LMFDB - Embedded newform 966.2.s.b.97.16

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			97.16
Character	$\chi$	$=$	966.97
Dual form			966.2.s.b.727.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 + 0.281733i) q^{2} +(0.755750 + 0.654861i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.518172 - 3.60397i) q^{5} +(0.540641 + 0.841254i) q^{6} +(1.65217 - 2.06648i) q^{7} +(0.654861 + 0.755750i) q^{8} +(0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(0.959493 + 0.281733i) q^{2} +(0.755750 + 0.654861i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.518172 - 3.60397i) q^{5} +(0.540641 + 0.841254i) q^{6} +(1.65217 - 2.06648i) q^{7} +(0.654861 + 0.755750i) q^{8} +(0.142315 + 0.989821i) q^{9} +(1.51254 - 3.31199i) q^{10} +(-0.691079 - 2.35360i) q^{11} +(0.281733 + 0.959493i) q^{12} +(0.123854 + 0.0565622i) q^{13} +(2.16744 - 1.51730i) q^{14} +(2.75170 - 2.38437i) q^{15} +(0.415415 + 0.909632i) q^{16} +(-0.733700 + 0.471520i) q^{17} +(-0.142315 + 0.989821i) q^{18} +(-5.42650 - 3.48740i) q^{19} +(2.38437 - 2.75170i) q^{20} +(2.60188 - 0.479800i) q^{21} -2.45296i q^{22} +(-1.70502 + 4.48251i) q^{23} +1.00000i q^{24} +(-7.92260 - 2.32629i) q^{25} +(0.102902 + 0.0891647i) q^{26} +(-0.540641 + 0.841254i) q^{27} +(2.50712 - 0.845203i) q^{28} +(-5.54185 + 3.56153i) q^{29} +(3.31199 - 1.51254i) q^{30} +(7.56647 - 6.55639i) q^{31} +(0.142315 + 0.989821i) q^{32} +(1.01900 - 2.23129i) q^{33} +(-0.836822 + 0.245713i) q^{34} +(-6.59141 - 7.02515i) q^{35} +(-0.415415 + 0.909632i) q^{36} +(10.8803 - 1.56435i) q^{37} +(-4.22417 - 4.87496i) q^{38} +(0.0565622 + 0.123854i) q^{39} +(3.06303 - 1.96849i) q^{40} +(5.50496 + 0.791494i) q^{41} +(2.63166 + 0.272670i) q^{42} +(6.23016 + 5.39846i) q^{43} +(0.691079 - 2.35360i) q^{44} +3.64103 q^{45} +(-2.89882 + 3.82058i) q^{46} +10.0300i q^{47} +(-0.281733 + 0.959493i) q^{48} +(-1.54067 - 6.82835i) q^{49} +(-6.94629 - 4.46411i) q^{50} +(-0.863273 - 0.124120i) q^{51} +(0.0736128 + 0.114544i) q^{52} +(-5.77411 + 2.63695i) q^{53} +(-0.755750 + 0.654861i) q^{54} +(-8.84038 + 1.27106i) q^{55} +(2.64368 - 0.104630i) q^{56} +(-1.81731 - 6.18920i) q^{57} +(-6.32076 + 1.85594i) q^{58} +(-1.09238 - 0.498873i) q^{59} +(3.60397 - 0.518172i) q^{60} +(4.42779 + 5.10994i) q^{61} +(9.10713 - 4.15909i) q^{62} +(2.28057 + 1.34126i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(0.268026 - 0.417057i) q^{65} +(1.60635 - 1.85382i) q^{66} +(-1.47500 + 5.02337i) q^{67} -0.872151 q^{68} +(-4.22399 + 2.27111i) q^{69} +(-4.34520 - 8.59760i) q^{70} +(13.4693 + 3.95493i) q^{71} +(-0.654861 + 0.755750i) q^{72} +(-5.77930 + 8.99276i) q^{73} +(10.8803 + 1.56435i) q^{74} +(-4.46411 - 6.94629i) q^{75} +(-2.67963 - 5.86757i) q^{76} +(-6.00544 - 2.46044i) q^{77} +(0.0193774 + 0.134772i) q^{78} +(8.89524 + 4.06232i) q^{79} +(3.49354 - 1.02580i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(5.05898 + 2.31036i) q^{82} +(1.12332 + 7.81289i) q^{83} +(2.44824 + 1.00305i) q^{84} +(1.31916 + 2.88856i) q^{85} +(4.45687 + 6.93502i) q^{86} +(-6.52055 - 0.937514i) q^{87} +(1.32617 - 2.06356i) q^{88} +(8.08770 - 9.33371i) q^{89} +(3.49354 + 1.02580i) q^{90} +(0.321512 - 0.162491i) q^{91} +(-3.85778 + 2.84913i) q^{92} +10.0119 q^{93} +(-2.82577 + 9.62370i) q^{94} +(-15.3803 + 17.7498i) q^{95} +(-0.540641 + 0.841254i) q^{96} +(-0.840059 + 5.84274i) q^{97} +(0.445503 - 6.98581i) q^{98} +(2.23129 - 1.01900i) 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 $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.959493	+	0.281733i	0.678464	+	0.199215i
$2$	0.959493	+	0.281733i	0.678464	+	0.199215i
$3$	0.755750	+	0.654861i	0.436332	+	0.378084i
$3$	0.755750	+	0.654861i	0.436332	+	0.378084i
$4$	0.841254	+	0.540641i	0.420627	+	0.270320i
$5$	0.518172	−	3.60397i	0.231734	−	1.61174i	−0.458866	−	0.888505i	$-0.651744\pi$
$5$	0.518172	−	3.60397i	0.231734	−	1.61174i	0.690600	−	0.723237i	$-0.257347\pi$
$6$	0.540641	+	0.841254i	0.220716	+	0.343440i
$7$	1.65217	−	2.06648i	0.624461	−	0.781056i
$7$	1.65217	−	2.06648i	0.624461	−	0.781056i
$8$	0.654861	+	0.755750i	0.231528	+	0.267198i
$9$	0.142315	+	0.989821i	0.0474383	+	0.329940i
$10$	1.51254	−	3.31199i	0.478306	−	1.04734i
$11$	−0.691079	−	2.35360i	−0.208368	−	0.709636i	−0.995661	−	0.0930570i	$-0.970336\pi$
$11$	−0.691079	−	2.35360i	−0.208368	−	0.709636i	0.787293	−	0.616579i	$-0.211482\pi$
$12$	0.281733	+	0.959493i	0.0813292	+	0.276982i
$13$	0.123854	+	0.0565622i	0.0343509	+	0.0156875i	0.432516	−	0.901626i	$-0.357626\pi$
$13$	0.123854	+	0.0565622i	0.0343509	+	0.0156875i	−0.398165	+	0.917314i	$0.630353\pi$
$14$	2.16744	−	1.51730i	0.579273	−	0.405516i
$15$	2.75170	−	2.38437i	0.710487	−	0.615640i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	−0.733700	+	0.471520i	−0.177948	+	0.114360i	−0.626583	−	0.779355i	$-0.715547\pi$
$17$	−0.733700	+	0.471520i	−0.177948	+	0.114360i	0.448634	+	0.893715i	$0.351911\pi$
$18$	−0.142315	+	0.989821i	−0.0335439	+	0.233303i
$19$	−5.42650	−	3.48740i	−1.24492	−	0.800064i	−0.258777	−	0.965937i	$-0.583320\pi$
$19$	−5.42650	−	3.48740i	−1.24492	−	0.800064i	−0.986147	+	0.165873i	$0.946956\pi$
$20$	2.38437	−	2.75170i	0.533160	−	0.615300i
$21$	2.60188	−	0.479800i	0.567777	−	0.104701i
$22$		−	2.45296i		−	0.522973i
$23$	−1.70502	+	4.48251i	−0.355520	+	0.934669i
$23$	−1.70502	+	4.48251i	−0.355520	+	0.934669i
$24$			1.00000i			0.204124i
$25$	−7.92260	−	2.32629i	−1.58452	−	0.465257i
$26$	0.102902	+	0.0891647i	0.0201807	+	0.0174866i
$27$	−0.540641	+	0.841254i	−0.104046	+	0.161899i
$28$	2.50712	−	0.845203i	0.473800	−	0.159728i
$29$	−5.54185	+	3.56153i	−1.02910	+	0.661359i	−0.942266	−	0.334864i	$-0.891310\pi$
$29$	−5.54185	+	3.56153i	−1.02910	+	0.661359i	−0.0868287	+	0.996223i	$0.527673\pi$
$30$	3.31199	−	1.51254i	0.604685	−	0.276150i
$31$	7.56647	−	6.55639i	1.35898	−	1.17756i	0.392820	−	0.919616i	$-0.371500\pi$
$31$	7.56647	−	6.55639i	1.35898	−	1.17756i	0.966159	−	0.257946i	$-0.0830458\pi$
$32$	0.142315	+	0.989821i	0.0251579	+	0.174977i
$33$	1.01900	−	2.23129i	0.177384	−	0.388418i
$34$	−0.836822	+	0.245713i	−0.143514	+	0.0421395i
$35$	−6.59141	−	7.02515i	−1.11415	−	1.18747i
$36$	−0.415415	+	0.909632i	−0.0692358	+	0.151605i
$37$	10.8803	−	1.56435i	1.78871	−	0.257177i	0.833373	−	0.552711i	$-0.186407\pi$
$37$	10.8803	−	1.56435i	1.78871	−	0.257177i	0.955332	+	0.295534i	$0.0954974\pi$
$38$	−4.22417	−	4.87496i	−0.685252	−	0.790822i
$39$	0.0565622	+	0.123854i	0.00905720	+	0.0198325i
$40$	3.06303	−	1.96849i	0.484307	−	0.311245i
$41$	5.50496	+	0.791494i	0.859731	+	0.123611i	0.558059	−	0.829801i	$-0.311546\pi$
$41$	5.50496	+	0.791494i	0.859731	+	0.123611i	0.301672	+	0.953412i	$0.402455\pi$
$42$	2.63166	+	0.272670i	0.406074	+	0.0420740i
$43$	6.23016	+	5.39846i	0.950090	+	0.823258i	0.984362	−	0.176155i	$-0.0563659\pi$
$43$	6.23016	+	5.39846i	0.950090	+	0.823258i	−0.0342724	+	0.999413i	$0.510911\pi$
$44$	0.691079	−	2.35360i	0.104184	−	0.354818i
$45$	3.64103			0.542772
$46$	−2.89882	+	3.82058i	−0.427408	+	0.563314i
$47$			10.0300i			1.46302i	0.681829	+	0.731512i	$0.261185\pi$
$47$			10.0300i			1.46302i	−0.681829	+	0.731512i	$0.738815\pi$
$48$	−0.281733	+	0.959493i	−0.0406646	+	0.138491i
$49$	−1.54067	−	6.82835i	−0.220096	−	0.975478i
$50$	−6.94629	−	4.46411i	−0.982354	−	0.631321i
$51$	−0.863273	−	0.124120i	−0.120882	−	0.0173803i
$52$	0.0736128	+	0.114544i	0.0102083	+	0.0158844i
$53$	−5.77411	+	2.63695i	−0.793136	+	0.362213i	−0.770426	−	0.637529i	$-0.779957\pi$
$53$	−5.77411	+	2.63695i	−0.793136	+	0.362213i	−0.0227095	+	0.999742i	$0.507229\pi$
$54$	−0.755750	+	0.654861i	−0.102844	+	0.0891153i
$55$	−8.84038	+	1.27106i	−1.19204	+	0.171389i
$56$	2.64368	−	0.104630i	0.353277	−	0.0139817i
$57$	−1.81731	−	6.18920i	−0.240709	−	0.819780i
$58$	−6.32076	+	1.85594i	−0.829957	+	0.243697i
$59$	−1.09238	−	0.498873i	−0.142216	−	0.0649478i	0.343036	−	0.939322i	$-0.388545\pi$
$59$	−1.09238	−	0.498873i	−0.142216	−	0.0649478i	−0.485252	+	0.874375i	$0.661272\pi$
$60$	3.60397	−	0.518172i	0.465270	−	0.0668957i
$61$	4.42779	+	5.10994i	0.566920	+	0.654261i	0.964741	−	0.263203i	$-0.0847788\pi$
$61$	4.42779	+	5.10994i	0.566920	+	0.654261i	−0.397821	+	0.917463i	$0.630233\pi$
$62$	9.10713	−	4.15909i	1.15661	−	0.528204i
$63$	2.28057	+	1.34126i	0.287325	+	0.168983i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	0.268026	−	0.417057i	0.0332445	−	0.0517295i
$66$	1.60635	−	1.85382i	0.197728	−	0.228190i
$67$	−1.47500	+	5.02337i	−0.180199	+	0.613703i	0.819004	+	0.573788i	$0.194527\pi$
$67$	−1.47500	+	5.02337i	−0.180199	+	0.613703i	−0.999203	+	0.0399145i	$0.987291\pi$
$68$	−0.872151			−0.105764
$69$	−4.22399	+	2.27111i	−0.508508	+	0.273409i
$70$	−4.34520	−	8.59760i	−0.519351	−	1.02761i
$71$	13.4693	+	3.95493i	1.59851	+	0.469364i	0.955130	−	0.296185i	$-0.0957146\pi$
$71$	13.4693	+	3.95493i	1.59851	+	0.469364i	0.643377	+	0.765550i	$0.277533\pi$
$72$	−0.654861	+	0.755750i	−0.0771761	+	0.0890659i
$73$	−5.77930	+	8.99276i	−0.676416	+	1.05252i	0.318112	+	0.948053i	$0.396951\pi$
$73$	−5.77930	+	8.99276i	−0.676416	+	1.05252i	−0.994528	+	0.104470i	$0.966685\pi$
$74$	10.8803	+	1.56435i	1.26481	+	0.181852i
$75$	−4.46411	−	6.94629i	−0.515471	−	0.802089i
$76$	−2.67963	−	5.86757i	−0.307375	−	0.673057i
$77$	−6.00544	−	2.46044i	−0.684383	−	0.280393i
