LMFDB - Embedded newform 975.2.bo.d.401.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(176,975)]

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, 0, 11]))

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

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

chi := DirichletCharacter("975.176");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bo (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.78541419707$
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			401.2
Root			$0.500000 + 0.564882i$ of defining polynomial
Character	$\chi$	$=$	975.401
Dual form			975.2.bo.d.851.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.45466 + 0.389774i) q^{2} +(-0.239203 + 1.71545i) q^{3} +(0.232051 + 0.133975i) q^{4} +(-1.01660 + 2.40216i) q^{6} +(-0.366025 - 1.36603i) q^{7} +(-1.84443 - 1.84443i) q^{8} +(-2.88556 - 0.820682i) q^{9} +O(q^{10})$	\(q+(1.45466 + 0.389774i) q^{2} +(-0.239203 + 1.71545i) q^{3} +(0.232051 + 0.133975i) q^{4} +(-1.01660 + 2.40216i) q^{6} +(-0.366025 - 1.36603i) q^{7} +(-1.84443 - 1.84443i) q^{8} +(-2.88556 - 0.820682i) q^{9} +(-1.06488 + 3.97420i) q^{11} +(-0.285334 + 0.366025i) q^{12} +(-3.59808 - 0.232051i) q^{13} -2.12976i q^{14} +(-2.23205 - 3.86603i) q^{16} +(-2.51954 + 4.36397i) q^{17} +(-3.87762 - 2.31853i) q^{18} +(-3.73205 + 1.00000i) q^{19} +(2.43091 - 0.301143i) q^{21} +(-3.09808 + 5.36603i) q^{22} +(3.60523 - 2.72284i) q^{24} +(-5.14352 - 1.73999i) q^{26} +(2.09808 - 4.75374i) q^{27} +(0.0980762 - 0.366025i) q^{28} +(-6.20840 + 3.58442i) q^{29} +(-2.46410 - 2.46410i) q^{31} +(-0.389774 - 1.45466i) q^{32} +(-6.56283 - 2.77739i) q^{33} +(-5.36603 + 5.36603i) q^{34} +(-0.559647 - 0.577032i) q^{36} +(5.23205 + 1.40192i) q^{37} -5.81863 q^{38} +(1.25874 - 6.11683i) q^{39} +(5.42885 + 1.45466i) q^{41} +(3.65351 + 0.509445i) q^{42} +(-1.90192 - 1.09808i) q^{43} +(-0.779548 + 0.779548i) q^{44} +(4.25953 + 4.25953i) q^{47} +(7.16590 - 2.90422i) q^{48} +(4.33013 - 2.50000i) q^{49} +(-6.88351 - 5.36603i) q^{51} +(-0.803848 - 0.535898i) q^{52} +0.779548i q^{53} +(4.90487 - 6.09729i) q^{54} +(-1.84443 + 3.19465i) q^{56} +(-0.822738 - 6.64136i) q^{57} +(-10.4282 + 2.79423i) q^{58} +(-2.90931 + 0.779548i) q^{59} +(3.50000 - 6.06218i) q^{61} +(-2.62398 - 4.54486i) q^{62} +(-0.0648824 + 4.24214i) q^{63} +6.66025i q^{64} +(-8.46410 - 6.59817i) q^{66} +(1.53590 - 5.73205i) q^{67} +(-1.16932 + 0.675108i) q^{68} +(-0.779548 - 2.90931i) q^{71} +(3.80853 + 6.83591i) q^{72} +(0.901924 - 0.901924i) q^{73} +(7.06440 + 4.07863i) q^{74} +(-1.00000 - 0.267949i) q^{76} +5.81863 q^{77} +(4.21522 - 8.40726i) q^{78} +2.00000 q^{79} +(7.65296 + 4.73626i) q^{81} +(7.33013 + 4.23205i) q^{82} +(-2.90931 + 2.90931i) q^{83} +(0.604440 + 0.255799i) q^{84} +(-2.33864 - 2.33864i) q^{86} +(-4.66384 - 11.5076i) q^{87} +(9.29423 - 5.36603i) q^{88} +(-2.41510 + 9.01327i) q^{89} +(1.00000 + 5.00000i) q^{91} +(4.81647 - 3.63763i) q^{93} +(4.53590 + 7.85641i) q^{94} +(2.58863 - 0.320682i) q^{96} +(-1.63397 + 0.437822i) q^{97} +(7.27328 - 1.94887i) q^{98} +(6.33434 - 10.5939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} - 12 q^{4} - 2 q^{6} + 4 q^{7} + 4 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 - 12 * q^4 - 2 * q^6 + 4 * q^7 + 4 * q^9	$ 8 q + 2 q^{3} - 12 q^{4} - 2 q^{6} + 4 q^{7} + 4 q^{9} - 8 q^{13} - 4 q^{16} - 4 q^{18} - 16 q^{19} + 4 q^{21} - 4 q^{22} + 18 q^{24} - 4 q^{27} - 20 q^{28} + 8 q^{31} - 16 q^{33} - 36 q^{34} - 36 q^{36} + 28 q^{37} - 14 q^{39} + 16 q^{42} - 36 q^{43} + 14 q^{48} - 48 q^{52} + 46 q^{54} - 16 q^{57} - 28 q^{58} + 28 q^{61} + 8 q^{63} - 40 q^{66} + 40 q^{67} - 12 q^{72} + 28 q^{73} - 8 q^{76} + 80 q^{78} + 16 q^{79} + 4 q^{81} + 24 q^{82} + 4 q^{84} + 34 q^{87} + 12 q^{88} + 8 q^{91} - 4 q^{93} + 64 q^{94} + 16 q^{96} - 20 q^{97} + 40 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 - 12 * q^4 - 2 * q^6 + 4 * q^7 + 4 * q^9 - 8 * q^13 - 4 * q^16 - 4 * q^18 - 16 * q^19 + 4 * q^21 - 4 * q^22 + 18 * q^24 - 4 * q^27 - 20 * q^28 + 8 * q^31 - 16 * q^33 - 36 * q^34 - 36 * q^36 + 28 * q^37 - 14 * q^39 + 16 * q^42 - 36 * q^43 + 14 * q^48 - 48 * q^52 + 46 * q^54 - 16 * q^57 - 28 * q^58 + 28 * q^61 + 8 * q^63 - 40 * q^66 + 40 * q^67 - 12 * q^72 + 28 * q^73 - 8 * q^76 + 80 * q^78 + 16 * q^79 + 4 * q^81 + 24 * q^82 + 4 * q^84 + 34 * q^87 + 12 * q^88 + 8 * q^91 - 4 * q^93 + 64 * q^94 + 16 * q^96 - 20 * 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 $

$2$	1.45466	+	0.389774i	1.02860	+	0.275612i	0.733380	−	0.679818i	$-0.237941\pi$
$2$	1.45466	+	0.389774i	1.02860	+	0.275612i	0.295217	+	0.955430i	$0.404608\pi$
$3$	−0.239203	+	1.71545i	−0.138104	+	0.990418i
$3$	−0.239203	+	1.71545i	−0.138104	+	0.990418i
$4$	0.232051	+	0.133975i	0.116025	+	0.0669873i
$5$		0			0
$5$		0			0
$6$	−1.01660	+	2.40216i	−0.415024	+	0.980678i
$7$	−0.366025	−	1.36603i	−0.138345	−	0.516309i	−0.999962	−	0.00875026i	$-0.997215\pi$
$7$	−0.366025	−	1.36603i	−0.138345	−	0.516309i	0.861617	−	0.507559i	$-0.169452\pi$
$8$	−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	$0.870357\pi$
$12$	−0.285334	+	0.366025i	−0.0823689	+	0.105662i
$13$	−3.59808	−	0.232051i	−0.997927	−	0.0643593i
$13$	−3.59808	−	0.232051i	−0.997927	−	0.0643593i
$14$		−	2.12976i		−	0.569204i
$15$		0			0
$16$	−2.23205	−	3.86603i	−0.558013	−	0.966506i
$17$	−2.51954	+	4.36397i	−0.611078	+	1.05842i	0.379981	+	0.924994i	$0.375930\pi$
$17$	−2.51954	+	4.36397i	−0.611078	+	1.05842i	−0.991059	+	0.133424i	$0.957403\pi$
$18$	−3.87762	−	2.31853i	−0.913965	−	0.546482i
$19$	−3.73205	+	1.00000i	−0.856191	+	0.229416i	−0.660107	−	0.751171i	$-0.729489\pi$
$19$	−3.73205	+	1.00000i	−0.856191	+	0.229416i	−0.196084	+	0.980587i	$0.562823\pi$
$20$		0			0
$21$	2.43091	−	0.301143i	0.530468	−	0.0657148i
$22$	−3.09808	+	5.36603i	−0.660512	+	1.14404i
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	3.60523	−	2.72284i	0.735914	−	0.555798i
$25$		0			0
$26$	−5.14352	−	1.73999i	−1.00873	−	0.341240i
$27$	2.09808	−	4.75374i	0.403775	−	0.914858i
$28$	0.0980762	−	0.366025i	0.0185347	−	0.0691723i
$29$	−6.20840	+	3.58442i	−1.15287	+	0.665610i	−0.949585	−	0.313509i	$-0.898495\pi$
$29$	−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	$0.851314\pi$
$32$	−0.389774	−	1.45466i	−0.0689030	−	0.257149i
$33$	−6.56283	−	2.77739i	−1.14244	−	0.483482i
$34$	−5.36603	+	5.36603i	−0.920266	+	0.920266i
$35$		0			0
$36$	−0.559647	−	0.577032i	−0.0932745	−	0.0961720i
$37$	5.23205	+	1.40192i	0.860144	+	0.230475i	0.661821	−	0.749662i	$-0.269784\pi$
$37$	5.23205	+	1.40192i	0.860144	+	0.230475i	0.198323	+	0.980137i	$0.436451\pi$
$38$	−5.81863			−0.943906
$39$	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	$0.438710\pi$
$42$	3.65351	+	0.509445i	0.563749	+	0.0786091i
$43$	−1.90192	−	1.09808i	−0.290041	−	0.167455i	0.347920	−	0.937524i	$-0.386888\pi$
$43$	−1.90192	−	1.09808i	−0.290041	−	0.167455i	−0.637960	+	0.770069i	$0.720222\pi$
$44$	−0.779548	+	0.779548i	−0.117521	+	0.117521i
$45$		0			0
$46$		0			0
$47$	4.25953	+	4.25953i	0.621316	+	0.621316i	0.945868	−	0.324552i	$-0.105213\pi$
$47$	4.25953	+	4.25953i	0.621316	+	0.621316i	−0.324552	+	0.945868i	$0.605213\pi$
$48$	7.16590	−	2.90422i	1.03431	−	0.419188i
$49$	4.33013	−	2.50000i	0.618590	−	0.357143i
$50$		0			0
$51$	−6.88351	−	5.36603i	−0.963884	−	0.751394i
$52$	−0.803848	−	0.535898i	−0.111474	−	0.0743157i
$53$			0.779548i			0.107079i	0.998566	+	0.0535396i	$0.0170503\pi$
$53$			0.779548i			0.107079i	−0.998566	+	0.0535396i	$0.982950\pi$
$54$	4.90487	−	6.09729i	0.667468	−	0.829736i
