LMFDB - Embedded newform 920.2.bb.b.251.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(11,920)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.34623698596$
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			251.20
Character	$\chi$	$=$	920.251
Dual form			920.2.bb.b.11.20

$q$-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 $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$-1$	$e\left(\frac{13}{22}\right)$	$-1$	$1$

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	−0.646934	−	0.762546i	$-0.723949\pi$
$3$	−0.417492	−	2.90372i	−0.241039	−	1.67647i	0.405895	−	0.913920i	$-0.366960\pi$
$4$	−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	0.00959057	+	0.999954i	$0.496947\pi$
$7$	−2.59694	+	2.99703i	−0.981550	+	1.13277i	−0.991141	+	0.132815i	$0.957598\pi$
$8$	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	0.988477	−	0.151369i	$-0.0483682\pi$
$11$	1.45984	+	2.27156i	0.440159	+	0.684901i	−0.548318	+	0.836270i	$0.684732\pi$
$12$	4.83731	+	3.32025i	1.39641	+	0.958473i
$13$	−1.80368	+	1.56290i	−0.500251	+	0.433470i	−0.868081	−	0.496423i	$-0.834646\pi$
$13$	−1.80368	+	1.56290i	−0.500251	+	0.433470i	0.367830	+	0.929893i	$0.380101\pi$
$14$	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	−0.582737	−	0.812661i	$-0.698018\pi$
$17$	−6.50839	−	2.97228i	−1.57852	−	0.720884i	−0.995780	+	0.0917766i	$0.970745\pi$
$18$	5.10025	+	6.06959i	1.20214	+	1.43062i
$19$	4.78524	−	2.18535i	1.09781	−	0.501353i	0.217648	−	0.976027i	$-0.430161\pi$
$19$	4.78524	−	2.18535i	1.09781	−	0.501353i	0.880162	+	0.474674i	$0.157434\pi$
$20$	−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	0.704047	−	0.710153i	$-0.251374\pi$
$29$	3.38405	+	1.54544i	0.628402	+	0.286982i	−0.0756452	+	0.997135i	$0.524102\pi$
$30$	−3.99793	+	1.10833i	−0.729919	+	0.202352i
$31$	8.17242	+	1.17502i	1.46781	+	0.211039i	0.829399	−	0.558656i	$-0.188683\pi$
$31$	8.17242	+	1.17502i	1.46781	+	0.211039i	0.638411	+	0.769696i	$0.279592\pi$
$32$	−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	−0.0855203	−	0.996336i	$-0.527255\pi$
$37$	2.31872	−	0.680838i	0.381195	−	0.111929i	0.466716	+	0.884407i	$0.345437\pi$
$38$	−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	0.824979	−	0.565164i	$-0.191187\pi$
$41$	7.76984	+	2.28143i	1.21344	+	0.356299i	0.388466	+	0.921463i	$0.373005\pi$
$42$	2.58808	−	16.2474i	0.399349	−	2.50703i
$43$	4.51454	−	0.649093i	0.688461	−	0.0989858i	0.210799	−	0.977529i	$-0.432393\pi$
$43$	4.51454	−	0.649093i	0.688461	−	0.0989858i	0.477662	+	0.878544i	$0.341484\pi$
$44$	−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	$-0.933854\pi$
$47$		−	2.82882i		−	0.412625i	0.978486	−	0.206313i	$-0.0661464\pi$
$48$	−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	0.0718021	+	0.997419i	$0.477125\pi$
$53$	−6.73907	+	7.77731i	−0.925683	+	1.06830i	−0.997485	+	0.0708763i	$0.977420\pi$
$54$	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	0.788849	−	0.614587i	$-0.210678\pi$
$59$	0.524253	+	0.605020i	0.0682519	+	0.0787669i	−0.720597	+	0.693354i	$0.756132\pi$
$60$	3.70595	+	4.54858i	0.478436	+	0.587220i
$61$	0.543398	−	3.77942i	0.0695750	−	0.483905i	−0.925007	−	0.379950i	$-0.875941\pi$
$61$	0.543398	−	3.77942i	0.0695750	−	0.483905i	0.994582	−	0.103955i	$-0.0331497\pi$
$62$	−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	−0.434705	+	0.900573i	$0.643148\pi$
$67$	−8.78544	+	13.6704i	−1.07331	+	1.67011i	−0.638607	+	0.769533i	$0.720489\pi$
$68$	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	0.347523	+	0.937671i	$0.387023\pi$
$71$	−5.47514	+	8.51948i	−0.649779	+	1.01108i	−0.997302	+	0.0734047i	$0.976614\pi$
$72$	−15.8395	−	0.721104i	−1.86670	−	0.0849830i
$73$	1.80492	+	3.95221i	0.211249	+	0.462572i	0.985362	−	0.170477i	$-0.0545308\pi$
$73$	1.80492	+	3.95221i	0.211249	+	0.462572i	−0.774112	+	0.633048i	$0.781803\pi$
