LMFDB - Embedded newform 462.2.p.b.241.5

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			241.5
Root			$0.500000 - 3.19339i$ of defining polynomial
Character	$\chi$	$=$	462.241
Dual form			462.2.p.b.439.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.01555 + 1.16368i) q^{5} +1.00000 q^{6} +(1.31629 + 2.29508i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.01555 + 1.16368i) q^{5} +1.00000 q^{6} +(1.31629 + 2.29508i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.16368 + 2.01555i) q^{10} +(2.46679 + 2.21696i) q^{11} +(0.866025 - 0.500000i) q^{12} +1.44095 q^{13} +(2.28748 + 1.32945i) q^{14} -2.32736 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.60782 - 2.78483i) q^{17} +(0.866025 + 0.500000i) q^{18} +(3.07901 + 5.33301i) q^{19} +2.32736i q^{20} +(-0.00760304 + 2.64574i) q^{21} +(3.24479 + 0.686549i) q^{22} +(-3.14645 - 5.44981i) q^{23} +(0.500000 - 0.866025i) q^{24} +(0.208304 - 0.360793i) q^{25} +(1.24790 - 0.720474i) q^{26} +1.00000i q^{27} +(2.64574 + 0.00760304i) q^{28} -3.26833i q^{29} +(-2.01555 + 1.16368i) q^{30} +(2.67692 + 1.54552i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.02783 + 3.15334i) q^{33} -3.21565i q^{34} +(-5.32378 - 3.09412i) q^{35} +1.00000 q^{36} +(-4.57056 - 7.91644i) q^{37} +(5.33301 + 3.07901i) q^{38} +(1.24790 + 0.720474i) q^{39} +(1.16368 + 2.01555i) q^{40} -3.41163 q^{41} +(1.31629 + 2.29508i) q^{42} -1.89247i q^{43} +(3.15334 - 1.02783i) q^{44} +(-2.01555 - 1.16368i) q^{45} +(-5.44981 - 3.14645i) q^{46} +(-9.22249 + 5.32461i) q^{47} -1.00000i q^{48} +(-3.53478 + 6.04196i) q^{49} -0.416608i q^{50} +(2.78483 - 1.60782i) q^{51} +(0.720474 - 1.24790i) q^{52} +(4.60856 - 7.98226i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-7.55179 - 1.59785i) q^{55} +(2.29508 - 1.31629i) q^{56} +6.15803i q^{57} +(-1.63416 - 2.83045i) q^{58} +(-0.461345 - 0.266358i) q^{59} +(-1.16368 + 2.01555i) q^{60} +(0.233713 + 0.404803i) q^{61} +3.09104 q^{62} +(-1.32945 + 2.28748i) q^{63} -1.00000 q^{64} +(-2.90431 + 1.67680i) q^{65} +(2.46679 + 2.21696i) q^{66} +(4.61347 - 7.99077i) q^{67} +(-1.60782 - 2.78483i) q^{68} -6.29290i q^{69} +(-6.15759 - 0.0176950i) q^{70} -3.25253 q^{71} +(0.866025 - 0.500000i) q^{72} +(2.50002 - 4.33016i) q^{73} +(-7.91644 - 4.57056i) q^{74} +(0.360793 - 0.208304i) q^{75} +6.15803 q^{76} +(-1.84110 + 8.57965i) q^{77} +1.44095 q^{78} +(7.21263 - 4.16421i) q^{79} +(2.01555 + 1.16368i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.95456 + 1.70582i) q^{82} -4.56130 q^{83} +(2.28748 + 1.32945i) q^{84} +7.48397i q^{85} +(-0.946236 - 1.63893i) q^{86} +(1.63416 - 2.83045i) q^{87} +(2.21696 - 2.46679i) q^{88} +(-3.79409 + 2.19052i) q^{89} -2.32736 q^{90} +(1.89670 + 3.30709i) q^{91} -6.29290 q^{92} +(1.54552 + 2.67692i) q^{93} +(-5.32461 + 9.22249i) q^{94} +(-12.4118 - 7.16598i) q^{95} +(-0.500000 - 0.866025i) q^{96} +17.8026i q^{97} +(-0.0402313 + 6.99988i) q^{98} +(-0.686549 + 3.24479i) 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 $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

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

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
$5$	−2.01555	+	1.16368i	−0.901383	+	0.520414i	−0.877649	−	0.479305i	$-0.840889\pi$
$5$	−2.01555	+	1.16368i	−0.901383	+	0.520414i	−0.0237343	+	0.999718i	$0.507556\pi$
$6$	1.00000			0.408248
$7$	1.31629	+	2.29508i	0.497509	+	0.867459i
$7$	1.31629	+	2.29508i	0.497509	+	0.867459i
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.16368	+	2.01555i	−0.367988	+	0.637374i
$11$	2.46679	+	2.21696i	0.743767	+	0.668439i
$11$	2.46679	+	2.21696i	0.743767	+	0.668439i
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$	1.44095			0.399647			0.199823	−	0.979832i	$-0.435963\pi$
$13$	1.44095			0.399647			0.199823	+	0.979832i	$0.435963\pi$
$14$	2.28748	+	1.32945i	0.611354	+	0.355312i
$15$	−2.32736			−0.600922
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.60782	−	2.78483i	0.389954	−	0.675421i	−0.602489	−	0.798127i	$-0.705824\pi$
$17$	1.60782	−	2.78483i	0.389954	−	0.675421i	0.992443	+	0.122707i	$0.0391575\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	3.07901	+	5.33301i	0.706374	+	1.22348i	0.966193	+	0.257819i	$0.0830038\pi$
$19$	3.07901	+	5.33301i	0.706374	+	1.22348i	−0.259819	+	0.965657i	$0.583663\pi$
$20$			2.32736i			0.520414i
$21$	−0.00760304	+	2.64574i	−0.00165912	+	0.577348i
$22$	3.24479	+	0.686549i	0.691791	+	0.146373i
$23$	−3.14645	−	5.44981i	−0.656080	−	1.13636i	−0.981622	−	0.190836i	$-0.938880\pi$
$23$	−3.14645	−	5.44981i	−0.656080	−	1.13636i	0.325542	−	0.945528i	$-0.394453\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	0.208304	−	0.360793i	0.0416608	−	0.0721586i
$26$	1.24790	−	0.720474i	0.244733	−	0.141297i
$27$			1.00000i			0.192450i
$28$	2.64574	+	0.00760304i	0.499998	+	0.00143684i
$29$		−	3.26833i		−	0.606913i	−0.952845	−	0.303456i	$-0.901859\pi$
$29$		−	3.26833i		−	0.606913i	0.952845	−	0.303456i	$-0.0981407\pi$
$30$	−2.01555	+	1.16368i	−0.367988	+	0.212458i
$31$	2.67692	+	1.54552i	0.480789	+	0.277584i	0.720745	−	0.693200i	$-0.243800\pi$
$31$	2.67692	+	1.54552i	0.480789	+	0.277584i	−0.239956	+	0.970784i	$0.577133\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	1.02783	+	3.15334i	0.178921	+	0.548927i
$34$		−	3.21565i		−	0.551479i
$35$	−5.32378	−	3.09412i	−0.899884	−	0.523002i
$36$	1.00000			0.166667
$37$	−4.57056	−	7.91644i	−0.751395	−	1.30145i	−0.947147	−	0.320801i	$-0.896048\pi$
$37$	−4.57056	−	7.91644i	−0.751395	−	1.30145i	0.195752	−	0.980653i	$-0.437285\pi$
$38$	5.33301	+	3.07901i	0.865128	+	0.499482i
$39$	1.24790	+	0.720474i	0.199823	+	0.115368i
$40$	1.16368	+	2.01555i	0.183994	+	0.318687i
$41$	−3.41163			−0.532808			−0.266404	−	0.963861i	$-0.585835\pi$
$41$	−3.41163			−0.532808			−0.266404	+	0.963861i	$0.585835\pi$
$42$	1.31629	+	2.29508i	0.203107	+	0.354139i
$43$		−	1.89247i		−	0.288599i	−0.989534	−	0.144300i	$-0.953907\pi$
$43$		−	1.89247i		−	0.288599i	0.989534	−	0.144300i	$-0.0460929\pi$
$44$	3.15334	−	1.02783i	0.475384	−	0.154951i
$45$	−2.01555	−	1.16368i	−0.300461	−	0.173471i
$46$	−5.44981	−	3.14645i	−0.803530	−	0.463919i
$47$	−9.22249	+	5.32461i	−1.34524	+	0.776674i	−0.987571	−	0.157175i	$-0.949761\pi$
$47$	−9.22249	+	5.32461i	−1.34524	+	0.776674i	−0.357668	+	0.933849i	$0.616428\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−3.53478	+	6.04196i	−0.504969	+	0.863137i
$50$		−	0.416608i		−	0.0589173i
$51$	2.78483	−	1.60782i	0.389954	−	0.225140i
$52$	0.720474	−	1.24790i	0.0999117	−	0.173052i
$53$	4.60856	−	7.98226i	0.633035	−	1.09645i	−0.353893	−	0.935286i	$-0.615142\pi$
$53$	4.60856	−	7.98226i	0.633035	−	1.09645i	0.986928	−	0.161162i	$-0.0515242\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−7.55179	−	1.59785i	−1.01828	−	0.215454i
$56$	2.29508	−	1.31629i	0.306693	−	0.175896i
$57$			6.15803i			0.815651i
$58$	−1.63416	−	2.83045i	−0.214576	−	0.371657i
$59$	−0.461345	−	0.266358i	−0.0600620	−	0.0346768i	0.469668	−	0.882843i	$-0.344374\pi$
$59$	−0.461345	−	0.266358i	−0.0600620	−	0.0346768i	−0.529730	+	0.848166i	$0.677707\pi$
$60$	−1.16368	+	2.01555i	−0.150230	+	0.260207i
$61$	0.233713	+	0.404803i	0.0299239	+	0.0518298i	0.880600	−	0.473861i	$-0.157140\pi$
$61$	0.233713	+	0.404803i	0.0299239	+	0.0518298i	−0.850676	+	0.525691i	$0.823807\pi$
$62$	3.09104			0.392563
$63$	−1.32945	+	2.28748i	−0.167496	+	0.288195i
$64$	−1.00000			−0.125000
$65$	−2.90431	+	1.67680i	−0.360235	+	0.207982i
$66$	2.46679	+	2.21696i	0.303641	+	0.272889i
$67$	4.61347	−	7.99077i	0.563625	−	0.976227i	−0.433551	−	0.901129i	$-0.642740\pi$
$67$	4.61347	−	7.99077i	0.563625	−	0.976227i	0.997176	−	0.0750984i	$-0.0239271\pi$
$68$	−1.60782	−	2.78483i	−0.194977	−	0.337710i
$69$		−	6.29290i		−	0.757576i
$70$	−6.15759	−	0.0176950i	−0.735973	−	0.00211496i
$71$	−3.25253			−0.386004			−0.193002	−	0.981198i	$-0.561822\pi$
$71$	−3.25253			−0.386004			−0.193002	+	0.981198i	$0.561822\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	2.50002	−	4.33016i	0.292605	−	0.506807i	−0.681820	−	0.731520i	$-0.738811\pi$
$73$	2.50002	−	4.33016i	0.292605	−	0.506807i	0.974425	+	0.224713i	$0.0721446\pi$
$74$	−7.91644	−	4.57056i	−0.920267	−	0.531316i
$75$	0.360793	−	0.208304i	0.0416608	−	0.0240529i
$76$	6.15803			0.706374
$77$	−1.84110	+	8.57965i	−0.209813	+	0.977742i
$78$	1.44095			0.163155
$79$	7.21263	−	4.16421i	0.811484	−	0.468510i	−0.0359870	−	0.999352i	$-0.511457\pi$
$79$	7.21263	−	4.16421i	0.811484	−	0.468510i	0.847471	+	0.530842i	$0.178124\pi$
$80$	2.01555	+	1.16368i	0.225346	+	0.130103i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.95456	+	1.70582i	−0.326277	+	0.188376i
