LMFDB - Embedded newform 507.2.k.e.488.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(80,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 1]))

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

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

chi := DirichletCharacter("507.80");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.k (of order $12$, degree $4$, not 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.56070144.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 $ x^8 - 4x^7 + 16x^6 - 34x^5 + 63x^4 - 74x^3 + 70x^2 - 38*x + 13
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			488.2
Root			$0.500000 - 1.56488i$ of defining polynomial
Character	$\chi$	$=$	507.488
Dual form			507.2.k.e.80.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.389774 + 1.45466i) q^{2} +(-1.60523 + 0.650571i) q^{3} +(-0.232051 + 0.133975i) q^{4} +(1.06488 - 1.06488i) q^{5} +(-1.57203 - 2.08148i) q^{6} +(-1.36603 - 0.366025i) q^{7} +(1.84443 + 1.84443i) q^{8} +(2.15351 - 2.08863i) q^{9} +O(q^{10})$	\(q+(0.389774 + 1.45466i) q^{2} +(-1.60523 + 0.650571i) q^{3} +(-0.232051 + 0.133975i) q^{4} +(1.06488 - 1.06488i) q^{5} +(-1.57203 - 2.08148i) q^{6} +(-1.36603 - 0.366025i) q^{7} +(1.84443 + 1.84443i) q^{8} +(2.15351 - 2.08863i) q^{9} +(1.96410 + 1.13397i) q^{10} +(3.97420 - 1.06488i) q^{11} +(0.285334 - 0.366025i) q^{12} -2.12976i q^{14} +(-1.01660 + 2.40216i) q^{15} +(-2.23205 + 3.86603i) q^{16} +(2.51954 + 4.36397i) q^{17} +(3.87762 + 2.31853i) q^{18} +(1.00000 - 3.73205i) q^{19} +(-0.104440 + 0.389774i) q^{20} +(2.43091 - 0.301143i) q^{21} +(3.09808 + 5.36603i) q^{22} +(-4.16067 - 1.76080i) q^{24} +2.73205i q^{25} +(-2.09808 + 4.75374i) q^{27} +(0.366025 - 0.0980762i) q^{28} +(6.20840 + 3.58442i) q^{29} +(-3.89056 - 0.542499i) q^{30} +(-2.46410 - 2.46410i) q^{31} +(-1.45466 - 0.389774i) q^{32} +(-5.68671 + 4.29488i) q^{33} +(-5.36603 + 5.36603i) q^{34} +(-1.84443 + 1.06488i) q^{35} +(-0.219901 + 0.773185i) q^{36} +(1.40192 + 5.23205i) q^{37} +5.81863 q^{38} +3.92820 q^{40} +(-1.45466 - 5.42885i) q^{41} +(1.38556 + 3.41876i) q^{42} +(-1.90192 + 1.09808i) q^{43} +(-0.779548 + 0.779548i) q^{44} +(0.0690922 - 4.51739i) q^{45} +(-4.25953 - 4.25953i) q^{47} +(1.06782 - 7.65796i) q^{48} +(-4.33013 - 2.50000i) q^{49} +(-3.97420 + 1.06488i) q^{50} +(-6.88351 - 5.36603i) q^{51} -0.779548i q^{53} +(-7.73284 - 1.19909i) q^{54} +(3.09808 - 5.36603i) q^{55} +(-1.84443 - 3.19465i) q^{56} +(0.822738 + 6.64136i) q^{57} +(-2.79423 + 10.4282i) q^{58} +(0.779548 - 2.90931i) q^{59} +(-0.0859264 - 0.693622i) q^{60} +(3.50000 + 6.06218i) q^{61} +(2.62398 - 4.54486i) q^{62} +(-3.70625 + 2.06488i) q^{63} +6.66025i q^{64} +(-8.46410 - 6.59817i) q^{66} +(5.73205 - 1.53590i) q^{67} +(-1.16932 - 0.675108i) q^{68} +(-2.26795 - 2.26795i) q^{70} +(2.90931 + 0.779548i) q^{71} +(7.82434 + 0.119671i) q^{72} +(-0.901924 + 0.901924i) q^{73} +(-7.06440 + 4.07863i) q^{74} +(-1.77739 - 4.38556i) q^{75} +(0.267949 + 1.00000i) q^{76} -5.81863 q^{77} +2.00000 q^{79} +(1.73999 + 6.49373i) q^{80} +(0.275241 - 8.99579i) q^{81} +(7.33013 - 4.23205i) q^{82} +(2.90931 - 2.90931i) q^{83} +(-0.523749 + 0.395560i) q^{84} +(7.33013 + 1.96410i) q^{85} +(-2.33864 - 2.33864i) q^{86} +(-12.2978 - 1.71481i) q^{87} +(9.29423 + 5.36603i) q^{88} +(9.01327 - 2.41510i) q^{89} +(6.59817 - 1.66025i) q^{90} +(5.55852 + 2.35237i) q^{93} +(4.53590 - 7.85641i) q^{94} +(-2.90931 - 5.03908i) q^{95} +(2.58863 - 0.320682i) q^{96} +(-0.437822 + 1.63397i) q^{97} +(1.94887 - 7.27328i) q^{98} +(6.33434 - 10.5939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 12 q^{4} - 14 q^{6} - 4 q^{7} + 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 12 * q^4 - 14 * q^6 - 4 * q^7 + 4 * q^9	$ 8 q - 2 q^{3} + 12 q^{4} - 14 q^{6} - 4 q^{7} + 4 q^{9} - 12 q^{10} - 2 q^{15} - 4 q^{16} + 4 q^{18} + 8 q^{19} + 4 q^{21} + 4 q^{22} - 30 q^{24} + 4 q^{27} - 4 q^{28} - 18 q^{30} + 8 q^{31} - 20 q^{33} - 36 q^{34} + 36 q^{36} + 32 q^{37} - 24 q^{40} - 16 q^{42} - 36 q^{43} + 16 q^{45} - 14 q^{48} - 38 q^{54} + 4 q^{55} + 16 q^{57} + 40 q^{58} + 44 q^{60} + 28 q^{61} + 16 q^{63} - 40 q^{66} + 32 q^{67} - 32 q^{70} + 24 q^{72} - 28 q^{73} - 12 q^{75} + 16 q^{76} + 16 q^{79} + 4 q^{81} + 24 q^{82} - 8 q^{84} + 24 q^{85} - 34 q^{87} + 12 q^{88} + 16 q^{93} + 64 q^{94} + 16 q^{96} - 52 q^{97} + 40 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 + 12 * q^4 - 14 * q^6 - 4 * q^7 + 4 * q^9 - 12 * q^10 - 2 * q^15 - 4 * q^16 + 4 * q^18 + 8 * q^19 + 4 * q^21 + 4 * q^22 - 30 * q^24 + 4 * q^27 - 4 * q^28 - 18 * q^30 + 8 * q^31 - 20 * q^33 - 36 * q^34 + 36 * q^36 + 32 * q^37 - 24 * q^40 - 16 * q^42 - 36 * q^43 + 16 * q^45 - 14 * q^48 - 38 * q^54 + 4 * q^55 + 16 * q^57 + 40 * q^58 + 44 * q^60 + 28 * q^61 + 16 * q^63 - 40 * q^66 + 32 * q^67 - 32 * q^70 + 24 * q^72 - 28 * q^73 - 12 * q^75 + 16 * q^76 + 16 * q^79 + 4 * q^81 + 24 * q^82 - 8 * q^84 + 24 * q^85 - 34 * q^87 + 12 * q^88 + 16 * q^93 + 64 * q^94 + 16 * q^96 - 52 * q^97 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{11}{12}\right)$

Coefficient data

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

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

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

$2$	0.389774	+	1.45466i	0.275612	+	1.02860i	0.955430	+	0.295217i	$0.0953919\pi$
$2$	0.389774	+	1.45466i	0.275612	+	1.02860i	−0.679818	+	0.733380i	$0.737941\pi$
$3$	−1.60523	+	0.650571i	−0.926779	+	0.375608i
$3$	−1.60523	+	0.650571i	−0.926779	+	0.375608i
$4$	−0.232051	+	0.133975i	−0.116025	+	0.0669873i
$5$	1.06488	−	1.06488i	0.476230	−	0.476230i	−0.427694	−	0.903924i	$-0.640674\pi$
$5$	1.06488	−	1.06488i	0.476230	−	0.476230i	0.903924	+	0.427694i	$0.140674\pi$
$6$	−1.57203	−	2.08148i	−0.641780	−	0.849760i
$7$	−1.36603	−	0.366025i	−0.516309	−	0.138345i	−0.00875026	−	0.999962i	$-0.502785\pi$
$7$	−1.36603	−	0.366025i	−0.516309	−	0.138345i	−0.507559	+	0.861617i	$0.669452\pi$
$8$	1.84443	+	1.84443i	0.652105	+	0.652105i
$9$	2.15351	−	2.08863i	0.717838	−	0.696210i
$10$	1.96410	+	1.13397i	0.621103	+	0.358594i
$11$	3.97420	−	1.06488i	1.19826	−	0.321074i	0.396117	−	0.918200i	$-0.370357\pi$
$11$	3.97420	−	1.06488i	1.19826	−	0.321074i	0.802148	+	0.597126i	$0.203691\pi$
$12$	0.285334	−	0.366025i	0.0823689	−	0.105662i
$13$		0			0
$13$		0			0
$14$		−	2.12976i		−	0.569204i
$15$	−1.01660	+	2.40216i	−0.262484	+	0.620235i
$16$	−2.23205	+	3.86603i	−0.558013	+	0.966506i
$17$	2.51954	+	4.36397i	0.611078	+	1.05842i	0.991059	+	0.133424i	$0.0425971\pi$
$17$	2.51954	+	4.36397i	0.611078	+	1.05842i	−0.379981	+	0.924994i	$0.624070\pi$
$18$	3.87762	+	2.31853i	0.913965	+	0.546482i
$19$	1.00000	−	3.73205i	0.229416	−	0.856191i	−0.751171	−	0.660107i	$-0.770511\pi$
$19$	1.00000	−	3.73205i	0.229416	−	0.856191i	0.980587	−	0.196084i	$-0.0628225\pi$
$20$	−0.104440	+	0.389774i	−0.0233534	+	0.0871561i
$21$	2.43091	−	0.301143i	0.530468	−	0.0657148i
$22$	3.09808	+	5.36603i	0.660512	+	1.14404i
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	−4.16067	−	1.76080i	−0.849292	−	0.359421i
$25$			2.73205i			0.546410i
$26$		0			0
$27$	−2.09808	+	4.75374i	−0.403775	+	0.914858i
$28$	0.366025	−	0.0980762i	0.0691723	−	0.0185347i
$29$	6.20840	+	3.58442i	1.15287	+	0.665610i	0.949585	−	0.313509i	$-0.101505\pi$
$29$	6.20840	+	3.58442i	1.15287	+	0.665610i	0.203286	+	0.979119i	$0.434838\pi$
$30$	−3.89056	−	0.542499i	−0.710316	−	0.0990463i
$31$	−2.46410	−	2.46410i	−0.442566	−	0.442566i	0.450308	−	0.892873i	$-0.351314\pi$
$31$	−2.46410	−	2.46410i	−0.442566	−	0.442566i	−0.892873	+	0.450308i	$0.851314\pi$
$32$	−1.45466	−	0.389774i	−0.257149	−	0.0689030i
$33$	−5.68671	+	4.29488i	−0.989929	+	0.747642i
$34$	−5.36603	+	5.36603i	−0.920266	+	0.920266i
$35$	−1.84443	+	1.06488i	−0.311766	+	0.179998i
$36$	−0.219901	+	0.773185i	−0.0366502	+	0.128864i
$37$	1.40192	+	5.23205i	0.230475	+	0.860144i	0.980137	+	0.198323i	$0.0635495\pi$
$37$	1.40192	+	5.23205i	0.230475	+	0.860144i	−0.749662	+	0.661821i	$0.769784\pi$
$38$	5.81863			0.943906
$39$		0			0
$40$	3.92820			0.621103
$41$	−1.45466	−	5.42885i	−0.227179	−	0.847844i	−0.981520	−	0.191361i	$-0.938710\pi$
$41$	−1.45466	−	5.42885i	−0.227179	−	0.847844i	0.754341	−	0.656483i	$-0.227957\pi$
$42$	1.38556	+	3.41876i	0.213797	+	0.527526i
$43$	−1.90192	+	1.09808i	−0.290041	+	0.167455i	−0.637960	−	0.770069i	$-0.720222\pi$
$43$	−1.90192	+	1.09808i	−0.290041	+	0.167455i	0.347920	+	0.937524i	$0.386888\pi$
$44$	−0.779548	+	0.779548i	−0.117521	+	0.117521i
$45$	0.0690922	−	4.51739i	0.0102997	−	0.673412i
$46$		0			0
$47$	−4.25953	−	4.25953i	−0.621316	−	0.621316i	0.324552	−	0.945868i	$-0.394787\pi$
$47$	−4.25953	−	4.25953i	−0.621316	−	0.621316i	−0.945868	+	0.324552i	$0.894787\pi$
$48$	1.06782	−	7.65796i	0.154127	−	1.10533i
$49$	−4.33013	−	2.50000i	−0.618590	−	0.357143i
$50$	−3.97420	+	1.06488i	−0.562036	+	0.150597i
$51$	−6.88351	−	5.36603i	−0.963884	−	0.751394i
$52$		0			0
$53$		−	0.779548i		−	0.107079i	−0.998566	−	0.0535396i	$-0.982950\pi$
$53$		−	0.779548i		−	0.107079i	0.998566	−	0.0535396i	$-0.0170503\pi$
$54$	−7.73284	−	1.19909i	−1.05231	−	0.163176i
$55$	3.09808	−	5.36603i	0.417745	−	0.723555i
$56$	−1.84443	−	3.19465i	−0.246472	−	0.426903i
$57$	0.822738	+	6.64136i	0.108974	+	0.879670i
$58$	−2.79423	+	10.4282i	−0.366900	+	1.36929i
