LMFDB - Embedded newform 360.2.bo.a.43.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(43,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 8, 9]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("360.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bo (of order $12$, degree $4$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$272$
Relative dimension:	$68$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			43.13
Character	$\chi$	$=$	360.43
Dual form			360.2.bo.a.67.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21505 - 0.723644i) q^{2} +(1.31796 - 1.12382i) q^{3} +(0.952679 + 1.75852i) q^{4} +(2.19583 + 0.422281i) q^{5} +(-2.41463 + 0.411761i) q^{6} +(-0.968556 + 0.259524i) q^{7} +(0.114995 - 2.82609i) q^{8} +(0.474050 - 2.96231i) q^{9} +O(q^{10})$	\(q+(-1.21505 - 0.723644i) q^{2} +(1.31796 - 1.12382i) q^{3} +(0.952679 + 1.75852i) q^{4} +(2.19583 + 0.422281i) q^{5} +(-2.41463 + 0.411761i) q^{6} +(-0.968556 + 0.259524i) q^{7} +(0.114995 - 2.82609i) q^{8} +(0.474050 - 2.96231i) q^{9} +(-2.36246 - 2.10209i) q^{10} +(0.0439296 - 0.0760883i) q^{11} +(3.23186 + 1.24703i) q^{12} +(0.755462 + 0.202425i) q^{13} +(1.36464 + 0.385556i) q^{14} +(3.36859 - 1.91117i) q^{15} +(-2.18481 + 3.35062i) q^{16} +(4.13408 - 4.13408i) q^{17} +(-2.71965 + 3.25630i) q^{18} +3.13250i q^{19} +(1.34933 + 4.26372i) q^{20} +(-0.984862 + 1.43053i) q^{21} +(-0.108437 + 0.0606615i) q^{22} +(3.50919 + 0.940285i) q^{23} +(-3.02446 - 3.85391i) q^{24} +(4.64336 + 1.85452i) q^{25} +(-0.771438 - 0.792642i) q^{26} +(-2.70433 - 4.43696i) q^{27} +(-1.37910 - 1.45599i) q^{28} +(1.77509 - 3.07454i) q^{29} +(-5.47601 - 0.115497i) q^{30} +(-8.48968 + 4.90152i) q^{31} +(5.07929 - 2.49013i) q^{32} +(-0.0276121 - 0.149651i) q^{33} +(-8.01471 + 2.03150i) q^{34} +(-2.23638 + 0.160868i) q^{35} +(5.66091 - 1.98850i) q^{36} +(-6.82169 - 6.82169i) q^{37} +(2.26682 - 3.80614i) q^{38} +(1.22316 - 0.582215i) q^{39} +(1.44591 - 6.15706i) q^{40} +(-0.468734 - 0.811870i) q^{41} +(2.23185 - 1.02547i) q^{42} +(8.76616 - 2.34889i) q^{43} +(0.175654 + 0.00476350i) q^{44} +(2.29186 - 6.30455i) q^{45} +(-3.58340 - 3.68190i) q^{46} +(-2.51100 + 0.672821i) q^{47} +(0.886001 + 6.87132i) q^{48} +(-5.19143 + 2.99727i) q^{49} +(-4.29989 - 5.61346i) q^{50} +(0.802594 - 10.0945i) q^{51} +(0.363743 + 1.52134i) q^{52} +(-2.88187 + 2.88187i) q^{53} +(0.0751062 + 7.34809i) q^{54} +(0.128593 - 0.148527i) q^{55} +(0.622058 + 2.76707i) q^{56} +(3.52038 + 4.12852i) q^{57} +(-4.38169 + 2.45118i) q^{58} +(-3.71726 + 2.14616i) q^{59} +(6.57003 + 4.10301i) q^{60} +(5.21098 + 3.00856i) q^{61} +(13.8623 + 0.187929i) q^{62} +(0.309646 + 2.99219i) q^{63} +(-7.97355 - 0.649972i) q^{64} +(1.57339 + 0.763510i) q^{65} +(-0.0747437 + 0.201814i) q^{66} +(-8.06532 - 2.16110i) q^{67} +(11.2083 + 3.33143i) q^{68} +(5.68170 - 2.70445i) q^{69} +(2.83372 + 1.42288i) q^{70} +5.67266i q^{71} +(-8.31724 - 1.68036i) q^{72} +(10.6328 + 10.6328i) q^{73} +(3.35220 + 13.2252i) q^{74} +(8.20392 - 2.77412i) q^{75} +(-5.50858 + 2.98427i) q^{76} +(-0.0228016 + 0.0850966i) q^{77} +(-1.90751 - 0.177714i) q^{78} +(-2.67568 + 4.63441i) q^{79} +(-6.21237 + 6.43479i) q^{80} +(-8.55055 - 2.80856i) q^{81} +(-0.0179717 + 1.32566i) q^{82} +(-14.3252 + 3.83843i) q^{83} +(-3.45387 - 0.369070i) q^{84} +(10.8235 - 7.33201i) q^{85} +(-12.3511 - 3.48957i) q^{86} +(-1.11574 - 6.04702i) q^{87} +(-0.209981 - 0.132899i) q^{88} -2.97912i q^{89} +(-7.34697 + 6.00184i) q^{90} -0.784242 q^{91} +(1.68962 + 7.06678i) q^{92} +(-5.68065 + 16.0009i) q^{93} +(3.53787 + 0.999562i) q^{94} +(-1.32280 + 6.87845i) q^{95} +(3.89585 - 8.99012i) q^{96} +(3.81348 + 14.2321i) q^{97} +(8.47679 + 0.114919i) q^{98} +(-0.204572 - 0.166203i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8}+O(q^{10}) $ 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8	$ 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8} - 8 q^{10} - 8 q^{11} - 10 q^{12} - 4 q^{16} - 16 q^{17} + 20 q^{18} + 14 q^{20} + 6 q^{22} - 4 q^{25} - 48 q^{26} - 8 q^{27} + 8 q^{28} - 34 q^{30} - 22 q^{32} + 4 q^{33} - 16 q^{35} - 8 q^{36} - 26 q^{38} - 2 q^{40} - 8 q^{41} - 66 q^{42} - 4 q^{43} - 40 q^{46} - 38 q^{48} - 42 q^{50} - 16 q^{51} + 14 q^{52} + 24 q^{56} + 16 q^{57} + 6 q^{58} + 14 q^{60} - 76 q^{62} - 4 q^{65} - 44 q^{66} - 4 q^{67} - 46 q^{68} + 18 q^{70} + 38 q^{72} - 16 q^{73} - 120 q^{75} - 38 q^{78} + 92 q^{80} - 32 q^{81} - 4 q^{83} - 40 q^{86} - 42 q^{88} - 14 q^{90} - 32 q^{91} + 52 q^{92} + 108 q^{96} - 4 q^{97} - 140 q^{98}+O(q^{100}) $ 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8 - 8 * q^10 - 8 * q^11 - 10 * q^12 - 4 * q^16 - 16 * q^17 + 20 * q^18 + 14 * q^20 + 6 * q^22 - 4 * q^25 - 48 * q^26 - 8 * q^27 + 8 * q^28 - 34 * q^30 - 22 * q^32 + 4 * q^33 - 16 * q^35 - 8 * q^36 - 26 * q^38 - 2 * q^40 - 8 * q^41 - 66 * q^42 - 4 * q^43 - 40 * q^46 - 38 * q^48 - 42 * q^50 - 16 * q^51 + 14 * q^52 + 24 * q^56 + 16 * q^57 + 6 * q^58 + 14 * q^60 - 76 * q^62 - 4 * q^65 - 44 * q^66 - 4 * q^67 - 46 * q^68 + 18 * q^70 + 38 * q^72 - 16 * q^73 - 120 * q^75 - 38 * q^78 + 92 * q^80 - 32 * q^81 - 4 * q^83 - 40 * q^86 - 42 * q^88 - 14 * q^90 - 32 * q^91 + 52 * q^92 + 108 * q^96 - 4 * q^97 - 140 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.21505	−	0.723644i	−0.859168	−	0.511694i
$2$	−1.21505	−	0.723644i	−0.859168	−	0.511694i
$3$	1.31796	−	1.12382i	0.760926	−	0.648839i
$3$	1.31796	−	1.12382i	0.760926	−	0.648839i
$4$	0.952679	+	1.75852i	0.476339	+	0.879261i
$5$	2.19583	+	0.422281i	0.982006	+	0.188850i
$5$	2.19583	+	0.422281i	0.982006	+	0.188850i
$6$	−2.41463	+	0.411761i	−0.985770	+	0.168101i
$7$	−0.968556	+	0.259524i	−0.366080	+	0.0980908i	−0.437170	−	0.899379i	$-0.644019\pi$
$7$	−0.968556	+	0.259524i	−0.366080	+	0.0980908i	0.0710897	+	0.997470i	$0.477352\pi$
$8$	0.114995	−	2.82609i	0.0406569	−	0.999173i
$9$	0.474050	−	2.96231i	0.158017	−	0.987436i
$10$	−2.36246	−	2.10209i	−0.747075	−	0.664740i
$11$	0.0439296	−	0.0760883i	0.0132453	−	0.0229415i	−0.859327	−	0.511427i	$-0.829117\pi$
$11$	0.0439296	−	0.0760883i	0.0132453	−	0.0229415i	0.872572	+	0.488485i	$0.162450\pi$
$12$	3.23186	+	1.24703i	0.932958	+	0.359985i
$13$	0.755462	+	0.202425i	0.209527	+	0.0561427i	0.362056	−	0.932156i	$-0.382075\pi$
$13$	0.755462	+	0.202425i	0.209527	+	0.0561427i	−0.152529	+	0.988299i	$0.548742\pi$
$14$	1.36464	+	0.385556i	0.364717	+	0.103044i
$15$	3.36859	−	1.91117i	0.869767	−	0.493463i
$16$	−2.18481	+	3.35062i	−0.546202	+	0.837654i
$17$	4.13408	−	4.13408i	1.00266	−	1.00266i	0.00266597	−	0.999996i	$-0.499151\pi$
$17$	4.13408	−	4.13408i	1.00266	−	1.00266i	0.999996	−	0.00266597i	$-0.000848605\pi$
$18$	−2.71965	+	3.25630i	−0.641028	+	0.767518i
$19$			3.13250i			0.718646i	0.933213	+	0.359323i	$0.116992\pi$
$19$			3.13250i			0.718646i	−0.933213	+	0.359323i	$0.883008\pi$
$20$	1.34933	+	4.26372i	0.301720	+	0.953397i
$21$	−0.984862	+	1.43053i	−0.214915	+	0.312167i
$22$	−0.108437	+	0.0606615i	−0.0231189	+	0.0129331i
$23$	3.50919	+	0.940285i	0.731717	+	0.196063i	0.605394	−	0.795926i	$-0.293016\pi$
$23$	3.50919	+	0.940285i	0.731717	+	0.196063i	0.126323	+	0.991989i	$0.459682\pi$
$24$	−3.02446	−	3.85391i	−0.617365	−	0.786677i
$25$	4.64336	+	1.85452i	0.928671	+	0.370904i
$26$	−0.771438	−	0.792642i	−0.151291	−	0.155450i
$27$	−2.70433	−	4.43696i	−0.520448	−	0.853893i
$28$	−1.37910	−	1.45599i	−0.260626	−	0.275155i
$29$	1.77509	−	3.07454i	0.329626	−	0.570929i	−0.652812	−	0.757520i	$-0.726411\pi$
$29$	1.77509	−	3.07454i	0.329626	−	0.570929i	0.982438	+	0.186592i	$0.0597441\pi$
$30$	−5.47601	−	0.115497i	−0.999778	−	0.0210868i
$31$	−8.48968	+	4.90152i	−1.52479	+	0.880339i	−0.525224	+	0.850964i	$0.676018\pi$
$31$	−8.48968	+	4.90152i	−1.52479	+	0.880339i	−0.999568	+	0.0293750i	$0.990648\pi$
$32$	5.07929	−	2.49013i	0.897901	−	0.440198i
$33$	−0.0276121	−	0.149651i	−0.00480665	−	0.0260508i
$34$	−8.01471	+	2.03150i	−1.37451	+	0.348400i
$35$	−2.23638	+	0.160868i	−0.378017	+	0.0271916i
$36$	5.66091	−	1.98850i	0.943484	−	0.331417i
$37$	−6.82169	−	6.82169i	−1.12148	−	1.12148i	−0.991519	−	0.129960i	$-0.958515\pi$
$37$	−6.82169	−	6.82169i	−1.12148	−	1.12148i	−0.129960	−	0.991519i	$-0.541485\pi$
$38$	2.26682	−	3.80614i	0.367726	−	0.617437i
$39$	1.22316	−	0.582215i	0.195862	−	0.0932291i
$40$	1.44591	−	6.15706i	0.228619	−	0.973516i
$41$	−0.468734	−	0.811870i	−0.0732039	−	0.126793i	0.827100	−	0.562055i	$-0.189989\pi$
$41$	−0.468734	−	0.811870i	−0.0732039	−	0.126793i	−0.900304	+	0.435262i	$0.856656\pi$
$42$	2.23185	−	1.02547i	0.344381	−	0.158233i
$43$	8.76616	−	2.34889i	1.33683	−	0.358202i	0.481571	−	0.876407i	$-0.340066\pi$
$43$	8.76616	−	2.34889i	1.33683	−	0.358202i	0.855256	+	0.518205i	$0.173400\pi$
$44$	0.175654	+	0.00476350i	0.0264808	+	0.000718125i
$45$	2.29186	−	6.30455i	0.341651	−	0.939827i
$46$	−3.58340	−	3.68190i	−0.528344	−	0.542866i
$47$	−2.51100	+	0.672821i	−0.366267	+	0.0981410i	−0.437258	−	0.899336i	$-0.644050\pi$
$47$	−2.51100	+	0.672821i	−0.366267	+	0.0981410i	0.0709911	+	0.997477i	$0.477384\pi$
$48$	0.886001	+	6.87132i	0.127883	+	0.991789i
$49$	−5.19143	+	2.99727i	−0.741633	+	0.428182i
$50$	−4.29989	−	5.61346i	−0.608096	−	0.793864i
$51$	0.802594	−	10.0945i	0.112386	−	1.41352i
$52$	0.363743	+	1.52134i	0.0504420	+	0.210972i
$53$	−2.88187	+	2.88187i	−0.395855	+	0.395855i	−0.876768	−	0.480913i	$-0.840305\pi$
$53$	−2.88187	+	2.88187i	−0.395855	+	0.395855i	0.480913	+	0.876768i	$0.340305\pi$
$54$	0.0751062	+	7.34809i	0.0102207	+	0.999948i
$55$	0.128593	−	0.148527i	0.0173394	−	0.0200273i
$56$	0.622058	+	2.76707i	0.0831260	+	0.369765i
$57$	3.52038	+	4.12852i	0.466285	+	0.546836i
$58$	−4.38169	+	2.45118i	−0.575344	+	0.321856i
$59$	−3.71726	+	2.14616i	−0.483946	+	0.279407i	−0.722060	−	0.691831i	$-0.756804\pi$
