LMFDB - Embedded newform 975.2.bp.f.674.1

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			674.1
Root			$0.500000 - 0.564882i$ of defining polynomial
Character	$\chi$	$=$	975.674
Dual form			975.2.bp.f.149.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.389774 + 1.45466i) q^{2} +(1.71545 + 0.239203i) q^{3} +(-0.232051 - 0.133975i) q^{4} +(-1.01660 + 2.40216i) q^{6} +(1.36603 - 0.366025i) q^{7} +(-1.84443 + 1.84443i) q^{8} +(2.88556 + 0.820682i) q^{9} +O(q^{10})$	\(q+(-0.389774 + 1.45466i) q^{2} +(1.71545 + 0.239203i) q^{3} +(-0.232051 - 0.133975i) q^{4} +(-1.01660 + 2.40216i) q^{6} +(1.36603 - 0.366025i) q^{7} +(-1.84443 + 1.84443i) q^{8} +(2.88556 + 0.820682i) 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} +(-2.31853 + 3.87762i) q^{18} +(3.73205 - 1.00000i) q^{19} +(2.43091 - 0.301143i) q^{21} +(-5.36603 - 3.09808i) q^{22} +(-3.60523 + 2.72284i) 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} +(-2.77739 + 6.56283i) q^{33} +(5.36603 - 5.36603i) q^{34} +(-0.559647 - 0.577032i) q^{36} +(-1.40192 + 5.23205i) q^{37} +5.81863i q^{38} +(-1.25874 + 6.11683i) q^{39} +(5.42885 + 1.45466i) q^{41} +(-0.509445 + 3.65351i) q^{42} +(-1.09808 + 1.90192i) q^{43} +(0.779548 - 0.779548i) q^{44} +(-4.25953 + 4.25953i) q^{47} +(-2.90422 - 7.16590i) q^{48} +(-4.33013 + 2.50000i) q^{49} +(-6.88351 - 5.36603i) q^{51} +(0.535898 - 0.803848i) q^{52} +0.779548 q^{53} +(-4.90487 + 6.09729i) q^{54} +(-1.84443 + 3.19465i) q^{56} +(6.64136 - 0.822738i) 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} +(4.24214 + 0.0648824i) 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} +(-6.83591 + 3.80853i) q^{72} +(-0.901924 - 0.901924i) q^{73} +(-7.06440 - 4.07863i) q^{74} +(-1.00000 - 0.267949i) q^{76} +5.81863i q^{77} +(-8.40726 - 4.21522i) q^{78} -2.00000 q^{79} +(7.65296 + 4.73626i) q^{81} +(-4.23205 + 7.33013i) q^{82} +(2.90931 + 2.90931i) q^{83} +(-0.604440 - 0.255799i) q^{84} +(-2.33864 - 2.33864i) q^{86} +(11.5076 - 4.66384i) q^{87} +(-5.36603 - 9.29423i) q^{88} +(2.41510 - 9.01327i) q^{89} +(1.00000 + 5.00000i) q^{91} +(-3.63763 - 4.81647i) q^{93} +(-4.53590 - 7.85641i) q^{94} +(2.58863 - 0.320682i) q^{96} +(-0.437822 - 1.63397i) q^{97} +(-1.94887 - 7.27328i) q^{98} +(-6.33434 + 10.5939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 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	$0.262059\pi$
$2$	−0.389774	+	1.45466i	−0.275612	+	1.02860i	−0.955430	+	0.295217i	$0.904608\pi$
$3$	1.71545	+	0.239203i	0.990418	+	0.138104i
$3$	1.71545	+	0.239203i	0.990418	+	0.138104i
$4$	−0.232051	−	0.133975i	−0.116025	−	0.0669873i
$5$		0			0
$5$		0			0
$6$	−1.01660	+	2.40216i	−0.415024	+	0.980678i
$7$	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
$9$	2.88556	+	0.820682i	0.961855	+	0.273561i
$10$		0			0
$11$	−1.06488	+	3.97420i	−0.321074	+	1.19826i	0.597126	+	0.802148i	$0.296309\pi$
$11$	−1.06488	+	3.97420i	−0.321074	+	1.19826i	−0.918200	+	0.396117i	$0.870357\pi$
$12$	−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	$-0.542597\pi$
$17$	−4.36397	−	2.51954i	−1.05842	−	0.611078i	−0.924994	+	0.379981i	$0.875930\pi$
$18$	−2.31853	+	3.87762i	−0.546482	+	0.913965i
$19$	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
$21$	2.43091	−	0.301143i	0.530468	−	0.0657148i
$22$	−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	$0.333333\pi$
$24$	−3.60523	+	2.72284i	−0.735914	+	0.555798i
$25$		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	$-0.434838\pi$
$29$	6.20840	−	3.58442i	1.15287	−	0.665610i	0.949585	+	0.313509i	$0.101505\pi$
$30$		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
$33$	−2.77739	+	6.56283i	−0.483482	+	1.14244i
$34$	5.36603	−	5.36603i	0.920266	−	0.920266i
$35$		0			0
$36$	−0.559647	−	0.577032i	−0.0932745	−	0.0961720i
$37$	−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
$39$	−1.25874	+	6.11683i	−0.201560	+	0.979476i
$40$		0			0
$41$	5.42885	+	1.45466i	0.847844	+	0.227179i	0.656483	−	0.754341i	$-0.272043\pi$
$41$	5.42885	+	1.45466i	0.847844	+	0.227179i	0.191361	+	0.981520i	$0.438710\pi$
$42$	−0.509445	+	3.65351i	−0.0786091	+	0.563749i
$43$	−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	−0.945868	−	0.324552i	$-0.894787\pi$
$47$	−4.25953	+	4.25953i	−0.621316	+	0.621316i	0.324552	+	0.945868i	$0.394787\pi$
$48$	−2.90422	−	7.16590i	−0.419188	−	1.03431i
$49$	−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	$-0.482950\pi$
$53$	0.779548			0.107079			0.0535396	+	0.998566i	$0.482950\pi$
$54$	−4.90487	+	6.09729i	−0.667468	+	0.829736i
$55$		0			0
$56$	−1.84443	+	3.19465i	−0.246472	+	0.426903i
$57$	6.64136	−	0.822738i	0.879670	−	0.108974i
$58$	2.79423	+	10.4282i	0.366900	+	1.36929i
$59$	2.90931	−	0.779548i	0.378760	−	0.101489i	−0.0644157	−	0.997923i	$-0.520518\pi$
$59$	2.90931	−	0.779548i	0.378760	−	0.101489i	0.443176	+	0.896435i	$0.353852\pi$
$60$		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
$63$	4.24214	+	0.0648824i	0.534460	+	0.00817442i
$64$		−	6.66025i		−	0.832532i
$65$		0			0
$66$	−8.46410	−	6.59817i	−1.04186	−	0.812179i
$67$	5.73205	+	1.53590i	0.700281	+	0.187640i	0.591357	−	0.806410i	$-0.298593\pi$
$67$	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	0.904116	−	0.427288i	$-0.140531\pi$
$71$	−0.779548	−	2.90931i	−0.0925153	−	0.345272i	−0.996631	+	0.0820158i	$0.973864\pi$
