LMFDB - Embedded newform 975.2.bp.f.674.2

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			674.2
Root			$0.500000 + 1.56488i$ of defining polynomial
Character	$\chi$	$=$	975.674
Dual form			975.2.bp.f.149.2

$q$-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 $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$-1$	$-1$

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	−0.679818	−	0.733380i	$-0.737941\pi$
$2$	0.389774	−	1.45466i	0.275612	−	1.02860i	0.955430	−	0.295217i	$-0.0953919\pi$
$3$	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	0.00875026	−	0.999962i	$-0.497215\pi$
$7$	1.36603	−	0.366025i	0.516309	−	0.138345i	0.507559	+	0.861617i	$0.330548\pi$
$8$	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	−0.597126	−	0.802148i	$-0.703691\pi$
$11$	1.06488	−	3.97420i	0.321074	−	1.19826i	0.918200	−	0.396117i	$-0.129643\pi$
$12$	−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	0.924994	−	0.379981i	$-0.124070\pi$
$17$	4.36397	+	2.51954i	1.05842	+	0.611078i	0.133424	+	0.991059i	$0.457403\pi$
$18$	−3.87762	+	2.31853i	−0.913965	+	0.546482i
$19$	3.73205	−	1.00000i	0.856191	−	0.229416i	0.196084	−	0.980587i	$-0.437177\pi$
$19$	3.73205	−	1.00000i	0.856191	−	0.229416i	0.660107	+	0.751171i	$0.270511\pi$
$20$		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	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$	−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	−0.949585	−	0.313509i	$-0.898495\pi$
$29$	−6.20840	+	3.58442i	−1.15287	+	0.665610i	−0.203286	+	0.979119i	$0.565162\pi$
$30$		0			0
$31$	−2.46410	−	2.46410i	−0.442566	−	0.442566i	0.450308	−	0.892873i	$-0.351314\pi$
$31$	−2.46410	−	2.46410i	−0.442566	−	0.442566i	−0.892873	+	0.450308i	$0.851314\pi$
$32$	−1.45466	+	0.389774i	−0.257149	+	0.0689030i
$33$	−5.68671	−	4.29488i	−0.989929	−	0.747642i
$34$	5.36603	−	5.36603i	0.920266	−	0.920266i
$35$		0			0
$36$	0.219901	+	0.773185i	0.0366502	+	0.128864i
$37$	−1.40192	+	5.23205i	−0.230475	+	0.860144i	0.749662	+	0.661821i	$0.230216\pi$
$37$	−1.40192	+	5.23205i	−0.230475	+	0.860144i	−0.980137	+	0.198323i	$0.936451\pi$
$38$		−	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	−0.191361	−	0.981520i	$-0.561290\pi$
$41$	−5.42885	−	1.45466i	−0.847844	−	0.227179i	−0.656483	+	0.754341i	$0.727957\pi$
$42$	−3.41876	−	1.38556i	−0.527526	−	0.213797i
$43$	−1.09808	+	1.90192i	−0.167455	+	0.290041i	−0.937524	−	0.347920i	$-0.886888\pi$
$43$	−1.09808	+	1.90192i	−0.167455	+	0.290041i	0.770069	+	0.637960i	$0.220222\pi$
$44$	−0.779548	+	0.779548i	−0.117521	+	0.117521i
$45$		0			0
$46$		0			0
$47$	4.25953	−	4.25953i	0.621316	−	0.621316i	−0.324552	−	0.945868i	$-0.605213\pi$
$47$	4.25953	−	4.25953i	0.621316	−	0.621316i	0.945868	+	0.324552i	$0.105213\pi$
$48$	−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	−0.443176	−	0.896435i	$-0.646148\pi$
$59$	−2.90931	+	0.779548i	−0.378760	+	0.101489i	0.0644157	+	0.997923i	$0.479482\pi$
$60$		0			0
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	−0.550135	−	0.835076i	$-0.685424\pi$
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	0.998264	+	0.0588933i	$0.0187572\pi$
$62$	−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	0.591357	−	0.806410i	$-0.298593\pi$
$67$	5.73205	+	1.53590i	0.700281	+	0.187640i	0.108925	+	0.994050i	$0.465259\pi$
$68$	−0.675108	−	1.16932i	−0.0818689	−	0.141801i
$69$		0			0
$70$		0			0
$71$	0.779548	+	2.90931i	0.0925153	+	0.345272i	0.996631	−	0.0820158i	$-0.0261358\pi$
$71$	0.779548	+	2.90931i	0.0925153	+	0.345272i	−0.904116	+	0.427288i	$0.859469\pi$
$72$	−7.82434	+	0.119671i	−0.922107	+	0.0141034i
$73$	−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
$75$		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	0.529174	−	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
$85$		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	0.711531	+	0.702654i	$0.248002\pi$
$89$	−2.41510	+	9.01327i	−0.256000	+	0.955405i	−0.967531	+	0.252751i	$0.918665\pi$
