LMFDB - Embedded newform 975.2.bp.f.149.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(149,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 5]))

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

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

chi := DirichletCharacter("975.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bp (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:	$7.78541419707$
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			149.2
Root			$0.500000 - 1.56488i$ of defining polynomial
Character	$\chi$	$=$	975.149
Dual form			975.2.bp.f.674.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.389774	+	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	$0.737941\pi$
$3$	0.650571	+	1.60523i	0.375608	+	0.926779i
$3$	0.650571	+	1.60523i	0.375608	+	0.926779i
$4$	−0.232051	+	0.133975i	−0.116025	+	0.0669873i
$5$		0			0
$5$		0			0
$6$	−2.08148	+	1.57203i	−0.849760	+	0.641780i
$7$	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
$9$	−2.15351	+	2.08863i	−0.717838	+	0.696210i
$10$		0			0
$11$	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	$0.703691\pi$
$12$	−0.366025	−	0.285334i	−0.105662	−	0.0823689i
$13$	−0.232051	−	3.59808i	−0.0643593	−	0.997927i
$13$	−0.232051	−	3.59808i	−0.0643593	−	0.997927i
$14$			2.12976i			0.569204i
$15$		0			0
$16$	−2.23205	+	3.86603i	−0.558013	+	0.966506i
$17$	4.36397	−	2.51954i	1.05842	−	0.611078i	0.133424	−	0.991059i	$-0.457403\pi$
$17$	4.36397	−	2.51954i	1.05842	−	0.611078i	0.924994	+	0.379981i	$0.124070\pi$
$18$	−3.87762	−	2.31853i	−0.913965	−	0.546482i
$19$	3.73205	+	1.00000i	0.856191	+	0.229416i	0.660107	−	0.751171i	$-0.270511\pi$
$19$	3.73205	+	1.00000i	0.856191	+	0.229416i	0.196084	+	0.980587i	$0.437177\pi$
$20$		0			0
$21$	0.301143	+	2.43091i	0.0657148	+	0.530468i
$22$	−5.36603	+	3.09808i	−1.14404	+	0.660512i
$23$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$23$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$24$	−1.76080	+	4.16067i	−0.359421	+	0.849292i
$25$		0			0
$26$	5.14352	−	1.73999i	1.00873	−	0.341240i
$27$	−4.75374	−	2.09808i	−0.914858	−	0.403775i
$28$	−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	$0.898495\pi$
$30$		0			0
$31$	−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	$0.351314\pi$
$32$	−1.45466	−	0.389774i	−0.257149	−	0.0689030i
$33$	−5.68671	+	4.29488i	−0.989929	+	0.747642i
$34$	5.36603	+	5.36603i	0.920266	+	0.920266i
$35$		0			0
$36$	0.219901	−	0.773185i	0.0366502	−	0.128864i
$37$	−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	$-0.230216\pi$
$38$			5.81863i			0.943906i
$39$	5.62477	−	2.71330i	0.900684	−	0.434476i
$40$		0			0
$41$	−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	$0.561290\pi$
$42$	−3.41876	+	1.38556i	−0.527526	+	0.213797i
$43$	−1.09808	−	1.90192i	−0.167455	−	0.290041i	0.770069	−	0.637960i	$-0.220222\pi$
$43$	−1.09808	−	1.90192i	−0.167455	−	0.290041i	−0.937524	+	0.347920i	$0.886888\pi$
$44$	−0.779548	−	0.779548i	−0.117521	−	0.117521i
$45$		0			0
$46$		0			0
$47$	4.25953	+	4.25953i	0.621316	+	0.621316i	0.945868	−	0.324552i	$-0.105213\pi$
$47$	4.25953	+	4.25953i	0.621316	+	0.621316i	−0.324552	+	0.945868i	$0.605213\pi$
$48$	−7.65796	−	1.06782i	−1.10533	−	0.154127i
$49$	−4.33013	−	2.50000i	−0.618590	−	0.357143i
$50$		0			0
$51$	6.88351	+	5.36603i	0.963884	+	0.751394i
$52$	0.535898	+	0.803848i	0.0743157	+	0.111474i
$53$	−0.779548			−0.107079			−0.0535396	−	0.998566i	$-0.517050\pi$
$53$	−0.779548			−0.107079			−0.0535396	+	0.998566i	$0.517050\pi$
$54$	1.19909	−	7.73284i	0.163176	−	1.05231i
$55$		0			0
$56$	1.84443	+	3.19465i	0.246472	+	0.426903i
$57$	0.822738	+	6.64136i	0.108974	+	0.879670i
$58$	2.79423	−	10.4282i	0.366900	−	1.36929i
$59$	−2.90931	−	0.779548i	−0.378760	−	0.101489i	0.0644157	−	0.997923i	$-0.479482\pi$
$59$	−2.90931	−	0.779548i	−0.378760	−	0.101489i	−0.443176	+	0.896435i	$0.646148\pi$
$60$		0			0
$61$	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	$0.685424\pi$
$62$	−4.54486	−	2.62398i	−0.577198	−	0.333246i
$63$	−3.70625	+	2.06488i	−0.466943	+	0.260151i
$64$			6.66025i			0.832532i
$65$		0			0
$66$	−8.46410	−	6.59817i	−1.04186	−	0.812179i
$67$	5.73205	−	1.53590i	0.700281	−	0.187640i	0.108925	−	0.994050i	$-0.465259\pi$
$67$	5.73205	−	1.53590i	0.700281	−	0.187640i	0.591357	+	0.806410i	$0.298593\pi$
$68$	−0.675108	+	1.16932i	−0.0818689	+	0.141801i
$69$		0			0
$70$		0			0
$71$	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	$0.0261358\pi$
$72$	−7.82434	−	0.119671i	−0.922107	−	0.0141034i
$73$	−0.901924	+	0.901924i	−0.105562	+	0.105562i	−0.757915	−	0.652353i	$-0.773782\pi$
$73$	−0.901924	+	0.901924i	−0.105562	+	0.105562i	0.652353	+	0.757915i	$0.273782\pi$
$74$	7.06440	−	4.07863i	0.821220	−	0.474132i
$75$		0			0
$76$	−1.00000	+	0.267949i	−0.114708	+	0.0307359i
$77$			5.81863i			0.663094i
$78$	6.13931	+	7.12453i	0.695140	+	0.806694i
$79$	−2.00000			−0.225018			−0.112509	−	0.993651i	$-0.535889\pi$
$79$	−2.00000			−0.225018			−0.112509	+	0.993651i	$0.535889\pi$
$80$		0			0
$81$	0.275241	−	8.99579i	0.0305823	−	0.999532i
$82$	−4.23205	−	7.33013i	−0.467352	−	0.809477i
$83$	−2.90931	+	2.90931i	−0.319339	+	0.319339i	−0.848513	−	0.529174i	$-0.822502\pi$
$83$	−2.90931	+	2.90931i	−0.319339	+	0.319339i	0.529174	+	0.848513i	$0.322502\pi$
$84$	−0.395560	−	0.523749i	−0.0431592	−	0.0571457i
$85$		0			0
$86$	2.33864	−	2.33864i	0.252182	−	0.252182i
$87$	1.71481	−	12.2978i	0.183846	−	1.31846i
$88$	−5.36603	+	9.29423i	−0.572020	+	0.990768i
$89$	−2.41510	−	9.01327i	−0.256000	−	0.955405i	−0.967531	−	0.252751i	$-0.918665\pi$
$89$	−2.41510	−	9.01327i	−0.256000	−	0.955405i	0.711531	−	0.702654i	$-0.248002\pi$
$90$		0			0
$91$	1.00000	−	5.00000i	0.104828	−	0.524142i
$92$		0			0
$93$	−5.55852	−	2.35237i	−0.576392	−	0.243929i
$94$	−4.53590	+	7.85641i	−0.467842	+	0.810326i
$95$		0			0
$96$	−0.320682	−	2.58863i	−0.0327295	−	0.264201i
$97$	−0.437822	+	1.63397i	−0.0444541	+	0.165905i	−0.984584	−	0.174910i	$-0.944036\pi$
$97$	−0.437822	+	1.63397i	−0.0444541	+	0.165905i	0.940130	+	0.340815i	$0.110703\pi$
$98$	1.94887	−	7.27328i	0.196866	−	0.734712i
$99$	−10.5939	−	6.33434i	−1.06472	−	0.636625i
$100$		0			0
$101$	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	$0.0697202\pi$
$102$	−5.12271	+	12.1047i	−0.507224	+	1.19854i
$103$	6.92820			0.682656			0.341328	−	0.939944i	$-0.389123\pi$
$103$	6.92820			0.682656			0.341328	+	0.939944i	$0.389123\pi$
$104$	6.20840	−	7.06440i	0.608784	−	0.692722i
$105$		0			0
$106$	−0.303848	−	1.13397i	−0.0295123	−	0.110141i
$107$	9.50749	−	16.4675i	0.919123	−	1.59197i	0.118374	−	0.992969i	$-0.462232\pi$
$107$	9.50749	−	16.4675i	0.919123	−	1.59197i	0.800749	−	0.598999i	$-0.204435\pi$
$108$	1.38420	−	0.150021i	0.133195	−	0.0144357i
$109$	13.1962	−	13.1962i	1.26396	−	1.26396i	0.314806	−	0.949156i	$-0.398060\pi$
$109$	13.1962	−	13.1962i	1.26396	−	1.26396i	0.949156	−	0.314806i	$-0.101940\pi$
