LMFDB - Embedded newform 966.2.s.b.475.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(97,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 1]))

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

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

chi := DirichletCharacter("966.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.s (of order $22$, degree $10$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			475.8
Character	$\chi$	$=$	966.475
Dual form			966.2.s.b.181.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 - 0.989821i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(2.43577 + 2.81103i) q^{5} +(0.281733 + 0.959493i) q^{6} +(-2.26148 - 1.37321i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(0.142315 - 0.989821i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(2.43577 + 2.81103i) q^{5} +(0.281733 + 0.959493i) q^{6} +(-2.26148 - 1.37321i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(0.654861 - 0.755750i) q^{9} +(3.12906 - 2.01093i) q^{10} +(-5.43364 + 0.781240i) q^{11} +(0.989821 - 0.142315i) q^{12} +(0.737541 + 1.14764i) q^{13} +(-1.68107 + 2.04304i) q^{14} +(-3.38340 - 1.54515i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-0.428654 + 0.125864i) q^{17} +(-0.654861 - 0.755750i) q^{18} +(3.85282 + 1.13129i) q^{19} +(-1.54515 - 3.38340i) q^{20} +(2.62757 + 0.309660i) q^{21} +5.48952i q^{22} +(-2.48580 - 4.10132i) q^{23} -1.00000i q^{24} +(-1.25733 + 8.74494i) q^{25} +(1.24092 - 0.566708i) q^{26} +(-0.281733 + 0.959493i) q^{27} +(1.78300 + 1.95472i) q^{28} +(-8.12381 + 2.38537i) q^{29} +(-2.01093 + 3.12906i) q^{30} +(-6.53827 - 2.98593i) q^{31} +(0.654861 - 0.755750i) q^{32} +(4.61808 - 2.96786i) q^{33} +(0.0635792 + 0.442203i) q^{34} +(-1.64833 - 9.70191i) q^{35} +(-0.841254 + 0.540641i) q^{36} +(-5.76375 - 4.99432i) q^{37} +(1.66809 - 3.65260i) q^{38} +(-1.14764 - 0.737541i) q^{39} +(-3.56886 + 1.04791i) q^{40} +(-5.00761 + 4.33912i) q^{41} +(0.680450 - 2.55675i) q^{42} +(0.454906 - 0.207749i) q^{43} +(5.43364 + 0.781240i) q^{44} +3.71952 q^{45} +(-4.41334 + 1.87682i) q^{46} -5.66812i q^{47} +(-0.989821 - 0.142315i) q^{48} +(3.22860 + 6.21097i) q^{49} +(8.47699 + 2.48907i) q^{50} +(0.337631 - 0.292559i) q^{51} +(-0.384339 - 1.30894i) q^{52} +(-4.15055 + 6.45838i) q^{53} +(0.909632 + 0.415415i) q^{54} +(-15.4312 - 13.3712i) q^{55} +(2.18857 - 1.48667i) q^{56} +(-3.97460 + 0.571461i) q^{57} +(1.20495 + 8.38060i) q^{58} +(3.71300 + 5.77755i) q^{59} +(2.81103 + 2.43577i) q^{60} +(-1.01557 + 2.22379i) q^{61} +(-3.88603 + 6.04678i) q^{62} +(-2.51876 + 0.809854i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-1.42956 + 4.86863i) q^{65} +(-2.28043 - 4.99344i) q^{66} +(2.31160 + 0.332358i) q^{67} +0.446750 q^{68} +(3.96491 + 2.69805i) q^{69} +(-9.83774 + 0.250822i) q^{70} +(-0.545983 + 3.79740i) q^{71} +(0.415415 + 0.909632i) q^{72} +(0.550021 - 1.87320i) q^{73} +(-5.76375 + 4.99432i) q^{74} +(-2.48907 - 8.47699i) q^{75} +(-3.37803 - 2.17093i) q^{76} +(13.3609 + 5.69476i) q^{77} +(-0.893359 + 1.03099i) q^{78} +(-4.93755 - 7.68297i) q^{79} +(0.529344 + 3.68167i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(3.58230 + 5.57416i) q^{82} +(-7.99401 + 9.22557i) q^{83} +(-2.43389 - 1.03739i) q^{84} +(-1.39791 - 0.898383i) q^{85} +(-0.140894 - 0.479842i) q^{86} +(6.39876 - 5.54456i) q^{87} +(1.54658 - 5.26716i) q^{88} +(-1.46177 - 3.20082i) q^{89} +(0.529344 - 3.68167i) q^{90} +(-0.0919931 - 3.60815i) q^{91} +(1.22964 + 4.63551i) q^{92} +7.18782 q^{93} +(-5.61043 - 0.806658i) q^{94} +(6.20449 + 13.5859i) q^{95} +(-0.281733 + 0.959493i) q^{96} +(6.92355 + 7.99020i) q^{97} +(6.60723 - 2.31183i) q^{98} +(-2.96786 + 4.61808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 16 q^{2} - 16 q^{4} + 16 q^{8} + 16 q^{9}+O(q^{10}) $ 160 * q + 16 * q^2 - 16 * q^4 + 16 * q^8 + 16 * q^9	$ 160 q + 16 q^{2} - 16 q^{4} + 16 q^{8} + 16 q^{9} + 22 q^{14} - 16 q^{16} - 16 q^{18} - 52 q^{23} - 48 q^{25} + 22 q^{28} - 12 q^{29} + 16 q^{32} + 22 q^{35} + 16 q^{36} + 22 q^{37} - 4 q^{39} + 154 q^{43} + 8 q^{46} + 4 q^{50} + 22 q^{51} + 88 q^{53} + 22 q^{57} + 56 q^{58} - 16 q^{64} + 16 q^{71} - 16 q^{72} + 22 q^{74} - 72 q^{77} + 4 q^{78} + 88 q^{79} - 16 q^{81} - 22 q^{84} - 68 q^{85} - 44 q^{86} + 44 q^{88} - 8 q^{92} - 8 q^{93} - 66 q^{95} + 66 q^{98} - 66 q^{99}+O(q^{100}) $ 160 * q + 16 * q^2 - 16 * q^4 + 16 * q^8 + 16 * q^9 + 22 * q^14 - 16 * q^16 - 16 * q^18 - 52 * q^23 - 48 * q^25 + 22 * q^28 - 12 * q^29 + 16 * q^32 + 22 * q^35 + 16 * q^36 + 22 * q^37 - 4 * q^39 + 154 * q^43 + 8 * q^46 + 4 * q^50 + 22 * q^51 + 88 * q^53 + 22 * q^57 + 56 * q^58 - 16 * q^64 + 16 * q^71 - 16 * q^72 + 22 * q^74 - 72 * q^77 + 4 * q^78 + 88 * q^79 - 16 * q^81 - 22 * q^84 - 68 * q^85 - 44 * q^86 + 44 * q^88 - 8 * q^92 - 8 * q^93 - 66 * q^95 + 66 * q^98 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$-1$	$e\left(\frac{17}{22}\right)$

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 $

$2$	0.142315	−	0.989821i	0.100632	−	0.699909i
$2$	0.142315	−	0.989821i	0.100632	−	0.699909i
$3$	−0.909632	+	0.415415i	−0.525176	+	0.239840i
$3$	−0.909632	+	0.415415i	−0.525176	+	0.239840i
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	2.43577	+	2.81103i	1.08931	+	1.25713i	0.964254	+	0.264981i	$0.0853656\pi$
$5$	2.43577	+	2.81103i	1.08931	+	1.25713i	0.125056	+	0.992150i	$0.460089\pi$
$6$	0.281733	+	0.959493i	0.115017	+	0.391711i
$7$	−2.26148	−	1.37321i	−0.854760	−	0.519024i
$7$	−2.26148	−	1.37321i	−0.854760	−	0.519024i
$8$	−0.415415	+	0.909632i	−0.146871	+	0.321603i
$9$	0.654861	−	0.755750i	0.218287	−	0.251917i
$10$	3.12906	−	2.01093i	0.989497	−	0.635911i
$11$	−5.43364	+	0.781240i	−1.63831	+	0.235553i	−0.899042	−	0.437863i	$-0.855735\pi$
$11$	−5.43364	+	0.781240i	−1.63831	+	0.235553i	−0.739264	+	0.673416i	$0.764826\pi$
$12$	0.989821	−	0.142315i	0.285737	−	0.0410828i
$13$	0.737541	+	1.14764i	0.204557	+	0.318297i	0.928341	−	0.371730i	$-0.121235\pi$
$13$	0.737541	+	1.14764i	0.204557	+	0.318297i	−0.723784	+	0.690027i	$0.757599\pi$
$14$	−1.68107	+	2.04304i	−0.449286	+	0.546024i
$15$	−3.38340	−	1.54515i	−0.873590	−	0.398955i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	−0.428654	+	0.125864i	−0.103964	+	0.0305265i	−0.333301	−	0.942821i	$-0.608162\pi$
$17$	−0.428654	+	0.125864i	−0.103964	+	0.0305265i	0.229337	+	0.973347i	$0.426344\pi$
$18$	−0.654861	−	0.755750i	−0.154352	−	0.178132i
$19$	3.85282	+	1.13129i	0.883897	+	0.259536i	0.692016	−	0.721882i	$-0.256723\pi$
$19$	3.85282	+	1.13129i	0.883897	+	0.259536i	0.191882	+	0.981418i	$0.438541\pi$
$20$	−1.54515	−	3.38340i	−0.345505	−	0.756551i
$21$	2.62757	+	0.309660i	0.573382	+	0.0675733i
$22$			5.48952i			1.17037i
$23$	−2.48580	−	4.10132i	−0.518326	−	0.855183i
$23$	−2.48580	−	4.10132i	−0.518326	−	0.855183i
$24$		−	1.00000i		−	0.204124i
$25$	−1.25733	+	8.74494i	−0.251466	+	1.74899i
$26$	1.24092	−	0.566708i	0.243364	−	0.111141i
$27$	−0.281733	+	0.959493i	−0.0542195	+	0.184655i
$28$	1.78300	+	1.95472i	0.336955	+	0.369407i
$29$	−8.12381	+	2.38537i	−1.50855	+	0.442951i	−0.928408	−	0.371561i	$-0.878823\pi$
$29$	−8.12381	+	2.38537i	−1.50855	+	0.442951i	−0.580146	+	0.814513i	$0.697004\pi$
$30$	−2.01093	+	3.12906i	−0.367143	+	0.571286i
$31$	−6.53827	−	2.98593i	−1.17431	−	0.536289i	−0.269872	−	0.962896i	$-0.586981\pi$
$31$	−6.53827	−	2.98593i	−1.17431	−	0.536289i	−0.904437	+	0.426608i	$0.859709\pi$
$32$	0.654861	−	0.755750i	0.115764	−	0.133599i
$33$	4.61808	−	2.96786i	0.803904	−	0.516638i
$34$	0.0635792	+	0.442203i	0.0109037	+	0.0758372i
$35$	−1.64833	−	9.70191i	−0.278618	−	1.63992i
$36$	−0.841254	+	0.540641i	−0.140209	+	0.0901068i
$37$	−5.76375	−	4.99432i	−0.947554	−	0.821061i	0.0364262	−	0.999336i	$-0.488403\pi$
$37$	−5.76375	−	4.99432i	−0.947554	−	0.821061i	−0.983981	+	0.178276i	$0.942948\pi$
$38$	1.66809	−	3.65260i	0.270600	−	0.592530i
$39$	−1.14764	−	0.737541i	−0.183769	−	0.118101i
$40$	−3.56886	+	1.04791i	−0.564286	+	0.165689i
$41$	−5.00761	+	4.33912i	−0.782057	+	0.677657i	−0.951420	−	0.307897i	$-0.900375\pi$
$41$	−5.00761	+	4.33912i	−0.782057	+	0.677657i	0.169362	+	0.985554i	$0.445829\pi$
$42$	0.680450	−	2.55675i	0.104996	−	0.394516i
$43$	0.454906	−	0.207749i	0.0693726	−	0.0316814i	−0.380427	−	0.924811i	$-0.624223\pi$
$43$	0.454906	−	0.207749i	0.0693726	−	0.0316814i	0.449799	+	0.893130i	$0.351496\pi$
$44$	5.43364	+	0.781240i	0.819153	+	0.117776i
$45$	3.71952			0.554474
$46$	−4.41334	+	1.87682i	−0.650711	+	0.276722i
$47$		−	5.66812i		−	0.826781i	−0.910554	−	0.413390i	$-0.864344\pi$
$47$		−	5.66812i		−	0.826781i	0.910554	−	0.413390i	$-0.135656\pi$
$48$	−0.989821	−	0.142315i	−0.142868	−	0.0205414i
$49$	3.22860	+	6.21097i	0.461229	+	0.887281i
$50$	8.47699	+	2.48907i	1.19883	+	0.352007i
$51$	0.337631	−	0.292559i	0.0472779	−	0.0409665i
$52$	−0.384339	−	1.30894i	−0.0532982	−	0.181517i
$53$	−4.15055	+	6.45838i	−0.570122	+	0.887127i	−0.999875	−	0.0158198i	$-0.994964\pi$
$53$	−4.15055	+	6.45838i	−0.570122	+	0.887127i	0.429753	+	0.902946i	$0.358601\pi$
$54$	0.909632	+	0.415415i	0.123785	+	0.0565308i
$55$	−15.4312	−	13.3712i	−2.08074	−	1.80297i
$56$	2.18857	−	1.48667i	0.292460	−	0.198664i
$57$	−3.97460	+	0.571461i	−0.526449	+	0.0756919i
$58$	1.20495	+	8.38060i	0.158217	+	1.10043i
$59$	3.71300	+	5.77755i	0.483392	+	0.752172i	0.994203	−	0.107521i	$-0.0342912\pi$
$59$	3.71300	+	5.77755i	0.483392	+	0.752172i	−0.510811	+	0.859693i	$0.670655\pi$
$60$	2.81103	+	2.43577i	0.362902	+	0.314457i
$61$	−1.01557	+	2.22379i	−0.130031	+	0.284728i	−0.963438	−	0.267932i	$-0.913660\pi$