$83$	−4.56130			−0.500668			−0.250334	−	0.968160i	$-0.580540\pi$
$83$	−4.56130			−0.500668			−0.250334	+	0.968160i	$0.580540\pi$
$84$	2.28748	+	1.32945i	0.249584	+	0.145055i
$85$			7.48397i			0.811750i
$86$	−0.946236	−	1.63893i	−0.102035	−	0.176730i
$87$	1.63416	−	2.83045i	0.175201	−	0.303456i
$88$	2.21696	−	2.46679i	0.236329	−	0.262961i
$89$	−3.79409	+	2.19052i	−0.402173	+	0.232195i	−0.687421	−	0.726259i	$-0.741257\pi$
$89$	−3.79409	+	2.19052i	−0.402173	+	0.232195i	0.285248	+	0.958454i	$0.407924\pi$
$90$	−2.32736			−0.245325
$91$	1.89670	+	3.30709i	0.198828	+	0.346677i
$92$	−6.29290			−0.656080
$93$	1.54552	+	2.67692i	0.160263	+	0.277584i
$94$	−5.32461	+	9.22249i	−0.549191	+	0.951227i
$95$	−12.4118	−	7.16598i	−1.27343	−	0.735214i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$			17.8026i			1.80758i	0.427977	+	0.903790i	$0.359226\pi$
$97$			17.8026i			1.80758i	−0.427977	+	0.903790i	$0.640774\pi$
$98$	−0.0402313	+	6.99988i	−0.00406398	+	0.707095i
$99$	−0.686549	+	3.24479i	−0.0690007	+	0.326113i
$100$	−0.208304	−	0.360793i	−0.0208304	−	0.0360793i
$101$	5.34857	−	9.26399i	0.532203	−	0.921802i	−0.467091	−	0.884209i	$-0.654698\pi$
$101$	5.34857	−	9.26399i	0.532203	−	0.921802i	0.999293	−	0.0375924i	$-0.0119688\pi$
$102$	1.60782	−	2.78483i	0.159198	−	0.275739i
$103$	11.7844	−	6.80370i	1.16115	−	0.670388i	0.209568	−	0.977794i	$-0.432794\pi$
$103$	11.7844	−	6.80370i	1.16115	−	0.670388i	0.951579	+	0.307406i	$0.0994609\pi$
$104$		−	1.44095i		−	0.141297i
$105$	−3.06347	−	5.34148i	−0.298964	−	0.521275i
$106$		−	9.21712i		−	0.895246i
$107$	8.13694	−	4.69786i	0.786627	−	0.454159i	−0.0521466	−	0.998639i	$-0.516606\pi$
$107$	8.13694	−	4.69786i	0.786627	−	0.454159i	0.838774	+	0.544480i	$0.183273\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	−6.18076	−	3.56846i	−0.592009	−	0.341797i	0.173882	−	0.984766i	$-0.444369\pi$
$109$	−6.18076	−	3.56846i	−0.592009	−	0.341797i	−0.765892	+	0.642970i	$0.777702\pi$
$110$	−7.33897	+	2.39212i	−0.699743	+	0.228080i
$111$		−	9.14111i		−	0.867636i
$112$	1.32945	−	2.28748i	0.125622	−	0.216146i
$113$	−3.15100			−0.296421			−0.148210	−	0.988956i	$-0.547351\pi$
$113$	−3.15100			−0.296421			−0.148210	+	0.988956i	$0.547351\pi$
$114$	3.07901	+	5.33301i	0.288376	+	0.499482i
$115$	12.6837	+	7.32292i	1.18276	+	0.682866i
$116$	−2.83045	−	1.63416i	−0.262801	−	0.151728i
$117$	0.720474	+	1.24790i	0.0666078	+	0.115368i
$118$	−0.532715			−0.0490404
$119$	8.50776	+	0.0244487i	0.779905	+	0.00224121i
$120$			2.32736i			0.212458i
$121$	1.17015	+	10.9376i	0.106377	+	0.994326i
$122$	0.404803	+	0.233713i	0.0366492	+	0.0211594i
$123$	−2.95456	−	1.70582i	−0.266404	−	0.153808i
$124$	2.67692	−	1.54552i	0.240395	−	0.138792i
$125$		−	10.6672i		−	0.954104i
$126$	−0.00760304	+	2.64574i	−0.000677332	+	0.235701i
$127$		−	10.8090i		−	0.959143i	−0.877503	−	0.479571i	$-0.840792\pi$
$127$		−	10.8090i		−	0.959143i	0.877503	−	0.479571i	$-0.159208\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	0.946236	−	1.63893i	0.0833115	−	0.144300i
$130$	−1.67680	+	2.90431i	−0.147065	+	0.254725i
$131$	−5.48559	−	9.50131i	−0.479278	−	0.830134i	0.520440	−	0.853898i	$-0.325768\pi$
$131$	−5.48559	−	9.50131i	−0.479278	−	0.830134i	−0.999718	+	0.0237647i	$0.992435\pi$
$132$	3.24479	+	0.686549i	0.282423	+	0.0597564i
$133$	−8.18682	+	14.0863i	−0.709887	+	1.22144i
$134$		−	9.22694i		−	0.797086i
$135$	−1.16368	−	2.01555i	−0.100154	−	0.173471i
$136$	−2.78483	−	1.60782i	−0.238797	−	0.137870i
$137$	−4.83301	+	8.37102i	−0.412912	+	0.715185i	−0.995207	−	0.0977932i	$-0.968822\pi$
$137$	−4.83301	+	8.37102i	−0.412912	+	0.715185i	0.582295	+	0.812978i	$0.302155\pi$
$138$	−3.14645	−	5.44981i	−0.267843	−	0.463919i
$139$	−23.3695			−1.98218			−0.991088	−	0.133208i	$-0.957472\pi$
$139$	−23.3695			−1.98218			−0.991088	+	0.133208i	$0.957472\pi$
$140$	−5.34148	+	3.06347i	−0.451437	+	0.258911i
$141$	−10.6492			−0.896826
$142$	−2.81677	+	1.62627i	−0.236378	+	0.136473i
$143$	3.55452	+	3.19453i	0.297244	+	0.267140i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	3.80329	+	6.58749i	0.315846	+	0.547061i
$146$		−	5.00004i		−	0.413806i
$147$	−6.08219	+	3.46510i	−0.501651	+	0.285797i
$148$	−9.14111			−0.751395
$149$	−13.0372	+	7.52705i	−1.06805	+	0.616640i	−0.927648	−	0.373455i	$-0.878173\pi$
$149$	−13.0372	+	7.52705i	−1.06805	+	0.616640i	−0.140403	+	0.990094i	$0.544840\pi$
$150$	0.208304	−	0.360793i	0.0170080	−	0.0294586i
$151$	11.2506	+	6.49554i	0.915561	+	0.528599i	0.882216	−	0.470845i	$-0.156051\pi$
$151$	11.2506	+	6.49554i	0.915561	+	0.528599i	0.0333445	+	0.999444i	$0.489384\pi$
$152$	5.33301	−	3.07901i	0.432564	−	0.249741i
$153$	3.21565			0.259970
$154$	2.69538	+	8.35074i	0.217200	+	0.672922i
$155$	−7.19397			−0.577833
$156$	1.24790	−	0.720474i	0.0999117	−	0.0576841i
$157$	−9.98402	−	5.76428i	−0.796812	−	0.460039i	0.0455434	−	0.998962i	$-0.485498\pi$
$157$	−9.98402	−	5.76428i	−0.796812	−	0.460039i	−0.842355	+	0.538923i	$0.818831\pi$
$158$	4.16421	−	7.21263i	0.331287	−	0.573806i
$159$	7.98226	−	4.60856i	0.633035	−	0.365483i
$160$	2.32736			0.183994
$161$	8.36612	−	14.3949i	0.659343	−	1.13447i
$162$			1.00000i			0.0785674i
$163$	4.15686	+	7.19989i	0.325590	+	0.563939i	0.981632	−	0.190786i	$-0.0611037\pi$
$163$	4.15686	+	7.19989i	0.325590	+	0.563939i	−0.656041	+	0.754725i	$0.727770\pi$
$164$	−1.70582	+	2.95456i	−0.133202	+	0.230713i
$165$	−5.74112	−	5.15967i	−0.446946	−	0.401680i
$166$	−3.95020	+	2.28065i	−0.306595	+	0.177013i
$167$	15.5338			1.20204			0.601022	−	0.799232i	$-0.294760\pi$
$167$	15.5338			1.20204			0.601022	+	0.799232i	$0.294760\pi$
$168$	2.64574	+	0.00760304i	0.204123	+	0.000586587i
$169$	−10.9237			−0.840282
$170$	3.74198	+	6.48131i	0.286997	+	0.497094i
$171$	−3.07901	+	5.33301i	−0.235458	+	0.407825i
$172$	−1.63893	−	0.946236i	−0.124967	−	0.0721499i
$173$	6.60240	+	11.4357i	0.501971	+	0.869439i	0.999997	+	0.00227722i	$0.000724861\pi$
$173$	6.60240	+	11.4357i	0.501971	+	0.869439i	−0.498027	+	0.867162i	$0.665942\pi$
$174$		−	3.26833i		−	0.247771i
$175$	1.10224	+	0.00316749i	0.0833213	+	0.000239439i
$176$	0.686549	−	3.24479i	0.0517506	−	0.244585i
$177$	−0.266358	−	0.461345i	−0.0200207	−	0.0346768i
$178$	−2.19052	+	3.79409i	−0.164186	+	0.284379i
$179$	9.43539	−	16.3426i	0.705234	−	1.22150i	−0.261373	−	0.965238i	$-0.584175\pi$
$179$	9.43539	−	16.3426i	0.705234	−	1.22150i	0.966607	−	0.256263i	$-0.0824913\pi$
$180$	−2.01555	+	1.16368i	−0.150230	+	0.0867356i
$181$		−	3.94448i		−	0.293191i	−0.989197	−	0.146595i	$-0.953168\pi$
$181$		−	3.94448i		−	0.293191i	0.989197	−	0.146595i	$-0.0468316\pi$
$182$	3.29613	+	1.91567i	0.244326	+	0.141999i
$183$			0.467427i			0.0345532i
$184$	−5.44981	+	3.14645i	−0.401765	+	0.231959i
$185$	18.4244	+	10.6373i	1.35459	+	0.782072i
$186$	2.67692	+	1.54552i	0.196281	+	0.113323i
$187$	10.1400	−	3.30512i	0.741513	−	0.241695i
$188$			10.6492i			0.776674i
$189$	−2.29508	+	1.31629i	−0.166942	+	0.0957457i
$190$	−14.3320			−1.03975
$191$	−11.7619	−	20.3722i	−0.851062	−	1.47408i	−0.880251	−	0.474508i	$-0.842626\pi$
$191$	−11.7619	−	20.3722i	−0.851062	−	1.47408i	0.0291897	−	0.999574i	$-0.490707\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	18.0103	+	10.3983i	1.29641	+	0.748484i	0.979782	−	0.200066i	$-0.0641156\pi$
$193$	18.0103	+	10.3983i	1.29641	+	0.748484i	0.316629	+	0.948549i	$0.397449\pi$
$194$	8.90130	+	15.4175i	0.639076	+	1.10691i
$195$	−3.35360			−0.240157
$196$	3.46510	+	6.08219i	0.247507	+	0.434442i
$197$			21.3675i			1.52237i	0.648534	+	0.761186i	$0.275382\pi$
$197$			21.3675i			1.52237i	−0.648534	+	0.761186i	$0.724618\pi$
$198$	1.02783	+	3.15334i	0.0730444	+	0.224098i
$199$	17.3579	+	10.0216i	1.23047	+	0.710410i	0.967127	−	0.254293i	$-0.0818429\pi$
$199$	17.3579	+	10.0216i	1.23047	+	0.710410i	0.263339	+	0.964703i	$0.415176\pi$
$200$	−0.360793	−	0.208304i	−0.0255119	−	0.0147293i
$201$	7.99077	−	4.61347i	0.563625	−	0.325409i
$202$		−	10.6971i		−	0.752648i
$203$	7.50107	−	4.30205i	0.526472	−	0.301945i
$204$		−	3.21565i		−	0.225140i
$205$	6.87633	−	3.97005i	0.480264	−	0.277280i
$206$	6.80370	−	11.7844i	0.474036	−	0.821055i
$207$	3.14645	−	5.44981i	0.218693	−	0.378788i
$208$	−0.720474	−	1.24790i	−0.0499559	−	0.0865261i
$209$	−4.22779	+	19.9815i	−0.292442	+	1.38215i
$210$	−5.32378	−	3.09412i	−0.367376	−	0.213515i
$211$			2.04651i			0.140887i	0.997516	+	0.0704437i	$0.0224415\pi$
$211$			2.04651i			0.140887i	−0.997516	+	0.0704437i	$0.977558\pi$
$212$	−4.60856	−	7.98226i	−0.316517	−	0.548224i
$213$	−2.81677	−	1.62627i	−0.193002	−	0.111430i
$214$	4.69786	−	8.13694i	0.321139	−	0.556229i
$215$	2.20223	+	3.81438i	0.150191	+	0.260139i
