pi$
$569$	−4.84248e9	+	3.86175e9i	−1.10198	+	0.878801i	−0.108649	+	0.994080i	$0.534652\pi$
$570$	2.87978e9	−	5.97993e9i	0.651325	−	1.35249i
$571$	−3.62220e9	+	4.54210e9i	−0.814229	+	1.02101i	0.185038	+	0.982731i	$0.440759\pi$
$571$	−3.62220e9	+	4.54210e9i	−0.814229	+	1.02101i	−0.999267	+	0.0382794i	$0.987812\pi$
$572$	4.17414e9	+	3.32877e9i	0.932569	+	0.743699i
$573$	2.17304e9	−	1.04648e9i	0.482532	−	0.232375i
$574$	5.66554e8	+	2.48224e9i	0.125040	+	0.547837i
$575$	−2.46897e8	+	1.08172e9i	−0.0541599	+	0.237290i
$576$	4.52339e9	+	2.17835e9i	0.986246	+	0.474951i
$577$	1.18061e9	+	2.45155e9i	0.255852	+	0.531283i	0.988844	−	0.148955i	$-0.0475909\pi$
$577$	1.18061e9	+	2.45155e9i	0.255852	+	0.531283i	−0.732992	+	0.680238i	$0.761877\pi$
$578$	7.35814e9	+	1.67945e9i	1.58497	+	0.361759i
$579$	4.13231e9			0.884745
$580$	1.65293e9	−	3.39646e9i	0.351768	−	0.722817i
$581$	2.49023e9			0.526772
$582$	−2.21211e9	−	5.04900e8i	−0.465132	−	0.106163i
$583$	−3.52394e9	−	7.31754e9i	−0.736527	−	1.52941i
$584$	7.23486e9	+	3.48412e9i	1.50309	+	0.723850i
$585$	2.07090e8	−	9.07321e8i	0.0427675	−	0.187377i
$586$	6.45295e8	+	2.82722e9i	0.132470	+	0.580388i
$587$	6.32008e9	−	3.04359e9i	1.28970	−	0.621087i	0.341836	−	0.939760i	$-0.388951\pi$
$587$	6.32008e9	−	3.04359e9i	1.28970	−	0.621087i	0.947865	+	0.318672i	$0.103237\pi$
$588$	−5.64007e9	−	4.49780e9i	−1.14410	−	0.912389i
$589$	−7.57594e9	+	9.49993e9i	−1.52768	+	1.91565i
$590$	−1.90282e9	+	3.95125e9i	−0.381431	+	0.792050i
$591$	8.22533e9	−	6.55948e9i	1.63907	−	1.30711i
$592$		−	3.06134e8i		−	0.0606436i
$593$	2.67715e9	+	3.35704e9i	0.527208	+	0.661097i	0.972122	−	0.234476i	$-0.0753373\pi$
$593$	2.67715e9	+	3.35704e9i	0.527208	+	0.661097i	−0.444914	+	0.895573i	$0.646766\pi$
$594$	−4.17134e9	+	9.52081e8i	−0.816626	+	0.186389i
$595$	5.09818e7	−	1.16363e7i	0.00992215	−	0.00226467i
$596$	5.36476e9	+	6.72720e9i	1.03798	+	1.30158i
$597$			1.17033e10i			2.25111i
$598$	1.22702e9	−	9.78512e8i	0.234637	−	0.187116i
$599$	−1.93250e9	+	4.01287e9i	−0.367388	+	0.762889i	−0.999932	−	0.0116349i	$-0.996296\pi$
$599$	−1.93250e9	+	4.01287e9i	−0.367388	+	0.762889i	0.632544	+	0.774524i	$0.282011\pi$
$600$	−3.45570e9	+	4.33331e9i	−0.653141	+	0.819013i
$601$	−1.87648e9	−	1.49644e9i	−0.352601	−	0.281190i	0.431131	−	0.902289i	$-0.358115\pi$
$601$	−1.87648e9	−	1.49644e9i	−0.352601	−	0.281190i	−0.783732	+	0.621100i	$0.786686\pi$
$602$	1.50806e9	−	7.26243e8i	0.281728	−	0.135673i
$603$	−4.61273e8	−	2.02097e9i	−0.0856737	−	0.375361i
$604$	−1.22769e9	+	5.37887e9i	−0.226705	+	0.993257i
$605$	−1.35142e9	−	6.50809e8i	−0.248111	−	0.119484i
$606$	−7.18100e9	−	1.49115e10i	−1.31078	−	2.72187i
$607$	7.40842e9	+	1.69092e9i	1.34451	+	0.306877i	0.833416	−	0.552646i	$-0.186382\pi$
$607$	7.40842e9	+	1.69092e9i	1.34451	+	0.306877i	0.511098	+	0.859523i	$0.329239\pi$
$608$	−7.59763e9			−1.37093
$609$	3.65786e9	+	1.78014e9i	0.656246	+	0.319370i
$610$	7.16775e9			1.27858
$611$	8.19678e8	+	1.87086e8i	0.145378	+	0.0331816i
$612$	−1.02996e8	−	2.13874e8i	−0.0181632	−	0.0377162i
$613$	−1.56757e9	−	7.54902e8i	−0.274862	−	0.132367i	0.291375	−	0.956609i	$-0.405887\pi$
$613$	−1.56757e9	−	7.54902e8i	−0.274862	−	0.132367i	−0.566238	+	0.824242i	$0.691602\pi$
$614$	2.91652e9	−	1.27781e10i	0.508481	−	2.22780i
$615$	4.97678e8	+	2.18047e9i	0.0862750	+	0.377996i
$616$	−3.89487e9	+	1.87567e9i	−0.671367	+	0.323313i
$617$	−1.12317e9	−	8.95700e8i	−0.192508	−	0.153520i	0.522493	−	0.852644i	$-0.325002\pi$
$617$	−1.12317e9	−	8.95700e8i	−0.192508	−	0.153520i	−0.715001	+	0.699124i	$0.753574\pi$
$618$	6.81209e9	−	8.54209e9i	1.16097	−	1.45581i
$619$	−9.21718e8	+	1.91397e9i	−0.156200	+	0.324353i	−0.964353	−	0.264621i	$-0.914753\pi$
$619$	−9.21718e8	+	1.91397e9i	−0.156200	+	0.324353i	0.808153	+	0.588973i	$0.200468\pi$
$620$	−6.26268e9	+	4.99432e9i	−1.05533	+	0.841599i
$621$			7.83166e8i			0.131230i
$622$	5.41487e9	+	6.79003e9i	0.902239	+	1.13137i
$623$	2.84362e9	−	6.49037e8i	0.471154	−	0.107538i
$624$	3.24611e8	−	7.40904e7i	0.0534832	−	0.0122072i
$625$	1.31094e9	+	1.64386e9i	0.214784	+	0.269331i
$626$		−	8.90785e9i		−	1.45132i
$627$	−1.14290e10	+	9.11436e9i	−1.85171	+	1.47669i
$628$	7.26082e9	−	1.50772e10i	1.16984	−	2.42920i
$629$	1.19735e8	−	1.50142e8i	0.0191841	−	0.0240561i
$630$	1.49513e9	+	1.19232e9i	0.238224	+	0.189978i
$631$	7.71732e9	−	3.71647e9i	1.22282	−	0.588881i	0.292727	−	0.956196i	$-0.405437\pi$
$631$	7.71732e9	−	3.71647e9i	1.22282	−	0.588881i	0.930097	+	0.367315i	$0.119723\pi$
$632$	−1.93408e9	−	8.47376e9i	−0.304765	−	1.33526i