$61$	−1.01557	+	2.22379i	−0.130031	+	0.284728i	0.833407	+	0.552660i	$0.186387\pi$
$62$	−3.88603	+	6.04678i	−0.493526	+	0.767942i
$63$	−2.51876	+	0.809854i	−0.317334	+	0.102032i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	−1.42956	+	4.86863i	−0.177315	+	0.603879i
$66$	−2.28043	−	4.99344i	−0.280701	−	0.614650i
$67$	2.31160	+	0.332358i	0.282407	+	0.0406040i	0.282063	−	0.959396i	$-0.408981\pi$
$67$	2.31160	+	0.332358i	0.282407	+	0.0406040i	0.000344144		1.00000i	$0.499890\pi$
$68$	0.446750			0.0541765
$69$	3.96491	+	2.69805i	0.477319	+	0.324807i
$70$	−9.83774	+	0.250822i	−1.17583	+	0.0299790i
$71$	−0.545983	+	3.79740i	−0.0647963	+	0.450668i	0.931433	+	0.363912i	$0.118559\pi$
$71$	−0.545983	+	3.79740i	−0.0647963	+	0.450668i	−0.996230	+	0.0867559i	$0.972350\pi$
$72$	0.415415	+	0.909632i	0.0489571	+	0.107201i
$73$	0.550021	−	1.87320i	0.0643751	−	0.219241i	−0.921023	−	0.389509i	$-0.872645\pi$
$73$	0.550021	−	1.87320i	0.0643751	−	0.219241i	0.985398	+	0.170267i	$0.0544631\pi$
$74$	−5.76375	+	4.99432i	−0.670022	+	0.580577i
$75$	−2.48907	−	8.47699i	−0.287413	−	0.978838i
$76$	−3.37803	−	2.17093i	−0.387487	−	0.249023i
$77$	13.3609	+	5.69476i	1.52262	+	0.648978i
$78$	−0.893359	+	1.03099i	−0.101153	+	0.116737i
$79$	−4.93755	−	7.68297i	−0.555518	−	0.864402i	0.443982	−	0.896036i	$-0.353565\pi$
$79$	−4.93755	−	7.68297i	−0.555518	−	0.864402i	−0.999500	+	0.0316335i	$0.989929\pi$
$80$	0.529344	+	3.68167i	0.0591824	+	0.411623i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	3.58230	+	5.57416i	0.395598	+	0.615563i
$83$	−7.99401	+	9.22557i	−0.877456	+	1.01264i	0.122341	+	0.992488i	$0.460960\pi$
$83$	−7.99401	+	9.22557i	−0.877456	+	1.01264i	−0.999797	+	0.0201502i	$0.993586\pi$
$84$	−2.43389	−	1.03739i	−0.265559	−	0.113188i
$85$	−1.39791	−	0.898383i	−0.151625	−	0.0974433i
$86$	−0.140894	−	0.479842i	−0.0151930	−	0.0517427i
$87$	6.39876	−	5.54456i	0.686019	−	0.594439i
$88$	1.54658	−	5.26716i	0.164866	−	0.561481i
$89$	−1.46177	−	3.20082i	−0.154947	−	0.339286i	0.816200	−	0.577770i	$-0.196077\pi$
$89$	−1.46177	−	3.20082i	−0.154947	−	0.339286i	−0.971147	+	0.238484i	$0.923350\pi$
$90$	0.529344	−	3.68167i	0.0557977	−	0.388082i
$91$	−0.0919931	−	3.60815i	−0.00964350	−	0.378237i
$92$	1.22964	+	4.63551i	0.128198	+	0.483286i
$93$	7.18782			0.745342
$94$	−5.61043	−	0.806658i	−0.578672	−	0.0832004i
$95$	6.20449	+	13.5859i	0.636568	+	1.39389i
$96$	−0.281733	+	0.959493i	−0.0287542	+	0.0979278i
$97$	6.92355	+	7.99020i	0.702980	+	0.811282i	0.989152	−	0.146896i	$-0.0469283\pi$
$97$	6.92355	+	7.99020i	0.702980	+	0.811282i	−0.286172	+	0.958178i	$0.592383\pi$
$98$	6.60723	−	2.31183i	0.667431	−	0.233530i
$99$	−2.96786	+	4.61808i	−0.298281	+	0.464134i
$100$	3.67014	−	8.03647i	0.367014	−	0.803647i
$101$	6.82169	+	5.91103i	0.678783	+	0.588169i	0.924504	−	0.381171i	$-0.124479\pi$
$101$	6.82169	+	5.91103i	0.678783	+	0.588169i	−0.245721	+	0.969341i	$0.579025\pi$
$102$	−0.241532	−	0.375830i	−0.0239152	−	0.0372128i
$103$	2.35220	+	16.3599i	0.231769	+	1.61199i	0.690446	+	0.723384i	$0.257414\pi$
$103$	2.35220	+	16.3599i	0.231769	+	1.61199i	−0.458678	+	0.888603i	$0.651677\pi$
$104$	−1.35031	+	0.194146i	−0.132409	+	0.0190375i
$105$	5.52969	+	8.14043i	0.539642	+	0.794425i
$106$	5.80196	+	5.02742i	0.563536	+	0.488307i
$107$	11.2675	+	5.14572i	1.08928	+	0.497455i	0.877360	−	0.479833i	$-0.159303\pi$
$107$	11.2675	+	5.14572i	1.08928	+	0.497455i	0.211915	+	0.977288i	$0.432030\pi$
$108$	0.540641	−	0.841254i	0.0520232	−	0.0809497i
$109$	−2.17327	−	7.40148i	−0.208162	−	0.708933i	−0.995697	−	0.0926644i	$-0.970462\pi$
$109$	−2.17327	−	7.40148i	−0.208162	−	0.708933i	0.787536	−	0.616269i	$-0.211357\pi$
$110$	−15.4312	+	13.3712i	−1.47131	+	1.27490i
$111$	7.31760	+	2.14864i	0.694556	+	0.203940i
$112$	−1.16007	−	2.37787i	−0.109616	−	0.224687i
$113$	−15.9106	−	2.28759i	−1.49674	−	0.215199i	−0.655226	−	0.755433i	$-0.727427\pi$
$113$	−15.9106	−	2.28759i	−1.49674	−	0.215199i	−0.841515	+	0.540234i	$0.818336\pi$
$114$			4.01547i			0.376084i
$115$	5.47407	−	16.9775i	0.510460	−	1.58316i
$116$	8.46678			0.786120
$117$	1.35031	+	0.194146i	0.124836	+	0.0179488i
$118$	6.24716	−	2.85298i	0.575097	−	0.262638i
$119$	1.14223	+	0.303991i	0.104708	+	0.0278668i
$120$	2.81103	−	2.43577i	0.256611	−	0.222354i
$121$	18.3597	−	5.39091i	1.66907	−	0.490082i
$122$	2.05663	+	1.32171i	0.186198	+	0.119662i
$123$	2.75255	−	6.02724i	0.248189	−	0.543458i
$124$	5.43219	+	4.70702i	0.487825	+	0.422703i
$125$	−11.9995	+	7.71163i	−1.07327	+	0.689749i
$126$	0.443155	+	2.60837i	0.0394794	+	0.232372i
$127$	−1.37586	−	9.56930i	−0.122088	−	0.849138i	−0.955184	−	0.296011i	$-0.904343\pi$
$127$	−1.37586	−	9.56930i	−0.122088	−	0.849138i	0.833097	−	0.553127i	$-0.186566\pi$
$128$	−0.841254	+	0.540641i	−0.0743570	+	0.0477863i
$129$	−0.327495	+	0.377950i	−0.0288344	+	0.0332766i
$130$	4.61562	+	2.10788i	0.404817	+	0.184874i
$131$	−7.66456	+	11.9263i	−0.669656	+	1.04200i	0.325675	+	0.945482i	$0.394408\pi$
$131$	−7.66456	+	11.9263i	−0.669656	+	1.04200i	−0.995331	+	0.0965228i	$0.969228\pi$
$132$	−5.26716	+	1.54658i	−0.458447	+	0.134612i
$133$	−7.15958	−	7.84911i	−0.620815	−	0.680604i
$134$	0.657950	−	2.24077i	0.0568382	−	0.193573i
$135$	−3.38340	+	1.54515i	−0.291197	+	0.132985i
$136$	0.0635792	−	0.442203i	0.00545187	−	0.0379186i
$137$		−	11.3000i		−	0.965421i	−0.875780	−	0.482710i	$-0.839652\pi$
$137$		−	11.3000i		−	0.965421i	0.875780	−	0.482710i	$-0.160348\pi$
$138$	3.23485	−	3.54058i	0.275369	−	0.301395i
$139$		−	14.7403i		−	1.25026i	−0.780521	−	0.625129i	$-0.785046\pi$
$139$		−	14.7403i		−	1.25026i	0.780521	−	0.625129i	$-0.214954\pi$
$140$	−1.15179	+	9.77330i	−0.0973438	+	0.825995i
$141$	2.35462	+	5.15591i	0.198295	+	0.434206i
$142$	3.68104	+	1.08085i	0.308906	+	0.0907030i
$143$	−4.90411	−	5.65965i	−0.410103	−	0.473284i
$144$	0.959493	−	0.281733i	0.0799577	−	0.0234777i
$145$	−26.4931	−	17.0261i	−2.20013	−	1.41394i
$146$	−1.77586	−	0.811006i	−0.146971	−	0.0671194i
$147$	−5.51697	−	4.30849i	−0.455032	−	0.355358i
$148$	4.12321	+	6.41585i	0.338926	+	0.527379i
$149$	19.4475	−	2.79613i	1.59320	−	0.229068i	0.712131	−	0.702047i	$-0.247730\pi$
$149$	19.4475	−	2.79613i	1.59320	−	0.229068i	0.881074	+	0.472978i	$0.156821\pi$
$150$	−8.74494	+	1.25733i	−0.714021	+	0.102661i
$151$	−9.31258	+	5.98483i	−0.757847	+	0.487039i	−0.861615	−	0.507563i	$-0.830546\pi$
$151$	−9.31258	+	5.98483i	−0.757847	+	0.487039i	0.103768	+	0.994602i	$0.466910\pi$
$152$	−2.62958	+	3.03469i	−0.213287	+	0.246146i
$153$	−0.185587	+	0.406379i	−0.0150038	+	0.0328538i
$154$	7.53825	−	12.4145i	0.607450	−	1.00039i
$155$	−7.53220	−	25.6523i	−0.605001	−	2.06044i
$156$	0.893359	+	1.03099i	0.0715260	+	0.0825454i
$157$	14.7645	+	4.33524i	1.17833	+	0.345990i	0.811532	−	0.584309i	$-0.198634\pi$
$157$	14.7645	+	4.33524i	1.17833	+	0.345990i	0.366803	+	0.930299i	$0.380452\pi$
$158$	−8.30746	+	3.79389i	−0.660906	+	0.301826i
$159$	1.09256	−	7.59895i	0.0866459	−	0.602636i
$160$	3.71952			0.294054
$161$	−0.0103599	+	12.6886i	−0.000816476	+	1.00000i
$162$	−1.00000			−0.0785674
$163$	0.556023	−	3.86722i	0.0435511	−	0.302904i	−0.956390	−	0.292091i	$-0.905649\pi$
$163$	0.556023	−	3.86722i	0.0435511	−	0.302904i	0.999942	−	0.0108132i	$-0.00344200\pi$
$164$	6.02724	−	2.75255i	0.470648	−	0.214938i
$165$	19.5913	+	5.75253i	1.52518	+	0.447834i
$166$	7.99401	+	9.22557i	0.620455	+	0.716043i
$167$	3.72568	+	12.6885i	0.288301	+	0.981865i	0.968537	+	0.248871i	$0.0800594\pi$
$167$	3.72568	+	12.6885i	0.288301	+	0.981865i	−0.680235	+	0.732994i	$0.738122\pi$
$168$	−1.37321	+	2.26148i	−0.105945	+	0.174477i
$169$	4.62729	−	10.1324i	0.355946	−	0.779412i
$170$	−1.08818	+	1.25583i	−0.0834597	+	0.0963177i
$171$	3.37803	−	2.17093i	0.258325	−	0.166015i
$172$	−0.495009	+	0.0711716i	−0.0377441	+	0.00542678i
$173$	8.81222	−	1.26701i	0.669981	−	0.0963287i	0.201073	−	0.979576i	$-0.435557\pi$
$173$	8.81222	−	1.26701i	0.669981	−	0.0963287i	0.468907	+	0.883248i	$0.344648\pi$
$174$	−4.57748	−	7.12270i	−0.347018	−	0.539971i
$175$	14.8520	−	18.0499i	1.12271	−	1.36445i
$176$	−4.99344	−	2.28043i	−0.376395	−	0.171894i
$177$	−5.77755	−	3.71300i	−0.434267	−	0.279086i
$178$	−3.37627	+	0.991363i	−0.253062	+	0.0743058i
$179$	9.77926	+	11.2859i	0.730936	+	0.843545i	0.992577	−	0.121620i	$-0.0388090\pi$
$179$	9.77926	+	11.2859i	0.730936	+	0.843545i	−0.261641	+	0.965165i	$0.584264\pi$
$180$	−3.56886	−	1.04791i	−0.266007	−	0.0781067i
$181$	−9.44569	−	20.6832i	−0.702093	−	1.53737i	−0.837415	−	0.546567i	$-0.815934\pi$
$181$	−9.44569	−	20.6832i	−0.702093	−	1.53737i	0.135323	−	0.990802i	$-0.456793\pi$
$182$	−3.58452	−	0.422437i	−0.265702	−	0.0313131i
$183$		−	2.44472i		−	0.180719i
$184$	4.76333	−	0.557417i	0.351157	−	0.0410933i
$185$		−	28.3671i		−	2.08559i
$186$	1.02293	−	7.11466i	0.0750051	−	0.521672i
$187$	2.23082	−	1.01878i	0.163134	−	0.0745008i
$188$	−1.59690	+	5.43853i	−0.116466	+	0.396645i
$189$	1.95472	−	1.78300i	0.142185	−	0.129694i
$190$	14.3307	−	4.20786i	1.03965	−	0.305270i
$191$	−0.607617	+	0.945470i	−0.0439656	+	0.0684118i	−0.862541	−	0.505988i	$-0.831128\pi$
$191$	−0.607617	+	0.945470i	−0.0439656	+	0.0684118i	0.818575	+	0.574400i	$0.194764\pi$
$192$	0.909632	+	0.415415i	0.0656470	+	0.0299800i
$193$	−6.29560	+	7.26551i	−0.453167	+	0.522983i	−0.935653	−	0.352921i	$-0.885189\pi$
$193$	−6.29560	+	7.26551i	−0.453167	+	0.522983i	0.482486	+	0.875904i	$0.339734\pi$
$194$	8.89420	−	5.71596i	0.638566	−	0.410382i
$195$	−0.722129	−	5.02252i	−0.0517127	−	0.359670i
$196$	−1.34799	−	6.86898i	−0.0962850	−	0.490642i
