LMFDB - Embedded newform 975.2.bp.f.449.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(149,975)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 5]))

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

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

chi := DirichletCharacter("975.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bp (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.56070144.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 $ x^8 - 4x^7 + 16x^6 - 34x^5 + 63x^4 - 74x^3 + 70x^2 - 38*x + 13
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			449.2
Root			$0.500000 - 1.19293i$ of defining polynomial
Character	$\chi$	$=$	975.449
Dual form			975.2.bp.f.899.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.31259 - 0.619657i) q^{2} +(1.16345 - 1.28311i) q^{3} +(3.23205 - 1.86603i) q^{4} +(1.89551 - 3.68825i) q^{6} +(-0.366025 + 1.36603i) q^{7} +(2.93225 - 2.93225i) q^{8} +(-0.292748 - 2.98568i) q^{9} +O(q^{10})$	\(q+(2.31259 - 0.619657i) q^{2} +(1.16345 - 1.28311i) q^{3} +(3.23205 - 1.86603i) q^{4} +(1.89551 - 3.68825i) q^{6} +(-0.366025 + 1.36603i) q^{7} +(2.93225 - 2.93225i) q^{8} +(-0.292748 - 2.98568i) q^{9} +(-1.69293 + 0.453620i) q^{11} +(1.36603 - 6.31812i) q^{12} +(3.23205 - 1.59808i) q^{13} +3.38587i q^{14} +(1.23205 - 2.13397i) q^{16} +(1.85897 - 1.07328i) q^{17} +(-2.52711 - 6.72326i) q^{18} +(0.267949 - 1.00000i) q^{19} +(1.32691 + 2.05896i) q^{21} +(-3.63397 + 2.09808i) q^{22} +(-0.350863 - 7.17394i) q^{24} +(6.48415 - 5.69846i) q^{26} +(-4.17156 - 3.09808i) q^{27} +(1.36603 + 5.09808i) q^{28} +(-4.79122 - 2.76621i) q^{29} +(4.46410 + 4.46410i) q^{31} +(-0.619657 + 2.31259i) q^{32} +(-1.38761 + 2.69999i) q^{33} +(3.63397 - 3.63397i) q^{34} +(-6.51754 - 9.10360i) q^{36} +(-6.59808 + 1.76795i) q^{37} -2.47863i q^{38} +(1.70983 - 6.00637i) q^{39} +(-0.166037 - 0.619657i) q^{41} +(4.34444 + 3.93930i) q^{42} +(4.09808 + 7.09808i) q^{43} +(-4.62518 + 4.62518i) q^{44} +(-6.77174 + 6.77174i) q^{47} +(-1.30469 - 4.06364i) q^{48} +(4.33013 + 2.50000i) q^{49} +(0.785693 - 3.63397i) q^{51} +(7.46410 - 11.1962i) q^{52} -4.62518 q^{53} +(-11.5669 - 4.57965i) q^{54} +(2.93225 + 5.07880i) q^{56} +(-0.971364 - 1.50726i) q^{57} +(-12.7942 - 3.42820i) q^{58} +(-1.23931 + 4.62518i) q^{59} +(3.50000 + 6.06218i) q^{61} +(13.0899 + 7.55743i) q^{62} +(4.18567 + 0.692934i) q^{63} +10.6603i q^{64} +(-1.53590 + 7.10381i) q^{66} +(2.26795 + 8.46410i) q^{67} +(4.00552 - 6.93777i) q^{68} +(4.62518 + 1.23931i) q^{71} +(-9.61317 - 7.89635i) q^{72} +(-6.09808 - 6.09808i) q^{73} +(-14.1631 + 8.17709i) q^{74} +(-1.00000 - 3.73205i) q^{76} -2.47863i q^{77} +(0.232259 - 14.9498i) q^{78} -2.00000 q^{79} +(-8.82860 + 1.74811i) q^{81} +(-0.767949 - 1.33013i) q^{82} +(-1.23931 - 1.23931i) q^{83} +(8.13071 + 4.17862i) q^{84} +(13.8755 + 13.8755i) q^{86} +(-9.12372 + 2.92931i) q^{87} +(-3.63397 + 6.29423i) q^{88} +(9.70398 - 2.60017i) q^{89} +(1.00000 + 5.00000i) q^{91} +(10.9217 - 0.534160i) q^{93} +(-11.4641 + 19.8564i) q^{94} +(2.24637 + 3.48568i) q^{96} +(-12.5622 - 3.36603i) q^{97} +(11.5630 + 3.09828i) q^{98} +(1.84997 + 4.92177i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} + 12 q^{4} - 2 q^{6} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q + 6 * q^3 + 12 * q^4 - 2 * q^6 + 4 * q^7 - 4 * q^9	$ 8 q + 6 q^{3} + 12 q^{4} - 2 q^{6} + 4 q^{7} - 4 q^{9} + 4 q^{12} + 12 q^{13} - 4 q^{16} - 4 q^{18} + 16 q^{19} + 4 q^{21} - 36 q^{22} - 18 q^{24} + 4 q^{28} + 8 q^{31} - 20 q^{33} + 36 q^{34} - 36 q^{36} - 32 q^{37} + 14 q^{39} + 12 q^{42} + 12 q^{43} - 18 q^{48} + 32 q^{52} - 46 q^{54} + 16 q^{57} - 40 q^{58} + 28 q^{61} + 16 q^{63} - 40 q^{66} + 32 q^{67} - 24 q^{72} - 28 q^{73} - 8 q^{76} - 16 q^{78} - 16 q^{79} + 4 q^{81} - 20 q^{82} - 4 q^{84} - 6 q^{87} - 36 q^{88} + 8 q^{91} - 16 q^{93} - 64 q^{94} + 16 q^{96} - 52 q^{97} - 40 q^{99}+O(q^{100}) $ 8 * q + 6 * q^3 + 12 * q^4 - 2 * q^6 + 4 * q^7 - 4 * q^9 + 4 * q^12 + 12 * q^13 - 4 * q^16 - 4 * q^18 + 16 * q^19 + 4 * q^21 - 36 * q^22 - 18 * q^24 + 4 * q^28 + 8 * q^31 - 20 * q^33 + 36 * q^34 - 36 * q^36 - 32 * q^37 + 14 * q^39 + 12 * q^42 + 12 * q^43 - 18 * q^48 + 32 * q^52 - 46 * q^54 + 16 * q^57 - 40 * q^58 + 28 * q^61 + 16 * q^63 - 40 * q^66 + 32 * q^67 - 24 * q^72 - 28 * q^73 - 8 * q^76 - 16 * q^78 - 16 * q^79 + 4 * q^81 - 20 * q^82 - 4 * q^84 - 6 * q^87 - 36 * q^88 + 8 * q^91 - 16 * q^93 - 64 * q^94 + 16 * q^96 - 52 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$-1$	$-1$

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 $

$2$	2.31259	−	0.619657i	1.63525	−	0.438164i	0.679818	−	0.733380i	$-0.262059\pi$
$2$	2.31259	−	0.619657i	1.63525	−	0.438164i	0.955430	+	0.295217i	$0.0953919\pi$
$3$	1.16345	−	1.28311i	0.671721	−	0.740805i
$3$	1.16345	−	1.28311i	0.671721	−	0.740805i
$4$	3.23205	−	1.86603i	1.61603	−	0.933013i
$5$		0			0
$5$		0			0
$6$	1.89551	−	3.68825i	0.773837	−	1.50572i
$7$	−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	$0.997215\pi$
$8$	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	−0.504840	−	0.863213i	$-0.668449\pi$
$11$	−1.69293	+	0.453620i	−0.510439	+	0.136772i	−0.00559833	+	0.999984i	$0.501782\pi$
$12$	1.36603	−	6.31812i	0.394338	−	1.82388i
$13$	3.23205	−	1.59808i	0.896410	−	0.443227i
$13$	3.23205	−	1.59808i	0.896410	−	0.443227i
$14$			3.38587i			0.904911i
$15$		0			0
$16$	1.23205	−	2.13397i	0.308013	−	0.533494i
$17$	1.85897	−	1.07328i	0.450867	−	0.260308i	−0.257330	−	0.966324i	$-0.582843\pi$
$17$	1.85897	−	1.07328i	0.450867	−	0.260308i	0.708196	+	0.706016i	$0.249509\pi$
$18$	−2.52711	−	6.72326i	−0.595644	−	1.58469i
$19$	0.267949	−	1.00000i	0.0614718	−	0.229416i	−0.928355	−	0.371695i	$-0.878777\pi$
$19$	0.267949	−	1.00000i	0.0614718	−	0.229416i	0.989826	+	0.142280i	$0.0454432\pi$
$20$		0			0
$21$	1.32691	+	2.05896i	0.289555	+	0.449302i
$22$	−3.63397	+	2.09808i	−0.774766	+	0.447311i
$23$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$23$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$24$	−0.350863	−	7.17394i	−0.0716197	−	1.46437i
$25$		0			0
$26$	6.48415	−	5.69846i	1.27165	−	1.11756i
$27$	−4.17156	−	3.09808i	−0.802817	−	0.596225i
$28$	1.36603	+	5.09808i	0.258155	+	0.963446i
$29$	−4.79122	−	2.76621i	−0.889707	−	0.513673i	−0.0158603	−	0.999874i	$-0.505049\pi$
$29$	−4.79122	−	2.76621i	−0.889707	−	0.513673i	−0.873847	+	0.486202i	$0.838382\pi$
$30$		0			0
$31$	4.46410	+	4.46410i	0.801776	+	0.801776i	0.983373	−	0.181597i	$-0.0581266\pi$
$31$	4.46410	+	4.46410i	0.801776	+	0.801776i	−0.181597	+	0.983373i	$0.558127\pi$
$32$	−0.619657	+	2.31259i	−0.109541	+	0.408812i
$33$	−1.38761	+	2.69999i	−0.241551	+	0.470008i
$34$	3.63397	−	3.63397i	0.623222	−	0.623222i
$35$		0			0
$36$	−6.51754	−	9.10360i	−1.08626	−	1.51727i
$37$	−6.59808	+	1.76795i	−1.08472	+	0.290649i	−0.756527	−	0.653963i	$-0.773105\pi$
$37$	−6.59808	+	1.76795i	−1.08472	+	0.290649i	−0.328190	+	0.944612i	$0.606439\pi$
$38$		−	2.47863i		−	0.402086i
$39$	1.70983	−	6.00637i	0.273793	−	0.961789i
$40$		0			0
$41$	−0.166037	−	0.619657i	−0.0259306	−	0.0967741i	0.951748	−	0.306881i	$-0.0992854\pi$
$41$	−0.166037	−	0.619657i	−0.0259306	−	0.0967741i	−0.977678	+	0.210107i	$0.932619\pi$
$42$	4.34444	+	3.93930i	0.670362	+	0.607848i
$43$	4.09808	+	7.09808i	0.624951	+	1.08245i	0.988550	+	0.150891i	$0.0482143\pi$
$43$	4.09808	+	7.09808i	0.624951	+	1.08245i	−0.363600	+	0.931555i	$0.618452\pi$
$44$	−4.62518	+	4.62518i	−0.697272	+	0.697272i
$45$		0			0
$46$		0			0
$47$	−6.77174	+	6.77174i	−0.987759	+	0.987759i	−0.999926	−	0.0121668i	$-0.996127\pi$
$47$	−6.77174	+	6.77174i	−0.987759	+	0.987759i	0.0121668	+	0.999926i	$0.496127\pi$
$48$	−1.30469	−	4.06364i	−0.188316	−	0.586536i
$49$	4.33013	+	2.50000i	0.618590	+	0.357143i
$50$		0			0
$51$	0.785693	−	3.63397i	0.110019	−	0.508858i
$52$	7.46410	−	11.1962i	1.03508	−	1.55263i
$53$	−4.62518			−0.635318			−0.317659	−	0.948205i	$-0.602897\pi$
$53$	−4.62518			−0.635318			−0.317659	+	0.948205i	$0.602897\pi$
$54$	−11.5669	−	4.57965i	−1.57405	−	0.623211i
$55$		0			0
$56$	2.93225	+	5.07880i	0.391838	+	0.678683i
$57$	−0.971364	−	1.50726i	−0.128660	−	0.199642i
$58$	−12.7942	−	3.42820i	−1.67996	−	0.450145i
