LMFDB - Embedded newform 135.2.q.a.122.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(2,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("135.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, 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:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			122.4
Character	$\chi$	$=$	135.122
Dual form			135.2.q.a.83.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.42277 - 0.996232i) q^{2} +(0.949962 + 1.44830i) q^{3} +(0.347747 + 0.955427i) q^{4} +(-0.893670 + 2.04972i) q^{5} +(0.0912678 - 3.00698i) q^{6} +(0.429055 + 0.920112i) q^{7} +(-0.442010 + 1.64960i) q^{8} +(-1.19514 + 2.75166i) q^{9} +O(q^{10})$	\(q+(-1.42277 - 0.996232i) q^{2} +(0.949962 + 1.44830i) q^{3} +(0.347747 + 0.955427i) q^{4} +(-0.893670 + 2.04972i) q^{5} +(0.0912678 - 3.00698i) q^{6} +(0.429055 + 0.920112i) q^{7} +(-0.442010 + 1.64960i) q^{8} +(-1.19514 + 2.75166i) q^{9} +(3.31348 - 2.02597i) q^{10} +(-0.759141 - 0.904709i) q^{11} +(-1.05340 + 1.41126i) q^{12} +(2.21505 + 3.16342i) q^{13} +(0.306200 - 1.73654i) q^{14} +(-3.81756 + 0.652855i) q^{15} +(3.83001 - 3.21376i) q^{16} +(0.144887 + 0.540727i) q^{17} +(4.44170 - 2.72433i) q^{18} +(3.83587 - 2.21464i) q^{19} +(-2.26913 - 0.141052i) q^{20} +(-0.925012 + 1.49547i) q^{21} +(0.178781 + 2.04347i) q^{22} +(4.21975 + 1.96770i) q^{23} +(-2.80901 + 0.926898i) q^{24} +(-3.40271 - 3.66355i) q^{25} -6.70752i q^{26} +(-5.12057 + 0.883047i) q^{27} +(-0.729897 + 0.729897i) q^{28} +(-1.44060 - 8.17007i) q^{29} +(6.08190 + 2.87432i) q^{30} +(-7.51688 + 2.73592i) q^{31} +(-5.24827 + 0.459164i) q^{32} +(0.589135 - 1.95890i) q^{33} +(0.332549 - 0.913671i) q^{34} +(-2.26941 + 0.0571670i) q^{35} +(-3.04462 - 0.184991i) q^{36} +(-5.30076 + 1.42034i) q^{37} +(-7.66385 - 0.670500i) q^{38} +(-2.47737 + 6.21319i) q^{39} +(-2.98621 - 2.38020i) q^{40} +(5.46773 + 0.964109i) q^{41} +(2.80591 - 1.20618i) q^{42} +(0.0660161 - 0.754568i) q^{43} +(0.600395 - 1.03991i) q^{44} +(-4.57207 - 4.90879i) q^{45} +(-4.04344 - 7.00343i) q^{46} +(11.1364 - 5.19301i) q^{47} +(8.29285 + 2.49405i) q^{48} +(3.83700 - 4.57275i) q^{49} +(1.19152 + 8.60226i) q^{50} +(-0.645498 + 0.723511i) q^{51} +(-2.25214 + 3.21639i) q^{52} +(-5.40763 - 5.40763i) q^{53} +(8.16510 + 3.84491i) q^{54} +(2.53282 - 0.747516i) q^{55} +(-1.70747 + 0.301072i) q^{56} +(6.85140 + 3.45167i) q^{57} +(-6.08964 + 13.0593i) q^{58} +(6.20310 + 5.20502i) q^{59} +(-1.95130 - 3.42037i) q^{60} +(10.5365 + 3.83498i) q^{61} +(13.4204 + 3.59598i) q^{62} +(-3.04462 + 0.0809482i) q^{63} +(-0.735277 - 0.424512i) q^{64} +(-8.46365 + 1.71318i) q^{65} +(-2.78972 + 2.20015i) q^{66} +(-1.29416 + 0.906180i) q^{67} +(-0.466241 + 0.326466i) q^{68} +(1.15878 + 7.98071i) q^{69} +(3.28579 + 2.17952i) q^{70} +(6.95937 + 4.01800i) q^{71} +(-4.01088 - 3.18777i) q^{72} +(-5.11087 - 1.36945i) q^{73} +(8.95674 + 3.25999i) q^{74} +(2.07347 - 8.40837i) q^{75} +(3.44984 + 2.89476i) q^{76} +(0.506721 - 1.08667i) q^{77} +(9.71449 - 6.37189i) q^{78} +(6.62789 - 1.16868i) q^{79} +(3.16454 + 10.7225i) q^{80} +(-6.14326 - 6.57726i) q^{81} +(-6.81884 - 6.81884i) q^{82} +(0.172108 - 0.245796i) q^{83} +(-1.75049 - 0.363735i) q^{84} +(-1.23782 - 0.186253i) q^{85} +(-0.845650 + 1.00781i) q^{86} +(10.4642 - 9.84768i) q^{87} +(1.82796 - 0.852391i) q^{88} +(-5.41601 - 9.38081i) q^{89} +(1.61470 + 11.5389i) q^{90} +(-1.96032 + 3.39538i) q^{91} +(-0.412590 + 4.71593i) q^{92} +(-11.1032 - 8.28768i) q^{93} +(-21.0180 - 3.70604i) q^{94} +(1.11139 + 9.84163i) q^{95} +(-5.65066 - 7.16487i) q^{96} +(-5.10194 - 0.446362i) q^{97} +(-10.0147 + 2.68342i) q^{98} +(3.39674 - 1.00764i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.42277	−	0.996232i	−1.00605	−	0.704443i	−0.0503320	−	0.998733i	$-0.516028\pi$
$2$	−1.42277	−	0.996232i	−1.00605	−	0.704443i	−0.955716	+	0.294290i	$0.904917\pi$
$3$	0.949962	+	1.44830i	0.548461	+	0.836176i
$3$	0.949962	+	1.44830i	0.548461	+	0.836176i
$4$	0.347747	+	0.955427i	0.173874	+	0.477714i
$5$	−0.893670	+	2.04972i	−0.399661	+	0.916663i
$5$	−0.893670	+	2.04972i	−0.399661	+	0.916663i
$6$	0.0912678	−	3.00698i	0.0372599	−	1.22759i
$7$	0.429055	+	0.920112i	0.162168	+	0.347770i	0.970554	−	0.240882i	$-0.0774367\pi$
$7$	0.429055	+	0.920112i	0.162168	+	0.347770i	−0.808387	+	0.588652i	$0.799659\pi$
$8$	−0.442010	+	1.64960i	−0.156274	+	0.583223i
$9$	−1.19514	+	2.75166i	−0.398381	+	0.917220i
$10$	3.31348	−	2.02597i	1.04781	−	0.640669i
$11$	−0.759141	−	0.904709i	−0.228890	−	0.272780i	0.639360	−	0.768908i	$-0.279199\pi$
$11$	−0.759141	−	0.904709i	−0.228890	−	0.272780i	−0.868250	+	0.496127i	$0.834755\pi$
$12$	−1.05340	+	1.41126i	−0.304090	+	0.407396i
$13$	2.21505	+	3.16342i	0.614345	+	0.877375i	0.998955	−	0.0457040i	$-0.0145531\pi$
$13$	2.21505	+	3.16342i	0.614345	+	0.877375i	−0.384610	+	0.923079i	$0.625664\pi$
$14$	0.306200	−	1.73654i	0.0818353	−	0.464111i
$15$	−3.81756	+	0.652855i	−0.985690	+	0.168567i
$16$	3.83001	−	3.21376i	0.957502	−	0.803439i
$17$	0.144887	+	0.540727i	0.0351404	+	0.131146i	0.981268	−	0.192649i	$-0.0617079\pi$
$17$	0.144887	+	0.540727i	0.0351404	+	0.131146i	−0.946127	+	0.323795i	$0.895041\pi$
$18$	4.44170	−	2.72433i	1.04692	−	0.642131i
