LMFDB - Embedded newform 216.2.t.a.13.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(13,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 8]))

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

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

chi := DirichletCharacter("216.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.t (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			13.20
Character	$\chi$	$=$	216.13
Dual form			216.2.t.a.133.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.289471 + 1.38427i) q^{2} +(-1.40283 + 1.01591i) q^{3} +(-1.83241 + 0.801412i) q^{4} +(-1.55785 + 1.85658i) q^{5} +(-1.81237 - 1.64782i) q^{6} +(0.763942 + 0.278052i) q^{7} +(-1.63980 - 2.30457i) q^{8} +(0.935847 - 2.85030i) q^{9} +O(q^{10})$	\(q+(0.289471 + 1.38427i) q^{2} +(-1.40283 + 1.01591i) q^{3} +(-1.83241 + 0.801412i) q^{4} +(-1.55785 + 1.85658i) q^{5} +(-1.81237 - 1.64782i) q^{6} +(0.763942 + 0.278052i) q^{7} +(-1.63980 - 2.30457i) q^{8} +(0.935847 - 2.85030i) q^{9} +(-3.02096 - 1.61907i) q^{10} +(-2.23007 - 2.65769i) q^{11} +(1.75640 - 2.98581i) q^{12} +(2.83964 + 0.500705i) q^{13} +(-0.163761 + 1.13799i) q^{14} +(0.299281 - 4.18710i) q^{15} +(2.71548 - 2.93704i) q^{16} +(-3.55127 + 6.15099i) q^{17} +(4.21648 + 0.470389i) q^{18} +(-5.16371 + 2.98127i) q^{19} +(1.36675 - 4.65050i) q^{20} +(-1.35415 + 0.386038i) q^{21} +(3.03343 - 3.85634i) q^{22} +(-6.58997 + 2.39855i) q^{23} +(4.64160 + 1.56702i) q^{24} +(-0.151733 - 0.860521i) q^{25} +(0.128881 + 4.07577i) q^{26} +(1.58282 + 4.94921i) q^{27} +(-1.62269 + 0.102726i) q^{28} +(6.59552 - 1.16297i) q^{29} +(5.88272 - 0.797758i) q^{30} +(2.55724 - 0.930757i) q^{31} +(4.85171 + 2.90877i) q^{32} +(5.82838 + 1.46273i) q^{33} +(-9.54262 - 3.13539i) q^{34} +(-1.70634 + 0.985154i) q^{35} +(0.569403 + 5.97292i) q^{36} +(3.59434 + 2.07519i) q^{37} +(-5.62163 - 6.28499i) q^{38} +(-4.49220 + 2.18242i) q^{39} +(6.83319 + 0.545766i) q^{40} +(-0.742124 + 4.20880i) q^{41} +(-0.926370 - 1.76277i) q^{42} +(-1.77034 - 2.10981i) q^{43} +(6.21631 + 3.08279i) q^{44} +(3.83389 + 6.17782i) q^{45} +(-5.22785 - 8.42800i) q^{46} +(2.80028 + 1.01922i) q^{47} +(-0.825575 + 6.87884i) q^{48} +(-4.85602 - 4.07468i) q^{49} +(1.14727 - 0.459136i) q^{50} +(-1.26704 - 12.2365i) q^{51} +(-5.60467 + 1.35822i) q^{52} +7.38929i q^{53} +(-6.39287 + 3.62370i) q^{54} +8.40834 q^{55} +(-0.611922 - 2.21651i) q^{56} +(4.21509 - 9.42808i) q^{57} +(3.51907 + 8.79334i) q^{58} +(-4.72368 + 5.62947i) q^{59} +(2.80719 + 7.91235i) q^{60} +(0.0900385 - 0.247379i) q^{61} +(2.02867 + 3.27048i) q^{62} +(1.50746 - 1.91725i) q^{63} +(-2.62210 + 7.55808i) q^{64} +(-5.35335 + 4.49199i) q^{65} +(-0.337669 + 8.49148i) q^{66} +(2.20513 + 0.388825i) q^{67} +(1.57793 - 14.1172i) q^{68} +(6.80787 - 10.0596i) q^{69} +(-1.85765 - 2.07686i) q^{70} +(2.69918 - 4.67512i) q^{71} +(-8.10332 + 2.51719i) q^{72} +(-1.97245 - 3.41639i) q^{73} +(-1.83217 + 5.57624i) q^{74} +(1.08707 + 1.05302i) q^{75} +(7.07283 - 9.60118i) q^{76} +(-0.964666 - 2.65040i) q^{77} +(-4.32142 - 5.58667i) q^{78} +(1.76846 + 10.0295i) q^{79} +(1.22252 + 9.61697i) q^{80} +(-7.24838 - 5.33489i) q^{81} +(-6.04094 + 0.191022i) q^{82} +(7.86515 - 1.38684i) q^{83} +(2.17200 - 1.79262i) q^{84} +(-5.88742 - 16.1756i) q^{85} +(2.40809 - 3.06136i) q^{86} +(-8.07090 + 8.33191i) q^{87} +(-2.46797 + 9.49744i) q^{88} +(2.14833 + 3.72101i) q^{89} +(-7.44198 + 7.09544i) q^{90} +(2.03010 + 1.17208i) q^{91} +(10.1533 - 9.67643i) q^{92} +(-2.64179 + 3.90362i) q^{93} +(-0.600276 + 4.17138i) q^{94} +(2.50935 - 14.2312i) q^{95} +(-9.76116 + 0.848403i) q^{96} +(4.28345 - 3.59424i) q^{97} +(4.23479 - 7.90155i) q^{98} +(-9.66221 + 3.86916i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.289471	+	1.38427i	0.204687	+	0.978828i
$2$	0.289471	+	1.38427i	0.204687	+	0.978828i
$3$	−1.40283	+	1.01591i	−0.809923	+	0.586537i
$3$	−1.40283	+	1.01591i	−0.809923	+	0.586537i
$4$	−1.83241	+	0.801412i	−0.916207	+	0.400706i
$5$	−1.55785	+	1.85658i	−0.696694	+	0.830287i	−0.992148	−	0.125070i	$-0.960085\pi$
$5$	−1.55785	+	1.85658i	−0.696694	+	0.830287i	0.295454	+	0.955357i	$0.404529\pi$
$6$	−1.81237	−	1.64782i	−0.739899	−	0.672718i
$7$	0.763942	+	0.278052i	0.288743	+	0.105094i	0.482331	−	0.875989i	$-0.339790\pi$
$7$	0.763942	+	0.278052i	0.288743	+	0.105094i	−0.193588	+	0.981083i	$0.562012\pi$
$8$	−1.63980	−	2.30457i	−0.579758	−	0.814789i
$9$	0.935847	−	2.85030i	0.311949	−	0.950099i
$10$	−3.02096	−	1.61907i	−0.955312	−	0.511994i
$11$	−2.23007	−	2.65769i	−0.672391	−	0.801324i	0.316716	−	0.948520i	$-0.397420\pi$
$11$	−2.23007	−	2.65769i	−0.672391	−	0.801324i	−0.989107	+	0.147196i	$0.952975\pi$
$12$	1.75640	−	2.98581i	0.507028	−	0.861930i
$13$	2.83964	+	0.500705i	0.787574	+	0.138871i	0.552949	−	0.833215i	$-0.313502\pi$
$13$	2.83964	+	0.500705i	0.787574	+	0.138871i	0.234626	+	0.972086i	$0.424614\pi$
$14$	−0.163761	+	1.13799i	−0.0437669	+	0.304141i
$15$	0.299281	−	4.18710i	0.0772740	−	1.08110i
$16$	2.71548	−	2.93704i	0.678869	−	0.734259i
$17$	−3.55127	+	6.15099i	−0.861310	+	1.49183i	0.00935441	+	0.999956i	$0.497022\pi$
$17$	−3.55127	+	6.15099i	−0.861310	+	1.49183i	−0.870665	+	0.491877i	$0.836311\pi$
$18$	4.21648	+	0.470389i	0.993835	+	0.110872i
$19$	−5.16371	+	2.98127i	−1.18464	+	0.683950i	−0.957083	−	0.289815i	$-0.906406\pi$
$19$	−5.16371	+	2.98127i	−1.18464	+	0.683950i	−0.227554	+	0.973765i	$0.573073\pi$
$20$	1.36675	−	4.65050i	0.305614	−	1.03988i
$21$	−1.35415	+	0.386038i	−0.295501	+	0.0842405i
$22$	3.03343	−	3.85634i	0.646729	−	0.822175i
$23$	−6.58997	+	2.39855i	−1.37410	+	0.500133i	−0.920386	−	0.391012i	$-0.872125\pi$
$23$	−6.58997	+	2.39855i	−1.37410	+	0.500133i	−0.453719	+	0.891145i	$0.649903\pi$
$24$	4.64160	+	1.56702i	0.947462	+	0.319867i
$25$	−0.151733	−	0.860521i	−0.0303466	−	0.172104i
$26$	0.128881	+	4.07577i	0.0252757	+	0.799325i
$27$	1.58282	+	4.94921i	0.304613	+	0.952476i
$28$	−1.62269	+	0.102726i	−0.306660	+	0.0194134i
$29$	6.59552	−	1.16297i	1.22476	−	0.215958i	0.476385	−	0.879237i	$-0.341947\pi$
$29$	6.59552	−	1.16297i	1.22476	−	0.215958i	0.748372	+	0.663279i	$0.230836\pi$
$30$	5.88272	−	0.797758i	1.07403	−	0.145650i
$31$	2.55724	−	0.930757i	0.459293	−	0.167169i	−0.102003	−	0.994784i	$-0.532525\pi$
$31$	2.55724	−	0.930757i	0.459293	−	0.167169i	0.561296	+	0.827615i	$0.310303\pi$
$32$	4.85171	+	2.90877i	0.857669	+	0.514203i
$33$	5.82838	+	1.46273i	1.01459	+	0.254629i
$34$	−9.54262	−	3.13539i	−1.63655	−	0.537716i
$35$	−1.70634	+	0.985154i	−0.288423	+	0.166521i
$36$	0.569403	+	5.97292i	0.0949005	+	0.995487i
$37$	3.59434	+	2.07519i	0.590905	+	0.341159i	0.765455	−	0.643489i	$-0.222514\pi$
$37$	3.59434	+	2.07519i	0.590905	+	0.341159i	−0.174550	+	0.984648i	$0.555847\pi$
$38$	−5.62163	−	6.28499i	−0.911949	−	1.01956i
$39$	−4.49220	+	2.18242i	−0.719327	+	0.349467i
$40$	6.83319	+	0.545766i	1.08042	+	0.0862932i
$41$	−0.742124	+	4.20880i	−0.115900	+	0.657304i	0.870400	+	0.492345i	$0.163860\pi$
$41$	−0.742124	+	4.20880i	−0.115900	+	0.657304i	−0.986301	+	0.164959i	$0.947251\pi$
$42$	−0.926370	−	1.76277i	−0.142942	−	0.272001i
$43$	−1.77034	−	2.10981i	−0.269975	−	0.321743i	0.613975	−	0.789326i	$-0.289570\pi$
$43$	−1.77034	−	2.10981i	−0.269975	−	0.321743i	−0.883950	+	0.467582i	$0.845125\pi$
$44$	6.21631	+	3.08279i	0.937145	+	0.464748i
$45$	3.83389	+	6.17782i	0.571522	+	0.920935i
$46$	−5.22785	−	8.42800i	−0.770805	−	1.24264i
$47$	2.80028	+	1.01922i	0.408463	+	0.148668i	0.538076	−	0.842896i	$-0.319151\pi$
$47$	2.80028	+	1.01922i	0.408463	+	0.148668i	−0.129613	+	0.991565i	$0.541374\pi$
$48$	−0.825575	+	6.87884i	−0.119162	+	0.992875i
$49$	−4.85602	−	4.07468i	−0.693717	−	0.582097i
$50$	1.14727	−	0.459136i	0.162249	−	0.0649316i
$51$	−1.26704	−	12.2365i	−0.177420	−	1.71346i
$52$	−5.60467	+	1.35822i	−0.777227	+	0.188352i
$53$			7.38929i			1.01500i	0.861653	+	0.507498i	$0.169430\pi$
$53$			7.38929i			1.01500i	−0.861653	+	0.507498i	$0.830570\pi$
$54$	−6.39287	+	3.62370i	−0.869960	+	0.493123i
$55$	8.40834			1.13378
$56$	−0.611922	−	2.21651i	−0.0817716	−	0.296194i
$57$	4.21509	−	9.42808i	0.558302	−	1.24878i
$58$	3.51907	+	8.79334i	0.462077	+	1.15462i
$59$	−4.72368	+	5.62947i	−0.614971	+	0.732894i	−0.980197	−	0.198025i	$-0.936547\pi$
$59$	−4.72368	+	5.62947i	−0.614971	+	0.732894i	0.365226	+	0.930919i	$0.380992\pi$
$60$	2.80719	+	7.91235i	0.362406	+	1.02148i
$61$	0.0900385	−	0.247379i	0.0115283	−	0.0316736i	−0.933795	−	0.357808i	$-0.883524\pi$
$61$	0.0900385	−	0.247379i	0.0115283	−	0.0316736i	0.945323	+	0.326135i	$0.105746\pi$
$62$	2.02867	+	3.27048i	0.257641	+	0.415351i
$63$	1.50746	−	1.91725i	0.189923	−	0.241550i
$64$	−2.62210	+	7.55808i	−0.327762	+	0.944760i
$65$	−5.35335	+	4.49199i	−0.664001	+	0.557163i
$66$	−0.337669	+	8.49148i	−0.0415642	+	1.04523i
$67$	2.20513	+	0.388825i	0.269400	+	0.0475025i	0.306716	−	0.951801i	$-0.400770\pi$
$67$	2.20513	+	0.388825i	0.269400	+	0.0475025i	−0.0373162	+	0.999304i	$0.511881\pi$
$68$	1.57793	−	14.1172i	0.191352	−	1.71196i
$69$	6.80787	−	10.0596i	0.819572	−	1.21103i
$70$	−1.85765	−	2.07686i	−0.222032	−	0.248232i
$71$	2.69918	−	4.67512i	0.320334	−	0.554835i	−0.660223	−	0.751070i	$-0.729538\pi$
$71$	2.69918	−	4.67512i	0.320334	−	0.554835i	0.980557	+	0.196235i	$0.0628714\pi$
$72$	−8.10332	+	2.51719i	−0.954985	+	0.296654i
$73$	−1.97245	−	3.41639i	−0.230858	−	0.399858i	0.727203	−	0.686423i	$-0.240820\pi$
