LMFDB - Embedded newform 39.2.k.b.32.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [39,2,Mod(2,39)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(39, 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("39.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 39 = 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	39.k (of order $12$, degree $4$, 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:	$0.311416567883$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			32.2
Root			$0.500000 - 0.564882i$ of defining polynomial
Character	$\chi$	$=$	39.32
Dual form			39.2.k.b.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.45466 - 0.389774i) q^{2} +(-1.60523 + 0.650571i) q^{3} +(0.232051 - 0.133975i) q^{4} +(-1.06488 - 1.06488i) q^{5} +(-2.08148 + 1.57203i) q^{6} +(0.366025 - 1.36603i) q^{7} +(-1.84443 + 1.84443i) q^{8} +(2.15351 - 2.08863i) q^{9} +(-1.96410 - 1.13397i) q^{10} +(1.06488 + 3.97420i) q^{11} +(-0.285334 + 0.366025i) q^{12} +(3.59808 - 0.232051i) q^{13} -2.12976i q^{14} +(2.40216 + 1.01660i) q^{15} +(-2.23205 + 3.86603i) q^{16} +(-2.51954 - 4.36397i) q^{17} +(2.31853 - 3.87762i) q^{18} +(-3.73205 - 1.00000i) q^{19} +(-0.389774 - 0.104440i) q^{20} +(0.301143 + 2.43091i) q^{21} +(3.09808 + 5.36603i) q^{22} +(1.76080 - 4.16067i) q^{24} -2.73205i q^{25} +(5.14352 - 1.73999i) q^{26} +(-2.09808 + 4.75374i) q^{27} +(-0.0980762 - 0.366025i) q^{28} +(6.20840 + 3.58442i) q^{29} +(3.89056 + 0.542499i) q^{30} +(-2.46410 + 2.46410i) q^{31} +(-0.389774 + 1.45466i) q^{32} +(-4.29488 - 5.68671i) q^{33} +(-5.36603 - 5.36603i) q^{34} +(-1.84443 + 1.06488i) q^{35} +(0.219901 - 0.773185i) q^{36} +(-5.23205 + 1.40192i) q^{37} -5.81863 q^{38} +(-5.62477 + 2.71330i) q^{39} +3.92820 q^{40} +(-5.42885 + 1.45466i) q^{41} +(1.38556 + 3.41876i) q^{42} +(1.90192 - 1.09808i) q^{43} +(0.779548 + 0.779548i) q^{44} +(-4.51739 - 0.0690922i) q^{45} +(4.25953 - 4.25953i) q^{47} +(1.06782 - 7.65796i) q^{48} +(4.33013 + 2.50000i) q^{49} +(-1.06488 - 3.97420i) q^{50} +(6.88351 + 5.36603i) q^{51} +(0.803848 - 0.535898i) q^{52} -0.779548i q^{53} +(-1.19909 + 7.73284i) q^{54} +(3.09808 - 5.36603i) q^{55} +(1.84443 + 3.19465i) q^{56} +(6.64136 - 0.822738i) q^{57} +(10.4282 + 2.79423i) q^{58} +(2.90931 + 0.779548i) q^{59} +(0.693622 - 0.0859264i) q^{60} +(3.50000 + 6.06218i) q^{61} +(-2.62398 + 4.54486i) q^{62} +(-2.06488 - 3.70625i) q^{63} -6.66025i q^{64} +(-4.07863 - 3.58442i) q^{65} +(-8.46410 - 6.59817i) q^{66} +(-1.53590 - 5.73205i) q^{67} +(-1.16932 - 0.675108i) q^{68} +(-2.26795 + 2.26795i) q^{70} +(0.779548 - 2.90931i) q^{71} +(-0.119671 + 7.82434i) q^{72} +(-0.901924 - 0.901924i) q^{73} +(-7.06440 + 4.07863i) q^{74} +(1.77739 + 4.38556i) q^{75} +(-1.00000 + 0.267949i) q^{76} +5.81863 q^{77} +(-7.12453 + 6.13931i) q^{78} +2.00000 q^{79} +(6.49373 - 1.73999i) q^{80} +(0.275241 - 8.99579i) q^{81} +(-7.33013 + 4.23205i) q^{82} +(-2.90931 - 2.90931i) q^{83} +(0.395560 + 0.523749i) q^{84} +(-1.96410 + 7.33013i) q^{85} +(2.33864 - 2.33864i) q^{86} +(-12.2978 - 1.71481i) q^{87} +(-9.29423 - 5.36603i) q^{88} +(2.41510 + 9.01327i) q^{89} +(-6.59817 + 1.66025i) q^{90} +(1.00000 - 5.00000i) q^{91} +(2.35237 - 5.55852i) q^{93} +(4.53590 - 7.85641i) q^{94} +(2.90931 + 5.03908i) q^{95} +(-0.320682 - 2.58863i) q^{96} +(1.63397 + 0.437822i) q^{97} +(7.27328 + 1.94887i) q^{98} +(10.5939 + 6.33434i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} - 12 q^{4} - 2 q^{6} - 4 q^{7} + 4 q^{9} + 12 q^{10} + 8 q^{13} - 14 q^{15} - 4 q^{16} + 4 q^{18} - 16 q^{19} + 4 q^{21} + 4 q^{22} + 18 q^{24} + 4 q^{27} + 20 q^{28} + 18 q^{30} + 8 q^{31}+ \cdots + 40 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 - 12 * q^4 - 2 * q^6 - 4 * q^7 + 4 * q^9 + 12 * q^10 + 8 * q^13 - 14 * q^15 - 4 * q^16 + 4 * q^18 - 16 * q^19 + 4 * q^21 + 4 * q^22 + 18 * q^24 + 4 * q^27 + 20 * q^28 + 18 * q^30 + 8 * q^31 + 16 * q^33 - 36 * q^34 - 36 * q^36 - 28 * q^37 - 14 * q^39 - 24 * q^40 - 16 * q^42 + 36 * q^43 - 20 * q^45 - 14 * q^48 + 48 * q^52 + 46 * q^54 + 4 * q^55 + 16 * q^57 + 28 * q^58 + 44 * q^60 + 28 * q^61 - 8 * q^63 - 40 * q^66 - 40 * q^67 - 32 * q^70 + 12 * q^72 - 28 * q^73 + 12 * q^75 - 8 * q^76 - 80 * q^78 + 16 * q^79 + 4 * q^81 - 24 * q^82 + 4 * q^84 + 12 * q^85 - 34 * q^87 - 12 * q^88 + 8 * q^91 + 4 * q^93 + 64 * q^94 + 16 * q^96 + 20 * q^97 + 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$.

$n$	$14$	$28$
$\chi(n)$	$-1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	1.45466	−	0.389774i	1.02860	−	0.275612i	0.295217	−	0.955430i	$-0.404608\pi$
$2$	1.45466	−	0.389774i	1.02860	−	0.275612i	0.733380	+	0.679818i	$0.237941\pi$
$3$	−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	$-0.359326\pi$
$5$	−1.06488	−	1.06488i	−0.476230	−	0.476230i	−0.903924	+	0.427694i	$0.859326\pi$
$6$	−2.08148	+	1.57203i	−0.849760	+	0.641780i
$7$	0.366025	−	1.36603i	0.138345	−	0.516309i	−0.861617	−	0.507559i	$-0.830548\pi$
$7$	0.366025	−	1.36603i	0.138345	−	0.516309i	0.999962	−	0.00875026i	$-0.00278533\pi$
$8$	−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
$11$	1.06488	+	3.97420i	0.321074	+	1.19826i	0.918200	+	0.396117i	$0.129643\pi$
$11$	1.06488	+	3.97420i	0.321074	+	1.19826i	−0.597126	+	0.802148i	$0.703691\pi$
$12$	−0.285334	+	0.366025i	−0.0823689	+	0.105662i
$13$	3.59808	−	0.232051i	0.997927	−	0.0643593i
$13$	3.59808	−	0.232051i	0.997927	−	0.0643593i
$14$		−	2.12976i		−	0.569204i
$15$	2.40216	+	1.01660i	0.620235	+	0.262484i
$16$	−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
$19$	−3.73205	−	1.00000i	−0.856191	−	0.229416i	−0.196084	−	0.980587i	$-0.562823\pi$
$19$	−3.73205	−	1.00000i	−0.856191	−	0.229416i	−0.660107	+	0.751171i	$0.729489\pi$
$20$	−0.389774	−	0.104440i	−0.0871561	−	0.0233534i
$21$	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	$0.166667\pi$
$24$	1.76080	−	4.16067i	0.359421	−	0.849292i
$25$		−	2.73205i		−	0.546410i
$26$	5.14352	−	1.73999i	1.00873	−	0.341240i
$27$	−2.09808	+	4.75374i	−0.403775	+	0.914858i
$28$	−0.0980762	−	0.366025i	−0.0185347	−	0.0691723i
$29$	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	−0.892873	−	0.450308i	$-0.851314\pi$
$31$	−2.46410	+	2.46410i	−0.442566	+	0.442566i	0.450308	+	0.892873i	$0.351314\pi$
$32$	−0.389774	+	1.45466i	−0.0689030	+	0.257149i
$33$	−4.29488	−	5.68671i	−0.747642	−	0.989929i
$34$	−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
$37$	−5.23205	+	1.40192i	−0.860144	+	0.230475i	−0.661821	−	0.749662i	$-0.730216\pi$
$37$	−5.23205	+	1.40192i	−0.860144	+	0.230475i	−0.198323	+	0.980137i	$0.563549\pi$
$38$	−5.81863			−0.943906
$39$	−5.62477	+	2.71330i	−0.900684	+	0.434476i
$40$	3.92820			0.621103
$41$	−5.42885	+	1.45466i	−0.847844	+	0.227179i	−0.656483	−	0.754341i	$-0.727957\pi$
$41$	−5.42885	+	1.45466i	−0.847844	+	0.227179i	−0.191361	+	0.981520i	$0.561290\pi$
$42$	1.38556	+	3.41876i	0.213797	+	0.527526i
$43$	1.90192	−	1.09808i	0.290041	−	0.167455i	−0.347920	−	0.937524i	$-0.613112\pi$
$43$	1.90192	−	1.09808i	0.290041	−	0.167455i	0.637960	+	0.770069i	$0.279778\pi$
$44$	0.779548	+	0.779548i	0.117521	+	0.117521i
$45$	−4.51739	−	0.0690922i	−0.673412	−	0.0102997i
$46$		0			0
$47$	4.25953	−	4.25953i	0.621316	−	0.621316i	−0.324552	−	0.945868i	$-0.605213\pi$
$47$	4.25953	−	4.25953i	0.621316	−	0.621316i	0.945868	+	0.324552i	$0.105213\pi$
$48$	1.06782	−	7.65796i	0.154127	−	1.10533i
$49$	4.33013	+	2.50000i	0.618590	+	0.357143i
$50$	−1.06488	−	3.97420i	−0.150597	−	0.562036i