$78$	0.0193774	+	0.134772i	0.00219405	+	0.0152600i
$79$	8.89524	+	4.06232i	1.00079	+	0.457047i	0.847306	−	0.531104i	$-0.178223\pi$
$79$	8.89524	+	4.06232i	1.00079	+	0.457047i	0.153486	+	0.988151i	$0.450950\pi$
$80$	3.49354	−	1.02580i	0.390590	−	0.114687i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	5.05898	+	2.31036i	0.558671	+	0.255137i
$83$	1.12332	+	7.81289i	0.123301	+	0.857576i	0.953776	+	0.300520i	$0.0971601\pi$
$83$	1.12332	+	7.81289i	0.123301	+	0.857576i	−0.830475	+	0.557056i	$0.811931\pi$
$84$	2.44824	+	1.00305i	0.267125	+	0.109442i
$85$	1.31916	+	2.88856i	0.143083	+	0.313308i
$86$	4.45687	+	6.93502i	0.480597	+	0.747823i
$87$	−6.52055	−	0.937514i	−0.699077	−	0.100512i
$88$	1.32617	−	2.06356i	0.141370	−	0.219976i
$89$	8.08770	−	9.33371i	0.857295	−	0.989371i	−0.142705	−	0.989765i	$-0.545580\pi$
$89$	8.08770	−	9.33371i	0.857295	−	0.989371i	1.00000		0.000394294i	$0.000125508\pi$
$90$	3.49354	+	1.02580i	0.368251	+	0.108128i
$91$	0.321512	−	0.162491i	0.0337037	−	0.0170337i
$92$	−3.85778	+	2.84913i	−0.402201	+	0.297042i
$93$	10.0119			1.03818
$94$	−2.82577	+	9.62370i	−0.291456	+	0.992609i
$95$	−15.3803	+	17.7498i	−1.57799	+	1.82110i
$96$	−0.540641	+	0.841254i	−0.0551789	+	0.0858601i
$97$	−0.840059	+	5.84274i	−0.0852951	+	0.593240i	0.901685	+	0.432395i	$0.142331\pi$
$97$	−0.840059	+	5.84274i	−0.0852951	+	0.593240i	−0.986980	+	0.160846i	$0.948578\pi$
$98$	0.445503	−	6.98581i	0.0450026	−	0.705673i
$99$	2.23129	−	1.01900i	0.224253	−	0.102413i
$100$	−5.40723	−	6.24028i	−0.540723	−	0.624028i
$101$	−9.63468	+	1.38526i	−0.958686	+	0.137838i	−0.603857	−	0.797093i	$-0.706370\pi$
$101$	−9.63468	+	1.38526i	−0.958686	+	0.137838i	−0.354829	+	0.934931i	$0.615461\pi$
$102$	−0.793336	−	0.362305i	−0.0785520	−	0.0358735i
$103$	9.35945	−	2.74818i	0.922214	−	0.270786i	0.214040	−	0.976825i	$-0.431338\pi$
$103$	9.35945	−	2.74818i	0.922214	−	0.270786i	0.708173	+	0.706038i	$0.249519\pi$
$104$	0.0383602	+	0.130643i	0.00376153	+	0.0128106i
$105$	−0.380960	−	9.62571i	−0.0371778	−	0.939374i
$106$	−6.28314	+	0.903379i	−0.610272	+	0.0877439i
$107$	−1.20868	+	1.04733i	−0.116848	+	0.101249i	−0.711325	−	0.702863i	$-0.751905\pi$
$107$	−1.20868	+	1.04733i	−0.116848	+	0.101249i	0.594477	+	0.804112i	$0.297359\pi$
$108$	−0.909632	+	0.415415i	−0.0875294	+	0.0399733i
$109$	−6.58021	−	10.2390i	−0.630270	−	0.980720i	−0.998695	−	0.0510622i	$-0.983739\pi$
$109$	−6.58021	−	10.2390i	−0.630270	−	0.980720i	0.368425	−	0.929657i	$-0.379897\pi$
$110$	−8.84038	−	1.27106i	−0.842897	−	0.121190i
$111$	9.24719	+	5.94281i	0.877704	+	0.564066i
$112$	2.56607	+	0.644420i	0.242471	+	0.0608919i
$113$	4.29984	−	14.6439i	0.404495	−	1.37758i	−0.465730	−	0.884927i	$-0.654208\pi$
$113$	4.29984	−	14.6439i	0.404495	−	1.37758i	0.870225	−	0.492655i	$-0.163974\pi$
$114$		−	6.45049i		−	0.604144i
$115$	15.2713	+	8.46753i	1.42406	+	0.789601i
$116$	−6.58761			−0.611644
$117$	−0.0383602	+	0.130643i	−0.00354641	+	0.0120779i
$118$	−0.907583	−	0.786425i	−0.0835497	−	0.0723963i
$119$	−0.237810	+	2.29521i	−0.0218000	+	0.210401i
$120$	3.60397	+	0.518172i	0.328996	+	0.0473024i
$121$	4.19196	−	2.69401i	0.381087	−	0.244910i
$122$	2.80879	+	6.15040i	0.254296	+	0.556831i
$123$	3.64206	+	4.20316i	0.328393	+	0.378986i
$124$	9.90997	−	1.42484i	0.889942	−	0.127954i
$125$	−4.92644	+	10.7874i	−0.440634	+	0.964855i
$126$	1.81032	+	1.92944i	0.161276	+	0.171888i
$127$	−14.9513	+	4.39010i	−1.32671	+	0.389558i	−0.866911	−	0.498463i	$-0.833898\pi$
$127$	−14.9513	+	4.39010i	−1.32671	+	0.389558i	−0.459803	+	0.888021i	$0.652080\pi$
$128$	−0.415415	+	0.909632i	−0.0367178	+	0.0804009i
$129$	1.17320	+	8.15977i	0.103294	+	0.718428i
$130$	0.374667	−	0.324651i	0.0328605	−	0.0284738i
$131$	−19.0131	+	8.68299i	−1.66118	+	0.758637i	−0.661218	+	0.750193i	$0.729960\pi$
$131$	−19.0131	+	8.68299i	−1.66118	+	0.758637i	−0.999964	+	0.00844326i	$0.997312\pi$
$132$	2.06356	−	1.32617i	0.179610	−	0.115428i
$133$	−16.1721	+	5.45197i	−1.40230	+	0.472746i
$134$	−2.83050	+	4.40434i	−0.244518	+	0.380477i
$135$	2.75170	+	2.38437i	0.236829	+	0.205213i
$136$	−0.836822	−	0.245713i	−0.0717569	−	0.0210697i
$137$		−	8.84070i		−	0.755312i	−0.925946	−	0.377656i	$-0.876730\pi$
$137$		−	8.84070i		−	0.755312i	0.925946	−	0.377656i	$-0.123270\pi$
$138$	−4.69273	+	0.989079i	−0.399472	+	0.0841960i
$139$			7.98091i			0.676932i	0.940979	+	0.338466i	$0.109908\pi$
$139$			7.98091i			0.676932i	−0.940979	+	0.338466i	$0.890092\pi$
$140$	−1.74696	−	9.47352i	−0.147645	−	0.800659i
$141$	−6.56824	+	7.58016i	−0.553146	+	0.638364i
$142$	11.8094	+	7.58946i	0.991025	+	0.636893i
$143$	0.0475319	−	0.330591i	0.00397481	−	0.0276454i
$144$	−0.841254	+	0.540641i	−0.0701045	+	0.0450534i
$145$	9.96400	+	21.8181i	0.827465	+	1.81190i
$146$	−8.07875	+	7.00028i	−0.668602	+	0.579347i
$147$	3.30725	−	6.16945i	0.272778	−	0.508847i
$148$	9.99882	+	4.56631i	0.821898	+	0.375348i
$149$	−1.34689	−	4.58709i	−0.110342	−	0.375789i	0.885745	−	0.464172i	$-0.153648\pi$
$149$	−1.34689	−	4.58709i	−0.110342	−	0.375789i	−0.996087	+	0.0883832i	$0.971830\pi$
$150$	−2.32629	−	7.92260i	−0.189940	−	0.646878i
$151$	7.49861	−	16.4197i	0.610228	−	1.33621i	−0.312190	−	0.950020i	$-0.601063\pi$
$151$	7.49861	−	16.4197i	0.610228	−	1.33621i	0.922418	−	0.386193i	$-0.126210\pi$
$152$	−0.918001	−	6.38484i	−0.0744597	−	0.517879i
$153$	−0.571137	−	0.659128i	−0.0461737	−	0.0532873i
$154$	−5.06899	−	4.05271i	−0.408471	−	0.326576i
$155$	−19.7083	−	30.6667i	−1.58301	−	2.46320i
$156$	−0.0193774	+	0.134772i	−0.00155143	+	0.0107904i
$157$	−4.98027	−	3.20063i	−0.397469	−	0.255438i	0.326604	−	0.945161i	$-0.394096\pi$
$157$	−4.98027	−	3.20063i	−0.397469	−	0.255438i	−0.724073	+	0.689724i	$0.757732\pi$
$158$	7.39043	+	6.40384i	0.587951	+	0.509462i
$159$	−6.09062	−	1.78837i	−0.483018	−	0.141827i
$160$	3.64103			0.287848
$161$	6.44604	+	10.9293i	0.508019	+	0.861346i
$162$	−1.00000			−0.0785674
$163$	2.36732	+	0.695109i	0.185423	+	0.0544451i	0.373126	−	0.927781i	$-0.378286\pi$
$163$	2.36732	+	0.695109i	0.185423	+	0.0544451i	−0.187703	+	0.982226i	$0.560104\pi$
$164$	4.20316	+	3.64206i	0.328211	+	0.284397i
$165$	−7.51348	−	4.82862i	−0.584924	−	0.375908i
$166$	−1.12332	+	7.81289i	−0.0871868	+	0.606398i
$167$	−1.56660	−	2.43768i	−0.121227	−	0.188633i	0.775336	−	0.631549i	$-0.217581\pi$
$167$	−1.56660	−	2.43768i	−0.121227	−	0.188633i	−0.896563	+	0.442916i	$0.853944\pi$
$168$	2.06648	+	1.65217i	0.159432	+	0.127468i
$169$	−8.50105	−	9.81073i	−0.653927	−	0.754672i
$170$	0.451924	+	3.14320i	0.0346610	+	0.241073i
$171$	2.67963	−	5.86757i	0.204917	−	0.448705i
$172$	2.32251	+	7.90975i	0.177090	+	0.603113i
$173$	−5.76768	−	19.6429i	−0.438508	−	1.49342i	−0.821790	−	0.569791i	$-0.807024\pi$
$173$	−5.76768	−	19.6429i	−0.438508	−	1.49342i	0.383282	−	0.923632i	$-0.374794\pi$
$174$	−5.99230	−	2.73659i	−0.454275	−	0.207460i
$175$	−17.8967	+	12.5285i	−1.35286	+	0.947064i
$176$	1.85382	−	1.60635i	0.139737	−	0.121083i
$177$	−0.498873	−	1.09238i	−0.0374976	−	0.0821084i
$178$	10.3897	−	6.67706i	0.778741	−	0.500467i
$179$	2.01333	−	14.0030i	0.150483	−	1.04663i	−0.764928	−	0.644116i	$-0.777226\pi$
$179$	2.01333	−	14.0030i	0.150483	−	1.04663i	0.915412	−	0.402519i	$-0.131865\pi$
$180$	3.06303	+	1.96849i	0.228304	+	0.146722i
$181$	−9.68287	+	11.1746i	−0.719722	+	0.830603i	−0.991274	−	0.131820i	$-0.957918\pi$
$181$	−9.68287	+	11.1746i	−0.719722	+	0.830603i	0.271552	+	0.962424i	$0.412463\pi$
$182$	0.354268	−	0.0653288i	0.0262601	−	0.00484249i
$183$			6.76142i			0.499818i
$184$	−4.50421	+	1.64686i	−0.332054	+	0.121408i
$185$		−	40.0227i		−	2.94253i
$186$	9.60633	+	2.82067i	0.704370	+	0.206822i
$187$	1.61681	+	1.40098i	0.118233	+	0.102450i
$188$	−5.42262	+	8.43776i	−0.395485	+	0.615387i
$189$	0.845203	+	2.50712i	0.0614794	+	0.182366i
$190$	−19.7580	+	12.6977i	−1.43340	+	0.921189i
$191$	−19.2852	+	8.80724i	−1.39543	+	0.637270i	−0.964249	−	0.264998i	$-0.914629\pi$
$191$	−19.2852	+	8.80724i	−1.39543	+	0.637270i	−0.431177	+	0.902267i	$0.641902\pi$
$192$	−0.755750	+	0.654861i	−0.0545415	+	0.0472605i
$193$	−0.593687	−	4.12918i	−0.0427345	−	0.297225i	−0.999969	−	0.00791083i	$-0.997482\pi$
$193$	−0.593687	−	4.12918i	−0.0427345	−	0.297225i	0.957234	−	0.289314i	$-0.0934272\pi$
$194$	−2.45212	+	5.36939i	−0.176052	+	0.385500i
$195$	0.475674	−	0.139671i	0.0340638	−	0.0100020i
$196$	2.39559	−	6.57732i	0.171113	−	0.469809i
$197$	−3.49731	+	7.65803i	−0.249173	+	0.545612i	−0.992346	−	0.123486i	$-0.960592\pi$
$197$	−3.49731	+	7.65803i	−0.249173	+	0.545612i	0.743173	+	0.669099i	$0.233320\pi$
$198$	2.42799	−	0.349093i	0.172550	−	0.0248089i
$199$	6.55806	+	7.56840i	0.464888	+	0.536510i	0.938983	−	0.343964i	$-0.111770\pi$
$199$	6.55806	+	7.56840i	0.464888	+	0.536510i	−0.474094	+	0.880474i	$0.657224\pi$
$200$	−3.43011	−	7.51090i	−0.242546	−	0.531101i
$201$	−4.40434	+	2.83050i	−0.310658	+	0.199648i
$202$	−9.63468	−	1.38526i	−0.677893	−	0.0974664i
$203$	−1.79625	+	17.3364i	−0.126072	+	1.21677i
$204$	−0.659128	−	0.571137i	−0.0461482	−	0.0399876i
$205$	5.70504	−	19.4296i	0.398457	−	1.35702i
$206$	9.75458			0.679633
$207$	−4.67954	−	1.04973i	−0.325250	−	0.0729615i
$208$			0.136158i			0.00944088i
$209$	−4.45780	+	15.1819i	−0.308352	+	1.05015i
$210$	2.34635	−	9.34313i	0.161913	−	0.644737i
