LMFDB - Embedded newform 975.2.bo.d.626.1

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			626.1
Root			$0.500000 - 1.19293i$ of defining polynomial
Character	$\chi$	$=$	975.626
Dual form			975.2.bo.d.176.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.619657 + 2.31259i) q^{2} +(1.28311 - 1.16345i) q^{3} +(-3.23205 - 1.86603i) q^{4} +(1.89551 + 3.68825i) q^{6} +(1.36603 - 0.366025i) q^{7} +(2.93225 - 2.93225i) q^{8} +(0.292748 - 2.98568i) q^{9} +O(q^{10})$	\(q+(-0.619657 + 2.31259i) q^{2} +(1.28311 - 1.16345i) q^{3} +(-3.23205 - 1.86603i) q^{4} +(1.89551 + 3.68825i) q^{6} +(1.36603 - 0.366025i) q^{7} +(2.93225 - 2.93225i) q^{8} +(0.292748 - 2.98568i) q^{9} +(-1.69293 - 0.453620i) q^{11} +(-6.31812 + 1.36603i) q^{12} +(1.59808 - 3.23205i) q^{13} +3.38587i q^{14} +(1.23205 + 2.13397i) q^{16} +(-1.07328 + 1.85897i) q^{17} +(6.72326 + 2.52711i) q^{18} +(-0.267949 - 1.00000i) q^{19} +(1.32691 - 2.05896i) q^{21} +(2.09808 - 3.63397i) q^{22} +(0.350863 - 7.17394i) q^{24} +(6.48415 + 5.69846i) q^{26} +(-3.09808 - 4.17156i) q^{27} +(-5.09808 - 1.36603i) q^{28} +(4.79122 - 2.76621i) q^{29} +(4.46410 - 4.46410i) q^{31} +(2.31259 - 0.619657i) q^{32} +(-2.69999 + 1.38761i) q^{33} +(-3.63397 - 3.63397i) q^{34} +(-6.51754 + 9.10360i) q^{36} +(1.76795 - 6.59808i) q^{37} +2.47863 q^{38} +(-1.70983 - 6.00637i) q^{39} +(-0.166037 + 0.619657i) q^{41} +(3.93930 + 4.34444i) q^{42} +(-7.09808 - 4.09808i) q^{43} +(4.62518 + 4.62518i) q^{44} +(6.77174 - 6.77174i) q^{47} +(4.06364 + 1.30469i) q^{48} +(-4.33013 + 2.50000i) q^{49} +(0.785693 + 3.63397i) q^{51} +(-11.1962 + 7.46410i) q^{52} +4.62518i q^{53} +(11.5669 - 4.57965i) q^{54} +(2.93225 - 5.07880i) q^{56} +(-1.50726 - 0.971364i) q^{57} +(3.42820 + 12.7942i) q^{58} +(1.23931 + 4.62518i) q^{59} +(3.50000 - 6.06218i) q^{61} +(7.55743 + 13.0899i) q^{62} +(-0.692934 - 4.18567i) q^{63} +10.6603i q^{64} +(-1.53590 - 7.10381i) q^{66} +(8.46410 + 2.26795i) q^{67} +(6.93777 - 4.00552i) q^{68} +(4.62518 - 1.23931i) q^{71} +(-7.89635 - 9.61317i) q^{72} +(6.09808 + 6.09808i) q^{73} +(14.1631 + 8.17709i) q^{74} +(-1.00000 + 3.73205i) q^{76} -2.47863 q^{77} +(14.9498 - 0.232259i) q^{78} +2.00000 q^{79} +(-8.82860 - 1.74811i) q^{81} +(-1.33013 - 0.767949i) q^{82} +(1.23931 + 1.23931i) q^{83} +(-8.13071 + 4.17862i) q^{84} +(13.8755 - 13.8755i) q^{86} +(2.92931 - 9.12372i) q^{87} +(-6.29423 + 3.63397i) q^{88} +(-9.70398 - 2.60017i) q^{89} +(1.00000 - 5.00000i) q^{91} +(0.534160 - 10.9217i) q^{93} +(11.4641 + 19.8564i) q^{94} +(2.24637 - 3.48568i) q^{96} +(-3.36603 - 12.5622i) q^{97} +(-3.09828 - 11.5630i) q^{98} +(-1.84997 + 4.92177i) 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 $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.619657	+	2.31259i	−0.438164	+	1.63525i	0.295217	+	0.955430i	$0.404608\pi$
$2$	−0.619657	+	2.31259i	−0.438164	+	1.63525i	−0.733380	+	0.679818i	$0.762059\pi$
$3$	1.28311	−	1.16345i	0.740805	−	0.671721i
$3$	1.28311	−	1.16345i	0.740805	−	0.671721i
$4$	−3.23205	−	1.86603i	−1.61603	−	0.933013i
$5$		0			0
$5$		0			0
$6$	1.89551	+	3.68825i	0.773837	+	1.50572i
$7$	1.36603	−	0.366025i	0.516309	−	0.138345i	0.00875026	−	0.999962i	$-0.497215\pi$
$7$	1.36603	−	0.366025i	0.516309	−	0.138345i	0.507559	+	0.861617i	$0.330548\pi$
$8$	2.93225	−	2.93225i	1.03671	−	1.03671i
$9$	0.292748	−	2.98568i	0.0975828	−	0.995227i
$10$		0			0
$11$	−1.69293	−	0.453620i	−0.510439	−	0.136772i	−0.00559833	−	0.999984i	$-0.501782\pi$
$11$	−1.69293	−	0.453620i	−0.510439	−	0.136772i	−0.504840	+	0.863213i	$0.668449\pi$
$12$	−6.31812	+	1.36603i	−1.82388	+	0.394338i
$13$	1.59808	−	3.23205i	0.443227	−	0.896410i
$13$	1.59808	−	3.23205i	0.443227	−	0.896410i
$14$			3.38587i			0.904911i
$15$		0			0
$16$	1.23205	+	2.13397i	0.308013	+	0.533494i
$17$	−1.07328	+	1.85897i	−0.260308	+	0.450867i	−0.966324	−	0.257330i	$-0.917157\pi$
$17$	−1.07328	+	1.85897i	−0.260308	+	0.450867i	0.706016	+	0.708196i	$0.250491\pi$
$18$	6.72326	+	2.52711i	1.58469	+	0.595644i
$19$	−0.267949	−	1.00000i	−0.0614718	−	0.229416i	0.928355	−	0.371695i	$-0.121223\pi$
$19$	−0.267949	−	1.00000i	−0.0614718	−	0.229416i	−0.989826	+	0.142280i	$0.954557\pi$
$20$		0			0
$21$	1.32691	−	2.05896i	0.289555	−	0.449302i
$22$	2.09808	−	3.63397i	0.447311	−	0.774766i
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	0.350863	−	7.17394i	0.0716197	−	1.46437i
$25$		0			0
$26$	6.48415	+	5.69846i	1.27165	+	1.11756i
$27$	−3.09808	−	4.17156i	−0.596225	−	0.802817i
$28$	−5.09808	−	1.36603i	−0.963446	−	0.258155i
$29$	4.79122	−	2.76621i	0.889707	−	0.513673i	0.0158603	−	0.999874i	$-0.494951\pi$
$29$	4.79122	−	2.76621i	0.889707	−	0.513673i	0.873847	+	0.486202i	$0.161618\pi$
$30$		0			0
$31$	4.46410	−	4.46410i	0.801776	−	0.801776i	−0.181597	−	0.983373i	$-0.558127\pi$
$31$	4.46410	−	4.46410i	0.801776	−	0.801776i	0.983373	+	0.181597i	$0.0581266\pi$
$32$	2.31259	−	0.619657i	0.408812	−	0.109541i
$33$	−2.69999	+	1.38761i	−0.470008	+	0.241551i
$34$	−3.63397	−	3.63397i	−0.623222	−	0.623222i
$35$		0			0
$36$	−6.51754	+	9.10360i	−1.08626	+	1.51727i
$37$	1.76795	−	6.59808i	0.290649	−	1.08472i	−0.653963	−	0.756527i	$-0.726895\pi$
$37$	1.76795	−	6.59808i	0.290649	−	1.08472i	0.944612	−	0.328190i	$-0.106439\pi$
$38$	2.47863			0.402086
$39$	−1.70983	−	6.00637i	−0.273793	−	0.961789i
$40$		0			0
$41$	−0.166037	+	0.619657i	−0.0259306	+	0.0967741i	−0.977678	−	0.210107i	$-0.932619\pi$
$41$	−0.166037	+	0.619657i	−0.0259306	+	0.0967741i	0.951748	+	0.306881i	$0.0992854\pi$
$42$	3.93930	+	4.34444i	0.607848	+	0.670362i
$43$	−7.09808	−	4.09808i	−1.08245	−	0.624951i	−0.150891	−	0.988550i	$-0.548214\pi$
$43$	−7.09808	−	4.09808i	−1.08245	−	0.624951i	−0.931555	+	0.363600i	$0.881548\pi$
$44$	4.62518	+	4.62518i	0.697272	+	0.697272i
$45$		0			0
$46$		0			0
$47$	6.77174	−	6.77174i	0.987759	−	0.987759i	−0.0121668	−	0.999926i	$-0.503873\pi$
$47$	6.77174	−	6.77174i	0.987759	−	0.987759i	0.999926	+	0.0121668i	$0.00387290\pi$
$48$	4.06364	+	1.30469i	0.586536	+	0.188316i
$49$	−4.33013	+	2.50000i	−0.618590	+	0.357143i
$50$		0			0
$51$	0.785693	+	3.63397i	0.110019	+	0.508858i
$52$	−11.1962	+	7.46410i	−1.55263	+	1.03508i
$53$			4.62518i			0.635318i	0.948205	+	0.317659i	$0.102897\pi$
$53$			4.62518i			0.635318i	−0.948205	+	0.317659i	$0.897103\pi$
$54$	11.5669	−	4.57965i	1.57405	−	0.623211i
$55$		0			0
$56$	2.93225	−	5.07880i	0.391838	−	0.678683i
$57$	−1.50726	−	0.971364i	−0.199642	−	0.128660i
$58$	3.42820	+	12.7942i	0.450145	+	1.67996i
$59$	1.23931	+	4.62518i	0.161345	+	0.602147i	0.998478	+	0.0551484i	$0.0175632\pi$
$59$	1.23931	+	4.62518i	0.161345	+	0.602147i	−0.837133	+	0.546999i	$0.815770\pi$
$60$		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	$0.0187572\pi$
$62$	7.55743	+	13.0899i	0.959794	+	1.66241i
$63$	−0.692934	−	4.18567i	−0.0873015	−	0.527345i
$64$			10.6603i			1.33253i
$65$		0			0
$66$	−1.53590	−	7.10381i	−0.189056	−	0.874418i
$67$	8.46410	+	2.26795i	1.03405	+	0.277074i	0.735647	−	0.677365i	$-0.236878\pi$
$67$	8.46410	+	2.26795i	1.03405	+	0.277074i	0.298407	+	0.954439i	$0.403545\pi$
$68$	6.93777	−	4.00552i	0.841328	−	0.485741i
$69$		0			0
$70$		0			0
$71$	4.62518	−	1.23931i	0.548908	−	0.147079i	0.0263025	−	0.999654i	$-0.491627\pi$
$71$	4.62518	−	1.23931i	0.548908	−	0.147079i	0.522606	+	0.852575i	$0.324960\pi$
$72$	−7.89635	−	9.61317i	−0.930594	−	1.13292i
$73$	6.09808	+	6.09808i	0.713726	+	0.713726i	0.967313	−	0.253587i	$-0.0816103\pi$
$73$	6.09808	+	6.09808i	0.713726	+	0.713726i	−0.253587	+	0.967313i	$0.581610\pi$
$74$	14.1631	+	8.17709i	1.64643	+	0.950567i
$75$		0			0
$76$	−1.00000	+	3.73205i	−0.114708	+	0.428096i
$77$	−2.47863			−0.282466
$78$	14.9498	−	0.232259i	1.69273	−	0.0262981i
$79$	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
$81$	−8.82860	−	1.74811i	−0.980955	−	0.194234i
$82$	−1.33013	−	0.767949i	−0.146888	−	0.0848058i
$83$	1.23931	+	1.23931i	0.136032	+	0.136032i	0.771844	−	0.635812i	$-0.219335\pi$
$83$	1.23931	+	1.23931i	0.136032	+	0.136032i	−0.635812	+	0.771844i	$0.719335\pi$
$84$	−8.13071	+	4.17862i	−0.887133	+	0.455924i
$85$		0			0
$86$	13.8755	−	13.8755i	1.49624	−	1.49624i
$87$	2.92931	−	9.12372i	0.314054	−	0.978165i