$72$	−6.83591	+	3.80853i	−0.805620	+	0.448840i
$73$	−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
$78$	−8.40726	−	4.21522i	−0.951934	−	0.477279i
$79$	−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
$81$	7.65296	+	4.73626i	0.850329	+	0.526251i
$82$	−4.23205	+	7.33013i	−0.467352	+	0.809477i
$83$	2.90931	+	2.90931i	0.319339	+	0.319339i	0.848513	−	0.529174i	$-0.177498\pi$
$83$	2.90931	+	2.90931i	0.319339	+	0.319339i	−0.529174	+	0.848513i	$0.677498\pi$
$84$	−0.604440	−	0.255799i	−0.0659498	−	0.0279100i
$85$		0			0
$86$	−2.33864	−	2.33864i	−0.252182	−	0.252182i
$87$	11.5076	−	4.66384i	1.23375	−	0.500017i
$88$	−5.36603	−	9.29423i	−0.572020	−	0.990768i
$89$	2.41510	−	9.01327i	0.256000	−	0.955405i	−0.711531	−	0.702654i	$-0.751998\pi$
$89$	2.41510	−	9.01327i	0.256000	−	0.955405i	0.967531	−	0.252751i	$-0.0813353\pi$
$90$		0			0
$91$	1.00000	+	5.00000i	0.104828	+	0.524142i
$92$		0			0
$93$	−3.63763	−	4.81647i	−0.377205	−	0.499445i
$94$	−4.53590	−	7.85641i	−0.467842	−	0.810326i
$95$		0			0
$96$	2.58863	−	0.320682i	0.264201	−	0.0327295i
$97$	−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
$99$	−6.33434	+	10.5939i	−0.636625	+	1.06472i
$100$		0			0
$101$	−3.01375	−	5.21997i	−0.299880	−	0.519407i	0.676229	−	0.736692i	$-0.263613\pi$
$101$	−3.01375	−	5.21997i	−0.299880	−	0.519407i	−0.976108	+	0.217285i	$0.930280\pi$
$102$	10.4887	−	7.92160i	1.03854	−	0.784356i
$103$	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	$-0.795565\pi$
$107$	−9.50749	−	16.4675i	−0.919123	−	1.59197i	−0.118374	−	0.992969i	$-0.537768\pi$
$108$	−0.822021	−	1.12374i	−0.0790990	−	0.108132i
$109$	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
$111$	−3.65646	+	8.64000i	−0.347055	+	0.820072i
$112$	−4.46410	−	4.46410i	−0.421818	−	0.421818i
$113$	5.14352	−	8.90883i	0.483861	−	0.838073i	−0.515967	−	0.856609i	$-0.672567\pi$
$113$	5.14352	−	8.90883i	0.483861	−	0.838073i	0.999828	+	0.0185360i	$0.00590054\pi$
$114$	−1.39183	+	9.98158i	−0.130357	+	0.934861i
$115$		0			0
$116$	−1.92089			−0.178350
$117$	−3.62247	+	10.1920i	−0.334898	+	0.942254i
$118$			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
$123$	8.96499	+	3.79399i	0.808346	+	0.342093i
$124$	0.241670	+	0.901924i	0.0217026	+	0.0809951i
$125$		0			0
$126$	−1.74786	+	6.14557i	−0.155712	+	0.547491i
$127$	−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	$0.112877\pi$
$131$			7.94839i			0.694454i	−0.937781	+	0.347227i	$0.887123\pi$
$132$	1.52375	−	1.15081i	0.132625	−	0.100165i
$133$	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	$-0.990614\pi$
$137$	−1.73999	−	6.49373i	−0.148657	−	0.554797i	0.850908	−	0.525315i	$-0.176052\pi$
$138$		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
$141$	−8.32592	+	6.28814i	−0.701169	+	0.529557i
$142$	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
$147$	−8.02614	+	3.25286i	−0.661985	+	0.268291i
$148$	1.02628	−	1.02628i	0.0843597	−	0.0843597i
$149$	−2.23420	−	8.33816i	−0.183033	−	0.683089i	−0.995043	−	0.0994454i	$-0.968293\pi$
$149$	−2.23420	−	8.33816i	−0.183033	−	0.683089i	0.812010	−	0.583644i	$-0.198374\pi$
$150$		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
$153$	−10.5248	−	10.8517i	−0.850878	−	0.877310i
$154$	−8.46410	−	2.26795i	−0.682057	−	0.182757i
$155$		0			0
$156$	1.11159	−	1.25078i	0.0889985	−	0.100142i
$157$			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
$159$	1.33728	+	0.186470i	0.106053	+	0.0147880i
$160$		0			0
$161$		0			0
$162$	−9.87256	+	9.28636i	−0.775661	+	0.729605i
$163$	4.00000	−	1.07180i	0.313304	−	0.0839496i	−0.0987406	−	0.995113i	$-0.531481\pi$
$163$	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	−0.281461	−	0.959573i	$-0.590819\pi$
$167$	−12.9875	−	3.47998i	−1.00500	−	0.269289i	−0.723539	+	0.690283i	$0.757486\pi$
$168$	−3.92820	+	5.03908i	−0.303067	+	0.388773i
$169$	−12.8923	−	1.66987i	−0.991716	−	0.128452i
$170$		0			0
$171$	11.5898	+	0.177262i	0.886291	+	0.0135556i
$172$	0.509619	−	0.294229i	0.0388581	−	0.0224347i
$173$	−15.1172	−	8.72794i	−1.14934	−	0.663573i	−0.200615	−	0.979670i	$-0.564294\pi$
$173$	−15.1172	−	8.72794i	−1.14934	−	0.663573i	−0.948727	+	0.316097i	$0.897627\pi$
$174$	2.29892	+	18.5575i	0.174281	+	1.40684i
$175$		0			0
$176$	17.7412	−	4.75374i	1.33729	−	0.358327i
$177$	5.17726	−	0.641364i	0.389147	−	0.0482078i
$178$	12.1699	+	7.02628i	0.912171	+	0.526642i
$179$	13.2728	+	22.9892i	0.992056	+	1.71829i	0.604972	+	0.796247i	$0.293184\pi$
$179$	13.2728	+	22.9892i	0.992056	+	1.71829i	0.387084	+	0.922045i	$0.373482\pi$
$180$		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
$186$	8.42417	−	3.41417i	0.617690	−	0.250339i
$187$	14.6603	−	14.6603i	1.07206	−	1.07206i
$188$	1.55910	−	0.417759i	0.113709	−	0.0304682i
$189$	7.26168	+	1.12603i	0.528210	+	0.0819070i
$190$		0			0
$191$	4.18307	+	2.41510i	0.302677	+	0.174750i	0.643645	−	0.765324i	$-0.277421\pi$
$191$	4.18307	+	2.41510i	0.302677	+	0.174750i	−0.340968	+	0.940075i	$0.610755\pi$
$192$	1.59315	−	11.4254i	0.114976	−	0.824554i
$193$	−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	−0.993429	−	0.114449i	$-0.963490\pi$
$197$	−1.06488	+	3.97420i	−0.0758697	+	0.283150i	0.917559	+	0.397599i	$0.130156\pi$
$198$	−12.9415	−	13.3435i	−0.919711	−	0.948281i
$199$	−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