$74$	−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	0.979763	−	0.200161i	$-0.0641467\pi$
$79$	5.70803	+	6.58742i	0.642204	+	0.741143i	−0.337559	+	0.941304i	$0.609601\pi$
$80$	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	0.827160	+	0.561967i	$0.189955\pi$
$83$	3.96423	+	13.5009i	0.435131	+	1.48192i	−0.392029	+	0.919953i	$0.628227\pi$
$84$	−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	−0.962885	−	0.269913i	$-0.913005\pi$
$89$	−17.0823	+	2.45607i	−1.81072	+	0.260343i	−0.847838	+	0.530256i	$0.822096\pi$
$90$	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	0.739697	+	0.672940i	$0.234969\pi$
$97$	−2.42670	+	8.26459i	−0.246394	+	0.839142i	−0.986092	+	0.166202i	$0.946850\pi$
$98$	−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	0.908823	−	0.417182i	$-0.136982\pi$
$101$	−0.816787	−	2.78172i	−0.0812733	−	0.276792i	−0.990096	+	0.140391i	$0.955164\pi$
$102$	29.4425	−	3.77843i	2.91524	−	0.374120i
$103$	9.50954	−	6.11141i	0.937003	−	0.602175i	0.0194595	−	0.999811i	$-0.493805\pi$
$103$	9.50954	−	6.11141i	0.937003	−	0.602175i	0.917544	+	0.397635i	$0.130169\pi$
$104$	−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	0.516730	−	0.856148i	$-0.327149\pi$
$107$	7.97864	+	1.14716i	0.771324	+	0.110900i	0.254594	+	0.967048i	$0.418058\pi$
$108$	−14.5326	−	4.75039i	−1.39840	−	0.457106i
$109$	−0.538879	+	1.17998i	−0.0516153	+	0.113022i	−0.933683	−	0.358102i	$-0.883424\pi$
$109$	−0.538879	+	1.17998i	−0.0516153	+	0.113022i	0.882067	+	0.471123i	$0.156151\pi$
$110$	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	−0.0595116	−	0.998228i	$-0.518954\pi$
$113$	9.28256	−	14.4440i	0.873230	−	1.35877i	0.932742	−	0.360545i	$-0.117409\pi$
$114$	−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	0.923328	−	0.384013i	$-0.125458\pi$
$127$	2.14629	+	3.33970i	0.190453	+	0.296350i	−0.732875	+	0.680363i	$0.761822\pi$
$128$	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	−0.868745	−	0.495259i	$-0.835073\pi$
$131$	−2.91737	+	3.36682i	−0.254892	+	0.294161i	0.613854	+	0.789420i	$0.289619\pi$
$132$	−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	$-0.994824\pi$
$137$		−	0.380632i		−	0.0325196i	0.999868	−	0.0162598i	$-0.00517588\pi$
$138$	−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	−0.942215	−	0.335008i	$-0.891261\pi$
$149$	−12.5592	+	8.07132i	−1.02889	+	0.661228i	−0.0866762	+	0.996237i	$0.527625\pi$
$150$	−4.14824	−	0.0629118i	−0.338702	−	0.00513673i
$151$	−11.8155	+	10.2382i	−0.961529	+	0.833169i	−0.986036	−	0.166530i	$-0.946744\pi$
$151$	−11.8155	+	10.2382i	−0.961529	+	0.833169i	0.0245076	+	0.999700i	$0.492198\pi$
$152$	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	0.853216	+	0.521557i	$0.174649\pi$
$157$	8.62870	+	18.8942i	0.688645	+	1.50792i	−0.164571	+	0.986365i	$0.552624\pi$
$158$	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	0.320079	−	0.947391i	$-0.396291\pi$
$163$	−5.21835	−	3.35363i	−0.408733	−	0.262677i	−0.728812	+	0.684714i	$0.759927\pi$
$164$	−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	0.409637	−	0.912249i	$-0.365655\pi$
$167$	−0.149124	−	0.0681026i	−0.0115396	−	0.00526994i	−0.421176	+	0.906979i	$0.638383\pi$
$168$	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	0.835155	−	0.550015i	$-0.185378\pi$
$173$	−0.159051	−	0.247488i	−0.0120924	−	0.0188161i	−0.847247	+	0.531199i	$0.821742\pi$
$174$	−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	0.792227	−	0.610227i	$-0.208922\pi$
$179$	15.1020	+	4.43435i	1.12878	+	0.331439i	0.336550	+	0.941666i	$0.390740\pi$
$180$	7.59576	−	8.24679i	0.566155	−	0.614679i
$181$	−1.10560	−	7.68959i	−0.0821783	−	0.571562i	−0.988758	−	0.149527i	$-0.952225\pi$
$181$	−1.10560	−	7.68959i	−0.0821783	−	0.571562i	0.906579	−	0.422035i	$-0.138684\pi$
$182$	−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	−0.687246	−	0.726425i	$-0.741181\pi$
