LMFDB - Embedded newform 966.2.s.a.475.2

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			475.2
Character	$\chi$	$=$	966.475
Dual form			966.2.s.a.181.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.32721 - 1.53168i) q^{5} +(-0.281733 - 0.959493i) q^{6} +(-2.59428 - 0.519336i) q^{7} +(0.415415 - 0.909632i) q^{8} +(0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.32721 - 1.53168i) q^{5} +(-0.281733 - 0.959493i) q^{6} +(-2.59428 - 0.519336i) q^{7} +(0.415415 - 0.909632i) q^{8} +(0.654861 - 0.755750i) q^{9} +(1.70498 - 1.09572i) q^{10} +(3.12743 - 0.449656i) q^{11} +(0.989821 - 0.142315i) q^{12} +(0.718675 + 1.11828i) q^{13} +(0.883254 - 2.49397i) q^{14} +(1.84356 + 0.841925i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-0.378462 + 0.111127i) q^{17} +(0.654861 + 0.755750i) q^{18} +(-1.61920 - 0.475439i) q^{19} +(0.841925 + 1.84356i) q^{20} +(2.57558 - 0.605299i) q^{21} +3.15959i q^{22} +(-0.441143 + 4.77550i) q^{23} +1.00000i q^{24} +(0.127009 - 0.883370i) q^{25} +(-1.20918 + 0.552212i) q^{26} +(-0.281733 + 0.959493i) q^{27} +(2.34288 + 1.22919i) q^{28} +(-1.23665 + 0.363114i) q^{29} +(-1.09572 + 1.70498i) q^{30} +(4.26375 + 1.94719i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(-2.65801 + 1.70820i) q^{33} +(-0.0561346 - 0.390425i) q^{34} +(2.64770 + 4.66289i) q^{35} +(-0.841254 + 0.540641i) q^{36} +(5.39648 + 4.67608i) q^{37} +(0.701036 - 1.53505i) q^{38} +(-1.11828 - 0.718675i) q^{39} +(-1.94461 + 0.570990i) q^{40} +(-8.14068 + 7.05394i) q^{41} +(0.232594 + 2.63551i) q^{42} +(-10.4406 + 4.76804i) q^{43} +(-3.12743 - 0.449656i) q^{44} -2.02671 q^{45} +(-4.66411 - 1.11628i) q^{46} +8.94459i q^{47} +(-0.989821 - 0.142315i) q^{48} +(6.46058 + 2.69461i) q^{49} +(0.856303 + 0.251433i) q^{50} +(0.298098 - 0.258303i) q^{51} +(-0.374508 - 1.27546i) q^{52} +(-3.63278 + 5.65271i) q^{53} +(-0.909632 - 0.415415i) q^{54} +(-4.83949 - 4.19344i) q^{55} +(-1.55011 + 2.14410i) q^{56} +(1.67038 - 0.240164i) q^{57} +(-0.183424 - 1.27574i) q^{58} +(2.47780 + 3.85553i) q^{59} +(-1.53168 - 1.32721i) q^{60} +(4.36150 - 9.55036i) q^{61} +(-2.53417 + 3.94324i) q^{62} +(-2.09138 + 1.62053i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(0.759018 - 2.58498i) q^{65} +(-1.31254 - 2.87406i) q^{66} +(13.0036 + 1.86963i) q^{67} +0.394440 q^{68} +(-1.58254 - 4.52720i) q^{69} +(-4.99223 + 1.95715i) q^{70} +(0.470265 - 3.27076i) q^{71} +(-0.415415 - 0.909632i) q^{72} +(1.62426 - 5.53174i) q^{73} +(-5.39648 + 4.67608i) q^{74} +(0.251433 + 0.856303i) q^{75} +(1.41966 + 0.912361i) q^{76} +(-8.34695 - 0.457651i) q^{77} +(0.870508 - 1.00462i) q^{78} +(6.66028 + 10.3636i) q^{79} +(-0.288431 - 2.00608i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-5.82360 - 9.06169i) q^{82} +(-4.12233 + 4.75742i) q^{83} +(-2.64178 - 0.144845i) q^{84} +(0.672510 + 0.432196i) q^{85} +(-3.23366 - 11.0128i) q^{86} +(0.974055 - 0.844023i) q^{87} +(0.890159 - 3.03160i) q^{88} +(-3.04528 - 6.66823i) q^{89} +(0.288431 - 2.00608i) q^{90} +(-1.28368 - 3.27437i) q^{91} +(1.76869 - 4.45777i) q^{92} -4.68734 q^{93} +(-8.85355 - 1.27295i) q^{94} +(1.42079 + 3.11111i) q^{95} +(0.281733 - 0.959493i) q^{96} +(7.96782 + 9.19535i) q^{97} +(-3.58661 + 6.01134i) q^{98} +(1.70820 - 2.65801i) 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} - 36 q^{23} + 96 q^{25} + 22 q^{28} - 20 q^{29} - 16 q^{32} - 50 q^{35} + 16 q^{36} + 22 q^{37} + 4 q^{39} - 110 q^{43} + 8 q^{46} - 36 q^{50} + 22 q^{51} - 88 q^{53} + 22 q^{57} + 24 q^{58} - 16 q^{64} - 72 q^{70} + 48 q^{71} + 16 q^{72} - 22 q^{74} + 24 q^{77} + 4 q^{78} + 88 q^{79} - 16 q^{81} + 22 q^{84} + 76 q^{85} + 44 q^{86} - 44 q^{88} + 8 q^{92} - 14 q^{95} + 22 q^{98} - 22 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 - 36 * q^23 + 96 * q^25 + 22 * q^28 - 20 * q^29 - 16 * q^32 - 50 * q^35 + 16 * q^36 + 22 * q^37 + 4 * q^39 - 110 * q^43 + 8 * q^46 - 36 * q^50 + 22 * q^51 - 88 * q^53 + 22 * q^57 + 24 * q^58 - 16 * q^64 - 72 * q^70 + 48 * q^71 + 16 * q^72 - 22 * q^74 + 24 * q^77 + 4 * q^78 + 88 * q^79 - 16 * q^81 + 22 * q^84 + 76 * q^85 + 44 * q^86 - 44 * q^88 + 8 * q^92 - 14 * q^95 + 22 * q^98 - 22 * 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
$5$	−1.32721	−	1.53168i	−0.593547	−	0.684990i	0.376914	−	0.926248i	$-0.376985\pi$
$5$	−1.32721	−	1.53168i	−0.593547	−	0.684990i	−0.970461	+	0.241258i	$0.922440\pi$
$6$	−0.281733	−	0.959493i	−0.115017	−	0.391711i
$7$	−2.59428	−	0.519336i	−0.980546	−	0.196290i
$7$	−2.59428	−	0.519336i	−0.980546	−	0.196290i
$8$	0.415415	−	0.909632i	0.146871	−	0.321603i
$9$	0.654861	−	0.755750i	0.218287	−	0.251917i
$10$	1.70498	−	1.09572i	0.539161	−	0.346497i
$11$	3.12743	−	0.449656i	0.942955	−	0.135576i	0.346344	−	0.938107i	$-0.387423\pi$
$11$	3.12743	−	0.449656i	0.942955	−	0.135576i	0.596610	+	0.802531i	$0.296514\pi$
$12$	0.989821	−	0.142315i	0.285737	−	0.0410828i
$13$	0.718675	+	1.11828i	0.199325	+	0.310155i	0.926499	−	0.376298i	$-0.122803\pi$
$13$	0.718675	+	1.11828i	0.199325	+	0.310155i	−0.727174	+	0.686453i	$0.759167\pi$
$14$	0.883254	−	2.49397i	0.236060	−	0.666540i
$15$	1.84356	+	0.841925i	0.476005	+	0.217384i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	−0.378462	+	0.111127i	−0.0917906	+	0.0269521i	−0.327305	−	0.944919i	$-0.606141\pi$
$17$	−0.378462	+	0.111127i	−0.0917906	+	0.0269521i	0.235515	+	0.971871i	$0.424322\pi$
$18$	0.654861	+	0.755750i	0.154352	+	0.178132i
$19$	−1.61920	−	0.475439i	−0.371469	−	0.109073i	0.0906690	−	0.995881i	$-0.471099\pi$
$19$	−1.61920	−	0.475439i	−0.371469	−	0.109073i	−0.462138	+	0.886808i	$0.652918\pi$
$20$	0.841925	+	1.84356i	0.188260	+	0.412232i
$21$	2.57558	−	0.605299i	0.562038	−	0.132087i
$22$			3.15959i			0.673626i
$23$	−0.441143	+	4.77550i	−0.0919847	+	0.995760i
$23$	−0.441143	+	4.77550i	−0.0919847	+	0.995760i
$24$			1.00000i			0.204124i
$25$	0.127009	−	0.883370i	0.0254019	−	0.176674i
$26$	−1.20918	+	0.552212i	−0.237139	+	0.108298i
$27$	−0.281733	+	0.959493i	−0.0542195	+	0.184655i
$28$	2.34288	+	1.22919i	0.442763	+	0.232296i
$29$	−1.23665	+	0.363114i	−0.229640	+	0.0674285i	−0.394528	−	0.918884i	$-0.629092\pi$
$29$	−1.23665	+	0.363114i	−0.229640	+	0.0674285i	0.164888	+	0.986312i	$0.447274\pi$
$30$	−1.09572	+	1.70498i	−0.200050	+	0.311285i
$31$	4.26375	+	1.94719i	0.765793	+	0.349726i	0.759715	−	0.650256i	$-0.225338\pi$
$31$	4.26375	+	1.94719i	0.765793	+	0.349726i	0.00607736	+	0.999982i	$0.498066\pi$
$32$	−0.654861	+	0.755750i	−0.115764	+	0.133599i
$33$	−2.65801	+	1.70820i	−0.462701	+	0.297360i
$34$	−0.0561346	−	0.390425i	−0.00962701	−	0.0669573i
$35$	2.64770	+	4.66289i	0.447543	+	0.788172i
$36$	−0.841254	+	0.540641i	−0.140209	+	0.0901068i
$37$	5.39648	+	4.67608i	0.887176	+	0.768742i	0.973778	−	0.227501i	$-0.0730553\pi$
$37$	5.39648	+	4.67608i	0.887176	+	0.768742i	−0.0866018	+	0.996243i	$0.527601\pi$
$38$	0.701036	−	1.53505i	0.113723	−	0.249019i
$39$	−1.11828	−	0.718675i	−0.179068	−	0.115080i
$40$	−1.94461	+	0.570990i	−0.307470	+	0.0902814i
$41$	−8.14068	+	7.05394i	−1.27136	+	1.10164i	−0.281505	+	0.959560i	$0.590833\pi$
$41$	−8.14068	+	7.05394i	−1.27136	+	1.10164i	−0.989855	+	0.142080i	$0.954621\pi$
$42$	0.232594	+	2.63551i	0.0358901	+	0.406668i
$43$	−10.4406	+	4.76804i	−1.59217	+	0.727119i	−0.997067	−	0.0765305i	$-0.975616\pi$
$43$	−10.4406	+	4.76804i	−1.59217	+	0.727119i	−0.595102	+	0.803650i	$0.702888\pi$
$44$	−3.12743	−	0.449656i	−0.471477	−	0.0677882i
$45$	−2.02671			−0.302124
$46$	−4.66411	−	1.11628i	−0.687686	−	0.164586i
$47$			8.94459i			1.30470i	0.757917	+	0.652352i	$0.226217\pi$
$47$			8.94459i			1.30470i	−0.757917	+	0.652352i	$0.773783\pi$
$48$	−0.989821	−	0.142315i	−0.142868	−	0.0205414i
$49$	6.46058	+	2.69461i	0.922940	+	0.384944i
$50$	0.856303	+	0.251433i	0.121100	+	0.0355580i
$51$	0.298098	−	0.258303i	0.0417420	−	0.0361697i
$52$	−0.374508	−	1.27546i	−0.0519349	−	0.176874i
$53$	−3.63278	+	5.65271i	−0.499000	+	0.776459i	−0.995814	−	0.0913976i	$-0.970867\pi$
$53$	−3.63278	+	5.65271i	−0.499000	+	0.776459i	0.496814	+	0.867857i	$0.334503\pi$
$54$	−0.909632	−	0.415415i	−0.123785	−	0.0565308i
$55$	−4.83949	−	4.19344i	−0.652557	−	0.565444i
$56$	−1.55011	+	2.14410i	−0.207142	+	0.286517i
$57$	1.67038	−	0.240164i	0.221247	−	0.0318105i
$58$	−0.183424	−	1.27574i	−0.0240847	−	0.167513i
$59$	2.47780	+	3.85553i	0.322582	+	0.501947i	0.964235	−	0.265047i	$-0.0853876\pi$
$59$	2.47780	+	3.85553i	0.322582	+	0.501947i	−0.641653	+	0.766995i	$0.721751\pi$
$60$	−1.53168	−	1.32721i	−0.197740	−	0.171342i
$61$	4.36150	−	9.55036i	0.558433	−	1.22280i	−0.394297	−	0.918983i	$-0.629012\pi$
$61$	4.36150	−	9.55036i	0.558433	−	1.22280i	0.952731	−	0.303816i	$-0.0982607\pi$
$62$	−2.53417	+	3.94324i	−0.321840	+	0.500792i
$63$	−2.09138	+	1.62053i	−0.263489	+	0.204168i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	0.759018	−	2.58498i	0.0941446	−	0.320627i
$66$	−1.31254	−	2.87406i	−0.161563	−	0.353773i
$67$	13.0036	+	1.86963i	1.58864	+	0.228412i	0.879234	−	0.476390i	$-0.158055\pi$
$67$	13.0036	+	1.86963i	1.58864	+	0.228412i	0.709404	+	0.704802i	$0.248964\pi$
$68$	0.394440			0.0478328
$69$	−1.58254	−	4.52720i	−0.190515	−	0.545011i
$70$	−4.99223	+	1.95715i	−0.596686	+	0.233925i
$71$	0.470265	−	3.27076i	0.0558102	−	0.388168i	−0.942702	−	0.333636i	$-0.891724\pi$
$71$	0.470265	−	3.27076i	0.0558102	−	0.388168i	0.998512	−	0.0545319i	$-0.0173666\pi$
$72$	−0.415415	−	0.909632i	−0.0489571	−	0.107201i
$73$	1.62426	−	5.53174i	0.190106	−	0.647441i	−0.808181	−	0.588934i	$-0.799548\pi$