$59$	0.779548	−	2.90931i	0.101489	−	0.378760i	−0.896435	−	0.443176i	$-0.853852\pi$
$59$	0.779548	−	2.90931i	0.101489	−	0.378760i	0.997923	+	0.0644157i	$0.0205184\pi$
$60$	−0.0859264	−	0.693622i	−0.0110931	−	0.0895462i
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	0.998264	−	0.0588933i	$-0.0187572\pi$
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	−0.550135	+	0.835076i	$0.685424\pi$
$62$	2.62398	−	4.54486i	0.333246	−	0.577198i
$63$	−3.70625	+	2.06488i	−0.466943	+	0.260151i
$64$			6.66025i			0.832532i
$65$		0			0
$66$	−8.46410	−	6.59817i	−1.04186	−	0.812179i
$67$	5.73205	−	1.53590i	0.700281	−	0.187640i	0.108925	−	0.994050i	$-0.465259\pi$
$67$	5.73205	−	1.53590i	0.700281	−	0.187640i	0.591357	+	0.806410i	$0.298593\pi$
$68$	−1.16932	−	0.675108i	−0.141801	−	0.0818689i
$69$		0			0
$70$	−2.26795	−	2.26795i	−0.271072	−	0.271072i
$71$	2.90931	+	0.779548i	0.345272	+	0.0925153i	0.427288	−	0.904116i	$-0.359469\pi$
$71$	2.90931	+	0.779548i	0.345272	+	0.0925153i	−0.0820158	+	0.996631i	$0.526136\pi$
$72$	7.82434	+	0.119671i	0.922107	+	0.0141034i
$73$	−0.901924	+	0.901924i	−0.105562	+	0.105562i	−0.757915	−	0.652353i	$-0.773782\pi$
$73$	−0.901924	+	0.901924i	−0.105562	+	0.105562i	0.652353	+	0.757915i	$0.273782\pi$
$74$	−7.06440	+	4.07863i	−0.821220	+	0.474132i
$75$	−1.77739	−	4.38556i	−0.205236	−	0.506401i
$76$	0.267949	+	1.00000i	0.0307359	+	0.114708i
$77$	−5.81863			−0.663094
$78$		0			0
$79$	2.00000			0.225018			0.112509	−	0.993651i	$-0.464111\pi$
$79$	2.00000			0.225018			0.112509	+	0.993651i	$0.464111\pi$
$80$	1.73999	+	6.49373i	0.194537	+	0.726022i
$81$	0.275241	−	8.99579i	0.0305823	−	0.999532i
$82$	7.33013	−	4.23205i	0.809477	−	0.467352i
$83$	2.90931	−	2.90931i	0.319339	−	0.319339i	−0.529174	−	0.848513i	$-0.677498\pi$
$83$	2.90931	−	2.90931i	0.319339	−	0.319339i	0.848513	+	0.529174i	$0.177498\pi$
$84$	−0.523749	+	0.395560i	−0.0571457	+	0.0431592i
$85$	7.33013	+	1.96410i	0.795064	+	0.213037i
$86$	−2.33864	−	2.33864i	−0.252182	−	0.252182i
$87$	−12.2978	−	1.71481i	−1.31846	−	0.183846i
$88$	9.29423	+	5.36603i	0.990768	+	0.572020i
$89$	9.01327	−	2.41510i	0.955405	−	0.256000i	0.252751	−	0.967531i	$-0.418665\pi$
$89$	9.01327	−	2.41510i	0.955405	−	0.256000i	0.702654	+	0.711531i	$0.251998\pi$
$90$	6.59817	−	1.66025i	0.695509	−	0.175006i
$91$		0			0
$92$		0			0
$93$	5.55852	+	2.35237i	0.576392	+	0.243929i
$94$	4.53590	−	7.85641i	0.467842	−	0.810326i
$95$	−2.90931	−	5.03908i	−0.298489	−	0.516998i
$96$	2.58863	−	0.320682i	0.264201	−	0.0327295i
$97$	−0.437822	+	1.63397i	−0.0444541	+	0.165905i	−0.984584	−	0.174910i	$-0.944036\pi$
$97$	−0.437822	+	1.63397i	−0.0444541	+	0.165905i	0.940130	+	0.340815i	$0.110703\pi$
$98$	1.94887	−	7.27328i	0.196866	−	0.734712i
$99$	6.33434	−	10.5939i	0.636625	−	1.06472i
$100$	−0.366025	−	0.633975i	−0.0366025	−	0.0633975i
$101$	−3.01375	+	5.21997i	−0.299880	+	0.519407i	−0.976108	−	0.217285i	$-0.930280\pi$
$101$	−3.01375	+	5.21997i	−0.299880	+	0.519407i	0.676229	+	0.736692i	$0.263613\pi$
$102$	5.12271	−	12.1047i	0.507224	−	1.19854i
$103$		−	6.92820i		−	0.682656i	−0.939944	−	0.341328i	$-0.889123\pi$
$103$		−	6.92820i		−	0.682656i	0.939944	−	0.341328i	$-0.110877\pi$
$104$		0			0
$105$	2.26795	−	2.90931i	0.221329	−	0.283920i
$106$	1.13397	−	0.303848i	0.110141	−	0.0295123i
$107$	−16.4675	−	9.50749i	−1.59197	−	0.919123i	−0.992969	−	0.118374i	$-0.962232\pi$
$107$	−16.4675	−	9.50749i	−1.59197	−	0.919123i	−0.598999	−	0.800749i	$-0.704435\pi$
$108$	−0.150021	−	1.38420i	−0.0144357	−	0.133195i
$109$	−13.1962	−	13.1962i	−1.26396	−	1.26396i	−0.949156	−	0.314806i	$-0.898060\pi$
$109$	−13.1962	−	13.1962i	−1.26396	−	1.26396i	−0.314806	−	0.949156i	$-0.601940\pi$
$110$	9.01327	+	2.41510i	0.859382	+	0.230271i
$111$	−5.65423	−	7.48658i	−0.536676	−	0.710595i
$112$	4.46410	−	4.46410i	0.421818	−	0.421818i
$113$	8.90883	−	5.14352i	0.838073	−	0.483861i	−0.0185360	−	0.999828i	$-0.505901\pi$
$113$	8.90883	−	5.14352i	0.838073	−	0.483861i	0.856609	+	0.515967i	$0.172567\pi$
$114$	−9.34022	+	3.78543i	−0.874792	+	0.354538i
$115$		0			0
$116$	−1.92089			−0.178350
$117$		0			0
$118$	4.53590			0.417563
$119$	−1.84443	−	6.88351i	−0.169079	−	0.631010i
$120$	−6.30566	+	2.55558i	−0.575626	+	0.233291i
$121$	5.13397	−	2.96410i	0.466725	−	0.269464i
$122$	−7.45418	+	7.45418i	−0.674869	+	0.674869i
$123$	5.86691	+	7.76819i	0.529002	+	0.700434i
$124$	0.901924	+	0.241670i	0.0809951	+	0.0217026i
$125$	8.23373	+	8.23373i	0.736447	+	0.736447i
$126$	−4.44829	−	4.58648i	−0.396285	−	0.408596i
$127$	−7.90192	−	4.56218i	−0.701182	−	0.404828i	0.106605	−	0.994301i	$-0.466002\pi$
$127$	−7.90192	−	4.56218i	−0.701182	−	0.404828i	−0.807788	+	0.589474i	$0.799335\pi$
$128$	−12.5977	+	3.37554i	−1.11349	+	0.298359i
$129$	2.33864	−	3.00000i	0.205906	−	0.264135i
$130$		0			0
$131$			7.94839i			0.694454i	0.937781	+	0.347227i	$0.112877\pi$
$131$			7.94839i			0.694454i	−0.937781	+	0.347227i	$0.887123\pi$
$132$	0.744201	−	1.75850i	0.0647743	−	0.153058i
$133$	−2.73205	+	4.73205i	−0.236899	+	0.410321i
$134$	4.46841	+	7.73951i	0.386012	+	0.668592i
$135$	2.82797	+	7.29638i	0.243393	+	0.627973i
$136$	−3.40192	+	12.6962i	−0.291713	+	1.08869i
$137$	−1.73999	+	6.49373i	−0.148657	+	0.554797i	0.850908	+	0.525315i	$0.176052\pi$
$137$	−1.73999	+	6.49373i	−0.148657	+	0.554797i	−0.999565	+	0.0294822i	$0.990614\pi$
$138$		0			0
$139$	−9.19615	−	15.9282i	−0.780007	−	1.35101i	−0.931937	−	0.362621i	$-0.881882\pi$
$139$	−9.19615	−	15.9282i	−0.780007	−	1.35101i	0.151929	−	0.988391i	$-0.451451\pi$
$140$	0.285334	−	0.494214i	0.0241152	−	0.0417687i
$141$	9.60864	+	4.06639i	0.809194	+	0.342452i
$142$			4.53590i			0.380644i
$143$		0			0
$144$	3.26795	+	12.9875i	0.272329	+	1.08229i
$145$	10.4282	−	2.79423i	0.866015	−	0.232048i
$146$	−1.66354	−	0.960443i	−0.137675	−	0.0794868i
$147$	8.57727	+	1.19601i	0.707441	+	0.0986455i
$148$	−1.02628	−	1.02628i	−0.0843597	−	0.0843597i
$149$	−8.33816	−	2.23420i	−0.683089	−	0.183033i	−0.0994454	−	0.995043i	$-0.531707\pi$
$149$	−8.33816	−	2.23420i	−0.683089	−	0.183033i	−0.583644	+	0.812010i	$0.698374\pi$
$150$	5.68671	−	4.29488i	0.464318	−	0.350675i
$151$	0.535898	−	0.535898i	0.0436108	−	0.0436108i	−0.684965	−	0.728576i	$-0.740183\pi$
$151$	0.535898	−	0.535898i	0.0436108	−	0.0436108i	0.728576	+	0.684965i	$0.240183\pi$
$152$	8.72794	−	5.03908i	0.707929	−	0.408723i
$153$	14.5406	+	4.13548i	1.17554	+	0.334334i
$154$	−2.26795	−	8.46410i	−0.182757	−	0.682057i
$155$	−5.24796			−0.421526
$156$		0			0
$157$	−4.80385			−0.383389			−0.191694	−	0.981455i	$-0.561398\pi$
$157$	−4.80385			−0.383389			−0.191694	+	0.981455i	$0.561398\pi$
$158$	0.779548	+	2.90931i	0.0620175	+	0.231453i
$159$	0.507152	+	1.25135i	0.0402197	+	0.0992387i
$160$	−1.96410	+	1.13397i	−0.155276	+	0.0896486i
$161$		0			0
$162$	13.1931	−	3.10594i	1.03655	−	0.244026i
$163$	4.00000	+	1.07180i	0.313304	+	0.0839496i	0.412045	−	0.911164i	$-0.364815\pi$
$163$	4.00000	+	1.07180i	0.313304	+	0.0839496i	−0.0987406	+	0.995113i	$0.531481\pi$
$164$	1.06488	+	1.06488i	0.0831533	+	0.0831533i
$165$	−1.48214	+	10.6292i	−0.115384	+	0.827483i
$166$	5.36603	+	3.09808i	0.416484	+	0.240457i
$167$	−12.9875	+	3.47998i	−1.00500	+	0.269289i	−0.723539	−	0.690283i	$-0.757486\pi$
$167$	−12.9875	+	3.47998i	−1.00500	+	0.269289i	−0.281461	+	0.959573i	$0.590819\pi$
$168$	5.03908	+	3.92820i	0.388773	+	0.303067i
$169$		0			0
$170$			11.4284i			0.876516i
$171$	−5.64136	−	10.1257i	−0.431406	−	0.774328i
$172$	0.294229	−	0.509619i	0.0224347	−	0.0388581i
$173$	−8.72794	−	15.1172i	−0.663573	−	1.14934i	−0.979670	−	0.200615i	$-0.935706\pi$
$173$	−8.72794	−	15.1172i	−0.663573	−	1.14934i	0.316097	−	0.948727i	$-0.397627\pi$
$174$	−2.29892	−	18.5575i	−0.174281	−	1.40684i
$175$	1.00000	−	3.73205i	0.0755929	−	0.282117i
$176$	−4.75374	+	17.7412i	−0.358327	+	1.33729i
$177$	0.641364	+	5.17726i	0.0482078	+	0.389147i
$178$	7.02628	+	12.1699i	0.526642	+	0.912171i
$179$	−13.2728	+	22.9892i	−0.992056	+	1.71829i	−0.387084	+	0.922045i	$0.626518\pi$
$179$	−13.2728	+	22.9892i	−0.992056	+	1.71829i	−0.604972	+	0.796247i	$0.706816\pi$
$180$	0.589182	+	1.05752i	0.0439150	+	0.0788228i
$181$		−	3.00000i		−	0.222988i	−0.993765	−	0.111494i	$-0.964436\pi$
$181$		−	3.00000i		−	0.222988i	0.993765	−	0.111494i	$-0.0355636\pi$
$182$		0			0
$183$	−9.56218	−	7.45418i	−0.706857	−	0.551029i
$184$		0			0
$185$	7.06440	+	4.07863i	0.519385	+	0.299867i
$186$	−1.25532	+	9.00263i	−0.0920449	+	0.660105i
$187$	14.6603	+	14.6603i	1.07206	+	1.07206i
$188$	1.55910	+	0.417759i	0.113709	+	0.0304682i
$189$	4.60602	−	5.72579i	0.335038	−	0.416490i
$190$	6.19615	−	6.19615i	0.449516	−	0.449516i
$191$	−4.18307	+	2.41510i	−0.302677	+	0.174750i	−0.643645	−	0.765324i	$-0.722579\pi$
$191$	−4.18307	+	2.41510i	−0.302677	+	0.174750i	0.340968	+	0.940075i	$0.389245\pi$
$192$	−4.33297	−	10.6912i	−0.312705	−	0.771573i
$193$	−0.0358984	−	0.133975i	−0.00258402	−	0.00964370i	0.964622	−	0.263638i	$-0.0849223\pi$
$193$	−0.0358984	−	0.133975i	−0.00258402	−	0.00964370i	−0.967206	+	0.253994i	$0.918256\pi$
$194$	−2.54752			−0.182902
$195$		0			0
$196$	1.33975			0.0956961
$197$	1.06488	+	3.97420i	0.0758697	+	0.283150i	0.993429	−	0.114449i	$-0.0365103\pi$
$197$	1.06488	+	3.97420i	0.0758697	+	0.283150i	−0.917559	+	0.397599i	$0.869844\pi$