$191$	1.79097	−	2.06689i	0.129590	−	0.149555i	0.816836	+	0.576870i	$0.195726\pi$
$192$	11.6486	−	20.3737i	0.840668	−	1.47035i
$193$	1.96732	−	0.577657i	0.141611	−	0.0415806i	−0.210159	−	0.977667i	$-0.567398\pi$
$193$	1.96732	−	0.577657i	0.141611	−	0.0415806i	0.351770	+	0.936087i	$0.385580\pi$
$194$	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	−0.650620	−	0.759404i	$-0.725491\pi$
$197$	0.118757	−	0.102904i	0.00846109	−	0.00733158i	0.659081	+	0.752072i	$0.270945\pi$
$198$	−6.34186	+	20.4462i	−0.450696	+	1.45305i
$199$	−2.62241	+	18.2392i	−0.185898	+	1.29295i	0.656597	+	0.754241i	$0.271995\pi$
$199$	−2.62241	+	18.2392i	−0.185898	+	1.29295i	−0.842495	+	0.538704i	$0.818914\pi$
$200$	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	0.662744	−	0.748846i	$-0.269392\pi$
$211$	−4.89813	−	10.7254i	−0.337201	−	0.738367i	−0.999945	+	0.0104787i	$0.996664\pi$
$212$	−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	0.162913	−	0.986640i	$-0.447911\pi$
$223$	−11.8047	−	10.2288i	−0.790500	−	0.684972i	−0.953413	+	0.301668i	$0.902457\pi$
$224$	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	−0.366191	−	0.930540i	$-0.619338\pi$
$227$	−6.86109	+	0.986475i	−0.455386	+	0.0654747i	−0.0891948	+	0.996014i	$0.528429\pi$
$228$	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	−0.716993	−	0.697080i	$-0.754482\pi$
$233$	−3.44109	−	23.9333i	−0.225433	−	1.56792i	0.491560	−	0.870844i	$-0.336427\pi$
$234$	−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	−0.989024	−	0.147754i	$-0.952796\pi$
$239$	−3.66216	−	12.4722i	−0.236886	−	0.806759i	0.752138	−	0.659005i	$-0.229022\pi$
$240$	−11.7128	−	0.711357i	−0.756055	−	0.0459179i
$241$	−7.57875	−	11.7928i	−0.488190	−	0.759639i	0.506534	−	0.862220i	$-0.330926\pi$
$241$	−7.57875	−	11.7928i	−0.488190	−	0.759639i	−0.994725	+	0.102581i	$0.967290\pi$
$242$	−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	−0.533835	−	0.845588i	$-0.679250\pi$
$251$	7.24186	−	11.2686i	0.457102	−	0.711265i	0.990938	+	0.134324i	$0.0428862\pi$
$252$	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	−0.999561	−	0.0296371i	$-0.990565\pi$
$257$	−5.88964	−	12.8965i	−0.367386	−	0.804463i	0.632175	−	0.774826i	$-0.282162\pi$
$258$	−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	0.789833	−	0.613322i	$-0.210167\pi$
$263$	1.14086	+	1.31662i	0.0703485	+	0.0811865i	−0.719484	+	0.694509i	$0.755622\pi$
$264$	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	0.791226	−	0.611524i	$-0.209443\pi$
$269$	4.89624	+	4.24261i	0.298529	+	0.258677i	−0.492697	+	0.870201i	$0.663989\pi$
$270$	9.18254	−	5.70638i	0.558831	−	0.347279i
$271$	5.41170	−	18.4306i	0.328737	−	1.11958i	−0.614903	−	0.788603i	$-0.710805\pi$
$271$	5.41170	−	18.4306i	0.328737	−	1.11958i	0.943640	−	0.330974i	$-0.107377\pi$
$272$	−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	$0.258897\pi$
$277$			24.1858i			1.45319i	−0.687068	+	0.726593i	$0.741103\pi$
$278$	−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	−0.878328	−	0.478059i	$-0.841341\pi$
$281$	1.99525	−	6.79520i	0.119027	−	0.405368i	0.997354	+	0.0726912i	$0.0231587\pi$
$282$	6.19449	+	9.96799i	0.368876	+	0.593585i
$283$	9.33245	+	8.08661i	0.554756	+	0.480699i	0.886537	−	0.462657i	$-0.153104\pi$
$283$	9.33245	+	8.08661i	0.554756	+	0.480699i	−0.331781	+	0.943356i	$0.607649\pi$
$284$	−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	−0.868729	−	0.495288i	$-0.835062\pi$
$293$	1.27492	−	2.79168i	0.0744815	−	0.163092i	0.943210	+	0.332197i	$0.107790\pi$
$294$	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	−0.635896	−	0.771775i	$-0.719369\pi$
$307$	3.35843	−	23.3584i	0.191676	−	1.33313i	0.827572	−	0.561360i	$-0.189722\pi$
$308$	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	0.850660	−	0.525716i	$-0.176203\pi$
$311$	0.336387	+	0.523428i	0.0190748	+	0.0296809i	−0.831585	+	0.555397i	$0.812566\pi$
