LMFDB - Embedded newform 930.2.bn.b.19.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(19,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 15, 4]))

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

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

chi := DirichletCharacter("930.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bn (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.12
Character	$\chi$	$=$	930.19
Dual form			930.2.bn.b.49.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{2} +(0.406737 - 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-1.25186 + 1.85280i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.38970 + 2.15169i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{2} +(0.406737 - 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-1.25186 + 1.85280i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.38970 + 2.15169i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +(0.763121 + 2.10182i) q^{10} +(1.84738 + 0.392674i) q^{11} +(-0.994522 - 0.104528i) q^{12} +(0.431848 - 0.0453891i) q^{13} +(3.14539 - 0.668572i) q^{14} +(1.18344 + 1.89723i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.51855 + 7.14422i) q^{17} +(-0.994522 + 0.104528i) q^{18} +(-0.0888569 + 0.845417i) q^{19} +(2.14896 + 0.618041i) q^{20} +(2.93765 - 1.30792i) q^{21} +(1.40355 - 1.26376i) q^{22} +(-0.0511067 - 0.0166056i) q^{23} +(-0.669131 + 0.743145i) q^{24} +(-1.86571 - 4.63887i) q^{25} +(0.217113 - 0.376051i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(1.30792 - 2.93765i) q^{28} +(8.30533 + 6.03417i) q^{29} +(2.23050 + 0.157741i) q^{30} +(-0.214136 - 5.56364i) q^{31} +1.00000i q^{32} +(1.11012 - 1.52796i) q^{33} +(6.67238 + 2.97073i) q^{34} +(-6.97821 + 1.73401i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.04448 - 0.603030i) q^{37} +(0.631728 + 0.568810i) q^{38} +(0.134183 - 0.412974i) q^{39} +(1.76313 - 1.37527i) q^{40} +(7.93895 - 3.53465i) q^{41} +(0.668572 - 3.14539i) q^{42} +(1.03247 + 0.108517i) q^{43} +(-0.197418 - 1.87831i) q^{44} +(2.21455 - 0.309452i) q^{45} +(-0.0434739 + 0.0315857i) q^{46} +(0.402620 + 0.554159i) q^{47} +(0.207912 + 0.978148i) q^{48} +(0.349171 + 3.32214i) q^{49} +(-4.84956 - 1.21727i) q^{50} +(7.14422 + 1.51855i) q^{51} +(-0.176616 - 0.396686i) q^{52} +(-4.80779 + 4.32895i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-3.04021 + 2.93126i) q^{55} +(-1.60783 - 2.78484i) q^{56} +(0.736185 + 0.425037i) q^{57} +(9.76350 - 3.17235i) q^{58} +(-2.79674 - 1.24519i) q^{59} +(1.43867 - 1.71179i) q^{60} +3.68567 q^{61} +(-4.62695 - 3.09699i) q^{62} -3.21565i q^{63} +(0.809017 + 0.587785i) q^{64} +(-0.456515 + 0.856947i) q^{65} +(-0.583627 - 1.79622i) q^{66} +(-6.92418 - 3.99768i) q^{67} +(6.32530 - 3.65191i) q^{68} +(-0.0359569 + 0.0399342i) q^{69} +(-2.69884 + 6.66472i) q^{70} +(-2.79470 - 3.10383i) q^{71} +(0.406737 + 0.913545i) q^{72} +(0.937540 - 4.41078i) q^{73} +(0.126068 - 1.19945i) q^{74} +(-4.99667 - 0.182388i) q^{75} +(0.831497 - 0.176740i) q^{76} +(3.56978 + 4.91338i) q^{77} +(-0.255232 - 0.351297i) q^{78} +(-0.505633 + 0.107476i) q^{79} +(-0.0762733 - 2.23477i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(1.80681 - 8.50036i) q^{82} +(-1.98050 - 4.44828i) q^{83} +(-2.15169 - 2.38970i) q^{84} +(-15.1378 - 6.12998i) q^{85} +(0.694666 - 0.771504i) q^{86} +(8.89057 - 5.13297i) q^{87} +(-1.63562 - 0.944328i) q^{88} +(-2.28647 - 7.03703i) q^{89} +(1.05133 - 1.97350i) q^{90} +(1.12965 + 0.820738i) q^{91} +0.0537367i q^{92} +(-5.16974 - 2.06731i) q^{93} +0.684978 q^{94} +(-1.45515 - 1.22297i) q^{95} +(0.913545 + 0.406737i) q^{96} +(-8.87702 + 2.88432i) q^{97} +(2.89290 + 1.67022i) q^{98} +(-0.944328 - 1.63562i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9}+O(q^{10}) $ 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9	$ 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9} - 18 q^{11} - 8 q^{14} - 36 q^{16} - 24 q^{19} - 2 q^{20} + 28 q^{21} - 18 q^{24} + 10 q^{25} - 12 q^{26} - 4 q^{30} - 4 q^{31} + 10 q^{34} - 2 q^{35} - 72 q^{36} + 16 q^{39} + 4 q^{41} - 2 q^{44} - 2 q^{45} - 2 q^{46} - 78 q^{49} + 32 q^{50} + 10 q^{51} + 36 q^{54} - 50 q^{55} - 12 q^{56} + 28 q^{59} + 88 q^{61} + 36 q^{64} - 124 q^{65} + 6 q^{66} - 46 q^{69} - 10 q^{70} + 140 q^{71} + 34 q^{74} - 32 q^{75} + 24 q^{76} + 16 q^{79} + 12 q^{80} + 18 q^{81} - 8 q^{84} + 74 q^{85} - 98 q^{86} + 148 q^{89} + 44 q^{91} - 108 q^{94} - 80 q^{95} + 18 q^{96} - 2 q^{99}+O(q^{100}) $ 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9 - 18 * q^11 - 8 * q^14 - 36 * q^16 - 24 * q^19 - 2 * q^20 + 28 * q^21 - 18 * q^24 + 10 * q^25 - 12 * q^26 - 4 * q^30 - 4 * q^31 + 10 * q^34 - 2 * q^35 - 72 * q^36 + 16 * q^39 + 4 * q^41 - 2 * q^44 - 2 * q^45 - 2 * q^46 - 78 * q^49 + 32 * q^50 + 10 * q^51 + 36 * q^54 - 50 * q^55 - 12 * q^56 + 28 * q^59 + 88 * q^61 + 36 * q^64 - 124 * q^65 + 6 * q^66 - 46 * q^69 - 10 * q^70 + 140 * q^71 + 34 * q^74 - 32 * q^75 + 24 * q^76 + 16 * q^79 + 12 * q^80 + 18 * q^81 - 8 * q^84 + 74 * q^85 - 98 * q^86 + 148 * q^89 + 44 * q^91 - 108 * q^94 - 80 * q^95 + 18 * q^96 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{15}\right)$

Coefficient data

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

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

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

$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$3$	0.406737	−	0.913545i	0.234830	−	0.527436i
$3$	0.406737	−	0.913545i	0.234830	−	0.527436i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	−1.25186	+	1.85280i	−0.559847	+	0.828596i
$5$	−1.25186	+	1.85280i	−0.559847	+	0.828596i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	2.38970	+	2.15169i	0.903221	+	0.813264i	0.983011	−	0.183548i	$-0.0587583\pi$
$7$	2.38970	+	2.15169i	0.903221	+	0.813264i	−0.0797900	+	0.996812i	$0.525425\pi$
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$	−0.669131	−	0.743145i	−0.223044	−	0.247715i
$10$	0.763121	+	2.10182i	0.241320	+	0.664654i
$11$	1.84738	+	0.392674i	0.557007	+	0.118396i	0.477810	−	0.878463i	$-0.341431\pi$
$11$	1.84738	+	0.392674i	0.557007	+	0.118396i	0.0791977	+	0.996859i	$0.474764\pi$
$12$	−0.994522	−	0.104528i	−0.287094	−	0.0301748i
$13$	0.431848	−	0.0453891i	0.119773	−	0.0125887i	−0.0444522	−	0.999012i	$-0.514154\pi$
$13$	0.431848	−	0.0453891i	0.119773	−	0.0125887i	0.164225	+	0.986423i	$0.447488\pi$
$14$	3.14539	−	0.668572i	0.840640	−	0.178683i
$15$	1.18344	+	1.89723i	0.305562	+	0.489862i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	1.51855	+	7.14422i	0.368303	+	1.73273i	0.638228	+	0.769847i	$0.279668\pi$
$17$	1.51855	+	7.14422i	0.368303	+	1.73273i	−0.269925	+	0.962881i	$0.586999\pi$
$18$	−0.994522	+	0.104528i	−0.234411	+	0.0246376i
$19$	−0.0888569	+	0.845417i	−0.0203852	+	0.193952i	−0.999975	−	0.00705440i	$-0.997754\pi$
$19$	−0.0888569	+	0.845417i	−0.0203852	+	0.193952i	0.979590	+	0.201006i	$0.0644212\pi$
$20$	2.14896	+	0.618041i	0.480522	+	0.138198i
$21$	2.93765	−	1.30792i	0.641047	−	0.285413i
$22$	1.40355	−	1.26376i	0.299237	−	0.269434i
$23$	−0.0511067	−	0.0166056i	−0.0106565	−	0.00346250i	0.303684	−	0.952773i	$-0.401783\pi$
$23$	−0.0511067	−	0.0166056i	−0.0106565	−	0.00346250i	−0.314340	+	0.949310i	$0.601783\pi$
$24$	−0.669131	+	0.743145i	−0.136586	+	0.151694i
$25$	−1.86571	−	4.63887i	−0.373142	−	0.927774i
$26$	0.217113	−	0.376051i	0.0425794	−	0.0737498i
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	1.30792	−	2.93765i	0.247175	−	0.555163i
$29$	8.30533	+	6.03417i	1.54226	+	1.12052i	0.948898	+	0.315583i	$0.102200\pi$
$29$	8.30533	+	6.03417i	1.54226	+	1.12052i	0.593363	+	0.804935i	$0.297800\pi$
$30$	2.23050	+	0.157741i	0.407231	+	0.0287995i
$31$	−0.214136	−	5.56364i	−0.0384600	−	0.999260i
$31$	−0.214136	−	5.56364i	−0.0384600	−	0.999260i
$32$			1.00000i			0.176777i
$33$	1.11012	−	1.52796i	0.193248	−	0.265983i
$34$	6.67238	+	2.97073i	1.14430	+	0.509477i
$35$	−6.97821	+	1.73401i	−1.17953	+	0.293101i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	1.04448	−	0.603030i	0.171711	−	0.0991374i	−0.411681	−	0.911328i	$-0.635058\pi$
$37$	1.04448	−	0.603030i	0.171711	−	0.0991374i	0.583392	+	0.812190i	$0.301725\pi$
$38$	0.631728	+	0.568810i	0.102480	+	0.0922732i
$39$	0.134183	−	0.412974i	0.0214866	−	0.0661288i
$40$	1.76313	−	1.37527i	0.278776	−	0.217449i
$41$	7.93895	−	3.53465i	1.23986	−	0.552020i	0.321175	−	0.947020i	$-0.395922\pi$
$41$	7.93895	−	3.53465i	1.23986	−	0.552020i	0.918681	+	0.395000i	$0.129255\pi$
$42$	0.668572	−	3.14539i	0.103163	−	0.485343i
$43$	1.03247	+	0.108517i	0.157451	+	0.0165488i	0.182926	−	0.983127i	$-0.441443\pi$
$43$	1.03247	+	0.108517i	0.157451	+	0.0165488i	−0.0254750	+	0.999675i	$0.508110\pi$
$44$	−0.197418	−	1.87831i	−0.0297619	−	0.283166i
$45$	2.21455	−	0.309452i	0.330126	−	0.0461304i
$46$	−0.0434739	+	0.0315857i	−0.00640988	+	0.00465705i
$47$	0.402620	+	0.554159i	0.0587282	+	0.0808324i	0.837371	−	0.546635i	$-0.184092\pi$
$47$	0.402620	+	0.554159i	0.0587282	+	0.0808324i	−0.778643	+	0.627468i	$0.784092\pi$
$48$	0.207912	+	0.978148i	0.0300095	+	0.141183i
$49$	0.349171	+	3.32214i	0.0498815	+	0.474591i
$50$	−4.84956	−	1.21727i	−0.685832	−	0.172148i
$51$	7.14422	+	1.51855i	1.00039	+	0.212640i
$52$	−0.176616	−	0.396686i	−0.0244922	−	0.0550104i
$53$	−4.80779	+	4.32895i	−0.660401	+	0.594627i	−0.929650	−	0.368443i	$-0.879891\pi$
$53$	−4.80779	+	4.32895i	−0.660401	+	0.594627i	0.269250	+	0.963070i	$0.413224\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$	−3.04021	+	2.93126i	−0.409941	+	0.395251i
$56$	−1.60783	−	2.78484i	−0.214855	−	0.372140i
$57$	0.736185	+	0.425037i	0.0975101	+	0.0562975i
$58$	9.76350	−	3.17235i	1.28201	−	0.416550i
$59$	−2.79674	−	1.24519i	−0.364104	−	0.162110i	0.216526	−	0.976277i	$-0.430527\pi$
