LMFDB - Embedded newform 507.2.k.f.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.f.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} +(0.239203 + 1.71545i) q^{3} +(-0.232051 + 0.133975i) q^{4} +(1.06488 - 1.06488i) q^{5} +(-2.40216 + 1.01660i) q^{6} +(1.36603 + 0.366025i) q^{7} +(1.84443 + 1.84443i) q^{8} +(-2.88556 + 0.820682i) q^{9} +(1.96410 + 1.13397i) q^{10} +(3.97420 - 1.06488i) q^{11} +(-0.285334 - 0.366025i) q^{12} +2.12976i q^{14} +(2.08148 + 1.57203i) q^{15} +(-2.23205 + 3.86603i) q^{16} +(-2.51954 - 4.36397i) q^{17} +(-2.31853 - 3.87762i) q^{18} +(-1.00000 + 3.73205i) q^{19} +(-0.104440 + 0.389774i) q^{20} +(-0.301143 + 2.43091i) q^{21} +(3.09808 + 5.36603i) q^{22} +(-2.72284 + 3.60523i) q^{24} +2.73205i q^{25} +(-2.09808 - 4.75374i) q^{27} +(-0.366025 + 0.0980762i) q^{28} +(-6.20840 - 3.58442i) q^{29} +(-1.47546 + 3.64058i) q^{30} +(2.46410 + 2.46410i) q^{31} +(-1.45466 - 0.389774i) q^{32} +(2.77739 + 6.56283i) q^{33} +(5.36603 - 5.36603i) q^{34} +(1.84443 - 1.06488i) q^{35} +(0.559647 - 0.577032i) q^{36} +(-1.40192 - 5.23205i) q^{37} -5.81863 q^{38} +3.92820 q^{40} +(-1.45466 - 5.42885i) q^{41} +(-3.65351 + 0.509445i) q^{42} +(-1.90192 + 1.09808i) q^{43} +(-0.779548 + 0.779548i) q^{44} +(-2.19886 + 3.94672i) q^{45} +(-4.25953 - 4.25953i) q^{47} +(-7.16590 - 2.90422i) q^{48} +(-4.33013 - 2.50000i) q^{49} +(-3.97420 + 1.06488i) q^{50} +(6.88351 - 5.36603i) q^{51} +0.779548i q^{53} +(6.09729 - 4.90487i) q^{54} +(3.09808 - 5.36603i) q^{55} +(1.84443 + 3.19465i) q^{56} +(-6.64136 - 0.822738i) q^{57} +(2.79423 - 10.4282i) q^{58} +(0.779548 - 2.90931i) q^{59} +(-0.693622 - 0.0859264i) q^{60} +(3.50000 + 6.06218i) q^{61} +(-2.62398 + 4.54486i) q^{62} +(-4.24214 + 0.0648824i) 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} +(-6.83591 - 3.80853i) q^{72} +(0.901924 - 0.901924i) q^{73} +(7.06440 - 4.07863i) q^{74} +(-4.68671 + 0.653513i) q^{75} +(-0.267949 - 1.00000i) q^{76} +5.81863 q^{77} +2.00000 q^{79} +(1.73999 + 6.49373i) q^{80} +(7.65296 - 4.73626i) q^{81} +(7.33013 - 4.23205i) q^{82} +(2.90931 - 2.90931i) q^{83} +(-0.255799 - 0.604440i) q^{84} +(-7.33013 - 1.96410i) q^{85} +(-2.33864 - 2.33864i) q^{86} +(4.66384 - 11.5076i) q^{87} +(9.29423 + 5.36603i) q^{88} +(9.01327 - 2.41510i) q^{89} +(-6.59817 - 1.66025i) q^{90} +(-3.63763 + 4.81647i) q^{93} +(4.53590 - 7.85641i) q^{94} +(2.90931 + 5.03908i) q^{95} +(0.320682 - 2.58863i) q^{96} +(0.437822 - 1.63397i) q^{97} +(1.94887 - 7.27328i) q^{98} +(-10.5939 + 6.33434i) 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} - 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}+ \cdots - 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

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	$0.737941\pi$
$3$	0.239203	+	1.71545i	0.138104	+	0.990418i
$3$	0.239203	+	1.71545i	0.138104	+	0.990418i
$4$	−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	$0.140674\pi$
$6$	−2.40216	+	1.01660i	−0.980678	+	0.415024i
$7$	1.36603	+	0.366025i	0.516309	+	0.138345i	0.507559	−	0.861617i	$-0.330548\pi$
$7$	1.36603	+	0.366025i	0.516309	+	0.138345i	0.00875026	+	0.999962i	$0.497215\pi$
$8$	1.84443	+	1.84443i	0.652105	+	0.652105i
$9$	−2.88556	+	0.820682i	−0.961855	+	0.273561i
$10$	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
$15$	2.08148	+	1.57203i	0.537436	+	0.405897i
$16$	−2.23205	+	3.86603i	−0.558013	+	0.966506i
$17$	−2.51954	−	4.36397i	−0.611078	−	1.05842i	−0.991059	−	0.133424i	$-0.957403\pi$
$17$	−2.51954	−	4.36397i	−0.611078	−	1.05842i	0.379981	−	0.924994i	$-0.375930\pi$
$18$	−2.31853	−	3.87762i	−0.546482	−	0.913965i
$19$	−1.00000	+	3.73205i	−0.229416	+	0.856191i	0.751171	+	0.660107i	$0.229489\pi$
$19$	−1.00000	+	3.73205i	−0.229416	+	0.856191i	−0.980587	+	0.196084i	$0.937177\pi$
$20$	−0.104440	+	0.389774i	−0.0233534	+	0.0871561i
$21$	−0.301143	+	2.43091i	−0.0657148	+	0.530468i
$22$	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	$0.166667\pi$
$24$	−2.72284	+	3.60523i	−0.555798	+	0.735914i
$25$			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	−0.203286	−	0.979119i	$-0.565162\pi$
$29$	−6.20840	−	3.58442i	−1.15287	−	0.665610i	−0.949585	+	0.313509i	$0.898495\pi$
$30$	−1.47546	+	3.64058i	−0.269381	+	0.664675i
$31$	2.46410	+	2.46410i	0.442566	+	0.442566i	0.892873	−	0.450308i	$-0.148686\pi$
$31$	2.46410	+	2.46410i	0.442566	+	0.442566i	−0.450308	+	0.892873i	$0.648686\pi$
$32$	−1.45466	−	0.389774i	−0.257149	−	0.0689030i
$33$	2.77739	+	6.56283i	0.483482	+	1.14244i
$34$	5.36603	−	5.36603i	0.920266	−	0.920266i
$35$	1.84443	−	1.06488i	0.311766	−	0.179998i
$36$	0.559647	−	0.577032i	0.0932745	−	0.0961720i
$37$	−1.40192	−	5.23205i	−0.230475	−	0.860144i	−0.980137	−	0.198323i	$-0.936451\pi$
$37$	−1.40192	−	5.23205i	−0.230475	−	0.860144i	0.749662	−	0.661821i	$-0.230216\pi$
$38$	−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	$-0.227957\pi$
$42$	−3.65351	+	0.509445i	−0.563749	+	0.0786091i
$43$	−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
$45$	−2.19886	+	3.94672i	−0.327786	+	0.588342i
$46$		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	$0.894787\pi$
$48$	−7.16590	−	2.90422i	−1.03431	−	0.419188i
$49$	−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	$0.0170503\pi$
$53$			0.779548i			0.107079i	−0.998566	+	0.0535396i	$0.982950\pi$
$54$	6.09729	−	4.90487i	0.829736	−	0.667468i
$55$	3.09808	−	5.36603i	0.417745	−	0.723555i
$56$	1.84443	+	3.19465i	0.246472	+	0.426903i
$57$	−6.64136	−	0.822738i	−0.879670	−	0.108974i
$58$	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	$0.0205184\pi$
$60$	−0.693622	−	0.0859264i	−0.0895462	−	0.0110931i
$61$	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
$63$	−4.24214	+	0.0648824i	−0.534460	+	0.00817442i
$64$			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	−0.591357	−	0.806410i	$-0.701407\pi$
$67$	−5.73205	+	1.53590i	−0.700281	+	0.187640i	−0.108925	+	0.994050i	$0.534741\pi$
$68$	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	$0.526136\pi$
$72$	−6.83591	−	3.80853i	−0.805620	−	0.448840i
$73$	0.901924	−	0.901924i	0.105562	−	0.105562i	−0.652353	−	0.757915i	$-0.726218\pi$
$73$	0.901924	−	0.901924i	0.105562	−	0.105562i	0.757915	+	0.652353i	$0.226218\pi$
$74$	7.06440	−	4.07863i	0.821220	−	0.474132i
$75$	−4.68671	+	0.653513i	−0.541174	+	0.0754612i
$76$	−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
$81$	7.65296	−	4.73626i	0.850329	−	0.526251i
