LMFDB - Embedded newform 920.2.bb.b.11.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [920,2,Mod(11,920)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(920, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 11, 0, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("920.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bb (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [480,2,0,-4,48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.20
Character	$\chi$	$=$	920.11
Dual form			920.2.bb.b.251.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.567911 + 1.29517i) q^{2} +(-0.417492 + 2.90372i) q^{3} +(-1.35496 - 1.47109i) q^{4} +(0.959493 - 0.281733i) q^{5} +(-3.52373 - 2.18978i) q^{6} +(-2.59694 - 2.99703i) q^{7} +(2.67481 - 0.919458i) q^{8} +(-5.37883 - 1.57937i) q^{9} +(-0.180013 + 1.40271i) q^{10} +(1.45984 - 2.27156i) q^{11} +(4.83731 - 3.32025i) q^{12} +(-1.80368 - 1.56290i) q^{13} +(5.35650 - 1.66145i) q^{14} +(0.417492 + 2.90372i) q^{15} +(-0.328193 + 3.98651i) q^{16} +(-6.50839 + 2.97228i) q^{17} +(5.10025 - 6.06959i) q^{18} +(4.78524 + 2.18535i) q^{19} +(-1.71452 - 1.02976i) q^{20} +(9.78674 - 6.28955i) q^{21} +(2.11301 + 3.18079i) q^{22} +(2.91434 - 3.80876i) q^{23} +(1.55314 + 8.15077i) q^{24} +(0.841254 - 0.540641i) q^{25} +(3.04856 - 1.44850i) q^{26} +(3.17571 - 6.95383i) q^{27} +(-0.890152 + 7.88116i) q^{28} +(3.38405 - 1.54544i) q^{29} +(-3.99793 - 1.10833i) q^{30} +(8.17242 - 1.17502i) q^{31} +(-4.97685 - 2.68905i) q^{32} +(5.98650 + 5.18734i) q^{33} +(-0.153441 - 10.1175i) q^{34} +(-3.33610 - 2.14398i) q^{35} +(4.96469 + 10.0527i) q^{36} +(2.31872 + 0.680838i) q^{37} +(-5.54800 + 4.95664i) q^{38} +(5.29125 - 4.58489i) q^{39} +(2.30742 - 1.63579i) q^{40} +(7.76984 - 2.28143i) q^{41} +(2.58808 + 16.2474i) q^{42} +(4.51454 + 0.649093i) q^{43} +(-5.31968 + 0.930305i) q^{44} -5.60591 q^{45} +(3.27792 + 5.93761i) q^{46} +2.82882i q^{47} +(-11.4387 - 2.61732i) q^{48} +(-1.24187 + 8.63743i) q^{49} +(0.222468 + 1.39661i) q^{50} +(-5.91348 - 20.1395i) q^{51} +(0.144747 + 4.77103i) q^{52} +(-6.73907 - 7.77731i) q^{53} +(7.20291 + 8.06225i) q^{54} +(0.760736 - 2.59083i) q^{55} +(-9.70195 - 5.62869i) q^{56} +(-8.34345 + 12.9827i) q^{57} +(0.0797819 + 5.26061i) q^{58} +(0.524253 - 0.605020i) q^{59} +(3.70595 - 4.54858i) q^{60} +(0.543398 + 3.77942i) q^{61} +(-3.11935 + 11.2520i) q^{62} +(9.23509 + 20.2220i) q^{63} +(6.30919 - 4.91875i) q^{64} +(-2.17094 - 0.991434i) q^{65} +(-10.1183 + 4.80763i) q^{66} +(-8.78544 - 13.6704i) q^{67} +(13.1911 + 5.54710i) q^{68} +(9.84286 + 10.0526i) q^{69} +(4.67144 - 3.10325i) q^{70} +(-5.47514 - 8.51948i) q^{71} +(-15.8395 + 0.721104i) q^{72} +(1.80492 - 3.95221i) q^{73} +(-2.19863 + 2.61649i) q^{74} +(1.21865 + 2.66848i) q^{75} +(-3.26895 - 10.0006i) q^{76} +(-10.5990 + 1.52391i) q^{77} +(2.93328 + 9.45690i) q^{78} +(5.70803 - 6.58742i) q^{79} +(0.808231 + 3.91749i) q^{80} +(4.71819 + 3.03220i) q^{81} +(-1.45772 + 11.3589i) q^{82} +(3.96423 - 13.5009i) q^{83} +(-22.5131 - 5.87508i) q^{84} +(-5.40737 + 4.68551i) q^{85} +(-3.40455 + 5.47849i) q^{86} +(3.07472 + 10.4716i) q^{87} +(1.81619 - 7.41824i) q^{88} +(-17.0823 - 2.45607i) q^{89} +(3.18366 - 7.26064i) q^{90} +9.46443i q^{91} +(-9.55181 + 0.873449i) q^{92} +24.2210i q^{93} +(-3.66381 - 1.60651i) q^{94} +(5.20709 + 0.748667i) q^{95} +(9.88606 - 13.3287i) q^{96} +(-2.42670 - 8.26459i) q^{97} +(-10.4817 - 6.51373i) q^{98} +(-11.4399 + 9.91271i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 2 q^{2} - 4 q^{4} + 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} - 2 q^{10} + 3 q^{12} - 56 q^{16} + 7 q^{18} + 4 q^{20} - 8 q^{21} - 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} - 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) $ 480 * q + 2 * q^2 - 4 * q^4 + 48 * q^5 + 5 * q^6 - q^8 - 48 * q^9 - 2 * q^10 + 3 * q^12 - 56 * q^16 + 7 * q^18 + 4 * q^20 - 8 * q^21 - 4 * q^23 + 2 * q^24 - 48 * q^25 + 7 * q^26 + 12 * q^27 - 5 * q^30 + 102 * q^32 + q^34 + 54 * q^36 - 8 * q^37 - 45 * q^38 + 45 * q^40 + 10 * q^42 + 23 * q^44 - 480 * q^45 + 32 * q^46 + 154 * q^48 - 48 * q^49 - 9 * q^50 - 7 * q^52 - 32 * q^53 - 27 * q^54 + 43 * q^56 - 40 * q^58 - 12 * q^59 + 8 * q^60 + 8 * q^61 + 158 * q^62 - 73 * q^64 - 88 * q^66 - 10 * q^68 + 20 * q^69 + 3 * q^72 - 11 * q^74 - 110 * q^76 - 300 * q^78 + 144 * q^79 + q^80 - 56 * q^81 - 59 * q^82 - 146 * q^84 + 18 * q^86 - 100 * q^88 - 7 * q^90 + 19 * q^92 - 316 * q^94 + 65 * q^96 - 98 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$-1$	$e\left(\frac{9}{22}\right)$	$-1$	$1$

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 $

$2$	−0.567911	+	1.29517i	−0.401573	+	0.915827i
$2$	−0.567911	+	1.29517i	−0.401573	+	0.915827i
$3$	−0.417492	+	2.90372i	−0.241039	+	1.67647i	0.405895	+	0.913920i	$0.366960\pi$
$3$	−0.417492	+	2.90372i	−0.241039	+	1.67647i	−0.646934	+	0.762546i	$0.723949\pi$
$4$	−1.35496	−	1.47109i	−0.677478	−	0.735543i
$5$	0.959493	−	0.281733i	0.429098	−	0.125995i
$5$	0.959493	−	0.281733i	0.429098	−	0.125995i
$6$	−3.52373	−	2.18978i	−1.43856	−	0.893974i
$7$	−2.59694	−	2.99703i	−0.981550	−	1.13277i	−0.991141	−	0.132815i	$-0.957598\pi$
$7$	−2.59694	−	2.99703i	−0.981550	−	1.13277i	0.00959057	−	0.999954i	$-0.496947\pi$
$8$	2.67481	−	0.919458i	0.945687	−	0.325077i
$9$	−5.37883	−	1.57937i	−1.79294	−	0.526456i
$10$	−0.180013	+	1.40271i	−0.0569252	+	0.443576i
$11$	1.45984	−	2.27156i	0.440159	−	0.684901i	−0.548318	−	0.836270i	$-0.684732\pi$
$11$	1.45984	−	2.27156i	0.440159	−	0.684901i	0.988477	+	0.151369i	$0.0483682\pi$
$12$	4.83731	−	3.32025i	1.39641	−	0.958473i
$13$	−1.80368	−	1.56290i	−0.500251	−	0.433470i	0.367830	−	0.929893i	$-0.380101\pi$
$13$	−1.80368	−	1.56290i	−0.500251	−	0.433470i	−0.868081	+	0.496423i	$0.834646\pi$
$14$	5.35650	−	1.66145i	1.43159	−	0.444040i
$15$	0.417492	+	2.90372i	0.107796	+	0.749738i
$16$	−0.328193	+	3.98651i	−0.0820483	+	0.996628i
$17$	−6.50839	+	2.97228i	−1.57852	+	0.720884i	−0.995780	−	0.0917766i	$-0.970745\pi$
$17$	−6.50839	+	2.97228i	−1.57852	+	0.720884i	−0.582737	+	0.812661i	$0.698018\pi$
$18$	5.10025	−	6.06959i	1.20214	−	1.43062i
$19$	4.78524	+	2.18535i	1.09781	+	0.501353i	0.880162	−	0.474674i	$-0.157434\pi$
$19$	4.78524	+	2.18535i	1.09781	+	0.501353i	0.217648	+	0.976027i	$0.430161\pi$
$20$	−1.71452	−	1.02976i	−0.383379	−	0.230262i
$21$	9.78674	−	6.28955i	2.13564	−	1.37249i
$22$	2.11301	+	3.18079i	0.450494	+	0.678147i
$23$	2.91434	−	3.80876i	0.607682	−	0.794181i
$23$	2.91434	−	3.80876i	0.607682	−	0.794181i
$24$	1.55314	+	8.15077i	0.317033	+	1.66377i
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	3.04856	−	1.44850i	0.597871	−	0.284073i
$27$	3.17571	−	6.95383i	0.611165	−	1.33827i
$28$	−0.890152	+	7.88116i	−0.168223	+	1.48940i
$29$	3.38405	−	1.54544i	0.628402	−	0.286982i	−0.0756452	−	0.997135i	$-0.524102\pi$
$29$	3.38405	−	1.54544i	0.628402	−	0.286982i	0.704047	+	0.710153i	$0.251374\pi$
$30$	−3.99793	−	1.10833i	−0.729919	−	0.202352i
$31$	8.17242	−	1.17502i	1.46781	−	0.211039i	0.638411	−	0.769696i	$-0.279592\pi$
$31$	8.17242	−	1.17502i	1.46781	−	0.211039i	0.829399	+	0.558656i	$0.188683\pi$
$32$	−4.97685	−	2.68905i	−0.879791	−	0.475362i
$33$	5.98650	+	5.18734i	1.04212	+	0.902999i
$34$	−0.153441	−	10.1175i	−0.0263149	−	1.73514i
$35$	−3.33610	−	2.14398i	−0.563904	−	0.362399i
$36$	4.96469	+	10.0527i	0.827449	+	1.67545i
$37$	2.31872	+	0.680838i	0.381195	+	0.111929i	0.466716	−	0.884407i	$-0.345437\pi$
$37$	2.31872	+	0.680838i	0.381195	+	0.111929i	−0.0855203	+	0.996336i	$0.527255\pi$
$38$	−5.54800	+	4.95664i	−0.900004	+	0.804074i
$39$	5.29125	−	4.58489i	0.847278	−	0.734170i
$40$	2.30742	−	1.63579i	0.364835	−	0.258642i
$41$	7.76984	−	2.28143i	1.21344	−	0.356299i	0.388466	−	0.921463i	$-0.373005\pi$
$41$	7.76984	−	2.28143i	1.21344	−	0.356299i	0.824979	+	0.565164i	$0.191187\pi$
$42$	2.58808	+	16.2474i	0.399349	+	2.50703i
$43$	4.51454	+	0.649093i	0.688461	+	0.0989858i	0.477662	−	0.878544i	$-0.341484\pi$
$43$	4.51454	+	0.649093i	0.688461	+	0.0989858i	0.210799	+	0.977529i	$0.432393\pi$
$44$	−5.31968	+	0.930305i	−0.801972	+	0.140249i
$45$	−5.60591			−0.835680
$46$	3.27792	+	5.93761i	0.483303	+	0.875453i
$47$			2.82882i			0.412625i	0.978486	+	0.206313i	$0.0661464\pi$
$47$			2.82882i			0.412625i	−0.978486	+	0.206313i	$0.933854\pi$
$48$	−11.4387	−	2.61732i	−1.65104	−	0.377778i
$49$	−1.24187	+	8.63743i	−0.177411	+	1.23392i
$50$	0.222468	+	1.39661i	0.0314617	+	0.197510i
$51$	−5.91348	−	20.1395i	−0.828053	−	2.82009i
$52$	0.144747	+	4.77103i	0.0200728	+	0.661622i
$53$	−6.73907	−	7.77731i	−0.925683	−	1.06830i	−0.997485	−	0.0708763i	$-0.977420\pi$
$53$	−6.73907	−	7.77731i	−0.925683	−	1.06830i	0.0718021	−	0.997419i	$-0.477125\pi$
$54$	7.20291	+	8.06225i	0.980192	+	1.09713i
$55$	0.760736	−	2.59083i	0.102578	−	0.349347i
$56$	−9.70195	−	5.62869i	−1.29648	−	0.752166i
$57$	−8.34345	+	12.9827i	−1.10512	+	1.71960i
$58$	0.0797819	+	5.26061i	0.0104759	+	0.690751i
$59$	0.524253	−	0.605020i	0.0682519	−	0.0787669i	−0.720597	−	0.693354i	$-0.756132\pi$
$59$	0.524253	−	0.605020i	0.0682519	−	0.0787669i	0.788849	+	0.614587i	$0.210678\pi$
$60$	3.70595	−	4.54858i	0.478436	−	0.587220i
$61$	0.543398	+	3.77942i	0.0695750	+	0.483905i	0.994582	+	0.103955i	$0.0331497\pi$
$61$	0.543398	+	3.77942i	0.0695750	+	0.483905i	−0.925007	+	0.379950i	$0.875941\pi$
$62$	−3.11935	+	11.2520i	−0.396158	+	1.42901i
$63$	9.23509	+	20.2220i	1.16351	+	2.54774i
$64$	6.30919	−	4.91875i	0.788649	−	0.614843i