$55$		0			0
$56$	−1.84443	+	3.19465i	−0.246472	+	0.426903i
$57$	−0.822738	−	6.64136i	−0.108974	−	0.879670i
$58$	−10.4282	+	2.79423i	−1.36929	+	0.366900i
$59$	−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	$0.0187572\pi$
$62$	−2.62398	−	4.54486i	−0.333246	−	0.577198i
$63$	−0.0648824	+	4.24214i	−0.00817442	+	0.534460i
$64$			6.66025i			0.832532i
$65$		0			0
$66$	−8.46410	−	6.59817i	−1.04186	−	0.812179i
$67$	1.53590	−	5.73205i	0.187640	−	0.700281i	−0.806410	−	0.591357i	$-0.798593\pi$
$67$	1.53590	−	5.73205i	0.187640	−	0.700281i	0.994050	−	0.108925i	$-0.0347408\pi$
$68$	−1.16932	+	0.675108i	−0.141801	+	0.0818689i
$69$		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	$0.973864\pi$
$72$	3.80853	+	6.83591i	0.448840	+	0.805620i
$73$	0.901924	−	0.901924i	0.105562	−	0.105562i	−0.652353	−	0.757915i	$-0.726218\pi$
$73$	0.901924	−	0.901924i	0.105562	−	0.105562i	0.757915	+	0.652353i	$0.226218\pi$
$74$	7.06440	+	4.07863i	0.821220	+	0.474132i
$75$		0			0
$76$	−1.00000	−	0.267949i	−0.114708	−	0.0307359i
$77$	5.81863			0.663094
$78$	4.21522	−	8.40726i	0.477279	−	0.951934i
$79$	2.00000			0.225018			0.112509	−	0.993651i	$-0.464111\pi$
$79$	2.00000			0.225018			0.112509	+	0.993651i	$0.464111\pi$
$80$		0			0
$81$	7.65296	+	4.73626i	0.850329	+	0.526251i
$82$	7.33013	+	4.23205i	0.809477	+	0.467352i
$83$	−2.90931	+	2.90931i	−0.319339	+	0.319339i	−0.848513	−	0.529174i	$-0.822502\pi$
$83$	−2.90931	+	2.90931i	−0.319339	+	0.319339i	0.529174	+	0.848513i	$0.322502\pi$
$84$	0.604440	+	0.255799i	0.0659498	+	0.0279100i
$85$		0			0
$86$	−2.33864	−	2.33864i	−0.252182	−	0.252182i
$87$	−4.66384	−	11.5076i	−0.500017	−	1.23375i
$88$	9.29423	−	5.36603i	0.990768	−	0.572020i
$89$	−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
$93$	4.81647	−	3.63763i	0.499445	−	0.377205i
$94$	4.53590	+	7.85641i	0.467842	+	0.810326i
$95$		0			0
$96$	2.58863	−	0.320682i	0.264201	−	0.0327295i
$97$	−1.63397	+	0.437822i	−0.165905	+	0.0444541i	−0.340815	−	0.940130i	$-0.610703\pi$
$97$	−1.63397	+	0.437822i	−0.165905	+	0.0444541i	0.174910	+	0.984584i	$0.444036\pi$
$98$	7.27328	−	1.94887i	0.734712	−	0.196866i
$99$	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	$0.930280\pi$
$102$	−7.92160	−	10.4887i	−0.784356	−	1.03854i
$103$			6.92820i			0.682656i	0.939944	+	0.341328i	$0.110877\pi$
$103$			6.92820i			0.682656i	−0.939944	+	0.341328i	$0.889123\pi$
$104$	6.20840	+	7.06440i	0.608784	+	0.692722i
$105$		0			0
$106$	−0.303848	+	1.13397i	−0.0295123	+	0.110141i
$107$	−16.4675	+	9.50749i	−1.59197	+	0.919123i	−0.598999	+	0.800749i	$0.704435\pi$
$107$	−16.4675	+	9.50749i	−1.59197	+	0.919123i	−0.992969	+	0.118374i	$0.962232\pi$
$108$	1.12374	−	0.822021i	0.108132	−	0.0790990i
$109$	−13.1962	−	13.1962i	−1.26396	−	1.26396i	−0.949156	−	0.314806i	$-0.898060\pi$
$109$	−13.1962	−	13.1962i	−1.26396	−	1.26396i	−0.314806	−	0.949156i	$-0.601940\pi$
$110$		0			0
$111$	−3.65646	+	8.64000i	−0.347055	+	0.820072i
$112$	−4.46410	+	4.46410i	−0.421818	+	0.421818i
$113$	8.90883	+	5.14352i	0.838073	+	0.483861i	0.856609	−	0.515967i	$-0.172567\pi$
$113$	8.90883	+	5.14352i	0.838073	+	0.483861i	−0.0185360	+	0.999828i	$0.505901\pi$
$114$	1.39183	−	9.98158i	0.130357	−	0.934861i
$115$		0			0
$116$	−1.92089			−0.178350
$117$	10.1920	+	3.62247i	0.942254	+	0.334898i
$118$	−4.53590			−0.417563
$119$	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
$123$	−3.79399	+	8.96499i	−0.342093	+	0.808346i
$124$	−0.241670	−	0.901924i	−0.0217026	−	0.0809951i
$125$		0			0
$126$	−1.74786	+	6.14557i	−0.155712	+	0.547491i
$127$	−7.90192	+	4.56218i	−0.701182	+	0.404828i	−0.807788	−	0.589474i	$-0.799335\pi$
$127$	−7.90192	+	4.56218i	−0.701182	+	0.404828i	0.106605	+	0.994301i	$0.466002\pi$
$128$	−3.37554	+	12.5977i	−0.298359	+	1.11349i
$129$	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	$0.887123\pi$
$132$	−1.15081	−	1.52375i	−0.100165	−	0.132625i
$133$	2.73205	+	4.73205i	0.236899	+	0.410321i
$134$	4.46841	−	7.73951i	0.386012	−	0.668592i
$135$		0			0
$136$	12.6962	−	3.40192i	1.08869	−	0.291713i
$137$	−6.49373	+	1.73999i	−0.554797	+	0.148657i	−0.525315	−	0.850908i	$-0.676052\pi$
$137$	−6.49373	+	1.73999i	−0.554797	+	0.148657i	−0.0294822	+	0.999565i	$0.509386\pi$
$138$		0			0
$139$	−9.19615	+	15.9282i	−0.780007	+	1.35101i	0.151929	+	0.988391i	$0.451451\pi$
$139$	−9.19615	+	15.9282i	−0.780007	+	1.35101i	−0.931937	+	0.362621i	$0.881882\pi$
$140$		0			0
$141$	−8.32592	+	6.28814i	−0.701169	+	0.529557i
$142$		−	4.53590i		−	0.380644i
$143$	4.75374	−	14.0524i	0.397528	−	1.17512i
$144$	3.26795	+	12.9875i	0.272329	+	1.08229i
$145$		0			0
$146$	1.66354	−	0.960443i	0.137675	−	0.0794868i
$147$	3.25286	+	8.02614i	0.268291	+	0.661985i
$148$	1.02628	+	1.02628i	0.0843597	+	0.0843597i
$149$	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	$0.240183\pi$
$152$	8.72794	+	5.03908i	0.707929	+	0.408723i
$153$	10.8517	−	10.5248i	0.877310	−	0.850878i
$154$	8.46410	+	2.26795i	0.682057	+	0.182757i
$155$		0			0
$156$	1.11159	−	1.25078i	0.0889985	−	0.100142i
$157$	4.80385			0.383389			0.191694	−	0.981455i	$-0.438602\pi$
$157$	4.80385			0.383389			0.191694	+	0.981455i	$0.438602\pi$
$158$	2.90931	+	0.779548i	0.231453	+	0.0620175i
$159$	−1.33728	−	0.186470i	−0.106053	−	0.0147880i
$160$		0			0
$161$		0			0
$162$	9.28636	+	9.87256i	0.729605	+	0.775661i
$163$	1.07180	+	4.00000i	0.0839496	+	0.313304i	0.995113	−	0.0987406i	$-0.0314814\pi$
$163$	1.07180	+	4.00000i	0.0839496	+	0.313304i	−0.911164	+	0.412045i	$0.864815\pi$
$164$	1.06488	+	1.06488i	0.0831533	+	0.0831533i
$165$		0			0
$166$	−5.36603	+	3.09808i	−0.416484	+	0.240457i
$167$	−3.47998	+	12.9875i	−0.269289	+	1.00500i	0.690283	+	0.723539i	$0.257486\pi$
$167$	−3.47998	+	12.9875i	−0.269289	+	1.00500i	−0.959573	+	0.281461i	$0.909181\pi$
$168$	−5.03908	−	3.92820i	−0.388773	−	0.303067i
$169$	12.8923	+	1.66987i	0.991716	+	0.128452i
$170$		0			0
$171$	11.5898	+	0.177262i	0.886291	+	0.0135556i
$172$	−0.294229	−	0.509619i	−0.0224347	−	0.0388581i
$173$	8.72794	−	15.1172i	0.663573	−	1.14934i	−0.316097	−	0.948727i	$-0.602373\pi$
$173$	8.72794	−	15.1172i	0.663573	−	1.14934i	0.979670	−	0.200615i	$-0.0642941\pi$
$174$	−2.29892	−	18.5575i	−0.174281	−	1.40684i
$175$		0			0
$176$	17.7412	−	4.75374i	1.33729	−	0.358327i
$177$	−0.641364	−	5.17726i	−0.0482078	−	0.389147i
$178$	−7.02628	+	12.1699i	−0.526642	+	0.912171i
$179$	−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	$-0.0355636\pi$
$182$	−0.494214	+	7.66306i	−0.0366336	+	0.568024i
$183$	9.56218	+	7.45418i	0.706857	+	0.551029i
$184$		0			0
$185$		0			0
$186$	8.42417	−	3.41417i	0.617690	−	0.250339i
$187$	−14.6603	−	14.6603i	−1.07206	−	1.07206i
$188$	0.417759	+	1.55910i	0.0304682	+	0.113709i
$189$	−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	$0.610755\pi$
$192$	−11.4254	−	1.59315i	−0.824554	−	0.114976i
$193$	−0.133975	−	0.0358984i	−0.00964370	−	0.00258402i	0.253994	−	0.967206i	$-0.418256\pi$
$193$	−0.133975	−	0.0358984i	−0.00964370	−	0.00258402i	−0.263638	+	0.964622i	$0.584922\pi$
$194$	−2.54752			−0.182902
$195$		0			0
$196$	1.33975			0.0956961
$197$	3.97420	+	1.06488i	0.283150	+	0.0758697i	0.397599	−	0.917559i	$-0.369844\pi$
$197$	3.97420	+	1.06488i	0.283150	+	0.0758697i	−0.114449	+	0.993429i	$0.536510\pi$
$198$	13.3435	−	12.9415i	0.948281	−	0.919711i
$199$	11.1962	+	6.46410i	0.793674	+	0.458228i	0.841254	−	0.540639i	$-0.181818\pi$
$199$	11.1962	+	6.46410i	0.793674	+	0.458228i	−0.0475802	+	0.998867i	$0.515151\pi$
$200$		0			0
$201$	9.46568	+	4.00588i	0.667657	+	0.282553i