$82$	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	$0.177498\pi$
$84$	−0.255799	−	0.604440i	−0.0279100	−	0.0659498i
$85$	−7.33013	−	1.96410i	−0.795064	−	0.213037i
$86$	−2.33864	−	2.33864i	−0.252182	−	0.252182i
$87$	4.66384	−	11.5076i	0.500017	−	1.23375i
$88$	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
$93$	−3.63763	+	4.81647i	−0.377205	+	0.499445i
$94$	4.53590	−	7.85641i	0.467842	−	0.810326i
$95$	2.90931	+	5.03908i	0.298489	+	0.516998i
$96$	0.320682	−	2.58863i	0.0327295	−	0.264201i
$97$	0.437822	−	1.63397i	0.0444541	−	0.165905i	−0.940130	−	0.340815i	$-0.889297\pi$
$97$	0.437822	−	1.63397i	0.0444541	−	0.165905i	0.984584	+	0.174910i	$0.0559636\pi$
$98$	1.94887	−	7.27328i	0.196866	−	0.734712i
$99$	−10.5939	+	6.33434i	−1.06472	+	0.636625i
$100$	−0.366025	−	0.633975i	−0.0366025	−	0.0633975i
$101$	3.01375	−	5.21997i	0.299880	−	0.519407i	−0.676229	−	0.736692i	$-0.736387\pi$
$101$	3.01375	−	5.21997i	0.299880	−	0.519407i	0.976108	+	0.217285i	$0.0697202\pi$
$102$	10.4887	+	7.92160i	1.03854	+	0.784356i
$103$		−	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	$0.0377682\pi$
$107$	16.4675	+	9.50749i	1.59197	+	0.919123i	0.598999	+	0.800749i	$0.295565\pi$
$108$	1.12374	+	0.822021i	0.108132	+	0.0790990i
$109$	13.1962	+	13.1962i	1.26396	+	1.26396i	0.949156	+	0.314806i	$0.101940\pi$
$109$	13.1962	+	13.1962i	1.26396	+	1.26396i	0.314806	+	0.949156i	$0.398060\pi$
$110$	9.01327	+	2.41510i	0.859382	+	0.230271i
$111$	8.64000	−	3.65646i	0.820072	−	0.347055i
$112$	−4.46410	+	4.46410i	−0.421818	+	0.421818i
$113$	−8.90883	+	5.14352i	−0.838073	+	0.483861i	−0.856609	−	0.515967i	$-0.827433\pi$
$113$	−8.90883	+	5.14352i	−0.838073	+	0.483861i	0.0185360	+	0.999828i	$0.494099\pi$
$114$	−1.39183	−	9.98158i	−0.130357	−	0.934861i
$115$		0			0
$116$	1.92089			0.178350
$117$		0			0
$118$	4.53590			0.417563
$119$	−1.84443	−	6.88351i	−0.169079	−	0.631010i
$120$	0.939636	+	6.73865i	0.0857767	+	0.615152i
$121$	5.13397	−	2.96410i	0.466725	−	0.269464i
$122$	−7.45418	+	7.45418i	−0.674869	+	0.674869i
$123$	8.96499	−	3.79399i	0.808346	−	0.342093i
$124$	−0.901924	−	0.241670i	−0.0809951	−	0.0217026i
$125$	8.23373	+	8.23373i	0.736447	+	0.736447i
$126$	−1.74786	−	6.14557i	−0.155712	−	0.547491i
$127$	−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	$-0.887123\pi$
$131$		−	7.94839i		−	0.694454i	0.937781	−	0.347227i	$-0.112877\pi$
$132$	−1.52375	−	1.15081i	−0.132625	−	0.100165i
$133$	−2.73205	+	4.73205i	−0.236899	+	0.410321i
$134$	−4.46841	−	7.73951i	−0.386012	−	0.668592i
$135$	−7.29638	−	2.82797i	−0.627973	−	0.243393i
$136$	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
$141$	6.28814	−	8.32592i	0.529557	−	0.701169i
$142$			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
$147$	3.25286	−	8.02614i	0.268291	−	0.661985i
$148$	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	$0.698374\pi$
$150$	−2.77739	−	6.56283i	−0.226773	−	0.535853i
$151$	−0.535898	+	0.535898i	−0.0436108	+	0.0436108i	−0.728576	−	0.684965i	$-0.759817\pi$
$151$	−0.535898	+	0.535898i	−0.0436108	+	0.0436108i	0.684965	+	0.728576i	$0.259817\pi$
$152$	−8.72794	+	5.03908i	−0.707929	+	0.408723i
$153$	10.8517	+	10.5248i	0.877310	+	0.850878i
$154$	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
$159$	−1.33728	+	0.186470i	−0.106053	+	0.0147880i
$160$	−1.96410	+	1.13397i	−0.155276	+	0.0896486i
$161$		0			0
$162$	9.87256	+	9.28636i	0.775661	+	0.729605i
$163$	−4.00000	−	1.07180i	−0.313304	−	0.0839496i	0.0987406	−	0.995113i	$-0.468519\pi$
$163$	−4.00000	−	1.07180i	−0.313304	−	0.0839496i	−0.412045	+	0.911164i	$0.635185\pi$
$164$	1.06488	+	1.06488i	0.0831533	+	0.0831533i
$165$	9.94624	+	4.03104i	0.774313	+	0.313816i
$166$	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
$171$	−0.177262	−	11.5898i	−0.0135556	−	0.886291i
$172$	0.294229	−	0.509619i	0.0224347	−	0.0388581i
$173$	8.72794	+	15.1172i	0.663573	+	1.14934i	0.979670	+	0.200615i	$0.0642941\pi$
$173$	8.72794	+	15.1172i	0.663573	+	1.14934i	−0.316097	+	0.948727i	$0.602373\pi$
$174$	18.5575	+	2.29892i	1.40684	+	0.174281i
$175$	−1.00000	+	3.73205i	−0.0755929	+	0.282117i
$176$	−4.75374	+	17.7412i	−0.358327	+	1.33729i
$177$	5.17726	+	0.641364i	0.389147	+	0.0482078i
$178$	7.02628	+	12.1699i	0.526642	+	0.912171i
$179$	13.2728	−	22.9892i	0.992056	−	1.71829i	0.387084	−	0.922045i	$-0.373482\pi$
$179$	13.2728	−	22.9892i	0.992056	−	1.71829i	0.604972	−	0.796247i	$-0.293184\pi$
$180$	−0.0185132	−	1.21043i	−0.00137989	−	0.0902201i
$181$		−	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
$186$	−8.42417	−	3.41417i	−0.617690	−	0.250339i
$187$	−14.6603	−	14.6603i	−1.07206	−	1.07206i
$188$	1.55910	+	0.417759i	0.113709	+	0.0304682i
$189$	−1.12603	−	7.26168i	−0.0819070	−	0.528210i
$190$	−6.19615	+	6.19615i	−0.449516	+	0.449516i
$191$	4.18307	−	2.41510i	0.302677	−	0.174750i	−0.340968	−	0.940075i	$-0.610755\pi$
$191$	4.18307	−	2.41510i	0.302677	−	0.174750i	0.643645	+	0.765324i	$0.277421\pi$
$192$	−11.4254	+	1.59315i	−0.824554	+	0.114976i
$193$	0.0358984	+	0.133975i	0.00258402	+	0.00964370i	0.967206	−	0.253994i	$-0.0817443\pi$
$193$	0.0358984	+	0.133975i	0.00258402	+	0.00964370i	−0.964622	+	0.263638i	$0.915078\pi$
$194$	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	$0.869844\pi$
$198$	−13.3435	−	12.9415i	−0.948281	−	0.919711i
$199$	−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
$201$	−4.00588	−	9.46568i	−0.282553	−	0.667657i
$202$	8.76795	+	2.34936i	0.616911	+	0.165301i
$203$	−7.16884	−	7.16884i	−0.503154	−	0.503154i
$204$	−0.878413	+	2.16741i	−0.0615012	+	0.151749i
$205$	−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
$210$	−3.34806	+	4.43306i	−0.231038	+	0.305910i
$211$	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
$213$	−0.641364	+	5.17726i	−0.0439455	+	0.354740i
$214$	−7.41154	+	27.6603i	−0.506643	+	1.89082i
$215$	−0.856003	+	3.19465i	−0.0583789	+	0.217873i
$216$	4.89819	−	12.6377i	0.333280	−	0.859887i
$217$	2.46410	+	4.26795i	0.167274	+	0.289727i
$218$	−14.0524	+	24.3394i	−0.951745	+	1.64847i
$219$	1.76295	+	1.33147i	0.119129	+	0.0899722i
$220$			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	0.709196	−	0.705011i	$-0.249058\pi$
$223$	25.0263	−	6.70577i	1.67588	−	0.449052i	0.966687	+	0.255960i	$0.0823914\pi$
$224$	−1.84443	−	1.06488i	−0.123236	−	0.0711505i
$225$	−2.24214	−	7.88351i	−0.149476	−	0.525567i
$226$	−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	$0.818285\pi$
