LMFDB - Embedded newform 525.2.bf.g.32.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(32,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

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

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

chi := DirichletCharacter("525.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bf (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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			32.13
Character	$\chi$	$=$	525.32
Dual form			525.2.bf.g.443.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.05572 + 0.282878i) q^{2} +(0.652459 - 1.60446i) q^{3} +(-0.697534 - 0.402722i) q^{4} +(1.14268 - 1.50929i) q^{6} +(-2.58881 + 0.545957i) q^{7} +(-2.16815 - 2.16815i) q^{8} +(-2.14860 - 2.09369i) q^{9} +O(q^{10})$	\(q+(1.05572 + 0.282878i) q^{2} +(0.652459 - 1.60446i) q^{3} +(-0.697534 - 0.402722i) q^{4} +(1.14268 - 1.50929i) q^{6} +(-2.58881 + 0.545957i) q^{7} +(-2.16815 - 2.16815i) q^{8} +(-2.14860 - 2.09369i) q^{9} +(-3.85168 - 2.22377i) q^{11} +(-1.10126 + 0.856408i) q^{12} +(0.728174 - 0.728174i) q^{13} +(-2.88749 - 0.155942i) q^{14} +(-0.870187 - 1.50721i) q^{16} +(0.535291 + 1.99773i) q^{17} +(-1.67605 - 2.81813i) q^{18} +(2.10724 - 1.21661i) q^{19} +(-0.813123 + 4.50986i) q^{21} +(-3.43722 - 3.43722i) q^{22} +(0.435895 - 1.62678i) q^{23} +(-4.89335 + 2.06409i) q^{24} +(0.974730 - 0.562761i) q^{26} +(-4.76112 + 2.08129i) q^{27} +(2.02565 + 0.661745i) q^{28} +9.39666 q^{29} +(4.76201 - 8.24805i) q^{31} +(1.09488 + 4.08616i) q^{32} +(-6.08101 + 4.72895i) q^{33} +2.26046i q^{34} +(0.655544 + 2.32571i) q^{36} +(-0.266530 + 0.994704i) q^{37} +(2.56880 - 0.688308i) q^{38} +(-0.693224 - 1.64343i) q^{39} -4.34602i q^{41} +(-2.13417 + 4.53112i) q^{42} +(1.05639 - 1.05639i) q^{43} +(1.79112 + 3.10231i) q^{44} +(0.920363 - 1.59412i) q^{46} +(-11.0874 - 2.97086i) q^{47} +(-2.98602 + 0.412791i) q^{48} +(6.40386 - 2.82676i) q^{49} +(3.55454 + 0.444584i) q^{51} +(-0.801178 + 0.214675i) q^{52} +(-8.97595 + 2.40510i) q^{53} +(-5.61514 + 0.850437i) q^{54} +(6.79665 + 4.42921i) q^{56} +(-0.577125 - 4.17477i) q^{57} +(9.92021 + 2.65811i) q^{58} +(-2.98943 + 5.17784i) q^{59} +(-4.99108 - 8.64480i) q^{61} +(7.36053 - 7.36053i) q^{62} +(6.70537 + 4.24712i) q^{63} +8.10429i q^{64} +(-7.75754 + 3.27225i) q^{66} +(10.2474 - 2.74579i) q^{67} +(0.431146 - 1.60906i) q^{68} +(-2.32571 - 1.76079i) q^{69} +2.85415i q^{71} +(0.119042 + 9.19792i) q^{72} +(0.547494 + 2.04328i) q^{73} +(-0.562761 + 0.974730i) q^{74} -1.95983 q^{76} +(11.1853 + 3.65405i) q^{77} +(-0.266957 - 1.93109i) q^{78} +(11.9404 - 6.89380i) q^{79} +(0.232921 + 8.99699i) q^{81} +(1.22939 - 4.58816i) q^{82} +(-2.87386 - 2.87386i) q^{83} +(2.38340 - 2.81832i) q^{84} +(1.41408 - 0.816417i) q^{86} +(6.13094 - 15.0766i) q^{87} +(3.52956 + 13.1725i) q^{88} +(-5.19347 - 8.99535i) q^{89} +(-1.48755 + 2.28266i) q^{91} +(-0.959192 + 0.959192i) q^{92} +(-10.1267 - 13.0220i) q^{93} +(-10.8647 - 6.27276i) q^{94} +(7.27046 + 0.909353i) q^{96} +(12.3520 + 12.3520i) q^{97} +(7.56029 - 1.17274i) q^{98} +(3.61981 + 12.8422i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 16 q^{6}+O(q^{10}) $ 80 * q + 16 * q^6	$ 80 q + 16 q^{6} + 72 q^{16} + 44 q^{21} + 72 q^{31} - 240 q^{36} - 92 q^{51} - 24 q^{61} - 216 q^{66} - 208 q^{76} - 20 q^{81} - 40 q^{91} - 156 q^{96}+O(q^{100}) $ 80 * q + 16 * q^6 + 72 * q^16 + 44 * q^21 + 72 * q^31 - 240 * q^36 - 92 * q^51 - 24 * q^61 - 216 * q^66 - 208 * q^76 - 20 * q^81 - 40 * q^91 - 156 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.05572	+	0.282878i	0.746504	+	0.200025i	0.611967	−	0.790883i	$-0.290379\pi$
$2$	1.05572	+	0.282878i	0.746504	+	0.200025i	0.134537	+	0.990909i	$0.457045\pi$
$3$	0.652459	−	1.60446i	0.376697	−	0.926336i
$3$	0.652459	−	1.60446i	0.376697	−	0.926336i
$4$	−0.697534	−	0.402722i	−0.348767	−	0.201361i
$5$		0			0
$5$		0			0
$6$	1.14268	−	1.50929i	0.466497	−	0.616165i
$7$	−2.58881	+	0.545957i	−0.978478	+	0.206352i
$7$	−2.58881	+	0.545957i	−0.978478	+	0.206352i
$8$	−2.16815	−	2.16815i	−0.766558	−	0.766558i
$9$	−2.14860	−	2.09369i	−0.716198	−	0.697897i
$10$		0			0
$11$	−3.85168	−	2.22377i	−1.16132	−	0.670491i	−0.209703	−	0.977765i	$-0.567250\pi$
$11$	−3.85168	−	2.22377i	−1.16132	−	0.670491i	−0.951621	+	0.307274i	$0.900583\pi$
$12$	−1.10126	+	0.856408i	−0.317908	+	0.247224i
$13$	0.728174	−	0.728174i	0.201959	−	0.201959i	−0.598880	−	0.800839i	$-0.704387\pi$
$13$	0.728174	−	0.728174i	0.201959	−	0.201959i	0.800839	+	0.598880i	$0.204387\pi$
$14$	−2.88749	−	0.155942i	−0.771713	−	0.0416772i
$15$		0			0
$16$	−0.870187	−	1.50721i	−0.217547	−	0.376802i
$17$	0.535291	+	1.99773i	0.129827	+	0.484521i	0.999966	−	0.00828584i	$-0.00263749\pi$
$17$	0.535291	+	1.99773i	0.129827	+	0.484521i	−0.870139	+	0.492807i	$0.835971\pi$
$18$	−1.67605	−	2.81813i	−0.395048	−	0.664240i
$19$	2.10724	−	1.21661i	0.483434	−	0.279110i	−0.238413	−	0.971164i	$-0.576627\pi$
$19$	2.10724	−	1.21661i	0.483434	−	0.279110i	0.721846	+	0.692053i	$0.243294\pi$
$20$		0			0
$21$	−0.813123	+	4.50986i	−0.177438	+	0.984132i
$22$	−3.43722	−	3.43722i	−0.732818	−	0.732818i
$23$	0.435895	−	1.62678i	0.0908904	−	0.339208i	−0.905474	−	0.424402i	$-0.860484\pi$
$23$	0.435895	−	1.62678i	0.0908904	−	0.339208i	0.996364	+	0.0851942i	$0.0271511\pi$
$24$	−4.89335	+	2.06409i	−0.998851	+	0.421330i
$25$		0			0
$26$	0.974730	−	0.562761i	0.191160	−	0.110366i
$27$	−4.76112	+	2.08129i	−0.916277	+	0.400545i
$28$	2.02565	+	0.661745i	0.382812	+	0.125058i
$29$	9.39666			1.74492			0.872458	−	0.488688i	$-0.162525\pi$
$29$	9.39666			1.74492			0.872458	+	0.488688i	$0.162525\pi$
$30$		0			0
$31$	4.76201	−	8.24805i	0.855283	−	1.48139i	−0.0210991	−	0.999777i	$-0.506717\pi$
$31$	4.76201	−	8.24805i	0.855283	−	1.48139i	0.876382	−	0.481616i	$-0.159950\pi$
$32$	1.09488	+	4.08616i	0.193550	+	0.722338i
$33$	−6.08101	+	4.72895i	−1.05857	+	0.823205i
$34$			2.26046i			0.387666i
$35$		0			0
$36$	0.655544	+	2.32571i	0.109257	+	0.387618i
$37$	−0.266530	+	0.994704i	−0.0438173	+	0.163528i	−0.984368	−	0.176126i	$-0.943643\pi$
$37$	−0.266530	+	0.994704i	−0.0438173	+	0.163528i	0.940550	+	0.339654i	$0.110310\pi$
$38$	2.56880	−	0.688308i	0.416714	−	0.111658i
$39$	−0.693224	−	1.64343i	−0.111005	−	0.263160i
$40$		0			0
$41$		−	4.34602i		−	0.678734i	−0.940654	−	0.339367i	$-0.889787\pi$
$41$		−	4.34602i		−	0.678734i	0.940654	−	0.339367i	$-0.110213\pi$
$42$	−2.13417	+	4.53112i	−0.329309	+	0.699166i
$43$	1.05639	−	1.05639i	0.161098	−	0.161098i	−0.621955	−	0.783053i	$-0.713661\pi$
$43$	1.05639	−	1.05639i	0.161098	−	0.161098i	0.783053	+	0.621955i	$0.213661\pi$
$44$	1.79112	+	3.10231i	0.270021	+	0.467690i
$45$		0			0
$46$	0.920363	−	1.59412i	0.135700	−	0.235039i
$47$	−11.0874	−	2.97086i	−1.61726	−	0.433344i	−0.667066	−	0.744999i	$-0.732450\pi$
$47$	−11.0874	−	2.97086i	−1.61726	−	0.433344i	−0.950195	+	0.311655i	$0.899117\pi$
$48$	−2.98602	+	0.412791i	−0.430995	+	0.0595812i
$49$	6.40386	−	2.82676i	0.914837	−	0.403823i
$50$		0			0
$51$	3.55454	+	0.444584i	0.497735	+	0.0622543i
$52$	−0.801178	+	0.214675i	−0.111103	+	0.0297701i
$53$	−8.97595	+	2.40510i	−1.23294	+	0.330366i	−0.815724	−	0.578441i	$-0.803661\pi$
$53$	−8.97595	+	2.40510i	−1.23294	+	0.330366i	−0.417218	+	0.908807i	$0.636995\pi$
$54$	−5.61514	+	0.850437i	−0.764124	+	0.115730i
$55$		0			0
$56$	6.79665	+	4.42921i	0.908241	+	0.591879i
$57$	−0.577125	−	4.17477i	−0.0764421	−	0.552962i
$58$	9.92021	+	2.65811i	1.30259	+	0.349027i
$59$	−2.98943	+	5.17784i	−0.389190	+	0.674097i	−0.992341	−	0.123530i	$-0.960578\pi$
$59$	−2.98943	+	5.17784i	−0.389190	+	0.674097i	0.603151	+	0.797627i	$0.293912\pi$
$60$		0			0
$61$	−4.99108	−	8.64480i	−0.639042	−	1.10685i	−0.985643	−	0.168841i	$-0.945998\pi$
$61$	−4.99108	−	8.64480i	−0.639042	−	1.10685i	0.346601	−	0.938013i	$-0.387336\pi$
$62$	7.36053	−	7.36053i	0.934788	−	0.934788i
$63$	6.70537	+	4.24712i	0.844797	+	0.535087i
$64$			8.10429i			1.01304i
$65$		0			0
$66$	−7.75754	+	3.27225i	−0.954887	+	0.402786i
$67$	10.2474	−	2.74579i	1.25192	−	0.335452i	0.428845	−	0.903378i	$-0.358921\pi$
$67$	10.2474	−	2.74579i	1.25192	−	0.335452i	0.823080	+	0.567926i	$0.192254\pi$
$68$	0.431146	−	1.60906i	0.0522842	−	0.195127i
$69$	−2.32571	−	1.76079i	−0.279982	−	0.211974i
$70$		0			0
$71$			2.85415i			0.338726i	0.985554	+	0.169363i	$0.0541710\pi$
$71$			2.85415i			0.338726i	−0.985554	+	0.169363i	$0.945829\pi$