$197$	9.61934	−	6.18198i	0.685350	−	0.440448i	−0.151080	−	0.988522i	$-0.548275\pi$
$197$	9.61934	−	6.18198i	0.685350	−	0.440448i	0.836430	+	0.548074i	$0.184639\pi$
$198$	4.14870	+	3.59487i	0.294835	+	0.255476i
$199$	−4.15466	+	9.09743i	−0.294516	+	0.644900i	−0.997820	−	0.0659889i	$-0.978980\pi$
$199$	−4.15466	+	9.09743i	−0.294516	+	0.644900i	0.703304	+	0.710889i	$0.251707\pi$
$200$	−7.43236	−	4.77649i	−0.525547	−	0.337749i
$201$	−2.24077	+	0.657950i	−0.158052	+	0.0464082i
$202$	6.82169	−	5.91103i	0.479972	−	0.415898i
$203$	21.6475	+	5.76122i	1.51935	+	0.404358i
$204$	−0.406379	+	0.185587i	−0.0284522	+	0.0129937i
$205$	−24.3948	−	3.50744i	−1.70381	−	0.244970i
$206$	16.5281			1.15157
$207$	−4.72742	−	0.807147i	−0.328579	−	0.0561006i
$208$			1.36420i			0.0945901i
$209$	−21.8187	−	3.13705i	−1.50923	−	0.216994i
$210$	8.84453	−	4.31490i	0.610330	−	0.297756i
$211$	−14.9472	−	4.38889i	−1.02901	−	0.302144i	−0.276700	−	0.960956i	$-0.589241\pi$
$211$	−14.9472	−	4.38889i	−1.02901	−	0.302144i	−0.752307	+	0.658812i	$0.771059\pi$
$212$	5.80196	−	5.02742i	0.398480	−	0.345285i
$213$	−1.08085	−	3.68104i	−0.0740587	−	0.252221i
$214$	6.69688	−	10.4205i	0.457789	−	0.712334i
$215$	1.69204	+	0.772727i	0.115396	+	0.0526995i
$216$	−0.755750	−	0.654861i	−0.0514222	−	0.0445576i
$217$	10.6859	+	15.7310i	0.725405	+	1.06789i
$218$	−7.63543	+	1.09781i	−0.517137	+	0.0743530i
$219$	0.277838	+	1.93241i	0.0187746	+	0.130580i
$220$	11.0390	+	17.1771i	0.744251	+	1.15808i
$221$	−0.460596	−	0.399109i	−0.0309830	−	0.0268470i
$222$	3.16818	−	6.93734i	0.212634	−	0.465604i
$223$	−9.29228	+	14.4591i	−0.622257	+	0.968251i	0.376861	+	0.926270i	$0.377003\pi$
$223$	−9.29228	+	14.4591i	−0.622257	+	0.968251i	−0.999118	+	0.0419815i	$0.986633\pi$
$224$	−2.51876	+	0.809854i	−0.168292	+	0.0541107i
$225$	5.78561	+	6.67694i	0.385707	+	0.445130i
$226$	−4.52862	+	15.4231i	−0.301239	+	1.02593i
$227$	−3.50781	−	7.68103i	−0.232822	−	0.509808i	0.756775	−	0.653675i	$-0.226774\pi$
$227$	−3.50781	−	7.68103i	−0.232822	−	0.509808i	−0.989597	+	0.143867i	$0.954046\pi$
$228$	3.97460	+	0.571461i	0.263224	+	0.0378460i
$229$	5.56911			0.368017			0.184009	−	0.982925i	$-0.441093\pi$
$229$	5.56911			0.368017			0.184009	+	0.982925i	$0.441093\pi$
$230$	−16.0257	−	7.83451i	−1.05670	−	0.516592i
$231$	−14.5192	+	0.370180i	−0.955292	+	0.0243560i
$232$	1.20495	−	8.38060i	0.0791087	−	0.550213i
$233$	6.10801	+	13.3747i	0.400149	+	0.876204i	0.997255	+	0.0740419i	$0.0235899\pi$
$233$	6.10801	+	13.3747i	0.400149	+	0.876204i	−0.597106	+	0.802162i	$0.703683\pi$
$234$	0.384339	−	1.30894i	0.0251250	−	0.0855679i
$235$	15.9333	−	13.8063i	1.03937	−	0.900621i
$236$	−1.93488	−	6.58959i	−0.125950	−	0.428946i
$237$	7.68297	+	4.93755i	0.499063	+	0.320728i
$238$	0.463453	−	1.08734i	0.0300412	−	0.0704819i
$239$	19.3013	−	22.2749i	1.24850	−	1.44085i	0.395890	−	0.918298i	$-0.370436\pi$
$239$	19.3013	−	22.2749i	1.24850	−	1.44085i	0.852610	−	0.522548i	$-0.175019\pi$
$240$	−2.01093	−	3.12906i	−0.129805	−	0.201980i
$241$	−3.73370	−	25.9684i	−0.240509	−	1.67277i	−0.649597	−	0.760279i	$-0.725062\pi$
$241$	−3.73370	−	25.9684i	−0.240509	−	1.67277i	0.409088	−	0.912495i	$-0.365847\pi$
$242$	−2.72317	−	18.9401i	−0.175052	−	1.21751i
$243$	0.540641	+	0.841254i	0.0346821	+	0.0539664i
$244$	1.60095	−	1.84759i	0.102490	−	0.118280i
$245$	−9.59508	+	24.2042i	−0.613007	+	1.54635i
$246$	−5.57416	−	3.58230i	−0.355396	−	0.228399i
$247$	1.54330	+	5.25600i	0.0981980	+	0.334432i
$248$	5.43219	−	4.70702i	0.344945	−	0.298896i
$249$	3.43916	−	11.7127i	0.217948	−	0.742263i
$250$	5.92543	+	12.9749i	0.374757	+	0.820603i
$251$	−1.71200	+	11.9072i	−0.108061	+	0.751578i	0.861682	+	0.507448i	$0.169411\pi$
$251$	−1.71200	+	11.9072i	−0.108061	+	0.751578i	−0.969743	+	0.244129i	$0.921498\pi$
$252$	2.64489	−	0.0674339i	0.166613	−	0.00424794i
$253$	16.7111	+	20.3431i	1.05062	+	1.27896i
$254$	−9.66771			−0.606606
$255$	1.64479	+	0.236484i	0.103000	+	0.0148092i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	1.95820	−	6.66903i	0.122149	−	0.416003i	−0.875601	−	0.483034i	$-0.839535\pi$
$257$	1.95820	−	6.66903i	0.122149	−	0.416003i	0.997751	+	0.0670315i	$0.0213528\pi$
$258$	0.327495	+	0.377950i	0.0203890	+	0.0235301i
$259$	6.17638	+	19.2094i	0.383782	+	1.19361i
$260$	2.74330	−	4.26866i	0.170132	−	0.264731i
$261$	−3.51723	+	7.70165i	−0.217711	+	0.476720i
$262$	10.7141	+	9.28383i	0.661920	+	0.573557i
$263$	−11.0172	−	17.1431i	−0.679350	−	1.05709i	−0.994158	−	0.107933i	$-0.965577\pi$
$263$	−11.0172	−	17.1431i	−0.679350	−	1.05709i	0.314809	−	0.949155i	$-0.398060\pi$
$264$	0.781240	+	5.43364i	0.0480820	+	0.334418i
$265$	−28.2645	+	4.06382i	−1.73627	+	0.249638i
$266$	−8.78813	+	5.96967i	−0.538835	+	0.366024i
$267$	2.65934	+	2.30433i	0.162749	+	0.141023i
$268$	−2.12433	−	0.970148i	−0.129764	−	0.0592612i
$269$	−13.8744	+	21.5890i	−0.845938	+	1.31631i	0.100999	+	0.994887i	$0.467796\pi$
$269$	−13.8744	+	21.5890i	−0.845938	+	1.31631i	−0.946937	+	0.321419i	$0.895840\pi$
$270$	1.04791	+	3.56886i	0.0637738	+	0.217194i
$271$	−16.9216	+	14.6626i	−1.02791	+	0.890691i	−0.994071	−	0.108736i	$-0.965320\pi$
$271$	−16.9216	+	14.6626i	−1.02791	+	0.890691i	−0.0338413	+	0.999427i	$0.510774\pi$
$272$	−0.428654	−	0.125864i	−0.0259910	−	0.00763164i
$273$	1.58256	+	3.24388i	0.0957810	+	0.196328i
$274$	−11.1849	−	1.60815i	−0.675707	−	0.0971520i
$275$		−	48.4992i		−	2.92461i
$276$	−3.04418	−	3.70580i	−0.183238	−	0.223063i
$277$	16.5710			0.995653			0.497826	−	0.867277i	$-0.334132\pi$
$277$	16.5710			0.995653			0.497826	+	0.867277i	$0.334132\pi$
$278$	−14.5903	−	2.09777i	−0.875068	−	0.125816i
$279$	−6.53827	+	2.98593i	−0.391436	+	0.178763i
$280$	9.50991	+	2.53095i	0.568326	+	0.151253i
$281$	−7.68112	+	6.65573i	−0.458217	+	0.397048i	−0.853153	−	0.521661i	$-0.825312\pi$
$281$	−7.68112	+	6.65573i	−0.458217	+	0.397048i	0.394935	+	0.918709i	$0.370767\pi$
$282$	5.43853	−	1.59690i	0.323860	−	0.0950937i
$283$	23.1700	+	14.8905i	1.37732	+	0.885147i	0.999175	−	0.0406007i	$-0.0129272\pi$
$283$	23.1700	+	14.8905i	1.37732	+	0.885147i	0.378141	+	0.925748i	$0.376564\pi$
$284$	1.59372	−	3.48975i	0.0945697	−	0.207079i
$285$	−11.2876	−	9.78077i	−0.668620	−	0.579363i
$286$	−6.29997	+	4.04875i	−0.372525	+	0.239407i
$287$	17.2831	−	2.93635i	1.02019	−	0.173327i
$288$	−0.142315	−	0.989821i	−0.00838598	−	0.0583258i
$289$	−14.1334	+	9.08299i	−0.831377	+	0.534294i
$290$	−20.6231	+	23.8004i	−1.21103	+	1.39760i
$291$	−9.61714	−	4.39200i	−0.563766	−	0.257464i
$292$	−1.05548	+	1.64236i	−0.0617674	+	0.0961120i
$293$	7.05521	−	2.07160i	0.412170	−	0.121024i	−0.0690723	−	0.997612i	$-0.522004\pi$
$293$	7.05521	−	2.07160i	0.412170	−	0.121024i	0.481242	+	0.876588i	$0.340186\pi$
$294$	−5.04978	+	4.84765i	−0.294509	+	0.282721i
$295$	−7.19683	+	24.5101i	−0.419015	+	1.42704i
$296$	6.93734	−	3.16818i	0.403225	−	0.184146i
$297$	0.781240	−	5.43364i	0.0453322	−	0.315292i
$298$		−	19.6475i		−	1.13815i
$299$	2.87344	−	5.87768i	0.166175	−	0.339915i
$300$			8.83486i			0.510081i
$301$	−1.31404	−	0.154861i	−0.0757403	−	0.00892602i
$302$	4.59860	+	10.0695i	0.264619	+	0.579436i
$303$	−8.66076	−	2.54303i	−0.497547	−	0.146093i
$304$	2.62958	+	3.03469i	0.150817	+	0.174052i
$305$	−8.72485	+	2.56185i	−0.499583	+	0.146691i
$306$	0.375830	+	0.241532i	0.0214848	+	0.0138074i
$307$	15.3008	+	6.98764i	0.873262	+	0.398805i	0.801060	−	0.598585i	$-0.204270\pi$
$307$	15.3008	+	6.98764i	0.873262	+	0.398805i	0.0722025	+	0.997390i	$0.476997\pi$
$308$	−11.2153	−	9.22828i	−0.639050	−	0.525830i
$309$	−8.93577	−	13.9043i	−0.508338	−	0.790990i
$310$	−26.4632	+	3.80483i	−1.50301	+	0.216100i
$311$	−7.84507	+	1.12795i	−0.444853	+	0.0639602i	−0.361102	−	0.932526i	$-0.617599\pi$
$311$	−7.84507	+	1.12795i	−0.444853	+	0.0639602i	−0.0837515	+	0.996487i	$0.526690\pi$
$312$	1.14764	−	0.737541i	0.0649721	−	0.0417550i
$313$	−3.63379	+	4.19362i	−0.205394	+	0.237037i	−0.849095	−	0.528239i	$-0.822852\pi$
$313$	−3.63379	+	4.19362i	−0.205394	+	0.237037i	0.643702	+	0.765277i	$0.277398\pi$
$314$	6.39232	−	13.9972i	0.360740	−	0.789910i
$315$	−8.41164	−	5.10768i	−0.473942	−	0.287785i
$316$	2.57300	+	8.76283i	0.144742	+	0.492948i
$317$	13.6370	+	15.7379i	0.765928	+	0.883928i	0.996010	−	0.0892431i	$-0.0284448\pi$
$317$	13.6370	+	15.7379i	0.765928	+	0.883928i	−0.230082	+	0.973171i	$0.573899\pi$
$318$	−7.36611	−	2.16289i	−0.413071	−	0.121289i
$319$	42.2784	−	19.3079i	2.36713	−	1.08103i
$320$	0.529344	−	3.68167i	0.0295912	−	0.205811i
$321$	−12.3869			−0.691371
$322$	12.5579	+	1.81603i	0.699827	+	0.101203i
$323$	−1.79391			−0.0998161
$324$	−0.142315	+	0.989821i	−0.00790638	+	0.0549901i
$325$	−10.9633	+	5.00679i	−0.608137	+	0.277727i
$326$	−3.74873	−	1.10073i	−0.207623	−	0.0609636i
$327$	5.05156	+	5.82981i	0.279352	+	0.322389i
$328$	−1.86677	−	6.35762i	−0.103075	−	0.351041i
$329$	−7.78351	+	12.8184i	−0.429119	+	0.706699i
$330$	8.48211	−	18.5732i	0.466925	−	1.02242i
$331$	−9.82778	+	11.3419i	−0.540183	+	0.623405i	−0.958568	−	0.284865i	$-0.908051\pi$
$331$	−9.82778	+	11.3419i	−0.540183	+	0.623405i	0.418384	+	0.908270i	$0.362597\pi$
$332$	10.2693	−	6.59970i	0.563603	−	0.362206i
$333$	−7.54891	+	1.08537i	−0.413677	+	0.0594778i
$334$	13.0896	−	1.88199i	0.716229	−	0.102978i
$335$	4.69626	+	7.30752i	0.256584	+	0.399253i
$336$	2.04304	+	1.68107i	0.111457	+	0.0917100i
$337$	1.39022	+	0.634893i	0.0757302	+	0.0345848i	0.452920	−	0.891551i	$-0.350382\pi$
$337$	1.39022	+	0.634893i	0.0757302	+	0.0345848i	−0.377190	+	0.926136i	$0.623110\pi$
$338$	−9.37069	−	6.02218i	−0.509699	−	0.327563i
$339$	15.4231	−	4.52862i	0.837666	−	0.245961i