$19$	3.83587	−	2.21464i	0.880010	−	0.508074i	0.00934815	−	0.999956i	$-0.497024\pi$
$19$	3.83587	−	2.21464i	0.880010	−	0.508074i	0.870662	+	0.491882i	$0.163691\pi$
$20$	−2.26913	−	0.141052i	−0.507393	−	0.0315402i
$21$	−0.925012	+	1.49547i	−0.201854	+	0.326339i
$22$	0.178781	+	2.04347i	0.0381162	+	0.435670i
$23$	4.21975	+	1.96770i	0.879879	+	0.410294i	0.809427	−	0.587221i	$-0.199778\pi$
$23$	4.21975	+	1.96770i	0.879879	+	0.410294i	0.0704523	+	0.997515i	$0.477556\pi$
$24$	−2.80901	+	0.926898i	−0.573387	+	0.189202i
$25$	−3.40271	−	3.66355i	−0.680542	−	0.732709i
$26$		−	6.70752i		−	1.31545i
$27$	−5.12057	+	0.883047i	−0.985454	+	0.169942i
$28$	−0.729897	+	0.729897i	−0.137938	+	0.137938i
$29$	−1.44060	−	8.17007i	−0.267513	−	1.51714i	−0.761782	−	0.647834i	$-0.775675\pi$
$29$	−1.44060	−	8.17007i	−0.267513	−	1.51714i	0.494268	−	0.869309i	$-0.335436\pi$
$30$	6.08190	+	2.87432i	1.11040	+	0.524776i
$31$	−7.51688	+	2.73592i	−1.35007	+	0.491386i	−0.912970	−	0.408026i	$-0.866217\pi$
$31$	−7.51688	+	2.73592i	−1.35007	+	0.491386i	−0.437102	+	0.899412i	$0.643995\pi$
$32$	−5.24827	+	0.459164i	−0.927771	+	0.0811694i
$33$	0.589135	−	1.95890i	0.102555	−	0.341001i
$34$	0.332549	−	0.913671i	0.0570317	−	0.156693i
$35$	−2.26941	+	0.0571670i	−0.383600	+	0.00966299i
$36$	−3.04462	−	0.184991i	−0.507436	−	0.0308319i
$37$	−5.30076	+	1.42034i	−0.871440	+	0.233502i	−0.666710	−	0.745317i	$-0.732298\pi$
$37$	−5.30076	+	1.42034i	−0.871440	+	0.233502i	−0.204730	+	0.978819i	$0.565632\pi$
$38$	−7.66385	−	0.670500i	−1.24324	−	0.108770i
$39$	−2.47737	+	6.21319i	−0.396696	+	0.994906i
$40$	−2.98621	−	2.38020i	−0.472162	−	0.376342i
$41$	5.46773	+	0.964109i	0.853917	+	0.150569i	0.583438	−	0.812157i	$-0.301707\pi$
$41$	5.46773	+	0.964109i	0.853917	+	0.150569i	0.270478	+	0.962726i	$0.412818\pi$
$42$	2.80591	−	1.20618i	0.432962	−	0.186118i
$43$	0.0660161	−	0.754568i	0.0100674	−	0.115070i	−0.989498	−	0.144546i	$-0.953828\pi$
$43$	0.0660161	−	0.754568i	0.0100674	−	0.115070i	0.999566	+	0.0294750i	$0.00938355\pi$
$44$	0.600395	−	1.03991i	0.0905129	−	0.156773i
$45$	−4.57207	−	4.90879i	−0.681564	−	0.731759i
$46$	−4.04344	−	7.00343i	−0.596172	−	1.03260i
$47$	11.1364	−	5.19301i	1.62442	−	0.757478i	0.624691	−	0.780872i	$-0.285225\pi$
$47$	11.1364	−	5.19301i	1.62442	−	0.757478i	0.999726	+	0.0233932i	$0.00744697\pi$
$48$	8.29285	+	2.49405i	1.19697	+	0.359985i
$49$	3.83700	−	4.57275i	0.548142	−	0.653250i
$50$	1.19152	+	8.60226i	0.168506	+	1.21654i
$51$	−0.645498	+	0.723511i	−0.0903877	+	0.101312i
$52$	−2.25214	+	3.21639i	−0.312316	+	0.446033i
$53$	−5.40763	−	5.40763i	−0.742795	−	0.742795i	0.230320	−	0.973115i	$-0.426023\pi$
$53$	−5.40763	−	5.40763i	−0.742795	−	0.742795i	−0.973115	+	0.230320i	$0.926023\pi$
$54$	8.16510	+	3.84491i	1.11113	+	0.523225i
$55$	2.53282	−	0.747516i	0.341526	−	0.100795i
$56$	−1.70747	+	0.301072i	−0.228170	+	0.0402325i
$57$	6.85140	+	3.45167i	0.907490	+	0.457185i
$58$	−6.08964	+	13.0593i	−0.799609	+	1.71477i
$59$	6.20310	+	5.20502i	0.807575	+	0.677636i	0.950028	−	0.312166i	$-0.101054\pi$
$59$	6.20310	+	5.20502i	0.807575	+	0.677636i	−0.142453	+	0.989802i	$0.545499\pi$
$60$	−1.95130	−	3.42037i	−0.251912	−	0.441568i
$61$	10.5365	+	3.83498i	1.34906	+	0.491018i	0.912655	−	0.408731i	$-0.134029\pi$
$61$	10.5365	+	3.83498i	1.34906	+	0.491018i	0.436407	+	0.899749i	$0.356251\pi$
$62$	13.4204	+	3.59598i	1.70439	+	0.456690i
$63$	−3.04462	+	0.0809482i	−0.383586	+	0.0101985i
$64$	−0.735277	−	0.424512i	−0.0919096	−	0.0530640i
$65$	−8.46365	+	1.71318i	−1.04979	+	0.212494i
$66$	−2.78972	+	2.20015i	−0.343391	+	0.270820i
$67$	−1.29416	+	0.906180i	−0.158107	+	0.110707i	−0.649953	−	0.759975i	$-0.725211\pi$
$67$	−1.29416	+	0.906180i	−0.158107	+	0.110707i	0.491846	+	0.870682i	$0.336322\pi$
$68$	−0.466241	+	0.326466i	−0.0565401	+	0.0395898i
$69$	1.15878	+	7.98071i	0.139501	+	0.960764i
$70$	3.28579	+	2.17952i	0.392727	+	0.260503i
$71$	6.95937	+	4.01800i	0.825926	+	0.476849i	0.852456	−	0.522800i	$-0.175112\pi$
$71$	6.95937	+	4.01800i	0.825926	+	0.476849i	−0.0265298	+	0.999648i	$0.508446\pi$
$72$	−4.01088	−	3.18777i	−0.472687	−	0.375683i
$73$	−5.11087	−	1.36945i	−0.598182	−	0.160282i	−0.0529922	−	0.998595i	$-0.516876\pi$
$73$	−5.11087	−	1.36945i	−0.598182	−	0.160282i	−0.545190	+	0.838312i	$0.683543\pi$
$74$	8.95674	+	3.25999i	1.04120	+	0.378966i
$75$	2.07347	−	8.40837i	0.239424	−	0.970915i
$76$	3.44984	+	2.89476i	0.395724	+	0.332052i
$77$	0.506721	−	1.08667i	0.0577462	−	0.123837i
$78$	9.71449	−	6.37189i	1.09995	−	0.721474i
$79$	6.62789	−	1.16868i	0.745696	−	0.131486i	0.212126	−	0.977242i	$-0.431961\pi$
$79$	6.62789	−	1.16868i	0.745696	−	0.131486i	0.533570	+	0.845756i	$0.320850\pi$
$80$	3.16454	+	10.7225i	0.353807	+	1.19881i
$81$	−6.14326	−	6.57726i	−0.682585	−	0.730806i
$82$	−6.81884	−	6.81884i	−0.753014	−	0.753014i
$83$	0.172108	−	0.245796i	0.0188913	−	0.0269796i	−0.809595	−	0.586988i	$-0.800313\pi$
$83$	0.172108	−	0.245796i	0.0188913	−	0.0269796i	0.828487	+	0.560009i	$0.189202\pi$
$84$	−1.75049	−	0.363735i	−0.190994	−	0.0396868i
$85$	−1.23782	−	0.186253i	−0.134261	−	0.0202020i
$86$	−0.845650	+	1.00781i	−0.0911888	+	0.108675i
$87$	10.4642	−	9.84768i	1.12188	−	1.05578i
$88$	1.82796	−	0.852391i	0.194861	−	0.0908652i