$59$	−1.23931	+	4.62518i	−0.161345	+	0.602147i	0.837133	+	0.546999i	$0.184230\pi$
$59$	−1.23931	+	4.62518i	−0.161345	+	0.602147i	−0.998478	+	0.0551484i	$0.982437\pi$
$60$		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	$0.685424\pi$
$62$	13.0899	+	7.55743i	1.66241	+	0.959794i
$63$	4.18567	+	0.692934i	0.527345	+	0.0873015i
$64$			10.6603i			1.33253i
$65$		0			0
$66$	−1.53590	+	7.10381i	−0.189056	+	0.874418i
$67$	2.26795	+	8.46410i	0.277074	+	1.03405i	0.954439	+	0.298407i	$0.0964553\pi$
$67$	2.26795	+	8.46410i	0.277074	+	1.03405i	−0.677365	+	0.735647i	$0.736878\pi$
$68$	4.00552	−	6.93777i	0.485741	−	0.841328i
$69$		0			0
$70$		0			0
$71$	4.62518	+	1.23931i	0.548908	+	0.147079i	0.522606	−	0.852575i	$-0.324960\pi$
$71$	4.62518	+	1.23931i	0.548908	+	0.147079i	0.0263025	+	0.999654i	$0.491627\pi$
$72$	−9.61317	−	7.89635i	−1.13292	−	0.930594i
$73$	−6.09808	−	6.09808i	−0.713726	−	0.713726i	0.253587	−	0.967313i	$-0.418390\pi$
$73$	−6.09808	−	6.09808i	−0.713726	−	0.713726i	−0.967313	+	0.253587i	$0.918390\pi$
$74$	−14.1631	+	8.17709i	−1.64643	+	0.950567i
$75$		0			0
$76$	−1.00000	−	3.73205i	−0.114708	−	0.428096i
$77$		−	2.47863i		−	0.282466i
$78$	0.232259	−	14.9498i	0.0262981	−	1.69273i
$79$	−2.00000			−0.225018			−0.112509	−	0.993651i	$-0.535889\pi$
$79$	−2.00000			−0.225018			−0.112509	+	0.993651i	$0.535889\pi$
$80$		0			0
$81$	−8.82860	+	1.74811i	−0.980955	+	0.194234i
$82$	−0.767949	−	1.33013i	−0.0848058	−	0.146888i
$83$	−1.23931	−	1.23931i	−0.136032	−	0.136032i	0.635812	−	0.771844i	$-0.280665\pi$
$83$	−1.23931	−	1.23931i	−0.136032	−	0.136032i	−0.771844	+	0.635812i	$0.780665\pi$
$84$	8.13071	+	4.17862i	0.887133	+	0.455924i
$85$		0			0
$86$	13.8755	+	13.8755i	1.49624	+	1.49624i
$87$	−9.12372	+	2.92931i	−0.978165	+	0.314054i
$88$	−3.63397	+	6.29423i	−0.387383	+	0.670967i
$89$	9.70398	−	2.60017i	1.02862	−	0.275618i	0.295230	−	0.955426i	$-0.404604\pi$
$89$	9.70398	−	2.60017i	1.02862	−	0.275618i	0.733390	+	0.679808i	$0.237937\pi$
$90$		0			0
$91$	1.00000	+	5.00000i	0.104828	+	0.524142i
$92$		0			0
$93$	10.9217	−	0.534160i	1.13253	−	0.0553898i
$94$	−11.4641	+	19.8564i	−1.18243	+	2.04803i
$95$		0			0
$96$	2.24637	+	3.48568i	0.229269	+	0.355756i
$97$	−12.5622	−	3.36603i	−1.27550	−	0.341768i	−0.443362	−	0.896343i	$-0.646214\pi$
$97$	−12.5622	−	3.36603i	−1.27550	−	0.341768i	−0.832134	+	0.554575i	$0.812881\pi$
$98$	11.5630	+	3.09828i	1.16803	+	0.312974i
$99$	1.84997	+	4.92177i	0.185929	+	0.494656i
$100$		0			0
$101$	9.87002	−	17.0954i	0.982104	−	1.70105i	0.327944	−	0.944697i	$-0.393644\pi$
$101$	9.87002	−	17.0954i	0.982104	−	1.70105i	0.654160	−	0.756356i	$-0.273022\pi$
$102$	−0.434830	−	8.89076i	−0.0430546	−	0.880316i
$103$	−6.92820			−0.682656			−0.341328	−	0.939944i	$-0.610877\pi$
$103$	−6.92820			−0.682656			−0.341328	+	0.939944i	$0.610877\pi$
$104$	4.79122	−	14.1631i	0.469818	−	1.38881i
$105$		0			0
$106$	−10.6962	+	2.86603i	−1.03890	+	0.278373i
$107$	8.34312	−	14.4507i	0.806560	−	1.39700i	−0.108673	−	0.994078i	$-0.534660\pi$
$107$	8.34312	−	14.4507i	0.806560	−	1.39700i	0.915233	−	0.402925i	$-0.132007\pi$
$108$	−19.2638	−	2.22890i	−1.85366	−	0.214476i
$109$	2.80385	+	2.80385i	0.268560	+	0.268560i	0.828520	−	0.559960i	$-0.189183\pi$
$109$	2.80385	+	2.80385i	0.268560	+	0.268560i	−0.559960	+	0.828520i	$0.689183\pi$
$110$		0			0
$111$	−5.40808	+	10.5230i	−0.513313	+	0.998798i
$112$	2.46410	+	2.46410i	0.232836	+	0.232836i
$113$	−6.48415	−	11.2309i	−0.609978	−	1.05651i	−0.991243	−	0.132047i	$-0.957845\pi$
$113$	−6.48415	−	11.2309i	−0.609978	−	1.05651i	0.381266	−	0.924465i	$-0.375488\pi$
$114$	−3.18035	−	2.88377i	−0.297867	−	0.270090i
$115$		0			0
$116$	−20.6473			−1.91705
$117$	−5.71753	−	9.18204i	−0.528585	−	0.848880i
$118$			11.4641i			1.05536i
$119$	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
$123$	−0.988265	−	0.507899i	−0.0891088	−	0.0457957i
$124$	22.7583	+	6.09808i	2.04376	+	0.547623i
$125$		0			0
$126$	10.1091	−	0.991207i	0.900592	−	0.0883037i
$127$	7.56218	−	13.0981i	0.671035	−	1.16227i	−0.306576	−	0.951846i	$-0.599183\pi$
$127$	7.56218	−	13.0981i	0.671035	−	1.16227i	0.977611	−	0.210420i	$-0.0674832\pi$
$128$	5.36639	+	20.0276i	0.474326	+	1.77021i
$129$	13.8755	+	3.00000i	1.22167	+	0.264135i
$130$		0			0
$131$			0.907241i			0.0792660i	0.999214	+	0.0396330i	$0.0126189\pi$
$131$			0.907241i			0.0792660i	−0.999214	+	0.0396330i	$0.987381\pi$
$132$	0.553435	+	11.3158i	0.0481703	+	0.984915i
$133$	1.26795	+	0.732051i	0.109945	+	0.0634769i
$134$	10.4897	+	18.1687i	0.906170	+	1.56953i
$135$		0			0
$136$	2.30385	−	8.59808i	0.197553	−	0.737279i
$137$	−5.69846	−	1.52690i	−0.486852	−	0.130452i	0.00703925	−	0.999975i	$-0.497759\pi$
$137$	−5.69846	−	1.52690i	−0.486852	−	0.130452i	−0.493891	+	0.869524i	$0.664426\pi$
$138$		0			0
$139$	−1.19615	−	2.07180i	−0.101456	−	0.175728i	0.810829	−	0.585284i	$-0.199017\pi$
$139$	−1.19615	−	2.07180i	−0.101456	−	0.175728i	−0.912285	+	0.409556i	$0.865684\pi$
$140$		0			0
$141$	0.810284	+	16.5675i	0.0682383	+	1.39523i
$142$	11.4641			0.962046
$143$	−4.74673	+	4.17156i	−0.396941	+	0.348843i
$144$	−6.73205	−	3.05379i	−0.561004	−	0.254483i
$145$		0			0
$146$	−17.8811	−	10.3236i	−1.47985	−	0.854391i
$147$	8.24568	−	2.64740i	0.680092	−	0.218354i
$148$	−18.0263	+	18.0263i	−1.48175	+	1.48175i
$149$	5.24484	+	1.40535i	0.429674	+	0.115131i	0.467173	−	0.884166i	$-0.345272\pi$
$149$	5.24484	+	1.40535i	0.429674	+	0.115131i	−0.0374992	+	0.999297i	$0.511939\pi$
$150$		0			0
$151$	7.46410	−	7.46410i	0.607420	−	0.607420i	−0.334851	−	0.942271i	$-0.608686\pi$
$151$	7.46410	−	7.46410i	0.607420	−	0.607420i	0.942271	+	0.334851i	$0.108686\pi$
$152$	−2.14655	−	3.71794i	−0.174109	−	0.301565i
$153$	−3.74867	−	5.23610i	−0.303062	−	0.423313i
$154$	−1.53590	−	5.73205i	−0.123766	−	0.461902i
$155$		0			0
$156$	−5.68177	−	22.6035i	−0.454905	−	1.80973i
$157$			15.1962i			1.21278i	0.795165	+	0.606392i	$0.207384\pi$
$157$			15.1962i			1.21278i	−0.795165	+	0.606392i	$0.792616\pi$
$158$	−4.62518	+	1.23931i	−0.367960	+	0.0985945i
$159$	−5.38119	+	5.93462i	−0.426756	+	0.470646i
$160$		0			0
$161$		0			0
$162$	−19.3337	+	9.51336i	−1.51900	+	0.747440i
$163$	4.00000	−	14.9282i	0.313304	−	1.16927i	−0.612254	−	0.790661i	$-0.709737\pi$
$163$	4.00000	−	14.9282i	0.313304	−	1.16927i	0.925558	−	0.378606i	$-0.123596\pi$
$164$	−1.69293	−	1.69293i	−0.132196	−	0.132196i
$165$		0			0
$166$	−3.63397	−	2.09808i	−0.282051	−	0.162842i
$167$	−3.05379	−	11.3969i	−0.236310	−	0.881920i	−0.977554	−	0.210685i	$-0.932431\pi$
$167$	−3.05379	−	11.3969i	−0.236310	−	0.881920i	0.741244	−	0.671235i	$-0.234236\pi$
$168$	9.92820	+	2.14655i	0.765978	+	0.165610i
$169$	7.89230	−	10.3301i	0.607100	−	0.794625i
$170$		0			0
$171$	−3.06412	−	0.507263i	−0.234319	−	0.0387914i
$172$	26.4904	+	15.2942i	2.01987	+	1.16617i
$173$	−6.43966	+	3.71794i	−0.489598	+	0.282670i	−0.724408	−	0.689372i	$-0.757887\pi$
$173$	−6.43966	+	3.71794i	−0.489598	+	0.282670i	0.234809	+	0.972041i	$0.424553\pi$
$174$	−19.2843	+	12.4279i	−1.46194	+	0.942154i
$175$		0			0
$176$	−1.11777	+	4.17156i	−0.0842548	+	0.314443i
$177$	4.49274	+	6.97136i	0.337695	+	0.524000i
$178$	20.8301	−	12.0263i	1.56128	−	0.901408i
$179$	9.37191	−	16.2326i	0.700489	−	1.21328i	−0.267805	−	0.963473i	$-0.586298\pi$
$179$	9.37191	−	16.2326i	0.700489	−	1.21328i	0.968295	−	0.249810i	$-0.0803683\pi$
$180$		0			0
$181$		−	3.00000i		−	0.222988i	−0.993765	−	0.111494i	$-0.964436\pi$
$181$		−	3.00000i		−	0.222988i	0.993765	−	0.111494i	$-0.0355636\pi$
$182$	5.41087	+	10.9433i	0.401081	+	0.811171i
$183$	11.8505	+	2.56218i	0.876017	+	0.189402i
$184$		0			0
$185$		0			0
$186$	24.9265	−	8.00301i	1.82770	−	0.586809i
$187$	−2.66025	+	2.66025i	−0.194537	+	0.194537i
$188$	−9.25036	+	34.5228i	−0.674652	+	2.51784i
$189$	5.75895	−	4.56448i	0.418902	−	0.332017i
$190$		0			0
$191$	−16.8078	+	9.70398i	−1.21617	+	0.702156i	−0.964096	−	0.265553i	$-0.914446\pi$
$191$	−16.8078	+	9.70398i	−1.21617	+	0.702156i	−0.252073	+	0.967708i	$0.581112\pi$
$192$	13.6783	+	12.4027i	0.987146	+	0.895089i
$193$	−6.96410	+	1.86603i	−0.501287	+	0.134319i	−0.500597	−	0.865680i	$-0.666886\pi$
$193$	−6.96410	+	1.86603i	−0.501287	+	0.134319i	−0.000689767		1.00000i	$0.500220\pi$
$194$	−31.1370			−2.23550
