LMFDB - Embedded newform 460.2.o.b.19.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(19,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 15]))

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

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

chi := DirichletCharacter("460.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.o (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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$64$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			19.15
Character	$\chi$	$=$	460.19
Dual form			460.2.o.b.339.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09031 - 0.900680i) q^{2} +(2.64511 - 0.776673i) q^{3} +(0.377553 + 1.96404i) q^{4} +(-2.22046 + 0.263774i) q^{5} +(-3.58352 - 1.53558i) q^{6} +(2.67954 - 0.385260i) q^{7} +(1.35732 - 2.48147i) q^{8} +(3.86960 - 2.48684i) q^{9} +O(q^{10})$	\(q+(-1.09031 - 0.900680i) q^{2} +(2.64511 - 0.776673i) q^{3} +(0.377553 + 1.96404i) q^{4} +(-2.22046 + 0.263774i) q^{5} +(-3.58352 - 1.53558i) q^{6} +(2.67954 - 0.385260i) q^{7} +(1.35732 - 2.48147i) q^{8} +(3.86960 - 2.48684i) q^{9} +(2.65856 + 1.71232i) q^{10} +(0.177262 - 0.388150i) q^{11} +(2.52408 + 4.90186i) q^{12} +(-0.0403963 - 0.00580811i) q^{13} +(-3.26852 - 1.99335i) q^{14} +(-5.66847 + 2.42228i) q^{15} +(-3.71491 + 1.48306i) q^{16} +(1.68439 + 1.94389i) q^{17} +(-6.45891 - 0.773842i) q^{18} +(3.71452 - 4.28679i) q^{19} +(-1.35640 - 4.26148i) q^{20} +(6.78844 - 3.10018i) q^{21} +(-0.542869 + 0.263547i) q^{22} +(2.22386 - 4.24905i) q^{23} +(1.66297 - 7.61794i) q^{24} +(4.86085 - 1.17140i) q^{25} +(0.0388132 + 0.0427168i) q^{26} +(2.88813 - 3.33308i) q^{27} +(1.76833 + 5.11727i) q^{28} +(-3.07588 - 3.54975i) q^{29} +(8.36209 + 2.46444i) q^{30} +(-2.43880 + 8.30579i) q^{31} +(5.38616 + 1.72895i) q^{32} +(0.167411 - 1.16437i) q^{33} +(-0.0856862 - 3.63654i) q^{34} +(-5.84818 + 1.56225i) q^{35} +(6.34524 + 6.66114i) q^{36} +(4.95991 - 3.18754i) q^{37} +(-7.91100 + 1.32833i) q^{38} +(-0.111363 + 0.0160116i) q^{39} +(-2.35932 + 5.86801i) q^{40} +(0.870309 + 0.559314i) q^{41} +(-10.1938 - 2.73406i) q^{42} +(1.20643 + 4.10871i) q^{43} +(0.829267 + 0.201603i) q^{44} +(-7.93631 + 6.54262i) q^{45} +(-6.25173 + 2.62980i) q^{46} -12.9936 q^{47} +(-8.67447 + 6.80811i) q^{48} +(0.315056 - 0.0925087i) q^{49} +(-6.35488 - 3.10088i) q^{50} +(5.96516 + 3.83358i) q^{51} +(-0.00384437 - 0.0815328i) q^{52} +(-0.635662 - 4.42112i) q^{53} +(-6.15100 + 1.03281i) q^{54} +(-0.291219 + 0.908626i) q^{55} +(2.68099 - 7.17211i) q^{56} +(6.49587 - 14.2240i) q^{57} +(0.156472 + 6.64071i) q^{58} +(7.66268 + 1.10173i) q^{59} +(-6.89760 - 10.2186i) q^{60} +(-2.02441 + 6.89449i) q^{61} +(10.1399 - 6.85931i) q^{62} +(9.41067 - 8.15439i) q^{63} +(-4.31536 - 6.73630i) q^{64} +(0.0912302 + 0.00224114i) q^{65} +(-1.23126 + 1.11874i) q^{66} +(4.83647 - 2.20874i) q^{67} +(-3.18194 + 4.04214i) q^{68} +(2.58221 - 12.9664i) q^{69} +(7.78341 + 3.56400i) q^{70} +(-13.3802 + 6.11053i) q^{71} +(-0.918725 - 12.9777i) q^{72} +(-5.06816 - 4.39159i) q^{73} +(-8.27880 - 0.991882i) q^{74} +(11.9477 - 6.87376i) q^{75} +(9.82185 + 5.67698i) q^{76} +(0.325442 - 1.10835i) q^{77} +(0.135842 + 0.0828451i) q^{78} +(-1.88910 + 13.1390i) q^{79} +(7.85759 - 4.27296i) q^{80} +(-0.681785 + 1.49290i) q^{81} +(-0.445145 - 1.39370i) q^{82} +(-2.59000 - 4.03012i) q^{83} +(8.65187 + 12.1623i) q^{84} +(-4.25287 - 3.87203i) q^{85} +(2.38525 - 5.56637i) q^{86} +(-10.8930 - 7.00052i) q^{87} +(-0.722579 - 0.966714i) q^{88} +(0.597645 + 2.03539i) q^{89} +(14.5459 + 0.0145852i) q^{90} -0.110481 q^{91} +(9.18494 + 2.76350i) q^{92} +23.8638i q^{93} +(14.1671 + 11.7031i) q^{94} +(-7.11719 + 10.4984i) q^{95} +(15.5898 + 0.389963i) q^{96} +(-15.9911 - 10.2768i) q^{97} +(-0.426829 - 0.182901i) q^{98} +(-0.279334 - 1.94281i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9}+O(q^{10}) $ 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9	$ 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9} - 11 q^{10} - 22 q^{14} + 2 q^{16} - 11 q^{20} - 44 q^{21} - 8 q^{24} - 38 q^{25} - 46 q^{26} - 52 q^{29} - 11 q^{30} - 44 q^{34} + 18 q^{36} - 11 q^{40} - 76 q^{41} - 154 q^{44} - 30 q^{46} - 100 q^{49} + 21 q^{50} + 178 q^{54} + 242 q^{56} - 11 q^{60} - 44 q^{61} + 6 q^{64} - 22 q^{65} + 44 q^{66} - 12 q^{69} + 22 q^{70} - 22 q^{74} + 88 q^{76} - 110 q^{80} - 252 q^{81} - 374 q^{84} + 94 q^{85} - 198 q^{86} - 44 q^{89} - 242 q^{90} - 62 q^{94} + 372 q^{96}+O(q^{100}) $ 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9 - 11 * q^10 - 22 * q^14 + 2 * q^16 - 11 * q^20 - 44 * q^21 - 8 * q^24 - 38 * q^25 - 46 * q^26 - 52 * q^29 - 11 * q^30 - 44 * q^34 + 18 * q^36 - 11 * q^40 - 76 * q^41 - 154 * q^44 - 30 * q^46 - 100 * q^49 + 21 * q^50 + 178 * q^54 + 242 * q^56 - 11 * q^60 - 44 * q^61 + 6 * q^64 - 22 * q^65 + 44 * q^66 - 12 * q^69 + 22 * q^70 - 22 * q^74 + 88 * q^76 - 110 * q^80 - 252 * q^81 - 374 * q^84 + 94 * q^85 - 198 * q^86 - 44 * q^89 - 242 * q^90 - 62 * q^94 + 372 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{15}{22}\right)$

Coefficient data

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

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

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

$2$	−1.09031	−	0.900680i	−0.770966	−	0.636877i
$2$	−1.09031	−	0.900680i	−0.770966	−	0.636877i
$3$	2.64511	−	0.776673i	1.52715	−	0.448412i	0.592975	−	0.805221i	$-0.297953\pi$
$3$	2.64511	−	0.776673i	1.52715	−	0.448412i	0.934178	+	0.356809i	$0.116135\pi$
$4$	0.377553	+	1.96404i	0.188776	+	0.982020i
$5$	−2.22046	+	0.263774i	−0.993018	+	0.117963i
$5$	−2.22046	+	0.263774i	−0.993018	+	0.117963i
$6$	−3.58352	−	1.53558i	−1.46297	−	0.626897i
$7$	2.67954	−	0.385260i	1.01277	−	0.145614i	0.384104	−	0.923290i	$-0.374510\pi$
$7$	2.67954	−	0.385260i	1.01277	−	0.145614i	0.628666	+	0.777675i	$0.283601\pi$
$8$	1.35732	−	2.48147i	0.479885	−	0.877331i
$9$	3.86960	−	2.48684i	1.28987	−	0.828947i
$10$	2.65856	+	1.71232i	0.840711	+	0.541484i
$11$	0.177262	−	0.388150i	0.0534465	−	0.117032i	−0.881025	−	0.473070i	$-0.843146\pi$
$11$	0.177262	−	0.388150i	0.0534465	−	0.117032i	0.934471	+	0.356039i	$0.115873\pi$
$12$	2.52408	+	4.90186i	0.728640	+	1.41504i
$13$	−0.0403963	−	0.00580811i	−0.0112039	−	0.00161088i	0.136711	−	0.990611i	$-0.456347\pi$
$13$	−0.0403963	−	0.00580811i	−0.0112039	−	0.00161088i	−0.147915	+	0.989000i	$0.547256\pi$
$14$	−3.26852	−	1.99335i	−0.873550	−	0.532746i
$15$	−5.66847	+	2.42228i	−1.46359	+	0.625430i
$16$	−3.71491	+	1.48306i	−0.928727	+	0.370764i
$17$	1.68439	+	1.94389i	0.408525	+	0.471463i	0.922307	−	0.386458i	$-0.126301\pi$
$17$	1.68439	+	1.94389i	0.408525	+	0.471463i	−0.513782	+	0.857921i	$0.671756\pi$
$18$	−6.45891	−	0.773842i	−1.52238	−	0.182396i
$19$	3.71452	−	4.28679i	0.852170	−	0.983456i	−0.147815	−	0.989015i	$-0.547224\pi$
$19$	3.71452	−	4.28679i	0.852170	−	0.983456i	0.999985	+	0.00555872i	$0.00176940\pi$
$20$	−1.35640	−	4.26148i	−0.303301	−	0.952895i
$21$	6.78844	−	3.10018i	1.48136	−	0.676514i
$22$	−0.542869	+	0.263547i	−0.115740	+	0.0561885i
$23$	2.22386	−	4.24905i	0.463706	−	0.885989i
$23$	2.22386	−	4.24905i	0.463706	−	0.885989i
$24$	1.66297	−	7.61794i	0.339452	−	1.55500i
$25$	4.86085	−	1.17140i	0.972169	−	0.234280i
$26$	0.0388132	+	0.0427168i	0.00761190	+	0.00837745i
$27$	2.88813	−	3.33308i	0.555821	−	0.641452i
$28$	1.76833	+	5.11727i	0.334184	+	0.967073i
$29$	−3.07588	−	3.54975i	−0.571176	−	0.659173i	0.394508	−	0.918893i	$-0.370915\pi$
$29$	−3.07588	−	3.54975i	−0.571176	−	0.659173i	−0.965684	+	0.259720i	$0.916370\pi$
$30$	8.36209	+	2.46444i	1.52670	+	0.449943i
$31$	−2.43880	+	8.30579i	−0.438021	+	1.49176i	0.384551	+	0.923104i	$0.374356\pi$
$31$	−2.43880	+	8.30579i	−0.438021	+	1.49176i	−0.822572	+	0.568660i	$0.807462\pi$
$32$	5.38616	+	1.72895i	0.952148	+	0.305638i
$33$	0.167411	−	1.16437i	0.0291426	−	0.202691i
$34$	−0.0856862	−	3.63654i	−0.0146951	−	0.623662i
$35$	−5.84818	+	1.56225i	−0.988522	+	0.264068i
$36$	6.34524	+	6.66114i	1.05754	+	1.11019i
$37$	4.95991	−	3.18754i	0.815405	−	0.524029i	−0.0652044	−	0.997872i	$-0.520770\pi$
$37$	4.95991	−	3.18754i	0.815405	−	0.524029i	0.880609	+	0.473843i	$0.157134\pi$
$38$	−7.91100	+	1.32833i	−1.28333	+	0.215484i
$39$	−0.111363	+	0.0160116i	−0.0178324	+	0.00256392i
$40$	−2.35932	+	5.86801i	−0.373042	+	0.927815i
$41$	0.870309	+	0.559314i	0.135919	+	0.0873501i	0.606834	−	0.794829i	$-0.292439\pi$
$41$	0.870309	+	0.559314i	0.135919	+	0.0873501i	−0.470914	+	0.882179i	$0.656076\pi$
$42$	−10.1938	−	2.73406i	−1.57293	−	0.421874i
$43$	1.20643	+	4.10871i	0.183978	+	0.626572i	0.998895	+	0.0469945i	$0.0149643\pi$
$43$	1.20643	+	4.10871i	0.183978	+	0.626572i	−0.814917	+	0.579578i	$0.803218\pi$
$44$	0.829267	+	0.201603i	0.125017	+	0.0303928i
$45$	−7.93631	+	6.54262i	−1.18308	+	0.975317i
$46$	−6.25173	+	2.62980i	−0.921767	+	0.387743i
$47$	−12.9936			−1.89532			−0.947659	−	0.319285i	$-0.896557\pi$
$47$	−12.9936			−1.89532			−0.947659	+	0.319285i	$0.896557\pi$
$48$	−8.67447	+	6.80811i	−1.25205	+	0.982667i
$49$	0.315056	−	0.0925087i	0.0450079	−	0.0132155i
$50$	−6.35488	−	3.10088i	−0.898716	−	0.438530i
$51$	5.96516	+	3.83358i	0.835290	+	0.536808i
$52$	−0.00384437	−	0.0815328i	−0.000533119	−	0.0113066i
$53$	−0.635662	−	4.42112i	−0.0873148	−	0.607288i	−0.985754	−	0.168191i	$-0.946208\pi$
$53$	−0.635662	−	4.42112i	−0.0873148	−	0.607288i	0.898440	−	0.439097i	$-0.144702\pi$
$54$	−6.15100	+	1.03281i	−0.837045	+	0.140548i
$55$	−0.291219	+	0.908626i	−0.0392679	+	0.122519i
$56$	2.68099	−	7.17211i	0.358262	−	0.958414i
$57$	6.49587	−	14.2240i	0.860399	−	1.88401i
$58$	0.156472	+	6.64071i	0.0205458	+	0.871968i
$59$	7.66268	+	1.10173i	0.997596	+	0.143433i	0.621722	−	0.783238i	$-0.286433\pi$
