LMFDB - Embedded newform 230.2.j.a.9.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(9,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 10]))

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

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

chi := DirichletCharacter("230.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.j (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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			9.10
Character	$\chi$	$=$	230.9
Dual form			230.2.j.a.179.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.281733 + 0.959493i) q^{2} +(0.0697998 - 0.0604819i) q^{3} +(-0.841254 + 0.540641i) q^{4} +(1.48028 + 1.67594i) q^{5} +(0.0776969 + 0.0499327i) q^{6} +(-1.04108 - 0.475445i) q^{7} +(-0.755750 - 0.654861i) q^{8} +(-0.425731 + 2.96102i) q^{9} +O(q^{10})$	\(q+(0.281733 + 0.959493i) q^{2} +(0.0697998 - 0.0604819i) q^{3} +(-0.841254 + 0.540641i) q^{4} +(1.48028 + 1.67594i) q^{5} +(0.0776969 + 0.0499327i) q^{6} +(-1.04108 - 0.475445i) q^{7} +(-0.755750 - 0.654861i) q^{8} +(-0.425731 + 2.96102i) q^{9} +(-1.19101 + 1.89248i) q^{10} +(3.69609 + 1.08527i) q^{11} +(-0.0260204 + 0.0886173i) q^{12} +(-1.25102 + 0.571322i) q^{13} +(0.162880 - 1.13286i) q^{14} +(0.204687 + 0.0274504i) q^{15} +(0.415415 - 0.909632i) q^{16} +(0.463067 - 0.720547i) q^{17} +(-2.96102 + 0.425731i) q^{18} +(-0.778520 + 0.500325i) q^{19} +(-2.15137 - 0.609593i) q^{20} +(-0.101423 + 0.0297805i) q^{21} +3.85213i q^{22} +(-0.229075 - 4.79036i) q^{23} -0.0923584 q^{24} +(-0.617556 + 4.96172i) q^{25} +(-0.900632 - 1.03939i) q^{26} +(0.299170 + 0.465518i) q^{27} +(1.13286 - 0.162880i) q^{28} +(0.00469088 + 0.00301465i) q^{29} +(0.0313286 + 0.204130i) q^{30} +(4.36818 - 5.04115i) q^{31} +(0.989821 + 0.142315i) q^{32} +(0.323626 - 0.147795i) q^{33} +(0.821820 + 0.241308i) q^{34} +(-0.744268 - 2.44858i) q^{35} +(-1.24270 - 2.72114i) q^{36} +(-1.06862 - 0.153645i) q^{37} +(-0.699392 - 0.606027i) q^{38} +(-0.0527664 + 0.115542i) q^{39} +(-0.0212112 - 2.23597i) q^{40} +(-0.702947 - 4.88910i) q^{41} +(-0.0571483 - 0.0889245i) q^{42} +(5.24726 - 4.54678i) q^{43} +(-3.69609 + 1.08527i) q^{44} +(-5.59270 + 3.66963i) q^{45} +(4.53178 - 1.56940i) q^{46} -7.27641i q^{47} +(-0.0260204 - 0.0886173i) q^{48} +(-3.72623 - 4.30030i) q^{49} +(-4.93472 + 0.805336i) q^{50} +(-0.0112580 - 0.0783012i) q^{51} +(0.743545 - 1.15698i) q^{52} +(-0.417802 - 0.190804i) q^{53} +(-0.362376 + 0.418204i) q^{54} +(3.65240 + 7.80094i) q^{55} +(0.475445 + 1.04108i) q^{56} +(-0.0240800 + 0.0820090i) q^{57} +(-0.00157096 + 0.00535019i) q^{58} +(0.895090 + 1.95997i) q^{59} +(-0.187035 + 0.0875695i) q^{60} +(6.33405 - 7.30988i) q^{61} +(6.06760 + 2.77098i) q^{62} +(1.85102 - 2.88025i) q^{63} +(0.142315 + 0.989821i) q^{64} +(-2.80936 - 1.25092i) q^{65} +(0.232984 + 0.268878i) q^{66} +(2.18008 + 7.42468i) q^{67} +0.856515i q^{68} +(-0.305719 - 0.320511i) q^{69} +(2.13971 - 1.40396i) q^{70} +(3.45459 - 1.01436i) q^{71} +(2.26080 - 1.95900i) q^{72} +(7.64561 + 11.8968i) q^{73} +(-0.153645 - 1.06862i) q^{74} +(0.256989 + 0.383678i) q^{75} +(0.384437 - 0.841800i) q^{76} +(-3.33194 - 2.88714i) q^{77} +(-0.125728 - 0.0180770i) q^{78} +(-0.879284 - 1.92536i) q^{79} +(2.13942 - 0.650297i) q^{80} +(-8.56185 - 2.51398i) q^{81} +(4.49301 - 2.05189i) q^{82} +(-10.1835 - 1.46416i) q^{83} +(0.0692219 - 0.0798863i) q^{84} +(1.89306 - 0.290536i) q^{85} +(5.84093 + 3.75374i) q^{86} +(0.000509755 - 7.32916e-5i) q^{87} +(-2.08262 - 3.24062i) q^{88} +(-4.67545 - 5.39575i) q^{89} +(-5.09663 - 4.33230i) q^{90} +1.57404 q^{91} +(2.78257 + 3.90606i) q^{92} -0.616067i q^{93} +(6.98167 - 2.05000i) q^{94} +(-1.99094 - 0.564135i) q^{95} +(0.0776969 - 0.0499327i) q^{96} +(-19.0564 + 2.73989i) q^{97} +(3.07630 - 4.78682i) q^{98} +(-4.78705 + 10.4822i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) $ 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9	$ 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9} + 8 q^{11} - 6 q^{15} - 12 q^{16} - 16 q^{19} - 22 q^{20} + 4 q^{24} - 52 q^{25} - 4 q^{26} - 8 q^{29} - 44 q^{30} + 12 q^{31} + 16 q^{35} - 8 q^{36} - 36 q^{39} - 28 q^{41} - 8 q^{44} + 16 q^{45} - 4 q^{46} - 58 q^{49} + 12 q^{50} - 24 q^{51} - 6 q^{54} - 36 q^{55} + 22 q^{56} - 102 q^{59} - 38 q^{60} + 72 q^{61} + 12 q^{64} - 138 q^{65} + 80 q^{66} - 212 q^{69} - 108 q^{70} + 176 q^{71} - 88 q^{74} - 100 q^{75} + 16 q^{76} - 104 q^{79} - 22 q^{80} - 28 q^{81} - 22 q^{84} + 2 q^{85} + 62 q^{86} + 48 q^{89} + 24 q^{90} - 56 q^{91} + 24 q^{94} + 18 q^{95} - 4 q^{96} + 188 q^{99}+O(q^{100}) $ 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9 + 8 * q^11 - 6 * q^15 - 12 * q^16 - 16 * q^19 - 22 * q^20 + 4 * q^24 - 52 * q^25 - 4 * q^26 - 8 * q^29 - 44 * q^30 + 12 * q^31 + 16 * q^35 - 8 * q^36 - 36 * q^39 - 28 * q^41 - 8 * q^44 + 16 * q^45 - 4 * q^46 - 58 * q^49 + 12 * q^50 - 24 * q^51 - 6 * q^54 - 36 * q^55 + 22 * q^56 - 102 * q^59 - 38 * q^60 + 72 * q^61 + 12 * q^64 - 138 * q^65 + 80 * q^66 - 212 * q^69 - 108 * q^70 + 176 * q^71 - 88 * q^74 - 100 * q^75 + 16 * q^76 - 104 * q^79 - 22 * q^80 - 28 * q^81 - 22 * q^84 + 2 * q^85 + 62 * q^86 + 48 * q^89 + 24 * q^90 - 56 * q^91 + 24 * q^94 + 18 * q^95 - 4 * q^96 + 188 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{5}{11}\right)$

Coefficient data

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

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

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

$2$	0.281733	+	0.959493i	0.199215	+	0.678464i
$2$	0.281733	+	0.959493i	0.199215	+	0.678464i
$3$	0.0697998	−	0.0604819i	0.0402990	−	0.0349192i	−0.634478	−	0.772941i	$-0.718785\pi$
$3$	0.0697998	−	0.0604819i	0.0402990	−	0.0349192i	0.674777	+	0.738021i	$0.264240\pi$
$4$	−0.841254	+	0.540641i	−0.420627	+	0.270320i
$5$	1.48028	+	1.67594i	0.662000	+	0.749504i
$5$	1.48028	+	1.67594i	0.662000	+	0.749504i
$6$	0.0776969	+	0.0499327i	0.0317196	+	0.0203850i
$7$	−1.04108	−	0.475445i	−0.393491	−	0.179701i	0.208836	−	0.977951i	$-0.433032\pi$
$7$	−1.04108	−	0.475445i	−0.393491	−	0.179701i	−0.602327	+	0.798249i	$0.705760\pi$
$8$	−0.755750	−	0.654861i	−0.267198	−	0.231528i
$9$	−0.425731	+	2.96102i	−0.141910	+	0.987007i
$10$	−1.19101	+	1.89248i	−0.376631	+	0.598456i
$11$	3.69609	+	1.08527i	1.11441	+	0.327222i	0.786564	−	0.617508i	$-0.211858\pi$
$11$	3.69609	+	1.08527i	1.11441	+	0.327222i	0.327850	+	0.944730i	$0.393676\pi$
$12$	−0.0260204	+	0.0886173i	−0.00751144	+	0.0255816i
$13$	−1.25102	+	0.571322i	−0.346971	+	0.158456i	−0.581275	−	0.813707i	$-0.697446\pi$
$13$	−1.25102	+	0.571322i	−0.346971	+	0.158456i	0.234305	+	0.972163i	$0.424719\pi$
$14$	0.162880	−	1.13286i	0.0435315	−	0.302769i
$15$	0.204687	+	0.0274504i	0.0528500	+	0.00708766i
$16$	0.415415	−	0.909632i	0.103854	−	0.227408i
$17$	0.463067	−	0.720547i	0.112310	−	0.174758i	−0.780548	−	0.625096i	$-0.785060\pi$
$17$	0.463067	−	0.720547i	0.112310	−	0.174758i	0.892858	+	0.450337i	$0.148696\pi$
$18$	−2.96102	+	0.425731i	−0.697919	+	0.100346i
$19$	−0.778520	+	0.500325i	−0.178605	+	0.114782i	−0.626888	−	0.779109i	$-0.715672\pi$
$19$	−0.778520	+	0.500325i	−0.178605	+	0.114782i	0.448284	+	0.893891i	$0.352035\pi$
$20$	−2.15137	−	0.609593i	−0.481061	−	0.136309i
$21$	−0.101423	+	0.0297805i	−0.0221323	+	0.00649863i
$22$			3.85213i			0.821277i
$23$	−0.229075	−	4.79036i	−0.0477655	−	0.998859i
$23$	−0.229075	−	4.79036i	−0.0477655	−	0.998859i
$24$	−0.0923584			−0.0188526
$25$	−0.617556	+	4.96172i	−0.123511	+	0.992343i
$26$	−0.900632	−	1.03939i	−0.176629	−	0.203840i
$27$	0.299170	+	0.465518i	0.0575754	+	0.0895890i
$28$	1.13286	−	0.162880i	0.214090	−	0.0307815i
$29$	0.00469088	+	0.00301465i	0.000871075	+	0.000559806i	0.541076	−	0.840974i	$-0.318017\pi$
$29$	0.00469088	+	0.00301465i	0.000871075	+	0.000559806i	−0.540205	+	0.841533i	$0.681653\pi$
$30$	0.0313286	+	0.204130i	0.00571979	+	0.0372688i
$31$	4.36818	−	5.04115i	0.784548	−	0.905416i	−0.212881	−	0.977078i	$-0.568285\pi$
$31$	4.36818	−	5.04115i	0.784548	−	0.905416i	0.997429	+	0.0716617i	$0.0228302\pi$
$32$	0.989821	+	0.142315i	0.174977	+	0.0251579i
$33$	0.323626	−	0.147795i	0.0563361	−	0.0257278i
$34$	0.821820	+	0.241308i	0.140941	+	0.0413840i
$35$	−0.744268	−	2.44858i	−0.125804	−	0.413885i
$36$	−1.24270	−	2.72114i	−0.207117	−	0.453523i
$37$	−1.06862	−	0.153645i	−0.175680	−	0.0252590i	0.0539132	−	0.998546i	$-0.482831\pi$
$37$	−1.06862	−	0.153645i	−0.175680	−	0.0252590i	−0.229593	+	0.973287i	$0.573740\pi$
$38$	−0.699392	−	0.606027i	−0.113456	−	0.0983105i
$39$	−0.0527664	+	0.115542i	−0.00844938	+	0.0185016i
$40$	−0.0212112	−	2.23597i	−0.00335379	−	0.353537i
$41$	−0.702947	−	4.88910i	−0.109782	−	0.763549i	−0.968124	−	0.250472i	$-0.919414\pi$
$41$	−0.702947	−	4.88910i	−0.109782	−	0.763549i	0.858342	−	0.513078i	$-0.171495\pi$
$42$	−0.0571483	−	0.0889245i	−0.00881817	−	0.0137213i
$43$	5.24726	−	4.54678i	0.800200	−	0.693377i	−0.155462	−	0.987842i	$-0.549687\pi$
$43$	5.24726	−	4.54678i	0.800200	−	0.693377i	0.955662	+	0.294465i	$0.0951413\pi$
$44$	−3.69609	+	1.08527i	−0.557207	+	0.163611i
$45$	−5.59270	+	3.66963i	−0.833710	+	0.547037i
$46$	4.53178	−	1.56940i	0.668174	−	0.231395i
$47$		−	7.27641i		−	1.06137i	−0.847568	−	0.530687i	$-0.821934\pi$
$47$		−	7.27641i		−	1.06137i	0.847568	−	0.530687i	$-0.178066\pi$
$48$	−0.0260204	−	0.0886173i	−0.00375572	−	0.0127908i
$49$	−3.72623	−	4.30030i	−0.532318	−	0.614328i
$50$	−4.93472	+	0.805336i	−0.697874	+	0.113892i
$51$	−0.0112580	−	0.0783012i	−0.00157644	−	0.0109644i
$52$	0.743545	−	1.15698i	0.103111	−	0.160444i
$53$	−0.417802	−	0.190804i	−0.0573896	−	0.0262089i	0.386513	−	0.922284i	$-0.373679\pi$
$53$	−0.417802	−	0.190804i	−0.0573896	−	0.0262089i	−0.443903	+	0.896075i	$0.646407\pi$
$54$	−0.362376	+	0.418204i	−0.0493131	+	0.0569103i
$55$	3.65240	+	7.80094i	0.492489	+	1.05188i
$56$	0.475445	+	1.04108i	0.0635340	+	0.139120i
