LMFDB - Embedded newform 29.7.c.a.12.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,7,Mod(12,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("29.12");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	29.c (of order $4$, degree $2$, 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:	$6.67156842498$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			12.10
Character	$\chi$	$=$	29.12
Dual form			29.7.c.a.17.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.72749 + 4.72749i) q^{2} +(-5.84368 - 5.84368i) q^{3} -19.3016i q^{4} -122.935i q^{5} -55.2519i q^{6} -317.611 q^{7} +(393.808 - 393.808i) q^{8} -660.703i q^{9} +O(q^{10})$	\(q+(4.72749 + 4.72749i) q^{2} +(-5.84368 - 5.84368i) q^{3} -19.3016i q^{4} -122.935i q^{5} -55.2519i q^{6} -317.611 q^{7} +(393.808 - 393.808i) q^{8} -660.703i q^{9} +(581.174 - 581.174i) q^{10} +(904.860 + 904.860i) q^{11} +(-112.792 + 112.792i) q^{12} -1220.31i q^{13} +(-1501.50 - 1501.50i) q^{14} +(-718.392 + 718.392i) q^{15} +2488.15 q^{16} +(5508.26 + 5508.26i) q^{17} +(3123.47 - 3123.47i) q^{18} +(-9024.37 - 9024.37i) q^{19} -2372.84 q^{20} +(1856.01 + 1856.01i) q^{21} +8555.44i q^{22} -9177.93 q^{23} -4602.57 q^{24} +511.993 q^{25} +(5768.99 - 5768.99i) q^{26} +(-8120.97 + 8120.97i) q^{27} +6130.40i q^{28} +(4826.87 + 23906.6i) q^{29} -6792.39 q^{30} +(21942.9 + 21942.9i) q^{31} +(-13441.0 - 13441.0i) q^{32} -10575.4i q^{33} +52080.5i q^{34} +39045.5i q^{35} -12752.6 q^{36} +(27321.6 - 27321.6i) q^{37} -85325.3i q^{38} +(-7131.08 + 7131.08i) q^{39} +(-48412.8 - 48412.8i) q^{40} +(75477.0 - 75477.0i) q^{41} +17548.6i q^{42} +(42100.3 + 42100.3i) q^{43} +(17465.2 - 17465.2i) q^{44} -81223.5 q^{45} +(-43388.6 - 43388.6i) q^{46} +(78079.2 - 78079.2i) q^{47} +(-14539.9 - 14539.9i) q^{48} -16772.4 q^{49} +(2420.44 + 2420.44i) q^{50} -64377.0i q^{51} -23553.9 q^{52} +187104. q^{53} -76783.7 q^{54} +(111239. - 111239. i) q^{55} +(-125078. + 125078. i) q^{56} +105471. i q^{57} +(-90199.2 + 135837. i) q^{58} -134740. q^{59} +(13866.1 + 13866.1i) q^{60} +(201963. + 201963. i) q^{61} +207469. i q^{62} +209846. i q^{63} -286326. i q^{64} -150018. q^{65} +(49995.2 - 49995.2i) q^{66} +156779. i q^{67} +(106318. - 106318. i) q^{68} +(53632.8 + 53632.8i) q^{69} +(-184587. + 184587. i) q^{70} -35515.7i q^{71} +(-260190. - 260190. i) q^{72} +(-178645. + 178645. i) q^{73} +258325. q^{74} +(-2991.92 - 2991.92i) q^{75} +(-174185. + 174185. i) q^{76} +(-287393. - 287393. i) q^{77} -67424.3 q^{78} +(164941. + 164941. i) q^{79} -305880. i q^{80} -386740. q^{81} +713634. q^{82} +137229. q^{83} +(35824.1 - 35824.1i) q^{84} +(677158. - 677158. i) q^{85} +398058. i q^{86} +(111496. - 167909. i) q^{87} +712682. q^{88} +(-862453. - 862453. i) q^{89} +(-383984. - 383984. i) q^{90} +387583. i q^{91} +177149. i q^{92} -256454. i q^{93} +738238. q^{94} +(-1.10941e6 + 1.10941e6i) q^{95} +157090. i q^{96} +(338869. - 338869. i) q^{97} +(-79291.4 - 79291.4i) q^{98} +(597844. - 597844. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8}+O(q^{10}) $ 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8	\( 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8} - 3714 q^{10} + 1934 q^{11} - 2706 q^{12} + 2648 q^{14} + 16280 q^{15} - 36632 q^{16} - 5236 q^{17} + 5258 q^{18} + 6718 q^{19} + 24828 q^{20} + 7380 q^{21} - 21524 q^{23} + 90648 q^{24} - 73196 q^{25} - 5394 q^{26} + 5824 q^{27} - 12510 q^{29} - 1780 q^{30} + 1150 q^{31} + 104646 q^{32} - 32904 q^{36} - 256832 q^{37} + 127752 q^{39} - 256374 q^{40} + 265716 q^{41} + 80590 q^{43} + 188482 q^{44} - 78008 q^{45} + 405572 q^{46} - 445250 q^{47} - 1016886 q^{48} + 532764 q^{49} - 80230 q^{50} + 619608 q^{52} + 143428 q^{53} + 373816 q^{54} - 533304 q^{55} - 619392 q^{56} + 326848 q^{58} - 957340 q^{59} + 1790622 q^{60} - 115640 q^{61} - 643584 q^{65} - 1821654 q^{66} + 1457028 q^{68} - 1049340 q^{69} + 3024084 q^{70} + 1480560 q^{72} - 627512 q^{73} - 3652060 q^{74} + 586518 q^{75} - 1343752 q^{76} - 115820 q^{77} + 1820304 q^{78} + 235966 q^{79} + 2710496 q^{81} + 796544 q^{82} + 3881892 q^{83} + 219332 q^{84} - 3064608 q^{85} + 900526 q^{87} - 9844332 q^{88} + 3821436 q^{89} - 4192912 q^{90} - 648556 q^{94} - 620200 q^{95} - 620288 q^{97} + 4735296 q^{98} + 4021770 q^{99}+O(q^{100}) \) 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8 - 3714 * q^10 + 1934 * q^11 - 2706 * q^12 + 2648 * q^14 + 16280 * q^15 - 36632 * q^16 - 5236 * q^17 + 5258 * q^18 + 6718 * q^19 + 24828 * q^20 + 7380 * q^21 - 21524 * q^23 + 90648 * q^24 - 73196 * q^25 - 5394 * q^26 + 5824 * q^27 - 12510 * q^29 - 1780 * q^30 + 1150 * q^31 + 104646 * q^32 - 32904 * q^36 - 256832 * q^37 + 127752 * q^39 - 256374 * q^40 + 265716 * q^41 + 80590 * q^43 + 188482 * q^44 - 78008 * q^45 + 405572 * q^46 - 445250 * q^47 - 1016886 * q^48 + 532764 * q^49 - 80230 * q^50 + 619608 * q^52 + 143428 * q^53 + 373816 * q^54 - 533304 * q^55 - 619392 * q^56 + 326848 * q^58 - 957340 * q^59 + 1790622 * q^60 - 115640 * q^61 - 643584 * q^65 - 1821654 * q^66 + 1457028 * q^68 - 1049340 * q^69 + 3024084 * q^70 + 1480560 * q^72 - 627512 * q^73 - 3652060 * q^74 + 586518 * q^75 - 1343752 * q^76 - 115820 * q^77 + 1820304 * q^78 + 235966 * q^79 + 2710496 * q^81 + 796544 * q^82 + 3881892 * q^83 + 219332 * q^84 - 3064608 * q^85 + 900526 * q^87 - 9844332 * q^88 + 3821436 * q^89 - 4192912 * q^90 - 648556 * q^94 - 620200 * q^95 - 620288 * q^97 + 4735296 * q^98 + 4021770 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	4.72749	+	4.72749i	0.590937	+	0.590937i	0.937884	−	0.346948i	$-0.112782\pi$
$2$	4.72749	+	4.72749i	0.590937	+	0.590937i	−0.346948	+	0.937884i	$0.612782\pi$
$3$	−5.84368	−	5.84368i	−0.216432	−	0.216432i	0.590561	−	0.806993i	$-0.298907\pi$
$3$	−5.84368	−	5.84368i	−0.216432	−	0.216432i	−0.806993	+	0.590561i	$0.798907\pi$
$4$		−	19.3016i		−	0.301588i
$5$		−	122.935i		−	0.983480i	−0.870742	−	0.491740i	$-0.836361\pi$
$5$		−	122.935i		−	0.983480i	0.870742	−	0.491740i	$-0.163639\pi$
$6$		−	55.2519i		−	0.255796i
$7$	−317.611			−0.925979			−0.462989	−	0.886364i	$-0.653223\pi$
$7$	−317.611			−0.925979			−0.462989	+	0.886364i	$0.653223\pi$
$8$	393.808	−	393.808i	0.769156	−	0.769156i
$9$		−	660.703i		−	0.906314i
$10$	581.174	−	581.174i	0.581174	−	0.581174i
$11$	904.860	+	904.860i	0.679835	+	0.679835i	0.959963	−	0.280128i	$-0.0903769\pi$
$11$	904.860	+	904.860i	0.679835	+	0.679835i	−0.280128	+	0.959963i	$0.590377\pi$
$12$	−112.792	+	112.792i	−0.0652733	+	0.0652733i
$13$		−	1220.31i		−	0.555442i	−0.960662	−	0.277721i	$-0.910421\pi$
$13$		−	1220.31i		−	0.555442i	0.960662	−	0.277721i	$-0.0895791\pi$
$14$	−1501.50	−	1501.50i	−0.547195	−	0.547195i
$15$	−718.392	+	718.392i	−0.212857	+	0.212857i
$16$	2488.15			0.607457
$17$	5508.26	+	5508.26i	1.12116	+	1.12116i	0.991567	+	0.129593i	$0.0413670\pi$
$17$	5508.26	+	5508.26i	1.12116	+	1.12116i	0.129593	+	0.991567i	$0.458633\pi$
$18$	3123.47	−	3123.47i	0.535574	−	0.535574i
$19$	−9024.37	−	9024.37i	−1.31570	−	1.31570i	−0.917146	−	0.398551i	$-0.869513\pi$
$19$	−9024.37	−	9024.37i	−1.31570	−	1.31570i	−0.398551	−	0.917146i	$-0.630487\pi$
$20$	−2372.84			−0.296605
$21$	1856.01	+	1856.01i	0.200412	+	0.200412i
$22$			8555.44i			0.803479i
$23$	−9177.93			−0.754330			−0.377165	−	0.926146i	$-0.623101\pi$
$23$	−9177.93			−0.754330			−0.377165	+	0.926146i	$0.623101\pi$
$24$	−4602.57			−0.332941
$25$	511.993			0.0327676
$26$	5768.99	−	5768.99i	0.328231	−	0.328231i
$27$	−8120.97	+	8120.97i	−0.412588	+	0.412588i
$28$			6130.40i			0.279264i
$29$	4826.87	+	23906.6i	0.197912	+	0.980220i
$29$	4826.87	+	23906.6i	0.197912	+	0.980220i
$30$	−6792.39			−0.251570
$31$	21942.9	+	21942.9i	0.736560	+	0.736560i	0.971911	−	0.235351i	$-0.0756238\pi$
$31$	21942.9	+	21942.9i	0.736560	+	0.736560i	−0.235351	+	0.971911i	$0.575624\pi$
$32$	−13441.0	−	13441.0i	−0.410187	−	0.410187i
$33$		−	10575.4i		−	0.294277i
$34$			52080.5i			1.32507i
$35$			39045.5i			0.910682i
$36$	−12752.6			−0.273333
$37$	27321.6	−	27321.6i	0.539387	−	0.539387i	−0.383962	−	0.923349i	$-0.625441\pi$
$37$	27321.6	−	27321.6i	0.539387	−	0.539387i	0.923349	+	0.383962i	$0.125441\pi$
$38$		−	85325.3i		−	1.55499i
$39$	−7131.08	+	7131.08i	−0.120216	+	0.120216i
$40$	−48412.8	−	48412.8i	−0.756449	−	0.756449i
$41$	75477.0	−	75477.0i	1.09512	−	1.09512i	0.100151	−	0.994972i	$-0.468068\pi$
$41$	75477.0	−	75477.0i	1.09512	−	1.09512i	0.994972	−	0.100151i	$-0.0319325\pi$
$42$			17548.6i			0.236862i
$43$	42100.3	+	42100.3i	0.529517	+	0.529517i	0.920428	−	0.390911i	$-0.127840\pi$
$43$	42100.3	+	42100.3i	0.529517	+	0.529517i	−0.390911	+	0.920428i	$0.627840\pi$
$44$	17465.2	−	17465.2i	0.205030	−	0.205030i
$45$	−81223.5			−0.891341
$46$	−43388.6	−	43388.6i	−0.445761	−	0.445761i
$47$	78079.2	−	78079.2i	0.752042	−	0.752042i	−0.222818	−	0.974860i	$-0.571526\pi$
$47$	78079.2	−	78079.2i	0.752042	−	0.752042i	0.974860	+	0.222818i	$0.0715256\pi$