$73$	−1.97245	−	3.41639i	−0.230858	−	0.399858i	−0.958061	+	0.286565i	$0.907487\pi$
$74$	−1.83217	+	5.57624i	−0.212986	+	0.648225i
$75$	1.08707	+	1.05302i	0.125524	+	0.121592i
$76$	7.07283	−	9.60118i	0.811309	−	1.10133i
$77$	−0.964666	−	2.65040i	−0.109934	−	0.302041i
$78$	−4.32142	−	5.58667i	−0.489305	−	0.632566i
$79$	1.76846	+	10.0295i	0.198968	+	1.12840i	0.906654	+	0.421875i	$0.138628\pi$
$79$	1.76846	+	10.0295i	0.198968	+	1.12840i	−0.707686	+	0.706527i	$0.750261\pi$
$80$	1.22252	+	9.61697i	0.136682	+	1.07521i
$81$	−7.24838	−	5.33489i	−0.805375	−	0.592765i
$82$	−6.04094	+	0.191022i	−0.667110	+	0.0210949i
$83$	7.86515	−	1.38684i	0.863312	−	0.152225i	0.275577	−	0.961279i	$-0.411131\pi$
$83$	7.86515	−	1.38684i	0.863312	−	0.152225i	0.587735	+	0.809054i	$0.300020\pi$
$84$	2.17200	−	1.79262i	0.236984	−	0.195591i
$85$	−5.88742	−	16.1756i	−0.638581	−	1.75449i
$86$	2.40809	−	3.06136i	0.259671	−	0.330115i
$87$	−8.07090	+	8.33191i	−0.865292	+	0.893274i
$88$	−2.46797	+	9.49744i	−0.263087	+	1.01243i
$89$	2.14833	+	3.72101i	0.227722	+	0.394426i	0.957133	−	0.289650i	$-0.0935389\pi$
$89$	2.14833	+	3.72101i	0.227722	+	0.394426i	−0.729410	+	0.684076i	$0.760206\pi$
$90$	−7.44198	+	7.09544i	−0.784454	+	0.747925i
$91$	2.03010	+	1.17208i	0.212812	+	0.122867i
$92$	10.1533	−	9.67643i	1.05856	−	1.00884i
$93$	−2.64179	+	3.90362i	−0.273941	+	0.404786i
$94$	−0.600276	+	4.17138i	−0.0619137	+	0.430245i
$95$	2.50935	−	14.2312i	0.257454	−	1.46009i
$96$	−9.76116	+	0.848403i	−0.996244	+	0.0865897i
$97$	4.28345	−	3.59424i	0.434918	−	0.364940i	−0.398886	−	0.917001i	$-0.630603\pi$
$97$	4.28345	−	3.59424i	0.434918	−	0.364940i	0.833804	+	0.552061i	$0.186159\pi$
$98$	4.23479	−	7.90155i	0.427778	−	0.798177i
$99$	−9.66221	+	3.86916i	−0.971089	+	0.388865i
$100$	0.967670	+	1.45523i	0.0967670	+	0.145523i
$101$	5.64914	−	15.5209i	0.562110	−	1.54438i	−0.254427	−	0.967092i	$-0.581887\pi$
$101$	5.64914	−	15.5209i	0.562110	−	1.54438i	0.816537	−	0.577293i	$-0.195891\pi$
$102$	16.5719	−	5.29604i	1.64087	−	0.524386i
$103$	14.0312	+	11.7736i	1.38254	+	1.16009i	0.968262	+	0.249938i	$0.0804101\pi$
$103$	14.0312	+	11.7736i	1.38254	+	1.16009i	0.414278	+	0.910151i	$0.364034\pi$
$104$	−3.50254	−	7.36521i	−0.343452	−	0.722218i
$105$	1.39287	−	3.11549i	0.135930	−	0.304040i
$106$	−10.2288	+	2.13898i	−0.993506	+	0.207756i
$107$		−	17.0660i		−	1.64983i	−0.565254	−	0.824917i	$-0.691222\pi$
$107$		−	17.0660i		−	1.64983i	0.565254	−	0.824917i	$-0.308778\pi$
$108$	−6.86673	−	7.80051i	−0.660752	−	0.750605i
$109$			18.3759i			1.76009i	0.474890	+	0.880045i	$0.342488\pi$
$109$			18.3759i			1.76009i	−0.474890	+	0.880045i	$0.657512\pi$
$110$	2.43397	+	11.6394i	0.232070	+	1.10978i
$111$	−7.15044	+	0.740394i	−0.678690	+	0.0702751i
$112$	2.89112	−	1.48868i	0.273185	−	0.140667i
$113$	6.55711	+	5.50207i	0.616841	+	0.517591i	0.896809	−	0.442418i	$-0.145879\pi$
$113$	6.55711	+	5.50207i	0.616841	+	0.517591i	−0.279968	+	0.960009i	$0.590324\pi$
$114$	14.2712	+	3.10567i	1.33662	+	0.290873i
$115$	5.81311	−	15.9714i	0.542076	−	1.48934i
$116$	−11.1537	+	7.41677i	−1.03560	+	0.688630i
$117$	4.08463	−	7.62523i	0.377624	−	0.704953i
$118$	−9.16008	−	4.90929i	−0.843254	−	0.451937i
$119$	−4.42326	+	3.71156i	−0.405480	+	0.340238i
$120$	−10.1402	+	6.17630i	−0.925673	+	0.563817i
$121$	−0.179992	+	1.02079i	−0.0163629	+	0.0927987i
$122$	0.368503	+	0.0530288i	0.0333627	+	0.00480100i
$123$	−3.23469	−	6.65815i	−0.291662	−	0.600345i
$124$	−3.93999	+	3.75493i	−0.353822	+	0.337203i
$125$	−8.66046	−	5.00012i	−0.774615	−	0.447224i
$126$	3.09036	+	1.53175i	0.275311	+	0.136459i
$127$	−2.28240	−	3.95324i	−0.202530	−	0.350793i	0.746813	−	0.665034i	$-0.231583\pi$
$127$	−2.28240	−	3.95324i	−0.202530	−	0.350793i	−0.949343	+	0.314242i	$0.898250\pi$
$128$	−11.2215	−	1.44185i	−0.991846	−	0.127443i
$129$	4.62687	+	1.16119i	0.407373	+	0.102237i
$130$	−7.76777	−	6.11018i	−0.681278	−	0.535898i
$131$	4.55139	+	12.5048i	0.397657	+	1.09255i	0.963422	+	0.267987i	$0.0863585\pi$
$131$	4.55139	+	12.5048i	0.397657	+	1.09255i	−0.565766	+	0.824566i	$0.691419\pi$
$132$	−11.8523	+	1.99061i	−1.03161	+	0.173260i
$133$	−4.77372	+	0.841736i	−0.413934	+	0.0729878i
$134$	0.100083	+	3.16506i	0.00864587	+	0.273419i
$135$	−11.6544	−	4.77153i	−1.00305	−	0.410668i
$136$	19.9988	−	1.90223i	1.71488	−	0.163115i
$137$	−0.374428	−	2.12348i	−0.0319895	−	0.181422i	0.964626	−	0.263621i	$-0.0849167\pi$
$137$	−0.374428	−	2.12348i	−0.0319895	−	0.181422i	−0.996616	+	0.0821992i	$0.973806\pi$
$138$	15.8959	+	6.51199i	1.35315	+	0.554337i
$139$	−0.200125	−	0.549839i	−0.0169744	−	0.0466367i	0.930916	−	0.365233i	$-0.119011\pi$
$139$	−0.200125	−	0.549839i	−0.0169744	−	0.0466367i	−0.947890	+	0.318596i	$0.896789\pi$
$140$	2.33720	−	3.17269i	0.197529	−	0.268141i
$141$	−4.96375	+	1.41505i	−0.418023	+	0.119169i
$142$	7.25297	+	2.38309i	0.608656	+	0.199985i
$143$	−5.00187	−	8.66350i	−0.418278	−	0.724478i
$144$	−5.83015	−	10.4885i	−0.485846	−	0.874044i
$145$	−8.11572	+	14.0568i	−0.673974	+	1.16736i
$146$	4.15824	−	3.71936i	0.344139	−	0.307816i
$147$	10.9517	+	0.782791i	0.903278	+	0.0645635i
$148$	−8.24940	−	0.922063i	−0.678096	−	0.0757931i
$149$	−21.5708	−	3.80351i	−1.76715	−	0.311596i	−0.806888	−	0.590705i	$-0.798850\pi$
$149$	−21.5708	−	3.80351i	−1.76715	−	0.311596i	−0.960259	+	0.279109i	$0.909961\pi$
$150$	−1.14298	+	1.80962i	−0.0933242	+	0.147754i
$151$	5.91767	−	4.96552i	0.481573	−	0.404088i	−0.369422	−	0.929262i	$-0.620444\pi$
$151$	5.91767	−	4.96552i	0.481573	−	0.404088i	0.850995	+	0.525174i	$0.176000\pi$
$152$	15.3380	+	7.01145i	1.24408	+	0.568704i
$153$	14.2087	+	15.8786i	1.14870	+	1.28371i
$154$	3.38963	−	2.10257i	0.273144	−	0.169430i
$155$	−2.25578	+	6.19769i	−0.181188	+	0.497811i
$156$	6.48254	−	7.59920i	0.519019	−	0.608423i
$157$	−0.882254	+	1.05143i	−0.0704116	+	0.0839132i	−0.800100	−	0.599866i	$-0.795220\pi$
$157$	−0.882254	+	1.05143i	−0.0704116	+	0.0839132i	0.729689	+	0.683779i	$0.239665\pi$
$158$	−13.3716	+	5.35127i	−1.06378	+	0.425724i
$159$	−7.50686	−	10.3659i	−0.595333	−	0.822068i
$160$	−12.9586	+	4.47613i	−1.02447	+	0.353869i
$161$	−5.70128			−0.449324
$162$	5.28673	−	11.5780i	0.415365	−	0.909655i
$163$			13.5989i			1.06515i	0.846383	+	0.532574i	$0.178775\pi$
$163$			13.5989i			1.06515i	−0.846383	+	0.532574i	$0.821225\pi$
$164$	−2.01310	−	8.30700i	−0.157197	−	0.648668i
$165$	−11.7954	+	8.54213i	−0.918274	+	0.665004i
$166$	4.19649	+	10.4861i	0.325711	+	0.813875i
$167$	3.38292	+	2.83861i	0.261778	+	0.219658i	0.764224	−	0.644950i	$-0.223122\pi$
$167$	3.38292	+	2.83861i	0.261778	+	0.219658i	−0.502446	+	0.864609i	$0.667566\pi$
$168$	3.11020	+	2.48772i	0.239957	+	0.191932i
$169$	−4.40315	−	1.60262i	−0.338704	−	0.123278i
$170$	20.6871	−	12.8321i	1.58663	−	0.984180i
$171$	3.66506	+	17.5081i	0.280274	+	1.33888i
$172$	4.93483	+	2.44727i	0.376277	+	0.186603i
$173$	12.4793	+	14.8722i	0.948781	+	1.13071i	0.991301	+	0.131617i	$0.0420169\pi$
$173$	12.4793	+	14.8722i	0.948781	+	1.13071i	−0.0425201	+	0.999096i	$0.513539\pi$
$174$	−13.8699	−	8.76047i	−1.05148	−	0.664130i
$175$	0.123355	−	0.699578i	0.00932472	−	0.0528831i
$176$	−13.8614	−	0.667109i	−1.04485	−	0.0502853i
$177$	0.907471	−	12.6960i	0.0682097	−	0.954291i
$178$	−4.52901	+	4.05099i	−0.339464	+	0.303635i
$179$	4.00038	+	2.30962i	0.299002	+	0.172629i	0.641995	−	0.766709i	$-0.278107\pi$
$179$	4.00038	+	2.30962i	0.299002	+	0.172629i	−0.342992	+	0.939338i	$0.611441\pi$
$180$	−11.9762	−	8.24780i	−0.892657	−	0.614755i
$181$	5.55052	−	3.20459i	0.412567	−	0.238195i	−0.279325	−	0.960197i	$-0.590111\pi$
$181$	5.55052	−	3.20459i	0.412567	−	0.238195i	0.691892	+	0.722001i	$0.256777\pi$
$182$	−1.03482	+	3.14949i	−0.0767059	+	0.233456i
$183$	0.125007	+	0.438501i	0.00924075	+	0.0324149i
$184$	16.3339	+	11.2539i	1.20415	+	0.829649i
$185$	−9.45221	+	3.44032i	−0.694940	+	0.252938i
$186$	−6.16839	−	2.52697i	−0.452288	−	0.185287i
$187$	24.2670	−	4.27893i	1.77458	−	0.312906i
$188$	−5.94809	+	0.376549i	−0.433809	+	0.0274626i
$189$	−0.166959	+	4.22102i	−0.0121444	+	0.307034i
$190$	20.4263	−	0.645905i	1.48188	−	0.0468588i
$191$	−3.51460	−	19.9323i	−0.254307	−	1.44225i	−0.797844	−	0.602864i	$-0.794026\pi$
$191$	−3.51460	−	19.9323i	−0.254307	−	1.44225i	0.543537	−	0.839385i	$-0.317085\pi$
$192$	−3.99999	−	13.2665i	−0.288674	−	0.957427i
$193$	5.28857	−	1.92488i	0.380680	−	0.138556i	−0.144590	−	0.989492i	$-0.546186\pi$
$193$	5.28857	−	1.92488i	0.380680	−	0.138556i	0.525270	+	0.850935i	$0.323964\pi$
$194$	6.21533	+	4.88902i	0.446235	+	0.351011i
$195$	2.94635	−	11.7400i	0.210993	−	0.840720i
$196$	12.1637	+	3.57483i	0.868838	+	0.255345i
$197$	3.79439	−	2.19069i	0.270339	−	0.156080i	−0.358703	−	0.933452i	$-0.616781\pi$
$197$	3.79439	−	2.19069i	0.270339	−	0.156080i	0.629042	+	0.777371i	$0.283447\pi$
$198$	−8.15290	−	12.2551i	−0.579401	−	0.870933i
$199$	−6.64564	+	11.5106i	−0.471097	+	0.815963i	−0.999453	−	0.0330592i	$-0.989475\pi$
$199$	−6.64564	+	11.5106i	−0.471097	+	0.815963i	0.528357	+	0.849022i	$0.322808\pi$
$200$	−1.73432	+	1.76076i	−0.122635	+	0.124505i
$201$	−3.48843	+	1.69477i	−0.246055	+	0.119540i
$202$	23.1204	+	3.32710i	1.62674	+	0.234094i
$203$	5.36196	+	0.945458i	0.376336	+	0.0663582i
$204$	12.1283	+	21.4070i	0.849147	+	1.49879i
$205$	−6.65784	−	7.93450i	−0.465004	−	0.554170i
$206$	−12.2362	+	22.8312i	−0.852539	+	1.59072i
$207$	0.669380	+	21.0281i	0.0465251	+	1.46155i
$208$	9.18157	−	6.98047i	0.636627	−	0.484009i