$57$	−0.0240800	+	0.0820090i	−0.00318947	+	0.0108624i
$58$	−0.00157096	+	0.00535019i	−0.000206277	+	0.000702515i
$59$	0.895090	+	1.95997i	0.116531	+	0.255167i	0.958906	−	0.283725i	$-0.0915704\pi$
$59$	0.895090	+	1.95997i	0.116531	+	0.255167i	−0.842375	+	0.538892i	$0.818843\pi$
$60$	−0.187035	+	0.0875695i	−0.0241461	+	0.0113052i
$61$	6.33405	−	7.30988i	0.810992	−	0.935934i	−0.187939	−	0.982181i	$-0.560181\pi$
$61$	6.33405	−	7.30988i	0.810992	−	0.935934i	0.998930	+	0.0462467i	$0.0147260\pi$
$62$	6.06760	+	2.77098i	0.770586	+	0.351915i
$63$	1.85102	−	2.88025i	0.233207	−	0.362877i
$64$	0.142315	+	0.989821i	0.0177894	+	0.123728i
$65$	−2.80936	−	1.25092i	−0.348458	−	0.155158i
$66$	0.232984	+	0.268878i	0.0286784	+	0.0330966i
$67$	2.18008	+	7.42468i	0.266339	+	0.907069i	0.978707	+	0.205262i	$0.0658047\pi$
$67$	2.18008	+	7.42468i	0.266339	+	0.907069i	−0.712368	+	0.701806i	$0.752377\pi$
$68$			0.856515i			0.103868i
$69$	−0.305719	−	0.320511i	−0.0368043	−	0.0385850i
$70$	2.13971	−	1.40396i	0.255744	−	0.167806i
$71$	3.45459	−	1.01436i	0.409984	−	0.120382i	−0.0702355	−	0.997530i	$-0.522375\pi$
$71$	3.45459	−	1.01436i	0.409984	−	0.120382i	0.480220	+	0.877148i	$0.340557\pi$
$72$	2.26080	−	1.95900i	0.266438	−	0.230870i
$73$	7.64561	+	11.8968i	0.894851	+	1.39242i	0.919657	+	0.392723i	$0.128467\pi$
$73$	7.64561	+	11.8968i	0.894851	+	1.39242i	−0.0248059	+	0.999692i	$0.507897\pi$
$74$	−0.153645	−	1.06862i	−0.0178608	−	0.124225i
$75$	0.256989	+	0.383678i	0.0296745	+	0.0443033i
$76$	0.384437	−	0.841800i	0.0440979	−	0.0965610i
$77$	−3.33194	−	2.88714i	−0.379710	−	0.329020i
$78$	−0.125728	−	0.0180770i	−0.0142359	−	0.00204681i
$79$	−0.879284	−	1.92536i	−0.0989272	−	0.216620i	0.853697	−	0.520770i	$-0.174355\pi$
$79$	−0.879284	−	1.92536i	−0.0989272	−	0.216620i	−0.952624	+	0.304150i	$0.901628\pi$
$80$	2.13942	−	0.650297i	0.239194	−	0.0727054i
$81$	−8.56185	−	2.51398i	−0.951316	−	0.279332i
$82$	4.49301	−	2.05189i	0.496170	−	0.226593i
$83$	−10.1835	−	1.46416i	−1.11778	−	0.160713i	−0.441433	−	0.897294i	$-0.645530\pi$
$83$	−10.1835	−	1.46416i	−1.11778	−	0.160713i	−0.676349	+	0.736581i	$0.736439\pi$
$84$	0.0692219	−	0.0798863i	0.00755273	−	0.00871631i
$85$	1.89306	−	0.290536i	0.205331	−	0.0315130i
$86$	5.84093	+	3.75374i	0.629843	+	0.404776i
$87$	0.000509755	0	7.32916e-5i	5.46514e−5	0	7.85769e-6i
$88$	−2.08262	−	3.24062i	−0.222008	−	0.345451i
$89$	−4.67545	−	5.39575i	−0.495597	−	0.571949i	0.451756	−	0.892142i	$-0.350798\pi$
$89$	−4.67545	−	5.39575i	−0.495597	−	0.571949i	−0.947352	+	0.320193i	$0.896252\pi$
$90$	−5.09663	−	4.33230i	−0.537232	−	0.456664i
$91$	1.57404			0.165005
$92$	2.78257	+	3.90606i	0.290103	+	0.407235i
$93$		−	0.616067i		−	0.0638832i
$94$	6.98167	−	2.05000i	0.720104	−	0.211442i
$95$	−1.99094	−	0.564135i	−0.204266	−	0.0578790i
$96$	0.0776969	−	0.0499327i	0.00792990	−	0.00509624i
$97$	−19.0564	+	2.73989i	−1.93488	+	0.278194i	−0.997533	−	0.0702015i	$-0.977636\pi$
$97$	−19.0564	+	2.73989i	−1.93488	+	0.278194i	−0.937348	+	0.348395i	$0.886727\pi$
$98$	3.07630	−	4.78682i	0.310754	−	0.483542i
$99$	−4.78705	+	10.4822i	−0.481117	+	1.05350i
$100$	−2.16298	−	4.50794i	−0.216298	−	0.450794i
$101$	−1.46183	+	10.1673i	−0.145458	+	1.01168i	0.778077	+	0.628169i	$0.216195\pi$
$101$	−1.46183	+	10.1673i	−0.145458	+	1.01168i	−0.923535	+	0.383514i	$0.874714\pi$
$102$	0.0719577	−	0.0328620i	0.00712488	−	0.00325382i
$103$	−4.19683	+	14.2931i	−0.413526	+	1.40834i	0.444983	+	0.895539i	$0.353210\pi$
$103$	−4.19683	+	14.2931i	−0.413526	+	1.40834i	−0.858508	+	0.512800i	$0.828608\pi$
$104$	1.31959	+	0.387468i	0.129397	+	0.0379943i
$105$	−0.200044	−	0.125896i	−0.0195223	−	0.0122861i
$106$	0.0653665	−	0.454634i	0.00634896	−	0.0441580i
$107$	−13.5230	−	11.7177i	−1.30732	−	1.13280i	−0.982347	−	0.187070i	$-0.940101\pi$
$107$	−13.5230	−	11.7177i	−1.30732	−	1.13280i	−0.324969	−	0.945725i	$-0.605354\pi$
$108$	−0.503356	−	0.229875i	−0.0484355	−	0.0221198i
$109$	11.5072	+	7.39525i	1.10219	+	0.708336i	0.959578	−	0.281442i	$-0.0908128\pi$
$109$	11.5072	+	7.39525i	1.10219	+	0.708336i	0.142614	+	0.989778i	$0.454449\pi$
$110$	−6.45595	+	5.70223i	−0.615550	+	0.543686i
$111$	−0.0838823	+	0.0539079i	−0.00796176	+	0.00511671i
$112$	−0.864960	+	0.749492i	−0.0817310	+	0.0708203i
$113$	4.35279	+	14.8243i	0.409476	+	1.39455i	0.863855	+	0.503740i	$0.168043\pi$
$113$	4.35279	+	14.8243i	0.409476	+	1.39455i	−0.454379	+	0.890809i	$0.650139\pi$
$114$	−0.0854711			−0.00800511
$115$	7.68926	−	7.47498i	0.717027	−	0.697045i
$116$	−0.00557606			−0.000517725
$117$	−1.15910	−	3.94753i	−0.107159	−	0.364949i
$118$	−1.62840	+	1.41102i	−0.149907	+	0.129895i
$119$	−0.824670	+	0.529983i	−0.0755973	+	0.0485835i
$120$	−0.136716	−	0.154787i	−0.0124804	−	0.0141301i
$121$	3.22951	+	2.07548i	0.293592	+	0.188680i
$122$	8.79828	+	4.01804i	0.796559	+	0.363776i
$123$	−0.344768	−	0.298743i	−0.0310867	−	0.0269367i
$124$	−0.949296	+	6.60250i	−0.0852493	+	0.592922i
$125$	−9.22970	+	6.30973i	−0.825529	+	0.564359i
$126$	3.28507	+	0.964583i	0.292657	+	0.0859319i
$127$	0.858846	−	2.92496i	0.0762103	−	0.259548i	−0.912571	−	0.408918i	$-0.865906\pi$
$127$	0.858846	−	2.92496i	0.0762103	−	0.259548i	0.988781	+	0.149370i	$0.0477244\pi$
$128$	−0.909632	+	0.415415i	−0.0804009	+	0.0367178i
$129$	0.0912602	−	0.634729i	0.00803502	−	0.0558848i
$130$	0.408762	−	3.04799i	0.0358508	−	0.267326i
$131$	2.74657	−	6.01415i	0.239969	−	0.525459i	−0.750879	−	0.660440i	$-0.770370\pi$
$131$	2.74657	−	6.01415i	0.239969	−	0.525459i	0.990848	+	0.134981i	$0.0430972\pi$
$132$	−0.192348	+	0.299299i	−0.0167417	+	0.0260506i
$133$	1.04838	−	0.150734i	0.0909059	−	0.0130703i
$134$	−6.50972	+	4.18355i	−0.562355	+	0.361403i
$135$	−0.337326	+	1.19049i	−0.0290324	+	0.102461i
$136$	−0.821820	+	0.241308i	−0.0704705	+	0.0206920i
$137$			12.2743i			1.04866i	0.851515	+	0.524330i	$0.175684\pi$
$137$			12.2743i			1.04866i	−0.851515	+	0.524330i	$0.824316\pi$
$138$	0.221397	−	0.383634i	0.0188466	−	0.0326571i
$139$	16.1706			1.37157			0.685785	−	0.727804i	$-0.259459\pi$
$139$	16.1706			1.37157			0.685785	+	0.727804i	$0.259459\pi$
$140$	1.94992	+	1.65749i	0.164798	+	0.140084i
$141$	−0.440091	−	0.507892i	−0.0370624	−	0.0427723i
$142$	1.94654	+	3.02888i	0.163350	+	0.254178i
$143$	−5.24393	+	0.753963i	−0.438519	+	0.0630495i
$144$	2.51658	+	1.61731i	0.209715	+	0.134776i
$145$	0.00189144	+	0.0123242i	0.000157075	+	0.00102347i
$146$	−9.26088	+	10.6876i	−0.766436	+	0.884514i
$147$	−0.520180	−	0.0747906i	−0.0429037	−	0.00616863i
$148$	0.982048	−	0.448486i	0.0807239	−	0.0368654i
$149$	−14.1219	−	4.14655i	−1.15691	−	0.339699i	−0.353678	−	0.935367i	$-0.615069\pi$
$149$	−14.1219	−	4.14655i	−1.15691	−	0.339699i	−0.803230	+	0.595668i	$0.796887\pi$
$150$	−0.295734	+	0.354673i	−0.0241466	+	0.0289590i
$151$	1.73764	+	3.80489i	0.141407	+	0.309638i	0.967064	−	0.254535i	$-0.0819224\pi$
$151$	1.73764	+	3.80489i	0.141407	+	0.309638i	−0.825657	+	0.564173i	$0.809195\pi$
$152$	0.916009	+	0.131702i	0.0742982	+	0.0106825i
$153$	1.93641	+	1.67791i	0.156550	+	0.135651i
$154$	1.83148	−	4.01037i	0.147585	−	0.323165i
$155$	14.9148	−	0.141487i	1.19798	−	0.0113645i
$156$	−0.0180770	−	0.125728i	−0.00144731	−	0.0100663i
$157$	−1.41025	−	2.19439i	−0.112550	−	0.175132i	0.780409	−	0.625270i	$-0.215011\pi$
$157$	−1.41025	−	2.19439i	−0.112550	−	0.175132i	−0.892959	+	0.450138i	$0.851375\pi$
$158$	1.59965	−	1.38610i	0.127261	−	0.110273i
$159$	−0.0407027	+	0.0119514i	−0.00322794	+	0.000947807i
$160$	1.22670	+	1.86955i	0.0969791	+	0.147801i
$161$	−2.03906	+	5.09605i	−0.160701	+	0.401625i
$162$		−	8.92330i		−	0.701081i
$163$	0.865221	+	2.94667i	0.0677693	+	0.230801i	0.986413	−	0.164287i	$-0.0525323\pi$
$163$	0.865221	+	2.94667i	0.0677693	+	0.230801i	−0.918643	+	0.395088i	$0.870714\pi$
$164$	3.23460	+	3.73293i	0.252580	+	0.291493i
$165$	0.726752	+	0.323600i	0.0565776	+	0.0251923i
$166$	−1.46416	−	10.1835i	−0.113641	−	0.790391i
$167$	7.41220	−	11.5336i	0.573573	−	0.892497i	−0.426354	−	0.904556i	$-0.640202\pi$
$167$	7.41220	−	11.5336i	0.573573	−	0.892497i	0.999927	+	0.0120592i	$0.00383865\pi$
$168$	0.0961524	+	0.0439113i	0.00741832	+	0.00338783i
$169$	−7.27455	+	8.39527i	−0.559581	+	0.645790i
$170$	0.812104	+	1.73453i	0.0622855	+	0.133032i
$171$	−1.15003	−	2.51822i	−0.0879451	−	0.192573i
$172$	−1.95610	+	6.66188i	−0.149152	+	0.507963i
$173$	4.49878	−	15.3214i	0.342036	−	1.16487i	−0.591477	−	0.806322i	$-0.701455\pi$
$173$	4.49878	−	15.3214i	0.342036	−	1.16487i	0.933513	−	0.358545i	$-0.116727\pi$
$174$	0.000213937	0	0.000468457i	1.62185e−5	0	3.55137e-5i
$175$	3.00195	−	4.87192i	0.226926	−	0.368283i
$176$	2.52261	−	2.91125i	0.190149	−	0.219444i
$177$	0.181020	+	0.0826691i	0.0136063	+	0.00621379i
$178$	3.85996	−	6.00622i	0.289316	−	0.450185i
$179$	−3.39154	−	23.5887i	−0.253496	−	1.76310i	−0.576876	−	0.816831i	$-0.695729\pi$
$179$	−3.39154	−	23.5887i	−0.253496	−	1.76310i	0.323381	−	0.946269i	$-0.395181\pi$
$180$	2.72092	−	6.11073i	0.202806	−	0.455467i
$181$	−1.14197	−	1.31790i	−0.0848820	−	0.0979591i	0.711720	−	0.702464i	$-0.247917\pi$
$181$	−1.14197	−	1.31790i	−0.0848820	−	0.0979591i	−0.796602	+	0.604504i	$0.793371\pi$
$182$	0.443459	+	1.51028i	0.0328714	+	0.111950i
$183$		−	0.893324i		−	0.0660364i
$184$	−2.96389	+	3.77032i	−0.218501	+	0.277952i
$185$	−1.32436	−	2.01838i	−0.0973687	−	0.148395i
$186$	0.591112	−	0.173566i	0.0433424	−	0.0127265i
$187$	2.49353	−	2.16065i	0.182345	−	0.158003i
$188$	3.93393	+	6.12131i	0.286911	+	0.446442i
$189$	−0.0901318	−	0.626880i	−0.00655612	−	0.0455988i
$190$	−0.0196295	−	2.06923i	−0.00142407	−	0.150118i
$191$	−6.27677	+	13.7442i	−0.454171	+	0.994496i	0.534607	+	0.845101i	$0.320460\pi$
$191$	−6.27677	+	13.7442i	−0.454171	+	0.994496i	−0.988778	+	0.149395i	$0.952267\pi$
$192$	0.0697998	+	0.0604819i	0.00503737	+	0.00436491i
$193$	23.5131	+	3.38067i	1.69251	+	0.243346i	0.920073	−	0.391747i	$-0.128129\pi$