$48$	−14539.9	−	14539.9i	−0.131474	−	0.131474i
$49$	−16772.4			−0.142563
$50$	2420.44	+	2420.44i	0.0193636	+	0.0193636i
$51$		−	64377.0i		−	0.485311i
$52$	−23553.9			−0.167514
$53$	187104.			1.25677			0.628383	−	0.777904i	$-0.283717\pi$
$53$	187104.			1.25677			0.628383	+	0.777904i	$0.283717\pi$
$54$	−76783.7			−0.487627
$55$	111239.	−	111239.i	0.668604	−	0.668604i
$56$	−125078.	+	125078.i	−0.712222	+	0.712222i
$57$			105471.i			0.569519i
$58$	−90199.2	+	135837.i	−0.462295	+	0.696201i
$59$	−134740.			−0.656055			−0.328028	−	0.944668i	$-0.606384\pi$
$59$	−134740.			−0.656055			−0.328028	+	0.944668i	$0.606384\pi$
$60$	13866.1	+	13866.1i	0.0641950	+	0.0641950i
$61$	201963.	+	201963.i	0.889781	+	0.889781i	0.994502	−	0.104721i	$-0.0333948\pi$
$61$	201963.	+	201963.i	0.889781	+	0.889781i	−0.104721	+	0.994502i	$0.533395\pi$
$62$			207469.i			0.870521i
$63$			209846.i			0.839228i
$64$		−	286326.i		−	1.09225i
$65$	−150018.			−0.546266
$66$	49995.2	−	49995.2i	0.173899	−	0.173899i
$67$			156779.i			0.521271i	0.965437	+	0.260635i	$0.0839320\pi$
$67$			156779.i			0.521271i	−0.965437	+	0.260635i	$0.916068\pi$
$68$	106318.	−	106318.i	0.338128	−	0.338128i
$69$	53632.8	+	53632.8i	0.163261	+	0.163261i
$70$	−184587.	+	184587.i	−0.538155	+	0.538155i
$71$		−	35515.7i		−	0.0992307i	−0.998768	−	0.0496153i	$-0.984200\pi$
$71$		−	35515.7i		−	0.0992307i	0.998768	−	0.0496153i	$-0.0157995\pi$
$72$	−260190.	−	260190.i	−0.697097	−	0.697097i
$73$	−178645.	+	178645.i	−0.459221	+	0.459221i	−0.898400	−	0.439178i	$-0.855270\pi$
$73$	−178645.	+	178645.i	−0.459221	+	0.459221i	0.439178	+	0.898400i	$0.355270\pi$
$74$	258325.			0.637487
$75$	−2991.92	−	2991.92i	−0.00709196	−	0.00709196i
$76$	−174185.	+	174185.i	−0.396798	+	0.396798i
$77$	−287393.	−	287393.i	−0.629513	−	0.629513i
$78$	−67424.3			−0.142080
$79$	164941.	+	164941.i	0.334539	+	0.334539i	0.854307	−	0.519768i	$-0.173982\pi$
$79$	164941.	+	164941.i	0.334539	+	0.334539i	−0.519768	+	0.854307i	$0.673982\pi$
$80$		−	305880.i		−	0.597422i
$81$	−386740.			−0.727719
$82$	713634.			1.29430
$83$	137229.			0.240001			0.120000	−	0.992774i	$-0.461710\pi$
$83$	137229.			0.240001			0.120000	+	0.992774i	$0.461710\pi$
$84$	35824.1	−	35824.1i	0.0604417	−	0.0604417i
$85$	677158.	−	677158.i	1.10264	−	1.10264i
$86$			398058.i			0.625822i
$87$	111496.	−	167909.i	0.169317	−	0.254986i
$88$	712682.			1.04580
$89$	−862453.	−	862453.i	−1.22339	−	1.22339i	−0.966419	−	0.256972i	$-0.917275\pi$
$89$	−862453.	−	862453.i	−1.22339	−	1.22339i	−0.256972	−	0.966419i	$-0.582725\pi$
$90$	−383984.	−	383984.i	−0.526726	−	0.526726i
$91$			387583.i			0.514328i
$92$			177149.i			0.227496i
$93$		−	256454.i		−	0.318831i
$94$	738238.			0.888818
$95$	−1.10941e6	+	1.10941e6i	−1.29396	+	1.29396i
$96$			157090.i			0.177556i
$97$	338869.	−	338869.i	0.371293	−	0.371293i	−0.496655	−	0.867948i	$-0.665438\pi$
$97$	338869.	−	338869.i	0.371293	−	0.371293i	0.867948	+	0.496655i	$0.165438\pi$
$98$	−79291.4	−	79291.4i	−0.0842457	−	0.0842457i
$99$	597844.	−	597844.i	0.616144	−	0.616144i
$100$		−	9882.29i		−	0.00988229i
$101$	188263.	+	188263.i	0.182727	+	0.182727i	0.792543	−	0.609816i	$-0.208757\pi$
$101$	188263.	+	188263.i	0.182727	+	0.182727i	−0.609816	+	0.792543i	$0.708757\pi$
$102$	304342.	−	304342.i	0.286788	−	0.286788i
$103$	−719994.			−0.658897			−0.329448	−	0.944174i	$-0.606863\pi$
$103$	−719994.			−0.658897			−0.329448	+	0.944174i	$0.606863\pi$
$104$	−480566.	−	480566.i	−0.427222	−	0.427222i
$105$	228169.	−	228169.i	0.197101	−	0.197101i
$106$	884531.	+	884531.i	0.742670	+	0.742670i
$107$	135778.			0.110835			0.0554175	−	0.998463i	$-0.482351\pi$
$107$	135778.			0.110835			0.0554175	+	0.998463i	$0.482351\pi$
$108$	156748.	+	156748.i	0.124431	+	0.124431i
$109$		−	52013.4i		−	0.0401639i	−0.999798	−	0.0200820i	$-0.993607\pi$
$109$		−	52013.4i		−	0.0401639i	0.999798	−	0.0200820i	$-0.00639271\pi$
$110$	1.05176e6			0.790205
$111$	−319317.			−0.233482
$112$	−790262.			−0.562493
$113$	−725535.	+	725535.i	−0.502832	+	0.502832i	−0.912317	−	0.409485i	$-0.865708\pi$
$113$	−725535.	+	725535.i	−0.502832	+	0.502832i	0.409485	+	0.912317i	$0.365708\pi$
$114$	−498613.	+	498613.i	−0.336550	+	0.336550i
$115$			1.12829e6i			0.741868i
$116$	461435.	−	93166.3i	0.295622	−	0.0596877i
$117$	−806260.			−0.503405
$118$	−636982.	−	636982.i	−0.387687	−	0.387687i
$119$	−1.74948e6	−	1.74948e6i	−1.03817	−	1.03817i
$120$			565817.i			0.327440i
$121$		−	134018.i		−	0.0756496i
$122$			1.90956e6i			1.05161i
$123$	−882126.			−0.474040
$124$	423532.	−	423532.i	0.222137	−	0.222137i
$125$		−	1.98380e6i		−	1.01571i
$126$	−992047.	+	992047.i	−0.495930	+	0.495930i
$127$	2.39389e6	+	2.39389e6i	1.16867	+	1.16867i	0.982521	+	0.186153i	$0.0596021\pi$
$127$	2.39389e6	+	2.39389e6i	1.16867	+	1.16867i	0.186153	+	0.982521i	$0.440398\pi$
$128$	493379.	−	493379.i	0.235262	−	0.235262i
$129$		−	492041.i		−	0.229209i
$130$	−709211.	−	709211.i	−0.322809	−	0.322809i
$131$	−1.31488e6	+	1.31488e6i	−0.584887	+	0.584887i	−0.936242	−	0.351356i	$-0.885721\pi$
$131$	−1.31488e6	+	1.31488e6i	−0.584887	+	0.584887i	0.351356	+	0.936242i	$0.385721\pi$
$132$	−204123.			−0.0887502
$133$	2.86624e6	+	2.86624e6i	1.21831	+	1.21831i
$134$	−741172.	+	741172.i	−0.308038	+	0.308038i
$135$	998352.	+	998352.i	0.405772	+	0.405772i
$136$	4.33839e6			1.72469
$137$	−1.41300e6	−	1.41300e6i	−0.549517	−	0.549517i	0.376784	−	0.926301i	$-0.377030\pi$
$137$	−1.41300e6	−	1.41300e6i	−0.549517	−	0.549517i	−0.926301	+	0.376784i	$0.877030\pi$
$138$			507098.i			0.192954i
$139$	−2.72008e6			−1.01283			−0.506415	−	0.862290i	$-0.669030\pi$
$139$	−2.72008e6			−1.01283			−0.506415	+	0.862290i	$0.669030\pi$
$140$	753640.			0.274650
$141$	−912540.			−0.325533
$142$	167900.	−	167900.i	0.0586391	−	0.0586391i
$143$	1.10421e6	−	1.10421e6i	0.377609	−	0.377609i
$144$		−	1.64392e6i		−	0.550547i
$145$	2.93895e6	−	593391.i	0.964026	−	0.194642i
$146$	−1.68909e6			−0.542742
$147$	98012.4	+	98012.4i	0.0308552	+	0.0308552i
$148$	−527350.	−	527350.i	−0.162672	−	0.162672i
$149$			1.14991e6i			0.347620i	0.984779	+	0.173810i	$0.0556078\pi$
$149$			1.14991e6i			0.347620i	−0.984779	+	0.173810i	$0.944392\pi$
$150$		−	28288.6i		−	0.00838180i
$151$		−	3.72841e6i		−	1.08291i	−0.840729	−	0.541456i	$-0.817873\pi$
$151$		−	3.72841e6i		−	1.08291i	0.840729	−	0.541456i	$-0.182127\pi$
$152$	−7.10773e6			−2.02395
$153$	3.63932e6	−	3.63932e6i	1.01612	−	1.01612i
$154$		−	2.71730e6i		−	0.744004i
$155$	2.69754e6	−	2.69754e6i	0.724392	−	0.724392i
$156$	137641.	+	137641.i	0.0362556	+	0.0362556i
$157$	2.16042e6	−	2.16042e6i	0.558264	−	0.558264i	−0.370549	−	0.928813i	$-0.620830\pi$
$157$	2.16042e6	−	2.16042e6i	0.558264	−	0.558264i	0.928813	+	0.370549i	$0.120830\pi$
$158$			1.55951e6i			0.395383i
$159$	−1.09337e6	−	1.09337e6i	−0.272005	−	0.272005i
$160$	−1.65237e6	+	1.65237e6i	−0.403411	+	0.403411i
$161$	2.91501e6			0.698493
$162$	−1.82831e6	−	1.82831e6i	−0.430036	−	0.430036i
$163$	−1.66974e6	+	1.66974e6i	−0.385555	+	0.385555i	−0.873099	−	0.487543i	$-0.837893\pi$
$163$	−1.66974e6	+	1.66974e6i	−0.385555	+	0.385555i	0.487543	+	0.873099i	$0.337893\pi$
$164$	−1.45683e6	−	1.45683e6i	−0.330275	−	0.330275i
$165$	−1.30009e6			−0.289415
$166$	648750.	+	648750.i	0.141825	+	0.141825i
$167$		−	1.69121e6i		−	0.363118i	−0.983380	−	0.181559i	$-0.941886\pi$
$167$		−	1.69121e6i		−	0.363118i	0.983380	−	0.181559i	$-0.0581143\pi$
$168$	1.46183e6			0.308296
$169$	3.33766e6			0.691484
$170$	6.40252e6			1.30318
$171$	−5.96243e6	+	5.96243e6i	−1.19243	+	1.19243i
$172$	812604.	−	812604.i	0.159696	−	0.159696i
$173$			2.87926e6i			0.556086i	0.960569	+	0.278043i	$0.0896858\pi$
$173$			2.87926e6i			0.556086i	−0.960569	+	0.278043i	$0.910314\pi$
$174$	1.32088e6	−	266694.i	0.250736	−	0.0506250i
$175$	−162615.			−0.0303421
$176$	2.25142e6	+	2.25142e6i	0.412971	+	0.412971i
$177$	787377.	+	787377.i	0.141992	+	0.141992i
$178$		−	8.15448e6i		−	1.44589i
$179$			1.04701e7i			1.82555i	0.408466	+	0.912774i	$0.366064\pi$
$179$			1.04701e7i			1.82555i	−0.408466	+	0.912774i	$0.633936\pi$
$180$			1.56774e6i			0.268817i
$181$	−9.18851e6			−1.54956			−0.774781	−	0.632229i	$-0.782140\pi$
$181$	−9.18851e6			−1.54956			−0.774781	+	0.632229i	$0.782140\pi$
$182$	−1.83229e6	+	1.83229e6i	−0.303935	+	0.303935i
$183$		−	2.36042e6i		−	0.385155i
$184$	−3.61434e6	+	3.61434e6i	−0.580197	+	0.580197i
$185$	−3.35878e6	−	3.35878e6i	−0.530476	−	0.530476i
$186$	1.21238e6	−	1.21238e6i	0.188409	−	0.188409i
$187$			9.96841e6i			1.52441i
$188$	−1.50705e6	−	1.50705e6i	−0.226806	−	0.226806i
$189$	2.57931e6	−	2.57931e6i	0.382048	−	0.382048i
$190$	−1.04895e7			−1.52930
$191$	8.20698e6	+	8.20698e6i	1.17783	+	1.17783i	0.980296	+	0.197536i	$0.0632938\pi$
$191$	8.20698e6	+	8.20698e6i	1.17783	+	1.17783i	0.197536	+	0.980296i	$0.436706\pi$
$192$	−1.67320e6	+	1.67320e6i	−0.236398	+	0.236398i
$193$	7.93918e6	+	7.93918e6i	1.10434	+	1.10434i	0.993880	+	0.110462i	$0.0352332\pi$