$195$		0			0
$196$	18.6603			1.33288
$197$	−1.69293	+	0.453620i	−0.120617	+	0.0323191i	−0.318622	−	0.947882i	$-0.603220\pi$
$197$	−1.69293	+	0.453620i	−0.120617	+	0.0323191i	0.198006	+	0.980201i	$0.436554\pi$
$198$	7.32803	+	10.2357i	0.520780	+	0.727418i
$199$	−0.803848	+	0.464102i	−0.0569832	+	0.0328993i	−0.528221	−	0.849107i	$-0.677141\pi$
$199$	−0.803848	+	0.464102i	−0.0569832	+	0.0328993i	0.471238	+	0.882006i	$0.343807\pi$
$200$		0			0
$201$	13.4990	+	6.93756i	0.952149	+	0.489338i
$202$	12.2321	−	45.6506i	0.860644	−	3.21197i
$203$	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
$208$	0.571797	−	8.86603i	0.0396470	−	0.614748i
$209$			1.81448i			0.125510i
$210$		0			0
$211$	6.09808	−	10.5622i	0.419809	−	0.727130i	−0.576111	−	0.817371i	$-0.695430\pi$
$211$	6.09808	−	10.5622i	0.419809	−	0.727130i	0.995920	+	0.0902411i	$0.0287638\pi$
$212$	−14.9488	+	8.63071i	−1.02669	+	0.592759i
$213$	6.97136	−	4.49274i	0.477670	−	0.307837i
$214$	10.3397	−	38.5885i	0.706810	−	2.63785i
$215$		0			0
$216$	−21.3164	+	3.14772i	−1.45040	+	0.214176i
$217$	−7.73205	+	4.46410i	−0.524886	+	0.303043i
$218$	8.22158	+	4.74673i	0.556835	+	0.321489i
$219$	−14.9193	+	0.729677i	−1.00816	+	0.0493070i
$220$		0			0
$221$	4.29311	−	6.43966i	0.288786	−	0.433179i
$222$	−5.98604	+	27.6865i	−0.401757	+	1.85820i
$223$	5.97372	+	22.2942i	0.400030	+	1.49293i	0.813041	+	0.582206i	$0.197810\pi$
$223$	5.97372	+	22.2942i	0.400030	+	1.49293i	−0.413011	+	0.910726i	$0.635523\pi$
$224$	−2.93225	−	1.69293i	−0.195919	−	0.113114i
$225$		0			0
$226$	−21.9545	−	21.9545i	−1.46039	−	1.46039i
$227$	−4.05001	+	15.1149i	−0.268809	+	1.00321i	0.691069	+	0.722789i	$0.257140\pi$
$227$	−4.05001	+	15.1149i	−0.268809	+	1.00321i	−0.959878	+	0.280419i	$0.909526\pi$
$228$	−5.95209	−	3.05896i	−0.394187	−	0.202585i
$229$	−10.1244	+	10.1244i	−0.669036	+	0.669036i	−0.957493	−	0.288457i	$-0.906858\pi$
$229$	−10.1244	+	10.1244i	−0.669036	+	0.669036i	0.288457	+	0.957493i	$0.406858\pi$
$230$		0			0
$231$	−3.18035	−	2.88377i	−0.209252	−	0.189738i
$232$	−22.1603	+	5.93782i	−1.45489	+	0.389837i
$233$		−	7.43588i		−	0.487141i	−0.969883	−	0.243570i	$-0.921681\pi$
$233$		−	7.43588i		−	0.487141i	0.969883	−	0.243570i	$-0.0783187\pi$
$234$	−18.9120	−	17.6914i	−1.23632	−	1.15652i
$235$		0			0
$236$	4.62518	+	17.2614i	0.301074	+	1.12362i
$237$	−2.32691	+	2.56622i	−0.151149	+	0.166694i
$238$	3.63397	+	6.29423i	0.235556	+	0.407994i
$239$	7.10381	−	7.10381i	0.459507	−	0.459507i	−0.438986	−	0.898494i	$-0.644662\pi$
$239$	7.10381	−	7.10381i	0.459507	−	0.459507i	0.898494	+	0.438986i	$0.144662\pi$
$240$		0			0
$241$	7.23205	+	1.93782i	0.465857	+	0.124826i	0.484110	−	0.875007i	$-0.339144\pi$
$241$	7.23205	+	1.93782i	0.465857	+	0.124826i	−0.0182524	+	0.999833i	$0.505810\pi$
$242$	−13.4219	+	13.4219i	−0.862794	+	0.862794i
$243$	−8.02865	+	13.3619i	−0.515038	+	0.857167i
$244$	22.6244	+	13.0622i	1.44838	+	0.836220i
$245$		0			0
$246$	−2.60017	−	0.562178i	−0.165781	−	0.0358431i
$247$	−0.732051	−	3.66025i	−0.0465793	−	0.232896i
$248$	26.1797			1.66241
$249$	−3.03206	+	0.148292i	−0.192149	+	0.00939765i
$250$		0			0
$251$	−10.9433	−	18.9543i	−0.690735	−	1.19639i	−0.971597	−	0.236640i	$-0.923954\pi$
$251$	−10.9433	−	18.9543i	−0.690735	−	1.19639i	0.280863	−	0.959748i	$-0.409379\pi$
$252$	14.8213	−	5.57097i	0.933656	−	0.350938i
$253$		0			0
$254$	9.37191	−	34.9764i	0.588046	−	2.19462i
$255$		0			0
$256$	14.1603	+	24.5263i	0.885016	+	1.53289i
$257$	−14.3737	−	8.29863i	−0.896604	−	0.517655i	−0.0205071	−	0.999790i	$-0.506528\pi$
$257$	−14.3737	−	8.29863i	−0.896604	−	0.517655i	−0.876097	+	0.482135i	$0.839861\pi$
$258$	33.9474	−	1.66030i	2.11347	−	0.103366i
$259$		−	9.66025i		−	0.600259i
$260$		0			0
$261$	−6.85641	+	15.1149i	−0.424401	+	0.935586i
$262$	0.562178	+	2.09808i	0.0347315	+	0.129620i
$263$	−5.98604	+	10.3681i	−0.369115	+	0.639326i	−0.989427	−	0.145029i	$-0.953673\pi$
$263$	−5.98604	+	10.3681i	−0.369115	+	0.639326i	0.620312	+	0.784355i	$0.287006\pi$
$264$	3.84823	+	11.9858i	0.236842	+	0.737677i
$265$		0			0
$266$	3.38587	+	0.907241i	0.207601	+	0.0556265i
$267$	7.95383	−	15.4765i	0.486766	−	0.947145i
$268$	23.1244	+	23.1244i	1.41254	+	1.41254i
$269$	−9.58244	+	5.53242i	−0.584251	+	0.337318i	−0.762821	−	0.646610i	$-0.776186\pi$
$269$	−9.58244	+	5.53242i	−0.584251	+	0.337318i	0.178570	+	0.983927i	$0.442853\pi$
$270$		0			0
$271$	0.535898	+	2.00000i	0.0325535	+	0.121491i	0.980291	−	0.197561i	$-0.0633021\pi$
$271$	0.535898	+	2.00000i	0.0325535	+	0.121491i	−0.947737	+	0.319052i	$0.896635\pi$
$272$		−	5.28933i		−	0.320713i
$273$	7.57901	+	4.53416i	0.458703	+	0.274420i
$274$	−14.1244			−0.853284
$275$		0			0
$276$		0			0
$277$	−1.79423	−	3.10770i	−0.107805	−	0.186723i	0.807076	−	0.590448i	$-0.201049\pi$
$277$	−1.79423	−	3.10770i	−0.107805	−	0.186723i	−0.914881	+	0.403724i	$0.867715\pi$
$278$	−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	0.998740	−	0.0501922i	$-0.0159834\pi$
$281$	15.9006	+	15.9006i	0.948547	+	0.948547i	−0.0501922	+	0.998740i	$0.515983\pi$
$282$	12.1400	+	37.8117i	0.722928	+	2.25166i
$283$	12.2942	−	21.2942i	0.730816	−	1.26581i	−0.225719	−	0.974192i	$-0.572473\pi$
$283$	12.2942	−	21.2942i	0.730816	−	1.26581i	0.956535	−	0.291618i	$-0.0941936\pi$
$284$	17.2614	−	4.62518i	1.02428	−	0.274454i
$285$		0			0
$286$	−8.39230	+	12.5885i	−0.496247	+	0.744371i
$287$	0.907241			0.0535527
$288$	7.08606	+	1.17309i	0.417550	+	0.0691251i
$289$	−6.19615	+	10.7321i	−0.364480	+	0.631297i
$290$		0			0
$291$	−18.9345	+	12.2025i	−1.10996	+	0.715320i
$292$	−31.0885	−	8.33013i	−1.81931	−	0.487484i
$293$	−21.2669	−	5.69846i	−1.24243	−	0.332908i	−0.423021	−	0.906120i	$-0.639030\pi$
$293$	−21.2669	−	5.69846i	−1.24243	−	0.332908i	−0.819407	+	0.573212i	$0.805697\pi$
$294$	17.4284	−	11.2318i	1.01645	−	0.655054i
$295$		0			0
$296$	−14.1631	+	24.5313i	−0.823215	+	1.42585i
$297$	8.46753	+	3.35253i	0.491336	+	0.194534i
$298$	13.0000			0.753070
$299$		0			0
$300$		0			0
$301$	−11.1962	+	3.00000i	−0.645335	+	0.172917i
$302$	12.6362	−	21.8866i	0.727133	−	1.25943i
$303$	−10.4520	−	32.5540i	−0.600449	−	1.87018i
$304$	−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	$0.583292\pi$
$308$	−4.62518	−	8.01105i	−0.263544	−	0.456472i
$309$	−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	$0.461159\pi$
$312$	−12.5985	−	22.6258i	−0.713250	−	1.28093i
$313$			2.00000i			0.113047i	0.998401	+	0.0565233i	$0.0180015\pi$
$313$			2.00000i			0.113047i	−0.998401	+	0.0565233i	$0.981998\pi$
$314$	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	$0.897793\pi$
$318$	−8.76706	+	17.0588i	−0.491632	+	0.956612i
$319$	9.36603	+	2.50962i	0.524397	+	0.140512i
$320$		0			0
$321$	−8.83503	−	27.5179i	−0.493123	−	1.53590i
$322$		0			0
$323$	−0.575167	−	2.14655i	−0.0320032	−	0.119437i
$324$	−25.2725	+	22.1244i	−1.40403	+	1.22913i
$325$		0			0
$326$		−	37.0015i		−	2.04932i
$327$	6.85980	−	0.335500i	0.379348	−	0.0185532i
$328$	−2.30385	−	1.33013i	−0.127209	−	0.0734440i
$329$	−6.77174	−	11.7290i	−0.373338	−	0.646640i
$330$		0			0
$331$	5.05256	−	18.8564i	0.277714	−	1.03644i	−0.676287	−	0.736638i	$-0.736412\pi$
$331$	5.05256	−	18.8564i	0.277714	−	1.03644i	0.954001	−	0.299804i	$-0.0969212\pi$
$332$	−6.31812	−	1.69293i	−0.346752	−	0.0929118i
$333$	7.21011	+	19.1822i	0.395112	+	1.05118i
$334$	−14.1244	−	24.4641i	−0.772850	−	1.33862i
$335$		0			0
$336$	6.02859	−	0.294847i	0.328886	−	0.0160852i
$337$	11.5359			0.628400			0.314200	−	0.949357i	$-0.398264\pi$
$337$	11.5359			0.628400			0.314200	+	0.949357i	$0.398264\pi$
$338$	11.8505	−	28.7799i	0.644584	−	1.56542i
$339$	−21.9545	−	4.74673i	−1.19240	−	0.257807i
$340$		0			0
$341$	−9.58244	−	5.53242i	−0.518918	−	0.299597i
$342$	−7.40039	+	0.725614i	−0.400167	+	0.0392367i
$343$	−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
$347$	−12.9683	−	22.4618i	−0.696175	−	1.20581i	−0.969783	−	0.243969i	$-0.921550\pi$
$347$	−12.9683	−	22.4618i	−0.696175	−	1.20581i	0.273608	−	0.961841i	$-0.411783\pi$
$348$	−24.0222	+	26.4928i	−1.28772	+	1.42016i
$349$	−1.50962	−	5.63397i	−0.0808080	−	0.301580i	0.913679	−	0.406436i	$-0.133228\pi$
$349$	−1.50962	−	5.63397i	−0.0808080	−	0.301580i	−0.994487	+	0.104856i	$0.966562\pi$
$350$		0			0