$198$	17.8794	+	5.08507i	1.27063	+	0.361380i
$199$	−11.1962	+	6.46410i	−0.793674	+	0.458228i	−0.841254	−	0.540639i	$-0.818182\pi$
$199$	−11.1962	+	6.46410i	−0.793674	+	0.458228i	0.0475802	+	0.998867i	$0.484849\pi$
$200$	−5.03908	+	5.03908i	−0.356317	+	0.356317i
$201$	−8.20204	+	6.19458i	−0.578527	+	0.436932i
$202$	−8.76795	−	2.34936i	−0.616911	−	0.165301i
$203$	−7.16884	−	7.16884i	−0.503154	−	0.503154i
$204$	2.31623	+	0.322975i	0.162169	+	0.0226128i
$205$	−7.33013	−	4.23205i	−0.511958	−	0.295579i
$206$	10.0782	−	2.70043i	0.702178	−	0.188148i
$207$		0			0
$208$		0			0
$209$		−	15.8968i		−	1.09960i
$210$	5.11604	+	2.16511i	0.353040	+	0.149407i
$211$	0.901924	−	1.56218i	0.0620910	−	0.107545i	−0.833309	−	0.552808i	$-0.813556\pi$
$211$	0.901924	−	1.56218i	0.0620910	−	0.107545i	0.895400	+	0.445263i	$0.146890\pi$
$212$	0.104440	+	0.180895i	0.00717294	+	0.0124239i
$213$	−5.17726	+	0.641364i	−0.354740	+	0.0439455i
$214$	7.41154	−	27.6603i	0.506643	−	1.89082i
$215$	−0.856003	+	3.19465i	−0.0583789	+	0.217873i
$216$	−12.6377	+	4.89819i	−0.859887	+	0.333280i
$217$	2.46410	+	4.26795i	0.167274	+	0.289727i
$218$	14.0524	−	24.3394i	0.951745	−	1.64847i
$219$	0.861027	−	2.03456i	0.0581828	−	0.137483i
$220$			1.66025i			0.111934i
$221$		0			0
$222$	8.68653	−	11.1430i	0.583002	−	0.747872i
$223$	−25.0263	+	6.70577i	−1.67588	+	0.449052i	−0.966687	−	0.255960i	$-0.917609\pi$
$223$	−25.0263	+	6.70577i	−1.67588	+	0.449052i	−0.709196	+	0.705011i	$0.750942\pi$
$224$	1.84443	+	1.06488i	0.123236	+	0.0711505i
$225$	5.70625	+	5.88351i	0.380416	+	0.392234i
$226$	10.9545	+	10.9545i	0.728681	+	0.728681i
$227$	−19.5856	−	5.24796i	−1.29994	−	0.348319i	−0.458515	−	0.888686i	$-0.651619\pi$
$227$	−19.5856	−	5.24796i	−1.29994	−	0.348319i	−0.841429	+	0.540367i	$0.818285\pi$
$228$	−1.08069	−	1.43091i	−0.0715705	−	0.0947642i
$229$	−14.1244	+	14.1244i	−0.933364	+	0.933364i	−0.997914	−	0.0645507i	$-0.979439\pi$
$229$	−14.1244	+	14.1244i	−0.933364	+	0.933364i	0.0645507	+	0.997914i	$0.479439\pi$
$230$		0			0
$231$	9.34022	−	3.78543i	0.614541	−	0.249063i
$232$	4.83975	+	18.0622i	0.317745	+	1.18584i
$233$	17.4559			1.14357			0.571786	−	0.820403i	$-0.306251\pi$
$233$	17.4559			1.14357			0.571786	+	0.820403i	$0.306251\pi$
$234$		0			0
$235$	−9.07180			−0.591779
$236$	0.208879	+	0.779548i	0.0135969	+	0.0507443i
$237$	−3.21046	+	1.30114i	−0.208542	+	0.0845183i
$238$	9.29423	−	5.36603i	0.602455	−	0.347828i
$239$	6.59817	−	6.59817i	0.426800	−	0.426800i	−0.460737	−	0.887537i	$-0.652415\pi$
$239$	6.59817	−	6.59817i	0.426800	−	0.426800i	0.887537	+	0.460737i	$0.152415\pi$
$240$	−7.01772	−	9.29194i	−0.452992	−	0.599792i
$241$	−14.0622	−	3.76795i	−0.905825	−	0.242715i	−0.224309	−	0.974518i	$-0.572012\pi$
$241$	−14.0622	−	3.76795i	−0.905825	−	0.242715i	−0.681516	+	0.731803i	$0.738679\pi$
$242$	6.31284	+	6.31284i	0.405805	+	0.405805i
$243$	5.41058	+	14.6194i	0.347089	+	0.937832i
$244$	−1.62436	−	0.937822i	−0.103989	−	0.0600379i
$245$	−7.27328	+	1.94887i	−0.464673	+	0.124509i
$246$	−9.01327	+	11.5622i	−0.574665	+	0.737178i
$247$		0			0
$248$		−	9.08973i		−	0.577198i
$249$	−2.77739	+	6.56283i	−0.176010	+	0.415902i
$250$	−8.76795	+	15.1865i	−0.554534	+	0.960481i
$251$	0.494214	+	0.856003i	0.0311945	+	0.0540304i	0.881201	−	0.472741i	$-0.156736\pi$
$251$	0.494214	+	0.856003i	0.0311945	+	0.0540304i	−0.850007	+	0.526772i	$0.823402\pi$
$252$	0.583396	−	0.975700i	0.0367505	−	0.0614634i
$253$		0			0
$254$	3.55644	−	13.2728i	0.223151	−	0.832810i
$255$	−13.0443	+	1.61594i	−0.816867	+	0.101194i
$256$	−3.16025	−	5.47372i	−0.197516	−	0.342108i
$257$	10.7533	−	18.6252i	0.670770	−	1.16181i	−0.306916	−	0.951737i	$-0.599297\pi$
$257$	10.7533	−	18.6252i	0.670770	−	1.16181i	0.977686	−	0.210071i	$-0.0673696\pi$
$258$	5.27551	+	2.23260i	0.328439	+	0.138996i
$259$		−	7.66025i		−	0.475985i
$260$		0			0
$261$	20.8564	−	5.24796i	1.29098	−	0.324840i
$262$	−11.5622	+	3.09808i	−0.714314	+	0.191400i
$263$	19.3003	+	11.1430i	1.19011	+	0.687109i	0.958331	−	0.285660i	$-0.0922127\pi$
$263$	19.3003	+	11.1430i	1.19011	+	0.687109i	0.231777	+	0.972769i	$0.425546\pi$
$264$	−18.4103	−	2.56713i	−1.13308	−	0.157996i
$265$	−0.830127	−	0.830127i	−0.0509943	−	0.0509943i
$266$	−7.94839	−	2.12976i	−0.487347	−	0.130584i
$267$	−12.8972	+	9.74056i	−0.789294	+	0.596113i
$268$	−1.12436	+	1.12436i	−0.0686810	+	0.0686810i
$269$	12.4168	−	7.16884i	0.757066	−	0.437092i	−0.0711756	−	0.997464i	$-0.522675\pi$
$269$	12.4168	−	7.16884i	0.757066	−	0.437092i	0.828241	+	0.560372i	$0.189342\pi$
$270$	−9.51146	+	6.95767i	−0.578849	+	0.423430i
$271$	−2.00000	−	7.46410i	−0.121491	−	0.453412i	0.878199	−	0.478295i	$-0.158745\pi$
$271$	−2.00000	−	7.46410i	−0.121491	−	0.453412i	−0.999690	+	0.0248835i	$0.992079\pi$
$272$	−22.4950			−1.36396
$273$		0			0
$274$	−10.1244			−0.611635
$275$	2.90931	+	10.8577i	0.175438	+	0.654744i
$276$		0			0
$277$	−23.8923	+	13.7942i	−1.43555	+	0.828815i	−0.997536	−	0.0701536i	$-0.977651\pi$
$277$	−23.8923	+	13.7942i	−1.43555	+	0.828815i	−0.438013	+	0.898969i	$0.644318\pi$
$278$	19.5856	−	19.5856i	1.17467	−	1.17467i
$279$	−10.4531	−	0.159877i	−0.625809	−	0.00957158i
$280$	−5.36603	−	1.43782i	−0.320681	−	0.0859263i
$281$	−12.1315	−	12.1315i	−0.723703	−	0.723703i	0.245655	−	0.969357i	$-0.420997\pi$
$281$	−12.1315	−	12.1315i	−0.723703	−	0.723703i	−0.969357	+	0.245655i	$0.920997\pi$
$282$	−2.17000	+	15.5622i	−0.129221	+	0.926718i
$283$	5.70577	+	3.29423i	0.339173	+	0.195822i	0.659906	−	0.751348i	$-0.270596\pi$
$283$	5.70577	+	3.29423i	0.339173	+	0.195822i	−0.320733	+	0.947170i	$0.603929\pi$
$284$	−0.779548	+	0.208879i	−0.0462577	+	0.0123947i
$285$	7.94839	+	6.19615i	0.470822	+	0.367028i
$286$		0			0
$287$			7.94839i			0.469179i
$288$	−3.94672	+	2.19886i	−0.232562	+	0.129569i
$289$	−4.19615	+	7.26795i	−0.246832	+	0.427526i
$290$	8.12929	+	14.0803i	0.477368	+	0.826826i
$291$	−0.360213	−	2.90774i	−0.0211161	−	0.170455i
$292$	0.0884573	−	0.330127i	0.00517657	−	0.0193192i
$293$	0.466229	−	1.73999i	0.0272374	−	0.101651i	−0.950969	−	0.309286i	$-0.899910\pi$
$293$	0.466229	−	1.73999i	0.0272374	−	0.101651i	0.978206	+	0.207635i	$0.0665766\pi$
$294$	1.60341	+	12.9432i	0.0935127	+	0.754860i
$295$	−2.26795	−	3.92820i	−0.132045	−	0.228709i
$296$	−7.06440	+	12.2359i	−0.410610	+	0.711198i
$297$	−3.27599	+	21.1265i	−0.190092	+	1.22588i
$298$		−	13.0000i		−	0.753070i
$299$		0			0
$300$	1.00000	+	0.779548i	0.0577350	+	0.0450072i
$301$	3.00000	−	0.803848i	0.172917	−	0.0463330i
$302$	0.988427	+	0.570669i	0.0568776	+	0.0328383i
$303$	1.44179	−	10.3399i	0.0828289	−	0.594012i
$304$	12.1962	+	12.1962i	0.699497	+	0.699497i
$305$	10.1826	+	2.72842i	0.583054	+	0.156229i
$306$	−0.348161	+	22.7635i	−0.0199030	+	1.30130i
$307$	8.39230	−	8.39230i	0.478974	−	0.478974i	−0.425829	−	0.904803i	$-0.640018\pi$
$307$	8.39230	−	8.39230i	0.478974	−	0.478974i	0.904803	+	0.425829i	$0.140018\pi$
$308$	1.35022	−	0.779548i	0.0769357	−	0.0444189i
$309$	4.50729	+	11.1213i	0.256411	+	0.632671i
$310$	−2.04552	−	7.63397i	−0.116178	−	0.433581i
$311$	10.0782			0.571480			0.285740	−	0.958307i	$-0.407761\pi$
$311$	10.0782			0.571480			0.285740	+	0.958307i	$0.407761\pi$
$312$		0			0
$313$	2.00000			0.113047			0.0565233	−	0.998401i	$-0.481998\pi$
$313$	2.00000			0.113047			0.0565233	+	0.998401i	$0.481998\pi$
$314$	−1.87241	−	6.98795i	−0.105666	−	0.394353i
$315$	−1.74786	+	6.14557i	−0.0984807	+	0.346264i
$316$	−0.464102	+	0.267949i	−0.0261078	+	0.0150733i
$317$	−11.3519	+	11.3519i	−0.637587	+	0.637587i	−0.949960	−	0.312373i	$-0.898876\pi$
$317$	−11.3519	+	11.3519i	−0.637587	+	0.637587i	0.312373	+	0.949960i	$0.398876\pi$
$318$	−1.62261	+	1.22548i	−0.0909916	+	0.0687213i
$319$	28.4904	+	7.63397i	1.59516	+	0.427421i
$320$	7.09239	+	7.09239i	0.396477	+	0.396477i
$321$	32.6193	+	4.54843i	1.82063	+	0.253869i
$322$		0			0
$323$	18.8061	−	5.03908i	1.04640	−	0.280382i
$324$	1.14134	+	2.12436i	0.0634076	+	0.118020i
$325$		0			0
$326$			6.23638i			0.345401i
$327$	29.7679	+	12.5978i	1.64617	+	0.696659i
$328$	7.33013	−	12.6962i	0.404739	−	0.701028i
$329$	4.25953	+	7.37772i	0.234835	+	0.406747i
$330$	−16.0396	+	1.98699i	−0.882948	+	0.109380i
$331$	8.85641	−	33.0526i	0.486792	−	1.81673i	−0.0850595	−	0.996376i	$-0.527108\pi$
$331$	8.85641	−	33.0526i	0.486792	−	1.81673i	0.571852	−	0.820357i	$-0.306225\pi$
$332$	−0.285334	+	1.06488i	−0.0156598	+	0.0584430i
$333$	13.9469	+	8.33919i	0.764285	+	0.456985i
$334$	−10.1244	−	17.5359i	−0.553980	−	0.959522i
$335$	4.46841	−	7.73951i	0.244135	−	0.422855i
$336$	−4.26168	+	10.0701i	−0.232494	+	0.549370i
$337$			18.4641i			1.00580i	0.864344	+	0.502902i	$0.167734\pi$
$337$			18.4641i			1.00580i	−0.864344	+	0.502902i	$0.832266\pi$
$338$		0			0
$339$	−10.9545	+	14.0524i	−0.594966	+	0.763219i
$340$	−1.96410	+	0.526279i	−0.106518	+	0.0285415i
$341$	−12.4168	−	7.16884i	−0.672407	−	0.388215i
$342$	12.5305	−	12.1530i	0.677571	−	0.657157i
$343$	12.0000	+	12.0000i	0.647939	+	0.647939i
$344$	−5.53329	−	1.48264i	−0.298335	−	0.0799386i
$345$		0			0
$346$	18.5885	−	18.5885i	0.999322	−	0.999322i
$347$	−17.8177	+	10.2870i	−0.956502	+	0.552237i	−0.895095	−	0.445876i	$-0.852892\pi$
$347$	−17.8177	+	10.2870i	−0.956502	+	0.552237i	−0.0614076	+	0.998113i	$0.519559\pi$
$348$	3.08346	−	1.24967i	0.165291	−	0.0669895i