$228$	1.65136	−	0.698857i	0.109364	−	0.0462829i
$229$	14.1244	−	14.1244i	0.933364	−	0.933364i	−0.0645507	−	0.997914i	$-0.520561\pi$
$229$	14.1244	−	14.1244i	0.933364	−	0.933364i	0.997914	+	0.0645507i	$0.0205614\pi$
$230$		0			0
$231$	1.39183	+	9.98158i	0.0915757	+	0.656740i
$232$	−4.83975	−	18.0622i	−0.317745	−	1.18584i
$233$	−17.4559			−1.14357			−0.571786	−	0.820403i	$-0.693749\pi$
$233$	−17.4559			−1.14357			−0.571786	+	0.820403i	$0.693749\pi$
$234$		0			0
$235$	−9.07180			−0.591779
$236$	0.208879	+	0.779548i	0.0135969	+	0.0507443i
$237$	0.478405	+	3.43091i	0.0310757	+	0.222861i
$238$	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	$0.152415\pi$
$240$	−10.7235	+	4.53819i	−0.692198	+	0.292939i
$241$	14.0622	+	3.76795i	0.905825	+	0.242715i	0.681516	−	0.731803i	$-0.261321\pi$
$241$	14.0622	+	3.76795i	0.905825	+	0.242715i	0.224309	+	0.974518i	$0.427988\pi$
$242$	6.31284	+	6.31284i	0.405805	+	0.405805i
$243$	9.95544	+	11.9954i	0.638642	+	0.769504i
$244$	−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
$249$	5.68671	+	4.29488i	0.360380	+	0.272177i
$250$	−8.76795	+	15.1865i	−0.554534	+	0.960481i
$251$	−0.494214	−	0.856003i	−0.0311945	−	0.0540304i	0.850007	−	0.526772i	$-0.176598\pi$
$251$	−0.494214	−	0.856003i	−0.0311945	−	0.0540304i	−0.881201	+	0.472741i	$0.843264\pi$
$252$	0.975700	−	0.583396i	0.0614634	−	0.0367505i
$253$		0			0
$254$	3.55644	−	13.2728i	0.223151	−	0.832810i
$255$	1.61594	−	13.0443i	0.101194	−	0.816867i
$256$	−3.16025	−	5.47372i	−0.197516	−	0.342108i
$257$	−10.7533	+	18.6252i	−0.670770	+	1.16181i	0.306916	+	0.951737i	$0.400703\pi$
$257$	−10.7533	+	18.6252i	−0.670770	+	1.16181i	−0.977686	+	0.210071i	$0.932630\pi$
$258$	3.45243	−	4.57125i	0.214939	−	0.284593i
$259$		−	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	−0.231777	−	0.972769i	$-0.574454\pi$
$263$	−19.3003	−	11.1430i	−1.19011	−	0.687109i	−0.958331	+	0.285660i	$0.907787\pi$
$264$	−6.98197	+	17.2274i	−0.429710	+	1.06027i
$265$	0.830127	+	0.830127i	0.0509943	+	0.0509943i
$266$	−7.94839	−	2.12976i	−0.487347	−	0.130584i
$267$	6.29899	+	14.8842i	0.385492	+	0.910896i
$268$	1.12436	−	1.12436i	0.0686810	−	0.0686810i
$269$	−12.4168	+	7.16884i	−0.757066	+	0.437092i	−0.828241	−	0.560372i	$-0.810658\pi$
$269$	−12.4168	+	7.16884i	−0.757066	+	0.437092i	0.0711756	+	0.997464i	$0.477325\pi$
$270$	1.26979	−	11.7160i	0.0772769	−	0.713013i
$271$	2.00000	+	7.46410i	0.121491	+	0.453412i	0.999690	−	0.0248835i	$-0.00792149\pi$
$271$	2.00000	+	7.46410i	0.121491	+	0.453412i	−0.878199	+	0.478295i	$0.841255\pi$
$272$	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
$279$	−9.13257	−	5.08808i	−0.546752	−	0.304615i
$280$	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	$0.920997\pi$
$282$	14.5623	+	5.90185i	0.867172	+	0.351450i
$283$	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
$288$	4.51739	−	0.0690922i	0.266189	−	0.00407129i
$289$	−4.19615	+	7.26795i	−0.246832	+	0.427526i
$290$	−8.12929	−	14.0803i	−0.477368	−	0.826826i
$291$	2.90774	+	0.360213i	0.170455	+	0.0211161i
$292$	−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	$0.0665766\pi$
$294$	12.9432	+	1.60341i	0.754860	+	0.0935127i
$295$	−2.26795	−	3.92820i	−0.132045	−	0.228709i
$296$	7.06440	−	12.2359i	0.410610	−	0.711198i
$297$	−13.4003	−	16.6581i	−0.777567	−	0.966601i
$298$		−	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
$303$	9.67552	+	3.92132i	0.555844	+	0.225274i
$304$	−12.1962	−	12.1962i	−0.699497	−	0.699497i
$305$	10.1826	+	2.72842i	0.583054	+	0.156229i
$306$	−11.0802	+	19.8878i	−0.633414	+	1.13691i
$307$	−8.39230	+	8.39230i	−0.478974	+	0.478974i	−0.904803	−	0.425829i	$-0.859982\pi$
$307$	−8.39230	+	8.39230i	−0.478974	+	0.478974i	0.425829	+	0.904803i	$0.359982\pi$
$308$	−1.35022	+	0.779548i	−0.0769357	+	0.0444189i
$309$	11.8850	−	1.65724i	0.676115	−	0.0942773i
$310$	2.04552	+	7.63397i	0.116178	+	0.433581i
$311$	−10.0782			−0.571480			−0.285740	−	0.958307i	$-0.592239\pi$
$311$	−10.0782			−0.571480			−0.285740	+	0.958307i	$0.592239\pi$
$312$		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
$315$	−4.44829	+	4.58648i	−0.250633	+	0.258419i
$316$	−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	$0.398876\pi$
$318$	−0.792486	−	1.87260i	−0.0444404	−	0.105010i
$319$	−28.4904	−	7.63397i	−1.59516	−	0.427421i
$320$	7.09239	+	7.09239i	0.396477	+	0.396477i
$321$	−12.3706	+	30.5234i	−0.690460	+	1.70365i
$322$		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
$327$	−19.4808	+	25.7939i	−1.07729	+	1.42641i
$328$	7.33013	−	12.6962i	0.404739	−	0.701028i
$329$	−4.25953	−	7.37772i	−0.234835	−	0.406747i
$330$	−1.98699	+	16.0396i	−0.109380	+	0.882948i
$331$	−8.85641	+	33.0526i	−0.486792	+	1.81673i	0.0850595	+	0.996376i	$0.472892\pi$
$331$	−8.85641	+	33.0526i	−0.486792	+	1.81673i	−0.571852	+	0.820357i	$0.693775\pi$
$332$	−0.285334	+	1.06488i	−0.0156598	+	0.0584430i
$333$	8.33919	+	13.9469i	0.456985	+	0.764285i
$334$	−10.1244	−	17.5359i	−0.553980	−	0.959522i
$335$	−4.46841	+	7.73951i	−0.244135	+	0.422855i
$336$	−8.72579	−	6.59014i	−0.476031	−	0.359521i
$337$			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
$342$	16.7900	−	4.77524i	0.907900	−	0.258215i
$343$	−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	0.0614076	−	0.998113i	$-0.480441\pi$
$347$	17.8177	−	10.2870i	0.956502	−	0.552237i	0.895095	+	0.445876i	$0.147108\pi$
$348$	0.459481	+	3.29519i	0.0246308	+	0.176641i
$349$	7.36603	+	27.4904i	0.394294	+	1.47153i	0.822979	+	0.568072i	$0.192311\pi$
$349$	7.36603	+	27.4904i	0.394294	+	1.47153i	−0.428684	+	0.903454i	$0.641023\pi$
$350$	−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	$-0.206178\pi$
$354$	1.08500	+	7.78112i	0.0576670	+	0.413562i
$355$	3.92820	−	2.26795i	0.208487	−	0.120370i
$356$	−1.76798	+	1.76798i	−0.0937025	+	0.0937025i
$357$	11.3671	−	4.81059i	0.601613	−	0.254603i
$358$	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	$0.511745\pi$
$360$	−11.3351	+	3.22381i	−0.597411	+	0.169909i
$361$	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
$366$	−14.5704	−	11.0042i	−0.761605	−	0.575201i
$367$	−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
$369$	8.65286	+	14.4715i	0.450450	+	0.753356i
$370$	3.17949	−	11.8660i	0.165294	−	0.616885i
$371$	−0.285334	+	1.06488i	−0.0148138	+	0.0552859i
$372$	0.198831	−	1.60502i	0.0103089	−	0.0832162i
$373$	−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
$375$	−12.1550	+	16.0941i	−0.627684	+	0.831096i