$202$	−2.34936	−	8.76795i	−0.165301	−	0.616911i
$203$	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
$208$	7.13397	+	14.4282i	0.494652	+	1.00042i
$209$		−	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	$0.813556\pi$
$212$	−0.104440	+	0.180895i	−0.00717294	+	0.0124239i
$213$	5.17726	−	0.641364i	0.354740	−	0.0439455i
$214$	−27.6603	+	7.41154i	−1.89082	+	0.506643i
$215$		0			0
$216$	−12.6377	+	4.89819i	−0.859887	+	0.333280i
$217$	−2.46410	+	4.26795i	−0.167274	+	0.289727i
$218$	−14.0524	−	24.3394i	−0.951745	−	1.64847i
$219$	1.33147	+	1.76295i	0.0899722	+	0.119129i
$220$		0			0
$221$	10.0782	−	15.1172i	0.677930	−	1.01690i
$222$	−8.68653	+	11.1430i	−0.583002	+	0.747872i
$223$	−6.70577	+	25.0263i	−0.449052	+	1.67588i	0.255960	+	0.966687i	$0.417609\pi$
$223$	−6.70577	+	25.0263i	−0.449052	+	1.67588i	−0.705011	+	0.709196i	$0.749058\pi$
$224$	−1.84443	+	1.06488i	−0.123236	+	0.0711505i
$225$		0			0
$226$	10.9545	+	10.9545i	0.728681	+	0.728681i
$227$	−5.24796	−	19.5856i	−0.348319	−	1.29994i	−0.888686	−	0.458515i	$-0.848381\pi$
$227$	−5.24796	−	19.5856i	−0.348319	−	1.29994i	0.540367	−	0.841429i	$-0.318285\pi$
$228$	0.698857	−	1.65136i	0.0462829	−	0.109364i
$229$	−14.1244	+	14.1244i	−0.933364	+	0.933364i	−0.997914	−	0.0645507i	$-0.979439\pi$
$229$	−14.1244	+	14.1244i	−0.933364	+	0.933364i	0.0645507	+	0.997914i	$0.479439\pi$
$230$		0			0
$231$	−1.39183	+	9.98158i	−0.0915757	+	0.656740i
$232$	18.0622	+	4.83975i	1.18584	+	0.317745i
$233$	−17.4559			−1.14357			−0.571786	−	0.820403i	$-0.693749\pi$
$233$	−17.4559			−1.14357			−0.571786	+	0.820403i	$0.693749\pi$
$234$	13.4140	+	9.24205i	0.876899	+	0.604172i
$235$		0			0
$236$	−0.779548	−	0.208879i	−0.0507443	−	0.0135969i
$237$	−0.478405	+	3.43091i	−0.0310757	+	0.222861i
$238$	9.29423	+	5.36603i	0.602455	+	0.347828i
$239$	6.59817	−	6.59817i	0.426800	−	0.426800i	−0.460737	−	0.887537i	$-0.652415\pi$
$239$	6.59817	−	6.59817i	0.426800	−	0.426800i	0.887537	+	0.460737i	$0.152415\pi$
$240$		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
$243$	−9.95544	+	11.9954i	−0.638642	+	0.769504i
$244$	1.62436	−	0.937822i	0.103989	−	0.0600379i
$245$		0			0
$246$	−9.01327	+	11.5622i	−0.574665	+	0.737178i
$247$	13.6603	−	2.73205i	0.869181	−	0.173836i
$248$			9.08973i			0.577198i
$249$	−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	$0.156736\pi$
$252$	−0.583396	+	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
$257$	−10.7533	−	18.6252i	−0.670770	−	1.16181i	−0.977686	−	0.210071i	$-0.932630\pi$
$257$	−10.7533	−	18.6252i	−0.670770	−	1.16181i	0.306916	−	0.951737i	$-0.400703\pi$
$258$	4.57125	−	3.45243i	0.284593	−	0.214939i
$259$		−	7.66025i		−	0.475985i
$260$		0			0
$261$	20.8564	−	5.24796i	1.29098	−	0.324840i
$262$	−3.09808	+	11.5622i	−0.191400	+	0.714314i
$263$	19.3003	−	11.1430i	1.19011	−	0.687109i	0.231777	−	0.972769i	$-0.425546\pi$
$263$	19.3003	−	11.1430i	1.19011	−	0.687109i	0.958331	+	0.285660i	$0.0922127\pi$
$264$	6.98197	+	17.2274i	0.429710	+	1.06027i
$265$		0			0
$266$	2.12976	+	7.94839i	0.130584	+	0.487347i
$267$	−14.8842	−	6.29899i	−0.910896	−	0.385492i
$268$	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	$0.507921\pi$
$272$	22.4950			1.36396
$273$	−8.81647	+	0.519441i	−0.533597	+	0.0314380i
$274$	−10.1244			−0.611635
$275$		0			0
$276$		0			0
$277$	−23.8923	−	13.7942i	−1.43555	−	0.828815i	−0.438013	−	0.898969i	$-0.644318\pi$
$277$	−23.8923	−	13.7942i	−1.43555	−	0.828815i	−0.997536	+	0.0701536i	$0.977651\pi$
$278$	−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	$0.920997\pi$
$282$	−14.5623	+	5.90185i	−0.867172	+	0.351450i
$283$	5.70577	−	3.29423i	0.339173	−	0.195822i	−0.320733	−	0.947170i	$-0.603929\pi$
$283$	5.70577	−	3.29423i	0.339173	−	0.195822i	0.659906	+	0.751348i	$0.270596\pi$
$284$	0.208879	−	0.779548i	0.0123947	−	0.0462577i
$285$		0			0
$286$	12.3923	−	18.5885i	0.732772	−	1.09916i
$287$		−	7.94839i		−	0.469179i
$288$	−0.0690922	+	4.51739i	−0.00407129	+	0.266189i
$289$	−4.19615	−	7.26795i	−0.246832	−	0.427526i
$290$		0			0
$291$	−0.360213	−	2.90774i	−0.0211161	−	0.170455i
$292$	0.330127	−	0.0884573i	0.0193192	−	0.00517657i
$293$	1.73999	−	0.466229i	0.101651	−	0.0272374i	−0.207635	−	0.978206i	$-0.566577\pi$
$293$	1.73999	−	0.466229i	0.101651	−	0.0272374i	0.309286	+	0.950969i	$0.399910\pi$
$294$	1.60341	+	12.9432i	0.0935127	+	0.754860i
$295$		0			0
$296$	−7.06440	−	12.2359i	−0.410610	−	0.711198i
$297$	16.6581	+	13.4003i	0.966601	+	0.777567i
$298$			13.0000i			0.753070i
$299$		0			0
$300$		0			0
$301$	−0.803848	+	3.00000i	−0.0463330	+	0.172917i
$302$	0.988427	−	0.570669i	0.0568776	−	0.0328383i
$303$	9.67552	−	3.92132i	0.555844	−	0.225274i
$304$	12.1962	+	12.1962i	0.699497	+	0.699497i
$305$		0			0
$306$	19.8878	−	11.0802i	1.13691	−	0.633414i
$307$	−8.39230	+	8.39230i	−0.478974	+	0.478974i	−0.904803	−	0.425829i	$-0.859982\pi$
$307$	−8.39230	+	8.39230i	−0.478974	+	0.478974i	0.425829	+	0.904803i	$0.359982\pi$
$308$	1.35022	+	0.779548i	0.0769357	+	0.0444189i
$309$	−11.8850	−	1.65724i	−0.676115	−	0.0942773i
$310$		0			0
$311$	10.0782			0.571480			0.285740	−	0.958307i	$-0.407761\pi$
$311$	10.0782			0.571480			0.285740	+	0.958307i	$0.407761\pi$
$312$	−13.6037	+	8.96040i	−0.770159	+	0.507283i
$313$	−2.00000			−0.113047			−0.0565233	−	0.998401i	$-0.518002\pi$
$313$	−2.00000			−0.113047			−0.0565233	+	0.998401i	$0.518002\pi$
$314$	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	$-0.601124\pi$
$317$	11.3519	−	11.3519i	0.637587	−	0.637587i	0.949960	+	0.312373i	$0.101124\pi$
$318$	−1.87260	−	0.792486i	−0.105010	−	0.0444404i
$319$	−7.63397	−	28.4904i	−0.427421	−	1.59516i
$320$		0			0
$321$	−12.3706	−	30.5234i	−0.690460	−	1.70365i
$322$		0			0
$323$	5.03908	−	18.8061i	0.280382	−	1.04640i
$324$	1.14134	+	2.12436i	0.0634076	+	0.118020i
$325$		0			0
$326$			6.23638i			0.345401i
$327$	25.7939	−	19.4808i	1.42641	−	1.07729i
$328$	−7.33013	−	12.6962i	−0.404739	−	0.701028i
$329$	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	$0.806225\pi$
$332$	−1.06488	+	0.285334i	−0.0584430	+	0.0156598i
$333$	−13.9469	−	8.33919i	−0.764285	−	0.456985i
$334$	−10.1244	+	17.5359i	−0.553980	+	0.959522i
$335$		0			0
$336$	−6.59014	−	8.72579i	−0.359521	−	0.476031i
$337$		−	18.4641i		−	1.00580i	−0.864344	−	0.502902i	$-0.832266\pi$
$337$		−	18.4641i		−	1.00580i	0.864344	−	0.502902i	$-0.167734\pi$
$338$	18.1030	+	7.45418i	0.984673	+	0.405454i
$339$	−10.9545	+	14.0524i	−0.594966	+	0.763219i
$340$		0			0
$341$	12.4168	−	7.16884i	0.672407	−	0.388215i
$342$	16.7900	+	4.77524i	0.907900	+	0.258215i
$343$	−12.0000	−	12.0000i	−0.647939	−	0.647939i
$344$	1.48264	+	5.53329i	0.0799386	+	0.298335i
$345$		0			0
$346$	18.5885	−	18.5885i	0.999322	−	0.999322i
$347$	−17.8177	−	10.2870i	−0.956502	−	0.552237i	−0.0614076	−	0.998113i	$-0.519559\pi$
$347$	−17.8177	−	10.2870i	−0.956502	−	0.552237i	−0.895095	+	0.445876i	$0.852892\pi$
$348$	0.459481	−	3.29519i	0.0246308	−	0.176641i
$349$	27.4904	+	7.36603i	1.47153	+	0.394294i	0.903454	−	0.428684i	$-0.141023\pi$
$349$	27.4904	+	7.36603i	1.47153	+	0.394294i	0.568072	+	0.822979i	$0.307689\pi$
$350$		0			0
$351$	−8.65215	+	16.6175i	−0.461818	+	0.886975i
$352$	6.19615			0.330256
$353$	−13.6626	−	3.66088i	−0.727186	−	0.194849i	−0.123810	−	0.992306i	$-0.539511\pi$
$353$	−13.6626	−	3.66088i	−0.727186	−	0.194849i	−0.603376	+	0.797457i	$0.706178\pi$
$354$	1.08500	−	7.78112i	0.0576670	−	0.413562i
$355$		0			0
$356$	−1.76798	+	1.76798i	−0.0937025	+	0.0937025i
$357$	−4.81059	+	11.3671i	−0.254603	+	0.601613i
$358$	−10.3468	−	38.6147i	−0.546845	−	2.04085i
