LMFDB - Embedded newform 429.2.bs.a.7.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [429,2,Mod(7,429)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(429, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([0, 42, 55])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("429.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bs (of order $60$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [224,0,-28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$14$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			7.5
Character	$\chi$	$=$	429.7
Dual form			429.2.bs.a.184.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.501760 + 1.30713i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(0.0294667 + 0.0265320i) q^{4} +(2.71725 + 0.430370i) q^{5} +(1.30713 - 0.501760i) q^{6} +(-2.18905 + 0.114723i) q^{7} +(-2.54451 + 1.29649i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(-1.92595 + 3.33585i) q^{10} +(-2.18977 + 2.49096i) q^{11} -0.0396514i q^{12} +(3.59111 + 0.322345i) q^{13} +(0.948417 - 2.91893i) q^{14} +(-1.49837 - 2.30728i) q^{15} +(-0.409660 - 3.89766i) q^{16} +(2.58353 + 1.15026i) q^{17} +(-1.24752 - 0.635643i) q^{18} +(-3.24490 + 4.99672i) q^{19} +(0.0686498 + 0.0847755i) q^{20} +(1.55001 + 1.55001i) q^{21} +(-2.15727 - 4.11218i) q^{22} +(7.32001 + 4.22621i) q^{23} +(2.66609 + 1.02341i) q^{24} +(2.44293 + 0.793756i) q^{25} +(-2.22322 + 4.53231i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-0.0675478 - 0.0546991i) q^{28} +(-1.40722 + 6.62045i) q^{29} +(3.76773 - 0.800857i) q^{30} +(-1.47593 - 9.31865i) q^{31} +(-0.216627 - 0.0580450i) q^{32} +(3.31639 - 0.0394581i) q^{33} +(-2.79985 + 2.79985i) q^{34} +(-5.99755 - 0.630368i) q^{35} +(-0.0294667 + 0.0265320i) q^{36} +(-6.96768 + 4.52487i) q^{37} +(-4.90319 - 6.74866i) q^{38} +(-2.16337 - 2.88441i) q^{39} +(-7.47202 + 2.42781i) q^{40} +(4.34650 + 0.227790i) q^{41} +(-2.80380 + 1.24833i) q^{42} +(0.655187 + 1.13482i) q^{43} +(-0.130616 + 0.0153014i) q^{44} +(-0.712042 + 2.65738i) q^{45} +(-9.19709 + 7.44766i) q^{46} +(-3.09092 - 6.06626i) q^{47} +(-2.62241 + 2.91248i) q^{48} +(-2.18290 + 0.229432i) q^{49} +(-2.26331 + 2.79495i) q^{50} +(-0.873908 - 2.68961i) q^{51} +(0.0972659 + 0.104778i) q^{52} +(9.35493 + 6.79675i) q^{53} +(0.362379 + 1.35242i) q^{54} +(-7.02219 + 5.82614i) q^{55} +(5.42130 - 3.12999i) q^{56} +(5.88455 - 0.932021i) q^{57} +(-7.94770 - 5.16129i) q^{58} +(-0.453512 - 8.65353i) q^{59} +(0.0170648 - 0.107743i) q^{60} +(0.987348 - 2.21762i) q^{61} +(12.9212 + 2.74650i) q^{62} +(0.114723 - 2.18905i) q^{63} +(4.79177 - 6.59531i) q^{64} +(9.61921 + 2.42140i) q^{65} +(-1.61245 + 4.35475i) q^{66} +(2.11791 - 0.567493i) q^{67} +(0.0456095 + 0.102441i) q^{68} +(-1.75736 - 8.26772i) q^{69} +(3.83330 - 7.52328i) q^{70} +(4.71417 + 12.2808i) q^{71} +(-1.02341 - 2.66609i) q^{72} +(5.38962 - 10.5777i) q^{73} +(-2.41848 - 11.3781i) q^{74} +(-1.04476 - 2.34658i) q^{75} +(-0.228189 + 0.0611431i) q^{76} +(4.50775 - 5.70404i) q^{77} +(4.85579 - 1.38053i) q^{78} +(-3.57582 + 4.92169i) q^{79} +(0.564285 - 10.7672i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-2.47865 + 5.56714i) q^{82} +(1.15136 - 7.26941i) q^{83} +(0.00454893 + 0.0867987i) q^{84} +(6.52505 + 4.23742i) q^{85} +(-1.81210 + 0.287008i) q^{86} +(5.86157 - 3.38418i) q^{87} +(2.34239 - 9.17729i) q^{88} +(-2.12907 - 7.94581i) q^{89} +(-3.11626 - 2.26409i) q^{90} +(-7.89809 - 0.293644i) q^{91} +(0.103567 + 0.318747i) q^{92} +(-5.93752 + 7.33223i) q^{93} +(9.48029 - 0.996418i) q^{94} +(-10.9676 + 12.1808i) q^{95} +(0.101816 + 0.199825i) q^{96} +(8.37084 - 6.77857i) q^{97} +(0.795392 - 2.96845i) q^{98} +(-2.24842 - 2.43816i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 28 q^{3} - 6 q^{5} + 28 q^{9} - 16 q^{11} - 10 q^{13} - 36 q^{14} + 8 q^{15} - 24 q^{16} + 50 q^{20} + 10 q^{22} - 48 q^{23} - 30 q^{24} + 10 q^{26} + 56 q^{27} + 20 q^{29} + 12 q^{31} - 32 q^{33}+ \cdots - 6 q^{99}+O(q^{100}) $ 224 * q - 28 * q^3 - 6 * q^5 + 28 * q^9 - 16 * q^11 - 10 * q^13 - 36 * q^14 + 8 * q^15 - 24 * q^16 + 50 * q^20 + 10 * q^22 - 48 * q^23 - 30 * q^24 + 10 * q^26 + 56 * q^27 + 20 * q^29 + 12 * q^31 - 32 * q^33 - 104 * q^34 + 20 * q^35 + 12 * q^37 + 20 * q^39 - 80 * q^40 + 190 * q^41 + 32 * q^42 - 24 * q^44 + 4 * q^45 - 40 * q^46 - 10 * q^47 + 44 * q^48 - 24 * q^49 - 180 * q^50 - 110 * q^52 + 28 * q^53 - 62 * q^55 - 72 * q^56 + 20 * q^58 - 118 * q^59 + 88 * q^60 - 20 * q^61 + 120 * q^62 - 20 * q^66 - 156 * q^67 - 60 * q^68 + 12 * q^69 - 20 * q^70 + 64 * q^71 - 30 * q^72 + 10 * q^73 - 60 * q^74 - 12 * q^75 + 84 * q^78 + 200 * q^79 + 188 * q^80 + 28 * q^81 - 138 * q^82 - 80 * q^83 - 60 * q^84 + 40 * q^85 - 42 * q^86 - 18 * q^88 + 216 * q^89 - 88 * q^91 + 16 * q^92 + 12 * q^93 - 40 * q^94 - 300 * q^95 - 100 * q^96 + 18 * q^97 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.501760	+	1.30713i	−0.354798	+	0.924280i	0.633773	+	0.773519i	$0.281505\pi$
$2$	−0.501760	+	1.30713i	−0.354798	+	0.924280i	−0.988570	+	0.150760i	$0.951828\pi$
$3$	−0.669131	−	0.743145i	−0.386323	−	0.429055i
$3$	−0.669131	−	0.743145i	−0.386323	−	0.429055i
$4$	0.0294667	+	0.0265320i	0.0147334	+	0.0132660i
$5$	2.71725	+	0.430370i	1.21519	+	0.192467i	0.730927	−	0.682456i	$-0.239088\pi$
$5$	2.71725	+	0.430370i	1.21519	+	0.192467i	0.484263	+	0.874923i	$0.339088\pi$
$6$	1.30713	−	0.501760i	0.533633	−	0.204843i
$7$	−2.18905	+	0.114723i	−0.827381	+	0.0433612i	−0.461325	−	0.887231i	$-0.652626\pi$
$7$	−2.18905	+	0.114723i	−0.827381	+	0.0433612i	−0.366057	+	0.930593i	$0.619292\pi$
$8$	−2.54451	+	1.29649i	−0.899619	+	0.458379i
$9$	−0.104528	+	0.994522i	−0.0348428	+	0.331507i
$10$	−1.92595	+	3.33585i	−0.609040	+	1.05489i
$11$	−2.18977	+	2.49096i	−0.660242	+	0.751053i
$11$	−2.18977	+	2.49096i	−0.660242	+	0.751053i
$12$		−	0.0396514i		−	0.0114464i
$13$	3.59111	+	0.322345i	0.995996	+	0.0894024i
$13$	3.59111	+	0.322345i	0.995996	+	0.0894024i
$14$	0.948417	−	2.91893i	0.253475	−	0.780116i
$15$	−1.49837	−	2.30728i	−0.386876	−	0.595738i
$16$	−0.409660	−	3.89766i	−0.102415	−	0.974414i
$17$	2.58353	+	1.15026i	0.626598	+	0.278980i	0.695369	−	0.718653i	$-0.255241\pi$
$17$	2.58353	+	1.15026i	0.626598	+	0.278980i	−0.0687707	+	0.997632i	$0.521908\pi$
$18$	−1.24752	−	0.635643i	−0.294043	−	0.149823i
$19$	−3.24490	+	4.99672i	−0.744432	+	1.14633i	0.240036	+	0.970764i	$0.422841\pi$
$19$	−3.24490	+	4.99672i	−0.744432	+	1.14633i	−0.984469	+	0.175561i	$0.943826\pi$
$20$	0.0686498	+	0.0847755i	0.0153506	+	0.0189564i
$21$	1.55001	+	1.55001i	0.338241	+	0.338241i
$22$	−2.15727	−	4.11218i	−0.459931	−	0.876720i
$23$	7.32001	+	4.22621i	1.52633	+	0.881226i	0.999512	+	0.0312470i	$0.00994785\pi$
$23$	7.32001	+	4.22621i	1.52633	+	0.881226i	0.526817	+	0.849979i	$0.323385\pi$
$24$	2.66609	+	1.02341i	0.544213	+	0.208904i
$25$	2.44293	+	0.793756i	0.488586	+	0.158751i
$26$	−2.22322	+	4.53231i	−0.436010	+	0.888859i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	−0.0675478	−	0.0546991i	−0.0127653	−	0.0103372i
$29$	−1.40722	+	6.62045i	−0.261314	+	1.22939i	0.630214	+	0.776422i	$0.282967\pi$
$29$	−1.40722	+	6.62045i	−0.261314	+	1.22939i	−0.891528	+	0.452965i	$0.850366\pi$
$30$	3.76773	−	0.800857i	0.687891	−	0.146216i
$31$	−1.47593	−	9.31865i	−0.265085	−	1.67368i	−0.657164	−	0.753748i	$-0.728244\pi$
$31$	−1.47593	−	9.31865i	−0.265085	−	1.67368i	0.392079	−	0.919932i	$-0.371756\pi$
$32$	−0.216627	−	0.0580450i	−0.0382946	−	0.0102610i
$33$	3.31639	−	0.0394581i	0.577309	−	0.00686878i
$34$	−2.79985	+	2.79985i	−0.480171	+	0.480171i
$35$	−5.99755	−	0.630368i	−1.01377	−	0.106552i
$36$	−0.0294667	+	0.0265320i	−0.00491112	+	0.00442199i
$37$	−6.96768	+	4.52487i	−1.14548	+	0.743883i	−0.970598	−	0.240706i	$-0.922621\pi$
$37$	−6.96768	+	4.52487i	−1.14548	+	0.743883i	−0.174882	+	0.984589i	$0.555954\pi$
$38$	−4.90319	−	6.74866i	−0.795402	−	1.09478i
$39$	−2.16337	−	2.88441i	−0.346417	−	0.461875i
$40$	−7.47202	+	2.42781i	−1.18143	+	0.383870i
$41$	4.34650	+	0.227790i	0.678809	+	0.0355749i	0.388625	−	0.921396i	$-0.372950\pi$
$41$	4.34650	+	0.227790i	0.678809	+	0.0355749i	0.290184	+	0.956971i	$0.406283\pi$
$42$	−2.80380	+	1.24833i	−0.432636	+	0.192622i
$43$	0.655187	+	1.13482i	0.0999150	+	0.173058i	0.911649	−	0.410969i	$-0.134810\pi$
$43$	0.655187	+	1.13482i	0.0999150	+	0.173058i	−0.811734	+	0.584027i	$0.801476\pi$
$44$	−0.130616	+	0.0153014i	−0.0196910	+	0.00230678i
$45$	−0.712042	+	2.65738i	−0.106145	+	0.396138i
$46$	−9.19709	+	7.44766i	−1.35604	+	1.09810i
$47$	−3.09092	−	6.06626i	−0.450856	−	0.884856i	−0.998830	−	0.0483599i	$-0.984601\pi$
$47$	−3.09092	−	6.06626i	−0.450856	−	0.884856i	0.547974	−	0.836496i	$-0.315399\pi$
$48$	−2.62241	+	2.91248i	−0.378512	+	0.420380i
$49$	−2.18290	+	0.229432i	−0.311842	+	0.0327759i
$50$	−2.26331	+	2.79495i	−0.320080	+	0.395266i
$51$	−0.873908	−	2.68961i	−0.122372	−	0.376621i
$52$	0.0972659	+	0.104778i	0.0134884	+	0.0145301i
$53$	9.35493	+	6.79675i	1.28500	+	0.933606i	0.999692	−	0.0248303i	$-0.00790455\pi$
$53$	9.35493	+	6.79675i	1.28500	+	0.933606i	0.285307	+	0.958436i	$0.407905\pi$
$54$	0.362379	+	1.35242i	0.0493135	+	0.184041i
$55$	−7.02219	+	5.82614i	−0.946872	+	0.785597i
$56$	5.42130	−	3.12999i	0.724452	−	0.418262i
$57$	5.88455	−	0.932021i	0.779427	−	0.123449i
$58$	−7.94770	−	5.16129i	−1.04358	−	0.677711i
$59$	−0.453512	−	8.65353i	−0.0590423	−	1.12659i	−0.854117	−	0.520082i	$-0.825901\pi$
$59$	−0.453512	−	8.65353i	−0.0590423	−	1.12659i	0.795074	−	0.606512i	$-0.207432\pi$
$60$	0.0170648	−	0.107743i	0.00220305	−	0.0139095i
$61$	0.987348	−	2.21762i	0.126417	−	0.283937i	−0.839238	−	0.543764i	$-0.816999\pi$
$61$	0.987348	−	2.21762i	0.126417	−	0.283937i	0.965655	+	0.259827i	$0.0836654\pi$
$62$	12.9212	+	2.74650i	1.64100	+	0.348805i