$209$	19.4387	+	7.07512i	1.34460	+	0.489396i
$210$	4.71587	+	1.02626i	0.325426	+	0.0708188i
$211$	−16.0858	+	19.1703i	−1.10739	+	1.31974i	−0.164597	+	0.986361i	$0.552632\pi$
$211$	−16.0858	+	19.1703i	−1.10739	+	1.31974i	−0.942794	+	0.333376i	$0.891812\pi$
$212$	−5.92186	−	13.5402i	−0.406715	−	0.929946i
$213$	0.963024	+	9.30052i	0.0659853	+	0.637261i
$214$	23.6240	−	4.94011i	1.61490	−	0.337699i
$215$	6.67497			0.455229
$216$	8.81031	−	11.7634i	0.599465	−	0.800401i
$217$	2.21238			0.150186
$218$	−25.4372	+	5.31928i	−1.72283	+	0.360267i
$219$	6.23776	+	2.78877i	0.421509	+	0.188447i
$220$	−15.4076	+	6.73854i	−1.03878	+	0.454313i
$221$	−13.1642	+	15.6884i	−0.885518	+	1.05532i
$222$	−3.09475	−	9.68383i	−0.207706	−	0.649936i
$223$	1.52221	+	0.554040i	0.101935	+	0.0371013i	0.392484	−	0.919759i	$-0.371616\pi$
$223$	1.52221	+	0.554040i	0.101935	+	0.0371013i	−0.290549	+	0.956860i	$0.593838\pi$
$224$	2.89763	+	3.57116i	0.193606	+	0.238608i
$225$	−2.59474	−	0.372832i	−0.172983	−	0.0248555i
$226$	−5.71827	+	10.6695i	−0.380373	+	0.709725i
$227$	4.47903	+	5.33790i	0.297284	+	0.354289i	0.893923	−	0.448221i	$-0.147942\pi$
$227$	4.47903	+	5.33790i	0.297284	+	0.354289i	−0.596639	+	0.802510i	$0.703498\pi$
$228$	−0.168004	+	20.6542i	−0.0111263	+	1.36786i
$229$	−24.7618	−	4.36618i	−1.63631	−	0.288525i	−0.721500	−	0.692415i	$-0.756547\pi$
$229$	−24.7618	−	4.36618i	−1.63631	−	0.288525i	−0.914808	+	0.403890i	$0.867658\pi$
$230$	23.7915	+	3.42367i	1.56876	+	0.225750i
$231$	4.04583	+	2.73803i	0.266196	+	0.180149i
$232$	−13.4955	−	13.2928i	−0.886022	−	0.872716i
$233$	7.86096	−	13.6156i	0.514989	−	0.891987i	−0.484860	−	0.874592i	$-0.661129\pi$
$233$	7.86096	−	13.6156i	0.514989	−	0.891987i	0.999849	−	0.0173948i	$-0.00553722\pi$
$234$	11.7378	+	3.44695i	0.767322	+	0.225334i
$235$	−6.25469	+	3.61115i	−0.408011	+	0.235565i
$236$	4.14422	−	14.1011i	0.269766	−	0.917905i
$237$	−12.6699	−	12.2730i	−0.822998	−	0.797216i
$238$	−6.41821	−	5.04861i	−0.416031	−	0.327253i
$239$	14.6050	−	5.31579i	0.944720	−	0.343850i	0.176692	−	0.984266i	$-0.443460\pi$
$239$	14.6050	−	5.31579i	0.944720	−	0.343850i	0.768028	+	0.640416i	$0.221238\pi$
$240$	−11.4850	−	12.2490i	−0.741352	−	0.790668i
$241$	−2.19088	−	12.4251i	−0.141127	−	0.800370i	−0.970396	−	0.241520i	$-0.922354\pi$
$241$	−2.19088	−	12.4251i	−0.141127	−	0.800370i	0.829269	−	0.558850i	$-0.188757\pi$
$242$	−1.46515	+	0.0463299i	−0.0941832	+	0.00297820i
$243$	15.5880	+	0.120210i	0.999970	+	0.00771147i
$244$	0.0332646	+	0.525458i	0.00212955	+	0.0336390i
$245$	15.1299	−	2.66782i	0.966616	−	0.170441i
$246$	8.28033	−	6.40503i	0.527935	−	0.408370i
$247$	−16.1558	+	5.88024i	−1.02797	+	0.374151i
$248$	−6.33836	−	4.36707i	−0.402486	−	0.277309i
$249$	−9.62454	+	9.93579i	−0.609930	+	0.629655i
$250$	4.41457	−	13.4358i	0.279202	−	0.849755i
$251$	4.86765	−	2.81034i	0.307244	−	0.177387i	−0.338449	−	0.940985i	$-0.609902\pi$
$251$	4.86765	−	2.81034i	0.307244	−	0.177387i	0.645692	+	0.763598i	$0.276569\pi$
$252$	−1.22579	+	4.72129i	−0.0772177	+	0.297413i
$253$	21.0707	+	12.1652i	1.32470	+	0.764818i
$254$	4.81166	−	4.30381i	0.301910	−	0.270045i
$255$	24.6920	+	16.7104i	1.54627	+	1.04645i
$256$	−1.25237	−	15.9509i	−0.0782730	−	0.996932i
$257$	3.35726	−	19.0399i	0.209420	−	1.18768i	−0.680911	−	0.732366i	$-0.738416\pi$
$257$	3.35726	−	19.0399i	0.209420	−	1.18768i	0.890331	−	0.455313i	$-0.150473\pi$
$258$	−0.268059	+	6.74097i	−0.0166886	+	0.419674i
$259$	2.16885	+	2.58474i	0.134766	+	0.160608i
$260$	6.20961	−	12.5214i	0.385103	−	0.776545i
$261$	2.85760	−	19.8876i	0.176881	−	1.23101i
$262$	−15.9926	+	9.92015i	−0.988026	+	0.612869i
$263$	10.8424	+	3.94631i	0.668571	+	0.243340i	0.653932	−	0.756553i	$-0.273118\pi$
$263$	10.8424	+	3.94631i	0.668571	+	0.243340i	0.0146383	+	0.999893i	$0.495340\pi$
$264$	−6.18642	−	15.8305i	−0.380748	−	0.974300i
$265$	−13.7188	−	11.5114i	−0.842739	−	0.707142i
$266$	−2.54705	−	6.36447i	−0.156169	−	0.390231i
$267$	−6.79395	−	3.03742i	−0.415783	−	0.185887i
$268$	−4.35233	+	1.05473i	−0.265861	+	0.0644281i
$269$			13.3630i			0.814758i	0.913259	+	0.407379i	$0.133557\pi$
$269$			13.3630i			0.814758i	−0.913259	+	0.407379i	$0.866443\pi$
$270$	3.23148	−	17.5141i	0.196662	−	1.06587i
$271$	3.26667			0.198436			0.0992182	−	0.995066i	$-0.468366\pi$
$271$	3.26667			0.198436			0.0992182	+	0.995066i	$0.468366\pi$
$272$	8.42227	+	27.1331i	0.510675	+	1.64518i
$273$	−4.03860	+	0.418178i	−0.244427	+	0.0253093i
$274$	2.83109	−	1.13300i	0.171033	−	0.0684468i
$275$	−1.94863	+	2.32228i	−0.117507	+	0.140039i
$276$	−4.41296	+	23.8892i	−0.265629	+	1.43796i
$277$	0.102104	−	0.280528i	0.00613482	−	0.0168553i	−0.936587	−	0.350434i	$-0.886034\pi$
$277$	0.102104	−	0.280528i	0.00613482	−	0.0168553i	0.942722	+	0.333579i	$0.108256\pi$
$278$	0.703196	−	0.436190i	0.0421749	−	0.0261609i
$279$	−0.259753	−	8.15992i	−0.0155510	−	0.488522i
$280$	5.06841	+	2.31692i	0.302895	+	0.138462i
$281$	−13.3262	+	11.1820i	−0.794976	+	0.667064i	−0.946972	−	0.321317i	$-0.895874\pi$
$281$	−13.3262	+	11.1820i	−0.794976	+	0.667064i	0.151996	+	0.988381i	$0.451430\pi$
$282$	−3.39567	−	6.46155i	−0.202209	−	0.384780i
$283$	−1.31422	−	0.231732i	−0.0781220	−	0.0137750i	0.134451	−	0.990920i	$-0.457073\pi$
$283$	−1.31422	−	0.231732i	−0.0781220	−	0.0137750i	−0.212573	+	0.977145i	$0.568184\pi$
$284$	−1.19932	+	10.7299i	−0.0711665	+	0.636704i
$285$	10.9375	+	22.5132i	0.647880	+	1.33357i
$286$	10.5447	−	9.43178i	0.623523	−	0.557713i
$287$	−1.73720	+	3.00893i	−0.102544	+	0.177611i
$288$	12.8313	−	11.1066i	0.756092	−	0.654465i
$289$	−16.7231	−	28.9652i	−0.983711	−	1.70384i
$290$	−21.8077	−	7.16531i	−1.28059	−	0.420762i
$291$	−2.35751	+	9.39370i	−0.138199	+	0.550668i
$292$	6.35229	+	4.67949i	0.371739	+	0.273846i
$293$	−2.77744	−	7.63095i	−0.162260	−	0.445805i	0.831743	−	0.555161i	$-0.187343\pi$
$293$	−2.77744	−	7.63095i	−0.162260	−	0.445805i	−0.994003	+	0.109356i	$0.965121\pi$
$294$	2.08659	+	15.3867i	0.121693	+	0.897369i
$295$	−3.09274	−	17.5398i	−0.180066	−	1.02121i
$296$	−1.11157	−	11.6863i	−0.0646089	−	0.679253i
$297$	9.62369	−	15.2437i	0.558423	−	0.884530i
$298$	−0.979021	−	30.9608i	−0.0567132	−	1.79351i
$299$	−19.9141	+	3.51140i	−1.15166	+	0.203069i
$300$	−2.83586	−	1.05837i	−0.163728	−	0.0611050i
$301$	−0.765801	−	2.10402i	−0.0441400	−	0.121274i
$302$	8.58661	+	6.75429i	0.494104	+	0.388666i
$303$	7.84307	+	27.5121i	0.450573	+	1.58053i
$304$	−5.26584	+	23.2616i	−0.302017	+	1.33414i
$305$	0.319011	+	0.552544i	0.0182665	+	0.0316386i
$306$	−17.8672	+	24.2651i	−1.02140	+	1.38714i
$307$	−22.1985	−	12.8163i	−1.26693	−	0.731464i	−0.292527	−	0.956257i	$-0.594496\pi$
$307$	−22.1985	−	12.8163i	−1.26693	−	0.731464i	−0.974406	+	0.224793i	$0.927829\pi$
$308$	3.89173	+	4.08353i	0.221752	+	0.232681i
$309$	−31.6444	−	2.26184i	−1.80018	−	0.128671i
$310$	−9.23227	−	1.32855i	−0.524358	−	0.0754568i
$311$	−3.08781	+	17.5119i	−0.175094	+	0.993007i	0.762942	+	0.646467i	$0.223754\pi$
$311$	−3.08781	+	17.5119i	−0.175094	+	0.993007i	−0.938035	+	0.346539i	$0.887357\pi$
$312$	12.3959	+	6.77385i	0.701777	+	0.383494i
$313$	−25.2201	+	21.1622i	−1.42553	+	1.19616i	−0.477226	+	0.878781i	$0.658358\pi$
$313$	−25.2201	+	21.1622i	−1.42553	+	1.19616i	−0.948299	+	0.317377i	$0.897198\pi$
$314$	−1.71085	−	0.916921i	−0.0965489	−	0.0517448i
$315$	1.21111	+	5.78552i	0.0682383	+	0.325977i
$316$	−11.2783	−	16.9608i	−0.634453	−	0.954122i
$317$	−2.41535	+	6.63611i	−0.135659	+	0.372721i	−0.988857	−	0.148866i	$-0.952438\pi$
$317$	−2.41535	+	6.63611i	−0.135659	+	0.372721i	0.853198	+	0.521587i	$0.174660\pi$
$318$	12.1762	−	13.3922i	0.682807	−	0.750995i
$319$	−17.7993	−	14.9354i	−0.996568	−	0.836220i
$320$	−9.94732	−	16.6425i	−0.556072	−	0.930346i
$321$	17.3376	+	23.9407i	0.967688	+	1.33624i
$322$	−1.65035	−	7.89212i	−0.0919706	−	0.439810i
$323$		−	42.3492i		−	2.35637i
$324$	17.5575	+	3.96678i	0.975415	+	0.220376i
$325$		−	2.51954i		−	0.139759i
$326$	−18.8246	+	3.93649i	−1.04260	+	0.218022i
$327$	−18.6683	−	25.7782i	−1.03236	−	1.42554i
$328$	10.9164	−	5.19131i	0.602758	−	0.286642i
$329$	1.85586	+	1.55725i	0.102317	+	0.0858539i
$330$	−15.2391	−	13.8554i	−0.838882	−	0.762714i
$331$	4.15163	−	11.4065i	0.228194	−	0.626958i	−0.771766	−	0.635907i	$-0.780626\pi$
$331$	4.15163	−	11.4065i	0.228194	−	0.626958i	0.999960	+	0.00894876i	$0.00284852\pi$
$332$	−13.3008	+	8.84449i	−0.729975	+	0.485404i
$333$	9.27866	−	8.30286i	0.508468	−	0.454994i
$334$	−2.95015	+	5.50457i	−0.161425	+	0.301197i
$335$	−4.15716	+	3.48827i	−0.227130	+	0.190585i
$336$	−2.54337	+	5.02548i	−0.138752	+	0.274162i
$337$	−4.48506	+	25.4361i	−0.244317	+	1.38559i	0.577757	+	0.816209i	$0.303928\pi$
$337$	−4.48506	+	25.4361i	−0.244317	+	1.38559i	−0.822074	+	0.569381i	$0.807183\pi$
$338$	0.943872	−	6.55907i	0.0513399	−	0.356766i
$339$	−14.7881	−	1.05701i	−0.803180	−	0.0574088i
$340$	23.7515	+	24.9221i	1.28811	+	1.35159i
$341$	−8.17648	−	4.72069i	−0.442781	−	0.255640i
$342$	−23.1751	+	10.1415i	−1.25316	+	0.548391i
$343$	−5.42214	−	9.39142i	−0.292768	−	0.507089i
$344$	−1.95920	+	7.53955i	−0.105633	+	0.406506i
$345$	8.07074	+	28.3107i	0.434514	+	1.52420i
$346$	−16.9748	+	21.5797i	−0.912570	+	1.16013i
$347$	4.43311	+	12.1799i	0.237982	+	0.653849i	0.999980	+	0.00627055i	$0.00199599\pi$
$347$	4.43311	+	12.1799i	0.237982	+	0.653849i	−0.761999	+	0.647578i	$0.775782\pi$
$348$	8.11194	−	21.7356i	0.434845	−	1.16515i
