LMFDB - Embedded newform 354.2.e.c.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, 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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$3$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			121.1
Character	$\chi$	$=$	354.121
Dual form			354.2.e.c.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.907575 - 0.419889i) q^{2} +(0.947653 + 0.319302i) q^{3} +(0.647386 - 0.762162i) q^{4} +(-2.35642 - 1.41781i) q^{5} +(0.994138 - 0.108119i) q^{6} +(0.260327 - 4.80144i) q^{7} +(0.267528 - 0.963550i) q^{8} +(0.796093 + 0.605174i) q^{9} +O(q^{10})$	\(q+(0.907575 - 0.419889i) q^{2} +(0.947653 + 0.319302i) q^{3} +(0.647386 - 0.762162i) q^{4} +(-2.35642 - 1.41781i) q^{5} +(0.994138 - 0.108119i) q^{6} +(0.260327 - 4.80144i) q^{7} +(0.267528 - 0.963550i) q^{8} +(0.796093 + 0.605174i) q^{9} +(-2.73396 - 0.297336i) q^{10} +(-0.0646256 + 0.394199i) q^{11} +(0.856857 - 0.515554i) q^{12} +(-0.265479 + 0.201812i) q^{13} +(-1.77981 - 4.46698i) q^{14} +(-1.78036 - 2.09601i) q^{15} +(-0.161782 - 0.986827i) q^{16} +(0.335166 + 6.18178i) q^{17} +(0.976621 + 0.214970i) q^{18} +(2.11735 - 2.00566i) q^{19} +(-2.60612 + 0.878104i) q^{20} +(1.77981 - 4.46698i) q^{21} +(0.106867 + 0.384901i) q^{22} +(1.98573 - 0.437093i) q^{23} +(0.561187 - 0.827689i) q^{24} +(1.20050 + 2.26438i) q^{25} +(-0.156203 + 0.294631i) q^{26} +(0.561187 + 0.827689i) q^{27} +(-3.49095 - 3.30680i) q^{28} +(7.13200 + 3.29962i) q^{29} +(-2.49590 - 1.15473i) q^{30} +(1.64829 + 1.56134i) q^{31} +(-0.561187 - 0.827689i) q^{32} +(-0.187111 + 0.352929i) q^{33} +(2.89985 + 5.46970i) q^{34} +(-7.42099 + 10.9451i) q^{35} +(0.976621 - 0.214970i) q^{36} +(-1.48398 - 5.34480i) q^{37} +(1.07950 - 2.70934i) q^{38} +(-0.316020 + 0.106480i) q^{39} +(-1.99654 + 1.89123i) q^{40} +(7.16970 + 1.57817i) q^{41} +(-0.260327 - 4.80144i) q^{42} +(1.70788 + 10.4176i) q^{43} +(0.258606 + 0.304454i) q^{44} +(-1.01791 - 2.55476i) q^{45} +(1.61867 - 1.23048i) q^{46} +(-2.53319 + 1.52417i) q^{47} +(0.161782 - 0.986827i) q^{48} +(-16.0271 - 1.74305i) q^{49} +(2.04033 + 1.55102i) q^{50} +(-1.65623 + 5.96520i) q^{51} +(-0.0180541 + 0.332988i) q^{52} +(-5.20304 + 0.565865i) q^{53} +(0.856857 + 0.515554i) q^{54} +(0.711186 - 0.837272i) q^{55} +(-4.55678 - 1.53536i) q^{56} +(2.64692 - 1.22460i) q^{57} +7.85830 q^{58} +(-5.19674 - 5.65632i) q^{59} -2.75008 q^{60} +(-6.26975 + 2.90069i) q^{61} +(2.15154 + 0.724937i) q^{62} +(3.11295 - 3.66485i) q^{63} +(-0.856857 - 0.515554i) q^{64} +(0.911712 - 0.0991546i) q^{65} +(-0.0216264 + 0.398875i) q^{66} +(3.04568 - 10.9695i) q^{67} +(4.92850 + 3.74655i) q^{68} +(2.02135 + 0.219835i) q^{69} +(-2.13936 + 13.0495i) q^{70} +(1.34623 - 0.810002i) q^{71} +(0.796093 - 0.605174i) q^{72} +(3.49566 + 8.77343i) q^{73} +(-3.59104 - 4.22770i) q^{74} +(0.414636 + 2.52917i) q^{75} +(-0.157895 - 2.91220i) q^{76} +(1.87590 + 0.412916i) q^{77} +(-0.242103 + 0.229332i) q^{78} +(10.7133 - 3.60972i) q^{79} +(-1.01791 + 2.55476i) q^{80} +(0.267528 + 0.963550i) q^{81} +(7.16970 - 1.57817i) q^{82} +(-7.76998 + 11.4599i) q^{83} +(-2.25234 - 4.24836i) q^{84} +(7.97482 - 15.0421i) q^{85} +(5.92427 + 8.73764i) q^{86} +(5.70509 + 5.40415i) q^{87} +(0.362541 + 0.167729i) q^{88} +(-10.8555 - 5.02227i) q^{89} +(-1.99654 - 1.89123i) q^{90} +(0.899876 + 1.32722i) q^{91} +(0.952400 - 1.79642i) q^{92} +(1.06347 + 2.00591i) q^{93} +(-1.65908 + 2.44696i) q^{94} +(-7.83303 + 1.72418i) q^{95} +(-0.267528 - 0.963550i) q^{96} +(1.82065 - 4.56949i) q^{97} +(-15.2777 + 5.14766i) q^{98} +(-0.290007 + 0.274709i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9	$ 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9} - 26 q^{11} + 3 q^{12} - 3 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} - 3 q^{18} + 4 q^{19} - q^{21} + 3 q^{22} - 2 q^{23} + 3 q^{24} + 41 q^{25} + 26 q^{26} + 3 q^{27} + q^{28} - 2 q^{29} + 8 q^{31} - 3 q^{32} - 3 q^{33} - 26 q^{34} + 83 q^{35} - 3 q^{36} - 53 q^{37} + 4 q^{38} + 3 q^{39} - 7 q^{41} - q^{42} + 119 q^{43} + 3 q^{44} - 31 q^{46} - 12 q^{47} + 3 q^{48} - 38 q^{49} - 133 q^{50} - 3 q^{51} - 32 q^{52} - 83 q^{53} + 3 q^{54} - 83 q^{55} + q^{56} - 4 q^{57} + 56 q^{58} - 57 q^{59} - 48 q^{61} - 21 q^{62} + q^{63} - 3 q^{64} - 33 q^{65} - 3 q^{66} - 88 q^{67} - 26 q^{68} + 89 q^{69} - 62 q^{70} - 35 q^{71} - 3 q^{72} - 71 q^{73} - 24 q^{74} + 17 q^{75} + 33 q^{76} + 113 q^{77} + 3 q^{78} - 5 q^{79} - 3 q^{81} - 7 q^{82} - 51 q^{83} - q^{84} + 125 q^{85} + 61 q^{86} + 31 q^{87} + 32 q^{88} - 58 q^{89} + 173 q^{91} - 2 q^{92} + 21 q^{93} + 17 q^{94} + 26 q^{95} + 3 q^{96} + 20 q^{98} + 3 q^{99}+O(q^{100}) $ 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9 - 26 * q^11 + 3 * q^12 - 3 * q^13 + q^14 - 3 * q^16 + 3 * q^17 - 3 * q^18 + 4 * q^19 - q^21 + 3 * q^22 - 2 * q^23 + 3 * q^24 + 41 * q^25 + 26 * q^26 + 3 * q^27 + q^28 - 2 * q^29 + 8 * q^31 - 3 * q^32 - 3 * q^33 - 26 * q^34 + 83 * q^35 - 3 * q^36 - 53 * q^37 + 4 * q^38 + 3 * q^39 - 7 * q^41 - q^42 + 119 * q^43 + 3 * q^44 - 31 * q^46 - 12 * q^47 + 3 * q^48 - 38 * q^49 - 133 * q^50 - 3 * q^51 - 32 * q^52 - 83 * q^53 + 3 * q^54 - 83 * q^55 + q^56 - 4 * q^57 + 56 * q^58 - 57 * q^59 - 48 * q^61 - 21 * q^62 + q^63 - 3 * q^64 - 33 * q^65 - 3 * q^66 - 88 * q^67 - 26 * q^68 + 89 * q^69 - 62 * q^70 - 35 * q^71 - 3 * q^72 - 71 * q^73 - 24 * q^74 + 17 * q^75 + 33 * q^76 + 113 * q^77 + 3 * q^78 - 5 * q^79 - 3 * q^81 - 7 * q^82 - 51 * q^83 - q^84 + 125 * q^85 + 61 * q^86 + 31 * q^87 + 32 * q^88 - 58 * q^89 + 173 * q^91 - 2 * q^92 + 21 * q^93 + 17 * q^94 + 26 * q^95 + 3 * q^96 + 20 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{25}{29}\right)$	$1$

Coefficient data

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

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

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

$2$	0.907575	−	0.419889i	0.641753	−	0.296906i
$2$	0.907575	−	0.419889i	0.641753	−	0.296906i
$3$	0.947653	+	0.319302i	0.547128	+	0.184349i
$3$	0.947653	+	0.319302i	0.547128	+	0.184349i
$4$	0.647386	−	0.762162i	0.323693	−	0.381081i
$5$	−2.35642	−	1.41781i	−1.05383	−	0.634066i	−0.120359	−	0.992730i	$-0.538404\pi$
$5$	−2.35642	−	1.41781i	−1.05383	−	0.634066i	−0.933466	+	0.358665i	$0.883232\pi$
$6$	0.994138	−	0.108119i	0.405855	−	0.0441394i
$7$	0.260327	−	4.80144i	0.0983942	−	1.81477i	−0.367597	−	0.929985i	$-0.619819\pi$
$7$	0.260327	−	4.80144i	0.0983942	−	1.81477i	0.465991	−	0.884789i	$-0.345698\pi$
$8$	0.267528	−	0.963550i	0.0945856	−	0.340666i
$9$	0.796093	+	0.605174i	0.265364	+	0.201725i
$10$	−2.73396	−	0.297336i	−0.864553	−	0.0940258i
$11$	−0.0646256	+	0.394199i	−0.0194853	+	0.118855i	−0.994778	−	0.102061i	$-0.967456\pi$
$11$	−0.0646256	+	0.394199i	−0.0194853	+	0.118855i	0.975293	+	0.220916i	$0.0709047\pi$
$12$	0.856857	−	0.515554i	0.247353	−	0.148828i
$13$	−0.265479	+	0.201812i	−0.0736305	+	0.0559725i	−0.641342	−	0.767255i	$-0.721622\pi$
$13$	−0.265479	+	0.201812i	−0.0736305	+	0.0559725i	0.567711	+	0.823228i	$0.307829\pi$
$14$	−1.77981	−	4.46698i	−0.475673	−	1.19385i
$15$	−1.78036	−	2.09601i	−0.459688	−	0.541186i
$16$	−0.161782	−	0.986827i	−0.0404455	−	0.246707i
$17$	0.335166	+	6.18178i	0.0812898	+	1.49930i	0.700260	+	0.713888i	$0.253067\pi$
$17$	0.335166	+	6.18178i	0.0812898	+	1.49930i	−0.618971	+	0.785414i	$0.712450\pi$
$18$	0.976621	+	0.214970i	0.230192	+	0.0506690i
$19$	2.11735	−	2.00566i	0.485753	−	0.460130i	−0.405198	−	0.914229i	$-0.632797\pi$
$19$	2.11735	−	2.00566i	0.485753	−	0.460130i	0.890951	+	0.454099i	$0.150039\pi$
$20$	−2.60612	+	0.878104i	−0.582746	+	0.196350i
$21$	1.77981	−	4.46698i	0.388386	−	0.974775i
$22$	0.106867	+	0.384901i	0.0227841	+	0.0820611i
$23$	1.98573	−	0.437093i	0.414054	−	0.0911401i	−0.00305809	−	0.999995i	$-0.500973\pi$
$23$	1.98573	−	0.437093i	0.414054	−	0.0911401i	0.417112	+	0.908855i	$0.363042\pi$
$24$	0.561187	−	0.827689i	0.114552	−	0.168951i
$25$	1.20050	+	2.26438i	0.240100	+	0.452876i
$26$	−0.156203	+	0.294631i	−0.0306340	+	0.0577819i
$27$	0.561187	+	0.827689i	0.108001	+	0.159289i
$28$	−3.49095	−	3.30680i	−0.659727	−	0.624926i
$29$	7.13200	+	3.29962i	1.32438	+	0.612723i	0.949330	−	0.314281i	$-0.101764\pi$
$29$	7.13200	+	3.29962i	1.32438	+	0.612723i	0.375050	+	0.927005i	$0.377626\pi$
$30$	−2.49590	−	1.15473i	−0.455688	−	0.210824i
$31$	1.64829	+	1.56134i	0.296042	+	0.280425i	0.821275	−	0.570533i	$-0.193263\pi$
$31$	1.64829	+	1.56134i	0.296042	+	0.280425i	−0.525233	+	0.850958i	$0.676022\pi$
$32$	−0.561187	−	0.827689i	−0.0992048	−	0.146316i
$33$	−0.187111	+	0.352929i	−0.0325718	+	0.0614370i
$34$	2.89985	+	5.46970i	0.497320	+	0.938046i
$35$	−7.42099	+	10.9451i	−1.25438	+	1.85007i
$36$	0.976621	−	0.214970i	0.162770	−	0.0358284i
$37$	−1.48398	−	5.34480i	−0.243964	−	0.878680i	−0.979542	−	0.201240i	$-0.935503\pi$
$37$	−1.48398	−	5.34480i	−0.243964	−	0.878680i	0.735578	−	0.677440i	$-0.236911\pi$
$38$	1.07950	−	2.70934i	0.175118	−	0.439513i
$39$	−0.316020	+	0.106480i	−0.0506038	+	0.0170504i
$40$	−1.99654	+	1.89123i	−0.315681	+	0.299029i
$41$	7.16970	+	1.57817i	1.11972	+	0.246469i	0.736001	−	0.676981i	$-0.236712\pi$
$41$	7.16970	+	1.57817i	1.11972	+	0.246469i	0.383719	+	0.923450i	$0.374643\pi$
$42$	−0.260327	−	4.80144i	−0.0401693	−	0.740879i
$43$	1.70788	+	10.4176i	0.260449	+	1.58867i	0.715766	+	0.698340i	$0.246078\pi$
$43$	1.70788	+	10.4176i	0.260449	+	1.58867i	−0.455317	+	0.890330i	$0.650474\pi$
$44$	0.258606	+	0.304454i	0.0389863	+	0.0458982i
$45$	−1.01791	−	2.55476i	−0.151741	−	0.380841i
$46$	1.61867	−	1.23048i	0.238660	−	0.181425i
$47$	−2.53319	+	1.52417i	−0.369504	+	0.222323i	−0.688179	−	0.725541i	$-0.741590\pi$
$47$	−2.53319	+	1.52417i	−0.369504	+	0.222323i	0.318675	+	0.947864i	$0.396762\pi$
$48$	0.161782	−	0.986827i	0.0233512	−	0.142436i
$49$	−16.0271	−	1.74305i	−2.28959	−	0.249008i
$50$	2.04033	+	1.55102i	0.288547	+	0.219348i
$51$	−1.65623	+	5.96520i	−0.231919	+	0.835295i