$51$	6.88351	+	5.36603i	0.963884	+	0.751394i
$52$	0.803848	−	0.535898i	0.111474	−	0.0743157i
$53$		−	0.779548i		−	0.107079i	−0.998566	−	0.0535396i	$-0.982950\pi$
$53$		−	0.779548i		−	0.107079i	0.998566	−	0.0535396i	$-0.0170503\pi$
$54$	−1.19909	+	7.73284i	−0.163176	+	1.05231i
$55$	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
$58$	10.4282	+	2.79423i	1.36929	+	0.366900i
$59$	2.90931	+	0.779548i	0.378760	+	0.101489i	0.443176	−	0.896435i	$-0.353852\pi$
$59$	2.90931	+	0.779548i	0.378760	+	0.101489i	−0.0644157	+	0.997923i	$0.520518\pi$
$60$	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
$63$	−2.06488	−	3.70625i	−0.260151	−	0.466943i
$64$		−	6.66025i		−	0.832532i
$65$	−4.07863	−	3.58442i	−0.505892	−	0.444593i
$66$	−8.46410	−	6.59817i	−1.04186	−	0.812179i
$67$	−1.53590	−	5.73205i	−0.187640	−	0.700281i	−0.994050	−	0.108925i	$-0.965259\pi$
$67$	−1.53590	−	5.73205i	−0.187640	−	0.700281i	0.806410	−	0.591357i	$-0.201407\pi$
$68$	−1.16932	−	0.675108i	−0.141801	−	0.0818689i
$69$		0			0
$70$	−2.26795	+	2.26795i	−0.271072	+	0.271072i
$71$	0.779548	−	2.90931i	0.0925153	−	0.345272i	−0.904116	−	0.427288i	$-0.859469\pi$
$71$	0.779548	−	2.90931i	0.0925153	−	0.345272i	0.996631	+	0.0820158i	$0.0261358\pi$
$72$	−0.119671	+	7.82434i	−0.0141034	+	0.922107i
$73$	−0.901924	−	0.901924i	−0.105562	−	0.105562i	0.652353	−	0.757915i	$-0.273782\pi$
$73$	−0.901924	−	0.901924i	−0.105562	−	0.105562i	−0.757915	+	0.652353i	$0.773782\pi$
$74$	−7.06440	+	4.07863i	−0.821220	+	0.474132i
$75$	1.77739	+	4.38556i	0.205236	+	0.506401i
$76$	−1.00000	+	0.267949i	−0.114708	+	0.0307359i
$77$	5.81863			0.663094
$78$	−7.12453	+	6.13931i	−0.806694	+	0.695140i
$79$	2.00000			0.225018			0.112509	−	0.993651i	$-0.464111\pi$
$79$	2.00000			0.225018			0.112509	+	0.993651i	$0.464111\pi$
$80$	6.49373	−	1.73999i	0.726022	−	0.194537i
$81$	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	$-0.322502\pi$
$83$	−2.90931	−	2.90931i	−0.319339	−	0.319339i	−0.848513	+	0.529174i	$0.822502\pi$
$84$	0.395560	+	0.523749i	0.0431592	+	0.0571457i
$85$	−1.96410	+	7.33013i	−0.213037	+	0.795064i
$86$	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
$89$	2.41510	+	9.01327i	0.256000	+	0.955405i	0.967531	+	0.252751i	$0.0813353\pi$
$89$	2.41510	+	9.01327i	0.256000	+	0.955405i	−0.711531	+	0.702654i	$0.751998\pi$
$90$	−6.59817	+	1.66025i	−0.695509	+	0.175006i
$91$	1.00000	−	5.00000i	0.104828	−	0.524142i
$92$		0			0
$93$	2.35237	−	5.55852i	0.243929	−	0.576392i
$94$	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
$97$	1.63397	+	0.437822i	0.165905	+	0.0444541i	0.340815	−	0.940130i	$-0.389297\pi$
$97$	1.63397	+	0.437822i	0.165905	+	0.0444541i	−0.174910	+	0.984584i	$0.555964\pi$
$98$	7.27328	+	1.94887i	0.734712	+	0.196866i
$99$	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	$0.0697202\pi$
$102$	12.1047	+	5.12271i	1.19854	+	0.507224i
$103$			6.92820i			0.682656i	0.939944	+	0.341328i	$0.110877\pi$
$103$			6.92820i			0.682656i	−0.939944	+	0.341328i	$0.889123\pi$
$104$	−6.20840	+	7.06440i	−0.608784	+	0.692722i
$105$	2.26795	−	2.90931i	0.221329	−	0.283920i
$106$	−0.303848	−	1.13397i	−0.0295123	−	0.110141i
$107$	−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	−0.314806	+	0.949156i	$0.601940\pi$
$109$	−13.1962	+	13.1962i	−1.26396	+	1.26396i	−0.949156	+	0.314806i	$0.898060\pi$
$110$	2.41510	−	9.01327i	0.230271	−	0.859382i
$111$	7.48658	−	5.65423i	0.710595	−	0.536676i
$112$	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
$117$	7.26384	−	8.01478i	0.671542	−	0.740967i
$118$	4.53590			0.417563
$119$	−6.88351	+	1.84443i	−0.631010	+	0.169079i
$120$	−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
$123$	7.76819	−	5.86691i	0.700434	−	0.529002i
$124$	−0.241670	+	0.901924i	−0.0217026	+	0.0809951i
$125$	−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	0.807788	−	0.589474i	$-0.200665\pi$
$127$	7.90192	+	4.56218i	0.701182	+	0.404828i	−0.106605	+	0.994301i	$0.533998\pi$
$128$	−3.37554	−	12.5977i	−0.298359	−	1.11349i
$129$	−2.33864	+	3.00000i	−0.205906	+	0.264135i
$130$	−7.33013	−	3.62436i	−0.642895	−	0.317877i
$131$			7.94839i			0.694454i	0.937781	+	0.347227i	$0.112877\pi$
$131$			7.94839i			0.694454i	−0.937781	+	0.347227i	$0.887123\pi$
$132$	−1.75850	−	0.744201i	−0.153058	−	0.0647743i
$133$	−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
$136$	12.6962	+	3.40192i	1.08869	+	0.291713i
$137$	−6.49373	−	1.73999i	−0.554797	−	0.148657i	−0.0294822	−	0.999565i	$-0.509386\pi$
$137$	−6.49373	−	1.73999i	−0.554797	−	0.148657i	−0.525315	+	0.850908i	$0.676052\pi$
$138$		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
$141$	−4.06639	+	9.60864i	−0.342452	+	0.809194i
$142$		−	4.53590i		−	0.380644i
$143$	4.75374	+	14.0524i	0.397528	+	1.17512i
$144$	3.26795	+	12.9875i	0.272329	+	1.08229i
$145$	−2.79423	−	10.4282i	−0.232048	−	0.866015i
$146$	−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
$149$	−2.23420	+	8.33816i	−0.183033	+	0.683089i	0.812010	+	0.583644i	$0.198374\pi$
$149$	−2.23420	+	8.33816i	−0.183033	+	0.683089i	−0.995043	+	0.0994454i	$0.968293\pi$
$150$	4.29488	+	5.68671i	0.350675	+	0.464318i
$151$	0.535898	+	0.535898i	0.0436108	+	0.0436108i	0.728576	−	0.684965i	$-0.240183\pi$
$151$	0.535898	+	0.535898i	0.0436108	+	0.0436108i	−0.684965	+	0.728576i	$0.740183\pi$
$152$	8.72794	−	5.03908i	0.707929	−	0.408723i
$153$	−14.5406	−	4.13548i	−1.17554	−	0.334334i
$154$	8.46410	−	2.26795i	0.682057	−	0.182757i
$155$	5.24796			0.421526
$156$	−0.941718	+	1.38320i	−0.0753978	+	0.110745i
$157$	−4.80385			−0.383389			−0.191694	−	0.981455i	$-0.561398\pi$
$157$	−4.80385			−0.383389			−0.191694	+	0.981455i	$0.561398\pi$
$158$	2.90931	−	0.779548i	0.231453	−	0.0620175i
$159$	0.507152	+	1.25135i	0.0402197	+	0.0992387i
$160$	1.96410	−	1.13397i	0.155276	−	0.0896486i
$161$		0			0
$162$	−3.10594	−	13.1931i	−0.244026	−	1.03655i
$163$	−1.07180	+	4.00000i	−0.0839496	+	0.313304i	−0.995113	−	0.0987406i	$-0.968519\pi$
$163$	−1.07180	+	4.00000i	−0.0839496	+	0.313304i	0.911164	+	0.412045i	$0.135185\pi$
$164$	−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
$167$	−3.47998	−	12.9875i	−0.269289	−	1.00500i	−0.959573	−	0.281461i	$-0.909181\pi$
$167$	−3.47998	−	12.9875i	−0.269289	−	1.00500i	0.690283	−	0.723539i	$-0.257486\pi$
$168$	−5.03908	−	3.92820i	−0.388773	−	0.303067i
$169$	12.8923	−	1.66987i	0.991716	−	0.128452i
$170$			11.4284i			0.876516i
$171$	−10.1257	+	5.64136i	−0.774328	+	0.431406i
$172$	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
$175$	−3.73205	−	1.00000i	−0.282117	−	0.0755929i
$176$	−17.7412	−	4.75374i	−1.33729	−	0.358327i
$177$	−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	$-0.293184\pi$
$180$	−1.05752	+	0.589182i	−0.0788228	+	0.0439150i
$181$			3.00000i			0.222988i	0.993765	+	0.111494i	$0.0355636\pi$
$181$			3.00000i			0.222988i	−0.993765	+	0.111494i	$0.964436\pi$
$182$	−0.494214	−	7.66306i	−0.0366336	−	0.568024i
$183$	−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
$188$	0.417759	−	1.55910i	0.0304682	−	0.113709i
$189$	5.72579	+	4.60602i	0.416490	+	0.335038i
$190$	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
$193$	0.133975	−	0.0358984i	0.00964370	−	0.00258402i	−0.253994	−	0.967206i	$-0.581744\pi$
$193$	0.133975	−	0.0358984i	0.00964370	−	0.00258402i	0.263638	+	0.964622i	$0.415078\pi$
$194$	2.54752			0.182902
$195$	8.87906	+	3.10037i	0.635843	+	0.222022i
$196$	1.33975			0.0956961
$197$	3.97420	−	1.06488i	0.283150	−	0.0758697i	−0.114449	−	0.993429i	$-0.536510\pi$
