LMFDB - Embedded newform 975.2.bo.d.851.1

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			851.1
Root			$0.500000 + 1.56488i$ of defining polynomial
Character	$\chi$	$=$	975.851
Dual form			975.2.bo.d.401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.45466 + 0.389774i) q^{2} +(1.60523 - 0.650571i) q^{3} +(0.232051 - 0.133975i) q^{4} +(-2.08148 + 1.57203i) q^{6} +(-0.366025 + 1.36603i) q^{7} +(1.84443 - 1.84443i) q^{8} +(2.15351 - 2.08863i) q^{9} +O(q^{10})$	\(q+(-1.45466 + 0.389774i) q^{2} +(1.60523 - 0.650571i) q^{3} +(0.232051 - 0.133975i) q^{4} +(-2.08148 + 1.57203i) q^{6} +(-0.366025 + 1.36603i) q^{7} +(1.84443 - 1.84443i) q^{8} +(2.15351 - 2.08863i) q^{9} +(1.06488 + 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} +(-2.31853 + 3.87762i) q^{18} +(-3.73205 - 1.00000i) q^{19} +(0.301143 + 2.43091i) q^{21} +(-3.09808 - 5.36603i) q^{22} +(1.76080 - 4.16067i) 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} +(4.29488 + 5.68671i) q^{33} +(-5.36603 - 5.36603i) q^{34} +(0.219901 - 0.773185i) q^{36} +(5.23205 - 1.40192i) q^{37} +5.81863 q^{38} +(-5.62477 + 2.71330i) q^{39} +(-5.42885 + 1.45466i) q^{41} +(-1.38556 - 3.41876i) q^{42} +(-1.90192 + 1.09808i) q^{43} +(0.779548 + 0.779548i) q^{44} +(-4.25953 + 4.25953i) q^{47} +(-1.06782 + 7.65796i) q^{48} +(4.33013 + 2.50000i) q^{49} +(6.88351 + 5.36603i) q^{51} +(-0.803848 + 0.535898i) q^{52} +0.779548i q^{53} +(-1.19909 + 7.73284i) q^{54} +(1.84443 + 3.19465i) q^{56} +(-6.64136 + 0.822738i) 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} +(2.06488 + 3.70625i) 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} +(0.119671 - 7.82434i) q^{72} +(0.901924 + 0.901924i) q^{73} +(-7.06440 + 4.07863i) q^{74} +(-1.00000 + 0.267949i) q^{76} -5.81863 q^{77} +(7.12453 - 6.13931i) q^{78} +2.00000 q^{79} +(0.275241 - 8.99579i) q^{81} +(7.33013 - 4.23205i) q^{82} +(2.90931 + 2.90931i) q^{83} +(0.395560 + 0.523749i) q^{84} +(2.33864 - 2.33864i) q^{86} +(12.2978 + 1.71481i) q^{87} +(9.29423 + 5.36603i) q^{88} +(2.41510 + 9.01327i) q^{89} +(1.00000 - 5.00000i) q^{91} +(-2.35237 + 5.55852i) q^{93} +(4.53590 - 7.85641i) q^{94} +(-0.320682 - 2.58863i) q^{96} +(-1.63397 - 0.437822i) q^{97} +(-7.27328 - 1.94887i) q^{98} +(10.5939 + 6.33434i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} - 12 q^{4} - 2 q^{6} + 4 q^{7} + 4 q^{9}+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 $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−1.45466	+	0.389774i	−1.02860	+	0.275612i	−0.733380	−	0.679818i	$-0.762059\pi$
$2$	−1.45466	+	0.389774i	−1.02860	+	0.275612i	−0.295217	+	0.955430i	$0.595392\pi$
$3$	1.60523	−	0.650571i	0.926779	−	0.375608i
$3$	1.60523	−	0.650571i	0.926779	−	0.375608i
$4$	0.232051	−	0.133975i	0.116025	−	0.0669873i
$5$		0			0
$5$		0			0
$6$	−2.08148	+	1.57203i	−0.849760	+	0.641780i
$7$	−0.366025	+	1.36603i	−0.138345	+	0.516309i	0.861617	+	0.507559i	$0.169452\pi$
$7$	−0.366025	+	1.36603i	−0.138345	+	0.516309i	−0.999962	+	0.00875026i	$0.997215\pi$
$8$	1.84443	−	1.84443i	0.652105	−	0.652105i
$9$	2.15351	−	2.08863i	0.717838	−	0.696210i
$10$		0			0
$11$	1.06488	+	3.97420i	0.321074	+	1.19826i	0.918200	+	0.396117i	$0.129643\pi$
$11$	1.06488	+	3.97420i	0.321074	+	1.19826i	−0.597126	+	0.802148i	$0.703691\pi$
$12$	0.285334	−	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	0.991059	+	0.133424i	$0.0425971\pi$
$17$	2.51954	+	4.36397i	0.611078	+	1.05842i	−0.379981	+	0.924994i	$0.624070\pi$
$18$	−2.31853	+	3.87762i	−0.546482	+	0.913965i
$19$	−3.73205	−	1.00000i	−0.856191	−	0.229416i	−0.196084	−	0.980587i	$-0.562823\pi$
$19$	−3.73205	−	1.00000i	−0.856191	−	0.229416i	−0.660107	+	0.751171i	$0.729489\pi$
$20$		0			0
$21$	0.301143	+	2.43091i	0.0657148	+	0.530468i
$22$	−3.09808	−	5.36603i	−0.660512	−	1.14404i
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	1.76080	−	4.16067i	0.359421	−	0.849292i
$25$		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	$-0.101505\pi$
$29$	6.20840	+	3.58442i	1.15287	+	0.665610i	0.203286	+	0.979119i	$0.434838\pi$
$30$		0			0
$31$	−2.46410	+	2.46410i	−0.442566	+	0.442566i	−0.892873	−	0.450308i	$-0.851314\pi$
$31$	−2.46410	+	2.46410i	−0.442566	+	0.442566i	0.450308	+	0.892873i	$0.351314\pi$
$32$	0.389774	−	1.45466i	0.0689030	−	0.257149i
$33$	4.29488	+	5.68671i	0.747642	+	0.989929i
$34$	−5.36603	−	5.36603i	−0.920266	−	0.920266i
$35$		0			0
$36$	0.219901	−	0.773185i	0.0366502	−	0.128864i
$37$	5.23205	−	1.40192i	0.860144	−	0.230475i	0.198323	−	0.980137i	$-0.436451\pi$
$37$	5.23205	−	1.40192i	0.860144	−	0.230475i	0.661821	+	0.749662i	$0.269784\pi$
$38$	5.81863			0.943906
$39$	−5.62477	+	2.71330i	−0.900684	+	0.434476i
$40$		0			0
$41$	−5.42885	+	1.45466i	−0.847844	+	0.227179i	−0.656483	−	0.754341i	$-0.727957\pi$
$41$	−5.42885	+	1.45466i	−0.847844	+	0.227179i	−0.191361	+	0.981520i	$0.561290\pi$
$42$	−1.38556	−	3.41876i	−0.213797	−	0.527526i
$43$	−1.90192	+	1.09808i	−0.290041	+	0.167455i	−0.637960	−	0.770069i	$-0.720222\pi$
$43$	−1.90192	+	1.09808i	−0.290041	+	0.167455i	0.347920	+	0.937524i	$0.386888\pi$
$44$	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	$0.394787\pi$
$48$	−1.06782	+	7.65796i	−0.154127	+	1.10533i
$49$	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	$0.982950\pi$
$54$	−1.19909	+	7.73284i	−0.163176	+	1.05231i
$55$		0			0
$56$	1.84443	+	3.19465i	0.246472	+	0.426903i
$57$	−6.64136	+	0.822738i	−0.879670	+	0.108974i
$58$	−10.4282	−	2.79423i	−1.36929	−	0.366900i
$59$	2.90931	+	0.779548i	0.378760	+	0.101489i	0.443176	−	0.896435i	$-0.353852\pi$
$59$	2.90931	+	0.779548i	0.378760	+	0.101489i	−0.0644157	+	0.997923i	$0.520518\pi$
$60$		0			0
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	0.998264	−	0.0588933i	$-0.0187572\pi$
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	−0.550135	+	0.835076i	$0.685424\pi$
$62$	2.62398	−	4.54486i	0.333246	−	0.577198i
$63$	2.06488	+	3.70625i	0.260151	+	0.466943i
$64$		−	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	0.994050	+	0.108925i	$0.0347408\pi$
$67$	1.53590	+	5.73205i	0.187640	+	0.700281i	−0.806410	+	0.591357i	$0.798593\pi$
$68$	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	$-0.859469\pi$
$71$	0.779548	−	2.90931i	0.0925153	−	0.345272i	0.996631	+	0.0820158i	$0.0261358\pi$
$72$	0.119671	−	7.82434i	0.0141034	−	0.922107i
$73$	0.901924	+	0.901924i	0.105562	+	0.105562i	0.757915	−	0.652353i	$-0.226218\pi$
$73$	0.901924	+	0.901924i	0.105562	+	0.105562i	−0.652353	+	0.757915i	$0.726218\pi$
$74$	−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
$78$	7.12453	−	6.13931i	0.806694	−	0.695140i
$79$	2.00000			0.225018			0.112509	−	0.993651i	$-0.464111\pi$
$79$	2.00000			0.225018			0.112509	+	0.993651i	$0.464111\pi$
$80$		0			0
$81$	0.275241	−	8.99579i	0.0305823	−	0.999532i
$82$	7.33013	−	4.23205i	0.809477	−	0.467352i
$83$	2.90931	+	2.90931i	0.319339	+	0.319339i	0.848513	−	0.529174i	$-0.177498\pi$
$83$	2.90931	+	2.90931i	0.319339	+	0.319339i	−0.529174	+	0.848513i	$0.677498\pi$
$84$	0.395560	+	0.523749i	0.0431592	+	0.0571457i
$85$		0			0
$86$	2.33864	−	2.33864i	0.252182	−	0.252182i
$87$	12.2978	+	1.71481i	1.31846	+	0.183846i
$88$	9.29423	+	5.36603i	0.990768	+	0.572020i