$59$	−3.71726	+	2.14616i	−0.483946	+	0.279407i	0.238113	+	0.971237i	$0.423471\pi$
$60$	6.57003	+	4.10301i	0.848187	+	0.529697i
$61$	5.21098	+	3.00856i	0.667197	+	0.385207i	0.795014	−	0.606591i	$-0.207464\pi$
$61$	5.21098	+	3.00856i	0.667197	+	0.385207i	−0.127817	+	0.991798i	$0.540797\pi$
$62$	13.8623	+	0.187929i	1.76052	+	0.0238671i
$63$	0.309646	+	2.99219i	0.0390117	+	0.376981i
$64$	−7.97355	−	0.649972i	−0.996694	−	0.0812465i
$65$	1.57339	+	0.763510i	0.195155	+	0.0947017i
$66$	−0.0747437	+	0.201814i	−0.00920032	+	0.0248416i
$67$	−8.06532	−	2.16110i	−0.985335	−	0.264020i	−0.270045	−	0.962848i	$-0.587039\pi$
$67$	−8.06532	−	2.16110i	−0.985335	−	0.264020i	−0.715290	+	0.698828i	$0.753705\pi$
$68$	11.2083	+	3.33143i	1.35921	+	0.403995i
$69$	5.68170	−	2.70445i	0.683996	−	0.325577i
$70$	2.83372	+	1.42288i	0.338694	+	0.170067i
$71$			5.67266i			0.673221i	0.941644	+	0.336611i	$0.109281\pi$
$71$			5.67266i			0.673221i	−0.941644	+	0.336611i	$0.890719\pi$
$72$	−8.31724	−	1.68036i	−0.980196	−	0.198032i
$73$	10.6328	+	10.6328i	1.24448	+	1.24448i	0.958124	+	0.286354i	$0.0924434\pi$
$73$	10.6328	+	10.6328i	1.24448	+	1.24448i	0.286354	+	0.958124i	$0.407557\pi$
$74$	3.35220	+	13.2252i	0.389686	+	1.53739i
$75$	8.20392	−	2.77412i	0.947307	−	0.320328i
$76$	−5.50858	+	2.98427i	−0.631877	+	0.342319i
$77$	−0.0228016	+	0.0850966i	−0.00259848	+	0.00969766i
$78$	−1.90751	−	0.177714i	−0.215983	−	0.0201221i
$79$	−2.67568	+	4.63441i	−0.301037	+	0.521412i	−0.976371	−	0.216100i	$-0.930666\pi$
$79$	−2.67568	+	4.63441i	−0.301037	+	0.521412i	0.675334	+	0.737512i	$0.264000\pi$
$80$	−6.21237	+	6.43479i	−0.694564	+	0.719431i
$81$	−8.55055	−	2.80856i	−0.950062	−	0.312063i
$82$	−0.0179717	+	1.32566i	−0.00198465	+	0.146394i
$83$	−14.3252	+	3.83843i	−1.57239	+	0.421322i	−0.936561	−	0.350504i	$-0.886010\pi$
$83$	−14.3252	+	3.83843i	−1.57239	+	0.421322i	−0.635834	+	0.771826i	$0.719344\pi$
$84$	−3.45387	−	0.369070i	−0.376848	−	0.0402688i
$85$	10.8235	−	7.33201i	1.17397	−	0.795268i
$86$	−12.3511	−	3.48957i	−1.33185	−	0.376290i
$87$	−1.11574	−	6.04702i	−0.119620	−	0.648308i
$88$	−0.209981	−	0.132899i	−0.0223840	−	0.0141671i
$89$		−	2.97912i		−	0.315786i	−0.987456	−	0.157893i	$-0.949530\pi$
$89$		−	2.97912i		−	0.315786i	0.987456	−	0.157893i	$-0.0504701\pi$
$90$	−7.34697	+	6.00184i	−0.774439	+	0.632649i
$91$	−0.784242			−0.0822108
$92$	1.68962	+	7.06678i	0.176155	+	0.736763i
$93$	−5.68065	+	16.0009i	−0.589056	+	1.65922i
$94$	3.53787	+	0.999562i	0.364903	+	0.103097i
$95$	−1.32280	+	6.87845i	−0.135716	+	0.705714i
$96$	3.89585	−	8.99012i	0.397619	−	0.917551i
$97$	3.81348	+	14.2321i	0.387201	+	1.44505i	0.834669	+	0.550752i	$0.185659\pi$
$97$	3.81348	+	14.2321i	0.387201	+	1.44505i	−0.447468	+	0.894300i	$0.647674\pi$
$98$	8.47679	+	0.114919i	0.856285	+	0.0116085i
$99$	−0.204572	−	0.166203i	−0.0205603	−	0.0167040i
$100$	1.16242	+	9.93221i	0.116242	+	0.993221i
$101$	−12.7842	−	7.38096i	−1.27208	−	0.734433i	−0.296697	−	0.954972i	$-0.595885\pi$
$101$	−12.7842	−	7.38096i	−1.27208	−	0.734433i	−0.975378	+	0.220539i	$0.929219\pi$
$102$	−8.28004	+	11.6845i	−0.819846	+	1.15694i
$103$	−5.36155	−	1.43662i	−0.528290	−	0.141555i	−0.0151913	−	0.999885i	$-0.504836\pi$
$103$	−5.36155	−	1.43662i	−0.528290	−	0.141555i	−0.513098	+	0.858330i	$0.671502\pi$
$104$	0.658946	−	2.11172i	0.0646150	−	0.207072i
$105$	−2.76668	+	2.72531i	−0.270000	+	0.265963i
$106$	5.58705	−	1.41616i	0.542662	−	0.137549i
$107$	5.32474	−	5.32474i	0.514762	−	0.514762i	−0.401220	−	0.915982i	$-0.631414\pi$
$107$	5.32474	−	5.32474i	0.514762	−	0.514762i	0.915982	+	0.401220i	$0.131414\pi$
$108$	5.22614	−	8.98262i	0.502886	−	0.864353i
$109$	13.5891			1.30160			0.650802	−	0.759248i	$-0.274433\pi$
$109$	13.5891			1.30160			0.650802	+	0.759248i	$0.274433\pi$
$110$	−0.263727	+	0.0874114i	−0.0251453	+	0.00833435i
$111$	−16.6571	−	1.32437i	−1.58102	−	0.125704i
$112$	1.24654	−	3.81227i	0.117787	−	0.360226i
$113$	−3.44677	+	12.8635i	−0.324245	+	1.21010i	0.590825	+	0.806800i	$0.298803\pi$
$113$	−3.44677	+	12.8635i	−0.324245	+	1.21010i	−0.915069	+	0.403297i	$0.867864\pi$
$114$	−1.28984	−	7.56385i	−0.120805	−	0.708419i
$115$	7.30853	+	3.54657i	0.681524	+	0.330720i
$116$	7.09775	+	0.192482i	0.659009	+	0.0178715i
$117$	0.957773	−	2.14195i	0.0885462	−	0.198024i
$118$	6.06971	+	0.0822861i	0.558762	+	0.00757505i
$119$	−2.93120	+	5.07699i	−0.268703	+	0.465406i
$120$	−5.01377	−	9.73972i	−0.457693	−	0.889110i
$121$	5.49614	+	9.51959i	0.499649	+	0.865418i
$122$	−4.15446	−	7.42643i	−0.376127	−	0.672358i
$123$	−1.53017	−	0.543242i	−0.137971	−	0.0489825i
$124$	−16.7074	−	10.2597i	−1.50037	−	0.921351i
$125$	9.41290	+	6.03301i	0.841916	+	0.539609i
$126$	1.78905	−	3.85973i	0.159381	−	0.343852i
$127$	−1.69446	−	1.69446i	−0.150359	−	0.150359i	0.627920	−	0.778278i	$-0.283907\pi$
$127$	−1.69446	−	1.69446i	−0.150359	−	0.150359i	−0.778278	+	0.627920i	$0.783907\pi$
$128$	9.21789	+	6.55976i	0.814754	+	0.579806i
$129$	8.91374	−	12.9473i	0.784811	−	1.13995i
$130$	−1.35923	−	2.06627i	−0.119212	−	0.181224i
$131$	0.365040	+	0.632268i	0.0318937	+	0.0552415i	0.881532	−	0.472125i	$-0.156513\pi$
$131$	0.365040	+	0.632268i	0.0318937	+	0.0552415i	−0.849638	+	0.527366i	$0.823180\pi$
$132$	0.236859	−	0.191126i	0.0206159	−	0.0166353i
$133$	−0.812959	−	3.03401i	−0.0704925	−	0.263082i
$134$	8.23588	+	8.46225i	0.711471	+	0.731027i
$135$	−4.06460	−	10.8848i	−0.349825	−	0.936815i
$136$	−11.2079	−	12.1587i	−0.961068	−	1.04260i
$137$	0.627180	+	2.34067i	0.0535836	+	0.199977i	0.987529	−	0.157440i	$-0.0503242\pi$
$137$	0.627180	+	2.34067i	0.0535836	+	0.199977i	−0.933945	+	0.357417i	$0.883657\pi$
$138$	−8.86058	−	0.825496i	−0.754263	−	0.0702709i
$139$	−5.70316	+	3.29272i	−0.483736	+	0.279285i	−0.721972	−	0.691922i	$-0.756764\pi$
$139$	−5.70316	+	3.29272i	−0.483736	+	0.279285i	0.238236	+	0.971207i	$0.423431\pi$
$140$	−2.41344	−	3.77947i	−0.203973	−	0.319423i
$141$	−2.55327	+	3.70867i	−0.215025	+	0.312326i
$142$	4.10499	−	6.89255i	0.344483	−	0.578410i
$143$	0.0485894	−	0.0485894i	0.00406325	−	0.00406325i
$144$	8.88985	+	8.06043i	0.740821	+	0.671703i
$145$	5.19612	−	6.00160i	0.431514	−	0.498405i
$146$	−5.22500	−	20.6138i	−0.432424	−	1.70601i
$147$	−3.47371	+	9.78453i	−0.286507	+	0.807015i
$148$	5.49722	−	18.4950i	0.451869	−	1.52028i
$149$	−1.71020	−	2.96216i	−0.140105	−	0.242669i	0.787431	−	0.616403i	$-0.211411\pi$
$149$	−1.71020	−	2.96216i	−0.140105	−	0.242669i	−0.927536	+	0.373734i	$0.878077\pi$
$150$	−11.9756	−	2.56603i	−0.977805	−	0.209515i
$151$	13.5895	+	7.84588i	1.10589	+	0.638489i	0.937763	−	0.347276i	$-0.112893\pi$
$151$	13.5895	+	7.84588i	1.10589	+	0.638489i	0.168132	+	0.985765i	$0.446227\pi$
$152$	8.85273	+	0.360222i	0.718051	+	0.0292179i
$153$	−10.2867	−	14.2062i	−0.831628	−	1.14850i
$154$	0.0892846	−	0.0868962i	0.00719476	−	0.00700229i
$155$	−20.7117	+	7.17788i	−1.66361	+	0.576541i
$156$	2.18912	+	1.59629i	0.175270	+	0.127806i
$157$	0.934662	−	3.48821i	0.0745941	−	0.278389i	−0.918547	−	0.395312i	$-0.870636\pi$
$157$	0.934662	−	3.48821i	0.0745941	−	0.278389i	0.993141	+	0.116923i	$0.0373031\pi$
$158$	6.60474	−	3.69479i	0.525445	−	0.293942i
$159$	−0.559488	+	7.03690i	−0.0443703	+	0.558062i
$160$	12.2048	−	3.32302i	0.964875	−	0.262708i
$161$	−3.64288			−0.287099
$162$	8.35692	+	9.60009i	0.656582	+	0.754255i
$163$	−12.7691	−	12.7691i	−1.00015	−	1.00015i	−1.00000		0.000149631i	$-0.999952\pi$
$163$	−12.7691	−	12.7691i	−1.00015	−	1.00015i	−0.000149631	−	1.00000i	$-0.500048\pi$
$164$	0.981140	−	1.59773i	0.0766142	−	0.124762i
$165$	0.00256306	−	0.340268i	0.000199534	−	0.0264898i
$166$	20.1834	+	5.70248i	1.56654	+	0.442598i
$167$	3.69435	−	13.7875i	0.285878	−	1.06691i	−0.662318	−	0.749223i	$-0.730427\pi$
$167$	3.69435	−	13.7875i	0.285878	−	1.06691i	0.948196	−	0.317687i	$-0.102906\pi$
$168$	3.92954	+	2.94781i	0.303171	+	0.227429i
$169$	−10.7286	−	6.19415i	−0.825276	−	0.476473i
$170$	−18.4568	+	1.07637i	−1.41557	+	0.0825541i
$171$	9.27944	+	1.48496i	0.709617	+	0.113558i
$172$	12.4819	+	13.1778i	0.951736	+	1.00479i
$173$	−2.12574	−	7.93336i	−0.161617	−	0.603162i	−0.998448	−	0.0557006i	$-0.982261\pi$
$173$	−2.12574	−	7.93336i	−0.161617	−	0.603162i	0.836831	−	0.547462i	$-0.184406\pi$
$174$	−3.02021	+	8.15481i	−0.228962	+	0.618214i
$175$	−4.97864	−	0.591143i	−0.376350	−	0.0446862i
$176$	0.158965	+	0.313430i	0.0119824	+	0.0236256i
$177$	−2.48731	+	7.00610i	−0.186958	+	0.526611i
$178$	−2.15582	+	3.61977i	−0.161586	+	0.271313i
$179$			7.52891i			0.562738i	0.959600	+	0.281369i	$0.0907884\pi$
$179$			7.52891i			0.562738i	−0.959600	+	0.281369i	$0.909212\pi$
$180$	13.2701	−	1.97592i	0.989095	−	0.147276i
$181$			6.06083i			0.450498i	0.974301	+	0.225249i	$0.0723195\pi$
$181$			6.06083i			0.450498i	−0.974301	+	0.225249i	$0.927680\pi$
$182$	0.952890	+	0.567512i	0.0706329	+	0.0420668i
$183$	10.2490	−	1.89104i	0.757625	−	0.139790i
$184$	3.06087	−	9.80916i	0.225650	−	0.723141i
$185$	−12.0986	−	17.8600i	−0.889508	−	1.31309i
$186$	18.4812	−	15.3311i	1.35511	−	1.12413i
$187$	−0.132947	−	0.496164i	−0.00972203	−	0.0362831i
$188$	−3.57535	−	3.77467i	−0.260759	−	0.275296i
$189$	3.77079	+	3.59561i	0.274285	+	0.261542i
$190$	6.58481	−	7.40041i	0.477712	−	0.536882i
$191$	19.4275	+	11.2165i	1.40572	+	0.811596i	0.994972	−	0.100151i	$-0.0319327\pi$
$191$	19.4275	+	11.2165i	1.40572	+	0.811596i	0.410753	+	0.911747i	$0.365266\pi$
$192$	−11.2393	+	8.10421i	−0.811126	+	0.584871i
$193$	−0.833146	+	3.10934i	−0.0599711	+	0.223815i	−0.989407	−	0.145169i	$-0.953628\pi$
$193$	−0.833146	+	3.10934i	−0.0599711	+	0.223815i	0.929436	+	0.368984i	$0.120294\pi$
$194$	5.66542	−	20.0523i	0.406754	−	1.43967i
$195$	2.93171	−	0.761929i	0.209944	−	0.0545629i
$196$	−10.2165	−	6.27381i	−0.729753	−	0.448129i