$197$	3.97420	−	1.06488i	0.283150	−	0.0758697i	0.397599	+	0.917559i	$0.369844\pi$
$198$	17.8794	+	5.08507i	1.27063	+	0.361380i
$199$	11.1962	−	6.46410i	0.793674	−	0.458228i	−0.0475802	−	0.998867i	$-0.515151\pi$
$199$	11.1962	−	6.46410i	0.793674	−	0.458228i	0.841254	+	0.540639i	$0.181818\pi$
$200$	5.03908	+	5.03908i	0.356317	+	0.356317i
$201$	6.19458	+	8.20204i	0.436932	+	0.578527i
$202$	2.34936	−	8.76795i	0.165301	−	0.616911i
$203$	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
$206$	2.70043	+	10.0782i	0.188148	+	0.702178i
$207$		0			0
$208$	−7.13397	+	14.4282i	−0.494652	+	1.00042i
$209$		−	15.8968i		−	1.09960i
$210$	2.16511	−	5.11604i	0.149407	−	0.353040i
$211$	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
$214$	−27.6603	−	7.41154i	−1.89082	−	0.506643i
$215$	−3.19465	−	0.856003i	−0.217873	−	0.0583789i
$216$	−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
$219$	2.03456	+	0.861027i	0.137483	+	0.0581828i
$220$		−	1.66025i		−	0.111934i
$221$	−10.0782	−	15.1172i	−0.677930	−	1.01690i
$222$	8.68653	−	11.1430i	0.583002	−	0.747872i
$223$	6.70577	+	25.0263i	0.449052	+	1.67588i	0.705011	+	0.709196i	$0.250942\pi$
$223$	6.70577	+	25.0263i	0.449052	+	1.67588i	−0.255960	+	0.966687i	$0.582391\pi$
$224$	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
$227$	−5.24796	+	19.5856i	−0.348319	+	1.29994i	0.540367	+	0.841429i	$0.318285\pi$
$227$	−5.24796	+	19.5856i	−0.348319	+	1.29994i	−0.888686	+	0.458515i	$0.848381\pi$
$228$	1.43091	−	1.08069i	0.0947642	−	0.0715705i
$229$	−14.1244	−	14.1244i	−0.933364	−	0.933364i	0.0645507	−	0.997914i	$-0.479439\pi$
$229$	−14.1244	−	14.1244i	−0.933364	−	0.933364i	−0.997914	+	0.0645507i	$0.979439\pi$
$230$		0			0
$231$	−9.34022	+	3.78543i	−0.614541	+	0.249063i
$232$	−18.0622	+	4.83975i	−1.18584	+	0.317745i
$233$	−17.4559			−1.14357			−0.571786	−	0.820403i	$-0.693749\pi$
$233$	−17.4559			−1.14357			−0.571786	+	0.820403i	$0.693749\pi$
$234$	7.44244	−	14.4900i	0.486527	−	0.947241i
$235$	−9.07180			−0.591779
$236$	0.779548	−	0.208879i	0.0507443	−	0.0135969i
$237$	−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	$-0.347585\pi$
$239$	−6.59817	−	6.59817i	−0.426800	−	0.426800i	−0.887537	+	0.460737i	$0.847585\pi$
$240$	−9.29194	+	7.01772i	−0.599792	+	0.452992i
$241$	3.76795	−	14.0622i	0.242715	−	0.905825i	−0.731803	−	0.681516i	$-0.761321\pi$
$241$	3.76795	−	14.0622i	0.242715	−	0.905825i	0.974518	−	0.224309i	$-0.0720123\pi$
$242$	−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
$245$	−1.94887	−	7.27328i	−0.124509	−	0.464673i
$246$	9.01327	−	11.5622i	0.574665	−	0.737178i
$247$	−13.6603	−	2.73205i	−0.869181	−	0.173836i
$248$		−	9.08973i		−	0.577198i
$249$	6.56283	+	2.77739i	0.415902	+	0.176010i
$250$	−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
$254$	13.2728	+	3.55644i	0.832810	+	0.223151i
$255$	−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	$0.932630\pi$
$258$	−2.23260	+	5.27551i	−0.138996	+	0.328439i
$259$			7.66025i			0.475985i
$260$	−1.42667	−	0.285334i	−0.0884784	−	0.0176957i
$261$	20.8564	−	5.24796i	1.29098	−	0.324840i
$262$	3.09808	+	11.5622i	0.191400	+	0.714314i
$263$	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
$266$	−2.12976	+	7.94839i	−0.130584	+	0.487347i
$267$	−9.74056	−	12.8972i	−0.596113	−	0.789294i
$268$	−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
$271$	7.46410	−	2.00000i	0.453412	−	0.121491i	−0.0248835	−	0.999690i	$-0.507921\pi$
$271$	7.46410	−	2.00000i	0.453412	−	0.121491i	0.478295	+	0.878199i	$0.341255\pi$
$272$	22.4950			1.36396
$273$	1.64763	+	8.67671i	0.0997191	+	0.525138i
$274$	−10.1244			−0.611635
$275$	10.8577	−	2.90931i	0.654744	−	0.175438i
$276$		0			0
$277$	23.8923	−	13.7942i	1.43555	−	0.828815i	0.438013	−	0.898969i	$-0.355682\pi$
$277$	23.8923	−	13.7942i	1.43555	−	0.828815i	0.997536	+	0.0701536i	$0.0223490\pi$
$278$	−19.5856	−	19.5856i	−1.17467	−	1.17467i
$279$	−0.159877	+	10.4531i	−0.00957158	+	0.625809i
$280$	1.43782	−	5.36603i	0.0859263	−	0.320681i
$281$	12.1315	−	12.1315i	0.723703	−	0.723703i	−0.245655	−	0.969357i	$-0.579003\pi$
$281$	12.1315	−	12.1315i	0.723703	−	0.723703i	0.969357	+	0.245655i	$0.0790030\pi$
$282$	−2.17000	+	15.5622i	−0.129221	+	0.926718i
$283$	−5.70577	−	3.29423i	−0.339173	−	0.195822i	0.320733	−	0.947170i	$-0.396071\pi$
$283$	−5.70577	−	3.29423i	−0.339173	−	0.195822i	−0.659906	+	0.751348i	$0.729404\pi$
$284$	−0.208879	−	0.779548i	−0.0123947	−	0.0462577i
$285$	−7.94839	−	6.19615i	−0.470822	−	0.367028i
$286$	12.3923	+	18.5885i	0.732772	+	1.09916i
$287$			7.94839i			0.469179i
$288$	2.19886	+	3.94672i	0.129569	+	0.232562i
$289$	−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
$292$	−0.330127	−	0.0884573i	−0.0193192	−	0.00517657i
$293$	1.73999	+	0.466229i	0.101651	+	0.0272374i	0.309286	−	0.950969i	$-0.399910\pi$
$293$	1.73999	+	0.466229i	0.101651	+	0.0272374i	−0.207635	+	0.978206i	$0.566577\pi$
$294$	−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
$297$	−21.1265	−	3.27599i	−1.22588	−	0.190092i
$298$			13.0000i			0.753070i
$299$		0			0
$300$	1.00000	+	0.779548i	0.0577350	+	0.0450072i
$301$	−0.803848	−	3.00000i	−0.0463330	−	0.172917i
$302$	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
$305$	2.72842	−	10.1826i	0.156229	−	0.583054i
$306$	−22.7635	−	0.348161i	−1.30130	−	0.0199030i
$307$	8.39230	+	8.39230i	0.478974	+	0.478974i	0.904803	−	0.425829i	$-0.140018\pi$
$307$	8.39230	+	8.39230i	0.478974	+	0.478974i	−0.425829	+	0.904803i	$0.640018\pi$
$308$	1.35022	−	0.779548i	0.0769357	−	0.0444189i
$309$	−4.50729	−	11.1213i	−0.256411	−	0.632671i
$310$	7.63397	−	2.04552i	0.433581	−	0.116178i
$311$	−10.0782			−0.571480			−0.285740	−	0.958307i	$-0.592239\pi$
$311$	−10.0782			−0.571480			−0.285740	+	0.958307i	$0.592239\pi$
$312$	5.37000	−	15.3790i	0.304016	−	0.870664i
$313$	2.00000			0.113047			0.0565233	−	0.998401i	$-0.481998\pi$
$313$	2.00000			0.113047			0.0565233	+	0.998401i	$0.481998\pi$
$314$	−6.98795	+	1.87241i	−0.394353	+	0.105666i
$315$	−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	$-0.101124\pi$
$317$	11.3519	+	11.3519i	0.637587	+	0.637587i	−0.312373	+	0.949960i	$0.601124\pi$
$318$	1.22548	+	1.62261i	0.0687213	+	0.0909916i
$319$	−7.63397	+	28.4904i	−0.427421	+	1.59516i
$320$	−7.09239	+	7.09239i	−0.396477	+	0.396477i
$321$	32.6193	+	4.54843i	1.82063	+	0.253869i
$322$		0			0
$323$	5.03908	+	18.8061i	0.280382	+	1.04640i
$324$	−1.14134	−	2.12436i	−0.0634076	−	0.118020i
$325$	−0.633975	−	9.83013i	−0.0351666	−	0.545277i
$326$			6.23638i			0.345401i
$327$	12.5978	−	29.7679i	0.696659	−	1.64617i
$328$	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
$331$	−33.0526	−	8.85641i	−1.81673	−	0.486792i	−0.820357	−	0.571852i	$-0.806225\pi$
$331$	−33.0526	−	8.85641i	−1.81673	−	0.486792i	−0.996376	+	0.0850595i	$0.972892\pi$
$332$	−1.06488	−	0.285334i	−0.0584430	−	0.0156598i
$333$	−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
$336$	−10.0701	−	4.26168i	−0.549370	−	0.232494i
$337$		−	18.4641i		−	1.00580i	−0.864344	−	0.502902i	$-0.832266\pi$
$337$		−	18.4641i		−	1.00580i	0.864344	−	0.502902i	$-0.167734\pi$
$338$	18.1030	−	7.45418i	0.984673	−	0.405454i
$339$	−10.9545	+	14.0524i	−0.594966	+	0.763219i
$340$	0.526279	+	1.96410i	0.0285415	+	0.106518i
$341$	−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
$344$	−1.48264	+	5.53329i	−0.0799386	+	0.298335i
$345$		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
$349$	27.4904	−	7.36603i	1.47153	−	0.394294i	0.568072	−	0.822979i	$-0.307689\pi$