$52$	−0.0180541	+	0.332988i	−0.00250365	+	0.0461771i
$53$	−5.20304	+	0.565865i	−0.714693	+	0.0777275i	−0.458239	−	0.888829i	$-0.651520\pi$
$53$	−5.20304	+	0.565865i	−0.714693	+	0.0777275i	−0.256454	+	0.966556i	$0.582554\pi$
$54$	0.856857	+	0.515554i	0.116603	+	0.0701580i
$55$	0.711186	−	0.837272i	0.0958962	−	0.112898i
$56$	−4.55678	−	1.53536i	−0.608926	−	0.205171i
$57$	2.64692	−	1.22460i	0.350594	−	0.162202i
$58$	7.85830			1.03185
$59$	−5.19674	−	5.65632i	−0.676558	−	0.736390i
$59$	−5.19674	−	5.65632i	−0.676558	−	0.736390i
$60$	−2.75008			−0.355034
$61$	−6.26975	+	2.90069i	−0.802759	+	0.371396i	−0.777974	−	0.628297i	$-0.783752\pi$
$61$	−6.26975	+	2.90069i	−0.802759	+	0.371396i	−0.0247852	+	0.999693i	$0.507890\pi$
$62$	2.15154	+	0.724937i	0.273246	+	0.0920672i
$63$	3.11295	−	3.66485i	0.392195	−	0.461728i
$64$	−0.856857	−	0.515554i	−0.107107	−	0.0644442i
$65$	0.911712	−	0.0991546i	0.113084	−	0.0122986i
$66$	−0.0216264	+	0.398875i	−0.00266202	+	0.0490981i
$67$	3.04568	−	10.9695i	0.372089	−	1.34014i	−0.506367	−	0.862318i	$-0.669012\pi$
$67$	3.04568	−	10.9695i	0.372089	−	1.34014i	0.878456	−	0.477824i	$-0.158574\pi$
$68$	4.92850	+	3.74655i	0.597668	+	0.454336i
$69$	2.02135	+	0.219835i	0.243342	+	0.0264650i
$70$	−2.13936	+	13.0495i	−0.255703	+	1.55972i
$71$	1.34623	−	0.810002i	0.159768	−	0.0961295i	−0.433424	−	0.901190i	$-0.642695\pi$
$71$	1.34623	−	0.810002i	0.159768	−	0.0961295i	0.593193	+	0.805061i	$0.297867\pi$
$72$	0.796093	−	0.605174i	0.0938205	−	0.0713205i
$73$	3.49566	+	8.77343i	0.409136	+	1.02685i	0.978771	+	0.204955i	$0.0657050\pi$
$73$	3.49566	+	8.77343i	0.409136	+	1.02685i	−0.569636	+	0.821897i	$0.692916\pi$
$74$	−3.59104	−	4.22770i	−0.417450	−	0.491461i
$75$	0.414636	+	2.52917i	0.0478781	+	0.292043i
$76$	−0.157895	−	2.91220i	−0.0181118	−	0.334052i
$77$	1.87590	+	0.412916i	0.213778	+	0.0470562i
$78$	−0.242103	+	0.229332i	−0.0274127	+	0.0259667i
$79$	10.7133	−	3.60972i	1.20534	−	0.406126i	0.356257	−	0.934388i	$-0.384053\pi$
$79$	10.7133	−	3.60972i	1.20534	−	0.406126i	0.849081	+	0.528263i	$0.177156\pi$
$80$	−1.01791	+	2.55476i	−0.113806	+	0.285631i
$81$	0.267528	+	0.963550i	0.0297254	+	0.107061i
$82$	7.16970	−	1.57817i	0.791761	−	0.174280i
$83$	−7.76998	+	11.4599i	−0.852866	+	1.25788i	0.111621	+	0.993751i	$0.464396\pi$
$83$	−7.76998	+	11.4599i	−0.852866	+	1.25788i	−0.964486	+	0.264132i	$0.914914\pi$
$84$	−2.25234	−	4.24836i	−0.245750	−	0.463534i
$85$	7.97482	−	15.0421i	0.864990	−	1.63154i
$86$	5.92427	+	8.73764i	0.638830	+	0.942204i
$87$	5.70509	+	5.40415i	0.611650	+	0.579386i
$88$	0.362541	+	0.167729i	0.0386470	+	0.0178800i
$89$	−10.8555	−	5.02227i	−1.15068	−	0.532360i	−0.250600	−	0.968091i	$-0.580628\pi$
$89$	−10.8555	−	5.02227i	−1.15068	−	0.532360i	−0.900077	+	0.435731i	$0.856490\pi$
$90$	−1.99654	−	1.89123i	−0.210454	−	0.199353i
$91$	0.899876	+	1.32722i	0.0943326	+	0.139130i
$92$	0.952400	−	1.79642i	0.0992946	−	0.187289i
$93$	1.06347	+	2.00591i	0.110276	+	0.208003i
$94$	−1.65908	+	2.44696i	−0.171121	+	0.252385i
$95$	−7.83303	+	1.72418i	−0.803652	+	0.176897i
$96$	−0.267528	−	0.963550i	−0.0273045	−	0.0983419i
$97$	1.82065	−	4.56949i	0.184859	−	0.463961i	−0.807116	−	0.590393i	$-0.798973\pi$
$97$	1.82065	−	4.56949i	0.184859	−	0.463961i	0.991975	+	0.126431i	$0.0403523\pi$
$98$	−15.2777	+	5.14766i	−1.54328	+	0.519992i
$99$	−0.290007	+	0.274709i	−0.0291468	+	0.0276093i
$100$	2.50301	+	0.550955i	0.250301	+	0.0550955i
$101$	0.0821777	+	1.51568i	0.00817698	+	0.150816i	0.999770	+	0.0214235i	$0.00681983\pi$
$101$	0.0821777	+	1.51568i	0.00817698	+	0.150816i	−0.991594	+	0.129392i	$0.958697\pi$
$102$	1.00157	+	6.10930i	0.0991702	+	0.604911i
$103$	8.48794	+	9.99277i	0.836341	+	0.984617i	0.999998	−	0.00190008i	$-0.000604815\pi$
$103$	8.48794	+	9.99277i	0.836341	+	0.984617i	−0.163657	+	0.986517i	$0.552329\pi$
$104$	0.123433	+	0.309792i	0.0121036	+	0.0303776i
$105$	−10.5273	+	8.00267i	−1.02736	+	0.780980i
$106$	−4.48455	+	2.69827i	−0.435578	+	0.262079i
$107$	−1.79157	+	10.9281i	−0.173198	+	1.05646i	0.746948	+	0.664883i	$0.231518\pi$
$107$	−1.79157	+	10.9281i	−0.173198	+	1.05646i	−0.920145	+	0.391577i	$0.871930\pi$
$108$	0.994138	+	0.108119i	0.0956610	+	0.0104038i
$109$	−15.8559	−	12.0533i	−1.51872	−	1.15450i	−0.941070	−	0.338213i	$-0.890178\pi$
$109$	−15.8559	−	12.0533i	−1.51872	−	1.15450i	−0.577648	−	0.816286i	$-0.696029\pi$
$110$	0.293893	−	1.05851i	0.0280216	−	0.100925i
$111$	0.300308	−	5.53885i	0.0285040	−	0.525725i
$112$	−4.78031	+	0.519890i	−0.451697	+	0.0491250i
$113$	0.585441	+	0.352248i	0.0550736	+	0.0331367i	0.542824	−	0.839846i	$-0.317355\pi$
$113$	0.585441	+	0.352248i	0.0550736	+	0.0331367i	−0.487751	+	0.872983i	$0.662183\pi$
$114$	1.88809	−	2.22283i	0.176836	−	0.208187i
$115$	−5.29894	−	1.78542i	−0.494129	−	0.166491i
$116$	7.13200	−	3.29962i	0.662190	−	0.306362i
$117$	−0.333477			−0.0308300
$118$	−7.09146	−	2.95148i	−0.652822	−	0.271706i
$119$	29.7687			2.72889
$120$	−2.49590	+	1.15473i	−0.227844	+	0.105412i
$121$	10.2730	+	3.46137i	0.933906	+	0.314670i
$122$	−4.47230	+	5.26520i	−0.404903	+	0.476688i
$123$	6.29048	+	3.78486i	0.567193	+	0.341269i
$124$	2.25708	−	0.245472i	0.202691	−	0.0220440i
$125$	−0.362846	+	6.69230i	−0.0324539	+	0.598577i
$126$	1.28641	−	4.63322i	0.114602	−	0.412760i
$127$	12.2689	+	9.32654i	1.08869	+	0.827597i	0.985938	−	0.167111i	$-0.0534437\pi$
$127$	12.2689	+	9.32654i	1.08869	+	0.827597i	0.102747	+	0.994708i	$0.467237\pi$
$128$	−0.994138	−	0.108119i	−0.0878702	−	0.00955646i
$129$	−1.70788	+	10.4176i	−0.150370	+	0.917219i
$130$	0.785813	−	0.472808i	0.0689204	−	0.0414680i
$131$	3.78175	−	2.87481i	0.330413	−	0.251174i	−0.426793	−	0.904349i	$-0.640357\pi$
$131$	3.78175	−	2.87481i	0.330413	−	0.251174i	0.757206	+	0.653176i	$0.226564\pi$
$132$	0.147856	+	0.371090i	0.0128692	+	0.0322992i
$133$	−9.07886	−	10.6885i	−0.787237	−	0.926807i
$134$	−1.84181	−	11.2345i	−0.159108	−	0.970515i
$135$	−0.148886	−	2.74605i	−0.0128141	−	0.236342i
$136$	6.04612	+	1.33085i	0.518451	+	0.114120i
$137$	4.80753	−	4.55393i	0.410735	−	0.389069i	−0.454244	−	0.890877i	$-0.650090\pi$
$137$	4.80753	−	4.55393i	0.410735	−	0.389069i	0.864979	+	0.501809i	$0.167332\pi$
$138$	1.92683	−	0.649226i	0.164023	−	0.0552658i
$139$	3.91329	−	9.82162i	0.331921	−	0.833059i	−0.664401	−	0.747376i	$-0.731313\pi$
$139$	3.91329	−	9.82162i	0.331921	−	0.833059i	0.996322	−	0.0856830i	$-0.0273072\pi$
$140$	3.53772	+	12.7417i	0.298992	+	1.07687i
$141$	−2.88726	+	0.635533i	−0.243151	+	0.0535215i
$142$	0.881697	−	1.30041i	0.0739904	−	0.109128i
$143$	−0.0623972	−	0.117694i	−0.00521791	−	0.00984203i
$144$	0.468408	−	0.883512i	0.0390340	−	0.0736260i
$145$	−12.1278	−	17.8871i	−1.00716	−	1.48545i
$146$	6.85644	+	6.49476i	0.567443	+	0.537511i
$147$	−14.6316	−	6.76929i	−1.20679	−	0.558322i
$148$	−5.03431	−	2.32912i	−0.413818	−	0.191453i
$149$	−13.6884	−	12.9664i	−1.12140	−	1.06225i	−0.997551	−	0.0699438i	$-0.977718\pi$
$149$	−13.6884	−	12.9664i	−1.12140	−	1.06225i	−0.123848	−	0.992301i	$-0.539523\pi$
$150$	1.43829	+	2.12131i	0.117435	+	0.173204i
$151$	7.95881	−	15.0119i	0.647679	−	1.22165i	−0.314506	−	0.949255i	$-0.601839\pi$
$151$	7.95881	−	15.0119i	0.647679	−	1.22165i	0.962185	−	0.272396i	$-0.0878162\pi$
$152$	−1.36610	−	2.57674i	−0.110806	−	0.209001i
$153$	−3.47423	+	5.12411i	−0.280875	+	0.414259i
$154$	1.87590	−	0.412916i	0.151164	−	0.0332738i
$155$	−1.67038	−	6.01615i	−0.134168	−	0.483229i
$156$	−0.123433	+	0.309792i	−0.00988251	+	0.0248032i
$157$	1.16633	−	0.392983i	0.0930835	−	0.0313635i	−0.272374	−	0.962191i	$-0.587809\pi$
$157$	1.16633	−	0.392983i	0.0930835	−	0.0313635i	0.365458	+	0.930828i	$0.380912\pi$
$158$	8.20742	−	7.77448i	0.652948	−	0.618505i
$159$	−5.11136	−	1.12510i	−0.405357	−	0.0892259i
$160$	0.148886	+	2.74605i	0.0117705	+	0.217094i
$161$	−1.58174	−	9.64816i	−0.124658	−	0.760382i
$162$	0.647386	+	0.762162i	0.0508635	+	0.0598811i
$163$	5.91193	+	14.8378i	0.463058	+	1.16219i	0.956324	+	0.292309i	$0.0944236\pi$
$163$	5.91193	+	14.8378i	0.463058	+	1.16219i	−0.493266	+	0.869879i	$0.664197\pi$
$164$	5.84439	−	4.44279i	0.456370	−	0.346924i
$165$	0.941300	−	0.566361i	0.0732801	−	0.0440912i
$166$	−2.23997	+	13.6632i	−0.173855	+	1.06047i
$167$	−8.78954	−	0.955921i	−0.680155	−	0.0739714i	−0.238482	−	0.971147i	$-0.576650\pi$
$167$	−8.78954	−	0.955921i	−0.680155	−	0.0739714i	−0.441674	+	0.897176i	$0.645615\pi$
$168$	−3.82801	−	2.90998i	−0.295337	−	0.224510i
$169$	−3.44812	+	12.4190i	−0.265240	+	0.955307i
$170$	0.921734	−	17.0004i	0.0706938	−	1.30387i
$171$	2.89938	−	0.315327i	0.221721	−	0.0241136i
$172$	9.04556	+	5.44253i	0.689718	+	0.414989i
$173$	9.04675	−	10.6507i	0.687812	−	0.809755i	−0.301823	−	0.953364i	$-0.597595\pi$
$173$	9.04675	−	10.6507i	0.687812	−	0.809755i	0.989634	+	0.143609i	$0.0458709\pi$
$174$	7.44695	+	2.50917i	0.564552	+	0.190220i
$175$	11.1848	−	5.17465i	0.845493	−	0.391167i
$176$	0.399461			0.0301105
$177$	−3.11863	−	7.01955i	−0.234411	−	0.527622i
$178$	−11.9610			−0.896511
$179$	−7.69207	+	3.55873i	−0.574932	+	0.265992i	−0.685736	−	0.727850i	$-0.740520\pi$
$179$	−7.69207	+	3.55873i	−0.574932	+	0.265992i	0.110804	+	0.993842i	$0.464657\pi$
$180$	−2.60612	−	0.878104i	−0.194249	−	0.0654500i
$181$	−5.94134	+	6.99469i	−0.441616	+	0.519911i	−0.937268	−	0.348611i	$-0.886654\pi$
$181$	−5.94134	+	6.99469i	−0.441616	+	0.519911i	0.495651	+	0.868522i	$0.334929\pi$
$182$	1.37399	+	0.826702i	0.101847	+	0.0612792i
$183$	−6.86774	+	0.746912i	−0.507678	+	0.0552133i
$184$	0.110079	−	2.03029i	0.00811512	−	0.149675i
$185$	−4.08105	+	14.6986i	−0.300045	+	1.08066i
$186$	1.80744	+	1.37398i	0.132528	+	0.100745i
$187$	−2.45851	−	0.267379i	−0.179784	−	0.0195527i
$188$	−0.478288	+	2.91743i	−0.0348827	+	0.212775i
$189$	4.12019	−	2.47904i	0.299700	−	0.180323i
$190$	−6.38510	+	4.85383i	−0.463224	+	0.352133i
$191$	−7.62191	−	19.1295i	−0.551502	−	1.38417i	−0.895444	−	0.445174i	$-0.853142\pi$
$191$	−7.62191	−	19.1295i	−0.551502	−	1.38417i	0.343942	−	0.938991i	$-0.388238\pi$
