LMFDB - Embedded newform 966.2.s.a.97.7

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			97.7
Character	$\chi$	$=$	966.97
Dual form			966.2.s.a.727.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 - 0.281733i) q^{2} +(-0.755750 - 0.654861i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.286709 - 1.99411i) q^{5} +(0.540641 + 0.841254i) q^{6} +(-2.61261 - 0.417427i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.959493 - 0.281733i) q^{2} +(-0.755750 - 0.654861i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.286709 - 1.99411i) q^{5} +(0.540641 + 0.841254i) q^{6} +(-2.61261 - 0.417427i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.142315 + 0.989821i) q^{9} +(-0.836900 + 1.83256i) q^{10} +(1.11026 + 3.78120i) q^{11} +(-0.281733 - 0.959493i) q^{12} +(4.06031 + 1.85428i) q^{13} +(2.38918 + 1.13658i) q^{14} +(-1.52254 + 1.31929i) q^{15} +(0.415415 + 0.909632i) q^{16} +(2.72263 - 1.74973i) q^{17} +(0.142315 - 0.989821i) q^{18} +(3.13503 + 2.01476i) q^{19} +(1.31929 - 1.52254i) q^{20} +(1.70113 + 2.02637i) q^{21} -3.94083i q^{22} +(-0.676160 - 4.74793i) q^{23} +1.00000i q^{24} +(0.903208 + 0.265206i) q^{25} +(-3.37343 - 2.92309i) q^{26} +(0.540641 - 0.841254i) q^{27} +(-1.97219 - 1.76365i) q^{28} +(5.74713 - 3.69346i) q^{29} +(1.83256 - 0.836900i) q^{30} +(0.313818 - 0.271924i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(1.63708 - 3.58470i) q^{33} +(-3.10530 + 0.911798i) q^{34} +(-1.58145 + 5.09015i) q^{35} +(-0.415415 + 0.909632i) q^{36} +(-7.16191 + 1.02973i) q^{37} +(-2.44042 - 2.81639i) q^{38} +(-1.85428 - 4.06031i) q^{39} +(-1.69480 + 1.08918i) q^{40} +(-0.634378 - 0.0912098i) q^{41} +(-1.06132 - 2.42355i) q^{42} +(-7.60846 - 6.59277i) q^{43} +(-1.11026 + 3.78120i) q^{44} +2.01461 q^{45} +(-0.688875 + 4.74610i) q^{46} -7.63441i q^{47} +(0.281733 - 0.959493i) q^{48} +(6.65151 + 2.18115i) q^{49} +(-0.791905 - 0.508926i) q^{50} +(-3.20345 - 0.460587i) q^{51} +(2.41325 + 3.75509i) q^{52} +(7.22190 - 3.29813i) q^{53} +(-0.755750 + 0.654861i) q^{54} +(7.85843 - 1.12987i) q^{55} +(1.39543 + 2.24784i) q^{56} +(-1.04991 - 3.57567i) q^{57} +(-6.55490 + 1.92469i) q^{58} +(-3.43221 - 1.56744i) q^{59} +(-1.99411 + 0.286709i) q^{60} +(-1.85829 - 2.14459i) q^{61} +(-0.377716 + 0.172497i) q^{62} +(0.0413642 - 2.64543i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(4.86176 - 7.56505i) q^{65} +(-2.58069 + 2.97828i) q^{66} +(-2.97423 + 10.1293i) q^{67} +3.23639 q^{68} +(-2.59822 + 4.03103i) q^{69} +(2.95145 - 4.43842i) q^{70} +(7.58801 + 2.22804i) q^{71} +(0.654861 - 0.755750i) q^{72} +(-5.14835 + 8.01099i) q^{73} +(7.16191 + 1.02973i) q^{74} +(-0.508926 - 0.791905i) q^{75} +(1.54809 + 3.38985i) q^{76} +(-1.32231 - 10.3423i) q^{77} +(0.635248 + 4.41825i) q^{78} +(-1.44542 - 0.660100i) q^{79} +(1.93301 - 0.567582i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(0.582985 + 0.266240i) q^{82} +(-0.973229 - 6.76895i) q^{83} +(0.335541 + 2.62439i) q^{84} +(-2.70854 - 5.93087i) q^{85} +(5.44286 + 8.46926i) q^{86} +(-6.76210 - 0.972243i) q^{87} +(2.13057 - 3.31524i) q^{88} +(11.1224 - 12.8359i) q^{89} +(-1.93301 - 0.567582i) q^{90} +(-9.83399 - 6.53940i) q^{91} +(1.99810 - 4.35977i) q^{92} -0.415240 q^{93} +(-2.15086 + 7.32517i) q^{94} +(4.91649 - 5.67394i) q^{95} +(-0.540641 + 0.841254i) q^{96} +(2.20348 - 15.3255i) q^{97} +(-5.76758 - 3.96675i) q^{98} +(-3.58470 + 1.63708i) 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 $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

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

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
$5$	0.286709	−	1.99411i	0.128220	−	0.891791i	−0.819589	−	0.572952i	$-0.805798\pi$
$5$	0.286709	−	1.99411i	0.128220	−	0.891791i	0.947809	−	0.318839i	$-0.103293\pi$
$6$	0.540641	+	0.841254i	0.220716	+	0.343440i
$7$	−2.61261	−	0.417427i	−0.987475	−	0.157772i
$7$	−2.61261	−	0.417427i	−0.987475	−	0.157772i
$8$	−0.654861	−	0.755750i	−0.231528	−	0.267198i
$9$	0.142315	+	0.989821i	0.0474383	+	0.329940i
$10$	−0.836900	+	1.83256i	−0.264651	+	0.579505i
$11$	1.11026	+	3.78120i	0.334756	+	1.14007i	0.939184	+	0.343414i	$0.111583\pi$
$11$	1.11026	+	3.78120i	0.334756	+	1.14007i	−0.604428	+	0.796660i	$0.706598\pi$
$12$	−0.281733	−	0.959493i	−0.0813292	−	0.276982i
$13$	4.06031	+	1.85428i	1.12613	+	0.514285i	0.889326	−	0.457273i	$-0.151174\pi$
$13$	4.06031	+	1.85428i	1.12613	+	0.514285i	0.236801	+	0.971558i	$0.423901\pi$
$14$	2.38918	+	1.13658i	0.638536	+	0.303763i
$15$	−1.52254	+	1.31929i	−0.393119	+	0.340639i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	2.72263	−	1.74973i	0.660334	−	0.424371i	−0.167095	−	0.985941i	$-0.553439\pi$
$17$	2.72263	−	1.74973i	0.660334	−	0.424371i	0.827429	+	0.561570i	$0.189802\pi$
$18$	0.142315	−	0.989821i	0.0335439	−	0.233303i
$19$	3.13503	+	2.01476i	0.719226	+	0.462218i	0.848367	−	0.529408i	$-0.177586\pi$
$19$	3.13503	+	2.01476i	0.719226	+	0.462218i	−0.129142	+	0.991626i	$0.541222\pi$
$20$	1.31929	−	1.52254i	0.295002	−	0.340451i
$21$	1.70113	+	2.02637i	0.371216	+	0.442190i
$22$		−	3.94083i		−	0.840188i
$23$	−0.676160	−	4.74793i	−0.140989	−	0.990011i
$23$	−0.676160	−	4.74793i	−0.140989	−	0.990011i
$24$			1.00000i			0.204124i
$25$	0.903208	+	0.265206i	0.180642	+	0.0530412i
$26$	−3.37343	−	2.92309i	−0.661583	−	0.573265i
$27$	0.540641	−	0.841254i	0.104046	−	0.161899i
$28$	−1.97219	−	1.76365i	−0.372709	−	0.333298i
$29$	5.74713	−	3.69346i	1.06722	−	0.685858i	0.115646	−	0.993290i	$-0.463106\pi$
$29$	5.74713	−	3.69346i	1.06722	−	0.685858i	0.951570	+	0.307432i	$0.0994698\pi$
$30$	1.83256	−	0.836900i	0.334577	−	0.152796i
$31$	0.313818	−	0.271924i	0.0563633	−	0.0488391i	−0.626224	−	0.779643i	$-0.715400\pi$
$31$	0.313818	−	0.271924i	0.0563633	−	0.0488391i	0.682587	+	0.730804i	$0.260855\pi$
$32$	−0.142315	−	0.989821i	−0.0251579	−	0.174977i
$33$	1.63708	−	3.58470i	0.284979	−	0.624017i
$34$	−3.10530	+	0.911798i	−0.532554	+	0.156372i
$35$	−1.58145	+	5.09015i	−0.267314	+	0.860392i
$36$	−0.415415	+	0.909632i	−0.0692358	+	0.151605i
$37$	−7.16191	+	1.02973i	−1.17741	+	0.169286i	−0.703113	−	0.711078i	$-0.748207\pi$
$37$	−7.16191	+	1.02973i	−1.17741	+	0.169286i	−0.474298	+	0.880364i	$0.657298\pi$
$38$	−2.44042	−	2.81639i	−0.395888	−	0.456879i
$39$	−1.85428	−	4.06031i	−0.296923	−	0.650170i
$40$	−1.69480	+	1.08918i	−0.267971	+	0.172215i
$41$	−0.634378	−	0.0912098i	−0.0990732	−	0.0142446i	0.0925999	−	0.995703i	$-0.470482\pi$
$41$	−0.634378	−	0.0912098i	−0.0990732	−	0.0142446i	−0.191673	+	0.981459i	$0.561391\pi$
$42$	−1.06132	−	2.42355i	−0.163766	−	0.373962i
$43$	−7.60846	−	6.59277i	−1.16028	−	1.00539i	−0.999832	−	0.0183430i	$-0.994161\pi$
$43$	−7.60846	−	6.59277i	−1.16028	−	1.00539i	−0.160447	−	0.987044i	$-0.551294\pi$
$44$	−1.11026	+	3.78120i	−0.167378	+	0.570037i
$45$	2.01461			0.300321
$46$	−0.688875	+	4.74610i	−0.101569	+	0.699774i
$47$		−	7.63441i		−	1.11359i	−0.830649	−	0.556797i	$-0.812030\pi$
$47$		−	7.63441i		−	1.11359i	0.830649	−	0.556797i	$-0.187970\pi$
$48$	0.281733	−	0.959493i	0.0406646	−	0.138491i
$49$	6.65151	+	2.18115i	0.950216	+	0.311593i
$50$	−0.791905	−	0.508926i	−0.111992	−	0.0719730i
$51$	−3.20345	−	0.460587i	−0.448573	−	0.0644951i
$52$	2.41325	+	3.75509i	0.334657	+	0.520737i
$53$	7.22190	−	3.29813i	0.992004	−	0.453033i	0.147778	−	0.989021i	$-0.452788\pi$
$53$	7.22190	−	3.29813i	0.992004	−	0.453033i	0.844226	+	0.535988i	$0.180061\pi$
$54$	−0.755750	+	0.654861i	−0.102844	+	0.0891153i
$55$	7.85843	−	1.12987i	1.05963	−	0.152352i
$56$	1.39543	+	2.24784i	0.186472	+	0.300380i
$57$	−1.04991	−	3.57567i	−0.139064	−	0.473608i
$58$	−6.55490	+	1.92469i	−0.860701	+	0.252725i
$59$	−3.43221	−	1.56744i	−0.446835	−	0.204063i	0.179272	−	0.983799i	$-0.442626\pi$
$59$	−3.43221	−	1.56744i	−0.446835	−	0.204063i	−0.626108	+	0.779737i	$0.715353\pi$
$60$	−1.99411	+	0.286709i	−0.257438	+	0.0370140i
$61$	−1.85829	−	2.14459i	−0.237930	−	0.274586i	0.624209	−	0.781257i	$-0.285421\pi$
$61$	−1.85829	−	2.14459i	−0.237930	−	0.274586i	−0.862139	+	0.506671i	$0.830876\pi$
$62$	−0.377716	+	0.172497i	−0.0479699	+	0.0219071i
$63$	0.0413642	−	2.64543i	0.00521139	−	0.333293i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	4.86176	−	7.56505i	0.603027	−	0.938329i
$66$	−2.58069	+	2.97828i	−0.317661	+	0.366601i
$67$	−2.97423	+	10.1293i	−0.363360	+	1.23749i	0.551656	+	0.834072i	$0.313996\pi$
$67$	−2.97423	+	10.1293i	−0.363360	+	1.23749i	−0.915016	+	0.403418i	$0.867822\pi$
$68$	3.23639			0.392471
$69$	−2.59822	+	4.03103i	−0.312789	+	0.485280i
$70$	2.95145	−	4.43842i	0.352766	−	0.530492i
$71$	7.58801	+	2.22804i	0.900531	+	0.264420i	0.699050	−	0.715073i	$-0.253606\pi$
$71$	7.58801	+	2.22804i	0.900531	+	0.264420i	0.201481	+	0.979492i	$0.435425\pi$
$72$	0.654861	−	0.755750i	0.0771761	−	0.0890659i
$73$	−5.14835	+	8.01099i	−0.602569	+	0.937615i	0.397233	+	0.917718i	$0.369970\pi$
$73$	−5.14835	+	8.01099i	−0.602569	+	0.937615i	−0.999802	+	0.0198977i	$0.993666\pi$
$74$	7.16191	+	1.02973i	0.832556	+	0.119703i
$75$	−0.508926	−	0.791905i	−0.0587657	−	0.0914413i
$76$	1.54809	+	3.38985i	0.177579	+	0.388843i
$77$	−1.32231	−	10.3423i	−0.150691	−	1.17861i
$78$	0.635248	+	4.41825i	0.0719277	+	0.500268i
$79$	−1.44542	−	0.660100i	−0.162622	−	0.0742670i	0.332441	−	0.943124i	$-0.392128\pi$