$349$	−7.36603	−	27.4904i	−0.394294	−	1.47153i	−0.822979	−	0.568072i	$-0.807689\pi$
$349$	−7.36603	−	27.4904i	−0.394294	−	1.47153i	0.428684	−	0.903454i	$-0.358977\pi$
$350$	5.81863			0.311019
$351$		0			0
$352$	−6.19615			−0.330256
$353$	−3.66088	−	13.6626i	−0.194849	−	0.727186i	−0.992306	−	0.123810i	$-0.960489\pi$
$353$	−3.66088	−	13.6626i	−0.194849	−	0.727186i	0.797457	−	0.603376i	$-0.206178\pi$
$354$	−7.28115	+	2.95093i	−0.386989	+	0.156840i
$355$	3.92820	−	2.26795i	0.208487	−	0.120370i
$356$	−1.76798	+	1.76798i	−0.0937025	+	0.0937025i
$357$	7.43895	+	9.84967i	0.393711	+	0.521300i
$358$	−38.6147	−	10.3468i	−2.04085	−	0.546845i
$359$	18.2354	+	18.2354i	0.962429	+	0.962429i	0.999319	−	0.0368904i	$-0.0117452\pi$
$359$	18.2354	+	18.2354i	0.962429	+	0.962429i	−0.0368904	+	0.999319i	$0.511745\pi$
$360$	8.45944	−	8.20457i	0.445852	−	0.432419i
$361$	3.52628	+	2.03590i	0.185594	+	0.107153i
$362$	4.36397	−	1.16932i	0.229365	−	0.0614582i
$363$	−6.31284	+	8.09808i	−0.331338	+	0.425039i
$364$		0			0
$365$			1.92089i			0.100544i
$366$	7.11618	−	16.8151i	0.371969	−	0.878941i
$367$	−15.1962	+	26.3205i	−0.793233	+	1.37392i	0.130723	+	0.991419i	$0.458270\pi$
$367$	−15.1962	+	26.3205i	−0.793233	+	1.37392i	−0.923955	+	0.382500i	$0.875063\pi$
$368$		0			0
$369$	−14.4715	−	8.65286i	−0.753356	−	0.450450i
$370$	−3.17949	+	11.8660i	−0.165294	+	0.616885i
$371$	−0.285334	+	1.06488i	−0.0148138	+	0.0552859i
$372$	−1.60502	+	0.198831i	−0.0832162	+	0.0103089i
$373$	−5.79423	−	10.0359i	−0.300014	−	0.519639i	0.676125	−	0.736787i	$-0.263658\pi$
$373$	−5.79423	−	10.0359i	−0.300014	−	0.519639i	−0.976139	+	0.217148i	$0.930325\pi$
$374$	−15.6114	+	27.0398i	−0.807249	+	1.39820i
$375$	−18.5736	−	7.86038i	−0.959138	−	0.405908i
$376$		−	15.7128i		−	0.810326i
$377$		0			0
$378$	10.1244	+	4.46841i	0.520741	+	0.229830i
$379$	−14.2942	+	3.83013i	−0.734245	+	0.196740i	−0.606519	−	0.795069i	$-0.707435\pi$
$379$	−14.2942	+	3.83013i	−0.734245	+	0.196740i	−0.127726	+	0.991809i	$0.540768\pi$
$380$	1.35022	+	0.779548i	0.0692647	+	0.0399900i
$381$	15.6524	+	2.18257i	0.801897	+	0.111816i
$382$	−5.14359	−	5.14359i	−0.263169	−	0.263169i
$383$	31.7936	+	8.51906i	1.62458	+	0.435304i	0.952341	−	0.305035i	$-0.0986682\pi$
$383$	31.7936	+	8.51906i	1.62458	+	0.435304i	0.672234	+	0.740339i	$0.265335\pi$
$384$	18.0261	−	13.6142i	0.919893	−	0.694748i
$385$	−6.19615	+	6.19615i	−0.315785	+	0.315785i
$386$	0.180895	−	0.104440i	0.00920730	−	0.00531584i
$387$	−1.80234	+	6.33714i	−0.0916182	+	0.322135i
$388$	−0.117314	−	0.437822i	−0.00595572	−	0.0222271i
$389$	22.4950			1.14054			0.570270	−	0.821457i	$-0.306839\pi$
$389$	22.4950			1.14054			0.570270	+	0.821457i	$0.306839\pi$
$390$		0			0
$391$		0			0
$392$	−3.37554	−	12.5977i	−0.170491	−	0.636280i
$393$	−5.17100	−	12.7590i	−0.260842	−	0.643605i
$394$	−5.36603	+	3.09808i	−0.270336	+	0.156079i
$395$	2.12976	−	2.12976i	0.107160	−	0.107160i
$396$	−0.0505790	+	3.30696i	−0.00254169	+	0.166181i
$397$	13.2942	+	3.56218i	0.667218	+	0.178781i	0.576501	−	0.817096i	$-0.304418\pi$
$397$	13.2942	+	3.56218i	0.667218	+	0.178781i	0.0907168	+	0.995877i	$0.471084\pi$
$398$	−13.7670	−	13.7670i	−0.690078	−	0.690078i
$399$	1.30703	−	9.37341i	0.0654332	−	0.469258i
$400$	−10.5622	−	6.09808i	−0.528109	−	0.304904i
$401$	12.0270	−	3.22263i	0.600601	−	0.160931i	0.0543073	−	0.998524i	$-0.482705\pi$
$401$	12.0270	−	3.22263i	0.600601	−	0.160931i	0.546294	+	0.837594i	$0.316038\pi$
$402$	−12.2079	−	9.51666i	−0.608876	−	0.474648i
$403$		0			0
$404$		−	1.61507i		−	0.0803525i
$405$	−9.28636	−	9.87256i	−0.461443	−	0.490571i
$406$	7.63397	−	13.2224i	0.378868	−	0.656218i
$407$	11.1430	+	19.3003i	0.552340	+	0.956681i
$408$	−2.79889	−	22.5934i	−0.138566	−	1.11854i
$409$	−7.76795	+	28.9904i	−0.384100	+	1.43348i	0.455480	+	0.890246i	$0.349468\pi$
$409$	−7.76795	+	28.9904i	−0.384100	+	1.43348i	−0.839580	+	0.543236i	$0.817199\pi$
$410$	3.29909	−	12.3124i	0.162930	−	0.608064i
$411$	−1.43156	−	11.5559i	−0.0706135	−	0.570011i
$412$	0.928203	+	1.60770i	0.0457293	+	0.0792055i
$413$	−2.12976	+	3.68886i	−0.104799	+	0.181517i
$414$		0			0
$415$		−	6.19615i		−	0.304157i
$416$		0			0
$417$	25.1244	+	19.5856i	1.23034	+	0.959113i
$418$	23.1244	−	6.19615i	1.13105	−	0.303064i
$419$	8.23373	+	4.75374i	0.402244	+	0.232236i	0.687452	−	0.726230i	$-0.258729\pi$
$419$	8.23373	+	4.75374i	0.402244	+	0.232236i	−0.285208	+	0.958466i	$0.592063\pi$
$420$	−0.136505	+	0.978956i	−0.00666078	+	0.0477682i
$421$	−7.83013	−	7.83013i	−0.381617	−	0.381617i	0.490067	−	0.871685i	$-0.336972\pi$
$421$	−7.83013	−	7.83013i	−0.381617	−	0.381617i	−0.871685	+	0.490067i	$0.836972\pi$
$422$	2.62398	+	0.703093i	0.127733	+	0.0342260i
$423$	−18.0695	−	0.276369i	−0.878571	−	0.0134375i
$424$	1.43782	−	1.43782i	0.0698268	−	0.0698268i
$425$	−11.9226	+	6.88351i	−0.578330	+	0.333899i
$426$	−2.95093	−	7.28115i	−0.142973	−	0.352773i
$427$	−2.56218	−	9.56218i	−0.123992	−	0.462746i
$428$	5.09505			0.246278
$429$		0			0
$430$	−4.98076			−0.240194
$431$	9.79282	+	36.5473i	0.471704	+	1.76042i	0.633648	+	0.773622i	$0.281557\pi$
$431$	9.79282	+	36.5473i	0.471704	+	1.76042i	−0.161944	+	0.986800i	$0.551776\pi$
$432$	−13.6951	−	18.7218i	−0.658905	−	0.900754i
$433$	26.8923	−	15.5263i	1.29236	−	0.746145i	0.313289	−	0.949658i	$-0.398569\pi$
$433$	26.8923	−	15.5263i	1.29236	−	0.746145i	0.979072	+	0.203512i	$0.0652357\pi$
$434$	−5.24796	+	5.24796i	−0.251910	+	0.251910i
$435$	−14.9218	+	11.2697i	−0.715445	+	0.540339i
$436$	4.83013	+	1.29423i	0.231321	+	0.0619823i
$437$		0			0
$438$	3.29519	+	0.459481i	0.157450	+	0.0219548i
$439$	−1.09808	−	0.633975i	−0.0524083	−	0.0302580i	0.473567	−	0.880758i	$-0.342966\pi$
$439$	−1.09808	−	0.633975i	−0.0524083	−	0.0302580i	−0.525975	+	0.850500i	$0.676300\pi$
$440$	15.6114	−	4.18307i	0.744247	−	0.199420i
$441$	−14.5466	+	3.66025i	−0.692694	+	0.174298i
$442$		0			0
$443$		−	11.2195i		−	0.533054i	−0.963827	−	0.266527i	$-0.914124\pi$
$443$		−	11.2195i		−	0.533054i	0.963827	−	0.266527i	$-0.0858762\pi$
$444$	2.31508	+	0.979744i	0.109869	+	0.0464966i
$445$	7.02628	−	12.1699i	0.333078	−	0.576907i
$446$	−19.5092	−	33.7909i	−0.923787	−	1.60005i
$447$	14.8382	−	1.83816i	0.701821	−	0.0869422i
$448$	2.43782	−	9.09808i	0.115176	−	0.429844i
$449$	5.32441	−	19.8710i	0.251275	−	0.937769i	−0.718851	−	0.695165i	$-0.755331\pi$
$449$	5.32441	−	19.8710i	0.251275	−	0.937769i	0.970125	−	0.242605i	$-0.0780018\pi$
$450$	−6.33434	+	10.5939i	−0.298603	+	0.499400i
$451$	−11.5622	−	20.0263i	−0.544442	−	0.943001i
$452$	−1.37820	+	2.38711i	−0.0648251	+	0.112280i
$453$	−0.511599	+	1.20888i	−0.0240370	+	0.0567981i
$454$		−	30.5359i		−	1.43312i
$455$		0			0
$456$	−10.7321	+	13.7670i	−0.502574	+	0.644700i
$457$	3.76795	−	1.00962i	0.176257	−	0.0472280i	−0.169611	−	0.985511i	$-0.554251\pi$
$457$	3.76795	−	1.00962i	0.176257	−	0.0472280i	0.345868	+	0.938283i	$0.387584\pi$
$458$	−26.0514	−	15.0408i	−1.21730	−	0.702809i
$459$	−26.0314	+	2.82130i	−1.21504	+	0.131687i
$460$		0			0
$461$	20.5461	+	5.50531i	0.956927	+	0.256408i	0.703299	−	0.710894i	$-0.251710\pi$
$461$	20.5461	+	5.50531i	0.956927	+	0.256408i	0.253628	+	0.967302i	$0.418376\pi$
$462$	9.14708	+	12.1113i	0.425561	+	0.563471i
$463$	23.0526	−	23.0526i	1.07134	−	1.07134i	0.0740918	−	0.997251i	$-0.476394\pi$
$463$	23.0526	−	23.0526i	1.07134	−	1.07134i	0.997251	−	0.0740918i	$-0.0236058\pi$
$464$	−27.7149	+	16.0012i	−1.28663	+	0.742838i
$465$	8.42417	−	3.41417i	0.390661	−	0.158328i
$466$	6.80385	+	25.3923i	0.315182	+	1.17628i
$467$	−19.1679			−0.886984			−0.443492	−	0.896278i	$-0.646261\pi$
$467$	−19.1679			−0.886984			−0.443492	+	0.896278i	$0.646261\pi$
$468$		0			0
$469$	−8.39230			−0.387521
$470$	−3.53595	−	13.1963i	−0.163101	−	0.608702i
$471$	7.71127	−	3.12525i	0.355317	−	0.144004i
$472$	6.80385	−	3.92820i	0.313172	−	0.180810i
$473$	−6.38929	+	6.38929i	−0.293780	+	0.293780i
$474$	−3.14407	−	4.16296i	−0.144412	−	0.191211i
$475$	10.1962	+	2.73205i	0.467832	+	0.125355i
$476$	1.35022	+	1.35022i	0.0618871	+	0.0618871i
$477$	−1.62819	−	1.67877i	−0.0745496	−	0.0768655i
$478$	12.1699	+	7.02628i	0.556637	+	0.321375i
$479$	−19.8710	+	5.32441i	−0.907928	+	0.243279i	−0.682418	−	0.730962i	$-0.739072\pi$
$479$	−19.8710	+	5.32441i	−0.907928	+	0.243279i	−0.225510	+	0.974241i	$0.572405\pi$
$480$	2.41510	−	3.09808i	0.110234	−	0.141407i
$481$		0			0
$482$		−	21.9243i		−	0.998624i
$483$		0			0
$484$	−0.794229	+	1.37564i	−0.0361013	+	0.0625293i
$485$	1.27376	+	2.20622i	0.0578385	+	0.100179i
$486$	−19.1572	+	13.5688i	−0.868990	+	0.615492i
$487$	−1.49038	+	5.56218i	−0.0675356	+	0.252046i	−0.991437	−	0.130584i	$-0.958315\pi$
$487$	−1.49038	+	5.56218i	−0.0675356	+	0.252046i	0.923902	+	0.382630i	$0.124982\pi$
$488$	−4.72576	+	17.6368i	−0.213925	+	0.798379i
$489$	−7.11819	+	0.881808i	−0.321896	+	0.0398767i
$490$	−5.66987	−	9.82051i	−0.256139	−	0.443645i
$491$	14.2612	−	24.7012i	0.643600	−	1.11475i	−0.341023	−	0.940055i	$-0.610773\pi$
$491$	14.2612	−	24.7012i	0.643600	−	1.11475i	0.984623	−	0.174693i	$-0.0558934\pi$
$492$	−2.40216	−	1.01660i	−0.108298	−	0.0458317i
$493$			36.1244i			1.62696i
$494$		0			0
$495$	−4.53590	−	18.0265i	−0.203873	−	0.810233i
$496$	15.0263	−	4.02628i	0.674700	−	0.180785i
$497$	−3.68886	−	2.12976i	−0.165468	−	0.0955330i
$498$	−10.6292	−	1.48214i	−0.476306	−	0.0664161i
