LMFDB - Embedded newform 462.2.p.b.439.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(241,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

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

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

chi := DirichletCharacter("462.241");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.p (of order $6$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + \cdots + 13417 $ x^16 - 8x^15 + 74x^14 - 378x^13 + 1878x^12 - 6718x^11 + 22086x^10 - 56904x^9 + 130215x^8 - 239606x^7 + 378750x^6 - 477124x^5 + 493030x^4 - 386266x^3 + 223844x^2 - 82874*x + 13417
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			439.2
Root			$0.500000 + 0.0286340i$ of defining polynomial
Character	$\chi$	$=$	462.439
Dual form			462.2.p.b.241.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.725202 + 0.418696i) q^{5} +1.00000 q^{6} +(-2.44037 - 1.02205i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.725202 + 0.418696i) q^{5} +1.00000 q^{6} +(-2.44037 - 1.02205i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.418696 - 0.725202i) q^{10} +(-3.15670 + 1.01748i) q^{11} +(-0.866025 - 0.500000i) q^{12} +2.59370 q^{13} +(1.60239 + 2.10531i) q^{14} -0.837391 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.98686 - 5.17339i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(1.55590 - 2.69491i) q^{19} +0.837391i q^{20} +(2.62445 - 0.335059i) q^{21} +(3.24252 + 0.697189i) q^{22} +(-1.43256 + 2.48126i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-2.14939 - 3.72285i) q^{25} +(-2.24621 - 1.29685i) q^{26} +1.00000i q^{27} +(-0.335059 - 2.62445i) q^{28} -5.38769i q^{29} +(0.725202 + 0.418696i) q^{30} +(-0.913399 + 0.527351i) q^{31} +(0.866025 - 0.500000i) q^{32} +(2.22504 - 2.45951i) q^{33} +5.97372i q^{34} +(-1.34183 - 1.76297i) q^{35} +1.00000 q^{36} +(5.49467 - 9.51705i) q^{37} +(-2.69491 + 1.55590i) q^{38} +(-2.24621 + 1.29685i) q^{39} +(0.418696 - 0.725202i) q^{40} -11.2350 q^{41} +(-2.44037 - 1.02205i) q^{42} +1.27527i q^{43} +(-2.45951 - 2.22504i) q^{44} +(0.725202 - 0.418696i) q^{45} +(2.48126 - 1.43256i) q^{46} +(-10.6034 - 6.12185i) q^{47} -1.00000i q^{48} +(4.91081 + 4.98838i) q^{49} +4.29878i q^{50} +(5.17339 + 2.98686i) q^{51} +(1.29685 + 2.24621i) q^{52} +(-2.58730 - 4.48134i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.71526 - 0.583820i) q^{55} +(-1.02205 + 2.44037i) q^{56} +3.11181i q^{57} +(-2.69384 + 4.66587i) q^{58} +(-8.38751 + 4.84253i) q^{59} +(-0.418696 - 0.725202i) q^{60} +(-2.03524 + 3.52514i) q^{61} +1.05470 q^{62} +(-2.10531 + 1.60239i) q^{63} -1.00000 q^{64} +(1.88096 + 1.08597i) q^{65} +(-3.15670 + 1.01748i) q^{66} +(-6.51916 - 11.2915i) q^{67} +(2.98686 - 5.17339i) q^{68} -2.86511i q^{69} +(0.280576 + 2.19769i) q^{70} +14.0795 q^{71} +(-0.866025 - 0.500000i) q^{72} +(4.95659 + 8.58507i) q^{73} +(-9.51705 + 5.49467i) q^{74} +(3.72285 + 2.14939i) q^{75} +3.11181 q^{76} +(8.74343 + 0.743301i) q^{77} +2.59370 q^{78} +(11.7018 + 6.75603i) q^{79} +(-0.725202 + 0.418696i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(9.72978 + 5.61749i) q^{82} +2.99287 q^{83} +(1.60239 + 2.10531i) q^{84} -5.00234i q^{85} +(0.637637 - 1.10442i) q^{86} +(2.69384 + 4.66587i) q^{87} +(1.01748 + 3.15670i) q^{88} +(7.28049 + 4.20339i) q^{89} -0.837391 q^{90} +(-6.32960 - 2.65091i) q^{91} -2.86511 q^{92} +(0.527351 - 0.913399i) q^{93} +(6.12185 + 10.6034i) q^{94} +(2.25669 - 1.30290i) q^{95} +(-0.500000 + 0.866025i) q^{96} -0.786131i q^{97} +(-1.75869 - 6.77547i) q^{98} +(-0.697189 + 3.24252i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 12 q^{5} + 16 q^{6} + 6 q^{7} + 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 12 * q^5 + 16 * q^6 + 6 * q^7 + 8 * q^9	$ 16 q + 8 q^{4} + 12 q^{5} + 16 q^{6} + 6 q^{7} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{14} - 4 q^{15} - 8 q^{16} + 10 q^{19} + 4 q^{21} + 2 q^{22} - 4 q^{23} + 8 q^{24} + 10 q^{25} + 12 q^{26} + 12 q^{30} + 6 q^{31} + 4 q^{33} + 8 q^{35} + 16 q^{36} + 14 q^{37} - 12 q^{38} + 12 q^{39} + 2 q^{40} - 32 q^{41} + 6 q^{42} + 4 q^{44} + 12 q^{45} - 18 q^{46} - 24 q^{47} - 6 q^{49} - 6 q^{51} + 8 q^{54} + 14 q^{55} + 4 q^{56} - 2 q^{60} - 28 q^{61} + 8 q^{62} + 6 q^{63} - 16 q^{64} - 72 q^{65} - 4 q^{66} - 16 q^{67} - 30 q^{70} - 56 q^{71} + 44 q^{73} - 24 q^{74} - 12 q^{75} + 20 q^{76} - 52 q^{77} + 30 q^{79} - 12 q^{80} - 8 q^{81} - 12 q^{82} - 8 q^{83} + 8 q^{84} - 12 q^{86} - 2 q^{88} - 36 q^{89} - 4 q^{90} - 8 q^{91} - 8 q^{92} + 4 q^{93} - 14 q^{94} - 72 q^{95} - 8 q^{96} + 40 q^{98} - 8 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 12 * q^5 + 16 * q^6 + 6 * q^7 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^14 - 4 * q^15 - 8 * q^16 + 10 * q^19 + 4 * q^21 + 2 * q^22 - 4 * q^23 + 8 * q^24 + 10 * q^25 + 12 * q^26 + 12 * q^30 + 6 * q^31 + 4 * q^33 + 8 * q^35 + 16 * q^36 + 14 * q^37 - 12 * q^38 + 12 * q^39 + 2 * q^40 - 32 * q^41 + 6 * q^42 + 4 * q^44 + 12 * q^45 - 18 * q^46 - 24 * q^47 - 6 * q^49 - 6 * q^51 + 8 * q^54 + 14 * q^55 + 4 * q^56 - 2 * q^60 - 28 * q^61 + 8 * q^62 + 6 * q^63 - 16 * q^64 - 72 * q^65 - 4 * q^66 - 16 * q^67 - 30 * q^70 - 56 * q^71 + 44 * q^73 - 24 * q^74 - 12 * q^75 + 20 * q^76 - 52 * q^77 + 30 * q^79 - 12 * q^80 - 8 * q^81 - 12 * q^82 - 8 * q^83 + 8 * q^84 - 12 * q^86 - 2 * q^88 - 36 * q^89 - 4 * q^90 - 8 * q^91 - 8 * q^92 + 4 * q^93 - 14 * q^94 - 72 * q^95 - 8 * q^96 + 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.725202	+	0.418696i	0.324320	+	0.187246i	0.653317	−	0.757085i	$-0.273377\pi$
$5$	0.725202	+	0.418696i	0.324320	+	0.187246i	−0.328996	+	0.944331i	$0.606710\pi$
$6$	1.00000			0.408248
$7$	−2.44037	−	1.02205i	−0.922373	−	0.386300i
$7$	−2.44037	−	1.02205i	−0.922373	−	0.386300i
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−0.418696	−	0.725202i	−0.132403	−	0.229329i
$11$	−3.15670	+	1.01748i	−0.951780	+	0.306781i
$11$	−3.15670	+	1.01748i	−0.951780	+	0.306781i
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$	2.59370			0.719364			0.359682	−	0.933075i	$-0.382885\pi$
$13$	2.59370			0.719364			0.359682	+	0.933075i	$0.382885\pi$
$14$	1.60239	+	2.10531i	0.428258	+	0.562668i
$15$	−0.837391			−0.216214
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.98686	−	5.17339i	−0.724420	−	1.25473i	−0.959212	−	0.282687i	$-0.908774\pi$
$17$	−2.98686	−	5.17339i	−0.724420	−	1.25473i	0.234792	−	0.972046i	$-0.424559\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	1.55590	−	2.69491i	0.356949	−	0.618254i	−0.630501	−	0.776189i	$-0.717150\pi$
$19$	1.55590	−	2.69491i	0.356949	−	0.618254i	0.987449	+	0.157935i	$0.0504837\pi$
$20$			0.837391i			0.187246i
$21$	2.62445	−	0.335059i	0.572702	−	0.0731160i
$22$	3.24252	+	0.697189i	0.691307	+	0.148641i
$23$	−1.43256	+	2.48126i	−0.298709	+	0.517379i	−0.975841	−	0.218483i	$-0.929889\pi$
$23$	−1.43256	+	2.48126i	−0.298709	+	0.517379i	0.677132	+	0.735862i	$0.263223\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−2.14939	−	3.72285i	−0.429878	−	0.744570i
$26$	−2.24621	−	1.29685i	−0.440519	−	0.254334i
$27$			1.00000i			0.192450i
$28$	−0.335059	−	2.62445i	−0.0633203	−	0.495974i
$29$		−	5.38769i		−	1.00047i	−0.865890	−	0.500234i	$-0.833247\pi$
$29$		−	5.38769i		−	1.00047i	0.865890	−	0.500234i	$-0.166753\pi$
$30$	0.725202	+	0.418696i	0.132403	+	0.0764430i
$31$	−0.913399	+	0.527351i	−0.164051	+	0.0947151i	−0.579778	−	0.814775i	$-0.696861\pi$
$31$	−0.913399	+	0.527351i	−0.164051	+	0.0947151i	0.415727	+	0.909490i	$0.363527\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	2.22504	−	2.45951i	0.387330	−	0.428146i
$34$			5.97372i			1.02448i
$35$	−1.34183	−	1.76297i	−0.226811	−	0.297996i
$36$	1.00000			0.166667
$37$	5.49467	−	9.51705i	0.903319	−	1.56459i	0.0801603	−	0.996782i	$-0.474457\pi$
$37$	5.49467	−	9.51705i	0.903319	−	1.56459i	0.823158	−	0.567812i	$-0.192210\pi$
$38$	−2.69491	+	1.55590i	−0.437171	+	0.252401i
$39$	−2.24621	+	1.29685i	−0.359682	+	0.207663i
$40$	0.418696	−	0.725202i	0.0662016	−	0.114665i
$41$	−11.2350			−1.75461			−0.877304	−	0.479934i	$-0.840661\pi$
$41$	−11.2350			−1.75461			−0.877304	+	0.479934i	$0.840661\pi$
$42$	−2.44037	−	1.02205i	−0.376557	−	0.157706i
$43$			1.27527i			0.194478i	0.995261	+	0.0972388i	$0.0310010\pi$
$43$			1.27527i			0.194478i	−0.995261	+	0.0972388i	$0.968999\pi$
$44$	−2.45951	−	2.22504i	−0.370785	−	0.335438i
$45$	0.725202	−	0.418696i	0.108107	−	0.0624155i
$46$	2.48126	−	1.43256i	0.365842	−	0.211219i
$47$	−10.6034	−	6.12185i	−1.54666	−	0.892964i	−0.998394	−	0.0566600i	$-0.981955\pi$
$47$	−10.6034	−	6.12185i	−1.54666	−	0.892964i	−0.548266	−	0.836304i	$-0.684712\pi$
$48$		−	1.00000i		−	0.144338i
$49$	4.91081	+	4.98838i	0.701544	+	0.712626i
$50$			4.29878i			0.607939i
$51$	5.17339	+	2.98686i	0.724420	+	0.418244i
$52$	1.29685	+	2.24621i	0.179841	+	0.311494i
$53$	−2.58730	−	4.48134i	−0.355394	−	0.615560i	0.631792	−	0.775138i	$-0.282320\pi$
$53$	−2.58730	−	4.48134i	−0.355394	−	0.615560i	−0.987185	+	0.159579i	$0.948986\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−2.71526	−	0.583820i	−0.366125	−	0.0787223i
$56$	−1.02205	+	2.44037i	−0.136578	+	0.326108i