$216$	1.00000			0.0680414
$217$	−0.0235013	+	8.17809i	−0.00159537	+	0.555165i
$218$	−7.13693			−0.483374
$219$	4.33016	−	2.50002i	0.292605	−	0.168936i
$220$	−5.15967	+	5.74112i	−0.347865	+	0.387066i
$221$	2.31679	−	4.01279i	0.155844	−	0.269930i
$222$	−4.57056	−	7.91644i	−0.306756	−	0.531316i
$223$		−	23.3804i		−	1.56567i	−0.622230	−	0.782835i	$-0.713773\pi$
$223$		−	23.3804i		−	1.56567i	0.622230	−	0.782835i	$-0.286227\pi$
$224$	0.00760304	−	2.64574i	0.000507999	−	0.176776i
$225$	0.416608			0.0277739
$226$	−2.72884	+	1.57550i	−0.181520	+	0.104801i
$227$	−6.97413	+	12.0796i	−0.462890	+	0.801748i	−0.999104	−	0.0423338i	$-0.986521\pi$
$227$	−6.97413	+	12.0796i	−0.462890	+	0.801748i	0.536214	+	0.844082i	$0.319854\pi$
$228$	5.33301	+	3.07901i	0.353187	+	0.203913i
$229$	−13.0033	+	7.50744i	−0.859281	+	0.496106i	−0.863771	−	0.503884i	$-0.831904\pi$
$229$	−13.0033	+	7.50744i	−0.859281	+	0.496106i	0.00449072	+	0.999990i	$0.498571\pi$
$230$	14.6458			0.965718
$231$	−5.88426	+	6.50964i	−0.387156	+	0.428303i
$232$	−3.26833			−0.214576
$233$	14.2393	−	8.22109i	0.932850	−	0.538581i	0.0451385	−	0.998981i	$-0.485627\pi$
$233$	14.2393	−	8.22109i	0.932850	−	0.538581i	0.887712	+	0.460399i	$0.152294\pi$
$234$	1.24790	+	0.720474i	0.0815776	+	0.0470988i
$235$	12.3923	−	21.4641i	0.808384	−	1.40016i
$236$	−0.461345	+	0.266358i	−0.0300310	+	0.0173384i
$237$	8.32842			0.540989
$238$	7.38016	−	4.23271i	0.478385	−	0.274366i
$239$			24.7950i			1.60386i	0.597419	+	0.801929i	$0.296193\pi$
$239$			24.7950i			1.60386i	−0.597419	+	0.801929i	$0.703807\pi$
$240$	1.16368	+	2.01555i	0.0751152	+	0.130103i
$241$	11.1098	−	19.2427i	0.715643	−	1.23953i	−0.247068	−	0.968998i	$-0.579467\pi$
$241$	11.1098	−	19.2427i	0.715643	−	1.23953i	0.962711	−	0.270532i	$-0.0871996\pi$
$242$	6.48217	+	8.88715i	0.416690	+	0.571288i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	0.467427			0.0299239
$245$	0.0936328	−	16.2913i	0.00598198	−	1.04081i
$246$	−3.41163			−0.217518
$247$	4.43670	+	7.68458i	0.282300	+	0.488958i
$248$	1.54552	−	2.67692i	0.0981407	−	0.169985i
$249$	−3.95020	−	2.28065i	−0.250334	−	0.144530i
$250$	−5.33360	−	9.23807i	−0.337327	−	0.584267i
$251$		−	4.73415i		−	0.298817i	−0.988776	−	0.149409i	$-0.952263\pi$
$251$		−	4.73415i		−	0.298817i	0.988776	−	0.149409i	$-0.0477370\pi$
$252$	1.31629	+	2.29508i	0.0829182	+	0.144576i
$253$	4.32038	−	20.4191i	0.271620	−	1.28374i
$254$	−5.40449	−	9.36086i	−0.339108	−	0.587353i
$255$	−3.74198	+	6.48131i	−0.234332	+	0.405875i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.5961	+	6.11764i	−0.660965	+	0.381608i	−0.792644	−	0.609684i	$-0.791296\pi$
$257$	−10.5961	+	6.11764i	−0.660965	+	0.381608i	0.131680	+	0.991292i	$0.457963\pi$
$258$		−	1.89247i		−	0.117820i
$259$	12.1527	−	20.9101i	0.755132	−	1.29929i
$260$			3.35360i			0.207982i
$261$	2.83045	−	1.63416i	0.175201	−	0.101152i
$262$	−9.50131	−	5.48559i	−0.586993	−	0.338901i
$263$	16.6883	+	9.63502i	1.02905	+	0.594121i	0.916712	−	0.399550i	$-0.130833\pi$
$263$	16.6883	+	9.63502i	1.02905	+	0.594121i	0.112336	+	0.993670i	$0.464167\pi$
$264$	3.15334	−	1.02783i	0.194075	−	0.0632583i
$265$			21.4516i			1.31776i
$266$	−0.0468197	+	16.2925i	−0.00287070	+	0.998960i
$267$	−4.38104			−0.268115
$268$	−4.61347	−	7.99077i	−0.281813	−	0.488114i
$269$	19.1299	+	11.0447i	1.16637	+	0.673405i	0.952823	−	0.303527i	$-0.0981644\pi$
$269$	19.1299	+	11.0447i	1.16637	+	0.673405i	0.213549	+	0.976932i	$0.431498\pi$
$270$	−2.01555	−	1.16368i	−0.122663	−	0.0708193i
$271$	−0.610555	−	1.05751i	−0.0370886	−	0.0642393i	0.846885	−	0.531776i	$-0.178475\pi$
$271$	−0.610555	−	1.05751i	−0.0370886	−	0.0642393i	−0.883974	+	0.467536i	$0.845142\pi$
$272$	−3.21565			−0.194977
$273$	−0.0109556	+	3.81237i	−0.000663062	+	0.230735i
$274$			9.66602i			0.583946i
$275$	1.31371	−	0.428200i	0.0792196	−	0.0258215i
$276$	−5.44981	−	3.14645i	−0.328040	−	0.189394i
$277$	−10.8330	−	6.25443i	−0.650891	−	0.375792i	0.137906	−	0.990445i	$-0.455963\pi$
$277$	−10.8330	−	6.25443i	−0.650891	−	0.375792i	−0.788798	+	0.614653i	$0.789296\pi$
$278$	−20.2386	+	11.6848i	−1.21383	+	0.700805i
$279$			3.09104i			0.185056i
$280$	−3.09412	+	5.32378i	−0.184909	+	0.318157i
$281$			25.3495i			1.51222i	0.654443	+	0.756111i	$0.272903\pi$
$281$			25.3495i			1.51222i	−0.654443	+	0.756111i	$0.727097\pi$
$282$	−9.22249	+	5.32461i	−0.549191	+	0.317076i
$283$	1.38222	−	2.39408i	0.0821646	−	0.142313i	−0.822015	−	0.569466i	$-0.807150\pi$
$283$	1.38222	−	2.39408i	0.0821646	−	0.142313i	0.904179	+	0.427153i	$0.140483\pi$
$284$	−1.62627	+	2.81677i	−0.0965011	+	0.167145i
$285$	−7.16598	−	12.4118i	−0.424476	−	0.735214i
$286$	4.67557	+	0.989280i	0.276472	+	0.0584974i
$287$	−4.49069	−	7.82997i	−0.265077	−	0.462189i
$288$		−	1.00000i		−	0.0589256i
$289$	3.32981	+	5.76740i	0.195871	+	0.339259i
$290$	6.58749	+	3.80329i	0.386831	+	0.223337i
$291$	−8.90130	+	15.4175i	−0.521803	+	0.903790i
$292$	−2.50002	−	4.33016i	−0.146303	−	0.253403i
$293$	9.03175			0.527640			0.263820	−	0.964572i	$-0.415017\pi$
$293$	9.03175			0.527640			0.263820	+	0.964572i	$0.415017\pi$
$294$	−3.53478	+	6.04196i	−0.206153	+	0.352374i
$295$	1.23982			0.0721851
$296$	−7.91644	+	4.57056i	−0.460134	+	0.265658i
$297$	−2.21696	+	2.46679i	−0.128641	+	0.143138i
$298$	−7.52705	+	13.0372i	−0.436030	+	0.755226i
$299$	−4.53387	−	7.85289i	−0.262200	−	0.454144i
$300$		−	0.416608i		−	0.0240529i
$301$	4.34338	−	2.49104i	0.250348	−	0.143581i
$302$	12.9911			0.747552
$303$	9.26399	−	5.34857i	0.532203	−	0.307267i
$304$	3.07901	−	5.33301i	0.176594	−	0.305869i
$305$	−0.942123	−	0.543935i	−0.0539458	−	0.0311456i
$306$	2.78483	−	1.60782i	0.159198	−	0.0919131i
$307$	−3.52291			−0.201063			−0.100531	−	0.994934i	$-0.532054\pi$
$307$	−3.52291			−0.201063			−0.100531	+	0.994934i	$0.532054\pi$
$308$	6.50964	+	5.88426i	0.370921	+	0.335287i
$309$	13.6074			0.774098
$310$	−6.23016	+	3.59698i	−0.353849	+	0.204295i
$311$	4.83852	+	2.79352i	0.274367	+	0.158406i	0.630871	−	0.775888i	$-0.282698\pi$
$311$	4.83852	+	2.79352i	0.274367	+	0.158406i	−0.356503	+	0.934294i	$0.616031\pi$
$312$	0.720474	−	1.24790i	0.0407888	−	0.0706483i
$313$	4.57178	−	2.63952i	0.258412	−	0.149194i	−0.365198	−	0.930930i	$-0.618999\pi$
$313$	4.57178	−	2.63952i	0.258412	−	0.149194i	0.623610	+	0.781736i	$0.285665\pi$
$314$	−11.5286			−0.650594
$315$	0.0176950	−	6.15759i	0.000997001	−	0.346941i
$316$		−	8.32842i		−	0.468510i
$317$	−15.8432	−	27.4412i	−0.889843	−	1.54125i	−0.840060	−	0.542493i	$-0.817480\pi$
$317$	−15.8432	−	27.4412i	−0.889843	−	1.54125i	−0.0497829	−	0.998760i	$-0.515853\pi$
$318$	4.60856	−	7.98226i	0.258435	−	0.447623i
$319$	7.24576	−	8.06229i	0.405685	−	0.451402i
$320$	2.01555	−	1.16368i	0.112673	−	0.0650517i
$321$	9.39572			0.524418
$322$	0.0478451	−	16.6494i	0.00266630	−	0.927833i
$323$	19.8020			1.10181
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	0.300155	−	0.519884i	0.0166496	−	0.0288380i
$326$	7.19989	+	4.15686i	0.398765	+	0.230227i
$327$	−3.56846	−	6.18076i	−0.197336	−	0.341797i
$328$			3.41163i			0.188376i
$329$	−24.3598	−	14.1577i	−1.34300	−	0.780537i
$330$	−7.55179	−	1.59785i	−0.415713	−	0.0879586i
$331$	1.95793	+	3.39124i	0.107618	+	0.186399i	0.914805	−	0.403896i	$-0.132344\pi$
$331$	1.95793	+	3.39124i	0.107618	+	0.186399i	−0.807187	+	0.590296i	$0.799011\pi$
$332$	−2.28065	+	3.95020i	−0.125167	+	0.216796i
$333$	4.57056	−	7.91644i	0.250465	−	0.433818i
$334$	13.4527	−	7.76692i	0.736099	−	0.424987i
$335$			21.4744i			1.17327i
$336$	2.29508	−	1.31629i	0.125207	−	0.0718093i
$337$			20.0534i			1.09238i	0.837662	+	0.546189i	$0.183922\pi$
$337$			20.0534i			1.09238i	−0.837662	+	0.546189i	$0.816078\pi$
$338$	−9.46018	+	5.46184i	−0.514566	+	0.297085i
$339$	−2.72884	−	1.57550i	−0.148210	−	0.0855694i
$340$	6.48131	+	3.74198i	0.351498	+	0.202938i
$341$	3.17705	+	9.74711i	0.172047	+	0.527836i
$342$			6.15803i			0.332988i
$343$	−18.5196	−	0.159662i	−0.999963	−	0.00862094i
$344$	−1.89247			−0.102035
$345$	7.32292	+	12.6837i	0.394253	+	0.682866i
$346$	11.4357	+	6.60240i	0.614786	+	0.354947i
$347$	24.6999	+	14.2605i	1.32596	+	0.765545i	0.984673	−	0.174413i	$-0.0558029\pi$
$347$	24.6999	+	14.2605i	1.32596	+	0.765545i	0.341290	+	0.939958i	$0.389136\pi$
$348$	−1.63416	−	2.83045i	−0.0876003	−	0.151728i
$349$	−15.3941			−0.824027			−0.412014	−	0.911178i	$-0.635174\pi$
$349$	−15.3941			−0.824027			−0.412014	+	0.911178i	$0.635174\pi$
$350$	0.956149	−	0.548375i	0.0511083	−	0.0293119i
$351$			1.44095i			0.0769121i
$352$	−1.02783	−	3.15334i	−0.0547833	−	0.168074i
$353$	4.80016	+	2.77137i	0.255487	+	0.147505i	0.622274	−	0.782800i	$-0.286209\pi$