$349$	1.00479	−	0.177171i	0.0537849	−	0.00948374i	−0.146691	−	0.989182i	$-0.546862\pi$
$349$	1.00479	−	0.177171i	0.0537849	−	0.00948374i	0.200476	+	0.979699i	$0.435751\pi$
$350$	1.00411	−	0.0317514i	0.0536721	−	0.00169718i
$351$	2.01653	+	14.8465i	0.107635	+	0.792448i
$352$	−3.08902	−	19.3811i	−0.164645	−	1.03302i
$353$	−2.87234	−	16.2899i	−0.152879	−	0.867022i	−0.960699	−	0.277592i	$-0.910464\pi$
$353$	−2.87234	−	16.2899i	−0.152879	−	0.867022i	0.807820	−	0.589430i	$-0.200648\pi$
$354$	17.8374	−	2.41894i	0.948048	−	0.128565i
$355$	4.47480	+	12.2944i	0.237498	+	0.652520i
$356$	−6.91869	−	5.09673i	−0.366690	−	0.270126i
$357$	2.43446	−	9.70032i	0.128845	−	0.513395i
$358$	−2.03915	+	6.20617i	−0.107772	+	0.328006i
$359$	9.03871	+	15.6555i	0.477045	+	0.826266i	0.999654	−	0.0263063i	$-0.00837453\pi$
$359$	9.03871	+	15.6555i	0.477045	+	0.826266i	−0.522609	+	0.852573i	$0.675041\pi$
$360$	7.95042	−	18.9659i	0.419024	−	0.999589i
$361$	8.27594	−	14.3343i	0.435576	−	0.754439i
$362$	6.04274	+	6.75579i	0.317599	+	0.355076i
$363$	−0.784531	−	1.61484i	−0.0411772	−	0.0847573i
$364$	−4.65930	−	0.520786i	−0.244213	−	0.0272966i
$365$	9.41559	+	1.66022i	0.492835	+	0.0869000i
$366$	−0.570818	+	0.299976i	−0.0298372	+	0.0156800i
$367$	−15.6345	+	13.1189i	−0.816112	+	0.684799i	−0.952058	−	0.305917i	$-0.901037\pi$
$367$	−15.6345	+	13.1189i	−0.816112	+	0.684799i	0.135946	+	0.990716i	$0.456593\pi$
$368$	−10.8503	+	25.8682i	−0.565610	+	1.34847i
$369$	11.3018	+	6.05407i	0.588348	+	0.315162i
$370$	−7.49848	−	12.0886i	−0.389827	−	0.628454i
$371$	−2.05461	+	5.64499i	−0.106670	+	0.293073i
$372$	1.71245	−	9.27020i	0.0887863	−	0.480638i
$373$	18.6443	−	22.2194i	0.965366	−	1.15048i	−0.0232061	−	0.999731i	$-0.507387\pi$
$373$	18.6443	−	22.2194i	0.965366	−	1.15048i	0.988572	−	0.150748i	$-0.0481681\pi$
$374$	12.9478	+	32.3535i	0.669514	+	1.67296i
$375$	17.2288	−	1.78396i	0.889691	−	0.0921232i
$376$	−2.24304	−	8.12476i	−0.115676	−	0.419003i
$377$	19.3112			0.994578
$378$	−5.89136	+	0.990745i	−0.303019	+	0.0509584i
$379$		−	18.7878i		−	0.965062i	−0.875879	−	0.482531i	$-0.839718\pi$
$379$		−	18.7878i		−	0.965062i	0.875879	−	0.482531i	$-0.160282\pi$
$380$	6.80691	+	28.0885i	0.349187	+	1.44091i
$381$	7.21795	+	3.22699i	0.369787	+	0.165324i
$382$	26.5743	−	10.6350i	1.35966	−	0.544132i
$383$	−11.4097	−	9.57391i	−0.583010	−	0.489204i	0.302924	−	0.953015i	$-0.402037\pi$
$383$	−11.4097	−	9.57391i	−0.583010	−	0.489204i	−0.885934	+	0.463811i	$0.846482\pi$
$384$	17.2066	−	9.37734i	0.878068	−	0.478535i
$385$	6.42348	+	2.33796i	0.327371	+	0.119153i
$386$	4.19545	+	6.76362i	0.213543	+	0.344259i
$387$	−7.67036	+	3.07154i	−0.389906	+	0.156135i
$388$	−4.96858	+	10.0189i	−0.252241	+	0.508634i
$389$	−11.3184	−	13.4888i	−0.573866	−	0.683907i	0.398553	−	0.917145i	$-0.369512\pi$
$389$	−11.3184	−	13.4888i	−0.573866	−	0.683907i	−0.972420	+	0.233238i	$0.925068\pi$
$390$	17.1042	+	0.680161i	0.866107	+	0.0344413i
$391$	8.64932	−	49.0527i	0.437415	−	2.48070i
$392$	−1.42749	+	17.8727i	−0.0720992	+	0.902708i
$393$	−19.0886	−	12.9183i	−0.962894	−	0.651643i
$394$	4.13088	+	4.61833i	0.208111	+	0.232668i
$395$	−21.3755	−	12.3411i	−1.07552	−	0.620950i
$396$	14.6044	−	14.8333i	0.733898	−	0.745402i
$397$	13.1290	−	7.58002i	0.658924	−	0.380430i	−0.132943	−	0.991124i	$-0.542443\pi$
$397$	13.1290	−	7.58002i	0.658924	−	0.380430i	0.791867	+	0.610694i	$0.209109\pi$
$398$	−17.8575	−	5.86739i	−0.895115	−	0.294105i
$399$	5.84158	−	6.03049i	0.292445	−	0.301902i
$400$	−2.93941	−	1.89108i	−0.146971	−	0.0945540i
$401$	0.563391	−	0.205057i	0.0281344	−	0.0102401i	−0.327915	−	0.944707i	$-0.606346\pi$
$401$	0.563391	−	0.205057i	0.0281344	−	0.0102401i	0.356049	+	0.934467i	$0.384124\pi$
$402$	−3.35582	−	4.33835i	−0.167373	−	0.216377i
$403$	7.72766	−	1.36260i	0.384942	−	0.0678757i
$404$	2.08706	+	32.9679i	0.103835	+	1.64022i
$405$	21.1966	−	5.14621i	1.05327	−	0.255717i
$406$	0.243360	+	7.69609i	0.0120778	+	0.381951i
$407$	−2.50040	−	14.1805i	−0.123940	−	0.702899i
$408$	−26.1223	+	22.9855i	−1.29325	+	1.13795i
$409$	26.7235	−	9.72655i	1.32139	−	0.480947i	0.417487	−	0.908683i	$-0.362911\pi$
$409$	26.7235	−	9.72655i	1.32139	−	0.480947i	0.903904	+	0.427736i	$0.140689\pi$
$410$	9.05626	−	11.5131i	0.447257	−	0.568590i
$411$	2.68253	+	2.59850i	0.132319	+	0.128174i
$412$	−35.1466	−	10.3293i	−1.73155	−	0.508889i
$413$	−5.17391	+	2.98716i	−0.254591	+	0.146988i
$414$	−28.9148	+	7.01361i	−1.42108	+	0.344700i
$415$	−9.67799	+	16.7628i	−0.475074	+	0.822852i
$416$	12.3207	+	10.6891i	0.604070	+	0.524078i
$417$	0.839329	+	0.568020i	0.0411021	+	0.0278160i
$418$	−4.16694	+	28.9565i	−0.203812	+	1.41631i
$419$	27.5479	+	4.85743i	1.34580	+	0.237301i	0.799691	−	0.600412i	$-0.204997\pi$
$419$	27.5479	+	4.85743i	1.34580	+	0.237301i	0.546110	+	0.837713i	$0.316108\pi$
$420$	−0.0555165	+	6.82512i	−0.00270893	+	0.333032i
$421$	21.0378	+	25.0719i	1.02532	+	1.22193i	0.974771	+	0.223208i	$0.0716530\pi$
$421$	21.0378	+	25.0719i	1.02532	+	1.22193i	0.0505502	+	0.998722i	$0.483903\pi$
$422$	−31.1932	−	16.7178i	−1.51846	−	0.813812i
$423$	5.52571	−	7.02780i	0.268669	−	0.341703i
$424$	17.0291	−	12.1170i	0.827008	−	0.588452i
$425$	5.83190	+	2.12264i	0.282889	+	0.102963i
$426$	−12.5957	+	4.02532i	−0.610263	+	0.195027i
$427$	0.137568	−	0.163948i	0.00665740	−	0.00793398i
$428$	13.6769	+	31.2720i	0.661098	+	1.51159i
$429$	15.8181	+	7.07193i	0.763705	+	0.341436i
$430$	1.93221	+	9.23997i	0.0931794	+	0.445591i
$431$	−9.98011			−0.480725			−0.240363	−	0.970683i	$-0.577266\pi$
$431$	−9.98011			−0.480725			−0.240363	+	0.970683i	$0.577266\pi$
$432$	18.8341	+	8.79068i	0.906157	+	0.422942i
$433$	17.4899			0.840513			0.420257	−	0.907405i	$-0.361940\pi$
$433$	17.4899			0.840513			0.420257	+	0.907405i	$0.361940\pi$
$434$	0.640419	+	3.06253i	0.0307411	+	0.147006i
$435$	−2.89555	−	27.9642i	−0.138831	−	1.34078i
$436$	−14.7267	−	33.6722i	−0.705279	−	1.61261i
$437$	26.8780	−	32.0319i	1.28575	−	1.53229i
$438$	−2.05476	+	9.44202i	−0.0981801	+	0.451157i
$439$	7.21777	+	2.62705i	0.344485	+	0.125382i	0.508468	−	0.861081i	$-0.330212\pi$
$439$	7.21777	+	2.62705i	0.344485	+	0.125382i	−0.163983	+	0.986463i	$0.552434\pi$
$440$	−13.7880	−	19.3776i	−0.657317	−	0.923792i
$441$	−16.1585	+	10.0278i	−0.769454	+	0.477515i
$442$	−25.5277	−	13.6814i	−1.21423	−	0.650759i
$443$	3.13735	+	3.73895i	0.149060	+	0.177643i	0.835408	−	0.549631i	$-0.185232\pi$
$443$	3.13735	+	3.73895i	0.149060	+	0.177643i	−0.686348	+	0.727274i	$0.740787\pi$
$444$	12.5092	−	7.08716i	0.593661	−	0.336342i
$445$	−10.2551	−	1.80826i	−0.486140	−	0.0857196i
$446$	−0.326306	+	2.26753i	−0.0154510	+	0.107371i
$447$	34.1241	−	16.5783i	1.61401	−	0.784129i
$448$	−4.10467	+	5.04486i	−0.193928	+	0.238347i
$449$	−2.49179	+	4.31590i	−0.117595	+	0.203680i	−0.918814	−	0.394691i	$-0.870852\pi$
$449$	−2.49179	+	4.31590i	−0.117595	+	0.203680i	0.801219	+	0.598371i	$0.204185\pi$
$450$	−0.235000	−	3.69975i	−0.0110780	−	0.174408i
$451$	12.8407	−	7.41357i	0.604644	−	0.349091i
$452$	−16.4248	−	4.82712i	−0.772556	−	0.227049i
$453$	−3.25694	+	12.9776i	−0.153025	+	0.609740i
$454$	−6.09255	+	7.74536i	−0.285938	+	0.363508i
$455$	−5.33865	+	1.94311i	−0.250280	+	0.0910944i
$456$	−28.6396	+	5.74621i	−1.34117	+	0.269091i
$457$	3.50014	+	19.8503i	0.163729	+	0.928556i	0.950365	+	0.311138i	$0.100710\pi$
$457$	3.50014	+	19.8503i	0.163729	+	0.928556i	−0.786635	+	0.617418i	$0.788179\pi$
$458$	−1.12385	−	35.5410i	−0.0525141	−	1.66072i
$459$	−36.0635	−	7.84012i	−1.68330	−	0.365945i
$460$	2.14765	+	33.9249i	0.100135	+	1.58176i
$461$	33.4428	−	5.89687i	1.55759	−	0.274645i	0.672510	−	0.740088i	$-0.265216\pi$
$461$	33.4428	−	5.89687i	1.55759	−	0.274645i	0.885077	+	0.465444i	$0.154105\pi$
$462$	−2.61903	+	6.39311i	−0.121848	+	0.297434i
$463$	−35.9891	+	13.0990i	−1.67256	+	0.608760i	−0.992260	−	0.124178i	$-0.960371\pi$
$463$	−35.9891	+	13.0990i	−1.67256	+	0.608760i	−0.680295	+	0.732938i	$0.738148\pi$
$464$	14.4943	−	22.5293i	0.672881	−	1.04590i
$465$	−3.13184	−	10.9860i	−0.145236	−	0.509462i
$466$	21.1232	+	6.94039i	0.978512	+	0.321507i
$467$	−9.53283	+	5.50378i	−0.441127	+	0.254685i	−0.704075	−	0.710125i	$-0.748638\pi$
$467$	−9.53283	+	5.50378i	−0.441127	+	0.254685i	0.262949	+	0.964810i	$0.415305\pi$
$468$	−1.37377	+	17.2460i	−0.0635027	+	0.797199i
$469$	1.57648	+	0.910182i	0.0727951	+	0.0420283i
$470$	−6.80936	−	7.61287i	−0.314092	−	0.351155i
$471$	0.169491	−	2.37127i	0.00780971	−	0.109262i
$472$	20.7194	+	1.65486i	0.953689	+	0.0761710i
$473$	−1.65925	+	9.41005i	−0.0762922	+	0.432675i
$474$	13.3216	−	21.0912i	0.611881	−	0.968753i
$475$	3.34895	+	3.99113i	0.153660	+	0.183125i
$476$	5.13076	−	10.3460i	0.235168	−	0.474206i
$477$	21.0617	+	6.91524i	0.964347	+	0.316627i
$478$	11.5862	+	18.6785i	0.529942	+	0.854337i
$479$	21.5794	+	7.85427i	0.985989	+	0.358871i	0.784166	−	0.620551i	$-0.213091\pi$
$479$	21.5794	+	7.85427i	0.985989	+	0.358871i	0.201823	+	0.979422i	$0.435313\pi$
$480$	13.6313	−	19.4440i	0.622183	−	0.887495i
$481$	9.16757	+	7.69250i	0.418005	+	0.350748i
$482$	16.5655	−	6.62947i	0.754537	−	0.301964i
$483$	7.99791	−	5.79200i	0.363917	−	0.263545i
$484$	−0.488250	−	2.01475i	−0.0221932	−	0.0915795i
$485$			13.5519i			0.615358i
$486$	4.34587	+	21.6128i	0.197132	+	0.980377i
$487$	8.81274			0.399343			0.199672	−	0.979863i	$-0.436012\pi$
$487$	8.81274			0.399343			0.199672	+	0.979863i	$0.436012\pi$