$376$		−	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	0.127726	−	0.991809i	$-0.459232\pi$
$379$	14.2942	−	3.83013i	0.734245	−	0.196740i	0.606519	+	0.795069i	$0.292565\pi$
$380$	−1.35022	−	0.779548i	−0.0692647	−	0.0399900i
$381$	5.93605	−	14.6467i	0.304113	−	0.750372i
$382$	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	$0.265335\pi$
$384$	−8.80399	−	20.8033i	−0.449277	−	1.06162i
$385$	6.19615	−	6.19615i	0.315785	−	0.315785i
$386$	−0.180895	+	0.104440i	−0.00920730	+	0.00531584i
$387$	4.58695	−	4.72944i	0.233168	−	0.240411i
$388$	0.117314	+	0.437822i	0.00595572	+	0.0222271i
$389$	−22.4950			−1.14054			−0.570270	−	0.821457i	$-0.693161\pi$
$389$	−22.4950			−1.14054			−0.570270	+	0.821457i	$0.693161\pi$
$390$		0			0
$391$		0			0
$392$	−3.37554	−	12.5977i	−0.170491	−	0.636280i
$393$	13.6351	−	1.90128i	0.687800	−	0.0959066i
$394$	−5.36603	+	3.09808i	−0.270336	+	0.156079i
$395$	2.12976	−	2.12976i	0.107160	−	0.107160i
$396$	1.60968	−	2.88920i	0.0808892	−	0.145188i
$397$	−13.2942	−	3.56218i	−0.667218	−	0.178781i	−0.0907168	−	0.995877i	$-0.528916\pi$
$397$	−13.2942	−	3.56218i	−0.667218	−	0.178781i	−0.576501	+	0.817096i	$0.695582\pi$
$398$	−13.7670	−	13.7670i	−0.690078	−	0.690078i
$399$	−8.77113	−	3.55479i	−0.439106	−	0.177962i
$400$	−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
$405$	3.10594	−	13.1931i	0.154336	−	0.655569i
$406$	7.63397	−	13.2224i	0.378868	−	0.656218i
$407$	−11.1430	−	19.3003i	−0.552340	−	0.956681i
$408$	22.5934	+	2.79889i	1.11854	+	0.138566i
$409$	7.76795	−	28.9904i	0.384100	−	1.43348i	−0.455480	−	0.890246i	$-0.650532\pi$
$409$	7.76795	−	28.9904i	0.384100	−	1.43348i	0.839580	−	0.543236i	$-0.182801\pi$
$410$	3.29909	−	12.3124i	0.162930	−	0.608064i
$411$	−11.5559	−	1.43156i	−0.570011	−	0.0706135i
$412$	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	0.285208	−	0.958466i	$-0.407937\pi$
$419$	−8.23373	−	4.75374i	−0.402244	−	0.232236i	−0.687452	+	0.726230i	$0.741271\pi$
$420$	−0.916053	−	0.371261i	−0.0446988	−	0.0181157i
$421$	7.83013	+	7.83013i	0.381617	+	0.381617i	0.871685	−	0.490067i	$-0.163028\pi$
$421$	7.83013	+	7.83013i	0.381617	+	0.381617i	−0.490067	+	0.871685i	$0.663028\pi$
$422$	2.62398	+	0.703093i	0.127733	+	0.0342260i
$423$	15.7869	+	8.79543i	0.767584	+	0.427648i
$424$	−1.43782	+	1.43782i	−0.0698268	+	0.0698268i
$425$	11.9226	−	6.88351i	0.578330	−	0.333899i
$426$	−7.78112	+	1.08500i	−0.376997	+	0.0525683i
$427$	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	$0.551776\pi$
$432$	23.0611	+	2.49938i	1.10953	+	0.120252i
$433$	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
$435$	−7.28782	−	17.2207i	−0.349424	−	0.825670i
$436$	−4.83013	−	1.29423i	−0.231321	−	0.0619823i
$437$		0			0
$438$	−1.24967	+	3.08346i	−0.0597117	+	0.147333i
$439$	−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	$0.0858762\pi$
$443$			11.2195i			0.533054i	−0.963827	+	0.266527i	$0.914124\pi$
$444$	−1.51505	+	2.00602i	−0.0719009	+	0.0952017i
$445$	7.02628	−	12.1699i	0.333078	−	0.576907i
$446$	19.5092	+	33.7909i	0.923787	+	1.60005i
$447$	1.83816	−	14.8382i	0.0869422	−	0.701821i
$448$	−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	$-0.0780018\pi$
$450$	10.5939	−	6.33434i	0.499400	−	0.298603i
$451$	−11.5622	−	20.0263i	−0.544442	−	0.943001i
$452$	1.37820	−	2.38711i	0.0648251	−	0.112280i
$453$	−1.04750	−	0.791121i	−0.0492157	−	0.0371701i
$454$		−	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	−0.345868	−	0.938283i	$-0.612416\pi$
$457$	−3.76795	+	1.00962i	−0.176257	+	0.0472280i	0.169611	+	0.985511i	$0.445749\pi$
$458$	26.0514	+	15.0408i	1.21730	+	0.702809i
$459$	−15.4590	+	21.1332i	−0.721565	+	0.986412i
$460$		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	$0.418376\pi$
$462$	−13.9773	+	5.91520i	−0.650282	+	0.275200i
$463$	−23.0526	+	23.0526i	−1.07134	+	1.07134i	−0.0740918	+	0.997251i	$0.523606\pi$
$463$	−23.0526	+	23.0526i	−1.07134	+	1.07134i	−0.997251	+	0.0740918i	$0.976394\pi$
$464$	27.7149	−	16.0012i	1.28663	−	0.742838i
$465$	1.25532	+	9.00263i	0.0582143	+	0.417487i
$466$	−6.80385	−	25.3923i	−0.315182	−	1.17628i
$467$	19.1679			0.886984			0.443492	−	0.896278i	$-0.353739\pi$
$467$	19.1679			0.886984			0.443492	+	0.896278i	$0.353739\pi$
$468$		0			0
$469$	−8.39230			−0.387521
$470$	−3.53595	−	13.1963i	−0.163101	−	0.608702i
$471$	−1.14909	−	8.24078i	−0.0529474	−	0.379715i
$472$	6.80385	−	3.92820i	0.313172	−	0.180810i
$473$	−6.38929	+	6.38929i	−0.293780	+	0.293780i
$474$	−4.80432	+	2.03319i	−0.220670	+	0.0933877i
$475$	−10.1962	−	2.73205i	−0.467832	−	0.125355i
$476$	1.35022	+	1.35022i	0.0618871	+	0.0618871i
$477$	−0.639761	−	2.24944i	−0.0292926	−	0.102995i
$478$	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
$486$	−13.5688	+	19.1572i	−0.615492	+	0.868990i
$487$	1.49038	−	5.56218i	0.0675356	−	0.252046i	−0.923902	−	0.382630i	$-0.875018\pi$
$487$	1.49038	−	5.56218i	0.0675356	−	0.252046i	0.991437	+	0.130584i	$0.0416851\pi$
$488$	−4.72576	+	17.6368i	−0.213925	+	0.798379i
$489$	0.881808	−	7.11819i	0.0398767	−	0.321896i
$490$	−5.66987	−	9.82051i	−0.256139	−	0.443645i
$491$	−14.2612	+	24.7012i	−0.643600	+	1.11475i	0.341023	+	0.940055i	$0.389227\pi$
$491$	−14.2612	+	24.7012i	−0.643600	+	1.11475i	−0.984623	+	0.174693i	$0.944107\pi$
$492$	−1.57203	+	2.08148i	−0.0708728	+	0.0938403i
$493$			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
$498$	−4.03104	+	9.94624i	−0.180635	+	0.445702i
$499$	2.46410	+	2.46410i	0.110308	+	0.110308i	0.760107	−	0.649798i	$-0.225147\pi$
$499$	2.46410	+	2.46410i	0.110308	+	0.110308i	−0.649798	+	0.760107i	$0.725147\pi$
$500$	−3.01375	−	0.807533i	−0.134779	−	0.0361140i
$501$	−9.07638	−	21.4470i	−0.405503	−	0.958181i
$502$	1.05256	−	1.05256i	0.0469780	−	0.0469780i
$503$	−2.83286	+	1.63555i	−0.126311	+	0.0729256i	−0.561824	−	0.827257i	$-0.689900\pi$
$503$	−2.83286	+	1.63555i	−0.126311	+	0.0729256i	0.435513	+	0.900182i	$0.356567\pi$
$504$	−7.94401	−	7.70467i	−0.353854	−	0.343193i
$505$	−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	$-0.188634\pi$
$510$	19.6048	−	2.73370i	0.868117	−	0.121050i
$511$	1.56218	−	0.901924i	0.0691067	−	0.0398988i
$512$	−11.7137	+	11.7137i	−0.517678	+	0.517678i
$513$	19.8393	−	3.07638i	0.875926	−	0.135826i
$514$	−31.2846	−	8.38269i	−1.37990	−	0.369744i
$515$	−7.37772	−	7.37772i	−0.325101	−	0.325101i
$516$	0.944608	+	0.382834i	0.0415841	+	0.0168533i
$517$	−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	$0.0173815\pi$