$63$	0.114723	−	2.18905i	0.0144537	−	0.275794i
$64$	4.79177	−	6.59531i	0.598972	−	0.824414i
$65$	9.61921	+	2.42140i	1.19312	+	0.300337i
$66$	−1.61245	+	4.35475i	−0.198479	+	0.536032i
$67$	2.11791	−	0.567493i	0.258744	−	0.0693303i	−0.127115	−	0.991888i	$-0.540572\pi$
$67$	2.11791	−	0.567493i	0.258744	−	0.0693303i	0.385859	+	0.922558i	$0.373905\pi$
$68$	0.0456095	+	0.102441i	0.00553096	+	0.0124227i
$69$	−1.75736	−	8.26772i	−0.211561	−	0.995316i
$70$	3.83330	−	7.52328i	0.458167	−	0.899204i
$71$	4.71417	+	12.2808i	0.559469	+	1.45747i	0.863276	+	0.504732i	$0.168409\pi$
$71$	4.71417	+	12.2808i	0.559469	+	1.45747i	−0.303807	+	0.952734i	$0.598258\pi$
$72$	−1.02341	−	2.66609i	−0.120611	−	0.314201i
$73$	5.38962	−	10.5777i	0.630808	−	1.23803i	−0.325465	−	0.945554i	$-0.605521\pi$
$73$	5.38962	−	10.5777i	0.630808	−	1.23803i	0.956273	−	0.292476i	$-0.0944790\pi$
$74$	−2.41848	−	11.3781i	−0.281143	−	1.32267i
$75$	−1.04476	−	2.34658i	−0.120639	−	0.270959i
$76$	−0.228189	+	0.0611431i	−0.0261751	+	0.00701360i
$77$	4.50775	−	5.70404i	0.513705	−	0.650036i
$78$	4.85579	−	1.38053i	0.549810	−	0.156314i
$79$	−3.57582	+	4.92169i	−0.402311	+	0.553733i	−0.961322	−	0.275427i	$-0.911181\pi$
$79$	−3.57582	+	4.92169i	−0.402311	+	0.553733i	0.559011	+	0.829160i	$0.311181\pi$
$80$	0.564285	−	10.7672i	0.0630890	−	1.20381i
$81$	−0.978148	−	0.207912i	−0.108683	−	0.0231013i
$82$	−2.47865	+	5.56714i	−0.273721	+	0.614788i
$83$	1.15136	−	7.26941i	0.126378	−	0.797921i	−0.840336	−	0.542065i	$-0.817643\pi$
$83$	1.15136	−	7.26941i	0.126378	−	0.797921i	0.966715	−	0.255856i	$-0.0823574\pi$
$84$	0.00454893	+	0.0867987i	0.000496328	+	0.00947051i
$85$	6.52505	+	4.23742i	0.707741	+	0.459613i
$86$	−1.81210	+	0.287008i	−0.195404	+	0.0309489i
$87$	5.86157	−	3.38418i	0.628426	−	0.362822i
$88$	2.34239	−	9.17729i	0.249699	−	0.978302i
$89$	−2.12907	−	7.94581i	−0.225681	−	0.842254i	−0.982130	−	0.188202i	$-0.939734\pi$
$89$	−2.12907	−	7.94581i	−0.225681	−	0.842254i	0.756449	−	0.654052i	$-0.226932\pi$
$90$	−3.11626	−	2.26409i	−0.328482	−	0.238657i
$91$	−7.89809	−	0.293644i	−0.827945	−	0.0307823i
$92$	0.103567	+	0.318747i	0.0107976	+	0.0332317i
$93$	−5.93752	+	7.33223i	−0.615692	+	0.760316i
$94$	9.48029	−	0.996418i	0.977817	−	0.102773i
$95$	−10.9676	+	12.1808i	−1.12526	+	1.24972i
$96$	0.101816	+	0.199825i	0.0103915	+	0.0203946i
$97$	8.37084	−	6.77857i	0.849930	−	0.688260i	−0.101930	−	0.994792i	$-0.532502\pi$
$97$	8.37084	−	6.77857i	0.849930	−	0.688260i	0.951860	+	0.306532i	$0.0991685\pi$
$98$	0.795392	−	2.96845i	0.0803468	−	0.299858i
$99$	−2.24842	−	2.43816i	−0.225975	−	0.245044i
$100$	0.0509252	+	0.0882051i	0.00509252	+	0.00882051i
$101$	−0.751950	+	0.334790i	−0.0748218	+	0.0333128i	−0.443806	−	0.896123i	$-0.646372\pi$
$101$	−0.751950	+	0.334790i	−0.0748218	+	0.0333128i	0.368985	+	0.929436i	$0.379706\pi$
$102$	3.95416	+	0.207229i	0.391520	+	0.0205187i
$103$	11.0493	−	3.59013i	1.08872	−	0.353746i	0.290968	−	0.956733i	$-0.406023\pi$
$103$	11.0493	−	3.59013i	1.08872	−	0.353746i	0.797751	+	0.602987i	$0.206023\pi$
$104$	−9.55553	+	3.83564i	−0.936996	+	0.376115i
$105$	3.54469	+	4.87885i	0.345926	+	0.476127i
$106$	−13.5782	+	8.81776i	−1.31883	+	0.856457i
$107$	3.40251	−	3.06363i	0.328933	−	0.296172i	−0.488072	−	0.872803i	$-0.662300\pi$
$107$	3.40251	−	3.06363i	0.328933	−	0.296172i	0.817005	+	0.576631i	$0.195633\pi$
$108$	0.0394342	+	0.00414470i	0.00379455	+	0.000398824i
$109$	3.00438	−	3.00438i	0.287768	−	0.287768i	−0.548429	−	0.836197i	$-0.684774\pi$
$109$	3.00438	−	3.00438i	0.287768	−	0.287768i	0.836197	+	0.548429i	$0.184774\pi$
$110$	−4.09207	−	12.1022i	−0.390163	−	1.15390i
$111$	8.02492	+	2.15027i	0.761692	+	0.204095i
$112$	1.34392	+	8.48515i	0.126988	+	0.801771i
$113$	16.1722	−	3.43751i	1.52135	−	0.323374i	0.629969	−	0.776620i	$-0.283068\pi$
$113$	16.1722	−	3.43751i	1.52135	−	0.323374i	0.891385	+	0.453246i	$0.149734\pi$
$114$	−1.73436	+	8.15951i	−0.162438	+	0.764208i
$115$	18.0715	+	14.6340i	1.68517	+	1.36462i
$116$	−0.217120	+	0.157747i	−0.0201591	+	0.0146464i
$117$	−0.695953	+	3.53775i	−0.0643408	+	0.327065i
$118$	11.5388	+	3.74919i	1.06224	+	0.345141i
$119$	−5.78743	−	2.22159i	−0.530533	−	0.203652i
$120$	6.80397	+	3.92827i	0.621115	+	0.358601i
$121$	−1.40977	−	10.9093i	−0.128161	−	0.991753i
$122$	2.40330	+	2.40330i	0.217585	+	0.217585i
$123$	−2.73909	−	3.38250i	−0.246976	−	0.304990i
$124$	0.203751	−	0.313749i	0.0182974	−	0.0281755i
$125$	−5.95988	−	3.03671i	−0.533068	−	0.271612i
$126$	2.80380	+	1.24833i	0.249782	+	0.111210i
$127$	−0.397602	−	3.78293i	−0.0352815	−	0.335681i	−0.997898	−	0.0648112i	$-0.979355\pi$
$127$	−0.397602	−	3.78293i	−0.0352815	−	0.335681i	0.962616	−	0.270870i	$-0.0873112\pi$
$128$	5.97231	+	9.19655i	0.527883	+	0.812868i
$129$	0.404928	−	1.24624i	0.0356519	−	0.109725i
$130$	−7.99161	+	11.3586i	−0.700911	+	0.996214i
$131$			9.05639i			0.791260i	0.918410	+	0.395630i	$0.129474\pi$
$131$			9.05639i			0.791260i	−0.918410	+	0.395630i	$0.870526\pi$
$132$	0.0987700	+	0.0868276i	0.00859683	+	0.00755737i
$133$	6.53001	−	11.3103i	0.566223	−	0.980727i
$134$	−0.320897	+	3.05313i	−0.0277213	+	0.263750i
$135$	2.45126	−	1.24898i	0.210971	−	0.107495i
$136$	−8.06511	+	0.422675i	−0.691578	+	0.0362441i
$137$	−6.46822	+	2.48292i	−0.552618	+	0.212130i	−0.618621	−	0.785689i	$-0.712308\pi$
$137$	−6.46822	+	2.48292i	−0.552618	+	0.212130i	0.0660036	+	0.997819i	$0.478975\pi$
$138$	11.6887	+	1.85132i	0.995012	+	0.157594i
$139$	−12.8825	−	11.5994i	−1.09268	−	0.983852i	−0.0927480	−	0.995690i	$-0.529565\pi$
$139$	−12.8825	−	11.5994i	−1.09268	−	0.983852i	−0.999930	+	0.0118380i	$0.996232\pi$
$140$	−0.160003	−	0.177702i	−0.0135227	−	0.0150185i
$141$	−2.43989	+	6.35612i	−0.205475	+	0.535282i
$142$	−18.4180			−1.54560
$143$	−8.66668	+	8.23946i	−0.724744	+	0.689018i
$144$	3.91913			0.326594
$145$	−6.67301	+	17.3838i	−0.554163	+	1.44364i
$146$	11.1222	+	12.3524i	0.920476	+	1.02229i
$147$	1.63114	+	1.46869i	0.134534	+	0.121135i
$148$	−0.325368	−	0.0515333i	−0.0267451	−	0.00423601i
$149$	−15.4387	+	5.92636i	−1.26479	+	0.485506i	−0.896019	−	0.444015i	$-0.853554\pi$
$149$	−15.4387	+	5.92636i	−1.26479	+	0.485506i	−0.368768	+	0.929522i	$0.620220\pi$
$150$	3.59150	−	0.188223i	0.293245	−	0.0153683i
$151$	7.73923	−	3.94333i	0.629810	−	0.320904i	−0.109786	−	0.993955i	$-0.535017\pi$
$151$	7.73923	−	3.94333i	0.629810	−	0.320904i	0.739596	+	0.673051i	$0.235017\pi$
$152$	1.77849	−	16.9212i	0.144254	−	1.37249i
$153$	−1.41401	+	2.44914i	−0.114316	+	0.198001i
$154$	5.19411	+	8.75426i	0.418554	+	0.705439i
$155$		−	25.9563i		−	2.08486i
$156$	0.0127814	−	0.142393i	0.00102333	−	0.0114005i
$157$	3.97347	−	12.2291i	0.317117	−	0.975987i	−0.657757	−	0.753230i	$-0.728495\pi$
$157$	3.97347	−	12.2291i	0.317117	−	0.975987i	0.974874	−	0.222756i	$-0.0715054\pi$
$158$	−4.63908	−	7.14356i	−0.369065	−	0.568311i
$159$	−1.20870	−	11.5000i	−0.0958559	−	0.912008i
$160$	−0.563648	−	0.250952i	−0.0445603	−	0.0198395i
$161$	−16.5087	−	8.41159i	−1.30107	−	0.662927i
$162$	0.762562	−	1.17424i	0.0599126	−	0.0922573i
$163$	12.7046	+	15.6889i	0.995103	+	1.22885i	0.973406	+	0.229086i	$0.0735736\pi$
$163$	12.7046	+	15.6889i	0.995103	+	1.22885i	0.0216971	+	0.999765i	$0.493093\pi$
$164$	0.122033	+	0.122033i	0.00952920	+	0.00952920i
$165$	9.02843	+	1.32006i	0.702863	+	0.102766i
$166$	8.92435	+	5.15248i	0.692664	+	0.399910i
$167$	−4.12669	−	1.58409i	−0.319333	−	0.122580i	0.193422	−	0.981116i	$-0.438041\pi$
$167$	−4.12669	−	1.58409i	−0.319333	−	0.122580i	−0.512754	+	0.858535i	$0.671375\pi$
$168$	−5.95359	−	1.93444i	−0.459330	−	0.149245i
$169$	12.7922	+	2.31515i	0.984014	+	0.178089i
$170$	−8.81286	+	6.40292i	−0.675916	+	0.491081i
$171$	−4.63016	−	3.74943i	−0.354077	−	0.286726i
$172$	−0.0108027	+	0.0508227i	−0.000823698	+	0.00387519i
$173$	18.0835	−	3.84376i	1.37486	−	0.292236i	0.539523	−	0.841971i	$-0.318605\pi$
$173$	18.0835	−	3.84376i	1.37486	−	0.292236i	0.835339	+	0.549735i	$0.185271\pi$
$174$	1.48246	+	9.35987i	0.112385	+	0.709570i
$175$	−5.43875	−	1.45731i	−0.411131	−	0.110162i
$176$	10.6060	+	7.51454i	0.799455	+	0.566430i
$177$	−6.12737	+	6.12737i	−0.460561	+	0.460561i
$178$	11.4545	+	1.20391i	0.858549	+	0.0902372i
$179$	2.71165	−	2.44158i	0.202678	−	0.182492i	−0.561541	−	0.827449i	$-0.689791\pi$
$179$	2.71165	−	2.44158i	0.202678	−	0.182492i	0.764219	+	0.644957i	$0.223125\pi$
$180$	−0.0914869	+	0.0594123i	−0.00681903	+	0.00442833i
$181$	6.44232	+	8.86709i	0.478854	+	0.659086i	0.978284	−	0.207268i	$-0.0664573\pi$
$181$	6.44232	+	8.86709i	0.478854	+	0.659086i	−0.499430	+	0.866354i	$0.666457\pi$
$182$	4.34677	−	10.1765i	0.322204	−	0.754331i
$183$	−2.30868	+	0.750135i	−0.170662	+	0.0554515i
$184$	−24.1051	−	1.26329i	−1.77705	−	0.0931312i
$185$	−20.8803	+	9.29650i	−1.53515	+	0.683492i
$186$	−6.60496	−	11.4401i	−0.484299	−	0.838830i
$187$	−8.52261	+	3.91666i	−0.623235	+	0.286414i
$188$	0.0698707	−	0.260761i	0.00509584	−	0.0190179i
$189$	−1.70354	+	1.37950i	−0.123914	+	0.100344i
$190$	−10.4188	−	20.4480i	−0.755856	−	1.48345i
$191$	−7.23770	+	8.03828i	−0.523702	+	0.581630i	−0.945730	−	0.324953i	$-0.894652\pi$
$191$	−7.23770	+	8.03828i	−0.523702	+	0.581630i	0.422029	+	0.906583i	$0.361318\pi$
$192$	−8.10760	+	0.852143i	−0.585115	+	0.0614981i
$193$	−4.99263	+	6.16539i	−0.359378	+	0.443794i	−0.924482	−	0.381225i	$-0.875502\pi$
$193$	−4.99263	+	6.16539i	−0.359378	+	0.443794i	0.565105	+	0.825019i	$0.308836\pi$
$194$	4.66032	+	14.3430i	0.334591	+	1.02977i
$195$	−4.63706	−	8.76870i	−0.332067	−	0.627940i
$196$	−0.0704100	−	0.0511559i	−0.00502929	−	0.00365399i
$197$	−4.47164	−	16.6884i	−0.318591	−	1.18900i	−0.920599	−	0.390509i	$-0.872299\pi$
$197$	−4.47164	−	16.6884i	−0.318591	−	1.18900i	0.602008	−	0.798490i	$-0.294368\pi$