$349$	27.4904	−	7.36603i	1.47153	−	0.394294i	0.903454	+	0.428684i	$0.141023\pi$
$350$	−5.81863			−0.311019
$351$	−6.44593	+	17.5912i	−0.344058	+	0.938948i
$352$	−6.19615			−0.330256
$353$	−13.6626	+	3.66088i	−0.727186	+	0.194849i	−0.603376	−	0.797457i	$-0.706178\pi$
$353$	−13.6626	+	3.66088i	−0.727186	+	0.194849i	−0.123810	+	0.992306i	$0.539511\pi$
$354$	−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
$357$	9.84967	−	7.43895i	0.521300	−	0.393711i
$358$	10.3468	−	38.6147i	0.546845	−	2.04085i
$359$	−18.2354	+	18.2354i	−0.962429	+	0.962429i	−0.999319	−	0.0368904i	$-0.988255\pi$
$359$	−18.2354	+	18.2354i	−0.962429	+	0.962429i	0.0368904	+	0.999319i	$0.488255\pi$
$360$	8.45944	−	8.20457i	0.445852	−	0.432419i
$361$	−3.52628	−	2.03590i	−0.185594	−	0.107153i
$362$	1.16932	+	4.36397i	0.0614582	+	0.229365i
$363$	6.31284	−	8.09808i	0.331338	−	0.425039i
$364$	−0.437822	−	1.29423i	−0.0229481	−	0.0678360i
$365$			1.92089i			0.100544i
$366$	−16.8151	−	7.11618i	−0.878941	−	0.371969i
$367$	−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
$370$	11.8660	+	3.17949i	0.616885	+	0.165294i
$371$	−1.06488	−	0.285334i	−0.0552859	−	0.0148138i
$372$	−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
$375$	7.86038	−	18.5736i	0.405908	−	0.959138i
$376$			15.7128i			0.810326i
$377$	23.1701	+	11.4564i	1.19332	+	0.590032i
$378$	10.1244	+	4.46841i	0.520741	+	0.229830i
$379$	3.83013	+	14.2942i	0.196740	+	0.734245i	0.991809	+	0.127726i	$0.0407679\pi$
$379$	3.83013	+	14.2942i	0.196740	+	0.734245i	−0.795069	+	0.606519i	$0.792565\pi$
$380$	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
$383$	8.51906	−	31.7936i	0.435304	−	1.62458i	−0.305035	−	0.952341i	$-0.598668\pi$
$383$	8.51906	−	31.7936i	0.435304	−	1.62458i	0.740339	−	0.672234i	$-0.234665\pi$
$384$	13.6142	+	18.0261i	0.694748	+	0.919893i
$385$	−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
$388$	0.437822	−	0.117314i	0.0222271	−	0.00595572i
$389$	−22.4950			−1.14054			−0.570270	−	0.821457i	$-0.693161\pi$
$389$	−22.4950			−1.14054			−0.570270	+	0.821457i	$0.693161\pi$
$390$	14.1244	+	1.04915i	0.715218	+	0.0531255i
$391$		0			0
$392$	−12.5977	+	3.37554i	−0.636280	+	0.170491i
$393$	−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
$396$	3.30696	+	0.0505790i	0.166181	+	0.00254169i
$397$	−3.56218	+	13.2942i	−0.178781	+	0.667218i	0.817096	+	0.576501i	$0.195582\pi$
$397$	−3.56218	+	13.2942i	−0.178781	+	0.667218i	−0.995877	+	0.0907168i	$0.971084\pi$
$398$	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
$401$	3.22263	+	12.0270i	0.160931	+	0.600601i	0.998524	+	0.0543073i	$0.0172951\pi$
$401$	3.22263	+	12.0270i	0.160931	+	0.600601i	−0.837594	+	0.546294i	$0.816038\pi$
$402$	12.2079	+	9.51666i	0.608876	+	0.474648i
$403$	−8.29423	+	9.43782i	−0.413165	+	0.470131i
$404$		−	1.61507i		−	0.0803525i
$405$	−9.87256	+	9.28636i	−0.490571	+	0.461443i
$406$	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
$409$	28.9904	+	7.76795i	1.43348	+	0.384100i	0.890246	−	0.455480i	$-0.150532\pi$
$409$	28.9904	+	7.76795i	1.43348	+	0.384100i	0.543236	+	0.839580i	$0.317199\pi$
$410$	12.3124	+	3.29909i	0.608064	+	0.162930i
$411$	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
$416$	−1.06488	+	5.32441i	−0.0522102	+	0.261051i
$417$	25.1244	+	19.5856i	1.23034	+	0.959113i
$418$	−6.19615	−	23.1244i	−0.303064	−	1.13105i
$419$	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	−0.871685	−	0.490067i	$-0.836972\pi$
$421$	−7.83013	+	7.83013i	−0.381617	+	0.381617i	0.490067	+	0.871685i	$0.336972\pi$
$422$	0.703093	−	2.62398i	0.0342260	−	0.127733i
$423$	0.276369	−	18.0695i	0.0134375	−	0.878571i
$424$	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
$427$	9.56218	−	2.56218i	0.462746	−	0.123992i
$428$	−5.09505			−0.246278
$429$	−16.7729	−	19.4646i	−0.809803	−	0.939759i
$430$	−4.98076			−0.240194
$431$	36.5473	−	9.79282i	1.76042	−	0.471704i	0.773622	−	0.633648i	$-0.218443\pi$
$431$	36.5473	−	9.79282i	1.76042	−	0.471704i	0.986800	+	0.161944i	$0.0517764\pi$
$432$	−13.6951	−	18.7218i	−0.658905	−	0.900754i
$433$	−26.8923	+	15.5263i	−1.29236	+	0.746145i	−0.979072	−	0.203512i	$-0.934764\pi$
$433$	−26.8923	+	15.5263i	−1.29236	+	0.746145i	−0.313289	+	0.949658i	$0.601431\pi$
$434$	5.24796	+	5.24796i	0.251910	+	0.251910i
$435$	11.2697	+	14.9218i	0.540339	+	0.715445i
$436$	−1.29423	+	4.83013i	−0.0619823	+	0.231321i
$437$		0			0
$438$	3.29519	+	0.459481i	0.157450	+	0.0219548i
$439$	1.09808	+	0.633975i	0.0524083	+	0.0302580i	0.525975	−	0.850500i	$-0.323700\pi$
$439$	1.09808	+	0.633975i	0.0524083	+	0.0302580i	−0.473567	+	0.880758i	$0.657034\pi$
$440$	4.18307	+	15.6114i	0.199420	+	0.744247i
$441$	14.5466	−	3.66025i	0.692694	−	0.174298i
$442$	−20.5526	−	18.0622i	−0.977586	−	0.859130i
$443$		−	11.2195i		−	0.533054i	−0.963827	−	0.266527i	$-0.914124\pi$
$443$		−	11.2195i		−	0.533054i	0.963827	−	0.266527i	$-0.0858762\pi$
$444$	0.979744	−	2.31508i	0.0464966	−	0.109869i
$445$	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
$448$	−9.09808	−	2.43782i	−0.429844	−	0.115176i
$449$	19.8710	+	5.32441i	0.937769	+	0.251275i	0.695165	−	0.718851i	$-0.255331\pi$
$449$	19.8710	+	5.32441i	0.937769	+	0.251275i	0.242605	+	0.970125i	$0.421998\pi$
$450$	−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
$453$	−1.20888	−	0.511599i	−0.0567981	−	0.0240370i
$454$			30.5359i			1.43312i
$455$	−6.38929	+	4.25953i	−0.299535	+	0.199690i
$456$	−10.7321	+	13.7670i	−0.502574	+	0.644700i
$457$	−1.00962	−	3.76795i	−0.0472280	−	0.176257i	0.938283	−	0.345868i	$-0.112416\pi$
$457$	−1.00962	−	3.76795i	−0.0472280	−	0.176257i	−0.985511	+	0.169611i	$0.945749\pi$
$458$	−26.0514	−	15.0408i	−1.21730	−	0.702809i
$459$	26.0314	−	2.82130i	1.21504	−	0.131687i
$460$		0			0
$461$	5.50531	−	20.5461i	0.256408	−	0.956927i	−0.710894	−	0.703299i	$-0.751710\pi$
$461$	5.50531	−	20.5461i	0.256408	−	0.956927i	0.967302	−	0.253628i	$-0.0816238\pi$
$462$	−12.1113	+	9.14708i	−0.563471	+	0.425561i
$463$	23.0526	+	23.0526i	1.07134	+	1.07134i	0.997251	+	0.0740918i	$0.0236058\pi$
$463$	23.0526	+	23.0526i	1.07134	+	1.07134i	0.0740918	+	0.997251i	$0.476394\pi$
$464$	−27.7149	+	16.0012i	−1.28663	+	0.742838i
$465$	−8.42417	+	3.41417i	−0.390661	+	0.158328i
$466$	−25.3923	+	6.80385i	−1.17628	+	0.315182i
$467$	19.1679			0.886984			0.443492	−	0.896278i	$-0.353739\pi$
$467$	19.1679			0.886984			0.443492	+	0.896278i	$0.353739\pi$
$468$	0.611803	−	2.83301i	0.0282806	−	0.130956i
$469$	−8.39230			−0.387521
$470$	−13.1963	+	3.53595i	−0.608702	+	0.163101i
$471$	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
$474$	−4.16296	+	3.14407i	−0.191211	+	0.144412i
$475$	−2.73205	+	10.1962i	−0.125355	+	0.467832i
$476$	−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
$479$	−5.32441	−	19.8710i	−0.243279	−	0.907928i	−0.974241	−	0.225510i	$-0.927595\pi$
$479$	−5.32441	−	19.8710i	−0.243279	−	0.907928i	0.730962	−	0.682418i	$-0.239072\pi$
$480$	−2.41510	+	3.09808i	−0.110234	+	0.141407i
$481$	−18.5000	+	6.25833i	−0.843527	+	0.285355i
$482$		−	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
$487$	5.56218	+	1.49038i	0.252046	+	0.0675356i	0.382630	−	0.923902i	$-0.375018\pi$
$487$	5.56218	+	1.49038i	0.252046	+	0.0675356i	−0.130584	+	0.991437i	$0.541685\pi$
$488$	−17.6368	−	4.72576i	−0.798379	−	0.213925i
$489$	−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	$0.944107\pi$
$492$	1.01660	−	2.40216i	0.0458317	−	0.108298i
$493$		−	36.1244i		−	1.62696i
$494$	−20.9359	+	1.35022i	−0.941949	+	0.0607491i