$211$	15.2587	+	9.80617i	1.05045	+	0.675084i	0.947550	−	0.319607i	$-0.103551\pi$
$211$	15.2587	+	9.80617i	1.05045	+	0.675084i	0.102902	+	0.994692i	$0.467187\pi$
$212$	−6.28314	−	0.903379i	−0.431528	−	0.0620443i
$213$	7.58946	+	11.8094i	0.520021	+	0.809169i
$214$	−1.45479	+	0.664379i	−0.0994472	+	0.0454160i
$215$	22.6842	−	19.6559i	1.54705	−	1.34052i
$216$	−0.989821	+	0.142315i	−0.0673488	+	0.00968330i
$217$	−1.04754	−	26.4682i	−0.0711117	−	1.79678i
$218$	−3.42901	−	11.6781i	−0.232242	−	0.790942i
$219$	−10.2567	+	3.01164i	−0.693084	+	0.203508i
$220$	−8.12419	−	3.71019i	−0.547733	−	0.250141i
$221$	−0.117542	+	0.0169000i	−0.00790672	+	0.00113682i
$222$	7.19833	+	8.30732i	0.483120	+	0.557551i
$223$	−1.13656	+	0.519050i	−0.0761098	+	0.0347582i	−0.453106	−	0.891457i	$-0.649684\pi$
$223$	−1.13656	+	0.519050i	−0.0761098	+	0.0347582i	0.376996	+	0.926215i	$0.376957\pi$
$224$	2.28057	+	1.34126i	0.152377	+	0.0896168i
$225$	1.17510	−	8.17303i	0.0783403	−	0.544868i
$226$	8.25133	−	12.8393i	0.548870	−	0.854059i
$227$	−9.31681	+	10.7522i	−0.618378	+	0.713647i	−0.975398	−	0.220450i	$-0.929247\pi$
$227$	−9.31681	+	10.7522i	−0.618378	+	0.713647i	0.357020	+	0.934097i	$0.383793\pi$
$228$	1.81731	−	6.18920i	0.120355	−	0.409890i
$229$	−18.3189			−1.21055			−0.605274	−	0.796017i	$-0.706936\pi$
$229$	−18.3189			−1.21055			−0.605274	+	0.796017i	$0.706936\pi$
$230$	12.2672	+	12.4270i	0.808872	+	0.819410i
$231$	−2.92736	−	5.79220i	−0.192606	−	0.381099i
$232$	−6.32076	−	1.85594i	−0.414978	−	0.121849i
$233$	−3.08176	+	3.55654i	−0.201892	+	0.232996i	−0.847663	−	0.530535i	$-0.821991\pi$
$233$	−3.08176	+	3.55654i	−0.201892	+	0.232996i	0.645770	+	0.763532i	$0.276536\pi$
$234$	−0.0736128	+	0.114544i	−0.00481222	+	0.00748795i
$235$	36.1477	+	5.19726i	2.35802	+	0.339032i
$236$	−0.649258	−	1.01026i	−0.0422631	−	0.0657626i
$237$	4.06232	+	8.89524i	0.263876	+	0.577808i
$238$	−0.874811	+	2.13524i	−0.0567056	+	0.138407i
$239$	1.55341	+	10.8042i	0.100482	+	0.698867i	0.976331	+	0.216282i	$0.0693931\pi$
$239$	1.55341	+	10.8042i	0.100482	+	0.698867i	−0.875849	+	0.482585i	$0.839698\pi$
$240$	3.31199	+	1.51254i	0.213788	+	0.0976338i
$241$	4.60816	−	1.35308i	0.296838	−	0.0871594i	−0.129923	−	0.991524i	$-0.541473\pi$
$241$	4.60816	−	1.35308i	0.296838	−	0.0871594i	0.426760	+	0.904365i	$0.359655\pi$
$242$	4.78114	−	1.40387i	0.307343	−	0.0902442i
$243$	−0.909632	−	0.415415i	−0.0583529	−	0.0266489i
$244$	0.962250	+	6.69260i	0.0616018	+	0.428450i
$245$	−25.4075	+	2.01427i	−1.62322	+	0.128687i
$246$	2.31036	+	5.05898i	0.147303	+	0.322549i
$247$	−0.474839	−	0.738863i	−0.0302133	−	0.0470127i
$248$	9.90997	+	1.42484i	0.629284	+	0.0904774i
$249$	−4.26740	+	6.64021i	−0.270436	+	0.420806i
$250$	−7.76605	+	8.96250i	−0.491168	+	0.566838i
$251$	15.1244	+	4.44093i	0.954644	+	0.280309i	0.721719	−	0.692186i	$-0.243352\pi$
$251$	15.1244	+	4.44093i	0.954644	+	0.280309i	0.232925	+	0.972495i	$0.425170\pi$
$252$	1.19340	+	2.36131i	0.0751771	+	0.148749i
$253$	11.7283	+	0.915152i	0.737354	+	0.0575351i
$254$	−15.5825			−0.977734
$255$	−0.894648	+	3.04689i	−0.0560251	+	0.190804i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	−7.55563	+	11.7568i	−0.471307	+	0.733368i	−0.992786	−	0.119896i	$-0.961744\pi$
$257$	−7.55563	+	11.7568i	−0.471307	+	0.733368i	0.521479	+	0.853264i	$0.325380\pi$
$258$	−1.17320	+	8.15977i	−0.0730401	+	0.508005i
$259$	14.7434	−	25.0684i	0.916108	−	1.55768i
$260$	0.450956	−	0.205945i	0.0279671	−	0.0127721i
$261$	−4.31396	−	4.97858i	−0.267028	−	0.308166i
$262$	−20.6892	+	2.97466i	−1.27818	+	0.183775i
$263$	−4.35773	−	1.99011i	−0.268709	−	0.122715i	0.276504	−	0.961013i	$-0.410824\pi$
$263$	−4.35773	−	1.99011i	−0.268709	−	0.122715i	−0.545213	+	0.838297i	$0.683551\pi$
$264$	2.35360	−	0.691079i	0.144854	−	0.0425329i
$265$	6.51149	+	22.1761i	0.399998	+	1.36227i
$266$	−17.0530	+	0.674913i	−1.04559	+	0.0413816i
$267$	12.2246	−	1.75763i	0.748131	−	0.107565i
$268$	−3.95669	+	3.42849i	−0.241693	+	0.209428i
$269$	−17.4908	+	7.98778i	−1.06643	+	0.487023i	−0.869775	−	0.493449i	$-0.835736\pi$
$269$	−17.4908	+	7.98778i	−1.06643	+	0.487023i	−0.196658	+	0.980472i	$0.563009\pi$
$270$	1.96849	+	3.06303i	0.119798	+	0.186410i
$271$	25.1011	+	3.60899i	1.52478	+	0.219231i	0.853154	−	0.521659i	$-0.174687\pi$
$271$	25.1011	+	3.60899i	1.52478	+	0.219231i	0.671627	+	0.740889i	$0.265596\pi$
$272$	−0.733700	−	0.471520i	−0.0444871	−	0.0285901i
$273$	0.349392	+	0.0877431i	0.0211462	+	0.00531045i
$274$	2.49071	−	8.48259i	0.150470	−	0.512452i
$275$			20.2543i			1.22138i
$276$	−4.78130	−	0.373081i	−0.287800	−	0.0224568i
$277$	−2.13649			−0.128369			−0.0641846	−	0.997938i	$-0.520445\pi$
$277$	−2.13649			−0.128369			−0.0641846	+	0.997938i	$0.520445\pi$
$278$	−2.24848	+	7.65763i	−0.134855	+	0.459274i
$279$	7.56647	+	6.55639i	0.452993	+	0.392521i
$280$	0.992800	−	9.58195i	0.0593311	−	0.572631i
$281$	1.75376	+	0.252153i	0.104621	+	0.0150422i	0.194426	−	0.980917i	$-0.437716\pi$
$281$	1.75376	+	0.252153i	0.104621	+	0.0150422i	−0.0898057	+	0.995959i	$0.528625\pi$
$282$	−8.43776	+	5.42262i	−0.502461	+	0.322912i
$283$	−3.87162	−	8.47766i	−0.230144	−	0.503945i	0.758965	−	0.651132i	$-0.225705\pi$
$283$	−3.87162	−	8.47766i	−0.230144	−	0.503945i	−0.989109	+	0.147187i	$0.952978\pi$
$284$	9.19287	+	10.6091i	0.545496	+	0.629536i
$285$	−23.2474	+	3.34246i	−1.37705	+	0.197991i
$286$	0.138745	−	0.303809i	0.00820415	−	0.0179646i
$287$	10.7307	−	10.0682i	0.633416	−	0.594308i
$288$	−0.959493	+	0.281733i	−0.0565387	+	0.0166013i
$289$	−6.74607	+	14.7718i	−0.396828	+	0.868931i
$290$	3.41351	+	23.7415i	0.200448	+	1.39415i
$291$	−4.46105	+	3.86553i	−0.261512	+	0.226601i
$292$	−9.72371	+	4.44067i	−0.569037	+	0.259871i
$293$	−15.3467	+	9.86274i	−0.896565	+	0.576188i	−0.905770	−	0.423770i	$-0.860706\pi$
$293$	−15.3467	+	9.86274i	−0.896565	+	0.576188i	0.00920436	+	0.999958i	$0.497070\pi$
$294$	4.91142	−	4.98778i	0.286440	−	0.290893i
$295$	−2.36396	+	3.67840i	−0.137635	+	0.214165i
$296$	8.30732	+	7.19833i	0.482853	+	0.418395i
$297$	2.35360	+	0.691079i	0.136570	+	0.0401004i
$298$		−	4.78074i		−	0.276941i
$299$	−0.464714	+	0.458738i	−0.0268751	+	0.0265295i
$300$		−	8.25707i		−	0.476722i
$301$	21.4491	−	3.95532i	1.23630	−	0.227981i
$302$	11.8208	−	13.6419i	0.680211	−	0.785006i
$303$	−8.18855	−	5.26246i	−0.470420	−	0.302321i
$304$	0.918001	−	6.38484i	0.0526510	−	0.366195i
$305$	20.7104	−	13.3098i	1.18587	−	0.762115i
$306$	−0.362305	−	0.793336i	−0.0207116	−	0.0453520i
$307$	−9.60342	+	8.32141i	−0.548096	+	0.474928i	−0.884338	−	0.466848i	$-0.845390\pi$
$307$	−9.60342	+	8.32141i	−0.548096	+	0.474928i	0.336242	+	0.941776i	$0.390844\pi$
$308$	−3.72188	−	5.31664i	−0.212074	−	0.302944i
$309$	8.87307	+	4.05220i	0.504772	+	0.230521i
$310$	−10.2701	−	34.9769i	−0.583305	−	1.98655i
$311$	−6.55132	−	22.3118i	−0.371491	−	1.26518i	−0.907171	−	0.420762i	$-0.861763\pi$
$311$	−6.55132	−	22.3118i	−0.371491	−	1.26518i	0.535680	−	0.844421i	$-0.320056\pi$
$312$	−0.0565622	+	0.123854i	−0.00320220	+	0.00701185i
$313$	0.659516	+	4.58704i	0.0372781	+	0.259275i	0.999934	−	0.0114516i	$-0.00364525\pi$
$313$	0.659516	+	4.58704i	0.0372781	+	0.259275i	−0.962656	+	0.270726i	$0.912736\pi$
$314$	−3.87681	−	4.47408i	−0.218781	−	0.252487i
$315$	6.01559	−	7.52410i	0.338940	−	0.423935i
$316$	5.28689	+	8.22657i	0.297411	+	0.462781i
$317$	−2.13423	+	14.8439i	−0.119870	+	0.833715i	0.837827	+	0.545936i	$0.183826\pi$
$317$	−2.13423	+	14.8439i	−0.119870	+	0.833715i	−0.957697	+	0.287779i	$0.907083\pi$
$318$	−5.34007	−	3.43185i	−0.299456	−	0.192449i
$319$	12.2123	+	10.5820i	0.683755	+	0.592477i
$320$	3.49354	+	1.02580i	0.195295	+	0.0573437i
$321$	−1.59931			−0.0892650
$322$	3.10581	+	12.3026i	0.173080	+	0.685597i
$323$	5.62580			0.313028
$324$	−0.959493	−	0.281733i	−0.0533052	−	0.0156518i
$325$	−0.849666	−	0.736240i	−0.0471310	−	0.0408392i
$326$	2.07559	+	1.33390i	0.114957	+	0.0738781i
$327$	1.73213	−	12.0473i	0.0957872	−	0.666215i
$328$	3.00681	+	4.67869i	0.166023	+	0.258338i
$329$	20.7268	+	16.5712i	1.14270	+	0.913602i
$330$	−5.84875	−	6.74982i	−0.321963	−	0.371565i
$331$	−2.34185	−	16.2879i	−0.128720	−	0.895265i	−0.947180	−	0.320702i	$-0.896081\pi$
$331$	−2.34185	−	16.2879i	−0.128720	−	0.895265i	0.818460	−	0.574563i	$-0.194828\pi$
$332$	−3.27897	+	7.17993i	−0.179957	+	0.394050i
$333$	3.09685	+	10.5469i	0.169706	+	0.577966i
$334$	−0.816370	−	2.78030i	−0.0446698	−	0.152131i
$335$	17.3398	+	7.91881i	0.947373	+	0.432651i
$336$	1.51730	+	2.16744i	0.0827756	+	0.118244i
$337$	18.1207	−	15.7017i	0.987098	−	0.855325i	−0.00238153	−	0.999997i	$-0.500758\pi$
$337$	18.1207	−	15.7017i	0.987098	−	0.855325i	0.989480	+	0.144672i	$0.0462126\pi$
$338$	−5.39269	−	11.8084i	−0.293324	−	0.642290i
$339$	12.8393	−	8.25133i	0.697336	−	0.448151i
$340$	−0.451924	+	3.14320i	−0.0245090	+	0.170464i
$341$	−20.6601	−	13.2775i	−1.11881	−	0.719015i
$342$	4.22417	−	4.87496i	0.228417	−	0.263607i
$343$	−16.6561	−	8.09782i	−0.899344	−	0.437241i
$344$			8.24368i			0.444469i
$345$	5.99625	+	16.3999i	0.322827	+	0.882942i
$346$		−	20.4722i		−	1.10059i
$347$	26.0314	+	7.64350i	1.39744	+	0.410324i	0.891803	−	0.452424i	$-0.149441\pi$
$347$	26.0314	+	7.64350i	1.39744	+	0.410324i	0.505633	+	0.862748i	$0.331259\pi$
$348$	−4.97858	−	4.31396i	−0.266880	−	0.231253i