$79$	−1.44542	−	0.660100i	−0.162622	−	0.0742670i	−0.495063	+	0.868857i	$0.664855\pi$
$80$	1.93301	−	0.567582i	0.216117	−	0.0634576i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	0.582985	+	0.266240i	0.0643799	+	0.0294013i
$83$	−0.973229	−	6.76895i	−0.106826	−	0.742989i	−0.970876	−	0.239583i	$-0.922989\pi$
$83$	−0.973229	−	6.76895i	−0.106826	−	0.742989i	0.864050	−	0.503406i	$-0.167920\pi$
$84$	0.335541	+	2.62439i	0.0366105	+	0.286344i
$85$	−2.70854	−	5.93087i	−0.293782	−	0.643293i
$86$	5.44286	+	8.46926i	0.586919	+	0.913264i
$87$	−6.76210	−	0.972243i	−0.724973	−	0.104235i
$88$	2.13057	−	3.31524i	0.227120	−	0.353405i
$89$	11.1224	−	12.8359i	1.17897	−	1.36061i	0.260326	−	0.965521i	$-0.416170\pi$
$89$	11.1224	−	12.8359i	1.17897	−	1.36061i	0.918645	−	0.395085i	$-0.129285\pi$
$90$	−1.93301	−	0.567582i	−0.203757	−	0.0598284i
$91$	−9.83399	−	6.53940i	−1.03088	−	0.685516i
$92$	1.99810	−	4.35977i	0.208316	−	0.454537i
$93$	−0.415240			−0.0430584
$94$	−2.15086	+	7.32517i	−0.221845	+	0.755533i
$95$	4.91649	−	5.67394i	0.504422	−	0.582133i
$96$	−0.540641	+	0.841254i	−0.0551789	+	0.0858601i
$97$	2.20348	−	15.3255i	0.223729	−	1.55607i	−0.500024	−	0.866011i	$-0.666676\pi$
$97$	2.20348	−	15.3255i	0.223729	−	1.55607i	0.723753	−	0.690059i	$-0.242415\pi$
$98$	−5.76758	−	3.96675i	−0.582613	−	0.400702i
$99$	−3.58470	+	1.63708i	−0.360276	+	0.164533i
$100$	0.616446	+	0.711416i	0.0616446	+	0.0711416i
$101$	14.5800	−	2.09629i	1.45077	−	0.208589i	0.628554	−	0.777766i	$-0.283647\pi$
$101$	14.5800	−	2.09629i	1.45077	−	0.208589i	0.822215	+	0.569177i	$0.192738\pi$
$102$	2.94393	+	1.34445i	0.291492	+	0.133120i
$103$	17.2774	−	5.07311i	1.70240	−	0.499868i	0.721174	−	0.692754i	$-0.243603\pi$
$103$	17.2774	−	5.07311i	1.70240	−	0.499868i	0.981221	+	0.192885i	$0.0617845\pi$
$104$	−1.25756	−	4.28287i	−0.123314	−	0.419970i
$105$	4.52852	−	2.81125i	0.441939	−	0.274350i
$106$	−7.85855	+	1.12989i	−0.763290	+	0.109745i
$107$	−2.12985	+	1.84553i	−0.205901	+	0.178414i	−0.751707	−	0.659498i	$-0.770769\pi$
$107$	−2.12985	+	1.84553i	−0.205901	+	0.178414i	0.545806	+	0.837912i	$0.316224\pi$
$108$	0.909632	−	0.415415i	0.0875294	−	0.0399733i
$109$	−5.17605	−	8.05410i	−0.495776	−	0.771443i	0.499726	−	0.866184i	$-0.333434\pi$
$109$	−5.17605	−	8.05410i	−0.495776	−	0.771443i	−0.995502	+	0.0947410i	$0.969798\pi$
$110$	−7.85843	−	1.12987i	−0.749272	−	0.107729i
$111$	6.08694	+	3.91184i	0.577747	+	0.371295i
$112$	−0.705615	−	2.54992i	−0.0666743	−	0.240945i
$113$	−4.81456	+	16.3969i	−0.452916	+	1.54249i	0.344338	+	0.938846i	$0.388103\pi$
$113$	−4.81456	+	16.3969i	−0.452916	+	1.54249i	−0.797254	+	0.603644i	$0.793715\pi$
$114$			3.72662i			0.349030i
$115$	−9.66173	−	0.0129390i	−0.900961	−	0.00120657i
$116$	6.83163			0.634301
$117$	−1.25756	+	4.28287i	−0.116262	+	0.395952i
$118$	2.85158	+	2.47091i	0.262509	+	0.227465i
$119$	−7.84356	+	3.43486i	−0.719018	+	0.314874i
$120$	1.99411	+	0.286709i	0.182036	+	0.0261728i
$121$	−3.81099	+	2.44917i	−0.346454	+	0.222652i
$122$	1.17882	+	2.58126i	0.106725	+	0.233696i
$123$	0.419701	+	0.484361i	0.0378432	+	0.0436734i
$124$	0.411014	−	0.0590948i	0.0369101	−	0.00530687i
$125$	4.97231	−	10.8878i	0.444737	−	0.973837i
$126$	−0.784992	+	2.52662i	−0.0699326	+	0.225089i
$127$	6.43149	−	1.88846i	0.570702	−	0.167573i	0.0163660	−	0.999866i	$-0.494790\pi$
$127$	6.43149	−	1.88846i	0.570702	−	0.167573i	0.554336	+	0.832293i	$0.312972\pi$
$128$	0.415415	−	0.909632i	0.0367178	−	0.0804009i
$129$	1.43275	+	9.96496i	0.126146	+	0.877366i
$130$	−6.79614	+	5.88889i	−0.596061	+	0.516490i
$131$	−3.94387	+	1.80110i	−0.344577	+	0.157363i	−0.580184	−	0.814485i	$-0.697019\pi$
$131$	−3.94387	+	1.80110i	−0.344577	+	0.157363i	0.235607	+	0.971848i	$0.424292\pi$
$132$	3.31524	−	2.13057i	0.288554	−	0.185443i
$133$	−7.34961	−	6.57244i	−0.637292	−	0.569903i
$134$	5.70750	−	8.88104i	0.493053	−	0.767205i
$135$	−1.52254	−	1.31929i	−0.131040	−	0.113546i
$136$	−3.10530	−	0.911798i	−0.266277	−	0.0781860i
$137$		−	10.9789i		−	0.937992i	−0.883200	−	0.468996i	$-0.844616\pi$
$137$		−	10.9789i		−	0.937992i	0.883200	−	0.468996i	$-0.155384\pi$
$138$	3.62865	−	3.13575i	0.308891	−	0.266932i
$139$		−	16.5053i		−	1.39996i	−0.714163	−	0.699980i	$-0.753192\pi$
$139$		−	16.5053i		−	1.39996i	0.714163	−	0.699980i	$-0.246808\pi$
$140$	−4.08235	+	3.42711i	−0.345021	+	0.289644i
$141$	−4.99948	+	5.76971i	−0.421032	+	0.485897i
$142$	−6.65293	−	4.27558i	−0.558302	−	0.358799i
$143$	−2.50340	+	17.4116i	−0.209345	+	1.45603i
$144$	−0.841254	+	0.540641i	−0.0701045	+	0.0450534i
$145$	−5.71739	−	12.5193i	−0.474804	−	1.03967i
$146$	7.19676	−	6.23603i	0.595608	−	0.516098i
$147$	−3.59853	−	6.00422i	−0.296801	−	0.495219i
$148$	−6.58170	−	3.00576i	−0.541012	−	0.247072i
$149$	3.40606	+	11.6000i	0.279036	+	0.950308i	0.973098	+	0.230393i	$0.0740012\pi$
$149$	3.40606	+	11.6000i	0.279036	+	0.950308i	−0.694062	+	0.719915i	$0.744181\pi$
$150$	0.265206	+	0.903208i	0.0216540	+	0.0737466i
$151$	−7.30167	+	15.9884i	−0.594202	+	1.30112i	0.338668	+	0.940906i	$0.390024\pi$
$151$	−7.30167	+	15.9884i	−0.594202	+	1.30112i	−0.932870	+	0.360214i	$0.882704\pi$
$152$	−0.530353	−	3.68869i	−0.0430173	−	0.299192i
$153$	2.11939	+	2.44590i	0.171342	+	0.197740i
$154$	−1.64501	+	10.2959i	−0.132558	+	0.829665i
$155$	−0.452272	−	0.703749i	−0.0363274	−	0.0565265i
$156$	0.635248	−	4.41825i	0.0508606	−	0.353743i
$157$	19.5886	+	12.5888i	1.56334	+	1.00470i	0.981515	+	0.191385i	$0.0612978\pi$
$157$	19.5886	+	12.5888i	1.56334	+	1.00470i	0.581826	+	0.813313i	$0.302339\pi$
$158$	1.20090	+	1.04058i	0.0955381	+	0.0827843i
$159$	−7.61776	−	2.23678i	−0.604128	−	0.177388i
$160$	−2.01461			−0.159269
$161$	−0.215366	+	12.6867i	−0.0169732	+	0.999856i
$162$	1.00000			0.0785674
$163$	21.0319	+	6.17552i	1.64735	+	0.483704i	0.968174	−	0.250276i	$-0.0805214\pi$
$163$	21.0319	+	6.17552i	1.64735	+	0.483704i	0.679171	+	0.733980i	$0.262340\pi$
$164$	−0.484361	−	0.419701i	−0.0378223	−	0.0327732i
$165$	−6.67891	−	4.29228i	−0.519953	−	0.334153i
$166$	−0.973229	+	6.76895i	−0.0755372	+	0.525373i
$167$	−1.23074	−	1.91507i	−0.0952377	−	0.148193i	0.790365	−	0.612636i	$-0.209891\pi$
$167$	−1.23074	−	1.91507i	−0.0952377	−	0.148193i	−0.885603	+	0.464443i	$0.846254\pi$
$168$	0.417427	−	2.61261i	0.0322052	−	0.201568i
$169$	4.53456	+	5.23316i	0.348812	+	0.402551i
$170$	0.927904	+	6.45371i	0.0711670	+	0.494977i
$171$	−1.54809	+	3.38985i	−0.118386	+	0.259228i
$172$	−2.83632	−	9.65963i	−0.216268	−	0.736540i
$173$	−2.15157	−	7.32756i	−0.163580	−	0.557104i	−0.999960	−	0.00895301i	$-0.997150\pi$
$173$	−2.15157	−	7.32756i	−0.163580	−	0.557104i	0.836379	−	0.548151i	$-0.184668\pi$
$174$	6.21427	+	2.83796i	0.471103	+	0.215145i
$175$	−2.24903	−	1.06990i	−0.170011	−	0.0808771i
$176$	−2.97828	+	2.58069i	−0.224496	+	0.194527i
$177$	1.56744	+	3.43221i	0.117816	+	0.257980i
$178$	−14.2882	+	9.18244i	−1.07094	+	0.688253i
$179$	−2.08152	+	14.4773i	−0.155580	+	1.08208i	0.751077	+	0.660215i	$0.229535\pi$
$179$	−2.08152	+	14.4773i	−0.155580	+	1.08208i	−0.906657	+	0.421868i	$0.861374\pi$
$180$	1.69480	+	1.08918i	0.126323	+	0.0811828i
$181$	−14.9986	+	17.3093i	−1.11484	+	1.28659i	−0.160773	+	0.986991i	$0.551399\pi$
$181$	−14.9986	+	17.3093i	−1.11484	+	1.28659i	−0.954065	+	0.299600i	$0.903147\pi$
$182$	7.59329	+	9.04507i	0.562852	+	0.670465i
$183$			2.83769i			0.209768i
$184$	−3.14545	+	3.62024i	−0.231886	+	0.266888i
$185$			14.5768i			1.07171i
$186$	0.398420	+	0.116987i	0.0292136	+	0.00857788i
$187$	9.63889	+	8.35214i	0.704865	+	0.610769i
$188$	4.12748	−	6.42248i	0.301027	−	0.468407i
$189$	−1.76365	+	1.97219i	−0.128287	+	0.143456i
$190$	−6.31587	+	4.05896i	−0.458202	+	0.294468i
$191$	8.90763	−	4.06798i	0.644534	−	0.294349i	−0.0662037	−	0.997806i	$-0.521089\pi$
$191$	8.90763	−	4.06798i	0.644534	−	0.294349i	0.710737	+	0.703457i	$0.248361\pi$
$192$	0.755750	−	0.654861i	0.0545415	−	0.0472605i
$193$	−0.0105782	−	0.0735732i	−0.000761437	−	0.00529591i	0.989437	−	0.144962i	$-0.0463061\pi$
$193$	−0.0105782	−	0.0735732i	−0.000761437	−	0.00529591i	−0.990199	+	0.139666i	$0.955397\pi$
$194$	−6.43192	+	14.0839i	−0.461785	+	1.01117i
$195$	−8.62832	+	2.53350i	−0.617887	+	0.181428i
$196$	4.41639	+	5.43098i	0.315456	+	0.387927i
$197$	7.00364	−	15.3358i	0.498988	−	1.09263i	−0.477808	−	0.878464i	$-0.658569\pi$
$197$	7.00364	−	15.3358i	0.498988	−	1.09263i	0.976797	−	0.214168i	$-0.0687040\pi$
$198$	3.90072	−	0.560838i	0.277212	−	0.0398571i
$199$	1.82158	+	2.10221i	0.129128	+	0.149022i	0.816632	−	0.577159i	$-0.195839\pi$
$199$	1.82158	+	2.10221i	0.129128	+	0.149022i	−0.687503	+	0.726181i	$0.741293\pi$
$200$	−0.391046	−	0.856272i	−0.0276512	−	0.0605476i
$201$	8.88104	−	5.70750i	0.626420	−	0.402576i
$202$	−14.5800	−	2.09629i	−1.02585	−	0.147495i
$203$	−16.5568	+	7.25058i	−1.16206	+	0.508891i
$204$	−2.44590	−	2.11939i	−0.171248	−	0.148387i
$205$	−0.363764	+	1.23887i	−0.0254064	+	0.0865262i
$206$	−18.0068			−1.25460
$207$	4.60337	−	1.34498i	0.319956	−	0.0934825i
$208$			4.46368i			0.309501i
$209$	−4.13752	+	14.0911i	−0.286198	+	0.974701i
$210$	−5.13711	+	1.42154i	−0.354494	+	0.0980955i
$211$	21.1036	+	13.5625i	1.45284	+	0.933680i	0.999094	+	0.0425465i	$0.0135471\pi$