$65$	−2.17094	−	0.991434i	−0.269272	−	0.122972i
$66$	−10.1183	+	4.80763i	−1.24548	+	0.591778i
$67$	−8.78544	−	13.6704i	−1.07331	−	1.67011i	−0.638607	−	0.769533i	$-0.720489\pi$
$67$	−8.78544	−	13.6704i	−1.07331	−	1.67011i	−0.434705	−	0.900573i	$-0.643148\pi$
$68$	13.1911	+	5.54710i	1.59965	+	0.672685i
$69$	9.84286	+	10.0526i	1.18494	+	1.21019i
$70$	4.67144	−	3.10325i	0.558344	−	0.370909i
$71$	−5.47514	−	8.51948i	−0.649779	−	1.01108i	−0.997302	−	0.0734047i	$-0.976614\pi$
$71$	−5.47514	−	8.51948i	−0.649779	−	1.01108i	0.347523	−	0.937671i	$-0.387023\pi$
$72$	−15.8395	+	0.721104i	−1.86670	+	0.0849830i
$73$	1.80492	−	3.95221i	0.211249	−	0.462572i	−0.774112	−	0.633048i	$-0.781803\pi$
$73$	1.80492	−	3.95221i	0.211249	−	0.462572i	0.985362	+	0.170477i	$0.0545308\pi$
$74$	−2.19863	+	2.61649i	−0.255586	+	0.304161i
$75$	1.21865	+	2.66848i	0.140718	+	0.308130i
$76$	−3.26895	−	10.0006i	−0.374975	−	1.14714i
$77$	−10.5990	+	1.52391i	−1.20787	+	0.173666i
$78$	2.93328	+	9.45690i	0.332129	+	1.07078i
$79$	5.70803	−	6.58742i	0.642204	−	0.741143i	−0.337559	−	0.941304i	$-0.609601\pi$
$79$	5.70803	−	6.58742i	0.642204	−	0.741143i	0.979763	+	0.200161i	$0.0641467\pi$
$80$	0.808231	+	3.91749i	0.0903630	+	0.437989i
$81$	4.71819	+	3.03220i	0.524243	+	0.336911i
$82$	−1.45772	+	11.3589i	−0.160978	+	1.25439i
$83$	3.96423	−	13.5009i	0.435131	−	1.48192i	−0.392029	−	0.919953i	$-0.628227\pi$
$83$	3.96423	−	13.5009i	0.435131	−	1.48192i	0.827160	−	0.561967i	$-0.189955\pi$
$84$	−22.5131	−	5.87508i	−2.45638	−	0.641024i
$85$	−5.40737	+	4.68551i	−0.586511	+	0.508215i
$86$	−3.40455	+	5.47849i	−0.367122	+	0.590761i
$87$	3.07472	+	10.4716i	0.329645	+	1.12267i
$88$	1.81619	−	7.41824i	0.193607	−	0.790788i
$89$	−17.0823	−	2.45607i	−1.81072	−	0.260343i	−0.847838	−	0.530256i	$-0.822096\pi$
$89$	−17.0823	−	2.45607i	−1.81072	−	0.260343i	−0.962885	+	0.269913i	$0.913005\pi$
$90$	3.18366	−	7.26064i	0.335587	−	0.765338i
$91$			9.46443i			0.992141i
$92$	−9.55181	+	0.873449i	−0.995845	+	0.0910634i
$93$			24.2210i			2.51160i
$94$	−3.66381	−	1.60651i	−0.377893	−	0.165699i
$95$	5.20709	+	0.748667i	0.534236	+	0.0768116i
$96$	9.88606	−	13.3287i	1.00899	−	1.36036i
$97$	−2.42670	−	8.26459i	−0.246394	−	0.839142i	−0.986092	−	0.166202i	$-0.946850\pi$
$97$	−2.42670	−	8.26459i	−0.246394	−	0.839142i	0.739697	−	0.672940i	$-0.234969\pi$
$98$	−10.4817	−	6.51373i	−1.05881	−	0.657986i
$99$	−11.4399	+	9.91271i	−1.14975	+	0.996265i
$100$	−1.93519	−	0.505013i	−0.193519	−	0.0505013i
$101$	−0.816787	+	2.78172i	−0.0812733	+	0.276792i	−0.990096	−	0.140391i	$-0.955164\pi$
$101$	−0.816787	+	2.78172i	−0.0812733	+	0.276792i	0.908823	+	0.417182i	$0.136982\pi$
$102$	29.4425	+	3.77843i	2.91524	+	0.374120i
$103$	9.50954	+	6.11141i	0.937003	+	0.602175i	0.917544	−	0.397635i	$-0.130169\pi$
$103$	9.50954	+	6.11141i	0.937003	+	0.602175i	0.0194595	+	0.999811i	$0.493805\pi$
$104$	−6.26152	−	2.52204i	−0.613992	−	0.247307i
$105$	7.61833	−	8.79203i	0.743473	−	0.858014i
$106$	13.9002	−	4.31146i	1.35010	−	0.418766i
$107$	7.97864	−	1.14716i	0.771324	−	0.110900i	0.254594	−	0.967048i	$-0.418058\pi$
$107$	7.97864	−	1.14716i	0.771324	−	0.110900i	0.516730	+	0.856148i	$0.327149\pi$
$108$	−14.5326	+	4.75039i	−1.39840	+	0.457106i
$109$	−0.538879	−	1.17998i	−0.0516153	−	0.113022i	0.882067	−	0.471123i	$-0.156151\pi$
$109$	−0.538879	−	1.17998i	−0.0516153	−	0.113022i	−0.933683	+	0.358102i	$0.883424\pi$
$110$	2.92355	+	2.45665i	0.278749	+	0.234232i
$111$	−2.94501	+	6.44868i	−0.279528	+	0.612082i
$112$	12.8000	−	9.36912i	1.20948	−	0.885299i
$113$	9.28256	+	14.4440i	0.873230	+	1.35877i	0.932742	+	0.360545i	$0.117409\pi$
$113$	9.28256	+	14.4440i	0.873230	+	1.35877i	−0.0595116	+	0.998228i	$0.518954\pi$
$114$	−12.0765	−	18.1792i	−1.13107	−	1.70264i
$115$	1.72324	−	4.47554i	0.160693	−	0.417346i
$116$	−6.85871	−	2.88422i	−0.636816	−	0.267793i
$117$	7.23331	+	11.2552i	0.668719	+	1.04055i
$118$	0.485878	+	1.02260i	0.0447287	+	0.0941376i
$119$	25.8099	+	11.7870i	2.36599	+	1.08051i
$120$	3.78656	+	7.38304i	0.345664	+	0.673976i
$121$	1.54073	+	3.37372i	0.140066	+	0.306702i
$122$	−5.20360	−	1.44257i	−0.471112	−	0.130605i
$123$	3.38079	+	23.5139i	0.304836	+	2.12018i
$124$	−12.8018	−	10.4302i	−1.14964	−	0.936664i
$125$	0.654861	−	0.755750i	0.0585725	−	0.0675963i
$126$	−31.4358	+	0.476752i	−2.80052	+	0.0424724i
$127$	2.14629	−	3.33970i	0.190453	−	0.296350i	−0.732875	−	0.680363i	$-0.761822\pi$
$127$	2.14629	−	3.33970i	0.190453	−	0.296350i	0.923328	+	0.384013i	$0.125458\pi$
$128$	2.78758	+	10.9649i	0.246389	+	0.969171i
$129$	−3.76957	+	12.8380i	−0.331893	+	1.13032i
$130$	2.51698	−	2.24870i	0.220754	−	0.197224i
$131$	−2.91737	−	3.36682i	−0.254892	−	0.294161i	0.613854	−	0.789420i	$-0.289619\pi$
$131$	−2.91737	−	3.36682i	−0.254892	−	0.294161i	−0.868745	+	0.495259i	$0.835073\pi$
$132$	−0.480423	−	15.8353i	−0.0418155	−	1.37828i
$133$	−5.87744	−	20.0167i	−0.509638	−	1.73567i
$134$	22.6949	−	3.61511i	1.96054	−	0.312298i
$135$	1.08795	−	7.56685i	0.0936358	−	0.651251i
$136$	−14.6758	+	13.9345i	−1.25844	+	1.19487i
$137$			0.380632i			0.0325196i	0.999868	+	0.0162598i	$0.00517588\pi$
$137$			0.380632i			0.0325196i	−0.999868	+	0.0162598i	$0.994824\pi$
$138$	−18.6097	+	7.03927i	−1.58416	+	0.599223i
$139$	7.59377			0.644095			0.322048	−	0.946723i	$-0.395629\pi$
$139$	7.59377			0.644095			0.322048	+	0.946723i	$0.395629\pi$
$140$	1.36628	+	7.81270i	0.115472	+	0.660294i
$141$	−8.21410	−	1.18101i	−0.691752	−	0.0994590i
$142$	14.1436	−	2.25296i	1.18690	−	0.189064i
$143$	−6.18330	+	1.81558i	−0.517074	+	0.151827i
$144$	8.06147	−	20.9245i	0.671789	−	1.74370i
$145$	2.81157	−	2.43624i	0.233488	−	0.202319i
$146$	4.09378	+	4.58218i	0.338803	+	0.379224i
$147$	−24.5622	−	7.21212i	−2.02586	−	0.594846i
$148$	−2.14019	−	4.33355i	−0.175923	−	0.356215i
$149$	−12.5592	−	8.07132i	−1.02889	−	0.661228i	−0.0866762	−	0.996237i	$-0.527625\pi$
$149$	−12.5592	−	8.07132i	−1.02889	−	0.661228i	−0.942215	+	0.335008i	$0.891261\pi$
$150$	−4.14824	+	0.0629118i	−0.338702	+	0.00513673i
$151$	−11.8155	−	10.2382i	−0.961529	−	0.833169i	0.0245076	−	0.999700i	$-0.492198\pi$
$151$	−11.8155	−	10.2382i	−0.961529	−	0.833169i	−0.986036	+	0.166530i	$0.946744\pi$
$152$	14.8089	+	1.44556i	1.20116	+	0.117250i
$153$	39.7019	−	5.70827i	3.20971	−	0.461486i
$154$	4.04557	−	14.5930i	0.326002	−	1.17594i
$155$	7.51034	−	3.42986i	0.603245	−	0.275493i
$156$	−13.9142	−	1.57156i	−1.11403	−	0.125826i
$157$	8.62870	−	18.8942i	0.688645	−	1.50792i	−0.164571	−	0.986365i	$-0.552624\pi$
$157$	8.62870	−	18.8942i	0.688645	−	1.50792i	0.853216	−	0.521557i	$-0.174649\pi$
$158$	5.29021	+	11.1340i	0.420867	+	0.885771i
$159$	25.3967	−	16.3214i	2.01409	−	1.29437i
$160$	−5.53284	−	1.17799i	−0.437410	−	0.0931279i
$161$	−18.9833	+	1.15676i	−1.49609	+	0.0911651i
$162$	−6.60673	+	4.38886i	−0.519074	+	0.344822i
$163$	−5.21835	+	3.35363i	−0.408733	+	0.262677i	−0.728812	−	0.684714i	$-0.759927\pi$
$163$	−5.21835	+	3.35363i	−0.408733	+	0.262677i	0.320079	+	0.947391i	$0.396291\pi$
$164$	−13.8840	−	8.33887i	−1.08416	−	0.651156i
$165$	7.20545	+	3.29062i	0.560944	+	0.256174i
$166$	15.2347	+	12.8017i	1.18244	+	0.993604i
$167$	−0.149124	+	0.0681026i	−0.0115396	+	0.00526994i	−0.421176	−	0.906979i	$-0.638383\pi$
$167$	−0.149124	+	0.0681026i	−0.0115396	+	0.00526994i	0.409637	+	0.912249i	$0.365655\pi$
$168$	20.3947	−	25.8218i	1.57348	−	1.99220i
$169$	−1.03948	−	7.22974i	−0.0799600	−	0.556134i
$170$	−2.99765	−	9.66443i	−0.229909	−	0.741228i
$171$	−22.2876	−	19.3123i	−1.70437	−	1.47685i
$172$	−5.16213	−	7.52078i	−0.393609	−	0.573454i
$173$	−0.159051	+	0.247488i	−0.0120924	+	0.0188161i	−0.847247	−	0.531199i	$-0.821742\pi$
$173$	−0.159051	+	0.247488i	−0.0120924	+	0.0188161i	0.835155	+	0.550015i	$0.185378\pi$
$174$	−15.3087	−	1.96460i	−1.16055	−	0.148936i
$175$	−3.80500	−	1.11725i	−0.287631	−	0.0844560i
$176$	8.57649	+	6.56519i	0.646477	+	0.494870i
$177$	1.53794	+	1.77488i	0.115599	+	0.133408i
$178$	12.8823	−	20.7298i	0.965567	−	1.55376i
$179$	15.1020	−	4.43435i	1.12878	−	0.331439i	0.336550	−	0.941666i	$-0.390740\pi$
$179$	15.1020	−	4.43435i	1.12878	−	0.331439i	0.792227	+	0.610227i	$0.208922\pi$
$180$	7.59576	+	8.24679i	0.566155	+	0.614679i
$181$	−1.10560	+	7.68959i	−0.0821783	+	0.571562i	0.906579	+	0.422035i	$0.138684\pi$
$181$	−1.10560	+	7.68959i	−0.0821783	+	0.571562i	−0.988758	+	0.149527i	$0.952225\pi$
$182$	−12.2581	−	5.37495i	−0.908630	−	0.398418i
$183$	−11.2012			−0.828020
$184$	4.29331	−	12.8673i	0.316507	−	0.948590i
$185$	2.41661			0.177673
$186$	−31.3704	−	13.7554i	−2.30019	−	1.00859i
$187$	−2.74951	+	19.1232i	−0.201064	+	1.39843i
$188$	4.16143	−	3.83292i	0.303504	−	0.279544i
$189$	−29.0879	+	8.54099i	−2.11584	+	0.621265i
$190$	−3.92682	+	6.31892i	−0.284881	+	0.458422i
$191$	1.79097	+	2.06689i	0.129590	+	0.149555i	0.816836	−	0.576870i	$-0.195726\pi$
$191$	1.79097	+	2.06689i	0.129590	+	0.149555i	−0.687246	+	0.726425i	$0.741181\pi$
$192$	11.6486	+	20.3737i	0.840668	+	1.47035i
$193$	1.96732	+	0.577657i	0.141611	+	0.0415806i	0.351770	−	0.936087i	$-0.385580\pi$
$193$	1.96732	+	0.577657i	0.141611	+	0.0415806i	−0.210159	+	0.977667i	$0.567398\pi$
$194$	12.0822	+	1.55054i	0.867454	+	0.111323i
$195$	3.78520	−	5.88989i	0.271064	−	0.421784i
$196$	14.3891	−	9.87642i	1.02779	−	0.705459i
$197$	0.118757	+	0.102904i	0.00846109	+	0.00733158i	0.659081	−	0.752072i	$-0.270945\pi$
$197$	0.118757	+	0.102904i	0.00846109	+	0.00733158i	−0.650620	+	0.759404i	$0.725491\pi$
$198$	−6.34186	−	20.4462i	−0.450696	−	1.45305i