$57$			3.11181i			0.412169i
$58$	−2.69384	+	4.66587i	−0.353719	+	0.612659i
$59$	−8.38751	+	4.84253i	−1.09196	+	0.630444i	−0.934098	−	0.357017i	$-0.883794\pi$
$59$	−8.38751	+	4.84253i	−1.09196	+	0.630444i	−0.157863	+	0.987461i	$0.550460\pi$
$60$	−0.418696	−	0.725202i	−0.0540534	−	0.0936232i
$61$	−2.03524	+	3.52514i	−0.260586	+	0.451348i	−0.966398	−	0.257051i	$-0.917249\pi$
$61$	−2.03524	+	3.52514i	−0.260586	+	0.451348i	0.705812	+	0.708399i	$0.250582\pi$
$62$	1.05470			0.133947
$63$	−2.10531	+	1.60239i	−0.265244	+	0.201883i
$64$	−1.00000			−0.125000
$65$	1.88096	+	1.08597i	0.233304	+	0.134698i
$66$	−3.15670	+	1.01748i	−0.388563	+	0.125243i
$67$	−6.51916	−	11.2915i	−0.796442	−	1.37948i	−0.921920	−	0.387381i	$-0.873380\pi$
$67$	−6.51916	−	11.2915i	−0.796442	−	1.37948i	0.125478	−	0.992096i	$-0.459954\pi$
$68$	2.98686	−	5.17339i	0.362210	−	0.627366i
$69$		−	2.86511i		−	0.344919i
$70$	0.280576	+	2.19769i	0.0335352	+	0.262674i
$71$	14.0795			1.67093			0.835467	−	0.549541i	$-0.185197\pi$
$71$	14.0795			1.67093			0.835467	+	0.549541i	$0.185197\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$	4.95659	+	8.58507i	0.580125	+	1.00481i	0.995464	+	0.0951394i	$0.0303297\pi$
$73$	4.95659	+	8.58507i	0.580125	+	1.00481i	−0.415339	+	0.909667i	$0.636337\pi$
$74$	−9.51705	+	5.49467i	−1.10633	+	0.638743i
$75$	3.72285	+	2.14939i	0.429878	+	0.248190i
$76$	3.11181			0.356949
$77$	8.74343	+	0.743301i	0.996406	+	0.0847070i
$78$	2.59370			0.293679
$79$	11.7018	+	6.75603i	1.31655	+	0.760113i	0.983173	−	0.182680i	$-0.0584771\pi$
$79$	11.7018	+	6.75603i	1.31655	+	0.760113i	0.333381	+	0.942792i	$0.391810\pi$
$80$	−0.725202	+	0.418696i	−0.0810801	+	0.0468116i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	9.72978	+	5.61749i	1.07447	+	0.620348i
$83$	2.99287			0.328510			0.164255	−	0.986418i	$-0.447478\pi$
$83$	2.99287			0.328510			0.164255	+	0.986418i	$0.447478\pi$
$84$	1.60239	+	2.10531i	0.174836	+	0.229708i
$85$		−	5.00234i		−	0.542580i
$86$	0.637637	−	1.10442i	0.0687582	−	0.119093i
$87$	2.69384	+	4.66587i	0.288810	+	0.500234i
$88$	1.01748	+	3.15670i	0.108463	+	0.336505i
$89$	7.28049	+	4.20339i	0.771730	+	0.445559i	0.833491	−	0.552532i	$-0.186338\pi$
$89$	7.28049	+	4.20339i	0.771730	+	0.445559i	−0.0617614	+	0.998091i	$0.519672\pi$
$90$	−0.837391			−0.0882688
$91$	−6.32960	−	2.65091i	−0.663522	−	0.277891i
$92$	−2.86511			−0.298709
$93$	0.527351	−	0.913399i	0.0546838	−	0.0947151i
$94$	6.12185	+	10.6034i	0.631421	+	1.09365i
$95$	2.25669	−	1.30290i	0.231532	−	0.133675i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$		−	0.786131i		−	0.0798195i	−0.999203	−	0.0399097i	$-0.987293\pi$
$97$		−	0.786131i		−	0.0798195i	0.999203	−	0.0399097i	$-0.0127070\pi$
$98$	−1.75869	−	6.77547i	−0.177655	−	0.684426i
$99$	−0.697189	+	3.24252i	−0.0700701	+	0.325885i
$100$	2.14939	−	3.72285i	0.214939	−	0.372285i
$101$	3.36113	+	5.82166i	0.334445	+	0.579276i	0.983378	−	0.181569i	$-0.0581177\pi$
$101$	3.36113	+	5.82166i	0.334445	+	0.579276i	−0.648933	+	0.760846i	$0.724784\pi$
$102$	−2.98686	−	5.17339i	−0.295743	−	0.512242i
$103$	−3.52596	−	2.03571i	−0.347423	−	0.200585i	0.316127	−	0.948717i	$-0.397618\pi$
$103$	−3.52596	−	2.03571i	−0.347423	−	0.200585i	−0.663550	+	0.748132i	$0.730951\pi$
$104$		−	2.59370i		−	0.254334i
$105$	2.04354	+	0.855860i	0.199430	+	0.0835234i
$106$			5.17461i			0.502602i
$107$	0.209477	+	0.120942i	0.0202509	+	0.0116919i	0.510091	−	0.860120i	$-0.329612\pi$
$107$	0.209477	+	0.120942i	0.0202509	+	0.0116919i	−0.489840	+	0.871812i	$0.662945\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	−15.1773	+	8.76259i	−1.45372	+	0.839304i	−0.998690	−	0.0511733i	$-0.983704\pi$
$109$	−15.1773	+	8.76259i	−1.45372	+	0.839304i	−0.455028	+	0.890477i	$0.650371\pi$
$110$	2.05957	+	1.86323i	0.196372	+	0.177652i
$111$			10.9893i			1.04306i
$112$	2.10531	−	1.60239i	0.198933	−	0.151412i
$113$	8.08949			0.760995			0.380498	−	0.924782i	$-0.375753\pi$
$113$	8.08949			0.760995			0.380498	+	0.924782i	$0.375753\pi$
$114$	1.55590	−	2.69491i	0.145724	−	0.252401i
$115$	−2.07779	+	1.19961i	−0.193755	+	0.111864i
$116$	4.66587	−	2.69384i	0.433216	−	0.250117i
$117$	1.29685	−	2.24621i	0.119894	−	0.207663i
$118$	9.68506			0.891582
$119$	2.00155	+	15.6777i	0.183482	+	1.43717i
$120$			0.837391i			0.0764430i
$121$	8.92949	−	6.42373i	0.811771	−	0.583975i
$122$	3.52514	−	2.03524i	0.319151	−	0.184262i
$123$	9.72978	−	5.61749i	0.877304	−	0.506512i
$124$	−0.913399	−	0.527351i	−0.0820257	−	0.0473575i
$125$		−	7.78672i		−	0.696465i
$126$	2.62445	−	0.335059i	0.233805	−	0.0298495i
$127$		−	12.1313i		−	1.07648i	−0.842791	−	0.538241i	$-0.819089\pi$
$127$		−	12.1313i		−	1.07648i	0.842791	−	0.538241i	$-0.180911\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−0.637637	−	1.10442i	−0.0561408	−	0.0972388i
$130$	−1.08597	−	1.88096i	−0.0952461	−	0.164971i
$131$	−1.02224	+	1.77058i	−0.0893139	+	0.154696i	−0.907221	−	0.420654i	$-0.861801\pi$
$131$	−1.02224	+	1.77058i	−0.0893139	+	0.154696i	0.817907	+	0.575350i	$0.195134\pi$
$132$	3.24252	+	0.697189i	0.282225	+	0.0606825i
$133$	−6.55132	+	4.98635i	−0.568072	+	0.432371i
$134$			13.0383i			1.12634i
$135$	−0.418696	+	0.725202i	−0.0360356	+	0.0624155i
$136$	−5.17339	+	2.98686i	−0.443615	+	0.256121i
$137$	6.60556	+	11.4412i	0.564351	+	0.977485i	0.997110	+	0.0759750i	$0.0242069\pi$
$137$	6.60556	+	11.4412i	0.564351	+	0.977485i	−0.432759	+	0.901510i	$0.642460\pi$
$138$	−1.43256	+	2.48126i	−0.121947	+	0.211219i
$139$	6.16293			0.522733			0.261367	−	0.965240i	$-0.415827\pi$
$139$	6.16293			0.522733			0.261367	+	0.965240i	$0.415827\pi$
$140$	0.855860	−	2.04354i	0.0723334	−	0.172711i
$141$	12.2437			1.03111
$142$	−12.1932	−	7.03977i	−1.02323	−	0.590764i
$143$	−8.18754	+	2.63903i	−0.684677	+	0.220687i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	2.25580	−	3.90716i	0.187334	−	0.324472i
$146$		−	9.91318i		−	0.820421i
$147$	−6.74708	−	1.86466i	−0.556489	−	0.153795i
$148$	10.9893			0.903319
$149$	3.80788	+	2.19848i	0.311954	+	0.180107i	0.647800	−	0.761810i	$-0.275689\pi$
$149$	3.80788	+	2.19848i	0.311954	+	0.180107i	−0.335847	+	0.941917i	$0.609022\pi$
$150$	−2.14939	−	3.72285i	−0.175497	−	0.303969i
$151$	−8.86874	+	5.12037i	−0.721728	+	0.416690i	−0.815388	−	0.578914i	$-0.803477\pi$
$151$	−8.86874	+	5.12037i	−0.721728	+	0.416690i	0.0936604	+	0.995604i	$0.470143\pi$
$152$	−2.69491	−	1.55590i	−0.218586	−	0.126200i
$153$	−5.97372			−0.482947
$154$	−7.20038	−	5.01543i	−0.580223	−	0.404155i
$155$	−0.883199			−0.0709402
$156$	−2.24621	−	1.29685i	−0.179841	−	0.103831i
$157$	−13.8444	+	7.99304i	−1.10490	+	0.637914i	−0.937504	−	0.347975i	$-0.886869\pi$
$157$	−13.8444	+	7.99304i	−1.10490	+	0.637914i	−0.167396	+	0.985890i	$0.553536\pi$
$158$	−6.75603	−	11.7018i	−0.537481	−	0.930944i
$159$	4.48134	+	2.58730i	0.355394	+	0.205187i
$160$	0.837391			0.0662016
$161$	6.03195	−	4.59104i	0.475385	−	0.361825i
$162$			1.00000i			0.0785674i
$163$	0.261926	−	0.453669i	0.0205156	−	0.0355341i	−0.855585	−	0.517662i	$-0.826803\pi$
$163$	0.261926	−	0.453669i	0.0205156	−	0.0355341i	0.876101	+	0.482128i	$0.160136\pi$
$164$	−5.61749	−	9.72978i	−0.438652	−	0.759768i
$165$	2.64339	−	0.852026i	0.205788	−	0.0663301i
$166$	−2.59190	−	1.49643i	−0.201170	−	0.116146i
$167$	−17.0544			−1.31971			−0.659855	−	0.751393i	$-0.729382\pi$
$167$	−17.0544			−1.31971			−0.659855	+	0.751393i	$0.729382\pi$
$168$	−0.335059	−	2.62445i	−0.0258504	−	0.202481i
$169$	−6.27269			−0.482515
$170$	−2.50117	+	4.33216i	−0.191831	+	0.332261i
$171$	−1.55590	−	2.69491i	−0.118983	−	0.206085i
$172$	−1.10442	+	0.637637i	−0.0842112	+	0.0486194i
$173$	3.61831	−	6.26710i	0.275095	−	0.476479i	−0.695064	−	0.718948i	$-0.744624\pi$
$173$	3.61831	−	6.26710i	0.275095	−	0.476479i	0.970159	+	0.242469i	$0.0779573\pi$
$174$		−	5.38769i		−	0.408440i
$175$	1.44035	+	11.2819i	0.108880	+	0.852833i
$176$	0.697189	−	3.24252i	0.0525526	−	0.244414i
$177$	4.84253	−	8.38751i	0.363987	−	0.630444i
$178$	−4.20339	−	7.28049i	−0.315057	−	0.545696i
$179$	−4.03318	−	6.98568i	−0.301454	−	0.522134i	0.675011	−	0.737807i	$-0.264139\pi$
$179$	−4.03318	−	6.98568i	−0.301454	−	0.522134i	−0.976466	+	0.215673i	$0.930805\pi$
$180$	0.725202	+	0.418696i	0.0540534	+	0.0312077i
$181$			5.61056i			0.417030i	0.978019	+	0.208515i	$0.0668630\pi$
$181$			5.61056i			0.417030i	−0.978019	+	0.208515i	$0.933137\pi$
$182$	4.15614	+	5.46055i	0.308074	+	0.404763i
$183$		−	4.07048i		−	0.300899i
$184$	2.48126	+	1.43256i	0.182921	+	0.105609i
$185$	7.96950	−	4.60119i	0.585929	−	0.338286i
$186$	−0.913399	+	0.527351i	−0.0669737	+	0.0386673i
$187$	14.6924	+	13.2918i	1.07442	+	0.971992i
$188$		−	12.2437i		−	0.892964i
$189$	1.02205	−	2.44037i	0.0743435	−	0.177511i
$190$	−2.60580			−0.189045
$191$	−5.89206	+	10.2053i	−0.426334	+	0.738433i	−0.996544	−	0.0830666i	$-0.973529\pi$
$191$	−5.89206	+	10.2053i	−0.426334	+	0.738433i	0.570210	+	0.821499i	$0.306862\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	15.6730	−	9.04882i	1.12817	−	0.651348i	0.184694	−	0.982796i	$-0.440870\pi$
$193$	15.6730	−	9.04882i	1.12817	−	0.651348i	0.943474	+	0.331448i	$0.107537\pi$