$312$	9.93746	+	17.1288i	0.562598	+	0.969726i
$313$	−0.772329	−	2.63031i	−0.0436546	−	0.148674i	0.934782	−	0.355223i	$-0.115595\pi$
$313$	−0.772329	−	2.63031i	−0.0436546	−	0.148674i	−0.978436	+	0.206549i	$0.933777\pi$
$314$	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	−0.953910	−	0.300092i	$-0.902983\pi$
$317$	0.192504	−	0.655608i	0.0108121	−	0.0368226i	0.964722	+	0.263269i	$0.0848008\pi$
$318$	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	−0.246364	−	0.969177i	$-0.579236\pi$
$331$	1.28006	−	0.375858i	0.0703582	−	0.0206590i	0.316722	+	0.948518i	$0.397418\pi$
$332$	−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	0.427746	−	0.903899i	$-0.359308\pi$
$337$	10.7118	+	1.54012i	0.583507	+	0.0838957i	0.155761	+	0.987795i	$0.450217\pi$
$338$	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	−0.998894	−	0.0470255i	$-0.985026\pi$
$347$	−27.1339	−	17.4379i	−1.45662	−	0.936116i	−0.457731	−	0.889091i	$-0.651338\pi$
$348$	11.2384	+	18.7117i	0.602444	+	1.00305i
$349$	8.97024	−	4.09657i	0.480166	−	0.219285i	−0.160602	−	0.987019i	$-0.551343\pi$
$349$	8.97024	−	4.09657i	0.480166	−	0.219285i	0.640768	+	0.767735i	$0.278616\pi$
$350$	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	−0.821842	−	0.569715i	$-0.807054\pi$
$353$	2.39019	−	16.6241i	0.127217	−	0.884813i	0.949059	−	0.315098i	$-0.102037\pi$
$354$	−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	−0.607252	−	0.794509i	$-0.707728\pi$
$359$	−13.0464	+	3.83076i	−0.688561	+	0.202180i	−0.0813088	+	0.996689i	$0.525910\pi$
$360$	−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	0.681318	−	0.731987i	$-0.261407\pi$
$373$	16.5850	+	4.86979i	0.858738	+	0.252148i	0.177419	+	0.984135i	$0.443225\pi$
$374$	−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	0.897069	−	0.441891i	$-0.145692\pi$
$379$	2.38394	+	3.70949i	0.122455	+	0.190543i	−0.774614	+	0.632434i	$0.782056\pi$
$380$	−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	−0.967173	−	0.254117i	$-0.918215\pi$
$383$	0.634390	−	4.41228i	0.0324158	−	0.225457i	0.999589	+	0.0286605i	$0.00912417\pi$
$384$	−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	0.638549	−	0.769581i	$-0.279535\pi$
$389$	4.01908	+	2.58291i	0.203775	+	0.130959i	−0.434773	+	0.900540i	$0.643171\pi$
$390$	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	0.738372	−	0.674394i	$-0.235595\pi$
$397$	14.1911	+	6.48085i	0.712230	+	0.325264i	−0.0261421	+	0.999658i	$0.508322\pi$
$398$	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	−0.317940	−	0.948111i	$-0.602991\pi$
$401$	11.5198	−	9.98198i	0.575272	−	0.498476i	0.893213	+	0.449634i	$0.148446\pi$
$402$	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	−0.536735	−	0.843751i	$-0.680342\pi$
$409$	−29.2118	−	8.57736i	−1.44443	−	0.424123i	−0.907696	+	0.419628i	$0.862161\pi$
$410$	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	0.831465	+	0.555577i	$0.187503\pi$
$419$	−3.44656	+	11.7379i	−0.168375	+	0.573434i	−0.999841	+	0.0178571i	$0.994316\pi$
$420$	−23.2563	−	0.705569i	−1.13479	−	0.0344283i
$421$	−23.9730	+	27.6663i	−1.16837	+	1.34837i	−0.242676	+	0.970107i	$0.578025\pi$
$421$	−23.9730	+	27.6663i	−1.16837	+	1.34837i	−0.925697	+	0.378267i	$0.876520\pi$
$422$	−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	0.555615	+	0.831440i	$0.312483\pi$
$431$	−9.06396	+	19.8473i	−0.436596	+	0.956011i	−0.992211	+	0.124571i	$0.960244\pi$
$432$	26.6793	−	14.9422i	1.28361	−	0.718907i
$433$	10.9007	−	4.97819i	0.523854	−	0.239236i	−0.135893	−	0.990723i	$-0.543390\pi$
$433$	10.9007	−	4.97819i	0.523854	−	0.239236i	0.659748	+	0.751487i	$0.270663\pi$
$434$	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	−0.163518	−	0.986540i	$-0.552284\pi$
$439$	16.7995	−	26.1406i	0.801799	−	1.24762i	0.965316	−	0.261083i	$-0.0840795\pi$
$440$	−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	−0.281081	−	0.959684i	$-0.590693\pi$