$110$		0			0
$111$	7.48658	−	5.65423i	0.710595	−	0.536676i
$112$	−4.46410	+	4.46410i	−0.421818	+	0.421818i
$113$	−5.14352	−	8.90883i	−0.483861	−	0.838073i	0.515967	−	0.856609i	$-0.327433\pi$
$113$	−5.14352	−	8.90883i	−0.483861	−	0.838073i	−0.999828	+	0.0185360i	$0.994099\pi$
$114$	−9.34022	+	3.78543i	−0.874792	+	0.354538i
$115$		0			0
$116$	1.92089			0.178350
$117$	8.01478	+	7.26384i	0.740967	+	0.671542i
$118$		−	4.53590i		−	0.417563i
$119$	6.88351	−	1.84443i	0.631010	−	0.169079i
$120$		0			0
$121$	−5.13397	+	2.96410i	−0.466725	+	0.269464i
$122$	−7.45418	+	7.45418i	−0.674869	+	0.674869i
$123$	−5.86691	−	7.76819i	−0.529002	−	0.700434i
$124$	0.241670	−	0.901924i	0.0217026	−	0.0809951i
$125$		0			0
$126$	−4.44829	−	4.58648i	−0.396285	−	0.408596i
$127$	−4.56218	+	7.90192i	−0.404828	+	0.701182i	−0.994301	−	0.106605i	$-0.966002\pi$
$127$	−4.56218	+	7.90192i	−0.404828	+	0.701182i	0.589474	+	0.807788i	$0.299335\pi$
$128$	−12.5977	+	3.37554i	−1.11349	+	0.298359i
$129$	2.33864	−	3.00000i	0.205906	−	0.264135i
$130$		0			0
$131$			7.94839i			0.694454i	0.937781	+	0.347227i	$0.112877\pi$
$131$			7.94839i			0.694454i	−0.937781	+	0.347227i	$0.887123\pi$
$132$	0.744201	−	1.75850i	0.0647743	−	0.153058i
$133$	4.73205	+	2.73205i	0.410321	+	0.236899i
$134$	4.46841	+	7.73951i	0.386012	+	0.668592i
$135$		0			0
$136$	12.6962	+	3.40192i	1.08869	+	0.291713i
$137$	1.73999	−	6.49373i	0.148657	−	0.554797i	−0.850908	−	0.525315i	$-0.823948\pi$
$137$	1.73999	−	6.49373i	0.148657	−	0.554797i	0.999565	−	0.0294822i	$-0.00938583\pi$
$138$		0			0
$139$	9.19615	+	15.9282i	0.780007	+	1.35101i	0.931937	+	0.362621i	$0.118118\pi$
$139$	9.19615	+	15.9282i	0.780007	+	1.35101i	−0.151929	+	0.988391i	$0.548549\pi$
$140$		0			0
$141$	−4.06639	+	9.60864i	−0.342452	+	0.809194i
$142$	4.53590			0.380644
$143$	14.0524	−	4.75374i	1.17512	−	0.397528i
$144$	−3.26795	−	12.9875i	−0.272329	−	1.08229i
$145$		0			0
$146$	−1.66354	−	0.960443i	−0.137675	−	0.0794868i
$147$	1.19601	−	8.57727i	0.0986455	−	0.707441i
$148$	1.02628	+	1.02628i	0.0843597	+	0.0843597i
$149$	2.23420	−	8.33816i	0.183033	−	0.683089i	−0.812010	−	0.583644i	$-0.801626\pi$
$149$	2.23420	−	8.33816i	0.183033	−	0.683089i	0.995043	−	0.0994454i	$-0.0317068\pi$
$150$		0			0
$151$	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	$0.740183\pi$
$152$	5.03908	+	8.72794i	0.408723	+	0.707929i
$153$	−4.13548	+	14.5406i	−0.334334	+	1.17554i
$154$	−8.46410	+	2.26795i	−0.682057	+	0.182757i
$155$		0			0
$156$	−0.941718	+	1.38320i	−0.0753978	+	0.110745i
$157$		−	4.80385i		−	0.383389i	−0.981455	−	0.191694i	$-0.938602\pi$
$157$		−	4.80385i		−	0.383389i	0.981455	−	0.191694i	$-0.0613982\pi$
$158$	−0.779548	−	2.90931i	−0.0620175	−	0.231453i
$159$	−0.507152	−	1.25135i	−0.0402197	−	0.0992387i
$160$		0			0
$161$		0			0
$162$	13.1931	−	3.10594i	1.03655	−	0.244026i
$163$	4.00000	+	1.07180i	0.313304	+	0.0839496i	0.412045	−	0.911164i	$-0.364815\pi$
$163$	4.00000	+	1.07180i	0.313304	+	0.0839496i	−0.0987406	+	0.995113i	$0.531481\pi$
$164$	1.06488	−	1.06488i	0.0831533	−	0.0831533i
$165$		0			0
$166$	−5.36603	−	3.09808i	−0.416484	−	0.240457i
$167$	12.9875	−	3.47998i	1.00500	−	0.269289i	0.281461	−	0.959573i	$-0.409181\pi$
$167$	12.9875	−	3.47998i	1.00500	−	0.269289i	0.723539	+	0.690283i	$0.242514\pi$
$168$	−3.92820	+	5.03908i	−0.303067	+	0.388773i
$169$	−12.8923	+	1.66987i	−0.991716	+	0.128452i
$170$		0			0
$171$	−10.1257	+	5.64136i	−0.774328	+	0.431406i
$172$	0.509619	+	0.294229i	0.0388581	+	0.0224347i
$173$	15.1172	−	8.72794i	1.14934	−	0.663573i	0.200615	−	0.979670i	$-0.435706\pi$
$173$	15.1172	−	8.72794i	1.14934	−	0.663573i	0.948727	+	0.316097i	$0.102373\pi$
$174$	18.5575	−	2.29892i	1.40684	−	0.174281i
$175$		0			0
$176$	−17.7412	−	4.75374i	−1.33729	−	0.358327i
$177$	−0.641364	−	5.17726i	−0.0482078	−	0.389147i
$178$	12.1699	−	7.02628i	0.912171	−	0.526642i
$179$	−13.2728	+	22.9892i	−0.992056	+	1.71829i	−0.387084	+	0.922045i	$0.626518\pi$
$179$	−13.2728	+	22.9892i	−0.992056	+	1.71829i	−0.604972	+	0.796247i	$0.706816\pi$
$180$		0			0
$181$			3.00000i			0.222988i	0.993765	+	0.111494i	$0.0355636\pi$
$181$			3.00000i			0.222988i	−0.993765	+	0.111494i	$0.964436\pi$
$182$	7.66306	−	0.494214i	0.568024	−	0.0366336i
$183$	−7.45418	+	9.56218i	−0.551029	+	0.706857i
$184$		0			0
$185$		0			0
$186$	1.25532	−	9.00263i	0.0920449	−	0.660105i
$187$	14.6603	+	14.6603i	1.07206	+	1.07206i
$188$	−1.55910	−	0.417759i	−0.113709	−	0.0304682i
$189$	−5.72579	−	4.60602i	−0.416490	−	0.335038i
$190$		0			0
$191$	−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	$0.389245\pi$
$192$	−10.6912	+	4.33297i	−0.771573	+	0.312705i
$193$	−0.0358984	−	0.133975i	−0.00258402	−	0.00964370i	0.964622	−	0.263638i	$-0.0849223\pi$
$193$	−0.0358984	−	0.133975i	−0.00258402	−	0.00964370i	−0.967206	+	0.253994i	$0.918256\pi$
$194$	−2.54752			−0.182902
$195$		0			0
$196$	1.33975			0.0956961
$197$	1.06488	+	3.97420i	0.0758697	+	0.283150i	0.993429	−	0.114449i	$-0.0365103\pi$
$197$	1.06488	+	3.97420i	0.0758697	+	0.283150i	−0.917559	+	0.397599i	$0.869844\pi$
$198$	5.08507	−	17.8794i	0.361380	−	1.27063i
$199$	−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	$0.484849\pi$
$200$		0			0
$201$	6.19458	+	8.20204i	0.436932	+	0.578527i
$202$	8.76795	+	2.34936i	0.616911	+	0.165301i
$203$	−7.16884	−	7.16884i	−0.503154	−	0.503154i
$204$	−2.31623	−	0.322975i	−0.162169	−	0.0226128i
$205$		0			0
$206$	2.70043	+	10.0782i	0.188148	+	0.702178i
$207$		0			0
$208$	14.4282	+	7.13397i	1.00042	+	0.494652i
$209$			15.8968i			1.09960i
$210$		0			0
$211$	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	$0.146890\pi$
$212$	0.180895	−	0.104440i	0.0124239	−	0.00717294i
$213$	5.17726	−	0.641364i	0.354740	−	0.0439455i
$214$	27.6603	+	7.41154i	1.89082	+	0.506643i
$215$		0			0
$216$	−4.89819	−	12.6377i	−0.333280	−	0.859887i
$217$	−4.26795	+	2.46410i	−0.289727	+	0.167274i
$218$	24.3394	+	14.0524i	1.64847	+	0.951745i
$219$	−2.03456	−	0.861027i	−0.137483	−	0.0581828i
$220$		0			0
$221$	−10.0782	−	15.1172i	−0.677930	−	1.01690i
$222$	11.1430	+	8.68653i	0.747872	+	0.583002i
$223$	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
$225$		0			0
$226$	10.9545	−	10.9545i	0.728681	−	0.728681i
$227$	−19.5856	−	5.24796i	−1.29994	−	0.348319i	−0.458515	−	0.888686i	$-0.651619\pi$
$227$	−19.5856	−	5.24796i	−1.29994	−	0.348319i	−0.841429	+	0.540367i	$0.818285\pi$
$228$	−1.08069	−	1.43091i	−0.0715705	−	0.0947642i
$229$	14.1244	+	14.1244i	0.933364	+	0.933364i	0.997914	−	0.0645507i	$-0.0205614\pi$
$229$	14.1244	+	14.1244i	0.933364	+	0.933364i	−0.0645507	+	0.997914i	$0.520561\pi$
$230$		0			0
$231$	−9.34022	+	3.78543i	−0.614541	+	0.249063i
$232$	−4.83975	−	18.0622i	−0.317745	−	1.18584i
$233$			17.4559i			1.14357i	0.820403	+	0.571786i	$0.193749\pi$
$233$			17.4559i			1.14357i	−0.820403	+	0.571786i	$0.806251\pi$