$353$	4.80016	+	2.77137i	0.255487	+	0.147505i	−0.366787	+	0.930305i	$0.619542\pi$
$354$	−0.461345	−	0.266358i	−0.0245202	−	0.0141567i
$355$	6.55565	−	3.78491i	0.347938	−	0.200882i
$356$			4.38104i			0.232195i
$357$	7.35572	+	4.27506i	0.389306	+	0.226260i
$358$		−	18.8708i		−	0.997351i
$359$	−17.9527	+	10.3650i	−0.947508	+	0.547044i	−0.892306	−	0.451431i	$-0.850914\pi$
$359$	−17.9527	+	10.3650i	−0.947508	+	0.547044i	−0.0552018	+	0.998475i	$0.517580\pi$
$360$	−1.16368	+	2.01555i	−0.0613313	+	0.106229i
$361$	−9.46065	+	16.3863i	−0.497929	+	0.862439i
$362$	−1.97224	−	3.41602i	−0.103659	−	0.179542i
$363$	−4.45541	+	10.0573i	−0.233848	+	0.527871i
$364$	3.81237	+	0.0109556i	0.199823	+	0.000574228i
$365$			11.6369i			0.609103i
$366$	0.233713	+	0.404803i	0.0122164	+	0.0211594i
$367$	−30.3880	−	17.5445i	−1.58624	−	0.915816i	−0.993919	−	0.110113i	$-0.964879\pi$
$367$	−30.3880	−	17.5445i	−1.58624	−	0.915816i	−0.592320	−	0.805703i	$-0.701788\pi$
$368$	−3.14645	+	5.44981i	−0.164020	+	0.284091i
$369$	−1.70582	−	2.95456i	−0.0888013	−	0.153808i
$370$	21.2747			1.10602
$371$	24.3861	+	0.0700781i	1.26606	+	0.00363827i
$372$	3.09104			0.160263
$373$	−21.2225	+	12.2528i	−1.09886	+	0.634427i	−0.935921	−	0.352210i	$-0.885430\pi$
$373$	−21.2225	+	12.2528i	−1.09886	+	0.634427i	−0.162938	+	0.986636i	$0.552097\pi$
$374$	7.12897	−	7.93234i	0.368630	−	0.410171i
$375$	5.33360	−	9.23807i	0.275426	−	0.477052i
$376$	5.32461	+	9.22249i	0.274596	+	0.475614i
$377$		−	4.70949i		−	0.242551i
$378$	−1.32945	+	2.28748i	−0.0683798	+	0.117655i
$379$	−3.42705			−0.176036			−0.0880179	−	0.996119i	$-0.528053\pi$
$379$	−3.42705			−0.176036			−0.0880179	+	0.996119i	$0.528053\pi$
$380$	−12.4118	+	7.16598i	−0.636714	+	0.367607i
$381$	5.40449	−	9.36086i	0.276881	−	0.479571i
$382$	−20.3722	−	11.7619i	−1.04233	−	0.601791i
$383$	−28.2806	+	16.3278i	−1.44507	+	0.834312i	−0.998182	−	0.0602779i	$-0.980801\pi$
$383$	−28.2806	+	16.3278i	−1.44507	+	0.834312i	−0.446889	+	0.894590i	$0.647468\pi$
$384$	−1.00000			−0.0510310
$385$	−6.27313	−	19.4352i	−0.319708	−	0.990509i
$386$	20.7965			1.05852
$387$	1.63893	−	0.946236i	0.0833115	−	0.0480999i
$388$	15.4175	+	8.90130i	0.782705	+	0.451895i
$389$	−9.28386	+	16.0801i	−0.470711	+	0.815295i	−0.999439	−	0.0334965i	$-0.989336\pi$
$389$	−9.28386	+	16.0801i	−0.470711	+	0.815295i	0.528728	+	0.848791i	$0.322669\pi$
$390$	−2.90431	+	1.67680i	−0.147065	+	0.0849082i
$391$	−20.2357			−1.02336
$392$	6.04196	+	3.53478i	0.305165	+	0.178534i
$393$		−	10.9712i		−	0.553422i
$394$	10.6837	+	18.5048i	0.538239	+	0.932258i
$395$	−9.69162	+	16.7864i	−0.487639	+	0.844615i
$396$	2.46679	+	2.21696i	0.123961	+	0.111407i
$397$	−4.84409	+	2.79674i	−0.243118	+	0.140364i	−0.616609	−	0.787270i	$-0.711494\pi$
$397$	−4.84409	+	2.79674i	−0.243118	+	0.140364i	0.373491	+	0.927634i	$0.378161\pi$
$398$	20.0431			1.00467
$399$	−14.1332	+	8.10572i	−0.707543	+	0.405794i
$400$	−0.416608			−0.0208304
$401$	5.17676	+	8.96641i	0.258515	+	0.447761i	0.965844	−	0.259123i	$-0.0834335\pi$
$401$	5.17676	+	8.96641i	0.258515	+	0.447761i	−0.707329	+	0.706884i	$0.750100\pi$
$402$	4.61347	−	7.99077i	0.230099	−	0.398543i
$403$	3.85730	+	2.22701i	0.192146	+	0.110935i
$404$	−5.34857	−	9.26399i	−0.266101	−	0.460901i
$405$		−	2.32736i		−	0.115647i
$406$	4.34509	−	7.47622i	0.215643	−	0.371039i
$407$	6.27582	−	29.6610i	0.311081	−	1.47024i
$408$	−1.60782	−	2.78483i	−0.0795991	−	0.137870i
$409$	−10.4458	+	18.0927i	−0.516512	+	0.894625i	0.483304	+	0.875452i	$0.339436\pi$
$409$	−10.4458	+	18.0927i	−0.516512	+	0.894625i	−0.999816	+	0.0191723i	$0.993897\pi$
$410$	3.97005	−	6.87633i	0.196067	−	0.339598i
$411$	−8.37102	+	4.83301i	−0.412912	+	0.238395i
$412$		−	13.6074i		−	0.670388i
$413$	0.00405025	−	1.40943i	0.000199300	−	0.0693533i
$414$		−	6.29290i		−	0.309279i
$415$	9.19355	−	5.30790i	0.451293	−	0.260554i
$416$	−1.24790	−	0.720474i	−0.0611832	−	0.0353241i
$417$	−20.2386	−	11.6848i	−0.991088	−	0.572205i
$418$	6.32938	+	19.4184i	0.309580	+	0.949784i
$419$			7.59471i			0.371026i	0.982642	+	0.185513i	$0.0593946\pi$
$419$			7.59471i			0.371026i	−0.982642	+	0.185513i	$0.940605\pi$
$420$	−6.15759	−	0.0176950i	−0.300460	−	0.000863428i
$421$	−29.9360			−1.45899			−0.729496	−	0.683985i	$-0.760246\pi$
$421$	−29.9360			−1.45899			−0.729496	+	0.683985i	$0.760246\pi$
$422$	1.02325	+	1.77233i	0.0498112	+	0.0862756i
$423$	−9.22249	−	5.32461i	−0.448413	−	0.258891i
$424$	−7.98226	−	4.60856i	−0.387653	−	0.223812i
$425$	−0.669832	−	1.16018i	−0.0324916	−	0.0562771i
$426$	−3.25253			−0.157586
$427$	−0.621422	+	1.06923i	−0.0300727	+	0.0517435i
$428$		−	9.39572i		−	0.454159i
$429$	1.48104	+	4.54380i	0.0715054	+	0.219377i
$430$	3.81438	+	2.20223i	0.183946	+	0.106201i
$431$	−28.8852	−	16.6769i	−1.39135	−	0.803297i	−0.397886	−	0.917435i	$-0.630256\pi$
$431$	−28.8852	−	16.6769i	−1.39135	−	0.803297i	−0.993465	+	0.114138i	$0.963590\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$		−	27.7837i		−	1.33520i	−0.744521	−	0.667599i	$-0.767322\pi$
$433$		−	27.7837i		−	1.33520i	0.744521	−	0.667599i	$-0.232678\pi$
$434$	4.06869	+	7.09419i	0.195304	+	0.340532i
$435$			7.60657i			0.364707i
$436$	−6.18076	+	3.56846i	−0.296005	+	0.170898i
$437$	19.3759	−	33.5601i	0.926876	−	1.60540i
$438$	2.50002	−	4.33016i	0.119456	−	0.206903i
$439$	−15.5488	−	26.9314i	−0.742105	−	1.28536i	−0.951535	−	0.307541i	$-0.900494\pi$
$439$	−15.5488	−	26.9314i	−0.742105	−	1.28536i	0.209429	−	0.977824i	$-0.432839\pi$
$440$	−1.59785	+	7.55179i	−0.0761743	+	0.360018i
$441$	−6.99988	−	0.0402313i	−0.333328	−	0.00191578i
$442$		−	4.63358i		−	0.220397i
$443$	2.50430	+	4.33757i	0.118983	+	0.206084i	0.919365	−	0.393406i	$-0.128703\pi$
$443$	2.50430	+	4.33757i	0.118983	+	0.206084i	−0.800382	+	0.599490i	$0.795370\pi$
$444$	−7.91644	−	4.57056i	−0.375697	−	0.216909i
$445$	5.09813	−	8.83022i	0.241675	−	0.418593i
$446$	−11.6902	−	20.2480i	−0.553548	−	0.958773i
$447$	−15.0541			−0.712034
$448$	−1.31629	−	2.29508i	−0.0621887	−	0.108432i
$449$	24.8715			1.17376			0.586880	−	0.809674i	$-0.300356\pi$
$449$	24.8715			1.17376			0.586880	+	0.809674i	$0.300356\pi$
$450$	0.360793	−	0.208304i	0.0170080	−	0.00981954i
$451$	−8.41580	−	7.56347i	−0.396285	−	0.356150i
$452$	−1.57550	+	2.72884i	−0.0741052	+	0.128354i
$453$	6.49554	+	11.2506i	0.305187	+	0.528599i
$454$			13.9483i			0.654625i
$455$	−7.67129	−	4.45846i	−0.359636	−	0.209016i
$456$	6.15803			0.288376
$457$	6.59453	−	3.80735i	0.308479	−	0.178100i	−0.337767	−	0.941230i	$-0.609671\pi$
$457$	6.59453	−	3.80735i	0.308479	−	0.178100i	0.646246	+	0.763129i	$0.276338\pi$
$458$	−7.50744	+	13.0033i	−0.350800	+	0.607603i
$459$	2.78483	+	1.60782i	0.129985	+	0.0750467i
$460$	12.6837	−	7.32292i	0.591379	−	0.341433i
$461$	−8.56061			−0.398707			−0.199354	−	0.979928i	$-0.563884\pi$
$461$	−8.56061			−0.398707			−0.199354	+	0.979928i	$0.563884\pi$
$462$	−1.84110	+	8.57965i	−0.0856557	+	0.399161i
$463$	−2.87221			−0.133483			−0.0667415	−	0.997770i	$-0.521260\pi$
$463$	−2.87221			−0.133483			−0.0667415	+	0.997770i	$0.521260\pi$
$464$	−2.83045	+	1.63416i	−0.131401	+	0.0758641i
$465$	−6.23016	−	3.59698i	−0.288917	−	0.166806i
$466$	8.22109	−	14.2393i	0.380835	−	0.659625i
$467$	−7.84052	+	4.52673i	−0.362816	+	0.209472i	−0.670315	−	0.742076i	$-0.733841\pi$
$467$	−7.84052	+	4.52673i	−0.362816	+	0.209472i	0.307499	+	0.951548i	$0.400508\pi$
$468$	1.44095			0.0666078
$469$	24.4121	+	0.0701528i	1.12725	+	0.00323935i
$470$		−	24.7846i		−	1.14323i
$471$	−5.76428	−	9.98402i	−0.265604	−	0.460039i
$472$	−0.266358	+	0.461345i	−0.0122601	+	0.0212351i
$473$	4.19554	−	4.66834i	0.192911	−	0.214651i
$474$	7.21263	−	4.16421i	0.331287	−	0.191269i
$475$	2.56548			0.117712
$476$	4.27506	−	7.35572i	0.195947	−	0.337149i
$477$	9.21712			0.422023
$478$	12.3975	+	21.4731i	0.567050	+	0.982159i
$479$	−15.5977	+	27.0160i	−0.712677	+	1.23439i	0.251172	+	0.967943i	$0.419184\pi$
$479$	−15.5977	+	27.0160i	−0.712677	+	1.23439i	−0.963849	+	0.266450i	$0.914149\pi$
$480$	2.01555	+	1.16368i	0.0919970	+	0.0531145i
$481$	−6.58593	−	11.4072i	−0.300293	−	0.520122i
$482$		−	22.2195i		−	1.01207i
$483$	14.4427	−	8.28325i	0.657166	−	0.376901i
$484$	10.0573	+	4.45541i	0.457150	+	0.202519i
$485$	−20.7165	−	35.8821i	−0.940689	−	1.62932i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−18.0368	+	31.2407i	−0.817327	+	1.41565i	0.0903185	+	0.995913i	$0.471211\pi$
$487$	−18.0368	+	31.2407i	−0.817327	+	1.41565i	−0.907645	+	0.419738i	$0.862122\pi$
$488$	0.404803	−	0.233713i	0.0183246	−	0.0105797i
$489$			8.31371i			0.375959i
$490$	−8.06454	−	14.1555i	−0.364319	−	0.639478i
$491$		−	26.7561i		−	1.20749i	−0.797179	−	0.603744i	$-0.793675\pi$