$88$	−6.29423	+	3.63397i	−0.670967	+	0.387383i
$89$	−9.70398	−	2.60017i	−1.02862	−	0.275618i	−0.295230	−	0.955426i	$-0.595396\pi$
$89$	−9.70398	−	2.60017i	−1.02862	−	0.275618i	−0.733390	+	0.679808i	$0.762063\pi$
$90$		0			0
$91$	1.00000	−	5.00000i	0.104828	−	0.524142i
$92$		0			0
$93$	0.534160	−	10.9217i	0.0553898	−	1.13253i
$94$	11.4641	+	19.8564i	1.18243	+	2.04803i
$95$		0			0
$96$	2.24637	−	3.48568i	0.229269	−	0.355756i
$97$	−3.36603	−	12.5622i	−0.341768	−	1.27550i	−0.896343	−	0.443362i	$-0.853786\pi$
$97$	−3.36603	−	12.5622i	−0.341768	−	1.27550i	0.554575	−	0.832134i	$-0.312881\pi$
$98$	−3.09828	−	11.5630i	−0.312974	−	1.16803i
$99$	−1.84997	+	4.92177i	−0.185929	+	0.494656i
$100$		0			0
$101$	9.87002	+	17.0954i	0.982104	+	1.70105i	0.654160	+	0.756356i	$0.273022\pi$
$101$	9.87002	+	17.0954i	0.982104	+	1.70105i	0.327944	+	0.944697i	$0.393644\pi$
$102$	−8.89076	−	0.434830i	−0.880316	−	0.0430546i
$103$			6.92820i			0.682656i	0.939944	+	0.341328i	$0.110877\pi$
$103$			6.92820i			0.682656i	−0.939944	+	0.341328i	$0.889123\pi$
$104$	−4.79122	−	14.1631i	−0.469818	−	1.38881i
$105$		0			0
$106$	−10.6962	−	2.86603i	−1.03890	−	0.278373i
$107$	−14.4507	+	8.34312i	−1.39700	+	0.806560i	−0.994078	−	0.108673i	$-0.965340\pi$
$107$	−14.4507	+	8.34312i	−1.39700	+	0.806560i	−0.402925	+	0.915233i	$0.632007\pi$
$108$	2.22890	+	19.2638i	0.214476	+	1.85366i
$109$	−2.80385	+	2.80385i	−0.268560	+	0.268560i	−0.828520	−	0.559960i	$-0.810817\pi$
$109$	−2.80385	+	2.80385i	−0.268560	+	0.268560i	0.559960	+	0.828520i	$0.310817\pi$
$110$		0			0
$111$	−5.40808	−	10.5230i	−0.513313	−	0.998798i
$112$	2.46410	+	2.46410i	0.232836	+	0.232836i
$113$	11.2309	+	6.48415i	1.05651	+	0.609978i	0.924465	−	0.381266i	$-0.124512\pi$
$113$	11.2309	+	6.48415i	1.05651	+	0.609978i	0.132047	+	0.991243i	$0.457845\pi$
$114$	3.18035	−	2.88377i	0.297867	−	0.270090i
$115$		0			0
$116$	−20.6473			−1.91705
$117$	−9.18204	−	5.71753i	−0.848880	−	0.528585i
$118$	−11.4641			−1.05536
$119$	−0.785693	+	2.93225i	−0.0720244	+	0.268799i
$120$		0			0
$121$	−6.86603	−	3.96410i	−0.624184	−	0.360373i
$122$	11.8505	+	11.8505i	1.07290	+	1.07290i
$123$	0.507899	+	0.988265i	0.0457957	+	0.0891088i
$124$	−22.7583	+	6.09808i	−2.04376	+	0.547623i
$125$		0			0
$126$	10.1091	+	0.991207i	0.900592	+	0.0883037i
$127$	−13.0981	+	7.56218i	−1.16227	+	0.671035i	−0.951846	−	0.306576i	$-0.900817\pi$
$127$	−13.0981	+	7.56218i	−1.16227	+	0.671035i	−0.210420	+	0.977611i	$0.567483\pi$
$128$	−20.0276	−	5.36639i	−1.77021	−	0.474326i
$129$	−13.8755	+	3.00000i	−1.22167	+	0.264135i
$130$		0			0
$131$		−	0.907241i		−	0.0792660i	−0.999214	−	0.0396330i	$-0.987381\pi$
$131$		−	0.907241i		−	0.0792660i	0.999214	−	0.0396330i	$-0.0126189\pi$
$132$	11.3158	+	0.553435i	0.984915	+	0.0481703i
$133$	−0.732051	−	1.26795i	−0.0634769	−	0.109945i
$134$	−10.4897	+	18.1687i	−0.906170	+	1.56953i
$135$		0			0
$136$	2.30385	+	8.59808i	0.197553	+	0.737279i
$137$	−1.52690	−	5.69846i	−0.130452	−	0.486852i	0.869524	−	0.493891i	$-0.164426\pi$
$137$	−1.52690	−	5.69846i	−0.130452	−	0.486852i	−0.999975	+	0.00703925i	$0.997759\pi$
$138$		0			0
$139$	1.19615	−	2.07180i	0.101456	−	0.175728i	−0.810829	−	0.585284i	$-0.800983\pi$
$139$	1.19615	−	2.07180i	0.101456	−	0.175728i	0.912285	+	0.409556i	$0.134316\pi$
$140$		0			0
$141$	0.810284	−	16.5675i	0.0682383	−	1.39523i
$142$			11.4641i			0.962046i
$143$	−4.17156	+	4.74673i	−0.348843	+	0.396941i
$144$	6.73205	−	3.05379i	0.561004	−	0.254483i
$145$		0			0
$146$	−17.8811	+	10.3236i	−1.47985	+	0.854391i
$147$	−2.64740	+	8.24568i	−0.218354	+	0.680092i
$148$	−18.0263	+	18.0263i	−1.48175	+	1.48175i
$149$	−5.24484	+	1.40535i	−0.429674	+	0.115131i	−0.467173	−	0.884166i	$-0.654728\pi$
$149$	−5.24484	+	1.40535i	−0.429674	+	0.115131i	0.0374992	+	0.999297i	$0.488061\pi$
$150$		0			0
$151$	7.46410	+	7.46410i	0.607420	+	0.607420i	0.942271	−	0.334851i	$-0.108686\pi$
$151$	7.46410	+	7.46410i	0.607420	+	0.607420i	−0.334851	+	0.942271i	$0.608686\pi$
$152$	−3.71794	−	2.14655i	−0.301565	−	0.174109i
$153$	5.23610	+	3.74867i	0.423313	+	0.303062i
$154$	1.53590	−	5.73205i	0.123766	−	0.461902i
$155$		0			0
$156$	−5.68177	+	22.6035i	−0.454905	+	1.80973i
$157$	15.1962			1.21278			0.606392	−	0.795165i	$-0.292616\pi$
$157$	15.1962			1.21278			0.606392	+	0.795165i	$0.292616\pi$
$158$	−1.23931	+	4.62518i	−0.0985945	+	0.367960i
$159$	5.38119	+	5.93462i	0.426756	+	0.470646i
$160$		0			0
$161$		0			0
$162$	9.51336	−	19.3337i	0.747440	−	1.51900i
$163$	14.9282	−	4.00000i	1.16927	−	0.313304i	0.378606	−	0.925558i	$-0.376404\pi$
$163$	14.9282	−	4.00000i	1.16927	−	0.313304i	0.790661	+	0.612254i	$0.209737\pi$
$164$	1.69293	−	1.69293i	0.132196	−	0.132196i
$165$		0			0
$166$	−3.63397	+	2.09808i	−0.282051	+	0.162842i
$167$	−11.3969	−	3.05379i	−0.881920	−	0.236310i	−0.210685	−	0.977554i	$-0.567569\pi$
$167$	−11.3969	−	3.05379i	−0.881920	−	0.236310i	−0.671235	+	0.741244i	$0.734236\pi$
$168$	−2.14655	−	9.92820i	−0.165610	−	0.765978i
$169$	−7.89230	−	10.3301i	−0.607100	−	0.794625i
$170$		0			0
$171$	−3.06412	+	0.507263i	−0.234319	+	0.0387914i
$172$	15.2942	+	26.4904i	1.16617	+	2.01987i
$173$	−3.71794	+	6.43966i	−0.282670	+	0.489598i	−0.972041	−	0.234809i	$-0.924553\pi$
$173$	−3.71794	+	6.43966i	−0.282670	+	0.489598i	0.689372	+	0.724408i	$0.257887\pi$
$174$	19.2843	+	12.4279i	1.46194	+	0.942154i
$175$		0			0
$176$	−1.11777	−	4.17156i	−0.0842548	−	0.314443i
$177$	6.97136	+	4.49274i	0.524000	+	0.337695i
$178$	12.0263	−	20.8301i	0.901408	−	1.56128i
$179$	−9.37191	−	16.2326i	−0.700489	−	1.21328i	−0.968295	−	0.249810i	$-0.919632\pi$
$179$	−9.37191	−	16.2326i	−0.700489	−	1.21328i	0.267805	−	0.963473i	$-0.413702\pi$
$180$		0			0
$181$			3.00000i			0.222988i	0.993765	+	0.111494i	$0.0355636\pi$
$181$			3.00000i			0.222988i	−0.993765	+	0.111494i	$0.964436\pi$
$182$	10.9433	+	5.41087i	0.811171	+	0.401081i
$183$	−2.56218	−	11.8505i	−0.189402	−	0.876017i
$184$		0			0
$185$		0			0
$186$	24.9265	+	8.00301i	1.82770	+	0.586809i
$187$	2.66025	−	2.66025i	0.194537	−	0.194537i
$188$	−34.5228	+	9.25036i	−2.51784	+	0.674652i
$189$	−5.75895	−	4.56448i	−0.418902	−	0.332017i
$190$		0			0
$191$	−16.8078	−	9.70398i	−1.21617	−	0.702156i	−0.252073	−	0.967708i	$-0.581112\pi$
$191$	−16.8078	−	9.70398i	−1.21617	−	0.702156i	−0.964096	+	0.265553i	$0.914446\pi$
$192$	12.4027	+	13.6783i	0.895089	+	0.987146i
$193$	−1.86603	+	6.96410i	−0.134319	+	0.501287i	0.865680	+	0.500597i	$0.166886\pi$
$193$	−1.86603	+	6.96410i	−0.134319	+	0.501287i	−1.00000		0.000689767i	$0.999780\pi$
$194$	31.1370			2.23550
$195$		0			0
$196$	18.6603			1.33288
$197$	0.453620	−	1.69293i	0.0323191	−	0.120617i	−0.947882	−	0.318622i	$-0.896780\pi$
$197$	0.453620	−	1.69293i	0.0323191	−	0.120617i	0.980201	+	0.198006i	$0.0634465\pi$
$198$	−10.2357	−	7.32803i	−0.727418	−	0.520780i
$199$	0.803848	+	0.464102i	0.0569832	+	0.0328993i	0.528221	−	0.849107i	$-0.322859\pi$
$199$	0.803848	+	0.464102i	0.0569832	+	0.0328993i	−0.471238	+	0.882006i	$0.656193\pi$
$200$		0			0
$201$	13.4990	−	6.93756i	0.952149	−	0.489338i
$202$	−45.6506	+	12.2321i	−3.21197	+	0.860644i
$203$	5.53242	−	5.53242i	0.388300	−	0.388300i
$204$	4.24169	−	13.2113i	0.296978	−	0.924977i
$205$		0			0
$206$	−16.0221	−	4.29311i	−1.11631	−	0.299115i
$207$		0			0
$208$	8.86603	−	0.571797i	0.614748	−	0.0396470i
$209$			1.81448i			0.125510i
$210$		0			0
$211$	6.09808	+	10.5622i	0.419809	+	0.727130i	0.995920	−	0.0902411i	$-0.0287638\pi$
$211$	6.09808	+	10.5622i	0.419809	+	0.727130i	−0.576111	+	0.817371i	$0.695430\pi$
$212$	8.63071	−	14.9488i	0.592759	−	1.02669i
$213$	4.49274	−	6.97136i	0.307837	−	0.477670i
$214$	−10.3397	−	38.5885i	−0.706810	−	2.63785i
$215$		0			0
$216$	−21.3164	−	3.14772i	−1.45040	−	0.214176i
$217$	4.46410	−	7.73205i	0.303043	−	0.524886i
$218$	−4.74673	−	8.22158i	−0.321489	−	0.556835i
$219$	14.9193	+	0.729677i	1.00816	+	0.0493070i
$220$		0			0
$221$	4.29311	+	6.43966i	0.288786	+	0.433179i
$222$	27.6865	−	5.98604i	1.85820	−	0.401757i
$223$	−22.2942	−	5.97372i	−1.49293	−	0.400030i	−0.582206	−	0.813041i	$-0.697810\pi$
$223$	−22.2942	−	5.97372i	−1.49293	−	0.400030i	−0.910726	+	0.413011i	$0.864477\pi$