$499$	−2.46410	−	2.46410i	−0.110308	−	0.110308i	0.649798	−	0.760107i	$-0.274853\pi$
$499$	−2.46410	−	2.46410i	−0.110308	−	0.110308i	−0.760107	+	0.649798i	$0.774853\pi$
$500$	−3.01375	−	0.807533i	−0.134779	−	0.0361140i
$501$	18.5839	−	14.0354i	0.830266	−	0.627057i
$502$	−1.05256	+	1.05256i	−0.0469780	+	0.0469780i
$503$	2.83286	−	1.63555i	0.126311	−	0.0729256i	−0.435513	−	0.900182i	$-0.643433\pi$
$503$	2.83286	−	1.63555i	0.126311	−	0.0729256i	0.561824	+	0.827257i	$0.310100\pi$
$504$	−10.6444	−	3.02738i	−0.474141	−	0.134850i
$505$	2.34936	+	8.76795i	0.104545	+	0.390169i
$506$		0			0
$507$		0			0
$508$	2.44486			0.108473
$509$	−3.79330	−	14.1568i	−0.168135	−	0.627489i	−0.997620	−	0.0689588i	$-0.978032\pi$
$509$	−3.79330	−	14.1568i	−0.168135	−	0.627489i	0.829484	−	0.558530i	$-0.188634\pi$
$510$	−7.43497	−	18.3451i	−0.329226	−	0.812337i
$511$	1.56218	−	0.901924i	0.0691067	−	0.0398988i
$512$	−11.7137	+	11.7137i	−0.517678	+	0.517678i
$513$	15.6431	+	12.5839i	0.690661	+	0.555591i
$514$	31.2846	+	8.38269i	1.37990	+	0.369744i
$515$	−7.37772	−	7.37772i	−0.325101	−	0.325101i
$516$	−0.140760	+	1.00947i	−0.00619663	+	0.0444395i
$517$	−21.4641	−	12.3923i	−0.943990	−	0.545013i
$518$	11.1430	−	2.98577i	0.489597	−	0.131187i
$519$	23.8452	+	18.5885i	1.04669	+	0.815943i
$520$		0			0
$521$		−	2.49155i		−	0.109157i	−0.998509	−	0.0545785i	$-0.982618\pi$
$521$		−	2.49155i		−	0.109157i	0.998509	−	0.0545785i	$-0.0173815\pi$
$522$	15.7633	+	28.2934i	0.689939	+	1.23837i
$523$	19.4904	−	33.7583i	0.852255	−	1.47615i	−0.0269137	−	0.999638i	$-0.508568\pi$
$523$	19.4904	−	33.7583i	0.852255	−	1.47615i	0.879169	−	0.476511i	$-0.158099\pi$
$524$	−1.06488	−	1.84443i	−0.0465196	−	0.0805743i
$525$	0.822738	+	6.64136i	0.0359072	+	0.289853i
$526$	−8.68653	+	32.4186i	−0.378751	+	1.41352i
$527$	4.54486	−	16.9617i	0.197977	−	0.738862i
$528$	−3.91108	−	31.5713i	−0.170208	−	1.37397i
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	0.883988	−	1.53111i	0.0383980	−	0.0665072i
$531$	−4.39771	−	7.89343i	−0.190845	−	0.342546i
$532$		−	1.46410i		−	0.0634769i
$533$		0			0
$534$	−19.1962	−	14.9643i	−0.830699	−	0.647570i
$535$	−27.6603	+	7.41154i	−1.19586	+	0.320429i
$536$	13.4052	+	7.73951i	0.579018	+	0.334296i
$537$	6.34978	−	45.5378i	0.274013	−	1.96510i
$538$	15.2679	+	15.2679i	0.658248	+	0.658248i
$539$	−19.8710	−	5.32441i	−0.855904	−	0.229339i
$540$	−1.63376	−	1.31425i	−0.0703060	−	0.0565565i
$541$	−12.6865	+	12.6865i	−0.545437	+	0.545437i	−0.925118	−	0.379681i	$-0.876034\pi$
$541$	−12.6865	+	12.6865i	−0.545437	+	0.545437i	0.379681	+	0.925118i	$0.376034\pi$
$542$	10.0782	−	5.81863i	0.432894	−	0.249931i
$543$	1.95171	+	4.81568i	0.0837561	+	0.206661i
$544$	−1.96410	−	7.33013i	−0.0842102	−	0.314277i
$545$	−28.1047			−1.20387
$546$		0			0
$547$	2.00000			0.0855138			0.0427569	−	0.999086i	$-0.486386\pi$
$547$	2.00000			0.0855138			0.0427569	+	0.999086i	$0.486386\pi$
$548$	−0.466229	−	1.73999i	−0.0199163	−	0.0743287i
$549$	20.1990	+	5.74477i	0.862070	+	0.245181i
$550$	−14.6603	+	8.46410i	−0.625115	+	0.360911i
$551$	19.5856	−	19.5856i	0.834376	−	0.834376i
$552$		0			0
$553$	−2.73205	−	0.732051i	−0.116179	−	0.0311300i
$554$	−29.3785	−	29.3785i	−1.24817	−	1.24817i
$555$	−13.9934	−	1.95124i	−0.593988	−	0.0828255i
$556$	4.26795	+	2.46410i	0.181001	+	0.104501i
$557$	−24.7292	+	6.62616i	−1.04781	+	0.280759i	−0.741346	−	0.671123i	$-0.765812\pi$
$557$	−24.7292	+	6.62616i	−1.04781	+	0.280759i	−0.306462	+	0.951883i	$0.599145\pi$
$558$	−3.84177	−	15.2679i	−0.162635	−	0.646344i
$559$		0			0
$560$		−	9.50749i		−	0.401765i
$561$	−33.0706	−	13.9955i	−1.39624	−	0.590891i
$562$	12.9186	−	22.3756i	0.544938	−	0.943860i
$563$	5.03908	+	8.72794i	0.212372	+	0.367839i	0.952456	−	0.304675i	$-0.0985479\pi$
$563$	5.03908	+	8.72794i	0.212372	+	0.367839i	−0.740085	+	0.672514i	$0.765215\pi$
$564$	−2.77449	+	0.343706i	−0.116827	+	0.0144726i
$565$	4.00962	−	14.9641i	0.168686	−	0.629544i
$566$	−2.56801	+	9.58394i	−0.107941	+	0.402843i
$567$	−3.66867	+	12.1877i	−0.154070	+	0.511837i
$568$	3.92820	+	6.80385i	0.164824	+	0.285483i
$569$	1.35022	−	2.33864i	0.0566040	−	0.0980411i	−0.836335	−	0.548219i	$-0.815306\pi$
$569$	1.35022	−	2.33864i	0.0566040	−	0.0980411i	0.892939	+	0.450178i	$0.148639\pi$
$570$	−5.91520	+	13.9773i	−0.247760	+	0.585444i
$571$		−	1.94744i		−	0.0814979i	−0.999169	−	0.0407489i	$-0.987026\pi$
$571$		−	1.94744i		−	0.0814979i	0.999169	−	0.0407489i	$-0.0129744\pi$
$572$		0			0
$573$	5.14359	−	6.59817i	0.214877	−	0.275643i
$574$	−11.5622	+	3.09808i	−0.482596	+	0.129311i
$575$		0			0
$576$	13.9108	+	14.3429i	0.579617	+	0.597623i
$577$	−22.4904	−	22.4904i	−0.936287	−	0.936287i	0.0618016	−	0.998088i	$-0.480315\pi$
$577$	−22.4904	−	22.4904i	−0.936287	−	0.936287i	−0.998088	+	0.0618016i	$0.980315\pi$
$578$	−12.2079	−	3.27110i	−0.507783	−	0.136060i
$579$	0.144785	+	0.191705i	0.00601707	+	0.00796700i
$580$	−2.04552	+	2.04552i	−0.0849355	+	0.0849355i
$581$	−5.03908	+	2.90931i	−0.209056	+	0.120699i
$582$	4.08936	−	1.65735i	0.169509	−	0.0686992i
$583$	−0.830127	−	3.09808i	−0.0343803	−	0.128309i
$584$	−3.32707			−0.137675
$585$		0			0
$586$	2.71281			0.112065
$587$	−4.83020	−	18.0265i	−0.199364	−	0.744035i	−0.991094	−	0.133164i	$-0.957486\pi$
$587$	−4.83020	−	18.0265i	−0.199364	−	0.744035i	0.791730	−	0.610871i	$-0.209181\pi$
$588$	−2.15060	+	0.871601i	−0.0886892	+	0.0359442i
$589$	−11.6603	+	6.73205i	−0.480452	+	0.277389i
$590$	4.83020	−	4.83020i	0.198856	−	0.198856i
$591$	−4.29488	−	5.68671i	−0.176668	−	0.233920i
$592$	−23.3564	−	6.25833i	−0.959942	−	0.257216i
$593$	10.3635	+	10.3635i	0.425578	+	0.425578i	0.887119	−	0.461541i	$-0.152703\pi$
$593$	10.3635	+	10.3635i	0.425578	+	0.425578i	−0.461541	+	0.887119i	$0.652703\pi$
$594$	−32.0087	+	3.46913i	−1.31333	+	0.142340i
$595$	−9.29423	−	5.36603i	−0.381026	−	0.219986i
$596$	2.23420	−	0.598653i	0.0915166	−	0.0245218i
$597$	13.7670	−	17.6603i	0.563446	−	0.722786i
$598$		0			0
$599$			20.7270i			0.846881i	0.905924	+	0.423441i	$0.139178\pi$
$599$			20.7270i			0.846881i	−0.905924	+	0.423441i	$0.860822\pi$
$600$	4.81059	−	11.3671i	0.196391	−	0.464062i
$601$	−11.7942	+	20.4282i	−0.481097	+	0.833284i	−0.999765	−	0.0216919i	$-0.993095\pi$
$601$	−11.7942	+	20.4282i	−0.481097	+	0.833284i	0.518668	+	0.854976i	$0.326428\pi$
$602$	2.33864	+	4.05065i	0.0953160	+	0.165092i
$603$	9.13612	−	15.2797i	0.372052	−	0.622238i
$604$	−0.0525589	+	0.196152i	−0.00213859	+	0.00798133i
$605$	2.31066	−	8.62350i	0.0939417	−	0.350595i
$606$	15.6030	−	1.93291i	0.633828	−	0.0785192i
$607$	0.0980762	+	0.169873i	0.00398079	+	0.00689493i	0.868009	−	0.496549i	$-0.165400\pi$
$607$	0.0980762	+	0.169873i	0.00398079	+	0.00689493i	−0.864028	+	0.503444i	$0.832066\pi$
$608$	−2.90931	+	5.03908i	−0.117988	+	0.204362i
$609$	16.1715	+	6.84378i	0.655301	+	0.277324i
$610$			15.8756i			0.642786i
$611$		0			0
$612$	−3.92820	+	0.988427i	−0.158788	+	0.0399548i
$613$	42.3827	−	11.3564i	1.71182	−	0.458681i	0.735951	−	0.677035i	$-0.236735\pi$
$613$	42.3827	−	11.3564i	1.71182	−	0.458681i	0.975870	+	0.218354i	$0.0700687\pi$
$614$	15.4790	+	8.93682i	0.624683	+	0.360661i
$615$	14.5198	+	2.02463i	0.585494	+	0.0816411i
$616$	−10.7321	−	10.7321i	−0.432407	−	0.432407i
$617$	17.8457	+	4.78173i	0.718439	+	0.192505i	0.599475	−	0.800393i	$-0.295376\pi$
$617$	17.8457	+	4.78173i	0.718439	+	0.192505i	0.118964	+	0.992899i	$0.462043\pi$
$618$	−14.4209	+	10.8914i	−0.580094	+	0.438115i
$619$	−31.6603	+	31.6603i	−1.27253	+	1.27253i	−0.327778	+	0.944755i	$0.606300\pi$
$619$	−31.6603	+	31.6603i	−1.27253	+	1.27253i	−0.944755	+	0.327778i	$0.893700\pi$
$620$	1.21779	−	0.703093i	0.0489077	−	0.0282369i
$621$		0			0
$622$	3.92820	+	14.6603i	0.157507	+	0.587823i
$623$	−13.1963			−0.528701
$624$		0			0
$625$	3.87564			0.155026
$626$	0.779548	+	2.90931i	0.0311570	+	0.116280i
$627$	10.3420	+	25.5180i	0.413019	+	1.01909i
$628$	1.11474	−	0.643594i	0.0444828	−	0.0256822i
$629$	−19.3003	+	19.3003i	−0.769554	+	0.769554i
$630$	−9.62097	−	0.147150i	−0.383309	−	0.00586260i
$631$	−21.3923	−	5.73205i	−0.851614	−	0.228189i	−0.193493	−	0.981102i	$-0.561982\pi$
$631$	−21.3923	−	5.73205i	−0.851614	−	0.228189i	−0.658121	+	0.752912i	$0.728648\pi$
$632$	3.68886	+	3.68886i	0.146735	+	0.146735i
$633$	−0.431485	+	3.09442i	−0.0171500	+	0.122992i
$634$	−20.9378	−	12.0885i	−0.831547	−	0.480094i
$635$	−13.2728	+	3.55644i	−0.526715	+	0.141133i
$636$	−0.285334	−	0.222432i	−0.0113142	−	0.00882000i
$637$		0			0
$638$			44.4192i			1.75857i
$639$	7.89343	−	4.39771i	0.312259	−	0.173971i
$640$	−9.82051	+	17.0096i	−0.388190	+	0.672364i
$641$	−22.6758	−	39.2757i	−0.895642	−	1.55130i	−0.833008	−	0.553261i	$-0.813383\pi$
$641$	−22.6758	−	39.2757i	−0.895642	−	1.55130i	−0.0626345	−	0.998037i	$-0.519950\pi$
$642$	6.09776	+	49.2228i	0.240659	+	1.94267i
$643$	−1.87564	+	7.00000i	−0.0739682	+	0.276053i	−0.992997	−	0.118136i	$-0.962308\pi$
$643$	−1.87564	+	7.00000i	−0.0739682	+	0.276053i	0.919029	+	0.394190i	$0.128975\pi$
$644$		0			0
$645$	−0.704266	−	5.68503i	−0.0277305	−	0.223848i
$646$	14.6603	+	25.3923i	0.576800	+	0.999047i
$647$	8.23373	−	14.2612i	0.323701	−	0.560667i	−0.657547	−	0.753413i	$-0.728406\pi$
$647$	8.23373	−	14.2612i	0.323701	−	0.560667i	0.981249	+	0.192746i	$0.0617394\pi$
$648$	17.0998	−	16.0844i	0.671742	−	0.631857i