$491$		−	26.7561i		−	1.20749i	0.797179	−	0.603744i	$-0.206325\pi$
$492$	−2.95456	+	1.70582i	−0.133202	+	0.0769042i
$493$	−9.10174	−	5.25489i	−0.409922	−	0.236668i
$494$	7.68458	+	4.43670i	0.345746	+	0.199616i
$495$	−2.39212	−	7.33897i	−0.107518	−	0.329862i
$496$		−	3.09104i		−	0.138792i
$497$	−4.28126	−	7.46482i	−0.192041	−	0.334843i
$498$	−4.56130			−0.204397
$499$	−14.0487	−	24.3330i	−0.628906	−	1.08930i	−0.987772	−	0.155907i	$-0.950170\pi$
$499$	−14.0487	−	24.3330i	−0.628906	−	1.08930i	0.358866	−	0.933389i	$-0.383164\pi$
$500$	−9.23807	−	5.33360i	−0.413139	−	0.238526i
$501$	13.4527	+	7.76692i	0.601022	+	0.347000i
$502$	−2.36708	−	4.09990i	−0.105648	−	0.182987i
$503$	16.3197			0.727660			0.363830	−	0.931465i	$-0.381469\pi$
$503$	16.3197			0.727660			0.363830	+	0.931465i	$0.381469\pi$
$504$	2.28748	+	1.32945i	0.101892	+	0.0592186i
$505$			24.8961i			1.10786i
$506$	−6.46800	−	19.8437i	−0.287538	−	0.882159i
$507$	−9.46018	−	5.46184i	−0.420141	−	0.242569i
$508$	−9.36086	−	5.40449i	−0.415321	−	0.239786i
$509$	3.92989	−	2.26892i	0.174189	−	0.100568i	−0.410370	−	0.911919i	$-0.634601\pi$
$509$	3.92989	−	2.26892i	0.174189	−	0.100568i	0.584560	+	0.811351i	$0.301267\pi$
$510$			7.48397i			0.331396i
$511$	13.2288	+	0.0380155i	0.585208	+	0.00168171i
$512$			1.00000i			0.0441942i
$513$	−5.33301	+	3.07901i	−0.235458	+	0.135942i
$514$	−6.11764	+	10.5961i	−0.269838	+	0.467373i
$515$	−15.8347	+	27.4264i	−0.697758	+	1.20855i
$516$	−0.946236	−	1.63893i	−0.0416557	−	0.0721499i
$517$	−34.5545	−	7.31121i	−1.51970	−	0.321546i
$518$	0.0695002	−	24.1850i	0.00305366	−	1.06263i
$519$			13.2048i			0.579626i
$520$	1.67680	+	2.90431i	0.0735326	+	0.127362i
$521$	−0.675518	−	0.390011i	−0.0295950	−	0.0170867i	0.485130	−	0.874442i	$-0.338772\pi$
$521$	−0.675518	−	0.390011i	−0.0295950	−	0.0170867i	−0.514725	+	0.857356i	$0.672106\pi$
$522$	1.63416	−	2.83045i	0.0715254	−	0.123886i
$523$	−5.88383	−	10.1911i	−0.257282	−	0.445626i	0.708231	−	0.705981i	$-0.249494\pi$
$523$	−5.88383	−	10.1911i	−0.257282	−	0.445626i	−0.965513	+	0.260355i	$0.916160\pi$
$524$	−10.9712			−0.479278
$525$	0.952981	+	0.553861i	0.0415915	+	0.0241725i
$526$	19.2700			0.840214
$527$	8.60803	−	4.96985i	0.374972	−	0.216490i
$528$	2.21696	−	2.46679i	0.0964809	−	0.107353i
$529$	−8.30028	+	14.3765i	−0.360882	+	0.625065i
$530$	10.7258	+	18.5776i	0.465898	+	0.806959i
$531$		−	0.532715i		−	0.0231179i
$532$	8.10572	+	14.1332i	0.351428	+	0.612750i
$533$	−4.91598			−0.212935
$534$	−3.79409	+	2.19052i	−0.164186	+	0.0947931i
$535$	−10.9336	+	18.9376i	−0.472702	+	0.818743i
$536$	−7.99077	−	4.61347i	−0.345149	−	0.199272i
$537$	16.3426	−	9.43539i	0.705234	−	0.407167i
$538$	22.0893			0.952338
$539$	−22.1144	+	7.06780i	−0.952534	+	0.304432i
$540$	−2.32736			−0.100154
$541$	9.27327	−	5.35393i	0.398689	−	0.230183i	−0.287229	−	0.957862i	$-0.592734\pi$
$541$	9.27327	−	5.35393i	0.398689	−	0.230183i	0.685918	+	0.727679i	$0.259401\pi$
$542$	−1.05751	−	0.610555i	−0.0454240	−	0.0262256i
$543$	1.97224	−	3.41602i	0.0846369	−	0.146595i
$544$	−2.78483	+	1.60782i	−0.119399	+	0.0689348i
$545$	16.6102			0.711503
$546$	1.89670	+	3.30709i	0.0811712	+	0.141530i
$547$		−	19.5154i		−	0.834419i	−0.908810	−	0.417210i	$-0.863008\pi$
$547$		−	19.5154i		−	0.834419i	0.908810	−	0.417210i	$-0.136992\pi$
$548$	4.83301	+	8.37102i	0.206456	+	0.357592i
$549$	−0.233713	+	0.404803i	−0.00997464	+	0.0172766i
$550$	0.923604	−	1.02769i	0.0393826	−	0.0438207i
$551$	17.4300	−	10.0632i	0.742544	−	0.428708i
$552$	−6.29290			−0.267843
$553$	19.0511	+	11.0723i	0.810134	+	0.470841i
$554$	−12.5089			−0.531450
$555$	10.6373	+	18.4244i	0.451530	+	0.782072i
$556$	−11.6848	+	20.2386i	−0.495544	+	0.858308i
$557$	5.25260	+	3.03259i	0.222560	+	0.128495i	0.607135	−	0.794599i	$-0.292319\pi$
$557$	5.25260	+	3.03259i	0.222560	+	0.128495i	−0.384575	+	0.923094i	$0.625652\pi$
$558$	1.54552	+	2.67692i	0.0654271	+	0.113323i
$559$		−	2.72695i		−	0.115338i
$560$	−0.0176950	+	6.15759i	−0.000747751	+	0.260206i
$561$	10.4341	+	2.20770i	0.440528	+	0.0932091i
$562$	12.6747	+	21.9533i	0.534651	+	0.926043i
$563$	0.122186	−	0.211633i	0.00514953	−	0.00891925i	−0.863439	−	0.504453i	$-0.831694\pi$
$563$	0.122186	−	0.211633i	0.00514953	−	0.00891925i	0.868589	+	0.495534i	$0.165028\pi$
$564$	−5.32461	+	9.22249i	−0.224206	+	0.388337i
$565$	6.35100	−	3.66675i	0.267189	−	0.154262i
$566$		−	2.76444i		−	0.116198i
$567$	−2.64574	−	0.00760304i	−0.111111	−	0.000319298i
$568$			3.25253i			0.136473i
$569$	−7.44979	+	4.30114i	−0.312311	+	0.180313i	−0.647960	−	0.761674i	$-0.724378\pi$
$569$	−7.44979	+	4.30114i	−0.312311	+	0.180313i	0.335649	+	0.941987i	$0.391044\pi$
$570$	−12.4118	−	7.16598i	−0.519875	−	0.300150i
$571$	26.9418	+	15.5548i	1.12748	+	0.650950i	0.943299	−	0.331943i	$-0.107704\pi$
$571$	26.9418	+	15.5548i	1.12748	+	0.650950i	0.184178	+	0.982893i	$0.441038\pi$
$572$	4.54380	−	1.48104i	0.189986	−	0.0619255i
$573$		−	23.5238i		−	0.982721i
$574$	−7.80403	−	4.53561i	−0.325734	−	0.189313i
$575$	−2.62167			−0.109331
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−35.4669	−	20.4768i	−1.47651	−	0.852462i	−0.476859	−	0.878980i	$-0.658225\pi$
$577$	−35.4669	−	20.4768i	−1.47651	−	0.852462i	−0.999648	+	0.0265176i	$0.991558\pi$
$578$	5.76740	+	3.32981i	0.239892	+	0.138502i
$579$	10.3983	+	18.0103i	0.432137	+	0.748484i
$580$	7.60657			0.315846
$581$	−6.00398	−	10.4686i	−0.249087	−	0.434309i
$582$			17.8026i			0.737941i
$583$	29.0648	−	9.47359i	1.20374	−	0.392356i
$584$	−4.33016	−	2.50002i	−0.179183	−	0.103451i
$585$	−2.90431	−	1.67680i	−0.120078	−	0.0693272i
$586$	7.82172	−	4.51587i	0.323112	−	0.186549i
$587$			33.6048i			1.38702i	0.720449	+	0.693508i	$0.243936\pi$
$587$			33.6048i			1.38702i	−0.720449	+	0.693508i	$0.756064\pi$
$588$	−0.0402313	+	6.99988i	−0.00165911	+	0.288670i
$589$			19.0347i			0.784312i
$590$	1.07372	−	0.619910i	0.0442042	−	0.0255213i
$591$	−10.6837	+	18.5048i	−0.439471	+	0.761186i
$592$	−4.57056	+	7.91644i	−0.187849	+	0.325364i
$593$	−13.3626	−	23.1448i	−0.548738	−	0.950442i	−0.998361	−	0.0572237i	$-0.981775\pi$
$593$	−13.3626	−	23.1448i	−0.548738	−	0.950442i	0.449624	−	0.893218i	$-0.351558\pi$
$594$	−0.686549	+	3.24479i	−0.0281694	+	0.133135i
$595$	−17.1763	+	9.85104i	−0.704160	+	0.403853i
$596$			15.0541i			0.616640i
$597$	10.0216	+	17.3579i	0.410155	+	0.710410i
$598$	−7.85289	−	4.53387i	−0.321128	−	0.185404i
$599$	−12.4072	+	21.4899i	−0.506945	+	0.878055i	0.493022	+	0.870017i	$0.335892\pi$
$599$	−12.4072	+	21.4899i	−0.506945	+	0.878055i	−0.999968	+	0.00803859i	$0.997441\pi$
$600$	−0.208304	−	0.360793i	−0.00850398	−	0.0147293i
$601$	17.8950			0.729952			0.364976	−	0.931017i	$-0.381077\pi$
$601$	17.8950			0.729952			0.364976	+	0.931017i	$0.381077\pi$
$602$	2.51596	−	4.32899i	0.102543	−	0.176436i
$603$	9.22694			0.375750
$604$	11.2506	−	6.49554i	0.457780	−	0.264300i
$605$	−15.0864	−	20.6836i	−0.613348	−	0.840908i
$606$	5.34857	−	9.26399i	0.217271	−	0.376324i
$607$	16.4712	+	28.5290i	0.668546	+	1.15796i	0.978311	+	0.207142i	$0.0664162\pi$
$607$	16.4712	+	28.5290i	0.668546	+	1.15796i	−0.309765	+	0.950813i	$0.600250\pi$
$608$		−	6.15803i		−	0.249741i
$609$	8.64714	+	0.0248492i	0.350400	+	0.00100694i
$610$	−1.08787			−0.0440466
$611$	−13.2891	+	7.67248i	−0.537620	+	0.310395i
$612$	1.60782	−	2.78483i	0.0649924	−	0.112570i
$613$	7.51244	+	4.33731i	0.303425	+	0.175182i	0.643980	−	0.765042i	$-0.277282\pi$
$613$	7.51244	+	4.33731i	0.303425	+	0.175182i	−0.340556	+	0.940224i	$0.610615\pi$
$614$	−3.05093	+	1.76145i	−0.123125	+	0.0710865i
$615$	7.94010			0.320176
$616$	8.57965	+	1.84110i	0.345684	+	0.0741800i
$617$	32.6421			1.31412			0.657061	−	0.753837i	$-0.271799\pi$
$617$	32.6421			1.31412			0.657061	+	0.753837i	$0.271799\pi$
$618$	11.7844	−	6.80370i	0.474036	−	0.273685i
$619$	−13.6975	−	7.90825i	−0.550549	−	0.317859i	0.198795	−	0.980041i	$-0.436297\pi$
$619$	−13.6975	−	7.90825i	−0.550549	−	0.317859i	−0.749343	+	0.662182i	$0.769631\pi$
$620$	−3.59698	+	6.23016i	−0.144458	+	0.250209i
$621$	5.44981	−	3.14645i	0.218693	−	0.126263i
$622$	5.58704			0.224020
$623$	−10.0215	−	5.82439i	−0.401504	−	0.233349i
$624$		−	1.44095i		−	0.0576841i
$625$	13.4547	+	23.3043i	0.538190	+	0.932172i
$626$	2.63952	−	4.57178i	0.105496	−	0.182725i
$627$	−13.6521	+	15.1906i	−0.545213	+	0.606654i
$628$	−9.98402	+	5.76428i	−0.398406	+	0.230020i
$629$	−29.3946			−1.17204
$630$	−3.06347	−	5.34148i	−0.122052	−	0.212810i
$631$	40.7984			1.62416			0.812080	−	0.583546i	$-0.198335\pi$
$631$	40.7984			1.62416			0.812080	+	0.583546i	$0.198335\pi$
$632$	−4.16421	−	7.21263i	−0.165643	−	0.286903i