$633$	2.64077e9	−	1.15700e10i	0.413826	−	1.81309i
$634$	−5.54308e9	−	2.66941e9i	−0.863850	−	0.416008i
$635$	1.60438e9	+	3.33152e9i	0.248656	+	0.516339i
$636$	−1.83734e10	−	4.19360e9i	−2.83197	−	0.646379i
$637$	2.57591e9			0.394860
$638$	−1.04800e10	+	8.28707e9i	−1.59767	+	1.26336i
$639$	5.62439e9			0.852752
$640$	−5.25834e9	−	1.20018e9i	−0.792900	−	0.180974i
$641$	−5.34021e9	−	1.10891e10i	−0.800858	−	1.66300i	−0.747350	−	0.664431i	$-0.768674\pi$
$641$	−5.34021e9	−	1.10891e10i	−0.800858	−	1.66300i	−0.0535079	−	0.998567i	$-0.517040\pi$
$642$	1.16321e10	+	5.60175e9i	1.73495	+	0.835509i
$643$	−1.65971e9	+	7.27166e9i	−0.246203	+	1.07869i	0.689052	+	0.724712i	$0.258027\pi$
$643$	−1.65971e9	+	7.27166e9i	−0.246203	+	1.07869i	−0.935255	+	0.353974i	$0.884830\pi$
$644$	4.46840e8	+	1.95773e9i	0.0659252	+	0.288837i
$645$	1.32472e9	−	6.37952e8i	0.194386	−	0.0936115i
$646$	4.72627e8	+	3.76908e8i	0.0689771	+	0.0550074i
$647$	−7.58152e9	+	9.50693e9i	−1.10050	+	1.37999i	−0.182599	+	0.983188i	$0.558451\pi$
$647$	−7.58152e9	+	9.50693e9i	−1.10050	+	1.37999i	−0.917905	+	0.396800i	$0.870121\pi$
$648$	−3.87049e9	+	8.03715e9i	−0.558796	+	1.16035i
$649$	7.55176e9	−	6.02233e9i	1.08441	−	0.864785i
$650$		−	5.02243e9i		−	0.717327i
$651$	−5.37869e9	−	6.74467e9i	−0.764088	−	0.958136i
$652$	1.31275e9	−	2.99627e8i	0.185488	−	0.0423364i
$653$	3.79713e9	−	8.66671e8i	0.533654	−	0.121803i	0.0528022	−	0.998605i	$-0.483185\pi$
$653$	3.79713e9	−	8.66671e8i	0.533654	−	0.121803i	0.480852	+	0.876802i	$0.340328\pi$
$654$	−6.56063e9	−	8.22677e9i	−0.917114	−	1.15002i
$655$		−	4.76530e9i		−	0.662591i
$656$	−2.53881e8	+	2.02464e8i	−0.0351129	+	0.0280016i
$657$	−3.39458e9	+	7.04892e9i	−0.466990	+	0.969714i
$658$	−1.07715e9	+	1.35070e9i	−0.147396	+	0.184829i
$659$	4.37566e8	+	3.48947e8i	0.0595587	+	0.0474964i	0.652817	−	0.757516i	$-0.273587\pi$
$659$	4.37566e8	+	3.48947e8i	0.0595587	+	0.0474964i	−0.593258	+	0.805012i	$0.702159\pi$
$660$	−8.68254e9	+	4.18129e9i	−1.17555	+	0.566117i
$661$	−7.81207e8	−	3.42269e9i	−0.105211	−	0.460959i	−0.999898	−	0.0142663i	$-0.995459\pi$
$661$	−7.81207e8	−	3.42269e9i	−0.105211	−	0.460959i	0.894687	−	0.446693i	$-0.147398\pi$
$662$	3.06756e9	−	1.34399e10i	0.410951	−	1.80049i
$663$	1.88183e8	+	9.06240e7i	0.0250774	+	0.0120766i
$664$	3.24465e9	+	6.73759e9i	0.430110	+	0.893133i
$665$	−2.95640e9	−	6.74779e8i	−0.389841	−	0.0889787i
$666$	7.02283e9			0.921196
$667$	1.05199e9	+	2.20772e9i	0.137269	+	0.288073i
$668$	8.75988e9			1.13705
$669$	−6.57764e9	−	1.50130e9i	−0.849334	−	0.193855i
$670$	1.50994e9	+	3.13541e9i	0.193953	+	0.402748i
$671$	−1.42234e10	−	6.84962e9i	−1.81750	−	0.875261i
$672$	1.20030e9	−	5.25885e9i	0.152580	−	0.668496i
$673$	−3.33919e8	−	1.46299e9i	−0.0422268	−	0.185008i	0.949416	−	0.314021i	$-0.101676\pi$
$673$	−3.33919e8	−	1.46299e9i	−0.0422268	−	0.185008i	−0.991643	+	0.129013i	$0.958819\pi$
$674$	−1.31718e10	+	6.34322e9i	−1.65705	+	0.797995i
$675$	1.95950e9	+	1.56265e9i	0.245234	+	0.195568i
$676$	5.50625e9	−	6.90462e9i	0.685555	−	0.859659i
$677$	1.18408e9	−	2.45877e9i	0.146663	−	0.304549i	−0.814676	−	0.579917i	$-0.803085\pi$
$677$	1.18408e9	−	2.45877e9i	0.146663	−	0.304549i	0.961339	+	0.275367i	$0.0887995\pi$
$678$	1.27377e9	−	1.01580e9i	0.156959	−	0.125171i
$679$			1.03667e9i			0.127085i
$680$	9.79101e7	+	1.22775e8i	0.0119411	+	0.0149737i
$681$	−1.02617e10	+	2.34218e9i	−1.24511	+	0.284187i
$682$	2.76224e10	−	6.30464e9i	3.33439	−	0.761053i
$683$	−7.66395e9	−	9.61029e9i	−0.920408	−	1.15416i	−0.987690	−	0.156421i	$-0.950004\pi$
$683$	−7.66395e9	−	9.61029e9i	−0.920408	−	1.15416i	0.0672824	−	0.997734i	$-0.478567\pi$
$684$			1.37656e10i			1.64475i
$685$	1.76804e9	−	1.40996e9i	0.210172	−	0.167606i
$686$	−5.65655e9	+	1.17460e10i	−0.668987	+	1.38917i
$687$	−3.68569e9	+	4.62171e9i	−0.433681	+	0.543819i
$688$	1.66905e8	+	1.33102e8i	0.0195393	+	0.0155821i
$689$	6.06298e9	−	2.91978e9i	0.706185	−	0.340081i
$690$	6.30363e8	+	2.76180e9i	0.0730497	+	0.320052i
$691$	5.72209e8	−	2.50701e9i	0.0659754	−	0.289057i	−0.931168	−	0.364591i	$-0.881209\pi$
$691$	5.72209e8	−	2.50701e9i	0.0659754	−	0.289057i	0.997143	+	0.0755338i	$0.0240661\pi$
$692$	1.29586e10	+	6.24054e9i	1.48658	+	0.715898i
$693$	−1.82746e9	−	3.79477e9i	−0.208585	−	0.433130i
$694$	1.78301e10	+	4.06961e9i	2.02487	+	0.462163i
$695$	5.93438e9			0.670546
$696$	−5.03477e7	+	1.22162e10i	−0.00566041	+	1.37342i
$697$	−2.03703e8			−0.0227867
$698$	1.36659e10	+	3.11914e9i	1.52105	+	0.347169i
$699$	7.76813e9	+	1.61307e10i	0.860293	+	1.78642i