$359$	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
$362$	1.16932	−	4.36397i	0.0614582	−	0.229365i
$363$	6.31284	−	8.09808i	0.331338	−	0.425039i
$364$	−0.437822	+	1.29423i	−0.0229481	+	0.0678360i
$365$		0			0
$366$	11.0042	+	14.5704i	0.575201	+	0.761605i
$367$	15.1962	+	26.3205i	0.793233	+	1.37392i	0.923955	+	0.382500i	$0.124937\pi$
$367$	15.1962	+	26.3205i	0.793233	+	1.37392i	−0.130723	+	0.991419i	$0.541730\pi$
$368$		0			0
$369$	−14.4715	−	8.65286i	−0.753356	−	0.450450i
$370$		0			0
$371$	1.06488	−	0.285334i	0.0552859	−	0.0148138i
$372$	1.60502	−	0.198831i	0.0832162	−	0.0103089i
$373$	5.79423	−	10.0359i	0.300014	−	0.519639i	−0.676125	−	0.736787i	$-0.736342\pi$
$373$	5.79423	−	10.0359i	0.300014	−	0.519639i	0.976139	+	0.217148i	$0.0696754\pi$
$374$	−15.6114	−	27.0398i	−0.807249	−	1.39820i
$375$		0			0
$376$		−	15.7128i		−	0.810326i
$377$	23.1701	−	11.4564i	1.19332	−	0.590032i
$378$	−10.1244	−	4.46841i	−0.520741	−	0.229830i
$379$	3.83013	−	14.2942i	0.196740	−	0.734245i	−0.795069	−	0.606519i	$-0.792565\pi$
$379$	3.83013	−	14.2942i	0.196740	−	0.734245i	0.991809	−	0.127726i	$-0.0407679\pi$
$380$		0			0
$381$	−5.93605	−	14.6467i	−0.304113	−	0.750372i
$382$	5.14359	+	5.14359i	0.263169	+	0.263169i
$383$	8.51906	+	31.7936i	0.435304	+	1.62458i	0.740339	+	0.672234i	$0.234665\pi$
$383$	8.51906	+	31.7936i	0.435304	+	1.62458i	−0.305035	+	0.952341i	$0.598668\pi$
$384$	−20.8033	−	8.80399i	−1.06162	−	0.449277i
$385$		0			0
$386$	−0.180895	−	0.104440i	−0.00920730	−	0.00531584i
$387$	4.58695	+	4.72944i	0.233168	+	0.240411i
$388$	−0.437822	−	0.117314i	−0.0222271	−	0.00595572i
$389$	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
$392$	−12.5977	−	3.37554i	−0.636280	−	0.170491i
$393$	−13.6351	−	1.90128i	−0.687800	−	0.0959066i
$394$	5.36603	+	3.09808i	0.270336	+	0.156079i
$395$		0			0
$396$	2.88920	−	1.60968i	0.145188	−	0.0808892i
$397$	3.56218	+	13.2942i	0.178781	+	0.667218i	0.995877	+	0.0907168i	$0.0289158\pi$
$397$	3.56218	+	13.2942i	0.178781	+	0.667218i	−0.817096	+	0.576501i	$0.804418\pi$
$398$	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	$0.982705\pi$
$402$	12.2079	+	9.51666i	0.608876	+	0.474648i
$403$	8.29423	+	9.43782i	0.413165	+	0.470131i
$404$		−	1.61507i		−	0.0803525i
$405$		0			0
$406$	7.63397	+	13.2224i	0.378868	+	0.656218i
$407$	−11.1430	+	19.3003i	−0.552340	+	0.956681i
$408$	2.79889	+	22.5934i	0.138566	+	1.11854i
$409$	28.9904	−	7.76795i	1.43348	−	0.384100i	0.543236	−	0.839580i	$-0.317199\pi$
$409$	28.9904	−	7.76795i	1.43348	−	0.384100i	0.890246	+	0.455480i	$0.150532\pi$
$410$		0			0
$411$	−1.43156	−	11.5559i	−0.0706135	−	0.570011i
$412$	−0.928203	+	1.60770i	−0.0457293	+	0.0792055i
$413$	2.12976	+	3.68886i	0.104799	+	0.181517i
$414$		0			0
$415$		0			0
$416$	1.06488	+	5.32441i	0.0522102	+	0.261051i
$417$	−25.1244	−	19.5856i	−1.23034	−	0.959113i
$418$	6.19615	−	23.1244i	0.303064	−	1.13105i
$419$	−8.23373	+	4.75374i	−0.402244	+	0.232236i	−0.687452	−	0.726230i	$-0.741271\pi$
$419$	−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	$0.836972\pi$
$422$	0.703093	+	2.62398i	0.0342260	+	0.127733i
$423$	−8.79543	−	15.7869i	−0.427648	−	0.767584i
$424$	1.43782	−	1.43782i	0.0698268	−	0.0698268i
$425$		0			0
$426$	7.78112	+	1.08500i	0.376997	+	0.0525683i
$427$	−9.56218	−	2.56218i	−0.462746	−	0.123992i
$428$	−5.09505			−0.246278
$429$	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	$0.948224\pi$
$432$	−23.0611	+	2.49938i	−1.10953	+	0.120252i
$433$	26.8923	+	15.5263i	1.29236	+	0.746145i	0.979072	−	0.203512i	$-0.0652357\pi$
$433$	26.8923	+	15.5263i	1.29236	+	0.746145i	0.313289	+	0.949658i	$0.398569\pi$
$434$	−5.24796	+	5.24796i	−0.251910	+	0.251910i
$435$		0			0
$436$	−1.29423	−	4.83013i	−0.0619823	−	0.231321i
$437$		0			0
$438$	1.24967	+	3.08346i	0.0597117	+	0.147333i
$439$	1.09808	−	0.633975i	0.0524083	−	0.0302580i	−0.473567	−	0.880758i	$-0.657034\pi$
$439$	1.09808	−	0.633975i	0.0524083	−	0.0302580i	0.525975	+	0.850500i	$0.323700\pi$
$440$		0			0
$441$	−14.5466	+	3.66025i	−0.692694	+	0.174298i
$442$	20.5526	−	18.0622i	0.977586	−	0.859130i
$443$			11.2195i			0.533054i	0.963827	+	0.266527i	$0.0858762\pi$
$443$			11.2195i			0.533054i	−0.963827	+	0.266527i	$0.914124\pi$
$444$	−2.00602	+	1.51505i	−0.0952017	+	0.0719009i
$445$		0			0
$446$	−19.5092	+	33.7909i	−0.923787	+	1.60005i
$447$	−14.8382	+	1.83816i	−0.701821	+	0.0869422i
$448$	9.09808	−	2.43782i	0.429844	−	0.115176i
$449$	−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
$452$	1.37820	+	2.38711i	0.0648251	+	0.112280i
$453$	0.791121	+	1.04750i	0.0371701	+	0.0492157i
$454$		−	30.5359i		−	1.43312i
$455$		0			0
$456$	−10.7321	+	13.7670i	−0.502574	+	0.644700i
$457$	1.00962	−	3.76795i	0.0472280	−	0.176257i	−0.938283	−	0.345868i	$-0.887584\pi$
$457$	1.00962	−	3.76795i	0.0472280	−	0.176257i	0.985511	+	0.169611i	$0.0542511\pi$
$458$	−26.0514	+	15.0408i	−1.21730	+	0.702809i
$459$	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	$-0.248290\pi$
$462$	−5.91520	+	13.9773i	−0.275200	+	0.650282i
$463$	−23.0526	+	23.0526i	−1.07134	+	1.07134i	−0.0740918	+	0.997251i	$0.523606\pi$
$463$	−23.0526	+	23.0526i	−1.07134	+	1.07134i	−0.997251	+	0.0740918i	$0.976394\pi$
$464$	27.7149	+	16.0012i	1.28663	+	0.742838i
$465$		0			0
$466$	−25.3923	−	6.80385i	−1.17628	−	0.315182i
$467$	19.1679			0.886984			0.443492	−	0.896278i	$-0.353739\pi$
$467$	19.1679			0.886984			0.443492	+	0.896278i	$0.353739\pi$
$468$	1.87975	+	2.20607i	0.0868916	+	0.101976i
$469$	−8.39230			−0.387521
$470$		0			0
$471$	−1.14909	+	8.24078i	−0.0529474	+	0.379715i
$472$	6.80385	+	3.92820i	0.313172	+	0.180810i
$473$	6.38929	−	6.38929i	0.293780	−	0.293780i
$474$	−2.03319	+	4.80432i	−0.0933877	+	0.220670i
$475$		0			0
$476$	1.35022	+	1.35022i	0.0618871	+	0.0618871i
$477$	0.639761	−	2.24944i	0.0292926	−	0.102995i
$478$	12.1699	−	7.02628i	0.556637	−	0.321375i
$479$	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
$482$			21.9243i			0.998624i
$483$		0			0
$484$	−0.794229	−	1.37564i	−0.0361013	−	0.0625293i
$485$		0			0
$486$	−19.1572	+	13.5688i	−0.868990	+	0.615492i
$487$	−5.56218	+	1.49038i	−0.252046	+	0.0675356i	−0.382630	−	0.923902i	$-0.624982\pi$
$487$	−5.56218	+	1.49038i	−0.252046	+	0.0675356i	0.130584	+	0.991437i	$0.458315\pi$
$488$	−17.6368	+	4.72576i	−0.798379	+	0.213925i
$489$	−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	$0.610773\pi$
$492$	−2.08148	+	1.57203i	−0.0938403	+	0.0708728i
$493$		−	36.1244i		−	1.62696i
$494$	20.9359	+	1.35022i	0.941949	+	0.0607491i
$495$		0			0
$496$	−4.02628	+	15.0263i	−0.180785	+	0.674700i
$497$	−3.68886	+	2.12976i	−0.165468	+	0.0955330i
$498$	−4.03104	−	9.94624i	−0.180635	−	0.445702i
$499$	−2.46410	−	2.46410i	−0.110308	−	0.110308i	0.649798	−	0.760107i	$-0.274853\pi$
$499$	−2.46410	−	2.46410i	−0.110308	−	0.110308i	−0.760107	+	0.649798i	$0.774853\pi$
$500$		0			0
$501$	−21.4470	−	9.07638i	−0.958181	−	0.405503i
$502$	1.05256	−	1.05256i	0.0469780	−	0.0469780i
$503$	2.83286	+	1.63555i	0.126311	+	0.0729256i	0.561824	−	0.827257i	$-0.310100\pi$
$503$	2.83286	+	1.63555i	0.126311	+	0.0729256i	−0.435513	+	0.900182i	$0.643433\pi$
$504$	7.94401	−	7.70467i	0.353854	−	0.343193i
$505$		0			0
$506$		0			0
$507$	−5.94846	+	21.7167i	−0.264180	+	0.964473i
$508$	−2.44486			−0.108473
$509$	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
$513$	−3.07638	+	19.8393i	−0.135826	+	0.875926i
$514$	−8.38269	−	31.2846i	−0.369744	−	1.37990i
$515$		0			0
$516$	0.944608	−	0.382834i	0.0415841	−	0.0168533i