$72$	0.119042	+	9.19792i	0.0140292	+	1.08399i
$73$	0.547494	+	2.04328i	0.0640793	+	0.239147i	0.990536	−	0.137255i	$-0.0438278\pi$
$73$	0.547494	+	2.04328i	0.0640793	+	0.239147i	−0.926456	+	0.376402i	$0.877161\pi$
$74$	−0.562761	+	0.974730i	−0.0654196	+	0.113310i
$75$		0			0
$76$	−1.95983			−0.224808
$77$	11.1853	+	3.65405i	1.27469	+	0.416418i
$78$	−0.266957	−	1.93109i	−0.0302269	−	0.218653i
$79$	11.9404	−	6.89380i	1.34340	−	0.775613i	0.356096	−	0.934449i	$-0.384108\pi$
$79$	11.9404	−	6.89380i	1.34340	−	0.775613i	0.987305	+	0.158836i	$0.0507742\pi$
$80$		0			0
$81$	0.232921	+	8.99699i	0.0258801	+	0.999665i
$82$	1.22939	−	4.58816i	0.135764	−	0.506678i
$83$	−2.87386	−	2.87386i	−0.315448	−	0.315448i	0.531568	−	0.847016i	$-0.321603\pi$
$83$	−2.87386	−	2.87386i	−0.315448	−	0.315448i	−0.847016	+	0.531568i	$0.821603\pi$
$84$	2.38340	−	2.81832i	0.260050	−	0.307504i
$85$		0			0
$86$	1.41408	−	0.816417i	0.152484	−	0.0880365i
$87$	6.13094	−	15.0766i	0.657305	−	1.61638i
$88$	3.52956	+	13.1725i	0.376252	+	1.40419i
$89$	−5.19347	−	8.99535i	−0.550506	−	0.953505i	−0.998238	−	0.0593369i	$-0.981101\pi$
$89$	−5.19347	−	8.99535i	−0.550506	−	0.953505i	0.447732	−	0.894168i	$-0.352232\pi$
$90$		0			0
$91$	−1.48755	+	2.28266i	−0.155938	+	0.239287i
$92$	−0.959192	+	0.959192i	−0.100003	+	0.100003i
$93$	−10.1267	−	13.0220i	−1.05009	−	1.35032i
$94$	−10.8647	−	6.27276i	−1.12061	−	0.646986i
$95$		0			0
$96$	7.27046	+	0.909353i	0.742038	+	0.0928105i
$97$	12.3520	+	12.3520i	1.25415	+	1.25415i	0.953841	+	0.300312i	$0.0970909\pi$
$97$	12.3520	+	12.3520i	1.25415	+	1.25415i	0.300312	+	0.953841i	$0.402909\pi$
$98$	7.56029	−	1.17274i	0.763704	−	0.118465i
$99$	3.61981	+	12.8422i	0.363805	+	1.29069i
$100$		0			0
$101$	5.85887	+	3.38262i	0.582979	+	0.336583i	0.762317	−	0.647204i	$-0.224062\pi$
$101$	5.85887	+	3.38262i	0.582979	+	0.336583i	−0.179337	+	0.983788i	$0.557395\pi$
$102$	3.62682	+	1.47486i	0.359109	+	0.146033i
$103$	−1.34753	−	0.361070i	−0.132776	−	0.0355773i	0.191819	−	0.981430i	$-0.438561\pi$
$103$	−1.34753	−	0.361070i	−0.132776	−	0.0355773i	−0.324595	+	0.945853i	$0.605228\pi$
$104$	−3.15759			−0.309627
$105$		0			0
$106$	−10.1564			−0.986478
$107$	1.95004	+	0.522512i	0.188518	+	0.0505132i	0.351843	−	0.936059i	$-0.385555\pi$
$107$	1.95004	+	0.522512i	0.188518	+	0.0505132i	−0.163325	+	0.986572i	$0.552222\pi$
$108$	4.15922	+	0.465632i	0.400221	+	0.0448055i
$109$	3.00677	+	1.73596i	0.287996	+	0.166275i	0.637038	−	0.770833i	$-0.280160\pi$
$109$	3.00677	+	1.73596i	0.287996	+	0.166275i	−0.349042	+	0.937107i	$0.613493\pi$
$110$		0			0
$111$	1.42207	+	1.07664i	0.134976	+	0.102190i
$112$	3.07562	+	3.42679i	0.290619	+	0.323801i
$113$	12.8909	+	12.8909i	1.21267	+	1.21267i	0.970145	+	0.242525i	$0.0779755\pi$
$113$	12.8909	+	12.8909i	1.21267	+	1.21267i	0.242525	+	0.970145i	$0.422024\pi$
$114$	0.571672	−	4.57063i	0.0535420	−	0.428079i
$115$		0			0
$116$	−6.55450	−	3.78424i	−0.608570	−	0.351358i
$117$	−3.08912	+	0.0399801i	−0.285589	+	0.00369617i
$118$	−4.62068	+	4.62068i	−0.425369	+	0.425369i
$119$	−2.47644	−	4.87950i	−0.227015	−	0.447303i
$120$		0			0
$121$	4.39027	+	7.60418i	0.399116	+	0.691289i
$122$	−2.82373	−	10.5383i	−0.255649	−	0.954095i
$123$	−6.97302	−	2.83560i	−0.628736	−	0.255677i
$124$	−6.64334	+	3.83553i	−0.596589	+	0.344441i
$125$		0			0
$126$	5.87755	+	6.38056i	0.523613	+	0.568425i
$127$	−10.8677	−	10.8677i	−0.964350	−	0.964350i	0.0350358	−	0.999386i	$-0.488845\pi$
$127$	−10.8677	−	10.8677i	−0.964350	−	0.964350i	−0.999386	+	0.0350358i	$0.988845\pi$
$128$	−0.102761	+	0.383510i	−0.00908289	+	0.0338978i
$129$	−1.00569	−	2.38419i	−0.0885456	−	0.209916i
$130$		0			0
$131$	−11.9389	+	6.89295i	−1.04311	+	0.602239i	−0.920712	−	0.390242i	$-0.872391\pi$
$131$	−11.9389	+	6.89295i	−1.04311	+	0.602239i	−0.122397	+	0.992481i	$0.539058\pi$
$132$	6.14616	−	0.849652i	0.534955	−	0.0739528i
$133$	−4.79102	+	4.30004i	−0.415434	+	0.372861i
$134$	11.5951			1.00167
$135$		0			0
$136$	3.17080	−	5.49198i	0.271894	−	0.470933i
$137$	−2.63799	−	9.84511i	−0.225379	−	0.841125i	−0.982252	−	0.187564i	$-0.939941\pi$
$137$	−2.63799	−	9.84511i	−0.225379	−	0.841125i	0.756874	−	0.653561i	$-0.226726\pi$
$138$	−1.95720	−	2.51678i	−0.166608	−	0.214243i
$139$		−	10.4292i		−	0.884591i	−0.896869	−	0.442295i	$-0.854164\pi$
$139$		−	10.4292i		−	0.884591i	0.896869	−	0.442295i	$-0.145836\pi$
$140$		0			0
$141$	−12.0007	+	15.8509i	−1.01064	+	1.33489i
$142$	−0.807378	+	3.01318i	−0.0677537	+	0.252860i
$143$	−4.42398	+	1.18540i	−0.369952	+	0.0991283i
$144$	−1.28595	+	5.06028i	−0.107162	+	0.421690i
$145$		0			0
$146$			2.31199i			0.191342i
$147$	−0.357170	−	12.1191i	−0.0294589	−	0.999566i
$148$	0.586503	−	0.586503i	0.0482103	−	0.0482103i
$149$	−5.41281	−	9.37526i	−0.443435	−	0.768051i	0.554507	−	0.832179i	$-0.312907\pi$
$149$	−5.41281	−	9.37526i	−0.443435	−	0.768051i	−0.997942	+	0.0641278i	$0.979573\pi$
$150$		0			0
$151$	−7.00027	+	12.1248i	−0.569674	+	0.986704i	0.426924	+	0.904287i	$0.359597\pi$
$151$	−7.00027	+	12.1248i	−0.569674	+	0.986704i	−0.996598	+	0.0824166i	$0.973736\pi$
$152$	−7.20662	−	1.93101i	−0.584534	−	0.156625i
$153$	3.03251	−	5.41305i	0.245164	−	0.437619i
$154$	10.7749	+	7.02173i	0.868265	+	0.565827i
$155$		0			0
$156$	−0.178298	+	1.42553i	−0.0142753	+	0.114133i
$157$	7.65525	−	2.05122i	0.610955	−	0.163705i	0.0599425	−	0.998202i	$-0.480908\pi$
$157$	7.65525	−	2.05122i	0.610955	−	0.163705i	0.551013	+	0.834497i	$0.314242\pi$
$158$	14.5558	−	3.90021i	1.15800	−	0.310284i
$159$	−1.99755	+	15.9708i	−0.158416	+	1.26657i
$160$		0			0
$161$	−0.240295	+	4.44941i	−0.0189379	+	0.350663i
$162$	−2.29915	+	9.56415i	−0.180639	+	0.751431i
$163$	4.05688	+	1.08704i	0.317760	+	0.0851434i	0.414174	−	0.910198i	$-0.364071\pi$
$163$	4.05688	+	1.08704i	0.317760	+	0.0851434i	−0.0964140	+	0.995341i	$0.530737\pi$
$164$	−1.75024	+	3.03150i	−0.136671	+	0.236720i
$165$		0			0
$166$	−2.22103	−	3.84694i	−0.172385	−	0.298580i
$167$	−13.8451	+	13.8451i	−1.07137	+	1.07137i	−0.0741166	+	0.997250i	$0.523614\pi$
$167$	−13.8451	+	13.8451i	−1.07137	+	1.07137i	−0.997250	+	0.0741166i	$0.976386\pi$
$168$	11.5410	−	8.01509i	0.890411	−	0.618377i
$169$			11.9395i			0.918425i
$170$		0			0
$171$	−7.07481	−	1.79789i	−0.541025	−	0.137488i
$172$	−1.16230	+	0.311437i	−0.0886244	+	0.0237468i
$173$	1.86235	−	6.95037i	0.141592	−	0.528427i	−0.858292	−	0.513162i	$-0.828474\pi$
$173$	1.86235	−	6.95037i	0.141592	−	0.528427i	0.999883	−	0.0152651i	$-0.00485921\pi$
$174$	10.7374	−	14.1823i	0.813998	−	1.07516i
$175$		0			0
$176$			7.74037i			0.583452i
$177$	6.35717	+	8.17475i	0.477834	+	0.614452i
$178$	−2.93824	−	10.9657i	−0.220230	−	0.821910i
$179$	−0.603111	+	1.04462i	−0.0450787	+	0.0780785i	−0.887684	−	0.460452i	$-0.847687\pi$
$179$	−0.603111	+	1.04462i	−0.0450787	+	0.0780785i	0.842606	+	0.538531i	$0.181021\pi$
$180$		0			0
$181$	−5.19945			−0.386472			−0.193236	−	0.981152i	$-0.561898\pi$
$181$	−5.19945			−0.386472			−0.193236	+	0.981152i	$0.561898\pi$
$182$	−2.21615	+	1.98904i	−0.164272	+	0.147437i
$183$	−17.1267	+	2.36762i	−1.26604	+	0.175019i
$184$	−4.47220	+	2.58203i	−0.329695	+	0.190349i
$185$		0			0
$186$	−7.00725	−	16.6121i	−0.513796	−	1.21806i
$187$	2.38072	−	8.88498i	0.174096	−	0.649734i
$188$	6.53740	+	6.53740i	0.476789	+	0.476789i
$189$	11.1893	−	7.98743i	0.813903	−	0.581000i
$190$		0			0
$191$	14.5157	−	8.38063i	1.05032	−	0.606401i	0.127579	−	0.991828i	$-0.459279\pi$
$191$	14.5157	−	8.38063i	1.05032	−	0.606401i	0.922738	+	0.385427i	$0.125946\pi$
$192$	13.0030	+	5.28772i	0.938413	+	0.381608i
$193$	−0.853891	−	3.18676i	−0.0614644	−	0.229388i	0.928360	−	0.371682i	$-0.121219\pi$
$193$	−0.853891	−	3.18676i	−0.0614644	−	0.229388i	−0.989824	+	0.142294i	$0.954552\pi$
$194$	9.54608	+	16.5343i	0.685368	+	1.18709i
$195$		0			0
$196$	−5.60531	−	0.607212i	−0.400379	−	0.0433723i
$197$	−6.81742	+	6.81742i	−0.485721	+	0.485721i	−0.906953	−	0.421232i	$-0.861598\pi$
$197$	−6.81742	+	6.81742i	−0.485721	+	0.485721i	0.421232	+	0.906953i	$0.361598\pi$
$198$	0.188719	+	14.5817i	0.0134117	+	1.03627i
$199$	−6.12618	−	3.53695i	−0.434273	−	0.250728i	0.266892	−	0.963726i	$-0.414003\pi$
$199$	−6.12618	−	3.53695i	−0.434273	−	0.250728i	−0.701165	+	0.712999i	$0.747337\pi$
$200$		0			0
$201$	2.28051	−	18.2331i	0.160855	−	1.28607i
$202$	5.22843	+	5.22843i	0.367871	+	0.367871i
$203$	−24.3262	+	5.13018i	−1.70736	+	0.360068i
$204$	−2.30037	−	1.74160i	−0.161058	−	0.121937i