$197$	−10.4494	−	10.4494i	−0.744486	−	0.744486i	0.228952	−	0.973438i	$-0.426470\pi$
$197$	−10.4494	−	10.4494i	−0.744486	−	0.744486i	−0.973438	+	0.228952i	$0.926470\pi$
$198$	0.128293	+	0.349982i	0.00911742	+	0.0248721i
$199$	1.64950			0.116930			0.0584651	−	0.998289i	$-0.481379\pi$
$199$	1.64950			0.116930			0.0584651	+	0.998289i	$0.481379\pi$
$200$	5.77499	−	12.9093i	0.408354	−	0.912824i
$201$	−13.0585	+	6.21574i	−0.921073	+	0.438424i
$202$	10.1922	+	18.2194i	0.717122	+	1.28191i
$203$	−0.921356	+	3.43855i	−0.0646665	+	0.241339i
$204$	18.5161	−	8.20547i	1.29639	−	0.574498i
$205$	−0.686423	−	1.98067i	−0.0479418	−	0.138336i
$206$	5.47494	+	5.62542i	0.381457	+	0.391942i
$207$	4.44895	−	9.94957i	0.309223	−	0.691543i
$208$	−2.32879	+	2.08900i	−0.161472	+	0.144846i
$209$	0.238347	+	0.137610i	0.0164868	+	0.00951866i
$210$	5.33380	−	1.30929i	0.368067	−	0.0903495i
$211$	−5.50448	−	9.53404i	−0.378944	−	0.656351i	0.611965	−	0.790885i	$-0.290379\pi$
$211$	−5.50448	−	9.53404i	−0.378944	−	0.656351i	−0.990909	+	0.134534i	$0.957046\pi$
$212$	−7.81332	−	2.32234i	−0.536621	−	0.159499i
$213$	6.37506	+	7.47636i	0.436812	+	0.512272i
$214$	−10.3230	+	2.61659i	−0.705668	+	0.178867i
$215$	20.2409	−	1.45597i	1.38042	−	0.0992965i
$216$	−12.8502	+	7.13244i	−0.874347	+	0.485301i
$217$	6.95067	−	6.95067i	0.471843	−	0.471843i
$218$	−16.5114	−	9.83370i	−1.11830	−	0.666022i
$219$	25.9631	+	2.06426i	1.75442	+	0.139490i
$220$	0.383695	+	0.0846352i	0.0258687	+	0.00570611i
$221$	3.95999	−	2.28630i	0.266377	−	0.153793i
$222$	19.2808	+	13.6630i	1.29404	+	0.916999i
$223$	−7.19983	−	26.8701i	−0.482136	−	1.79936i	−0.592625	−	0.805478i	$-0.701908\pi$
$223$	−7.19983	−	26.8701i	−0.482136	−	1.79936i	0.110489	−	0.993877i	$-0.464758\pi$
$224$	−4.27333	+	3.73003i	−0.285524	+	0.249223i
$225$	7.69484	−	12.8759i	0.512989	−	0.858395i
$226$	13.4966	−	13.1355i	0.897779	−	0.873763i
$227$	2.75248	+	10.2724i	0.182688	+	0.681803i	0.995114	+	0.0987370i	$0.0314803\pi$
$227$	2.75248	+	10.2724i	0.182688	+	0.681803i	−0.812425	+	0.583066i	$0.801853\pi$
$228$	−3.90631	+	10.1238i	−0.258702	+	0.670466i
$229$	7.31805	+	12.6752i	0.483591	+	0.837603i	0.999822	−	0.0188455i	$-0.00599906\pi$
$229$	7.31805	+	12.6752i	0.483591	+	0.837603i	−0.516232	+	0.856449i	$0.672666\pi$
$230$	−6.31375	−	9.59803i	−0.416316	−	0.632875i
$231$	0.0655818	+	0.137779i	0.00431497	+	0.00906520i
$232$	−8.48481	−	5.37012i	−0.557055	−	0.352565i
$233$	−5.82842	−	5.82842i	−0.381832	−	0.381832i	0.489930	−	0.871762i	$-0.337022\pi$
$233$	−5.82842	−	5.82842i	−0.381832	−	0.381832i	−0.871762	+	0.489930i	$0.837022\pi$
$234$	−2.71375	+	1.90949i	−0.177403	+	0.124827i
$235$	−5.79786	+	0.417053i	−0.378210	+	0.0272055i
$236$	−7.31543	−	4.49229i	−0.476194	−	0.292423i
$237$	1.68181	+	9.11497i	0.109245	+	0.592081i
$238$	7.23547	−	4.04763i	0.469006	−	0.262369i
$239$	−9.78217	−	16.9432i	−0.632756	−	1.09597i	−0.986986	−	0.160807i	$-0.948590\pi$
$239$	−9.78217	−	16.9432i	−0.632756	−	1.09597i	0.354230	−	0.935158i	$-0.384743\pi$
$240$	−0.956118	+	15.4624i	−0.0617172	+	0.998094i
$241$	−3.48623	+	6.03834i	−0.224568	+	0.388963i	−0.956190	−	0.292747i	$-0.905430\pi$
$241$	−3.48623	+	6.03834i	−0.224568	+	0.388963i	0.731622	+	0.681711i	$0.238764\pi$
$242$	0.210728	−	15.5440i	0.0135461	−	0.999206i
$243$	−14.4256	+	5.90772i	−0.925405	+	0.378980i
$244$	−0.326233	+	12.0298i	−0.0208849	+	0.770130i
$245$	−12.6652	+	4.38926i	−0.809150	+	0.280420i
$246$	1.46612	+	1.76736i	0.0934761	+	0.112683i
$247$	−0.634098	+	2.36649i	−0.0403467	+	0.150576i
$248$	12.8759	+	24.5562i	0.817618	+	1.55932i
$249$	−14.5664	+	21.1579i	−0.923106	+	1.34083i
$250$	−7.07137	−	14.1420i	−0.447233	−	0.894418i
$251$	1.79803			0.113490			0.0567452	−	0.998389i	$-0.481928\pi$
$251$	1.79803			0.113490			0.0567452	+	0.998389i	$0.481928\pi$
$252$	−4.96684	+	3.39512i	−0.312882	+	0.213872i
$253$	0.225702	−	0.225702i	0.0141898	−	0.0141898i
$254$	0.832661	+	3.28503i	0.0522458	+	0.206121i
$255$	6.02510	−	21.8270i	0.377306	−	1.36686i
$256$	−6.45324	−	14.6409i	−0.403328	−	0.915056i
$257$	−15.8334	−	4.24254i	−0.987659	−	0.264643i	−0.271392	−	0.962469i	$-0.587484\pi$
$257$	−15.8334	−	4.24254i	−0.987659	−	0.264643i	−0.716267	+	0.697826i	$0.754151\pi$
$258$	−20.1999	+	9.28126i	−1.25759	+	0.577826i
$259$	8.37759	+	4.83680i	0.520558	+	0.300544i
$260$	0.156283	+	3.49422i	0.00969227	+	0.216702i
$261$	−8.26627	−	6.71585i	−0.511669	−	0.415701i
$262$	0.0139960	−	1.03239i	0.000864677	−	0.0637815i
$263$	6.91447	+	25.8052i	0.426365	+	1.59121i	0.760925	+	0.648840i	$0.224746\pi$
$263$	6.91447	+	25.8052i	0.426365	+	1.59121i	−0.334560	+	0.942374i	$0.608588\pi$
$264$	−0.426101	+	0.0608253i	−0.0262247	+	0.00374354i
$265$	−7.54505	+	5.11114i	−0.463489	+	0.313975i
$266$	−1.20776	+	4.27475i	−0.0740523	+	0.262102i
$267$	−3.34800	−	3.92637i	−0.204894	−	0.240290i
$268$	−3.88332	−	16.2419i	−0.237212	−	0.992130i
$269$	−10.7400			−0.654830			−0.327415	−	0.944881i	$-0.606178\pi$
$269$	−10.7400			−0.654830			−0.327415	+	0.944881i	$0.606178\pi$
$270$	−2.93804	+	16.1669i	−0.178803	+	0.983885i
$271$			24.3275i			1.47779i	0.673822	+	0.738894i	$0.264652\pi$
$271$			24.3275i			1.47779i	−0.673822	+	0.738894i	$0.735348\pi$
$272$	4.81955	+	22.8839i	0.292228	+	1.38754i
$273$	−1.03360	+	0.881348i	−0.0625564	+	0.0533416i
$274$	0.931757	−	3.29788i	0.0562895	−	0.199232i
$275$	0.345088	−	0.271837i	0.0208096	−	0.0163924i
$276$	10.1687	+	7.41492i	0.612081	+	0.446326i
$277$	−25.4979	+	6.83214i	−1.53202	+	0.410503i	−0.923677	−	0.383172i	$-0.874832\pi$
$277$	−25.4979	+	6.83214i	−1.53202	+	0.410503i	−0.608342	+	0.793675i	$0.708165\pi$
$278$	9.31237	+	0.126246i	0.558519	+	0.00757176i
$279$	10.4953	+	27.4726i	0.628337	+	1.64474i
$280$	0.197454	+	6.33870i	0.0118001	+	0.378810i
$281$	5.91016	−	10.2367i	0.352571	−	0.610670i	−0.634129	−	0.773228i	$-0.718641\pi$
$281$	5.91016	−	10.2367i	0.352571	−	0.610670i	0.986699	+	0.162558i	$0.0519743\pi$
$282$	5.78611	−	2.65855i	0.344558	−	0.158314i
$283$	2.20106	−	8.21445i	0.130839	−	0.488298i	−0.869141	−	0.494564i	$-0.835328\pi$
$283$	2.20106	−	8.21445i	0.130839	−	0.488298i	0.999980	+	0.00626564i	$0.00199443\pi$
$284$	−9.97551	+	5.40423i	−0.591938	+	0.320682i
$285$	5.98676	+	10.5521i	0.354625	+	0.625054i
$286$	−0.0941998	+	0.0238770i	−0.00557015	+	0.00141187i
$287$	0.664695	+	0.664695i	0.0392357	+	0.0392357i
$288$	−4.96871	−	16.2269i	−0.292784	−	0.956179i
$289$		−	17.1813i		−	1.01066i
$290$	−10.6565	+	3.53208i	−0.625774	+	0.207411i
$291$	21.0204	+	14.4717i	1.23224	+	0.848347i
$292$	−8.56840	+	28.8277i	−0.501428	+	1.68702i
$293$	−23.6794	−	6.34489i	−1.38337	−	0.370672i	−0.511024	−	0.859566i	$-0.670734\pi$
$293$	−23.6794	−	6.34489i	−1.38337	−	0.370672i	−0.872343	+	0.488894i	$0.837401\pi$
$294$	11.3012	−	9.37494i	0.659102	−	0.546758i
$295$	−9.06877	+	3.14288i	−0.528004	+	0.182986i
$296$	−20.0632	+	18.4942i	−1.16615	+	1.07496i
$297$	−0.456401	+	0.0108538i	−0.0264831	+	0.000629803i
$298$	−0.0655709	+	4.83674i	−0.00379842	+	0.280185i
$299$	2.46072	+	1.42070i	0.142307	+	0.0821611i
$300$	12.6941	+	11.7839i	0.732891	+	0.680346i
$301$	−7.88093	+	4.55006i	−0.454249	+	0.262261i
$302$	−10.8342	−	19.3670i	−0.623439	−	1.11445i
$303$	−25.1440	+	4.63933i	−1.44448	+	0.266523i
$304$	−10.4958	−	6.84391i	−0.601976	−	0.392525i
$305$	10.1720	+	8.80679i	0.582445	+	0.504275i
$306$	2.21856	+	24.7051i	0.126827	+	1.41230i
$307$	22.7157	−	22.7157i	1.29645	−	1.29645i	0.365735	−	0.930719i	$-0.380818\pi$
$307$	22.7157	−	22.7157i	1.29645	−	1.29645i	0.930719	−	0.365735i	$-0.119182\pi$
$308$	−0.171367	+	0.0409727i	−0.00976454	+	0.00233463i
$309$	−8.68084	+	4.13201i	−0.493835	+	0.235062i
$310$	30.3600	+	6.26646i	1.72433	+	0.355911i
$311$	27.1770	−	15.6906i	1.54107	−	0.889735i	0.542294	−	0.840189i	$-0.317556\pi$
$311$	27.1770	−	15.6906i	1.54107	−	0.889735i	0.998772	−	0.0495458i	$-0.0157774\pi$
$312$	−1.50473	−	3.52371i	−0.0851888	−	0.199491i
$313$	21.7091	−	5.81692i	1.22707	−	0.328792i	0.413631	−	0.910445i	$-0.364260\pi$
$313$	21.7091	−	5.81692i	1.22707	−	0.328792i	0.813437	+	0.581653i	$0.197594\pi$
$314$	−3.65988	+	3.56197i	−0.206539	+	0.201014i
$315$	−0.583615	+	6.70111i	−0.0328830	+	0.377565i
$316$	−10.6988	−	0.290137i	−0.601854	−	0.0163215i
$317$	0.734396	−	0.196781i	0.0412478	−	0.0110523i	−0.238136	−	0.971232i	$-0.576536\pi$
$317$	0.734396	−	0.196781i	0.0412478	−	0.0110523i	0.279384	+	0.960179i	$0.409870\pi$
$318$	5.77201	−	8.14529i	0.323678	−	0.456765i
$319$	−0.155958	−	0.270127i	−0.00873197	−	0.0151242i
$320$	−17.2341	−	4.79431i	−0.963416	−	0.268010i
$321$	1.03375	−	13.0019i	0.0576983	−	0.725694i
$322$	4.42627	+	2.63615i	0.246666	+	0.146907i
$323$	12.9500	+	12.9500i	0.720559	+	0.720559i
$324$	−3.20701	−	17.7120i	−0.178167	−	0.984000i
$325$	3.13248	+	2.34095i	0.173759	+	0.129853i
$326$	6.27475	+	24.7553i	0.347526	+	1.37107i
$327$	17.9100	−	15.2718i	0.990424	−	0.844531i
$328$	−2.34832	+	1.23132i	−0.129664	+	0.0679884i
$329$	2.25743	−	1.30333i	0.124456	−	0.0718549i
$330$	−0.249347	+	0.411587i	−0.0137261	+	0.0226571i
$331$	−5.12649	+	8.87934i	−0.281777	+	0.488053i	−0.971823	−	0.235714i	$-0.924257\pi$
$331$	−5.12649	+	8.87934i	−0.281777	+	0.488053i	0.690045	+	0.723766i	$0.257591\pi$
$332$	−20.3973	−	21.5344i	−1.11945	−	1.18185i
$333$	−23.4418	+	16.9741i	−1.28460	+	0.930177i
$334$	−14.4661	+	14.0791i	−0.791548	+	0.770373i
$335$	−16.7975	−	8.15123i	−0.917745	−	0.445350i
$336$	−2.64141	−	6.42532i	−0.144101	−	0.350530i
$337$	−21.8198	−	5.84661i	−1.18860	−	0.318485i	−0.390269	−	0.920701i	$-0.627618\pi$
$337$	−21.8198	−	5.84661i	−1.18860	−	0.318485i	−0.798333	+	0.602216i	$0.794285\pi$
$338$	8.55337	+	15.2899i	0.465242	+	0.831659i
$339$	9.91358	+	20.8272i	0.538432	+	1.13118i
$340$	23.2048	+	12.0483i	1.25846	+	0.653412i
$341$			0.861288i			0.0466414i