$234$	−7.44244	+	14.4900i	−0.486527	+	0.947241i
$235$		0			0
$236$	0.779548	−	0.208879i	0.0507443	−	0.0135969i
$237$	−1.30114	−	3.21046i	−0.0845183	−	0.208542i
$238$	5.36603	+	9.29423i	0.347828	+	0.602455i
$239$	6.59817	+	6.59817i	0.426800	+	0.426800i	0.887537	−	0.460737i	$-0.152415\pi$
$239$	6.59817	+	6.59817i	0.426800	+	0.426800i	−0.460737	+	0.887537i	$0.652415\pi$
$240$		0			0
$241$	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
$243$	14.6194	−	5.41058i	0.937832	−	0.347089i
$244$	−1.62436	−	0.937822i	−0.103989	−	0.0600379i
$245$		0			0
$246$	9.01327	−	11.5622i	0.574665	−	0.737178i
$247$	2.73205	−	13.6603i	0.173836	−	0.869181i
$248$	−9.08973			−0.577198
$249$	−6.56283	−	2.77739i	−0.415902	−	0.176010i
$250$		0			0
$251$	−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	$0.843264\pi$
$252$	0.583396	−	0.975700i	0.0367505	−	0.0614634i
$253$		0			0
$254$	−13.2728	−	3.55644i	−0.832810	−	0.223151i
$255$		0			0
$256$	−3.16025	−	5.47372i	−0.197516	−	0.342108i
$257$	−18.6252	−	10.7533i	−1.16181	−	0.670770i	−0.210071	−	0.977686i	$-0.567370\pi$
$257$	−18.6252	−	10.7533i	−1.16181	−	0.670770i	−0.951737	+	0.306916i	$0.900703\pi$
$258$	5.27551	+	2.23260i	0.328439	+	0.138996i
$259$		−	7.66025i		−	0.475985i
$260$		0			0
$261$	20.8564	−	5.24796i	1.29098	−	0.324840i
$262$	−11.5622	+	3.09808i	−0.714314	+	0.191400i
$263$	11.1430	−	19.3003i	0.687109	−	1.19011i	−0.285660	−	0.958331i	$-0.592213\pi$
$263$	11.1430	−	19.3003i	0.687109	−	1.19011i	0.972769	−	0.231777i	$-0.0744539\pi$
$264$	−18.4103	−	2.56713i	−1.13308	−	0.157996i
$265$		0			0
$266$	−2.12976	+	7.94839i	−0.130584	+	0.487347i
$267$	12.8972	−	9.74056i	0.789294	−	0.596113i
$268$	−1.12436	+	1.12436i	−0.0686810	+	0.0686810i
$269$	−12.4168	+	7.16884i	−0.757066	+	0.437092i	−0.828241	−	0.560372i	$-0.810658\pi$
$269$	−12.4168	+	7.16884i	−0.757066	+	0.437092i	0.0711756	+	0.997464i	$0.477325\pi$
$270$		0			0
$271$	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	$0.341255\pi$
$272$			22.4950i			1.36396i
$273$	8.67671	−	1.64763i	0.525138	−	0.0997191i
$274$	10.1244			0.611635
$275$		0			0
$276$		0			0
$277$	13.7942	+	23.8923i	0.828815	+	1.43555i	0.898969	+	0.438013i	$0.144318\pi$
$277$	13.7942	+	23.8923i	0.828815	+	1.43555i	−0.0701536	+	0.997536i	$0.522349\pi$
$278$	−19.5856	+	19.5856i	−1.17467	+	1.17467i
$279$	0.159877	−	10.4531i	0.00957158	−	0.625809i
$280$		0			0
$281$	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	$0.0790030\pi$
$282$	−15.5622	−	2.17000i	−0.926718	−	0.129221i
$283$	−3.29423	+	5.70577i	−0.195822	+	0.339173i	−0.947170	−	0.320733i	$-0.896071\pi$
$283$	−3.29423	+	5.70577i	−0.195822	+	0.339173i	0.751348	+	0.659906i	$0.229404\pi$
$284$	0.208879	+	0.779548i	0.0123947	+	0.0462577i
$285$		0			0
$286$	12.3923	+	18.5885i	0.732772	+	1.09916i
$287$	−7.94839			−0.469179
$288$	3.94672	−	2.19886i	0.232562	−	0.129569i
$289$	4.19615	−	7.26795i	0.246832	−	0.427526i
$290$		0			0
$291$	−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
$295$		0			0
$296$	7.06440	−	12.2359i	0.410610	−	0.711198i
$297$	3.27599	−	21.1265i	0.190092	−	1.22588i
$298$	13.0000			0.753070
$299$		0			0
$300$		0			0
$301$	−0.803848	−	3.00000i	−0.0463330	−	0.172917i
$302$	−0.570669	+	0.988427i	−0.0328383	+	0.0568776i
$303$	10.3399	+	1.44179i	0.594012	+	0.0828289i
$304$	−12.1962	+	12.1962i	−0.699497	+	0.699497i
$305$		0			0
$306$	−22.7635	−	0.348161i	−1.30130	−	0.0199030i
$307$	−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	$0.359982\pi$
$308$	−0.779548	−	1.35022i	−0.0444189	−	0.0769357i
$309$	4.50729	+	11.1213i	0.256411	+	0.632671i
$310$		0			0
$311$	−10.0782			−0.571480			−0.285740	−	0.958307i	$-0.592239\pi$
$311$	−10.0782			−0.571480			−0.285740	+	0.958307i	$0.592239\pi$
$312$	15.3790	+	5.37000i	0.870664	+	0.304016i
$313$		−	2.00000i		−	0.113047i	−0.998401	−	0.0565233i	$-0.981998\pi$
$313$		−	2.00000i		−	0.113047i	0.998401	−	0.0565233i	$-0.0180015\pi$
$314$	6.98795	−	1.87241i	0.394353	−	0.105666i
$315$		0			0
$316$	0.464102	−	0.267949i	0.0261078	−	0.0150733i
$317$	−11.3519	+	11.3519i	−0.637587	+	0.637587i	−0.949960	−	0.312373i	$-0.898876\pi$
$317$	−11.3519	+	11.3519i	−0.637587	+	0.637587i	0.312373	+	0.949960i	$0.398876\pi$
$318$	1.62261	−	1.22548i	0.0909916	−	0.0687213i
$319$	7.63397	−	28.4904i	0.427421	−	1.59516i
$320$		0			0
$321$	32.6193	+	4.54843i	1.82063	+	0.253869i
$322$		0			0
$323$	18.8061	−	5.03908i	1.04640	−	0.280382i
$324$	1.14134	+	2.12436i	0.0634076	+	0.118020i
$325$		0			0
$326$			6.23638i			0.345401i
$327$	29.7679	+	12.5978i	1.64617	+	0.696659i
$328$	−12.6962	−	7.33013i	−0.701028	−	0.404739i
$329$	4.25953	+	7.37772i	0.234835	+	0.406747i
$330$		0			0
$331$	−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	$0.972892\pi$
$332$	0.285334	−	1.06488i	0.0156598	−	0.0584430i
$333$	13.9469	+	8.33919i	0.764285	+	0.456985i
$334$	10.1244	+	17.5359i	0.553980	+	0.959522i
$335$		0			0
$336$	−10.0701	−	4.26168i	−0.549370	−	0.232494i
$337$	18.4641			1.00580			0.502902	−	0.864344i	$-0.332266\pi$
$337$	18.4641			1.00580			0.502902	+	0.864344i	$0.332266\pi$
$338$	−7.45418	−	18.1030i	−0.405454	−	0.984673i
$339$	10.9545	−	14.0524i	0.594966	−	0.763219i
$340$		0			0
$341$	−12.4168	−	7.16884i	−0.672407	−	0.388215i
$342$	−12.1530	−	12.5305i	−0.657157	−	0.677571i
$343$	−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
$347$	−10.2870	−	17.8177i	−0.552237	−	0.956502i	−0.998113	−	0.0614076i	$-0.980441\pi$
$347$	−10.2870	−	17.8177i	−0.552237	−	0.956502i	0.445876	−	0.895095i	$-0.352892\pi$
$348$	1.24967	+	3.08346i	0.0669895	+	0.165291i
$349$	−27.4904	+	7.36603i	−1.47153	+	0.394294i	−0.903454	−	0.428684i	$-0.858977\pi$
$349$	−27.4904	+	7.36603i	−1.47153	+	0.394294i	−0.568072	+	0.822979i	$0.692311\pi$
$350$		0			0
$351$	−6.44593	+	17.5912i	−0.344058	+	0.938948i
$352$		−	6.19615i		−	0.330256i
$353$	3.66088	+	13.6626i	0.194849	+	0.727186i	0.992306	+	0.123810i	$0.0395113\pi$
$353$	3.66088	+	13.6626i	0.194849	+	0.727186i	−0.797457	+	0.603376i	$0.793822\pi$
$354$	7.28115	−	2.95093i	0.386989	−	0.156840i
$355$		0			0
$356$	1.76798	+	1.76798i	0.0937025	+	0.0937025i
$357$	7.43895	+	9.84967i	0.393711	+	0.521300i
$358$	−38.6147	−	10.3468i	−2.04085	−	0.546845i
$359$	18.2354	−	18.2354i	0.962429	−	0.962429i	−0.0368904	−	0.999319i	$-0.511745\pi$
$359$	18.2354	−	18.2354i	0.962429	−	0.962429i	0.999319	+	0.0368904i	$0.0117452\pi$
$360$		0			0
$361$	−3.52628	−	2.03590i	−0.185594	−	0.107153i
$362$	−4.36397	+	1.16932i	−0.229365	+	0.0614582i
$363$	−8.09808	−	6.31284i	−0.425039	−	0.331338i
$364$	0.437822	+	1.29423i	0.0229481	+	0.0678360i
$365$		0			0
$366$	−16.8151	−	7.11618i	−0.878941	−	0.371969i
$367$	−26.3205	−	15.1962i	−1.37392	−	0.793233i	−0.382500	−	0.923955i	$-0.624937\pi$
$367$	−26.3205	−	15.1962i	−1.37392	−	0.793233i	−0.991419	+	0.130723i	$0.958270\pi$
$368$		0			0
$369$	8.65286	−	14.4715i	0.450450	−	0.753356i
$370$		0			0