$59$	7.66268	+	1.10173i	0.997596	+	0.143433i	0.375874	+	0.926671i	$0.377342\pi$
$60$	−6.89760	−	10.2186i	−0.890477	−	1.31921i
$61$	−2.02441	+	6.89449i	−0.259199	+	0.882750i	0.722348	+	0.691529i	$0.243063\pi$
$61$	−2.02441	+	6.89449i	−0.259199	+	0.882750i	−0.981547	+	0.191220i	$0.938756\pi$
$62$	10.1399	−	6.85931i	1.28777	−	0.871133i
$63$	9.41067	−	8.15439i	1.18563	−	1.02736i
$64$	−4.31536	−	6.73630i	−0.539420	−	0.842037i
$65$	0.0912302	+	0.00224114i	0.0113157	+	0.000277980i
$66$	−1.23126	+	1.11874i	−0.151557	+	0.137708i
$67$	4.83647	−	2.20874i	0.590869	−	0.269841i	−0.0974602	−	0.995239i	$-0.531072\pi$
$67$	4.83647	−	2.20874i	0.590869	−	0.269841i	0.688329	+	0.725399i	$0.258345\pi$
$68$	−3.18194	+	4.04214i	−0.385866	+	0.490181i
$69$	2.58221	−	12.9664i	0.310862	−	1.56097i
$70$	7.78341	+	3.56400i	0.930295	+	0.425980i
$71$	−13.3802	+	6.11053i	−1.58794	+	0.725186i	−0.996689	−	0.0813044i	$-0.974091\pi$
$71$	−13.3802	+	6.11053i	−1.58794	+	0.725186i	−0.591247	+	0.806491i	$0.701364\pi$
$72$	−0.918725	−	12.9777i	−0.108273	−	1.52944i
$73$	−5.06816	−	4.39159i	−0.593183	−	0.513996i	0.305733	−	0.952117i	$-0.401099\pi$
$73$	−5.06816	−	4.39159i	−0.593183	−	0.513996i	−0.898916	+	0.438121i	$0.855644\pi$
$74$	−8.27880	−	0.991882i	−0.962391	−	0.115304i
$75$	11.9477	−	6.87376i	1.37960	−	0.793714i
$76$	9.82185	+	5.67698i	1.12664	+	0.651194i
$77$	0.325442	−	1.10835i	0.0370876	−	0.126309i
$78$	0.135842	+	0.0828451i	0.0153811	+	0.00938036i
$79$	−1.88910	+	13.1390i	−0.212541	+	1.47825i	0.552090	+	0.833785i	$0.313830\pi$
$79$	−1.88910	+	13.1390i	−0.212541	+	1.47825i	−0.764631	+	0.644469i	$0.777079\pi$
$80$	7.85759	−	4.27296i	0.878506	−	0.477732i
$81$	−0.681785	+	1.49290i	−0.0757538	+	0.165878i
$82$	−0.445145	−	1.39370i	−0.0491580	−	0.153908i
$83$	−2.59000	−	4.03012i	−0.284290	−	0.442364i	0.669512	−	0.742802i	$-0.266503\pi$
$83$	−2.59000	−	4.03012i	−0.284290	−	0.442364i	−0.953801	+	0.300438i	$0.902867\pi$
$84$	8.65187	+	12.1623i	0.943997	+	1.32702i
$85$	−4.25287	−	3.87203i	−0.461288	−	0.419980i
$86$	2.38525	−	5.56637i	0.257208	−	0.600237i
$87$	−10.8930	−	7.00052i	−1.16785	−	0.750535i
$88$	−0.722579	−	0.966714i	−0.0770272	−	0.103052i
$89$	0.597645	+	2.03539i	0.0633503	+	0.215751i	0.985085	−	0.172071i	$-0.0550457\pi$
$89$	0.597645	+	2.03539i	0.0633503	+	0.215751i	−0.921734	+	0.387822i	$0.873228\pi$
$90$	14.5459	+	0.0145852i	1.53327	+	0.00153741i
$91$	−0.110481			−0.0115816
$92$	9.18494	+	2.76350i	0.957596	+	0.288115i
$93$			23.8638i			2.47457i
$94$	14.1671	+	11.7031i	1.46123	+	1.20708i
$95$	−7.11719	+	10.4984i	−0.730208	+	1.07711i
$96$	15.5898	+	0.389963i	1.59113	+	0.0398005i
$97$	−15.9911	−	10.2768i	−1.62365	−	1.04346i	−0.953573	−	0.301162i	$-0.902626\pi$
$97$	−15.9911	−	10.2768i	−1.62365	−	1.04346i	−0.670075	−	0.742293i	$-0.733738\pi$
$98$	−0.426829	−	0.182901i	−0.0431162	−	0.0184758i
$99$	−0.279334	−	1.94281i	−0.0280741	−	0.195259i
$100$	4.13590	+	9.10463i	0.413590	+	0.910463i
$101$	−8.67567	+	5.57551i	−0.863261	+	0.554784i	−0.895685	−	0.444690i	$-0.853314\pi$
$101$	−8.67567	+	5.57551i	−0.863261	+	0.554784i	0.0324233	+	0.999474i	$0.489678\pi$
$102$	−3.05105	−	9.55249i	−0.302099	−	0.945838i
$103$	8.44072	+	3.85475i	0.831688	+	0.379819i	0.785309	−	0.619104i	$-0.212504\pi$
$103$	8.44072	+	3.85475i	0.831688	+	0.379819i	0.0463798	+	0.998924i	$0.485232\pi$
$104$	−0.0692434	+	0.0923586i	−0.00678987	+	0.00905651i
$105$	−14.2557	+	8.67443i	−1.39121	+	0.846537i
$106$	−3.28895	+	5.39292i	−0.319451	+	0.523807i
$107$	−2.66242	+	9.06737i	−0.257386	+	0.876576i	0.724847	+	0.688910i	$0.241910\pi$
$107$	−2.66242	+	9.06737i	−0.257386	+	0.876576i	−0.982233	+	0.187666i	$0.939908\pi$
$108$	7.63673	+	4.41399i	0.734845	+	0.424737i
$109$	10.2320	−	8.86607i	0.980047	−	0.849216i	−0.00852482	−	0.999964i	$-0.502714\pi$
$109$	10.2320	−	8.86607i	0.980047	−	0.849216i	0.988572	+	0.150748i	$0.0481681\pi$
$110$	1.13590	−	0.728390i	0.108304	−	0.0694493i
$111$	10.6438	−	12.2836i	1.01027	−	1.16591i
$112$	−9.38288	+	5.40512i	−0.886599	+	0.510735i
$113$	4.95030	+	10.8397i	0.465685	+	1.01971i	0.986155	+	0.165828i	$0.0530298\pi$
$113$	4.95030	+	10.8397i	0.465685	+	1.01971i	−0.520469	+	0.853880i	$0.674243\pi$
$114$	−19.8938	+	9.65785i	−1.86322	+	0.904540i
$115$	−3.81719	+	10.0214i	−0.355955	+	0.934503i
$116$	5.81055	−	7.38137i	0.539496	−	0.685343i
$117$	−0.170761	+	0.0779841i	−0.0157869	+	0.00720963i
$118$	−7.36240	−	8.10284i	−0.677764	−	0.745927i
$119$	5.26230	+	4.55981i	0.482394	+	0.417997i
$120$	−1.68313	+	17.3539i	−0.153648	+	1.58419i
$121$	7.08423	+	8.17564i	0.644021	+	0.743240i
$122$	8.41696	−	5.69380i	0.762036	−	0.515492i
$123$	2.73646	+	0.803498i	0.246739	+	0.0724490i
$124$	−17.2337	−	1.65403i	−1.54763	−	0.148536i
$125$	−10.4843	+	3.88320i	−0.937745	+	0.347324i
$126$	−17.6050	+	0.414819i	−1.56838	+	0.0369551i
$127$	−4.58323	+	10.0359i	−0.406696	+	0.890539i	0.589852	+	0.807512i	$0.299186\pi$
$127$	−4.58323	+	10.0359i	−0.406696	+	0.890539i	−0.996547	+	0.0830275i	$0.973541\pi$
$128$	−1.36216	+	11.2314i	−0.120399	+	0.992726i
$129$	6.38225	+	9.93097i	0.561926	+	0.874373i
$130$	−0.0974507	−	0.0846127i	−0.00854699	−	0.00742103i
$131$	−3.42368	+	0.492251i	−0.299128	+	0.0430082i	−0.290245	−	0.956952i	$-0.593737\pi$
$131$	−3.42368	+	0.492251i	−0.299128	+	0.0430082i	−0.00888340	+	0.999961i	$0.502828\pi$
$132$	2.35008	−	0.110809i	0.204548	−	0.00964470i
$133$	8.30168	−	12.9177i	0.719847	−	1.12010i
$134$	−7.26262	−	1.94790i	−0.627395	−	0.168273i
$135$	−5.53379	+	8.16278i	−0.476273	+	0.702540i
$136$	7.10997	−	1.54128i	0.609675	−	0.132164i
$137$	11.9577			1.02161			0.510806	−	0.859696i	$-0.329347\pi$
$137$	11.9577			1.02161			0.510806	+	0.859696i	$0.329347\pi$
$138$	−14.4940	+	11.8117i	−1.23381	+	1.00548i
$139$		−	2.39621i		−	0.203244i	−0.994823	−	0.101622i	$-0.967597\pi$
$139$		−	2.39621i		−	0.203244i	0.994823	−	0.101622i	$-0.0324031\pi$
$140$	−5.27631	−	10.8962i	−0.445929	−	0.920899i
$141$	−34.3696	+	10.0918i	−2.89444	+	0.849884i
$142$	20.0922	+	5.38889i	1.68610	+	0.452226i
$143$	−0.00941515	+	0.0146503i	−0.000787334	+	0.00122512i
$144$	−10.6871	+	14.9772i	−0.890590	+	1.24810i
$145$	7.76619	+	7.07073i	0.644947	+	0.587192i
$146$	1.57046	+	9.35298i	0.129972	+	0.774058i
$147$	0.761506	−	0.489390i	0.0628080	−	0.0403642i
$148$	8.13309	+	8.53801i	0.668536	+	0.701820i
$149$	10.6920	+	4.88286i	0.875920	+	0.400019i	0.802056	−	0.597249i	$-0.203740\pi$
$149$	10.6920	+	4.88286i	0.875920	+	0.400019i	0.0738641	+	0.997268i	$0.476467\pi$
$150$	−19.2177	−	3.26648i	−1.56912	−	0.266707i
$151$	3.72111	+	0.535014i	0.302819	+	0.0435388i	0.292050	−	0.956403i	$-0.405663\pi$
$151$	3.72111	+	0.535014i	0.302819	+	0.0435388i	0.0107697	+	0.999942i	$0.496572\pi$
$152$	−5.59572	−	15.0360i	−0.453873	−	1.21958i
$153$	11.3521	+	3.33327i	0.917761	+	0.269479i
$154$	−1.35310	+	0.915331i	−0.109036	+	0.0737595i
$155$	3.22439	−	19.0859i	0.258990	−	1.53302i
$156$	−0.0734931	−	0.212677i	−0.00588416	−	0.0170278i
$157$	−10.1352	+	11.6966i	−0.808874	+	0.933491i	−0.998833	−	0.0483015i	$-0.984619\pi$
$157$	−10.1352	+	11.6966i	−0.808874	+	0.933491i	0.189959	+	0.981792i	$0.439165\pi$
$158$	13.8937	−	12.6241i	1.10533	−	1.00432i
$159$	−5.11516	−	11.2006i	−0.405659	−	0.888268i
$160$	−12.4158	−	2.41832i	−0.981554	−	0.191185i
$161$	4.32193	−	12.2423i	0.340616	−	0.964826i
$162$	2.08798	−	1.01365i	0.164047	−	0.0796402i
$163$	−1.58036	−	3.46051i	−0.123783	−	0.271048i	0.837588	−	0.546303i	$-0.183965\pi$
$163$	−1.58036	−	3.46051i	−0.123783	−	0.271048i	−0.961371	+	0.275255i	$0.911238\pi$
$164$	−0.769927	+	1.92049i	−0.0601212	+	0.149965i
$165$	−0.0645981	+	2.62959i	−0.00502896	+	0.204714i
$166$	−0.805943	+	6.72685i	−0.0625533	+	0.522105i
$167$	4.50125	+	5.19472i	0.348317	+	0.401980i	0.902692	−	0.430288i	$-0.141588\pi$
$167$	4.50125	+	5.19472i	0.348317	+	0.401980i	−0.554375	+	0.832267i	$0.687042\pi$
$168$	1.52111	−	21.0532i	0.117356	−	1.62429i
$169$	−12.4718	−	3.66205i	−0.959370	−	0.281696i
$170$	1.14949	+	8.05218i	0.0881618	+	0.617574i
$171$	3.71316	−	25.8256i	0.283952	−	1.97493i
$172$	−7.61418	+	3.92072i	−0.580576	+	0.298952i
$173$	13.6358	+	6.22725i	1.03671	+	0.473449i	0.859721	−	0.510764i	$-0.170638\pi$
$173$	13.6358	+	6.22725i	1.03671	+	0.473449i	0.176987	+	0.984213i	$0.443365\pi$
$174$	5.57155	+	17.4439i	0.422378	+	1.32242i
$175$	12.5735	−	5.01150i	0.950470	−	0.378833i
$176$	−0.0828636	+	1.70483i	−0.00624608	+	0.128506i
$177$	21.1243	−	3.03721i	1.58780	−	0.228291i
$178$	1.18162	−	2.75750i	0.0885660	−	0.206683i
$179$	−5.09195	+	7.92322i	−0.380590	+	0.592209i	−0.977714	−	0.209939i	$-0.932673\pi$
$179$	−5.09195	+	7.92322i	−0.380590	+	0.592209i	0.597125	+	0.802149i	$0.296310\pi$
$180$	−15.8464	−	13.1171i	−1.18112	−	0.977687i
$181$	−2.14895	−	7.31865i	−0.159730	−	0.543991i	−0.999998	−	0.00181979i	$-0.999421\pi$
$181$	−2.14895	−	7.31865i	−0.159730	−	0.543991i	0.840268	−	0.542171i	$-0.182397\pi$
$182$	0.120459	+	0.0995081i	0.00892899	+	0.00737603i
$183$			19.8090i			1.46432i
$184$	−7.52540	−	11.2858i	−0.554780	−	0.831997i
$185$	−10.1725	+	8.38610i	−0.747895	+	0.616558i
$186$	21.4937	−	26.0190i	1.57599	−	1.90781i
$187$	1.05310	−	0.309218i	0.0770103	−	0.0226123i
$188$	−4.90579	−	25.5200i	−0.357791	−	1.86124i
$189$	6.45476	−	10.0438i	0.469515	−	0.730579i
$190$	17.2156	−	5.03623i	1.24895	−	0.365366i
$191$	−2.24112	−	15.5873i	−0.162162	−	1.12786i	−0.894548	−	0.446971i	$-0.852503\pi$
$191$	−2.24112	−	15.5873i	−0.162162	−	1.12786i	0.732386	−	0.680889i	$-0.238406\pi$
$192$	−16.6465	−	14.4666i	−1.20136	−	1.04404i
$193$	−14.6960	−	22.8674i	−1.05784	−	1.64603i	−0.703145	−	0.711047i	$-0.748221\pi$
$193$	−14.6960	−	22.8674i	−1.05784	−	1.64603i	−0.354694	−	0.934983i	$-0.615415\pi$
$194$	8.17910	+	25.6078i	0.587225	+	1.83853i
$195$	0.243054	−	0.0649280i	0.0174055	−	0.00464959i