$73$	1.62426	−	5.53174i	0.190106	−	0.647441i	0.998287	−	0.0585069i	$-0.0186340\pi$
$74$	−5.39648	+	4.67608i	−0.627328	+	0.543583i
$75$	0.251433	+	0.856303i	0.0290330	+	0.0988773i
$76$	1.41966	+	0.912361i	0.162846	+	0.104655i
$77$	−8.34695	−	0.457651i	−0.951223	−	0.0521542i
$78$	0.870508	−	1.00462i	0.0985657	−	0.113751i
$79$	6.66028	+	10.3636i	0.749340	+	1.16600i	0.981153	+	0.193235i	$0.0618979\pi$
$79$	6.66028	+	10.3636i	0.749340	+	1.16600i	−0.231813	+	0.972760i	$0.574466\pi$
$80$	−0.288431	−	2.00608i	−0.0322475	−	0.224286i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	−5.82360	−	9.06169i	−0.643109	−	1.00070i
$83$	−4.12233	+	4.75742i	−0.452484	+	0.522194i	−0.935457	−	0.353441i	$-0.885012\pi$
$83$	−4.12233	+	4.75742i	−0.452484	+	0.522194i	0.482973	+	0.875635i	$0.339557\pi$
$84$	−2.64178	−	0.144845i	−0.288242	−	0.0158039i
$85$	0.672510	+	0.432196i	0.0729440	+	0.0468782i
$86$	−3.23366	−	11.0128i	−0.348695	−	1.18755i
$87$	0.974055	−	0.844023i	0.104430	−	0.0904888i
$88$	0.890159	−	3.03160i	0.0948912	−	0.323170i
$89$	−3.04528	−	6.66823i	−0.322799	−	0.706831i	0.676770	−	0.736195i	$-0.263379\pi$
$89$	−3.04528	−	6.66823i	−0.322799	−	0.706831i	−0.999569	+	0.0293637i	$0.990652\pi$
$90$	0.288431	−	2.00608i	0.0304033	−	0.211459i
$91$	−1.28368	−	3.27437i	−0.134566	−	0.343247i
$92$	1.76869	−	4.45777i	0.184398	−	0.464755i
$93$	−4.68734			−0.486054
$94$	−8.85355	−	1.27295i	−0.913174	−	0.131295i
$95$	1.42079	+	3.11111i	0.145770	+	0.319193i
$96$	0.281733	−	0.959493i	0.0287542	−	0.0979278i
$97$	7.96782	+	9.19535i	0.809010	+	0.933647i	0.998839	−	0.0481703i	$-0.0153390\pi$
$97$	7.96782	+	9.19535i	0.809010	+	0.933647i	−0.189830	+	0.981817i	$0.560794\pi$
$98$	−3.58661	+	6.01134i	−0.362303	+	0.607237i
$99$	1.70820	−	2.65801i	0.171681	−	0.267141i
$100$	−0.370739	+	0.811804i	−0.0370739	+	0.0811804i
$101$	13.5057	+	11.7027i	1.34386	+	1.16446i	0.971679	+	0.236307i	$0.0759370\pi$
$101$	13.5057	+	11.7027i	1.34386	+	1.16446i	0.372186	+	0.928158i	$0.378608\pi$
$102$	0.213250	+	0.331824i	0.0211149	+	0.0328555i
$103$	−0.751671	−	5.22798i	−0.0740643	−	0.515129i	−0.992756	−	0.120152i	$-0.961662\pi$
$103$	−0.751671	−	5.22798i	−0.0740643	−	0.515129i	0.918691	−	0.394977i	$-0.129247\pi$
$104$	1.31577	−	0.189180i	0.129022	−	0.0185506i
$105$	−4.34547	−	3.14162i	−0.424074	−	0.306590i
$106$	−5.07817	−	4.40026i	−0.493236	−	0.427391i
$107$	4.92190	+	2.24776i	0.475818	+	0.217299i	0.638864	−	0.769320i	$-0.279405\pi$
$107$	4.92190	+	2.24776i	0.475818	+	0.217299i	−0.163046	+	0.986618i	$0.552132\pi$
$108$	0.540641	−	0.841254i	0.0520232	−	0.0809497i
$109$	−4.42672	−	15.0760i	−0.424003	−	1.44402i	−0.843925	−	0.536461i	$-0.819761\pi$
$109$	−4.42672	−	15.0760i	−0.424003	−	1.44402i	0.419922	−	0.907560i	$-0.362057\pi$
$110$	4.83949	−	4.19344i	0.461427	−	0.399829i
$111$	−6.85133	−	2.01173i	−0.650299	−	0.190945i
$112$	−1.90167	−	1.83947i	−0.179691	−	0.173813i
$113$	−11.9625	−	1.71995i	−1.12534	−	0.161799i	−0.445585	−	0.895240i	$-0.647004\pi$
$113$	−11.9625	−	1.71995i	−1.12534	−	0.161799i	−0.679754	+	0.733440i	$0.737913\pi$
$114$			1.68755i			0.158054i
$115$	7.90005	−	5.66241i	0.736683	−	0.528022i
$116$	1.28886			0.119668
$117$	1.31577	+	0.189180i	0.121643	+	0.0174897i
$118$	−4.16891	+	1.90388i	−0.383780	+	0.175266i
$119$	1.03955	−	0.0917444i	0.0952953	−	0.00841020i
$120$	1.53168	−	1.32721i	0.139823	−	0.121157i
$121$	−0.975808	+	0.286523i	−0.0887098	+	0.0260476i
$122$	8.83245	+	5.67627i	0.799652	+	0.513905i
$123$	4.47471	−	9.79824i	0.403471	−	0.883478i
$124$	−3.54245	−	3.06955i	−0.318122	−	0.275654i
$125$	−10.0465	+	6.45649i	−0.898585	+	0.577486i
$126$	−1.30640	−	2.30072i	−0.116384	−	0.204964i
$127$	1.83189	+	12.7411i	0.162554	+	1.13059i	0.893797	+	0.448471i	$0.148031\pi$
$127$	1.83189	+	12.7411i	0.162554	+	1.13059i	−0.731243	+	0.682117i	$0.761060\pi$
$128$	0.841254	−	0.540641i	0.0743570	−	0.0477863i
$129$	7.51635	−	8.67433i	0.661777	−	0.763732i
$130$	2.45065	+	1.11917i	0.214936	+	0.0981580i
$131$	−9.35824	+	14.5617i	−0.817633	+	1.27226i	0.141679	+	0.989913i	$0.454750\pi$
$131$	−9.35824	+	14.5617i	−0.817633	+	1.27226i	−0.959312	+	0.282349i	$0.908886\pi$
$132$	3.03160	−	0.890159i	0.263867	−	0.0774784i
$133$	3.95374	+	2.07433i	0.342833	+	0.179867i
$134$	−3.70120	+	12.6051i	−0.319735	+	1.08892i
$135$	1.84356	−	0.841925i	0.158668	−	0.0724614i
$136$	−0.0561346	+	0.390425i	−0.00481350	+	0.0334787i
$137$		−	3.54600i		−	0.302955i	−0.988461	−	0.151478i	$-0.951597\pi$
$137$		−	3.54600i		−	0.302955i	0.988461	−	0.151478i	$-0.0484031\pi$
$138$	4.70634	−	0.922140i	0.400630	−	0.0784978i
$139$			9.80085i			0.831297i	0.909525	+	0.415649i	$0.136445\pi$
$139$			9.80085i			0.831297i	−0.909525	+	0.415649i	$0.863555\pi$
$140$	−1.22676	−	5.21995i	−0.103680	−	0.441166i
$141$	−3.71572	−	8.13629i	−0.312920	−	0.685199i
$142$	3.17055	+	0.930956i	0.266066	+	0.0781241i
$143$	2.75045	+	3.17419i	0.230004	+	0.265439i
$144$	0.959493	−	0.281733i	0.0799577	−	0.0234777i
$145$	2.19747	+	1.41223i	0.182490	+	0.117279i
$146$	5.24427	+	2.39498i	0.434019	+	0.198210i
$147$	−6.99613	+	0.232723i	−0.577031	+	0.0191947i
$148$	−3.86048	−	6.00703i	−0.317330	−	0.493775i
$149$	−0.940885	+	0.135279i	−0.0770803	+	0.0110825i	−0.180747	−	0.983530i	$-0.557852\pi$
$149$	−0.940885	+	0.135279i	−0.0770803	+	0.0110825i	0.103667	+	0.994612i	$0.466942\pi$
$150$	−0.883370	+	0.127009i	−0.0721268	+	0.0103703i
$151$	−7.13841	+	4.58758i	−0.580916	+	0.373332i	−0.797852	−	0.602854i	$-0.794030\pi$
$151$	−7.13841	+	4.58758i	−0.580916	+	0.373332i	0.216936	+	0.976186i	$0.430394\pi$
$152$	−1.10511	+	1.27537i	−0.0896365	+	0.103446i
$153$	−0.163856	+	0.358795i	−0.0132470	+	0.0290069i
$154$	1.64089	−	8.19686i	0.132226	−	0.660522i
$155$	−2.67642	−	9.11506i	−0.214975	−	0.732139i
$156$	0.870508	+	1.00462i	0.0696964	+	0.0804340i
$157$	10.9162	+	3.20529i	0.871209	+	0.255810i	0.686630	−	0.727007i	$-0.259089\pi$
$157$	10.9162	+	3.20529i	0.871209	+	0.255810i	0.184580	+	0.982818i	$0.440908\pi$
$158$	−11.2060	+	5.11759i	−0.891498	+	0.407134i
$159$	0.956269	−	6.65099i	0.0758370	−	0.527458i
$160$	2.02671			0.160225
$161$	3.62454	−	12.1599i	0.285654	−	0.958333i
$162$	1.00000			0.0785674
$163$	2.14267	−	14.9026i	0.167827	−	1.16726i	−0.715537	−	0.698574i	$-0.753818\pi$
$163$	2.14267	−	14.9026i	0.167827	−	1.16726i	0.883364	−	0.468687i	$-0.155273\pi$
$164$	9.79824	−	4.47471i	0.765114	−	0.349416i
$165$	6.14417	+	1.80409i	0.478323	+	0.140448i
$166$	−4.12233	−	4.75742i	−0.319955	−	0.369247i
$167$	4.93275	+	16.7994i	0.381707	+	1.29998i	0.896646	+	0.442749i	$0.145997\pi$
$167$	4.93275	+	16.7994i	0.381707	+	1.29998i	−0.514938	+	0.857227i	$0.672185\pi$
$168$	0.519336	−	2.59428i	0.0400676	−	0.200153i
$169$	4.66634	−	10.2179i	0.358949	−	0.785989i
$170$	−0.523505	+	0.604157i	−0.0401510	+	0.0463367i
$171$	−1.41966	+	0.912361i	−0.108564	+	0.0697700i
$172$	11.3610	−	1.63346i	0.866264	−	0.124550i
$173$	10.5419	−	1.51570i	0.801487	−	0.115236i	0.270614	−	0.962688i	$-0.412773\pi$
$173$	10.5419	−	1.51570i	0.801487	−	0.115236i	0.530873	+	0.847451i	$0.321864\pi$
$174$	0.696810	+	1.08426i	0.0528250	+	0.0821973i
$175$	−0.788263	+	2.22575i	−0.0595871	+	0.168251i
$176$	2.87406	+	1.31254i	0.216641	+	0.0989364i
$177$	−3.85553	−	2.47780i	−0.289799	−	0.186243i
$178$	7.03374	−	2.06529i	0.527201	−	0.154800i
$179$	−2.87966	−	3.32330i	−0.215236	−	0.248395i	0.637857	−	0.770155i	$-0.279821\pi$
$179$	−2.87966	−	3.32330i	−0.215236	−	0.248395i	−0.853092	+	0.521760i	$0.825276\pi$
$180$	1.94461	+	0.570990i	0.144943	+	0.0425591i
$181$	0.581138	+	1.27252i	0.0431957	+	0.0945853i	0.930000	−	0.367561i	$-0.119807\pi$
$181$	0.581138	+	1.27252i	0.0431957	+	0.0945853i	−0.886804	+	0.462146i	$0.847080\pi$
$182$	3.42373	−	0.804625i	0.253783	−	0.0596428i
$183$			10.4991i			0.776119i
$184$	4.16069	+	2.38509i	0.306730	+	0.175831i
$185$		−	14.4718i		−	1.06399i
$186$	0.667078	−	4.63963i	0.0489125	−	0.340194i
$187$	−1.13364	+	0.517718i	−0.0829003	+	0.0378593i
$188$	2.51998	−	8.58227i	0.183789	−	0.625927i
$189$	1.22919	−	2.34288i	0.0894106	−	0.170419i
$190$	−3.28164	+	0.963577i	−0.238075	+	0.0699052i
$191$	6.89190	−	10.7240i	0.498680	−	0.775962i	−0.497104	−	0.867691i	$-0.665603\pi$
$191$	6.89190	−	10.7240i	0.498680	−	0.775962i	0.995784	+	0.0917295i	$0.0292395\pi$
$192$	0.909632	+	0.415415i	0.0656470	+	0.0299800i
$193$	5.56024	−	6.41686i	0.400235	−	0.461896i	−0.519480	−	0.854483i	$-0.673874\pi$
$193$	5.56024	−	6.41686i	0.400235	−	0.461896i	0.919715	+	0.392587i	$0.128420\pi$
$194$	−10.2357	+	6.57808i	−0.734880	+	0.472279i
$195$	0.383412	+	2.66669i	0.0274567	+	0.190965i
$196$	−5.43972	−	4.40561i	−0.388552	−	0.314686i
$197$	−8.49587	+	5.45997i	−0.605306	+	0.389006i	−0.807094	−	0.590423i	$-0.798961\pi$
$197$	−8.49587	+	5.45997i	−0.605306	+	0.389006i	0.201788	+	0.979429i	$0.435325\pi$
$198$	2.38786	+	2.06909i	0.169698	+	0.147044i
$199$	4.21994	−	9.24037i	0.299143	−	0.655033i	−0.699053	−	0.715070i	$-0.746395\pi$
$199$	4.21994	−	9.24037i	0.299143	−	0.655033i	0.998196	+	0.0600375i	$0.0191220\pi$
$200$	−0.750780	−	0.482497i	−0.0530881	−	0.0341177i
$201$	−12.6051	+	3.70120i	−0.889097	+	0.261063i
$202$	−13.5057	+	11.7027i	−0.950255	+	0.823401i
$203$	3.39680	−	0.299781i	0.238408	−	0.0210405i
$204$	−0.358795	+	0.163856i	−0.0251207	+	0.0114722i
$205$	21.6088	+	3.10688i	1.50922	+	0.216994i
$206$	5.28174			0.367997
$207$	3.32019	+	3.46068i	0.230769	+	0.240534i
$208$			1.32930i			0.0921706i
$209$	−5.27771	−	0.758820i	−0.365067	−	0.0524887i