$495$	−4.53590	−	18.0265i	−0.203873	−	0.810233i
$496$	−4.02628	−	15.0263i	−0.180785	−	0.674700i
$497$	−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	−0.760107	−	0.649798i	$-0.774853\pi$
$499$	−2.46410	+	2.46410i	−0.110308	+	0.110308i	0.649798	+	0.760107i	$0.274853\pi$
$500$	−0.807533	+	3.01375i	−0.0361140	+	0.134779i
$501$	14.0354	+	18.5839i	0.627057	+	0.830266i
$502$	−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
$505$	−8.76795	+	2.34936i	−0.390169	+	0.104545i
$506$		0			0
$507$	−19.6087	+	11.0679i	−0.870854	+	0.491542i
$508$	2.44486			0.108473
$509$	−14.1568	+	3.79330i	−0.627489	+	0.168135i	−0.558530	−	0.829484i	$-0.688634\pi$
$509$	−14.1568	+	3.79330i	−0.627489	+	0.168135i	−0.0689588	+	0.997620i	$0.521968\pi$
$510$	−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
$513$	12.5839	−	15.6431i	0.555591	−	0.690661i
$514$	−8.38269	+	31.2846i	−0.369744	+	1.37990i
$515$	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
$518$	2.98577	+	11.1430i	0.131187	+	0.489597i
$519$	−23.8452	−	18.5885i	−1.04669	−	0.815943i
$520$	14.1340	−	0.911543i	0.619816	−	0.0399738i
$521$		−	2.49155i		−	0.109157i	−0.998509	−	0.0545785i	$-0.982618\pi$
$521$		−	2.49155i		−	0.109157i	0.998509	−	0.0545785i	$-0.0173815\pi$
$522$	28.2934	−	15.7633i	1.23837	−	0.689939i
$523$	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
$526$	32.4186	+	8.68653i	1.41352	+	0.378751i
$527$	16.9617	+	4.54486i	0.738862	+	0.197977i
$528$	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
$531$	7.89343	−	4.39771i	0.342546	−	0.190845i
$532$			1.46410i			0.0634769i
$533$	−19.1959	+	6.49373i	−0.831465	+	0.281275i
$534$	−19.1962	−	14.9643i	−0.830699	−	0.647570i
$535$	7.41154	+	27.6603i	0.320429	+	1.19586i
$536$	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
$539$	−5.32441	+	19.8710i	−0.229339	+	0.855904i
$540$	1.31425	−	1.63376i	0.0565565	−	0.0703060i
$541$	−12.6865	−	12.6865i	−0.545437	−	0.545437i	0.379681	−	0.925118i	$-0.376034\pi$
$541$	−12.6865	−	12.6865i	−0.545437	−	0.545437i	−0.925118	+	0.379681i	$0.876034\pi$
$542$	10.0782	−	5.81863i	0.432894	−	0.249931i
$543$	−1.95171	−	4.81568i	−0.0837561	−	0.206661i
$544$	7.33013	−	1.96410i	0.314277	−	0.0842102i
$545$	28.1047			1.20387
$546$	5.77869	+	11.9794i	0.247305	+	0.512672i
$547$	2.00000			0.0855138			0.0427569	−	0.999086i	$-0.486386\pi$
$547$	2.00000			0.0855138			0.0427569	+	0.999086i	$0.486386\pi$
$548$	−1.73999	+	0.466229i	−0.0743287	+	0.0199163i
$549$	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
$553$	0.732051	−	2.73205i	0.0311300	−	0.116179i
$554$	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
$557$	−6.62616	−	24.7292i	−0.280759	−	1.04781i	−0.951883	−	0.306462i	$-0.900855\pi$
$557$	−6.62616	−	24.7292i	−0.280759	−	1.04781i	0.671123	−	0.741346i	$-0.265812\pi$
$558$	3.84177	+	15.2679i	0.162635	+	0.646344i
$559$	6.58846	−	4.39230i	0.278662	−	0.185775i
$560$		−	9.50749i		−	0.401765i
$561$	−13.9955	+	33.0706i	−0.590891	+	1.39624i
$562$	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
$565$	−14.9641	−	4.00962i	−0.629544	−	0.168686i
$566$	−9.58394	−	2.56801i	−0.402843	−	0.107941i
$567$	−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	$0.184694\pi$
$570$	−13.9773	−	5.91520i	−0.585444	−	0.247760i
$571$			1.94744i			0.0814979i	0.999169	+	0.0407489i	$0.0129744\pi$
$571$			1.94744i			0.0814979i	−0.999169	+	0.0407489i	$0.987026\pi$
$572$	2.98577	+	2.62398i	0.124841	+	0.109714i
$573$	5.14359	−	6.59817i	0.214877	−	0.275643i
$574$	3.09808	+	11.5622i	0.129311	+	0.482596i
$575$		0			0
$576$	−13.9108	−	14.3429i	−0.579617	−	0.597623i
$577$	−22.4904	+	22.4904i	−0.936287	+	0.936287i	−0.998088	−	0.0618016i	$-0.980315\pi$
$577$	−22.4904	+	22.4904i	−0.936287	+	0.936287i	0.0618016	+	0.998088i	$0.480315\pi$
$578$	−3.27110	+	12.2079i	−0.136060	+	0.507783i
$579$	−0.191705	+	0.144785i	−0.00796700	+	0.00601707i
$580$	−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
$583$	3.09808	−	0.830127i	0.128309	−	0.0343803i
$584$	3.32707			0.137675
$585$	−16.2699	+	0.799664i	−0.672679	+	0.0330620i
$586$	2.71281			0.112065
$587$	−18.0265	+	4.83020i	−0.744035	+	0.199364i	−0.610871	−	0.791730i	$-0.709181\pi$
$587$	−18.0265	+	4.83020i	−0.744035	+	0.199364i	−0.133164	+	0.991094i	$0.542514\pi$
$588$	−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
$591$	−5.68671	+	4.29488i	−0.233920	+	0.176668i
$592$	6.25833	−	23.3564i	0.257216	−	0.959942i
$593$	−10.3635	+	10.3635i	−0.425578	+	0.425578i	−0.887119	−	0.461541i	$-0.847297\pi$
$593$	−10.3635	+	10.3635i	−0.425578	+	0.425578i	0.461541	+	0.887119i	$0.347297\pi$
$594$	−32.0087	+	3.46913i	−1.31333	+	0.142340i
$595$	9.29423	+	5.36603i	0.381026	+	0.219986i
$596$	0.598653	+	2.23420i	0.0245218	+	0.0915166i
$597$	−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	$0.860822\pi$
$600$	−11.3671	−	4.81059i	−0.464062	−	0.196391i
$601$	−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
$604$	0.196152	+	0.0525589i	0.00798133	+	0.00213859i
$605$	8.62350	+	2.31066i	0.350595	+	0.0939417i
$606$	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
$609$	−6.84378	+	16.1715i	−0.277324	+	0.655301i
$610$		−	15.8756i		−	0.642786i
$611$	14.3377	−	16.3145i	0.580041	−	0.660016i
$612$	−3.92820	+	0.988427i	−0.158788	+	0.0399548i
$613$	−11.3564	−	42.3827i	−0.458681	−	1.71182i	−0.677035	−	0.735951i	$-0.736735\pi$
$613$	−11.3564	−	42.3827i	−0.458681	−	1.71182i	0.218354	−	0.975870i	$-0.429931\pi$
$614$	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
$617$	4.78173	−	17.8457i	0.192505	−	0.718439i	−0.800393	−	0.599475i	$-0.795376\pi$
$617$	4.78173	−	17.8457i	0.192505	−	0.718439i	0.992899	−	0.118964i	$-0.0379573\pi$
$618$	−10.8914	−	14.4209i	−0.438115	−	0.580094i
$619$	−31.6603	−	31.6603i	−1.27253	−	1.27253i	−0.944755	−	0.327778i	$-0.893700\pi$
$619$	−31.6603	−	31.6603i	−1.27253	−	1.27253i	−0.327778	−	0.944755i	$-0.606300\pi$
$620$	1.21779	−	0.703093i	0.0489077	−	0.0282369i
$621$		0			0
$622$	−14.6603	+	3.92820i	−0.587823	+	0.157507i
$623$	13.1963			0.528701
$624$	2.06508	−	27.8017i	0.0826693	−	1.11296i
$625$	3.87564			0.155026
$626$	2.90931	−	0.779548i	0.116280	−	0.0311570i
$627$	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
$630$	−0.147150	+	9.62097i	−0.00586260	+	0.383309i
$631$	5.73205	−	21.3923i	0.228189	−	0.851614i	−0.752912	−	0.658121i	$-0.771352\pi$
$631$	5.73205	−	21.3923i	0.228189	−	0.851614i	0.981102	−	0.193493i	$-0.0619818\pi$
$632$	−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
$635$	−3.55644	−	13.2728i	−0.141133	−	0.526715i
$636$	0.285334	+	0.222432i	0.0113142	+	0.00882000i
$637$	16.1603	+	7.99038i	0.640293	+	0.316590i
$638$			44.4192i			1.75857i
$639$	−4.39771	−	7.89343i	−0.173971	−	0.312259i
$640$	−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
$643$	7.00000	+	1.87564i	0.276053	+	0.0739682i	0.394190	−	0.919029i	$-0.371025\pi$
$643$	7.00000	+	1.87564i	0.276053	+	0.0739682i	−0.118136	+	0.992997i	$0.537692\pi$
$644$		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	$0.271594\pi$
$648$	16.0844	+	17.0998i	0.631857	+	0.671742i
$649$			12.3923i			0.486441i
$650$	−4.75374	−	14.0524i	−0.186457	−	0.551179i
$651$	−6.73205	−	5.24796i	−0.263850	−	0.205684i
$652$	0.287187	+	1.07180i	0.0112471	+	0.0419748i
$653$	−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
$656$	6.49373	−	24.2349i	0.253538	−	0.946216i
$657$	−3.82609	−	0.0585190i	−0.149270	−	0.00228304i
$658$	−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