$443$	13.2235	−	28.9555i	0.628269	−	1.37572i	0.909350	−	0.416033i	$-0.136580\pi$
$444$	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	−0.968611	−	0.248583i	$-0.920035\pi$
$449$	−24.2593	+	15.5905i	−1.14487	+	0.735761i	−0.176256	+	0.984344i	$0.556399\pi$
$450$	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	0.162857	−	0.986650i	$-0.447929\pi$
$457$	12.7643	−	1.83523i	0.597089	−	0.0858485i	0.434232	+	0.900801i	$0.357020\pi$
$458$	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	$0.120146\pi$
$461$			15.8262i			0.737100i	−0.929608	+	0.368550i	$0.879854\pi$
$462$	40.6852	−	17.8397i	1.89285	−	0.829979i
$463$	−9.06780	+	1.30375i	−0.421417	+	0.0605905i	−0.349761	−	0.936839i	$-0.613737\pi$
$463$	−9.06780	+	1.30375i	−0.421417	+	0.0605905i	−0.0716554	+	0.997429i	$0.522828\pi$
$464$	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	0.918256	−	0.395986i	$-0.129597\pi$
$467$	14.1975	+	12.3022i	0.656982	+	0.569278i	−0.261274	+	0.965265i	$0.584143\pi$
$468$	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	−0.915261	−	0.402861i	$-0.868016\pi$
$479$	−13.5771	−	29.7298i	−0.620355	−	1.35839i	0.294906	−	0.955526i	$-0.404712\pi$
$480$	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	−0.152336	−	0.988329i	$-0.548680\pi$
$487$	10.9200	−	4.98701i	0.494833	−	0.225983i	0.647170	+	0.762346i	$0.275952\pi$
$488$	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	0.944892	+	0.327383i	$0.106167\pi$
$491$	−1.19567	+	8.31607i	−0.0539598	+	0.375299i	−0.998851	+	0.0479154i	$0.984742\pi$
$492$	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	−0.507131	−	0.861869i	$-0.669294\pi$
$499$	9.34048	−	10.7795i	0.418137	−	0.482556i	0.925269	+	0.379313i	$0.123840\pi$
$500$	−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	0.977225	−	0.212208i	$-0.0680654\pi$
$503$	−0.453070	−	3.15117i	−0.0202014	−	0.140504i	−0.997426	+	0.0717040i	$0.977156\pi$
$504$	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	−0.620490	−	0.784214i	$-0.713066\pi$
$509$	−22.4461	+	3.22727i	−0.994908	+	0.143046i	−0.374418	+	0.927260i	$0.622157\pi$
$510$	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	0.528167	−	0.849140i	$-0.322879\pi$
$521$	18.1624	+	2.61136i	0.795710	+	0.114406i	0.267543	+	0.963546i	$0.413788\pi$
$522$	7.87930	+	28.4219i	0.344868	+	1.24399i
$523$	28.2381	+	12.8959i	1.23477	+	0.563899i	0.922464	−	0.386083i	$-0.126172\pi$
$523$	28.2381	+	12.8959i	1.23477	+	0.563899i	0.312304	+	0.949982i	$0.398899\pi$
$524$	−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	0.880048	+	0.474884i	$0.157510\pi$
$541$	22.0135	+	34.2536i	0.946433	+	1.47268i	0.0663844	+	0.997794i	$0.478854\pi$
$542$	−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	−0.222044	−	0.975037i	$-0.571273\pi$
$547$	−21.8908	−	6.42773i	−0.935985	−	0.274830i	−0.713940	+	0.700207i	$0.753091\pi$
$548$	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	−0.573036	−	0.819530i	$-0.694235\pi$
$557$	−35.3582	−	10.3821i	−1.49818	−	0.439904i	−0.925140	+	0.379626i	$0.876053\pi$
$558$	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	0.996287	+	0.0860933i	$0.0274383\pi$
$563$	15.6775	+	24.3947i	0.660728	+	1.02811i	−0.335559	+	0.942019i	$0.608925\pi$
$564$	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	0.377088	−	0.926177i	$-0.376925\pi$
$569$	−1.81120	−	0.827150i	−0.0759297	−	0.0346759i	−0.453018	+	0.891501i	$0.649653\pi$
$570$	−16.7090	+	14.0405i	−0.699862	+	0.588091i
$571$	33.2637	−	15.1910i	1.39204	−	0.635725i	0.428565	−	0.903511i	$-0.359019\pi$
$571$	33.2637	−	15.1910i	1.39204	−	0.635725i	0.963479	+	0.267786i	$0.0862919\pi$
$572$	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	0.920785	−	0.390071i	$-0.127550\pi$
$577$	22.7831	+	14.6418i	0.948471	+	0.609545i	0.0276862	+	0.999617i	$0.491186\pi$