$201$	9.46568	+	4.00588i	0.667657	+	0.282553i
$202$	8.76795	−	2.34936i	0.616911	−	0.165301i
$203$	7.16884	−	7.16884i	0.503154	−	0.503154i
$204$	0.878413	+	2.16741i	0.0615012	+	0.151749i
$205$		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
$213$	−0.641364	−	5.17726i	−0.0439455	−	0.354740i
$214$	27.6603	−	7.41154i	1.89082	−	0.506643i
$215$		0			0
$216$	−12.6377	+	4.89819i	−0.859887	+	0.333280i
$217$	−4.26795	−	2.46410i	−0.289727	−	0.167274i
$218$	−24.3394	+	14.0524i	−1.64847	+	0.951745i
$219$	−1.33147	−	1.76295i	−0.0899722	−	0.119129i
$220$		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	0.458515	−	0.888686i	$-0.348381\pi$
$227$	19.5856	−	5.24796i	1.29994	−	0.348319i	0.841429	+	0.540367i	$0.181715\pi$
$228$	−1.65136	−	0.698857i	−0.109364	−	0.0462829i
$229$	14.1244	−	14.1244i	0.933364	−	0.933364i	−0.0645507	−	0.997914i	$-0.520561\pi$
$229$	14.1244	−	14.1244i	0.933364	−	0.933364i	0.997914	+	0.0645507i	$0.0205614\pi$
$230$		0			0
$231$	−1.39183	+	9.98158i	−0.0915757	+	0.656740i
$232$	−4.83975	+	18.0622i	−0.317745	+	1.18584i
$233$			17.4559i			1.14357i	0.820403	+	0.571786i	$0.193749\pi$
$233$			17.4559i			1.14357i	−0.820403	+	0.571786i	$0.806251\pi$
$234$	−13.4140	−	9.24205i	−0.876899	−	0.604172i
$235$		0			0
$236$	−0.779548	−	0.208879i	−0.0507443	−	0.0135969i
$237$	−3.43091	−	0.478405i	−0.222861	−	0.0310757i
$238$	5.36603	−	9.29423i	0.347828	−	0.602455i
$239$	−6.59817	+	6.59817i	−0.426800	+	0.426800i	−0.887537	−	0.460737i	$-0.847585\pi$
$239$	−6.59817	+	6.59817i	−0.426800	+	0.426800i	0.460737	+	0.887537i	$0.347585\pi$
$240$		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
$243$	11.9954	+	9.95544i	0.769504	+	0.638642i
$244$	−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
$249$	4.29488	+	5.68671i	0.272177	+	0.360380i
$250$		0			0
$251$	0.494214	−	0.856003i	0.0311945	−	0.0540304i	−0.850007	−	0.526772i	$-0.823402\pi$
$251$	0.494214	−	0.856003i	0.0311945	−	0.0540304i	0.881201	+	0.472741i	$0.156736\pi$
$252$	−0.975700	−	0.583396i	−0.0614634	−	0.0367505i
$253$		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	$-0.432630\pi$
$257$	18.6252	−	10.7533i	1.16181	−	0.670770i	0.951737	+	0.306916i	$0.0992970\pi$
$258$	−3.45243	−	4.57125i	−0.214939	−	0.284593i
$259$			7.66025i			0.475985i
$260$		0			0
$261$	20.8564	−	5.24796i	1.29098	−	0.324840i
$262$	−11.5622	−	3.09808i	−0.714314	−	0.191400i
$263$	−11.1430	−	19.3003i	−0.687109	−	1.19011i	−0.972769	−	0.231777i	$-0.925546\pi$
$263$	−11.1430	−	19.3003i	−0.687109	−	1.19011i	0.285660	−	0.958331i	$-0.407787\pi$
$264$	−6.98197	−	17.2274i	−0.429710	−	1.06027i
$265$		0			0
$266$	2.12976	+	7.94839i	0.130584	+	0.487347i
$267$	6.29899	−	14.8842i	0.385492	−	0.910896i
$268$	−1.12436	−	1.12436i	−0.0686810	−	0.0686810i
$269$	12.4168	+	7.16884i	0.757066	+	0.437092i	0.828241	−	0.560372i	$-0.189342\pi$
$269$	12.4168	+	7.16884i	0.757066	+	0.437092i	−0.0711756	+	0.997464i	$0.522675\pi$
$270$		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
$273$	0.519441	+	8.81647i	0.0314380	+	0.533597i
$274$	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
$279$	−5.08808	−	9.13257i	−0.304615	−	0.546752i
$280$		0			0
$281$	−12.1315	−	12.1315i	−0.723703	−	0.723703i	0.245655	−	0.969357i	$-0.420997\pi$
$281$	−12.1315	−	12.1315i	−0.723703	−	0.723703i	−0.969357	+	0.245655i	$0.920997\pi$
$282$	−5.90185	−	14.5623i	−0.351450	−	0.867172i
$283$	−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
$288$	4.51739	+	0.0690922i	0.266189	+	0.00407129i
$289$	4.19615	+	7.26795i	0.246832	+	0.427526i
$290$		0			0
$291$	−0.360213	−	2.90774i	−0.0211161	−	0.170455i
$292$	0.0884573	+	0.330127i	0.00517657	+	0.0193192i
$293$	−0.466229	−	1.73999i	−0.0272374	−	0.101651i	0.950969	−	0.309286i	$-0.100090\pi$
$293$	−0.466229	−	1.73999i	−0.0272374	−	0.101651i	−0.978206	+	0.207635i	$0.933423\pi$
$294$	−1.60341	−	12.9432i	−0.0935127	−	0.754860i
$295$		0			0
$296$	−7.06440	−	12.2359i	−0.410610	−	0.711198i
$297$	−13.4003	+	16.6581i	−0.777567	+	0.966601i
$298$	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
$303$	−3.92132	−	9.67552i	−0.225274	−	0.555844i
$304$	−12.1962	−	12.1962i	−0.699497	−	0.699497i
$305$		0			0
$306$	19.8878	−	11.0802i	1.13691	−	0.633414i
$307$	−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
$309$	11.8850	+	1.65724i	0.676115	+	0.0942773i
$310$		0			0
$311$	10.0782			0.571480			0.285740	−	0.958307i	$-0.407761\pi$
$311$	10.0782			0.571480			0.285740	+	0.958307i	$0.407761\pi$
$312$	−8.96040	−	13.6037i	−0.507283	−	0.770159i
$313$			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	0.949960	−	0.312373i	$-0.101124\pi$
$317$	11.3519	+	11.3519i	0.637587	+	0.637587i	−0.312373	+	0.949960i	$0.601124\pi$
$318$	−0.792486	+	1.87260i	−0.0444404	+	0.105010i
$319$	7.63397	+	28.4904i	0.427421	+	1.59516i
$320$		0			0
$321$	−12.3706	−	30.5234i	−0.690460	−	1.70365i
$322$		0			0
$323$	−18.8061	−	5.03908i	−1.04640	−	0.280382i
$324$	−1.14134	−	2.12436i	−0.0634076	−	0.118020i
$325$		0			0
$326$			6.23638i			0.345401i
$327$	19.4808	+	25.7939i	1.07729	+	1.42641i
$328$	−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
$333$	−8.33919	+	13.9469i	−0.456985	+	0.764285i
$334$	10.1244	−	17.5359i	0.553980	−	0.959522i
$335$		0			0
$336$	−6.59014	−	8.72579i	−0.359521	−	0.476031i
$337$	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