$521$			2.49155i			0.109157i	−0.998509	+	0.0545785i	$0.982618\pi$
$522$	0.495311	+	32.3844i	0.0216792	+	1.41743i
$523$	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
$525$	−6.64136	−	0.822738i	−0.289853	−	0.0359072i
$526$	8.68653	−	32.4186i	0.378751	−	1.41352i
$527$	4.54486	−	16.9617i	0.197977	−	0.738862i
$528$	−31.5713	−	3.91108i	−1.37397	−	0.170208i
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	−0.883988	+	1.53111i	−0.0383980	+	0.0665072i
$531$	0.138184	+	9.03477i	0.00599669	+	0.392076i
$532$		−	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
$537$	42.6117	+	17.2698i	1.83883	+	0.745247i
$538$	−15.2679	−	15.2679i	−0.658248	−	0.658248i
$539$	−19.8710	−	5.32441i	−0.855904	−	0.229339i
$540$	2.07201	−	0.321296i	0.0891650	−	0.0138264i
$541$	12.6865	−	12.6865i	0.545437	−	0.545437i	−0.379681	−	0.925118i	$-0.623966\pi$
$541$	12.6865	−	12.6865i	0.545437	−	0.545437i	0.925118	+	0.379681i	$0.123966\pi$
$542$	−10.0782	+	5.81863i	−0.432894	+	0.249931i
$543$	5.14636	−	0.717608i	0.220852	−	0.0307955i
$544$	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
$549$	−15.0746	−	14.6204i	−0.643368	−	0.623984i
$550$	−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
$555$	5.30689	−	13.0943i	0.225265	−	0.555821i
$556$	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
$561$	21.6422	−	28.6558i	0.913735	−	1.20985i
$562$	12.9186	−	22.3756i	0.544938	−	0.943860i
$563$	−5.03908	−	8.72794i	−0.212372	−	0.367839i	0.740085	−	0.672514i	$-0.234785\pi$
$563$	−5.03908	−	8.72794i	−0.212372	−	0.367839i	−0.952456	+	0.304675i	$0.901452\pi$
$564$	−0.343706	+	2.77449i	−0.0144726	+	0.116827i
$565$	−4.00962	+	14.9641i	−0.168686	+	0.629544i
$566$	−2.56801	+	9.58394i	−0.107941	+	0.402843i
$567$	12.1877	−	3.66867i	0.511837	−	0.154070i
$568$	3.92820	+	6.80385i	0.164824	+	0.285483i
$569$	−1.35022	+	2.33864i	−0.0566040	+	0.0980411i	−0.892939	−	0.450178i	$-0.851361\pi$
$569$	−1.35022	+	2.33864i	−0.0566040	+	0.0980411i	0.836335	+	0.548219i	$0.184694\pi$
$570$	−12.1113	−	9.14708i	−0.507289	−	0.383129i
$571$		−	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
$576$	−5.46595	−	19.2186i	−0.227748	−	0.800775i
$577$	22.4904	+	22.4904i	0.936287	+	0.936287i	0.998088	−	0.0618016i	$-0.0196846\pi$
$577$	22.4904	+	22.4904i	0.936287	+	0.936287i	−0.0618016	+	0.998088i	$0.519685\pi$
$578$	−12.2079	−	3.27110i	−0.507783	−	0.136060i
$579$	−0.221240	+	0.0936291i	−0.00919443	+	0.00389109i
$580$	2.04552	−	2.04552i	0.0849355	−	0.0849355i
$581$	5.03908	−	2.90931i	0.209056	−	0.120699i
$582$	0.609374	+	4.37016i	0.0252594	+	0.181149i
$583$	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	$-0.209181\pi$
$588$	0.320471	+	2.29827i	0.0132160	+	0.0947792i
$589$	−11.6603	+	6.73205i	−0.480452	+	0.277389i
$590$	4.83020	−	4.83020i	0.198856	−	0.198856i
$591$	−6.56283	+	2.77739i	−0.269959	+	0.114247i
$592$	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	$0.652703\pi$
$594$	19.0087	−	25.9858i	0.779937	−	1.06621i
$595$	−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	$-0.860822\pi$
$599$		−	20.7270i		−	0.846881i	0.905924	−	0.423441i	$-0.139178\pi$
$600$	−9.84967	−	7.43895i	−0.402111	−	0.303694i
$601$	−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
$603$	15.2797	−	9.13612i	0.622238	−	0.372052i
$604$	0.0525589	−	0.196152i	0.00213859	−	0.00798133i
$605$	2.31066	−	8.62350i	0.0939417	−	0.350595i
$606$	−1.93291	+	15.6030i	−0.0785192	+	0.633828i
$607$	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
$609$	10.5830	−	14.0126i	0.428845	−	0.567820i
$610$			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	−0.975870	−	0.218354i	$-0.929931\pi$
$613$	−42.3827	+	11.3564i	−1.71182	+	0.458681i	−0.735951	+	0.677035i	$0.763265\pi$
$614$	−15.4790	−	8.93682i	−0.624683	−	0.360661i
$615$	5.50650	−	13.5868i	0.222044	−	0.547873i
$616$	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	$0.462043\pi$
$618$	7.04319	+	16.6427i	0.283319	+	0.669466i
$619$	31.6603	−	31.6603i	1.27253	−	1.27253i	0.327778	−	0.944755i	$-0.393700\pi$
$619$	31.6603	−	31.6603i	1.27253	−	1.27253i	0.944755	−	0.327778i	$-0.106300\pi$
$620$	−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
$627$	−27.2702	+	3.80255i	−1.08907	+	0.151859i
$628$	1.11474	−	0.643594i	0.0444828	−	0.0256822i
$629$	−19.3003	+	19.3003i	−0.769554	+	0.769554i
$630$	−8.40558	−	4.68305i	−0.334886	−	0.186577i
$631$	21.3923	+	5.73205i	0.851614	+	0.228189i	0.658121	−	0.752912i	$-0.271352\pi$
$631$	21.3923	+	5.73205i	0.851614	+	0.228189i	0.193493	+	0.981102i	$0.438018\pi$
$632$	3.68886	+	3.68886i	0.146735	+	0.146735i
$633$	2.89559	+	1.17353i	0.115089	+	0.0466437i
$634$	−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
$639$	−9.03477	+	0.138184i	−0.357410	+	0.00546649i
$640$	−9.82051	+	17.0096i	−0.388190	+	0.672364i
$641$	22.6758	+	39.2757i	0.895642	+	1.55130i	0.833008	+	0.553261i	$0.186617\pi$
$641$	22.6758	+	39.2757i	0.895642	+	1.55130i	0.0626345	+	0.998037i	$0.480050\pi$
$642$	−49.2228	−	6.09776i	−1.94267	−	0.240659i
$643$	1.87564	−	7.00000i	0.0739682	−	0.276053i	−0.919029	−	0.394190i	$-0.871025\pi$
$643$	1.87564	−	7.00000i	0.0739682	−	0.276053i	0.992997	+	0.118136i	$0.0376920\pi$
$644$		0			0
$645$	−5.68503	−	0.704266i	−0.223848	−	0.0277305i
$646$	14.6603	+	25.3923i	0.576800	+	0.999047i
$647$	−8.23373	+	14.2612i	−0.323701	+	0.560667i	−0.981249	−	0.192746i	$-0.938261\pi$
$647$	−8.23373	+	14.2612i	−0.323701	+	0.560667i	0.657547	+	0.753413i	$0.271594\pi$
$648$	22.8511	+	5.37965i	0.897674	+	0.211333i
$649$		−	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	0.654683	−	0.755904i	$-0.272802\pi$
$653$	8.36615	+	4.83020i	0.327393	+	0.189020i	−0.327290	+	0.944924i	$0.606135\pi$
$654$	−45.1145	−	18.2841i	−1.76411	−	0.714966i
$655$	−8.46410	−	8.46410i	−0.330720	−	0.330720i
$656$	24.2349	+	6.49373i	0.946216	+	0.253538i
$657$	−1.86237	+	3.34275i	−0.0726578	+	0.130413i
$658$	9.07180	−	9.07180i	0.353655	−	0.353655i
$659$	−23.4834	+	13.5581i	−0.914783	+	0.528150i	−0.881967	−	0.471311i	$-0.843781\pi$
$659$	−23.4834	+	13.5581i	−0.914783	+	0.528150i	−0.0328158	+	0.999461i	$0.510447\pi$
$660$	−2.84809	+	0.397137i	−0.110862	+	0.0154585i
$661$	2.52628	+	9.42820i	0.0982609	+	0.366715i	0.997494	−	0.0707559i	$-0.0225411\pi$
$661$	2.52628	+	9.42820i	0.0982609	+	0.366715i	−0.899233	+	0.437470i	$0.855874\pi$
$662$	−51.5321			−2.00285
$663$		0			0
$664$	10.7321			0.416484
$665$	2.12976	+	7.94839i	0.0825887	+	0.308225i