$351$	−18.4337	−	3.34667i	−0.983916	−	0.178632i
$352$		−	4.19615i		−	0.223656i
$353$	−26.3457	+	7.05932i	−1.40224	+	0.375730i	−0.879149	−	0.476546i	$-0.841889\pi$
$353$	−26.3457	+	7.05932i	−1.40224	+	0.375730i	−0.523093	+	0.852276i	$0.675222\pi$
$354$	14.7097	+	13.3380i	0.781813	+	0.708904i
$355$		0			0
$356$	26.5118	−	26.5118i	1.40512	−	1.40512i
$357$	4.67652	+	2.40340i	0.247508	+	0.127202i
$358$	11.6147	−	43.3468i	0.613858	−	2.29095i
$359$	12.0611	+	12.0611i	0.636559	+	0.636559i	0.949705	−	0.313146i	$-0.101383\pi$
$359$	12.0611	+	12.0611i	0.636559	+	0.636559i	−0.313146	+	0.949705i	$0.601383\pi$
$360$		0			0
$361$	15.5263	+	8.96410i	0.817173	+	0.471795i
$362$	−1.85897	−	6.93777i	−0.0977053	−	0.364641i
$363$	−2.90192	+	13.4219i	−0.152311	+	0.704468i
$364$	12.5622	+	14.2942i	0.658437	+	0.749221i
$365$		0			0
$366$	28.9931	−	1.41800i	1.51549	−	0.0741199i
$367$	8.32051	+	4.80385i	0.434327	+	0.250759i	0.701188	−	0.712976i	$-0.252653\pi$
$367$	8.32051	+	4.80385i	0.434327	+	0.250759i	−0.266861	+	0.963735i	$0.585987\pi$
$368$		0			0
$369$	−1.80149	+	0.677136i	−0.0937819	+	0.0352503i
$370$		0			0
$371$	1.69293	−	6.31812i	0.0878928	−	0.328020i
$372$	34.3028	−	22.1066i	1.77852	−	1.14618i
$373$	−16.9641	+	9.79423i	−0.878368	+	0.507126i	−0.870120	−	0.492840i	$-0.835959\pi$
$373$	−16.9641	+	9.79423i	−0.878368	+	0.507126i	−0.00824796	+	0.999966i	$0.502625\pi$
$374$	−4.50363	+	7.80052i	−0.232877	+	0.403355i
$375$		0			0
$376$			39.7128i			2.04803i
$377$	−19.9061	−	1.28380i	−1.02522	−	0.0661192i
$378$	10.4897	−	14.1244i	0.539531	−	0.726478i
$379$	4.83013	−	1.29423i	0.248107	−	0.0664801i	−0.132622	−	0.991167i	$-0.542340\pi$
$379$	4.83013	−	1.29423i	0.248107	−	0.0664801i	0.380729	+	0.924687i	$0.375673\pi$
$380$		0			0
$381$	−8.00804	−	24.9421i	−0.410264	−	1.27782i
$382$	−32.8564	+	32.8564i	−1.68108	+	1.68108i
$383$	3.62896	−	13.5435i	0.185431	−	0.692039i	−0.809106	−	0.587662i	$-0.800048\pi$
$383$	3.62896	−	13.5435i	0.185431	−	0.692039i	0.994538	−	0.104377i	$-0.0332849\pi$
$384$	31.9412	+	16.4156i	1.62999	+	0.837703i
$385$		0			0
$386$	−14.9488	+	8.63071i	−0.760875	+	0.439291i
$387$	19.9929	−	14.3135i	1.01630	−	0.727596i
$388$	−46.8827	+	12.5622i	−2.38011	+	0.637748i
$389$	5.28933			0.268180			0.134090	−	0.990969i	$-0.457189\pi$
$389$	5.28933			0.268180			0.134090	+	0.990969i	$0.457189\pi$
$390$		0			0
$391$		0			0
$392$	20.0276	−	5.36639i	1.01155	−	0.271043i
$393$	1.16409	+	1.05553i	0.0587206	+	0.0532446i
$394$	−3.63397	+	2.09808i	−0.183077	+	0.105700i
$395$		0			0
$396$	15.1633	+	12.4553i	0.761986	+	0.625903i
$397$	2.29423	−	8.56218i	0.115144	−	0.429723i	−0.884154	−	0.467196i	$-0.845264\pi$
$397$	2.29423	−	8.56218i	0.115144	−	0.429723i	0.999298	+	0.0374729i	$0.0119308\pi$
$398$	−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	0.492946	−	0.870060i	$-0.335920\pi$
$401$	27.1314	−	7.26985i	1.35488	−	0.363039i	0.861933	+	0.507021i	$0.169253\pi$
$402$	35.5167	+	7.67898i	1.77141	+	0.382993i
$403$	21.5622	+	7.29423i	1.07409	+	0.363351i
$404$		−	73.6708i		−	3.66526i
$405$		0			0
$406$	9.36603	−	16.2224i	0.464828	−	0.805106i
$407$	10.3681	−	5.98604i	0.513929	−	0.296717i
$408$	−8.35187	−	12.9596i	−0.413479	−	0.641594i
$409$	−3.00962	+	11.2321i	−0.148816	+	0.555389i	0.850740	+	0.525587i	$0.176154\pi$
$409$	−3.00962	+	11.2321i	−0.148816	+	0.555389i	−0.999556	+	0.0298020i	$0.990512\pi$
$410$		0			0
$411$	−8.58908	+	5.53528i	−0.423668	+	0.273035i
$412$	−22.3923	+	12.9282i	−1.10319	+	0.636927i
$413$	−5.86450	−	3.38587i	−0.288573	−	0.166608i
$414$		0			0
$415$		0			0
$416$	1.69293	+	8.46467i	0.0830029	+	0.415015i
$417$	−4.05001	−	0.875644i	−0.198330	−	0.0428805i
$418$	1.12436	+	4.19615i	0.0549940	+	0.205241i
$419$	7.22536	+	4.17156i	0.352982	+	0.203794i	0.665998	−	0.745954i	$-0.268006\pi$
$419$	7.22536	+	4.17156i	0.352982	+	0.203794i	−0.313016	+	0.949748i	$0.601339\pi$
$420$		0			0
$421$	0.830127	+	0.830127i	0.0404579	+	0.0404579i	0.727046	−	0.686588i	$-0.240893\pi$
$421$	0.830127	+	0.830127i	0.0404579	+	0.0404579i	−0.686588	+	0.727046i	$0.740893\pi$
$422$	7.55743	−	28.2047i	0.367890	−	1.37298i
$423$	22.2007	+	18.2358i	1.07943	+	0.886657i
$424$	−13.5622	+	13.5622i	−0.658638	+	0.658638i
$425$		0			0
$426$	13.3380	−	14.7097i	0.646226	−	0.712688i
$427$	−9.56218	+	2.56218i	−0.462746	+	0.123992i
$428$		−	62.2739i		−	3.01012i
$429$	−0.170025	+	10.9440i	−0.00820890	+	0.528381i
$430$		0			0
$431$	0.542599	+	2.02501i	0.0261361	+	0.0975412i	0.977762	−	0.209718i	$-0.0672547\pi$
$431$	0.542599	+	2.02501i	0.0261361	+	0.0975412i	−0.951626	+	0.307260i	$0.900588\pi$
$432$	−11.7508	+	5.08502i	−0.565360	+	0.244653i
$433$	−3.52628	−	6.10770i	−0.169462	−	0.293517i	0.768769	−	0.639527i	$-0.220870\pi$
$433$	−3.52628	−	6.10770i	−0.169462	−	0.293517i	−0.938231	+	0.346010i	$0.887536\pi$
$434$	−15.1149	+	15.1149i	−0.725536	+	0.725536i
$435$		0			0
$436$	14.2942	+	3.83013i	0.684569	+	0.183430i
$437$		0			0
$438$	−34.0502	+	10.9323i	−1.62698	+	0.522366i
$439$	4.09808	+	2.36603i	0.195591	+	0.112924i	0.594597	−	0.804024i	$-0.297312\pi$
$439$	4.09808	+	2.36603i	0.195591	+	0.112924i	−0.399007	+	0.916948i	$0.630645\pi$
$440$		0			0
$441$	6.19657	−	13.6603i	0.295075	−	0.650488i
$442$	5.93782	−	17.5526i	0.282433	−	0.834890i
$443$	29.5656			1.40470			0.702351	−	0.711830i	$-0.252134\pi$
$443$	29.5656			1.40470			0.702351	+	0.711830i	$0.252134\pi$
$444$	2.15697	+	44.1025i	0.102365	+	2.09301i
$445$		0			0
$446$	27.6295	+	47.8558i	1.30830	+	2.26604i
$447$	7.90535	−	5.09465i	0.373910	−	0.240969i
$448$	−14.5622	−	3.90192i	−0.687998	−	0.184349i
$449$	2.26810	−	8.46467i	0.107038	−	0.399472i	−0.891530	−	0.452961i	$-0.850368\pi$
$449$	2.26810	−	8.46467i	0.107038	−	0.399472i	0.998568	+	0.0534890i	$0.0170342\pi$
$450$		0			0
$451$	0.562178	+	0.973721i	0.0264719	+	0.0458507i
$452$	−41.9142	−	24.1992i	−1.97148	−	1.13823i
$453$	−0.893131	−	18.2614i	−0.0419629	−	0.857996i
$454$			37.4641i			1.75828i
$455$		0			0
$456$	−7.26795	−	1.57139i	−0.340353	−	0.0735869i
$457$	7.23205	+	26.9904i	0.338301	+	1.26256i	0.900246	+	0.435382i	$0.143387\pi$
$457$	7.23205	+	26.9904i	0.338301	+	1.26256i	−0.561945	+	0.827175i	$0.689947\pi$
$458$	−17.1399	+	29.6871i	−0.800893	+	1.38719i
$459$	−11.0799	−	1.28199i	−0.517166	−	0.0598382i
$460$		0			0
$461$	−23.4135	−	6.27363i	−1.09048	−	0.292192i	−0.331595	−	0.943422i	$-0.607587\pi$
$461$	−23.4135	−	6.27363i	−1.09048	−	0.292192i	−0.758880	+	0.651230i	$0.774253\pi$
$462$	−9.14181	−	4.69825i	−0.425315	−	0.218582i
$463$	−15.0526	−	15.0526i	−0.699552	−	0.699552i	0.264762	−	0.964314i	$-0.414707\pi$
$463$	−15.0526	−	15.0526i	−0.699552	−	0.699552i	−0.964314	+	0.264762i	$0.914707\pi$
$464$	−11.8060	+	6.81623i	−0.548082	+	0.316435i
$465$		0			0
$466$	−4.60770	−	17.1962i	−0.213447	−	0.796596i
$467$			30.4728i			1.41011i	0.709151	+	0.705057i	$0.249079\pi$
$467$			30.4728i			1.41011i	−0.709151	+	0.705057i	$0.750921\pi$
$468$	−35.6133	−	19.0078i	−1.64622	−	0.878635i
$469$	−12.3923			−0.572223
$470$		0			0
$471$	19.4984	+	17.6800i	0.898437	+	0.814653i
$472$	9.92820	+	17.1962i	0.456983	+	0.791517i
$473$	−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
$477$	1.35401	+	13.8093i	0.0619960	+	0.632285i
$478$	12.0263	−	20.8301i	0.550069	−	0.952748i
$479$	−8.46467	+	2.26810i	−0.386761	+	0.103632i	−0.446959	−	0.894554i	$-0.647493\pi$
$479$	−8.46467	+	2.26810i	−0.386761	+	0.103632i	0.0601988	+	0.998186i	$0.480827\pi$
$480$		0			0
$481$	−18.5000	+	16.2583i	−0.843527	+	0.741316i
$482$	17.9256			0.816487
$483$		0			0
$484$	−14.7942	+	25.6244i	−0.672465	+	1.16474i
$485$		0			0
$486$	−10.2872	+	35.8756i	−0.466636	+	1.62735i
$487$	24.4904	+	6.56218i	1.10977	+	0.297361i	0.766735	−	0.641964i	$-0.221880\pi$
$487$	24.4904	+	6.56218i	1.10977	+	0.297361i	0.343030	+	0.939324i	$0.388547\pi$
$488$	28.0387	+	7.51294i	1.26925	+	0.340095i
$489$	−14.5007	−	22.5007i	−0.655746	−	1.01752i
$490$		0			0
$491$	−12.5147	+	21.6761i	−0.564780	+	0.978227i	0.432290	+	0.901734i	$0.357706\pi$
$491$	−12.5147	+	21.6761i	−0.564780	+	0.978227i	−0.997070	+	0.0764928i	$0.975628\pi$
$492$	−4.14187	+	0.202571i	−0.186730	+	0.00913261i
$493$	−11.8756			−0.534852
$494$	−3.96104	−	8.01105i	−0.178215	−	0.360434i
$495$		0			0