$198$	4.31515	−	1.71561i	0.306664	−	0.121923i
$199$	7.30389	−	4.21690i	0.517759	−	0.298928i	−0.218258	−	0.975891i	$-0.570037\pi$
$199$	7.30389	−	4.21690i	0.517759	−	0.298928i	0.736017	+	0.676963i	$0.236704\pi$
$200$	−7.24515	+	1.14752i	−0.512309	+	0.0811418i
$201$	−1.83889	−	1.19419i	−0.129705	−	0.0842316i
$202$	−0.0603151	−	1.15088i	−0.00424375	−	0.0809756i
$203$	2.32095	−	14.6539i	0.162899	−	1.02850i
$204$	0.0456095	−	0.102441i	0.00319330	−	0.00717227i
$205$	11.7125	+	2.48956i	0.818035	+	0.173879i
$206$	−0.851324	+	16.2442i	−0.0593146	+	1.13179i
$207$	−4.96821	+	6.83815i	−0.345314	+	0.475285i
$208$	−0.214746	−	14.1290i	−0.0148900	−	0.979668i
$209$	−5.34101	−	19.0246i	−0.369445	−	1.31596i
$210$	−8.15586	+	2.18536i	−0.562808	+	0.150804i
$211$	−7.36560	−	16.5434i	−0.507069	−	1.13890i	−0.967884	−	0.251399i	$-0.919109\pi$
$211$	−7.36560	−	16.5434i	−0.507069	−	1.13890i	0.460815	−	0.887496i	$-0.347557\pi$
$212$	0.0953279	+	0.448483i	0.00654715	+	0.0308019i
$213$	5.97204	−	11.7208i	0.409197	−	0.803095i
$214$	2.29732	+	5.98472i	0.157041	+	0.409107i
$215$	1.29191	+	3.36555i	0.0881078	+	0.229529i
$216$	−1.29649	+	2.54451i	−0.0882150	+	0.173132i
$217$	4.29994	+	20.2296i	0.291899	+	1.37328i
$218$	2.41964	+	5.43460i	0.163879	+	0.368077i
$219$	−11.4671	+	3.07261i	−0.774878	+	0.207628i
$220$	−0.361500	−	0.0146352i	−0.0243723	−	0.000986704i
$221$	8.90697	+	4.96351i	0.599148	+	0.333882i
$222$	−6.83726	+	9.41068i	−0.458887	+	0.631604i
$223$	−1.09920	+	20.9740i	−0.0736081	+	1.40453i	0.673187	+	0.739472i	$0.264925\pi$
$223$	−1.09920	+	20.9740i	−0.0736081	+	1.40453i	−0.746795	+	0.665054i	$0.768409\pi$
$224$	0.480865	+	0.102211i	0.0321292	+	0.00682927i
$225$	−1.04476	+	2.34658i	−0.0696509	+	0.156439i
$226$	−3.62130	+	22.8640i	−0.240885	+	1.52089i
$227$	0.377495	+	7.20304i	0.0250552	+	0.478083i	0.982126	+	0.188227i	$0.0602740\pi$
$227$	0.377495	+	7.20304i	0.0250552	+	0.478083i	−0.957070	+	0.289856i	$0.906393\pi$
$228$	0.198127	+	0.128665i	0.0131213	+	0.00852105i
$229$	8.25441	−	1.30737i	0.545467	−	0.0863935i	0.122381	−	0.992483i	$-0.460947\pi$
$229$	8.25441	−	1.30737i	0.545467	−	0.0863935i	0.423086	+	0.906090i	$0.360947\pi$
$230$	−28.1960	+	16.2790i	−1.85919	+	1.07340i
$231$	−7.25520	+	0.466842i	−0.477357	+	0.0307159i
$232$	−5.00267	−	18.6702i	−0.328442	−	1.22576i
$233$	−11.9095	−	8.65277i	−0.780218	−	0.566862i	0.124826	−	0.992179i	$-0.460163\pi$
$233$	−11.9095	−	8.65277i	−0.780218	−	0.566862i	−0.905045	+	0.425317i	$0.860163\pi$
$234$	−4.27509	−	2.68480i	−0.279471	−	0.175511i
$235$	−5.78805	−	17.8138i	−0.377570	−	1.16204i
$236$	0.216232	−	0.267024i	0.0140755	−	0.0173818i
$237$	6.05022	−	0.635903i	0.393004	−	0.0413064i
$238$	5.80780	−	6.45021i	0.376463	−	0.418105i
$239$	1.77785	+	3.48923i	0.115000	+	0.225700i	0.941331	−	0.337485i	$-0.109576\pi$
$239$	1.77785	+	3.48923i	0.115000	+	0.225700i	−0.826331	+	0.563184i	$0.809576\pi$
$240$	−8.37917	+	6.78532i	−0.540873	+	0.437990i
$241$	−2.39093	+	8.92306i	−0.154013	+	0.574785i	0.845175	+	0.534490i	$0.179496\pi$
$241$	−2.39093	+	8.92306i	−0.154013	+	0.574785i	−0.999188	+	0.0402947i	$0.987170\pi$
$242$	14.9672	+	3.63109i	0.962129	+	0.233415i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	0.0879317	−	0.0391497i	0.00562925	−	0.00250630i
$245$	−6.03021	−	0.316030i	−0.385256	−	0.0201904i
$246$	5.79573	−	1.88315i	0.369522	−	0.120065i
$247$	−13.2635	+	16.8978i	−0.843935	+	1.07518i
$248$	15.8371	+	21.7978i	1.00565	+	1.38416i
$249$	−6.17264	+	4.00856i	−0.391175	+	0.254032i
$250$	6.95980	−	6.26663i	0.440177	−	0.396337i
$251$	−12.5363	−	1.31762i	−0.791285	−	0.0831674i	−0.299742	−	0.954020i	$-0.596900\pi$
$251$	−12.5363	−	1.31762i	−0.791285	−	0.0831674i	−0.491544	+	0.870853i	$0.663567\pi$
$252$	0.0614602	−	0.0614602i	0.00387163	−	0.00387163i
$253$	−26.5565	+	8.97941i	−1.66959	+	0.564531i
$254$	5.14428	+	1.37840i	0.322781	+	0.0864888i
$255$	−1.21710	−	7.68445i	−0.0762176	−	0.481219i
$256$	0.930469	−	0.197777i	0.0581543	−	0.0123611i
$257$	−3.93527	+	18.5140i	−0.245476	+	1.15487i	0.666781	+	0.745253i	$0.267671\pi$
$257$	−3.93527	+	18.5140i	−0.245476	+	1.15487i	−0.912257	+	0.409618i	$0.865662\pi$
$258$	1.42582	+	1.15461i	0.0887676	+	0.0718826i
$259$	14.7335	−	10.7045i	0.915493	−	0.665145i
$260$	0.219202	+	0.326567i	0.0135943	+	0.0202528i
$261$	−6.43709	−	2.09154i	−0.398446	−	0.129463i
$262$	−11.8379	−	4.54413i	−0.731346	−	0.280737i
$263$	−1.03565	−	0.597933i	−0.0638609	−	0.0368701i	0.467730	−	0.883872i	$-0.345072\pi$
$263$	−1.03565	−	0.597933i	−0.0638609	−	0.0368701i	−0.531590	+	0.847002i	$0.678405\pi$
$264$	−8.38742	+	4.40007i	−0.516210	+	0.270806i
$265$	22.4945	+	22.4945i	1.38183	+	1.38183i
$266$	11.5075	+	14.2106i	0.705572	+	0.871309i
$267$	−4.48026	+	6.89899i	−0.274187	+	0.422212i
$268$	0.0774646	+	0.0394702i	0.00473190	+	0.00241103i
$269$	−17.9977	−	8.01311i	−1.09734	−	0.488568i	−0.223463	−	0.974712i	$-0.571736\pi$
$269$	−17.9977	−	8.01311i	−1.09734	−	0.488568i	−0.873878	+	0.486145i	$0.838403\pi$
$270$	0.402634	+	3.83081i	0.0245035	+	0.233135i
$271$	0.781613	+	1.20358i	0.0474796	+	0.0731122i	0.861613	−	0.507565i	$-0.169454\pi$
$271$	0.781613	+	1.20358i	0.0474796	+	0.0731122i	−0.814134	+	0.580678i	$0.802788\pi$
$272$	3.42496	−	10.5409i	0.207668	−	0.639138i
$273$	5.06663	+	6.06591i	0.306647	+	0.367126i
$274$		−	9.70063i		−	0.586037i
$275$	−7.32668	+	4.34710i	−0.441816	+	0.262140i
$276$	0.167575	−	0.290249i	0.0100868	−	0.0174709i
$277$	0.147736	−	1.40562i	0.00887660	−	0.0844552i	−0.989187	−	0.146662i	$-0.953147\pi$
$277$	0.147736	−	1.40562i	0.00887660	−	0.0844552i	0.998063	+	0.0622066i	$0.0198138\pi$
$278$	21.6259	−	11.0189i	1.29703	−	0.660872i
$279$	9.42188	−	0.493780i	0.564073	−	0.0295618i
$280$	16.0781	−	6.17179i	0.960848	−	0.368835i
$281$	27.5761	+	4.36763i	1.64505	+	0.260551i	0.909129	−	0.416514i	$-0.136748\pi$
$281$	27.5761	+	4.36763i	1.64505	+	0.260551i	0.735924	+	0.677065i	$0.236748\pi$
$282$	−7.08403	−	6.37849i	−0.421848	−	0.379834i
$283$	13.4996	+	14.9928i	0.802469	+	0.891232i	0.995953	−	0.0898713i	$-0.0286456\pi$
$283$	13.4996	+	14.9928i	0.802469	+	0.891232i	−0.193484	+	0.981103i	$0.561979\pi$
$284$	−0.186923	+	0.486952i	−0.0110919	+	0.0288953i
$285$	16.3909			0.970912
$286$	−6.42144	−	15.4627i	−0.379708	−	0.914328i
$287$	−9.54082			−0.563177
$288$	0.0803708	−	0.209373i	0.00473589	−	0.0123374i
$289$	−6.02369	−	6.68999i	−0.354335	−	0.393529i
$290$	−19.3746	−	17.4450i	−1.13772	−	1.02440i
$291$	−10.6386	−	1.68500i	−0.623649	−	0.0987762i
$292$	0.439462	−	0.168694i	0.0257176	−	0.00987206i
$293$	−5.59143	+	0.293034i	−0.326655	+	0.0171193i	−0.214959	−	0.976623i	$-0.568962\pi$
$293$	−5.59143	+	0.293034i	−0.326655	+	0.0171193i	−0.111696	+	0.993742i	$0.535628\pi$
$294$	−2.73821	+	1.39519i	−0.159695	+	0.0813689i
$295$	2.49191	−	23.7090i	0.145085	−	1.38039i
$296$	11.8629	−	20.5471i	0.689515	−	1.19427i
$297$	−0.307415	+	3.30235i	−0.0178380	+	0.191622i
$298$		−	23.1540i		−	1.34127i
$299$	24.9247	+	17.5364i	1.44143	+	1.01415i
$300$	0.0314735	−	0.0968656i	0.00181713	−	0.00559254i
$301$	−1.56442	−	2.40900i	−0.0901718	−	0.138852i
$302$	1.27121	+	12.0948i	0.0731500	+	0.695976i
$303$	0.751950	+	0.334790i	0.0431984	+	0.0192332i
$304$	20.8048	+	10.6006i	1.19324	+	0.607984i
$305$	3.63726	−	5.60089i	0.208269	−	0.320706i
$306$	−2.49185	−	3.07718i	−0.142450	−	0.175911i
$307$	12.2713	+	12.2713i	0.700359	+	0.700359i	0.964487	−	0.264129i	$-0.0850844\pi$
$307$	12.2713	+	12.2713i	0.700359	+	0.700359i	−0.264129	+	0.964487i	$0.585084\pi$
$308$	0.284168	−	0.0484801i	0.0161920	−	0.00276241i
$309$	−10.0614	−	5.80896i	−0.572373	−	0.330460i
$310$	33.9282	+	13.0238i	1.92699	+	0.739703i
$311$	−12.3872	−	4.02485i	−0.702415	−	0.228228i	−0.0640325	−	0.997948i	$-0.520396\pi$
$311$	−12.3872	−	4.02485i	−0.702415	−	0.228228i	−0.638382	+	0.769719i	$0.720396\pi$
$312$	9.24433	+	4.53460i	0.523357	+	0.256721i
$313$	−4.55679	+	3.31070i	−0.257565	+	0.187132i	−0.709073	−	0.705135i	$-0.750886\pi$
$313$	−4.55679	+	3.31070i	−0.257565	+	0.187132i	0.451508	+	0.892267i	$0.350886\pi$
$314$	13.9913	+	11.3299i	0.789572	+	0.639383i
$315$	1.25383	−	5.89880i	0.0706453	−	0.332360i
$316$	−0.235950	+	0.0501526i	−0.0132732	+	0.00282131i
$317$	1.40552	+	8.87408i	0.0789417	+	0.498418i	0.995203	+	0.0978360i	$0.0311921\pi$
$317$	1.40552	+	8.87408i	0.0789417	+	0.498418i	−0.916261	+	0.400582i	$0.868808\pi$
$318$	15.6384	+	4.19031i	0.876960	+	0.234981i
$319$	−13.4098	−	18.0026i	−0.750804	−	1.00795i
$320$	15.8589	−	15.8589i	0.886537	−	0.886537i
$321$	−4.55344	−	0.478586i	−0.254148	−	0.0267121i
$322$	19.2784	−	17.3584i	1.07434	−	0.967345i
$323$	−14.1308	+	9.17668i	−0.786261	+	0.510604i
$324$	−0.0233065	−	0.0320786i	−0.00129481	−	0.00178215i
$325$	8.51698	+	3.63793i	0.472437	+	0.201796i
$326$	−26.8821	+	8.73452i	−1.48886	+	0.483761i
$327$	−4.24302	−	0.222367i	−0.234639	−	0.0122969i
$328$	−11.3550	+	5.05558i	−0.626976	+	0.279148i
$329$	7.46209	+	12.9247i	0.411399	+	0.712563i
$330$	−6.25559	+	11.1390i	−0.344359	+	0.613180i
$331$	−2.48387	+	9.26993i	−0.136526	+	0.509521i	0.863461	+	0.504415i	$0.168292\pi$
$331$	−2.48387	+	9.26993i	−0.136526	+	0.509521i	−0.999987	+	0.00510603i	$0.998375\pi$
$332$	0.226798	−	0.183658i	0.0124472	−	0.0100795i
$333$	−3.77176	−	7.40249i	−0.206691	−	0.405654i
$334$	4.14121	−	4.59928i	0.226597	−	0.251662i
$335$	5.99912	−	0.630533i	0.327767	−	0.0344497i
$336$	5.40644	−	6.67640i	0.294945	−	0.364227i
$337$	−0.488844	−	1.50451i	−0.0266290	−	0.0819557i	0.936859	−	0.349708i	$-0.113719\pi$
$337$	−0.488844	−	1.50451i	−0.0266290	−	0.0819557i	−0.963488	+	0.267752i	$0.913719\pi$
$338$	−9.44481	+	15.5594i	−0.513730	+	0.846319i
$339$	−13.3759	−	9.71816i	−0.726479	−	0.527818i
$340$	0.0798449	+	0.297985i	0.00433020	+	0.0161605i
$341$	26.4444	+	16.7293i	1.43204	+	0.905941i