$488$	−0.717747	+	0.198152i	−0.0324909	+	0.00896992i
$489$	−13.8153	−	19.0769i	−0.624749	−	0.862688i
$490$	8.07266	+	20.1717i	0.364685	+	0.911264i
$491$	7.55920	−	9.00870i	0.341142	−	0.406557i	−0.568010	−	0.823022i	$-0.692287\pi$
$491$	7.55920	−	9.00870i	0.341142	−	0.406557i	0.909152	+	0.416465i	$0.136731\pi$
$492$	11.2632	+	9.60815i	0.507785	+	0.433169i
$493$	−16.2691	+	44.6990i	−0.732723	+	2.01314i
$494$	−12.8165	−	20.6619i	−0.576641	−	0.929622i
$495$	7.86892	−	23.9663i	0.353682	−	1.07720i
$496$	4.21044	−	10.0381i	0.189055	−	0.450726i
$497$	3.36195	−	2.82101i	0.150804	−	0.126540i
$498$	−16.5399	−	10.4469i	−0.741168	−	0.468135i
$499$	−17.3768	−	3.06399i	−0.777891	−	0.137163i	−0.229414	−	0.973329i	$-0.573681\pi$
$499$	−17.3768	−	3.06399i	−0.777891	−	0.137163i	−0.548477	+	0.836166i	$0.684792\pi$
$500$	19.8767	+	2.22169i	0.888913	+	0.0993568i
$501$	−7.62943	−	0.545327i	−0.340858	−	0.0243634i
$502$	5.29932	+	5.92464i	0.236520	+	0.264430i
$503$	−10.0037	+	17.3268i	−0.446041	+	0.772565i	−0.998124	−	0.0612236i	$-0.980500\pi$
$503$	−10.0037	+	17.3268i	−0.446041	+	0.772565i	0.552083	+	0.833789i	$0.313833\pi$
$504$	−6.89037	−	0.330154i	−0.306922	−	0.0147062i
$505$	20.0152	+	34.6673i	0.890664	+	1.54268i
$506$	−10.7406	+	32.6890i	−0.477476	+	1.45320i
$507$	7.80498	−	2.22502i	0.346631	−	0.0988166i
$508$	7.35047	+	5.41482i	0.326125	+	0.240244i
$509$	−3.57485	−	9.82182i	−0.158452	−	0.435345i	0.834908	−	0.550390i	$-0.185521\pi$
$509$	−3.57485	−	9.82182i	−0.158452	−	0.435345i	−0.993360	+	0.115045i	$0.963299\pi$
$510$	−15.9841	+	39.0176i	−0.707790	+	1.72773i
$511$	−0.556906	−	3.15837i	−0.0246361	−	0.139718i
$512$	21.7179	−	6.35094i	0.959803	−	0.280675i
$513$	−22.9281	−	20.8375i	−1.01230	−	0.919998i
$514$	27.3283	−	0.864155i	1.20540	−	0.0381163i
$515$	−43.7173	+	7.70853i	−1.92641	+	0.339679i
$516$	−9.40892	+	1.58025i	−0.414205	+	0.0695665i
$517$	−3.53605	−	9.71521i	−0.155515	−	0.427274i
$518$	−2.95016	+	3.75049i	−0.129623	+	0.164787i
$519$	−32.6151	−	8.18530i	−1.43164	−	0.359295i
$520$	19.1305	+	4.97119i	0.838930	+	0.218001i
$521$	−10.0111	−	17.3397i	−0.438593	−	0.759665i	0.558988	−	0.829175i	$-0.311190\pi$
$521$	−10.0111	−	17.3397i	−0.438593	−	0.759665i	−0.997581	+	0.0695105i	$0.977856\pi$
$522$	28.3570	−	1.80118i	1.24115	−	0.0788353i
$523$	−17.8863	−	10.3267i	−0.782114	−	0.451554i	0.0550649	−	0.998483i	$-0.482463\pi$
$523$	−17.8863	−	10.3267i	−0.782114	−	0.451554i	−0.837179	+	0.546929i	$0.815797\pi$
$524$	−18.3616	−	19.2665i	−0.802129	−	0.841661i
$525$	0.537664	+	1.10670i	0.0234656	+	0.0483005i
$526$	−2.32421	+	16.1512i	−0.101340	+	0.704224i
$527$	−3.35636	+	19.0349i	−0.146206	+	0.829173i
$528$	20.1229	−	13.1462i	0.875738	−	0.572113i
$529$	20.0556	−	16.8287i	0.871985	−	0.731682i
$530$	11.9638	−	22.3228i	0.519672	−	0.969638i
$531$	11.6250	+	18.7322i	0.504482	+	0.812909i
$532$	8.07286	−	5.36813i	0.350003	−	0.232738i
$533$	−4.21473	+	11.5799i	−0.182560	+	0.501580i
$534$	2.23797	−	10.2839i	0.0968464	−	0.445028i
$535$	31.6844	+	26.5864i	1.36984	+	1.14943i
$536$	−2.71991	−	5.71949i	−0.117482	−	0.247044i
$537$	−7.95820	+	0.824033i	−0.343422	+	0.0355597i
$538$	−18.4981	+	3.86821i	−0.797508	+	0.166770i
$539$			21.9926i			0.947289i
$540$	25.1796	−	0.596567i	1.08356	−	0.0256722i
$541$		−	31.7185i		−	1.36368i	−0.731499	−	0.681842i	$-0.761179\pi$
$541$		−	31.7185i		−	1.36368i	0.731499	−	0.681842i	$-0.238821\pi$
$542$	0.945607	+	4.52196i	0.0406173	+	0.194235i
$543$	−4.53083	+	10.1343i	−0.194437	+	0.434905i
$544$	−35.1215	+	19.5129i	−1.50582	+	0.836610i
$545$	−34.1163	−	28.6270i	−1.46138	−	1.22624i
$546$	−1.74793	−	5.46947i	−0.0748045	−	0.234072i
$547$	−2.69951	+	7.41685i	−0.115423	+	0.317122i	−0.983930	−	0.178555i	$-0.942858\pi$
$547$	−2.69951	+	7.41685i	−0.115423	+	0.317122i	0.868507	+	0.495677i	$0.165080\pi$
$548$	2.38789	+	3.59103i	0.102006	+	0.153401i
$549$	−0.620841	−	0.488145i	−0.0264968	−	0.0208335i
$550$	−3.77874	−	2.02519i	−0.161126	−	0.0863545i
$551$	−30.5902	+	25.6683i	−1.30319	+	1.09350i
$552$	−34.3466	+	0.806496i	−1.46189	+	0.0343268i
$553$	−1.43771	+	8.15365i	−0.0611376	+	0.346728i
$554$	0.417883	+	0.0601347i	0.0177541	+	0.00255488i
$555$	9.76475	−	14.4288i	0.414491	−	0.612468i
$556$	0.807359	+	0.847150i	0.0342397	+	0.0359271i
$557$	11.9380	+	6.89241i	0.505829	+	0.292041i	0.731118	−	0.682251i	$-0.238999\pi$
$557$	11.9380	+	6.89241i	0.505829	+	0.292041i	−0.225288	+	0.974292i	$0.572332\pi$
$558$	11.2204	−	2.72163i	0.474996	−	0.115216i
$559$	−3.97074	−	6.87753i	−0.167944	−	0.290888i
$560$	−1.74008	+	7.68673i	−0.0735320	+	0.324824i
$561$	−29.6954	+	30.6557i	−1.25374	+	1.29429i
$562$	−19.3365	−	15.2102i	−0.815662	−	0.641605i
$563$	4.49431	+	12.3480i	0.189413	+	0.520407i	0.997655	−	0.0684431i	$-0.0218032\pi$
$563$	4.49431	+	12.3480i	0.189413	+	0.520407i	−0.808242	+	0.588850i	$0.799581\pi$
$564$	7.96159	−	6.57096i	0.335244	−	0.276687i
$565$	−20.4301	+	3.60237i	−0.859499	+	0.151553i
$566$	−0.0596476	−	1.88631i	−0.00250718	−	0.0792876i
$567$	−4.05396	−	6.09097i	−0.170251	−	0.255797i
$568$	−15.2003	+	1.44581i	−0.637790	+	0.0606650i
$569$	−6.12718	−	34.7490i	−0.256865	−	1.45675i	−0.791241	−	0.611505i	$-0.790564\pi$
$569$	−6.12718	−	34.7490i	−0.256865	−	1.45675i	0.534376	−	0.845247i	$-0.320547\pi$
$570$	−27.9983	+	21.6574i	−1.17272	+	0.907127i
$571$	13.0508	+	35.8568i	0.546159	+	1.50056i	0.838856	+	0.544354i	$0.183225\pi$
$571$	13.0508	+	35.8568i	0.546159	+	1.50056i	−0.292697	+	0.956205i	$0.594553\pi$
$572$	16.1085	+	11.8665i	0.673531	+	0.496165i
$573$	25.1798	+	24.3910i	1.05190	+	1.01895i
$574$	−4.66804	−	1.53377i	−0.194840	−	0.0640182i
$575$	3.06392	+	5.30687i	0.127774	+	0.221312i
$576$	19.0889	+	14.5470i	0.795370	+	0.606124i
$577$	−13.9536	+	24.1683i	−0.580895	+	1.00614i	0.414478	+	0.910059i	$0.363964\pi$
$577$	−13.9536	+	24.1683i	−0.580895	+	1.00614i	−0.995374	+	0.0960807i	$0.969369\pi$
$578$	35.2549	−	31.5339i	1.46641	−	1.31164i
$579$	−5.46344	+	8.07300i	−0.227053	+	0.335503i
$580$	3.60603	−	32.2620i	0.149732	−	1.33961i
$581$	6.39413	+	1.12746i	0.265273	+	0.0467748i
$582$	−13.6859	−	0.544227i	−0.567297	−	0.0225589i
$583$	19.6384	−	16.4786i	0.813341	−	0.682474i
$584$	−4.63888	+	10.1479i	−0.191958	+	0.419921i
$585$	7.79359	+	19.4624i	0.322225	+	0.804673i
$586$	9.75931	−	6.05366i	0.403153	−	0.250074i
$587$	−3.04495	+	8.36592i	−0.125678	+	0.345299i	−0.986535	−	0.163549i	$-0.947706\pi$
$587$	−3.04495	+	8.36592i	−0.125678	+	0.345299i	0.860857	+	0.508847i	$0.169928\pi$
$588$	−20.6953	+	7.34240i	−0.853461	+	0.302796i
$589$	−10.4300	+	12.4300i	−0.429760	+	0.512168i
$590$	23.3846	−	9.35844i	0.962727	−	0.385281i
$591$	−3.09733	+	6.92793i	−0.127407	+	0.284977i
$592$	15.8553	−	4.92156i	0.651647	−	0.202275i
$593$	−13.6477			−0.560446			−0.280223	−	0.959935i	$-0.590408\pi$
$593$	−13.6477			−0.560446			−0.280223	+	0.959935i	$0.590408\pi$
$594$	23.8872	+	8.90918i	0.980104	+	0.365548i
$595$		−	13.9942i		−	0.573706i
$596$	42.5748	−	10.3175i	1.74393	−	0.422621i
$597$	−2.37105	−	22.8987i	−0.0970407	−	0.937183i
$598$	−10.6253	−	26.5501i	−0.434500	−	1.08571i
$599$	23.2233	+	19.4867i	0.948878	+	0.796203i	0.979108	−	0.203340i	$-0.0651796\pi$
$599$	23.2233	+	19.4867i	0.948878	+	0.796203i	−0.0302302	+	0.999543i	$0.509624\pi$
$600$	0.644171	−	4.23196i	0.0262982	−	0.172769i
$601$	2.85426	+	1.03887i	0.116428	+	0.0423762i	0.399577	−	0.916700i	$-0.369157\pi$
$601$	2.85426	+	1.03887i	0.116428	+	0.0423762i	−0.283149	+	0.959076i	$0.591379\pi$
$602$	2.69086	−	1.66913i	0.109671	−	0.0680286i
$603$	3.17193	−	5.92141i	0.129171	−	0.241138i
$604$	−6.86419	+	13.8414i	−0.279300	+	0.563197i
$605$	−1.61477	−	1.92441i	−0.0656497	−	0.0782382i
$606$	−35.8139	+	18.8209i	−1.45484	+	0.764547i
$607$	−4.34423	+	24.6374i	−0.176327	+	0.999999i	0.760274	+	0.649602i	$0.225065\pi$
$607$	−4.34423	+	24.6374i	−0.176327	+	0.999999i	−0.936601	+	0.350397i	$0.886047\pi$
$608$	−33.7246	−	0.555803i	−1.36771	−	0.0225408i
$609$	−8.48241	+	4.12096i	−0.343724	+	0.166990i
$610$	−0.672526	+	0.601543i	−0.0272298	+	0.0243558i
$611$	7.44146	+	4.29633i	0.301049	+	0.173811i
$612$	−38.7615	−	17.7091i	−1.56684	−	0.715847i
$613$	−11.1629	+	6.44490i	−0.450865	+	0.260307i	−0.708195	−	0.706017i	$-0.750490\pi$
$613$	−11.1629	+	6.44490i	−0.450865	+	0.260307i	0.257331	+	0.966323i	$0.417157\pi$
$614$	11.3154	−	34.4386i	0.456653	−	1.38983i
$615$	17.4006	+	4.36696i	0.701658	+	0.176093i
$616$	−4.52617	+	6.56927i	−0.182365	+	0.264683i
$617$	23.2620	−	8.46669i	0.936495	−	0.340856i	0.171714	−	0.985147i	$-0.445070\pi$
$617$	23.2620	−	8.46669i	0.936495	−	0.340856i	0.764781	+	0.644291i	$0.222847\pi$
$618$	−6.02912	−	44.4591i	−0.242527	−	1.78841i
$619$	−7.07392	+	1.24732i	−0.284325	+	0.0501341i	−0.313992	−	0.949426i	$-0.601666\pi$
$619$	−7.07392	+	1.24732i	−0.284325	+	0.0501341i	0.0296670	+	0.999560i	$0.490555\pi$
$620$	−0.833393	−	13.1645i	−0.0334699	−	0.528701i
$621$	−22.3017	−	28.8187i	−0.894935	−	1.15645i
$622$	−25.1350	+	0.794801i	−1.00782	+	0.0318686i
$623$	0.606562	+	3.43998i	0.0243014	+	0.137820i
$624$	−5.78861	+	19.1201i	−0.231730	+	0.765415i
$625$	26.8803	−	9.78364i	1.07521	−	0.391346i
$626$	−36.5947	−	28.7856i	−1.46262	−	1.15051i
$627$	−34.4569	+	9.82286i	−1.37607	+	0.392287i
$628$	0.774026	−	2.63370i	0.0308870	−	0.105096i
$629$	−25.5289	+	14.7391i	−1.01791	+	0.587688i
$630$	−7.65815	+	3.35124i	−0.305108	+	0.133517i
$631$	19.7806	−	34.2610i	0.787453	−	1.36391i	−0.140070	−	0.990142i	$-0.544733\pi$