$196$	0.300641	+	0.583855i	0.0214743	+	0.0417039i
$197$	−7.14906	−	1.02788i	−0.509349	−	0.0732334i	−0.117151	−	0.993114i	$-0.537376\pi$
$197$	−7.14906	−	1.02788i	−0.509349	−	0.0732334i	−0.392198	+	0.919881i	$0.628285\pi$
$198$	−1.44529	+	2.36985i	−0.102712	+	0.168418i
$199$	5.54551	+	1.62831i	0.393111	+	0.115428i	0.472313	−	0.881431i	$-0.343419\pi$
$199$	5.54551	+	1.62831i	0.393111	+	0.115428i	−0.0792024	+	0.996859i	$0.525237\pi$
$200$	3.69094	−	13.6520i	0.260989	−	0.965342i
$201$	11.0775	−	9.59871i	0.781347	−	0.677041i
$202$	14.4809	+	1.73496i	1.01887	+	0.122071i
$203$	−9.60952	−	8.32669i	−0.674456	−	0.584419i
$204$	−5.27714	+	13.1632i	−0.369474	+	0.921608i
$205$	−2.08002	−	1.01237i	−0.145275	−	0.0707067i
$206$	−5.73111	−	11.8052i	−0.399305	−	0.822511i
$207$	−1.96128	−	21.9725i	−0.136318	−	1.52720i
$208$	0.158682	−	0.0383334i	0.0110026	−	0.00265795i
$209$	−1.00547	−	2.20168i	−0.0695499	−	0.152293i
$210$	23.3560	+	3.38199i	1.61172	+	0.233380i
$211$	6.29177	+	5.45185i	0.433144	+	0.375321i	0.843968	−	0.536393i	$-0.180214\pi$
$211$	6.29177	+	5.45185i	0.433144	+	0.375321i	−0.410824	+	0.911714i	$0.634759\pi$
$212$	8.44327	−	2.91767i	0.579886	−	0.200387i
$213$	−30.6461	+	26.5550i	−2.09984	+	1.81952i
$214$	11.0697	−	7.48826i	0.756706	−	0.511887i
$215$	−3.76259	−	8.80498i	−0.256606	−	0.600495i
$216$	−4.35081	−	11.6909i	−0.296035	−	0.795463i
$217$	−3.33498	+	23.1953i	−0.226393	+	1.57460i
$218$	−19.1415	+	0.451023i	−1.29643	+	0.0305471i
$219$	−16.8166	−	7.67991i	−1.13636	−	0.518960i
$220$	−1.89453	−	0.228910i	−0.127729	−	0.0154331i
$221$	−0.0567529	−	0.0883092i	−0.00381761	−	0.00594032i
$222$	−22.6687	+	3.80629i	−1.52142	+	0.255461i
$223$	−2.57643	−	17.9195i	−0.172531	−	1.19998i	−0.873514	−	0.486799i	$-0.838164\pi$
$223$	−2.57643	−	17.9195i	−0.172531	−	1.19998i	0.700984	−	0.713177i	$-0.252745\pi$
$224$	15.0985	+	2.55771i	1.00881	+	0.170894i
$225$	15.8965	−	16.6210i	1.05976	−	1.10807i
$226$	4.36569	−	16.2772i	0.290401	−	1.08274i
$227$	−3.53951	−	12.0545i	−0.234925	−	0.800083i	−0.989583	−	0.143964i	$-0.954015\pi$
$227$	−3.53951	−	12.0545i	−0.234925	−	0.800083i	0.754657	−	0.656119i	$-0.227803\pi$
$228$	30.3890	+	7.38785i	2.01256	+	0.489272i
$229$			5.22911i			0.345549i	0.984961	+	0.172775i	$0.0552732\pi$
$229$			5.22911i			0.345549i	−0.984961	+	0.172775i	$0.944727\pi$
$230$	13.1880	−	7.48841i	0.869592	−	0.493771i
$231$		−	3.18448i		−	0.209523i
$232$	−12.9836	+	2.81454i	−0.852412	+	0.184783i
$233$	0.939167	+	3.19851i	0.0615269	+	0.209541i	0.984519	−	0.175277i	$-0.0560822\pi$
$233$	0.939167	+	3.19851i	0.0615269	+	0.209541i	−0.922992	+	0.384819i	$0.874264\pi$
$234$	0.256422	+	0.0687744i	0.0167628	+	0.00449592i
$235$	28.8518	−	3.42739i	1.88208	−	0.223578i
$236$	0.729230	+	15.4658i	0.0474689	+	1.00674i
$237$	5.20783	+	36.2213i	0.338285	+	2.35282i
$238$	−1.63061	−	9.71125i	−0.105697	−	0.629487i
$239$	2.57575	+	4.00795i	0.166612	+	0.259253i	0.914512	−	0.404558i	$-0.132575\pi$
$239$	2.57575	+	4.00795i	0.166612	+	0.259253i	−0.747901	+	0.663811i	$0.768938\pi$
$240$	17.4655	−	17.4052i	1.12739	−	1.12350i
$241$	12.1319	+	5.54046i	0.781485	+	0.356892i	0.765878	−	0.642986i	$-0.222305\pi$
$241$	12.1319	+	5.54046i	0.781485	+	0.356892i	0.0156072	+	0.999878i	$0.495032\pi$
$242$	−0.360380	−	15.2946i	−0.0231661	−	0.983174i
$243$	−2.52685	+	17.5746i	−0.162098	+	1.12741i
$244$	−14.3054	−	1.37298i	−0.915808	−	0.0878960i
$245$	−0.675165	+	0.288515i	−0.0431347	+	0.0184325i
$246$	−2.25990	−	3.34074i	−0.144086	−	0.212998i
$247$	−0.174951	+	0.151596i	−0.0111319	+	0.00964582i
$248$	17.3003	+	17.3254i	1.09857	+	1.10017i
$249$	−9.98092	−	8.64852i	−0.632515	−	0.548077i
$250$	14.9287	+	5.20910i	0.944172	+	0.329453i
$251$	0.216544	+	0.474165i	0.0136681	+	0.0299291i	0.916343	−	0.400394i	$-0.131127\pi$
$251$	0.216544	+	0.474165i	0.0136681	+	0.0299291i	−0.902675	+	0.430323i	$0.858400\pi$
$252$	19.5686	+	15.4042i	1.23270	+	0.970375i
$253$	−1.25506	−	1.61639i	−0.0789051	−	0.101621i
$254$	14.0362	−	6.81419i	0.880712	−	0.427560i
$255$	−14.2566	−	6.93883i	−0.892782	−	0.434527i
$256$	11.6011	−	11.0188i	0.725067	−	0.688678i
$257$	8.83023	+	7.65144i	0.550815	+	0.477284i	0.885237	−	0.465140i	$-0.153996\pi$
$257$	8.83023	+	7.65144i	0.550815	+	0.477284i	−0.334423	+	0.942423i	$0.608541\pi$
$258$	1.98599	−	16.5762i	0.123642	−	1.03199i
$259$	12.0623	−	10.4520i	0.749512	−	0.649456i
$260$	0.0300425	+	0.180026i	0.00186316	+	0.0111647i
$261$	−20.7301	−	6.08691i	−1.28316	−	0.376770i
$262$	4.17623	+	2.54693i	0.258009	+	0.157350i
$263$	−12.8191	−	1.84311i	−0.790459	−	0.113651i	−0.264752	−	0.964317i	$-0.585290\pi$
$263$	−12.8191	−	1.84311i	−0.790459	−	0.113651i	−0.525707	+	0.850666i	$0.676199\pi$
$264$	−2.66212	−	1.99585i	−0.163842	−	0.122836i
$265$	2.57764	+	9.64924i	0.158343	+	0.592748i
$266$	−20.6861	+	6.60711i	−1.26835	+	0.405108i
$267$	3.16167	+	4.91966i	0.193491	+	0.301078i
$268$	6.16408	+	8.66510i	0.376531	+	0.529305i
$269$	−4.27927	−	29.7630i	−0.260911	−	1.81468i	−0.526033	−	0.850464i	$-0.676321\pi$
$269$	−4.27927	−	29.7630i	−0.260911	−	1.81468i	0.265121	−	0.964215i	$-0.414588\pi$
$270$	13.3856	−	3.91579i	0.814621	−	0.238307i
$271$	−14.2771	+	22.2157i	−0.867275	+	1.34951i	0.0687731	+	0.997632i	$0.478092\pi$
$271$	−14.2771	+	22.2157i	−0.867275	+	1.34951i	−0.936048	+	0.351873i	$0.885545\pi$
$272$	−9.14027	−	4.72333i	−0.554210	−	0.286394i
$273$	−0.292234	+	0.0858077i	−0.0176868	+	0.00519332i
$274$	−13.0376	−	10.7700i	−0.787627	−	0.650640i
$275$	0.406965	−	2.09438i	0.0245409	−	0.126296i
$276$	26.4415	+	0.176069i	1.59159	+	0.0105981i
$277$		−	30.6954i		−	1.84431i	−0.386826	−	0.922153i	$-0.626429\pi$
$277$		−	30.6954i		−	1.84431i	0.386826	−	0.922153i	$-0.373571\pi$
$278$	−2.15821	+	2.61261i	−0.129441	+	0.156694i
$279$	11.2180	+	38.2050i	0.671604	+	2.28727i
$280$	−4.06119	+	16.6325i	−0.242703	+	0.993984i
$281$	6.17425	−	9.60733i	0.368325	−	0.573125i	−0.606780	−	0.794870i	$-0.707539\pi$
$281$	6.17425	−	9.60733i	0.368325	−	0.573125i	0.975105	+	0.221745i	$0.0711753\pi$
$282$	46.5630	+	19.9528i	2.77278	+	1.18817i
$283$	−24.1088	+	3.46633i	−1.43312	+	0.206052i	−0.814740	−	0.579826i	$-0.803121\pi$
$283$	−24.1088	+	3.46633i	−1.43312	+	0.206052i	−0.618382	+	0.785878i	$0.712211\pi$
$284$	−17.0530	−	23.9722i	−1.01191	−	1.42249i
$285$	−10.6719	+	33.2971i	−0.632147	+	1.97235i
$286$	0.0234606	−	0.00749329i	0.00138726	−	0.000443088i
$287$	2.54751	+	1.16341i	0.150375	+	0.0686738i
$288$	25.1419	−	6.70419i	1.48150	−	0.395048i
$289$	1.47781	−	10.2784i	0.0869301	−	0.604612i
$290$	−2.09909	−	14.7041i	−0.123263	−	0.863457i
$291$	−50.2798	−	14.7635i	−2.94746	−	0.865451i
$292$	6.71175	−	11.6121i	0.392776	−	0.679548i
$293$	−13.6328	−	15.7331i	−0.796436	−	0.919137i	0.201744	−	0.979438i	$-0.435339\pi$
$293$	−13.6328	−	15.7331i	−0.796436	−	0.919137i	−0.998180	+	0.0603018i	$0.980794\pi$
$294$	−1.27106	−	0.152286i	−0.0741298	−	0.00888149i
$295$	−17.3053	−	0.425118i	−1.00755	−	0.0247513i
$296$	−1.17759	−	16.6344i	−0.0684459	−	0.966854i
$297$	−0.781779	−	1.71186i	−0.0453634	−	0.0993320i
$298$	−7.25967	−	14.9539i	−0.420541	−	0.866254i
$299$	−0.114515	+	0.158730i	−0.00662255	+	0.00917957i
$300$	18.0112	+	20.8705i	1.03988	+	1.20496i
$301$	4.81558	+	10.5447i	0.277566	+	0.607784i
$302$	−3.57528	−	3.93486i	−0.205734	−	0.226426i
$303$	−18.6177	+	21.4860i	−1.06956	+	1.23434i
$304$	−7.44155	+	21.4339i	−0.426802	+	1.22932i
$305$	2.67651	−	15.8429i	0.153257	−	0.907162i
$306$	−9.37508	−	13.8589i	−0.535938	−	0.792260i
$307$	−11.3532	−	3.33361i	−0.647964	−	0.190259i	−0.0587958	−	0.998270i	$-0.518726\pi$
$307$	−11.3532	−	3.33361i	−0.647964	−	0.190259i	−0.589168	+	0.808011i	$0.700544\pi$
$308$	2.29972	+	0.220719i	0.131039	+	0.0125766i
$309$	25.3205	+	3.64053i	1.44043	+	0.207103i
$310$	−20.7059	+	17.9054i	−1.17602	+	1.01696i
$311$	16.5151	+	7.54220i	0.936486	+	0.427679i	0.824392	−	0.566019i	$-0.191517\pi$
$311$	16.5151	+	7.54220i	0.936486	+	0.427679i	0.112094	+	0.993698i	$0.464244\pi$
$312$	−0.111424	+	0.298078i	−0.00630812	+	0.0168753i
$313$	4.05685	−	2.60718i	0.229307	−	0.147366i	−0.420943	−	0.907087i	$-0.638301\pi$
$313$	4.05685	−	2.60718i	0.229307	−	0.147366i	0.650249	+	0.759721i	$0.274664\pi$
$314$	21.5854	−	3.62439i	1.21813	−	0.204536i
$315$	−18.7451	+	20.5888i	−1.05616	+	1.16005i
$316$	−26.5188	+	1.25039i	−1.49180	+	0.0703401i
$317$	10.1766	−	15.8351i	0.571576	−	0.889390i	−0.428322	−	0.903626i	$-0.640895\pi$
$317$	10.1766	−	15.8351i	0.571576	−	0.889390i	0.999899	+	0.0142358i	$0.00453155\pi$
$318$	−4.51107	+	16.8193i	−0.252968	+	0.943179i
$319$	−1.92307	+	0.564665i	−0.107671	+	0.0316152i
$320$	11.3589	+	13.8194i	0.634983	+	0.772526i
$321$			26.0520i			1.45408i
$322$	−15.7386	+	9.45520i	−0.877078	+	0.526918i
$323$	14.5898			0.811796
$324$	−3.18953	−	0.775404i	−0.177196	−	0.0430780i
$325$	−0.203164	+	0.0190878i	−0.0112695	+	0.00105880i
$326$	−1.39373	+	5.19643i	−0.0771913	+	0.287804i
$327$	20.1787	−	31.3986i	1.11588	−	1.73635i
$328$	2.56921	−	1.40048i	0.141861	−	0.0773283i
$329$	−34.8170	+	5.00593i	−1.91952	+	0.275986i
$330$	2.43885	−	2.80889i	0.134254	−	0.154624i
$331$	0.616439	+	0.959198i	0.0338826	+	0.0527223i	0.857782	−	0.514014i	$-0.171842\pi$
$331$	0.616439	+	0.959198i	0.0338826	+	0.0527223i	−0.823899	+	0.566736i	$0.808206\pi$
$332$	6.93746	−	6.60846i	0.380743	−	0.362686i
$333$	11.2660	−	24.6690i	0.617372	−	1.35186i
$334$	−0.228982	−	9.71804i	−0.0125293	−	0.531748i
$335$	−10.1566	+	6.18015i	−0.554912	+	0.337658i
$336$	−20.6207	+	21.5845i	−1.12495	+	1.17753i
$337$	−17.5048	−	5.13988i	−0.953549	−	0.279987i	−0.232285	−	0.972648i	$-0.574620\pi$
$337$	−17.5048	−	5.13988i	−0.953549	−	0.279987i	−0.721264	+	0.692660i	$0.756438\pi$
$338$	10.2998	+	15.2259i	0.560236	+	0.828179i
$339$	21.5129	+	24.8273i	1.16842	+	1.34843i
