LMFDB - Embedded newform 418.2.v.a.13.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(13,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([9, 25]))

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

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

chi := DirichletCharacter("418.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.v (of order $90$, degree $24$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$10$ over $\Q(\zeta_{90})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{90}]$

Embedding invariants

Embedding label			13.8
Character	$\chi$	$=$	418.13
Dual form			418.2.v.a.193.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.374607 + 0.927184i) q^{2} +(0.682065 + 2.37864i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(-1.17948 + 0.627143i) q^{5} +(-1.94993 + 1.52345i) q^{6} +(1.45204 + 3.26133i) q^{7} +(-0.913545 - 0.406737i) q^{8} +(-2.64858 + 1.65502i) q^{9} +O(q^{10})$	\(q+(0.374607 + 0.927184i) q^{2} +(0.682065 + 2.37864i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(-1.17948 + 0.627143i) q^{5} +(-1.94993 + 1.52345i) q^{6} +(1.45204 + 3.26133i) q^{7} +(-0.913545 - 0.406737i) q^{8} +(-2.64858 + 1.65502i) q^{9} +(-1.02332 - 0.858667i) q^{10} +(3.15389 - 1.02616i) q^{11} +(-2.14298 - 1.23725i) q^{12} +(-0.0825347 - 2.36349i) q^{13} +(-2.47991 + 2.56802i) q^{14} +(-2.29623 - 2.37782i) q^{15} +(0.0348995 - 0.999391i) q^{16} +(0.552050 - 0.883465i) q^{17} +(-2.52668 - 1.83574i) q^{18} +(-3.95934 - 1.82309i) q^{19} +(0.412800 - 1.27047i) q^{20} +(-6.76715 + 5.67832i) q^{21} +(2.13290 + 2.53983i) q^{22} +(0.735339 - 4.17031i) q^{23} +(0.344384 - 2.45042i) q^{24} +(-1.79809 + 2.66578i) q^{25} +(2.16047 - 0.961902i) q^{26} +(-0.226459 - 0.203905i) q^{27} +(-3.31002 - 1.33733i) q^{28} +(1.11302 + 4.46407i) q^{29} +(1.34449 - 3.01978i) q^{30} +(4.72871 - 4.25775i) q^{31} +(0.939693 - 0.342020i) q^{32} +(4.59202 + 6.80206i) q^{33} +(1.02594 + 0.180900i) q^{34} +(-3.75798 - 2.93605i) q^{35} +(0.755558 - 3.03038i) q^{36} +(-2.90535 + 3.99887i) q^{37} +(0.207141 - 4.35397i) q^{38} +(5.56559 - 1.80837i) q^{39} +(1.33259 - 0.0931841i) q^{40} +(-0.0430701 + 0.0123501i) q^{41} +(-7.79986 - 4.14726i) q^{42} +(-1.43465 + 0.252967i) q^{43} +(-1.55589 + 2.92903i) q^{44} +(2.08603 - 3.61310i) q^{45} +(4.14211 - 0.880433i) q^{46} +(4.27470 + 0.298916i) q^{47} +(2.40100 - 0.598636i) q^{48} +(-3.84395 + 4.26914i) q^{49} +(-3.14524 - 0.668542i) q^{50} +(2.47798 + 0.710549i) q^{51} +(1.70119 + 1.64282i) q^{52} +(6.00514 - 11.2940i) q^{53} +(0.104224 - 0.286353i) q^{54} +(-3.07641 + 3.18828i) q^{55} -3.56997i q^{56} +(1.63594 - 10.6613i) q^{57} +(-3.72207 + 2.70424i) q^{58} +(0.698580 + 9.99015i) q^{59} +(3.30354 + 0.115362i) q^{60} +(0.555646 + 3.95363i) q^{61} +(5.71912 + 2.78940i) q^{62} +(-9.24340 - 6.23475i) q^{63} +(0.669131 + 0.743145i) q^{64} +(1.57959 + 2.73593i) q^{65} +(-4.58656 + 6.80574i) q^{66} +(-0.642603 + 0.765824i) q^{67} +(0.216595 + 1.01900i) q^{68} +(10.4212 - 1.09532i) q^{69} +(1.31450 - 4.58420i) q^{70} +(0.930136 + 1.74933i) q^{71} +(3.09275 - 0.434658i) q^{72} +(3.87956 - 2.61679i) q^{73} +(-4.79605 - 1.19579i) q^{74} +(-7.56734 - 2.45878i) q^{75} +(4.11453 - 1.43897i) q^{76} +(7.92621 + 8.79584i) q^{77} +(3.76160 + 4.48290i) q^{78} +(-2.79258 + 3.57433i) q^{79} +(0.585597 + 1.20065i) q^{80} +(-3.77674 + 7.74346i) q^{81} +(-0.0275852 - 0.0353074i) q^{82} +(1.31206 - 6.17278i) q^{83} +(0.923393 - 8.78550i) q^{84} +(-0.0970757 + 1.38825i) q^{85} +(-0.771975 - 1.23542i) q^{86} +(-9.85928 + 5.69226i) q^{87} +(-3.29859 - 0.345358i) q^{88} +(3.51836 + 9.66661i) q^{89} +(4.13145 + 0.580637i) q^{90} +(7.58827 - 3.70104i) q^{91} +(2.36798 + 3.51068i) q^{92} +(13.3529 + 8.34384i) q^{93} +(1.32418 + 4.07541i) q^{94} +(5.81331 - 0.332771i) q^{95} +(1.45447 + 2.00191i) q^{96} +(-15.4258 + 6.23245i) q^{97} +(-5.39824 - 1.96480i) q^{98} +(-6.65501 + 7.93760i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9}+O(q^{10}) $ 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9	$ 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9} - 3 q^{11} - 6 q^{13} - 18 q^{14} + 21 q^{15} + 21 q^{17} - 60 q^{18} + 45 q^{19} + 12 q^{20} + 48 q^{21} - 12 q^{22} + 12 q^{24} - 18 q^{25} - 96 q^{26} - 9 q^{27} - 6 q^{28} + 18 q^{29} + 9 q^{31} + 87 q^{33} - 24 q^{34} - 36 q^{35} - 12 q^{36} - 36 q^{38} + 60 q^{41} - 6 q^{42} - 12 q^{43} + 18 q^{44} + 48 q^{45} + 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} - 21 q^{50} - 75 q^{51} + 3 q^{52} - 39 q^{53} + 27 q^{54} - 126 q^{55} - 90 q^{57} - 24 q^{58} + 69 q^{59} - 42 q^{60} + 66 q^{61} - 45 q^{62} - 9 q^{63} + 30 q^{64} - 12 q^{66} - 9 q^{67} + 12 q^{68} - 54 q^{69} + 9 q^{70} + 48 q^{71} + 6 q^{72} - 12 q^{74} + 72 q^{77} - 36 q^{79} - 27 q^{81} + 45 q^{82} + 36 q^{83} + 36 q^{84} - 210 q^{85} + 3 q^{86} + 216 q^{87} + 3 q^{88} + 18 q^{89} - 96 q^{90} - 108 q^{91} - 30 q^{92} + 147 q^{93} - 18 q^{94} + 66 q^{95} - 9 q^{97} - 12 q^{98} - 42 q^{99}+O(q^{100}) $ 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9 - 3 * q^11 - 6 * q^13 - 18 * q^14 + 21 * q^15 + 21 * q^17 - 60 * q^18 + 45 * q^19 + 12 * q^20 + 48 * q^21 - 12 * q^22 + 12 * q^24 - 18 * q^25 - 96 * q^26 - 9 * q^27 - 6 * q^28 + 18 * q^29 + 9 * q^31 + 87 * q^33 - 24 * q^34 - 36 * q^35 - 12 * q^36 - 36 * q^38 + 60 * q^41 - 6 * q^42 - 12 * q^43 + 18 * q^44 + 48 * q^45 + 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 - 21 * q^50 - 75 * q^51 + 3 * q^52 - 39 * q^53 + 27 * q^54 - 126 * q^55 - 90 * q^57 - 24 * q^58 + 69 * q^59 - 42 * q^60 + 66 * q^61 - 45 * q^62 - 9 * q^63 + 30 * q^64 - 12 * q^66 - 9 * q^67 + 12 * q^68 - 54 * q^69 + 9 * q^70 + 48 * q^71 + 6 * q^72 - 12 * q^74 + 72 * q^77 - 36 * q^79 - 27 * q^81 + 45 * q^82 + 36 * q^83 + 36 * q^84 - 210 * q^85 + 3 * q^86 + 216 * q^87 + 3 * q^88 + 18 * q^89 - 96 * q^90 - 108 * q^91 - 30 * q^92 + 147 * q^93 - 18 * q^94 + 66 * q^95 - 9 * q^97 - 12 * q^98 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	0.374607	+	0.927184i	0.264887	+	0.655618i
$2$	0.374607	+	0.927184i	0.264887	+	0.655618i
$3$	0.682065	+	2.37864i	0.393790	+	1.37331i	0.869598	+	0.493760i	$0.164378\pi$
$3$	0.682065	+	2.37864i	0.393790	+	1.37331i	−0.475808	+	0.879549i	$0.657844\pi$
$4$	−0.719340	+	0.694658i	−0.359670	+	0.347329i
$5$	−1.17948	+	0.627143i	−0.527481	+	0.280467i	−0.711779	−	0.702404i	$-0.752110\pi$
$5$	−1.17948	+	0.627143i	−0.527481	+	0.280467i	0.184297	+	0.982871i	$0.440999\pi$
$6$	−1.94993	+	1.52345i	−0.796057	+	0.621948i
$7$	1.45204	+	3.26133i	0.548819	+	1.23267i	0.948723	+	0.316110i	$0.102377\pi$
$7$	1.45204	+	3.26133i	0.548819	+	1.23267i	−0.399904	+	0.916557i	$0.630956\pi$
$8$	−0.913545	−	0.406737i	−0.322987	−	0.143803i
$9$	−2.64858	+	1.65502i	−0.882860	+	0.551672i
$10$	−1.02332	−	0.858667i	−0.323602	−	0.271534i
$11$	3.15389	−	1.02616i	0.950932	−	0.309399i
$11$	3.15389	−	1.02616i	0.950932	−	0.309399i
$12$	−2.14298	−	1.23725i	−0.618625	−	0.357163i
$13$	−0.0825347	−	2.36349i	−0.0228910	−	0.655513i	−0.955563	−	0.294787i	$-0.904751\pi$
$13$	−0.0825347	−	2.36349i	−0.0228910	−	0.655513i	0.932672	−	0.360726i	$-0.117471\pi$
$14$	−2.47991	+	2.56802i	−0.662784	+	0.686333i
$15$	−2.29623	−	2.37782i	−0.592885	−	0.613950i
$16$	0.0348995	−	0.999391i	0.00872487	−	0.249848i
$17$	0.552050	−	0.883465i	0.133892	−	0.214272i	−0.774308	−	0.632809i	$-0.781902\pi$
$17$	0.552050	−	0.883465i	0.133892	−	0.214272i	0.908199	+	0.418538i	$0.137457\pi$
$18$	−2.52668	−	1.83574i	−0.595544	−	0.432688i
$19$	−3.95934	−	1.82309i	−0.908335	−	0.418244i
$19$	−3.95934	−	1.82309i	−0.908335	−	0.418244i
$20$	0.412800	−	1.27047i	0.0923048	−	0.284085i
$21$	−6.76715	+	5.67832i	−1.47671	+	1.23911i
$22$	2.13290	+	2.53983i	0.454737	+	0.541493i
$23$	0.735339	−	4.17031i	0.153329	−	0.869570i	−0.806969	−	0.590594i	$-0.798894\pi$
$23$	0.735339	−	4.17031i	0.153329	−	0.869570i	0.960298	−	0.278977i	$-0.0899952\pi$
$24$	0.344384	−	2.45042i	0.0702970	−	0.500189i
$25$	−1.79809	+	2.66578i	−0.359618	+	0.533156i
$26$	2.16047	−	0.961902i	0.423703	−	0.188645i
$27$	−0.226459	−	0.203905i	−0.0435821	−	0.0392415i
$28$	−3.31002	−	1.33733i	−0.625535	−	0.252732i
$29$	1.11302	+	4.46407i	0.206682	+	0.828957i	0.980656	+	0.195740i	$0.0627107\pi$
$29$	1.11302	+	4.46407i	0.206682	+	0.828957i	−0.773974	+	0.633218i	$0.781734\pi$
$30$	1.34449	−	3.01978i	0.245469	−	0.551333i
$31$	4.72871	−	4.25775i	0.849301	−	0.764714i	−0.124475	−	0.992223i	$-0.539725\pi$
$31$	4.72871	−	4.25775i	0.849301	−	0.764714i	0.973776	+	0.227509i	$0.0730580\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	4.59202	+	6.80206i	0.799368	+	1.18409i
$34$	1.02594	+	0.180900i	0.175947	+	0.0310241i
$35$	−3.75798	−	2.93605i	−0.635214	−	0.496283i
$36$	0.755558	−	3.03038i	0.125926	−	0.505063i
$37$	−2.90535	+	3.99887i	−0.477636	+	0.657410i	−0.978048	−	0.208378i	$-0.933182\pi$
$37$	−2.90535	+	3.99887i	−0.477636	+	0.657410i	0.500412	+	0.865787i	$0.333182\pi$
$38$	0.207141	−	4.35397i	0.0336027	−	0.706308i
$39$	5.56559	−	1.80837i	0.891208	−	0.289571i
$40$	1.33259	−	0.0931841i	0.210702	−	0.0147337i
$41$	−0.0430701	+	0.0123501i	−0.00672642	+	0.00192877i	−0.278999	−	0.960291i	$-0.590003\pi$
$41$	−0.0430701	+	0.0123501i	−0.00672642	+	0.00192877i	0.272272	+	0.962220i	$0.412225\pi$
$42$	−7.79986	−	4.14726i	−1.20355	−	0.639936i
$43$	−1.43465	+	0.252967i	−0.218782	+	0.0385771i	−0.281964	−	0.959425i	$-0.590986\pi$
$43$	−1.43465	+	0.252967i	−0.218782	+	0.0385771i	0.0631828	+	0.998002i	$0.479875\pi$
$44$	−1.55589	+	2.92903i	−0.234559	+	0.441568i
$45$	2.08603	−	3.61310i	0.310966	−	0.538610i
$46$	4.14211	−	0.880433i	0.610721	−	0.129813i
$47$	4.27470	+	0.298916i	0.623530	+	0.0436014i	0.378027	−	0.925795i	$-0.376603\pi$
$47$	4.27470	+	0.298916i	0.623530	+	0.0436014i	0.245502	+	0.969396i	$0.421047\pi$
$48$	2.40100	−	0.598636i	0.346554	−	0.0864056i
$49$	−3.84395	+	4.26914i	−0.549136	+	0.609877i
$50$	−3.14524	−	0.668542i	−0.444805	−	0.0945461i
$51$	2.47798	+	0.710549i	0.346987	+	0.0994968i
$52$	1.70119	+	1.64282i	0.235912	+	0.227818i