$349$	−4.50005	+	7.00222i	−0.240882	+	0.374820i	−0.940554	−	0.339644i	$-0.889693\pi$
$349$	−4.50005	+	7.00222i	−0.240882	+	0.374820i	0.699672	+	0.714465i	$0.253330\pi$
$350$	−20.7014	+	6.97890i	−1.10654	+	0.373038i
$351$	−0.114544	+	0.0736128i	−0.00611389	+	0.00392916i
$352$	2.23129	−	1.01900i	0.118928	−	0.0543127i
$353$	2.61684	−	2.26751i	0.139280	−	0.120687i	−0.582434	−	0.812878i	$-0.697900\pi$
$353$	2.61684	−	2.26751i	0.139280	−	0.120687i	0.721715	+	0.692191i	$0.243354\pi$
$354$	−0.170906	−	1.18868i	−0.00908357	−	0.0631776i
$355$	21.2328	−	46.4934i	1.12692	−	2.46761i
$356$	11.8500	−	3.47947i	0.628048	−	0.184412i
$357$	−1.68277	+	1.57887i	−0.0890614	+	0.0835626i
$358$	5.87688	−	12.8686i	0.310603	−	0.680126i
$359$	−19.2255	+	2.76420i	−1.01468	+	0.145889i	−0.629540	−	0.776968i	$-0.716756\pi$
$359$	−19.2255	+	2.76420i	−1.01468	+	0.145889i	−0.385142	+	0.922857i	$0.625847\pi$
$360$	2.38437	+	2.75170i	0.125667	+	0.145028i
$361$	9.39206	+	20.5657i	0.494319	+	1.08241i
$362$	−12.4389	+	7.99400i	−0.653774	+	0.420155i
$363$	4.93227	+	0.709153i	0.258877	+	0.0372209i
$364$	0.358323	+	0.0371263i	0.0187812	+	0.00194595i
$365$	29.4149	+	25.4882i	1.53965	+	1.33411i
$366$	−1.90491	+	6.48753i	−0.0995713	+	0.339109i
$367$	−12.1677			−0.635148			−0.317574	−	0.948233i	$-0.602868\pi$
$367$	−12.1677			−0.635148			−0.317574	+	0.948233i	$0.602868\pi$
$368$	−4.78573	+	0.311166i	−0.249473	+	0.0162207i
$369$			5.56157i			0.289524i
$370$	11.2757	−	38.4015i	0.586196	−	1.99640i
$371$	−4.09061	+	16.2888i	−0.212374	+	0.845671i
$372$	8.42253	+	5.41283i	0.436688	+	0.280642i
$373$	−19.5860	−	2.81604i	−1.01412	−	0.145809i	−0.384839	−	0.922984i	$-0.625743\pi$
$373$	−19.5860	−	2.81604i	−1.01412	−	0.145809i	−0.629285	+	0.777175i	$0.716652\pi$
$374$	1.15662	+	1.79974i	0.0598074	+	0.0930621i
$375$	−10.7874	+	4.92644i	−0.557059	+	0.254400i
$376$	−7.58016	+	6.56824i	−0.390917	+	0.338731i
$377$	−0.887828	+	0.127650i	−0.0457255	+	0.00657433i
$378$	0.104630	+	2.64368i	0.00538157	+	0.135976i
$379$	−1.86893	−	6.36499i	−0.0960005	−	0.326948i	0.897464	−	0.441087i	$-0.145407\pi$
$379$	−1.86893	−	6.36499i	−0.0960005	−	0.326948i	−0.993465	+	0.114140i	$0.963589\pi$
$380$	−22.5350	+	6.61689i	−1.15602	+	0.339439i
$381$	−14.1743	−	6.47321i	−0.726174	−	0.331633i
$382$	−20.9853	+	3.01723i	−1.07370	+	0.154375i
$383$	−5.93068	−	6.84437i	−0.303044	−	0.349731i	0.583719	−	0.811956i	$-0.301597\pi$
$383$	−5.93068	−	6.84437i	−0.303044	−	0.349731i	−0.886763	+	0.462225i	$0.847051\pi$
$384$	−0.909632	+	0.415415i	−0.0464195	+	0.0211991i
$385$	−11.9792	+	20.3685i	−0.610517	+	1.03807i
$386$	0.593687	−	4.12918i	0.0302179	−	0.210170i
$387$	−4.45687	+	6.93502i	−0.226555	+	0.352527i
$388$	−3.86553	+	4.46105i	−0.196242	+	0.226476i
$389$	3.08466	−	10.5054i	0.156399	−	0.532645i	−0.843592	−	0.536985i	$-0.819563\pi$
$389$	3.08466	−	10.5054i	0.156399	−	0.532645i	0.999991	+	0.00433977i	$0.00138140\pi$
$390$	0.495756			0.0251036
$391$	−0.862626	−	4.09277i	−0.0436249	−	0.206980i
$392$	4.15159	−	5.63598i	0.209687	−	0.284660i
$393$	−20.0553	−	5.88877i	−1.01166	−	0.297049i
$394$	−5.51316	+	6.36253i	−0.277749	+	0.320539i
$395$	19.2497	−	29.9532i	0.968559	−	1.50711i
$396$	2.42799	+	0.349093i	0.122011	+	0.0175426i
$397$	−0.348071	−	0.541609i	−0.0174692	−	0.0271826i	0.832409	−	0.554162i	$-0.186961\pi$
$397$	−0.348071	−	0.541609i	−0.0174692	−	0.0271826i	−0.849878	+	0.526979i	$0.823325\pi$
$398$	4.16014	+	9.10944i	0.208529	+	0.456615i
$399$	−15.7924	−	6.47017i	−0.790607	−	0.323914i
$400$	−1.17510	−	8.17303i	−0.0587552	−	0.408651i
$401$	−14.4186	−	6.58475i	−0.720030	−	0.328827i	0.0214793	−	0.999769i	$-0.493162\pi$
$401$	−14.4186	−	6.58475i	−0.720030	−	0.328827i	−0.741509	+	0.670943i	$0.765890\pi$
$402$	−5.02337	+	1.47500i	−0.250543	+	0.0735661i
$403$	1.30798	−	0.384058i	0.0651552	−	0.0191313i
$404$	−8.85413	−	4.04355i	−0.440510	−	0.201174i
$405$	0.518172	+	3.60397i	0.0257482	+	0.179083i
$406$	−6.60770	+	16.1281i	−0.327935	+	0.800422i
$407$	−11.2010	−	24.5267i	−0.555211	−	1.21574i
$408$	−0.471520	−	0.733700i	−0.0233437	−	0.0363236i
$409$	12.3894	+	1.78132i	0.612616	+	0.0880808i	0.441637	−	0.897194i	$-0.354398\pi$
$409$	12.3894	+	1.78132i	0.612616	+	0.0880808i	0.170979	+	0.985275i	$0.445307\pi$
$410$	10.9479	−	17.0352i	0.540678	−	0.841311i
$411$	5.78943	−	6.68136i	0.285572	−	0.329567i
$412$	9.35945	+	2.74818i	0.461107	+	0.135393i
$413$	−2.83571	+	1.43316i	−0.139536	+	0.0705211i
$414$	−4.19424	−	2.32559i	−0.206136	−	0.114296i
$415$	28.7395			1.41076
$416$	−0.0383602	+	0.130643i	−0.00188077	+	0.00640530i
$417$	−5.22638	+	6.03157i	−0.255937	+	0.295367i
$418$	−8.55445	+	13.3110i	−0.418412	+	0.651062i
$419$	−2.30541	+	16.0344i	−0.112626	+	0.783334i	0.852721	+	0.522366i	$0.174951\pi$
$419$	−2.30541	+	16.0344i	−0.112626	+	0.783334i	−0.965348	+	0.260968i	$0.915958\pi$
$420$	4.88357	−	8.30363i	0.238294	−	0.405176i
$421$	−6.93602	+	3.16757i	−0.338041	+	0.154378i	−0.577201	−	0.816602i	$-0.695855\pi$
$421$	−6.93602	+	3.16757i	−0.338041	+	0.154378i	0.239160	+	0.970980i	$0.423128\pi$
$422$	11.8779	+	13.7078i	0.578207	+	0.667286i
$423$	−9.92789	+	1.42742i	−0.482711	+	0.0694033i
$424$	−5.77411	−	2.63695i	−0.280416	−	0.128062i
$425$	6.90970	−	2.02887i	0.335170	−	0.0984147i
$426$	3.95493	+	13.4693i	0.191617	+	0.652588i
$427$	17.8750	−	0.707445i	0.865034	−	0.0342357i
$428$	−1.58304	+	0.227606i	−0.0765189	+	0.0110018i
$429$	0.252413	−	0.218718i	0.0121866	−	0.0105598i
$430$	27.3030	−	12.4689i	1.31667	−	0.601302i
$431$	7.24822	+	11.2784i	0.349134	+	0.543264i	0.970760	−	0.240051i	$-0.0771640\pi$
$431$	7.24822	+	11.2784i	0.349134	+	0.543264i	−0.621626	+	0.783314i	$0.713528\pi$
$432$	−0.989821	−	0.142315i	−0.0476228	−	0.00684713i
$433$	7.98594	+	5.13225i	0.383780	+	0.246640i	0.718278	−	0.695756i	$-0.244931\pi$
$433$	7.98594	+	5.13225i	0.383780	+	0.246640i	−0.334498	+	0.942396i	$0.608567\pi$
$434$	6.45185	−	25.6912i	0.309699	−	1.23322i
$435$	−6.75754	+	23.0141i	−0.323999	+	1.10344i
$436$		−	12.1711i		−	0.582892i
$437$	24.8846	−	18.3783i	1.19039	−	0.879153i
$438$	−10.6897			−0.510774
$439$	2.77263	−	9.44272i	0.132331	−	0.450676i	−0.866492	−	0.499191i	$-0.833631\pi$
$439$	2.77263	−	9.44272i	0.132331	−	0.450676i	0.998822	+	0.0485146i	$0.0154487\pi$
$440$	−6.74982	−	5.84875i	−0.321785	−	0.278828i
$441$	6.53958	−	2.49677i	0.311409	−	0.118894i
$442$	−0.117542	−	0.0169000i	−0.00559090	−	0.000803850i
$443$	5.20062	−	3.34223i	0.247089	−	0.158794i	−0.411235	−	0.911530i	$-0.634902\pi$
$443$	5.20062	−	3.34223i	0.247089	−	0.158794i	0.658323	+	0.752735i	$0.271266\pi$
$444$	4.56631	+	9.99882i	0.216707	+	0.474523i
$445$	−29.4475	−	33.9843i	−1.39595	−	1.61101i
$446$	−1.23676	+	0.177819i	−0.0585621	+	0.00841996i
$447$	1.98599	−	4.34872i	0.0939342	−	0.205687i
$448$	1.81032	+	1.92944i	0.0855294	+	0.0911576i
$449$	−19.4820	+	5.72044i	−0.919413	+	0.269964i	−0.706998	−	0.707215i	$-0.749951\pi$
$449$	−19.4820	+	5.72044i	−0.919413	+	0.269964i	−0.212415	+	0.977180i	$0.568133\pi$
$450$	3.43011	−	7.51090i	0.161697	−	0.354067i
$451$	−1.94150	−	13.5035i	−0.0914218	−	0.635853i
$452$	11.5343	−	9.99457i	0.542530	−	0.470105i
$453$	16.4197	−	7.49861i	0.771463	−	0.352315i
$454$	−11.9686	+	7.69178i	−0.561717	+	0.360993i
$455$	−0.419014	−	1.24292i	−0.0196437	−	0.0582689i
$456$	3.48740	−	5.42650i	0.163312	−	0.254119i
$457$	−7.41003	−	6.42082i	−0.346626	−	0.300353i	0.464095	−	0.885785i	$-0.346380\pi$
$457$	−7.41003	−	6.42082i	−0.346626	−	0.300353i	−0.810722	+	0.585432i	$0.800925\pi$
$458$	−17.5769	−	5.16103i	−0.821313	−	0.241159i
$459$		−	0.872151i		−	0.0407085i
$460$	8.26917	+	15.3796i	0.385552	+	0.717080i
$461$		−	3.89980i		−	0.181632i	−0.995868	−	0.0908160i	$-0.971053\pi$
$461$		−	3.89980i		−	0.181632i	0.995868	−	0.0908160i	$-0.0289475\pi$
$462$	−1.17693	−	6.38231i	−0.0547557	−	0.296932i
$463$	−9.69138	+	11.1844i	−0.450397	+	0.519785i	−0.934855	−	0.355029i	$-0.884471\pi$
$463$	−9.69138	+	11.1844i	−0.450397	+	0.519785i	0.484459	+	0.874814i	$0.339017\pi$
$464$	−5.54185	−	3.56153i	−0.257274	−	0.165340i
$465$	5.18788	−	36.0825i	0.240582	−	1.67328i
$466$	−3.95891	+	2.54424i	−0.183393	+	0.117860i
$467$	0.673574	+	1.47492i	0.0311693	+	0.0682512i	0.924576	−	0.380997i	$-0.124419\pi$
$467$	0.673574	+	1.47492i	0.0311693	+	0.0682512i	−0.893407	+	0.449248i	$0.851692\pi$
$468$	−0.102902	+	0.0891647i	−0.00475663	+	0.00412164i
$469$	7.94375	+	11.3475i	0.366808	+	0.523979i
$470$	33.2192	+	15.1707i	1.53229	+	0.699773i
$471$	−1.66787	−	5.68026i	−0.0768516	−	0.261732i
$472$	−0.338334	−	1.15226i	−0.0155731	−	0.0530370i
$473$	8.40028	−	18.3940i	0.386245	−	0.845759i
$474$	1.39169	+	9.67941i	0.0639224	+	0.444590i
$475$	34.8793	+	40.2529i	1.60037	+	1.84693i
$476$	−1.44094	+	1.80228i	−0.0660454	+	0.0826074i
$477$	−3.43185	−	5.34007i	−0.157134	−	0.244505i
$478$	−1.55341	+	10.8042i	−0.0710515	+	0.494174i
$479$	−22.5802	−	14.5114i	−1.03172	−	0.663044i	−0.0887921	−	0.996050i	$-0.528301\pi$
$479$	−22.5802	−	14.5114i	−1.03172	−	0.663044i	−0.942925	+	0.333006i	$0.891937\pi$
$480$	2.75170	+	2.38437i	0.125598	+	0.108831i
$481$	1.43605	+	0.421662i	0.0654781	+	0.0192261i
$482$	4.80270			0.218757
$483$	−2.28554	+	12.4810i	−0.103996	+	0.567907i
$484$	4.98299			0.226499
$485$	20.6217	+	6.05509i	0.936385	+	0.274947i