$371$	−1.06488	−	0.285334i	−0.0552859	−	0.0148138i
$372$	1.60502	−	0.198831i	0.0832162	−	0.0103089i
$373$	−10.0359	+	5.79423i	−0.519639	+	0.300014i	−0.736787	−	0.676125i	$-0.763658\pi$
$373$	−10.0359	+	5.79423i	−0.519639	+	0.300014i	0.217148	+	0.976139i	$0.430325\pi$
$374$	−15.6114	+	27.0398i	−0.807249	+	1.39820i
$375$		0			0
$376$			15.7128i			0.810326i
$377$	−11.4564	+	23.1701i	−0.590032	+	1.19332i
$378$	4.46841	−	10.1244i	0.229830	−	0.520741i
$379$	−3.83013	−	14.2942i	−0.196740	−	0.734245i	−0.991809	−	0.127726i	$-0.959232\pi$
$379$	−3.83013	−	14.2942i	−0.196740	−	0.734245i	0.795069	−	0.606519i	$-0.207435\pi$
$380$		0			0
$381$	−15.6524	−	2.18257i	−0.801897	−	0.111816i
$382$	−5.14359	−	5.14359i	−0.263169	−	0.263169i
$383$	−31.7936	−	8.51906i	−1.62458	−	0.435304i	−0.672234	−	0.740339i	$-0.734665\pi$
$383$	−31.7936	−	8.51906i	−1.62458	−	0.435304i	−0.952341	+	0.305035i	$0.901332\pi$
$384$	−13.6142	−	18.0261i	−0.694748	−	0.919893i
$385$		0			0
$386$	0.180895	−	0.104440i	0.00920730	−	0.00531584i
$387$	6.33714	+	1.80234i	0.322135	+	0.0916182i
$388$	−0.117314	−	0.437822i	−0.00595572	−	0.0222271i
$389$	22.4950			1.14054			0.570270	−	0.821457i	$-0.306839\pi$
$389$	22.4950			1.14054			0.570270	+	0.821457i	$0.306839\pi$
$390$		0			0
$391$		0			0
$392$	−3.37554	−	12.5977i	−0.170491	−	0.636280i
$393$	−12.7590	+	5.17100i	−0.643605	+	0.260842i
$394$	−5.36603	+	3.09808i	−0.270336	+	0.156079i
$395$		0			0
$396$	3.30696	+	0.0505790i	0.166181	+	0.00254169i
$397$	−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
$399$	−1.30703	+	9.37341i	−0.0654332	+	0.469258i
$400$		0			0
$401$	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	$0.816038\pi$
$402$	−9.51666	+	12.2079i	−0.474648	+	0.608876i
$403$	9.43782	+	8.29423i	0.470131	+	0.413165i
$404$			1.61507i			0.0803525i
$405$		0			0
$406$	7.63397	−	13.2224i	0.378868	−	0.656218i
$407$	19.3003	−	11.1430i	0.956681	−	0.552340i
$408$	2.79889	+	22.5934i	0.138566	+	1.11854i
$409$	−28.9904	−	7.76795i	−1.43348	−	0.384100i	−0.543236	−	0.839580i	$-0.682801\pi$
$409$	−28.9904	−	7.76795i	−1.43348	−	0.384100i	−0.890246	+	0.455480i	$0.849468\pi$
$410$		0			0
$411$	11.5559	−	1.43156i	0.570011	−	0.0706135i
$412$	−1.60770	+	0.928203i	−0.0792055	+	0.0457293i
$413$	−3.68886	−	2.12976i	−0.181517	−	0.104799i
$414$		0			0
$415$		0			0
$416$	−1.06488	+	5.32441i	−0.0522102	+	0.261051i
$417$	−19.5856	+	25.1244i	−0.959113	+	1.23034i
$418$	−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			0
$421$	−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	$0.336972\pi$
$422$	2.62398	+	0.703093i	0.127733	+	0.0342260i
$423$	−18.0695	−	0.276369i	−0.878571	−	0.0134375i
$424$	−1.43782	−	1.43782i	−0.0698268	−	0.0698268i
$425$		0			0
$426$	2.95093	+	7.28115i	0.142973	+	0.352773i
$427$	2.56218	+	9.56218i	0.123992	+	0.462746i
$428$			5.09505i			0.246278i
$429$	16.7729	+	19.4646i	0.809803	+	0.939759i
$430$		0			0
$431$	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	$0.0517764\pi$
$432$	18.7218	−	13.6951i	0.900754	−	0.658905i
$433$	15.5263	+	26.8923i	0.746145	+	1.29236i	0.949658	+	0.313289i	$0.101431\pi$
$433$	15.5263	+	26.8923i	0.746145	+	1.29236i	−0.203512	+	0.979072i	$0.565236\pi$
$434$	−5.24796	−	5.24796i	−0.251910	−	0.251910i
$435$		0			0
$436$	−1.29423	+	4.83013i	−0.0619823	+	0.231321i
$437$		0			0
$438$	0.459481	−	3.29519i	0.0219548	−	0.157450i
$439$	−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	$0.676300\pi$
$440$		0			0
$441$	14.5466	−	3.66025i	0.692694	−	0.174298i
$442$	18.0622	−	20.5526i	0.859130	−	0.977586i
$443$	−11.2195			−0.533054			−0.266527	−	0.963827i	$-0.585876\pi$
$443$	−11.2195			−0.533054			−0.266527	+	0.963827i	$0.585876\pi$
$444$	−0.979744	+	2.31508i	−0.0464966	+	0.109869i
$445$		0			0
$446$	19.5092	+	33.7909i	0.923787	+	1.60005i
$447$	14.8382	−	1.83816i	0.701821	−	0.0869422i
$448$	−2.43782	+	9.09808i	−0.115176	+	0.429844i
$449$	−19.8710	−	5.32441i	−0.937769	−	0.251275i	−0.242605	−	0.970125i	$-0.578002\pi$
$449$	−19.8710	−	5.32441i	−0.937769	−	0.251275i	−0.695165	+	0.718851i	$0.744669\pi$
$450$		0			0
$451$	−11.5622	−	20.0263i	−0.544442	−	0.943001i
$452$	2.38711	+	1.37820i	0.112280	+	0.0648251i
$453$	−0.511599	+	1.20888i	−0.0240370	+	0.0567981i
$454$		−	30.5359i		−	1.43312i
$455$		0			0
$456$	−10.7321	+	13.7670i	−0.502574	+	0.644700i
$457$	3.76795	−	1.00962i	0.176257	−	0.0472280i	−0.169611	−	0.985511i	$-0.554251\pi$
$457$	3.76795	−	1.00962i	0.176257	−	0.0472280i	0.345868	+	0.938283i	$0.387584\pi$
$458$	−15.0408	+	26.0514i	−0.702809	+	1.21730i
$459$	−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	$-0.0816238\pi$
$462$	−9.14708	−	12.1113i	−0.425561	−	0.563471i
$463$	23.0526	−	23.0526i	1.07134	−	1.07134i	0.0740918	−	0.997251i	$-0.476394\pi$
$463$	23.0526	−	23.0526i	1.07134	−	1.07134i	0.997251	−	0.0740918i	$-0.0236058\pi$
$464$	27.7149	−	16.0012i	1.28663	−	0.742838i
$465$		0			0
$466$	−25.3923	+	6.80385i	−1.17628	+	0.315182i
$467$			19.1679i			0.886984i	0.896278	+	0.443492i	$0.146261\pi$
$467$			19.1679i			0.886984i	−0.896278	+	0.443492i	$0.853739\pi$
$468$	−2.83301	−	0.611803i	−0.130956	−	0.0282806i
$469$	8.39230			0.387521
$470$		0			0
$471$	7.71127	−	3.12525i	0.355317	−	0.144004i
$472$	−3.92820	−	6.80385i	−0.180810	−	0.313172i
$473$	6.38929	−	6.38929i	0.293780	−	0.293780i
$474$	4.16296	−	3.14407i	0.191211	−	0.144412i
$475$		0			0
$476$	−1.35022	+	1.35022i	−0.0618871	+	0.0618871i
$477$	1.67877	−	1.62819i	0.0768655	−	0.0745496i
$478$	−7.02628	+	12.1699i	−0.321375	+	0.556637i
$479$	5.32441	+	19.8710i	0.243279	+	0.907928i	0.974241	+	0.225510i	$0.0724049\pi$
$479$	5.32441	+	19.8710i	0.243279	+	0.907928i	−0.730962	+	0.682418i	$0.760928\pi$
$480$		0			0
$481$	−18.5000	+	6.25833i	−0.843527	+	0.285355i
$482$	21.9243			0.998624
$483$		0			0
$484$	0.794229	−	1.37564i	0.0361013	−	0.0625293i
$485$		0			0
$486$	13.5688	+	19.1572i	0.615492	+	0.868990i
$487$	−1.49038	+	5.56218i	−0.0675356	+	0.252046i	−0.991437	−	0.130584i	$-0.958315\pi$
$487$	−1.49038	+	5.56218i	−0.0675356	+	0.252046i	0.923902	+	0.382630i	$0.124982\pi$
$488$	−4.72576	+	17.6368i	−0.213925	+	0.798379i
$489$	0.881808	+	7.11819i	0.0398767	+	0.321896i
$490$		0			0
$491$	−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	$0.944107\pi$
$492$	2.40216	+	1.01660i	0.108298	+	0.0458317i
$493$	−36.1244			−1.62696
$494$	20.9359	−	1.35022i	0.941949	−	0.0607491i
$495$		0			0
$496$	−4.02628	−	15.0263i	−0.180785	−	0.674700i
$497$	2.12976	−	3.68886i	0.0955330	−	0.165468i
$498$	1.48214	−	10.6292i	0.0664161	−	0.476306i
$499$	2.46410	−	2.46410i	0.110308	−	0.110308i	−0.649798	−	0.760107i	$-0.725147\pi$
$499$	2.46410	−	2.46410i	0.110308	−	0.110308i	0.760107	+	0.649798i	$0.225147\pi$
$500$		0			0
$501$	14.0354	+	18.5839i	0.627057	+	0.830266i
$502$	1.05256	−	1.05256i	0.0469780	−	0.0469780i
$503$	−1.63555	−	2.83286i	−0.0729256	−	0.126311i	0.827257	−	0.561824i	$-0.189900\pi$