$194$	−0.393065	+	0.680809i	−0.0282204	+	0.0488792i
$195$	−2.17195			−0.155536
$196$	−1.86466	+	6.74708i	−0.133190	+	0.481934i
$197$			6.23110i			0.443948i	0.975053	+	0.221974i	$0.0712500\pi$
$197$			6.23110i			0.443948i	−0.975053	+	0.221974i	$0.928750\pi$
$198$	2.22504	−	2.45951i	0.158127	−	0.174790i
$199$	−15.8196	+	9.13344i	−1.12142	+	0.647453i	−0.941763	−	0.336276i	$-0.890832\pi$
$199$	−15.8196	+	9.13344i	−1.12142	+	0.647453i	−0.179658	+	0.983729i	$0.557499\pi$
$200$	−3.72285	+	2.14939i	−0.263245	+	0.151985i
$201$	11.2915	+	6.51916i	0.796442	+	0.459826i
$202$		−	6.72227i		−	0.472977i
$203$	−5.50651	+	13.1479i	−0.386481	+	0.922805i
$204$			5.97372i			0.418244i
$205$	−8.14763	−	4.70404i	−0.569055	−	0.328544i
$206$	2.03571	+	3.52596i	0.141835	+	0.245665i
$207$	1.43256	+	2.48126i	0.0995696	+	0.172460i
$208$	−1.29685	+	2.24621i	−0.0899205	+	0.155747i
$209$	−2.16952	+	10.0901i	−0.150069	+	0.697947i
$210$	−1.34183	−	1.76297i	−0.0925952	−	0.121656i
$211$		−	10.2446i		−	0.705269i	−0.935761	−	0.352635i	$-0.885286\pi$
$211$		−	10.2446i		−	0.705269i	0.935761	−	0.352635i	$-0.114714\pi$
$212$	2.58730	−	4.48134i	0.177697	−	0.307780i
$213$	−12.1932	+	7.03977i	−0.835467	+	0.482357i
$214$	−0.120942	−	0.209477i	−0.00826740	−	0.0143196i
$215$	−0.533952	+	0.924832i	−0.0364152	+	0.0630730i
$216$	1.00000			0.0680414
$217$	2.76801	−	0.353388i	0.187905	−	0.0239895i
$218$	17.5252			1.18696
$219$	−8.58507	−	4.95659i	−0.580125	−	0.334935i
$220$	−0.852026	−	2.64339i	−0.0574436	−	0.178217i
$221$	−7.74703	−	13.4183i	−0.521122	−	0.902610i
$222$	5.49467	−	9.51705i	0.368778	−	0.638743i
$223$		−	15.6665i		−	1.04911i	−0.851377	−	0.524554i	$-0.824232\pi$
$223$		−	15.6665i		−	1.04911i	0.851377	−	0.524554i	$-0.175768\pi$
$224$	−2.62445	+	0.335059i	−0.175353	+	0.0223871i
$225$	−4.29878			−0.286585
$226$	−7.00571	−	4.04475i	−0.466013	−	0.269053i
$227$	7.86025	+	13.6143i	0.521703	+	0.903616i	0.999681	+	0.0252443i	$0.00803637\pi$
$227$	7.86025	+	13.6143i	0.521703	+	0.903616i	−0.477978	+	0.878372i	$0.658630\pi$
$228$	−2.69491	+	1.55590i	−0.178474	+	0.103042i
$229$	−2.16867	−	1.25208i	−0.143310	−	0.0827400i	0.426631	−	0.904426i	$-0.359700\pi$
$229$	−2.16867	−	1.25208i	−0.143310	−	0.0827400i	−0.569940	+	0.821686i	$0.693034\pi$
$230$	2.39922			0.158200
$231$	−7.94368	+	3.72800i	−0.522656	+	0.245284i
$232$	−5.38769			−0.353719
$233$	−0.0479052	−	0.0276581i	−0.00313837	−	0.00181194i	0.498430	−	0.866930i	$-0.333910\pi$
$233$	−0.0479052	−	0.0276581i	−0.00313837	−	0.00181194i	−0.501568	+	0.865118i	$0.667243\pi$
$234$	−2.24621	+	1.29685i	−0.146840	+	0.0847779i
$235$	−5.12639	−	8.87916i	−0.334409	−	0.579213i
$236$	−8.38751	−	4.84253i	−0.545981	−	0.315222i
$237$	−13.5121			−0.877702
$238$	6.10547	−	14.5781i	0.395759	−	0.944957i
$239$		−	5.74465i		−	0.371591i	−0.982588	−	0.185795i	$-0.940514\pi$
$239$		−	5.74465i		−	0.371591i	0.982588	−	0.185795i	$-0.0594861\pi$
$240$	0.418696	−	0.725202i	0.0270267	−	0.0468116i
$241$	−3.67123	−	6.35875i	−0.236484	−	0.409603i	0.723219	−	0.690619i	$-0.242662\pi$
$241$	−3.67123	−	6.35875i	−0.236484	−	0.409603i	−0.959703	+	0.281016i	$0.909329\pi$
$242$	−10.9450	+	1.09837i	−0.703573	+	0.0706058i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−4.07048			−0.260586
$245$	1.47271	+	5.67372i	0.0940883	+	0.362481i
$246$	−11.2350			−0.716316
$247$	4.03556	−	6.98979i	0.256776	−	0.444750i
$248$	0.527351	+	0.913399i	0.0334868	+	0.0580009i
$249$	−2.59190	+	1.49643i	−0.164255	+	0.0948326i
$250$	−3.89336	+	6.74349i	−0.246238	+	0.426496i
$251$		−	4.20803i		−	0.265608i	−0.991142	−	0.132804i	$-0.957602\pi$
$251$		−	4.20803i		−	0.265608i	0.991142	−	0.132804i	$-0.0423981\pi$
$252$	−2.44037	−	1.02205i	−0.153729	−	0.0643834i
$253$	1.99753	−	9.29019i	0.125583	−	0.584069i
$254$	−6.06567	+	10.5060i	−0.380594	+	0.659208i
$255$	2.50117	+	4.33216i	0.156629	+	0.271290i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−21.3446	−	12.3233i	−1.33144	−	0.768706i	−0.345918	−	0.938265i	$-0.612432\pi$
$257$	−21.3446	−	12.3233i	−1.33144	−	0.768706i	−0.985520	+	0.169559i	$0.945766\pi$
$258$			1.27527i			0.0793951i
$259$	−23.1360	+	17.6093i	−1.43760	+	1.09419i
$260$			2.17195i			0.134698i
$261$	−4.66587	−	2.69384i	−0.288810	−	0.166745i
$262$	1.77058	−	1.02224i	0.109387	−	0.0631545i
$263$	26.3130	−	15.1918i	1.62253	−	0.936768i	0.636290	−	0.771450i	$-0.280468\pi$
$263$	26.3130	−	15.1918i	1.62253	−	0.936768i	0.986240	−	0.165318i	$-0.0528651\pi$
$264$	−2.45951	−	2.22504i	−0.151372	−	0.136942i
$265$		−	4.33317i		−	0.266185i
$266$	8.16678	−	1.04264i	0.500738	−	0.0639284i
$267$	−8.40678			−0.514487
$268$	6.51916	−	11.2915i	0.398221	−	0.689739i
$269$	17.2977	−	9.98686i	1.05466	−	0.608910i	0.130711	−	0.991420i	$-0.458274\pi$
$269$	17.2977	−	9.98686i	1.05466	−	0.608910i	0.923951	+	0.382511i	$0.124941\pi$
$270$	0.725202	−	0.418696i	0.0441344	−	0.0254810i
$271$	−0.807639	+	1.39887i	−0.0490606	+	0.0849754i	−0.889513	−	0.456910i	$-0.848956\pi$
$271$	−0.807639	+	1.39887i	−0.0490606	+	0.0849754i	0.840452	+	0.541886i	$0.182289\pi$
$272$	5.97372			0.362210
$273$	6.80705	−	0.869045i	0.411981	−	0.0525970i
$274$		−	13.2111i		−	0.798113i
$275$	10.5729	+	9.56496i	0.637568	+	0.576789i
$276$	2.48126	−	1.43256i	0.149354	−	0.0862298i
$277$	−4.48663	+	2.59035i	−0.269575	+	0.155639i	−0.628695	−	0.777652i	$-0.716410\pi$
$277$	−4.48663	+	2.59035i	−0.269575	+	0.155639i	0.359119	+	0.933292i	$0.383077\pi$
$278$	−5.33726	−	3.08147i	−0.320107	−	0.184814i
$279$			1.05470i			0.0631434i
$280$	−1.76297	+	1.34183i	−0.105358	+	0.0801898i
$281$		−	25.1883i		−	1.50261i	−0.659956	−	0.751304i	$-0.729425\pi$
$281$		−	25.1883i		−	1.50261i	0.659956	−	0.751304i	$-0.270575\pi$
$282$	−10.6034	−	6.12185i	−0.631421	−	0.364551i
$283$	−11.5167	−	19.9475i	−0.684598	−	1.18576i	−0.973563	−	0.228419i	$-0.926644\pi$
$283$	−11.5167	−	19.9475i	−0.684598	−	1.18576i	0.288965	−	0.957340i	$-0.406689\pi$
$284$	7.03977	+	12.1932i	0.417733	+	0.723536i
$285$	−1.30290	+	2.25669i	−0.0771772	+	0.133675i
$286$	8.41014	+	1.80830i	0.497302	+	0.106927i
$287$	27.4175	+	11.4828i	1.61840	+	0.677806i
$288$		−	1.00000i		−	0.0589256i
$289$	−9.34267	+	16.1820i	−0.549569	+	0.951881i
$290$	−3.90716	+	2.25580i	−0.229437	+	0.132465i
$291$	0.393065	+	0.680809i	0.0230419	+	0.0399097i
$292$	−4.95659	+	8.58507i	−0.290063	+	0.502403i
$293$	−4.18076			−0.244242			−0.122121	−	0.992515i	$-0.538970\pi$
$293$	−4.18076			−0.244242			−0.122121	+	0.992515i	$0.538970\pi$
$294$	4.91081	+	4.98838i	0.286404	+	0.290928i
$295$	−8.11019			−0.472194
$296$	−9.51705	−	5.49467i	−0.553167	−	0.319371i
$297$	−1.01748	−	3.15670i	−0.0590399	−	0.183170i
$298$	−2.19848	−	3.80788i	−0.127355	−	0.220585i
$299$	−3.71563	+	6.43566i	−0.214880	+	0.372184i
$300$			4.29878i			0.248190i
$301$	1.30340	−	3.11214i	0.0751267	−	0.179381i
$302$	10.2407			0.589288
$303$	−5.82166	−	3.36113i	−0.334445	−	0.193092i
$304$	1.55590	+	2.69491i	0.0892372	+	0.154563i
$305$	−2.95192	+	1.70429i	−0.169027	+	0.0975876i
$306$	5.17339	+	2.98686i	0.295743	+	0.170747i
$307$	10.0657			0.574478			0.287239	−	0.957859i	$-0.407263\pi$
$307$	10.0657			0.574478			0.287239	+	0.957859i	$0.407263\pi$
$308$	3.72800	+	7.94368i	0.212422	+	0.452633i
$309$	4.07143			0.231615
$310$	0.764873	+	0.441599i	0.0434418	+	0.0250812i
$311$	1.23817	−	0.714858i	0.0702102	−	0.0405359i	−0.464484	−	0.885582i	$-0.653760\pi$
$311$	1.23817	−	0.714858i	0.0702102	−	0.0405359i	0.534694	+	0.845046i	$0.320427\pi$
$312$	1.29685	+	2.24621i	0.0734198	+	0.127167i
$313$	26.3211	+	15.1965i	1.48776	+	0.858958i	0.999902	−	0.0139662i	$-0.00444572\pi$
$313$	26.3211	+	15.1965i	1.48776	+	0.858958i	0.487856	+	0.872924i	$0.337779\pi$
$314$	15.9861			0.902147
$315$	−2.19769	+	0.280576i	−0.123826	+	0.0158087i
$316$			13.5121i			0.760113i
$317$	−5.42610	+	9.39829i	−0.304760	+	0.527860i	−0.977208	−	0.212284i	$-0.931910\pi$
$317$	−5.42610	+	9.39829i	−0.304760	+	0.527860i	0.672448	+	0.740145i	$0.265243\pi$
$318$	−2.58730	−	4.48134i	−0.145089	−	0.251301i
$319$	5.48184	+	17.0073i	0.306924	+	0.952226i
$320$	−0.725202	−	0.418696i	−0.0405400	−	0.0234058i
$321$	−0.241883			−0.0135006
$322$	−7.51935	+	0.959984i	−0.419037	+	0.0534978i
$323$	−18.5891			−1.03432
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−5.57488	−	9.65597i	−0.309239	−	0.535617i
$326$	−0.453669	+	0.261926i	−0.0251264	+	0.0145067i
$327$	8.76259	−	15.1773i	0.484572	−	0.839304i
$328$			11.2350i			0.620348i
$329$	19.6193	+	25.7768i	1.08164	+	1.42112i
$330$	−2.71526	−	0.583820i	−0.149470	−	0.0321382i
$331$	6.45747	−	11.1847i	0.354935	−	0.614765i	−0.632172	−	0.774828i	$-0.717836\pi$
$331$	6.45747	−	11.1847i	0.354935	−	0.614765i	0.987107	+	0.160063i	$0.0511697\pi$
$332$	1.49643	+	2.59190i	0.0821274	+	0.142249i
$333$	−5.49467	−	9.51705i	−0.301106	−	0.521531i
$334$	14.7695	+	8.52720i	0.808154	+	0.466588i
$335$		−	10.9182i		−	0.596523i
$336$	−1.02205	+	2.44037i	−0.0557577	+	0.133133i
$337$		−	16.4809i		−	0.897772i	−0.893589	−	0.448886i	$-0.851821\pi$
$337$		−	16.4809i		−	0.897772i	0.893589	−	0.448886i	$-0.148179\pi$
$338$	5.43231	+	3.13635i	0.295479	+	0.170595i
$339$	−7.00571	+	4.04475i	−0.380498	+	0.219680i
$340$	4.33216	−	2.50117i	0.234944	−	0.135645i