$340$	1.08818	+	1.25583i	0.0590149	+	0.0681069i
$341$	37.8594	+	11.1165i	2.05020	+	0.601993i
$342$	−1.66809	−	3.65260i	−0.0901999	−	0.197510i
$343$	1.22752	−	18.4795i	0.0662799	−	0.997801i
$344$			0.500099i			0.0269636i
$345$	2.07333	+	17.7173i	0.111624	+	0.953868i
$346$		−	8.90284i		−	0.478619i
$347$	−3.91988	+	27.2634i	−0.210430	+	1.46358i	0.561293	+	0.827617i	$0.310304\pi$
$347$	−3.91988	+	27.2634i	−0.210430	+	1.46358i	−0.771723	+	0.635958i	$0.780605\pi$
$348$	−7.70165	+	3.51723i	−0.412852	+	0.188543i
$349$	1.22193	−	4.16151i	0.0654084	−	0.222761i	−0.920302	−	0.391208i	$-0.872057\pi$
$349$	1.22193	−	4.16151i	0.0654084	−	0.222761i	0.985711	+	0.168448i	$0.0538754\pi$
$350$	−15.7526	−	17.2696i	−0.842009	−	0.923102i
$351$	−1.30894	+	0.384339i	−0.0698659	+	0.0205145i
$352$	−2.96786	+	4.61808i	−0.158187	+	0.246144i
$353$	11.8587	+	5.41571i	0.631177	+	0.288249i	0.705201	−	0.709007i	$-0.250857\pi$
$353$	11.8587	+	5.41571i	0.631177	+	0.288249i	−0.0740236	+	0.997256i	$0.523584\pi$
$354$	−4.49744	+	5.19032i	−0.239036	+	0.275863i
$355$	−12.0045	+	7.71481i	−0.637132	+	0.409460i
$356$	0.500779	+	3.48299i	0.0265412	+	0.184598i
$357$	−1.16529	+	0.197980i	−0.0616738	+	0.0104782i
$358$	12.5627	−	8.07357i	0.663961	−	0.426702i
$359$	−3.52808	−	3.05710i	−0.186205	−	0.161348i	0.556770	−	0.830667i	$-0.312040\pi$
$359$	−3.52808	−	3.05710i	−0.186205	−	0.161348i	−0.742975	+	0.669319i	$0.766586\pi$
$360$	−1.54515	+	3.38340i	−0.0814364	+	0.178321i
$361$	−2.41942	−	1.55487i	−0.127338	−	0.0818352i
$362$	−21.8169	+	6.40602i	−1.14667	+	0.336693i
$363$	−14.4611	+	12.5307i	−0.759013	+	0.657689i
$364$	−0.928268	+	3.48792i	−0.0486545	+	0.182816i
$365$	6.60534	−	3.01656i	0.345739	−	0.157894i
$366$	−2.41983	−	0.347920i	−0.126487	−	0.0181860i
$367$	11.9056			0.621469			0.310734	−	0.950497i	$-0.399425\pi$
$367$	11.9056			0.621469			0.310734	+	0.950497i	$0.399425\pi$
$368$	0.126149	−	4.79417i	0.00657595	−	0.249913i
$369$			6.62602i			0.344937i
$370$	−28.0783	−	4.03706i	−1.45972	−	0.209877i
$371$	18.2551	−	8.90594i	0.947757	−	0.462374i
$372$	−6.89666	−	2.02504i	−0.357575	−	0.104994i
$373$	11.7110	−	10.1476i	0.606372	−	0.525425i	−0.296668	−	0.954981i	$-0.595875\pi$
$373$	11.7110	−	10.1476i	0.606372	−	0.525425i	0.903040	+	0.429556i	$0.141330\pi$
$374$	−0.690934	−	2.35310i	−0.0357273	−	0.121676i
$375$	7.71163	−	11.9995i	0.398227	−	0.619653i
$376$	5.15591	+	2.35462i	0.265896	+	0.121430i
$377$	−8.72917	−	7.56387i	−0.449575	−	0.389559i
$378$	−1.48667	−	2.18857i	−0.0764658	−	0.112568i
$379$	−5.96227	+	0.857245i	−0.306261	+	0.0440337i	−0.293732	−	0.955888i	$-0.594897\pi$
$379$	−5.96227	+	0.857245i	−0.306261	+	0.0440337i	−0.0125292	+	0.999922i	$0.503988\pi$
$380$	−2.12556	−	14.7836i	−0.109039	−	0.758384i
$381$	5.22676	+	8.13299i	0.267775	+	0.416666i
$382$	0.849373	+	0.735986i	0.0434577	+	0.0376563i
$383$	5.46180	−	11.9597i	0.279085	−	0.611111i	−0.717234	−	0.696832i	$-0.754592\pi$
$383$	5.46180	−	11.9597i	0.279085	−	0.611111i	0.996319	+	0.0857213i	$0.0273195\pi$
$384$	0.540641	−	0.841254i	0.0275895	−	0.0429300i
$385$	16.5359	+	51.4290i	0.842749	+	2.62106i
$386$	6.29560	+	7.26551i	0.320438	+	0.369805i
$387$	0.140894	−	0.479842i	0.00716206	−	0.0243917i
$388$	−4.39200	−	9.61714i	−0.222970	−	0.488236i
$389$	−34.6193	−	4.97750i	−1.75527	−	0.252369i	−0.811823	−	0.583904i	$-0.801525\pi$
$389$	−34.6193	−	4.97750i	−1.75527	−	0.252369i	−0.943443	+	0.331534i	$0.892434\pi$
$390$	−5.07417			−0.256940
$391$	1.58176	+	1.44517i	0.0799929	+	0.0730855i
$392$	−6.99091	+	0.356711i	−0.353094	+	0.0180166i
$393$	2.01757	−	14.0325i	0.101773	−	0.707846i
$394$	−4.75008	−	10.4012i	−0.239305	−	0.524006i
$395$	9.57033	−	32.5936i	0.481536	−	1.63996i
$396$	4.14870	−	3.59487i	0.208480	−	0.180649i
$397$	−4.82102	−	16.4189i	−0.241960	−	0.824039i	−0.987505	−	0.157585i	$-0.949629\pi$
$397$	−4.82102	−	16.4189i	−0.241960	−	0.824039i	0.745546	−	0.666455i	$-0.232189\pi$
$398$	8.41357	+	5.40707i	0.421734	+	0.271032i
$399$	9.77323	+	4.16560i	0.489273	+	0.208541i
$400$	−5.78561	+	6.67694i	−0.289280	+	0.333847i
$401$	18.2531	+	28.4023i	0.911514	+	1.41834i	0.908287	+	0.418348i	$0.137391\pi$
$401$	18.2531	+	28.4023i	0.911514	+	1.41834i	0.00322726	+	0.999995i	$0.498973\pi$
$402$	0.332358	+	2.31160i	0.0165765	+	0.115292i
$403$	−1.39548	−	9.70580i	−0.0695140	−	0.483480i
$404$	−4.88003	−	7.59348i	−0.242791	−	0.377790i
$405$	2.43577	−	2.81103i	0.121034	−	0.139681i
$406$	8.78333	−	20.6072i	0.435909	−	1.02272i
$407$	35.2199	+	22.6345i	1.74579	+	1.12195i
$408$	0.125864	+	0.428654i	0.00623120	+	0.0212215i
$409$	6.31802	−	5.47460i	0.312406	−	0.270701i	−0.484518	−	0.874782i	$-0.661005\pi$
$409$	6.31802	−	5.47460i	0.312406	−	0.270701i	0.796923	+	0.604080i	$0.206459\pi$
$410$	−6.94348	+	23.6473i	−0.342914	+	1.16786i
$411$	4.69417	+	10.2788i	0.231546	+	0.507016i
$412$	2.35220	−	16.3599i	0.115884	−	0.805993i
$413$	−0.463121	−	18.1645i	−0.0227887	−	0.893819i
$414$	−1.47171	+	4.56443i	−0.0723308	+	0.224330i
$415$	−45.4049			−2.22884
$416$	1.35031	+	0.194146i	0.0662045	+	0.00951877i
$417$	6.12336	+	13.4083i	0.299862	+	0.656606i
$418$	−6.21024	+	21.1501i	−0.303753	+	1.03449i
$419$	−18.1336	−	20.9272i	−0.885882	−	1.02236i	−0.999584	−	0.0288476i	$-0.990816\pi$
$419$	−18.1336	−	20.9272i	−0.885882	−	1.02236i	0.113702	−	0.993515i	$-0.463729\pi$
$420$	−3.01227	−	9.36858i	−0.146984	−	0.457140i
$421$	6.13237	−	9.54216i	0.298874	−	0.465056i	−0.659042	−	0.752106i	$-0.729038\pi$
$421$	6.13237	−	9.54216i	0.298874	−	0.465056i	0.957916	+	0.287050i	$0.0926745\pi$
$422$	−6.47143	+	14.1705i	−0.315024	+	0.689807i
$423$	−4.28368	−	3.71183i	−0.208280	−	0.180475i
$424$	−4.15055	−	6.45838i	−0.201568	−	0.313647i
$425$	−0.561714	−	3.90680i	−0.0272471	−	0.189508i
$426$	−3.79740	+	0.545983i	−0.183984	+	0.0264530i
$427$	5.35043	−	3.63448i	0.258925	−	0.175885i
$428$	−9.36142	−	8.11171i	−0.452501	−	0.392095i
$429$	6.81204	+	3.11096i	0.328888	+	0.150198i
$430$	1.00566	−	1.56484i	0.0484974	−	0.0754634i
$431$	3.12340	+	10.6373i	0.150449	+	0.512382i	0.999883	−	0.0153134i	$-0.00487459\pi$
$431$	3.12340	+	10.6373i	0.150449	+	0.512382i	−0.849434	+	0.527695i	$0.823056\pi$
$432$	−0.755750	+	0.654861i	−0.0363610	+	0.0315070i
$433$	−1.10097	−	0.323275i	−0.0529094	−	0.0155356i	0.255171	−	0.966896i	$-0.417868\pi$
$433$	−1.10097	−	0.323275i	−0.0529094	−	0.0155356i	−0.308080	+	0.951360i	$0.599686\pi$
$434$	17.0917	−	8.33836i	0.820426	−	0.400254i
$435$	31.1718	+	4.48183i	1.49458	+	0.214887i
$436$			7.71395i			0.369431i
$437$	−4.93757	−	18.6138i	−0.236196	−	0.890418i
$438$	1.95228			0.0932835
$439$	30.8716	+	4.43866i	1.47342	+	0.211846i	0.831757	−	0.555141i	$-0.187336\pi$
$439$	30.8716	+	4.43866i	1.47342	+	0.211846i	0.641663	+	0.766986i	$0.278245\pi$
$440$	18.5732	−	8.48211i	0.885444	−	0.404369i
$441$	6.80822	+	1.62730i	0.324201	+	0.0774907i
$442$	−0.460596	+	0.399109i	−0.0219083	+	0.0189837i
$443$	−19.0098	+	5.58179i	−0.903184	+	0.265199i	−0.700169	−	0.713977i	$-0.746892\pi$
$443$	−19.0098	+	5.58179i	−0.903184	+	0.265199i	−0.203015	+	0.979176i	$0.565074\pi$
$444$	−6.41585	−	4.12321i	−0.304483	−	0.195679i
$445$	5.43707	−	11.9055i	0.257742	−	0.564376i
$446$	12.9895	+	11.2554i	0.615069	+	0.532961i
$447$	−16.5286	+	10.6223i	−0.781774	+	0.502415i
$448$	0.443155	+	2.60837i	0.0209371	+	0.123234i
$449$	4.27213	+	29.7133i	0.201614	+	1.40226i	0.799495	+	0.600673i	$0.205101\pi$
$449$	4.27213	+	29.7133i	0.201614	+	1.40226i	−0.597880	+	0.801585i	$0.703990\pi$
$450$	7.43236	−	4.77649i	0.350365	−	0.225166i
$451$	23.8197	−	27.4894i	1.12163	−	1.29442i
$452$	14.6216	+	6.67746i	0.687742	+	0.314081i
$453$	5.98483	−	9.31258i	0.281192	−	0.437543i
$454$	−8.10207	+	2.37898i	−0.380249	+	0.111651i
$455$	9.91855	−	9.04723i	0.464989	−	0.424141i
$456$	1.13129	−	3.85282i	0.0529775	−	0.180425i
$457$	19.2780	−	8.80397i	0.901787	−	0.411832i	0.0901052	−	0.995932i	$-0.471280\pi$
$457$	19.2780	−	8.80397i	0.901787	−	0.411832i	0.811682	+	0.584100i	$0.198552\pi$
$458$	0.792567	−	5.51242i	0.0370342	−	0.257579i
$459$		−	0.446750i		−	0.0208525i
$460$	−10.0355	+	14.7476i	−0.467906	+	0.687610i
$461$		−	2.68854i		−	0.125218i	−0.998038	−	0.0626089i	$-0.980058\pi$
$461$		−	2.68854i		−	0.125218i	0.998038	−	0.0626089i	$-0.0199421\pi$
$462$	−1.69988	+	14.4241i	−0.0790858	+	0.671069i
$463$	−2.50588	−	5.48712i	−0.116458	−	0.255008i	0.842422	−	0.538818i	$-0.181129\pi$
$463$	−2.50588	−	5.48712i	−0.116458	−	0.255008i	−0.958881	+	0.283810i	$0.908402\pi$
$464$	−8.12381	−	2.38537i	−0.377138	−	0.110738i
$465$	17.5079	+	20.2052i	0.811909	+	0.936993i
$466$	14.1078	−	4.14242i	0.653531	−	0.191894i
$467$	−27.5182	−	17.6849i	−1.27339	−	0.818359i	−0.283334	−	0.959021i	$-0.591440\pi$
$467$	−27.5182	−	17.6849i	−1.27339	−	0.818359i	−0.990058	+	0.140663i	$0.955077\pi$
$468$	−1.24092	−	0.566708i	−0.0573614	−	0.0261961i
$469$	−4.77125	−	3.92593i	−0.220316	−	0.181283i
$470$	−11.3982	−	17.7359i	−0.525759	−	0.818097i
$471$	−15.2312	+	2.18991i	−0.701815	+	0.100906i
$472$	−6.79788	+	0.977387i	−0.312898	+	0.0449879i
$473$	−2.30950	+	1.48422i	−0.106191	+	0.0682447i
$474$	5.98069	−	6.90209i	0.274702	−	0.317023i
$475$	−14.7373	+	32.2703i	−0.676195	+	1.48066i
$476$	−1.01032	−	0.613481i	−0.0463079	−	0.0281189i
$477$	2.16289	+	7.36611i	0.0990318	+	0.337271i
$478$	−19.3013	−	22.2749i	−0.882823	−	1.01883i
$479$	−14.4245	−	4.23541i	−0.659071	−	0.193521i	−0.0649401	−	0.997889i	$-0.520686\pi$
$479$	−14.4245	−	4.23541i	−0.659071	−	0.193521i	−0.594131	+	0.804369i	$0.702504\pi$
$480$	−3.38340	+	1.54515i	−0.154430	+	0.0705260i
$481$	1.48066	−	10.2982i	0.0675122	−	0.469557i