$53$	6.00514	−	11.2940i	0.824869	−	1.55135i	−0.00937295	−	0.999956i	$-0.502984\pi$
$53$	6.00514	−	11.2940i	0.824869	−	1.55135i	0.834242	−	0.551398i	$-0.185905\pi$
$54$	0.104224	−	0.286353i	0.0141831	−	0.0389678i
$55$	−3.07641	+	3.18828i	−0.414823	+	0.429907i
$56$		−	3.56997i		−	0.477057i
$57$	1.63594	−	10.6613i	0.216686	−	1.41212i
$58$	−3.72207	+	2.70424i	−0.488732	+	0.355085i
$59$	0.698580	+	9.99015i	0.0909473	+	1.30061i	0.801939	+	0.597406i	$0.203802\pi$
$59$	0.698580	+	9.99015i	0.0909473	+	1.30061i	−0.710991	+	0.703201i	$0.751753\pi$
$60$	3.30354	+	0.115362i	0.426485	+	0.0148932i
$61$	0.555646	+	3.95363i	0.0711432	+	0.506210i	0.992948	+	0.118555i	$0.0378261\pi$
$61$	0.555646	+	3.95363i	0.0711432	+	0.506210i	−0.921804	+	0.387655i	$0.873285\pi$
$62$	5.71912	+	2.78940i	0.726329	+	0.354254i
$63$	−9.24340	−	6.23475i	−1.16456	−	0.785505i
$64$	0.669131	+	0.743145i	0.0836413	+	0.0928931i
$65$	1.57959	+	2.73593i	0.195924	+	0.339351i
$66$	−4.58656	+	6.80574i	−0.564566	+	0.837729i
$67$	−0.642603	+	0.765824i	−0.0785064	+	0.0935603i	−0.803868	−	0.594808i	$-0.797228\pi$
$67$	−0.642603	+	0.765824i	−0.0785064	+	0.0935603i	0.725362	+	0.688368i	$0.241673\pi$
$68$	0.216595	+	1.01900i	0.0262660	+	0.123572i
$69$	10.4212	−	1.09532i	1.25457	−	0.131860i
$70$	1.31450	−	4.58420i	0.157113	−	0.547917i
$71$	0.930136	+	1.74933i	0.110387	+	0.207607i	0.932018	−	0.362412i	$-0.118047\pi$
$71$	0.930136	+	1.74933i	0.110387	+	0.207607i	−0.821631	+	0.570020i	$0.806936\pi$
$72$	3.09275	−	0.434658i	0.364485	−	0.0512250i
$73$	3.87956	−	2.61679i	0.454068	−	0.306273i	−0.310782	−	0.950481i	$-0.600591\pi$
$73$	3.87956	−	2.61679i	0.454068	−	0.306273i	0.764850	+	0.644209i	$0.222813\pi$
$74$	−4.79605	−	1.19579i	−0.557529	−	0.139008i
$75$	−7.56734	−	2.45878i	−0.873802	−	0.283915i
$76$	4.11453	−	1.43897i	0.471969	−	0.165061i
$77$	7.92621	+	8.79584i	0.903275	+	1.00238i
$78$	3.76160	+	4.48290i	0.425917	+	0.507588i
$79$	−2.79258	+	3.57433i	−0.314189	+	0.402144i	−0.919021	−	0.394210i	$-0.871018\pi$
$79$	−2.79258	+	3.57433i	−0.314189	+	0.402144i	0.604831	+	0.796354i	$0.293241\pi$
$80$	0.585597	+	1.20065i	0.0654718	+	0.134237i
$81$	−3.77674	+	7.74346i	−0.419638	+	0.860384i
$82$	−0.0275852	−	0.0353074i	−0.00304627	−	0.00389905i
$83$	1.31206	−	6.17278i	0.144018	−	0.677551i	−0.845599	−	0.533819i	$-0.820756\pi$
$83$	1.31206	−	6.17278i	0.144018	−	0.677551i	0.989617	−	0.143732i	$-0.0459103\pi$
$84$	0.923393	−	8.78550i	0.100750	−	0.958576i
$85$	−0.0970757	+	1.38825i	−0.0105293	+	0.150577i
$86$	−0.771975	−	1.23542i	−0.0832442	−	0.133219i
$87$	−9.85928	+	5.69226i	−1.05703	+	0.610274i
$88$	−3.29859	−	0.345358i	−0.351631	−	0.0368153i
$89$	3.51836	+	9.66661i	0.372945	+	1.02466i	0.974217	+	0.225614i	$0.0724387\pi$
$89$	3.51836	+	9.66661i	0.372945	+	1.02466i	−0.601272	+	0.799045i	$0.705339\pi$
$90$	4.13145	+	0.580637i	0.435493	+	0.0612046i
$91$	7.58827	−	3.70104i	0.795466	−	0.387975i
$92$	2.36798	+	3.51068i	0.246879	+	0.366014i
$93$	13.3529	+	8.34384i	1.38464	+	0.865216i
$94$	1.32418	+	4.07541i	0.136579	+	0.420347i
$95$	5.81331	−	0.332771i	0.596433	−	0.0341415i
$96$	1.45447	+	2.00191i	0.148447	+	0.204319i
$97$	−15.4258	+	6.23245i	−1.56626	+	0.632809i	−0.983674	−	0.179961i	$-0.942403\pi$
$97$	−15.4258	+	6.23245i	−1.56626	+	0.632809i	−0.582584	+	0.812770i	$0.697958\pi$
$98$	−5.39824	−	1.96480i	−0.545305	−	0.198475i
$99$	−6.65501	+	7.93760i	−0.668854	+	0.797759i
$100$	−0.558367	−	3.16666i	−0.0558367	−	0.316666i
$101$	2.57253	−	0.0898347i	0.255976	−	0.00893889i	0.0933760	−	0.995631i	$-0.470234\pi$
$101$	2.57253	−	0.0898347i	0.255976	−	0.00893889i	0.162600	+	0.986692i	$0.448012\pi$
$102$	0.269458	+	2.56372i	0.0266803	+	0.253846i
$103$	4.09697	+	0.430609i	0.403687	+	0.0424292i	0.304196	−	0.952609i	$-0.401612\pi$
$103$	4.09697	+	0.430609i	0.403687	+	0.0424292i	0.0994904	+	0.995039i	$0.468279\pi$
$104$	−0.885917	+	2.19272i	−0.0868713	+	0.215014i
$105$	4.42063	−	10.9415i	0.431410	−	1.06778i
$106$	12.7212	+	1.33705i	1.23559	+	0.129866i
$107$	−1.83266	−	17.4366i	−0.177170	−	1.68566i	−0.616515	−	0.787343i	$-0.711456\pi$
$107$	−1.83266	−	17.4366i	−0.177170	−	1.68566i	0.439345	−	0.898319i	$-0.355211\pi$
$108$	0.304545	−	0.0106350i	0.0293049	−	0.00102335i
$109$	−3.36062	−	19.0590i	−0.321889	−	1.82552i	−0.530692	−	0.847564i	$-0.678068\pi$
$109$	−3.36062	−	19.0590i	−0.321889	−	1.82552i	0.208804	−	0.977958i	$-0.433043\pi$
$110$	−4.10856	−	1.65805i	−0.391736	−	0.158089i
$111$	−11.4935	−	4.18329i	−1.09092	−	0.397061i
$112$	3.31002	−	1.33733i	0.312767	−	0.126366i
$113$	8.43182	+	11.6054i	0.793199	+	1.09174i	0.993702	+	0.112052i	$0.0357422\pi$
$113$	8.43182	+	11.6054i	0.793199	+	1.09174i	−0.200503	+	0.979693i	$0.564258\pi$
$114$	10.4978	−	2.47698i	0.983212	−	0.231990i
$115$	1.74806	+	5.37998i	0.163008	+	0.501686i
$116$	−3.90164	−	2.43802i	−0.362258	−	0.226364i
$117$	4.13021	+	6.12329i	0.381838	+	0.566098i
$118$	−9.00102	+	4.39009i	−0.828611	+	0.404140i
$119$	3.68287	+	0.517594i	0.337608	+	0.0474477i
$120$	1.13057	+	3.10621i	0.103206	+	0.283557i
$121$	8.89399	−	6.47278i	0.808545	−	0.588434i
$122$	−3.45759	+	1.99624i	−0.313036	+	0.180731i
$123$	−0.0587531	−	0.0940247i	−0.00529759	−	0.00847792i
$124$	−0.443868	+	6.34760i	−0.0398605	+	0.570032i
$125$	1.14717	−	10.9146i	0.102606	−	0.976227i
$126$	2.31812	−	10.9059i	0.206515	−	0.971575i
$127$	−10.4972	−	13.4358i	−0.931474	−	1.19223i	−0.981107	−	0.193465i	$-0.938027\pi$
$127$	−10.4972	−	13.4358i	−0.931474	−	1.19223i	0.0496328	−	0.998768i	$-0.484195\pi$
$128$	−0.438371	+	0.898794i	−0.0387469	+	0.0794429i
$129$	−1.58024	−	3.23997i	−0.139132	−	0.285263i
$130$	−1.94499	+	2.48947i	−0.170587	+	0.218341i
$131$	2.80299	+	3.34048i	0.244899	+	0.291859i	0.874466	−	0.485087i	$-0.161212\pi$
$131$	2.80299	+	3.34048i	0.244899	+	0.291859i	−0.629567	+	0.776946i	$0.716768\pi$
$132$	−8.02833	−	1.70311i	−0.698776	−	0.148236i
$133$	0.196574	−	15.5599i	0.0170451	−	1.34921i
$134$	−0.950783	−	0.308928i	−0.0821352	−	0.0266873i
$135$	0.394983	+	0.0984802i	0.0339947	+	0.00847583i
$136$	−0.863661	+	0.582546i	−0.0740583	+	0.0499529i
$137$	21.3419	−	2.99941i	1.82336	−	0.256257i	0.857345	−	0.514742i	$-0.172112\pi$
$137$	21.3419	−	2.99941i	1.82336	−	0.256257i	0.966015	+	0.258485i	$0.0832233\pi$
$138$	4.91942	+	9.25208i	0.418769	+	0.787590i
$139$	−1.92544	+	6.71480i	−0.163313	+	0.569542i	0.836455	+	0.548035i	$0.184624\pi$
$139$	−1.92544	+	6.71480i	−0.163313	+	0.569542i	−0.999769	+	0.0215064i	$0.993154\pi$
$140$	4.74281	−	0.498490i	0.400841	−	0.0421301i
$141$	2.20461	+	10.3719i	0.185662	+	0.873469i
$142$	−1.27352	+	1.51772i	−0.106871	+	0.127364i
$143$	−2.68562	−	7.36947i	−0.224583	−	0.616266i
$144$	1.56157	+	2.70473i	0.130131	+	0.225394i
$145$	−4.11240	−	4.56728i	−0.341516	−	0.379292i
$146$	3.87956	+	2.61679i	0.321074	+	0.216567i
$147$	−12.7766	−	6.23155i	−1.05379	−	0.513970i
$148$	−0.687915	−	4.89477i	−0.0565462	−	0.402347i
$149$	12.3485	+	0.431217i	1.01162	+	0.0353267i	0.535912	−	0.844274i	$-0.319968\pi$
$149$	12.3485	+	0.431217i	1.01162	+	0.0353267i	0.475713	+	0.879601i	$0.342190\pi$
$150$	−0.555037	−	7.93739i	−0.0453186	−	0.648086i
$151$	7.16483	−	5.20555i	0.583066	−	0.423622i	−0.256762	−	0.966475i	$-0.582656\pi$
$151$	7.16483	−	5.20555i	0.583066	−	0.423622i	0.839828	+	0.542853i	$0.182656\pi$
$152$	2.87552	+	3.27588i	0.233235	+	0.265709i
$153$			3.25358i			0.263036i
$154$	−5.18615	+	10.6440i	−0.417912	+	0.857721i
$155$	−2.90722	+	7.98752i	−0.233513	+	0.641573i
$156$	−2.74735	+	5.16702i	−0.219964	+	0.413693i
$157$	−9.92629	−	9.58571i	−0.792204	−	0.765023i	0.183756	−	0.982972i	$-0.441174\pi$
$157$	−9.92629	−	9.58571i	−0.792204	−	0.765023i	−0.975960	+	0.217949i	$0.930063\pi$
$158$	−4.36018	−	1.25026i	−0.346878	−	0.0994655i
$159$	30.9603	+	6.58082i	2.45531	+	0.521893i
$160$	−0.893857	+	0.992729i	−0.0706656	+	0.0784821i
$161$	14.6685	−	3.65727i	1.15604	−	0.288233i
$162$	−8.59440	−	0.600979i	−0.675240	−	0.0472174i
$163$	−20.8129	+	4.42391i	−1.63019	+	0.346507i	−0.930031	−	0.367481i	$-0.880220\pi$
$163$	−20.8129	+	4.42391i	−1.63019	+	0.346507i	−0.700157	+	0.713988i	$0.746887\pi$
$164$	0.0224029	−	0.0388029i	0.00174937	−	0.00303000i
$165$	−9.68207	−	5.14307i	−0.753748	−	0.400387i
$166$	6.21481	−	1.09584i	0.482363	−	0.0850536i
$167$	−20.0973	−	10.6859i	−1.55518	−	0.826903i	−0.555191	−	0.831723i	$-0.687355\pi$
$167$	−20.0973	−	10.6859i	−1.55518	−	0.826903i	−0.999988	+	0.00481966i	$0.998466\pi$
$168$	8.49168	−	2.43495i	0.655147	−	0.187861i
$169$	7.38908	−	0.516695i	0.568391	−	0.0397457i
$170$	−1.32353	+	0.430039i	−0.101510	+	0.0329825i
$171$	13.5039	−	1.72418i	1.03267	−	0.131852i
$172$	0.856273	−	1.17856i	0.0652902	−	0.0898642i
$173$	−2.69903	+	10.8252i	−0.205204	+	0.823027i	0.776108	+	0.630600i	$0.217191\pi$
$173$	−2.69903	+	10.8252i	−0.205204	+	0.823027i	−0.981311	+	0.192426i	$0.938364\pi$
$174$	−8.97112	−	7.00901i	−0.680099	−	0.531351i
$175$	−11.3049	−	1.99336i	−0.854569	−	0.150683i
$176$	−0.915465	−	3.18778i	−0.0690058	−	0.240288i
$177$	−23.2865	+	8.47560i	−1.75032	+	0.637065i
$178$	−7.64472	+	6.88334i	−0.572996	+	0.515928i
$179$	−0.577586	+	1.29728i	−0.0431708	+	0.0969632i	−0.933843	−	0.357682i	$-0.883567\pi$
$179$	−0.577586	+	1.29728i	−0.0431708	+	0.0969632i	0.890673	+	0.454645i	$0.150234\pi$
$180$	1.00931	+	4.04812i	0.0752296	+	0.301729i
$181$	−22.7967	−	9.21047i	−1.69447	−	0.684609i	−0.695056	−	0.718956i	$-0.744620\pi$
$181$	−22.7967	−	9.21047i	−1.69447	−	0.684609i	−0.999410	+	0.0343469i	$0.989065\pi$
$182$	6.27416	+	5.64928i	0.465072	+	0.418753i
$183$	−9.02528	+	4.01831i	−0.667168	+	0.297042i
$184$	−2.36798	+	3.51068i	−0.174570	+	0.258811i
$185$	0.918950	−	6.53867i	0.0675625	−	0.480732i
$186$	−2.73418	+	15.5063i	−0.200480	+	1.13698i
$187$	0.834528	−	3.35284i	0.0610267	−	0.245184i
$188$	−3.28261	+	2.75444i	−0.239409	+	0.200888i
$189$	0.336174	−	1.03464i	0.0244530	−	0.0752587i
$190$	2.48624	+	5.26535i	0.180371	+	0.381989i
$191$	−5.52865	−	4.01680i	−0.400039	−	0.290645i	0.369518	−	0.929224i	$-0.379523\pi$