$341$	2.34676	−	2.59405i	0.127084	−	0.140476i
$342$			3.11181i			0.168267i
$343$	−6.88579	−	17.1926i	−0.371798	−	0.928314i
$344$	1.27527			0.0687582
$345$	1.19961	−	2.07779i	0.0645849	−	0.111864i
$346$	−6.26710	+	3.61831i	−0.336922	+	0.194522i
$347$	9.92748	−	5.73163i	0.532935	−	0.307690i	−0.209276	−	0.977857i	$-0.567111\pi$
$347$	9.92748	−	5.73163i	0.532935	−	0.307690i	0.742211	+	0.670166i	$0.233777\pi$
$348$	−2.69384	+	4.66587i	−0.144405	+	0.250117i
$349$	−20.9561			−1.12176			−0.560878	−	0.827899i	$-0.689536\pi$
$349$	−20.9561			−1.12176			−0.560878	+	0.827899i	$0.689536\pi$
$350$	4.39358	−	10.4906i	0.234847	−	0.560746i
$351$			2.59370i			0.138442i
$352$	−2.22504	+	2.45951i	−0.118595	+	0.131092i
$353$	17.2530	−	9.96104i	0.918286	−	0.530173i	0.0351983	−	0.999380i	$-0.488794\pi$
$353$	17.2530	−	9.96104i	0.918286	−	0.530173i	0.883088	+	0.469208i	$0.155460\pi$
$354$	−8.38751	+	4.84253i	−0.445791	+	0.257378i
$355$	10.2105	+	5.89504i	0.541918	+	0.312876i
$356$			8.40678i			0.445559i
$357$	−9.57226	−	12.5765i	−0.506618	−	0.665621i
$358$			8.06636i			0.426321i
$359$	−3.38989	−	1.95715i	−0.178912	−	0.103295i	0.407870	−	0.913040i	$-0.366272\pi$
$359$	−3.38989	−	1.95715i	−0.178912	−	0.103295i	−0.586781	+	0.809746i	$0.699605\pi$
$360$	−0.418696	−	0.725202i	−0.0220672	−	0.0382215i
$361$	4.65832	+	8.06845i	0.245175	+	0.424655i
$362$	2.80528	−	4.85889i	0.147442	−	0.255378i
$363$	−4.52130	+	10.0279i	−0.237307	+	0.526326i
$364$	−0.869045	−	6.80705i	−0.0455504	−	0.356786i
$365$			8.30121i			0.434505i
$366$	−2.03524	+	3.52514i	−0.106384	+	0.184262i
$367$	10.4720	−	6.04600i	0.546633	−	0.315599i	−0.201130	−	0.979565i	$-0.564461\pi$
$367$	10.4720	−	6.04600i	0.546633	−	0.315599i	0.747763	+	0.663966i	$0.231128\pi$
$368$	−1.43256	−	2.48126i	−0.0746772	−	0.129345i
$369$	−5.61749	+	9.72978i	−0.292435	+	0.506512i
$370$	−9.20238			−0.478409
$371$	1.73380	+	13.5805i	0.0900145	+	0.705064i
$372$	1.05470			0.0546838
$373$	15.3231	+	8.84681i	0.793401	+	0.458070i	0.841158	−	0.540789i	$-0.181874\pi$
$373$	15.3231	+	8.84681i	0.793401	+	0.458070i	−0.0477575	+	0.998859i	$0.515207\pi$
$374$	−6.07812	−	18.8572i	−0.314292	−	0.975084i
$375$	3.89336	+	6.74349i	0.201052	+	0.348232i
$376$	−6.12185	+	10.6034i	−0.315711	+	0.546827i
$377$		−	13.9741i		−	0.719701i
$378$	−2.10531	+	1.60239i	−0.108285	+	0.0824183i
$379$	19.6577			1.00975			0.504874	−	0.863193i	$-0.331539\pi$
$379$	19.6577			1.00975			0.504874	+	0.863193i	$0.331539\pi$
$380$	2.25669	+	1.30290i	0.115766	+	0.0668374i
$381$	6.06567	+	10.5060i	0.310754	+	0.538241i
$382$	10.2053	−	5.89206i	0.522151	−	0.301464i
$383$	1.18944	+	0.686725i	0.0607777	+	0.0350900i	0.530081	−	0.847947i	$-0.322162\pi$
$383$	1.18944	+	0.686725i	0.0607777	+	0.0350900i	−0.469303	+	0.883037i	$0.655495\pi$
$384$	−1.00000			−0.0510310
$385$	6.02954	+	4.19988i	0.307294	+	0.214046i
$386$	−18.0976			−0.921145
$387$	1.10442	+	0.637637i	0.0561408	+	0.0324129i
$388$	0.680809	−	0.393065i	0.0345628	−	0.0199549i
$389$	−15.6896	−	27.1752i	−0.795496	−	1.37784i	−0.922524	−	0.385941i	$-0.873877\pi$
$389$	−15.6896	−	27.1752i	−0.795496	−	1.37784i	0.127027	−	0.991899i	$-0.459456\pi$
$390$	1.88096	+	1.08597i	0.0952461	+	0.0549904i
$391$	17.1154			0.865562
$392$	4.98838	−	4.91081i	0.251951	−	0.248033i
$393$		−	2.04449i		−	0.103131i
$394$	3.11555	−	5.39629i	0.156959	−	0.271861i
$395$	5.65744	+	9.79897i	0.284657	+	0.493040i
$396$	−3.15670	+	1.01748i	−0.158630	+	0.0511301i
$397$	−30.5464	−	17.6360i	−1.53308	−	0.885123i	−0.999218	−	0.0395508i	$-0.987407\pi$
$397$	−30.5464	−	17.6360i	−1.53308	−	0.885123i	−0.533861	−	0.845572i	$-0.679259\pi$
$398$	18.2669			0.915636
$399$	3.18044	−	7.59396i	0.159221	−	0.380174i
$400$	4.29878			0.214939
$401$	−4.48309	+	7.76494i	−0.223875	+	0.387763i	−0.955981	−	0.293428i	$-0.905204\pi$
$401$	−4.48309	+	7.76494i	−0.223875	+	0.387763i	0.732106	+	0.681190i	$0.238537\pi$
$402$	−6.51916	−	11.2915i	−0.325146	−	0.563169i
$403$	−2.36909	+	1.36779i	−0.118013	+	0.0681347i
$404$	−3.36113	+	5.82166i	−0.167223	+	0.289638i
$405$		−	0.837391i		−	0.0416103i
$406$	11.3428	−	8.63320i	0.562931	−	0.428459i
$407$	−7.66165	+	35.6332i	−0.379774	+	1.76627i
$408$	2.98686	−	5.17339i	0.147872	−	0.256121i
$409$	17.9762	+	31.1357i	0.888867	+	1.53956i	0.841217	+	0.540698i	$0.181840\pi$
$409$	17.9762	+	31.1357i	0.888867	+	1.53956i	0.0476498	+	0.998864i	$0.484827\pi$
$410$	4.70404	+	8.14763i	0.232316	+	0.402383i
$411$	−11.4412	−	6.60556i	−0.564351	−	0.325828i
$412$		−	4.07143i		−	0.200585i
$413$	25.4180	−	3.24507i	1.25074	−	0.159680i
$414$		−	2.86511i		−	0.140813i
$415$	2.17043	+	1.25310i	0.106542	+	0.0615123i
$416$	2.24621	−	1.29685i	0.110130	−	0.0635834i
$417$	−5.33726	+	3.08147i	−0.261367	+	0.150900i
$418$	6.92391	−	7.65352i	0.338659	−	0.374346i
$419$			0.724634i			0.0354007i	0.999843	+	0.0177004i	$0.00563449\pi$
$419$			0.724634i			0.0354007i	−0.999843	+	0.0177004i	$0.994366\pi$
$420$	0.280576	+	2.19769i	0.0136907	+	0.107236i
$421$	3.71423			0.181021			0.0905103	−	0.995896i	$-0.471150\pi$
$421$	3.71423			0.181021			0.0905103	+	0.995896i	$0.471150\pi$
$422$	−5.12231	+	8.87211i	−0.249350	+	0.431887i
$423$	−10.6034	+	6.12185i	−0.515553	+	0.297655i
$424$	−4.48134	+	2.58730i	−0.217633	+	0.125651i
$425$	−12.8398	+	22.2393i	−0.622824	+	1.07876i
$426$	14.0795			0.682156
$427$	8.56963	−	6.52252i	0.414714	−	0.315647i
$428$			0.241883i			0.0116919i
$429$	5.77110	−	6.37924i	0.278632	−	0.307993i
$430$	0.924832	−	0.533952i	0.0445994	−	0.0257495i
$431$	3.53752	−	2.04239i	0.170396	−	0.0983784i	−0.412376	−	0.911014i	$-0.635301\pi$
$431$	3.53752	−	2.04239i	0.170396	−	0.0983784i	0.582773	+	0.812635i	$0.301968\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$			30.3109i			1.45665i	0.685232	+	0.728325i	$0.259701\pi$
$433$			30.3109i			1.45665i	−0.685232	+	0.728325i	$0.740299\pi$
$434$	−2.57386	−	1.07796i	−0.123549	−	0.0517439i
$435$			4.51160i			0.216315i
$436$	−15.1773	−	8.76259i	−0.726859	−	0.419652i
$437$	4.45784	+	7.72121i	0.213248	+	0.369356i
$438$	4.95659	+	8.58507i	0.236835	+	0.410210i
$439$	−6.30512	+	10.9208i	−0.300927	+	0.521221i	−0.976346	−	0.216213i	$-0.930629\pi$
$439$	−6.30512	+	10.9208i	−0.300927	+	0.521221i	0.675419	+	0.737434i	$0.263963\pi$
$440$	−0.583820	+	2.71526i	−0.0278325	+	0.129445i
$441$	6.77547	−	1.75869i	0.322641	−	0.0837473i
$442$			15.4941i			0.736978i
$443$	−7.61859	+	13.1958i	−0.361970	+	0.626951i	−0.988285	−	0.152619i	$-0.951229\pi$
$443$	−7.61859	+	13.1958i	−0.361970	+	0.626951i	0.626315	+	0.779570i	$0.284562\pi$
$444$	−9.51705	+	5.49467i	−0.451659	+	0.260766i
$445$	3.51988	+	6.09662i	0.166858	+	0.289007i
$446$	−7.83326	+	13.5676i	−0.370916	+	0.642445i
$447$	−4.39696			−0.207969
$448$	2.44037	+	1.02205i	0.115297	+	0.0482875i
$449$	32.2780			1.52329			0.761647	−	0.647993i	$-0.224391\pi$
$449$	32.2780			1.52329			0.761647	+	0.647993i	$0.224391\pi$
$450$	3.72285	+	2.14939i	0.175497	+	0.101323i
$451$	35.4654	−	11.4313i	1.67000	−	0.538280i
$452$	4.04475	+	7.00571i	0.190249	+	0.329521i
$453$	5.12037	−	8.86874i	0.240576	−	0.416690i
$454$		−	15.7205i		−	0.737799i
$455$	−3.48032	−	4.57262i	−0.163160	−	0.214368i
$456$	3.11181			0.145724
$457$	−26.2793	−	15.1724i	−1.22929	−	0.709733i	−0.262412	−	0.964956i	$-0.584518\pi$
$457$	−26.2793	−	15.1724i	−1.22929	−	0.709733i	−0.966882	+	0.255223i	$0.917851\pi$
$458$	1.25208	+	2.16867i	0.0585060	+	0.101335i
$459$	5.17339	−	2.98686i	0.241473	−	0.139415i
$460$	−2.07779	−	1.19961i	−0.0968773	−	0.0559321i
$461$	4.81402			0.224211			0.112106	−	0.993696i	$-0.464240\pi$
$461$	4.81402			0.224211			0.112106	+	0.993696i	$0.464240\pi$
$462$	8.74343	+	0.743301i	0.406781	+	0.0345815i
$463$	−33.1197			−1.53920			−0.769600	−	0.638526i	$-0.779545\pi$
$463$	−33.1197			−1.53920			−0.769600	+	0.638526i	$0.779545\pi$
$464$	4.66587	+	2.69384i	0.216608	+	0.125059i
$465$	0.764873	−	0.441599i	0.0354701	−	0.0204787i
$466$	0.0276581	+	0.0479052i	0.00128123	+	0.00221916i
$467$	−12.4591	−	7.19328i	−0.576539	−	0.332865i	0.183218	−	0.983072i	$-0.441349\pi$
$467$	−12.4591	−	7.19328i	−0.576539	−	0.332865i	−0.759757	+	0.650207i	$0.774682\pi$
$468$	2.59370			0.119894
$469$	4.36861	+	34.2184i	0.201724	+	1.58006i
$470$			10.2528i			0.472925i
$471$	7.99304	−	13.8444i	0.368300	−	0.637914i
$472$	4.84253	+	8.38751i	0.222896	+	0.386067i
$473$	−1.29756	−	4.02566i	−0.0596619	−	0.185100i
$474$	11.7018	+	6.75603i	0.537481	+	0.310315i
$475$	−13.3770			−0.613777
$476$	−12.5765	+	9.57226i	−0.576445	+	0.438744i
$477$	−5.17461			−0.236929
$478$	−2.87233	+	4.97501i	−0.131377	+	0.227552i
$479$	−3.23604	−	5.60499i	−0.147859	−	0.256099i	0.782577	−	0.622554i	$-0.213905\pi$
$479$	−3.23604	−	5.60499i	−0.147859	−	0.256099i	−0.930436	+	0.366455i	$0.880571\pi$
$480$	−0.725202	+	0.418696i	−0.0331008	+	0.0191108i
$481$	14.2516	−	24.6844i	0.649815	−	1.12551i
$482$			7.34245i			0.334440i
$483$	−2.92830	+	6.99194i	−0.133242	+	0.318144i
$484$	10.0279	+	4.52130i	0.455812	+	0.205514i
$485$	0.329150	−	0.570104i	0.0149459	−	0.0258871i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	2.64048	+	4.57345i	0.119652	+	0.207243i	0.919630	−	0.392787i	$-0.128489\pi$