$89$	−5.41601	−	9.38081i	−0.574096	−	0.994364i	−0.996139	−	0.0877879i	$-0.972020\pi$
$89$	−5.41601	−	9.38081i	−0.574096	−	0.994364i	0.422043	−	0.906576i	$-0.361313\pi$
$90$	1.61470	+	11.5389i	0.170204	+	1.21631i
$91$	−1.96032	+	3.39538i	−0.205498	+	0.355932i
$92$	−0.412590	+	4.71593i	−0.0430155	+	0.491670i
$93$	−11.1032	−	8.28768i	−1.15135	−	0.859392i
$94$	−21.0180	−	3.70604i	−2.16784	−	0.382249i
$95$	1.11139	+	9.84163i	0.114027	+	1.00973i
$96$	−5.65066	−	7.16487i	−0.576718	−	0.731262i
$97$	−5.10194	−	0.446362i	−0.518023	−	0.0453212i	−0.174853	−	0.984595i	$-0.555945\pi$
$97$	−5.10194	−	0.446362i	−0.518023	−	0.0453212i	−0.343170	+	0.939273i	$0.611501\pi$
$98$	−10.0147	+	2.68342i	−1.01163	+	0.271067i
$99$	3.39674	−	1.00764i	0.341385	−	0.101272i
$100$	2.31697	−	4.52503i	0.231697	−	0.452503i
$101$	−6.63190	+	18.2210i	−0.659899	+	1.81306i	−0.0825062	+	0.996591i	$0.526292\pi$
$101$	−6.63190	+	18.2210i	−0.659899	+	1.81306i	−0.577393	+	0.816467i	$0.695930\pi$
$102$	1.63918	−	0.386322i	0.162303	−	0.0382516i
$103$	14.8525	−	1.29943i	1.46346	−	0.128036i	0.672589	−	0.740016i	$-0.265182\pi$
$103$	14.8525	−	1.29943i	1.46346	−	0.128036i	0.790873	+	0.611980i	$0.209627\pi$
$104$	−6.19746	+	2.25569i	−0.607711	+	0.221189i
$105$	−2.23865	−	3.23247i	−0.218469	−	0.315457i
$106$	2.30654	+	13.0811i	0.224031	+	1.27054i
$107$	3.20052	−	3.20052i	0.309406	−	0.309406i	−0.535273	−	0.844679i	$-0.679791\pi$
$107$	3.20052	−	3.20052i	0.309406	−	0.309406i	0.844679	+	0.535273i	$0.179791\pi$
$108$	−2.62435	−	4.58525i	−0.252528	−	0.441216i
$109$			10.7258i			1.02735i	0.857986	+	0.513673i	$0.171716\pi$
$109$			10.7258i			1.02735i	−0.857986	+	0.513673i	$0.828284\pi$
$110$	−4.34832	−	1.45974i	−0.414596	−	0.139181i
$111$	−7.09260	−	6.32783i	−0.673200	−	0.600611i
$112$	4.60030	+	2.14516i	0.434688	+	0.202698i
$113$	−1.10011	−	12.5744i	−0.103490	−	1.18290i	−0.853364	−	0.521316i	$-0.825441\pi$
$113$	−1.10011	−	12.5744i	−0.103490	−	1.18290i	0.749874	−	0.661581i	$-0.230114\pi$
$114$	−6.30929	−	11.7365i	−0.590919	−	1.09922i
$115$	−7.80431	+	6.89084i	−0.727755	+	0.642574i
$116$	7.30494	−	4.21751i	0.678247	−	0.391586i
$117$	−11.3520	+	2.31432i	−1.04949	+	0.213959i
$118$	−3.64016	−	13.5853i	−0.335104	−	1.25062i
$119$	−0.435365	+	0.365315i	−0.0399099	+	0.0334883i
$120$	0.610448	−	6.58603i	0.0557260	−	0.601220i
$121$	1.66793	−	9.45928i	0.151630	−	0.859935i
$122$	−11.1705	−	15.9531i	−1.01133	−	1.44432i
$123$	3.79782	+	8.83479i	0.342438	+	0.796606i
$124$	−5.22795	−	6.23043i	−0.469484	−	0.559509i
$125$	10.5501	−	3.70060i	0.943634	−	0.330992i
$126$	4.41243	+	2.91798i	0.393090	+	0.259954i
$127$	−4.56717	+	17.0449i	−0.405270	+	1.51249i	0.398286	+	0.917261i	$0.369605\pi$
$127$	−4.56717	+	17.0449i	−0.405270	+	1.51249i	−0.803556	+	0.595229i	$0.797061\pi$
$128$	5.07618	+	10.8859i	0.448676	+	0.962188i
$129$	1.15555	−	0.621200i	0.101741	−	0.0546936i
$130$	13.7485	+	5.99430i	1.20583	+	0.525735i
$131$	−0.988469	−	2.71580i	−0.0863629	−	0.237280i	0.888992	−	0.457923i	$-0.151407\pi$
$131$	−0.988469	−	2.71580i	−0.0863629	−	0.237280i	−0.975355	+	0.220643i	$0.929184\pi$
$132$	2.07646	−	0.118328i	0.180733	−	0.0102991i
$133$	3.68352	+	2.57923i	0.319402	+	0.223648i
$134$	2.74405			0.237050
$135$	2.76610	−	11.2849i	0.238068	−	0.971249i
$136$	−0.956027			−0.0819787
$137$	−6.89836	−	4.83028i	−0.589367	−	0.412679i	0.240493	−	0.970651i	$-0.422691\pi$
$137$	−6.89836	−	4.83028i	−0.589367	−	0.412679i	−0.829860	+	0.557972i	$0.811580\pi$
$138$	6.30196	−	12.5091i	0.536459	−	1.06485i
$139$	−3.42050	−	9.39775i	−0.290123	−	0.797107i	−0.996048	−	0.0888198i	$-0.971690\pi$
$139$	−3.42050	−	9.39775i	−0.290123	−	0.797107i	0.705925	−	0.708287i	$-0.250532\pi$
$140$	−0.843798	−	2.14837i	−0.0713140	−	0.181571i
$141$	18.1002	+	11.1957i	1.52432	+	0.942852i
$142$	−5.89871	−	12.6498i	−0.495009	−	1.06155i
$143$	1.18044	−	4.40546i	0.0987133	−	0.368403i
$144$	4.26576	+	14.3798i	0.355480	+	1.19831i
$145$	18.0338	+	4.34851i	1.49762	+	0.361124i
$146$	5.90728	+	7.04003i	0.488890	+	0.582637i
$147$	10.2677	+	1.21318i	0.846867	+	0.100061i
$148$	−3.20035	−	4.57058i	−0.263067	−	0.375699i
$149$	−2.48868	+	14.1140i	−0.203881	+	1.15626i	0.695311	+	0.718709i	$0.255267\pi$
$149$	−2.48868	+	14.1140i	−0.203881	+	1.15626i	−0.899191	+	0.437555i	$0.855844\pi$
$150$	−11.3268	+	9.89750i	−0.924826	+	0.808127i
$151$	4.12708	−	3.46303i	0.335857	−	0.281818i	−0.459224	−	0.888320i	$-0.651873\pi$
$151$	4.12708	−	3.46303i	0.335857	−	0.281818i	0.795081	+	0.606503i	$0.207428\pi$
$152$	1.95779	+	7.30656i	0.158798	+	0.592640i
$153$	−1.66106	−	0.247566i	−0.134289	−	0.0200145i
$154$	−1.80352	+	1.04126i	−0.145332	+	0.0839072i
$155$	1.10974	−	17.8525i	0.0891362	−	1.43395i
$156$	−6.79775	−	0.206325i	−0.544255	−	0.0165193i
$157$	−0.694063	−	7.93317i	−0.0553922	−	0.633136i	−0.972253	−	0.233930i	$-0.924841\pi$
$157$	−0.694063	−	7.93317i	−0.0553922	−	0.633136i	0.916861	−	0.399206i	$-0.130714\pi$
$158$	−10.5942	−	4.94016i	−0.842831	−	0.393018i
$159$	2.69482	−	12.9689i	0.213713	−	1.02850i
$160$	3.74906	−	11.1678i	0.296389	−	0.882893i
$161$			4.72690i			0.372532i
$162$	2.18796	+	15.4780i	0.171902	+	1.21607i
$163$	−11.3432	+	11.3432i	−0.888466	+	0.888466i	−0.994376	−	0.105910i	$-0.966224\pi$
$163$	−11.3432	+	11.3432i	−0.888466	+	0.888466i	0.105910	+	0.994376i	$0.466224\pi$