$633$	−1.02325	+	1.77233i	−0.0406707	+	0.0704437i
$634$	−27.4412	−	15.8432i	−1.08983	−	0.629214i
$635$	12.5782	+	21.7861i	0.499151	+	0.864555i
$636$		−	9.21712i		−	0.365483i
$637$	−5.09344	+	8.70615i	−0.201809	+	0.344950i
$638$	2.24387	−	10.6050i	0.0888355	−	0.419857i
$639$	−1.62627	−	2.81677i	−0.0643341	−	0.111430i
$640$	1.16368	−	2.01555i	0.0459985	−	0.0796717i
$641$	−11.9591	+	20.7137i	−0.472354	+	0.818142i	−0.999500	−	0.0316335i	$-0.989929\pi$
$641$	−11.9591	+	20.7137i	−0.472354	+	0.818142i	0.527145	+	0.849775i	$0.323262\pi$
$642$	8.13694	−	4.69786i	0.321139	−	0.185410i
$643$		−	19.6140i		−	0.773502i	−0.922184	−	0.386751i	$-0.873597\pi$
$643$		−	19.6140i		−	0.773502i	0.922184	−	0.386751i	$-0.126403\pi$
$644$	−8.28325	−	14.4427i	−0.326406	−	0.569122i
$645$			4.40447i			0.173426i
$646$	17.1491	−	9.90102i	0.674721	−	0.389550i
$647$	22.5941	+	13.0447i	0.888267	+	0.512841i	0.873375	−	0.487048i	$-0.161926\pi$
$647$	22.5941	+	13.0447i	0.888267	+	0.512841i	0.0148918	+	0.999889i	$0.495260\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−0.547538	−	1.67983i	−0.0214928	−	0.0659392i
$650$		−	0.600310i		−	0.0235461i
$651$	−4.10940	+	7.07068i	−0.161060	+	0.277122i
$652$	8.31371			0.325590
$653$	10.8589	+	18.8082i	0.424942	+	0.736020i	0.996415	−	0.0846002i	$-0.0269613\pi$
$653$	10.8589	+	18.8082i	0.424942	+	0.736020i	−0.571473	+	0.820621i	$0.693628\pi$
$654$	−6.18076	−	3.56846i	−0.241687	−	0.139538i
$655$	22.1130	+	12.7669i	0.864026	+	0.498846i
$656$	1.70582	+	2.95456i	0.0666010	+	0.115356i
$657$	5.00004			0.195070
$658$	−28.1751	−	0.0809664i	−1.09838	−	0.00315640i
$659$		−	12.7596i		−	0.497044i	−0.968626	−	0.248522i	$-0.920055\pi$
$659$		−	12.7596i		−	0.497044i	0.968626	−	0.248522i	$-0.0799448\pi$
$660$	−7.33897	+	2.39212i	−0.285669	+	0.0931132i
$661$	−19.9646	−	11.5266i	−0.776533	−	0.448332i	0.0586670	−	0.998278i	$-0.481315\pi$
$661$	−19.9646	−	11.5266i	−0.776533	−	0.448332i	−0.835200	+	0.549946i	$0.814648\pi$
$662$	3.39124	+	1.95793i	0.131804	+	0.0760972i
$663$	4.01279	−	2.31679i	0.155844	−	0.0899766i
$664$			4.56130i			0.177013i
$665$	0.108966	−	37.9186i	0.00422553	−	1.47042i
$666$		−	9.14111i		−	0.354211i
$667$	−17.8118	+	10.2836i	−0.689674	+	0.398183i
$668$	7.76692	−	13.4527i	0.300511	−	0.520500i
$669$	11.6902	−	20.2480i	0.451970	−	0.782835i
$670$	10.7372	+	18.5974i	0.414815	+	0.718480i
$671$	−0.320911	+	1.51670i	−0.0123886	+	0.0585516i
$672$	1.32945	−	2.28748i	0.0512848	−	0.0882413i
$673$		−	10.4212i		−	0.401709i	−0.979621	−	0.200854i	$-0.935628\pi$
$673$		−	10.4212i		−	0.401709i	0.979621	−	0.200854i	$-0.0643718\pi$
$674$	10.0267	+	17.3668i	0.386214	+	0.668942i
$675$	0.360793	+	0.208304i	0.0138869	+	0.00801762i
$676$	−5.46184	+	9.46018i	−0.210071	+	0.363853i
$677$	−7.14285	−	12.3718i	−0.274522	−	0.475486i	0.695492	−	0.718534i	$-0.255186\pi$
$677$	−7.14285	−	12.3718i	−0.274522	−	0.475486i	−0.970014	+	0.243047i	$0.921853\pi$
$678$	−3.15100			−0.121013
$679$	−40.8584	+	23.4333i	−1.56800	+	0.899287i
$680$	7.48397			0.286997
$681$	−12.0796	+	6.97413i	−0.462890	+	0.267249i
$682$	7.62496	+	6.85272i	0.291975	+	0.262404i
$683$	17.3671	−	30.0806i	0.664532	−	1.15100i	−0.314880	−	0.949132i	$-0.601964\pi$
$683$	17.3671	−	30.0806i	0.664532	−	1.15100i	0.979412	−	0.201872i	$-0.0647025\pi$
$684$	3.07901	+	5.33301i	0.117729	+	0.203913i
$685$		−	22.4963i		−	0.859540i
$686$	−16.1182	+	9.12151i	−0.615398	+	0.348261i
$687$	−15.0149			−0.572854
$688$	−1.63893	+	0.946236i	−0.0624836	+	0.0360749i
$689$	6.64069	−	11.5020i	0.252990	−	0.438192i
$690$	12.6837	+	7.32292i	0.482859	+	0.278779i
$691$	7.08434	−	4.09015i	0.269501	−	0.155596i	−0.359160	−	0.933276i	$-0.616937\pi$
$691$	7.08434	−	4.09015i	0.269501	−	0.155596i	0.628661	+	0.777680i	$0.283603\pi$
$692$	13.2048			0.501971
$693$	−8.35074	+	2.69538i	−0.317218	+	0.102389i
$694$	28.5210			1.08264
$695$	47.1025	−	27.1946i	1.78670	−	1.03155i
$696$	−2.83045	−	1.63416i	−0.107288	−	0.0619428i
$697$	−5.48530	+	9.50082i	−0.207771	+	0.359869i
$698$	−13.3317	+	7.69705i	−0.504612	+	0.291338i
$699$	16.4422			0.621900
$700$	0.553861	−	0.952981i	0.0209340	−	0.0360193i
$701$			15.9970i			0.604198i	0.953277	+	0.302099i	$0.0976874\pi$
$701$			15.9970i			0.604198i	−0.953277	+	0.302099i	$0.902313\pi$
$702$	0.720474	+	1.24790i	0.0271925	+	0.0470988i
$703$	28.1456	−	48.7496i	1.06153	−	1.83863i
$704$	−2.46679	−	2.21696i	−0.0929708	−	0.0835549i
$705$	21.4641	−	12.3923i	0.808384	−	0.466720i
$706$	5.54275			0.208604
$707$	28.3019	+	0.0813307i	1.06440	+	0.00305876i
$708$	−0.532715			−0.0200207
$709$	4.39355	+	7.60985i	0.165003	+	0.285794i	0.936656	−	0.350250i	$-0.113903\pi$
$709$	4.39355	+	7.60985i	0.165003	+	0.285794i	−0.771653	+	0.636043i	$0.780570\pi$
$710$	3.78491	−	6.55565i	0.142045	−	0.246029i
$711$	7.21263	+	4.16421i	0.270495	+	0.156170i
$712$	2.19052	+	3.79409i	0.0820932	+	0.142190i
$713$		−	19.4516i		−	0.728468i
$714$	8.50776	+	0.0244487i	0.318395	+	0.000914969i
$715$	−10.8817	−	2.30241i	−0.406954	−	0.0861053i
$716$	−9.43539	−	16.3426i	−0.352617	−	0.610750i
$717$	−12.3975	+	21.4731i	−0.462994	+	0.801929i
$718$	−10.3650	+	17.9527i	−0.386818	+	0.669989i
$719$	−27.2393	+	15.7266i	−1.01585	+	0.586503i	−0.912900	−	0.408183i	$-0.866163\pi$
$719$	−27.2393	+	15.7266i	−1.01585	+	0.586503i	−0.102953	+	0.994686i	$0.532829\pi$
$720$			2.32736i			0.0867356i
$721$	31.1266	+	18.0904i	1.15922	+	0.673722i
$722$			18.9213i			0.704178i
$723$	19.2427	−	11.1098i	0.715643	−	0.413177i
$724$	−3.41602	−	1.97224i	−0.126955	−	0.0732977i
$725$	−1.17919	−	0.680805i	−0.0437940	−	0.0252845i
$726$	1.17015	+	10.9376i	0.0434284	+	0.405932i
$727$			50.7040i			1.88051i	0.340475	+	0.940254i	$0.389412\pi$
$727$			50.7040i			1.88051i	−0.340475	+	0.940254i	$0.610588\pi$
$728$	3.30709	−	1.89670i	0.122569	−	0.0702963i
$729$	−1.00000			−0.0370370
$730$	5.81844	+	10.0778i	0.215350	+	0.372998i
$731$	−5.27022	−	3.04276i	−0.194926	−	0.112541i
$732$	0.404803	+	0.233713i	0.0149620	+	0.00863829i
$733$	−3.99023	−	6.91128i	−0.147382	−	0.255274i	0.782877	−	0.622177i	$-0.213751\pi$
$733$	−3.99023	−	6.91128i	−0.147382	−	0.255274i	−0.930259	+	0.366903i	$0.880418\pi$
$734$	−35.0890			−1.29516
$735$	8.22672	−	14.0618i	0.303447	−	0.518678i
$736$			6.29290i			0.231959i
$737$	29.0957	−	9.48369i	1.07175	−	0.349336i
$738$	−2.95456	−	1.70582i	−0.108759	−	0.0627920i
$739$	38.2867	+	22.1048i	1.40840	+	0.813140i	0.995234	−	0.0975161i	$-0.0310898\pi$
$739$	38.2867	+	22.1048i	1.40840	+	0.813140i	0.413166	+	0.910656i	$0.364423\pi$
$740$	18.4244	−	10.6373i	0.677295	−	0.391036i
$741$			8.87339i			0.325972i
$742$	21.1540	−	12.1324i	0.776589	−	0.445393i
$743$		−	17.1346i		−	0.628607i	−0.949323	−	0.314304i	$-0.898229\pi$
$743$		−	17.1346i		−	0.628607i	0.949323	−	0.314304i	$-0.101771\pi$
$744$	2.67692	−	1.54552i	0.0981407	−	0.0566615i
$745$	17.5182	−	30.3423i	0.641815	−	1.11166i
$746$	−12.2528	+	21.2225i	−0.448607	+	0.777011i
$747$	−2.28065	−	3.95020i	−0.0834446	−	0.144530i
$748$	2.20770	−	10.4341i	0.0807214	−	0.381508i
$749$	21.4925	+	12.4912i	0.785319	+	0.456418i
$750$		−	10.6672i		−	0.389511i
$751$	20.4417	+	35.4061i	0.745928	+	1.29199i	0.949760	+	0.312979i	$0.101327\pi$
$751$	20.4417	+	35.4061i	0.745928	+	1.29199i	−0.203832	+	0.979006i	$0.565340\pi$
$752$	9.22249	+	5.32461i	0.336310	+	0.194168i
$753$	2.36708	−	4.09990i	0.0862611	−	0.149409i
$754$	−2.35474	−	4.07853i	−0.0857547	−	0.148531i
$755$	−30.2349			−1.10036
$756$	−0.00760304	+	2.64574i	−0.000276520	+	0.0962246i
$757$	−20.2420			−0.735709			−0.367855	−	0.929883i	$-0.619908\pi$
$757$	−20.2420			−0.735709			−0.367855	+	0.929883i	$0.619908\pi$
$758$	−2.96791	+	1.71353i	−0.107799	+	0.0622380i
$759$	13.9511	−	15.5233i	0.506394	−	0.563460i
$760$	−7.16598	+	12.4118i	−0.259937	+	0.450225i
$761$	22.7554	+	39.4136i	0.824884	+	1.42874i	0.902008	+	0.431719i	$0.142093\pi$
$761$	22.7554	+	39.4136i	0.824884	+	1.42874i	−0.0771248	+	0.997021i	$0.524574\pi$
$762$		−	10.8090i		−	0.391568i
$763$	0.0542623	−	18.8825i	0.00196443	−	0.683591i
$764$	−23.5238			−0.851062
$765$	−6.48131	+	3.74198i	−0.234332	+	0.135292i
$766$	−16.3278	+	28.2806i	−0.589947	+	1.02182i
$767$	−0.664773	−	0.383807i	−0.0240036	−	0.0138585i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	−2.76998			−0.0998881			−0.0499440	−	0.998752i	$-0.515904\pi$
$769$	−2.76998			−0.0998881			−0.0499440	+	0.998752i	$0.515904\pi$
$770$	−15.1503	−	13.6948i	−0.545978	−	0.493526i
$771$	−12.2353			−0.440643
$772$	18.0103	−	10.3983i	0.648206	−	0.374242i
$773$	−9.93494	−	5.73594i	−0.357335	−	0.206307i	0.310576	−	0.950548i	$-0.399478\pi$
$773$	−9.93494	−	5.73594i	−0.357335	−	0.206307i	−0.667911	+	0.744241i	$0.732811\pi$