$199$	−2.62241	−	18.2392i	−0.185898	−	1.29295i	−0.842495	−	0.538704i	$-0.818914\pi$
$199$	−2.62241	−	18.2392i	−0.185898	−	1.29295i	0.656597	−	0.754241i	$-0.271995\pi$
$200$	1.75310	−	2.21961i	0.123963	−	0.156950i
$201$	43.3629	−	19.8032i	3.05859	−	1.39681i
$202$	−3.13895	−	2.63765i	−0.220856	−	0.185584i
$203$	−13.4199	−	6.12866i	−0.941892	−	0.430148i
$204$	−21.6144	+	35.9873i	−1.51331	+	2.51962i
$205$	6.81235	−	4.37803i	0.475795	−	0.305775i
$206$	−13.3159	+	8.84578i	−0.927764	+	0.616315i
$207$	−21.6912	+	15.8839i	−1.50764	+	1.10400i
$208$	6.82247	−	6.67746i	0.473053	−	0.462999i
$209$	11.9498	−	7.67970i	0.826588	−	0.531216i
$210$	7.06068	+	14.8602i	0.487233	+	1.02545i
$211$	−4.89813	+	10.7254i	−0.337201	+	0.738367i	−0.999945	−	0.0104787i	$-0.996664\pi$
$211$	−4.89813	+	10.7254i	−0.337201	+	0.738367i	0.662744	+	0.748846i	$0.269392\pi$
$212$	−2.30995	+	20.4517i	−0.158648	+	1.40463i
$213$	27.0240	−	12.3415i	1.85166	−	0.845623i
$214$	−3.04539	+	10.9852i	−0.208178	+	0.750934i
$215$	4.51454	−	0.649093i	0.307889	−	0.0442678i
$216$	2.10066	−	21.5201i	0.142932	−	1.46426i
$217$	−24.7448	−	21.4415i	−1.67979	−	1.45554i
$218$	1.83432	−	0.0278191i	0.124236	−	0.00188415i
$219$	10.7226	+	6.89099i	0.724566	+	0.465650i
$220$	−4.84210	+	2.39135i	−0.326454	+	0.161225i
$221$	16.3844	+	4.81090i	1.10214	+	0.323616i
$222$	−6.67967	−	7.47658i	−0.448310	−	0.501795i
$223$	−11.8047	+	10.2288i	−0.790500	+	0.684972i	−0.953413	−	0.301668i	$-0.902457\pi$
$223$	−11.8047	+	10.2288i	−0.790500	+	0.684972i	0.162913	+	0.986640i	$0.447911\pi$
$224$	4.86541	+	21.8990i	0.325084	+	1.46319i
$225$	−5.37883	+	1.57937i	−0.358589	+	0.105291i
$226$	−23.9791	+	3.81967i	−1.59507	+	0.254081i
$227$	−6.86109	−	0.986475i	−0.455386	−	0.0654747i	−0.0891948	−	0.996014i	$-0.528429\pi$
$227$	−6.86109	−	0.986475i	−0.455386	−	0.0654747i	−0.366191	+	0.930540i	$0.619338\pi$
$228$	30.4036	−	5.31698i	2.01353	−	0.352126i
$229$	−13.4293			−0.887433			−0.443717	−	0.896167i	$-0.646340\pi$
$229$	−13.4293			−0.887433			−0.443717	+	0.896167i	$0.646340\pi$
$230$	4.81796	+	4.77360i	0.317687	+	0.314762i
$231$		−	31.4129i		−	2.06682i
$232$	7.63071	−	7.24525i	0.500981	−	0.475674i
$233$	−3.44109	+	23.9333i	−0.225433	+	1.56792i	0.491560	+	0.870844i	$0.336427\pi$
$233$	−3.44109	+	23.9333i	−0.225433	+	1.56792i	−0.716993	+	0.697080i	$0.754482\pi$
$234$	−18.6854	+	2.97642i	−1.22150	+	0.194575i
$235$	0.796970	+	2.71423i	0.0519886	+	0.177057i
$236$	−1.60038	+	0.0485535i	−0.104176	+	0.00316056i
$237$	16.7450	+	19.3248i	1.08770	+	1.25528i
$238$	−29.9239	+	26.7344i	−1.93968	+	1.73293i
$239$	−3.66216	+	12.4722i	−0.236886	+	0.806759i	0.752138	+	0.659005i	$0.229022\pi$
$239$	−3.66216	+	12.4722i	−0.236886	+	0.806759i	−0.989024	+	0.147754i	$0.952796\pi$
$240$	−11.7128	+	0.711357i	−0.756055	+	0.0459179i
$241$	−7.57875	+	11.7928i	−0.488190	+	0.759639i	−0.994725	−	0.102581i	$-0.967290\pi$
$241$	−7.57875	+	11.7928i	−0.488190	+	0.759639i	0.506534	+	0.862220i	$0.330926\pi$
$242$	−5.24455	+	0.0795384i	−0.337133	+	0.00511292i
$243$	4.24410	−	4.89795i	0.272259	−	0.314204i
$244$	4.82357	−	5.92032i	0.308797	−	0.379010i
$245$	1.24187	+	8.63743i	0.0793405	+	0.551825i
$246$	−32.3746	−	8.97510i	−2.06413	−	0.572231i
$247$	−5.21557	−	11.4205i	−0.331859	−	0.726670i
$248$	20.7793	−	10.6571i	1.31949	−	0.676729i
$249$	37.5479	+	17.1476i	2.37950	+	1.08668i
$250$	0.606925	+	1.27736i	0.0383853	+	0.0807872i
$251$	7.24186	+	11.2686i	0.457102	+	0.711265i	0.990938	−	0.134324i	$-0.0428862\pi$
$251$	7.24186	+	11.2686i	0.457102	+	0.711265i	−0.533835	+	0.845588i	$0.679250\pi$
$252$	17.2352	−	40.9856i	1.08572	−	2.58185i
$253$	−4.39734	−	12.1803i	−0.276458	−	0.765767i
$254$	3.10659	+	4.67647i	0.194925	+	0.293428i
$255$	−11.3479	−	17.6577i	−0.710633	−	1.10577i
$256$	−15.7846	−	2.61669i	−0.986536	−	0.163543i
$257$	−5.88964	+	12.8965i	−0.367386	+	0.804463i	0.632175	+	0.774826i	$0.282162\pi$
$257$	−5.88964	+	12.8965i	−0.367386	+	0.804463i	−0.999561	+	0.0296371i	$0.990565\pi$
$258$	−14.4867	−	12.1731i	−0.901900	−	0.757863i
$259$	−3.98109	−	8.71736i	−0.247373	−	0.541671i
$260$	1.48304	+	4.53699i	0.0919741	+	0.281372i
$261$	−20.6431	+	2.96802i	−1.27777	+	0.183716i
$262$	6.01743	−	1.86645i	0.371758	−	0.115310i
$263$	1.14086	−	1.31662i	0.0703485	−	0.0811865i	−0.719484	−	0.694509i	$-0.755622\pi$
$263$	1.14086	−	1.31662i	0.0703485	−	0.0811865i	0.789833	+	0.613322i	$0.210167\pi$
$264$	20.7823	+	8.37079i	1.27906	+	0.515186i
$265$	−8.65721	−	5.56365i	−0.531808	−	0.341773i
$266$	29.2630	+	3.75539i	1.79423	+	0.230258i
$267$	14.2635	−	48.5770i	0.872911	−	2.97286i
$268$	−8.20648	+	31.4469i	−0.501291	+	1.92093i
$269$	4.89624	−	4.24261i	0.298529	−	0.258677i	−0.492697	−	0.870201i	$-0.663989\pi$
$269$	4.89624	−	4.24261i	0.298529	−	0.258677i	0.791226	+	0.611524i	$0.209443\pi$
$270$	9.18254	+	5.70638i	0.558831	+	0.347279i
$271$	5.41170	+	18.4306i	0.328737	+	1.11958i	0.943640	+	0.330974i	$0.107377\pi$
$271$	5.41170	+	18.4306i	0.328737	+	1.11958i	−0.614903	+	0.788603i	$0.710805\pi$
$272$	−9.71303	−	26.9213i	−0.588939	−	1.63234i
$273$	−27.4821	−	3.95133i	−1.66329	−	0.239145i
$274$	−0.492985	−	0.216165i	−0.0297823	−	0.0130590i
$275$		−	2.70021i		−	0.162829i
$276$	1.45155	−	28.1005i	0.0873733	−	1.69145i
$277$		−	24.1858i		−	1.45319i	−0.687068	−	0.726593i	$-0.741103\pi$
$277$		−	24.1858i		−	1.45319i	0.687068	−	0.726593i	$-0.258897\pi$
$278$	−4.31258	+	9.83526i	−0.258652	+	0.589880i
$279$	−45.8139	−	6.58704i	−2.74281	−	0.394356i
$280$	−10.8947	−	2.66734i	−0.651085	−	0.159404i
$281$	1.99525	+	6.79520i	0.119027	+	0.405368i	0.997354	−	0.0726912i	$-0.0231587\pi$
$281$	1.99525	+	6.79520i	0.119027	+	0.405368i	−0.878328	+	0.478059i	$0.841341\pi$
$282$	6.19449	−	9.96799i	0.368876	−	0.593585i
$283$	9.33245	−	8.08661i	0.554756	−	0.480699i	−0.331781	−	0.943356i	$-0.607649\pi$
$283$	9.33245	−	8.08661i	0.554756	−	0.480699i	0.886537	+	0.462657i	$0.153104\pi$
$284$	−5.11433	+	19.5979i	−0.303480	+	1.16292i
$285$	−4.34784	+	14.8074i	−0.257544	+	0.877114i
$286$	1.16007	−	9.03954i	0.0685962	−	0.534519i
$287$	−27.0153	−	17.3617i	−1.59466	−	1.02483i
$288$	22.5226	+	22.3242i	1.32716	+	1.31547i
$289$	22.3920	−	25.8418i	1.31718	−	1.52011i
$290$	1.55863	+	5.02504i	0.0915262	+	0.295080i
$291$	25.0112	−	3.59607i	1.46618	−	0.210805i
$292$	−8.25963	+	2.69988i	−0.483358	+	0.157999i
$293$	1.27492	+	2.79168i	0.0744815	+	0.163092i	0.943210	−	0.332197i	$-0.107790\pi$
$293$	1.27492	+	2.79168i	0.0744815	+	0.163092i	−0.868729	+	0.495288i	$0.835062\pi$
$294$	23.2901	−	27.7165i	1.35831	−	1.61646i
$295$	0.332563	−	0.728212i	0.0193626	−	0.0423981i
$296$	6.82814	−	0.310855i	0.396877	−	0.0180681i
$297$	−11.1600	−	17.3653i	−0.647569	−	1.00764i
$298$	17.5863	−	11.6826i	1.01875	−	0.676755i
$299$	−11.2092	+	2.31497i	−0.648247	+	0.133878i
$300$	2.27435	−	5.40842i	0.131309	−	0.312255i
$301$	−9.77864	−	15.2159i	−0.563631	−	0.877027i
$302$	19.9703	−	9.48873i	1.14916	−	0.546015i
$303$	−7.73635	−	3.53307i	−0.444442	−	0.202970i
$304$	−10.2824	+	18.3592i	−0.589736	+	1.05297i
$305$	1.58617	+	3.47323i	0.0908239	+	0.198877i
$306$	−15.1539	+	54.6627i	−0.866292	+	3.12486i
$307$	3.35843	+	23.3584i	0.191676	+	1.33313i	0.827572	+	0.561360i	$0.189722\pi$
$307$	3.35843	+	23.3584i	0.191676	+	1.33313i	−0.635896	+	0.771775i	$0.719369\pi$
$308$	16.6030	+	13.5273i	0.946045	+	0.770788i
$309$	−21.7160	+	25.0616i	−1.23538	+	1.42571i
$310$	0.177063	+	11.6751i	0.0100565	+	0.663099i
$311$	0.336387	−	0.523428i	0.0190748	−	0.0296809i	−0.831585	−	0.555397i	$-0.812566\pi$
$311$	0.336387	−	0.523428i	0.0190748	−	0.0296809i	0.850660	+	0.525716i	$0.176203\pi$
$312$	9.93746	−	17.1288i	0.562598	−	0.969726i
$313$	−0.772329	+	2.63031i	−0.0436546	+	0.148674i	−0.978436	−	0.206549i	$-0.933777\pi$
$313$	−0.772329	+	2.63031i	−0.0436546	+	0.148674i	0.934782	+	0.355223i	$0.115595\pi$
$314$	19.5710	+	21.9059i	1.10445	+	1.23622i
$315$	14.5582	+	16.8011i	0.820262	+	0.946633i
$316$	−17.4248	+	0.528648i	−0.980222	+	0.0297388i
$317$	0.192504	+	0.655608i	0.0108121	+	0.0368226i	0.964722	−	0.263269i	$-0.0848008\pi$
$317$	0.192504	+	0.655608i	0.0108121	+	0.0368226i	−0.953910	+	0.300092i	$0.902983\pi$
$318$	6.71609	+	42.1622i	0.376620	+	2.36434i
$319$	1.42961	−	9.94316i	0.0800428	−	0.556710i
$320$	4.66786	−	6.49701i	0.260941	−	0.363194i
$321$			23.6467i			1.31983i
$322$	9.28262	−	25.2436i	0.517300	−	1.40677i
$323$	−37.6397			−2.09433
$324$	−1.93231	−	11.0494i	−0.107351	−	0.613853i
$325$	−2.36232	−	0.339650i	−0.131038	−	0.0188404i
$326$	−1.37998	−	8.66324i	−0.0764301	−	0.479812i
$327$	3.65132	−	1.07212i	0.201918	−	0.0592886i
$328$	18.6851	−	13.2464i	1.03171	−	0.731411i
$329$	8.47804	−	7.34626i	0.467409	−	0.405012i
$330$	−8.35398	+	7.46354i	−0.459871	+	0.410854i
$331$	1.28006	+	0.375858i	0.0703582	+	0.0206590i	0.316722	−	0.948518i	$-0.397418\pi$
$331$	1.28006	+	0.375858i	0.0703582	+	0.0206590i	−0.246364	+	0.969177i	$0.579236\pi$
$332$	−25.2324	+	12.4614i	−1.38481	+	0.683910i
$333$	−11.3967	−	7.32423i	−0.624537	−	0.401365i
$334$	−0.00351573	−	0.231818i	−0.000192372	−	0.0126845i
$335$	−12.2810	−	10.6415i	−0.670981	−	0.581408i
$336$	21.8615	+	41.0792i	1.19264	+	2.24105i
$337$	10.7118	−	1.54012i	0.583507	−	0.0838957i	0.155761	−	0.987795i	$-0.450217\pi$
$337$	10.7118	−	1.54012i	0.583507	−	0.0838957i	0.427746	+	0.903899i	$0.359308\pi$
$338$	9.95411	+	2.75954i	0.541432	+	0.150099i
$339$	−45.8167	+	20.9238i	−2.48842	+	1.13642i
$340$	14.2195	+	1.60605i	0.771162	+	0.0871003i