$193$	7.93918e6	+	7.93918e6i	1.10434	+	1.10434i	0.110462	+	0.993880i	$0.464767\pi$
$194$	3.20401e6			0.438822
$195$	876659.	+	876659.i	0.118230	+	0.118230i
$196$			323734.i			0.0429952i
$197$	3.69272e6			0.483001			0.241501	−	0.970401i	$-0.422360\pi$
$197$	3.69272e6			0.483001			0.241501	+	0.970401i	$0.422360\pi$
$198$	5.65260e6			0.728204
$199$	−2.98062e6			−0.378222			−0.189111	−	0.981956i	$-0.560561\pi$
$199$	−2.98062e6			−0.378222			−0.189111	+	0.981956i	$0.560561\pi$
$200$	201627.	−	201627.i	0.0252034	−	0.0252034i
$201$	916165.	−	916165.i	0.112820	−	0.112820i
$202$			1.78003e6i			0.215960i
$203$	−1.53307e6	−	7.59299e6i	−0.183262	−	0.907663i
$204$	−1.24258e6			−0.146364
$205$	−9.27876e6	−	9.27876e6i	−1.07703	−	1.07703i
$206$	−3.40377e6	−	3.40377e6i	−0.389366	−	0.389366i
$207$			6.06388e6i			0.683660i
$208$		−	3.03630e6i		−	0.337408i
$209$		−	1.63316e7i		−	1.78891i
$210$	2.15734e6			0.232949
$211$	−9.30621e6	+	9.30621e6i	−0.990662	+	0.990662i	−0.999957	−	0.00929462i	$-0.997041\pi$
$211$	−9.30621e6	+	9.30621e6i	−0.990662	+	0.990662i	0.00929462	+	0.999957i	$0.497041\pi$
$212$		−	3.61140e6i		−	0.379025i
$213$	−207543.	+	207543.i	−0.0214767	+	0.0214767i
$214$	641888.	+	641888.i	0.0654965	+	0.0654965i
$215$	5.17560e6	−	5.17560e6i	0.520769	−	0.520769i
$216$			6.39621e6i			0.634689i
$217$	−6.96929e6	−	6.96929e6i	−0.682039	−	0.682039i
$218$	245893.	−	245893.i	0.0237343	−	0.0237343i
$219$	2.08789e6			0.198781
$220$	−2.14709e6	−	2.14709e6i	−0.201643	−	0.201643i
$221$	6.72177e6	−	6.72177e6i	0.622740	−	0.622740i
$222$	−1.50957e6	−	1.50957e6i	−0.137973	−	0.137973i
$223$	6.16919e6			0.556306			0.278153	−	0.960537i	$-0.410278\pi$
$223$	6.16919e6			0.556306			0.278153	+	0.960537i	$0.410278\pi$
$224$	4.26901e6	+	4.26901e6i	0.379825	+	0.379825i
$225$		−	338275.i		−	0.0296977i
$226$	−6.85993e6			−0.594284
$227$	1.69352e7			1.44782			0.723908	−	0.689897i	$-0.242344\pi$
$227$	1.69352e7			1.44782			0.723908	+	0.689897i	$0.242344\pi$
$228$	2.03576e6			0.171760
$229$	1.05454e7	−	1.05454e7i	0.878129	−	0.878129i	−0.115212	−	0.993341i	$-0.536755\pi$
$229$	1.05454e7	−	1.05454e7i	0.878129	−	0.878129i	0.993341	+	0.115212i	$0.0367548\pi$
$230$	−5.33398e6	+	5.33398e6i	−0.438397	+	0.438397i
$231$			3.35887e6i			0.272494i
$232$	1.13155e7	+	7.51374e6i	0.906167	+	0.601717i
$233$	−7.43449e6			−0.587738			−0.293869	−	0.955846i	$-0.594943\pi$
$233$	−7.43449e6			−0.587738			−0.293869	+	0.955846i	$0.594943\pi$
$234$	−3.81159e6	−	3.81159e6i	−0.297481	−	0.297481i
$235$	−9.59867e6	−	9.59867e6i	−0.739618	−	0.739618i
$236$			2.60070e6i			0.197858i
$237$		−	1.92772e6i		−	0.144810i
$238$		−	1.65413e7i		−	1.22699i
$239$	−99657.7			−0.00729991			−0.00364995	−	0.999993i	$-0.501162\pi$
$239$	−99657.7			−0.00729991			−0.00364995	+	0.999993i	$0.501162\pi$
$240$	−1.78746e6	+	1.78746e6i	−0.129302	+	0.129302i
$241$			2.07984e7i			1.48586i	0.669369	+	0.742930i	$0.266564\pi$
$241$			2.07984e7i			1.48586i	−0.669369	+	0.742930i	$0.733436\pi$
$242$	633569.	−	633569.i	0.0447041	−	0.0447041i
$243$	8.18017e6	+	8.18017e6i	0.570090	+	0.570090i
$244$	3.89822e6	−	3.89822e6i	0.268347	−	0.268347i
$245$			2.06191e6i			0.140208i
$246$	−4.17025e6	−	4.17025e6i	−0.280128	−	0.280128i
$247$	−1.10125e7	+	1.10125e7i	−0.730794	+	0.730794i
$248$	1.72825e7			1.13306
$249$	−801923.	−	801923.i	−0.0519439	−	0.0519439i
$250$	9.37841e6	−	9.37841e6i	0.600218	−	0.600218i
$251$	−7.01168e6	−	7.01168e6i	−0.443405	−	0.443405i	0.449749	−	0.893155i	$-0.351513\pi$
$251$	−7.01168e6	−	7.01168e6i	−0.443405	−	0.443405i	−0.893155	+	0.449749i	$0.851513\pi$
$252$	4.05037e6			0.253101
$253$	−8.30474e6	−	8.30474e6i	−0.512819	−	0.512819i
$254$			2.26342e7i			1.38122i
$255$	−7.91418e6			−0.477293
$256$	−1.36600e7			−0.814197
$257$	1.07862e7			0.635430			0.317715	−	0.948186i	$-0.397084\pi$
$257$	1.07862e7			0.635430			0.317715	+	0.948186i	$0.397084\pi$
$258$	2.32612e6	−	2.32612e6i	0.135448	−	0.135448i
$259$	−8.67762e6	+	8.67762e6i	−0.499461	+	0.499461i
$260$			2.89559e6i			0.164747i
$261$	1.57951e7	−	3.18913e6i	0.888387	−	0.179370i
$262$	−1.24322e7			−0.691262
$263$	−1.09364e7	−	1.09364e7i	−0.601185	−	0.601185i	0.339442	−	0.940627i	$-0.389762\pi$
$263$	−1.09364e7	−	1.09364e7i	−0.601185	−	0.601185i	−0.940627	+	0.339442i	$0.889762\pi$
$264$	−4.16468e6	−	4.16468e6i	−0.226345	−	0.226345i
$265$		−	2.30016e7i		−	1.23600i
$266$			2.71002e7i			1.43989i
$267$			1.00798e7i			0.529563i
$268$	3.02609e6			0.157209
$269$	−2.03996e7	+	2.03996e7i	−1.04801	+	1.04801i	−0.0492186	+	0.998788i	$0.515673\pi$
$269$	−2.03996e7	+	2.03996e7i	−1.04801	+	1.04801i	−0.998788	+	0.0492186i	$0.984327\pi$
$270$			9.43940e6i			0.479571i
$271$	−4.70212e6	+	4.70212e6i	−0.236257	+	0.236257i	−0.815298	−	0.579041i	$-0.803427\pi$
$271$	−4.70212e6	+	4.70212e6i	−0.236257	+	0.236257i	0.579041	+	0.815298i	$0.303427\pi$
$272$	1.37054e7	+	1.37054e7i	0.681057	+	0.681057i
$273$	2.26491e6	−	2.26491e6i	0.111317	−	0.111317i
$274$		−	1.33599e7i		−	0.649460i
$275$	463282.	+	463282.i	0.0222765	+	0.0222765i
$276$	1.03520e6	−	1.03520e6i	0.0492376	−	0.0492376i
$277$	−4.72418e6			−0.222273			−0.111137	−	0.993805i	$-0.535449\pi$
$277$	−4.72418e6			−0.222273			−0.111137	+	0.993805i	$0.535449\pi$
$278$	−1.28591e7	−	1.28591e7i	−0.598519	−	0.598519i
$279$	1.44977e7	−	1.44977e7i	0.667555	−	0.667555i
$280$	1.53764e7	+	1.53764e7i	0.700456	+	0.700456i
$281$	−6.63951e6			−0.299238			−0.149619	−	0.988744i	$-0.547805\pi$
$281$	−6.63951e6			−0.299238			−0.149619	+	0.988744i	$0.547805\pi$
$282$	−4.31403e6	−	4.31403e6i	−0.192369	−	0.192369i
$283$		−	3.25017e7i		−	1.43399i	−0.697078	−	0.716996i	$-0.745517\pi$
$283$		−	3.25017e7i		−	1.43399i	0.697078	−	0.716996i	$-0.254483\pi$
$284$	−685511.			−0.0299267
$285$	1.29661e7			0.560111
$286$	1.04403e7			0.446286
$287$	−2.39723e7	+	2.39723e7i	−1.01406	+	1.01406i
$288$	−8.88051e6	+	8.88051e6i	−0.371758	+	0.371758i
$289$			3.65443e7i			1.51400i
$290$	1.66991e7	+	1.10886e7i	0.684700	+	0.454657i
$291$	−3.96049e6			−0.160720
$292$	3.44813e6	+	3.44813e6i	0.138495	+	0.138495i
$293$	−1.10664e7	−	1.10664e7i	−0.439952	−	0.439952i	0.452044	−	0.891996i	$-0.350695\pi$
$293$	−1.10664e7	−	1.10664e7i	−0.439952	−	0.439952i	−0.891996	+	0.452044i	$0.850695\pi$
$294$			926706.i			0.0364670i
$295$			1.65643e7i			0.645217i
$296$		−	2.15189e7i		−	0.829745i
$297$	−1.46967e7			−0.560984
$298$	−5.43618e6	+	5.43618e6i	−0.205421	+	0.205421i
$299$			1.11999e7i			0.418987i
$300$	−57748.9	+	57748.9i	−0.00213885	+	0.00213885i
$301$	−1.33715e7	−	1.33715e7i	−0.490322	−	0.490322i
$302$	1.76260e7	−	1.76260e7i	0.639932	−	0.639932i
$303$		−	2.20030e6i		−	0.0790959i
$304$	−2.24539e7	−	2.24539e7i	−0.799230	−	0.799230i
$305$	2.48284e7	−	2.48284e7i	0.875082	−	0.875082i
$306$	3.44098e7			1.20093
$307$	−1.44488e7	−	1.44488e7i	−0.499363	−	0.499363i	0.411877	−	0.911240i	$-0.364873\pi$
$307$	−1.44488e7	−	1.44488e7i	−0.499363	−	0.499363i	−0.911240	+	0.411877i	$0.864873\pi$
$308$	−5.54715e6	+	5.54715e6i	−0.189853	+	0.189853i
$309$	4.20741e6	+	4.20741e6i	0.142607	+	0.142607i
$310$	2.55053e7			0.856139
$311$	−655722.	−	655722.i	−0.0217991	−	0.0217991i	0.696123	−	0.717922i	$-0.254907\pi$
$311$	−655722.	−	655722.i	−0.0217991	−	0.0217991i	−0.717922	+	0.696123i	$0.754907\pi$
$312$			5.61655e6i			0.184929i
$313$	5.60571e7			1.82809			0.914045	−	0.405613i	$-0.132942\pi$
$313$	5.60571e7			1.82809			0.914045	+	0.405613i	$0.132942\pi$
$314$	2.04268e7			0.659797
$315$	2.57975e7			0.825363
$316$	3.18362e6	−	3.18362e6i	0.100893	−	0.100893i
$317$	−3.14600e7	+	3.14600e7i	−0.987600	+	0.987600i	−0.999924	−	0.0123245i	$-0.996077\pi$
$317$	−3.14600e7	+	3.14600e7i	−0.987600	+	0.987600i	0.0123245	+	0.999924i	$0.496077\pi$
$318$		−	1.03378e7i		−	0.321476i
$319$	−1.72645e7	+	2.59998e7i	−0.531840	+	0.800935i
$320$	−3.51995e7			−1.07420
$321$	−793440.	−	793440.i	−0.0239883	−	0.0239883i
$322$	1.37807e7	+	1.37807e7i	0.412765	+	0.412765i
$323$		−	9.94171e7i		−	2.95021i
$324$			7.46470e6i			0.219471i
$325$		−	624789.i		−	0.0182005i
$326$	−1.57874e7			−0.455678
$327$	−303950.	+	303950.i	−0.00869277	+	0.00869277i
$328$		−	5.94468e7i		−	1.68464i
$329$	−2.47988e7	+	2.47988e7i	−0.696375	+	0.696375i
$330$	−6.14616e6	−	6.14616e6i	−0.171026	−	0.171026i
$331$	−2.99623e7	+	2.99623e7i	−0.826211	+	0.826211i	−0.986990	−	0.160780i	$-0.948599\pi$
$331$	−2.99623e7	+	2.99623e7i	−0.826211	+	0.826211i	0.160780	+	0.986990i	$0.448599\pi$
$332$		−	2.64874e6i		−	0.0723812i
$333$	−1.80514e7	−	1.80514e7i	−0.488854	−	0.488854i
$334$	7.99518e6	−	7.99518e6i	0.214580	−	0.214580i
$335$	1.92736e7			0.512659
$336$	4.61803e6	+	4.61803e6i	0.121742	+	0.121742i
$337$	2.60271e7	−	2.60271e7i	0.680042	−	0.680042i	−0.279968	−	0.960009i	$-0.590324\pi$
$337$	2.60271e7	−	2.60271e7i	0.680042	−	0.680042i	0.960009	+	0.279968i	$0.0903238\pi$
$338$	1.57788e7	+	1.57788e7i	0.408623	+	0.408623i