$700$	5.78987e9	+	2.78825e9i	0.638007	+	0.307248i
$701$	−2.58642e9	+	1.13318e10i	−0.283587	+	1.24247i	0.609571	+	0.792731i	$0.291342\pi$
$701$	−2.58642e9	+	1.13318e10i	−0.283587	+	1.24247i	−0.893158	+	0.449743i	$0.851515\pi$
$702$	−7.88851e8	−	3.45618e9i	−0.0860627	−	0.377065i
$703$	−1.00334e10	+	4.83183e9i	−1.08919	+	0.524527i
$704$	1.45136e10	+	1.15742e10i	1.56773	+	1.25022i
$705$	−9.46200e8	+	1.18650e9i	−0.101700	+	0.127528i
$706$	−7.63924e9	+	1.58630e10i	−0.817022	+	1.69656i
$707$	−5.91193e9	+	4.71461e9i	−0.629160	+	0.501739i
$708$		−	2.24128e10i		−	2.37345i
$709$	3.25405e7	+	4.08046e7i	0.00342896	+	0.00429979i	0.783543	−	0.621338i	$-0.213410\pi$
$709$	3.25405e7	+	4.08046e7i	0.00342896	+	0.00429979i	−0.780114	+	0.625637i	$0.784839\pi$
$710$	−9.20547e9	+	2.10109e9i	−0.965254	+	0.220313i
$711$	8.25598e9	−	1.88437e9i	0.861440	−	0.196618i
$712$	5.46114e9	+	6.84805e9i	0.567026	+	0.711028i
$713$		−	5.18609e9i		−	0.535830i
$714$	−3.35552e8	+	2.67593e8i	−0.0344997	+	0.0275126i
$715$	1.49304e9	−	3.10032e9i	0.152756	−	0.317202i
$716$	−5.04670e9	+	6.32836e9i	−0.513821	+	0.644312i
$717$	−5.23736e7	−	4.17666e7i	−0.00530635	−	0.00423167i
$718$	−7.27311e9	+	3.50255e9i	−0.733305	+	0.353141i
$719$	4.86759e8	+	2.13263e9i	0.0488385	+	0.213976i	0.993459	−	0.114189i	$-0.0364270\pi$
$719$	4.86759e8	+	2.13263e9i	0.0488385	+	0.213976i	−0.944620	+	0.328165i	$0.893570\pi$
$720$	−5.42728e7	+	2.37785e8i	−0.00541899	+	0.0237422i
$721$	−4.49744e9	−	2.16585e9i	−0.446881	−	0.215206i
$722$	−8.06658e9	−	1.67504e10i	−0.797644	−	1.65633i
$723$	1.69567e10	+	3.87025e9i	1.66862	+	0.380851i
$724$	−1.18398e10			−1.15947
$725$	7.62279e9	+	1.77294e9i	0.742901	+	0.172787i
$726$	1.23107e10			1.19400
$727$	1.72518e9	+	3.93761e8i	0.166519	+	0.0380069i	0.304968	−	0.952363i	$-0.401354\pi$
$727$	1.72518e9	+	3.93761e8i	0.166519	+	0.0380069i	−0.138448	+	0.990370i	$0.544212\pi$
$728$	−1.55409e9	−	3.22711e9i	−0.149285	−	0.309994i
$729$	−2.80258e9	−	1.34965e9i	−0.267924	−	0.129025i
$730$	2.92268e9	−	1.28051e10i	0.278068	−	1.21830i
$731$	2.97992e7	+	1.30559e8i	0.00282159	+	0.0123622i
$732$	−3.30038e10	+	1.58938e10i	−3.11011	+	1.49775i
$733$	5.19967e9	+	4.14660e9i	0.487654	+	0.388891i	0.836221	−	0.548393i	$-0.184760\pi$
$733$	5.19967e9	+	4.14660e9i	0.487654	+	0.388891i	−0.348567	+	0.937284i	$0.613331\pi$
$734$	−1.30398e10	+	1.63513e10i	−1.21712	+	1.52622i
$735$	−2.01738e9	+	4.18913e9i	−0.187405	+	0.389151i
$736$	2.53527e9	−	2.02181e9i	0.234397	−	0.186925i
$737$		−	7.66471e9i		−	0.705276i
$738$	−4.64459e9	−	5.82413e9i	−0.425354	−	0.533377i
$739$	−1.76064e9	+	4.01855e8i	−0.160478	+	0.0366281i	−0.302005	−	0.953306i	$-0.597656\pi$
$739$	−1.76064e9	+	4.01855e8i	−0.160478	+	0.0366281i	0.141527	+	0.989934i	$0.454799\pi$
$740$	−7.15732e9	+	1.63361e9i	−0.649291	+	0.148196i
$741$	−7.55174e9	−	9.46958e9i	−0.681841	−	0.855002i
$742$			1.38278e10i			1.24262i
$743$	1.59277e10	−	1.27019e10i	1.42460	−	1.13608i	0.455260	−	0.890359i	$-0.349546\pi$
$743$	1.59277e10	−	1.27019e10i	1.42460	−	1.13608i	0.969340	−	0.245722i	$-0.0790250\pi$
$744$	1.12403e10	−	2.33406e10i	1.00062	−	2.07782i
$745$	3.45774e9	−	4.33587e9i	0.306370	−	0.384176i
$746$	−2.00059e10	−	1.59542e10i	−1.76430	−	1.40698i
$747$	−6.56443e9	+	3.16126e9i	−0.576202	+	0.277484i
$748$	−1.95311e8	−	8.55714e8i	−0.0170636	−	0.0747606i
$749$	1.31258e9	−	5.75078e9i	0.114140	−	0.500081i
$750$	1.88765e10	+	9.09045e9i	1.63383	+	0.786812i
$751$	6.77282e9	+	1.40639e10i	0.583485	+	1.21162i	0.958630	+	0.284654i	$0.0918787\pi$
$751$	6.77282e9	+	1.40639e10i	0.583485	+	1.21162i	−0.375145	+	0.926966i	$0.622407\pi$
$752$	−2.14816e8	−	4.90303e7i	−0.0184206	−	0.00420438i
$753$	7.32084e9			0.624854
$754$	−6.86628e9	−	8.68322e9i	−0.583340	−	0.737702i
$755$	3.55600e9			0.300709
$756$	4.42223e9	+	1.00934e9i	0.372233	+	0.0849597i
$757$	−4.67389e8	−	9.70544e8i	−0.0391600	−	0.0813167i	0.880471	−	0.474100i	$-0.157227\pi$
$757$	−4.67389e8	−	9.70544e8i	−0.0391600	−	0.0813167i	−0.919631	+	0.392783i	$0.871512\pi$
$758$	−3.02762e10	−	1.45803e10i	−2.52499	−	1.21597i
$759$	1.38836e9	−	6.08279e9i	0.115254	−	0.504959i
$760$	−2.02636e9	−	8.87807e9i	−0.167444	−	0.733619i
$761$	−1.75522e9	+	8.45268e8i	−0.144373	+	0.0695262i	−0.504675	−	0.863309i	$-0.668388\pi$
$761$	−1.75522e9	+	8.45268e8i	−0.144373	+	0.0695262i	0.360303	+	0.932835i	$0.382673\pi$
$762$	−2.37274e10	−	1.89219e10i	−1.94271	−	1.54926i
$763$	−2.99743e9	+	3.75866e9i	−0.244295	+	0.306336i
$764$	3.64366e9	−	7.56614e9i	0.295605	−	0.613829i
$765$	−1.19620e8	+	9.53937e7i	−0.00966025	+	0.00770380i