$342$	7.22421	−	4.17090i	0.390641	−	0.225536i
$343$	19.9076	−	3.15305i	1.07491	−	0.170249i
$344$	−3.13841	−	2.03810i	−0.169211	−	0.109887i
$345$	−1.21700	−	23.2217i	−0.0655211	−	1.25022i
$346$	−4.04927	+	25.5661i	−0.217690	+	1.37444i
$347$	−0.301157	+	0.676409i	−0.0161669	+	0.0363115i	−0.921448	−	0.388501i	$-0.872993\pi$
$347$	−0.301157	+	0.676409i	−0.0161669	+	0.0363115i	0.905282	+	0.424812i	$0.139660\pi$
$348$	0.262510	+	0.0557982i	0.0140720	+	0.00299110i
$349$	0.694059	−	13.2434i	0.0371521	−	0.708905i	−0.915032	−	0.403381i	$-0.867835\pi$
$349$	0.694059	−	13.2434i	0.0371521	−	0.708905i	0.952184	−	0.305524i	$-0.0988316\pi$
$350$	4.63383	−	6.37793i	0.247689	−	0.340914i
$351$	3.09474	−	1.85002i	0.165185	−	0.0987468i
$352$	0.618952	−	0.412504i	0.0329903	−	0.0219865i
$353$	−15.1069	+	4.04788i	−0.804060	+	0.215447i	−0.637366	−	0.770562i	$-0.719976\pi$
$353$	−15.1069	+	4.04788i	−0.804060	+	0.215447i	−0.166694	+	0.986009i	$0.553309\pi$
$354$	−4.93479	−	11.0837i	−0.262281	−	0.589093i
$355$	7.52426	+	35.3989i	0.399346	+	1.87878i
$356$	0.148081	−	0.290625i	0.00784828	−	0.0154031i
$357$	2.22159	+	5.78743i	0.117579	+	0.306303i
$358$	1.83087	+	4.76957i	0.0967642	+	0.252079i
$359$	−9.90113	+	19.4321i	−0.522562	+	1.02558i	0.467373	+	0.884060i	$0.345200\pi$
$359$	−9.90113	+	19.4321i	−0.522562	+	1.02558i	−0.989935	+	0.141525i	$0.954800\pi$
$360$	−1.63347	−	7.68486i	−0.0860913	−	0.405028i
$361$	−6.70976	−	15.0704i	−0.353145	−	0.793177i
$362$	−14.8229	+	3.97179i	−0.779076	+	0.208753i
$363$	−7.16386	+	8.34740i	−0.376005	+	0.438125i
$364$	−0.224940	−	0.218204i	−0.0117901	−	0.0114370i
$365$	19.1973	−	26.4228i	1.00483	−	1.38303i
$366$	0.177879	−	3.39413i	0.00929786	−	0.177414i
$367$	−17.6597	−	3.75369i	−0.921830	−	0.195941i	−0.277533	−	0.960716i	$-0.589517\pi$
$367$	−17.6597	−	3.75369i	−0.921830	−	0.195941i	−0.644297	+	0.764775i	$0.722850\pi$
$368$	13.4736	−	30.2622i	0.702360	−	1.57753i
$369$	−0.680875	+	4.29888i	−0.0354450	+	0.223791i
$370$	−1.67484	−	31.9578i	−0.0870707	−	1.66141i
$371$	−21.2581	−	13.8052i	−1.10367	−	0.716729i
$372$	−0.369498	+	0.0585227i	−0.0191576	+	0.00303426i
$373$	−7.38528	+	4.26389i	−0.382395	+	0.220776i	−0.678860	−	0.734268i	$-0.737526\pi$
$373$	−7.38528	+	4.26389i	−0.382395	+	0.220776i	0.296465	+	0.955044i	$0.404192\pi$
$374$	−0.843276	−	13.1054i	−0.0436047	−	0.677662i
$375$	1.73122	+	6.46101i	0.0894000	+	0.333645i
$376$	15.7297	+	11.4283i	0.811198	+	0.589370i
$377$	−7.18756	+	23.3212i	−0.370178	+	1.20110i
$378$	−0.948417	−	2.91893i	−0.0487813	−	0.150133i
$379$	−5.03382	+	6.21625i	−0.258570	+	0.319307i	−0.889855	−	0.456244i	$-0.849195\pi$
$379$	−5.03382	+	6.21625i	−0.258570	+	0.319307i	0.631285	+	0.775551i	$0.282528\pi$
$380$	−0.646361	+	0.0679353i	−0.0331576	+	0.00348501i
$381$	−2.54522	+	2.82675i	−0.130395	+	0.144819i
$382$	−6.87548	−	13.4939i	−0.351780	−	0.690408i
$383$	22.5375	−	18.2505i	1.15161	−	0.932556i	0.153160	−	0.988201i	$-0.451055\pi$
$383$	22.5375	−	18.2505i	1.15161	−	0.932556i	0.998451	+	0.0556451i	$0.0177215\pi$
$384$	2.83811	−	10.5920i	0.144832	−	0.540520i
$385$	14.7035	−	13.5593i	0.749360	−	0.691046i
$386$	−5.55385	−	9.61956i	−0.282684	−	0.489623i
$387$	−1.19709	+	0.532977i	−0.0608513	+	0.0270927i
$388$	0.426510	+	0.0223524i	0.0216528	+	0.00113477i
$389$	−21.2373	+	6.90042i	−1.07677	+	0.349865i	−0.793122	−	0.609062i	$-0.791546\pi$
$389$	−21.2373	+	6.90042i	−1.07677	+	0.349865i	−0.283652	+	0.958927i	$0.591546\pi$
$390$	13.7885	−	1.66146i	0.698208	−	0.0841311i
$391$	14.0502	+	19.3385i	0.710551	+	0.977989i
$392$	5.25693	−	3.41389i	0.265515	−	0.172428i
$393$	6.73021	−	6.05991i	0.339494	−	0.305682i
$394$	24.0576	+	2.52855i	1.21200	+	0.127387i
$395$	−11.8345	+	11.8345i	−0.595459	+	0.595459i
$396$	−0.00156457	−	0.131499i	−7.86226e−5	−	0.00660810i
$397$	1.37160	+	0.367519i	0.0688386	+	0.0184452i	0.293074	−	0.956090i	$-0.405322\pi$
$397$	1.37160	+	0.367519i	0.0688386	+	0.0184452i	−0.224235	+	0.974535i	$0.571988\pi$
$398$	1.84724	+	11.6630i	0.0925937	+	0.584613i
$399$	−12.7746	+	2.71533i	−0.639531	+	0.135936i
$400$	2.09302	−	9.84687i	0.104651	−	0.492344i
$401$	11.0305	+	8.93233i	0.550837	+	0.446059i	0.863893	−	0.503675i	$-0.168019\pi$
$401$	11.0305	+	8.93233i	0.550837	+	0.446059i	−0.313055	+	0.949735i	$0.601353\pi$
$402$	2.48364	−	1.80447i	0.123873	−	0.0899987i
$403$	−2.29641	−	33.9401i	−0.114392	−	1.69068i
$404$	−0.0310401	−	0.0100856i	−0.00154430	−	0.000501775i
$405$	−2.56839	−	0.985912i	−0.127624	−	0.0489904i
$406$	17.9900	+	10.3865i	0.892828	+	0.515475i
$407$	3.98639	−	27.2647i	0.197598	−	1.35146i
$408$	5.71072	+	5.71072i	0.282723	+	0.282723i
$409$	−24.0171	−	29.6587i	−1.18757	−	1.46653i	−0.851235	−	0.524785i	$-0.824146\pi$
$409$	−24.0171	−	29.6587i	−1.18757	−	1.46653i	−0.336335	−	0.941742i	$-0.609188\pi$
$410$	−9.13103	+	14.0606i	−0.450949	+	0.694401i
$411$	6.17325	+	3.14543i	0.304504	+	0.155153i
$412$	0.420840	+	0.187370i	0.0207333	+	0.00923105i
$413$	1.98552	+	18.8909i	0.0977010	+	0.929563i
$414$	−6.44550	−	9.92520i	−0.316779	−	0.487797i
$415$	6.25707	−	19.2573i	0.307147	−	0.945302i
$416$	−0.759222	−	0.278275i	−0.0372239	−	0.0136436i
$417$			17.3351i			0.848903i
$418$	27.5475	+	2.56440i	1.34739	+	0.125429i
$419$	−2.63841	+	4.56985i	−0.128895	+	0.223252i	−0.923249	−	0.384203i	$-0.874476\pi$
$419$	−2.63841	+	4.56985i	−0.128895	+	0.223252i	0.794354	+	0.607455i	$0.207810\pi$
$420$	−0.0249950	+	0.237811i	−0.00121963	+	0.0116040i
$421$	0.505346	−	0.257487i	0.0246290	−	0.0125491i	−0.441633	−	0.897196i	$-0.645601\pi$
$421$	0.505346	−	0.257487i	0.0246290	−	0.0125491i	0.466262	+	0.884647i	$0.345601\pi$
$422$	25.3201	−	1.32697i	1.23256	−	0.0645960i
$423$	6.35612	−	2.43989i	0.309045	−	0.118631i
$424$	−32.6156	−	5.16580i	−1.58395	−	0.250874i
$425$	5.39836	+	4.86070i	0.261859	+	0.235779i
$426$	12.3240	+	13.6872i	0.597102	+	0.663149i
$427$	−1.90694	+	4.96774i	−0.0922831	+	0.240406i
$428$	0.181545			0.00877530
$429$	11.9223	+	0.927323i	0.575612	+	0.0447716i
$430$	−5.04744			−0.243409
$431$	7.66257	−	19.9617i	0.369093	−	0.961521i	−0.615729	−	0.787958i	$-0.711139\pi$
$431$	7.66257	−	19.9617i	0.369093	−	0.961521i	0.984823	−	0.173563i	$-0.0555281\pi$
$432$	−2.62241	−	2.91248i	−0.126171	−	0.140127i
$433$	−4.28139	−	3.85498i	−0.205751	−	0.185259i	0.559813	−	0.828619i	$-0.310873\pi$
$433$	−4.28139	−	3.85498i	−0.205751	−	0.185259i	−0.765563	+	0.643360i	$0.777540\pi$
$434$	−28.6003	−	4.52984i	−1.37286	−	0.217439i
$435$	17.3838	−	6.67301i	0.833488	−	0.319946i
$436$	0.168241	−	0.00881716i	0.00805731	−	0.000422266i
$437$	−44.8699	+	22.8624i	−2.14642	+	1.09366i
$438$	1.73745	−	16.5308i	0.0830187	−	0.789870i
$439$	10.5583	−	18.2875i	0.503919	−	0.872814i	−0.496071	−	0.868282i	$-0.665224\pi$
$439$	10.5583	−	18.2875i	0.503919	−	0.872814i	0.999990	−	0.00453133i	$-0.00144237\pi$
$440$	10.3145	−	23.9289i	0.491723	−	1.14076i
$441$		−	2.19492i		−	0.104520i
$442$	−10.9571	+	9.15207i	−0.521176	+	0.435319i
$443$	3.21259	−	9.88735i	0.152635	−	0.469762i	−0.845279	−	0.534326i	$-0.820566\pi$
$443$	3.21259	−	9.88735i	0.152635	−	0.469762i	0.997914	+	0.0645637i	$0.0205656\pi$
$444$	0.179417	+	0.276278i	0.00851476	+	0.0131116i
$445$	−2.36558	−	22.5070i	−0.112139	−	1.06693i
$446$	−26.8642	−	11.9607i	−1.27206	−	0.566357i
$447$	14.7346	+	7.50768i	0.696925	+	0.355101i
$448$	−9.73278	+	14.9872i	−0.459831	+	0.708077i
$449$	3.65476	+	4.51325i	0.172479	+	0.212993i	0.856054	−	0.516887i	$-0.172909\pi$
$449$	3.65476	+	4.51325i	0.172479	+	0.212993i	−0.683575	+	0.729880i	$0.739576\pi$
$450$	−2.54306	−	2.54306i	−0.119881	−	0.119881i
$451$	−10.0853	+	10.3281i	−0.474897	+	0.486334i
$452$	0.567746	+	0.327788i	0.0267045	+	0.0154179i
$453$	−8.10902	−	3.11276i	−0.380995	−	0.146250i
$454$	−9.60471	−	3.12076i	−0.450772	−	0.146465i
$455$	−21.3347	−	4.19700i	−1.00019	−	0.196759i
$456$	−13.7649	+	10.0008i	−0.644601	+	0.468330i
$457$	−13.4671	−	10.9055i	−0.629966	−	0.510136i	0.260330	−	0.965520i	$-0.416169\pi$
$457$	−13.4671	−	10.9055i	−0.629966	−	0.510136i	−0.890295	+	0.455384i	$0.849502\pi$
$458$	−2.43283	+	11.4456i	−0.113679	+	0.534816i
$459$	2.76623	−	0.587980i	0.129116	−	0.0274445i
$460$	0.144238	+	0.910686i	0.00672515	+	0.0424610i
$461$	11.2896	+	3.02504i	0.525810	+	0.140890i	0.511953	−	0.859014i	$-0.328922\pi$
$461$	11.2896	+	3.02504i	0.525810	+	0.140890i	0.0138572	+	0.999904i	$0.495589\pi$
$462$	3.03015	−	9.71773i	0.140975	−	0.452109i
$463$	−0.450446	+	0.450446i	−0.0209340	+	0.0209340i	−0.717496	−	0.696562i	$-0.754712\pi$
$463$	−0.450446	+	0.450446i	−0.0209340	+	0.0209340i	0.696562	+	0.717496i	$0.254712\pi$
$464$	26.3807	+	2.77273i	1.22469	+	0.128721i
$465$	−19.2893	+	17.3681i	−0.894519	+	0.805428i
$466$	17.2860	−	11.2257i	0.800758	−	0.520019i
$467$	−2.39297	−	3.29364i	−0.110734	−	0.152412i	0.750053	−	0.661378i	$-0.230028\pi$
$467$	−2.39297	−	3.29364i	−0.110734	−	0.152412i	−0.860787	+	0.508966i	$0.830028\pi$
$468$	−0.114371	+	0.0857808i	−0.00528679	+	0.00396522i
$469$	−4.57110	+	1.48524i	−0.211074	+	0.0685820i
$470$	26.1891	+	1.37251i	1.20801	+	0.0633093i
$471$	−11.7467	+	5.22999i	−0.541261	+	0.240985i
$472$	12.3732	+	21.4310i	0.569522	+	0.986441i
$473$	−4.26150	−	0.852949i	−0.195944	−	0.0392186i
$474$	−2.20455	+	8.22748i	−0.101258	+	0.377901i
$475$	−11.8933	+	9.63097i	−0.545700	+	0.441899i
$476$	−0.111593	−	0.219015i	−0.00511488	−	0.0100385i
$477$	−7.73738	+	8.59323i	−0.354270	+	0.393457i
$478$	−5.45293	+	0.573126i	−0.249411	+	0.0262142i
$479$	17.8640	−	22.0601i	0.816225	−	1.00795i	−0.183464	−	0.983026i	$-0.558731\pi$
$479$	17.8640	−	22.0601i	0.816225	−	1.00795i	0.999689	−	0.0249274i	$-0.00793547\pi$
$480$	0.190660	+	0.586792i	0.00870242	+	0.0267833i
$481$	−26.4803	+	14.0033i	−1.20740	+	0.638496i
$482$	−10.4639	−	7.60248i	−0.476618	−	0.346284i