$192$	−0.647386	−	0.762162i	−0.0467211	−	0.0550043i
$193$	−1.20906	−	7.37494i	−0.0870301	−	0.530860i	−0.993975	−	0.109610i	$-0.965040\pi$
$193$	−1.20906	−	7.37494i	−0.0870301	−	0.530860i	0.906945	−	0.421250i	$-0.138408\pi$
$194$	−0.266301	−	4.91163i	−0.0191193	−	0.352634i
$195$	0.895647	+	0.197147i	0.0641386	+	0.0141180i
$196$	−11.7042	+	11.0868i	−0.836016	+	0.791916i
$197$	−12.7548	+	4.29758i	−0.908739	+	0.306190i	−0.734576	−	0.678527i	$-0.762619\pi$
$197$	−12.7548	+	4.29758i	−0.908739	+	0.306190i	−0.174163	+	0.984717i	$0.555722\pi$
$198$	−0.147856	+	0.371090i	−0.0105076	+	0.0263722i
$199$	4.46661	+	16.0873i	0.316629	+	1.14040i	0.935040	+	0.354541i	$0.115363\pi$
$199$	4.46661	+	16.0873i	0.316629	+	1.14040i	−0.618411	+	0.785855i	$0.712223\pi$
$200$	2.50301	−	0.550955i	0.176990	−	0.0389584i
$201$	6.38883	−	9.42282i	0.450634	−	0.664635i
$202$	0.710999	+	1.34109i	0.0500257	+	0.0943585i
$203$	17.6996	−	33.3849i	1.24227	−	2.34316i
$204$	3.47423	+	5.12411i	0.243245	+	0.358759i
$205$	−14.6573	−	13.8841i	−1.02371	−	0.969711i
$206$	11.8993	+	5.50520i	0.829064	+	0.383566i
$207$	1.84534	+	0.853747i	0.128260	+	0.0593395i
$208$	0.242103	+	0.229332i	0.0167868	+	0.0159013i
$209$	0.653793	+	0.964273i	0.0452238	+	0.0667002i
$210$	−6.19411	+	11.6833i	−0.427434	+	0.806226i
$211$	−4.03464	−	7.61014i	−0.277756	−	0.523903i	0.704908	−	0.709299i	$-0.250988\pi$
$211$	−4.03464	−	7.61014i	−0.277756	−	0.523903i	−0.982664	+	0.185395i	$0.940643\pi$
$212$	−2.93710	+	4.33189i	−0.201721	+	0.297516i
$213$	1.53440	−	0.337746i	0.105135	−	0.0231420i
$214$	2.96260	+	10.6703i	0.202519	+	0.729409i
$215$	10.7457	−	26.9698i	0.732853	−	1.83932i
$216$	0.947653	−	0.319302i	0.0644796	−	0.0217257i
$217$	7.92579	−	7.50771i	0.538038	−	0.509656i
$218$	−19.4515	−	4.28159i	−1.31742	−	0.289986i
$219$	0.511298	+	9.43034i	0.0345503	+	0.637243i
$220$	−0.177725	−	1.08408i	−0.0119822	−	0.0730885i
$221$	−1.33653	−	1.57349i	−0.0899051	−	0.105844i
$222$	−2.05315	−	5.15302i	−0.137799	−	0.345848i
$223$	−14.2539	+	10.8356i	−0.954514	+	0.725603i	−0.961624	−	0.274372i	$-0.911530\pi$
$223$	−14.2539	+	10.8356i	−0.954514	+	0.725603i	0.00710931	+	0.999975i	$0.497737\pi$
$224$	−4.12019	+	2.47904i	−0.275292	+	0.165638i
$225$	−0.414636	+	2.52917i	−0.0276424	+	0.168611i
$226$	0.679237	+	0.0738715i	0.0451822	+	0.00491386i
$227$	3.89948	+	2.96430i	0.258817	+	0.196748i	0.726534	−	0.687131i	$-0.241130\pi$
$227$	3.89948	+	2.96430i	0.258817	+	0.196748i	−0.467716	+	0.883879i	$0.654923\pi$
$228$	0.780240	−	2.81017i	0.0516727	−	0.186108i
$229$	−0.845160	+	15.5881i	−0.0558497	+	1.03009i	0.827527	+	0.561425i	$0.189747\pi$
$229$	−0.845160	+	15.5881i	−0.0558497	+	1.03009i	−0.883377	+	0.468663i	$0.844736\pi$
$230$	−5.55887	+	0.604563i	−0.366541	+	0.0398637i
$231$	1.64586	+	0.990279i	0.108289	+	0.0651556i
$232$	5.08736	−	5.98930i	0.334001	−	0.393217i
$233$	−14.5084	−	4.88846i	−0.950479	−	0.320254i	−0.198991	−	0.980001i	$-0.563767\pi$
$233$	−14.5084	−	4.88846i	−0.950479	−	0.320254i	−0.751487	+	0.659748i	$0.770663\pi$
$234$	−0.302655	+	0.140023i	−0.0197852	+	0.00915361i
$235$	8.13026			0.530360
$236$	−7.67533	+	0.298934i	−0.499621	+	0.0194590i
$237$	11.3051			0.734343
$238$	27.0173	−	12.4996i	1.75127	−	0.810226i
$239$	22.0597	+	7.43277i	1.42692	+	0.480786i	0.923615	−	0.383321i	$-0.125220\pi$
$239$	22.0597	+	7.43277i	1.42692	+	0.480786i	0.503307	+	0.864108i	$0.332116\pi$
$240$	−1.78036	+	2.09601i	−0.114922	+	0.135297i
$241$	−13.7618	−	8.28021i	−0.886477	−	0.533376i	−0.00202038	−	0.999998i	$-0.500643\pi$
$241$	−13.7618	−	8.28021i	−0.886477	−	0.533376i	−0.884457	+	0.466622i	$0.845471\pi$
$242$	10.7769	−	1.17206i	0.692764	−	0.0753427i
$243$	−0.0541389	+	0.998533i	−0.00347301	+	0.0640559i
$244$	−1.84815	+	6.65643i	−0.118316	+	0.426134i
$245$	35.2954	+	26.8308i	2.25494	+	1.71416i
$246$	7.29830	+	0.793738i	0.465323	+	0.0506069i
$247$	−0.157346	+	0.959766i	−0.0100117	+	0.0610684i
$248$	1.94540	−	1.17051i	0.123533	−	0.0743272i
$249$	−11.0224	+	8.37901i	−0.698516	+	0.530998i
$250$	2.48071	+	6.22612i	0.156894	+	0.393774i
$251$	12.0667	+	14.2061i	0.761646	+	0.896679i	0.997169	−	0.0751898i	$-0.0239563\pi$
$251$	12.0667	+	14.2061i	0.761646	+	0.896679i	−0.235523	+	0.971869i	$0.575680\pi$
$252$	−0.777928	−	4.74515i	−0.0490048	−	0.298916i
$253$	0.0439722	+	0.811020i	0.00276451	+	0.0509884i
$254$	15.0510	+	3.31298i	0.944385	+	0.207875i
$255$	12.3603	−	11.7083i	0.774034	−	0.733204i
$256$	−0.947653	+	0.319302i	−0.0592283	+	0.0199563i
$257$	11.3385	−	28.4576i	0.707279	−	1.77514i	0.0793755	−	0.996845i	$-0.474707\pi$
$257$	11.3385	−	28.4576i	0.707279	−	1.77514i	0.627903	−	0.778291i	$-0.283913\pi$
$258$	2.82421	+	10.1719i	0.175828	+	0.633274i
$259$	−26.0491	+	5.73383i	−1.61861	+	0.356283i
$260$	0.514658	−	0.759064i	0.0319177	−	0.0470751i
$261$	3.68090	+	6.94291i	0.227842	+	0.429755i
$262$	2.22512	−	4.19703i	0.137469	−	0.259293i
$263$	−5.42275	−	7.99796i	−0.334381	−	0.493176i	0.622913	−	0.782291i	$-0.285949\pi$
$263$	−5.42275	−	7.99796i	−0.334381	−	0.493176i	−0.957294	+	0.289116i	$0.906639\pi$
$264$	0.290007	+	0.274709i	0.0178487	+	0.0169072i
$265$	13.0629	+	6.04353i	0.802446	+	0.371251i
$266$	−12.7277	−	5.88847i	−0.780386	−	0.361045i
$267$	−8.68360	−	8.22554i	−0.531428	−	0.503395i
$268$	−6.38883	−	9.42282i	−0.390260	−	0.575591i
$269$	−7.74730	+	14.6130i	−0.472361	+	0.890968i	0.526799	+	0.849990i	$0.323392\pi$
$269$	−7.74730	+	14.6130i	−0.472361	+	0.890968i	−0.999160	+	0.0409778i	$0.986953\pi$
$270$	−1.28816	−	2.42973i	−0.0783949	−	0.147869i
$271$	−3.48231	+	5.13603i	−0.211536	+	0.311992i	−0.918623	−	0.395134i	$-0.870698\pi$
$271$	−3.48231	+	5.13603i	−0.211536	+	0.311992i	0.707088	+	0.707126i	$0.250008\pi$
$272$	6.04612	−	1.33085i	0.366600	−	0.0806947i
$273$	0.428988	+	1.54507i	0.0259635	+	0.0935121i
$274$	2.45105	−	6.15167i	0.148073	−	0.371636i
$275$	−0.970200	+	0.326898i	−0.0585052	+	0.0197127i
$276$	1.47614	−	1.39828i	0.0888534	−	0.0841664i
$277$	4.37530	+	0.963076i	0.262886	+	0.0578656i	0.344458	−	0.938802i	$-0.388063\pi$
$277$	4.37530	+	0.963076i	0.262886	+	0.0578656i	−0.0815714	+	0.996667i	$0.525994\pi$
$278$	−0.572384	−	10.5570i	−0.0343293	−	0.633167i
$279$	0.367307	+	2.24048i	0.0219901	+	0.134134i
$280$	8.56087	+	10.0786i	0.511610	+	0.602313i
$281$	−3.13822	−	7.87635i	−0.187211	−	0.469864i	0.805174	−	0.593038i	$-0.202072\pi$
$281$	−3.13822	−	7.87635i	−0.187211	−	0.469864i	−0.992385	+	0.123175i	$0.960692\pi$
$282$	−2.35355	+	1.78912i	−0.140152	+	0.106541i
$283$	−11.9873	+	7.21251i	−0.712571	+	0.428739i	−0.825158	−	0.564902i	$-0.808914\pi$
$283$	−11.9873	+	7.21251i	−0.712571	+	0.428739i	0.112587	+	0.993642i	$0.464086\pi$
$284$	0.254180	−	1.55043i	0.0150828	−	0.0920012i
$285$	−7.97352	−	0.867173i	−0.472311	−	0.0513669i
$286$	−0.106048	−	0.0806159i	−0.00627077	−	0.00476692i
$287$	9.44396	−	34.0141i	0.557459	−	2.00779i
$288$	0.0541389	−	0.998533i	0.00319017	−	0.0588391i
$289$	−21.2017	+	2.30583i	−1.24716	+	0.135637i
$290$	−18.5175	−	11.1416i	−1.08739	−	0.654258i
$291$	3.18439	−	3.74896i	0.186672	−	0.219768i
$292$	8.94982	+	3.01554i	0.523748	+	0.176471i
$293$	−26.8564	+	12.4251i	−1.56897	+	0.725882i	−0.995625	−	0.0934341i	$-0.970216\pi$
$293$	−26.8564	+	12.4251i	−1.56897	+	0.725882i	−0.573342	+	0.819316i	$0.694354\pi$
$294$	−16.1216			−0.940232
$295$	4.22612	+	20.6967i	0.246054	+	1.20501i
$296$	−5.54699			−0.322412
$297$	−0.362541	+	0.167729i	−0.0210368	+	0.00973264i
$298$	−17.8677	−	6.02033i	−1.03505	−	0.348748i
$299$	−0.438959	+	0.516782i	−0.0253857	+	0.0298863i
$300$	2.19607	+	1.32133i	0.126790	+	0.0762870i
$301$	50.4641	−	5.48831i	2.90870	−	0.316341i
$302$	0.919884	−	16.9663i	0.0529334	−	0.976298i
$303$	−0.406082	+	1.46258i	−0.0233288	+	0.0840228i
$304$	−2.32179	−	1.76498i	−0.133164	−	0.101228i
$305$	18.8868	+	2.05407i	1.08146	+	0.117615i
$306$	−1.00157	+	6.10930i	−0.0572559	+	0.349246i
$307$	−16.8554	+	10.1415i	−0.961987	+	0.578809i	−0.907656	−	0.419714i	$-0.862130\pi$
$307$	−16.8554	+	10.1415i	−0.961987	+	0.578809i	−0.0543311	+	0.998523i	$0.517303\pi$
$308$	1.52914	−	1.16242i	0.0871308	−	0.0662351i
$309$	4.85291	+	12.1799i	0.276073	+	0.692890i
$310$	−4.04211	−	4.75874i	−0.229576	−	0.270278i
$311$	0.753125	+	4.59386i	0.0427058	+	0.260494i	0.999546	−	0.0301198i	$-0.00958889\pi$
$311$	0.753125	+	4.59386i	0.0427058	+	0.260494i	−0.956841	+	0.290614i	$0.906141\pi$
$312$	0.0180541	+	0.332988i	0.00102211	+	0.0188517i
$313$	−26.2975	−	5.78852i	−1.48642	−	0.327187i	−0.603750	−	0.797174i	$-0.706328\pi$
$313$	−26.2975	−	5.78852i	−1.48642	−	0.327187i	−0.882673	+	0.469987i	$0.844259\pi$
$314$	0.893526	−	0.846393i	0.0504246	−	0.0477647i
$315$	−12.5315	+	4.22236i	−0.706071	+	0.237903i
$316$	4.18443	−	10.5021i	0.235393	−	0.590791i
$317$	3.21279	+	11.5714i	0.180448	+	0.649915i	0.997324	+	0.0731024i	$0.0232900\pi$
$317$	3.21279	+	11.5714i	0.180448	+	0.649915i	−0.816876	+	0.576813i	$0.804296\pi$
$318$	−5.11136	+	1.12510i	−0.286631	+	0.0630922i
$319$	−1.76161	+	2.59819i	−0.0986314	+	0.145471i
$320$	1.28816	+	2.42973i	0.0720103	+	0.135826i
$321$	−5.18715	+	9.78400i	−0.289518	+	0.546089i
$322$	−5.48670	−	8.09228i	−0.305762	−	0.450965i
$323$	13.1082	+	12.4168i	0.729360	+	0.690887i
$324$	0.907575	+	0.419889i	0.0504209	+	0.0233272i
$325$	−0.775686	−	0.358870i	−0.0430273	−	0.0199066i
$326$	11.5958	+	10.9841i	0.642230	+	0.608352i
$327$	−11.1772	−	16.4852i	−0.618102	−	0.911632i
$328$	3.43875	−	6.48616i	0.189873	−	0.358138i
$329$	6.65876	+	12.5598i	0.367109	+	0.692441i
$330$	0.616492	−	0.909257i	0.0339367	−	0.0500529i
$331$	10.6002	−	2.33327i	0.582638	−	0.128248i	0.0861353	−	0.996283i	$-0.472548\pi$
$331$	10.6002	−	2.33327i	0.582638	−	0.128248i	0.496503	+	0.868035i	$0.334617\pi$
$332$	3.70409	+	13.3409i	0.203289	+	0.732179i
$333$	2.05315	−	5.15302i	0.112512	−	0.282384i
$334$	−8.37855	+	2.82306i	−0.458454	+	0.154471i
$335$	−22.7297	+	21.5307i	−1.24185	+	1.17635i