$224$	2.93225	−	1.69293i	0.195919	−	0.113114i
$225$		0			0
$226$	−21.9545	+	21.9545i	−1.46039	+	1.46039i
$227$	15.1149	−	4.05001i	1.00321	−	0.268809i	0.280419	−	0.959878i	$-0.409526\pi$
$227$	15.1149	−	4.05001i	1.00321	−	0.268809i	0.722789	+	0.691069i	$0.242860\pi$
$228$	3.05896	+	5.95209i	0.202585	+	0.394187i
$229$	10.1244	+	10.1244i	0.669036	+	0.669036i	0.957493	−	0.288457i	$-0.0931421\pi$
$229$	10.1244	+	10.1244i	0.669036	+	0.669036i	−0.288457	+	0.957493i	$0.593142\pi$
$230$		0			0
$231$	−3.18035	+	2.88377i	−0.209252	+	0.189738i
$232$	5.93782	−	22.1603i	0.389837	−	1.45489i
$233$	7.43588			0.487141			0.243570	−	0.969883i	$-0.421681\pi$
$233$	7.43588			0.487141			0.243570	+	0.969883i	$0.421681\pi$
$234$	18.9120	−	17.6914i	1.23632	−	1.15652i
$235$		0			0
$236$	4.62518	−	17.2614i	0.301074	−	1.12362i
$237$	2.56622	−	2.32691i	0.166694	−	0.151149i
$238$	−6.29423	−	3.63397i	−0.407994	−	0.235556i
$239$	−7.10381	−	7.10381i	−0.459507	−	0.459507i	0.438986	−	0.898494i	$-0.355338\pi$
$239$	−7.10381	−	7.10381i	−0.459507	−	0.459507i	−0.898494	+	0.438986i	$0.855338\pi$
$240$		0			0
$241$	7.23205	−	1.93782i	0.465857	−	0.124826i	−0.0182524	−	0.999833i	$-0.505810\pi$
$241$	7.23205	−	1.93782i	0.465857	−	0.124826i	0.484110	+	0.875007i	$0.339144\pi$
$242$	13.4219	−	13.4219i	0.862794	−	0.862794i
$243$	−13.3619	+	8.02865i	−0.857167	+	0.515038i
$244$	−22.6244	+	13.0622i	−1.44838	+	0.836220i
$245$		0			0
$246$	−2.60017	+	0.562178i	−0.165781	+	0.0358431i
$247$	−3.66025	−	0.732051i	−0.232896	−	0.0465793i
$248$		−	26.1797i		−	1.66241i
$249$	3.03206	+	0.148292i	0.192149	+	0.00939765i
$250$		0			0
$251$	−10.9433	+	18.9543i	−0.690735	+	1.19639i	0.280863	+	0.959748i	$0.409379\pi$
$251$	−10.9433	+	18.9543i	−0.690735	+	1.19639i	−0.971597	+	0.236640i	$0.923954\pi$
$252$	−5.57097	+	14.8213i	−0.350938	+	0.933656i
$253$		0			0
$254$	−9.37191	−	34.9764i	−0.588046	−	2.19462i
$255$		0			0
$256$	14.1603	−	24.5263i	0.885016	−	1.53289i
$257$	−8.29863	−	14.3737i	−0.517655	−	0.896604i	−0.999790	−	0.0205071i	$-0.993472\pi$
$257$	−8.29863	−	14.3737i	−0.517655	−	0.896604i	0.482135	−	0.876097i	$-0.339861\pi$
$258$	1.66030	−	33.9474i	0.103366	−	2.11347i
$259$		−	9.66025i		−	0.600259i
$260$		0			0
$261$	−6.85641	−	15.1149i	−0.424401	−	0.935586i
$262$	2.09808	+	0.562178i	0.129620	+	0.0347315i
$263$	−10.3681	+	5.98604i	−0.639326	+	0.369115i	−0.784355	−	0.620312i	$-0.787006\pi$
$263$	−10.3681	+	5.98604i	−0.639326	+	0.369115i	0.145029	+	0.989427i	$0.453673\pi$
$264$	−3.84823	+	11.9858i	−0.236842	+	0.737677i
$265$		0			0
$266$	3.38587	−	0.907241i	0.207601	−	0.0556265i
$267$	−15.4765	+	7.95383i	−0.947145	+	0.486766i
$268$	−23.1244	−	23.1244i	−1.41254	−	1.41254i
$269$	9.58244	+	5.53242i	0.584251	+	0.337318i	0.762821	−	0.646610i	$-0.223814\pi$
$269$	9.58244	+	5.53242i	0.584251	+	0.337318i	−0.178570	+	0.983927i	$0.557147\pi$
$270$		0			0
$271$	0.535898	−	2.00000i	0.0325535	−	0.121491i	−0.947737	−	0.319052i	$-0.896635\pi$
$271$	0.535898	−	2.00000i	0.0325535	−	0.121491i	0.980291	+	0.197561i	$0.0633021\pi$
$272$	−5.28933			−0.320713
$273$	−4.53416	−	7.57901i	−0.274420	−	0.458703i
$274$	14.1244			0.853284
$275$		0			0
$276$		0			0
$277$	−3.10770	−	1.79423i	−0.186723	−	0.107805i	0.403724	−	0.914881i	$-0.367715\pi$
$277$	−3.10770	−	1.79423i	−0.186723	−	0.107805i	−0.590448	+	0.807076i	$0.701049\pi$
$278$	4.05001	+	4.05001i	0.242904	+	0.242904i
$279$	−12.0215	−	14.6352i	−0.719710	−	0.876189i
$280$		0			0
$281$	15.9006	−	15.9006i	0.948547	−	0.948547i	−0.0501922	−	0.998740i	$-0.515983\pi$
$281$	15.9006	−	15.9006i	0.948547	−	0.948547i	0.998740	+	0.0501922i	$0.0159834\pi$
$282$	37.8117	+	12.1400i	2.25166	+	0.722928i
$283$	21.2942	−	12.2942i	1.26581	−	0.730816i	0.291618	−	0.956535i	$-0.405806\pi$
$283$	21.2942	−	12.2942i	1.26581	−	0.730816i	0.974192	+	0.225719i	$0.0724731\pi$
$284$	−17.2614	−	4.62518i	−1.02428	−	0.274454i
$285$		0			0
$286$	−8.39230	−	12.5885i	−0.496247	−	0.744371i
$287$			0.907241i			0.0535527i
$288$	−1.17309	−	7.08606i	−0.0691251	−	0.417550i
$289$	6.19615	+	10.7321i	0.364480	+	0.631297i
$290$		0			0
$291$	−18.9345	−	12.2025i	−1.10996	−	0.715320i
$292$	−8.33013	−	31.0885i	−0.487484	−	1.81931i
$293$	5.69846	+	21.2669i	0.332908	+	1.24243i	0.906120	+	0.423021i	$0.139030\pi$
$293$	5.69846	+	21.2669i	0.332908	+	1.24243i	−0.573212	+	0.819407i	$0.694303\pi$
$294$	−17.4284	−	11.2318i	−1.01645	−	0.655054i
$295$		0			0
$296$	−14.1631	−	24.5313i	−0.823215	−	1.42585i
$297$	3.35253	+	8.46753i	0.194534	+	0.491336i
$298$		−	13.0000i		−	0.753070i
$299$		0			0
$300$		0			0
$301$	−11.1962	−	3.00000i	−0.645335	−	0.172917i
$302$	−21.8866	+	12.6362i	−1.25943	+	0.727133i
$303$	32.5540	+	10.4520i	1.87018	+	0.600449i
$304$	1.80385	−	1.80385i	0.103458	−	0.103458i
$305$		0			0
$306$	−11.9137	+	9.78605i	−0.681063	+	0.559431i
$307$	12.3923	+	12.3923i	0.707266	+	0.707266i	0.965960	−	0.258693i	$-0.0832919\pi$
$307$	12.3923	+	12.3923i	0.707266	+	0.707266i	−0.258693	+	0.965960i	$0.583292\pi$
$308$	8.01105	+	4.62518i	0.456472	+	0.263544i
$309$	8.06065	+	8.88965i	0.458554	+	0.505715i
$310$		0			0
$311$	4.29311			0.243440			0.121720	−	0.992564i	$-0.461159\pi$
$311$	4.29311			0.243440			0.121720	+	0.992564i	$0.461159\pi$
$312$	−22.6258	−	12.5985i	−1.28093	−	0.713250i
$313$	−2.00000			−0.113047			−0.0565233	−	0.998401i	$-0.518002\pi$
$313$	−2.00000			−0.113047			−0.0565233	+	0.998401i	$0.518002\pi$
$314$	−9.41640	+	35.1425i	−0.531398	+	1.98321i
$315$		0			0
$316$	−6.46410	−	3.73205i	−0.363634	−	0.209944i
$317$	−11.2754	−	11.2754i	−0.633288	−	0.633288i	0.315603	−	0.948891i	$-0.397793\pi$
$317$	−11.2754	−	11.2754i	−0.633288	−	0.633288i	−0.948891	+	0.315603i	$0.897793\pi$
$318$	−17.0588	+	8.76706i	−0.956612	+	0.491632i
$319$	−9.36603	+	2.50962i	−0.524397	+	0.140512i
$320$		0			0
$321$	−8.83503	+	27.5179i	−0.493123	+	1.53590i
$322$		0			0
$323$	2.14655	+	0.575167i	0.119437	+	0.0320032i
$324$	25.2725	+	22.1244i	1.40403	+	1.22913i
$325$		0			0
$326$			37.0015i			2.04932i
$327$	−0.335500	+	6.85980i	−0.0185532	+	0.379348i
$328$	1.33013	+	2.30385i	0.0734440	+	0.127209i
$329$	6.77174	−	11.7290i	0.373338	−	0.646640i
$330$		0			0
$331$	5.05256	+	18.8564i	0.277714	+	1.03644i	0.954001	+	0.299804i	$0.0969212\pi$
$331$	5.05256	+	18.8564i	0.277714	+	1.03644i	−0.676287	+	0.736638i	$0.736412\pi$
$332$	−1.69293	−	6.31812i	−0.0929118	−	0.346752i
$333$	−19.1822	−	7.21011i	−1.05118	−	0.395112i
$334$	14.1244	−	24.4641i	0.772850	−	1.33862i
$335$		0			0
$336$	6.02859	+	0.294847i	0.328886	+	0.0160852i
$337$			11.5359i			0.628400i	0.949357	+	0.314200i	$0.101736\pi$
$337$			11.5359i			0.628400i	−0.949357	+	0.314200i	$0.898264\pi$
$338$	28.7799	−	11.8505i	1.56542	−	0.644584i
$339$	21.9545	−	4.74673i	1.19240	−	0.257807i
$340$		0			0
$341$	−9.58244	+	5.53242i	−0.518918	+	0.299597i
$342$	0.725614	−	7.40039i	0.0392367	−	0.400167i
$343$	−12.0000	+	12.0000i	−0.647939	+	0.647939i
$344$	−32.8299	+	8.79674i	−1.77007	+	0.474289i
$345$		0			0
$346$	−12.5885	−	12.5885i	−0.676760	−	0.676760i
$347$	−22.4618	−	12.9683i	−1.20581	−	0.696175i	−0.243969	−	0.969783i	$-0.578450\pi$
$347$	−22.4618	−	12.9683i	−1.20581	−	0.696175i	−0.961841	+	0.273608i	$0.911783\pi$
$348$	−26.4928	+	24.0222i	−1.42016	+	1.28772i
$349$	1.50962	−	5.63397i	0.0808080	−	0.301580i	−0.913679	−	0.406436i	$-0.866772\pi$
$349$	1.50962	−	5.63397i	0.0808080	−	0.301580i	0.994487	+	0.104856i	$0.0334382\pi$
$350$		0			0
$351$	−18.4337	+	3.34667i	−0.983916	+	0.178632i
$352$	−4.19615			−0.223656
$353$	−7.05932	+	26.3457i	−0.375730	+	1.40224i	0.476546	+	0.879149i	$0.341889\pi$
$353$	−7.05932	+	26.3457i	−0.375730	+	1.40224i	−0.852276	+	0.523093i	$0.824778\pi$
$354$	−14.7097	+	13.3380i	−0.781813	+	0.708904i
$355$		0			0
$356$	26.5118	+	26.5118i	1.40512	+	1.40512i
$357$	2.40340	+	4.67652i	0.127202	+	0.247508i
$358$	43.3468	−	11.6147i	2.29095	−	0.613858i
$359$	−12.0611	+	12.0611i	−0.636559	+	0.636559i	−0.949705	−	0.313146i	$-0.898617\pi$
$359$	−12.0611	+	12.0611i	−0.636559	+	0.636559i	0.313146	+	0.949705i	$0.398617\pi$
$360$		0			0
$361$	15.5263	−	8.96410i	0.817173	−	0.471795i
$362$	−6.93777	−	1.85897i	−0.364641	−	0.0977053i