$517$	−21.4641	+	12.3923i	−0.943990	+	0.545013i
$518$	2.98577	−	11.1430i	0.131187	−	0.489597i
$519$	23.8452	+	18.5885i	1.04669	+	0.815943i
$520$		0			0
$521$		−	2.49155i		−	0.109157i	−0.998509	−	0.0545785i	$-0.982618\pi$
$521$		−	2.49155i		−	0.109157i	0.998509	−	0.0545785i	$-0.0173815\pi$
$522$	32.3844	+	0.495311i	1.41743	+	0.0216792i
$523$	−19.4904	−	33.7583i	−0.852255	−	1.47615i	−0.879169	−	0.476511i	$-0.841901\pi$
$523$	−19.4904	−	33.7583i	−0.852255	−	1.47615i	0.0269137	−	0.999638i	$-0.491432\pi$
$524$	−1.06488	+	1.84443i	−0.0465196	+	0.0805743i
$525$		0			0
$526$	32.4186	−	8.68653i	1.41352	−	0.378751i
$527$	16.9617	−	4.54486i	0.738862	−	0.197977i
$528$	3.91108	+	31.5713i	0.170208	+	1.37397i
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$		0			0
$531$	9.03477	+	0.138184i	0.392076	+	0.00599669i
$532$			1.46410i			0.0634769i
$533$	−19.1959	−	6.49373i	−0.831465	−	0.281275i
$534$	−19.1962	−	14.9643i	−0.830699	−	0.647570i
$535$		0			0
$536$	−13.4052	+	7.73951i	−0.579018	+	0.334296i
$537$	42.6117	−	17.2698i	1.83883	−	0.745247i
$538$	−15.2679	−	15.2679i	−0.658248	−	0.658248i
$539$	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	$0.376034\pi$
$542$	10.0782	+	5.81863i	0.432894	+	0.249931i
$543$	5.14636	+	0.717608i	0.220852	+	0.0307955i
$544$	7.33013	+	1.96410i	0.314277	+	0.0842102i
$545$		0			0
$546$	−13.0274	−	2.68082i	−0.557521	−	0.114729i
$547$	−2.00000			−0.0855138			−0.0427569	−	0.999086i	$-0.513614\pi$
$547$	−2.00000			−0.0855138			−0.0427569	+	0.999086i	$0.513614\pi$
$548$	−1.73999	−	0.466229i	−0.0743287	−	0.0199163i
$549$	−15.0746	+	14.6204i	−0.643368	+	0.623984i
$550$		0			0
$551$	19.5856	−	19.5856i	0.834376	−	0.834376i
$552$		0			0
$553$	−0.732051	−	2.73205i	−0.0311300	−	0.116179i
$554$	−29.3785	−	29.3785i	−1.24817	−	1.24817i
$555$		0			0
$556$	−4.26795	+	2.46410i	−0.181001	+	0.104501i
$557$	−6.62616	+	24.7292i	−0.280759	+	1.04781i	0.671123	+	0.741346i	$0.265812\pi$
$557$	−6.62616	+	24.7292i	−0.280759	+	1.04781i	−0.951883	+	0.306462i	$0.900855\pi$
$558$	3.84177	+	15.2679i	0.162635	+	0.646344i
$559$	6.58846	+	4.39230i	0.278662	+	0.185775i
$560$		0			0
$561$	28.6558	−	21.6422i	1.20985	−	0.913735i
$562$	−12.9186	−	22.3756i	−0.544938	−	0.943860i
$563$	−5.03908	+	8.72794i	−0.212372	+	0.367839i	−0.952456	−	0.304675i	$-0.901452\pi$
$563$	−5.03908	+	8.72794i	−0.212372	+	0.367839i	0.740085	+	0.672514i	$0.234785\pi$
$564$	−2.77449	+	0.343706i	−0.116827	+	0.0144726i
$565$		0			0
$566$	9.58394	−	2.56801i	0.402843	−	0.107941i
$567$	3.66867	−	12.1877i	0.154070	−	0.511837i
$568$	−3.92820	+	6.80385i	−0.164824	+	0.285483i
$569$	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	$-0.0129744\pi$
$572$	2.98577	−	2.62398i	0.124841	−	0.109714i
$573$	−5.14359	+	6.59817i	−0.214877	+	0.275643i
$574$	3.09808	−	11.5622i	0.129311	−	0.482596i
$575$		0			0
$576$	5.46595	−	19.2186i	0.227748	−	0.800775i
$577$	22.4904	+	22.4904i	0.936287	+	0.936287i	0.998088	−	0.0618016i	$-0.0196846\pi$
$577$	22.4904	+	22.4904i	0.936287	+	0.936287i	−0.0618016	+	0.998088i	$0.519685\pi$
$578$	−3.27110	−	12.2079i	−0.136060	−	0.507783i
$579$	0.0936291	−	0.221240i	0.00389109	−	0.00919443i
$580$		0			0
$581$	5.03908	+	2.90931i	0.209056	+	0.120699i
$582$	0.609374	−	4.37016i	0.0252594	−	0.181149i
$583$	−3.09808	−	0.830127i	−0.128309	−	0.0343803i
$584$	−3.32707			−0.137675
$585$		0			0
$586$	2.71281			0.112065
$587$	−18.0265	−	4.83020i	−0.744035	−	0.199364i	−0.133164	−	0.991094i	$-0.542514\pi$
$587$	−18.0265	−	4.83020i	−0.744035	−	0.199364i	−0.610871	+	0.791730i	$0.709181\pi$
$588$	−0.320471	+	2.29827i	−0.0132160	+	0.0947792i
$589$	11.6603	+	6.73205i	0.480452	+	0.277389i
$590$		0			0
$591$	−2.77739	+	6.56283i	−0.114247	+	0.269959i
$592$	−6.25833	−	23.3564i	−0.257216	−	0.959942i
$593$	−10.3635	−	10.3635i	−0.425578	−	0.425578i	0.461541	−	0.887119i	$-0.347297\pi$
$593$	−10.3635	−	10.3635i	−0.425578	−	0.425578i	−0.887119	+	0.461541i	$0.847297\pi$
$594$	19.0087	+	25.9858i	0.779937	+	1.06621i
$595$		0			0
$596$	−0.598653	+	2.23420i	−0.0245218	+	0.0915166i
$597$	−13.7670	+	17.6603i	−0.563446	+	0.722786i
$598$		0			0
$599$			20.7270i			0.846881i	0.905924	+	0.423441i	$0.139178\pi$
$599$			20.7270i			0.846881i	−0.905924	+	0.423441i	$0.860822\pi$
$600$		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	$0.993095\pi$
$602$	−2.33864	+	4.05065i	−0.0953160	+	0.165092i
$603$	−9.13612	+	15.2797i	−0.372052	+	0.622238i
$604$	0.196152	−	0.0525589i	0.00798133	−	0.00213859i
$605$		0			0
$606$	15.6030	−	1.93291i	0.633828	−	0.0785192i
$607$	−0.0980762	+	0.169873i	−0.00398079	+	0.00689493i	−0.868009	−	0.496549i	$-0.834600\pi$
$607$	−0.0980762	+	0.169873i	−0.00398079	+	0.00689493i	0.864028	+	0.503444i	$0.167934\pi$
$608$	2.90931	+	5.03908i	0.117988	+	0.204362i
$609$	−14.0126	+	10.5830i	−0.567820	+	0.428845i
$610$		0			0
$611$	−14.3377	−	16.3145i	−0.580041	−	0.660016i
$612$	3.92820	−	0.988427i	0.158788	−	0.0399548i
$613$	11.3564	−	42.3827i	0.458681	−	1.71182i	−0.218354	−	0.975870i	$-0.570069\pi$
$613$	11.3564	−	42.3827i	0.458681	−	1.71182i	0.677035	−	0.735951i	$-0.263265\pi$
$614$	−15.4790	+	8.93682i	−0.624683	+	0.360661i
$615$		0			0
$616$	−10.7321	−	10.7321i	−0.432407	−	0.432407i
$617$	4.78173	+	17.8457i	0.192505	+	0.718439i	0.992899	+	0.118964i	$0.0379573\pi$
$617$	4.78173	+	17.8457i	0.192505	+	0.718439i	−0.800393	+	0.599475i	$0.795376\pi$
$618$	−16.6427	−	7.04319i	−0.669466	−	0.283319i
$619$	−31.6603	+	31.6603i	−1.27253	+	1.27253i	−0.327778	+	0.944755i	$0.606300\pi$
$619$	−31.6603	+	31.6603i	−1.27253	+	1.27253i	−0.944755	+	0.327778i	$0.893700\pi$
$620$		0			0
$621$		0			0
$622$	14.6603	+	3.92820i	0.587823	+	0.157507i
$623$	13.1963			0.528701
$624$	−26.4574	+	8.78674i	−1.05914	+	0.351751i
$625$		0			0
$626$	−2.90931	−	0.779548i	−0.116280	−	0.0311570i
$627$	27.2702	+	3.80255i	1.08907	+	0.151859i
$628$	1.11474	+	0.643594i	0.0444828	+	0.0256822i
$629$	−19.3003	+	19.3003i	−0.769554	+	0.769554i
$630$		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
$633$	−2.89559	+	1.17353i	−0.115089	+	0.0466437i
$634$	20.9378	−	12.0885i	0.831547	−	0.480094i
$635$		0			0
$636$	−0.285334	−	0.222432i	−0.0113142	−	0.00882000i
$637$	−16.1603	+	7.99038i	−0.640293	+	0.316590i
$638$		−	44.4192i		−	1.75857i
$639$	−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	$0.813383\pi$
$642$	−6.09776	−	49.2228i	−0.240659	−	1.94267i
$643$	−7.00000	+	1.87564i	−0.276053	+	0.0739682i	−0.394190	−	0.919029i	$-0.628975\pi$
$643$	−7.00000	+	1.87564i	−0.276053	+	0.0739682i	0.118136	+	0.992997i	$0.462308\pi$
$644$		0			0
$645$		0			0
$646$	14.6603	−	25.3923i	0.576800	−	0.999047i
$647$	−8.23373	−	14.2612i	−0.323701	−	0.560667i	0.657547	−	0.753413i	$-0.271594\pi$
$647$	−8.23373	−	14.2612i	−0.323701	−	0.560667i	−0.981249	+	0.192746i	$0.938261\pi$
$648$	−5.37965	−	22.8511i	−0.211333	−	0.897674i
$649$		−	12.3923i		−	0.486441i
$650$		0			0
$651$	−6.73205	−	5.24796i	−0.263850	−	0.205684i
$652$	−0.287187	+	1.07180i	−0.0112471	+	0.0419748i
$653$	−8.36615	+	4.83020i	−0.327393	+	0.189020i	−0.654683	−	0.755904i	$-0.727198\pi$
$653$	−8.36615	+	4.83020i	−0.327393	+	0.189020i	0.327290	+	0.944924i	$0.393865\pi$
$654$	45.1145	−	18.2841i	1.76411	−	0.714966i
$655$		0			0
$656$	−6.49373	−	24.2349i	−0.253538	−	0.946216i
$657$	−3.34275	+	1.86237i	−0.130413	+	0.0726578i
$658$	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	$0.522541\pi$
$662$	−51.5321			−2.00285
$663$	23.5222	+	20.9047i	0.913526	+	0.811871i
$664$	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
$672$	−1.38556	−	3.41876i	−0.0534493	−	0.131881i