$59$	−2.79674	−	1.24519i	−0.364104	−	0.162110i	−0.580631	+	0.814167i	$0.697194\pi$
$60$	1.43867	−	1.71179i	0.185731	−	0.220991i
$61$	3.68567			0.471902			0.235951	−	0.971765i	$-0.424180\pi$
$61$	3.68567			0.471902			0.235951	+	0.971765i	$0.424180\pi$
$62$	−4.62695	−	3.09699i	−0.587623	−	0.393318i
$63$		−	3.21565i		−	0.405134i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	−0.456515	+	0.856947i	−0.0566237	+	0.106291i
$66$	−0.583627	−	1.79622i	−0.0718395	−	0.221099i
$67$	−6.92418	−	3.99768i	−0.845924	−	0.488394i	0.0133496	−	0.999911i	$-0.495751\pi$
$67$	−6.92418	−	3.99768i	−0.845924	−	0.488394i	−0.859273	+	0.511517i	$0.829084\pi$
$68$	6.32530	−	3.65191i	0.767055	−	0.442860i
$69$	−0.0359569	+	0.0399342i	−0.00432870	+	0.00480751i
$70$	−2.69884	+	6.66472i	−0.322573	+	0.796586i
$71$	−2.79470	−	3.10383i	−0.331670	−	0.368357i	0.554125	−	0.832433i	$-0.313053\pi$
$71$	−2.79470	−	3.10383i	−0.331670	−	0.368357i	−0.885795	+	0.464077i	$0.846386\pi$
$72$	0.406737	+	0.913545i	0.0479344	+	0.107662i
$73$	0.937540	−	4.41078i	0.109731	−	0.516243i	−0.888610	−	0.458663i	$-0.848328\pi$
$73$	0.937540	−	4.41078i	0.109731	−	0.516243i	0.998341	−	0.0575794i	$-0.0183382\pi$
$74$	0.126068	−	1.19945i	0.0146550	−	0.139433i
$75$	−4.99667	−	0.182388i	−0.576966	−	0.0210603i
$76$	0.831497	−	0.176740i	0.0953793	−	0.0202735i
$77$	3.56978	+	4.91338i	0.406814	+	0.559931i
$78$	−0.255232	−	0.351297i	−0.0288993	−	0.0397765i
$79$	−0.505633	+	0.107476i	−0.0568882	+	0.0120920i	−0.236268	−	0.971688i	$-0.575924\pi$
$79$	−0.505633	+	0.107476i	−0.0568882	+	0.0120920i	0.179380	+	0.983780i	$0.442591\pi$
$80$	−0.0762733	−	2.23477i	−0.00852761	−	0.249855i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	1.80681	−	8.50036i	0.199529	−	0.938708i
$83$	−1.98050	−	4.44828i	−0.217388	−	0.488263i	0.771627	−	0.636075i	$-0.219443\pi$
$83$	−1.98050	−	4.44828i	−0.217388	−	0.488263i	−0.989015	+	0.147813i	$0.952777\pi$
$84$	−2.15169	−	2.38970i	−0.234769	−	0.260737i
$85$	−15.1378	−	6.12998i	−1.64192	−	0.664889i
$86$	0.694666	−	0.771504i	0.0749077	−	0.0831934i
$87$	8.89057	−	5.13297i	0.953169	−	0.550313i
$88$	−1.63562	−	0.944328i	−0.174358	−	0.100666i
$89$	−2.28647	−	7.03703i	−0.242365	−	0.745923i	−0.996059	−	0.0886971i	$-0.971730\pi$
$89$	−2.28647	−	7.03703i	−0.242365	−	0.745923i	0.753694	−	0.657226i	$-0.228270\pi$
$90$	1.05133	−	1.97350i	0.110820	−	0.208025i
$91$	1.12965	+	0.820738i	0.118419	+	0.0860368i
$92$			0.0537367i			0.00560244i
$93$	−5.16974	−	2.06731i	−0.536077	−	0.214371i
$94$	0.684978			0.0706501
$95$	−1.45515	−	1.22297i	−0.149295	−	0.125474i
$96$	0.913545	+	0.406737i	0.0932383	+	0.0415124i
$97$	−8.87702	+	2.88432i	−0.901325	+	0.292858i	−0.722784	−	0.691074i	$-0.757138\pi$
$97$	−8.87702	+	2.88432i	−0.901325	+	0.292858i	−0.178541	+	0.983932i	$0.557138\pi$
$98$	2.89290	+	1.67022i	0.292227	+	0.168718i
$99$	−0.944328	−	1.63562i	−0.0949086	−	0.164386i
$100$	−3.83529	+	3.20789i	−0.383529	+	0.320789i
$101$	1.70311	−	5.24164i	0.169466	−	0.521562i	−0.829872	−	0.557954i	$-0.811586\pi$
$101$	1.70311	−	5.24164i	0.169466	−	0.521562i	0.999338	+	0.0363919i	$0.0115865\pi$
$102$	5.42780	−	4.88722i	0.537433	−	0.483906i
$103$	3.55032	+	7.97415i	0.349823	+	0.785716i	0.999671	+	0.0256516i	$0.00816606\pi$
$103$	3.55032	+	7.97415i	0.349823	+	0.785716i	−0.649848	+	0.760065i	$0.725167\pi$
$104$	−0.424738	−	0.0902808i	−0.0416490	−	0.00885276i
$105$	−1.25419	+	7.08020i	−0.122397	+	0.690956i
$106$	0.676249	+	6.43408i	0.0656831	+	0.624933i
$107$	1.65713	+	7.79620i	0.160201	+	0.753687i	0.982742	+	0.184981i	$0.0592225\pi$
$107$	1.65713	+	7.79620i	0.160201	+	0.753687i	−0.822541	+	0.568706i	$0.807444\pi$
$108$	0.587785	+	0.809017i	0.0565597	+	0.0778477i
$109$	−1.98877	+	1.44492i	−0.190489	+	0.138399i	−0.678942	−	0.734192i	$-0.737561\pi$
$109$	−1.98877	+	1.44492i	−0.190489	+	0.138399i	0.488453	+	0.872590i	$0.337561\pi$
$110$	0.584449	+	4.18253i	0.0557250	+	0.398788i
$111$	−0.126068	−	1.19945i	−0.0119658	−	0.113847i
$112$	−3.19804	−	0.336127i	−0.302186	−	0.0317611i
$113$	−3.35978	+	15.8065i	−0.316062	+	1.48695i	0.477591	+	0.878582i	$0.341510\pi$
$113$	−3.35978	+	15.8065i	−0.316062	+	1.48695i	−0.793653	+	0.608371i	$0.791823\pi$
$114$	0.776581	−	0.345756i	0.0727334	−	0.0323830i
$115$	0.0947450	−	0.0739025i	0.00883501	−	0.00689144i
$116$	3.17235	−	9.76350i	0.294546	−	0.906518i
$117$	−0.322693	−	0.290554i	−0.0298330	−	0.0268618i
$118$	−2.65126	+	1.53070i	−0.244068	+	0.140913i
$119$	−11.7433	+	20.3400i	−1.07651	+	1.86456i
$120$	−0.539241	−	2.17007i	−0.0492257	−	0.198100i
$121$	−6.79036	−	3.02326i	−0.617306	−	0.274842i
$122$	2.16638	−	2.98177i	0.196135	−	0.269957i
$123$		−	8.69027i		−	0.783575i
$124$	−5.22517	+	1.92292i	−0.469234	+	0.172683i
$125$	10.9305	+	2.35042i	0.977652	+	0.210228i
$126$	−2.60152	−	1.89011i	−0.231762	−	0.168385i
$127$	−0.984596	+	2.21144i	−0.0873688	+	0.196234i	−0.951946	−	0.306267i	$-0.900920\pi$
$127$	−0.984596	+	2.21144i	−0.0873688	+	0.196234i	0.864577	+	0.502501i	$0.167587\pi$
$128$	0.951057	−	0.309017i	0.0840623	−	0.0273135i
$129$	0.519081	−	0.899074i	0.0457025	−	0.0791591i
$130$	0.424952	+	0.873029i	0.0372708	+	0.0765697i
$131$	2.10739	−	2.34049i	0.184123	−	0.204490i	−0.644016	−	0.765012i	$-0.722733\pi$
$131$	2.10739	−	2.34049i	0.184123	−	0.204490i	0.828139	+	0.560522i	$0.189400\pi$
$132$	−1.79622	−	0.583627i	−0.156341	−	0.0507982i
$133$	−2.03142	+	1.82910i	−0.176146	+	0.158603i
$134$	−7.30412	+	3.25201i	−0.630980	+	0.280931i
$135$	0.618041	−	2.14896i	0.0531925	−	0.184953i
$136$	0.763458	−	7.26382i	0.0654660	−	0.622867i
$137$	−19.2760	+	2.02599i	−1.64686	+	0.173092i	−0.882047	−	0.471162i	$-0.843835\pi$
$137$	−19.2760	+	2.02599i	−1.64686	+	0.173092i	−0.764812	+	0.644254i	$0.777168\pi$
$138$	0.0111725	+	0.0525625i	0.000951066	+	0.00447441i
$139$	10.5698	−	7.67939i	0.896516	−	0.651357i	−0.0410525	−	0.999157i	$-0.513071\pi$
$139$	10.5698	−	7.67939i	0.896516	−	0.651357i	0.937569	+	0.347800i	$0.113071\pi$
$140$	3.80553	+	6.10083i	0.321626	+	0.515614i
$141$	0.670010	−	0.142415i	0.0564250	−	0.0119935i
$142$	−4.15373	+	0.436575i	−0.348573	+	0.0366365i
$143$	0.815613	+	0.0857243i	0.0682049	+	0.00716863i
$144$	0.978148	+	0.207912i	0.0815123	+	0.0173260i
$145$	−21.5772	+	7.83416i	−1.79189	+	0.650592i
$146$	−3.01732	−	3.35108i	−0.249715	−	0.277337i
$147$	3.17694	+	1.03225i	0.262030	+	0.0851387i
$148$	−0.896277	−	0.807011i	−0.0736735	−	0.0663359i
$149$	8.46335	+	14.6589i	0.693344	+	1.20091i	0.970736	+	0.240151i	$0.0771969\pi$
$149$	8.46335	+	14.6589i	0.693344	+	1.20091i	−0.277391	+	0.960757i	$0.589470\pi$
$150$	−3.08453	+	3.93519i	−0.251850	+	0.321307i
$151$	−5.07714	−	15.6258i	−0.413172	−	1.27161i	−0.913876	−	0.405994i	$-0.866925\pi$
$151$	−5.07714	−	15.6258i	−0.413172	−	1.27161i	0.500704	−	0.865619i	$-0.333075\pi$
$152$	0.345756	−	0.776581i	0.0280445	−	0.0629890i
$153$	4.29308	−	5.90892i	0.347075	−	0.477708i
$154$	6.07327			0.489398
$155$	10.5764	+	6.56813i	0.849515	+	0.527565i
$156$	−0.434227			−0.0347660
$157$	3.15286	−	4.33954i	0.251626	−	0.346333i	−0.664454	−	0.747329i	$-0.731336\pi$
$157$	3.15286	−	4.33954i	0.251626	−	0.346333i	0.916080	+	0.400996i	$0.131336\pi$
$158$	−0.210254	+	0.472239i	−0.0167269	+	0.0375693i
$159$	1.99919	+	6.15288i	0.158546	+	0.487955i
$160$	−1.85280	−	1.25186i	−0.146476	−	0.0989680i
$161$	−0.0863994	−	0.149648i	−0.00680923	−	0.0117939i
$162$	0.743145	+	0.669131i	0.0583870	+	0.0525719i
$163$	21.8738	+	7.10723i	1.71329	+	0.556681i	0.990875	−	0.134782i	$-0.0430334\pi$
$163$	21.8738	+	7.10723i	1.71329	+	0.556681i	0.722412	+	0.691463i	$0.243033\pi$
$164$	−5.81492	−	6.45813i	−0.454069	−	0.504295i
$165$	1.44127	+	3.96962i	0.112203	+	0.309034i
$166$	−4.76285	−	1.01237i	−0.369669	−	0.0785755i
$167$	12.5177	+	1.31566i	0.968649	+	0.101809i	0.575620	−	0.817717i	$-0.304761\pi$
$167$	12.5177	+	1.31566i	0.968649	+	0.101809i	0.393029	+	0.919526i	$0.371427\pi$
$168$	−3.19804	+	0.336127i	−0.246734	+	0.0259328i
$169$	−12.5315	+	2.66365i	−0.963960	+	0.204896i
$170$	−13.8570	+	8.64363i	−1.06279	+	0.662936i
$171$	0.687724	−	0.499661i	0.0525916	−	0.0382100i
$172$	−0.215846	−	1.01548i	−0.0164581	−	0.0774293i
$173$	1.93017	−	0.202869i	0.146748	−	0.0154238i	−0.0308696	−	0.999523i	$-0.509828\pi$
$173$	1.93017	−	0.202869i	0.146748	−	0.0154238i	0.177618	+	0.984100i	$0.443161\pi$
$174$	1.07308	−	10.2097i	0.0813503	−	0.773996i
$175$	5.52294	−	15.0999i	0.417495	−	1.14145i
$176$	−1.72537	+	0.768186i	−0.130055	+	0.0579042i
$177$	−2.27507	+	2.04848i	−0.171005	+	0.153973i
$178$	−7.03703	−	2.28647i	−0.527447	−	0.171378i
$179$	−11.0156	+	12.2340i	−0.823342	+	0.914414i	−0.997526	−	0.0702992i	$-0.977605\pi$
$179$	−11.0156	+	12.2340i	−0.823342	+	0.914414i	0.174184	+	0.984713i	$0.444271\pi$
$180$	−0.978641	−	2.01054i	−0.0729436	−	0.149857i
$181$	−5.63298	+	9.75661i	−0.418696	+	0.725203i	−0.995809	−	0.0914618i	$-0.970846\pi$
$181$	−5.63298	+	9.75661i	−0.418696	+	0.725203i	0.577113	+	0.816665i	$0.304179\pi$
$182$	1.32798	−	0.431488i	0.0984366	−	0.0319840i
$183$	1.49910	−	3.36703i	0.110816	−	0.248898i
$184$	0.0434739	+	0.0315857i	0.00320494	+	0.00232853i
$185$	−0.190245	+	2.69011i	−0.0139871	+	0.197781i
$186$	−4.71119	+	2.96727i	−0.345441	+	0.217571i
$187$			13.7944i			1.00875i
$188$	0.402620	−	0.554159i	0.0293641	−	0.0404162i
$189$	−2.93765	−	1.30792i	−0.213682	−	0.0951375i
$190$	−1.84472	+	0.458394i	−0.133830	+	0.0332554i
$191$	6.52281	−	11.2978i	0.471974	−	0.817483i	−0.527512	−	0.849548i	$-0.676875\pi$
$191$	6.52281	−	11.2978i	0.471974	−	0.817483i	0.999486	+	0.0320650i	$0.0102084\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	1.42234	+	1.28068i	0.102382	+	0.0921853i	0.718732	−	0.695287i	$-0.244723\pi$
$193$	1.42234	+	1.28068i	0.102382	+	0.0921853i	−0.616350	+	0.787472i	$0.711389\pi$
$194$	−2.88432	+	8.87702i	−0.207082	+	0.637333i