$503$	−1.63555	−	2.83286i	−0.0729256	−	0.126311i	−0.900182	+	0.435513i	$0.856567\pi$
$504$	−10.6444	−	3.02738i	−0.474141	−	0.134850i
$505$		0			0
$506$		0			0
$507$	−11.0679	−	19.6087i	−0.491542	−	0.870854i
$508$		−	2.44486i		−	0.108473i
$509$	14.1568	−	3.79330i	0.627489	−	0.168135i	0.0689588	−	0.997620i	$-0.478032\pi$
$509$	14.1568	−	3.79330i	0.627489	−	0.168135i	0.558530	+	0.829484i	$0.311366\pi$
$510$		0			0
$511$	−1.56218	+	0.901924i	−0.0691067	+	0.0398988i
$512$	−11.7137	+	11.7137i	−0.517678	+	0.517678i
$513$	−15.6431	−	12.5839i	−0.690661	−	0.555591i
$514$	8.38269	−	31.2846i	0.369744	−	1.37990i
$515$		0			0
$516$	−0.140760	+	1.00947i	−0.00619663	+	0.0444395i
$517$	−12.3923	+	21.4641i	−0.545013	+	0.943990i
$518$	11.1430	−	2.98577i	0.489597	−	0.131187i
$519$	23.8452	+	18.5885i	1.04669	+	0.815943i
$520$		0			0
$521$		−	2.49155i		−	0.109157i	−0.998509	−	0.0545785i	$-0.982618\pi$
$521$		−	2.49155i		−	0.109157i	0.998509	−	0.0545785i	$-0.0173815\pi$
$522$	15.7633	+	28.2934i	0.689939	+	1.23837i
$523$	−33.7583	−	19.4904i	−1.47615	−	0.852255i	−0.476511	−	0.879169i	$-0.658099\pi$
$523$	−33.7583	−	19.4904i	−1.47615	−	0.852255i	−0.999638	+	0.0269137i	$0.991432\pi$
$524$	−1.06488	−	1.84443i	−0.0465196	−	0.0805743i
$525$		0			0
$526$	32.4186	+	8.68653i	1.41352	+	0.378751i
$527$	−4.54486	+	16.9617i	−0.197977	+	0.738862i
$528$	−3.91108	−	31.5713i	−0.170208	−	1.37397i
$529$	−11.5000	−	19.9186i	−0.500000	−	0.866025i
$530$		0			0
$531$	7.89343	−	4.39771i	0.342546	−	0.190845i
$532$	−1.46410			−0.0634769
$533$	6.49373	+	19.1959i	0.281275	+	0.831465i
$534$	19.1962	+	14.9643i	0.830699	+	0.647570i
$535$		0			0
$536$	13.4052	+	7.73951i	0.579018	+	0.334296i
$537$	−45.5378	−	6.34978i	−1.96510	−	0.274013i
$538$	−15.2679	−	15.2679i	−0.658248	−	0.658248i
$539$	5.32441	−	19.8710i	0.229339	−	0.855904i
$540$		0			0
$541$	−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	$0.876034\pi$
$542$	5.81863	+	10.0782i	0.249931	+	0.432894i
$543$	−4.81568	+	1.95171i	−0.206661	+	0.0837561i
$544$	−7.33013	+	1.96410i	−0.314277	+	0.0842102i
$545$		0			0
$546$	5.77869	+	11.9794i	0.247305	+	0.512672i
$547$			2.00000i			0.0855138i	0.999086	+	0.0427569i	$0.0136141\pi$
$547$			2.00000i			0.0855138i	−0.999086	+	0.0427569i	$0.986386\pi$
$548$	0.466229	+	1.73999i	0.0199163	+	0.0743287i
$549$	−20.1990	−	5.74477i	−0.862070	−	0.245181i
$550$		0			0
$551$	−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
$555$		0			0
$556$	−4.26795	−	2.46410i	−0.181001	−	0.104501i
$557$	24.7292	−	6.62616i	1.04781	−	0.280759i	0.306462	−	0.951883i	$-0.400855\pi$
$557$	24.7292	−	6.62616i	1.04781	−	0.280759i	0.741346	+	0.671123i	$0.234188\pi$
$558$	15.2679	−	3.84177i	0.646344	−	0.162635i
$559$	−6.58846	+	4.39230i	−0.278662	+	0.185775i
$560$		0			0
$561$	−13.9955	+	33.0706i	−0.590891	+	1.39624i
$562$	22.3756	+	12.9186i	0.943860	+	0.544938i
$563$	−8.72794	+	5.03908i	−0.367839	+	0.212372i	−0.672514	−	0.740085i	$-0.734785\pi$
$563$	−8.72794	+	5.03908i	−0.367839	+	0.212372i	0.304675	+	0.952456i	$0.401452\pi$
$564$	−0.343706	−	2.77449i	−0.0144726	−	0.116827i
$565$		0			0
$566$	−9.58394	−	2.56801i	−0.402843	−	0.107941i
$567$	3.66867	−	12.1877i	0.154070	−	0.511837i
$568$	6.80385	−	3.92820i	0.285483	−	0.164824i
$569$	1.35022	−	2.33864i	0.0566040	−	0.0980411i	−0.836335	−	0.548219i	$-0.815306\pi$
$569$	1.35022	−	2.33864i	0.0566040	−	0.0980411i	0.892939	+	0.450178i	$0.148639\pi$
$570$		0			0
$571$			1.94744i			0.0814979i	0.999169	+	0.0407489i	$0.0129744\pi$
$571$			1.94744i			0.0814979i	−0.999169	+	0.0407489i	$0.987026\pi$
$572$	−2.62398	+	2.98577i	−0.109714	+	0.124841i
$573$	−6.59817	−	5.14359i	−0.275643	−	0.214877i
$574$	−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	0.0618016	−	0.998088i	$-0.480315\pi$
$577$	−22.4904	−	22.4904i	−0.936287	−	0.936287i	−0.998088	+	0.0618016i	$0.980315\pi$
$578$	12.2079	+	3.27110i	0.507783	+	0.136060i
$579$	0.191705	−	0.144785i	0.00796700	−	0.00601707i
$580$		0			0
$581$	−5.03908	+	2.90931i	−0.209056	+	0.120699i
$582$	−1.65735	−	4.08936i	−0.0686992	−	0.169509i
$583$	−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	$-0.209181\pi$
$588$	0.871601	+	2.15060i	0.0359442	+	0.0886892i
$589$	−11.6603	+	6.73205i	−0.480452	+	0.277389i
$590$		0			0
$591$	−5.68671	+	4.29488i	−0.233920	+	0.176668i
$592$	23.3564	+	6.25833i	0.959942	+	0.257216i
$593$	10.3635	+	10.3635i	0.425578	+	0.425578i	0.887119	−	0.461541i	$-0.152703\pi$
$593$	10.3635	+	10.3635i	0.425578	+	0.425578i	−0.461541	+	0.887119i	$0.652703\pi$
$594$	32.0087	−	3.46913i	1.31333	−	0.142340i
$595$		0			0
$596$	0.598653	+	2.23420i	0.0245218	+	0.0915166i
$597$	−17.6603	−	13.7670i	−0.722786	−	0.563446i
$598$		0			0
$599$		−	20.7270i		−	0.846881i	−0.905924	−	0.423441i	$-0.860822\pi$
$599$		−	20.7270i		−	0.846881i	0.905924	−	0.423441i	$-0.139178\pi$
$600$		0			0
$601$	−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	$0.326428\pi$
$602$	4.05065	−	2.33864i	0.165092	−	0.0953160i
$603$	−9.13612	+	15.2797i	−0.372052	+	0.622238i
$604$	−0.196152	−	0.0525589i	−0.00798133	−	0.00213859i
$605$		0			0
$606$	1.93291	+	15.6030i	0.0785192	+	0.633828i
$607$	−0.169873	+	0.0980762i	−0.00689493	+	0.00398079i	−0.503444	−	0.864028i	$-0.667934\pi$
$607$	−0.169873	+	0.0980762i	−0.00689493	+	0.00398079i	0.496549	+	0.868009i	$0.334600\pi$
$608$	−5.03908	−	2.90931i	−0.204362	−	0.117988i
$609$	6.84378	−	16.1715i	0.277324	−	0.655301i
$610$		0			0
$611$	14.3377	−	16.3145i	0.580041	−	0.660016i
$612$	−0.988427	−	3.92820i	−0.0399548	−	0.158788i
$613$	−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
$615$		0			0
$616$	−10.7321	+	10.7321i	−0.432407	+	0.432407i
$617$	17.8457	+	4.78173i	0.718439	+	0.192505i	0.599475	−	0.800393i	$-0.295376\pi$
$617$	17.8457	+	4.78173i	0.718439	+	0.192505i	0.118964	+	0.992899i	$0.462043\pi$
$618$	−14.4209	+	10.8914i	−0.580094	+	0.438115i
$619$	31.6603	+	31.6603i	1.27253	+	1.27253i	0.944755	+	0.327778i	$0.106300\pi$
$619$	31.6603	+	31.6603i	1.27253	+	1.27253i	0.327778	+	0.944755i	$0.393700\pi$
$620$		0			0
$621$		0			0
$622$	−3.92820	−	14.6603i	−0.157507	−	0.587823i
$623$		−	13.1963i		−	0.528701i
$624$	−2.06508	+	27.8017i	−0.0826693	+	1.11296i
$625$		0			0
$626$	2.90931	−	0.779548i	0.116280	−	0.0311570i
$627$	−25.5180	+	10.3420i	−1.01909	+	0.413019i
$628$	0.643594	+	1.11474i	0.0256822	+	0.0444828i
$629$	−19.3003	−	19.3003i	−0.769554	−	0.769554i
$630$		0			0
$631$	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
$633$	3.09442	+	0.431485i	0.122992	+	0.0171500i
$634$	−20.9378	−	12.0885i	−0.831547	−	0.480094i
$635$		0			0
$636$	0.285334	+	0.222432i	0.0113142	+	0.00882000i
$637$	−7.99038	+	16.1603i	−0.316590	+	0.640293i
$638$	44.4192			1.75857
$639$	4.39771	+	7.89343i	0.173971	+	0.312259i
$640$		0			0
$641$	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	$0.480050\pi$
$642$	6.09776	+	49.2228i	0.240659	+	1.94267i