$673$	36.9904	−	21.3564i	1.42587	−	0.823229i	0.429082	−	0.903265i	$-0.358837\pi$
$673$	36.9904	−	21.3564i	1.42587	−	0.823229i	0.996792	+	0.0800364i	$0.0255036\pi$
$674$	7.19683	−	26.8589i	0.277211	−	1.03457i
$675$		0			0
$676$	2.76795	+	2.11474i	0.106460	+	0.0813360i
$677$		−	9.66040i		−	0.371279i	−0.982618	−	0.185640i	$-0.940564\pi$
$677$		−	9.66040i		−	0.371279i	0.982618	−	0.185640i	$-0.0594357\pi$
$678$	−21.4123	+	16.1716i	−0.822333	+	0.621065i
$679$	1.19615	+	2.07180i	0.0459041	+	0.0795083i
$680$		0			0
$681$	34.8536	−	4.31769i	1.33559	−	0.165454i
$682$	20.8564	−	5.58846i	0.798633	−	0.213993i
$683$	−45.2752	+	12.1315i	−1.73241	+	0.464198i	−0.980736	−	0.195338i	$-0.937420\pi$
$683$	−45.2752	+	12.1315i	−1.73241	+	0.464198i	−0.751673	+	0.659536i	$0.770753\pi$
$684$	2.66566	+	1.59387i	0.101924	+	0.0609430i
$685$		0			0
$686$	−12.7786	−	22.1332i	−0.487889	−	0.845048i
$687$	−20.8511	−	27.6083i	−0.795519	−	1.05332i
$688$			9.80385i			0.373768i
$689$	0.180895	−	2.80487i	0.00689154	−	0.106857i
$690$		0			0
$691$	4.88269	−	18.2224i	0.185746	−	0.693214i	−0.808723	−	0.588189i	$-0.799841\pi$
$691$	4.88269	−	18.2224i	0.185746	−	0.693214i	0.994470	−	0.105025i	$-0.0334922\pi$
$692$	4.05065	−	2.33864i	0.153983	−	0.0889019i
$693$	−16.7900	−	4.77524i	−0.637800	−	0.181396i
$694$	−21.9090	−	21.9090i	−0.831653	−	0.831653i
$695$		0			0
$696$	−12.6229	+	29.8272i	−0.478469	+	1.13060i
$697$	−20.0263	+	20.0263i	−0.758549	+	0.758549i
$698$	37.1180	+	21.4301i	1.40494	+	0.811140i
$699$	4.17549	−	29.9448i	0.157932	−	1.13261i
$700$		0			0
$701$	12.7786			0.482641			0.241320	−	0.970446i	$-0.422420\pi$
$701$	12.7786			0.482641			0.241320	+	0.970446i	$0.422420\pi$
$702$	−19.0630	+	20.8003i	−0.719485	+	0.785058i
$703$	−20.9282			−0.789322
$704$	−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
$708$	0.544793	−	1.28731i	0.0204746	−	0.0483802i
$709$	−3.03590	−	11.3301i	−0.114016	−	0.425512i	0.885196	−	0.465219i	$-0.154024\pi$
$709$	−3.03590	−	11.3301i	−0.114016	−	0.425512i	−0.999211	+	0.0397068i	$0.987358\pi$
$710$		0			0
$711$	−5.77113	−	1.64136i	−0.216434	−	0.0615559i
$712$	21.0788	−	12.1699i	0.789963	−	0.456085i
$713$		0			0
$714$	−11.4284	+	14.6603i	−0.427696	+	0.548646i
$715$		0			0
$716$		−	7.11287i		−	0.265821i
$717$	9.74056	+	12.8972i	0.363768	+	0.481653i
$718$	19.4186	+	33.6340i	0.724695	+	1.25521i
$719$	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
$722$	−5.92307	+	1.58708i	−0.220434	+	0.0590650i
$723$	−25.0243	+	3.10003i	−0.930665	+	0.115292i
$724$	0.401924	−	0.696152i	0.0149374	−	0.0258723i
$725$		0			0
$726$	12.3394	−	9.31934i	0.457959	−	0.345873i
$727$		−	19.5167i		−	0.723833i	−0.932211	−	0.361916i	$-0.882123\pi$
$727$		−	19.5167i		−	0.723833i	0.932211	−	0.361916i	$-0.117877\pi$
$728$	7.37772	−	11.0666i	0.273437	−	0.410155i
$729$	−18.1962	−	19.9474i	−0.673932	−	0.738794i
$730$		0			0
$731$	9.58394	−	5.53329i	0.354475	−	0.204656i
$732$	1.22024	+	3.01084i	0.0451014	+	0.111284i
$733$	6.77757	+	6.77757i	0.250335	+	0.250335i	0.821108	−	0.570773i	$-0.193356\pi$
$733$	6.77757	+	6.77757i	0.250335	+	0.250335i	−0.570773	+	0.821108i	$0.693356\pi$
$734$	11.8461	+	44.2104i	0.437249	+	1.63183i
$735$		0			0
$736$		0			0
$737$	21.1447	+	12.2079i	0.778876	+	0.449685i
$738$	−17.6784	−	18.2276i	−0.650750	−	0.670966i
$739$	−11.1244	−	2.98076i	−0.409216	−	0.109649i	0.0483378	−	0.998831i	$-0.484608\pi$
$739$	−11.1244	−	2.98076i	−0.409216	−	0.109649i	−0.457554	+	0.889182i	$0.651274\pi$
$740$		0			0
$741$	1.41914	+	24.0870i	0.0521334	+	0.884860i
$742$	1.66025			0.0609498
$743$	8.51906	+	2.28268i	0.312534	+	0.0837432i	0.411677	−	0.911330i	$-0.364943\pi$
$743$	8.51906	+	2.28268i	0.312534	+	0.0837432i	−0.0991426	+	0.995073i	$0.531610\pi$
$744$	−15.5930	−	2.17429i	−0.571667	−	0.0797132i
$745$		0			0
$746$	12.3403	−	12.3403i	0.451812	−	0.451812i
$747$	10.7826	−	6.00739i	0.394516	−	0.219799i
$748$	−1.43782	−	5.36603i	−0.0525720	−	0.196201i
$749$	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	$0.544888\pi$
$752$	6.95996	−	25.9749i	0.253804	−	0.947208i
$753$	1.35022	+	1.05256i	0.0492046	+	0.0383574i
$754$	38.1699	−	7.63397i	1.39006	−	0.278013i
$755$		0			0
$756$	−1.53422	−	1.23418i	−0.0557990	−	0.0448866i
$757$	8.39230	+	14.5359i	0.305024	+	0.528316i	0.977267	−	0.212014i	$-0.0680023\pi$
$757$	8.39230	+	14.5359i	0.305024	+	0.528316i	−0.672243	+	0.740331i	$0.734669\pi$
$758$	11.1430	−	19.3003i	0.404733	−	0.701019i
$759$		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	$0.308639\pi$
$762$	−2.92602	−	23.6196i	−0.105998	−	0.855647i
$763$	−13.1962	+	22.8564i	−0.477733	+	0.827457i
$764$	0.647124	+	1.12085i	0.0234121	+	0.0405510i
$765$		0			0
$766$			49.5692i			1.79101i
$767$	10.6488	−	2.12976i	0.384507	−	0.0769014i
$768$	−8.63397	−	6.73060i	−0.311552	−	0.242870i
$769$	−10.8301	+	40.4186i	−0.390544	+	1.45753i	0.438694	+	0.898636i	$0.355441\pi$
$769$	−10.8301	+	40.4186i	−0.390544	+	1.45753i	−0.829238	+	0.558895i	$0.811225\pi$
$770$		0			0
$771$	34.5229	−	13.9915i	1.24331	−	0.503893i
$772$	−0.0262794	−	0.0262794i	−0.000945818	−	0.000945818i
$773$	−11.1430	−	41.5864i	−0.400787	−	1.49576i	−0.811695	−	0.584081i	$-0.801455\pi$
$773$	−11.1430	−	41.5864i	−0.400787	−	1.49576i	0.410908	−	0.911677i	$-0.365212\pi$
$774$	4.82903	+	8.66759i	0.173576	+	0.311550i
$775$		0			0
$776$	3.82129	+	2.20622i	0.137176	+	0.0791987i
$777$	13.1408	+	1.83235i	0.471424	+	0.0657353i
$778$	32.7224	+	8.76795i	1.17316	+	0.314346i
$779$	−21.7154			−0.778035
$780$		0			0
$781$	12.3923			0.443432
$782$		0			0
$783$	4.01372	+	37.0335i	0.143439	+	1.32347i
$784$	−19.3301	−	11.1603i	−0.690362	−	0.398581i
$785$		0			0
$786$	−19.0933	−	8.08031i	−0.681036	−	0.288215i
$787$	−4.29423	−	16.0263i	−0.153073	−	0.571275i	−0.999263	−	0.0383938i	$-0.987776\pi$
$787$	−4.29423	−	16.0263i	−0.153073	−	0.571275i	0.846190	−	0.532881i	$-0.178891\pi$
$788$	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
$792$	−31.2229	+	7.85641i	−1.10946	+	0.279165i
$793$	−14.0000	+	21.0000i	−0.497155	+	0.745732i
$794$			20.7270i			0.735573i
$795$		0			0
$796$	1.73205	+	3.00000i	0.0613909	+	0.106332i
$797$	−20.1563	+	34.9118i	−0.713973	+	1.23664i	0.249381	+	0.968405i	$0.419773\pi$
$797$	−20.1563	+	34.9118i	−0.713973	+	1.23664i	−0.963354	+	0.268232i	$0.913561\pi$
$798$	−14.1445	+	1.75224i	−0.500711	+	0.0620286i
$799$	−29.3205	+	7.85641i	−1.03729	+	0.277940i
$800$		0			0
$801$	14.3660	−	24.0264i	0.507596	−	0.848929i
$802$	−9.37564	+	16.2391i	−0.331066	+	0.573422i
$803$	2.62398	+	4.54486i	0.0925982	+	0.160385i
$804$	1.65983	+	2.19773i	0.0585377	+	0.0775079i
$805$		0			0
$806$	8.38664	+	16.9617i	0.295407	+	0.597449i
$807$	15.2679	−	19.5856i	0.537457	−	0.689447i
$808$	−4.06922	+	15.1865i	−0.143155	+	0.534260i
$809$	24.0261	−	13.8715i	0.844712	−	0.487694i	−0.0141514	−	0.999900i	$-0.504505\pi$
$809$	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	$0.593616\pi$
$812$	0.703093	+	2.62398i	0.0246737	+	0.0920836i
$813$	−5.21634	+	12.3259i	−0.182945	+	0.432289i
$814$	−23.7321	+	23.7321i	−0.831808	+	0.831808i
$815$		0			0
$816$	−5.38085	+	38.5891i	−0.188367	+	1.35089i
$817$	8.19615	+	2.19615i	0.286747	+	0.0768336i
$818$	45.1988			1.58034
$819$	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	$0.853900\pi$
$822$	2.42177	−	17.3679i	0.0844690	−	0.605774i
$823$	7.39230	+	4.26795i	0.257680	+	0.148771i	0.623276	−	0.782002i	$-0.285801\pi$
$823$	7.39230	+	4.26795i	0.257680	+	0.148771i	−0.365596	+	0.930774i	$0.619135\pi$
$824$	12.7786	−	12.7786i	0.445163	−	0.445163i