$191$	−5.52865	−	4.01680i	−0.400039	−	0.290645i	−0.769557	+	0.638578i	$0.779523\pi$
$192$	−1.31129	+	2.09849i	−0.0946338	+	0.151446i
$193$	−0.153752	+	4.40288i	−0.0110673	+	0.316926i	0.981214	+	0.192921i	$0.0617961\pi$
$193$	−0.153752	+	4.40288i	−0.0110673	+	0.316926i	−0.992282	+	0.124005i	$0.960426\pi$
$194$	−11.5572	−	11.9679i	−0.829762	−	0.859244i
$195$	−5.43042	+	5.62337i	−0.388880	+	0.402698i
$196$	−0.200487	−	5.74119i	−0.0143205	−	0.410085i
$197$	5.24957	+	3.03084i	0.374016	+	0.215938i	0.675212	−	0.737624i	$-0.264052\pi$
$197$	5.24957	+	3.03084i	0.374016	+	0.215938i	−0.301195	+	0.953562i	$0.597386\pi$
$198$	−9.85262	−	3.19694i	−0.700195	−	0.227197i
$199$	13.3247	+	11.1807i	0.944561	+	0.792581i	0.978373	−	0.206847i	$-0.0663203\pi$
$199$	13.3247	+	11.1807i	0.944561	+	0.792581i	−0.0338121	+	0.999428i	$0.510765\pi$
$200$	2.72691	−	1.70396i	0.192821	−	0.120488i
$201$	−2.25992	−	1.00618i	−0.159402	−	0.0709705i
$202$	1.04698	+	2.35155i	0.0736652	+	0.165455i
$203$	−12.9427	+	10.1119i	−0.908397	+	0.709718i
$204$	−2.27610	+	1.21022i	−0.159359	+	0.0847326i
$205$	0.0430552	−	0.0415779i	0.00300710	−	0.00290393i
$206$	1.13550	+	3.95996i	0.0791140	+	0.275903i
$207$	4.95433	+	12.2624i	0.344350	+	0.852296i
$208$	−2.36493			−0.163978
$209$	−14.3581	−	1.68689i	−0.993169	−	0.116685i
$210$	11.8007			0.814328
$211$	1.10447	+	2.73366i	0.0760348	+	0.188193i	0.960414	−	0.278576i	$-0.0898625\pi$
$211$	1.10447	+	2.73366i	0.0760348	+	0.188193i	−0.884379	+	0.466769i	$0.845418\pi$
$212$	3.52575	+	12.2958i	0.242150	+	0.844477i
$213$	−3.52662	+	3.40562i	−0.241640	+	0.233349i
$214$	15.4804	−	8.23109i	1.05822	−	0.562666i
$215$	1.53350	−	1.19810i	0.104584	−	0.0817096i
$216$	0.123945	+	0.278386i	0.00843341	+	0.0189417i
$217$	20.7522	+	9.23947i	1.40875	+	0.627216i
$218$	16.4123	−	10.2555i	1.11158	−	0.694593i
$219$	8.87052	+	7.44325i	0.599415	+	0.502969i
$220$	−0.00177792	−	4.43051i	−0.000119868	−	0.298705i
$221$	−2.13362	−	1.23185i	−0.143523	−	0.0828629i
$222$	−0.426860	−	12.2237i	−0.0286490	−	0.820400i
$223$	17.6026	−	18.2280i	1.17876	−	1.22064i	0.208643	−	0.977992i	$-0.433095\pi$
$223$	17.6026	−	18.2280i	1.17876	−	1.22064i	0.970115	−	0.242647i	$-0.0780156\pi$
$224$	2.47991	+	2.56802i	0.165696	+	0.171583i
$225$	0.350479	−	10.0364i	0.0233652	−	0.669093i
$226$	−7.60173	+	12.1653i	−0.505659	+	0.809224i
$227$	−9.75660	−	7.08859i	−0.647568	−	0.470486i	0.214874	−	0.976642i	$-0.431066\pi$
$227$	−9.75660	−	7.08859i	−0.647568	−	0.470486i	−0.862442	+	0.506156i	$0.831066\pi$
$228$	6.22917	+	8.80552i	0.412537	+	0.583160i
$229$	−5.38226	+	16.5649i	−0.355670	+	1.09464i	0.599950	+	0.800037i	$0.295187\pi$
$229$	−5.38226	+	16.5649i	−0.355670	+	1.09464i	−0.955620	+	0.294602i	$0.904813\pi$
$230$	−4.33339	+	3.63615i	−0.285736	+	0.239761i
$231$	−15.5160	+	24.8529i	−1.02088	+	1.63520i
$232$	0.798909	−	4.53084i	0.0524509	−	0.297464i
$233$	3.98024	−	28.3209i	0.260754	−	1.85536i	−0.216091	−	0.976373i	$-0.569331\pi$
$233$	3.98024	−	28.3209i	0.260754	−	1.85536i	0.476844	−	0.878988i	$-0.341780\pi$
$234$	−4.13021	+	6.12329i	−0.270000	+	0.400292i
$235$	−5.22941	+	2.32828i	−0.341129	+	0.151880i
$236$	−7.44226	−	6.70104i	−0.484450	−	0.436201i
$237$	−10.4068	−	4.20461i	−0.675993	−	0.273119i
$238$	0.899723	+	3.60859i	0.0583204	+	0.233910i
$239$	7.80519	−	17.5308i	0.504876	−	1.13397i	−0.463867	−	0.885905i	$-0.653539\pi$
$239$	7.80519	−	17.5308i	0.504876	−	1.13397i	0.968743	−	0.248065i	$-0.0797948\pi$
$240$	−2.45651	+	2.21185i	−0.158567	+	0.142774i
$241$	−12.6046	+	4.58770i	−0.811934	+	0.295520i	−0.714423	−	0.699714i	$-0.753311\pi$
$241$	−12.6046	+	4.58770i	−0.811934	+	0.295520i	−0.0975117	+	0.995234i	$0.531088\pi$
$242$	9.33320	+	5.82162i	0.599961	+	0.374228i
$243$	−21.8952	−	3.86071i	−1.40458	−	0.247665i
$244$	−3.14612	−	2.45802i	−0.201410	−	0.157358i
$245$	1.85652	−	7.44608i	0.118609	−	0.475713i
$246$	0.0651689	−	0.0896972i	0.00415501	−	0.00571889i
$247$	−3.98205	+	9.50831i	−0.253372	+	0.604999i
$248$	−6.05167	+	1.96631i	−0.384282	+	0.124861i
$249$	15.5777	−	1.08930i	0.987200	−	0.0690317i
$250$	10.5495	−	3.02503i	0.667211	−	0.191320i
$251$	−2.79123	−	1.48412i	−0.176181	−	0.0936771i	0.379039	−	0.925381i	$-0.376255\pi$
$251$	−2.79123	−	1.48412i	−0.176181	−	0.0936771i	−0.555220	+	0.831704i	$0.687366\pi$
$252$	10.9802	−	1.93610i	0.691685	−	0.121963i
$253$	−1.96023	−	13.9073i	−0.123239	−	0.874342i
$254$	8.52513	−	14.7660i	0.534914	−	0.926498i
$255$	−3.36835	+	0.715966i	−0.210935	+	0.0448355i
$256$	−0.997564	−	0.0697565i	−0.0623478	−	0.00435978i
$257$	−6.85273	+	1.70858i	−0.427462	+	0.106578i	−0.449711	−	0.893174i	$-0.648473\pi$
$257$	−6.85273	+	1.70858i	−0.427462	+	0.106578i	0.0222490	+	0.999752i	$0.492917\pi$
$258$	2.41208	−	2.67889i	0.150170	−	0.166780i
$259$	−17.2603	−	3.66879i	−1.07250	−	0.227967i
$260$	−3.03680	−	0.870789i	−0.188334	−	0.0540040i
$261$	−10.3360	−	9.98139i	−0.639784	−	0.617832i
$262$	−2.04722	+	3.85025i	−0.126477	+	0.237870i
$263$	6.33397	−	17.4024i	0.390569	−	1.07308i	−0.576173	−	0.817328i	$-0.695455\pi$
$263$	6.33397	−	17.4024i	0.390569	−	1.07308i	0.966742	−	0.255752i	$-0.0823231\pi$
$264$	−1.42837	−	8.08173i	−0.0879102	−	0.497396i
$265$			17.0872i			1.04966i
$266$	14.5005	−	5.64658i	0.889084	−	0.346214i
$267$	−20.5936	+	14.9622i	−1.26031	+	0.915669i
$268$	−0.0697364	−	0.997277i	−0.00425983	−	0.0609184i
$269$	−19.3754	−	0.676604i	−1.18134	−	0.0412532i	−0.562518	−	0.826785i	$-0.690167\pi$
$269$	−19.3754	−	0.676604i	−1.18134	−	0.0412532i	−0.618821	+	0.785532i	$0.712389\pi$
$270$	0.0566538	+	0.403113i	0.00344784	+	0.0245327i
$271$	12.1949	+	5.94785i	0.740788	+	0.361306i	0.769811	−	0.638272i	$-0.220351\pi$
$271$	12.1949	+	5.94785i	0.740788	+	0.361306i	−0.0290229	+	0.999579i	$0.509240\pi$
$272$	−0.863661	−	0.582546i	−0.0523671	−	0.0353221i
$273$	13.9791	+	15.5254i	0.846056	+	0.939641i
$274$	10.7758	+	18.6643i	0.650991	+	1.12755i
$275$	−2.93546	+	10.2527i	−0.177015	+	0.618260i
$276$	−6.73553	+	8.02710i	−0.405432	+	0.483174i
$277$	−4.49902	−	21.1662i	−0.270320	−	1.27176i	−0.878418	−	0.477894i	$-0.841400\pi$
$277$	−4.49902	−	21.1662i	−0.270320	−	1.27176i	0.608098	−	0.793862i	$-0.291933\pi$
$278$	−6.94713	+	0.730173i	−0.416661	+	0.0437929i
$279$	−5.47772	+	19.1031i	−0.327942	+	1.14367i
$280$	2.23888	+	4.21072i	0.133799	+	0.251639i
$281$	1.70778	−	0.240012i	0.101877	−	0.0143179i	−0.0880501	−	0.996116i	$-0.528064\pi$
$281$	1.70778	−	0.240012i	0.101877	−	0.0143179i	0.189928	+	0.981798i	$0.439175\pi$
$282$	−8.79077	+	5.92945i	−0.523483	+	0.353093i
$283$	8.35767	+	2.08380i	0.496812	+	0.123869i	0.482266	−	0.876025i	$-0.339814\pi$
$283$	8.35767	+	2.08380i	0.496812	+	0.123869i	0.0145463	+	0.999894i	$0.495370\pi$
$284$	−1.88427	−	0.612237i	−0.111811	−	0.0363296i
$285$	4.75660	+	13.6008i	0.281756	+	0.805643i
$286$	5.82680	−	5.25071i	0.344546	−	0.310481i
$287$	−0.102817	−	0.122533i	−0.00606911	−	0.00723289i
$288$	−1.92280	+	2.46107i	−0.113302	+	0.145020i
$289$	6.97656	+	14.3041i	0.410386	+	0.841416i
$290$	2.69418	−	5.52388i	0.158208	−	0.324374i
$291$	−25.3462	−	32.4416i	−1.48582	−	1.90176i
$292$	−0.972942	+	4.57733i	−0.0569371	+	0.267868i
$293$	1.87801	−	17.8681i	0.109715	−	1.04386i	−0.791701	−	0.610909i	$-0.790804\pi$
$293$	1.87801	−	17.8681i	0.109715	−	1.04386i	0.901415	−	0.432955i	$-0.142529\pi$
$294$	0.991605	−	14.1806i	0.0578316	−	0.827030i
$295$	−7.08922	−	11.3451i	−0.412750	−	0.660538i
$296$	4.28065	−	2.47144i	0.248808	−	0.143649i
$297$	−0.923466	−	0.410709i	−0.0535849	−	0.0238318i
$298$	4.22599	+	11.6108i	0.244805	+	0.672597i
$299$	−9.91717	−	1.39377i	−0.573525	−	0.0806036i
$300$	7.15150	−	3.48802i	0.412892	−	0.201381i
$301$	−2.90817	−	4.31154i	−0.167624	−	0.248513i
$302$	7.51050	+	4.69308i	0.432181	+	0.270056i
$303$	1.96832	+	6.05785i	0.113077	+	0.348014i
$304$	−1.96015	+	3.89330i	−0.112423	+	0.223296i
$305$	−3.13486	−	4.31477i	−0.179502	−	0.247063i
$306$	−3.01667	+	1.21881i	−0.172451	+	0.0696749i
$307$	−26.7883	−	9.75016i	−1.52889	−	0.556471i	−0.565541	−	0.824720i	$-0.691333\pi$
$307$	−26.7883	−	9.75016i	−1.52889	−	0.556471i	−0.963350	+	0.268249i	$0.913555\pi$
$308$	−11.8117	−	0.821194i	−0.673036	−	0.0467919i
$309$	1.77014	+	10.0389i	0.100699	+	0.571095i
$310$	−8.49496	+	0.296651i	−0.482481	+	0.0168486i
$311$	0.0468955	+	0.446180i	0.00265920	+	0.0253006i	0.995771	−	0.0918697i	$-0.0292843\pi$
$311$	0.0468955	+	0.446180i	0.00265920	+	0.0253006i	−0.993112	+	0.117170i	$0.962618\pi$
$312$	−5.81995	−	0.611702i	−0.329490	−	0.0346308i
$313$	−2.81478	+	6.96682i	−0.159101	+	0.393788i	−0.985587	−	0.169169i	$-0.945892\pi$
$313$	−2.81478	+	6.96682i	−0.159101	+	0.393788i	0.826486	+	0.562957i	$0.190336\pi$
$314$	5.16926	−	12.7944i	0.291718	−	0.722028i
$315$	14.8125	+	1.55686i	0.834591	+	0.0877190i
$316$	−0.474130	−	4.51105i	−0.0266719	−	0.253766i
$317$	23.6337	−	0.825307i	1.32740	−	0.0463539i	0.637608	−	0.770361i	$-0.279924\pi$
$317$	23.6337	−	0.825307i	1.32740	−	0.0463539i	0.689793	+	0.724007i	$0.257702\pi$
$318$	5.49631	+	31.1711i	0.308218	+	1.74799i
$319$	8.09118	+	12.9370i	0.453019	+	0.724335i
$320$	−1.25529	−	0.456887i	−0.0701727	−	0.0255408i
$321$	40.2255	−	16.2521i	2.24517	−	0.907107i
$322$	8.88588	+	12.2304i	0.495191	+	0.681572i
$323$	−3.79639	+	2.49150i	−0.211237	+	0.138631i
$324$	−2.66230	−	8.19372i	−0.147906	−	0.455207i
$325$	6.44893	+	4.02974i	0.357722	+	0.223530i
$326$	−11.8984	−	17.6401i	−0.658992	−	0.976996i
$327$	43.0424	−	20.9932i	2.38025	−	1.16093i
$328$	0.0443697	+	0.00623576i	0.00244991	+	0.000344312i
$329$	5.23217	+	14.3753i	0.288459	+	0.792534i
$330$	1.14160	−	10.9037i	0.0628430	−	0.600228i
$331$	13.2610	−	7.65623i	0.728890	−	0.420825i	−0.0891262	−	0.996020i	$-0.528407\pi$
$331$	13.2610	−	7.65623i	0.728890	−	0.420825i	0.818016	+	0.575196i	$0.195074\pi$
$332$	3.34415	+	5.35176i	0.183534	+	0.293716i
$333$	1.07685	−	15.3997i	0.0590112	−	0.843899i
$334$	2.37924	−	22.6370i	0.130186	−	1.23864i
$335$	0.277659	−	1.30628i	0.0151701	−	0.0713698i
$336$	5.43869	+	6.96120i	0.296705	+	0.379765i
$337$	−13.6944	+	28.0777i	−0.745982	+	1.52949i	0.0992328	+	0.995064i	$0.468361\pi$