$487$	2.64048	+	4.57345i	0.119652	+	0.207243i	−0.799978	+	0.600029i	$0.795156\pi$
$488$	3.52514	+	2.03524i	0.159576	+	0.0921311i
$489$			0.523852i			0.0236894i
$490$	1.56145	−	5.64994i	0.0705392	−	0.255238i
$491$		−	11.3633i		−	0.512820i	−0.966568	−	0.256410i	$-0.917460\pi$
$491$		−	11.3633i		−	0.512820i	0.966568	−	0.256410i	$-0.0825398\pi$
$492$	9.72978	+	5.61749i	0.438652	+	0.253256i
$493$	−27.8726	+	16.0923i	−1.25532	+	0.724759i
$494$	−6.98979	+	4.03556i	−0.314485	+	0.181568i
$495$	−1.86323	+	2.05957i	−0.0837460	+	0.0925709i
$496$		−	1.05470i		−	0.0473575i
$497$	−34.3593	−	14.3901i	−1.54122	−	0.645482i
$498$	2.99287			0.134114
$499$	14.5860	−	25.2638i	0.652961	−	1.13096i	−0.329440	−	0.944176i	$-0.606860\pi$
$499$	14.5860	−	25.2638i	0.652961	−	1.13096i	0.982401	−	0.186785i	$-0.0598066\pi$
$500$	6.74349	−	3.89336i	0.301578	−	0.174116i
$501$	14.7695	−	8.52720i	0.659855	−	0.380967i
$502$	−2.10401	+	3.64426i	−0.0939067	+	0.162651i
$503$	22.4317			1.00018			0.500090	−	0.865973i	$-0.333300\pi$
$503$	22.4317			1.00018			0.500090	+	0.865973i	$0.333300\pi$
$504$	1.60239	+	2.10531i	0.0713763	+	0.0937780i
$505$			5.62917i			0.250495i
$506$	−6.37500	+	7.04677i	−0.283403	+	0.313267i
$507$	5.43231	−	3.13635i	0.241257	−	0.139290i
$508$	10.5060	−	6.06567i	0.466130	−	0.269121i
$509$	−23.7016	−	13.6841i	−1.05055	−	0.606537i	−0.127749	−	0.991807i	$-0.540775\pi$
$509$	−23.7016	−	13.6841i	−1.05055	−	0.606537i	−0.922804	+	0.385269i	$0.874109\pi$
$510$		−	5.00234i		−	0.221507i
$511$	−3.32151	−	26.0166i	−0.146935	−	1.15091i
$512$			1.00000i			0.0441942i
$513$	2.69491	+	1.55590i	0.118983	+	0.0686948i
$514$	12.3233	+	21.3446i	0.543557	+	0.941469i
$515$	−1.70469	−	2.95261i	−0.0751176	−	0.130107i
$516$	0.637637	−	1.10442i	0.0280704	−	0.0486194i
$517$	39.7005	+	8.53618i	1.74602	+	0.375421i
$518$	28.8410	−	3.68208i	1.26720	−	0.161782i
$519$			7.23663i			0.317653i
$520$	1.08597	−	1.88096i	0.0476231	−	0.0824856i
$521$	30.3032	−	17.4955i	1.32761	−	0.766493i	0.342676	−	0.939454i	$-0.388667\pi$
$521$	30.3032	−	17.4955i	1.32761	−	0.766493i	0.984929	+	0.172960i	$0.0553332\pi$
$522$	2.69384	+	4.66587i	0.117906	+	0.204220i
$523$	−19.1224	+	33.1210i	−0.836165	+	1.44828i	0.0569142	+	0.998379i	$0.481874\pi$
$523$	−19.1224	+	33.1210i	−0.836165	+	1.44828i	−0.893079	+	0.449900i	$0.851459\pi$
$524$	−2.04449			−0.0893139
$525$	−6.88834	−	9.05026i	−0.300632	−	0.394986i
$526$	−30.3837			−1.32479
$527$	5.45639	+	3.15025i	0.237684	+	0.137227i
$528$	1.01748	+	3.15670i	0.0442800	+	0.137378i
$529$	7.39556	+	12.8095i	0.321546	+	0.556934i
$530$	−2.16659	+	3.75264i	−0.0941105	+	0.163004i
$531$			9.68506i			0.420296i
$532$	−7.59396	−	3.18044i	−0.329240	−	0.137889i
$533$	−29.1402			−1.26220
$534$	7.28049	+	4.20339i	0.315057	+	0.181899i
$535$	0.101275	+	0.175414i	0.00437852	+	0.00758382i
$536$	−11.2915	+	6.51916i	−0.487719	+	0.281585i
$537$	6.98568	+	4.03318i	0.301454	+	0.174045i
$538$	−19.9737			−0.861128
$539$	−20.5775	−	10.7502i	−0.886336	−	0.463043i
$540$	−0.837391			−0.0360356
$541$	−2.73079	−	1.57662i	−0.117406	−	0.0677842i	0.440147	−	0.897926i	$-0.354926\pi$
$541$	−2.73079	−	1.57662i	−0.117406	−	0.0677842i	−0.557553	+	0.830141i	$0.688260\pi$
$542$	1.39887	−	0.807639i	0.0600867	−	0.0346911i
$543$	−2.80528	−	4.85889i	−0.120386	−	0.208515i
$544$	−5.17339	−	2.98686i	−0.221807	−	0.128061i
$545$	−14.6754			−0.628627
$546$	−6.32960	−	2.65091i	−0.270882	−	0.113448i
$547$		−	20.6313i		−	0.882131i	−0.897475	−	0.441065i	$-0.854601\pi$
$547$		−	20.6313i		−	0.882131i	0.897475	−	0.441065i	$-0.145399\pi$
$548$	−6.60556	+	11.4412i	−0.282176	+	0.488742i
$549$	2.03524	+	3.52514i	0.0868620	+	0.150449i
$550$	−4.37390	−	13.5699i	−0.186504	−	0.578624i
$551$	−14.5193	−	8.38273i	−0.618543	−	0.357116i
$552$	−2.86511			−0.121947
$553$	−21.6516	−	28.4471i	−0.920722	−	1.20969i
$554$	5.18071			0.220107
$555$	−4.60119	+	7.96950i	−0.195310	+	0.338286i
$556$	3.08147	+	5.33726i	0.130683	+	0.226350i
$557$	−1.10046	+	0.635353i	−0.0466281	+	0.0269208i	−0.523133	−	0.852251i	$-0.675237\pi$
$557$	−1.10046	+	0.635353i	−0.0466281	+	0.0269208i	0.476505	+	0.879172i	$0.341904\pi$
$558$	0.527351	−	0.913399i	0.0223246	−	0.0386673i
$559$			3.30769i			0.139900i
$560$	2.19769	−	0.280576i	0.0928694	−	0.0118565i
$561$	−19.3699	−	4.16481i	−0.817798	−	0.175839i
$562$	−12.5942	+	21.8137i	−0.531252	+	0.920156i
$563$	−20.1729	−	34.9405i	−0.850187	−	1.47257i	−0.881039	−	0.473043i	$-0.843155\pi$
$563$	−20.1729	−	34.9405i	−0.850187	−	1.47257i	0.0308519	−	0.999524i	$-0.490178\pi$
$564$	6.12185	+	10.6034i	0.257777	+	0.446482i
$565$	5.86652	+	3.38704i	0.246806	+	0.142494i
$566$			23.0334i			0.968168i
$567$	0.335059	+	2.62445i	0.0140712	+	0.110217i
$568$		−	14.0795i		−	0.590764i
$569$	2.40837	+	1.39047i	0.100964	+	0.0582917i	0.549632	−	0.835407i	$-0.314768\pi$
$569$	2.40837	+	1.39047i	0.100964	+	0.0582917i	−0.448668	+	0.893699i	$0.648101\pi$
$570$	2.25669	−	1.30290i	0.0945224	−	0.0545725i
$571$	33.0674	−	19.0915i	1.38383	−	0.798953i	0.391217	−	0.920299i	$-0.372054\pi$
$571$	33.0674	−	19.0915i	1.38383	−	0.798953i	0.992610	+	0.121346i	$0.0387209\pi$
$572$	−6.37924	−	5.77110i	−0.266729	−	0.241302i
$573$		−	11.7841i		−	0.492288i
$574$	−18.0029	−	23.6531i	−0.751425	−	0.987262i
$575$	12.3165			0.513633
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	5.92826	−	3.42268i	0.246797	−	0.142488i	−0.371500	−	0.928433i	$-0.621156\pi$
$577$	5.92826	−	3.42268i	0.246797	−	0.142488i	0.618297	+	0.785945i	$0.287823\pi$
$578$	16.1820	−	9.34267i	0.673081	−	0.388604i
$579$	−9.04882	+	15.6730i	−0.376056	+	0.651348i
$580$	4.51160			0.187334
$581$	−7.30370	−	3.05887i	−0.303009	−	0.126903i
$582$		−	0.786131i		−	0.0325862i
$583$	12.7270	+	11.5137i	0.527098	+	0.476850i
$584$	8.58507	−	4.95659i	0.355253	−	0.205105i
$585$	1.88096	−	1.08597i	0.0777682	−	0.0448995i
$586$	3.62064	+	2.09038i	0.149567	+	0.0863527i
$587$			22.7050i			0.937135i	0.883428	+	0.468568i	$0.155230\pi$
$587$			22.7050i			0.937135i	−0.883428	+	0.468568i	$0.844770\pi$
$588$	−1.75869	−	6.77547i	−0.0725273	−	0.279416i
$589$			3.28203i			0.135234i
$590$	7.02363	+	4.05510i	0.289158	+	0.166946i
$591$	−3.11555	−	5.39629i	−0.128157	−	0.221974i
$592$	5.49467	+	9.51705i	0.225830	+	0.391148i
$593$	−5.05558	+	8.75652i	−0.207608	+	0.359587i	−0.950960	−	0.309313i	$-0.899901\pi$
$593$	−5.05558	+	8.75652i	−0.207608	+	0.359587i	0.743353	+	0.668900i	$0.233234\pi$
$594$	−0.697189	+	3.24252i	−0.0286060	+	0.133042i
$595$	−5.11267	+	12.2076i	−0.209599	+	0.500461i
$596$			4.39696i			0.180107i
$597$	9.13344	−	15.8196i	0.373807	−	0.647453i
$598$	6.43566	−	3.71563i	0.263174	−	0.151943i
$599$	1.45219	+	2.51527i	0.0593349	+	0.102771i	0.894167	−	0.447734i	$-0.147769\pi$
$599$	1.45219	+	2.51527i	0.0593349	+	0.102771i	−0.834832	+	0.550505i	$0.814435\pi$
$600$	2.14939	−	3.72285i	0.0877484	−	0.151985i
$601$	−8.68237			−0.354161			−0.177081	−	0.984196i	$-0.556665\pi$
$601$	−8.68237			−0.354161			−0.177081	+	0.984196i	$0.556665\pi$
$602$	−2.68485	+	2.04349i	−0.109426	+	0.0832866i
$603$	−13.0383			−0.530961
$604$	−8.86874	−	5.12037i	−0.360864	−	0.208345i
$605$	9.16527	−	0.919765i	0.372621	−	0.0373938i
$606$	3.36113	+	5.82166i	0.136537	+	0.236489i
$607$	11.7341	−	20.3240i	0.476272	−	0.824927i	−0.523359	−	0.852113i	$-0.675321\pi$
$607$	11.7341	−	20.3240i	0.476272	−	0.824927i	0.999630	+	0.0271855i	$0.00865449\pi$
$608$		−	3.11181i		−	0.126200i
$609$	−1.80520	−	14.1397i	−0.0731502	−	0.572970i
$610$	3.40859			0.138010
$611$	−27.5020	−	15.8783i	−1.11261	−	0.642367i
$612$	−2.98686	−	5.17339i	−0.120737	−	0.209122i
$613$	−26.8294	+	15.4899i	−1.08363	+	0.625633i	−0.931873	−	0.362785i	$-0.881826\pi$
$613$	−26.8294	+	15.4899i	−1.08363	+	0.625633i	−0.151756	+	0.988418i	$0.548493\pi$
$614$	−8.71712	−	5.03283i	−0.351794	−	0.203108i
$615$	9.40808			0.379370
$616$	0.743301	−	8.74343i	0.0299485	−	0.352283i
$617$	7.35346			0.296039			0.148020	−	0.988984i	$-0.452710\pi$
$617$	7.35346			0.296039			0.148020	+	0.988984i	$0.452710\pi$
$618$	−3.52596	−	2.03571i	−0.141835	−	0.0818884i
$619$	−3.16686	+	1.82839i	−0.127287	+	0.0734892i	−0.562292	−	0.826939i	$-0.690080\pi$
$619$	−3.16686	+	1.82839i	−0.127287	+	0.0734892i	0.435005	+	0.900428i	$0.356747\pi$
$620$	−0.441599	−	0.764873i	−0.0177351	−	0.0307180i
$621$	−2.48126	−	1.43256i	−0.0995696	−	0.0574865i
$622$	−1.42972			−0.0573264
$623$	−13.4710	−	17.6989i	−0.539704	−	0.709091i
$624$		−	2.59370i		−	0.103831i
$625$	−7.48667	+	12.9673i	−0.299467	+	0.518692i
$626$	−15.1965	−	26.3211i	−0.607375	−	1.05200i
$627$	−3.16619	−	9.82304i	−0.126445	−	0.392294i
$628$	−13.8444	−	7.99304i	−0.552450	−	0.318957i
$629$	−65.6473			−2.61753
$630$	2.04354	+	0.855860i	0.0814168	+	0.0340983i
$631$	22.5757			0.898724			0.449362	−	0.893350i	$-0.351651\pi$
$631$	22.5757			0.898724			0.449362	+	0.893350i	$0.351651\pi$
$632$	6.75603	−	11.7018i	0.268740	−	0.465472i
$633$	5.12231	+	8.87211i	0.203594	+	0.352635i
$634$	9.39829	−	5.42610i	0.373254	−	0.215498i
$635$	5.07934	−	8.79767i	0.201567	−	0.349125i
$636$			5.17461i			0.205187i
$637$	12.7372	+	12.9384i	0.504666	+	0.512638i
$638$	3.75624	−	17.4697i	0.148711	−	0.691631i