$825$		0			0
$826$	1.66025	+	6.19615i	0.0577676	+	0.215592i
$827$	31.7936	+	31.7936i	1.10557	+	1.10557i	0.993726	+	0.111845i	$0.0356760\pi$
$827$	31.7936	+	31.7936i	1.10557	+	1.10557i	0.111845	+	0.993726i	$0.464324\pi$
$828$		0			0
$829$	41.6769	−	24.0622i	1.44750	−	0.835714i	0.449167	−	0.893448i	$-0.351721\pi$
$829$	41.6769	−	24.0622i	1.44750	−	0.835714i	0.998332	+	0.0577338i	$0.0183875\pi$
$830$		0			0
$831$	29.3785	−	37.6865i	1.01913	−	1.30733i
$832$	1.54552	−	23.9641i	0.0535812	−	0.830806i
$833$			25.1954i			0.872968i
$834$	−28.9133	−	38.2832i	−1.00119	−	1.32564i
$835$		0			0
$836$	2.12976	−	3.68886i	0.0736595	−	0.127582i
$837$	−16.8836	+	6.54383i	−0.583582	+	0.226188i
$838$	−13.8301	+	3.70577i	−0.477754	+	0.128014i
$839$	−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
$842$	−8.33816	−	14.4421i	−0.287352	−	0.497708i
$843$	23.7128	−	17.9091i	0.816714	−	0.616822i
$844$			0.483340i			0.0166372i
$845$		0			0
$846$	−6.64102	−	26.3927i	−0.228323	−	0.907400i
$847$	−2.16987	+	8.09808i	−0.0745577	+	0.278253i
$848$	3.01375	−	1.73999i	0.103493	−	0.0597515i
$849$	4.28626	+	10.5760i	0.147104	+	0.362967i
$850$		0			0
$851$		0			0
$852$	1.28731	+	0.544793i	0.0441027	+	0.0186643i
$853$	22.3660	−	22.3660i	0.765798	−	0.765798i	−0.211566	−	0.977364i	$-0.567856\pi$
$853$	22.3660	−	22.3660i	0.765798	−	0.765798i	0.977364	+	0.211566i	$0.0678562\pi$
$854$	−12.9110	−	7.45418i	−0.441806	−	0.255077i
$855$		0			0
$856$	47.9090	+	12.8372i	1.63749	+	0.438765i
$857$	−3.32707			−0.113651			−0.0568253	−	0.998384i	$-0.518098\pi$
$857$	−3.32707			−0.113651			−0.0568253	+	0.998384i	$0.518098\pi$
$858$	28.9234	+	25.7048i	0.987428	+	0.877549i
$859$	39.1769			1.33670			0.668350	−	0.743847i	$-0.267001\pi$
$859$	39.1769			1.33670			0.668350	+	0.743847i	$0.267001\pi$
$860$		0			0
$861$	13.6351	+	1.90128i	0.464683	+	0.0647953i
$862$	−49.3468	−	28.4904i	−1.68076	−	0.970386i
$863$	18.2354	−	18.2354i	0.620741	−	0.620741i	−0.324980	−	0.945721i	$-0.605358\pi$
$863$	18.2354	−	18.2354i	0.620741	−	0.620741i	0.945721	+	0.324980i	$0.105358\pi$
$864$	−7.73284	−	1.19909i	−0.263077	−	0.0407940i
$865$		0			0
$866$	33.0673	+	33.0673i	1.12367	+	1.12367i
$867$	13.4716	−	5.45979i	0.457518	−	0.185424i
$868$	−1.14359	+	0.660254i	−0.0388161	+	0.0224105i
$869$	−2.12976	+	7.94839i	−0.0722473	+	0.269631i
$870$		0			0
$871$	−6.85641	+	20.2679i	−0.232320	+	0.686753i
$872$			48.6788i			1.64847i
$873$	5.07425	+	0.0776093i	0.171737	+	0.00262668i
$874$		0			0
$875$		0			0
$876$	0.0727771	+	0.587477i	0.00245891	+	0.0198490i
$877$	−28.9904	+	7.76795i	−0.978936	+	0.262305i	−0.712596	−	0.701574i	$-0.752481\pi$
$877$	−28.9904	+	7.76795i	−0.978936	+	0.262305i	−0.266339	+	0.963879i	$0.585814\pi$
$878$	1.84443	−	0.494214i	0.0622465	−	0.0166789i
$879$	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	$0.703874\pi$
$882$	−22.5869	−	0.345461i	−0.760541	−	0.0116323i
$883$			33.3731i			1.12309i	0.827445	+	0.561547i	$0.189793\pi$
$883$			33.3731i			1.12309i	−0.827445	+	0.561547i	$0.810207\pi$
$884$	4.36397	−	2.15775i	0.146776	−	0.0725730i
$885$		0			0
$886$	−4.37307	+	16.3205i	−0.146916	+	0.548298i
$887$	21.8683	−	12.6257i	0.734266	−	0.423929i	−0.0857146	−	0.996320i	$-0.527317\pi$
$887$	21.8683	−	12.6257i	0.734266	−	0.423929i	0.819981	+	0.572391i	$0.193984\pi$
$888$	22.6800	−	9.19180i	0.761089	−	0.308457i
$889$	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
$893$	−20.1563	−	11.6373i	−0.674505	−	0.389426i
$894$	−22.3009	−	3.10963i	−0.745854	−	0.104002i
$895$		0			0
$896$	18.4443			0.616181
$897$		0			0
$898$	−30.9808			−1.03384
$899$	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
$903$	−4.95408	−	2.09657i	−0.164861	−	0.0697695i
$904$	−6.94486	−	25.9186i	−0.230983	−	0.862039i
$905$		0			0
$906$	0.742522	+	1.83211i	0.0246686	+	0.0608677i
$907$	15.0000	−	8.66025i	0.498067	−	0.287559i	−0.229848	−	0.973227i	$-0.573823\pi$
$907$	15.0000	−	8.66025i	0.498067	−	0.287559i	0.727915	+	0.685668i	$0.240490\pi$
$908$	1.40619	−	5.24796i	0.0466659	−	0.174160i
$909$	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	$0.991778\pi$
$912$	−23.8393	+	18.0046i	−0.789398	+	0.596191i
$913$	−8.46410	−	14.6603i	−0.280121	−	0.485184i
$914$	2.93730	−	5.08755i	0.0971572	−	0.168281i
$915$		0			0
$916$	−5.16987	+	1.38526i	−0.170817	+	0.0457704i
$917$	10.8577	−	2.90931i	0.358553	−	0.0960740i
$918$	14.2504	+	36.7670i	0.470333	+	1.21349i
$919$	−6.70577	+	11.6147i	−0.221203	+	0.383135i	−0.955174	−	0.296046i	$-0.904332\pi$
$919$	−6.70577	+	11.6147i	−0.221203	+	0.383135i	0.733971	+	0.679181i	$0.237665\pi$
$920$		0			0
$921$	−12.3892	−	16.4041i	−0.408236	−	0.540533i
$922$		−	32.0333i		−	1.05496i
$923$	2.12976	+	10.6488i	0.0701021	+	0.350510i
$924$	−1.66025	+	2.12976i	−0.0546183	+	0.0700641i
$925$		0			0
$926$	−42.5188	+	24.5483i	−1.39726	+	0.806706i
$927$	5.68585	−	19.9918i	0.186748	−	0.656616i
$928$	7.63397	+	7.63397i	0.250597	+	0.250597i
$929$	−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
$932$	−4.05065	−	2.33864i	−0.132683	−	0.0766048i
$933$	−2.41072	+	17.2886i	−0.0789234	+	0.566004i
$934$	27.8827	+	7.47114i	0.912349	+	0.244463i
$935$		0			0
$936$	−12.1171	−	25.4799i	−0.396060	−	0.832837i
$937$	37.0000			1.20874			0.604369	−	0.796705i	$-0.293425\pi$
$937$	37.0000			1.20874			0.604369	+	0.796705i	$0.293425\pi$
$938$	−12.2079	−	3.27110i	−0.398603	−	0.106805i
$939$	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	$0.317613\pi$
$942$	−4.88358	+	11.5396i	−0.159116	+	0.375981i
$943$		0			0
$944$	9.50749	+	9.50749i	0.309442	+	0.309442i
$945$		0			0
$946$	11.7846	−	6.80385i	0.383151	−	0.221212i
$947$	2.77689	−	10.3635i	0.0902368	−	0.336768i	−0.906018	−	0.423240i	$-0.860893\pi$
$947$	2.77689	−	10.3635i	0.0902368	−	0.336768i	0.996254	+	0.0864720i	$0.0275593\pi$
$948$	−0.570669	+	0.732051i	−0.0185345	+	0.0237759i
$949$	−3.45448	+	3.03590i	−0.112137	+	0.0985494i
$950$		0			0
$951$	16.7583	+	22.1891i	0.543425	+	0.719531i
$952$	−9.29423	−	16.0981i	−0.301228	−	0.521742i
$953$	0.988427	−	1.71201i	0.0320183	−	0.0554573i	−0.849572	−	0.527472i	$-0.823140\pi$
$953$	0.988427	−	1.71201i	0.0320183	−	0.0554573i	0.881591	+	0.472015i	$0.156473\pi$
$954$	1.80740	−	3.02279i	0.0585169	−	0.0978666i
$955$		0			0
$956$	2.41510	−	0.647124i	0.0781099	−	0.0209295i
$957$	50.7000	−	6.28076i	1.63890	−	0.203028i
$958$	15.4904	−	26.8301i	0.500471	−	0.866842i
$959$	4.75374	+	8.23373i	0.153506	+	0.265881i
$960$		0			0
$961$		−	18.8564i		−	0.608271i
$962$	−24.4718	−	16.3145i	−0.789003	−	0.526002i
$963$	55.3205	−	13.9199i	1.78268	−	0.448563i
$964$	−1.00962	+	3.76795i	−0.0325176	+	0.121357i
$965$		0			0
$966$		0			0
$967$	27.8564	+	27.8564i	0.895802	+	0.895802i	0.995062	−	0.0992599i	$-0.0316475\pi$
$967$	27.8564	+	27.8564i	0.895802	+	0.895802i	−0.0992599	+	0.995062i	$0.531648\pi$
$968$	4.00218	+	14.9363i	0.128635	+	0.480072i
$969$	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	$0.388077\pi$
$972$	−3.91725	+	1.44976i	−0.125646	+	0.0465011i
$973$	25.1244	+	6.73205i	0.805450	+	0.215820i
$974$	−8.67197			−0.277868
$975$		0			0
$976$	−31.2487			−1.00025
$977$	−22.8847	−	6.13194i	−0.732147	−	0.196178i	−0.126562	−	0.991959i	$-0.540394\pi$
$977$	−22.8847	−	6.13194i	−0.732147	−	0.196178i	−0.605585	+	0.795780i	$0.707061\pi$
$978$	−10.6982	−	1.49176i	−0.342092	−	0.0477012i
$979$	−33.2487	−	19.1962i	−1.06263	−	0.613512i
$980$		0			0
$981$	27.2485	+	48.9082i	0.869978	+	1.56152i
$982$	11.1173	+	41.4904i	0.354768	+	1.32401i
$983$	30.4433	+	30.4433i	0.970992	+	0.970992i	0.999591	−	0.0285990i	$-0.00910459\pi$