$211$	21.1036	+	13.5625i	1.45284	+	0.933680i	0.453741	+	0.891134i	$0.350089\pi$
$212$	7.85855	+	1.12989i	0.539727	+	0.0776011i
$213$	−4.27558	−	6.65293i	−0.292958	−	0.455851i
$214$	2.56352	−	1.17072i	0.175239	−	0.0800289i
$215$	−15.3281	+	13.2819i	−1.04537	+	0.905816i
$216$	−0.989821	+	0.142315i	−0.0673488	+	0.00968330i
$217$	−0.933393	+	0.579438i	−0.0633628	+	0.0393348i
$218$	2.69729	+	9.18611i	0.182683	+	0.622162i
$219$	9.13695	−	2.68285i	0.617418	−	0.181290i
$220$	7.22179	+	3.29808i	0.486893	+	0.222356i
$221$	14.2992	−	2.05591i	0.961868	−	0.138296i
$222$	−4.73829	−	5.46827i	−0.318013	−	0.367006i
$223$	0.593212	−	0.270911i	0.0397244	−	0.0181415i	−0.395454	−	0.918486i	$-0.629413\pi$
$223$	0.593212	−	0.270911i	0.0397244	−	0.0181415i	0.435178	+	0.900344i	$0.356685\pi$
$224$	−0.0413642	+	2.64543i	−0.00276376	+	0.176755i
$225$	−0.133966	+	0.931757i	−0.00893110	+	0.0621172i
$226$	9.23908	−	14.3763i	0.614574	−	0.956296i
$227$	−12.6614	+	14.6121i	−0.840368	+	0.969836i	−0.999849	−	0.0173649i	$-0.994472\pi$
$227$	−12.6614	+	14.6121i	−0.840368	+	0.969836i	0.159481	+	0.987201i	$0.449018\pi$
$228$	1.04991	−	3.57567i	0.0695320	−	0.236804i
$229$	12.8375			0.848327			0.424163	−	0.905586i	$-0.360568\pi$
$229$	12.8375			0.848327			0.424163	+	0.905586i	$0.360568\pi$
$230$	9.26672	+	2.73444i	0.611029	+	0.180304i
$231$	−5.77341	+	8.68209i	−0.379862	+	0.571240i
$232$	−6.55490	−	1.92469i	−0.430350	−	0.126362i
$233$	−4.14720	+	4.78613i	−0.271692	+	0.313550i	−0.875156	−	0.483841i	$-0.839241\pi$
$233$	−4.14720	+	4.78613i	−0.271692	+	0.313550i	0.603464	+	0.797390i	$0.293787\pi$
$234$	2.41325	−	3.75509i	0.157759	−	0.245478i
$235$	−15.2238	−	2.18886i	−0.993093	−	0.142785i
$236$	−2.03993	−	3.17420i	−0.132788	−	0.206623i
$237$	0.660100	+	1.44542i	0.0428781	+	0.0938899i
$238$	8.49356	−	1.08594i	0.550555	−	0.0703911i
$239$	−0.751051	−	5.22367i	−0.0485814	−	0.337891i	−0.999588	−	0.0287191i	$-0.990857\pi$
$239$	−0.751051	−	5.22367i	−0.0485814	−	0.337891i	0.951006	−	0.309172i	$-0.100052\pi$
$240$	−1.83256	−	0.836900i	−0.118291	−	0.0540217i
$241$	−14.8576	+	4.36258i	−0.957062	+	0.281019i	−0.722724	−	0.691137i	$-0.757110\pi$
$241$	−14.8576	+	4.36258i	−0.957062	+	0.281019i	−0.234338	+	0.972155i	$0.575292\pi$
$242$	4.34663	−	1.27629i	0.279412	−	0.0820428i
$243$	0.909632	+	0.415415i	0.0583529	+	0.0266489i
$244$	−0.403846	−	2.80881i	−0.0258536	−	0.179816i
$245$	6.25649	−	12.6385i	0.399713	−	0.807442i
$246$	−0.266240	−	0.582985i	−0.0169749	−	0.0371697i
$247$	8.99326	+	13.9938i	0.572227	+	0.890403i
$248$	−0.411014	−	0.0590948i	−0.0260994	−	0.00375253i
$249$	−3.69721	+	5.75296i	−0.234301	+	0.364579i
$250$	−7.83835	+	9.04594i	−0.495741	+	0.572115i
$251$	−13.9919	−	4.10840i	−0.883162	−	0.259320i	−0.191458	−	0.981501i	$-0.561322\pi$
$251$	−13.9919	−	4.10840i	−0.883162	−	0.259320i	−0.691704	+	0.722181i	$0.743140\pi$
$252$	1.46502	−	2.20311i	0.0922878	−	0.138783i
$253$	17.2021	−	7.82813i	1.08149	−	0.492150i
$254$	−6.70301			−0.420584
$255$	−1.83692	+	6.25597i	−0.115032	+	0.391764i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	13.9087	−	21.6424i	0.867603	−	1.35002i	−0.0682648	−	0.997667i	$-0.521746\pi$
$257$	13.9087	−	21.6424i	0.867603	−	1.35002i	0.935868	−	0.352350i	$-0.114617\pi$
$258$	1.43275	−	9.96496i	0.0891988	−	0.620391i
$259$	19.1412	+	0.299293i	1.18937	+	0.0185972i
$260$	8.17995	−	3.73566i	0.507299	−	0.231676i
$261$	4.47377	+	5.16300i	0.276919	+	0.319582i
$262$	4.29154	−	0.617031i	0.265132	−	0.0381203i
$263$	−5.62874	−	2.57056i	−0.347083	−	0.158508i	0.234243	−	0.972178i	$-0.424739\pi$
$263$	−5.62874	−	2.57056i	−0.347083	−	0.158508i	−0.581326	+	0.813670i	$0.697466\pi$
$264$	−3.78120	+	1.11026i	−0.232717	+	0.0683318i
$265$	−4.50624	−	15.3468i	−0.276816	−	0.942748i
$266$	5.20023	+	8.37684i	0.318847	+	0.513617i
$267$	−16.8115	+	2.41713i	−1.02885	+	0.147926i
$268$	−7.97839	+	6.91331i	−0.487357	+	0.422298i
$269$	−14.0041	+	6.39546i	−0.853845	+	0.389938i	−0.793742	−	0.608254i	$-0.791870\pi$
$269$	−14.0041	+	6.39546i	−0.853845	+	0.389938i	−0.0601027	+	0.998192i	$0.519143\pi$
$270$	1.08918	+	1.69480i	0.0662855	+	0.103142i
$271$	−14.1770	−	2.03835i	−0.861194	−	0.123821i	−0.302454	−	0.953164i	$-0.597806\pi$
$271$	−14.1770	−	2.03835i	−0.861194	−	0.123821i	−0.558740	+	0.829343i	$0.688715\pi$
$272$	2.72263	+	1.74973i	0.165084	+	0.106093i
$273$	3.14964	+	11.3820i	0.190625	+	0.688873i
$274$	−3.09312	+	10.5342i	−0.186862	+	0.636394i
$275$			3.70966i			0.223701i
$276$	−4.36511	+	1.98642i	−0.262748	+	0.119568i
$277$	5.67918			0.341229			0.170614	−	0.985338i	$-0.445425\pi$
$277$	5.67918			0.341229			0.170614	+	0.985338i	$0.445425\pi$
$278$	−4.65008	+	15.8367i	−0.278893	+	0.949822i
$279$	0.313818	+	0.271924i	0.0187878	+	0.0162797i
$280$	4.88251	−	2.13816i	0.291786	−	0.127779i
$281$	−21.1346	−	3.03869i	−1.26078	−	0.181273i	−0.520671	−	0.853757i	$-0.674318\pi$
$281$	−21.1346	−	3.03869i	−1.26078	−	0.181273i	−0.740111	+	0.672484i	$0.765227\pi$
$282$	6.42248	−	4.12748i	0.382453	−	0.245788i
$283$	1.08118	+	2.36745i	0.0642694	+	0.140730i	0.939041	−	0.343805i	$-0.111716\pi$
$283$	1.08118	+	2.36745i	0.0642694	+	0.140730i	−0.874772	+	0.484535i	$0.838989\pi$
$284$	5.17887	+	5.97674i	0.307310	+	0.354654i
$285$	−7.43127	+	1.06846i	−0.440191	+	0.0632899i
$286$	7.30740	−	16.0010i	0.432096	−	0.946158i
$287$	1.61931	+	0.503103i	0.0955850	+	0.0296972i
$288$	0.959493	−	0.281733i	0.0565387	−	0.0166013i
$289$	−2.71089	+	5.93603i	−0.159464	+	0.349178i
$290$	1.95869	+	13.6230i	0.115018	+	0.799970i
$291$	−11.7014	+	10.1393i	−0.685945	+	0.594375i
$292$	−8.66214	+	3.95587i	−0.506913	+	0.231499i
$293$	1.56117	−	1.00330i	0.0912045	−	0.0586135i	−0.494244	−	0.869323i	$-0.664555\pi$
$293$	1.56117	−	1.00330i	0.0912045	−	0.0586135i	0.585448	+	0.810710i	$0.300919\pi$
$294$	1.76118	+	6.77483i	0.102714	+	0.395116i
$295$	−4.10968	+	6.39478i	−0.239275	+	0.372319i
$296$	5.46827	+	4.73829i	0.317837	+	0.275407i
$297$	3.78120	+	1.11026i	0.219407	+	0.0644238i
$298$		−	12.0897i		−	0.700338i
$299$	6.05857	−	20.5318i	0.350376	−	1.18739i
$300$		−	0.941339i		−	0.0543482i
$301$	17.1260	+	20.4003i	0.987125	+	1.17586i
$302$	11.5104	−	13.2837i	0.662347	−	0.764389i
$303$	−12.3916	−	7.96363i	−0.711881	−	0.457498i
$304$	−0.530353	+	3.68869i	−0.0304178	+	0.211561i
$305$	−4.80932	+	3.09076i	−0.275381	+	0.176977i
$306$	−1.34445	−	2.94393i	−0.0768569	−	0.168293i
$307$	8.27790	−	7.17284i	0.472445	−	0.409376i	−0.385827	−	0.922571i	$-0.626084\pi$
$307$	8.27790	−	7.17284i	0.472445	−	0.409376i	0.858272	+	0.513195i	$0.171538\pi$
$308$	4.47905	−	9.41536i	0.255218	−	0.536490i
$309$	−16.3796	−	7.48031i	−0.931802	−	0.425540i
$310$	0.235683	+	0.802662i	0.0133859	+	0.0455881i
$311$	−0.337336	−	1.14886i	−0.0191286	−	0.0651459i	0.949376	−	0.314143i	$-0.101717\pi$
$311$	−0.337336	−	1.14886i	−0.0191286	−	0.0651459i	−0.968504	+	0.248997i	$0.919899\pi$
$312$	−1.85428	+	4.06031i	−0.104978	+	0.229870i
$313$	0.647342	+	4.50236i	0.0365899	+	0.254489i	0.999904	−	0.0138897i	$-0.00442136\pi$
$313$	0.647342	+	4.50236i	0.0365899	+	0.254489i	−0.963314	+	0.268378i	$0.913512\pi$
$314$	−15.2484	−	17.5976i	−0.860520	−	0.993092i
$315$	−5.26340	−	0.840953i	−0.296559	−	0.0473823i
$316$	−0.859085	−	1.33676i	−0.0483273	−	0.0751988i
$317$	2.56379	−	17.8316i	0.143997	−	1.00152i	−0.781808	−	0.623519i	$-0.785702\pi$
$317$	2.56379	−	17.8316i	0.143997	−	1.00152i	0.925805	−	0.378002i	$-0.123389\pi$
$318$	6.67902	+	4.29234i	0.374541	+	0.240703i
$319$	20.3465	+	17.6304i	1.13919	+	0.987110i
$320$	1.93301	+	0.567582i	0.108058	+	0.0317288i
$321$	2.81820			0.157296
$322$	3.78091	−	12.1122i	0.210702	−	0.674985i
$323$	12.0608			0.671082
$324$	−0.959493	−	0.281733i	−0.0533052	−	0.0156518i
$325$	3.17554	+	2.75162i	0.176147	+	0.152632i
$326$	−18.4401	−	11.8507i	−1.02130	−	0.656352i
$327$	−1.36251	+	9.47647i	−0.0753470	+	0.524050i
$328$	0.346498	+	0.539161i	0.0191321	+	0.0297702i
$329$	−3.18681	+	19.9458i	−0.175694	+	1.09965i
$330$	5.19910	+	6.00008i	0.286201	+	0.330293i
$331$	−3.24857	−	22.5943i	−0.178557	−	1.24189i	−0.860104	−	0.510119i	$-0.829601\pi$
$331$	−3.24857	−	22.5943i	−0.178557	−	1.24189i	0.681546	−	0.731775i	$-0.261308\pi$
$332$	2.84084	−	6.22057i	0.155911	−	0.341398i
$333$	−2.03849	−	6.94247i	−0.111709	−	0.380445i
$334$	0.641350	+	2.18424i	0.0350931	+	0.119516i
$335$	19.3461	+	8.83508i	1.05699	+	0.482712i
$336$	−1.13658	+	2.38918i	−0.0620053	+	0.130341i
$337$	8.67839	−	7.51987i	0.472742	−	0.409633i	−0.385636	−	0.922651i	$-0.626018\pi$
$337$	8.67839	−	7.51987i	0.472742	−	0.409633i	0.858378	+	0.513018i	$0.171473\pi$
$338$	−2.87653	−	6.29871i	−0.156462	−	0.342605i
$339$	14.3763	−	9.23908i	0.780812	−	0.501798i
$340$	0.927904	−	6.45371i	0.0503227	−	0.350002i
$341$	1.37662	+	0.884699i	0.0745481	+	0.0479092i
$342$	2.44042	−	2.81639i	0.131963	−	0.152293i
$343$	−16.4674	−	8.47502i	−0.889154	−	0.457608i
$344$			10.0674i			0.542800i
$345$	7.29338	+	6.33687i	0.392662	+	0.341165i
$346$			7.63691i			0.410563i
$347$	3.64110	+	1.06912i	0.195465	+	0.0573936i	0.378000	−	0.925806i	$-0.376612\pi$
$347$	3.64110	+	1.06912i	0.195465	+	0.0573936i	−0.182535	+	0.983199i	$0.558430\pi$
$348$	−5.16300	−	4.47377i	−0.276766	−	0.239819i
$349$	1.98368	−	3.08667i	0.106184	−	0.165226i	−0.784095	−	0.620641i	$-0.786873\pi$