$578$	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	−0.333936	−	0.942596i	$-0.608377\pi$
$587$	9.32193	−	5.99084i	0.384757	−	0.247268i	0.718693	+	0.695327i	$0.244741\pi$
$588$	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	0.0420319	−	0.999116i	$-0.486617\pi$
$593$	−11.2692	−	3.30894i	−0.462772	−	0.135882i	−0.504804	+	0.863234i	$0.668435\pi$
$594$	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	$-0.949479\pi$
$599$		−	7.73638i		−	0.316100i	0.987431	−	0.158050i	$-0.0505207\pi$
$600$	5.71322	−	6.01717i	0.233241	−	0.245650i
$601$	0.791496	+	5.50498i	0.0322858	+	0.224553i	0.999576	−	0.0291200i	$-0.00927048\pi$
$601$	0.791496	+	5.50498i	0.0322858	+	0.224553i	−0.967290	+	0.253673i	$0.918361\pi$
$602$	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	−0.999975	−	0.00703109i	$-0.997762\pi$
$607$	−4.00465	−	13.6386i	−0.162544	−	0.553573i	0.837431	−	0.546542i	$-0.184056\pi$
$608$	−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	0.677905	+	0.735150i	$0.262888\pi$
$613$	−4.44807	+	30.9370i	−0.179656	+	1.24953i	−0.857560	+	0.514383i	$0.828021\pi$
$614$	−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	−0.284108	−	0.958792i	$-0.591698\pi$
$617$	6.32033	−	2.88640i	0.254447	−	0.116202i	0.538555	+	0.842590i	$0.318970\pi$
$618$	−20.1264	+	42.3588i	−0.809603	+	1.70392i
$619$	4.44057	−	6.90965i	0.178481	−	0.277722i	−0.740473	−	0.672086i	$-0.765399\pi$
$619$	4.44057	−	6.90965i	0.178481	−	0.277722i	0.918955	+	0.394363i	$0.129035\pi$
$620$	−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	0.793314	−	0.608812i	$-0.208354\pi$
$631$	1.95427	+	2.25535i	0.0777983	+	0.0897840i	−0.715516	+	0.698596i	$0.753808\pi$
$632$	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	−0.549799	−	0.835297i	$-0.685296\pi$
$641$	−21.3177	+	3.06502i	−0.841998	+	0.121061i	−0.292198	+	0.956358i	$0.594387\pi$
$642$	−30.6266	+	13.4292i	−1.20874	+	0.530009i
$643$		−	13.8501i		−	0.546194i	−0.961987	−	0.273097i	$-0.911952\pi$
$643$		−	13.8501i		−	0.546194i	0.961987	−	0.273097i	$-0.0880480\pi$
$644$	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	−0.819519	−	0.573052i	$-0.805759\pi$
$647$	−36.7399	+	5.28240i	−1.44439	+	0.207673i	−0.624875	+	0.780725i	$0.714850\pi$
$648$	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	−0.983647	−	0.180109i	$-0.942355\pi$
$653$	−6.47854	−	22.0639i	−0.253525	−	0.863426i	0.730122	−	0.683317i	$-0.239463\pi$
$654$	−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	0.0819189	−	0.996639i	$-0.473895\pi$
$659$	−3.08735	−	0.443894i	−0.120266	−	0.0172917i	−0.202185	+	0.979347i	$0.564804\pi$
$660$	−4.92228	+	15.0585i	−0.191599	+	0.586151i
$661$	−8.05791	+	17.6444i	−0.313416	+	0.686286i	−0.999135	−	0.0415805i	$-0.986761\pi$
$661$	−8.05791	+	17.6444i	−0.313416	+	0.686286i	0.685719	+	0.727867i	$0.259488\pi$
$662$	−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	−0.946541	−	0.322584i	$-0.895449\pi$
$673$	−2.15050	+	4.70894i	−0.0828958	+	0.181516i	0.863645	+	0.504100i	$0.168176\pi$
$674$	−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	0.998065	+	0.0621825i	$0.0198061\pi$
$677$	23.8746	+	27.5527i	0.917575	+	1.05894i	−0.0804899	+	0.996755i	$0.525648\pi$
$678$	−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	−0.106670	+	0.994294i	$0.534019\pi$
$683$	−28.1117	+	32.4426i	−1.07566	+	1.24138i	−0.968993	+	0.247087i	$0.920527\pi$
$684$	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	0.276729	−	0.960948i	$-0.410750\pi$
$701$	33.5137	−	21.5380i	1.26580	−	0.813477i	0.989066	+	0.147471i	$0.0471132\pi$
$702$	−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	0.952096	−	0.305801i	$-0.0989241\pi$
$709$	2.59606	+	5.68457i	0.0974969	+	0.213488i	−0.854599	+	0.519289i	$0.826197\pi$
$710$	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	0.765545	−	0.643383i	$-0.222470\pi$
$719$	20.9320	+	9.55935i	0.780634	+	0.356503i	0.0150889	+	0.999886i	$0.495197\pi$