$164$	0.980253	+	5.55929i	0.0765449	+	0.434108i
$165$	3.48871	+	2.95818i	0.271596	+	0.230294i
$166$	−0.489740	+	0.178251i	−0.0380112	+	0.0138349i
$167$	−0.422026	+	0.0369225i	−0.0326574	+	0.00285715i	−0.103473	−	0.994632i	$-0.532995\pi$
$167$	−0.422026	+	0.0369225i	−0.0326574	+	0.00285715i	0.0708153	+	0.997489i	$0.477440\pi$
$168$	−2.05807	−	2.18692i	−0.158784	−	0.168724i
$169$	−0.654517	+	1.79827i	−0.0503475	+	0.138329i
$170$	1.57558	+	1.49815i	0.120842	+	0.114903i
$171$	1.50952	+	13.2018i	0.115436	+	1.00957i
$172$	0.743891	−	0.199325i	0.0567212	−	0.0151984i
$173$	−8.04840	−	0.704144i	−0.611909	−	0.0535351i	−0.223011	−	0.974816i	$-0.571589\pi$
$173$	−8.04840	−	0.704144i	−0.611909	−	0.0535351i	−0.388898	+	0.921281i	$0.627144\pi$
$174$	−24.6987	+	3.58619i	−1.87240	+	0.271869i
$175$	1.91092	−	4.70274i	0.144452	−	0.355494i
$176$	−5.81503	−	1.02535i	−0.438325	−	0.0772885i
$177$	−1.64572	+	13.9285i	−0.123700	+	1.04693i
$178$	−1.63974	+	18.7423i	−0.122904	+	1.40480i
$179$	6.38218	−	11.0543i	0.477026	−	0.826234i	−0.522627	−	0.852561i	$-0.675048\pi$
$179$	6.38218	−	11.0543i	0.477026	−	0.826234i	0.999653	+	0.0263277i	$0.00838135\pi$
$180$	3.10006	−	6.07530i	0.231065	−	0.452826i
$181$	−9.24880	−	16.0194i	−0.687458	−	1.19071i	−0.972657	−	0.232244i	$-0.925393\pi$
$181$	−9.24880	−	16.0194i	−0.687458	−	1.19071i	0.285199	−	0.958468i	$-0.407940\pi$
$182$	6.17167	−	2.87790i	0.457474	−	0.213324i
$183$	4.45509	+	18.9031i	0.329330	+	1.39736i
$184$	−5.11110	+	6.09117i	−0.376795	+	0.449047i
$185$	1.82584	−	12.1344i	0.134239	−	0.892139i
$186$	7.54080	+	22.8528i	0.552918	+	1.67565i
$187$	0.379211	−	0.541570i	0.0277307	−	0.0396035i
$188$	8.83421	+	8.83421i	0.644301	+	0.644301i
$189$	−3.00951	−	4.33262i	−0.218910	−	0.315152i
$190$	8.22329	−	15.1096i	0.596580	−	1.09616i
$191$	4.20349	−	0.741189i	0.304154	−	0.0536306i	−0.0194882	−	0.999810i	$-0.506204\pi$
$191$	4.20349	−	0.741189i	0.304154	−	0.0536306i	0.323642	+	0.946180i	$0.395093\pi$
$192$	−0.0836642	−	1.46817i	−0.00603794	−	0.105956i
$193$	−4.28212	+	9.18304i	−0.308234	+	0.661010i	−0.998013	−	0.0630104i	$-0.979930\pi$
$193$	−4.28212	+	9.18304i	−0.308234	+	0.661010i	0.689779	+	0.724020i	$0.257708\pi$
$194$	6.81419	+	5.71778i	0.489230	+	0.410513i
$195$	−10.5214	−	10.6304i	−0.753450	−	0.761262i
$196$	5.70324	+	2.07581i	0.407374	+	0.148272i
$197$	−11.4519	−	3.06853i	−0.815916	−	0.218624i	−0.173356	−	0.984859i	$-0.555461\pi$
$197$	−11.4519	−	3.06853i	−0.815916	−	0.218624i	−0.642560	+	0.766235i	$0.722128\pi$
$198$	−5.83661	−	1.95030i	−0.414790	−	0.138602i
$199$	5.06551	+	2.92457i	0.359084	+	0.207317i	0.668679	−	0.743551i	$-0.266860\pi$
$199$	5.06551	+	2.92457i	0.359084	+	0.207317i	−0.309595	+	0.950869i	$0.600193\pi$
$200$	7.54743	−	3.99379i	0.533684	−	0.282404i
$201$	−2.54182	−	1.01349i	−0.179286	−	0.0714863i
$202$	27.5880	−	19.3173i	1.94108	−	1.35916i
$203$	6.89928	−	4.83093i	0.484234	−	0.339065i
$204$	−0.915732	−	0.365127i	−0.0641141	−	0.0255640i
$205$	−6.86250	+	10.3457i	−0.479298	+	0.722577i
$206$	−22.4262	−	12.9478i	−1.56251	−	0.902114i
$207$	−10.4577	+	9.25963i	−0.726857	+	0.643589i
$208$	18.6501	+	4.99729i	1.29315	+	0.346500i
$209$	−4.91558	−	1.78912i	−0.340018	−	0.123756i
$210$	−0.0352239	+	6.82927i	−0.00243068	+	0.471264i
$211$	−5.44373	−	4.56783i	−0.374762	−	0.314462i	0.435880	−	0.900005i	$-0.356437\pi$
$211$	−5.44373	−	4.56783i	−0.374762	−	0.314462i	−0.810642	+	0.585542i	$0.800882\pi$
$212$	3.28611	−	7.04709i	0.225691	−	0.483996i
$213$	0.791880	+	13.8962i	0.0542587	+	0.952152i
$214$	−7.74205	+	1.36513i	−0.529236	+	0.0933186i
$215$	1.48766	+	0.809649i	0.101457	+	0.0552176i
$216$	0.806665	−	8.83722i	0.0548866	−	0.601297i
$217$	−5.74251	−	5.74251i	−0.389827	−	0.389827i
$218$	10.6854	−	15.2603i	0.723707	−	1.03356i
$219$	−2.87176	−	8.70300i	−0.194055	−	0.588094i
$220$	1.59498	+	2.15998i	0.107533	+	0.145626i
$221$	−1.38961	+	1.65608i	−0.0934756	+	0.111400i
$222$	3.78713	+	16.0689i	0.254175	+	1.07847i
$223$	2.00892	−	0.936774i	0.134527	−	0.0627310i	−0.354189	−	0.935174i	$-0.615243\pi$
$223$	2.00892	−	0.936774i	0.134527	−	0.0627310i	0.488716	+	0.872443i	$0.337465\pi$
$224$	−2.67428	−	4.63199i	−0.178683	−	0.309488i
$225$	14.1476	−	4.98463i	0.943171	−	0.332309i
$226$	−10.9618	+	18.9864i	−0.729167	+	1.26295i
$227$	−0.837726	+	9.57526i	−0.0556018	+	0.635532i	0.916354	+	0.400369i	$0.131118\pi$
$227$	−0.837726	+	9.57526i	−0.0556018	+	0.635532i	−0.971956	+	0.235163i	$0.924438\pi$
$228$	−0.915263	+	7.74632i	−0.0606147	+	0.513013i
$229$	−9.88832	−	1.74358i	−0.653438	−	0.115219i	−0.162906	−	0.986642i	$-0.552087\pi$
$229$	−9.88832	−	1.74358i	−0.653438	−	0.115219i	−0.490533	+	0.871423i	$0.663198\pi$
$230$	17.9686	−	2.02915i	1.18481	−	0.133798i
$231$	2.05518	−	0.298408i	0.135221	−	0.0196338i
$232$	14.1141	+	1.23483i	0.926638	+	0.0810703i
$233$	−11.6282	+	3.11576i	−0.761788	+	0.204120i	−0.618741	−	0.785595i	$-0.712357\pi$
$233$	−11.6282	+	3.11576i	−0.761788	+	0.204120i	−0.143047	+	0.989716i	$0.545690\pi$
$234$	18.4568	+	8.01644i	1.20656	+	0.524051i
$235$	0.691913	+	27.4674i	0.0451354	+	1.79178i
$236$	−2.81591	+	7.73664i	−0.183300	+	0.503613i
$237$	7.98884	+	8.48897i	0.518931	+	0.551418i