$210$	3.72806	−	3.85414i	0.257261	−	0.265961i
$211$	8.81784	+	2.58915i	0.607045	+	0.178245i	0.570787	−	0.821098i	$-0.306638\pi$
$211$	8.81784	+	2.58915i	0.607045	+	0.178245i	0.0362579	+	0.999342i	$0.488456\pi$
$212$	5.07817	−	4.40026i	0.348770	−	0.302211i
$213$	0.930956	+	3.17055i	0.0637881	+	0.217242i
$214$	−2.92534	+	4.55191i	−0.199972	+	0.311162i
$215$	21.1600	+	9.66343i	1.44310	+	0.659040i
$216$	0.755750	+	0.654861i	0.0514222	+	0.0445576i
$217$	−10.0501	−	7.26588i	−0.682247	−	0.493240i
$218$	15.5526	−	2.23612i	1.05335	−	0.151449i
$219$	0.820484	+	5.70659i	0.0554431	+	0.385616i
$220$	3.46203	+	5.38702i	0.233410	+	0.363193i
$221$	−0.396262	−	0.343363i	−0.0266555	−	0.0230971i
$222$	2.96630	−	6.49529i	0.199085	−	0.435935i
$223$	−1.54733	+	2.40769i	−0.103617	+	0.161231i	−0.889190	−	0.457537i	$-0.848732\pi$
$223$	−1.54733	+	2.40769i	−0.103617	+	0.161231i	0.785574	+	0.618768i	$0.212368\pi$
$224$	2.09138	−	1.62053i	0.139736	−	0.108276i
$225$	−0.584433	−	0.674471i	−0.0389622	−	0.0449648i
$226$	3.40489	−	11.5960i	0.226490	−	0.771353i
$227$	3.04279	+	6.66279i	0.201957	+	0.442225i	0.983328	−	0.181843i	$-0.0582062\pi$
$227$	3.04279	+	6.66279i	0.201957	+	0.442225i	−0.781370	+	0.624068i	$0.785479\pi$
$228$	−1.67038	−	0.240164i	−0.110623	−	0.0159053i
$229$	0.0980447			0.00647898			0.00323949	−	0.999995i	$-0.498969\pi$
$229$	0.0980447			0.00647898			0.00323949	+	0.999995i	$0.498969\pi$
$230$	4.48048	+	8.62548i	0.295434	+	0.568747i
$231$	7.78277	−	3.05115i	0.512068	−	0.200751i
$232$	−0.183424	+	1.27574i	−0.0120424	+	0.0837564i
$233$	−9.23313	−	20.2177i	−0.604883	−	1.32451i	−0.926020	−	0.377476i	$-0.876792\pi$
$233$	−9.23313	−	20.2177i	−0.604883	−	1.32451i	0.321137	−	0.947033i	$-0.395935\pi$
$234$	−0.374508	+	1.27546i	−0.0244823	+	0.0833792i
$235$	13.7003	−	11.8714i	0.893708	−	0.774403i
$236$	−1.29120	−	4.39743i	−0.0840501	−	0.286248i
$237$	−10.3636	−	6.66028i	−0.673188	−	0.432631i
$238$	−0.0571327	+	1.04202i	−0.00370336	+	0.0675444i
$239$	7.53937	−	8.70090i	0.487681	−	0.562814i	−0.457563	−	0.889177i	$-0.651278\pi$
$239$	7.53937	−	8.70090i	0.487681	−	0.562814i	0.945245	+	0.326363i	$0.105823\pi$
$240$	1.09572	+	1.70498i	0.0707285	+	0.110056i
$241$	−1.10351	−	7.67509i	−0.0710834	−	0.494396i	−0.993999	−	0.109393i	$-0.965109\pi$
$241$	−1.10351	−	7.67509i	−0.0710834	−	0.494396i	0.922915	−	0.385003i	$-0.125800\pi$
$242$	−0.144735	−	1.00665i	−0.00930390	−	0.0647101i
$243$	0.540641	+	0.841254i	0.0346821	+	0.0539664i
$244$	−6.87548	+	7.93473i	−0.440158	+	0.507969i
$245$	−4.44727	−	13.4719i	−0.284126	−	0.860687i
$246$	9.06169	+	5.82360i	0.577753	+	0.371299i
$247$	−0.632003	−	2.15240i	−0.0402134	−	0.136954i
$248$	3.54245	−	3.06955i	0.224946	−	0.194917i
$249$	1.77350	−	6.03998i	0.112391	−	0.382768i
$250$	−4.96100	−	10.8631i	−0.313761	−	0.687042i
$251$	−0.514062	+	3.57538i	−0.0324473	+	0.225676i	−0.999592	−	0.0285492i	$-0.990911\pi$
$251$	−0.514062	+	3.57538i	−0.0324473	+	0.225676i	0.967145	+	0.254225i	$0.0818204\pi$
$252$	2.46322	−	0.965681i	0.155168	−	0.0608322i
$253$	0.767690	+	15.1334i	0.0482642	+	0.951428i
$254$	−12.8721			−0.807667
$255$	−0.791277	−	0.113769i	−0.0495517	−	0.00712446i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	−3.51355	+	11.9660i	−0.219169	+	0.746421i	0.774350	+	0.632757i	$0.218077\pi$
$257$	−3.51355	+	11.9660i	−0.219169	+	0.746421i	−0.993519	+	0.113664i	$0.963741\pi$
$258$	7.51635	+	8.67433i	0.467947	+	0.540040i
$259$	−11.5715	−	14.9336i	−0.719020	−	0.927931i
$260$	−1.45655	+	2.26643i	−0.0903311	+	0.140558i
$261$	−0.535411	+	1.17239i	−0.0331411	+	0.0725690i
$262$	−13.0817	−	11.3353i	−0.808188	−	0.700299i
$263$	14.7276	+	22.9166i	0.908144	+	1.41310i	0.910684	+	0.413103i	$0.135555\pi$
$263$	14.7276	+	22.9166i	0.908144	+	1.41310i	−0.00253990	+	0.999997i	$0.500808\pi$
$264$	0.449656	+	3.12743i	0.0276744	+	0.192480i
$265$	13.4796	−	1.93808i	0.828047	−	0.119055i
$266$	−2.61589	+	3.61829i	−0.160391	+	0.221851i
$267$	5.54016	+	4.80058i	0.339053	+	0.293791i
$268$	−11.9501	−	5.45742i	−0.729968	−	0.333365i
$269$	−9.17804	+	14.2813i	−0.559595	+	0.870747i	−0.999629	−	0.0272341i	$-0.991330\pi$
$269$	−9.17804	+	14.2813i	−0.559595	+	0.870747i	0.440034	+	0.897981i	$0.354966\pi$
$270$	0.570990	+	1.94461i	0.0347493	+	0.118345i
$271$	−18.7777	+	16.2709i	−1.14066	+	0.988388i	−0.999999	−	0.00166916i	$-0.999469\pi$
$271$	−18.7777	+	16.2709i	−1.14066	+	0.988388i	−0.140662	+	0.990058i	$0.544923\pi$
$272$	−0.378462	−	0.111127i	−0.0229476	−	0.00673803i
$273$	2.52790	+	2.44521i	0.152995	+	0.147991i
$274$	3.50991	+	0.504648i	0.212041	+	0.0304869i
$275$		−	2.81979i		−	0.170039i
$276$	0.242971	+	4.78967i	0.0146252	+	0.288304i
$277$	−16.7109			−1.00406			−0.502031	−	0.864850i	$-0.667414\pi$
$277$	−16.7109			−1.00406			−0.502031	+	0.864850i	$0.667414\pi$
$278$	−9.70109	−	1.39481i	−0.581833	−	0.0836549i
$279$	4.26375	−	1.94719i	0.255264	−	0.116575i
$280$	5.34140	−	0.471401i	0.319210	−	0.0281716i
$281$	12.8503	−	11.1349i	0.766586	−	0.664250i	−0.181097	−	0.983465i	$-0.557965\pi$
$281$	12.8503	−	11.1349i	0.766586	−	0.664250i	0.947682	+	0.319215i	$0.103419\pi$
$282$	8.58227	−	2.51998i	0.511067	−	0.150063i
$283$	4.69481	+	3.01717i	0.279077	+	0.179352i	0.672690	−	0.739924i	$-0.265139\pi$
$283$	4.69481	+	3.01717i	0.279077	+	0.179352i	−0.393613	+	0.919276i	$0.628775\pi$
$284$	−1.37270	+	3.00579i	−0.0814545	+	0.178361i
$285$	−2.58480	−	2.23974i	−0.153110	−	0.132671i
$286$	−3.53331	+	2.27072i	−0.208929	+	0.134270i
$287$	24.7826	−	14.0721i	1.46287	−	0.830652i
$288$	0.142315	+	0.989821i	0.00838598	+	0.0583258i
$289$	−14.1704	+	9.10678i	−0.833554	+	0.535693i
$290$	−1.71059	+	1.97412i	−0.100449	+	0.115925i
$291$	−11.0677	−	5.05444i	−0.648798	−	0.296296i
$292$	−3.11694	+	4.85005i	−0.182405	+	0.283828i
$293$	−2.89873	+	0.851144i	−0.169346	+	0.0497244i	−0.365306	−	0.930887i	$-0.619036\pi$
$293$	−2.89873	+	0.851144i	−0.169346	+	0.0497244i	0.195961	+	0.980612i	$0.437218\pi$
$294$	0.765299	−	6.95804i	0.0446331	−	0.405801i
$295$	2.61689	−	8.91231i	0.152361	−	0.518895i
$296$	6.49529	−	2.96630i	0.377531	−	0.172413i
$297$	−0.449656	+	3.12743i	−0.0260917	+	0.181472i
$298$		−	0.950561i		−	0.0550645i
$299$	−5.65739	+	2.93871i	−0.327175	+	0.169950i
$300$		−	0.892454i		−	0.0515258i
$301$	29.5619	−	6.94748i	1.70392	−	0.400446i
$302$	−3.52498	−	7.71863i	−0.202840	−	0.444157i
$303$	−17.1467	−	5.03472i	−0.985051	−	0.289237i
$304$	−1.10511	−	1.27537i	−0.0633826	−	0.0731474i
$305$	−20.4168	+	5.99491i	−1.16906	+	0.343267i
$306$	−0.331824	−	0.213250i	−0.0189691	−	0.0121907i
$307$	−29.0536	−	13.2683i	−1.65818	−	0.757265i	−0.999990	−	0.00441114i	$-0.998596\pi$
$307$	−29.0536	−	13.2683i	−1.65818	−	0.757265i	−0.658188	−	0.752854i	$-0.728677\pi$
$308$	7.87990	+	2.79072i	0.448999	+	0.159016i
$309$	2.85553	+	4.44329i	0.162445	+	0.252770i
$310$	9.40317	−	1.35197i	0.534064	−	0.0767869i
$311$	10.9391	−	1.57280i	0.620298	−	0.0891854i	0.175001	−	0.984568i	$-0.444007\pi$
$311$	10.9391	−	1.57280i	0.620298	−	0.0891854i	0.445297	+	0.895383i	$0.353098\pi$
$312$	−1.11828	+	0.718675i	−0.0633102	+	0.0406870i
$313$	−2.65387	+	3.06273i	−0.150006	+	0.173116i	−0.825779	−	0.563993i	$-0.809264\pi$
$313$	−2.65387	+	3.06273i	−0.150006	+	0.173116i	0.675773	+	0.737109i	$0.263810\pi$
$314$	−4.72621	+	10.3489i	−0.266715	+	0.584025i
$315$	5.25785	+	1.05254i	0.296246	+	0.0593040i
$316$	−3.47073	−	11.8202i	−0.195244	−	0.664939i
$317$	13.6041	+	15.7000i	0.764082	+	0.881797i	0.995853	−	0.0909730i	$-0.0289977\pi$
$317$	13.6041	+	15.7000i	0.764082	+	0.881797i	−0.231772	+	0.972770i	$0.574452\pi$
$318$	6.44720	+	1.89307i	0.361541	+	0.106158i
$319$	−3.70426	+	1.69168i	−0.207399	+	0.0947159i
$320$	−0.288431	+	2.00608i	−0.0161238	+	0.112143i
$321$	−5.41087			−0.302005
$322$	11.5203	+	5.31818i	0.642000	+	0.296370i
$323$	0.665639			0.0370371
$324$	−0.142315	+	0.989821i	−0.00790638	+	0.0549901i
$325$	1.07913	−	0.492824i	0.0598596	−	0.0273370i
$326$	14.4460	+	4.24172i	0.800089	+	0.234927i
$327$	10.2895	+	11.8747i	0.569010	+	0.656673i
$328$	3.03473	+	10.3353i	0.167565	+	0.570673i
$329$	4.64525	−	23.2048i	0.256101	−	1.27932i
$330$	−2.66014	+	5.82489i	−0.146436	+	0.320649i
$331$	−0.704765	+	0.813342i	−0.0387374	+	0.0447053i	−0.774788	−	0.632222i	$-0.782143\pi$
$331$	−0.704765	+	0.813342i	−0.0387374	+	0.0447053i	0.736050	+	0.676927i	$0.236689\pi$
$332$	5.29566	−	3.40332i	0.290637	−	0.186781i
$333$	7.06789	−	1.01621i	0.387318	−	0.0556879i
$334$	−17.3304	+	2.49174i	−0.948277	+	0.136342i
$335$	−14.3948	−	22.3987i	−0.786472	−	1.22377i
$336$	2.49397	+	0.883254i	0.136057	+	0.0481855i
$337$	−25.4323	−	11.6145i	−1.38538	−	0.632684i	−0.423439	−	0.905925i	$-0.639177\pi$
$337$	−25.4323	−	11.6145i	−1.38538	−	0.632684i	−0.961946	+	0.273241i	$0.911904\pi$
$338$	9.44976	+	6.07299i	0.513999	+	0.330327i
$339$	11.5960	−	3.40489i	0.629807	−	0.184928i
$340$	−0.523505	−	0.604157i	−0.0283910	−	0.0327650i
$341$	14.2101	+	4.17248i	0.769523	+	0.225952i
$342$	−0.701036	−	1.53505i	−0.0379077	−	0.0830062i
$343$	−15.3612	−	10.3458i	−0.829424	−	0.558619i
$344$			11.4778i			0.618840i
$345$	−4.83389	+	8.43250i	−0.260248	+	0.453991i
$346$			10.6503i			0.572565i
$347$	−2.46335	+	17.1330i	−0.132240	+	0.919746i	0.810386	+	0.585896i	$0.199257\pi$
$347$	−2.46335	+	17.1330i	−0.132240	+	0.919746i	−0.942626	+	0.333851i	$0.891652\pi$
$348$	−1.17239	+	0.535411i	−0.0628466	+	0.0287011i
$349$	−3.73321	+	12.7141i	−0.199834	+	0.680573i	0.797207	+	0.603706i	$0.206310\pi$