$339$	8.47958e6			0.217658
$340$	−1.30702e7	−	1.30702e7i	−0.332542	−	0.332542i
$341$			3.97104e7i			1.00148i
$342$	−5.63747e7			−1.40931
$343$	4.26937e7			1.05799
$344$	3.31589e7			0.814563
$345$	6.59335e6	−	6.59335e6i	0.160564	−	0.160564i
$346$	−1.36117e7	+	1.36117e7i	−0.328612	+	0.328612i
$347$		−	5.37295e7i		−	1.28595i	−0.765887	−	0.642975i	$-0.777700\pi$
$347$		−	5.37295e7i		−	1.28595i	0.765887	−	0.642975i	$-0.222300\pi$
$348$	−3.24091e6	−	2.15204e6i	−0.0769006	−	0.0510639i
$349$	2.07475e6			0.0488078			0.0244039	−	0.999702i	$-0.492231\pi$
$349$	2.07475e6			0.0488078			0.0244039	+	0.999702i	$0.492231\pi$
$350$	−768759.	−	768759.i	−0.0179302	−	0.0179302i
$351$	9.91008e6	+	9.91008e6i	0.229169	+	0.229169i
$352$		−	2.43245e7i		−	0.557719i
$353$		−	3.99219e7i		−	0.907584i	−0.891108	−	0.453792i	$-0.850071\pi$
$353$		−	3.99219e7i		−	0.907584i	0.891108	−	0.453792i	$-0.149929\pi$
$354$			7.44464e6i			0.167816i
$355$	−4.36613e6			−0.0975914
$356$	−1.66467e7	+	1.66467e7i	−0.368960	+	0.368960i
$357$			2.04468e7i			0.449388i
$358$	−4.94975e7	+	4.94975e7i	−1.07878	+	1.07878i
$359$	5.82289e7	+	5.82289e7i	1.25850	+	1.25850i	0.951807	+	0.306698i	$0.0992242\pi$
$359$	5.82289e7	+	5.82289e7i	1.25850	+	1.25850i	0.306698	+	0.951807i	$0.400776\pi$
$360$	−3.19864e7	+	3.19864e7i	−0.685581	+	0.685581i
$361$			1.15832e8i			2.46212i
$362$	−4.34386e7	−	4.34386e7i	−0.915694	−	0.915694i
$363$	−783157.	+	783157.i	−0.0163730	+	0.0163730i
$364$	7.48096e6			0.155115
$365$	2.19617e7	+	2.19617e7i	0.451635	+	0.451635i
$366$	1.11589e7	−	1.11589e7i	0.227602	−	0.227602i
$367$	4.03011e7	+	4.03011e7i	0.815303	+	0.815303i	0.985423	−	0.170120i	$-0.0544156\pi$
$367$	4.03011e7	+	4.03011e7i	0.815303	+	0.815303i	−0.170120	+	0.985423i	$0.554416\pi$
$368$	−2.28360e7			−0.458223
$369$	−4.98679e7	−	4.98679e7i	−0.992525	−	0.992525i
$370$		−	3.17572e7i		−	0.626956i
$371$	−5.94261e7			−1.16374
$372$	−4.94997e6			−0.0961554
$373$	3.61122e7			0.695870			0.347935	−	0.937519i	$-0.386883\pi$
$373$	3.61122e7			0.695870			0.347935	+	0.937519i	$0.386883\pi$
$374$	−4.71256e7	+	4.71256e7i	−0.900828	+	0.900828i
$375$	−1.15927e7	+	1.15927e7i	−0.219832	+	0.219832i
$376$		−	6.14964e7i		−	1.15687i
$377$	2.91734e7	−	5.89026e6i	0.544456	−	0.109929i
$378$	2.43873e7			0.451532
$379$	7.23680e7	+	7.23680e7i	1.32932	+	1.32932i	0.905965	+	0.423353i	$0.139147\pi$
$379$	7.23680e7	+	7.23680e7i	1.32932	+	1.32932i	0.423353	+	0.905965i	$0.360853\pi$
$380$	2.14134e7	+	2.14134e7i	0.390243	+	0.390243i
$381$		−	2.79783e7i		−	0.505878i
$382$			7.75969e7i			1.39205i
$383$		−	5.19363e7i		−	0.924432i	−0.886767	−	0.462216i	$-0.847054\pi$
$383$		−	5.19363e7i		−	0.924432i	0.886767	−	0.462216i	$-0.152946\pi$
$384$	−5.76630e6			−0.101837
$385$	−3.53307e7	+	3.53307e7i	−0.619113	+	0.619113i
$386$			7.50649e7i			1.30519i
$387$	2.78158e7	−	2.78158e7i	0.479909	−	0.479909i
$388$	−6.54072e6	−	6.54072e6i	−0.111977	−	0.111977i
$389$	1.10090e7	−	1.10090e7i	0.187025	−	0.187025i	−0.607384	−	0.794409i	$-0.707781\pi$
$389$	1.10090e7	−	1.10090e7i	0.187025	−	0.187025i	0.794409	+	0.607384i	$0.207781\pi$
$390$			8.28880e6i			0.139733i
$391$	−5.05544e7	−	5.05544e7i	−0.845724	−	0.845724i
$392$	−6.60510e6	+	6.60510e6i	−0.109653	+	0.109653i
$393$	1.53674e7			0.253177
$394$	1.74573e7	+	1.74573e7i	0.285423	+	0.285423i
$395$	2.02770e7	−	2.02770e7i	0.329012	−	0.329012i
$396$	−1.15393e7	−	1.15393e7i	−0.185821	−	0.185821i
$397$	3.46845e6			0.0554324			0.0277162	−	0.999616i	$-0.491177\pi$
$397$	3.46845e6			0.0554324			0.0277162	+	0.999616i	$0.491177\pi$
$398$	−1.40908e7	−	1.40908e7i	−0.223505	−	0.223505i
$399$		−	3.34987e7i		−	0.527363i
$400$	1.27391e6			0.0199049
$401$	−6.43750e7			−0.998354			−0.499177	−	0.866500i	$-0.666364\pi$
$401$	−6.43750e7			−0.998354			−0.499177	+	0.866500i	$0.666364\pi$
$402$	8.66233e6			0.133339
$403$	2.67770e7	−	2.67770e7i	0.409117	−	0.409117i
$404$	3.63379e6	−	3.63379e6i	0.0551081	−	0.0551081i
$405$			4.75438e7i			0.715697i
$406$	2.86482e7	−	4.31434e7i	0.428075	−	0.644668i
$407$	4.94444e7			0.733388
$408$	−2.53522e7	−	2.53522e7i	−0.373280	−	0.373280i
$409$	−3.20066e7	−	3.20066e7i	−0.467811	−	0.467811i	0.433394	−	0.901205i	$-0.357316\pi$
$409$	−3.20066e7	−	3.20066e7i	−0.467811	−	0.467811i	−0.901205	+	0.433394i	$0.857316\pi$
$410$		−	8.77306e7i		−	1.27291i
$411$			1.65143e7i			0.237867i
$412$			1.38970e7i			0.198715i
$413$	4.27949e7			0.607493
$414$	−2.86670e7	+	2.86670e7i	−0.404000	+	0.404000i
$415$		−	1.68703e7i		−	0.236036i
$416$	−1.64022e7	+	1.64022e7i	−0.227835	+	0.227835i
$417$	1.58952e7	+	1.58952e7i	0.219209	+	0.219209i
$418$	7.72074e7	−	7.72074e7i	1.05713	−	1.05713i
$419$		−	6.29150e7i		−	0.855288i	−0.903947	−	0.427644i	$-0.859344\pi$
$419$		−	6.29150e7i		−	0.855288i	0.903947	−	0.427644i	$-0.140656\pi$
$420$	−4.40403e6	−	4.40403e6i	−0.0594432	−	0.0594432i
$421$	1.18573e7	−	1.18573e7i	0.158906	−	0.158906i	−0.623176	−	0.782082i	$-0.714158\pi$
$421$	1.18573e7	−	1.18573e7i	0.158906	−	0.158906i	0.782082	+	0.623176i	$0.214158\pi$
$422$	−8.79901e7			−1.17084
$423$	−5.15872e7	−	5.15872e7i	−0.681586	−	0.681586i
$424$	7.36829e7	−	7.36829e7i	0.966649	−	0.966649i
$425$	2.82019e6	+	2.82019e6i	0.0367377	+	0.0367377i
$426$	−1.96231e6			−0.0253828
$427$	−6.41458e7	−	6.41458e7i	−0.823919	−	0.823919i
$428$		−	2.62073e6i		−	0.0334264i
$429$	−1.29053e7			−0.163454
$430$	4.89353e7			0.615484
$431$	1.01498e8			1.26773			0.633863	−	0.773446i	$-0.281468\pi$
$431$	1.01498e8			1.26773			0.633863	+	0.773446i	$0.281468\pi$
$432$	−2.02062e7	+	2.02062e7i	−0.250630	+	0.250630i
$433$	−8.01800e7	+	8.01800e7i	−0.987648	+	0.987648i	−0.999925	−	0.0122768i	$-0.996092\pi$
$433$	−8.01800e7	+	8.01800e7i	−0.987648	+	0.987648i	0.0122768	+	0.999925i	$0.496092\pi$
$434$		−	6.58945e7i		−	0.806084i
$435$	−2.06419e7	−	1.37067e7i	−0.250773	−	0.166520i
$436$	−1.00394e6			−0.0121129
$437$	8.28250e7	+	8.28250e7i	0.992469	+	0.992469i
$438$	9.87047e6	+	9.87047e6i	0.117467	+	0.117467i
$439$		−	3.99711e7i		−	0.472446i	−0.971699	−	0.236223i	$-0.924090\pi$
$439$		−	3.99711e7i		−	0.472446i	0.971699	−	0.236223i	$-0.0759096\pi$
$440$		−	8.76135e7i		−	1.02852i
$441$			1.10816e7i			0.129207i
$442$	6.35542e7			0.736000
$443$	−8.36153e7	+	8.36153e7i	−0.961778	+	0.961778i	−0.999296	−	0.0375180i	$-0.988055\pi$
$443$	−8.36153e7	+	8.36153e7i	−0.961778	+	0.961778i	0.0375180	+	0.999296i	$0.488055\pi$
$444$			6.16333e6i			0.0704152i
$445$	−1.06026e8	+	1.06026e8i	−1.20318	+	1.20318i
$446$	2.91648e7	+	2.91648e7i	0.328741	+	0.328741i
$447$	6.71969e6	−	6.71969e6i	0.0752362	−	0.0752362i
$448$			9.09402e7i			1.01140i
$449$	−3.93443e7	−	3.93443e7i	−0.434653	−	0.434653i	0.455555	−	0.890208i	$-0.349441\pi$
$449$	−3.93443e7	−	3.93443e7i	−0.434653	−	0.434653i	−0.890208	+	0.455555i	$0.849441\pi$
$450$	1.59919e6	−	1.59919e6i	0.0175495	−	0.0175495i
$451$	1.36592e8			1.48901
$452$	1.40040e7	+	1.40040e7i	0.151648	+	0.151648i
$453$	−2.17876e7	+	2.17876e7i	−0.234377	+	0.234377i
$454$	8.00612e7	+	8.00612e7i	0.855568	+	0.855568i
$455$	4.76475e7			0.505831
$456$	4.15353e7	+	4.15353e7i	0.438049	+	0.438049i
$457$			6.20946e6i			0.0650587i	0.999471	+	0.0325294i	$0.0103562\pi$
$457$			6.20946e6i			0.0650587i	−0.999471	+	0.0325294i	$0.989644\pi$
$458$	9.97070e7			1.03784
$459$	−8.94649e7			−0.925155
$460$	2.17778e7			0.223738
$461$	−5.99215e6	+	5.99215e6i	−0.0611617	+	0.0611617i	−0.737026	−	0.675864i	$-0.763771\pi$
$461$	−5.99215e6	+	5.99215e6i	−0.0611617	+	0.0611617i	0.675864	+	0.737026i	$0.263771\pi$
$462$	−1.58790e7	+	1.58790e7i	−0.161027	+	0.161027i
$463$			5.27044e7i			0.531011i	0.964109	+	0.265506i	$0.0855389\pi$
$463$			5.27044e7i			0.531011i	−0.964109	+	0.265506i	$0.914461\pi$
$464$	1.20100e7	+	5.94831e7i	0.120223	+	0.595442i
$465$	−3.15272e7			−0.313564
$466$	−3.51465e7	−	3.51465e7i	−0.347316	−	0.347316i
$467$	−1.01046e8	−	1.01046e8i	−0.992129	−	0.992129i	0.00784039	−	0.999969i	$-0.497504\pi$
$467$	−1.01046e8	−	1.01046e8i	−0.992129	−	0.992129i	−0.999969	+	0.00784039i	$0.997504\pi$
$468$			1.55621e7i			0.151821i
$469$		−	4.97947e7i		−	0.482686i
$470$		−	9.07553e7i		−	0.874135i
$471$	−2.52496e7			−0.241653
$472$	−5.30616e7	+	5.30616e7i	−0.504609	+	0.504609i
$473$			7.61898e7i			0.719968i
$474$	9.11328e6	−	9.11328e6i	0.0855736	−	0.0855736i
$475$	−4.62041e6	−	4.62041e6i	−0.0431122	−	0.0431122i
$476$	−3.37678e7	+	3.37678e7i	−0.313099	+	0.313099i
$477$		−	1.23620e8i		−	1.13903i
$478$	−471131.	−	471131.i	−0.00431378	−	0.00431378i
$479$	−7.41231e7	+	7.41231e7i	−0.674446	+	0.674446i	−0.958738	−	0.284292i	$-0.908242\pi$
$479$	−7.41231e7	+	7.41231e7i	−0.674446	+	0.674446i	0.284292	+	0.958738i	$0.408242\pi$
$480$	1.93118e7			0.174622
$481$	−3.33407e7	−	3.33407e7i	−0.299598	−	0.299598i
$482$	−9.83241e7	+	9.83241e7i	−0.878049	+	0.878049i
$483$	−1.70344e7	−	1.70344e7i	−0.151177	−	0.151177i
$484$	−2.58676e6			−0.0228150
$485$	−4.16589e7	−	4.16589e7i	−0.365160	−	0.365160i