$89$	2.41510	+	9.01327i	0.256000	+	0.955405i	0.967531	+	0.252751i	$0.0813353\pi$
$89$	2.41510	+	9.01327i	0.256000	+	0.955405i	−0.711531	+	0.702654i	$0.751998\pi$
$90$		0			0
$91$	1.00000	−	5.00000i	0.104828	−	0.524142i
$92$		0			0
$93$	−2.35237	+	5.55852i	−0.243929	+	0.576392i
$94$	4.53590	−	7.85641i	0.467842	−	0.810326i
$95$		0			0
$96$	−0.320682	−	2.58863i	−0.0327295	−	0.264201i
$97$	−1.63397	−	0.437822i	−0.165905	−	0.0444541i	0.174910	−	0.984584i	$-0.444036\pi$
$97$	−1.63397	−	0.437822i	−0.165905	−	0.0444541i	−0.340815	+	0.940130i	$0.610703\pi$
$98$	−7.27328	−	1.94887i	−0.734712	−	0.196866i
$99$	10.5939	+	6.33434i	1.06472	+	0.636625i
$100$		0			0
$101$	3.01375	−	5.21997i	0.299880	−	0.519407i	−0.676229	−	0.736692i	$-0.736387\pi$
$101$	3.01375	−	5.21997i	0.299880	−	0.519407i	0.976108	+	0.217285i	$0.0697202\pi$
$102$	−12.1047	−	5.12271i	−1.19854	−	0.507224i
$103$		−	6.92820i		−	0.682656i	−0.939944	−	0.341328i	$-0.889123\pi$
$103$		−	6.92820i		−	0.682656i	0.939944	−	0.341328i	$-0.110877\pi$
$104$	−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	0.992969	+	0.118374i	$0.0377682\pi$
$107$	16.4675	+	9.50749i	1.59197	+	0.919123i	0.598999	+	0.800749i	$0.295565\pi$
$108$	−0.150021	−	1.38420i	−0.0144357	−	0.133195i
$109$	−13.1962	+	13.1962i	−1.26396	+	1.26396i	−0.314806	+	0.949156i	$0.601940\pi$
$109$	−13.1962	+	13.1962i	−1.26396	+	1.26396i	−0.949156	+	0.314806i	$0.898060\pi$
$110$		0			0
$111$	7.48658	−	5.65423i	0.710595	−	0.536676i
$112$	−4.46410	−	4.46410i	−0.421818	−	0.421818i
$113$	−8.90883	+	5.14352i	−0.838073	+	0.483861i	−0.856609	−	0.515967i	$-0.827433\pi$
$113$	−8.90883	+	5.14352i	−0.838073	+	0.483861i	0.0185360	+	0.999828i	$0.494099\pi$
$114$	9.34022	−	3.78543i	0.874792	−	0.354538i
$115$		0			0
$116$	1.92089			0.178350
$117$	−7.26384	+	8.01478i	−0.671542	+	0.740967i
$118$	−4.53590			−0.417563
$119$	−6.88351	+	1.84443i	−0.631010	+	0.169079i
$120$		0			0
$121$	−5.13397	+	2.96410i	−0.466725	+	0.269464i
$122$	−7.45418	−	7.45418i	−0.674869	−	0.674869i
$123$	−7.76819	+	5.86691i	−0.700434	+	0.529002i
$124$	−0.241670	+	0.901924i	−0.0217026	+	0.0809951i
$125$		0			0
$126$	−4.44829	−	4.58648i	−0.396285	−	0.408596i
$127$	−7.90192	−	4.56218i	−0.701182	−	0.404828i	0.106605	−	0.994301i	$-0.466002\pi$
$127$	−7.90192	−	4.56218i	−0.701182	−	0.404828i	−0.807788	+	0.589474i	$0.799335\pi$
$128$	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	$0.887123\pi$
$132$	1.75850	+	0.744201i	0.153058	+	0.0647743i
$133$	2.73205	−	4.73205i	0.236899	−	0.410321i
$134$	−4.46841	−	7.73951i	−0.386012	−	0.668592i
$135$		0			0
$136$	12.6962	+	3.40192i	1.08869	+	0.291713i
$137$	6.49373	+	1.73999i	0.554797	+	0.148657i	0.525315	−	0.850908i	$-0.323948\pi$
$137$	6.49373	+	1.73999i	0.554797	+	0.148657i	0.0294822	+	0.999565i	$0.490614\pi$
$138$		0			0
$139$	−9.19615	−	15.9282i	−0.780007	−	1.35101i	−0.931937	−	0.362621i	$-0.881882\pi$
$139$	−9.19615	−	15.9282i	−0.780007	−	1.35101i	0.151929	−	0.988391i	$-0.451451\pi$
$140$		0			0
$141$	−4.06639	+	9.60864i	−0.342452	+	0.809194i
$142$			4.53590i			0.380644i
$143$	−4.75374	−	14.0524i	−0.397528	−	1.17512i
$144$	3.26795	+	12.9875i	0.272329	+	1.08229i
$145$		0			0
$146$	−1.66354	−	0.960443i	−0.137675	−	0.0794868i
$147$	8.57727	+	1.19601i	0.707441	+	0.0986455i
$148$	1.02628	−	1.02628i	0.0843597	−	0.0843597i
$149$	−2.23420	+	8.33816i	−0.183033	+	0.683089i	0.812010	+	0.583644i	$0.198374\pi$
$149$	−2.23420	+	8.33816i	−0.183033	+	0.683089i	−0.995043	+	0.0994454i	$0.968293\pi$
$150$		0			0
$151$	0.535898	+	0.535898i	0.0436108	+	0.0436108i	0.728576	−	0.684965i	$-0.240183\pi$
$151$	0.535898	+	0.535898i	0.0436108	+	0.0436108i	−0.684965	+	0.728576i	$0.740183\pi$
$152$	−8.72794	+	5.03908i	−0.707929	+	0.408723i
$153$	14.5406	+	4.13548i	1.17554	+	0.334334i
$154$	8.46410	−	2.26795i	0.682057	−	0.182757i
$155$		0			0
$156$	−0.941718	+	1.38320i	−0.0753978	+	0.110745i
$157$	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
$159$	0.507152	+	1.25135i	0.0402197	+	0.0992387i
$160$		0			0
$161$		0			0
$162$	3.10594	+	13.1931i	0.244026	+	1.03655i
$163$	1.07180	−	4.00000i	0.0839496	−	0.313304i	−0.911164	−	0.412045i	$-0.864815\pi$
$163$	1.07180	−	4.00000i	0.0839496	−	0.313304i	0.995113	+	0.0987406i	$0.0314814\pi$
$164$	−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	0.959573	+	0.281461i	$0.0908192\pi$
$167$	3.47998	+	12.9875i	0.269289	+	1.00500i	−0.690283	+	0.723539i	$0.742514\pi$
$168$	5.03908	+	3.92820i	0.388773	+	0.303067i
$169$	12.8923	−	1.66987i	0.991716	−	0.128452i
$170$		0			0
$171$	−10.1257	+	5.64136i	−0.774328	+	0.431406i
$172$	−0.294229	+	0.509619i	−0.0224347	+	0.0388581i
$173$	−8.72794	−	15.1172i	−0.663573	−	1.14934i	−0.979670	−	0.200615i	$-0.935706\pi$
$173$	−8.72794	−	15.1172i	−0.663573	−	1.14934i	0.316097	−	0.948727i	$-0.397627\pi$
$174$	−18.5575	+	2.29892i	−1.40684	+	0.174281i
$175$		0			0
$176$	−17.7412	−	4.75374i	−1.33729	−	0.358327i
$177$	5.17726	−	0.641364i	0.389147	−	0.0482078i
$178$	−7.02628	−	12.1699i	−0.526642	−	0.912171i
$179$	13.2728	−	22.9892i	0.992056	−	1.71829i	0.387084	−	0.922045i	$-0.373482\pi$
$179$	13.2728	−	22.9892i	0.992056	−	1.71829i	0.604972	−	0.796247i	$-0.293184\pi$
$180$		0			0
$181$			3.00000i			0.222988i	0.993765	+	0.111494i	$0.0355636\pi$
$181$			3.00000i			0.222988i	−0.993765	+	0.111494i	$0.964436\pi$
$182$	0.494214	+	7.66306i	0.0366336	+	0.568024i
$183$	9.56218	+	7.45418i	0.706857	+	0.551029i
$184$		0			0
$185$		0			0
$186$	1.25532	−	9.00263i	0.0920449	−	0.660105i
$187$	−14.6603	+	14.6603i	−1.07206	+	1.07206i
$188$	−0.417759	+	1.55910i	−0.0304682	+	0.113709i
$189$	5.72579	+	4.60602i	0.416490	+	0.335038i
$190$		0			0
$191$	−4.18307	+	2.41510i	−0.302677	+	0.174750i	−0.643645	−	0.765324i	$-0.722579\pi$
$191$	−4.18307	+	2.41510i	−0.302677	+	0.174750i	0.340968	+	0.940075i	$0.389245\pi$
$192$	−4.33297	−	10.6912i	−0.312705	−	0.771573i
$193$	−0.133975	+	0.0358984i	−0.00964370	+	0.00258402i	−0.263638	−	0.964622i	$-0.584922\pi$
$193$	−0.133975	+	0.0358984i	−0.00964370	+	0.00258402i	0.253994	+	0.967206i	$0.418256\pi$
$194$	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	$-0.630156\pi$
$197$	−3.97420	+	1.06488i	−0.283150	+	0.0758697i	0.114449	+	0.993429i	$0.463490\pi$
$198$	−17.8794	−	5.08507i	−1.27063	−	0.361380i
$199$	11.1962	−	6.46410i	0.793674	−	0.458228i	−0.0475802	−	0.998867i	$-0.515151\pi$
$199$	11.1962	−	6.46410i	0.793674	−	0.458228i	0.841254	+	0.540639i	$0.181818\pi$
$200$		0			0
$201$	6.19458	+	8.20204i	0.436932	+	0.578527i
$202$	−2.34936	+	8.76795i	−0.165301	+	0.616911i
$203$	−7.16884	+	7.16884i	−0.503154	+	0.503154i
$204$	2.31623	+	0.322975i	0.162169	+	0.0226128i
$205$		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	−0.833309	−	0.552808i	$-0.813556\pi$
$211$	0.901924	−	1.56218i	0.0620910	−	0.107545i	0.895400	+	0.445263i	$0.146890\pi$
$212$	0.104440	+	0.180895i	0.00717294	+	0.0124239i
$213$	−0.641364	−	5.17726i	−0.0439455	−	0.354740i
$214$	−27.6603	−	7.41154i	−1.89082	−	0.506643i
$215$		0			0
$216$	−4.89819	−	12.6377i	−0.333280	−	0.859887i
$217$	−2.46410	−	4.26795i	−0.167274	−	0.289727i
$218$	14.0524	−	24.3394i	0.951745	−	1.64847i
$219$	2.03456	+	0.861027i	0.137483	+	0.0581828i
$220$		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	−0.705011	−	0.709196i	$-0.749058\pi$