$720$	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	−0.909435	−	0.415847i	$-0.863485\pi$
$727$	−39.0875	+	11.4771i	−1.44968	+	0.425663i	−0.540242	+	0.841510i	$0.681667\pi$
$728$	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	−0.808916	−	0.587924i	$-0.799945\pi$
$733$	−5.37159	−	37.3602i	−0.198404	−	1.37993i	0.610512	−	0.792007i	$-0.290964\pi$
$734$	−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	0.947476	+	0.319827i	$0.103625\pi$
$739$	3.49281	+	24.2930i	0.128485	+	0.893633i	−0.818991	+	0.573806i	$0.805466\pi$
$740$	−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	−0.669884	−	0.742466i	$-0.733656\pi$
$743$	4.37107	−	5.04448i	0.160359	−	0.185064i	0.830243	+	0.557402i	$0.188202\pi$
$744$	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	0.849360	+	0.527813i	$0.176988\pi$
$751$	−3.13224	+	21.7852i	−0.114297	+	0.794954i	−0.963658	+	0.267141i	$0.913921\pi$
$752$	−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	0.424785	−	0.905294i	$-0.360350\pi$
$757$	−6.11457	−	3.92959i	−0.222238	−	0.142823i	−0.647023	+	0.762471i	$0.723986\pi$
$758$	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	−0.00253575	−	0.999997i	$-0.500807\pi$
$761$	−25.1922	−	16.1901i	−0.913218	−	0.586890i	−0.910682	+	0.413107i	$0.864444\pi$
$762$	−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	−0.841189	−	0.540741i	$-0.818144\pi$
$769$	−11.8041	+	10.2283i	−0.425665	+	0.368841i	0.415524	+	0.909582i	$0.363598\pi$
$770$	−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	−0.383960	−	0.923350i	$-0.625440\pi$
$773$	−5.77655	+	1.69615i	−0.207768	+	0.0610062i	0.176192	+	0.984356i	$0.443622\pi$
$774$	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	−0.998058	−	0.0622894i	$-0.980160\pi$
$787$	−3.50001	+	11.9200i	−0.124762	+	0.424900i	0.873296	+	0.487190i	$0.161978\pi$
$788$	−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	−0.762105	−	0.647453i	$-0.775834\pi$
$797$	4.27810	−	29.7548i	0.151538	−	1.05397i	0.913643	−	0.406517i	$-0.133257\pi$
$798$	−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	−0.990925	−	0.134414i	$-0.957085\pi$
$809$	−12.6170	−	27.6274i	−0.443591	−	0.971328i	0.547334	−	0.836914i	$-0.315643\pi$
$810$	−5.10263	−	6.07242i	−0.179288	−	0.213363i
$811$	14.7235	−	32.2401i	0.517014	−	1.13210i	−0.453544	−	0.891234i	$-0.649841\pi$
$811$	14.7235	−	32.2401i	0.517014	−	1.13210i	0.970558	−	0.240868i	$-0.0774322\pi$
$812$	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	−0.105320	−	0.994438i	$-0.533587\pi$
$821$	−31.6509	−	27.4257i	−1.10463	−	0.957163i	−0.999305	+	0.0372753i	$0.988132\pi$
$822$	0.833501	+	1.34125i	0.0290717	+	0.0467813i
$823$	3.29630	−	11.2262i	0.114902	−	0.391320i	−0.881881	−	0.471473i	$-0.843723\pi$
$823$	3.29630	−	11.2262i	0.114902	−	0.391320i	0.996783	+	0.0801528i	$0.0255408\pi$
$824$	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	$0.0476425\pi$
$827$			8.57638i			0.298230i	−0.988820	+	0.149115i	$0.952358\pi$
$828$	52.7571	−	10.3877i	1.83344	−	0.360997i
$829$			33.8755i			1.17654i	0.808663	+	0.588272i	$0.200192\pi$
$829$			33.8755i			1.17654i	−0.808663	+	0.588272i	$0.799808\pi$
$830$	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	−0.891055	−	0.453896i	$-0.850034\pi$
$839$	−24.5724	+	15.7917i	−0.848334	+	0.545191i	0.0427205	+	0.999087i	$0.486397\pi$
$840$	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	−0.831766	−	0.555126i	$-0.812670\pi$
$853$	0.546803	−	0.850842i	0.0187222	−	0.0291323i	0.850489	+	0.525994i	$0.176306\pi$
$854$	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	−0.908346	−	0.418220i	$-0.862654\pi$
$857$	0.0750635	−	0.164366i	0.00256412	−	0.00561464i	0.910910	+	0.412606i	$0.135381\pi$
$858$	25.7640	−	7.14246i	0.879569	−	0.243840i
$859$	−6.23836	+	43.3888i	−0.212850	+	1.48041i	0.550725	+	0.834687i	$0.314351\pi$