$238$	0.983361	−	0.0860330i	0.0637418	−	0.00557669i
$239$	−1.69787	+	0.617976i	−0.109826	+	0.0399735i	−0.396349	−	0.918100i	$-0.629723\pi$
$239$	−1.69787	+	0.617976i	−0.109826	+	0.0399735i	0.286522	+	0.958074i	$0.407501\pi$
$240$	−12.5232	+	14.7692i	−0.808367	+	0.953345i
$241$	−2.79425	−	15.8470i	−0.179994	−	1.02079i	−0.932221	−	0.361890i	$-0.882131\pi$
$241$	−2.79425	−	15.8470i	−0.179994	−	1.02079i	0.752227	−	0.658904i	$-0.228980\pi$
$242$	−11.7967	+	11.7967i	−0.758321	+	0.758321i
$243$	3.68997	−	15.1454i	0.236712	−	0.971580i
$244$			11.4005i			0.729840i
$245$	5.94386	+	11.9513i	0.379739	+	0.763541i
$246$	3.39808	−	16.3534i	0.216654	−	1.04265i
$247$	15.5025	+	7.22894i	0.986401	+	0.459966i
$248$	−1.19065	−	13.6092i	−0.0756063	−	0.864184i
$249$	0.519483	+	0.0157674i	0.0329209	+	0.000999216i
$250$	−18.6971	−	5.24530i	−1.18251	−	0.331742i
$251$	−15.8224	+	9.13506i	−0.998700	+	0.576600i	−0.907863	−	0.419266i	$-0.862287\pi$
$251$	−15.8224	+	9.13506i	−0.998700	+	0.576600i	−0.0908365	+	0.995866i	$0.528954\pi$
$252$	−1.13610	−	2.88076i	−0.0715674	−	0.181471i
$253$	−1.42319	−	5.31141i	−0.0894751	−	0.333926i
$254$	23.4787	−	19.7010i	1.47318	−	1.23615i
$255$	−0.906134	−	1.96967i	−0.0567443	−	0.123346i
$256$	3.32781	−	18.8729i	0.207988	−	1.17956i
$257$	−8.13228	−	11.6141i	−0.507278	−	0.724468i	0.481070	−	0.876682i	$-0.340248\pi$
$257$	−8.13228	−	11.6141i	−0.507278	−	0.724468i	−0.988347	+	0.152215i	$0.951359\pi$
$258$	−2.26294	−	0.267377i	−0.140885	−	0.0166461i
$259$	−3.58119	−	4.26790i	−0.222524	−	0.265194i
$260$	−4.58003	−	7.49065i	−0.284041	−	0.464550i
$261$	24.2030	+	5.80035i	1.49813	+	0.359033i
$262$	−1.29920	+	4.84869i	−0.0802650	+	0.299553i
$263$	−1.55072	−	3.32553i	−0.0956215	−	0.205061i	0.852679	−	0.522436i	$-0.174977\pi$
$263$	−1.55072	−	3.32553i	−0.0956215	−	0.205061i	−0.948300	+	0.317375i	$0.897199\pi$
$264$	2.97101	+	1.83769i	0.182853	+	0.113102i
$265$	15.9168	−	6.25149i	0.977759	−	0.384026i
$266$	−2.67128	−	7.33929i	−0.163787	−	0.450000i
$267$	8.44121	−	16.7554i	0.516594	−	1.02542i
$268$	−1.31583	−	0.921353i	−0.0803770	−	0.0562806i
$269$	−11.1677			−0.680904			−0.340452	−	0.940262i	$-0.610580\pi$
$269$	−11.1677			−0.680904			−0.340452	+	0.940262i	$0.610580\pi$
$270$	−15.1779	+	13.3001i	−0.923697	+	0.809418i
$271$	23.0328			1.39914			0.699572	−	0.714562i	$-0.253374\pi$
$271$	23.0328			1.39914			0.699572	+	0.714562i	$0.253374\pi$
$272$	2.29269	+	1.60536i	0.139015	+	0.0973390i
$273$	−6.77976	+	0.386347i	−0.410330	+	0.0233828i
$274$	5.00267	+	13.7447i	0.302223	+	0.830350i
$275$	−0.731309	+	5.85961i	−0.0440996	+	0.353348i
$276$	−7.22202	+	3.88240i	−0.434715	+	0.233693i
$277$	5.25770	+	11.2752i	0.315905	+	0.677460i	0.998581	−	0.0532613i	$-0.0169616\pi$
$277$	5.25770	+	11.2752i	0.315905	+	0.677460i	−0.682676	+	0.730721i	$0.739184\pi$
$278$	−4.49577	+	16.7784i	−0.269638	+	1.00630i
$279$	1.45543	−	23.9537i	0.0871343	−	1.43407i
$280$	0.908797	−	3.76889i	0.0543110	−	0.225234i
$281$	5.39196	+	6.42589i	0.321657	+	0.383336i	0.902507	−	0.430674i	$-0.141724\pi$
$281$	5.39196	+	6.42589i	0.321657	+	0.383336i	−0.580850	+	0.814011i	$0.697280\pi$
$282$	−14.5989	−	33.9610i	−0.869349	−	2.02235i
$283$	−6.92088	−	9.88404i	−0.411404	−	0.587545i	0.558960	−	0.829195i	$-0.311201\pi$
$283$	−6.92088	−	9.88404i	−0.411404	−	0.587545i	−0.970364	+	0.241649i	$0.922312\pi$
$284$	−1.41880	+	8.04642i	−0.0841904	+	0.477467i
$285$	−13.1978	+	10.9588i	−0.781773	+	0.649144i
$286$	−6.06835	+	5.09195i	−0.358829	+	0.301093i
$287$	1.45887	+	5.44459i	0.0861145	+	0.321384i
$288$	5.00897	−	14.9902i	0.295156	−	0.883306i
$289$	14.4510	−	8.34331i	0.850061	−	0.490783i
$290$	−21.3257	−	24.1527i	−1.25229	−	1.41830i
$291$	−4.20018	−	7.81316i	−0.246219	−	0.458015i
$292$	−0.468877	−	5.35929i	−0.0274390	−	0.313629i
$293$	19.4978	+	9.09195i	1.13907	+	0.531157i	0.898282	−	0.439420i	$-0.144816\pi$
$293$	19.4978	+	9.09195i	1.13907	+	0.531157i	0.240789	+	0.970577i	$0.422594\pi$
$294$	−13.4000	−	11.9551i	−0.781502	−	0.697235i
$295$	−16.2124	+	8.06305i	−0.943920	+	0.469449i
$296$		−	9.37196i		−	0.544734i
$297$	4.68614	+	3.96227i	0.271917	+	0.229914i
$298$	17.6016	−	17.6016i	1.01964	−	1.01964i
$299$	3.12229	+	17.7074i	0.180567	+	1.02405i
$300$	8.75463	−	0.942938i	0.505449	−	0.0544405i
$301$	0.722611	−	0.263009i	0.0416506	−	0.0151596i
$302$	−9.32186	+	0.815557i	−0.536413	+	0.0469301i
$303$	−32.6895	+	7.70428i	−1.87796	+	0.442599i
$304$	7.57410	−	20.8097i	0.434404	−	1.19352i
$305$	−17.2768	+	18.1697i	−0.989266	+	1.04039i
$306$	2.11667	+	2.00703i	0.121002	+	0.114734i
$307$	−11.9453	+	3.20074i	−0.681757	+	0.182676i	−0.583045	−	0.812440i	$-0.698139\pi$
$307$	−11.9453	+	3.20074i	−0.681757	+	0.182676i	−0.0987117	+	0.995116i	$0.531472\pi$
$308$	1.21444	+	0.106250i	0.0691992	+	0.00605414i
$309$	15.9913	+	20.2765i	0.909713	+	1.15349i
$310$	−19.3642	+	24.2944i	−1.09981	+	1.37983i
$311$	−13.5294	−	2.38560i	−0.767181	−	0.135275i	−0.223656	−	0.974668i	$-0.571799\pi$
$311$	−13.5294	−	2.38560i	−0.767181	−	0.135275i	−0.543524	+	0.839393i	$0.682910\pi$
$312$	−9.15427	−	6.83296i	−0.518259	−	0.386840i
$313$	2.60145	−	29.7347i	0.147043	−	1.68071i	−0.461465	−	0.887159i	$-0.652676\pi$
$313$	2.60145	−	29.7347i	0.147043	−	1.68071i	0.608507	−	0.793548i	$-0.291769\pi$