$341$	9.26132	−	20.2795i	0.501529	−	1.09819i
$342$	37.6701	−	17.8986i	2.03697	−	0.967847i
$343$	5.75895	−	3.70105i	0.310954	−	0.199838i
$344$	12.6723	−	2.41473i	0.683247	−	0.130194i
$345$	12.2763	+	6.87231i	0.660933	+	0.369993i
$346$	−0.230213	−	0.346549i	−0.0123763	−	0.0186306i
$347$	−27.1339	+	17.4379i	−1.45662	+	0.936116i	−0.457731	+	0.889091i	$0.651338\pi$
$347$	−27.1339	+	17.4379i	−1.45662	+	0.936116i	−0.998894	+	0.0470255i	$0.985026\pi$
$348$	11.2384	−	18.7117i	0.602444	−	1.00305i
$349$	8.97024	+	4.09657i	0.480166	+	0.219285i	0.640768	−	0.767735i	$-0.278616\pi$
$349$	8.97024	+	4.09657i	0.480166	+	0.219285i	−0.160602	+	0.987019i	$0.551343\pi$
$350$	3.60793	−	4.29364i	0.192852	−	0.229505i
$351$	−16.5961	+	7.57918i	−0.885834	+	0.404547i
$352$	−13.3737	+	7.37961i	−0.712823	+	0.393334i
$353$	2.39019	+	16.6241i	0.127217	+	0.884813i	0.949059	+	0.315098i	$0.102037\pi$
$353$	2.39019	+	16.6241i	0.127217	+	0.884813i	−0.821842	+	0.569715i	$0.807054\pi$
$354$	−3.17219	+	0.983929i	−0.168600	+	0.0522952i
$355$	−7.65357	−	6.63186i	−0.406209	−	0.351982i
$356$	19.5327	+	28.4574i	1.03523	+	1.50824i
$357$	−45.0016	+	70.0238i	−2.38174	+	3.70605i
$358$	−2.83333	+	22.0781i	−0.149746	+	1.16686i
$359$	−13.0464	−	3.83076i	−0.688561	−	0.202180i	−0.0813088	−	0.996689i	$-0.525910\pi$
$359$	−13.0464	−	3.83076i	−0.688561	−	0.202180i	−0.607252	+	0.794509i	$0.707728\pi$
$360$	−14.9947	+	5.15440i	−0.790292	+	0.271661i
$361$	5.68045	+	6.55559i	0.298971	+	0.345031i
$362$	−9.33148	−	5.79894i	−0.490452	−	0.304785i
$363$	−10.4396	+	3.06534i	−0.547937	+	0.160889i
$364$	13.9230	−	12.8239i	0.729763	−	0.672154i
$365$	0.618336	−	4.30062i	0.0323652	−	0.225105i
$366$	6.36130	−	14.5076i	0.332511	−	0.758323i
$367$	28.7128			1.49880			0.749398	−	0.662119i	$-0.230343\pi$
$367$	28.7128			1.49880			0.749398	+	0.662119i	$0.230343\pi$
$368$	14.2272	+	12.8681i	0.741644	+	0.670794i
$369$	−45.3959			−2.36321
$370$	−1.37242	+	3.12993i	−0.0713487	+	0.162718i
$371$	−5.80783	+	40.3944i	−0.301528	+	2.09717i
$372$	35.6312	−	32.8184i	1.84739	−	1.70155i
$373$	16.5850	−	4.86979i	0.858738	−	0.252148i	0.177419	−	0.984135i	$-0.443225\pi$
$373$	16.5850	−	4.86979i	0.858738	−	0.252148i	0.681318	+	0.731987i	$0.261407\pi$
$374$	−23.2065	−	14.4214i	−1.19998	−	0.745712i
$375$	1.92109	+	2.21705i	0.0992046	+	0.114488i
$376$	2.60098	+	7.56654i	0.134135	+	0.390215i
$377$	−8.51911	−	2.50144i	−0.438757	−	0.128831i
$378$	5.45727	−	42.5245i	0.280692	−	2.18722i
$379$	2.38394	−	3.70949i	0.122455	−	0.190543i	−0.774614	−	0.632434i	$-0.782056\pi$
$379$	2.38394	−	3.70949i	0.122455	−	0.190543i	0.897069	+	0.441891i	$0.145692\pi$
$380$	−5.95402	−	8.67449i	−0.305435	−	0.444992i
$381$	8.80150	+	7.62654i	0.450914	+	0.390719i
$382$	−3.69410	+	1.14581i	−0.189007	+	0.0586248i
$383$	0.634390	+	4.41228i	0.0324158	+	0.225457i	0.999589	−	0.0286605i	$-0.00912417\pi$
$383$	0.634390	+	4.41228i	0.0324158	+	0.225457i	−0.967173	+	0.254117i	$0.918215\pi$
$384$	−33.0029	+	3.51658i	−1.68417	+	0.179455i
$385$	−9.74037	+	4.44828i	−0.496415	+	0.226705i
$386$	−1.86543	+	2.21996i	−0.0949477	+	0.112993i
$387$	−23.2578	−	10.6215i	−1.18226	−	0.539921i
$388$	−8.86986	+	14.7680i	−0.450299	+	0.749734i
$389$	4.01908	−	2.58291i	0.203775	−	0.130959i	−0.434773	−	0.900540i	$-0.643171\pi$
$389$	4.01908	−	2.58291i	0.203775	−	0.130959i	0.638549	+	0.769581i	$0.279535\pi$
$390$	5.47878	+	8.24743i	0.277429	+	0.417625i
$391$	−7.64695	+	33.4511i	−0.386723	+	1.69170i
$392$	4.61998	+	24.2453i	0.233344	+	1.22457i
$393$	10.9943	−	7.06561i	0.554589	−	0.356413i
$394$	−0.200722	+	0.0953712i	−0.0101122	+	0.00480473i
$395$	3.62093	−	7.92872i	0.182189	−	0.398937i
$396$	30.0830	+	3.39778i	1.51173	+	0.170745i
$397$	14.1911	−	6.48085i	0.712230	−	0.325264i	−0.0261421	−	0.999658i	$-0.508322\pi$
$397$	14.1911	−	6.48085i	0.712230	−	0.325264i	0.738372	+	0.674394i	$0.235595\pi$
$398$	25.1123	+	6.96178i	1.25877	+	0.348963i
$399$	60.5768	−	8.70963i	3.03263	−	0.436027i
$400$	1.87918	+	3.53110i	0.0939589	+	0.176555i
$401$	11.5198	+	9.98198i	0.575272	+	0.498476i	0.893213	−	0.449634i	$-0.148446\pi$
$401$	11.5198	+	9.98198i	0.575272	+	0.498476i	−0.317940	+	0.948111i	$0.602991\pi$
$402$	1.02232	+	67.4090i	0.0509887	+	3.36206i
$403$	−16.5769	−	10.6533i	−0.825753	−	0.530679i
$404$	5.19886	−	2.56754i	0.258653	−	0.127740i
$405$	5.38134	+	1.58010i	0.267401	+	0.0785160i
$406$	15.5590	−	13.9006i	0.772179	−	0.689874i
$407$	4.93153	−	4.27320i	0.244447	−	0.211814i
$408$	−34.3348	−	48.4320i	−1.69983	−	2.39774i
$409$	−29.2118	+	8.57736i	−1.44443	+	0.424123i	−0.907696	−	0.419628i	$-0.862161\pi$
$409$	−29.2118	+	8.57736i	−1.44443	+	0.424123i	−0.536735	+	0.843751i	$0.680342\pi$
$410$	1.80151	+	11.3095i	0.0889702	+	0.558537i
$411$	−1.10525	−	0.158911i	−0.0545180	−	0.00783850i
$412$	−3.89458	−	22.2700i	−0.191872	−	1.09717i
$413$	−3.17471			−0.156217
$414$	−8.25372	−	37.1145i	−0.405648	−	1.82408i
$415$		−	14.0709i		−	0.690713i
$416$	4.77393	+	12.6285i	0.234061	+	0.619163i
$417$	−3.17034	+	22.0502i	−0.155252	+	1.07980i
$418$	3.16011	+	19.8385i	0.154566	+	0.970333i
$419$	−3.44656	−	11.7379i	−0.168375	−	0.573434i	−0.999841	−	0.0178571i	$-0.994316\pi$
$419$	−3.44656	−	11.7379i	−0.168375	−	0.573434i	0.831465	−	0.555577i	$-0.187503\pi$
$420$	−23.2563	+	0.705569i	−1.13479	+	0.0344283i
$421$	−23.9730	−	27.6663i	−1.16837	−	1.34837i	−0.925697	−	0.378267i	$-0.876520\pi$
$421$	−23.9730	−	27.6663i	−1.16837	−	1.34837i	−0.242676	−	0.970107i	$-0.578025\pi$
$422$	−11.1096	−	12.4350i	−0.540806	−	0.605326i
$423$	4.46774	−	15.2157i	0.217229	−	0.739814i
$424$	−25.1766	−	14.6065i	−1.22269	−	0.709355i
$425$	−3.86827	+	6.01914i	−0.187639	+	0.291971i
$426$	0.637116	+	42.0097i	0.0308684	+	2.03538i
$427$	9.91583	−	11.4435i	0.479861	−	0.553789i
$428$	−12.4983	−	10.1829i	−0.604126	−	0.492210i
$429$	−2.69046	−	18.7126i	−0.129897	−	0.903453i
$430$	−1.72317	+	6.21575i	−0.0830985	+	0.299750i
$431$	−9.06396	−	19.8473i	−0.436596	−	0.956011i	−0.992211	−	0.124571i	$-0.960244\pi$
$431$	−9.06396	−	19.8473i	−0.436596	−	0.956011i	0.555615	−	0.831440i	$-0.312483\pi$
$432$	26.6793	+	14.9422i	1.28361	+	0.718907i
$433$	10.9007	+	4.97819i	0.523854	+	0.239236i	0.659748	−	0.751487i	$-0.270663\pi$
$433$	10.9007	+	4.97819i	0.523854	+	0.239236i	−0.135893	+	0.990723i	$0.543390\pi$
$434$	41.8234	−	19.8720i	2.00759	−	0.953887i
$435$	5.90035	+	9.18113i	0.282900	+	0.440201i
$436$	−1.00570	+	2.39156i	−0.0481642	+	0.114535i
$437$	22.2693	−	11.8570i	1.06528	−	0.567196i
$438$	−15.0145	+	9.97417i	−0.717421	+	0.476584i
$439$	16.7995	+	26.1406i	0.801799	+	1.24762i	0.965316	+	0.261083i	$0.0840795\pi$
$439$	16.7995	+	26.1406i	0.801799	+	1.24762i	−0.163518	+	0.986540i	$0.552284\pi$
$440$	−0.347335	−	7.62943i	−0.0165585	−	0.363719i
$441$	20.3215	−	44.4979i	0.967692	−	2.11895i
$442$	−15.5359	+	18.4885i	−0.738965	+	0.879410i
$443$	13.2235	+	28.9555i	0.628269	+	1.37572i	0.909350	+	0.416033i	$0.136580\pi$
$443$	13.2235	+	28.9555i	0.628269	+	1.37572i	−0.281081	+	0.959684i	$0.590693\pi$
$444$	13.4769	−	4.40530i	0.639587	−	0.209066i
$445$	−17.0823	+	2.45607i	−0.809780	+	0.116429i
$446$	−6.54410	−	21.0982i	−0.309872	−	0.999028i
$447$	28.6803	−	33.0988i	1.35653	−	1.56552i
$448$	−31.1262	−	6.13514i	−1.47057	−	0.289858i
$449$	−24.2593	−	15.5905i	−1.14487	−	0.735761i	−0.176256	−	0.984344i	$-0.556399\pi$
$449$	−24.2593	−	15.5905i	−1.14487	−	0.735761i	−0.968611	+	0.248583i	$0.920035\pi$
$450$	1.00914	−	7.86347i	0.0475713	−	0.370688i
$451$	6.16033	−	20.9802i	0.290079	−	0.987917i
$452$	8.67085	−	33.2264i	0.407843	−	1.56284i
$453$	34.6617	−	30.0345i	1.62855	−	1.41114i
$454$	5.17414	−	8.32607i	0.242834	−	0.390762i
$455$	2.66644	+	9.08105i	0.125004	+	0.425726i
$456$	−10.3801	+	42.3976i	−0.486093	+	1.98545i
$457$	12.7643	+	1.83523i	0.597089	+	0.0858485i	0.434232	−	0.900801i	$-0.357020\pi$
$457$	12.7643	+	1.83523i	0.597089	+	0.0858485i	0.162857	+	0.986650i	$0.447929\pi$
$458$	7.62664	−	17.3933i	0.356370	−	0.812735i
$459$			54.6973i			2.55305i
$460$	−8.91882	+	3.52912i	−0.415842	+	0.164546i
$461$		−	15.8262i		−	0.737100i	−0.929608	−	0.368550i	$-0.879854\pi$
$461$		−	15.8262i		−	0.737100i	0.929608	−	0.368550i	$-0.120146\pi$
$462$	40.6852	+	17.8397i	1.89285	+	0.829979i
$463$	−9.06780	−	1.30375i	−0.421417	−	0.0605905i	−0.0716554	−	0.997429i	$-0.522828\pi$
$463$	−9.06780	−	1.30375i	−0.421417	−	0.0605905i	−0.349761	+	0.936839i	$0.613737\pi$
$464$	5.05031	+	13.9978i	0.234455	+	0.649829i
$465$	6.82385	+	23.2399i	0.316448	+	1.07772i
$466$	−29.0436	−	18.0488i	−1.34542	−	0.836095i
$467$	14.1975	−	12.3022i	0.656982	−	0.569278i	−0.261274	−	0.965265i	$-0.584143\pi$
$467$	14.1975	−	12.3022i	0.656982	−	0.569278i	0.918256	+	0.395986i	$0.129597\pi$
$468$	6.75664	−	25.8912i	0.312326	−	1.19682i
$469$	−18.1553	+	61.8314i	−0.838335	+	2.85511i
$470$	−3.96801	−	0.509225i	−0.183031	−	0.0234888i
$471$	51.2612	+	32.9435i	2.36199	+	1.51796i
$472$	0.845985	−	2.10034i	0.0389396	−	0.0966760i
$473$	8.06497	−	9.30747i	0.370828	−	0.427958i
$474$	−34.5386	+	10.7130i	−1.58641	+	0.492063i
$475$	5.20709	−	0.748667i	0.238918	−	0.0343512i
$476$	−17.6316	−	53.9394i	−0.808142	−	2.47231i
$477$	23.9651	+	52.4763i	1.09729	+	2.40273i
$478$	−14.0739	−	11.8262i	−0.643724	−	0.540919i
$479$	−13.5771	+	29.7298i	−0.620355	+	1.35839i	0.294906	+	0.955526i	$0.404712\pi$
$479$	−13.5771	+	29.7298i	−0.620355	+	1.35839i	−0.915261	+	0.402861i	$0.868016\pi$
$480$	5.73047	−	15.5740i	0.261559	−	0.710855i
$481$	−3.11815	−	4.85194i	−0.142176	−	0.221229i