$486$			7.73434e7i			0.673775i
$487$	2.61163e7			0.226113			0.113056	−	0.993589i	$-0.463936\pi$
$487$	2.61163e7			0.226113			0.113056	+	0.993589i	$0.463936\pi$
$488$	1.59070e8			1.36876
$489$	1.95149e7			0.166893
$490$	−9.74768e6	+	9.74768e6i	−0.0828539	+	0.0828539i
$491$	−5.32496e6	+	5.32496e6i	−0.0449854	+	0.0449854i	−0.729242	−	0.684256i	$-0.760127\pi$
$491$	−5.32496e6	+	5.32496e6i	−0.0449854	+	0.0449854i	0.684256	+	0.729242i	$0.260127\pi$
$492$			1.70264e7i			0.142965i
$493$	−1.05096e8	+	1.58271e8i	−0.877093	+	1.32087i
$494$	−1.04123e8			−0.863706
$495$	−7.34959e7	−	7.34959e7i	−0.605965	−	0.605965i
$496$	5.45970e7	+	5.45970e7i	0.447429	+	0.447429i
$497$			1.12802e7i			0.0918855i
$498$		−	7.58217e6i		−	0.0613911i
$499$		−	1.68848e7i		−	0.135892i	−0.997689	−	0.0679460i	$-0.978355\pi$
$499$		−	1.68848e7i		−	0.135892i	0.997689	−	0.0679460i	$-0.0216446\pi$
$500$	−3.82905e7			−0.306324
$501$	−9.88287e6	+	9.88287e6i	−0.0785905	+	0.0785905i
$502$		−	6.62954e7i		−	0.524049i
$503$	1.43874e8	−	1.43874e8i	1.13052	−	1.13052i	0.140426	−	0.990091i	$-0.455153\pi$
$503$	1.43874e8	−	1.43874e8i	1.13052	−	1.13052i	0.990091	−	0.140426i	$-0.0448472\pi$
$504$	8.26391e7	+	8.26391e7i	0.645497	+	0.645497i
$505$	2.31442e7	−	2.31442e7i	0.179708	−	0.179708i
$506$		−	7.85212e7i		−	0.606088i
$507$	−1.95042e7	−	1.95042e7i	−0.149660	−	0.149660i
$508$	4.62060e7	−	4.62060e7i	0.352458	−	0.352458i
$509$	3.17972e7			0.241121			0.120561	−	0.992706i	$-0.461531\pi$
$509$	3.17972e7			0.241121			0.120561	+	0.992706i	$0.461531\pi$
$510$	−3.74142e7	−	3.74142e7i	−0.282050	−	0.282050i
$511$	5.67396e7	−	5.67396e7i	0.425229	−	0.425229i
$512$	−9.61537e7	−	9.61537e7i	−0.716401	−	0.716401i
$513$	1.46573e8			1.08568
$514$	5.09915e7	+	5.09915e7i	0.375499	+	0.375499i
$515$			8.85125e7i			0.648012i
$516$	−9.49719e6			−0.0691267
$517$	1.41302e8			1.02253
$518$	−8.20468e7			−0.590300
$519$	1.68254e7	−	1.68254e7i	0.120355	−	0.120355i
$520$	−5.90784e7	+	5.90784e7i	−0.420164	+	0.420164i
$521$			4.39775e7i			0.310969i	0.987838	+	0.155484i	$0.0496939\pi$
$521$			4.39775e7i			0.310969i	−0.987838	+	0.155484i	$0.950306\pi$
$522$	8.97480e7	+	5.95949e7i	0.630977	+	0.418984i
$523$	−1.61758e8			−1.13073			−0.565366	−	0.824840i	$-0.691265\pi$
$523$	−1.61758e8			−1.13073			−0.565366	+	0.824840i	$0.691265\pi$
$524$	2.53793e7	+	2.53793e7i	0.176394	+	0.176394i
$525$	950267.	+	950267.i	0.00656701	+	0.00656701i
$526$		−	1.03404e8i		−	0.710525i
$527$			2.41734e8i			1.65160i
$528$		−	2.63132e7i		−	0.178760i
$529$	−6.38015e7			−0.430987
$530$	1.08740e8	−	1.08740e8i	0.730400	−	0.730400i
$531$			8.90231e7i			0.594592i
$532$	5.53230e7	−	5.53230e7i	0.367426	−	0.367426i
$533$	−9.21051e7	−	9.21051e7i	−0.608278	−	0.608278i
$534$	−4.76521e7	+	4.76521e7i	−0.312938	+	0.312938i
$535$		−	1.66918e7i		−	0.109004i
$536$	6.17408e7	+	6.17408e7i	0.400938	+	0.400938i
$537$	6.11841e7	−	6.11841e7i	0.395108	−	0.395108i
$538$	−1.92878e8			−1.23861
$539$	−1.51767e7	−	1.51767e7i	−0.0969192	−	0.0969192i
$540$	1.92698e7	−	1.92698e7i	0.122376	−	0.122376i
$541$	−1.04421e8	−	1.04421e8i	−0.659472	−	0.659472i	0.295783	−	0.955255i	$-0.404420\pi$
$541$	−1.04421e8	−	1.04421e8i	−0.659472	−	0.659472i	−0.955255	+	0.295783i	$0.904420\pi$
$542$	−4.44585e7			−0.279226
$543$	5.36947e7	+	5.36947e7i	0.335376	+	0.335376i
$544$		−	1.48073e8i		−	0.919771i
$545$	−6.39427e6			−0.0395004
$546$	2.14147e7			0.131563
$547$	7.05481e7			0.431046			0.215523	−	0.976499i	$-0.430854\pi$
$547$	7.05481e7			0.431046			0.215523	+	0.976499i	$0.430854\pi$
$548$	−2.72732e7	+	2.72732e7i	−0.165728	+	0.165728i
$549$	1.33438e8	−	1.33438e8i	0.806421	−	0.806421i
$550$			4.38033e6i			0.0263280i
$551$	1.72182e8	−	2.59301e8i	1.02928	−	1.55006i
$552$	4.22421e7			0.251147
$553$	−5.23869e7	−	5.23869e7i	−0.309776	−	0.309776i
$554$	−2.23335e7	−	2.23335e7i	−0.131349	−	0.131349i
$555$			3.92552e7i			0.229624i
$556$			5.25018e7i			0.305457i
$557$			1.70837e8i			0.988589i	0.869294	+	0.494295i	$0.164574\pi$
$557$			1.70837e8i			0.988589i	−0.869294	+	0.494295i	$0.835426\pi$
$558$	1.37076e8			0.788965
$559$	5.13753e7	−	5.13753e7i	0.294116	−	0.294116i
$560$			9.71508e7i			0.553200i
$561$	5.82521e7	−	5.82521e7i	0.329931	−	0.329931i
$562$	−3.13882e7	−	3.13882e7i	−0.176831	−	0.176831i
$563$	−1.65656e7	+	1.65656e7i	−0.0928286	+	0.0928286i	−0.751996	−	0.659168i	$-0.770909\pi$
$563$	−1.65656e7	+	1.65656e7i	−0.0928286	+	0.0928286i	0.659168	+	0.751996i	$0.270909\pi$
$564$			1.76135e7i			0.0981766i
$565$	8.91936e7	+	8.91936e7i	0.494525	+	0.494525i
$566$	1.53652e8	−	1.53652e8i	0.847398	−	0.847398i
$567$	1.22833e8			0.673853
$568$	−1.39864e7	−	1.39864e7i	−0.0763239	−	0.0763239i
$569$	−1.43213e7	+	1.43213e7i	−0.0777404	+	0.0777404i	−0.744908	−	0.667167i	$-0.767507\pi$
$569$	−1.43213e7	+	1.43213e7i	−0.0777404	+	0.0777404i	0.667167	+	0.744908i	$0.267507\pi$
$570$	6.12970e7	+	6.12970e7i	0.330990	+	0.330990i
$571$	−2.84909e8			−1.53038			−0.765189	−	0.643806i	$-0.777354\pi$
$571$	−2.84909e8			−1.53038			−0.765189	+	0.643806i	$0.777354\pi$
$572$	−2.13130e7	−	2.13130e7i	−0.113882	−	0.113882i
$573$		−	9.59178e7i		−	0.509842i
$574$	−2.26658e8			−1.19849
$575$	−4.69904e6			−0.0247175
$576$	−1.89176e8			−0.989918
$577$	2.49333e7	−	2.49333e7i	0.129793	−	0.129793i	−0.639226	−	0.769019i	$-0.720745\pi$
$577$	2.49333e7	−	2.49333e7i	0.129793	−	0.129793i	0.769019	+	0.639226i	$0.220745\pi$
$578$	−1.72763e8	+	1.72763e8i	−0.894678	+	0.894678i
$579$		−	9.27880e7i		−	0.478031i
$580$	−1.14534e7	−	5.67265e7i	−0.0587017	−	0.290738i
$581$	−4.35855e7			−0.222235
$582$	−1.87232e7	−	1.87232e7i	−0.0949753	−	0.0949753i
$583$	1.69303e8	+	1.69303e8i	0.854394	+	0.854394i
$584$			1.40704e8i			0.706426i
$585$			9.91176e7i			0.495089i
$586$		−	1.04633e8i		−	0.519967i
$587$	−6.81715e7			−0.337045			−0.168523	−	0.985698i	$-0.553900\pi$
$587$	−6.81715e7			−0.337045			−0.168523	+	0.985698i	$0.553900\pi$
$588$	1.89180e6	−	1.89180e6i	0.00930556	−	0.00930556i
$589$		−	3.96041e8i		−	1.93818i
$590$	−7.83074e7	+	7.83074e7i	−0.381282	+	0.381282i
$591$	−2.15791e7	−	2.15791e7i	−0.104537	−	0.104537i
$592$	6.79800e7	−	6.79800e7i	0.327655	−	0.327655i
$593$			3.35240e8i			1.60765i	0.594865	+	0.803826i	$0.297206\pi$
$593$			3.35240e8i			1.60765i	−0.594865	+	0.803826i	$0.702794\pi$
$594$	−6.94785e7	−	6.94785e7i	−0.331506	−	0.331506i
$595$	−2.15073e8	+	2.15073e8i	−1.02102	+	1.02102i
$596$	2.21951e7			0.104838
$597$	1.74177e7	+	1.74177e7i	0.0818595	+	0.0818595i
$598$	−5.29474e7	+	5.29474e7i	−0.247595	+	0.247595i
$599$	2.71002e6	+	2.71002e6i	0.0126093	+	0.0126093i	0.713383	−	0.700774i	$-0.247162\pi$
$599$	2.71002e6	+	2.71002e6i	0.0126093	+	0.0126093i	−0.700774	+	0.713383i	$0.747162\pi$
$600$	−2.35648e6			−0.0109097
$601$	1.11582e8	+	1.11582e8i	0.514008	+	0.514008i	0.915752	−	0.401744i	$-0.131596\pi$
$601$	1.11582e8	+	1.11582e8i	0.514008	+	0.514008i	−0.401744	+	0.915752i	$0.631596\pi$
$602$		−	1.26428e8i		−	0.579498i
$603$	1.03584e8			0.472435
$604$	−7.19643e7			−0.326593
$605$	−1.64755e7			−0.0743998
$606$	1.04019e7	−	1.04019e7i	0.0467407	−	0.0467407i
$607$	2.45365e8	−	2.45365e8i	1.09710	−	1.09710i	0.102351	−	0.994748i	$-0.467363\pi$
$607$	2.45365e8	−	2.45365e8i	1.09710	−	1.09710i	0.994748	−	0.102351i	$-0.0326366\pi$
$608$			2.42593e8i			1.07936i
$609$	−3.54122e7	+	5.33297e7i	−0.156784	+	0.236112i
$610$	2.34752e8			1.03424
$611$	−9.52806e7	−	9.52806e7i	−0.417716	−	0.417716i
$612$	−7.02448e7	−	7.02448e7i	−0.306450	−	0.306450i
$613$			3.60075e8i			1.56319i	0.623785	+	0.781596i	$0.285594\pi$
$613$			3.60075e8i			1.56319i	−0.623785	+	0.781596i	$0.714406\pi$
$614$		−	1.36613e8i		−	0.590184i
$615$			1.08444e8i			0.466209i
$616$	−2.26355e8			−0.968387
$617$	−1.40583e8	+	1.40583e8i	−0.598519	+	0.598519i	−0.939918	−	0.341400i	$-0.889099\pi$
$617$	−1.40583e8	+	1.40583e8i	−0.598519	+	0.598519i	0.341400	+	0.939918i	$0.389099\pi$
$618$			3.97811e7i			0.168543i
$619$	−1.29705e8	+	1.29705e8i	−0.546869	+	0.546869i	−0.925534	−	0.378665i	$-0.876383\pi$
$619$	−1.29705e8	+	1.29705e8i	−0.546869	+	0.546869i	0.378665	+	0.925534i	$0.376383\pi$
$620$	−5.20669e7	−	5.20669e7i	−0.218468	−	0.218468i
$621$	7.45337e7	−	7.45337e7i	0.311228	−	0.311228i
$622$		−	6.19984e6i		−	0.0257638i
$623$	2.73924e8	+	2.73924e8i	1.13283	+	1.13283i
$624$	−1.77432e7	+	1.77432e7i	−0.0730259	+	0.0730259i
$625$	−2.35879e8			−0.966159
$626$	2.65010e8	+	2.65010e8i	1.08029	+	1.08029i
$627$	−9.54364e7	+	9.54364e7i	−0.387179	+	0.387179i
$628$	−4.16996e7	−	4.16996e7i	−0.168365	−	0.168365i
$629$	3.00989e8			1.20948
$630$	1.21957e8	+	1.21957e8i	0.487738	+	0.487738i
$631$			2.95675e8i			1.17686i	0.808547	+	0.588431i	$0.200254\pi$
$631$			2.95675e8i			1.17686i	−0.808547	+	0.588431i	$0.799746\pi$
$632$	1.29910e8			0.514625
$633$	1.08765e8			0.428823
$634$	−2.97454e8			−1.16722
$635$	2.94293e8	−	2.94293e8i	1.14937	−	1.14937i
$636$	−2.11039e7	+	2.11039e7i	−0.0820333	+	0.0820333i