$314$	−6.91579	+	11.9785i	−0.390281	+	0.675986i
$315$	2.55496	−	6.31296i	0.143956	−	0.355695i
$316$	3.42141	+	5.92606i	0.192470	+	0.333367i
$317$	−19.3873	+	9.04044i	−1.08890	+	0.507762i	−0.882311	−	0.470666i	$-0.844014\pi$
$317$	−19.3873	+	9.04044i	−1.08890	+	0.507762i	−0.206588	+	0.978428i	$0.566236\pi$
$318$	−16.7542	+	15.7671i	−0.939526	+	0.884173i
$319$	−6.29792	+	7.50556i	−0.352616	+	0.420231i
$320$	1.52723	−	1.12774i	0.0853745	−	0.0630425i
$321$	7.67568	+	1.59494i	0.428415	+	0.0890208i
$322$	4.70909	−	6.72527i	0.262427	−	0.374785i
$323$	1.75329	+	1.75329i	0.0975556	+	0.0975556i
$324$	4.14779	−	8.15666i	0.230433	−	0.453148i
$325$	4.05217	−	18.8791i	0.224774	−	1.04723i
$326$	27.4391	−	4.83826i	1.51971	−	0.267966i
$327$	−15.5342	+	10.1891i	−0.859043	+	0.563460i
$328$	−4.00719	+	8.59345i	−0.221260	+	0.474494i
$329$	9.55630	+	8.01869i	0.526856	+	0.442085i
$330$	−2.01660	−	7.68436i	−0.111010	−	0.423010i
$331$	−24.1329	−	8.78365i	−1.32646	−	0.482793i	−0.420939	−	0.907089i	$-0.638299\pi$
$331$	−24.1329	−	8.78365i	−1.32646	−	0.482793i	−0.905524	+	0.424296i	$0.860522\pi$
$332$	0.294691	+	0.0789621i	0.0161732	+	0.00433361i
$333$	2.42689	−	16.2834i	0.132993	−	0.892325i
$334$	0.637228	+	0.367904i	0.0348676	+	0.0201308i
$335$	−0.700864	−	3.46249i	−0.0382923	−	0.189176i
$336$	1.26328	+	8.70043i	0.0689178	+	0.474648i
$337$	−0.778831	+	0.545344i	−0.0424256	+	0.0297068i	−0.594597	−	0.804024i	$-0.702688\pi$
$337$	−0.778831	+	0.545344i	−0.0424256	+	0.0297068i	0.552171	+	0.833731i	$0.313799\pi$
$338$	2.72272	−	1.90647i	0.148096	−	0.103698i
$339$	17.1664	−	13.5385i	0.932350	−	0.735309i
$340$	−0.252498	−	1.24742i	−0.0136936	−	0.0676507i
$341$	8.18159	+	4.72364i	0.443058	+	0.255800i
$342$	11.0044	−	20.2870i	0.595049	−	1.09699i
$343$	12.7182	+	3.40783i	0.686718	+	0.184006i
$344$	1.21556	+	0.442427i	0.0655385	+	0.0238540i
$345$	−17.3938	−	4.75694i	−0.936450	−	0.256105i
$346$	10.7495	+	9.01991i	0.577897	+	0.484913i
$347$	0.861237	−	1.84693i	0.0462336	−	0.0991483i	−0.881834	−	0.471560i	$-0.843691\pi$
$347$	0.861237	−	1.84693i	0.0462336	−	0.0991483i	0.928068	+	0.372411i	$0.121469\pi$
$348$	13.0476	+	6.57327i	0.699426	+	0.352364i
$349$	13.3172	−	2.34817i	0.712851	−	0.125695i	0.194549	−	0.980893i	$-0.437676\pi$
$349$	13.3172	−	2.34817i	0.712851	−	0.125695i	0.518302	+	0.855198i	$0.326564\pi$
$350$	−7.40382	+	4.78718i	−0.395751	+	0.255885i
$351$	−14.1358	−	14.2425i	−0.754512	−	0.760209i
$352$	4.39958	+	4.39958i	0.234499	+	0.234499i
$353$	−4.28254	+	6.11610i	−0.227936	+	0.325527i	−0.916787	−	0.399376i	$-0.869227\pi$
$353$	−4.28254	+	6.11610i	−0.227936	+	0.325527i	0.688851	+	0.724903i	$0.258116\pi$
$354$	16.2175	−	18.1775i	0.861951	−	0.966125i
$355$	−14.4552	+	10.6740i	−0.767200	+	0.566518i
$356$	7.07928	−	8.43675i	0.375201	−	0.447147i
$357$	−0.942665	−	0.283504i	−0.0498911	−	0.0150046i
$358$	−20.0930	+	9.36950i	−1.06195	+	0.495193i
$359$	4.40107	+	7.62287i	0.232279	+	0.402320i	0.958479	−	0.285165i	$-0.0920483\pi$
$359$	4.40107	+	7.62287i	0.232279	+	0.402320i	−0.726199	+	0.687484i	$0.758715\pi$
$360$	10.1184	−	5.37237i	0.533289	−	0.283149i
$361$	0.309285	−	0.535697i	0.0162782	−	0.0281946i
$362$	−2.80015	+	32.0058i	−0.147172	+	1.68219i
$363$	15.2843	−	6.57030i	0.802220	−	0.344851i
$364$	−3.92573	−	0.692213i	−0.205764	−	0.0362818i
$365$	7.37443	−	9.25202i	0.385995	−	0.484273i
$366$	12.4933	−	31.3330i	0.653036	−	1.63780i
$367$	−27.1913	−	2.37893i	−1.41938	−	0.124179i	−0.648524	−	0.761194i	$-0.724613\pi$
$367$	−27.1913	−	2.37893i	−1.41938	−	0.124179i	−0.770852	+	0.637015i	$0.780169\pi$
$368$	22.4854	−	6.02494i	1.17213	−	0.314072i
$369$	−9.18763	+	13.8931i	−0.478289	+	0.723246i
$370$	−14.6864	+	15.4455i	−0.763511	+	0.802971i
$371$	2.65545	−	7.29580i	0.137864	−	0.378779i
$372$	4.05717	−	13.4903i	0.210354	−	0.699440i
$373$	12.1103	−	1.05951i	0.627046	−	0.0548594i	0.230796	−	0.973002i	$-0.425867\pi$
$373$	12.1103	−	1.05951i	0.627046	−	0.0548594i	0.396250	+	0.918143i	$0.370311\pi$
$374$	−1.07906	+	0.392745i	−0.0557968	+	0.0203084i
$375$	15.3818	+	11.7643i	0.794314	+	0.607508i
$376$	3.64399	+	20.6661i	0.187924	+	1.06577i
$377$	22.6543	−	22.6543i	1.16676	−	1.16676i
$378$	−0.0344665	+	9.16248i	−0.00177277	+	0.471267i
$379$			22.6602i			1.16398i	0.813198	+	0.581988i	$0.197725\pi$
$379$			22.6602i			1.16398i	−0.813198	+	0.581988i	$0.802275\pi$
$380$	−9.01648	+	4.48425i	−0.462535	+	0.230037i
$381$	−29.0248	+	9.57738i	−1.48698	+	0.490664i
$382$	−6.71899	−	3.13312i	−0.343773	−	0.160304i
$383$	1.66185	+	18.9950i	0.0849166	+	0.970601i	0.912451	+	0.409186i	$0.134187\pi$
$383$	1.66185	+	18.9950i	0.0849166	+	0.970601i	−0.827534	+	0.561415i	$0.810257\pi$
$384$	−10.9439	+	17.6930i	−0.558478	+	0.902894i
$385$	1.77452	+	2.00976i	0.0904379	+	0.102427i
$386$	15.2409	−	8.79934i	0.775741	−	0.447874i
$387$	1.99741	+	1.08347i	0.101534	+	0.0550759i
$388$	−1.34772	−	5.02975i	−0.0684200	−	0.255347i
$389$	11.9485	−	10.0260i	0.605814	−	0.508338i	−0.287495	−	0.957782i	$-0.592822\pi$
$389$	11.9485	−	10.0260i	0.605814	−	0.508338i	0.893309	+	0.449444i	$0.148378\pi$
$390$	4.37904	+	25.6064i	0.221741	+	1.29663i
$391$	−0.452602	+	2.56683i	−0.0228890	+	0.129810i
$392$	5.84724	+	8.35072i	0.295330	+	0.421775i