$639$	7.03977	−	12.1932i	0.278489	−	0.482357i
$640$	0.418696	+	0.725202i	0.0165504	+	0.0286661i
$641$	22.2802	+	38.5905i	0.880017	+	1.52423i	0.851321	+	0.524646i	$0.175802\pi$
$641$	22.2802	+	38.5905i	0.880017	+	1.52423i	0.0286961	+	0.999588i	$0.490864\pi$
$642$	0.209477	+	0.120942i	0.00826740	+	0.00477319i
$643$		−	14.8587i		−	0.585968i	−0.956117	−	0.292984i	$-0.905352\pi$
$643$		−	14.8587i		−	0.585968i	0.956117	−	0.292984i	$-0.0946483\pi$
$644$	6.99194	+	2.92830i	0.275521	+	0.115391i
$645$		−	1.06790i		−	0.0420487i
$646$	16.0986	+	9.29454i	0.633391	+	0.365689i
$647$	41.5179	−	23.9704i	1.63224	−	0.942373i	0.648836	−	0.760928i	$-0.275256\pi$
$647$	41.5179	−	23.9704i	1.63224	−	0.942373i	0.983401	−	0.181445i	$-0.0580774\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	21.5497	−	23.8205i	0.845899	−	0.935037i
$650$			11.1498i			0.437329i
$651$	−2.22048	+	1.69005i	−0.0870273	+	0.0662383i
$652$	0.523852			0.0205156
$653$	−12.9160	+	22.3711i	−0.505440	+	0.875448i	0.494540	+	0.869155i	$0.335337\pi$
$653$	−12.9160	+	22.3711i	−0.505440	+	0.875448i	−0.999980	+	0.00629344i	$0.997997\pi$
$654$	−15.1773	+	8.76259i	−0.593478	+	0.342644i
$655$	−1.48267	+	0.856019i	−0.0579326	+	0.0334474i
$656$	5.61749	−	9.72978i	0.219326	−	0.379884i
$657$	9.91318			0.386750
$658$	−4.10237	−	32.1330i	−0.159927	−	1.25267i
$659$		−	28.7951i		−	1.12170i	−0.827918	−	0.560850i	$-0.810475\pi$
$659$		−	28.7951i		−	1.12170i	0.827918	−	0.560850i	$-0.189525\pi$
$660$	2.05957	+	1.86323i	0.0801687	+	0.0725262i
$661$	−23.0670	+	13.3177i	−0.897201	+	0.517999i	−0.876291	−	0.481782i	$-0.839990\pi$
$661$	−23.0670	+	13.3177i	−0.897201	+	0.517999i	−0.0209100	+	0.999781i	$0.506656\pi$
$662$	−11.1847	+	6.45747i	−0.434705	+	0.250977i
$663$	13.4183	+	7.74703i	0.521122	+	0.300870i
$664$		−	2.99287i		−	0.116146i
$665$	−6.83880	+	0.873099i	−0.265197	+	0.0338573i
$666$			10.9893i			0.425829i
$667$	13.3683	+	7.71817i	0.517621	+	0.298849i
$668$	−8.52720	−	14.7695i	−0.329927	−	0.571451i
$669$	7.83326	+	13.5676i	0.302851	+	0.524554i
$670$	−5.45909	+	9.45541i	−0.210903	+	0.365295i
$671$	2.83790	−	13.1986i	0.109556	−	0.509527i
$672$	2.10531	−	1.60239i	0.0812141	−	0.0618137i
$673$			12.3054i			0.474337i	0.971469	+	0.237168i	$0.0762193\pi$
$673$			12.3054i			0.474337i	−0.971469	+	0.237168i	$0.923781\pi$
$674$	−8.24045	+	14.2729i	−0.317410	+	0.549771i
$675$	3.72285	−	2.14939i	0.143293	−	0.0827300i
$676$	−3.13635	−	5.43231i	−0.120629	−	0.208935i
$677$	5.73042	−	9.92539i	0.220238	−	0.381464i	−0.734642	−	0.678455i	$-0.762650\pi$
$677$	5.73042	−	9.92539i	0.220238	−	0.381464i	0.954880	+	0.296991i	$0.0959832\pi$
$678$	8.08949			0.310675
$679$	−0.803469	+	1.91845i	−0.0308343	+	0.0736233i
$680$	−5.00234			−0.191831
$681$	−13.6143	−	7.86025i	−0.521703	−	0.301205i
$682$	−3.32938	+	1.07313i	−0.127488	+	0.0410924i
$683$	3.78001	+	6.54717i	0.144638	+	0.250520i	0.929238	−	0.369482i	$-0.120465\pi$
$683$	3.78001	+	6.54717i	0.144638	+	0.250520i	−0.784600	+	0.620003i	$0.787132\pi$
$684$	1.55590	−	2.69491i	0.0594915	−	0.103042i
$685$			11.0629i			0.422691i
$686$	−2.63304	+	18.3321i	−0.100530	+	0.699924i
$687$	2.50417			0.0955399
$688$	−1.10442	−	0.637637i	−0.0421056	−	0.0243097i
$689$	−6.71070	−	11.6233i	−0.255657	−	0.442812i
$690$	−2.07779	+	1.19961i	−0.0791000	+	0.0456684i
$691$	−16.4626	−	9.50471i	−0.626268	−	0.361576i	0.153037	−	0.988220i	$-0.451095\pi$
$691$	−16.4626	−	9.50471i	−0.626268	−	0.361576i	−0.779305	+	0.626644i	$0.784428\pi$
$692$	7.23663			0.275095
$693$	5.01543	−	7.20038i	0.190520	−	0.273520i
$694$	−11.4633			−0.435140
$695$	4.46937	+	2.58039i	0.169533	+	0.0978799i
$696$	4.66587	−	2.69384i	0.176860	−	0.102110i
$697$	33.5573	+	58.1230i	1.27107	+	2.20156i
$698$	18.1485	+	10.4781i	0.686932	+	0.396600i
$699$	0.0553161			0.00209225
$700$	−9.05026	+	6.88834i	−0.342068	+	0.260355i
$701$		−	32.6349i		−	1.23260i	−0.787510	−	0.616302i	$-0.788630\pi$
$701$		−	32.6349i		−	1.23260i	0.787510	−	0.616302i	$-0.211370\pi$
$702$	1.29685	−	2.24621i	0.0489465	−	0.0847779i
$703$	−17.0984	−	29.6152i	−0.644877	−	1.11696i
$704$	3.15670	−	1.01748i	0.118973	−	0.0383476i
$705$	8.87916	+	5.12639i	0.334409	+	0.193071i
$706$	−19.9221			−0.749778
$707$	−2.25236	−	17.6423i	−0.0847087	−	0.663505i
$708$	9.68506			0.363987
$709$	−7.57532	+	13.1208i	−0.284497	+	0.492764i	−0.972487	−	0.232957i	$-0.925160\pi$
$709$	−7.57532	+	13.1208i	−0.284497	+	0.492764i	0.687990	+	0.725720i	$0.258493\pi$
$710$	−5.89504	−	10.2105i	−0.221237	−	0.383194i
$711$	11.7018	−	6.75603i	0.438851	−	0.253371i
$712$	4.20339	−	7.28049i	0.157529	−	0.272848i
$713$		−	3.02184i		−	0.113169i
$714$	2.00155	+	15.6777i	0.0749062	+	0.586724i
$715$	−7.04258	−	1.51426i	−0.263377	−	0.0566300i
$716$	4.03318	−	6.98568i	0.150727	−	0.261067i
$717$	2.87233	+	4.97501i	0.107269	+	0.185795i
$718$	1.95715	+	3.38989i	0.0730403	+	0.126510i
$719$	4.46410	+	2.57735i	0.166483	+	0.0961189i	0.580926	−	0.813956i	$-0.302690\pi$
$719$	4.46410	+	2.57735i	0.166483	+	0.0961189i	−0.414444	+	0.910075i	$0.636024\pi$
$720$			0.837391i			0.0312077i
$721$	6.52403	+	8.57162i	0.242968	+	0.319224i
$722$		−	9.31665i		−	0.346730i
$723$	6.35875	+	3.67123i	0.236484	+	0.136534i
$724$	−4.85889	+	2.80528i	−0.180579	+	0.104257i
$725$	−20.0575	+	11.5802i	−0.744919	+	0.430079i
$726$	8.92949	−	6.42373i	0.331404	−	0.238407i
$727$			24.1329i			0.895041i	0.894274	+	0.447520i	$0.147693\pi$
$727$			24.1329i			0.895041i	−0.894274	+	0.447520i	$0.852307\pi$
$728$	−2.65091	+	6.32960i	−0.0982492	+	0.234591i
$729$	−1.00000			−0.0370370
$730$	4.15061	−	7.18906i	0.153621	−	0.266079i
$731$	6.59750	−	3.80907i	0.244017	−	0.140883i
$732$	3.52514	−	2.03524i	0.130293	−	0.0752247i
$733$	26.0520	−	45.1235i	0.962254	−	1.66667i	0.245436	−	0.969413i	$-0.421069\pi$
$733$	26.0520	−	45.1235i	0.962254	−	1.66667i	0.716818	−	0.697260i	$-0.245598\pi$
$734$	−12.0920			−0.446324
$735$	−4.11227	−	4.17723i	−0.151683	−	0.154079i
$736$			2.86511i			0.105609i
$737$	32.0678	+	29.0108i	1.18123	+	1.06863i
$738$	9.72978	−	5.61749i	0.358158	−	0.206783i
$739$	−4.80361	+	2.77336i	−0.176704	+	0.102020i	−0.585743	−	0.810497i	$-0.699197\pi$
$739$	−4.80361	+	2.77336i	−0.176704	+	0.102020i	0.409039	+	0.912517i	$0.365864\pi$
$740$	7.96950	+	4.60119i	0.292965	+	0.169143i
$741$			8.07111i			0.296500i
$742$	5.28873	−	12.6280i	0.194155	−	0.463587i
$743$			18.2750i			0.670443i	0.942139	+	0.335222i	$0.108811\pi$
$743$			18.2750i			0.670443i	−0.942139	+	0.335222i	$0.891189\pi$
$744$	−0.913399	−	0.527351i	−0.0334868	−	0.0193336i
$745$	1.84099	+	3.18869i	0.0674486	+	0.116824i
$746$	−8.84681	−	15.3231i	−0.323905	−	0.561019i
$747$	1.49643	−	2.59190i	0.0547516	−	0.0948326i
$748$	−4.16481	+	19.3699i	−0.152281	+	0.708234i
$749$	−0.387592	−	0.509239i	−0.0141623	−	0.0186072i
$750$		−	7.78672i		−	0.284331i
$751$	7.35764	−	12.7438i	0.268484	−	0.465028i	−0.699986	−	0.714156i	$-0.746811\pi$
$751$	7.35764	−	12.7438i	0.268484	−	0.465028i	0.968471	+	0.249128i	$0.0801440\pi$
$752$	10.6034	−	6.12185i	0.386665	−	0.223241i
$753$	2.10401	+	3.64426i	0.0766745	+	0.132804i
$754$	−6.98704	+	12.1019i	−0.254453	+	0.440725i
$755$	−8.57551			−0.312095
$756$	2.62445	−	0.335059i	0.0954503	−	0.0121860i
$757$	−46.8890			−1.70421			−0.852105	−	0.523371i	$-0.824674\pi$
$757$	−46.8890			−1.70421			−0.852105	+	0.523371i	$0.824674\pi$
$758$	−17.0241	−	9.82884i	−0.618342	−	0.357000i
$759$	2.91518	+	9.04430i	0.105814	+	0.328287i
$760$	−1.30290	−	2.25669i	−0.0472612	−	0.0818588i
$761$	18.5206	−	32.0787i	0.671373	−	1.16285i	−0.306142	−	0.951986i	$-0.599038\pi$
$761$	18.5206	−	32.0787i	0.671373	−	1.16285i	0.977515	−	0.210866i	$-0.0676283\pi$
$762$		−	12.1313i		−	0.439472i
$763$	45.9940	−	5.87198i	1.66509	−	0.212580i
$764$	−11.7841			−0.426334
$765$	−4.33216	−	2.50117i	−0.156629	−	0.0904300i
$766$	−0.686725	−	1.18944i	−0.0248124	−	0.0429763i
$767$	−21.7547	+	12.5601i	−0.785518	+	0.453519i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	−10.3666			−0.373830			−0.186915	−	0.982376i	$-0.559849\pi$
$769$	−10.3666			−0.373830			−0.186915	+	0.982376i	$0.559849\pi$
$770$	−3.12179	−	6.65197i	−0.112502	−	0.239720i
$771$	24.6466			0.887625
$772$	15.6730	+	9.04882i	0.564084	+	0.325674i
$773$	−18.7188	+	10.8073i	−0.673268	+	0.388712i	−0.797314	−	0.603565i	$-0.793746\pi$
$773$	−18.7188	+	10.8073i	−0.673268	+	0.388712i	0.124045	+	0.992277i	$0.460413\pi$
$774$	−0.637637	−	1.10442i	−0.0229194	−	0.0396976i
$775$	3.92650	+	2.26696i	0.141044	+	0.0814318i
$776$	−0.786131			−0.0282204
$777$	11.2317	−	26.8181i	0.402935	−	0.962093i
$778$			31.3793i			1.12500i
$779$	−17.4806	+	30.2772i	−0.626306	+	1.08479i
$780$	−1.08597	−	1.88096i	−0.0388841	−	0.0673492i
$781$	−44.4449	+	14.3256i	−1.59036	+	0.512610i
$782$	−14.8224	−	8.55769i	−0.530047	−	0.306023i
$783$	5.38769			0.192540
$784$	−6.77547	+	1.75869i	−0.241981	+	0.0628105i
$785$	−13.3866			−0.477789
$786$	−1.02224	+	1.77058i	−0.0364622	+	0.0631545i
$787$	−24.3455	−	42.1677i	−0.867824	−	1.50312i	−0.864215	−	0.503122i	$-0.832185\pi$
$787$	−24.3455	−	42.1677i	−0.867824	−	1.50312i	−0.00360891	−	0.999993i	$-0.501149\pi$
$788$	−5.39629	+	3.11555i	−0.192235	+	0.110987i