$496$	15.0263	−	4.02628i	0.674700	−	0.180785i
$497$	−3.38587	+	5.86450i	−0.151877	+	0.263059i
$498$	−6.92003	+	2.22178i	−0.310094	+	0.0995602i
$499$	−4.46410	−	4.46410i	−0.199841	−	0.199841i	0.600091	−	0.799932i	$-0.295131\pi$
$499$	−4.46410	−	4.46410i	−0.199841	−	0.199841i	−0.799932	+	0.600091i	$0.795131\pi$
$500$		0			0
$501$	−18.1765	−	9.34143i	−0.812064	−	0.417345i
$502$	−37.0526	−	37.0526i	−1.65374	−	1.65374i
$503$	14.3292	+	24.8188i	0.638906	+	1.10662i	0.985673	+	0.168666i	$0.0539460\pi$
$503$	14.3292	+	24.8188i	0.638906	+	1.10662i	−0.346767	+	0.937951i	$0.612721\pi$
$504$	14.3053	−	10.2416i	0.637208	−	0.456196i
$505$		0			0
$506$		0			0
$507$	−4.07236	−	22.1453i	−0.180860	−	0.983509i
$508$		−	56.4449i		−	2.50434i
$509$	3.88398	+	14.4952i	0.172154	+	0.642489i	0.997019	+	0.0771582i	$0.0245846\pi$
$509$	3.88398	+	14.4952i	0.172154	+	0.642489i	−0.824865	+	0.565330i	$0.808749\pi$
$510$		0			0
$511$	10.5622	−	6.09808i	0.467243	−	0.269763i
$512$	18.6223	+	18.6223i	0.822996	+	0.822996i
$513$	−4.21584	+	3.34143i	−0.186134	+	0.147528i
$514$	−38.3827	−	10.2846i	−1.69299	−	0.453635i
$515$		0			0
$516$	50.4445	−	16.1960i	2.22070	−	0.712988i
$517$	8.39230	−	14.5359i	0.369093	−	0.639288i
$518$	−5.98604	−	22.3402i	−0.263012	−	0.981573i
$519$	−2.72172	+	12.5885i	−0.119470	+	0.552572i
$520$		0			0
$521$		−	33.2835i		−	1.45818i	−0.684419	−	0.729089i	$-0.739944\pi$
$521$		−	33.2835i		−	1.45818i	0.684419	−	0.729089i	$-0.260056\pi$
$522$	−6.49004	+	39.2031i	−0.284061	+	1.71587i
$523$	−11.2417	−	6.49038i	−0.491564	−	0.283805i	0.233659	−	0.972319i	$-0.424930\pi$
$523$	−11.2417	−	6.49038i	−0.491564	−	0.283805i	−0.725223	+	0.688514i	$0.758263\pi$
$524$	1.69293	+	2.93225i	0.0739562	+	0.128096i
$525$		0			0
$526$	−7.41858	+	27.6865i	−0.323466	+	1.20719i
$527$	13.0899	+	3.50742i	0.570203	+	0.152785i
$528$	4.05211	+	6.28764i	0.176345	+	0.273634i
$529$	−11.5000	−	19.9186i	−0.500000	−	0.866025i
$530$		0			0
$531$	14.1721	+	2.34618i	0.615018	+	0.101816i
$532$	5.46410			0.236899
$533$	−1.52690	−	1.73742i	−0.0661373	−	0.0752562i
$534$	8.80385	−	40.7194i	0.380980	−	1.76210i
$535$		0			0
$536$	31.4690	+	18.1687i	1.35926	+	0.784766i
$537$	−9.92447	−	30.9111i	−0.428273	−	1.33391i
$538$	−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	0.0185354	−	0.999828i	$-0.494100\pi$
$541$	23.6865	−	23.6865i	1.01836	−	1.01836i	0.999828	−	0.0185354i	$-0.00590034\pi$
$542$	2.47863	+	4.29311i	0.106466	+	0.184405i
$543$	−3.84933	−	3.49036i	−0.165191	−	0.149786i
$544$	1.33013	+	4.96410i	0.0570287	+	0.212834i
$545$		0			0
$546$	20.3368	+	5.78927i	0.870333	+	0.247758i
$547$		−	2.00000i		−	0.0855138i	−0.999086	−	0.0427569i	$-0.986386\pi$
$547$		−	2.00000i		−	0.0855138i	0.999086	−	0.0427569i	$-0.0136141\pi$
$548$	−21.2669	+	5.69846i	−0.908479	+	0.243426i
$549$	17.0751	−	12.2246i	0.728748	−	0.521732i
$550$		0			0
$551$	−4.05001	+	4.05001i	−0.172536	+	0.172536i
$552$		0			0
$553$	0.732051	−	2.73205i	0.0311300	−	0.116179i
$554$	−6.07502	−	6.07502i	−0.258103	−	0.258103i
$555$		0			0
$556$	−7.73205	−	4.46410i	−0.327912	−	0.189320i
$557$	10.5342	+	39.3140i	0.446347	+	1.66579i	0.712355	+	0.701819i	$0.247628\pi$
$557$	10.5342	+	39.3140i	0.446347	+	1.66579i	−0.266009	+	0.963971i	$0.585705\pi$
$558$	18.7321	−	41.2946i	0.792991	−	1.74814i
$559$	24.5885	+	16.3923i	1.03998	+	0.693321i
$560$		0			0
$561$	0.318318	+	6.50849i	0.0134394	+	0.274788i
$562$	46.6244	+	26.9186i	1.96673	+	1.13549i
$563$	−3.71794	+	2.14655i	−0.156693	+	0.0904665i	−0.576296	−	0.817241i	$-0.695502\pi$
$563$	−3.71794	+	2.14655i	−0.156693	+	0.0904665i	0.419603	+	0.907708i	$0.362169\pi$
$564$	33.5342	+	52.0350i	1.41205	+	2.19107i
$565$		0			0
$566$	15.2364	−	56.8630i	0.640434	−	2.39013i
$567$	0.843533	−	12.6999i	0.0354250	−	0.533347i
$568$	17.1962	−	9.92820i	0.721535	−	0.416578i
$569$	−8.01105	+	13.8755i	−0.335841	+	0.581693i	−0.983646	−	0.180113i	$-0.942354\pi$
$569$	−8.01105	+	13.8755i	−0.335841	+	0.581693i	0.647805	+	0.761806i	$0.275687\pi$
$570$		0			0
$571$		−	40.0526i		−	1.67615i	−0.545557	−	0.838074i	$-0.683682\pi$
$571$		−	40.0526i		−	1.67615i	0.545557	−	0.838074i	$-0.316318\pi$
$572$	−7.55743	+	22.3402i	−0.315992	+	0.934091i
$573$	−7.10381	+	32.8564i	−0.296766	+	1.37260i
$574$	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	−0.630711	−	0.776018i	$-0.717237\pi$
$577$	3.49038	−	3.49038i	0.145306	−	0.145306i	0.776018	+	0.630711i	$0.217237\pi$
$578$	−7.67898	+	28.6583i	−0.319403	+	1.19203i
$579$	−5.70810	+	11.1068i	−0.237220	+	0.461581i
$580$		0			0
$581$	2.14655	−	1.23931i	0.0890541	−	0.0514154i
$582$	−36.2264	+	39.9522i	−1.50163	+	1.65607i
$583$	7.83013	−	2.09808i	0.324291	−	0.0868934i
$584$	−35.7621			−1.47985
$585$		0			0
$586$	−52.7128			−2.17755
$587$	19.4080	−	5.20035i	0.801053	−	0.214641i	0.165006	−	0.986292i	$-0.447235\pi$
$587$	19.4080	−	5.20035i	0.801053	−	0.214641i	0.636046	+	0.771651i	$0.280569\pi$
$588$	21.7104	−	23.9432i	0.895320	−	0.987400i
$589$	5.66025	−	3.26795i	0.233227	−	0.134654i
$590$		0			0
$591$	−1.38761	+	2.69999i	−0.0570785	+	0.111063i
$592$	−4.35641	+	16.2583i	−0.179047	+	0.668213i
$593$	−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
$597$	−0.339746	+	1.57139i	−0.0139049	+	0.0643126i
$598$		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	−0.778205	−	0.628010i	$-0.783870\pi$
$601$	3.79423	−	6.57180i	0.154770	−	0.268069i	0.932975	+	0.359941i	$0.117203\pi$
$602$	−24.0331	+	13.8755i	−0.979518	+	0.565525i
$603$	24.6072	−	9.24923i	1.00208	−	0.376658i
$604$	10.1962	−	38.0526i	0.414876	−	1.54834i
$605$		0			0
$606$	−44.3434	−	68.8075i	−1.80133	−	2.79511i
$607$	−8.83013	+	5.09808i	−0.358404	+	0.206925i	−0.668380	−	0.743820i	$-0.733012\pi$
$607$	−8.83013	+	5.09808i	−0.358404	+	0.206925i	0.309977	+	0.950744i	$0.399679\pi$
$608$	2.14655	+	1.23931i	0.0870543	+	0.0502608i
$609$	−0.661992	−	13.5354i	−0.0268253	−	0.548483i
$610$		0			0
$611$	−11.0648	+	32.7083i	−0.447636	+	1.32324i
$612$	−21.8866	−	9.92820i	−0.884713	−	0.401324i
$613$	4.38269	+	16.3564i	0.177015	+	0.660629i	0.996200	+	0.0870991i	$0.0277597\pi$
$613$	4.38269	+	16.3564i	0.177015	+	0.660629i	−0.819185	+	0.573530i	$0.805574\pi$
$614$	36.3373	+	20.9794i	1.46645	+	0.846658i
$615$		0			0
$616$	−7.26795	−	7.26795i	−0.292834	−	0.292834i
$617$	9.74847	−	36.3818i	0.392459	−	1.46468i	−0.433607	−	0.901102i	$-0.642759\pi$
$617$	9.74847	−	36.3818i	0.392459	−	1.46468i	0.826066	−	0.563574i	$-0.190574\pi$
$618$	−13.1324	+	25.5530i	−0.528264	+	1.02789i
$619$	14.3397	−	14.3397i	0.576363	−	0.576363i	−0.357536	−	0.933899i	$-0.616383\pi$
$619$	14.3397	−	14.3397i	0.576363	−	0.576363i	0.933899	+	0.357536i	$0.116383\pi$
$620$		0			0
$621$		0			0
$622$	9.92820	−	2.66025i	0.398085	−	0.106666i
$623$			14.2076i			0.569216i
$624$	−10.7108	−	11.0489i	−0.428777	−	0.442310i
$625$		0			0
$626$	1.23931	+	4.62518i	0.0495329	+	0.184859i
$627$	2.32818	+	2.11107i	0.0929786	+	0.0843078i
$628$	28.3564	+	49.1147i	1.13154	+	1.95989i
$629$	−10.3681	+	10.3681i	−0.413404	+	0.413404i
$630$		0			0
$631$	2.26795	+	0.607695i	0.0902856	+	0.0241920i	0.303679	−	0.952774i	$-0.401785\pi$
$631$	2.26795	+	0.607695i	0.0902856	+	0.0241920i	−0.213393	+	0.976966i	$0.568452\pi$
$632$	−5.86450	+	5.86450i	−0.233277	+	0.233277i
$633$	−6.45761	−	20.1131i	−0.256667	−	0.799425i
$634$	−33.0622	−	19.0885i	−1.31307	−	0.758099i
$635$		0			0
$636$	−6.31812	+	29.2224i	−0.250530	+	1.15874i
$637$	17.9904	+	1.16025i	0.712805	+	0.0459709i
$638$	23.2149			0.919086
$639$	2.34618	−	14.1721i	0.0928136	−	0.560641i
$640$		0			0
$641$	−9.65949	−	16.7307i	−0.381527	−	0.660824i	0.609754	−	0.792591i	$-0.291268\pi$
$641$	−9.65949	−	16.7307i	−0.381527	−	0.660824i	−0.991281	+	0.131767i	$0.957935\pi$
$642$	−37.4835	−	58.1629i	−1.47935	−	2.29551i
$643$	26.1244	+	7.00000i	1.03024	+	0.276053i	0.734065	−	0.679079i	$-0.237621\pi$
$643$	26.1244	+	7.00000i	1.03024	+	0.276053i	0.296179	+	0.955132i	$0.404287\pi$
$644$		0			0
$645$		0			0
$646$	−2.66025	−	4.60770i	−0.104666	−	0.181287i
$647$	−12.5147	−	7.22536i	−0.492003	−	0.284058i	0.233402	−	0.972380i	$-0.425014\pi$
$647$	−12.5147	−	7.22536i	−0.492003	−	0.284058i	−0.725405	+	0.688322i	$0.758348\pi$
$648$	−20.7618	+	31.0135i	−0.815599	+	1.21833i
$649$		−	8.39230i		−	0.329427i