$766$		−	2.11741e10i		−	1.70217i
$767$	4.98982e9	+	6.25704e9i	0.399302	+	0.500709i
$768$	1.77103e10	−	4.04226e9i	1.41079	−	0.322003i
$769$	−1.36808e9	+	3.12256e8i	−0.108485	+	0.0247610i	−0.276419	−	0.961037i	$-0.589148\pi$
$769$	−1.36808e9	+	3.12256e8i	−0.108485	+	0.0247610i	0.167934	+	0.985798i	$0.446291\pi$
$770$	4.40862e9	+	5.52823e9i	0.348004	+	0.436384i
$771$			1.46055e10i			1.14770i
$772$	1.12490e10	−	8.97077e9i	0.879939	−	0.701728i
$773$	−8.38728e9	+	1.74164e10i	−0.653120	+	1.35622i	0.266663	+	0.963790i	$0.414079\pi$
$773$	−8.38728e9	+	1.74164e10i	−0.653120	+	1.35622i	−0.919783	+	0.392427i	$0.871635\pi$
$774$	−3.05341e9	+	3.82886e9i	−0.236697	+	0.296808i
$775$	−1.29757e10	−	1.03478e10i	−1.00132	−	0.798529i
$776$	−2.80481e9	+	1.35073e9i	−0.215470	+	0.103765i
$777$	−1.75934e9	−	7.70816e9i	−0.134548	−	0.589491i
$778$	−6.76156e8	+	2.96243e9i	−0.0514776	+	0.225538i
$779$	1.06428e10	+	5.12528e9i	0.806628	+	0.388451i
$780$	−3.46442e9	−	7.19395e9i	−0.261397	−	0.542796i
$781$	2.02748e10	+	4.62759e9i	1.52292	+	0.347597i
$782$	−2.58011e8			−0.0192937
$783$	5.52408e9	+	2.27669e7i	0.411238	+	0.00169488i
$784$	−6.75078e8			−0.0500320
$785$	−1.05154e10	−	2.40008e9i	−0.775860	−	0.177085i
$786$	1.69694e10	+	3.52373e10i	1.24649	+	2.58836i
$787$	−2.05816e10	−	9.91159e9i	−1.50511	−	0.724823i	−0.513991	−	0.857796i	$-0.671833\pi$
$787$	−2.05816e10	−	9.91159e9i	−1.50511	−	0.724823i	−0.991120	+	0.132973i	$0.957548\pi$
$788$	8.15113e9	−	3.57124e10i	0.593439	−	2.60003i
$789$	1.67465e9	+	7.33713e9i	0.121382	+	0.531810i
$790$	−1.28087e10	+	6.16833e9i	−0.924292	+	0.445115i
$791$	−5.81962e8	−	4.64099e8i	−0.0418097	−	0.0333421i
$792$	7.88605e9	−	9.88880e9i	0.564055	−	0.707303i
$793$	5.67528e9	−	1.17848e10i	0.404139	−	0.839204i
$794$	−8.22820e9	+	6.56177e9i	−0.583355	+	0.465210i
$795$			1.21467e10i			0.857381i
$796$	2.54064e10	+	3.18587e10i	1.78545	+	2.23889i
$797$	−1.90304e9	+	4.34356e8i	−0.133151	+	0.0303908i	−0.288577	−	0.957457i	$-0.593182\pi$
$797$	−1.90304e9	+	4.34356e8i	−0.133151	+	0.0303908i	0.155426	+	0.987848i	$0.450325\pi$
$798$	2.42642e10	−	5.53815e9i	1.69027	−	0.385793i
$799$	−8.61791e7	−	1.08065e8i	−0.00597707	−	0.00749501i
$800$		−	1.03774e10i		−	0.716595i
$801$	−6.67205e9	+	5.32078e9i	−0.458718	+	0.365815i
$802$	−7.32851e9	+	1.52178e10i	−0.501656	+	1.04170i
$803$	−1.80364e10	+	2.26169e10i	−1.22927	+	1.54145i
$804$	−1.39050e10	−	1.10888e10i	−0.943569	−	0.752471i
$805$	1.16609e9	−	5.61561e8i	0.0787858	−	0.0379413i
$806$	5.22373e9	+	2.28867e10i	0.351405	+	1.53961i
$807$	2.65240e9	−	1.16209e10i	0.177657	−	0.778365i
$808$	−2.04588e10	−	9.85246e9i	−1.36440	−	0.657060i
$809$	1.90865e9	+	3.96336e9i	0.126738	+	0.263174i	0.954677	−	0.297644i	$-0.0962009\pi$
$809$	1.90865e9	+	3.96336e9i	0.126738	+	0.263174i	−0.827939	+	0.560818i	$0.810487\pi$
$810$	1.42251e10	+	3.24678e9i	0.940497	+	0.214662i
$811$	−1.89630e9			−0.124834			−0.0624172	−	0.998050i	$-0.519881\pi$
$811$	−1.89630e9			−0.124834			−0.0624172	+	0.998050i	$0.519881\pi$
$812$	1.38219e10	−	3.09488e9i	0.905987	−	0.202861i
$813$	2.25436e10			1.47132
$814$	2.53159e10	+	5.77818e9i	1.64516	+	0.375496i
$815$	−3.76553e8	−	7.81920e8i	−0.0243654	−	0.0505954i
$816$	−4.93177e7	−	2.37501e7i	−0.00317751	−	0.00153021i
$817$	1.72804e9	−	7.57102e9i	0.110860	−	0.485710i
$818$	−3.08817e9	−	1.35302e10i	−0.197272	−	0.864304i
$819$	3.14417e9	−	1.51415e9i	0.199992	−	0.0963110i
$820$	6.08832e9	+	4.85527e9i	0.385611	+	0.307514i
$821$	1.89231e10	−	2.37288e10i	1.19342	−	1.49650i	0.370024	−	0.929022i	$-0.379349\pi$
$821$	1.89231e10	−	2.37288e10i	1.19342	−	1.49650i	0.823391	−	0.567474i	$-0.192079\pi$
$822$	−8.05295e9	+	1.67221e10i	−0.505712	+	1.05012i
$823$	−1.34509e10	+	1.07267e10i	−0.841107	+	0.670761i	−0.946158	−	0.323706i	$-0.895071\pi$
$823$	−1.34509e10	+	1.07267e10i	−0.841107	+	0.670761i	0.105050	+	0.994467i	$0.466500\pi$
$824$		−	1.49903e10i		−	0.933394i
$825$	−1.24491e10	−	1.56106e10i	−0.771877	−	0.967903i
$826$	−1.60326e10	+	3.65934e9i	−0.989862	+	0.225930i
$827$	−1.29660e10	+	2.95941e9i	−0.797145	+	0.181943i	−0.601648	−	0.798761i	$-0.705489\pi$
$827$	−1.29660e10	+	2.95941e9i	−0.797145	+	0.181943i	−0.195497	+	0.980704i	$0.562632\pi$
$828$	−3.66318e9	−	4.59348e9i	−0.224260	−	0.281213i
$829$			1.47147e10i			0.897039i	0.893773	+	0.448520i	$0.148049\pi$
$829$			1.47147e10i			0.897039i	−0.893773	+	0.448520i	$0.851951\pi$
$830$	9.56308e9	−	7.62630e9i	0.580530	−	0.462957i
$831$	8.77624e9	−	1.82241e10i	0.530524	−	1.10164i
$832$	−9.58987e9	+	1.20253e10i	−0.577273	+	0.723877i