$483$	4.79543	+	17.8968i	0.218200	+	0.814333i
$484$	0.247903	−	0.358865i	0.0112683	−	0.0163120i
$485$	25.6629	−	14.8165i	1.16529	−	0.672783i
$486$	−1.38289	+	0.219028i	−0.0627290	+	0.00993530i
$487$	14.4907	+	9.41035i	0.656635	+	0.426424i	0.829488	−	0.558524i	$-0.188632\pi$
$487$	14.4907	+	9.41035i	0.656635	+	0.426424i	−0.172854	+	0.984948i	$0.555299\pi$
$488$	0.362810	+	6.92283i	0.0164236	+	0.313382i
$489$	3.15808	−	19.9393i	0.142813	−	0.901687i
$490$	3.43881	−	7.72369i	0.155349	−	0.348921i
$491$	39.8857	+	8.47796i	1.80001	+	0.382605i	0.981436	−	0.191790i	$-0.0614291\pi$
$491$	39.8857	+	8.47796i	1.80001	+	0.382605i	0.818579	+	0.574395i	$0.194762\pi$
$492$	0.00903220	−	0.172345i	0.000407203	−	0.00776990i
$493$	−11.2509	+	15.4855i	−0.506713	+	0.697430i
$494$	−15.4325	−	25.8157i	−0.694341	−	1.16150i
$495$	−5.06021	−	7.59272i	−0.227439	−	0.341268i
$496$	−35.7163	+	9.57015i	−1.60371	+	0.429712i
$497$	−11.7284	−	26.3425i	−0.526092	−	1.18162i
$498$	−2.14252	−	10.0798i	−0.0960086	−	0.451685i
$499$	−7.32403	+	14.3742i	−0.327869	+	0.643478i	−0.994823	−	0.101620i	$-0.967597\pi$
$499$	−7.32403	+	14.3742i	−0.327869	+	0.643478i	0.666955	+	0.745098i	$0.267597\pi$
$500$	−0.0950483	−	0.247609i	−0.00425069	−	0.0110734i
$501$	1.58409	+	4.12669i	0.0707718	+	0.184367i
$502$	8.01252	−	15.7255i	0.357616	−	0.701861i
$503$	−3.51763	−	16.5491i	−0.156843	−	0.737890i	−0.984320	−	0.176390i	$-0.943558\pi$
$503$	−3.51763	−	16.5491i	−0.156843	−	0.737890i	0.827477	−	0.561500i	$-0.189775\pi$
$504$	2.54616	+	5.71878i	0.113415	+	0.254735i
$505$	−2.18732	+	0.586090i	−0.0973344	+	0.0260807i
$506$	1.58774	−	39.2183i	0.0705835	−	1.74347i
$507$	−6.83915	−	11.0556i	−0.303737	−	0.490996i
$508$	0.0886525	−	0.122020i	0.00393332	−	0.00541375i
$509$	−1.13137	+	21.5879i	−0.0501472	+	0.956865i	0.851490	+	0.524371i	$0.175700\pi$
$509$	−1.13137	+	21.5879i	−0.0501472	+	0.956865i	−0.901637	+	0.432494i	$0.857634\pi$
$510$	10.6553	+	2.26484i	0.471822	+	0.100289i
$511$	−10.5846	+	23.7734i	−0.468236	+	1.05168i
$512$	−3.63916	+	22.9767i	−0.160830	+	1.01544i
$513$	0.311812	+	5.94973i	0.0137669	+	0.262687i
$514$	−22.2256	−	14.4335i	−0.980330	−	0.636634i
$515$	31.5687	−	5.00000i	1.39108	−	0.220326i
$516$	0.0449970	−	0.0259791i	0.00198088	−	0.00114366i
$517$	21.8792	+	5.58440i	0.962248	+	0.245602i
$518$	6.59949	+	24.6296i	0.289965	+	1.08216i
$519$	−14.9567	−	10.8667i	−0.656526	−	0.476994i
$520$	−27.6155	+	6.30996i	−1.21102	+	0.276710i
$521$	−1.20664	−	3.71366i	−0.0528640	−	0.162699i	0.921139	−	0.389234i	$-0.127260\pi$
$521$	−1.20664	−	3.71366i	−0.0528640	−	0.162699i	−0.974003	+	0.226535i	$0.927260\pi$
$522$	5.96378	−	7.36466i	0.261028	−	0.322342i
$523$	−20.8744	+	2.19398i	−0.912772	+	0.0959362i	−0.549258	−	0.835653i	$-0.685090\pi$
$523$	−20.8744	+	2.19398i	−0.912772	+	0.0959362i	−0.363514	+	0.931589i	$0.618423\pi$
$524$	−0.240284	+	0.266862i	−0.0104968	+	0.0116579i
$525$	2.55624	+	5.01691i	0.111564	+	0.218956i
$526$	1.30122	−	1.05371i	0.0567360	−	0.0459439i
$527$	6.90578	−	25.7727i	0.300821	−	1.12268i
$528$	−1.51239	−	12.9100i	−0.0658182	−	0.561835i
$529$	24.2217	+	41.9533i	1.05312	+	1.82405i
$530$	−40.6901	+	18.1164i	−1.76747	+	0.786926i
$531$	8.65353	+	0.453512i	0.375531	+	0.0196808i
$532$	0.492502	−	0.160024i	0.0213527	−	0.00693791i
$533$	15.5353	+	2.21909i	0.672910	+	0.0961196i
$534$	−6.76986	−	9.31791i	−0.292960	−	0.403225i
$535$	10.5639	−	6.86030i	0.456719	−	0.296597i
$536$	−4.65329	+	4.18984i	−0.200992	+	0.180974i
$537$	−3.62890	−	0.381413i	−0.156599	−	0.0164592i
$538$	19.5047	−	19.5047i	0.840908	−	0.840908i
$539$	4.20854	−	5.93991i	0.181275	−	0.255850i
$540$	0.105369	+	0.0282334i	0.00453434	+	0.00121497i
$541$	−2.40086	−	15.1585i	−0.103221	−	0.651713i	−0.983998	−	0.178181i	$-0.942979\pi$
$541$	−2.40086	−	15.1585i	−0.103221	−	0.651713i	0.880777	−	0.473532i	$-0.157021\pi$
$542$	−1.96541	+	0.417762i	−0.0844218	+	0.0179444i
$543$	2.27878	−	10.7208i	0.0977918	−	0.460074i
$544$	−0.492896	−	0.399139i	−0.0211327	−	0.0171129i
$545$	9.45665	−	6.87066i	0.405078	−	0.294307i
$546$	−10.4712	+	3.57911i	−0.448124	+	0.153172i
$547$	−21.3067	−	6.92298i	−0.911010	−	0.296005i	−0.184236	−	0.982882i	$-0.558981\pi$
$547$	−21.3067	−	6.92298i	−0.911010	−	0.296005i	−0.726774	+	0.686877i	$0.758981\pi$
$548$	−0.256474	−	0.0984512i	−0.0109560	−	0.00420562i
$549$	2.10226	+	1.21374i	0.0897225	+	0.0518013i
$550$	−2.00598	−	11.7581i	−0.0855353	−	0.501368i
$551$	−28.5142	−	28.5142i	−1.21475	−	1.21475i
$552$	15.1906	+	18.7589i	0.646556	+	0.798430i
$553$	7.26299	−	11.1840i	0.308854	−	0.475593i
$554$	1.76319	+	0.898391i	0.0749109	+	0.0381690i
$555$	20.8803	+	9.29650i	0.886318	+	0.394614i
$556$	−0.0718487	−	0.683595i	−0.00304706	−	0.0289909i
$557$	18.5096	+	28.5023i	0.784279	+	1.20768i	0.974156	+	0.225875i	$0.0725242\pi$
$557$	18.5096	+	28.5023i	0.784279	+	1.20768i	−0.189878	+	0.981808i	$0.560809\pi$
$558$	−4.08209	+	12.5634i	−0.172809	+	0.531850i
$559$	1.98705	+	4.28645i	0.0840431	+	0.181298i
$560$			23.6346i			0.998745i
$561$	8.61338	+	3.71278i	0.363657	+	0.156754i
$562$	−19.5456	+	33.8540i	−0.824483	+	1.42805i
$563$	−2.17363	+	20.6807i	−0.0916074	+	0.871587i	0.848153	+	0.529752i	$0.177715\pi$
$563$	−2.17363	+	20.6807i	−0.0916074	+	0.871587i	−0.939760	+	0.341835i	$0.888952\pi$
$564$	−0.240536	+	0.122559i	−0.0101284	+	0.00516067i
$565$	45.4233	−	2.38053i	1.91097	−	0.100150i
$566$	−26.3711	+	10.1229i	−1.10846	+	0.425499i
$567$	2.16506	+	0.342912i	0.0909240	+	0.0144010i
$568$	−27.9172	−	25.1368i	−1.17138	−	1.05472i
$569$	9.11460	+	10.1228i	0.382104	+	0.424369i	0.903261	−	0.429091i	$-0.141166\pi$
$569$	9.11460	+	10.1228i	0.382104	+	0.424369i	−0.521157	+	0.853461i	$0.674499\pi$
$570$	−8.22429	+	21.4250i	−0.344477	+	0.897394i
$571$	−5.30887			−0.222169			−0.111085	−	0.993811i	$-0.535432\pi$
$571$	−5.30887			−0.222169			−0.111085	+	0.993811i	$0.535432\pi$
$572$	−0.473988	+	0.0128459i	−0.0198184	+	0.000537115i
$573$	10.8166			0.451869
$574$	4.78720	−	12.4711i	0.199814	−	0.520533i
$575$	14.5277	+	16.1346i	0.605847	+	0.672861i
$576$	6.05831	+	5.45492i	0.252429	+	0.227288i
$577$	−22.1648	−	3.51055i	−0.922731	−	0.146146i	−0.323047	−	0.946383i	$-0.604707\pi$
$577$	−22.1648	−	3.51055i	−0.922731	−	0.146146i	−0.599684	+	0.800237i	$0.704707\pi$
$578$	11.7671	−	4.51698i	0.489448	−	0.187881i
$579$	7.92250	−	0.415201i	0.329248	−	0.0172551i
$580$	−0.657857	+	0.335195i	−0.0273160	+	0.0139182i
$581$	−1.68641	+	16.0452i	−0.0699642	+	0.665665i
$582$	7.54055	−	13.0606i	0.312566	−	0.541380i
$583$	−37.4156	+	8.41940i	−1.54960	+	0.348696i
$584$			33.9027i			1.40290i
$585$	−3.41361	+	9.31341i	−0.141136	+	0.385062i
$586$	2.42252	−	7.45575i	0.100073	−	0.307994i
$587$	0.499342	+	0.768920i	0.0206101	+	0.0317367i	0.848825	−	0.528673i	$-0.177310\pi$
$587$	0.499342	+	0.768920i	0.0206101	+	0.0317367i	−0.828215	+	0.560410i	$0.810644\pi$
$588$	0.00909728	+	0.0865548i	0.000375165	+	0.00356946i
$589$	51.3519	+	22.8633i	2.11592	+	0.942068i
$590$	29.7403	+	15.1535i	1.22439	+	0.623858i
$591$	−9.40979	+	14.4898i	−0.387067	+	0.596031i
$592$	20.4907	+	25.3040i	0.842165	+	1.03999i
$593$	−14.0947	−	14.0947i	−0.578798	−	0.578798i	0.355774	−	0.934572i	$-0.384217\pi$
$593$	−14.0947	−	14.0947i	−0.578798	−	0.578798i	−0.934572	+	0.355774i	$0.884217\pi$
$594$	−4.16234	−	2.05882i	−0.170783	−	0.0844742i
$595$	−14.7698	−	8.52733i	−0.605501	−	0.349586i
$596$	−0.612165	−	0.234988i	−0.0250753	−	0.00962550i
$597$	−8.02103	−	2.60619i	−0.328279	−	0.106664i
$598$	−35.4285	+	23.7807i	−1.44878	+	0.972467i
$599$	−8.89197	+	6.46040i	−0.363316	+	0.263965i	−0.754434	−	0.656376i	$-0.772089\pi$
$599$	−8.89197	+	6.46040i	−0.363316	+	0.263965i	0.391118	+	0.920341i	$0.372089\pi$
$600$	5.70072	+	4.61636i	0.232731	+	0.188462i
$601$	4.22486	−	19.8764i	0.172336	−	0.810775i	−0.804020	−	0.594603i	$-0.797309\pi$
$601$	4.22486	−	19.8764i	0.172336	−	0.810775i	0.976355	−	0.216172i	$-0.0693573\pi$
$602$	3.93384	−	0.836163i	0.160331	−	0.0340795i
$603$	0.343002	+	2.16563i	0.0139681	+	0.0881912i
$604$	0.332674	+	0.0891397i	0.0135363	+	0.00362704i
$605$	0.864330	−	30.2500i	0.0351400	−	1.22984i
$606$	−0.814912	+	0.814912i	−0.0331035	+	0.0331035i
$607$	14.1571	+	1.48797i	0.574617	+	0.0603947i	0.387380	−	0.921920i	$-0.373380\pi$
$607$	14.1571	+	1.48797i	0.574617	+	0.0603947i	0.187237	+	0.982315i	$0.440047\pi$
$608$	0.992969	−	0.894073i	0.0402702	−	0.0362594i
$609$	−12.4430	+	8.08058i	−0.504216	+	0.327441i
$610$	5.49606	+	7.56468i	0.222529	+	0.306285i
$611$	−9.14440	−	22.7810i	−0.369943	−	0.921620i
$612$	−0.106647	+	0.0346517i	−0.00431094	+	0.00140071i
$613$	37.5234	+	1.96652i	1.51556	+	0.0794269i	0.791865	−	0.610697i	$-0.209111\pi$
$613$	37.5234	+	1.96652i	1.51556	+	0.0794269i	0.723691	+	0.690124i	$0.242444\pi$
$614$	−22.1974	+	9.88290i	−0.895813	+	0.398842i
$615$	−5.98707	−	10.3699i	−0.241422	−	0.418155i
$616$	−4.07475	+	20.3582i	−0.164176	+	0.820256i
$617$	4.82990	−	18.0254i	0.194445	−	0.725677i	−0.797965	−	0.602703i	$-0.794090\pi$
$617$	4.82990	−	18.0254i	0.194445	−	0.725677i	0.992410	−	0.122974i	$-0.0392431\pi$
$618$	12.6415	−	10.2369i	0.508514	−	0.411787i
$619$	22.2936	+	43.7536i	0.896055	+	1.75861i	0.591965	+	0.805964i	$0.298352\pi$
$619$	22.2936	+	43.7536i	0.896055	+	1.75861i	0.304090	+	0.952643i	$0.401648\pi$
$620$	0.688671	−	0.764846i	0.0276577	−	0.0307170i
$621$	8.40612	−	0.883519i	0.337326	−	0.0354544i
$622$	11.4764	−	14.1722i	0.460162	−	0.568253i
$623$	5.57220	+	17.1495i	0.223246	+	0.687079i
$624$	−10.3562	+	9.61372i	−0.414579	+	0.384857i
$625$	−25.2780	−	18.3655i	−1.01112	−	0.734621i
$626$	−2.04110	−	7.61748i	−0.0815787	−	0.304456i
$627$	−10.5642	+	16.6991i	−0.421894	+	0.666898i
$628$	0.441546	−	0.254927i	0.0176196	−	0.0101727i