$195$	0.597179	+	0.765599i	0.0427649	+	0.0548257i
$196$	3.05164	−	1.35868i	0.217974	−	0.0970484i
$197$	2.13324	−	10.0361i	0.151987	−	0.715044i	−0.834474	−	0.551048i	$-0.814228\pi$
$197$	2.13324	−	10.0361i	0.151987	−	0.715044i	0.986461	−	0.163996i	$-0.0524385\pi$
$198$	−1.87831	−	0.197418i	−0.133486	−	0.0140299i
$199$	−1.35837	−	12.9240i	−0.0962923	−	0.916160i	−0.930890	−	0.365300i	$-0.880967\pi$
$199$	−1.35837	−	12.9240i	−0.0962923	−	0.916160i	0.834598	−	0.550860i	$-0.185700\pi$
$200$	0.340906	+	4.98836i	0.0241057	+	0.352731i
$201$	−6.46838	+	4.69955i	−0.456244	+	0.331481i
$202$	−3.23951	−	4.45880i	−0.227931	−	0.313720i
$203$	6.86353	+	32.2904i	0.481725	+	2.26634i
$204$	−0.763458	−	7.26382i	−0.0534528	−	0.508569i
$205$	−3.38944	+	19.1341i	−0.236729	+	1.33639i
$206$	8.53805	+	1.81482i	0.594874	+	0.126444i
$207$	0.0218567	+	0.0490910i	0.00151915	+	0.00341206i
$208$	−0.322693	+	0.290554i	−0.0223748	+	0.0201463i
$209$	−0.496126	+	1.52692i	−0.0343177	+	0.105619i
$210$	4.99080	+	5.17630i	0.344398	+	0.357199i
$211$	−10.2646	−	17.7787i	−0.706641	−	1.22394i	−0.966096	−	0.258183i	$-0.916876\pi$
$211$	−10.2646	−	17.7787i	−0.706641	−	1.22394i	0.259455	−	0.965755i	$-0.416457\pi$
$212$	5.60277	+	3.23476i	0.384800	+	0.222164i
$213$	−3.97219	+	1.29064i	−0.272170	+	0.0884335i
$214$	7.28130	+	3.24184i	0.497739	+	0.221608i
$215$	−1.49357	+	1.77712i	−0.101861	+	0.121198i
$216$	1.00000			0.0680414
$217$	11.4595	−	13.7562i	0.777924	−	0.933831i
$218$			2.45825i			0.166494i
$219$	−3.64811	−	2.65051i	−0.246517	−	0.179105i
$220$	3.72727	+	1.98560i	0.251292	+	0.133869i
$221$	0.980053	+	3.01629i	0.0659255	+	0.202898i
$222$	−1.04448	−	0.603030i	−0.0701008	−	0.0404727i
$223$	10.9847	−	6.34204i	0.735592	−	0.424694i	−0.0848722	−	0.996392i	$-0.527048\pi$
$223$	10.9847	−	6.34204i	0.735592	−	0.424694i	0.820465	+	0.571697i	$0.193715\pi$
$224$	−2.15169	+	2.38970i	−0.143766	+	0.159668i
$225$	−2.19895	+	4.49050i	−0.146597	+	0.299367i
$226$	10.8129	+	12.0090i	0.719265	+	0.798825i
$227$	7.49701	+	16.8386i	0.497594	+	1.11761i	0.971500	+	0.237039i	$0.0761769\pi$
$227$	7.49701	+	16.8386i	0.497594	+	1.11761i	−0.473906	+	0.880575i	$0.657156\pi$
$228$	0.176740	−	0.831497i	0.0117049	−	0.0550672i
$229$	1.87826	−	17.8705i	0.124119	−	1.18091i	−0.738212	−	0.674569i	$-0.764329\pi$
$229$	1.87826	−	17.8705i	0.124119	−	1.18091i	0.862331	−	0.506345i	$-0.169004\pi$
$230$	−0.00409868	−	0.120089i	−0.000270259	−	0.00791844i
$231$	5.94055	−	1.26270i	0.390860	−	0.0830798i
$232$	−6.03417	−	8.30533i	−0.396163	−	0.545271i
$233$	−2.84963	−	3.92218i	−0.186685	−	0.256950i	0.705408	−	0.708802i	$-0.250764\pi$
$233$	−2.84963	−	3.92218i	−0.186685	−	0.256950i	−0.892093	+	0.451851i	$0.850764\pi$
$234$	−0.424738	+	0.0902808i	−0.0277660	+	0.00590184i
$235$	−1.53077	+	0.0522455i	−0.0998562	+	0.00340812i
$236$	−0.320004	+	3.04464i	−0.0208305	+	0.198189i
$237$	−0.107476	+	0.505633i	−0.00698130	+	0.0328444i
$238$	9.55286	+	21.4561i	0.619220	+	1.39079i
$239$	−9.52459	−	10.5781i	−0.616095	−	0.684242i	0.351663	−	0.936127i	$-0.385616\pi$
$239$	−9.52459	−	10.5781i	−0.616095	−	0.684242i	−0.967757	+	0.251884i	$0.918950\pi$
$240$	−2.07258	−	0.839282i	−0.133785	−	0.0541754i
$241$	12.3692	−	13.7374i	0.796771	−	0.884903i	−0.198692	−	0.980062i	$-0.563669\pi$
$241$	12.3692	−	13.7374i	0.796771	−	0.884903i	0.995462	+	0.0951587i	$0.0303358\pi$
$242$	−6.43715	+	3.71649i	−0.413795	+	0.238905i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−1.13894	−	3.50528i	−0.0729129	−	0.224403i
$245$	−6.59236	−	3.51190i	−0.421170	−	0.224367i
$246$	−7.03057	−	5.10801i	−0.448253	−	0.325675i
$247$			0.369125i			0.0234868i
$248$	−1.51561	+	5.35751i	−0.0962410	+	0.340202i
$249$	−4.86925			−0.308576
$250$	8.32631	−	7.46141i	0.526602	−	0.471901i
$251$	−18.7112	−	8.33076i	−1.18104	−	0.525833i	−0.280182	−	0.959947i	$-0.590395\pi$
$251$	−18.7112	−	8.33076i	−1.18104	−	0.525833i	−0.900858	+	0.434114i	$0.857062\pi$
$252$	−3.05827	+	0.993692i	−0.192653	+	0.0625967i
$253$	−0.0878931	−	0.0507451i	−0.00552579	−	0.00319032i
$254$	1.21036	+	2.09641i	0.0759448	+	0.131540i
$255$	−11.7571	+	11.3358i	−0.736259	+	0.709874i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−9.25790	+	8.33585i	−0.577492	+	0.519976i	−0.905303	−	0.424767i	$-0.860356\pi$
$257$	−9.25790	+	8.33585i	−0.577492	+	0.519976i	0.327810	+	0.944744i	$0.393689\pi$
$258$	−0.422258	−	0.948408i	−0.0262887	−	0.0590453i
$259$	3.79352	+	0.806338i	0.235718	+	0.0501034i
$260$	0.956076	+	0.169360i	0.0592933	+	0.0105033i
$261$	−1.07308	−	10.2097i	−0.0664222	−	0.631965i
$262$	−0.654806	−	3.08062i	−0.0404541	−	0.190321i
$263$	−15.7895	−	21.7324i	−0.973625	−	1.34008i	−0.940194	−	0.340639i	$-0.889357\pi$
$263$	−15.7895	−	21.7324i	−0.973625	−	1.34008i	−0.0334310	−	0.999441i	$-0.510643\pi$
$264$	−1.52796	+	1.11012i	−0.0940391	+	0.0683234i
$265$	−2.00201	−	14.3271i	−0.122982	−	0.880106i
$266$	0.285733	+	2.71857i	0.0175194	+	0.166686i
$267$	−7.35863	−	0.773423i	−0.450341	−	0.0473327i
$268$	−1.66233	+	7.82064i	−0.101543	+	0.477722i
$269$	−15.2307	+	6.78116i	−0.928634	+	0.413454i	−0.814600	−	0.580023i	$-0.803044\pi$
$269$	−15.2307	+	6.78116i	−0.928634	+	0.413454i	−0.114033	+	0.993477i	$0.536377\pi$
$270$	−1.37527	−	1.76313i	−0.0836962	−	0.107301i
$271$	4.67235	−	14.3800i	0.283825	−	0.873524i	−0.702923	−	0.711266i	$-0.748122\pi$
$271$	4.67235	−	14.3800i	0.283825	−	0.873524i	0.986748	−	0.162258i	$-0.0518778\pi$
$272$	−5.42780	−	4.88722i	−0.329109	−	0.296331i
$273$	1.20925	−	0.698162i	0.0731872	−	0.0422547i
$274$	−9.69108	+	16.7854i	−0.585459	+	1.01405i
$275$	−1.62512	−	9.30239i	−0.0979985	−	0.560956i
$276$	0.0490910	+	0.0218567i	0.00295493	+	0.00131562i
$277$	−4.21274	+	5.79833i	−0.253119	+	0.348388i	−0.916600	−	0.399804i	$-0.869078\pi$
$277$	−4.21274	+	5.79833i	−0.253119	+	0.348388i	0.663482	+	0.748192i	$0.269078\pi$
$278$		−	13.0650i		−	0.783584i
$279$	−3.99131	+	3.88194i	−0.238953	+	0.232406i
$280$	7.17251	+	0.507242i	0.428639	+	0.0303135i
$281$	−19.1683	−	13.9266i	−1.14348	−	0.830789i	−0.155883	−	0.987776i	$-0.549822\pi$
$281$	−19.1683	−	13.9266i	−1.14348	−	0.830789i	−0.987601	+	0.156986i	$0.949822\pi$
$282$	0.278606	−	0.625759i	0.0165907	−	0.0372634i
$283$	18.6182	−	6.04941i	1.10674	−	0.359600i	0.302044	−	0.953294i	$-0.402331\pi$
$283$	18.6182	−	6.04941i	1.10674	−	0.359600i	0.804691	+	0.593694i	$0.202331\pi$
$284$	−2.08831	+	3.61705i	−0.123918	+	0.214633i
$285$	−1.70910	+	0.831916i	−0.101239	+	0.0492785i
$286$	0.548757	−	0.609457i	0.0324487	−	0.0360379i
$287$	26.5772	+	8.63545i	1.56880	+	0.509734i
$288$	0.743145	−	0.669131i	0.0437902	−	0.0394289i
$289$	−33.2036	+	14.7832i	−1.95316	+	0.869601i
$290$	−6.34477	+	22.0611i	−0.372578	+	1.29547i
$291$	−0.975653	+	9.28272i	−0.0571938	+	0.544163i
$292$	−4.48462	+	0.471352i	−0.262442	+	0.0275838i
$293$	−5.59675	−	26.3306i	−0.326966	−	1.53825i	−0.767815	−	0.640671i	$-0.778656\pi$
$293$	−5.59675	−	26.3306i	−0.326966	−	1.53825i	0.440850	−	0.897581i	$-0.354677\pi$
$294$	2.70247	−	1.96346i	0.157611	−	0.114511i
$295$	5.80819	−	3.62299i	0.338166	−	0.210938i
$296$	−1.17970	+	0.250754i	−0.0685689	+	0.0145748i
$297$	−1.87831	+	0.197418i	−0.108991	+	0.0114554i
$298$	16.8340	+	1.76932i	0.975166	+	0.102494i
$299$	−0.0228240	−	0.00485140i	−0.00131995	−	0.000280564i
$300$	1.37060	+	4.80848i	0.0791314	+	0.277618i
$301$	2.23380	+	2.48089i	0.128754	+	0.142996i
$302$	−15.6258	−	5.07714i	−0.899166	−	0.292157i
$303$	−4.09576	−	3.68783i	−0.235295	−	0.211861i
$304$	−0.425037	−	0.736185i	−0.0243775	−	0.0422231i
$305$	−4.61393	+	6.82880i	−0.264193	+	0.391016i
$306$	−2.25701	−	6.94635i	−0.129025	−	0.397097i
$307$	−11.4745	+	25.7722i	−0.654885	+	1.47090i	0.214481	+	0.976728i	$0.431194\pi$
$307$	−11.4745	+	25.7722i	−0.654885	+	1.47090i	−0.869366	+	0.494168i	$0.835473\pi$
$308$	3.56978	−	4.91338i	0.203407	−	0.279966i
$309$	8.72879			0.496564
$310$	11.5304	−	4.69581i	0.654881	−	0.266704i
$311$	28.0548			1.59084			0.795421	−	0.606057i	$-0.207250\pi$
$311$	28.0548			1.59084			0.795421	+	0.606057i	$0.207250\pi$
$312$	−0.255232	+	0.351297i	−0.0144497	+	0.0198883i
$313$	−8.23226	+	18.4900i	−0.465315	+	1.04511i	0.516675	+	0.856182i	$0.327170\pi$
$313$	−8.23226	+	18.4900i	−0.465315	+	1.04511i	−0.981990	+	0.188933i	$0.939497\pi$
$314$	−1.65756	−	5.10144i	−0.0935414	−	0.287891i
$315$	5.95795	+	4.02554i	0.335693	+	0.226813i
$316$	0.258465	+	0.447674i	0.0145398	+	0.0251836i
$317$	−18.4441	−	16.6072i	−1.03593	−	0.932751i	−0.0381400	−	0.999272i	$-0.512143\pi$
$317$	−18.4441	−	16.6072i	−1.03593	−	0.932751i	−0.997785	+	0.0665213i	$0.978810\pi$
$318$	6.15288	+	1.99919i	0.345036	+	0.112109i
$319$	12.9737	+	14.4087i	0.726386	+	0.806734i
$320$	−2.10182	+	0.763121i	−0.117495	+	0.0426598i
$321$	7.79620	+	1.65713i	0.435142	+	0.0924922i
$322$	−0.171852	−	0.0180624i	−0.00957695	−	0.00100658i
$323$	−6.17478	+	0.648995i	−0.343574	+	0.0361111i
$324$	0.978148	−	0.207912i	0.0543415	−	0.0115506i
$325$	−1.01626	−	1.91860i	−0.0563718	−	0.106425i
$326$	18.6070	−	13.5187i	1.03054	−	0.748734i
$327$	0.511099	+	2.40453i	0.0282638	+	0.132971i
$328$	−8.64266	+	0.908380i	−0.477211	+	0.0501569i
$329$	−0.230240	+	2.19059i	−0.0126935	+	0.120771i
$330$	4.05865	+	1.16727i	0.223421	+	0.0642559i
$331$	−1.28521	+	0.572212i	−0.0706415	+	0.0314516i	−0.441753	−	0.897137i	$-0.645643\pi$
$331$	−1.28521	+	0.572212i	−0.0706415	+	0.0314516i	0.371112	+	0.928588i	$0.378977\pi$
$332$	−3.61856	+	3.25817i	−0.198594	+	0.178815i
$333$	−1.14703	−	0.372693i	−0.0628569	−	0.0204234i
$334$	8.42212	−	9.35371i	0.460838	−	0.511812i
$335$	16.0750	−	7.82458i	0.878270	−	0.427503i
$336$	−1.60783	+	2.78484i	−0.0877142	+	0.151925i
$337$	7.55945	−	2.45621i	0.411790	−	0.133799i	−0.0957938	−	0.995401i	$-0.530539\pi$
$337$	7.55945	−	2.45621i	0.411790	−	0.133799i	0.507583	+	0.861603i	$0.330539\pi$