$649$		−	12.3923i		−	0.486441i
$650$		0			0
$651$	−6.73205	−	5.24796i	−0.263850	−	0.205684i
$652$	−1.07180	+	0.287187i	−0.0419748	+	0.0112471i
$653$	−8.36615	−	4.83020i	−0.327393	−	0.189020i	0.327290	−	0.944924i	$-0.393865\pi$
$653$	−8.36615	−	4.83020i	−0.327393	−	0.189020i	−0.654683	+	0.755904i	$0.727198\pi$
$654$	−6.72272	+	48.2123i	−0.262879	+	1.88525i
$655$	8.46410	+	8.46410i	0.330720	+	0.330720i
$656$	24.2349	+	6.49373i	0.946216	+	0.253538i
$657$	−0.0585190	+	3.82609i	−0.00228304	+	0.149270i
$658$	−9.07180	+	9.07180i	−0.353655	+	0.353655i
$659$	23.4834	−	13.5581i	0.914783	−	0.528150i	0.0328158	−	0.999461i	$-0.489553\pi$
$659$	23.4834	−	13.5581i	0.914783	−	0.528150i	0.881967	+	0.471311i	$0.156219\pi$
$660$	−1.08011	−	2.66509i	−0.0420434	−	0.103738i
$661$	−2.52628	−	9.42820i	−0.0982609	−	0.366715i	0.899233	−	0.437470i	$-0.144126\pi$
$661$	−2.52628	−	9.42820i	−0.0982609	−	0.366715i	−0.997494	+	0.0707559i	$0.977459\pi$
$662$	51.5321			2.00285
$663$		0			0
$664$	10.7321			0.416484
$665$	2.12976	+	7.94839i	0.0825887	+	0.308225i
$666$	−6.69452	+	23.5383i	−0.259408	+	0.912092i
$667$		0			0
$668$	2.54752	−	2.54752i	0.0985666	−	0.0985666i
$669$	35.8103	−	27.0457i	1.38451	−	1.04565i
$670$	13.0000	+	3.48334i	0.502234	+	0.134573i
$671$	20.3652	+	20.3652i	0.786189	+	0.786189i
$672$	−3.65351	−	0.509445i	−0.140937	−	0.0196523i
$673$	36.9904	+	21.3564i	1.42587	+	0.823229i	0.996792	−	0.0800364i	$-0.0255036\pi$
$673$	36.9904	+	21.3564i	1.42587	+	0.823229i	0.429082	+	0.903265i	$0.358837\pi$
$674$	−26.8589	+	7.19683i	−1.03457	+	0.277211i
$675$	−12.9875	−	5.73205i	−0.499888	−	0.220627i
$676$		0			0
$677$			9.66040i			0.371279i	0.982618	+	0.185640i	$0.0594357\pi$
$677$			9.66040i			0.371279i	−0.982618	+	0.185640i	$0.940564\pi$
$678$	−24.7111	−	10.4578i	−0.949025	−	0.401628i
$679$	1.19615	−	2.07180i	0.0459041	−	0.0795083i
$680$	9.89726	+	17.1426i	0.379543	+	0.657387i
$681$	34.8536	−	4.31769i	1.33559	−	0.165454i
$682$	5.58846	−	20.8564i	0.213993	−	0.798633i
$683$	−12.1315	+	45.2752i	−0.464198	+	1.73241i	0.195338	+	0.980736i	$0.437420\pi$
$683$	−12.1315	+	45.2752i	−0.464198	+	1.73241i	−0.659536	+	0.751673i	$0.729247\pi$
$684$	2.66566	+	1.59387i	0.101924	+	0.0609430i
$685$	5.06218	+	8.76795i	0.193416	+	0.335006i
$686$	−12.7786	+	22.1332i	−0.487889	+	0.845048i
$687$	13.4839	−	31.8617i	0.514443	−	1.21560i
$688$		−	9.80385i		−	0.373768i
$689$		0			0
$690$		0			0
$691$	−18.2224	+	4.88269i	−0.693214	+	0.185746i	−0.588189	−	0.808723i	$-0.700159\pi$
$691$	−18.2224	+	4.88269i	−0.693214	+	0.185746i	−0.105025	+	0.994470i	$0.533492\pi$
$692$	4.05065	+	2.33864i	0.153983	+	0.0889019i
$693$	−12.5305	+	12.1530i	−0.475994	+	0.461653i
$694$	−21.9090	−	21.9090i	−0.831653	−	0.831653i
$695$	−26.7545	−	7.16884i	−1.01486	−	0.271930i
$696$	−19.5196	−	25.8453i	−0.739890	−	0.979664i
$697$	20.0263	−	20.0263i	0.758549	−	0.758549i
$698$	37.1180	−	21.4301i	1.40494	−	0.811140i
$699$	−28.0207	+	11.3563i	−1.05984	+	0.429535i
$700$	0.267949	+	1.00000i	0.0101275	+	0.0377964i
$701$	12.7786			0.482641			0.241320	−	0.970446i	$-0.422420\pi$
$701$	12.7786			0.482641			0.241320	+	0.970446i	$0.422420\pi$
$702$		0			0
$703$	20.9282			0.789322
$704$	7.09239	+	26.4692i	0.267304	+	0.997594i
$705$	14.5623	−	5.90185i	0.548448	−	0.222277i
$706$	18.4474	−	10.6506i	0.694279	−	0.400842i
$707$	6.02751	−	6.02751i	0.226688	−	0.226688i
$708$	−0.842451	−	1.11546i	−0.0316612	−	0.0419216i
$709$	11.3301	+	3.03590i	0.425512	+	0.114016i	0.465219	−	0.885196i	$-0.345976\pi$
$709$	11.3301	+	3.03590i	0.425512	+	0.114016i	−0.0397068	+	0.999211i	$0.512642\pi$
$710$	4.83020	+	4.83020i	0.181274	+	0.181274i
$711$	4.30703	−	4.17726i	0.161526	−	0.156660i
$712$	21.0788	+	12.1699i	0.789963	+	0.456085i
$713$		0			0
$714$	−11.4284	+	14.6603i	−0.427696	+	0.548646i
$715$		0			0
$716$		−	7.11287i		−	0.265821i
$717$	−6.29899	+	14.8842i	−0.235240	+	0.555859i
$718$	−19.4186	+	33.6340i	−0.724695	+	1.25521i
$719$	3.68886	+	6.38929i	0.137571	+	0.238280i	0.926577	−	0.376106i	$-0.122737\pi$
$719$	3.68886	+	6.38929i	0.137571	+	0.238280i	−0.789005	+	0.614386i	$0.789404\pi$
$720$	17.3101	+	10.3501i	0.645110	+	0.385727i
$721$	−2.53590	+	9.46410i	−0.0944418	+	0.352462i
$722$	−1.58708	+	5.92307i	−0.0590650	+	0.220434i
$723$	25.0243	−	3.10003i	0.930665	−	0.115292i
$724$	0.401924	+	0.696152i	0.0149374	+	0.0258723i
$725$	−9.79282	+	16.9617i	−0.363696	+	0.629940i
$726$	−14.2405	−	6.02659i	−0.528515	−	0.223668i
$727$			19.5167i			0.723833i	0.932211	+	0.361916i	$0.117877\pi$
$727$			19.5167i			0.723833i	−0.932211	+	0.361916i	$0.882123\pi$
$728$		0			0
$729$	−18.1962	−	19.9474i	−0.673932	−	0.738794i
$730$	−2.79423	+	0.748711i	−0.103419	+	0.0277110i
$731$	−9.58394	−	5.53329i	−0.354475	−	0.204656i
$732$	3.21758	+	0.448659i	0.118925	+	0.0165829i
$733$	−6.77757	−	6.77757i	−0.250335	−	0.250335i	0.570773	−	0.821108i	$-0.306644\pi$
$733$	−6.77757	−	6.77757i	−0.250335	−	0.250335i	−0.821108	+	0.570773i	$0.806644\pi$
$734$	−44.2104	−	11.8461i	−1.63183	−	0.437249i
$735$	10.4074	−	7.86017i	0.383883	−	0.289927i
$736$		0			0
$737$	21.1447	−	12.2079i	0.778876	−	0.449685i
$738$	6.94633	−	24.4237i	0.255698	−	0.899049i
$739$	2.98076	+	11.1244i	0.109649	+	0.409216i	0.998831	−	0.0483378i	$-0.0153924\pi$
$739$	2.98076	+	11.1244i	0.109649	+	0.409216i	−0.889182	+	0.457554i	$0.848726\pi$
$740$	−2.18573			−0.0803492
$741$		0			0
$742$	−1.66025			−0.0609498
$743$	2.28268	+	8.51906i	0.0837432	+	0.312534i	0.995073	−	0.0991426i	$-0.0316100\pi$
$743$	2.28268	+	8.51906i	0.0837432	+	0.312534i	−0.911330	+	0.411677i	$0.864943\pi$
$744$	5.91352	+	14.5911i	0.216800	+	0.534935i
$745$	−11.2583	+	6.50000i	−0.412473	+	0.238142i
$746$	12.3403	−	12.3403i	0.451812	−	0.451812i
$747$	0.188763	−	12.3417i	0.00690649	−	0.451560i
$748$	−5.36603	−	1.43782i	−0.196201	−	0.0525720i
$749$	19.0150	+	19.0150i	0.694792	+	0.694792i
$750$	4.19463	−	30.0820i	0.153166	−	1.09844i
$751$	29.2750	+	16.9019i	1.06826	+	0.616760i	0.927705	−	0.373313i	$-0.121778\pi$
$751$	29.2750	+	16.9019i	1.06826	+	0.616760i	0.140554	+	0.990073i	$0.455112\pi$
$752$	25.9749	−	6.95996i	0.947208	−	0.253804i
$753$	−1.35022	−	1.05256i	−0.0492046	−	0.0383574i
$754$		0			0
$755$		−	1.14134i		−	0.0415375i
$756$	−0.301720	+	1.94576i	−0.0109735	+	0.0707667i
$757$	−8.39230	+	14.5359i	−0.305024	+	0.528316i	−0.977267	−	0.212014i	$-0.931998\pi$
$757$	−8.39230	+	14.5359i	−0.305024	+	0.528316i	0.672243	+	0.740331i	$0.265331\pi$
$758$	−11.1430	−	19.3003i	−0.404733	−	0.701019i
$759$		0			0
$760$	3.92820	−	14.6603i	0.142491	−	0.531783i
$761$	−4.75374	+	17.7412i	−0.172323	+	0.643118i	0.824669	+	0.565616i	$0.191361\pi$
$761$	−4.75374	+	17.7412i	−0.172323	+	0.643118i	−0.996992	+	0.0775029i	$0.975305\pi$
$762$	2.92602	+	23.6196i	0.105998	+	0.855647i
$763$	13.1962	+	22.8564i	0.477733	+	0.827457i
$764$	0.647124	−	1.12085i	0.0234121	−	0.0405510i
$765$	19.8878	−	11.0802i	0.719045	−	0.400606i
$766$			49.5692i			1.79101i
$767$		0			0
$768$	8.63397	+	6.73060i	0.311552	+	0.242870i
$769$	40.4186	−	10.8301i	1.45753	−	0.390544i	0.558895	−	0.829238i	$-0.311225\pi$
$769$	40.4186	−	10.8301i	1.45753	−	0.390544i	0.898636	+	0.438694i	$0.144559\pi$
$770$	−11.4284	−	6.59817i	−0.411850	−	0.237782i
$771$	−5.14442	+	36.8935i	−0.185272	+	1.32869i
$772$	0.0262794	+	0.0262794i	0.000945818	+	0.000945818i
$773$	−41.5864	−	11.1430i	−1.49576	−	0.400787i	−0.584081	−	0.811695i	$-0.698545\pi$
$773$	−41.5864	−	11.1430i	−1.49576	−	0.400787i	−0.911677	+	0.410908i	$0.865212\pi$
$774$	−9.92087	−	0.151737i	−0.356598	−	0.00545407i
$775$	6.73205	−	6.73205i	0.241822	−	0.241822i
$776$	−3.82129	+	2.20622i	−0.137176	+	0.0791987i
$777$	4.98354	+	12.2965i	0.178784	+	0.441133i
$778$	8.76795	+	32.7224i	0.314346	+	1.17316i
$779$	−21.7154			−0.778035
$780$		0			0
$781$	12.3923			0.443432
$782$		0			0
$783$	−30.0651	+	21.9928i	−1.07444	+	0.785957i
$784$	19.3301	−	11.1603i	0.690362	−	0.398581i
$785$	−5.11553	+	5.11553i	−0.182581	+	0.182581i
$786$	16.5444	−	12.4951i	0.590120	−	0.445687i
$787$	−16.0263	−	4.29423i	−0.571275	−	0.153073i	−0.0383938	−	0.999263i	$-0.512224\pi$
$787$	−16.0263	−	4.29423i	−0.571275	−	0.153073i	−0.532881	+	0.846190i	$0.678891\pi$
$788$	−0.779548	−	0.779548i	−0.0277702	−	0.0277702i
$789$	−38.2307	−	5.33089i	−1.36105	−	0.189785i
$790$	3.92820	+	2.26795i	0.139759	+	0.0806900i
$791$	−14.0524	+	3.76532i	−0.499644	+	0.133879i
$792$	31.2229	−	7.85641i	1.10946	−	0.279165i
$793$		0			0
$794$			20.7270i			0.735573i
$795$	1.87260	+	0.792486i	0.0664143	+	0.0281066i
$796$	1.73205	−	3.00000i	0.0613909	−	0.106332i
$797$	20.1563	+	34.9118i	0.713973	+	1.23664i	0.963354	+	0.268232i	$0.0864395\pi$
$797$	20.1563	+	34.9118i	0.713973	+	1.23664i	−0.249381	+	0.968405i	$0.580227\pi$
$798$	14.1445	−	1.75224i	0.500711	−	0.0620286i
$799$	7.85641	−	29.3205i	0.277940	−	1.03729i
$800$	1.06488	−	3.97420i	0.0376493	−	0.140509i
$801$	14.3660	−	24.0264i	0.507596	−	0.848929i
$802$	9.37564	+	16.2391i	0.331066	+	0.573422i
$803$	−2.62398	+	4.54486i	−0.0925982	+	0.160385i
$804$	1.07337	−	2.53632i	0.0378550	−	0.0894491i
$805$		0			0
$806$		0			0
$807$	−15.2679	+	19.5856i	−0.537457	+	0.689447i
$808$	−15.1865	+	4.06922i	−0.534260	+	0.143155i
$809$	−24.0261	−	13.8715i	−0.844712	−	0.487694i	0.0141514	−	0.999900i	$-0.495495\pi$