$661$	9.42820	−	2.52628i	0.366715	−	0.0982609i	−0.0707559	−	0.997494i	$-0.522541\pi$
$661$	9.42820	−	2.52628i	0.366715	−	0.0982609i	0.437470	+	0.899233i	$0.355874\pi$
$662$	−51.5321			−2.00285
$663$	26.0126	+	17.7100i	1.01024	+	0.687801i
$664$	10.7321			0.416484
$665$	7.94839	−	2.12976i	0.308225	−	0.0825887i
$666$	−6.69452	+	23.5383i	−0.259408	+	0.912092i
$667$		0			0
$668$	−2.54752	−	2.54752i	−0.0985666	−	0.0985666i
$669$	−27.0457	−	35.8103i	−1.04565	−	1.38451i
$670$	−3.48334	+	13.0000i	−0.134573	+	0.502234i
$671$	−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	−0.429082	−	0.903265i	$-0.641163\pi$
$673$	−36.9904	−	21.3564i	−1.42587	−	0.823229i	−0.996792	+	0.0800364i	$0.974496\pi$
$674$	−7.19683	−	26.8589i	−0.277211	−	1.03457i
$675$	12.9875	+	5.73205i	0.499888	+	0.220627i
$676$	2.76795	−	2.11474i	0.106460	−	0.0813360i
$677$			9.66040i			0.371279i	0.982618	+	0.185640i	$0.0594357\pi$
$677$			9.66040i			0.371279i	−0.982618	+	0.185640i	$0.940564\pi$
$678$	−10.4578	+	24.7111i	−0.401628	+	0.949025i
$679$	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
$682$	−20.8564	−	5.58846i	−0.798633	−	0.213993i
$683$	−45.2752	−	12.1315i	−1.73241	−	0.464198i	−0.751673	−	0.659536i	$-0.770753\pi$
$683$	−45.2752	−	12.1315i	−1.73241	−	0.464198i	−0.980736	+	0.195338i	$0.937420\pi$
$684$	−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
$687$	31.8617	+	13.4839i	1.21560	+	0.514443i
$688$			9.80385i			0.373768i
$689$	−0.180895	−	2.80487i	−0.00689154	−	0.106857i
$690$		0			0
$691$	4.88269	+	18.2224i	0.185746	+	0.693214i	0.994470	+	0.105025i	$0.0334922\pi$
$691$	4.88269	+	18.2224i	0.185746	+	0.693214i	−0.808723	+	0.588189i	$0.799841\pi$
$692$	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
$695$	−7.16884	+	26.7545i	−0.271930	+	1.01486i
$696$	25.8453	−	19.5196i	0.979664	−	0.739890i
$697$	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
$700$	−1.00000	+	0.267949i	−0.0377964	+	0.0101275i
$701$	−12.7786			−0.482641			−0.241320	−	0.970446i	$-0.577580\pi$
$701$	−12.7786			−0.482641			−0.241320	+	0.970446i	$0.577580\pi$
$702$	−2.52002	+	28.1016i	−0.0951121	+	1.06063i
$703$	20.9282			0.789322
$704$	26.4692	−	7.09239i	0.997594	−	0.267304i
$705$	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
$708$	−1.11546	+	0.842451i	−0.0419216	+	0.0316612i
$709$	−3.03590	+	11.3301i	−0.114016	+	0.425512i	−0.999211	−	0.0397068i	$-0.987358\pi$
$709$	−3.03590	+	11.3301i	−0.114016	+	0.425512i	0.885196	+	0.465219i	$0.154024\pi$
$710$	−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
$715$	9.90192	−	20.0263i	0.370311	−	0.748940i
$716$		−	7.11287i		−	0.265821i
$717$	14.8842	+	6.29899i	0.555859	+	0.235240i
$718$	−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
$721$	9.46410	+	2.53590i	0.352462	+	0.0944418i
$722$	−5.92307	−	1.58708i	−0.220434	−	0.0590650i
$723$	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
$726$	6.02659	−	14.2405i	0.223668	−	0.528515i
$727$		−	19.5167i		−	0.723833i	−0.932211	−	0.361916i	$-0.882123\pi$
$727$		−	19.5167i		−	0.723833i	0.932211	−	0.361916i	$-0.117877\pi$
$728$	7.37772	+	11.0666i	0.273437	+	0.410155i
$729$	−18.1962	−	19.9474i	−0.673932	−	0.738794i
$730$	0.748711	+	2.79423i	0.0277110	+	0.103419i
$731$	−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	−0.821108	−	0.570773i	$-0.806644\pi$
$733$	−6.77757	+	6.77757i	−0.250335	+	0.250335i	0.570773	+	0.821108i	$0.306644\pi$
$734$	−11.8461	+	44.2104i	−0.437249	+	1.63183i
$735$	7.86017	+	10.4074i	0.289927	+	0.383883i
$736$		0			0
$737$	21.1447	−	12.2079i	0.778876	−	0.449685i
$738$	−6.94633	+	24.4237i	−0.255698	+	0.899049i
$739$	−11.1244	+	2.98076i	−0.409216	+	0.109649i	−0.457554	−	0.889182i	$-0.651274\pi$
$739$	−11.1244	+	2.98076i	−0.409216	+	0.109649i	0.0483378	+	0.998831i	$0.484608\pi$
$740$	2.18573			0.0803492
$741$	23.7052	−	4.50141i	0.870833	−	0.165363i
$742$	−1.66025			−0.0609498
$743$	8.51906	−	2.28268i	0.312534	−	0.0837432i	−0.0991426	−	0.995073i	$-0.531610\pi$
$743$	8.51906	−	2.28268i	0.312534	−	0.0837432i	0.411677	+	0.911330i	$0.364943\pi$
$744$	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
$747$	−12.3417	−	0.188763i	−0.451560	−	0.00690649i
$748$	1.43782	−	5.36603i	0.0525720	−	0.196201i
$749$	−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	−0.140554	−	0.990073i	$-0.544888\pi$
$751$	−29.2750	−	16.9019i	−1.06826	−	0.616760i	−0.927705	+	0.373313i	$0.878222\pi$
$752$	6.95996	+	25.9749i	0.253804	+	0.947208i
$753$	1.35022	+	1.05256i	0.0492046	+	0.0383574i
$754$	38.1699	+	7.63397i	1.39006	+	0.278013i
$755$		−	1.14134i		−	0.0415375i
$756$	1.94576	+	0.301720i	0.0707667	+	0.0109735i
$757$	−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
$760$	−14.6603	−	3.92820i	−0.531783	−	0.142491i
$761$	−17.7412	−	4.75374i	−0.643118	−	0.172323i	−0.0775029	−	0.996992i	$-0.524695\pi$
$761$	−17.7412	−	4.75374i	−0.643118	−	0.172323i	−0.565616	+	0.824669i	$0.691361\pi$
$762$	−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
$765$	11.0802	+	19.8878i	0.400606	+	0.719045i
$766$		−	49.5692i		−	1.79101i
$767$	10.6488	+	2.12976i	0.384507	+	0.0769014i
$768$	8.63397	+	6.73060i	0.311552	+	0.242870i
$769$	−10.8301	−	40.4186i	−0.390544	−	1.45753i	−0.829238	−	0.558895i	$-0.811225\pi$
$769$	−10.8301	−	40.4186i	−0.390544	−	1.45753i	0.438694	−	0.898636i	$-0.355441\pi$
$770$	−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
$773$	−11.1430	+	41.5864i	−0.400787	+	1.49576i	0.410908	+	0.911677i	$0.365212\pi$
$773$	−11.1430	+	41.5864i	−0.400787	+	1.49576i	−0.811695	+	0.584081i	$0.801455\pi$
$774$	0.151737	−	9.92087i	0.00545407	−	0.356598i
$775$	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
$778$	−32.7224	+	8.76795i	−1.17316	+	0.314346i
$779$	21.7154			0.778035
$780$	2.47576	−	0.470125i	0.0886466	−	0.0168332i
$781$	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
$786$	−12.4951	−	16.5444i	−0.445687	−	0.590120i
$787$	4.29423	−	16.0263i	0.153073	−	0.571275i	−0.846190	−	0.532881i	$-0.821109\pi$
$787$	4.29423	−	16.0263i	0.153073	−	0.571275i	0.999263	−	0.0383938i	$-0.0122241\pi$
$788$	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
$791$	−3.76532	−	14.0524i	−0.133879	−	0.499644i
$792$	−31.2229	+	7.85641i	−1.10946	+	0.279165i
$793$	14.0000	+	21.0000i	0.497155	+	0.745732i
$794$			20.7270i			0.735573i
$795$	0.792486	−	1.87260i	0.0281066	−	0.0664143i
$796$	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
$799$	−29.3205	−	7.85641i	−1.03729	−	0.277940i
$800$	3.97420	+	1.06488i	0.140509	+	0.0376493i
$801$	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
$804$	2.53632	+	1.07337i	0.0894491	+	0.0378550i
$805$		0			0
$806$	−8.38664	+	16.9617i	−0.295407	+	0.597449i
$807$	−15.2679	+	19.5856i	−0.537457	+	0.689447i
$808$	4.06922	+	15.1865i	0.143155	+	0.534260i
$809$	−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	−0.289882	−	0.957062i	$-0.593616\pi$
$811$	19.0000	−	19.0000i	0.667180	−	0.667180i	0.957062	+	0.289882i	$0.0936161\pi$
$812$	0.703093	−	2.62398i	0.0246737	−	0.0920836i
$813$	−10.6804	+	8.06639i	−0.374579	+	0.282901i
$814$	−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
$817$	−8.19615	+	2.19615i	−0.286747	+	0.0768336i
$818$	45.1988			1.58034
$819$	−8.28964	−	12.8562i	−0.289664	−	0.449232i
$820$	2.26795			0.0792002
$821$	41.5864	−	11.1430i	1.45137	−	0.388895i	0.554873	−	0.831935i	$-0.312767\pi$
$821$	41.5864	−	11.1430i	1.45137	−	0.388895i	0.896502	+	0.443040i	$0.146100\pi$
$822$	16.2519	−	6.58662i	0.566850	−	0.229735i