$336$	−4.69607	−	1.03368i	−0.256192	−	0.0563921i
$337$	0.482801	+	8.90474i	0.0262998	+	0.485072i	0.981781	+	0.190018i	$0.0608548\pi$
$337$	0.482801	+	8.90474i	0.0262998	+	0.485072i	−0.955481	+	0.295054i	$0.904662\pi$
$338$	2.08517	+	12.7190i	0.113419	+	0.691823i
$339$	0.442321	+	0.520741i	0.0240236	+	0.0282828i
$340$	−6.30173	−	15.8162i	−0.341759	−	0.857751i
$341$	−0.722001	+	0.548851i	−0.0390985	+	0.0297219i
$342$	2.49900	−	1.50360i	0.135131	−	0.0813054i
$343$	−7.09596	+	43.2834i	−0.383146	+	2.33709i
$344$	10.4948	+	1.14138i	0.565841	+	0.0615389i
$345$	−4.45147	−	3.38392i	−0.239659	−	0.182184i
$346$	3.73851	−	13.4649i	0.200984	−	0.723878i
$347$	−1.46879	+	27.0903i	−0.0788490	+	1.45428i	0.644925	+	0.764246i	$0.276889\pi$
$347$	−1.46879	+	27.0903i	−0.0788490	+	1.45428i	−0.723774	+	0.690038i	$0.757594\pi$
$348$	7.81224	−	0.849632i	0.418780	−	0.0455451i
$349$	−0.759268	−	0.456836i	−0.0406427	−	0.0244539i	0.495088	−	0.868843i	$-0.335136\pi$
$349$	−0.759268	−	0.456836i	−0.0406427	−	0.0244539i	−0.535730	+	0.844389i	$0.679964\pi$
$350$	7.97829	−	9.39277i	0.426458	−	0.502065i
$351$	−0.316020	−	0.106480i	−0.0168679	−	0.00568347i
$352$	0.362541	−	0.167729i	0.0193235	−	0.00894000i
$353$	8.77352			0.466967			0.233484	−	0.972361i	$-0.424987\pi$
$353$	8.77352			0.466967			0.233484	+	0.972361i	$0.424987\pi$
$354$	−5.77783	−	5.06129i	−0.307088	−	0.269005i
$355$	−4.32073			−0.229320
$356$	−10.8555	+	5.02227i	−0.575339	+	0.266180i
$357$	28.2104	+	9.50519i	1.49305	+	0.503068i
$358$	−5.48686	+	6.45963i	−0.289990	+	0.341402i
$359$	18.5398	+	11.1551i	0.978496	+	0.588741i	0.912499	−	0.409078i	$-0.134150\pi$
$359$	18.5398	+	11.1551i	0.978496	+	0.588741i	0.0659966	+	0.997820i	$0.478977\pi$
$360$	−2.73396	+	0.297336i	−0.144092	+	0.0156710i
$361$	−0.568142	+	10.4788i	−0.0299022	+	0.551514i
$362$	−2.45522	+	8.84291i	−0.129044	+	0.464773i
$363$	8.62999	+	6.56035i	0.452957	+	0.344329i
$364$	1.59412	+	0.173371i	0.0835547	+	0.00908712i
$365$	4.20185	−	25.6301i	0.219935	−	1.34154i
$366$	−5.91937	+	3.56157i	−0.309411	+	0.186166i
$367$	−18.1555	+	13.8015i	−0.947711	+	0.720431i	−0.960148	−	0.279491i	$-0.909834\pi$
$367$	−18.1555	+	13.8015i	−0.947711	+	0.720431i	0.0124369	+	0.999923i	$0.496041\pi$
$368$	−0.752590	−	1.88886i	−0.0392315	−	0.0984636i
$369$	4.75268	+	5.59529i	0.247415	+	0.291279i
$370$	2.46793	+	15.0537i	0.128302	+	0.782605i
$371$	1.36248	+	25.1294i	0.0707363	+	1.30465i
$372$	2.21730	+	0.488066i	0.114962	+	0.0253050i
$373$	3.64419	−	3.45196i	0.188689	−	0.178736i	−0.587523	−	0.809207i	$-0.699897\pi$
$373$	3.64419	−	3.45196i	0.188689	−	0.178736i	0.776213	+	0.630471i	$0.217138\pi$
$374$	−2.34355	+	0.789635i	−0.121182	+	0.0408310i
$375$	−2.48071	+	6.22612i	−0.128103	+	0.321515i
$376$	0.790914	+	2.84861i	0.0407883	+	0.146906i
$377$	−2.55930	+	0.563344i	−0.131810	+	0.0290137i
$378$	2.69846	−	3.97994i	0.138794	−	0.204706i
$379$	−4.36279	−	8.22909i	−0.224101	−	0.422700i	0.745810	−	0.666159i	$-0.232063\pi$
$379$	−4.36279	−	8.22909i	−0.224101	−	0.422700i	−0.969911	+	0.243459i	$0.921718\pi$
$380$	−3.75689	+	7.08625i	−0.192724	+	0.363517i
$381$	8.64864	+	12.7558i	0.443083	+	0.653499i
$382$	−14.9497	−	14.1611i	−0.764895	−	0.724547i
$383$	−20.8571	−	9.64951i	−1.06575	−	0.493067i	−0.192979	−	0.981203i	$-0.561815\pi$
$383$	−20.8571	−	9.64951i	−1.06575	−	0.493067i	−0.872768	+	0.488136i	$0.837677\pi$
$384$	−0.907575	−	0.419889i	−0.0463145	−	0.0214274i
$385$	−3.83497	−	3.63268i	−0.195448	−	0.185139i
$386$	−4.19397	−	6.18565i	−0.213468	−	0.314841i
$387$	−4.94484	+	9.32695i	−0.251360	+	0.474115i
$388$	−2.30403	−	4.34586i	−0.116969	−	0.220627i
$389$	16.3485	−	24.1123i	0.828903	−	1.22254i	−0.143597	−	0.989636i	$-0.545867\pi$
$389$	16.3485	−	24.1123i	0.828903	−	1.22254i	0.972500	−	0.232904i	$-0.0748228\pi$
$390$	0.895647	−	0.197147i	0.0453528	−	0.00998292i
$391$	3.36756	+	12.1289i	0.170305	+	0.613383i
$392$	−5.96723	+	14.9766i	−0.301390	+	0.756433i
$393$	4.50172	−	1.51681i	0.227082	−	0.0765128i
$394$	−9.77140	+	9.25596i	−0.492276	+	0.466309i
$395$	−30.3629	−	6.68339i	−1.52773	−	0.336278i
$396$	0.0216264	+	0.398875i	0.00108677	+	0.0200442i
$397$	3.36562	+	20.5294i	0.168916	+	1.03034i	0.926139	+	0.377183i	$0.123107\pi$
$397$	3.36562	+	20.5294i	0.168916	+	1.03034i	−0.757223	+	0.653156i	$0.773444\pi$
$398$	10.8087	+	12.7249i	0.541789	+	0.637843i
$399$	−5.19077	−	13.0278i	−0.259863	−	0.652208i
$400$	2.04033	−	1.55102i	0.102017	−	0.0775511i
$401$	10.6515	−	6.40878i	0.531909	−	0.320039i	−0.224137	−	0.974558i	$-0.571956\pi$
$401$	10.6515	−	6.40878i	0.531909	−	0.320039i	0.756046	+	0.654519i	$0.227129\pi$
$402$	1.84181	−	11.2345i	0.0918610	−	0.560327i
$403$	−0.752683	−	0.0818592i	−0.0374938	−	0.00407770i
$404$	1.20839	+	0.918596i	0.0601198	+	0.0457019i
$405$	0.735724	−	2.64984i	0.0365584	−	0.131672i
$406$	2.04573	−	37.7312i	0.101528	−	1.87257i
$407$	2.20282	−	0.239571i	0.109190	−	0.0118751i
$408$	5.30468	+	3.19172i	0.262621	+	0.158014i
$409$	10.1944	−	12.0017i	0.504079	−	0.593448i	−0.449990	−	0.893033i	$-0.648573\pi$
$409$	10.1944	−	12.0017i	0.504079	−	0.593448i	0.954069	+	0.299586i	$0.0968484\pi$
$410$	−19.1324	−	6.44646i	−0.944883	−	0.318368i
$411$	6.00995	−	2.78050i	0.296449	−	0.137152i
$412$	13.1111			0.645937
$413$	−28.5113	+	23.4793i	−1.40295	+	1.15534i
$414$	2.03327			0.0999297
$415$	34.5573	−	15.9879i	1.69635	−	0.784816i
$416$	0.316020	+	0.106480i	0.0154942	+	0.00522060i
$417$	6.84450	−	8.05797i	0.335177	−	0.394600i
$418$	0.998255	+	0.600630i	0.0488262	+	0.0293778i
$419$	−21.1582	+	2.30110i	−1.03365	+	0.112416i	−0.609184	−	0.793029i	$-0.708503\pi$
$419$	−21.1582	+	2.30110i	−1.03365	+	0.112416i	−0.424464	+	0.905445i	$0.639537\pi$
$420$	−0.715919	+	13.2043i	−0.0349333	+	0.644306i
$421$	8.02861	−	28.9164i	0.391291	−	1.40930i	−0.461543	−	0.887118i	$-0.652704\pi$
$421$	8.02861	−	28.9164i	0.391291	−	1.40930i	0.852833	−	0.522183i	$-0.174882\pi$
$422$	−6.85715	−	5.21267i	−0.333801	−	0.253749i
$423$	−2.93904	−	0.319640i	−0.142901	−	0.0155414i
$424$	−0.846722	+	5.16478i	−0.0411205	+	0.250824i
$425$	−13.5955	+	8.18017i	−0.659481	+	0.396796i
$426$	1.25076	−	0.950807i	0.0605998	−	0.0460667i
$427$	12.2953	+	30.8589i	0.595013	+	1.49337i
$428$	7.16914	+	8.44017i	0.346534	+	0.407971i
$429$	−0.0215511	−	0.131456i	−0.00104050	−	0.00634676i
$430$	−1.57174	−	28.9891i	−0.0757962	−	1.39798i
$431$	2.25954	+	0.497363i	0.108838	+	0.0239571i	0.269056	−	0.963125i	$-0.413288\pi$
$431$	2.25954	+	0.497363i	0.108838	+	0.0239571i	−0.160217	+	0.987082i	$0.551219\pi$
$432$	0.725995	−	0.687699i	0.0349295	−	0.0330870i
$433$	37.9115	−	12.7739i	1.82191	−	0.613874i	0.822960	−	0.568099i	$-0.192321\pi$
$433$	37.9115	−	12.7739i	1.82191	−	0.613874i	0.998952	−	0.0457745i	$-0.0145756\pi$
$434$	4.04085	−	10.1418i	0.193967	−	0.486820i
$435$	−5.78154	−	20.8232i	−0.277204	−	0.998398i
$436$	−19.4515	+	4.28159i	−0.931556	+	0.205051i
$437$	3.32783	−	4.90818i	0.159192	−	0.234790i
$438$	4.42374	+	8.34406i	0.211374	+	0.398694i
$439$	8.46017	−	15.9576i	0.403782	−	0.761613i	−0.595342	−	0.803473i	$-0.702983\pi$
$439$	8.46017	−	15.9576i	0.403782	−	0.761613i	0.999124	+	0.0418593i	$0.0133281\pi$
$440$	−0.616492	−	0.909257i	−0.0293901	−	0.0433471i
$441$	−11.7042	−	11.0868i	−0.557344	−	0.527944i
$442$	−1.87370	−	0.866865i	−0.0891227	−	0.0412326i
$443$	−25.6048	−	11.8461i	−1.21652	−	0.562823i	−0.296629	−	0.954993i	$-0.595862\pi$
$443$	−25.6048	−	11.8461i	−1.21652	−	0.562823i	−0.919893	+	0.392170i	$0.871725\pi$
$444$	−4.02709	−	3.81466i	−0.191117	−	0.181036i
$445$	18.4594	+	27.2256i	0.875061	+	1.29062i
$446$	−8.38679	+	15.8192i	−0.397126	+	0.749059i
$447$	−8.83169	−	16.6583i	−0.417725	−	0.787912i
$448$	−2.69846	+	3.97994i	−0.127490	+	0.188034i
$449$	−17.5166	+	3.85569i	−0.826658	+	0.181961i	−0.608098	−	0.793862i	$-0.708067\pi$
$449$	−17.5166	+	3.85569i	−0.826658	+	0.181961i	−0.218560	+	0.975823i	$0.570136\pi$
$450$	0.685657	+	2.46951i	0.0323222	+	0.116414i
$451$	−1.08546	+	2.72430i	−0.0511123	+	0.128282i
$452$	0.647476	−	0.218160i	0.0304547	−	0.0102614i
$453$	12.3355	−	11.6848i	0.579573	−	0.549001i
$454$	4.78375	+	1.05298i	0.224512	+	0.0494189i
$455$	−0.238742	−	4.40334i	−0.0111924	−	0.206432i
$456$	−0.471833	−	2.87806i	−0.0220956	−	0.134777i
$457$	20.9713	+	24.6893i	0.980997	+	1.15492i	0.987923	+	0.154942i	$0.0495192\pi$
$457$	20.9713	+	24.6893i	0.980997	+	1.15492i	−0.00692690	+	0.999976i	$0.502205\pi$
$458$	5.77821	+	14.5022i	0.269998	+	0.677644i
$459$	−4.92850	+	3.74655i	−0.230043	+	0.174874i
$460$	−4.79124	+	2.88280i	−0.223393	+	0.134411i
$461$	3.83344	−	23.3829i	0.178541	−	1.08905i	−0.733723	−	0.679449i	$-0.762219\pi$
$461$	3.83344	−	23.3829i	0.178541	−	1.08905i	0.912264	−	0.409603i	$-0.134333\pi$
$462$	1.90955	+	0.207676i	0.0888401	+	0.00966194i
$463$	−24.8242	−	18.8709i	−1.15368	−	0.877004i	−0.159764	−	0.987155i	$-0.551073\pi$
$463$	−24.8242	−	18.8709i	−1.15368	−	0.877004i	−0.993915	+	0.110151i	$0.964866\pi$
$464$	2.10232	−	7.57187i	0.0975977	−	0.351515i
$465$	0.338029	−	6.23458i	0.0156757	−	0.289122i
$466$	−15.2201	+	1.65529i	−0.705058	+	0.0766796i
$467$	−15.7726	−	9.49005i	−0.729868	−	0.439147i	0.101524	−	0.994833i	$-0.467628\pi$
$467$	−15.7726	−	9.49005i	−0.729868	−	0.439147i	−0.831392	+	0.555686i	$0.812456\pi$
$468$	−0.215888	+	0.254163i	−0.00997945	+	0.0117487i
$469$	−51.8767	−	17.4793i	−2.39544	−	0.807119i
$470$	7.37883	−	3.41381i	0.340360	−	0.157467i
$471$	1.23076			0.0567104
$472$	−6.84042	+	3.49409i	−0.314856	+	0.160829i
$473$	−4.21698			−0.193897
$474$	10.2602	−	4.74687i	0.471266	−	0.218031i
$475$	7.08346	+	2.38669i	0.325011	+	0.109509i
$476$	19.2719	−	22.6886i	0.883324	−	1.03993i
$477$	−4.48455	−	2.69827i	−0.205334	−	0.123545i
$478$	23.1418	−	2.51682i	1.05848	−	0.115117i
$479$	−0.218574	+	4.03135i	−0.00998688	+	0.184197i	0.989284	+	0.146007i	$0.0466421\pi$
$479$	−0.218574	+	4.03135i	−0.00998688	+	0.184197i	−0.999270	+	0.0381905i	$0.987841\pi$
$480$	−0.735724	+	2.64984i	−0.0335811	+	0.120948i