$789$	−15.1918	+	26.3130i	−0.540843	+	0.936768i
$790$		−	11.3149i		−	0.402565i
$791$	−19.7414	−	8.26790i	−0.701922	−	0.293973i
$792$	3.24252	+	0.697189i	0.115218	+	0.0247735i
$793$	−5.27882	+	9.14318i	−0.187456	+	0.324684i
$794$	17.6360	+	30.5464i	0.625877	+	1.08405i
$795$	2.16659	+	3.75264i	0.0768409	+	0.133092i
$796$	−15.8196	−	9.13344i	−0.560711	−	0.323726i
$797$		−	36.0374i		−	1.27651i	−0.769825	−	0.638255i	$-0.779657\pi$
$797$		−	36.0374i		−	1.27651i	0.769825	−	0.638255i	$-0.220343\pi$
$798$	−6.55132	+	4.98635i	−0.231914	+	0.176515i
$799$			73.1405i			2.58752i
$800$	−3.72285	−	2.14939i	−0.131623	−	0.0759923i
$801$	7.28049	−	4.20339i	0.257243	−	0.148520i
$802$	7.76494	−	4.48309i	0.274190	−	0.158303i
$803$	−24.3816	−	22.0573i	−0.860407	−	0.778384i
$804$			13.0383i			0.459826i
$805$	6.29664	−	0.803882i	0.221927	−	0.0283331i
$806$	2.73559			0.0963569
$807$	−9.98686	+	17.2977i	−0.351554	+	0.608910i
$808$	5.82166	−	3.36113i	0.204805	−	0.118244i
$809$	25.9030	−	14.9551i	0.910700	−	0.525793i	0.0300439	−	0.999549i	$-0.490435\pi$
$809$	25.9030	−	14.9551i	0.910700	−	0.525793i	0.880656	+	0.473756i	$0.157102\pi$
$810$	−0.418696	+	0.725202i	−0.0147115	+	0.0254810i
$811$	18.1295			0.636611			0.318306	−	0.947988i	$-0.396886\pi$
$811$	18.1295			0.636611			0.318306	+	0.947988i	$0.396886\pi$
$812$	−14.1397	+	1.80520i	−0.496207	+	0.0633500i
$813$		−	1.61528i		−	0.0566503i
$814$	24.4518	−	27.0284i	0.857034	−	0.947345i
$815$	0.379899	−	0.219335i	0.0133073	−	0.00768296i
$816$	−5.17339	+	2.98686i	−0.181105	+	0.104561i
$817$	3.43674	+	1.98420i	0.120236	+	0.0694185i
$818$		−	35.9524i		−	1.25705i
$819$	−5.46055	+	4.15614i	−0.190807	+	0.145227i
$820$		−	9.40808i		−	0.328544i
$821$	−16.8684	−	9.73899i	−0.588712	−	0.339893i	0.175876	−	0.984412i	$-0.443724\pi$
$821$	−16.8684	−	9.73899i	−0.588712	−	0.339893i	−0.764588	+	0.644519i	$0.777058\pi$
$822$	6.60556	+	11.4412i	0.230395	+	0.399057i
$823$	−14.0931	−	24.4100i	−0.491255	−	0.850879i	0.508694	−	0.860947i	$-0.330128\pi$
$823$	−14.0931	−	24.4100i	−0.491255	−	0.850879i	−0.999949	+	0.0100686i	$0.996795\pi$
$824$	−2.03571	+	3.52596i	−0.0709174	+	0.122833i
$825$	−13.9389	−	2.99706i	−0.485289	−	0.104344i
$826$	−23.6351	−	9.89867i	−0.822372	−	0.344419i
$827$			25.7981i			0.897089i	0.893761	+	0.448544i	$0.148057\pi$
$827$			25.7981i			0.897089i	−0.893761	+	0.448544i	$0.851943\pi$
$828$	−1.43256	+	2.48126i	−0.0497848	+	0.0862298i
$829$	31.9716	−	18.4588i	1.11042	−	0.641100i	0.171480	−	0.985188i	$-0.445145\pi$
$829$	31.9716	−	18.4588i	1.11042	−	0.641100i	0.938938	+	0.344087i	$0.111812\pi$
$830$	−1.25310	−	2.17043i	−0.0434958	−	0.0753369i
$831$	2.59035	−	4.48663i	0.0898584	−	0.155639i
$832$	−2.59370			−0.0899205
$833$	11.1390	−	40.3051i	0.385942	−	1.39649i
$834$	6.16293			0.213405
$835$	−12.3679	−	7.14060i	−0.428008	−	0.247111i
$836$	−9.82304	+	3.16619i	−0.339737	+	0.109505i
$837$	−0.527351	−	0.913399i	−0.0182279	−	0.0315717i
$838$	0.362317	−	0.627552i	0.0125160	−	0.0216784i
$839$		−	6.71611i		−	0.231866i	−0.993257	−	0.115933i	$-0.963014\pi$
$839$		−	6.71611i		−	0.231866i	0.993257	−	0.115933i	$-0.0369858\pi$
$840$	0.855860	−	2.04354i	0.0295300	−	0.0705090i
$841$	−0.0271771			−0.000937142
$842$	−3.21662	−	1.85712i	−0.110852	−	0.0640005i
$843$	12.5942	+	21.8137i	0.433766	+	0.751304i
$844$	8.87211	−	5.12231i	0.305390	−	0.176317i
$845$	−4.54897	−	2.62635i	−0.156489	−	0.0903492i
$846$	12.2437			0.420947
$847$	−28.3566	+	6.54985i	−0.974346	+	0.225055i
$848$	5.17461			0.177697
$849$	19.9475	+	11.5167i	0.684598	+	0.395253i
$850$	22.2393	−	12.8398i	0.762800	−	0.440403i
$851$	15.7429	+	27.2674i	0.539658	+	0.934716i
$852$	−12.1932	−	7.03977i	−0.417733	−	0.241179i
$853$	39.8993			1.36613			0.683063	−	0.730360i	$-0.260648\pi$
$853$	39.8993			1.36613			0.683063	+	0.730360i	$0.260648\pi$
$854$	−10.6828	+	1.36385i	−0.365557	+	0.0466701i
$855$		−	2.60580i		−	0.0891165i
$856$	0.120942	−	0.209477i	0.00413370	−	0.00715978i
$857$	7.85467	+	13.6047i	0.268310	+	0.464727i	0.968426	−	0.249303i	$-0.0802014\pi$
$857$	7.85467	+	13.6047i	0.268310	+	0.464727i	−0.700115	+	0.714030i	$0.746868\pi$
$858$	−8.18754	+	2.63903i	−0.279518	+	0.0900951i
$859$	16.6977	+	9.64043i	0.569719	+	0.328927i	0.757037	−	0.653372i	$-0.226646\pi$
$859$	16.6977	+	9.64043i	0.569719	+	0.328927i	−0.187318	+	0.982299i	$0.559980\pi$
$860$	−1.06790			−0.0364152
$861$	−29.4856	+	3.76439i	−1.00487	+	0.128290i
$862$	−4.08478			−0.139128
$863$	−19.0761	+	33.0408i	−0.649358	+	1.12472i	0.333918	+	0.942602i	$0.391629\pi$
$863$	−19.0761	+	33.0408i	−0.649358	+	1.12472i	−0.983276	+	0.182119i	$0.941704\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	5.24802	−	3.02995i	0.178438	−	0.103021i
$866$	15.1555	−	26.2500i	0.515003	−	0.892012i
$867$		−	18.6853i		−	0.634587i
$868$	1.69005	+	2.22048i	0.0573640	+	0.0753679i
$869$	−43.8131	−	9.42046i	−1.48626	−	0.319567i
$870$	2.25580	−	3.90716i	0.0764788	−	0.132465i
$871$	−16.9088	−	29.2868i	−0.572932	−	0.992347i
$872$	8.76259	+	15.1773i	0.296739	+	0.513967i
$873$	−0.680809	−	0.393065i	−0.0230419	−	0.0133032i
$874$		−	8.91569i		−	0.301578i
$875$	−7.95845	+	19.0025i	−0.269045	+	0.642401i
$876$		−	9.91318i		−	0.334935i
$877$	7.92511	+	4.57556i	0.267612	+	0.154506i	0.627802	−	0.778373i	$-0.283955\pi$
$877$	7.92511	+	4.57556i	0.267612	+	0.154506i	−0.360190	+	0.932879i	$0.617288\pi$
$878$	10.9208	−	6.30512i	0.368559	−	0.212787i
$879$	3.62064	−	2.09038i	0.122121	−	0.0705067i
$880$	1.86323	−	2.05957i	0.0628095	−	0.0694282i
$881$			47.7019i			1.60712i	0.595225	+	0.803559i	$0.297063\pi$
$881$			47.7019i			1.60712i	−0.595225	+	0.803559i	$0.702937\pi$
$882$	−6.74708	−	1.86466i	−0.227186	−	0.0627864i
$883$	43.7932			1.47376			0.736879	−	0.676025i	$-0.236299\pi$
$883$	43.7932			1.47376			0.736879	+	0.676025i	$0.236299\pi$
$884$	7.74703	−	13.4183i	0.260561	−	0.451305i
$885$	7.02363	−	4.05510i	0.236097	−	0.136311i
$886$	13.1958	−	7.61859i	0.443321	−	0.255952i
$887$	−25.2896	+	43.8029i	−0.849142	+	1.47076i	0.0328338	+	0.999461i	$0.489547\pi$
$887$	−25.2896	+	43.8029i	−0.849142	+	1.47076i	−0.881975	+	0.471296i	$0.843787\pi$
$888$	10.9893			0.368778
$889$	−12.3989	+	29.6049i	−0.415845	+	0.992918i
$890$		−	7.03977i		−	0.235974i
$891$	2.45951	+	2.22504i	0.0823967	+	0.0745417i
$892$	13.5676	−	7.83326i	0.454277	−	0.262277i
$893$	−32.9956	+	19.0500i	−1.10416	+	0.637485i
$894$	3.80788	+	2.19848i	0.127355	+	0.0735282i
$895$		−	6.75470i		−	0.225785i
$896$	−1.60239	−	2.10531i	−0.0535323	−	0.0703335i
$897$		−	7.43126i		−	0.248123i
$898$	−27.9536	−	16.1390i	−0.932823	−	0.538566i
$899$	2.84120	+	4.92111i	0.0947595	+	0.164128i
$900$	−2.14939	−	3.72285i	−0.0716463	−	0.124095i
$901$	−15.4558	+	26.7703i	−0.514908	+	0.891847i
$902$	−36.4296	−	7.83291i	−1.21297	−	0.260807i
$903$	0.427293	+	3.34689i	0.0142194	+	0.111378i
$904$		−	8.08949i		−	0.269053i
$905$	−2.34912	+	4.06879i	−0.0780873	+	0.135251i
$906$	−8.86874	+	5.12037i	−0.294644	+	0.170113i
$907$	28.9344	+	50.1159i	0.960752	+	1.66407i	0.720620	+	0.693330i	$0.243857\pi$
$907$	28.9344	+	50.1159i	0.960752	+	1.66407i	0.240132	+	0.970740i	$0.422809\pi$
$908$	−7.86025	+	13.6143i	−0.260851	+	0.451808i
$909$	6.72227			0.222964
$910$	0.727731	+	5.70016i	0.0241241	+	0.188959i
$911$	25.4860			0.844389			0.422195	−	0.906505i	$-0.361260\pi$
$911$	25.4860			0.844389			0.422195	+	0.906505i	$0.361260\pi$
$912$	−2.69491	−	1.55590i	−0.0892372	−	0.0515211i
$913$	−9.44758	+	3.04517i	−0.312669	+	0.100780i
$914$	15.1724	+	26.2793i	0.501857	+	0.869242i
$915$	1.70429	−	2.95192i	0.0563422	−	0.0975876i
$916$		−	2.50417i		−	0.0827400i
$917$	4.30428	−	3.27608i	0.142140	−	0.108186i
$918$	−5.97372			−0.197162
$919$	11.2495	+	6.49491i	0.371087	+	0.214247i	0.673933	−	0.738792i	$-0.264604\pi$
$919$	11.2495	+	6.49491i	0.371087	+	0.214247i	−0.302846	+	0.953039i	$0.597937\pi$
$920$	1.19961	+	2.07779i	0.0395500	+	0.0685026i
$921$	−8.71712	+	5.03283i	−0.287239	+	0.165837i
$922$	−4.16907	−	2.40701i	−0.137301	−	0.0792707i
$923$	36.5182			1.20201
$924$	−7.20038	−	5.01543i	−0.236875	−	0.164996i
$925$	−47.2407			−1.55327
$926$	28.6825	+	16.5598i	0.942564	+	0.544190i
$927$	−3.52596	+	2.03571i	−0.115808	+	0.0668616i
$928$	−2.69384	−	4.66587i	−0.0884298	−	0.153165i
$929$	−18.8834	−	10.9024i	−0.619545	−	0.357695i	0.157147	−	0.987575i	$-0.449770\pi$
$929$	−18.8834	−	10.9024i	−0.619545	−	0.357695i	−0.776692	+	0.629881i	$0.783104\pi$
$930$	−0.883199			−0.0289612
$931$	21.0840	−	5.47272i	0.690999	−	0.179361i
$932$		−	0.0553161i		−	0.00181194i
$933$	−0.714858	+	1.23817i	−0.0234034	+	0.0405359i
$934$	7.19328	+	12.4591i	0.235371	+	0.407675i
$935$	5.08976	+	15.7909i	0.166453	+	0.516417i
$936$	−2.24621	−	1.29685i	−0.0734198	−	0.0423889i
$937$	31.2647			1.02137			0.510686	−	0.859767i	$-0.329391\pi$
$937$	31.2647			1.02137			0.510686	+	0.859767i	$0.329391\pi$
$938$	13.3259	−	31.8183i	0.435105	−	1.03890i
$939$	−30.3930			−0.991839
$940$	5.12639	−	8.87916i	0.167204	−	0.289606i
$941$	9.38779	+	16.2601i	0.306033	+	0.530065i	0.977491	−	0.210978i	$-0.0676648\pi$
$941$	9.38779	+	16.2601i	0.306033	+	0.530065i	−0.671458	+	0.741043i	$0.734332\pi$