$482$	−26.2355			−1.19499
$483$	−5.26160	−	11.5462i	−0.239411	−	0.525372i
$484$	−19.1348			−0.869765
$485$	−5.59651	+	38.9246i	−0.254125	+	1.76748i
$486$	0.909632	−	0.415415i	0.0412617	−	0.0188436i
$487$	5.61860	+	1.64977i	0.254603	+	0.0747582i	0.406543	−	0.913631i	$-0.366734\pi$
$487$	5.61860	+	1.64977i	0.254603	+	0.0747582i	−0.151940	+	0.988390i	$0.548552\pi$
$488$	−1.60095	−	1.84759i	−0.0724716	−	0.0836367i
$489$	1.10073	+	3.74873i	0.0497766	+	0.169523i
$490$	22.5923	+	12.9420i	1.02062	+	0.584661i
$491$	−8.81747	+	19.3076i	−0.397927	+	0.871338i	0.599550	+	0.800338i	$0.295346\pi$
$491$	−8.81747	+	19.3076i	−0.397927	+	0.871338i	−0.997476	+	0.0710004i	$0.977381\pi$
$492$	−4.33912	+	5.00761i	−0.195623	+	0.225761i
$493$	3.18207	−	2.04499i	0.143313	−	0.0921019i
$494$	5.42214	−	0.779586i	0.243954	−	0.0350752i
$495$	−20.2106	+	2.90584i	−0.908398	+	0.130608i
$496$	−3.88603	−	6.04678i	−0.174488	−	0.271508i
$497$	6.44934	−	7.83799i	0.289293	−	0.351582i
$498$	−11.1040	−	5.07105i	−0.497584	−	0.227239i
$499$	−24.6250	−	15.8255i	−1.10236	−	0.708447i	−0.142748	−	0.989759i	$-0.545594\pi$
$499$	−24.6250	−	15.8255i	−1.10236	−	0.708447i	−0.959616	+	0.281312i	$0.909230\pi$
$500$	13.6861	−	4.01860i	0.612060	−	0.179717i
$501$	−8.65998	−	9.99415i	−0.386899	−	0.446506i
$502$	11.5424	+	3.38915i	0.515162	+	0.151265i
$503$	16.1018	+	35.2580i	0.717943	+	1.57208i	0.816764	+	0.576971i	$0.195766\pi$
$503$	16.1018	+	35.2580i	0.717943	+	1.57208i	−0.0988212	+	0.995105i	$0.531507\pi$
$504$	0.309660	−	2.62757i	0.0137933	−	0.117041i
$505$			33.5739i			1.49402i
$506$	22.5143	−	13.6459i	1.00088	−	0.606633i
$507$			11.1390i			0.494699i
$508$	−1.37586	+	9.56930i	−0.0610438	+	0.424569i
$509$	−15.2732	+	6.97502i	−0.676971	+	0.309162i	−0.724069	−	0.689728i	$-0.757730\pi$
$509$	−15.2732	+	6.97502i	−0.676971	+	0.309162i	0.0470975	+	0.998890i	$0.485003\pi$
$510$	0.468155	−	1.59439i	0.0207302	−	0.0706007i
$511$	−3.81615	+	3.48091i	−0.168817	+	0.153987i
$512$	0.959493	−	0.281733i	0.0424040	−	0.0124509i
$513$	−2.17093	+	3.37803i	−0.0958488	+	0.149144i
$514$	−6.32247	−	2.88738i	−0.278872	−	0.127357i
$515$	−40.2587	+	46.4610i	−1.77401	+	2.04732i
$516$	0.420710	−	0.270374i	0.0185207	−	0.0119026i
$517$	4.42817	+	30.7986i	0.194751	+	1.35452i
$518$	19.8928	−	3.37973i	0.874041	−	0.148497i
$519$	−7.48954	+	4.81324i	−0.328754	+	0.211278i
$520$	−3.83480	−	3.32287i	−0.168167	−	0.145718i
$521$	0.541789	−	1.18635i	0.0237362	−	0.0519750i	−0.897393	−	0.441233i	$-0.854541\pi$
$521$	0.541789	−	1.18635i	0.0237362	−	0.0519750i	0.921129	+	0.389258i	$0.127269\pi$
$522$	7.12270	+	4.57748i	0.311752	+	0.200351i
$523$	−17.1629	+	5.03948i	−0.750481	+	0.220361i	−0.634535	−	0.772894i	$-0.718808\pi$
$523$	−17.1629	+	5.03948i	−0.750481	+	0.220361i	−0.115946	+	0.993255i	$0.536990\pi$
$524$	10.7141	−	9.28383i	0.468048	−	0.405566i
$525$	−6.01168	+	22.5886i	−0.262371	+	0.985846i
$526$	−18.5365	+	8.46534i	−0.808230	+	0.369106i
$527$	3.17848	+	0.456996i	0.138457	+	0.0199071i
$528$	5.48952			0.238901
$529$	−10.6416	+	20.3901i	−0.462677	+	0.886527i
$530$			28.5551i			1.24036i
$531$	6.79788	+	0.977387i	0.295003	+	0.0424150i
$532$	4.65822	+	9.54825i	0.201960	+	0.413969i
$533$	−8.67305	−	2.54664i	−0.375671	−	0.110307i
$534$	2.65934	−	2.30433i	0.115081	−	0.0997181i
$535$	12.9804	+	44.2072i	0.561192	+	1.91124i
$536$	−1.26260	+	1.96464i	−0.0545359	+	0.0848595i
$537$	−13.5838	−	6.20353i	−0.586186	−	0.267702i
$538$	19.3947	+	16.8056i	0.836167	+	0.724542i
$539$	−22.3953	−	31.2259i	−0.964635	−	1.34499i
$540$	3.68167	−	0.529344i	0.158434	−	0.0227793i
$541$	3.06234	+	21.2990i	0.131660	+	0.915717i	0.943390	+	0.331684i	$0.107617\pi$
$541$	3.06234	+	21.2990i	0.131660	+	0.915717i	−0.811730	+	0.584033i	$0.801474\pi$
$542$	12.1052	+	18.8360i	0.519962	+	0.809077i
$543$	17.1842	+	14.8902i	0.737445	+	0.639000i
$544$	−0.185587	+	0.406379i	−0.00795697	+	0.0174233i
$545$	15.5122	−	24.1374i	0.664469	−	1.03393i
$546$	3.43608	−	1.10480i	0.147051	−	0.0472811i
$547$	24.6438	+	28.4405i	1.05369	+	1.21603i	0.975708	+	0.219073i	$0.0703034\pi$
$547$	24.6438	+	28.4405i	1.05369	+	1.21603i	0.0779857	+	0.996954i	$0.475151\pi$
$548$	−3.18357	+	10.8422i	−0.135995	+	0.463157i
$549$	1.01557	+	2.22379i	0.0433436	+	0.0949092i
$550$	−48.0055	−	6.90215i	−2.04696	−	0.294309i
$551$	−33.9981			−1.44837
$552$	−4.10132	+	2.48580i	−0.174564	+	0.105803i
$553$	0.615858	+	24.1552i	0.0261890	+	1.02718i
$554$	2.35829	−	16.4023i	0.100194	−	0.696867i
$555$	11.7841	+	25.8036i	0.500208	+	1.09530i
$556$	−4.15283	+	14.1432i	−0.176119	+	0.599807i
$557$	−25.4566	+	22.0583i	−1.07863	+	0.934640i	−0.998069	−	0.0621093i	$-0.980217\pi$
$557$	−25.4566	+	22.0583i	−1.07863	+	0.934640i	−0.0805629	+	0.996750i	$0.525672\pi$
$558$	2.02504	+	6.89666i	0.0857269	+	0.291959i
$559$	0.573932	+	0.368844i	0.0242747	+	0.0156004i
$560$	3.85859	−	9.05292i	0.163055	−	0.382556i
$561$	−1.60601	+	1.85343i	−0.0678058	+	0.0782521i
$562$	5.49485	+	8.55015i	0.231786	+	0.360666i
$563$	−3.41619	−	23.7601i	−0.143975	−	1.00137i	−0.925839	−	0.377919i	$-0.876640\pi$
$563$	−3.41619	−	23.7601i	−0.143975	−	1.00137i	0.781863	−	0.623450i	$-0.214269\pi$
$564$	−0.806658	−	5.61043i	−0.0339664	−	0.236242i
$565$	−32.3240	−	50.2971i	−1.35988	−	2.11602i
$566$	18.0364	−	20.8151i	0.758125	−	0.874923i
$567$	−1.03739	+	2.43389i	−0.0435662	+	0.102214i
$568$	−3.22742	−	2.07414i	−0.135420	−	0.0870289i
$569$	−9.67439	−	32.9480i	−0.405572	−	1.38125i	−0.868867	−	0.495046i	$-0.835151\pi$
$569$	−9.67439	−	32.9480i	−0.405572	−	1.38125i	0.463295	−	0.886204i	$-0.346667\pi$
$570$	−11.2876	+	9.78077i	−0.472786	+	0.409671i
$571$	−0.703963	+	2.39748i	−0.0294599	+	0.100331i	−0.972911	−	0.231182i	$-0.925741\pi$
$571$	−0.703963	+	2.39748i	−0.0294599	+	0.100331i	0.943451	+	0.331513i	$0.107559\pi$
$572$	3.11096	+	6.81204i	0.130076	+	0.284826i
$573$	0.159945	−	1.11244i	0.00668180	−	0.0464730i
$574$	−0.446818	−	17.5251i	−0.0186498	−	0.731484i
$575$	38.9912	−	16.5815i	1.62605	−	0.691495i
$576$	−1.00000			−0.0416667
$577$	−31.1210	−	4.47453i	−1.29558	−	0.186277i	−0.540188	−	0.841544i	$-0.681647\pi$
$577$	−31.1210	−	4.47453i	−1.29558	−	0.186277i	−0.755397	+	0.655267i	$0.772556\pi$
$578$	6.97914	+	15.2822i	0.290294	+	0.635655i
$579$	2.70848	−	9.22423i	0.112561	−	0.383346i
$580$	20.6231	+	23.8004i	0.856329	+	0.988256i
$581$	30.7469	−	9.88604i	1.27560	−	0.410142i
$582$	−5.71596	+	8.89420i	−0.236934	+	0.368676i
$583$	17.5071	−	38.3351i	0.725068	−	1.58768i
$584$	1.47543	+	1.27847i	0.0610539	+	0.0529035i
$585$	2.74330	+	4.26866i	0.113422	+	0.176487i
$586$	−1.04645	−	7.27822i	−0.0432285	−	0.300661i
$587$	14.2006	−	2.04173i	0.586120	−	0.0842713i	0.157126	−	0.987579i	$-0.449777\pi$
$587$	14.2006	−	2.04173i	0.586120	−	0.0842713i	0.428994	+	0.903307i	$0.358868\pi$
$588$	4.07965	+	5.68827i	0.168242	+	0.234580i
$589$	−21.8128	−	18.9009i	−0.898782	−	0.778799i
$590$	23.2364	+	10.6117i	0.956629	+	0.436878i
$591$	−6.18198	+	9.61934i	−0.254293	+	0.395687i
$592$	−2.14864	−	7.31760i	−0.0883087	−	0.300752i
$593$	0.0833018	−	0.0721814i	0.00342079	−	0.00296413i	−0.653149	−	0.757230i	$-0.726552\pi$
$593$	0.0833018	−	0.0721814i	0.00342079	−	0.00296413i	0.656569	+	0.754266i	$0.272007\pi$
$594$	−5.26716	−	1.54658i	−0.216114	−	0.0634568i
$595$	1.92768	+	3.95130i	0.0790273	+	0.161987i
$596$	−19.4475	−	2.79613i	−0.796602	−	0.114534i
$597$		−	10.0012i		−	0.409323i
$598$	−5.40892	−	3.68067i	−0.221187	−	0.150514i
$599$	−28.3385			−1.15788			−0.578939	−	0.815371i	$-0.696533\pi$
$599$	−28.3385			−1.15788			−0.578939	+	0.815371i	$0.696533\pi$
$600$	8.74494	+	1.25733i	0.357011	+	0.0513304i
$601$	−28.5854	+	13.0545i	−1.16602	+	0.532504i	−0.901883	−	0.431980i	$-0.857815\pi$
$601$	−28.5854	+	13.0545i	−1.16602	+	0.532504i	−0.264139	+	0.964485i	$0.585088\pi$
$602$	−0.340293	+	1.27863i	−0.0138693	+	0.0521131i
$603$	1.76496	−	1.52934i	0.0718745	−	0.0622796i
$604$	10.6215	−	3.11875i	0.432182	−	0.126900i
$605$	59.8741	+	38.4788i	2.43423	+	1.56438i
$606$	−3.74970	+	8.21069i	−0.152321	+	0.333537i
$607$	−0.161701	−	0.140114i	−0.00656322	−	0.00568707i	0.651573	−	0.758586i	$-0.274109\pi$
$607$	−0.161701	−	0.140114i	−0.00656322	−	0.00568707i	−0.658136	+	0.752899i	$0.728655\pi$
$608$	3.37803	−	2.17093i	0.136997	−	0.0880428i
$609$	−22.0845	+	3.75209i	−0.894910	+	0.152042i
$610$	1.29410	+	9.00063i	0.0523964	+	0.364425i
$611$	6.50494	−	4.18047i	0.263162	−	0.169124i
$612$	0.292559	−	0.337631i	0.0118260	−	0.0136479i
$613$	−8.81647	−	4.02635i	−0.356094	−	0.162623i	0.229333	−	0.973348i	$-0.426346\pi$
$613$	−8.81647	−	4.02635i	−0.356094	−	0.162623i	−0.585426	+	0.810726i	$0.699073\pi$
$614$	9.09404	−	14.1506i	0.367006	−	0.571072i
$615$	23.6473	−	6.94348i	0.953552	−	0.279988i
$616$	−10.7305	+	9.78781i	−0.432342	+	0.394362i
$617$	−10.4511	+	35.5931i	−0.420744	+	1.43292i	0.427835	+	0.903857i	$0.359276\pi$
$617$	−10.4511	+	35.5931i	−0.420744	+	1.43292i	−0.848580	+	0.529067i	$0.822542\pi$
$618$	−15.0345	+	6.86602i	−0.604776	+	0.276192i
$619$	−4.62763	+	32.1858i	−0.186000	+	1.29366i	0.656239	+	0.754553i	$0.272147\pi$
$619$	−4.62763	+	32.1858i	−0.186000	+	1.29366i	−0.842239	+	0.539105i	$0.818763\pi$
$620$			26.7353i			1.07371i
$621$	4.63551	−	1.22964i	0.186017	−	0.0493436i
$622$			7.92574i			0.317793i
$623$	−1.08963	+	9.24591i	−0.0436552	+	0.370429i
$624$	−0.566708	−	1.24092i	−0.0226865	−	0.0496765i
$625$	−8.52078	−	2.50193i	−0.340831	−	0.100077i
$626$	3.63379	+	4.19362i	0.145235	+	0.167611i
$627$	21.1501	−	6.21024i	0.844655	−	0.248013i
$628$	−12.9450	−	8.31927i	−0.516563	−	0.331975i