$340$	5.99914	−	9.81470i	0.325349	−	0.532277i
$341$	2.79158	+	2.41892i	0.151173	+	0.130992i
$342$	−27.3091	+	24.8135i	−1.47671	+	1.34176i
$343$	−16.4286	+	7.50271i	−0.887064	+	0.405108i
$344$	11.8331	+	2.58313i	0.638000	+	0.139273i
$345$	−2.31349	+	29.4724i	−0.124554	+	1.58674i
$346$	−9.25846	−	19.0711i	−0.497738	−	1.02527i
$347$	11.6847	+	25.5858i	0.627266	+	1.37352i	0.910115	+	0.414356i	$0.135993\pi$
$347$	11.6847	+	25.5858i	0.627266	+	1.37352i	−0.282849	+	0.959164i	$0.591280\pi$
$348$	9.63661	−	24.0374i	0.516577	−	1.28854i
$349$	9.60955	−	11.0900i	0.514387	−	0.593635i	−0.437829	−	0.899058i	$-0.644253\pi$
$349$	9.60955	−	11.0900i	0.514387	−	0.593635i	0.952217	+	0.305423i	$0.0987980\pi$
$350$	−18.2228	−	5.86064i	−0.974050	−	0.313264i
$351$	−0.136029	+	0.117870i	−0.00726068	+	0.00629141i
$352$	1.62585	−	1.78416i	0.0866582	−	0.0950961i
$353$	−1.78984	+	6.09563i	−0.0952635	+	0.324438i	−0.993312	−	0.115458i	$-0.963166\pi$
$353$	−1.78984	+	6.09563i	−0.0952635	+	0.324438i	0.898049	+	0.439896i	$0.144985\pi$
$354$	−25.7676	−	15.7147i	−1.36953	−	0.835227i
$355$	28.0983	−	17.0975i	1.49130	−	0.907441i
$356$	−3.77195	+	1.94227i	−0.199913	+	0.102940i
$357$	17.4608	+	7.97409i	0.924124	+	0.422033i
$358$	12.6881	−	4.05256i	0.670586	−	0.214184i
$359$	−12.8119	+	8.23368i	−0.676184	+	0.434557i	−0.833150	−	0.553047i	$-0.813465\pi$
$359$	−12.8119	+	8.23368i	−0.676184	+	0.434557i	0.156966	+	0.987604i	$0.449829\pi$
$360$	5.46318	+	28.5741i	0.287935	+	1.50599i
$361$	−1.87489	−	13.0401i	−0.0986782	−	0.686322i
$362$	−4.24873	+	9.91511i	−0.223308	+	0.521126i
$363$	25.0883	+	16.1233i	1.31680	+	0.846253i
$364$	−0.0417124	−	0.216989i	−0.00218633	−	0.0113733i
$365$	12.4120	+	8.41447i	0.649675	+	0.440434i
$366$	17.8415	−	21.5979i	0.932592	−	1.12894i
$367$			4.90639i			0.256112i	0.991767	+	0.128056i	$0.0408736\pi$
$367$			4.90639i			0.256112i	−0.991767	+	0.128056i	$0.959126\pi$
$368$	−1.95984	+	19.0830i	−0.102163	+	0.994768i
$369$	4.75868			0.247727
$370$	18.6443	+	0.0186947i	0.969273	+	0.000971892i
$371$	−3.40656	−	11.6017i	−0.176860	−	0.602329i
$372$	−46.8696	+	9.00986i	−2.43007	+	0.467140i
$373$	−23.0703	−	14.8264i	−1.19454	−	0.767682i	−0.216534	−	0.976275i	$-0.569475\pi$
$373$	−23.0703	−	14.8264i	−1.19454	−	0.767682i	−0.978002	+	0.208593i	$0.933112\pi$
$374$	−1.42671	−	0.611362i	−0.0737735	−	0.0316128i
$375$	−24.7161	+	18.4144i	−1.27634	+	0.950914i
$376$	−17.6365	+	32.2433i	−0.909535	+	1.66282i
$377$	0.103637	+	0.161262i	0.00533756	+	0.00830541i
$378$	−16.0839	+	5.13719i	−0.827269	+	0.264229i
$379$	13.3196	−	29.1659i	0.684182	−	1.49815i	−0.173968	−	0.984751i	$-0.555659\pi$
$379$	13.3196	−	29.1659i	0.684182	−	1.49815i	0.858150	−	0.513399i	$-0.171614\pi$
$380$	−23.3064	−	10.0147i	−1.19559	−	0.513745i
$381$	−4.32853	+	30.1056i	−0.221757	+	1.54236i
$382$	−11.5957	+	19.0136i	−0.593287	+	0.972819i
$383$	7.24937	−	24.6891i	0.370425	−	1.26155i	−0.537800	−	0.843072i	$-0.680745\pi$
$383$	7.24937	−	24.6891i	0.370425	−	1.26155i	0.908226	−	0.418481i	$-0.137437\pi$
$384$	5.12007	+	30.7662i	0.261282	+	1.57003i
$385$	−0.430274	+	2.54689i	−0.0219288	+	0.129802i
$386$	−4.57301	+	38.1689i	−0.232760	+	1.94274i
$387$	14.8861	+	12.8989i	0.756703	+	0.655687i
$388$	14.1467	−	35.2872i	0.718188	−	1.79143i
$389$	33.5561	−	15.3245i	1.70136	−	0.776985i	0.703564	−	0.710632i	$-0.251591\pi$
$389$	33.5561	−	15.3245i	1.70136	−	0.776985i	0.997796	−	0.0663532i	$-0.0211364\pi$
$390$	−0.323484	−	0.148122i	−0.0163802	−	0.00750046i
$391$	12.0056	−	2.83413i	0.607147	−	0.143328i
$392$	0.198074	−	0.907364i	0.0100043	−	0.0458288i
$393$	−8.67368	+	3.96114i	−0.437529	+	0.199813i
$394$	6.86890	+	7.55972i	0.346050	+	0.380853i
$395$	0.728938	−	29.6729i	0.0366769	−	1.49300i
$396$	3.71029	−	1.28213i	0.186449	−	0.0644297i
$397$	−11.4304	+	9.90452i	−0.573677	+	0.497094i	−0.892699	−	0.450654i	$-0.851191\pi$
$397$	−11.4304	+	9.90452i	−0.573677	+	0.497094i	0.319022	+	0.947747i	$0.396646\pi$
$398$	−4.57974	−	6.77009i	−0.229562	−	0.339354i
$399$	11.9260	−	40.6163i	0.597048	−	2.03336i
$400$	−16.3203	+	11.5606i	−0.816017	+	0.578028i
$401$	−10.6602	−	1.53270i	−0.532343	−	0.0765393i	−0.129099	−	0.991632i	$-0.541208\pi$
$401$	−10.6602	−	1.53270i	−0.532343	−	0.0765393i	−0.403244	+	0.915092i	$0.632117\pi$
$402$	−20.7233	+	0.488293i	−1.03358	+	0.0243538i
$403$	0.146759	−	0.321358i	0.00731061	−	0.0160080i
$404$	−14.2261	−	14.9343i	−0.707773	−	0.743010i
$405$	1.12008	−	3.49476i	0.0556574	−	0.173656i
$406$	2.97767	+	17.7338i	0.147779	+	0.880112i
$407$	−0.358040	−	2.49022i	−0.0177474	−	0.123436i
$408$	17.6095	−	9.59896i	0.871802	−	0.475220i
$409$	−0.151393	−	0.0972942i	−0.00748589	−	0.00481089i	0.536893	−	0.843651i	$-0.319598\pi$
$409$	−0.151393	−	0.0972942i	−0.00748589	−	0.00481089i	−0.544378	+	0.838840i	$0.683234\pi$
$410$	1.35604	+	2.97722i	0.0669703	+	0.147034i
$411$	31.6293	−	9.28719i	1.56016	−	0.458103i
$412$	−4.38406	+	18.0333i	−0.215987	+	0.888436i
$413$	20.9569			1.03122
$414$	−17.6518	+	25.7234i	−0.867539	+	1.26423i
$415$	6.81403	+	8.26553i	0.334488	+	0.405739i
$416$	−0.207539	−	0.101127i	−0.0101754	−	0.00495814i
$417$	−1.86107	−	6.33822i	−0.0911369	−	0.310384i
$418$	−0.886728	+	3.30612i	−0.0433713	+	0.161707i
$419$	11.1884	+	7.19032i	0.546587	+	0.351270i	0.784610	−	0.619989i	$-0.212863\pi$
$419$	11.1884	+	7.19032i	0.546587	+	0.351270i	−0.238023	+	0.971259i	$0.576499\pi$
$420$	−22.4192	−	24.7237i	−1.09394	−	1.20639i
$421$	18.3741	−	2.64179i	0.895497	−	0.128753i	0.320826	−	0.947138i	$-0.396039\pi$
$421$	18.3741	−	2.64179i	0.895497	−	0.128753i	0.574670	+	0.818385i	$0.305130\pi$
$422$	−1.94961	−	11.6111i	−0.0949057	−	0.565219i
$423$	−50.2802	+	32.3131i	−2.44471	+	1.57112i
$424$	−11.8337	−	4.42351i	−0.574694	−	0.214825i
$425$	10.4646	+	7.47587i	0.507610	+	0.362633i
$426$	57.3314	−	1.35087i	2.77771	−	0.0654500i
$427$	−2.76831	+	19.2540i	−0.133968	+	0.931766i
$428$	−18.8139	−	1.80569i	−0.909403	−	0.0872813i
$429$	−0.0135256	+	0.0460640i	−0.000653022	+	0.00222399i
$430$	−3.82808	+	12.9890i	−0.184606	+	0.626387i
$431$	12.9228	+	14.9137i	0.622470	+	0.718368i	0.976174	−	0.216989i	$-0.0696236\pi$
$431$	12.9228	+	14.9137i	0.622470	+	0.718368i	−0.353704	+	0.935357i	$0.615078\pi$
$432$	−5.78599	+	16.6654i	−0.278379	+	0.801812i
$433$	6.09375	−	7.03256i	0.292847	−	0.337963i	−0.590192	−	0.807263i	$-0.700948\pi$
$433$	6.09375	−	7.03256i	0.292847	−	0.337963i	0.883039	+	0.469299i	$0.155494\pi$
$434$	24.5277	−	22.2863i	1.17737	−	1.06978i
$435$	26.0340	+	12.6710i	1.24824	+	0.607530i
$436$	21.2764	+	16.7486i	1.01896	+	0.802114i
$437$	−9.95422	−	25.3164i	−0.476175	−	1.21105i
$438$	11.4182	+	23.5199i	0.545584	+	1.12382i
$439$	−16.0950	+	7.35035i	−0.768174	+	0.350813i	−0.760653	−	0.649159i	$-0.775121\pi$
$439$	−16.0950	+	7.35035i	−0.768174	+	0.350813i	−0.00752047	+	0.999972i	$0.502394\pi$
$440$	1.85945	+	1.95595i	0.0886458	+	0.0932461i
$441$	0.989085	−	1.14147i	0.0470993	−	0.0543555i
$442$	−0.0176600	+	0.147401i	−0.000840003	+	0.00701113i
$443$	5.80920	+	6.70417i	0.276003	+	0.318525i	0.876780	−	0.480892i	$-0.159687\pi$
$443$	5.80920	+	6.70417i	0.276003	+	0.318525i	−0.600776	+	0.799417i	$0.705142\pi$
$444$	28.1441	+	16.2672i	1.33566	+	0.772006i
$445$	−1.86393	−	4.36186i	−0.0883587	−	0.206772i
$446$	−13.3306	+	21.8583i	−0.631222	+	1.03502i
$447$	32.0738	+	4.61151i	1.51704	+	0.218117i
$448$	−14.1584	−	16.3876i	−0.668921	−	0.774243i
$449$	−11.2017	+	24.5283i	−0.528642	+	1.15756i	0.437421	+	0.899257i	$0.355892\pi$
$449$	−11.2017	+	24.5283i	−0.528642	+	1.15756i	−0.966063	+	0.258307i	$0.916835\pi$
$450$	−32.3023	+	3.80444i	−1.52274	+	0.179343i
$451$	0.371370	−	0.238665i	0.0174871	−	0.0112383i
$452$	−19.4205	+	13.8151i	−0.913464	+	0.649809i
$453$	10.2583	−	1.47491i	0.481975	−	0.0692975i
$454$	−6.99804	+	16.3311i	−0.328434	+	0.766455i
$455$	0.245318	−	0.0291421i	0.0115007	−	0.00136620i
$456$	−26.4793	−	35.4258i	−1.24001	−	1.65896i
$457$	−23.0200	+	6.75927i	−1.07683	+	0.316186i	−0.771610	−	0.636097i	$-0.780548\pi$
$457$	−23.0200	+	6.75927i	−1.07683	+	0.316186i	−0.305219	+	0.952282i	$0.598730\pi$
$458$	4.70975	−	5.70135i	0.220072	−	0.266407i
$459$	11.3439			0.529488
$460$	−21.1237	−	3.71349i	−0.984897	−	0.173142i
$461$	−9.17672			−0.427403			−0.213701	−	0.976899i	$-0.568552\pi$
$461$	−9.17672			−0.427403			−0.213701	+	0.976899i	$0.568552\pi$
$462$	−2.86819	+	3.47207i	−0.133440	+	0.161535i
$463$	29.6127	−	8.69508i	1.37622	−	0.404095i	0.491768	−	0.870726i	$-0.336351\pi$
$463$	29.6127	−	8.69508i	1.37622	−	0.404095i	0.884452	+	0.466632i	$0.154533\pi$
$464$	16.6911	+	8.62530i	0.774865	+	0.400420i
$465$	−6.29467	−	52.9886i	−0.291908	−	2.45729i
$466$	1.85685	−	4.33326i	0.0860168	−	0.200734i
$467$	20.6840	−	2.97390i	0.957139	−	0.137616i	0.353994	−	0.935248i	$-0.384823\pi$
$467$	20.6840	−	2.97390i	0.957139	−	0.137616i	0.603145	+	0.797632i	$0.293914\pi$
$468$	−0.217635	−	0.305939i	−0.0100602	−	0.0141420i
$469$	12.1086	−	7.78171i	0.559122	−	0.359326i
$470$	−34.5444	−	22.2493i	−1.59341	−	1.02628i
$471$	−17.7241	+	38.8105i	−0.816685	+	1.78829i
$472$	13.1346	−	17.5193i	0.604570	−	0.806391i
$473$	1.80865	+	0.260044i	0.0831617	+	0.0119568i
$474$	26.9456	−	44.1830i	1.23765	−	2.02939i
$475$	13.0342	−	25.1886i	0.598049	−	1.15573i
$476$	−6.96885	+	12.0569i	−0.319417	+	0.552629i
$477$	−13.4544	−	15.5272i	−0.616034	−	0.710941i
$478$	0.801509	−	6.68984i	0.0366602	−	0.305986i
$479$	10.2824	−	11.8665i	0.469813	−	0.542193i	−0.470547	−	0.882375i	$-0.655943\pi$
$479$	10.2824	−	11.8665i	0.469813	−	0.542193i	0.940360	+	0.340182i	$0.110489\pi$
$480$	−34.7193	+	3.24629i	−1.58471	+	0.148172i
$481$	−0.218876	+	0.0999572i	−0.00997988	+	0.00455766i
$482$	−8.23737	−	16.9678i	−0.375202	−	0.772862i
$483$	1.92371	−	35.7388i	0.0875319	−	1.62617i
$484$	−13.3826	+	17.0004i	−0.608300	+	0.772748i