$193$	23.5131	+	3.38067i	1.69251	+	0.243346i	0.772435	+	0.635093i	$0.219038\pi$
$194$	−7.99770	−	17.5125i	−0.574202	−	1.25733i
$195$	−0.271751	+	0.0826013i	−0.0194605	+	0.00591520i
$196$	5.45962	+	1.60309i	0.389973	+	0.114506i
$197$	8.75402	−	3.99783i	0.623698	−	0.284834i	−0.0783906	−	0.996923i	$-0.524978\pi$
$197$	8.75402	−	3.99783i	0.623698	−	0.284834i	0.702089	+	0.712089i	$0.252251\pi$
$198$	−11.4062	−	1.63997i	−0.810607	−	0.116548i
$199$	−3.28145	+	3.78700i	−0.232616	+	0.268453i	−0.860042	−	0.510223i	$-0.829563\pi$
$199$	−3.28145	+	3.78700i	−0.232616	+	0.268453i	0.627426	+	0.778676i	$0.284108\pi$
$200$	3.71595	−	3.34540i	0.262757	−	0.236556i
$201$	0.601228	+	0.386386i	0.0424073	+	0.0272535i
$202$	−10.1673	+	1.46183i	−0.715367	+	0.102854i
$203$	−0.00345028	−	0.00536874i	−0.000242162	−	0.000376812i
$204$	0.0518037	+	0.0597846i	0.00362698	+	0.00418576i
$205$	7.15329	−	8.41532i	0.499607	−	0.587752i
$206$	−14.8965			−1.03789
$207$	14.2819	+	1.36110i	0.992659	+	0.0946033i
$208$			1.37530i			0.0953601i
$209$	−3.42047	+	1.00434i	−0.236599	+	0.0694717i
$210$	0.0644368	−	0.227410i	0.00444656	−	0.0156928i
$211$	−18.3831	+	11.8141i	−1.26555	+	0.813317i	−0.989033	−	0.147693i	$-0.952815\pi$
$211$	−18.3831	+	11.8141i	−1.26555	+	0.813317i	−0.276513	+	0.961010i	$0.589179\pi$
$212$	0.454634	−	0.0653665i	0.0312244	−	0.00448939i
$213$	0.179779	−	0.279742i	0.0123183	−	0.0191676i
$214$	7.43321	−	16.2765i	0.508124	−	1.11264i
$215$	15.3875	+	2.06361i	1.04942	+	0.140737i
$216$	0.0787517	−	0.547730i	0.00535838	−	0.0372683i
$217$	−6.94440	+	3.17140i	−0.471417	+	0.215289i
$218$	−3.85373	+	13.1246i	−0.261007	+	0.888909i
$219$	1.25320	+	0.367974i	0.0846836	+	0.0248654i
$220$	−7.29010	−	4.58793i	−0.491498	−	0.309318i
$221$	−0.167642	+	1.16598i	−0.0112768	+	0.0784322i
$222$	−0.0753566	−	0.0652969i	−0.00505761	−	0.00438244i
$223$	−18.5392	−	8.46657i	−1.24148	−	0.566964i	−0.317081	−	0.948398i	$-0.602703\pi$
$223$	−18.5392	−	8.46657i	−1.24148	−	0.566964i	−0.924396	+	0.381435i	$0.875430\pi$
$224$	−0.962819	−	0.618766i	−0.0643311	−	0.0413431i
$225$	−14.4288	−	3.94095i	−0.961922	−	0.262730i
$226$	−12.9974	+	8.35295i	−0.864577	+	0.555630i
$227$	−2.24627	+	1.94640i	−0.149090	+	0.129187i	−0.726212	−	0.687471i	$-0.758721\pi$
$227$	−2.24627	+	1.94640i	−0.149090	+	0.129187i	0.577122	+	0.816658i	$0.304176\pi$
$228$	−0.0240800	−	0.0820090i	−0.00159474	−	0.00543118i
$229$	22.4667			1.48464			0.742320	−	0.670046i	$-0.233726\pi$
$229$	22.4667			1.48464			0.742320	+	0.670046i	$0.233726\pi$
$230$	9.33850	+	5.27185i	0.615763	+	0.347615i
$231$	−0.407189			−0.0267910
$232$	−0.00157096	−	0.00535019i	−0.000103138	−	0.000351257i
$233$	10.5253	−	9.12026i	0.689538	−	0.597488i	−0.237979	−	0.971270i	$-0.576485\pi$
$233$	10.5253	−	9.12026i	0.689538	−	0.597488i	0.927516	+	0.373783i	$0.121939\pi$
$234$	3.46107	−	2.22429i	0.226257	−	0.145407i
$235$	12.1948	−	10.7711i	0.795504	−	0.702630i
$236$	−1.81264	−	1.16491i	−0.117993	−	0.0758293i
$237$	−0.177824	−	0.0812093i	−0.0115509	−	0.00527511i
$238$	−0.740851	−	0.641951i	−0.0480222	−	0.0416115i
$239$	1.65603	−	11.5180i	0.107120	−	0.745036i	−0.863488	−	0.504370i	$-0.831725\pi$
$239$	1.65603	−	11.5180i	0.107120	−	0.745036i	0.970608	−	0.240666i	$-0.0773660\pi$
$240$	0.110000	−	0.174787i	0.00710046	−	0.0112824i
$241$	−17.8128	−	5.23031i	−1.14742	−	0.336914i	−0.347890	−	0.937535i	$-0.613102\pi$
$241$	−17.8128	−	5.23031i	−1.14742	−	0.336914i	−0.799534	+	0.600621i	$0.794920\pi$
$242$	−1.08155	+	3.68342i	−0.0695247	+	0.236779i
$243$	−2.25974	+	1.03199i	−0.144962	+	0.0662020i
$244$	−1.37652	+	9.57391i	−0.0881227	+	0.612907i
$245$	1.69119	−	12.6106i	0.108046	−	0.805660i
$246$	0.189509	−	0.414968i	0.0120827	−	0.0264574i
$247$	0.688098	−	1.07070i	0.0437826	−	0.0681271i
$248$	−6.60250	+	0.949296i	−0.419259	+	0.0602803i
$249$	−0.799361	+	0.513718i	−0.0506574	+	0.0325555i
$250$	−8.65445	−	7.07817i	−0.547355	−	0.447663i
$251$	−6.14302	+	1.80375i	−0.387744	+	0.113852i	−0.469793	−	0.882776i	$-0.655672\pi$
$251$	−6.14302	+	1.80375i	−0.387744	+	0.113852i	0.0820495	+	0.996628i	$0.473853\pi$
$252$			3.42375i			0.215676i
$253$	4.35215	−	17.9542i	0.273617	−	1.12877i
$254$	3.04844			0.191276
$255$	0.114563	−	0.134775i	0.00717423	−	0.00843996i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	6.44307	+	10.0256i	0.401908	+	0.625380i	0.981935	−	0.189216i	$-0.0605947\pi$
$257$	6.44307	+	10.0256i	0.401908	+	0.625380i	−0.580028	+	0.814597i	$0.696958\pi$
$258$	0.634729	−	0.0912602i	0.0395165	−	0.00568161i
$259$	1.03947	+	0.668027i	0.0645895	+	0.0415092i
$260$	3.03968	−	0.466512i	0.188513	−	0.0289319i
$261$	−0.0109235	+	0.0126064i	−0.000676147	+	0.000780315i
$262$	6.54433	+	0.940933i	0.404310	+	0.0581310i
$263$	−8.46647	+	3.86651i	−0.522065	+	0.238419i	−0.658975	−	0.752164i	$-0.729010\pi$
$263$	−8.46647	+	3.86651i	−0.522065	+	0.238419i	0.136911	+	0.990583i	$0.456283\pi$
$264$	−0.341365	−	0.100234i	−0.0210096	−	0.00616897i
$265$	−0.298687	−	0.982655i	−0.0183482	−	0.0603640i
$266$	0.439990	+	0.963444i	0.0269775	+	0.0590726i
$267$	−0.652691	−	0.0938428i	−0.0399440	−	0.00574309i
$268$	−5.84808	−	5.06739i	−0.357229	−	0.309540i
$269$	12.2184	−	26.7546i	0.744970	−	1.63126i	−0.0302316	−	0.999543i	$-0.509624\pi$
$269$	12.2184	−	26.7546i	0.744970	−	1.63126i	0.775202	−	0.631714i	$-0.217648\pi$
$270$	−1.23730	+	0.0117375i	−0.0752997	+	0.000714321i
$271$	−2.18178	−	15.1746i	−0.132534	−	0.921793i	−0.942236	−	0.334951i	$-0.891280\pi$
$271$	−2.18178	−	15.1746i	−0.132534	−	0.921793i	0.809702	−	0.586842i	$-0.199629\pi$
$272$	−0.463067	−	0.720547i	−0.0280776	−	0.0436895i
$273$	0.109868	−	0.0952011i	0.00664951	−	0.00576183i
$274$	−11.7771	+	3.45806i	−0.711479	+	0.208909i
$275$	−7.66735	+	17.6688i	−0.462359	+	1.06547i
$276$	0.430469	+	0.104347i	0.0259112	+	0.00628094i
$277$		−	18.2644i		−	1.09740i	−0.836018	−	0.548702i	$-0.815122\pi$
$277$		−	18.2644i		−	1.09740i	0.836018	−	0.548702i	$-0.184878\pi$
$278$	4.55578	+	15.5156i	0.273237	+	0.930561i
$279$	13.0673	+	15.0804i	0.782317	+	0.902842i
$280$	−1.04100	+	2.33790i	−0.0622114	+	0.139716i
$281$	3.16822	+	22.0354i	0.189000	+	1.31452i	0.834604	+	0.550851i	$0.185697\pi$
$281$	3.16822	+	22.0354i	0.189000	+	1.31452i	−0.645604	+	0.763673i	$0.723394\pi$
$282$	0.363331	−	0.565354i	0.0216361	−	0.0336664i
$283$	−17.6388	−	8.05536i	−1.04852	−	0.478842i	−0.184778	−	0.982780i	$-0.559156\pi$
$283$	−17.6388	−	8.05536i	−1.04852	−	0.478842i	−0.863739	+	0.503939i	$0.831884\pi$
$284$	−2.35778	+	2.72102i	−0.139909	+	0.161463i
$285$	−0.173087	+	0.0810394i	−0.0102528	+	0.00480036i
$286$	−2.20081	−	4.81910i	−0.130136	−	0.284959i
$287$	−1.59267	+	5.42415i	−0.0940126	+	0.320178i
$288$	−0.842794	+	2.87029i	−0.0496621	+	0.169134i
$289$	6.75730	+	14.7964i	0.397488	+	0.870378i
$290$	−0.0112921	+	0.00528694i	−0.000663093	+	0.000310460i
$291$	−1.16442	+	1.34381i	−0.0682593	+	0.0787755i
$292$	−12.8638	−	5.87470i	−0.752796	−	0.343791i
$293$	6.21266	−	9.66709i	0.362948	−	0.564757i	−0.610972	−	0.791652i	$-0.709221\pi$
$293$	6.21266	−	9.66709i	0.362948	−	0.564757i	0.973919	+	0.226895i	$0.0728574\pi$
$294$	−0.0747906	−	0.520180i	−0.00436188	−	0.0303375i
$295$	−1.95982	+	4.40142i	−0.114105	+	0.256261i
$296$	0.706995	+	0.815915i	0.0410932	+	0.0474241i
$297$	0.600549	+	2.04528i	0.0348474	+	0.118679i
$298$		−	14.7180i		−	0.852594i
$299$	3.02341	+	5.86196i	0.174849	+	0.339006i
$300$	−0.423625	−	0.183832i	−0.0244580	−	0.0106135i
$301$	−7.62456	+	2.23877i	−0.439472	+	0.129041i
$302$	−3.16122	+	2.73921i	−0.181908	+	0.157624i
$303$	0.512901	+	0.798089i	0.0294654	+	0.0458490i
$304$	0.131702	+	0.916009i	0.00755364	+	0.0525367i
$305$	21.6271	−	0.205162i	1.23836	−	0.0117476i
$306$	−1.06439	+	2.33070i	−0.0608473	+	0.133237i
$307$	5.79883	+	5.02472i	0.330957	+	0.286776i	0.804448	−	0.594023i	$-0.202461\pi$
$307$	5.79883	+	5.02472i	0.330957	+	0.286776i	−0.473491	+	0.880798i	$0.657007\pi$
$308$	4.36391	+	0.627436i	0.248657	+	0.0357515i
$309$	0.571535	+	1.25149i	0.0325135	+	0.0711946i
$310$	4.33773	+	14.2708i	0.246367	+	0.810525i
$311$	0.619013	+	0.181759i	0.0351010	+	0.0103066i	0.299236	−	0.954179i	$-0.403268\pi$
$311$	0.619013	+	0.181759i	0.0351010	+	0.0103066i	−0.264135	+	0.964486i	$0.585086\pi$
$312$	0.115542	−	0.0527664i	0.00654129	−	0.00298731i
$313$	3.65395	+	0.525358i	0.206533	+	0.0296950i	0.244805	−	0.969572i	$-0.421276\pi$
$313$	3.65395	+	0.525358i	0.206533	+	0.0296950i	−0.0382716	+	0.999267i	$0.512185\pi$
$314$	1.70819	−	1.97136i	0.0963989	−	0.111250i
$315$	7.56715	−	1.16136i	0.426360	−	0.0654352i
$316$	1.78063	+	1.14434i	0.100168	+	0.0643743i
$317$	−18.2009	+	2.61689i	−1.02226	+	0.146979i	−0.633004	−	0.774148i	$-0.718178\pi$
$317$	−18.2009	+	2.61689i	−1.02226	+	0.146979i	−0.389260	+	0.921128i	$0.627269\pi$
$318$	−0.0229346	−	0.0356869i	−0.00128611	−	0.00200122i
$319$	0.0140662	+	0.0162333i	0.000787558	+	0.000908890i
$320$	−1.44822	+	1.70372i	−0.0809578	+	0.0952409i
$321$	−1.65261			−0.0922398
$322$	−5.46410	−	0.520744i	−0.304502	−	0.0290200i
$323$			0.792644i			0.0441039i
$324$	8.56185	−	2.51398i	0.475658	−	0.139666i
$325$	−2.06216	−	6.56003i	−0.114388	−	0.363885i
$326$	−2.58355	+	1.66035i	−0.143090	+	0.0919581i
$327$	1.25048	−	0.179792i	0.0691518	−	0.00994252i
$328$	−2.67043	+	4.15527i	−0.147450	+	0.229436i
$329$	−3.45953	+	7.57532i	−0.190730	+	0.417641i
$330$	−0.105743	+	0.788482i	−0.00582094	+	0.0434045i
$331$	−4.58706	+	31.9037i	−0.252128	+	1.75359i	0.333262	+	0.942834i	$0.391851\pi$
$331$	−4.58706	+	31.9037i	−0.252128	+	1.75359i	−0.585390	+	0.810752i	$0.699058\pi$
$332$	9.35847	−	4.27387i	0.513613	−	0.234559i
$333$	0.909890	−	3.09880i	0.0498617	−	0.169813i
$334$	13.1547	+	3.86256i	0.719792	+	0.211350i
$335$	−9.21619	+	14.6443i	−0.503534	+	0.800102i
$336$	−0.0150434	+	0.104629i	−0.000820682	+	0.00570797i
$337$	7.50022	+	6.49898i	0.408563	+	0.354022i	0.834765	−	0.550606i	$-0.185603\pi$