$650$		0			0
$651$	−3.26795	+	15.1149i	−0.128081	+	0.592398i
$652$	−14.9282	−	55.7128i	−0.584634	−	2.18188i
$653$	19.4080	−	33.6156i	0.759492	−	1.31548i	−0.183617	−	0.982998i	$-0.558781\pi$
$653$	19.4080	−	33.6156i	0.759492	−	1.31548i	0.943110	−	0.332482i	$-0.107886\pi$
$654$	15.6560	−	5.02659i	0.612198	−	0.196555i
$655$		0			0
$656$	−1.52690	−	0.409131i	−0.0596153	−	0.0159739i
$657$	−16.4217	+	19.9921i	−0.640672	+	0.779967i
$658$	−22.9282	−	22.9282i	−0.893834	−	0.893834i
$659$	−27.1759	+	15.6900i	−1.05862	+	0.611197i	−0.925051	−	0.379842i	$-0.875978\pi$
$659$	−27.1759	+	15.6900i	−1.05862	+	0.611197i	−0.133572	+	0.991039i	$0.542645\pi$
$660$		0			0
$661$	−4.42820	−	16.5263i	−0.172237	−	0.642798i	−0.997006	−	0.0773274i	$-0.975361\pi$
$661$	−4.42820	−	16.5263i	−0.172237	−	0.642798i	0.824769	−	0.565470i	$-0.191305\pi$
$662$		−	46.7380i		−	1.81652i
$663$	−3.26797	−	13.0008i	−0.126917	−	0.504909i
$664$	−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
$672$	−5.58376	+	1.79275i	−0.215398	+	0.0691568i
$673$	6.35641	−	11.0096i	0.245021	−	0.424390i	−0.717116	−	0.696954i	$-0.754538\pi$
$673$	6.35641	−	11.0096i	0.245021	−	0.424390i	0.962138	+	0.272564i	$0.0878717\pi$
$674$	26.6778	−	7.14830i	1.02759	−	0.275342i
$675$		0			0
$676$	6.23205	−	48.1147i	0.239694	−	1.85057i
$677$	38.8159			1.49182			0.745909	−	0.666048i	$-0.232015\pi$
$677$	38.8159			1.49182			0.745909	+	0.666048i	$0.232015\pi$
$678$	−53.7131	+	2.62700i	−2.06284	+	0.100889i
$679$	9.19615	−	15.9282i	0.352916	−	0.611268i
$680$		0			0
$681$	14.6820	+	22.7821i	0.562617	+	0.873011i
$682$	−25.5885	−	6.85641i	−0.979833	−	0.262545i
$683$	−15.9006	−	4.26054i	−0.608418	−	0.163025i	−0.0585607	−	0.998284i	$-0.518651\pi$
$683$	−15.9006	−	4.26054i	−0.608418	−	0.163025i	−0.549857	+	0.835259i	$0.685318\pi$
$684$	−10.8500	+	4.07823i	−0.414859	+	0.155935i
$685$		0			0
$686$	−20.3152	+	35.1870i	−0.775638	+	1.34344i
$687$	1.21145	+	24.7699i	0.0462196	+	0.945031i
$688$	20.1962			0.769971
$689$	−14.9488	+	7.39139i	−0.569505	+	0.281590i
$690$		0			0
$691$	−41.8827	+	11.2224i	−1.59329	+	0.426921i	−0.943008	−	0.332770i	$-0.892017\pi$
$691$	−41.8827	+	11.2224i	−1.59329	+	0.426921i	−0.650284	+	0.759691i	$0.725350\pi$
$692$	−13.8755	+	24.0331i	−0.527469	+	0.913603i
$693$	−7.40039	+	0.725614i	−0.281118	+	0.0275638i
$694$	−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
$698$	−6.98226	−	12.0936i	−0.264283	−	0.457751i
$699$	−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	$0.374668\pi$
$702$	−44.7033	+	3.68307i	−1.68722	+	0.139009i
$703$			7.07180i			0.266718i
$704$	−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
$708$	27.5295	+	14.1482i	1.03462	+	0.531724i
$709$	9.96410	+	2.66987i	0.374210	+	0.100269i	0.441022	−	0.897496i	$-0.354616\pi$
$709$	9.96410	+	2.66987i	0.374210	+	0.100269i	−0.0668121	+	0.997766i	$0.521283\pi$
$710$		0			0
$711$	0.585497	+	5.97136i	0.0219578	+	0.223944i
$712$	20.8301	−	36.0788i	0.780642	−	1.35211i
$713$		0			0
$714$	12.3042	+	2.66025i	0.460472	+	0.0995575i
$715$		0			0
$716$		−	69.9529i		−	2.61426i
$717$	−0.850019	−	17.3799i	−0.0317446	−	0.649065i
$718$	35.3660	+	20.4186i	1.31985	+	0.762015i
$719$	5.86450	+	10.1576i	0.218709	+	0.378815i	0.954413	−	0.298488i	$-0.0964822\pi$
$719$	5.86450	+	10.1576i	0.218709	+	0.378815i	−0.735705	+	0.677302i	$0.763149\pi$
$720$		0			0
$721$	2.53590	−	9.46410i	0.0944418	−	0.352462i
$722$	41.4606	+	11.1093i	1.54300	+	0.413447i
$723$	10.9006	−	7.02496i	0.405398	−	0.261261i
$724$	−5.59808	−	9.69615i	−0.208051	−	0.360355i
$725$		0			0
$726$	1.60603	+	32.8376i	0.0596052	+	1.21872i
$727$	−25.5167			−0.946361			−0.473180	−	0.880966i	$-0.656894\pi$
$727$	−25.5167			−0.946361			−0.473180	+	0.880966i	$0.656894\pi$
$728$	17.5935	+	11.7290i	0.652058	+	0.434705i
$729$	7.80385	+	25.8476i	0.289031	+	0.957320i
$730$		0			0
$731$	15.2364	+	8.79674i	0.563539	+	0.325359i
$732$	43.0826	−	13.8323i	1.59238	−	0.511257i
$733$	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
$737$	−7.67898	−	13.3004i	−0.282859	−	0.489926i
$738$	−3.74652	+	2.68224i	−0.137911	+	0.0987348i
$739$	−13.1244	−	48.9808i	−0.482787	−	1.80179i	−0.589825	−	0.807531i	$-0.700803\pi$
$739$	−13.1244	−	48.9808i	−0.482787	−	1.80179i	0.107037	−	0.994255i	$-0.465864\pi$
$740$		0			0
$741$	−5.54822	−	3.31924i	−0.203819	−	0.121935i
$742$		−	15.6603i		−	0.574906i
$743$	50.5449	−	13.5435i	1.85431	−	0.496862i	0.854566	−	0.519343i	$-0.173823\pi$
$743$	50.5449	−	13.5435i	1.85431	−	0.496862i	0.999747	+	0.0224808i	$0.00715645\pi$
$744$	30.4589	−	33.5915i	1.11668	−	1.23152i
$745$		0			0
$746$	−33.1620	+	33.1620i	−1.21415	+	1.21415i
$747$	−3.33739	+	4.06300i	−0.122109	+	0.148658i
$748$	−3.63397	+	13.5622i	−0.132871	+	0.495882i
$749$	16.6862	+	16.6862i	0.609702	+	0.609702i
$750$		0			0
$751$	38.2750	+	22.0981i	1.39667	+	0.806370i	0.994043	−	0.108992i	$-0.0347622\pi$
$751$	38.2750	+	22.0981i	1.39667	+	0.806370i	0.402632	+	0.915362i	$0.368096\pi$
$752$	6.10759	+	22.7938i	0.222721	+	0.831206i
$753$	−37.0526	−	8.01105i	−1.35027	−	0.291939i
$754$	−46.8301	+	9.36603i	−1.70545	+	0.341091i
$755$		0			0
$756$	10.0958	−	25.4990i	0.367180	−	0.927389i
$757$	−21.4641	−	12.3923i	−0.780126	−	0.450406i	0.0563489	−	0.998411i	$-0.482054\pi$
$757$	−21.4641	−	12.3923i	−0.780126	−	0.450406i	−0.836475	+	0.548005i	$0.815387\pi$
$758$	10.3681	−	5.98604i	0.376587	−	0.217423i
$759$		0			0
$760$		0			0
$761$	−1.11777	+	4.17156i	−0.0405190	+	0.151219i	−0.983222	−	0.182415i	$-0.941608\pi$
$761$	−1.11777	+	4.17156i	−0.0405190	+	0.151219i	0.942703	+	0.333634i	$0.108275\pi$
$762$	−33.9749	−	52.7187i	−1.23078	−	1.90980i
$763$	−4.85641	+	2.80385i	−0.175814	+	0.101506i
$764$	−36.2158	+	62.7275i	−1.31024	+	2.26940i
$765$		0			0
$766$		−	33.5692i		−	1.21291i
$767$	3.38587	+	16.9293i	0.122257	+	0.611283i
$768$	47.9447	+	10.3660i	1.73006	+	0.374052i
$769$	2.16987	−	0.581416i	0.0782476	−	0.0209664i	−0.219483	−	0.975616i	$-0.570437\pi$
$769$	2.16987	−	0.581416i	0.0782476	−	0.0209664i	0.297730	+	0.954650i	$0.403770\pi$
$770$		0			0
$771$	−27.3712	+	8.78792i	−0.985748	+	0.316489i
$772$	−19.0263	+	19.0263i	−0.684771	+	0.684771i
$773$	−1.60396	+	5.98604i	−0.0576903	+	0.215303i	−0.988753	−	0.149555i	$-0.952216\pi$
$773$	−1.60396	+	5.98604i	−0.0576903	+	0.215303i	0.931063	+	0.364858i	$0.118883\pi$
$774$	37.3659	−	45.4900i	1.34309	−	1.63510i
$775$		0			0
$776$	−46.7054	+	26.9654i	−1.67663	+	0.968001i
$777$	−12.3952	−	11.2393i	−0.444675	−	0.403206i
$778$	12.2321	−	3.27757i	0.438540	−	0.117507i
$779$	−0.664146			−0.0237955
$780$		0			0
$781$	−8.39230			−0.300300
$782$		0			0
$783$	11.4169	+	26.3830i	0.408008	+	0.942851i
$784$	10.6699	−	6.16025i	0.381067	−	0.220009i
$785$		0			0
$786$	3.34613	+	1.71968i	0.119353	+	0.0613389i
$787$	−3.02628	+	11.2942i	−0.107875	+	0.402596i	−0.998655	−	0.0518385i	$-0.983492\pi$
$787$	−3.02628	+	11.2942i	−0.107875	+	0.402596i	0.890780	+	0.454434i	$0.150159\pi$
$788$	−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
$792$	19.8564	+	9.00727i	0.705567	+	0.320059i
$793$	21.0000	+	14.0000i	0.745732	+	0.497155i
$794$		−	21.2224i		−	0.753157i
$795$		0			0
$796$	−1.73205	+	3.00000i	−0.0613909	+	0.106332i
$797$	14.8718	−	8.58622i	0.526785	−	0.304139i	−0.212921	−	0.977069i	$-0.568298\pi$
$797$	14.8718	−	8.58622i	0.526785	−	0.304139i	0.739706	+	0.672930i	$0.234964\pi$
$798$	5.10339	−	3.28891i	0.180658	−	0.116426i
$799$	−5.32051	+	19.8564i	−0.188226	+	0.702469i
$800$		0			0
$801$	−10.6041	−	28.2118i	−0.374678	−	0.996815i
$802$	58.2391	−	33.6244i	2.05649	−	1.18732i
$803$	13.0899	+	7.55743i	0.461931	+	0.266696i
$804$	56.5752	−	2.76699i	1.99526	−	0.0975841i
$805$		0			0
$806$	54.3844	+	3.50742i	1.91561	+	0.123543i
$807$	−4.05001	+	18.7321i	−0.142567	+	0.659399i
$808$	−21.1865	−	79.0692i	−0.745340	−	2.78165i
$809$	−17.6705	−	10.2021i	−0.621263	−	0.358686i	0.156097	−	0.987742i	$-0.450109\pi$
$809$	−17.6705	−	10.2021i	−0.621263	−	0.358686i	−0.777361	+	0.629055i	$0.783442\pi$
$810$		0			0
$811$	19.0000	+	19.0000i	0.667180	+	0.667180i	0.957062	−	0.289882i	$-0.0936161\pi$
$811$	19.0000	+	19.0000i	0.667180	+	0.667180i	−0.289882	+	0.957062i	$0.593616\pi$
$812$	7.55743	−	28.2047i	0.265214	−	0.989791i
$813$	3.18972	+	1.63929i	0.111868	+	0.0574925i