$363$	−13.4219	+	2.90192i	−0.704468	+	0.152311i
$364$	−12.5622	+	14.2942i	−0.658437	+	0.749221i
$365$		0			0
$366$	28.9931	+	1.41800i	1.51549	+	0.0741199i
$367$	4.80385	+	8.32051i	0.250759	+	0.434327i	0.963735	−	0.266861i	$-0.0859866\pi$
$367$	4.80385	+	8.32051i	0.250759	+	0.434327i	−0.712976	+	0.701188i	$0.752653\pi$
$368$		0			0
$369$	1.80149	+	0.677136i	0.0937819	+	0.0352503i
$370$		0			0
$371$	1.69293	+	6.31812i	0.0878928	+	0.328020i
$372$	−22.1066	+	34.3028i	−1.14618	+	1.77852i
$373$	−9.79423	+	16.9641i	−0.507126	+	0.878368i	0.492840	+	0.870120i	$0.335959\pi$
$373$	−9.79423	+	16.9641i	−0.507126	+	0.878368i	−0.999966	+	0.00824796i	$0.997375\pi$
$374$	4.50363	+	7.80052i	0.232877	+	0.403355i
$375$		0			0
$376$		−	39.7128i		−	2.04803i
$377$	−1.28380	−	19.9061i	−0.0661192	−	1.02522i
$378$	14.1244	−	10.4897i	0.726478	−	0.539531i
$379$	−4.83013	−	1.29423i	−0.248107	−	0.0664801i	0.132622	−	0.991167i	$-0.457660\pi$
$379$	−4.83013	−	1.29423i	−0.248107	−	0.0664801i	−0.380729	+	0.924687i	$0.624327\pi$
$380$		0			0
$381$	−8.00804	+	24.9421i	−0.410264	+	1.27782i
$382$	32.8564	−	32.8564i	1.68108	−	1.68108i
$383$	13.5435	−	3.62896i	0.692039	−	0.185431i	0.104377	−	0.994538i	$-0.466715\pi$
$383$	13.5435	−	3.62896i	0.692039	−	0.185431i	0.587662	+	0.809106i	$0.300048\pi$
$384$	−31.9412	+	16.4156i	−1.62999	+	0.837703i
$385$		0			0
$386$	−14.9488	−	8.63071i	−0.760875	−	0.439291i
$387$	−14.3135	+	19.9929i	−0.727596	+	1.01630i
$388$	−12.5622	+	46.8827i	−0.637748	+	2.38011i
$389$	−5.28933			−0.268180			−0.134090	−	0.990969i	$-0.542811\pi$
$389$	−5.28933			−0.268180			−0.134090	+	0.990969i	$0.542811\pi$
$390$		0			0
$391$		0			0
$392$	−5.36639	+	20.0276i	−0.271043	+	1.01155i
$393$	−1.05553	−	1.16409i	−0.0532446	−	0.0587206i
$394$	3.63397	+	2.09808i	0.183077	+	0.105700i
$395$		0			0
$396$	15.1633	−	12.4553i	0.761986	−	0.625903i
$397$	−8.56218	+	2.29423i	−0.429723	+	0.115144i	−0.467196	−	0.884154i	$-0.654736\pi$
$397$	−8.56218	+	2.29423i	−0.429723	+	0.115144i	0.0374729	+	0.999298i	$0.488069\pi$
$398$	−1.57139	+	1.57139i	−0.0787665	+	0.0787665i
$399$	−2.41450	−	0.775212i	−0.120876	−	0.0388091i
$400$		0			0
$401$	27.1314	+	7.26985i	1.35488	+	0.363039i	0.861933	−	0.507021i	$-0.169253\pi$
$401$	27.1314	+	7.26985i	1.35488	+	0.363039i	0.492946	+	0.870060i	$0.335920\pi$
$402$	7.67898	+	35.5167i	0.382993	+	1.77141i
$403$	−7.29423	−	21.5622i	−0.363351	−	1.07409i
$404$		−	73.6708i		−	3.66526i
$405$		0			0
$406$	9.36603	+	16.2224i	0.464828	+	0.805106i
$407$	−5.98604	+	10.3681i	−0.296717	+	0.513929i
$408$	12.9596	+	8.35187i	0.641594	+	0.413479i
$409$	3.00962	+	11.2321i	0.148816	+	0.555389i	0.999556	+	0.0298020i	$0.00948767\pi$
$409$	3.00962	+	11.2321i	0.148816	+	0.555389i	−0.850740	+	0.525587i	$0.823846\pi$
$410$		0			0
$411$	−8.58908	−	5.53528i	−0.423668	−	0.273035i
$412$	12.9282	−	22.3923i	0.636927	−	1.10319i
$413$	3.38587	+	5.86450i	0.166608	+	0.288573i
$414$		0			0
$415$		0			0
$416$	1.69293	−	8.46467i	0.0830029	−	0.415015i
$417$	−0.875644	−	4.05001i	−0.0428805	−	0.198330i
$418$	−4.19615	−	1.12436i	−0.205241	−	0.0549940i
$419$	−7.22536	+	4.17156i	−0.352982	+	0.203794i	−0.665998	−	0.745954i	$-0.731994\pi$
$419$	−7.22536	+	4.17156i	−0.352982	+	0.203794i	0.313016	+	0.949748i	$0.398661\pi$
$420$		0			0
$421$	0.830127	−	0.830127i	0.0404579	−	0.0404579i	−0.686588	−	0.727046i	$-0.740893\pi$
$421$	0.830127	−	0.830127i	0.0404579	−	0.0404579i	0.727046	+	0.686588i	$0.240893\pi$
$422$	−28.2047	+	7.55743i	−1.37298	+	0.367890i
$423$	−18.2358	−	22.2007i	−0.886657	−	1.07943i
$424$	13.5622	+	13.5622i	0.658638	+	0.658638i
$425$		0			0
$426$	13.3380	+	14.7097i	0.646226	+	0.712688i
$427$	2.56218	−	9.56218i	0.123992	−	0.462746i
$428$	62.2739			3.01012
$429$	0.170025	+	10.9440i	0.00820890	+	0.528381i
$430$		0			0
$431$	0.542599	−	2.02501i	0.0261361	−	0.0975412i	−0.951626	−	0.307260i	$-0.900588\pi$
$431$	0.542599	−	2.02501i	0.0261361	−	0.0975412i	0.977762	+	0.209718i	$0.0672547\pi$
$432$	5.08502	−	11.7508i	0.244653	−	0.565360i
$433$	6.10770	+	3.52628i	0.293517	+	0.169462i	0.639527	−	0.768769i	$-0.279130\pi$
$433$	6.10770	+	3.52628i	0.293517	+	0.169462i	−0.346010	+	0.938231i	$0.612464\pi$
$434$	15.1149	+	15.1149i	0.725536	+	0.725536i
$435$		0			0
$436$	14.2942	−	3.83013i	0.684569	−	0.183430i
$437$		0			0
$438$	−10.9323	+	34.0502i	−0.522366	+	1.62698i
$439$	−4.09808	+	2.36603i	−0.195591	+	0.112924i	−0.594597	−	0.804024i	$-0.702688\pi$
$439$	−4.09808	+	2.36603i	−0.195591	+	0.112924i	0.399007	+	0.916948i	$0.369355\pi$
$440$		0			0
$441$	6.19657	+	13.6603i	0.295075	+	0.650488i
$442$	−17.5526	+	5.93782i	−0.834890	+	0.282433i
$443$		−	29.5656i		−	1.40470i	−0.711830	−	0.702351i	$-0.752134\pi$
$443$		−	29.5656i		−	1.40470i	0.711830	−	0.702351i	$-0.247866\pi$
$444$	−2.15697	+	44.1025i	−0.102365	+	2.09301i
$445$		0			0
$446$	27.6295	−	47.8558i	1.30830	−	2.26604i
$447$	−5.09465	+	7.90535i	−0.240969	+	0.373910i
$448$	3.90192	+	14.5622i	0.184349	+	0.687998i
$449$	−2.26810	−	8.46467i	−0.107038	−	0.399472i	0.891530	−	0.452961i	$-0.149632\pi$
$449$	−2.26810	−	8.46467i	−0.107038	−	0.399472i	−0.998568	+	0.0534890i	$0.982966\pi$
$450$		0			0
$451$	0.562178	−	0.973721i	0.0264719	−	0.0458507i
$452$	−24.1992	−	41.9142i	−1.13823	−	1.97148i
$453$	18.2614	+	0.893131i	0.857996	+	0.0419629i
$454$			37.4641i			1.75828i
$455$		0			0
$456$	−7.26795	+	1.57139i	−0.340353	+	0.0735869i
$457$	26.9904	+	7.23205i	1.26256	+	0.338301i	0.827175	−	0.561945i	$-0.189947\pi$
$457$	26.9904	+	7.23205i	1.26256	+	0.338301i	0.435382	+	0.900246i	$0.356613\pi$
$458$	−29.6871	+	17.1399i	−1.38719	+	0.800893i
$459$	11.0799	−	1.28199i	0.517166	−	0.0598382i
$460$		0			0
$461$	−23.4135	+	6.27363i	−1.09048	+	0.292192i	−0.758880	−	0.651230i	$-0.774253\pi$
$461$	−23.4135	+	6.27363i	−1.09048	+	0.292192i	−0.331595	+	0.943422i	$0.607587\pi$
$462$	−4.69825	−	9.14181i	−0.218582	−	0.425315i
$463$	15.0526	+	15.0526i	0.699552	+	0.699552i	0.964314	−	0.264762i	$-0.0852934\pi$
$463$	15.0526	+	15.0526i	0.699552	+	0.699552i	−0.264762	+	0.964314i	$0.585293\pi$
$464$	11.8060	+	6.81623i	0.548082	+	0.316435i
$465$		0			0
$466$	−4.60770	+	17.1962i	−0.213447	+	0.796596i
$467$	30.4728			1.41011			0.705057	−	0.709151i	$-0.250921\pi$
$467$	30.4728			1.41011			0.705057	+	0.709151i	$0.250921\pi$
$468$	19.0078	+	35.6133i	0.878635	+	1.64622i
$469$	12.3923			0.572223
$470$		0			0
$471$	19.4984	−	17.6800i	0.898437	−	0.814653i
$472$	17.1962	+	9.92820i	0.791517	+	0.456983i
$473$	10.1576	+	10.1576i	0.467047	+	0.467047i
$474$	3.79101	+	7.37651i	0.174127	+	0.338814i
$475$		0			0
$476$	8.01105	−	8.01105i	0.367186	−	0.367186i
$477$	13.8093	+	1.35401i	0.632285	+	0.0619960i
$478$	20.8301	−	12.0263i	0.952748	−	0.550069i
$479$	8.46467	+	2.26810i	0.386761	+	0.103632i	0.446959	−	0.894554i	$-0.352507\pi$
$479$	8.46467	+	2.26810i	0.386761	+	0.103632i	−0.0601988	+	0.998186i	$0.519173\pi$
$480$		0			0
$481$	−18.5000	−	16.2583i	−0.843527	−	0.741316i
$482$			17.9256i			0.816487i
$483$		0			0
$484$	14.7942	+	25.6244i	0.672465	+	1.16474i
$485$		0			0
$486$	−10.2872	−	35.8756i	−0.466636	−	1.62735i
$487$	6.56218	+	24.4904i	0.297361	+	1.10977i	0.939324	+	0.343030i	$0.111453\pi$
$487$	6.56218	+	24.4904i	0.297361	+	1.10977i	−0.641964	+	0.766735i	$0.721880\pi$
$488$	−7.51294	−	28.0387i	−0.340095	−	1.26925i
$489$	14.5007	−	22.5007i	0.655746	−	1.01752i
$490$		0			0
$491$	−12.5147	−	21.6761i	−0.564780	−	0.978227i	−0.997070	−	0.0764928i	$-0.975628\pi$
$491$	−12.5147	−	21.6761i	−0.564780	−	0.978227i	0.432290	−	0.901734i	$-0.357706\pi$
$492$	0.202571	−	4.14187i	0.00913261	−	0.186730i
$493$			11.8756i			0.534852i
$494$	3.96104	−	8.01105i	0.178215	−	0.360434i
$495$		0			0
$496$	15.0263	+	4.02628i	0.674700	+	0.180785i
$497$	5.86450	−	3.38587i	0.263059	−	0.151877i
$498$	−2.22178	+	6.92003i	−0.0995602	+	0.310094i
$499$	4.46410	−	4.46410i	0.199841	−	0.199841i	−0.600091	−	0.799932i	$-0.704869\pi$
$499$	4.46410	−	4.46410i	0.199841	−	0.199841i	0.799932	+	0.600091i	$0.204869\pi$
$500$		0			0
$501$	−18.1765	+	9.34143i	−0.812064	+	0.417345i
$502$	−37.0526	−	37.0526i	−1.65374	−	1.65374i
$503$	−24.8188	−	14.3292i	−1.10662	−	0.638906i	−0.168666	−	0.985673i	$-0.553946\pi$