$205$		0			0
$206$	−1.32047	−	0.762376i	−0.0920017	−	0.0531172i
$207$	−4.34254	+	2.58267i	−0.301827	+	0.179508i
$208$	−1.73116	−	0.463862i	−0.120034	−	0.0321631i
$209$	−10.8219			−0.748564
$210$		0			0
$211$	13.1131			0.902745			0.451372	−	0.892336i	$-0.350935\pi$
$211$	13.1131			0.902745			0.451372	+	0.892336i	$0.350935\pi$
$212$	7.22962	+	1.93717i	0.496532	+	0.133045i
$213$	4.57938	+	1.86222i	0.313774	+	0.127597i
$214$	1.91088	+	1.10325i	0.130625	+	0.0754166i
$215$		0			0
$216$	14.8354	+	5.81027i	1.00942	+	0.395339i
$217$	−7.82486	+	23.9525i	−0.531186	+	1.62600i
$218$	2.68323	+	2.68323i	0.181731	+	0.181731i
$219$	3.63558	+	0.454720i	0.245669	+	0.0307271i
$220$		0			0
$221$	1.84448	+	1.06491i	0.124073	+	0.0716337i
$222$	1.19674	+	1.53890i	0.0803198	+	0.103284i
$223$	9.97114	−	9.97114i	0.667717	−	0.667717i	−0.289470	−	0.957187i	$-0.593479\pi$
$223$	9.97114	−	9.97114i	0.667717	−	0.667717i	0.957187	+	0.289470i	$0.0934790\pi$
$224$	−5.06532	−	9.98053i	−0.338441	−	0.666852i
$225$		0			0
$226$	9.96254	+	17.2556i	0.662698	+	1.14783i
$227$	−2.62406	−	9.79314i	−0.174165	−	0.649994i	−0.996692	−	0.0812676i	$-0.974103\pi$
$227$	−2.62406	−	9.79314i	−0.174165	−	0.649994i	0.822527	−	0.568726i	$-0.192564\pi$
$228$	−1.27871	+	3.14447i	−0.0846844	+	0.208248i
$229$	0.769340	−	0.444179i	0.0508394	−	0.0293522i	−0.474365	−	0.880328i	$-0.657322\pi$
$229$	0.769340	−	0.444179i	0.0508394	−	0.0293522i	0.525204	+	0.850976i	$0.323989\pi$
$230$		0			0
$231$	13.1608	−	15.5623i	0.865914	−	1.02393i
$232$	−20.3734	−	20.3734i	−1.33758	−	1.33758i
$233$	−2.33670	+	8.72070i	−0.153083	+	0.571312i	0.846179	+	0.532898i	$0.178897\pi$
$233$	−2.33670	+	8.72070i	−0.153083	+	0.571312i	−0.999262	+	0.0384138i	$0.987769\pi$
$234$	−3.27255	−	0.831638i	−0.213933	−	0.0543659i
$235$		0			0
$236$	4.17046	−	2.40781i	0.271474	−	0.156735i
$237$	−3.27021	−	23.6559i	−0.212423	−	1.53661i
$238$	−1.23412	−	5.85190i	−0.0799958	−	0.379322i
$239$	−3.80497			−0.246123			−0.123061	−	0.992399i	$-0.539271\pi$
$239$	−3.80497			−0.246123			−0.123061	+	0.992399i	$0.539271\pi$
$240$		0			0
$241$	11.6152	−	20.1180i	0.748198	−	1.29592i	−0.200488	−	0.979696i	$-0.564253\pi$
$241$	11.6152	−	20.1180i	0.748198	−	1.29592i	0.948686	−	0.316221i	$-0.102414\pi$
$242$	2.48383	+	9.26976i	0.159666	+	0.595883i
$243$	14.5873	+	5.49645i	0.935775	+	0.352597i
$244$			8.04006i			0.514712i
$245$		0			0
$246$	−6.55940	−	4.96610i	−0.418212	−	0.316627i
$247$	0.648529	−	2.42034i	0.0412649	−	0.154003i
$248$	−28.2078	+	7.55826i	−1.79120	+	0.479950i
$249$	−6.48608	+	2.73593i	−0.411039	+	0.173382i
$250$		0			0
$251$		−	17.3870i		−	1.09746i	−0.836001	−	0.548728i	$-0.815112\pi$
$251$		−	17.3870i		−	1.09746i	0.836001	−	0.548728i	$-0.184888\pi$
$252$	−2.96682	−	5.66291i	−0.186892	−	0.356730i
$253$	−5.29651	+	5.29651i	−0.332989	+	0.332989i
$254$	−8.39895	−	14.5474i	−0.526997	−	0.912786i
$255$		0			0
$256$	7.88732	−	13.6612i	0.492958	−	0.853828i
$257$	28.5609	+	7.65288i	1.78158	+	0.477373i	0.990871	−	0.134817i	$-0.0430446\pi$
$257$	28.5609	+	7.65288i	1.78158	+	0.477373i	0.790711	+	0.612190i	$0.209711\pi$
$258$	−0.387284	−	2.80151i	−0.0241112	−	0.174414i
$259$	0.146930	−	2.72061i	0.00912976	−	0.169051i
$260$		0			0
$261$	−20.1896	−	19.6737i	−1.24971	−	1.21777i
$262$	−14.5540	+	3.89973i	−0.899148	+	0.240926i
$263$	13.2642	−	3.55414i	0.817907	−	0.219158i	0.174476	−	0.984661i	$-0.444177\pi$
$263$	13.2642	−	3.55414i	0.817907	−	0.219158i	0.643431	+	0.765504i	$0.277510\pi$
$264$	23.4376	+	2.93147i	1.44249	+	0.180419i
$265$		0			0
$266$	−6.27434	+	3.18435i	−0.384705	+	0.195245i
$267$	−17.8212	+	2.46362i	−1.09064	+	0.150771i
$268$	−8.25373	−	2.21158i	−0.504177	−	0.135094i
$269$	−12.3641	+	21.4152i	−0.753850	+	1.30571i	0.192094	+	0.981377i	$0.438472\pi$
$269$	−12.3641	+	21.4152i	−0.753850	+	1.30571i	−0.945944	+	0.324330i	$0.894861\pi$
$270$		0			0
$271$	6.56869	+	11.3773i	0.399019	+	0.691122i	0.993605	−	0.112910i	$-0.0360173\pi$
$271$	6.56869	+	11.3773i	0.399019	+	0.691122i	−0.594586	+	0.804032i	$0.702684\pi$
$272$	2.54520	−	2.54520i	0.154325	−	0.154325i
$273$	2.69187	+	3.87606i	0.162919	+	0.234590i
$274$		−	11.1399i		−	0.672984i
$275$		0			0
$276$	0.913154	+	2.16482i	0.0549654	+	0.130307i
$277$	−8.84604	+	2.37029i	−0.531507	+	0.142417i	−0.514584	−	0.857440i	$-0.672054\pi$
$277$	−8.84604	+	2.37029i	−0.531507	+	0.142417i	−0.0169230	+	0.999857i	$0.505387\pi$
$278$	2.95019	−	11.0102i	0.176940	−	0.660351i
$279$	−27.5005	+	7.75154i	−1.64641	+	0.464072i
$280$		0			0
$281$		−	17.5674i		−	1.04798i	−0.851723	−	0.523992i	$-0.824442\pi$
$281$		−	17.5674i		−	1.04798i	0.851723	−	0.523992i	$-0.175558\pi$
$282$	−17.1532	+	13.3393i	−1.02146	+	0.794346i
$283$	−6.60367	−	24.6452i	−0.392547	−	1.46501i	−0.825918	−	0.563790i	$-0.809343\pi$
$283$	−6.60367	−	24.6452i	−0.392547	−	1.46501i	0.433371	−	0.901216i	$-0.357324\pi$
$284$	1.14943	−	1.99087i	0.0682061	−	0.118136i
$285$		0			0
$286$	−5.00579			−0.295999
$287$	2.37274	+	11.2510i	0.140059	+	0.664126i
$288$	6.20270	−	11.0719i	0.365497	−	0.652415i
$289$	11.0180	−	6.36126i	0.648120	−	0.374192i
$290$		0			0
$291$	27.8774	−	11.7591i	1.63420	−	0.689332i
$292$	0.440976	−	1.64574i	0.0258061	−	0.0963098i
$293$	−3.30875	−	3.30875i	−0.193299	−	0.193299i	0.603821	−	0.797120i	$-0.293644\pi$
$293$	−3.30875	−	3.30875i	−0.193299	−	0.193299i	−0.797120	+	0.603821i	$0.793644\pi$
$294$	3.05116	−	12.8954i	0.177947	−	0.752073i
$295$		0			0
$296$	2.73455	−	1.57879i	0.158942	−	0.0917655i
$297$	22.9666	+	2.57115i	1.33266	+	0.149193i
$298$	−3.06233	−	11.4288i	−0.177396	−	0.662051i
$299$	−0.867173	−	1.50199i	−0.0501499	−	0.0868622i
$300$		0			0
$301$	−2.15805	+	3.31153i	−0.124388	+	0.190874i
$302$	−10.8201	+	10.8201i	−0.622629	+	0.622629i
$303$	9.24996	−	7.19331i	0.531396	−	0.413245i
$304$	−3.66738	−	2.11736i	−0.210339	−	0.121439i
$305$		0			0
$306$	4.73270	−	4.85681i	0.270551	−	0.277646i
$307$	−6.83669	−	6.83669i	−0.390191	−	0.390191i	0.484565	−	0.874755i	$-0.338978\pi$
$307$	−6.83669	−	6.83669i	−0.390191	−	0.390191i	−0.874755	+	0.484565i	$0.838978\pi$
$308$	−6.33059	−	7.05341i	−0.360719	−	0.401905i
$309$	−1.45853	+	1.92648i	−0.0829731	+	0.109594i
$310$		0			0
$311$	−17.7059	−	10.2225i	−1.00401	−	0.579665i	−0.0945773	−	0.995518i	$-0.530150\pi$
$311$	−17.7059	−	10.2225i	−1.00401	−	0.579665i	−0.909432	+	0.415852i	$0.863483\pi$
$312$	−2.06019	+	5.06623i	−0.116636	+	0.286819i
$313$	5.16189	+	1.38312i	0.291767	+	0.0781788i	0.401734	−	0.915757i	$-0.368408\pi$
$313$	5.16189	+	1.38312i	0.291767	+	0.0781788i	−0.109967	+	0.993935i	$0.535074\pi$
$314$	8.66201			0.488826
$315$		0			0
$316$	−11.1051			−0.624712
$317$	−3.12046	−	0.836124i	−0.175262	−	0.0469614i	0.170121	−	0.985423i	$-0.445584\pi$
$317$	−3.12046	−	0.836124i	−0.175262	−	0.0469614i	−0.345383	+	0.938462i	$0.612251\pi$
$318$	−6.62664	+	16.2956i	−0.371603	+	0.913810i
$319$	−36.1929	−	20.8960i	−2.02641	−	1.16995i
$320$		0			0
$321$	2.11067	−	2.78785i	0.117806	−	0.155603i
$322$	−1.51232	+	4.62934i	−0.0842785	+	0.257983i
$323$	3.55845	+	3.55845i	0.197998	+	0.197998i
$324$	3.46081	−	6.36951i	0.192267	−	0.353862i
$325$		0			0
$326$	3.97542	+	2.29521i	0.220178	+	0.127120i
$327$	4.74707	−	3.69160i	0.262514	−	0.204146i
$328$	−9.42284	+	9.42284i	−0.520289	+	0.520289i
$329$	30.3251	+	1.63774i	1.67188	+	0.0902914i
$330$		0			0
$331$	14.2422	+	24.6682i	0.782822	+	1.35589i	0.930292	+	0.366821i	$0.119554\pi$
$331$	14.2422	+	24.6682i	0.782822	+	1.35589i	−0.147470	+	0.989067i	$0.547113\pi$
$332$	0.847252	+	3.16199i	0.0464990	+	0.173537i
$333$	2.65527	−	1.57919i	0.145508	−	0.0865388i
$334$	−18.5330	+	10.7000i	−1.01408	+	0.585479i
$335$		0			0
$336$	7.50487	−	2.69888i	0.409424	−	0.147236i
$337$	14.8944	+	14.8944i	0.811349	+	0.811349i	0.984836	−	0.173487i	$-0.0555036\pi$
$337$	14.8944	+	14.8944i	0.811349	+	0.811349i	−0.173487	+	0.984836i	$0.555504\pi$
$338$	−3.37743	+	12.6047i	−0.183708	+	0.685608i
$339$	29.0936	−	12.2721i	1.58015	−	0.666531i
$340$		0			0
$341$	−36.6835	+	21.1792i	−1.98652	+	1.14692i
$342$	−6.96041	−	3.89938i	−0.376376	−	0.210854i
$343$	−15.0351	+	10.8142i	−0.811818	+	0.583910i
$344$	−4.58082			−0.246981
$345$		0			0
$346$	3.93222	−	6.81080i	0.211397	−	0.366151i
$347$	−2.25181	−	8.40389i	−0.120884	−	0.451144i	0.878776	−	0.477235i	$-0.158361\pi$
$347$	−2.25181	−	8.40389i	−0.120884	−	0.451144i	−0.999660	+	0.0260905i	$0.991694\pi$
$348$	−10.3482	+	8.04738i	−0.554722	+	0.431385i