$643$	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
$645$		0			0
$646$	14.6603	+	25.3923i	0.576800	+	0.999047i
$647$	−14.2612	−	8.23373i	−0.560667	−	0.323701i	0.192746	−	0.981249i	$-0.438261\pi$
$647$	−14.2612	−	8.23373i	−0.560667	−	0.323701i	−0.753413	+	0.657547i	$0.771594\pi$
$648$	17.0998	−	16.0844i	0.671742	−	0.631857i
$649$		−	12.3923i		−	0.486441i
$650$		0			0
$651$	−6.73205	−	5.24796i	−0.263850	−	0.205684i
$652$	−1.07180	+	0.287187i	−0.0419748	+	0.0112471i
$653$	−4.83020	+	8.36615i	−0.189020	+	0.327393i	−0.944924	−	0.327290i	$-0.893865\pi$
$653$	−4.83020	+	8.36615i	−0.189020	+	0.327393i	0.755904	+	0.654683i	$0.227198\pi$
$654$	−6.72272	+	48.2123i	−0.262879	+	1.88525i
$655$		0			0
$656$	6.49373	−	24.2349i	0.253538	−	0.946216i
$657$	0.0585190	−	3.82609i	0.00228304	−	0.149270i
$658$	−9.07180	+	9.07180i	−0.353655	+	0.353655i
$659$	−23.4834	+	13.5581i	−0.914783	+	0.528150i	−0.881967	−	0.471311i	$-0.843781\pi$
$659$	−23.4834	+	13.5581i	−0.914783	+	0.528150i	−0.0328158	+	0.999461i	$0.510447\pi$
$660$		0			0
$661$	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	$0.355874\pi$
$662$		−	51.5321i		−	2.00285i
$663$	17.7100	−	26.0126i	0.687801	−	1.01024i
$664$	−10.7321			−0.416484
$665$		0			0
$666$	−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
$670$		0			0
$671$	−20.3652	+	20.3652i	−0.786189	+	0.786189i
$672$	0.509445	−	3.65351i	0.0196523	−	0.140937i
$673$	−21.3564	+	36.9904i	−0.823229	+	1.42587i	0.0800364	+	0.996792i	$0.474496\pi$
$673$	−21.3564	+	36.9904i	−0.823229	+	1.42587i	−0.903265	+	0.429082i	$0.858837\pi$
$674$	7.19683	+	26.8589i	0.277211	+	1.03457i
$675$		0			0
$676$	2.76795	−	2.11474i	0.106460	−	0.0813360i
$677$	−9.66040			−0.371279			−0.185640	−	0.982618i	$-0.559436\pi$
$677$	−9.66040			−0.371279			−0.185640	+	0.982618i	$0.559436\pi$
$678$	24.7111	+	10.4578i	0.949025	+	0.401628i
$679$	−1.19615	+	2.07180i	−0.0459041	+	0.0795083i
$680$		0			0
$681$	−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
$685$		0			0
$686$	12.7786	−	22.1332i	0.487889	−	0.845048i
$687$	−13.4839	+	31.8617i	−0.514443	+	1.21560i
$688$	9.80385			0.373768
$689$	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	$0.799841\pi$
$692$	−2.33864	+	4.05065i	−0.0889019	+	0.153983i
$693$	−12.1530	−	12.5305i	−0.461653	−	0.475994i
$694$	21.9090	−	21.9090i	0.831653	−	0.831653i
$695$		0			0
$696$	25.8453	−	19.5196i	0.979664	−	0.739890i
$697$	−20.0263	+	20.0263i	−0.758549	+	0.758549i
$698$	−21.4301	−	37.1180i	−0.811140	−	1.40494i
$699$	−28.0207	+	11.3563i	−1.05984	+	0.429535i
$700$		0			0
$701$	−12.7786			−0.482641			−0.241320	−	0.970446i	$-0.577580\pi$
$701$	−12.7786			−0.482641			−0.241320	+	0.970446i	$0.577580\pi$
$702$	−28.1016	−	2.52002i	−1.06063	−	0.0951121i
$703$		−	20.9282i		−	0.789322i
$704$	−26.4692	+	7.09239i	−0.997594	+	0.267304i
$705$		0			0
$706$	−18.4474	+	10.6506i	−0.694279	+	0.400842i
$707$	6.02751	−	6.02751i	0.226688	−	0.226688i
$708$	0.842451	+	1.11546i	0.0316612	+	0.0419216i
$709$	3.03590	−	11.3301i	0.114016	−	0.425512i	−0.885196	−	0.465219i	$-0.845976\pi$
$709$	3.03590	−	11.3301i	0.114016	−	0.425512i	0.999211	+	0.0397068i	$0.0126424\pi$
$710$		0			0
$711$	4.30703	−	4.17726i	0.161526	−	0.156660i
$712$	12.1699	−	21.0788i	0.456085	−	0.789963i
$713$		0			0
$714$	−11.4284	+	14.6603i	−0.427696	+	0.548646i
$715$		0			0
$716$		−	7.11287i		−	0.265821i
$717$	−6.29899	+	14.8842i	−0.235240	+	0.555859i
$718$	33.6340	+	19.4186i	1.25521	+	0.724695i
$719$	3.68886	+	6.38929i	0.137571	+	0.238280i	0.926577	−	0.376106i	$-0.122737\pi$
$719$	3.68886	+	6.38929i	0.137571	+	0.238280i	−0.789005	+	0.614386i	$0.789404\pi$
$720$		0			0
$721$	9.46410	+	2.53590i	0.352462	+	0.0944418i
$722$	1.58708	−	5.92307i	0.0590650	−	0.220434i
$723$	25.0243	−	3.10003i	0.930665	−	0.115292i
$724$	−0.401924	−	0.696152i	−0.0149374	−	0.0258723i
$725$		0			0
$726$	6.02659	−	14.2405i	0.223668	−	0.528515i
$727$	19.5167			0.723833			0.361916	−	0.932211i	$-0.382123\pi$
$727$	19.5167			0.723833			0.361916	+	0.932211i	$0.382123\pi$
$728$	11.0666	−	7.37772i	0.410155	−	0.273437i
$729$	18.1962	+	19.9474i	0.673932	+	0.738794i
$730$		0			0
$731$	−9.58394	−	5.53329i	−0.354475	−	0.204656i
$732$	0.448659	−	3.21758i	0.0165829	−	0.118925i
$733$	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	$0.693356\pi$
$734$	11.8461	−	44.2104i	0.437249	−	1.63183i
$735$		0			0
$736$		0			0
$737$	12.2079	+	21.1447i	0.449685	+	0.778876i
$738$	24.4237	+	6.94633i	0.899049	+	0.255698i
$739$	11.1244	−	2.98076i	0.409216	−	0.109649i	−0.0483378	−	0.998831i	$-0.515392\pi$
$739$	11.1244	−	2.98076i	0.409216	−	0.109649i	0.457554	+	0.889182i	$0.348726\pi$
$740$		0			0
$741$	23.7052	−	4.50141i	0.870833	−	0.165363i
$742$		−	1.66025i		−	0.0609498i
$743$	−2.28268	−	8.51906i	−0.0837432	−	0.312534i	0.911330	−	0.411677i	$-0.135057\pi$
$743$	−2.28268	−	8.51906i	−0.0837432	−	0.312534i	−0.995073	+	0.0991426i	$0.968390\pi$
$744$	−5.91352	−	14.5911i	−0.216800	−	0.534935i
$745$		0			0
$746$	−12.3403	−	12.3403i	−0.451812	−	0.451812i
$747$	0.188763	−	12.3417i	0.00690649	−	0.451560i
$748$	−5.36603	−	1.43782i	−0.196201	−	0.0525720i
$749$	19.0150	−	19.0150i	0.694792	−	0.694792i
$750$		0			0
$751$	−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	$0.878222\pi$
$752$	−25.9749	+	6.95996i	−0.947208	+	0.253804i
$753$	1.05256	−	1.35022i	0.0383574	−	0.0492046i
$754$	−38.1699	−	7.63397i	−1.39006	−	0.278013i
$755$		0			0
$756$	1.94576	+	0.301720i	0.0707667	+	0.0109735i
$757$	−14.5359	−	8.39230i	−0.528316	−	0.305024i	0.212014	−	0.977267i	$-0.431998\pi$
$757$	−14.5359	−	8.39230i	−0.528316	−	0.305024i	−0.740331	+	0.672243i	$0.765331\pi$
$758$	19.3003	−	11.1430i	0.701019	−	0.404733i
$759$		0			0
$760$		0			0
$761$	−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	$0.691361\pi$
$762$	−2.92602	−	23.6196i	−0.105998	−	0.855647i
$763$	22.8564	−	13.1962i	0.827457	−	0.477733i
$764$	0.647124	−	1.12085i	0.0234121	−	0.0405510i
$765$		0			0
$766$		−	49.5692i		−	1.79101i
$767$	−2.12976	+	10.6488i	−0.0769014	+	0.384507i
$768$	6.73060	−	8.63397i	0.242870	−	0.311552i
$769$	10.8301	+	40.4186i	0.390544	+	1.45753i	0.829238	+	0.558895i	$0.188775\pi$
$769$	10.8301	+	40.4186i	0.390544	+	1.45753i	−0.438694	+	0.898636i	$0.644559\pi$
$770$		0			0
$771$	5.14442	−	36.8935i	0.185272	−	1.32869i
$772$	0.0262794	+	0.0262794i	0.000945818	+	0.000945818i
$773$	41.5864	+	11.1430i	1.49576	+	0.400787i	0.911677	−	0.410908i	$-0.134788\pi$
$773$	41.5864	+	11.1430i	1.49576	+	0.400787i	0.584081	+	0.811695i	$0.301455\pi$
$774$	−0.151737	+	9.92087i	−0.00545407	+	0.356598i
$775$		0			0
$776$	−3.82129	+	2.20622i	−0.137176	+	0.0791987i
$777$	12.2965	−	4.98354i	0.441133	−	0.178784i
$778$	8.76795	+	32.7224i	0.314346	+	1.17316i
$779$	−21.7154			−0.778035
$780$		0			0
$781$	12.3923			0.443432
$782$		0			0
$783$	21.9928	+	30.0651i	0.785957	+	1.07444i
$784$	19.3301	−	11.1603i	0.690362	−	0.398581i
$785$		0			0