$342$	−10.2004	−	8.51931i	−0.551573	−	0.460672i
$343$	9.21355	−	9.21355i	0.497485	−	0.497485i
$344$	−5.63009	−	25.0441i	−0.303554	−	1.35029i
$345$	13.6181	−	3.53923i	0.733173	−	0.190546i
$346$	−3.15806	+	11.1777i	−0.169778	+	0.600916i
$347$	8.14862	+	2.18342i	0.437441	+	0.117212i	0.470817	−	0.882231i	$-0.343959\pi$
$347$	8.14862	+	2.18342i	0.437441	+	0.117212i	−0.0333761	+	0.999443i	$0.510626\pi$
$348$	9.57088	−	7.72292i	0.513053	−	0.413992i
$349$	10.5696	−	18.3071i	0.565779	−	0.979958i	−0.431198	−	0.902257i	$-0.641909\pi$
$349$	10.5696	−	18.3071i	0.565779	−	0.979958i	0.996977	−	0.0777003i	$-0.0247577\pi$
$350$	5.62151	+	4.32103i	0.300482	+	0.230969i
$351$	−1.14486	−	3.89938i	−0.0611083	−	0.208133i
$352$	0.0336614	−	0.495866i	0.00179416	−	0.0264297i
$353$	32.6273	−	8.74246i	1.73658	−	0.465314i	0.754895	−	0.655846i	$-0.227688\pi$
$353$	32.6273	−	8.74246i	1.73658	−	0.465314i	0.981681	+	0.190531i	$0.0610211\pi$
$354$	8.09212	−	6.71282i	0.430091	−	0.356782i
$355$	−2.39546	+	12.4562i	−0.127138	+	0.661107i
$356$	5.23885	−	2.83815i	0.277659	−	0.150421i
$357$	1.84242	+	9.98542i	0.0975110	+	0.528484i
$358$	5.44825	−	9.14799i	0.287949	−	0.483486i
$359$	−12.6718			−0.668792			−0.334396	−	0.942433i	$-0.608532\pi$
$359$	−12.6718			−0.668792			−0.334396	+	0.942433i	$0.608532\pi$
$360$	−17.5537	−	7.20200i	−0.925160	−	0.379578i
$361$	9.18742			0.483548
$362$	4.38588	−	7.36419i	0.230517	−	0.387053i
$363$	17.9420	+	6.36979i	0.941712	+	0.334327i
$364$	−0.747130	−	1.37911i	−0.0391603	−	0.0722848i
$365$	18.8579	+	27.8379i	0.987065	+	1.45710i
$366$	−13.8214	−	5.11889i	−0.722456	−	0.267569i
$367$	12.8046	−	3.43098i	0.668395	−	0.179096i	0.0913631	−	0.995818i	$-0.470878\pi$
$367$	12.8046	−	3.43098i	0.668395	−	0.179096i	0.577032	+	0.816722i	$0.304211\pi$
$368$	−10.8174	+	9.70361i	−0.563898	+	0.505836i
$369$	−2.62721	+	1.00367i	−0.136767	+	0.0522488i
$370$	1.77614	+	30.4558i	0.0923369	+	1.58332i
$371$	2.04334	−	3.53916i	0.106085	−	0.183744i
$372$	−33.5498	+	5.25418i	−1.73948	+	0.272416i
$373$	16.0737	+	4.30692i	0.832262	+	0.223004i	0.649700	−	0.760190i	$-0.274894\pi$
$373$	16.0737	+	4.30692i	0.832262	+	0.223004i	0.182562	+	0.983194i	$0.441561\pi$
$374$	−0.197510	+	0.699069i	−0.0102130	+	0.0361480i
$375$	19.1859	−	2.62714i	0.990755	−	0.135665i
$376$	1.61270	+	7.17368i	0.0831686	+	0.369954i
$377$	1.96338	−	1.96338i	0.101119	−	0.101119i
$378$	−1.97975	−	7.09754i	−0.101827	−	0.365058i
$379$		−	8.75353i		−	0.449639i	−0.974400	−	0.224819i	$-0.927821\pi$
$379$		−	8.75353i		−	0.449639i	0.974400	−	0.224819i	$-0.0721792\pi$
$380$	−13.3561	+	4.22679i	−0.685154	+	0.216830i
$381$	−4.13750	−	0.328963i	−0.211970	−	0.0168533i
$382$	−15.4886	−	27.6871i	−0.792466	−	1.41660i
$383$	−27.4505	−	7.35533i	−1.40265	−	0.375840i	−0.523356	−	0.852114i	$-0.675320\pi$
$383$	−27.4505	−	7.35533i	−1.40265	−	0.375840i	−0.879297	+	0.476274i	$0.841987\pi$
$384$	19.5208	−	1.71375i	0.996169	−	0.0874545i
$385$	−0.0860031	+	0.177229i	−0.00438313	+	0.00903244i
$386$	3.26237	−	3.17510i	0.166050	−	0.161608i
$387$	−2.80253	−	27.0816i	−0.142461	−	1.37663i
$388$	−21.3945	+	20.2647i	−1.08614	+	1.02879i
$389$	18.7426	−	32.4631i	0.950287	−	1.64595i	0.205485	−	0.978660i	$-0.434123\pi$
$389$	18.7426	−	32.4631i	0.950287	−	1.64595i	0.744802	−	0.667285i	$-0.232544\pi$
$390$	−4.11354	−	1.19574i	−0.208297	−	0.0605485i
$391$	18.3945	−	10.6201i	0.930250	−	0.537080i
$392$	7.87357	+	15.0161i	0.397675	+	0.758428i
$393$	1.19167	+	0.423065i	0.0601116	+	0.0213408i
$394$	5.13485	+	20.2581i	0.258690	+	1.02059i
$395$	−7.83237	+	9.04650i	−0.394089	+	0.455179i
$396$	0.0973797	−	0.518083i	0.00489351	−	0.0260347i
$397$	−18.8036	−	18.8036i	−0.943727	−	0.943727i	0.0547717	−	0.998499i	$-0.482557\pi$
$397$	−18.8036	−	18.8036i	−0.943727	−	0.943727i	−0.998499	+	0.0547717i	$0.982557\pi$
$398$	−2.00422	−	1.19365i	−0.100463	−	0.0598324i
$399$	−4.48113	−	3.08508i	−0.224337	−	0.154447i
$400$	−16.3586	+	11.5063i	−0.817931	+	0.575317i
$401$	5.80716	+	10.0583i	0.289996	+	0.502287i	0.973808	−	0.227371i	$-0.0730128\pi$
$401$	5.80716	+	10.0583i	0.289996	+	0.502287i	−0.683813	+	0.729657i	$0.739680\pi$
$402$	20.3646	+	1.89727i	1.01570	+	0.0946273i
$403$	−7.40582	+	1.98438i	−0.368910	+	0.0988492i
$404$	0.800354	−	29.5130i	0.0398191	−	1.46833i
$405$	−17.5896	−	9.77787i	−0.874033	−	0.485866i
$406$	3.60777	−	3.51126i	0.179051	−	0.174261i
$407$	−0.818726	+	0.219377i	−0.0405827	+	0.0108741i
$408$	−28.4358	−	3.42902i	−1.40778	−	0.169762i
$409$	−4.81991	+	2.78278i	−0.238329	+	0.137600i	−0.614409	−	0.788988i	$-0.710605\pi$
$409$	−4.81991	+	2.78278i	−0.238329	+	0.137600i	0.376079	+	0.926587i	$0.377272\pi$
$410$	−0.599263	+	2.90333i	−0.0295955	+	0.143385i
$411$	3.45709	+	2.38007i	0.170526	+	0.117400i
$412$	−2.58150	−	10.7971i	−0.127181	−	0.531933i
$413$	3.04340	−	3.04340i	0.149756	−	0.149756i
$414$	−12.6056	+	8.86974i	−0.619533	+	0.435924i
$415$	−33.0766	+	2.37927i	−1.62367	+	0.116794i
$416$	4.34128	−	0.853022i	0.212849	−	0.0418229i
$417$	−3.81612	+	10.7490i	−0.186876	+	0.526382i
$418$	−0.190022	−	0.339681i	−0.00929430	−	0.0166143i
$419$	29.8006	−	17.2054i	1.45586	−	0.840538i	0.457052	−	0.889440i	$-0.348905\pi$
$419$	29.8006	−	17.2054i	1.45586	−	0.840538i	0.998804	+	0.0489019i	$0.0155722\pi$
$420$	−7.42827	−	2.26892i	−0.362463	−	0.110712i
$421$	31.2347	+	18.0334i	1.52229	+	0.878894i	0.999653	+	0.0263371i	$0.00838432\pi$
$421$	31.2347	+	18.0334i	1.52229	+	0.878894i	0.522635	+	0.852556i	$0.324949\pi$
$422$	−0.211048	+	15.5676i	−0.0102736	+	0.757819i
$423$	0.802764	+	7.75731i	0.0390317	+	0.377173i
$424$	7.81301	+	8.47581i	0.379433	+	0.411622i
$425$	26.8628	−	11.5293i	1.30303	−	0.559253i
$426$	−2.33578	−	13.6974i	−0.113169	−	0.663641i
$427$	−5.82792	−	1.56159i	−0.282033	−	0.0755704i
$428$	14.4364	+	4.29091i	0.697812	+	0.207409i
$429$	0.00943318	−	0.118645i	0.000455438	−	0.00572822i
$430$	−25.6473	−	12.8781i	−1.23682	−	0.621039i
$431$		−	15.2229i		−	0.733262i	−0.930366	−	0.366631i	$-0.880511\pi$
$431$		−	15.2229i		−	0.733262i	0.930366	−	0.366631i	$-0.119489\pi$
$432$	20.7750	+	0.632736i	0.999537	+	0.0304425i
$433$	−12.0363	−	12.0363i	−0.578428	−	0.578428i	0.356042	−	0.934470i	$-0.384126\pi$
$433$	−12.0363	−	12.0363i	−0.578428	−	0.578428i	−0.934470	+	0.356042i	$0.884126\pi$
$434$	−13.4752	+	3.41558i	−0.646831	+	0.163953i
$435$	0.103567	−	13.7494i	0.00496566	−	0.659233i
$436$	12.9461	+	23.8968i	0.620005	+	1.14445i
$437$	−2.94545	+	10.9926i	−0.140900	+	0.525845i
$438$	−30.0525	−	21.2962i	−1.43597	−	1.01757i
$439$	−8.70022	+	15.0692i	−0.415239	+	0.719215i	−0.995453	−	0.0952490i	$-0.969635\pi$
$439$	−8.70022	+	15.0692i	−0.415239	+	0.719215i	0.580215	+	0.814464i	$0.302969\pi$
$440$	−0.404962	−	0.380494i	−0.0193058	−	0.0181394i
$441$	6.41785	+	16.7995i	0.305612	+	0.799975i
$442$	−6.46603	−	0.0876591i	−0.307558	−	0.00416952i
$443$	21.7957	−	5.84014i	1.03554	−	0.277473i	0.299279	−	0.954166i	$-0.403254\pi$
$443$	21.7957	−	5.84014i	1.03554	−	0.277473i	0.736266	+	0.676692i	$0.236587\pi$
$444$	−13.5399	−	30.5536i	−0.642577	−	1.45001i
$445$	1.25803	−	6.54165i	0.0596362	−	0.310104i
$446$	−10.6963	+	37.8586i	−0.506483	+	1.79265i
$447$	−5.58292	−	1.98205i	−0.264063	−	0.0937477i
$448$	7.89152	−	1.43979i	0.372839	−	0.0680238i
$449$		−	19.2896i		−	0.910334i	−0.890406	−	0.455167i	$-0.849580\pi$
$449$		−	19.2896i		−	0.910334i	0.890406	−	0.455167i	$-0.150420\pi$
$450$	−18.6672	+	10.0765i	−0.879979	+	0.475012i
$451$	−0.0823652			−0.00387842
$452$	−25.9044	+	6.19357i	−1.21844	+	0.291321i
$453$	26.7278	−	4.93156i	1.25578	−	0.231705i
$454$	4.08916	−	14.4733i	0.191914	−	0.679263i
$455$	−1.72206	−	0.331171i	−0.0807315	−	0.0155255i
$456$	12.0724	−	9.47413i	0.565342	−	0.443667i
$457$	3.10128	+	11.5741i	0.145072	+	0.541415i	0.999752	+	0.0222604i	$0.00708629\pi$
$457$	3.10128	+	11.5741i	0.145072	+	0.541415i	−0.854681	+	0.519154i	$0.826247\pi$
$458$	0.280582	−	20.6967i	0.0131107	−	0.967092i
$459$	−29.5227	−	7.16285i	−1.37800	−	0.334333i
$460$	0.725950	+	16.2310i	0.0338476	+	0.756773i
$461$	−13.2759	−	7.66487i	−0.618323	−	0.356989i	0.157893	−	0.987456i	$-0.449530\pi$
$461$	−13.2759	−	7.66487i	−0.618323	−	0.356989i	−0.776216	+	0.630468i	$0.782863\pi$
$462$	0.0200180	−	0.214866i	0.000931321	−	0.00999647i
$463$	−5.39648	−	1.44598i	−0.250796	−	0.0672005i	0.131231	−	0.991352i	$-0.458107\pi$
$463$	−5.39648	−	1.44598i	−0.250796	−	0.0672005i	−0.382027	+	0.924151i	$0.624774\pi$
$464$	6.42339	+	12.6649i	0.298198	+	0.587954i
$465$	−19.2306	+	32.7365i	−0.891799	+	1.51812i
$466$	2.86410	+	11.2995i	0.132677	+	0.523439i
$467$	1.29633	−	1.29633i	0.0599868	−	0.0599868i	−0.676477	−	0.736464i	$-0.736494\pi$
$467$	1.29633	−	1.29633i	0.0599868	−	0.0599868i	0.736464	+	0.676477i	$0.236494\pi$
$468$	4.67912	−	0.356326i	0.216292	−	0.0164712i
$469$	8.37257			0.386609
$470$	7.34647	+	3.68885i	0.338867	+	0.170154i
$471$	−2.68827	−	5.64772i	−0.123869	−	0.260233i
$472$	5.63778	+	10.7521i	0.259500	+	0.494906i
$473$	0.206371	−	0.770188i	0.00948896	−	0.0354133i
$474$	4.55252	−	12.2921i	0.209104	−	0.564597i
$475$	−5.80928	+	14.5453i	−0.266548	+	0.667386i
$476$	−11.7205	−	0.317844i	−0.537208	−	0.0145684i
$477$	7.17083	+	9.90313i	0.328330	+	0.453433i
$478$	−0.375059	+	27.6656i	−0.0171548	+	1.26540i
$479$	−0.756609	+	1.31049i	−0.0345704	+	0.0598776i	−0.882793	−	0.469762i	$-0.844340\pi$
$479$	−0.756609	+	1.31049i	−0.0345704	+	0.0598776i	0.848223	+	0.529640i	$0.177673\pi$
$480$	12.3510	−	18.0957i	0.563744	−	0.825950i
$481$	−3.77265	−	6.53441i	−0.172018	−	0.297944i
$482$	8.60554	−	4.81407i	0.391972	−	0.219275i
$483$	−4.80117	+	4.09394i	−0.218461	+	0.186281i
$484$	−11.5044	+	18.7342i	−0.522926	+	0.851555i
$485$	2.36381	+	32.8617i	0.107335	+	1.49217i
$486$	21.8029	+	3.26087i	0.989000	+	0.147916i