$393$	2.99428	−	4.01150i	0.151041	−	0.202354i
$394$	13.2364	+	15.7746i	0.666842	+	0.794712i
$395$	−3.52769	+	14.6297i	−0.177497	+	0.736102i
$396$	2.14393	+	2.89493i	0.107737	+	0.145476i
$397$	2.30277	−	8.59405i	0.115573	−	0.431323i	−0.883756	−	0.467947i	$-0.844994\pi$
$397$	2.30277	−	8.59405i	0.115573	−	0.431323i	0.999329	+	0.0366240i	$0.0116604\pi$
$398$	−4.29348	−	9.20740i	−0.215213	−	0.461525i
$399$	−0.236291	+	7.78501i	−0.0118293	+	0.389738i
$400$	−24.8062	−	3.09593i	−1.24031	−	0.154797i
$401$	−0.377837	−	1.03810i	−0.0188683	−	0.0518401i	0.929901	−	0.367810i	$-0.119892\pi$
$401$	−0.377837	−	1.03810i	−0.0188683	−	0.0518401i	−0.948769	+	0.315970i	$0.897670\pi$
$402$	2.60675	+	3.97421i	0.130013	+	0.198216i
$403$	−25.3051	−	17.7189i	−1.26054	−	0.882639i
$404$	−19.7151			−0.980861
$405$	18.9716	−	6.71408i	0.942706	−	0.333625i
$406$	−14.6288			−0.726015
$407$	5.30902	+	3.71742i	0.263158	+	0.184265i
$408$	−0.908190	−	1.38461i	−0.0449621	−	0.0685486i
$409$	−0.248916	−	0.683891i	−0.0123081	−	0.0338162i	0.933386	−	0.358873i	$-0.116839\pi$
$409$	−0.248916	−	0.683891i	−0.0123081	−	0.0338162i	−0.945695	+	0.325057i	$0.894617\pi$
$410$	20.0705	−	7.88292i	0.991211	−	0.389310i
$411$	0.442517	−	14.5795i	0.0218277	−	0.719153i
$412$	6.40643	+	13.7386i	0.315622	+	0.676854i
$413$	−2.12773	+	7.94079i	−0.104699	+	0.390741i
$414$	24.1036	−	2.75605i	1.18463	−	0.135452i
$415$	0.350005	+	0.572435i	0.0171811	+	0.0280997i
$416$	−13.0777	−	15.5854i	−0.641187	−	0.764137i
$417$	10.3614	−	13.8814i	0.507401	−	0.679776i
$418$	5.21134	+	7.44256i	0.254895	+	0.364028i
$419$	−3.40845	+	19.3303i	−0.166514	+	0.944347i	0.780976	+	0.624561i	$0.214722\pi$
$419$	−3.40845	+	19.3303i	−0.166514	+	0.944347i	−0.947490	+	0.319786i	$0.896389\pi$
$420$	2.30991	−	3.26295i	0.112712	−	0.159215i
$421$	−8.09926	+	6.79608i	−0.394734	+	0.331221i	−0.818454	−	0.574572i	$-0.805168\pi$
$421$	−8.09926	+	6.79608i	−0.394734	+	0.331221i	0.423720	+	0.905793i	$0.360724\pi$
$422$	3.19454	+	11.9222i	0.155508	+	0.580362i
$423$	0.979745	+	36.8501i	0.0476368	+	1.79171i
$424$	11.3107	−	6.53022i	0.549295	−	0.317135i
$425$	1.48797	−	2.37074i	0.0721772	−	0.114998i
$426$	12.7172	−	20.5600i	0.616150	−	0.996133i
$427$	0.992138	+	11.3402i	0.0480129	+	0.548790i
$428$	4.17083	+	1.94489i	0.201605	+	0.0940099i
$429$	7.50180	−	2.47539i	0.362190	−	0.119513i
$430$	−1.30999	−	2.63399i	−0.0631733	−	0.127022i
$431$		−	16.6095i		−	0.800052i	−0.916504	−	0.400026i	$-0.869001\pi$
$431$		−	16.6095i		−	0.800052i	0.916504	−	0.400026i	$-0.130999\pi$
$432$	−16.7739	+	19.8383i	−0.807036	+	0.954473i
$433$	−14.3203	+	14.3203i	−0.688189	+	0.688189i	−0.961831	−	0.273643i	$-0.911771\pi$
$433$	−14.3203	+	14.3203i	−0.688189	+	0.688189i	0.273643	+	0.961831i	$0.411771\pi$
$434$	2.44938	+	13.8911i	0.117574	+	0.666796i
$435$	10.8335	+	30.2492i	0.519425	+	1.45034i
$436$	−10.2477	+	3.72987i	−0.490778	+	0.178628i
$437$	20.5442	−	1.79738i	0.982762	−	0.0859805i
$438$	−4.58437	+	15.2433i	−0.219050	+	0.728352i
$439$	4.05583	−	11.1433i	0.193574	−	0.531840i	−0.804495	−	0.593960i	$-0.797564\pi$
$439$	4.05583	−	11.1433i	0.193574	−	0.531840i	0.998069	+	0.0621195i	$0.0197860\pi$
$440$	0.113572	+	4.50856i	0.00541434	+	0.214937i
$441$	7.99690	+	16.0232i	0.380805	+	0.763010i
$442$	3.62694	−	0.971835i	0.172516	−	0.0462255i
$443$	22.1937	+	1.94169i	1.05445	+	0.0922527i	0.601176	−	0.799117i	$-0.294699\pi$
$443$	22.1937	+	1.94169i	1.05445	+	0.0922527i	0.453277	+	0.891369i	$0.350255\pi$
$444$	3.57935	−	8.97695i	0.169868	−	0.426027i
$445$	24.0682	−	2.71797i	1.14094	−	0.128844i
$446$	−3.79147	−	0.668538i	−0.179531	−	0.0316562i
$447$	−22.8055	+	9.80342i	−1.07866	+	0.463686i
$448$	0.0751244	−	0.858676i	0.00354930	−	0.0405686i
$449$	2.63657	−	4.56667i	0.124427	−	0.215514i	−0.797082	−	0.603872i	$-0.793624\pi$
$449$	2.63657	−	4.56667i	0.124427	−	0.215514i	0.921509	+	0.388357i	$0.126957\pi$
$450$	−25.0945	−	7.00229i	−1.18297	−	0.330091i
$451$	−3.27855	−	5.67861i	−0.154381	−	0.267395i
$452$	11.6313	−	5.42378i	0.547092	−	0.255113i
$453$	8.93608	+	2.68750i	0.419854	+	0.126270i
$454$	10.7311	−	12.7888i	0.503634	−	0.600208i
$455$	−5.20769	−	7.05246i	−0.244140	−	0.330624i
$456$	−8.72227	+	9.77642i	−0.408458	+	0.457823i
$457$	−5.51211	+	7.87211i	−0.257846	+	0.368242i	−0.927114	−	0.374779i	$-0.877719\pi$
$457$	−5.51211	+	7.87211i	−0.257846	+	0.368242i	0.669269	+	0.743021i	$0.266608\pi$
$458$	12.3318	+	12.3318i	0.576225	+	0.576225i
$459$	−1.21939	−	2.64089i	−0.0569164	−	0.123266i
$460$	−9.29762	−	5.06018i	−0.433504	−	0.235932i
$461$	10.5760	−	1.86484i	0.492575	−	0.0868543i	0.0781574	−	0.996941i	$-0.475096\pi$
$461$	10.5760	−	1.86484i	0.492575	−	0.0868543i	0.414418	+	0.910087i	$0.363985\pi$
$462$	−3.22133	−	1.62287i	−0.149870	−	0.0755029i
$463$	15.1325	−	32.4518i	0.703268	−	1.50816i	−0.151113	−	0.988516i	$-0.548286\pi$
$463$	15.1325	−	32.4518i	0.703268	−	1.50816i	0.854381	−	0.519647i	$-0.173936\pi$
$464$	−31.7741	−	26.6617i	−1.47508	−	1.23774i
$465$	26.9100	−	15.3520i	1.24792	−	0.711931i
$466$	19.6482	+	7.15137i	0.910187	+	0.331281i
$467$	23.5963	+	6.32261i	1.09191	+	0.292575i	0.759465	−	0.650549i	$-0.225461\pi$
$467$	23.5963	+	6.32261i	1.09191	+	0.292575i	0.332441	+	0.943124i	$0.392128\pi$
$468$	−6.15878	−	10.0412i	−0.284690	−	0.464153i