$337$	−13.6944	+	28.0777i	−0.745982	+	1.52949i	−0.845215	+	0.534426i	$0.820528\pi$
$338$	3.24707	+	6.65748i	0.176617	+	0.362119i
$339$	−21.8541	+	27.9719i	−1.18695	+	1.51923i
$340$	−0.894527	−	1.06606i	−0.0485125	−	0.0578150i
$341$	10.5447	−	18.2809i	0.571026	−	0.989964i
$342$	6.65727	+	11.8747i	0.359984	+	0.642109i
$343$	4.26208	+	1.38483i	0.230131	+	0.0747740i
$344$	1.41351	+	0.352426i	0.0762111	+	0.0190016i
$345$	−11.6048	+	7.82751i	−0.624779	+	0.421419i
$346$	−11.0480	+	1.55270i	−0.593947	+	0.0834738i
$347$	2.88118	+	5.41871i	0.154670	+	0.290892i	0.948221	−	0.317612i	$-0.102881\pi$
$347$	2.88118	+	5.41871i	0.154670	+	0.290892i	−0.793551	+	0.608504i	$0.791770\pi$
$348$	3.13800	−	10.9435i	0.168214	−	0.586633i
$349$	5.66778	−	0.595707i	0.303389	−	0.0318875i	0.0483892	−	0.998829i	$-0.484591\pi$
$349$	5.66778	−	0.595707i	0.303389	−	0.0318875i	0.255000	+	0.966941i	$0.417925\pi$
$350$	−2.38668	−	11.2284i	−0.127573	−	0.600185i
$351$	−0.463235	+	0.552063i	−0.0247257	+	0.0294669i
$352$	2.61272	−	2.04297i	0.139258	−	0.108890i
$353$	14.1020	+	24.4254i	0.750574	+	1.30003i	0.947545	+	0.319624i	$0.103556\pi$
$353$	14.1020	+	24.4254i	0.750574	+	1.30003i	−0.196970	+	0.980409i	$0.563110\pi$
$354$	−16.5817	−	18.4159i	−0.881309	−	0.978792i
$355$	−2.19416	−	1.47998i	−0.116454	−	0.0785492i
$356$	−9.24588	−	4.50952i	−0.490031	−	0.239004i
$357$	1.28078	+	9.11326i	0.0677863	+	0.482325i
$358$	−1.41918	−	0.0495590i	−0.0750062	−	0.00261927i
$359$	−0.0885092	−	1.26574i	−0.00467134	−	0.0668032i	0.994669	−	0.103119i	$-0.0328822\pi$
$359$	−0.0885092	−	1.26574i	−0.00467134	−	0.0668032i	−0.999340	+	0.0363158i	$0.988438\pi$
$360$	−3.37526	+	2.45227i	−0.177892	+	0.129246i
$361$	12.3527	+	14.4364i	0.650143	+	0.759812i
$362$		−	24.5870i		−	1.29227i
$363$	21.4627	+	16.7408i	1.12650	+	0.878663i
$364$	−2.88758	+	7.93356i	−0.151350	+	0.415832i
$365$	−2.93477	+	5.51950i	−0.153613	+	0.288904i
$366$	−7.10664	−	6.86280i	−0.371470	−	0.358725i
$367$	−3.58735	−	1.02866i	−0.187258	−	0.0536954i	0.180698	−	0.983539i	$-0.442164\pi$
$367$	−3.58735	−	1.02866i	−0.187258	−	0.0536954i	−0.367956	+	0.929843i	$0.619942\pi$
$368$	−4.14211	−	0.880433i	−0.215922	−	0.0458957i
$369$	0.0936349	−	0.103992i	0.00487444	−	0.00541361i
$370$	6.40679	−	1.59739i	0.333073	−	0.0830445i
$371$	45.5532	+	3.18539i	2.36501	+	0.165377i
$372$	−15.4014	+	3.27367i	−0.798527	+	0.169732i
$373$	8.73399	−	15.1277i	0.452229	−	0.783283i	−0.546295	−	0.837593i	$-0.683962\pi$
$373$	8.73399	−	15.1277i	0.452229	−	0.783283i	0.998524	+	0.0543093i	$0.0172957\pi$
$374$	3.42132	−	0.482235i	0.176912	−	0.0249358i
$375$	26.7443	−	4.71573i	1.38107	−	0.243519i
$376$	−3.78356	−	2.01175i	−0.195122	−	0.103748i
$377$	10.4589	−	2.99904i	0.538661	−	0.154459i
$378$	1.08523	−	0.0758867i	0.0558182	−	0.00390319i
$379$	−14.7713	+	4.79948i	−0.758749	+	0.246533i	−0.662742	−	0.748848i	$-0.730607\pi$
$379$	−14.7713	+	4.79948i	−0.758749	+	0.246533i	−0.0960076	+	0.995381i	$0.530607\pi$
$380$	−3.95058	+	4.27764i	−0.202661	+	0.219438i
$381$	24.7992	−	34.1331i	1.27050	−	1.74869i
$382$	1.65324	−	6.63080i	0.0845873	−	0.339261i
$383$	−9.32261	−	7.28362i	−0.476363	−	0.372176i	0.348683	−	0.937241i	$-0.386629\pi$
$383$	−9.32261	−	7.28362i	−0.476363	−	0.372176i	−0.825046	+	0.565065i	$0.808851\pi$
$384$	−2.43691	−	0.429692i	−0.124358	−	0.0219276i
$385$	−14.8651	−	5.40369i	−0.757595	−	0.275398i
$386$	−4.13987	+	1.50679i	−0.210714	+	0.0766937i
$387$	3.38111	−	3.04437i	0.171872	−	0.154754i
$388$	6.76701	−	15.1989i	0.343543	−	0.771609i
$389$	6.71594	+	26.9362i	0.340512	+	1.36572i	0.859587	+	0.510989i	$0.170721\pi$
$389$	6.71594	+	26.9362i	0.340512	+	1.36572i	−0.519076	+	0.854728i	$0.673724\pi$
$390$	−7.24816	−	2.92845i	−0.367025	−	0.148288i
$391$	−3.27838	−	2.95187i	−0.165795	−	0.149282i
$392$	5.24804	−	2.33658i	0.265066	−	0.118015i
$393$	−6.03398	+	8.94574i	−0.304374	+	0.451253i
$394$	−0.843623	+	6.00269i	−0.0425011	+	0.302411i
$395$	1.05218	−	5.96721i	0.0529410	−	0.300243i
$396$	−0.726706	−	10.3328i	−0.0365183	−	0.519242i
$397$	−10.7383	+	9.01048i	−0.538938	+	0.452223i	−0.871175	−	0.490973i	$-0.836641\pi$
$397$	−10.7383	+	9.01048i	−0.538938	+	0.452223i	0.332236	+	0.943196i	$0.392197\pi$
$398$	−5.37508	+	16.5428i	−0.269428	+	0.829215i
$399$	37.1455	−	10.1453i	1.85960	−	0.507899i
$400$	2.60140	+	1.89003i	0.130070	+	0.0945015i
$401$	17.5355	−	28.0627i	0.875683	−	1.40139i	−0.0398771	−	0.999205i	$-0.512697\pi$
$401$	17.5355	−	28.0627i	0.875683	−	1.40139i	0.915560	−	0.402181i	$-0.131748\pi$
$402$	0.0863340	−	2.47228i	0.00430595	−	0.123306i
$403$	−10.4534	−	10.8248i	−0.520721	−	0.539223i
$404$	−1.78812	+	1.85165i	−0.0889622	+	0.0921230i
$405$	−0.401653	−	11.5018i	−0.0199583	−	0.571531i
$406$	−14.2240	−	8.21224i	−0.705926	−	0.407567i
$407$	−5.05966	+	15.5933i	−0.250798	+	0.772932i
$408$	−1.97474	−	1.65700i	−0.0977643	−	0.0820340i
$409$	−6.93777	+	4.33520i	−0.343051	+	0.214362i	−0.690492	−	0.723340i	$-0.742606\pi$
$409$	−6.93777	+	4.33520i	−0.343051	+	0.214362i	0.347442	+	0.937702i	$0.387050\pi$
$410$	0.0546791	+	0.0243447i	0.00270041	+	0.00120230i
$411$	21.6911	+	48.7189i	1.06994	+	2.40313i
$412$	−3.24624	+	2.53624i	−0.159931	+	0.124952i
$413$	−31.5668	+	16.7844i	−1.55330	+	0.825905i
$414$	−9.51358	+	9.18716i	−0.467567	+	0.451524i
$415$	2.32365	+	8.10355i	0.114064	+	0.397788i
$416$	−0.885917	−	2.19272i	−0.0434357	−	0.107507i
$417$	−17.2854			−0.846468
$418$	−3.81457	−	13.9445i	−0.186577	−	0.682048i
$419$	−13.4783			−0.658459			−0.329229	−	0.944250i	$-0.606789\pi$
$419$	−13.4783			−0.658459			−0.329229	+	0.944250i	$0.606789\pi$
$420$	4.42063	+	10.9415i	0.215705	+	0.533888i
$421$	−4.15572	−	14.4927i	−0.202537	−	0.706332i	−0.995303	−	0.0968057i	$-0.969137\pi$
$421$	−4.15572	−	14.4927i	−0.202537	−	0.706332i	0.792766	−	0.609526i	$-0.208640\pi$
$422$	−2.12086	+	2.04809i	−0.103242	+	0.0996995i
$423$	−11.8166	+	6.28300i	−0.574543	+	0.305490i
$424$	−10.0797	+	7.87510i	−0.489512	+	0.382448i
$425$	1.36249	+	3.06019i	0.0660903	+	0.148441i
$426$	−4.47873	−	1.99406i	−0.216995	−	0.0966124i
$427$	−12.0873	+	7.55296i	−0.584944	+	0.365513i
$428$	13.4308	+	11.2698i	0.649202	+	0.544745i
$429$	15.6976	−	11.4146i	0.757886	−	0.551101i
$430$	1.68532	+	0.973017i	0.0812731	+	0.0469231i
$431$	−0.509243	−	14.5828i	−0.0245294	−	0.702429i	−0.947909	−	0.318541i	$-0.896807\pi$
$431$	−0.509243	−	14.5828i	−0.0245294	−	0.702429i	0.923380	−	0.383888i	$-0.125415\pi$
$432$	−0.211684	+	0.219205i	−0.0101846	+	0.0105465i
$433$	14.5944	+	15.1130i	0.701364	+	0.726284i	0.971631	−	0.236501i	$-0.0760008\pi$
$433$	14.5944	+	15.1130i	0.701364	+	0.726284i	−0.270267	+	0.962785i	$0.587112\pi$
$434$	−0.792780	+	22.7023i	−0.0380547	+	1.08974i
$435$	8.05900	−	12.8971i	0.386400	−	0.618369i
$436$	15.6569	+	11.3754i	0.749831	+	0.544784i
$437$	−10.5143	+	15.1711i	−0.502967	+	0.725732i
$438$	−3.57831	+	11.0129i	−0.170978	+	0.526217i
$439$	27.5473	−	23.1149i	1.31476	−	1.10322i	0.327373	−	0.944895i	$-0.393837\pi$
$439$	27.5473	−	23.1149i	1.31476	−	1.10322i	0.987388	−	0.158320i	$-0.0506078\pi$
$440$	4.10723	−	1.66135i	0.195804	−	0.0792015i
$441$	3.11551	−	17.6690i	0.148358	−	0.841379i
$442$	0.342880	−	2.43972i	0.0163091	−	0.116045i
$443$	18.9956	−	28.1621i	0.902509	−	1.33802i	−0.0383642	−	0.999264i	$-0.512215\pi$
$443$	18.9956	−	28.1621i	0.902509	−	1.33802i	0.940873	−	0.338760i	$-0.110008\pi$
$444$	11.1737	−	4.97485i	0.530280	−	0.236096i
$445$	−10.2122	−	9.19510i	−0.484104	−	0.435889i
$446$	23.4948	+	9.49251i	1.11251	+	0.449483i
$447$	7.39673	+	29.6667i	0.349853	+	1.40318i
$448$	−1.45204	+	3.26133i	−0.0686023	+	0.154083i
$449$	5.41096	−	4.87205i	0.255359	−	0.229926i	−0.531501	−	0.847058i	$-0.678372\pi$
$449$	5.41096	−	4.87205i	0.255359	−	0.229926i	0.786860	+	0.617131i	$0.211705\pi$
$450$	9.43688	−	3.43474i	0.444859	−	0.161915i
$451$	−0.123165	+	0.0831477i	−0.00579961	+	0.00391527i
$452$	−14.1271	−	2.49100i	−0.664485	−	0.117167i
$453$	17.2690	+	13.4920i	0.811370	+	0.633911i
$454$	2.91754	−	11.7016i	0.136927	−	0.549183i
$455$	−6.62915	+	9.12425i	−0.310780	+	0.427751i
$456$	−5.83085	+	9.07419i	−0.273055	+	0.424938i
$457$	0.313837	−	0.101972i	0.0146807	−	0.00477004i	−0.301667	−	0.953413i	$-0.597543\pi$
$457$	0.313837	−	0.101972i	0.0146807	−	0.00477004i	0.316348	+	0.948643i	$0.397543\pi$
$458$	−17.3749	+	1.21497i	−0.811877	+	0.0567720i
$459$	−0.305160	+	0.0875031i	−0.0142436	+	0.00408430i
$460$	−4.99470	−	2.65573i	−0.232879	−	0.123824i
$461$	−28.5591	+	5.03574i	−1.33013	+	0.234538i	−0.793134	−	0.609048i	$-0.791552\pi$
$461$	−28.5591	+	5.03574i	−1.33013	+	0.234538i	−0.536995	+	0.843585i	$0.680441\pi$
$462$	−28.8556	−	5.07609i	−1.34249	−	0.236161i
$463$	−3.59003	+	6.21811i	−0.166843	+	0.288980i	−0.937308	−	0.348502i	$-0.886691\pi$
$463$	−3.59003	+	6.21811i	−0.166843	+	0.288980i	0.770465	+	0.637482i	$0.220024\pi$
$464$	4.50020	−	0.956546i	0.208916	−	0.0444065i
$465$	−20.9824	−	1.46723i	−0.973034	−	0.0680411i
$466$	27.7497	−	6.91877i	1.28548	−	0.320506i
$467$	5.47957	−	6.08568i	0.253564	−	0.281612i	−0.602901	−	0.797816i	$-0.705989\pi$
$467$	5.47957	−	6.08568i	0.253564	−	0.281612i	0.856466	+	0.516204i	$0.172655\pi$
$468$	−7.22461	−	1.53564i	−0.333958	−	0.0709850i
$469$	−3.43069	−	0.983734i	−0.158415	−	0.0454246i
$470$	−4.11772	−	3.97643i	−0.189936	−	0.183419i
$471$	16.0306	−	30.1492i	0.738651	−	1.38920i
$472$	3.42518	−	9.41060i	0.157657	−	0.433158i
$473$	−4.26513	+	2.27000i	−0.196111	+	0.104375i
$474$		−	11.2241i		−	0.515539i
$475$	11.9792	−	7.27665i	0.549643	−	0.333875i
$476$	−3.00879	+	2.18601i	−0.137907	+	0.100196i
$477$	2.78671	+	39.8517i	0.127594	+	1.82469i
$478$	19.1781	+	0.669714i	0.877186	+	0.0306320i
$479$	1.24293	+	8.84389i	0.0567908	+	0.404087i	0.997833	+	0.0657981i	$0.0209593\pi$
$479$	1.24293	+	8.84389i	0.0567908	+	0.404087i	−0.941042	+	0.338289i	$0.890152\pi$
$480$	−2.97101	−	1.44906i	−0.135608	−	0.0661403i
$481$	9.69106	+	6.53670i	0.441874	+	0.298048i
$482$	−8.97541	−	9.96821i	−0.408819	−	0.454039i