$983$	30.4433	+	30.4433i	0.970992	+	0.970992i	−0.0285990	+	0.999591i	$0.509105\pi$
$984$	23.5330	−	9.53754i	0.750206	−	0.304046i
$985$		0			0
$986$	14.0803	−	52.5485i	0.448409	−	1.67349i
$987$	11.6373	+	9.07180i	0.370418	+	0.288758i
$988$	3.53590	+	1.19615i	0.112492	+	0.0380547i
$989$		0			0
$990$		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	$0.466017\pi$
$992$	−2.62398	+	4.54486i	−0.0833114	+	0.144300i
$993$	−7.28650	−	58.8186i	−0.231230	−	1.86655i
$994$	−6.19615	+	1.66025i	−0.196530	+	0.0526601i
$995$		0			0
$996$	−0.234755	−	1.89501i	−0.00743851	−	0.0600457i
$997$	−3.50000	+	6.06218i	−0.110846	+	0.191991i	−0.916112	−	0.400923i	$-0.868689\pi$
$997$	−3.50000	+	6.06218i	−0.110846	+	0.191991i	0.805266	+	0.592914i	$0.202023\pi$
$998$	−2.62398	−	4.54486i	−0.0830606	−	0.143865i
$999$	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.bo.d.401.2		8
3.2	odd	2	inner	975.2.bo.d.401.1		8
5.2	odd	4		975.2.bp.f.674.1		8
5.3	odd	4		975.2.bp.e.674.2		8
5.4	even	2		39.2.k.b.11.1	✓	8
13.6	odd	12	inner	975.2.bo.d.851.1		8
15.2	even	4		975.2.bp.f.674.2		8
15.8	even	4		975.2.bp.e.674.1		8
15.14	odd	2		39.2.k.b.11.2	yes	8
20.19	odd	2		624.2.cn.c.401.1		8
39.32	even	12	inner	975.2.bo.d.851.2		8
60.59	even	2		624.2.cn.c.401.2		8
65.4	even	6		507.2.k.f.488.1		8
65.9	even	6		507.2.k.e.488.2		8
65.19	odd	12		39.2.k.b.32.2	yes	8
65.24	odd	12		507.2.f.e.239.3		8
65.29	even	6		507.2.f.f.437.3		8
65.32	even	12		975.2.bp.e.149.1		8
65.34	odd	4		507.2.k.f.80.2		8
65.44	odd	4		507.2.k.e.80.1		8
65.49	even	6		507.2.f.e.437.2		8
65.54	odd	12		507.2.f.f.239.2		8
65.58	even	12		975.2.bp.f.149.2		8
65.59	odd	12		507.2.k.d.188.1		8
65.64	even	2		507.2.k.d.89.2		8
195.29	odd	6		507.2.f.f.437.2		8
195.32	odd	12		975.2.bp.e.149.2		8
195.44	even	4		507.2.k.e.80.2		8
195.59	even	12		507.2.k.d.188.2		8
195.74	odd	6		507.2.k.e.488.1		8
195.89	even	12		507.2.f.e.239.2		8
195.119	even	12		507.2.f.f.239.3		8
195.134	odd	6		507.2.k.f.488.2		8
195.149	even	12		39.2.k.b.32.1	yes	8
195.164	even	4		507.2.k.f.80.1		8
195.179	odd	6		507.2.f.e.437.3		8
195.188	odd	12		975.2.bp.f.149.1		8
195.194	odd	2		507.2.k.d.89.1		8
260.19	even	12		624.2.cn.c.305.2		8
780.539	odd	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	5.4	even	2
39.2.k.b.11.2	yes	8	15.14	odd	2
39.2.k.b.32.1	yes	8	195.149	even	12
39.2.k.b.32.2	yes	8	65.19	odd	12
507.2.f.e.239.2		8	195.89	even	12
507.2.f.e.239.3		8	65.24	odd	12
507.2.f.e.437.2		8	65.49	even	6
507.2.f.e.437.3		8	195.179	odd	6
507.2.f.f.239.2		8	65.54	odd	12
507.2.f.f.239.3		8	195.119	even	12
507.2.f.f.437.2		8	195.29	odd	6
507.2.f.f.437.3		8	65.29	even	6
507.2.k.d.89.1		8	195.194	odd	2
507.2.k.d.89.2		8	65.64	even	2
507.2.k.d.188.1		8	65.59	odd	12
507.2.k.d.188.2		8	195.59	even	12
507.2.k.e.80.1		8	65.44	odd	4
507.2.k.e.80.2		8	195.44	even	4
507.2.k.e.488.1		8	195.74	odd	6
507.2.k.e.488.2		8	65.9	even	6
507.2.k.f.80.1		8	195.164	even	4
507.2.k.f.80.2		8	65.34	odd	4
507.2.k.f.488.1		8	65.4	even	6
507.2.k.f.488.2		8	195.134	odd	6
624.2.cn.c.305.1		8	780.539	odd	12
624.2.cn.c.305.2		8	260.19	even	12
624.2.cn.c.401.1		8	20.19	odd	2
624.2.cn.c.401.2		8	60.59	even	2
975.2.bo.d.401.1		8	3.2	odd	2	inner
975.2.bo.d.401.2		8	1.1	even	1	trivial
975.2.bo.d.851.1		8	13.6	odd	12	inner
975.2.bo.d.851.2		8	39.32	even	12	inner
975.2.bp.e.149.1		8	65.32	even	12
975.2.bp.e.149.2		8	195.32	odd	12
975.2.bp.e.674.1		8	15.8	even	4
975.2.bp.e.674.2		8	5.3	odd	4
975.2.bp.f.149.1		8	195.188	odd	12
975.2.bp.f.149.2		8	65.58	even	12
975.2.bp.f.674.1		8	5.2	odd	4
975.2.bp.f.674.2		8	15.2	even	4

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.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.45466 + 0.389774i) q^{2} +(-0.239203 + 1.71545i) q^{3} +(0.232051 + 0.133975i) q^{4} +(-1.01660 + 2.40216i) q^{6} +(-0.366025 - 1.36603i) q^{7} +(-1.84443 - 1.84443i) q^{8} +(-2.88556 - 0.820682i) q^{9} +O(q^{10})\)	\(q+(1.45466 + 0.389774i) q^{2} +(-0.239203 + 1.71545i) q^{3} +(0.232051 + 0.133975i) q^{4} +(-1.01660 + 2.40216i) q^{6} +(-0.366025 - 1.36603i) q^{7} +(-1.84443 - 1.84443i) q^{8} +(-2.88556 - 0.820682i) q^{9} +(-1.06488 + 3.97420i) q^{11} +(-0.285334 + 0.366025i) q^{12} +(-3.59808 - 0.232051i) q^{13} -2.12976i q^{14} +(-2.23205 - 3.86603i) q^{16} +(-2.51954 + 4.36397i) q^{17} +(-3.87762 - 2.31853i) q^{18} +(-3.73205 + 1.00000i) q^{19} +(2.43091 - 0.301143i) q^{21} +(-3.09808 + 5.36603i) q^{22} +(3.60523 - 2.72284i) q^{24} +(-5.14352 - 1.73999i) q^{26} +(2.09808 - 4.75374i) q^{27} +(0.0980762 - 0.366025i) q^{28} +(-6.20840 + 3.58442i) q^{29} +(-2.46410 - 2.46410i) q^{31} +(-0.389774 - 1.45466i) q^{32} +(-6.56283 - 2.77739i) q^{33} +(-5.36603 + 5.36603i) q^{34} +(-0.559647 - 0.577032i) q^{36} +(5.23205 + 1.40192i) q^{37} -5.81863 q^{38} +(1.25874 - 6.11683i) q^{39} +(5.42885 + 1.45466i) q^{41} +(3.65351 + 0.509445i) q^{42} +(-1.90192 - 1.09808i) q^{43} +(-0.779548 + 0.779548i) q^{44} +(4.25953 + 4.25953i) q^{47} +(7.16590 - 2.90422i) q^{48} +(4.33013 - 2.50000i) q^{49} +(-6.88351 - 5.36603i) q^{51} +(-0.803848 - 0.535898i) q^{52} +0.779548i q^{53} +(4.90487 - 6.09729i) q^{54} +(-1.84443 + 3.19465i) q^{56} +(-0.822738 - 6.64136i) q^{57} +(-10.4282 + 2.79423i) q^{58} +(-2.90931 + 0.779548i) q^{59} +(3.50000 - 6.06218i) q^{61} +(-2.62398 - 4.54486i) q^{62} +(-0.0648824 + 4.24214i) q^{63} +6.66025i q^{64} +(-8.46410 - 6.59817i) q^{66} +(1.53590 - 5.73205i) q^{67} +(-1.16932 + 0.675108i) q^{68} +(-0.779548 - 2.90931i) q^{71} +(3.80853 + 6.83591i) q^{72} +(0.901924 - 0.901924i) q^{73} +(7.06440 + 4.07863i) q^{74} +(-1.00000 - 0.267949i) q^{76} +5.81863 q^{77} +(4.21522 - 8.40726i) q^{78} +2.00000 q^{79} +(7.65296 + 4.73626i) q^{81} +(7.33013 + 4.23205i) q^{82} +(-2.90931 + 2.90931i) q^{83} +(0.604440 + 0.255799i) q^{84} +(-2.33864 - 2.33864i) q^{86} +(-4.66384 - 11.5076i) q^{87} +(9.29423 - 5.36603i) q^{88} +(-2.41510 + 9.01327i) q^{89} +(1.00000 + 5.00000i) q^{91} +(4.81647 - 3.63763i) q^{93} +(4.53590 + 7.85641i) q^{94} +(2.58863 - 0.320682i) q^{96} +(-1.63397 + 0.437822i) q^{97} +(7.27328 - 1.94887i) q^{98} +(6.33434 - 10.5939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} - 12 q^{4} - 2 q^{6} + 4 q^{7} + 4 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 - 12 * q^4 - 2 * q^6 + 4 * q^7 + 4 * q^9	\( 8 q + 2 q^{3} - 12 q^{4} - 2 q^{6} + 4 q^{7} + 4 q^{9} - 8 q^{13} - 4 q^{16} - 4 q^{18} - 16 q^{19} + 4 q^{21} - 4 q^{22} + 18 q^{24} - 4 q^{27} - 20 q^{28} + 8 q^{31} - 16 q^{33} - 36 q^{34} - 36 q^{36} + 28 q^{37} - 14 q^{39} + 16 q^{42} - 36 q^{43} + 14 q^{48} - 48 q^{52} + 46 q^{54} - 16 q^{57} - 28 q^{58} + 28 q^{61} + 8 q^{63} - 40 q^{66} + 40 q^{67} - 12 q^{72} + 28 q^{73} - 8 q^{76} + 80 q^{78} + 16 q^{79} + 4 q^{81} + 24 q^{82} + 4 q^{84} + 34 q^{87} + 12 q^{88} + 8 q^{91} - 4 q^{93} + 64 q^{94} + 16 q^{96} - 20 q^{97} + 40 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 - 12 * q^4 - 2 * q^6 + 4 * q^7 + 4 * q^9 - 8 * q^13 - 4 * q^16 - 4 * q^18 - 16 * q^19 + 4 * q^21 - 4 * q^22 + 18 * q^24 - 4 * q^27 - 20 * q^28 + 8 * q^31 - 16 * q^33 - 36 * q^34 - 36 * q^36 + 28 * q^37 - 14 * q^39 + 16 * q^42 - 36 * q^43 + 14 * q^48 - 48 * q^52 + 46 * q^54 - 16 * q^57 - 28 * q^58 + 28 * q^61 + 8 * q^63 - 40 * q^66 + 40 * q^67 - 12 * q^72 + 28 * q^73 - 8 * q^76 + 80 * q^78 + 16 * q^79 + 4 * q^81 + 24 * q^82 + 4 * q^84 + 34 * q^87 + 12 * q^88 + 8 * q^91 - 4 * q^93 + 64 * q^94 + 16 * q^96 - 20 * q^97 + 40 * q^99

Introduction

L-functions

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