$833$	−3.31090e8	−	2.64035e8i	−0.0198467	−	0.0158272i
$834$	−4.38822e10	+	2.11326e10i	−2.61943	+	1.26145i
$835$	−1.25635e9	−	5.50444e9i	−0.0746808	−	0.327198i
$836$	−1.13260e10	+	4.96223e10i	−0.670429	+	2.93734i
$837$	−1.05545e10	−	5.08277e9i	−0.622154	−	0.299614i
$838$	1.06662e10	+	2.21486e10i	0.626118	+	1.30015i
$839$	−1.51684e9	−	3.46209e8i	−0.0886693	−	0.0202382i	0.177956	−	0.984038i	$-0.443051\pi$
$839$	−1.51684e9	−	3.46209e8i	−0.0886693	−	0.0202382i	−0.266625	+	0.963800i	$0.585909\pi$
$840$	6.46527e9			0.376365
$841$	1.56028e10	−	7.35608e9i	0.904515	−	0.426443i
$842$	−2.93057e10			−1.69184
$843$	−3.20788e10	−	7.32177e9i	−1.84426	−	0.420939i
$844$	−1.79283e10	−	3.72286e10i	−1.02646	−	2.13146i
$845$	−5.12836e9	−	2.46969e9i	−0.292402	−	0.140813i
$846$	1.12477e9	−	4.92796e9i	0.0638659	−	0.279815i
$847$	−1.25158e9	−	5.48353e9i	−0.0707728	−	0.310076i
$848$	−1.58895e9	+	7.65196e8i	−0.0894795	+	0.0430911i
$849$	−1.81743e10	−	1.44935e10i	−1.01925	−	0.812826i
$850$	−5.14808e8	+	6.45549e8i	−0.0287527	+	0.0360548i
$851$	2.06226e9	−	4.28234e9i	0.114707	−	0.238192i
$852$	3.77275e10	−	3.00867e10i	2.08987	−	1.66662i
$853$		−	9.64534e9i		−	0.532103i	−0.963959	−	0.266052i	$-0.914281\pi$
$853$		−	9.64534e9i		−	0.532103i	0.963959	−	0.266052i	$-0.0857192\pi$
$854$	1.67579e10	+	2.10137e10i	0.920698	+	1.15452i
$855$	8.64990e9	−	1.97428e9i	0.473292	−	0.108026i
$856$	1.72696e10	−	3.94167e9i	0.941074	−	0.214794i
$857$	1.62292e10	+	2.03508e10i	0.880773	+	1.10445i	0.993835	+	0.110867i	$0.0353626\pi$
$857$	1.62292e10	+	2.03508e10i	0.880773	+	1.10445i	−0.113062	+	0.993588i	$0.536066\pi$
$858$			2.82423e10i			1.52649i
$859$	−1.37660e9	+	1.09780e9i	−0.0741025	+	0.0590948i	−0.659841	−	0.751406i	$-0.729376\pi$
$859$	−1.37660e9	+	1.09780e9i	−0.0741025	+	0.0590948i	0.585738	+	0.810500i	$0.300805\pi$
$860$	2.22124e9	−	4.61245e9i	0.119083	−	0.247279i
$861$	−5.22895e9	+	6.55689e9i	−0.279192	+	0.350096i
$862$	1.31644e10	+	1.04983e10i	0.700047	+	0.558269i
$863$	1.33460e10	−	6.42708e9i	0.706826	−	0.340390i	−0.0456969	−	0.998955i	$-0.514551\pi$
$863$	1.33460e10	−	6.42708e9i	0.706826	−	0.340390i	0.752523	+	0.658566i	$0.228837\pi$
$864$	−1.62993e9	−	7.14119e9i	−0.0859747	−	0.376680i
$865$	2.06283e9	−	9.03783e9i	0.108369	−	0.474797i
$866$	3.44851e10	+	1.66071e10i	1.80434	+	0.868925i
$867$	1.07866e10	+	2.23985e10i	0.562104	+	1.16722i
$868$	−2.92838e10	−	6.68383e9i	−1.51988	−	0.346902i
$869$	3.13115e10			1.61858
$870$	1.94987e10	−	4.36599e9i	1.00390	−	0.224784i
$871$	6.35062e9			0.325651
$872$	−1.40750e10	−	3.21252e9i	−0.718853	−	0.164074i
$873$	−1.31601e9	−	2.73272e9i	−0.0669437	−	0.139010i
$874$	1.34802e10	+	6.49172e9i	0.682978	+	0.328905i
$875$	2.13004e9	−	9.33230e9i	0.107488	−	0.470935i
$876$	1.49366e10	+	6.54417e10i	0.750738	+	3.28920i
$877$	7.35984e8	−	3.54431e8i	0.0368443	−	0.0177433i	−0.415371	−	0.909652i	$-0.636348\pi$
$877$	7.35984e8	−	3.54431e8i	0.0368443	−	0.0177433i	0.452215	+	0.891909i	$0.350634\pi$
$878$	1.29089e10	+	1.02945e10i	0.643662	+	0.513303i
$879$	−5.95567e9	+	7.46818e9i	−0.295781	+	0.370897i
$880$	−3.91285e8	+	8.12512e8i	−0.0193555	+	0.0401921i
$881$	1.65042e10	−	1.31617e10i	0.813166	−	0.648478i	−0.125966	−	0.992035i	$-0.540203\pi$
$881$	1.65042e10	−	1.31617e10i	0.813166	−	0.648478i	0.939132	+	0.343557i	$0.111632\pi$
$882$		−	1.54866e10i		−	0.760002i
$883$	−1.46937e10	−	1.84253e10i	−0.718238	−	0.900642i	0.279999	−	0.960000i	$-0.409666\pi$
$883$	−1.46937e10	−	1.84253e10i	−0.718238	−	0.900642i	−0.998237	+	0.0593585i	$0.981095\pi$
$884$	7.09005e8	−	1.61826e8i	0.0345196	−	0.00787888i
$885$	−1.40835e10	+	3.21447e9i	−0.682983	+	0.155886i
$886$	−1.37715e10	−	1.72689e10i	−0.665217	−	0.834156i
$887$		−	1.26105e10i		−	0.606736i	−0.952873	−	0.303368i	$-0.901889\pi$
$887$		−	1.26105e10i		−	0.606736i	0.952873	−	0.303368i	$-0.0981112\pi$
$888$	1.85629e10	−	1.48034e10i	0.889613	−	0.709443i
$889$	−6.01608e9	+	1.24925e10i	−0.287182	+	0.596340i
$890$	8.93250e9	−	1.12010e10i	0.424725	−	0.532589i
$891$	−2.51250e10	−	2.00365e10i	−1.18996	−	0.948965i
$892$	−2.11648e10	+	1.01924e10i	−0.998475	+	0.480840i
$893$	1.78357e9	+	7.81435e9i	0.0838130	+	0.367209i
$894$	−1.01283e10	+	4.43751e10i	−0.474085	+	2.07710i
$895$	4.70036e9	+	2.26357e9i	0.219154	+	0.105539i
$896$	−8.77520e9	−	1.82219e10i	−0.407548	−	0.846282i
$897$	5.03992e9	+	1.15033e9i	0.233158	+	0.0532167i
$898$	1.48849e9			0.0685929
$899$	−3.65802e10	−	1.50762e8i	−1.67914	−	0.00692041i
$900$	−1.88021e10			−0.859721
$901$	−1.07858e9	−	2.46178e8i	−0.0491263	−	0.0112128i