$631$	19.7806	−	34.2610i	0.787453	−	1.36391i	0.927523	−	0.373767i	$-0.121934\pi$
$632$	20.2137	−	20.5219i	0.804057	−	0.816316i
$633$	3.09025	−	43.2343i	0.122827	−	1.71841i
$634$	−9.88534	−	1.42253i	−0.392597	−	0.0564960i
$635$	10.8951	+	1.92111i	0.432361	+	0.0762368i
$636$	22.0630	+	12.9785i	0.874856	+	0.514631i
$637$	−11.7491	−	14.0021i	−0.465517	−	0.554782i
$638$	15.5222	−	28.9624i	0.614531	−	1.14663i
$639$	−10.7995	−	12.0687i	−0.427220	−	0.477430i
$640$	20.1583	−	18.5873i	0.796827	−	0.734728i
$641$	20.4795	+	7.45392i	0.808891	+	0.294412i	0.713166	−	0.700995i	$-0.247261\pi$
$641$	20.4795	+	7.45392i	0.808891	+	0.294412i	0.0957255	+	0.995408i	$0.469483\pi$
$642$	−28.1216	+	30.9300i	−1.10987	+	1.22071i
$643$	24.0829	−	28.7008i	0.949735	−	1.13185i	−0.0414197	−	0.999142i	$-0.513188\pi$
$643$	24.0829	−	28.7008i	0.949735	−	1.13185i	0.991155	−	0.132709i	$-0.0423675\pi$
$644$	10.4471	−	4.56907i	0.411673	−	0.180047i
$645$	−9.36383	+	6.78118i	−0.368700	+	0.267009i
$646$	58.6228	−	12.2589i	2.30648	−	0.482318i
$647$	−13.9531			−0.548554			−0.274277	−	0.961651i	$-0.588439\pi$
$647$	−13.9531			−0.548554			−0.274277	+	0.961651i	$0.588439\pi$
$648$	−0.408720	+	25.4526i	−0.0160560	+	0.999871i
$649$	25.4955			1.00079
$650$	3.48773	−	0.729335i	0.136800	−	0.0286069i
$651$	−3.10358	+	2.24758i	−0.121639	+	0.0880896i
$652$	−10.8983	−	24.9188i	−0.426812	−	0.975896i
$653$	−16.3129	+	19.4409i	−0.638372	+	0.760782i	−0.984112	−	0.177548i	$-0.943183\pi$
$653$	−16.3129	+	19.4409i	−0.638372	+	0.760782i	0.345740	+	0.938330i	$0.387628\pi$
$654$	30.2801	−	33.3040i	1.18405	−	1.30229i
$655$	−30.3066	−	11.0307i	−1.18418	−	0.431006i
$656$	10.3462	+	13.6085i	0.403950	+	0.531324i
$657$	−11.5836	+	2.42486i	−0.451921	+	0.0946027i
$658$	−1.61844	+	3.01979i	−0.0630933	+	0.117724i
$659$	−23.0007	−	27.4112i	−0.895981	−	1.06779i	−0.997336	−	0.0729384i	$-0.976762\pi$
$659$	−23.0007	−	27.4112i	−0.895981	−	1.06779i	0.101355	−	0.994850i	$-0.467682\pi$
$660$	14.7684	−	25.1057i	0.574858	−	0.977239i
$661$	29.1329	+	5.13692i	1.13314	+	0.199803i	0.708603	−	0.705608i	$-0.249326\pi$
$661$	29.1329	+	5.13692i	1.13314	+	0.199803i	0.424536	+	0.905411i	$0.360437\pi$
$662$	16.9915	+	2.44513i	0.660392	+	0.0950326i
$663$	2.52898	−	35.3818i	0.0982174	−	1.37412i
$664$	−16.0934	−	15.8517i	−0.624543	−	0.615164i
$665$	5.87402	−	10.1741i	0.227785	−	0.394535i
$666$	14.1793	+	10.4407i	0.549437	+	0.404571i
$667$	−40.6749	+	23.4836i	−1.57494	+	0.909290i
$668$	−8.47380	−	2.49039i	−0.327861	−	0.0963560i
$669$	−2.69826	+	0.769211i	−0.104321	+	0.0297394i
$670$	−6.03209	−	4.74489i	−0.233040	−	0.183311i
$671$	−0.858249	+	0.312377i	−0.0331323	+	0.0120592i
$672$	−7.69286	−	2.06598i	−0.296758	−	0.0796969i
$673$	3.21781	+	18.2491i	0.124038	+	0.703452i	0.981875	+	0.189531i	$0.0606967\pi$
$673$	3.21781	+	18.2491i	0.124038	+	0.703452i	−0.857837	+	0.513922i	$0.828192\pi$
$674$	−36.5087	+	1.15445i	−1.40626	+	0.0444678i
$675$	4.01874	−	2.11301i	0.154681	−	0.0813297i
$676$	9.35275	−	0.592084i	0.359721	−	0.0227725i
$677$	−31.1495	+	5.49250i	−1.19717	+	0.211094i	−0.736477	−	0.676463i	$-0.763512\pi$
$677$	−31.1495	+	5.49250i	−1.19717	+	0.211094i	−0.460698	+	0.887557i	$0.652401\pi$
$678$	−2.81754	−	20.7767i	−0.108207	−	0.797926i
$679$	4.27169	−	1.55477i	0.163932	−	0.0596665i
$680$	−27.6235	+	40.0927i	−1.05931	+	1.53748i
$681$	−11.7061	−	2.93785i	−0.448580	−	0.112579i
$682$	4.16787	−	12.6850i	0.159596	−	0.485732i
$683$	29.5187	−	17.0426i	1.12950	−	0.652117i	0.185691	−	0.982608i	$-0.440548\pi$
$683$	29.5187	−	17.0426i	1.12950	−	0.652117i	0.943809	+	0.330491i	$0.107214\pi$
$684$	−20.7471	−	29.1449i	−0.793286	−	1.11438i
$685$	4.52572	+	2.61293i	0.172919	+	0.0998348i
$686$	11.4307	−	10.2242i	0.436427	−	0.390364i
$687$	39.1722	−	19.0308i	1.49451	−	0.726072i
$688$	−11.0039	−	0.529586i	−0.419520	−	0.0201903i
$689$	−3.69985	+	20.9829i	−0.140953	+	0.799385i
$690$	−36.8535	+	19.3672i	−1.40299	+	0.737297i
$691$	5.27112	+	6.28188i	0.200523	+	0.238974i	0.856930	−	0.515433i	$-0.172369\pi$
$691$	5.27112	+	6.28188i	0.200523	+	0.238974i	−0.656407	+	0.754407i	$0.727925\pi$
$692$	−34.7859	−	17.2510i	−1.32236	−	0.655784i
$693$	−8.45720	+	0.269216i	−0.321262	+	0.0102267i
$694$	−15.5770	+	9.66233i	−0.591294	+	0.366777i
$695$	1.33259	+	0.485021i	0.0505478	+	0.0183979i
$696$	32.4362	+	4.93729i	1.22949	+	0.187148i
$697$	−23.2528	−	19.5114i	−0.880761	−	0.739046i
$698$	0.536109	+	1.33961i	0.0202920	+	0.0507050i
$699$	2.80466	+	27.0864i	0.106082	+	1.02450i
$700$	0.334614	+	1.38077i	0.0126472	+	0.0521884i
$701$		−	1.97965i		−	0.0747704i	−0.999301	−	0.0373852i	$-0.988097\pi$
$701$		−	1.97965i		−	0.0747704i	0.999301	−	0.0373852i	$-0.0119029\pi$
$702$	−19.9679	+	7.08906i	−0.753638	+	0.267559i
$703$	−24.7468			−0.933344
$704$	25.9345	−	9.88631i	0.977444	−	0.372604i
$705$	5.10564	−	11.4200i	0.192290	−	0.430103i
$706$	21.7181	−	8.69154i	0.817373	−	0.327110i
$707$	8.63122	−	10.2863i	0.324611	−	0.386856i
$708$	8.51188	+	23.9916i	0.319896	+	0.901660i
$709$	5.97488	−	16.4158i	0.224391	−	0.616510i	−0.775499	−	0.631349i	$-0.782501\pi$
$709$	5.97488	−	16.4158i	0.224391	−	0.616510i	0.999890	+	0.0148394i	$0.00472370\pi$
$710$	−15.7235	+	9.75321i	−0.590092	+	0.366031i
$711$	30.2419	+	4.34540i	1.13416	+	0.162965i
$712$	5.05251	−	11.0527i	0.189351	−	0.414217i
$713$	−14.6196	+	12.2673i	−0.547510	+	0.459415i
$714$	14.1326	+	0.561991i	0.528898	+	0.0210320i
$715$	23.8767	+	4.21010i	0.892936	+	0.157449i
$716$	−9.18130	−	1.02622i	−0.343121	−	0.0383518i
$717$	−15.0879	+	22.2945i	−0.563470	+	0.832605i
$718$	−19.0550	+	17.0438i	−0.711127	+	0.636071i
$719$	17.2073	−	29.8038i	0.641722	−	1.11150i	−0.343326	−	0.939216i	$-0.611554\pi$
$719$	17.2073	−	29.8038i	0.641722	−	1.11150i	0.985048	−	0.172279i	$-0.0551131\pi$
$720$	28.5553	+	5.51547i	1.06419	+	0.205550i
$721$	7.44538	+	12.8958i	0.277280	+	0.480264i
$722$	22.2383	+	7.30677i	0.827623	+	0.271930i
$723$	15.6962	+	15.2045i	0.583748	+	0.565462i
$724$	−7.60264	+	10.3204i	−0.282550	+	0.383554i
$725$	−2.00152	−	5.49913i	−0.0743345	−	0.204232i
$726$	2.00828	−	1.55345i	0.0745343	−	0.0576540i
$727$	4.21802	+	23.9216i	0.156438	+	0.887203i	0.957460	+	0.288567i	$0.0931789\pi$
$727$	4.21802	+	23.9216i	0.156438	+	0.887203i	−0.801022	+	0.598635i	$0.795710\pi$
$728$	−0.627822	−	6.60048i	−0.0232686	−	0.244630i
$729$	−21.9894	+	15.6674i	−0.814422	+	0.580274i
$730$	0.427340	+	13.5143i	0.0158166	+	0.500187i
$731$	19.2644	−	3.39683i	0.712519	−	0.125636i
$732$	−0.580483	−	0.703333i	−0.0214553	−	0.0259959i
$733$	7.76866	+	21.3442i	0.286942	+	0.788366i	0.996490	+	0.0837095i	$0.0266768\pi$
$733$	7.76866	+	21.3442i	0.286942	+	0.788366i	−0.709548	+	0.704657i	$0.751101\pi$
$734$	−22.6858	−	17.8448i	−0.837348	−	0.658663i
$735$	−18.5144	+	19.1132i	−0.682915	+	0.705000i
$736$	−38.9494	−	7.53164i	−1.43570	−	0.277620i
$737$	−3.88422	−	6.72767i	−0.143077	−	0.247817i
$738$	−5.10893	+	17.3972i	−0.188062	+	0.640401i
$739$	0.214406	+	0.123787i	0.00788706	+	0.00455360i	0.503938	−	0.863740i	$-0.331884\pi$
$739$	0.214406	+	0.123787i	0.00788706	+	0.00455360i	−0.496051	+	0.868293i	$0.665217\pi$
$740$	14.5632	−	13.8792i	0.535355	−	0.510210i
$741$	16.6900	−	24.6618i	0.613123	−	0.905975i
$742$	−8.40894	−	1.21007i	−0.308702	−	0.0444232i
$743$	0.843956	−	4.78631i	0.0309618	−	0.175593i	−0.965406	−	0.260753i	$-0.916029\pi$
$743$	0.843956	−	4.78631i	0.0309618	−	0.175593i	0.996367	+	0.0851603i	$0.0271402\pi$
$744$	13.3282	−	0.312960i	0.488635	−	0.0114737i
$745$	40.6657	−	34.1225i	1.48987	−	1.25015i
$746$	36.1547	+	19.3769i	1.32372	+	0.709439i
$747$	3.40768	−	23.7159i	0.124681	−	0.867719i
$748$	−41.0380	+	27.2886i	−1.50050	+	0.997772i
$749$	4.74524	−	13.0374i	0.173387	−	0.476378i
$750$	7.45672	+	23.3329i	0.272281	+	0.851998i
$751$	23.6852	+	19.8743i	0.864287	+	0.725223i	0.962887	−	0.269905i	$-0.0869921\pi$
$751$	23.6852	+	19.8743i	0.864287	+	0.725223i	−0.0986005	+	0.995127i	$0.531437\pi$
$752$	10.5976	−	5.45686i	0.386454	−	0.198991i
$753$	−3.97342	+	8.88753i	−0.144799	+	0.323879i
$754$	5.59003	+	26.7320i	0.203577	+	0.973520i
$755$			18.7222i			0.681370i
$756$	−3.07684	−	7.86845i	−0.111903	−	0.286173i
$757$			15.9221i			0.578697i	0.957224	+	0.289349i	$0.0934387\pi$
$757$			15.9221i			0.578697i	−0.957224	+	0.289349i	$0.906561\pi$
$758$	26.0074	−	5.43851i	0.944630	−	0.197535i
$759$	−41.9173	+	4.34033i	−1.52150	+	0.157544i
$760$	−36.9117	+	17.5534i	−1.33893	+	0.636729i
$761$	12.1040	+	10.1564i	0.438768	+	0.368170i	0.835248	−	0.549873i	$-0.185324\pi$
$761$	12.1040	+	10.1564i	0.438768	+	0.368170i	−0.396480	+	0.918043i	$0.629768\pi$
$762$	−2.37764	+	10.9257i	−0.0861328	+	0.395797i
$763$	−5.10946	+	14.0381i	−0.184975	+	0.508214i
$764$	22.4142	+	33.7075i	0.810916	+	1.21950i
$765$	−51.6149	+	1.64304i	−1.86614	+	0.0594043i
$766$	9.95010	−	18.5655i	0.359512	−	0.670800i
$767$	−16.2323	+	13.6205i	−0.586113	+	0.491807i
$768$	17.9616	+	21.1041i	0.648132	+	0.761528i
$769$	−7.98567	+	45.2890i	−0.287970	+	1.63316i	0.406507	+	0.913648i	$0.366747\pi$
$769$	−7.98567	+	45.2890i	−0.287970	+	1.63316i	−0.694478	+	0.719514i	$0.744365\pi$
$770$	−1.37696	+	9.56861i	−0.0496220	+	0.344829i
$771$	14.6332	+	30.1204i	0.527004	+	1.08476i
$772$	−8.14823	+	7.76551i	−0.293261	+	0.279487i
$773$	35.6666	+	20.5921i	1.28284	+	0.740647i	0.977366	−	0.211554i	$-0.0678526\pi$
$773$	35.6666	+	20.5921i	1.28284	+	0.740647i	0.305472	+	0.952201i	$0.401186\pi$