$666$	−17.0375	+	17.5668i	−0.660191	+	0.680699i
$667$		0			0
$668$	2.54752	−	2.54752i	0.0985666	−	0.0985666i
$669$	17.4898	+	41.3274i	0.676194	+	1.59781i
$670$	−13.0000	−	3.48334i	−0.502234	−	0.134573i
$671$	20.3652	+	20.3652i	0.786189	+	0.786189i
$672$	1.38556	−	3.41876i	0.0534493	−	0.131881i
$673$	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	$-0.940564\pi$
$677$		−	9.66040i		−	0.371279i	0.982618	−	0.185640i	$-0.0594357\pi$
$678$	16.1716	−	21.4123i	0.621065	−	0.822333i
$679$	1.19615	−	2.07180i	0.0459041	−	0.0795083i
$680$	−9.89726	−	17.1426i	−0.379543	−	0.657387i
$681$	4.31769	−	34.8536i	0.165454	−	1.33559i
$682$	−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	$0.729247\pi$
$684$	1.59387	+	2.66566i	0.0609430	+	0.101924i
$685$	5.06218	+	8.76795i	0.193416	+	0.335006i
$686$	12.7786	−	22.1332i	0.487889	−	0.845048i
$687$	27.6083	+	20.8511i	1.05332	+	0.795519i
$688$		−	9.80385i		−	0.373768i
$689$		0			0
$690$		0			0
$691$	18.2224	−	4.88269i	0.693214	−	0.185746i	0.105025	−	0.994470i	$-0.466508\pi$
$691$	18.2224	−	4.88269i	0.693214	−	0.185746i	0.588189	+	0.808723i	$0.299841\pi$
$692$	−4.05065	−	2.33864i	−0.153983	−	0.0889019i
$693$	−16.7900	+	4.77524i	−0.637800	+	0.181396i
$694$	21.9090	+	21.9090i	0.831653	+	0.831653i
$695$	−26.7545	−	7.16884i	−1.01486	−	0.271930i
$696$	29.8272	−	12.6229i	1.13060	−	0.478469i
$697$	−20.0263	+	20.0263i	−0.758549	+	0.758549i
$698$	−37.1180	+	21.4301i	−1.40494	+	0.811140i
$699$	−4.17549	−	29.9448i	−0.157932	−	1.13261i
$700$	−0.267949	−	1.00000i	−0.0101275	−	0.0377964i
$701$	−12.7786			−0.482641			−0.241320	−	0.970446i	$-0.577580\pi$
$701$	−12.7786			−0.482641			−0.241320	+	0.970446i	$0.577580\pi$
$702$		0			0
$703$	20.9282			0.789322
$704$	7.09239	+	26.4692i	0.267304	+	0.997594i
$705$	−2.17000	−	15.5622i	−0.0817268	−	0.586108i
$706$	18.4474	−	10.6506i	0.694279	−	0.400842i
$707$	6.02751	−	6.02751i	0.226688	−	0.226688i
$708$	−1.28731	+	0.544793i	−0.0483802	+	0.0204746i
$709$	−11.3301	−	3.03590i	−0.425512	−	0.114016i	0.0397068	−	0.999211i	$-0.487358\pi$
$709$	−11.3301	−	3.03590i	−0.425512	−	0.114016i	−0.465219	+	0.885196i	$0.654024\pi$
$710$	4.83020	+	4.83020i	0.181274	+	0.181274i
$711$	−5.77113	+	1.64136i	−0.216434	+	0.0615559i
$712$	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
$717$	12.8972	+	9.74056i	0.481653	+	0.363768i
$718$	−19.4186	+	33.6340i	−0.724695	+	1.25521i
$719$	−3.68886	−	6.38929i	−0.137571	−	0.238280i	0.789005	−	0.614386i	$-0.210596\pi$
$719$	−3.68886	−	6.38929i	−0.137571	−	0.238280i	−0.926577	+	0.376106i	$0.877263\pi$
$720$	−10.3501	−	17.3101i	−0.385727	−	0.645110i
$721$	2.53590	−	9.46410i	0.0944418	−	0.352462i
$722$	−1.58708	+	5.92307i	−0.0590650	+	0.220434i
$723$	−3.10003	+	25.0243i	−0.115292	+	0.930665i
$724$	0.401924	+	0.696152i	0.0149374	+	0.0258723i
$725$	9.79282	−	16.9617i	0.363696	−	0.629940i
$726$	−9.31934	+	12.3394i	−0.345873	+	0.457959i
$727$			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
$732$	1.22024	−	3.01084i	0.0451014	−	0.111284i
$733$	6.77757	+	6.77757i	0.250335	+	0.250335i	0.821108	−	0.570773i	$-0.193356\pi$
$733$	6.77757	+	6.77757i	0.250335	+	0.250335i	−0.570773	+	0.821108i	$0.693356\pi$
$734$	−44.2104	−	11.8461i	−1.63183	−	0.437249i
$735$	−5.08298	−	12.0108i	−0.187489	−	0.443025i
$736$		0			0
$737$	−21.1447	+	12.2079i	−0.778876	+	0.449685i
$738$	−17.6784	+	18.2276i	−0.650750	+	0.670966i
$739$	−2.98076	−	11.1244i	−0.109649	−	0.409216i	0.889182	−	0.457554i	$-0.151274\pi$
$739$	−2.98076	−	11.1244i	−0.109649	−	0.409216i	−0.998831	+	0.0483378i	$0.984608\pi$
$740$	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	$0.864943\pi$
$744$	−15.5930	+	2.17429i	−0.571667	+	0.0797132i
$745$	−11.2583	+	6.50000i	−0.412473	+	0.238142i
$746$	12.3403	−	12.3403i	0.451812	−	0.451812i
$747$	−6.00739	+	10.7826i	−0.219799	+	0.394516i
$748$	5.36603	+	1.43782i	0.196201	+	0.0525720i
$749$	19.0150	+	19.0150i	0.694792	+	0.694792i
$750$	−28.1491	−	11.4084i	−1.02786	−	0.416574i
$751$	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
$756$	1.23418	+	1.53422i	0.0448866	+	0.0557990i
$757$	−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	$0.975305\pi$
$762$	23.6196	+	2.92602i	0.855647	+	0.105998i
$763$	13.1962	+	22.8564i	0.477733	+	0.827457i
$764$	−0.647124	+	1.12085i	−0.0234121	+	0.0405510i
$765$	22.7635	−	0.348161i	0.823014	−	0.0125878i
$766$			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	−0.898636	−	0.438694i	$-0.855441\pi$
$769$	−40.4186	+	10.8301i	−1.45753	+	0.390544i	−0.558895	+	0.829238i	$0.688775\pi$
$770$	11.4284	+	6.59817i	0.411850	+	0.237782i
$771$	−34.5229	−	13.9915i	−1.24331	−	0.503893i
$772$	−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	$0.865212\pi$
$774$	8.66759	+	4.82903i	0.311550	+	0.173576i
$775$	−6.73205	+	6.73205i	−0.241822	+	0.241822i
$776$	3.82129	−	2.20622i	0.137176	−	0.0791987i
$777$	13.1408	−	1.83235i	0.471424	−	0.0657353i
$778$	−8.76795	−	32.7224i	−0.314346	−	1.17316i
$779$	21.7154			0.778035
$780$		0			0
$781$	12.3923			0.443432
$782$		0			0
$783$	−4.01372	+	37.0335i	−0.143439	+	1.32347i
$784$	19.3301	−	11.1603i	0.690362	−	0.398581i
$785$	−5.11553	+	5.11553i	−0.182581	+	0.182581i
$786$	8.08031	+	19.0933i	0.288215	+	0.681036i
$787$	16.0263	+	4.29423i	0.571275	+	0.153073i	0.532881	−	0.846190i	$-0.321109\pi$
$787$	16.0263	+	4.29423i	0.571275	+	0.153073i	0.0383938	+	0.999263i	$0.487776\pi$
$788$	−0.779548	−	0.779548i	−0.0277702	−	0.0277702i
$789$	14.4987	−	35.7742i	0.516167	−	1.27360i
$790$	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
$795$	−1.22548	+	1.62261i	−0.0434632	+	0.0575482i
$796$	1.73205	−	3.00000i	0.0613909	−	0.106332i
$797$	−20.1563	−	34.9118i	−0.713973	−	1.23664i	−0.963354	−	0.268232i	$-0.913561\pi$
$797$	−20.1563	−	34.9118i	−0.713973	−	1.23664i	0.249381	−	0.968405i	$-0.419773\pi$
$798$	1.75224	−	14.1445i	0.0620286	−	0.500711i
$799$	−7.85641	+	29.3205i	−0.277940	+	1.03729i
$800$	1.06488	−	3.97420i	0.0376493	−	0.140509i
$801$	−24.0264	+	14.3660i	−0.848929	+	0.507596i
$802$	9.37564	+	16.2391i	0.331066	+	0.573422i
$803$	2.62398	−	4.54486i	0.0925982	−	0.160385i
$804$	2.19773	+	1.65983i	0.0775079	+	0.0585377i
$805$		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	0.858863	−	0.512205i	$-0.171171\pi$
$809$	24.0261	+	13.8715i	0.844712	+	0.487694i	−0.0141514	+	0.999900i	$0.504505\pi$
$810$	20.4020	−	0.624232i	0.716853	−	0.0219333i