$349$			8.03952i			0.430346i	0.976576	+	0.215173i	$0.0690315\pi$
$349$			8.03952i			0.430346i	−0.976576	+	0.215173i	$0.930969\pi$
$350$		0			0
$351$	−1.95138	+	4.98246i	−0.104157	+	0.265944i
$352$	4.86953	−	18.1733i	0.259547	−	0.968642i
$353$	10.3932	−	2.78484i	0.553173	−	0.148222i	0.0286049	−	0.999591i	$-0.490894\pi$
$353$	10.3932	−	2.78484i	0.553173	−	0.148222i	0.524568	+	0.851369i	$0.324227\pi$
$354$	4.39891	+	10.4285i	0.233799	+	0.554270i
$355$		0			0
$356$			8.36609i			0.443402i
$357$	−9.44475	+	0.789683i	−0.499869	+	0.0417945i
$358$	−0.932215	+	0.932215i	−0.0492691	+	0.0492691i
$359$	9.72321	+	16.8411i	0.513171	+	0.888839i	0.999883	+	0.0152765i	$0.00486284\pi$
$359$	9.72321	+	16.8411i	0.513171	+	0.888839i	−0.486712	+	0.873563i	$0.661804\pi$
$360$		0			0
$361$	−6.53970	+	11.3271i	−0.344195	+	0.596163i
$362$	−5.48914	−	1.47081i	−0.288503	−	0.0773041i
$363$	15.0651	−	2.08261i	0.790712	−	0.109309i
$364$	1.95689	−	0.993162i	0.102569	−	0.0520558i
$365$		0			0
$366$	−18.7507	−	2.34525i	−0.980115	−	0.122588i
$367$	−27.0614	+	7.25109i	−1.41260	+	0.378504i	−0.882851	−	0.469653i	$-0.844379\pi$
$367$	−27.0614	+	7.25109i	−1.41260	+	0.378504i	−0.529745	+	0.848157i	$0.677712\pi$
$368$	−2.83121	+	0.758621i	−0.147587	+	0.0395458i
$369$	−9.09922	+	9.33784i	−0.473686	+	0.486108i
$370$		0			0
$371$	21.9239	−	11.1268i	1.13823	−	0.577676i
$372$	1.81946	+	13.1615i	0.0943347	+	0.682392i
$373$	4.96003	+	1.32904i	0.256821	+	0.0688149i	0.384932	−	0.922945i	$-0.374225\pi$
$373$	4.96003	+	1.32904i	0.256821	+	0.0688149i	−0.128111	+	0.991760i	$0.540892\pi$
$374$	5.02674	−	8.70656i	0.259926	−	0.450206i
$375$		0			0
$376$	17.5979	+	30.4804i	0.907541	+	1.57191i
$377$	6.84241	−	6.84241i	0.352402	−	0.352402i
$378$	14.0722	−	5.26725i	0.723797	−	0.270918i
$379$			15.5022i			0.796297i	0.917321	+	0.398148i	$0.130347\pi$
$379$			15.5022i			0.796297i	−0.917321	+	0.398148i	$0.869653\pi$
$380$		0			0
$381$	−24.5275	+	10.3461i	−1.25658	+	0.530045i
$382$	17.6951	−	4.74140i	0.905362	−	0.242591i
$383$	6.48458	−	24.2008i	0.331347	−	1.23660i	−0.576429	−	0.817147i	$-0.695554\pi$
$383$	6.48458	−	24.2008i	0.331347	−	1.23660i	0.907776	−	0.419455i	$-0.137779\pi$
$384$	0.548280	+	0.415101i	0.0279793	+	0.0211830i
$385$		0			0
$386$		−	3.60586i		−	0.183534i
$387$	−4.48150	+	0.0580007i	−0.227808	+	0.00294834i
$388$	−3.64152	−	13.5903i	−0.184870	−	0.689945i
$389$	4.26338	−	7.38439i	0.216162	−	0.374403i	−0.737469	−	0.675380i	$-0.763979\pi$
$389$	4.26338	−	7.38439i	0.216162	−	0.374403i	0.953631	+	0.300977i	$0.0973128\pi$
$390$		0			0
$391$	3.48321			0.176153
$392$	−20.0134	−	7.75570i	−1.01083	−	0.391722i
$393$	3.26981	+	23.6529i	0.164940	+	1.19313i
$394$	−9.12576	+	5.26876i	−0.459749	+	0.265436i
$395$		0			0
$396$	2.64688	−	10.4156i	0.133011	−	0.523406i
$397$	−1.86525	+	6.96120i	−0.0936141	+	0.349372i	−0.996806	−	0.0798651i	$-0.974551\pi$
$397$	−1.86525	+	6.96120i	−0.0936141	+	0.349372i	0.903192	+	0.429238i	$0.141218\pi$
$398$	−5.46698	−	5.46698i	−0.274035	−	0.274035i
$399$	3.77332	+	10.4926i	0.188902	+	0.525287i
$400$		0			0
$401$	−6.84251	+	3.95052i	−0.341698	+	0.197280i	−0.661023	−	0.750366i	$-0.729877\pi$
$401$	−6.84251	+	3.95052i	−0.341698	+	0.197280i	0.319324	+	0.947645i	$0.396544\pi$
$402$	7.56534	−	18.6039i	0.377325	−	0.927879i
$403$	−2.53844	−	9.47359i	−0.126449	−	0.471913i
$404$	−2.72451	−	4.71899i	−0.135549	−	0.234778i
$405$		0			0
$406$	−27.1327	−	1.46533i	−1.34658	−	0.0727232i
$407$	3.23858	−	3.23858i	0.160530	−	0.160530i
$408$	−6.74286	−	8.67071i	−0.333821	−	0.429264i
$409$	−22.2128	−	12.8246i	−1.09835	−	0.634135i	−0.162566	−	0.986698i	$-0.551977\pi$
$409$	−22.2128	−	12.8246i	−1.09835	−	0.634135i	−0.935788	+	0.352563i	$0.885310\pi$
$410$		0			0
$411$	−17.5173	−	2.19098i	−0.864064	−	0.108073i
$412$	0.794540	+	0.794540i	0.0391442	+	0.0391442i
$413$	4.91218	−	15.0365i	0.241712	−	0.739900i
$414$	−5.31507	+	1.49815i	−0.261221	+	0.0736302i
$415$		0			0
$416$	3.77270	+	2.17817i	0.184972	+	0.106794i
$417$	−16.7332	−	6.80461i	−0.819429	−	0.333223i
$418$	−11.4248	−	3.06127i	−0.558806	−	0.149732i
$419$	16.1468			0.788823			0.394412	−	0.918934i	$-0.370948\pi$
$419$	16.1468			0.788823			0.394412	+	0.918934i	$0.370948\pi$
$420$		0			0
$421$	3.49287			0.170232			0.0851160	−	0.996371i	$-0.472874\pi$
$421$	3.49287			0.170232			0.0851160	+	0.996371i	$0.472874\pi$
$422$	13.8437	+	3.70942i	0.673903	+	0.180572i
$423$	17.6022	+	29.5967i	0.855851	+	1.43904i
$424$	24.6759	+	14.2466i	1.19837	+	0.691877i
$425$		0			0
$426$	4.30774	+	3.26138i	0.208711	+	0.158014i
$427$	17.6406	+	19.6548i	0.853690	+	0.951163i
$428$	−1.14979	−	1.14979i	−0.0555774	−	0.0555774i
$429$	−0.984533	+	7.87153i	−0.0475337	+	0.380041i
$430$		0			0
$431$	26.7589	+	15.4493i	1.28893	+	0.744166i	0.978464	−	0.206418i	$-0.0661806\pi$
$431$	26.7589	+	15.4493i	1.28893	+	0.744166i	0.310469	+	0.950583i	$0.399514\pi$
$432$	7.28000	+	5.36488i	0.350259	+	0.258118i
$433$	−13.1840	+	13.1840i	−0.633582	+	0.633582i	−0.948965	−	0.315382i	$-0.897867\pi$
$433$	−13.1840	+	13.1840i	−0.633582	+	0.633582i	0.315382	+	0.948965i	$0.397867\pi$
$434$	−15.0365	+	23.0735i	−0.721774	+	1.10757i
$435$		0			0
$436$	−1.39822	−	2.42178i	−0.0669624	−	0.115982i
$437$	−1.06063	−	3.95833i	−0.0507369	−	0.189353i
$438$	3.70951	+	1.50848i	0.177247	+	0.0720780i
$439$	18.3366	−	10.5867i	0.875159	−	0.505273i	0.00609995	−	0.999981i	$-0.498058\pi$
$439$	18.3366	−	10.5867i	0.875159	−	0.505273i	0.869059	+	0.494708i	$0.164725\pi$
$440$		0			0
$441$	−19.6777	−	7.33414i	−0.937031	−	0.349245i
$442$	1.64601	+	1.64601i	0.0782927	+	0.0782927i
$443$	8.55398	−	31.9239i	0.406412	−	1.51675i	−0.395024	−	0.918671i	$-0.629264\pi$
$443$	8.55398	−	31.9239i	0.406412	−	1.51675i	0.801437	−	0.598080i	$-0.204069\pi$
$444$	−0.558353	−	1.32369i	−0.0264982	−	0.0628196i
$445$		0			0
$446$	13.3473	−	7.70608i	0.632014	−	0.364893i
$447$	−18.5739	+	2.56767i	−0.878514	+	0.121447i
$448$	−4.42460	−	20.9805i	−0.209043	−	0.991234i
$449$	4.61196			0.217652			0.108826	−	0.994061i	$-0.465291\pi$
$449$	4.61196			0.217652			0.108826	+	0.994061i	$0.465291\pi$
$450$		0			0
$451$	−9.66453	+	16.7395i	−0.455085	+	0.788230i
$452$	−3.80039	−	14.1832i	−0.178755	−	0.667124i
$453$	14.8864	+	19.1426i	0.699425	+	0.899398i
$454$		−	11.0811i		−	0.520060i
$455$		0			0
$456$	−7.80025	+	10.3028i	−0.365280	+	0.482475i
$457$	4.24682	−	15.8493i	0.198658	−	0.741401i	−0.792632	−	0.609701i	$-0.791290\pi$
$457$	4.24682	−	15.8493i	0.198658	−	0.741401i	0.991290	−	0.131700i	$-0.0420437\pi$
$458$	0.937853	−	0.251297i	0.0438230	−	0.0117423i
$459$	−6.70645	−	8.39734i	−0.313030	−	0.391954i
$460$		0			0
$461$			34.6764i			1.61504i	0.589841	+	0.807520i	$0.299191\pi$
$461$			34.6764i			1.61504i	−0.589841	+	0.807520i	$0.700809\pi$
$462$	18.2963	−	12.7065i	0.851220	−	0.591160i
$463$	12.3396	−	12.3396i	0.573472	−	0.573472i	−0.359625	−	0.933097i	$-0.617095\pi$
$463$	12.3396	−	12.3396i	0.573472	−	0.573472i	0.933097	+	0.359625i	$0.117095\pi$
$464$	−8.17686	−	14.1627i	−0.379601	−	0.657488i
$465$		0			0
$466$	−4.93379	+	8.54558i	−0.228554	+	0.395866i
$467$	−6.09334	−	1.63270i	−0.281966	−	0.0755526i	0.115064	−	0.993358i	$-0.463293\pi$
$467$	−6.09334	−	1.63270i	−0.281966	−	0.0755526i	−0.397030	+	0.917805i	$0.629959\pi$
$468$	2.17087	+	1.21617i	0.100349	+	0.0562174i
$469$	−25.0296	+	12.7030i	−1.15576	+	0.586570i
$470$		0			0
$471$	1.70363	−	13.6209i	0.0784993	−	0.627617i
$472$	17.7079	−	4.74481i	0.815071	−	0.218398i
$473$	−6.41803	+	1.71971i	−0.295101	+	0.0790721i
$474$	3.23931	−	25.8989i	0.148787	−	1.18958i
$475$		0			0
$476$	−0.237677	+	4.40094i	−0.0108939	+	0.201717i
$477$	24.3212	+	13.6253i	1.11359	+	0.623859i
$478$	−4.01696	−	1.07634i	−0.183732	−	0.0492308i
$479$	7.77601	−	13.4684i	0.355295	−	0.615389i	−0.631873	−	0.775072i	$-0.717714\pi$
$479$	7.77601	−	13.4684i	0.355295	−	0.615389i	0.987168	+	0.159683i	$0.0510471\pi$
$480$		0			0
$481$	0.530238	+	0.918398i	0.0241768	+	0.0418754i
$482$	17.9533	−	17.9533i	0.817749	−	0.817749i
$483$	6.98212	+	3.28860i	0.317698	+	0.149636i
$484$		−	7.07223i		−	0.321465i
$485$		0			0
$486$	13.8452	+	9.92912i	0.628032	+	0.450394i
$487$	−7.87188	+	2.10926i	−0.356709	+	0.0955799i	−0.432723	−	0.901527i	$-0.642447\pi$
$487$	−7.87188	+	2.10926i	−0.356709	+	0.0955799i	0.0760141	+	0.997107i	$0.475781\pi$
$488$	−7.92183	+	29.5647i	−0.358604	+	1.33833i
$489$	4.39106	−	5.79987i	0.198571	−	0.262279i
$490$		0			0