$823$	−7.39230	+	4.26795i	−0.257680	+	0.148771i	−0.623276	−	0.782002i	$-0.714199\pi$
$823$	−7.39230	+	4.26795i	−0.257680	+	0.148771i	0.365596	+	0.930774i	$0.380865\pi$
$824$	−12.7786	−	12.7786i	−0.445163	−	0.445163i
$825$	−15.5364	+	11.7338i	−0.540907	+	0.408519i
$826$	1.66025	−	6.19615i	0.0577676	−	0.215592i
$827$	31.7936	−	31.7936i	1.10557	−	1.10557i	0.111845	−	0.993726i	$-0.464324\pi$
$827$	31.7936	−	31.7936i	1.10557	−	1.10557i	0.993726	−	0.111845i	$-0.0356760\pi$
$828$		0			0
$829$	41.6769	+	24.0622i	1.44750	+	0.835714i	0.998332	−	0.0577338i	$-0.0183875\pi$
$829$	41.6769	+	24.0622i	1.44750	+	0.835714i	0.449167	+	0.893448i	$0.351721\pi$
$830$	2.41510	+	9.01327i	0.0838293	+	0.312855i
$831$	−29.3785	+	37.6865i	−1.01913	+	1.30733i
$832$	−1.54552	−	23.9641i	−0.0535812	−	0.830806i
$833$		−	25.1954i		−	0.872968i
$834$	44.1813	+	18.6976i	1.52987	+	0.647444i
$835$	−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
$838$	13.8301	+	3.70577i	0.477754	+	0.128014i
$839$	9.79282	+	2.62398i	0.338086	+	0.0905898i	0.423868	−	0.905724i	$-0.360672\pi$
$839$	9.79282	+	2.62398i	0.338086	+	0.0905898i	−0.0857819	+	0.996314i	$0.527339\pi$
$840$	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
$843$	−11.5814	+	27.3662i	−0.398884	+	0.942540i
$844$		−	0.483340i		−	0.0166372i
$845$	−15.5070	−	11.9506i	−0.533457	−	0.411112i
$846$	−6.64102	−	26.3927i	−0.228323	−	0.907400i
$847$	2.16987	+	8.09808i	0.0745577	+	0.278253i
$848$	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
$852$	0.842451	+	1.11546i	0.0288619	+	0.0382151i
$853$	−22.3660	−	22.3660i	−0.765798	−	0.765798i	0.211566	−	0.977364i	$-0.432144\pi$
$853$	−22.3660	−	22.3660i	−0.765798	−	0.765798i	−0.977364	+	0.211566i	$0.932144\pi$
$854$	12.9110	−	7.45418i	0.441806	−	0.255077i
$855$	16.7900	+	4.77524i	0.574207	+	0.163310i
$856$	47.9090	−	12.8372i	1.63749	−	0.438765i
$857$	−3.32707			−0.113651			−0.0568253	−	0.998384i	$-0.518098\pi$
$857$	−3.32707			−0.113651			−0.0568253	+	0.998384i	$0.518098\pi$
$858$	−31.9856	−	21.7766i	−1.09197	−	0.743442i
$859$	39.1769			1.33670			0.668350	−	0.743847i	$-0.267001\pi$
$859$	39.1769			1.33670			0.668350	+	0.743847i	$0.267001\pi$
$860$	−0.856003	+	0.229365i	−0.0291895	+	0.00782129i
$861$	−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	$-0.105358\pi$
$863$	18.2354	+	18.2354i	0.620741	+	0.620741i	−0.324980	+	0.945721i	$0.605358\pi$
$864$	−6.09729	−	4.90487i	−0.207434	−	0.166867i
$865$	6.80385	−	25.3923i	0.231338	−	0.863364i
$866$	−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
$869$	2.12976	+	7.94839i	0.0722473	+	0.269631i
$870$	22.2096	+	17.3135i	0.752977	+	0.586981i
$871$	−6.85641	−	20.2679i	−0.232320	−	0.686753i
$872$		−	48.6788i		−	1.64847i
$873$	4.43324	−	2.46991i	0.150042	−	0.0835939i
$874$		0			0
$875$	8.23373	+	14.2612i	0.278351	+	0.482118i
$876$	0.587477	−	0.0727771i	0.0198490	−	0.00245891i
$877$	28.9904	+	7.76795i	0.978936	+	0.262305i	0.712596	−	0.701574i	$-0.247519\pi$
$877$	28.9904	+	7.76795i	0.978936	+	0.262305i	0.266339	+	0.963879i	$0.414186\pi$
$878$	1.84443	+	0.494214i	0.0622465	+	0.0166789i
$879$	−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	$0.296126\pi$
$882$	19.7336	−	10.9943i	0.664464	−	0.370197i
$883$			33.3731i			1.12309i	0.827445	+	0.561547i	$0.189793\pi$
$883$			33.3731i			1.12309i	−0.827445	+	0.561547i	$0.810207\pi$
$884$	−4.36397	−	2.15775i	−0.146776	−	0.0725730i
$885$	6.19615	+	4.83020i	0.208281	+	0.162365i
$886$	−4.37307	−	16.3205i	−0.146916	−	0.548298i
$887$	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
$890$	5.47732	−	20.4416i	0.183600	−	0.685206i
$891$	36.0441	−	8.48560i	1.20752	−	0.284278i
$892$	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
$895$	−38.6147	+	10.3468i	−1.29075	+	0.345855i
$896$	−18.4443			−0.616181
$897$		0			0
$898$	30.9808			1.03384
$899$	−24.1305	+	6.46575i	−0.804797	+	0.215645i
$900$	−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
$903$	3.24207	+	4.29272i	0.107889	+	0.142853i
$904$	−6.94486	+	25.9186i	−0.230983	+	0.862039i
$905$	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	0.229848	−	0.973227i	$-0.426177\pi$
$907$	−15.0000	−	8.66025i	−0.498067	−	0.287559i	−0.727915	+	0.685668i	$0.759510\pi$
$908$	1.40619	+	5.24796i	0.0466659	+	0.174160i
$909$	−4.41244	−	17.5359i	−0.146351	−	0.581629i
$910$	−7.63397	+	8.68653i	−0.253064	+	0.287956i
$911$			1.55910i			0.0516552i	0.999666	+	0.0258276i	$0.00822209\pi$
$911$			1.55910i			0.0516552i	−0.999666	+	0.0258276i	$0.991778\pi$
$912$	−11.6431	+	27.5121i	−0.385543	+	0.911016i
$913$	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
$916$	−5.16987	−	1.38526i	−0.170817	−	0.0457704i
$917$	10.8577	+	2.90931i	0.358553	+	0.0960740i
$918$	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
$921$	−18.9314	−	8.01177i	−0.623809	−	0.263997i
$922$		−	32.0333i		−	1.05496i
$923$	2.12976	−	10.6488i	0.0701021	−	0.350510i
$924$	−1.66025	+	2.12976i	−0.0546183	+	0.0700641i
$925$	3.83013	+	14.2942i	0.125934	+	0.469991i
$926$	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
$929$	5.27594	−	19.6901i	0.173098	−	0.646011i	−0.823770	−	0.566924i	$-0.808133\pi$
$929$	5.27594	−	19.6901i	0.173098	−	0.646011i	0.996868	−	0.0790861i	$-0.0252002\pi$
$930$	−10.9235	+	8.24997i	−0.358196	+	0.270527i
$931$	−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
$934$	27.8827	−	7.47114i	0.912349	−	0.244463i
$935$	−31.2229			−1.02110
$936$	1.38506	+	28.1803i	0.0452721	+	0.921103i
$937$	−37.0000			−1.20874			−0.604369	−	0.796705i	$-0.706575\pi$
$937$	−37.0000			−1.20874			−0.604369	+	0.796705i	$0.706575\pi$
$938$	−12.2079	+	3.27110i	−0.398603	+	0.106805i
$939$	−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	$-0.182387\pi$
$941$	9.14570	+	9.14570i	0.298141	+	0.298141i	−0.542144	+	0.840285i	$0.682387\pi$
$942$	9.99911	−	7.55181i	0.325789	−	0.246051i
$943$		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
$947$	2.77689	+	10.3635i	0.0902368	+	0.336768i	0.996254	−	0.0864720i	$-0.0275593\pi$
$947$	2.77689	+	10.3635i	0.0902368	+	0.336768i	−0.906018	+	0.423240i	$0.860893\pi$
$948$	−0.570669	+	0.732051i	−0.0185345	+	0.0237759i
$949$	−3.45448	−	3.03590i	−0.112137	−	0.0985494i
$950$			15.8968i			0.515760i
$951$	−25.6076	−	10.8372i	−0.830385	−	0.351420i
$952$	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
$955$	7.02628	+	1.88269i	0.227365	+	0.0609223i
$956$	−2.41510	−	0.647124i	−0.0781099	−	0.0209295i
$957$	−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
$960$	6.77079	−	15.9990i	0.218526	−	0.516366i
$961$			18.8564i			0.608271i
$962$	−24.4718	+	16.3145i	−0.789003	+	0.526002i
$963$	−55.3205	+	13.9199i	−1.78268	+	0.448563i
$964$	−1.00962	−	3.76795i	−0.0325176	−	0.121357i
$965$	−0.180895	−	0.104440i	−0.00582321	−	0.00336203i
$966$		0			0
$967$	−27.8564	+	27.8564i	−0.895802	+	0.895802i	−0.995062	−	0.0992599i	$-0.968352\pi$
$967$	−27.8564	+	27.8564i	−0.895802	+	0.895802i	0.0992599	+	0.995062i	$0.468352\pi$
$968$	4.00218	−	14.9363i	0.128635	−	0.480072i
$969$	−20.3236	−	26.9098i	−0.652887	−	0.864467i
$970$	−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
$973$	−25.1244	+	6.73205i	−0.805450	+	0.215820i
$974$	8.67197			0.277868
$975$	7.41287	+	15.3671i	0.237402	+	0.492143i
$976$	−31.2487			−1.00025
$977$	−22.8847	+	6.13194i	−0.732147	+	0.196178i	−0.605585	−	0.795780i	$-0.707061\pi$
$977$	−22.8847	+	6.13194i	−0.732147	+	0.196178i	−0.126562	+	0.991959i	$0.540394\pi$
$978$	−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
$981$	−0.856198	+	55.9800i	−0.0273363	+	1.78730i