$338$	−5.21088	+	11.7038i	−0.283435	+	0.636605i
$339$	13.0734	+	9.49841i	0.710052	+	0.515883i
$340$	−1.15212	+	16.2912i	−0.0624822	+	0.883513i
$341$	1.78910	−	10.3623i	0.0968855	−	0.561149i
$342$		−	0.850073i		−	0.0459667i
$343$	6.91699	−	9.52043i	0.373483	−	0.514055i
$344$	−0.948408	−	0.422258i	−0.0511347	−	0.0227666i
$345$	−0.0289770	−	0.116613i	−0.00156007	−	0.00627822i
$346$	0.970400	−	1.68078i	0.0521691	−	0.0903595i
$347$	14.6526	−	8.45971i	0.786595	−	0.454141i	−0.0521675	−	0.998638i	$-0.516613\pi$
$347$	14.6526	−	8.45971i	0.786595	−	0.454141i	0.838762	+	0.544498i	$0.183280\pi$
$348$	−7.62909	−	6.86926i	−0.408962	−	0.368231i
$349$	4.90493	−	15.0958i	0.262555	−	0.808060i	−0.729692	−	0.683776i	$-0.760337\pi$
$349$	4.90493	−	15.0958i	0.262555	−	0.808060i	0.992247	−	0.124284i	$-0.0396635\pi$
$350$	−8.96980	−	13.3437i	−0.479456	−	0.713249i
$351$	−0.396686	+	0.176616i	−0.0211735	+	0.00942706i
$352$	−0.392674	+	1.84738i	−0.0209296	+	0.0984659i
$353$	−35.7800	−	3.76062i	−1.90437	−	0.200158i	−0.922015	−	0.387155i	$-0.873458\pi$
$353$	−35.7800	−	3.76062i	−1.90437	−	0.200158i	−0.982360	+	0.186997i	$0.940124\pi$
$354$	0.320004	+	3.04464i	0.0170080	+	0.161821i
$355$	9.24932	−	1.29246i	0.490903	−	0.0685967i
$356$	−5.98605	+	4.34912i	−0.317260	+	0.230503i
$357$	13.8051	+	19.0011i	0.730642	+	1.00564i
$358$	3.42275	+	16.1028i	0.180898	+	0.851057i
$359$	3.44861	+	32.8113i	0.182011	+	1.73172i	0.580254	+	0.814436i	$0.302953\pi$
$359$	3.44861	+	32.8113i	0.182011	+	1.73172i	−0.398243	+	0.917280i	$0.630380\pi$
$360$	−2.20179	−	0.390028i	−0.116045	−	0.0205563i
$361$	17.8780	+	3.80008i	0.940946	+	0.200004i
$362$	4.58228	+	10.2920i	0.240839	+	0.540934i
$363$	−5.52378	+	4.97363i	−0.289923	+	0.261048i
$364$	0.431488	−	1.32798i	0.0226161	−	0.0696052i
$365$	6.99861	+	7.25873i	0.366324	+	0.379939i
$366$	−1.84284	−	3.19189i	−0.0963266	−	0.166843i
$367$	−23.8260	−	13.7560i	−1.24371	−	0.718055i	−0.273861	−	0.961769i	$-0.588301\pi$
$367$	−23.8260	−	13.7560i	−1.24371	−	0.718055i	−0.969847	+	0.243714i	$0.921634\pi$
$368$	0.0511067	−	0.0166056i	0.00266412	−	0.000865625i
$369$	−7.93895	−	3.53465i	−0.413285	−	0.184007i
$370$	2.06452	+	1.73512i	0.107329	+	0.0902046i
$371$	−20.8037			−1.08008
$372$	−0.368596	+	5.55555i	−0.0191108	+	0.288042i
$373$		−	28.4031i		−	1.47066i	−0.677710	−	0.735329i	$-0.737027\pi$
$373$		−	28.4031i		−	1.47066i	0.677710	−	0.735329i	$-0.262973\pi$
$374$	11.1599	+	8.10816i	0.577066	+	0.419263i
$375$	6.59304	−	9.02949i	0.340463	−	0.466281i
$376$	−0.211670	−	0.651453i	−0.0109160	−	0.0335961i
$377$	3.86053	+	2.22888i	0.198827	+	0.114793i
$378$	−2.78484	+	1.60783i	−0.143237	+	0.0826977i
$379$	−12.5091	+	13.8927i	−0.642548	+	0.713622i	−0.973156	−	0.230146i	$-0.926079\pi$
$379$	−12.5091	+	13.8927i	−0.642548	+	0.713622i	0.330608	+	0.943768i	$0.392746\pi$
$380$	−0.713452	+	1.76185i	−0.0365993	+	0.0903809i
$381$	1.61978	+	1.79895i	0.0829838	+	0.0921628i
$382$	−5.30613	−	11.9178i	−0.271485	−	0.609766i
$383$	7.73126	−	36.3727i	0.395049	−	1.85856i	−0.107782	−	0.994175i	$-0.534375\pi$
$383$	7.73126	−	36.3727i	0.395049	−	1.85856i	0.502831	−	0.864385i	$-0.332292\pi$
$384$	0.104528	−	0.994522i	0.00533420	−	0.0507515i
$385$	−13.5723	+	0.463228i	−0.691710	+	0.0236083i
$386$	1.87212	−	0.397931i	0.0952884	−	0.0202542i
$387$	−0.610216	−	0.839890i	−0.0310190	−	0.0426940i
$388$	5.48630	+	7.55124i	0.278525	+	0.383356i
$389$	19.6275	−	4.17196i	0.995155	−	0.211527i	0.318577	−	0.947897i	$-0.396795\pi$
$389$	19.6275	−	4.17196i	0.995155	−	0.211527i	0.676579	+	0.736370i	$0.263462\pi$
$390$	0.970396	−	0.0331199i	0.0491379	−	0.00167709i
$391$	0.0410257	−	0.390334i	0.00207476	−	0.0197400i
$392$	0.694516	−	3.26744i	0.0350783	−	0.165031i
$393$	−1.28099	−	2.87716i	−0.0646176	−	0.145134i
$394$	−6.86551	−	7.62492i	−0.345879	−	0.384138i
$395$	0.433850	−	1.07138i	0.0218294	−	0.0539070i
$396$	−1.26376	+	1.40355i	−0.0635062	+	0.0705308i
$397$	5.06592	−	2.92481i	0.254251	−	0.146792i	−0.367458	−	0.930040i	$-0.619772\pi$
$397$	5.06592	−	2.92481i	0.254251	−	0.146792i	0.621709	+	0.783248i	$0.286439\pi$
$398$	−11.2542	−	6.49761i	−0.564121	−	0.325696i
$399$	0.844711	+	2.59975i	0.0422885	+	0.130150i
$400$	4.23605	+	2.65629i	0.211803	+	0.132814i
$401$	24.4799	+	17.7857i	1.22247	+	0.888176i	0.996303	−	0.0859130i	$-0.0273807\pi$
$401$	24.4799	+	17.7857i	1.22247	+	0.888176i	0.226166	+	0.974089i	$0.427381\pi$
$402$			7.99536i			0.398772i
$403$	−0.345003	−	2.39293i	−0.0171858	−	0.119200i
$404$	−5.51138			−0.274202
$405$	−1.71179	−	1.43867i	−0.0850596	−	0.0714880i
$406$	30.1577	+	13.4271i	1.49670	+	0.666375i
$407$	2.16635	−	0.703889i	0.107382	−	0.0348905i
$408$	−6.32530	−	3.65191i	−0.313149	−	0.180797i
$409$	−8.20150	−	14.2054i	−0.405538	−	0.702413i	0.588846	−	0.808245i	$-0.299583\pi$
$409$	−8.20150	−	14.2054i	−0.405538	−	0.702413i	−0.994384	+	0.105833i	$0.966249\pi$
$410$	13.4876	+	13.9889i	0.666104	+	0.690862i
$411$	−5.98942	+	18.4335i	−0.295436	+	0.909259i
$412$	6.48676	−	5.84070i	0.319580	−	0.287751i
$413$	−4.00409	−	8.99334i	−0.197028	−	0.442533i
$414$	0.0525625	+	0.0111725i	0.00258330	+	0.000549098i
$415$	10.7211	+	1.89914i	0.526277	+	0.0932253i
$416$	0.0453891	+	0.431848i	0.00222538	+	0.0211731i
$417$	−2.71636	−	12.7795i	−0.133021	−	0.625813i
$418$	0.943687	+	1.29887i	0.0461572	+	0.0635300i
$419$	21.5167	−	15.6328i	1.05116	−	0.763712i	0.0787268	−	0.996896i	$-0.474915\pi$
$419$	21.5167	−	15.6328i	1.05116	−	0.763712i	0.972433	+	0.233184i	$0.0749145\pi$
$420$	7.12123	−	0.995091i	0.347481	−	0.0485555i
$421$	1.46275	+	13.9172i	0.0712902	+	0.678281i	0.970556	+	0.240877i	$0.0774352\pi$
$421$	1.46275	+	13.9172i	0.0712902	+	0.678281i	−0.899265	+	0.437404i	$0.855898\pi$
$422$	−20.4166	−	2.14588i	−0.993867	−	0.104460i
$423$	0.142415	−	0.670010i	0.00692445	−	0.0325770i
$424$	5.91020	−	2.63139i	0.287025	−	0.127792i
$425$	30.3080	−	20.3734i	1.47015	−	0.988256i
$426$	−1.29064	+	3.97219i	−0.0625319	+	0.192453i
$427$	8.80764	+	7.93043i	0.426232	+	0.383781i
$428$	6.90255	−	3.98519i	0.333647	−	0.192631i
$429$	0.410053	−	0.710232i	0.0197975	−	0.0342903i
$430$	0.559819	+	2.25289i	0.0269969	+	0.108644i
$431$	−19.6389	−	8.74380i	−0.945972	−	0.421174i	−0.125010	−	0.992156i	$-0.539896\pi$
$431$	−19.6389	−	8.74380i	−0.945972	−	0.421174i	−0.820963	+	0.570981i	$0.806563\pi$
$432$	0.587785	−	0.809017i	0.0282798	−	0.0389238i
$433$		−	24.0805i		−	1.15723i	−0.815599	−	0.578617i	$-0.803593\pi$
$433$		−	24.0805i		−	1.15723i	0.815599	−	0.578617i	$-0.196407\pi$
$434$	−4.39324	−	17.3566i	−0.210882	−	0.833145i
$435$	−1.61936	+	22.8982i	−0.0776426	+	1.09788i
$436$	1.98877	+	1.44492i	0.0952446	+	0.0691993i
$437$	0.0185798	−	0.0417309i	0.000888792	−	0.00199626i
$438$	−4.28862	+	1.39346i	−0.204918	+	0.0665819i
$439$	−1.73213	+	3.00013i	−0.0826699	+	0.143188i	−0.904396	−	0.426694i	$-0.859678\pi$
$439$	−1.73213	+	3.00013i	−0.0826699	+	0.143188i	0.821726	+	0.569883i	$0.193011\pi$
$440$	3.79722	−	1.84832i	0.181025	−	0.0881150i
$441$	2.23519	−	2.48243i	0.106438	−	0.118211i
$442$	3.01629	+	0.980053i	0.143470	+	0.0466164i
$443$	1.66954	−	1.50326i	0.0793222	−	0.0714220i	−0.628516	−	0.777797i	$-0.716337\pi$
$443$	1.66954	−	1.50326i	0.0793222	−	0.0714220i	0.707838	+	0.706375i	$0.249671\pi$
$444$	−1.10179	+	0.490548i	−0.0522886	+	0.0232804i
$445$	15.9005	+	4.57299i	0.753756	+	0.216780i
$446$	1.32585	−	12.6146i	0.0627807	−	0.597318i
$447$	16.8340	−	1.76932i	0.796219	−	0.0836860i
$448$	0.668572	+	3.14539i	0.0315871	+	0.148605i
$449$	26.0152	−	18.9011i	1.22773	−	0.891999i	0.231013	−	0.972951i	$-0.425796\pi$
$449$	26.0152	−	18.9011i	1.22773	−	0.891999i	0.996718	+	0.0809516i	$0.0257959\pi$
$450$	2.34038	+	4.41844i	0.110327	+	0.208287i
$451$	16.0543	−	3.41244i	0.755966	−	0.160686i
$452$	16.0711	−	1.68914i	0.755923	−	0.0794507i
$453$	−16.3400	−	1.71740i	−0.767719	−	0.0806905i
$454$	18.0293	+	3.83225i	0.846158	+	0.179856i
$455$	−2.93482	+	1.06556i	−0.137587	+	0.0499544i
$456$	−0.568810	−	0.631728i	−0.0266370	−	0.0295834i
$457$	−1.03916	−	0.337643i	−0.0486098	−	0.0157943i	0.284611	−	0.958643i	$-0.408136\pi$
$457$	−1.03916	−	0.337643i	−0.0486098	−	0.0157943i	−0.333221	+	0.942849i	$0.608136\pi$
$458$	−13.3535	−	12.0236i	−0.623968	−	0.561824i
$459$	−3.65191	−	6.32530i	−0.170457	−	0.295240i
$460$	−0.0995632	−	0.0672707i	−0.00464216	−	0.00313651i
$461$	4.84173	+	14.9013i	0.225502	+	0.694023i	0.998240	+	0.0592986i	$0.0188864\pi$
$461$	4.84173	+	14.9013i	0.225502	+	0.694023i	−0.772739	+	0.634724i	$0.781114\pi$
$462$	2.47022	−	5.54821i	0.114925	−	0.258126i
$463$	−11.2411	+	15.4720i	−0.522418	+	0.719046i	−0.985951	−	0.167033i	$-0.946581\pi$
$463$	−11.2411	+	15.4720i	−0.522418	+	0.719046i	0.463534	+	0.886079i	$0.346581\pi$
$464$	−10.2659			−0.476585
$465$	10.3021	−	6.99049i	0.477748	−	0.324176i
$466$	−4.84808			−0.224583
$467$	−14.7356	+	20.2819i	−0.681884	+	0.938533i	−0.999955	−	0.00953395i	$-0.996965\pi$
$467$	−14.7356	+	20.2819i	−0.681884	+	0.938533i	0.318070	+	0.948067i	$0.396965\pi$
$468$	−0.176616	+	0.396686i	−0.00816408	+	0.0183368i
$469$	−7.94493	−	24.4520i	−0.366863	−	1.12909i
$470$	−0.857494	+	1.26912i	−0.0395533	+	0.0585404i
$471$	−2.68199	−	4.64533i	−0.123579	−	0.214046i
$472$	2.27507	+	2.04848i	0.104719	+	0.0942890i
$473$	1.86477	+	0.605899i	0.0857420	+	0.0278593i
$474$	0.345893	+	0.384153i	0.0158874	+	0.0176448i
$475$	4.08756	−	1.16511i	0.187550	−	0.0534588i
$476$	22.9734	+	4.88314i	1.05298	+	0.223818i
$477$	6.43408	+	0.676249i	0.294596	+	0.0309633i
$478$	−14.1563	+	1.48789i	−0.647494	+	0.0680544i
$479$	25.6445	−	5.45091i	1.17173	−	0.249059i	0.419372	−	0.907815i	$-0.362250\pi$
$479$	25.6445	−	5.45091i	1.17173	−	0.249059i	0.752357	+	0.658756i	$0.228917\pi$
$480$	−1.89723	+	1.18344i	−0.0865962	+	0.0540163i
$481$	0.423685	−	0.307825i	0.0193184	−	0.0140356i
$482$	−3.84335	−	18.0815i	−0.175060	−	0.823591i