$349$	−3.73321	+	12.7141i	−0.199834	+	0.680573i	−0.997041	+	0.0768668i	$0.975508\pi$
$350$	−2.09091	−	1.09700i	−0.111764	−	0.0586370i
$351$	−1.27546	+	0.374508i	−0.0680788	+	0.0199898i
$352$	−1.70820	+	2.65801i	−0.0910475	+	0.141673i
$353$	−20.6957	−	9.45143i	−1.10152	−	0.503049i	−0.220148	−	0.975466i	$-0.570654\pi$
$353$	−20.6957	−	9.45143i	−1.10152	−	0.503049i	−0.881375	+	0.472418i	$0.843381\pi$
$354$	3.00128	−	3.46366i	0.159516	−	0.184091i
$355$	−5.63392	+	3.62070i	−0.299017	+	0.192167i
$356$	1.04327	+	7.25607i	0.0552930	+	0.384571i
$357$	−0.907495	+	0.515298i	−0.0480297	+	0.0272725i
$358$	3.69929	−	2.37739i	0.195514	−	0.125649i
$359$	−23.9577	−	20.7595i	−1.26444	−	1.09564i	−0.991015	−	0.133751i	$-0.957298\pi$
$359$	−23.9577	−	20.7595i	−1.26444	−	1.09564i	−0.273426	−	0.961893i	$-0.588157\pi$
$360$	−0.841925	+	1.84356i	−0.0443733	+	0.0971641i
$361$	−13.5881	−	8.73252i	−0.715161	−	0.459606i
$362$	−1.34227	+	0.394125i	−0.0705480	+	0.0207148i
$363$	0.768600	−	0.665996i	0.0403411	−	0.0349557i
$364$	0.309188	+	3.50339i	0.0162059	+	0.183627i
$365$	−10.6286	+	4.85393i	−0.556327	+	0.254066i
$366$	−10.3923	−	1.49418i	−0.543213	−	0.0781023i
$367$	21.6902			1.13222			0.566110	−	0.824330i	$-0.308448\pi$
$367$	21.6902			1.13222			0.566110	+	0.824330i	$0.308448\pi$
$368$	−2.95294	+	3.77891i	−0.153933	+	0.196989i
$369$			10.7717i			0.560750i
$370$	14.3245	+	2.05956i	0.744698	+	0.107071i
$371$	12.3601	−	12.7781i	0.641704	−	0.663405i
$372$	4.49747	+	1.32058i	0.233183	+	0.0684687i
$373$	−9.89014	+	8.56985i	−0.512092	+	0.443730i	−0.872178	−	0.489189i	$-0.837293\pi$
$373$	−9.89014	+	8.56985i	−0.512092	+	0.443730i	0.360086	+	0.932919i	$0.382747\pi$
$374$	−0.351114	−	1.19578i	−0.0181557	−	0.0618325i
$375$	6.45649	−	10.0465i	0.333412	−	0.518798i
$376$	8.13629	+	3.71572i	0.419597	+	0.191624i
$377$	−1.29481	−	1.12196i	−0.0666863	−	0.0577840i
$378$	2.14410	+	1.55011i	0.110281	+	0.0797289i
$379$	−0.0996937	+	0.0143338i	−0.00512092	+	0.000736277i	−0.144875	−	0.989450i	$-0.546278\pi$
$379$	−0.0996937	+	0.0143338i	−0.00512092	+	0.000736277i	0.139754	+	0.990186i	$0.455369\pi$
$380$	−0.486743	−	3.38537i	−0.0249694	−	0.173666i
$381$	−6.95918	−	10.8287i	−0.356530	−	0.554771i
$382$	9.63403	+	8.34793i	0.492920	+	0.427117i
$383$	−2.63533	+	5.77057i	−0.134659	+	0.294862i	−0.964934	−	0.262491i	$-0.915456\pi$
$383$	−2.63533	+	5.77057i	−0.134659	+	0.294862i	0.830275	+	0.557354i	$0.188183\pi$
$384$	−0.540641	+	0.841254i	−0.0275895	+	0.0429300i
$385$	10.3772	+	13.3923i	0.528871	+	0.682534i
$386$	5.56024	+	6.41686i	0.283009	+	0.326610i
$387$	−3.23366	+	11.0128i	−0.164376	+	0.559814i
$388$	−5.05444	−	11.0677i	−0.256600	−	0.561876i
$389$	−1.52574	−	0.219369i	−0.0773582	−	0.0111224i	0.103527	−	0.994627i	$-0.466987\pi$
$389$	−1.52574	−	0.219369i	−0.0773582	−	0.0111224i	−0.180885	+	0.983504i	$0.557896\pi$
$390$	−2.69411			−0.136422
$391$	−0.363729	−	1.85637i	−0.0183945	−	0.0938806i
$392$	5.13492	−	4.75737i	0.259353	−	0.240284i
$393$	2.46340	−	17.1333i	0.124262	−	0.864263i
$394$	−4.19530	−	9.18643i	−0.211356	−	0.462806i
$395$	7.03415	−	23.9561i	0.353927	−	1.20536i
$396$	−2.38786	+	2.06909i	−0.119994	+	0.103976i
$397$	−1.30492	−	4.44416i	−0.0654922	−	0.223046i	0.920244	−	0.391346i	$-0.127990\pi$
$397$	−1.30492	−	4.44416i	−0.0654922	−	0.223046i	−0.985736	+	0.168300i	$0.946172\pi$
$398$	8.54576	+	5.49203i	0.428360	+	0.275290i
$399$	−4.45815	−	0.244434i	−0.223187	−	0.0122370i
$400$	0.584433	−	0.674471i	0.0292216	−	0.0337236i
$401$	−2.97498	−	4.62916i	−0.148564	−	0.231169i	0.758994	−	0.651098i	$-0.225691\pi$
$401$	−2.97498	−	4.62916i	−0.148564	−	0.231169i	−0.907557	+	0.419929i	$0.862055\pi$
$402$	−1.86963	−	13.0036i	−0.0932487	−	0.648559i
$403$	0.886749	+	6.16747i	0.0441721	+	0.307224i
$404$	−9.66155	−	15.0337i	−0.480680	−	0.747953i
$405$	−1.32721	+	1.53168i	−0.0659497	+	0.0761100i
$406$	−0.186685	+	3.40489i	−0.00926502	+	0.168982i
$407$	18.9797	+	12.1975i	0.940791	+	0.604609i
$408$	−0.111127	−	0.378462i	−0.00550158	−	0.0187367i
$409$	17.6738	−	15.3144i	0.873912	−	0.757249i	−0.0973533	−	0.995250i	$-0.531038\pi$
$409$	17.6738	−	15.3144i	0.873912	−	0.757249i	0.971265	+	0.238001i	$0.0764922\pi$
$410$	−6.15051	+	20.9467i	−0.303752	+	1.03448i
$411$	1.47306	+	3.22555i	0.0726607	+	0.159105i
$412$	−0.751671	+	5.22798i	−0.0370322	+	0.257564i
$413$	−4.42579	−	11.2891i	−0.217779	−	0.555502i
$414$	−3.89797	+	2.79389i	−0.191575	+	0.137312i
$415$	12.7581			0.626268
$416$	−1.31577	−	0.189180i	−0.0645111	−	0.00927529i
$417$	−4.07142	−	8.91517i	−0.199378	−	0.436578i
$418$	1.50219	−	5.11600i	0.0734746	−	0.250232i
$419$	−3.75591	−	4.33455i	−0.183488	−	0.211757i	0.656552	−	0.754281i	$-0.272014\pi$
$419$	−3.75591	−	4.33455i	−0.183488	−	0.211757i	−0.840040	+	0.542524i	$0.817469\pi$
$420$	3.28435	+	4.23862i	0.160260	+	0.206823i
$421$	3.59887	−	5.59995i	0.175398	−	0.272925i	−0.742413	−	0.669943i	$-0.766319\pi$
$421$	3.59887	−	5.59995i	0.175398	−	0.272925i	0.917811	+	0.397018i	$0.129955\pi$
$422$	−3.81771	+	8.35961i	−0.185843	+	0.406940i
$423$	6.75987	+	5.85746i	0.328676	+	0.284800i
$424$	3.63278	+	5.65271i	0.176423	+	0.274520i
$425$	0.0500975	+	0.348436i	0.00243009	+	0.0169016i
$426$	−3.27076	+	0.470265i	−0.158469	+	0.0227844i
$427$	−16.2748	+	22.5112i	−0.787593	+	1.08939i
$428$	−4.08926	−	3.54337i	−0.197662	−	0.171275i
$429$	−3.82050	−	1.74476i	−0.184455	−	0.0842380i
$430$	−12.5764	+	19.5693i	−0.606490	+	0.943717i
$431$	2.56015	+	8.71906i	0.123318	+	0.419982i	0.997891	−	0.0649113i	$-0.0206765\pi$
$431$	2.56015	+	8.71906i	0.123318	+	0.419982i	−0.874573	+	0.484894i	$0.838858\pi$
$432$	−0.755750	+	0.654861i	−0.0363610	+	0.0315070i
$433$	−12.5085	−	3.67282i	−0.601118	−	0.176504i	−0.0330058	−	0.999455i	$-0.510508\pi$
$433$	−12.5085	−	3.67282i	−0.601118	−	0.176504i	−0.568113	+	0.822951i	$0.692326\pi$
$434$	8.62221	−	8.91379i	0.413879	−	0.427876i
$435$	−2.58555	−	0.371746i	−0.123968	−	0.0178239i
$436$			15.7125i			0.752492i
$437$	2.98476	−	7.52274i	0.142780	−	0.359861i
$438$	−5.76527			−0.275475
$439$	20.3243	+	2.92219i	0.970025	+	0.139469i	0.609072	−	0.793115i	$-0.291542\pi$
$439$	20.3243	+	2.92219i	0.970025	+	0.139469i	0.360953	+	0.932584i	$0.382451\pi$
$440$	−5.82489	+	2.66014i	−0.277691	+	0.126817i
$441$	6.26723	−	3.11799i	0.298439	−	0.148476i
$442$	0.396262	−	0.343363i	0.0188483	−	0.0163321i
$443$	−10.6173	+	3.11751i	−0.504442	+	0.148117i	−0.524045	−	0.851690i	$-0.675578\pi$
$443$	−10.6173	+	3.11751i	−0.504442	+	0.148117i	0.0196037	+	0.999808i	$0.493760\pi$
$444$	6.00703	+	3.86048i	0.285081	+	0.183210i
$445$	−6.17189	+	13.5146i	−0.292576	+	0.640651i
$446$	−2.16298	−	1.87423i	−0.102420	−	0.0887473i
$447$	0.799662	−	0.513912i	0.0378227	−	0.0243072i
$448$	1.30640	+	2.30072i	0.0617218	+	0.108699i
$449$	3.62645	+	25.2225i	0.171143	+	1.19032i	0.876475	+	0.481447i	$0.159888\pi$
$449$	3.62645	+	25.2225i	0.171143	+	1.19032i	−0.705333	+	0.708876i	$0.749202\pi$
$450$	0.750780	−	0.482497i	0.0353921	−	0.0227451i
$451$	−22.2875	+	25.7212i	−1.04948	+	1.21116i
$452$	10.9934	+	5.02051i	0.517085	+	0.236145i
$453$	4.58758	−	7.13841i	0.215543	−	0.335392i
$454$	−7.02800	+	2.06361i	−0.329841	+	0.0968499i
$455$	−3.31158	+	6.31197i	−0.155249	+	0.295910i
$456$	0.475439	−	1.61920i	0.0222645	−	0.0758259i
$457$	−17.6448	+	8.05809i	−0.825387	+	0.376942i	−0.782894	−	0.622155i	$-0.786257\pi$
$457$	−17.6448	+	8.05809i	−0.825387	+	0.376942i	−0.0424932	+	0.999097i	$0.513530\pi$
$458$	−0.0139532	+	0.0970468i	−0.000651991	+	0.00453470i
$459$		−	0.394440i		−	0.0184109i
$460$	−9.17532	+	3.20734i	−0.427802	+	0.149543i
$461$		−	18.7787i		−	0.874611i	−0.899313	−	0.437306i	$-0.855933\pi$
$461$		−	18.7787i		−	0.874611i	0.899313	−	0.437306i	$-0.144067\pi$
$462$	1.91249	+	8.13777i	0.0889773	+	0.378603i
$463$	−1.81148	−	3.96660i	−0.0841868	−	0.184343i	0.862857	−	0.505449i	$-0.168673\pi$
$463$	−1.81148	−	3.96660i	−0.0841868	−	0.184343i	−0.947044	+	0.321105i	$0.895946\pi$
$464$	−1.23665	−	0.363114i	−0.0574101	−	0.0168571i
$465$	6.22109	+	7.17952i	0.288496	+	0.332942i
$466$	21.3260	−	6.26187i	0.987906	−	0.290075i
$467$	−12.4006	−	7.96938i	−0.573832	−	0.368779i	0.221310	−	0.975204i	$-0.428967\pi$
$467$	−12.4006	−	7.96938i	−0.573832	−	0.368779i	−0.795141	+	0.606424i	$0.792603\pi$
$468$	−1.20918	−	0.552212i	−0.0558942	−	0.0255260i
$469$	−32.7639	−	11.6036i	−1.51290	−	0.535803i
$470$	9.80078	+	15.2503i	0.452076	+	0.703444i
$471$	−11.2613	+	1.61913i	−0.518892	+	0.0746054i
$472$	4.53643	−	0.652240i	0.208806	−	0.0300218i
$473$	−30.5081	+	19.6064i	−1.40276	+	0.901502i
$474$	8.06738	−	9.31025i	0.370547	−	0.427634i
$475$	−0.625642	+	1.36996i	−0.0287064	+	0.0628583i
$476$	−1.02329	−	0.204847i	−0.0469023	−	0.00938913i
$477$	1.89307	+	6.44720i	0.0866777	+	0.295197i
$478$	7.53937	+	8.70090i	0.344843	+	0.397970i
$479$	−37.1905	−	10.9201i	−1.69928	−	0.498952i	−0.718737	−	0.695282i	$-0.755280\pi$
$479$	−37.1905	−	10.9201i	−1.69928	−	0.498952i	−0.980538	+	0.196330i	$0.937098\pi$
$480$	−1.84356	+	0.841925i	−0.0841466	+	0.0384284i
$481$	−1.35085	+	9.39536i	−0.0615934	+	0.428392i
$482$	7.75401			0.353186
$483$	1.75440	+	12.5667i	0.0798281	+	0.571805i
$484$	1.01700			0.0462275
$485$	3.50939	−	24.4084i	0.159353	−	1.10833i
$486$	−0.909632	+	0.415415i	−0.0412617	+	0.0188436i
$487$	11.2215	+	3.29492i	0.508493	+	0.149307i	0.525908	−	0.850541i	$-0.323726\pi$
$487$	11.2215	+	3.29492i	0.508493	+	0.149307i	−0.0174151	+	0.999848i	$0.505544\pi$
$488$	−6.87548	−	7.93473i	−0.311238	−	0.359188i