$349$	1.98368	−	3.08667i	0.106184	−	0.165226i	0.890279	+	0.455415i	$0.150509\pi$
$350$	1.85650	+	1.66019i	0.0992342	+	0.0887409i
$351$	3.75509	−	2.41325i	0.200432	−	0.128810i
$352$	3.58470	−	1.63708i	0.191065	−	0.0872566i
$353$	−18.0347	+	15.6271i	−0.959889	+	0.831748i	−0.985801	−	0.167916i	$-0.946296\pi$
$353$	−18.0347	+	15.6271i	−0.959889	+	0.831748i	0.0259124	+	0.999664i	$0.491751\pi$
$354$	−0.536979	−	3.73477i	−0.0285401	−	0.198501i
$355$	6.61850	−	14.4925i	0.351274	−	0.769182i
$356$	16.2964	−	4.78505i	0.863706	−	0.253607i
$357$	8.17713	+	2.54054i	0.432779	+	0.134460i
$358$	6.07592	−	13.3044i	0.321123	−	0.703160i
$359$	−24.3393	+	3.49947i	−1.28458	+	0.184695i	−0.750575	−	0.660785i	$-0.770223\pi$
$359$	−24.3393	+	3.49947i	−1.28458	+	0.184695i	−0.534007	+	0.845480i	$0.679314\pi$
$360$	−1.31929	−	1.52254i	−0.0695327	−	0.0802450i
$361$	−2.12373	−	4.65032i	−0.111775	−	0.244754i
$362$	19.2677	−	12.3826i	1.01269	−	0.650814i
$363$	4.48402	+	0.644705i	0.235350	+	0.0338382i
$364$	−4.73741	−	10.8180i	−0.248308	−	0.567015i
$365$	14.4987	+	12.5632i	0.758896	+	0.657587i
$366$	0.799471	−	2.72275i	0.0417890	−	0.142320i
$367$	−25.2866			−1.31995			−0.659975	−	0.751288i	$-0.729433\pi$
$367$	−25.2866			−1.31995			−0.659975	+	0.751288i	$0.729433\pi$
$368$	4.03798	−	2.58742i	0.210494	−	0.134878i
$369$		−	0.640902i		−	0.0333640i
$370$	4.10677	−	13.9864i	0.213501	−	0.727117i
$371$	−20.2448	+	5.60213i	−1.05106	+	0.290848i
$372$	−0.349322	−	0.224496i	−0.0181115	−	0.0116396i
$373$	−12.3500	−	1.77567i	−0.639460	−	0.0919405i	−0.185044	−	0.982730i	$-0.559243\pi$
$373$	−12.3500	−	1.77567i	−0.639460	−	0.0919405i	−0.454416	+	0.890790i	$0.650152\pi$
$374$	−6.89537	−	10.7294i	−0.356551	−	0.554805i
$375$	−10.8878	+	4.97231i	−0.562245	+	0.256769i
$376$	−5.76971	+	4.99948i	−0.297550	+	0.257828i
$377$	30.1838	−	4.33978i	1.55455	−	0.223510i
$378$	2.24784	−	1.39543i	0.115616	−	0.0717731i
$379$	7.56600	+	25.7674i	0.388639	+	1.32358i	0.889056	+	0.457799i	$0.151362\pi$
$379$	7.56600	+	25.7674i	0.388639	+	1.32358i	−0.500416	+	0.865785i	$0.666820\pi$
$380$	7.20358	−	2.11516i	0.369536	−	0.108505i
$381$	−6.09727	−	2.78453i	−0.312373	−	0.142656i
$382$	−9.69289	+	1.39363i	−0.495932	+	0.0713042i
$383$	−12.5656	−	14.5015i	−0.642071	−	0.740990i	0.337668	−	0.941265i	$-0.390362\pi$
$383$	−12.5656	−	14.5015i	−0.642071	−	0.740990i	−0.979740	+	0.200275i	$0.935816\pi$
$384$	−0.909632	+	0.415415i	−0.0464195	+	0.0211991i
$385$	−21.0027	−	0.328400i	−1.07040	−	0.0167368i
$386$	−0.0105782	+	0.0735732i	−0.000538418	+	0.00374478i
$387$	5.44286	−	8.46926i	0.276676	−	0.430517i
$388$	10.1393	−	11.7014i	0.514744	−	0.594046i
$389$	−0.664343	+	2.26254i	−0.0336835	+	0.114716i	−0.974619	−	0.223871i	$-0.928131\pi$
$389$	−0.664343	+	2.26254i	−0.0336835	+	0.114716i	0.940935	+	0.338586i	$0.109949\pi$
$390$	8.99259			0.455357
$391$	−10.1485	−	11.7437i	−0.513232	−	0.593907i
$392$	−2.70741	−	6.45523i	−0.136745	−	0.326038i
$393$	4.16005	+	1.22150i	0.209847	+	0.0616166i
$394$	−11.0405	+	12.7415i	−0.556214	+	0.641906i
$395$	−1.73072	+	2.69306i	−0.0870821	+	0.135502i
$396$	−3.90072	−	0.560838i	−0.196018	−	0.0281832i
$397$	3.01808	+	4.69622i	0.151473	+	0.235696i	0.908695	−	0.417461i	$-0.137080\pi$
$397$	3.01808	+	4.69622i	0.151473	+	0.235696i	−0.757222	+	0.653158i	$0.773444\pi$
$398$	−1.15553	−	2.53026i	−0.0579214	−	0.126830i
$399$	1.25043	+	9.78010i	0.0625999	+	0.489617i
$400$	0.133966	+	0.931757i	0.00669832	+	0.0465879i
$401$	−9.06756	−	4.14102i	−0.452813	−	0.206793i	0.175935	−	0.984402i	$-0.443705\pi$
$401$	−9.06756	−	4.14102i	−0.452813	−	0.206793i	−0.628748	+	0.777609i	$0.716432\pi$
$402$	−10.1293	+	2.97423i	−0.505203	+	0.148341i
$403$	1.77842	−	0.522191i	0.0885894	−	0.0260122i
$404$	13.3989	+	6.11905i	0.666618	+	0.304434i
$405$	0.286709	+	1.99411i	0.0142467	+	0.0990879i
$406$	17.9289	−	2.29229i	0.889794	−	0.113764i
$407$	−11.8452	−	25.9373i	−0.587144	−	1.28567i
$408$	1.74973	+	2.72263i	0.0866244	+	0.134790i
$409$	9.25291	+	1.33037i	0.457527	+	0.0657824i	0.367225	−	0.930132i	$-0.380308\pi$
$409$	9.25291	+	1.33037i	0.457527	+	0.0657824i	0.0903015	+	0.995914i	$0.471217\pi$
$410$	0.698058	−	1.08620i	0.0344746	−	0.0536436i
$411$	−7.18966	+	8.29731i	−0.354640	+	0.409276i
$412$	17.2774	+	5.07311i	0.851198	+	0.249934i
$413$	8.31274	+	5.52780i	0.409043	+	0.272005i
$414$	−4.79583	−	0.00642257i	−0.235702	−	0.000315652i
$415$	−13.7770			−0.676289
$416$	1.25756	−	4.28287i	0.0616572	−	0.209985i
$417$	−10.8087	+	12.4739i	−0.529302	+	0.610848i
$418$	7.93983	−	12.3546i	0.388350	−	0.604284i
$419$	2.38976	−	16.6212i	0.116748	−	0.811998i	−0.844351	−	0.535791i	$-0.820013\pi$
$419$	2.38976	−	16.6212i	0.116748	−	0.811998i	0.961098	−	0.276207i	$-0.0890774\pi$
$420$	5.32951	+	0.0833327i	0.260053	+	0.00406622i
$421$	18.5527	−	8.47272i	0.904202	−	0.412935i	0.0916279	−	0.995793i	$-0.470793\pi$
$421$	18.5527	−	8.47272i	0.904202	−	0.412935i	0.812574	+	0.582858i	$0.198066\pi$
$422$	−16.4278	−	18.9587i	−0.799693	−	0.922895i
$423$	7.55671	−	1.08649i	0.367420	−	0.0528270i
$424$	−7.22190	−	3.29813i	−0.350726	−	0.160171i
$425$	2.92314	−	0.858311i	0.141793	−	0.0416342i
$426$	2.22804	+	7.58801i	0.107949	+	0.367640i
$427$	3.95980	+	6.37868i	0.191628	+	0.308686i
$428$	−2.78951	+	0.401071i	−0.134836	+	0.0193865i
$429$	13.2941	−	11.5194i	0.641845	−	0.556162i
$430$	18.4491	−	8.42543i	0.889696	−	0.406311i
$431$	17.0218	+	26.4864i	0.819912	+	1.27581i	0.958396	+	0.285443i	$0.0921406\pi$
$431$	17.0218	+	26.4864i	0.819912	+	1.27581i	−0.138484	+	0.990365i	$0.544223\pi$
$432$	0.989821	+	0.142315i	0.0476228	+	0.00684713i
$433$	0.572723	+	0.368067i	0.0275233	+	0.0176882i	0.554330	−	0.832297i	$-0.312975\pi$
$433$	0.572723	+	0.368067i	0.0275233	+	0.0176882i	−0.526807	+	0.849985i	$0.676611\pi$
$434$	1.05883	−	0.293000i	0.0508255	−	0.0140644i
$435$	−3.87751	+	13.2056i	−0.185912	+	0.633159i
$436$		−	9.57392i		−	0.458508i
$437$	7.44616	−	16.2472i	0.356198	−	0.777209i
$438$	−9.52268			−0.455011
$439$	−1.01988	+	3.47338i	−0.0486760	+	0.165775i	−0.980244	−	0.197792i	$-0.936623\pi$
$439$	−1.01988	+	3.47338i	−0.0486760	+	0.165775i	0.931568	+	0.363567i	$0.118441\pi$
$440$	−6.00008	−	5.19910i	−0.286042	−	0.247857i
$441$	−1.21234	+	6.89422i	−0.0577305	+	0.328296i
$442$	−14.2992	−	2.05591i	−0.680143	−	0.0977899i
$443$	−6.28879	+	4.04156i	−0.298790	+	0.192020i	−0.681442	−	0.731872i	$-0.738647\pi$
$443$	−6.28879	+	4.04156i	−0.298790	+	0.192020i	0.382653	+	0.923892i	$0.375011\pi$
$444$	3.00576	+	6.58170i	0.142647	+	0.312354i
$445$	−22.4073	−	25.8594i	−1.06221	−	1.22585i
$446$	−0.645507	+	0.0928099i	−0.0305656	+	0.00439468i
$447$	5.02225	−	10.9972i	0.237544	−	0.520149i
$448$	0.784992	−	2.52662i	0.0370874	−	0.119371i
$449$	−38.9655	+	11.4413i	−1.83890	+	0.539948i	−0.999991	−	0.00432980i	$-0.998622\pi$
$449$	−38.9655	+	11.4413i	−1.83890	+	0.539948i	−0.838905	+	0.544278i	$0.816804\pi$
$450$	0.391046	−	0.856272i	0.0184341	−	0.0403650i
$451$	−0.359442	−	2.49998i	−0.0169255	−	0.117719i
$452$	−12.9151	+	11.1910i	−0.607475	+	0.526380i
$453$	15.9884	−	7.30167i	0.751202	−	0.343063i
$454$	16.2652	−	10.4530i	0.763365	−	0.490585i
$455$	−15.8598	+	17.7351i	−0.743517	+	0.831435i
$456$	−2.01476	+	3.13503i	−0.0943499	+	0.146811i
$457$	18.1393	+	15.7178i	0.848520	+	0.735247i	0.966197	−	0.257805i	$-0.0829993\pi$
$457$	18.1393	+	15.7178i	0.848520	+	0.735247i	−0.117677	+	0.993052i	$0.537545\pi$
$458$	−12.3175	−	3.61675i	−0.575559	−	0.168999i
$459$		−	3.23639i		−	0.151062i
$460$	−8.12097	−	5.23441i	−0.378642	−	0.244056i
$461$			10.0106i			0.466239i	0.972448	+	0.233119i	$0.0748933\pi$
$461$			10.0106i			0.466239i	−0.972448	+	0.233119i	$0.925107\pi$
$462$	7.98557	−	6.70385i	0.371522	−	0.311891i
$463$	−14.7855	+	17.0634i	−0.687142	+	0.793004i	−0.986955	−	0.160994i	$-0.948530\pi$
$463$	−14.7855	+	17.0634i	−0.687142	+	0.793004i	0.299814	+	0.953998i	$0.403076\pi$
$464$	5.74713	+	3.69346i	0.266804	+	0.171465i
$465$	−0.119053	+	0.828033i	−0.00552096	+	0.0383991i
$466$	5.32762	−	3.42385i	0.246797	−	0.158607i
$467$	6.31689	+	13.8321i	0.292311	+	0.640072i	0.997629	−	0.0688191i	$-0.0219231\pi$
$467$	6.31689	+	13.8321i	0.292311	+	0.640072i	−0.705318	+	0.708891i	$0.749196\pi$
$468$	−3.37343	+	2.92309i	−0.155937	+	0.135120i
$469$	11.9987	−	25.2224i	0.554051	−	1.16466i
$470$	13.9905	+	6.38924i	0.645333	+	0.294714i
$471$	−6.56015	−	22.3418i	−0.302276	−	1.02946i
$472$	1.06303	+	3.62034i	0.0489298	+	0.166640i
$473$	16.4812	−	36.0888i	0.757806	−	1.65936i
$474$	−0.226140	−	1.57284i	−0.0103870	−	0.0722429i
$475$	2.29726	+	2.65118i	0.105405	+	0.121644i
$476$	−8.45545	−	1.35096i	−0.387555	−	0.0619210i
$477$	4.29234	+	6.67902i	0.196533	+	0.305811i
$478$	−0.751051	+	5.22367i	−0.0343523	+	0.238925i
$479$	7.34755	+	4.72198i	0.335718	+	0.215753i	0.697628	−	0.716460i	$-0.254239\pi$
$479$	7.34755	+	4.72198i	0.335718	+	0.215753i	−0.361910	+	0.932213i	$0.617875\pi$
$480$	1.52254	+	1.31929i	0.0694942	+	0.0602171i
$481$	−30.9890	−	9.09919i	−1.41298	−	0.414887i
$482$	15.4848			0.705315
$483$	8.47082	−	9.44697i	0.385436	−	0.429852i
$484$	−4.53013			−0.205915
$485$	−29.9289	−	8.78793i	−1.35900	−	0.399039i
$486$	−0.755750	−	0.654861i	−0.0342815	−	0.0297051i
$487$	−6.37731	−	4.09845i	−0.288983	−	0.185718i	0.388115	−	0.921611i	$-0.373126\pi$