$482$	−10.9696	−	16.5130i	−0.499653	−	0.752148i
$483$	4.56648	−	55.6052i	0.207782	−	2.53012i
$484$	2.87542	−	6.83778i	0.130701	−	0.310808i
$485$	−4.65681	−	7.24613i	−0.211455	−	0.329030i
$486$	3.93344	+	8.27845i	0.178424	+	0.375518i
$487$	10.9200	+	4.98701i	0.494833	+	0.225983i	0.647170	−	0.762346i	$-0.275952\pi$
$487$	10.9200	+	4.98701i	0.494833	+	0.225983i	−0.152336	+	0.988329i	$0.548680\pi$
$488$	4.92850	+	9.60958i	0.223103	+	0.435005i
$489$	−7.55940	−	16.5528i	−0.341848	−	0.748542i
$490$	−11.8923	−	3.29684i	−0.537237	−	0.148936i
$491$	−1.19567	−	8.31607i	−0.0539598	−	0.375299i	−0.998851	−	0.0479154i	$-0.984742\pi$
$491$	−1.19567	−	8.31607i	−0.0539598	−	0.375299i	0.944892	−	0.327383i	$-0.106167\pi$
$492$	30.0102	−	36.8338i	1.35297	−	1.66059i
$493$	−17.4312	+	20.1167i	−0.785062	+	0.906010i
$494$	17.7535	−	0.269249i	0.798770	−	0.0121141i
$495$	−8.18375	+	12.7342i	−0.367832	+	0.572358i
$496$	2.00209	+	32.9651i	0.0898963	+	1.48018i
$497$	−11.3145	+	38.5337i	−0.507525	+	1.72847i
$498$	−43.5330	+	38.8929i	−1.95076	+	1.74283i
$499$	9.34048	+	10.7795i	0.418137	+	0.482556i	0.925269	−	0.379313i	$-0.123840\pi$
$499$	9.34048	+	10.7795i	0.418137	+	0.482556i	−0.507131	+	0.861869i	$0.669294\pi$
$500$	−1.99908	+	0.0606497i	−0.0894016	+	0.00271234i
$501$	−0.135493	−	0.461447i	−0.00605339	−	0.0206159i
$502$	−18.7075	+	2.97994i	−0.834955	+	0.133001i
$503$	−0.453070	+	3.15117i	−0.0202014	+	0.140504i	−0.997426	−	0.0717040i	$-0.977156\pi$
$503$	−0.453070	+	3.15117i	−0.0202014	+	0.140504i	0.977225	+	0.212208i	$0.0680654\pi$
$504$	43.2954	+	45.5988i	1.92853	+	2.03113i
$505$			2.89916i			0.129011i
$506$	18.2729	+	1.22198i	0.812328	+	0.0543238i
$507$	21.4271			0.951613
$508$	−7.82111	+	1.36776i	−0.347006	+	0.0606844i
$509$	−22.4461	−	3.22727i	−0.994908	−	0.143046i	−0.374418	−	0.927260i	$-0.622157\pi$
$509$	−22.4461	−	3.22727i	−0.994908	−	0.143046i	−0.620490	+	0.784214i	$0.713066\pi$
$510$	29.3143	−	4.66953i	1.29806	−	0.206770i
$511$	−16.5321	+	4.85427i	−0.731339	+	0.214740i
$512$	12.3533	−	18.9577i	0.545944	−	0.837822i
$513$	30.3931	−	26.3357i	1.34189	−	1.16275i
$514$	−13.3585	−	14.9522i	−0.589216	−	0.659513i
$515$	10.8461	+	3.18471i	0.477937	+	0.140335i
$516$	23.9934	−	11.8495i	1.05625	−	0.521647i
$517$	6.42582	+	4.12962i	0.282607	+	0.181621i
$518$	13.5514	−	0.205520i	0.595415	−	0.00903001i
$519$	−0.652233	−	0.565163i	−0.0286299	−	0.0248079i
$520$	−6.71842	−	0.655810i	−0.294622	−	0.0287592i
$521$	18.1624	−	2.61136i	0.795710	−	0.114406i	0.267543	−	0.963546i	$-0.413788\pi$
$521$	18.1624	−	2.61136i	0.795710	−	0.114406i	0.528167	+	0.849140i	$0.322879\pi$
$522$	7.87930	−	28.4219i	0.344868	−	1.24399i
$523$	28.2381	−	12.8959i	1.23477	−	0.563899i	0.312304	−	0.949982i	$-0.398899\pi$
$523$	28.2381	−	12.8959i	1.23477	−	0.563899i	0.922464	+	0.386083i	$0.126172\pi$
$524$	−0.999985	+	8.85360i	−0.0436846	+	0.386771i
$525$	4.83274	−	10.5822i	0.210918	−	0.461846i
$526$	1.05735	+	2.22534i	0.0461027	+	0.0970294i
$527$	−49.6968	+	31.9382i	−2.16483	+	1.39125i
$528$	−22.6441	+	22.1628i	−0.985459	+	0.964513i
$529$	−6.01326	−	22.2000i	−0.261446	−	0.965218i
$530$	12.1224	−	8.05295i	0.526565	−	0.349798i
$531$	−3.77542	+	2.42631i	−0.163839	+	0.105293i
$532$	−21.4827	+	35.7680i	−0.931391	+	1.55074i
$533$	−17.5799	−	8.02849i	−0.761472	−	0.347753i
$534$	54.8153	+	46.0611i	2.37209	+	1.99326i
$535$	7.33226	−	3.34853i	0.317001	−	0.144770i
$536$	−36.0687	−	28.4879i	−1.55793	−	1.23049i
$537$	6.57115	+	45.7034i	0.283566	+	1.97225i
$538$	2.71430	+	8.75091i	0.117022	+	0.377278i
$539$	17.8075	+	15.4303i	0.767023	+	0.664629i
$540$	−12.6056	+	8.65228i	−0.542460	+	0.372335i
$541$	22.0135	−	34.2536i	0.946433	−	1.47268i	0.0663844	−	0.997794i	$-0.478854\pi$
$541$	22.0135	−	34.2536i	0.946433	−	1.47268i	0.880048	−	0.474884i	$-0.157510\pi$
$542$	−26.9442	−	3.45781i	−1.15735	−	0.148526i
$543$	−21.8669	−	6.42069i	−0.938397	−	0.275538i
$544$	40.3839	+	2.70880i	1.73144	+	0.116139i
$545$	−0.849490	−	0.980364i	−0.0363881	−	0.0419942i
$546$	20.7250	−	33.3501i	0.886949	−	1.42725i
$547$	−21.8908	+	6.42773i	−0.935985	+	0.274830i	−0.713940	−	0.700207i	$-0.753091\pi$
$547$	−21.8908	+	6.42773i	−0.935985	+	0.274830i	−0.222044	+	0.975037i	$0.571273\pi$
$548$	0.559943	−	0.515739i	0.0239196	−	0.0220313i
$549$	3.04624	−	21.1871i	0.130010	−	0.904242i
$550$	3.49724	+	1.53348i	0.149123	+	0.0653876i
$551$	19.5708			0.833745
$552$	35.5707	+	17.8386i	1.51399	+	0.759260i
$553$	−34.5661			−1.46990
$554$	31.3249	+	13.7354i	1.33087	+	0.583561i
$555$	−1.00892	+	7.01717i	−0.0428261	+	0.297862i
$556$	−10.2892	−	11.1711i	−0.436360	−	0.473760i
$557$	−35.3582	+	10.3821i	−1.49818	+	0.439904i	−0.925140	−	0.379626i	$-0.876053\pi$
$557$	−35.3582	+	10.3821i	−1.49818	+	0.439904i	−0.573036	+	0.819530i	$0.694235\pi$
$558$	34.5496	−	55.5961i	1.46260	−	2.35357i
$559$	−7.12832	−	8.22653i	−0.301496	−	0.347945i
$560$	9.64191	−	12.5958i	0.407445	−	0.532269i
$561$	−54.3807	−	15.9676i	−2.29596	−	0.674154i
$562$	−9.93410	−	1.27487i	−0.419045	−	0.0537771i
$563$	15.6775	−	24.3947i	0.660728	−	1.02811i	−0.335559	−	0.942019i	$-0.608925\pi$
$563$	15.6775	−	24.3947i	0.660728	−	1.02811i	0.996287	−	0.0860933i	$-0.0274383\pi$
$564$	9.39237	+	13.6839i	0.395490	+	0.576195i
$565$	12.9759	+	11.2437i	0.545900	+	0.473025i
$566$	5.17358	+	16.6796i	0.217462	+	0.701097i
$567$	−3.16527	−	22.0150i	−0.132929	−	0.924542i
$568$	−22.4782	−	17.7538i	−0.943166	−	0.744933i
$569$	−1.81120	+	0.827150i	−0.0759297	+	0.0346759i	−0.453018	−	0.891501i	$-0.649653\pi$
$569$	−1.81120	+	0.827150i	−0.0759297	+	0.0346759i	0.377088	+	0.926177i	$0.376925\pi$
$570$	−16.7090	−	14.0405i	−0.699862	−	0.588091i
$571$	33.2637	+	15.1910i	1.39204	+	0.635725i	0.963479	−	0.267786i	$-0.0862919\pi$
$571$	33.2637	+	15.1910i	1.39204	+	0.635725i	0.428565	+	0.903511i	$0.359019\pi$
$572$	11.0490	+	6.63614i	0.461981	+	0.277471i
$573$	−6.74940	+	4.33758i	−0.281960	+	0.181205i
$574$	37.8287	−	25.1296i	1.57894	−	1.04889i
$575$	0.392528	−	4.77974i	0.0163696	−	0.199329i
$576$	−41.7046	+	16.4926i	−1.73769	+	0.687191i
$577$	22.7831	−	14.6418i	0.948471	−	0.609545i	0.0276862	−	0.999617i	$-0.491186\pi$
$577$	22.7831	−	14.6418i	0.948471	−	0.609545i	0.920785	+	0.390071i	$0.127550\pi$
$578$	20.7530	+	43.6774i	0.863210	+	1.81674i
$579$	−2.49870	+	5.47138i	−0.103842	+	0.227383i
$580$	−7.39347	−	0.835068i	−0.306997	−	0.0346743i
$581$	−50.7575	+	23.1802i	−2.10578	+	0.961676i
$582$	−9.54660	+	34.4361i	−0.395719	+	1.42742i
$583$	−27.5046	+	3.95456i	−1.13912	+	0.163781i
$584$	1.19391	−	12.2310i	0.0494043	−	0.506120i
$585$	10.1113	+	8.76147i	0.418050	+	0.362242i
$586$	−4.33975	+	0.0658163i	−0.179274	+	0.00271885i
$587$	9.32193	+	5.99084i	0.384757	+	0.247268i	0.718693	−	0.695327i	$-0.244741\pi$
$587$	9.32193	+	5.99084i	0.384757	+	0.247268i	−0.333936	+	0.942596i	$0.608377\pi$
$588$	22.6711	+	45.9053i	0.934939	+	1.89310i
$589$	41.6748	+	12.2368i	1.71718	+	0.504210i
$590$	0.754295	+	0.844286i	0.0310538	+	0.0347587i
$591$	−0.348384	+	0.301876i	−0.0143306	+	0.0124175i
$592$	−3.47516	+	9.02017i	−0.142828	+	0.370727i
$593$	−11.2692	+	3.30894i	−0.462772	+	0.135882i	−0.504804	−	0.863234i	$-0.668435\pi$
$593$	−11.2692	+	3.30894i	−0.462772	+	0.135882i	0.0420319	+	0.999116i	$0.486617\pi$
$594$	28.8290	−	4.59221i	1.18287	−	0.188421i
$595$	28.0852	+	4.03804i	1.15138	+	0.165544i
$596$	5.14357	+	29.4120i	0.210689	+	1.20476i
$597$	54.0566			2.21239
$598$	3.36756	−	15.8326i	0.137710	−	0.647444i
$599$			7.73638i			0.316100i	0.987431	+	0.158050i	$0.0505207\pi$
$599$			7.73638i			0.316100i	−0.987431	+	0.158050i	$0.949479\pi$
$600$	5.71322	+	6.01717i	0.233241	+	0.245650i
$601$	0.791496	−	5.50498i	0.0322858	−	0.224553i	−0.967290	−	0.253673i	$-0.918361\pi$
$601$	0.791496	−	5.50498i	0.0322858	−	0.224553i	0.999576	+	0.0291200i	$0.00927048\pi$
$602$	25.2606	−	4.02380i	1.02954	−	0.163998i
$603$	25.6648	+	87.4063i	1.04515	+	3.55946i
$604$	0.948203	+	31.2538i	0.0385819	+	1.27170i
$605$	2.42880	+	2.80299i	0.0987449	+	0.113958i
$606$	8.96950	−	8.01345i	0.364361	−	0.325524i
$607$	−4.00465	+	13.6386i	−0.162544	+	0.553573i	0.837431	+	0.546542i	$0.184056\pi$
$607$	−4.00465	+	13.6386i	−0.162544	+	0.553573i	−0.999975	+	0.00703109i	$0.997762\pi$
$608$	−17.9389	−	23.7439i	−0.727519	−	0.962942i
$609$	23.3986	−	36.4090i	0.948161	−	1.47537i
$610$	−5.39924	+	0.0818844i	−0.218609	+	0.00331540i
$611$	4.42115	−	5.10228i	0.178861	−	0.206416i
$612$	−62.1916	−	50.6705i	−2.51395	−	2.04823i
$613$	−4.44807	−	30.9370i	−0.179656	−	1.24953i	−0.857560	−	0.514383i	$-0.828021\pi$
$613$	−4.44807	−	30.9370i	−0.179656	−	1.24953i	0.677905	−	0.735150i	$-0.262888\pi$
$614$	−32.1605	−	8.91573i	−1.29789	−	0.359809i
$615$	9.86849	+	21.6090i	0.397936	+	0.871358i
$616$	−26.9492	+	13.8215i	−1.08581	+	0.556886i
$617$	6.32033	+	2.88640i	0.254447	+	0.116202i	0.538555	−	0.842590i	$-0.318970\pi$
$617$	6.32033	+	2.88640i	0.254447	+	0.116202i	−0.284108	+	0.958792i	$0.591698\pi$
$618$	−20.1264	−	42.3588i	−0.809603	−	1.70392i
$619$	4.44057	+	6.90965i	0.178481	+	0.277722i	0.918955	−	0.394363i	$-0.129035\pi$
$619$	4.44057	+	6.90965i	0.178481	+	0.277722i	−0.740473	+	0.672086i	$0.765399\pi$
$620$	−15.2218	−	6.40106i	−0.611322	−	0.257073i
$621$	−17.2304	−	32.3613i	−0.691431	−	1.29862i
$622$	0.486893	+	0.732940i	0.0195226	+	0.0293882i
$623$	37.0008	+	57.5744i	1.48241	+	2.30667i
$624$	16.5412	+	22.5984i	0.662177	+	0.904658i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	−2.96810	−	2.49408i	−0.118629	−	0.0996835i