$489$	4.24172	+	14.4460i	0.191817	+	0.653270i
$490$	13.9677	−	2.48476i	0.630995	−	0.112250i
$491$	−8.71981	+	19.0937i	−0.393519	+	0.861687i	0.604367	+	0.796706i	$0.293426\pi$
$491$	−8.71981	+	19.0937i	−0.393519	+	0.861687i	−0.997886	+	0.0649813i	$0.979301\pi$
$492$	−7.05394	+	8.14068i	−0.318016	+	0.367010i
$493$	0.427674	−	0.274849i	0.0192615	−	0.0123786i
$494$	2.22044	−	0.319251i	0.0999022	−	0.0143638i
$495$	−6.33838	+	0.911322i	−0.284889	+	0.0409609i
$496$	2.53417	+	3.94324i	0.113787	+	0.177057i
$497$	−2.91862	+	8.24105i	−0.130918	+	0.369662i
$498$	5.72610	+	2.61502i	0.256593	+	0.117182i
$499$	21.8262	+	14.0268i	0.977073	+	0.627927i	0.928672	−	0.370901i	$-0.120951\pi$
$499$	21.8262	+	14.0268i	0.977073	+	0.627927i	0.0484008	+	0.998828i	$0.484588\pi$
$500$	11.4585	−	3.36453i	0.512441	−	0.150466i
$501$	−11.4657	−	13.2321i	−0.512250	−	0.591168i
$502$	−3.46583	−	1.01766i	−0.154687	−	0.0454203i
$503$	−15.6893	−	34.3548i	−0.699551	−	1.53180i	−0.840515	−	0.541788i	$-0.817747\pi$
$503$	−15.6893	−	34.3548i	−0.699551	−	1.53180i	0.140964	−	0.990015i	$-0.454980\pi$
$504$	0.605299	+	2.57558i	0.0269621	+	0.114725i
$505$		−	36.2184i		−	1.61170i
$506$	−15.0886	−	1.39383i	−0.670771	−	0.0619633i
$507$			11.2330i			0.498873i
$508$	1.83189	−	12.7411i	0.0812770	−	0.565294i
$509$	0.985219	−	0.449935i	0.0436691	−	0.0199430i	−0.393461	−	0.919341i	$-0.628722\pi$
$509$	0.985219	−	0.449935i	0.0436691	−	0.0199430i	0.437130	+	0.899398i	$0.355995\pi$
$510$	0.225221	−	0.767032i	0.00997295	−	0.0339648i
$511$	−7.08663	+	13.5073i	−0.313494	+	0.597529i
$512$	−0.959493	+	0.281733i	−0.0424040	+	0.0124509i
$513$	0.912361	−	1.41966i	0.0402817	−	0.0626796i
$514$	−11.3442	−	5.18073i	−0.500372	−	0.228512i
$515$	−7.00999	+	8.08996i	−0.308897	+	0.356486i
$516$	−9.65572	+	6.20536i	−0.425069	+	0.273176i
$517$	4.02199	+	27.9736i	0.176887	+	1.23028i
$518$	16.4284	−	9.32847i	0.721824	−	0.409869i
$519$	−8.95962	+	5.75800i	−0.393284	+	0.252748i
$520$	−2.03607	−	1.76427i	−0.0892877	−	0.0773682i
$521$	13.1783	−	28.8565i	0.577353	−	1.26423i	−0.365436	−	0.930836i	$-0.619080\pi$
$521$	13.1783	−	28.8565i	0.577353	−	1.26423i	0.942789	−	0.333390i	$-0.108192\pi$
$522$	−1.08426	−	0.696810i	−0.0474566	−	0.0304985i
$523$	17.0834	−	5.01614i	0.747004	−	0.219340i	0.113992	−	0.993482i	$-0.463636\pi$
$523$	17.0834	−	5.01614i	0.747004	−	0.219340i	0.633013	+	0.774141i	$0.281818\pi$
$524$	13.0817	−	11.3353i	0.571475	−	0.495186i
$525$	−0.207580	−	2.35207i	−0.00905951	−	0.102653i
$526$	−24.7793	+	11.3163i	−1.08043	+	0.493416i
$527$	−1.83005	−	0.263122i	−0.0797184	−	0.0114618i
$528$	−3.15959			−0.137503
$529$	−22.6108	−	4.21336i	−0.983078	−	0.183189i
$530$			13.6182i			0.591538i
$531$	4.53643	+	0.652240i	0.196864	+	0.0283048i
$532$	−3.20918	−	3.10420i	−0.139136	−	0.134584i
$533$	−13.7388	−	4.03407i	−0.595093	−	0.174735i
$534$	−5.54016	+	4.80058i	−0.239746	+	0.207741i
$535$	−3.08955	−	10.5220i	−0.133573	−	0.454908i
$536$	7.10255	−	11.0518i	0.306783	−	0.477364i
$537$	3.99998	+	1.82673i	0.172612	+	0.0788291i
$538$	−12.8298	−	11.1171i	−0.553131	−	0.479291i
$539$	21.4166	+	5.52214i	0.922480	+	0.237856i
$540$	−2.00608	+	0.288431i	−0.0863279	+	0.0124121i
$541$	4.81173	+	33.4663i	0.206872	+	1.43883i	0.783281	+	0.621667i	$0.213544\pi$
$541$	4.81173	+	33.4663i	0.206872	+	1.43883i	−0.576409	+	0.817161i	$0.695547\pi$
$542$	−13.4330	−	20.9021i	−0.576996	−	0.897823i
$543$	−1.05724	−	0.916107i	−0.0453707	−	0.0393139i
$544$	0.163856	−	0.358795i	0.00702528	−	0.0153832i
$545$	−17.2165	+	26.7894i	−0.737474	+	1.14753i
$546$	−2.78008	+	2.15418i	−0.118976	+	0.0921904i
$547$	21.6818	+	25.0222i	0.927049	+	1.06987i	0.997379	+	0.0723475i	$0.0230491\pi$
$547$	21.6818	+	25.0222i	0.927049	+	1.06987i	−0.0703308	+	0.997524i	$0.522405\pi$
$548$	−0.999023	+	3.40236i	−0.0426762	+	0.145342i
$549$	−4.36150	−	9.55036i	−0.186144	−	0.407600i
$550$	2.79108	+	0.401297i	0.119012	+	0.0171114i
$551$	2.17502			0.0926590
$552$	−4.77550	−	0.441143i	−0.203259	−	0.0187763i
$553$	−11.8964	−	30.3450i	−0.505888	−	1.29040i
$554$	2.37821	−	16.5408i	0.101040	−	0.702752i
$555$	6.01182	+	13.1641i	0.255188	+	0.558783i
$556$	2.76122	−	9.40385i	0.117102	−	0.398812i
$557$	−12.2212	+	10.5898i	−0.517830	+	0.448702i	−0.874146	−	0.485663i	$-0.838578\pi$
$557$	−12.2212	+	10.5898i	−0.517830	+	0.448702i	0.356316	+	0.934366i	$0.384033\pi$
$558$	1.32058	+	4.49747i	0.0559044	+	0.190393i
$559$	−12.8354	−	8.24880i	−0.542879	−	0.348887i
$560$	−0.293559	+	5.35412i	−0.0124051	+	0.226253i
$561$	0.816131	−	0.941866i	0.0344571	−	0.0397656i
$562$	9.19274	+	14.3042i	0.387772	+	0.603385i
$563$	5.05548	+	35.1617i	0.213063	+	1.48189i	0.762846	+	0.646580i	$0.223801\pi$
$563$	5.05548	+	35.1617i	0.213063	+	1.48189i	−0.549783	+	0.835307i	$0.685290\pi$
$564$	1.27295	+	8.85355i	0.0536008	+	0.372802i
$565$	13.2424	+	20.6055i	0.557111	+	0.866881i
$566$	−3.65460	+	4.21763i	−0.153614	+	0.177280i
$567$	−0.144845	+	2.64178i	−0.00608292	+	0.110944i
$568$	−2.77984	−	1.78649i	−0.116639	−	0.0749595i
$569$	−8.20931	−	27.9583i	−0.344152	−	1.17207i	−0.931804	−	0.362961i	$-0.881766\pi$
$569$	−8.20931	−	27.9583i	−0.344152	−	1.17207i	0.587652	−	0.809113i	$-0.300052\pi$
$570$	2.58480	−	2.23974i	0.108265	−	0.0938125i
$571$	5.15610	−	17.5601i	0.215776	−	0.734865i	−0.778464	−	0.627689i	$-0.784001\pi$
$571$	5.15610	−	17.5601i	0.215776	−	0.734865i	0.994240	−	0.107176i	$-0.0341809\pi$
$572$	−1.74476	−	3.82050i	−0.0729522	−	0.159743i
$573$	−1.81418	+	12.6179i	−0.0757884	+	0.527120i
$574$	10.4020	+	26.5330i	0.434170	+	1.10747i
$575$	4.16250	+	0.996226i	0.173588	+	0.0415455i
$576$	−1.00000			−0.0416667
$577$	−3.34121	−	0.480393i	−0.139096	−	0.0199990i	0.0724149	−	0.997375i	$-0.476929\pi$
$577$	−3.34121	−	0.480393i	−0.139096	−	0.0199990i	−0.211511	+	0.977376i	$0.567839\pi$
$578$	−6.99742	−	15.3222i	−0.291054	−	0.637320i
$579$	−2.39211	+	8.14679i	−0.0994129	+	0.338569i
$580$	−1.71059	−	1.97412i	−0.0710283	−	0.0819711i
$581$	13.1652	−	10.2012i	0.546183	−	0.423217i
$582$	6.57808	−	10.2357i	0.272670	−	0.424283i
$583$	−8.81947	+	19.3119i	−0.365265	+	0.799819i
$584$	−4.35710	−	3.77545i	−0.180298	−	0.156229i
$585$	−1.45655	−	2.26643i	−0.0602207	−	0.0937053i
$586$	−0.429948	−	2.99036i	−0.0177610	−	0.123530i
$587$	−12.4108	+	1.78440i	−0.512247	+	0.0736501i	−0.393592	−	0.919285i	$-0.628768\pi$
$587$	−12.4108	+	1.78440i	−0.512247	+	0.0736501i	−0.118656	+	0.992935i	$0.537858\pi$
$588$	6.77830	+	1.74774i	0.279533	+	0.0720756i
$589$	−5.97809	−	5.18004i	−0.246323	−	0.213440i
$590$	8.44917	+	3.85861i	0.347847	+	0.158856i
$591$	5.45997	−	8.49587i	0.224593	−	0.349474i
$592$	2.01173	+	6.85133i	0.0826816	+	0.281588i
$593$	14.8339	−	12.8536i	0.609155	−	0.527836i	−0.294747	−	0.955575i	$-0.595235\pi$
$593$	14.8339	−	12.8536i	0.609155	−	0.527836i	0.903902	+	0.427740i	$0.140690\pi$
$594$	−3.03160	−	0.890159i	−0.124388	−	0.0365237i
$595$	−1.52022	−	1.47050i	−0.0623231	−	0.0602845i
$596$	0.940885	+	0.135279i	0.0385402	+	0.00554124i
$597$			10.1584i			0.415754i
$598$	−2.10367	−	6.01803i	−0.0860255	−	0.246095i
$599$	7.92967			0.323998			0.161999	−	0.986791i	$-0.448206\pi$
$599$	7.92967			0.323998			0.161999	+	0.986791i	$0.448206\pi$
$600$	0.883370	+	0.127009i	0.0360634	+	0.00518514i
$601$	−3.25760	+	1.48770i	−0.132880	+	0.0606844i	−0.480746	−	0.876860i	$-0.659634\pi$
$601$	−3.25760	+	1.48770i	−0.132880	+	0.0606844i	0.347865	+	0.937545i	$0.386907\pi$
$602$	2.66966	+	30.2498i	0.108807	+	1.23289i
$603$	9.92850	−	8.60309i	0.404320	−	0.350345i
$604$	8.14173	−	2.39063i	0.331282	−	0.0972732i
$605$	1.73397	+	1.11435i	0.0704958	+	0.0453049i
$606$	7.42370	−	16.2556i	0.301567	−	0.660340i
$607$	4.43826	+	3.84577i	0.180143	+	0.156095i	0.740265	−	0.672315i	$-0.234700\pi$
$607$	4.43826	+	3.84577i	0.180143	+	0.156095i	−0.560121	+	0.828411i	$0.689246\pi$
$608$	1.41966	−	0.912361i	0.0575749	−	0.0370011i
$609$	−2.96530	+	1.68377i	−0.120160	+	0.0682298i
$610$	−3.02828	−	21.0621i	−0.122611	−	0.852781i
$611$	−10.0026	+	6.42826i	−0.404661	+	0.260060i
$612$	0.258303	−	0.298098i	0.0104413	−	0.0120499i
$613$	15.8186	+	7.22412i	0.638908	+	0.291780i	0.708409	−	0.705802i	$-0.249413\pi$
$613$	15.8186	+	7.22412i	0.638908	+	0.291780i	−0.0695007	+	0.997582i	$0.522141\pi$
$614$	17.2681	−	26.8696i	0.696882	−	1.08437i
$615$	−20.9467	+	6.15051i	−0.844652	+	0.248012i
$616$	−3.88374	+	7.40254i	−0.156480	+	0.298257i
$617$	7.53258	−	25.6536i	0.303250	−	1.03278i	−0.657059	−	0.753839i	$-0.728200\pi$
$617$	7.53258	−	25.6536i	0.303250	−	1.03278i	0.960309	−	0.278937i	$-0.0899820\pi$
$618$	−4.80444	+	2.19412i	−0.193263	+	0.0882603i
$619$	−1.16464	+	8.10026i	−0.0468109	+	0.325577i	0.952938	+	0.303165i	$0.0980435\pi$
$619$	−1.16464	+	8.10026i	−0.0468109	+	0.325577i	−0.999749	+	0.0224115i	$0.992866\pi$
$620$			9.49987i			0.381524i
$621$	−4.45777	−	1.76869i	−0.178884	−	0.0709750i
$622$			11.0516i			0.443127i
$623$	4.43726	+	18.8808i	0.177775	+	0.756442i
$624$	−0.552212	−	1.20918i	−0.0221062	−	0.0484058i
$625$	18.9416	+	5.56176i	0.757664	+	0.222470i
$626$	−2.65387	−	3.06273i	−0.106070	−	0.122411i
$627$	5.11600	−	1.50219i	0.204313	−	0.0599918i
$628$	−9.57100	−	6.15091i	−0.381925	−	0.245448i
$629$	−2.56200	−	1.17003i	−0.102154	−	0.0466520i
$630$	−1.79010	+	5.05454i	−0.0713192	+	0.201378i
$631$	18.9792	+	29.5321i	0.755548	+	1.17566i	0.979576	+	0.201073i	$0.0644429\pi$
$631$	18.9792	+	29.5321i	0.755548	+	1.17566i	−0.224028	+	0.974583i	$0.571921\pi$
$632$	12.1938	−	1.75321i	0.485045	−	0.0697389i