$483$	18.7042	+	32.3966i	0.851071	+	1.47410i
$484$	−1.90144	+	10.8344i	−0.0864289	+	0.492473i
$485$	14.2859	−	17.0253i	0.648690	−	0.773078i
$486$	−4.62249	−	21.7471i	−0.209681	−	0.986470i
$487$	−1.52935	+	0.160741i	−0.0693013	+	0.00728386i	−0.139116	−	0.990276i	$-0.544426\pi$
$487$	−1.52935	+	0.160741i	−0.0693013	+	0.00728386i	0.0698144	+	0.997560i	$0.477759\pi$
$488$	1.10048	−	3.83782i	0.0498163	−	0.173730i
$489$	−24.7186	−	46.4889i	−1.11781	−	2.10230i
$490$	7.59935	−	1.06802i	0.343304	−	0.0482482i
$491$	1.85026	−	1.24802i	0.0835011	−	0.0563222i	−0.516733	−	0.856147i	$-0.672852\pi$
$491$	1.85026	−	1.24802i	0.0835011	−	0.0563222i	0.600234	+	0.799825i	$0.295074\pi$
$492$	0.107579	+	0.0268223i	0.00485001	+	0.00120924i
$493$	4.55829	+	1.48108i	0.205295	+	0.0667045i
$494$	−10.3077	−	0.130220i	−0.463763	−	0.00585889i
$495$	2.87147	−	13.5359i	0.129063	−	0.608394i
$496$	−4.09012	−	4.87442i	−0.183652	−	0.218868i
$497$	−4.35455	+	5.57357i	−0.195328	+	0.250009i
$498$	6.84551	+	14.0354i	0.306755	+	0.628940i
$499$	0.801291	−	1.64289i	0.0358707	−	0.0735459i	−0.880106	−	0.474777i	$-0.842529\pi$
$499$	0.801291	−	1.64289i	0.0358707	−	0.0735459i	0.915977	+	0.401231i	$0.131418\pi$
$500$	6.75668	+	8.64816i	0.302168	+	0.386758i
$501$	11.7104	−	55.0929i	0.523180	−	2.46137i
$502$	0.330442	−	3.14395i	0.0147484	−	0.140321i
$503$	−0.0564886	+	0.807825i	−0.00251870	+	0.0360191i	−0.998661	−	0.0517355i	$-0.983525\pi$
$503$	−0.0564886	+	0.807825i	−0.00251870	+	0.0360191i	0.996142	+	0.0877547i	$0.0279692\pi$
$504$	5.90836	+	9.45535i	0.263179	+	0.421175i
$505$	−2.97792	+	1.71930i	−0.132516	+	0.0765079i
$506$	12.1603	−	7.02725i	0.540590	−	0.312399i
$507$	6.26886	+	17.2236i	0.278410	+	0.764925i
$508$	16.8843	+	2.37294i	0.749121	+	0.105282i
$509$	−14.4721	+	7.05850i	−0.641463	+	0.312862i	−0.730242	−	0.683189i	$-0.760592\pi$
$509$	−14.4721	+	7.05850i	−0.641463	+	0.312862i	0.0887787	+	0.996051i	$0.471704\pi$
$510$	−1.92564	−	2.85488i	−0.0852688	−	0.126416i
$511$	14.1675	+	8.85283i	0.626733	+	0.391626i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	0.524893	+	1.22018i	0.0231746	+	0.0538724i
$514$	−4.15124	−	5.71370i	−0.183103	−	0.252020i
$515$	−5.10237	+	2.06149i	−0.224837	+	0.0908401i
$516$	3.38740	+	1.23291i	0.149122	+	0.0542760i
$517$	13.7887	−	3.44378i	0.606425	−	0.151457i
$518$	−3.06418	−	17.3778i	−0.134632	−	0.763538i
$519$	−27.5902	+	0.963473i	−1.21108	+	0.0422918i
$520$	−0.330225	−	3.14188i	−0.0144813	−	0.137780i
$521$	−22.3257	−	2.34653i	−0.978107	−	0.102803i	−0.398037	−	0.917370i	$-0.630308\pi$
$521$	−22.3257	−	2.34653i	−0.978107	−	0.102803i	−0.580070	+	0.814566i	$0.696975\pi$
$522$	5.38264	−	13.3225i	0.235592	−	0.583110i
$523$	−10.7980	+	26.7261i	−0.472165	+	1.16865i	0.483802	+	0.875177i	$0.339255\pi$
$523$	−10.7980	+	26.7261i	−0.472165	+	1.16865i	−0.955967	+	0.293473i	$0.905189\pi$
$524$	−4.33679	−	0.455815i	−0.189454	−	0.0199124i
$525$	−2.96918	−	28.2499i	−0.129586	−	1.23292i
$526$	18.5080	−	0.646314i	0.806987	−	0.0281806i
$527$	−1.15109	−	6.52814i	−0.0501421	−	0.284370i
$528$	6.95817	−	4.35183i	0.302816	−	0.189389i
$529$	4.76214	+	1.73328i	0.207050	+	0.0753599i
$530$	−15.8430	+	6.40098i	−0.688175	+	0.278041i
$531$	−18.3841	−	25.3036i	−0.797803	−	1.09808i
$532$	10.6674	+	11.3294i	0.462491	+	0.491192i
$533$	0.0327442	+	0.100776i	0.00141831	+	0.00436510i
$534$	−21.5872	−	13.4892i	−0.934169	−	0.583734i
$535$	13.0968	+	19.4169i	0.566226	+	0.839465i
$536$	0.898536	−	0.438245i	0.0388108	−	0.0189293i
$537$	−3.47971	−	0.489042i	−0.150161	−	0.0211037i
$538$	−6.63081	−	18.2180i	−0.285875	−	0.785434i
$539$	−7.74256	+	17.4089i	−0.333496	+	0.749853i
$540$	−0.352537	+	0.203537i	−0.0151708	+	0.00875885i
$541$	13.8702	+	22.1970i	0.596326	+	0.954322i	0.999236	+	0.0390820i	$0.0124434\pi$
$541$	13.8702	+	22.1970i	0.596326	+	0.954322i	−0.402910	+	0.915240i	$0.632001\pi$
$542$	−0.946461	+	13.5350i	−0.0406540	+	0.581379i
$543$	6.35958	−	60.5073i	0.272916	−	2.59662i
$544$	0.216595	−	1.01900i	0.00928642	−	0.0436892i
$545$	15.9165	+	20.3722i	0.681789	+	0.872650i
$546$	−9.15823	+	18.7772i	−0.391936	+	0.803588i
$547$	16.0054	+	32.8160i	0.684342	+	1.40311i	0.904000	+	0.427533i	$0.140617\pi$
$547$	16.0054	+	32.8160i	0.684342	+	1.40311i	−0.219658	+	0.975577i	$0.570494\pi$
$548$	−13.2685	+	16.9829i	−0.566803	+	0.725474i
$549$	−8.01499	−	9.55190i	−0.342072	−	0.407665i
$550$	−10.6058	+	1.11901i	−0.452231	+	0.0477149i
$551$	3.73157	−	19.7039i	0.158970	−	0.839414i
$552$	−9.96577	−	3.23808i	−0.424171	−	0.137822i
$553$	−15.7120	−	3.91744i	−0.668143	−	0.166587i
$554$	17.9396	−	12.1004i	0.762182	−	0.514098i
$555$	16.1799	−	2.27394i	0.686800	−	0.0965234i
$556$	−3.27945	−	6.16774i	−0.139079	−	0.261570i
$557$	−9.38847	+	32.7415i	−0.397802	+	1.38730i	0.466586	+	0.884476i	$0.345484\pi$
$557$	−9.38847	+	32.7415i	−0.397802	+	1.38730i	−0.864388	+	0.502825i	$0.832294\pi$
$558$	−19.7641	+	2.07729i	−0.836679	+	0.0879385i
$559$	0.716292	+	3.36989i	0.0302959	+	0.142531i
$560$	−3.06542	+	3.65322i	−0.129537	+	0.154377i
$561$	8.54441	−	0.301810i	0.360745	−	0.0127424i
$562$	0.862280	+	1.49351i	0.0363731	+	0.0630000i
$563$	−2.34618	−	2.60569i	−0.0988795	−	0.109817i	0.691674	−	0.722210i	$-0.256874\pi$
$563$	−2.34618	−	2.60569i	−0.0988795	−	0.109817i	−0.790553	+	0.612393i	$0.790207\pi$
$564$	−8.79077	−	5.92945i	−0.370158	−	0.249675i
$565$	−17.2234	−	8.40043i	−0.724596	−	0.353409i
$566$	1.19877	+	8.52970i	0.0503881	+	0.358530i
$567$	−30.7380	−	1.07339i	−1.29087	−	0.0450783i
$568$	−0.138204	−	1.97641i	−0.00579892	−	0.0829285i
$569$	−34.2588	+	24.8905i	−1.43620	+	1.04346i	−0.447386	+	0.894341i	$0.647645\pi$
$569$	−34.2588	+	24.8905i	−1.43620	+	1.04346i	−0.988819	+	0.149123i	$0.952355\pi$
$570$	−10.8286	+	9.50519i	−0.453560	+	0.398129i
$571$		−	35.1090i		−	1.46926i	−0.678465	−	0.734632i	$-0.737355\pi$
$571$		−	35.1090i		−	1.46926i	0.678465	−	0.734632i	$-0.262645\pi$
$572$	7.05114	+	3.43557i	0.294823	+	0.143648i
$573$	5.78363	−	15.8904i	0.241615	−	0.663831i
$574$	0.0750945	−	0.141232i	0.00313438	−	0.00589492i
$575$	9.79492	+	9.45885i	0.408477	+	0.394461i
$576$	−3.00216	−	0.860856i	−0.125090	−	0.0358690i
$577$	6.94597	+	1.47641i	0.289165	+	0.0614638i	0.350210	−	0.936671i	$-0.386110\pi$
$577$	6.94597	+	1.47641i	0.289165	+	0.0614638i	−0.0610456	+	0.998135i	$0.519443\pi$
$578$	−10.6490	+	11.8269i	−0.442941	+	0.491936i
$579$	−10.5777	+	2.63733i	−0.439596	+	0.109604i
$580$	6.13091	+	0.428715i	0.254572	+	0.0178014i
$581$	22.0366	−	4.68403i	0.914234	−	0.194326i
$582$	20.5845	−	35.6534i	0.853256	−	1.47788i
$583$	7.35006	−	41.7823i	0.304408	−	1.73045i
$584$	−4.60850	+	0.812603i	−0.190701	+	0.0336257i
$585$	−8.71169	−	4.63209i	−0.360184	−	0.191513i
$586$	17.2705	−	4.95224i	0.713438	−	0.204575i
$587$	−23.9301	+	1.67336i	−0.987703	+	0.0690669i	−0.554460	−	0.832210i	$-0.687075\pi$
$587$	−23.9301	+	1.67336i	−0.987703	+	0.0690669i	−0.433243	+	0.901277i	$0.642631\pi$
$588$	13.5195	−	4.39275i	0.557535	−	0.181154i
$589$	−26.4848	+	8.23703i	−1.09129	+	0.339401i
$590$	7.86334	−	10.8230i	0.323729	−	0.445574i
$591$	−3.62874	+	14.5541i	−0.149266	+	0.598675i
$592$	3.89504	+	3.04313i	0.160085	+	0.125072i
$593$	0.453870	+	0.0800295i	0.0186382	+	0.00328642i	0.182960	−	0.983120i	$-0.441432\pi$
$593$	0.453870	+	0.0800295i	0.0186382	+	0.00328642i	−0.164321	+	0.986407i	$0.552543\pi$
$594$	0.0348668	−	1.01008i	0.00143060	−	0.0414440i
$595$	−4.66849	+	1.69919i	−0.191389	+	0.0696601i
$596$	−9.18228	+	8.26776i	−0.376121	+	0.338661i
$597$	−17.5067	+	39.3206i	−0.716500	+	1.60929i
$598$	−2.42276	−	9.71715i	−0.0990739	−	0.397364i
$599$	27.2511	+	11.0102i	1.11345	+	0.449863i	0.856285	−	0.516504i	$-0.172767\pi$
$599$	27.2511	+	11.0102i	1.11345	+	0.449863i	0.257166	+	0.966367i	$0.417211\pi$
$600$	5.91304	+	5.32412i	0.241399	+	0.217356i
$601$	−27.7656	+	12.3621i	−1.13258	+	0.504259i	−0.885456	−	0.464724i	$-0.846154\pi$
$601$	−27.7656	+	12.3621i	−1.13258	+	0.504259i	−0.247129	+	0.968983i	$0.579487\pi$
$602$	2.90817	−	4.31154i	0.118528	−	0.175725i
$603$	0.434533	−	3.09187i	0.0176956	−	0.125910i
$604$	−1.53787	+	8.72167i	−0.0625749	+	0.354880i
$605$	−6.43097	+	13.2123i	−0.261456	+	0.537158i
$606$	−4.87940	+	4.09430i	−0.198212	+	0.166320i
$607$	1.53044	−	4.71022i	0.0621187	−	0.191182i	−0.915181	−	0.403043i	$-0.867953\pi$
$607$	1.53044	−	4.71022i	0.0621187	−	0.191182i	0.977300	+	0.211861i	$0.0679525\pi$
$608$	−4.34409	−	0.358966i	−0.176176	−	0.0145580i
$609$	−32.8804	−	23.8890i	−1.33238	−	0.968031i
$610$	2.82625	−	4.52294i	0.114431	−	0.183128i
$611$	0.353673	−	10.1279i	0.0143081	−	0.409730i
$612$	−2.26013	−	2.34043i	−0.0913602	−	0.0946063i
$613$	−26.4301	+	27.3691i	−1.06750	+	1.10543i	−0.0733622	+	0.997305i	$0.523373\pi$
$613$	−26.4301	+	27.3691i	−1.06750	+	1.10543i	−0.994138	+	0.108123i	$0.965516\pi$
$614$	−0.994899	−	28.4902i	−0.0401509	−	1.14977i
$615$	0.128265	+	0.0740540i	0.00517216	+	0.00298615i
$616$	−3.66336	−	11.2593i	−0.147601	−	0.453649i
$617$	31.6462	+	26.5543i	1.27403	+	1.06904i	0.994038	+	0.109034i	$0.0347756\pi$
$617$	31.6462	+	26.5543i	1.27403	+	1.06904i	0.279990	+	0.960003i	$0.409669\pi$
$618$	−8.64483	+	5.40189i	−0.347746	+	0.217296i
$619$	−14.3562	−	6.39180i	−0.577025	−	0.256908i	0.0974075	−	0.995245i	$-0.468945\pi$
$619$	−14.3562	−	6.39180i	−0.577025	−	0.256908i	−0.674433	+	0.738337i	$0.735612\pi$
$620$	−3.45732	−	7.76527i	−0.138849	−	0.311861i
$621$	−1.01687	+	0.794467i	−0.0408056	+	0.0318809i
$622$	−0.396124	+	0.210623i	−0.0158831	+	0.00844521i
$623$	−26.4172	+	25.5108i	−1.05838	+	1.02207i
$624$	−1.61303	−	5.62531i	−0.0645730	−	0.225193i
$625$	−0.530836	−	1.31386i	−0.0212334	−	0.0525546i
$626$	−7.51396			−0.300318
$627$	−5.78062	−	35.3033i	−0.230856	−	1.40988i
$628$	13.7992			0.550647
$629$	1.92896	+	4.77435i	0.0769127	+	0.190366i
$630$	4.10537	+	14.3171i	0.163562	+	0.570408i
$631$	16.6493	−	16.0780i	0.662798	−	0.640057i	−0.285149	−	0.958483i	$-0.592043\pi$
$631$	16.6493	−	16.0780i	0.662798	−	0.640057i	0.947948	+	0.318426i	$0.103154\pi$
$632$	4.00496	−	2.12947i	0.159309	−	0.0847059i