$942$	−13.8444	+	7.99304i	−0.451074	+	0.260427i
$943$	16.0947	−	27.8769i	0.524117	−	0.907797i
$944$		−	9.68506i		−	0.315222i
$945$	1.76297	−	1.34183i	0.0573494	−	0.0436498i
$946$	−0.889107	+	4.13510i	−0.0289074	+	0.134444i
$947$	19.7729	−	34.2477i	0.642534	−	1.11290i	−0.342331	−	0.939580i	$-0.611216\pi$
$947$	19.7729	−	34.2477i	0.642534	−	1.11290i	0.984865	−	0.173323i	$-0.0554503\pi$
$948$	−6.75603	−	11.7018i	−0.219426	−	0.380056i
$949$	12.8559	+	22.2671i	0.417321	+	0.722822i
$950$	11.5848	+	6.68848i	0.375860	+	0.217003i
$951$		−	10.8522i		−	0.351907i
$952$	15.6777	−	2.00155i	0.508118	−	0.0648707i
$953$			2.98673i			0.0967495i	0.998829	+	0.0483748i	$0.0154042\pi$
$953$			2.98673i			0.0967495i	−0.998829	+	0.0483748i	$0.984596\pi$
$954$	4.48134	+	2.58730i	0.145089	+	0.0837671i
$955$	−8.54587	+	4.93396i	−0.276538	+	0.159659i
$956$	4.97501	−	2.87233i	0.160903	−	0.0928976i
$957$	−13.2511	−	11.9878i	−0.428346	−	0.387512i
$958$			6.47208i			0.209104i
$959$	−4.42651	−	34.6719i	−0.142940	−	1.11961i
$960$	0.837391			0.0270267
$961$	−14.9438	+	25.8834i	−0.482058	+	0.834949i
$962$	−24.6844	+	14.2516i	−0.795858	+	0.459489i
$963$	0.209477	−	0.120942i	0.00675030	−	0.00389729i
$964$	3.67123	−	6.35875i	0.118242	−	0.204802i
$965$	15.1548			0.487850
$966$	6.03195	−	4.59104i	0.194075	−	0.147714i
$967$		−	3.61655i		−	0.116300i	−0.998308	−	0.0581502i	$-0.981480\pi$
$967$		−	3.61655i		−	0.116300i	0.998308	−	0.0581502i	$-0.0185202\pi$
$968$	−6.42373	−	8.92949i	−0.206466	−	0.287005i
$969$	16.0986	−	9.29454i	0.517162	−	0.298584i
$970$	−0.570104	+	0.329150i	−0.0183049	+	0.0105684i
$971$	23.9499	+	13.8275i	0.768587	+	0.443744i	0.832370	−	0.554220i	$-0.186983\pi$
$971$	23.9499	+	13.8275i	0.768587	+	0.443744i	−0.0637831	+	0.997964i	$0.520317\pi$
$972$			1.00000i			0.0320750i
$973$	−15.0398	−	6.29886i	−0.482155	−	0.201932i
$974$		−	5.28096i		−	0.169213i
$975$	9.65597	+	5.57488i	0.309239	+	0.178539i
$976$	−2.03524	−	3.52514i	−0.0651465	−	0.112837i
$977$	−17.4175	−	30.1679i	−0.557234	−	0.965158i	−0.997726	−	0.0674010i	$-0.978529\pi$
$977$	−17.4175	−	30.1679i	−0.557234	−	0.965158i	0.440492	−	0.897757i	$-0.354804\pi$
$978$	0.261926	−	0.453669i	0.00837547	−	0.0145067i
$979$	−27.2591	−	5.86112i	−0.871206	−	0.187322i
$980$	−4.17723	+	4.11227i	−0.133437	+	0.131362i
$981$			17.5252i			0.559536i
$982$	−5.68167	+	9.84094i	−0.181309	+	0.314037i
$983$	19.2919	−	11.1382i	0.615317	−	0.355254i	−0.159726	−	0.987161i	$-0.551061\pi$
$983$	19.2919	−	11.1382i	0.615317	−	0.355254i	0.775044	+	0.631908i	$0.217728\pi$
$984$	−5.61749	−	9.72978i	−0.179079	−	0.310174i
$985$	−2.60894	+	4.51881i	−0.0831276	+	0.143981i
$986$	32.1845			1.02496
$987$	−29.8792	−	12.5137i	−0.951065	−	0.398317i
$988$	8.07111			0.256776
$989$	−3.16429	−	1.82690i	−0.100619	−	0.0580921i
$990$	2.64339	−	0.852026i	0.0840125	−	0.0270792i
$991$	−27.3088	−	47.3002i	−0.867493	−	1.50254i	−0.864550	−	0.502546i	$-0.832397\pi$
$991$	−27.3088	−	47.3002i	−0.867493	−	1.50254i	−0.00294265	−	0.999996i	$-0.500937\pi$
$992$	−0.527351	+	0.913399i	−0.0167434	+	0.0290005i
$993$			12.9149i			0.409843i
$994$	22.5610	+	29.6418i	0.715591	+	0.940181i
$995$	−15.2965			−0.484933
$996$	−2.59190	−	1.49643i	−0.0821274	−	0.0474163i
$997$	8.45911	+	14.6516i	0.267903	+	0.464021i	0.968320	−	0.249712i	$-0.0803361\pi$
$997$	8.45911	+	14.6516i	0.267903	+	0.464021i	−0.700417	+	0.713734i	$0.747003\pi$
$998$	−25.2638	+	14.5860i	−0.799710	+	0.461713i
$999$	9.51705	+	5.49467i	0.301106	+	0.173844i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.p.b.439.2	yes	16
3.2	odd	2		1386.2.bk.b.901.7		16
7.2	even	3		3234.2.e.b.2155.12		16
7.3	odd	6		462.2.p.a.241.6	✓	16
7.5	odd	6		3234.2.e.a.2155.13		16
11.10	odd	2		462.2.p.a.439.6	yes	16
21.17	even	6		1386.2.bk.a.703.3		16
33.32	even	2		1386.2.bk.a.901.3		16
77.10	even	6	inner	462.2.p.b.241.2	yes	16
77.54	even	6		3234.2.e.b.2155.5		16
77.65	odd	6		3234.2.e.a.2155.4		16
231.164	odd	6		1386.2.bk.b.703.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.p.a.241.6	✓	16	7.3	odd	6
462.2.p.a.439.6	yes	16	11.10	odd	2
462.2.p.b.241.2	yes	16	77.10	even	6	inner
462.2.p.b.439.2	yes	16	1.1	even	1	trivial
1386.2.bk.a.703.3		16	21.17	even	6
1386.2.bk.a.901.3		16	33.32	even	2
1386.2.bk.b.703.7		16	231.164	odd	6
1386.2.bk.b.901.7		16	3.2	odd	2
3234.2.e.a.2155.4		16	77.65	odd	6
3234.2.e.a.2155.13		16	7.5	odd	6
3234.2.e.b.2155.5		16	77.54	even	6
3234.2.e.b.2155.12		16	7.2	even	3

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.725202 + 0.418696i) q^{5} +1.00000 q^{6} +(-2.44037 - 1.02205i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.725202 + 0.418696i) q^{5} +1.00000 q^{6} +(-2.44037 - 1.02205i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.418696 - 0.725202i) q^{10} +(-3.15670 + 1.01748i) q^{11} +(-0.866025 - 0.500000i) q^{12} +2.59370 q^{13} +(1.60239 + 2.10531i) q^{14} -0.837391 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.98686 - 5.17339i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(1.55590 - 2.69491i) q^{19} +0.837391i q^{20} +(2.62445 - 0.335059i) q^{21} +(3.24252 + 0.697189i) q^{22} +(-1.43256 + 2.48126i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-2.14939 - 3.72285i) q^{25} +(-2.24621 - 1.29685i) q^{26} +1.00000i q^{27} +(-0.335059 - 2.62445i) q^{28} -5.38769i q^{29} +(0.725202 + 0.418696i) q^{30} +(-0.913399 + 0.527351i) q^{31} +(0.866025 - 0.500000i) q^{32} +(2.22504 - 2.45951i) q^{33} +5.97372i q^{34} +(-1.34183 - 1.76297i) q^{35} +1.00000 q^{36} +(5.49467 - 9.51705i) q^{37} +(-2.69491 + 1.55590i) q^{38} +(-2.24621 + 1.29685i) q^{39} +(0.418696 - 0.725202i) q^{40} -11.2350 q^{41} +(-2.44037 - 1.02205i) q^{42} +1.27527i q^{43} +(-2.45951 - 2.22504i) q^{44} +(0.725202 - 0.418696i) q^{45} +(2.48126 - 1.43256i) q^{46} +(-10.6034 - 6.12185i) q^{47} -1.00000i q^{48} +(4.91081 + 4.98838i) q^{49} +4.29878i q^{50} +(5.17339 + 2.98686i) q^{51} +(1.29685 + 2.24621i) q^{52} +(-2.58730 - 4.48134i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.71526 - 0.583820i) q^{55} +(-1.02205 + 2.44037i) q^{56} +3.11181i q^{57} +(-2.69384 + 4.66587i) q^{58} +(-8.38751 + 4.84253i) q^{59} +(-0.418696 - 0.725202i) q^{60} +(-2.03524 + 3.52514i) q^{61} +1.05470 q^{62} +(-2.10531 + 1.60239i) q^{63} -1.00000 q^{64} +(1.88096 + 1.08597i) q^{65} +(-3.15670 + 1.01748i) q^{66} +(-6.51916 - 11.2915i) q^{67} +(2.98686 - 5.17339i) q^{68} -2.86511i q^{69} +(0.280576 + 2.19769i) q^{70} +14.0795 q^{71} +(-0.866025 - 0.500000i) q^{72} +(4.95659 + 8.58507i) q^{73} +(-9.51705 + 5.49467i) q^{74} +(3.72285 + 2.14939i) q^{75} +3.11181 q^{76} +(8.74343 + 0.743301i) q^{77} +2.59370 q^{78} +(11.7018 + 6.75603i) q^{79} +(-0.725202 + 0.418696i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(9.72978 + 5.61749i) q^{82} +2.99287 q^{83} +(1.60239 + 2.10531i) q^{84} -5.00234i q^{85} +(0.637637 - 1.10442i) q^{86} +(2.69384 + 4.66587i) q^{87} +(1.01748 + 3.15670i) q^{88} +(7.28049 + 4.20339i) q^{89} -0.837391 q^{90} +(-6.32960 - 2.65091i) q^{91} -2.86511 q^{92} +(0.527351 - 0.913399i) q^{93} +(6.12185 + 10.6034i) q^{94} +(2.25669 - 1.30290i) q^{95} +(-0.500000 + 0.866025i) q^{96} -0.786131i q^{97} +(-1.75869 - 6.77547i) q^{98} +(-0.697189 + 3.24252i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 12 q^{5} + 16 q^{6} + 6 q^{7} + 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 12 * q^5 + 16 * q^6 + 6 * q^7 + 8 * q^9	\( 16 q + 8 q^{4} + 12 q^{5} + 16 q^{6} + 6 q^{7} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{14} - 4 q^{15} - 8 q^{16} + 10 q^{19} + 4 q^{21} + 2 q^{22} - 4 q^{23} + 8 q^{24} + 10 q^{25} + 12 q^{26} + 12 q^{30} + 6 q^{31} + 4 q^{33} + 8 q^{35} + 16 q^{36} + 14 q^{37} - 12 q^{38} + 12 q^{39} + 2 q^{40} - 32 q^{41} + 6 q^{42} + 4 q^{44} + 12 q^{45} - 18 q^{46} - 24 q^{47} - 6 q^{49} - 6 q^{51} + 8 q^{54} + 14 q^{55} + 4 q^{56} - 2 q^{60} - 28 q^{61} + 8 q^{62} + 6 q^{63} - 16 q^{64} - 72 q^{65} - 4 q^{66} - 16 q^{67} - 30 q^{70} - 56 q^{71} + 44 q^{73} - 24 q^{74} - 12 q^{75} + 20 q^{76} - 52 q^{77} + 30 q^{79} - 12 q^{80} - 8 q^{81} - 12 q^{82} - 8 q^{83} + 8 q^{84} - 12 q^{86} - 2 q^{88} - 36 q^{89} - 4 q^{90} - 8 q^{91} - 8 q^{92} + 4 q^{93} - 14 q^{94} - 72 q^{95} - 8 q^{96} + 40 q^{98} - 8 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 12 * q^5 + 16 * q^6 + 6 * q^7 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^14 - 4 * q^15 - 8 * q^16 + 10 * q^19 + 4 * q^21 + 2 * q^22 - 4 * q^23 + 8 * q^24 + 10 * q^25 + 12 * q^26 + 12 * q^30 + 6 * q^31 + 4 * q^33 + 8 * q^35 + 16 * q^36 + 14 * q^37 - 12 * q^38 + 12 * q^39 + 2 * q^40 - 32 * q^41 + 6 * q^42 + 4 * q^44 + 12 * q^45 - 18 * q^46 - 24 * q^47 - 6 * q^49 - 6 * q^51 + 8 * q^54 + 14 * q^55 + 4 * q^56 - 2 * q^60 - 28 * q^61 + 8 * q^62 + 6 * q^63 - 16 * q^64 - 72 * q^65 - 4 * q^66 - 16 * q^67 - 30 * q^70 - 56 * q^71 + 44 * q^73 - 24 * q^74 - 12 * q^75 + 20 * q^76 - 52 * q^77 + 30 * q^79 - 12 * q^80 - 8 * q^81 - 12 * q^82 - 8 * q^83 + 8 * q^84 - 12 * q^86 - 2 * q^88 - 36 * q^89 - 4 * q^90 - 8 * q^91 - 8 * q^92 + 4 * q^93 - 14 * q^94 - 72 * q^95 - 8 * q^96 + 40 * q^98 - 8 * q^99

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