$342$	−4.77524	+	16.7900i	−0.258215	+	0.907900i
$343$	−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	$-0.647108\pi$
$347$	10.2870	−	17.8177i	0.552237	−	0.956502i	0.998113	−	0.0614076i	$-0.0195590\pi$
$348$	−3.29519	−	0.459481i	−0.176641	−	0.0246308i
$349$	−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
$351$	−8.65215	+	16.6175i	−0.461818	+	0.886975i
$352$			6.19615i			0.330256i
$353$	−3.66088	+	13.6626i	−0.194849	+	0.727186i	0.797457	+	0.603376i	$0.206178\pi$
$353$	−3.66088	+	13.6626i	−0.194849	+	0.727186i	−0.992306	+	0.123810i	$0.960489\pi$
$354$	−1.08500	+	7.78112i	−0.0576670	+	0.413562i
$355$		0			0
$356$	−1.76798	+	1.76798i	−0.0937025	+	0.0937025i
$357$	−11.3671	−	4.81059i	−0.601613	−	0.254603i
$358$	−38.6147	+	10.3468i	−2.04085	+	0.546845i
$359$	−18.2354	−	18.2354i	−0.962429	−	0.962429i	0.0368904	−	0.999319i	$-0.488255\pi$
$359$	−18.2354	−	18.2354i	−0.962429	−	0.962429i	−0.999319	+	0.0368904i	$0.988255\pi$
$360$		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
$366$	11.0042	+	14.5704i	0.575201	+	0.761605i
$367$	−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
$369$	14.4715	+	8.65286i	0.753356	+	0.450450i
$370$		0			0
$371$	1.06488	−	0.285334i	0.0552859	−	0.0148138i
$372$	0.198831	+	1.60502i	0.0103089	+	0.0832162i
$373$	−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
$381$	−5.93605	−	14.6467i	−0.304113	−	0.750372i
$382$	−5.14359	+	5.14359i	−0.263169	+	0.263169i
$383$	31.7936	−	8.51906i	1.62458	−	0.435304i	0.672234	−	0.740339i	$-0.265335\pi$
$383$	31.7936	−	8.51906i	1.62458	−	0.435304i	0.952341	+	0.305035i	$0.0986682\pi$
$384$	20.8033	+	8.80399i	1.06162	+	0.449277i
$385$		0			0
$386$	−0.180895	−	0.104440i	−0.00920730	−	0.00531584i
$387$	−4.72944	+	4.58695i	−0.240411	+	0.233168i
$388$	−0.117314	+	0.437822i	−0.00595572	+	0.0222271i
$389$	−22.4950			−1.14054			−0.570270	−	0.821457i	$-0.693161\pi$
$389$	−22.4950			−1.14054			−0.570270	+	0.821457i	$0.693161\pi$
$390$		0			0
$391$		0			0
$392$	3.37554	−	12.5977i	0.170491	−	0.636280i
$393$	−1.90128	+	13.6351i	−0.0959066	+	0.687800i
$394$	−5.36603	−	3.09808i	−0.270336	−	0.156079i
$395$		0			0
$396$	2.88920	−	1.60968i	0.145188	−	0.0808892i
$397$	−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
$399$	8.77113	−	3.55479i	0.439106	−	0.177962i
$400$		0			0
$401$	−3.22263	+	12.0270i	−0.160931	+	0.600601i	0.837594	+	0.546294i	$0.183962\pi$
$401$	−3.22263	+	12.0270i	−0.160931	+	0.600601i	−0.998524	+	0.0543073i	$0.982705\pi$
$402$	−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
$408$	22.5934	−	2.79889i	1.11854	−	0.138566i
$409$	−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
$411$	−1.43156	−	11.5559i	−0.0706135	−	0.570011i
$412$	−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	$-0.592063\pi$
$419$	8.23373	−	4.75374i	0.402244	−	0.232236i	0.687452	+	0.726230i	$0.258729\pi$
$420$		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
$423$	−15.7869	+	8.79543i	−0.767584	+	0.427648i
$424$	−1.43782	+	1.43782i	−0.0698268	+	0.0698268i
$425$		0			0
$426$	7.78112	+	1.08500i	0.376997	+	0.0525683i
$427$	2.56218	−	9.56218i	0.123992	−	0.462746i
$428$			5.09505i			0.246278i
$429$	−22.9691	−	11.5162i	−1.10896	−	0.556007i
$430$		0			0
$431$	−36.5473	−	9.79282i	−1.76042	−	0.471704i	−0.773622	−	0.633648i	$-0.781557\pi$
$431$	−36.5473	−	9.79282i	−1.76042	−	0.471704i	−0.986800	+	0.161944i	$0.948224\pi$
$432$	−2.49938	−	23.0611i	−0.120252	−	1.10953i
$433$	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
$438$	3.08346	−	1.24967i	0.147333	−	0.0597117i
$439$	−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	$-0.414124\pi$
$443$	11.2195			0.533054			0.266527	+	0.963827i	$0.414124\pi$
$444$	2.00602	−	1.51505i	0.0952017	−	0.0719009i
$445$		0			0
$446$	−19.5092	+	33.7909i	−0.923787	+	1.60005i
$447$	−1.83816	−	14.8382i	−0.0869422	−	0.701821i
$448$	−2.43782	−	9.09808i	−0.115176	−	0.429844i
$449$	19.8710	−	5.32441i	0.937769	−	0.251275i	0.242605	−	0.970125i	$-0.421998\pi$
$449$	19.8710	−	5.32441i	0.937769	−	0.251275i	0.695165	+	0.718851i	$0.255331\pi$
$450$		0			0
$451$	−11.5622	+	20.0263i	−0.544442	+	0.943001i
$452$	−2.38711	+	1.37820i	−0.112280	+	0.0648251i
$453$	1.04750	−	0.791121i	0.0492157	−	0.0371701i
$454$			30.5359i			1.43312i
$455$		0			0
$456$	−10.7321	+	13.7670i	−0.502574	+	0.644700i
$457$	3.76795	+	1.00962i	0.176257	+	0.0472280i	0.345868	−	0.938283i	$-0.387584\pi$
$457$	3.76795	+	1.00962i	0.176257	+	0.0472280i	−0.169611	+	0.985511i	$0.554251\pi$
$458$	15.0408	+	26.0514i	0.702809	+	1.21730i
$459$	−15.4590	−	21.1332i	−0.721565	−	0.986412i
$460$		0			0
$461$	−5.50531	−	20.5461i	−0.256408	−	0.956927i	−0.967302	−	0.253628i	$-0.918376\pi$
$461$	−5.50531	−	20.5461i	−0.256408	−	0.956927i	0.710894	−	0.703299i	$-0.248290\pi$
$462$	−13.9773	−	5.91520i	−0.650282	−	0.275200i
$463$	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	$0.146261\pi$
$467$			19.1679i			0.886984i	−0.896278	+	0.443492i	$0.853739\pi$
$468$	2.20607	−	1.87975i	0.101976	−	0.0868916i
$469$	8.39230			0.387521
$470$		0			0
$471$	−1.14909	+	8.24078i	−0.0529474	+	0.379715i
$472$	−3.92820	+	6.80385i	−0.180810	+	0.313172i
$473$	−6.38929	−	6.38929i	−0.293780	−	0.293780i
$474$	2.03319	−	4.80432i	0.0933877	−	0.220670i
$475$		0			0
$476$	1.35022	+	1.35022i	0.0618871	+	0.0618871i