$337$	7.50022	+	6.49898i	0.408563	+	0.354022i	−0.426202	+	0.904628i	$0.640149\pi$
$338$	−10.1047	−	4.61465i	−0.549622	−	0.251004i
$339$	1.20042	+	0.771465i	0.0651981	+	0.0419002i
$340$	−1.43547	+	1.26788i	−0.0778492	+	0.0687605i
$341$	21.6162	−	13.8919i	1.17058	−	0.752288i
$342$	2.09221	−	1.81291i	0.113134	−	0.0980310i
$343$	4.09186	+	13.9356i	0.220939	+	0.752451i
$344$	−6.94312			−0.374348
$345$	0.0846084	−	0.986813i	0.00455516	−	0.0531282i
$346$	15.9683			0.858459
$347$	0.511743	+	1.74284i	0.0274718	+	0.0935604i	0.972088	−	0.234617i	$-0.0753837\pi$
$347$	0.511743	+	1.74284i	0.0274718	+	0.0935604i	−0.944616	+	0.328178i	$0.893566\pi$
$348$	−0.000389208	0	0.000337251i	−2.08638e−5	0	1.80786e-5i
$349$	−7.67643	+	4.93334i	−0.410910	+	0.264076i	−0.729724	−	0.683741i	$-0.760352\pi$
$349$	−7.67643	+	4.93334i	−0.410910	+	0.264076i	0.318815	+	0.947817i	$0.396715\pi$
$350$	5.52032	+	1.50777i	0.295074	+	0.0805936i
$351$	−0.640229	−	0.411450i	−0.0341729	−	0.0219616i
$352$	3.50402	+	1.60023i	0.186765	+	0.0852927i
$353$	11.6061	+	10.0567i	0.617730	+	0.535266i	0.906540	−	0.422121i	$-0.138714\pi$
$353$	11.6061	+	10.0567i	0.617730	+	0.535266i	−0.288810	+	0.957386i	$0.593260\pi$
$354$	−0.0283212	+	0.196978i	−0.00150525	+	0.0104693i
$355$	6.81376	+	4.28815i	0.361637	+	0.227592i
$356$	6.85040	+	2.01146i	0.363071	+	0.106607i
$357$	−0.0255074	+	0.0868703i	−0.00135000	+	0.00459766i
$358$	21.6777	−	9.89986i	1.14570	−	0.523224i
$359$	−0.348942	+	2.42695i	−0.0184165	+	0.128089i	−0.996956	−	0.0779719i	$-0.975156\pi$
$359$	−0.348942	+	2.42695i	−0.0184165	+	0.128089i	0.978539	+	0.206061i	$0.0660646\pi$
$360$	6.62978	+	0.889113i	0.349420	+	0.0468604i
$361$	−7.53712	+	16.5040i	−0.396690	+	0.868631i
$362$	0.942790	−	1.46701i	0.0495519	−	0.0771043i
$363$	0.350948	−	0.0504587i	0.0184200	−	0.00264840i
$364$	−1.32417	+	0.850992i	−0.0694053	+	0.0446041i
$365$	−8.62071	+	30.4242i	−0.451229	+	1.59247i
$366$	0.857138	−	0.251678i	0.0448033	−	0.0131554i
$367$			22.7391i			1.18697i	0.804845	+	0.593485i	$0.202248\pi$
$367$			22.7391i			1.18697i	−0.804845	+	0.593485i	$0.797752\pi$
$368$	−4.45262	−	1.78161i	−0.232109	−	0.0928729i
$369$	14.7760			0.769208
$370$	1.56351	−	1.83936i	0.0812830	−	0.0956236i
$371$	0.344248	+	0.397284i	0.0178725	+	0.0206259i
$372$	0.333071	+	0.518268i	0.0172689	+	0.0268710i
$373$	−34.5081	+	4.96151i	−1.78676	+	0.256897i	−0.954654	−	0.297717i	$-0.903775\pi$
$373$	−34.5081	+	4.96151i	−1.78676	+	0.256897i	−0.832107	+	0.554615i	$0.812866\pi$
$374$	2.77564	+	1.78380i	0.143525	+	0.0922379i
$375$	−0.262607	+	0.998648i	−0.0135610	+	0.0515700i
$376$	−4.76504	+	5.49915i	−0.245738	+	0.283597i
$377$	−0.00759072	−	0.00109138i	−0.000390942	−	5.62090e-5i
$378$	0.576094	−	0.263093i	0.0296311	−	0.0135321i
$379$	−30.1488	−	8.85248i	−1.54864	−	0.454721i	−0.607945	−	0.793979i	$-0.708006\pi$
$379$	−30.1488	−	8.85248i	−1.54864	−	0.454721i	−0.940693	+	0.339258i	$0.889824\pi$
$380$	1.97988	−	0.601803i	0.101566	−	0.0308719i
$381$	−0.116960	−	0.256107i	−0.00599204	−	0.0131207i
$382$	−14.9558	−	2.15032i	−0.765207	−	0.110020i
$383$	−25.2467	−	21.8764i	−1.29004	−	1.11783i	−0.986280	−	0.165083i	$-0.947211\pi$
$383$	−25.2467	−	21.8764i	−1.29004	−	1.11783i	−0.303765	−	0.952747i	$-0.598244\pi$
$384$	−0.0383671	+	0.0840122i	−0.00195791	+	0.00428723i
$385$	−0.0935158	−	9.85791i	−0.00476600	−	0.502405i
$386$	3.38067	+	23.5131i	0.172072	+	1.19678i
$387$	11.2292	+	17.4730i	0.570812	+	0.888200i
$388$	14.5499	−	12.6076i	0.738661	−	0.640053i
$389$	−7.19341	+	2.11218i	−0.364720	+	0.107092i	−0.458957	−	0.888458i	$-0.651777\pi$
$389$	−7.19341	+	2.11218i	−0.364720	+	0.107092i	0.0942372	+	0.995550i	$0.469959\pi$
$390$	−0.155816	−	0.237472i	−0.00789007	−	0.0120248i
$391$	−3.55775	−	2.05320i	−0.179923	−	0.103835i
$392$			5.69011i			0.287394i
$393$	−0.172037	−	0.585905i	−0.00867813	−	0.0295550i
$394$	6.30218	+	7.27311i	0.317499	+	0.366414i
$395$	1.92521	−	4.32370i	0.0968679	−	0.217549i
$396$	−1.63997	−	11.4062i	−0.0824116	−	0.573185i
$397$	14.2718	−	22.2073i	0.716279	−	1.11455i	−0.272060	−	0.962280i	$-0.587705\pi$
$397$	14.2718	−	22.2073i	0.716279	−	1.11455i	0.988339	−	0.152271i	$-0.0486588\pi$
$398$	−4.55809	−	2.08161i	−0.228476	−	0.104342i
$399$	0.0640599	−	0.0739291i	0.00320701	−	0.00370108i
$400$	4.25679	+	2.62292i	0.212840	+	0.131146i
$401$	3.29610	+	7.21746i	0.164600	+	0.360423i	0.973902	−	0.226970i	$-0.0728818\pi$
$401$	3.29610	+	7.21746i	0.164600	+	0.360423i	−0.809302	+	0.587392i	$0.800155\pi$
$402$	−0.201349	+	0.685731i	−0.0100424	+	0.0342012i
$403$	−2.58456	+	8.80221i	−0.128746	+	0.438469i
$404$	−4.26707	−	9.34359i	−0.212295	−	0.464861i
$405$	−8.46062	−	18.0705i	−0.420412	−	0.897933i
$406$	0.00417921	−	0.00482307i	0.000207411	−	0.000239365i
$407$	−3.78298	−	1.72763i	−0.187515	−	0.0856354i
$408$	−0.0427682	+	0.0665485i	−0.00211734	+	0.00329464i
$409$	−1.73550	−	12.0707i	−0.0858150	−	0.596856i	−0.986670	−	0.162736i	$-0.947968\pi$
$409$	−1.73550	−	12.0707i	−0.0858150	−	0.596856i	0.900855	−	0.434121i	$-0.142941\pi$
$410$	10.0898	+	4.49266i	0.498298	+	0.221877i
$411$	0.742371	+	0.856741i	0.0366184	+	0.0422599i
$412$	−4.19683	−	14.2931i	−0.206763	−	0.704169i
$413$		−	2.46605i		−	0.121347i
$414$	2.71770	+	14.0868i	0.133568	+	0.692330i
$415$	−12.6205	−	19.2343i	−0.619517	−	0.944174i
$416$	−1.31959	+	0.387468i	−0.0646984	+	0.0189972i
$417$	1.12870	−	0.978028i	0.0552729	−	0.0478942i
$418$	−1.92732	−	2.99896i	−0.0942681	−	0.146684i
$419$	−2.14712	−	14.9335i	−0.104894	−	0.729550i	−0.972602	−	0.232477i	$-0.925317\pi$
$419$	−2.14712	−	14.9335i	−0.104894	−	0.729550i	0.867708	−	0.497074i	$-0.165592\pi$
$420$	0.236352	−	0.00224213i	0.0115328	−	0.000109405i
$421$	8.54469	−	18.7103i	0.416443	−	0.911883i	−0.578892	−	0.815404i	$-0.696515\pi$
$421$	8.54469	−	18.7103i	0.416443	−	0.911883i	0.995335	−	0.0964786i	$-0.0307579\pi$
$422$	−16.5147	−	14.3101i	−0.803923	−	0.696603i
$423$	21.5456	+	3.09779i	1.04758	+	0.150620i
$424$	0.190804	+	0.417802i	0.00926626	+	0.0202903i
$425$	3.28918	+	2.74259i	0.159549	+	0.133035i
$426$	0.319060	+	0.0936846i	0.0154585	+	0.00453903i
$427$	−10.0697	+	4.59867i	−0.487306	+	0.222545i
$428$	17.7113	+	2.54650i	0.856109	+	0.123090i
$429$	−0.320424	+	0.369789i	−0.0154702	+	0.0178536i
$430$	2.35515	+	15.3456i	0.113576	+	0.740032i
$431$	−12.7650	−	8.20355i	−0.614867	−	0.395151i	0.195812	−	0.980641i	$-0.437266\pi$
$431$	−12.7650	−	8.20355i	−0.614867	−	0.395151i	−0.810679	+	0.585490i	$0.800902\pi$
$432$	0.547730	−	0.0787517i	0.0263527	−	0.00378894i
$433$	−1.83241	−	2.85128i	−0.0880599	−	0.137024i	0.794429	−	0.607357i	$-0.207770\pi$
$433$	−1.83241	−	2.85128i	−0.0880599	−	0.137024i	−0.882489	+	0.470333i	$0.844134\pi$
$434$	−4.99940	−	5.76962i	−0.239979	−	0.276951i
$435$	0.000877411	0	0.000745827i	4.20686e−5	0	3.57596e-5i
$436$	−13.6787			−0.655089
$437$	2.57507	+	3.61478i	0.123182	+	0.172918i
$438$			1.30611i			0.0624084i
$439$	−15.2146	+	4.46741i	−0.726154	+	0.213218i	−0.623860	−	0.781536i	$-0.714436\pi$
$439$	−15.2146	+	4.46741i	−0.726154	+	0.213218i	−0.102294	+	0.994754i	$0.532618\pi$
$440$	2.34823	−	8.28737i	0.111948	−	0.395085i
$441$	14.3196	−	9.20267i	0.681887	−	0.438222i
$442$	−1.16598	+	0.167642i	−0.0554599	+	0.00797394i
$443$	−16.5079	+	25.6868i	−0.784314	+	1.22042i	0.186940	+	0.982371i	$0.440143\pi$
$443$	−16.5079	+	25.6868i	−0.784314	+	1.22042i	−0.971254	+	0.238045i	$0.923493\pi$
$444$	0.0414215	−	0.0907004i	0.00196578	−	0.00430445i
$445$	2.12201	−	15.8230i	0.100593	−	0.750082i
$446$	2.90052	−	20.1735i	0.137344	−	0.955245i
$447$	−1.23650	+	0.564688i	−0.0584842	+	0.0267088i
$448$	0.322444	−	1.09815i	0.0152341	−	0.0518825i
$449$	−6.20596	−	1.82224i	−0.292878	−	0.0859966i	0.131993	−	0.991251i	$-0.457862\pi$
$449$	−6.20596	−	1.82224i	−0.292878	−	0.0859966i	−0.424871	+	0.905254i	$0.639680\pi$
$450$	−0.283756	−	14.9547i	−0.0133764	−	0.704969i
$451$	2.70784	−	18.8335i	0.127507	−	0.886833i
$452$	−11.6764	−	10.1177i	−0.549212	−	0.475895i
$453$	0.351414	+	0.160485i	0.0165109	+	0.00754026i
$454$	−2.50041	−	1.60691i	−0.117350	−	0.0754162i
$455$	2.33002	+	2.63800i	0.109233	+	0.123671i
$456$	0.0719029	−	0.0462092i	0.00336716	−	0.00216394i
$457$	−15.0484	+	13.0395i	−0.703935	+	0.609963i	−0.931475	−	0.363806i	$-0.881477\pi$
$457$	−15.0484	+	13.0395i	−0.703935	+	0.609963i	0.227540	+	0.973769i	$0.426932\pi$
$458$	6.32959	+	21.5566i	0.295762	+	1.00727i
$459$	0.473964			0.0221227
$460$	−2.42734	+	10.4455i	−0.113175	+	0.487023i
$461$	−13.0285			−0.606796			−0.303398	−	0.952864i	$-0.598121\pi$
$461$	−13.0285			−0.606796			−0.303398	+	0.952864i	$0.598121\pi$
$462$	−0.114718	−	0.390695i	−0.00533718	−	0.0181768i
$463$	−14.3298	+	12.4168i	−0.665962	+	0.577059i	−0.920853	−	0.389911i	$-0.872506\pi$
$463$	−14.3298	+	12.4168i	−0.665962	+	0.577059i	0.254891	+	0.966970i	$0.417960\pi$
$464$	0.00469088	−	0.00301465i	0.000217769	−	0.000139952i
$465$	1.03249	−	0.911950i	0.0478807	−	0.0422907i
$466$	11.7162	+	7.52951i	0.542740	+	0.348798i
$467$	29.8041	+	13.6111i	1.37917	+	0.629846i	0.960497	−	0.278291i	$-0.0897681\pi$
$467$	29.8041	+	13.6111i	1.37917	+	0.629846i	0.418673	+	0.908137i	$0.362495\pi$
$468$	3.10929	+	2.69421i	0.143727	+	0.124540i
$469$	1.26039	−	8.76618i	0.0581993	−	0.404785i
$470$	13.7705	+	8.66629i	0.635185	+	0.399746i
$471$	−0.231156	−	0.0678737i	−0.0106511	−	0.00312745i
$472$	0.607046	−	2.06741i	0.0279415	−	0.0951602i
$473$	24.3289	−	11.1106i	1.11864	−	0.510867i
$474$	0.0278211	−	0.193500i	0.00127786	−	0.00888774i
$475$	−2.00169	−	4.17177i	−0.0918437	−	0.191414i
$476$	0.407226	−	0.891700i	0.0186652	−	0.0408710i
$477$	0.742846	−	1.15589i	0.0340126	−	0.0529246i
$478$	11.5180	−	1.65603i	0.526820	−	0.0757453i
$479$	17.9599	−	11.5421i	0.820608	−	0.527373i	−0.0616728	−	0.998096i	$-0.519644\pi$
$479$	17.9599	−	11.5421i	0.820608	−	0.527373i	0.882281	+	0.470724i	$0.156007\pi$