$627$	17.3107	+	37.9053i	0.691325	+	1.51379i
$628$	−39.4865	+	12.9072i	−1.57568	+	0.515055i
$629$	−17.1148	+	2.46074i	−0.682411	+	0.0981159i
$630$	−30.0281	+	9.31392i	−1.19635	+	0.371075i
$631$	1.95427	−	2.25535i	0.0777983	−	0.0897840i	−0.715516	−	0.698596i	$-0.753808\pi$
$631$	1.95427	−	2.25535i	0.0777983	−	0.0897840i	0.793314	+	0.608812i	$0.208354\pi$
$632$	9.21104	−	22.8684i	0.366395	−	0.909656i
$633$	−29.0987	−	18.7006i	−1.15657	−	0.743282i
$634$	−0.958452	−	0.123001i	−0.0380650	−	0.00488498i
$635$	1.11845	−	3.80910i	0.0443844	−	0.151159i
$636$	−58.4216	−	15.2459i	−2.31657	−	0.604538i
$637$	15.7394	−	13.6382i	0.623616	−	0.540367i
$638$	12.0662	+	7.49842i	0.477707	+	0.296865i
$639$	15.9945	+	54.4721i	0.632731	+	2.15488i
$640$	5.76383	+	9.73541i	0.227836	+	0.384826i
$641$	−21.3177	−	3.06502i	−0.841998	−	0.121061i	−0.292198	−	0.956358i	$-0.594387\pi$
$641$	−21.3177	−	3.06502i	−0.841998	−	0.121061i	−0.549799	+	0.835297i	$0.685296\pi$
$642$	−30.6266	−	13.4292i	−1.20874	−	0.530009i
$643$			13.8501i			0.546194i	0.961987	+	0.273097i	$0.0880480\pi$
$643$			13.8501i			0.546194i	−0.961987	+	0.273097i	$0.911952\pi$
$644$	27.4232	+	26.3587i	1.08063	+	1.03868i
$645$			13.3800i			0.526836i
$646$	21.3760	−	48.7500i	0.841027	−	1.91804i
$647$	−36.7399	−	5.28240i	−1.44439	−	0.207673i	−0.624875	−	0.780725i	$-0.714850\pi$
$647$	−36.7399	−	5.28240i	−1.44439	−	0.207673i	−0.819519	+	0.573052i	$0.805759\pi$
$648$	15.4082	+	3.77237i	0.605292	+	0.148193i
$649$	−0.609012	−	2.07410i	−0.0239058	−	0.0814157i
$650$	1.78149	−	2.86673i	0.0698759	−	0.112442i
$651$	72.5910	−	62.9005i	2.84507	−	2.46526i
$652$	12.0041	+	3.13263i	0.470117	+	0.122683i
$653$	−6.47854	+	22.0639i	−0.253525	+	0.863426i	0.730122	+	0.683317i	$0.239463\pi$
$653$	−6.47854	+	22.0639i	−0.253525	+	0.863426i	−0.983647	+	0.180109i	$0.942355\pi$
$654$	−0.685034	+	5.33796i	−0.0267870	+	0.208731i
$655$	−3.74774	−	2.40852i	−0.146436	−	0.0941089i
$656$	6.54494	+	31.7233i	0.255537	+	1.23859i
$657$	−15.9503	+	18.4077i	−0.622282	+	0.718152i
$658$	4.69992	+	15.1526i	0.183222	+	0.590708i
$659$	−3.08735	+	0.443894i	−0.120266	+	0.0172917i	−0.202185	−	0.979347i	$-0.564804\pi$
$659$	−3.08735	+	0.443894i	−0.120266	+	0.0172917i	0.0819189	+	0.996639i	$0.473895\pi$
$660$	−4.92228	−	15.0585i	−0.191599	−	0.586151i
$661$	−8.05791	−	17.6444i	−0.313416	−	0.686286i	0.685719	−	0.727867i	$-0.259488\pi$
$661$	−8.05791	−	17.6444i	−0.313416	−	0.686286i	−0.999135	+	0.0415805i	$0.986761\pi$
$662$	−1.21376	+	1.44444i	−0.0471741	+	0.0561398i
$663$	−20.8099	+	45.5673i	−0.808190	+	1.76969i
$664$	−1.80998	−	39.7573i	−0.0702408	−	1.54288i
$665$	−11.2787	−	17.5500i	−0.437370	−	0.680561i
$666$	15.9585	−	10.6012i	0.618379	−	0.410790i
$667$	3.97605	−	17.3930i	0.153953	−	0.673458i
$668$	0.302241	+	0.127098i	0.0116941	+	0.00491758i
$669$	−24.7733	−	38.5480i	−0.957791	−	1.49035i
$670$	20.7571	−	9.86256i	0.801917	−	0.381024i
$671$	9.37844	+	4.28299i	0.362050	+	0.165343i
$672$	−65.6200	+	4.98511i	−2.53135	+	0.192305i
$673$	−2.15050	−	4.70894i	−0.0828958	−	0.181516i	0.863645	−	0.504100i	$-0.168176\pi$
$673$	−2.15050	−	4.70894i	−0.0828958	−	0.181516i	−0.946541	+	0.322584i	$0.895449\pi$
$674$	−4.08860	+	14.7483i	−0.157487	+	0.568082i
$675$	−1.08795	−	7.56685i	−0.0418752	−	0.291248i
$676$	−9.22713	+	11.3251i	−0.354890	+	0.435582i
$677$	23.8746	−	27.5527i	0.917575	−	1.05894i	−0.0804899	−	0.996755i	$-0.525648\pi$
$677$	23.8746	−	27.5527i	0.917575	−	1.05894i	0.998065	−	0.0621825i	$-0.0198061\pi$
$678$	−1.08017	−	71.2234i	−0.0414836	−	2.73532i
$679$	−18.4672	+	28.7355i	−0.708706	+	1.10277i
$680$	−10.1555	+	17.5047i	−0.389447	+	0.671274i
$681$	5.72890	−	19.5109i	0.219532	−	0.747657i
$682$	21.0059	+	23.5120i	0.804356	+	0.900319i
$683$	−28.1117	−	32.4426i	−1.07566	−	1.24138i	−0.968993	−	0.247087i	$-0.920527\pi$
$683$	−28.1117	−	32.4426i	−1.07566	−	1.24138i	−0.106670	−	0.994294i	$-0.534019\pi$
$684$	1.78860	+	58.9542i	0.0683888	+	2.25417i
$685$	0.107236	+	0.365214i	0.00409729	+	0.0139541i
$686$	1.52294	+	9.56071i	0.0581462	+	0.365030i
$687$	5.60663	−	38.9950i	0.213906	−	1.48775i
$688$	−4.06926	+	17.7843i	−0.155139	+	0.678018i
$689$			24.5603i			0.935671i
$690$	−15.8727	+	11.9971i	−0.604262	+	0.456721i
$691$	41.1915			1.56700			0.783499	−	0.621394i	$-0.213433\pi$
$691$	41.1915			1.56700			0.783499	+	0.621394i	$0.213433\pi$
$692$	0.579582	−	0.101357i	0.0220324	−	0.00385303i
$693$	59.4173	+	8.54292i	2.25708	+	0.324519i
$694$	−7.17550	−	45.0463i	−0.272378	−	1.70994i
$695$	7.28617	−	2.13941i	0.276380	−	0.0811526i
$696$	17.8524	+	25.1823i	0.676695	+	0.954533i
$697$	−43.7881	+	37.9426i	−1.65859	+	1.43718i
$698$	−10.4001	+	9.29155i	−0.393649	+	0.351690i
$699$	−68.0591	−	19.9840i	−2.57423	−	0.755863i
$700$	3.51203	+	7.11130i	0.132742	+	0.268782i
$701$	33.5137	+	21.5380i	1.26580	+	0.813477i	0.989066	−	0.147471i	$-0.0471132\pi$
$701$	33.5137	+	21.5380i	1.26580	+	0.813477i	0.276729	+	0.960948i	$0.410750\pi$
$702$	−0.391267	−	25.7991i	−0.0147674	−	0.973726i
$703$	9.60778	+	8.32519i	0.362364	+	0.313990i
$704$	−1.96279	−	21.5123i	−0.0739755	−	0.810775i
$705$	−8.21410	+	1.18101i	−0.309361	+	0.0444794i
$706$	−22.8886	−	6.34531i	−0.861422	−	0.238809i
$707$	10.4580	−	4.77602i	0.393315	−	0.179621i
$708$	0.527159	−	4.66732i	0.0198118	−	0.175409i
$709$	2.59606	−	5.68457i	0.0974969	−	0.213488i	−0.854599	−	0.519289i	$-0.826197\pi$
$709$	2.59606	−	5.68457i	0.0974969	−	0.213488i	0.952096	+	0.305801i	$0.0989241\pi$
$710$	12.9360	−	6.14641i	0.485478	−	0.230671i
$711$	−41.1065	+	26.4176i	−1.54162	+	0.990736i
$712$	−47.9502	+	9.13697i	−1.79701	+	0.342422i
$713$	19.3419	−	34.5512i	0.724358	−	1.29395i
$714$	−65.1362	−	98.0522i	−2.43766	−	3.66951i
$715$	−5.42133	+	3.48407i	−0.202746	+	0.130297i
$716$	−26.9859	−	16.2080i	−1.00851	−	0.605722i
$717$	−34.6869	−	15.8410i	−1.29540	−	0.591591i
$718$	12.3707	−	14.7218i	0.461669	−	0.549413i
$719$	20.9320	−	9.55935i	0.780634	−	0.356503i	0.0150889	−	0.999886i	$-0.495197\pi$
$719$	20.9320	−	9.55935i	0.780634	−	0.356503i	0.765545	+	0.643383i	$0.222470\pi$
$720$	1.83982	−	22.3480i	0.0685662	−	0.832863i
$721$	−6.37963	−	44.3713i	−0.237590	−	1.65247i
$722$	−11.7166	+	3.63419i	−0.436048	+	0.135250i
$723$	−31.0789	−	26.9300i	−1.15584	−	1.00154i
$724$	12.8101	−	8.79262i	0.476083	−	0.326775i
$725$	2.01131	−	3.12966i	0.0746983	−	0.116233i
$726$	1.95860	−	15.2619i	0.0726906	−	0.566424i
$727$	−39.0875	−	11.4771i	−1.44968	−	0.425663i	−0.540242	−	0.841510i	$-0.681667\pi$
$727$	−39.0875	−	11.4771i	−1.44968	−	0.425663i	−0.909435	+	0.415847i	$0.863485\pi$
$728$	8.70214	+	25.3155i	0.322523	+	0.938256i
$729$	23.4688	+	27.0845i	0.869216	+	1.00313i
$730$	5.21890	+	3.24322i	0.193160	+	0.120037i
$731$	−31.3117	+	9.19394i	−1.15810	+	0.340050i
$732$	15.1772	+	16.4780i	0.560965	+	0.609044i
$733$	−5.37159	+	37.3602i	−0.198404	+	1.37993i	0.610512	+	0.792007i	$0.290964\pi$
$733$	−5.37159	+	37.3602i	−0.198404	+	1.37993i	−0.808916	+	0.587924i	$0.799945\pi$
$734$	−16.3063	+	37.1881i	−0.601877	+	1.37264i
$735$	−25.5992			−0.944240
$736$	−24.7462	+	11.1188i	−0.912156	+	0.409844i
$737$	−43.8785			−1.61628
$738$	25.7808	−	58.7956i	0.949004	−	2.16430i
$739$	3.49281	−	24.2930i	0.128485	−	0.893633i	−0.818991	−	0.573806i	$-0.805466\pi$
$739$	3.49281	−	24.2930i	0.128485	−	0.893633i	0.947476	−	0.319827i	$-0.103625\pi$
$740$	−3.27440	−	3.55505i	−0.120369	−	0.130686i
$741$	35.3395	−	10.3766i	1.29823	−	0.381194i
$742$	−49.0194	−	30.4625i	−1.79956	−	1.11832i
$743$	4.37107	+	5.04448i	0.160359	+	0.185064i	0.830243	−	0.557402i	$-0.188202\pi$
$743$	4.37107	+	5.04448i	0.160359	+	0.185064i	−0.669884	+	0.742466i	$0.733656\pi$
$744$	22.2702	+	64.7866i	0.816465	+	2.37519i
$745$	−14.3244	−	4.20603i	−0.524807	−	0.154097i
$746$	−3.11156	+	24.2461i	−0.113922	+	0.887711i
$747$	−42.6459	+	66.3583i	−1.56033	+	2.42792i
$748$	31.8574	−	21.8664i	1.16482	−	0.799514i
$749$	−24.1581	−	20.9331i	−0.882717	−	0.764879i
$750$	−3.96248	+	1.22906i	−0.144689	+	0.0448788i
$751$	−3.13224	−	21.7852i	−0.114297	−	0.794954i	−0.963658	−	0.267141i	$-0.913921\pi$
$751$	−3.13224	−	21.7852i	−0.114297	−	0.794954i	0.849360	−	0.527813i	$-0.176988\pi$
$752$	−11.2771	−	0.928399i	−0.411234	−	0.0338552i
$753$	−35.7442	+	16.3238i	−1.30259	+	0.594873i
$754$	8.07789	−	9.61314i	0.294179	−	0.350090i
$755$	−14.2213	−	6.49464i	−0.517565	−	0.236364i
$756$	51.9774	+	31.2182i	1.89040	+	1.13540i
$757$	−6.11457	+	3.92959i	−0.222238	+	0.142823i	−0.647023	−	0.762471i	$-0.723986\pi$
$757$	−6.11457	+	3.92959i	−0.222238	+	0.142823i	0.424785	+	0.905294i	$0.360350\pi$
$758$	3.45057	+	5.19428i	0.125330	+	0.188665i
$759$	37.2040	−	7.68349i	1.35042	−	0.278893i
$760$	14.6163	−	2.78516i	0.530190	−	0.101028i
$761$	−25.1922	+	16.1901i	−0.913218	+	0.586890i	−0.910682	−	0.413107i	$-0.864444\pi$
$761$	−25.1922	+	16.1901i	−0.913218	+	0.586890i	−0.00253575	+	0.999997i	$0.500807\pi$
$762$	−14.8762	+	7.06828i	−0.538907	+	0.256057i
$763$	−2.13700	+	4.67937i	−0.0773645	+	0.169405i
$764$	0.613891	−	5.43522i	0.0222098	−	0.196639i
$765$	36.4855	−	16.6624i	1.31913	−	0.602429i
$766$	−6.07495	−	1.68413i	−0.219497	−	0.0608502i
$767$	−1.89117	+	0.271909i	−0.0682862	+	0.00981807i
$768$	14.1881	−	44.7416i	0.511969	−	1.61447i
$769$	−11.8041	−	10.2283i	−0.425665	−	0.368841i	0.415524	−	0.909582i	$-0.363598\pi$
$769$	−11.8041	−	10.2283i	−0.425665	−	0.368841i	−0.841189	+	0.540741i	$0.818144\pi$
$770$	−0.229638	−	15.1417i	−0.00827557	−	0.545669i
$771$	−34.9891	−	22.4861i	−1.26010	−	0.809817i