$503$	−24.8188	−	14.3292i	−1.10662	−	0.638906i	−0.937951	+	0.346767i	$0.887279\pi$
$504$	−14.3053	−	10.2416i	−0.637208	−	0.456196i
$505$		0			0
$506$		0			0
$507$	−22.1453	−	4.07236i	−0.983509	−	0.180860i
$508$	56.4449			2.50434
$509$	−3.88398	+	14.4952i	−0.172154	+	0.642489i	0.824865	+	0.565330i	$0.191251\pi$
$509$	−3.88398	+	14.4952i	−0.172154	+	0.642489i	−0.997019	+	0.0771582i	$0.975415\pi$
$510$		0			0
$511$	10.5622	+	6.09808i	0.467243	+	0.269763i
$512$	18.6223	+	18.6223i	0.822996	+	0.822996i
$513$	−3.34143	+	4.21584i	−0.147528	+	0.186134i
$514$	38.3827	−	10.2846i	1.69299	−	0.453635i
$515$		0			0
$516$	50.4445	+	16.1960i	2.22070	+	0.712988i
$517$	−14.5359	+	8.39230i	−0.639288	+	0.369093i
$518$	22.3402	+	5.98604i	0.981573	+	0.263012i
$519$	2.72172	+	12.5885i	0.119470	+	0.552572i
$520$		0			0
$521$			33.2835i			1.45818i	0.684419	+	0.729089i	$0.260056\pi$
$521$			33.2835i			1.45818i	−0.684419	+	0.729089i	$0.739944\pi$
$522$	39.2031	−	6.49004i	1.71587	−	0.284061i
$523$	6.49038	+	11.2417i	0.283805	+	0.491564i	0.972319	−	0.233659i	$-0.0750700\pi$
$523$	6.49038	+	11.2417i	0.283805	+	0.491564i	−0.688514	+	0.725223i	$0.741737\pi$
$524$	−1.69293	+	2.93225i	−0.0739562	+	0.128096i
$525$		0			0
$526$	−7.41858	−	27.6865i	−0.323466	−	1.20719i
$527$	3.50742	+	13.0899i	0.152785	+	0.570203i
$528$	−6.28764	−	4.05211i	−0.273634	−	0.176345i
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$		0			0
$531$	14.1721	−	2.34618i	0.615018	−	0.101816i
$532$			5.46410i			0.236899i
$533$	1.73742	+	1.52690i	0.0752562	+	0.0661373i
$534$	−8.80385	−	40.7194i	−0.380980	−	1.76210i
$535$		0			0
$536$	31.4690	−	18.1687i	1.35926	−	0.784766i
$537$	−30.9111	−	9.92447i	−1.33391	−	0.428273i
$538$	−18.7321	+	18.7321i	−0.807596	+	0.807596i
$539$	8.46467	−	2.26810i	0.364599	−	0.0976940i
$540$		0			0
$541$	23.6865	+	23.6865i	1.01836	+	1.01836i	0.999828	+	0.0185354i	$0.00590034\pi$
$541$	23.6865	+	23.6865i	1.01836	+	1.01836i	0.0185354	+	0.999828i	$0.494100\pi$
$542$	4.29311	+	2.47863i	0.184405	+	0.106466i
$543$	3.49036	+	3.84933i	0.149786	+	0.165191i
$544$	−1.33013	+	4.96410i	−0.0570287	+	0.212834i
$545$		0			0
$546$	20.3368	−	5.78927i	0.870333	−	0.247758i
$547$	−2.00000			−0.0855138			−0.0427569	−	0.999086i	$-0.513614\pi$
$547$	−2.00000			−0.0855138			−0.0427569	+	0.999086i	$0.513614\pi$
$548$	−5.69846	+	21.2669i	−0.243426	+	0.908479i
$549$	−17.0751	−	12.2246i	−0.728748	−	0.521732i
$550$		0			0
$551$	−4.05001	−	4.05001i	−0.172536	−	0.172536i
$552$		0			0
$553$	2.73205	−	0.732051i	0.116179	−	0.0311300i
$554$	6.07502	−	6.07502i	0.258103	−	0.258103i
$555$		0			0
$556$	−7.73205	+	4.46410i	−0.327912	+	0.189320i
$557$	39.3140	+	10.5342i	1.66579	+	0.446347i	0.963971	−	0.266009i	$-0.0857049\pi$
$557$	39.3140	+	10.5342i	1.66579	+	0.446347i	0.701819	+	0.712355i	$0.252372\pi$
$558$	41.2946	−	18.7321i	1.74814	−	0.792991i
$559$	−24.5885	+	16.3923i	−1.03998	+	0.693321i
$560$		0			0
$561$	0.318318	−	6.50849i	0.0134394	−	0.274788i
$562$	26.9186	+	46.6244i	1.13549	+	1.96673i
$563$	−2.14655	+	3.71794i	−0.0904665	+	0.156693i	−0.907708	−	0.419603i	$-0.862169\pi$
$563$	−2.14655	+	3.71794i	−0.0904665	+	0.156693i	0.817241	+	0.576296i	$0.195502\pi$
$564$	−33.5342	+	52.0350i	−1.41205	+	2.19107i
$565$		0			0
$566$	15.2364	+	56.8630i	0.640434	+	2.39013i
$567$	−12.6999	+	0.843533i	−0.533347	+	0.0354250i
$568$	9.92820	−	17.1962i	0.416578	−	0.721535i
$569$	8.01105	+	13.8755i	0.335841	+	0.581693i	0.983646	−	0.180113i	$-0.0576463\pi$
$569$	8.01105	+	13.8755i	0.335841	+	0.581693i	−0.647805	+	0.761806i	$0.724313\pi$
$570$		0			0
$571$			40.0526i			1.67615i	0.545557	+	0.838074i	$0.316318\pi$
$571$			40.0526i			1.67615i	−0.545557	+	0.838074i	$0.683682\pi$
$572$	22.3402	−	7.55743i	0.934091	−	0.315992i
$573$	−32.8564	+	7.10381i	−1.37260	+	0.296766i
$574$	−2.09808	−	0.562178i	−0.0875720	−	0.0234648i
$575$		0			0
$576$	31.8281	+	3.12077i	1.32617	+	0.130032i
$577$	−3.49038	+	3.49038i	−0.145306	+	0.145306i	−0.776018	−	0.630711i	$-0.782763\pi$
$577$	−3.49038	+	3.49038i	−0.145306	+	0.145306i	0.630711	+	0.776018i	$0.282763\pi$
$578$	−28.6583	+	7.67898i	−1.19203	+	0.319403i
$579$	5.70810	+	11.1068i	0.237220	+	0.461581i
$580$		0			0
$581$	2.14655	+	1.23931i	0.0890541	+	0.0514154i
$582$	39.9522	−	36.2264i	1.65607	−	1.50163i
$583$	2.09808	−	7.83013i	0.0868934	−	0.324291i
$584$	35.7621			1.47985
$585$		0			0
$586$	−52.7128			−2.17755
$587$	−5.20035	+	19.4080i	−0.214641	+	0.801053i	0.771651	+	0.636046i	$0.219431\pi$
$587$	−5.20035	+	19.4080i	−0.214641	+	0.801053i	−0.986292	+	0.165006i	$0.947235\pi$
$588$	23.9432	−	21.7104i	0.987400	−	0.895320i
$589$	−5.66025	−	3.26795i	−0.233227	−	0.134654i
$590$		0			0
$591$	−1.38761	−	2.69999i	−0.0570785	−	0.111063i
$592$	16.2583	−	4.35641i	0.668213	−	0.179047i
$593$	−10.6112	+	10.6112i	−0.435751	+	0.435751i	−0.890579	−	0.454828i	$-0.849701\pi$
$593$	−10.6112	+	10.6112i	−0.435751	+	0.435751i	0.454828	+	0.890579i	$0.349701\pi$
$594$	−21.6593	+	2.50608i	−0.888694	+	0.102826i
$595$		0			0
$596$	19.5740	+	5.24484i	0.801782	+	0.214837i
$597$	1.57139	−	0.339746i	0.0643126	−	0.0139049i
$598$		0			0
$599$		−	21.2224i		−	0.867126i	−0.901123	−	0.433563i	$-0.857256\pi$
$599$		−	21.2224i		−	0.867126i	0.901123	−	0.433563i	$-0.142744\pi$
$600$		0			0
$601$	3.79423	+	6.57180i	0.154770	+	0.268069i	0.932975	−	0.359941i	$-0.117203\pi$
$601$	3.79423	+	6.57180i	0.154770	+	0.268069i	−0.778205	+	0.628010i	$0.783870\pi$
$602$	13.8755	−	24.0331i	0.565525	−	0.979518i
$603$	9.24923	−	24.6072i	0.376658	−	1.00208i
$604$	−10.1962	−	38.0526i	−0.414876	−	1.54834i
$605$		0			0
$606$	−44.3434	+	68.8075i	−1.80133	+	2.79511i
$607$	5.09808	−	8.83013i	0.206925	−	0.358404i	−0.743820	−	0.668380i	$-0.766988\pi$
$607$	5.09808	−	8.83013i	0.206925	−	0.358404i	0.950744	+	0.309977i	$0.100321\pi$
$608$	−1.23931	−	2.14655i	−0.0502608	−	0.0870543i
$609$	0.661992	−	13.5354i	0.0268253	−	0.548483i
$610$		0			0
$611$	−11.0648	−	32.7083i	−0.447636	−	1.32324i
$612$	−9.92820	−	21.8866i	−0.401324	−	0.884713i
$613$	−16.3564	−	4.38269i	−0.660629	−	0.177015i	−0.0870991	−	0.996200i	$-0.527760\pi$
$613$	−16.3564	−	4.38269i	−0.660629	−	0.177015i	−0.573530	+	0.819185i	$0.694426\pi$
$614$	−36.3373	+	20.9794i	−1.46645	+	0.846658i
$615$		0			0
$616$	−7.26795	+	7.26795i	−0.292834	+	0.292834i
$617$	−36.3818	+	9.74847i	−1.46468	+	0.392459i	−0.901102	−	0.433607i	$-0.857241\pi$
$617$	−36.3818	+	9.74847i	−1.46468	+	0.392459i	−0.563574	+	0.826066i	$0.690574\pi$
$618$	−25.5530	+	13.1324i	−1.02789	+	0.528264i
$619$	−14.3397	−	14.3397i	−0.576363	−	0.576363i	0.357536	−	0.933899i	$-0.383617\pi$
$619$	−14.3397	−	14.3397i	−0.576363	−	0.576363i	−0.933899	+	0.357536i	$0.883617\pi$
$620$		0			0
$621$		0			0
$622$	−2.66025	+	9.92820i	−0.106666	+	0.398085i
$623$	−14.2076			−0.569216
$624$	10.7108	−	11.0489i	0.428777	−	0.442310i
$625$		0			0
$626$	1.23931	−	4.62518i	0.0495329	−	0.184859i
$627$	2.11107	+	2.32818i	0.0843078	+	0.0929786i
$628$	−49.1147	−	28.3564i	−1.95989	−	1.13154i
$629$	10.3681	+	10.3681i	0.413404	+	0.413404i
$630$		0			0
$631$	2.26795	−	0.607695i	0.0902856	−	0.0241920i	−0.213393	−	0.976966i	$-0.568452\pi$
$631$	2.26795	−	0.607695i	0.0902856	−	0.0241920i	0.303679	+	0.952774i	$0.401785\pi$
$632$	5.86450	−	5.86450i	0.233277	−	0.233277i
$633$	20.1131	+	6.45761i	0.799425	+	0.256667i
$634$	33.0622	−	19.0885i	1.31307	−	0.758099i
$635$		0			0
$636$	−6.31812	−	29.2224i	−0.250530	−	1.15874i
$637$	1.16025	+	17.9904i	0.0459709	+	0.712805i
$638$		−	23.2149i		−	0.919086i
$639$	−2.34618	−	14.1721i	−0.0928136	−	0.560641i
$640$		0			0
$641$	−9.65949	+	16.7307i	−0.381527	+	0.660824i	−0.991281	−	0.131767i	$-0.957935\pi$
$641$	−9.65949	+	16.7307i	−0.381527	+	0.660824i	0.609754	+	0.792591i	$0.291268\pi$
$642$	−58.1629	−	37.4835i	−2.29551	−	1.47935i
$643$	−7.00000	−	26.1244i	−0.276053	−	1.03024i	−0.955132	−	0.296179i	$-0.904287\pi$
$643$	−7.00000	−	26.1244i	−0.276053	−	1.03024i	0.679079	−	0.734065i	$-0.262379\pi$
$644$		0			0
$645$		0			0
$646$	−2.66025	+	4.60770i	−0.104666	+	0.181287i
$647$	−7.22536	−	12.5147i	−0.284058	−	0.492003i	0.688322	−	0.725405i	$-0.258348\pi$