$774$	0.946236	−	1.63893i	0.0340118	−	0.0589101i
$775$	1.11523	−	0.643876i	0.0400601	−	0.0231287i
$776$	17.8026			0.639076
$777$	20.9796	−	12.0323i	0.752639	−	0.431657i
$778$			18.5677i			0.665685i
$779$	−10.5045	−	18.1943i	−0.376362	−	0.651877i
$780$	−1.67680	+	2.90431i	−0.0600391	+	0.103991i
$781$	−8.02332	−	7.21074i	−0.287097	−	0.258021i
$782$	−17.5247	+	10.1179i	−0.626680	+	0.361814i
$783$	3.26833			0.116800
$784$	6.99988	+	0.0402313i	0.249996	+	0.00143683i
$785$	26.8311			0.957643
$786$	−5.48559	−	9.50131i	−0.195664	−	0.338901i
$787$	−14.7757	+	25.5923i	−0.526698	+	0.912268i	0.472818	+	0.881160i	$0.343237\pi$
$787$	−14.7757	+	25.5923i	−0.526698	+	0.912268i	−0.999516	+	0.0311080i	$0.990096\pi$
$788$	18.5048	+	10.6837i	0.659206	+	0.380593i
$789$	9.63502	+	16.6883i	0.343016	+	0.594121i
$790$			19.3832i			0.689625i
$791$	−4.14761	−	7.23179i	−0.147472	−	0.257133i
$792$	3.24479	+	0.686549i	0.115299	+	0.0243954i
$793$	0.336769	+	0.583300i	0.0119590	+	0.0207136i
$794$	−2.79674	+	4.84409i	−0.0992525	+	0.171910i
$795$	−10.7258	+	18.5776i	−0.380404	+	0.658880i
$796$	17.3579	−	10.0216i	0.615233	−	0.355205i
$797$		−	3.17035i		−	0.112300i	−0.998422	−	0.0561498i	$-0.982118\pi$
$797$		−	3.17035i		−	0.112300i	0.998422	−	0.0561498i	$-0.0178824\pi$
$798$	−8.18682	+	14.0863i	−0.289810	+	0.498651i
$799$			34.2441i			1.21147i
$800$	−0.360793	+	0.208304i	−0.0127560	+	0.00736466i
$801$	−3.79409	−	2.19052i	−0.134058	−	0.0773982i
$802$	8.96641	+	5.17676i	0.316615	+	0.182798i
$803$	15.7668	−	5.13917i	0.556399	−	0.181357i
$804$		−	9.22694i		−	0.325409i
$805$	−0.111353	+	38.7491i	−0.00392467	+	1.36573i
$806$	4.45403			0.156886
$807$	11.0447	+	19.1299i	0.388791	+	0.673405i
$808$	−9.26399	−	5.34857i	−0.325906	−	0.188162i
$809$	−34.3262	−	19.8183i	−1.20685	−	0.696773i	−0.244777	−	0.969579i	$-0.578715\pi$
$809$	−34.3262	−	19.8183i	−1.20685	−	0.696773i	−0.962069	+	0.272806i	$0.912048\pi$
$810$	−1.16368	−	2.01555i	−0.0408876	−	0.0708193i
$811$	24.9006			0.874377			0.437188	−	0.899370i	$-0.355974\pi$
$811$	24.9006			0.874377			0.437188	+	0.899370i	$0.355974\pi$
$812$	0.0248492	−	8.64714i	0.000872036	−	0.303455i
$813$		−	1.22111i		−	0.0428262i
$814$	−9.39547	−	28.8251i	−0.329311	−	1.01032i
$815$	−16.7567	−	9.67451i	−0.586963	−	0.338883i
$816$	−2.78483	−	1.60782i	−0.0974886	−	0.0562851i
$817$	10.0926	−	5.82695i	0.353094	−	0.203859i
$818$			20.8916i			0.730458i
$819$	−1.91567	+	3.29613i	−0.0669391	+	0.115176i
$820$		−	7.94010i		−	0.277280i
$821$	11.6214	−	6.70962i	0.405590	−	0.234167i	−0.283303	−	0.959030i	$-0.591430\pi$
$821$	11.6214	−	6.70962i	0.405590	−	0.234167i	0.688893	+	0.724863i	$0.258097\pi$
$822$	−4.83301	+	8.37102i	−0.168571	+	0.291973i
$823$	13.2288	−	22.9130i	0.461127	−	0.798696i	−0.537890	−	0.843015i	$-0.680778\pi$
$823$	13.2288	−	22.9130i	0.461127	−	0.798696i	0.999017	+	0.0443189i	$0.0141118\pi$
$824$	−6.80370	−	11.7844i	−0.237018	−	0.410527i
$825$	1.35180	+	0.286022i	0.0470638	+	0.00995800i
$826$	−0.701205	−	1.22262i	−0.0243981	−	0.0425405i
$827$		−	43.1986i		−	1.50216i	−0.660209	−	0.751081i	$-0.729533\pi$
$827$		−	43.1986i		−	1.50216i	0.660209	−	0.751081i	$-0.270467\pi$
$828$	−3.14645	−	5.44981i	−0.109347	−	0.189394i
$829$	−4.77405	−	2.75630i	−0.165810	−	0.0957303i	0.414799	−	0.909913i	$-0.363852\pi$
$829$	−4.77405	−	2.75630i	−0.165810	−	0.0957303i	−0.580609	+	0.814183i	$0.697185\pi$
$830$	5.30790	−	9.19355i	0.184240	−	0.319113i
$831$	−6.25443	−	10.8330i	−0.216964	−	0.375792i
$832$	−1.44095			−0.0499559
$833$	11.1425	+	19.5582i	0.386066	+	0.677651i
$834$	−23.3695			−0.809220
$835$	−31.3093	+	18.0764i	−1.08350	+	0.625560i
$836$	15.1906	+	13.6521i	0.525378	+	0.472168i
$837$	−1.54552	+	2.67692i	−0.0534210	+	0.0925279i
$838$	3.79735	+	6.57721i	0.131177	+	0.227206i
$839$		−	25.5783i		−	0.883062i	−0.897246	−	0.441531i	$-0.854436\pi$
$839$		−	25.5783i		−	0.883062i	0.897246	−	0.441531i	$-0.145564\pi$
$840$	−5.34148	+	3.06347i	−0.184299	+	0.105700i
$841$	18.3180			0.631657
$842$	−25.9254	+	14.9680i	−0.893447	+	0.515832i
$843$	−12.6747	+	21.9533i	−0.436541	+	0.756111i
$844$	1.77233	+	1.02325i	0.0610060	+	0.0352219i
$845$	22.0172	−	12.7117i	0.757416	−	0.437294i
$846$	−10.6492			−0.366128
$847$	−23.5624	+	17.0826i	−0.809613	+	0.586964i
$848$	−9.21712			−0.316517
$849$	2.39408	−	1.38222i	0.0821646	−	0.0474378i
$850$	−1.16018	−	0.669832i	−0.0397939	−	0.0229750i
$851$	−28.7620	+	49.8173i	−0.985950	+	1.70772i
$852$	−2.81677	+	1.62627i	−0.0965011	+	0.0557149i
$853$	26.6616			0.912877			0.456439	−	0.889755i	$-0.349125\pi$
$853$	26.6616			0.912877			0.456439	+	0.889755i	$0.349125\pi$
$854$	−0.00355386	+	1.23669i	−0.000121611	+	0.0423186i
$855$		−	14.3320i		−	0.490142i
$856$	−4.69786	−	8.13694i	−0.160570	−	0.278115i
$857$	−16.9270	+	29.3183i	−0.578214	+	1.00150i	0.417470	+	0.908690i	$0.362917\pi$
$857$	−16.9270	+	29.3183i	−0.578214	+	1.00150i	−0.995684	+	0.0928052i	$0.970417\pi$
$858$	3.55452	+	3.19453i	0.121349	+	0.109059i
$859$	−9.66594	+	5.58063i	−0.329798	+	0.190409i	−0.655751	−	0.754977i	$-0.727648\pi$
$859$	−9.66594	+	5.58063i	−0.329798	+	0.190409i	0.325954	+	0.945386i	$0.394315\pi$
$860$	4.40447			0.150191
$861$	0.0259388	−	9.02630i	0.000883991	−	0.307615i
$862$	−33.3538			−1.13603
$863$	−7.56384	−	13.1010i	−0.257476	−	0.445962i	0.708089	−	0.706123i	$-0.249558\pi$
$863$	−7.56384	−	13.1010i	−0.257476	−	0.445962i	−0.965565	+	0.260161i	$0.916224\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	−26.6150	−	15.3662i	−0.904936	−	0.522465i
$866$	−13.8918	−	24.0614i	−0.472064	−	0.817639i
$867$			6.65962i			0.226173i
$868$	7.07068	+	4.10940i	0.239995	+	0.139482i
$869$	27.0240	+	5.71787i	0.916726	+	0.193965i
$870$	3.80329	+	6.58749i	0.128944	+	0.223337i
$871$	6.64777	−	11.5143i	0.225251	−	0.390146i
$872$	−3.56846	+	6.18076i	−0.120843	+	0.209307i
$873$	−15.4175	+	8.90130i	−0.521803	+	0.301263i
$874$		−	38.7518i		−	1.31080i
$875$	24.4821	−	14.0411i	0.827646	−	0.474676i
$876$		−	5.00004i		−	0.168936i
$877$	8.64012	−	4.98837i	0.291756	−	0.168445i	−0.346977	−	0.937873i	$-0.612792\pi$
$877$	8.64012	−	4.98837i	0.291756	−	0.168445i	0.638733	+	0.769428i	$0.279459\pi$
$878$	−26.9314	−	15.5488i	−0.908890	−	0.524748i
$879$	7.82172	+	4.51587i	0.263820	+	0.152317i
$880$	2.39212	+	7.33897i	0.0806384	+	0.247397i
$881$			3.10955i			0.104763i	0.998627	+	0.0523816i	$0.0166812\pi$
$881$			3.10955i			0.104763i	−0.998627	+	0.0523816i	$0.983319\pi$
$882$	−6.08219	+	3.46510i	−0.204798	+	0.116676i
$883$	28.8971			0.972465			0.486233	−	0.873829i	$-0.338371\pi$
$883$	28.8971			0.972465			0.486233	+	0.873829i	$0.338371\pi$
$884$	−2.31679	−	4.01279i	−0.0779220	−	0.134965i
$885$	1.07372	+	0.619910i	0.0360926	+	0.0208380i
$886$	4.33757	+	2.50430i	0.145723	+	0.0841335i
$887$	6.85833	+	11.8790i	0.230280	+	0.398857i	0.957890	−	0.287134i	$-0.0927024\pi$
$887$	6.85833	+	11.8790i	0.230280	+	0.398857i	−0.727610	+	0.685991i	$0.759369\pi$
$888$	−9.14111			−0.306756
$889$	24.8075	−	14.2277i	0.832017	−	0.477182i
$890$		−	10.1963i		−	0.341779i
$891$	−3.15334	+	1.02783i	−0.105641	+	0.0344334i
$892$	−20.2480	−	11.6902i	−0.677955	−	0.391417i
$893$	−56.7924	−	32.7891i	−1.90048	−	1.09724i
$894$	−13.0372	+	7.52705i	−0.436030	+	0.251742i
$895$			43.9191i			1.46805i
$896$	−2.28748	−	1.32945i	−0.0764192	−	0.0444140i
$897$		−	9.06773i		−	0.302763i
$898$	21.5394	−	12.4358i	0.718778	−	0.414987i
$899$	5.05127	−	8.74905i	0.168469	−	0.291797i
$900$	0.208304	−	0.360793i	0.00694347	−	0.0120264i
$901$	−14.8195	−	25.6681i	−0.493709	−	0.855129i
$902$	−11.0700	−	2.34225i	−0.368592	−	0.0779885i
$903$	5.00699	+	0.0143885i	0.166622	+	0.000478821i
$904$			3.15100i			0.104801i
$905$	4.59012	+	7.95031i	0.152581	+	0.264277i
$906$	11.2506	+	6.49554i	0.373776	+	0.215800i
$907$	24.4939	−	42.4247i	0.813307	−	1.40869i	−0.0972300	−	0.995262i	$-0.530998\pi$
$907$	24.4939	−	42.4247i	0.813307	−	1.40869i	0.910537	−	0.413427i	$-0.135668\pi$
$908$	6.97413	+	12.0796i	0.231445	+	0.400874i
$909$	10.6971			0.354802
$910$	−8.87277	−	0.0254976i	−0.294129	−	0.000845236i
$911$	−26.6937			−0.884401			−0.442200	−	0.896916i	$-0.645802\pi$
$911$	−26.6937			−0.884401			−0.442200	+	0.896916i	$0.645802\pi$
$912$	5.33301	−	3.07901i	0.176594	−	0.101956i
$913$	−11.2518	−	10.1122i	−0.372380	−	0.334666i
$914$	3.80735	−	6.59453i	0.125936	−	0.218128i
$915$	−0.543935	−	0.942123i	−0.0179819	−	0.0311456i
$916$			15.0149i			0.496106i
$917$	14.5857	−	25.0963i	0.481661	−	0.828753i
$918$	3.21565			0.106132
$919$	−39.8952	+	23.0335i	−1.31602	+	0.759806i	−0.983086	−	0.183144i	$-0.941373\pi$
$919$	−39.8952	+	23.0335i	−1.31602	+	0.759806i	−0.332936	+	0.942949i	$0.608039\pi$