$487$	10.3914	+	10.3914i	0.470877	+	0.470877i	0.902198	−	0.431321i	$-0.141952\pi$
$487$	10.3914	+	10.3914i	0.470877	+	0.470877i	−0.431321	+	0.902198i	$0.641952\pi$
$488$	9.10169	−	14.3807i	0.412014	−	0.650984i
$489$	−31.1793	−	2.47899i	−1.40998	−	0.112104i
$490$	18.5651	+	3.83193i	0.838685	+	0.173109i
$491$	−5.84414	−	10.1223i	−0.263742	−	0.456815i	0.703491	−	0.710704i	$-0.251623\pi$
$491$	−5.84414	−	10.1223i	−0.263742	−	0.456815i	−0.967233	+	0.253889i	$0.918290\pi$
$492$	−0.502458	−	3.20838i	−0.0226526	−	0.144645i
$493$	−5.37206	−	20.0488i	−0.241945	−	0.902952i
$494$	2.48295	−	2.41653i	0.111713	−	0.108725i
$495$	−0.379022	−	0.451340i	−0.0170358	−	0.0202862i
$496$	2.12520	−	39.1545i	0.0954244	−	1.75809i
$497$	−1.47219	−	5.49429i	−0.0660368	−	0.246453i
$498$	33.0096	−	15.1669i	1.47919	−	0.679647i
$499$	19.0411	−	10.9934i	0.852397	−	0.492132i	−0.00906166	−	0.999959i	$-0.502884\pi$
$499$	19.0411	−	10.9934i	0.852397	−	0.492132i	0.861459	+	0.507827i	$0.169551\pi$
$500$	−1.64172	+	22.3003i	−0.0734198	+	0.997301i
$501$	−10.6257	−	22.3232i	−0.474721	−	0.997327i
$502$	−2.18469	−	1.30113i	−0.0975073	−	0.0580723i
$503$	18.2051	−	18.2051i	0.811727	−	0.811727i	−0.173166	−	0.984893i	$-0.555400\pi$
$503$	18.2051	−	18.2051i	0.811727	−	0.811727i	0.984893	+	0.173166i	$0.0553996\pi$
$504$	8.49180	−	0.531000i	0.378255	−	0.0236526i
$505$	−24.9551	−	21.6059i	−1.11049	−	0.961449i
$506$	−0.437567	+	0.110911i	−0.0194522	+	0.00493058i
$507$	−21.1010	+	3.89336i	−0.937128	+	0.172910i
$508$	1.36547	−	4.59401i	0.0605828	−	0.203826i
$509$	8.50307	+	14.7277i	0.376892	+	0.652796i	0.990608	−	0.136731i	$-0.0436595\pi$
$509$	8.50307	+	14.7277i	0.376892	+	0.652796i	−0.613716	+	0.789527i	$0.710326\pi$
$510$	−23.1157	+	22.1608i	−1.02358	+	0.981297i
$511$	−13.0580	−	7.53902i	−0.577650	−	0.333506i
$512$	−2.75380	+	22.4592i	−0.121702	+	0.992567i
$513$	13.8988	−	8.47132i	0.613647	−	0.374018i
$514$	16.1682	+	16.6126i	0.713150	+	0.732751i
$515$	−11.1664	−	5.41867i	−0.492051	−	0.238775i
$516$	31.2601	+	3.34036i	1.37615	+	0.147051i
$517$	−0.0591135	+	0.220615i	−0.00259981	+	0.00970262i
$518$	−6.67904	−	11.9393i	−0.293460	−	0.524584i
$519$	−11.7173	−	8.06692i	−0.514334	−	0.354099i
$520$	2.33868	−	4.35873i	0.102558	−	0.191143i
$521$	−22.4720			−0.984518			−0.492259	−	0.870449i	$-0.663829\pi$
$521$	−22.4720			−0.984518			−0.492259	+	0.870449i	$0.663829\pi$
$522$	5.18402	+	14.1419i	0.226899	+	0.618975i
$523$	−6.15000	−	6.15000i	−0.268921	−	0.268921i	0.559744	−	0.828665i	$-0.310899\pi$
$523$	−6.15000	−	6.15000i	−0.268921	−	0.268921i	−0.828665	+	0.559744i	$0.810899\pi$
$524$	−0.764092	+	1.24428i	−0.0333795	+	0.0543566i
$525$	−7.22600	+	4.81600i	−0.315369	+	0.210188i
$526$	10.2723	−	36.3581i	0.447895	−	1.58529i
$527$	−14.8338	+	55.3604i	−0.646169	+	2.41153i
$528$	0.561749	+	0.234440i	0.0244470	+	0.0102027i
$529$	−8.48829	−	4.90072i	−0.369056	−	0.213075i
$530$	12.8662	−	0.750339i	0.558874	−	0.0325927i
$531$	4.59543	+	12.0291i	0.199425	+	0.522017i
$532$	4.56088	−	4.32004i	0.197739	−	0.187298i
$533$	−0.189767	−	0.708221i	−0.00821973	−	0.0306764i
$534$	1.22668	+	7.19348i	0.0530838	+	0.311292i
$535$	13.9408	−	9.44370i	0.602712	−	0.408287i
$536$	−7.03492	+	22.5448i	−0.303862	+	0.973786i
$537$	8.46116	+	9.92283i	0.365126	+	0.428202i
$538$	13.0496	+	7.77195i	0.562609	+	0.335072i
$539$			0.526676i			0.0226856i
$540$	15.2689	−	17.5174i	0.657070	−	0.753830i
$541$			4.17430i			0.179467i	0.995966	+	0.0897337i	$0.0286016\pi$
$541$			4.17430i			0.179467i	−0.995966	+	0.0897337i	$0.971398\pi$
$542$	17.6044	−	29.5590i	0.756175	−	1.26967i
$543$	6.81129	+	7.98795i	0.292300	+	0.342796i
$544$	10.7038	−	31.2926i	0.458922	−	1.34166i
$545$	29.8395	+	5.73844i	1.27818	+	0.245808i
$546$	1.89366	−	0.322920i	0.0810410	−	0.0138197i
$547$	−5.90557	−	22.0399i	−0.252504	−	0.942357i	−0.969462	−	0.245241i	$-0.921133\pi$
$547$	−5.90557	−	22.0399i	−0.252504	−	0.942357i	0.716958	−	0.697116i	$-0.245534\pi$
$548$	−3.51862	+	3.33282i	−0.150308	+	0.142371i
$549$	11.3825	−	14.0103i	0.485795	−	0.597946i
$550$	−0.616012	+	0.0805739i	−0.0262668	+	0.00343568i
$551$	9.63102	+	5.56047i	0.410295	+	0.236884i
$552$	−6.98964	−	16.3680i	−0.297499	−	0.696667i
$553$	1.38881	−	5.18309i	0.0590580	−	0.220408i
$554$	35.9252	+	10.1500i	1.52631	+	0.431233i
$555$	−36.0169	−	9.94207i	−1.52883	−	0.422018i
$556$	−11.2236	−	6.89224i	−0.475987	−	0.292296i
$557$	10.3900	+	10.3900i	0.440239	+	0.440239i	0.892092	−	0.451853i	$-0.149237\pi$
$557$	10.3900	+	10.3900i	0.440239	+	0.440239i	−0.451853	+	0.892092i	$0.649237\pi$
$558$	7.12814	−	40.9754i	0.301758	−	1.73463i
$559$	7.09797			0.300212
$560$	4.34705	−	7.84471i	0.183696	−	0.331499i
$561$	−0.732819	−	0.504517i	−0.0309396	−	0.0213007i
$562$	−14.5888	+	8.16122i	−0.615393	+	0.344260i
$563$	5.89487	−	21.9999i	0.248439	−	0.927187i	−0.723185	−	0.690655i	$-0.757322\pi$
$563$	5.89487	−	21.9999i	0.248439	−	0.927187i	0.971624	−	0.236532i	$-0.0760109\pi$
$564$	−8.95423	−	0.956821i	−0.377041	−	0.0402894i
$565$	−13.0005	+	26.7906i	−0.546937	+	1.12709i
$566$	−8.61872	+	8.38816i	−0.362272	+	0.352581i
$567$	9.01058	+	0.501180i	0.378409	+	0.0210476i
$568$	16.0315	+	0.652328i	0.672665	+	0.0273711i
$569$	17.8331	+	10.2960i	0.747604	+	0.431630i	0.824828	−	0.565384i	$-0.191272\pi$
$569$	17.8331	+	10.2960i	0.747604	+	0.431630i	−0.0772233	+	0.997014i	$0.524605\pi$
$570$	0.361795	−	17.1536i	0.0151539	−	0.718486i
$571$	−9.95955	−	17.2504i	−0.416794	−	0.721908i	0.578821	−	0.815455i	$-0.303513\pi$
$571$	−9.95955	−	17.2504i	−0.416794	−	0.721908i	−0.995615	+	0.0935462i	$0.970180\pi$
$572$	0.131736	+	0.0391555i	0.00550814	+	0.00163717i
$573$	38.2100	−	7.05016i	1.59625	−	0.294525i
$574$	−0.326633	−	1.28864i	−0.0136334	−	0.0537867i
$575$	14.5507	+	10.8739i	0.606804	+	0.453475i
$576$	−5.70528	+	23.3120i	−0.237720	+	0.971334i
$577$	−20.0298	+	20.0298i	−0.833853	+	0.833853i	−0.988041	−	0.154188i	$-0.950724\pi$
$577$	−20.0298	+	20.0298i	−0.833853	+	0.833853i	0.154188	+	0.988041i	$0.450724\pi$
$578$	−12.4331	+	20.8761i	−0.517150	+	0.868330i
$579$	2.39629	+	5.03430i	0.0995865	+	0.209218i
$580$	15.5042	+	3.41990i	0.643776	+	0.142004i
$581$	12.8786	−	7.43546i	0.534294	−	0.308475i
$582$	−15.0684	−	32.7951i	−0.624605	−	1.35940i
$583$	0.0926771	+	0.345876i	0.00383829	+	0.0143247i
$584$	31.2720	−	28.8266i	1.29405	−	1.19285i
$585$	3.00762	−	4.29892i	0.124350	−	0.177738i
$586$	24.1802	+	24.8448i	0.998875	+	1.02633i
$587$	6.75834	+	25.2225i	0.278947	+	1.04104i	0.953150	+	0.302497i	$0.0978203\pi$
$587$	6.75834	+	25.2225i	0.278947	+	1.04104i	−0.674204	+	0.738545i	$0.735513\pi$
$588$	−20.5157	+	3.21292i	−0.846051	+	0.132499i
$589$	−15.3540	−	26.5940i	−0.632652	−	1.09579i
$590$	13.2933	+	2.74381i	0.547277	+	0.112961i
$591$	−25.5151	−	2.02865i	−1.04955	−	0.0834474i
$592$	37.7609	−	7.95279i	1.55197	−	0.326858i
$593$	−0.403643	−	0.403643i	−0.0165756	−	0.0165756i	0.698770	−	0.715346i	$-0.253731\pi$
$593$	−0.403643	−	0.403643i	−0.0165756	−	0.0165756i	−0.715346	+	0.698770i	$0.753731\pi$
$594$	0.562403	+	0.317084i	0.0230757	+	0.0130101i
$595$	−8.58034	+	9.91042i	−0.351759	+	0.406287i
$596$	3.57975	−	5.82941i	0.146632	−	0.238782i
$597$	2.17398	−	1.85375i	0.0889752	−	0.0758688i
$598$	−1.96181	−	3.50690i	−0.0802245	−	0.143408i
$599$	0.147747	+	0.255905i	0.00603676	+	0.0104560i	0.869028	−	0.494763i	$-0.164745\pi$
$599$	0.147747	+	0.255905i	0.00603676	+	0.0104560i	−0.862991	+	0.505219i	$0.831412\pi$
$600$	−6.89650	−	23.5040i	−0.281548	−	0.959547i
$601$	2.09775	−	3.63342i	0.0855691	−	0.148210i	−0.820064	−	0.572271i	$-0.806062\pi$
$601$	2.09775	−	3.63342i	0.0855691	−	0.148210i	0.905634	+	0.424061i	$0.139396\pi$
$602$	12.8683	+	0.174454i	0.524474	+	0.00711021i
$603$	−10.2252	+	22.8675i	−0.416402	+	0.931236i
$604$	−0.850767	+	31.3720i	−0.0346172	+	1.27651i
$605$	8.04865	+	23.2243i	0.327224	+	0.944204i
$606$	33.9083	+	12.5583i	1.37743	+	0.510145i
$607$	−8.03856	+	30.0003i	−0.326275	+	1.21767i	0.586749	+	0.809769i	$0.300408\pi$
$607$	−8.03856	+	30.0003i	−0.326275	+	1.21767i	−0.913024	+	0.407906i	$0.866259\pi$
$608$	7.80035	+	15.9109i	0.316346	+	0.645273i
$609$	2.65000	+	5.56732i	0.107383	+	0.225599i
$610$	−5.98645	−	18.0615i	−0.242384	−	0.731291i
$611$	−2.03316			−0.0822529
$612$	15.1820	−	31.6233i	0.613697	−	1.27830i
$613$	−3.63280	+	3.63280i	−0.146727	+	0.146727i	−0.776654	−	0.629927i	$-0.783085\pi$
$613$	−3.63280	+	3.63280i	−0.146727	+	0.146727i	0.629927	+	0.776654i	$0.283085\pi$
$614$	−44.0387	+	11.1626i	−1.77726	+	0.450485i
$615$	−3.13060	−	1.83903i	−0.126238	−	0.0741569i
$616$	0.237869	+	0.0742249i	0.00958400	+	0.00299061i
$617$	3.16893	+	0.849112i	0.127576	+	0.0341840i	0.322042	−	0.946725i	$-0.395631\pi$
$617$	3.16893	+	0.849112i	0.127576	+	0.0341840i	−0.194466	+	0.980909i	$0.562297\pi$
$618$	13.5377	+	1.26124i	0.544567	+	0.0507346i
$619$	9.41115	+	5.43353i	0.378266	+	0.218392i	0.677064	−	0.735925i	$-0.263252\pi$
$619$	9.41115	+	5.43353i	0.378266	+	0.218392i	−0.298798	+	0.954317i	$0.596586\pi$
$620$	−32.3541	−	29.5839i	−1.29937	−	1.18812i
$621$	−5.31800	−	18.1130i	−0.213404	−	0.726849i
$622$	−44.3758	−	0.601596i	−1.77931	−	0.0241218i
$623$	0.773153	+	2.88545i	0.0309757	+	0.115603i
$624$	−0.721589	+	5.37037i	−0.0288867	+	0.214987i
$625$	18.1215	+	17.2224i	0.724861	+	0.688895i
$626$	−30.5869	−	8.64179i	−1.22250	−	0.345395i
$627$	0.468781	−	0.0864951i	0.0187213	−	0.00345428i
$628$	7.02452	−	1.67952i	0.280309	−	0.0670199i
$629$	−56.4029			−2.24893
$630$	5.55833	−	7.71983i	0.221449	−	0.307565i
$631$		−	7.07227i		−	0.281543i	−0.990042	−	0.140771i	$-0.955042\pi$
$631$		−	7.07227i		−	0.281543i	0.990042	−	0.140771i	$-0.0449582\pi$
$632$	12.7896	+	8.09464i	0.508742	+	0.321988i
$633$	−17.9693	−	6.37945i	−0.714214	−	0.253561i
$634$	−1.03472	−	0.292343i	−0.0410942	−	0.0116104i