$90$		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	0.940130	−	0.340815i	$-0.110703\pi$
$97$	−0.437822	−	1.63397i	−0.0444541	−	0.165905i	−0.984584	+	0.174910i	$0.944036\pi$
$98$	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	0.976108	−	0.217285i	$-0.0697202\pi$
$101$	3.01375	+	5.21997i	0.299880	+	0.519407i	−0.676229	+	0.736692i	$0.736387\pi$
$102$	−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	0.800749	+	0.598999i	$0.204435\pi$
$107$	9.50749	+	16.4675i	0.919123	+	1.59197i	0.118374	+	0.992969i	$0.462232\pi$
$108$	1.38420	+	0.150021i	0.133195	+	0.0144357i
$109$	13.1962	+	13.1962i	1.26396	+	1.26396i	0.949156	+	0.314806i	$0.101940\pi$
$109$	13.1962	+	13.1962i	1.26396	+	1.26396i	0.314806	+	0.949156i	$0.398060\pi$
$110$		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	−0.999828	−	0.0185360i	$-0.994099\pi$
$113$	−5.14352	+	8.90883i	−0.483861	+	0.838073i	0.515967	+	0.856609i	$0.327433\pi$
$114$	−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	0.589474	−	0.807788i	$-0.299335\pi$
$127$	−4.56218	−	7.90192i	−0.404828	−	0.701182i	−0.994301	+	0.106605i	$0.966002\pi$
$128$	−12.5977	−	3.37554i	−1.11349	−	0.298359i
$129$	2.33864	+	3.00000i	0.205906	+	0.264135i
$130$		0			0
$131$		−	7.94839i		−	0.694454i	−0.937781	−	0.347227i	$-0.887123\pi$
$131$		−	7.94839i		−	0.694454i	0.937781	−	0.347227i	$-0.112877\pi$
$132$	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	0.999565	+	0.0294822i	$0.00938583\pi$
$137$	1.73999	+	6.49373i	0.148657	+	0.554797i	−0.850908	+	0.525315i	$0.823948\pi$
$138$		0			0
$139$	9.19615	−	15.9282i	0.780007	−	1.35101i	−0.151929	−	0.988391i	$-0.548549\pi$
$139$	9.19615	−	15.9282i	0.780007	−	1.35101i	0.931937	−	0.362621i	$-0.118118\pi$
$140$		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	0.995043	+	0.0994454i	$0.0317068\pi$
$149$	2.23420	+	8.33816i	0.183033	+	0.683089i	−0.812010	+	0.583644i	$0.801626\pi$
$150$		0			0
$151$	0.535898	−	0.535898i	0.0436108	−	0.0436108i	−0.684965	−	0.728576i	$-0.740183\pi$
$151$	0.535898	−	0.535898i	0.0436108	−	0.0436108i	0.728576	+	0.684965i	$0.240183\pi$
$152$	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	$0.0613982\pi$
$157$			4.80385i			0.383389i	−0.981455	+	0.191694i	$0.938602\pi$
$158$	−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	−0.0987406	−	0.995113i	$-0.531481\pi$
$163$	4.00000	−	1.07180i	0.313304	−	0.0839496i	0.412045	+	0.911164i	$0.364815\pi$
$164$	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	0.723539	−	0.690283i	$-0.242514\pi$
$167$	12.9875	+	3.47998i	1.00500	+	0.269289i	0.281461	+	0.959573i	$0.409181\pi$
$168$	−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	0.948727	−	0.316097i	$-0.102373\pi$
$173$	15.1172	+	8.72794i	1.14934	+	0.663573i	0.200615	+	0.979670i	$0.435706\pi$
$174$	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	−0.604972	−	0.796247i	$-0.706816\pi$
$179$	−13.2728	−	22.9892i	−0.992056	−	1.71829i	−0.387084	−	0.922045i	$-0.626518\pi$
$180$		0			0
$181$		−	3.00000i		−	0.222988i	−0.993765	−	0.111494i	$-0.964436\pi$
$181$		−	3.00000i		−	0.222988i	0.993765	−	0.111494i	$-0.0355636\pi$
$182$	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	0.340968	−	0.940075i	$-0.389245\pi$
$191$	−4.18307	−	2.41510i	−0.302677	−	0.174750i	−0.643645	+	0.765324i	$0.722579\pi$
$192$	−10.6912	−	4.33297i	−0.771573	−	0.312705i
$193$	−0.0358984	+	0.133975i	−0.00258402	+	0.00964370i	−0.967206	−	0.253994i	$-0.918256\pi$
$193$	−0.0358984	+	0.133975i	−0.00258402	+	0.00964370i	0.964622	+	0.263638i	$0.0849223\pi$
$194$	−2.54752			−0.182902
$195$		0			0
$196$	1.33975			0.0956961
$197$	1.06488	−	3.97420i	0.0758697	−	0.283150i	−0.917559	−	0.397599i	$-0.869844\pi$
$197$	1.06488	−	3.97420i	0.0758697	−	0.283150i	0.993429	+	0.114449i	$0.0365103\pi$
$198$	5.08507	+	17.8794i	0.361380	+	1.27063i
$199$	−11.1962	−	6.46410i	−0.793674	−	0.458228i	0.0475802	−	0.998867i	$-0.484849\pi$
$199$	−11.1962	−	6.46410i	−0.793674	−	0.458228i	−0.841254	+	0.540639i	$0.818182\pi$