$485$	38.2182	+	18.6012i	1.73540	+	0.844639i
$486$	18.5842	−	16.8859i	0.842995	−	0.765961i
$487$	21.9236	−	25.3012i	0.993454	−	1.14651i	0.00424622	−	0.999991i	$-0.498648\pi$
$487$	21.9236	−	25.3012i	0.993454	−	1.14651i	0.989208	−	0.146517i	$-0.0468062\pi$
$488$	14.3607	+	14.3815i	0.650078	+	0.651022i
$489$	−6.86791	−	7.92599i	−0.310578	−	0.358426i
$490$	0.995999	+	0.293537i	0.0449947	+	0.0132606i
$491$	−0.544856	+	1.85561i	−0.0245890	+	0.0837425i	−0.970873	−	0.239593i	$-0.922986\pi$
$491$	−0.544856	+	1.85561i	−0.0245890	+	0.0837425i	0.946284	+	0.323335i	$0.104804\pi$
$492$	−0.544943	+	5.67789i	−0.0245679	+	0.255979i
$493$	1.71935	−	11.9584i	0.0774357	−	0.538577i
$494$	0.327290	−	0.00771179i	0.0147255	−	0.000346970i
$495$	1.13271	+	4.24024i	0.0509115	+	0.190584i
$496$	−3.25805	−	34.4721i	−0.146291	−	1.54784i
$497$	−33.4986	+	21.5282i	−1.50262	+	0.965674i
$498$	3.09276	+	18.4192i	0.138590	+	0.825383i
$499$	−6.16262	+	0.886051i	−0.275877	+	0.0396651i	−0.278865	−	0.960330i	$-0.589958\pi$
$499$	−6.16262	+	0.886051i	−0.275877	+	0.0396651i	0.00298775	+	0.999996i	$0.499049\pi$
$500$	−11.5852	−	19.1255i	−0.518104	−	0.855318i
$501$	15.9409	+	10.2446i	0.712186	+	0.457694i
$502$	0.190971	−	0.712024i	0.00852345	−	0.0317792i
$503$	2.74710	+	9.35576i	0.122487	+	0.417153i	0.997792	−	0.0664190i	$-0.0211574\pi$
$503$	2.74710	+	9.35576i	0.122487	+	0.417153i	−0.875305	+	0.483572i	$0.839339\pi$
$504$	−7.46156	−	34.4204i	−0.332364	−	1.53321i
$505$	17.7933	−	14.6686i	0.791790	−	0.652744i
$506$	−0.0874372	+	2.89277i	−0.00388706	+	0.128599i
$507$	−35.8335			−1.59142
$508$	−21.4413	−	5.21257i	−0.951302	−	0.231270i
$509$	28.1569	−	8.26762i	1.24803	−	0.366456i	0.410006	−	0.912083i	$-0.365527\pi$
$509$	28.1569	−	8.26762i	1.24803	−	0.366456i	0.838028	+	0.545627i	$0.183708\pi$
$510$	9.29443	+	20.4061i	0.411564	+	0.903597i
$511$	−15.2722	−	9.81487i	−0.675604	−	0.434184i
$512$	−22.5732	+	1.56511i	−0.997605	+	0.0691686i
$513$	−3.56018	−	24.7616i	−0.157186	−	1.09325i
$514$	−2.73620	−	16.2957i	−0.120688	−	0.718770i
$515$	−19.7590	−	6.33285i	−0.870686	−	0.279059i
$516$	−17.0952	+	16.2845i	−0.752574	+	0.716883i
$517$	−2.30328	+	5.04348i	−0.101298	+	0.221812i
$518$	−22.5655	+	0.531700i	−0.991471	+	0.0233616i
$519$	40.9046	+	5.88119i	1.79551	+	0.258156i
$520$	0.129390	−	0.223343i	0.00567413	−	0.00979423i
$521$	2.81671	−	9.59282i	0.123402	−	0.420269i	−0.874499	−	0.485028i	$-0.838810\pi$
$521$	2.81671	−	9.59282i	0.123402	−	0.420269i	0.997901	+	0.0647586i	$0.0206277\pi$
$522$	17.1199	+	25.3078i	0.749317	+	1.10769i
$523$	−17.2477	+	14.9452i	−0.754188	+	0.653507i	−0.944610	−	0.328195i	$-0.893560\pi$
$523$	−17.2477	+	14.9452i	−0.754188	+	0.653507i	0.190422	+	0.981702i	$0.439014\pi$
$524$	−2.25942	−	6.53840i	−0.0987033	−	0.285631i
$525$	29.3660	−	23.0215i	1.28164	−	1.00474i
$526$	12.3167	+	13.5554i	0.537035	+	0.591046i
$527$	−20.2535	+	9.24945i	−0.882255	+	0.402912i
$528$	1.10491	+	4.57381i	0.0480852	+	0.199050i
$529$	−13.1089	−	18.8986i	−0.569953	−	0.821678i
$530$	5.88045	−	12.8423i	0.255430	−	0.557833i
$531$	32.3913	−	14.7926i	1.40566	−	0.641946i
$532$	28.5051	+	11.4277i	1.23585	+	0.495455i
$533$	−0.0319087	−	0.0276491i	−0.00138212	−	0.00119761i
$534$	0.983831	−	8.21160i	0.0425745	−	0.355351i
$535$	3.52005	−	20.8360i	0.152185	−	0.900818i
$536$	1.08372	−	14.9995i	0.0468097	−	0.647880i
$537$	−7.31498	+	24.9125i	−0.315665	+	1.07506i
$538$	−22.1412	+	36.3051i	−0.954573	+	1.56522i
$539$	0.0199402	−	0.138687i	0.000858884	−	0.00597367i
$540$	−18.1213	−	7.78670i	−0.779817	−	0.335086i
$541$	−3.76788	+	8.25050i	−0.161994	+	0.354717i	−0.973171	−	0.230084i	$-0.926100\pi$
$541$	−3.76788	+	8.25050i	−0.161994	+	0.354717i	0.811177	+	0.584801i	$0.198827\pi$
$542$	35.5757	−	11.3628i	1.52811	−	0.488076i
$543$	−11.3684	−	17.6896i	−0.487864	−	0.759132i
$544$	5.71152	+	13.3823i	0.244879	+	0.573763i
$545$	−20.3810	+	22.3857i	−0.873028	+	0.958896i
$546$	0.395911	+	0.169652i	0.0169434	+	0.00726045i
$547$	16.0328	+	10.3037i	0.685514	+	0.440553i	0.836488	−	0.547985i	$-0.184605\pi$
$547$	16.0328	+	10.3037i	0.685514	+	0.440553i	−0.150974	+	0.988538i	$0.548241\pi$
$548$	4.51465	+	23.4853i	0.192856	+	1.00324i
$549$	9.31187	+	31.7133i	0.397421	+	1.35349i
$550$	−2.33008	+	1.91698i	−0.0993551	+	0.0817403i
$551$	−26.6425			−1.13501
$552$	−28.6708	−	24.0073i	−1.22031	−	1.02182i
$553$			35.9343i			1.52808i
$554$	−27.6467	+	33.4675i	−1.17460	+	1.42190i
$555$	−20.3940	+	30.0828i	−0.865678	+	1.27694i
$556$	4.70624	−	0.904694i	0.199589	−	0.0383676i
$557$	14.7741	+	9.49474i	0.625999	+	0.402305i	0.814826	−	0.579705i	$-0.196832\pi$
$557$	14.7741	+	9.49474i	0.625999	+	0.402305i	−0.188827	+	0.982010i	$0.560469\pi$
$558$	22.1794	−	51.7591i	0.938928	−	2.19114i
$559$	−0.0248713	−	0.172984i	−0.00105194	−	0.00731643i
$560$	19.4085	−	14.4768i	0.820160	−	0.611756i
$561$	2.54540	−	1.63583i	0.107467	−	0.0690648i
$562$	−15.3850	+	4.91394i	−0.648976	+	0.207282i
$563$	33.1231	+	15.1268i	1.39597	+	0.637518i	0.964373	−	0.264548i	$-0.0852226\pi$
$563$	33.1231	+	15.1268i	1.39597	+	0.637518i	0.431598	+	0.902066i	$0.357950\pi$
$564$	−32.7971	−	63.6930i	−1.38100	−	2.68196i
$565$	−13.8512	−	22.7632i	−0.582722	−	0.957655i
$566$	29.4082	+	17.9350i	1.23612	+	0.753863i
$567$	−1.25171	+	4.26295i	−0.0525671	+	0.179027i
$568$	−2.99814	+	41.4964i	−0.125799	+	1.74115i
$569$	−34.2281	+	29.6588i	−1.43492	+	1.24336i	−0.511656	+	0.859191i	$0.670968\pi$
$569$	−34.2281	+	29.6588i	−1.43492	+	1.24336i	−0.923261	+	0.384172i	$0.874487\pi$
$570$	41.6257	−	26.6923i	1.74351	−	1.11802i
$571$	−2.53915	+	2.93034i	−0.106260	+	0.122631i	−0.806388	−	0.591387i	$-0.798581\pi$
$571$	−2.53915	+	2.93034i	−0.106260	+	0.122631i	0.700128	+	0.714017i	$0.253126\pi$
$572$	−0.0323284	−	0.0129605i	−0.00135172	−	0.000541905i
$573$	−18.0343	−	39.4895i	−0.753392	−	1.64970i
$574$	−1.72972	−	3.56297i	−0.0721970	−	0.148715i
$575$	5.83250	−	23.2590i	0.243232	−	0.969968i
$576$	−33.4508	−	15.3352i	−1.39378	−	0.638965i
$577$	11.7366	−	5.35994i	0.488602	−	0.223137i	−0.155851	−	0.987781i	$-0.549812\pi$
$577$	11.7366	−	5.35994i	0.488602	−	0.223137i	0.644454	+	0.764643i	$0.277085\pi$
$578$	−10.8688	+	9.87562i	−0.452084	+	0.410772i
$579$	−56.6328	−	49.0726i	−2.35358	−	2.03939i
$580$	−10.9551	+	17.9227i	−0.454884	+	0.744199i
$581$	−8.49266	−	9.80105i	−0.352335	−	0.406616i
$582$	41.5234	+	61.3828i	1.72120	+	2.54440i
$583$	−1.82874	−	0.536965i	−0.0757385	−	0.0222388i
$584$	−17.7767	+	6.61568i	−0.735605	+	0.273759i
$585$	0.358598	−	0.218203i	0.0148262	−	0.00902157i
$586$	0.693509	+	29.4327i	0.0286486	+	1.21585i
$587$	−12.3999	+	27.1521i	−0.511801	+	1.12069i	0.460651	+	0.887581i	$0.347616\pi$
$587$	−12.3999	+	27.1521i	−0.511801	+	1.12069i	−0.972451	+	0.233106i	$0.925111\pi$
$588$	1.24869	+	1.31086i	0.0514952	+	0.0540589i
$589$	26.5462	+	41.3067i	1.09382	+	1.70201i
$590$	18.4852	+	16.0500i	0.761024	+	0.660768i
$591$	−19.7083	+	2.83363i	−0.810693	+	0.116560i
$592$	−13.6983	+	19.1973i	−0.562997	+	0.789003i
$593$	−14.4259	+	22.4472i	−0.592402	+	0.921795i	0.407561	+	0.913178i	$0.366379\pi$
$593$	−14.4259	+	22.4472i	−0.592402	+	0.921795i	−0.999963	+	0.00861712i	$0.997257\pi$
$594$	−0.689453	+	2.57059i	−0.0282886	+	0.105472i
$595$	−12.8875	−	8.73679i	−0.528334	−	0.358174i
$596$	−5.55335	+	22.8430i	−0.227474	+	0.935685i
$597$	15.9331			0.652099
$598$	0.267821	−	0.0699236i	0.0109520	−	0.00285939i
$599$			21.2241i			0.867192i	0.901107	+	0.433596i	$0.142755\pi$
$599$			21.2241i			0.867192i	−0.901107	+	0.433596i	$0.857245\pi$
$600$	−0.840206	−	38.9776i	−0.0343013	−	1.59125i
$601$	5.62208	−	1.65079i	0.229329	−	0.0673372i	−0.165049	−	0.986285i	$-0.552778\pi$
$601$	5.62208	−	1.65079i	0.229329	−	0.0673372i	0.394378	+	0.918948i	$0.370960\pi$
$602$	4.24688	−	15.8342i	0.173090	−	0.645356i
$603$	13.2224	−	20.5745i	0.538459	−	0.837858i
$604$	0.354125	+	7.51040i	0.0144091	+	0.305594i
$605$	−17.8867	−	16.2850i	−0.727199	−	0.662079i
$606$	39.6511	−	6.65780i	1.61071	−	0.270454i
$607$	−2.07804	+	1.33548i	−0.0843451	+	0.0542053i	−0.582134	−	0.813093i	$-0.697782\pi$
$607$	−2.07804	+	1.33548i	−0.0843451	+	0.0542053i	0.497789	+	0.867298i	$0.334146\pi$
$608$	27.4186	−	16.6671i	1.11197	−	0.675941i
$609$	−31.8853	−	14.5615i	−1.29206	−	0.590063i
$610$	−17.1876	+	14.8630i	−0.695906	+	0.601785i
$611$	0.524895	+	0.0754685i	0.0212350	+	0.00305313i
$612$	−2.26067	+	23.5544i	−0.0913821	+	0.952131i
$613$	41.1504	+	12.0828i	1.66205	+	0.488021i	0.971850	−	0.235600i	$-0.0757055\pi$
$613$	41.1504	+	12.0828i	1.66205	+	0.488021i	0.690197	+	0.723621i	$0.257524\pi$
$614$	9.37604	+	13.8603i	0.378386	+	0.559356i
$615$	−6.28814	−	1.06232i	−0.253562	−	0.0428370i
$616$	−2.30862	−	2.31197i	−0.0930168	−	0.0931518i
$617$	−4.66878	+	5.38806i	−0.187958	+	0.216915i	−0.841906	−	0.539625i	$-0.818566\pi$
$617$	−4.66878	+	5.38806i	−0.187958	+	0.216915i	0.653948	+	0.756540i	$0.273112\pi$
$618$	−24.3282	−	26.7749i	−0.978624	−	1.07705i
$619$	16.5555	+	36.2515i	0.665422	+	1.45707i	0.877382	+	0.479793i	$0.159288\pi$
$619$	16.5555	+	36.2515i	0.665422	+	1.45707i	−0.211960	+	0.977278i	$0.567984\pi$
$620$	38.7029	−	0.873111i	1.55435	−	0.0350650i
$621$	−7.73965	−	19.6841i	−0.310581	−	0.789897i
$622$	−11.2135	−	23.0982i	−0.449620	−	0.926152i
$623$	2.38557	+	5.22367i	0.0955758	+	0.209282i
$624$	0.389959	−	0.224640i	0.0156108	−	0.00899281i
$625$	22.2557	−	11.3880i	0.890226	−	0.455519i
$626$	−6.77145	−	0.811287i	−0.270642	−	0.0324256i
$627$	−4.36956	−	5.04274i	−0.174503	−	0.201388i
$628$	−26.7992	−	15.4898i	−1.06940	−	0.618110i
$629$	14.5507	+	4.27247i	0.580174	+	0.170354i
$630$	38.9818	−	5.56485i	1.55307	−	0.221709i
$631$	2.38424	−	16.5828i	0.0949151	−	0.660149i	−0.885708	−	0.464243i	$-0.846326\pi$