$480$	0.198697	+	0.0563010i	0.00906925	+	0.00256978i
$481$	1.42465	−	0.418314i	0.0649583	−	0.0190735i
$482$		−	18.5648i		−	0.845604i
$483$	0.165893	+	0.479030i	0.00754837	+	0.0217966i
$484$	−3.83893			−0.174497
$485$	−32.8006	−	27.8815i	−1.48940	−	1.26604i
$486$	−1.62682	−	1.87746i	−0.0737943	−	0.0851631i
$487$	11.3067	+	17.5936i	0.512357	+	0.797243i	0.996995	−	0.0774722i	$-0.0246849\pi$
$487$	11.3067	+	17.5936i	0.512357	+	0.797243i	−0.484638	+	0.874715i	$0.661049\pi$
$488$	−9.57391	+	1.37652i	−0.433390	+	0.0623121i
$489$	0.238613	+	0.153347i	0.0107904	+	0.00693459i
$490$	12.5762	−	1.93012i	0.568136	−	0.0871940i
$491$	27.0112	−	31.1726i	1.21900	−	1.40680i	0.333118	−	0.942885i	$-0.391899\pi$
$491$	27.0112	−	31.1726i	1.21900	−	1.40680i	0.885881	−	0.463913i	$-0.153555\pi$
$492$	0.451550	+	0.0649230i	0.0203574	+	0.00292696i
$493$	0.00434439	−	0.00198402i	0.000195661	−	8.93556e-5i
$494$	1.22119	+	0.358574i	0.0549439	+	0.0161330i
$495$	−24.6537	+	7.49372i	−1.10810	+	0.336818i
$496$	−2.77098	−	6.06760i	−0.124421	−	0.272443i
$497$	−4.07877	−	0.586439i	−0.182958	−	0.0263054i
$498$	−0.718115	−	0.622250i	−0.0321795	−	0.0278837i
$499$	−14.7053	+	32.2001i	−0.658300	+	1.44148i	0.225798	+	0.974174i	$0.427501\pi$
$499$	−14.7053	+	32.2001i	−0.658300	+	1.44148i	−0.884098	+	0.467301i	$0.845226\pi$
$500$	4.35322	−	10.2980i	0.194682	−	0.460542i
$501$	−0.180204	−	1.25335i	−0.00805093	−	0.0559954i
$502$	−3.46138	−	5.38601i	−0.154489	−	0.240389i
$503$	3.70454	−	3.21001i	0.165177	−	0.143127i	−0.568350	−	0.822787i	$-0.692418\pi$
$503$	3.70454	−	3.21001i	0.165177	−	0.143127i	0.733527	+	0.679660i	$0.237873\pi$
$504$	−3.28507	+	0.964583i	−0.146329	+	0.0429659i
$505$	−19.2037	+	12.6005i	−0.854553	+	0.560713i
$506$	18.4531	−	0.882429i	0.820340	−	0.0392288i
$507$			1.02597i			0.0455648i
$508$	0.858846	+	2.92496i	0.0381051	+	0.129774i
$509$	−6.24616	−	7.20845i	−0.276856	−	0.319509i	0.600244	−	0.799817i	$-0.295070\pi$
$509$	−6.24616	−	7.20845i	−0.276856	−	0.319509i	−0.877100	+	0.480308i	$0.840525\pi$
$510$	0.161592	+	0.0719520i	0.00715542	+	0.00318609i
$511$	−2.30341	−	16.0206i	−0.101897	−	0.708708i
$512$	0.540641	−	0.841254i	0.0238932	−	0.0371785i
$513$	−0.465821	−	0.212733i	−0.0205665	−	0.00939240i
$514$	−7.80428	+	9.00662i	−0.344232	+	0.397265i
$515$	−30.1668	+	14.1241i	−1.32931	+	0.622382i
$516$	0.266387	+	0.583307i	0.0117270	+	0.0256787i
$517$	7.89688	−	26.8943i	0.347304	−	1.18281i
$518$	−0.348114	+	1.18557i	−0.0152953	+	0.0520909i
$519$	−0.612655	−	1.34153i	−0.0268926	−	0.0588865i
$520$	1.30399	+	2.78512i	0.0571839	+	0.122136i
$521$	15.2873	−	17.6425i	0.669748	−	0.772930i	−0.314589	−	0.949228i	$-0.601867\pi$
$521$	15.2873	−	17.6425i	0.669748	−	0.772930i	0.984337	+	0.176298i	$0.0564121\pi$
$522$	−0.0151732	−	0.00692938i	−0.000664114	−	0.000303291i
$523$	−2.28976	+	3.56293i	−0.100124	+	0.155796i	−0.887701	−	0.460420i	$-0.847699\pi$
$523$	−2.28976	+	3.56293i	−0.100124	+	0.155796i	0.787577	+	0.616216i	$0.211335\pi$
$524$	0.940933	+	6.54433i	0.0411049	+	0.285891i
$525$	−0.0851278	−	0.521623i	−0.00371528	−	0.0227655i
$526$	−6.09516	−	7.03419i	−0.265762	−	0.306705i
$527$	−1.60962	−	5.48186i	−0.0701162	−	0.238794i
$528$		−	0.355777i		−	0.0154832i
$529$	−22.8950	+	2.19471i	−0.995437	+	0.0954220i
$530$	0.858700	−	0.563434i	0.0372996	−	0.0244740i
$531$	−6.18459	+	1.81596i	−0.268388	+	0.0788059i
$532$	−0.800458	+	0.693601i	−0.0347043	+	0.0300714i
$533$	3.67265	+	5.71475i	0.159080	+	0.247533i
$534$	−0.0938428	−	0.652691i	−0.00406098	−	0.0282447i
$535$	−0.379542	−	40.0092i	−0.0164090	−	1.72975i
$536$	3.21453	−	7.03885i	0.138847	−	0.304032i
$537$	−1.66342	−	1.44136i	−0.0717817	−	0.0621992i
$538$	29.1132	+	4.18584i	1.25516	+	0.180465i
$539$	−9.10550	−	19.9383i	−0.392202	−	0.858802i
$540$	−0.359850	−	1.18387i	−0.0154855	−	0.0509459i
$541$	19.2376	+	5.64867i	0.827089	+	0.242855i	0.667766	−	0.744371i	$-0.267251\pi$
$541$	19.2376	+	5.64867i	0.827089	+	0.242855i	0.159323	+	0.987227i	$0.449069\pi$
$542$	13.9453	−	6.36859i	0.599000	−	0.273554i
$543$	−0.159419	−	0.0229210i	−0.00684131	−	0.000983632i
$544$	0.560898	−	0.647311i	0.0240483	−	0.0277532i
$545$	4.63990	+	30.2325i	0.198751	+	1.29502i
$546$	0.122298	+	0.0785963i	0.00523388	+	0.00336361i
$547$	5.59151	−	0.803938i	0.239076	−	0.0343739i	−0.0217354	−	0.999764i	$-0.506919\pi$
$547$	5.59151	−	0.803938i	0.239076	−	0.0343739i	0.260811	+	0.965390i	$0.416010\pi$
$548$	−6.63597	−	10.3258i	−0.283474	−	0.441095i
$549$	18.9481	+	21.8673i	0.808686	+	0.933273i
$550$	−19.1132	−	2.37891i	−0.814989	−	0.101437i
$551$	−0.00516025			−0.000219834
$552$	0.0211571	+	0.442430i	0.000900504	+	0.0188311i
$553$			2.42251i			0.103015i
$554$	17.5246	−	5.14569i	0.744549	−	0.218619i
$555$	−0.214516	−	0.0607832i	−0.00910568	−	0.00258010i
$556$	−13.6036	+	8.74248i	−0.576919	+	0.370764i
$557$	34.5963	−	4.97419i	1.46589	−	0.210763i	0.637299	−	0.770617i	$-0.280052\pi$
$557$	34.5963	−	4.97419i	1.46589	−	0.210763i	0.828592	+	0.559853i	$0.189143\pi$
$558$	−10.7881	+	16.7866i	−0.456696	+	0.710634i
$559$	−3.96676	+	8.68599i	−0.167776	+	0.367378i
$560$	−2.53648	−	0.340165i	−0.107186	−	0.0143746i
$561$	0.0433674	−	0.301627i	0.00183097	−	0.0127347i
$562$	−20.2503	+	9.24798i	−0.854205	+	0.390103i
$563$	4.00533	−	13.6409i	0.168804	−	0.574895i	−0.831022	−	0.556240i	$-0.812243\pi$
$563$	4.00533	−	13.6409i	0.168804	−	0.574895i	0.999826	−	0.0186549i	$-0.00593840\pi$
$564$	0.644816	+	0.189335i	0.0271516	+	0.00797244i
$565$	−18.4012	+	29.2390i	−0.774146	+	1.23010i
$566$	2.75964	−	19.1938i	0.115997	−	0.806774i
$567$	7.71830	+	6.68794i	0.324138	+	0.280867i
$568$	−3.27507	−	1.49567i	−0.137419	−	0.0627571i
$569$	11.0496	+	7.10113i	0.463222	+	0.297695i	0.751358	−	0.659895i	$-0.229399\pi$
$569$	11.0496	+	7.10113i	0.463222	+	0.297695i	−0.288136	+	0.957590i	$0.593035\pi$
$570$	−0.126521	−	0.143245i	−0.00529938	−	0.00599986i
$571$	6.97446	−	4.48221i	0.291872	−	0.187575i	−0.386508	−	0.922286i	$-0.626319\pi$
$571$	6.97446	−	4.48221i	0.291872	−	0.187575i	0.678380	+	0.734711i	$0.262682\pi$
$572$	4.00385	−	3.46936i	0.167409	−	0.145061i
$573$	0.393158	+	1.33897i	0.0164244	+	0.0559365i
$574$	−5.65314			−0.235958
$575$	23.9099	+	1.82171i	0.997110	+	0.0759705i
$576$	−2.99147			−0.124645
$577$	−5.22928	−	17.8093i	−0.217698	−	0.741410i	−0.993837	−	0.110849i	$-0.964643\pi$
$577$	−5.22928	−	17.8093i	−0.217698	−	0.741410i	0.776140	−	0.630561i	$-0.217175\pi$
$578$	−12.2933	+	10.6522i	−0.511334	+	0.443074i
$579$	1.84568	−	1.18615i	0.0767038	−	0.0492945i
$580$	−0.00825412	−	0.00934515i	−0.000342734	−	0.000388036i
$581$	9.90568	+	6.36599i	0.410957	+	0.264106i
$582$	−1.61743	−	0.738655i	−0.0670446	−	0.0306183i
$583$	−1.33716	−	1.15866i	−0.0553796	−	0.0479867i
$584$	2.01258	−	13.9978i	0.0832812	−	0.579234i
$585$	4.90003	−	7.78601i	0.202591	−	0.321912i
$586$	11.0258	+	3.23747i	0.455472	+	0.133739i
$587$	4.20940	−	14.3359i	0.173741	−	0.591706i	−0.825872	−	0.563858i	$-0.809316\pi$
$587$	4.20940	−	14.3359i	0.173741	−	0.591706i	0.999612	−	0.0278477i	$-0.00886534\pi$
$588$	0.478038	−	0.218313i	0.0197140	−	0.00900307i
$589$	−0.878505	+	6.11014i	−0.0361982	+	0.251764i
$590$	−4.77528	−	0.640408i	−0.196595	−	0.0263652i
$591$	0.369233	−	0.808508i	0.0151882	−	0.0332576i
$592$	−0.583682	+	0.908226i	−0.0239892	+	0.0373279i
$593$	44.3260	−	6.37311i	1.82025	−	0.261712i	0.854177	−	0.519983i	$-0.174062\pi$
$593$	44.3260	−	6.37311i	1.82025	−	0.261712i	0.966073	+	0.258270i	$0.0831525\pi$
$594$	−1.79324	+	1.15244i	−0.0735775	+	0.0472854i
$595$	−2.10896	−	0.597576i	−0.0864589	−	0.0244982i
$596$	14.1219	−	4.14655i	0.578454	−	0.169849i
$597$			0.462800i			0.0189411i
$598$	−4.77271	+	4.55245i	−0.195171	+	0.186163i
$599$	−24.3359			−0.994336			−0.497168	−	0.867654i	$-0.665627\pi$
$599$	−24.3359			−0.994336			−0.497168	+	0.867654i	$0.665627\pi$
$600$	0.0570365	−	0.458256i	0.00232851	−	0.0187082i
$601$	−17.3309	−	20.0009i	−0.706940	−	0.815853i	0.282732	−	0.959199i	$-0.408759\pi$
$601$	−17.3309	−	20.0009i	−0.706940	−	0.815853i	−0.989673	+	0.143346i	$0.954214\pi$
$602$	−4.29617	−	6.68497i	−0.175099	−	0.272459i
$603$	−22.9127	+	3.29436i	−0.933079	+	0.134157i
$604$	−3.51887	−	2.26144i	−0.143181	−	0.0920168i
$605$	1.30219	+	8.48476i	0.0529415	+	0.344954i
$606$	−0.621260	+	0.716972i	−0.0252370	+	0.0291250i
$607$	−5.88323	−	0.845881i	−0.238793	−	0.0343333i	0.0218792	−	0.999761i	$-0.493035\pi$
$607$	−5.88323	−	0.845881i	−0.238793	−	0.0343333i	−0.260672	+	0.965427i	$0.583944\pi$
$608$	−0.841800	+	0.384437i	−0.0341395	+	0.0155910i
$609$	−0.000565541	0	0.000166058i	−2.29169e−5	0	6.72900e-6i
$610$	6.28990	+	20.6932i	0.254671	+	0.837844i
$611$	4.15717	+	9.10294i	0.168181	+	0.368266i
$612$	−2.53616	−	0.364645i	−0.102518	−	0.0147399i
$613$	14.5319	+	12.5920i	0.586940	+	0.508586i	0.896941	−	0.442150i	$-0.145784\pi$
$613$	14.5319	+	12.5920i	0.586940	+	0.508586i	−0.310002	+	0.950736i	$0.600330\pi$
$614$	−3.18746	+	6.97957i	−0.128635	+	0.281672i
$615$	−0.00967641	−	1.02003i	−0.000390190	−	0.0411317i
$616$	0.627436	+	4.36391i	0.0252801	+	0.175827i
$617$	7.50772	+	11.6822i	0.302250	+	0.470310i	0.958844	−	0.283935i	$-0.0916399\pi$
$617$	7.50772	+	11.6822i	0.302250	+	0.470310i	−0.656594	+	0.754244i	$0.728004\pi$
$618$	−1.03977	+	0.900968i	−0.0418258	+	0.0362422i
$619$	38.2748	−	11.2385i	1.53840	−	0.451714i	0.600788	−	0.799408i	$-0.294854\pi$
$619$	38.2748	−	11.2385i	1.53840	−	0.451714i	0.937608	+	0.347695i	$0.113035\pi$
$620$	−12.4706	+	8.18256i	−0.500832	+	0.328620i
$621$	2.16147	−	1.53977i	0.0867367	−	0.0617889i
$622$			0.645146i			0.0258680i
$623$	2.30213	+	7.84032i	0.0922328	+	0.314116i
$624$	0.0831810	+	0.0959960i	0.00332990	+	0.00384291i
$625$	−24.2372	−	6.12828i	−0.969490	−	0.245131i
$626$	0.525358	+	3.65395i	0.0209975	+	0.146041i
$627$	−0.178004	+	0.276980i	−0.00710879	+	0.0110615i
$628$	2.37276	+	1.08360i	0.0946834	+	0.0432404i