$223$	−6.70577	−	25.0263i	−0.449052	−	1.67588i	0.255960	−	0.966687i	$-0.417609\pi$
$224$	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	−0.540367	−	0.841429i	$-0.681715\pi$
$227$	5.24796	−	19.5856i	0.348319	−	1.29994i	0.888686	−	0.458515i	$-0.151619\pi$
$228$	−1.43091	+	1.08069i	−0.0947642	+	0.0715705i
$229$	−14.1244	−	14.1244i	−0.933364	−	0.933364i	0.0645507	−	0.997914i	$-0.479439\pi$
$229$	−14.1244	−	14.1244i	−0.933364	−	0.933364i	−0.997914	+	0.0645507i	$0.979439\pi$
$230$		0			0
$231$	−9.34022	+	3.78543i	−0.614541	+	0.249063i
$232$	18.0622	−	4.83975i	1.18584	−	0.317745i
$233$	17.4559			1.14357			0.571786	−	0.820403i	$-0.306251\pi$
$233$	17.4559			1.14357			0.571786	+	0.820403i	$0.306251\pi$
$234$	7.44244	−	14.4900i	0.486527	−	0.947241i
$235$		0			0
$236$	0.779548	−	0.208879i	0.0507443	−	0.0135969i
$237$	3.21046	−	1.30114i	0.208542	−	0.0845183i
$238$	9.29423	−	5.36603i	0.602455	−	0.347828i
$239$	−6.59817	−	6.59817i	−0.426800	−	0.426800i	0.460737	−	0.887537i	$-0.347585\pi$
$239$	−6.59817	−	6.59817i	−0.426800	−	0.426800i	−0.887537	+	0.460737i	$0.847585\pi$
$240$		0			0
$241$	3.76795	−	14.0622i	0.242715	−	0.905825i	−0.731803	−	0.681516i	$-0.761321\pi$
$241$	3.76795	−	14.0622i	0.242715	−	0.905825i	0.974518	−	0.224309i	$-0.0720123\pi$
$242$	6.31284	−	6.31284i	0.405805	−	0.405805i
$243$	−5.41058	−	14.6194i	−0.347089	−	0.937832i
$244$	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
$249$	6.56283	+	2.77739i	0.415902	+	0.176010i
$250$		0			0
$251$	−0.494214	−	0.856003i	−0.0311945	−	0.0540304i	0.850007	−	0.526772i	$-0.176598\pi$
$251$	−0.494214	−	0.856003i	−0.0311945	−	0.0540304i	−0.881201	+	0.472741i	$0.843264\pi$
$252$	0.975700	+	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
$257$	10.7533	−	18.6252i	0.670770	−	1.16181i	−0.306916	−	0.951737i	$-0.599297\pi$
$257$	10.7533	−	18.6252i	0.670770	−	1.16181i	0.977686	−	0.210071i	$-0.0673696\pi$
$258$	2.23260	−	5.27551i	0.138996	−	0.328439i
$259$			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	$-0.574454\pi$
$263$	−19.3003	−	11.1430i	−1.19011	−	0.687109i	−0.958331	+	0.285660i	$0.907787\pi$
$264$	18.4103	+	2.56713i	1.13308	+	0.157996i
$265$		0			0
$266$	−2.12976	+	7.94839i	−0.130584	+	0.487347i
$267$	9.74056	+	12.8972i	0.596113	+	0.789294i
$268$	1.12436	+	1.12436i	0.0686810	+	0.0686810i
$269$	12.4168	−	7.16884i	0.757066	−	0.437092i	−0.0711756	−	0.997464i	$-0.522675\pi$
$269$	12.4168	−	7.16884i	0.757066	−	0.437092i	0.828241	+	0.560372i	$0.189342\pi$
$270$		0			0
$271$	7.46410	−	2.00000i	0.453412	−	0.121491i	−0.0248835	−	0.999690i	$-0.507921\pi$
$271$	7.46410	−	2.00000i	0.453412	−	0.121491i	0.478295	+	0.878199i	$0.341255\pi$
$272$	−22.4950			−1.36396
$273$	−1.64763	−	8.67671i	−0.0997191	−	0.525138i
$274$	−10.1244			−0.611635
$275$		0			0
$276$		0			0
$277$	−23.8923	+	13.7942i	−1.43555	+	0.828815i	−0.997536	−	0.0701536i	$-0.977651\pi$
$277$	−23.8923	+	13.7942i	−1.43555	+	0.828815i	−0.438013	+	0.898969i	$0.644318\pi$
$278$	19.5856	+	19.5856i	1.17467	+	1.17467i
$279$	−0.159877	+	10.4531i	−0.00957158	+	0.625809i
$280$		0			0
$281$	12.1315	−	12.1315i	0.723703	−	0.723703i	−0.245655	−	0.969357i	$-0.579003\pi$
$281$	12.1315	−	12.1315i	0.723703	−	0.723703i	0.969357	+	0.245655i	$0.0790030\pi$
$282$	2.17000	−	15.5622i	0.129221	−	0.926718i
$283$	5.70577	+	3.29423i	0.339173	+	0.195822i	0.659906	−	0.751348i	$-0.270596\pi$
$283$	5.70577	+	3.29423i	0.339173	+	0.195822i	−0.320733	+	0.947170i	$0.603929\pi$
$284$	−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
$288$	−2.19886	−	3.94672i	−0.129569	−	0.232562i
$289$	−4.19615	+	7.26795i	−0.246832	+	0.427526i
$290$		0			0
$291$	−2.90774	+	0.360213i	−0.170455	+	0.0211161i
$292$	0.330127	+	0.0884573i	0.0193192	+	0.00517657i
$293$	−1.73999	−	0.466229i	−0.101651	−	0.0272374i	0.207635	−	0.978206i	$-0.433423\pi$
$293$	−1.73999	−	0.466229i	−0.101651	−	0.0272374i	−0.309286	+	0.950969i	$0.600090\pi$
$294$	−12.9432	+	1.60341i	−0.754860	+	0.0935127i
$295$		0			0
$296$	7.06440	−	12.2359i	0.410610	−	0.711198i
$297$	21.1265	+	3.27599i	1.22588	+	0.190092i
$298$		−	13.0000i		−	0.753070i
$299$		0			0
$300$		0			0
$301$	−0.803848	−	3.00000i	−0.0463330	−	0.172917i
$302$	−0.988427	−	0.570669i	−0.0568776	−	0.0328383i
$303$	1.44179	−	10.3399i	0.0828289	−	0.594012i
$304$	12.1962	−	12.1962i	0.699497	−	0.699497i
$305$		0			0
$306$	−22.7635	−	0.348161i	−1.30130	−	0.0199030i
$307$	−8.39230	−	8.39230i	−0.478974	−	0.478974i	0.425829	−	0.904803i	$-0.359982\pi$
$307$	−8.39230	−	8.39230i	−0.478974	−	0.478974i	−0.904803	+	0.425829i	$0.859982\pi$
$308$	−1.35022	+	0.779548i	−0.0769357	+	0.0444189i
$309$	−4.50729	−	11.1213i	−0.256411	−	0.632671i
$310$		0			0
$311$	−10.0782			−0.571480			−0.285740	−	0.958307i	$-0.592239\pi$
$311$	−10.0782			−0.571480			−0.285740	+	0.958307i	$0.592239\pi$
$312$	−5.37000	+	15.3790i	−0.304016	+	0.870664i
$313$	−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	$-0.398876\pi$
$317$	−11.3519	−	11.3519i	−0.637587	−	0.637587i	−0.949960	+	0.312373i	$0.898876\pi$
$318$	−1.22548	−	1.62261i	−0.0687213	−	0.0909916i
$319$	−7.63397	+	28.4904i	−0.427421	+	1.59516i
$320$		0			0
$321$	32.6193	+	4.54843i	1.82063	+	0.253869i
$322$		0			0
$323$	−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
$327$	−12.5978	+	29.7679i	−0.696659	+	1.64617i
$328$	−7.33013	+	12.6962i	−0.404739	+	0.701028i
$329$	−4.25953	−	7.37772i	−0.234835	−	0.406747i
$330$		0			0
$331$	−33.0526	−	8.85641i	−1.81673	−	0.486792i	−0.820357	−	0.571852i	$-0.806225\pi$
$331$	−33.0526	−	8.85641i	−1.81673	−	0.486792i	−0.996376	+	0.0850595i	$0.972892\pi$
$332$	1.06488	+	0.285334i	0.0584430	+	0.0156598i
$333$	8.33919	−	13.9469i	0.456985	−	0.764285i
$334$	−10.1244	−	17.5359i	−0.553980	−	0.959522i
$335$		0			0
$336$	−10.0701	−	4.26168i	−0.549370	−	0.232494i
$337$			18.4641i			1.00580i	0.864344	+	0.502902i	$0.167734\pi$
$337$			18.4641i			1.00580i	−0.864344	+	0.502902i	$0.832266\pi$
$338$	−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
$342$	12.5305	−	12.1530i	0.677571	−	0.657157i
$343$	−12.0000	+	12.0000i	−0.647939	+	0.647939i
$344$	−1.48264	+	5.53329i	−0.0799386	+	0.298335i
$345$		0			0
$346$	18.5885	+	18.5885i	0.999322	+	0.999322i
$347$	17.8177	−	10.2870i	0.956502	−	0.552237i	0.0614076	−	0.998113i	$-0.480441\pi$
$347$	17.8177	−	10.2870i	0.956502	−	0.552237i	0.895095	+	0.445876i	$0.147108\pi$
$348$	3.08346	−	1.24967i	0.165291	−	0.0669895i
$349$	27.4904	−	7.36603i	1.47153	−	0.394294i	0.568072	−	0.822979i	$-0.307689\pi$
$349$	27.4904	−	7.36603i	1.47153	−	0.394294i	0.903454	+	0.428684i	$0.141023\pi$
$350$		0			0
$351$	−6.44593	+	17.5912i	−0.344058	+	0.938948i
$352$	6.19615			0.330256
$353$	13.6626	−	3.66088i	0.727186	−	0.194849i	0.123810	−	0.992306i	$-0.460489\pi$
$353$	13.6626	−	3.66088i	0.727186	−	0.194849i	0.603376	+	0.797457i	$0.293822\pi$
$354$	−7.28115	+	2.95093i	−0.386989	+	0.156840i
$355$		0			0
$356$	1.76798	+	1.76798i	0.0937025	+	0.0937025i
$357$	−9.84967	+	7.43895i	−0.521300	+	0.393711i
$358$	−10.3468	+	38.6147i	−0.546845	+	2.04085i
$359$	−18.2354	+	18.2354i	−0.962429	+	0.962429i	−0.999319	−	0.0368904i	$-0.988255\pi$
$359$	−18.2354	+	18.2354i	−0.962429	+	0.962429i	0.0368904	+	0.999319i	$0.488255\pi$