$637$			2.04675e7i			0.0791855i
$638$	−2.04531e8	+	4.12960e7i	−0.787586	+	0.159018i
$639$	−2.34654e7			−0.0899341
$640$	−6.06536e7	−	6.06536e7i	−0.231375	−	0.231375i
$641$	−2.66857e8	−	2.66857e8i	−1.01322	−	1.01322i	−0.999911	−	0.0133118i	$-0.995763\pi$
$641$	−2.66857e8	−	2.66857e8i	−1.01322	−	1.01322i	−0.0133118	−	0.999911i	$-0.504237\pi$
$642$		−	7.50197e6i		−	0.0283511i
$643$		−	1.03211e8i		−	0.388232i	−0.980979	−	0.194116i	$-0.937816\pi$
$643$		−	1.03211e8i		−	0.388232i	0.980979	−	0.194116i	$-0.0621838\pi$
$644$		−	5.62644e7i		−	0.210657i
$645$	−6.04891e7			−0.225423
$646$	4.69994e8	−	4.69994e8i	1.74339	−	1.74339i
$647$		−	2.36248e8i		−	0.872277i	−0.899880	−	0.436139i	$-0.856346\pi$
$647$		−	2.36248e8i		−	0.872277i	0.899880	−	0.436139i	$-0.143654\pi$
$648$	−1.52301e8	+	1.52301e8i	−0.559729	+	0.559729i
$649$	−1.21921e8	−	1.21921e8i	−0.446009	−	0.446009i
$650$	2.95368e6	−	2.95368e6i	0.0107553	−	0.0107553i
$651$			8.14525e7i			0.295231i
$652$	3.22287e7	+	3.22287e7i	0.116279	+	0.116279i
$653$	−1.01983e8	+	1.01983e8i	−0.366258	+	0.366258i	−0.866110	−	0.499853i	$-0.833388\pi$
$653$	−1.01983e8	+	1.01983e8i	−0.366258	+	0.366258i	0.499853	+	0.866110i	$0.333388\pi$
$654$	−2.87384e6			−0.0102738
$655$	1.61645e8	+	1.61645e8i	0.575224	+	0.575224i
$656$	1.87798e8	−	1.87798e8i	0.665241	−	0.665241i
$657$	1.18031e8	+	1.18031e8i	0.416199	+	0.416199i
$658$	−2.34472e8			−0.823027
$659$	−6.77905e7	−	6.77905e7i	−0.236871	−	0.236871i	0.578682	−	0.815553i	$-0.303567\pi$
$659$	−6.77905e7	−	6.77905e7i	−0.236871	−	0.236871i	−0.815553	+	0.578682i	$0.803567\pi$
$660$			2.50938e7i			0.0872840i
$661$	−1.55112e8			−0.537082			−0.268541	−	0.963268i	$-0.586542\pi$
$661$	−1.55112e8			−0.537082			−0.268541	+	0.963268i	$0.586542\pi$
$662$	−2.83293e8			−0.976476
$663$	−7.85597e7			−0.269562
$664$	5.40419e7	−	5.40419e7i	0.184598	−	0.184598i
$665$	3.52361e8	−	3.52361e8i	1.19818	−	1.19818i
$666$		−	1.70676e8i		−	0.577763i
$667$	−4.43007e7	−	2.19413e8i	−0.149291	−	0.739409i
$668$	−3.26430e7			−0.109512
$669$	−3.60507e7	−	3.60507e7i	−0.120403	−	0.120403i
$670$	9.11159e7	+	9.11159e7i	0.302949	+	0.302949i
$671$			3.65497e8i			1.20981i
$672$		−	4.98934e7i		−	0.164413i
$673$		−	3.29039e8i		−	1.07945i	−0.841842	−	0.539724i	$-0.818529\pi$
$673$		−	3.29039e8i		−	1.07945i	0.841842	−	0.539724i	$-0.181471\pi$
$674$	2.46086e8			0.803723
$675$	−4.15788e6	+	4.15788e6i	−0.0135195	+	0.0135195i
$676$		−	6.44222e7i		−	0.208543i
$677$	3.24538e8	−	3.24538e8i	1.04592	−	1.04592i	0.0470301	−	0.998893i	$-0.485024\pi$
$677$	3.24538e8	−	3.24538e8i	1.04592	−	1.04592i	0.998893	−	0.0470301i	$-0.0149757\pi$
$678$	4.00872e7	+	4.00872e7i	0.128622	+	0.128622i
$679$	−1.07629e8	+	1.07629e8i	−0.343810	+	0.343810i
$680$		−	5.33340e8i		−	1.69620i
$681$	−9.89640e7	−	9.89640e7i	−0.313354	−	0.313354i
$682$	−1.87731e8	+	1.87731e8i	−0.591810	+	0.591810i
$683$	1.57703e8			0.494968			0.247484	−	0.968892i	$-0.420396\pi$
$683$	1.57703e8			0.494968			0.247484	+	0.968892i	$0.420396\pi$
$684$	1.15084e8	+	1.15084e8i	0.359623	+	0.359623i
$685$	−1.73707e8	+	1.73707e8i	−0.540439	+	0.540439i
$686$	2.01834e8	+	2.01834e8i	0.625205	+	0.625205i
$687$	−1.23248e8			−0.380111
$688$	1.04752e8	+	1.04752e8i	0.321659	+	0.321659i
$689$		−	2.28324e8i		−	0.698061i
$690$	6.23401e7			0.189767
$691$	−5.94101e8			−1.80064			−0.900318	−	0.435232i	$-0.856666\pi$
$691$	−5.94101e8			−1.80064			−0.900318	+	0.435232i	$0.856666\pi$
$692$	5.55742e7			0.167709
$693$	−1.89882e8	+	1.89882e8i	−0.570536	+	0.570536i
$694$	2.54006e8	−	2.54006e8i	0.759915	−	0.759915i
$695$			3.34392e8i			0.996098i
$696$	−2.22160e7	−	1.10032e8i	−0.0658929	−	0.326355i
$697$	8.31493e8			2.45562
$698$	9.80836e6	+	9.80836e6i	0.0288423	+	0.0288423i
$699$	4.34448e7	+	4.34448e7i	0.127206	+	0.127206i
$700$			3.13872e6i			0.00915079i
$701$		−	5.56425e8i		−	1.61530i	−0.589664	−	0.807649i	$-0.700740\pi$
$701$		−	5.56425e8i		−	1.61530i	0.589664	−	0.807649i	$-0.299260\pi$
$702$			9.36997e7i			0.270849i
$703$	−4.93120e8			−1.41934
$704$	2.59085e8	−	2.59085e8i	0.742547	−	0.742547i
$705$			1.12183e8i			0.320155i
$706$	1.88731e8	−	1.88731e8i	0.536325	−	0.536325i
$707$	−5.97945e7	−	5.97945e7i	−0.169201	−	0.169201i
$708$	1.51976e7	−	1.51976e7i	0.0428229	−	0.0428229i
$709$			2.48941e8i			0.698485i	0.937032	+	0.349242i	$0.113561\pi$
$709$			2.48941e8i			0.698485i	−0.937032	+	0.349242i	$0.886439\pi$
$710$	−2.06408e7	−	2.06408e7i	−0.0576703	−	0.0576703i
$711$	1.08977e8	−	1.08977e8i	0.303197	−	0.303197i
$712$	−6.79281e8			−1.88196
$713$	−2.01390e8	−	2.01390e8i	−0.555609	−	0.555609i
$714$	−9.66622e7	+	9.66622e7i	−0.265560	+	0.265560i
$715$	−1.35746e8	−	1.35746e8i	−0.371371	−	0.371371i
$716$	2.02090e8			0.550562
$717$	582367.	+	582367.i	0.00157994	+	0.00157994i
$718$			5.50553e8i			1.48739i
$719$	1.64413e8			0.442333			0.221167	−	0.975236i	$-0.429014\pi$
$719$	1.64413e8			0.442333			0.221167	+	0.975236i	$0.429014\pi$
$720$	−2.02096e8			−0.541452
$721$	2.28678e8			0.610125
$722$	−5.47597e8	+	5.47597e8i	−1.45496	+	1.45496i
$723$	1.21539e8	−	1.21539e8i	0.321588	−	0.321588i
$724$			1.77353e8i			0.467329i
$725$	2.47132e6	+	1.22400e7i	0.00648509	+	0.0321194i
$726$	−7.40474e6			−0.0193508
$727$	1.30815e8	+	1.30815e8i	0.340450	+	0.340450i	0.856536	−	0.516086i	$-0.172612\pi$
$727$	1.30815e8	+	1.30815e8i	0.340450	+	0.340450i	−0.516086	+	0.856536i	$0.672612\pi$
$728$	1.52633e8	+	1.52633e8i	0.395598	+	0.395598i
$729$			1.86329e8i			0.480947i
$730$			2.07648e8i			0.533775i
$731$			4.63799e8i			1.18735i
$732$	−4.55598e7			−0.116158
$733$	2.16552e8	−	2.16552e8i	0.549859	−	0.549859i	−0.376541	−	0.926400i	$-0.622887\pi$
$733$	2.16552e8	−	2.16552e8i	0.549859	−	0.549859i	0.926400	+	0.376541i	$0.122887\pi$
$734$			3.81047e8i			0.963585i
$735$	1.20492e7	−	1.20492e7i	0.0303455	−	0.0303455i
$736$	1.23361e8	+	1.23361e8i	0.309416	+	0.309416i
$737$	−1.41863e8	+	1.41863e8i	−0.354378	+	0.354378i
$738$		−	4.71500e8i		−	1.17304i
$739$	1.56149e8	+	1.56149e8i	0.386906	+	0.386906i	0.873582	−	0.486676i	$-0.161791\pi$
$739$	1.56149e8	+	1.56149e8i	0.386906	+	0.386906i	−0.486676	+	0.873582i	$0.661791\pi$
$740$	−6.48298e7	+	6.48298e7i	−0.159985	+	0.159985i
$741$	1.28707e8			0.316335
$742$	−2.80937e8	−	2.80937e8i	−0.687696	−	0.687696i
$743$	−4.19241e8	+	4.19241e8i	−1.02211	+	1.02211i	−0.0223596	+	0.999750i	$0.507118\pi$
$743$	−4.19241e8	+	4.19241e8i	−1.02211	+	1.02211i	−0.999750	+	0.0223596i	$0.992882\pi$
$744$	−1.00994e8	−	1.00994e8i	−0.245231	−	0.245231i
$745$	1.41364e8			0.341877
$746$	1.70720e8	+	1.70720e8i	0.411215	+	0.411215i
$747$		−	9.06677e7i		−	0.217516i
$748$	1.92406e8			0.459742
$749$	−4.31244e7			−0.102631
$750$	−1.09609e8			−0.259813
$751$	2.21530e8	−	2.21530e8i	0.523013	−	0.523013i	−0.395467	−	0.918480i	$-0.629417\pi$
$751$	2.21530e8	−	2.21530e8i	0.523013	−	0.523013i	0.918480	+	0.395467i	$0.129417\pi$
$752$	1.94273e8	−	1.94273e8i	0.456833	−	0.456833i
$753$			8.19480e7i			0.191935i
$754$	1.65763e8	+	1.10071e8i	0.386700	+	0.256778i
$755$	−4.58352e8			−1.06502
$756$	−4.97848e7	−	4.97848e7i	−0.115221	−	0.115221i
$757$	−8.73073e7	−	8.73073e7i	−0.201263	−	0.201263i	0.599278	−	0.800541i	$-0.295454\pi$
$757$	−8.73073e7	−	8.73073e7i	−0.201263	−	0.201263i	−0.800541	+	0.599278i	$0.795454\pi$
$758$			6.84238e8i			1.57109i
$759$			9.70604e7i			0.221982i
$760$			8.73789e8i			1.99052i
$761$	2.33723e8			0.530331			0.265166	−	0.964203i	$-0.414573\pi$
$761$	2.33723e8			0.530331			0.265166	+	0.964203i	$0.414573\pi$
$762$	1.32267e8	−	1.32267e8i	0.298942	−	0.298942i
$763$			1.65200e7i			0.0371909i
$764$	1.58408e8	−	1.58408e8i	0.355219	−	0.355219i
$765$	−4.47400e8	−	4.47400e8i	−0.999337	−	0.999337i
$766$	2.45529e8	−	2.45529e8i	0.546281	−	0.546281i
$767$			1.64424e8i			0.364401i
$768$	7.98244e7	+	7.98244e7i	0.176219	+	0.176219i
$769$	−5.27012e7	+	5.27012e7i	−0.115889	+	0.115889i	−0.762673	−	0.646784i	$-0.776113\pi$
$769$	−5.27012e7	+	5.27012e7i	−0.115889	+	0.115889i	0.646784	+	0.762673i	$0.276113\pi$
$770$	−3.34051e8			−0.731713
$771$	−6.30309e7	−	6.30309e7i	−0.137528	−	0.137528i
$772$	1.53239e8	−	1.53239e8i	0.333056	−	0.333056i
$773$	−2.72290e8	−	2.72290e8i	−0.589513	−	0.589513i	0.347986	−	0.937500i	$-0.386866\pi$
$773$	−2.72290e8	−	2.72290e8i	−0.589513	−	0.589513i	−0.937500	+	0.347986i	$0.886866\pi$
$774$	2.62998e8			0.567192
$775$	1.12346e7	+	1.12346e7i	0.0241353	+	0.0241353i
$776$		−	2.66899e8i		−	0.571165i
$777$	1.01418e8			0.216199
$778$	1.04090e8			0.221040
$779$	−1.36226e9			−2.88170
$780$	1.69209e7	−	1.69209e7i	0.0356566	−	0.0356566i
$781$	3.21368e7	−	3.21368e7i	0.0674605	−	0.0674605i
$782$		−	4.77991e8i		−	0.999539i
$783$	−2.33344e8	−	1.54946e8i	−0.486083	−	0.322771i
$784$	−4.17321e7			−0.0866009
$785$	−2.65591e8	−	2.65591e8i	−0.549041	−	0.549041i
$786$	7.26495e7	+	7.26495e7i	0.149612	+	0.149612i
$787$			1.80049e8i			0.369375i	0.982797	+	0.184688i	$0.0591273\pi$
$787$			1.80049e8i			0.369375i	−0.982797	+	0.184688i	$0.940873\pi$