$631$	2.38424	−	16.5828i	0.0949151	−	0.660149i	0.980623	−	0.195906i	$-0.0627646\pi$
$632$	30.0399	+	22.5216i	1.19492	+	0.895861i
$633$	20.8767	+	9.53408i	0.829775	+	0.378946i
$634$	−25.3581	+	8.09934i	−1.00710	+	0.321666i
$635$	7.52965	−	23.4931i	0.298805	−	0.932297i
$636$	20.0673	−	14.2752i	0.795718	−	0.566049i
$637$	−0.0132644	+	0.00190713i	−0.000525554	+	7.55632e-5i
$638$	2.60533	+	1.11641i	0.103146	+	0.0441992i
$639$	−36.5801	+	56.9197i	−1.44709	+	2.25171i
$640$	0.0620646	−	25.2981i	0.00245332	−	0.999997i
$641$	−4.01558	−	13.6758i	−0.158606	−	0.540162i	0.841394	−	0.540422i	$-0.181735\pi$
$641$	−4.01558	−	13.6758i	−0.158606	−	0.540162i	−1.00000		0.000260110i	$0.999917\pi$
$642$	23.4645	−	28.4047i	0.926069	−	1.12105i
$643$		−	9.70011i		−	0.382535i	−0.981538	−	0.191267i	$-0.938740\pi$
$643$		−	9.70011i		−	0.382535i	0.981538	−	0.191267i	$-0.0612598\pi$
$644$	25.6761	+	3.86633i	1.01178	+	0.152355i
$645$	−16.7910	−	20.3678i	−0.661146	−	0.801982i
$646$	−15.9074	−	13.1407i	−0.625867	−	0.517014i
$647$	−0.723117	+	0.212326i	−0.0284286	+	0.00834740i	−0.295916	−	0.955214i	$-0.595625\pi$
$647$	−0.723117	+	0.212326i	−0.0284286	+	0.00834740i	0.267487	+	0.963561i	$0.413807\pi$
$648$	2.77918	+	3.71817i	0.109177	+	0.146064i
$649$	1.78594	−	2.77897i	0.0701042	−	0.109084i
$650$	0.238704	+	0.162174i	0.00936272	+	0.00636098i
$651$	9.19378	+	63.9441i	0.360332	+	2.50617i
$652$	6.19991	−	4.41042i	0.242807	−	0.172725i
$653$	1.13623	+	1.76800i	0.0444639	+	0.0691872i	0.862774	−	0.505590i	$-0.168725\pi$
$653$	1.13623	+	1.76800i	0.0444639	+	0.0691872i	−0.818310	+	0.574777i	$0.805089\pi$
$654$	−50.2811	+	16.0597i	−1.96615	+	0.627985i
$655$	7.47229	−	1.99610i	0.291966	−	0.0779941i
$656$	−4.06261	−	0.787080i	−0.158618	−	0.0307303i
$657$	−30.5329	−	4.38997i	−1.19120	−	0.171269i
$658$	42.4700	+	25.9009i	1.65565	+	1.00972i
$659$	−38.3273	−	11.2539i	−1.49302	−	0.438390i	−0.569515	−	0.821981i	$-0.692869\pi$
$659$	−38.3273	−	11.2539i	−1.49302	−	0.438390i	−0.923503	+	0.383591i	$0.874687\pi$
$660$	−5.18902	+	0.865937i	−0.201982	+	0.0337066i
$661$	10.9114	−	9.45478i	0.424404	−	0.367748i	−0.416314	−	0.909221i	$-0.636678\pi$
$661$	10.9114	−	9.45478i	0.424404	−	0.367748i	0.840718	+	0.541473i	$0.182133\pi$
$662$	0.191820	−	1.60104i	0.00745530	−	0.0622261i
$663$	−0.218705	−	0.189509i	−0.00849379	−	0.00735991i
$664$	−13.5161	+	0.956837i	−0.524526	+	0.0371325i
$665$	−15.0262	+	30.8729i	−0.582690	+	1.19720i
$666$	−34.5023	+	16.7499i	−1.33694	+	0.649045i
$667$	−21.9234	+	5.17543i	−0.848878	+	0.200393i
$668$	−8.50318	+	10.8019i	−0.328998	+	0.417939i
$669$	−20.7325	−	45.3978i	−0.801565	−	1.75518i
$670$	16.6401	+	2.40952i	0.642864	+	0.0930880i
$671$	2.31725	+	2.00790i	0.0894563	+	0.0775143i
$672$	41.9237	−	4.96120i	1.61724	−	0.191382i
$673$	27.9179	−	24.1910i	1.07615	−	0.932494i	0.0782334	−	0.996935i	$-0.475072\pi$
$673$	27.9179	−	24.1910i	1.07615	−	0.932494i	0.997921	+	0.0644415i	$0.0205266\pi$
$674$	14.4563	+	21.3703i	0.556836	+	0.823154i
$675$	10.1344	−	19.5848i	0.390073	−	0.753817i
$676$	2.48365	−	25.8778i	0.0955251	−	0.995298i
$677$	−1.86731	+	12.9874i	−0.0717665	+	0.499147i	0.921958	+	0.387290i	$0.126589\pi$
$677$	−1.86731	+	12.9874i	−0.0717665	+	0.499147i	−0.993724	+	0.111857i	$0.964320\pi$
$678$	−1.09438	−	46.4457i	−0.0420293	−	1.78374i
$679$	−46.8080	−	21.3765i	−1.79633	−	0.820354i
$680$	−15.3808	+	5.29777i	−0.589827	+	0.203160i
$681$	−18.7248	−	29.1363i	−0.717534	−	1.11650i
$682$	−0.865020	−	5.15170i	−0.0331233	−	0.197269i
$683$	−3.77898	−	26.2834i	−0.144599	−	1.00570i	−0.924875	−	0.380270i	$-0.875831\pi$
$683$	−3.77898	−	26.2834i	−0.144599	−	1.00570i	0.780277	−	0.625434i	$-0.215078\pi$
$684$	52.1244	−	2.45773i	1.99303	−	0.0939737i
$685$	−26.5514	+	3.15412i	−1.01448	+	0.120513i
$686$	24.6699	+	6.61666i	0.941900	+	0.252625i
$687$	4.06131	+	13.8315i	0.154949	+	0.527706i
$688$	−10.5752	−	13.4743i	−0.403176	−	0.513702i
$689$			0.182289i			0.00694466i
$690$	29.0676	−	30.0504i	1.10659	−	1.14400i
$691$		−	29.3255i		−	1.11560i	−0.829977	−	0.557798i	$-0.811647\pi$
$691$		−	29.3255i		−	1.11560i	0.829977	−	0.557798i	$-0.188353\pi$
$692$	−7.08234	+	29.1323i	−0.269230	+	1.10744i
$693$	−1.49697	−	5.09821i	−0.0568652	−	0.193665i
$694$	10.3047	−	38.4207i	0.391163	−	1.45843i
$695$	0.632058	+	5.32067i	0.0239753	+	0.201824i
$696$	−32.1569	+	17.5287i	−1.21890	+	0.664425i
$697$	0.378696	+	2.63389i	0.0143442	+	0.0997658i
$698$	−20.4659	+	3.43643i	−0.774647	+	0.130071i
$699$	4.96839	+	7.73097i	0.187922	+	0.292412i
$700$	14.5900	+	22.8028i	0.551448	+	0.861866i
$701$	42.5433	+	19.4289i	1.60684	+	0.733819i	0.998220	−	0.0596438i	$-0.0189965\pi$
$701$	42.5433	+	19.4289i	1.60684	+	0.733819i	0.608619	+	0.793462i	$0.291724\pi$
$702$	0.254476	−	0.00599610i	0.00960459	−	0.000226308i
$703$	4.75939	−	33.1023i	0.179504	−	1.24848i
$704$	−3.37964	+	0.480916i	−0.127375	+	0.0181252i
$705$	73.6541	−	31.4742i	2.77397	−	1.18539i
$706$	7.44169	−	5.03406i	0.280072	−	0.189459i
$707$	−21.0988	+	18.2822i	−0.793501	+	0.687573i
$708$	13.9407	+	40.3422i	0.523925	+	1.51615i
$709$	−12.2082	−	10.5785i	−0.458490	−	0.397284i	0.394761	−	0.918784i	$-0.370827\pi$
$709$	−12.2082	−	10.5785i	−0.458490	−	0.397284i	−0.853251	+	0.521500i	$0.825373\pi$
$710$	−46.0353	−	6.66599i	−1.72767	−	0.250170i
$711$	25.3645	+	55.5406i	0.951245	+	2.08294i
$712$	5.86196	+	1.27964i	0.219686	+	0.0479567i
$713$	29.8682	+	28.8335i	1.11857	+	1.07982i
$714$	−11.8556	−	24.4208i	−0.443685	−	0.913927i
$715$	0.0170416	−	0.0350137i	0.000637318	−	0.00130944i
$716$	−17.4840	−	7.00935i	−0.653408	−	0.261952i
$717$	9.92601	+	8.60094i	0.370694	+	0.321208i
$718$	21.3848	+	2.56211i	0.798074	+	0.0956171i
$719$	7.66917	−	6.64538i	0.286012	−	0.247831i	−0.500024	−	0.866012i	$-0.666675\pi$
$719$	7.66917	−	6.64538i	0.286012	−	0.247831i	0.786036	+	0.618181i	$0.212130\pi$
$720$	19.7796	−	36.0753i	0.737142	−	1.34445i
$721$	24.1023	+	7.07708i	0.897617	+	0.263564i
$722$	−9.70076	+	15.9064i	−0.361025	+	0.591977i
$723$	36.3933	+	5.23257i	1.35348	+	0.194601i
$724$	13.5628	−	6.98380i	0.504056	−	0.259551i
$725$	−19.1096	−	13.6517i	−0.709711	−	0.507012i
$726$	−12.8321	−	40.1759i	−0.476246	−	1.49107i
$727$	23.8449	+	37.1034i	0.884360	+	1.37609i	0.926227	+	0.376967i	$0.123033\pi$
$727$	23.8449	+	37.1034i	0.884360	+	1.37609i	−0.0418670	+	0.999123i	$0.513331\pi$
$728$	−0.149958	+	0.274155i	−0.00555782	+	0.0101609i
$729$	6.26525	+	43.5758i	0.232046	+	1.61392i
$730$	−5.95420	−	20.3536i	−0.220375	−	0.753322i
$731$	−5.95479	+	9.26584i	−0.220246	+	0.342709i
$732$	−38.9056	+	7.47893i	−1.43799	+	0.276429i
$733$	16.4200	−	4.82136i	0.606488	−	0.178081i	0.0359517	−	0.999354i	$-0.488554\pi$
$733$	16.4200	−	4.82136i	0.606488	−	0.178081i	0.570536	+	0.821273i	$0.306736\pi$
$734$	4.41909	−	5.34949i	0.163111	−	0.197453i
$735$	−1.56180	+	1.28754i	−0.0576079	+	0.0474915i
$736$	19.3245	−	19.0412i	0.712309	−	0.701866i
$737$		−	2.26880i		−	0.0835723i
$738$	−5.18843	−	4.28604i	−0.190989	−	0.157771i
$739$	−6.48253	−	22.0775i	−0.238464	−	0.812132i	−0.988563	−	0.150807i	$-0.951813\pi$
$739$	−6.48253	−	22.0775i	−0.238464	−	0.812132i	0.750100	−	0.661325i	$-0.230006\pi$
$740$	−20.3113	−	16.8130i	−0.746658	−	0.618057i
$741$	−0.345023	+	0.536867i	−0.0126748	+	0.0197223i
$742$	−6.73519	+	15.7176i	−0.247256	+	0.577013i
$743$	14.5085	−	2.08601i	0.532265	−	0.0765282i	0.129058	−	0.991637i	$-0.458805\pi$
$743$	14.5085	−	2.08601i	0.532265	−	0.0765282i	0.403207	+	0.915109i	$0.367895\pi$
$744$	59.2174	+	32.3909i	2.17101	+	1.18751i
$745$	−25.0290	−	8.02190i	−0.916992	−	0.293900i
$746$	11.8000	+	36.9443i	0.432028	+	1.35263i
$747$	−20.0446	−	9.15404i	−0.733392	−	0.334929i
$748$	1.00492	+	1.95158i	0.0367434	+	0.0713570i
$749$	−3.64077	+	25.3221i	−0.133031	+	0.925249i
$750$	43.5337	+	2.18393i	1.58963	+	0.0797459i
$751$	12.7855	+	3.75415i	0.466548	+	0.136991i	0.506554	−	0.862208i	$-0.330919\pi$
$751$	12.7855	+	3.75415i	0.466548	+	0.136991i	−0.0400051	+	0.999199i	$0.512737\pi$
$752$	48.2702	−	19.2703i	1.76023	−	0.702716i
$753$	0.941054	+	1.08603i	0.0342939	+	0.0395773i
$754$	0.0322491	−	0.269169i	0.00117444	−	0.00980256i
$755$	−8.40367	−	0.206443i	−0.305841	−	0.00751323i
$756$	22.1634	+	8.88534i	0.806077	+	0.323157i
$757$	−21.5661	−	47.2231i	−0.783832	−	1.71635i	−0.693519	−	0.720439i	$-0.743941\pi$
$757$	−21.5661	−	47.2231i	−0.783832	−	1.71635i	−0.0903130	−	0.995913i	$-0.528787\pi$
$758$	−40.7916	+	19.8031i	−1.48162	+	0.719283i
$759$	−4.57518	−	3.30074i	−0.166068	−	0.119809i
$760$	16.3912	+	31.9108i	0.594570	+	1.15753i
$761$	−6.33288	−	13.8671i	−0.229567	−	0.502681i	0.759435	−	0.650583i	$-0.225475\pi$
$761$	−6.33288	−	13.8671i	−0.229567	−	0.502681i	−0.989002	+	0.147902i	$0.952748\pi$
$762$	31.8349	−	28.9258i	1.15326	−	1.04787i
$763$	24.0013	−	27.6990i	0.868905	−	1.00277i
$764$	29.7680	−	10.2867i	1.07697	−	0.372160i
$765$	−26.0860	−	4.40699i	−0.943142	−	0.159335i
$766$	−30.1410	+	20.3894i	−1.08904	+	0.736699i
$767$	−0.303145	−	0.0890114i	−0.0109459	−	0.00321402i
$768$	22.1280	−	38.1563i	0.798477	−	1.37685i
$769$	40.3226	+	5.79751i	1.45407	+	0.209064i	0.823609	−	0.567158i	$-0.191957\pi$
$769$	40.3226	+	5.79751i	1.45407	+	0.209064i	0.630460	+	0.776222i	$0.282866\pi$
$770$	2.76307	−	2.38937i	0.0995741	−	0.0861068i
$771$	29.2996	+	13.3807i	1.05520	+	0.481893i
$772$	39.3639	−	37.4971i	1.41674	−	1.34955i
$773$	−3.32844	+	2.13906i	−0.119716	+	0.0769367i	−0.599128	−	0.800653i	$-0.704486\pi$
$773$	−3.32844	+	2.13906i	−0.119716	+	0.0769367i	0.479413	+	0.877590i	$0.340850\pi$
$774$	−4.61271	−	27.4714i	−0.165800	−	0.987438i
$775$	−2.12524	+	43.2300i	−0.0763410	+	1.55287i
$776$	−47.2067	+	25.7324i	−1.69462	+	0.923738i
$777$	23.7881	−	37.0151i	0.853395	−	1.32791i
$778$	−50.3890	−	13.5148i	−1.80653	−	0.484528i
$779$	5.63044	−	1.65325i	0.201732	−	0.0592337i