$360$		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
$366$	−16.8151	−	7.11618i	−0.878941	−	0.371969i
$367$	15.1962	−	26.3205i	0.793233	−	1.37392i	−0.130723	−	0.991419i	$-0.541730\pi$
$367$	15.1962	−	26.3205i	0.793233	−	1.37392i	0.923955	−	0.382500i	$-0.124937\pi$
$368$		0			0
$369$	−8.65286	+	14.4715i	−0.450450	+	0.753356i
$370$		0			0
$371$	−1.06488	−	0.285334i	−0.0552859	−	0.0148138i
$372$	0.198831	+	1.60502i	0.0103089	+	0.0832162i
$373$	5.79423	+	10.0359i	0.300014	+	0.519639i	0.976139	−	0.217148i	$-0.0696754\pi$
$373$	5.79423	+	10.0359i	0.300014	+	0.519639i	−0.676125	+	0.736787i	$0.736342\pi$
$374$	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	0.991809	+	0.127726i	$0.0407679\pi$
$379$	3.83013	+	14.2942i	0.196740	+	0.734245i	−0.795069	+	0.606519i	$0.792565\pi$
$380$		0			0
$381$	−15.6524	−	2.18257i	−0.801897	−	0.111816i
$382$	5.14359	−	5.14359i	0.263169	−	0.263169i
$383$	−8.51906	+	31.7936i	−0.435304	+	1.62458i	0.305035	+	0.952341i	$0.401332\pi$
$383$	−8.51906	+	31.7936i	−0.435304	+	1.62458i	−0.740339	+	0.672234i	$0.765335\pi$
$384$	13.6142	+	18.0261i	0.694748	+	0.919893i
$385$		0			0
$386$	0.180895	−	0.104440i	0.00920730	−	0.00531584i
$387$	−1.80234	+	6.33714i	−0.0916182	+	0.322135i
$388$	−0.437822	+	0.117314i	−0.0222271	+	0.00595572i
$389$	−22.4950			−1.14054			−0.570270	−	0.821457i	$-0.693161\pi$
$389$	−22.4950			−1.14054			−0.570270	+	0.821457i	$0.693161\pi$
$390$		0			0
$391$		0			0
$392$	12.5977	−	3.37554i	0.636280	−	0.170491i
$393$	5.17100	+	12.7590i	0.260842	+	0.643605i
$394$	5.36603	−	3.09808i	0.270336	−	0.156079i
$395$		0			0
$396$	3.30696	+	0.0505790i	0.166181	+	0.00254169i
$397$	3.56218	−	13.2942i	0.178781	−	0.667218i	−0.817096	−	0.576501i	$-0.804418\pi$
$397$	3.56218	−	13.2942i	0.178781	−	0.667218i	0.995877	−	0.0907168i	$-0.0289158\pi$
$398$	−13.7670	+	13.7670i	−0.690078	+	0.690078i
$399$	1.30703	−	9.37341i	0.0654332	−	0.469258i
$400$		0			0
$401$	3.22263	+	12.0270i	0.160931	+	0.600601i	0.998524	+	0.0543073i	$0.0172951\pi$
$401$	3.22263	+	12.0270i	0.160931	+	0.600601i	−0.837594	+	0.546294i	$0.816038\pi$
$402$	−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
$408$	22.5934	−	2.79889i	1.11854	−	0.138566i
$409$	28.9904	+	7.76795i	1.43348	+	0.384100i	0.890246	−	0.455480i	$-0.150532\pi$
$409$	28.9904	+	7.76795i	1.43348	+	0.384100i	0.543236	+	0.839580i	$0.317199\pi$
$410$		0			0
$411$	11.5559	−	1.43156i	0.570011	−	0.0706135i
$412$	−0.928203	−	1.60770i	−0.0457293	−	0.0792055i
$413$	−2.12976	+	3.68886i	−0.104799	+	0.181517i
$414$		0			0
$415$		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	$-0.258729\pi$
$419$	8.23373	+	4.75374i	0.402244	+	0.232236i	−0.285208	+	0.958466i	$0.592063\pi$
$420$		0			0
$421$	−7.83013	+	7.83013i	−0.381617	+	0.381617i	−0.871685	−	0.490067i	$-0.836972\pi$
$421$	−7.83013	+	7.83013i	−0.381617	+	0.381617i	0.490067	+	0.871685i	$0.336972\pi$
$422$	−0.703093	+	2.62398i	−0.0342260	+	0.127733i
$423$	−0.276369	+	18.0695i	−0.0134375	+	0.878571i
$424$	1.43782	+	1.43782i	0.0698268	+	0.0698268i
$425$		0			0
$426$	2.95093	+	7.28115i	0.142973	+	0.352773i
$427$	−9.56218	+	2.56218i	−0.462746	+	0.123992i
$428$	5.09505			0.246278
$429$	−16.7729	−	19.4646i	−0.809803	−	0.939759i
$430$		0			0
$431$	36.5473	−	9.79282i	1.76042	−	0.471704i	0.773622	−	0.633648i	$-0.218443\pi$
$431$	36.5473	−	9.79282i	1.76042	−	0.471704i	0.986800	+	0.161944i	$0.0517764\pi$
$432$	13.6951	+	18.7218i	0.658905	+	0.900754i
$433$	26.8923	−	15.5263i	1.29236	−	0.746145i	0.313289	−	0.949658i	$-0.398569\pi$
$433$	26.8923	−	15.5263i	1.29236	−	0.746145i	0.979072	+	0.203512i	$0.0652357\pi$
$434$	5.24796	+	5.24796i	0.251910	+	0.251910i
$435$		0			0
$436$	−1.29423	+	4.83013i	−0.0619823	+	0.231321i
$437$		0			0
$438$	−3.29519	−	0.459481i	−0.157450	−	0.0219548i
$439$	1.09808	+	0.633975i	0.0524083	+	0.0302580i	0.525975	−	0.850500i	$-0.323700\pi$
$439$	1.09808	+	0.633975i	0.0524083	+	0.0302580i	−0.473567	+	0.880758i	$0.657034\pi$
$440$		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	$0.914124\pi$
$444$	0.979744	−	2.31508i	0.0464966	−	0.109869i
$445$		0			0
$446$	19.5092	+	33.7909i	0.923787	+	1.60005i
$447$	1.83816	+	14.8382i	0.0869422	+	0.701821i
$448$	9.09808	+	2.43782i	0.429844	+	0.115176i
$449$	19.8710	+	5.32441i	0.937769	+	0.251275i	0.695165	−	0.718851i	$-0.255331\pi$
$449$	19.8710	+	5.32441i	0.937769	+	0.251275i	0.242605	+	0.970125i	$0.421998\pi$
$450$		0			0
$451$	−11.5622	−	20.0263i	−0.544442	−	0.943001i
$452$	−1.37820	+	2.38711i	−0.0648251	+	0.112280i
$453$	1.20888	+	0.511599i	0.0567981	+	0.0240370i
$454$			30.5359i			1.43312i
$455$		0			0
$456$	−10.7321	+	13.7670i	−0.502574	+	0.644700i
$457$	1.00962	+	3.76795i	0.0472280	+	0.176257i	0.985511	−	0.169611i	$-0.0542511\pi$
$457$	1.00962	+	3.76795i	0.0472280	+	0.176257i	−0.938283	+	0.345868i	$0.887584\pi$
$458$	26.0514	+	15.0408i	1.21730	+	0.702809i
$459$	26.0314	−	2.82130i	1.21504	−	0.131687i
$460$		0			0
$461$	5.50531	−	20.5461i	0.256408	−	0.956927i	−0.710894	−	0.703299i	$-0.751710\pi$
$461$	5.50531	−	20.5461i	0.256408	−	0.956927i	0.967302	−	0.253628i	$-0.0816238\pi$
$462$	12.1113	−	9.14708i	0.563471	−	0.425561i
$463$	−23.0526	−	23.0526i	−1.07134	−	1.07134i	−0.997251	−	0.0740918i	$-0.976394\pi$
$463$	−23.0526	−	23.0526i	−1.07134	−	1.07134i	−0.0740918	−	0.997251i	$-0.523606\pi$
$464$	−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	$-0.646261\pi$
$467$	−19.1679			−0.886984			−0.443492	+	0.896278i	$0.646261\pi$
$468$	−0.611803	+	2.83301i	−0.0282806	+	0.130956i
$469$	−8.39230			−0.387521
$470$		0			0
$471$	7.71127	−	3.12525i	0.355317	−	0.144004i
$472$	6.80385	−	3.92820i	0.313172	−	0.180810i
$473$	−6.38929	−	6.38929i	−0.293780	−	0.293780i
$474$	−4.16296	+	3.14407i	−0.191211	+	0.144412i
$475$		0			0
$476$	−1.35022	+	1.35022i	−0.0618871	+	0.0618871i
$477$	1.62819	+	1.67877i	0.0745496	+	0.0768655i
$478$	12.1699	+	7.02628i	0.556637	+	0.321375i
$479$	−5.32441	−	19.8710i	−0.243279	−	0.907928i	−0.974241	−	0.225510i	$-0.927595\pi$
$479$	−5.32441	−	19.8710i	−0.243279	−	0.907928i	0.730962	−	0.682418i	$-0.239072\pi$
$480$		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
$486$	13.5688	+	19.1572i	0.615492	+	0.868990i
$487$	−5.56218	−	1.49038i	−0.252046	−	0.0675356i	0.130584	−	0.991437i	$-0.458315\pi$
$487$	−5.56218	−	1.49038i	−0.252046	−	0.0675356i	−0.382630	+	0.923902i	$0.624982\pi$
$488$	17.6368	+	4.72576i	0.798379	+	0.213925i
$489$	−0.881808	−	7.11819i	−0.0398767	−	0.321896i
$490$		0			0
$491$	−14.2612	+	24.7012i	−0.643600	+	1.11475i	0.341023	+	0.940055i	$0.389227\pi$
$491$	−14.2612	+	24.7012i	−0.643600	+	1.11475i	−0.984623	+	0.174693i	$0.944107\pi$
$492$	−1.01660	+	2.40216i	−0.0458317	+	0.108298i
$493$			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
$498$	−10.6292	−	1.48214i	−0.476306	−	0.0664161i
$499$	−2.46410	+	2.46410i	−0.110308	+	0.110308i	−0.760107	−	0.649798i	$-0.774853\pi$
$499$	−2.46410	+	2.46410i	−0.110308	+	0.110308i	0.649798	+	0.760107i	$0.274853\pi$
$500$		0			0
$501$	14.0354	+	18.5839i	0.627057	+	0.830266i
$502$	1.05256	+	1.05256i	0.0469780	+	0.0469780i
$503$	−2.83286	+	1.63555i	−0.126311	+	0.0729256i	−0.561824	−	0.827257i	$-0.689900\pi$