$491$		−	23.5077i		−	1.06089i	−0.847721	−	0.530443i	$-0.822026\pi$
$491$		−	23.5077i		−	1.06089i	0.847721	−	0.530443i	$-0.177974\pi$
$492$	3.72197	+	4.78612i	0.167799	+	0.215775i
$493$	5.02995	+	18.7720i	0.226537	+	0.845449i
$494$	1.36933	−	2.37174i	0.0616088	−	0.106710i
$495$		0			0
$496$	−16.5754			−0.744256
$497$	−1.55825	−	7.38886i	−0.0698969	−	0.331436i
$498$	−7.62140	+	1.05359i	−0.341523	+	0.0472125i
$499$	1.16468	−	0.672430i	0.0521383	−	0.0301021i	−0.473704	−	0.880684i	$-0.657083\pi$
$499$	1.16468	−	0.672430i	0.0521383	−	0.0301021i	0.525843	+	0.850582i	$0.323750\pi$
$500$		0			0
$501$	13.1806	+	31.2473i	0.588865	+	1.39603i
$502$	4.91840	−	18.3557i	0.219519	−	0.819256i
$503$	18.5696	+	18.5696i	0.827976	+	0.827976i	0.987237	−	0.159261i	$-0.0509111\pi$
$503$	18.5696	+	18.5696i	0.827976	+	0.827976i	−0.159261	+	0.987237i	$0.550911\pi$
$504$	−5.32985	−	23.7467i	−0.237410	−	1.05776i
$505$		0			0
$506$	−7.08988	+	4.09334i	−0.315184	+	0.181971i
$507$	19.1565	+	7.79005i	0.850771	+	0.345968i
$508$	3.20393	+	11.9572i	0.142151	+	0.530516i
$509$	−2.13443	−	3.69695i	−0.0946071	−	0.163864i	0.814837	−	0.579689i	$-0.196826\pi$
$509$	−2.13443	−	3.69695i	−0.0946071	−	0.163864i	−0.909445	+	0.415825i	$0.863493\pi$
$510$		0			0
$511$	−2.53290	−	4.99074i	−0.112049	−	0.220777i
$512$	12.7527	−	12.7527i	0.563597	−	0.563597i
$513$	−7.50067	+	10.1782i	−0.331163	+	0.449379i
$514$	27.9874	+	16.1585i	1.23447	+	0.712722i
$515$		0			0
$516$	−0.258663	+	2.06806i	−0.0113870	+	0.0910414i
$517$	36.0985	+	36.0985i	1.58761	+	1.58761i
$518$	0.924718	−	2.83063i	0.0406298	−	0.124371i
$519$	−9.93650	−	7.52289i	−0.436164	−	0.330218i
$520$		0			0
$521$	22.6559	+	13.0804i	0.992575	+	0.573063i	0.906043	−	0.423186i	$-0.139088\pi$
$521$	22.6559	+	13.0804i	0.992575	+	0.573063i	0.0865318	+	0.996249i	$0.472422\pi$
$522$	−15.7492	−	26.4811i	−0.689326	−	1.15904i
$523$	23.6667	+	6.34148i	1.03487	+	0.277293i	0.735987	−	0.676995i	$-0.236718\pi$
$523$	23.6667	+	6.34148i	1.03487	+	0.277293i	0.298886	+	0.954289i	$0.403385\pi$
$524$	11.1038			0.485070
$525$		0			0
$526$	15.0087			0.654408
$527$	19.0265	+	5.09812i	0.828806	+	0.222078i
$528$	12.4191	+	5.05027i	0.540473	+	0.219785i
$529$	17.4622	+	10.0818i	0.759225	+	0.438339i
$530$		0			0
$531$	17.2639	−	4.86615i	0.749188	−	0.211173i
$532$	5.07362	−	1.06998i	0.219969	−	0.0463896i
$533$	−3.16466	−	3.16466i	−0.137077	−	0.137077i
$534$	−19.5110	−	2.44035i	−0.844326	−	0.105604i
$535$		0			0
$536$	−28.1713	−	16.2647i	−1.21682	−	0.702529i
$537$	1.28255	+	1.64924i	0.0553460	+	0.0711700i
$538$	−19.1108	+	19.1108i	−0.823926	+	0.823926i
$539$	−30.9516	−	3.35293i	−1.33318	−	0.144421i
$540$		0			0
$541$	−6.23503	−	10.7994i	−0.268065	−	0.464302i	0.700297	−	0.713852i	$-0.253051\pi$
$541$	−6.23503	−	10.7994i	−0.268065	−	0.464302i	−0.968362	+	0.249549i	$0.919718\pi$
$542$	3.71628	+	13.8693i	0.159628	+	0.595739i
$543$	−3.39242	+	8.34231i	−0.145583	+	0.358003i
$544$	−7.57698	+	4.37457i	−0.324860	+	0.187558i
$545$		0			0
$546$	1.74540	+	4.85349i	0.0746960	+	0.207710i
$547$	10.7444	+	10.7444i	0.459396	+	0.459396i	0.898457	−	0.439061i	$-0.144689\pi$
$547$	10.7444	+	10.7444i	0.459396	+	0.459396i	−0.439061	+	0.898457i	$0.644689\pi$
$548$	−2.12475	+	7.92968i	−0.0907649	+	0.338739i
$549$	−7.37573	+	29.0239i	−0.314788	+	1.23871i
$550$		0			0
$551$	19.8010	−	11.4321i	0.843551	−	0.487025i
$552$	1.22484	+	8.86014i	0.0521325	+	0.377113i
$553$	−27.1477	+	24.3657i	−1.15444	+	1.03613i
$554$	−10.0094			−0.425259
$555$		0			0
$556$	−4.20005	+	7.27471i	−0.178122	+	0.308516i
$557$	−2.74806	−	10.2559i	−0.116439	−	0.434557i	0.882951	−	0.469464i	$-0.155553\pi$
$557$	−2.74806	−	10.2559i	−0.116439	−	0.434557i	−0.999391	+	0.0349077i	$0.988886\pi$
$558$	−31.2255	+	0.404127i	−1.32188	+	0.0171081i
$559$		−	1.53847i		−	0.0650703i
$560$		0			0
$561$	−12.7023	−	9.61686i	−0.536291	−	0.406024i
$562$	4.96944	−	18.5462i	0.209623	−	0.782324i
$563$	−2.35096	+	0.629938i	−0.0990811	+	0.0265487i	−0.308019	−	0.951380i	$-0.599666\pi$
$563$	−2.35096	+	0.629938i	−0.0990811	+	0.0265487i	0.208938	+	0.977929i	$0.432999\pi$
$564$	14.7544	−	6.22363i	0.621272	−	0.262062i
$565$		0			0
$566$		−	27.8864i		−	1.17215i
$567$	−5.51496	−	23.1643i	−0.231607	−	0.972810i
$568$	6.18824	−	6.18824i	0.259653	−	0.259653i
$569$	18.8578	+	32.6626i	0.790559	+	1.36929i	0.925621	+	0.378451i	$0.123543\pi$
$569$	18.8578	+	32.6626i	0.790559	+	1.36929i	−0.135062	+	0.990837i	$0.543123\pi$
$570$		0			0
$571$	−7.75315	+	13.4288i	−0.324459	+	0.561980i	−0.981403	−	0.191960i	$-0.938516\pi$
$571$	−7.75315	+	13.4288i	−0.324459	+	0.561980i	0.656944	+	0.753940i	$0.271849\pi$
$572$	3.56327	+	0.954774i	0.148988	+	0.0399211i
$573$	−3.97552	−	28.7579i	−0.166080	−	1.20138i
$574$	−0.677726	+	12.5491i	−0.0282877	+	0.523788i
$575$		0			0
$576$	16.9679	−	17.4128i	0.706995	−	0.725535i
$577$	−33.4083	+	8.95172i	−1.39081	+	0.372665i	−0.875034	−	0.484061i	$-0.839161\pi$
$577$	−33.4083	+	8.95172i	−1.39081	+	0.372665i	−0.515771	+	0.856726i	$0.672495\pi$
$578$	13.4314	−	3.59893i	0.558672	−	0.149696i
$579$	−5.67017	−	0.709197i	−0.235644	−	0.0294732i
$580$		0			0
$581$	9.00889	+	5.87088i	0.373752	+	0.243565i
$582$	32.7571	−	4.52837i	1.35782	−	0.187707i
$583$	39.9208	+	10.6968i	1.65335	+	0.443014i
$584$	3.24308	−	5.61719i	0.134200	−	0.232441i
$585$		0			0
$586$	−2.55713	−	4.42908i	−0.105634	−	0.182964i
$587$	−6.59879	+	6.59879i	−0.272361	+	0.272361i	−0.830050	−	0.557689i	$-0.811688\pi$
$587$	−6.59879	+	6.59879i	−0.272361	+	0.272361i	0.557689	+	0.830050i	$0.311688\pi$
$588$	−4.63148	+	8.59733i	−0.190999	+	0.354548i
$589$		−	23.1741i		−	0.954874i
$590$		0			0
$591$	6.49021	+	15.3864i	0.266971	+	0.632911i
$592$	1.73116	−	0.463862i	0.0711502	−	0.0190646i
$593$	−5.76848	+	21.5283i	−0.236883	+	0.884059i	0.740408	+	0.672158i	$0.234632\pi$
$593$	−5.76848	+	21.5283i	−0.236883	+	0.884059i	−0.977291	+	0.211902i	$0.932034\pi$
$594$	23.5189	+	9.21115i	0.964991	+	0.377938i
$595$		0			0
$596$			8.71942i			0.357161i
$597$	−9.67198	+	7.52150i	−0.395848	+	0.307835i
$598$	−0.490609	−	1.83098i	−0.0200625	−	0.0748743i
$599$	−9.24781	+	16.0177i	−0.377855	+	0.654464i	−0.990750	−	0.135700i	$-0.956672\pi$
$599$	−9.24781	+	16.0177i	−0.377855	+	0.654464i	0.612895	+	0.790164i	$0.290005\pi$
$600$		0			0
$601$	−15.3237			−0.625066			−0.312533	−	0.949907i	$-0.601177\pi$
$601$	−15.3237			−0.625066			−0.312533	+	0.949907i	$0.601177\pi$
$602$	−3.21504	+	2.88557i	−0.131035	+	0.117607i
$603$	−27.7664	−	15.5554i	−1.13074	−	0.633464i
$604$	9.76586	−	5.63832i	0.397367	−	0.229420i
$605$		0			0
$606$	11.8002	−	4.97748i	0.479349	−	0.202196i
$607$	1.31641	−	4.91291i	0.0534315	−	0.199409i	−0.934050	−	0.357141i	$-0.883752\pi$
$607$	1.31641	−	4.91291i	0.0534315	−	0.199409i	0.987482	+	0.157732i	$0.0504182\pi$
$608$	7.27846	+	7.27846i	0.295181	+	0.295181i
$609$	−7.64065	+	42.3776i	−0.309615	+	1.71723i
$610$		0			0
$611$	−10.2368	+	5.91025i	−0.414139	+	0.239103i
$612$	−4.29523	+	2.55453i	−0.173624	+	0.103261i
$613$	−2.39852	−	8.95140i	−0.0968753	−	0.361544i	0.900422	−	0.435018i	$-0.143258\pi$
$613$	−2.39852	−	8.95140i	−0.0968753	−	0.361544i	−0.997297	+	0.0734743i	$0.976591\pi$
$614$	−5.28365	−	9.15156i	−0.213231	−	0.369327i
$615$		0			0
$616$	−16.3290	−	32.1741i	−0.657913	−	1.29633i
$617$	16.4753	−	16.4753i	0.663272	−	0.663272i	−0.292878	−	0.956150i	$-0.594613\pi$
$617$	16.4753	−	16.4753i	0.663272	−	0.663272i	0.956150	+	0.292878i	$0.0946128\pi$
$618$	−2.08476	+	1.62123i	−0.0838612	+	0.0652154i
$619$	16.8522	+	9.72960i	0.677346	+	0.391066i	0.798854	−	0.601525i	$-0.205440\pi$
$619$	16.8522	+	9.72960i	0.677346	+	0.391066i	−0.121509	+	0.992590i	$0.538773\pi$
$620$		0			0
$621$	1.31046	+	8.65253i	0.0525870	+	0.347214i
$622$	−15.8007	−	15.8007i	−0.633549	−	0.633549i
$623$	18.3560	+	20.4518i	0.735416	+	0.819385i
$624$	−1.87376	+	2.47493i	−0.0750104	+	0.0990763i
$625$		0			0
$626$	5.05823	+	2.92037i	0.202168	+	0.116722i
$627$	−7.06082	+	17.3633i	−0.281982	+	0.693422i
$628$	−6.16587	−	1.65214i	−0.246045	−	0.0659275i
$629$	−2.12982			−0.0849217
$630$		0			0
$631$	19.7802			0.787437			0.393718	−	0.919231i	$-0.371189\pi$
$631$	19.7802			0.787437			0.393718	+	0.919231i	$0.371189\pi$
$632$	−40.8354	−	10.9418i	−1.62435	−	0.435242i
$633$	8.55578	−	21.0395i	0.340062	−	0.836246i
$634$	−3.05780	−	1.76542i	−0.121441	−	0.0701137i
$635$		0			0
$636$	7.82515	−	10.3357i	0.310287	−	0.409838i
$637$	2.60475	−	6.72150i	0.103204	−	0.266315i