$200$		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	0.895400	−	0.445263i	$-0.146890\pi$
$211$	0.901924	+	1.56218i	0.0620910	+	0.107545i	−0.833309	+	0.552808i	$0.813556\pi$
$212$	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	0.966687	−	0.255960i	$-0.0823914\pi$
$223$	25.0263	+	6.70577i	1.67588	+	0.449052i	0.709196	+	0.705011i	$0.249058\pi$
$224$	−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	−0.841429	−	0.540367i	$-0.818285\pi$
$227$	−19.5856	+	5.24796i	−1.29994	+	0.348319i	−0.458515	+	0.888686i	$0.651619\pi$
$228$	−1.08069	+	1.43091i	−0.0715705	+	0.0947642i
$229$	14.1244	−	14.1244i	0.933364	−	0.933364i	−0.0645507	−	0.997914i	$-0.520561\pi$
$229$	14.1244	−	14.1244i	0.933364	−	0.933364i	0.997914	+	0.0645507i	$0.0205614\pi$
$230$		0			0
$231$	−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	$-0.806251\pi$
$233$		−	17.4559i		−	1.14357i	0.820403	−	0.571786i	$-0.193749\pi$
$234$	−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	−0.460737	−	0.887537i	$-0.652415\pi$
$239$	6.59817	−	6.59817i	0.426800	−	0.426800i	0.887537	+	0.460737i	$0.152415\pi$
$240$		0			0
$241$	3.76795	+	14.0622i	0.242715	+	0.905825i	0.974518	+	0.224309i	$0.0720123\pi$
$241$	3.76795	+	14.0622i	0.242715	+	0.905825i	−0.731803	+	0.681516i	$0.761321\pi$
$242$	−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	−0.881201	−	0.472741i	$-0.843264\pi$
$251$	−0.494214	+	0.856003i	−0.0311945	+	0.0540304i	0.850007	+	0.526772i	$0.176598\pi$
$252$	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	−0.951737	−	0.306916i	$-0.900703\pi$
$257$	−18.6252	+	10.7533i	−1.16181	+	0.670770i	−0.210071	+	0.977686i	$0.567370\pi$
$258$	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	0.972769	+	0.231777i	$0.0744539\pi$
$263$	11.1430	+	19.3003i	0.687109	+	1.19011i	−0.285660	+	0.958331i	$0.592213\pi$
$264$	−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	0.0711756	−	0.997464i	$-0.477325\pi$
$269$	−12.4168	−	7.16884i	−0.757066	−	0.437092i	−0.828241	+	0.560372i	$0.810658\pi$
$270$		0			0
$271$	7.46410	+	2.00000i	0.453412	+	0.121491i	0.478295	−	0.878199i	$-0.341255\pi$
$271$	7.46410	+	2.00000i	0.453412	+	0.121491i	−0.0248835	+	0.999690i	$0.507921\pi$
$272$		−	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	−0.0701536	−	0.997536i	$-0.522349\pi$
$277$	13.7942	−	23.8923i	0.828815	−	1.43555i	0.898969	−	0.438013i	$-0.144318\pi$
$278$	−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	0.969357	−	0.245655i	$-0.0790030\pi$
$281$	12.1315	+	12.1315i	0.723703	+	0.723703i	−0.245655	+	0.969357i	$0.579003\pi$
$282$	−15.5622	+	2.17000i	−0.926718	+	0.129221i
$283$	−3.29423	−	5.70577i	−0.195822	−	0.339173i	0.751348	−	0.659906i	$-0.229404\pi$
$283$	−3.29423	−	5.70577i	−0.195822	−	0.339173i	−0.947170	+	0.320733i	$0.896071\pi$
$284$	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	0.978206	−	0.207635i	$-0.0665766\pi$
$293$	0.466229	+	1.73999i	0.0272374	+	0.101651i	−0.950969	+	0.309286i	$0.899910\pi$
$294$	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	0.425829	−	0.904803i	$-0.359982\pi$
$307$	−8.39230	−	8.39230i	−0.478974	−	0.478974i	−0.904803	+	0.425829i	$0.859982\pi$
$308$	−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	$0.0180015\pi$
$313$			2.00000i			0.113047i	−0.998401	+	0.0565233i	$0.981998\pi$
$314$	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	0.312373	−	0.949960i	$-0.398876\pi$
$317$	−11.3519	−	11.3519i	−0.637587	−	0.637587i	−0.949960	+	0.312373i	$0.898876\pi$
$318$	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	−0.996376	−	0.0850595i	$-0.972892\pi$
$331$	−33.0526	+	8.85641i	−1.81673	+	0.486792i	−0.820357	+	0.571852i	$0.806225\pi$
$332$	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	0.445876	+	0.895095i	$0.352892\pi$
$347$	−10.2870	+	17.8177i	−0.552237	+	0.956502i	−0.998113	+	0.0614076i	$0.980441\pi$
$348$	1.24967	−	3.08346i	0.0669895	−	0.165291i
$349$	−27.4904	−	7.36603i	−1.47153	−	0.394294i	−0.568072	−	0.822979i	$-0.692311\pi$