$483$	−0.171852	+	0.0180624i	−0.00781955	+	0.000821867i
$484$	−0.776958	+	7.39226i	−0.0353163	+	0.336012i
$485$	5.76870	−	20.0581i	0.261943	−	0.910790i
$486$	0.913545	−	0.406737i	0.0414393	−	0.0184499i
$487$	8.61596	−	7.75785i	0.390427	−	0.351542i	−0.450418	−	0.892818i	$-0.648725\pi$
$487$	8.61596	−	7.75785i	0.390427	−	0.351542i	0.840845	+	0.541276i	$0.182059\pi$
$488$	−3.50528	−	1.13894i	−0.158677	−	0.0515572i
$489$	15.3896	−	17.0919i	0.695944	−	0.772924i
$490$	−6.71607	+	3.26909i	−0.303401	+	0.147682i
$491$	−17.4999	+	30.3107i	−0.789759	+	1.36790i	0.136356	+	0.990660i	$0.456461\pi$
$491$	−17.4999	+	30.3107i	−0.789759	+	1.36790i	−0.926114	+	0.377243i	$0.876872\pi$
$492$	−8.26494	+	2.68544i	−0.372612	+	0.121069i
$493$	−30.4974	+	68.4983i	−1.37353	+	3.08501i
$494$	0.298628	+	0.216966i	0.0134359	+	0.00976176i
$495$	4.21264	+	0.297919i	0.189344	+	0.0133905i
$496$	3.44347	+	4.37522i	0.154616	+	0.196453i
$497$		−	13.4305i		−	0.602442i
$498$	−2.86207	+	3.93931i	−0.128253	+	0.176525i
$499$	19.9377	+	8.87683i	0.892533	+	0.397381i	0.801170	−	0.598436i	$-0.204211\pi$
$499$	19.9377	+	8.87683i	0.892533	+	0.397381i	0.0913628	+	0.995818i	$0.470878\pi$
$500$	−1.14232	−	11.1218i	−0.0510863	−	0.497383i
$501$	6.29333	−	10.9004i	0.281165	−	0.486992i
$502$	−17.7379	+	10.2410i	−0.791681	+	0.457077i
$503$	14.2939	+	12.8703i	0.637334	+	0.573859i	0.923157	−	0.384424i	$-0.125600\pi$
$503$	14.2939	+	12.8703i	0.637334	+	0.573859i	−0.285822	+	0.958283i	$0.592267\pi$
$504$	−0.993692	+	3.05827i	−0.0442626	+	0.136226i
$505$	7.57964	+	9.71729i	0.337289	+	0.432414i
$506$	−0.0927159	+	0.0412798i	−0.00412173	+	0.00183511i
$507$	−2.66365	+	12.5315i	−0.118297	+	0.556543i
$508$	2.40746	+	0.253034i	0.106814	+	0.0112266i
$509$	0.604766	+	5.75396i	0.0268058	+	0.255040i	0.999715	+	0.0238543i	$0.00759378\pi$
$509$	0.604766	+	5.75396i	0.0268058	+	0.255040i	−0.972910	+	0.231186i	$0.925740\pi$
$510$	2.26019	+	16.1747i	0.100083	+	0.716228i
$511$	11.7311	−	8.52313i	0.518952	−	0.377041i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$	−0.176740	−	0.831497i	−0.00780327	−	0.0367115i
$514$	1.30219	+	12.3895i	0.0574371	+	0.546477i
$515$	−19.2190	−	3.40447i	−0.846889	−	0.150019i
$516$	−1.01548	−	0.215846i	−0.0447038	−	0.00950209i
$517$	0.526190	+	1.18184i	0.0231418	+	0.0519774i
$518$	2.88212	−	2.59507i	0.126633	−	0.114021i
$519$	0.599740	−	1.84581i	0.0263257	−	0.0810221i
$520$	0.698983	−	0.673934i	0.0306524	−	0.0295540i
$521$	−7.04007	−	12.1938i	−0.308431	−	0.534218i	0.669588	−	0.742732i	$-0.266471\pi$
$521$	−7.04007	−	12.1938i	−0.308431	−	0.534218i	−0.978019	+	0.208514i	$0.933137\pi$
$522$	−8.89057	−	5.13297i	−0.389130	−	0.224664i
$523$	14.4353	−	4.69031i	0.631211	−	0.205093i	0.0240995	−	0.999710i	$-0.492328\pi$
$523$	14.4353	−	4.69031i	0.631211	−	0.205093i	0.607111	+	0.794617i	$0.292328\pi$
$524$	−2.87716	−	1.28099i	−0.125689	−	0.0559605i
$525$	−11.5481	−	11.1872i	−0.504000	−	0.488248i
$526$	−26.8628			−1.17127
$527$	39.4227	−	9.97852i	1.71728	−	0.434671i
$528$			1.88866i			0.0821932i
$529$	−18.6051	−	13.5174i	−0.808915	−	0.587711i
$530$	−12.7676	−	6.80159i	−0.554589	−	0.295442i
$531$	0.946027	+	2.91157i	0.0410541	+	0.126351i
$532$	2.36732	+	1.36677i	0.102636	+	0.0592571i
$533$	3.26799	−	1.88677i	0.141552	−	0.0817252i
$534$	−4.95101	+	5.49865i	−0.214251	+	0.237950i
$535$	−16.5193	−	6.68940i	−0.714190	−	0.289208i
$536$	5.34994	+	5.94171i	0.231082	+	0.256643i
$537$	6.69590	+	15.0392i	0.288950	+	0.648991i
$538$	−3.46633	+	16.3078i	−0.149444	+	0.703078i
$539$	−0.659463	+	6.27438i	−0.0284051	+	0.270257i
$540$	−2.23477	+	0.0762733i	−0.0961690	+	0.00328228i
$541$	13.3015	−	2.82732i	0.571877	−	0.121556i	0.0871085	−	0.996199i	$-0.472237\pi$
$541$	13.3015	−	2.82732i	0.571877	−	0.121556i	0.484768	+	0.874643i	$0.338904\pi$
$542$	−8.88734	−	12.2324i	−0.381744	−	0.525426i
$543$	6.62196	+	9.11435i	0.284176	+	0.391134i
$544$	−7.14422	+	1.51855i	−0.306306	+	0.0651074i
$545$	−0.187499	−	5.49362i	−0.00803156	−	0.235321i
$546$	0.145956	−	1.38867i	0.00624632	−	0.0594298i
$547$	4.28626	−	20.1653i	0.183267	−	0.862205i	−0.786389	−	0.617732i	$-0.788052\pi$
$547$	4.28626	−	20.1653i	0.183267	−	0.862205i	0.969656	−	0.244473i	$-0.0786149\pi$
$548$	7.88343	+	17.7065i	0.336764	+	0.756383i
$549$	−2.46620	−	2.73899i	−0.105255	−	0.116897i
$550$	−8.48102	−	4.15306i	−0.361632	−	0.177087i
$551$	−5.83938	+	6.48528i	−0.248766	+	0.276282i
$552$	0.0465374	−	0.0268684i	0.00198076	−	0.00114359i
$553$	−1.43957	−	0.831133i	−0.0612165	−	0.0353434i
$554$	2.21477	+	6.81635i	0.0940964	+	0.289599i
$555$	2.38016	+	1.26796i	0.101032	+	0.0538221i
$556$	−10.5698	−	7.67939i	−0.448258	−	0.325679i
$557$		−	11.3392i		−	0.480459i	−0.970716	−	0.240229i	$-0.922777\pi$
$557$		−	11.3392i		−	0.480459i	0.970716	−	0.240229i	$-0.0772227\pi$
$558$	0.794523	+	5.51078i	0.0336348	+	0.233290i
$559$	0.450798			0.0190667
$560$	4.62626	−	5.50453i	0.195495	−	0.232609i
$561$	12.6018	+	5.61070i	0.532050	+	0.236884i
$562$	−22.5337	+	7.32163i	−0.950525	+	0.308844i
$563$	−7.94424	−	4.58661i	−0.334810	−	0.193303i	0.323165	−	0.946343i	$-0.395253\pi$
$563$	−7.94424	−	4.58661i	−0.334810	−	0.193303i	−0.657975	+	0.753040i	$0.728587\pi$
$564$	−0.342489	−	0.593208i	−0.0144214	−	0.0249786i
$565$	−25.0803	−	26.0125i	−1.05514	−	1.09435i
$566$	6.04941	−	18.6182i	0.254276	−	0.782580i
$567$	−2.38970	+	2.15169i	−0.100358	+	0.0903626i
$568$	1.69878	+	3.81552i	0.0712793	+	0.160096i
$569$	−2.12149	−	0.450937i	−0.0889376	−	0.0189043i	0.163228	−	0.986588i	$-0.447809\pi$
$569$	−2.12149	−	0.450937i	−0.0889376	−	0.0189043i	−0.252166	+	0.967684i	$0.581143\pi$
$570$	−0.331552	+	1.87168i	−0.0138872	+	0.0783962i
$571$	−1.70351	−	16.2078i	−0.0712898	−	0.678277i	−0.970556	−	0.240875i	$-0.922565\pi$
$571$	−1.70351	−	16.2078i	−0.0712898	−	0.678277i	0.899266	−	0.437402i	$-0.144101\pi$
$572$	−0.170509	−	0.802184i	−0.00712936	−	0.0335410i
$573$	−7.66802	−	10.5541i	−0.320336	−	0.440905i
$574$	22.6079	−	16.4256i	0.943636	−	0.685591i
$575$	0.0183192	+	0.268058i	0.000763962	+	0.0111788i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	−13.6770	−	1.43751i	−0.569381	−	0.0598443i	−0.184536	−	0.982826i	$-0.559078\pi$
$577$	−13.6770	−	1.43751i	−0.569381	−	0.0598443i	−0.384845	+	0.922981i	$0.625745\pi$
$578$	−7.55674	+	35.5517i	−0.314319	+	1.47875i
$579$	1.74848	−	0.778471i	0.0726642	−	0.0323522i
$580$	14.1184	+	18.1002i	0.586237	+	0.751571i
$581$	4.83854	−	14.8915i	0.200736	−	0.617803i
$582$	6.93640	+	6.24557i	0.287523	+	0.258887i
$583$	−10.5817	+	6.10935i	−0.438249	+	0.253023i
$584$	−2.25466	+	3.90518i	−0.0932984	+	0.161598i
$585$	0.942304	−	0.234153i	0.0389595	−	0.00968102i
$586$	−24.5916	−	10.9489i	−1.01587	−	0.452295i
$587$	−4.95205	+	6.81591i	−0.204393	+	0.281323i	−0.898891	−	0.438171i	$-0.855626\pi$
$587$	−4.95205	+	6.81591i	−0.204393	+	0.281323i	0.694499	+	0.719494i	$0.255626\pi$
$588$		−	3.34044i		−	0.137757i
$589$	4.72263	+	0.313334i	0.194592	+	0.0129107i
$590$	0.482911	−	6.82846i	0.0198811	−	0.281123i
$591$	−8.30079	−	6.03088i	−0.341449	−	0.248077i
$592$	−0.490548	+	1.10179i	−0.0201614	+	0.0452833i
$593$	24.1424	−	7.84435i	0.991411	−	0.322129i	0.231982	−	0.972720i	$-0.425479\pi$
$593$	24.1424	−	7.84435i	0.991411	−	0.322129i	0.759428	+	0.650591i	$0.225479\pi$
$594$	−0.944328	+	1.63562i	−0.0387463	+	0.0671105i
$595$	−22.9849	−	47.2207i	−0.942290	−	1.93586i
$596$	11.3262	−	12.5790i	0.463938	−	0.515255i
$597$	−12.3592	−	4.01574i	−0.505828	−	0.164353i
$598$	−0.0173405	+	0.0156134i	−0.000709105	+	0.000638481i
$599$	21.9977	−	9.79402i	0.898803	−	0.400173i	0.0952827	−	0.995450i	$-0.469625\pi$
$599$	21.9977	−	9.79402i	0.898803	−	0.400173i	0.803520	+	0.595277i	$0.202958\pi$
$600$	4.69576	+	1.71752i	0.191703	+	0.0701174i
$601$	0.979858	−	9.32273i	0.0399692	−	0.380282i	−0.956192	−	0.292741i	$-0.905433\pi$
$601$	0.979858	−	9.32273i	0.0399692	−	0.380282i	0.996161	−	0.0875407i	$-0.0279008\pi$
$602$	3.32008	−	0.348955i	0.135316	−	0.0142223i
$603$	1.66233	+	7.82064i	0.0676953	+	0.318481i
$604$	−13.2921	+	9.65730i	−0.540849	+	0.392950i
$605$	14.1021	−	8.79647i	0.573330	−	0.357627i
$606$	−5.39095	+	1.14588i	−0.218992	+	0.0465482i
$607$	1.06069	−	0.111483i	0.0430522	−	0.00452496i	−0.0829779	−	0.996551i	$-0.526443\pi$
$607$	1.06069	−	0.111483i	0.0430522	−	0.00452496i	0.126030	+	0.992026i	$0.459776\pi$
$608$	−0.845417	−	0.0888569i	−0.0342862	−	0.00360362i
$609$	32.2904	+	6.86353i	1.30847	+	0.278124i
$610$	2.81261	+	7.74662i	0.113879	+	0.313651i
$611$	0.199023	+	0.221038i	0.00805163	+	0.00894224i
$612$	−6.94635	−	2.25701i	−0.280790	−	0.0912341i
$613$	27.9423	+	25.1594i	1.12858	+	1.01618i	0.999699	+	0.0245166i	$0.00780467\pi$
$613$	27.9423	+	25.1594i	1.12858	+	1.01618i	0.128879	+	0.991660i	$0.458862\pi$
$614$	14.1056	+	24.4316i	0.569255	+	0.985979i
$615$	16.1013	+	10.8790i	0.649267	+	0.438682i
$616$	−1.87674	−	5.77602i	−0.0756161	−	0.232722i
$617$	8.55197	−	19.2080i	0.344290	−	0.773287i	−0.655546	−	0.755155i	$-0.727562\pi$
$617$	8.55197	−	19.2080i	0.344290	−	0.773287i	0.999836	−	0.0181317i	$-0.00577183\pi$
$618$	5.13066	−	7.06174i	0.206385	−	0.284065i
$619$	7.53007			0.302659			0.151330	−	0.988483i	$-0.451645\pi$
$619$	7.53007			0.302659			0.151330	+	0.988483i	$0.451645\pi$
$620$	2.97839	−	12.0884i	0.119615	−	0.485481i
$621$	0.0537367			0.00215638
$622$	16.4902	−	22.6968i	0.661197	−	0.910060i
$623$	9.67755	−	21.7361i	0.387723	−	0.870840i
$624$	0.134183	+	0.412974i	0.00537164	+	0.0165322i
$625$	−18.0383	+	17.3096i	−0.721530	+	0.692383i
$626$	10.1199	+	17.5282i	0.404472	+	0.700566i
$627$	1.19312	+	1.07429i	0.0476485	+	0.0429029i
$628$	−5.10144	−	1.65756i	−0.203570	−	0.0661438i
$629$	5.89427	+	6.54625i	0.235020	+	0.261016i
$630$	6.75873	−	2.45393i	0.269274	−	0.0977671i
$631$	22.1945	+	4.71760i	0.883551	+	0.187804i	0.627274	−	0.778799i	$-0.284171\pi$