$633$	−9.09656	+	1.30789i	−0.361556	+	0.0519839i
$634$	−17.4762	+	11.2313i	−0.694069	+	0.446051i
$635$	17.0840	−	19.7160i	0.677958	−	0.782405i
$636$	−2.79133	+	6.11217i	−0.110684	+	0.242363i
$637$	1.62974	+	9.16129i	0.0645725	+	0.362984i
$638$	−1.14729	−	3.90731i	−0.0454216	−	0.154692i
$639$	−2.16392	−	2.49730i	−0.0856033	−	0.0987915i
$640$	−1.94461	−	0.570990i	−0.0768676	−	0.0225703i
$641$	4.73216	−	2.16111i	0.186909	−	0.0853586i	−0.319762	−	0.947498i	$-0.603603\pi$
$641$	4.73216	−	2.16111i	0.186909	−	0.0853586i	0.506671	+	0.862139i	$0.330876\pi$
$642$	0.770047	−	5.35579i	0.0303913	−	0.211376i
$643$	−24.0749			−0.949420			−0.474710	−	0.880142i	$-0.657447\pi$
$643$	−24.0749			−0.949420			−0.474710	+	0.880142i	$0.657447\pi$
$644$	−6.90355	+	10.6462i	−0.272038	+	0.419518i
$645$	−23.2621			−0.915945
$646$	−0.0947303	+	0.658863i	−0.00372711	+	0.0259226i
$647$	−7.00822	+	3.20055i	−0.275522	+	0.125827i	−0.548384	−	0.836227i	$-0.684757\pi$
$647$	−7.00822	+	3.20055i	−0.275522	+	0.125827i	0.272863	+	0.962053i	$0.412030\pi$
$648$	−0.959493	−	0.281733i	−0.0376924	−	0.0110675i
$649$	9.48280	+	10.9437i	0.372233	+	0.429579i
$650$	0.334231	+	1.13829i	0.0131096	+	0.0446472i
$651$	12.1603	+	2.43430i	0.476599	+	0.0954079i
$652$	−6.25442	+	13.6953i	−0.244942	+	0.536348i
$653$	−29.9476	+	34.5614i	−1.17194	+	1.35249i	−0.248556	+	0.968617i	$0.579956\pi$
$653$	−29.9476	+	34.5614i	−1.17194	+	1.35249i	−0.923385	+	0.383875i	$0.874589\pi$
$654$	−13.2182	+	8.49481i	−0.516872	+	0.332173i
$655$	34.7243	−	4.99260i	1.35679	−	0.195077i
$656$	−10.6620	+	1.53297i	−0.416282	+	0.0598523i
$657$	−3.11694	−	4.85005i	−0.121603	−	0.189219i
$658$	22.3075	+	7.90035i	0.869637	+	0.307988i
$659$	−23.7361	−	10.8399i	−0.924626	−	0.422263i	−0.104552	−	0.994519i	$-0.533341\pi$
$659$	−23.7361	−	10.8399i	−0.924626	−	0.422263i	−0.820075	+	0.572257i	$0.806068\pi$
$660$	−5.38702	−	3.46203i	−0.209689	−	0.134759i
$661$	43.4872	−	12.7690i	1.69145	−	0.496656i	0.712662	−	0.701508i	$-0.247490\pi$
$661$	43.4872	−	12.7690i	1.69145	−	0.496656i	0.978793	+	0.204852i	$0.0656714\pi$
$662$	−0.704765	−	0.813342i	−0.0273915	−	0.0316114i
$663$	0.503091	+	0.147721i	0.0195384	+	0.00573700i
$664$	2.61502	+	5.72610i	0.101483	+	0.222216i
$665$	−2.07023	−	8.80895i	−0.0802801	−	0.341597i
$666$			7.14057i			0.276691i
$667$	−1.18851	−	6.06581i	−0.0460192	−	0.234869i
$668$		−	17.5086i		−	0.677429i
$669$	0.407309	−	2.83290i	0.0157475	−	0.109526i
$670$	24.2194	−	11.0606i	0.935675	−	0.427309i
$671$	9.34591	−	31.8292i	0.360795	−	1.22875i
$672$	−1.22919	+	2.34288i	−0.0474171	+	0.0903786i
$673$	−25.3245	+	7.43594i	−0.976187	+	0.286634i	−0.730649	−	0.682753i	$-0.760783\pi$
$673$	−25.3245	+	7.43594i	−0.976187	+	0.286634i	−0.245537	+	0.969387i	$0.578964\pi$
$674$	15.1157	−	23.5205i	0.582235	−	0.905976i
$675$	0.811804	+	0.370739i	0.0312464	+	0.0142697i
$676$	−7.35602	+	8.48930i	−0.282924	+	0.326512i
$677$	−1.84616	+	1.18645i	−0.0709536	+	0.0455991i	−0.575637	−	0.817706i	$-0.695246\pi$
$677$	−1.84616	+	1.18645i	−0.0709536	+	0.0455991i	0.504683	+	0.863305i	$0.331609\pi$
$678$	1.71995	+	11.9625i	0.0660543	+	0.459418i
$679$	−15.8953	−	27.9933i	−0.610005	−	1.07428i
$680$	0.672510	−	0.432196i	0.0257896	−	0.0165740i
$681$	−5.53564	−	4.79666i	−0.212126	−	0.183808i
$682$	−6.15232	+	13.4717i	−0.235585	+	0.515858i
$683$	26.0968	+	16.7714i	0.998565	+	0.641739i	0.934409	−	0.356201i	$-0.115928\pi$
$683$	26.0968	+	16.7714i	0.998565	+	0.641739i	0.0641560	+	0.997940i	$0.479564\pi$
$684$	1.61920	−	0.475439i	0.0619115	−	0.0181789i
$685$	−5.43135	+	4.70629i	−0.207521	+	0.179818i
$686$	12.4266	−	13.7324i	0.474449	−	0.524307i
$687$	−0.0891846	+	0.0407293i	−0.00340261	+	0.00155392i
$688$	−11.3610	−	1.63346i	−0.433132	−	0.0622750i
$689$	−8.93210			−0.340286
$690$	−7.65874	−	5.98475i	−0.291563	−	0.227836i
$691$			30.9880i			1.17884i	0.807827	+	0.589420i	$0.200644\pi$
$691$			30.9880i			1.17884i	−0.807827	+	0.589420i	$0.799356\pi$
$692$	−10.5419	−	1.51570i	−0.400743	−	0.0576182i
$693$	−5.81196	+	6.00850i	−0.220778	+	0.228244i
$694$	−16.6080	−	4.87655i	−0.630432	−	0.185111i
$695$	15.0118	−	13.0078i	0.569430	−	0.493414i
$696$	−0.363114	−	1.23665i	−0.0137638	−	0.0468751i
$697$	2.29706	−	3.57429i	0.0870073	−	0.135386i
$698$	−12.0534	−	5.50462i	−0.456229	−	0.208353i
$699$	16.7975	+	14.5551i	0.635340	+	0.550525i
$700$	1.38340	−	1.91351i	0.0522876	−	0.0723239i
$701$	37.6105	−	5.40758i	1.42053	−	0.204241i	0.611145	−	0.791519i	$-0.290709\pi$
$701$	37.6105	−	5.40758i	1.42053	−	0.204241i	0.809386	+	0.587277i	$0.199800\pi$
$702$	−0.189180	−	1.31577i	−0.00714012	−	0.0496606i
$703$	−6.51478	−	10.1372i	−0.245709	−	0.382331i
$704$	−2.38786	−	2.06909i	−0.0899958	−	0.0779818i
$705$	−7.53068	+	16.4899i	−0.283622	+	0.621045i
$706$	12.3005	−	19.1400i	0.462937	−	0.720344i
$707$	−28.9598	−	37.3741i	−1.08915	−	1.40560i
$708$	3.00128	+	3.46366i	0.112795	+	0.130172i
$709$	7.35810	−	25.0594i	0.276339	−	0.941125i	−0.698011	−	0.716087i	$-0.745931\pi$
$709$	7.35810	−	25.0594i	0.276339	−	0.941125i	0.974350	−	0.225038i	$-0.0722505\pi$
$710$	−2.78205	−	6.09185i	−0.104409	−	0.228623i
$711$	12.1938	+	1.75321i	0.457304	+	0.0657505i
$712$	−7.33069			−0.274729
$713$	−11.1797	+	19.5026i	−0.418684	+	0.730377i
$714$	−0.380903	−	0.971592i	−0.0142549	−	0.0363609i
$715$	1.21142	−	8.42563i	0.0453047	−	0.315101i
$716$	1.82673	+	3.99998i	0.0682680	+	0.149486i
$717$	−3.24357	+	11.0466i	−0.121133	+	0.412542i
$718$	23.9577	−	20.7595i	0.894095	−	0.774737i
$719$	0.311066	+	1.05939i	0.0116008	+	0.0395087i	0.965090	−	0.261918i	$-0.0843552\pi$
$719$	0.311066	+	1.05939i	0.0116008	+	0.0395087i	−0.953489	+	0.301427i	$0.902537\pi$
$720$	−1.70498	−	1.09572i	−0.0635407	−	0.0408351i
$721$	−0.765035	+	13.9532i	−0.0284914	+	0.519645i
$722$	10.5774	−	12.2070i	0.393651	−	0.454297i
$723$	4.19213	+	6.52309i	0.155907	+	0.242596i
$724$	−0.199089	−	1.38470i	−0.00739909	−	0.0514618i
$725$	0.163697	+	1.13854i	0.00607956	+	0.0422843i
$726$	0.549834	+	0.855558i	0.0204063	+	0.0317527i
$727$	−8.91459	+	10.2880i	−0.330624	+	0.381560i	−0.896585	−	0.442872i	$-0.853960\pi$
$727$	−8.91459	+	10.2880i	−0.330624	+	0.381560i	0.565961	+	0.824432i	$0.308505\pi$
$728$	−3.51173	−	0.192543i	−0.130153	−	0.00713612i
$729$	−0.841254	−	0.540641i	−0.0311575	−	0.0200237i
$730$	−3.29191	−	11.2112i	−0.121839	−	0.414946i
$731$	3.42150	−	2.96475i	0.126549	−	0.109655i
$732$	2.95795	−	10.0739i	0.109329	−	0.372341i
$733$	21.8718	+	47.8926i	0.807854	+	1.76895i	0.616368	+	0.787459i	$0.288604\pi$
$733$	21.8718	+	47.8926i	0.807854	+	1.76895i	0.191486	+	0.981495i	$0.438669\pi$
$734$	−3.08684	+	21.4694i	−0.113937	+	0.792451i
$735$	9.64180	+	10.4070i	0.355643	+	0.383868i
$736$	−3.32019	−	3.46068i	−0.122384	−	0.127562i
$737$	41.5084			1.52898
$738$	−10.6620	−	1.53297i	−0.392474	−	0.0564293i
$739$	−13.4379	−	29.4250i	−0.494322	−	1.08241i	−0.978273	−	0.207320i	$-0.933526\pi$
$739$	−13.4379	−	29.4250i	−0.494322	−	1.08241i	0.483951	−	0.875095i	$-0.339201\pi$
$740$	−4.07719	+	13.8856i	−0.149881	+	0.510446i
$741$	1.46903	+	1.69535i	0.0539662	+	0.0622803i
$742$	10.8890	+	14.0528i	0.399748	+	0.515894i
$743$	2.39026	−	3.71932i	0.0876903	−	0.136449i	−0.794637	−	0.607084i	$-0.792339\pi$
$743$	2.39026	−	3.71932i	0.0876903	−	0.136449i	0.882328	+	0.470636i	$0.155975\pi$
$744$	−1.94719	+	4.26375i	−0.0713875	+	0.156317i
$745$	1.45596	+	1.26160i	0.0533422	+	0.0462213i
$746$	−7.07511	−	11.0091i	−0.259038	−	0.403071i
$747$	0.895867	+	6.23089i	0.0327781	+	0.227976i
$748$	1.23358	−	0.177362i	0.0451042	−	0.00648501i
$749$	−11.6014	−	8.38743i	−0.423908	−	0.306470i
$750$	9.02538	+	7.82053i	0.329560	+	0.285565i
$751$	−31.3250	−	14.3057i	−1.14307	−	0.522021i	−0.248357	−	0.968669i	$-0.579891\pi$
$751$	−31.3250	−	14.3057i	−1.14307	−	0.522021i	−0.894710	+	0.446647i	$0.852618\pi$
$752$	−4.83581	+	7.52467i	−0.176344	+	0.274397i
$753$	−1.01766	−	3.46583i	−0.0370855	−	0.126302i
$754$	1.29481	−	1.12196i	0.0471543	−	0.0408595i
$755$	16.5009	+	4.84510i	0.600529	+	0.176331i
$756$	−1.83947	+	1.90167i	−0.0669008	+	0.0691632i
$757$	53.3474	+	7.67020i	1.93895	+	0.278778i	0.998181	−	0.0602844i	$-0.0192008\pi$
$757$	53.3474	+	7.67020i	1.93895	+	0.278778i	0.940764	+	0.339063i	$0.110110\pi$
$758$		−	0.100719i		−	0.00365827i
$759$	−6.98495	−	13.4469i	−0.253538	−	0.488092i
$760$	3.42018			0.124063
$761$	12.0544	+	1.73316i	0.436972	+	0.0628271i	0.357291	−	0.933993i	$-0.383701\pi$
$761$	12.0544	+	1.73316i	0.436972	+	0.0628271i	0.0796815	+	0.996820i	$0.474610\pi$
$762$	11.7089	−	5.34726i	0.424168	−	0.193711i
$763$	3.65463	+	41.4104i	0.132307	+	1.49916i
$764$	−9.63403	+	8.34793i	−0.348547	+	0.302018i
$765$	0.767032	−	0.225221i	0.0277321	−	0.00814288i
$766$	−5.33679	−	3.42974i	−0.192826	−	0.123922i
$767$	−2.53083	+	5.54175i	−0.0913831	+	0.200101i
$768$	−0.755750	−	0.654861i	−0.0272708	−	0.0236303i
$769$	39.0754	−	25.1123i	1.40910	−	0.905571i	0.409120	−	0.912480i	$-0.365836\pi$
$769$	39.0754	−	25.1123i	1.40910	−	0.905571i	0.999976	+	0.00690925i	$0.00219930\pi$
$770$	−14.7328	+	8.36564i	−0.530933	+	0.301477i
$771$	−1.77484	−	12.3443i	−0.0639192	−	0.444568i
$772$	−7.14285	+	4.59043i	−0.257077	+	0.165213i
$773$	0.212027	−	0.244692i	0.00762609	−	0.00880098i	−0.751924	−	0.659250i	$-0.770874\pi$
$773$	0.212027	−	0.244692i	0.00762609	−	0.00880098i	0.759550	+	0.650449i	$0.225419\pi$
$774$	−10.4406	−	4.76804i	−0.375278	−	0.171384i
$775$	2.26163	−	3.51916i	0.0812400	−	0.126412i
$776$	11.6743	−	3.42790i	0.419084	−	0.123054i