$477$	2.24944	+	0.639761i	0.102995	+	0.0292926i
$478$	−7.02628	−	12.1699i	−0.321375	−	0.556637i
$479$	−5.32441	+	19.8710i	−0.243279	+	0.907928i	0.730962	+	0.682418i	$0.239072\pi$
$479$	−5.32441	+	19.8710i	−0.243279	+	0.907928i	−0.974241	+	0.225510i	$0.927595\pi$
$480$		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
$486$	−19.1572	+	13.5688i	−0.868990	+	0.615492i
$487$	−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
$489$	7.11819	−	0.881808i	0.321896	−	0.0398767i
$490$		0			0
$491$	14.2612	+	24.7012i	0.643600	+	1.11475i	0.984623	+	0.174693i	$0.0558934\pi$
$491$	14.2612	+	24.7012i	0.643600	+	1.11475i	−0.341023	+	0.940055i	$0.610773\pi$
$492$	−1.57203	−	2.08148i	−0.0708728	−	0.0938403i
$493$	−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
$498$	−9.94624	+	4.03104i	−0.445702	+	0.180635i
$499$	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
$501$	−21.4470	−	9.07638i	−0.958181	−	0.405503i
$502$	1.05256	+	1.05256i	0.0469780	+	0.0469780i
$503$	1.63555	−	2.83286i	0.0729256	−	0.126311i	−0.827257	−	0.561824i	$-0.810100\pi$
$503$	1.63555	−	2.83286i	0.0729256	−	0.126311i	0.900182	+	0.435513i	$0.143433\pi$
$504$	−7.94401	+	7.70467i	−0.353854	+	0.343193i
$505$		0			0
$506$		0			0
$507$	−21.7167	−	5.94846i	−0.964473	−	0.264180i
$508$			2.44486i			0.108473i
$509$	−14.1568	−	3.79330i	−0.627489	−	0.168135i	−0.0689588	−	0.997620i	$-0.521968\pi$
$509$	−14.1568	−	3.79330i	−0.627489	−	0.168135i	−0.558530	+	0.829484i	$0.688634\pi$
$510$		0			0
$511$	−1.56218	−	0.901924i	−0.0691067	−	0.0398988i
$512$	11.7137	+	11.7137i	0.517678	+	0.517678i
$513$	19.8393	+	3.07638i	0.875926	+	0.135826i
$514$	8.38269	+	31.2846i	0.369744	+	1.37990i
$515$		0			0
$516$	0.944608	−	0.382834i	0.0415841	−	0.0168533i
$517$	−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	$-0.0173815\pi$
$522$	−0.495311	+	32.3844i	−0.0216792	+	1.41743i
$523$	−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
$528$	31.5713	−	3.91108i	1.37397	−	0.170208i
$529$	−11.5000	+	19.9186i	−0.500000	+	0.866025i
$530$		0			0
$531$	9.03477	+	0.138184i	0.392076	+	0.00599669i
$532$	−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
$537$	17.2698	+	42.6117i	0.745247	+	1.83883i
$538$	−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
$543$	0.717608	−	5.14636i	0.0307955	−	0.220852i
$544$	−7.33013	−	1.96410i	−0.314277	−	0.0842102i
$545$		0			0
$546$	−13.0274	−	2.68082i	−0.557521	−	0.114729i
$547$		−	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
$549$	15.0746	−	14.6204i	0.643368	−	0.623984i
$550$		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	$-0.599145\pi$
$557$	−24.7292	−	6.62616i	−1.04781	−	0.280759i	−0.741346	+	0.671123i	$0.765812\pi$
$558$	15.2679	−	3.84177i	0.646344	−	0.162635i
$559$	−6.58846	−	4.39230i	−0.278662	−	0.185775i
$560$		0			0
$561$	28.6558	−	21.6422i	1.20985	−	0.913735i
$562$	22.3756	−	12.9186i	0.943860	−	0.544938i
$563$	8.72794	+	5.03908i	0.367839	+	0.212372i	0.672514	−	0.740085i	$-0.265215\pi$
$563$	8.72794	+	5.03908i	0.367839	+	0.212372i	−0.304675	+	0.952456i	$0.598548\pi$
$564$	2.77449	−	0.343706i	0.116827	−	0.0144726i
$565$		0			0
$566$	9.58394	−	2.56801i	0.402843	−	0.107941i
$567$	12.1877	+	3.66867i	0.511837	+	0.154070i
$568$	6.80385	+	3.92820i	0.285483	+	0.164824i
$569$	−1.35022	−	2.33864i	−0.0566040	−	0.0980411i	0.836335	−	0.548219i	$-0.184694\pi$
$569$	−1.35022	−	2.33864i	−0.0566040	−	0.0980411i	−0.892939	+	0.450178i	$0.851361\pi$
$570$		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
$576$	5.46595	−	19.2186i	0.227748	−	0.800775i
$577$	−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
$579$	−0.0936291	+	0.221240i	−0.00389109	+	0.00919443i
$580$		0			0
$581$	5.03908	+	2.90931i	0.209056	+	0.120699i
$582$	4.37016	+	0.609374i	0.181149	+	0.0252594i
$583$	−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	$-0.790819\pi$
$587$	4.83020	−	18.0265i	0.199364	−	0.744035i	0.991094	−	0.133164i	$-0.0425138\pi$
$588$	2.29827	+	0.320471i	0.0947792	+	0.0132160i
$589$	−11.6603	−	6.73205i	−0.480452	−	0.277389i
$590$		0			0
$591$	−2.77739	+	6.56283i	−0.114247	+	0.269959i
$592$	23.3564	−	6.25833i	0.959942	−	0.257216i
$593$	−10.3635	+	10.3635i	−0.425578	+	0.425578i	−0.887119	−	0.461541i	$-0.847297\pi$
$593$	−10.3635	+	10.3635i	−0.425578	+	0.425578i	0.461541	+	0.887119i	$0.347297\pi$
$594$	−19.0087	−	25.9858i	−0.779937	−	1.06621i
$595$		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	0.518668	−	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
$603$	15.2797	+	9.13612i	0.622238	+	0.372052i
$604$	−0.196152	+	0.0525589i	−0.00798133	+	0.00213859i
$605$		0			0
$606$	15.6030	−	1.93291i	0.633828	−	0.0785192i
$607$	−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
$609$	14.0126	−	10.5830i	0.567820	−	0.428845i
$610$		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	−0.599475	−	0.800393i	$-0.704624\pi$
$617$	−17.8457	+	4.78173i	−0.718439	+	0.192505i	−0.118964	+	0.992899i	$0.537957\pi$
$618$	−7.04319	+	16.6427i	−0.283319	+	0.669466i
$619$	31.6603	−	31.6603i	1.27253	−	1.27253i	0.327778	−	0.944755i	$-0.393700\pi$
$619$	31.6603	−	31.6603i	1.27253	−	1.27253i	0.944755	−	0.327778i	$-0.106300\pi$
$620$		0			0
$621$		0			0
$622$	−3.92820	+	14.6603i	−0.157507	+	0.587823i
$623$		−	13.1963i		−	0.528701i
$624$	26.4574	−	8.78674i	1.05914	−	0.351751i