$902$	−1.19509e10	−	2.48163e10i	−0.542222	−	1.12594i
$903$	4.96744e9	+	2.39219e9i	0.224505	+	0.108116i
$904$	4.97401e8	−	2.17926e9i	0.0223933	−	0.0981113i
$905$	1.69807e9	+	7.43974e9i	0.0761528	+	0.333647i
$906$	−2.62951e10	+	1.26630e10i	−1.17470	+	0.565704i
$907$	−1.27229e10	−	1.01462e10i	−0.566190	−	0.451521i	0.298087	−	0.954539i	$-0.403652\pi$
$907$	−1.27229e10	−	1.01462e10i	−0.566190	−	0.451521i	−0.864276	+	0.503018i	$0.832223\pi$
$908$	−2.28499e10	+	2.86529e10i	−1.01294	+	1.27019i
$909$	9.59924e9	−	1.99330e10i	0.423900	−	0.880237i
$910$	−4.58044e9	+	3.65278e9i	−0.201494	+	0.160686i
$911$			1.66672e10i			0.730379i	0.930933	+	0.365189i	$0.118996\pi$
$911$			1.66672e10i			0.730379i	−0.930933	+	0.365189i	$0.881004\pi$
$912$	1.97911e9	+	2.48173e9i	0.0863949	+	0.108336i
$913$	−2.62644e10	+	5.99468e9i	−1.14214	+	0.260686i
$914$	3.72303e10	−	8.49757e9i	1.61282	−	0.368115i
$915$	1.47206e10	+	1.84591e10i	0.635261	+	0.796592i
$916$			2.05824e10i			0.884836i
$917$	1.39705e10	−	1.11411e10i	0.598299	−	0.477127i
$918$	−2.52871e8	+	5.25092e8i	−0.0107882	+	0.0224020i
$919$	1.28754e10	−	1.61452e10i	0.547211	−	0.686181i	−0.428925	−	0.903340i	$-0.641108\pi$
$919$	1.28754e10	−	1.61452e10i	0.547211	−	0.686181i	0.976136	+	0.217159i	$0.0696790\pi$
$920$	3.03873e9	+	2.42331e9i	0.128657	+	0.102601i
$921$	3.88971e10	−	1.87319e10i	1.64062	−	0.790082i
$922$	−1.06268e10	−	4.65591e10i	−0.446524	−	1.95635i
$923$	−3.83421e9	+	1.67988e10i	−0.160498	+	0.703187i
$924$	−3.25577e10	−	1.56790e10i	−1.35770	−	0.653832i
$925$	−6.59966e9	−	1.37043e10i	−0.274174	−	0.569327i
$926$	−2.34218e10	−	5.34588e9i	−0.969354	−	0.221249i
$927$	1.46050e10			0.602176
$928$	−1.41872e10	−	1.79413e10i	−0.582744	−	0.736949i
$929$	1.99161e10			0.814983			0.407492	−	0.913209i	$-0.366404\pi$
$929$	1.99161e10			0.814983			0.407492	+	0.913209i	$0.366404\pi$
$930$	−4.13110e10	−	9.42896e9i	−1.68413	−	0.384391i
$931$	1.06550e10	+	2.21254e10i	0.432743	+	0.898601i
$932$	5.61643e10	+	2.70473e10i	2.27250	+	1.09438i
$933$	−6.36566e9	+	2.78898e10i	−0.256601	+	1.12424i
$934$	1.21362e9	+	5.31721e9i	0.0487380	+	0.213535i
$935$	−5.09693e8	+	2.45455e8i	−0.0203924	+	0.00982045i
$936$	8.19340e9	+	6.53402e9i	0.326587	+	0.260444i
$937$	−2.75592e10	+	3.45581e10i	−1.09440	+	1.37234i	−0.172460	+	0.985017i	$0.555172\pi$
$937$	−2.75592e10	+	3.45581e10i	−1.09440	+	1.37234i	−0.921944	+	0.387323i	$0.873400\pi$
$938$	−5.66195e9	+	1.17572e10i	−0.224004	+	0.465149i
$939$	2.29404e10	−	1.82943e10i	0.904213	−	0.721085i
$940$			5.28397e9i			0.207498i
$941$	−1.80074e10	−	2.25806e10i	−0.704512	−	0.883430i	0.292840	−	0.956162i	$-0.405400\pi$
$941$	−1.80074e10	−	2.25806e10i	−0.704512	−	0.883430i	−0.997352	+	0.0727318i	$0.976828\pi$
$942$	8.63039e10	−	1.96983e10i	3.36397	−	0.767804i
$943$	−4.91530e9	+	1.12188e9i	−0.190879	+	0.0435670i
$944$	−1.30770e9	−	1.63981e9i	−0.0505949	−	0.0634440i
$945$		−	2.92355e9i		−	0.112694i
$946$	−1.41572e10	+	1.12900e10i	−0.543699	+	0.433585i
$947$	−2.10126e10	+	4.36332e10i	−0.803999	+	1.66952i	−0.0630016	+	0.998013i	$0.520067\pi$
$947$	−2.10126e10	+	4.36332e10i	−0.803999	+	1.66952i	−0.740997	+	0.671508i	$0.765647\pi$
$948$	4.52997e10	−	5.68040e10i	1.72689	−	2.16546i
$949$	−1.87394e10	−	1.49441e10i	−0.711743	−	0.567596i
$950$	4.31394e10	−	2.07748e10i	1.63246	−	0.786149i
$951$	−4.50948e9	−	1.97573e10i	−0.170018	−	0.744896i
$952$	−1.31032e8	+	5.74087e8i	−0.00492206	+	0.0215650i
$953$	3.20803e10	+	1.54491e10i	1.20064	+	0.578198i	0.923858	−	0.382735i	$-0.125018\pi$
$953$	3.20803e10	+	1.54491e10i	1.20064	+	0.578198i	0.276782	+	0.960933i	$0.410732\pi$
$954$	−1.75539e10	−	3.64510e10i	−0.654567	−	1.35922i
$955$	−5.27691e9	−	1.20442e9i	−0.196051	−	0.0447472i
$956$	−2.33242e8			−0.00863384
$957$	−4.28647e10	−	9.96963e9i	−1.58091	−	0.367694i
$958$	−4.21700e10			−1.54962
$959$	8.26720e9	+	1.88693e9i	0.302687	+	0.0690863i
$960$	−1.20459e10	−	2.50136e10i	−0.439430	−	0.912487i
$961$	4.51033e10	+	2.17206e10i	1.63937	+	0.789478i
$962$	−4.78753e9	+	2.09756e10i	−0.173380	+	0.759627i
$963$	3.84037e9	+	1.68258e10i	0.138574	+	0.607131i
$964$	5.45614e10	−	2.62754e10i	1.96162	−	0.944668i
$965$	−7.25030e9	−	5.78192e9i	−0.259723	−	0.207122i
$966$	−6.62303e9	+	8.30501e9i	−0.236394	+	0.296429i
$967$	1.37418e10	−	2.85351e10i	0.488708	−	1.01481i	−0.500148	−	0.865940i	$-0.666721\pi$
$967$	1.37418e10	−	2.85351e10i	0.488708	−	1.01481i	0.988856	−	0.148874i	$-0.0475647\pi$
$968$	1.32055e10	−	1.05311e10i	0.467942	−	0.373171i
$969$			1.99122e9i			0.0703050i