$777$	16.7295	+	8.77713i	0.600167	+	0.314878i
$778$	0.434272	−	1.47899i	0.0155694	−	0.0530245i
$779$	16.5351	−	7.55132i	0.592431	−	0.270554i
$780$	0.383412	−	2.66669i	0.0137283	−	0.0954827i
$781$		−	10.4405i		−	0.373592i
$782$	1.88924	−	0.0958376i	0.0675590	−	0.00342714i
$783$		−	1.28886i		−	0.0460601i
$784$	3.97817	+	5.75970i	0.142078	+	0.205704i
$785$	−9.57864	−	20.9743i	−0.341876	−	0.748605i
$786$	16.6084	+	4.87666i	0.592401	+	0.173945i
$787$	−1.70843	−	1.97163i	−0.0608988	−	0.0702810i	0.724483	−	0.689293i	$-0.242079\pi$
$787$	−1.70843	−	1.97163i	−0.0608988	−	0.0702810i	−0.785382	+	0.619012i	$0.787533\pi$
$788$	9.68998	−	2.84523i	0.345191	−	0.101357i
$789$	−22.9166	−	14.7276i	−0.815854	−	0.524317i
$790$	22.7112	+	10.3719i	0.808029	+	0.369014i
$791$	30.1409	+	10.6746i	1.07169	+	0.379545i
$792$	−1.70820	−	2.65801i	−0.0606983	−	0.0944484i
$793$	13.8145	−	1.98622i	0.490567	−	0.0705329i
$794$	4.58463	−	0.659171i	0.162703	−	0.0233931i
$795$	−11.4564	+	7.36258i	−0.406316	+	0.261124i
$796$	−6.65231	+	7.67718i	−0.235785	+	0.272110i
$797$	4.74132	−	10.3820i	0.167946	−	0.367751i	−0.806881	−	0.590715i	$-0.798846\pi$
$797$	4.74132	−	10.3820i	0.167946	−	0.367751i	0.974827	+	0.222964i	$0.0715732\pi$
$798$	0.876408	−	4.37799i	0.0310245	−	0.154979i
$799$	−0.993981	−	3.38519i	−0.0351645	−	0.119759i
$800$	0.584433	+	0.674471i	0.0206628	+	0.0238462i
$801$	−7.03374	−	2.06529i	−0.248525	−	0.0729736i
$802$	5.00543	−	2.28590i	0.176748	−	0.0807180i
$803$	2.59239	−	18.0305i	0.0914835	−	0.636281i
$804$	13.1373			0.463316
$805$	−23.4356	+	10.5871i	−0.825997	+	0.373146i
$806$	−6.23089			−0.219474
$807$	2.41597	−	16.8034i	0.0850462	−	0.591509i
$808$	16.2556	−	7.42370i	0.571871	−	0.261165i
$809$	−19.9169	−	5.84814i	−0.700242	−	0.205610i	−0.0878149	−	0.996137i	$-0.527988\pi$
$809$	−19.9169	−	5.84814i	−0.700242	−	0.205610i	−0.612427	+	0.790527i	$0.709807\pi$
$810$	−1.32721	−	1.53168i	−0.0466335	−	0.0538179i
$811$	−13.7346	−	46.7757i	−0.482287	−	1.64252i	−0.737290	−	0.675577i	$-0.763895\pi$
$811$	−13.7346	−	46.7757i	−0.482287	−	1.64252i	0.255003	−	0.966940i	$-0.417924\pi$
$812$	−3.34366	−	0.669351i	−0.117340	−	0.0234896i
$813$	10.3216	−	22.6011i	0.361993	−	0.792654i
$814$	−14.7745	+	17.0507i	−0.517845	+	0.597625i
$815$	−25.6698	+	16.4970i	−0.899175	+	0.577865i
$816$	0.390425	−	0.0561346i	0.0136676	−	0.00196511i
$817$	19.1722	−	2.75655i	0.670751	−	0.0964395i
$818$	12.6433	+	19.6733i	0.442062	+	0.687862i
$819$	−3.31523	−	1.17411i	−0.115844	−	0.0410268i
$820$	−19.8582	−	9.06893i	−0.693478	−	0.316701i
$821$	22.1436	+	14.2308i	0.772815	+	0.496658i	0.866642	−	0.498930i	$-0.166274\pi$
$821$	22.1436	+	14.2308i	0.772815	+	0.496658i	−0.0938268	+	0.995589i	$0.529910\pi$
$822$	−3.40236	+	0.999023i	−0.118671	+	0.0348449i
$823$	−28.8277	−	33.2689i	−1.00487	−	1.15968i	−0.987143	−	0.159839i	$-0.948902\pi$
$823$	−28.8277	−	33.2689i	−1.00487	−	1.15968i	−0.0177271	−	0.999843i	$-0.505643\pi$
$824$	−5.06780	−	1.48804i	−0.176545	−	0.0518383i
$825$	1.17138	+	2.56497i	0.0407823	+	0.0893007i
$826$	11.8041	−	2.77413i	0.410717	−	0.0965243i
$827$			28.2279i			0.981580i	0.871278	+	0.490790i	$0.163292\pi$
$827$			28.2279i			0.981580i	−0.871278	+	0.490790i	$0.836708\pi$
$828$	−2.21072	−	4.25591i	−0.0768277	−	0.147903i
$829$			8.83288i			0.306778i	0.988166	+	0.153389i	$0.0490188\pi$
$829$			8.83288i			0.306778i	−0.988166	+	0.153389i	$0.950981\pi$
$830$	−1.81566	+	12.6282i	−0.0630225	+	0.438331i
$831$	15.2008	−	6.94196i	0.527309	−	0.240814i
$832$	0.374508	−	1.27546i	0.0129837	−	0.0442185i
$833$	−2.74453	−	0.301864i	−0.0950922	−	0.0104590i
$834$	9.40385	−	2.76122i	0.325629	−	0.0956132i
$835$	19.1846	−	29.8518i	0.663909	−	1.03306i
$836$	4.85014	+	2.21498i	0.167746	+	0.0766068i
$837$	−3.06955	+	3.54245i	−0.106099	+	0.122445i
$838$	4.82496	−	3.10081i	0.166675	−	0.107116i
$839$	5.55276	+	38.6203i	0.191703	+	1.33332i	0.827500	+	0.561465i	$0.189762\pi$
$839$	5.55276	+	38.6203i	0.191703	+	1.33332i	−0.635798	+	0.771856i	$0.719329\pi$
$840$	−4.66289	+	2.64770i	−0.160885	+	0.0913544i
$841$	−22.9989	+	14.7805i	−0.793065	+	0.509672i
$842$	5.03077	+	4.35919i	0.173372	+	0.150228i
$843$	−7.06347	+	15.4668i	−0.243279	+	0.532706i
$844$	−7.73121	−	4.96855i	−0.266119	−	0.171024i
$845$	−21.8437	+	6.41390i	−0.751448	+	0.220645i
$846$	−6.75987	+	5.85746i	−0.232409	+	0.201384i
$847$	2.68032	−	0.236549i	0.0920969	−	0.00812793i
$848$	−6.11217	+	2.79133i	−0.209893	+	0.0958548i
$849$	−5.52392	−	0.794220i	−0.189581	−	0.0272576i
$850$	−0.352019			−0.0120742
$851$	−24.7112	+	23.7081i	−0.847090	+	0.812702i
$852$		−	3.30440i		−	0.113207i
$853$	37.6765	+	5.41707i	1.29002	+	0.185477i	0.752959	−	0.658067i	$-0.228626\pi$
$853$	37.6765	+	5.41707i	1.29002	+	0.185477i	0.537060	+	0.843544i	$0.319535\pi$
$854$	−19.9660	−	19.3128i	−0.683221	−	0.660872i
$855$	3.28164	+	0.963577i	0.112230	+	0.0329536i
$856$	4.08926	−	3.54337i	0.139768	−	0.121110i
$857$	−8.41892	−	28.6722i	−0.287585	−	0.979424i	−0.968904	−	0.247437i	$-0.920412\pi$
$857$	−8.41892	−	28.6722i	−0.287585	−	0.979424i	0.681319	−	0.731986i	$-0.261407\pi$
$858$	2.27072	−	3.53331i	0.0775210	−	0.120625i
$859$	7.96482	+	3.63741i	0.271756	+	0.124107i	0.546632	−	0.837373i	$-0.315910\pi$
$859$	7.96482	+	3.63741i	0.271756	+	0.124107i	−0.274876	+	0.961480i	$0.588637\pi$
$860$	−17.5803	−	15.2334i	−0.599484	−	0.519456i
$861$	−16.6972	+	23.0955i	−0.569040	+	0.787093i
$862$	−8.99466	+	1.29324i	−0.306359	+	0.0440478i
$863$	−2.31676	−	16.1134i	−0.0788635	−	0.548507i	−0.990500	−	0.137511i	$-0.956090\pi$
$863$	−2.31676	−	16.1134i	−0.0788635	−	0.548507i	0.911637	−	0.410997i	$-0.134819\pi$
$864$	−0.540641	−	0.841254i	−0.0183930	−	0.0286200i
$865$	−16.3129	−	14.1352i	−0.554656	−	0.480612i
$866$	5.41557	−	11.8584i	0.184029	−	0.402967i
$867$	9.10678	−	14.1704i	0.309282	−	0.481253i
$868$	7.59599	+	9.80301i	0.257825	+	0.332736i
$869$	25.4896	+	29.4165i	0.864675	+	0.997888i
$870$	0.735925	−	2.50633i	0.0249502	−	0.0849726i
$871$	7.25457	+	15.8853i	0.245812	+	0.538253i
$872$	−15.5526	−	2.23612i	−0.526676	−	0.0757246i
$873$	12.1672			0.411797
$874$	7.02139	+	4.02497i	0.237502	+	0.136147i
$875$	29.4165	−	11.5324i	0.994459	−	0.389867i
$876$	0.820484	−	5.70659i	0.0277216	−	0.192808i
$877$	21.0146	+	46.0155i	0.709612	+	1.55383i	0.827914	+	0.560855i	$0.189527\pi$
$877$	21.0146	+	46.0155i	0.709612	+	1.55383i	−0.118303	+	0.992978i	$0.537745\pi$
$878$	−5.78489	+	19.7015i	−0.195231	+	0.664895i
$879$	2.28320	−	1.97840i	0.0770104	−	0.0667299i
$880$	−1.80409	−	6.14417i	−0.0608159	−	0.207120i
$881$	11.4235	+	7.34141i	0.384866	+	0.247338i	0.718739	−	0.695280i	$-0.244719\pi$
$881$	11.4235	+	7.34141i	0.384866	+	0.247338i	−0.333873	+	0.942618i	$0.608356\pi$
$882$	2.19433	+	6.64717i	0.0738871	+	0.223822i
$883$	30.6953	−	35.4243i	1.03298	−	1.19212i	0.0518732	−	0.998654i	$-0.483481\pi$
$883$	30.6953	−	35.4243i	1.03298	−	1.19212i	0.981106	−	0.193468i	$-0.0619737\pi$
$884$	0.283474	+	0.441094i	0.00953427	+	0.0148356i
$885$	1.32190	+	9.19402i	0.0444352	+	0.309054i
$886$	−1.57478	−	10.9529i	−0.0529059	−	0.367969i
$887$	−25.5307	−	39.7266i	−0.857238	−	1.33389i	−0.941350	−	0.337432i	$-0.890442\pi$
$887$	−25.5307	−	39.7266i	−0.857238	−	1.33389i	0.0841122	−	0.996456i	$-0.473195\pi$
$888$	−4.67608	+	5.39648i	−0.156919	+	0.181094i
$889$	1.86446	−	34.0053i	0.0625320	−	1.14050i
$890$	−12.4986	−	8.03239i	−0.418956	−	0.269246i
$891$	−0.890159	−	3.03160i	−0.0298214	−	0.101563i
$892$	2.16298	−	1.87423i	0.0724218	−	0.0627538i
$893$	4.25261	−	14.4831i	0.142308	−	0.484657i
$894$	0.394877	+	0.864660i	0.0132067	+	0.0289186i
$895$	−1.26833	+	8.82145i	−0.0423957	+	0.294868i
$896$	−2.46322	+	0.965681i	−0.0822905	+	0.0322611i
$897$	3.92536	−	5.02331i	0.131064	−	0.167723i
$898$	−25.4819			−0.850341
$899$	−5.97983	−	0.859769i	−0.199438	−	0.0286749i
$900$	0.370739	+	0.811804i	0.0123580	+	0.0270601i
$901$	0.746702	−	2.54303i	0.0248763	−	0.0847207i
$902$	−22.2875	−	25.7212i	−0.742094	−	0.856422i
$903$	−24.0044	+	18.6001i	−0.798816	+	0.618973i
$904$	−6.53393	+	10.1670i	−0.217315	+	0.338149i
$905$	1.17780	−	2.57902i	0.0391513	−	0.0857294i
$906$	6.41287	+	5.55679i	0.213053	+	0.184612i
$907$	14.2967	+	22.2462i	0.474716	+	0.738672i	0.993201	−	0.116415i	$-0.0371401\pi$
$907$	14.2967	+	22.2462i	0.474716	+	0.738672i	−0.518485	+	0.855087i	$0.673504\pi$
$908$	−1.04241	−	7.25015i	−0.0345937	−	0.240605i
$909$	17.6887	−	2.54325i	0.586696	−	0.0843541i
$910$	−5.77644	−	4.17616i	−0.191487	−	0.138438i
$911$	10.2811	+	8.90865i	0.340629	+	0.295157i	0.808330	−	0.588730i	$-0.200372\pi$
$911$	10.2811	+	8.90865i	0.340629	+	0.295157i	−0.467701	+	0.883887i	$0.654917\pi$
$912$	1.53505	+	0.701036i	0.0508307	+	0.0232136i
$913$	−10.7531	+	16.7321i	−0.355875	+	0.553752i
$914$	−5.46496	−	18.6120i	−0.180765	−	0.615629i
$915$	16.0814	−	13.9346i	0.531634	−	0.460663i
$916$	−0.0940732	−	0.0276224i	−0.00310827	−	0.000912670i
$917$	31.8403	−	32.9171i	1.05146	−	1.08702i
$918$	0.390425	+	0.0561346i	0.0128859	+	0.00185272i
$919$			2.96298i			0.0977398i	0.998805	+	0.0488699i	$0.0155620\pi$
$919$			2.96298i			0.0977398i	−0.998805	+	0.0488699i	$0.984438\pi$
$920$	−1.86891	−	9.53838i	−0.0616161	−	0.314471i
$921$	31.9400			1.05246
$922$	18.5876	+	2.67249i	0.612149	+	0.0880137i
$923$	3.99560	−	1.82473i	0.131517	−	0.0600617i
$924$	−8.32712	+	0.734902i	−0.273942	+	0.0241765i
$925$	4.81611	−	4.17318i	0.158353	−	0.137213i
$926$	4.18402	−	1.22854i	0.137496	−	0.0403723i