$635$	−3.00520	−	4.43628i	−0.119258	−	0.176048i
$636$	−12.9076	+	5.72003i	−0.511818	+	0.226814i
$637$	−4.52865	+	1.21345i	−0.179432	+	0.0480786i
$638$	−0.00597959	+	0.441075i	−0.000236734	+	0.0174623i
$639$	16.8042	+	2.68913i	0.664763	+	0.106380i
$640$	17.4709	+	18.2967i	0.690597	+	0.723240i
$641$	−18.9625	+	32.8441i	−0.748976	+	1.29726i	0.199339	+	0.979931i	$0.436121\pi$
$641$	−18.9625	+	32.8441i	−0.748976	+	1.29726i	−0.948314	+	0.317333i	$0.897213\pi$
$642$	−10.6648	+	15.0498i	−0.420905	+	0.593969i
$643$	−8.18748	+	30.5561i	−0.322883	+	1.20501i	0.593540	+	0.804804i	$0.297730\pi$
$643$	−8.18748	+	30.5561i	−0.322883	+	1.20501i	−0.916423	+	0.400211i	$0.868937\pi$
$644$	−3.47049	−	6.40608i	−0.136757	−	0.252435i
$645$	25.0405	−	24.6661i	0.985969	−	0.971226i
$646$	−6.36369	−	25.1061i	−0.250376	−	0.987787i
$647$	0.462255	+	0.462255i	0.0181731	+	0.0181731i	0.716135	−	0.697962i	$-0.245909\pi$
$647$	0.462255	+	0.462255i	0.0181731	+	0.0181731i	−0.697962	+	0.716135i	$0.745909\pi$
$648$	−8.92052	+	23.8417i	−0.350431	+	0.936588i
$649$			0.377120i			0.0148033i
$650$	−2.11209	−	5.11116i	−0.0828431	−	0.200476i
$651$	1.34941	−	16.9720i	0.0528875	−	0.665187i
$652$	10.2899	−	34.6195i	0.402982	−	1.35580i
$653$	27.8579	+	7.46449i	1.09016	+	0.292108i	0.758753	−	0.651379i	$-0.225809\pi$
$653$	27.8579	+	7.46449i	1.09016	+	0.292108i	0.331410	+	0.943487i	$0.392476\pi$
$654$	−32.8128	+	5.59547i	−1.28308	+	0.218800i
$655$	0.534572	+	1.54250i	0.0208874	+	0.0602706i
$656$	3.74436	+	0.203234i	0.146193	+	0.00793494i
$657$	36.5382	−	26.4572i	1.42549	−	1.03219i
$658$	−3.68603	−	0.0499710i	−0.143697	−	0.00194807i
$659$	−27.5806	−	15.9236i	−1.07439	−	0.620297i	−0.145010	−	0.989430i	$-0.546321\pi$
$659$	−27.5806	−	15.9236i	−1.07439	−	0.620297i	−0.929377	+	0.369133i	$0.879655\pi$
$660$	0.600810	−	0.319659i	0.0233865	−	0.0124427i
$661$	−22.1416	+	12.7835i	−0.861210	+	0.497220i	−0.864417	−	0.502775i	$-0.832312\pi$
$661$	−22.1416	+	12.7835i	−0.861210	+	0.497220i	0.00320714	+	0.999995i	$0.498979\pi$
$662$	12.6544	−	7.07906i	0.491827	−	0.275136i
$663$	2.64972	−	7.46357i	0.102907	−	0.289861i
$664$	9.20040	+	40.9257i	0.357045	+	1.58822i
$665$	−0.503918	−	7.00547i	−0.0195411	−	0.271660i
$666$	40.7661	−	3.66088i	1.57965	−	0.141856i
$667$	9.12008	−	9.12008i	0.353131	−	0.353131i
$668$	27.7652	−	6.63846i	1.07427	−	0.256850i
$669$	−39.6863	−	27.3225i	−1.53436	−	1.05635i
$670$	14.5112	+	22.0595i	0.560615	+	0.852234i
$671$	0.457832	−	0.264330i	0.0176744	−	0.0102043i
$672$	−1.44020	+	9.71851i	−0.0555570	+	0.374900i
$673$	−17.8584	+	4.78515i	−0.688392	+	0.184454i	−0.586026	−	0.810293i	$-0.699308\pi$
$673$	−17.8584	+	4.78515i	−0.688392	+	0.184454i	−0.102367	+	0.994747i	$0.532642\pi$
$674$	22.2813	+	22.8937i	0.858242	+	0.881832i
$675$	−4.32874	−	25.6176i	−0.166613	−	0.986022i
$676$	0.671662	−	24.7675i	0.0258332	−	0.952596i
$677$	47.0179	−	12.5984i	1.80705	−	0.484196i	0.812003	−	0.583653i	$-0.198377\pi$
$677$	47.0179	−	12.5984i	1.80705	−	0.484196i	0.995042	+	0.0994566i	$0.0317104\pi$
$678$	3.02599	−	32.4799i	0.116212	−	1.24738i
$679$	−7.38715	−	12.7949i	−0.283493	−	0.491024i
$680$	−19.4763	−	31.4313i	−0.746880	−	1.20534i
$681$	15.1720	+	10.4453i	0.581392	+	0.400266i
$682$	0.623266	−	1.04651i	0.0238661	−	0.0400728i
$683$	−9.44286	−	9.44286i	−0.361321	−	0.361321i	0.502978	−	0.864299i	$-0.332238\pi$
$683$	−9.44286	−	9.44286i	−0.361321	−	0.361321i	−0.864299	+	0.502978i	$0.832238\pi$
$684$	6.22899	+	17.7328i	0.238171	+	0.678031i
$685$	0.388762	+	5.40456i	0.0148538	+	0.206498i
$686$	−17.8622	+	4.52757i	−0.681983	+	0.172863i
$687$	23.8896	+	8.48130i	0.911446	+	0.323582i
$688$	−11.2822	+	34.5039i	−0.430128	+	1.31545i
$689$	−2.76050	+	1.59378i	−0.105167	+	0.0607181i
$690$	−19.1078	−	5.55431i	−0.727420	−	0.211449i
$691$	−18.3157	+	31.7237i	−0.696762	+	1.20683i	0.272822	+	0.962065i	$0.412043\pi$
$691$	−18.3157	+	31.7237i	−0.696762	+	1.20683i	−0.969583	+	0.244762i	$0.921290\pi$
$692$	11.9259	−	11.2961i	0.453353	−	0.429414i
$693$	0.241273	+	0.107885i	0.00916522	+	0.00409823i
$694$	−8.32094	−	8.54965i	−0.315859	−	0.324540i
$695$	−13.9136	+	4.82193i	−0.527775	+	0.182906i
$696$	−17.2177	+	2.45780i	−0.652636	+	0.0931627i
$697$	−5.29412	−	1.41856i	−0.200529	−	0.0537316i
$698$	−26.0904	+	14.5954i	−0.987537	+	0.552443i
$699$	−14.2317	−	1.13153i	−0.538294	−	0.0427985i
$700$	−3.70351	−	9.31823i	−0.139980	−	0.352196i
$701$		−	37.1852i		−	1.40447i	−0.711947	−	0.702233i	$-0.752186\pi$
$701$		−	37.1852i		−	1.40447i	0.711947	−	0.702233i	$-0.247814\pi$
$702$	−1.43070	+	5.56640i	−0.0539983	+	0.210090i
$703$	21.3690	−	21.3690i	0.805946	−	0.805946i
$704$	−0.399730	+	0.578141i	−0.0150654	+	0.0217895i
$705$	−7.17266	+	7.06542i	−0.270138	+	0.266099i
$706$	−45.9701	−	12.9881i	−1.73011	−	0.488812i
$707$	14.2978	+	3.83107i	0.537722	+	0.144082i
$708$	−14.6900	+	2.30058i	−0.552084	+	0.0864609i
$709$	0.856737	−	1.48391i	0.0321754	−	0.0557295i	−0.849489	−	0.527606i	$-0.823090\pi$
$709$	0.856737	−	1.48391i	0.0321754	−	0.0557295i	0.881665	+	0.471876i	$0.156423\pi$
$710$	11.9245	−	13.4014i	0.447517	−	0.502947i
$711$	12.4602	+	10.1231i	0.467292	+	0.379647i
$712$	−8.41926	−	0.342584i	−0.315525	−	0.0128389i
$713$	−34.4008	+	9.21765i	−1.28832	+	0.345204i
$714$	4.98727	−	13.4660i	0.186644	−	0.503953i
$715$	0.127212	−	0.0861757i	0.00475748	−	0.00322279i
$716$	−13.2398	+	7.17264i	−0.494793	+	0.268054i
$717$	−31.9337	−	11.3371i	−1.19259	−	0.423392i
$718$	15.3968	+	9.16988i	0.574605	+	0.342217i
$719$	−1.38913			−0.0518059			−0.0259029	−	0.999664i	$-0.508246\pi$
$719$	−1.38913			−0.0518059			−0.0259029	+	0.999664i	$0.508246\pi$
$720$	16.1169	+	21.4534i	0.600640	+	0.799520i
$721$	5.56580			0.207281
$722$	−11.1631	−	6.64842i	−0.415449	−	0.247429i
$723$	2.19129	+	11.8762i	0.0814948	+	0.441681i
$724$	−10.6581	+	5.77402i	−0.396105	+	0.214590i
$725$	13.9442	−	10.9843i	0.517873	−	0.407946i
$726$	−17.1910	−	20.7232i	−0.638016	−	0.769111i
$727$	15.8468	−	4.24613i	0.587725	−	0.157480i	0.0473116	−	0.998880i	$-0.484935\pi$
$727$	15.8468	−	4.24613i	0.587725	−	0.157480i	0.540413	+	0.841400i	$0.318268\pi$
$728$	−0.0901838	+	2.21634i	−0.00334243	+	0.0821429i
$729$	−12.3732	+	23.9980i	−0.458268	+	0.888814i
$730$	−2.76842	−	47.4708i	−0.102464	−	1.75697i
$731$	26.5295	−	45.9505i	0.981231	−	1.69954i
$732$	13.0894	+	16.2215i	0.483798	+	0.599563i
$733$	−24.8942	−	6.67038i	−0.919488	−	0.246376i	−0.232121	−	0.972687i	$-0.574567\pi$
$733$	−24.8942	−	6.67038i	−0.919488	−	0.246376i	−0.687366	+	0.726311i	$0.741233\pi$
$734$	−18.0410	−	5.09717i	−0.665906	−	0.188140i
$735$	−11.7595	+	20.0183i	−0.433756	+	0.738387i
$736$	20.1657	−	3.96237i	0.743316	−	0.146055i
$737$	−0.518740	+	0.518740i	−0.0191081	+	0.0191081i
$738$	3.91849	+	0.681665i	0.144241	+	0.0250924i
$739$			35.8807i			1.31989i	0.751313	+	0.659946i	$0.229421\pi$
$739$			35.8807i			1.31989i	−0.751313	+	0.659946i	$0.770579\pi$
$740$	19.8811	−	38.2905i	0.730842	−	1.40759i
$741$	1.82379	+	3.83155i	0.0669987	+	0.140756i
$742$	−5.04384	+	2.82160i	−0.185165	+	0.103584i
$743$	−29.5389	−	7.91492i	−1.08368	−	0.290370i	−0.327575	−	0.944825i	$-0.606232\pi$
$743$	−29.5389	−	7.91492i	−1.08368	−	0.290370i	−0.756101	+	0.654455i	$0.772898\pi$
$744$	44.5667	+	17.8940i	1.63390	+	0.656027i
$745$	−2.50445	−	7.22658i	−0.0917560	−	0.264761i
$746$	−16.4136	−	16.8647i	−0.600944	−	0.617461i
$747$	4.57975	+	44.2553i	0.167564	+	1.61922i
$748$	0.745861	−	0.706475i	0.0272714	−	0.0258313i
$749$	−3.77541	+	6.53921i	−0.137951	+	0.238938i
$750$	−25.2129	−	10.6916i	−0.920644	−	0.390404i
$751$	−4.98688	+	2.87918i	−0.181974	+	0.105063i	−0.588220	−	0.808701i	$-0.700171\pi$
$751$	−4.98688	+	2.87918i	−0.181974	+	0.105063i	0.406246	+	0.913764i	$0.366838\pi$
$752$	3.23169	−	9.88338i	0.117848	−	0.360410i
$753$	2.36973	−	2.02066i	0.0863578	−	0.0736370i
$754$	−3.80638	+	0.964810i	−0.138620	+	0.0351363i
$755$	26.5270	+	22.9668i	0.965417	+	0.835848i
$756$	−2.73061	+	10.0565i	−0.0993112	+	0.365751i
$757$	−10.6316	−	10.6316i	−0.386411	−	0.386411i	0.486994	−	0.873405i	$-0.338093\pi$
$757$	−10.6316	−	10.6316i	−0.386411	−	0.386411i	−0.873405	+	0.486994i	$0.838093\pi$
$758$	−6.33444	+	10.6360i	−0.230077	+	0.386315i
$759$	0.0438180	−	0.551116i	0.00159049	−	0.0200042i
$760$	19.2870	+	4.52933i	0.699613	+	0.164296i
$761$	22.0530	+	38.1969i	0.799420	+	1.38464i	0.919994	+	0.391933i	$0.128193\pi$
$761$	22.0530	+	38.1969i	0.799420	+	1.38464i	−0.120573	+	0.992704i	$0.538473\pi$
$762$	4.78920	+	3.39378i	0.173494	+	0.122944i
$763$	−13.1618	+	3.52671i	−0.476491	+	0.127675i
$764$	−1.21626	+	44.8494i	−0.0440026	+	1.62259i
$765$	−16.5888	−	35.5383i	−0.599769	−	1.28489i
$766$	28.0310	+	28.8014i	1.01280	+	1.04064i
$767$	−3.24269	+	0.868876i	−0.117087	+	0.0313733i
$768$	−24.9589	−	12.0438i	−0.900626	−	0.434595i
$769$	35.9752	−	20.7703i	1.29730	−	0.748995i	0.317362	−	0.948305i	$-0.397203\pi$
$769$	35.9752	−	20.7703i	1.29730	−	0.748995i	0.979937	+	0.199309i	$0.0638698\pi$
$770$	0.232749	−	0.153106i	0.00838768	−	0.00551756i
$771$	−25.6357	+	12.2024i	−0.923246	+	0.439458i
$772$	−6.26157	+	1.49710i	−0.225359	+	0.0538817i
$773$	−3.87082	+	3.87082i	−0.139224	+	0.139224i	−0.773284	−	0.634060i	$-0.781387\pi$
$773$	−3.87082	+	3.87082i	−0.139224	+	0.139224i	0.634060	+	0.773284i	$0.281387\pi$
$774$	−16.1922	+	34.9334i	−0.582017	+	1.25566i
$775$	−48.5106	+	7.01524i	−1.74255	+	0.251995i
$776$	40.6597	−	9.14062i	1.45960	−	0.328129i
$777$	16.4770	−	3.04019i	0.591111	−	0.109066i
$778$	−46.2649	+	25.8813i	−1.65868	+	0.927888i
$779$	2.54319	−	1.46831i	0.0911191	−	0.0526077i
$780$	4.13285	+	4.42961i	0.147980	+	0.158606i
$781$	0.431624	+	0.249198i	0.0154447	+	0.00891701i
$782$	−30.0353	−	0.407185i	−1.07406	−	0.0145609i
$783$	−18.4421	+	0.438577i	−0.659065	+	0.0156735i