$982$	−11.1173	+	41.4904i	−0.354768	+	1.32401i
$983$	30.4433	−	30.4433i	0.970992	−	0.970992i	−0.0285990	−	0.999591i	$-0.509105\pi$
$983$	30.4433	−	30.4433i	0.970992	−	0.970992i	0.999591	+	0.0285990i	$0.00910459\pi$
$984$	−3.50677	+	25.1490i	−0.111792	+	0.801721i
$985$	−5.36603	−	3.09808i	−0.170976	−	0.0987129i
$986$	−14.0803	−	52.5485i	−0.448409	−	1.67349i
$987$	11.6373	+	9.07180i	0.370418	+	0.288758i
$988$	−3.53590	+	1.19615i	−0.112492	+	0.0380547i
$989$		0			0
$990$	−13.6245	−	24.4545i	−0.433014	−	0.777214i
$991$	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
$994$	−6.19615	−	1.66025i	−0.196530	−	0.0526601i
$995$	−18.8061	−	5.03908i	−0.596193	−	0.159750i
$996$	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
$999$	4.31286	−	27.8132i	0.136453	−	0.879970i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.2.k.b.32.2	yes	8
3.2	odd	2	inner	39.2.k.b.32.1	yes	8
4.3	odd	2		624.2.cn.c.305.2		8
5.2	odd	4		975.2.bp.f.149.2		8
5.3	odd	4		975.2.bp.e.149.1		8
5.4	even	2		975.2.bo.d.851.1		8
12.11	even	2		624.2.cn.c.305.1		8
13.2	odd	12		507.2.k.d.89.2		8
13.3	even	3		507.2.k.e.80.1		8
13.4	even	6		507.2.f.e.239.3		8
13.5	odd	4		507.2.k.f.488.1		8
13.6	odd	12		507.2.f.e.437.2		8
13.7	odd	12		507.2.f.f.437.3		8
13.8	odd	4		507.2.k.e.488.2		8
13.9	even	3		507.2.f.f.239.2		8
13.10	even	6		507.2.k.f.80.2		8
13.11	odd	12	inner	39.2.k.b.11.1	✓	8
13.12	even	2		507.2.k.d.188.1		8
15.2	even	4		975.2.bp.f.149.1		8
15.8	even	4		975.2.bp.e.149.2		8
15.14	odd	2		975.2.bo.d.851.2		8
39.2	even	12		507.2.k.d.89.1		8
39.5	even	4		507.2.k.f.488.2		8
39.8	even	4		507.2.k.e.488.1		8
39.11	even	12	inner	39.2.k.b.11.2	yes	8
39.17	odd	6		507.2.f.e.239.2		8
39.20	even	12		507.2.f.f.437.2		8
39.23	odd	6		507.2.k.f.80.1		8
39.29	odd	6		507.2.k.e.80.2		8
39.32	even	12		507.2.f.e.437.3		8
39.35	odd	6		507.2.f.f.239.3		8
39.38	odd	2		507.2.k.d.188.2		8
52.11	even	12		624.2.cn.c.401.1		8
65.24	odd	12		975.2.bo.d.401.2		8
65.37	even	12		975.2.bp.e.674.2		8
65.63	even	12		975.2.bp.f.674.1		8
156.11	odd	12		624.2.cn.c.401.2		8
195.89	even	12		975.2.bo.d.401.1		8
195.128	odd	12		975.2.bp.f.674.2		8
195.167	odd	12		975.2.bp.e.674.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.k.b.11.1	✓	8	13.11	odd	12	inner
39.2.k.b.11.2	yes	8	39.11	even	12	inner
39.2.k.b.32.1	yes	8	3.2	odd	2	inner
39.2.k.b.32.2	yes	8	1.1	even	1	trivial
507.2.f.e.239.2		8	39.17	odd	6
507.2.f.e.239.3		8	13.4	even	6
507.2.f.e.437.2		8	13.6	odd	12
507.2.f.e.437.3		8	39.32	even	12
507.2.f.f.239.2		8	13.9	even	3
507.2.f.f.239.3		8	39.35	odd	6
507.2.f.f.437.2		8	39.20	even	12
507.2.f.f.437.3		8	13.7	odd	12
507.2.k.d.89.1		8	39.2	even	12
507.2.k.d.89.2		8	13.2	odd	12
507.2.k.d.188.1		8	13.12	even	2
507.2.k.d.188.2		8	39.38	odd	2
507.2.k.e.80.1		8	13.3	even	3
507.2.k.e.80.2		8	39.29	odd	6
507.2.k.e.488.1		8	39.8	even	4
507.2.k.e.488.2		8	13.8	odd	4
507.2.k.f.80.1		8	39.23	odd	6
507.2.k.f.80.2		8	13.10	even	6
507.2.k.f.488.1		8	13.5	odd	4
507.2.k.f.488.2		8	39.5	even	4
624.2.cn.c.305.1		8	12.11	even	2
624.2.cn.c.305.2		8	4.3	odd	2
624.2.cn.c.401.1		8	52.11	even	12
624.2.cn.c.401.2		8	156.11	odd	12
975.2.bo.d.401.1		8	195.89	even	12
975.2.bo.d.401.2		8	65.24	odd	12
975.2.bo.d.851.1		8	5.4	even	2
975.2.bo.d.851.2		8	15.14	odd	2
975.2.bp.e.149.1		8	5.3	odd	4
975.2.bp.e.149.2		8	15.8	even	4
975.2.bp.e.674.1		8	195.167	odd	12
975.2.bp.e.674.2		8	65.37	even	12
975.2.bp.f.149.1		8	15.2	even	4
975.2.bp.f.149.2		8	5.2	odd	4
975.2.bp.f.674.1		8	65.63	even	12
975.2.bp.f.674.2		8	195.128	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:	\( N \)	\(=\)	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	39.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.45466 - 0.389774i) q^{2} +(-1.60523 + 0.650571i) q^{3} +(0.232051 - 0.133975i) q^{4} +(-1.06488 - 1.06488i) q^{5} +(-2.08148 + 1.57203i) q^{6} +(0.366025 - 1.36603i) q^{7} +(-1.84443 + 1.84443i) q^{8} +(2.15351 - 2.08863i) q^{9} +(-1.96410 - 1.13397i) q^{10} +(1.06488 + 3.97420i) q^{11} +(-0.285334 + 0.366025i) q^{12} +(3.59808 - 0.232051i) q^{13} -2.12976i q^{14} +(2.40216 + 1.01660i) q^{15} +(-2.23205 + 3.86603i) q^{16} +(-2.51954 - 4.36397i) q^{17} +(2.31853 - 3.87762i) q^{18} +(-3.73205 - 1.00000i) q^{19} +(-0.389774 - 0.104440i) q^{20} +(0.301143 + 2.43091i) q^{21} +(3.09808 + 5.36603i) q^{22} +(1.76080 - 4.16067i) q^{24} -2.73205i q^{25} +(5.14352 - 1.73999i) q^{26} +(-2.09808 + 4.75374i) q^{27} +(-0.0980762 - 0.366025i) q^{28} +(6.20840 + 3.58442i) q^{29} +(3.89056 + 0.542499i) q^{30} +(-2.46410 + 2.46410i) q^{31} +(-0.389774 + 1.45466i) q^{32} +(-4.29488 - 5.68671i) q^{33} +(-5.36603 - 5.36603i) q^{34} +(-1.84443 + 1.06488i) q^{35} +(0.219901 - 0.773185i) q^{36} +(-5.23205 + 1.40192i) q^{37} -5.81863 q^{38} +(-5.62477 + 2.71330i) q^{39} +3.92820 q^{40} +(-5.42885 + 1.45466i) q^{41} +(1.38556 + 3.41876i) q^{42} +(1.90192 - 1.09808i) q^{43} +(0.779548 + 0.779548i) q^{44} +(-4.51739 - 0.0690922i) q^{45} +(4.25953 - 4.25953i) q^{47} +(1.06782 - 7.65796i) q^{48} +(4.33013 + 2.50000i) q^{49} +(-1.06488 - 3.97420i) q^{50} +(6.88351 + 5.36603i) q^{51} +(0.803848 - 0.535898i) q^{52} -0.779548i q^{53} +(-1.19909 + 7.73284i) q^{54} +(3.09808 - 5.36603i) q^{55} +(1.84443 + 3.19465i) q^{56} +(6.64136 - 0.822738i) q^{57} +(10.4282 + 2.79423i) q^{58} +(2.90931 + 0.779548i) q^{59} +(0.693622 - 0.0859264i) q^{60} +(3.50000 + 6.06218i) q^{61} +(-2.62398 + 4.54486i) q^{62} +(-2.06488 - 3.70625i) q^{63} -6.66025i q^{64} +(-4.07863 - 3.58442i) q^{65} +(-8.46410 - 6.59817i) q^{66} +(-1.53590 - 5.73205i) q^{67} +(-1.16932 - 0.675108i) q^{68} +(-2.26795 + 2.26795i) q^{70} +(0.779548 - 2.90931i) q^{71} +(-0.119671 + 7.82434i) q^{72} +(-0.901924 - 0.901924i) q^{73} +(-7.06440 + 4.07863i) q^{74} +(1.77739 + 4.38556i) q^{75} +(-1.00000 + 0.267949i) q^{76} +5.81863 q^{77} +(-7.12453 + 6.13931i) q^{78} +2.00000 q^{79} +(6.49373 - 1.73999i) q^{80} +(0.275241 - 8.99579i) q^{81} +(-7.33013 + 4.23205i) q^{82} +(-2.90931 - 2.90931i) q^{83} +(0.395560 + 0.523749i) q^{84} +(-1.96410 + 7.33013i) q^{85} +(2.33864 - 2.33864i) q^{86} +(-12.2978 - 1.71481i) q^{87} +(-9.29423 - 5.36603i) q^{88} +(2.41510 + 9.01327i) q^{89} +(-6.59817 + 1.66025i) q^{90} +(1.00000 - 5.00000i) q^{91} +(2.35237 - 5.55852i) q^{93} +(4.53590 - 7.85641i) q^{94} +(2.90931 + 5.03908i) q^{95} +(-0.320682 - 2.58863i) q^{96} +(1.63397 + 0.437822i) q^{97} +(7.27328 + 1.94887i) q^{98} +(10.5939 + 6.33434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} - 12 q^{4} - 2 q^{6} - 4 q^{7} + 4 q^{9} + 12 q^{10} + 8 q^{13} - 14 q^{15} - 4 q^{16} + 4 q^{18} - 16 q^{19} + 4 q^{21} + 4 q^{22} + 18 q^{24} + 4 q^{27} + 20 q^{28} + 18 q^{30} + 8 q^{31}+ \cdots + 40 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 - 12 * q^4 - 2 * q^6 - 4 * q^7 + 4 * q^9 + 12 * q^10 + 8 * q^13 - 14 * q^15 - 4 * q^16 + 4 * q^18 - 16 * q^19 + 4 * q^21 + 4 * q^22 + 18 * q^24 + 4 * q^27 + 20 * q^28 + 18 * q^30 + 8 * q^31 + 16 * q^33 - 36 * q^34 - 36 * q^36 - 28 * q^37 - 14 * q^39 - 24 * q^40 - 16 * q^42 + 36 * q^43 - 20 * q^45 - 14 * q^48 + 48 * q^52 + 46 * q^54 + 4 * q^55 + 16 * q^57 + 28 * q^58 + 44 * q^60 + 28 * q^61 - 8 * q^63 - 40 * q^66 - 40 * q^67 - 32 * q^70 + 12 * q^72 - 28 * q^73 + 12 * q^75 - 8 * q^76 - 80 * q^78 + 16 * q^79 + 4 * q^81 - 24 * q^82 + 4 * q^84 + 12 * q^85 - 34 * q^87 - 12 * q^88 + 8 * q^91 + 4 * q^93 + 64 * q^94 + 16 * q^96 + 20 * q^97 + 40 * q^99

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