$503$	−2.83286	+	1.63555i	−0.126311	+	0.0729256i	0.435513	+	0.900182i	$0.356567\pi$
$504$	10.6444	+	3.02738i	0.474141	+	0.134850i
$505$		0			0
$506$		0			0
$507$	19.6087	−	11.0679i	0.870854	−	0.491542i
$508$	−2.44486			−0.108473
$509$	−14.1568	+	3.79330i	−0.627489	+	0.168135i	−0.558530	−	0.829484i	$-0.688634\pi$
$509$	−14.1568	+	3.79330i	−0.627489	+	0.168135i	−0.0689588	+	0.997620i	$0.521968\pi$
$510$		0			0
$511$	−1.56218	+	0.901924i	−0.0691067	+	0.0398988i
$512$	−11.7137	−	11.7137i	−0.517678	−	0.517678i
$513$	−12.5839	+	15.6431i	−0.555591	+	0.690661i
$514$	−8.38269	+	31.2846i	−0.369744	+	1.37990i
$515$		0			0
$516$	−0.140760	+	1.00947i	−0.00619663	+	0.0444395i
$517$	−21.4641	−	12.3923i	−0.943990	−	0.545013i
$518$	−2.98577	−	11.1430i	−0.131187	−	0.489597i
$519$	−23.8452	−	18.5885i	−1.04669	−	0.815943i
$520$		0			0
$521$		−	2.49155i		−	0.109157i	−0.998509	−	0.0545785i	$-0.982618\pi$
$521$		−	2.49155i		−	0.109157i	0.998509	−	0.0545785i	$-0.0173815\pi$
$522$	−28.2934	+	15.7633i	−1.23837	+	0.689939i
$523$	−19.4904	+	33.7583i	−0.852255	+	1.47615i	0.0269137	+	0.999638i	$0.491432\pi$
$523$	−19.4904	+	33.7583i	−0.852255	+	1.47615i	−0.879169	+	0.476511i	$0.841901\pi$
$524$	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
$528$	−31.5713	+	3.91108i	−1.37397	+	0.170208i
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$		0			0
$531$	7.89343	−	4.39771i	0.342546	−	0.190845i
$532$		−	1.46410i		−	0.0634769i
$533$	19.1959	−	6.49373i	0.831465	−	0.281275i
$534$	−19.1962	−	14.9643i	−0.830699	−	0.647570i
$535$		0			0
$536$	13.4052	+	7.73951i	0.579018	+	0.334296i
$537$	6.34978	−	45.5378i	0.274013	−	1.96510i
$538$	−15.2679	+	15.2679i	−0.658248	+	0.658248i
$539$	−5.32441	+	19.8710i	−0.229339	+	0.855904i
$540$		0			0
$541$	−12.6865	−	12.6865i	−0.545437	−	0.545437i	0.379681	−	0.925118i	$-0.376034\pi$
$541$	−12.6865	−	12.6865i	−0.545437	−	0.545437i	−0.925118	+	0.379681i	$0.876034\pi$
$542$	−10.0782	+	5.81863i	−0.432894	+	0.249931i
$543$	1.95171	+	4.81568i	0.0837561	+	0.206661i
$544$	7.33013	−	1.96410i	0.314277	−	0.0842102i
$545$		0			0
$546$	5.77869	+	11.9794i	0.247305	+	0.512672i
$547$	−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
$549$	20.1990	+	5.74477i	0.862070	+	0.245181i
$550$		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	0.951883	+	0.306462i	$0.0991454\pi$
$557$	6.62616	+	24.7292i	0.280759	+	1.04781i	−0.671123	+	0.741346i	$0.734188\pi$
$558$	−3.84177	−	15.2679i	−0.162635	−	0.646344i
$559$	6.58846	−	4.39230i	0.278662	−	0.185775i
$560$		0			0
$561$	−13.9955	+	33.0706i	−0.590891	+	1.39624i
$562$	−12.9186	+	22.3756i	−0.544938	+	0.943860i
$563$	5.03908	+	8.72794i	0.212372	+	0.367839i	0.952456	−	0.304675i	$-0.0985479\pi$
$563$	5.03908	+	8.72794i	0.212372	+	0.367839i	−0.740085	+	0.672514i	$0.765215\pi$
$564$	0.343706	+	2.77449i	0.0144726	+	0.116827i
$565$		0			0
$566$	−9.58394	−	2.56801i	−0.402843	−	0.107941i
$567$	12.1877	+	3.66867i	0.511837	+	0.154070i
$568$	−3.92820	−	6.80385i	−0.164824	−	0.285483i
$569$	−1.35022	+	2.33864i	−0.0566040	+	0.0980411i	−0.892939	−	0.450178i	$-0.851361\pi$
$569$	−1.35022	+	2.33864i	−0.0566040	+	0.0980411i	0.836335	+	0.548219i	$0.184694\pi$
$570$		0			0
$571$			1.94744i			0.0814979i	0.999169	+	0.0407489i	$0.0129744\pi$
$571$			1.94744i			0.0814979i	−0.999169	+	0.0407489i	$0.987026\pi$
$572$	−2.98577	−	2.62398i	−0.124841	−	0.109714i
$573$	−5.14359	+	6.59817i	−0.214877	+	0.275643i
$574$	3.09808	+	11.5622i	0.129311	+	0.482596i
$575$		0			0
$576$	−13.9108	−	14.3429i	−0.579617	−	0.597623i
$577$	22.4904	−	22.4904i	0.936287	−	0.936287i	−0.0618016	−	0.998088i	$-0.519685\pi$
$577$	22.4904	−	22.4904i	0.936287	−	0.936287i	0.998088	+	0.0618016i	$0.0196846\pi$
$578$	3.27110	−	12.2079i	0.136060	−	0.507783i
$579$	−0.191705	+	0.144785i	−0.00796700	+	0.00601707i
$580$		0			0
$581$	−5.03908	+	2.90931i	−0.209056	+	0.120699i
$582$	4.08936	−	1.65735i	0.169509	−	0.0686992i
$583$	−3.09808	+	0.830127i	−0.128309	+	0.0343803i
$584$	3.32707			0.137675
$585$		0			0
$586$	2.71281			0.112065
$587$	18.0265	−	4.83020i	0.744035	−	0.199364i	0.133164	−	0.991094i	$-0.457486\pi$
$587$	18.0265	−	4.83020i	0.744035	−	0.199364i	0.610871	+	0.791730i	$0.290819\pi$
$588$	2.15060	−	0.871601i	0.0886892	−	0.0359442i
$589$	11.6603	−	6.73205i	0.480452	−	0.277389i
$590$		0			0
$591$	−5.68671	+	4.29488i	−0.233920	+	0.176668i
$592$	−6.25833	+	23.3564i	−0.257216	+	0.959942i
$593$	10.3635	−	10.3635i	0.425578	−	0.425578i	−0.461541	−	0.887119i	$-0.652703\pi$
$593$	10.3635	−	10.3635i	0.425578	−	0.425578i	0.887119	+	0.461541i	$0.152703\pi$
$594$	−32.0087	+	3.46913i	−1.31333	+	0.142340i
$595$		0			0
$596$	0.598653	+	2.23420i	0.0245218	+	0.0915166i
$597$	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	−0.999765	−	0.0216919i	$-0.993095\pi$
$601$	−11.7942	+	20.4282i	−0.481097	+	0.833284i	0.518668	+	0.854976i	$0.326428\pi$
$602$	2.33864	+	4.05065i	0.0953160	+	0.165092i
$603$	15.2797	+	9.13612i	0.622238	+	0.372052i
$604$	0.196152	+	0.0525589i	0.00798133	+	0.00213859i
$605$		0			0
$606$	1.93291	+	15.6030i	0.0785192	+	0.633828i
$607$	−0.0980762	−	0.169873i	−0.00398079	−	0.00689493i	0.864028	−	0.503444i	$-0.167934\pi$
$607$	−0.0980762	−	0.169873i	−0.00398079	−	0.00689493i	−0.868009	+	0.496549i	$0.834600\pi$
$608$	−2.90931	+	5.03908i	−0.117988	+	0.204362i
$609$	−6.84378	+	16.1715i	−0.277324	+	0.655301i
$610$		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	0.677035	+	0.735951i	$0.263265\pi$
$613$	11.3564	+	42.3827i	0.458681	+	1.71182i	−0.218354	+	0.975870i	$0.570069\pi$
$614$	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	0.800393	+	0.599475i	$0.204624\pi$
$617$	−4.78173	+	17.8457i	−0.192505	+	0.718439i	−0.992899	+	0.118964i	$0.962043\pi$
$618$	10.8914	+	14.4209i	0.438115	+	0.580094i
$619$	−31.6603	−	31.6603i	−1.27253	−	1.27253i	−0.944755	−	0.327778i	$-0.893700\pi$
$619$	−31.6603	−	31.6603i	−1.27253	−	1.27253i	−0.327778	−	0.944755i	$-0.606300\pi$
$620$		0			0
$621$		0			0
$622$	14.6603	−	3.92820i	0.587823	−	0.157507i
$623$	−13.1963			−0.528701
$624$	2.06508	−	27.8017i	0.0826693	−	1.11296i
$625$		0			0
$626$	2.90931	−	0.779548i	0.116280	−	0.0311570i
$627$	−10.3420	−	25.5180i	−0.413019	−	1.01909i
$628$	1.11474	−	0.643594i	0.0444828	−	0.0256822i
$629$	19.3003	+	19.3003i	0.769554	+	0.769554i
$630$		0			0
$631$	5.73205	−	21.3923i	0.228189	−	0.851614i	−0.752912	−	0.658121i	$-0.771352\pi$
$631$	5.73205	−	21.3923i	0.228189	−	0.851614i	0.981102	−	0.193493i	$-0.0619818\pi$
$632$	3.68886	−	3.68886i	0.146735	−	0.146735i
$633$	0.431485	−	3.09442i	0.0171500	−	0.122992i
$634$	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
$639$	−4.39771	−	7.89343i	−0.173971	−	0.312259i
$640$		0			0
$641$	22.6758	+	39.2757i	0.895642	+	1.55130i	0.833008	+	0.553261i	$0.186617\pi$
$641$	22.6758	+	39.2757i	0.895642	+	1.55130i	0.0626345	+	0.998037i	$0.480050\pi$
$642$	−49.2228	+	6.09776i	−1.94267	+	0.240659i
$643$	−7.00000	−	1.87564i	−0.276053	−	0.0739682i	0.118136	−	0.992997i	$-0.462308\pi$
$643$	−7.00000	−	1.87564i	−0.276053	−	0.0739682i	−0.394190	+	0.919029i	$0.628975\pi$
$644$		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	$-0.728406\pi$
$647$	8.23373	−	14.2612i	0.323701	−	0.560667i	0.981249	+	0.192746i	$0.0617394\pi$