$629$	3.09926	+	1.41538i	0.123576	+	0.0564351i
$630$	−6.25279	+	7.59912i	−0.249117	+	0.302756i
$631$	−4.22203	−	6.56960i	−0.168076	−	0.261532i	0.746990	−	0.664835i	$-0.231498\pi$
$631$	−4.22203	−	6.56960i	−0.168076	−	0.261532i	−0.915066	+	0.403304i	$0.867862\pi$
$632$	9.03981	−	1.29973i	0.359584	−	0.0517004i
$633$	15.4197	−	2.21701i	0.612877	−	0.0881184i
$634$	17.5184	−	11.2584i	0.695746	−	0.447129i
$635$	23.5483	−	27.1762i	0.934487	−	1.07845i
$636$	−3.18918	+	6.98333i	−0.126459	+	0.276907i
$637$	−4.74670	+	8.28610i	−0.188071	+	0.328307i
$638$	−13.0945	−	44.5958i	−0.518417	−	1.76557i
$639$	2.51234	+	2.89939i	0.0993865	+	0.114698i
$640$	−3.56886	−	1.04791i	−0.141071	−	0.0414223i
$641$	33.9239	−	15.4925i	1.33991	−	0.611918i	0.388961	−	0.921254i	$-0.372834\pi$
$641$	33.9239	−	15.4925i	1.33991	−	0.611918i	0.950953	+	0.309336i	$0.100107\pi$
$642$	−1.76284	+	12.2608i	−0.0695739	+	0.483897i
$643$	−35.1147			−1.38479			−0.692394	−	0.721520i	$-0.743444\pi$
$643$	−35.1147			−1.38479			−0.692394	+	0.721520i	$0.743444\pi$
$644$	3.58472	−	12.1717i	0.141258	−	0.479631i
$645$	−1.86013			−0.0732426
$646$	−0.255301	+	1.77566i	−0.0100447	+	0.0698622i
$647$	−42.7584	+	19.5271i	−1.68100	+	0.767689i	−0.681654	+	0.731675i	$0.738739\pi$
$647$	−42.7584	+	19.5271i	−1.68100	+	0.767689i	−0.999351	+	0.0360141i	$0.988534\pi$
$648$	0.959493	+	0.281733i	0.0376924	+	0.0110675i
$649$	−24.6888	−	28.4924i	−0.969120	−	1.11842i
$650$	3.39558	+	11.5643i	0.133186	+	0.453589i
$651$	−16.2551	−	9.87037i	−0.637089	−	0.386850i
$652$	−1.62302	+	3.55393i	−0.0635625	+	0.139182i
$653$	26.5706	−	30.6641i	1.03979	−	1.19998i	0.0603597	−	0.998177i	$-0.480775\pi$
$653$	26.5706	−	30.6641i	1.03979	−	1.19998i	0.979427	−	0.201801i	$-0.0646793\pi$
$654$	6.48939	−	4.17048i	0.253755	−	0.163079i
$655$	−52.1942	+	7.50440i	−2.03940	+	0.293221i
$656$	−6.55858	+	0.942981i	−0.256069	+	0.0368172i
$657$	−1.05548	−	1.64236i	−0.0411783	−	0.0640747i
$658$	11.5802	+	9.52853i	0.451442	+	0.371461i
$659$	−24.0297	−	10.9740i	−0.936066	−	0.427487i	−0.111826	−	0.993728i	$-0.535670\pi$
$659$	−24.0297	−	10.9740i	−0.936066	−	0.427487i	−0.824240	+	0.566241i	$0.808397\pi$
$660$	−17.1771	−	11.0390i	−0.668616	−	0.429693i
$661$	−22.9506	+	6.73890i	−0.892674	+	0.262113i	−0.695731	−	0.718302i	$-0.744920\pi$
$661$	−22.9506	+	6.73890i	−0.892674	+	0.262113i	−0.196943	+	0.980415i	$0.563101\pi$
$662$	9.82778	+	11.3419i	0.381967	+	0.440814i
$663$	0.584769	+	0.171704i	0.0227105	+	0.00666841i
$664$	−5.07105	−	11.1040i	−0.196795	−	0.430921i
$665$	4.62497	−	39.2444i	0.179349	−	1.52183i
$666$			7.62653i			0.295522i
$667$	29.9773	+	27.3888i	1.16073	+	1.06050i
$668$		−	13.2242i		−	0.511658i
$669$	2.44604	−	17.0126i	0.0945694	−	0.657745i
$670$	7.90149	−	3.60849i	0.305261	−	0.139408i
$671$	3.78094	−	12.8767i	0.145962	−	0.497100i
$672$	1.95472	−	1.78300i	0.0754048	−	0.0687807i
$673$	16.9538	−	4.97810i	0.653523	−	0.191892i	0.0618697	−	0.998084i	$-0.480294\pi$
$673$	16.9538	−	4.97810i	0.653523	−	0.191892i	0.591653	+	0.806193i	$0.298476\pi$
$674$	0.826280	−	1.28572i	0.0318271	−	0.0495240i
$675$	−8.03647	−	3.67014i	−0.309324	−	0.141264i
$676$	−7.29447	+	8.41827i	−0.280557	+	0.323780i
$677$	14.7310	−	9.46707i	0.566160	−	0.363849i	−0.226033	−	0.974120i	$-0.572576\pi$
$677$	14.7310	−	9.46707i	0.566160	−	0.363849i	0.792193	+	0.610271i	$0.208939\pi$
$678$	−2.28759	−	15.9106i	−0.0878545	−	0.611042i
$679$	−4.68528	−	27.5772i	−0.179805	−	1.05831i
$680$	1.39791	−	0.898383i	0.0536074	−	0.0344514i
$681$	6.38163	+	5.52972i	0.244545	+	0.211899i
$682$	16.3913	−	35.8920i	0.627656	−	1.37437i
$683$	11.5344	+	7.41271i	0.441352	+	0.283639i	0.742384	−	0.669974i	$-0.233695\pi$
$683$	11.5344	+	7.41271i	0.441352	+	0.283639i	−0.301033	+	0.953614i	$0.597331\pi$
$684$	−3.85282	+	1.13129i	−0.147316	+	0.0432559i
$685$	31.7645	−	27.5241i	1.21366	−	1.05164i
$686$	−18.1167	−	3.84494i	−0.691701	−	0.146800i
$687$	−5.06584	+	2.31349i	−0.193274	+	0.0882652i
$688$	0.495009	+	0.0711716i	0.0188720	+	0.00271339i
$689$	−10.4731			−0.398992
$690$	17.8320	+	0.469213i	0.678854	+	0.0178626i
$691$		−	19.6453i		−	0.747342i	−0.927561	−	0.373671i	$-0.878099\pi$
$691$		−	19.6453i		−	0.747342i	0.927561	−	0.373671i	$-0.121901\pi$
$692$	−8.81222	−	1.26701i	−0.334990	−	0.0481643i
$693$	13.0533	−	6.36822i	0.495855	−	0.241909i
$694$	26.4280	+	7.75997i	1.00319	+	0.294564i
$695$	41.4355	−	35.9041i	1.57174	−	1.36192i
$696$	2.38537	+	8.12381i	0.0904171	+	0.307932i
$697$	1.60039	−	2.49026i	0.0606192	−	0.0943253i
$698$	−3.94525	−	1.80174i	−0.149330	−	0.0681968i
$699$	−11.1121	−	9.62867i	−0.420298	−	0.364190i
$700$	−19.3357	+	13.1345i	−0.730820	+	0.496437i
$701$	−39.7499	+	5.71518i	−1.50133	+	0.215859i	−0.843429	−	0.537241i	$-0.819467\pi$
$701$	−39.7499	+	5.71518i	−1.50133	+	0.215859i	−0.657906	+	0.753100i	$0.728557\pi$
$702$	0.194146	+	1.35031i	0.00732755	+	0.0509642i
$703$	−16.5567	−	25.7627i	−0.624446	−	0.971657i
$704$	4.14870	+	3.59487i	0.156360	+	0.135487i
$705$	−8.75808	+	19.1775i	−0.329848	+	0.722267i
$706$	7.04826	−	10.9673i	0.265265	−	0.412760i
$707$	−7.31006	−	22.7353i	−0.274923	−	0.855048i
$708$	4.49744	+	5.19032i	0.169024	+	0.195064i
$709$	1.27796	−	4.35232i	0.0479947	−	0.163455i	−0.932009	−	0.362436i	$-0.881945\pi$
$709$	1.27796	−	4.35232i	0.0479947	−	0.163455i	0.980003	+	0.198981i	$0.0637633\pi$
$710$	5.92787	+	12.9802i	0.222469	+	0.487139i
$711$	−9.03981	−	1.29973i	−0.339019	−	0.0487436i
$712$	3.51881			0.131873
$713$	4.00661	+	34.2379i	0.150049	+	1.28222i
$714$	0.0301261	+	1.18161i	0.00112744	+	0.0442205i
$715$	3.96414	−	27.5712i	0.148251	−	1.03110i
$716$	−6.20353	−	13.5838i	−0.231837	−	0.507652i
$717$	−8.30378	+	28.2801i	−0.310110	+	1.05614i
$718$	−3.52808	+	3.05710i	−0.131667	+	0.114090i
$719$	−13.5421	−	46.1203i	−0.505037	−	1.72000i	−0.677994	−	0.735068i	$-0.737150\pi$
$719$	−13.5421	−	46.1203i	−0.505037	−	1.72000i	0.172957	−	0.984929i	$-0.444668\pi$
$720$	3.12906	+	2.01093i	0.116613	+	0.0749428i
$721$	17.1461	−	40.2276i	0.638553	−	1.49815i
$722$	−1.88336	+	2.17352i	−0.0700915	+	0.0808899i
$723$	14.1840	+	22.0707i	0.527507	+	0.820817i
$724$	3.23595	+	22.5065i	0.120263	+	0.836448i
$725$	−10.6455	−	74.0414i	−0.395366	−	2.74983i
$726$	10.3451	+	16.0972i	0.383942	+	0.597425i
$727$	−2.29665	+	2.65047i	−0.0851780	+	0.0983006i	−0.796739	−	0.604324i	$-0.793443\pi$
$727$	−2.29665	+	2.65047i	−0.0851780	+	0.0983006i	0.711561	+	0.702625i	$0.247989\pi$
$728$	3.32031	+	1.41520i	0.123059	+	0.0524509i
$729$	−0.841254	−	0.540641i	−0.0311575	−	0.0200237i
$730$	−2.04582	−	6.96741i	−0.0757191	−	0.257875i
$731$	−0.168849	+	0.146309i	−0.00624512	+	0.00541142i
$732$	−0.688757	+	2.34569i	−0.0254572	+	0.0866992i
$733$	−0.205946	−	0.450959i	−0.00760680	−	0.0166566i	0.905790	−	0.423726i	$-0.139278\pi$
$733$	−0.205946	−	0.450959i	−0.00760680	−	0.0166566i	−0.913397	+	0.407069i	$0.866551\pi$
$734$	1.69435	−	11.7844i	0.0625395	−	0.434972i
$735$	−1.32679	−	26.0028i	−0.0489395	−	0.959129i
$736$	−4.72742	−	0.807147i	−0.174255	−	0.0297518i
$737$	−12.8201			−0.472233
$738$	6.55858	+	0.942981i	0.241424	+	0.0347116i
$739$	13.6028	+	29.7860i	0.500387	+	1.09570i	0.976343	+	0.216226i	$0.0693750\pi$
$739$	13.6028	+	29.7860i	0.500387	+	1.09570i	−0.475956	+	0.879469i	$0.657898\pi$
$740$	−7.99193	+	27.2180i	−0.293789	+	1.00055i
$741$	−3.58726	−	4.13992i	−0.131781	−	0.152084i
$742$	−6.21733	−	19.3367i	−0.228245	−	0.709873i
$743$	−25.5982	+	39.8316i	−0.939107	+	1.46128i	−0.0525714	+	0.998617i	$0.516742\pi$
$743$	−25.5982	+	39.8316i	−0.939107	+	1.46128i	−0.886535	+	0.462661i	$0.846895\pi$
$744$	−2.98593	+	6.53827i	−0.109469	+	0.239705i
$745$	55.2298	+	47.8569i	2.02346	+	1.75334i
$746$	−8.37770	−	13.0360i	−0.306729	−	0.477280i
$747$	1.73726	+	12.0829i	0.0635631	+	0.442091i
$748$	−2.42748	+	0.349019i	−0.0887576	+	0.0127614i
$749$	−18.4152	−	27.1096i	−0.672878	−	0.990564i
$750$	−10.7799	−	9.34085i	−0.393627	−	0.341080i
$751$	−39.5310	−	18.0532i	−1.44251	−	0.658770i	−0.468122	−	0.883664i	$-0.655069\pi$
$751$	−39.5310	−	18.0532i	−1.44251	−	0.658770i	−0.974383	+	0.224894i	$0.927796\pi$
$752$	3.06442	−	4.76833i	0.111748	−	0.173883i
$753$	−3.38915	−	11.5424i	−0.123508	−	0.420628i
$754$	−8.72917	+	7.56387i	−0.317898	+	0.275460i
$755$	−39.5068	−	11.6003i	−1.43780	−	0.422177i
$756$	−2.37787	+	1.16007i	−0.0864821	+	0.0421913i
$757$	−15.4761	−	2.22513i	−0.562490	−	0.0808738i	−0.144796	−	0.989462i	$-0.546253\pi$
$757$	−15.4761	−	2.22513i	−0.562490	−	0.0808738i	−0.417694	+	0.908588i	$0.637162\pi$
$758$			6.02358i			0.218786i
$759$	−23.6518	−	11.5627i	−0.858504	−	0.419699i
$760$	−14.9357			−0.541773
$761$	39.8653	+	5.73176i	1.44512	+	0.207776i	0.819824	−	0.572615i	$-0.194071\pi$
$761$	39.8653	+	5.73176i	1.44512	+	0.207776i	0.625291	+	0.780391i	$0.284980\pi$
$762$	8.79406	−	4.01611i	0.318575	−	0.145488i
$763$	−5.24896	+	19.7227i	−0.190025	+	0.714008i
$764$	0.849373	−	0.735986i	0.0307293	−	0.0266271i
$765$	−1.59439	+	0.468155i	−0.0576453	+	0.0169262i
$766$	−11.0606	−	7.10825i	−0.399637	−	0.256831i
$767$	−3.89203	+	8.52235i	−0.140533	+	0.307724i
$768$	−0.755750	−	0.654861i	−0.0272708	−	0.0236303i
$769$	23.8709	−	15.3409i	0.860806	−	0.553206i	−0.0341219	−	0.999418i	$-0.510863\pi$
$769$	23.8709	−	15.3409i	0.860806	−	0.553206i	0.894928	+	0.446211i	$0.147227\pi$
$770$	53.2588	−	9.04852i	1.91932	−	0.326086i
$771$	0.989171	+	6.87983i	0.0356241	+	0.247771i
$772$	8.08752	−	5.19753i	0.291076	−	0.187063i
$773$	−23.1587	+	26.7266i	−0.832962	+	0.961290i	−0.999695	−	0.0247125i	$-0.992133\pi$
$773$	−23.1587	+	26.7266i	−0.832962	+	0.961290i	0.166732	+	0.986002i	$0.446678\pi$