$920$	7.32292	−	12.6837i	0.241430	−	0.418168i
$921$	−3.05093	−	1.76145i	−0.100531	−	0.0580419i
$922$	−7.41371	+	4.28031i	−0.244157	+	0.140964i
$923$	−4.68672			−0.154265
$924$	2.69538	+	8.35074i	0.0886716	+	0.274719i
$925$	−3.80826			−0.125215
$926$	−2.48741	+	1.43611i	−0.0817413	+	0.0471933i
$927$	11.7844	+	6.80370i	0.387049	+	0.223463i
$928$	−1.63416	+	2.83045i	−0.0536440	+	0.0929142i
$929$	10.5117	−	6.06892i	0.344877	−	0.199115i	−0.317550	−	0.948242i	$-0.602860\pi$
$929$	10.5117	−	6.06892i	0.344877	−	0.199115i	0.662427	+	0.749127i	$0.269527\pi$
$930$	−7.19397			−0.235899
$931$	−43.1055	−	0.247746i	−1.41273	−	0.00811953i
$932$		−	16.4422i		−	0.538581i
$933$	2.79352	+	4.83852i	0.0914557	+	0.158406i
$934$	−4.52673	+	7.84052i	−0.148119	+	0.256550i
$935$	−16.5917	+	18.4614i	−0.542606	+	0.603753i
$936$	1.24790	−	0.720474i	0.0407888	−	0.0235494i
$937$	−43.9719			−1.43650			−0.718250	−	0.695786i	$-0.755056\pi$
$937$	−43.9719			−1.43650			−0.718250	+	0.695786i	$0.755056\pi$
$938$	21.1766	−	12.1453i	0.691439	−	0.396558i
$939$	5.27903			0.172275
$940$	−12.3923	−	21.4641i	−0.404192	−	0.700081i
$941$	20.8247	−	36.0694i	0.678866	−	1.17583i	−0.296457	−	0.955046i	$-0.595805\pi$
$941$	20.8247	−	36.0694i	0.678866	−	1.17583i	0.975323	−	0.220784i	$-0.0708615\pi$
$942$	−9.98402	−	5.76428i	−0.325297	−	0.187810i
$943$	10.7345	+	18.5928i	0.349564	+	0.605463i
$944$			0.532715i			0.0173384i
$945$	3.09412	−	5.32378i	0.100652	−	0.173183i
$946$	1.29927	−	6.14067i	0.0422431	−	0.199651i
$947$	9.94370	+	17.2230i	0.323127	+	0.559672i	0.981131	−	0.193342i	$-0.0619326\pi$
$947$	9.94370	+	17.2230i	0.323127	+	0.559672i	−0.658005	+	0.753014i	$0.728599\pi$
$948$	4.16421	−	7.21263i	0.135247	−	0.234255i
$949$	3.60239	−	6.23953i	0.116939	−	0.202544i
$950$	2.22177	−	1.28274i	0.0720839	−	0.0416176i
$951$		−	31.6864i		−	1.02750i
$952$	0.0244487	−	8.50776i	0.000792386	−	0.275738i
$953$		−	42.1430i		−	1.36514i	−0.730818	−	0.682572i	$-0.760861\pi$
$953$		−	42.1430i		−	1.36514i	0.730818	−	0.682572i	$-0.239139\pi$
$954$	7.98226	−	4.60856i	0.258435	−	0.149208i
$955$	47.4135	+	27.3742i	1.53426	+	0.885808i
$956$	21.4731	+	12.3975i	0.694491	+	0.400965i
$957$	10.3062	−	3.35927i	0.333151	−	0.108590i
$958$			31.1954i			1.00788i
$959$	−25.5738	−	0.0734911i	−0.825821	−	0.00237315i
$960$	2.32736			0.0751152
$961$	−10.7227	−	18.5723i	−0.345895	−	0.599107i
$962$	−11.4072	−	6.58593i	−0.367782	−	0.212339i
$963$	8.13694	+	4.69786i	0.262209	+	0.151386i
$964$	−11.1098	−	19.2427i	−0.357822	−	0.619765i
$965$	−48.4010			−1.55808
$966$	8.36612	−	14.3949i	0.269176	−	0.463147i
$967$		−	32.5204i		−	1.04578i	−0.852399	−	0.522892i	$-0.824853\pi$
$967$		−	32.5204i		−	1.04578i	0.852399	−	0.522892i	$-0.175147\pi$
$968$	10.9376	−	1.17015i	0.351547	−	0.0376101i
$969$	17.1491	+	9.90102i	0.550907	+	0.318067i
$970$	−35.8821	−	20.7165i	−1.15210	−	0.665168i
$971$	−35.8435	+	20.6943i	−1.15027	+	0.664111i	−0.948954	−	0.315415i	$-0.897856\pi$
$971$	−35.8435	+	20.6943i	−1.15027	+	0.664111i	−0.201319	+	0.979526i	$0.564523\pi$
$972$			1.00000i			0.0320750i
$973$	−30.7610	−	53.6349i	−0.986151	−	1.71946i
$974$			36.0737i			1.15587i
$975$	0.519884	−	0.300155i	0.0166496	−	0.00961266i
$976$	0.233713	−	0.404803i	0.00748098	−	0.0129574i
$977$	−7.05105	+	12.2128i	−0.225583	+	0.390721i	−0.956494	−	0.291751i	$-0.905762\pi$
$977$	−7.05105	+	12.2128i	−0.225583	+	0.390721i	0.730911	+	0.682473i	$0.239095\pi$
$978$	4.15686	+	7.19989i	0.132922	+	0.230227i
$979$	−14.2155	−	3.00780i	−0.454331	−	0.0961296i
$980$	−14.0618	−	8.22672i	−0.449189	−	0.262793i
$981$		−	7.13693i		−	0.227865i
$982$	−13.3781	−	23.1715i	−0.426911	−	0.739432i
$983$	38.2844	+	22.1035i	1.22108	+	0.704992i	0.965149	−	0.261703i	$-0.0842840\pi$
$983$	38.2844	+	22.1035i	1.22108	+	0.704992i	0.255933	+	0.966695i	$0.417617\pi$
$984$	−1.70582	+	2.95456i	−0.0543795	+	0.0941880i
$985$	−24.8649	−	43.0673i	−0.792263	−	1.37224i
$986$	−10.5098			−0.334700
$987$	−14.0174	−	24.4408i	−0.446179	−	0.777959i
$988$	8.87339			0.282300
$989$	−10.3136	+	5.95457i	−0.327954	+	0.189344i
$990$	−5.74112	−	5.15967i	−0.182465	−	0.163985i
$991$	−22.7546	+	39.4121i	−0.722824	+	1.25197i	0.237039	+	0.971500i	$0.423823\pi$
$991$	−22.7546	+	39.4121i	−0.722824	+	1.25197i	−0.959863	+	0.280468i	$0.909510\pi$
$992$	−1.54552	−	2.67692i	−0.0490703	−	0.0849923i
$993$			3.91587i			0.124266i
$994$	−7.44009	−	4.32409i	−0.235985	−	0.137152i
$995$	−46.6476			−1.47883
$996$	−3.95020	+	2.28065i	−0.125167	+	0.0722652i
$997$	24.1616	−	41.8491i	0.765205	−	1.32537i	−0.174934	−	0.984580i	$-0.555971\pi$
$997$	24.1616	−	41.8491i	0.765205	−	1.32537i	0.940138	−	0.340793i	$-0.110696\pi$
$998$	−24.3330	−	14.0487i	−0.770249	−	0.444703i
$999$	7.91644	−	4.57056i	0.250465	−	0.144606i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.p.b.241.5	yes	16
3.2	odd	2		1386.2.bk.b.703.4		16
7.3	odd	6		3234.2.e.a.2155.15		16
7.4	even	3		3234.2.e.b.2155.10		16
7.5	odd	6		462.2.p.a.439.1	yes	16
11.10	odd	2		462.2.p.a.241.1	✓	16
21.5	even	6		1386.2.bk.a.901.8		16
33.32	even	2		1386.2.bk.a.703.8		16
77.10	even	6		3234.2.e.b.2155.7		16
77.32	odd	6		3234.2.e.a.2155.2		16
77.54	even	6	inner	462.2.p.b.439.5	yes	16
231.131	odd	6		1386.2.bk.b.901.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.p.a.241.1	✓	16	11.10	odd	2
462.2.p.a.439.1	yes	16	7.5	odd	6
462.2.p.b.241.5	yes	16	1.1	even	1	trivial
462.2.p.b.439.5	yes	16	77.54	even	6	inner
1386.2.bk.a.703.8		16	33.32	even	2
1386.2.bk.a.901.8		16	21.5	even	6
1386.2.bk.b.703.4		16	3.2	odd	2
1386.2.bk.b.901.4		16	231.131	odd	6
3234.2.e.a.2155.2		16	77.32	odd	6
3234.2.e.a.2155.15		16	7.3	odd	6
3234.2.e.b.2155.7		16	77.10	even	6
3234.2.e.b.2155.10		16	7.4	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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.01555 + 1.16368i) q^{5} +1.00000 q^{6} +(1.31629 + 2.29508i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.01555 + 1.16368i) q^{5} +1.00000 q^{6} +(1.31629 + 2.29508i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.16368 + 2.01555i) q^{10} +(2.46679 + 2.21696i) q^{11} +(0.866025 - 0.500000i) q^{12} +1.44095 q^{13} +(2.28748 + 1.32945i) q^{14} -2.32736 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.60782 - 2.78483i) q^{17} +(0.866025 + 0.500000i) q^{18} +(3.07901 + 5.33301i) q^{19} +2.32736i q^{20} +(-0.00760304 + 2.64574i) q^{21} +(3.24479 + 0.686549i) q^{22} +(-3.14645 - 5.44981i) q^{23} +(0.500000 - 0.866025i) q^{24} +(0.208304 - 0.360793i) q^{25} +(1.24790 - 0.720474i) q^{26} +1.00000i q^{27} +(2.64574 + 0.00760304i) q^{28} -3.26833i q^{29} +(-2.01555 + 1.16368i) q^{30} +(2.67692 + 1.54552i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.02783 + 3.15334i) q^{33} -3.21565i q^{34} +(-5.32378 - 3.09412i) q^{35} +1.00000 q^{36} +(-4.57056 - 7.91644i) q^{37} +(5.33301 + 3.07901i) q^{38} +(1.24790 + 0.720474i) q^{39} +(1.16368 + 2.01555i) q^{40} -3.41163 q^{41} +(1.31629 + 2.29508i) q^{42} -1.89247i q^{43} +(3.15334 - 1.02783i) q^{44} +(-2.01555 - 1.16368i) q^{45} +(-5.44981 - 3.14645i) q^{46} +(-9.22249 + 5.32461i) q^{47} -1.00000i q^{48} +(-3.53478 + 6.04196i) q^{49} -0.416608i q^{50} +(2.78483 - 1.60782i) q^{51} +(0.720474 - 1.24790i) q^{52} +(4.60856 - 7.98226i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-7.55179 - 1.59785i) q^{55} +(2.29508 - 1.31629i) q^{56} +6.15803i q^{57} +(-1.63416 - 2.83045i) q^{58} +(-0.461345 - 0.266358i) q^{59} +(-1.16368 + 2.01555i) q^{60} +(0.233713 + 0.404803i) q^{61} +3.09104 q^{62} +(-1.32945 + 2.28748i) q^{63} -1.00000 q^{64} +(-2.90431 + 1.67680i) q^{65} +(2.46679 + 2.21696i) q^{66} +(4.61347 - 7.99077i) q^{67} +(-1.60782 - 2.78483i) q^{68} -6.29290i q^{69} +(-6.15759 - 0.0176950i) q^{70} -3.25253 q^{71} +(0.866025 - 0.500000i) q^{72} +(2.50002 - 4.33016i) q^{73} +(-7.91644 - 4.57056i) q^{74} +(0.360793 - 0.208304i) q^{75} +6.15803 q^{76} +(-1.84110 + 8.57965i) q^{77} +1.44095 q^{78} +(7.21263 - 4.16421i) q^{79} +(2.01555 + 1.16368i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.95456 + 1.70582i) q^{82} -4.56130 q^{83} +(2.28748 + 1.32945i) q^{84} +7.48397i q^{85} +(-0.946236 - 1.63893i) q^{86} +(1.63416 - 2.83045i) q^{87} +(2.21696 - 2.46679i) q^{88} +(-3.79409 + 2.19052i) q^{89} -2.32736 q^{90} +(1.89670 + 3.30709i) q^{91} -6.29290 q^{92} +(1.54552 + 2.67692i) q^{93} +(-5.32461 + 9.22249i) q^{94} +(-12.4118 - 7.16598i) q^{95} +(-0.500000 - 0.866025i) q^{96} +17.8026i q^{97} +(-0.0402313 + 6.99988i) q^{98} +(-0.686549 + 3.24479i) 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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