$780$	0.219287	+	0.452854i	0.00785173	+	0.0162148i
$781$			6.27668i			0.224597i
$782$	−15.6424	−	7.72307i	−0.559372	−	0.276176i
$783$	−20.7152			−0.740300
$784$	−1.03321	+	0.810907i	−0.0369002	+	0.0289610i
$785$	19.4194	−	28.6452i	0.693109	−	1.02239i
$786$	13.0247	+	3.49334i	0.464576	+	0.124603i
$787$	6.90434	−	10.7434i	0.246113	−	0.382959i	−0.696116	−	0.717930i	$-0.745090\pi$
$787$	6.90434	−	10.7434i	0.246113	−	0.382959i	0.942229	+	0.334970i	$0.108726\pi$
$788$	−0.680351	−	14.4291i	−0.0242365	−	0.514016i
$789$	−35.3393	+	5.08103i	−1.25811	+	0.180889i
$790$	−27.5205	+	31.6961i	−0.979136	+	1.12770i
$791$	17.4406	+	27.1381i	0.620117	+	0.964921i
$792$	−5.20016	−	1.94386i	−0.184780	−	0.0690719i
$793$	0.121822	−	0.266754i	0.00432604	−	0.00947271i
$794$	21.3835	−	0.503850i	0.758872	−	0.0178810i
$795$	14.3124	+	23.5213i	0.507609	+	0.834213i
$796$	−1.10434	+	11.5064i	−0.0391423	+	0.407833i
$797$	−19.8464	−	5.82743i	−0.702995	−	0.206418i	−0.0893505	−	0.996000i	$-0.528479\pi$
$797$	−19.8464	−	5.82743i	−0.702995	−	0.206418i	−0.613645	+	0.789582i	$0.710297\pi$
$798$	−49.5853	+	33.5428i	−1.75530	+	1.18740i
$799$	−21.8864	−	25.2582i	−0.774285	−	0.893573i
$800$	28.2066	+	2.09481i	0.997254	+	0.0740627i
$801$	7.37435	+	6.38991i	0.260560	+	0.225776i
$802$	10.2424	+	11.2725i	0.361672	+	0.398046i
$803$	−2.60299	+	1.18874i	−0.0918574	+	0.0419499i
$804$	23.0346	+	18.1326i	0.812368	+	0.639489i
$805$	−6.36745	+	28.3234i	−0.224423	+	0.998270i
$806$	−0.449454	+	0.218197i	−0.0158314	+	0.00768566i
$807$	−34.4352	−	75.4026i	−1.21218	−	2.65430i
$808$	2.05979	+	29.0962i	0.0724631	+	1.02360i
$809$	−23.9639	+	27.6558i	−0.842525	+	0.972326i	−0.999884	−	0.0152155i	$-0.995157\pi$
$809$	−23.9639	+	27.6558i	−0.842525	+	0.972326i	0.157359	+	0.987541i	$0.449702\pi$
$810$	−4.36889	+	2.80153i	−0.153507	+	0.0984358i
$811$	−11.5611	+	10.0178i	−0.405965	+	0.351771i	−0.833781	−	0.552095i	$-0.813829\pi$
$811$	−11.5611	+	10.0178i	−0.405965	+	0.351771i	0.427816	+	0.903866i	$0.359283\pi$
$812$	12.7259	−	22.0172i	0.446590	−	0.772654i
$813$	−20.5102	+	69.8515i	−0.719325	+	2.44980i
$814$	−1.85252	+	3.03759i	−0.0649306	+	0.106468i
$815$	4.42192	+	7.26705i	0.154893	+	0.254554i
$816$	−27.8455	−	5.39471i	−0.974786	−	0.188852i
$817$	22.0945	+	10.0902i	0.772987	+	0.353011i
$818$	0.0774341	+	0.242437i	0.00270742	+	0.00847661i
$819$	−0.427518	+	0.274749i	−0.0149387	+	0.00960051i
$820$	1.20301	−	4.46746i	0.0420110	−	0.156010i
$821$	−3.39933	−	23.6429i	−0.118637	−	0.825141i	−0.959059	−	0.283208i	$-0.908601\pi$
$821$	−3.39933	−	23.6429i	−0.118637	−	0.825141i	0.840421	−	0.541934i	$-0.182308\pi$
$822$	−42.8505	−	18.3619i	−1.49458	−	0.640445i
$823$	−32.2635	−	20.7345i	−1.12464	−	0.722760i	−0.160202	−	0.987084i	$-0.551215\pi$
$823$	−32.2635	−	20.7345i	−1.12464	−	0.722760i	−0.964434	+	0.264325i	$0.914851\pi$
$824$	21.0222	−	15.7132i	0.732343	−	0.547396i
$825$	−0.550182	−	5.85594i	−0.0191549	−	0.203878i
$826$	−22.8495	−	18.8755i	−0.795037	−	0.656761i
$827$			22.8852i			0.795797i	0.917429	+	0.397899i	$0.130260\pi$
$827$			22.8852i			0.795797i	−0.917429	+	0.397899i	$0.869740\pi$
$828$	42.4144	−	12.1478i	1.47400	−	0.422166i
$829$	−10.1488			−0.352482			−0.176241	−	0.984347i	$-0.556394\pi$
$829$	−10.1488			−0.352482			−0.176241	+	0.984347i	$0.556394\pi$
$830$	0.0151902	−	15.1493i	0.000527259	−	0.525838i
$831$	−23.8403	−	81.1925i	−0.827009	−	2.81654i
$832$	0.135199	+	0.297185i	0.00468719	+	0.0103031i
$833$	0.710504	+	0.456613i	0.0246175	+	0.0158207i
$834$	−3.67956	+	8.58685i	−0.127413	+	0.297338i
$835$	−11.3651	−	10.3473i	−0.393304	−	0.358084i
$836$	3.94456	−	2.80603i	0.136425	−	0.0970487i
$837$	20.6403	+	32.1169i	0.713433	+	1.11012i
$838$	−5.72261	−	17.9168i	−0.197684	−	0.618926i
$839$	9.45311	−	20.6994i	0.326358	−	0.714623i	−0.673337	−	0.739336i	$-0.735140\pi$
$839$	9.45311	−	20.6994i	0.326358	−	0.714623i	0.999695	+	0.0247124i	$0.00786699\pi$
$840$	2.17576	+	47.1490i	0.0750707	+	1.62680i
$841$	0.987411	−	6.86760i	0.0340487	−	0.236814i
$842$	−22.4128	−	13.6688i	−0.772397	−	0.471057i
$843$	8.86980	−	30.2078i	0.305492	−	1.04041i
$844$	−8.33218	+	14.4157i	−0.286806	+	0.496207i
$845$	28.6591	+	4.84168i	0.985902	+	0.166559i
$846$	83.9248	+	10.0550i	2.88539	+	0.345699i
$847$	22.1322	+	19.1777i	0.760472	+	0.658953i
$848$	8.91821	+	15.4813i	0.306252	+	0.531631i
$849$	−61.0782	+	27.8935i	−2.09620	+	0.957302i
$850$	−4.67635	−	17.5763i	−0.160397	−	0.602862i
$851$	−2.51390	−	28.1636i	−0.0861753	−	0.965435i
$852$	−63.7257	−	50.1643i	−2.18321	−	1.71860i
$853$	16.1077	−	7.35614i	0.551517	−	0.251869i	−0.120108	−	0.992761i	$-0.538324\pi$
$853$	16.1077	−	7.35614i	0.551517	−	0.251869i	0.671625	+	0.740891i	$0.265597\pi$
$854$	20.3600	−	18.4995i	0.696704	−	0.633039i
$855$	−1.43278	+	58.3240i	−0.0489999	+	1.99464i
$856$	18.8866	+	18.9140i	0.645532	+	0.646469i
$857$	9.16502	−	7.94153i	0.313071	−	0.271278i	−0.484124	−	0.874999i	$-0.660862\pi$
$857$	9.16502	−	7.94153i	0.313071	−	0.271278i	0.797195	+	0.603722i	$0.206316\pi$
$858$	0.0562360	−	0.0380418i	0.00191986	−	0.00129872i
$859$	−2.96530	+	10.0989i	−0.101175	+	0.344570i	−0.994486	−	0.104869i	$-0.966558\pi$
$859$	−2.96530	+	10.0989i	−0.101175	+	0.344570i	0.893311	+	0.449439i	$0.148376\pi$
$860$	15.8728	−	10.7142i	0.541257	−	0.365352i
$861$	7.64202	+	1.09876i	0.260439	+	0.0374455i
$862$	−0.657392	−	27.8999i	−0.0223909	−	0.950274i
$863$	−4.31214	+	9.44227i	−0.146787	+	0.321419i	−0.968716	−	0.248171i	$-0.920171\pi$
$863$	−4.31214	+	9.44227i	−0.146787	+	0.321419i	0.821929	+	0.569590i	$0.192898\pi$
$864$	21.3187	−	12.9591i	0.725276	−	0.440877i
$865$	−31.9202	−	10.2306i	−1.08532	−	0.347849i
$866$	−12.9782	+	2.17916i	−0.441016	+	0.0740508i
$867$	−4.07399	−	28.3353i	−0.138360	−	0.962316i
$868$	−46.8156	+	2.20741i	−1.58902	+	0.0749245i
$869$	4.76503	+	3.06230i	0.161643	+	0.103881i
$870$	−16.9726	−	37.2637i	−0.575426	−	1.26336i
$871$	−0.208204	+	0.0611342i	−0.00705473	+	0.00207145i
$872$	−8.11277	−	37.4245i	−0.274733	−	1.26735i
$873$	−87.4360			−2.95926
$874$	−11.9488	+	36.5683i	−0.404174	+	1.23694i
$875$	−26.5971	+	14.4444i	−0.899145	+	0.488309i
$876$	8.73447	−	35.9281i	0.295110	−	1.21390i
$877$	6.38431	+	21.7430i	0.215583	+	0.734208i	0.994280	+	0.106808i	$0.0340629\pi$
$877$	6.38431	+	21.7430i	0.215583	+	0.734208i	−0.778697	+	0.627400i	$0.784119\pi$
$878$	24.1689	+	6.48229i	0.815660	+	0.218767i
$879$	−48.2796	−	31.0274i	−1.62843	−	1.04653i
$880$	−0.265696	−	3.80736i	−0.00895660	−	0.128346i
$881$	−2.00543	+	0.288338i	−0.0675648	+	0.00971435i	−0.176014	−	0.984388i	$-0.556321\pi$
$881$	−2.00543	+	0.288338i	−0.0675648	+	0.00971435i	0.108450	+	0.994102i	$0.465411\pi$
$882$	−2.10650	+	0.353702i	−0.0709297	+	0.0119098i
$883$	7.41982	−	4.76843i	0.249697	−	0.160470i	−0.409805	−	0.912173i	$-0.634403\pi$
$883$	7.41982	−	4.76843i	0.249697	−	0.160470i	0.659502	+	0.751703i	$0.270767\pi$
$884$	0.152016	−	0.144806i	0.00511284	−	0.00487036i
$885$	−46.1044	+	12.3160i	−1.54978	+	0.413999i
$886$	−0.295518	−	12.5419i	−0.00992812	−	0.421352i
$887$	−2.09344	+	14.5602i	−0.0702907	+	0.488883i	0.924018	+	0.382348i	$0.124885\pi$
$887$	−2.09344	+	14.5602i	−0.0702907	+	0.488883i	−0.994309	+	0.106535i	$0.966025\pi$
$888$	−16.0343	−	43.0851i	−0.538077	−	1.44584i
$889$	−8.41452	+	28.6572i	−0.282214	+	0.961133i
$890$	−1.89637	+	6.43458i	−0.0635666	+	0.215688i
$891$	0.458614	+	0.529269i	0.0153642	+	0.0177312i
$892$	34.2218	−	11.8258i	1.14583	−	0.395956i
$893$	−48.2652	+	55.7010i	−1.61513	+	1.86396i
$894$	−30.8169	−	33.9162i	−1.03067	−	1.13433i
$895$	9.21650	−	18.9363i	0.308074	−	0.632970i
$896$	0.677039	+	30.6198i	0.0226183	+	1.02294i
$897$	−0.179622	+	0.508797i	−0.00599741	+	0.0169882i
$898$	34.3055	−	16.6543i	1.14479	−	0.555763i
$899$	36.9850	−	16.8905i	1.23352	−	0.563329i
$900$	38.6461	+	24.9460i	1.28820	+	0.831532i
$901$	7.52348	−	8.68256i	0.250644	−	0.289258i
$902$	−0.619870	−	0.0742665i	−0.0206394	−	0.00247280i
$903$	20.9275	+	24.1516i	0.696423	+	0.803715i
$904$	33.6174	+	2.42887i	1.11810	+	0.0807831i
$905$	6.70211	+	15.6839i	0.222786	+	0.521350i
$906$	−12.5131	−	7.63128i	−0.415720	−	0.253532i
$907$	−6.28253	−	0.903291i	−0.208608	−	0.0299933i	0.0372185	−	0.999307i	$-0.488150\pi$
$907$	−6.28253	−	0.903291i	−0.208608	−	0.0299933i	−0.245826	+	0.969314i	$0.579059\pi$
$908$	22.3391	−	11.5029i	0.741349	−	0.381738i
$909$	−19.7060	+	43.1500i	−0.653605	+	1.43120i
$910$	−0.293721	−	0.189179i	−0.00973675	−	0.00627123i
$911$	34.2032	−	21.9810i	1.13320	−	0.728264i	0.166975	−	0.985961i	$-0.446600\pi$
$911$	34.2032	−	21.9810i	1.13320	−	0.728264i	0.966226	+	0.257697i	$0.0829636\pi$
$912$	−3.03658	+	62.4745i	−0.100551	+	2.06874i
$913$	−2.02340	+	0.290921i	−0.0669648	+	0.00962808i
$914$	31.1869	+	13.3639i	1.03157	+	0.442039i
$915$	−5.22510	−	43.9849i	−0.172736	−	1.45410i
$916$	−10.2702	+	1.97427i	−0.339336	+	0.0652316i
$917$	−8.98424	+	2.63801i	−0.296686	+	0.0871148i
$918$	−12.3684	−	10.2172i	−0.408217	−	0.337218i
$919$	6.26901			0.206796			0.103398	−	0.994640i	$-0.467029\pi$
$919$	6.26901			0.206796			0.103398	+	0.994640i	$0.467029\pi$
$920$	19.6867	+	23.0745i	0.649051	+	0.760745i
$921$	−32.6196			−1.07485
$922$	10.0055	+	8.26529i	0.329513	+	0.272203i
$923$	0.576001	−	0.169129i	0.0189593	−	0.00556695i
$924$	6.25444	−	1.20231i	0.205756	−	0.0395530i
$925$	20.3755	−	21.3042i	0.669942	−	0.700478i
$926$	−40.1185	−	17.1912i	−1.31838	−	0.564939i
$927$	42.2484	−	6.07440i	1.38762	−	0.199509i
$928$	−10.4298	−	24.4376i	−0.342376	−	0.802203i
$929$	−2.85921	+	1.83750i	−0.0938077	+	0.0602865i	−0.586704	−	0.809802i	$-0.699575\pi$
$929$	−2.85921	+	1.83750i	−0.0938077	+	0.0602865i	0.492896	+	0.870088i	$0.335938\pi$
$930$	−40.8626	+	63.4435i	−1.33994	+	2.08039i
$931$	0.773716	−	1.69420i	0.0253575	−	0.0555252i