$629$	−23.2060	+	3.67547i	−0.925284	+	0.146551i
$630$	7.08137	+	4.59870i	0.282129	+	0.183217i
$631$	0.0839471	+	1.60181i	0.00334188	+	0.0637669i	0.999791	−	0.0204258i	$-0.00650220\pi$
$631$	0.0839471	+	1.60181i	0.00334188	+	0.0637669i	−0.996449	+	0.0841927i	$0.973169\pi$
$632$	2.71776	−	17.1593i	0.108107	−	0.682560i
$633$	−7.36560	+	16.5434i	−0.292756	+	0.657542i
$634$	−12.3048	−	2.61547i	−0.488686	−	0.103873i
$635$	0.547675	−	10.4503i	0.0217338	−	0.414706i
$636$	0.269501	−	0.370936i	0.0106864	−	0.0147086i
$637$	−7.91298	+	0.120269i	−0.313524	+	0.00476525i
$638$	30.2602	−	8.49533i	1.19801	−	0.336333i
$639$	−12.7063	+	3.40465i	−0.502654	+	0.134686i
$640$	12.2703	+	27.5596i	0.485027	+	1.08939i
$641$	1.58675	+	7.46508i	0.0626729	+	0.294853i	0.998310	−	0.0581102i	$-0.0185075\pi$
$641$	1.58675	+	7.46508i	0.0626729	+	0.294853i	−0.935637	+	0.352963i	$0.885174\pi$
$642$	2.91031	−	5.71180i	0.114861	−	0.225427i
$643$	−6.19208	−	16.1309i	−0.244192	−	0.636141i	0.755631	−	0.654998i	$-0.227331\pi$
$643$	−6.19208	−	16.1309i	−0.244192	−	0.636141i	−0.999822	+	0.0188572i	$0.993997\pi$
$644$	−0.263281	−	0.685870i	−0.0103747	−	0.0270271i
$645$	1.63663	−	3.21207i	0.0644423	−	0.126475i
$646$	−4.90481	−	23.0753i	−0.192977	−	0.907886i
$647$	−5.48601	−	12.3218i	−0.215677	−	0.484420i	0.773013	−	0.634390i	$-0.218749\pi$
$647$	−5.48601	−	12.3218i	−0.215677	−	0.484420i	−0.988690	+	0.149971i	$0.952082\pi$
$648$	2.75846	−	0.739127i	0.108362	−	0.0290356i
$649$	22.5487	+	17.8196i	0.885114	+	0.699481i
$650$	−9.02873	+	9.30742i	−0.354136	+	0.365067i
$651$	12.1563	−	16.7317i	0.476444	−	0.655769i
$652$	−0.0418937	+	0.799379i	−0.00164068	+	0.0313061i
$653$	5.17400	+	1.09977i	0.202474	+	0.0430372i	0.308032	−	0.951376i	$-0.400330\pi$
$653$	5.17400	+	1.09977i	0.202474	+	0.0430372i	−0.105558	+	0.994413i	$0.533663\pi$
$654$	2.41964	−	5.43460i	0.0946153	−	0.212509i
$655$	−3.89759	+	24.6084i	−0.152292	+	0.961531i
$656$	−0.892739	−	17.0345i	−0.0348556	−	0.665084i
$657$	9.95641	+	6.46577i	0.388437	+	0.252254i
$658$	−20.6385	+	3.26881i	−0.804571	+	0.127432i
$659$	−3.38393	+	1.95371i	−0.131819	+	0.0761058i	−0.564459	−	0.825461i	$-0.690915\pi$
$659$	−3.38393	+	1.95371i	−0.131819	+	0.0761058i	0.432640	+	0.901567i	$0.357582\pi$
$660$	0.231015	+	0.278440i	0.00899223	+	0.0108382i
$661$	−3.22625	−	12.0405i	−0.125487	−	0.468322i	0.874370	−	0.485260i	$-0.161275\pi$
$661$	−3.22625	−	12.0405i	−0.125487	−	0.468322i	−0.999857	+	0.0169377i	$0.994608\pi$
$662$	−10.8707	−	7.89802i	−0.422501	−	0.306965i
$663$	−2.27132	−	9.94040i	−0.0882108	−	0.386053i
$664$	6.49508	+	19.9898i	0.252058	+	0.775754i
$665$	22.6112	−	27.9226i	0.876827	−	1.08279i
$666$	11.5685	−	1.21590i	0.448271	−	0.0471152i
$667$	−38.2803	+	42.5146i	−1.48222	+	1.64617i
$668$	−0.0795710	−	0.156167i	−0.00307870	−	0.00604228i
$669$	16.3223	−	13.2175i	0.631055	−	0.511018i
$670$	−2.18593	+	8.15800i	−0.0844498	+	0.315171i
$671$	3.36193	+	7.31553i	0.129786	+	0.282413i
$672$	−0.245804	−	0.425745i	−0.00948210	−	0.0164235i
$673$	−6.39379	+	2.84670i	−0.246463	+	0.109732i	−0.526250	−	0.850330i	$-0.676403\pi$
$673$	−6.39379	+	2.84670i	−0.246463	+	0.109732i	0.279788	+	0.960062i	$0.409736\pi$
$674$	2.21187	+	0.115919i	0.0851979	+	0.00446503i
$675$	2.44293	−	0.793756i	0.0940284	−	0.0305517i
$676$	0.315518	+	0.407622i	0.0121353	+	0.0156778i
$677$	3.64499	+	5.01690i	0.140088	+	0.192815i	0.873296	−	0.487189i	$-0.161978\pi$
$677$	3.64499	+	5.01690i	0.140088	+	0.192815i	−0.733208	+	0.680004i	$0.761978\pi$
$678$	19.4144	−	12.6078i	0.745604	−	0.484201i
$679$	−17.5465	+	15.7989i	−0.673373	+	0.606307i
$680$	−22.0968	−	2.32247i	−0.847374	−	0.0890626i
$681$	5.10031	−	5.10031i	0.195444	−	0.195444i
$682$	−35.1360	+	26.1721i	−1.34543	+	1.00218i
$683$	−18.7017	−	5.01109i	−0.715599	−	0.191744i	−0.117392	−	0.993086i	$-0.537453\pi$
$683$	−18.7017	−	5.01109i	−0.715599	−	0.191744i	−0.598207	+	0.801341i	$0.704120\pi$
$684$	−0.0369559	−	0.233330i	−0.00141304	−	0.00892161i
$685$	−18.6443	+	3.96298i	−0.712363	+	0.151418i
$686$	−5.86737	+	27.6038i	−0.224017	+	1.05392i
$687$	−6.49485	−	5.25942i	−0.247794	−	0.200659i
$688$	4.15472	−	3.01858i	0.158397	−	0.115082i
$689$	31.4037	+	27.4234i	1.19639	+	1.04475i
$690$	30.9645	+	10.0610i	1.17880	+	0.383014i
$691$	19.1042	+	7.33343i	0.726760	+	0.278977i	0.693487	−	0.720469i	$-0.256074\pi$
$691$	19.1042	+	7.33343i	0.726760	+	0.278977i	0.0332730	+	0.999446i	$0.489407\pi$
$692$	0.634844	+	0.366527i	0.0241331	+	0.0139333i
$693$	5.20161	+	5.07929i	0.197593	+	0.192946i
$694$	−0.733045	−	0.733045i	−0.0278260	−	0.0278260i
$695$	−30.0128	−	37.0628i	−1.13845	−	1.40587i
$696$	−10.5272	+	16.2105i	−0.399034	+	0.614459i
$697$	10.9673	+	5.58812i	0.415416	+	0.211665i
$698$	16.9626	+	7.55224i	0.642045	+	0.285857i
$699$	1.53876	+	14.6403i	0.0582013	+	0.553748i
$700$	−0.121597	−	0.187243i	−0.00459593	−	0.00707711i
$701$	−7.30407	+	22.4796i	−0.275871	+	0.849044i	0.713117	+	0.701046i	$0.247283\pi$
$701$	−7.30407	+	22.4796i	−0.275871	+	0.849044i	−0.988988	+	0.147998i	$0.952717\pi$
$702$	0.865399	+	4.97349i	0.0326624	+	0.187712i
$703$		−	49.4983i		−	1.86686i
$704$	5.93576	+	26.3784i	0.223712	+	0.994172i
$705$	−9.36525	+	16.2211i	−0.352716	+	0.610922i
$706$	2.28893	−	21.7777i	0.0861451	−	0.819616i
$707$	1.60764	−	0.819136i	0.0604617	−	0.0308068i
$708$	−0.343124	+	0.0179824i	−0.0128954	+	0.000675820i
$709$	−14.4952	+	5.56419i	−0.544379	+	0.208968i	−0.614988	−	0.788537i	$-0.710839\pi$
$709$	−14.4952	+	5.56419i	−0.544379	+	0.208968i	0.0706089	+	0.997504i	$0.477506\pi$
$710$	−50.0463	−	7.92655i	−1.87820	−	0.297478i
$711$	−4.52095	−	4.07068i	−0.169549	−	0.152663i
$712$	15.7191	+	17.4578i	0.589098	+	0.654260i
$713$	28.5788	−	74.4503i	1.07028	−	2.78818i
$714$	−8.67961			−0.324826
$715$	−27.0955	+	18.6588i	−1.01331	+	0.697798i
$716$	0.144683			0.00540708
$717$	1.40339	−	3.65595i	0.0524105	−	0.136534i
$718$	−20.4322	−	22.6923i	−0.762524	−	0.846868i
$719$	−6.35514	−	5.72219i	−0.237007	−	0.213402i	0.542065	−	0.840336i	$-0.317643\pi$
$719$	−6.35514	−	5.72219i	−0.237007	−	0.213402i	−0.779072	+	0.626935i	$0.784309\pi$
$720$	10.6492	+	1.68667i	0.396873	+	0.0628586i
$721$	−23.7755	+	9.12657i	−0.885447	+	0.339891i
$722$	23.0656	−	1.20882i	0.858413	−	0.0449875i
$723$	8.23097	−	4.19389i	0.306113	−	0.155972i
$724$	−0.0454272	+	0.432211i	−0.00168829	+	0.0160630i
$725$	−8.69277	+	15.0563i	−0.322841	+	0.559177i
$726$	−7.31659	−	13.5525i	−0.271544	−	0.502980i
$727$			15.5006i			0.574886i	0.957798	+	0.287443i	$0.0928051\pi$
$727$			15.5006i			0.574886i	−0.957798	+	0.287443i	$0.907195\pi$
$728$	20.4774	−	9.49262i	0.758945	−	0.351820i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	24.9056	+	38.3512i	0.921796	+	1.41944i
$731$	0.387358	+	3.68547i	0.0143270	+	0.136312i
$732$	−0.0879317	−	0.0391497i	−0.00325005	−	0.00144701i
$733$	−27.9059	−	14.2188i	−1.03073	−	0.525182i	−0.145022	−	0.989429i	$-0.546325\pi$
$733$	−27.9059	−	14.2188i	−1.03073	−	0.525182i	−0.885706	+	0.464247i	$0.846325\pi$
$734$	13.7675	−	21.2001i	0.508168	−	0.782510i
$735$	3.80014	+	4.69278i	0.140170	+	0.173096i
$736$	−1.34040	−	1.34040i	−0.0494079	−	0.0494079i
$737$	−3.22415	+	6.51832i	−0.118763	+	0.240105i
$738$	−5.27755	−	3.04700i	−0.194269	−	0.112161i
$739$	39.6416	+	15.2170i	1.45824	+	0.559766i	0.952935	−	0.303174i	$-0.0980463\pi$
$739$	39.6416	+	15.2170i	1.45824	+	0.559766i	0.505306	+	0.862940i	$0.331380\pi$
$740$	−0.861928	−	0.280057i	−0.0316851	−	0.0102951i
$741$	21.4325	−	1.45014i	0.787343	−	0.0532722i
$742$	28.7116	−	20.8602i	1.05404	−	0.765802i
$743$	−18.3631	−	14.8702i	−0.673677	−	0.545533i	0.230297	−	0.973120i	$-0.426030\pi$
$743$	−18.3631	−	14.8702i	−0.673677	−	0.545533i	−0.903974	+	0.427587i	$0.859364\pi$
$744$	5.60189	−	26.3548i	0.205375	−	0.966215i
$745$	−44.5013	+	9.45904i	−1.63040	+	0.346552i
$746$	−1.86782	−	11.7930i	−0.0683858	−	0.431771i
$747$	7.10924	+	1.90491i	0.260113	+	0.0696972i
$748$	−0.355050	−	0.110710i	−0.0129819	−	0.00404797i
$749$	−7.09677	+	7.09677i	−0.259310	+	0.259310i
$750$	−9.31403	−	0.978944i	−0.340100	−	0.0357460i
$751$	7.02394	−	6.32438i	0.256307	−	0.230780i	−0.530953	−	0.847401i	$-0.678166\pi$
$751$	7.02394	−	6.32438i	0.256307	−	0.230780i	0.787260	+	0.616622i	$0.211499\pi$
$752$	−22.3780	+	14.5324i	−0.816041	+	0.529943i
$753$	7.40925	+	10.1980i	0.270008	+	0.371634i
$754$	−26.8774	−	21.0967i	−0.978816	−	0.768296i
$755$	22.7265	−	7.38428i	0.827102	−	0.268742i
$756$	−0.0867987	−	0.00454893i	−0.00315684	−	0.000165443i
$757$	40.2531	−	17.9218i	1.46302	−	0.651380i	0.487871	−	0.872916i	$-0.337774\pi$
$757$	40.2531	−	17.9218i	1.46302	−	0.651380i	0.975152	+	0.221536i	$0.0711069\pi$
$758$	−5.59967	−	9.69891i	−0.203389	−	0.352280i
$759$	24.4428	+	13.7269i	0.887217	+	0.498256i
$760$	12.1149	−	45.2136i	0.439455	−	1.64007i
$761$	−5.92628	+	4.79901i	−0.214828	+	0.173964i	−0.730694	−	0.682705i	$-0.760803\pi$
$761$	−5.92628	+	4.79901i	−0.214828	+	0.173964i	0.515866	+	0.856669i	$0.327470\pi$
$762$	−2.41784	−	4.74528i	−0.0875891	−	0.171903i
$763$	−6.23206	+	6.92140i	−0.225616	+	0.250572i
$764$	−0.426543	+	0.0448314i	−0.0154318	+	0.00162194i
$765$	−4.89626	+	6.04638i	−0.177025	+	0.218607i
$766$	12.5473	+	38.6167i	0.453354	+	1.39528i
$767$	1.16081	−	31.2220i	0.0419143	−	1.12736i
$768$	−0.769583	−	0.559135i	−0.0277699	−	0.0201760i
$769$	0.884547	+	3.30118i	0.0318976	+	0.119043i	0.980039	−	0.198805i	$-0.0637062\pi$
$769$	0.884547	+	3.30118i	0.0318976	+	0.119043i	−0.948141	+	0.317849i	$0.897040\pi$
$770$	10.3461	+	26.0229i	0.372848	+	0.937800i
$771$	16.3918	−	9.46381i	0.590336	−	0.340831i
$772$	−0.310696	+	0.0492095i	−0.0111822	+	0.00177109i
$773$	21.4156	+	13.9075i	0.770267	+	0.500217i	0.868949	−	0.494902i	$-0.164796\pi$
$773$	21.4156	+	13.9075i	0.770267	+	0.500217i	−0.0986820	+	0.995119i	$0.531463\pi$