$629$	−0.605552	+	0.698844i	−0.0241449	+	0.0278647i
$630$	3.24623	+	6.93343i	0.129333	+	0.276234i
$631$	15.3213	+	33.5491i	0.609933	+	1.33557i	0.922620	+	0.385711i	$0.126044\pi$
$631$	15.3213	+	33.5491i	0.609933	+	1.33557i	−0.312687	+	0.949856i	$0.601229\pi$
$632$	−0.596326	+	2.03090i	−0.0237206	+	0.0807849i
$633$	−0.568599	+	1.93647i	−0.0225998	+	0.0769678i
$634$	−7.63868	−	16.7264i	−0.303371	−	0.664289i
$635$	6.17339	−	2.89038i	0.244984	−	0.114701i
$636$	0.0277799	−	0.0320597i	0.00110154	−	0.00127125i
$637$	7.11844	+	3.25088i	0.282043	+	0.128805i
$638$	−0.0116128	+	0.0180699i	−0.000459756	+	0.000715394i
$639$	1.53281	+	10.6610i	0.0606372	+	0.421741i
$640$	−2.04272	−	0.909560i	−0.0807456	−	0.0359535i
$641$	10.1816	+	11.7502i	0.402148	+	0.464103i	0.920316	−	0.391175i	$-0.127931\pi$
$641$	10.1816	+	11.7502i	0.402148	+	0.464103i	−0.518168	+	0.855279i	$0.673386\pi$
$642$	−0.465595	−	1.58567i	−0.0183756	−	0.0625814i
$643$		−	28.4579i		−	1.12227i	−0.827724	−	0.561136i	$-0.810365\pi$
$643$		−	28.4579i		−	1.12227i	0.827724	−	0.561136i	$-0.189635\pi$
$644$	−1.03976	−	5.38947i	−0.0409724	−	0.212375i
$645$	1.19886	−	0.786628i	0.0472050	−	0.0309735i
$646$	−0.760536	+	0.223314i	−0.0299229	+	0.00878616i
$647$	−24.7703	+	21.4636i	−0.973820	+	0.843820i	−0.987744	−	0.156083i	$-0.950113\pi$
$647$	−24.7703	+	21.4636i	−0.973820	+	0.843820i	0.0139238	+	0.999903i	$0.495568\pi$
$648$	4.82430	+	7.50676i	0.189516	+	0.294893i
$649$	1.18123	+	8.21566i	0.0463675	+	0.322493i
$650$	5.71332	−	3.82680i	0.224095	−	0.150100i
$651$	−0.292906	+	0.641374i	−0.0114799	+	0.0251374i
$652$	−2.32096	−	2.01112i	−0.0908959	−	0.0787617i
$653$	14.3223	+	2.05924i	0.560475	+	0.0805841i	0.416729	−	0.909031i	$-0.363176\pi$
$653$	14.3223	+	2.05924i	0.560475	+	0.0805841i	0.143745	+	0.989615i	$0.454085\pi$
$654$	0.524811	+	1.14917i	0.0205217	+	0.0449363i
$655$	14.1450	−	4.29952i	0.552693	−	0.167996i
$656$	−4.73930	−	1.39158i	−0.185038	−	0.0543322i
$657$	−38.4816	+	17.5740i	−1.50131	+	0.685626i
$658$	−8.24313	−	1.18518i	−0.321351	−	0.0462032i
$659$	−11.7391	+	13.5477i	−0.457292	+	0.527743i	−0.936833	−	0.349776i	$-0.886258\pi$
$659$	−11.7391	+	13.5477i	−0.457292	+	0.527743i	0.479541	+	0.877519i	$0.340803\pi$
$660$	−0.786334	+	0.120682i	−0.0306080	+	0.00469754i
$661$	1.44448	+	0.928308i	0.0561836	+	0.0361070i	0.568431	−	0.822731i	$-0.307551\pi$
$661$	1.44448	+	0.928308i	0.0561836	+	0.0361070i	−0.512248	+	0.858838i	$0.671187\pi$
$662$	−31.9037	+	4.58706i	−1.23997	+	0.178281i
$663$	0.0588192	+	0.0915245i	0.00228435	+	0.00355452i
$664$	6.73734	+	7.77530i	0.261459	+	0.301740i
$665$	1.80451	+	1.53389i	0.0699759	+	0.0594817i
$666$	3.22962			0.125145
$667$	0.0133667	−	0.0231616i	0.000517560	−	0.000896820i
$668$			13.7100i			0.530457i
$669$	−1.80611	+	0.530321i	−0.0698282	+	0.0205034i
$670$	−16.6476	−	4.71710i	−0.643152	−	0.182238i
$671$	31.3444	−	20.1438i	1.21004	−	0.777644i
$672$	−0.104629	+	0.0150434i	−0.00403614	+	0.000580310i
$673$	−20.2803	+	31.5567i	−0.781747	+	1.21642i	0.190321	+	0.981722i	$0.439047\pi$
$673$	−20.2803	+	31.5567i	−0.781747	+	1.21642i	−0.972068	+	0.234700i	$0.924589\pi$
$674$	−4.12267	+	9.02738i	−0.158799	+	0.347722i
$675$	−2.49452	+	1.19692i	−0.0960143	+	0.0460693i
$676$	1.58091	−	10.9955i	0.0608042	−	0.422903i
$677$	−4.43279	+	2.02439i	−0.170366	+	0.0778035i	−0.498772	−	0.866733i	$-0.666216\pi$
$677$	−4.43279	+	2.02439i	−0.170366	+	0.0778035i	0.328407	+	0.944536i	$0.393488\pi$
$678$	−0.402017	+	1.36914i	−0.0154394	+	0.0525817i
$679$	21.1418	+	6.20781i	0.811350	+	0.238234i
$680$	−1.62094	−	1.02012i	−0.0621602	−	0.0391198i
$681$	−0.0390670	+	0.271717i	−0.00149705	+	0.0104122i
$682$	19.4192	+	16.8268i	0.743598	+	0.644331i
$683$	−27.0727	−	12.3637i	−1.03591	−	0.473084i	−0.176461	−	0.984308i	$-0.556465\pi$
$683$	−27.0727	−	12.3637i	−1.03591	−	0.473084i	−0.859448	+	0.511224i	$0.829192\pi$
$684$	2.32892	+	1.49671i	0.0890485	+	0.0572280i
$685$	−20.5709	+	18.1693i	−0.785975	+	0.694214i
$686$	−12.2183	+	7.85221i	−0.466496	+	0.299799i
$687$	1.56817	−	1.35883i	0.0598294	−	0.0518425i
$688$	−1.95610	−	6.66188i	−0.0745758	−	0.253982i
$689$	0.631689			0.0240655
$690$	0.970677	−	0.196836i	0.0369531	−	0.00749343i
$691$	4.16285			0.158362			0.0791812	−	0.996860i	$-0.474769\pi$
$691$	4.16285			0.158362			0.0791812	+	0.996860i	$0.474769\pi$
$692$	4.49878	+	15.3214i	0.171018	+	0.582433i
$693$	9.96740	−	8.63680i	0.378630	−	0.328085i
$694$	−1.52807	+	0.982028i	−0.0580046	+	0.0372773i
$695$	23.9369	+	27.1009i	0.907980	+	1.02800i
$696$	−0.000433243	0	0.000278428i	−1.64220e−5	0	1.05538e-5i
$697$	−3.84834	−	1.75748i	−0.145766	−	0.0665691i
$698$	−6.89621	−	5.97560i	−0.261025	−	0.226180i
$699$	0.183056	−	1.27318i	0.00692383	−	0.0481563i
$700$	0.108562	+	5.72150i	0.00410327	+	0.216252i
$701$	10.5790	+	3.10627i	0.399563	+	0.117322i	0.475339	−	0.879802i	$-0.342325\pi$
$701$	10.5790	+	3.10627i	0.399563	+	0.117322i	−0.0757762	+	0.997125i	$0.524143\pi$
$702$	0.214410	−	0.730214i	0.00809239	−	0.0275602i
$703$	0.908816	−	0.415042i	0.0342766	−	0.0156536i
$704$	−0.548216	+	3.81292i	−0.0206617	+	0.143705i
$705$	0.199740	−	1.48939i	0.00752266	−	0.0560936i
$706$	−6.37955	+	13.9693i	−0.240098	+	0.525740i
$707$	6.35587	−	9.88992i	0.239037	−	0.371949i
$708$	−0.196978	+	0.0283212i	−0.00740289	+	0.00106437i
$709$	−5.17991	+	3.32892i	−0.194535	+	0.125020i	−0.634283	−	0.773101i	$-0.718704\pi$
$709$	−5.17991	+	3.32892i	−0.194535	+	0.125020i	0.439747	+	0.898122i	$0.355068\pi$
$710$	−2.19480	+	7.74586i	−0.0823693	+	0.290697i
$711$	6.07538	−	1.78389i	0.227845	−	0.0669012i
$712$			7.13961i			0.267568i
$713$	−25.1495	−	19.7703i	−0.941857	−	0.740405i
$714$	−0.0905377			−0.00338829
$715$	−9.02607	−	7.67244i	−0.337556	−	0.286933i
$716$	15.6061	+	18.0105i	0.583229	+	0.673082i
$717$	−0.581038	−	0.904113i	−0.0216993	−	0.0337647i
$718$	−2.42695	+	0.348942i	−0.0905729	+	0.0130224i
$719$	−18.6063	−	11.9575i	−0.693897	−	0.445940i	0.145572	−	0.989348i	$-0.453498\pi$
$719$	−18.6063	−	11.9575i	−0.693897	−	0.445940i	−0.839469	+	0.543407i	$0.817134\pi$
$720$	1.01473	+	6.61172i	0.0378166	+	0.246404i
$721$	11.1648	−	12.8849i	0.415799	−	0.479857i
$722$	−17.9589	−	2.58210i	−0.668361	−	0.0960958i
$723$	−1.55967	+	0.712278i	−0.0580048	+	0.0264899i
$724$	1.67320	+	0.491296i	0.0621840	+	0.0182589i
$725$	−0.0178547	+	0.0214131i	−0.000663107	+	0.000795263i
$726$	0.147288	+	0.322517i	0.00546638	+	0.0119697i
$727$	14.0078	+	2.01402i	0.519520	+	0.0746957i	0.397087	−	0.917781i	$-0.370021\pi$
$727$	14.0078	+	2.01402i	0.519520	+	0.0746957i	0.122433	+	0.992477i	$0.460930\pi$
$728$	−1.18958	−	1.03078i	−0.0440888	−	0.0382032i
$729$	11.0253	−	24.1421i	0.408345	−	0.894150i
$730$	−31.6205	+	0.299964i	−1.17033	+	0.0111022i
$731$	−0.846331	−	5.88636i	−0.0313027	−	0.217715i
$732$	0.482967	+	0.751512i	0.0178510	+	0.0277767i
$733$	7.77249	−	6.73490i	0.287084	−	0.248759i	−0.499399	−	0.866372i	$-0.666446\pi$
$733$	7.77249	−	6.73490i	0.287084	−	0.248759i	0.786482	+	0.617613i	$0.211900\pi$
$734$	−21.8180	+	6.40634i	−0.805316	+	0.236462i
$735$	−0.644666	−	0.982502i	−0.0237789	−	0.0362401i
$736$	0.454995	−	4.77420i	0.0167713	−	0.175979i
$737$			29.8083i			1.09800i
$738$	4.16288	+	14.1775i	0.153238	+	0.521880i
$739$	29.5389	+	34.0897i	1.08660	+	1.25401i	0.965230	+	0.261402i	$0.0841849\pi$
$739$	29.5389	+	34.0897i	1.08660	+	1.25401i	0.121375	+	0.992607i	$0.461270\pi$
$740$	2.20534	+	0.981971i	0.0810699	+	0.0360980i
$741$	−0.0167289	−	0.116352i	−0.000614553	−	0.00427431i
$742$	−0.284205	+	0.442232i	−0.0104335	+	0.0162348i
$743$	−35.1049	−	16.0319i	−1.28788	−	0.588153i	−0.350529	−	0.936552i	$-0.613998\pi$
$743$	−35.1049	−	16.0319i	−1.28788	−	0.588153i	−0.937346	+	0.348399i	$0.886726\pi$
$744$	−0.403438	+	0.465592i	−0.0147908	+	0.0170694i
$745$	−13.9549	−	29.8055i	−0.511268	−	1.09199i
$746$	−14.4826	−	31.7125i	−0.530245	−	1.16108i
$747$	8.67084	−	29.5302i	0.317249	−	1.08045i
$748$	−0.929551	+	3.16576i	−0.0339878	+	0.115752i
$749$	8.50735	+	18.6285i	0.310852	+	0.680671i
$750$	−1.03218	+	0.0293820i	−0.0376899	+	0.00107288i
$751$	−17.2821	+	19.9446i	−0.630632	+	0.727788i	−0.977689	−	0.210056i	$-0.932635\pi$
$751$	−17.2821	+	19.9446i	−0.630632	+	0.727788i	0.347057	+	0.937844i	$0.387181\pi$
$752$	−6.61886	−	3.02273i	−0.241365	−	0.110228i
$753$	−0.319687	+	0.497443i	−0.0116501	+	0.0181278i
$754$	−0.00109138	−	0.00759072i	−3.97458e−5	−	0.000276438i
$755$	−3.80459	+	8.54448i	−0.138463	+	0.310965i
$756$	0.414741	+	0.478636i	0.0150840	+	0.0174078i
$757$	−8.31937	−	28.3332i	−0.302373	−	1.02979i	−0.960823	−	0.277162i	$-0.910606\pi$
$757$	−8.31937	−	28.3332i	−0.302373	−	1.02979i	0.658451	−	0.752624i	$-0.271212\pi$
$758$		−	31.4216i		−	1.14128i
$759$	−0.782126	−	1.51643i	−0.0283894	−	0.0550429i
$760$	1.13522	+	1.73013i	0.0411789	+	0.0627585i
$761$	−35.4871	+	10.4200i	−1.28641	+	0.377723i	−0.852260	−	0.523119i	$-0.824768\pi$
$761$	−35.4871	+	10.4200i	−1.28641	+	0.377723i	−0.434147	+	0.900842i	$0.642950\pi$
$762$	0.212781	−	0.184376i	0.00770824	−	0.00667923i
$763$	−8.46390	−	13.1701i	−0.306414	−	0.476789i
$764$	−2.15032	−	14.9558i	−0.0777960	−	0.541083i
$765$	0.0543482	+	5.72908i	0.00196496	+	0.207135i
$766$	13.8774	−	30.3873i	0.501411	−	1.09794i
$767$	−2.23955	−	1.94058i	−0.0808655	−	0.0700703i
$768$	−0.0914184	−	0.0131440i	−0.00329878	−	0.000474292i
$769$	−4.58637	−	10.0427i	−0.165389	−	0.362151i	0.808733	−	0.588176i	$-0.200154\pi$
$769$	−4.58637	−	10.0427i	−0.165389	−	0.362151i	−0.974121	+	0.226026i	$0.927427\pi$
$770$	9.43224	−	2.86702i	0.339914	−	0.103320i
$771$	1.05609	+	0.310097i	0.0380343	+	0.0111679i
$772$	−21.6082	+	9.86813i	−0.777696	+	0.355162i
$773$	12.4731	+	1.79336i	0.448625	+	0.0645026i	0.362925	−	0.931818i	$-0.381778\pi$
$773$	12.4731	+	1.79336i	0.448625	+	0.0645026i	0.0857004	+	0.996321i	$0.472687\pi$
$774$	−13.6016	+	15.6970i	−0.488898	+	0.564218i