$648$	−16.0844	−	17.0998i	−0.631857	−	0.671742i
$649$			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	$-0.272802\pi$
$653$	8.36615	+	4.83020i	0.327393	+	0.189020i	−0.327290	+	0.944924i	$0.606135\pi$
$654$	6.72272	−	48.2123i	0.262879	−	1.88525i
$655$		0			0
$656$	6.49373	−	24.2349i	0.253538	−	0.946216i
$657$	3.82609	+	0.0585190i	0.149270	+	0.00228304i
$658$	9.07180	+	9.07180i	0.353655	+	0.353655i
$659$	23.4834	−	13.5581i	0.914783	−	0.528150i	0.0328158	−	0.999461i	$-0.489553\pi$
$659$	23.4834	−	13.5581i	0.914783	−	0.528150i	0.881967	+	0.471311i	$0.156219\pi$
$660$		0			0
$661$	9.42820	−	2.52628i	0.366715	−	0.0982609i	−0.0707559	−	0.997494i	$-0.522541\pi$
$661$	9.42820	−	2.52628i	0.366715	−	0.0982609i	0.437470	+	0.899233i	$0.355874\pi$
$662$	51.5321			2.00285
$663$	−26.0126	−	17.7100i	−1.01024	−	0.687801i
$664$	10.7321			0.416484
$665$		0			0
$666$	−6.69452	+	23.5383i	−0.259408	+	0.912092i
$667$		0			0
$668$	2.54752	+	2.54752i	0.0985666	+	0.0985666i
$669$	−27.0457	−	35.8103i	−1.04565	−	1.38451i
$670$		0			0
$671$	−20.3652	+	20.3652i	−0.786189	+	0.786189i
$672$	3.65351	+	0.509445i	0.140937	+	0.0196523i
$673$	36.9904	+	21.3564i	1.42587	+	0.823229i	0.996792	−	0.0800364i	$-0.0255036\pi$
$673$	36.9904	+	21.3564i	1.42587	+	0.823229i	0.429082	+	0.903265i	$0.358837\pi$
$674$	−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	$-0.0594357\pi$
$678$	10.4578	−	24.7111i	0.401628	−	0.949025i
$679$	1.19615	−	2.07180i	0.0459041	−	0.0795083i
$680$		0			0
$681$	−4.31769	−	34.8536i	−0.165454	−	1.33559i
$682$	20.8564	+	5.58846i	0.798633	+	0.213993i
$683$	45.2752	+	12.1315i	1.73241	+	0.464198i	0.980736	−	0.195338i	$-0.0625804\pi$
$683$	45.2752	+	12.1315i	1.73241	+	0.464198i	0.751673	+	0.659536i	$0.229247\pi$
$684$	−1.59387	+	2.66566i	−0.0609430	+	0.101924i
$685$		0			0
$686$	12.7786	−	22.1332i	0.487889	−	0.845048i
$687$	−31.8617	−	13.4839i	−1.21560	−	0.514443i
$688$		−	9.80385i		−	0.373768i
$689$	−0.180895	−	2.80487i	−0.00689154	−	0.106857i
$690$		0			0
$691$	4.88269	+	18.2224i	0.185746	+	0.693214i	0.994470	+	0.105025i	$0.0334922\pi$
$691$	4.88269	+	18.2224i	0.185746	+	0.693214i	−0.808723	+	0.588189i	$0.799841\pi$
$692$	−4.05065	−	2.33864i	−0.153983	−	0.0889019i
$693$	−12.5305	+	12.1530i	−0.475994	+	0.461653i
$694$	−21.9090	+	21.9090i	−0.831653	+	0.831653i
$695$		0			0
$696$	25.8453	−	19.5196i	0.979664	−	0.739890i
$697$	−20.0263	−	20.0263i	−0.758549	−	0.758549i
$698$	−37.1180	+	21.4301i	−1.40494	+	0.811140i
$699$	28.0207	−	11.3563i	1.05984	−	0.429535i
$700$		0			0
$701$	−12.7786			−0.482641			−0.241320	−	0.970446i	$-0.577580\pi$
$701$	−12.7786			−0.482641			−0.241320	+	0.970446i	$0.577580\pi$
$702$	2.52002	−	28.1016i	0.0951121	−	1.06063i
$703$	−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
$708$	1.11546	−	0.842451i	0.0419216	−	0.0316612i
$709$	−3.03590	+	11.3301i	−0.114016	+	0.425512i	−0.999211	−	0.0397068i	$-0.987358\pi$
$709$	−3.03590	+	11.3301i	−0.114016	+	0.425512i	0.885196	+	0.465219i	$0.154024\pi$
$710$		0			0
$711$	4.30703	−	4.17726i	0.161526	−	0.156660i
$712$	21.0788	+	12.1699i	0.789963	+	0.456085i
$713$		0			0
$714$	11.4284	−	14.6603i	0.427696	−	0.548646i
$715$		0			0
$716$		−	7.11287i		−	0.265821i
$717$	−14.8842	−	6.29899i	−0.555859	−	0.235240i
$718$	19.4186	−	33.6340i	0.724695	−	1.25521i
$719$	−3.68886	−	6.38929i	−0.137571	−	0.238280i	0.789005	−	0.614386i	$-0.210596\pi$
$719$	−3.68886	−	6.38929i	−0.137571	−	0.238280i	−0.926577	+	0.376106i	$0.877263\pi$
$720$		0			0
$721$	9.46410	+	2.53590i	0.352462	+	0.0944418i
$722$	5.92307	+	1.58708i	0.220434	+	0.0590650i
$723$	−3.10003	−	25.0243i	−0.115292	−	0.930665i
$724$	0.401924	+	0.696152i	0.0149374	+	0.0258723i
$725$		0			0
$726$	6.02659	−	14.2405i	0.223668	−	0.528515i
$727$			19.5167i			0.723833i	0.932211	+	0.361916i	$0.117877\pi$
$727$			19.5167i			0.723833i	−0.932211	+	0.361916i	$0.882123\pi$
$728$	−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
$732$	3.21758	+	0.448659i	0.118925	+	0.0165829i
$733$	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
$737$	−21.1447	+	12.2079i	−0.778876	+	0.449685i
$738$	6.94633	−	24.4237i	0.255698	−	0.899049i
$739$	−11.1244	+	2.98076i	−0.409216	+	0.109649i	−0.457554	−	0.889182i	$-0.651274\pi$
$739$	−11.1244	+	2.98076i	−0.409216	+	0.109649i	0.0483378	+	0.998831i	$0.484608\pi$
$740$		0			0
$741$	23.7052	−	4.50141i	0.870833	−	0.165363i
$742$	1.66025			0.0609498
$743$	−8.51906	+	2.28268i	−0.312534	+	0.0837432i	−0.411677	−	0.911330i	$-0.635057\pi$
$743$	−8.51906	+	2.28268i	−0.312534	+	0.0837432i	0.0991426	+	0.995073i	$0.468390\pi$
$744$	5.91352	+	14.5911i	0.216800	+	0.534935i
$745$		0			0
$746$	−12.3403	−	12.3403i	−0.451812	−	0.451812i
$747$	12.3417	+	0.188763i	0.451560	+	0.00690649i
$748$	−1.43782	+	5.36603i	−0.0525720	+	0.196201i
$749$	−19.0150	+	19.0150i	−0.694792	+	0.694792i
$750$		0			0
$751$	−29.2750	−	16.9019i	−1.06826	−	0.616760i	−0.140554	−	0.990073i	$-0.544888\pi$
$751$	−29.2750	−	16.9019i	−1.06826	−	0.616760i	−0.927705	+	0.373313i	$0.878222\pi$
$752$	−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
$756$	1.94576	+	0.301720i	0.0707667	+	0.0109735i
$757$	8.39230	−	14.5359i	0.305024	−	0.528316i	−0.672243	−	0.740331i	$-0.734669\pi$
$757$	8.39230	−	14.5359i	0.305024	−	0.528316i	0.977267	+	0.212014i	$0.0680023\pi$
$758$	−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	$-0.524695\pi$
$761$	−17.7412	−	4.75374i	−0.643118	−	0.172323i	−0.565616	+	0.824669i	$0.691361\pi$
$762$	23.6196	−	2.92602i	0.855647	−	0.105998i
$763$	−13.1962	−	22.8564i	−0.477733	−	0.827457i
$764$	−0.647124	+	1.12085i	−0.0234121	+	0.0405510i
$765$		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	−0.829238	−	0.558895i	$-0.811225\pi$
$769$	−10.8301	−	40.4186i	−0.390544	−	1.45753i	0.438694	−	0.898636i	$-0.355441\pi$
$770$		0			0
$771$	5.14442	−	36.8935i	0.185272	−	1.32869i
$772$	−0.0262794	+	0.0262794i	−0.000945818	+	0.000945818i
$773$	11.1430	−	41.5864i	0.400787	−	1.49576i	−0.410908	−	0.911677i	$-0.634788\pi$
$773$	11.1430	−	41.5864i	0.400787	−	1.49576i	0.811695	−	0.584081i	$-0.198545\pi$
$774$	0.151737	−	9.92087i	0.00545407	−	0.356598i
$775$		0			0
$776$	−3.82129	+	2.20622i	−0.137176	+	0.0791987i
$777$	4.98354	+	12.2965i	0.178784	+	0.441133i
$778$	32.7224	−	8.76795i	1.17316	−	0.314346i
$779$	21.7154			0.778035
$780$		0			0
$781$	12.3923			0.443432
$782$		0			0
$783$	30.0651	−	21.9928i	1.07444	−	0.785957i
$784$	−19.3301	+	11.1603i	−0.690362	+	0.398581i
$785$		0			0
$786$	−12.4951	−	16.5444i	−0.445687	−	0.590120i
$787$	−4.29423	+	16.0263i	−0.153073	+	0.571275i	0.846190	+	0.532881i	$0.178891\pi$
$787$	−4.29423	+	16.0263i	−0.153073	+	0.571275i	−0.999263	+	0.0383938i	$0.987776\pi$
$788$	−0.779548	+	0.779548i	−0.0277702	+	0.0277702i
$789$	−38.2307	−	5.33089i	−1.36105	−	0.189785i
$790$		0			0
$791$	−3.76532	−	14.0524i	−0.133879	−	0.499644i
$792$	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	0.963354	+	0.268232i	$0.0864395\pi$
$797$	20.1563	+	34.9118i	0.713973	+	1.23664i	−0.249381	+	0.968405i	$0.580227\pi$
$798$	1.75224	+	14.1445i	0.0620286	+	0.500711i
$799$	−29.3205	−	7.85641i	−1.03729	−	0.277940i
$800$		0			0
$801$	24.0264	+	14.3660i	0.848929	+	0.507596i