$481$	1.47261	+	1.11945i	0.0671451	+	0.0510424i
$482$	−15.9667	−	1.73648i	−0.727262	−	0.0790945i
$483$	1.58174	−	9.64816i	0.0719715	−	0.439007i
$484$	9.28870	−	5.58883i	0.422214	−	0.254038i
$485$	−10.7689	+	8.18632i	−0.488991	+	0.371721i
$486$	0.370138	+	0.928977i	0.0167898	+	0.0421392i
$487$	18.7813	+	22.1111i	0.851064	+	1.00195i	0.999914	+	0.0130900i	$0.00416681\pi$
$487$	18.7813	+	22.1111i	0.851064	+	1.00195i	−0.148851	+	0.988860i	$0.547557\pi$
$488$	1.11763	+	6.81723i	0.0505927	+	0.308602i
$489$	0.864718	+	15.9488i	0.0391039	+	0.721229i
$490$	43.2992	+	9.53087i	1.95606	+	0.430561i
$491$	22.9470	−	21.7366i	1.03559	−	0.980958i	0.0357545	−	0.999361i	$-0.488617\pi$
$491$	22.9470	−	21.7366i	1.03559	−	0.980958i	0.999831	+	0.0184022i	$0.00585793\pi$
$492$	6.95704	−	2.34410i	0.313648	−	0.105680i
$493$	−18.0071	+	45.1944i	−0.810999	+	2.03545i
$494$	0.260192	+	0.937127i	0.0117066	+	0.0421634i
$495$	1.07287	−	0.236156i	0.0482217	−	0.0106144i
$496$	1.27411	−	1.87917i	0.0572093	−	0.0843774i
$497$	−3.53872	−	6.67473i	−0.158733	−	0.299402i
$498$	−6.48540	+	12.2328i	−0.290618	+	0.548163i
$499$	−1.27107	−	1.87468i	−0.0569008	−	0.0839224i	0.798174	−	0.602427i	$-0.205799\pi$
$499$	−1.27107	−	1.87468i	−0.0569008	−	0.0839224i	−0.855075	+	0.518504i	$0.826489\pi$
$500$	4.86571	+	4.60905i	0.217601	+	0.206123i
$501$	−8.02421	−	3.71240i	−0.358495	−	0.165858i
$502$	16.9164	+	7.82638i	0.755018	+	0.349309i
$503$	−1.55403	−	1.47205i	−0.0692906	−	0.0656355i	0.652271	−	0.757986i	$-0.273817\pi$
$503$	−1.55403	−	1.47205i	−0.0692906	−	0.0656355i	−0.721561	+	0.692351i	$0.756575\pi$
$504$	−2.69846	−	3.97994i	−0.120199	−	0.177281i
$505$	1.95530	−	3.68809i	0.0870099	−	0.164118i
$506$	0.380447	+	0.717598i	0.0169129	+	0.0319011i
$507$	−7.23302	+	10.6679i	−0.321230	+	0.473779i
$508$	15.0510	−	3.31298i	0.667781	−	0.146990i
$509$	6.15717	+	22.1761i	0.272912	+	0.982939i	0.965242	+	0.261358i	$0.0841705\pi$
$509$	6.15717	+	22.1761i	0.272912	+	0.982939i	−0.692330	+	0.721581i	$0.743416\pi$
$510$	6.30173	−	15.8162i	0.279045	−	0.700351i
$511$	43.0351	−	14.5002i	1.90376	−	0.641452i
$512$	−0.725995	+	0.687699i	−0.0320848	+	0.0303923i
$513$	2.84829	+	0.626956i	0.125755	+	0.0276808i
$514$	−1.65845	−	30.5883i	−0.0731512	−	1.34919i
$515$	−5.83330	−	35.5815i	−0.257046	−	1.56791i
$516$	6.83425	+	8.04590i	0.300861	+	0.354201i
$517$	−0.437117	−	1.09708i	−0.0192244	−	0.0482496i
$518$	−21.2339	+	16.1416i	−0.932965	+	0.709222i
$519$	11.9740	−	7.20449i	0.525598	−	0.316242i
$520$	0.148368	−	0.905007i	0.00650638	−	0.0396872i
$521$	14.2403	+	1.54873i	0.623880	+	0.0678511i	0.414599	−	0.910004i	$-0.363922\pi$
$521$	14.2403	+	1.54873i	0.623880	+	0.0678511i	0.209282	+	0.977855i	$0.432887\pi$
$522$	6.25594	+	4.75564i	0.273815	+	0.208149i
$523$	8.45015	−	30.4347i	0.369499	−	1.33082i	−0.512144	−	0.858900i	$-0.671148\pi$
$523$	8.45015	−	30.4347i	0.369499	−	1.33082i	0.881643	−	0.471917i	$-0.156438\pi$
$524$	0.257181	−	4.74342i	0.0112350	−	0.207217i
$525$	12.2516	−	1.33244i	0.534704	−	0.0581526i
$526$	−8.27981	−	4.98180i	−0.361017	−	0.217217i
$527$	−9.09943	+	10.7127i	−0.396377	+	0.466651i
$528$	0.378550	+	0.127548i	0.0164743	+	0.00555084i
$529$	−17.1222	+	7.92155i	−0.744442	+	0.344415i
$530$	14.3932			0.625199
$531$	−0.714030	−	7.64789i	−0.0309863	−	0.331890i
$532$	−14.0239			−0.608012
$533$	−2.22190	+	1.02796i	−0.0962410	+	0.0445258i
$534$	−11.3348	−	3.81915i	−0.490506	−	0.165271i
$535$	19.7157	−	23.2111i	0.852385	−	1.00350i
$536$	−9.75489	−	5.86932i	−0.421347	−	0.253516i
$537$	−8.42572	+	0.916352i	−0.363597	+	0.0395435i
$538$	−0.895437	+	16.5154i	−0.0386050	+	0.712028i
$539$	1.72287	−	6.20522i	0.0742093	−	0.267278i
$540$	−2.18932	−	1.66428i	−0.0942133	−	0.0716191i
$541$	−0.950595	−	0.103383i	−0.0408693	−	0.00444480i	0.0876615	−	0.996150i	$-0.472061\pi$
$541$	−0.950595	−	0.103383i	−0.0408693	−	0.00444480i	−0.128531	+	0.991706i	$0.541026\pi$
$542$	−1.00390	+	6.12352i	−0.0431212	+	0.263028i
$543$	−7.86375	+	4.73146i	−0.337466	+	0.203046i
$544$	4.92850	−	3.74655i	0.211308	−	0.160632i
$545$	20.2738	+	50.8834i	0.868435	+	2.17961i
$546$	1.03810	+	1.22214i	0.0444265	+	0.0523029i
$547$	−1.79234	−	10.9328i	−0.0766350	−	0.467453i	−0.997066	−	0.0765476i	$-0.975610\pi$
$547$	−1.79234	−	10.9328i	−0.0766350	−	0.467453i	0.920431	−	0.390905i	$-0.127838\pi$
$548$	−0.358507	−	6.61227i	−0.0153147	−	0.282462i
$549$	−6.74673	−	1.48507i	−0.287943	−	0.0633811i
$550$	−0.743268	+	0.704061i	−0.0316931	+	0.0300213i
$551$	21.7188	−	7.31793i	0.925254	−	0.311754i
$552$	0.752590	−	1.88886i	0.0320324	−	0.0803952i
$553$	−14.5429	−	52.3789i	−0.618428	−	2.22738i
$554$	4.37530	−	0.963076i	0.185889	−	0.0409172i
$555$	−8.56072	+	12.6261i	−0.363382	+	0.535949i
$556$	−4.95225	−	9.34094i	−0.210022	−	0.396144i
$557$	6.09472	−	11.4959i	0.258242	−	0.487095i	−0.720160	−	0.693808i	$-0.755932\pi$
$557$	6.09472	−	11.4959i	0.258242	−	0.487095i	0.978402	+	0.206713i	$0.0662765\pi$
$558$	1.27411	+	1.87917i	0.0539374	+	0.0795517i
$559$	−2.55580	−	2.42098i	−0.108099	−	0.102397i
$560$	12.0015	+	5.55250i	0.507158	+	0.234636i
$561$	−2.24444	−	1.03839i	−0.0947603	−	0.0438408i
$562$	−6.15537	−	5.83068i	−0.259649	−	0.245952i
$563$	6.55876	+	9.67345i	0.276419	+	0.407687i	0.940404	−	0.340058i	$-0.110447\pi$
$563$	6.55876	+	9.67345i	0.276419	+	0.407687i	−0.663986	+	0.747745i	$0.731136\pi$
$564$	−1.38479	+	2.61199i	−0.0583102	+	0.109985i
$565$	−0.880125	−	1.66009i	−0.0370271	−	0.0698406i
$566$	−7.85092	+	11.5792i	−0.329999	+	0.486712i
$567$	4.69607	−	1.03368i	0.197217	−	0.0434107i
$568$	−0.420322	−	1.51386i	−0.0176363	−	0.0635202i
$569$	8.35757	−	20.9759i	0.350367	−	0.879356i	−0.643157	−	0.765735i	$-0.722376\pi$
$569$	8.35757	−	20.9759i	0.350367	−	0.879356i	0.993524	−	0.113621i	$-0.0362451\pi$
$570$	−7.60069	+	2.56097i	−0.318358	+	0.107267i
$571$	22.6805	−	21.4841i	0.949148	−	0.899081i	−0.0458524	−	0.998948i	$-0.514600\pi$
$571$	22.6805	−	21.4841i	0.949148	−	0.899081i	0.995001	+	0.0998671i	$0.0318418\pi$
$572$	−0.130097	−	0.0286364i	−0.00543961	−	0.00119735i
$573$	−1.11483	−	20.5619i	−0.0465728	−	0.858984i
$574$	−5.71103	−	34.8358i	−0.238374	−	1.45402i
$575$	3.37361	+	3.97173i	0.140689	+	0.165632i
$576$	−0.370138	−	0.928977i	−0.0154224	−	0.0387074i
$577$	27.5572	−	20.9484i	1.14722	−	0.872094i	0.153968	−	0.988076i	$-0.450795\pi$
$577$	27.5572	−	20.9484i	1.14722	−	0.872094i	0.993251	+	0.115982i	$0.0370016\pi$
$578$	−18.2740	+	10.9951i	−0.760097	+	0.457335i
$579$	1.20906	−	7.37494i	0.0502468	−	0.306492i
$580$	−21.4843	−	2.33655i	−0.892086	−	0.0970202i
$581$	53.0011	+	40.2904i	2.19886	+	1.67153i
$582$	1.31593	−	4.73955i	0.0545470	−	0.196461i
$583$	0.113186	−	2.08760i	0.00468771	−	0.0864596i
$584$	9.38883	−	1.02110i	0.388512	−	0.0422533i
$585$	0.785813	+	0.472808i	0.0324894	+	0.0195482i
$586$	−19.1570	+	22.5534i	−0.791370	+	0.931673i
$587$	−30.7471	−	10.3599i	−1.26907	−	0.427599i	−0.397378	−	0.917655i	$-0.630080\pi$
$587$	−30.7471	−	10.3599i	−1.26907	−	0.427599i	−0.871691	+	0.490056i	$0.836976\pi$
$588$	−14.6316	+	6.76929i	−0.603396	+	0.279161i
$589$	6.62153			0.272835
$590$	12.5258	+	17.0093i	0.515680	+	0.700262i
$591$	−13.4593			−0.553642
$592$	−5.03431	+	2.32912i	−0.206909	+	0.0957263i
$593$	−37.9043	−	12.7714i	−1.55654	−	0.524460i	−0.596092	−	0.802916i	$-0.703281\pi$
$593$	−37.9043	−	12.7714i	−1.55654	−	0.524460i	−0.960449	+	0.278456i	$0.910177\pi$
$594$	−0.258606	+	0.304454i	−0.0106107	+	0.0124919i
$595$	−70.1477	−	42.2065i	−2.87578	−	1.73030i
$596$	−18.7442	+	2.03855i	−0.767790	+	0.0835022i
$597$	−0.903894	+	16.6713i	−0.0369939	+	0.682313i
$598$	−0.181397	+	0.653333i	−0.00741788	+	0.0267168i
$599$	12.8439	+	9.76367i	0.524787	+	0.398933i	0.833751	−	0.552141i	$-0.186189\pi$
$599$	12.8439	+	9.76367i	0.524787	+	0.398933i	−0.308964	+	0.951074i	$0.599982\pi$
$600$	2.54791	+	0.277102i	0.104018	+	0.0113126i
$601$	−3.41761	+	20.8465i	−0.139407	+	0.850347i	0.820832	+	0.571169i	$0.193510\pi$
$601$	−3.41761	+	20.8465i	−0.139407	+	0.850347i	−0.960240	+	0.279177i	$0.909938\pi$
$602$	43.4955	−	26.1704i	1.77275	−	1.06663i
$603$	9.06312	−	6.88961i	0.369079	−	0.280566i
$604$	−6.28908	−	15.7844i	−0.255899	−	0.642258i
$605$	−19.2999	−	22.7216i	−0.784653	−	0.923765i
$606$	0.245570	+	1.49791i	0.00997558	+	0.0608484i
$607$	−0.220696	−	4.07049i	−0.00895776	−	0.165216i	−0.999589	−	0.0286548i	$-0.990878\pi$
$607$	−0.220696	−	4.07049i	−0.00895776	−	0.165216i	0.990632	−	0.136561i	$-0.0436051\pi$
$608$	−2.84829	−	0.626956i	−0.115513	−	0.0254264i
$609$	27.4329	−	25.9858i	1.11164	−	1.05300i
$610$	18.0037	−	6.06615i	0.728948	−	0.245611i
$611$	0.364913	−	0.915862i	0.0147628	−	0.0370518i
$612$	1.65623	+	5.96520i	0.0669491	+	0.241129i
$613$	−46.7125	+	10.2822i	−1.88670	+	0.415294i	−0.998983	−	0.0450937i	$-0.985641\pi$
$613$	−46.7125	+	10.2822i	−1.88670	+	0.415294i	−0.887718	+	0.460388i	$0.847710\pi$
$614$	−11.0392	+	16.2816i	−0.445506	+	0.657072i
$615$	−9.45682	−	17.8375i	−0.381336	−	0.719276i
$616$	0.899722	−	1.69705i	0.0362508	−	0.0683763i
$617$	14.3241	+	21.1264i	0.576665	+	0.850518i	0.998420	−	0.0561921i	$-0.0178959\pi$
$617$	14.3241	+	21.1264i	0.576665	+	0.850518i	−0.421754	+	0.906710i	$0.638586\pi$
$618$	9.51859	+	9.01649i	0.382894	+	0.362696i
$619$	−14.0124	−	6.48281i	−0.563204	−	0.260566i	0.117563	−	0.993065i	$-0.462492\pi$
$619$	−14.0124	−	6.48281i	−0.563204	−	0.260566i	−0.680768	+	0.732499i	$0.738354\pi$
$620$	−5.66666	−	2.62168i	−0.227579	−	0.105289i
$621$	1.47614	+	1.39828i	0.0592356	+	0.0561109i
$622$	2.61243	+	3.85304i	0.104749	+	0.154493i
$623$	−26.9401	+	50.8145i	−1.07933	+	2.03584i
$624$	0.156203	+	0.294631i	0.00625314	+	0.0117947i
$625$	17.5349	−	25.8620i	0.701395	−	1.03448i
$626$	−26.2975	+	5.78852i	−1.05106	+	0.231356i
$627$	0.311676	+	1.12255i	0.0124471	+	0.0448305i
$628$	0.455551	−	1.14335i	0.0181785	−	0.0456245i
$629$	32.5430	−	10.9650i	1.29757	−	0.437204i
$630$	−9.60037	+	9.09396i	−0.382488	+	0.362312i