$774$	−0.454906	−	0.207749i	−0.0163513	−	0.00746738i
$775$	34.3325	−	53.4225i	1.23326	−	1.91899i
$776$	−10.1443	+	2.97863i	−0.364159	+	0.106927i
$777$	−13.5981	−	14.9077i	−0.487829	−	0.534811i
$778$	−9.85367	+	33.5585i	−0.353271	+	1.20313i
$779$	−24.2022	+	11.0528i	−0.867134	+	0.396007i
$780$	−0.722129	+	5.02252i	−0.0258564	+	0.179835i
$781$		−	21.0602i		−	0.753595i
$782$	1.65557	−	1.35999i	0.0592030	−	0.0486331i
$783$		−	8.46678i		−	0.302578i
$784$	−0.641830	+	6.97051i	−0.0229225	+	0.248947i
$785$	23.7764	+	52.0631i	0.848616	+	1.85821i
$786$	−13.6025	−	3.99407i	−0.485187	−	0.142464i
$787$	−5.12632	−	5.91609i	−0.182734	−	0.210886i	0.656991	−	0.753898i	$-0.271829\pi$
$787$	−5.12632	−	5.91609i	−0.182734	−	0.210886i	−0.839724	+	0.543013i	$0.817284\pi$
$788$	−10.9714	+	3.22148i	−0.390838	+	0.114760i
$789$	17.1431	+	11.0172i	0.610310	+	0.392223i
$790$	−30.8998	−	14.1115i	−1.09937	−	0.502063i
$791$	32.8401	+	27.0219i	1.16766	+	0.960787i
$792$	−2.96786	−	4.61808i	−0.105458	−	0.164096i
$793$	−3.30113	+	0.474631i	−0.117227	+	0.0168546i
$794$	−16.9379	+	2.43530i	−0.601102	+	0.0864254i
$795$	24.0221	−	15.4381i	0.851976	−	0.547532i
$796$	6.54941	−	7.55842i	0.232138	−	0.267901i
$797$	20.1944	−	44.2195i	0.715321	−	1.56634i	−0.105026	−	0.994469i	$-0.533493\pi$
$797$	20.1944	−	44.2195i	0.715321	−	1.56634i	0.820347	−	0.571866i	$-0.193780\pi$
$798$	5.51408	−	9.08092i	0.195196	−	0.321461i
$799$	0.713414	+	2.42966i	0.0252388	+	0.0859553i
$800$	5.78561	+	6.67694i	0.204552	+	0.236066i
$801$	−3.37627	−	0.991363i	−0.119295	−	0.0350281i
$802$	30.7109	−	14.0252i	1.08444	−	0.495247i
$803$	−1.52520	+	10.6080i	−0.0538231	+	0.374348i
$804$	2.33537			0.0823622
$805$	−35.6932	+	30.8773i	−1.25802	+	1.08828i
$806$	−9.80561			−0.345388
$807$	3.65221	−	25.4017i	0.128564	−	0.894182i
$808$	−8.21069	+	3.74970i	−0.288851	+	0.131914i
$809$	−36.1791	−	10.6231i	−1.27199	−	0.373490i	−0.425045	−	0.905172i	$-0.639742\pi$
$809$	−36.1791	−	10.6231i	−1.27199	−	0.373490i	−0.846944	+	0.531683i	$0.821560\pi$
$810$	−2.43577	−	2.81103i	−0.0855843	−	0.0987695i
$811$	9.37411	+	31.9253i	0.329169	+	1.12105i	0.943327	+	0.331865i	$0.107678\pi$
$811$	9.37411	+	31.9253i	0.329169	+	1.12105i	−0.614158	+	0.789183i	$0.710504\pi$
$812$	−19.1475	−	11.6266i	−0.671944	−	0.408015i
$813$	9.30133	−	20.3671i	0.326212	−	0.714304i
$814$	27.4164	−	31.6402i	0.960944	−	1.10899i
$815$	12.2252	−	7.85668i	0.428231	−	0.275207i
$816$	0.442203	−	0.0635792i	0.0154802	−	0.00222572i
$817$	1.98770	−	0.285788i	0.0695407	−	0.00999844i
$818$	−4.51972	−	7.03283i	−0.158028	−	0.245897i
$819$	−2.78710	−	2.29331i	−0.0973893	−	0.0801349i
$820$	22.4185	+	10.2382i	0.782887	+	0.357532i
$821$	8.06399	+	5.18241i	0.281435	+	0.180867i	0.673741	−	0.738967i	$-0.264686\pi$
$821$	8.06399	+	5.18241i	0.281435	+	0.180867i	−0.392306	+	0.919835i	$0.628323\pi$
$822$	10.8422	−	3.18357i	0.378166	−	0.111040i
$823$	7.11865	+	8.21536i	0.248141	+	0.286369i	0.866132	−	0.499815i	$-0.166599\pi$
$823$	7.11865	+	8.21536i	0.248141	+	0.286369i	−0.617991	+	0.786185i	$0.712053\pi$
$824$	−15.8586	−	4.65651i	−0.552461	−	0.162217i
$825$	20.1473	+	44.1164i	0.701438	+	1.53594i
$826$	−18.0456	−	2.12668i	−0.627885	−	0.0739965i
$827$		−	43.6991i		−	1.51957i	−0.650177	−	0.759783i	$-0.725305\pi$
$827$		−	43.6991i		−	1.51957i	0.650177	−	0.759783i	$-0.274695\pi$
$828$	4.30853	+	2.10632i	0.149732	+	0.0731997i
$829$			8.12001i			0.282020i	0.990008	+	0.141010i	$0.0450349\pi$
$829$			8.12001i			0.282020i	−0.990008	+	0.141010i	$0.954965\pi$
$830$	−6.46179	+	44.9428i	−0.224292	+	1.55999i
$831$	−15.0735	+	6.88383i	−0.522893	+	0.238797i
$832$	0.384339	−	1.30894i	0.0133246	−	0.0453793i
$833$	−2.16569	−	2.25599i	−0.0750368	−	0.0781654i
$834$	14.1432	−	4.15283i	0.489741	−	0.143801i
$835$	−26.5928	+	41.3792i	−0.920282	+	1.43199i
$836$	20.0510	+	9.15700i	0.693480	+	0.316702i
$837$	4.70702	−	5.43219i	0.162698	−	0.187764i
$838$	−23.2949	+	14.9707i	−0.804709	+	0.517155i
$839$	1.44212	+	10.0302i	0.0497875	+	0.346280i	0.999455	+	0.0330192i	$0.0105122\pi$
$839$	1.44212	+	10.0302i	0.0497875	+	0.346280i	−0.949667	+	0.313261i	$0.898579\pi$
$840$	−9.70191	+	1.64833i	−0.334748	+	0.0568726i
$841$	35.9100	−	23.0779i	1.23828	−	0.795791i
$842$	−8.57231	−	7.42795i	−0.295421	−	0.255984i
$843$	4.22210	−	9.24512i	0.145417	−	0.318419i
$844$	13.1052	+	8.42223i	0.451101	+	0.289905i
$845$	39.7534	−	11.6726i	1.36756	−	0.401551i
$846$	−4.28368	+	3.71183i	−0.147276	+	0.127615i
$847$	−48.9231	−	13.0203i	−1.68102	−	0.447383i
$848$	−6.98333	+	3.18918i	−0.239808	+	0.109517i
$849$	−27.2619	−	3.91968i	−0.935628	−	0.134523i
$850$	−3.94698			−0.135380
$851$	−6.15573	+	36.0538i	−0.211016	+	1.23591i
$852$			3.83645i			0.131434i
$853$	−12.7268	−	1.82984i	−0.435758	−	0.0626525i	−0.0790546	−	0.996870i	$-0.525190\pi$
$853$	−12.7268	−	1.82984i	−0.435758	−	0.0626525i	−0.356703	+	0.934218i	$0.616099\pi$
$854$	−2.83604	−	5.81321i	−0.0970472	−	0.198924i
$855$	14.3307	+	4.20786i	0.490098	+	0.143906i
$856$	−9.36142	+	8.11171i	−0.319967	+	0.277253i
$857$	3.09614	+	10.5445i	0.105762	+	0.360192i	0.995320	−	0.0966290i	$-0.0308060\pi$
$857$	3.09614	+	10.5445i	0.105762	+	0.360192i	−0.889558	+	0.456821i	$0.848988\pi$
$858$	4.04875	−	6.29997i	0.138222	−	0.215077i
$859$	9.11064	+	4.16069i	0.310851	+	0.141961i	0.564732	−	0.825275i	$-0.308980\pi$
$859$	9.11064	+	4.16069i	0.310851	+	0.141961i	−0.253880	+	0.967236i	$0.581707\pi$
$860$	−1.40579	−	1.21813i	−0.0479372	−	0.0415378i
$861$	−14.5015	+	9.85067i	−0.494209	+	0.335710i
$862$	10.9736	−	1.57776i	0.373761	−	0.0537387i
$863$	−3.38217	−	23.5235i	−0.115130	−	0.800750i	−0.962798	−	0.270222i	$-0.912903\pi$
$863$	−3.38217	−	23.5235i	−0.115130	−	0.800750i	0.847668	−	0.530528i	$-0.178006\pi$
$864$	0.540641	+	0.841254i	0.0183930	+	0.0286200i
$865$	25.0261	+	21.6853i	0.850914	+	0.737321i
$866$	−0.476669	+	1.04376i	−0.0161979	+	0.0354684i
$867$	9.08299	−	14.1334i	0.308474	−	0.479996i
$868$	−5.82109	−	18.1044i	−0.197581	−	0.614502i
$869$	32.8311	+	37.8891i	1.11372	+	1.28530i
$870$	8.87243	−	30.2167i	0.300804	−	1.02444i
$871$	1.32347	+	2.89800i	0.0448442	+	0.0981951i
$872$	7.63543	+	1.09781i	0.258568	+	0.0371765i
$873$	10.5726			0.357827
$874$	−19.1270	+	2.23829i	−0.646981	+	0.0757114i
$875$	37.7264	−	0.961868i	1.27538	−	0.0325171i
$876$	0.277838	−	1.93241i	0.00938729	−	0.0652900i
$877$	15.6495	+	34.2677i	0.528448	+	1.15714i	0.966141	+	0.258015i	$0.0830683\pi$
$877$	15.6495	+	34.2677i	0.528448	+	1.15714i	−0.437693	+	0.899124i	$0.644204\pi$
$878$	8.78697	−	29.9257i	0.296546	−	1.00994i
$879$	−5.55707	+	4.81523i	−0.187435	+	0.162414i
$880$	−5.75253	−	19.5913i	−0.193918	−	0.660423i
$881$	33.9373	+	21.8102i	1.14338	+	0.734803i	0.968309	−	0.249754i	$-0.0803498\pi$
$881$	33.9373	+	21.8102i	1.14338	+	0.734803i	0.175066	+	0.984557i	$0.443986\pi$
$882$	2.57965	−	6.50733i	0.0868614	−	0.219113i
$883$	33.4723	−	38.6291i	1.12643	−	1.29997i	0.177631	−	0.984097i	$-0.443157\pi$
$883$	33.4723	−	38.6291i	1.12643	−	1.29997i	0.948801	−	0.315875i	$-0.102298\pi$
$884$	0.329497	+	0.512707i	0.0110822	+	0.0172442i
$885$	−3.63542	−	25.2849i	−0.122203	−	0.849942i
$886$	2.81959	+	19.6107i	0.0947261	+	0.658835i
$887$	24.7221	+	38.4683i	0.830086	+	1.29164i	0.954139	+	0.299363i	$0.0967743\pi$
$887$	24.7221	+	38.4683i	0.830086	+	1.29164i	−0.124053	+	0.992276i	$0.539589\pi$
$888$	−4.99432	+	5.76375i	−0.167598	+	0.193419i
$889$	−10.0292	+	23.5301i	−0.336367	+	0.789176i
$890$	−11.0106	−	7.07607i	−0.369075	−	0.237190i
$891$	1.54658	+	5.26716i	0.0518123	+	0.176456i
$892$	12.9895	−	11.2554i	0.434920	−	0.376860i
$893$	6.41229	−	21.8383i	0.214579	−	0.730789i
$894$	8.16188	+	17.8720i	0.272974	+	0.597730i
$895$	−7.90487	+	54.9796i	−0.264231	+	1.83776i
$896$	2.64489	−	0.0674339i	0.0883596	−	0.00225281i
$897$	−0.172092	+	6.54020i	−0.00574597	+	0.218371i
$898$	30.0189			1.00174
$899$	60.2382	+	8.66095i	2.00906	+	0.288859i
$900$	−3.67014	−	8.03647i	−0.122338	−	0.267882i
$901$	0.966270	−	3.29081i	0.0321911	−	0.109633i
$902$	−23.8197	−	27.4894i	−0.793109	−	0.915296i
$903$	1.25963	−	0.405008i	0.0419178	−	0.0134778i
$904$	8.69036	−	13.5225i	0.289037	−	0.449750i
$905$	35.1335	−	76.9316i	1.16788	−	2.55729i
$906$	−8.36606	−	7.24923i	−0.277944	−	0.240840i
$907$	−5.44558	−	8.47348i	−0.180817	−	0.281357i	0.738999	−	0.673707i	$-0.235299\pi$
$907$	−5.44558	−	8.47348i	−0.180817	−	0.281357i	−0.919816	+	0.392349i	$0.871662\pi$
$908$	1.20172	+	8.35816i	0.0398806	+	0.277375i
$909$	8.93451	−	1.28459i	0.296339	−	0.0426071i
$910$	−7.54359	−	11.1052i	−0.250067	−	0.368132i
$911$	−34.9123	−	30.2517i	−1.15670	−	1.00228i	−0.999893	−	0.0146534i	$-0.995336\pi$
$911$	−34.9123	−	30.2517i	−1.15670	−	1.00228i	−0.156804	−	0.987630i	$-0.550119\pi$
$912$	−3.65260	−	1.66809i	−0.120950	−	0.0552359i
$913$	36.2292	−	56.3737i	1.19901	−	1.86570i
$914$	−5.97081	−	20.3347i	−0.197497	−	0.672613i
$915$	6.87217	−	5.95477i	0.227187	−	0.196859i
$916$	−5.34352	−	1.56900i	−0.176555	−	0.0518412i
$917$	33.7105	−	16.4461i	1.11322	−	0.543097i
$918$	−0.442203	−	0.0635792i	−0.0145949	−	0.00209843i
$919$		−	13.1523i		−	0.433854i	−0.976188	−	0.216927i	$-0.930397\pi$
$919$		−	13.1523i		−	0.433854i	0.976188	−	0.216927i	$-0.0696033\pi$
$920$	13.1693	+	12.0321i	0.434179	+	0.396687i
$921$	−16.8209			−0.554266
$922$	−2.66118	−	0.382619i	−0.0876412	−	0.0126009i
$923$	−4.76071	+	2.17414i	−0.156701	+	0.0715628i
$924$	14.0353	+	3.73534i	0.461729	+	0.122884i
$925$	50.9219	−	44.1241i	1.67430	−	1.45079i
$926$	−5.78789	+	1.69948i	−0.190202	+	0.0558483i
$927$	13.9043	+	8.93577i	0.456678	+	0.293489i