$349$	−27.4904	−	7.36603i	−1.47153	−	0.394294i	−0.903454	+	0.428684i	$0.858977\pi$
$350$		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	−0.797457	−	0.603376i	$-0.793822\pi$
$353$	3.66088	−	13.6626i	0.194849	−	0.727186i	0.992306	−	0.123810i	$-0.0395113\pi$
$354$	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	0.999319	−	0.0368904i	$-0.0117452\pi$
$359$	18.2354	+	18.2354i	0.962429	+	0.962429i	−0.0368904	+	0.999319i	$0.511745\pi$
$360$		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	−0.991419	−	0.130723i	$-0.958270\pi$
$367$	−26.3205	+	15.1962i	−1.37392	+	0.793233i	−0.382500	+	0.923955i	$0.624937\pi$
$368$		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	0.217148	−	0.976139i	$-0.430325\pi$
$373$	−10.0359	−	5.79423i	−0.519639	−	0.300014i	−0.736787	+	0.676125i	$0.763658\pi$
$374$	−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	0.795069	+	0.606519i	$0.207435\pi$
$379$	−3.83013	+	14.2942i	−0.196740	+	0.734245i	−0.991809	+	0.127726i	$0.959232\pi$
$380$		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	−0.952341	−	0.305035i	$-0.901332\pi$
$383$	−31.7936	+	8.51906i	−1.62458	+	0.435304i	−0.672234	+	0.740339i	$0.734665\pi$
$384$	−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	−0.576501	−	0.817096i	$-0.695582\pi$
$397$	−13.2942	+	3.56218i	−0.667218	+	0.178781i	−0.0907168	+	0.995877i	$0.528916\pi$
$398$	−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	−0.837594	−	0.546294i	$-0.816038\pi$
$401$	3.22263	−	12.0270i	0.160931	−	0.600601i	0.998524	−	0.0543073i	$-0.0172951\pi$
$402$	−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	−0.890246	−	0.455480i	$-0.849468\pi$
$409$	−28.9904	+	7.76795i	−1.43348	+	0.384100i	−0.543236	+	0.839580i	$0.682801\pi$
$410$		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	−0.687452	−	0.726230i	$-0.741271\pi$
$419$	−8.23373	+	4.75374i	−0.402244	+	0.232236i	0.285208	+	0.958466i	$0.407937\pi$
$420$		0			0
$421$	−7.83013	−	7.83013i	−0.381617	−	0.381617i	0.490067	−	0.871685i	$-0.336972\pi$
$421$	−7.83013	−	7.83013i	−0.381617	−	0.381617i	−0.871685	+	0.490067i	$0.836972\pi$
$422$	2.62398	−	0.703093i	0.127733	−	0.0342260i
$423$	−18.0695	+	0.276369i	−0.878571	+	0.0134375i
$424$	−1.43782	+	1.43782i	−0.0698268	+	0.0698268i
$425$		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	0.986800	−	0.161944i	$-0.0517764\pi$
$431$	36.5473	+	9.79282i	1.76042	+	0.471704i	0.773622	+	0.633648i	$0.218443\pi$
$432$	18.7218	+	13.6951i	0.900754	+	0.658905i
$433$	15.5263	−	26.8923i	0.746145	−	1.29236i	−0.203512	−	0.979072i	$-0.565236\pi$
$433$	15.5263	−	26.8923i	0.746145	−	1.29236i	0.949658	−	0.313289i	$-0.101431\pi$
$434$	−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	−0.525975	−	0.850500i	$-0.676300\pi$
$439$	−1.09808	+	0.633975i	−0.0524083	+	0.0302580i	0.473567	+	0.880758i	$0.342966\pi$
$440$		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	−0.695165	−	0.718851i	$-0.744669\pi$
$449$	−19.8710	+	5.32441i	−0.937769	+	0.251275i	−0.242605	+	0.970125i	$0.578002\pi$
$450$		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	0.345868	−	0.938283i	$-0.387584\pi$
$457$	3.76795	+	1.00962i	0.176257	+	0.0472280i	−0.169611	+	0.985511i	$0.554251\pi$
$458$	−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	0.967302	+	0.253628i	$0.0816238\pi$
$461$	5.50531	+	20.5461i	0.256408	+	0.956927i	−0.710894	+	0.703299i	$0.751710\pi$
$462$	−9.14708	+	12.1113i	−0.425561	+	0.563471i
$463$	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
$465$		0			0
$466$	−25.3923	−	6.80385i	−1.17628	−	0.315182i
$467$		−	19.1679i		−	0.886984i	−0.896278	−	0.443492i	$-0.853739\pi$
$467$		−	19.1679i		−	0.886984i	0.896278	−	0.443492i	$-0.146261\pi$
$468$	−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	−0.730962	−	0.682418i	$-0.760928\pi$
$479$	5.32441	−	19.8710i	0.243279	−	0.907928i	0.974241	−	0.225510i	$-0.0724049\pi$
$480$		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	0.923902	−	0.382630i	$-0.124982\pi$