$487$	−6.37731	−	4.09845i	−0.288983	−	0.185718i	−0.677098	+	0.735893i	$0.736763\pi$
$488$	−0.403846	+	2.80881i	−0.0182813	+	0.127149i
$489$	−11.8507	−	18.4401i	−0.535909	−	0.833891i
$490$	−9.56373	+	10.3639i	−0.432045	+	0.468191i
$491$	4.07253	+	4.69995i	0.183791	+	0.212106i	0.840167	−	0.542328i	$-0.182457\pi$
$491$	4.07253	+	4.69995i	0.183791	+	0.212106i	−0.656376	+	0.754434i	$0.727912\pi$
$492$	0.0912098	+	0.634378i	0.00411206	+	0.0286000i
$493$	9.18477	−	20.1118i	0.413661	−	0.905791i
$494$	−4.68647	−	15.9606i	−0.210854	−	0.718103i
$495$	2.23674	+	7.61765i	0.100534	+	0.342388i
$496$	0.377716	+	0.172497i	0.0169599	+	0.00774534i
$497$	−18.8945	−	8.98845i	−0.847535	−	0.403187i
$498$	5.16824	−	4.47830i	0.231594	−	0.200678i
$499$	7.29286	+	15.9691i	0.326473	+	0.714877i	0.999698	−	0.0245610i	$-0.00781880\pi$
$499$	7.29286	+	15.9691i	0.326473	+	0.714877i	−0.673225	+	0.739438i	$0.735092\pi$
$500$	10.0694	−	6.47120i	0.450316	−	0.289401i
$501$	−0.323973	+	2.25328i	−0.0144740	+	0.100669i
$502$	12.2677	+	7.88396i	0.547533	+	0.351878i
$503$	−11.0358	+	12.7360i	−0.492061	+	0.567869i	−0.946415	−	0.322952i	$-0.895325\pi$
$503$	−11.0358	+	12.7360i	−0.492061	+	0.567869i	0.454354	+	0.890821i	$0.349870\pi$
$504$	−2.02637	+	1.70113i	−0.0902616	+	0.0757742i
$505$		−	29.6752i		−	1.32053i
$506$	−18.7108	+	2.66463i	−0.831795	+	0.118457i
$507$		−	6.92446i		−	0.307526i
$508$	6.43149	+	1.88846i	0.285351	+	0.0837867i
$509$	10.7687	+	9.33110i	0.477313	+	0.413594i	0.860008	−	0.510281i	$-0.170459\pi$
$509$	10.7687	+	9.33110i	0.477313	+	0.413594i	−0.382695	+	0.923875i	$0.625004\pi$
$510$	3.52502	−	5.48504i	0.156091	−	0.242882i
$511$	16.7947	−	18.7806i	0.742952	−	0.830803i
$512$	0.841254	−	0.540641i	0.0371785	−	0.0238932i
$513$	3.38985	−	1.54809i	0.149666	−	0.0683500i
$514$	−19.4427	+	16.8472i	−0.857581	+	0.743099i
$515$	−5.16272	−	35.9075i	−0.227497	−	1.58227i
$516$	−4.18216	+	9.15766i	−0.184109	+	0.403143i
$517$	28.8672	−	8.47618i	1.26958	−	0.372782i
$518$	−18.2815	−	5.67986i	−0.803242	−	0.249559i
$519$	−3.17249	+	6.94677i	−0.139257	+	0.304930i
$520$	−8.90106	+	1.27978i	−0.390337	+	0.0561220i
$521$	2.77783	+	3.20579i	0.121699	+	0.140448i	0.813329	−	0.581803i	$-0.197653\pi$
$521$	2.77783	+	3.20579i	0.121699	+	0.140448i	−0.691630	+	0.722252i	$0.743107\pi$
$522$	−2.83796	−	6.21427i	−0.124214	−	0.271991i
$523$	16.3889	−	10.5325i	0.716637	−	0.460554i	−0.130829	−	0.991405i	$-0.541764\pi$
$523$	16.3889	−	10.5325i	0.716637	−	0.460554i	0.847465	+	0.530851i	$0.178127\pi$
$524$	−4.29154	−	0.617031i	−0.187477	−	0.0269551i
$525$	0.999066	+	2.28138i	0.0436028	+	0.0995676i
$526$	4.67653	+	4.05223i	0.203906	+	0.176686i
$527$	0.378615	−	1.28944i	0.0164927	−	0.0561691i
$528$	3.94083			0.171503
$529$	−22.0856	+	6.42072i	−0.960244	+	0.279162i
$530$			15.9947i			0.694767i
$531$	1.06303	−	3.62034i	0.0461315	−	0.157109i
$532$	−2.62956	−	9.50259i	−0.114006	−	0.411990i
$533$	−2.40664	−	1.54666i	−0.104243	−	0.0669931i
$534$	16.8115	+	2.41713i	0.727504	+	0.104599i
$535$	3.06953	+	4.77628i	0.132707	+	0.206497i
$536$	9.60291	−	4.38550i	0.414782	−	0.189425i
$537$	11.0537	−	9.57810i	0.477003	−	0.413325i
$538$	15.2386	−	2.19099i	0.656984	−	0.0944601i
$539$	−0.862457	+	27.5723i	−0.0371487	+	1.18762i
$540$	−0.567582	−	1.93301i	−0.0244248	−	0.0831833i
$541$	4.81272	−	1.41314i	0.206915	−	0.0607557i	−0.176633	−	0.984277i	$-0.556520\pi$
$541$	4.81272	−	1.41314i	0.206915	−	0.0607557i	0.383547	+	0.923521i	$0.374702\pi$
$542$	13.0285	+	5.94992i	0.559622	+	0.255571i
$543$	22.6704	−	3.25951i	0.972880	−	0.139879i
$544$	−2.11939	−	2.44590i	−0.0908680	−	0.104867i
$545$	−17.5447	+	8.01242i	−0.751534	+	0.343214i
$546$	0.184636	−	11.8084i	0.00790171	−	0.505351i
$547$	−1.01704	+	7.07369i	−0.0434857	+	0.302449i	0.956458	+	0.291869i	$0.0942771\pi$
$547$	−1.01704	+	7.07369i	−0.0434857	+	0.302449i	−0.999944	+	0.0105806i	$0.996632\pi$
$548$	5.93565	−	9.23605i	0.253558	−	0.394544i
$549$	1.85829	−	2.14459i	0.0793101	−	0.0915287i
$550$	1.04513	−	3.55939i	0.0445645	−	0.151773i
$551$	25.4589			1.08459
$552$	4.74793	−	0.676160i	0.202085	−	0.0287793i
$553$	3.50077	+	2.32794i	0.148868	+	0.0989942i
$554$	−5.44914	−	1.60001i	−0.231512	−	0.0679779i
$555$	9.54581	−	11.0164i	0.405197	−	0.467622i
$556$	8.92343	−	13.8851i	0.378438	−	0.588861i
$557$	8.14384	+	1.17091i	0.345066	+	0.0496130i	0.312669	−	0.949862i	$-0.398777\pi$
$557$	8.14384	+	1.17091i	0.345066	+	0.0496130i	0.0323966	+	0.999475i	$0.489686\pi$
$558$	−0.224496	−	0.349322i	−0.00950366	−	0.0147880i
$559$	−18.6678	−	40.8769i	−0.789566	−	1.72891i
$560$	−5.28712	+	0.675984i	−0.223422	+	0.0285655i
$561$	−1.81509	−	12.6243i	−0.0766333	−	0.532997i
$562$	19.4224	+	8.86990i	0.819283	+	0.374154i
$563$	−1.47043	+	0.431756i	−0.0619710	+	0.0181963i	−0.312571	−	0.949894i	$-0.601190\pi$
$563$	−1.47043	+	0.431756i	−0.0619710	+	0.0181963i	0.250600	+	0.968091i	$0.419372\pi$
$564$	−7.32517	+	2.15086i	−0.308445	+	0.0905677i
$565$	31.3168	+	14.3019i	1.31751	+	0.601685i
$566$	−0.370395	−	2.57616i	−0.0155689	−	0.108284i
$567$	2.62439	−	0.335541i	0.110214	−	0.0140914i
$568$	−3.28525	−	7.19369i	−0.137846	−	0.301841i
$569$	0.367450	+	0.571763i	0.0154043	+	0.0239696i	0.848870	−	0.528601i	$-0.177283\pi$
$569$	0.367450	+	0.571763i	0.0154043	+	0.0239696i	−0.833466	+	0.552571i	$0.813647\pi$
$570$	7.43127	+	1.06846i	0.311262	+	0.0447527i
$571$	2.61885	−	4.07501i	0.109595	−	0.170534i	−0.782123	−	0.623123i	$-0.785863\pi$
$571$	2.61885	−	4.07501i	0.109595	−	0.170534i	0.891719	+	0.452590i	$0.149500\pi$
$572$	−11.5194	+	13.2941i	−0.481650	+	0.555854i
$573$	−9.39590	−	2.75889i	−0.392519	−	0.115254i
$574$	−1.41198	−	0.938936i	−0.0589348	−	0.0391904i
$575$	0.648464	−	4.46769i	0.0270428	−	0.186315i
$576$	−1.00000			−0.0416667
$577$	8.58625	−	29.2421i	0.357450	−	1.21736i	−0.562984	−	0.826468i	$-0.690347\pi$
$577$	8.58625	−	29.2421i	0.357450	−	1.21736i	0.920435	−	0.390896i	$-0.127835\pi$
$578$	4.27346	−	4.93183i	0.177752	−	0.205137i
$579$	−0.0401857	+	0.0625302i	−0.00167006	+	0.00259867i
$580$	1.95869	−	13.6230i	0.0813302	−	0.565664i
$581$	−0.282871	+	18.0909i	−0.0117355	+	0.750538i
$582$	14.0839	−	6.43192i	0.583798	−	0.266611i
$583$	20.4891	+	23.6456i	0.848570	+	0.979302i
$584$	9.42575	−	1.35522i	0.390041	−	0.0560794i
$585$	8.17995	+	3.73566i	0.338199	+	0.154450i
$586$	−1.78059	+	0.522829i	−0.0735556	+	0.0215979i
$587$	−2.96095	−	10.0841i	−0.122211	−	0.416214i	0.875547	−	0.483133i	$-0.160501\pi$
$587$	−2.96095	−	10.0841i	−0.122211	−	0.416214i	−0.997758	+	0.0669190i	$0.978683\pi$
$588$	0.218852	−	6.99658i	0.00902530	−	0.288534i
$589$	1.53169	−	0.220224i	0.0631122	−	0.00907417i
$590$	5.74482	−	4.97792i	0.236511	−	0.204938i
$591$	−15.3358	+	7.00364i	−0.630831	+	0.288091i
$592$	−3.91184	−	6.08694i	−0.160776	−	0.250172i
$593$	20.9496	+	3.01210i	0.860298	+	0.123692i	0.558323	−	0.829624i	$-0.311445\pi$
$593$	20.9496	+	3.01210i	0.860298	+	0.123692i	0.301975	+	0.953316i	$0.402354\pi$
$594$	−3.31524	−	2.13057i	−0.136026	−	0.0874185i
$595$	4.60066	+	16.6257i	0.188609	+	0.681587i
$596$	−3.40606	+	11.6000i	−0.139518	+	0.475154i
$597$		−	2.78163i		−	0.113844i
$598$	−11.5976	+	17.9933i	−0.474263	+	0.735799i
$599$	37.2750			1.52302			0.761508	−	0.648156i	$-0.224459\pi$
$599$	37.2750			1.52302			0.761508	+	0.648156i	$0.224459\pi$
$600$	−0.265206	+	0.903208i	−0.0108270	+	0.0368733i
$601$	15.4926	+	13.4244i	0.631958	+	0.547595i	0.910855	−	0.412726i	$-0.135423\pi$
$601$	15.4926	+	13.4244i	0.631958	+	0.547595i	−0.278897	+	0.960321i	$0.589969\pi$
$602$	−10.6848	−	24.3989i	−0.435480	−	0.994426i
$603$	−10.4495	−	1.50241i	−0.425535	−	0.0611827i
$604$	−14.7866	+	9.50275i	−0.601657	+	0.386661i
$605$	3.79127	+	8.30172i	0.154137	+	0.337513i
$606$	9.64608	+	11.1322i	0.391845	+	0.452214i
$607$	21.1923	−	3.04699i	0.860168	−	0.123673i	0.301905	−	0.953338i	$-0.402377\pi$
$607$	21.1923	−	3.04699i	0.860168	−	0.123673i	0.558262	+	0.829664i	$0.311468\pi$
$608$	1.54809	−	3.38985i	0.0627835	−	0.137477i
$609$	17.2609	+	5.36277i	0.699447	+	0.217311i
$610$	5.48528	−	1.61062i	0.222093	−	0.0652122i
$611$	14.1563	−	30.9981i	0.572705	−	1.25405i
$612$	0.460587	+	3.20345i	0.0186181	+	0.129492i
$613$	−15.1550	+	13.1319i	−0.612104	+	0.530391i	−0.904812	−	0.425811i	$-0.859989\pi$
$613$	−15.1550	+	13.1319i	−0.612104	+	0.530391i	0.292709	+	0.956202i	$0.405443\pi$
$614$	−9.96341	+	4.55014i	−0.402090	+	0.183629i
$615$	1.08620	−	0.698058i	0.0437998	−	0.0281484i
$616$	−6.95023	+	7.77208i	−0.280033	+	0.313146i
$617$	−20.5811	+	32.0248i	−0.828564	+	1.28927i	0.126229	+	0.992001i	$0.459713\pi$
$617$	−20.5811	+	32.0248i	−0.828564	+	1.28927i	−0.954793	+	0.297270i	$0.903924\pi$
$618$	13.6087	+	11.7920i	0.547420	+	0.474342i
$619$	−16.2324	−	4.76628i	−0.652437	−	0.191573i	−0.0612691	−	0.998121i	$-0.519515\pi$
$619$	−16.2324	−	4.76628i	−0.652437	−	0.191573i	−0.591168	+	0.806548i	$0.701333\pi$
$620$		−	0.836548i		−	0.0335966i
$621$	−4.35977	−	1.99810i	−0.174952	−	0.0801810i
$622$			1.19736i			0.0480098i
$623$	−34.4166	+	28.8925i	−1.37887	+	1.15756i
$624$	2.92309	−	3.37343i	0.117017	−	0.135045i
$625$	−16.3264	−	10.4923i	−0.653055	−	0.419693i
$626$	0.647342	−	4.50236i	0.0258730	−	0.179951i
$627$	12.3546	−	7.93983i	0.493396	−	0.317086i