$774$	−6.47219	−	9.72874i	−0.232638	−	0.349692i
$775$	−1.18895	−	2.05933i	−0.0427085	−	0.0739733i
$776$	−15.3072	−	3.97767i	−0.549496	−	0.142790i
$777$	−5.66839	−	1.42258i	−0.203352	−	0.0510347i
$778$	15.3957	−	19.5724i	0.551964	−	0.701703i
$779$	−8.71544	−	23.9455i	−0.312263	−	0.857936i
$780$	4.00965	+	23.8738i	0.143569	+	0.854819i
$781$	−18.4444	+	3.25225i	−0.659993	+	0.116375i
$782$	70.4060	−	2.22633i	2.51771	−	0.0796134i
$783$	16.1953	+	30.8019i	0.578772	+	1.10077i
$784$	−25.1539	+	3.19759i	−0.898353	+	0.114200i
$785$	−0.577638	−	3.27595i	−0.0206168	−	0.116924i
$786$	12.3569	−	30.1633i	0.440755	−	1.07589i
$787$	6.23669	+	17.1352i	0.222314	+	0.610803i	0.999837	−	0.0180518i	$-0.00574638\pi$
$787$	6.23669	+	17.1352i	0.222314	+	0.610803i	−0.777523	+	0.628854i	$0.783524\pi$
$788$	−5.19725	+	7.05513i	−0.185144	+	0.251329i
$789$	−19.2191	+	5.47892i	−0.684218	+	0.195055i
$790$	10.8959	−	33.1619i	0.387659	−	1.17985i
$791$	3.47939	+	6.02648i	0.123713	+	0.214277i
$792$	24.7609	+	15.9226i	0.879839	+	0.565785i
$793$	0.379541	−	0.657384i	0.0134779	−	0.0233444i
$794$	14.2933	+	15.9799i	0.507249	+	0.567104i
$795$	30.9397	+	2.21147i	1.09732	+	0.0784328i
$796$	2.95283	−	26.4180i	0.104660	−	0.936362i
$797$	−40.7976	−	7.19372i	−1.44512	−	0.254814i	−0.604575	−	0.796548i	$-0.706657\pi$
$797$	−40.7976	−	7.19372i	−1.44512	−	0.254814i	−0.840550	+	0.541734i	$0.817768\pi$
$798$	10.0388	+	6.34068i	0.355370	+	0.224458i
$799$	−16.2138	+	13.6050i	−0.573602	+	0.481309i
$800$	1.76689	−	4.61635i	0.0624692	−	0.163213i
$801$	12.6165	−	2.64107i	0.445782	−	0.0933176i
$802$	0.446940	+	0.720527i	0.0157820	+	0.0254427i
$803$	−4.68101	+	12.8610i	−0.165189	+	0.453853i
$804$	5.03404	−	5.90119i	0.177537	−	0.208119i
$805$	8.88176	−	10.5849i	0.313041	−	0.373068i
$806$	4.12313	+	10.3027i	0.145231	+	0.362899i
$807$	−13.5757	−	18.7460i	−0.477886	−	0.659891i
$808$	−45.0324	+	12.4323i	−1.58424	+	0.437367i
$809$	−19.2719			−0.677564			−0.338782	−	0.940865i	$-0.610015\pi$
$809$	−19.2719			−0.677564			−0.338782	+	0.940865i	$0.610015\pi$
$810$	13.2595	+	27.8521i	0.465893	+	0.978623i
$811$		−	15.7750i		−	0.553935i	−0.960879	−	0.276968i	$-0.910671\pi$
$811$		−	15.7750i		−	0.553935i	0.960879	−	0.276968i	$-0.0893295\pi$
$812$	−10.5830	+	2.56467i	−0.371392	+	0.0900023i
$813$	−4.58258	+	3.31865i	−0.160718	+	0.116390i
$814$	18.9058	−	7.56606i	0.662648	−	0.265190i
$815$	−25.2474	−	21.1851i	−0.884380	−	0.742083i
$816$	−39.3798	−	29.5067i	−1.37857	−	1.03294i
$817$	15.4315	+	5.61659i	0.539878	+	0.196500i
$818$	21.1999	+	34.1770i	0.741236	+	1.19497i
$819$	5.24063	−	4.68950i	0.183122	−	0.163864i
$820$	18.5587	+	9.20362i	0.648099	+	0.321404i
$821$	−6.66717	−	7.94562i	−0.232686	−	0.277304i	0.637049	−	0.770823i	$-0.280155\pi$
$821$	−6.66717	−	7.94562i	−0.232686	−	0.277304i	−0.869735	+	0.493519i	$0.835710\pi$
$822$	−2.82051	+	4.46554i	−0.0983766	+	0.155753i
$823$	9.20557	−	52.2074i	0.320886	−	1.81983i	−0.216249	−	0.976338i	$-0.569382\pi$
$823$	9.20557	−	52.2074i	0.320886	−	1.81983i	0.537135	−	0.843496i	$-0.319507\pi$
$824$	4.12467	−	51.6424i	0.143690	−	1.79905i
$825$	0.374352	−	5.23739i	0.0130333	−	0.182343i
$826$	−5.63273	−	6.29740i	−0.195988	−	0.219114i
$827$	23.9359	+	13.8194i	0.832332	+	0.480547i	0.854650	−	0.519204i	$-0.173771\pi$
$827$	23.9359	+	13.8194i	0.832332	+	0.480547i	−0.0223184	+	0.999751i	$0.507105\pi$
$828$	−18.0787	−	37.9956i	−0.628279	−	1.32044i
$829$	34.2649	−	19.7829i	1.19007	−	0.687088i	0.231748	−	0.972776i	$-0.425555\pi$
$829$	34.2649	−	19.7829i	1.19007	−	0.687088i	0.958323	+	0.285688i	$0.0922221\pi$
$830$	−26.0057	−	8.54463i	−0.902671	−	0.296588i
$831$	0.141757	+	0.497260i	0.00491751	+	0.0172498i
$832$	−11.2302	+	20.1493i	−0.389337	+	0.698552i
$833$	42.3084	−	15.3990i	1.46590	−	0.533543i
$834$	−0.543332	+	1.32628i	−0.0188141	+	0.0459254i
$835$	−10.5402	+	1.85852i	−0.364759	+	0.0643168i
$836$	−41.2899	+	2.61389i	−1.42804	+	0.0904033i
$837$	8.65415	+	11.1831i	0.299131	+	0.386544i
$838$	1.25030	+	39.5398i	0.0431909	+	1.36588i
$839$	4.95699	+	28.1125i	0.171134	+	0.970551i	0.942512	+	0.334173i	$0.108457\pi$
$839$	4.95699	+	28.1125i	0.171134	+	0.970551i	−0.771378	+	0.636378i	$0.780432\pi$
$840$	−9.46389	+	1.89882i	−0.326535	+	0.0655156i
$841$	14.8973	−	5.42218i	0.513700	−	0.186972i
$842$	−28.6165	+	36.3796i	−0.986189	+	1.25373i
$843$	7.33444	−	29.2247i	0.252611	−	1.00655i
$844$	14.1125	−	48.0192i	0.485772	−	1.65289i
$845$	9.83486	−	5.67816i	0.338329	−	0.195335i
$846$	11.3279	+	5.61474i	0.389461	+	0.193039i
$847$	−0.421335	+	0.729774i	−0.0144773	+	0.0250753i
$848$	21.7026	+	20.0654i	0.745270	+	0.689050i
$849$	2.07904	−	1.01005i	0.0713524	−	0.0346647i
$850$	−1.25014	+	8.68737i	−0.0428795	+	0.297974i
$851$	−28.6640	−	5.05424i	−0.982591	−	0.173257i
$852$	−9.21821	−	16.2706i	−0.315811	−	0.557422i
$853$	−4.41611	−	5.26292i	−0.151205	−	0.180199i	0.685125	−	0.728425i	$-0.259748\pi$
$853$	−4.41611	−	5.26292i	−0.151205	−	0.180199i	−0.836330	+	0.548227i	$0.815303\pi$
$854$	0.266770	+	0.142974i	0.00912868	+	0.00489247i
$855$	−38.2148	−	20.4706i	−1.30692	−	0.700081i
$856$	−39.3298	+	27.9849i	−1.34427	+	0.956503i
$857$	−26.6254	−	9.69084i	−0.909505	−	0.331033i	−0.155450	−	0.987844i	$-0.549683\pi$
$857$	−26.6254	−	9.69084i	−0.909505	−	0.331033i	−0.754055	+	0.656811i	$0.771905\pi$
$858$	−5.21059	+	23.9437i	−0.177886	+	0.817423i
$859$	−14.7282	+	17.5524i	−0.502520	+	0.598879i	−0.956355	−	0.292206i	$-0.905611\pi$
$859$	−14.7282	+	17.5524i	−0.502520	+	0.598879i	0.453836	+	0.891085i	$0.350055\pi$
$860$	−12.2313	+	5.34940i	−0.417084	+	0.182413i
$861$	−0.619806	−	5.98585i	−0.0211229	−	0.203997i
$862$	−2.88895	−	13.8152i	−0.0983981	−	0.470547i
$863$	24.0297			0.817980			0.408990	−	0.912539i	$-0.365881\pi$
$863$	24.0297			0.817980			0.408990	+	0.912539i	$0.365881\pi$
$864$	−6.71676	+	28.6162i	−0.228509	+	0.973542i
$865$	−47.0523			−1.59983
$866$	5.06283	+	24.2108i	0.172042	+	0.822717i
$867$	52.8857	+	23.6440i	1.79609	+	0.802994i
$868$	−4.05399	+	1.77303i	−0.137601	+	0.0601805i
$869$	22.7114	−	27.0664i	0.770432	−	0.918165i
$870$	37.8718	−	12.1030i	1.28397	−	0.410332i
$871$	6.06710	+	2.20824i	0.205576	+	0.0748235i
$872$	42.3485	−	30.1328i	1.43410	−	1.02043i
$873$	−6.23599	−	15.5727i	−0.211056	−	0.527058i
$874$	52.1213	+	27.9341i	1.76303	+	0.944885i
$875$	−5.22579	−	6.22786i	−0.176664	−	0.210540i
$876$	−13.6651	−	0.111154i	−0.461701	−	0.00375554i
$877$	0.500115	+	0.0881838i	0.0168877	+	0.00297776i	0.182086	−	0.983283i	$-0.441715\pi$
$877$	0.500115	+	0.0881838i	0.0168877	+	0.00297776i	−0.165198	+	0.986260i	$0.552826\pi$
$878$	−1.54722	+	10.7518i	−0.0522162	+	0.362856i
$879$	11.6486	+	7.88327i	0.392899	+	0.265896i
$880$	22.8326	−	24.6956i	0.769688	−	0.832488i
$881$	−11.2219	+	19.4369i	−0.378076	+	0.654847i	−0.990782	−	0.135464i	$-0.956747\pi$
$881$	−11.2219	+	19.4369i	−0.378076	+	0.654847i	0.612706	+	0.790311i	$0.290081\pi$
$882$	−18.5586	−	19.4650i	−0.624902	−	0.655422i
$883$	45.9402	−	26.5236i	1.54601	−	0.892589i	0.547570	−	0.836760i	$-0.315553\pi$
$883$	45.9402	−	26.5236i	1.54601	−	0.892589i	0.998440	−	0.0558294i	$-0.0177803\pi$
$884$	11.5493	−	39.2976i	0.388445	−	1.32172i
$885$	22.1574	+	21.4633i	0.744814	+	0.721482i
$886$	−4.26755	+	5.42526i	−0.143371	+	0.182265i
$887$	−26.2975	+	9.57151i	−0.882984	+	0.321380i	−0.743413	−	0.668832i	$-0.766794\pi$
$887$	−26.2975	+	9.57151i	−0.882984	+	0.321380i	−0.139571	+	0.990212i	$0.544572\pi$
$888$	13.4316	+	15.2646i	0.450735	+	0.512247i
$889$	−0.644417	−	3.65467i	−0.0216130	−	0.122574i
$890$	−0.465444	−	14.7193i	−0.0156017	−	0.493393i
$891$	1.98590	+	31.1611i	0.0665301	+	1.04394i
$892$	−3.23334	+	0.204689i	−0.108260	+	0.00685351i
$893$	−17.4984	+	3.08544i	−0.585562	+	0.103250i
$894$	32.8268	+	42.4381i	1.09789	+	1.41934i
$895$	−10.5200	+	3.82896i	−0.351644	+	0.127988i
$896$	−8.17163	−	4.22164i	−0.272995	−	0.141035i
$897$	24.3688	−	25.1569i	0.813650	−	0.839963i
$898$	−6.69567	−	2.19998i	−0.223438	−	0.0734143i
$899$	15.7839	−	9.11281i	0.526421	−	0.303929i
$900$	5.05343	−	1.39627i	0.168448	−	0.0465424i
$901$	−45.4514	−	26.2414i	−1.51421	−	0.874227i
$902$	13.9794	+	15.6290i	0.465463	+	0.520387i
$903$	3.21179	+	2.17359i	0.106882	+	0.0723326i
$904$	1.92755	−	24.1336i	0.0641094	−	0.802673i
$905$	−2.69732	+	15.2973i	−0.0896620	+	0.508498i
$906$	−18.9073	−	0.751861i	−0.628153	−	0.0249789i
$907$	−17.3874	−	20.7215i	−0.577338	−	0.688045i	0.395781	−	0.918345i	$-0.370474\pi$
$907$	−17.3874	−	20.7215i	−0.577338	−	0.688045i	−0.973120	+	0.230300i	$0.926029\pi$
$908$	−12.4853	−	6.19169i	−0.414339	−	0.205478i
$909$	−38.9524	−	30.6269i	−1.29197	−	1.01583i
$910$	−4.23518	−	6.82767i	−0.140395	−	0.226335i
$911$	9.03367	+	3.28799i	0.299299	+	0.108936i	0.487305	−	0.873232i	$-0.337980\pi$
$911$	9.03367	+	3.28799i	0.299299	+	0.108936i	−0.188006	+	0.982168i	$0.560202\pi$
$912$	−16.2446	−	37.9816i	−0.537914	−	1.25770i
$913$	−21.2256	−	17.8104i	−0.702465	−	0.589438i
$914$	−26.4649	+	10.5912i	−0.875383	+	0.350326i
$915$	−1.00885	−	0.451036i	−0.0333517	−	0.0149108i
$916$	48.8730	−	11.8438i	1.61481	−	0.391330i
$917$			10.8185i			0.357258i
$918$	0.413507	−	52.1912i	0.0136478	−	1.72257i
$919$	0.257674			0.00849989			0.00424994	−	0.999991i	$-0.498647\pi$
$919$	0.257674			0.00849989			0.00424994	+	0.999991i	$0.498647\pi$
$920$	−46.3396	+	12.7932i	−1.52777	+	0.421779i
$921$	44.1608	−	4.57264i	1.45515	−	0.150674i