$786$	−12.4951	−	16.5444i	−0.445687	−	0.590120i
$787$	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
$789$	38.2307	+	5.33089i	1.36105	+	0.189785i
$790$		0			0
$791$	−3.76532	−	14.0524i	−0.133879	−	0.499644i
$792$	−7.85641	−	31.2229i	−0.279165	−	1.10946i
$793$	21.0000	−	14.0000i	0.745732	−	0.497155i
$794$		−	20.7270i		−	0.735573i
$795$		0			0
$796$	1.73205	−	3.00000i	0.0613909	−	0.106332i
$797$	34.9118	−	20.1563i	1.23664	−	0.713973i	0.268232	−	0.963354i	$-0.413561\pi$
$797$	34.9118	−	20.1563i	1.23664	−	0.713973i	0.968405	+	0.249381i	$0.0802272\pi$
$798$	−14.1445	+	1.75224i	−0.500711	+	0.0620286i
$799$	29.3205	+	7.85641i	1.03729	+	0.277940i
$800$		0			0
$801$	24.0264	+	14.3660i	0.848929	+	0.507596i
$802$	−16.2391	+	9.37564i	−0.573422	+	0.331066i
$803$	−4.54486	−	2.62398i	−0.160385	−	0.0925982i
$804$	−2.53632	−	1.07337i	−0.0894491	−	0.0378550i
$805$		0			0
$806$	−8.38664	+	16.9617i	−0.295407	+	0.597449i
$807$	−19.5856	−	15.2679i	−0.689447	−	0.537457i
$808$	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	$0.504505\pi$
$810$		0			0
$811$	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	$0.0936161\pi$
$812$	2.62398	+	0.703093i	0.0920836	+	0.0246737i
$813$	8.06639	+	10.6804i	0.282901	+	0.374579i
$814$	23.7321	+	23.7321i	0.831808	+	0.831808i
$815$		0			0
$816$	−36.1095	+	14.6346i	−1.26409	+	0.512313i
$817$	−2.19615	−	8.19615i	−0.0768336	−	0.286747i
$818$		−	45.1988i		−	1.58034i
$819$	8.28964	+	12.8562i	0.289664	+	0.449232i
$820$		0			0
$821$	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	$0.146100\pi$
$822$	6.58662	+	16.2519i	0.229735	+	0.566850i
$823$	4.26795	+	7.39230i	0.148771	+	0.257680i	0.930774	−	0.365596i	$-0.119135\pi$
$823$	4.26795	+	7.39230i	0.148771	+	0.257680i	−0.782002	+	0.623276i	$0.785801\pi$
$824$	12.7786	+	12.7786i	0.445163	+	0.445163i
$825$		0			0
$826$	1.66025	−	6.19615i	0.0577676	−	0.215592i
$827$	31.7936	+	31.7936i	1.10557	+	1.10557i	0.993726	+	0.111845i	$0.0356760\pi$
$827$	31.7936	+	31.7936i	1.10557	+	1.10557i	0.111845	+	0.993726i	$0.464324\pi$
$828$		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	$0.981613\pi$
$830$		0			0
$831$	−29.3785	+	37.6865i	−1.01913	+	1.30733i
$832$	23.9641	−	1.54552i	0.830806	−	0.0535812i
$833$	−25.1954			−0.872968
$834$	−44.1813	−	18.6976i	−1.52987	−	0.647444i
$835$		0			0
$836$	−2.12976	−	3.68886i	−0.0736595	−	0.127582i
$837$	16.8836	−	6.54383i	0.583582	−	0.226188i
$838$	3.70577	−	13.8301i	0.128014	−	0.477754i
$839$	−9.79282	−	2.62398i	−0.338086	−	0.0905898i	0.0857819	−	0.996314i	$-0.472661\pi$
$839$	−9.79282	−	2.62398i	−0.338086	−	0.0905898i	−0.423868	+	0.905724i	$0.639328\pi$
$840$		0			0
$841$	11.1962	+	19.3923i	0.386074	+	0.668700i
$842$	−14.4421	−	8.33816i	−0.497708	−	0.287352i
$843$	27.3662	+	11.5814i	0.942540	+	0.398884i
$844$			0.483340i			0.0166372i
$845$		0			0
$846$	−6.64102	−	26.3927i	−0.228323	−	0.907400i
$847$	−8.09808	+	2.16987i	−0.278253	+	0.0745577i
$848$	1.73999	−	3.01375i	0.0597515	−	0.103493i
$849$	−11.3022	−	1.57598i	−0.387890	−	0.0540873i
$850$		0			0
$851$		0			0
$852$	−1.11546	+	0.842451i	−0.0382151	+	0.0288619i
$853$	−22.3660	+	22.3660i	−0.765798	+	0.765798i	−0.977364	−	0.211566i	$-0.932144\pi$
$853$	−22.3660	+	22.3660i	−0.765798	+	0.765798i	0.211566	+	0.977364i	$0.432144\pi$
$854$	−12.9110	+	7.45418i	−0.441806	+	0.255077i
$855$		0			0
$856$	47.9090	−	12.8372i	1.63749	−	0.438765i
$857$		−	3.32707i		−	0.113651i	−0.998384	−	0.0568253i	$-0.981902\pi$
$857$		−	3.32707i		−	0.113651i	0.998384	−	0.0568253i	$-0.0180978\pi$
$858$	−21.7766	+	31.9856i	−0.743442	+	1.09197i
$859$	−39.1769			−1.33670			−0.668350	−	0.743847i	$-0.732999\pi$
$859$	−39.1769			−1.33670			−0.668350	+	0.743847i	$0.732999\pi$
$860$		0			0
$861$	−5.17100	−	12.7590i	−0.176227	−	0.434825i
$862$	28.4904	+	49.3468i	0.970386	+	1.68076i
$863$	18.2354	−	18.2354i	0.620741	−	0.620741i	−0.324980	−	0.945721i	$-0.605358\pi$
$863$	18.2354	−	18.2354i	0.620741	−	0.620741i	0.945721	+	0.324980i	$0.105358\pi$
$864$	6.09729	+	4.90487i	0.207434	+	0.166867i
$865$		0			0
$866$	−33.0673	+	33.0673i	−1.12367	+	1.12367i
$867$	14.3966	+	2.00746i	0.488935	+	0.0681769i
$868$	0.660254	−	1.14359i	0.0224105	−	0.0388161i
$869$	−2.12976	−	7.94839i	−0.0722473	−	0.269631i
$870$		0			0
$871$	−6.85641	−	20.2679i	−0.232320	−	0.686753i
$872$	48.6788			1.64847
$873$	−2.46991	−	4.43324i	−0.0835939	−	0.150042i
$874$		0			0
$875$		0			0
$876$	0.587477	−	0.0727771i	0.0198490	−	0.00245891i
$877$	−7.76795	+	28.9904i	−0.262305	+	0.978936i	0.701574	+	0.712596i	$0.252481\pi$
$877$	−7.76795	+	28.9904i	−0.262305	+	0.978936i	−0.963879	+	0.266339i	$0.914186\pi$
$878$	0.494214	−	1.84443i	0.0166789	−	0.0622465i
$879$	3.09640	−	0.383584i	0.104439	−	0.0129380i
$880$		0			0
$881$	−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	$0.296126\pi$
$882$	10.9943	+	19.7336i	0.370197	+	0.664464i
$883$	33.3731			1.12309			0.561547	−	0.827445i	$-0.310207\pi$
$883$	33.3731			1.12309			0.561547	+	0.827445i	$0.310207\pi$
$884$	4.36397	+	2.15775i	0.146776	+	0.0725730i
$885$		0			0
$886$	−4.37307	−	16.3205i	−0.146916	−	0.548298i
$887$	−12.6257	+	21.8683i	−0.423929	+	0.734266i	−0.996320	−	0.0857146i	$-0.972683\pi$
$887$	−12.6257	+	21.8683i	−0.423929	+	0.734266i	0.572391	+	0.819981i	$0.306016\pi$
$888$	24.2373	+	3.37965i	0.813351	+	0.113414i
$889$	−9.12436	+	9.12436i	−0.306021	+	0.306021i
$890$		0			0
$891$	36.0441	−	8.48560i	1.20752	−	0.284278i
$892$	−4.90897	+	4.90897i	−0.164364	+	0.164364i
$893$	11.6373	+	20.1563i	0.389426	+	0.674505i
$894$	8.45743	+	20.8680i	0.282859	+	0.697929i
$895$		0			0
$896$	−18.4443			−0.616181
$897$		0			0
$898$		−	30.9808i		−	1.03384i
$899$	24.1305	−	6.46575i	0.804797	−	0.215645i
$900$		0			0
$901$	−3.40192	+	1.96410i	−0.113335	+	0.0654337i
$902$	24.6247	−	24.6247i	0.819913	−	0.819913i
$903$	4.29272	−	3.24207i	0.142853	−	0.107889i
$904$	6.94486	−	25.9186i	0.230983	−	0.862039i
$905$		0			0
$906$	−1.95791	−	0.273011i	−0.0650473	−	0.00907018i
$907$	8.66025	−	15.0000i	0.287559	−	0.498067i	−0.685668	−	0.727915i	$-0.740490\pi$
$907$	8.66025	−	15.0000i	0.287559	−	0.498067i	0.973227	+	0.229848i	$0.0738229\pi$
$908$	5.24796	−	1.40619i	0.174160	−	0.0466659i
$909$	4.41244	+	17.5359i	0.146351	+	0.581629i
$910$		0			0
$911$			1.55910i			0.0516552i	0.999666	+	0.0258276i	$0.00822209\pi$
$911$			1.55910i			0.0516552i	−0.999666	+	0.0258276i	$0.991778\pi$
$912$	−27.5121	−	11.6431i	−0.911016	−	0.385543i
$913$	−14.6603	−	8.46410i	−0.485184	−	0.280121i
$914$	2.93730	+	5.08755i	0.0971572	+	0.168281i
$915$		0			0
$916$	−5.16987	−	1.38526i	−0.170817	−	0.0457704i
$917$	−2.90931	+	10.8577i	−0.0960740	+	0.358553i
$918$	−14.2504	−	36.7670i	−0.470333	−	1.21349i
$919$	6.70577	+	11.6147i	0.221203	+	0.383135i	0.955174	−	0.296046i	$-0.0956683\pi$
$919$	6.70577	+	11.6147i	0.221203	+	0.383135i	−0.733971	+	0.679181i	$0.762335\pi$
$920$		0			0