$859$	−6.23836	+	43.3888i	−0.212850	+	1.48041i	−0.763575	+	0.645719i	$0.776558\pi$
$860$	−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	0.957112	+	0.289718i	$0.0935614\pi$
$863$	24.1786	+	37.6227i	0.823050	+	1.28069i	−0.134062	+	0.990973i	$0.542802\pi$
$864$	−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	0.712302	−	0.701873i	$-0.247653\pi$
$877$	47.1899	−	6.78489i	1.59349	−	0.229109i	0.881189	+	0.472764i	$0.156744\pi$
$878$	−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	0.824686	−	0.565590i	$-0.191352\pi$
$881$	11.3449	+	9.83038i	0.382218	+	0.331194i	−0.442468	+	0.896784i	$0.645897\pi$
$882$	46.0918	−	51.5908i	1.55199	−	1.73715i
$883$	7.36183	−	2.16163i	0.247745	−	0.0727446i	−0.155502	−	0.987836i	$-0.549700\pi$
$883$	7.36183	−	2.16163i	0.247745	−	0.0727446i	0.403248	+	0.915091i	$0.367881\pi$
$884$	−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	0.226084	−	0.974108i	$-0.427408\pi$
$887$	36.4077	−	31.5475i	1.22245	−	1.05926i	0.996368	−	0.0851529i	$-0.0271379\pi$
$888$	−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	−0.211202	−	0.977442i	$-0.567738\pi$
$907$	21.8716	−	18.9518i	0.726234	−	0.629286i	0.937436	+	0.348157i	$0.113192\pi$
$908$	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	−0.993554	−	0.113356i	$-0.963840\pi$
$911$	−53.3662	+	15.6697i	−1.76810	+	0.519161i	−0.774546	+	0.632517i	$0.782022\pi$
$912$	−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	0.250231	−	0.968186i	$-0.419494\pi$
$929$	29.9973	−	8.80800i	0.984179	−	0.288981i	0.733948	+	0.679205i	$0.237675\pi$
$930$	−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	0.712795	−	0.701372i	$-0.247429\pi$
$937$	19.8820	+	9.07979i	0.649515	+	0.296624i	−0.0632799	+	0.997996i	$0.520156\pi$
$938$	−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	0.0716404	−	0.997431i	$-0.477177\pi$
$941$	−24.7214	−	15.8875i	−0.805894	−	0.517916i	−0.877534	+	0.479514i	$0.840813\pi$
$942$	−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	0.999993	−	0.00366193i	$-0.00116563\pi$
$947$	10.5359	+	23.0703i	0.342369	+	0.749685i	−0.657624	+	0.753346i	$0.728438\pi$
$948$	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	0.400752	−	0.916187i	$-0.368749\pi$
$953$	42.1276	−	36.5038i	1.36465	−	1.18247i	0.963894	−	0.266286i	$-0.0857965\pi$
$954$	−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	$-0.947312\pi$
$967$		−	10.2475i		−	0.329537i	0.986332	−	0.164768i	$-0.0526877\pi$
$968$	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	0.474151	+	0.880443i	$0.342755\pi$
$971$	−12.4872	+	42.5275i	−0.400734	+	1.36477i	−0.874885	+	0.484330i	$0.839063\pi$
$972$	−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	0.623821	−	0.781567i	$-0.285579\pi$
$977$	−10.8231	−	16.8411i	−0.346262	−	0.538794i	−0.970083	+	0.242773i	$0.921943\pi$
$978$	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	−0.0265612	+	0.999647i	$0.508456\pi$
$983$	−23.9740	+	52.4956i	−0.764650	+	1.67435i	−0.738089	+	0.674703i	$0.764272\pi$
$984$	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	−0.804553	−	0.593881i	$-0.797595\pi$
$991$	2.19995	−	3.42319i	0.0698837	−	0.108741i	0.874437	+	0.485140i	$0.161231\pi$
$992$	−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	0.627353	−	0.778735i	$-0.284138\pi$
$997$	31.8879	+	4.58478i	1.00990	+	0.145202i	0.382546	+	0.923936i	$0.375047\pi$
$998$	−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.251.20	yes	480
8.3	odd	2		920.2.bb.a.251.2	yes	480
23.11	odd	22		920.2.bb.a.11.2	✓	480
184.11	even	22	inner	920.2.bb.b.11.20	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bb.a.11.2	✓	480	23.11	odd	22
920.2.bb.a.251.2	yes	480	8.3	odd	2
920.2.bb.b.11.20	yes	480	184.11	even	22	inner
920.2.bb.b.251.20	yes	480	1.1	even	1	trivial

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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