$788$		−	7.12755e7i		−	0.145667i
$789$			1.27818e8i			0.260232i
$790$	1.91719e8			0.388851
$791$	2.30438e8	−	2.30438e8i	0.465612	−	0.465612i
$792$		−	4.70871e8i		−	0.947821i
$793$	2.46457e8	−	2.46457e8i	0.494222	−	0.494222i
$794$	1.63971e7	+	1.63971e7i	0.0327571	+	0.0327571i
$795$	−1.34414e8	+	1.34414e8i	−0.267511	+	0.267511i
$796$			5.75306e7i			0.114067i
$797$	5.83366e8	+	5.83366e8i	1.15230	+	1.15230i	0.986090	+	0.166211i	$0.0531533\pi$
$797$	5.83366e8	+	5.83366e8i	1.15230	+	1.15230i	0.166211	+	0.986090i	$0.446847\pi$
$798$	1.58365e8	−	1.58365e8i	0.311638	−	0.311638i
$799$	8.60162e8			1.68632
$800$	−6.88170e6	−	6.88170e6i	−0.0134408	−	0.0134408i
$801$	−5.69825e8	+	5.69825e8i	−1.10878	+	1.10878i
$802$	−3.04333e8	−	3.04333e8i	−0.589964	−	0.589964i
$803$	−3.23297e8			−0.624389
$804$	−1.76835e7	−	1.76835e7i	−0.0340251	−	0.0340251i
$805$		−	3.58357e8i		−	0.686954i
$806$	2.53176e8			0.483524
$807$	2.38417e8			0.453645
$808$	1.48279e8			0.281091
$809$	2.71347e8	−	2.71347e8i	0.512484	−	0.512484i	−0.402803	−	0.915287i	$-0.631964\pi$
$809$	2.71347e8	−	2.71347e8i	0.512484	−	0.512484i	0.915287	+	0.402803i	$0.131964\pi$
$810$	−2.24763e8	+	2.24763e8i	−0.422932	+	0.422932i
$811$		−	5.07416e8i		−	0.951265i	−0.879644	−	0.475633i	$-0.842219\pi$
$811$		−	5.07416e8i		−	0.951265i	0.879644	−	0.475633i	$-0.157781\pi$
$812$	−1.46557e8	+	2.95906e7i	−0.273740	+	0.0552696i
$813$	5.49553e7			0.102268
$814$	2.33748e8	+	2.33748e8i	0.433386	+	0.433386i
$815$	2.05270e8	+	2.05270e8i	0.379186	+	0.379186i
$816$		−	1.60179e8i		−	0.294806i
$817$		−	7.59857e8i		−	1.39337i
$818$		−	3.02622e8i		−	0.552893i
$819$	2.56077e8			0.466143
$820$	−1.79095e8	+	1.79095e8i	−0.324819	+	0.324819i
$821$		−	2.70076e8i		−	0.488042i	−0.969770	−	0.244021i	$-0.921533\pi$
$821$		−	2.70076e8i		−	0.488042i	0.969770	−	0.244021i	$-0.0784665\pi$
$822$	−7.80711e7	+	7.80711e7i	−0.140564	+	0.140564i
$823$	2.07967e8	+	2.07967e8i	0.373073	+	0.373073i	0.868595	−	0.495522i	$-0.165023\pi$
$823$	2.07967e8	+	2.07967e8i	0.373073	+	0.373073i	−0.495522	+	0.868595i	$0.665023\pi$
$824$	−2.83539e8	+	2.83539e8i	−0.506794	+	0.506794i
$825$		−	5.41454e6i		−	0.00964273i
$826$	2.02312e8	+	2.02312e8i	0.358990	+	0.358990i
$827$	4.02535e8	−	4.02535e8i	0.711685	−	0.711685i	−0.255203	−	0.966888i	$-0.582142\pi$
$827$	4.02535e8	−	4.02535e8i	0.711685	−	0.711685i	0.966888	+	0.255203i	$0.0821423\pi$
$828$	1.17043e8			0.206183
$829$	5.21769e8	+	5.21769e8i	0.915830	+	0.915830i	0.996723	−	0.0808930i	$-0.0257772\pi$
$829$	5.21769e8	+	5.21769e8i	0.915830	+	0.915830i	−0.0808930	+	0.996723i	$0.525777\pi$
$830$	7.97541e7	−	7.97541e7i	0.139482	−	0.139482i
$831$	2.76066e7	+	2.76066e7i	0.0481071	+	0.0481071i
$832$	−3.49405e8			−0.606680
$833$	−9.23867e7	−	9.23867e7i	−0.159836	−	0.159836i
$834$			1.50289e8i			0.259078i
$835$	−2.07909e8			−0.357119
$836$	−3.15226e8			−0.539514
$837$	−3.56395e8			−0.607792
$838$	2.97430e8	−	2.97430e8i	0.505421	−	0.505421i
$839$	−6.48103e7	+	6.48103e7i	−0.109738	+	0.109738i	−0.759844	−	0.650106i	$-0.774725\pi$
$839$	−6.48103e7	+	6.48103e7i	−0.109738	+	0.109738i	0.650106	+	0.759844i	$0.274725\pi$
$840$		−	1.79710e8i		−	0.303203i
$841$	−5.48226e8	+	2.30788e8i	−0.921662	+	0.387994i
$842$	1.12111e8			0.187806
$843$	3.87991e7	+	3.87991e7i	0.0647649	+	0.0647649i
$844$	1.79625e8	+	1.79625e8i	0.298771	+	0.298771i
$845$		−	4.10315e8i		−	0.680060i
$846$		−	4.87756e8i		−	0.805548i
$847$			4.25655e7i			0.0700499i
$848$	4.65541e8			0.763432
$849$	−1.89929e8	+	1.89929e8i	−0.310362	+	0.310362i
$850$			2.66649e7i			0.0434193i
$851$	−2.50755e8	+	2.50755e8i	−0.406876	+	0.406876i
$852$	4.00590e6	+	4.00590e6i	0.00647712	+	0.00647712i
$853$	−4.36163e8	+	4.36163e8i	−0.702751	+	0.702751i	−0.965000	−	0.262249i	$-0.915536\pi$
$853$	−4.36163e8	+	4.36163e8i	−0.702751	+	0.702751i	0.262249	+	0.965000i	$0.415536\pi$
$854$		−	6.06497e8i		−	0.973768i
$855$	7.32991e8	+	7.32991e8i	1.17274	+	1.17274i
$856$	5.34703e7	−	5.34703e7i	0.0852494	−	0.0852494i
$857$	−3.40824e8			−0.541487			−0.270743	−	0.962652i	$-0.587270\pi$
$857$	−3.40824e8			−0.541487			−0.270743	+	0.962652i	$0.587270\pi$
$858$	−6.10095e7	−	6.10095e7i	−0.0965908	−	0.0965908i
$859$	1.70336e8	−	1.70336e8i	0.268737	−	0.268737i	−0.559854	−	0.828591i	$-0.689143\pi$
$859$	1.70336e8	−	1.70336e8i	0.268737	−	0.268737i	0.828591	+	0.559854i	$0.189143\pi$
$860$	−9.98974e7	−	9.98974e7i	−0.157058	−	0.157058i
$861$	2.80173e8			0.438951
$862$	4.79831e8	+	4.79831e8i	0.749145	+	0.749145i
$863$			1.51502e8i			0.235715i	0.993031	+	0.117857i	$0.0376026\pi$
$863$			1.51502e8i			0.235715i	−0.993031	+	0.117857i	$0.962397\pi$
$864$	2.18308e8			0.338477
$865$	3.53961e8			0.546899
$866$	−7.58100e8			−1.16727
$867$	2.13553e8	−	2.13553e8i	0.327679	−	0.327679i
$868$	−1.34518e8	+	1.34518e8i	−0.205694	+	0.205694i
$869$			2.98496e8i			0.454862i
$870$	−3.27860e7	−	1.62383e8i	−0.0497887	−	0.246594i
$871$	1.91318e8			0.289536
$872$	−2.04833e7	−	2.04833e7i	−0.0308923	−	0.0308923i
$873$	−2.23892e8	−	2.23892e8i	−0.336508	−	0.336508i
$874$			7.83109e8i			1.17297i
$875$			6.30077e8i			0.940522i
$876$		−	4.02996e7i		−	0.0599498i
$877$	5.94335e8			0.881114			0.440557	−	0.897725i	$-0.354781\pi$
$877$	5.94335e8			0.881114			0.440557	+	0.897725i	$0.354781\pi$
$878$	1.88963e8	−	1.88963e8i	0.279186	−	0.279186i
$879$			1.29337e8i			0.190440i
$880$	2.76779e8	−	2.76779e8i	0.406148	−	0.406148i
$881$	−4.39837e8	−	4.39837e8i	−0.643226	−	0.643226i	0.308121	−	0.951347i	$-0.400300\pi$
$881$	−4.39837e8	−	4.39837e8i	−0.643226	−	0.643226i	−0.951347	+	0.308121i	$0.900300\pi$
$882$	−5.23880e7	+	5.23880e7i	−0.0763530	+	0.0763530i
$883$		−	8.79699e8i		−	1.27777i	−0.769303	−	0.638884i	$-0.779396\pi$
$883$		−	8.79699e8i		−	1.27777i	0.769303	−	0.638884i	$-0.220604\pi$
$884$	−1.29741e8	−	1.29741e8i	−0.187811	−	0.187811i
$885$	9.67961e7	−	9.67961e7i	0.139646	−	0.139646i
$886$	−7.90582e8			−1.13670
$887$	−1.82146e8	−	1.82146e8i	−0.261005	−	0.261005i	0.564457	−	0.825462i	$-0.309085\pi$
$887$	−1.82146e8	−	1.82146e8i	−0.261005	−	0.261005i	−0.825462	+	0.564457i	$0.809085\pi$
$888$	−1.25749e8	+	1.25749e8i	−0.179584	+	0.179584i
$889$	−7.60326e8	−	7.60326e8i	−1.08217	−	1.08217i
$890$	−1.00247e9			−1.42201
$891$	−3.49945e8	−	3.49945e8i	−0.494729	−	0.494729i
$892$		−	1.19075e8i		−	0.167775i
$893$	−1.40923e9			−1.97892
$894$	6.35346e7			0.0889196
$895$	1.28715e9			1.79539
$896$	−1.56703e8	+	1.56703e8i	−0.217847	+	0.217847i
$897$	6.54485e7	−	6.54485e7i	0.0906823	−	0.0906823i
$898$		−	3.72000e8i		−	0.513705i
$899$	−4.18663e8	+	6.30494e8i	−0.576217	+	0.867765i
$900$	−6.52926e6			−0.00895646
$901$	1.03062e9	+	1.03062e9i	1.40904	+	1.40904i
$902$	6.45739e8	+	6.45739e8i	0.879908	+	0.879908i
$903$			1.56278e8i			0.212243i
$904$			5.71443e8i			0.773513i
$905$			1.12959e9i			1.52396i
$906$	−2.06002e8			−0.277004
$907$	−3.16311e8	+	3.16311e8i	−0.423928	+	0.423928i	−0.886554	−	0.462626i	$-0.846907\pi$
$907$	−3.16311e8	+	3.16311e8i	−0.423928	+	0.423928i	0.462626	+	0.886554i	$0.346907\pi$
$908$		−	3.26877e8i		−	0.436643i
$909$	1.24386e8	−	1.24386e8i	0.165608	−	0.165608i
$910$	2.25253e8	+	2.25253e8i	0.298914	+	0.298914i
$911$	6.46278e8	−	6.46278e8i	0.854799	−	0.854799i	−0.135921	−	0.990720i	$-0.543399\pi$
$911$	6.46278e8	−	6.46278e8i	0.854799	−	0.854799i	0.990720	+	0.135921i	$0.0433992\pi$
$912$			2.62427e8i			0.345959i
$913$	1.24173e8	+	1.24173e8i	0.163161	+	0.163161i
$914$	−2.93552e7	+	2.93552e7i	−0.0384456	+	0.0384456i
$915$	−2.90178e8			−0.378792
$916$	−2.03544e8	−	2.03544e8i	−0.264833	−	0.264833i
$917$	4.17620e8	−	4.17620e8i	0.541593	−	0.541593i
$918$	−4.22945e8	−	4.22945e8i	−0.546708	−	0.546708i
$919$	−1.30309e9			−1.67891			−0.839454	−	0.543430i	$-0.817125\pi$
$919$	−1.30309e9			−1.67891			−0.839454	+	0.543430i	$0.817125\pi$
$920$	4.44329e8	+	4.44329e8i	0.570612	+	0.570612i
$921$			1.68868e8i			0.216157i
$922$	−5.66557e7			−0.0722854
$923$	−4.33401e7			−0.0551169
$924$	6.48315e7			0.0821808
$925$	1.39885e7	−	1.39885e7i	0.0176744	−	0.0176744i
$926$	−2.49160e8	+	2.49160e8i	−0.313794	+	0.313794i
$927$			4.75702e8i			0.597167i
$928$	2.56451e8	−	3.86207e8i	0.320893	−	0.483254i
$929$	3.55521e8			0.443422			0.221711	−	0.975112i	$-0.428836\pi$
$929$	3.55521e8			0.443422			0.221711	+	0.975112i	$0.428836\pi$
$930$	−1.49044e8	−	1.49044e8i	−0.185296	−	0.185296i
$931$	1.51360e8	+	1.51360e8i	0.187570	+	0.187570i
$932$			1.43498e8i			0.177254i
$933$			7.66365e6i			0.00943607i
$934$		−	9.55388e8i		−	1.17257i
$935$	1.22547e9			1.49922
$936$	−3.17512e8	+	3.17512e8i	−0.387197	+	0.387197i
$937$			1.27826e9i			1.55382i	0.629611	+	0.776910i	$0.283214\pi$
$937$			1.27826e9i			1.55382i	−0.629611	+	0.776910i	$0.716786\pi$
$938$	2.35404e8	−	2.35404e8i	0.285237	−	0.285237i
$939$	−3.27579e8	−	3.27579e8i	−0.395658	−	0.395658i
$940$	−1.85270e8	+	1.85270e8i	−0.223060	+	0.223060i
$941$			2.34789e6i			0.00281779i	0.999999	+	0.00140890i	$0.000448465\pi$