$802$	−9.37564	−	16.2391i	−0.331066	−	0.573422i
$803$	−2.62398	+	4.54486i	−0.0925982	+	0.160385i
$804$	2.53632	+	1.07337i	0.0894491	+	0.0378550i
$805$		0			0
$806$	−8.38664	+	16.9617i	−0.295407	+	0.597449i
$807$	15.2679	−	19.5856i	0.537457	−	0.689447i
$808$	−4.06922	−	15.1865i	−0.143155	−	0.534260i
$809$	−24.0261	−	13.8715i	−0.844712	−	0.487694i	0.0141514	−	0.999900i	$-0.495495\pi$
$809$	−24.0261	−	13.8715i	−0.844712	−	0.487694i	−0.858863	+	0.512205i	$0.828829\pi$
$810$		0			0
$811$	19.0000	−	19.0000i	0.667180	−	0.667180i	−0.289882	−	0.957062i	$-0.593616\pi$
$811$	19.0000	−	19.0000i	0.667180	−	0.667180i	0.957062	+	0.289882i	$0.0936161\pi$
$812$	−0.703093	+	2.62398i	−0.0246737	+	0.0920836i
$813$	10.6804	−	8.06639i	0.374579	−	0.282901i
$814$	−23.7321	−	23.7321i	−0.831808	−	0.831808i
$815$		0			0
$816$	−36.1095	+	14.6346i	−1.26409	+	0.512313i
$817$	8.19615	−	2.19615i	0.286747	−	0.0768336i
$818$	−45.1988			−1.58034
$819$	−8.28964	−	12.8562i	−0.289664	−	0.449232i
$820$		0			0
$821$	41.5864	−	11.1430i	1.45137	−	0.388895i	0.554873	−	0.831935i	$-0.312767\pi$
$821$	41.5864	−	11.1430i	1.45137	−	0.388895i	0.896502	+	0.443040i	$0.146100\pi$
$822$	−16.2519	+	6.58662i	−0.566850	+	0.229735i
$823$	7.39230	−	4.26795i	0.257680	−	0.148771i	−0.365596	−	0.930774i	$-0.619135\pi$
$823$	7.39230	−	4.26795i	0.257680	−	0.148771i	0.623276	+	0.782002i	$0.285801\pi$
$824$	−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	$-0.0183875\pi$
$829$	41.6769	+	24.0622i	1.44750	+	0.835714i	0.449167	+	0.893448i	$0.351721\pi$
$830$		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
$834$	44.1813	+	18.6976i	1.52987	+	0.647444i
$835$		0			0
$836$	−2.12976	−	3.68886i	−0.0736595	−	0.127582i
$837$	6.54383	+	16.8836i	0.226188	+	0.583582i
$838$	−13.8301	−	3.70577i	−0.477754	−	0.128014i
$839$	9.79282	+	2.62398i	0.338086	+	0.0905898i	0.423868	−	0.905724i	$-0.360672\pi$
$839$	9.79282	+	2.62398i	0.338086	+	0.0905898i	−0.0857819	+	0.996314i	$0.527339\pi$
$840$		0			0
$841$	11.1962	+	19.3923i	0.386074	+	0.668700i
$842$	8.33816	−	14.4421i	0.287352	−	0.497708i
$843$	11.5814	−	27.3662i	0.398884	−	0.942540i
$844$		−	0.483340i		−	0.0166372i
$845$		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
$849$	11.3022	+	1.57598i	0.387890	+	0.0540873i
$850$		0			0
$851$		0			0
$852$	−0.842451	−	1.11546i	−0.0288619	−	0.0382151i
$853$	22.3660	+	22.3660i	0.765798	+	0.765798i	0.977364	−	0.211566i	$-0.0678562\pi$
$853$	22.3660	+	22.3660i	0.765798	+	0.765798i	−0.211566	+	0.977364i	$0.567856\pi$
$854$	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	$-0.481902\pi$
$857$	3.32707			0.113651			0.0568253	+	0.998384i	$0.481902\pi$
$858$	31.9856	+	21.7766i	1.09197	+	0.743442i
$859$	39.1769			1.33670			0.668350	−	0.743847i	$-0.267001\pi$
$859$	39.1769			1.33670			0.668350	+	0.743847i	$0.267001\pi$
$860$		0			0
$861$	−5.17100	−	12.7590i	−0.176227	−	0.434825i
$862$	−49.3468	+	28.4904i	−1.68076	+	0.970386i
$863$	−18.2354	−	18.2354i	−0.620741	−	0.620741i	0.324980	−	0.945721i	$-0.394642\pi$
$863$	−18.2354	−	18.2354i	−0.620741	−	0.620741i	−0.945721	+	0.324980i	$0.894642\pi$
$864$	−6.09729	−	4.90487i	−0.207434	−	0.166867i
$865$		0			0
$866$	−33.0673	+	33.0673i	−1.12367	+	1.12367i
$867$	−2.00746	+	14.3966i	−0.0681769	+	0.488935i
$868$	−1.14359	−	0.660254i	−0.0388161	−	0.0224105i
$869$	2.12976	+	7.94839i	0.0722473	+	0.269631i
$870$		0			0
$871$	−6.85641	−	20.2679i	−0.232320	−	0.686753i
$872$			48.6788i			1.64847i
$873$	−4.43324	+	2.46991i	−0.150042	+	0.0835939i
$874$		0			0
$875$		0			0
$876$	0.587477	−	0.0727771i	0.0198490	−	0.00245891i
$877$	−28.9904	−	7.76795i	−0.978936	−	0.262305i	−0.266339	−	0.963879i	$-0.585814\pi$
$877$	−28.9904	−	7.76795i	−0.978936	−	0.262305i	−0.712596	+	0.701574i	$0.752481\pi$
$878$	−1.84443	−	0.494214i	−0.0622465	−	0.0166789i
$879$	−3.09640	+	0.383584i	−0.104439	+	0.0129380i
$880$		0			0
$881$	−11.7417	+	20.3372i	−0.395588	+	0.685178i	−0.993176	−	0.116625i	$-0.962792\pi$
$881$	−11.7417	+	20.3372i	−0.395588	+	0.685178i	0.597588	+	0.801803i	$0.296126\pi$
$882$	−19.7336	+	10.9943i	−0.664464	+	0.370197i
$883$		−	33.3731i		−	1.12309i	−0.827445	−	0.561547i	$-0.810207\pi$
$883$		−	33.3731i		−	1.12309i	0.827445	−	0.561547i	$-0.189793\pi$
$884$	−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	$-0.472683\pi$
$887$	−21.8683	−	12.6257i	−0.734266	−	0.423929i	−0.819981	+	0.572391i	$0.806016\pi$
$888$	3.37965	−	24.2373i	0.113414	−	0.813351i
$889$	9.12436	−	9.12436i	0.306021	−	0.306021i
$890$		0			0
$891$	36.0441	−	8.48560i	1.20752	−	0.284278i
$892$	−4.90897	−	4.90897i	−0.164364	−	0.164364i
$893$	20.1563	−	11.6373i	0.674505	−	0.389426i
$894$	−8.45743	−	20.8680i	−0.282859	−	0.697929i
$895$		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
$903$	−3.24207	−	4.29272i	−0.107889	−	0.142853i
$904$	−6.94486	+	25.9186i	−0.230983	+	0.862039i
$905$		0			0
$906$	−1.95791	−	0.273011i	−0.0650473	−	0.00907018i
$907$	15.0000	+	8.66025i	0.498067	+	0.287559i	0.727915	−	0.685668i	$-0.240490\pi$
$907$	15.0000	+	8.66025i	0.498067	+	0.287559i	−0.229848	+	0.973227i	$0.573823\pi$
$908$	−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	$0.991778\pi$
$912$	11.6431	−	27.5121i	0.385543	−	0.911016i
$913$	−8.46410	+	14.6603i	−0.280121	+	0.485184i
$914$	−2.93730	−	5.08755i	−0.0971572	−	0.168281i
$915$		0			0
$916$	−5.16987	−	1.38526i	−0.170817	−	0.0457704i
$917$	−10.8577	−	2.90931i	−0.358553	−	0.0960740i
$918$	−36.7670	+	14.2504i	−1.21349	+	0.470333i
$919$	−6.70577	−	11.6147i	−0.221203	−	0.383135i	0.733971	−	0.679181i	$-0.237665\pi$
$919$	−6.70577	−	11.6147i	−0.221203	−	0.383135i	−0.955174	+	0.296046i	$0.904332\pi$
$920$		0			0
$921$	−18.9314	−	8.01177i	−0.623809	−	0.263997i
$922$			32.0333i			1.05496i
$923$	−2.12976	+	10.6488i	−0.0701021	+	0.350510i
$924$	−1.66025	+	2.12976i	−0.0546183	+	0.0700641i
$925$		0			0
$926$	42.5188	+	24.5483i	1.39726	+	0.806706i
$927$	−14.4705	−	14.9200i	−0.475272	−	0.490036i
$928$	7.63397	−	7.63397i	0.250597	−	0.250597i
$929$	5.27594	−	19.6901i	0.173098	−	0.646011i	−0.823770	−	0.566924i	$-0.808133\pi$
$929$	5.27594	−	19.6901i	0.173098	−	0.646011i	0.996868	−	0.0790861i	$-0.0252002\pi$
$930$		0			0
$931$	−13.6603	−	13.6603i	−0.447697	−	0.447697i
$932$	4.05065	−	2.33864i	0.132683	−	0.0766048i
$933$	−16.1777	+	6.55656i	−0.529635	+	0.214652i
$934$	27.8827	−	7.47114i	0.912349	−	0.244463i
$935$		0			0
$936$	1.38506	+	28.1803i	0.0452721	+	0.921103i
$937$	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
$939$	−3.21046	+	1.30114i	−0.104769	+	0.0424612i
$940$		0			0
$941$	9.14570	+	9.14570i	0.298141	+	0.298141i	0.840285	−	0.542144i	$-0.182387\pi$
$941$	9.14570	+	9.14570i	0.298141	+	0.298141i	−0.542144	+	0.840285i	$0.682387\pi$
$942$	−9.99911	+	7.55181i	−0.325789	+	0.246051i
$943$		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	$-0.139107\pi$
$947$	−2.77689	−	10.3635i	−0.0902368	−	0.336768i	−0.996254	+	0.0864720i	$0.972441\pi$
$948$	0.570669	−	0.732051i	0.0185345	−	0.0237759i
$949$	−3.45448	−	3.03590i	−0.112137	−	0.0985494i
$950$		0			0
$951$	−25.6076	−	10.8372i	−0.830385	−	0.351420i
$952$	−9.29423	+	16.0981i	−0.301228	+	0.521742i
$953$	−0.988427	−	1.71201i	−0.0320183	−	0.0554573i	0.849572	−	0.527472i	$-0.176860\pi$