$809$	−24.0261	−	13.8715i	−0.844712	−	0.487694i	−0.858863	+	0.512205i	$0.828829\pi$
$810$	10.7416	−	17.3565i	0.377421	−	0.609846i
$811$	19.0000	+	19.0000i	0.667180	+	0.667180i	0.957062	−	0.289882i	$-0.0936161\pi$
$811$	19.0000	+	19.0000i	0.667180	+	0.667180i	−0.289882	+	0.957062i	$0.593616\pi$
$812$	2.62398	+	0.703093i	0.0920836	+	0.0246737i
$813$	8.06639	+	10.6804i	0.282901	+	0.374579i
$814$	−23.7321	+	23.7321i	−0.831808	+	0.831808i
$815$	5.40087	−	3.11819i	0.189184	−	0.109226i
$816$	36.1095	−	14.6346i	1.26409	−	0.512313i
$817$	2.19615	+	8.19615i	0.0768336	+	0.286747i
$818$	−45.1988			−1.58034
$819$		0			0
$820$	2.26795			0.0792002
$821$	11.1430	+	41.5864i	0.388895	+	1.45137i	0.831935	+	0.554873i	$0.187233\pi$
$821$	11.1430	+	41.5864i	0.388895	+	1.45137i	−0.443040	+	0.896502i	$0.646100\pi$
$822$	16.2519	−	6.58662i	0.566850	−	0.229735i
$823$	7.39230	−	4.26795i	0.257680	−	0.148771i	−0.365596	−	0.930774i	$-0.619135\pi$
$823$	7.39230	−	4.26795i	0.257680	−	0.148771i	0.623276	+	0.782002i	$0.285801\pi$
$824$	12.7786	−	12.7786i	0.445163	−	0.445163i
$825$	−11.7338	−	15.5364i	−0.408519	−	0.540907i
$826$	−6.19615	−	1.66025i	−0.215592	−	0.0577676i
$827$	−31.7936	−	31.7936i	−1.10557	−	1.10557i	−0.993726	−	0.111845i	$-0.964324\pi$
$827$	−31.7936	−	31.7936i	−1.10557	−	1.10557i	−0.111845	−	0.993726i	$-0.535676\pi$
$828$		0			0
$829$	−41.6769	−	24.0622i	−1.44750	−	0.835714i	−0.449167	−	0.893448i	$-0.648279\pi$
$829$	−41.6769	−	24.0622i	−1.44750	−	0.835714i	−0.998332	+	0.0577338i	$0.981613\pi$
$830$	9.01327	−	2.41510i	0.312855	−	0.0838293i
$831$	29.3785	−	37.6865i	1.01913	−	1.30733i
$832$		0			0
$833$		−	25.1954i		−	0.872968i
$834$	−18.6976	+	44.1813i	−0.647444	+	1.52987i
$835$	−10.1244	+	17.5359i	−0.350368	+	0.606855i
$836$	2.12976	+	3.68886i	0.0736595	+	0.127582i
$837$	16.8836	−	6.54383i	0.583582	−	0.226188i
$838$	−3.70577	+	13.8301i	−0.128014	+	0.477754i
$839$	2.62398	−	9.79282i	0.0905898	−	0.338086i	−0.905724	−	0.423868i	$-0.860672\pi$
$839$	2.62398	−	9.79282i	0.0905898	−	0.338086i	0.996314	+	0.0857819i	$0.0273388\pi$
$840$	9.54910	−	1.18295i	0.329475	−	0.0408157i
$841$	11.1962	+	19.3923i	0.386074	+	0.668700i
$842$	8.33816	−	14.4421i	0.287352	−	0.497708i
$843$	27.3662	+	11.5814i	0.942540	+	0.398884i
$844$			0.483340i			0.0166372i
$845$		0			0
$846$	−6.64102	−	26.3927i	−0.228323	−	0.907400i
$847$	−8.09808	+	2.16987i	−0.278253	+	0.0745577i
$848$	3.01375	+	1.73999i	0.103493	+	0.0597515i
$849$	−11.3022	−	1.57598i	−0.387890	−	0.0540873i
$850$	−14.6603	−	14.6603i	−0.502843	−	0.502843i
$851$		0			0
$852$	1.11546	−	0.842451i	0.0382151	−	0.0288619i
$853$	−22.3660	+	22.3660i	−0.765798	+	0.765798i	−0.977364	−	0.211566i	$-0.932144\pi$
$853$	−22.3660	+	22.3660i	−0.765798	+	0.765798i	0.211566	+	0.977364i	$0.432144\pi$
$854$	12.9110	−	7.45418i	0.441806	−	0.255077i
$855$	−16.7900	−	4.77524i	−0.574207	−	0.163310i
$856$	−12.8372	−	47.9090i	−0.438765	−	1.63749i
$857$	3.32707			0.113651			0.0568253	−	0.998384i	$-0.481902\pi$
$857$	3.32707			0.113651			0.0568253	+	0.998384i	$0.481902\pi$
$858$		0			0
$859$	39.1769			1.33670			0.668350	−	0.743847i	$-0.267001\pi$
$859$	39.1769			1.33670			0.668350	+	0.743847i	$0.267001\pi$
$860$	−0.229365	−	0.856003i	−0.00782129	−	0.0291895i
$861$	−5.17100	−	12.7590i	−0.176227	−	0.434825i
$862$	−49.3468	+	28.4904i	−1.68076	+	0.970386i
$863$	−18.2354	+	18.2354i	−0.620741	+	0.620741i	−0.945721	−	0.324980i	$-0.894642\pi$
$863$	−18.2354	+	18.2354i	−0.620741	+	0.620741i	0.324980	+	0.945721i	$0.394642\pi$
$864$	4.90487	−	6.09729i	0.166867	−	0.207434i
$865$	−25.3923	−	6.80385i	−0.863364	−	0.231338i
$866$	33.0673	+	33.0673i	1.12367	+	1.12367i
$867$	2.00746	−	14.3966i	0.0681769	−	0.488935i
$868$	−1.14359	−	0.660254i	−0.0388161	−	0.0224105i
$869$	7.94839	−	2.12976i	0.269631	−	0.0722473i
$870$	−22.2096	−	17.3135i	−0.752977	−	0.586981i
$871$		0			0
$872$		−	48.6788i		−	1.64847i
$873$	2.46991	+	4.43324i	0.0835939	+	0.150042i
$874$		0			0
$875$	−8.23373	−	14.2612i	−0.278351	−	0.482118i
$876$	0.0727771	+	0.587477i	0.00245891	+	0.0198490i
$877$	−7.76795	+	28.9904i	−0.262305	+	0.978936i	0.701574	+	0.712596i	$0.252481\pi$
$877$	−7.76795	+	28.9904i	−0.262305	+	0.978936i	−0.963879	+	0.266339i	$0.914186\pi$
$878$	0.494214	−	1.84443i	0.0166789	−	0.0622465i
$879$	0.383584	+	3.09640i	0.0129380	+	0.104439i
$880$	13.8301	+	23.9545i	0.466213	+	0.807505i
$881$	11.7417	−	20.3372i	0.395588	−	0.685178i	−0.597588	−	0.801803i	$-0.703874\pi$
$881$	11.7417	−	20.3372i	0.395588	−	0.685178i	0.993176	+	0.116625i	$0.0372076\pi$
$882$	−10.9943	−	19.7336i	−0.370197	−	0.664464i
$883$		−	33.3731i		−	1.12309i	−0.827445	−	0.561547i	$-0.810207\pi$
$883$		−	33.3731i		−	1.12309i	0.827445	−	0.561547i	$-0.189793\pi$
$884$		0			0
$885$	6.19615	+	4.83020i	0.208281	+	0.162365i
$886$	16.3205	−	4.37307i	0.548298	−	0.146916i
$887$	21.8683	+	12.6257i	0.734266	+	0.423929i	0.819981	−	0.572391i	$-0.193984\pi$
$887$	21.8683	+	12.6257i	0.734266	+	0.423929i	−0.0857146	+	0.996320i	$0.527317\pi$
$888$	3.37965	−	24.2373i	0.113414	−	0.813351i
$889$	9.12436	+	9.12436i	0.306021	+	0.306021i
$890$	20.4416	+	5.47732i	0.685206	+	0.183600i
$891$	−8.48560	−	36.0441i	−0.284278	−	1.20752i
$892$	4.90897	−	4.90897i	0.164364	−	0.164364i
$893$	−20.1563	+	11.6373i	−0.674505	+	0.389426i
$894$	8.45743	+	20.8680i	0.282859	+	0.697929i
$895$	10.3468	+	38.6147i	0.345855	+	1.29075i
$896$	18.4443			0.616181
$897$		0			0
$898$	30.9808			1.03384
$899$	−6.46575	−	24.1305i	−0.215645	−	0.804797i
$900$	−2.11238	−	0.600781i	−0.0704127	−	0.0200260i
$901$	3.40192	−	1.96410i	0.113335	−	0.0654337i
$902$	24.6247	−	24.6247i	0.819913	−	0.819913i
$903$	−4.29272	+	3.24207i	−0.142853	+	0.107889i
$904$	25.9186	+	6.94486i	0.862039	+	0.230983i
$905$	−3.19465	−	3.19465i	−0.106194	−	0.106194i
$906$	−1.95791	−	0.273011i	−0.0650473	−	0.00907018i
$907$	15.0000	+	8.66025i	0.498067	+	0.287559i	0.727915	−	0.685668i	$-0.240490\pi$
$907$	15.0000	+	8.66025i	0.498067	+	0.287559i	−0.229848	+	0.973227i	$0.573823\pi$
$908$	5.24796	−	1.40619i	0.174160	−	0.0466659i
$909$	4.41244	+	17.5359i	0.146351	+	0.581629i
$910$		0			0
$911$			1.55910i			0.0516552i	0.999666	+	0.0258276i	$0.00822209\pi$
$911$			1.55910i			0.0516552i	−0.999666	+	0.0258276i	$0.991778\pi$
$912$	−27.5121	−	11.6431i	−0.911016	−	0.385543i
$913$	8.46410	−	14.6603i	0.280121	−	0.485184i
$914$	2.93730	+	5.08755i	0.0971572	+	0.168281i
$915$	−18.1204	+	2.24477i	−0.599043	+	0.0742099i
$916$	1.38526	−	5.16987i	0.0457704	−	0.170817i
$917$	2.90931	−	10.8577i	0.0960740	−	0.358553i
$918$	−14.2504	−	36.7670i	−0.470333	−	1.21349i
$919$	−6.70577	−	11.6147i	−0.221203	−	0.383135i	0.733971	−	0.679181i	$-0.237665\pi$
$919$	−6.70577	−	11.6147i	−0.221203	−	0.383135i	−0.955174	+	0.296046i	$0.904332\pi$
$920$		0			0
$921$	−8.01177	+	18.9314i	−0.263997	+	0.623809i
$922$			32.0333i			1.05496i
$923$		0			0
$924$	−1.66025	+	2.12976i	−0.0546183	+	0.0700641i
$925$	−14.2942	+	3.83013i	−0.469991	+	0.125934i
$926$	42.5188	+	24.5483i	1.39726	+	0.806706i
$927$	−14.4705	−	14.9200i	−0.475272	−	0.490036i
$928$	−7.63397	−	7.63397i	−0.250597	−	0.250597i
$929$	19.6901	+	5.27594i	0.646011	+	0.173098i	0.566924	−	0.823770i	$-0.308133\pi$
$929$	19.6901	+	5.27594i	0.646011	+	0.173098i	0.0790861	+	0.996868i	$0.474800\pi$
$930$	8.24997	+	10.9235i	0.270527	+	0.358196i
$931$	−13.6603	+	13.6603i	−0.447697	+	0.447697i
$932$	−4.05065	+	2.33864i	−0.132683	+	0.0766048i
$933$	−16.1777	+	6.55656i	−0.529635	+	0.214652i
$934$	−7.47114	−	27.8827i	−0.244463	−	0.912349i
$935$	31.2229			1.02110
$936$		0			0
$937$	−37.0000			−1.20874			−0.604369	−	0.796705i	$-0.706575\pi$
$937$	−37.0000			−1.20874			−0.604369	+	0.796705i	$0.706575\pi$
$938$	−3.27110	−	12.2079i	−0.106805	−	0.398603i
$939$	−3.21046	+	1.30114i	−0.104769	+	0.0424612i
$940$	2.10512	−	1.21539i	0.0686614	−	0.0396417i
$941$	−9.14570	+	9.14570i	−0.298141	+	0.298141i	−0.840285	−	0.542144i	$-0.817613\pi$
$941$	−9.14570	+	9.14570i	−0.298141	+	0.298141i	0.542144	+	0.840285i	$0.317613\pi$
$942$	7.55181	+	9.99911i	0.246051	+	0.325789i
$943$		0			0
$944$	9.50749	+	9.50749i	0.309442	+	0.309442i
$945$	−1.19242	−	11.0022i	−0.0387895	−	0.357900i
$946$	−11.7846	−	6.80385i	−0.383151	−	0.221212i
$947$	10.3635	−	2.77689i	0.336768	−	0.0902368i	−0.0864720	−	0.996254i	$-0.527559\pi$
$947$	10.3635	−	2.77689i	0.336768	−	0.0902368i	0.423240	+	0.906018i	$0.360893\pi$
$948$	0.570669	−	0.732051i	0.0185345	−	0.0237759i
$949$		0			0
$950$			15.8968i			0.515760i
$951$	10.8372	−	25.6076i	0.351420	−	0.830385i
$952$	9.29423	−	16.0981i	0.301228	−	0.521742i
$953$	−0.988427	−	1.71201i	−0.0320183	−	0.0554573i	0.849572	−	0.527472i	$-0.176860\pi$
$953$	−0.988427	−	1.71201i	−0.0320183	−	0.0554573i	−0.881591	+	0.472015i	$0.843527\pi$
$954$	1.80740	−	3.02279i	0.0585169	−	0.0978666i
$955$	−1.88269	+	7.02628i	−0.0609223	+	0.227365i
$956$	−0.647124	+	2.41510i	−0.0209295	+	0.0781099i
$957$	−50.7000	+	6.28076i	−1.63890	+	0.203028i
$958$	−15.4904	−	26.8301i	−0.500471	−	0.866842i
$959$	4.75374	−	8.23373i	0.153506	−	0.265881i
$960$	−15.9990	−	6.77079i	−0.516366	−	0.218526i
$961$		−	18.8564i		−	0.608271i
$962$		0			0
$963$	−55.3205	+	13.9199i	−1.78268	+	0.448563i
$964$	3.76795	−	1.00962i	0.121357	−	0.0325176i
$965$	−0.180895	−	0.104440i	−0.00582321	−	0.00336203i
$966$		0			0