$647$	−7.22536	−	12.5147i	−0.284058	−	0.492003i	−0.972380	+	0.233402i	$0.925014\pi$
$648$	−31.0135	+	20.7618i	−1.21833	+	0.815599i
$649$		−	8.39230i		−	0.329427i
$650$		0			0
$651$	−3.26795	−	15.1149i	−0.128081	−	0.592398i
$652$	−55.7128	−	14.9282i	−2.18188	−	0.584634i
$653$	33.6156	−	19.4080i	1.31548	−	0.759492i	0.332482	−	0.943110i	$-0.392114\pi$
$653$	33.6156	−	19.4080i	1.31548	−	0.759492i	0.982998	+	0.183617i	$0.0587807\pi$
$654$	−15.6560	−	5.02659i	−0.612198	−	0.196555i
$655$		0			0
$656$	−1.52690	+	0.409131i	−0.0596153	+	0.0159739i
$657$	19.9921	−	16.4217i	0.779967	−	0.640672i
$658$	22.9282	+	22.9282i	0.893834	+	0.893834i
$659$	27.1759	+	15.6900i	1.05862	+	0.611197i	0.925051	−	0.379842i	$-0.124022\pi$
$659$	27.1759	+	15.6900i	1.05862	+	0.611197i	0.133572	+	0.991039i	$0.457355\pi$
$660$		0			0
$661$	−4.42820	+	16.5263i	−0.172237	+	0.642798i	0.824769	+	0.565470i	$0.191305\pi$
$661$	−4.42820	+	16.5263i	−0.172237	+	0.642798i	−0.997006	+	0.0773274i	$0.975361\pi$
$662$	−46.7380			−1.81652
$663$	13.0008	+	3.26797i	0.504909	+	0.126917i
$664$	7.26795			0.282051
$665$		0			0
$666$	28.5604	−	39.8928i	1.10669	−	1.54581i
$667$		0			0
$668$	31.1370	+	31.1370i	1.20473	+	1.20473i
$669$	−35.5561	+	18.2734i	−1.37468	+	0.706489i
$670$		0			0
$671$	−8.67520	+	8.67520i	−0.334902	+	0.334902i
$672$	1.79275	−	5.58376i	0.0691568	−	0.215398i
$673$	11.0096	−	6.35641i	0.424390	−	0.245021i	−0.272564	−	0.962138i	$-0.587872\pi$
$673$	11.0096	−	6.35641i	0.424390	−	0.245021i	0.696954	+	0.717116i	$0.254538\pi$
$674$	−26.6778	−	7.14830i	−1.02759	−	0.275342i
$675$		0			0
$676$	6.23205	+	48.1147i	0.239694	+	1.85057i
$677$			38.8159i			1.49182i	0.666048	+	0.745909i	$0.267985\pi$
$677$			38.8159i			1.49182i	−0.666048	+	0.745909i	$0.732015\pi$
$678$	−2.62700	+	53.7131i	−0.100889	+	2.06284i
$679$	−9.19615	−	15.9282i	−0.352916	−	0.611268i
$680$		0			0
$681$	14.6820	−	22.7821i	0.562617	−	0.873011i
$682$	−6.85641	−	25.5885i	−0.262545	−	0.979833i
$683$	4.26054	+	15.9006i	0.163025	+	0.608418i	0.998284	+	0.0585607i	$0.0186511\pi$
$683$	4.26054	+	15.9006i	0.163025	+	0.608418i	−0.835259	+	0.549857i	$0.814682\pi$
$684$	10.8500	+	4.07823i	0.414859	+	0.155935i
$685$		0			0
$686$	−20.3152	−	35.1870i	−0.775638	−	1.34344i
$687$	24.7699	+	1.21145i	0.945031	+	0.0462196i
$688$		−	20.1962i		−	0.769971i
$689$	14.9488	+	7.39139i	0.569505	+	0.281590i
$690$		0			0
$691$	−41.8827	−	11.2224i	−1.59329	−	0.426921i	−0.650284	−	0.759691i	$-0.725350\pi$
$691$	−41.8827	−	11.2224i	−1.59329	−	0.426921i	−0.943008	+	0.332770i	$0.892017\pi$
$692$	24.0331	−	13.8755i	0.913603	−	0.527469i
$693$	−0.725614	+	7.40039i	−0.0275638	+	0.281118i
$694$	43.9090	−	43.9090i	1.66676	−	1.66676i
$695$		0			0
$696$	−18.1636	−	35.3425i	−0.688488	−	1.33965i
$697$	−0.973721	−	0.973721i	−0.0368823	−	0.0368823i
$698$	12.0936	+	6.98226i	0.457751	+	0.264283i
$699$	9.54106	−	8.65131i	0.360876	−	0.327223i
$700$		0			0
$701$	20.3152			0.767295			0.383647	−	0.923480i	$-0.374668\pi$
$701$	20.3152			0.767295			0.383647	+	0.923480i	$0.374668\pi$
$702$	3.68307	−	44.7033i	0.139009	−	1.68722i
$703$	−7.07180			−0.266718
$704$	4.83571	−	18.0471i	0.182253	−	0.680176i
$705$		0			0
$706$	−56.5526	−	32.6506i	−2.12838	−	1.22882i
$707$	19.7400	+	19.7400i	0.742401	+	0.742401i
$708$	−14.1482	−	27.5295i	−0.531724	−	1.03462i
$709$	−9.96410	+	2.66987i	−0.374210	+	0.100269i	−0.441022	−	0.897496i	$-0.645384\pi$
$709$	−9.96410	+	2.66987i	−0.374210	+	0.100269i	0.0668121	+	0.997766i	$0.478717\pi$
$710$		0			0
$711$	0.585497	−	5.97136i	0.0219578	−	0.223944i
$712$	−36.0788	+	20.8301i	−1.35211	+	0.780642i
$713$		0			0
$714$	−12.3042	+	2.66025i	−0.460472	+	0.0995575i
$715$		0			0
$716$			69.9529i			2.61426i
$717$	−17.3799	−	0.850019i	−0.649065	−	0.0317446i
$718$	−20.4186	−	35.3660i	−0.762015	−	1.31985i
$719$	−5.86450	+	10.1576i	−0.218709	+	0.378815i	−0.954413	−	0.298488i	$-0.903518\pi$
$719$	−5.86450	+	10.1576i	−0.218709	+	0.378815i	0.735705	+	0.677302i	$0.236851\pi$
$720$		0			0
$721$	2.53590	+	9.46410i	0.0944418	+	0.352462i
$722$	11.1093	+	41.4606i	0.413447	+	1.54300i
$723$	7.02496	−	10.9006i	0.261261	−	0.405398i
$724$	5.59808	−	9.69615i	0.208051	−	0.360355i
$725$		0			0
$726$	1.60603	−	32.8376i	0.0596052	−	1.21872i
$727$		−	25.5167i		−	0.946361i	−0.880966	−	0.473180i	$-0.843106\pi$
$727$		−	25.5167i		−	0.946361i	0.880966	−	0.473180i	$-0.156894\pi$
$728$	−11.7290	−	17.5935i	−0.434705	−	0.652058i
$729$	−7.80385	+	25.8476i	−0.289031	+	0.957320i
$730$		0			0
$731$	15.2364	−	8.79674i	0.563539	−	0.325359i
$732$	−13.8323	+	43.0826i	−0.511257	+	1.59238i
$733$	36.2224	−	36.2224i	1.33791	−	1.33791i	0.439820	−	0.898086i	$-0.355042\pi$
$733$	36.2224	−	36.2224i	1.33791	−	1.33791i	0.898086	−	0.439820i	$-0.144958\pi$
$734$	−22.2187	+	5.95347i	−0.820106	+	0.219747i
$735$		0			0
$736$		0			0
$737$	−13.3004	−	7.67898i	−0.489926	−	0.282859i
$738$	−2.68224	+	3.74652i	−0.0987348	+	0.137911i
$739$	13.1244	−	48.9808i	0.482787	−	1.80179i	−0.107037	−	0.994255i	$-0.534136\pi$
$739$	13.1244	−	48.9808i	0.482787	−	1.80179i	0.589825	−	0.807531i	$-0.299197\pi$
$740$		0			0
$741$	−5.54822	+	3.31924i	−0.203819	+	0.121935i
$742$	−15.6603			−0.574906
$743$	13.5435	−	50.5449i	0.496862	−	1.85431i	−0.0224808	−	0.999747i	$-0.507156\pi$
$743$	13.5435	−	50.5449i	0.496862	−	1.85431i	0.519343	−	0.854566i	$-0.326177\pi$
$744$	−30.4589	−	33.5915i	−1.11668	−	1.23152i
$745$		0			0
$746$	−33.1620	−	33.1620i	−1.21415	−	1.21415i
$747$	4.06300	−	3.33739i	0.148658	−	0.122109i
$748$	−13.5622	+	3.63397i	−0.495882	+	0.132871i
$749$	−16.6862	+	16.6862i	−0.609702	+	0.609702i
$750$		0			0
$751$	38.2750	−	22.0981i	1.39667	−	0.806370i	0.402632	−	0.915362i	$-0.368096\pi$
$751$	38.2750	−	22.0981i	1.39667	−	0.806370i	0.994043	+	0.108992i	$0.0347622\pi$
$752$	22.7938	+	6.10759i	0.831206	+	0.222721i
$753$	8.01105	+	37.0526i	0.291939	+	1.35027i
$754$	46.8301	+	9.36603i	1.70545	+	0.341091i
$755$		0			0
$756$	10.0958	+	25.4990i	0.367180	+	0.927389i
$757$	−12.3923	−	21.4641i	−0.450406	−	0.780126i	0.548005	−	0.836475i	$-0.315387\pi$
$757$	−12.3923	−	21.4641i	−0.450406	−	0.780126i	−0.998411	+	0.0563489i	$0.982054\pi$
$758$	5.98604	−	10.3681i	0.217423	−	0.376587i
$759$		0			0
$760$		0			0
$761$	−1.11777	−	4.17156i	−0.0405190	−	0.151219i	0.942703	−	0.333634i	$-0.108275\pi$
$761$	−1.11777	−	4.17156i	−0.0405190	−	0.151219i	−0.983222	+	0.182415i	$0.941608\pi$
$762$	−52.7187	−	33.9749i	−1.90980	−	1.23078i
$763$	−2.80385	+	4.85641i	−0.101506	+	0.175814i
$764$	36.2158	+	62.7275i	1.31024	+	2.26940i
$765$		0			0
$766$			33.5692i			1.21291i
$767$	16.9293	+	3.38587i	0.611283	+	0.122257i
$768$	−10.3660	−	47.9447i	−0.374052	−	1.73006i
$769$	−2.16987	−	0.581416i	−0.0782476	−	0.0209664i	0.219483	−	0.975616i	$-0.429563\pi$
$769$	−2.16987	−	0.581416i	−0.0782476	−	0.0209664i	−0.297730	+	0.954650i	$0.596230\pi$
$770$		0			0
$771$	−27.3712	−	8.78792i	−0.985748	−	0.316489i
$772$	19.0263	−	19.0263i	0.684771	−	0.684771i
$773$	−5.98604	+	1.60396i	−0.215303	+	0.0576903i	−0.364858	−	0.931063i	$-0.618883\pi$
$773$	−5.98604	+	1.60396i	−0.215303	+	0.0576903i	0.149555	+	0.988753i	$0.452216\pi$
$774$	−37.3659	−	45.4900i	−1.34309	−	1.63510i
$775$		0			0
$776$	−46.7054	−	26.9654i	−1.67663	−	0.968001i
$777$	−11.2393	−	12.3952i	−0.403206	−	0.444675i
$778$	3.27757	−	12.2321i	0.117507	−	0.438540i
$779$	0.664146			0.0237955
$780$		0			0
$781$	−8.39230			−0.300300
$782$		0			0
$783$	−26.3830	−	11.4169i	−0.942851	−	0.408008i
$784$	−10.6699	−	6.16025i	−0.381067	−	0.220009i
$785$		0			0
$786$	3.34613	−	1.71968i	0.119353	−	0.0613389i
$787$	11.2942	−	3.02628i	0.402596	−	0.107875i	−0.0518385	−	0.998655i	$-0.516508\pi$
$787$	11.2942	−	3.02628i	0.402596	−	0.107875i	0.454434	+	0.890780i	$0.349841\pi$
$788$	−4.62518	+	4.62518i	−0.164765	+	0.164765i
$789$	−6.33898	+	19.7436i	−0.225674	+	0.702891i
$790$		0			0
$791$	17.7150	+	4.74673i	0.629874	+	0.168774i
$792$	9.00727	+	19.8564i	0.320059	+	0.705567i
$793$	−14.0000	−	21.0000i	−0.497155	−	0.745732i
$794$		−	21.2224i		−	0.753157i
$795$		0			0
$796$	−1.73205	−	3.00000i	−0.0613909	−	0.106332i
$797$	−8.58622	+	14.8718i	−0.304139	+	0.526785i	−0.977069	−	0.212921i	$-0.931702\pi$