$932$	−5.92742	+	3.05217i	−0.194159	+	0.0999771i
$933$	49.5420	+	7.12307i	1.62193	+	0.233199i
$934$	−25.2305	−	15.3871i	−0.825566	−	0.503482i
$935$	−2.25680	+	0.964386i	−0.0738052	+	0.0315388i
$936$	−0.0382630	+	0.529588i	−0.00125067	+	0.0173101i
$937$	−4.21431	−	4.86357i	−0.137676	−	0.158886i	0.682725	−	0.730676i	$-0.260795\pi$
$937$	−4.21431	−	4.86357i	−0.137676	−	0.158886i	−0.820400	+	0.571790i	$0.806249\pi$
$938$	−20.2109	−	2.42147i	−0.659910	−	0.0790637i
$939$	8.70587	−	10.0471i	0.284105	−	0.327875i
$940$	17.6246	+	55.3721i	0.574852	+	1.80604i
$941$	−18.4065	+	8.40596i	−0.600034	+	0.274026i	−0.692187	−	0.721719i	$-0.743352\pi$
$941$	−18.4065	+	8.40596i	−0.600034	+	0.274026i	0.0921526	+	0.995745i	$0.470625\pi$
$942$	54.2806	−	26.3517i	1.76856	−	0.858584i
$943$	4.31200	−	2.45416i	0.140418	−	0.0799183i
$944$	−30.1001	+	7.27138i	−0.979674	+	0.236663i
$945$	−11.6832	+	24.0044i	−0.380055	+	0.780864i
$946$	−1.73777	−	1.91254i	−0.0564998	−	0.0621821i
$947$	22.5637	−	26.0399i	0.733221	−	0.846182i	−0.259610	−	0.965714i	$-0.583594\pi$
$947$	22.5637	−	26.0399i	0.733221	−	0.846182i	0.992830	+	0.119532i	$0.0381393\pi$
$948$	−69.1738	+	23.9038i	−2.24666	+	0.776360i
$949$	0.179228	+	0.206840i	0.00581799	+	0.00671432i
$950$	−36.8982	+	15.7238i	−1.19713	+	0.510146i
$951$	14.6195	−	49.7895i	0.474071	−	1.61454i
$952$	18.4576	−	6.86910i	0.598216	−	0.222629i
$953$	−2.70579	+	18.8192i	−0.0876490	+	0.609612i	0.897897	+	0.440205i	$0.145094\pi$
$953$	−2.70579	+	18.8192i	−0.0876490	+	0.609612i	−0.985546	+	0.169407i	$0.945815\pi$
$954$	0.684434	+	29.0476i	0.0221594	+	0.940449i
$955$	9.08785	+	34.0198i	0.294076	+	1.10086i
$956$	−6.89929	+	6.57210i	−0.223139	+	0.212557i
$957$	−4.64817	+	2.98720i	−0.150254	+	0.0965624i
$958$	−21.8988	+	3.67703i	−0.707520	+	0.118799i
$959$	32.0410	−	4.60680i	1.03466	−	0.148761i
$960$	40.7787	+	27.7315i	1.31613	+	0.895030i
$961$	−36.9596	−	23.7525i	−1.19224	−	0.766209i
$962$	0.328672	+	0.0881525i	0.0105968	+	0.00284215i
$963$	12.2466	+	41.7081i	0.394642	+	1.34403i
$964$	−6.30125	+	25.9194i	−0.202949	+	0.834807i
$965$	38.6636	+	46.8996i	1.24462	+	1.50975i
$966$	−34.2867	+	37.2337i	−1.10316	+	1.19798i
$967$	−13.9175			−0.447557			−0.223779	−	0.974640i	$-0.571839\pi$
$967$	−13.9175			−0.447557			−0.223779	+	0.974640i	$0.571839\pi$
$968$	29.9031	−	6.48232i	0.961124	−	0.208350i
$969$	38.5915	−	11.3315i	1.23974	−	0.364019i
$970$	−24.9160	−	54.7035i	−0.800004	−	1.75642i
$971$	−20.8406	−	13.3935i	−0.668808	−	0.429817i	0.161688	−	0.986842i	$-0.448306\pi$
$971$	−20.8406	−	13.3935i	−0.668808	−	0.429817i	−0.830496	+	0.557025i	$0.811943\pi$
$972$	−35.4713	+	1.67252i	−1.13774	+	0.0536460i
$973$	−0.923161	−	6.42073i	−0.0295952	−	0.205839i
$974$	−46.6918	+	7.84001i	−1.49610	+	0.251210i
$975$	−0.522565	+	0.208281i	−0.0167355	+	0.00667034i
$976$	−2.70445	−	28.6147i	−0.0865674	−	0.915935i
$977$	−9.50621	+	20.8157i	−0.304130	+	0.665953i	−0.998562	−	0.0536058i	$-0.982929\pi$
$977$	−9.50621	+	20.8157i	−0.304130	+	0.665953i	0.694432	+	0.719559i	$0.255656\pi$
$978$	0.349375	+	14.8276i	0.0111718	+	0.474133i
$979$	0.895977	+	0.128822i	0.0286356	+	0.00411717i
$980$	−0.821566	−	1.21712i	−0.0262439	−	0.0388796i
$981$	17.5452	−	59.7535i	0.560176	−	1.90778i
$982$	2.26537	−	1.53245i	0.0722909	−	0.0489024i
$983$	−6.38270	+	5.53064i	−0.203576	+	0.176400i	−0.750682	−	0.660664i	$-0.770275\pi$
$983$	−6.38270	+	5.53064i	−0.203576	+	0.176400i	0.547106	+	0.837064i	$0.315730\pi$
$984$	5.70811	−	5.69984i	0.181968	−	0.181704i
$985$	16.1453	+	0.396622i	0.514432	+	0.0126374i
$986$	−12.6453	+	11.4897i	−0.402708	+	0.365908i
$987$	−88.2066	+	40.2826i	−2.80765	+	1.28221i
$988$	−0.363794	−	0.286375i	−0.0115738	−	0.00911082i
$989$	20.1410	+	4.01102i	0.640448	+	0.127543i
$990$	2.58409	−	5.64338i	0.0821277	−	0.179358i
$991$	−39.8756	+	18.2106i	−1.26669	+	0.578478i	−0.931523	−	0.363682i	$-0.881520\pi$
$991$	−39.8756	+	18.2106i	−1.26669	+	0.578478i	−0.335166	+	0.942159i	$0.608792\pi$
$992$	−27.4961	+	40.5198i	−0.873001	+	1.28650i
$993$	2.37553	+	2.05841i	0.0753851	+	0.0653216i
$994$	55.9139	+	6.69904i	1.77348	+	0.212481i
$995$	−12.7431	−	2.15282i	−0.403982	−	0.0682491i
$996$	13.2177	−	22.8682i	0.418819	−	0.724607i
$997$	6.89549	−	23.4839i	0.218382	−	0.743742i	−0.775308	−	0.631584i	$-0.782405\pi$
$997$	6.89549	−	23.4839i	0.218382	−	0.743742i	0.993690	−	0.112159i	$-0.0357765\pi$
$998$	7.51722	+	4.58448i	0.237953	+	0.145119i
$999$	3.70054	−	25.7378i	0.117080	−	0.814309i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.o.b.19.15	✓	640
4.3	odd	2	inner	460.2.o.b.19.32	yes	640
5.4	even	2	inner	460.2.o.b.19.50	yes	640
20.19	odd	2	inner	460.2.o.b.19.33	yes	640
23.17	odd	22	inner	460.2.o.b.339.33	yes	640
92.63	even	22	inner	460.2.o.b.339.50	yes	640
115.109	odd	22	inner	460.2.o.b.339.32	yes	640
460.339	even	22	inner	460.2.o.b.339.15	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.o.b.19.15	✓	640	1.1	even	1	trivial
460.2.o.b.19.32	yes	640	4.3	odd	2	inner
460.2.o.b.19.33	yes	640	20.19	odd	2	inner
460.2.o.b.19.50	yes	640	5.4	even	2	inner
460.2.o.b.339.15	yes	640	460.339	even	22	inner
460.2.o.b.339.32	yes	640	115.109	odd	22	inner
460.2.o.b.339.33	yes	640	23.17	odd	22	inner
460.2.o.b.339.50	yes	640	92.63	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09031 - 0.900680i) q^{2} +(2.64511 - 0.776673i) q^{3} +(0.377553 + 1.96404i) q^{4} +(-2.22046 + 0.263774i) q^{5} +(-3.58352 - 1.53558i) q^{6} +(2.67954 - 0.385260i) q^{7} +(1.35732 - 2.48147i) q^{8} +(3.86960 - 2.48684i) q^{9} +O(q^{10})\)	\(q+(-1.09031 - 0.900680i) q^{2} +(2.64511 - 0.776673i) q^{3} +(0.377553 + 1.96404i) q^{4} +(-2.22046 + 0.263774i) q^{5} +(-3.58352 - 1.53558i) q^{6} +(2.67954 - 0.385260i) q^{7} +(1.35732 - 2.48147i) q^{8} +(3.86960 - 2.48684i) q^{9} +(2.65856 + 1.71232i) q^{10} +(0.177262 - 0.388150i) q^{11} +(2.52408 + 4.90186i) q^{12} +(-0.0403963 - 0.00580811i) q^{13} +(-3.26852 - 1.99335i) q^{14} +(-5.66847 + 2.42228i) q^{15} +(-3.71491 + 1.48306i) q^{16} +(1.68439 + 1.94389i) q^{17} +(-6.45891 - 0.773842i) q^{18} +(3.71452 - 4.28679i) q^{19} +(-1.35640 - 4.26148i) q^{20} +(6.78844 - 3.10018i) q^{21} +(-0.542869 + 0.263547i) q^{22} +(2.22386 - 4.24905i) q^{23} +(1.66297 - 7.61794i) q^{24} +(4.86085 - 1.17140i) q^{25} +(0.0388132 + 0.0427168i) q^{26} +(2.88813 - 3.33308i) q^{27} +(1.76833 + 5.11727i) q^{28} +(-3.07588 - 3.54975i) q^{29} +(8.36209 + 2.46444i) q^{30} +(-2.43880 + 8.30579i) q^{31} +(5.38616 + 1.72895i) q^{32} +(0.167411 - 1.16437i) q^{33} +(-0.0856862 - 3.63654i) q^{34} +(-5.84818 + 1.56225i) q^{35} +(6.34524 + 6.66114i) q^{36} +(4.95991 - 3.18754i) q^{37} +(-7.91100 + 1.32833i) q^{38} +(-0.111363 + 0.0160116i) q^{39} +(-2.35932 + 5.86801i) q^{40} +(0.870309 + 0.559314i) q^{41} +(-10.1938 - 2.73406i) q^{42} +(1.20643 + 4.10871i) q^{43} +(0.829267 + 0.201603i) q^{44} +(-7.93631 + 6.54262i) q^{45} +(-6.25173 + 2.62980i) q^{46} -12.9936 q^{47} +(-8.67447 + 6.80811i) q^{48} +(0.315056 - 0.0925087i) q^{49} +(-6.35488 - 3.10088i) q^{50} +(5.96516 + 3.83358i) q^{51} +(-0.00384437 - 0.0815328i) q^{52} +(-0.635662 - 4.42112i) q^{53} +(-6.15100 + 1.03281i) q^{54} +(-0.291219 + 0.908626i) q^{55} +(2.68099 - 7.17211i) q^{56} +(6.49587 - 14.2240i) q^{57} +(0.156472 + 6.64071i) q^{58} +(7.66268 + 1.10173i) q^{59} +(-6.89760 - 10.2186i) q^{60} +(-2.02441 + 6.89449i) q^{61} +(10.1399 - 6.85931i) q^{62} +(9.41067 - 8.15439i) q^{63} +(-4.31536 - 6.73630i) q^{64} +(0.0912302 + 0.00224114i) q^{65} +(-1.23126 + 1.11874i) q^{66} +(4.83647 - 2.20874i) q^{67} +(-3.18194 + 4.04214i) q^{68} +(2.58221 - 12.9664i) q^{69} +(7.78341 + 3.56400i) q^{70} +(-13.3802 + 6.11053i) q^{71} +(-0.918725 - 12.9777i) q^{72} +(-5.06816 - 4.39159i) q^{73} +(-8.27880 - 0.991882i) q^{74} +(11.9477 - 6.87376i) q^{75} +(9.82185 + 5.67698i) q^{76} +(0.325442 - 1.10835i) q^{77} +(0.135842 + 0.0828451i) q^{78} +(-1.88910 + 13.1390i) q^{79} +(7.85759 - 4.27296i) q^{80} +(-0.681785 + 1.49290i) q^{81} +(-0.445145 - 1.39370i) q^{82} +(-2.59000 - 4.03012i) q^{83} +(8.65187 + 12.1623i) q^{84} +(-4.25287 - 3.87203i) q^{85} +(2.38525 - 5.56637i) q^{86} +(-10.8930 - 7.00052i) q^{87} +(-0.722579 - 0.966714i) q^{88} +(0.597645 + 2.03539i) q^{89} +(14.5459 + 0.0145852i) q^{90} -0.110481 q^{91} +(9.18494 + 2.76350i) q^{92} +23.8638i q^{93} +(14.1671 + 11.7031i) q^{94} +(-7.11719 + 10.4984i) q^{95} +(15.5898 + 0.389963i) q^{96} +(-15.9911 - 10.2768i) q^{97} +(-0.426829 - 0.182901i) q^{98} +(-0.279334 - 1.94281i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9}+O(q^{10}) \) 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9	\( 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9} - 11 q^{10} - 22 q^{14} + 2 q^{16} - 11 q^{20} - 44 q^{21} - 8 q^{24} - 38 q^{25} - 46 q^{26} - 52 q^{29} - 11 q^{30} - 44 q^{34} + 18 q^{36} - 11 q^{40} - 76 q^{41} - 154 q^{44} - 30 q^{46} - 100 q^{49} + 21 q^{50} + 178 q^{54} + 242 q^{56} - 11 q^{60} - 44 q^{61} + 6 q^{64} - 22 q^{65} + 44 q^{66} - 12 q^{69} + 22 q^{70} - 22 q^{74} + 88 q^{76} - 110 q^{80} - 252 q^{81} - 374 q^{84} + 94 q^{85} - 198 q^{86} - 44 q^{89} - 242 q^{90} - 62 q^{94} + 372 q^{96}+O(q^{100}) \) 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9 - 11 * q^10 - 22 * q^14 + 2 * q^16 - 11 * q^20 - 44 * q^21 - 8 * q^24 - 38 * q^25 - 46 * q^26 - 52 * q^29 - 11 * q^30 - 44 * q^34 + 18 * q^36 - 11 * q^40 - 76 * q^41 - 154 * q^44 - 30 * q^46 - 100 * q^49 + 21 * q^50 + 178 * q^54 + 242 * q^56 - 11 * q^60 - 44 * q^61 + 6 * q^64 - 22 * q^65 + 44 * q^66 - 12 * q^69 + 22 * q^70 - 22 * q^74 + 88 * q^76 - 110 * q^80 - 252 * q^81 - 374 * q^84 + 94 * q^85 - 198 * q^86 - 44 * q^89 - 242 * q^90 - 62 * q^94 + 372 * q^96

Introduction

L-functions

Modular forms

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