$772$	−1.81584	−	3.67679i	−0.0653537	−	0.132331i
$773$	−5.77655	−	1.69615i	−0.207768	−	0.0610062i	0.176192	−	0.984356i	$-0.443622\pi$
$773$	−5.77655	−	1.69615i	−0.207768	−	0.0610062i	−0.383960	+	0.923350i	$0.625440\pi$
$774$	26.9650	−	24.0909i	0.969238	−	0.865929i
$775$	6.23982	−	5.40683i	0.224141	−	0.194219i
$776$	−14.0899	−	19.8749i	−0.505798	−	0.713469i
$777$	26.9749	−	7.92054i	0.967719	−	0.284148i
$778$	1.06284	+	6.67227i	0.0381045	+	0.239212i
$779$	42.1663	+	6.06259i	1.51076	+	0.217215i
$780$	−13.7933	+	2.41217i	−0.493880	+	0.0863697i
$781$	−27.3453			−0.978493
$782$	−38.9823	−	28.9014i	−1.39400	−	1.03351i
$783$		−	28.4400i		−	1.01636i
$784$	−34.0257	−	7.78550i	−1.21520	−	0.278053i
$785$	2.95606	−	20.5598i	0.105506	−	0.733812i
$786$	2.90742	+	18.2522i	0.103704	+	0.651034i
$787$	−3.50001	−	11.9200i	−0.124762	−	0.424900i	0.873296	−	0.487190i	$-0.161978\pi$
$787$	−3.50001	−	11.9200i	−0.124762	−	0.424900i	−0.998058	+	0.0622894i	$0.980160\pi$
$788$	−0.00953038	−	0.314132i	−0.000339506	−	0.0111905i
$789$	3.34681	+	3.86243i	0.119150	+	0.137506i
$790$	8.21272	+	9.19254i	0.292196	+	0.327056i
$791$	19.1827	−	65.3301i	0.682057	−	2.32287i
$792$	−21.4851	+	37.0331i	−0.763442	+	1.31591i
$793$	4.92672	−	7.66613i	0.174953	−	0.272232i
$794$	0.334567	+	22.0605i	0.0118733	+	0.782897i
$795$	19.7696	−	22.8154i	0.701157	−	0.809178i
$796$	−23.2783	+	28.5711i	−0.825076	+	1.01268i
$797$	4.27810	+	29.7548i	0.151538	+	1.05397i	0.913643	+	0.406517i	$0.133257\pi$
$797$	4.27810	+	29.7548i	0.151538	+	1.05397i	−0.762105	+	0.647453i	$0.775834\pi$
$798$	−23.1217	+	83.4038i	−0.818500	+	2.95246i
$799$	−8.40804	−	18.4110i	−0.297455	−	0.651336i
$800$	−5.64060	+	0.428513i	−0.199425	+	0.0151502i
$801$	88.0039	+	40.1901i	3.10947	+	1.42005i
$802$	−19.4706	+	9.25131i	−0.687532	+	0.326675i
$803$	−6.34279	−	9.86957i	−0.223832	−	0.348290i
$804$	−87.8871	−	36.9582i	−3.09954	−	1.30342i
$805$	−17.8884	+	6.45811i	−0.630485	+	0.227619i
$806$	23.2121	−	15.4198i	0.817610	−	0.543140i
$807$	10.2752	+	15.9886i	0.361705	+	0.562825i
$808$	0.372927	+	8.19157i	0.0131195	+	0.288178i
$809$	−12.6170	+	27.6274i	−0.443591	+	0.971328i	0.547334	+	0.836914i	$0.315643\pi$
$809$	−12.6170	+	27.6274i	−0.443591	+	0.971328i	−0.990925	+	0.134414i	$0.957085\pi$
$810$	−5.10263	+	6.07242i	−0.179288	+	0.213363i
$811$	14.7235	+	32.2401i	0.517014	+	1.13210i	0.970558	+	0.240868i	$0.0774322\pi$
$811$	14.7235	+	32.2401i	0.517014	+	1.13210i	−0.453544	+	0.891234i	$0.649841\pi$
$812$	9.16756	+	28.0459i	0.321718	+	0.984218i
$813$	−55.7766	+	8.01947i	−1.95617	+	0.281255i
$814$	2.73387	+	8.81399i	0.0958220	+	0.308930i
$815$	−4.06214	+	4.68797i	−0.142291	+	0.164212i
$816$	82.2270	−	16.9645i	2.87852	−	0.593878i
$817$	20.1847	+	12.9719i	0.706173	+	0.453830i
$818$	5.48052	−	42.7056i	0.191622	−	1.49317i
$819$	14.9478	−	50.9076i	0.522319	−	1.77885i
$820$	−15.6709	−	4.08952i	−0.547251	−	0.142812i
$821$	−31.6509	+	27.4257i	−1.10463	+	0.957163i	−0.999305	−	0.0372753i	$-0.988132\pi$
$821$	−31.6509	+	27.4257i	−1.10463	+	0.957163i	−0.105320	+	0.994438i	$0.533587\pi$
$822$	0.833501	−	1.34125i	0.0290717	−	0.0467813i
$823$	3.29630	+	11.2262i	0.114902	+	0.391320i	0.996783	−	0.0801528i	$-0.0255408\pi$
$823$	3.29630	+	11.2262i	0.114902	+	0.391320i	−0.881881	+	0.471473i	$0.843723\pi$
$824$	31.0554	+	7.60323i	1.08187	+	0.264871i
$825$	7.84065	+	1.12732i	0.272977	+	0.0392481i
$826$	1.80295	−	4.11181i	0.0627328	−	0.143068i
$827$		−	8.57638i		−	0.298230i	−0.988820	−	0.149115i	$-0.952358\pi$
$827$		−	8.57638i		−	0.298230i	0.988820	−	0.149115i	$-0.0476425\pi$
$828$	52.7571	+	10.3877i	1.83344	+	0.360997i
$829$		−	33.8755i		−	1.17654i	−0.808663	−	0.588272i	$-0.799808\pi$
$829$		−	33.8755i		−	1.17654i	0.808663	−	0.588272i	$-0.200192\pi$
$830$	18.2243	+	7.99101i	0.632574	+	0.277372i
$831$	70.2290	+	10.0974i	2.43622	+	0.350275i
$832$	−19.0673	−	0.988782i	−0.661039	−	0.0342799i
$833$	−17.5903	−	59.9070i	−0.609467	−	2.07565i
$834$	−26.7584	−	16.6287i	−0.926568	−	0.575805i
$835$	−0.123897	+	0.107357i	−0.00428762	+	0.00371525i
$836$	−27.4890	−	7.17361i	−0.950727	−	0.248104i
$837$	17.7824	−	60.5612i	0.614648	−	2.09330i
$838$	17.1600	+	2.20218i	0.592781	+	0.0760732i
$839$	−24.5724	−	15.7917i	−0.848334	−	0.545191i	0.0427205	−	0.999087i	$-0.486397\pi$
$839$	−24.5724	−	15.7917i	−0.848334	−	0.545191i	−0.891055	+	0.453896i	$0.850034\pi$
$840$	12.2937	−	30.5217i	0.424172	−	1.05310i
$841$	−9.92758	+	11.4570i	−0.342330	+	0.395070i
$842$	49.4472	−	15.3372i	1.70406	−	0.528556i
$843$	−20.5644	+	2.95671i	−0.708275	+	0.101835i
$844$	22.4147	−	7.32687i	0.771547	−	0.252201i
$845$	−3.03423	−	6.64403i	−0.104381	−	0.228562i
$846$	17.1698	+	14.4277i	0.590308	+	0.496034i
$847$	6.10996	−	13.3789i	0.209941	−	0.459706i
$848$	33.2161	−	24.3130i	1.14064	−	0.834910i
$849$	19.5851	+	30.4749i	0.672157	+	1.04590i
$850$	−5.59901	−	8.42842i	−0.192045	−	0.289092i
$851$	9.35069	−	6.84725i	0.320537	−	0.234721i
$852$	−54.7717	−	23.0326i	−1.87645	−	0.789083i
$853$	0.546803	+	0.850842i	0.0187222	+	0.0291323i	0.850489	−	0.525994i	$-0.176306\pi$
$853$	0.546803	+	0.850842i	0.0187222	+	0.0291323i	−0.831766	+	0.555126i	$0.812670\pi$
$854$	9.19000	+	19.3416i	0.314475	+	0.661856i
$855$	−26.8257	−	12.2509i	−0.917418	−	0.418971i
$856$	20.2866	−	10.4044i	0.693381	−	0.355617i
$857$	0.0750635	+	0.164366i	0.00256412	+	0.00561464i	0.910910	−	0.412606i	$-0.135381\pi$
$857$	0.0750635	+	0.164366i	0.00256412	+	0.00561464i	−0.908346	+	0.418220i	$0.862654\pi$
$858$	25.7640	+	7.14246i	0.879569	+	0.243840i
$859$	−6.23836	−	43.3888i	−0.212850	−	1.48041i	−0.763575	−	0.645719i	$-0.776558\pi$
$859$	−6.23836	−	43.3888i	−0.212850	−	1.48041i	0.550725	−	0.834687i	$-0.314351\pi$
$860$	−7.07187	−	5.76179i	−0.241149	−	0.196475i
$861$	61.6922	−	71.1966i	2.10246	−	2.42637i
$862$	30.8533	−	0.467918i	1.05087	−	0.0159373i
$863$	24.1786	−	37.6227i	0.823050	−	1.28069i	−0.134062	−	0.990973i	$-0.542802\pi$
$863$	24.1786	−	37.6227i	0.823050	−	1.28069i	0.957112	−	0.289718i	$-0.0935614\pi$
$864$	−34.5042	+	26.0685i	−1.17386	+	0.886869i
$865$	−0.0828827	+	0.282272i	−0.00281809	+	0.00959755i
$866$	−12.6382	+	11.2912i	−0.429465	+	0.383689i
$867$	65.6889	+	75.8091i	2.23091	+	2.57461i
$868$	1.98580	+	65.4541i	0.0674024	+	2.22166i
$869$	−6.63089	−	22.5827i	−0.224937	−	0.766067i
$870$	−15.2420	+	2.42793i	−0.516754	+	0.0823145i
$871$	−5.51933	+	38.3878i	−0.187015	+	1.30072i
$872$	−2.52634	−	2.66075i	−0.0855527	−	0.0901042i
$873$			48.2865i			1.63425i
$874$	2.70991	+	35.5763i	0.0916641	+	1.20339i
$875$	−3.96563			−0.134063
$876$	−4.39139	−	25.1109i	−0.148371	−	0.848417i
$877$	47.1899	+	6.78489i	1.59349	+	0.229109i	0.881189	−	0.472764i	$-0.156744\pi$
$877$	47.1899	+	6.78489i	1.59349	+	0.229109i	0.712302	+	0.701873i	$0.247653\pi$
$878$	−43.3973	+	6.91282i	−1.46459	+	0.233296i
$879$	−8.63854	+	2.53650i	−0.291371	+	0.0855542i
$880$	10.0787	+	3.88298i	0.339753	+	0.130895i
$881$	11.3449	−	9.83038i	0.382218	−	0.331194i	−0.442468	−	0.896784i	$-0.645897\pi$
$881$	11.3449	−	9.83038i	0.382218	−	0.331194i	0.824686	+	0.565590i	$0.191352\pi$
$882$	46.0918	+	51.5908i	1.55199	+	1.73715i
$883$	7.36183	+	2.16163i	0.247745	+	0.0727446i	0.403248	−	0.915091i	$-0.367881\pi$
$883$	7.36183	+	2.16163i	0.247745	+	0.0727446i	−0.155502	+	0.987836i	$0.549700\pi$
$884$	−15.1229	−	30.6215i	−0.508639	−	1.02991i
$885$	1.97568	+	1.26969i	0.0664118	+	0.0426803i
$886$	−45.0122	+	0.682651i	−1.51221	+	0.0229341i
$887$	36.4077	+	31.5475i	1.22245	+	1.05926i	0.996368	+	0.0851529i	$0.0271379\pi$
$887$	36.4077	+	31.5475i	1.22245	+	1.05926i	0.226084	+	0.974108i	$0.427408\pi$
$888$	−1.94806	+	19.9568i	−0.0653725	+	0.669707i
$889$	−15.5829	+	2.24049i	−0.522635	+	0.0751436i
$890$	6.52020	−	23.5194i	0.218557	−	0.788373i
$891$	13.7756	−	6.29111i	0.461501	−	0.210760i
$892$	31.0423	+	3.50613i	1.03937	+	0.117394i
$893$	−6.18195	+	13.5366i	−0.206871	+	0.452984i
$894$	26.5809	+	55.9431i	0.888998	+	1.87102i
$895$	13.2410	−	8.50945i	0.442597	−	0.284440i
$896$	25.6230	−	36.8296i	0.856004	−	1.23039i
$897$	−2.04225	−	33.5150i	−0.0681888	−	1.11903i
$898$	33.9695	−	22.5660i	1.13358	−	0.753038i
$899$	25.8399	−	16.6063i	0.861810	−	0.553852i
$900$	9.61147	+	5.77276i	0.320382	+	0.192425i
$901$	66.9769	+	30.5873i	2.23132	+	1.01901i
$902$	23.6745	+	19.8936i	0.788273	+	0.662383i
$903$	48.2651	−	22.0420i	1.60616	−	0.733510i
$904$	38.1097	+	30.0999i	1.26751	+	1.00111i
$905$	1.10560	+	7.68959i	0.0367512	+	0.255610i
$906$	19.2152	+	61.9498i	0.638382	+	2.05814i
$907$	21.8716	+	18.9518i	0.726234	+	0.629286i	0.937436	−	0.348157i	$-0.113192\pi$
$907$	21.8716	+	18.9518i	0.726234	+	0.629286i	−0.211202	+	0.977442i	$0.567738\pi$
$908$	7.84527	+	11.4299i	0.260354	+	0.379314i
$909$	8.78672	−	13.6724i	0.291437	−	0.453485i
$910$	−13.2758	−	1.70372i	−0.440090	−	0.0564779i
$911$	−53.3662	−	15.6697i	−1.76810	−	0.519161i	−0.774546	−	0.632517i	$-0.782022\pi$
$911$	−53.3662	−	15.6697i	−1.76810	−	0.519161i	−0.993554	+	0.113356i	$0.963840\pi$
$912$	−49.0173	−	37.5221i	−1.62312	−	1.24248i
$913$	−24.8810	−	28.7142i	−0.823441	−	0.950301i
$914$	−9.62593	+	15.4898i	−0.318397	+	0.512356i
$915$	−10.7475	+	3.15575i	−0.355302	+	0.104326i
$916$	18.1961	+	19.7557i	0.601216	+	0.652746i
$917$	−2.51423	+	17.4869i	−0.0830272	+	0.577467i
$918$	−70.8426	−	31.0632i	−2.33815	−	1.02524i
$919$	−43.0788			−1.42104			−0.710519	−	0.703678i	$-0.751540\pi$
$919$	−43.0788			−1.42104			−0.710519	+	0.703678i	$0.751540\pi$
$920$	0.494257	−	13.5557i	0.0162952	−	0.446917i