$631$	22.1945	+	4.71760i	0.883551	+	0.187804i	0.256277	+	0.966603i	$0.417504\pi$
$632$	0.514098	+	0.0540338i	0.0204497	+	0.00214935i
$633$	−20.4166	+	2.14588i	−0.811489	+	0.0852909i
$634$	−24.2767	+	5.16016i	−0.964149	+	0.204936i
$635$	−2.86477	−	4.59266i	−0.113685	−	0.182254i
$636$	5.23395	−	3.80269i	0.207540	−	0.150786i
$637$	0.301577	+	1.41881i	0.0119489	+	0.0562153i
$638$	19.2826	−	2.02669i	0.763407	−	0.0802373i
$639$	−0.436575	+	4.15373i	−0.0172706	+	0.164319i
$640$	−0.618041	+	2.14896i	−0.0244302	+	0.0849451i
$641$	−19.4320	+	8.65167i	−0.767516	+	0.341720i	−0.752867	−	0.658172i	$-0.771330\pi$
$641$	−19.4320	+	8.65167i	−0.767516	+	0.341720i	−0.0146491	+	0.999893i	$0.504663\pi$
$642$	5.92314	−	5.33322i	0.233768	−	0.210485i
$643$	29.2045	+	9.48912i	1.15171	+	0.374214i	0.821788	−	0.569793i	$-0.192977\pi$
$643$	29.2045	+	9.48912i	1.15171	+	0.374214i	0.329925	+	0.944007i	$0.392977\pi$
$644$	−0.115625	+	0.128415i	−0.00455626	+	0.00506024i
$645$	1.01599	+	2.08726i	0.0400044	+	0.0821859i
$646$	−3.10440	+	5.37697i	−0.122141	+	0.211554i
$647$	6.30784	−	2.04954i	0.247987	−	0.0805758i	−0.182386	−	0.983227i	$-0.558382\pi$
$647$	6.30784	−	2.04954i	0.247987	−	0.0805758i	0.430373	+	0.902651i	$0.358382\pi$
$648$	0.406737	−	0.913545i	0.0159781	−	0.0358875i
$649$	−4.67770	−	3.39854i	−0.183616	−	0.133405i
$650$	−2.14952	−	0.305558i	−0.0843113	−	0.0119850i
$651$	−7.90589	−	16.0640i	−0.309856	−	0.629596i
$652$		−	22.9995i		−	0.900729i
$653$	−15.1090	+	20.7958i	−0.591262	+	0.813803i	−0.994873	−	0.101128i	$-0.967755\pi$
$653$	−15.1090	+	20.7958i	−0.591262	+	0.813803i	0.403611	+	0.914931i	$0.367755\pi$
$654$	2.24572	+	0.999860i	0.0878147	+	0.0390976i
$655$	1.69831	+	6.83453i	0.0663584	+	0.267047i
$656$	−4.34513	+	7.52599i	−0.169649	+	0.293841i
$657$	−3.90518	+	2.25466i	−0.152356	+	0.0879626i
$658$	1.63689	+	1.47386i	0.0638126	+	0.0574571i
$659$	−15.2562	+	46.9538i	−0.594297	+	1.82906i	−0.0361030	+	0.999348i	$0.511494\pi$
$659$	−15.2562	+	46.9538i	−0.594297	+	1.82906i	−0.558194	+	0.829710i	$0.688506\pi$
$660$	3.32995	−	2.59741i	0.129618	−	0.101104i
$661$	−29.9893	+	13.3521i	−1.16645	+	0.519336i	−0.896285	−	0.443479i	$-0.853744\pi$
$661$	−29.9893	+	13.3521i	−1.16645	+	0.519336i	−0.270163	+	0.962815i	$0.587077\pi$
$662$	−0.292498	+	1.37609i	−0.0113682	+	0.0534834i
$663$	3.15414	+	0.331514i	0.122497	+	0.0128749i
$664$	0.508975	+	4.84258i	0.0197521	+	0.187928i
$665$	−0.845901	−	6.05357i	−0.0328026	−	0.234747i
$666$	−0.975722	+	0.708904i	−0.0378085	+	0.0274695i
$667$	−0.324257	−	0.446301i	−0.0125553	−	0.0172809i
$668$	−2.61691	−	12.3116i	−0.101251	−	0.476350i
$669$	−1.32585	−	12.6146i	−0.0512602	−	0.487708i
$670$	3.11841	−	17.6041i	0.120475	−	0.680106i
$671$	6.80885	+	1.44727i	0.262853	+	0.0558711i
$672$	1.30792	+	2.93765i	0.0504543	+	0.113322i
$673$	−32.6221	+	29.3731i	−1.25749	+	1.13225i	−0.272040	+	0.962286i	$0.587698\pi$
$673$	−32.6221	+	29.3731i	−1.25749	+	1.13225i	−0.985450	+	0.169963i	$0.945635\pi$
$674$	2.45621	−	7.55945i	0.0946098	−	0.291179i
$675$	3.20789	+	3.83529i	0.123472	+	0.147620i
$676$	6.40572	+	11.0950i	0.246374	+	0.426732i
$677$	42.8900	+	24.7626i	1.64840	+	0.951703i	0.977709	+	0.209964i	$0.0673348\pi$
$677$	42.8900	+	24.7626i	1.64840	+	0.951703i	0.670689	+	0.741739i	$0.265999\pi$
$678$	15.3687	−	4.99361i	0.590233	−	0.191778i
$679$	−27.4196	−	12.2080i	−1.05227	−	0.468499i
$680$	12.5026	+	10.5078i	0.479454	+	0.402955i
$681$	18.4321			0.706320
$682$	−7.33165	−	7.53821i	−0.280743	−	0.288653i
$683$		−	46.8094i		−	1.79111i	−0.444949	−	0.895556i	$-0.646778\pi$
$683$		−	46.8094i		−	1.79111i	0.444949	−	0.895556i	$-0.353222\pi$
$684$	−0.687724	−	0.499661i	−0.0262958	−	0.0191050i
$685$	20.3770	−	38.2507i	0.778566	−	1.46148i
$686$	−3.63648	−	11.1919i	−0.138841	−	0.427310i
$687$	−15.5615	−	8.98446i	−0.593710	−	0.342778i
$688$	−0.899074	+	0.519081i	−0.0342769	+	0.0197898i
$689$	−1.87975	+	2.08767i	−0.0716127	+	0.0795339i
$690$	−0.111374	−	0.0451003i	−0.00423993	−	0.00171694i
$691$	20.2671	+	22.5089i	0.770998	+	0.856280i	0.992920	−	0.118785i	$-0.0378998\pi$
$691$	20.2671	+	22.5089i	0.770998	+	0.856280i	−0.221922	+	0.975064i	$0.571233\pi$
$692$	−0.789395	−	1.77301i	−0.0300083	−	0.0673997i
$693$	1.26270	−	5.94055i	0.0479661	−	0.225663i
$694$	1.76856	−	16.8267i	0.0671336	−	0.638734i
$695$	0.996507	+	29.1971i	0.0377997	+	1.10751i
$696$	−10.0416	+	2.13441i	−0.380626	+	0.0809046i
$697$	37.3080	+	51.3501i	1.41314	+	1.94502i
$698$	−9.32973	−	12.8413i	−0.353135	−	0.486049i
$699$	−4.74214	+	1.00797i	−0.179364	+	0.0381250i
$700$	−16.0676	−	0.586496i	−0.607297	−	0.0221675i
$701$	0.802672	−	7.63692i	0.0303165	−	0.288442i	−0.968851	−	0.247645i	$-0.920343\pi$
$701$	0.802672	−	7.63692i	0.0303165	−	0.288442i	0.999167	−	0.0407976i	$-0.0129899\pi$
$702$	−0.0902808	+	0.424738i	−0.00340743	+	0.0160307i
$703$	0.417002	+	0.936602i	0.0157275	+	0.0353246i
$704$	1.26376	+	1.40355i	0.0476297	+	0.0528981i
$705$	−0.574890	+	1.41967i	−0.0216516	+	0.0534680i
$706$	−24.0733	+	26.7362i	−0.906012	+	1.00623i
$707$	15.3483	−	8.86135i	0.577233	−	0.333265i
$708$	2.65126	+	1.53070i	0.0996404	+	0.0575274i
$709$	9.08076	+	27.9477i	0.341035	+	1.04960i	0.963672	+	0.267088i	$0.0860613\pi$
$709$	9.08076	+	27.9477i	0.341035	+	1.04960i	−0.622637	+	0.782511i	$0.713939\pi$
$710$	4.39099	−	8.24255i	0.164791	−	0.309337i
$711$	0.418205	+	0.303843i	0.0156839	+	0.0113950i
$712$			7.39917i			0.277295i
$713$	−0.0814437	+	0.287895i	−0.00305009	+	0.0107818i
$714$	23.4866			0.878964
$715$	−1.17986	+	1.40385i	−0.0441243	+	0.0525010i
$716$	15.0392	+	6.69590i	0.562043	+	0.250238i
$717$	−13.5376	+	4.39863i	−0.505571	+	0.164270i
$718$	28.5720	+	16.4960i	1.06630	+	0.615626i
$719$	−24.5599	−	42.5390i	−0.915931	−	1.58644i	−0.805533	−	0.592551i	$-0.798121\pi$
$719$	−24.5599	−	42.5390i	−0.915931	−	1.58644i	−0.110398	−	0.993888i	$-0.535212\pi$
$720$	−1.60972	+	1.55203i	−0.0599907	+	0.0578409i
$721$	−8.67373	+	26.6950i	−0.323027	+	0.994174i
$722$	13.5827	−	12.2300i	0.505497	−	0.455152i
$723$	−7.51873	−	16.8873i	−0.279624	−	0.628047i
$724$	11.0198	+	2.34232i	0.409547	+	0.0870518i
$725$	12.4964	−	49.7854i	0.464105	−	1.84898i
$726$	0.776958	+	7.39226i	0.0288356	+	0.274352i
$727$	−3.43277	−	16.1499i	−0.127315	−	0.598968i	−0.994830	−	0.101557i	$-0.967618\pi$
$727$	−3.43277	−	16.1499i	−0.127315	−	0.598968i	0.867515	−	0.497411i	$-0.165716\pi$
$728$	−0.820738	−	1.12965i	−0.0304186	−	0.0418676i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	9.98612	−	1.39542i	0.369603	−	0.0516467i
$731$	0.792593	+	7.54102i	0.0293151	+	0.278915i
$732$	−3.66548	−	0.385258i	−0.135480	−	0.0142395i
$733$	−8.94277	+	42.0724i	−0.330309	+	1.55398i	0.429033	+	0.903289i	$0.358855\pi$
$733$	−8.94277	+	42.0724i	−0.330309	+	1.55398i	−0.759342	+	0.650692i	$0.774479\pi$
$734$	−25.1334	+	11.1901i	−0.927690	+	0.413034i
$735$	−5.88963	+	4.59400i	−0.217242	+	0.169452i
$736$	0.0166056	−	0.0511067i	0.000612089	−	0.00188382i
$737$	−11.2218	−	10.1042i	−0.413362	−	0.372193i
$738$	−7.52599	+	4.34513i	−0.277036	+	0.159947i
$739$	10.8136	−	18.7297i	0.397785	−	0.688983i	−0.595668	−	0.803231i	$-0.703112\pi$
$739$	10.8136	−	18.7297i	0.397785	−	0.688983i	0.993452	+	0.114248i	$0.0364457\pi$
$740$	2.61724	−	0.650356i	0.0962115	−	0.0239076i
$741$	0.337212	+	0.150137i	0.0123878	+	0.00551540i
$742$	−12.2281	+	16.8306i	−0.448909	+	0.617870i
$743$		−	30.5463i		−	1.12063i	−0.828278	−	0.560317i	$-0.810679\pi$
$743$		−	30.5463i		−	1.12063i	0.828278	−	0.560317i	$-0.189321\pi$
$744$	4.27788	+	3.56367i	0.156835	+	0.130651i
$745$	−37.7549	−	2.67004i	−1.38323	−	0.0978227i
$746$	−22.9786	−	16.6949i	−0.841307	−	0.611245i
$747$	−1.98050	+	4.44828i	−0.0724628	+	0.162754i
$748$	13.1193	−	4.26271i	0.479688	−	0.155860i
$749$	−12.8150	+	22.1962i	−0.468249	+	0.811032i
$750$	−3.42972	−	10.6413i	−0.125236	−	0.388565i
$751$	−21.1602	+	23.5008i	−0.772146	+	0.857555i	−0.993044	−	0.117742i	$-0.962435\pi$
$751$	−21.1602	+	23.5008i	−0.772146	+	0.857555i	0.220898	+	0.975297i	$0.429101\pi$
$752$	−0.651453	−	0.211670i	−0.0237560	−	0.00771881i
$753$	−15.2211	+	13.7051i	−0.554686	+	0.499442i
$754$	4.07236	−	1.81313i	0.148307	−	0.0660303i
$755$	35.3074	+	10.1544i	1.28497	+	0.369556i
$756$	−0.336127	+	3.19804i	−0.0122248	+	0.116312i
$757$	12.4320	−	1.30666i	0.451849	−	0.0474913i	0.124129	−	0.992266i	$-0.460386\pi$
$757$	12.4320	−	1.30666i	0.451849	−	0.0474913i	0.327720	+	0.944775i	$0.393720\pi$
$758$	3.88681	+	18.2860i	0.141175	+	0.664177i
$759$	−0.0821073	+	0.0596545i	−0.00298031	+	0.00216532i
$760$	1.00601	+	1.61278i	0.0364918	+	0.0585018i
$761$	21.7638	−	4.62604i	0.788937	−	0.167694i	0.204213	−	0.978926i	$-0.434536\pi$
$761$	21.7638	−	4.62604i	0.788937	−	0.167694i	0.584723	+	0.811233i	$0.301203\pi$
$762$	2.40746	−	0.253034i	0.0872131	−	0.00916647i
$763$	−7.86158	−	0.826285i	−0.284608	−	0.0299135i
$764$	−12.7605	−	2.71234i	−0.461660	−	0.0981289i
$765$	5.57371	+	15.3513i	0.201518	+	0.555029i
$766$	−24.8818	−	27.6341i	−0.899017	−	0.998460i
$767$	−1.26428	−	0.410790i	−0.0456506	−	0.0148328i
$768$	−0.743145	−	0.669131i	−0.0268159	−	0.0241452i
$769$	27.2670	+	47.2278i	0.983273	+	1.70308i	0.649374	+	0.760469i	$0.275031\pi$
$769$	27.2670	+	47.2278i	0.983273	+	1.70308i	0.333899	+	0.942609i	$0.391636\pi$
$770$	−7.60286	+	11.2525i	−0.273988	+	0.405513i
$771$	3.84965	+	11.8480i	0.138642	+	0.426696i
$772$	0.778471	−	1.74848i	0.0280178	−	0.0629290i
$773$	−8.85438	+	12.1870i	−0.318470	+	0.438336i	−0.937999	−	0.346637i	$-0.887323\pi$
$773$	−8.85438	+	12.1870i	−0.318470	+	0.438336i	0.619529	+	0.784973i	$0.287323\pi$
$774$	−1.03816			−0.0373159
$775$	−25.4095	+	11.3735i	−0.912737	+	0.408548i
$776$	9.33385			0.335066
$777$	2.27959	−	3.13759i	0.0817798	−	0.112560i
$778$	8.16159	−	18.3312i	0.292607	−	0.657206i