$967$	−27.8564	−	27.8564i	−0.895802	−	0.895802i	0.0992599	−	0.995062i	$-0.468352\pi$
$967$	−27.8564	−	27.8564i	−0.895802	−	0.895802i	−0.995062	+	0.0992599i	$0.968352\pi$
$968$	14.9363	+	4.00218i	0.480072	+	0.128635i
$969$	−26.9098	+	20.3236i	−0.864467	+	0.652887i
$970$	−2.71281	+	2.71281i	−0.0871032	+	0.0871032i
$971$	−41.4335	+	23.9216i	−1.32966	+	0.767682i	−0.985247	−	0.171136i	$-0.945256\pi$
$971$	−41.4335	+	23.9216i	−1.32966	+	0.767682i	−0.344416	+	0.938817i	$0.611923\pi$
$972$	−3.21415	−	2.66755i	−0.103094	−	0.0855618i
$973$	6.73205	+	25.1244i	0.215820	+	0.805450i
$974$	−8.67197			−0.277868
$975$		0			0
$976$	−31.2487			−1.00025
$977$	−6.13194	−	22.8847i	−0.196178	−	0.732147i	−0.991959	−	0.126562i	$-0.959606\pi$
$977$	−6.13194	−	22.8847i	−0.196178	−	0.732147i	0.795780	−	0.605585i	$-0.207061\pi$
$978$	−4.05721	−	10.0108i	−0.129735	−	0.320111i
$979$	33.2487	−	19.1962i	1.06263	−	0.613512i
$980$	1.42667	−	1.42667i	0.0455734	−	0.0455734i
$981$	−55.9800	−	0.856198i	−1.78730	−	0.0273363i
$982$	41.4904	+	11.1173i	1.32401	+	0.354768i
$983$	−30.4433	−	30.4433i	−0.970992	−	0.970992i	0.0285990	−	0.999591i	$-0.490895\pi$
$983$	−30.4433	−	30.4433i	−0.970992	−	0.970992i	−0.999591	+	0.0285990i	$0.990895\pi$
$984$	−3.50677	+	25.1490i	−0.111792	+	0.801721i
$985$	5.36603	+	3.09808i	0.170976	+	0.0987129i
$986$	−52.5485	+	14.0803i	−1.67349	+	0.448409i
$987$	−11.6373	−	9.07180i	−0.370418	−	0.288758i
$988$		0			0
$989$		0			0
$990$	24.4545	−	13.6245i	0.777214	−	0.433014i
$991$	28.7846	−	49.8564i	0.914373	−	1.58374i	0.106557	−	0.994307i	$-0.466017\pi$
$991$	28.7846	−	49.8564i	0.914373	−	1.58374i	0.807816	−	0.589434i	$-0.200649\pi$
$992$	2.62398	+	4.54486i	0.0833114	+	0.144300i
$993$	7.28650	+	58.8186i	0.231230	+	1.86655i
$994$	1.66025	−	6.19615i	0.0526601	−	0.196530i
$995$	−5.03908	+	18.8061i	−0.159750	+	0.596193i
$996$	−0.234755	−	1.89501i	−0.00743851	−	0.0600457i
$997$	3.50000	+	6.06218i	0.110846	+	0.191991i	0.916112	−	0.400923i	$-0.131311\pi$
$997$	3.50000	+	6.06218i	0.110846	+	0.191991i	−0.805266	+	0.592914i	$0.797977\pi$
$998$	2.62398	−	4.54486i	0.0830606	−	0.143865i
$999$	−27.8132	−	4.31286i	−0.879970	−	0.136453i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.k.e.488.2		8
3.2	odd	2	inner	507.2.k.e.488.1		8
13.2	odd	12	inner	507.2.k.e.80.1		8
13.3	even	3		39.2.k.b.11.1	✓	8
13.4	even	6		507.2.f.e.437.2		8
13.5	odd	4		39.2.k.b.32.2	yes	8
13.6	odd	12		507.2.f.f.239.2		8
13.7	odd	12		507.2.f.e.239.3		8
13.8	odd	4		507.2.k.d.188.1		8
13.9	even	3		507.2.f.f.437.3		8
13.10	even	6		507.2.k.d.89.2		8
13.11	odd	12		507.2.k.f.80.2		8
13.12	even	2		507.2.k.f.488.1		8
39.2	even	12	inner	507.2.k.e.80.2		8
39.5	even	4		39.2.k.b.32.1	yes	8
39.8	even	4		507.2.k.d.188.2		8
39.11	even	12		507.2.k.f.80.1		8
39.17	odd	6		507.2.f.e.437.3		8
39.20	even	12		507.2.f.e.239.2		8
39.23	odd	6		507.2.k.d.89.1		8
39.29	odd	6		39.2.k.b.11.2	yes	8
39.32	even	12		507.2.f.f.239.3		8
39.35	odd	6		507.2.f.f.437.2		8
39.38	odd	2		507.2.k.f.488.2		8
52.3	odd	6		624.2.cn.c.401.1		8
52.31	even	4		624.2.cn.c.305.2		8
65.3	odd	12		975.2.bp.f.674.1		8
65.18	even	4		975.2.bp.e.149.1		8
65.29	even	6		975.2.bo.d.401.2		8
65.42	odd	12		975.2.bp.e.674.2		8
65.44	odd	4		975.2.bo.d.851.1		8
65.57	even	4		975.2.bp.f.149.2		8
156.83	odd	4		624.2.cn.c.305.1		8
156.107	even	6		624.2.cn.c.401.2		8
195.29	odd	6		975.2.bo.d.401.1		8
195.44	even	4		975.2.bo.d.851.2		8
195.68	even	12		975.2.bp.f.674.2		8
195.83	odd	4		975.2.bp.e.149.2		8
195.107	even	12		975.2.bp.e.674.1		8
195.122	odd	4		975.2.bp.f.149.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.k.b.11.1	✓	8	13.3	even	3
39.2.k.b.11.2	yes	8	39.29	odd	6
39.2.k.b.32.1	yes	8	39.5	even	4
39.2.k.b.32.2	yes	8	13.5	odd	4
507.2.f.e.239.2		8	39.20	even	12
507.2.f.e.239.3		8	13.7	odd	12
507.2.f.e.437.2		8	13.4	even	6
507.2.f.e.437.3		8	39.17	odd	6
507.2.f.f.239.2		8	13.6	odd	12
507.2.f.f.239.3		8	39.32	even	12
507.2.f.f.437.2		8	39.35	odd	6
507.2.f.f.437.3		8	13.9	even	3
507.2.k.d.89.1		8	39.23	odd	6
507.2.k.d.89.2		8	13.10	even	6
507.2.k.d.188.1		8	13.8	odd	4
507.2.k.d.188.2		8	39.8	even	4
507.2.k.e.80.1		8	13.2	odd	12	inner
507.2.k.e.80.2		8	39.2	even	12	inner
507.2.k.e.488.1		8	3.2	odd	2	inner
507.2.k.e.488.2		8	1.1	even	1	trivial
507.2.k.f.80.1		8	39.11	even	12
507.2.k.f.80.2		8	13.11	odd	12
507.2.k.f.488.1		8	13.12	even	2
507.2.k.f.488.2		8	39.38	odd	2
624.2.cn.c.305.1		8	156.83	odd	4
624.2.cn.c.305.2		8	52.31	even	4
624.2.cn.c.401.1		8	52.3	odd	6
624.2.cn.c.401.2		8	156.107	even	6
975.2.bo.d.401.1		8	195.29	odd	6
975.2.bo.d.401.2		8	65.29	even	6
975.2.bo.d.851.1		8	65.44	odd	4
975.2.bo.d.851.2		8	195.44	even	4
975.2.bp.e.149.1		8	65.18	even	4
975.2.bp.e.149.2		8	195.83	odd	4
975.2.bp.e.674.1		8	195.107	even	12
975.2.bp.e.674.2		8	65.42	odd	12
975.2.bp.f.149.1		8	195.122	odd	4
975.2.bp.f.149.2		8	65.57	even	4
975.2.bp.f.674.1		8	65.3	odd	12
975.2.bp.f.674.2		8	195.68	even	12

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.k (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.389774 + 1.45466i) q^{2} +(-1.60523 + 0.650571i) q^{3} +(-0.232051 + 0.133975i) q^{4} +(1.06488 - 1.06488i) q^{5} +(-1.57203 - 2.08148i) q^{6} +(-1.36603 - 0.366025i) q^{7} +(1.84443 + 1.84443i) q^{8} +(2.15351 - 2.08863i) q^{9} +O(q^{10})\)	\(q+(0.389774 + 1.45466i) q^{2} +(-1.60523 + 0.650571i) q^{3} +(-0.232051 + 0.133975i) q^{4} +(1.06488 - 1.06488i) q^{5} +(-1.57203 - 2.08148i) q^{6} +(-1.36603 - 0.366025i) q^{7} +(1.84443 + 1.84443i) q^{8} +(2.15351 - 2.08863i) q^{9} +(1.96410 + 1.13397i) q^{10} +(3.97420 - 1.06488i) q^{11} +(0.285334 - 0.366025i) q^{12} -2.12976i q^{14} +(-1.01660 + 2.40216i) q^{15} +(-2.23205 + 3.86603i) q^{16} +(2.51954 + 4.36397i) q^{17} +(3.87762 + 2.31853i) q^{18} +(1.00000 - 3.73205i) q^{19} +(-0.104440 + 0.389774i) q^{20} +(2.43091 - 0.301143i) q^{21} +(3.09808 + 5.36603i) q^{22} +(-4.16067 - 1.76080i) q^{24} +2.73205i q^{25} +(-2.09808 + 4.75374i) q^{27} +(0.366025 - 0.0980762i) q^{28} +(6.20840 + 3.58442i) q^{29} +(-3.89056 - 0.542499i) q^{30} +(-2.46410 - 2.46410i) q^{31} +(-1.45466 - 0.389774i) q^{32} +(-5.68671 + 4.29488i) q^{33} +(-5.36603 + 5.36603i) q^{34} +(-1.84443 + 1.06488i) q^{35} +(-0.219901 + 0.773185i) q^{36} +(1.40192 + 5.23205i) q^{37} +5.81863 q^{38} +3.92820 q^{40} +(-1.45466 - 5.42885i) q^{41} +(1.38556 + 3.41876i) q^{42} +(-1.90192 + 1.09808i) q^{43} +(-0.779548 + 0.779548i) q^{44} +(0.0690922 - 4.51739i) q^{45} +(-4.25953 - 4.25953i) q^{47} +(1.06782 - 7.65796i) q^{48} +(-4.33013 - 2.50000i) q^{49} +(-3.97420 + 1.06488i) q^{50} +(-6.88351 - 5.36603i) q^{51} -0.779548i q^{53} +(-7.73284 - 1.19909i) q^{54} +(3.09808 - 5.36603i) q^{55} +(-1.84443 - 3.19465i) q^{56} +(0.822738 + 6.64136i) q^{57} +(-2.79423 + 10.4282i) q^{58} +(0.779548 - 2.90931i) q^{59} +(-0.0859264 - 0.693622i) q^{60} +(3.50000 + 6.06218i) q^{61} +(2.62398 - 4.54486i) q^{62} +(-3.70625 + 2.06488i) q^{63} +6.66025i q^{64} +(-8.46410 - 6.59817i) q^{66} +(5.73205 - 1.53590i) q^{67} +(-1.16932 - 0.675108i) q^{68} +(-2.26795 - 2.26795i) q^{70} +(2.90931 + 0.779548i) q^{71} +(7.82434 + 0.119671i) q^{72} +(-0.901924 + 0.901924i) q^{73} +(-7.06440 + 4.07863i) q^{74} +(-1.77739 - 4.38556i) q^{75} +(0.267949 + 1.00000i) q^{76} -5.81863 q^{77} +2.00000 q^{79} +(1.73999 + 6.49373i) q^{80} +(0.275241 - 8.99579i) q^{81} +(7.33013 - 4.23205i) q^{82} +(2.90931 - 2.90931i) q^{83} +(-0.523749 + 0.395560i) q^{84} +(7.33013 + 1.96410i) q^{85} +(-2.33864 - 2.33864i) q^{86} +(-12.2978 - 1.71481i) q^{87} +(9.29423 + 5.36603i) q^{88} +(9.01327 - 2.41510i) q^{89} +(6.59817 - 1.66025i) q^{90} +(5.55852 + 2.35237i) q^{93} +(4.53590 - 7.85641i) q^{94} +(-2.90931 - 5.03908i) q^{95} +(2.58863 - 0.320682i) q^{96} +(-0.437822 + 1.63397i) q^{97} +(1.94887 - 7.27328i) q^{98} +(6.33434 - 10.5939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 12 q^{4} - 14 q^{6} - 4 q^{7} + 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 12 * q^4 - 14 * q^6 - 4 * q^7 + 4 * q^9	\( 8 q - 2 q^{3} + 12 q^{4} - 14 q^{6} - 4 q^{7} + 4 q^{9} - 12 q^{10} - 2 q^{15} - 4 q^{16} + 4 q^{18} + 8 q^{19} + 4 q^{21} + 4 q^{22} - 30 q^{24} + 4 q^{27} - 4 q^{28} - 18 q^{30} + 8 q^{31} - 20 q^{33} - 36 q^{34} + 36 q^{36} + 32 q^{37} - 24 q^{40} - 16 q^{42} - 36 q^{43} + 16 q^{45} - 14 q^{48} - 38 q^{54} + 4 q^{55} + 16 q^{57} + 40 q^{58} + 44 q^{60} + 28 q^{61} + 16 q^{63} - 40 q^{66} + 32 q^{67} - 32 q^{70} + 24 q^{72} - 28 q^{73} - 12 q^{75} + 16 q^{76} + 16 q^{79} + 4 q^{81} + 24 q^{82} - 8 q^{84} + 24 q^{85} - 34 q^{87} + 12 q^{88} + 16 q^{93} + 64 q^{94} + 16 q^{96} - 52 q^{97} + 40 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 + 12 * q^4 - 14 * q^6 - 4 * q^7 + 4 * q^9 - 12 * q^10 - 2 * q^15 - 4 * q^16 + 4 * q^18 + 8 * q^19 + 4 * q^21 + 4 * q^22 - 30 * q^24 + 4 * q^27 - 4 * q^28 - 18 * q^30 + 8 * q^31 - 20 * q^33 - 36 * q^34 + 36 * q^36 + 32 * q^37 - 24 * q^40 - 16 * q^42 - 36 * q^43 + 16 * q^45 - 14 * q^48 - 38 * q^54 + 4 * q^55 + 16 * q^57 + 40 * q^58 + 44 * q^60 + 28 * q^61 + 16 * q^63 - 40 * q^66 + 32 * q^67 - 32 * q^70 + 24 * q^72 - 28 * q^73 - 12 * q^75 + 16 * q^76 + 16 * q^79 + 4 * q^81 + 24 * q^82 - 8 * q^84 + 24 * q^85 - 34 * q^87 + 12 * q^88 + 16 * q^93 + 64 * q^94 + 16 * q^96 - 52 * q^97 + 40 * q^99

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