$633$	−5.74907	+	4.49167i	−0.228505	+	0.178528i
$634$	9.61855	+	21.6036i	0.382001	+	0.857989i
$635$	20.8074	+	9.26406i	0.825717	+	0.367633i
$636$	−26.8424	+	16.7730i	−1.06437	+	0.665093i
$637$	10.4073	+	8.73277i	0.412352	+	0.346005i
$638$	−8.96401	+	12.3483i	−0.354888	+	0.488874i
$639$	−5.35871	−	3.09385i	−0.211987	−	0.122391i
$640$	−0.0466204	−	1.33503i	−0.00184283	−	0.0527719i
$641$	−19.9189	+	20.6267i	−0.786751	+	0.814704i	−0.986262	−	0.165191i	$-0.947176\pi$
$641$	−19.9189	+	20.6267i	−0.786751	+	0.814704i	0.199511	+	0.979896i	$0.436065\pi$
$642$	30.1375	+	31.2083i	1.18943	+	1.23169i
$643$	0.369365	−	10.5772i	0.0145664	−	0.417126i	−0.970103	−	0.242694i	$-0.921969\pi$
$643$	0.369365	−	10.5772i	0.0145664	−	0.417126i	0.984669	−	0.174432i	$-0.0558089\pi$
$644$	−8.01109	+	12.8204i	−0.315681	+	0.505195i
$645$	3.89579	+	2.83046i	0.153397	+	0.111449i
$646$	−3.73223	−	2.58661i	−0.146843	−	0.101769i
$647$	−7.95229	+	24.4746i	−0.312637	+	0.962197i	0.664079	+	0.747662i	$0.268824\pi$
$647$	−7.95229	+	24.4746i	−0.312637	+	0.962197i	−0.976716	+	0.214535i	$0.931176\pi$
$648$	6.59977	−	5.53787i	0.259263	−	0.217548i
$649$	12.4547	+	30.7910i	0.488891	+	1.20865i
$650$	−1.32050	+	7.48892i	−0.0517942	+	0.293739i
$651$	−7.82305	+	55.6639i	−0.306610	+	2.18164i
$652$	11.8984	−	17.6401i	0.465978	−	0.690840i
$653$	−13.5772	+	6.04498i	−0.531319	+	0.236558i	−0.654818	−	0.755786i	$-0.727255\pi$
$653$	−13.5772	+	6.04498i	−0.531319	+	0.236558i	0.123500	+	0.992345i	$0.460588\pi$
$654$	35.5885	+	32.0440i	1.39162	+	1.25302i
$655$	−5.40104	−	2.18216i	−0.211036	−	0.0852641i
$656$	0.0108395	+	0.0434749i	0.000423211	+	0.00169741i
$657$	−5.94448	+	13.3515i	−0.231916	+	0.520892i
$658$	−11.3685	+	10.2362i	−0.443190	+	0.399050i
$659$	−17.2475	+	6.27758i	−0.671868	+	0.244540i	−0.655352	−	0.755324i	$-0.727480\pi$
$659$	−17.2475	+	6.27758i	−0.671868	+	0.244540i	−0.0165160	+	0.999864i	$0.505257\pi$
$660$	10.5374	−	3.02612i	0.410167	−	0.117792i
$661$	−11.5982	−	2.04508i	−0.451119	−	0.0795444i	−0.0565272	−	0.998401i	$-0.518003\pi$
$661$	−11.5982	−	2.04508i	−0.451119	−	0.0795444i	−0.394591	+	0.918857i	$0.629114\pi$
$662$	12.0664	+	9.42730i	0.468973	+	0.366402i
$663$	1.47485	−	5.91532i	0.0572786	−	0.229732i
$664$	−3.70933	+	5.10545i	−0.143950	+	0.198130i
$665$	9.52642	+	18.4759i	0.369419	+	0.716466i
$666$	14.6818	−	4.77039i	0.568907	−	0.184849i
$667$	19.4350	−	1.35903i	0.752527	−	0.0526218i
$668$	21.8799	−	6.27396i	0.846559	−	0.242747i
$669$	55.3641	+	29.4376i	2.14050	+	1.13812i
$670$	1.31518	−	0.231901i	0.0508097	−	0.00895911i
$671$	5.80950	+	11.8991i	0.224273	+	0.459360i
$672$	−4.41695	+	7.65037i	−0.170387	+	0.295120i
$673$	−18.8314	+	4.00274i	−0.725898	+	0.154294i	−0.556018	−	0.831170i	$-0.687671\pi$
$673$	−18.8314	+	4.00274i	−0.725898	+	0.154294i	−0.169880	+	0.985465i	$0.554338\pi$
$674$	−31.1632	−	2.17914i	−1.20036	−	0.0839375i
$675$	0.950759	−	0.237051i	0.0365947	−	0.00912409i
$676$	−4.95633	+	5.50456i	−0.190628	+	0.211714i
$677$	−11.1336	−	2.36653i	−0.427900	−	0.0909530i	−0.0110730	−	0.999939i	$-0.503525\pi$
$677$	−11.1336	−	2.36653i	−0.427900	−	0.0909530i	−0.416827	+	0.908986i	$0.636858\pi$
$678$	−34.1218	−	9.78426i	−1.31044	−	0.375762i
$679$	−42.7250	−	41.2590i	−1.63963	−	1.58338i
$680$	0.653334	−	1.22874i	0.0250542	−	0.0471201i
$681$	10.2066	−	28.0423i	0.391117	−	1.07458i
$682$	20.8998	+	2.92873i	0.800296	+	0.112147i
$683$			13.5542i			0.518636i	0.965792	+	0.259318i	$0.0834978\pi$
$683$			13.5542i			0.518636i	−0.965792	+	0.259318i	$0.916502\pi$
$684$	−8.51615	+	10.6208i	−0.325623	+	0.406098i
$685$	−23.2914	+	16.9222i	−0.889917	+	0.646563i
$686$	0.312608	+	4.47050i	0.0119354	+	0.170684i
$687$	−43.0730	−	1.50414i	−1.64334	−	0.0573866i
$688$	0.202744	+	1.44260i	0.00772955	+	0.0549986i
$689$	−27.1889	−	13.2609i	−1.03581	−	0.505201i
$690$	−11.6048	−	7.82751i	−0.441785	−	0.297988i
$691$	−13.8491	−	15.3810i	−0.526845	−	0.585120i	0.419712	−	0.907657i	$-0.362131\pi$
$691$	−13.8491	−	15.3810i	−0.526845	−	0.585120i	−0.946557	+	0.322537i	$0.895464\pi$
$692$	−5.57831	−	9.66192i	−0.212056	−	0.367291i
$693$	−35.5505	−	10.1785i	−1.35045	−	0.386649i
$694$	−3.94483	+	4.70127i	−0.149744	+	0.178458i
$695$	−1.94011	−	9.12752i	−0.0735927	−	0.346227i
$696$	11.3221	−	1.19001i	0.429165	−	0.0451070i
$697$	−0.0128659	+	0.0448688i	−0.000487332	+	0.00169953i
$698$	2.67552	+	5.03191i	0.101270	+	0.190461i
$699$	70.0799	−	9.84909i	2.65067	−	0.372527i
$700$	9.51675	−	6.41913i	0.359699	−	0.242620i
$701$	−41.2315	−	10.2802i	−1.55729	−	0.388277i	−0.634299	−	0.773088i	$-0.718711\pi$
$701$	−41.2315	−	10.2802i	−1.55729	−	0.388277i	−0.922995	+	0.384811i	$0.874267\pi$
$702$	−0.685395	−	0.222698i	−0.0258686	−	0.00840520i
$703$	18.7935	−	10.5362i	0.708811	−	0.397379i
$704$	2.87295	+	1.65716i	0.108278	+	0.0624566i
$705$	−9.10494	−	10.8508i	−0.342912	−	0.408667i
$706$	−17.3641	+	22.2251i	−0.653508	+	0.836452i
$707$	4.02839	+	8.25942i	0.151503	+	0.310628i
$708$	10.8633	−	22.2730i	0.408267	−	0.837071i
$709$	−5.39548	−	6.90590i	−0.202631	−	0.259356i	0.675952	−	0.736946i	$-0.263733\pi$
$709$	−5.39548	−	6.90590i	−0.202631	−	0.259356i	−0.878583	+	0.477590i	$0.841511\pi$
$710$	0.550267	−	2.58880i	0.0206511	−	0.0971559i
$711$	1.48078	−	14.0887i	0.0555336	−	0.528366i
$712$	0.717584	−	10.2619i	0.0268926	−	0.384582i
$713$	−14.2789	−	22.8511i	−0.534750	−	0.855780i
$714$	−7.96988	+	4.60141i	−0.298265	+	0.172203i
$715$	7.78935	+	7.00791i	0.291305	+	0.262081i
$716$	−0.485685	−	1.33441i	−0.0181509	−	0.0498692i
$717$	47.0230	+	6.60866i	1.75611	+	0.246805i
$718$	1.14042	−	0.556219i	0.0425600	−	0.0207579i
$719$	−0.145378	−	0.215532i	−0.00542170	−	0.00803800i	0.826317	−	0.563205i	$-0.190432\pi$
$719$	−0.145378	−	0.215532i	−0.00542170	−	0.00803800i	−0.831739	+	0.555167i	$0.812654\pi$
$720$	−3.53810	−	2.21085i	−0.131857	−	0.0823936i
$721$	4.54460	+	13.9868i	0.169250	+	0.520897i
$722$	−8.75781	+	16.8612i	−0.325932	+	0.627510i
$723$	−19.5097	−	26.8527i	−0.725572	−	0.998664i
$724$	22.7967	−	9.21047i	0.847233	−	0.342304i
$725$	−13.9015	−	5.05974i	−0.516290	−	0.187914i
$726$	−7.48171	+	26.1711i	−0.277672	+	0.971300i
$727$	4.61578	+	26.1774i	0.171190	+	0.970865i	0.942450	+	0.334346i	$0.108515\pi$
$727$	4.61578	+	26.1774i	0.171190	+	0.970865i	−0.771261	+	0.636519i	$0.780374\pi$
$728$	−8.43758	+	0.294647i	−0.312717	+	0.0109203i
$729$	−3.04902	−	29.0095i	−0.112927	−	1.07443i
$730$	−6.21698	−	0.653431i	−0.230101	−	0.0241846i
$731$	−0.568509	+	1.40711i	−0.0210271	+	0.0520438i
$732$	3.70089	−	9.16002i	0.136789	−	0.338564i
$733$	−4.44101	−	0.466769i	−0.164033	−	0.0172405i	0.0221562	−	0.999755i	$-0.492947\pi$
$733$	−4.44101	−	0.466769i	−0.164033	−	0.0172405i	−0.186189	+	0.982514i	$0.559614\pi$
$734$	−0.390091	−	3.71147i	−0.0143985	−	0.136993i
$735$	18.9778	−	0.662720i	0.700008	−	0.0244448i
$736$	−0.735339	−	4.17031i	−0.0271049	−	0.153720i
$737$	−1.24084	+	3.07474i	−0.0457069	+	0.113259i
$738$	0.131496	+	0.0478606i	0.00484043	+	0.00176177i
$739$	7.04581	−	2.84669i	0.259184	−	0.104717i	−0.241337	−	0.970441i	$-0.577586\pi$
$739$	7.04581	−	2.84669i	0.259184	−	0.104717i	0.500522	+	0.865724i	$0.333142\pi$
$740$	3.88110	+	5.34188i	0.142672	+	0.196371i
$741$	−25.3329	−	2.98660i	−0.930626	−	0.109715i
$742$	14.1111	+	43.4295i	0.518035	+	1.59435i
$743$	−36.2395	−	22.6450i	−1.32950	−	0.830763i	−0.335701	−	0.941969i	$-0.608973\pi$
$743$	−36.2395	−	22.6450i	−1.32950	−	0.830763i	−0.993797	+	0.111206i	$0.964529\pi$
$744$	−8.80477	−	13.0536i	−0.322799	−	0.478569i
$745$	−14.8352	+	7.23563i	−0.543521	+	0.265093i
$746$	17.2980	+	2.43107i	0.633324	+	0.0890079i
$747$	6.74094	+	18.5206i	0.246638	+	0.677633i
$748$	1.72877	+	2.99154i	0.0632100	+	0.109382i
$749$	54.2055	−	31.2956i	1.98063	−	1.14351i
$750$	14.3909	+	23.0303i	0.525482	+	0.840947i
$751$	−2.05187	+	29.3432i	−0.0748739	+	1.07075i	0.804293	+	0.594233i	$0.202544\pi$
$751$	−2.05187	+	29.3432i	−0.0748739	+	1.07075i	−0.879167	+	0.476514i	$0.841900\pi$
$752$	0.447919	−	4.26167i	0.0163339	−	0.155407i
$753$	1.62640	−	7.65161i	0.0592693	−	0.278840i
$754$	6.69864	+	8.57387i	0.243950	+	0.312242i
$755$	−5.18618	+	10.6332i	−0.188744	+	0.386983i
$756$	0.476896	+	0.977781i	0.0173445	+	0.0355615i
$757$	14.0622	−	17.9988i	0.511100	−	0.654178i	−0.461370	−	0.887208i	$-0.652642\pi$
$757$	14.0622	−	17.9988i	0.511100	−	0.654178i	0.972470	+	0.233030i	$0.0748641\pi$
$758$	−9.98342	−	11.8978i	−0.362614	−	0.432147i
$759$	31.7434	−	14.1483i	1.15221	−	0.513552i
$760$	−5.44607	−	2.06049i	−0.197550	−	0.0747417i
$761$	−23.7489	−	7.71649i	−0.860898	−	0.279723i	−0.154894	−	0.987931i	$-0.549504\pi$
$761$	−23.7489	−	7.71649i	−0.860898	−	0.279723i	−0.706004	+	0.708208i	$0.749504\pi$
$762$	40.9376	+	10.2069i	1.48301	+	0.369757i
$763$	57.2780	−	38.6345i	2.07360	−	1.39866i
$764$	6.76728	−	0.951080i	0.244832	−	0.0344089i
$765$	−2.04046	−	3.83755i	−0.0737730	−	0.138747i
$766$	3.26094	−	11.3723i	0.117823	−	0.410897i
$767$	23.5539	−	2.47562i	0.850483	−	0.0893894i
$768$	−0.514477	−	2.42043i	−0.0185646	−	0.0873396i
$769$	−18.0231	+	21.4791i	−0.649929	+	0.774555i	−0.985903	−	0.167316i	$-0.946490\pi$
$769$	−18.0231	+	21.4791i	−0.649929	+	0.774555i	0.335975	+	0.941871i	$0.390934\pi$
$770$	−0.558341	−	15.8069i	−0.0201212	−	0.569642i
$771$	−8.73810	−	15.1348i	−0.314695	−	0.545068i
$772$	−2.94790	−	3.27397i	−0.106097	−	0.117833i
$773$	22.9348	+	15.4697i	0.824906	+	0.556406i	0.897530	−	0.440953i	$-0.145360\pi$
$773$	22.9348	+	15.4697i	0.824906	+	0.556406i	−0.0726240	+	0.997359i	$0.523137\pi$
$774$	4.08927	+	1.99447i	0.146986	+	0.0716898i
$775$	2.84757	+	20.2615i	0.102288	+	0.727815i
$776$	16.6272	+	0.580634i	0.596881	+	0.0208435i
$777$	−3.04590	−	43.5584i	−0.109271	−	1.56265i
$778$	−22.4589	+	16.3174i	−0.805192	+	0.585006i
$779$	0.193044	+	0.0296220i	0.00691653	+	0.00106132i
$780$		−	7.81740i		−	0.279908i
$781$	4.72863	+	4.56272i	0.169204	+	0.163267i
$782$	1.50882	−	4.14545i	0.0539553	−	0.148241i
$783$	0.658193	−	1.23788i	0.0235219	−	0.0442382i
$784$	4.13239	+	3.99060i	0.147585	+	0.142521i