$779$	2.28282	+	7.02580i	0.0817906	+	0.251725i
$780$	0.543590	−	0.804534i	0.0194636	−	0.0288069i
$781$	−3.94409	−	6.83137i	−0.141131	−	0.244446i
$782$	−0.291672	−	0.262623i	−0.0104302	−	0.00939138i
$783$	−9.76350	−	3.17235i	−0.348919	−	0.113371i
$784$	−2.23519	−	2.48243i	−0.0798282	−	0.0886582i
$785$	4.09336	+	11.2741i	0.146098	+	0.402390i
$786$	−3.08062	−	0.654806i	−0.109882	−	0.0233562i
$787$	17.5257	+	1.84202i	0.624723	+	0.0656610i	0.411600	−	0.911364i	$-0.364970\pi$
$787$	17.5257	+	1.84202i	0.624723	+	0.0656610i	0.213123	+	0.977025i	$0.431637\pi$
$788$	−10.2041	+	1.07250i	−0.363507	+	0.0382061i
$789$	−26.2758	+	5.58509i	−0.935442	+	0.198834i
$790$	−0.611754	−	0.980733i	−0.0217652	−	0.0348929i
$791$	−42.0397	+	30.5436i	−1.49476	+	1.08601i
$792$	0.392674	+	1.84738i	0.0139531	+	0.0656440i
$793$	1.59165	−	0.167289i	0.0565212	−	0.00594061i
$794$	0.611451	−	5.81757i	0.0216996	−	0.206458i
$795$	−13.9027	−	3.99843i	−0.493079	−	0.141810i
$796$	−11.8717	+	5.28563i	−0.420782	+	0.187344i
$797$	−31.9542	+	28.7717i	−1.13188	+	1.01914i	−0.132265	+	0.991214i	$0.542225\pi$
$797$	−31.9542	+	28.7717i	−1.13188	+	1.01914i	−0.999610	+	0.0279306i	$0.991108\pi$
$798$	2.59975	+	0.844711i	0.0920303	+	0.0299024i
$799$	−3.34764	+	3.71793i	−0.118431	+	0.131531i
$800$	4.63887	−	1.86571i	0.164009	−	0.0659628i
$801$	−3.69958	+	6.40787i	−0.130718	+	0.226411i
$802$	28.7779	−	9.35050i	1.01618	−	0.330178i
$803$	3.46399	−	7.78026i	0.122242	−	0.274559i
$804$	6.46838	+	4.69955i	0.228122	+	0.165741i
$805$	0.385427	+	0.0272575i	0.0135845	+	0.000960701i
$806$	−2.13871	−	1.12742i	−0.0753328	−	0.0397115i
$807$			16.6721i			0.586886i
$808$	−3.23951	+	4.45880i	−0.113966	+	0.156860i
$809$	−40.9145	−	18.2163i	−1.43848	−	0.640451i	−0.468459	−	0.883485i	$-0.655191\pi$
$809$	−40.9145	−	18.2163i	−1.43848	−	0.640451i	−0.970018	+	0.243034i	$0.921857\pi$
$810$	−2.17007	+	0.539241i	−0.0762486	+	0.0189470i
$811$	−3.11635	+	5.39768i	−0.109430	+	0.189538i	−0.915539	−	0.402228i	$-0.868236\pi$
$811$	−3.11635	+	5.39768i	−0.109430	+	0.189538i	0.806110	+	0.591766i	$0.201569\pi$
$812$	28.5890	−	16.5059i	1.00328	−	0.579243i
$813$	−11.2364	−	10.1173i	−0.394077	−	0.354829i
$814$	0.703889	−	2.16635i	0.0246713	−	0.0759304i
$815$	−40.5511	+	31.6305i	−1.42044	+	1.10797i
$816$	−6.67238	+	2.97073i	−0.233580	+	0.103997i
$817$	−0.183485	+	0.863228i	−0.00641932	+	0.0302005i
$818$	−16.3131	−	1.71458i	−0.570376	−	0.0599489i
$819$	−0.145956	−	1.38867i	−0.00510010	−	0.0485242i
$820$	19.2450	−	2.68922i	0.672066	−	0.0939117i
$821$	−33.2930	+	24.1888i	−1.16193	+	0.844195i	−0.990021	−	0.140917i	$-0.954995\pi$
$821$	−33.2930	+	24.1888i	−1.16193	+	0.844195i	−0.171913	+	0.985112i	$0.554995\pi$
$822$	11.3925	+	15.6805i	0.397361	+	0.546920i
$823$	−1.20672	−	5.67719i	−0.0420638	−	0.197894i	0.952098	−	0.305792i	$-0.0989214\pi$
$823$	−1.20672	−	5.67719i	−0.0420638	−	0.197894i	−0.994162	+	0.107898i	$0.965588\pi$
$824$	−0.912407	−	8.68098i	−0.0317852	−	0.302416i
$825$	−9.15916	−	2.29900i	−0.318881	−	0.0800410i
$826$	−9.62931	−	2.04677i	−0.335047	−	0.0712163i
$827$	15.1862	+	34.1088i	0.528077	+	1.18608i	0.958926	+	0.283656i	$0.0915472\pi$
$827$	15.1862	+	34.1088i	0.528077	+	1.18608i	−0.430850	+	0.902424i	$0.641786\pi$
$828$	0.0399342	−	0.0359569i	0.00138781	−	0.00124959i
$829$	6.57584	−	20.2384i	0.228388	−	0.702907i	−0.769542	−	0.638597i	$-0.779515\pi$
$829$	6.57584	−	20.2384i	0.228388	−	0.702907i	0.997930	−	0.0643104i	$-0.0204848\pi$
$830$	7.83813	−	7.55724i	0.272065	−	0.262316i
$831$	3.58357	+	6.20692i	0.124313	+	0.215316i
$832$	0.376051	+	0.217113i	0.0130372	+	0.00752705i
$833$	−23.2039	+	7.53939i	−0.803966	+	0.261224i
$834$	−11.9354	−	5.31400i	−0.413290	−	0.184009i
$835$	−18.1080	+	21.5457i	−0.626654	+	0.745621i
$836$	1.60550			0.0555273
$837$	1.92292	+	5.22517i	0.0664657	+	0.180608i
$838$		−	26.5961i		−	0.918747i
$839$	14.7410	+	10.7100i	0.508916	+	0.369749i	0.812412	−	0.583084i	$-0.198154\pi$
$839$	14.7410	+	10.7100i	0.508916	+	0.369749i	−0.303496	+	0.952833i	$0.598154\pi$
$840$	3.38071	−	6.34610i	0.116646	−	0.218961i
$841$	23.6057	+	72.6509i	0.813990	+	2.50520i
$842$	12.1190	+	6.99691i	0.417648	+	0.241129i
$843$	−20.5190	+	11.8466i	−0.706712	+	0.408020i
$844$	−13.7367	+	15.2561i	−0.472835	+	0.525137i
$845$	10.7524	−	26.5528i	0.369895	−	0.913444i
$846$	−0.458340	−	0.509038i	−0.0157580	−	0.0175011i
$847$	−9.72177	−	21.8355i	−0.334044	−	0.750275i
$848$	1.34509	−	6.32814i	0.0461905	−	0.217309i
$849$	2.04628	−	19.4691i	0.0702282	−	0.668176i
$850$	1.33213	−	36.4948i	0.0456916	−	1.25176i
$851$	−0.0633934	+	0.0134747i	−0.00217310	+	0.000461906i
$852$	2.45495	+	3.37895i	0.0841052	+	0.115761i
$853$	5.56321	+	7.65710i	0.190481	+	0.262174i	0.893566	−	0.448931i	$-0.148195\pi$
$853$	5.56321	+	7.65710i	0.190481	+	0.262174i	−0.703086	+	0.711105i	$0.748195\pi$
$854$	11.5929	−	2.46414i	0.396699	−	0.0843211i
$855$	0.0648379	+	1.89972i	0.00221741	+	0.0649689i
$856$	0.833131	−	7.92671i	0.0284758	−	0.270929i
$857$	−4.63738	+	21.8172i	−0.158410	+	0.745260i	0.825184	+	0.564864i	$0.191071\pi$
$857$	−4.63738	+	21.8172i	−0.158410	+	0.745260i	−0.983594	+	0.180396i	$0.942262\pi$
$858$	−0.333567	−	0.749203i	−0.0113878	−	0.0255774i
$859$	−24.3156	−	27.0052i	−0.829636	−	0.921404i	0.168293	−	0.985737i	$-0.446175\pi$
$859$	−24.3156	−	27.0052i	−0.829636	−	0.921404i	−0.997928	+	0.0643331i	$0.979508\pi$
$860$	2.15168	+	0.871311i	0.0733716	+	0.0297114i
$861$	18.6988	−	20.7671i	0.637253	−	0.707741i
$862$	−18.6173	+	10.7487i	−0.634109	+	0.366103i
$863$	−21.8150	−	12.5949i	−0.742591	−	0.428735i	0.0804194	−	0.996761i	$-0.474374\pi$
$863$	−21.8150	−	12.5949i	−0.742591	−	0.428735i	−0.823011	+	0.568026i	$0.807707\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	−2.04042	+	3.83017i	−0.0693764	+	0.130230i
$866$	−19.4815	−	14.1542i	−0.662009	−	0.480978i
$867$			36.3459i			1.23437i
$868$	−16.6241	−	6.64777i	−0.564259	−	0.225640i
$869$	−0.976302			−0.0331188
$870$	17.5732	+	14.7693i	0.595786	+	0.500726i
$871$	−3.17165	−	1.41211i	−0.107467	−	0.0478475i
$872$	2.33793	−	0.759641i	0.0791725	−	0.0257247i
$873$	8.08335	+	4.66693i	0.273580	+	0.157952i
$874$	−0.0228401	−	0.0395602i	−0.000772577	−	0.00133814i
$875$	21.0632	+	29.1358i	0.712065	+	0.984971i
$876$	−1.39346	+	4.28862i	−0.0470805	+	0.144899i
$877$	−1.86976	+	1.68354i	−0.0631373	+	0.0568491i	−0.700095	−	0.714049i	$-0.746859\pi$
$877$	−1.86976	+	1.68354i	−0.0631373	+	0.0568491i	0.636958	+	0.770899i	$0.280192\pi$
$878$	1.40904	+	3.16475i	0.0475527	+	0.106805i
$879$	−26.3306	−	5.59675i	−0.888110	−	0.188774i
$880$	0.736628	−	4.15842i	0.0248317	−	0.140180i
$881$	−2.50275	−	23.8121i	−0.0843199	−	0.802250i	−0.952200	−	0.305476i	$-0.901184\pi$
$881$	−2.50275	−	23.8121i	−0.0843199	−	0.802250i	0.867880	−	0.496774i	$-0.165482\pi$
$882$	−0.694516	−	3.26744i	−0.0233856	−	0.110020i
$883$	27.5150	+	37.8711i	0.925952	+	1.27446i	0.961418	+	0.275093i	$0.0887085\pi$
$883$	27.5150	+	37.8711i	0.925952	+	1.27446i	−0.0354659	+	0.999371i	$0.511292\pi$
$884$	2.56581	−	1.86417i	0.0862976	−	0.0626989i
$885$	−0.947360	−	6.77965i	−0.0318451	−	0.227895i
$886$	−0.234832	−	2.23428i	−0.00788934	−	0.0750620i
$887$	−56.4522	−	5.93336i	−1.89548	−	0.199223i	−0.916057	−	0.401047i	$-0.868646\pi$
$887$	−56.4522	−	5.93336i	−1.89548	−	0.199223i	−0.979422	+	0.201824i	$0.935313\pi$
$888$	−0.250754	+	1.17970i	−0.00841475	+	0.0395883i
$889$	−7.11123	+	3.16612i	−0.238503	+	0.106188i
$890$	13.0457	−	10.1758i	0.437293	−	0.341095i
$891$	−0.583627	+	1.79622i	−0.0195522	+	0.0601756i
$892$	−9.42611	−	8.48731i	−0.315609	−	0.284176i
$893$	−0.504271	+	0.291141i	−0.0168748	+	0.00974265i
$894$	8.46335	−	14.6589i	0.283057	−	0.490269i
$895$	−8.87725	−	35.7248i	−0.296734	−	1.19415i
$896$	2.93765	+	1.30792i	0.0981399	+	0.0436947i
$897$	−0.0137153	+	0.0188775i	−0.000457942	+	0.000630303i
$898$		−	32.1565i		−	1.07308i
$899$	31.7935	−	47.5000i	1.06037	−	1.58421i
$900$	4.95024	+	0.703683i	0.165008	+	0.0234561i
$901$	−38.2279	−	27.7742i	−1.27356	−	0.925292i
$902$	6.67574	−	14.9940i	0.222278	−	0.499244i
$903$	3.17498	−	1.03161i	0.105657	−	0.0343299i
$904$	8.07983	−	13.9947i	0.268731	−	0.465456i
$905$	−11.0253	−	22.6506i	−0.366494	−	0.752933i
$906$	−10.9938	+	12.2099i	−0.365245	+	0.405645i
$907$	−1.39800	−	0.454236i	−0.0464197	−	0.0150827i	0.285715	−	0.958315i	$-0.407769\pi$
$907$	−1.39800	−	0.454236i	−0.0464197	−	0.0150827i	−0.332135	+	0.943232i	$0.607769\pi$
$908$	13.6977	−	12.3335i	0.454575	−	0.409301i
$909$	−5.03490	+	2.24168i	−0.166997	+	0.0743519i
$910$	−0.862985	+	3.00064i	−0.0286077	+	0.0994703i
$911$	2.99968	−	28.5400i	0.0993838	−	0.945574i	−0.825263	−	0.564748i	$-0.808973\pi$
$911$	2.99968	−	28.5400i	0.0993838	−	0.945574i	0.924647	−	0.380825i	$-0.124360\pi$
$912$	−0.845417	+	0.0888569i	−0.0279945	+	0.00294234i
$913$	−1.91203	−	8.99538i	−0.0632789	−	0.297704i
$914$	−0.883962	+	0.642236i	−0.0292388	+	0.0212433i
$915$	4.36176	+	6.99256i	0.144195	+	0.231167i
$916$	−17.5763	+	3.73595i	−0.580736	+	0.123439i
$917$	10.0720	−	1.05861i	0.332608	−	0.0349585i
$918$	−7.26382	−	0.763458i	−0.239742	−	0.0251979i
$919$	35.3152	+	7.50648i	1.16494	+	0.247616i	0.749500	−	0.662004i	$-0.230294\pi$
$919$	35.3152	+	7.50648i	1.16494	+	0.247616i	0.415441	+	0.909620i	$0.363627\pi$
$920$	−0.112945	+	0.0410076i	−0.00372368	+	0.00135198i
$921$	18.8770	+	20.9650i	0.622017	+	0.690820i
$922$	14.9013	+	4.84173i	0.490748	+	0.159454i
$923$	−1.34776	−	1.21353i	−0.0443622	−	0.0399439i
$924$	−3.03663	−	5.25960i	−0.0998979	−	0.173028i
$925$	−4.74607	−	3.72012i	−0.156050	−	0.122317i
$926$	5.90979	+	18.1885i	0.194208	+	0.597710i
$927$	3.55032	−	7.97415i	0.116608	−	0.261905i
$928$	−6.03417	+	8.30533i	−0.198081	+	0.272636i
$929$	−9.88848			−0.324431			−0.162215	−	0.986755i	$-0.551864\pi$
$929$	−9.88848			−0.324431			−0.162215	+	0.986755i	$0.551864\pi$