$941$			2.34789e6i			0.00281779i	−0.999999	+	0.00140890i	$0.999552\pi$
$942$	−1.19367e8	−	1.19367e8i	−0.142802	−	0.142802i
$943$	−6.92722e8	+	6.92722e8i	−0.826084	+	0.826084i
$944$	−3.35253e8			−0.398526
$945$	−3.17087e8	−	3.17087e8i	−0.375736	−	0.375736i
$946$	−3.60187e8	+	3.60187e8i	−0.425456	+	0.425456i
$947$	6.68762e8	+	6.68762e8i	0.787447	+	0.787447i	0.981075	−	0.193628i	$-0.0620255\pi$
$947$	6.68762e8	+	6.68762e8i	0.787447	+	0.787447i	−0.193628	+	0.981075i	$0.562025\pi$
$948$	−3.72081e7			−0.0436729
$949$	2.18002e8	+	2.18002e8i	0.255071	+	0.255071i
$950$		−	4.36860e7i		−	0.0509531i
$951$	3.67684e8			0.427497
$952$	−1.37792e9			−1.59703
$953$	1.34436e9			1.55323			0.776616	−	0.629974i	$-0.216935\pi$
$953$	1.34436e9			1.55323			0.776616	+	0.629974i	$0.216935\pi$
$954$	5.84412e8	−	5.84412e8i	0.673092	−	0.673092i
$955$	1.00892e9	−	1.00892e9i	1.15837	−	1.15837i
$956$			1.92355e6i			0.00220156i
$957$	2.52822e8	−	5.10462e7i	0.288456	−	0.0582408i
$958$	−7.00833e8			−0.797110
$959$	4.48785e8	+	4.48785e8i	0.508841	+	0.508841i
$960$	2.05694e8	+	2.05694e8i	0.232492	+	0.232492i
$961$			7.54743e7i			0.0850412i
$962$		−	3.15236e8i		−	0.354087i
$963$		−	8.97087e7i		−	0.100451i
$964$	4.01441e8			0.448117
$965$	9.76003e8	−	9.76003e8i	1.08610	−	1.08610i
$966$		−	1.61060e8i		−	0.178672i
$967$	−3.34370e8	+	3.34370e8i	−0.369784	+	0.369784i	−0.867398	−	0.497614i	$-0.834209\pi$
$967$	−3.34370e8	+	3.34370e8i	−0.369784	+	0.369784i	0.497614	+	0.867398i	$0.334209\pi$
$968$	−5.27773e7	−	5.27773e7i	−0.0581863	−	0.0581863i
$969$	−5.80961e8	+	5.80961e8i	−0.638522	+	0.638522i
$970$		−	3.93884e8i		−	0.431572i
$971$	−2.90418e8	−	2.90418e8i	−0.317224	−	0.317224i	0.530476	−	0.847700i	$-0.322013\pi$
$971$	−2.90418e8	−	2.90418e8i	−0.317224	−	0.317224i	−0.847700	+	0.530476i	$0.822013\pi$
$972$	1.57890e8	−	1.57890e8i	0.171932	−	0.171932i
$973$	8.63925e8			0.937859
$974$	1.23465e8	+	1.23465e8i	0.133618	+	0.133618i
$975$	−3.65106e6	+	3.65106e6i	−0.00393918	+	0.00393918i
$976$	5.02514e8	+	5.02514e8i	0.540504	+	0.540504i
$977$	−7.77146e8			−0.833334			−0.416667	−	0.909059i	$-0.636802\pi$
$977$	−7.77146e8			−0.833334			−0.416667	+	0.909059i	$0.636802\pi$
$978$	9.22565e7	+	9.22565e7i	0.0986235	+	0.0986235i
$979$		−	1.56080e9i		−	1.66341i
$980$	3.97982e7			0.0422849
$981$	−3.43654e7			−0.0364011
$982$	−5.03474e7			−0.0531671
$983$	2.17651e8	−	2.17651e8i	0.229140	−	0.229140i	−0.583194	−	0.812333i	$-0.698197\pi$
$983$	2.17651e8	−	2.17651e8i	0.229140	−	0.229140i	0.812333	+	0.583194i	$0.198197\pi$
$984$	−3.47388e8	+	3.47388e8i	−0.364611	+	0.364611i
$985$		−	4.53965e8i		−	0.475022i
$986$	−1.24507e9	+	2.51386e8i	−1.29886	+	0.262247i
$987$	2.89832e8			0.301436
$988$	2.12559e8	+	2.12559e8i	0.220398	+	0.220398i
$989$	−3.86394e8	−	3.86394e8i	−0.399431	−	0.399431i
$990$		−	6.94903e8i		−	0.716174i
$991$		−	1.57898e9i		−	1.62239i	−0.584774	−	0.811196i	$-0.698817\pi$
$991$		−	1.57898e9i		−	1.62239i	0.584774	−	0.811196i	$-0.301183\pi$
$992$		−	5.89868e8i		−	0.604255i
$993$	3.50180e8			0.357638
$994$	−5.33270e7	+	5.33270e7i	−0.0542985	+	0.0542985i
$995$			3.66422e8i			0.371974i
$996$	−1.54784e7	+	1.54784e7i	−0.0156656	+	0.0156656i
$997$	−6.50839e8	−	6.50839e8i	−0.656731	−	0.656731i	0.297874	−	0.954605i	$-0.403723\pi$
$997$	−6.50839e8	−	6.50839e8i	−0.656731	−	0.656731i	−0.954605	+	0.297874i	$0.903723\pi$
$998$	7.98227e7	−	7.98227e7i	0.0803036	−	0.0803036i
$999$			4.43755e8i			0.445089i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.7.c.a.12.10	✓	28
29.17	odd	4	inner	29.7.c.a.17.10	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.7.c.a.12.10	✓	28	1.1	even	1	trivial
29.7.c.a.17.10	yes	28	29.17	odd	4	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:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.72749 + 4.72749i) q^{2} +(-5.84368 - 5.84368i) q^{3} -19.3016i q^{4} -122.935i q^{5} -55.2519i q^{6} -317.611 q^{7} +(393.808 - 393.808i) q^{8} -660.703i q^{9} +O(q^{10})\)	\(q+(4.72749 + 4.72749i) q^{2} +(-5.84368 - 5.84368i) q^{3} -19.3016i q^{4} -122.935i q^{5} -55.2519i q^{6} -317.611 q^{7} +(393.808 - 393.808i) q^{8} -660.703i q^{9} +(581.174 - 581.174i) q^{10} +(904.860 + 904.860i) q^{11} +(-112.792 + 112.792i) q^{12} -1220.31i q^{13} +(-1501.50 - 1501.50i) q^{14} +(-718.392 + 718.392i) q^{15} +2488.15 q^{16} +(5508.26 + 5508.26i) q^{17} +(3123.47 - 3123.47i) q^{18} +(-9024.37 - 9024.37i) q^{19} -2372.84 q^{20} +(1856.01 + 1856.01i) q^{21} +8555.44i q^{22} -9177.93 q^{23} -4602.57 q^{24} +511.993 q^{25} +(5768.99 - 5768.99i) q^{26} +(-8120.97 + 8120.97i) q^{27} +6130.40i q^{28} +(4826.87 + 23906.6i) q^{29} -6792.39 q^{30} +(21942.9 + 21942.9i) q^{31} +(-13441.0 - 13441.0i) q^{32} -10575.4i q^{33} +52080.5i q^{34} +39045.5i q^{35} -12752.6 q^{36} +(27321.6 - 27321.6i) q^{37} -85325.3i q^{38} +(-7131.08 + 7131.08i) q^{39} +(-48412.8 - 48412.8i) q^{40} +(75477.0 - 75477.0i) q^{41} +17548.6i q^{42} +(42100.3 + 42100.3i) q^{43} +(17465.2 - 17465.2i) q^{44} -81223.5 q^{45} +(-43388.6 - 43388.6i) q^{46} +(78079.2 - 78079.2i) q^{47} +(-14539.9 - 14539.9i) q^{48} -16772.4 q^{49} +(2420.44 + 2420.44i) q^{50} -64377.0i q^{51} -23553.9 q^{52} +187104. q^{53} -76783.7 q^{54} +(111239. - 111239. i) q^{55} +(-125078. + 125078. i) q^{56} +105471. i q^{57} +(-90199.2 + 135837. i) q^{58} -134740. q^{59} +(13866.1 + 13866.1i) q^{60} +(201963. + 201963. i) q^{61} +207469. i q^{62} +209846. i q^{63} -286326. i q^{64} -150018. q^{65} +(49995.2 - 49995.2i) q^{66} +156779. i q^{67} +(106318. - 106318. i) q^{68} +(53632.8 + 53632.8i) q^{69} +(-184587. + 184587. i) q^{70} -35515.7i q^{71} +(-260190. - 260190. i) q^{72} +(-178645. + 178645. i) q^{73} +258325. q^{74} +(-2991.92 - 2991.92i) q^{75} +(-174185. + 174185. i) q^{76} +(-287393. - 287393. i) q^{77} -67424.3 q^{78} +(164941. + 164941. i) q^{79} -305880. i q^{80} -386740. q^{81} +713634. q^{82} +137229. q^{83} +(35824.1 - 35824.1i) q^{84} +(677158. - 677158. i) q^{85} +398058. i q^{86} +(111496. - 167909. i) q^{87} +712682. q^{88} +(-862453. - 862453. i) q^{89} +(-383984. - 383984. i) q^{90} +387583. i q^{91} +177149. i q^{92} -256454. i q^{93} +738238. q^{94} +(-1.10941e6 + 1.10941e6i) q^{95} +157090. i q^{96} +(338869. - 338869. i) q^{97} +(-79291.4 - 79291.4i) q^{98} +(597844. - 597844. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8}+O(q^{10}) \) 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8	\( 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8} - 3714 q^{10} + 1934 q^{11} - 2706 q^{12} + 2648 q^{14} + 16280 q^{15} - 36632 q^{16} - 5236 q^{17} + 5258 q^{18} + 6718 q^{19} + 24828 q^{20} + 7380 q^{21} - 21524 q^{23} + 90648 q^{24} - 73196 q^{25} - 5394 q^{26} + 5824 q^{27} - 12510 q^{29} - 1780 q^{30} + 1150 q^{31} + 104646 q^{32} - 32904 q^{36} - 256832 q^{37} + 127752 q^{39} - 256374 q^{40} + 265716 q^{41} + 80590 q^{43} + 188482 q^{44} - 78008 q^{45} + 405572 q^{46} - 445250 q^{47} - 1016886 q^{48} + 532764 q^{49} - 80230 q^{50} + 619608 q^{52} + 143428 q^{53} + 373816 q^{54} - 533304 q^{55} - 619392 q^{56} + 326848 q^{58} - 957340 q^{59} + 1790622 q^{60} - 115640 q^{61} - 643584 q^{65} - 1821654 q^{66} + 1457028 q^{68} - 1049340 q^{69} + 3024084 q^{70} + 1480560 q^{72} - 627512 q^{73} - 3652060 q^{74} + 586518 q^{75} - 1343752 q^{76} - 115820 q^{77} + 1820304 q^{78} + 235966 q^{79} + 2710496 q^{81} + 796544 q^{82} + 3881892 q^{83} + 219332 q^{84} - 3064608 q^{85} + 900526 q^{87} - 9844332 q^{88} + 3821436 q^{89} - 4192912 q^{90} - 648556 q^{94} - 620200 q^{95} - 620288 q^{97} + 4735296 q^{98} + 4021770 q^{99}+O(q^{100}) \) 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8 - 3714 * q^10 + 1934 * q^11 - 2706 * q^12 + 2648 * q^14 + 16280 * q^15 - 36632 * q^16 - 5236 * q^17 + 5258 * q^18 + 6718 * q^19 + 24828 * q^20 + 7380 * q^21 - 21524 * q^23 + 90648 * q^24 - 73196 * q^25 - 5394 * q^26 + 5824 * q^27 - 12510 * q^29 - 1780 * q^30 + 1150 * q^31 + 104646 * q^32 - 32904 * q^36 - 256832 * q^37 + 127752 * q^39 - 256374 * q^40 + 265716 * q^41 + 80590 * q^43 + 188482 * q^44 - 78008 * q^45 + 405572 * q^46 - 445250 * q^47 - 1016886 * q^48 + 532764 * q^49 - 80230 * q^50 + 619608 * q^52 + 143428 * q^53 + 373816 * q^54 - 533304 * q^55 - 619392 * q^56 + 326848 * q^58 - 957340 * q^59 + 1790622 * q^60 - 115640 * q^61 - 643584 * q^65 - 1821654 * q^66 + 1457028 * q^68 - 1049340 * q^69 + 3024084 * q^70 + 1480560 * q^72 - 627512 * q^73 - 3652060 * q^74 + 586518 * q^75 - 1343752 * q^76 - 115820 * q^77 + 1820304 * q^78 + 235966 * q^79 + 2710496 * q^81 + 796544 * q^82 + 3881892 * q^83 + 219332 * q^84 - 3064608 * q^85 + 900526 * q^87 - 9844332 * q^88 + 3821436 * q^89 - 4192912 * q^90 - 648556 * q^94 - 620200 * q^95 - 620288 * q^97 + 4735296 * q^98 + 4021770 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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