$814$	20.2679	−	20.2679i	0.710391	−	0.710391i
$815$		0			0
$816$	−6.78680	−	6.15389i	−0.237585	−	0.215429i
$817$	8.19615	−	2.19615i	0.286747	−	0.0768336i
$818$			27.8401i			0.973405i
$819$	14.6357	−	4.44942i	0.511411	−	0.155475i
$820$		0			0
$821$	−1.60396	−	5.98604i	−0.0559784	−	0.208914i	0.932272	−	0.361758i	$-0.117823\pi$
$821$	−1.60396	−	5.98604i	−0.0559784	−	0.208914i	−0.988250	+	0.152844i	$0.951157\pi$
$822$	−16.4330	+	18.1231i	−0.573168	+	0.632116i
$823$	7.73205	+	13.3923i	0.269522	+	0.466826i	0.968739	−	0.248084i	$-0.0798009\pi$
$823$	7.73205	+	13.3923i	0.269522	+	0.466826i	−0.699216	+	0.714910i	$0.746468\pi$
$824$	−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	−0.767382	−	0.641190i	$-0.778441\pi$
$827$	−3.62896	+	3.62896i	−0.126191	+	0.126191i	0.641190	+	0.767382i	$0.278441\pi$
$828$		0			0
$829$	20.6769	+	11.9378i	0.718139	+	0.414618i	0.814067	−	0.580771i	$-0.197249\pi$
$829$	20.6769	+	11.9378i	0.718139	+	0.414618i	−0.0959284	+	0.995388i	$0.530582\pi$
$830$		0			0
$831$	−6.07502	−	1.31347i	−0.210740	−	0.0455636i
$832$	17.0359	+	34.4545i	0.590614	+	1.19449i
$833$	10.7328			0.371868
$834$	−9.90862	+	0.484612i	−0.343108	+	0.0167807i
$835$		0			0
$836$	3.38587	+	5.86450i	0.117103	+	0.202828i
$837$	−4.79215	−	32.4524i	−0.165641	−	1.12172i
$838$	19.2942	+	5.16987i	0.666508	+	0.178590i
$839$	−2.02501	+	7.55743i	−0.0699110	+	0.260911i	−0.992031	−	0.125992i	$-0.959789\pi$
$839$	−2.02501	+	7.55743i	−0.0699110	+	0.260911i	0.922120	+	0.386903i	$0.126455\pi$
$840$		0			0
$841$	0.803848	+	1.39230i	0.0277189	+	0.0480105i
$842$	2.43414	+	1.40535i	0.0838859	+	0.0484316i
$843$	38.9017	−	1.90261i	1.33985	−	0.0655294i
$844$		−	45.5167i		−	1.56675i
$845$		0			0
$846$	62.6410	+	28.4152i	2.15364	+	0.976936i
$847$	−2.90192	−	10.8301i	−0.0997113	−	0.372128i
$848$	−5.69846	+	9.87002i	−0.195686	+	0.338938i
$849$	−13.0191	−	40.5497i	−0.446814	−	1.39166i
$850$		0			0
$851$		0			0
$852$	14.1482	−	27.5295i	0.484711	−	0.943145i
$853$	−20.6340	−	20.6340i	−0.706494	−	0.706494i	0.259302	−	0.965796i	$-0.416507\pi$
$853$	−20.6340	−	20.6340i	−0.706494	−	0.706494i	−0.965796	+	0.259302i	$0.916507\pi$
$854$	−20.5257	+	11.8505i	−0.702376	+	0.405517i
$855$		0			0
$856$	−17.9090	−	66.8372i	−0.612116	−	2.28445i
$857$			35.7621i			1.22161i	0.791781	+	0.610806i	$0.209154\pi$
$857$			35.7621i			1.22161i	−0.791781	+	0.610806i	$0.790846\pi$
$858$	6.38833	+	25.4144i	0.218094	+	0.867632i
$859$	23.1769			0.790786			0.395393	−	0.918512i	$-0.370608\pi$
$859$	23.1769			0.790786			0.395393	+	0.918512i	$0.370608\pi$
$860$		0			0
$861$	1.05553	−	1.16409i	0.0359725	−	0.0396721i
$862$	2.50962	+	4.34679i	0.0854780	+	0.148052i
$863$	12.0611	+	12.0611i	0.410563	+	0.410563i	0.881935	−	0.471371i	$-0.156241\pi$
$863$	12.0611	+	12.0611i	0.410563	+	0.410563i	−0.471371	+	0.881935i	$0.656241\pi$
$864$	9.74952	−	7.72737i	0.331685	−	0.262890i
$865$		0			0
$866$	−11.9395	−	11.9395i	−0.405721	−	0.405721i
$867$	6.56147	+	20.4366i	0.222839	+	0.694063i
$868$	−16.6603	+	28.8564i	−0.565486	+	0.979450i
$869$	3.38587	−	0.907241i	0.114858	−	0.0307760i
$870$		0			0
$871$	20.8564	+	23.7321i	0.706692	+	0.804130i
$872$	16.4432			0.556835
$873$	−6.37233	+	38.4921i	−0.215671	+	1.30276i
$874$		0			0
$875$		0			0
$876$	−46.8585	+	30.1982i	−1.58320	+	1.02030i
$877$	−11.2321	−	3.00962i	−0.379279	−	0.101628i	0.0641422	−	0.997941i	$-0.479569\pi$
$877$	−11.2321	−	3.00962i	−0.379279	−	0.101628i	−0.443422	+	0.896313i	$0.646236\pi$
$878$	10.9433	+	2.93225i	0.369318	+	0.0989586i
$879$	−32.0549	+	20.6579i	−1.08118	+	0.696775i
$880$		0			0
$881$	−13.5880	+	23.5350i	−0.457790	+	0.792916i	−0.998844	−	0.0480724i	$-0.984692\pi$
$881$	−13.5880	+	23.5350i	−0.457790	+	0.792916i	0.541054	+	0.840988i	$0.318026\pi$
$882$	5.86546	−	35.4303i	0.197500	−	1.19300i
$883$	−39.3731			−1.32501			−0.662505	−	0.749058i	$-0.730506\pi$
$883$	−39.3731			−1.32501			−0.662505	+	0.749058i	$0.730506\pi$
$884$	1.85897	−	28.8244i	0.0625239	−	0.969468i
$885$		0			0
$886$	68.3731	−	18.3205i	2.29704	−	0.615490i
$887$	−26.8438	+	46.4949i	−0.901328	+	1.56115i	−0.0755567	+	0.997142i	$0.524073\pi$
$887$	−26.8438	+	46.4949i	−0.901328	+	1.56115i	−0.825772	+	0.564005i	$0.809260\pi$
$888$	14.9982	+	46.7139i	0.503306	+	1.56761i
$889$	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
$893$	4.95725	+	8.58622i	0.165888	+	0.287327i
$894$	15.1249	−	16.6804i	0.505853	−	0.557878i
$895$		0			0
$896$	−29.3225			−0.979595
$897$		0			0
$898$		−	20.9808i		−	0.700137i
$899$	−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
$903$	−9.17688	+	17.8563i	−0.305387	+	0.594219i
$904$	−51.9449	−	13.9186i	−1.72766	−	0.462925i
$905$		0			0
$906$	−13.3813	−	41.6777i	−0.444562	−	1.38465i
$907$	−8.66025	+	15.0000i	−0.287559	+	0.498067i	−0.973227	−	0.229848i	$-0.926177\pi$
$907$	−8.66025	+	15.0000i	−0.287559	+	0.498067i	0.685668	+	0.727915i	$0.259510\pi$
$908$	15.1149	+	56.4094i	0.501604	+	1.87201i
$909$	−53.9308	−	24.4641i	−1.78877	−	0.811423i
$910$		0			0
$911$		−	9.25036i		−	0.306478i	−0.988189	−	0.153239i	$-0.951030\pi$
$911$		−	9.25036i		−	0.306478i	0.988189	−	0.153239i	$-0.0489705\pi$
$912$	−4.41323	+	0.215843i	−0.146137	+	0.00714727i
$913$	2.66025	+	1.53590i	0.0880416	+	0.0508308i
$914$	33.4495	+	57.9363i	1.10641	+	1.91636i
$915$		0			0
$916$	−13.8301	+	51.6147i	−0.456960	+	1.70540i
$917$	−1.23931	−	0.332073i	−0.0409257	−	0.0109660i
$918$	−26.4177	+	3.90102i	−0.871913	+	0.128753i
$919$	22.2942	+	38.6147i	0.735419	+	1.27378i	0.954539	+	0.298085i	$0.0963478\pi$
$919$	22.2942	+	38.6147i	0.735419	+	1.27378i	−0.219121	+	0.975698i	$0.570319\pi$
$920$		0			0
$921$	30.3186	−	1.48282i	0.999031	−	0.0488607i
$922$	−58.0333			−1.91123
$923$	16.9293	−	3.38587i	0.557236	−	0.111447i
$924$	−15.6603	−	3.38587i	−0.515185	−	0.111387i
$925$		0			0
$926$	−44.1378	−	25.4830i	−1.45046	−	0.837423i
$927$	2.02822	+	20.6854i	0.0666155	+	0.679398i
$928$	9.36603	−	9.36603i	0.307455	−	0.307455i
$929$	−47.3251	−	12.6807i	−1.55269	−	0.416041i	−0.622347	−	0.782742i	$-0.713821\pi$
$929$	−47.3251	−	12.6807i	−1.55269	−	0.416041i	−0.930339	+	0.366701i	$0.880487\pi$
$930$		0			0
$931$	3.66025	−	3.66025i	0.119960	−	0.119960i
$932$	−13.8755	−	24.0331i	−0.454509	−	0.787232i
$933$	4.99484	−	5.50854i	0.163524	−	0.180341i
$934$	18.8827	+	70.4711i	0.617860	+	2.30589i
$935$		0			0
$936$	−43.6892	−	10.1588i	−1.42803	−	0.332052i
$937$			37.0000i			1.20874i	0.796705	+	0.604369i	$0.206575\pi$
$937$			37.0000i			1.20874i	−0.796705	+	0.604369i	$0.793425\pi$
$938$	−28.6583	+	7.67898i	−0.935728	+	0.250727i
$939$	2.56622	+	2.32691i	0.0837455	+	0.0759358i
$940$		0			0
$941$	38.2408	−	38.2408i	1.24661	−	1.24661i	0.289407	−	0.957206i	$-0.406542\pi$
$941$	38.2408	−	38.2408i	1.24661	−	1.24661i	0.957206	−	0.289407i	$-0.0934582\pi$
$942$	56.0473	+	28.8044i	1.82612	+	0.938498i
$943$		0			0
$944$	8.34312	+	8.34312i	0.271546	+	0.271546i
$945$		0			0
$946$	−29.7846	−	17.1962i	−0.968381	−	0.559095i
$947$	10.6112	+	39.6016i	0.344818	+	1.28688i	0.892824	+	0.450405i	$0.148721\pi$
$947$	10.6112	+	39.6016i	0.344818	+	1.28688i	−0.548006	+	0.836475i	$0.684613\pi$
$948$	−2.73205	+	12.6362i	−0.0887329	+	0.410406i
$949$	−29.4545	−	9.96410i	−0.956133	−	0.323448i
$950$		0			0
$951$	−27.5859	+	1.34918i	−0.894535	+	0.0437500i
$952$	10.9019	+	6.29423i	0.353333	+	0.203997i
$953$	−37.9087	+	21.8866i	−1.22798	+	0.708976i	−0.966608	−	0.256261i	$-0.917509\pi$
$953$	−37.9087	+	21.8866i	−1.22798	+	0.708976i	−0.261375	+	0.965237i	$0.584176\pi$
$954$	11.6883	+	31.0963i	0.378423	+	1.00678i
$955$		0			0
$956$	9.70398	−	36.2158i	0.313849	−	1.17130i
$957$	14.1171	−	9.09782i	0.456340	−	0.294091i
$958$	−18.1699	+	10.4904i	−0.587042	+	0.338929i
$959$	4.17156	−	7.22536i	0.134707	−	0.233319i
$960$		0			0
$961$			8.85641i			0.285691i
$962$	−32.7083	+	49.0625i	−1.05456	+	1.58184i
$963$	−45.5877	−	20.6795i	−1.46904	−	0.666387i
$964$	26.9904	−	7.23205i	0.869302	−	0.232929i
$965$		0			0
$966$		0			0
$967$	−0.143594	+	0.143594i	−0.00461766	+	0.00461766i	−0.709412	−	0.704794i	$-0.751039\pi$
$967$	−0.143594	+	0.143594i	−0.00461766	+	0.00461766i	0.704794	+	0.709412i	$0.251039\pi$
$968$	−8.50916	+	31.7566i	−0.273495	+	1.02070i