$775$	22.3151	+	24.7868i	0.801583	+	0.890370i
$776$	16.1961	+	10.4086i	0.581406	+	0.373647i
$777$	0.112958	−	0.0162410i	0.00405236	−	0.000582641i
$778$	−4.05324	−	6.30696i	−0.145316	−	0.226115i
$779$	2.99339	+	3.45456i	0.107250	+	0.123773i
$780$	0.183954	−	0.216408i	0.00658660	−	0.00774866i
$781$	13.8693			0.496284
$782$	0.967694	−	3.99209i	0.0346047	−	0.142757i
$783$			0.00308559i			0.000110270i
$784$	−5.45962	+	1.60309i	−0.194986	+	0.0572532i
$785$	1.59011	−	5.61181i	0.0567535	−	0.200294i
$786$	0.513703	−	0.330137i	0.0183232	−	0.0117756i
$787$	50.2644	−	7.22693i	1.79173	−	0.257612i	0.835348	−	0.549721i	$-0.185266\pi$
$787$	50.2644	−	7.22693i	1.79173	−	0.257612i	0.956385	+	0.292109i	$0.0943569\pi$
$788$	−5.20296	+	8.09597i	−0.185348	+	0.288407i
$789$	−0.357104	+	0.781949i	−0.0127133	+	0.0278381i
$790$	4.69096	+	0.629099i	0.166897	+	0.0223824i
$791$	2.51651	−	17.5027i	0.0894769	−	0.622326i
$792$	10.4822	−	4.78705i	0.372468	−	0.170100i
$793$	−3.74773	+	12.7636i	−0.133086	+	0.453248i
$794$	25.3286	+	7.43713i	0.898877	+	0.263934i
$795$	−0.0802811	−	0.0505240i	−0.00284728	−	0.00179190i
$796$	0.713127	−	4.95991i	0.0252761	−	0.175799i
$797$	15.3428	+	13.2946i	0.543469	+	0.470919i	0.882800	−	0.469748i	$-0.155655\pi$
$797$	15.3428	+	13.2946i	0.543469	+	0.470919i	−0.339331	+	0.940667i	$0.610201\pi$
$798$	0.0889822	+	0.0406368i	0.00314994	+	0.00143853i
$799$	−5.24299	−	3.36947i	−0.185484	−	0.119203i
$800$	−1.31740	+	4.82333i	−0.0465770	+	0.170530i
$801$	17.9674	−	11.5470i	0.634848	−	0.407992i
$802$	−5.99648	+	5.19598i	−0.211743	+	0.183477i
$803$	15.3476	+	52.2693i	0.541606	+	1.84454i
$804$	−0.714681			−0.0252049
$805$	−11.5591	+	4.12622i	−0.407404	+	0.145430i
$806$	−9.17381			−0.323134
$807$	−0.765326	−	2.60646i	−0.0269407	−	0.0917517i
$808$	7.76293	−	6.72662i	0.273099	−	0.236642i
$809$	−11.0408	+	7.09548i	−0.388173	+	0.249464i	−0.720142	−	0.693827i	$-0.755923\pi$
$809$	−11.0408	+	7.09548i	−0.388173	+	0.249464i	0.331969	+	0.943290i	$0.392287\pi$
$810$	14.9549	−	13.2090i	0.525463	−	0.464116i
$811$	−1.87623	−	1.20578i	−0.0658835	−	0.0423408i	0.507284	−	0.861779i	$-0.330649\pi$
$811$	−1.87623	−	1.20578i	−0.0658835	−	0.0423408i	−0.573168	+	0.819438i	$0.694286\pi$
$812$	0.00580512	+	0.00265111i	0.000203720	+	9.30357e-5i
$813$	−1.07008	−	0.927228i	−0.0375293	−	0.0325193i
$814$	0.591859	−	4.11647i	0.0207447	−	0.144282i
$815$	−3.65768	+	5.81195i	−0.128123	+	0.203584i
$816$	−0.0759020	−	0.0222868i	−0.00265710	−	0.000780196i
$817$	−1.81023	+	6.16509i	−0.0633321	+	0.215689i
$818$	11.0928	−	5.06590i	0.387850	−	0.177125i
$819$	−0.670118	+	4.66077i	−0.0234158	+	0.162861i
$820$	−1.46806	+	10.9468i	−0.0512669	+	0.382278i
$821$	−2.63898	+	5.77857i	−0.0921011	+	0.201673i	−0.950076	−	0.312018i	$-0.898995\pi$
$821$	−2.63898	+	5.77857i	−0.0921011	+	0.201673i	0.857975	+	0.513691i	$0.171722\pi$
$822$	−0.612887	+	0.953671i	−0.0213769	+	0.0332631i
$823$	39.8392	−	5.72802i	1.38871	−	0.199666i	0.592930	−	0.805254i	$-0.297971\pi$
$823$	39.8392	−	5.72802i	1.38871	−	0.199666i	0.795779	+	0.605588i	$0.207062\pi$
$824$	12.5317	−	8.05365i	0.436563	−	0.280562i
$825$	0.533460	+	1.69701i	0.0185727	+	0.0590824i
$826$	2.36616	−	0.694767i	0.0823292	−	0.0241740i
$827$			2.40620i			0.0836717i	0.999124	+	0.0418358i	$0.0133206\pi$
$827$			2.40620i			0.0836717i	−0.999124	+	0.0418358i	$0.986679\pi$
$828$	−12.7505	+	6.57633i	−0.443112	+	0.228543i
$829$	9.27482			0.322128			0.161064	−	0.986944i	$-0.448507\pi$
$829$	9.27482			0.322128			0.161064	+	0.986944i	$0.448507\pi$
$830$	14.8995	−	17.5282i	0.517171	−	0.608414i
$831$	−1.10467	−	1.27485i	−0.0383205	−	0.0442242i
$832$	−0.743545	−	1.15698i	−0.0257778	−	0.0401110i
$833$	−4.82406	+	0.693595i	−0.167144	+	0.0240316i
$834$	1.25640	+	0.807441i	0.0435057	+	0.0279594i
$835$	30.3018	−	4.65053i	1.04864	−	0.160938i
$836$	2.33450	−	2.69415i	0.0807402	−	0.0931792i
$837$	3.65358	+	0.525305i	0.126286	+	0.0181572i
$838$	13.7237	−	6.26740i	0.474077	−	0.216504i
$839$	−38.2396	−	11.2282i	−1.32018	−	0.387639i	−0.455621	−	0.890174i	$-0.650583\pi$
$839$	−38.2396	−	11.2282i	−1.32018	−	0.387639i	−0.864557	+	0.502535i	$0.832401\pi$
$840$	0.0687395	+	0.226147i	0.00237174	+	0.00780280i
$841$	−12.0470	−	26.3793i	−0.415415	−	0.909631i
$842$	20.3597	+	2.92728i	0.701641	+	0.100881i
$843$	1.55389	+	1.34645i	0.0535187	+	0.0463742i
$844$	9.07768	−	19.8773i	0.312467	−	0.684206i
$845$	−24.8383	+	0.235626i	−0.854465	+	0.00810577i
$846$	3.09779	+	21.5456i	0.106504	+	0.740753i
$847$	−2.37540	−	3.69619i	−0.0816197	−	0.127003i
$848$	−0.347123	+	0.300783i	−0.0119202	+	0.0103289i
$849$	−1.71839	+	0.504564i	−0.0589749	+	0.0173166i
$850$	−1.70482	+	3.92862i	−0.0584750	+	0.134750i
$851$	−0.491217	+	5.15428i	−0.0168387	+	0.176686i
$852$			0.332530i			0.0113923i
$853$	6.09719	+	20.7651i	0.208764	+	0.710984i	0.995590	+	0.0938097i	$0.0299045\pi$
$853$	6.09719	+	20.7651i	0.208764	+	0.710984i	−0.786826	+	0.617174i	$0.788277\pi$
$854$	−7.24935	−	8.36620i	−0.248068	−	0.286285i
$855$	2.51802	−	5.65505i	0.0861144	−	0.193399i
$856$	2.54650	+	17.7113i	0.0870377	+	0.605361i
$857$	−18.8802	+	29.3781i	−0.644934	+	1.00354i	0.352763	+	0.935713i	$0.385242\pi$
$857$	−18.8802	+	29.3781i	−0.644934	+	1.00354i	−0.997697	+	0.0678248i	$0.978394\pi$
$858$	−0.445084	−	0.203263i	−0.0151949	−	0.00693929i
$859$	−11.1462	+	12.8634i	−0.380303	+	0.438893i	−0.913339	−	0.407199i	$-0.866505\pi$
$859$	−11.1462	+	12.8634i	−0.380303	+	0.438893i	0.533036	+	0.846092i	$0.321051\pi$
$860$	−14.0605	+	6.58311i	−0.479459	+	0.224482i
$861$	0.216895	+	0.474933i	0.00739175	+	0.0161857i
$862$	4.27494	−	14.5591i	0.145605	−	0.495885i
$863$	9.67164	−	32.9386i	0.329227	−	1.12124i	−0.614059	−	0.789260i	$-0.710464\pi$
$863$	9.67164	−	32.9386i	0.329227	−	1.12124i	0.943286	−	0.331983i	$-0.107718\pi$
$864$	0.229875	+	0.503356i	0.00782051	+	0.0171245i
$865$	32.3372	−	15.1403i	1.09950	−	0.514785i
$866$	2.21954	−	2.56148i	0.0754229	−	0.0870427i
$867$	1.36657	+	0.624094i	0.0464113	+	0.0211953i
$868$	4.12741	−	6.42238i	0.140094	−	0.217990i
$869$	−1.16038	−	8.07059i	−0.0393630	−	0.273776i
$870$	−0.000468420		0.00105199i	−1.58809e−5		3.56659e-5i
$871$	−6.96920	−	8.04289i	−0.236143	−	0.272523i
$872$	−3.85373	−	13.1246i	−0.130504	−	0.444455i
$873$		−	57.5927i		−	1.94922i
$874$	−2.74287	+	3.48917i	−0.0927790	+	0.118023i
$875$	12.6088	−	2.18071i	0.426254	−	0.0737216i
$876$	−1.25320	+	0.367974i	−0.0423418	+	0.0124327i
$877$	20.6077	−	17.8566i	0.695871	−	0.602976i	−0.233397	−	0.972382i	$-0.574984\pi$
$877$	20.6077	−	17.8566i	0.695871	−	0.602976i	0.929268	+	0.369406i	$0.120439\pi$
$878$	−8.57291	−	13.3397i	−0.289322	−	0.450193i
$879$	−0.151041	−	1.05052i	−0.00509450	−	0.0354330i
$880$	8.61324	−	0.0817084i	0.290352	−	0.00275439i
$881$	−14.0150	+	30.6886i	−0.472178	+	1.03393i	0.512363	+	0.858769i	$0.328770\pi$
$881$	−14.0150	+	30.6886i	−0.472178	+	1.03393i	−0.984541	+	0.175156i	$0.943957\pi$
$882$	12.8642	+	11.1469i	0.433160	+	0.375336i
$883$	−17.7979	−	2.55896i	−0.598948	−	0.0861158i	−0.163829	−	0.986489i	$-0.552385\pi$
$883$	−17.7979	−	2.55896i	−0.598948	−	0.0861158i	−0.435119	+	0.900373i	$0.643294\pi$
$884$	−0.489346	−	1.07152i	−0.0164585	−	0.0360390i
$885$	0.129411	+	0.425752i	0.00435012	+	0.0143115i
$886$	−29.2971	−	8.60241i	−0.984255	−	0.289003i
$887$	19.1629	−	8.75141i	0.643427	−	0.293843i	−0.0668524	−	0.997763i	$-0.521296\pi$
$887$	19.1629	−	8.75141i	0.643427	−	0.293843i	0.710280	+	0.703919i	$0.248568\pi$
$888$	0.0986962	+	0.0141904i	0.00331203	+	0.000476198i
$889$	−2.28478	+	2.63678i	−0.0766292	+	0.0884348i
$890$	15.7799	−	2.42180i	0.528943	−	0.0811790i
$891$	−28.9170	−	18.5838i	−0.968757	−	0.622582i
$892$	20.1735	−	2.90052i	0.675460	−	0.0971165i
$893$	3.64057	+	5.66483i	0.121827	+	0.189566i
$894$	−0.890176	−	1.02732i	−0.0297719	−	0.0343586i
$895$	34.5128	−	40.6018i	1.15364	−	1.35717i
$896$	1.14451			0.0382352
$897$	0.565576	+	0.226302i	0.0188840	+	0.00755600i
$898$		−	6.46796i		−	0.215839i
$899$	0.0356879	−	0.0104789i	0.00119026	−	0.000349491i
$900$	14.2689	−	4.48548i	0.475632	−	0.149516i
$901$	−0.330954	+	0.212691i	−0.0110257	+	0.00708576i
$902$	18.8335	−	2.70784i	0.627086	−	0.0901613i
$903$	−0.396788	+	0.617414i	−0.0132043	+	0.0205462i
$904$	6.41820	−	14.0539i	0.213466	−	0.467426i
$905$	0.518296	−	3.86474i	0.0172288	−	0.128468i
$906$	−0.0549798	+	0.382393i	−0.00182658	+	0.0127042i
$907$	−11.5674	+	5.28265i	−0.384089	+	0.175408i	−0.598096	−	0.801425i	$-0.704076\pi$
$907$	−11.5674	+	5.28265i	−0.384089	+	0.175408i	0.214007	+	0.976832i	$0.431349\pi$
$908$	0.837376	−	2.85184i	0.0277893	−	0.0946417i
$909$	−29.4832	−	8.65704i	−0.977896	−	0.287136i
$910$	−1.87470	+	2.97885i	−0.0621458	+	0.0987479i
$911$	−5.54472	+	38.5644i	−0.183705	+	1.27770i	0.664203	+	0.747552i	$0.268771\pi$
$911$	−5.54472	+	38.5644i	−0.183705	+	1.27770i	−0.847908	+	0.530143i	$0.822138\pi$
$912$	0.0645948	+	0.0559717i	0.00213895	+	0.00185341i
$913$	−36.0501	−	16.4635i	−1.19308	−	0.544863i
$914$	−16.7509	−	10.7652i	−0.554072	−	0.356081i
$915$	1.49716	−	1.32237i	0.0494945	−	0.0437161i
$916$	−18.9002	+	12.1464i	−0.624479	+	0.401328i
$917$	−5.71879	+	4.95536i	−0.188851	+	0.163641i
$918$	0.133531	+	0.454765i	0.00440718	+	0.0150095i
$919$	39.1217			1.29050			0.645252	−	0.763970i	$-0.276752\pi$
$919$	39.1217			1.29050			0.645252	+	0.763970i	$0.276752\pi$
$920$	−10.7062	+	0.613815i	−0.352974	+	0.0202369i
$921$	0.708662			0.0233512
$922$	−3.67054	−	12.5007i	−0.120883	−	0.411689i
$923$	−3.74224	+	3.24267i	−0.123177	+	0.106734i
$924$	0.342549	−	0.220143i	0.0112690	−	0.00724217i
$925$	1.42227	−	5.20731i	0.0467641	−	0.171215i
$926$	−15.9510	−	10.2511i	−0.524183	−	0.336872i
$927$	−40.5354	−	18.5119i	−1.33136	−	0.608010i
$928$	0.00421411	+	0.00365155i	0.000138335	+	0.000119868i
$929$	7.65577	−	53.2471i	0.251178	−	1.74698i	−0.339988	−	0.940430i	$-0.610423\pi$