$930$	0.399986	−	12.4435i	0.0131161	−	0.408038i
$931$	−2.83962			−0.0930647
$932$	−2.84963	+	3.92218i	−0.0933427	+	0.128475i
$933$	11.4109	−	25.6294i	0.373577	−	0.839067i
$934$	7.74699	+	23.8428i	0.253489	+	0.780159i
$935$	−25.5583	−	17.2686i	−0.835844	−	0.564745i
$936$	0.217113	+	0.376051i	0.00709657	+	0.0122916i
$937$	20.7855	+	18.7154i	0.679034	+	0.611405i	0.934733	−	0.355352i	$-0.115639\pi$
$937$	20.7855	+	18.7154i	0.679034	+	0.611405i	−0.255699	+	0.966756i	$0.582306\pi$
$938$	−24.4520	−	7.94493i	−0.798385	−	0.259411i
$939$	13.5431	+	15.0411i	0.441961	+	0.490847i
$940$	0.522721	+	1.43970i	0.0170493	+	0.0469578i
$941$	−28.8447	−	6.13112i	−0.940309	−	0.199869i	−0.287835	−	0.957680i	$-0.592935\pi$
$941$	−28.8447	−	6.13112i	−0.940309	−	0.199869i	−0.652474	+	0.757811i	$0.726269\pi$
$942$	−5.33459	−	0.560688i	−0.173810	−	0.0182682i
$943$	−0.464428	+	0.0488134i	−0.0151239	+	0.00158958i
$944$	2.99451	−	0.636503i	0.0974630	−	0.0207164i
$945$	6.10083	−	3.80553i	0.198460	−	0.123794i
$946$	1.58626	−	1.15249i	0.0515739	−	0.0374706i
$947$	−1.83296	−	8.62339i	−0.0595631	−	0.280222i	0.938279	−	0.345879i	$-0.112419\pi$
$947$	−1.83296	−	8.62339i	−0.0595631	−	0.280222i	−0.997842	+	0.0656565i	$0.979086\pi$
$948$	0.514098	−	0.0540338i	0.0166971	−	0.00175494i
$949$	0.204674	−	1.94734i	0.00664399	−	0.0632133i
$950$	1.46002	−	3.99174i	0.0473692	−	0.129509i
$951$	−22.6733	+	10.0948i	−0.735232	+	0.327346i
$952$	17.4539	−	15.7156i	0.565685	−	0.509345i
$953$	27.9813	+	9.09168i	0.906404	+	0.294508i	0.724878	−	0.688878i	$-0.241896\pi$
$953$	27.9813	+	9.09168i	0.906404	+	0.294508i	0.181526	+	0.983386i	$0.441896\pi$
$954$	4.32895	−	4.80779i	0.140155	−	0.155658i
$955$	12.7670	+	26.2287i	0.413129	+	0.848741i
$956$	−7.11714	+	12.3272i	−0.230185	+	0.398692i
$957$	18.4399	−	5.99148i	0.596077	−	0.193677i
$958$	10.6636	−	23.9508i	0.344525	−	0.773816i
$959$	−50.4231	−	36.6345i	−1.62825	−	1.18299i
$960$	−0.157741	+	2.23050i	−0.00509108	+	0.0719890i
$961$	−30.9083	+	2.38276i	−0.997042	+	0.0768631i
$962$		−	0.523703i		−	0.0168849i
$963$	4.68487	−	6.44817i	0.150968	−	0.207789i
$964$	−16.8873	−	7.51873i	−0.543904	−	0.242162i
$965$	−4.15340	+	1.03208i	−0.133703	+	0.0332237i
$966$	−0.0863994	+	0.149648i	−0.00277986	+	0.00481485i
$967$	−16.1364	+	9.31635i	−0.518911	+	0.299594i	−0.736489	−	0.676449i	$-0.763518\pi$
$967$	−16.1364	+	9.31635i	−0.518911	+	0.299594i	0.217578	+	0.976043i	$0.430184\pi$
$968$	5.52378	+	4.97363i	0.177541	+	0.159859i
$969$	−1.91862	+	5.90491i	−0.0616350	+	0.189693i
$970$	−12.8366	−	16.4568i	−0.412157	−	0.528396i
$971$	−31.0388	+	13.8193i	−0.996081	+	0.443484i	−0.839017	−	0.544105i	$-0.816869\pi$
$971$	−31.0388	+	13.8193i	−0.996081	+	0.443484i	−0.157064	+	0.987588i	$0.550203\pi$
$972$	0.207912	−	0.978148i	0.00666877	−	0.0313741i
$973$	41.7822	+	4.39149i	1.33948	+	0.140785i
$974$	−1.21190	−	11.5304i	−0.0388316	−	0.369458i
$975$	−2.16608	+	0.148030i	−0.0693701	+	0.00474077i
$976$	−2.98177	+	2.16638i	−0.0954442	+	0.0693442i
$977$	−32.3848	−	44.5738i	−1.03608	−	1.42604i	−0.900282	−	0.435306i	$-0.856640\pi$
$977$	−32.3848	−	44.5738i	−1.03608	−	1.42604i	−0.135798	−	0.990736i	$-0.543360\pi$
$978$	−4.78186	−	22.4969i	−0.152907	−	0.719371i
$979$	−1.46073	−	13.8979i	−0.0466852	−	0.444180i
$980$	−1.30286	+	7.35494i	−0.0416184	+	0.234945i
$981$	2.40453	+	0.511099i	0.0767708	+	0.0163181i
$982$	14.2357	+	31.9739i	0.454279	+	1.02033i
$983$	22.8910	−	20.6111i	0.730109	−	0.657393i	−0.217778	−	0.975998i	$-0.569881\pi$
$983$	22.8910	−	20.6111i	0.730109	−	0.657393i	0.947888	+	0.318605i	$0.103214\pi$
$984$	−2.68544	+	8.26494i	−0.0856087	+	0.263477i
$985$	15.9244	+	16.5163i	0.507393	+	0.526252i
$986$	37.4904	+	64.9352i	1.19394	+	2.06796i
$987$	1.90755	+	1.10133i	0.0607181	+	0.0350556i
$988$	0.351058	−	0.114066i	0.0111687	−	0.00362892i
$989$	−0.0509643	−	0.0226908i	−0.00162057	−	0.000721525i
$990$	2.71715	−	3.23299i	0.0863567	−	0.102751i
$991$	−40.3678			−1.28233			−0.641163	−	0.767405i	$-0.721548\pi$
$991$	−40.3678			−1.28233			−0.641163	+	0.767405i	$0.721548\pi$
$992$	5.56364	−	0.214136i	0.176646	−	0.00679884i
$993$			1.40684i			0.0446446i
$994$	−10.8655	−	7.89427i	−0.344634	−	0.250391i
$995$	25.6461	+	13.6622i	0.813035	+	0.433122i
$996$	1.50468	+	4.63093i	0.0476777	+	0.146737i
$997$	−28.0778	−	16.2107i	−0.889233	−	0.513399i	−0.0155412	−	0.999879i	$-0.504947\pi$
$997$	−28.0778	−	16.2107i	−0.889233	−	0.513399i	−0.873691	+	0.486481i	$0.838280\pi$
$998$	18.9006	−	10.9123i	0.598287	−	0.345421i
$999$	−0.807011	+	0.896277i	−0.0255327	+	0.0283569i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bn.b.19.12	yes	144
5.4	even	2	inner	930.2.bn.b.19.4	✓	144
31.18	even	15	inner	930.2.bn.b.49.4	yes	144
155.49	even	30	inner	930.2.bn.b.49.12	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bn.b.19.4	✓	144	5.4	even	2	inner
930.2.bn.b.19.12	yes	144	1.1	even	1	trivial
930.2.bn.b.49.4	yes	144	31.18	even	15	inner
930.2.bn.b.49.12	yes	144	155.49	even	30	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bn (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{2} +(0.406737 - 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-1.25186 + 1.85280i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.38970 + 2.15169i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{2} +(0.406737 - 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-1.25186 + 1.85280i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.38970 + 2.15169i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +(0.763121 + 2.10182i) q^{10} +(1.84738 + 0.392674i) q^{11} +(-0.994522 - 0.104528i) q^{12} +(0.431848 - 0.0453891i) q^{13} +(3.14539 - 0.668572i) q^{14} +(1.18344 + 1.89723i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.51855 + 7.14422i) q^{17} +(-0.994522 + 0.104528i) q^{18} +(-0.0888569 + 0.845417i) q^{19} +(2.14896 + 0.618041i) q^{20} +(2.93765 - 1.30792i) q^{21} +(1.40355 - 1.26376i) q^{22} +(-0.0511067 - 0.0166056i) q^{23} +(-0.669131 + 0.743145i) q^{24} +(-1.86571 - 4.63887i) q^{25} +(0.217113 - 0.376051i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(1.30792 - 2.93765i) q^{28} +(8.30533 + 6.03417i) q^{29} +(2.23050 + 0.157741i) q^{30} +(-0.214136 - 5.56364i) q^{31} +1.00000i q^{32} +(1.11012 - 1.52796i) q^{33} +(6.67238 + 2.97073i) q^{34} +(-6.97821 + 1.73401i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.04448 - 0.603030i) q^{37} +(0.631728 + 0.568810i) q^{38} +(0.134183 - 0.412974i) q^{39} +(1.76313 - 1.37527i) q^{40} +(7.93895 - 3.53465i) q^{41} +(0.668572 - 3.14539i) q^{42} +(1.03247 + 0.108517i) q^{43} +(-0.197418 - 1.87831i) q^{44} +(2.21455 - 0.309452i) q^{45} +(-0.0434739 + 0.0315857i) q^{46} +(0.402620 + 0.554159i) q^{47} +(0.207912 + 0.978148i) q^{48} +(0.349171 + 3.32214i) q^{49} +(-4.84956 - 1.21727i) q^{50} +(7.14422 + 1.51855i) q^{51} +(-0.176616 - 0.396686i) q^{52} +(-4.80779 + 4.32895i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-3.04021 + 2.93126i) q^{55} +(-1.60783 - 2.78484i) q^{56} +(0.736185 + 0.425037i) q^{57} +(9.76350 - 3.17235i) q^{58} +(-2.79674 - 1.24519i) q^{59} +(1.43867 - 1.71179i) q^{60} +3.68567 q^{61} +(-4.62695 - 3.09699i) q^{62} -3.21565i q^{63} +(0.809017 + 0.587785i) q^{64} +(-0.456515 + 0.856947i) q^{65} +(-0.583627 - 1.79622i) q^{66} +(-6.92418 - 3.99768i) q^{67} +(6.32530 - 3.65191i) q^{68} +(-0.0359569 + 0.0399342i) q^{69} +(-2.69884 + 6.66472i) q^{70} +(-2.79470 - 3.10383i) q^{71} +(0.406737 + 0.913545i) q^{72} +(0.937540 - 4.41078i) q^{73} +(0.126068 - 1.19945i) q^{74} +(-4.99667 - 0.182388i) q^{75} +(0.831497 - 0.176740i) q^{76} +(3.56978 + 4.91338i) q^{77} +(-0.255232 - 0.351297i) q^{78} +(-0.505633 + 0.107476i) q^{79} +(-0.0762733 - 2.23477i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(1.80681 - 8.50036i) q^{82} +(-1.98050 - 4.44828i) q^{83} +(-2.15169 - 2.38970i) q^{84} +(-15.1378 - 6.12998i) q^{85} +(0.694666 - 0.771504i) q^{86} +(8.89057 - 5.13297i) q^{87} +(-1.63562 - 0.944328i) q^{88} +(-2.28647 - 7.03703i) q^{89} +(1.05133 - 1.97350i) q^{90} +(1.12965 + 0.820738i) q^{91} +0.0537367i q^{92} +(-5.16974 - 2.06731i) q^{93} +0.684978 q^{94} +(-1.45515 - 1.22297i) q^{95} +(0.913545 + 0.406737i) q^{96} +(-8.87702 + 2.88432i) q^{97} +(2.89290 + 1.67022i) q^{98} +(-0.944328 - 1.63562i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9}+O(q^{10}) \) 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9	\( 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9} - 18 q^{11} - 8 q^{14} - 36 q^{16} - 24 q^{19} - 2 q^{20} + 28 q^{21} - 18 q^{24} + 10 q^{25} - 12 q^{26} - 4 q^{30} - 4 q^{31} + 10 q^{34} - 2 q^{35} - 72 q^{36} + 16 q^{39} + 4 q^{41} - 2 q^{44} - 2 q^{45} - 2 q^{46} - 78 q^{49} + 32 q^{50} + 10 q^{51} + 36 q^{54} - 50 q^{55} - 12 q^{56} + 28 q^{59} + 88 q^{61} + 36 q^{64} - 124 q^{65} + 6 q^{66} - 46 q^{69} - 10 q^{70} + 140 q^{71} + 34 q^{74} - 32 q^{75} + 24 q^{76} + 16 q^{79} + 12 q^{80} + 18 q^{81} - 8 q^{84} + 74 q^{85} - 98 q^{86} + 148 q^{89} + 44 q^{91} - 108 q^{94} - 80 q^{95} + 18 q^{96} - 2 q^{99}+O(q^{100}) \) 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9 - 18 * q^11 - 8 * q^14 - 36 * q^16 - 24 * q^19 - 2 * q^20 + 28 * q^21 - 18 * q^24 + 10 * q^25 - 12 * q^26 - 4 * q^30 - 4 * q^31 + 10 * q^34 - 2 * q^35 - 72 * q^36 + 16 * q^39 + 4 * q^41 - 2 * q^44 - 2 * q^45 - 2 * q^46 - 78 * q^49 + 32 * q^50 + 10 * q^51 + 36 * q^54 - 50 * q^55 - 12 * q^56 + 28 * q^59 + 88 * q^61 + 36 * q^64 - 124 * q^65 + 6 * q^66 - 46 * q^69 - 10 * q^70 + 140 * q^71 + 34 * q^74 - 32 * q^75 + 24 * q^76 + 16 * q^79 + 12 * q^80 + 18 * q^81 - 8 * q^84 + 74 * q^85 - 98 * q^86 + 148 * q^89 + 44 * q^91 - 108 * q^94 - 80 * q^95 + 18 * q^96 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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