$486$	−0.755750	−	0.654861i	−0.0342815	−	0.0297051i
$487$	20.2288	+	13.0003i	0.916656	+	0.589099i	0.911685	−	0.410889i	$-0.134782\pi$
$487$	20.2288	+	13.0003i	0.916656	+	0.589099i	0.00497025	+	0.999988i	$0.498418\pi$
$488$	−0.962250	+	6.69260i	−0.0435590	+	0.302960i
$489$	1.33390	+	2.07559i	0.0603212	+	0.0938616i
$490$	−24.9458	−	5.22543i	−1.12693	−	0.236061i
$491$	5.75899	+	6.64623i	0.259900	+	0.299940i	0.870670	−	0.491868i	$-0.163686\pi$
$491$	5.75899	+	6.64623i	0.259900	+	0.299940i	−0.610770	+	0.791808i	$0.709140\pi$
$492$	0.791494	+	5.50496i	0.0356833	+	0.248183i
$493$	2.38672	−	5.22619i	0.107492	−	0.235376i
$494$	−0.247442	−	0.842711i	−0.0111330	−	0.0379154i
$495$	−2.51624	−	8.56951i	−0.113096	−	0.385171i
$496$	9.10713	+	4.15909i	0.408922	+	0.186748i
$497$	30.4263	−	21.2997i	1.36481	−	0.955424i
$498$	−5.96530	+	5.16897i	−0.267312	+	0.231627i
$499$	−17.3806	−	38.0583i	−0.778064	−	1.70372i	−0.708036	−	0.706177i	$-0.750418\pi$
$499$	−17.3806	−	38.0583i	−0.778064	−	1.70372i	−0.0700280	−	0.997545i	$-0.522309\pi$
$500$	−9.97650	+	6.41150i	−0.446162	+	0.286731i
$501$	0.412382	−	2.86818i	0.0184239	−	0.128141i
$502$	13.2606	+	8.52208i	0.591850	+	0.380359i
$503$	10.7027	−	12.3516i	0.477211	−	0.550731i	−0.465192	−	0.885210i	$-0.654015\pi$
$503$	10.7027	−	12.3516i	0.477211	−	0.550731i	0.942403	+	0.334478i	$0.108560\pi$
$504$	0.479800	+	2.60188i	0.0213720	+	0.115897i
$505$			35.4408i			1.57710i
$506$	10.9954	+	4.18233i	0.488806	+	0.185927i
$507$		−	12.9815i		−	0.576527i
$508$	−14.9513	−	4.39010i	−0.663357	−	0.194779i
$509$	13.6217	+	11.8033i	0.603771	+	0.523171i	0.902232	−	0.431251i	$-0.141928\pi$
$509$	13.6217	+	11.8033i	0.603771	+	0.523171i	−0.298461	+	0.954422i	$0.596473\pi$
$510$	−1.71682	+	2.67142i	−0.0760220	+	0.118292i
$511$	9.03498	+	26.8004i	0.399684	+	1.18558i
$512$	−0.841254	+	0.540641i	−0.0371785	+	0.0238932i
$513$	5.86757	−	2.67963i	0.259060	−	0.118309i
$514$	−10.5618	+	9.15189i	−0.465863	+	0.403672i
$515$	−5.05455	−	35.1552i	−0.222730	−	1.54912i
$516$	−3.42455	+	7.49871i	−0.150757	+	0.330112i
$517$	23.6065	−	6.93151i	1.03821	−	0.304847i
$518$	21.2087	−	19.8993i	0.931859	−	0.874325i
$519$	8.50445	−	18.6221i	0.373304	−	0.817421i
$520$	0.490710	−	0.0705534i	0.0215191	−	0.00309397i
$521$	11.6097	+	13.3983i	0.508631	+	0.586992i	0.950748	−	0.309966i	$-0.100318\pi$
$521$	11.6097	+	13.3983i	0.508631	+	0.586992i	−0.442116	+	0.896958i	$0.645772\pi$
$522$	−2.73659	−	5.99230i	−0.119777	−	0.262276i
$523$	−4.18595	+	2.69015i	−0.183039	+	0.117632i	−0.628951	−	0.777445i	$-0.716516\pi$
$523$	−4.18595	+	2.69015i	−0.183039	+	0.117632i	0.445913	+	0.895077i	$0.352879\pi$
$524$	−20.6892	−	2.97466i	−0.903813	−	0.129949i
$525$	−21.7298	−	2.25146i	−0.948368	−	0.0982617i
$526$	−3.62053	−	3.13721i	−0.157863	−	0.136789i
$527$	−2.46005	+	8.37817i	−0.107162	+	0.364959i
$528$	2.45296			0.106751
$529$	−17.1858	−	15.2855i	−0.747211	−	0.664587i
$530$			23.1123i			1.00393i
$531$	0.338334	−	1.15226i	0.0146824	−	0.0500038i
$532$	−16.5524	−	4.15682i	−0.717639	−	0.180221i
$533$	0.637043	+	0.409403i	0.0275934	+	0.0177332i
$534$	12.2246	+	1.75763i	0.529008	+	0.0760599i
$535$	3.14823	+	4.89874i	0.136110	+	0.211791i
$536$	−4.76233	+	2.17488i	−0.205701	+	0.0939406i
$537$	10.6916	−	9.26433i	0.461377	−	0.399785i
$538$	−19.0327	+	2.73649i	−0.820559	+	0.117979i
$539$	−15.0065	+	8.34505i	−0.646374	+	0.359447i
$540$	1.02580	+	3.49354i	0.0441432	+	0.150338i
$541$	24.2549	−	7.12189i	1.04280	−	0.306194i	0.284896	−	0.958559i	$-0.408041\pi$
$541$	24.2549	−	7.12189i	1.04280	−	0.306194i	0.757905	+	0.652364i	$0.226223\pi$
$542$	23.0675	+	10.5346i	0.990835	+	0.452499i
$543$	−14.6356	+	2.10429i	−0.628076	+	0.0903037i
$544$	−0.571137	−	0.659128i	−0.0244873	−	0.0282599i
$545$	−40.3107	+	18.4093i	−1.72672	+	0.788568i
$546$	0.310519	+	0.182624i	0.0132890	+	0.00781559i
$547$	−6.42700	+	44.7008i	−0.274799	+	1.91127i	0.120498	+	0.992714i	$0.461551\pi$
$547$	−6.42700	+	44.7008i	−0.274799	+	1.91127i	−0.395297	+	0.918553i	$0.629358\pi$
$548$	4.77965	−	7.43727i	0.204176	−	0.317705i
$549$	−4.42779	+	5.10994i	−0.188973	+	0.218087i
$550$	−5.70629	+	19.4338i	−0.243317	+	0.828661i
$551$	42.4933			1.81028
$552$	−4.48251	−	1.70502i	−0.190788	−	0.0725703i
$553$	23.0911	−	11.6702i	0.981935	−	0.496267i
$554$	−2.04995	−	0.601918i	−0.0870939	−	0.0255731i
$555$	26.2093	−	30.2472i	1.11252	−	1.28392i
$556$	−4.31480	+	6.71397i	−0.182988	+	0.284736i
$557$	−12.5803	−	1.80877i	−0.533044	−	0.0766401i	−0.129463	−	0.991584i	$-0.541325\pi$
$557$	−12.5803	−	1.80877i	−0.533044	−	0.0766401i	−0.403581	+	0.914944i	$0.632235\pi$
$558$	5.41283	+	8.42253i	0.229143	+	0.356554i
$559$	0.466281	+	1.02101i	0.0197216	+	0.0431842i
$560$	3.65213	−	8.91411i	0.154331	−	0.376690i
$561$	0.304461	+	2.11758i	0.0128544	+	0.0894041i
$562$	1.61168	+	0.736030i	0.0679847	+	0.0310475i
$563$	5.54666	−	1.62865i	0.233764	−	0.0686393i	−0.162752	−	0.986667i	$-0.552037\pi$
$563$	5.54666	−	1.62865i	0.233764	−	0.0686393i	0.396516	+	0.918028i	$0.370219\pi$
$564$	−9.62370	+	2.82577i	−0.405231	+	0.118987i
$565$	−50.5481	−	23.0845i	−2.12657	−	0.971173i
$566$	−1.32636	−	9.22502i	−0.0557510	−	0.387756i
$567$	−1.00305	+	2.44824i	−0.0421242	+	0.102817i
$568$	5.83155	+	12.7693i	0.244687	+	0.535789i
$569$	−3.43722	−	5.34841i	−0.144096	−	0.224217i	0.761702	−	0.647927i	$-0.224364\pi$
$569$	−3.43722	−	5.34841i	−0.144096	−	0.224217i	−0.905798	+	0.423710i	$0.860728\pi$
$570$	−23.2474	−	3.34246i	−0.973725	−	0.140000i
$571$	−2.30318	+	3.58382i	−0.0963850	+	0.149978i	−0.886097	−	0.463500i	$-0.846594\pi$
$571$	−2.30318	+	3.58382i	−0.0963850	+	0.149978i	0.789712	+	0.613478i	$0.210230\pi$
$572$	0.218718	−	0.252413i	0.00914504	−	0.0105539i
$573$	−20.3423	−	5.97303i	−0.849811	−	0.249527i
$574$	13.1326	−	6.63718i	0.548145	−	0.277030i
$575$	23.9358	−	31.5468i	0.998191	−	1.31559i
$576$	−1.00000			−0.0416667
$577$	9.67432	−	32.9477i	0.402747	−	1.37163i	−0.469658	−	0.882848i	$-0.655623\pi$
$577$	9.67432	−	32.9477i	0.402747	−	1.37163i	0.872405	−	0.488783i	$-0.162559\pi$
$578$	−10.6345	+	12.2729i	−0.442337	+	0.510485i
$579$	2.25536	−	3.50941i	0.0937296	−	0.145846i
$580$	−3.41351	+	23.7415i	−0.141738	+	0.985812i
$581$	18.0011	+	10.5869i	0.746811	+	0.439218i
$582$	−5.36939	+	2.45212i	−0.222569	+	0.101644i
$583$	10.1967	+	11.7676i	0.422304	+	0.487364i
$584$	−10.5809	+	1.52131i	−0.437841	+	0.0629521i
$585$	0.450956	+	0.205945i	0.0186447	+	0.00851476i
$586$	−17.5037	+	5.13956i	−0.723073	+	0.212313i
$587$	−7.63212	−	25.9926i	−0.315011	−	1.07283i	−0.953047	−	0.302823i	$-0.902071\pi$
$587$	−7.63212	−	25.9926i	−0.315011	−	1.07283i	0.638036	−	0.770007i	$-0.279747\pi$
$588$	6.11769	−	3.40203i	0.252289	−	0.140297i
$589$	−63.9242	+	9.19091i	−2.63395	+	0.378705i
$590$	−3.30453	+	2.86339i	−0.136045	+	0.117884i
$591$	−7.65803	+	3.49731i	−0.315009	+	0.143860i
$592$	5.94281	+	9.24719i	0.244248	+	0.380057i
$593$	22.6475	+	3.25622i	0.930021	+	0.133717i	0.590643	−	0.806933i	$-0.298874\pi$
$593$	22.6475	+	3.25622i	0.930021	+	0.133717i	0.339378	+	0.940650i	$0.389783\pi$
$594$	2.06356	+	1.32617i	0.0846689	+	0.0544134i
$595$	8.14862	+	2.04637i	0.334061	+	0.0838930i
$596$	1.34689	−	4.58709i	0.0551708	−	0.187895i
$597$			10.0144i			0.409863i
$598$	−0.575131	+	0.309230i	−0.0235189	+	0.0126454i
$599$	27.2815			1.11469			0.557347	−	0.830280i	$-0.311819\pi$
$599$	27.2815			1.11469			0.557347	+	0.830280i	$0.311819\pi$
$600$	2.32629	−	7.92260i	0.0949702	−	0.323439i
$601$	−25.2524	−	21.8813i	−1.03007	−	0.892557i	−0.0357853	−	0.999359i	$-0.511393\pi$
$601$	−25.2524	−	21.8813i	−1.03007	−	0.892557i	−0.994280	+	0.106803i	$0.965939\pi$
$602$	21.6946	+	2.24781i	0.884205	+	0.0916138i
$603$	−5.18216	−	0.745082i	−0.211034	−	0.0303421i
$604$	15.1854	−	9.75904i	0.617884	−	0.397090i
$605$	−7.53695	−	16.5036i	−0.306421	−	0.670968i
$606$	−6.37425	−	7.35628i	−0.258936	−	0.298828i
$607$	23.0492	−	3.31397i	0.935538	−	0.134510i	0.342349	−	0.939573i	$-0.388778\pi$
$607$	23.0492	−	3.31397i	0.935538	−	0.134510i	0.593189	+	0.805063i	$0.297868\pi$
$608$	2.67963	−	5.86757i	0.108673	−	0.237962i
$609$	−12.7104	+	11.9257i	−0.515052	+	0.483252i
$610$	23.6213	−	6.93583i	0.956398	−	0.280824i
$611$	−0.567318	+	1.24225i	−0.0229512	+	0.0502562i
$612$	−0.124120	−	0.863273i	−0.00501725	−	0.0348958i
$613$	−22.6030	+	19.5856i	−0.912925	+	0.791054i	−0.978383	−	0.206802i	$-0.933695\pi$
$613$	−22.6030	+	19.5856i	−0.912925	+	0.791054i	0.0654582	+	0.997855i	$0.479149\pi$
$614$	−11.5588	+	5.27874i	−0.466476	+	0.213033i
$615$	17.0352	−	10.9479i	0.686927	−	0.441461i
$616$	−2.07325	−	6.14986i	−0.0835335	−	0.247785i
$617$	20.6230	−	32.0901i	0.830252	−	1.29190i	−0.123815	−	0.992305i	$-0.539513\pi$
$617$	20.6230	−	32.0901i	0.830252	−	1.29190i	0.954067	−	0.299592i	$-0.0968506\pi$
$618$	7.37202	+	6.38789i	0.296546	+	0.256959i
$619$	17.3828	+	5.10405i	0.698674	+	0.205149i	0.611733	−	0.791064i	$-0.290473\pi$
$619$	17.3828	+	5.10405i	0.698674	+	0.205149i	0.0869407	+	0.996213i	$0.472291\pi$
$620$		−	36.4535i		−	1.46401i
$621$	−2.84913	−	3.85778i	−0.114332	−	0.154807i
$622$		−	23.2537i		−	0.932388i
$623$	−5.92566	−	32.1339i	−0.237406	−	1.28742i
$624$	−0.0891647	+	0.102902i	−0.00356945	+	0.00411936i
$625$	1.59323	+	1.02391i	0.0637292	+	0.0409563i
$626$	−0.659516	+	4.58704i	−0.0263596	+	0.183335i