$921$	−69.2285			−2.28116
$922$	20.4977	+	8.98788i	0.675056	+	0.296000i
$923$	−3.43968	+	23.9235i	−0.113218	+	0.787452i
$924$	−46.2111	+	42.5631i	−1.52023	+	1.40022i
$925$	2.31872	−	0.680838i	0.0762391	−	0.0223858i
$926$	6.83829	−	11.0040i	0.224720	−	0.361613i
$927$	−41.4981	−	47.8913i	−1.36298	−	1.57296i
$928$	−20.9977	−	1.40844i	−0.689282	−	0.0462344i
$929$	29.9973	+	8.80800i	0.984179	+	0.288981i	0.733948	−	0.679205i	$-0.237675\pi$
$929$	29.9973	+	8.80800i	0.984179	+	0.288981i	0.250231	+	0.968186i	$0.419494\pi$
$930$	−33.9751	−	4.36011i	−1.11409	−	0.142974i
$931$	−24.8185	+	38.6183i	−0.813392	+	1.26566i
$932$	39.8705	−	27.3664i	1.30600	−	0.896417i
$933$	1.37945	+	1.19530i	0.0451612	+	0.0391324i
$934$	7.87060	+	25.3748i	0.257534	+	0.830289i
$935$	2.74951	+	19.1232i	0.0899185	+	0.625397i
$936$	29.6964	+	23.4549i	0.970658	+	0.766647i
$937$	19.8820	−	9.07979i	0.649515	−	0.296624i	−0.0632799	−	0.997996i	$-0.520156\pi$
$937$	19.8820	−	9.07979i	0.649515	−	0.296624i	0.712795	+	0.701372i	$0.247429\pi$
$938$	−69.7718	−	58.6290i	−2.27813	−	1.91431i
$939$	−7.31525	−	3.34076i	−0.238724	−	0.109022i
$940$	2.91301	−	4.85007i	0.0950119	−	0.158192i
$941$	−24.7214	+	15.8875i	−0.805894	+	0.517916i	−0.877534	−	0.479514i	$-0.840813\pi$
$941$	−24.7214	+	15.8875i	−0.805894	+	0.517916i	0.0716404	+	0.997431i	$0.477177\pi$
$942$	−71.7794	+	47.6832i	−2.33870	+	1.55360i
$943$	13.9545	−	36.2423i	0.454422	−	1.18021i
$944$	2.23986	+	2.28850i	0.0729014	+	0.0744845i
$945$	−25.5034	+	16.3900i	−0.829625	+	0.533168i
$946$	7.47462	+	15.7314i	0.243021	+	0.511470i
$947$	10.5359	−	23.0703i	0.342369	−	0.749685i	−0.657624	−	0.753346i	$-0.728438\pi$
$947$	10.5359	−	23.0703i	0.342369	−	0.749685i	0.999993	+	0.00366193i	$0.00116563\pi$
$948$	5.73968	−	50.8175i	0.186416	−	1.65048i
$949$	−9.43240	+	4.30763i	−0.306189	+	0.139832i
$950$	−1.98751	+	7.16927i	−0.0644833	+	0.232602i
$951$	−1.98407	+	0.285267i	−0.0643380	+	0.00925041i
$952$	79.8741	+	7.79681i	2.58874	+	0.252696i
$953$	42.1276	+	36.5038i	1.36465	+	1.18247i	0.963894	+	0.266286i	$0.0857965\pi$
$953$	42.1276	+	36.5038i	1.36465	+	1.18247i	0.400752	+	0.916187i	$0.368749\pi$
$954$	−81.5761	+	1.23718i	−2.64112	+	0.0400550i
$955$	2.30074	+	1.47859i	0.0744501	+	0.0478462i
$956$	23.3097	−	11.5119i	0.753891	−	0.372321i
$957$	28.2753	+	8.30239i	0.914012	+	0.268378i
$958$	−30.7946	−	34.4686i	−0.994930	−	1.11363i
$959$	1.14076	−	0.988478i	0.0368372	−	0.0319196i
$960$	16.9167	+	16.2666i	0.545985	+	0.525003i
$961$	35.6635	−	10.4718i	1.15044	−	0.337799i
$962$	8.05494	−	1.28308i	0.259702	−	0.0413683i
$963$	−44.7276	−	6.43085i	−1.44133	−	0.207231i
$964$	27.6170	−	4.82967i	0.889485	−	0.155553i
$965$	2.05037			0.0660038
$966$	69.4251	+	37.4932i	2.23372	+	1.20632i
$967$			10.2475i			0.329537i	0.986332	+	0.164768i	$0.0526877\pi$
$967$			10.2475i			0.329537i	−0.986332	+	0.164768i	$0.947312\pi$
$968$	7.22314	+	7.60742i	0.232161	+	0.244512i
$969$	15.7143	−	109.295i	0.504816	−	3.51107i
$970$	12.0297	−	1.91622i	0.386249	−	0.0615262i
$971$	−12.4872	−	42.5275i	−0.400734	−	1.36477i	−0.874885	−	0.484330i	$-0.839063\pi$
$971$	−12.4872	−	42.5275i	−0.400734	−	1.36477i	0.474151	−	0.880443i	$-0.342755\pi$
$972$	−12.9559	+	0.393066i	−0.415560	+	0.0126076i
$973$	−19.7206	−	22.7587i	−0.632212	−	0.729611i
$974$	−12.6606	+	11.3112i	−0.405673	+	0.362433i
$975$	1.97250	−	6.71772i	0.0631706	−	0.215139i
$976$	−15.2450	+	0.925884i	−0.487981	+	0.0296368i
$977$	−10.8231	+	16.8411i	−0.346262	+	0.538794i	−0.970083	−	0.242773i	$-0.921943\pi$
$977$	−10.8231	+	16.8411i	−0.346262	+	0.538794i	0.623821	+	0.781567i	$0.285579\pi$
$978$	25.7318	−	0.390246i	0.822812	−	0.0124787i
$979$	−30.5166	+	35.2180i	−0.975314	+	1.12557i
$980$	11.0237	−	13.5302i	0.352140	−	0.432208i
$981$	1.03492	+	7.19801i	0.0330424	+	0.229815i
$982$	11.4498	+	3.17418i	0.365378	+	0.101292i
$983$	−23.9740	−	52.4956i	−0.764650	−	1.67435i	−0.738089	−	0.674703i	$-0.764272\pi$
$983$	−23.9740	−	52.4956i	−0.764650	−	1.67435i	−0.0265612	−	0.999647i	$-0.508456\pi$
$984$	30.6630	+	59.7868i	0.977502	+	1.90593i
$985$	0.142938	+	0.0652776i	0.00455438	+	0.00207992i
$986$	−16.1553	−	34.0009i	−0.514488	−	1.08281i
$987$	17.7920	+	27.6849i	0.566325	+	0.881220i
$988$	−9.73370	+	23.1468i	−0.309670	+	0.736399i
$989$	15.6291	−	15.3031i	0.496978	−	0.486611i
$990$	−11.8453	−	17.8312i	−0.376469	−	0.566714i
$991$	2.19995	+	3.42319i	0.0698837	+	0.108741i	0.874437	−	0.485140i	$-0.161231\pi$
$991$	2.19995	+	3.42319i	0.0698837	+	0.108741i	−0.804553	+	0.593881i	$0.797595\pi$
$992$	−43.8326	−	16.1282i	−1.39169	−	0.512070i
$993$	−1.62580	+	3.56001i	−0.0515933	+	0.112973i
$994$	−43.4822	−	36.5380i	−1.37917	−	1.15891i
$995$	−7.65477	−	16.7616i	−0.242673	−	0.531379i
$996$	−25.6502	−	78.4705i	−0.812758	−	2.48643i
$997$	31.8879	−	4.58478i	1.00990	−	0.145202i	0.382546	−	0.923936i	$-0.375047\pi$
$997$	31.8879	−	4.58478i	1.00990	−	0.145202i	0.627353	+	0.778735i	$0.284138\pi$
$998$	−19.2659	+	5.97577i	−0.609851	+	0.189160i
$999$	12.0980	−	13.9619i	0.382764	−	0.441734i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bb.b.11.20	yes	480
8.3	odd	2		920.2.bb.a.11.2	✓	480
23.21	odd	22		920.2.bb.a.251.2	yes	480
184.67	even	22	inner	920.2.bb.b.251.20	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bb.a.11.2	✓	480	8.3	odd	2
920.2.bb.a.251.2	yes	480	23.21	odd	22
920.2.bb.b.11.20	yes	480	1.1	even	1	trivial
920.2.bb.b.251.20	yes	480	184.67	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.567911 + 1.29517i) q^{2} +(-0.417492 + 2.90372i) q^{3} +(-1.35496 - 1.47109i) q^{4} +(0.959493 - 0.281733i) q^{5} +(-3.52373 - 2.18978i) q^{6} +(-2.59694 - 2.99703i) q^{7} +(2.67481 - 0.919458i) q^{8} +(-5.37883 - 1.57937i) q^{9} +(-0.180013 + 1.40271i) q^{10} +(1.45984 - 2.27156i) q^{11} +(4.83731 - 3.32025i) q^{12} +(-1.80368 - 1.56290i) q^{13} +(5.35650 - 1.66145i) q^{14} +(0.417492 + 2.90372i) q^{15} +(-0.328193 + 3.98651i) q^{16} +(-6.50839 + 2.97228i) q^{17} +(5.10025 - 6.06959i) q^{18} +(4.78524 + 2.18535i) q^{19} +(-1.71452 - 1.02976i) q^{20} +(9.78674 - 6.28955i) q^{21} +(2.11301 + 3.18079i) q^{22} +(2.91434 - 3.80876i) q^{23} +(1.55314 + 8.15077i) q^{24} +(0.841254 - 0.540641i) q^{25} +(3.04856 - 1.44850i) q^{26} +(3.17571 - 6.95383i) q^{27} +(-0.890152 + 7.88116i) q^{28} +(3.38405 - 1.54544i) q^{29} +(-3.99793 - 1.10833i) q^{30} +(8.17242 - 1.17502i) q^{31} +(-4.97685 - 2.68905i) q^{32} +(5.98650 + 5.18734i) q^{33} +(-0.153441 - 10.1175i) q^{34} +(-3.33610 - 2.14398i) q^{35} +(4.96469 + 10.0527i) q^{36} +(2.31872 + 0.680838i) q^{37} +(-5.54800 + 4.95664i) q^{38} +(5.29125 - 4.58489i) q^{39} +(2.30742 - 1.63579i) q^{40} +(7.76984 - 2.28143i) q^{41} +(2.58808 + 16.2474i) q^{42} +(4.51454 + 0.649093i) q^{43} +(-5.31968 + 0.930305i) q^{44} -5.60591 q^{45} +(3.27792 + 5.93761i) q^{46} +2.82882i q^{47} +(-11.4387 - 2.61732i) q^{48} +(-1.24187 + 8.63743i) q^{49} +(0.222468 + 1.39661i) q^{50} +(-5.91348 - 20.1395i) q^{51} +(0.144747 + 4.77103i) q^{52} +(-6.73907 - 7.77731i) q^{53} +(7.20291 + 8.06225i) q^{54} +(0.760736 - 2.59083i) q^{55} +(-9.70195 - 5.62869i) q^{56} +(-8.34345 + 12.9827i) q^{57} +(0.0797819 + 5.26061i) q^{58} +(0.524253 - 0.605020i) q^{59} +(3.70595 - 4.54858i) q^{60} +(0.543398 + 3.77942i) q^{61} +(-3.11935 + 11.2520i) q^{62} +(9.23509 + 20.2220i) q^{63} +(6.30919 - 4.91875i) q^{64} +(-2.17094 - 0.991434i) q^{65} +(-10.1183 + 4.80763i) q^{66} +(-8.78544 - 13.6704i) q^{67} +(13.1911 + 5.54710i) q^{68} +(9.84286 + 10.0526i) q^{69} +(4.67144 - 3.10325i) q^{70} +(-5.47514 - 8.51948i) q^{71} +(-15.8395 + 0.721104i) q^{72} +(1.80492 - 3.95221i) q^{73} +(-2.19863 + 2.61649i) q^{74} +(1.21865 + 2.66848i) q^{75} +(-3.26895 - 10.0006i) q^{76} +(-10.5990 + 1.52391i) q^{77} +(2.93328 + 9.45690i) q^{78} +(5.70803 - 6.58742i) q^{79} +(0.808231 + 3.91749i) q^{80} +(4.71819 + 3.03220i) q^{81} +(-1.45772 + 11.3589i) q^{82} +(3.96423 - 13.5009i) q^{83} +(-22.5131 - 5.87508i) q^{84} +(-5.40737 + 4.68551i) q^{85} +(-3.40455 + 5.47849i) q^{86} +(3.07472 + 10.4716i) q^{87} +(1.81619 - 7.41824i) q^{88} +(-17.0823 - 2.45607i) q^{89} +(3.18366 - 7.26064i) q^{90} +9.46443i q^{91} +(-9.55181 + 0.873449i) q^{92} +24.2210i q^{93} +(-3.66381 - 1.60651i) q^{94} +(5.20709 + 0.748667i) q^{95} +(9.88606 - 13.3287i) q^{96} +(-2.42670 - 8.26459i) q^{97} +(-10.4817 - 6.51373i) q^{98} +(-11.4399 + 9.91271i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 2 q^{2} - 4 q^{4} + 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} - 2 q^{10} + 3 q^{12} - 56 q^{16} + 7 q^{18} + 4 q^{20} - 8 q^{21} - 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} - 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) \) 480 * q + 2 * q^2 - 4 * q^4 + 48 * q^5 + 5 * q^6 - q^8 - 48 * q^9 - 2 * q^10 + 3 * q^12 - 56 * q^16 + 7 * q^18 + 4 * q^20 - 8 * q^21 - 4 * q^23 + 2 * q^24 - 48 * q^25 + 7 * q^26 + 12 * q^27 - 5 * q^30 + 102 * q^32 + q^34 + 54 * q^36 - 8 * q^37 - 45 * q^38 + 45 * q^40 + 10 * q^42 + 23 * q^44 - 480 * q^45 + 32 * q^46 + 154 * q^48 - 48 * q^49 - 9 * q^50 - 7 * q^52 - 32 * q^53 - 27 * q^54 + 43 * q^56 - 40 * q^58 - 12 * q^59 + 8 * q^60 + 8 * q^61 + 158 * q^62 - 73 * q^64 - 88 * q^66 - 10 * q^68 + 20 * q^69 + 3 * q^72 - 11 * q^74 - 110 * q^76 - 300 * q^78 + 144 * q^79 + q^80 - 56 * q^81 - 59 * q^82 - 146 * q^84 + 18 * q^86 - 100 * q^88 - 7 * q^90 + 19 * q^92 - 316 * q^94 + 65 * q^96 - 98 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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