$625$		0			0
$626$	−2.90931	−	0.779548i	−0.116280	−	0.0311570i
$627$	−3.80255	+	27.2702i	−0.151859	+	1.08907i
$628$	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
$633$	1.17353	+	2.89559i	0.0466437	+	0.115089i
$634$	−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
$639$	0.138184	−	9.03477i	0.00546649	−	0.357410i
$640$		0			0
$641$	−22.6758	+	39.2757i	−0.895642	+	1.55130i	−0.0626345	+	0.998037i	$0.519950\pi$
$641$	−22.6758	+	39.2757i	−0.895642	+	1.55130i	−0.833008	+	0.553261i	$0.813383\pi$
$642$	49.2228	−	6.09776i	1.94267	−	0.240659i
$643$	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	−0.192746	−	0.981249i	$-0.561739\pi$
$647$	14.2612	−	8.23373i	0.560667	−	0.323701i	0.753413	+	0.657547i	$0.228406\pi$
$648$	−22.8511	+	5.37965i	−0.897674	+	0.211333i
$649$			12.3923i			0.486441i
$650$		0			0
$651$	−6.73205	−	5.24796i	−0.263850	−	0.205684i
$652$	−1.07180	−	0.287187i	−0.0419748	−	0.0112471i
$653$	4.83020	+	8.36615i	0.189020	+	0.327393i	0.944924	−	0.327290i	$-0.106135\pi$
$653$	4.83020	+	8.36615i	0.189020	+	0.327393i	−0.755904	+	0.654683i	$0.772802\pi$
$654$	−45.1145	+	18.2841i	−1.76411	+	0.714966i
$655$		0			0
$656$	−6.49373	−	24.2349i	−0.253538	−	0.946216i
$657$	−1.86237	−	3.34275i	−0.0726578	−	0.130413i
$658$	−9.07180	−	9.07180i	−0.353655	−	0.353655i
$659$	23.4834	+	13.5581i	0.914783	+	0.528150i	0.881967	−	0.471311i	$-0.156219\pi$
$659$	23.4834	+	13.5581i	0.914783	+	0.528150i	0.0328158	+	0.999461i	$0.489553\pi$
$660$		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
$663$	20.9047	−	23.5222i	0.811871	−	0.913526i
$664$	−10.7321			−0.416484
$665$		0			0
$666$	−17.0375	−	17.5668i	−0.660191	−	0.680699i
$667$		0			0
$668$	2.54752	+	2.54752i	0.0985666	+	0.0985666i
$669$	41.3274	+	17.4898i	1.59781	+	0.676194i
$670$		0			0
$671$	20.3652	+	20.3652i	0.786189	+	0.786189i
$672$	3.41876	−	1.38556i	0.131881	−	0.0534493i
$673$	−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	$-0.440564\pi$
$677$	9.66040			0.371279			0.185640	+	0.982618i	$0.440564\pi$
$678$	16.1716	+	21.4123i	0.621065	+	0.822333i
$679$	−1.19615	−	2.07180i	−0.0459041	−	0.0795083i
$680$		0			0
$681$	34.8536	−	4.31769i	1.33559	−	0.165454i
$682$	5.58846	+	20.8564i	0.213993	+	0.798633i
$683$	12.1315	+	45.2752i	0.464198	+	1.73241i	0.659536	+	0.751673i	$0.270753\pi$
$683$	12.1315	+	45.2752i	0.464198	+	1.73241i	−0.195338	+	0.980736i	$0.562580\pi$
$684$	−2.66566	−	1.59387i	−0.101924	−	0.0609430i
$685$		0			0
$686$	−12.7786	−	22.1332i	−0.487889	−	0.845048i
$687$	27.6083	−	20.8511i	1.05332	−	0.795519i
$688$	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
$693$	−4.77524	+	16.7900i	−0.181396	+	0.637800i
$694$	21.9090	+	21.9090i	0.831653	+	0.831653i
$695$		0			0
$696$	−12.6229	+	29.8272i	−0.478469	+	1.13060i
$697$	−20.0263	−	20.0263i	−0.758549	−	0.758549i
$698$	21.4301	−	37.1180i	0.811140	−	1.40494i
$699$	−4.17549	+	29.9448i	−0.157932	+	1.13261i
$700$		0			0
$701$	12.7786			0.482641			0.241320	−	0.970446i	$-0.422420\pi$
$701$	12.7786			0.482641			0.241320	+	0.970446i	$0.422420\pi$
$702$	−20.8003	−	19.0630i	−0.785058	−	0.719485i
$703$			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
$708$	−1.28731	−	0.544793i	−0.0483802	−	0.0204746i
$709$	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
$711$	−5.77113	−	1.64136i	−0.216434	−	0.0615559i
$712$	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
$717$	−12.8972	+	9.74056i	−0.481653	+	0.363768i
$718$	33.6340	−	19.4186i	1.25521	−	0.724695i
$719$	−3.68886	+	6.38929i	−0.137571	+	0.238280i	−0.926577	−	0.376106i	$-0.877263\pi$
$719$	−3.68886	+	6.38929i	−0.137571	+	0.238280i	0.789005	+	0.614386i	$0.210596\pi$
$720$		0			0
$721$	9.46410	−	2.53590i	0.352462	−	0.0944418i
$722$	−1.58708	−	5.92307i	−0.0590650	−	0.220434i
$723$	3.10003	+	25.0243i	0.115292	+	0.930665i
$724$	−0.401924	+	0.696152i	−0.0149374	+	0.0258723i
$725$		0			0
$726$	12.3394	−	9.31934i	0.457959	−	0.345873i
$727$	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
$732$	−3.01084	+	1.22024i	−0.111284	+	0.0451014i
$733$	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
$738$	−18.2276	+	17.6784i	−0.670966	+	0.650750i
$739$	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
$741$	1.41914	+	24.0870i	0.0521334	+	0.884860i
$742$			1.66025i			0.0609498i
$743$	2.28268	−	8.51906i	0.0837432	−	0.312534i	−0.911330	−	0.411677i	$-0.864943\pi$
$743$	2.28268	−	8.51906i	0.0837432	−	0.312534i	0.995073	+	0.0991426i	$0.0316100\pi$
$744$	15.5930	+	2.17429i	0.571667	+	0.0797132i
$745$		0			0
$746$	12.3403	−	12.3403i	0.451812	−	0.451812i
$747$	6.00739	+	10.7826i	0.219799	+	0.394516i
$748$	−5.36603	+	1.43782i	−0.196201	+	0.0525720i
$749$	−19.0150	−	19.0150i	−0.694792	−	0.694792i
$750$		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
$756$	−1.53422	−	1.23418i	−0.0557990	−	0.0448866i
$757$	−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	0.0775029	−	0.996992i	$-0.475305\pi$
$761$	17.7412	−	4.75374i	0.643118	−	0.172323i	0.565616	+	0.824669i	$0.308639\pi$
$762$	23.6196	−	2.92602i	0.855647	−	0.105998i
$763$	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
$771$	34.5229	−	13.9915i	1.24331	−	0.503893i
$772$	0.0262794	−	0.0262794i	0.000945818	−	0.000945818i
$773$	−41.5864	+	11.1430i	−1.49576	+	0.400787i	−0.911677	−	0.410908i	$-0.865212\pi$