$784$	1.29956	−	23.9429i	0.0464128	−	0.855105i
$785$	3.52536	−	7.26482i	0.125826	−	0.259293i
$786$	−1.14178	−	1.37639i	−0.0407260	−	0.0490941i
$787$	−1.61508	−	0.432761i	−0.0575715	−	0.0154262i	0.229918	−	0.973210i	$-0.426154\pi$
$787$	−1.61508	−	0.432761i	−0.0575715	−	0.0154262i	−0.287490	+	0.957784i	$0.592821\pi$
$788$	8.42056	−	28.3303i	0.299970	−	1.00923i
$789$	38.1134	+	26.2396i	1.35687	+	0.934155i
$790$	16.0631	−	5.32408i	0.571501	−	0.189422i
$791$		−	13.3536i		−	0.474798i
$792$	−0.493229	+	0.559027i	−0.0175261	+	0.0198642i
$793$	3.32769	+	3.32769i	0.118170	+	0.118170i
$794$	9.24016	+	36.4544i	0.327921	+	1.29372i
$795$	−4.20009	+	15.2156i	−0.148962	+	0.539641i
$796$	1.57145	+	2.90069i	0.0556984	+	0.102812i
$797$	−0.328117	+	1.22455i	−0.0116225	+	0.0433758i	−0.971494	−	0.237066i	$-0.923814\pi$
$797$	−0.328117	+	1.22455i	−0.0116225	+	0.0433758i	0.959871	+	0.280442i	$0.0904809\pi$
$798$	3.21228	+	6.99127i	0.113714	+	0.247488i
$799$	−7.59919	+	13.1622i	−0.268840	+	0.465645i
$800$	28.2030	−	2.14294i	0.997126	−	0.0757642i
$801$	−8.82508	−	1.41225i	−0.311819	−	0.0498995i
$802$	0.222652	−	16.4236i	0.00786213	−	0.579938i
$803$	1.27613	−	0.341938i	0.0450336	−	0.0120667i
$804$	−23.3710	−	17.0420i	−0.824233	−	0.601026i
$805$	−7.99914	−	1.53832i	−0.281933	−	0.0542186i
$806$	10.4344	+	2.94806i	0.367537	+	0.103841i
$807$	−14.1549	+	12.0699i	−0.498277	+	0.424879i
$808$	−22.3294	+	35.2805i	−0.785544	+	1.24116i
$809$			6.81601i			0.239638i	0.992796	+	0.119819i	$0.0382315\pi$
$809$			6.81601i			0.239638i	−0.992796	+	0.119819i	$0.961769\pi$
$810$	14.2965	+	24.6092i	0.502326	+	0.864678i
$811$	15.7832			0.554224			0.277112	−	0.960838i	$-0.410623\pi$
$811$	15.7832			0.554224			0.277112	+	0.960838i	$0.410623\pi$
$812$	−6.92452	+	1.65561i	−0.243003	+	0.0581004i
$813$	27.3397	+	32.0627i	0.958846	+	1.12449i
$814$	1.15354	+	0.325913i	0.0404316	+	0.0114232i
$815$	−22.6466	−	33.4308i	−0.793275	−	1.17103i
$816$	32.0694	+	24.7438i	1.12265	+	0.866206i
$817$	7.35789	+	27.4600i	0.257420	+	0.960705i
$818$	7.87016	+	0.106695i	0.275174	+	0.00373049i
$819$	−0.371770	+	2.32317i	−0.0129907	+	0.0811780i
$820$	2.82911	−	3.09403i	0.0987968	−	0.108048i
$821$	4.74624	+	2.74024i	0.165645	+	0.0956352i	0.580531	−	0.814238i	$-0.302845\pi$
$821$	4.74624	+	2.74024i	0.165645	+	0.0956352i	−0.414886	+	0.909874i	$0.636178\pi$
$822$	−2.47821	−	5.39361i	−0.0864373	−	0.188124i
$823$	48.8218	+	13.0818i	1.70182	+	0.456002i	0.973397	−	0.229124i	$-0.0735861\pi$
$823$	48.8218	+	13.0818i	1.70182	+	0.456002i	0.728425	+	0.685126i	$0.240253\pi$
$824$	−4.67658	+	14.9870i	−0.162916	+	0.522098i
$825$	0.149317	−	0.746088i	0.00519854	−	0.0259755i
$826$	−5.90021	+	1.49553i	−0.205294	+	0.0520363i
$827$	−22.7111	+	22.7111i	−0.789741	+	0.789741i	−0.981452	−	0.191710i	$-0.938597\pi$
$827$	−22.7111	+	22.7111i	−0.789741	+	0.789741i	0.191710	+	0.981452i	$0.438597\pi$
$828$	21.7350	−	1.65517i	0.755342	−	0.0575211i
$829$	17.3616			0.602995			0.301497	−	0.953467i	$-0.402514\pi$
$829$	17.3616			0.602995			0.301497	+	0.953467i	$0.402514\pi$
$830$	41.9114	+	21.0448i	1.45477	+	0.730475i
$831$	−25.9271	+	37.6596i	−0.899403	+	1.30640i
$832$	−5.89214	−	2.10508i	−0.204273	−	0.0729805i
$833$	−9.07082	+	33.8528i	−0.314285	+	1.17293i
$834$	12.4152	−	10.2991i	0.429904	−	0.356627i
$835$	13.9344	−	28.7150i	0.482219	−	0.993723i
$836$	−0.0149217	+	0.550237i	−0.000516078	+	0.0190303i
$837$	44.7067	+	24.4131i	1.54529	+	0.843839i
$838$	−48.6597	−	0.659673i	−1.68092	−	0.0227880i
$839$	17.4135	−	30.1611i	0.601181	−	1.04128i	−0.391462	−	0.920194i	$-0.628030\pi$
$839$	17.4135	−	30.1611i	0.601181	−	1.04128i	0.992643	−	0.121082i	$-0.0386362\pi$
$840$	7.38381	+	8.13227i	0.254766	+	0.280590i
$841$	8.19812	+	14.1996i	0.282694	+	0.489640i
$842$	−24.9019	−	44.5142i	−0.858177	−	1.53406i
$843$	−3.71485	−	20.1335i	−0.127946	−	0.693436i
$844$	11.5218	−	18.7626i	0.396598	−	0.645837i
$845$	−20.9425	−	18.1318i	−0.720444	−	0.623753i
$846$	4.63814	−	10.0064i	0.159462	−	0.344028i
$847$	−7.79388	−	7.79388i	−0.267801	−	0.267801i
$848$	−3.35971	−	15.9523i	−0.115373	−	0.547806i
$849$	−6.33067	−	13.2999i	−0.217268	−	0.456452i
$850$	−40.9826	−	5.43044i	−1.40569	−	0.186262i
$851$	−17.5243	−	30.3530i	−0.600725	−	1.04049i
$852$	−7.07396	+	18.3333i	−0.242350	+	0.628087i
$853$	11.5223	+	43.0018i	0.394516	+	1.47235i	0.822603	+	0.568616i	$0.192521\pi$
$853$	11.5223	+	43.0018i	0.394516	+	1.47235i	−0.428087	+	0.903737i	$0.640812\pi$
$854$	5.95116	+	6.11474i	0.203645	+	0.209242i
$855$	19.7490	+	7.17926i	0.675403	+	0.245526i
$856$	−14.4359	−	15.6605i	−0.493408	−	0.535265i
$857$	0.177031	+	0.660690i	0.00604727	+	0.0225687i	0.968884	−	0.247517i	$-0.0796146\pi$
$857$	0.177031	+	0.660690i	0.00604727	+	0.0225687i	−0.962836	+	0.270086i	$0.912948\pi$
$858$	−0.0973183	+	0.137333i	−0.00332239	+	0.00468846i
$859$	−21.6134	+	12.4785i	−0.737441	+	0.425762i	−0.821138	−	0.570729i	$-0.806661\pi$
$859$	−21.6134	+	12.4785i	−0.737441	+	0.425762i	0.0836970	+	0.996491i	$0.473327\pi$
$860$	21.8434	+	34.2070i	0.744855	+	1.16645i
$861$	1.62304	+	0.129044i	0.0553131	+	0.00439782i
$862$	−11.0160	+	18.4966i	−0.375206	+	0.629995i
$863$	1.42563	−	1.42563i	0.0485288	−	0.0485288i	−0.682426	−	0.730955i	$-0.739075\pi$
$863$	1.42563	−	1.42563i	0.0485288	−	0.0485288i	0.730955	+	0.682426i	$0.239075\pi$
$864$	−24.7847	−	15.8025i	−0.843193	−	0.537612i
$865$	−1.31765	−	18.3180i	−0.0448016	−	0.622830i
$866$	5.91468	+	23.3347i	0.200989	+	0.792945i
$867$	−19.3087	−	22.6443i	−0.655758	−	0.769040i
$868$	18.8447	+	5.60116i	0.639630	+	0.190116i
$869$	0.235083	+	0.407176i	0.00797465	+	0.0138125i
$870$	−10.0755	+	16.6312i	−0.341592	+	0.563851i
$871$	−5.65558	−	3.26525i	−0.191632	−	0.110639i
$872$	1.56268	−	38.4041i	0.0529191	−	1.30053i
$873$	43.9677	−	4.54999i	1.48808	−	0.153994i
$874$	11.5336	−	11.2250i	0.390128	−	0.379692i
$875$	−10.6826	−	3.40044i	−0.361139	−	0.114956i
$876$	21.1044	+	47.6232i	0.713052	+	1.60904i
$877$	−5.34873	+	19.9617i	−0.180614	+	0.674060i	0.814913	+	0.579583i	$0.196784\pi$
$877$	−5.34873	+	19.9617i	−0.180614	+	0.674060i	−0.995527	+	0.0944768i	$0.969882\pi$
$878$	21.4759	−	12.0139i	0.724777	−	0.405451i
$879$	−38.3391	+	18.2491i	−1.29315	+	0.615528i
$880$	0.216705	+	0.755367i	0.00730513	+	0.0254634i
$881$	−39.1851			−1.32018			−0.660090	−	0.751186i	$-0.729482\pi$
$881$	−39.1851			−1.32018			−0.660090	+	0.751186i	$0.729482\pi$
$882$	4.35884	−	25.0564i	0.146770	−	0.843693i
$883$	−13.1389	−	13.1389i	−0.442158	−	0.442158i	0.450579	−	0.892737i	$-0.351218\pi$
$883$	−13.1389	−	13.1389i	−0.442158	−	0.442158i	−0.892737	+	0.450579i	$0.851218\pi$
$884$	7.79310	+	4.78562i	0.262110	+	0.160958i
$885$	−8.42026	+	14.3339i	−0.283044	+	0.481828i
$886$	−30.7090	−	8.67628i	−1.03169	−	0.291485i
$887$	−12.0896	+	45.1188i	−0.405927	+	1.51494i	0.396411	+	0.918073i	$0.370255\pi$
$887$	−12.0896	+	45.1188i	−0.405927	+	1.51494i	−0.802339	+	0.596869i	$0.796411\pi$
$888$	−5.65827	+	46.9222i	−0.189879	+	1.57460i
$889$	2.08093	+	1.20142i	0.0697921	+	0.0402945i
$890$	−6.26239	+	7.03805i	−0.209916	+	0.235916i
$891$	−0.589322	+	0.527218i	−0.0197430	+	0.0176625i
$892$	40.3926	−	38.2596i	1.35244	−	1.28103i
$893$	−2.10761	−	7.86572i	−0.0705286	−	0.263216i
$894$	5.34921	+	6.44833i	0.178904	+	0.215664i
$895$	−3.17932	+	16.5322i	−0.106273	+	0.552612i
$896$	−10.6305	−	3.96123i	−0.355139	−	0.132336i
$897$	4.83975	−	0.892986i	0.161595	−	0.0298159i
$898$	−13.9588	+	23.4378i	−0.465812	+	0.782130i
$899$			34.8025i			1.16073i
$900$	29.9733	+	1.26493i	0.999111	+	0.0421642i
$901$			23.8278i			0.793818i
$902$	0.100078	+	0.0596031i	0.00333222	+	0.00198456i
$903$	−5.27332	+	14.8536i	−0.175485	+	0.494296i
$904$	35.9571	+	11.2201i	1.19591	+	0.373175i
$905$	−2.55938	+	13.3086i	−0.0850765	+	0.442392i
$906$	−36.0442	−	13.3493i	−1.19749	−	0.443501i
$907$	−2.00595	−	7.48632i	−0.0666065	−	0.248579i	0.924593	−	0.380957i	$-0.124405\pi$
$907$	−2.00595	−	7.48632i	−0.0666065	−	0.248579i	−0.991199	+	0.132378i	$0.957739\pi$
$908$	−15.4420	+	14.6266i	−0.512461	+	0.485400i
$909$	−27.9250	+	34.3718i	−0.926215	+	1.14004i
$910$	1.85274	+	1.64855i	0.0614177	+	0.0546488i
$911$	−28.8797	−	16.6737i	−0.956829	−	0.552425i	−0.0616331	−	0.998099i	$-0.519631\pi$
$911$	−28.8797	−	16.6737i	−0.956829	−	0.552425i	−0.895196	+	0.445674i	$0.852964\pi$
$912$	−21.5244	+	2.77540i	−0.712745	+	0.0919028i
$913$	−0.337241	+	1.25860i	−0.0111611	+	0.0416536i
$914$	4.60735	−	16.3073i	0.152397	−	0.539398i
$915$	23.3035	+	0.175533i	0.770391	+	0.00580296i
$916$	−15.3179	+	24.9444i	−0.506119	+	0.824186i
$917$	−0.517650	−	0.517650i	−0.0170943	−	0.0170943i
$918$	30.6881	+	30.0671i	1.01286	+	0.992362i
$919$	52.8678			1.74395			0.871974	−	0.489553i	$-0.162840\pi$
$919$	52.8678			1.74395			0.871974	+	0.489553i	$0.162840\pi$
$920$	10.8634	−	20.2467i	0.358155	−	0.667515i
$921$	4.41004	−	55.4669i	0.145316	−	1.82770i
$922$	10.5843	+	18.9202i	0.348574	+	0.623105i
$923$	−1.14829	+	4.28548i	−0.0377965	+	0.141058i
$924$	−0.179809	+	0.246586i	−0.00591529	+	0.00811209i
$925$	−19.0246	−	44.3265i	−0.625525	−	1.45745i
$926$	5.51060	+	5.66207i	0.181090	+	0.186067i
$927$	−6.79737	+	15.2016i	−0.223255	+	0.499284i
$928$	1.36018	−	20.0367i	0.0446499	−	0.657738i
$929$	1.27080	+	0.733698i	0.0416937	+	0.0240718i	0.520702	−	0.853739i	$-0.325670\pi$
$929$	1.27080	+	0.733698i	0.0416937	+	0.0240718i	−0.479008	+	0.877810i	$0.659004\pi$
$930$	47.0557	−	25.8602i	1.54302	−	0.847990i
$931$	−9.38897	−	16.2622i	−0.307711	−	0.532971i
$932$	4.69679	−	15.8020i	0.153849	−	0.517612i
$933$	18.1848	−	51.2218i	0.595343	−	1.67693i
$934$	−2.51318	+	0.637019i	−0.0822336	+	0.0208439i
$935$	−0.0824080	−	1.14563i	−0.00269503	−	0.0374662i
$936$	−5.94321	−	2.95307i	−0.194260	−	0.0965240i