$631$	−1.02758	−	0.226188i	−0.0409075	−	0.00900441i	0.194470	−	0.980909i	$-0.437701\pi$
$631$	−1.02758	−	0.226188i	−0.0409075	−	0.00900441i	−0.235377	+	0.971904i	$0.575632\pi$
$632$	−0.612044	−	11.2885i	−0.0243458	−	0.449032i
$633$	−1.39351	−	8.50004i	−0.0553871	−	0.337846i
$634$	7.77456	+	9.15291i	0.308767	+	0.363509i
$635$	−15.6873	−	39.3723i	−0.622533	−	1.56244i
$636$	−4.16653	+	3.16731i	−0.165214	+	0.125592i
$637$	4.60662	−	2.77171i	0.182521	−	0.109819i
$638$	−0.507847	+	3.09773i	−0.0201059	+	0.122640i
$639$	1.56192	+	0.169869i	0.0617886	+	0.00671991i
$640$	2.18932	+	1.66428i	0.0865404	+	0.0657863i
$641$	1.09299	−	3.93660i	0.0431706	−	0.155487i	−0.938823	−	0.344399i	$-0.888083\pi$
$641$	1.09299	−	3.93660i	0.0431706	−	0.155487i	0.981994	+	0.188913i	$0.0604964\pi$
$642$	−0.599533	+	11.0577i	−0.0236617	+	0.436414i
$643$	36.9925	−	4.02318i	1.45884	−	0.158659i	0.655959	−	0.754796i	$-0.272264\pi$
$643$	36.9925	−	4.02318i	1.45884	−	0.158659i	0.802882	+	0.596138i	$0.203299\pi$
$644$	−8.37746	−	5.04055i	−0.330118	−	0.198625i
$645$	18.7947	−	22.1268i	0.740041	−	0.871244i
$646$	17.1103	+	5.76515i	0.673198	+	0.226827i
$647$	−7.37674	+	3.41284i	−0.290009	+	0.134173i	−0.559500	−	0.828830i	$-0.689007\pi$
$647$	−7.37674	+	3.41284i	−0.290009	+	0.134173i	0.269490	+	0.963003i	$0.413145\pi$
$648$	1.00000			0.0392837
$649$	2.56555	−	1.68300i	0.100707	−	0.0660637i
$650$	−0.854679			−0.0335233
$651$	9.90812	−	4.58399i	0.388330	−	0.179661i
$652$	15.1361	+	5.09995i	0.592776	+	0.199730i
$653$	−9.46225	+	11.1398i	−0.370286	+	0.435935i	−0.915473	−	0.402380i	$-0.868183\pi$
$653$	−9.46225	+	11.1398i	−0.370286	+	0.435935i	0.545186	+	0.838315i	$0.316459\pi$
$654$	−17.0661	−	10.2683i	−0.667338	−	0.401524i
$655$	−12.9874	+	1.41246i	−0.507458	+	0.0551894i
$656$	0.397452	−	7.33057i	0.0155179	−	0.286211i
$657$	−2.52659	+	9.09995i	−0.0985716	+	0.355023i
$658$	11.3170	+	8.60298i	0.441184	+	0.335379i
$659$	19.3360	+	2.10291i	0.753222	+	0.0819179i	0.476672	−	0.879081i	$-0.341843\pi$
$659$	19.3360	+	2.10291i	0.753222	+	0.0819179i	0.276551	+	0.960999i	$0.410809\pi$
$660$	0.177725	−	1.08408i	0.00691795	−	0.0421977i
$661$	−0.669528	+	0.402842i	−0.0260416	+	0.0156687i	−0.528515	−	0.848924i	$-0.677251\pi$
$661$	−0.669528	+	0.402842i	−0.0260416	+	0.0156687i	0.502474	+	0.864593i	$0.332423\pi$
$662$	8.64074	−	6.56852i	0.335832	−	0.255293i
$663$	−0.764153	−	1.91788i	−0.0296773	−	0.0744843i
$664$	8.96346	+	10.5526i	0.347850	+	0.409520i
$665$	6.23940	+	38.0587i	0.241954	+	1.47585i
$666$	−0.300308	−	5.53885i	−0.0116367	−	0.214626i
$667$	15.6045	+	3.43481i	0.604208	+	0.132996i
$668$	−6.41880	+	6.08021i	−0.248351	+	0.235250i
$669$	−16.9676	+	5.71705i	−0.656005	+	0.221034i
$670$	−11.5884	+	29.0847i	−0.447698	+	1.12364i
$671$	−0.738263	−	2.65898i	−0.0285003	−	0.102649i
$672$	−4.69607	+	1.03368i	−0.181155	+	0.0398752i
$673$	−4.51954	+	6.66582i	−0.174215	+	0.256948i	−0.904765	−	0.425911i	$-0.859954\pi$
$673$	−4.51954	+	6.66582i	−0.174215	+	0.256948i	0.730550	+	0.682860i	$0.239264\pi$
$674$	4.17718	+	7.87900i	0.160899	+	0.303488i
$675$	−1.20050	+	2.26438i	−0.0462073	+	0.0871561i
$676$	7.23302	+	10.6679i	0.278193	+	0.410304i
$677$	−8.61798	−	8.16339i	−0.331216	−	0.313744i	0.503960	−	0.863727i	$-0.331876\pi$
$677$	−8.61798	−	8.16339i	−0.331216	−	0.313744i	−0.835176	+	0.549982i	$0.814634\pi$
$678$	0.620094	+	0.286886i	0.0238146	+	0.0110178i
$679$	−21.4662	−	9.93131i	−0.823796	−	0.381129i
$680$	−12.3603	−	11.7083i	−0.473997	−	0.448994i
$681$	2.74884	+	4.05424i	0.105336	+	0.155359i
$682$	−0.424814	+	0.801284i	−0.0162670	+	0.0306827i
$683$	12.7498	+	24.0487i	0.487858	+	0.920197i	0.998185	+	0.0602173i	$0.0191794\pi$
$683$	12.7498	+	24.0487i	0.487858	+	0.920197i	−0.510328	+	0.859980i	$0.670476\pi$
$684$	1.63669	−	2.41394i	0.0625804	−	0.0922991i
$685$	−17.7852	+	3.91482i	−0.679538	+	0.149578i
$686$	11.7341	+	42.2625i	0.448011	+	1.61359i
$687$	−5.77821	+	14.5022i	−0.220452	+	0.553294i
$688$	10.0041	−	3.37076i	0.381401	−	0.128509i
$689$	1.26710	−	1.20026i	0.0482726	−	0.0457263i
$690$	−5.46092	−	1.20204i	−0.207894	−	0.0457608i
$691$	2.40197	+	44.3018i	0.0913754	+	1.68532i	0.581405	+	0.813614i	$0.302503\pi$
$691$	2.40197	+	44.3018i	0.0913754	+	1.68532i	−0.490030	+	0.871706i	$0.663014\pi$
$692$	−2.26079	−	13.7902i	−0.0859422	−	0.524224i
$693$	1.24350	+	1.46397i	0.0472368	+	0.0556114i
$694$	10.0419	+	25.2032i	0.381185	+	0.956701i
$695$	−23.1466	+	17.5956i	−0.878001	+	0.667439i
$696$	6.73344	−	4.05138i	0.255231	−	0.153567i
$697$	−7.35286	+	44.8505i	−0.278510	+	1.69883i
$698$	−0.880914	−	0.0958051i	−0.0333431	−	0.00362628i
$699$	−12.1881	−	9.26512i	−0.460995	−	0.350439i
$700$	3.29698	−	11.8746i	0.124614	−	0.448819i
$701$	1.03065	−	19.0092i	0.0389271	−	0.717969i	−0.912308	−	0.409504i	$-0.865702\pi$
$701$	1.03065	−	19.0092i	0.0389271	−	0.717969i	0.951236	−	0.308465i	$-0.0998153\pi$
$702$	−0.331522	+	0.0360552i	−0.0125125	+	0.00136082i
$703$	−13.8619	−	8.34046i	−0.522813	−	0.314566i
$704$	0.258606	−	0.304454i	0.00974656	−	0.0114745i
$705$	7.70467	+	2.59601i	0.290175	+	0.0977712i
$706$	7.96263	−	3.68390i	0.299677	−	0.138646i
$707$	7.29883			0.274501
$708$	−7.36900	−	2.16746i	−0.276944	−	0.0814580i
$709$	−51.1808			−1.92213			−0.961067	−	0.276316i	$-0.910887\pi$
$709$	−51.1808			−1.92213			−0.961067	+	0.276316i	$0.910887\pi$
$710$	−3.92139	+	1.81423i	−0.147167	+	0.0680867i
$711$	10.7133	+	3.60972i	0.401779	+	0.135375i
$712$	−7.74336	+	9.11618i	−0.290195	+	0.341643i
$713$	3.95551	+	2.37995i	0.148135	+	0.0891299i
$714$	29.5942	−	3.21856i	1.10754	−	0.120452i
$715$	−0.0198333	+	0.365804i	−0.000741723	+	0.0136803i
$716$	−2.26741	+	8.16648i	−0.0847371	+	0.305196i
$717$	18.5316	+	14.0874i	0.692077	+	0.526103i
$718$	21.5102	+	2.33937i	0.802753	+	0.0873047i
$719$	6.54641	−	39.9314i	0.244140	−	1.48919i	−0.525546	−	0.850765i	$-0.676139\pi$
$719$	6.54641	−	39.9314i	0.244140	−	1.48919i	0.769686	−	0.638423i	$-0.220413\pi$
$720$	−2.35642	+	1.41781i	−0.0878188	+	0.0528388i
$721$	50.1894	−	38.1530i	1.86915	−	1.42089i
$722$	3.88429	+	9.74883i	0.144558	+	0.362814i
$723$	−10.3976	−	12.2409i	−0.386689	−	0.455246i
$724$	1.48474	+	9.05653i	0.0551800	+	0.336583i
$725$	1.09037	+	20.1108i	0.0404955	+	0.746895i
$726$	10.5870	+	2.33037i	0.392920	+	0.0864882i
$727$	6.10987	−	5.78758i	0.226603	−	0.214649i	−0.565972	−	0.824425i	$-0.691499\pi$
$727$	6.10987	−	5.78758i	0.226603	−	0.214649i	0.792574	+	0.609775i	$0.208740\pi$
$728$	1.51958	−	0.512007i	0.0563195	−	0.0189762i
$729$	−0.370138	+	0.928977i	−0.0137088	+	0.0344065i
$730$	−6.94832	−	25.0256i	−0.257169	−	0.926238i
$731$	−63.8269	+	14.0494i	−2.36072	+	0.519635i
$732$	−3.87681	+	5.71787i	−0.143291	+	0.211339i
$733$	−2.12550	−	4.00911i	−0.0785070	−	0.148080i	0.841151	−	0.540801i	$-0.181879\pi$
$733$	−2.12550	−	4.00911i	−0.0785070	−	0.148080i	−0.919658	+	0.392721i	$0.871534\pi$
$734$	−10.6824	+	20.1492i	−0.394296	+	0.743720i
$735$	24.8806	+	36.6962i	0.917736	+	1.35356i
$736$	−1.47614	−	1.39828i	−0.0544114	−	0.0515412i
$737$	4.12735	+	1.90951i	0.152033	+	0.0703379i
$738$	6.66282	+	3.08255i	0.245262	+	0.113470i
$739$	30.9821	+	29.3478i	1.13969	+	1.07957i	0.995945	+	0.0899605i	$0.0286741\pi$
$739$	30.9821	+	29.3478i	1.13969	+	1.07957i	0.143748	+	0.989614i	$0.454085\pi$
$740$	8.56072	+	12.6261i	0.314698	+	0.464145i
$741$	−0.455564	+	0.859284i	−0.0167356	+	0.0315666i
$742$	11.7881	+	22.2348i	0.432755	+	0.816263i
$743$	8.34151	−	12.3028i	0.306020	−	0.451346i	−0.643319	−	0.765598i	$-0.722443\pi$
$743$	8.34151	−	12.3028i	0.306020	−	0.451346i	0.949340	+	0.314252i	$0.101754\pi$
$744$	2.21730	−	0.488066i	0.0812903	−	0.0178934i
$745$	13.8718	+	49.9619i	0.508225	+	1.83046i
$746$	1.85794	−	4.66307i	0.0680239	−	0.170727i
$747$	−13.1208	+	4.42093i	−0.480066	+	0.161753i
$748$	−1.79539	+	1.70069i	−0.0656460	+	0.0621832i
$749$	52.0042	+	11.4470i	1.90019	+	0.418264i
$750$	0.362846	+	6.69230i	0.0132493	+	0.244368i
$751$	−3.92925	−	23.9674i	−0.143380	−	0.874581i	−0.956339	−	0.292260i	$-0.905593\pi$
$751$	−3.92925	−	23.9674i	−0.143380	−	0.874581i	0.812959	−	0.582322i	$-0.197856\pi$
$752$	1.91392	+	2.25324i	0.0697933	+	0.0821671i
$753$	6.89907	+	17.3154i	0.251416	+	0.631007i
$754$	−2.08621	+	1.58590i	−0.0759754	+	0.0577550i
$755$	−40.0384	+	24.0903i	−1.45715	+	0.876737i
$756$	0.777928	−	4.74515i	0.0282930	−	0.172579i
$757$	−32.8168	−	3.56904i	−1.19275	−	0.129719i	−0.509870	−	0.860252i	$-0.670306\pi$
$757$	−32.8168	−	3.56904i	−1.19275	−	0.129719i	−0.682878	+	0.730533i	$0.739272\pi$
$758$	−7.41486	−	5.63663i	−0.269320	−	0.204732i
$759$	−0.217290	+	0.782606i	−0.00788711	+	0.0284068i
$760$	−0.434223	+	8.00878i	−0.0157509	+	0.290509i
$761$	−26.7154	+	2.90547i	−0.968432	+	0.105323i	−0.578643	−	0.815581i	$-0.696418\pi$
$761$	−26.7154	+	2.90547i	−0.968432	+	0.105323i	−0.389789	+	0.920904i	$0.627452\pi$
$762$	13.2053	+	7.94537i	0.478378	+	0.287831i
$763$	−62.0010	+	72.9933i	−2.24459	+	2.64253i
$764$	−19.5141	−	6.57508i	−0.705996	−	0.237878i
$765$	15.4518	−	7.14876i	0.558661	−	0.258464i
$766$	−22.9811			−0.830341
$767$	2.52113	+	0.452869i	0.0910329	+	0.0163522i
$768$	−1.00000			−0.0360844
$769$	−3.45127	+	1.59673i	−0.124456	+	0.0575795i	−0.481129	−	0.876650i	$-0.659773\pi$
$769$	−3.45127	+	1.59673i	−0.124456	+	0.0575795i	0.356673	+	0.934229i	$0.383911\pi$
$770$	−5.00585	−	1.68667i	−0.180398	−	0.0607833i
$771$	19.8316	−	23.3475i	0.714216	−	0.840840i
$772$	−6.40363	−	3.85294i	−0.230472	−	0.138670i
$773$	4.93036	−	0.536209i	0.177333	−	0.0192861i	−0.0190217	−	0.999819i	$-0.506055\pi$
$773$	4.93036	−	0.536209i	0.177333	−	0.0192861i	0.196355	+	0.980533i	$0.437090\pi$
$774$	−0.571527	+	10.5412i	−0.0205431	+	0.378895i
$775$	−1.55671	+	5.60675i	−0.0559185	+	0.201400i
$776$	−3.91586	−	2.97676i	−0.140571	−	0.106859i
$777$	−26.5163	−	2.88382i	−0.951267	−	0.103457i
$778$	4.71304	−	28.7483i	0.168971	−	1.03068i
$779$	18.3460	−	11.0384i	0.657315	−	0.395493i
$780$	0.730087	−	0.554998i	0.0261413	−	0.0198721i