$773$	−41.5864	+	11.1430i	−1.49576	+	0.400787i	−0.584081	+	0.811695i	$0.698545\pi$
$774$	−4.82903	−	8.66759i	−0.173576	−	0.311550i
$775$		0			0
$776$	3.82129	+	2.20622i	0.137176	+	0.0791987i
$777$	−1.83235	+	13.1408i	−0.0657353	+	0.471424i
$778$	8.76795	−	32.7224i	0.314346	−	1.17316i
$779$	21.7154			0.778035
$780$		0			0
$781$	12.3923			0.443432
$782$		0			0
$783$	37.0335	−	4.01372i	1.32347	−	0.143439i
$784$	19.3301	+	11.1603i	0.690362	+	0.398581i
$785$		0			0
$786$	−19.0933	−	8.08031i	−0.681036	−	0.288215i
$787$	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
$789$	−14.4987	−	35.7742i	−0.516167	−	1.27360i
$790$		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	$-0.586439\pi$
$797$	−34.9118	−	20.1563i	−1.23664	−	0.713973i	−0.968405	+	0.249381i	$0.919773\pi$
$798$	1.75224	+	14.1445i	0.0620286	+	0.500711i
$799$	29.3205	−	7.85641i	1.03729	−	0.277940i
$800$		0			0
$801$	14.3660	−	24.0264i	0.507596	−	0.848929i
$802$	−16.2391	−	9.37564i	−0.573422	−	0.331066i
$803$	4.54486	−	2.62398i	0.160385	−	0.0925982i
$804$	−1.65983	−	2.19773i	−0.0585377	−	0.0775079i
$805$		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	$-0.828829\pi$
$809$	−24.0261	+	13.8715i	−0.844712	+	0.487694i	0.0141514	+	0.999900i	$0.495495\pi$
$810$		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
$813$	12.3259	+	5.21634i	0.432289	+	0.182945i
$814$	23.7321	−	23.7321i	0.831808	−	0.831808i
$815$		0			0
$816$	−5.38085	+	38.5891i	−0.188367	+	1.35089i
$817$	−2.19615	+	8.19615i	−0.0768336	+	0.286747i
$818$		−	45.1988i		−	1.58034i
$819$	−1.21785	+	15.2485i	−0.0425549	+	0.532826i
$820$		0			0
$821$	−41.5864	−	11.1430i	−1.45137	−	0.388895i	−0.554873	−	0.831935i	$-0.687233\pi$
$821$	−41.5864	−	11.1430i	−1.45137	−	0.388895i	−0.896502	+	0.443040i	$0.853900\pi$
$822$	17.3679	+	2.42177i	0.605774	+	0.0844690i
$823$	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	$0.535676\pi$
$827$	−31.7936	+	31.7936i	−1.10557	+	1.10557i	−0.993726	+	0.111845i	$0.964324\pi$
$828$		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
$834$	28.9133	+	38.2832i	1.00119	+	1.32564i
$835$		0			0
$836$	2.12976	−	3.68886i	0.0736595	−	0.127582i
$837$	−6.54383	−	16.8836i	−0.226188	−	0.583582i
$838$	3.70577	+	13.8301i	0.128014	+	0.477754i
$839$	9.79282	−	2.62398i	0.338086	−	0.0905898i	−0.0857819	−	0.996314i	$-0.527339\pi$
$839$	9.79282	−	2.62398i	0.338086	−	0.0905898i	0.423868	+	0.905724i	$0.360672\pi$
$840$		0			0
$841$	11.1962	−	19.3923i	0.386074	−	0.668700i
$842$	14.4421	−	8.33816i	0.497708	−	0.287352i
$843$	−17.9091	−	23.7128i	−0.616822	−	0.816714i
$844$		−	0.483340i		−	0.0166372i
$845$		0			0
$846$	−6.64102	−	26.3927i	−0.228323	−	0.907400i
$847$	−8.09808	−	2.16987i	−0.278253	−	0.0745577i
$848$	−1.73999	−	3.01375i	−0.0597515	−	0.103493i
$849$	−4.28626	−	10.5760i	−0.147104	−	0.362967i
$850$		0			0
$851$		0			0
$852$	−0.544793	+	1.28731i	−0.0186643	+	0.0441027i
$853$	−22.3660	−	22.3660i	−0.765798	−	0.765798i	0.211566	−	0.977364i	$-0.432144\pi$
$853$	−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	$-0.981902\pi$
$857$		−	3.32707i		−	0.113651i	0.998384	−	0.0568253i	$-0.0180978\pi$
$858$	25.7048	−	28.9234i	0.877549	−	0.987428i
$859$	−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
$861$	13.6351	+	1.90128i	0.464683	+	0.0647953i
$862$	28.4904	−	49.3468i	0.970386	−	1.68076i
$863$	−18.2354	−	18.2354i	−0.620741	−	0.620741i	0.324980	−	0.945721i	$-0.394642\pi$
$863$	−18.2354	−	18.2354i	−0.620741	−	0.620741i	−0.945721	+	0.324980i	$0.894642\pi$
$864$	7.73284	+	1.19909i	0.263077	+	0.0407940i
$865$		0			0
$866$	33.0673	+	33.0673i	1.12367	+	1.12367i
$867$	5.45979	+	13.4716i	0.185424	+	0.457518i
$868$	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
$873$	0.0776093	−	5.07425i	0.00262668	−	0.171737i
$874$		0			0
$875$		0			0
$876$	0.0727771	+	0.587477i	0.00245891	+	0.0198490i
$877$	−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
$879$	−0.383584	−	3.09640i	−0.0129380	−	0.104439i
$880$		0			0
$881$	11.7417	+	20.3372i	0.395588	+	0.685178i	0.993176	−	0.116625i	$-0.0372076\pi$
$881$	11.7417	+	20.3372i	0.395588	+	0.685178i	−0.597588	+	0.801803i	$0.703874\pi$
$882$	0.345461	−	22.5869i	0.0116323	−	0.760541i
$883$	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	$-0.0273173\pi$
$887$	12.6257	+	21.8683i	0.423929	+	0.734266i	−0.572391	+	0.819981i	$0.693984\pi$
$888$	−9.19180	−	22.6800i	−0.308457	−	0.761089i
$889$	−9.12436	−	9.12436i	−0.306021	−	0.306021i
$890$		0			0
$891$	−26.9723	+	25.3708i	−0.903607	+	0.849954i
$892$	−4.90897	−	4.90897i	−0.164364	−	0.164364i
$893$	−11.6373	+	20.1563i	−0.389426	+	0.674505i
$894$	22.3009	+	3.10963i	0.745854	+	0.104002i
$895$		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
$903$	−2.09657	+	4.95408i	−0.0697695	+	0.164861i
$904$	6.94486	+	25.9186i	0.230983	+	0.862039i
$905$		0			0
$906$	0.742522	+	1.83211i	0.0246686	+	0.0608677i
$907$	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	$0.00822209\pi$
$911$			1.55910i			0.0516552i	−0.999666	+	0.0258276i	$0.991778\pi$
$912$	−18.0046	−	23.8393i	−0.596191	−	0.789398i
$913$	−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
$918$	36.7670	−	14.2504i	1.21349	−	0.470333i
$919$	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
$921$	−12.3892	−	16.4041i	−0.408236	−	0.540533i