$921$	−18.9314	−	8.01177i	−0.623809	−	0.263997i
$922$	32.0333			1.05496
$923$	−10.6488	−	2.12976i	−0.350510	−	0.0701021i
$924$	1.66025	−	2.12976i	0.0546183	−	0.0700641i
$925$		0			0
$926$	42.5188	+	24.5483i	1.39726	+	0.806706i
$927$	−14.9200	+	14.4705i	−0.490036	+	0.475272i
$928$	7.63397	+	7.63397i	0.250597	+	0.250597i
$929$	−5.27594	+	19.6901i	−0.173098	+	0.646011i	0.823770	+	0.566924i	$0.191867\pi$
$929$	−5.27594	+	19.6901i	−0.173098	+	0.646011i	−0.996868	+	0.0790861i	$0.974800\pi$
$930$		0			0
$931$	−13.6603	−	13.6603i	−0.447697	−	0.447697i
$932$	−2.33864	−	4.05065i	−0.0766048	−	0.132683i
$933$	−6.55656	−	16.1777i	−0.214652	−	0.529635i
$934$	−27.8827	+	7.47114i	−0.912349	+	0.244463i
$935$		0			0
$936$	1.38506	+	28.1803i	0.0452721	+	0.921103i
$937$		−	37.0000i		−	1.20874i	−0.796705	−	0.604369i	$-0.793425\pi$
$937$		−	37.0000i		−	1.20874i	0.796705	−	0.604369i	$-0.206575\pi$
$938$	3.27110	+	12.2079i	0.106805	+	0.398603i
$939$	3.21046	−	1.30114i	0.104769	−	0.0424612i
$940$		0			0
$941$	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	$0.682387\pi$
$942$	7.55181	+	9.99911i	0.246051	+	0.325789i
$943$		0			0
$944$	9.50749	−	9.50749i	0.309442	−	0.309442i
$945$		0			0
$946$	11.7846	+	6.80385i	0.383151	+	0.221212i
$947$	−10.3635	+	2.77689i	−0.336768	+	0.0902368i	−0.423240	−	0.906018i	$-0.639107\pi$
$947$	−10.3635	+	2.77689i	−0.336768	+	0.0902368i	0.0864720	+	0.996254i	$0.472441\pi$
$948$	0.732051	+	0.570669i	0.0237759	+	0.0185345i
$949$	3.45448	+	3.03590i	0.112137	+	0.0985494i
$950$		0			0
$951$	−25.6076	−	10.8372i	−0.830385	−	0.351420i
$952$	16.0981	+	9.29423i	0.521742	+	0.301228i
$953$	1.71201	−	0.988427i	0.0554573	−	0.0320183i	−0.472015	−	0.881591i	$-0.656473\pi$
$953$	1.71201	−	0.988427i	0.0554573	−	0.0320183i	0.527472	+	0.849572i	$0.323140\pi$
$954$	3.02279	+	1.80740i	0.0978666	+	0.0585169i
$955$		0			0
$956$	−2.41510	−	0.647124i	−0.0781099	−	0.0209295i
$957$	50.7000	−	6.28076i	1.63890	−	0.203028i
$958$	−26.8301	+	15.4904i	−0.866842	+	0.500471i
$959$	4.75374	−	8.23373i	0.153506	−	0.265881i
$960$		0			0
$961$			18.8564i			0.608271i
$962$	−16.3145	−	24.4718i	−0.526002	−	0.789003i
$963$	13.9199	+	55.3205i	0.448563	+	1.78268i
$964$	1.00962	+	3.76795i	0.0325176	+	0.121357i
$965$		0			0
$966$		0			0
$967$	−27.8564	−	27.8564i	−0.895802	−	0.895802i	0.0992599	−	0.995062i	$-0.468352\pi$
$967$	−27.8564	−	27.8564i	−0.895802	−	0.895802i	−0.995062	+	0.0992599i	$0.968352\pi$
$968$	−14.9363	−	4.00218i	−0.480072	−	0.128635i
$969$	20.3236	+	26.9098i	0.652887	+	0.864467i
$970$		0			0
$971$	−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	$0.611923\pi$
$972$	−2.66755	+	3.21415i	−0.0855618	+	0.103094i
$973$	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	$-0.207061\pi$
$978$	−10.0108	+	4.05721i	−0.320111	+	0.129735i
$979$	33.2487	−	19.1962i	1.06263	−	0.613512i
$980$		0			0
$981$	−0.856198	+	55.9800i	−0.0273363	+	1.78730i
$982$	−41.4904	−	11.1173i	−1.32401	−	0.354768i
$983$	−30.4433	−	30.4433i	−0.970992	−	0.970992i	0.0285990	−	0.999591i	$-0.490895\pi$
$983$	−30.4433	−	30.4433i	−0.970992	−	0.970992i	−0.999591	+	0.0285990i	$0.990895\pi$
$984$	3.50677	−	25.1490i	0.111792	−	0.801721i
$985$		0			0
$986$	−14.0803	−	52.5485i	−0.448409	−	1.67349i
$987$	−9.07180	+	11.6373i	−0.288758	+	0.370418i
$988$	1.19615	+	3.53590i	0.0380547	+	0.112492i
$989$		0			0
$990$		0			0
$991$	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	$-0.200649\pi$
$992$	4.54486	−	2.62398i	0.144300	−	0.0833114i
$993$	−7.28650	−	58.8186i	−0.231230	−	1.86655i
$994$	6.19615	+	1.66025i	0.196530	+	0.0526601i
$995$		0			0
$996$	1.89501	−	0.234755i	0.0600457	−	0.00743851i
$997$	−6.06218	+	3.50000i	−0.191991	+	0.110846i	−0.592914	−	0.805266i	$-0.702023\pi$
$997$	−6.06218	+	3.50000i	−0.191991	+	0.110846i	0.400923	+	0.916112i	$0.368689\pi$
$998$	4.54486	+	2.62398i	0.143865	+	0.0830606i
$999$	−4.31286	+	27.8132i	−0.136453	+	0.879970i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bp.f.149.2		8
3.2	odd	2	inner	975.2.bp.f.149.1		8
5.2	odd	4		975.2.bo.d.851.1		8
5.3	odd	4		39.2.k.b.32.2	yes	8
5.4	even	2		975.2.bp.e.149.1		8
13.11	odd	12		975.2.bp.e.674.2		8
15.2	even	4		975.2.bo.d.851.2		8
15.8	even	4		39.2.k.b.32.1	yes	8
15.14	odd	2		975.2.bp.e.149.2		8
20.3	even	4		624.2.cn.c.305.2		8
39.11	even	12		975.2.bp.e.674.1		8
60.23	odd	4		624.2.cn.c.305.1		8
65.3	odd	12		507.2.k.e.80.1		8
65.8	even	4		507.2.k.e.488.2		8
65.18	even	4		507.2.k.f.488.1		8
65.23	odd	12		507.2.k.f.80.2		8
65.24	odd	12	inner	975.2.bp.f.674.1		8
65.28	even	12		507.2.k.d.89.2		8
65.33	even	12		507.2.f.f.437.3		8
65.37	even	12		975.2.bo.d.401.2		8
65.38	odd	4		507.2.k.d.188.1		8
65.43	odd	12		507.2.f.e.239.3		8
65.48	odd	12		507.2.f.f.239.2		8
65.58	even	12		507.2.f.e.437.2		8
65.63	even	12		39.2.k.b.11.1	✓	8
195.8	odd	4		507.2.k.e.488.1		8
195.23	even	12		507.2.k.f.80.1		8
195.38	even	4		507.2.k.d.188.2		8
195.68	even	12		507.2.k.e.80.2		8
195.83	odd	4		507.2.k.f.488.2		8
195.89	even	12	inner	975.2.bp.f.674.2		8
195.98	odd	12		507.2.f.f.437.2		8
195.113	even	12		507.2.f.f.239.3		8
195.128	odd	12		39.2.k.b.11.2	yes	8
195.158	odd	12		507.2.k.d.89.1		8
195.167	odd	12		975.2.bo.d.401.1		8
195.173	even	12		507.2.f.e.239.2		8
195.188	odd	12		507.2.f.e.437.3		8
260.63	odd	12		624.2.cn.c.401.1		8
780.323	even	12		624.2.cn.c.401.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.k.b.11.1	✓	8	65.63	even	12
39.2.k.b.11.2	yes	8	195.128	odd	12
39.2.k.b.32.1	yes	8	15.8	even	4
39.2.k.b.32.2	yes	8	5.3	odd	4
507.2.f.e.239.2		8	195.173	even	12
507.2.f.e.239.3		8	65.43	odd	12
507.2.f.e.437.2		8	65.58	even	12
507.2.f.e.437.3		8	195.188	odd	12
507.2.f.f.239.2		8	65.48	odd	12
507.2.f.f.239.3		8	195.113	even	12
507.2.f.f.437.2		8	195.98	odd	12
507.2.f.f.437.3		8	65.33	even	12
507.2.k.d.89.1		8	195.158	odd	12
507.2.k.d.89.2		8	65.28	even	12
507.2.k.d.188.1		8	65.38	odd	4
507.2.k.d.188.2		8	195.38	even	4
507.2.k.e.80.1		8	65.3	odd	12
507.2.k.e.80.2		8	195.68	even	12
507.2.k.e.488.1		8	195.8	odd	4
507.2.k.e.488.2		8	65.8	even	4
507.2.k.f.80.1		8	195.23	even	12
507.2.k.f.80.2		8	65.23	odd	12
507.2.k.f.488.1		8	65.18	even	4
507.2.k.f.488.2		8	195.83	odd	4
624.2.cn.c.305.1		8	60.23	odd	4
624.2.cn.c.305.2		8	20.3	even	4
624.2.cn.c.401.1		8	260.63	odd	12
624.2.cn.c.401.2		8	780.323	even	12
975.2.bo.d.401.1		8	195.167	odd	12
975.2.bo.d.401.2		8	65.37	even	12
975.2.bo.d.851.1		8	5.2	odd	4
975.2.bo.d.851.2		8	15.2	even	4
975.2.bp.e.149.1		8	5.4	even	2
975.2.bp.e.149.2		8	15.14	odd	2
975.2.bp.e.674.1		8	39.11	even	12
975.2.bp.e.674.2		8	13.11	odd	12
975.2.bp.f.149.1		8	3.2	odd	2	inner
975.2.bp.f.149.2		8	1.1	even	1	trivial
975.2.bp.f.674.1		8	65.24	odd	12	inner
975.2.bp.f.674.2		8	195.89	even	12	inner

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bp (of order \(12\), degree \(4\), not minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more