$927$	−4.44329	−	2.85553i	−0.145937	−	0.0937878i
$928$	0.535411	−	1.17239i	0.0175757	−	0.0384855i
$929$	31.0993	+	26.9477i	1.02033	+	0.884125i	0.993306	−	0.115510i	$-0.0368503\pi$
$929$	31.0993	+	26.9477i	1.02033	+	0.884125i	0.0270278	+	0.999635i	$0.491396\pi$
$930$	−7.99180	+	5.13602i	−0.262061	+	0.168417i
$931$	−9.17983	−	7.43471i	−0.300857	−	0.243663i
$932$	3.16313	+	22.0001i	0.103612	+	0.720636i
$933$	−9.29717	+	5.97493i	−0.304376	+	0.195610i
$934$	9.65306	−	11.1402i	0.315858	−	0.364519i
$935$	2.29757	+	1.04926i	0.0751385	+	0.0343146i
$936$	0.718675	−	1.11828i	0.0234906	−	0.0365521i
$937$	14.0908	−	4.13742i	0.460325	−	0.135164i	−0.0433440	−	0.999060i	$-0.513801\pi$
$937$	14.0908	−	4.13742i	0.460325	−	0.135164i	0.503669	+	0.863896i	$0.331983\pi$
$938$	16.1482	−	30.7791i	0.527259	−	1.00497i
$939$	1.14174	−	3.88842i	0.0372594	−	0.126894i
$940$	−16.4899	+	7.53068i	−0.537841	+	0.245624i
$941$	1.30684	−	9.08928i	0.0426018	−	0.296302i	−0.957371	−	0.288863i	$-0.906723\pi$
$941$	1.30684	−	9.08928i	0.0426018	−	0.296302i	0.999972	−	0.00743926i	$-0.00236801\pi$
$942$		−	11.3771i		−	0.370685i
$943$	−30.0949	−	41.9876i	−0.980023	−	1.36730i
$944$			4.58308i			0.149166i
$945$	−5.21995	+	1.22676i	−0.169805	+	0.0399066i
$946$	−15.0650	−	32.9878i	−0.489807	−	1.07253i
$947$	−3.09959	−	0.910121i	−0.100723	−	0.0295750i	0.230983	−	0.972958i	$-0.425806\pi$
$947$	−3.09959	−	0.910121i	−0.100723	−	0.0295750i	−0.331706	+	0.943383i	$0.607624\pi$
$948$	8.06738	+	9.31025i	0.262016	+	0.302383i
$949$	7.35335	−	2.15914i	0.238700	−	0.0700886i
$950$	−1.26698	−	0.814240i	−0.0411063	−	0.0264174i
$951$	−18.8967	−	8.62984i	−0.612768	−	0.279842i
$952$	0.348391	−	0.983719i	0.0112914	−	0.0318825i
$953$	−0.459030	−	0.714265i	−0.0148694	−	0.0231373i	0.833739	−	0.552158i	$-0.186196\pi$
$953$	−0.459030	−	0.714265i	−0.0148694	−	0.0231373i	−0.848609	+	0.529021i	$0.822559\pi$
$954$	−6.65099	+	0.956269i	−0.215334	+	0.0309603i
$955$	−25.5728	+	3.67681i	−0.827516	+	0.118979i
$956$	−9.68530	+	6.22437i	−0.313245	+	0.201310i
$957$	2.66677	−	3.07761i	0.0862043	−	0.0994850i
$958$	16.1017	−	35.2578i	0.520222	−	1.13913i
$959$	−1.84156	+	9.19931i	−0.0594672	+	0.297061i
$960$	−0.570990	−	1.94461i	−0.0184286	−	0.0627621i
$961$	−5.91264	−	6.82355i	−0.190730	−	0.220114i
$962$	−9.10749	−	2.67420i	−0.293637	−	0.0862196i
$963$	4.92190	−	2.24776i	0.158606	−	0.0724329i
$964$	−1.10351	+	7.67509i	−0.0355417	+	0.247198i
$965$	−17.2082			−0.553952
$966$	−12.6885	−	0.0518828i	−0.408245	−	0.00166930i
$967$	9.87934			0.317698			0.158849	−	0.987303i	$-0.449222\pi$
$967$	9.87934			0.317698			0.158849	+	0.987303i	$0.449222\pi$
$968$	−0.144735	+	1.00665i	−0.00465195	+	0.0323550i
$969$	−0.605486	+	0.276516i	−0.0194510	+	0.00888298i
$970$	23.6605	+	6.94734i	0.759692	+	0.223066i
$971$	14.8071	+	17.0883i	0.475183	+	0.548390i	0.941846	−	0.336045i	$-0.109089\pi$
$971$	14.8071	+	17.0883i	0.475183	+	0.548390i	−0.466663	+	0.884435i	$0.654544\pi$
$972$	−0.281733	−	0.959493i	−0.00903658	−	0.0307758i
$973$	5.08993	−	25.4262i	0.163176	−	0.815125i
$974$	−4.85836	+	10.6383i	−0.155672	+	0.340874i
$975$	−0.776888	+	0.896577i	−0.0248803	+	0.0287134i
$976$	8.83245	−	5.67627i	0.282720	−	0.181693i
$977$	59.4596	−	8.54900i	1.90228	−	0.273507i	0.911745	−	0.410756i	$-0.134735\pi$
$977$	59.4596	−	8.54900i	1.90228	−	0.273507i	0.990537	+	0.137249i	$0.0438260\pi$
$978$	−14.9026	+	2.14267i	−0.476532	+	0.0685150i
$979$	−12.5223	−	19.4851i	−0.400214	−	0.622746i
$980$	0.471662	+	14.1791i	0.0150667	+	0.452935i
$981$	−14.2926	−	6.52720i	−0.456327	−	0.208398i
$982$	−17.6584	−	11.3484i	−0.563502	−	0.362141i
$983$	18.8869	−	5.54570i	0.602399	−	0.176880i	0.0337084	−	0.999432i	$-0.489268\pi$
$983$	18.8869	−	5.54570i	0.602399	−	0.176880i	0.568691	+	0.822551i	$0.307450\pi$
$984$	−7.05394	−	8.14068i	−0.224871	−	0.259515i
$985$	19.6388	+	5.76646i	0.625743	+	0.183735i
$986$	0.211188	+	0.462436i	0.00672558	+	0.0147270i
$987$	5.41415	+	23.0375i	0.172334	+	0.733292i
$988$			2.24327i			0.0713680i
$989$	−18.1640	−	51.9622i	−0.577582	−	1.65230i
$990$		−	6.40356i		−	0.203519i
$991$	6.18807	−	43.0389i	0.196570	−	1.36718i	−0.617573	−	0.786514i	$-0.711884\pi$
$991$	6.18807	−	43.0389i	0.196570	−	1.36718i	0.814143	−	0.580664i	$-0.197207\pi$
$992$	−4.26375	+	1.94719i	−0.135374	+	0.0618234i
$993$	0.303202	−	1.03261i	0.00962183	−	0.0327689i
$994$	−7.74181	−	4.06174i	−0.245555	−	0.128831i
$995$	−19.7541	+	5.80032i	−0.626246	+	0.183883i
$996$	−3.40332	+	5.29566i	−0.107838	+	0.167799i
$997$	−44.3882	−	20.2714i	−1.40579	−	0.642002i	−0.439213	−	0.898383i	$-0.644743\pi$
$997$	−44.3882	−	20.2714i	−1.40579	−	0.642002i	−0.966576	+	0.256381i	$0.917470\pi$
$998$	−16.9902	+	19.6078i	−0.537817	+	0.620673i
$999$	−6.00703	+	3.86048i	−0.190054	+	0.122140i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.s.a.475.2	yes	160
7.6	odd	2	inner	966.2.s.a.475.15	yes	160
23.20	odd	22	inner	966.2.s.a.181.15	yes	160
161.20	even	22	inner	966.2.s.a.181.2	✓	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.s.a.181.2	✓	160	161.20	even	22	inner
966.2.s.a.181.15	yes	160	23.20	odd	22	inner
966.2.s.a.475.2	yes	160	1.1	even	1	trivial
966.2.s.a.475.15	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)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.32721 - 1.53168i) q^{5} +(-0.281733 - 0.959493i) q^{6} +(-2.59428 - 0.519336i) q^{7} +(0.415415 - 0.909632i) q^{8} +(0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.32721 - 1.53168i) q^{5} +(-0.281733 - 0.959493i) q^{6} +(-2.59428 - 0.519336i) q^{7} +(0.415415 - 0.909632i) q^{8} +(0.654861 - 0.755750i) q^{9} +(1.70498 - 1.09572i) q^{10} +(3.12743 - 0.449656i) q^{11} +(0.989821 - 0.142315i) q^{12} +(0.718675 + 1.11828i) q^{13} +(0.883254 - 2.49397i) q^{14} +(1.84356 + 0.841925i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-0.378462 + 0.111127i) q^{17} +(0.654861 + 0.755750i) q^{18} +(-1.61920 - 0.475439i) q^{19} +(0.841925 + 1.84356i) q^{20} +(2.57558 - 0.605299i) q^{21} +3.15959i q^{22} +(-0.441143 + 4.77550i) q^{23} +1.00000i q^{24} +(0.127009 - 0.883370i) q^{25} +(-1.20918 + 0.552212i) q^{26} +(-0.281733 + 0.959493i) q^{27} +(2.34288 + 1.22919i) q^{28} +(-1.23665 + 0.363114i) q^{29} +(-1.09572 + 1.70498i) q^{30} +(4.26375 + 1.94719i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(-2.65801 + 1.70820i) q^{33} +(-0.0561346 - 0.390425i) q^{34} +(2.64770 + 4.66289i) q^{35} +(-0.841254 + 0.540641i) q^{36} +(5.39648 + 4.67608i) q^{37} +(0.701036 - 1.53505i) q^{38} +(-1.11828 - 0.718675i) q^{39} +(-1.94461 + 0.570990i) q^{40} +(-8.14068 + 7.05394i) q^{41} +(0.232594 + 2.63551i) q^{42} +(-10.4406 + 4.76804i) q^{43} +(-3.12743 - 0.449656i) q^{44} -2.02671 q^{45} +(-4.66411 - 1.11628i) q^{46} +8.94459i q^{47} +(-0.989821 - 0.142315i) q^{48} +(6.46058 + 2.69461i) q^{49} +(0.856303 + 0.251433i) q^{50} +(0.298098 - 0.258303i) q^{51} +(-0.374508 - 1.27546i) q^{52} +(-3.63278 + 5.65271i) q^{53} +(-0.909632 - 0.415415i) q^{54} +(-4.83949 - 4.19344i) q^{55} +(-1.55011 + 2.14410i) q^{56} +(1.67038 - 0.240164i) q^{57} +(-0.183424 - 1.27574i) q^{58} +(2.47780 + 3.85553i) q^{59} +(-1.53168 - 1.32721i) q^{60} +(4.36150 - 9.55036i) q^{61} +(-2.53417 + 3.94324i) q^{62} +(-2.09138 + 1.62053i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(0.759018 - 2.58498i) q^{65} +(-1.31254 - 2.87406i) q^{66} +(13.0036 + 1.86963i) q^{67} +0.394440 q^{68} +(-1.58254 - 4.52720i) q^{69} +(-4.99223 + 1.95715i) q^{70} +(0.470265 - 3.27076i) q^{71} +(-0.415415 - 0.909632i) q^{72} +(1.62426 - 5.53174i) q^{73} +(-5.39648 + 4.67608i) q^{74} +(0.251433 + 0.856303i) q^{75} +(1.41966 + 0.912361i) q^{76} +(-8.34695 - 0.457651i) q^{77} +(0.870508 - 1.00462i) q^{78} +(6.66028 + 10.3636i) q^{79} +(-0.288431 - 2.00608i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-5.82360 - 9.06169i) q^{82} +(-4.12233 + 4.75742i) q^{83} +(-2.64178 - 0.144845i) q^{84} +(0.672510 + 0.432196i) q^{85} +(-3.23366 - 11.0128i) q^{86} +(0.974055 - 0.844023i) q^{87} +(0.890159 - 3.03160i) q^{88} +(-3.04528 - 6.66823i) q^{89} +(0.288431 - 2.00608i) q^{90} +(-1.28368 - 3.27437i) q^{91} +(1.76869 - 4.45777i) q^{92} -4.68734 q^{93} +(-8.85355 - 1.27295i) q^{94} +(1.42079 + 3.11111i) q^{95} +(0.281733 - 0.959493i) q^{96} +(7.96782 + 9.19535i) q^{97} +(-3.58661 + 6.01134i) q^{98} +(1.70820 - 2.65801i) 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	\( 160 q - 16 q^{2} - 16 q^{4} - 16 q^{8} + 16 q^{9} - 22 q^{14} - 16 q^{16} + 16 q^{18} - 36 q^{23} + 96 q^{25} + 22 q^{28} - 20 q^{29} - 16 q^{32} - 50 q^{35} + 16 q^{36} + 22 q^{37} + 4 q^{39} - 110 q^{43} + 8 q^{46} - 36 q^{50} + 22 q^{51} - 88 q^{53} + 22 q^{57} + 24 q^{58} - 16 q^{64} - 72 q^{70} + 48 q^{71} + 16 q^{72} - 22 q^{74} + 24 q^{77} + 4 q^{78} + 88 q^{79} - 16 q^{81} + 22 q^{84} + 76 q^{85} + 44 q^{86} - 44 q^{88} + 8 q^{92} - 14 q^{95} + 22 q^{98} - 22 q^{99}+O(q^{100}) \) 160 * q - 16 * q^2 - 16 * q^4 - 16 * q^8 + 16 * q^9 - 22 * q^14 - 16 * q^16 + 16 * q^18 - 36 * q^23 + 96 * q^25 + 22 * q^28 - 20 * q^29 - 16 * q^32 - 50 * q^35 + 16 * q^36 + 22 * q^37 + 4 * q^39 - 110 * q^43 + 8 * q^46 - 36 * q^50 + 22 * q^51 - 88 * q^53 + 22 * q^57 + 24 * q^58 - 16 * q^64 - 72 * q^70 + 48 * q^71 + 16 * q^72 - 22 * q^74 + 24 * q^77 + 4 * q^78 + 88 * q^79 - 16 * q^81 + 22 * q^84 + 76 * q^85 + 44 * q^86 - 44 * q^88 + 8 * q^92 - 14 * q^95 + 22 * q^98 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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