$922$	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
$927$	19.9918	+	5.68585i	0.656616	+	0.186748i
$928$	7.63397	−	7.63397i	0.250597	−	0.250597i
$929$	5.27594	+	19.6901i	0.173098	+	0.646011i	0.996868	+	0.0790861i	$0.0252002\pi$
$929$	5.27594	+	19.6901i	0.173098	+	0.646011i	−0.823770	+	0.566924i	$0.808133\pi$
$930$		0			0
$931$	−13.6603	+	13.6603i	−0.447697	+	0.447697i
$932$	2.33864	−	4.05065i	0.0766048	−	0.132683i
$933$	17.2886	+	2.41072i	0.566004	+	0.0789234i
$934$	−27.8827	−	7.47114i	−0.912349	−	0.244463i
$935$		0			0
$936$	−12.1171	−	25.4799i	−0.396060	−	0.832837i
$937$			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
$939$	−0.478405	+	3.43091i	−0.0156122	+	0.111963i
$940$		0			0
$941$	−9.14570	+	9.14570i	−0.298141	+	0.298141i	−0.840285	−	0.542144i	$-0.817613\pi$
$941$	−9.14570	+	9.14570i	−0.298141	+	0.298141i	0.542144	+	0.840285i	$0.317613\pi$
$942$	−11.5396	−	4.88358i	−0.375981	−	0.159116i
$943$		0			0
$944$	−9.50749	−	9.50749i	−0.309442	−	0.309442i
$945$		0			0
$946$	11.7846	−	6.80385i	0.383151	−	0.221212i
$947$	10.3635	+	2.77689i	0.336768	+	0.0902368i	0.423240	−	0.906018i	$-0.360893\pi$
$947$	10.3635	+	2.77689i	0.336768	+	0.0902368i	−0.0864720	+	0.996254i	$0.527559\pi$
$948$	0.732051	+	0.570669i	0.0237759	+	0.0185345i
$949$	3.45448	−	3.03590i	0.112137	−	0.0985494i
$950$		0			0
$951$	16.7583	+	22.1891i	0.543425	+	0.719531i
$952$	16.0981	−	9.29423i	0.521742	−	0.301228i
$953$	−1.71201	−	0.988427i	−0.0554573	−	0.0320183i	0.472015	−	0.881591i	$-0.343527\pi$
$953$	−1.71201	−	0.988427i	−0.0554573	−	0.0320183i	−0.527472	+	0.849572i	$0.676860\pi$
$954$	−1.80740	+	3.02279i	−0.0585169	+	0.0978666i
$955$		0			0
$956$	2.41510	−	0.647124i	0.0781099	−	0.0209295i
$957$	6.28076	+	50.7000i	0.203028	+	1.63890i
$958$	−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
$969$	−31.0556	−	13.1428i	−0.997651	−	0.422207i
$970$		0			0
$971$	41.4335	+	23.9216i	1.32966	+	0.767682i	0.985247	−	0.171136i	$-0.0547436\pi$
$971$	41.4335	+	23.9216i	1.32966	+	0.767682i	0.344416	+	0.938817i	$0.388077\pi$
$972$	−1.44976	−	3.91725i	−0.0465011	−	0.125646i
$973$	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	$-0.792939\pi$
$977$	6.13194	−	22.8847i	0.196178	−	0.732147i	0.991959	−	0.126562i	$-0.0403943\pi$
$978$	−1.49176	+	10.6982i	−0.0477012	+	0.342092i
$979$	33.2487	+	19.1962i	1.06263	+	0.613512i
$980$		0			0
$981$	27.2485	+	48.9082i	0.869978	+	1.56152i
$982$	−41.4904	+	11.1173i	−1.32401	+	0.354768i
$983$	30.4433	−	30.4433i	0.970992	−	0.970992i	−0.0285990	−	0.999591i	$-0.509105\pi$
$983$	30.4433	−	30.4433i	0.970992	−	0.970992i	0.999591	+	0.0285990i	$0.00910459\pi$
$984$	−23.5330	+	9.53754i	−0.750206	+	0.304046i
$985$		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
$993$	−58.8186	+	7.28650i	−1.86655	+	0.231230i
$994$	6.19615	−	1.66025i	0.196530	−	0.0526601i
$995$		0			0
$996$	−0.234755	−	1.89501i	−0.00743851	−	0.0600457i
$997$	−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
$999$	−17.6416	+	21.9305i	−0.558156	+	0.693850i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.389774 + 1.45466i) q^{2} +(1.71545 + 0.239203i) q^{3} +(-0.232051 - 0.133975i) q^{4} +(-1.01660 + 2.40216i) q^{6} +(1.36603 - 0.366025i) q^{7} +(-1.84443 + 1.84443i) q^{8} +(2.88556 + 0.820682i) q^{9} +O(q^{10})\)	\(q+(-0.389774 + 1.45466i) q^{2} +(1.71545 + 0.239203i) q^{3} +(-0.232051 - 0.133975i) q^{4} +(-1.01660 + 2.40216i) q^{6} +(1.36603 - 0.366025i) q^{7} +(-1.84443 + 1.84443i) q^{8} +(2.88556 + 0.820682i) 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} +(-2.31853 + 3.87762i) q^{18} +(3.73205 - 1.00000i) q^{19} +(2.43091 - 0.301143i) q^{21} +(-5.36603 - 3.09808i) q^{22} +(-3.60523 + 2.72284i) 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} +(-2.77739 + 6.56283i) q^{33} +(5.36603 - 5.36603i) q^{34} +(-0.559647 - 0.577032i) q^{36} +(-1.40192 + 5.23205i) q^{37} +5.81863i q^{38} +(-1.25874 + 6.11683i) q^{39} +(5.42885 + 1.45466i) q^{41} +(-0.509445 + 3.65351i) q^{42} +(-1.09808 + 1.90192i) q^{43} +(0.779548 - 0.779548i) q^{44} +(-4.25953 + 4.25953i) q^{47} +(-2.90422 - 7.16590i) q^{48} +(-4.33013 + 2.50000i) q^{49} +(-6.88351 - 5.36603i) q^{51} +(0.535898 - 0.803848i) q^{52} +0.779548 q^{53} +(-4.90487 + 6.09729i) q^{54} +(-1.84443 + 3.19465i) q^{56} +(6.64136 - 0.822738i) 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} +(4.24214 + 0.0648824i) 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} +(-6.83591 + 3.80853i) q^{72} +(-0.901924 - 0.901924i) q^{73} +(-7.06440 - 4.07863i) q^{74} +(-1.00000 - 0.267949i) q^{76} +5.81863i q^{77} +(-8.40726 - 4.21522i) q^{78} -2.00000 q^{79} +(7.65296 + 4.73626i) q^{81} +(-4.23205 + 7.33013i) q^{82} +(2.90931 + 2.90931i) q^{83} +(-0.604440 - 0.255799i) q^{84} +(-2.33864 - 2.33864i) q^{86} +(11.5076 - 4.66384i) q^{87} +(-5.36603 - 9.29423i) q^{88} +(2.41510 - 9.01327i) q^{89} +(1.00000 + 5.00000i) q^{91} +(-3.63763 - 4.81647i) q^{93} +(-4.53590 - 7.85641i) q^{94} +(2.58863 - 0.320682i) q^{96} +(-0.437822 - 1.63397i) q^{97} +(-1.94887 - 7.27328i) q^{98} +(-6.33434 + 10.5939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} + 12 q^{4} - 2 q^{6} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 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

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