$638$	−32.2984	−	32.2984i	−1.27871	−	1.27871i
$639$	5.97571	−	6.13242i	0.236396	−	0.242595i
$640$		0			0
$641$	−7.19737	−	4.15540i	−0.284279	−	0.164128i	0.351080	−	0.936345i	$-0.385815\pi$
$641$	−7.19737	−	4.15540i	−0.284279	−	0.164128i	−0.635359	+	0.772217i	$0.719148\pi$
$642$	3.01689	−	2.34612i	0.119067	−	0.0925938i
$643$	18.0898	−	18.0898i	0.713390	−	0.713390i	−0.253852	−	0.967243i	$-0.581698\pi$
$643$	18.0898	−	18.0898i	0.713390	−	0.713390i	0.967243	+	0.253852i	$0.0816978\pi$
$644$	1.95949	−	3.00684i	0.0772146	−	0.118486i
$645$		0			0
$646$	2.75011	+	4.76333i	0.108202	+	0.187411i
$647$	10.7836	+	40.2450i	0.423947	+	1.58219i	0.766211	+	0.642589i	$0.222140\pi$
$647$	10.7836	+	40.2450i	0.423947	+	1.58219i	−0.342264	+	0.939604i	$0.611194\pi$
$648$	19.0018	−	20.0118i	0.746462	−	0.786140i
$649$	23.0286	−	13.2956i	0.903952	−	0.521897i
$650$		0			0
$651$	33.3254	+	28.1827i	1.30613	+	1.10457i
$652$	−2.39204	−	2.39204i	−0.0936796	−	0.0936796i
$653$	−2.51288	+	9.37818i	−0.0983365	+	0.366997i	−0.997504	−	0.0706075i	$-0.977506\pi$
$653$	−2.51288	+	9.37818i	−0.0983365	+	0.366997i	0.899168	+	0.437604i	$0.144173\pi$
$654$	6.05583	−	2.55444i	0.236802	−	0.0998865i
$655$		0			0
$656$	−6.55036	+	3.78185i	−0.255748	+	0.147656i
$657$	3.10164	−	5.53646i	0.121007	−	0.215998i
$658$	31.5514	+	10.3073i	1.23000	+	0.401820i
$659$	21.6306			0.842610			0.421305	−	0.906919i	$-0.361572\pi$
$659$	21.6306			0.842610			0.421305	+	0.906919i	$0.361572\pi$
$660$		0			0
$661$	19.8390	−	34.3622i	0.771648	−	1.33653i	−0.165012	−	0.986292i	$-0.552766\pi$
$661$	19.8390	−	34.3622i	0.771648	−	1.33653i	0.936659	−	0.350242i	$-0.113901\pi$
$662$	8.05762	+	30.0714i	0.313168	+	1.16876i
$663$	2.91206	−	2.26459i	0.113095	−	0.0879494i
$664$			12.4620i			0.483618i
$665$		0			0
$666$	3.24993	−	0.916053i	0.125932	−	0.0354963i
$667$	4.09596	−	15.2863i	0.158596	−	0.591889i
$668$	15.2332	−	4.08171i	0.589389	−	0.157926i
$669$	−9.49256	−	22.5041i	−0.367004	−	0.870058i
$670$		0			0
$671$			44.3960i			1.71389i
$672$	−19.3183	+	1.61522i	−0.745219	+	0.0623084i
$673$	−5.06190	+	5.06190i	−0.195122	+	0.195122i	−0.797905	−	0.602783i	$-0.794058\pi$
$673$	−5.06190	+	5.06190i	−0.195122	+	0.195122i	0.602783	+	0.797905i	$0.294058\pi$
$674$	11.5109	+	19.9375i	0.443385	+	0.767965i
$675$		0			0
$676$	4.80831	−	8.32823i	0.184935	−	0.320317i
$677$	−11.2707	−	3.01996i	−0.433167	−	0.116067i	0.0356456	−	0.999364i	$-0.488651\pi$
$677$	−11.2707	−	3.01996i	−0.433167	−	0.116067i	−0.468812	+	0.883298i	$0.655318\pi$
$678$	34.1861	−	4.72593i	1.31291	−	0.181498i
$679$	−38.7206	−	25.2333i	−1.48596	−	0.968363i
$680$		0			0
$681$	−17.4248	−	2.17941i	−0.667720	−	0.0835152i
$682$	−44.7185	+	11.9823i	−1.71236	+	0.458825i
$683$	−30.7776	+	8.24684i	−1.17767	+	0.315556i	−0.794003	−	0.607914i	$-0.792007\pi$
$683$	−30.7776	+	8.24684i	−1.17767	+	0.315556i	−0.383670	+	0.923470i	$0.625340\pi$
$684$	4.21088	+	4.10327i	0.161007	+	0.156893i
$685$		0			0
$686$	−18.9319	+	7.16360i	−0.722822	+	0.273507i
$687$	−0.210705	−	1.52418i	−0.00803890	−	0.0581513i
$688$	−2.51145	−	0.672942i	−0.0957483	−	0.0256557i
$689$	−4.78473	+	8.28739i	−0.182284	+	0.315724i
$690$		0			0
$691$	−13.1446	−	22.7672i	−0.500045	−	0.866104i	−1.00000		5.22217e-5i	$-0.999983\pi$
$691$	−13.1446	−	22.7672i	−0.500045	−	0.866104i	0.499955	−	0.866052i	$-0.333350\pi$
$692$	−4.09811	+	4.09811i	−0.155787	+	0.155787i
$693$	−16.3823	−	31.2697i	−0.622312	−	1.18784i
$694$		−	9.50911i		−	0.360961i
$695$		0			0
$696$	−45.9812	+	19.3955i	−1.74291	+	0.735186i
$697$	8.68218	−	2.32638i	0.328861	−	0.0881181i
$698$	−2.27421	+	8.48745i	−0.0860800	+	0.321255i
$699$	12.4674	+	9.43905i	0.471561	+	0.357018i
$700$		0			0
$701$		−	3.66115i		−	0.138280i	−0.997607	−	0.0691398i	$-0.977975\pi$
$701$		−	3.66115i		−	0.138280i	0.997607	−	0.0691398i	$-0.0220254\pi$
$702$	−3.46953	+	4.70807i	−0.130949	+	0.177694i
$703$	0.648529	+	2.42034i	0.0244597	+	0.0912850i
$704$	18.0221	−	31.2151i	0.679232	−	1.17646i
$705$		0			0
$706$	11.7600			0.442594
$707$	−17.0143	−	5.55826i	−0.639887	−	0.209040i
$708$	−1.14219	−	8.26234i	−0.0429263	−	0.310518i
$709$	−29.2851	+	16.9077i	−1.09982	+	0.634983i	−0.936175	−	0.351535i	$-0.885660\pi$
$709$	−29.2851	+	16.9077i	−1.09982	+	0.634983i	−0.163649	+	0.986519i	$0.552326\pi$
$710$		0			0
$711$	−40.0886	−	10.1875i	−1.50344	−	0.382063i
$712$	−8.24306	+	30.7635i	−0.308922	+	1.15291i
$713$	−11.3420	−	11.3420i	−0.424763	−	0.424763i
$714$	−10.1944	−	1.83803i	−0.381514	−	0.0687867i
$715$		0			0
$716$	0.841382	−	0.485772i	0.0314439	−	0.0181542i
$717$	−2.48258	+	6.10492i	−0.0927138	+	0.227993i
$718$	5.50097	+	20.5299i	0.205294	+	0.766169i
$719$	−20.4436	−	35.4093i	−0.762416	−	1.32054i	−0.941602	−	0.336728i	$-0.890680\pi$
$719$	−20.4436	−	35.4093i	−0.762416	−	1.32054i	0.179186	−	0.983815i	$-0.442654\pi$
$720$		0			0
$721$	3.68563	+	0.199047i	0.137260	+	0.00741288i
$722$	−10.1083	+	10.1083i	−0.376190	+	0.376190i
$723$	−24.7002	−	31.7623i	−0.918611	−	1.18125i
$724$	3.62679	+	2.09393i	0.134789	+	0.0778203i
$725$		0			0
$726$	16.4936	+	2.06294i	0.612134	+	0.0765627i
$727$	−23.4186	−	23.4186i	−0.868547	−	0.868547i	0.123764	−	0.992312i	$-0.460503\pi$
$727$	−23.4186	−	23.4186i	−0.868547	−	0.868547i	−0.992312	+	0.123764i	$0.960503\pi$
$728$	8.17439	−	1.72391i	0.302963	−	0.0638923i
$729$	18.3364	−	19.8185i	0.679128	−	0.734020i
$730$		0			0
$731$	2.67586	+	1.54491i	0.0989701	+	0.0571404i
$732$	12.9000	+	5.24581i	0.476797	+	0.193891i
$733$	2.36139	+	0.632731i	0.0872198	+	0.0233705i	0.302165	−	0.953256i	$-0.402291\pi$
$733$	2.36139	+	0.632731i	0.0872198	+	0.0233705i	−0.214945	+	0.976626i	$0.568957\pi$
$734$	−30.6204			−1.13022
$735$		0			0
$736$	7.12455			0.262614
$737$	−45.5758	−	12.2120i	−1.67881	−	0.449835i
$738$	−12.2477	+	7.28413i	−0.450843	+	0.268133i
$739$	26.6330	+	15.3766i	0.979711	+	0.565636i	0.902183	−	0.431354i	$-0.141964\pi$
$739$	26.6330	+	15.3766i	0.979711	+	0.565636i	0.0775282	+	0.996990i	$0.475297\pi$
$740$		0			0
$741$	−3.46021	−	2.61971i	−0.127114	−	0.0962376i
$742$	26.2930	−	5.54497i	0.965246	−	0.203562i
$743$	0.474519	+	0.474519i	0.0174084	+	0.0174084i	0.715757	−	0.698349i	$-0.246082\pi$
$743$	0.474519	+	0.474519i	0.0174084	+	0.0174084i	−0.698349	+	0.715757i	$0.746082\pi$
$744$	−6.27750	+	50.1898i	−0.230144	+	1.84005i
$745$		0			0
$746$	4.86043	+	2.80617i	0.177953	+	0.102741i
$747$	0.157788	+	12.1918i	0.00577318	+	0.446073i
$748$	−5.23881	+	5.23881i	−0.191550	+	0.191550i
$749$	−5.33356	−	0.288044i	−0.194884	−	0.0105249i
$750$		0			0
$751$	5.43251	+	9.40938i	0.198235	+	0.343353i	0.947956	−	0.318401i	$-0.103146\pi$
$751$	5.43251	+	9.40938i	0.198235	+	0.343353i	−0.749721	+	0.661754i	$0.769812\pi$
$752$	5.17040	+	19.2962i	0.188545	+	0.703660i
$753$	−27.8967	−	11.3443i	−1.01661	−	0.413409i
$754$	9.15921	−	5.28807i	0.333559	−	0.192580i
$755$		0			0
$756$	−11.0216	+	1.06533i	−0.400854	+	0.0387456i
$757$	−6.14130	−	6.14130i	−0.223209	−	0.223209i	0.586639	−	0.809849i	$-0.300451\pi$
$757$	−6.14130	−	6.14130i	−0.223209	−	0.223209i	−0.809849	+	0.586639i	$0.800451\pi$
$758$	−4.38525	+	16.3660i	−0.159279	+	0.594439i
$759$	5.04229	+	11.9538i	0.183024	+	0.433896i
$760$		0			0
$761$	18.8392	−	10.8768i	0.682919	−	0.394284i	−0.118035	−	0.993009i	$-0.537659\pi$
$761$	18.8392	−	10.8768i	0.682919	−	0.394284i	0.800954	+	0.598726i	$0.204326\pi$
$762$	−28.8207	+	3.98421i	−1.04406	+	0.144333i
$763$	−8.73170	−	2.85250i	−0.316109	−	0.103267i
$764$	−13.5002			−0.488422
$765$		0			0
$766$	13.6918	−	23.7148i	0.494703	−	0.856851i
$767$	1.59355	+	5.94719i	0.0575396	+	0.214741i
$768$	−16.7728	−	21.5683i	−0.605236	−	0.778279i
$769$			4.90055i			0.176718i	0.996089	+	0.0883592i	$0.0281623\pi$
$769$			4.90055i			0.176718i	−0.996089	+	0.0883592i	$0.971838\pi$
$770$		0			0
$771$	30.9136	−	40.8317i	1.11333	−	1.47052i
$772$	−0.687760	+	2.56676i	−0.0247530	+	0.0923796i
$773$	34.6404	−	9.28188i	1.24593	−	0.333846i	0.425167	−	0.905115i	$-0.360215\pi$
$773$	34.6404	−	9.28188i	1.24593	−	0.333846i	0.820763	+	0.571269i	$0.193549\pi$
$774$	−4.74760	−	1.20649i	−0.170649	−	0.0433663i
$775$		0			0
$776$		−	53.5619i		−	1.92276i
$777$	−4.26925	−	2.01083i	−0.153159	−	0.0721382i
$778$	6.58980	−	6.58980i	0.236256	−	0.236256i
$779$	−5.28743	−	9.15810i	−0.189442	−	0.328123i
$780$		0			0
$781$	6.34697	−	10.9933i	0.227112	−	0.393370i
$782$	3.67728	+	0.985324i	0.131499	+	0.0352351i
$783$	−44.7386	+	19.5572i	−1.59883	+	0.698917i