$628$	9.67295	+	21.1808i	0.385993	+	0.845206i
$629$	−17.6975	+	15.3350i	−0.705645	+	0.611445i
$630$	4.81328	+	2.28976i	0.191765	+	0.0912263i
$631$	−1.31611	−	0.601047i	−0.0523935	−	0.0239273i	0.389046	−	0.921218i	$-0.372805\pi$
$631$	−1.31611	−	0.601047i	−0.0523935	−	0.0239273i	−0.441439	+	0.897291i	$0.645532\pi$
$632$	0.447677	+	1.52465i	0.0178076	+	0.0606472i
$633$	−7.06753	−	24.0698i	−0.280909	−	0.956689i
$634$	−7.48368	+	16.3870i	−0.297215	+	0.650809i
$635$	−1.92181	−	13.3665i	−0.0762648	−	0.530434i
$636$	−5.19918	−	6.00017i	−0.206161	−	0.237922i
$637$	22.9627	+	21.1899i	0.909816	+	0.839575i
$638$	−14.5553	−	22.6485i	−0.576249	−	0.896662i
$639$	−1.12548	+	7.82786i	−0.0445232	+	0.309665i
$640$	−1.69480	−	1.08918i	−0.0669928	−	0.0430537i
$641$	25.8590	+	22.4069i	1.02137	+	0.885021i	0.993413	−	0.114588i	$-0.0365548\pi$
$641$	25.8590	+	22.4069i	1.02137	+	0.885021i	0.0279557	+	0.999609i	$0.491100\pi$
$642$	−2.70404	−	0.793978i	−0.106720	−	0.0313358i
$643$	−38.2538			−1.50858			−0.754292	−	0.656539i	$-0.772020\pi$
$643$	−38.2538			−1.50858			−0.754292	+	0.656539i	$0.772020\pi$
$644$	−7.04015	+	10.5563i	−0.277421	+	0.415978i
$645$	20.2820			0.798602
$646$	−11.5723	−	3.39792i	−0.455305	−	0.133690i
$647$	10.5188	+	9.11456i	0.413535	+	0.358330i	0.836643	−	0.547749i	$-0.184515\pi$
$647$	10.5188	+	9.11456i	0.413535	+	0.358330i	−0.423107	+	0.906080i	$0.639061\pi$
$648$	0.841254	+	0.540641i	0.0330476	+	0.0212384i
$649$	2.11614	−	14.7181i	0.0830659	−	0.577736i
$650$	−2.27169	−	3.53481i	−0.0891028	−	0.138647i
$651$	1.08486	+	0.173332i	0.0425191	+	0.00679343i
$652$	14.3544	+	16.5659i	0.562162	+	0.648770i
$653$	2.79761	+	19.4578i	0.109479	+	0.761442i	0.968412	+	0.249355i	$0.0802185\pi$
$653$	2.79761	+	19.4578i	0.109479	+	0.761442i	−0.858933	+	0.512087i	$0.828872\pi$
$654$	3.97715	−	8.70875i	0.155519	−	0.340539i
$655$	2.46085	+	8.38088i	0.0961533	+	0.327468i
$656$	−0.180563	−	0.614941i	−0.00704980	−	0.0240094i
$657$	−8.66214	−	3.95587i	−0.337942	−	0.154333i
$658$	8.67710	−	18.2400i	0.338268	−	0.711070i
$659$	6.36468	−	5.51502i	0.247933	−	0.214835i	−0.522024	−	0.852931i	$-0.674823\pi$
$659$	6.36468	−	5.51502i	0.247933	−	0.214835i	0.769957	+	0.638096i	$0.220278\pi$
$660$	−3.29808	−	7.22179i	−0.128378	−	0.281108i
$661$	20.8705	−	13.4126i	0.811768	−	0.521691i	−0.0676686	−	0.997708i	$-0.521556\pi$
$661$	20.8705	−	13.4126i	0.811768	−	0.521691i	0.879436	+	0.476016i	$0.157920\pi$
$662$	−3.24857	+	22.5943i	−0.126259	+	0.878152i
$663$	−12.1529	−	7.81023i	−0.471981	−	0.303324i
$664$	−4.47830	+	5.16824i	−0.173792	+	0.200567i
$665$	−15.2134	+	12.7715i	−0.589949	+	0.495259i
$666$			7.23556i			0.280372i
$667$	−21.4223	−	24.7896i	−0.829473	−	0.959857i
$668$		−	2.27645i		−	0.0880785i
$669$	−0.625728	−	0.183730i	−0.0241921	−	0.00710343i
$670$	−16.0733	−	13.9276i	−0.620968	−	0.538072i
$671$	6.04592	−	9.40763i	0.233400	−	0.363177i
$672$	1.76365	−	1.97219i	0.0680342	−	0.0760790i
$673$	−21.7630	+	13.9862i	−0.838900	+	0.539129i	−0.888095	−	0.459661i	$-0.847971\pi$
$673$	−21.7630	+	13.9862i	−0.838900	+	0.539129i	0.0491942	+	0.998789i	$0.484335\pi$
$674$	−10.4454	+	4.77027i	−0.402343	+	0.183744i
$675$	0.711416	−	0.616446i	0.0273824	−	0.0237270i
$676$	0.985454	+	6.85398i	0.0379021	+	0.263615i
$677$	−16.2446	+	35.5708i	−0.624332	+	1.36710i	0.287994	+	0.957632i	$0.407012\pi$
$677$	−16.2446	+	35.5708i	−0.624332	+	1.36710i	−0.912326	+	0.409465i	$0.865715\pi$
$678$	−16.3969	+	4.81456i	−0.629719	+	0.184902i
$679$	−12.1541	+	39.1199i	−0.466432	+	1.50128i
$680$	−2.70854	+	5.93087i	−0.103868	+	0.227439i
$681$	19.1377	−	2.75159i	0.733359	−	0.105441i
$682$	−1.07161	−	1.23670i	−0.0410340	−	0.0473557i
$683$	−1.89707	−	4.15401i	−0.0725894	−	0.158949i	0.869859	−	0.493301i	$-0.164210\pi$
$683$	−1.89707	−	4.15401i	−0.0725894	−	0.158949i	−0.942448	+	0.334352i	$0.891483\pi$
$684$	−3.13503	+	2.01476i	−0.119871	+	0.0770364i
$685$	−21.8931	−	3.14775i	−0.836493	−	0.120270i
$686$	13.4126	+	12.7711i	0.512096	+	0.487604i
$687$	−9.70195	−	8.40678i	−0.370152	−	0.320739i
$688$	2.83632	−	9.65963i	0.108134	−	0.368270i
$689$	35.4388			1.35011
$690$	−5.21264	−	8.13496i	−0.198442	−	0.309693i
$691$		−	20.2686i		−	0.771055i	−0.922696	−	0.385528i	$-0.874019\pi$
$691$		−	20.2686i		−	0.771055i	0.922696	−	0.385528i	$-0.125981\pi$
$692$	2.15157	−	7.32756i	0.0817902	−	0.278552i
$693$	10.0488	−	2.78071i	0.381723	−	0.105630i
$694$	−3.19241	−	2.05163i	−0.121182	−	0.0778790i
$695$	−32.9133	−	4.73222i	−1.24847	−	0.179503i
$696$	3.69346	+	5.74713i	0.140000	+	0.217845i
$697$	−1.88677	+	0.861658i	−0.0714665	+	0.0326376i
$698$	−2.77295	+	2.40277i	−0.104958	+	0.0909463i
$699$	6.26850	−	0.901274i	0.237096	−	0.0340893i
$700$	−1.31357	−	2.11598i	−0.0496483	−	0.0799765i
$701$	−6.67660	−	22.7384i	−0.252172	−	0.858818i	−0.984127	−	0.177465i	$-0.943210\pi$
$701$	−6.67660	−	22.7384i	−0.252172	−	0.858818i	0.731955	−	0.681352i	$-0.238608\pi$
$702$	−4.28287	+	1.25756i	−0.161647	+	0.0474637i
$703$	−24.5275	−	11.2013i	−0.925072	−	0.422466i
$704$	−3.90072	+	0.560838i	−0.147014	+	0.0211374i
$705$	10.0720	+	11.6237i	0.379334	+	0.437775i
$706$	21.7068	−	9.91317i	0.816947	−	0.373087i
$707$	−38.9671	−	0.609293i	−1.46551	−	0.0229148i
$708$	−0.536979	+	3.73477i	−0.0201809	+	0.140361i
$709$	22.9914	−	35.7754i	0.863461	−	1.34357i	−0.0746399	−	0.997211i	$-0.523781\pi$
$709$	22.9914	−	35.7754i	0.863461	−	1.34357i	0.938101	−	0.346361i	$-0.112583\pi$
$710$	−10.4334	+	12.0408i	−0.391559	+	0.451883i
$711$	0.447677	−	1.52465i	0.0167892	−	0.0571787i
$712$	−16.9844			−0.636516
$713$	−1.50327	−	1.30612i	−0.0562978	−	0.0489145i
$714$	−7.13014	−	4.74140i	−0.266839	−	0.177442i
$715$	34.0028	+	9.98411i	1.27163	+	0.373384i
$716$	−9.57810	+	11.0537i	−0.357950	+	0.413097i
$717$	−2.85317	+	4.43962i	−0.106554	+	0.165801i
$718$	24.3393	+	3.49947i	0.908336	+	0.130599i
$719$	−13.7612	−	21.4128i	−0.513205	−	0.798563i	0.483858	−	0.875147i	$-0.339235\pi$
$719$	−13.7612	−	21.4128i	−0.513205	−	0.798563i	−0.997063	+	0.0765835i	$0.975599\pi$
$720$	0.836900	+	1.83256i	0.0311894	+	0.0682953i
$721$	−47.2569	+	6.04202i	−1.75994	+	0.225017i
$722$	0.727557	+	5.06027i	0.0270769	+	0.188324i
$723$	14.0855	+	6.43264i	0.523846	+	0.239232i
$724$	−21.9758	+	6.45267i	−0.816723	+	0.239811i
$725$	6.17039	−	1.81179i	0.229162	−	0.0672881i
$726$	−4.12075	−	1.88188i	−0.152935	−	0.0698433i
$727$	1.19458	+	8.30846i	0.0443044	+	0.308144i	0.999909	+	0.0134917i	$0.00429466\pi$
$727$	1.19458	+	8.30846i	0.0443044	+	0.308144i	−0.955605	+	0.294652i	$0.904796\pi$
$728$	1.49775	+	11.7144i	0.0555102	+	0.434166i
$729$	−0.415415	−	0.909632i	−0.0153857	−	0.0336901i
$730$	−10.3719	−	16.1390i	−0.383882	−	0.597333i
$731$	−32.2505	−	4.63693i	−1.19283	−	0.171503i
$732$	−1.53417	+	2.38722i	−0.0567047	+	0.0882342i
$733$	−18.5485	+	21.4061i	−0.685105	+	0.790653i	−0.986660	−	0.162796i	$-0.947949\pi$
$733$	−18.5485	+	21.4061i	−0.685105	+	0.790653i	0.301555	+	0.953449i	$0.402494\pi$
$734$	24.2623	+	7.12406i	0.895538	+	0.262954i
$735$	−13.0048	+	5.45438i	−0.479688	+	0.201188i
$736$	−4.60337	+	1.34498i	−0.169683	+	0.0495766i
$737$	−41.6030			−1.53247
$738$	−0.180563	+	0.614941i	−0.00664661	+	0.0226363i
$739$	21.7246	−	25.0715i	0.799152	−	0.922271i	−0.199182	−	0.979962i	$-0.563829\pi$
$739$	21.7246	−	25.0715i	0.799152	−	0.922271i	0.998334	+	0.0576918i	$0.0183741\pi$
$740$	−7.88084	+	12.2628i	−0.289705	+	0.450790i
$741$	2.36733	−	16.4651i	0.0869660	−	0.604862i
$742$	21.0030	+	0.328405i	0.771045	+	0.0120561i
$743$	−20.5907	+	9.40347i	−0.755400	+	0.344980i	−0.755611	−	0.655020i	$-0.772660\pi$
$743$	−20.5907	+	9.40347i	−0.755400	+	0.344980i	0.000210996		1.00000i	$0.499933\pi$
$744$	0.271924	+	0.313818i	0.00996924	+	0.0115051i
$745$	24.1082	−	3.46623i	0.883255	−	0.126993i
$746$	11.3495	+	5.18314i	0.415535	+	0.189768i
$747$	6.56155	−	1.92665i	0.240075	−	0.0704923i
$748$	3.59324	+	12.2374i	0.131382	+	0.447445i
$749$	6.33485	−	3.93259i	0.231471	−	0.143694i
$750$	11.8477	−	1.70344i	0.432615	−	0.0622007i
$751$	15.0443	−	13.0360i	0.548976	−	0.475690i	−0.335653	−	0.941986i	$-0.608957\pi$
$751$	15.0443	−	13.0360i	0.548976	−	0.475690i	0.884629	+	0.466296i	$0.154412\pi$
$752$	6.94451	−	3.17145i	0.253240	−	0.115651i
$753$	7.88396	+	12.2677i	0.287307	+	0.447059i
$754$	−30.1838	−	4.33978i	−1.09923	−	0.158046i
$755$	29.7892	+	19.1443i	1.08414	+	0.696734i
$756$	−2.54992	+	0.705615i	−0.0927398	+	0.0256630i
$757$	12.0321	−	40.9777i	0.437316	−	1.48936i	−0.386386	−	0.922337i	$-0.626277\pi$
$757$	12.0321	−	40.9777i	0.437316	−	1.48936i	0.823702	−	0.567023i	$-0.191905\pi$
$758$		−	26.8553i		−	0.975427i
$759$	−18.1268	−	5.34890i	−0.657963	−	0.194153i
$760$	−7.50769			−0.272333
$761$	−14.0389	+	47.8122i	−0.508911	+	1.73319i	0.157418	+	0.987532i	$0.449683\pi$
$761$	−14.0389	+	47.8122i	−0.508911	+	1.73319i	−0.666329	+	0.745658i	$0.732135\pi$
$762$	5.06579	+	4.38954i	0.183514	+	0.159016i
$763$	10.1610	+	23.2029i	0.367854	+	0.840000i
$764$	9.69289	+	1.39363i	0.350677	+	0.0504197i
$765$	5.48504	−	3.52502i	0.198312	−	0.127447i
$766$	7.97106	+	17.4542i	0.288006	+	0.630645i
$767$	−11.0293	−	12.7285i	−0.398247	−	0.459601i
$768$	0.989821	−	0.142315i	0.0357171	−	0.00513534i
$769$	−20.2765	+	44.3993i	−0.731189	+	1.60108i	0.0663379	+	0.997797i	$0.478868\pi$