$969$	−3.42345	−	1.75941i	−0.109977	−	0.0565205i
$970$		0			0
$971$	−45.5551	+	26.3013i	−1.46193	+	0.844047i	−0.999101	−	0.0423987i	$-0.986500\pi$
$971$	−45.5551	+	26.3013i	−1.46193	+	0.844047i	−0.462832	+	0.886446i	$0.653167\pi$
$972$	−1.01535	+	58.1681i	−0.0325673	+	1.86574i
$973$	3.26795	−	0.875644i	0.104766	−	0.0280719i
$974$	60.7025			1.94503
$975$		0			0
$976$	17.2487			0.552118
$977$	−28.3707	+	7.60192i	−0.907661	+	0.243207i	−0.682303	−	0.731069i	$-0.739022\pi$
$977$	−28.3707	+	7.60192i	−0.907661	+	0.243207i	−0.225357	+	0.974276i	$0.572355\pi$
$978$	−47.4770	−	43.0495i	−1.51815	−	1.37657i
$979$	−15.2487	+	8.80385i	−0.487351	+	0.281372i
$980$		0			0
$981$	7.55058	−	9.19222i	0.241071	−	0.293485i
$982$	−15.5096	+	57.8827i	−0.494932	+	1.84711i
$983$	−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
$987$	−22.9282	−	4.95725i	−0.729813	−	0.157791i
$988$	−9.19615	−	10.4641i	−0.292569	−	0.332907i
$989$		0			0
$990$		0			0
$991$	−12.7846	+	22.1436i	−0.406117	+	0.703414i	−0.994451	−	0.105203i	$-0.966451\pi$
$991$	−12.7846	+	22.1436i	−0.406117	+	0.703414i	0.588334	+	0.808618i	$0.299784\pi$
$992$	−13.0899	+	7.55743i	−0.415603	+	0.239949i
$993$	−18.3164	−	28.4216i	−0.581255	−	0.901931i
$994$	−4.19615	+	15.6603i	−0.133094	+	0.496713i
$995$		0			0
$996$	−9.52306	+	6.13719i	−0.301750	+	0.194464i
$997$	6.06218	−	3.50000i	0.191991	−	0.110846i	−0.400923	−	0.916112i	$-0.631311\pi$
$997$	6.06218	−	3.50000i	0.191991	−	0.110846i	0.592914	+	0.805266i	$0.297977\pi$
$998$	−13.0899	−	7.55743i	−0.414352	−	0.239226i
$999$	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.bp.f.449.2		8
3.2	odd	2	inner	975.2.bp.f.449.1		8
5.2	odd	4		39.2.k.b.20.2	yes	8
5.3	odd	4		975.2.bo.d.176.1		8
5.4	even	2		975.2.bp.e.449.1		8
13.2	odd	12		975.2.bp.e.899.2		8
15.2	even	4		39.2.k.b.20.1	yes	8
15.8	even	4		975.2.bo.d.176.2		8
15.14	odd	2		975.2.bp.e.449.2		8
20.7	even	4		624.2.cn.c.449.2		8
39.2	even	12		975.2.bp.e.899.1		8
60.47	odd	4		624.2.cn.c.449.1		8
65.2	even	12		39.2.k.b.2.1	✓	8
65.7	even	12		507.2.f.e.239.4		8
65.12	odd	4		507.2.k.d.488.1		8
65.17	odd	12		507.2.f.e.437.1		8
65.22	odd	12		507.2.f.f.437.4		8
65.28	even	12		975.2.bo.d.626.2		8
65.32	even	12		507.2.f.f.239.1		8
65.37	even	12		507.2.k.d.80.2		8
65.42	odd	12		507.2.k.e.89.1		8
65.47	even	4		507.2.k.f.188.1		8
65.54	odd	12	inner	975.2.bp.f.899.1		8
65.57	even	4		507.2.k.e.188.2		8
65.62	odd	12		507.2.k.f.89.2		8
195.2	odd	12		39.2.k.b.2.2	yes	8
195.17	even	12		507.2.f.e.437.4		8
195.32	odd	12		507.2.f.f.239.4		8
195.47	odd	4		507.2.k.f.188.2		8
195.62	even	12		507.2.k.f.89.1		8
195.77	even	4		507.2.k.d.488.2		8
195.107	even	12		507.2.k.e.89.2		8
195.119	even	12	inner	975.2.bp.f.899.2		8
195.122	odd	4		507.2.k.e.188.1		8
195.137	odd	12		507.2.f.e.239.1		8
195.152	even	12		507.2.f.f.437.1		8
195.158	odd	12		975.2.bo.d.626.1		8
195.167	odd	12		507.2.k.d.80.1		8
260.67	odd	12		624.2.cn.c.353.1		8
780.587	even	12		624.2.cn.c.353.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.k.b.2.1	✓	8	65.2	even	12
39.2.k.b.2.2	yes	8	195.2	odd	12
39.2.k.b.20.1	yes	8	15.2	even	4
39.2.k.b.20.2	yes	8	5.2	odd	4
507.2.f.e.239.1		8	195.137	odd	12
507.2.f.e.239.4		8	65.7	even	12
507.2.f.e.437.1		8	65.17	odd	12
507.2.f.e.437.4		8	195.17	even	12
507.2.f.f.239.1		8	65.32	even	12
507.2.f.f.239.4		8	195.32	odd	12
507.2.f.f.437.1		8	195.152	even	12
507.2.f.f.437.4		8	65.22	odd	12
507.2.k.d.80.1		8	195.167	odd	12
507.2.k.d.80.2		8	65.37	even	12
507.2.k.d.488.1		8	65.12	odd	4
507.2.k.d.488.2		8	195.77	even	4
507.2.k.e.89.1		8	65.42	odd	12
507.2.k.e.89.2		8	195.107	even	12
507.2.k.e.188.1		8	195.122	odd	4
507.2.k.e.188.2		8	65.57	even	4
507.2.k.f.89.1		8	195.62	even	12
507.2.k.f.89.2		8	65.62	odd	12
507.2.k.f.188.1		8	65.47	even	4
507.2.k.f.188.2		8	195.47	odd	4
624.2.cn.c.353.1		8	260.67	odd	12
624.2.cn.c.353.2		8	780.587	even	12
624.2.cn.c.449.1		8	60.47	odd	4
624.2.cn.c.449.2		8	20.7	even	4
975.2.bo.d.176.1		8	5.3	odd	4
975.2.bo.d.176.2		8	15.8	even	4
975.2.bo.d.626.1		8	195.158	odd	12
975.2.bo.d.626.2		8	65.28	even	12
975.2.bp.e.449.1		8	5.4	even	2
975.2.bp.e.449.2		8	15.14	odd	2
975.2.bp.e.899.1		8	39.2	even	12
975.2.bp.e.899.2		8	13.2	odd	12
975.2.bp.f.449.1		8	3.2	odd	2	inner
975.2.bp.f.449.2		8	1.1	even	1	trivial
975.2.bp.f.899.1		8	65.54	odd	12	inner
975.2.bp.f.899.2		8	195.119	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bp (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.31259 - 0.619657i) q^{2} +(1.16345 - 1.28311i) q^{3} +(3.23205 - 1.86603i) q^{4} +(1.89551 - 3.68825i) q^{6} +(-0.366025 + 1.36603i) q^{7} +(2.93225 - 2.93225i) q^{8} +(-0.292748 - 2.98568i) q^{9} +O(q^{10})\)	\(q+(2.31259 - 0.619657i) q^{2} +(1.16345 - 1.28311i) q^{3} +(3.23205 - 1.86603i) q^{4} +(1.89551 - 3.68825i) q^{6} +(-0.366025 + 1.36603i) q^{7} +(2.93225 - 2.93225i) q^{8} +(-0.292748 - 2.98568i) q^{9} +(-1.69293 + 0.453620i) q^{11} +(1.36603 - 6.31812i) q^{12} +(3.23205 - 1.59808i) q^{13} +3.38587i q^{14} +(1.23205 - 2.13397i) q^{16} +(1.85897 - 1.07328i) q^{17} +(-2.52711 - 6.72326i) q^{18} +(0.267949 - 1.00000i) q^{19} +(1.32691 + 2.05896i) q^{21} +(-3.63397 + 2.09808i) q^{22} +(-0.350863 - 7.17394i) q^{24} +(6.48415 - 5.69846i) q^{26} +(-4.17156 - 3.09808i) q^{27} +(1.36603 + 5.09808i) q^{28} +(-4.79122 - 2.76621i) q^{29} +(4.46410 + 4.46410i) q^{31} +(-0.619657 + 2.31259i) q^{32} +(-1.38761 + 2.69999i) q^{33} +(3.63397 - 3.63397i) q^{34} +(-6.51754 - 9.10360i) q^{36} +(-6.59808 + 1.76795i) q^{37} -2.47863i q^{38} +(1.70983 - 6.00637i) q^{39} +(-0.166037 - 0.619657i) q^{41} +(4.34444 + 3.93930i) q^{42} +(4.09808 + 7.09808i) q^{43} +(-4.62518 + 4.62518i) q^{44} +(-6.77174 + 6.77174i) q^{47} +(-1.30469 - 4.06364i) q^{48} +(4.33013 + 2.50000i) q^{49} +(0.785693 - 3.63397i) q^{51} +(7.46410 - 11.1962i) q^{52} -4.62518 q^{53} +(-11.5669 - 4.57965i) q^{54} +(2.93225 + 5.07880i) q^{56} +(-0.971364 - 1.50726i) q^{57} +(-12.7942 - 3.42820i) q^{58} +(-1.23931 + 4.62518i) q^{59} +(3.50000 + 6.06218i) q^{61} +(13.0899 + 7.55743i) q^{62} +(4.18567 + 0.692934i) q^{63} +10.6603i q^{64} +(-1.53590 + 7.10381i) q^{66} +(2.26795 + 8.46410i) q^{67} +(4.00552 - 6.93777i) q^{68} +(4.62518 + 1.23931i) q^{71} +(-9.61317 - 7.89635i) q^{72} +(-6.09808 - 6.09808i) q^{73} +(-14.1631 + 8.17709i) q^{74} +(-1.00000 - 3.73205i) q^{76} -2.47863i q^{77} +(0.232259 - 14.9498i) q^{78} -2.00000 q^{79} +(-8.82860 + 1.74811i) q^{81} +(-0.767949 - 1.33013i) q^{82} +(-1.23931 - 1.23931i) q^{83} +(8.13071 + 4.17862i) q^{84} +(13.8755 + 13.8755i) q^{86} +(-9.12372 + 2.92931i) q^{87} +(-3.63397 + 6.29423i) q^{88} +(9.70398 - 2.60017i) q^{89} +(1.00000 + 5.00000i) q^{91} +(10.9217 - 0.534160i) q^{93} +(-11.4641 + 19.8564i) q^{94} +(2.24637 + 3.48568i) q^{96} +(-12.5622 - 3.36603i) q^{97} +(11.5630 + 3.09828i) q^{98} +(1.84997 + 4.92177i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} + 12 q^{4} - 2 q^{6} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q + 6 * q^3 + 12 * q^4 - 2 * q^6 + 4 * q^7 - 4 * q^9	\( 8 q + 6 q^{3} + 12 q^{4} - 2 q^{6} + 4 q^{7} - 4 q^{9} + 4 q^{12} + 12 q^{13} - 4 q^{16} - 4 q^{18} + 16 q^{19} + 4 q^{21} - 36 q^{22} - 18 q^{24} + 4 q^{28} + 8 q^{31} - 20 q^{33} + 36 q^{34} - 36 q^{36} - 32 q^{37} + 14 q^{39} + 12 q^{42} + 12 q^{43} - 18 q^{48} + 32 q^{52} - 46 q^{54} + 16 q^{57} - 40 q^{58} + 28 q^{61} + 16 q^{63} - 40 q^{66} + 32 q^{67} - 24 q^{72} - 28 q^{73} - 8 q^{76} - 16 q^{78} - 16 q^{79} + 4 q^{81} - 20 q^{82} - 4 q^{84} - 6 q^{87} - 36 q^{88} + 8 q^{91} - 16 q^{93} - 64 q^{94} + 16 q^{96} - 52 q^{97} - 40 q^{99}+O(q^{100}) \) 8 * q + 6 * q^3 + 12 * q^4 - 2 * q^6 + 4 * q^7 - 4 * q^9 + 4 * q^12 + 12 * q^13 - 4 * q^16 - 4 * q^18 + 16 * q^19 + 4 * q^21 - 36 * q^22 - 18 * q^24 + 4 * q^28 + 8 * q^31 - 20 * q^33 + 36 * q^34 - 36 * q^36 - 32 * q^37 + 14 * q^39 + 12 * q^42 + 12 * q^43 - 18 * q^48 + 32 * q^52 - 46 * q^54 + 16 * q^57 - 40 * q^58 + 28 * q^61 + 16 * q^63 - 40 * q^66 + 32 * q^67 - 24 * q^72 - 28 * q^73 - 8 * q^76 - 16 * q^78 - 16 * q^79 + 4 * q^81 - 20 * q^82 - 4 * q^84 - 6 * q^87 - 36 * q^88 + 8 * q^91 - 16 * q^93 - 64 * q^94 + 16 * q^96 - 52 * q^97 - 40 * q^99

Introduction

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