$784$	−9.83307	−	7.19214i	−0.351181	−	0.256862i
$785$		0			0
$786$	−3.23891	+	25.8957i	−0.115528	+	0.923670i
$787$	−18.8078	+	5.03952i	−0.670424	+	0.179640i	−0.577946	−	0.816075i	$-0.696146\pi$
$787$	−18.8078	+	5.03952i	−0.670424	+	0.179640i	−0.0924782	+	0.995715i	$0.529479\pi$
$788$	7.50091	−	2.00986i	0.267209	−	0.0715984i
$789$	2.95188	−	23.6009i	0.105090	−	0.840214i
$790$		0			0
$791$	−40.4098	−	26.3341i	−1.43681	−	0.936333i
$792$	19.9955	−	35.6921i	0.710510	−	1.26827i
$793$	−9.92929	−	2.66055i	−0.352600	−	0.0944788i
$794$	−3.93834	+	6.82141i	−0.139767	+	0.242083i
$795$		0			0
$796$	2.84881	+	4.93429i	0.100974	+	0.174891i
$797$	−12.3468	+	12.3468i	−0.437346	+	0.437346i	−0.891118	−	0.453772i	$-0.850078\pi$
$797$	−12.3468	+	12.3468i	−0.437346	+	0.437346i	0.453772	+	0.891118i	$0.350078\pi$
$798$	1.01542	+	12.1446i	0.0359455	+	0.429914i
$799$		−	23.7399i		−	0.839857i
$800$		0			0
$801$	−7.67482	+	30.2009i	−0.271176	+	1.06710i
$802$	−8.34126	+	2.23503i	−0.294540	+	0.0789218i
$803$	2.43500	−	9.08754i	0.0859292	−	0.320692i
$804$	−8.93362	+	11.7998i	−0.315064	+	0.416148i
$805$		0			0
$806$		−	10.7195i		−	0.377578i
$807$	26.2928	+	33.8102i	0.925550	+	1.19017i
$808$	−5.36889	−	20.0370i	−0.188877	−	0.704898i
$809$	−10.6763	+	18.4919i	−0.375360	+	0.650142i	−0.990381	−	0.138368i	$-0.955814\pi$
$809$	−10.6763	+	18.4919i	−0.375360	+	0.650142i	0.615021	+	0.788511i	$0.289148\pi$
$810$		0			0
$811$	−47.0797			−1.65319			−0.826596	−	0.562795i	$-0.809726\pi$
$811$	−47.0797			−1.65319			−0.826596	+	0.562795i	$0.809726\pi$
$812$	19.0344	+	6.21820i	0.667975	+	0.218216i
$813$	22.5402	−	3.11599i	0.790521	−	0.109282i
$814$	4.33514	−	2.50290i	0.151947	−	0.0877265i
$815$		0			0
$816$	−2.42303	−	5.74430i	−0.0848231	−	0.201091i
$817$	0.940845	−	3.51128i	0.0329160	−	0.122844i
$818$	−19.8226	−	19.8226i	−0.693083	−	0.693083i
$819$	7.97532	−	1.79003i	0.278680	−	0.0625487i
$820$		0			0
$821$	−29.7367	+	17.1685i	−1.03782	+	0.599185i	−0.919215	−	0.393756i	$-0.871175\pi$
$821$	−29.7367	+	17.1685i	−1.03782	+	0.599185i	−0.118604	+	0.992942i	$0.537842\pi$
$822$	−17.8735	−	7.26831i	−0.623410	−	0.253511i
$823$	−4.02040	−	15.0043i	−0.140142	−	0.523018i	−0.999924	−	0.0123558i	$-0.996067\pi$
$823$	−4.02040	−	15.0043i	−0.140142	−	0.523018i	0.859781	−	0.510662i	$-0.170600\pi$
$824$	2.13880	+	3.70451i	0.0745087	+	0.129053i
$825$		0			0
$826$	9.43937	−	14.4848i	0.328438	−	0.503989i
$827$	20.1828	−	20.1828i	0.701825	−	0.701825i	−0.262977	−	0.964802i	$-0.584704\pi$
$827$	20.1828	−	20.1828i	0.701825	−	0.701825i	0.964802	+	0.262977i	$0.0847045\pi$
$828$	4.06917	−	0.0526641i	0.141413	−	0.00183020i
$829$	25.1138	+	14.4994i	0.872237	+	0.503586i	0.868091	−	0.496405i	$-0.165347\pi$
$829$	25.1138	+	14.4994i	0.872237	+	0.503586i	0.00414604	+	0.999991i	$0.498680\pi$
$830$		0			0
$831$	−1.96864	+	15.7397i	−0.0682913	+	0.546003i
$832$	5.90134	+	5.90134i	0.204592	+	0.204592i
$833$	9.07503	+	11.2801i	0.314431	+	0.390831i
$834$	−15.7406	−	11.9172i	−0.545054	−	0.412659i
$835$		0			0
$836$	7.54862	+	4.35820i	0.261075	+	0.150731i
$837$	−5.50590	+	49.1811i	−0.190312	+	1.69995i
$838$	17.0464	+	4.56758i	0.588860	+	0.157784i
$839$	−11.4710			−0.396024			−0.198012	−	0.980200i	$-0.563449\pi$
$839$	−11.4710			−0.396024			−0.198012	+	0.980200i	$0.563449\pi$
$840$		0			0
$841$	59.2973			2.04473
$842$	3.68748	+	0.988057i	0.127079	+	0.0340507i
$843$	−28.1862	−	11.4620i	−0.970785	−	0.394772i
$844$	−9.14686	−	5.28094i	−0.314848	−	0.181777i
$845$		0			0
$846$	10.2107	+	36.2250i	0.351051	+	1.24544i
$847$	−15.5171	−	17.2889i	−0.533175	−	0.594052i
$848$	11.4357	+	11.4357i	0.392705	+	0.392705i
$849$	−43.8509	−	5.48466i	−1.50496	−	0.188233i
$850$		0			0
$851$	1.50199	+	0.867173i	0.0514875	+	0.0297263i
$852$	−2.44432	−	3.14318i	−0.0837410	−	0.107683i
$853$	−1.70484	+	1.70484i	−0.0583726	+	0.0583726i	−0.735691	−	0.677318i	$-0.763142\pi$
$853$	−1.70484	+	1.70484i	−0.0583726	+	0.0583726i	0.677318	+	0.735691i	$0.263142\pi$
$854$	13.0636	+	25.7401i	0.447027	+	0.880807i
$855$		0			0
$856$	−3.09510	−	5.36088i	−0.105788	−	0.183231i
$857$	1.68698	+	6.29588i	0.0576260	+	0.215063i	0.988735	−	0.149679i	$-0.0478239\pi$
$857$	1.68698	+	6.29588i	0.0576260	+	0.215063i	−0.931109	+	0.364742i	$0.881157\pi$
$858$	−3.26607	+	8.03160i	−0.111502	+	0.274194i
$859$	11.1215	−	6.42098i	0.379460	−	0.219081i	−0.298123	−	0.954527i	$-0.596361\pi$
$859$	11.1215	−	6.42098i	0.379460	−	0.219081i	0.677583	+	0.735446i	$0.263027\pi$
$860$		0			0
$861$	19.5999	+	3.53385i	0.667964	+	0.120433i
$862$	23.8796	+	23.8796i	0.813342	+	0.813342i
$863$	0.306345	−	1.14330i	0.0104281	−	0.0389183i	−0.960516	−	0.278226i	$-0.910254\pi$
$863$	0.306345	−	1.14330i	0.0104281	−	0.0389183i	0.970944	+	0.239307i	$0.0769204\pi$
$864$	−13.7174	−	17.1759i	−0.466674	−	0.584337i
$865$		0			0
$866$	−17.6480	+	10.1891i	−0.599704	+	0.346239i
$867$	−3.01759	−	21.8285i	−0.102483	−	0.741334i
$868$	15.1043	−	13.5564i	0.512673	−	0.460136i
$869$	−61.3208			−2.08017
$870$		0			0
$871$	5.46251	−	9.46134i	0.185090	−	0.320585i
$872$	−2.75531	−	10.2830i	−0.0933065	−	0.348225i
$873$	−0.678181	−	52.4006i	−0.0229529	−	1.77349i
$874$		−	4.47891i		−	0.151501i
$875$		0			0
$876$	−2.35281	−	1.78131i	−0.0794942	−	0.0601848i
$877$	12.0949	−	45.1386i	0.408414	−	1.52422i	−0.389256	−	0.921130i	$-0.627268\pi$
$877$	12.0949	−	45.1386i	0.408414	−	1.52422i	0.797670	−	0.603094i	$-0.206065\pi$
$878$	22.3530	−	5.98947i	0.754377	−	0.202135i
$879$	−7.46759	+	3.14994i	−0.251876	+	0.106245i
$880$		0			0
$881$		−	22.7347i		−	0.765950i	−0.923759	−	0.382975i	$-0.874900\pi$
$881$		−	22.7347i		−	0.765950i	0.923759	−	0.382975i	$-0.125100\pi$
$882$	−18.6994	−	13.3092i	−0.629640	−	0.448143i
$883$	38.7135	−	38.7135i	1.30281	−	1.30281i	0.376326	−	0.926487i	$-0.377187\pi$
$883$	38.7135	−	38.7135i	1.30281	−	1.30281i	0.926487	−	0.376326i	$-0.122813\pi$
$884$	−0.857726	−	1.48563i	−0.0288485	−	0.0499670i
$885$		0			0
$886$	18.0612	−	31.2828i	0.606776	−	1.05097i
$887$	−18.9845	−	5.08688i	−0.637437	−	0.170801i	−0.0743949	−	0.997229i	$-0.523703\pi$
$887$	−18.9845	−	5.08688i	−0.637437	−	0.170801i	−0.563042	+	0.826428i	$0.690369\pi$
$888$	−0.748932	−	5.41758i	−0.0251325	−	0.181802i
$889$	34.0676	+	22.2010i	1.14259	+	0.744599i
$890$		0			0
$891$	19.1101	−	35.1714i	0.640211	−	1.17829i
$892$	−10.9708	+	2.93962i	−0.367330	+	0.0984258i
$893$	−26.9781	+	7.22877i	−0.902789	+	0.241902i
$894$	−20.3351	−	2.54341i	−0.680107	−	0.0850644i
$895$		0			0
$896$	0.0566490	−	1.04894i	0.00189251	−	0.0350425i
$897$	−2.97568	+	0.411361i	−0.0993550	+	0.0137349i
$898$	4.86892	+	1.30462i	0.162478	+	0.0435358i
$899$	44.7471	−	77.5042i	1.49240	−	2.58491i
$900$		0			0
$901$	−9.60949	−	16.6441i	−0.320139	−	0.554496i
$902$	−14.9382	+	14.9382i	−0.497389	+	0.497389i
$903$	3.90519	+	5.62314i	0.129957	+	0.187126i
$904$		−	55.8987i		−	1.85916i
$905$		0			0
$906$	10.3008	+	24.4202i	0.342222	+	0.811307i
$907$	26.9380	−	7.21802i	0.894463	−	0.239671i	0.217826	−	0.975988i	$-0.430103\pi$
$907$	26.9380	−	7.21802i	0.894463	−	0.239671i	0.676637	+	0.736317i	$0.263437\pi$
$908$	−2.11354	+	7.88782i	−0.0701401	+	0.261767i
$909$	−5.50618	−	19.5345i	−0.182628	−	0.647920i
$910$		0			0
$911$			18.1819i			0.602393i	0.953562	+	0.301197i	$0.0973860\pi$
$911$			18.1819i			0.602393i	−0.953562	+	0.301197i	$0.902614\pi$
$912$	−5.79005	+	4.50268i	−0.191728	+	0.149099i
$913$	4.67839	+	17.4600i	0.154832	+	0.577842i
$914$	8.96687	−	15.5311i	0.296598	−	0.513722i
$915$		0			0
$916$	−0.715521			−0.0236415
$917$	27.1444	−	24.3627i	0.896386	−	0.804526i
$918$	−4.70468	−	10.7623i	−0.155278	−	0.355209i
$919$	3.06431	−	1.76918i	0.101082	−	0.0583598i	−0.448607	−	0.893729i	$-0.648080\pi$
$919$	3.06431	−	1.76918i	0.101082	−	0.0583598i	0.549689	+	0.835369i	$0.314746\pi$
$920$		0			0
$921$	−15.4299	+	6.50855i	−0.508432	+	0.214464i
$922$	−9.80919	+	36.6084i	−0.323048	+	1.20563i
$923$	2.07832	+	2.07832i	0.0684088	+	0.0684088i
$924$	−15.4474	+	5.55513i	−0.508181	+	0.182750i
$925$		0			0
$926$	16.5178	−	9.53654i	0.542808	−	0.313390i
$927$	2.13933	+	3.59711i	0.0702649	+	0.118145i
$928$	10.2883	+	38.3963i	0.337729	+	1.26042i
$929$	1.11983	+	1.93960i	0.0367403	+	0.0636361i	0.883811	−	0.467844i	$-0.154969\pi$
$929$	1.11983	+	1.93960i	0.0367403	+	0.0636361i	−0.847071	+	0.531480i	$0.821636\pi$
$930$		0			0
$931$	10.0554	−	13.7477i	0.329552	−	0.450562i
$932$	5.14195	−	5.14195i	0.168430	−	0.168430i