$928$	−3.51723	+	7.70165i	−0.115459	+	0.252819i
$929$	−8.34751	−	7.23316i	−0.273873	−	0.237312i	0.507085	−	0.861896i	$-0.330723\pi$
$929$	−8.34751	−	7.23316i	−0.273873	−	0.237312i	−0.780958	+	0.624584i	$0.785269\pi$
$930$	22.4911	−	14.4542i	0.737514	−	0.473971i
$931$	5.41282	+	27.5822i	0.177398	+	0.903971i
$932$	−2.09251	−	14.5537i	−0.0685425	−	0.476723i
$933$	6.66756	−	4.28498i	0.218286	−	0.140284i
$934$	−21.4211	+	24.7213i	−0.700921	+	0.808906i
$935$	8.29760	+	3.78939i	0.271361	+	0.123926i
$936$	−0.737541	+	1.14764i	−0.0241073	+	0.0375117i
$937$	−19.1362	+	5.61890i	−0.625153	+	0.183562i	−0.578940	−	0.815370i	$-0.696534\pi$
$937$	−19.1362	+	5.61890i	−0.625153	+	0.183562i	−0.0462132	+	0.998932i	$0.514715\pi$
$938$	−4.56499	+	4.16396i	−0.149052	+	0.135958i
$939$	1.56332	−	5.32418i	0.0510170	−	0.173748i
$940$	−19.1775	+	8.75808i	−0.625502	+	0.285657i
$941$	−4.70745	+	32.7410i	−0.153458	+	1.06733i	0.756907	+	0.653522i	$0.226709\pi$
$941$	−4.70745	+	32.7410i	−0.153458	+	1.06733i	−0.910366	+	0.413805i	$0.864200\pi$
$942$			15.3878i			0.501362i
$943$	30.2440	+	9.75160i	0.984881	+	0.317556i
$944$			6.86778i			0.223527i
$945$	9.77330	+	1.15179i	0.317926	+	0.0374676i
$946$	1.14044	+	2.49722i	0.0370789	+	0.0811916i
$947$	27.8690	+	8.18308i	0.905621	+	0.265914i	0.701197	−	0.712968i	$-0.252649\pi$
$947$	27.8690	+	8.18308i	0.905621	+	0.265914i	0.204425	+	0.978882i	$0.434468\pi$
$948$	−5.98069	−	6.90209i	−0.194244	−	0.224169i
$949$	2.55541	−	0.750337i	0.0829522	−	0.0243570i
$950$	29.8444	+	19.1799i	0.968282	+	0.622277i
$951$	−18.9424	−	8.65069i	−0.614249	−	0.280518i
$952$	−0.751020	+	0.912727i	−0.0243407	+	0.0295817i
$953$	−6.64607	−	10.3415i	−0.215287	−	0.334994i	0.716767	−	0.697313i	$-0.245621\pi$
$953$	−6.64607	−	10.3415i	−0.215287	−	0.334994i	−0.932054	+	0.362320i	$0.881985\pi$
$954$	7.59895	−	1.09256i	0.246025	−	0.0353731i
$955$	−4.13776	+	0.594920i	−0.133895	+	0.0192512i
$956$	−24.7951	+	15.9348i	−0.801930	+	0.515369i
$957$	−30.4370	+	35.1261i	−0.983887	+	1.13547i
$958$	−6.24511	+	13.6749i	−0.201770	+	0.441816i
$959$	−15.5172	+	25.5547i	−0.501076	+	0.825203i
$960$	1.04791	+	3.56886i	0.0338212	+	0.115184i
$961$	13.5325	+	15.6174i	0.436534	+	0.503787i
$962$	−9.98266	−	2.93117i	−0.321854	−	0.0945048i
$963$	11.2675	−	5.14572i	0.363092	−	0.165818i
$964$	−3.73370	+	25.9684i	−0.120254	+	0.836387i
$965$	−35.7582			−1.15110
$966$	−12.1775	+	3.56484i	−0.391805	+	0.114697i
$967$	30.8833			0.993140			0.496570	−	0.867997i	$-0.334593\pi$
$967$	30.8833			0.993140			0.496570	+	0.867997i	$0.334593\pi$
$968$	−2.72317	+	18.9401i	−0.0875260	+	0.608757i
$969$	1.63180	−	0.745219i	0.0524210	−	0.0239399i
$970$	37.7319	+	11.0791i	1.21150	+	0.355728i
$971$	−21.5151	−	24.8298i	−0.690453	−	0.796825i	0.296977	−	0.954885i	$-0.404022\pi$
$971$	−21.5151	−	24.8298i	−0.690453	−	0.796825i	−0.987430	+	0.158060i	$0.949476\pi$
$972$	−0.281733	−	0.959493i	−0.00903658	−	0.0307758i
$973$	−20.2415	+	33.3350i	−0.648914	+	1.06867i
$974$	2.43259	−	5.32662i	0.0779451	−	0.170676i
$975$	7.89271	−	9.10867i	0.252769	−	0.291711i
$976$	−2.05663	+	1.32171i	−0.0658310	+	0.0423070i
$977$	−1.52002	+	0.218547i	−0.0486299	+	0.00699192i	−0.166587	−	0.986027i	$-0.553275\pi$
$977$	−1.52002	+	0.218547i	−0.0486299	+	0.00699192i	0.117957	+	0.993019i	$0.462366\pi$
$978$	3.86722	−	0.556023i	0.123660	−	0.0177797i
$979$	10.4433	+	16.2501i	0.333770	+	0.519356i
$980$	16.0255	−	20.5205i	0.511916	−	0.655503i
$981$	−7.01686	−	3.20449i	−0.224031	−	0.102312i
$982$	17.8562	+	11.4755i	0.569814	+	0.366197i
$983$	35.5172	−	10.4288i	1.13282	−	0.332627i	0.339006	−	0.940784i	$-0.389909\pi$
$983$	35.5172	−	10.4288i	1.13282	−	0.332627i	0.793816	+	0.608157i	$0.208091\pi$
$984$	4.33912	+	5.00761i	0.138326	+	0.159637i
$985$	40.8082	+	11.9824i	1.30026	+	0.381790i
$986$	−1.57132	−	3.44072i	−0.0500411	−	0.109575i
$987$	1.75519	−	14.8934i	0.0558683	−	0.474062i
$988$		−	5.47790i		−	0.174275i
$989$	−1.98285	−	1.34929i	−0.0630510	−	0.0429050i
$990$			20.4184i			0.648940i
$991$	4.53495	−	31.5412i	0.144057	−	1.00194i	−0.781655	−	0.623711i	$-0.785624\pi$
$991$	4.53495	−	31.5412i	0.144057	−	1.00194i	0.925712	−	0.378229i	$-0.123467\pi$
$992$	−6.53827	+	2.98593i	−0.207590	+	0.0948033i
$993$	4.22808	−	14.3995i	0.134174	−	0.456955i
$994$	−6.84038	−	7.49916i	−0.216964	−	0.237859i
$995$	−35.6929	+	10.4804i	−1.13154	+	0.332251i
$996$	−6.59970	+	10.2693i	−0.209120	+	0.325396i
$997$	−49.8283	−	22.7558i	−1.57808	−	0.720684i	−0.582342	−	0.812944i	$-0.697864\pi$
$997$	−49.8283	−	22.7558i	−1.57808	−	0.720684i	−0.995735	+	0.0922602i	$0.970591\pi$
$998$	−19.1689	+	22.1221i	−0.606781	+	0.700263i
$999$	6.41585	−	4.12321i	0.202988	−	0.130453i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.s.b.475.8	yes	160
7.6	odd	2	inner	966.2.s.b.475.9	yes	160
23.20	odd	22	inner	966.2.s.b.181.9	yes	160
161.20	even	22	inner	966.2.s.b.181.8	✓	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.s.b.181.8	✓	160	161.20	even	22	inner
966.2.s.b.181.9	yes	160	23.20	odd	22	inner
966.2.s.b.475.8	yes	160	1.1	even	1	trivial
966.2.s.b.475.9	yes	160	7.6	odd	2	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 - 0.989821i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(2.43577 + 2.81103i) q^{5} +(0.281733 + 0.959493i) q^{6} +(-2.26148 - 1.37321i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.142315 - 0.989821i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(2.43577 + 2.81103i) q^{5} +(0.281733 + 0.959493i) q^{6} +(-2.26148 - 1.37321i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(0.654861 - 0.755750i) q^{9} +(3.12906 - 2.01093i) q^{10} +(-5.43364 + 0.781240i) q^{11} +(0.989821 - 0.142315i) q^{12} +(0.737541 + 1.14764i) q^{13} +(-1.68107 + 2.04304i) q^{14} +(-3.38340 - 1.54515i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-0.428654 + 0.125864i) q^{17} +(-0.654861 - 0.755750i) q^{18} +(3.85282 + 1.13129i) q^{19} +(-1.54515 - 3.38340i) q^{20} +(2.62757 + 0.309660i) q^{21} +5.48952i q^{22} +(-2.48580 - 4.10132i) q^{23} -1.00000i q^{24} +(-1.25733 + 8.74494i) q^{25} +(1.24092 - 0.566708i) q^{26} +(-0.281733 + 0.959493i) q^{27} +(1.78300 + 1.95472i) q^{28} +(-8.12381 + 2.38537i) q^{29} +(-2.01093 + 3.12906i) q^{30} +(-6.53827 - 2.98593i) q^{31} +(0.654861 - 0.755750i) q^{32} +(4.61808 - 2.96786i) q^{33} +(0.0635792 + 0.442203i) q^{34} +(-1.64833 - 9.70191i) q^{35} +(-0.841254 + 0.540641i) q^{36} +(-5.76375 - 4.99432i) q^{37} +(1.66809 - 3.65260i) q^{38} +(-1.14764 - 0.737541i) q^{39} +(-3.56886 + 1.04791i) q^{40} +(-5.00761 + 4.33912i) q^{41} +(0.680450 - 2.55675i) q^{42} +(0.454906 - 0.207749i) q^{43} +(5.43364 + 0.781240i) q^{44} +3.71952 q^{45} +(-4.41334 + 1.87682i) q^{46} -5.66812i q^{47} +(-0.989821 - 0.142315i) q^{48} +(3.22860 + 6.21097i) q^{49} +(8.47699 + 2.48907i) q^{50} +(0.337631 - 0.292559i) q^{51} +(-0.384339 - 1.30894i) q^{52} +(-4.15055 + 6.45838i) q^{53} +(0.909632 + 0.415415i) q^{54} +(-15.4312 - 13.3712i) q^{55} +(2.18857 - 1.48667i) q^{56} +(-3.97460 + 0.571461i) q^{57} +(1.20495 + 8.38060i) q^{58} +(3.71300 + 5.77755i) q^{59} +(2.81103 + 2.43577i) q^{60} +(-1.01557 + 2.22379i) q^{61} +(-3.88603 + 6.04678i) q^{62} +(-2.51876 + 0.809854i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-1.42956 + 4.86863i) q^{65} +(-2.28043 - 4.99344i) q^{66} +(2.31160 + 0.332358i) q^{67} +0.446750 q^{68} +(3.96491 + 2.69805i) q^{69} +(-9.83774 + 0.250822i) q^{70} +(-0.545983 + 3.79740i) q^{71} +(0.415415 + 0.909632i) q^{72} +(0.550021 - 1.87320i) q^{73} +(-5.76375 + 4.99432i) q^{74} +(-2.48907 - 8.47699i) q^{75} +(-3.37803 - 2.17093i) q^{76} +(13.3609 + 5.69476i) q^{77} +(-0.893359 + 1.03099i) q^{78} +(-4.93755 - 7.68297i) q^{79} +(0.529344 + 3.68167i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(3.58230 + 5.57416i) q^{82} +(-7.99401 + 9.22557i) q^{83} +(-2.43389 - 1.03739i) q^{84} +(-1.39791 - 0.898383i) q^{85} +(-0.140894 - 0.479842i) q^{86} +(6.39876 - 5.54456i) q^{87} +(1.54658 - 5.26716i) q^{88} +(-1.46177 - 3.20082i) q^{89} +(0.529344 - 3.68167i) q^{90} +(-0.0919931 - 3.60815i) q^{91} +(1.22964 + 4.63551i) q^{92} +7.18782 q^{93} +(-5.61043 - 0.806658i) q^{94} +(6.20449 + 13.5859i) q^{95} +(-0.281733 + 0.959493i) q^{96} +(6.92355 + 7.99020i) q^{97} +(6.60723 - 2.31183i) q^{98} +(-2.96786 + 4.61808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 16 q^{2} - 16 q^{4} + 16 q^{8} + 16 q^{9}+O(q^{10}) \) 160 * q + 16 * q^2 - 16 * q^4 + 16 * q^8 + 16 * q^9	\( 160 q + 16 q^{2} - 16 q^{4} + 16 q^{8} + 16 q^{9} + 22 q^{14} - 16 q^{16} - 16 q^{18} - 52 q^{23} - 48 q^{25} + 22 q^{28} - 12 q^{29} + 16 q^{32} + 22 q^{35} + 16 q^{36} + 22 q^{37} - 4 q^{39} + 154 q^{43} + 8 q^{46} + 4 q^{50} + 22 q^{51} + 88 q^{53} + 22 q^{57} + 56 q^{58} - 16 q^{64} + 16 q^{71} - 16 q^{72} + 22 q^{74} - 72 q^{77} + 4 q^{78} + 88 q^{79} - 16 q^{81} - 22 q^{84} - 68 q^{85} - 44 q^{86} + 44 q^{88} - 8 q^{92} - 8 q^{93} - 66 q^{95} + 66 q^{98} - 66 q^{99}+O(q^{100}) \) 160 * q + 16 * q^2 - 16 * q^4 + 16 * q^8 + 16 * q^9 + 22 * q^14 - 16 * q^16 - 16 * q^18 - 52 * q^23 - 48 * q^25 + 22 * q^28 - 12 * q^29 + 16 * q^32 + 22 * q^35 + 16 * q^36 + 22 * q^37 - 4 * q^39 + 154 * q^43 + 8 * q^46 + 4 * q^50 + 22 * q^51 + 88 * q^53 + 22 * q^57 + 56 * q^58 - 16 * q^64 + 16 * q^71 - 16 * q^72 + 22 * q^74 - 72 * q^77 + 4 * q^78 + 88 * q^79 - 16 * q^81 - 22 * q^84 - 68 * q^85 - 44 * q^86 + 44 * q^88 - 8 * q^92 - 8 * q^93 - 66 * q^95 + 66 * q^98 - 66 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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