$785$	17.7195	+	5.08099i	0.632436	+	0.181348i
$786$	−10.5547	−	2.24347i	−0.376474	−	0.0800220i
$787$	21.0323	−	23.3587i	0.749721	−	0.832649i	−0.240719	−	0.970595i	$-0.577383\pi$
$787$	21.0323	−	23.3587i	0.749721	−	0.832649i	0.990440	+	0.137946i	$0.0440499\pi$
$788$	−5.88162	+	1.46645i	−0.209524	+	0.0522402i
$789$	45.7143	+	3.19666i	1.62747	+	0.113804i
$790$	5.92686	−	1.25979i	0.210868	−	0.0448214i
$791$	−25.6057	+	44.3504i	−0.910435	+	1.57692i
$792$	9.30817	−	4.54452i	0.330751	−	0.161483i
$793$	9.29848	−	1.63957i	0.330199	−	0.0582230i
$794$	−12.3770	−	6.58097i	−0.439243	−	0.233550i
$795$	−40.6443	+	11.6546i	−1.44151	+	0.413345i
$796$	−17.3518	+	1.21335i	−0.615017	+	0.0430062i
$797$	26.6694	−	8.66540i	0.944677	−	0.306944i	0.204126	−	0.978945i	$-0.434565\pi$
$797$	26.6694	−	8.66540i	0.944677	−	0.306944i	0.740551	+	0.672000i	$0.234565\pi$
$798$	23.3215	+	30.6402i	0.825572	+	1.08465i
$799$	2.62393	−	3.61153i	0.0928281	−	0.127767i
$800$	−0.777902	+	3.12000i	−0.0275030	+	0.110308i
$801$	−25.3170	−	19.7798i	−0.894534	−	0.698886i
$802$	32.5882	+	5.74619i	1.15073	+	0.202905i
$803$	9.55043	−	12.2341i	0.337028	−	0.431733i
$804$	2.32460	−	0.846085i	0.0819823	−	0.0298391i
$805$	−15.0076	+	13.5129i	−0.528950	+	0.476269i
$806$	6.12068	−	13.7473i	0.215592	−	0.484227i
$807$	−11.6059	−	46.5486i	−0.408546	−	1.63859i
$808$	−2.38666	−	0.964274i	−0.0839624	−	0.0339230i
$809$	−30.8549	−	27.7819i	−1.08480	−	0.976759i	−0.0849938	−	0.996381i	$-0.527087\pi$
$809$	−30.8549	−	27.7819i	−1.08480	−	0.976759i	−0.999807	+	0.0196221i	$0.993754\pi$
$810$	10.5139	−	4.68107i	0.369419	−	0.164476i
$811$	−7.45193	+	11.0479i	−0.261673	+	0.387946i	−0.936862	−	0.349699i	$-0.886284\pi$
$811$	−7.45193	+	11.0479i	−0.261673	+	0.387946i	0.675190	+	0.737644i	$0.264062\pi$
$812$	2.28585	−	16.2646i	0.0802175	−	0.570777i
$813$	−5.83010	+	33.0641i	−0.204470	+	1.15961i
$814$	−16.3533	+	1.15013i	−0.573181	+	0.0403119i
$815$	21.7740	−	18.2706i	0.762710	−	0.639990i
$816$	0.796597	−	2.45167i	0.0278865	−	0.0858257i
$817$	6.14143	+	1.61390i	0.214861	+	0.0564632i
$818$	−6.61846	−	4.80859i	−0.231409	−	0.168128i
$819$	−13.9728	+	22.3612i	−0.488251	+	0.781364i
$820$	−0.00208886	+	0.0598173i	−7.29463e−5	+	0.00208891i
$821$	18.1868	+	18.8330i	0.634725	+	0.657277i	0.957242	−	0.289287i	$-0.0934181\pi$
$821$	18.1868	+	18.8330i	0.634725	+	0.657277i	−0.322518	+	0.946563i	$0.604529\pi$
$822$	−37.0458	+	38.3620i	−1.29212	+	1.33803i
$823$	−1.68925	−	48.3737i	−0.0588835	−	1.68620i	−0.566063	−	0.824362i	$-0.691534\pi$
$823$	−1.68925	−	48.3737i	−0.0588835	−	1.68620i	0.507179	−	0.861840i	$-0.330688\pi$
$824$	−3.56763	−	2.05977i	−0.124284	−	0.0717555i
$825$	−26.3896	+	0.0105899i	−0.918769	+	0.000368694i
$826$	−27.3873	−	22.9807i	−0.952928	−	0.799601i
$827$	3.33569	−	2.08437i	0.115993	−	0.0724806i	−0.470682	−	0.882303i	$-0.655992\pi$
$827$	3.33569	−	2.08437i	0.115993	−	0.0724806i	0.586675	+	0.809822i	$0.300437\pi$
$828$	−12.0820	−	5.37927i	−0.419880	−	0.186942i
$829$	−5.63342	−	12.6529i	−0.195657	−	0.439453i	0.788899	−	0.614523i	$-0.210651\pi$
$829$	−5.63342	−	12.6529i	−0.195657	−	0.439453i	−0.984556	+	0.175070i	$0.943985\pi$
$830$	−6.64302	+	5.19010i	−0.230583	+	0.180151i
$831$	47.2783	−	25.1383i	1.64006	−	0.872038i
$832$	1.70119	−	1.64282i	0.0589780	−	0.0569544i
$833$	1.64958	+	5.75277i	0.0571546	+	0.199322i
$834$	−6.47521	−	16.0267i	−0.224218	−	0.554960i
$835$	30.4061			1.05225
$836$	11.5002	−	8.76051i	0.397741	−	0.302989i
$837$	−1.93904			−0.0670229
$838$	−5.04906	−	12.4969i	−0.174417	−	0.431697i
$839$	−4.83355	−	16.8566i	−0.166873	−	0.581954i	−0.999600	−	0.0282714i	$-0.991000\pi$
$839$	−4.83355	−	16.8566i	−0.166873	−	0.581954i	0.832728	−	0.553683i	$-0.186778\pi$
$840$	−8.48874	+	8.19748i	−0.292889	+	0.282840i
$841$	6.91635	−	3.67749i	0.238495	−	0.126810i
$842$	11.8807	−	9.28219i	0.409434	−	0.319885i
$843$	1.73572	+	3.89849i	0.0597813	+	0.134271i
$844$	−2.69345	−	1.19920i	−0.0927122	−	0.0412781i
$845$	−8.39126	+	5.24344i	−0.288668	+	0.180380i
$846$	−10.2521	−	8.60251i	−0.352474	−	0.295760i
$847$	34.0243	+	19.6075i	1.16909	+	0.673723i
$848$	−11.0776	−	6.39564i	−0.380405	−	0.219627i
$849$	0.743854	+	21.3012i	0.0255290	+	0.731055i
$850$	−2.32697	+	2.40964i	−0.0798143	+	0.0826501i
$851$	14.5401	+	15.0567i	0.498429	+	0.516138i
$852$	0.171097	−	4.89959i	0.00586170	−	0.167857i
$853$	−26.2754	+	42.0495i	−0.899654	+	1.43975i	−0.00153226	+	0.999999i	$0.500488\pi$
$853$	−26.2754	+	42.0495i	−0.899654	+	1.43975i	−0.898121	+	0.439748i	$0.855068\pi$
$854$	−11.5310	−	8.37773i	−0.394581	−	0.286680i
$855$	−14.8463	+	10.5025i	−0.507732	+	0.359178i
$856$	−5.41789	+	16.6746i	−0.185180	+	0.569925i
$857$	3.72928	−	3.12923i	0.127390	−	0.106893i	−0.576867	−	0.816838i	$-0.695725\pi$
$857$	3.72928	−	3.12923i	0.127390	−	0.106893i	0.704257	+	0.709946i	$0.251280\pi$
$858$	16.4638	+	10.2786i	0.562066	+	0.350904i
$859$	7.66972	−	43.4971i	0.261687	−	1.48410i	−0.516618	−	0.856216i	$-0.672809\pi$
$859$	7.66972	−	43.4971i	0.261687	−	1.48410i	0.778305	−	0.627887i	$-0.216080\pi$
$860$	−0.270836	+	1.92710i	−0.00923542	+	0.0657134i
$861$	0.221334	−	0.328141i	0.00754304	−	0.0111830i
$862$	13.3302	−	5.93497i	0.454027	−	0.202146i
$863$	−3.42029	−	3.07965i	−0.116428	−	0.104832i	0.608860	−	0.793277i	$-0.291627\pi$
$863$	−3.42029	−	3.07965i	−0.116428	−	0.104832i	−0.725289	+	0.688445i	$0.758294\pi$
$864$	−0.282542	−	0.114154i	−0.00961226	−	0.00388361i
$865$	−3.60550	−	14.4609i	−0.122591	−	0.491684i
$866$	−8.54535	+	19.1932i	−0.290383	+	0.652210i
$867$	−29.2658	+	26.3510i	−0.993918	+	0.894928i
$868$	−21.3461	+	7.76936i	−0.724535	+	0.263709i
$869$	−5.13963	+	14.1387i	−0.174350	+	0.479622i
$870$	14.9769	+	2.64084i	0.507766	+	0.0895328i
$871$	1.86305	+	1.45558i	0.0631271	+	0.0493203i
$872$	−4.68192	+	18.7782i	−0.158550	+	0.635909i
$873$	30.5418	−	42.0372i	1.03368	−	1.42274i
$874$	−18.0051	−	4.06549i	−0.609032	−	0.137517i
$875$	37.2617	−	12.1071i	1.25968	−	0.409293i
$876$	−11.5514	+	0.807755i	−0.390287	+	0.0272915i
$877$	0.455802	−	0.130699i	0.0153913	−	0.00441339i	−0.267933	−	0.963438i	$-0.586341\pi$
$877$	0.455802	−	0.130699i	0.0153913	−	0.00441339i	0.283324	+	0.959024i	$0.408563\pi$
$878$	31.7512	+	16.8824i	1.07155	+	0.569754i
$879$	43.7827	−	7.72007i	1.47675	−	0.260391i
$880$	3.07897	+	3.18581i	0.103792	+	0.107393i
$881$	24.7605	−	42.8864i	0.834202	−	1.44488i	−0.0604759	−	0.998170i	$-0.519262\pi$
$881$	24.7605	−	42.8864i	0.834202	−	1.44488i	0.894678	−	0.446711i	$-0.147405\pi$
$882$	17.5495	−	3.73025i	0.590921	−	0.125604i
$883$	−18.8918	−	1.32104i	−0.635760	−	0.0444567i	−0.251760	−	0.967790i	$-0.581009\pi$
$883$	−18.8918	−	1.32104i	−0.635760	−	0.0444567i	−0.384000	+	0.923333i	$0.625454\pi$
$884$	2.39051	−	0.596021i	0.0804016	−	0.0200464i
$885$	22.1507	−	24.6008i	0.744587	−	0.826947i
$886$	33.2274	+	7.06269i	1.11630	+	0.237276i
$887$	−28.9383	−	8.29792i	−0.971653	−	0.278617i	−0.247984	−	0.968764i	$-0.579768\pi$
$887$	−28.9383	−	8.29792i	−0.971653	−	0.278617i	−0.723669	+	0.690147i	$0.757546\pi$
$888$	8.79834	+	8.49646i	0.295253	+	0.285122i
$889$	28.5762	−	53.7440i	0.958416	−	1.80252i
$890$	4.69999	−	12.9131i	0.157544	−	0.432849i
$891$	−3.96538	+	28.2975i	−0.132845	+	0.948003i
$892$			25.3399i			0.848444i
$893$	−16.3800	−	8.97666i	−0.548137	−	0.300392i
$894$	−24.7356	+	17.9715i	−0.827282	+	0.601055i
$895$	−0.132326	−	1.89235i	−0.00442317	−	0.0632543i
$896$	−3.56780	−	0.124590i	−0.119192	−	0.00416227i
$897$	−3.44888	−	24.5400i	−0.115155	−	0.819368i
$898$	6.54427	+	3.19185i	0.218385	+	0.106514i
$899$	24.2700	+	16.3703i	0.809451	+	0.545981i
$900$	6.71975	+	7.46304i	0.223992	+	0.248768i
$901$	−6.66274	−	11.5402i	−0.221968	−	0.384460i
$902$	−0.123232	−	0.0830488i	−0.00410316	−	0.00276522i
$903$	8.27205	−	9.85824i	0.275276	−	0.328062i
$904$	−2.98251	−	14.0316i	−0.0991967	−	0.466684i
$905$	32.6646	−	3.43319i	1.08581	−	0.114123i
$906$	−6.04051	+	21.0658i	−0.200683	+	0.699863i
$907$	−25.0325	−	47.0792i	−0.831190	−	1.56324i	−0.826285	−	0.563253i	$-0.809550\pi$
$907$	−25.0325	−	47.0792i	−0.831190	−	1.56324i	−0.00490523	−	0.999988i	$-0.501561\pi$
$908$	11.9425	−	1.67840i	0.396324	−	0.0556998i
$909$	−6.66487	+	4.49551i	−0.221060	+	0.149107i
$910$	−10.9432	−	2.72844i	−0.362763	−	0.0904470i
$911$	15.7364	+	5.11308i	0.521372	+	0.169404i	0.557868	−	0.829930i	$-0.311620\pi$
$911$	15.7364	+	5.11308i	0.521372	+	0.169404i	−0.0364961	+	0.999334i	$0.511620\pi$
$912$	−10.5977	−	2.00702i	−0.350926	−	0.0664591i
$913$	−2.19615	−	20.8146i	−0.0726820	−	0.688864i
$914$	0.212112	+	0.252785i	0.00701604	+	0.00836139i
$915$	8.12511	−	10.3997i	0.268608	−	0.343803i
$916$	−7.63527	−	15.6546i	−0.252276	−	0.517243i
$917$	−6.82435	+	13.9920i	−0.225360	+	0.462056i
$918$	−0.195446	−	0.250160i	−0.00645069	−	0.00825651i
$919$	9.39630	−	44.2061i	0.309955	−	1.45823i	−0.497071	−	0.867710i	$-0.665591\pi$
$919$	9.39630	−	44.2061i	0.309955	−	1.45823i	0.807026	−	0.590515i	$-0.201076\pi$
$920$	0.591301	−	5.62586i	0.0194946	−	0.185479i
$921$	4.92076	−	70.3701i	0.162144	−	2.31877i
$922$	−15.3675	−	24.5931i	−0.506101	−	0.809931i
$923$	4.05775	−	2.34274i	0.133562	−	0.0771123i
$924$	−6.10304	−	28.6560i	−0.200775	−	0.942714i
$925$	−5.43602	−	14.9353i	−0.178735	−	0.491071i
$926$	−7.11018	−	0.999271i	−0.233655	−	0.0328381i
$927$	−11.5638	+	5.64006i	−0.379806	+	0.185244i
$928$	2.57270	+	3.81418i	0.0844529	+	0.125207i
$929$	20.0506	+	12.5290i	0.657839	+	0.411064i	0.817357	−	0.576131i	$-0.195438\pi$
$929$	20.0506	+	12.5290i	0.657839	+	0.411064i	−0.159518	+	0.987195i	$0.550994\pi$
$930$	−6.49974	−	20.0041i	−0.213135	−	0.655962i
$931$	23.0025	−	9.89511i	0.753876	−	0.324299i
$932$	16.8102	+	23.1372i	0.550636	+	0.757885i
$933$	−1.02932	+	0.415871i	−0.0336984	+	0.0136150i
$934$	7.69523	+	2.80083i	0.251796	+	0.0916461i
$935$	1.11840	+	4.47799i	0.0365755	+	0.146446i
$936$	−1.28257	−	7.27381i	−0.0419221	−	0.237752i
$937$	25.6638	−	0.896201i	0.838401	−	0.0292776i	0.387520	−	0.921861i	$-0.373332\pi$
$937$	25.6638	−	0.896201i	0.838401	−	0.0292776i	0.450881	+	0.892584i	$0.351110\pi$