$487$	−1.49038	−	5.56218i	−0.0675356	−	0.252046i	−0.991437	+	0.130584i	$0.958315\pi$
$488$	−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	−0.984623	−	0.174693i	$-0.944107\pi$
$491$	−14.2612	−	24.7012i	−0.643600	−	1.11475i	0.341023	−	0.940055i	$-0.389227\pi$
$492$	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	0.760107	−	0.649798i	$-0.225147\pi$
$499$	2.46410	+	2.46410i	0.110308	+	0.110308i	−0.649798	+	0.760107i	$0.725147\pi$
$500$		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	−0.900182	−	0.435513i	$-0.856567\pi$
$503$	−1.63555	+	2.83286i	−0.0729256	+	0.126311i	0.827257	+	0.561824i	$0.189900\pi$
$504$	−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	0.558530	−	0.829484i	$-0.311366\pi$
$509$	14.1568	+	3.79330i	0.627489	+	0.168135i	0.0689588	+	0.997620i	$0.478032\pi$
$510$		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	$0.0173815\pi$
$521$			2.49155i			0.109157i	−0.998509	+	0.0545785i	$0.982618\pi$
$522$	15.7633	−	28.2934i	0.689939	−	1.23837i
$523$	−33.7583	+	19.4904i	−1.47615	+	0.852255i	−0.999638	−	0.0269137i	$-0.991432\pi$
$523$	−33.7583	+	19.4904i	−1.47615	+	0.852255i	−0.476511	+	0.879169i	$0.658099\pi$
$524$	−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	−0.925118	−	0.379681i	$-0.876034\pi$
$541$	−12.6865	+	12.6865i	−0.545437	+	0.545437i	0.379681	+	0.925118i	$0.376034\pi$
$542$	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	$-0.986386\pi$
$547$		−	2.00000i		−	0.0855138i	0.999086	−	0.0427569i	$-0.0136141\pi$
$548$	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	0.741346	−	0.671123i	$-0.234188\pi$
$557$	24.7292	+	6.62616i	1.04781	+	0.280759i	0.306462	+	0.951883i	$0.400855\pi$
$558$	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	0.304675	−	0.952456i	$-0.401452\pi$
$563$	−8.72794	−	5.03908i	−0.367839	−	0.212372i	−0.672514	+	0.740085i	$0.734785\pi$
$564$	−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	0.892939	−	0.450178i	$-0.148639\pi$
$569$	1.35022	+	2.33864i	0.0566040	+	0.0980411i	−0.836335	+	0.548219i	$0.815306\pi$
$570$		0			0
$571$		−	1.94744i		−	0.0814979i	−0.999169	−	0.0407489i	$-0.987026\pi$
$571$		−	1.94744i		−	0.0814979i	0.999169	−	0.0407489i	$-0.0129744\pi$
$572$	−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	−0.998088	−	0.0618016i	$-0.980315\pi$
$577$	−22.4904	+	22.4904i	−0.936287	+	0.936287i	0.0618016	+	0.998088i	$0.480315\pi$
$578$	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	0.791730	+	0.610871i	$0.209181\pi$
$587$	−4.83020	+	18.0265i	−0.199364	+	0.744035i	−0.991094	+	0.133164i	$0.957486\pi$
$588$	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	−0.461541	−	0.887119i	$-0.652703\pi$
$593$	10.3635	−	10.3635i	0.425578	−	0.425578i	0.887119	+	0.461541i	$0.152703\pi$
$594$	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	$0.139178\pi$
$599$			20.7270i			0.846881i	−0.905924	+	0.423441i	$0.860822\pi$
$600$		0			0
$601$	−11.7942	−	20.4282i	−0.481097	−	0.833284i	0.518668	−	0.854976i	$-0.326428\pi$
$601$	−11.7942	−	20.4282i	−0.481097	−	0.833284i	−0.999765	+	0.0216919i	$0.993095\pi$
$602$	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	0.496549	−	0.868009i	$-0.334600\pi$
$607$	−0.169873	−	0.0980762i	−0.00689493	−	0.00398079i	−0.503444	+	0.864028i	$0.667934\pi$
$608$	−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	−0.735951	−	0.677035i	$-0.763265\pi$
$613$	−42.3827	−	11.3564i	−1.71182	−	0.458681i	−0.975870	+	0.218354i	$0.929931\pi$
$614$	−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	0.118964	−	0.992899i	$-0.462043\pi$
$617$	17.8457	−	4.78173i	0.718439	−	0.192505i	0.599475	+	0.800393i	$0.295376\pi$
$618$	−14.4209	−	10.8914i	−0.580094	−	0.438115i
$619$	31.6603	−	31.6603i	1.27253	−	1.27253i	0.327778	−	0.944755i	$-0.393700\pi$
$619$	31.6603	−	31.6603i	1.27253	−	1.27253i	0.944755	−	0.327778i	$-0.106300\pi$
$620$		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	0.981102	+	0.193493i	$0.0619818\pi$