$929$	7.65577	−	53.2471i	0.251178	−	1.74698i	0.591166	−	0.806550i	$-0.298668\pi$
$930$	1.16590	+	0.733742i	0.0382312	+	0.0240604i
$931$	5.05249	+	1.48354i	0.165589	+	0.0486212i
$932$	−3.92369	+	13.3629i	−0.128525	+	0.437716i
$933$	0.0542002	−	0.0247524i	0.00177443	−	0.000810357i
$934$	−4.66295	+	32.4315i	−0.152576	+	1.06119i
$935$	7.31224	+	0.980638i	0.239136	+	0.0320703i
$936$	−1.70909	+	3.74239i	−0.0558634	+	0.122324i
$937$	−22.2862	+	34.6781i	−0.728060	+	1.13288i	0.257944	+	0.966160i	$0.416955\pi$
$937$	−22.2862	+	34.6781i	−0.728060	+	1.13288i	−0.986004	+	0.166723i	$0.946681\pi$
$938$	8.76618	−	1.26039i	0.286226	−	0.0411531i
$939$	0.286820	−	0.184328i	0.00936000	−	0.00601531i
$940$	−4.43565	+	15.6543i	−0.144675	+	0.510586i
$941$	−51.8062	+	15.2117i	−1.68883	+	0.495887i	−0.978198	−	0.207673i	$-0.933411\pi$
$941$	−51.8062	+	15.2117i	−1.68883	+	0.495887i	−0.710636	+	0.703559i	$0.751593\pi$
$942$		−	0.240915i		−	0.00784944i
$943$	−23.2595	+	4.48734i	−0.757434	+	0.146128i
$944$	2.15469			0.0701291
$945$	0.917194	−	1.07901i	0.0298363	−	0.0351003i
$946$	17.5148	+	20.2132i	0.569455	+	0.657186i
$947$	−23.1085	−	35.9576i	−0.750927	−	1.16847i	−0.980757	−	0.195234i	$-0.937453\pi$
$947$	−23.1085	−	35.9576i	−0.750927	−	1.16847i	0.229830	−	0.973231i	$-0.426183\pi$
$948$	0.193500	−	0.0278211i	0.00628458	−	0.000903586i
$949$	−16.3617	−	10.5150i	−0.531124	−	0.341332i
$950$	3.43885	−	3.09593i	0.111571	−	0.100445i
$951$	−1.11214	+	1.28348i	−0.0360638	+	0.0416198i
$952$	0.970309	+	0.139509i	0.0314479	+	0.00452152i
$953$	39.6359	−	18.1011i	1.28393	−	0.586353i	0.347658	−	0.937621i	$-0.386977\pi$
$953$	39.6359	−	18.1011i	1.28393	−	0.586353i	0.936275	+	0.351269i	$0.114250\pi$
$954$	1.31835	+	0.387103i	0.0426832	+	0.0125329i
$955$	−32.3258	+	9.82575i	−1.04604	+	0.317954i
$956$	4.83394	+	10.5849i	0.156341	+	0.342339i
$957$	0.00196364		0.000282329i	6.34755e−5		9.12640e-6i
$958$	16.1345	+	13.9806i	0.521281	+	0.451692i
$959$	5.83573	−	12.7785i	0.188446	−	0.412638i
$960$	0.00195903	+	0.206510i	6.32276e−5	+	0.00666510i
$961$	−1.92041	−	13.3568i	−0.0619488	−	0.430863i
$962$	0.802739	+	1.24909i	0.0258814	+	0.0402722i
$963$	40.4536	−	35.0532i	1.30360	−	1.12957i
$964$	17.8128	−	5.23031i	0.573712	−	0.168457i
$965$	29.1401	+	44.4109i	0.938052	+	1.42964i
$966$	−0.412889	+	0.294131i	−0.0132845	+	0.00946352i
$967$		−	25.3908i		−	0.816512i	−0.912867	−	0.408256i	$-0.866137\pi$
$967$		−	25.3908i		−	0.816512i	0.912867	−	0.408256i	$-0.133863\pi$
$968$	−1.08155	−	3.68342i	−0.0347623	−	0.118390i
$969$	0.0479406	+	0.0553264i	0.00154007	+	0.00177734i
$970$	17.5111	−	39.3271i	0.562249	−	1.26272i
$971$	−1.58233	−	11.0053i	−0.0507793	−	0.353178i	−0.999332	−	0.0365572i	$-0.988361\pi$
$971$	−1.58233	−	11.0053i	−0.0507793	−	0.353178i	0.948552	−	0.316621i	$-0.102548\pi$
$972$	1.34308	−	2.08987i	0.0430792	−	0.0670325i
$973$	−16.8349	−	7.68822i	−0.539701	−	0.246473i
$974$	−13.6955	+	15.8054i	−0.438831	+	0.506438i
$975$	−0.540702	−	0.333166i	−0.0173163	−	0.0106698i
$976$	−4.01804	−	8.79828i	−0.128614	−	0.281626i
$977$	−6.14059	+	20.9129i	−0.196455	+	0.669064i	0.801059	+	0.598586i	$0.204271\pi$
$977$	−6.14059	+	20.9129i	−0.196455	+	0.669064i	−0.997513	+	0.0704776i	$0.977548\pi$
$978$	−0.0799105	+	0.272150i	−0.00255525	+	0.00870240i
$979$	−11.4250	−	25.0173i	−0.365146	−	0.799558i
$980$	5.39507	+	11.5230i	0.172339	+	0.368089i
$981$	−26.7965	+	30.9248i	−0.855545	+	0.987352i
$982$	37.5198	+	17.1347i	1.19731	+	0.546791i
$983$	−12.6370	+	19.6636i	−0.403058	+	0.627171i	−0.982152	−	0.188090i	$-0.939770\pi$
$983$	−12.6370	+	19.6636i	−0.403058	+	0.627171i	0.579093	+	0.815261i	$0.303407\pi$
$984$	0.0649230	+	0.451550i	0.00206967	+	0.0143949i
$985$	19.6585	+	8.75333i	0.626372	+	0.278904i
$986$	0.00312760	+	0.00360945i	9.96032e−5	+	0.000114948i
$987$	0.216695	+	0.737995i	0.00689748	+	0.0234907i
$988$			1.27275i			0.0404914i
$989$	−22.9827	−	24.0947i	−0.730808	−	0.766167i
$990$	−14.1359	−	21.5438i	−0.449269	−	0.684707i
$991$	43.0587	−	12.6432i	1.36780	−	0.401624i	0.486297	−	0.873794i	$-0.338347\pi$
$991$	43.0587	−	12.6432i	1.36780	−	0.401624i	0.881508	+	0.472170i	$0.156529\pi$
$992$	5.04115	−	4.36818i	0.160057	−	0.138690i
$993$	1.60942	+	2.50431i	0.0510734	+	0.0794718i
$994$	−0.586439	−	4.07877i	−0.0186007	−	0.129371i
$995$	−11.2042	+	0.106288i	−0.355198	+	0.00336954i
$996$	0.394728	−	0.864334i	0.0125074	−	0.0273875i
$997$	24.2432	+	21.0068i	0.767789	+	0.665293i	0.947977	−	0.318339i	$-0.103125\pi$
$997$	24.2432	+	21.0068i	0.767789	+	0.665293i	−0.180188	+	0.983632i	$0.557670\pi$
$998$	−35.0388	−	5.03781i	−1.10913	−	0.159469i
$999$	−0.248176	−	0.543429i	−0.00785193	−	0.0171933i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.j.a.9.10	yes	120
5.4	even	2	inner	230.2.j.a.9.3	✓	120
23.18	even	11	inner	230.2.j.a.179.3	yes	120
115.64	even	22	inner	230.2.j.a.179.10	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.j.a.9.3	✓	120	5.4	even	2	inner
230.2.j.a.9.10	yes	120	1.1	even	1	trivial
230.2.j.a.179.3	yes	120	23.18	even	11	inner
230.2.j.a.179.10	yes	120	115.64	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.281733 + 0.959493i) q^{2} +(0.0697998 - 0.0604819i) q^{3} +(-0.841254 + 0.540641i) q^{4} +(1.48028 + 1.67594i) q^{5} +(0.0776969 + 0.0499327i) q^{6} +(-1.04108 - 0.475445i) q^{7} +(-0.755750 - 0.654861i) q^{8} +(-0.425731 + 2.96102i) q^{9} +O(q^{10})\)	\(q+(0.281733 + 0.959493i) q^{2} +(0.0697998 - 0.0604819i) q^{3} +(-0.841254 + 0.540641i) q^{4} +(1.48028 + 1.67594i) q^{5} +(0.0776969 + 0.0499327i) q^{6} +(-1.04108 - 0.475445i) q^{7} +(-0.755750 - 0.654861i) q^{8} +(-0.425731 + 2.96102i) q^{9} +(-1.19101 + 1.89248i) q^{10} +(3.69609 + 1.08527i) q^{11} +(-0.0260204 + 0.0886173i) q^{12} +(-1.25102 + 0.571322i) q^{13} +(0.162880 - 1.13286i) q^{14} +(0.204687 + 0.0274504i) q^{15} +(0.415415 - 0.909632i) q^{16} +(0.463067 - 0.720547i) q^{17} +(-2.96102 + 0.425731i) q^{18} +(-0.778520 + 0.500325i) q^{19} +(-2.15137 - 0.609593i) q^{20} +(-0.101423 + 0.0297805i) q^{21} +3.85213i q^{22} +(-0.229075 - 4.79036i) q^{23} -0.0923584 q^{24} +(-0.617556 + 4.96172i) q^{25} +(-0.900632 - 1.03939i) q^{26} +(0.299170 + 0.465518i) q^{27} +(1.13286 - 0.162880i) q^{28} +(0.00469088 + 0.00301465i) q^{29} +(0.0313286 + 0.204130i) q^{30} +(4.36818 - 5.04115i) q^{31} +(0.989821 + 0.142315i) q^{32} +(0.323626 - 0.147795i) q^{33} +(0.821820 + 0.241308i) q^{34} +(-0.744268 - 2.44858i) q^{35} +(-1.24270 - 2.72114i) q^{36} +(-1.06862 - 0.153645i) q^{37} +(-0.699392 - 0.606027i) q^{38} +(-0.0527664 + 0.115542i) q^{39} +(-0.0212112 - 2.23597i) q^{40} +(-0.702947 - 4.88910i) q^{41} +(-0.0571483 - 0.0889245i) q^{42} +(5.24726 - 4.54678i) q^{43} +(-3.69609 + 1.08527i) q^{44} +(-5.59270 + 3.66963i) q^{45} +(4.53178 - 1.56940i) q^{46} -7.27641i q^{47} +(-0.0260204 - 0.0886173i) q^{48} +(-3.72623 - 4.30030i) q^{49} +(-4.93472 + 0.805336i) q^{50} +(-0.0112580 - 0.0783012i) q^{51} +(0.743545 - 1.15698i) q^{52} +(-0.417802 - 0.190804i) q^{53} +(-0.362376 + 0.418204i) q^{54} +(3.65240 + 7.80094i) q^{55} +(0.475445 + 1.04108i) q^{56} +(-0.0240800 + 0.0820090i) q^{57} +(-0.00157096 + 0.00535019i) q^{58} +(0.895090 + 1.95997i) q^{59} +(-0.187035 + 0.0875695i) q^{60} +(6.33405 - 7.30988i) q^{61} +(6.06760 + 2.77098i) q^{62} +(1.85102 - 2.88025i) q^{63} +(0.142315 + 0.989821i) q^{64} +(-2.80936 - 1.25092i) q^{65} +(0.232984 + 0.268878i) q^{66} +(2.18008 + 7.42468i) q^{67} +0.856515i q^{68} +(-0.305719 - 0.320511i) q^{69} +(2.13971 - 1.40396i) q^{70} +(3.45459 - 1.01436i) q^{71} +(2.26080 - 1.95900i) q^{72} +(7.64561 + 11.8968i) q^{73} +(-0.153645 - 1.06862i) q^{74} +(0.256989 + 0.383678i) q^{75} +(0.384437 - 0.841800i) q^{76} +(-3.33194 - 2.88714i) q^{77} +(-0.125728 - 0.0180770i) q^{78} +(-0.879284 - 1.92536i) q^{79} +(2.13942 - 0.650297i) q^{80} +(-8.56185 - 2.51398i) q^{81} +(4.49301 - 2.05189i) q^{82} +(-10.1835 - 1.46416i) q^{83} +(0.0692219 - 0.0798863i) q^{84} +(1.89306 - 0.290536i) q^{85} +(5.84093 + 3.75374i) q^{86} +(0.000509755 - 7.32916e-5i) q^{87} +(-2.08262 - 3.24062i) q^{88} +(-4.67545 - 5.39575i) q^{89} +(-5.09663 - 4.33230i) q^{90} +1.57404 q^{91} +(2.78257 + 3.90606i) q^{92} -0.616067i q^{93} +(6.98167 - 2.05000i) q^{94} +(-1.99094 - 0.564135i) q^{95} +(0.0776969 - 0.0499327i) q^{96} +(-19.0564 + 2.73989i) q^{97} +(3.07630 - 4.78682i) q^{98} +(-4.78705 + 10.4822i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) \) 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9	\( 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9} + 8 q^{11} - 6 q^{15} - 12 q^{16} - 16 q^{19} - 22 q^{20} + 4 q^{24} - 52 q^{25} - 4 q^{26} - 8 q^{29} - 44 q^{30} + 12 q^{31} + 16 q^{35} - 8 q^{36} - 36 q^{39} - 28 q^{41} - 8 q^{44} + 16 q^{45} - 4 q^{46} - 58 q^{49} + 12 q^{50} - 24 q^{51} - 6 q^{54} - 36 q^{55} + 22 q^{56} - 102 q^{59} - 38 q^{60} + 72 q^{61} + 12 q^{64} - 138 q^{65} + 80 q^{66} - 212 q^{69} - 108 q^{70} + 176 q^{71} - 88 q^{74} - 100 q^{75} + 16 q^{76} - 104 q^{79} - 22 q^{80} - 28 q^{81} - 22 q^{84} + 2 q^{85} + 62 q^{86} + 48 q^{89} + 24 q^{90} - 56 q^{91} + 24 q^{94} + 18 q^{95} - 4 q^{96} + 188 q^{99}+O(q^{100}) \) 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9 + 8 * q^11 - 6 * q^15 - 12 * q^16 - 16 * q^19 - 22 * q^20 + 4 * q^24 - 52 * q^25 - 4 * q^26 - 8 * q^29 - 44 * q^30 + 12 * q^31 + 16 * q^35 - 8 * q^36 - 36 * q^39 - 28 * q^41 - 8 * q^44 + 16 * q^45 - 4 * q^46 - 58 * q^49 + 12 * q^50 - 24 * q^51 - 6 * q^54 - 36 * q^55 + 22 * q^56 - 102 * q^59 - 38 * q^60 + 72 * q^61 + 12 * q^64 - 138 * q^65 + 80 * q^66 - 212 * q^69 - 108 * q^70 + 176 * q^71 - 88 * q^74 - 100 * q^75 + 16 * q^76 - 104 * q^79 - 22 * q^80 - 28 * q^81 - 22 * q^84 + 2 * q^85 + 62 * q^86 + 48 * q^89 + 24 * q^90 - 56 * q^91 + 24 * q^94 + 18 * q^95 - 4 * q^96 + 188 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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