$953$	−0.988427	−	1.71201i	−0.0320183	−	0.0554573i	−0.881591	+	0.472015i	$0.843527\pi$
$954$	−3.02279	−	1.80740i	−0.0978666	−	0.0585169i
$955$		0			0
$956$	−2.41510	−	0.647124i	−0.0781099	−	0.0209295i
$957$	6.28076	+	50.7000i	0.203028	+	1.63890i
$958$	15.4904	+	26.8301i	0.500471	+	0.866842i
$959$	−4.75374	+	8.23373i	−0.153506	+	0.265881i
$960$		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	−0.0992599	−	0.995062i	$-0.531648\pi$
$967$	27.8564	−	27.8564i	0.895802	−	0.895802i	0.995062	+	0.0992599i	$0.0316475\pi$
$968$	−4.00218	+	14.9363i	−0.128635	+	0.480072i
$969$	−20.3236	−	26.9098i	−0.652887	−	0.864467i
$970$		0			0
$971$	−41.4335	+	23.9216i	−1.32966	+	0.767682i	−0.985247	−	0.171136i	$-0.945256\pi$
$971$	−41.4335	+	23.9216i	−1.32966	+	0.767682i	−0.344416	+	0.938817i	$0.611923\pi$
$972$	−3.21415	−	2.66755i	−0.103094	−	0.0855618i
$973$	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	$-0.459606\pi$
$977$	22.8847	−	6.13194i	0.732147	−	0.196178i	0.605585	+	0.795780i	$0.292939\pi$
$978$	4.05721	+	10.0108i	0.129735	+	0.320111i
$979$	−33.2487	+	19.1962i	−1.06263	+	0.613512i
$980$		0			0
$981$	−0.856198	+	55.9800i	−0.0273363	+	1.78730i
$982$	11.1173	−	41.4904i	0.354768	−	1.32401i
$983$	−30.4433	+	30.4433i	−0.970992	+	0.970992i	−0.999591	−	0.0285990i	$-0.990895\pi$
$983$	−30.4433	+	30.4433i	−0.970992	+	0.970992i	0.0285990	+	0.999591i	$0.490895\pi$
$984$	−3.50677	+	25.1490i	−0.111792	+	0.801721i
$985$		0			0
$986$	−14.0803	−	52.5485i	−0.448409	−	1.67349i
$987$	−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	0.106557	−	0.994307i	$-0.466017\pi$
$991$	28.7846	−	49.8564i	0.914373	−	1.58374i	0.807816	−	0.589434i	$-0.200649\pi$
$992$	2.62398	+	4.54486i	0.0833114	+	0.144300i
$993$	−58.8186	+	7.28650i	−1.86655	+	0.231230i
$994$	−6.19615	−	1.66025i	−0.196530	−	0.0526601i
$995$		0			0
$996$	1.89501	−	0.234755i	0.0600457	−	0.00743851i
$997$	−3.50000	−	6.06218i	−0.110846	−	0.191991i	0.805266	−	0.592914i	$-0.202023\pi$
$997$	−3.50000	−	6.06218i	−0.110846	−	0.191991i	−0.916112	+	0.400923i	$0.868689\pi$
$998$	2.62398	−	4.54486i	0.0830606	−	0.143865i
$999$	4.31286	−	27.8132i	0.136453	−	0.879970i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bo.d.851.1		8
3.2	odd	2	inner	975.2.bo.d.851.2		8
5.2	odd	4		975.2.bp.e.149.1		8
5.3	odd	4		975.2.bp.f.149.2		8
5.4	even	2		39.2.k.b.32.2	yes	8
13.11	odd	12	inner	975.2.bo.d.401.2		8
15.2	even	4		975.2.bp.e.149.2		8
15.8	even	4		975.2.bp.f.149.1		8
15.14	odd	2		39.2.k.b.32.1	yes	8
20.19	odd	2		624.2.cn.c.305.2		8
39.11	even	12	inner	975.2.bo.d.401.1		8
60.59	even	2		624.2.cn.c.305.1		8
65.4	even	6		507.2.f.e.239.3		8
65.9	even	6		507.2.f.f.239.2		8
65.19	odd	12		507.2.f.e.437.2		8
65.24	odd	12		39.2.k.b.11.1	✓	8
65.29	even	6		507.2.k.e.80.1		8
65.34	odd	4		507.2.k.e.488.2		8
65.37	even	12		975.2.bp.f.674.1		8
65.44	odd	4		507.2.k.f.488.1		8
65.49	even	6		507.2.k.f.80.2		8
65.54	odd	12		507.2.k.d.89.2		8
65.59	odd	12		507.2.f.f.437.3		8
65.63	even	12		975.2.bp.e.674.2		8
65.64	even	2		507.2.k.d.188.1		8
195.29	odd	6		507.2.k.e.80.2		8
195.44	even	4		507.2.k.f.488.2		8
195.59	even	12		507.2.f.f.437.2		8
195.74	odd	6		507.2.f.f.239.3		8
195.89	even	12		39.2.k.b.11.2	yes	8
195.119	even	12		507.2.k.d.89.1		8
195.128	odd	12		975.2.bp.e.674.1		8
195.134	odd	6		507.2.f.e.239.2		8
195.149	even	12		507.2.f.e.437.3		8
195.164	even	4		507.2.k.e.488.1		8
195.167	odd	12		975.2.bp.f.674.2		8
195.179	odd	6		507.2.k.f.80.1		8
195.194	odd	2		507.2.k.d.188.2		8
260.219	even	12		624.2.cn.c.401.1		8
780.479	odd	12		624.2.cn.c.401.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.k.b.11.1	✓	8	65.24	odd	12
39.2.k.b.11.2	yes	8	195.89	even	12
39.2.k.b.32.1	yes	8	15.14	odd	2
39.2.k.b.32.2	yes	8	5.4	even	2
507.2.f.e.239.2		8	195.134	odd	6
507.2.f.e.239.3		8	65.4	even	6
507.2.f.e.437.2		8	65.19	odd	12
507.2.f.e.437.3		8	195.149	even	12
507.2.f.f.239.2		8	65.9	even	6
507.2.f.f.239.3		8	195.74	odd	6
507.2.f.f.437.2		8	195.59	even	12
507.2.f.f.437.3		8	65.59	odd	12
507.2.k.d.89.1		8	195.119	even	12
507.2.k.d.89.2		8	65.54	odd	12
507.2.k.d.188.1		8	65.64	even	2
507.2.k.d.188.2		8	195.194	odd	2
507.2.k.e.80.1		8	65.29	even	6
507.2.k.e.80.2		8	195.29	odd	6
507.2.k.e.488.1		8	195.164	even	4
507.2.k.e.488.2		8	65.34	odd	4
507.2.k.f.80.1		8	195.179	odd	6
507.2.k.f.80.2		8	65.49	even	6
507.2.k.f.488.1		8	65.44	odd	4
507.2.k.f.488.2		8	195.44	even	4
624.2.cn.c.305.1		8	60.59	even	2
624.2.cn.c.305.2		8	20.19	odd	2
624.2.cn.c.401.1		8	260.219	even	12
624.2.cn.c.401.2		8	780.479	odd	12
975.2.bo.d.401.1		8	39.11	even	12	inner
975.2.bo.d.401.2		8	13.11	odd	12	inner
975.2.bo.d.851.1		8	1.1	even	1	trivial
975.2.bo.d.851.2		8	3.2	odd	2	inner
975.2.bp.e.149.1		8	5.2	odd	4
975.2.bp.e.149.2		8	15.2	even	4
975.2.bp.e.674.1		8	195.128	odd	12
975.2.bp.e.674.2		8	65.63	even	12
975.2.bp.f.149.1		8	15.8	even	4
975.2.bp.f.149.2		8	5.3	odd	4
975.2.bp.f.674.1		8	65.37	even	12
975.2.bp.f.674.2		8	195.167	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.45466 + 0.389774i) q^{2} +(1.60523 - 0.650571i) q^{3} +(0.232051 - 0.133975i) q^{4} +(-2.08148 + 1.57203i) q^{6} +(-0.366025 + 1.36603i) q^{7} +(1.84443 - 1.84443i) q^{8} +(2.15351 - 2.08863i) q^{9} +O(q^{10})\)	\(q+(-1.45466 + 0.389774i) q^{2} +(1.60523 - 0.650571i) q^{3} +(0.232051 - 0.133975i) q^{4} +(-2.08148 + 1.57203i) q^{6} +(-0.366025 + 1.36603i) q^{7} +(1.84443 - 1.84443i) q^{8} +(2.15351 - 2.08863i) q^{9} +(1.06488 + 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} +(-2.31853 + 3.87762i) q^{18} +(-3.73205 - 1.00000i) q^{19} +(0.301143 + 2.43091i) q^{21} +(-3.09808 - 5.36603i) q^{22} +(1.76080 - 4.16067i) 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} +(4.29488 + 5.68671i) q^{33} +(-5.36603 - 5.36603i) q^{34} +(0.219901 - 0.773185i) q^{36} +(5.23205 - 1.40192i) q^{37} +5.81863 q^{38} +(-5.62477 + 2.71330i) q^{39} +(-5.42885 + 1.45466i) q^{41} +(-1.38556 - 3.41876i) q^{42} +(-1.90192 + 1.09808i) q^{43} +(0.779548 + 0.779548i) q^{44} +(-4.25953 + 4.25953i) q^{47} +(-1.06782 + 7.65796i) q^{48} +(4.33013 + 2.50000i) q^{49} +(6.88351 + 5.36603i) q^{51} +(-0.803848 + 0.535898i) q^{52} +0.779548i q^{53} +(-1.19909 + 7.73284i) q^{54} +(1.84443 + 3.19465i) q^{56} +(-6.64136 + 0.822738i) 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} +(2.06488 + 3.70625i) 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} +(0.119671 - 7.82434i) q^{72} +(0.901924 + 0.901924i) q^{73} +(-7.06440 + 4.07863i) q^{74} +(-1.00000 + 0.267949i) q^{76} -5.81863 q^{77} +(7.12453 - 6.13931i) q^{78} +2.00000 q^{79} +(0.275241 - 8.99579i) q^{81} +(7.33013 - 4.23205i) q^{82} +(2.90931 + 2.90931i) q^{83} +(0.395560 + 0.523749i) q^{84} +(2.33864 - 2.33864i) q^{86} +(12.2978 + 1.71481i) q^{87} +(9.29423 + 5.36603i) q^{88} +(2.41510 + 9.01327i) q^{89} +(1.00000 - 5.00000i) q^{91} +(-2.35237 + 5.55852i) q^{93} +(4.53590 - 7.85641i) q^{94} +(-0.320682 - 2.58863i) q^{96} +(-1.63397 - 0.437822i) q^{97} +(-7.27328 - 1.94887i) q^{98} +(10.5939 + 6.33434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} - 12 q^{4} - 2 q^{6} + 4 q^{7} + 4 q^{9}+O(q^{10}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more