$631$	5.73205	+	21.3923i	0.228189	+	0.851614i	−0.752912	+	0.658121i	$0.771352\pi$
$632$	−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	0.0626345	−	0.998037i	$-0.480050\pi$
$641$	22.6758	−	39.2757i	0.895642	−	1.55130i	0.833008	−	0.553261i	$-0.186617\pi$
$642$	6.09776	−	49.2228i	0.240659	−	1.94267i
$643$	1.87564	+	7.00000i	0.0739682	+	0.276053i	0.992997	−	0.118136i	$-0.0376920\pi$
$643$	1.87564	+	7.00000i	0.0739682	+	0.276053i	−0.919029	+	0.394190i	$0.871025\pi$
$644$		0			0
$645$		0			0
$646$	14.6603	−	25.3923i	0.576800	−	0.999047i
$647$	−14.2612	+	8.23373i	−0.560667	+	0.323701i	−0.753413	−	0.657547i	$-0.771594\pi$
$647$	−14.2612	+	8.23373i	−0.560667	+	0.323701i	0.192746	+	0.981249i	$0.438261\pi$
$648$	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	0.755904	−	0.654683i	$-0.227198\pi$
$653$	−4.83020	−	8.36615i	−0.189020	−	0.327393i	−0.944924	+	0.327290i	$0.893865\pi$
$654$	−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	−0.0328158	−	0.999461i	$-0.510447\pi$
$659$	−23.4834	−	13.5581i	−0.914783	−	0.528150i	−0.881967	+	0.471311i	$0.843781\pi$
$660$		0			0
$661$	9.42820	+	2.52628i	0.366715	+	0.0982609i	0.437470	−	0.899233i	$-0.355874\pi$
$661$	9.42820	+	2.52628i	0.366715	+	0.0982609i	−0.0707559	+	0.997494i	$0.522541\pi$
$662$			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	−0.903265	−	0.429082i	$-0.858837\pi$
$673$	−21.3564	−	36.9904i	−0.823229	−	1.42587i	0.0800364	−	0.996792i	$-0.474496\pi$
$674$	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	−0.659536	−	0.751673i	$-0.729247\pi$
$683$	−12.1315	−	45.2752i	−0.464198	−	1.73241i	0.195338	−	0.980736i	$-0.437420\pi$
$684$	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	−0.808723	−	0.588189i	$-0.799841\pi$
$691$	4.88269	−	18.2224i	0.185746	−	0.693214i	0.994470	−	0.105025i	$-0.0334922\pi$
$692$	−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	0.999211	−	0.0397068i	$-0.0126424\pi$
$709$	3.03590	+	11.3301i	0.114016	+	0.425512i	−0.885196	+	0.465219i	$0.845976\pi$
$710$		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	−0.789005	−	0.614386i	$-0.789404\pi$
$719$	3.68886	−	6.38929i	0.137571	−	0.238280i	0.926577	+	0.376106i	$0.122737\pi$
$720$		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	−0.570773	−	0.821108i	$-0.693356\pi$
$733$	6.77757	−	6.77757i	0.250335	−	0.250335i	0.821108	+	0.570773i	$0.193356\pi$
$734$	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	0.457554	−	0.889182i	$-0.348726\pi$
$739$	11.1244	+	2.98076i	0.409216	+	0.109649i	−0.0483378	+	0.998831i	$0.515392\pi$
$740$		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	−0.995073	−	0.0991426i	$-0.968390\pi$
$743$	−2.28268	+	8.51906i	−0.0837432	+	0.312534i	0.911330	+	0.411677i	$0.135057\pi$
$744$	−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	−0.927705	−	0.373313i	$-0.878222\pi$
$751$	−29.2750	+	16.9019i	−1.06826	+	0.616760i	−0.140554	+	0.990073i	$0.544888\pi$
$752$	−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	−0.740331	−	0.672243i	$-0.765331\pi$
$757$	−14.5359	+	8.39230i	−0.528316	+	0.305024i	0.212014	+	0.977267i	$0.431998\pi$
$758$	19.3003	+	11.1430i	0.701019	+	0.404733i
$759$		0			0
$760$		0			0
$761$	−17.7412	+	4.75374i	−0.643118	+	0.172323i	−0.565616	−	0.824669i	$-0.691361\pi$
$761$	−17.7412	+	4.75374i	−0.643118	+	0.172323i	−0.0775029	+	0.996992i	$0.524695\pi$
$762$	−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	−0.438694	−	0.898636i	$-0.644559\pi$
$769$	10.8301	−	40.4186i	0.390544	−	1.45753i	0.829238	−	0.558895i	$-0.188775\pi$
$770$		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	0.584081	−	0.811695i	$-0.301455\pi$
$773$	41.5864	−	11.1430i	1.49576	−	0.400787i	0.911677	+	0.410908i	$0.134788\pi$
$774$	−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	0.0383938	−	0.999263i	$-0.487776\pi$
$787$	16.0263	−	4.29423i	0.571275	−	0.153073i	0.532881	+	0.846190i	$0.321109\pi$
$788$	−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	0.968405	−	0.249381i	$-0.0802272\pi$