$627$	−13.3110	+	8.55445i	−0.531590	+	0.341632i
$628$	−2.45928	−	5.38508i	−0.0981360	−	0.214888i
$629$	−7.24523	+	6.27803i	−0.288886	+	0.250321i
$630$	7.89170	−	5.52454i	0.314413	−	0.220103i
$631$	−5.97634	−	2.72930i	−0.237914	−	0.108652i	0.292890	−	0.956146i	$-0.405383\pi$
$631$	−5.97634	−	2.72930i	−0.237914	−	0.108652i	−0.530805	+	0.847494i	$0.678110\pi$
$632$	2.75505	+	9.38282i	0.109590	+	0.373229i
$633$	5.11008	+	17.4033i	0.203107	+	0.691720i
$634$	−6.22978	+	13.6413i	−0.247416	+	0.541765i
$635$	8.07442	+	56.1588i	0.320424	+	2.22860i
$636$	−4.15689	−	4.79731i	−0.164831	−	0.190226i
$637$	0.195408	−	0.932862i	0.00774235	−	0.0369613i
$638$	8.73629	+	13.5939i	0.345873	+	0.538189i
$639$	−1.99780	+	13.8950i	−0.0790318	+	0.549678i
$640$	3.06303	+	1.96849i	0.121077	+	0.0778113i
$641$	−23.5173	−	20.3779i	−0.928877	−	0.804877i	0.0521714	−	0.998638i	$-0.483386\pi$
$641$	−23.5173	−	20.3779i	−0.928877	−	0.804877i	−0.981049	+	0.193761i	$0.937931\pi$
$642$	−1.53453	−	0.450579i	−0.0605631	−	0.0177829i
$643$	33.4202			1.31796			0.658981	−	0.752159i	$-0.270988\pi$
$643$	33.4202			1.31796			0.658981	+	0.752159i	$0.270988\pi$
$644$	−0.486041	+	12.6793i	−0.0191527	+	0.499633i
$645$	30.0155			1.18186
$646$	5.39792	+	1.58497i	0.212378	+	0.0623599i
$647$	15.2320	+	13.1986i	0.598831	+	0.518890i	0.900690	−	0.434463i	$-0.143062\pi$
$647$	15.2320	+	13.1986i	0.598831	+	0.518890i	−0.301859	+	0.953353i	$0.597607\pi$
$648$	−0.841254	−	0.540641i	−0.0330476	−	0.0212384i
$649$	−0.419227	+	2.91579i	−0.0164561	+	0.114455i
$650$	−0.607826	−	0.945795i	−0.0238409	−	0.0370971i
$651$	16.5413	−	20.6893i	0.648306	−	0.810879i
$652$	1.61571	+	1.86463i	0.0632763	+	0.0730247i
$653$	5.69429	+	39.6046i	0.222835	+	1.54985i	0.727240	+	0.686383i	$0.240803\pi$
$653$	5.69429	+	39.6046i	0.222835	+	1.54985i	−0.504406	+	0.863467i	$0.668288\pi$
$654$	5.05607	−	11.0713i	0.197708	−	0.432920i
$655$	21.4412	+	73.0219i	0.837775	+	2.85320i
$656$	1.56688	+	5.33629i	0.0611762	+	0.208347i
$657$	−9.72371	−	4.44067i	−0.379358	−	0.173247i
$658$	15.2185	+	21.7394i	0.593280	+	0.847489i
$659$	27.1020	−	23.4840i	1.05574	−	0.914806i	0.0592295	−	0.998244i	$-0.481136\pi$
$659$	27.1020	−	23.4840i	1.05574	−	0.914806i	0.996513	+	0.0834383i	$0.0265902\pi$
$660$	−3.71019	−	8.12419i	−0.144419	−	0.316234i
$661$	4.64506	−	2.98520i	0.180672	−	0.116111i	−0.447179	−	0.894445i	$-0.647571\pi$
$661$	4.64506	−	2.98520i	0.180672	−	0.116111i	0.627851	+	0.778334i	$0.283935\pi$
$662$	2.34185	−	16.2879i	0.0910186	−	0.633048i
$663$	−0.0998994	−	0.0642014i	−0.00387977	−	0.00249338i
$664$	−5.16897	+	5.96530i	−0.200595	+	0.231499i
$665$	11.2688	+	61.1089i	0.436984	+	2.36970i
$666$			10.9922i			0.425937i
$667$	−6.51566	−	30.9139i	−0.252287	−	1.19699i
$668$		−	2.89768i		−	0.112114i
$669$	−1.19886	−	0.352018i	−0.0463507	−	0.0136098i
$670$	14.4064	+	12.4832i	0.556568	+	0.482269i
$671$	8.96679	−	13.9526i	0.346159	−	0.538634i
$672$	0.845203	+	2.50712i	0.0326044	+	0.0967141i
$673$	−34.3673	+	22.0865i	−1.32476	+	0.851373i	−0.995673	−	0.0929263i	$-0.970378\pi$
$673$	−34.3673	+	22.0865i	−1.32476	+	0.851373i	−0.329089	+	0.944299i	$0.606742\pi$
$674$	21.8104	−	9.96046i	0.840104	−	0.383663i
$675$	6.24028	−	5.40723i	0.240188	−	0.208124i
$676$	−1.84745	−	12.8493i	−0.0710559	−	0.494205i
$677$	5.56214	−	12.1794i	0.213771	−	0.468092i	−0.772121	−	0.635475i	$-0.780804\pi$
$677$	5.56214	−	12.1794i	0.213771	−	0.468092i	0.985892	+	0.167383i	$0.0535316\pi$
$678$	14.6439	−	4.29984i	0.562396	−	0.165134i
$679$	10.6860	+	11.3892i	0.410090	+	0.437076i
$680$	−1.31916	+	2.88856i	−0.0505875	+	0.110771i
$681$	−14.0823	+	2.02474i	−0.539637	+	0.0775881i
$682$	−16.0826	−	18.5603i	−0.615833	−	0.710709i
$683$	8.37175	+	18.3316i	0.320336	+	0.701438i	0.999469	−	0.0325771i	$-0.0103714\pi$
$683$	8.37175	+	18.3316i	0.320336	+	0.701438i	−0.679133	+	0.734015i	$0.737644\pi$
$684$	5.42650	−	3.48740i	0.207487	−	0.133344i
$685$	−31.8616	−	4.58101i	−1.21737	−	0.175031i
$686$	−13.7000	−	12.4624i	−0.523068	−	0.475815i
$687$	−13.8445	−	11.9963i	−0.528201	−	0.457689i
$688$	−2.32251	+	7.90975i	−0.0885450	+	0.301556i
$689$	−0.864299			−0.0329272
$690$	1.13296	+	17.4250i	0.0431312	+	0.663357i
$691$		−	51.6894i		−	1.96636i	−0.182649	−	0.983178i	$-0.558467\pi$
$691$		−	51.6894i		−	1.96636i	0.182649	−	0.983178i	$-0.441533\pi$
$692$	5.76768	−	19.6429i	0.219254	−	0.746711i
$693$	1.58074	−	6.29447i	0.0600472	−	0.239107i
$694$	22.8235	+	14.6678i	0.866367	+	0.556781i
$695$	28.7629	+	4.13548i	1.09104	+	0.156868i
$696$	−3.56153	−	5.54185i	−0.134999	−	0.210063i
$697$	−4.41220	+	2.01498i	−0.167124	+	0.0763229i
$698$	−6.29052	+	5.45077i	−0.238100	+	0.206315i
$699$	−4.65807	+	0.669729i	−0.176184	+	0.0253315i
$700$	−21.8291	+	0.863935i	−0.825061	+	0.0326537i
$701$	−6.67474	−	22.7321i	−0.252101	−	0.858578i	−0.984152	−	0.177328i	$-0.943255\pi$
$701$	−6.67474	−	22.7321i	−0.252101	−	0.858578i	0.732051	−	0.681250i	$-0.238563\pi$
$702$	−0.130643	+	0.0383602i	−0.00493080	+	0.00144781i
$703$	−64.4973	−	29.4549i	−2.43256	−	1.11091i
$704$	2.42799	−	0.349093i	0.0915084	−	0.0131569i
$705$	23.9151	+	27.5995i	0.900696	+	1.03946i
$706$	3.14967	−	1.43841i	0.118539	−	0.0541351i
$707$	−13.0555	+	22.1985i	−0.491003	+	0.834862i
$708$	0.170906	−	1.18868i	0.00642306	−	0.0446733i
$709$	20.2696	−	31.5400i	0.761239	−	1.18451i	−0.216826	−	0.976210i	$-0.569570\pi$
$709$	20.2696	−	31.5400i	0.761239	−	1.18451i	0.978065	−	0.208301i	$-0.0667933\pi$
$710$	33.4715	−	38.6281i	1.25616	−	1.44969i
$711$	−2.75505	+	9.38282i	−0.103322	+	0.351883i
$712$	12.3503			0.462846
$713$	16.4881	+	45.0956i	0.617485	+	1.68884i
$714$	−2.05942	+	1.04082i	−0.0770719	+	0.0389519i
$715$	−1.16681	−	0.342606i	−0.0436362	−	0.0128128i
$716$	9.26433	−	10.6916i	0.346224	−	0.399564i
$717$	−5.90127	+	9.18256i	−0.220387	+	0.342929i
$718$	−19.2255	−	2.76420i	−0.717488	−	0.103159i
$719$	6.38350	+	9.93292i	0.238064	+	0.370435i	0.939643	−	0.342157i	$-0.111157\pi$
$719$	6.38350	+	9.93292i	0.238064	+	0.370435i	−0.701578	+	0.712592i	$0.747521\pi$
$720$	1.51254	+	3.31199i	0.0563689	+	0.123431i
$721$	9.78433	−	23.8816i	0.364388	−	0.889396i
$722$	3.21758	+	22.3787i	0.119746	+	0.832850i
$723$	4.36869	+	1.99512i	0.162473	+	0.0741991i
$724$	−14.1872	+	4.16574i	−0.527263	+	0.154819i
$725$	52.1910	−	15.3247i	1.93832	−	0.569143i
$726$	4.53269	+	2.07001i	0.168224	+	0.0768252i
$727$	2.92544	+	20.3469i	0.108499	+	0.754624i	0.969335	+	0.245743i	$0.0790318\pi$
$727$	2.92544	+	20.3469i	0.108499	+	0.754624i	−0.860837	+	0.508882i	$0.830059\pi$
$728$	0.333349	+	0.136574i	0.0123547	+	0.00506176i
$729$	−0.415415	−	0.909632i	−0.0153857	−	0.0336901i
$730$	21.0426	+	32.7429i	0.778821	+	1.21187i
$731$	−7.11655	−	1.02321i	−0.263215	−	0.0378446i
$732$	−3.65550	+	5.68807i	−0.135111	+	0.210237i
$733$	12.3248	−	14.2236i	0.455227	−	0.525359i	−0.481017	−	0.876711i	$-0.659732\pi$
$733$	12.3248	−	14.2236i	0.455227	−	0.525359i	0.936243	+	0.351352i	$0.114278\pi$
$734$	−11.6748	−	3.42803i	−0.430925	−	0.126531i
$735$	−20.5207	−	15.1161i	−0.756919	−	0.557564i
$736$	−4.67954	−	1.04973i	−0.172490	−	0.0386937i
$737$	12.8423			0.473054
$738$	−1.56688	+	5.33629i	−0.0576775	+	0.196432i
$739$	−8.47514	+	9.78083i	−0.311763	+	0.359794i	−0.889908	−	0.456141i	$-0.849231\pi$
$739$	−8.47514	+	9.78083i	−0.311763	+	0.359794i	0.578145	+	0.815934i	$0.303777\pi$
$740$	21.6379	−	33.6693i	0.795426	−	1.23771i
$741$	0.124993	−	0.869349i	0.00459175	−	0.0319363i
$742$	−8.51399	+	14.4765i	−0.312559	+	0.531449i
$743$	−6.75715	+	3.08589i	−0.247896	+	0.113210i	−0.535488	−	0.844543i	$-0.679872\pi$
$743$	−6.75715	+	3.08589i	−0.247896	+	0.113210i	0.287592	+	0.957753i	$0.407145\pi$
$744$	6.55639	+	7.56647i	0.240369	+	0.277400i
$745$	−17.2296	+	2.47725i	−0.631245	+	0.0907593i
$746$	−17.9992	−	8.21997i	−0.658999	−	0.300955i
$747$	−7.57350	+	2.22378i	−0.277100	+	0.0813638i
$748$	0.602725	+	2.05269i	0.0220378	+	0.0750538i
$749$	0.167336	+	4.22808i	0.00611432	+	0.154491i
$750$	−11.7384	+	1.68772i	−0.428625	+	0.0616270i
$751$	−19.1114	+	16.5601i	−0.697385	+	0.604288i	−0.929685	−	0.368357i	$-0.879921\pi$
$751$	−19.1114	+	16.5601i	−0.697385	+	0.604288i	0.232299	+	0.972644i	$0.425375\pi$
$752$	−9.12359	+	4.16661i	−0.332703	+	0.151940i
$753$	8.52208	+	13.2606i	0.310562	+	0.483243i
$754$	−0.887828	−	0.127650i	−0.0323328	−	0.00464875i
$755$	−55.2903	−	35.5329i	−2.01222	−	1.29318i
$756$	−0.644420	+	2.56607i	−0.0234373	+	0.0933271i
$757$	3.79711	−	12.9318i	0.138008	−	0.470014i	−0.861264	−	0.508158i	$-0.830327\pi$
$757$	3.79711	−	12.9318i	0.138008	−	0.470014i	0.999272	+	0.0381445i	$0.0121447\pi$
$758$		−	6.63370i		−	0.240947i
$759$	8.26438	+	8.37205i	0.299978	+	0.303886i
$760$	−23.4864			−0.851942
$761$	−1.17228	+	3.99243i	−0.0424952	+	0.144725i	−0.978008	−	0.208568i	$-0.933120\pi$
$761$	−1.17228	+	3.99243i	−0.0424952	+	0.144725i	0.935513	+	0.353293i	$0.114938\pi$
$762$	−11.7765	−	10.2044i	−0.426617	−	0.369665i
$763$	−32.0303	−	3.31871i	−1.15958	−	0.120145i
$764$	−20.9853	−	3.01723i	−0.759221	−	0.109159i
$765$	−2.67142	+	1.71682i	−0.0965854	+	0.0620717i
$766$	−3.76217	−	8.23799i	−0.135933	−	0.297651i
$767$	−0.107078	−	0.123575i	−0.00386637	−	0.00446203i
$768$	−0.989821	+	0.142315i	−0.0357171	+	0.00513534i
$769$	9.56075	−	20.9351i	0.344769	−	0.754940i	−0.655230	−	0.755429i	$-0.727428\pi$