$797$	−8.58622	+	14.8718i	−0.304139	+	0.526785i	0.672930	+	0.739706i	$0.265036\pi$
$798$	3.28891	−	5.10339i	0.116426	−	0.180658i
$799$	5.32051	+	19.8564i	0.188226	+	0.702469i
$800$		0			0
$801$	−10.6041	+	28.2118i	−0.374678	+	0.996815i
$802$	−33.6244	+	58.2391i	−1.18732	+	2.05649i
$803$	−7.55743	−	13.0899i	−0.266696	−	0.461931i
$804$	−56.5752	−	2.76699i	−1.99526	−	0.0975841i
$805$		0			0
$806$	54.3844	−	3.50742i	1.91561	−	0.123543i
$807$	18.7321	−	4.05001i	0.659399	−	0.142567i
$808$	79.0692	+	21.1865i	2.78165	+	0.745340i
$809$	17.6705	−	10.2021i	0.621263	−	0.358686i	−0.156097	−	0.987742i	$-0.549891\pi$
$809$	17.6705	−	10.2021i	0.621263	−	0.358686i	0.777361	+	0.629055i	$0.216558\pi$
$810$		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	$0.0936161\pi$
$812$	−28.2047	+	7.55743i	−0.989791	+	0.265214i
$813$	−1.63929	−	3.18972i	−0.0574925	−	0.111868i
$814$	−20.2679	−	20.2679i	−0.710391	−	0.710391i
$815$		0			0
$816$	−6.78680	+	6.15389i	−0.237585	+	0.215429i
$817$	−2.19615	+	8.19615i	−0.0768336	+	0.286747i
$818$	−27.8401			−0.973405
$819$	−14.6357	−	4.44942i	−0.511411	−	0.155475i
$820$		0			0
$821$	−1.60396	+	5.98604i	−0.0559784	+	0.208914i	−0.988250	−	0.152844i	$-0.951157\pi$
$821$	−1.60396	+	5.98604i	−0.0559784	+	0.208914i	0.932272	+	0.361758i	$0.117823\pi$
$822$	18.1231	−	16.4330i	0.632116	−	0.573168i
$823$	−13.3923	−	7.73205i	−0.466826	−	0.269522i	0.248084	−	0.968739i	$-0.420199\pi$
$823$	−13.3923	−	7.73205i	−0.466826	−	0.269522i	−0.714910	+	0.699216i	$0.753532\pi$
$824$	20.3152	+	20.3152i	0.707714	+	0.707714i
$825$		0			0
$826$	−15.6603	+	4.19615i	−0.544890	+	0.146003i
$827$	3.62896	−	3.62896i	0.126191	−	0.126191i	−0.641190	−	0.767382i	$-0.721559\pi$
$827$	3.62896	−	3.62896i	0.126191	−	0.126191i	0.767382	+	0.641190i	$0.221559\pi$
$828$		0			0
$829$	−20.6769	+	11.9378i	−0.718139	+	0.414618i	−0.814067	−	0.580771i	$-0.802751\pi$
$829$	−20.6769	+	11.9378i	−0.718139	+	0.414618i	0.0959284	+	0.995388i	$0.469418\pi$
$830$		0			0
$831$	−6.07502	+	1.31347i	−0.210740	+	0.0455636i
$832$	34.4545	+	17.0359i	1.19449	+	0.590614i
$833$		−	10.7328i		−	0.371868i
$834$	9.90862	+	0.484612i	0.343108	+	0.0167807i
$835$		0			0
$836$	3.38587	−	5.86450i	0.117103	−	0.202828i
$837$	−32.4524	−	4.79215i	−1.12172	−	0.165641i
$838$	−5.16987	−	19.2942i	−0.178590	−	0.666508i
$839$	2.02501	+	7.55743i	0.0699110	+	0.260911i	0.992031	−	0.125992i	$-0.0402114\pi$
$839$	2.02501	+	7.55743i	0.0699110	+	0.260911i	−0.922120	+	0.386903i	$0.873545\pi$
$840$		0			0
$841$	0.803848	−	1.39230i	0.0277189	−	0.0480105i
$842$	1.40535	+	2.43414i	0.0484316	+	0.0838859i
$843$	1.90261	−	38.9017i	0.0655294	−	1.33985i
$844$		−	45.5167i		−	1.56675i
$845$		0			0
$846$	62.6410	−	28.4152i	2.15364	−	0.976936i
$847$	−10.8301	−	2.90192i	−0.372128	−	0.0997113i
$848$	−9.87002	+	5.69846i	−0.338938	+	0.195686i
$849$	13.0191	−	40.5497i	0.446814	−	1.39166i
$850$		0			0
$851$		0			0
$852$	−27.5295	+	14.1482i	−0.943145	+	0.484711i
$853$	20.6340	+	20.6340i	0.706494	+	0.706494i	0.965796	−	0.259302i	$-0.0834926\pi$
$853$	20.6340	+	20.6340i	0.706494	+	0.706494i	−0.259302	+	0.965796i	$0.583493\pi$
$854$	20.5257	+	11.8505i	0.702376	+	0.405517i
$855$		0			0
$856$	−17.9090	+	66.8372i	−0.612116	+	2.28445i
$857$	35.7621			1.22161			0.610806	−	0.791781i	$-0.290846\pi$
$857$	35.7621			1.22161			0.610806	+	0.791781i	$0.290846\pi$
$858$	−25.4144	−	6.38833i	−0.867632	−	0.218094i
$859$	−23.1769			−0.790786			−0.395393	−	0.918512i	$-0.629392\pi$
$859$	−23.1769			−0.790786			−0.395393	+	0.918512i	$0.629392\pi$
$860$		0			0
$861$	1.05553	+	1.16409i	0.0359725	+	0.0396721i
$862$	4.34679	+	2.50962i	0.148052	+	0.0854780i
$863$	−12.0611	−	12.0611i	−0.410563	−	0.410563i	0.471371	−	0.881935i	$-0.343759\pi$
$863$	−12.0611	−	12.0611i	−0.410563	−	0.410563i	−0.881935	+	0.471371i	$0.843759\pi$
$864$	−9.74952	−	7.72737i	−0.331685	−	0.262890i
$865$		0			0
$866$	−11.9395	+	11.9395i	−0.405721	+	0.405721i
$867$	20.4366	+	6.56147i	0.694063	+	0.222839i
$868$	−28.8564	+	16.6603i	−0.979450	+	0.565486i
$869$	−3.38587	−	0.907241i	−0.114858	−	0.0307760i
$870$		0			0
$871$	20.8564	−	23.7321i	0.706692	−	0.804130i
$872$			16.4432i			0.556835i
$873$	−38.4921	+	6.37233i	−1.30276	+	0.215671i
$874$		0			0
$875$		0			0
$876$	−46.8585	−	30.1982i	−1.58320	−	1.02030i
$877$	−3.00962	−	11.2321i	−0.101628	−	0.379279i	0.896313	−	0.443422i	$-0.146236\pi$
$877$	−3.00962	−	11.2321i	−0.101628	−	0.379279i	−0.997941	+	0.0641422i	$0.979569\pi$
$878$	−2.93225	−	10.9433i	−0.0989586	−	0.369318i
$879$	32.0549	+	20.6579i	1.08118	+	0.696775i
$880$		0			0
$881$	−13.5880	−	23.5350i	−0.457790	−	0.792916i	0.541054	−	0.840988i	$-0.318026\pi$
$881$	−13.5880	−	23.5350i	−0.457790	−	0.792916i	−0.998844	+	0.0480724i	$0.984692\pi$
$882$	−35.4303	+	5.86546i	−1.19300	+	0.197500i
$883$			39.3731i			1.32501i	0.749058	+	0.662505i	$0.230506\pi$
$883$			39.3731i			1.32501i	−0.749058	+	0.662505i	$0.769494\pi$
$884$	−1.85897	−	28.8244i	−0.0625239	−	0.969468i
$885$		0			0
$886$	68.3731	+	18.3205i	2.29704	+	0.615490i
$887$	46.4949	−	26.8438i	1.56115	−	0.901328i	0.564005	−	0.825772i	$-0.309260\pi$
$887$	46.4949	−	26.8438i	1.56115	−	0.901328i	0.997142	−	0.0755567i	$-0.0240734\pi$
$888$	−46.7139	−	14.9982i	−1.56761	−	0.503306i
$889$	−15.1244	+	15.1244i	−0.507255	+	0.507255i
$890$		0			0
$891$	14.1533	+	6.96426i	0.474152	+	0.233311i
$892$	60.9090	+	60.9090i	2.03938	+	2.03938i
$893$	−8.58622	−	4.95725i	−0.287327	−	0.165888i
$894$	−15.1249	−	16.6804i	−0.505853	−	0.557878i
$895$		0			0
$896$	−29.3225			−0.979595
$897$		0			0
$898$	20.9808			0.700137
$899$	9.03984	−	33.7371i	0.301495	−	1.12520i
$900$		0			0
$901$	−8.59808	−	4.96410i	−0.286443	−	0.165378i
$902$	1.90346	+	1.90346i	0.0633783	+	0.0633783i
$903$	−17.8563	+	9.17688i	−0.594219	+	0.305387i
$904$	51.9449	−	13.9186i	1.72766	−	0.462925i
$905$		0			0
$906$	−13.3813	+	41.6777i	−0.444562	+	1.38465i
$907$	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	$0.240490\pi$
$908$	−56.4094	−	15.1149i	−1.87201	−	0.501604i
$909$	53.9308	−	24.4641i	1.78877	−	0.811423i
$910$		0			0
$911$			9.25036i			0.306478i	0.988189	+	0.153239i	$0.0489705\pi$
$911$			9.25036i			0.306478i	−0.988189	+	0.153239i	$0.951030\pi$
$912$	0.215843	−	4.41323i	0.00714727	−	0.146137i
$913$	−1.53590	−	2.66025i	−0.0508308	−	0.0880416i
$914$	−33.4495	+	57.9363i	−1.10641	+	1.91636i
$915$		0			0
$916$	−13.8301	−	51.6147i	−0.456960	−	1.70540i
$917$	−0.332073	−	1.23931i	−0.0109660	−	0.0409257i
$918$	−3.90102	+	26.4177i	−0.128753	+	0.871913i
$919$	−22.2942	+	38.6147i	−0.735419	+	1.27378i	0.219121	+	0.975698i	$0.429681\pi$
$919$	−22.2942	+	38.6147i	−0.735419	+	1.27378i	−0.954539	+	0.298085i	$0.903652\pi$
$920$		0			0
$921$	30.3186	+	1.48282i	0.999031	+	0.0488607i
$922$		−	58.0333i		−	1.91123i
$923$	3.38587	−	16.9293i	0.111447	−	0.557236i
$924$	15.6603	−	3.38587i	0.515185	−	0.111387i
$925$		0			0
$926$	−44.1378	+	25.4830i	−1.45046	+	0.837423i
$927$	20.6854	+	2.02822i	0.679398	+	0.0666155i
$928$	9.36603	−	9.36603i	0.307455	−	0.307455i
$929$	47.3251	−	12.6807i	1.55269	−	0.416041i	0.622347	−	0.782742i	$-0.286179\pi$
$929$	47.3251	−	12.6807i	1.55269	−	0.416041i	0.930339	+	0.366701i	$0.119513\pi$
$930$		0			0
$931$	3.66025	+	3.66025i	0.119960	+	0.119960i
$932$	−24.0331	−	13.8755i	−0.787232	−	0.454509i
$933$	5.50854	−	4.99484i	0.180341	−	0.163524i
$934$	−18.8827	+	70.4711i	−0.617860	+	2.30589i
$935$		0			0
$936$	−43.6892	+	10.1588i	−1.42803	+	0.332052i
$937$	37.0000			1.20874			0.604369	−	0.796705i	$-0.293425\pi$
$937$	37.0000			1.20874			0.604369	+	0.796705i	$0.293425\pi$
$938$	−7.67898	+	28.6583i	−0.250727	+	0.935728i
$939$	−2.56622	+	2.32691i	−0.0837455	+	0.0759358i
$940$		0			0
$941$	38.2408	+	38.2408i	1.24661	+	1.24661i	0.957206	+	0.289407i	$0.0934582\pi$
$941$	38.2408	+	38.2408i	1.24661	+	1.24661i	0.289407	+	0.957206i	$0.406542\pi$
$942$	28.8044	+	56.0473i	0.938498	+	1.82612i
$943$		0			0
$944$	−8.34312	+	8.34312i	−0.271546	+	0.271546i
$945$		0			0
$946$	−29.7846	+	17.1962i	−0.968381	+	0.559095i
$947$	39.6016	+	10.6112i	1.28688	+	0.344818i	0.836475	−	0.548006i	$-0.184613\pi$