$922$	17.8436	+	44.5870i	0.587647	+	1.46839i
$923$	10.0056	−	11.9242i	0.329337	−	0.392489i
$924$	−9.60793	−	1.77483i	−0.316078	−	0.0583878i
$925$	1.24037	−	3.40788i	0.0407830	−	0.112050i
$926$	−28.5503	−	46.0269i	−0.938221	−	1.51254i
$927$	46.6894	−	28.9749i	1.53348	−	0.951660i
$928$	35.3823	+	13.5425i	1.16148	+	0.444554i
$929$	−27.9758	+	23.4745i	−0.917856	+	0.770173i	−0.973597	−	0.228273i	$-0.926692\pi$
$929$	−27.9758	+	23.4745i	−0.917856	+	0.770173i	0.0557411	+	0.998445i	$0.482248\pi$
$930$	14.3010	−	7.51544i	0.468947	−	0.246441i
$931$	37.2228	+	6.56338i	1.21993	+	0.215106i
$932$	−3.49284	+	31.2492i	−0.114412	+	1.02360i
$933$	−13.4588	−	27.7031i	−0.440622	−	0.906957i
$934$	−10.3782	−	11.6028i	−0.339585	−	0.379656i
$935$	−29.8603	+	51.7196i	−0.976536	+	1.69141i
$936$	−24.2709	+	3.09055i	−0.793318	+	0.101018i
$937$	−4.21635	−	7.30293i	−0.137742	−	0.238576i	0.788899	−	0.614522i	$-0.210651\pi$
$937$	−4.21635	−	7.30293i	−0.137742	−	0.238576i	−0.926642	+	0.375946i	$0.877318\pi$
$938$	−0.803593	+	2.44575i	−0.0262382	+	0.0798565i
$939$	13.8806	−	55.3083i	0.452975	−	1.80492i
$940$	8.56716	−	11.6297i	0.279430	−	0.379319i
$941$	−6.23285	−	17.1246i	−0.203185	−	0.558246i	0.795688	−	0.605707i	$-0.207109\pi$
$941$	−6.23285	−	17.1246i	−0.203185	−	0.558246i	−0.998873	+	0.0474602i	$0.984887\pi$
$942$	3.33154	−	0.451791i	0.108547	−	0.0147202i
$943$	−5.20444	−	29.5159i	−0.169480	−	0.961169i
$944$	3.70690	+	29.1603i	0.120649	+	0.949088i
$945$	−7.57655	−	6.88570i	−0.246465	−	0.223992i
$946$	−13.5064	+	0.427089i	−0.439130	+	0.0138859i
$947$	30.4479	−	5.36879i	0.989424	−	0.174462i	0.344564	−	0.938763i	$-0.388027\pi$
$947$	30.4479	−	5.36879i	0.989424	−	0.174462i	0.644860	+	0.764301i	$0.276916\pi$
$948$	33.0522	+	12.3354i	1.07349	+	0.400635i
$949$	−3.89045	−	10.6889i	−0.126289	−	0.346977i
$950$	−4.55538	+	5.79117i	−0.147796	+	0.187890i
$951$	−3.35339	−	11.7631i	−0.108741	−	0.381444i
$952$	15.8068	+	4.10750i	0.512302	+	0.133125i
$953$	17.3439	+	30.0406i	0.561825	+	0.973109i	0.997337	+	0.0729266i	$0.0232339\pi$
$953$	17.3439	+	30.0406i	0.561825	+	0.973109i	−0.435512	+	0.900183i	$0.643433\pi$
$954$	−3.47584	+	31.1568i	−0.112534	+	1.00874i
$955$	42.4811	+	24.5265i	1.37466	+	0.793658i
$956$	−22.5023	+	21.4454i	−0.727776	+	0.693593i
$957$	40.1423	+	2.86925i	1.29762	+	0.0927495i
$958$	−4.62583	+	32.1454i	−0.149454	+	1.03857i
$959$	0.304398	−	1.72633i	0.00982954	−	0.0557461i
$960$	30.8617	+	13.2410i	0.996057	+	0.427351i
$961$	−18.0742	+	15.1661i	−0.583040	+	0.489229i
$962$	−7.99476	+	14.9172i	−0.257762	+	0.480948i
$963$	−48.6432	−	15.9712i	−1.56750	−	0.514664i
$964$	13.9722	+	21.0121i	0.450015	+	0.676754i
$965$	−4.66513	+	12.8173i	−0.150176	+	0.412605i
$966$	10.3329	+	9.39466i	0.332454	+	0.302268i
$967$	23.6086	+	19.8100i	0.759202	+	0.637046i	0.937919	−	0.346854i	$-0.112750\pi$
$967$	23.6086	+	19.8100i	0.759202	+	0.637046i	−0.178717	+	0.983901i	$0.557195\pi$
$968$	2.64763	−	1.25908i	0.0850979	−	0.0404684i
$969$	43.0231	+	59.4086i	1.38210	+	1.90848i
$970$	−18.7594	+	3.92287i	−0.602329	+	0.125956i
$971$			43.2999i			1.38956i	0.719223	+	0.694779i	$0.244498\pi$
$971$			43.2999i			1.38956i	−0.719223	+	0.694779i	$0.755502\pi$
$972$	−28.6600	+	12.2721i	−0.919269	+	0.393629i
$973$		−	0.475690i		−	0.0152499i
$974$	2.55103	+	12.1992i	0.0817403	+	0.390888i
$975$	2.55963	+	3.53449i	0.0819739	+	0.113194i
$976$	−0.482063	−	0.936198i	−0.0154305	−	0.0299670i
$977$	4.11710	+	3.45466i	0.131718	+	0.110524i	0.706267	−	0.707946i	$-0.250378\pi$
$977$	4.11710	+	3.45466i	0.131718	+	0.110524i	−0.574549	+	0.818470i	$0.694822\pi$
$978$	22.4085	−	24.6463i	0.716545	−	0.788102i
$979$	5.09839	−	14.0077i	0.162945	−	0.447688i
$980$	−25.5863	+	17.0139i	−0.817324	+	0.543488i
$981$	52.3767	+	17.1970i	1.67226	+	0.549059i
$982$	14.6587	+	7.85622i	0.467776	+	0.250702i
$983$	0.806129	−	0.676422i	0.0257115	−	0.0215745i	−0.629841	−	0.776724i	$-0.716880\pi$
$983$	0.806129	−	0.676422i	0.0257115	−	0.0215745i	0.655553	+	0.755149i	$0.272436\pi$
$984$	−10.0399	+	18.3726i	−0.320061	+	0.585698i
$985$	−1.84392	+	10.4574i	−0.0587521	+	0.333200i
$986$	−66.5849	−	9.58179i	−2.12050	−	0.305146i
$987$	−4.18547	−	0.299164i	−0.133225	−	0.00952250i
$988$	24.8916	−	23.7225i	0.791909	−	0.754713i
$989$	16.7270	+	9.65734i	0.531888	+	0.307086i
$990$	35.4536	+	3.95519i	1.12679	+	0.125704i
$991$	10.7235	+	18.5737i	0.340644	+	0.590013i	0.984553	−	0.175090i	$-0.0560215\pi$
$991$	10.7235	+	18.5737i	0.340644	+	0.590013i	−0.643908	+	0.765103i	$0.722688\pi$
$992$	15.1143	+	2.92265i	0.479880	+	0.0927942i
$993$	5.76398	+	20.2190i	0.182914	+	0.641632i
$994$	4.87823	+	3.83725i	0.154728	+	0.121710i
$995$	−11.0174	−	30.2700i	−0.349274	−	0.959622i
$996$	9.67347	−	25.9197i	0.306516	−	0.821297i
$997$	−9.02724	+	1.59175i	−0.285896	+	0.0504111i	−0.314757	−	0.949172i	$-0.601923\pi$
$997$	−9.02724	+	1.59175i	−0.285896	+	0.0504111i	0.0288614	+	0.999583i	$0.490812\pi$
$998$	−0.788669	−	24.9411i	−0.0249649	−	0.789496i
$999$	−4.58138	+	21.0738i	−0.144949	+	0.666745i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.13.20	yes	204
3.2	odd	2		648.2.t.a.253.15		204
4.3	odd	2		864.2.bf.a.337.29		204
8.3	odd	2		864.2.bf.a.337.6		204
8.5	even	2	inner	216.2.t.a.13.19	✓	204
24.5	odd	2		648.2.t.a.253.16		204
27.2	odd	18		648.2.t.a.397.16		204
27.25	even	9	inner	216.2.t.a.133.19	yes	204
108.79	odd	18		864.2.bf.a.241.6		204
216.29	odd	18		648.2.t.a.397.15		204
216.133	even	18	inner	216.2.t.a.133.20	yes	204
216.187	odd	18		864.2.bf.a.241.29		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.19	✓	204	8.5	even	2	inner
216.2.t.a.13.20	yes	204	1.1	even	1	trivial
216.2.t.a.133.19	yes	204	27.25	even	9	inner
216.2.t.a.133.20	yes	204	216.133	even	18	inner
648.2.t.a.253.15		204	3.2	odd	2
648.2.t.a.253.16		204	24.5	odd	2
648.2.t.a.397.15		204	216.29	odd	18
648.2.t.a.397.16		204	27.2	odd	18
864.2.bf.a.241.6		204	108.79	odd	18
864.2.bf.a.241.29		204	216.187	odd	18
864.2.bf.a.337.6		204	8.3	odd	2
864.2.bf.a.337.29		204	4.3	odd	2

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.289471 + 1.38427i) q^{2} +(-1.40283 + 1.01591i) q^{3} +(-1.83241 + 0.801412i) q^{4} +(-1.55785 + 1.85658i) q^{5} +(-1.81237 - 1.64782i) q^{6} +(0.763942 + 0.278052i) q^{7} +(-1.63980 - 2.30457i) q^{8} +(0.935847 - 2.85030i) q^{9} +O(q^{10})\)	\(q+(0.289471 + 1.38427i) q^{2} +(-1.40283 + 1.01591i) q^{3} +(-1.83241 + 0.801412i) q^{4} +(-1.55785 + 1.85658i) q^{5} +(-1.81237 - 1.64782i) q^{6} +(0.763942 + 0.278052i) q^{7} +(-1.63980 - 2.30457i) q^{8} +(0.935847 - 2.85030i) q^{9} +(-3.02096 - 1.61907i) q^{10} +(-2.23007 - 2.65769i) q^{11} +(1.75640 - 2.98581i) q^{12} +(2.83964 + 0.500705i) q^{13} +(-0.163761 + 1.13799i) q^{14} +(0.299281 - 4.18710i) q^{15} +(2.71548 - 2.93704i) q^{16} +(-3.55127 + 6.15099i) q^{17} +(4.21648 + 0.470389i) q^{18} +(-5.16371 + 2.98127i) q^{19} +(1.36675 - 4.65050i) q^{20} +(-1.35415 + 0.386038i) q^{21} +(3.03343 - 3.85634i) q^{22} +(-6.58997 + 2.39855i) q^{23} +(4.64160 + 1.56702i) q^{24} +(-0.151733 - 0.860521i) q^{25} +(0.128881 + 4.07577i) q^{26} +(1.58282 + 4.94921i) q^{27} +(-1.62269 + 0.102726i) q^{28} +(6.59552 - 1.16297i) q^{29} +(5.88272 - 0.797758i) q^{30} +(2.55724 - 0.930757i) q^{31} +(4.85171 + 2.90877i) q^{32} +(5.82838 + 1.46273i) q^{33} +(-9.54262 - 3.13539i) q^{34} +(-1.70634 + 0.985154i) q^{35} +(0.569403 + 5.97292i) q^{36} +(3.59434 + 2.07519i) q^{37} +(-5.62163 - 6.28499i) q^{38} +(-4.49220 + 2.18242i) q^{39} +(6.83319 + 0.545766i) q^{40} +(-0.742124 + 4.20880i) q^{41} +(-0.926370 - 1.76277i) q^{42} +(-1.77034 - 2.10981i) q^{43} +(6.21631 + 3.08279i) q^{44} +(3.83389 + 6.17782i) q^{45} +(-5.22785 - 8.42800i) q^{46} +(2.80028 + 1.01922i) q^{47} +(-0.825575 + 6.87884i) q^{48} +(-4.85602 - 4.07468i) q^{49} +(1.14727 - 0.459136i) q^{50} +(-1.26704 - 12.2365i) q^{51} +(-5.60467 + 1.35822i) q^{52} +7.38929i q^{53} +(-6.39287 + 3.62370i) q^{54} +8.40834 q^{55} +(-0.611922 - 2.21651i) q^{56} +(4.21509 - 9.42808i) q^{57} +(3.51907 + 8.79334i) q^{58} +(-4.72368 + 5.62947i) q^{59} +(2.80719 + 7.91235i) q^{60} +(0.0900385 - 0.247379i) q^{61} +(2.02867 + 3.27048i) q^{62} +(1.50746 - 1.91725i) q^{63} +(-2.62210 + 7.55808i) q^{64} +(-5.35335 + 4.49199i) q^{65} +(-0.337669 + 8.49148i) q^{66} +(2.20513 + 0.388825i) q^{67} +(1.57793 - 14.1172i) q^{68} +(6.80787 - 10.0596i) q^{69} +(-1.85765 - 2.07686i) q^{70} +(2.69918 - 4.67512i) q^{71} +(-8.10332 + 2.51719i) q^{72} +(-1.97245 - 3.41639i) q^{73} +(-1.83217 + 5.57624i) q^{74} +(1.08707 + 1.05302i) q^{75} +(7.07283 - 9.60118i) q^{76} +(-0.964666 - 2.65040i) q^{77} +(-4.32142 - 5.58667i) q^{78} +(1.76846 + 10.0295i) q^{79} +(1.22252 + 9.61697i) q^{80} +(-7.24838 - 5.33489i) q^{81} +(-6.04094 + 0.191022i) q^{82} +(7.86515 - 1.38684i) q^{83} +(2.17200 - 1.79262i) q^{84} +(-5.88742 - 16.1756i) q^{85} +(2.40809 - 3.06136i) q^{86} +(-8.07090 + 8.33191i) q^{87} +(-2.46797 + 9.49744i) q^{88} +(2.14833 + 3.72101i) q^{89} +(-7.44198 + 7.09544i) q^{90} +(2.03010 + 1.17208i) q^{91} +(10.1533 - 9.67643i) q^{92} +(-2.64179 + 3.90362i) q^{93} +(-0.600276 + 4.17138i) q^{94} +(2.50935 - 14.2312i) q^{95} +(-9.76116 + 0.848403i) q^{96} +(4.28345 - 3.59424i) q^{97} +(4.23479 - 7.90155i) q^{98} +(-9.66221 + 3.86916i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Introduction

L-functions

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