$933$	−27.9540	+	21.7387i	−0.915173	+	0.711692i
$934$	−5.97098	−	3.44735i	−0.195376	−	0.112801i
$935$		0			0
$936$	6.78437	+	6.61101i	0.221754	+	0.216088i
$937$	−5.03306	−	5.03306i	−0.164423	−	0.164423i	0.620100	−	0.784523i	$-0.287092\pi$
$937$	−5.03306	−	5.03306i	−0.164423	−	0.164423i	−0.784523	+	0.620100i	$0.787092\pi$
$938$	−30.0175	+	6.33044i	−0.980107	+	0.206696i
$939$	5.58709	−	7.37962i	0.182328	−	0.240825i
$940$		0			0
$941$	−16.9467	−	9.78419i	−0.552447	−	0.318955i	0.197661	−	0.980270i	$-0.436665\pi$
$941$	−16.9467	−	9.78419i	−0.552447	−	0.318955i	−0.750108	+	0.661315i	$0.769999\pi$
$942$	5.65161	−	13.8979i	0.184139	−	0.452817i
$943$	−7.07003	−	1.89441i	−0.230232	−	0.0616904i
$944$	10.4054			0.338668
$945$		0			0
$946$	−7.26208			−0.236111
$947$	18.9567	+	5.07942i	0.616008	+	0.165059i	0.553313	−	0.832974i	$-0.313364\pi$
$947$	18.9567	+	5.07942i	0.616008	+	0.165059i	0.0626958	+	0.998033i	$0.480030\pi$
$948$	−7.24564	+	17.8178i	−0.235327	+	0.578694i
$949$	1.88653	+	1.08919i	0.0612394	+	0.0353566i
$950$		0			0
$951$	−3.37750	+	4.46112i	−0.109523	+	0.144662i
$952$	−5.21020	+	15.9488i	−0.168864	+	0.516904i
$953$	11.6458	+	11.6458i	0.377245	+	0.377245i	0.870107	−	0.492862i	$-0.164049\pi$
$953$	11.6458	+	11.6458i	0.377245	+	0.377245i	−0.492862	+	0.870107i	$0.664049\pi$
$954$	21.8220	+	21.2644i	0.706514	+	0.688460i
$955$		0			0
$956$	2.65409	+	1.53234i	0.0858396	+	0.0495595i
$957$	−57.1412	+	44.4364i	−1.84711	+	1.43642i
$958$	12.0192	−	12.0192i	0.388322	−	0.388322i
$959$	12.2043	+	24.0469i	0.394096	+	0.776514i
$960$		0			0
$961$	−29.8536	−	51.7079i	−0.963018	−	1.66800i
$962$	0.299985	+	1.11956i	0.00967192	+	0.0360961i
$963$	−3.09587	−	5.20545i	−0.0997631	−	0.167743i
$964$	−16.2039	+	9.35535i	−0.521894	+	0.301316i
$965$		0			0
$966$	6.44087	+	5.44692i	0.207232	+	0.175252i
$967$	15.8281	+	15.8281i	0.508996	+	0.508996i	0.914218	−	0.405222i	$-0.132806\pi$
$967$	15.8281	+	15.8281i	0.508996	+	0.508996i	−0.405222	+	0.914218i	$0.632806\pi$
$968$	6.96823	−	26.0058i	0.223967	−	0.835858i
$969$	8.03115	−	3.38766i	0.257998	−	0.108827i
$970$		0			0
$971$	31.2518	−	18.0432i	1.00292	−	0.579035i	0.0938076	−	0.995590i	$-0.470096\pi$
$971$	31.2518	−	18.0432i	1.00292	−	0.579035i	0.909110	+	0.416555i	$0.136763\pi$
$972$	−7.96160	−	9.70858i	−0.255368	−	0.311403i
$973$	5.69388	+	26.9991i	0.182538	+	0.865553i
$974$	−8.90714			−0.285403
$975$		0			0
$976$	−8.68634	+	15.0452i	−0.278043	+	0.481585i
$977$	10.8465	+	40.4796i	0.347010	+	1.29506i	0.890247	+	0.455479i	$0.150532\pi$
$977$	10.8465	+	40.4796i	0.347010	+	1.29506i	−0.543237	+	0.839580i	$0.682801\pi$
$978$	6.27637	−	4.88088i	0.200696	−	0.156073i
$979$			46.1962i			1.47644i
$980$		0			0
$981$	−2.82577	−	10.0251i	−0.0902198	−	0.320077i
$982$	6.64980	−	24.8174i	0.212204	−	0.791955i
$983$	−38.4216	+	10.2950i	−1.22546	+	0.328361i	−0.812810	−	0.582529i	$-0.802063\pi$
$983$	−38.4216	+	10.2950i	−1.22546	+	0.328361i	−0.412650	+	0.910890i	$0.635397\pi$
$984$	8.97057	+	21.2666i	0.285971	+	0.677954i
$985$		0			0
$986$			21.2408i			0.676444i
$987$	22.4136	−	47.5869i	0.713431	−	1.51471i
$988$	−1.42710	+	1.42710i	−0.0454020	+	0.0454020i
$989$	−1.25804	−	2.17899i	−0.0400033	−	0.0692878i
$990$		0			0
$991$	−21.7329	+	37.6425i	−0.690368	+	1.19575i	0.281349	+	0.959605i	$0.409218\pi$
$991$	−21.7329	+	37.6425i	−0.690368	+	1.19575i	−0.971717	+	0.236147i	$0.924115\pi$
$992$	38.9167	+	10.4277i	1.23561	+	0.331080i
$993$	48.8716	−	6.75607i	1.55089	−	0.214397i
$994$	0.445082	−	8.24133i	0.0141171	−	0.261399i
$995$		0			0
$996$	5.62608	+	0.703683i	0.178269	+	0.0222970i
$997$	−9.29172	+	2.48971i	−0.294272	+	0.0788498i	−0.402934	−	0.915229i	$-0.632010\pi$
$997$	−9.29172	+	2.48971i	−0.294272	+	0.0788498i	0.108663	+	0.994079i	$0.465343\pi$
$998$	1.41979	−	0.380432i	0.0449427	−	0.0120423i
$999$	−0.801289	−	5.29063i	−0.0253517	−	0.167388i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bf.g.32.13	yes	80
3.2	odd	2	inner	525.2.bf.g.32.7	✓	80
5.2	odd	4	inner	525.2.bf.g.368.7	yes	80
5.3	odd	4	inner	525.2.bf.g.368.14	yes	80
5.4	even	2	inner	525.2.bf.g.32.8	yes	80
7.2	even	3	inner	525.2.bf.g.107.8	yes	80
15.2	even	4	inner	525.2.bf.g.368.13	yes	80
15.8	even	4	inner	525.2.bf.g.368.8	yes	80
15.14	odd	2	inner	525.2.bf.g.32.14	yes	80
21.2	odd	6	inner	525.2.bf.g.107.14	yes	80
35.2	odd	12	inner	525.2.bf.g.443.14	yes	80
35.9	even	6	inner	525.2.bf.g.107.13	yes	80
35.23	odd	12	inner	525.2.bf.g.443.7	yes	80
105.2	even	12	inner	525.2.bf.g.443.8	yes	80
105.23	even	12	inner	525.2.bf.g.443.13	yes	80
105.44	odd	6	inner	525.2.bf.g.107.7	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bf.g.32.7	✓	80	3.2	odd	2	inner
525.2.bf.g.32.8	yes	80	5.4	even	2	inner
525.2.bf.g.32.13	yes	80	1.1	even	1	trivial
525.2.bf.g.32.14	yes	80	15.14	odd	2	inner
525.2.bf.g.107.7	yes	80	105.44	odd	6	inner
525.2.bf.g.107.8	yes	80	7.2	even	3	inner
525.2.bf.g.107.13	yes	80	35.9	even	6	inner
525.2.bf.g.107.14	yes	80	21.2	odd	6	inner
525.2.bf.g.368.7	yes	80	5.2	odd	4	inner
525.2.bf.g.368.8	yes	80	15.8	even	4	inner
525.2.bf.g.368.13	yes	80	15.2	even	4	inner
525.2.bf.g.368.14	yes	80	5.3	odd	4	inner
525.2.bf.g.443.7	yes	80	35.23	odd	12	inner
525.2.bf.g.443.8	yes	80	105.2	even	12	inner
525.2.bf.g.443.13	yes	80	105.23	even	12	inner
525.2.bf.g.443.14	yes	80	35.2	odd	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.05572 + 0.282878i) q^{2} +(0.652459 - 1.60446i) q^{3} +(-0.697534 - 0.402722i) q^{4} +(1.14268 - 1.50929i) q^{6} +(-2.58881 + 0.545957i) q^{7} +(-2.16815 - 2.16815i) q^{8} +(-2.14860 - 2.09369i) q^{9} +O(q^{10})\)	\(q+(1.05572 + 0.282878i) q^{2} +(0.652459 - 1.60446i) q^{3} +(-0.697534 - 0.402722i) q^{4} +(1.14268 - 1.50929i) q^{6} +(-2.58881 + 0.545957i) q^{7} +(-2.16815 - 2.16815i) q^{8} +(-2.14860 - 2.09369i) q^{9} +(-3.85168 - 2.22377i) q^{11} +(-1.10126 + 0.856408i) q^{12} +(0.728174 - 0.728174i) q^{13} +(-2.88749 - 0.155942i) q^{14} +(-0.870187 - 1.50721i) q^{16} +(0.535291 + 1.99773i) q^{17} +(-1.67605 - 2.81813i) q^{18} +(2.10724 - 1.21661i) q^{19} +(-0.813123 + 4.50986i) q^{21} +(-3.43722 - 3.43722i) q^{22} +(0.435895 - 1.62678i) q^{23} +(-4.89335 + 2.06409i) q^{24} +(0.974730 - 0.562761i) q^{26} +(-4.76112 + 2.08129i) q^{27} +(2.02565 + 0.661745i) q^{28} +9.39666 q^{29} +(4.76201 - 8.24805i) q^{31} +(1.09488 + 4.08616i) q^{32} +(-6.08101 + 4.72895i) q^{33} +2.26046i q^{34} +(0.655544 + 2.32571i) q^{36} +(-0.266530 + 0.994704i) q^{37} +(2.56880 - 0.688308i) q^{38} +(-0.693224 - 1.64343i) q^{39} -4.34602i q^{41} +(-2.13417 + 4.53112i) q^{42} +(1.05639 - 1.05639i) q^{43} +(1.79112 + 3.10231i) q^{44} +(0.920363 - 1.59412i) q^{46} +(-11.0874 - 2.97086i) q^{47} +(-2.98602 + 0.412791i) q^{48} +(6.40386 - 2.82676i) q^{49} +(3.55454 + 0.444584i) q^{51} +(-0.801178 + 0.214675i) q^{52} +(-8.97595 + 2.40510i) q^{53} +(-5.61514 + 0.850437i) q^{54} +(6.79665 + 4.42921i) q^{56} +(-0.577125 - 4.17477i) q^{57} +(9.92021 + 2.65811i) q^{58} +(-2.98943 + 5.17784i) q^{59} +(-4.99108 - 8.64480i) q^{61} +(7.36053 - 7.36053i) q^{62} +(6.70537 + 4.24712i) q^{63} +8.10429i q^{64} +(-7.75754 + 3.27225i) q^{66} +(10.2474 - 2.74579i) q^{67} +(0.431146 - 1.60906i) q^{68} +(-2.32571 - 1.76079i) q^{69} +2.85415i q^{71} +(0.119042 + 9.19792i) q^{72} +(0.547494 + 2.04328i) q^{73} +(-0.562761 + 0.974730i) q^{74} -1.95983 q^{76} +(11.1853 + 3.65405i) q^{77} +(-0.266957 - 1.93109i) q^{78} +(11.9404 - 6.89380i) q^{79} +(0.232921 + 8.99699i) q^{81} +(1.22939 - 4.58816i) q^{82} +(-2.87386 - 2.87386i) q^{83} +(2.38340 - 2.81832i) q^{84} +(1.41408 - 0.816417i) q^{86} +(6.13094 - 15.0766i) q^{87} +(3.52956 + 13.1725i) q^{88} +(-5.19347 - 8.99535i) q^{89} +(-1.48755 + 2.28266i) q^{91} +(-0.959192 + 0.959192i) q^{92} +(-10.1267 - 13.0220i) q^{93} +(-10.8647 - 6.27276i) q^{94} +(7.27046 + 0.909353i) q^{96} +(12.3520 + 12.3520i) q^{97} +(7.56029 - 1.17274i) q^{98} +(3.61981 + 12.8422i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{6}+O(q^{10}) \) 80 * q + 16 * q^6	\( 80 q + 16 q^{6} + 72 q^{16} + 44 q^{21} + 72 q^{31} - 240 q^{36} - 92 q^{51} - 24 q^{61} - 216 q^{66} - 208 q^{76} - 20 q^{81} - 40 q^{91} - 156 q^{96}+O(q^{100}) \) 80 * q + 16 * q^6 + 72 * q^16 + 44 * q^21 + 72 * q^31 - 240 * q^36 - 92 * q^51 - 24 * q^61 - 216 * q^66 - 208 * q^76 - 20 * q^81 - 40 * q^91 - 156 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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