$947$	39.6016	+	10.6112i	1.28688	+	0.344818i	0.450405	+	0.892824i	$0.351279\pi$
$948$	−12.6362	+	2.73205i	−0.410406	+	0.0887329i
$949$	29.4545	−	9.96410i	0.956133	−	0.323448i
$950$		0			0
$951$	−27.5859	−	1.34918i	−0.894535	−	0.0437500i
$952$	6.29423	+	10.9019i	0.203997	+	0.353333i
$953$	−21.8866	+	37.9087i	−0.708976	+	1.22798i	0.256261	+	0.966608i	$0.417509\pi$
$953$	−21.8866	+	37.9087i	−0.708976	+	1.22798i	−0.965237	+	0.261375i	$0.915824\pi$
$954$	−11.6883	+	31.0963i	−0.378423	+	1.00678i
$955$		0			0
$956$	9.70398	+	36.2158i	0.313849	+	1.17130i
$957$	−9.09782	+	14.1171i	−0.294091	+	0.456340i
$958$	−10.4904	+	18.1699i	−0.338929	+	0.587042i
$959$	−4.17156	−	7.22536i	−0.134707	−	0.233319i
$960$		0			0
$961$		−	8.85641i		−	0.285691i
$962$	49.0625	−	32.7083i	1.58184	−	1.05456i
$963$	20.6795	+	45.5877i	0.666387	+	1.46904i
$964$	−26.9904	−	7.23205i	−0.869302	−	0.232929i
$965$		0			0
$966$		0			0
$967$	0.143594	−	0.143594i	0.00461766	−	0.00461766i	−0.704794	−	0.709412i	$-0.748961\pi$
$967$	0.143594	−	0.143594i	0.00461766	−	0.00461766i	0.709412	+	0.704794i	$0.248961\pi$
$968$	−31.7566	+	8.50916i	−1.02070	+	0.273495i
$969$	3.42345	−	1.75941i	0.109977	−	0.0565205i
$970$		0			0
$971$	−45.5551	−	26.3013i	−1.46193	−	0.844047i	−0.462832	−	0.886446i	$-0.653167\pi$
$971$	−45.5551	−	26.3013i	−1.46193	−	0.844047i	−0.999101	+	0.0423987i	$0.986500\pi$
$972$	58.1681	−	1.01535i	1.86574	−	0.0325673i
$973$	0.875644	−	3.26795i	0.0280719	−	0.104766i
$974$	−60.7025			−1.94503
$975$		0			0
$976$	17.2487			0.552118
$977$	7.60192	−	28.3707i	0.243207	−	0.907661i	−0.731069	−	0.682303i	$-0.760978\pi$
$977$	7.60192	−	28.3707i	0.243207	−	0.907661i	0.974276	−	0.225357i	$-0.0723550\pi$
$978$	43.0495	+	47.4770i	1.37657	+	1.51815i
$979$	15.2487	+	8.80385i	0.487351	+	0.281372i
$980$		0			0
$981$	7.55058	+	9.19222i	0.241071	+	0.293485i
$982$	57.8827	−	15.5096i	1.84711	−	0.494932i
$983$	−4.38209	+	4.38209i	−0.139767	+	0.139767i	−0.773528	−	0.633762i	$-0.781510\pi$
$983$	−4.38209	+	4.38209i	−0.139767	+	0.139767i	0.633762	+	0.773528i	$0.281510\pi$
$984$	4.38712	+	1.40855i	0.139856	+	0.0449029i
$985$		0			0
$986$	−27.4635	−	7.35882i	−0.874616	−	0.234353i
$987$	−4.95725	−	22.9282i	−0.157791	−	0.729813i
$988$	10.4641	+	9.19615i	0.332907	+	0.292569i
$989$		0			0
$990$		0			0
$991$	−12.7846	−	22.1436i	−0.406117	−	0.703414i	0.588334	−	0.808618i	$-0.299784\pi$
$991$	−12.7846	−	22.1436i	−0.406117	−	0.703414i	−0.994451	+	0.105203i	$0.966451\pi$
$992$	7.55743	−	13.0899i	0.239949	−	0.415603i
$993$	28.4216	+	18.3164i	0.901931	+	0.581255i
$994$	4.19615	+	15.6603i	0.133094	+	0.496713i
$995$		0			0
$996$	−9.52306	−	6.13719i	−0.301750	−	0.194464i
$997$	−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	$0.202023\pi$
$998$	7.55743	+	13.0899i	0.239226	+	0.414352i
$999$	−33.0015	+	13.0662i	−1.04412	+	0.413397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bo.d.626.1		8
3.2	odd	2	inner	975.2.bo.d.626.2		8
5.2	odd	4		975.2.bp.e.899.1		8
5.3	odd	4		975.2.bp.f.899.2		8
5.4	even	2		39.2.k.b.2.2	yes	8
13.7	odd	12	inner	975.2.bo.d.176.2		8
15.2	even	4		975.2.bp.e.899.2		8
15.8	even	4		975.2.bp.f.899.1		8
15.14	odd	2		39.2.k.b.2.1	✓	8
20.19	odd	2		624.2.cn.c.353.2		8
39.20	even	12	inner	975.2.bo.d.176.1		8
60.59	even	2		624.2.cn.c.353.1		8
65.4	even	6		507.2.k.f.188.2		8
65.7	even	12		975.2.bp.f.449.1		8
65.9	even	6		507.2.k.e.188.1		8
65.19	odd	12		507.2.k.d.488.2		8
65.24	odd	12		507.2.f.f.437.1		8
65.29	even	6		507.2.f.f.239.4		8
65.33	even	12		975.2.bp.e.449.2		8
65.34	odd	4		507.2.k.e.89.2		8
65.44	odd	4		507.2.k.f.89.1		8
65.49	even	6		507.2.f.e.239.1		8
65.54	odd	12		507.2.f.e.437.4		8
65.59	odd	12		39.2.k.b.20.1	yes	8
65.64	even	2		507.2.k.d.80.1		8
195.29	odd	6		507.2.f.f.239.1		8
195.44	even	4		507.2.k.f.89.2		8
195.59	even	12		39.2.k.b.20.2	yes	8
195.74	odd	6		507.2.k.e.188.2		8
195.89	even	12		507.2.f.f.437.4		8
195.98	odd	12		975.2.bp.e.449.1		8
195.119	even	12		507.2.f.e.437.1		8
195.134	odd	6		507.2.k.f.188.1		8
195.137	odd	12		975.2.bp.f.449.2		8
195.149	even	12		507.2.k.d.488.1		8
195.164	even	4		507.2.k.e.89.1		8
195.179	odd	6		507.2.f.e.239.4		8
195.194	odd	2		507.2.k.d.80.2		8
260.59	even	12		624.2.cn.c.449.1		8
780.59	odd	12		624.2.cn.c.449.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.k.b.2.1	✓	8	15.14	odd	2
39.2.k.b.2.2	yes	8	5.4	even	2
39.2.k.b.20.1	yes	8	65.59	odd	12
39.2.k.b.20.2	yes	8	195.59	even	12
507.2.f.e.239.1		8	65.49	even	6
507.2.f.e.239.4		8	195.179	odd	6
507.2.f.e.437.1		8	195.119	even	12
507.2.f.e.437.4		8	65.54	odd	12
507.2.f.f.239.1		8	195.29	odd	6
507.2.f.f.239.4		8	65.29	even	6
507.2.f.f.437.1		8	65.24	odd	12
507.2.f.f.437.4		8	195.89	even	12
507.2.k.d.80.1		8	65.64	even	2
507.2.k.d.80.2		8	195.194	odd	2
507.2.k.d.488.1		8	195.149	even	12
507.2.k.d.488.2		8	65.19	odd	12
507.2.k.e.89.1		8	195.164	even	4
507.2.k.e.89.2		8	65.34	odd	4
507.2.k.e.188.1		8	65.9	even	6
507.2.k.e.188.2		8	195.74	odd	6
507.2.k.f.89.1		8	65.44	odd	4
507.2.k.f.89.2		8	195.44	even	4
507.2.k.f.188.1		8	195.134	odd	6
507.2.k.f.188.2		8	65.4	even	6
624.2.cn.c.353.1		8	60.59	even	2
624.2.cn.c.353.2		8	20.19	odd	2
624.2.cn.c.449.1		8	260.59	even	12
624.2.cn.c.449.2		8	780.59	odd	12
975.2.bo.d.176.1		8	39.20	even	12	inner
975.2.bo.d.176.2		8	13.7	odd	12	inner
975.2.bo.d.626.1		8	1.1	even	1	trivial
975.2.bo.d.626.2		8	3.2	odd	2	inner
975.2.bp.e.449.1		8	195.98	odd	12
975.2.bp.e.449.2		8	65.33	even	12
975.2.bp.e.899.1		8	5.2	odd	4
975.2.bp.e.899.2		8	15.2	even	4
975.2.bp.f.449.1		8	65.7	even	12
975.2.bp.f.449.2		8	195.137	odd	12
975.2.bp.f.899.1		8	15.8	even	4
975.2.bp.f.899.2		8	5.3	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.619657 + 2.31259i) q^{2} +(1.28311 - 1.16345i) q^{3} +(-3.23205 - 1.86603i) q^{4} +(1.89551 + 3.68825i) q^{6} +(1.36603 - 0.366025i) q^{7} +(2.93225 - 2.93225i) q^{8} +(0.292748 - 2.98568i) q^{9} +O(q^{10})\)	\(q+(-0.619657 + 2.31259i) q^{2} +(1.28311 - 1.16345i) q^{3} +(-3.23205 - 1.86603i) q^{4} +(1.89551 + 3.68825i) q^{6} +(1.36603 - 0.366025i) q^{7} +(2.93225 - 2.93225i) q^{8} +(0.292748 - 2.98568i) q^{9} +(-1.69293 - 0.453620i) q^{11} +(-6.31812 + 1.36603i) q^{12} +(1.59808 - 3.23205i) q^{13} +3.38587i q^{14} +(1.23205 + 2.13397i) q^{16} +(-1.07328 + 1.85897i) q^{17} +(6.72326 + 2.52711i) q^{18} +(-0.267949 - 1.00000i) q^{19} +(1.32691 - 2.05896i) q^{21} +(2.09808 - 3.63397i) q^{22} +(0.350863 - 7.17394i) q^{24} +(6.48415 + 5.69846i) q^{26} +(-3.09808 - 4.17156i) q^{27} +(-5.09808 - 1.36603i) q^{28} +(4.79122 - 2.76621i) q^{29} +(4.46410 - 4.46410i) q^{31} +(2.31259 - 0.619657i) q^{32} +(-2.69999 + 1.38761i) q^{33} +(-3.63397 - 3.63397i) q^{34} +(-6.51754 + 9.10360i) q^{36} +(1.76795 - 6.59808i) q^{37} +2.47863 q^{38} +(-1.70983 - 6.00637i) q^{39} +(-0.166037 + 0.619657i) q^{41} +(3.93930 + 4.34444i) q^{42} +(-7.09808 - 4.09808i) q^{43} +(4.62518 + 4.62518i) q^{44} +(6.77174 - 6.77174i) q^{47} +(4.06364 + 1.30469i) q^{48} +(-4.33013 + 2.50000i) q^{49} +(0.785693 + 3.63397i) q^{51} +(-11.1962 + 7.46410i) q^{52} +4.62518i q^{53} +(11.5669 - 4.57965i) q^{54} +(2.93225 - 5.07880i) q^{56} +(-1.50726 - 0.971364i) q^{57} +(3.42820 + 12.7942i) q^{58} +(1.23931 + 4.62518i) q^{59} +(3.50000 - 6.06218i) q^{61} +(7.55743 + 13.0899i) q^{62} +(-0.692934 - 4.18567i) q^{63} +10.6603i q^{64} +(-1.53590 - 7.10381i) q^{66} +(8.46410 + 2.26795i) q^{67} +(6.93777 - 4.00552i) q^{68} +(4.62518 - 1.23931i) q^{71} +(-7.89635 - 9.61317i) q^{72} +(6.09808 + 6.09808i) q^{73} +(14.1631 + 8.17709i) q^{74} +(-1.00000 + 3.73205i) q^{76} -2.47863 q^{77} +(14.9498 - 0.232259i) q^{78} +2.00000 q^{79} +(-8.82860 - 1.74811i) q^{81} +(-1.33013 - 0.767949i) q^{82} +(1.23931 + 1.23931i) q^{83} +(-8.13071 + 4.17862i) q^{84} +(13.8755 - 13.8755i) q^{86} +(2.92931 - 9.12372i) q^{87} +(-6.29423 + 3.63397i) q^{88} +(-9.70398 - 2.60017i) q^{89} +(1.00000 - 5.00000i) q^{91} +(0.534160 - 10.9217i) q^{93} +(11.4641 + 19.8564i) q^{94} +(2.24637 - 3.48568i) q^{96} +(-3.36603 - 12.5622i) q^{97} +(-3.09828 - 11.5630i) q^{98} +(-1.84997 + 4.92177i) 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

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