$970$	3.17478e9	+	3.98104e9i	0.111689	+	0.140054i
$971$	−1.92939e10	+	4.40371e9i	−0.676322	+	0.154366i	−0.546867	−	0.837219i	$-0.684180\pi$
$971$	−1.92939e10	+	4.40371e9i	−0.676322	+	0.154366i	−0.129455	+	0.991585i	$0.541323\pi$
$972$	−5.37549e10	+	1.22692e10i	−1.87753	+	0.428533i
$973$	1.38743e10	+	1.73979e10i	0.482856	+	0.605482i
$974$		−	6.54309e10i		−	2.26896i
$975$	1.29343e10	−	1.03147e10i	0.446915	−	0.356403i
$976$	−1.48734e9	+	3.08849e9i	−0.0512078	+	0.106334i
$977$	−2.52557e10	+	3.16696e10i	−0.866419	+	1.08646i	0.129075	+	0.991635i	$0.458799\pi$
$977$	−2.52557e10	+	3.16696e10i	−0.866419	+	1.08646i	−0.995494	+	0.0948206i	$0.969772\pi$
$978$	5.56889e9	+	4.44104e9i	0.190363	+	0.151810i
$979$	−2.84292e10	+	1.36908e10i	−0.968333	+	0.466325i
$980$	3.60240e9	+	1.57831e10i	0.122264	+	0.535676i
$981$	3.12996e9	−	1.37132e10i	0.105852	−	0.463766i
$982$	−8.01058e10	−	3.85769e10i	−2.69944	−	1.29998i
$983$	5.39362e9	+	1.12000e10i	0.181110	+	0.376079i	0.971683	−	0.236289i	$-0.0759312\pi$
$983$	5.39362e9	+	1.12000e10i	0.181110	+	0.376079i	−0.790573	+	0.612368i	$0.790217\pi$
$984$	−2.45534e10	−	5.60416e9i	−0.821541	−	0.187511i
$985$	−2.36097e10			−0.787160
$986$	−7.50048e6	+	1.81989e9i	−0.000249184	+	0.0604610i
$987$	−5.69064e9			−0.188387
$988$	−4.11147e10	−	9.38416e9i	−1.35628	−	0.309561i
$989$	1.43810e9	+	2.98624e9i	0.0472717	+	0.0981607i
$990$	−1.86393e10	−	8.97623e9i	−0.610530	−	0.294016i
$991$	−8.15022e9	+	3.57084e10i	−0.266018	+	1.16550i	0.648583	+	0.761144i	$0.275362\pi$
$991$	−8.15022e9	+	3.57084e10i	−0.266018	+	1.16550i	−0.914601	+	0.404358i	$0.867495\pi$
$992$	1.07933e10	+	4.72886e10i	0.351046	+	1.53803i
$993$	4.09115e10	−	1.97020e10i	1.32594	−	0.638539i
$994$	−2.76818e10	−	2.20755e10i	−0.894009	−	0.712948i
$995$	1.63752e10	−	2.05338e10i	0.526994	−	0.660829i
$996$	−2.71225e10	+	5.63204e10i	−0.869805	+	1.80617i
$997$	−1.01573e10	+	8.10017e9i	−0.324597	+	0.258858i	−0.772207	−	0.635371i	$-0.780847\pi$
$997$	−1.01573e10	+	8.10017e9i	−0.324597	+	0.258858i	0.447609	+	0.894229i	$0.352276\pi$
$998$		−	8.80301e10i		−	2.80333i
$999$	−6.69403e9	−	8.39404e9i	−0.212426	−	0.266374i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.8.e.a.4.15	✓	96
29.22	even	14	inner	29.8.e.a.22.15	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.8.e.a.4.15	✓	96	1.1	even	1	trivial
29.8.e.a.22.15	yes	96	29.22	even	14	inner

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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	29.e (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(17.9566 + 4.09849i) q^{2} +(26.3233 + 54.6609i) q^{3} +(190.320 + 91.6531i) q^{4} +(30.2961 - 132.736i) q^{5} +(248.651 + 1089.41i) q^{6} +(459.975 - 221.512i) q^{7} +(1198.65 + 955.891i) q^{8} +(-931.324 + 1167.84i) q^{9} +O(q^{10})\)	\(q+(17.9566 + 4.09849i) q^{2} +(26.3233 + 54.6609i) q^{3} +(190.320 + 91.6531i) q^{4} +(30.2961 - 132.736i) q^{5} +(248.651 + 1089.41i) q^{6} +(459.975 - 221.512i) q^{7} +(1198.65 + 955.891i) q^{8} +(-931.324 + 1167.84i) q^{9} +(1088.03 - 2259.33i) q^{10} +(-4318.10 + 3443.57i) q^{11} +12815.7i q^{12} +(-2853.18 - 3577.78i) q^{13} +(9167.47 - 2092.41i) q^{14} +(8052.97 - 1838.04i) q^{15} +(747.744 + 937.641i) q^{16} +752.320i q^{17} +(-21509.9 + 17153.5i) q^{18} +(18928.8 - 39306.1i) q^{19} +(17931.6 - 22485.5i) q^{20} +(24216.1 + 19311.7i) q^{21} +(-91652.1 + 44137.3i) q^{22} +(4143.38 + 18153.3i) q^{23} +(-20697.4 + 90681.4i) q^{24} +(53687.2 + 25854.4i) q^{25} +(-36570.1 - 75938.7i) q^{26} +(41005.6 + 9359.26i) q^{27} +107844. q^{28} +(128165. - 28697.7i) q^{29} +152137. q^{30} +(-271537. - 61976.6i) q^{31} +(-75561.6 - 156905. i) q^{32} +(-301895. - 145385. i) q^{33} +(-3083.37 + 13509.1i) q^{34} +(-15467.2 - 67766.2i) q^{35} +(-284286. + 136905. i) q^{36} +(-199573. - 159154. i) q^{37} +(500994. - 628227. i) q^{38} +(120459. - 250137. i) q^{39} +(163196. - 130144. i) q^{40} +270766. i q^{41} +(355691. + 446023. i) q^{42} +(173542. - 39609.8i) q^{43} +(-1.13743e6 + 259612. i) q^{44} +(126799. + 159001. i) q^{45} +342954. i q^{46} +(-143643. + 114551. i) q^{47} +(-31569.2 + 65554.2i) q^{48} +(-350962. + 440092. i) q^{49} +(858078. + 684294. i) q^{50} +(-41122.5 + 19803.5i) q^{51} +(-215102. - 942425. i) q^{52} +(-327225. + 1.43367e6i) q^{53} +(697964. + 336122. i) q^{54} +(326264. + 677495. i) q^{55} +(763090. + 174170. i) q^{56} +2.64678e6 q^{57} +(2.41903e6 + 9969.81i) q^{58} -1.74886e6 q^{59} +(1.70110e6 + 388265. i) q^{60} +(1.24019e6 + 2.57527e6i) q^{61} +(-4.62189e6 - 