$769$	−20.2765	+	44.3993i	−0.731189	+	1.60108i	−0.797527	+	0.603283i	$0.793859\pi$
$770$	20.0594	+	6.23224i	0.722891	+	0.224594i
$771$	−24.6843	+	7.24796i	−0.888983	+	0.261029i
$772$	0.0308777	−	0.0676127i	0.00111131	−	0.00243344i
$773$	−2.87758	−	20.0140i	−0.103500	−	0.719855i	−0.973812	−	0.227355i	$-0.926992\pi$
$773$	−2.87758	−	20.0140i	−0.103500	−	0.719855i	0.870312	−	0.492500i	$-0.163917\pi$
$774$	−7.60846	+	6.59277i	−0.273480	+	0.236972i
$775$	0.355559	−	0.162378i	0.0127720	−	0.00583280i
$776$	−13.0252	+	8.37080i	−0.467578	+	0.300494i
$777$	−14.2699	−	12.7610i	−0.511931	−	0.457798i
$778$	1.27486	−	1.98373i	0.0457061	−	0.0711201i
$779$	−1.80503	−	1.56407i	−0.0646719	−	0.0560385i
$780$	−8.62832	−	2.53350i	−0.308944	−	0.0907140i
$781$			31.1655i			1.11519i
$782$	6.42883	+	14.1272i	0.229894	+	0.505188i
$783$		−	6.83163i		−	0.244143i
$784$	0.779093	+	6.95651i	0.0278247	+	0.248447i
$785$	30.7197	−	35.4524i	1.09643	−	1.26535i
$786$	−3.64740	−	2.34404i	−0.130098	−	0.0836092i
$787$	4.67168	−	32.4922i	0.166527	−	1.15822i	−0.719467	−	0.694527i	$-0.755614\pi$
$787$	4.67168	−	32.4922i	0.166527	−	1.15822i	0.885994	−	0.463696i	$-0.153477\pi$
$788$	14.1830	−	9.11486i	0.505249	−	0.324704i
$789$	2.57056	+	5.62874i	0.0915144	+	0.200388i
$790$	2.41934	−	2.09637i	0.0860762	−	0.0745855i
$791$	19.4231	−	40.8290i	0.690606	−	1.45171i
$792$	3.58470	+	1.63708i	0.127377	+	0.0581711i
$793$	−3.56858	−	12.1535i	−0.126724	−	0.431583i
$794$	−1.57275	−	5.35628i	−0.0558146	−	0.190087i
$795$	−6.64445	+	14.5493i	−0.235654	+	0.516011i
$796$	0.395867	+	2.75331i	0.0140311	+	0.0975886i
$797$	−7.10271	−	8.19696i	−0.251591	−	0.290351i	0.615879	−	0.787840i	$-0.288801\pi$
$797$	−7.10271	−	8.19696i	−0.251591	−	0.290351i	−0.867470	+	0.497489i	$0.834255\pi$
$798$	1.55559	−	9.73622i	0.0550673	−	0.344658i
$799$	−13.3581	−	20.7857i	−0.472577	−	0.735344i
$800$	0.133966	−	0.931757i	0.00473643	−	0.0329426i
$801$	14.2882	+	9.18244i	0.504847	+	0.324446i
$802$	7.53360	+	6.52791i	0.266021	+	0.230508i
$803$	−36.0071	−	10.5727i	−1.27066	−	0.373101i
$804$	10.5569			0.372314
$805$	25.2370	+	4.06687i	0.889487	+	0.143338i
$806$	−1.85350			−0.0652868
$807$	14.7717	+	4.33737i	0.519989	+	0.152683i
$808$	−11.1322	−	9.64608i	−0.391628	−	0.339348i
$809$	8.94574	+	5.74908i	0.314516	+	0.202127i	0.688369	−	0.725361i	$-0.258327\pi$
$809$	8.94574	+	5.74908i	0.314516	+	0.202127i	−0.373853	+	0.927488i	$0.621964\pi$
$810$	0.286709	−	1.99411i	0.0100739	−	0.0700657i
$811$	27.1830	+	42.2975i	0.954523	+	1.48527i	0.872487	+	0.488638i	$0.162506\pi$
$811$	27.1830	+	42.2975i	0.954523	+	1.48527i	0.0820368	+	0.996629i	$0.473857\pi$
$812$	−17.8484	−	2.85171i	−0.626357	−	0.100075i
$813$	9.37946	+	10.8245i	0.328952	+	0.379631i
$814$	4.05798	+	28.2239i	0.142232	+	0.989246i
$815$	18.3447	−	40.1693i	0.642586	−	1.40707i
$816$	−0.911798	−	3.10530i	−0.0319193	−	0.108707i
$817$	−10.5699	−	35.9978i	−0.369794	−	1.25940i
$818$	−8.50329	−	3.88332i	−0.297311	−	0.135777i
$819$	5.07332	−	10.6646i	0.177276	−	0.372650i
$820$	−0.975800	+	0.845535i	−0.0340764	+	0.0295274i
$821$	19.6520	+	43.0318i	0.685859	+	1.50182i	0.856314	+	0.516455i	$0.172749\pi$
$821$	19.6520	+	43.0318i	0.685859	+	1.50182i	−0.170456	+	0.985365i	$0.554524\pi$
$822$	9.23605	−	5.93565i	0.322144	−	0.207030i
$823$	−4.83057	+	33.5974i	−0.168383	+	1.17113i	0.713843	+	0.700306i	$0.246953\pi$
$823$	−4.83057	+	33.5974i	−0.168383	+	1.17113i	−0.882226	+	0.470825i	$0.843956\pi$
$824$	−15.1483	−	9.73523i	−0.527716	−	0.339143i
$825$	2.42931	−	2.80357i	0.0845776	−	0.0976078i
$826$	−6.41865	−	7.64585i	−0.223334	−	0.266033i
$827$			34.9649i			1.21585i	0.793995	+	0.607925i	$0.207998\pi$
$827$			34.9649i			1.21585i	−0.793995	+	0.607925i	$0.792002\pi$
$828$	4.59975	+	1.35730i	0.159852	+	0.0471695i
$829$			46.5366i			1.61628i	0.588989	+	0.808141i	$0.299526\pi$
$829$			46.5366i			1.61628i	−0.588989	+	0.808141i	$0.700474\pi$
$830$	13.2190	+	3.88144i	0.458837	+	0.134727i
$831$	−4.29204	−	3.71907i	−0.148889	−	0.129013i
$832$	−2.41325	+	3.75509i	−0.0836644	+	0.130184i
$833$	21.9260	−	5.69986i	0.759691	−	0.197489i
$834$	13.8851	−	8.92343i	0.480803	−	0.308993i
$835$	−4.17172	+	1.90516i	−0.144368	+	0.0659308i
$836$	−11.0989	+	9.61727i	−0.383864	+	0.332620i
$837$	−0.0590948	−	0.411014i	−0.00204262	−	0.0142067i
$838$	−6.97569	+	15.2746i	−0.240971	+	0.527653i
$839$	−48.0502	+	14.1088i	−1.65888	+	0.487090i	−0.971068	−	0.238803i	$-0.923245\pi$
$839$	−48.0502	+	14.1088i	−1.65888	+	0.487090i	−0.687808	+	0.725893i	$0.741427\pi$
$840$	−5.09015	−	1.58145i	−0.175627	−	0.0545653i
$841$	7.34088	−	16.0743i	0.253134	−	0.554286i
$842$	−20.1882	+	2.90262i	−0.695731	+	0.100031i
$843$	13.9825	+	16.1367i	0.481583	+	0.555777i
$844$	10.4211	+	22.8190i	0.358708	+	0.785462i
$845$	11.7356	−	7.54199i	0.403716	−	0.259453i
$846$	−7.55671	−	1.08649i	−0.259805	−	0.0373543i
$847$	10.9790	−	4.80794i	0.377243	−	0.165203i
$848$	6.00017	+	5.19918i	0.206047	+	0.178540i
$849$	0.733250	−	2.49722i	0.0251651	−	0.0857044i
$850$	−3.04654			−0.104496
$851$	9.73167	+	33.3080i	0.333597	+	1.14178i
$852$		−	7.90836i		−	0.270936i
$853$	−12.0669	+	41.0959i	−0.413161	+	1.40710i	0.445835	+	0.895115i	$0.352907\pi$
$853$	−12.0669	+	41.0959i	−0.413161	+	1.40710i	−0.858996	+	0.511982i	$0.828911\pi$
$854$	−2.00232	−	7.23590i	−0.0685179	−	0.247608i
$855$	6.31587	+	4.05896i	0.215998	+	0.138814i
$856$	2.78951	+	0.401071i	0.0953436	+	0.0137083i
$857$	−21.2264	−	33.0289i	−0.725079	−	1.12824i	−0.986618	−	0.163052i	$-0.947866\pi$
$857$	−21.2264	−	33.0289i	−0.725079	−	1.12824i	0.261539	−	0.965193i	$-0.415770\pi$
$858$	−16.0010	+	7.30740i	−0.546264	+	0.249471i
$859$	−2.98316	+	2.58492i	−0.101784	+	0.0881965i	−0.704266	−	0.709936i	$-0.748724\pi$
$859$	−2.98316	+	2.58492i	−0.101784	+	0.0881965i	0.602482	+	0.798132i	$0.294178\pi$
$860$	−20.0755	+	2.88643i	−0.684570	+	0.0984263i
$861$	−0.894333	−	1.44064i	−0.0304788	−	0.0490970i
$862$	−8.87021	−	30.2092i	−0.302121	−	1.02893i
$863$	−51.0771	+	14.9976i	−1.73868	+	0.510524i	−0.988567	−	0.150781i	$-0.951821\pi$
$863$	−51.0771	+	14.9976i	−1.73868	+	0.510524i	−0.750117	+	0.661305i	$0.770003\pi$
$864$	−0.909632	−	0.415415i	−0.0309463	−	0.0141327i
$865$	−15.2288	+	2.18957i	−0.517795	+	0.0744476i
$866$	−0.445828	−	0.514512i	−0.0151498	−	0.0174838i
$867$	5.93603	−	2.71089i	0.201598	−	0.0920668i
$868$	−1.09849	−	0.0171761i	−0.0372851	−	0.000582993i
$869$	0.891179	−	6.19829i	0.0302312	−	0.210263i
$870$	7.44089	−	11.5782i	0.252270	−	0.392539i
$871$	−30.8588	+	35.6130i	−1.04561	+	1.20670i
$872$	−2.69729	+	9.18611i	−0.0913416	+	0.311081i
$873$	15.4831			0.524024
$874$	−11.7219	+	13.4913i	−0.396499	+	0.456348i
$875$	−17.5356	+	26.3701i	−0.592811	+	0.891473i
$876$	9.13695	+	2.68285i	0.308709	+	0.0906451i
$877$	−20.3998	+	23.5426i	−0.688852	+	0.794978i	−0.987201	−	0.159479i	$-0.949019\pi$
$877$	−20.3998	+	23.5426i	−0.688852	+	0.794978i	0.298349	+	0.954457i	$0.403564\pi$
$878$	1.95713	−	3.04535i	0.0660499	−	0.102776i
$879$	−1.83688	−	0.264103i	−0.0619563	−	0.00890797i
$880$	4.29228	+	6.67891i	0.144693	+	0.225146i
$881$	−18.2153	−	39.8860i	−0.613690	−	1.34379i	−0.920021	−	0.391869i	$-0.871829\pi$
$881$	−18.2153	−	39.8860i	−0.613690	−	1.34379i	0.306331	−	0.951925i	$-0.400899\pi$
$882$	3.10556	−	6.27340i	0.104570	−	0.211236i
$883$	−1.97126	−	13.7104i	−0.0663383	−	0.461393i	−0.995731	−	0.0923011i	$-0.970578\pi$
$883$	−1.97126	−	13.7104i	−0.0663383	−	0.461393i	0.929393	−	0.369092i	$-0.120331\pi$
$884$	13.1408	+	6.00118i	0.441972	+	0.201842i
$885$	7.29358	−	2.14159i	0.245171	−	0.0719887i
$886$	7.17269	−	2.10609i	0.240971	−	0.0707556i
$887$	34.4710	+	15.7424i	1.15742	+	0.528577i	0.899212	−	0.437512i	$-0.144140\pi$
$887$	34.4710	+	15.7424i	1.15742	+	0.528577i	0.258209	+	0.966089i	$0.416868\pi$
$888$	−1.02973	−	7.16191i	−0.0345554	−	0.240338i
$889$	−17.5913	+	2.24913i	−0.589993	+	0.0754334i
$890$	14.2142	+	31.1248i	0.476462	+	1.04331i
$891$	−2.13057	−	3.31524i	−0.0713769	−	0.111065i
$892$	0.645507	+	0.0928099i	0.0216132	+	0.00310750i
$893$	15.3815	−	23.9341i	0.514723	−	0.800925i
$894$	−7.91707	+	9.13679i	−0.264787	+	0.305580i
$895$	28.2724	+	8.30154i	0.945044	+	0.277490i
$896$	−1.46502	+	2.20311i	−0.0489430	+	0.0736008i
$897$	−18.0243	+	11.5494i	−0.601812	+	0.385623i
$898$	40.6105			1.35519
$899$	0.799210	−	2.72186i	0.0266551	−	0.0907791i
$900$	−0.616446	+	0.711416i	−0.0205482	+	0.0237139i
$901$	13.8917	−	21.6159i	0.462800	−	0.720131i
$902$	−0.359442	+	2.49998i	−0.0119681	+	0.0832401i
$903$	0.416431	−	26.6327i	0.0138580	−	0.886280i
$904$	15.5448	−	7.09908i	0.517013	−	0.236112i
$905$	30.2164	+	34.8716i	1.00443	+	1.15917i
$906$	−17.3979	+	2.50144i	−0.578007	+	0.0831048i
$907$	−30.7951	−	14.0637i	−1.02254	−	0.466976i	−0.167680	−	0.985842i	$-0.553627\pi$
$907$	−30.7951	−	14.0637i	−1.02254	−	0.466976i	−0.854856	+	0.518865i	$0.826355\pi$
$908$	−18.5513	+	5.44716i	−0.615648	+	0.180770i
$909$	4.14991	+	14.1333i	0.137644	+	0.468772i
$910$	20.2139	−	12.5485i	0.670084	−	0.415979i
$911$	−14.9478	+	2.14917i	−0.495242	+	0.0712051i	−0.385411	−	0.922745i	$-0.625940\pi$
$911$	−14.9478	+	2.14917i	−0.495242	+	0.0712051i	−0.109832	+	0.993950i	$0.535031\pi$
$912$	2.81639	−	2.44042i	0.0932600	−	0.0808103i
$913$	24.5142	−	11.1953i	0.811302	−	0.370509i