$797$	34.9118	+	20.1563i	1.23664	+	0.713973i	0.268232	+	0.963354i	$0.413561\pi$
$798$	−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	−0.0141514	−	0.999900i	$-0.504505\pi$
$809$	24.0261	−	13.8715i	0.844712	−	0.487694i	0.858863	+	0.512205i	$0.171171\pi$
$810$		0			0
$811$	19.0000	+	19.0000i	0.667180	+	0.667180i	0.957062	−	0.289882i	$-0.0936161\pi$
$811$	19.0000	+	19.0000i	0.667180	+	0.667180i	−0.289882	+	0.957062i	$0.593616\pi$
$812$	2.62398	−	0.703093i	0.0920836	−	0.0246737i
$813$	8.06639	−	10.6804i	0.282901	−	0.374579i
$814$	23.7321	−	23.7321i	0.831808	−	0.831808i
$815$		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	0.896502	−	0.443040i	$-0.146100\pi$
$821$	41.5864	+	11.1430i	1.45137	+	0.388895i	0.554873	+	0.831935i	$0.312767\pi$
$822$	6.58662	−	16.2519i	0.229735	−	0.566850i
$823$	4.26795	−	7.39230i	0.148771	−	0.257680i	−0.782002	−	0.623276i	$-0.785801\pi$
$823$	4.26795	−	7.39230i	0.148771	−	0.257680i	0.930774	+	0.365596i	$0.119135\pi$
$824$	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	0.111845	−	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	$-0.981613\pi$
$829$	−41.6769	+	24.0622i	−1.44750	+	0.835714i	−0.449167	+	0.893448i	$0.648279\pi$
$830$		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	−0.423868	−	0.905724i	$-0.639328\pi$
$839$	−9.79282	+	2.62398i	−0.338086	+	0.0905898i	0.0857819	+	0.996314i	$0.472661\pi$
$840$		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	0.211566	−	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
$855$		0			0
$856$	47.9090	+	12.8372i	1.63749	+	0.438765i
$857$			3.32707i			0.113651i	0.998384	+	0.0568253i	$0.0180978\pi$
$857$			3.32707i			0.113651i	−0.998384	+	0.0568253i	$0.981902\pi$
$858$	−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	0.945721	−	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
$865$		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	−0.963879	−	0.266339i	$-0.914186\pi$
$877$	−7.76795	−	28.9904i	−0.262305	−	0.978936i	0.701574	−	0.712596i	$-0.252481\pi$
$878$	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	0.597588	−	0.801803i	$-0.296126\pi$
$881$	−11.7417	−	20.3372i	−0.395588	−	0.685178i	−0.993176	+	0.116625i	$0.962792\pi$
$882$	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	0.572391	−	0.819981i	$-0.306016\pi$
$887$	−12.6257	−	21.8683i	−0.423929	−	0.734266i	−0.996320	+	0.0857146i	$0.972683\pi$
$888$	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	0.973227	−	0.229848i	$-0.0738229\pi$
$907$	8.66025	+	15.0000i	0.287559	+	0.498067i	−0.685668	+	0.727915i	$0.740490\pi$
$908$	5.24796	+	1.40619i	0.174160	+	0.0466659i
$909$	4.41244	−	17.5359i	0.146351	−	0.581629i
$910$		0			0
$911$		−	1.55910i		−	0.0516552i	−0.999666	−	0.0258276i	$-0.991778\pi$
$911$		−	1.55910i		−	0.0516552i	0.999666	−	0.0258276i	$-0.00822209\pi$
$912$	−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	−0.733971	−	0.679181i	$-0.762335\pi$
$919$	6.70577	−	11.6147i	0.221203	−	0.383135i	0.955174	+	0.296046i	$0.0956683\pi$
$920$		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	−0.996868	−	0.0790861i	$-0.974800\pi$
$929$	−5.27594	−	19.6901i	−0.173098	−	0.646011i	0.823770	−	0.566924i	$-0.191867\pi$
$930$		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	$0.206575\pi$
$937$			37.0000i			1.20874i	−0.796705	+	0.604369i	$0.793425\pi$
$938$	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	−0.542144	−	0.840285i	$-0.682387\pi$
$941$	9.14570	−	9.14570i	0.298141	−	0.298141i	0.840285	+	0.542144i	$0.182387\pi$
$942$	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	0.0864720	−	0.996254i	$-0.472441\pi$
$947$	−10.3635	−	2.77689i	−0.336768	−	0.0902368i	−0.423240	+	0.906018i	$0.639107\pi$
$948$	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	0.527472	−	0.849572i	$-0.323140\pi$
$953$	1.71201	+	0.988427i	0.0554573	+	0.0320183i	−0.472015	+	0.881591i	$0.656473\pi$