$937$	−2.11852	+	2.11852i	−0.0692091	+	0.0692091i	−0.740864	−	0.671655i	$-0.765584\pi$
$937$	−2.11852	+	2.11852i	−0.0692091	+	0.0692091i	0.671655	+	0.740864i	$0.265584\pi$
$938$	−10.1731	−	6.05876i	−0.332162	−	0.197825i
$939$	22.0745	−	32.0636i	0.720375	−	1.04636i
$940$	−6.25689	−	9.79835i	−0.204077	−	0.319587i
$941$	33.8409	−	19.5380i	1.10318	−	0.636922i	0.166126	−	0.986105i	$-0.446874\pi$
$941$	33.8409	−	19.5380i	1.10318	−	0.636922i	0.937055	+	0.349183i	$0.113541\pi$
$942$	−0.820560	+	8.80759i	−0.0267353	+	0.286967i
$943$	−0.881486	−	3.28975i	−0.0287051	−	0.107129i
$944$	0.930533	−	17.1441i	0.0302863	−	0.557992i
$945$	6.76166	+	9.48768i	0.219957	+	0.308634i
$946$	−0.808093	+	0.786476i	−0.0262734	+	0.0255705i
$947$	−12.1065	−	45.1822i	−0.393410	−	1.46823i	−0.824472	−	0.565903i	$-0.808528\pi$
$947$	−12.1065	−	45.1822i	−0.393410	−	1.46823i	0.431062	−	0.902322i	$-0.358139\pi$
$948$	−14.4267	+	11.6411i	−0.468556	+	0.378087i
$949$	5.88034	+	10.1850i	0.190884	+	0.330621i
$950$	17.5842	−	13.4694i	0.570507	−	0.437005i
$951$	0.746760	−	1.08468i	0.0242153	−	0.0351731i
$952$	14.0109	+	8.86765i	0.454097	+	0.287402i
$953$	−22.4838	−	22.4838i	−0.728323	−	0.728323i	0.241963	−	0.970286i	$-0.422209\pi$
$953$	−22.4838	−	22.4838i	−0.728323	−	0.728323i	−0.970286	+	0.241963i	$0.922209\pi$
$954$	−1.54656	−	17.2219i	−0.0500717	−	0.557580i
$955$	37.9230	+	32.8334i	1.22716	+	1.06246i
$956$	20.4758	−	33.3436i	0.662234	−	1.07841i
$957$	−0.509121	−	0.180748i	−0.0164576	−	0.00584277i
$958$	1.86764	−	1.04479i	0.0603407	−	0.0337555i
$959$	−1.21492	−	2.10430i	−0.0392318	−	0.0679514i
$960$	−28.1019	+	13.0493i	−0.906984	+	0.421166i
$961$	32.5498	−	56.3779i	1.04999	−	1.81864i
$962$	−0.144647	+	10.6697i	−0.00466361	+	0.344004i
$963$	−13.2493	−	18.2977i	−0.426954	−	0.589636i
$964$	−13.9398	−	0.378030i	−0.448971	−	0.0121755i
$965$	−3.14246	+	6.47577i	−0.101160	+	0.208462i
$966$	8.79621	−	1.49999i	0.283013	−	0.0482615i
$967$	8.27302	−	30.8753i	0.266042	−	0.992884i	−0.695567	−	0.718461i	$-0.744847\pi$
$967$	8.27302	−	30.8753i	0.266042	−	0.992884i	0.961609	−	0.274422i	$-0.0884866\pi$
$968$	27.5352	−	14.4379i	0.885016	−	0.464051i
$969$	31.6212	+	2.51413i	1.01582	+	0.0807654i
$970$	20.9080	−	41.6391i	0.671316	−	1.33695i
$971$	26.2238			0.841562			0.420781	−	0.907162i	$-0.361756\pi$
$971$	26.2238			0.841562			0.420781	+	0.907162i	$0.361756\pi$
$972$	−24.1318	−	19.7397i	−0.774029	−	0.633150i
$973$	4.66929	−	4.66929i	0.149691	−	0.149691i
$974$	−5.10635	−	20.1456i	−0.163618	−	0.645508i
$975$	6.75930	−	0.435061i	0.216471	−	0.0139331i
$976$	−21.4655	+	10.8869i	−0.687094	+	0.348480i
$977$	−26.0328	−	6.97547i	−0.832864	−	0.223165i	−0.182901	−	0.983131i	$-0.558549\pi$
$977$	−26.0328	−	6.97547i	−0.832864	−	0.223165i	−0.649963	+	0.759966i	$0.725215\pi$
$978$	36.0904	+	25.5748i	1.15404	+	0.817792i
$979$	−0.226676	−	0.130872i	−0.00724461	−	0.00418268i
$980$	−19.7845	−	18.0905i	−0.631992	−	0.577879i
$981$	6.44193	−	40.2552i	0.205675	−	1.28525i
$982$	−0.224070	+	16.5282i	−0.00715037	+	0.527436i
$983$	8.36554	+	31.2206i	0.266819	+	0.995783i	0.961127	+	0.276105i	$0.0890438\pi$
$983$	8.36554	+	31.2206i	0.266819	+	0.995783i	−0.694308	+	0.719678i	$0.744290\pi$
$984$	−1.71121	+	4.26193i	−0.0545514	+	0.135865i
$985$	−18.5325	−	27.3576i	−0.590494	−	0.871686i
$986$	−7.98088	+	28.2477i	−0.254163	+	0.899589i
$987$	1.51050	−	4.25469i	0.0480798	−	0.135428i
$988$	−4.76561	+	1.13943i	−0.151614	+	0.0362500i
$989$	32.9708			1.04841
$990$	0.133920	+	0.822677i	0.00425626	+	0.0261464i
$991$		−	45.3516i		−	1.44064i	−0.693641	−	0.720321i	$-0.743995\pi$
$991$		−	45.3516i		−	1.44064i	0.693641	−	0.720321i	$-0.256005\pi$
$992$	−30.9162	+	46.0367i	−0.981589	+	1.46167i
$993$	3.22227	+	17.4639i	0.102256	+	0.554200i
$994$	−2.18713	+	7.74117i	−0.0693716	+	0.245535i
$995$	3.62203	+	0.696554i	0.114826	+	0.0220822i
$996$	−51.0837	−	5.45864i	−1.61865	−	0.172964i
$997$	32.7518	−	8.77582i	1.03726	−	0.277933i	0.300283	−	0.953850i	$-0.402919\pi$
$997$	32.7518	−	8.77582i	1.03726	−	0.277933i	0.736977	+	0.675917i	$0.236252\pi$
$998$	−31.0912	−	0.421498i	−0.984173	−	0.0133423i
$999$	−11.8195	+	48.7157i	−0.373952	+	1.54130i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bo.a.43.13	✓	272
5.2	odd	4	inner	360.2.bo.a.187.47	yes	272
8.3	odd	2	inner	360.2.bo.a.43.44	yes	272
9.4	even	3	inner	360.2.bo.a.283.58	yes	272
40.27	even	4	inner	360.2.bo.a.187.58	yes	272
45.22	odd	12	inner	360.2.bo.a.67.44	yes	272
72.67	odd	6	inner	360.2.bo.a.283.47	yes	272
360.67	even	12	inner	360.2.bo.a.67.13	yes	272

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bo.a.43.13	✓	272	1.1	even	1	trivial
360.2.bo.a.43.44	yes	272	8.3	odd	2	inner
360.2.bo.a.67.13	yes	272	360.67	even	12	inner
360.2.bo.a.67.44	yes	272	45.22	odd	12	inner
360.2.bo.a.187.47	yes	272	5.2	odd	4	inner
360.2.bo.a.187.58	yes	272	40.27	even	4	inner
360.2.bo.a.283.47	yes	272	72.67	odd	6	inner
360.2.bo.a.283.58	yes	272	9.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21505 - 0.723644i) q^{2} +(1.31796 - 1.12382i) q^{3} +(0.952679 + 1.75852i) q^{4} +(2.19583 + 0.422281i) q^{5} +(-2.41463 + 0.411761i) q^{6} +(-0.968556 + 0.259524i) q^{7} +(0.114995 - 2.82609i) q^{8} +(0.474050 - 2.96231i) q^{9} +O(q^{10})\)	\(q+(-1.21505 - 0.723644i) q^{2} +(1.31796 - 1.12382i) q^{3} +(0.952679 + 1.75852i) q^{4} +(2.19583 + 0.422281i) q^{5} +(-2.41463 + 0.411761i) q^{6} +(-0.968556 + 0.259524i) q^{7} +(0.114995 - 2.82609i) q^{8} +(0.474050 - 2.96231i) q^{9} +(-2.36246 - 2.10209i) q^{10} +(0.0439296 - 0.0760883i) q^{11} +(3.23186 + 1.24703i) q^{12} +(0.755462 + 0.202425i) q^{13} +(1.36464 + 0.385556i) q^{14} +(3.36859 - 1.91117i) q^{15} +(-2.18481 + 3.35062i) q^{16} +(4.13408 - 4.13408i) q^{17} +(-2.71965 + 3.25630i) q^{18} +3.13250i q^{19} +(1.34933 + 4.26372i) q^{20} +(-0.984862 + 1.43053i) q^{21} +(-0.108437 + 0.0606615i) q^{22} +(3.50919 + 0.940285i) q^{23} +(-3.02446 - 3.85391i) q^{24} +(4.64336 + 1.85452i) q^{25} +(-0.771438 - 0.792642i) q^{26} +(-2.70433 - 4.43696i) q^{27} +(-1.37910 - 1.45599i) q^{28} +(1.77509 - 3.07454i) q^{29} +(-5.47601 - 0.115497i) q^{30} +(-8.48968 + 4.90152i) q^{31} +(5.07929 - 2.49013i) q^{32} +(-0.0276121 - 0.149651i) q^{33} +(-8.01471 + 2.03150i) q^{34} +(-2.23638 + 0.160868i) q^{35} +(5.66091 - 1.98850i) q^{36} +(-6.82169 - 6.82169i) q^{37} +(2.26682 - 3.80614i) q^{38} +(1.22316 - 0.582215i) q^{39} +(1.44591 - 6.15706i) q^{40} +(-0.468734 - 0.811870i) q^{41} +(2.23185 - 1.02547i) q^{42} +(8.76616 - 2.34889i) q^{43} +(0.175654 + 0.00476350i) q^{44} +(2.29186 - 6.30455i) q^{45} +(-3.58340 - 3.68190i) q^{46} +(-2.51100 + 0.672821i) q^{47} +(0.886001 + 6.87132i) q^{48} +(-5.19143 + 2.99727i) q^{49} +(-4.29989 - 5.61346i) q^{50} +(0.802594 - 10.0945i) q^{51} +(0.363743 + 1.52134i) q^{52} +(-2.88187 + 2.88187i) q^{53} +(0.0751062 + 7.34809i) q^{54} +(0.128593 - 0.148527i) q^{55} +(0.622058 + 2.76707i) q^{56} +(3.52038 + 4.12852i) q^{57} +(-4.38169 + 2.45118i) q^{58} +(-3.71726 + 2.14616i) q^{59} +(6.57003 + 4.10301i) q^{60} +(5.21098 + 3.00856i) q^{61} +(13.8623 + 0.187929i) q^{62} +(0.309646 + 2.99219i) q^{63} +(-7.97355 - 0.649972i) q^{64} +(1.57339 + 0.763510i) q^{65} +(-0.0747437 + 0.201814i) q^{66} +(-8.06532 - 2.16110i) q^{67} +(11.2083 + 3.33143i) q^{68} +(5.68170 - 2.70445i) q^{69} +(2.83372 + 1.42288i) q^{70} +5.67266i q^{71} +(-8.31724 - 1.68036i) q^{72} +(10.6328 + 10.6328i) q^{73} +(3.35220 + 13.2252i) q^{74} +(8.20392 - 2.77412i) q^{75} +(-5.50858 + 2.98427i) q^{76} +(-0.0228016 + 0.0850966i) q^{77} +(-1.90751 - 0.177714i) q^{78} +(-2.67568 + 4.63441i) q^{79} +(-6.21237 + 6.43479i) q^{80} +(-8.55055 - 2.80856i) q^{81} +(-0.0179717 + 1.32566i) q^{82} +(-14.3252 + 3.83843i) q^{83} +(-3.45387 - 0.369070i) q^{84} +(10.8235 - 7.33201i) q^{85} +(-12.3511 - 3.48957i) q^{86} +(-1.11574 - 6.04702i) q^{87} +(-0.209981 - 0.132899i) q^{88} -2.97912i q^{89} +(-7.34697 + 6.00184i) q^{90} -0.784242 q^{91} +(1.68962 + 7.06678i) q^{92} +(-5.68065 + 16.0009i) q^{93} +(3.53787 + 0.999562i) q^{94} +(-1.32280 + 6.87845i) q^{95} +(3.89585 - 8.99012i) q^{96} +(3.81348 + 14.2321i) q^{97} +(8.47679 + 0.114919i) q^{98} +(-0.204572 - 0.166203i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8}+O(q^{10}) \) 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8	\( 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8} - 8 q^{10} - 8 q^{11} - 10 q^{12} - 4 q^{16} - 16 q^{17} + 20 q^{18} + 14 q^{20} + 6 q^{22} - 4 q^{25} - 48 q^{26} - 8 q^{27} + 8 q^{28} - 34 q^{30} - 22 q^{32} + 4 q^{33} - 16 q^{35} - 8 q^{36} - 26 q^{38} - 2 q^{40} - 8 q^{41} - 66 q^{42} - 4 q^{43} - 40 q^{46} - 38 q^{48} - 42 q^{50} - 16 q^{51} + 14 q^{52} + 24 q^{56} + 16 q^{57} + 6 q^{58} + 14 q^{60} - 76 q^{62} - 4 q^{65} - 44 q^{66} - 4 q^{67} - 46 q^{68} + 18 q^{70} + 38 q^{72} - 16 q^{73} - 120 q^{75} - 38 q^{78} + 92 q^{80} - 32 q^{81} - 4 q^{83} - 40 q^{86} - 42 q^{88} - 14 q^{90} - 32 q^{91} + 52 q^{92} + 108 q^{96} - 4 q^{97} - 140 q^{98}+O(q^{100}) \) 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8 - 8 * q^10 - 8 * q^11 - 10 * q^12 - 4 * q^16 - 16 * q^17 + 20 * q^18 + 14 * q^20 + 6 * q^22 - 4 * q^25 - 48 * q^26 - 8 * q^27 + 8 * q^28 - 34 * q^30 - 22 * q^32 + 4 * q^33 - 16 * q^35 - 8 * q^36 - 26 * q^38 - 2 * q^40 - 8 * q^41 - 66 * q^42 - 4 * q^43 - 40 * q^46 - 38 * q^48 - 42 * q^50 - 16 * q^51 + 14 * q^52 + 24 * q^56 + 16 * q^57 + 6 * q^58 + 14 * q^60 - 76 * q^62 - 4 * q^65 - 44 * q^66 - 4 * q^67 - 46 * q^68 + 18 * q^70 + 38 * q^72 - 16 * q^73 - 120 * q^75 - 38 * q^78 + 92 * q^80 - 32 * q^81 - 4 * q^83 - 40 * q^86 - 42 * q^88 - 14 * q^90 - 32 * q^91 + 52 * q^92 + 108 * q^96 - 4 * q^97 - 140 * q^98

Introduction

L-functions

Modular forms

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