$914$	−12.9763	−	20.1915i	−0.429218	−	0.667876i
$915$	5.65866	+	0.813593i	0.187070	+	0.0268966i
$916$	10.7996	+	6.94048i	0.356829	+	0.229320i
$917$	11.0556	−	3.05931i	0.365089	−	0.101027i
$918$	−0.911798	+	3.10530i	−0.0300938	+	0.102490i
$919$		−	0.231297i		−	0.00762979i	−0.999993	−	0.00381489i	$-0.998786\pi$
$919$		−	0.231297i		−	0.00762979i	0.999993	−	0.00381489i	$-0.00121432\pi$
$920$	6.31731	+	7.31032i	0.208276	+	0.241014i
$921$	−10.9532			−0.360921
$922$	2.82030	−	9.60507i	0.0928818	−	0.316326i
$923$	26.6783	+	23.1168i	0.878126	+	0.760900i
$924$	−9.55079	+	4.18250i	−0.314198	+	0.137594i
$925$	−6.74179	−	0.969323i	−0.221669	−	0.0318711i
$926$	18.9939	−	12.2067i	0.624179	−	0.401136i
$927$	7.48031	+	16.3796i	0.245686	+	0.537976i
$928$	−4.47377	−	5.16300i	−0.146859	−	0.169484i
$929$	−16.4895	+	2.37083i	−0.541003	+	0.0777845i	−0.407399	−	0.913250i	$-0.633564\pi$
$929$	−16.4895	+	2.37083i	−0.541003	+	0.0777845i	−0.133604	+	0.991035i	$0.542655\pi$
$930$	0.347515	−	0.760951i	0.0113954	−	0.0249526i
$931$	16.4582	+	20.2392i	0.539396	+	0.663313i
$932$	−6.07643	+	1.78420i	−0.199040	+	0.0584434i
$933$	−0.497402	+	1.08916i	−0.0162842	+	0.0356574i
$934$	−2.16407	−	15.0514i	−0.0708106	−	0.492498i
$935$	19.4186	−	16.8263i	0.635057	−	0.550280i
$936$	4.06031	−	1.85428i	0.132715	−	0.0606091i
$937$	−16.1932	+	10.4067i	−0.529009	+	0.339974i	−0.777727	−	0.628602i	$-0.783627\pi$
$937$	−16.1932	+	10.4067i	−0.529009	+	0.339974i	0.248718	+	0.968576i	$0.419991\pi$
$938$	−18.6187	+	20.8203i	−0.607922	+	0.679806i
$939$	2.45919	−	3.82658i	0.0802527	−	0.124876i
$940$	−11.6237	−	10.0720i	−0.379124	−	0.328513i
$941$	40.7886	+	11.9766i	1.32967	+	0.390426i	0.867973	−	0.496611i	$-0.165423\pi$
$941$	40.7886	+	11.9766i	1.32967	+	0.390426i	0.461697	+	0.887038i	$0.347241\pi$
$942$			23.2850i			0.758667i
$943$	−0.00411624	+	3.07365i	−0.000134043	+	0.100092i
$944$		−	3.77318i		−	0.122807i
$945$	3.42711	+	4.08235i	0.111484	+	0.132799i
$946$	−25.9810	+	29.9836i	−0.844714	+	0.974852i
$947$	1.81518	+	1.16655i	0.0589856	+	0.0379077i	0.569801	−	0.821783i	$-0.307020\pi$
$947$	1.81518	+	1.16655i	0.0589856	+	0.0379077i	−0.510816	+	0.859690i	$0.670657\pi$
$948$	−0.226140	+	1.57284i	−0.00734469	+	0.0510834i
$949$	−35.7585	+	22.9806i	−1.16077	+	0.745982i
$950$	−1.45728	−	3.19100i	−0.0472804	−	0.103530i
$951$	−13.6148	+	11.7973i	−0.441490	+	0.382553i
$952$	7.73234	+	3.67841i	0.250607	+	0.119218i
$953$	39.6157	+	18.0919i	1.28328	+	0.586053i	0.936096	−	0.351744i	$-0.114411\pi$
$953$	39.6157	+	18.0919i	1.28328	+	0.586053i	0.347182	+	0.937798i	$0.387139\pi$
$954$	−2.23678	−	7.61776i	−0.0724183	−	0.246634i
$955$	−5.55808	−	18.9291i	−0.179855	−	0.612531i
$956$	2.19231	−	4.80048i	0.0709042	−	0.155259i
$957$	−3.83144	−	26.6483i	−0.123853	−	0.861416i
$958$	−5.71958	−	6.60075i	−0.184791	−	0.213261i
$959$	−4.58289	+	28.6837i	−0.147989	+	0.926244i
$960$	−1.08918	−	1.69480i	−0.0351532	−	0.0546994i
$961$	−4.38722	+	30.5138i	−0.141523	+	0.984316i
$962$	27.1702	+	17.4612i	0.876002	+	0.562972i
$963$	−2.12985	−	1.84553i	−0.0686335	−	0.0594713i
$964$	−14.8576	−	4.36258i	−0.478531	−	0.140509i
$965$	−0.149746			−0.00482048
$966$	−10.7892	+	6.67780i	−0.347137	+	0.214855i
$967$	53.7688			1.72909			0.864544	−	0.502557i	$-0.167607\pi$
$967$	53.7688			1.72909			0.864544	+	0.502557i	$0.167607\pi$
$968$	4.34663	+	1.27629i	0.139706	+	0.0410214i
$969$	−9.11495	−	7.89815i	−0.292814	−	0.253725i
$970$	26.2408	+	16.8639i	0.842540	+	0.541468i
$971$	7.88887	−	54.8683i	0.253166	−	1.76081i	−0.325784	−	0.945444i	$-0.605628\pi$
$971$	7.88887	−	54.8683i	0.253166	−	1.76081i	0.578950	−	0.815363i	$-0.303463\pi$
$972$	0.540641	+	0.841254i	0.0173411	+	0.0269832i
$973$	−6.88975	+	43.1219i	−0.220875	+	1.38243i
$974$	4.96432	+	5.72913i	0.159067	+	0.183573i
$975$	−0.597984	−	4.15907i	−0.0191508	−	0.133197i
$976$	1.17882	−	2.58126i	0.0377331	−	0.0826240i
$977$	−12.1718	−	41.4533i	−0.389410	−	1.32621i	−0.888188	−	0.459479i	$-0.848036\pi$
$977$	−12.1718	−	41.4533i	−0.389410	−	1.32621i	0.498778	−	0.866730i	$-0.333782\pi$
$978$	6.17552	+	21.0319i	0.197471	+	0.672526i
$979$	60.8839	+	27.8048i	1.94586	+	0.888644i
$980$	12.0962	−	7.24963i	0.386398	−	0.231581i
$981$	7.23549	−	6.26959i	0.231011	−	0.200172i
$982$	−2.58344	−	5.65694i	−0.0824408	−	0.180520i
$983$	−40.8296	+	26.2396i	−1.30226	+	0.836913i	−0.993456	−	0.114212i	$-0.963566\pi$
$983$	−40.8296	+	26.2396i	−1.30226	+	0.836913i	−0.308806	+	0.951125i	$0.599929\pi$
$984$	0.0912098	−	0.634378i	0.00290766	−	0.0202232i
$985$	−28.5733	−	18.3629i	−0.910420	−	0.585091i
$986$	−14.4789	+	16.7095i	−0.461101	+	0.532139i
$987$	15.4701	−	12.9871i	0.492420	−	0.413384i
$988$			16.6344i			0.529212i
$989$	−26.1574	+	40.5822i	−0.831758	+	1.29044i
$990$		−	7.93924i		−	0.252326i
$991$	11.8339	+	3.47475i	0.375917	+	0.110379i	0.464232	−	0.885713i	$-0.346330\pi$
$991$	11.8339	+	3.47475i	0.375917	+	0.110379i	−0.0883156	+	0.996093i	$0.528148\pi$
$992$	−0.313818	−	0.271924i	−0.00996372	−	0.00863361i
$993$	−12.3410	+	19.2030i	−0.391630	+	0.609388i
$994$	15.5968	+	13.9476i	0.494701	+	0.442390i
$995$	4.71430	−	3.02969i	0.149453	−	0.0960478i
$996$	−6.22057	+	2.84084i	−0.197106	+	0.0900155i
$997$	4.97663	−	4.31228i	0.157612	−	0.136571i	−0.572485	−	0.819915i	$-0.694021\pi$
$997$	4.97663	−	4.31228i	0.157612	−	0.136571i	0.730097	+	0.683344i	$0.239475\pi$
$998$	−2.49842	−	17.3769i	−0.0790862	−	0.550056i
$999$	−3.00576	+	6.58170i	−0.0950981	+	0.208236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.s.a.97.7	✓	160
7.6	odd	2	inner	966.2.s.a.97.10	yes	160
23.14	odd	22	inner	966.2.s.a.727.10	yes	160
161.83	even	22	inner	966.2.s.a.727.7	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.s.a.97.7	✓	160	1.1	even	1	trivial
966.2.s.a.97.10	yes	160	7.6	odd	2	inner
966.2.s.a.727.7	yes	160	161.83	even	22	inner
966.2.s.a.727.10	yes	160	23.14	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.959493 - 0.281733i) q^{2} +(-0.755750 - 0.654861i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.286709 - 1.99411i) q^{5} +(0.540641 + 0.841254i) q^{6} +(-2.61261 - 0.417427i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.959493 - 0.281733i) q^{2} +(-0.755750 - 0.654861i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.286709 - 1.99411i) q^{5} +(0.540641 + 0.841254i) q^{6} +(-2.61261 - 0.417427i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.142315 + 0.989821i) q^{9} +(-0.836900 + 1.83256i) q^{10} +(1.11026 + 3.78120i) q^{11} +(-0.281733 - 0.959493i) q^{12} +(4.06031 + 1.85428i) q^{13} +(2.38918 + 1.13658i) q^{14} +(-1.52254 + 1.31929i) q^{15} +(0.415415 + 0.909632i) q^{16} +(2.72263 - 1.74973i) q^{17} +(0.142315 - 0.989821i) q^{18} +(3.13503 + 2.01476i) q^{19} +(1.31929 - 1.52254i) q^{20} +(1.70113 + 2.02637i) q^{21} -3.94083i q^{22} +(-0.676160 - 4.74793i) q^{23} +1.00000i q^{24} +(0.903208 + 0.265206i) q^{25} +(-3.37343 - 2.92309i) q^{26} +(0.540641 - 0.841254i) q^{27} +(-1.97219 - 1.76365i) q^{28} +(5.74713 - 3.69346i) q^{29} +(1.83256 - 0.836900i) q^{30} +(0.313818 - 0.271924i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(1.63708 - 3.58470i) q^{33} +(-3.10530 + 0.911798i) q^{34} +(-1.58145 + 5.09015i) q^{35} +(-0.415415 + 0.909632i) q^{36} +(-7.16191 + 1.02973i) q^{37} +(-2.44042 - 2.81639i) q^{38} +(-1.85428 - 4.06031i) q^{39} +(-1.69480 + 1.08918i) q^{40} +(-0.634378 - 0.0912098i) q^{41} +(-1.06132 - 2.42355i) q^{42} +(-7.60846 - 6.59277i) q^{43} +(-1.11026 + 3.78120i) q^{44} +2.01461 q^{45} +(-0.688875 + 4.74610i) q^{46} -7.63441i q^{47} +(0.281733 - 0.959493i) q^{48} +(6.65151 + 2.18115i) q^{49} +(-0.791905 - 0.508926i) q^{50} +(-3.20345 - 0.460587i) q^{51} +(2.41325 + 3.75509i) q^{52} +(7.22190 - 3.29813i) q^{53} +(-0.755750 + 0.654861i) q^{54} +(7.85843 - 1.12987i) q^{55} +(1.39543 + 2.24784i) q^{56} +(-1.04991 - 3.57567i) q^{57} +(-6.55490 + 1.92469i) q^{58} +(-3.43221 - 1.56744i) q^{59} +(-1.99411 + 0.286709i) q^{60} +(-1.85829 - 2.14459i) q^{61} +(-0.377716 + 0.172497i) q^{62} +(0.0413642 - 2.64543i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(4.86176 - 7.56505i) q^{65} +(-2.58069 + 2.97828i) q^{66} +(-2.97423 + 10.1293i) q^{67} +3.23639 q^{68} +(-2.59822 + 4.03103i) q^{69} +(2.95145 - 4.43842i) q^{70} +(7.58801 + 2.22804i) q^{71} +(0.654861 - 0.755750i) q^{72} +(-5.14835 + 8.01099i) q^{73} +(7.16191 + 1.02973i) q^{74} +(-0.508926 - 0.791905i) q^{75} +(1.54809 + 3.38985i) q^{76} +(-1.32231 - 10.3423i) q^{77} +(0.635248 + 4.41825i) q^{78} +(-1.44542 - 0.660100i) q^{79} +(1.93301 - 0.567582i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(0.582985 + 0.266240i) q^{82} +(-0.973229 - 6.76895i) q^{83} +(0.335541 + 2.62439i) q^{84} +(-2.70854 - 5.93087i) q^{85} +(5.44286 + 8.46926i) q^{86} +(-6.76210 - 0.972243i) q^{87} +(2.13057 - 3.31524i) q^{88} +(11.1224 - 12.8359i) q^{89} +(-1.93301 - 0.567582i) q^{90} +(-9.83399 - 6.53940i) q^{91} +(1.99810 - 4.35977i) q^{92} -0.415240 q^{93} +(-2.15086 + 7.32517i) q^{94} +(4.91649 - 5.67394i) q^{95} +(-0.540641 + 0.841254i) q^{96} +(2.20348 - 15.3255i) q^{97} +(-5.76758 - 3.96675i) q^{98} +(-3.58470 + 1.63708i) 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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