$811$	−19.0000	−	19.0000i	−0.667180	−	0.667180i	0.289882	−	0.957062i	$-0.406384\pi$
$811$	−19.0000	−	19.0000i	−0.667180	−	0.667180i	−0.957062	+	0.289882i	$0.906384\pi$
$812$	2.62398	+	0.703093i	0.0920836	+	0.0246737i
$813$	−12.3259	+	5.21634i	−0.432289	+	0.182945i
$814$	23.7321	−	23.7321i	0.831808	−	0.831808i
$815$	−5.40087	+	3.11819i	−0.189184	+	0.109226i
$816$	5.38085	+	38.5891i	0.188367	+	1.35089i
$817$	−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	$0.646100\pi$
$822$	−2.42177	−	17.3679i	−0.0844690	−	0.605774i
$823$	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
$825$	−17.9300	+	7.58798i	−0.624242	+	0.264180i
$826$	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
$834$	38.2832	+	28.9133i	1.32564	+	1.00119i
$835$	−10.1244	+	17.5359i	−0.350368	+	0.606855i
$836$	−2.12976	−	3.68886i	−0.0736595	−	0.127582i
$837$	6.54383	−	16.8836i	0.226188	−	0.583582i
$838$	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	$0.0273388\pi$
$840$	−1.18295	+	9.54910i	−0.0408157	+	0.329475i
$841$	11.1962	+	19.3923i	0.386074	+	0.668700i
$842$	−8.33816	+	14.4421i	−0.287352	+	0.497708i
$843$	17.9091	−	23.7128i	0.616822	−	0.816714i
$844$			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
$849$	−4.28626	+	10.5760i	−0.147104	+	0.362967i
$850$	14.6603	+	14.6603i	0.502843	+	0.502843i
$851$		0			0
$852$	−0.544793	−	1.28731i	−0.0186643	−	0.0441027i
$853$	22.3660	−	22.3660i	0.765798	−	0.765798i	−0.211566	−	0.977364i	$-0.567856\pi$
$853$	22.3660	−	22.3660i	0.765798	−	0.765798i	0.977364	+	0.211566i	$0.0678562\pi$
$854$	−12.9110	+	7.45418i	−0.441806	+	0.255077i
$855$	−12.5305	−	12.1530i	−0.428534	−	0.415623i
$856$	12.8372	+	47.9090i	0.438765	+	1.63749i
$857$	−3.32707			−0.113651			−0.0568253	−	0.998384i	$-0.518098\pi$
$857$	−3.32707			−0.113651			−0.0568253	+	0.998384i	$0.518098\pi$
$858$		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
$861$	13.6351	−	1.90128i	0.464683	−	0.0647953i
$862$	−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	$0.394642\pi$
$864$	1.19909	+	7.73284i	0.0407940	+	0.263077i
$865$	25.3923	+	6.80385i	0.863364	+	0.231338i
$866$	33.0673	+	33.0673i	1.12367	+	1.12367i
$867$	−13.4716	−	5.45979i	−0.457518	−	0.185424i
$868$	−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
$873$	0.0776093	+	5.07425i	0.00262668	+	0.171737i
$874$		0			0
$875$	8.23373	+	14.2612i	0.278351	+	0.482118i
$876$	−0.587477	−	0.0727771i	−0.0198490	−	0.00245891i
$877$	7.76795	−	28.9904i	0.262305	−	0.978936i	−0.701574	−	0.712596i	$-0.747519\pi$
$877$	7.76795	−	28.9904i	0.262305	−	0.978936i	0.963879	−	0.266339i	$-0.0858142\pi$
$878$	0.494214	−	1.84443i	0.0166789	−	0.0622465i
$879$	3.09640	+	0.383584i	0.104439	+	0.0129380i
$880$	13.8301	+	23.9545i	0.466213	+	0.807505i
$881$	−11.7417	+	20.3372i	−0.395588	+	0.685178i	−0.993176	−	0.116625i	$-0.962792\pi$
$881$	−11.7417	+	20.3372i	−0.395588	+	0.685178i	0.597588	+	0.801803i	$0.296126\pi$
$882$	0.345461	+	22.5869i	0.0116323	+	0.760541i
$883$		−	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	0.0857146	−	0.996320i	$-0.472683\pi$
$887$	−21.8683	−	12.6257i	−0.734266	−	0.423929i	−0.819981	+	0.572391i	$0.806016\pi$
$888$	22.6800	+	9.19180i	0.761089	+	0.308457i
$889$	−9.12436	−	9.12436i	−0.306021	−	0.306021i
$890$	20.4416	+	5.47732i	0.685206	+	0.183600i
$891$	25.3708	−	26.9723i	0.849954	−	0.903607i
$892$	−4.90897	+	4.90897i	−0.164364	+	0.164364i
$893$	20.1563	−	11.6373i	0.674505	−	0.389426i
$894$	22.3009	−	3.10963i	0.745854	−	0.104002i
$895$	−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
$900$	1.57648	+	1.52898i	0.0525494	+	0.0509661i
$901$	3.40192	−	1.96410i	0.113335	−	0.0654337i
$902$	24.6247	−	24.6247i	0.819913	−	0.819913i
$903$	−2.09657	−	4.95408i	−0.0697695	−	0.164861i
$904$	−25.9186	−	6.94486i	−0.862039	−	0.230983i
$905$	−3.19465	−	3.19465i	−0.106194	−	0.106194i
$906$	0.742522	−	1.83211i	0.0246686	−	0.0608677i
$907$	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	$-0.991778\pi$
$911$		−	1.55910i		−	0.0516552i	0.999666	−	0.0258276i	$-0.00822209\pi$
$912$	18.0046	−	23.8393i	0.596191	−	0.789398i
$913$	8.46410	−	14.6603i	0.280121	−	0.485184i
$914$	−2.93730	−	5.08755i	−0.0971572	−	0.168281i
$915$	−2.24477	+	18.1204i	−0.0742099	+	0.599043i
$916$	−1.38526	+	5.16987i	−0.0457704	+	0.170817i
$917$	2.90931	−	10.8577i	0.0960740	−	0.358553i
$918$	−36.7670	−	14.2504i	−1.21349	−	0.470333i
$919$	−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
$921$	−16.4041	−	12.3892i	−0.540533	−	0.408236i
$922$			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
$927$	5.68585	+	19.9918i	0.186748	+	0.656616i
$928$	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	$0.474800\pi$
$930$	−12.6064	+	5.33506i	−0.413381	+	0.174943i
$931$	13.6603	−	13.6603i	0.447697	−	0.447697i
$932$	4.05065	−	2.33864i	0.132683	−	0.0766048i
$933$	−2.41072	−	17.2886i	−0.0789234	−	0.566004i
$934$	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
$939$	0.478405	+	3.43091i	0.0156122	+	0.111963i
$940$	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	$0.317613\pi$
$942$	11.5396	−	4.88358i	0.375981	−	0.159116i
$943$		0			0
$944$	9.50749	+	9.50749i	0.309442	+	0.309442i
$945$	−8.93193	−	6.53374i	−0.290556	−	0.212543i
$946$	−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
$951$	−22.1891	−	16.7583i	−0.719531	−	0.543425i
$952$	9.29423	−	16.0981i	0.301228	−	0.521742i
$953$	0.988427	+	1.71201i	0.0320183	+	0.0554573i	0.881591	−	0.472015i	$-0.156473\pi$
$953$	0.988427	+	1.71201i	0.0320183	+	0.0554573i	−0.849572	+	0.527472i	$0.823140\pi$
$954$	3.02279	−	1.80740i	0.0978666	−	0.0585169i
$955$	1.88269	−	7.02628i	0.0609223	−	0.227365i
$956$	−0.647124	+	2.41510i	−0.0209295	+	0.0781099i
$957$	6.28076	−	50.7000i	0.203028	−	1.63890i
$958$	−15.4904	−	26.8301i	−0.500471	−	0.866842i
$959$	−4.75374	+	8.23373i	−0.153506	+	0.265881i
$960$	−10.4701	+	13.8632i	−0.337923	+	0.447432i
$961$		−	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	0.995062	−	0.0992599i	$-0.0316475\pi$
$967$	27.8564	+	27.8564i	0.895802	+	0.895802i	−0.0992599	+	0.995062i	$0.531648\pi$
$968$	14.9363	+	4.00218i	0.480072	+	0.128635i
$969$	13.1428	+	31.0556i	0.422207	+	0.997651i
$970$	2.71281	−	2.71281i	0.0871032	−	0.0871032i
$971$	41.4335	−	23.9216i	1.32966	−	0.767682i	0.344416	−	0.938817i	$-0.388077\pi$
$971$	41.4335	−	23.9216i	1.32966	−	0.767682i	0.985247	+	0.171136i	$0.0547436\pi$
$972$	−3.91725	−	1.44976i	−0.125646	−	0.0465011i