$781$	0.232300	+	0.583030i	0.00831236	+	0.0208625i
$782$	8.14909	+	9.59385i	0.291411	+	0.343075i
$783$	1.27133	+	7.75478i	0.0454337	+	0.277133i
$784$	0.872807	+	16.0980i	0.0311717	+	0.574928i
$785$	−3.30555	−	0.727607i	−0.117980	−	0.0259694i
$786$	3.44876	−	3.26684i	0.123013	−	0.116524i
$787$	−3.81019	+	1.28380i	−0.135819	+	0.0457626i	−0.386390	−	0.922336i	$-0.626278\pi$
$787$	−3.81019	+	1.28380i	−0.135819	+	0.0457626i	0.250571	+	0.968098i	$0.419382\pi$
$788$	−4.98180	+	12.5034i	−0.177469	+	0.445415i
$789$	−2.58513	−	9.31079i	−0.0920330	−	0.331473i
$790$	−30.3629	+	6.68339i	−1.08027	+	0.237784i
$791$	1.84370	−	2.71926i	0.0655546	−	0.0966858i
$792$	0.187111	+	0.352929i	0.00664870	+	0.0125408i
$793$	1.07909	−	2.03538i	0.0383196	−	0.0722785i
$794$	11.6746	+	17.2188i	0.414316	+	0.611071i
$795$	10.4494	+	9.89816i	0.370601	+	0.351052i
$796$	15.1527	+	7.01040i	0.537074	+	0.248477i
$797$	−16.4714	−	7.62048i	−0.583447	−	0.269931i	0.105883	−	0.994379i	$-0.466233\pi$
$797$	−16.4714	−	7.62048i	−0.583447	−	0.269931i	−0.689330	+	0.724447i	$0.742095\pi$
$798$	−10.1813	−	9.64420i	−0.360413	−	0.341401i
$799$	−10.2711	−	15.1488i	−0.363366	−	0.535925i
$800$	1.20050	−	2.26438i	0.0424441	−	0.0800580i
$801$	−5.60261	−	10.5676i	−0.197959	−	0.373389i
$802$	6.97604	−	10.2889i	0.246332	−	0.363313i
$803$	−3.68438	+	0.810994i	−0.130019	+	0.0286194i
$804$	−3.04568	−	10.9695i	−0.107413	−	0.386866i
$805$	−9.95205	+	24.9778i	−0.350764	+	0.880351i
$806$	−0.717488	+	0.241750i	−0.0252724	+	0.00851528i
$807$	−12.0077	+	11.3743i	−0.422691	+	0.400394i
$808$	1.48242	+	0.326305i	0.0521512	+	0.0114794i
$809$	2.74539	+	50.6357i	0.0965228	+	1.78026i	0.500743	+	0.865596i	$0.333060\pi$
$809$	2.74539	+	50.6357i	0.0965228	+	1.78026i	−0.404220	+	0.914662i	$0.632457\pi$
$810$	−0.444913	−	2.71385i	−0.0156327	−	0.0953550i
$811$	−5.08791	−	5.98995i	−0.178661	−	0.210335i	0.665541	−	0.746361i	$-0.268201\pi$
$811$	−5.08791	−	5.98995i	−0.178661	−	0.210335i	−0.844202	+	0.536026i	$0.819925\pi$
$812$	−13.9863	−	35.1029i	−0.490822	−	1.23187i
$813$	−4.93997	+	3.75527i	−0.173252	+	0.131703i
$814$	1.89863	−	1.14237i	0.0665469	−	0.0400399i
$815$	7.10625	−	43.3462i	0.248921	−	1.51835i
$816$	6.15457	+	0.669350i	0.215453	+	0.0234319i
$817$	24.5104	+	18.6323i	0.857509	+	0.651861i
$818$	4.21276	−	15.1730i	0.147296	−	0.530511i
$819$	−0.0868129	+	1.60117i	−0.00303349	+	0.0559494i
$820$	−20.0709	+	2.18284i	−0.700907	+	0.0762282i
$821$	−16.1513	−	9.71791i	−0.563684	−	0.339157i	0.205025	−	0.978757i	$-0.434273\pi$
$821$	−16.1513	−	9.71791i	−0.563684	−	0.339157i	−0.768708	+	0.639600i	$0.779100\pi$
$822$	4.28698	−	5.04702i	0.149526	−	0.176035i
$823$	−9.11336	−	3.07065i	−0.317672	−	0.107036i	0.155949	−	0.987765i	$-0.450157\pi$
$823$	−9.11336	−	3.07065i	−0.317672	−	0.107036i	−0.473620	+	0.880729i	$0.657053\pi$
$824$	11.8993	−	5.50520i	0.414532	−	0.191783i
$825$	−1.02379			−0.0356439
$826$	−16.0175	+	33.2809i	−0.557319	+	1.15799i
$827$	−38.5540			−1.34065			−0.670327	−	0.742065i	$-0.733846\pi$
$827$	−38.5540			−1.34065			−0.670327	+	0.742065i	$0.733846\pi$
$828$	1.84534	−	0.853747i	0.0641301	−	0.0296698i
$829$	29.3234	+	9.88021i	1.01844	+	0.343154i	0.778508	−	0.627635i	$-0.215977\pi$
$829$	29.3234	+	9.88021i	1.01844	+	0.343154i	0.239936	+	0.970789i	$0.422873\pi$
$830$	24.6502	−	29.0205i	0.855622	−	1.00732i
$831$	3.83875	+	2.30970i	0.133165	+	0.0801226i
$832$	0.331522	−	0.0360552i	0.0114935	−	0.00124999i
$833$	5.40342	−	99.6603i	0.187218	−	3.45302i
$834$	2.82845	−	10.1871i	0.0979411	−	0.352752i
$835$	19.3566	+	14.7145i	0.669862	+	0.509216i
$836$	1.15819	+	0.125961i	0.0400568	+	0.00435644i
$837$	−0.367307	+	2.24048i	−0.0126960	+	0.0774422i
$838$	−18.2365	+	10.9725i	−0.629969	+	0.379040i
$839$	−16.3207	+	12.4067i	−0.563454	+	0.428327i	−0.847739	−	0.530413i	$-0.822037\pi$
$839$	−16.3207	+	12.4067i	−0.563454	+	0.428327i	0.284285	+	0.958740i	$0.408244\pi$
$840$	4.89461	+	12.2845i	0.168880	+	0.423857i
$841$	21.2038	+	24.9630i	0.731165	+	0.860794i
$842$	−4.85513	−	29.6150i	−0.167319	−	1.02060i
$843$	−0.459018	−	8.46609i	−0.0158094	−	0.291588i
$844$	−8.41213	−	1.85165i	−0.289557	−	0.0637364i
$845$	25.7331	−	24.3756i	0.885244	−	0.838548i
$846$	−2.80162	+	0.943975i	−0.0963216	+	0.0324545i
$847$	19.2939	−	48.4240i	0.662945	−	1.66387i
$848$	1.40017	+	5.04295i	0.0480820	+	0.173176i
$849$	−13.6628	+	3.00740i	−0.468905	+	0.103214i
$850$	−8.90422	+	13.1327i	−0.305412	+	0.450449i
$851$	−5.28295	−	9.96470i	−0.181097	−	0.341586i
$852$	0.735930	−	1.38811i	0.0252125	−	0.0475559i
$853$	7.64435	+	11.2746i	0.261738	+	0.386034i	0.935737	−	0.352697i	$-0.114735\pi$
$853$	7.64435	+	11.2746i	0.261738	+	0.386034i	−0.674000	+	0.738732i	$0.735425\pi$
$854$	24.1163	+	22.8441i	0.825242	+	0.781711i
$855$	−7.27925	−	3.36774i	−0.248945	−	0.115174i
$856$	10.0505	+	4.64984i	0.343518	+	0.158928i
$857$	−2.62020	−	2.48199i	−0.0895044	−	0.0847831i	0.641639	−	0.767006i	$-0.278255\pi$
$857$	−2.62020	−	2.48199i	−0.0895044	−	0.0847831i	−0.731144	+	0.682223i	$0.761013\pi$
$858$	−0.0747563	−	0.110257i	−0.00255214	−	0.00376412i
$859$	−8.60046	+	16.2222i	−0.293444	+	0.553494i	−0.985772	−	0.168089i	$-0.946240\pi$
$859$	−8.60046	+	16.2222i	−0.293444	+	0.553494i	0.692328	+	0.721583i	$0.256585\pi$
$860$	−13.5987	−	25.6498i	−0.463711	−	0.874652i
$861$	19.8103	−	29.2181i	0.675135	−	0.995749i
$862$	2.25954	−	0.497363i	0.0769604	−	0.0169403i
$863$	8.03418	+	28.9365i	0.273487	+	0.985010i	0.964914	+	0.262564i	$0.0845682\pi$
$863$	8.03418	+	28.9365i	0.273487	+	0.985010i	−0.691428	+	0.722446i	$0.743018\pi$
$864$	0.370138	−	0.928977i	0.0125924	−	0.0316044i
$865$	−36.4186	+	12.2709i	−1.23827	+	0.417222i
$866$	29.0440	−	27.5119i	0.986954	−	0.934892i
$867$	−20.8281	−	4.58462i	−0.707360	−	0.155702i
$868$	−0.591042	−	10.9011i	−0.0200613	−	0.370008i
$869$	0.730596	+	4.45644i	0.0247838	+	0.151174i
$870$	−13.9906	−	16.4710i	−0.474327	−	0.558421i
$871$	1.40522	+	3.52683i	0.0476140	+	0.119502i
$872$	−15.8559	+	12.0533i	−0.536948	+	0.408177i
$873$	4.21475	−	2.53593i	0.142648	−	0.0858282i
$874$	0.959364	−	5.85186i	0.0324510	−	0.197942i
$875$	32.0382	+	3.48437i	1.08309	+	0.117793i
$876$	7.51845	+	5.71538i	0.254025	+	0.193105i
$877$	11.5833	−	41.7193i	0.391140	−	1.40876i	−0.461908	−	0.886928i	$-0.652835\pi$
$877$	11.5833	−	41.7193i	0.391140	−	1.40876i	0.853048	−	0.521832i	$-0.174751\pi$
$878$	0.977831	−	18.0350i	0.0330002	−	0.608653i
$879$	−29.4179	+	3.19939i	−0.992241	+	0.107913i
$880$	−0.941300	−	0.566361i	−0.0317312	−	0.0190920i
$881$	10.8276	−	12.7472i	0.364791	−	0.429465i	−0.548892	−	0.835893i	$-0.684950\pi$
$881$	10.8276	−	12.7472i	0.364791	−	0.429465i	0.913683	+	0.406429i	$0.133226\pi$
$882$	−15.2777	−	5.14766i	−0.514427	−	0.173331i
$883$	7.58192	−	3.50777i	0.255152	−	0.118046i	−0.288144	−	0.957587i	$-0.593038\pi$
$883$	7.58192	−	3.50777i	0.255152	−	0.118046i	0.543296	+	0.839541i	$0.317176\pi$
$884$	−2.06451			−0.0694369
$885$	−2.60359	+	20.9627i	−0.0875188	+	0.704653i
$886$	−28.2123			−0.947812
$887$	34.3971	−	15.9138i	1.15494	−	0.534333i	0.253544	−	0.967324i	$-0.418404\pi$
$887$	34.3971	−	15.9138i	1.15494	−	0.534333i	0.901399	+	0.432990i	$0.142542\pi$
$888$	−5.25662	−	1.77116i	−0.176401	−	0.0594363i
$889$	47.9748	−	56.4803i	1.60902	−	1.89429i
$890$	28.1851	+	16.9584i	0.944766	+	0.568447i
$891$	−0.397119	+	0.0431893i	−0.0133040	+	0.00144690i
$892$	−0.969350	+	17.8786i	−0.0324562	+	0.598620i
$893$	−2.30668	+	8.30792i	−0.0771902	+	0.278014i
$894$	−15.0101	−	11.4104i	−0.502012	−	0.381620i
$895$	23.1714	+	2.52004i	0.774534	+	0.0842357i
$896$	−0.777928	+	4.74515i	−0.0259887	+	0.158524i
$897$	−0.580990	+	0.349570i	−0.0193987	+	0.0116718i
$898$	−14.2786	+	10.8543i	−0.476484	+	0.362214i
$899$	6.60377	+	16.5742i	0.220248	+	0.552781i
$900$	1.65921	+	1.95337i	0.0553069	+	0.0651123i
$901$	−5.24194	−	31.9744i	−0.174634	−	1.06522i
$902$	0.158767	+	2.92828i	0.00528635	+	0.0975010i
$903$	49.5749	+	10.9123i	1.64975	+	0.363137i
$904$	0.496031	−	0.469865i	0.0164977	−	0.0156275i
$905$	23.9175	−	8.05874i	0.795044	−	0.267882i
$906$	6.28908	−	15.7844i	0.208941	−	0.524402i
$907$	3.75277	+	13.5163i	0.124609	+	0.448800i	0.999360	−	0.0357722i	$-0.0113891\pi$
$907$	3.75277	+	13.5163i	0.124609	+	0.448800i	−0.874751	+	0.484572i	$0.838975\pi$
$908$	4.78375	−	1.05298i	0.158754	−	0.0349445i
$909$	−0.851828	+	1.25635i	−0.0282534	+	0.0416706i
$910$	−2.06559	−	3.89612i	−0.0684737	−	0.129155i
$911$	24.4737	−	46.1623i	0.810850	−	1.52943i	−0.0370761	−	0.999312i	$-0.511804\pi$
$911$	24.4737	−	46.1623i	0.810850	−	1.52943i	0.847927	−	0.530114i	$-0.177851\pi$
$912$	−1.63669	−	2.41394i	−0.0541962	−	0.0799334i
$913$	−4.01532	−	3.80352i	−0.132888	−	0.125878i
$914$	29.3998	+	13.6018i	0.972460	+	0.449908i
$915$	17.2423	+	7.97714i	0.570013	+	0.263716i
$916$	11.3335	+	10.7356i	0.374469	+	0.354716i
$917$	−12.8188	−	18.9063i	−0.423313	−	0.624340i
$918$	−2.89985	+	5.46970i	−0.0957093	+	0.180527i
$919$	−7.71383	−	14.5498i	−0.254456	−	0.479954i	0.723069	−	0.690776i	$-0.242731\pi$
$919$	−7.71383	−	14.5498i	−0.254456	−	0.479954i	−0.977525	+	0.210822i	$0.932386\pi$
$920$	−3.13796	+	4.62814i	−0.103455	+	0.152585i
$921$	−19.2113	+	4.22872i	−0.633033	+	0.139341i
$922$	−6.33911	−	22.8314i	−0.208767	−	0.751912i
$923$	−0.193928	+	0.486724i	−0.00638323	+	0.0160207i
$924$	1.82026	−	0.613316i	0.0598821	−	0.0201766i
$925$	10.3212	−	9.77672i	0.339358	−	0.321457i
$926$	−30.4535	−	6.70333i	−1.00076	−	0.220285i
$927$	0.709820	+	13.0919i	0.0233135	+	0.429993i
$928$	−1.27133	−	7.75478i	−0.0417335	−	0.254563i
$929$	20.7534	+	24.4328i	0.680898	+	0.801615i	0.988712	−	0.149831i	$-0.0478731\pi$
$929$	20.7534	+	24.4328i	0.680898	+	0.801615i	−0.307813	+	0.951447i	$0.599597\pi$
$930$	−2.31105	−	5.80029i	−0.0757822	−	0.190199i
$931$	−37.4310	+	28.4543i	−1.22675	+	0.932551i
$932$	−13.1184	+	7.89305i	−0.429706	+	0.258545i
$933$	−0.753125	+	4.59386i	−0.0246562	+	0.150396i
$934$	−18.2996	−	1.99020i	−0.598781	−	0.0651213i