$938$	−0.373056	−	3.54939i	−0.0121807	−	0.115892i
$939$	−18.4914	−	1.94353i	−0.603445	−	0.0634247i
$940$	2.14436	−	5.30748i	0.0699413	−	0.173111i
$941$	−10.3583	+	25.6376i	−0.337670	+	0.835762i	0.658840	+	0.752283i	$0.271047\pi$
$941$	−10.3583	+	25.6376i	−0.337670	+	0.835762i	−0.996510	+	0.0834784i	$0.973397\pi$
$942$	33.9590	+	3.56923i	1.10644	+	0.116292i
$943$	0.0198329	+	0.188697i	0.000645847	+	0.00614483i
$944$	10.0084	−	0.349503i	0.325747	−	0.0113753i
$945$	0.252353	+	1.43117i	0.00820905	+	0.0465558i
$946$	−3.70246	−	3.10420i	−0.120377	−	0.100926i
$947$	−15.2654	−	5.55614i	−0.496058	−	0.180550i	0.0818621	−	0.996644i	$-0.473913\pi$
$947$	−15.2654	−	5.55614i	−0.496058	−	0.180550i	−0.577920	+	0.816093i	$0.696136\pi$
$948$	10.4068	−	4.20461i	0.337996	−	0.136559i
$949$	−6.50496	−	8.95330i	−0.211160	−	0.290637i
$950$	11.2343	+	8.38103i	0.364488	+	0.271917i
$951$	18.0828	+	55.6532i	0.586375	+	1.80468i
$952$	−3.15394	−	1.97080i	−0.102220	−	0.0638741i
$953$	−23.2497	−	34.4692i	−0.753133	−	1.11657i	−0.989448	−	0.144889i	$-0.953718\pi$
$953$	−23.2497	−	34.4692i	−0.753133	−	1.11657i	0.236315	−	0.971676i	$-0.424060\pi$
$954$	−35.9060	+	17.5125i	−1.16250	+	0.566989i
$955$	9.04006	+	1.27050i	0.292530	+	0.0411124i
$956$	6.56330	+	18.0325i	0.212272	+	0.583213i
$957$	−25.2539	+	28.0699i	−0.816342	+	0.907372i
$958$	−7.73430	+	4.46540i	−0.249884	+	0.144271i
$959$	40.7713	+	65.2477i	1.31657	+	2.10696i
$960$	0.230584	−	3.29750i	0.00744206	−	0.106426i
$961$	0.991880	−	9.43711i	0.0319961	−	0.304423i
$962$	−2.43039	+	11.4341i	−0.0783589	+	0.368650i
$963$	33.7119	+	43.1492i	1.08635	+	1.39046i
$964$	5.88011	−	12.0560i	0.189386	−	0.388298i
$965$	−2.57989	−	5.28955i	−0.0830495	−	0.170277i
$966$	−23.0309	+	29.4782i	−0.741008	+	0.948446i
$967$	−5.12966	−	6.11330i	−0.164959	−	0.196590i	0.677232	−	0.735769i	$-0.263179\pi$
$967$	−5.12966	−	6.11330i	−0.164959	−	0.196590i	−0.842191	+	0.539179i	$0.818735\pi$
$968$	−10.7578	+	2.29566i	−0.345768	+	0.0737854i
$969$	−8.51577	−	7.33088i	−0.273566	−	0.235502i
$970$	21.1372	+	6.86788i	0.678673	+	0.220514i
$971$	−37.3684	−	9.31699i	−1.19921	−	0.298996i	−0.409403	−	0.912353i	$-0.634263\pi$
$971$	−37.3684	−	9.31699i	−1.19921	−	0.298996i	−0.789806	+	0.613357i	$0.789819\pi$
$972$	18.4320	−	12.4325i	0.591206	−	0.398773i
$973$	−24.6950	+	3.47065i	−0.791685	+	0.111264i
$974$	−0.721939	−	1.35777i	−0.0231324	−	0.0435058i
$975$	−5.18672	+	18.0882i	−0.166108	+	0.579288i
$976$	3.97061	−	0.417328i	0.127096	−	0.0133583i
$977$	−7.91626	−	37.2431i	−0.253263	−	1.19151i	−0.902420	−	0.430857i	$-0.858212\pi$
$977$	−7.91626	−	37.2431i	−0.253263	−	1.19151i	0.649157	−	0.760654i	$-0.275122\pi$
$978$	33.8440	−	40.3337i	1.08221	−	1.28973i
$979$	21.0160	+	26.8770i	0.671673	+	0.858992i
$980$	3.83702	+	6.64591i	0.122569	+	0.212296i
$981$	40.4438	+	44.9174i	1.29127	+	1.43410i
$982$	1.85026	+	1.24802i	0.0590442	+	0.0398258i
$983$	31.0965	+	15.1668i	0.991825	+	0.483745i	0.861517	−	0.507728i	$-0.169515\pi$
$983$	31.0965	+	15.1668i	0.991825	+	0.483745i	0.130307	+	0.991474i	$0.458404\pi$
$984$	0.0154304	+	0.109793i	0.000491903	+	0.00350007i
$985$	−8.09255	−	0.282598i	−0.257850	−	0.00900433i
$986$	0.334334	+	4.78120i	0.0106474	+	0.152264i
$987$	−30.6249	+	22.2503i	−0.974802	+	0.708235i
$988$	−3.74058	−	9.60587i	−0.119004	−	0.305603i
$989$			6.16894i			0.196161i
$990$	13.6260	−	2.40826i	0.433061	−	0.0765396i
$991$	−14.5337	+	39.9311i	−0.461679	+	1.26845i	0.462544	+	0.886597i	$0.346937\pi$
$991$	−14.5337	+	39.9311i	−0.461679	+	1.26845i	−0.924222	+	0.381855i	$0.875285\pi$
$992$	2.98730	−	5.61829i	0.0948468	−	0.178381i
$993$	27.2563	+	26.3211i	0.864952	+	0.835274i
$994$	−6.79897	−	1.94957i	−0.215650	−	0.0618367i
$995$	−22.7282	−	4.83102i	−0.720531	−	0.153154i
$996$	−10.4490	+	11.6048i	−0.331089	+	0.367712i
$997$	60.4074	−	15.0612i	1.91312	−	0.476995i	0.915999	−	0.401181i	$-0.131400\pi$
$997$	60.4074	−	15.0612i	1.91312	−	0.476995i	0.997122	−	0.0758131i	$-0.0241552\pi$
$998$	1.82343	+	0.127507i	0.0577197	+	0.00403615i
$999$	1.47333	−	0.313166i	0.0466141	−	0.00990814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.v.a.13.8	✓	240
11.6	odd	10		418.2.v.b.127.3	yes	240
19.3	odd	18		418.2.v.b.79.3	yes	240
209.193	even	90	inner	418.2.v.a.193.8	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.v.a.13.8	✓	240	1.1	even	1	trivial
418.2.v.a.193.8	yes	240	209.193	even	90	inner
418.2.v.b.79.3	yes	240	19.3	odd	18
418.2.v.b.127.3	yes	240	11.6	odd	10

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.v (of order \(90\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.374607 + 0.927184i) q^{2} +(0.682065 + 2.37864i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(-1.17948 + 0.627143i) q^{5} +(-1.94993 + 1.52345i) q^{6} +(1.45204 + 3.26133i) q^{7} +(-0.913545 - 0.406737i) q^{8} +(-2.64858 + 1.65502i) q^{9} +O(q^{10})\)	\(q+(0.374607 + 0.927184i) q^{2} +(0.682065 + 2.37864i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(-1.17948 + 0.627143i) q^{5} +(-1.94993 + 1.52345i) q^{6} +(1.45204 + 3.26133i) q^{7} +(-0.913545 - 0.406737i) q^{8} +(-2.64858 + 1.65502i) q^{9} +(-1.02332 - 0.858667i) q^{10} +(3.15389 - 1.02616i) q^{11} +(-2.14298 - 1.23725i) q^{12} +(-0.0825347 - 2.36349i) q^{13} +(-2.47991 + 2.56802i) q^{14} +(-2.29623 - 2.37782i) q^{15} +(0.0348995 - 0.999391i) q^{16} +(0.552050 - 0.883465i) q^{17} +(-2.52668 - 1.83574i) q^{18} +(-3.95934 - 1.82309i) q^{19} +(0.412800 - 1.27047i) q^{20} +(-6.76715 + 5.67832i) q^{21} +(2.13290 + 2.53983i) q^{22} +(0.735339 - 4.17031i) q^{23} +(0.344384 - 2.45042i) q^{24} +(-1.79809 + 2.66578i) q^{25} +(2.16047 - 0.961902i) q^{26} +(-0.226459 - 0.203905i) q^{27} +(-3.31002 - 1.33733i) q^{28} +(1.11302 + 4.46407i) q^{29} +(1.34449 - 3.01978i) q^{30} +(4.72871 - 4.25775i) q^{31} +(0.939693 - 0.342020i) q^{32} +(4.59202 + 6.80206i) q^{33} +(1.02594 + 0.180900i) q^{34} +(-3.75798 - 2.93605i) q^{35} +(0.755558 - 3.03038i) q^{36} +(-2.90535 + 3.99887i) q^{37} +(0.207141 - 4.35397i) q^{38} +(5.56559 - 1.80837i) q^{39} +(1.33259 - 0.0931841i) q^{40} +(-0.0430701 + 0.0123501i) q^{41} +(-7.79986 - 4.14726i) q^{42} +(-1.43465 + 0.252967i) q^{43} +(-1.55589 + 2.92903i) q^{44} +(2.08603 - 3.61310i) q^{45} +(4.14211 - 0.880433i) q^{46} +(4.27470 + 0.298916i) q^{47} +(2.40100 - 0.598636i) q^{48} +(-3.84395 + 4.26914i) q^{49} +(-3.14524 - 0.668542i) q^{50} +(2.47798 + 0.710549i) q^{51} +(1.70119 + 1.64282i) q^{52} +(6.00514 - 11.2940i) q^{53} +(0.104224 - 0.286353i) q^{54} +(-3.07641 + 3.18828i) q^{55} -3.56997i q^{56} +(1.63594 - 10.6613i) q^{57} +(-3.72207 + 2.70424i) q^{58} +(0.698580 + 9.99015i) q^{59} +(3.30354 + 0.115362i) q^{60} +(0.555646 + 3.95363i) q^{61} +(5.71912 + 2.78940i) q^{62} +(-9.24340 - 6.23475i) q^{63} +(0.669131 + 0.743145i) q^{64} +(1.57959 + 2.73593i) q^{65} +(-4.58656 + 6.80574i) q^{66} +(-0.642603 + 0.765824i) q^{67} +(0.216595 + 1.01900i) q^{68} +(10.4212 - 1.09532i) q^{69} +(1.31450 - 4.58420i) q^{70} +(0.930136 + 1.74933i) q^{71} +(3.09275 - 0.434658i) q^{72} +(3.87956 - 2.61679i) q^{73} +(-4.79605 - 1.19579i) q^{74} +(-7.56734 - 2.45878i) q^{75} +(4.11453 - 1.43897i) q^{76} +(7.92621 + 8.79584i) q^{77} +(3.76160 + 4.48290i) q^{78} +(-2.79258 + 3.57433i) q^{79} +(0.585597 + 1.20065i) q^{80} +(-3.77674 + 7.74346i) q^{81} +(-0.0275852 - 0.0353074i) q^{82} +(1.31206 - 6.17278i) q^{83} +(0.923393 - 8.78550i) q^{84} +(-0.0970757 + 1.38825i) q^{85} +(-0.771975 - 1.23542i) q^{86} +(-9.85928 + 5.69226i) q^{87} +(-3.29859 - 0.345358i) q^{88} +(3.51836 + 9.66661i) q^{89} +(4.13145 + 0.580637i) q^{90} +(7.58827 - 3.70104i) q^{91} +(2.36798 + 3.51068i) q^{92} +(13.3529 + 8.34384i) q^{93} +(1.32418 + 4.07541i) q^{94} +(5.81331 - 0.332771i) q^{95} +(1.45447 + 2.00191i) q^{96} +(-15.4258 + 6.23245i) q^{97} +(-5.39824 - 1.96480i) q^{98} +(-6.65501 + 7.93760i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9}+O(q^{10}) \) 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9	\( 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9} - 3 q^{11} - 6 q^{13} - 18 q^{14} + 21 q^{15} + 21 q^{17} - 60 q^{18} + 45 q^{19} + 12 q^{20} + 48 q^{21} - 12 q^{22} + 12 q^{24} - 18 q^{25} - 96 q^{26} - 9 q^{27} - 6 q^{28} + 18 q^{29} + 9 q^{31} + 87 q^{33} - 24 q^{34} - 36 q^{35} - 12 q^{36} - 36 q^{38} + 60 q^{41} - 6 q^{42} - 12 q^{43} + 18 q^{44} + 48 q^{45} + 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} - 21 q^{50} - 75 q^{51} + 3 q^{52} - 39 q^{53} + 27 q^{54} - 126 q^{55} - 90 q^{57} - 24 q^{58} + 69 q^{59} - 42 q^{60} + 66 q^{61} - 45 q^{62} - 9 q^{63} + 30 q^{64} - 12 q^{66} - 9 q^{67} + 12 q^{68} - 54 q^{69} + 9 q^{70} + 48 q^{71} + 6 q^{72} - 12 q^{74} + 72 q^{77} - 36 q^{79} - 27 q^{81} + 45 q^{82} + 36 q^{83} + 36 q^{84} - 210 q^{85} + 3 q^{86} + 216 q^{87} + 3 q^{88} + 18 q^{89} - 96 q^{90} - 108 q^{91} - 30 q^{92} + 147 q^{93} - 18 q^{94} + 66 q^{95} - 9 q^{97} - 12 q^{98} - 42 q^{99}+O(q^{100}) \) 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9 - 3 * q^11 - 6 * q^13 - 18 * q^14 + 21 * q^15 + 21 * q^17 - 60 * q^18 + 45 * q^19 + 12 * q^20 + 48 * q^21 - 12 * q^22 + 12 * q^24 - 18 * q^25 - 96 * q^26 - 9 * q^27 - 6 * q^28 + 18 * q^29 + 9 * q^31 + 87 * q^33 - 24 * q^34 - 36 * q^35 - 12 * q^36 - 36 * q^38 + 60 * q^41 - 6 * q^42 - 12 * q^43 + 18 * q^44 + 48 * q^45 + 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 - 21 * q^50 - 75 * q^51 + 3 * q^52 - 39 * q^53 + 27 * q^54 - 126 * q^55 - 90 * q^57 - 24 * q^58 + 69 * q^59 - 42 * q^60 + 66 * q^61 - 45 * q^62 - 9 * q^63 + 30 * q^64 - 12 * q^66 - 9 * q^67 + 12 * q^68 - 54 * q^69 + 9 * q^70 + 48 * q^71 + 6 * q^72 - 12 * q^74 + 72 * q^77 - 36 * q^79 - 27 * q^81 + 45 * q^82 + 36 * q^83 + 36 * q^84 - 210 * q^85 + 3 * q^86 + 216 * q^87 + 3 * q^88 + 18 * q^89 - 96 * q^90 - 108 * q^91 - 30 * q^92 + 147 * q^93 - 18 * q^94 + 66 * q^95 - 9 * q^97 - 12 * q^98 - 42 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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