$973$	−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	$-0.207061\pi$
$978$	10.6982	−	1.49176i	0.342092	−	0.0477012i
$979$	33.2487	−	19.1962i	1.06263	−	0.613512i
$980$	1.42667	−	1.42667i	0.0455734	−	0.0455734i
$981$	−48.9082	−	27.2485i	−1.56152	−	0.869978i
$982$	−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	$0.990895\pi$
$984$	23.5330	+	9.53754i	0.750206	+	0.304046i
$985$	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
$990$	−27.9904	+	0.428106i	−0.889594	+	0.0136061i
$991$	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
$993$	−58.8186	−	7.28650i	−1.86655	−	0.231230i
$994$	−1.66025	+	6.19615i	−0.0526601	+	0.196530i
$995$	−5.03908	+	18.8061i	−0.159750	+	0.596193i
$996$	−1.89501	−	0.234755i	−0.0600457	−	0.00743851i
$997$	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
$999$	−21.9305	+	17.6416i	−0.693850	+	0.558156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.k.f.488.2		8
3.2	odd	2	inner	507.2.k.f.488.1		8
13.2	odd	12	inner	507.2.k.f.80.1		8
13.3	even	3		507.2.k.d.89.1		8
13.4	even	6		507.2.f.f.437.2		8
13.5	odd	4		507.2.k.d.188.2		8
13.6	odd	12		507.2.f.e.239.2		8
13.7	odd	12		507.2.f.f.239.3		8
13.8	odd	4		39.2.k.b.32.1	yes	8
13.9	even	3		507.2.f.e.437.3		8
13.10	even	6		39.2.k.b.11.2	yes	8
13.11	odd	12		507.2.k.e.80.2		8
13.12	even	2		507.2.k.e.488.1		8
39.2	even	12	inner	507.2.k.f.80.2		8
39.5	even	4		507.2.k.d.188.1		8
39.8	even	4		39.2.k.b.32.2	yes	8
39.11	even	12		507.2.k.e.80.1		8
39.17	odd	6		507.2.f.f.437.3		8
39.20	even	12		507.2.f.f.239.2		8
39.23	odd	6		39.2.k.b.11.1	✓	8
39.29	odd	6		507.2.k.d.89.2		8
39.32	even	12		507.2.f.e.239.3		8
39.35	odd	6		507.2.f.e.437.2		8
39.38	odd	2		507.2.k.e.488.2		8
52.23	odd	6		624.2.cn.c.401.2		8
52.47	even	4		624.2.cn.c.305.1		8
65.8	even	4		975.2.bp.e.149.2		8
65.23	odd	12		975.2.bp.f.674.2		8
65.34	odd	4		975.2.bo.d.851.2		8
65.47	even	4		975.2.bp.f.149.1		8
65.49	even	6		975.2.bo.d.401.1		8
65.62	odd	12		975.2.bp.e.674.1		8
156.23	even	6		624.2.cn.c.401.1		8
156.47	odd	4		624.2.cn.c.305.2		8
195.8	odd	4		975.2.bp.e.149.1		8
195.23	even	12		975.2.bp.f.674.1		8
195.47	odd	4		975.2.bp.f.149.2		8
195.62	even	12		975.2.bp.e.674.2		8
195.164	even	4		975.2.bo.d.851.1		8
195.179	odd	6		975.2.bo.d.401.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.k.b.11.1	✓	8	39.23	odd	6
39.2.k.b.11.2	yes	8	13.10	even	6
39.2.k.b.32.1	yes	8	13.8	odd	4
39.2.k.b.32.2	yes	8	39.8	even	4
507.2.f.e.239.2		8	13.6	odd	12
507.2.f.e.239.3		8	39.32	even	12
507.2.f.e.437.2		8	39.35	odd	6
507.2.f.e.437.3		8	13.9	even	3
507.2.f.f.239.2		8	39.20	even	12
507.2.f.f.239.3		8	13.7	odd	12
507.2.f.f.437.2		8	13.4	even	6
507.2.f.f.437.3		8	39.17	odd	6
507.2.k.d.89.1		8	13.3	even	3
507.2.k.d.89.2		8	39.29	odd	6
507.2.k.d.188.1		8	39.5	even	4
507.2.k.d.188.2		8	13.5	odd	4
507.2.k.e.80.1		8	39.11	even	12
507.2.k.e.80.2		8	13.11	odd	12
507.2.k.e.488.1		8	13.12	even	2
507.2.k.e.488.2		8	39.38	odd	2
507.2.k.f.80.1		8	13.2	odd	12	inner
507.2.k.f.80.2		8	39.2	even	12	inner
507.2.k.f.488.1		8	3.2	odd	2	inner
507.2.k.f.488.2		8	1.1	even	1	trivial
624.2.cn.c.305.1		8	52.47	even	4
624.2.cn.c.305.2		8	156.47	odd	4
624.2.cn.c.401.1		8	156.23	even	6
624.2.cn.c.401.2		8	52.23	odd	6
975.2.bo.d.401.1		8	65.49	even	6
975.2.bo.d.401.2		8	195.179	odd	6
975.2.bo.d.851.1		8	195.164	even	4
975.2.bo.d.851.2		8	65.34	odd	4
975.2.bp.e.149.1		8	195.8	odd	4
975.2.bp.e.149.2		8	65.8	even	4
975.2.bp.e.674.1		8	65.62	odd	12
975.2.bp.e.674.2		8	195.62	even	12
975.2.bp.f.149.1		8	65.47	even	4
975.2.bp.f.149.2		8	195.47	odd	4
975.2.bp.f.674.1		8	195.23	even	12
975.2.bp.f.674.2		8	65.23	odd	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} +(0.239203 + 1.71545i) q^{3} +(-0.232051 + 0.133975i) q^{4} +(1.06488 - 1.06488i) q^{5} +(-2.40216 + 1.01660i) q^{6} +(1.36603 + 0.366025i) q^{7} +(1.84443 + 1.84443i) q^{8} +(-2.88556 + 0.820682i) q^{9} +(1.96410 + 1.13397i) q^{10} +(3.97420 - 1.06488i) q^{11} +(-0.285334 - 0.366025i) q^{12} +2.12976i q^{14} +(2.08148 + 1.57203i) q^{15} +(-2.23205 + 3.86603i) q^{16} +(-2.51954 - 4.36397i) q^{17} +(-2.31853 - 3.87762i) q^{18} +(-1.00000 + 3.73205i) q^{19} +(-0.104440 + 0.389774i) q^{20} +(-0.301143 + 2.43091i) q^{21} +(3.09808 + 5.36603i) q^{22} +(-2.72284 + 3.60523i) q^{24} +2.73205i q^{25} +(-2.09808 - 4.75374i) q^{27} +(-0.366025 + 0.0980762i) q^{28} +(-6.20840 - 3.58442i) q^{29} +(-1.47546 + 3.64058i) q^{30} +(2.46410 + 2.46410i) q^{31} +(-1.45466 - 0.389774i) q^{32} +(2.77739 + 6.56283i) q^{33} +(5.36603 - 5.36603i) q^{34} +(1.84443 - 1.06488i) q^{35} +(0.559647 - 0.577032i) q^{36} +(-1.40192 - 5.23205i) q^{37} -5.81863 q^{38} +3.92820 q^{40} +(-1.45466 - 5.42885i) q^{41} +(-3.65351 + 0.509445i) q^{42} +(-1.90192 + 1.09808i) q^{43} +(-0.779548 + 0.779548i) q^{44} +(-2.19886 + 3.94672i) q^{45} +(-4.25953 - 4.25953i) q^{47} +(-7.16590 - 2.90422i) q^{48} +(-4.33013 - 2.50000i) q^{49} +(-3.97420 + 1.06488i) q^{50} +(6.88351 - 5.36603i) q^{51} +0.779548i q^{53} +(6.09729 - 4.90487i) q^{54} +(3.09808 - 5.36603i) q^{55} +(1.84443 + 3.19465i) q^{56} +(-6.64136 - 0.822738i) q^{57} +(2.79423 - 10.4282i) q^{58} +(0.779548 - 2.90931i) q^{59} +(-0.693622 - 0.0859264i) q^{60} +(3.50000 + 6.06218i) q^{61} +(-2.62398 + 4.54486i) q^{62} +(-4.24214 + 0.0648824i) 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} +(-6.83591 - 3.80853i) q^{72} +(0.901924 - 0.901924i) q^{73} +(7.06440 - 4.07863i) q^{74} +(-4.68671 + 0.653513i) q^{75} +(-0.267949 - 1.00000i) q^{76} +5.81863 q^{77} +2.00000 q^{79} +(1.73999 + 6.49373i) q^{80} +(7.65296 - 4.73626i) q^{81} +(7.33013 - 4.23205i) q^{82} +(2.90931 - 2.90931i) q^{83} +(-0.255799 - 0.604440i) q^{84} +(-7.33013 - 1.96410i) q^{85} +(-2.33864 - 2.33864i) q^{86} +(4.66384 - 11.5076i) q^{87} +(9.29423 + 5.36603i) q^{88} +(9.01327 - 2.41510i) q^{89} +(-6.59817 - 1.66025i) q^{90} +(-3.63763 + 4.81647i) q^{93} +(4.53590 - 7.85641i) q^{94} +(2.90931 + 5.03908i) q^{95} +(0.320682 - 2.58863i) q^{96} +(0.437822 - 1.63397i) q^{97} +(1.94887 - 7.27328i) q^{98} +(-10.5939 + 6.33434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 12 q^{4} + 14 q^{6} + 4 q^{7} + 4 q^{9} - 12 q^{10} + 2 q^{15} - 4 q^{16} - 4 q^{18} - 8 q^{19} - 4 q^{21} + 4 q^{22} + 30 q^{24} + 4 q^{27} + 4 q^{28} - 18 q^{30} - 8 q^{31} + 20 q^{33}+ \cdots - 40 q^{99}+O(q^{100}) \) 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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