$769$	9.56075	−	20.9351i	0.344769	−	0.754940i	1.00000		0.000489285i	$0.000155744\pi$
$770$	−17.2324	+	16.1685i	−0.621013	+	0.582671i
$771$	−13.4092	+	3.93730i	−0.482921	+	0.141798i
$772$	1.73296	−	3.79466i	0.0623707	−	0.136573i
$773$	0.319409	+	2.22154i	0.0114883	+	0.0799031i	0.994759	−	0.102247i	$-0.0326033\pi$
$773$	0.319409	+	2.22154i	0.0114883	+	0.0799031i	−0.983271	+	0.182150i	$0.941694\pi$
$774$	−6.23016	+	5.39846i	−0.223938	+	0.194044i
$775$	−75.1982	+	34.3419i	−2.70120	+	1.23360i
$776$	−4.96577	+	3.19131i	−0.178261	+	0.114561i
$777$	27.5586	−	9.29060i	0.988660	−	0.333298i
$778$	5.91943	−	9.21081i	0.212222	−	0.330224i
$779$	−27.1124	−	23.4931i	−0.971404	−	0.841726i
$780$	0.475674	+	0.139671i	0.0170319	+	0.00500101i
$781$		−	34.4344i		−	1.23216i
$782$	0.325383	−	4.17001i	0.0116357	−	0.149119i
$783$		−	6.58761i		−	0.235422i
$784$	5.57126	−	4.23804i	0.198974	−	0.151359i
$785$	−14.1156	+	16.2903i	−0.503807	+	0.581424i
$786$	−17.5839	−	11.3005i	−0.627196	−	0.403074i
$787$	3.54146	−	24.6314i	0.126240	−	0.878015i	−0.824021	−	0.566559i	$-0.808274\pi$
$787$	3.54146	−	24.6314i	0.126240	−	0.878015i	0.950261	−	0.311456i	$-0.100817\pi$
$788$	−7.08237	+	4.55156i	−0.252299	+	0.162143i
$789$	−1.99011	−	4.35773i	−0.0708497	−	0.155139i
$790$	26.9088	−	23.3166i	0.957370	−	0.829566i
$791$	−23.1573	−	33.0797i	−0.823377	−	1.17618i
$792$	2.23129	+	1.01900i	0.0792855	+	0.0362085i
$793$	0.259370	+	0.883332i	0.00921048	+	0.0313680i
$794$	−0.181383	−	0.617733i	−0.00643703	−	0.0219225i
$795$	−9.60120	+	21.0237i	−0.340520	+	0.745634i
$796$	1.42520	+	9.91249i	0.0505149	+	0.351339i
$797$	10.2256	+	11.8009i	0.362208	+	0.418010i	0.907378	−	0.420315i	$-0.138080\pi$
$797$	10.2256	+	11.8009i	0.362208	+	0.418010i	−0.545170	+	0.838325i	$0.683535\pi$
$798$	−13.3298	−	10.6573i	−0.471870	−	0.377265i
$799$	−4.72934	−	7.35900i	−0.167312	−	0.260343i
$800$	1.17510	−	8.17303i	0.0415462	−	0.288960i
$801$	10.3897	+	6.67706i	0.367102	+	0.235922i
$802$	−11.9794	−	10.3802i	−0.423007	−	0.366538i
$803$	25.1593	+	7.38744i	0.887852	+	0.260697i
$804$	−5.23545			−0.184640
$805$	42.7288	−	17.5681i	1.50599	−	0.619194i
$806$	1.36320			0.0480167
$807$	−18.4495	−	5.41727i	−0.649455	−	0.190697i
$808$	−7.35628	−	6.37425i	−0.258793	−	0.224245i
$809$	−24.2708	−	15.5979i	−0.853316	−	0.548393i	0.0392912	−	0.999228i	$-0.487490\pi$
$809$	−24.2708	−	15.5979i	−0.853316	−	0.548393i	−0.892607	+	0.450835i	$0.851126\pi$
$810$	−0.518172	+	3.60397i	−0.0182067	+	0.126630i
$811$	16.1341	+	25.1051i	0.566543	+	0.881558i	0.999806	−	0.0197093i	$-0.00627409\pi$
$811$	16.1341	+	25.1051i	0.566543	+	0.881558i	−0.433263	+	0.901268i	$0.642638\pi$
$812$	−10.8838	+	13.6132i	−0.381948	+	0.477728i
$813$	16.6067	+	19.1652i	0.582424	+	0.672153i
$814$	−3.83728	−	26.6889i	−0.134497	−	0.935444i
$815$	3.73183	−	8.17156i	0.130720	−	0.286237i
$816$	−0.245713	−	0.836822i	−0.00860168	−	0.0292946i
$817$	−14.9814	−	51.0218i	−0.524131	−	1.78503i
$818$	11.3857	+	5.19966i	0.398091	+	0.181802i
$819$	0.206593	+	0.295115i	0.00721896	+	0.0103122i
$820$	15.3038	−	13.2608i	0.534432	−	0.463088i
$821$	−21.3108	−	46.6641i	−0.743751	−	1.62859i	−0.777285	−	0.629149i	$-0.783403\pi$
$821$	−21.3108	−	46.6641i	−0.743751	−	1.62859i	0.0335340	−	0.999438i	$-0.489324\pi$
$822$	7.43727	−	4.77965i	0.259405	−	0.166709i
$823$	4.65167	−	32.3531i	0.162147	−	1.12776i	−0.732430	−	0.680842i	$-0.761614\pi$
$823$	4.65167	−	32.3531i	0.162147	−	1.12776i	0.894577	−	0.446914i	$-0.147477\pi$
$824$	8.20607	+	5.27372i	0.285872	+	0.183719i
$825$	−13.2637	+	15.3072i	−0.461784	+	0.532927i
$826$	−3.12461	+	0.576194i	−0.108719	+	0.0200483i
$827$			36.2346i			1.26000i	0.776594	+	0.630001i	$0.216946\pi$
$827$			36.2346i			1.26000i	−0.776594	+	0.630001i	$0.783054\pi$
$828$	−3.36915	−	3.41304i	−0.117086	−	0.118611i
$829$		−	2.09406i		−	0.0727296i	−0.999339	−	0.0363648i	$-0.988422\pi$
$829$		−	2.09406i		−	0.0727296i	0.999339	−	0.0363648i	$-0.0115778\pi$
$830$	27.5753	+	8.09684i	0.957153	+	0.281045i
$831$	−1.61465	−	1.39910i	−0.0560116	−	0.0485343i
$832$	−0.0736128	+	0.114544i	−0.00255206	+	0.00397109i
$833$	4.35010	+	4.28350i	0.150722	+	0.148414i
$834$	−6.71397	+	4.31480i	−0.232486	+	0.149409i
$835$	−9.59709	+	4.38284i	−0.332121	+	0.151675i
$836$	−11.9581	+	10.3617i	−0.413579	+	0.358368i
$837$	1.42484	+	9.90997i	0.0492496	+	0.342539i
$838$	−6.72945	+	14.7354i	−0.232465	+	0.509027i
$839$	2.35088	−	0.690280i	0.0811614	−	0.0238311i	−0.240900	−	0.970550i	$-0.577443\pi$
$839$	2.35088	−	0.690280i	0.0811614	−	0.0238311i	0.322061	+	0.946719i	$0.395624\pi$
$840$	7.02515	−	6.59141i	0.242391	−	0.227425i
$841$	5.98055	−	13.0956i	0.206226	−	0.451571i
$842$	−7.54747	+	1.08516i	−0.260103	+	0.0373971i
$843$	1.16028	+	1.33903i	0.0399621	+	0.0461187i
$844$	7.53482	+	16.4989i	0.259359	+	0.567917i
$845$	−39.7626	+	25.5538i	−1.36787	+	0.879079i
$846$	−9.92789	−	1.42742i	−0.341328	−	0.0490756i
$847$	1.35871	−	13.1135i	0.0466859	−	0.450587i
$848$	−4.79731	−	4.15689i	−0.164740	−	0.142748i
$849$	2.62571	−	8.94236i	0.0901143	−	0.306901i
$850$	7.20141			0.247006
$851$	−11.5388	+	51.4382i	−0.395546	+	1.76328i
$852$			14.0379i			0.480930i
$853$	−1.78773	+	6.08846i	−0.0612108	+	0.208465i	−0.984420	−	0.175833i	$-0.943738\pi$
$853$	−1.78773	+	6.08846i	−0.0612108	+	0.208465i	0.923209	+	0.384298i	$0.125556\pi$
$854$	17.3503	+	4.35719i	0.593714	+	0.149100i
$855$	−19.7580	−	12.6977i	−0.675710	−	0.434253i
$856$	−1.58304	−	0.227606i	−0.0541071	−	0.00777942i
$857$	17.6359	+	27.4420i	0.602430	+	0.937399i	0.999805	+	0.0197431i	$0.00628485\pi$
$857$	17.6359	+	27.4420i	0.602430	+	0.937399i	−0.397375	+	0.917656i	$0.630079\pi$
$858$	0.303809	−	0.138745i	0.0103719	−	0.00473667i
$859$	−42.2014	+	36.5677i	−1.43989	+	1.24767i	−0.520773	+	0.853695i	$0.674356\pi$
$859$	−42.2014	+	36.5677i	−1.43989	+	1.24767i	−0.919120	+	0.393979i	$0.871098\pi$
$860$	29.7099	−	4.27164i	1.01310	−	0.145662i
$861$	14.7030	−	0.581906i	0.501078	−	0.0198313i
$862$	3.77711	+	12.8636i	0.128649	+	0.438138i
$863$	22.4118	−	6.58069i	0.762906	−	0.224009i	0.122941	−	0.992414i	$-0.460767\pi$
$863$	22.4118	−	6.58069i	0.762906	−	0.224009i	0.639964	+	0.768405i	$0.278949\pi$
$864$	−0.909632	−	0.415415i	−0.0309463	−	0.0141327i
$865$	−73.7810	+	10.6081i	−2.50863	+	0.360686i
$866$	6.21653	+	7.17426i	0.211246	+	0.243791i
$867$	−14.7718	+	6.74607i	−0.501678	+	0.229109i
$868$	13.4286	−	22.8328i	0.455795	−	0.774997i
$869$	3.41376	−	23.7432i	0.115804	−	0.805433i
$870$	−12.9676	+	20.1780i	−0.439644	+	0.684099i
$871$	−0.466817	+	0.538736i	−0.0158175	+	0.0182544i
$872$	3.42901	−	11.6781i	0.116121	−	0.395471i
$873$	−5.90282			−0.199780
$874$	29.0543	−	10.6230i	0.982778	−	0.359330i
$875$	14.1526	+	28.0030i	0.478446	+	0.946674i
$876$	−10.2567	−	3.01164i	−0.346542	−	0.101754i
$877$	−1.34367	+	1.55067i	−0.0453724	+	0.0523625i	−0.777982	−	0.628286i	$-0.783757\pi$
$877$	−1.34367	+	1.55067i	−0.0453724	+	0.0523625i	0.732610	+	0.680649i	$0.238302\pi$
$878$	5.32064	−	8.27908i	0.179563	−	0.279406i
$879$	−18.0570	−	2.59621i	−0.609048	−	0.0875678i
$880$	−4.82862	−	7.51348i	−0.162773	−	0.253279i
$881$	16.7220	+	36.6160i	0.563378	+	1.23363i	0.950249	+	0.311492i	$0.100829\pi$
$881$	16.7220	+	36.6160i	0.563378	+	1.23363i	−0.386871	+	0.922134i	$0.626444\pi$
$882$	6.97811	−	0.553215i	0.234965	−	0.0186277i
$883$	6.53889	+	45.4790i	0.220051	+	1.53049i	0.737836	+	0.674980i	$0.235848\pi$
$883$	6.53889	+	45.4790i	0.220051	+	1.53049i	−0.517785	+	0.855511i	$0.673243\pi$
$884$	−0.108019	−	0.0493308i	−0.00363308	−	0.00165917i
$885$	−4.19540	+	1.23188i	−0.141027	+	0.0414093i
$886$	5.93157	−	1.74167i	0.199275	−	0.0585124i
$887$	−11.6885	−	5.33795i	−0.392461	−	0.179231i	0.209403	−	0.977829i	$-0.432848\pi$
$887$	−11.6885	−	5.33795i	−0.392461	−	0.179231i	−0.601864	+	0.798598i	$0.705575\pi$
$888$	1.56435	+	10.8803i	0.0524960	+	0.365118i
$889$	−15.6300	+	38.1498i	−0.524215	+	1.27950i
$890$	−18.6802	−	40.9040i	−0.626163	−	1.37111i
$891$	1.32617	+	2.06356i	0.0444284	+	0.0691319i
$892$	−1.23676	−	0.177819i	−0.0414097	−	0.00595381i
$893$	34.9786	−	54.4277i	1.17051	−	1.82135i
$894$	3.13072	−	3.61305i	0.104707	−	0.120838i
$895$	−49.4232	−	14.5119i	−1.65203	−	0.485081i
$896$	1.19340	+	2.36131i	0.0398687	+	0.0788859i
$897$	−0.651617	+	0.0423679i	−0.0217568	+	0.00141462i
$898$	−20.3045			−0.677570
$899$	−18.5815	+	63.2827i	−0.619727	+	2.11060i
$900$	5.40723	−	6.24028i	0.180241	−	0.208009i
$901$	2.99309	−	4.65734i	0.0997144	−	0.155159i
$902$	1.94150	−	13.5035i	0.0646450	−	0.449616i
$903$	18.8003	+	11.0569i	0.625635	+	0.367952i
$904$	13.8829	−	6.34012i	0.461739	−	0.210869i
$905$	35.2556	+	40.6871i	1.17194	+	1.35249i
$906$	17.8671	−	2.56891i	0.593596	−	0.0853462i
$907$	36.8695	+	16.8377i	1.22423	+	0.559087i	0.919402	−	0.393320i	$-0.128674\pi$
$907$	36.8695	+	16.8377i	1.22423	+	0.559087i	0.304828	+	0.952407i	$0.401401\pi$
$908$	−13.6509	+	4.00825i	−0.453020	+	0.133019i
$909$	−2.74231	−	9.33947i	−0.0909568	−	0.309771i
$910$	−0.0518708	−	1.31062i	−0.00171950	−	0.0434467i
$911$	9.63008	−	1.38460i	0.319059	−	0.0458737i	0.0190750	−	0.999818i	$-0.493928\pi$
$911$	9.63008	−	1.38460i	0.319059	−	0.0458737i	0.299984	+	0.953944i	$0.403019\pi$
$912$	4.87496	−	4.22417i	0.161426	−	0.139876i
$913$	17.6121	−	8.04317i	0.582875	−	0.266190i