$774$	−0.0960200	−	1.83217i	−0.00345137	−	0.0658560i
$775$	3.79115	−	23.9364i	0.136182	−	0.859819i
$776$	−12.5113	+	28.1008i	−0.449129	+	1.00876i
$777$	−17.8136	−	3.78640i	−0.639059	−	0.135836i
$778$	1.63629	−	31.2222i	0.0586638	−	1.11937i
$779$	−15.2422	+	20.9791i	−0.546108	+	0.751653i
$780$	0.0960117	−	0.381415i	0.00343777	−	0.0136569i
$781$	−40.9140	−	15.1494i	−1.46402	−	0.542090i
$782$	−32.3277	+	8.66219i	−1.15604	+	0.309759i
$783$	2.75294	+	6.18320i	0.0983820	+	0.220970i
$784$	1.78849	+	8.41419i	0.0638747	+	0.300507i
$785$	16.0599	−	31.5194i	0.573203	−	1.12497i
$786$	4.54413	+	11.8379i	0.162084	+	0.422243i
$787$	−5.95633	−	15.5168i	−0.212320	−	0.553113i	0.785517	−	0.618840i	$-0.212397\pi$
$787$	−5.95633	−	15.5168i	−0.212320	−	0.553113i	−0.997838	+	0.0657263i	$0.979064\pi$
$788$	0.311011	−	0.610394i	0.0110793	−	0.0217444i
$789$	0.248634	+	1.16973i	0.00885162	+	0.0416436i
$790$	−9.53116	−	21.4073i	−0.339103	−	0.761639i
$791$	−35.0074	+	9.38019i	−1.24472	+	0.333521i
$792$	8.88217	+	3.28884i	0.315614	+	0.116864i
$793$	4.26052	−	7.64545i	0.151295	−	0.271498i
$794$	−1.16861	+	1.60845i	−0.0414724	+	0.0570818i
$795$	1.66492	−	31.7685i	0.0590485	−	1.12671i
$796$	0.327104	+	0.0695282i	0.0115939	+	0.00246436i
$797$	7.32189	−	16.4452i	0.259355	−	0.582520i	−0.736194	−	0.676771i	$-0.763379\pi$
$797$	7.32189	−	16.4452i	0.259355	−	0.582520i	0.995549	+	0.0942506i	$0.0300455\pi$
$798$	2.86050	−	18.0605i	0.101261	−	0.639335i
$799$	−1.00768	−	19.2277i	−0.0356493	−	0.680229i
$800$	−0.483131	−	0.313749i	−0.0170813	−	0.0110927i
$801$	8.12483	−	1.28685i	0.287077	−	0.0454685i
$802$	−17.2104	+	9.93642i	−0.607720	+	0.350867i
$803$	14.5466	+	36.5882i	0.513340	+	1.29117i
$804$	−0.0225019	−	0.0839781i	−0.000793580	−	0.00296168i
$805$	−41.2381	−	29.9612i	−1.45345	−	1.05599i
$806$	45.5163	+	14.0281i	1.60324	+	0.494118i
$807$	6.08794	+	18.7367i	0.214306	+	0.659565i
$808$	1.47929	−	1.82677i	0.0520412	−	0.0642656i
$809$	−22.3013	+	2.34396i	−0.784072	+	0.0824093i	−0.488100	−	0.872787i	$-0.662310\pi$
$809$	−22.3013	+	2.34396i	−0.784072	+	0.0824093i	−0.295972	+	0.955197i	$0.595643\pi$
$810$	2.57743	−	2.86253i	0.0905616	−	0.100579i
$811$	−13.2035	−	25.9134i	−0.463638	−	0.909941i	−0.997909	−	0.0646281i	$-0.979414\pi$
$811$	−13.2035	−	25.9134i	−0.463638	−	0.909941i	0.534271	−	0.845313i	$-0.320586\pi$
$812$	0.457188	−	0.370223i	0.0160441	−	0.0129923i
$813$	0.371432	−	1.38620i	0.0130267	−	0.0486163i
$814$	33.6382	+	18.8910i	1.17902	+	0.662131i
$815$	27.7696	+	48.0983i	0.972726	+	1.68481i
$816$	−10.1252	+	4.50802i	−0.354452	+	0.157812i
$817$	−7.79637	−	0.408591i	−0.272761	−	0.0142948i
$818$	50.8185	−	16.5119i	1.77683	−	0.577327i
$819$	1.11761	−	7.82413i	0.0390525	−	0.273397i
$820$	0.279075	+	0.384114i	0.00974573	+	0.0134139i
$821$	−43.6295	+	28.3333i	−1.52268	+	0.988839i	−0.532908	+	0.846173i	$0.678901\pi$
$821$	−43.6295	+	28.3333i	−1.52268	+	0.988839i	−0.989771	+	0.142666i	$0.954432\pi$
$822$	−7.20897	+	6.49099i	−0.251442	+	0.226399i
$823$	−15.8794	−	1.66899i	−0.553522	−	0.0581775i	−0.176362	−	0.984325i	$-0.556433\pi$
$823$	−15.8794	−	1.66899i	−0.553522	−	0.0581775i	−0.377160	+	0.926148i	$0.623099\pi$
$824$	−23.4604	+	23.4604i	−0.817282	+	0.817282i
$825$	8.13303	+	2.53601i	0.283156	+	0.0882926i
$826$	−25.6891	−	6.88339i	−0.893840	−	0.239504i
$827$	1.98703	+	12.5456i	0.0690958	+	0.436254i	0.997849	+	0.0655551i	$0.0208818\pi$
$827$	1.98703	+	12.5456i	0.0690958	+	0.436254i	−0.928753	+	0.370699i	$0.879118\pi$
$828$	−0.327826	+	0.0696817i	−0.0113928	+	0.00242160i
$829$	5.30753	−	24.9700i	0.184338	−	0.867243i	−0.784612	−	0.619987i	$-0.787138\pi$
$829$	5.30753	−	24.9700i	0.184338	−	0.867243i	0.968950	−	0.247256i	$-0.0795289\pi$
$830$	22.0322	+	17.8413i	0.764749	+	0.619281i
$831$	−1.14343	+	0.830751i	−0.0396652	+	0.0288184i
$832$	19.3338	−	22.1399i	0.670278	−	0.767563i
$833$	−5.90348	−	1.91816i	−0.204544	−	0.0664602i
$834$	−22.6592	−	8.69805i	−0.784624	−	0.301189i
$835$	−10.5315	−	6.08036i	−0.364457	−	0.210419i
$836$	0.347378	−	0.702300i	0.0120143	−	0.0242896i
$837$	−6.67142	−	6.67142i	−0.230598	−	0.230598i
$838$	−4.64954	−	5.74170i	−0.160616	−	0.198344i
$839$	3.68823	−	5.67938i	0.127332	−	0.196074i	−0.769255	−	0.638942i	$-0.779372\pi$
$839$	3.68823	−	5.67938i	0.127332	−	0.196074i	0.896587	+	0.442868i	$0.146039\pi$
$840$	−15.3449	−	7.81860i	−0.529448	−	0.269767i
$841$	−15.3573	−	6.83751i	−0.529562	−	0.235776i
$842$	0.0830059	+	0.789748i	0.00286057	+	0.0272165i
$843$	−15.2062	−	23.4156i	−0.523731	−	0.806475i
$844$	0.221889	−	0.682904i	0.00763773	−	0.0235065i
$845$	33.7632	+	11.7962i	1.16149	+	0.405802i
$846$			9.53251i			0.327734i
$847$	4.33760	+	23.7192i	0.149042	+	0.815001i
$848$	22.6591	−	39.2467i	0.778115	−	1.34774i
$849$	2.10885	−	20.0643i	0.0723754	−	0.688606i
$850$	−9.06225	+	4.61744i	−0.310832	+	0.158377i
$851$	−70.1266	+	3.67518i	−2.40391	+	0.125983i
$852$	0.486952	−	0.186923i	0.0166827	−	0.00640389i
$853$	−20.9575	−	3.31934i	−0.717570	−	0.113652i	−0.213037	−	0.977044i	$-0.568335\pi$
$853$	−20.9575	−	3.31934i	−0.717570	−	0.113652i	−0.504533	+	0.863392i	$0.668335\pi$
$854$	−5.53665	−	4.98522i	−0.189460	−	0.170591i
$855$	−10.9676	−	12.1808i	−0.375085	−	0.416575i
$856$	−4.68573	+	12.2067i	−0.160155	+	0.417218i
$857$	−19.8122			−0.676773			−0.338386	−	0.941007i	$-0.609881\pi$
$857$	−19.8122			−0.676773			−0.338386	+	0.941007i	$0.609881\pi$
$858$	−7.19424	+	15.1186i	−0.245607	+	0.516141i
$859$	−0.246868			−0.00842303			−0.00421151	−	0.999991i	$-0.501341\pi$
$859$	−0.246868			−0.00842303			−0.00421151	+	0.999991i	$0.501341\pi$
$860$	−0.0512262	+	0.133449i	−0.00174680	+	0.00455056i
$861$	6.38405	+	7.09021i	0.217568	+	0.241634i
$862$	22.2477	+	20.0319i	0.757761	+	0.682291i
$863$	24.0759	+	3.81325i	0.819554	+	0.129805i	0.552112	−	0.833770i	$-0.313822\pi$
$863$	24.0759	+	3.81325i	0.819554	+	0.129805i	0.267441	+	0.963574i	$0.413822\pi$
$864$	−0.209373	+	0.0803708i	−0.00712301	+	0.00273427i
$865$	50.7915	−	2.66187i	1.72696	−	0.0905064i
$866$	7.18719	−	3.66206i	0.244231	−	0.124442i
$867$	−0.940993	+	8.95295i	−0.0319578	+	0.304058i
$868$	−0.410027	+	0.710187i	−0.0139172	+	0.0241053i
$869$	−4.42950	−	19.6846i	−0.150261	−	0.667755i
$870$			26.0711i			0.883892i
$871$	7.78859	−	1.35523i	0.263906	−	0.0459203i
$872$	−3.74952	+	11.5398i	−0.126975	+	0.390788i
$873$	5.86645	+	9.03354i	0.198549	+	0.305739i
$874$	−7.37014	−	70.1222i	−0.249299	−	2.37192i
$875$	13.3948	+	5.96376i	0.452828	+	0.201612i
$876$	−0.419422	−	0.213706i	−0.0141709	−	0.00722046i
$877$	−7.11009	+	10.9486i	−0.240091	+	0.369707i	−0.938090	−	0.346391i	$-0.887407\pi$
$877$	−7.11009	+	10.9486i	−0.240091	+	0.369707i	0.698000	+	0.716098i	$0.254074\pi$
$878$	18.6064	+	22.9769i	0.627934	+	0.775434i
$879$	3.95916	+	3.95916i	0.133539	+	0.133539i
$880$	25.5850	+	24.9834i	0.862471	+	0.842189i
$881$	−33.2261	−	19.1831i	−1.11942	−	0.646295i	−0.178164	−	0.984001i	$-0.557016\pi$
$881$	−33.2261	−	19.1831i	−1.11942	−	0.646295i	−0.941252	+	0.337706i	$0.890349\pi$
$882$	2.86904	+	1.10132i	0.0966057	+	0.0370834i
$883$	29.6733	+	9.64145i	0.998587	+	0.324461i	0.762301	−	0.647223i	$-0.224070\pi$
$883$	29.6733	+	9.64145i	0.998587	+	0.324461i	0.236286	+	0.971683i	$0.424070\pi$
$884$	0.130768	+	0.382578i	0.00439819	+	0.0128675i
$885$	−19.2866	+	14.0125i	−0.648312	+	0.471026i
$886$	11.3121	+	9.16035i	0.380037	+	0.307748i
$887$	10.2692	−	48.3128i	0.344806	−	1.62219i	−0.374315	−	0.927301i	$-0.622122\pi$
$887$	10.2692	−	48.3128i	0.344806	−	1.62219i	0.719122	−	0.694884i	$-0.244544\pi$
$888$	−23.2073	+	4.93286i	−0.778785	+	0.165536i
$889$	1.30436	+	8.23539i	0.0437468	+	0.276206i
$890$	30.6065	+	8.20099i	1.02593	+	0.274898i
$891$	2.65982	−	1.98125i	0.0891074	−	0.0663743i
$892$	−0.588872	+	0.588872i	−0.0197169	+	0.0197169i
$893$	40.3411	+	4.24002i	1.34996	+	0.141887i
$894$	−17.2068	+	15.4930i	−0.575480	+	0.518164i
$895$	8.41901	−	5.46737i	0.281417	−	0.182754i
$896$	−14.1287	−	19.4465i	−0.472007	−	0.649662i
$897$	−3.64581	−	30.2568i	−0.121730	−	1.01024i
$898$	−7.73321	+	2.51267i	−0.258060	+	0.0838489i
$899$	63.7707	+	3.34208i	2.12687	+	0.111465i
$900$	−0.0930451	+	0.0414263i	−0.00310150	+	0.00138088i
$901$	16.3507	+	28.3202i	0.544721	+	0.943484i
$902$	−8.43984	−	18.3650i	−0.281016	−	0.611488i
$903$	−0.743433	+	2.77453i	−0.0247399	+	0.0923305i
$904$	−36.6936	+	29.7139i	−1.22041	+	0.988270i
$905$	13.6892	+	26.8667i	0.455046	+	0.893078i
$906$	8.13756	−	9.03768i	0.270352	−	0.300257i
$907$	−11.0029	+	1.15645i	−0.365345	+	0.0383993i	−0.285422	−	0.958402i	$-0.592134\pi$
$907$	−11.0029	+	1.15645i	−0.365345	+	0.0383993i	−0.0799223	+	0.996801i	$0.525467\pi$
$908$	−0.179987	+	0.222266i	−0.00597308	+	0.00737615i
$909$	−0.254356	−	0.782826i	−0.00843644	−	0.0259647i
$910$	16.1909	−	25.7813i	0.536723	−	0.854642i
$911$	−34.2988	−	24.9195i	−1.13637	−	0.825620i	−0.149760	−	0.988722i	$-0.547850\pi$
$911$	−34.2988	−	24.9195i	−1.13637	−	0.825620i	−0.986609	+	0.163102i	$0.947850\pi$
$912$	−6.04336	−	22.5541i	−0.200116	−	0.746842i
$913$	15.5866	+	18.7864i	0.515841	+	0.621738i
$914$	21.0121	−	12.1313i	0.695019	−	0.401269i
$915$	−6.59608	+	1.04472i	−0.218060	+	0.0345373i
$916$	0.277918	+	0.180482i	0.00918265	+	0.00596329i
$917$	−1.03898	−	19.8248i	−0.0343100	−	0.654674i
$918$	−0.619416	+	3.91084i	−0.0204438	+	0.129077i
$919$	19.8355	−	44.5513i	0.654313	−	1.46961i	−0.215638	−	0.976473i	$-0.569183\pi$
$919$	19.8355	−	44.5513i	0.654313	−	1.46961i	0.869951	−	0.493138i	$-0.164150\pi$
$920$	−64.9557	−	13.8068i	−2.14153	−	0.455196i
$921$	0.908249	−	17.3304i	0.0299278	−	0.571057i
$922$	−9.61880	+	13.2391i	−0.316778	+	0.436008i
$923$	12.9704	+	45.6214i	0.426927	+	1.50165i
$924$	−0.226173	−	0.178738i	−0.00744055	−	0.00588006i