$954$	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	−0.995062	−	0.0992599i	$-0.968352\pi$
$967$	−27.8564	+	27.8564i	−0.895802	+	0.895802i	0.0992599	+	0.995062i	$0.468352\pi$
$968$	−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	−0.344416	−	0.938817i	$-0.611923\pi$
$971$	−41.4335	−	23.9216i	−1.32966	−	0.767682i	−0.985247	+	0.171136i	$0.945256\pi$
$972$	−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	0.795780	+	0.605585i	$0.207061\pi$
$977$	−6.13194	+	22.8847i	−0.196178	+	0.732147i	−0.991959	+	0.126562i	$0.959606\pi$
$978$	−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	−0.999591	−	0.0285990i	$-0.990895\pi$
$983$	−30.4433	+	30.4433i	−0.970992	+	0.970992i	0.0285990	+	0.999591i	$0.490895\pi$
$984$	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	0.807816	+	0.589434i	$0.200649\pi$
$991$	28.7846	+	49.8564i	0.914373	+	1.58374i	0.106557	+	0.994307i	$0.466017\pi$
$992$	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	0.400923	−	0.916112i	$-0.368689\pi$
$997$	−6.06218	−	3.50000i	−0.191991	−	0.110846i	−0.592914	+	0.805266i	$0.702023\pi$
$998$	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.674.2		8
3.2	odd	2	inner	975.2.bp.f.674.1		8
5.2	odd	4		39.2.k.b.11.2	yes	8
5.3	odd	4		975.2.bo.d.401.1		8
5.4	even	2		975.2.bp.e.674.1		8
13.6	odd	12		975.2.bp.e.149.2		8
15.2	even	4		39.2.k.b.11.1	✓	8
15.8	even	4		975.2.bo.d.401.2		8
15.14	odd	2		975.2.bp.e.674.2		8
20.7	even	4		624.2.cn.c.401.2		8
39.32	even	12		975.2.bp.e.149.1		8
60.47	odd	4		624.2.cn.c.401.1		8
65.2	even	12		507.2.f.f.239.3		8
65.7	even	12		507.2.k.d.188.2		8
65.12	odd	4		507.2.k.d.89.1		8
65.17	odd	12		507.2.k.f.488.2		8
65.19	odd	12	inner	975.2.bp.f.149.1		8
65.22	odd	12		507.2.k.e.488.1		8
65.32	even	12		39.2.k.b.32.1	yes	8
65.37	even	12		507.2.f.e.239.2		8
65.42	odd	12		507.2.f.f.437.2		8
65.47	even	4		507.2.k.f.80.1		8
65.57	even	4		507.2.k.e.80.2		8
65.58	even	12		975.2.bo.d.851.2		8
65.62	odd	12		507.2.f.e.437.3		8
195.2	odd	12		507.2.f.f.239.2		8
195.17	even	12		507.2.k.f.488.1		8
195.32	odd	12		39.2.k.b.32.2	yes	8
195.47	odd	4		507.2.k.f.80.2		8
195.62	even	12		507.2.f.e.437.2		8
195.77	even	4		507.2.k.d.89.2		8
195.107	even	12		507.2.f.f.437.3		8
195.122	odd	4		507.2.k.e.80.1		8
195.137	odd	12		507.2.k.d.188.1		8
195.149	even	12	inner	975.2.bp.f.149.2		8
195.152	even	12		507.2.k.e.488.2		8
195.167	odd	12		507.2.f.e.239.3		8
195.188	odd	12		975.2.bo.d.851.1		8
260.227	odd	12		624.2.cn.c.305.1		8
780.227	even	12		624.2.cn.c.305.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.k.b.11.1	✓	8	15.2	even	4
39.2.k.b.11.2	yes	8	5.2	odd	4
39.2.k.b.32.1	yes	8	65.32	even	12
39.2.k.b.32.2	yes	8	195.32	odd	12
507.2.f.e.239.2		8	65.37	even	12
507.2.f.e.239.3		8	195.167	odd	12
507.2.f.e.437.2		8	195.62	even	12
507.2.f.e.437.3		8	65.62	odd	12
507.2.f.f.239.2		8	195.2	odd	12
507.2.f.f.239.3		8	65.2	even	12
507.2.f.f.437.2		8	65.42	odd	12
507.2.f.f.437.3		8	195.107	even	12
507.2.k.d.89.1		8	65.12	odd	4
507.2.k.d.89.2		8	195.77	even	4
507.2.k.d.188.1		8	195.137	odd	12
507.2.k.d.188.2		8	65.7	even	12
507.2.k.e.80.1		8	195.122	odd	4
507.2.k.e.80.2		8	65.57	even	4
507.2.k.e.488.1		8	65.22	odd	12
507.2.k.e.488.2		8	195.152	even	12
507.2.k.f.80.1		8	65.47	even	4
507.2.k.f.80.2		8	195.47	odd	4
507.2.k.f.488.1		8	195.17	even	12
507.2.k.f.488.2		8	65.17	odd	12
624.2.cn.c.305.1		8	260.227	odd	12
624.2.cn.c.305.2		8	780.227	even	12
624.2.cn.c.401.1		8	60.47	odd	4
624.2.cn.c.401.2		8	20.7	even	4
975.2.bo.d.401.1		8	5.3	odd	4
975.2.bo.d.401.2		8	15.8	even	4
975.2.bo.d.851.1		8	195.188	odd	12
975.2.bo.d.851.2		8	65.58	even	12
975.2.bp.e.149.1		8	39.32	even	12
975.2.bp.e.149.2		8	13.6	odd	12
975.2.bp.e.674.1		8	5.4	even	2
975.2.bp.e.674.2		8	15.14	odd	2
975.2.bp.f.149.1		8	65.19	odd	12	inner
975.2.bp.f.149.2		8	195.149	even	12	inner
975.2.bp.f.674.1		8	3.2	odd	2	inner
975.2.bp.f.674.2		8	1.1	even	1	trivial

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

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