$935$	5.41420	+	4.11577i	0.177063	+	0.134600i
$936$	−0.0892145	+	0.321322i	−0.00291607	+	0.0105027i
$937$	−1.68283	+	31.0379i	−0.0549755	+	1.01396i	0.832767	+	0.553624i	$0.186755\pi$
$937$	−1.68283	+	31.0379i	−0.0549755	+	1.01396i	−0.887742	+	0.460340i	$0.847727\pi$
$938$	−54.4214	+	5.91868i	−1.77692	+	0.193252i
$939$	−23.0726	−	13.8823i	−0.752947	−	0.453033i
$940$	5.26342	−	6.19658i	0.171674	−	0.202110i
$941$	28.2398	+	9.51509i	0.920590	+	0.310183i	0.739401	−	0.673265i	$-0.235109\pi$
$941$	28.2398	+	9.51509i	0.920590	+	0.310183i	0.181189	+	0.983448i	$0.442005\pi$
$942$	1.11701	−	0.516782i	0.0363941	−	0.0168377i
$943$	14.9269			0.486087
$944$	−4.74106	+	6.04337i	−0.154309	+	0.196695i
$945$	−13.2237			−0.430168
$946$	−3.82723	+	1.77066i	−0.124434	+	0.0575692i
$947$	7.18287	+	2.42019i	0.233412	+	0.0786456i	0.433577	−	0.901117i	$-0.357251\pi$
$947$	7.18287	+	2.42019i	0.233412	+	0.0786456i	−0.200165	+	0.979762i	$0.564148\pi$
$948$	7.31874	−	8.61629i	0.237702	−	0.279844i
$949$	−2.69860	−	1.62370i	−0.0876004	−	0.0527074i
$950$	7.43092	−	0.808161i	0.241091	−	0.0262202i
$951$	−0.650162	+	11.9915i	−0.0210829	+	0.388852i
$952$	7.96397	−	28.6836i	0.258114	−	0.929642i
$953$	−17.5881	−	13.3702i	−0.569736	−	0.433102i	0.280235	−	0.959931i	$-0.409587\pi$
$953$	−17.5881	−	13.3702i	−0.569736	−	0.433102i	−0.849971	+	0.526830i	$0.823381\pi$
$954$	−5.20304	−	0.565865i	−0.168455	−	0.0183206i
$955$	−9.16168	+	55.8838i	−0.296465	+	1.80836i
$956$	19.9461	−	12.0012i	0.645103	−	0.388146i
$957$	−2.49900	+	1.89969i	−0.0807813	+	0.0614084i
$958$	1.49435	+	3.75053i	0.0482802	+	0.121174i
$959$	−20.6139	−	24.2686i	−0.665658	−	0.783674i
$960$	0.444913	+	2.71385i	0.0143595	+	0.0875892i
$961$	−1.39924	−	25.8074i	−0.0451367	−	0.832498i
$962$	1.80655	+	0.397651i	0.0582454	+	0.0128208i
$963$	−8.03966	+	7.61557i	−0.259074	+	0.245408i
$964$	−15.2201	+	5.12824i	−0.490206	+	0.165170i
$965$	−7.60724	+	19.0927i	−0.244886	+	0.614616i
$966$	−2.61561	−	9.42059i	−0.0841560	−	0.303102i
$967$	50.5951	−	11.1368i	1.62703	−	0.358136i	0.694574	−	0.719422i	$-0.255593\pi$
$967$	50.5951	−	11.1368i	1.62703	−	0.358136i	0.932455	+	0.361286i	$0.117662\pi$
$968$	6.08351	−	8.97251i	0.195531	−	0.288387i
$969$	8.45735	+	15.9522i	0.271689	+	0.512460i
$970$	−6.33626	+	11.9514i	−0.203445	+	0.383738i
$971$	22.4308	+	33.0829i	0.719838	+	1.06168i	0.994960	+	0.100272i	$0.0319714\pi$
$971$	22.4308	+	33.0829i	0.719838	+	1.06168i	−0.275122	+	0.961409i	$0.588718\pi$
$972$	0.725995	+	0.687699i	0.0232863	+	0.0220580i
$973$	−46.1392	−	21.3463i	−1.47915	−	0.684330i
$974$	26.3297	+	12.1814i	0.843658	+	0.390318i
$975$	−0.620493	−	0.587762i	−0.0198717	−	0.0188235i
$976$	3.87681	+	5.71787i	0.124094	+	0.183025i
$977$	−1.88087	+	3.54770i	−0.0601745	+	0.113501i	−0.911775	−	0.410691i	$-0.865288\pi$
$977$	−1.88087	+	3.54770i	−0.0601745	+	0.113501i	0.851600	+	0.524192i	$0.175632\pi$
$978$	7.48152	+	14.1116i	0.239233	+	0.451241i
$979$	2.68131	−	3.95464i	0.0856952	−	0.126391i
$980$	43.2992	−	9.53087i	1.38314	−	0.304452i
$981$	−5.32839	−	19.1911i	−0.170122	−	0.612726i
$982$	11.6992	−	29.3628i	0.373337	−	0.937005i
$983$	4.89712	−	1.65003i	0.156194	−	0.0526278i	−0.240118	−	0.970744i	$-0.577186\pi$
$983$	4.89712	−	1.65003i	0.156194	−	0.0526278i	0.396312	+	0.918116i	$0.370290\pi$
$984$	5.32978	−	5.04864i	0.169907	−	0.160945i
$985$	36.1488	+	7.95695i	1.15180	+	0.253530i
$986$	2.63384	+	48.5783i	0.0838785	+	1.54705i
$987$	2.29985	+	14.0284i	0.0732049	+	0.446530i
$988$	0.629634	+	0.741262i	0.0200313	+	0.0235827i
$989$	7.94485	+	19.9401i	0.252631	+	0.634057i
$990$	0.874547	−	0.664814i	0.0277949	−	0.0211292i
$991$	5.36576	−	3.22847i	0.170449	−	0.102556i	−0.427773	−	0.903886i	$-0.640702\pi$
$991$	5.36576	−	3.22847i	0.170449	−	0.102556i	0.598222	+	0.801330i	$0.295874\pi$
$992$	0.367307	−	2.24048i	0.0116620	−	0.0711352i
$993$	10.7903	+	1.17352i	0.342420	+	0.0372404i
$994$	−6.01430	−	4.57195i	−0.190762	−	0.145013i
$995$	12.2835	−	44.2413i	0.389414	−	1.40254i
$996$	−0.749586	+	13.8253i	−0.0237516	+	0.438072i
$997$	−35.6900	+	3.88152i	−1.13031	+	0.122929i	−0.654105	−	0.756404i	$-0.726955\pi$
$997$	−35.6900	+	3.88152i	−1.13031	+	0.122929i	−0.476208	+	0.879333i	$0.657989\pi$
$998$	−1.94075	−	1.16771i	−0.0614333	−	0.0369632i
$999$	3.59104	−	4.22770i	0.113616	−	0.133759i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.c.121.1	yes	84
59.20	even	29	inner	354.2.e.c.79.1	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.c.79.1	✓	84	59.20	even	29	inner
354.2.e.c.121.1	yes	84	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(0.907575 - 0.419889i) q^{2} +(0.947653 + 0.319302i) q^{3} +(0.647386 - 0.762162i) q^{4} +(-2.35642 - 1.41781i) q^{5} +(0.994138 - 0.108119i) q^{6} +(0.260327 - 4.80144i) q^{7} +(0.267528 - 0.963550i) q^{8} +(0.796093 + 0.605174i) q^{9} +O(q^{10})\)	\(q+(0.907575 - 0.419889i) q^{2} +(0.947653 + 0.319302i) q^{3} +(0.647386 - 0.762162i) q^{4} +(-2.35642 - 1.41781i) q^{5} +(0.994138 - 0.108119i) q^{6} +(0.260327 - 4.80144i) q^{7} +(0.267528 - 0.963550i) q^{8} +(0.796093 + 0.605174i) q^{9} +(-2.73396 - 0.297336i) q^{10} +(-0.0646256 + 0.394199i) q^{11} +(0.856857 - 0.515554i) q^{12} +(-0.265479 + 0.201812i) q^{13} +(-1.77981 - 4.46698i) q^{14} +(-1.78036 - 2.09601i) q^{15} +(-0.161782 - 0.986827i) q^{16} +(0.335166 + 6.18178i) q^{17} +(0.976621 + 0.214970i) q^{18} +(2.11735 - 2.00566i) q^{19} +(-2.60612 + 0.878104i) q^{20} +(1.77981 - 4.46698i) q^{21} +(0.106867 + 0.384901i) q^{22} +(1.98573 - 0.437093i) q^{23} +(0.561187 - 0.827689i) q^{24} +(1.20050 + 2.26438i) q^{25} +(-0.156203 + 0.294631i) q^{26} +(0.561187 + 0.827689i) q^{27} +(-3.49095 - 3.30680i) q^{28} +(7.13200 + 3.29962i) q^{29} +(-2.49590 - 1.15473i) q^{30} +(1.64829 + 1.56134i) q^{31} +(-0.561187 - 0.827689i) q^{32} +(-0.187111 + 0.352929i) q^{33} +(2.89985 + 5.46970i) q^{34} +(-7.42099 + 10.9451i) q^{35} +(0.976621 - 0.214970i) q^{36} +(-1.48398 - 5.34480i) q^{37} +(1.07950 - 2.70934i) q^{38} +(-0.316020 + 0.106480i) q^{39} +(-1.99654 + 1.89123i) q^{40} +(7.16970 + 1.57817i) q^{41} +(-0.260327 - 4.80144i) q^{42} +(1.70788 + 10.4176i) q^{43} +(0.258606 + 0.304454i) q^{44} +(-1.01791 - 2.55476i) q^{45} +(1.61867 - 1.23048i) q^{46} +(-2.53319 + 1.52417i) q^{47} +(0.161782 - 0.986827i) q^{48} +(-16.0271 - 1.74305i) q^{49} +(2.04033 + 1.55102i) q^{50} +(-1.65623 + 5.96520i) q^{51} +(-0.0180541 + 0.332988i) q^{52} +(-5.20304 + 0.565865i) q^{53} +(0.856857 + 0.515554i) q^{54} +(0.711186 - 0.837272i) q^{55} +(-4.55678 - 1.53536i) q^{56} +(2.64692 - 1.22460i) q^{57} +7.85830 q^{58} +(-5.19674 - 5.65632i) q^{59} -2.75008 q^{60} +(-6.26975 + 2.90069i) q^{61} +(2.15154 + 0.724937i) q^{62} +(3.11295 - 3.66485i) q^{63} +(-0.856857 - 0.515554i) q^{64} +(0.911712 - 0.0991546i) q^{65} +(-0.0216264 + 0.398875i) q^{66} +(3.04568 - 10.9695i) q^{67} +(4.92850 + 3.74655i) q^{68} +(2.02135 + 0.219835i) q^{69} +(-2.13936 + 13.0495i) q^{70} +(1.34623 - 0.810002i) q^{71} +(0.796093 - 0.605174i) q^{72} +(3.49566 + 8.77343i) q^{73} +(-3.59104 - 4.22770i) q^{74} +(0.414636 + 2.52917i) q^{75} +(-0.157895 - 2.91220i) q^{76} +(1.87590 + 0.412916i) q^{77} +(-0.242103 + 0.229332i) q^{78} +(10.7133 - 3.60972i) q^{79} +(-1.01791 + 2.55476i) q^{80} +(0.267528 + 0.963550i) q^{81} +(7.16970 - 1.57817i) q^{82} +(-7.76998 + 11.4599i) q^{83} +(-2.25234 - 4.24836i) q^{84} +(7.97482 - 15.0421i) q^{85} +(5.92427 + 8.73764i) q^{86} +(5.70509 + 5.40415i) q^{87} +(0.362541 + 0.167729i) q^{88} +(-10.8555 - 5.02227i) q^{89} +(-1.99654 - 1.89123i) q^{90} +(0.899876 + 1.32722i) q^{91} +(0.952400 - 1.79642i) q^{92} +(1.06347 + 2.00591i) q^{93} +(-1.65908 + 2.44696i) q^{94} +(-7.83303 + 1.72418i) q^{95} +(-0.267528 - 0.963550i) q^{96} +(1.82065 - 4.56949i) q^{97} +(-15.2777 + 5.14766i) q^{98} +(-0.290007 + 0.274709i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9	\( 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9} - 26 q^{11} + 3 q^{12} - 3 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} - 3 q^{18} + 4 q^{19} - q^{21} + 3 q^{22} - 2 q^{23} + 3 q^{24} + 41 q^{25} + 26 q^{26} + 3 q^{27} + q^{28} - 2 q^{29} + 8 q^{31} - 3 q^{32} - 3 q^{33} - 26 q^{34} + 83 q^{35} - 3 q^{36} - 53 q^{37} + 4 q^{38} + 3 q^{39} - 7 q^{41} - q^{42} + 119 q^{43} + 3 q^{44} - 31 q^{46} - 12 q^{47} + 3 q^{48} - 38 q^{49} - 133 q^{50} - 3 q^{51} - 32 q^{52} - 83 q^{53} + 3 q^{54} - 83 q^{55} + q^{56} - 4 q^{57} + 56 q^{58} - 57 q^{59} - 48 q^{61} - 21 q^{62} + q^{63} - 3 q^{64} - 33 q^{65} - 3 q^{66} - 88 q^{67} - 26 q^{68} + 89 q^{69} - 62 q^{70} - 35 q^{71} - 3 q^{72} - 71 q^{73} - 24 q^{74} + 17 q^{75} + 33 q^{76} + 113 q^{77} + 3 q^{78} - 5 q^{79} - 3 q^{81} - 7 q^{82} - 51 q^{83} - q^{84} + 125 q^{85} + 61 q^{86} + 31 q^{87} + 32 q^{88} - 58 q^{89} + 173 q^{91} - 2 q^{92} + 21 q^{93} + 17 q^{94} + 26 q^{95} + 3 q^{96} + 20 q^{98} + 3 q^{99}+O(q^{100}) \) 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9 - 26 * q^11 + 3 * q^12 - 3 * q^13 + q^14 - 3 * q^16 + 3 * q^17 - 3 * q^18 + 4 * q^19 - q^21 + 3 * q^22 - 2 * q^23 + 3 * q^24 + 41 * q^25 + 26 * q^26 + 3 * q^27 + q^28 - 2 * q^29 + 8 * q^31 - 3 * q^32 - 3 * q^33 - 26 * q^34 + 83 * q^35 - 3 * q^36 - 53 * q^37 + 4 * q^38 + 3 * q^39 - 7 * q^41 - q^42 + 119 * q^43 + 3 * q^44 - 31 * q^46 - 12 * q^47 + 3 * q^48 - 38 * q^49 - 133 * q^50 - 3 * q^51 - 32 * q^52 - 83 * q^53 + 3 * q^54 - 83 * q^55 + q^56 - 4 * q^57 + 56 * q^58 - 57 * q^59 - 48 * q^61 - 21 * q^62 + q^63 - 3 * q^64 - 33 * q^65 - 3 * q^66 - 88 * q^67 - 26 * q^68 + 89 * q^69 - 62 * q^70 - 35 * q^71 - 3 * q^72 - 71 * q^73 - 24 * q^74 + 17 * q^75 + 33 * q^76 + 113 * q^77 + 3 * q^78 - 5 * q^79 - 3 * q^81 - 7 * q^82 - 51 * q^83 - q^84 + 125 * q^85 + 61 * q^86 + 31 * q^87 + 32 * q^88 - 58 * q^89 + 173 * q^91 - 2 * q^92 + 21 * q^93 + 17 * q^94 + 26 * q^95 + 3 * q^96 + 20 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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