$914$	−5.30091	−	8.24838i	−0.175339	−	0.272832i
$915$	24.3679	+	3.50358i	0.805579	+	0.115825i
$916$	−15.4108	−	9.90395i	−0.509189	−	0.327236i
$917$	−13.4696	+	53.6360i	−0.444807	+	1.77122i
$918$	0.245713	−	0.836822i	0.00810975	−	0.0276193i
$919$			36.5490i			1.20564i	0.797877	+	0.602820i	$0.205956\pi$
$919$			36.5490i			1.20564i	−0.797877	+	0.602820i	$0.794044\pi$
$920$	3.60126	+	17.0864i	0.118730	+	0.563320i
$921$	−12.7071			−0.418715
$922$	1.09870	−	3.74183i	0.0361838	−	0.123231i
$923$	1.44452	+	1.25169i	0.0475470	+	0.0411997i
$924$	0.668849	−	6.45536i	0.0220035	−	0.212366i
$925$	−89.8392	−	12.9169i	−2.95389	−	0.424706i
$926$	−12.4498	+	8.00102i	−0.409127	+	0.262930i
$927$	4.05220	+	8.87307i	0.133092	+	0.291430i
$928$	−4.31396	−	4.97858i	−0.141613	−	0.163430i
$929$	−10.2729	+	1.47702i	−0.337043	+	0.0484594i	−0.308758	−	0.951140i	$-0.599913\pi$
$929$	−10.2729	+	1.47702i	−0.337043	+	0.0484594i	−0.0282843	+	0.999600i	$0.509004\pi$
$930$	15.1433	−	33.1593i	0.496570	−	1.08734i
$931$	−15.4527	+	42.4270i	−0.506442	+	1.39049i
$932$	−4.51535	+	1.32583i	−0.147905	+	0.0434288i
$933$	9.65993	−	21.1523i	0.316252	−	0.692495i
$934$	0.230756	+	1.60494i	0.00755057	+	0.0525154i
$935$	5.88686	−	5.10099i	0.192521	−	0.166820i
$936$	−0.123854	+	0.0565622i	−0.00404829	+	0.00184879i
$937$	−11.6043	+	7.45764i	−0.379097	+	0.243631i	−0.716287	−	0.697806i	$-0.754160\pi$
$937$	−11.6043	+	7.45764i	−0.379097	+	0.243631i	0.337190	+	0.941437i	$0.390523\pi$
$938$	4.42501	+	13.1259i	0.144482	+	0.428575i
$939$	−2.50544	+	3.89854i	−0.0817620	+	0.127224i
$940$	27.5995	+	23.9151i	0.900198	+	0.780026i
$941$	−39.5120	−	11.6018i	−1.28806	−	0.378207i	−0.435190	−	0.900338i	$-0.643319\pi$
$941$	−39.5120	−	11.6018i	−1.28806	−	0.378207i	−0.852865	+	0.522131i	$0.825137\pi$
$942$		−	5.92006i		−	0.192886i
$943$	−12.9339	+	23.3266i	−0.421187	+	0.759617i
$944$		−	1.20090i		−	0.0390861i
$945$	9.47352	−	1.74696i	0.308174	−	0.0568287i
$946$	13.2422	−	15.2823i	0.430541	−	0.496871i
$947$	−12.1846	−	7.83055i	−0.395945	−	0.254459i	0.327485	−	0.944857i	$-0.393799\pi$
$947$	−12.1846	−	7.83055i	−0.395945	−	0.254459i	−0.723430	+	0.690398i	$0.757435\pi$
$948$	−1.39169	+	9.67941i	−0.0451999	+	0.314372i
$949$	−1.22444	+	0.786900i	−0.0397470	+	0.0255438i
$950$	22.1259	+	48.4490i	0.717859	+	1.57189i
$951$	−11.3336	+	9.82063i	−0.367517	+	0.318456i
$952$	−1.89033	+	1.32332i	−0.0612661	+	0.0428889i
$953$	8.19526	+	3.74265i	0.265470	+	0.121236i	0.543704	−	0.839277i	$-0.317022\pi$
$953$	8.19526	+	3.74265i	0.265470	+	0.121236i	−0.278233	+	0.960514i	$0.589749\pi$
$954$	−1.78837	−	6.09062i	−0.0579005	−	0.197191i
$955$	21.7480	+	74.0668i	0.703748	+	2.39674i
$956$	−4.53439	+	9.92893i	−0.146653	+	0.321125i
$957$	2.29968	+	15.9947i	0.0743382	+	0.517034i
$958$	−17.5772	−	20.2852i	−0.567894	−	0.655385i
$959$	−18.2691	−	14.6063i	−0.589941	−	0.471663i
$960$	1.96849	+	3.06303i	0.0635327	+	0.0988587i
$961$	9.85356	−	68.5330i	0.317857	−	2.21074i
$962$	1.25908	+	0.809163i	0.0405944	+	0.0260885i
$963$	−1.20868	−	1.04733i	−0.0389492	−	0.0337497i
$964$	4.60816	+	1.35308i	0.148419	+	0.0435797i
$965$	−15.1891			−0.488953
$966$	−5.70928	+	11.3316i	−0.183693	+	0.364587i
$967$	6.73600			0.216615			0.108308	−	0.994117i	$-0.465457\pi$
$967$	6.73600			0.216615			0.108308	+	0.994117i	$0.465457\pi$
$968$	4.78114	+	1.40387i	0.153672	+	0.0451221i
$969$	4.25170	+	3.68412i	0.136584	+	0.118351i
$970$	18.0805	+	11.6196i	0.580530	+	0.373084i
$971$	3.17107	−	22.0553i	0.101764	−	0.707787i	−0.873513	−	0.486802i	$-0.838163\pi$
$971$	3.17107	−	22.0553i	0.101764	−	0.707787i	0.975277	−	0.220986i	$-0.0709274\pi$
$972$	−0.540641	−	0.841254i	−0.0173411	−	0.0269832i
$973$	16.4924	+	13.1858i	0.528721	+	0.422718i
$974$	15.7468	+	18.1728i	0.504561	+	0.582294i
$975$	−0.160000	−	1.11283i	−0.00512411	−	0.0356389i
$976$	−2.80879	+	6.15040i	−0.0899073	+	0.196870i
$977$	4.28653	+	14.5986i	0.137138	+	0.467050i	0.999210	−	0.0397358i	$-0.0126516\pi$
$977$	4.28653	+	14.5986i	0.137138	+	0.467050i	−0.862072	+	0.506786i	$0.830833\pi$
$978$	0.695109	+	2.36732i	0.0222271	+	0.0756986i
$979$	−27.5570	−	12.5849i	−0.880726	−	0.402214i
$980$	−22.4631	−	12.0418i	−0.717558	−	0.384661i
$981$	9.19833	−	7.97040i	0.293680	−	0.254475i
$982$	3.65325	+	7.99950i	0.116580	+	0.255274i
$983$	−3.62274	+	2.32819i	−0.115547	+	0.0742578i	−0.597138	−	0.802138i	$-0.703696\pi$
$983$	−3.62274	+	2.32819i	−0.115547	+	0.0742578i	0.481591	+	0.876396i	$0.340059\pi$
$984$	−0.791494	+	5.50496i	−0.0252319	+	0.175492i
$985$	25.7871	+	16.5724i	0.821645	+	0.528039i
$986$	3.76243	−	4.34207i	0.119820	−	0.138280i
$987$	4.81239	+	26.0968i	0.153180	+	0.830672i
$988$		−	0.878288i		−	0.0279421i
$989$	−34.8212	+	18.7223i	−1.10725	+	0.595334i
$990$		−	8.93129i		−	0.283855i
$991$	19.3716	+	5.68802i	0.615359	+	0.180686i	0.574534	−	0.818481i	$-0.305183\pi$
$991$	19.3716	+	5.68802i	0.615359	+	0.180686i	0.0408250	+	0.999166i	$0.487001\pi$
$992$	7.56647	+	6.55639i	0.240236	+	0.208166i
$993$	8.89647	−	13.8432i	0.282321	−	0.439300i
$994$	35.1946	−	11.8649i	1.11631	−	0.376331i
$995$	30.6745	−	19.7133i	0.972446	−	0.624953i
$996$	−7.17993	+	3.27897i	−0.227505	+	0.103898i
$997$	26.2970	−	22.7865i	0.832834	−	0.721655i	−0.130068	−	0.991505i	$-0.541520\pi$
$997$	26.2970	−	22.7865i	0.832834	−	0.721655i	0.962902	+	0.269850i	$0.0869742\pi$
$998$	−5.95434	−	41.4133i	−0.188481	−	1.31092i
$999$	−4.56631	+	9.99882i	−0.144472	+	0.316349i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.s.b.97.16	yes	160
7.6	odd	2	inner	966.2.s.b.97.1	✓	160
23.14	odd	22	inner	966.2.s.b.727.1	yes	160
161.83	even	22	inner	966.2.s.b.727.16	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.s.b.97.1	✓	160	7.6	odd	2	inner
966.2.s.b.97.16	yes	160	1.1	even	1	trivial
966.2.s.b.727.1	yes	160	23.14	odd	22	inner
966.2.s.b.727.16	yes	160	161.83	even	22	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)

\(f(q)\)	\(=\)	\(q+(0.959493 + 0.281733i) q^{2} +(0.755750 + 0.654861i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.518172 - 3.60397i) q^{5} +(0.540641 + 0.841254i) q^{6} +(1.65217 - 2.06648i) q^{7} +(0.654861 + 0.755750i) q^{8} +(0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.959493 + 0.281733i) q^{2} +(0.755750 + 0.654861i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.518172 - 3.60397i) q^{5} +(0.540641 + 0.841254i) q^{6} +(1.65217 - 2.06648i) q^{7} +(0.654861 + 0.755750i) q^{8} +(0.142315 + 0.989821i) q^{9} +(1.51254 - 3.31199i) q^{10} +(-0.691079 - 2.35360i) q^{11} +(0.281733 + 0.959493i) q^{12} +(0.123854 + 0.0565622i) q^{13} +(2.16744 - 1.51730i) q^{14} +(2.75170 - 2.38437i) q^{15} +(0.415415 + 0.909632i) q^{16} +(-0.733700 + 0.471520i) q^{17} +(-0.142315 + 0.989821i) q^{18} +(-5.42650 - 3.48740i) q^{19} +(2.38437 - 2.75170i) q^{20} +(2.60188 - 0.479800i) q^{21} -2.45296i q^{22} +(-1.70502 + 4.48251i) q^{23} +1.00000i q^{24} +(-7.92260 - 2.32629i) q^{25} +(0.102902 + 0.0891647i) q^{26} +(-0.540641 + 0.841254i) q^{27} +(2.50712 - 0.845203i) q^{28} +(-5.54185 + 3.56153i) q^{29} +(3.31199 - 1.51254i) q^{30} +(7.56647 - 6.55639i) q^{31} +(0.142315 + 0.989821i) q^{32} +(1.01900 - 2.23129i) q^{33} +(-0.836822 + 0.245713i) q^{34} +(-6.59141 - 7.02515i) q^{35} +(-0.415415 + 0.909632i) q^{36} +(10.8803 - 1.56435i) q^{37} +(-4.22417 - 4.87496i) q^{38} +(0.0565622 + 0.123854i) q^{39} +(3.06303 - 1.96849i) q^{40} +(5.50496 + 0.791494i) q^{41} +(2.63166 + 0.272670i) q^{42} +(6.23016 + 5.39846i) q^{43} +(0.691079 - 2.35360i) q^{44} +3.64103 q^{45} +(-2.89882 + 3.82058i) q^{46} +10.0300i q^{47} +(-0.281733 + 0.959493i) q^{48} +(-1.54067 - 6.82835i) q^{49} +(-6.94629 - 4.46411i) q^{50} +(-0.863273 - 0.124120i) q^{51} +(0.0736128 + 0.114544i) q^{52} +(-5.77411 + 2.63695i) q^{53} +(-0.755750 + 0.654861i) q^{54} +(-8.84038 + 1.27106i) q^{55} +(2.64368 - 0.104630i) q^{56} +(-1.81731 - 6.18920i) q^{57} +(-6.32076 + 1.85594i) q^{58} +(-1.09238 - 0.498873i) q^{59} +(3.60397 - 0.518172i) q^{60} +(4.42779 + 5.10994i) q^{61} +(9.10713 - 4.15909i) q^{62} +(2.28057 + 1.34126i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(0.268026 - 0.417057i) q^{65} +(1.60635 - 1.85382i) q^{66} +(-1.47500 + 5.02337i) q^{67} -0.872151 q^{68} +(-4.22399 + 2.27111i) q^{69} +(-4.34520 - 8.59760i) q^{70} +(13.4693 + 3.95493i) q^{71} +(-0.654861 + 0.755750i) q^{72} +(-5.77930 + 8.99276i) q^{73} +(10.8803 + 1.56435i) q^{74} +(-4.46411 - 6.94629i) q^{75} +(-2.67963 - 5.86757i) q^{76} +(-6.00544 - 2.46044i) q^{77} +(0.0193774 + 0.134772i) q^{78} +(8.89524 + 4.06232i) q^{79} +(3.49354 - 1.02580i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(5.05898 + 2.31036i) q^{82} +(1.12332 + 7.81289i) q^{83} +(2.44824 + 1.00305i) q^{84} +(1.31916 + 2.88856i) q^{85} +(4.45687 + 6.93502i) q^{86} +(-6.52055 - 0.937514i) q^{87} +(1.32617 - 2.06356i) q^{88} +(8.08770 - 9.33371i) q^{89} +(3.49354 + 1.02580i) q^{90} +(0.321512 - 0.162491i) q^{91} +(-3.85778 + 2.84913i) q^{92} +10.0119 q^{93} +(-2.82577 + 9.62370i) q^{94} +(-15.3803 + 17.7498i) q^{95} +(-0.540641 + 0.841254i) q^{96} +(-0.840059 + 5.84274i) q^{97} +(0.445503 - 6.98581i) q^{98} +(2.23129 - 1.01900i) 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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