2.22578e6i) q^{62} +(-169694. + 743478. i) q^{63} +(-747917. - 3.27684e6i) q^{64} +(-561341. + 270328. i) q^{65} +(-4.82517e6 - 3.84794e6i) q^{66} +(-865257. + 1.08500e6i) q^{67} +(-68952.4 + 143181. i) q^{68} +(-883209. + 704336. i) q^{69} -1.28025e6i q^{70} +(-2.34765e6 - 2.94386e6i) q^{71} +(-2.23266e6 + 509591. i) q^{72} +(5.10639e6 - 1.16550e6i) q^{73} +(-2.93136e6 - 3.67581e6i) q^{74} +3.61516e6i q^{75} +(7.20506e6 - 5.74584e6i) q^{76} +(-1.22342e6 + 2.54047e6i) q^{77} +(3.18823e6 - 3.99791e6i) q^{78} +(-4.43239e6 - 3.53471e6i) q^{79} +(147113. - 70845.7i) q^{80} +(1.29474e6 + 5.67265e6i) q^{81} +(-1.10973e6 + 4.86205e6i) q^{82} +(4.39466e6 + 2.11636e6i) q^{83} +(2.83882e6 + 5.89487e6i) q^{84} +(99860.0 + 22792.4i) q^{85} +3.27857e6 q^{86} +(4.94237e6 + 6.25021e6i) q^{87} -8.46757e6 q^{88} +(5.56990e6 + 1.27129e6i) q^{89} +(1.62523e6 + 3.37482e6i) q^{90} +(-2.10491e6 - 1.01367e6i) q^{91} +(-875242. + 3.83469e6i) q^{92} +(-3.76006e6 - 1.64739e7i) q^{93} +(-3.04883e6 + 1.46824e6i) q^{94} +(-4.64387e6 - 3.70336e6i) q^{95} +(6.58755e6 - 8.26052e6i) q^{96} +(-881024. + 1.82947e6i) q^{97} +(-8.10581e6 + 6.46417e6i) q^{98} -8.24995e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 7 q^{2} - 7 q^{3} + 709 q^{4} + 191 q^{5} + 1801 q^{6} - 667 q^{7} + 9086 q^{8} + 9103 q^{9}+O(q^{10}) \) 96 * q - 7 * q^2 - 7 * q^3 + 709 * q^4 + 191 * q^5 + 1801 * q^6 - 667 * q^7 + 9086 * q^8 + 9103 * q^9	\( 96 q - 7 q^{2} - 7 q^{3} + 709 q^{4} + 191 q^{5} + 1801 q^{6} - 667 q^{7} + 9086 q^{8} + 9103 q^{9} - 7 q^{10} + 4207 q^{11} + 377 q^{13} - 7 q^{14} - 74473 q^{15} - 125851 q^{16} - 194880 q^{18} - 7 q^{19} + 162901 q^{20} + 86933 q^{21} + 252614 q^{22} + 238675 q^{23} - 490819 q^{24} - 107349 q^{25} + 367017 q^{26} + 75593 q^{27} + 1397540 q^{28} + 379863 q^{29} - 175646 q^{30} - 143885 q^{31} + 473172 q^{32} - 1419437 q^{33} - 2314463 q^{34} - 1018325 q^{35} + 1720462 q^{36} + 662991 q^{37} - 2763860 q^{38} + 42189 q^{39} + 580601 q^{40} - 3296492 q^{42} - 1587425 q^{43} + 2344398 q^{44} + 6508254 q^{45} + 526673 q^{47} + 6175806 q^{48} - 1391517 q^{49} - 4194526 q^{50} - 68204 q^{51} - 7720808 q^{52} + 1762640 q^{53} - 2032428 q^{54} + 2655709 q^{55} + 17091081 q^{56} + 4906842 q^{57} + 13231229 q^{58} - 8638324 q^{59} - 9957136 q^{60} + 2797697 q^{61} - 884069 q^{62} - 20232301 q^{63} - 17528026 q^{64} - 7454088 q^{65} - 17541475 q^{66} - 4890949 q^{67} + 22029140 q^{68} + 13204429 q^{69} - 1091301 q^{71} + 25137595 q^{72} + 14363636 q^{73} + 3185328 q^{74} - 41019881 q^{76} - 25204627 q^{77} - 15753743 q^{78} + 31186057 q^{79} + 24146022 q^{80} - 29435757 q^{81} - 51438506 q^{82} - 8367235 q^{83} + 78906093 q^{84} + 41540198 q^{85} + 65794492 q^{86} + 11089375 q^{87} + 39260390 q^{88} + 6628699 q^{89} + 32127214 q^{90} + 24315293 q^{91} - 39469980 q^{92} - 31050649 q^{93} - 102445588 q^{94} - 75684679 q^{95} - 95069050 q^{96} + 38131380 q^{97} + 19581828 q^{98}+O(q^{100}) \) 96 * q - 7 * q^2 - 7 * q^3 + 709 * q^4 + 191 * q^5 + 1801 * q^6 - 667 * q^7 + 9086 * q^8 + 9103 * q^9 - 7 * q^10 + 4207 * q^11 + 377 * q^13 - 7 * q^14 - 74473 * q^15 - 125851 * q^16 - 194880 * q^18 - 7 * q^19 + 162901 * q^20 + 86933 * q^21 + 252614 * q^22 + 238675 * q^23 - 490819 * q^24 - 107349 * q^25 + 367017 * q^26 + 75593 * q^27 + 1397540 * q^28 + 379863 * q^29 - 175646 * q^30 - 143885 * q^31 + 473172 * q^32 - 1419437 * q^33 - 2314463 * q^34 - 1018325 * q^35 + 1720462 * q^36 + 662991 * q^37 - 2763860 * q^38 + 42189 * q^39 + 580601 * q^40 - 3296492 * q^42 - 1587425 * q^43 + 2344398 * q^44 + 6508254 * q^45 + 526673 * q^47 + 6175806 * q^48 - 1391517 * q^49 - 4194526 * q^50 - 68204 * q^51 - 7720808 * q^52 + 1762640 * q^53 - 2032428 * q^54 + 2655709 * q^55 + 17091081 * q^56 + 4906842 * q^57 + 13231229 * q^58 - 8638324 * q^59 - 9957136 * q^60 + 2797697 * q^61 - 884069 * q^62 - 20232301 * q^63 - 17528026 * q^64 - 7454088 * q^65 - 17541475 * q^66 - 4890949 * q^67 + 22029140 * q^68 + 13204429 * q^69 - 1091301 * q^71 + 25137595 * q^72 + 14363636 * q^73 + 3185328 * q^74 - 41019881 * q^76 - 25204627 * q^77 - 15753743 * q^78 + 31186057 * q^79 + 24146022 * q^80 - 29435757 * q^81 - 51438506 * q^82 - 8367235 * q^83 + 78906093 * q^84 + 41540198 * q^85 + 65794492 * q^86 + 11089375 * q^87 + 39260390 * q^88 + 6628699 * q^89 + 32127214 * q^90 + 24315293 * q^91 - 39469980 * q^92 - 31050649 * q^93 - 102445588 * q^94 - 75684679 * q^95 - 95069050 * q^96 + 38131380 * q^97 + 19581828 * q^98

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