$925$	−20.6132	+	5.52329i	−0.677758	+	0.181605i
$926$	−0.362775	−	0.814806i	−0.0119215	−	0.0267762i
$927$	2.41550	+	11.3640i	0.0793354	+	0.373244i
$928$	0.689126	−	1.35249i	0.0226217	−	0.0443975i
$929$	12.0369	+	31.3573i	0.394920	+	1.02880i	0.976539	+	0.215340i	$0.0690859\pi$
$929$	12.0369	+	31.3573i	0.394920	+	1.02880i	−0.581620	+	0.813461i	$0.697581\pi$
$930$	−13.0238	−	33.9282i	−0.427068	−	1.11255i
$931$	5.93688	−	11.6518i	0.194574	−	0.381872i
$932$	−0.121359	−	0.570951i	−0.00397526	−	0.0187021i
$933$	5.29762	+	11.8986i	0.173436	+	0.389544i
$934$	5.50592	−	1.47531i	0.180159	−	0.0482735i
$935$	−24.8436	+	6.97466i	−0.812474	+	0.228096i
$936$	−2.81580	−	9.90411i	−0.0920373	−	0.323726i
$937$	−4.06324	+	5.59257i	−0.132740	+	0.182701i	−0.870213	−	0.492675i	$-0.836019\pi$
$937$	−4.06324	+	5.59257i	−0.132740	+	0.182701i	0.737473	+	0.675377i	$0.236019\pi$
$938$	0.352193	−	6.72025i	0.0114995	−	0.219424i
$939$	5.50941	+	1.17106i	0.179793	+	0.0382162i
$940$	0.302079	−	0.678482i	0.00985275	−	0.0221296i
$941$	−4.23633	+	26.7471i	−0.138100	+	0.871931i	0.817213	+	0.576336i	$0.195518\pi$
$941$	−4.23633	+	26.7471i	−0.138100	+	0.871931i	−0.955313	+	0.295595i	$0.904482\pi$
$942$	−0.942224	−	17.9787i	−0.0306993	−	0.585778i
$943$	30.8537	+	20.0367i	1.00474	+	0.652483i
$944$	−33.5427	+	5.31264i	−1.09172	+	0.172912i
$945$	−5.22264	+	3.01529i	−0.169893	+	0.0980875i
$946$	3.25316	−	5.14235i	0.105769	−	0.167192i
$947$	−12.3340	−	46.0309i	−0.400800	−	1.49580i	−0.811673	−	0.584112i	$-0.801443\pi$
$947$	−12.3340	−	46.0309i	−0.400800	−	1.49580i	0.410874	−	0.911692i	$-0.365224\pi$
$948$	0.195152	+	0.141786i	0.00633823	+	0.00460500i
$949$	22.7644	−	36.2485i	0.738964	−	1.17668i
$950$	−6.62136	−	20.3784i	−0.214825	−	0.661164i
$951$	5.65425	−	6.98242i	0.183352	−	0.226421i
$952$	17.6064	−	1.85051i	0.570627	−	0.0599753i
$953$	9.49219	−	10.5421i	0.307482	−	0.341493i	−0.569522	−	0.821976i	$-0.692872\pi$
$953$	9.49219	−	10.5421i	0.307482	−	0.341493i	0.877004	+	0.480482i	$0.159538\pi$
$954$	−7.35015	−	14.4255i	−0.237970	−	0.467042i
$955$	−23.1261	+	18.7271i	−0.748342	+	0.605995i
$956$	−0.0401886	+	0.149986i	−0.00129979	+	0.00485090i
$957$	−4.40566	+	22.0115i	−0.142415	+	0.711532i
$958$	19.8720	+	34.4194i	0.642036	+	1.11204i
$959$	13.8744	−	6.17728i	0.448027	−	0.199475i
$960$	−22.3971	−	1.17378i	−0.722862	−	0.0378836i
$961$	−55.1762	+	17.9278i	−1.77988	+	0.578317i
$962$	−5.01738	−	41.6395i	−0.161767	−	1.34251i
$963$	2.69119	+	3.70410i	0.0867223	+	0.119363i
$964$	−0.307199	+	0.199497i	−0.00989421	+	0.00642538i
$965$	−16.2196	+	14.6042i	−0.522128	+	0.470126i
$966$	−25.7996	−	2.71164i	−0.830088	−	0.0872457i
$967$	34.8429	−	34.8429i	1.12047	−	1.12047i	0.128801	−	0.991670i	$-0.458887\pi$
$967$	34.8429	−	34.8429i	1.12047	−	1.12047i	0.991670	−	0.128801i	$-0.0411129\pi$
$968$	17.7310	+	25.9310i	0.569895	+	0.833454i
$969$	16.2750	+	4.36087i	0.522828	+	0.140091i
$970$	6.49045	+	40.9791i	0.208396	+	1.31576i
$971$	51.7702	−	11.0041i	1.66139	−	0.353138i	0.720918	−	0.693021i	$-0.243721\pi$
$971$	51.7702	−	11.0041i	1.66139	−	0.353138i	0.940468	+	0.339882i	$0.110387\pi$
$972$	−0.00824399	+	0.0387849i	−0.000264426	+	0.00124403i
$973$	29.5311	+	23.9138i	0.946722	+	0.766641i
$974$	−19.5714	+	14.2194i	−0.627107	+	0.455620i
$975$	−2.99546	−	8.76360i	−0.0959314	−	0.280660i
$976$	−9.04799	−	2.93987i	−0.289619	−	0.0941030i
$977$	31.8581	+	12.2292i	1.01923	+	0.391246i	0.809881	−	0.586595i	$-0.199532\pi$
$977$	31.8581	+	12.2292i	1.01923	+	0.391246i	0.209350	+	0.977841i	$0.432865\pi$
$978$	24.4787	+	14.1328i	0.782741	+	0.451916i
$979$	24.4549	+	12.0961i	0.781582	+	0.386593i
$980$	−0.169306	−	0.169306i	−0.00540827	−	0.00540827i
$981$	2.67388	+	3.30197i	0.0853705	+	0.105424i
$982$	−31.0948	+	47.8818i	−0.992275	+	1.52797i
$983$	46.6294	+	23.7589i	1.48725	+	0.757790i	0.993715	−	0.111938i	$-0.0357057\pi$
$983$	46.6294	+	23.7589i	1.48725	+	0.757790i	0.493532	+	0.869728i	$0.335706\pi$
$984$	11.3550	+	5.05558i	0.361985	+	0.161166i
$985$	−4.96838	−	47.2710i	−0.158306	−	1.50618i
$986$	−14.5963	−	22.4763i	−0.464840	−	0.715791i
$987$	4.61183	−	14.1937i	0.146796	−	0.451792i
$988$	−0.839163	+	0.146016i	−0.0266973	+	0.00464540i
$989$			11.0758i			0.352191i
$990$	12.4637	−	2.80462i	0.396122	−	0.0891367i
$991$	8.86929	−	15.3621i	0.281742	−	0.487992i	−0.690072	−	0.723741i	$-0.742421\pi$
$991$	8.86929	−	15.3621i	0.281742	−	0.487992i	0.971814	+	0.235749i	$0.0757543\pi$
$992$	−0.221175	+	2.10434i	−0.00702232	+	0.0668130i
$993$	8.55093	−	4.35692i	0.271356	−	0.138263i
$994$	40.3178	−	2.11297i	1.27880	−	0.0670193i
$995$	21.6613	−	8.31500i	0.686710	−	0.263603i
$996$	−0.288242	−	0.0456531i	−0.00913330	−	0.00144657i
$997$	−7.71774	−	6.94909i	−0.244423	−	0.220080i	0.537809	−	0.843067i	$-0.319252\pi$
$997$	−7.71774	−	6.94909i	−0.244423	−	0.220080i	−0.782232	+	0.622987i	$0.785919\pi$
$998$	−15.1140	−	16.7859i	−0.478427	−	0.531347i
$999$	−2.97732	+	7.75619i	−0.0941984	+	0.245395i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bs.a.7.5	✓	224
11.8	odd	10	inner	429.2.bs.a.85.5	yes	224
13.2	odd	12	inner	429.2.bs.a.106.5	yes	224
143.41	even	60	inner	429.2.bs.a.184.5	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bs.a.7.5	✓	224	1.1	even	1	trivial
429.2.bs.a.85.5	yes	224	11.8	odd	10	inner
429.2.bs.a.106.5	yes	224	13.2	odd	12	inner
429.2.bs.a.184.5	yes	224	143.41	even	60	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bs (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.501760 + 1.30713i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(0.0294667 + 0.0265320i) q^{4} +(2.71725 + 0.430370i) q^{5} +(1.30713 - 0.501760i) q^{6} +(-2.18905 + 0.114723i) q^{7} +(-2.54451 + 1.29649i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(-1.92595 + 3.33585i) q^{10} +(-2.18977 + 2.49096i) q^{11} -0.0396514i q^{12} +(3.59111 + 0.322345i) q^{13} +(0.948417 - 2.91893i) q^{14} +(-1.49837 - 2.30728i) q^{15} +(-0.409660 - 3.89766i) q^{16} +(2.58353 + 1.15026i) q^{17} +(-1.24752 - 0.635643i) q^{18} +(-3.24490 + 4.99672i) q^{19} +(0.0686498 + 0.0847755i) q^{20} +(1.55001 + 1.55001i) q^{21} +(-2.15727 - 4.11218i) q^{22} +(7.32001 + 4.22621i) q^{23} +(2.66609 + 1.02341i) q^{24} +(2.44293 + 0.793756i) q^{25} +(-2.22322 + 4.53231i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-0.0675478 - 0.0546991i) q^{28} +(-1.40722 + 6.62045i) q^{29} +(3.76773 - 0.800857i) q^{30} +(-1.47593 - 9.31865i) q^{31} +(-0.216627 - 0.0580450i) q^{32} +(3.31639 - 0.0394581i) q^{33} +(-2.79985 + 2.79985i) q^{34} +(-5.99755 - 0.630368i) q^{35} +(-0.0294667 + 0.0265320i) q^{36} +(-6.96768 + 4.52487i) q^{37} +(-4.90319 - 6.74866i) q^{38} +(-2.16337 - 2.88441i) q^{39} +(-7.47202 + 2.42781i) q^{40} +(4.34650 + 0.227790i) q^{41} +(-2.80380 + 1.24833i) q^{42} +(0.655187 + 1.13482i) q^{43} +(-0.130616 + 0.0153014i) q^{44} +(-0.712042 + 2.65738i) q^{45} +(-9.19709 + 7.44766i) q^{46} +(-3.09092 - 6.06626i) q^{47} +(-2.62241 + 2.91248i) q^{48} +(-2.18290 + 0.229432i) q^{49} +(-2.26331 + 2.79495i) q^{50} +(-0.873908 - 2.68961i) q^{51} +(0.0972659 + 0.104778i) q^{52} +(9.35493 + 6.79675i) q^{53} +(0.362379 + 1.35242i) q^{54} +(-7.02219 + 5.82614i) q^{55} +(5.42130 - 3.12999i) q^{56} +(5.88455 - 0.932021i) q^{57} +(-7.94770 - 5.16129i) q^{58} +(-0.453512 - 8.65353i) q^{59} +(0.0170648 - 0.107743i) q^{60} +(0.987348 - 2.21762i) q^{61} +(12.9212 + 2.74650i) q^{62} +(0.114723 - 2.18905i) q^{63} +(4.79177 - 6.59531i) q^{64} +(9.61921 + 2.42140i) q^{65} +(-1.61245 + 4.35475i) q^{66} +(2.11791 - 0.567493i) q^{67} +(0.0456095 + 0.102441i) q^{68} +(-1.75736 - 8.26772i) q^{69} +(3.83330 - 7.52328i) q^{70} +(4.71417 + 12.2808i) q^{71} +(-1.02341 - 2.66609i) q^{72} +(5.38962 - 10.5777i) q^{73} +(-2.41848 - 11.3781i) q^{74} +(-1.04476 - 2.34658i) q^{75} +(-0.228189 + 0.0611431i) q^{76} +(4.50775 - 5.70404i) q^{77} +(4.85579 - 1.38053i) q^{78} +(-3.57582 + 4.92169i) q^{79} +(0.564285 - 10.7672i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-2.47865 + 5.56714i) q^{82} +(1.15136 - 7.26941i) q^{83} +(0.00454893 + 0.0867987i) q^{84} +(6.52505 + 4.23742i) q^{85} +(-1.81210 + 0.287008i) q^{86} +(5.86157 - 3.38418i) q^{87} +(2.34239 - 9.17729i) q^{88} +(-2.12907 - 7.94581i) q^{89} +(-3.11626 - 2.26409i) q^{90} +(-7.89809 - 0.293644i) q^{91} +(0.103567 + 0.318747i) q^{92} +(-5.93752 + 7.33223i) q^{93} +(9.48029 - 0.996418i) q^{94} +(-10.9676 + 12.1808i) q^{95} +(0.101816 + 0.199825i) q^{96} +(8.37084 - 6.77857i) q^{97} +(0.795392 - 2.96845i) q^{98} +(-2.24842 - 2.43816i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 28 q^{3} - 6 q^{5} + 28 q^{9} - 16 q^{11} - 10 q^{13} - 36 q^{14} + 8 q^{15} - 24 q^{16} + 50 q^{20} + 10 q^{22} - 48 q^{23} - 30 q^{24} + 10 q^{26} + 56 q^{27} + 20 q^{29} + 12 q^{31} - 32 q^{33}+ \cdots - 6 q^{99}+O(q^{100}) \) 224 * q - 28 * q^3 - 6 * q^5 + 28 * q^9 - 16 * q^11 - 10 * q^13 - 36 * q^14 + 8 * q^15 - 24 * q^16 + 50 * q^20 + 10 * q^22 - 48 * q^23 - 30 * q^24 + 10 * q^26 + 56 * q^27 + 20 * q^29 + 12 * q^31 - 32 * q^33 - 104 * q^34 + 20 * q^35 + 12 * q^37 + 20 * q^39 - 80 * q^40 + 190 * q^41 + 32 * q^42 - 24 * q^44 + 4 * q^45 - 40 * q^46 - 10 * q^47 + 44 * q^48 - 24 * q^49 - 180 * q^50 - 110 * q^52 + 28 * q^53 - 62 * q^55 - 72 * q^56 + 20 * q^58 - 118 * q^59 + 88 * q^60 - 20 * q^61 + 120 * q^62 - 20 * q^66 - 156 * q^67 - 60 * q^68 + 12 * q^69 - 20 * q^70 + 64 * q^71 - 30 * q^72 + 10 * q^73 - 60 * q^74 - 12 * q^75 + 84 * q^78 + 200 * q^79 + 188 * q^80 + 28 * q^81 - 138 * q^82 - 80 * q^83 - 60 * q^84 + 40 * q^85 - 42 * q^86 - 18 * q^88 + 216 * q^89 - 88 * q^91 + 16 * q^92 + 12 * q^93 - 40 * q^94 - 300 * q^95 - 100 * q^96 + 18 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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