$469$	−1.38905	−	0.801970i	−0.0641405	−	0.0370315i
$470$	26.3795	−	39.7691i	1.21680	−	1.83441i
$471$	10.8303	−	8.54143i	0.499033	−	0.393568i
$472$	−11.3280	+	7.93199i	−0.521416	+	0.365099i
$473$	−0.732780	+	0.513098i	−0.0336933	+	0.0235923i
$474$	−2.90927	−	20.0366i	−0.133627	−	0.920310i
$475$	−21.1658	−	6.51712i	−0.971154	−	0.299026i
$476$	−0.500429	−	0.288923i	−0.0229371	−	0.0132427i
$477$	21.3429	−	8.41706i	0.977222	−	0.385391i
$478$	3.03133	+	0.812242i	0.138650	+	0.0371511i
$479$	−38.3549	−	13.9601i	−1.75248	−	0.637851i	−0.752692	−	0.658373i	$-0.771245\pi$
$479$	−38.3549	−	13.9601i	−1.75248	−	0.637851i	−0.999789	+	0.0205215i	$0.993467\pi$
$480$	19.7358	−	5.17924i	0.900812	−	0.236399i
$481$	−16.2346	−	13.6224i	−0.740233	−	0.621129i
$482$	−11.8117	+	25.3303i	−0.538009	+	1.15376i
$483$	−6.84597	+	4.49037i	−0.311502	+	0.204319i
$484$	9.61767	−	1.69585i	0.437167	−	0.0770843i
$485$	5.47436	−	10.0586i	0.248578	−	0.456739i
$486$	−20.3383	+	17.8724i	−0.922566	+	0.810706i
$487$	−23.5238	−	23.5238i	−1.06596	−	1.06596i	−0.997665	−	0.0682997i	$-0.978243\pi$
$487$	−23.5238	−	23.5238i	−1.06596	−	1.06596i	−0.0682997	−	0.997665i	$-0.521757\pi$
$488$	−10.9834	+	15.6860i	−0.497196	+	0.710070i
$489$	−27.2039	−	5.65273i	−1.23020	−	0.255625i
$490$	3.44954	−	22.9254i	0.155834	−	1.03566i
$491$	−3.19936	+	3.81285i	−0.144385	+	0.172071i	−0.833390	−	0.552685i	$-0.813603\pi$
$491$	−3.19936	+	3.81285i	−0.144385	+	0.172071i	0.689005	+	0.724756i	$0.258048\pi$
$492$	−7.12031	+	6.70081i	−0.321009	+	0.302096i
$493$	4.20905	−	1.96271i	0.189566	−	0.0883962i
$494$	−14.8548	−	25.7292i	−0.668347	−	1.15761i
$495$	−0.970178	+	7.86286i	−0.0436062	+	0.353409i
$496$	−19.9971	+	34.6360i	−0.897897	+	1.55520i
$497$	−0.711051	+	8.12735i	−0.0318950	+	0.364561i
$498$	−0.723395	−	0.539959i	−0.0324161	−	0.0241961i
$499$	6.36453	+	1.12224i	0.284916	+	0.0502383i	0.314280	−	0.949330i	$-0.398237\pi$
$499$	6.36453	+	1.12224i	0.284916	+	0.0502383i	−0.0293640	+	0.999569i	$0.509348\pi$
$500$	7.20444	+	8.79302i	0.322192	+	0.393236i
$501$	−0.454384	−	0.576145i	−0.0203004	−	0.0257403i
$502$	31.6122	+	2.76571i	1.41092	+	0.123440i
$503$	24.7077	−	6.62040i	1.10166	−	0.295189i	0.338220	−	0.941067i	$-0.390175\pi$
$503$	24.7077	−	6.62040i	1.10166	−	0.295189i	0.763441	+	0.645878i	$0.223509\pi$
$504$	1.21222	−	5.05819i	0.0539965	−	0.225310i
$505$	−31.4212	−	29.8771i	−1.39823	−	1.32951i
$506$	−3.26654	+	8.97473i	−0.145215	+	0.398975i
$507$	−3.22620	+	0.760353i	−0.143281	+	0.0337684i
$508$	−17.8734	+	1.56372i	−0.793003	+	0.0693788i
$509$	−22.5637	+	8.21250i	−1.00012	+	0.364013i	−0.789630	−	0.613584i	$-0.789727\pi$
$509$	−22.5637	+	8.21250i	−1.00012	+	0.364013i	−0.210487	+	0.977597i	$0.567505\pi$
$510$	−0.673031	+	3.70510i	−0.0298023	+	0.164065i
$511$	−0.932796	−	5.29015i	−0.0412644	−	0.234022i
$512$	−6.55000	+	6.55000i	−0.289472	+	0.289472i
$513$	−17.6862	+	14.7275i	−0.780866	+	0.650234i
$514$			24.6258i			1.08620i
$515$	−10.6098	+	31.6048i	−0.467523	+	1.39267i
$516$	0.995351	+	0.888026i	0.0438179	+	0.0390932i
$517$	−13.1523	−	6.13302i	−0.578438	−	0.269730i
$518$	0.843383	+	9.63992i	0.0370561	+	0.423554i
$519$	−6.62587	−	12.3254i	−0.290843	−	0.541025i
$520$	0.914947	−	14.7189i	0.0401231	−	0.645467i
$521$	10.1059	−	5.83464i	0.442747	−	0.255620i	−0.262015	−	0.965064i	$-0.584387\pi$
$521$	10.1059	−	5.83464i	0.442747	−	0.255620i	0.704762	+	0.709444i	$0.251054\pi$
$522$	−28.6567	−	32.3643i	−1.25427	−	1.41655i
$523$	−9.07224	−	33.8581i	−0.396701	−	1.48051i	−0.818863	−	0.573989i	$-0.805395\pi$
$523$	−9.07224	−	33.8581i	−0.396701	−	1.48051i	0.422162	−	0.906521i	$-0.361272\pi$
$524$	2.25101	−	1.88882i	0.0983358	−	0.0825135i
$525$	8.62628	−	1.69983i	0.376482	−	0.0741868i
$526$	−1.10669	+	6.27633i	−0.0482539	+	0.273661i
$527$	−2.56849	−	3.66818i	−0.111885	−	0.159789i
$528$	−4.03905	−	9.39595i	−0.175777	−	0.408906i
$529$	−0.849663	−	1.01259i	−0.0369419	−	0.0440256i
$530$	−28.8738	−	6.96238i	−1.25420	−	0.302426i
$531$	−21.7360	+	10.8481i	−0.943264	+	0.470767i
$532$	−1.18333	+	4.41626i	−0.0513040	+	0.191469i
$533$	9.06143	+	19.4323i	0.392494	+	0.841706i
$534$	−28.7022	+	15.4297i	−1.24206	+	0.667706i
$535$	3.69996	+	9.42038i	0.159963	+	0.407278i
$536$	−0.922806	−	2.53539i	−0.0398591	−	0.109512i
$537$	22.0727	−	1.25782i	0.952507	−	0.0542789i
$538$	15.8890	+	11.1256i	0.685022	+	0.479658i
$539$	−7.04983			−0.303658
$540$	11.7438	−	1.28148i	0.505372	−	0.0551461i
$541$	32.8530			1.41246			0.706230	−	0.707983i	$-0.250394\pi$
$541$	32.8530			1.41246			0.706230	+	0.707983i	$0.250394\pi$
$542$	−32.7703	−	22.9460i	−1.40761	−	0.985617i
$543$	14.4149	−	28.6129i	0.618602	−	1.22790i
$544$	−1.00869	−	2.77135i	−0.0432472	−	0.118821i
$545$	−21.9849	−	9.58534i	−0.941731	−	0.410591i
$546$	10.0309	+	6.20453i	0.429283	+	0.265529i
$547$	18.7126	+	40.1294i	0.800094	+	1.71581i	0.692271	+	0.721638i	$0.256610\pi$
$547$	18.7126	+	40.1294i	0.800094	+	1.71581i	0.107823	+	0.994170i	$0.465612\pi$
$548$	2.21610	−	8.27060i	0.0946671	−	0.353302i
$549$	−23.1452	+	24.4095i	−0.987813	+	1.04177i
$550$	6.87802	−	7.60831i	0.293280	−	0.324419i
$551$	−23.6198	−	28.1489i	−1.00624	−	1.19918i
$552$	−13.6772	−	1.61602i	−0.582140	−	0.0687824i
$553$	3.91904	+	5.59698i	0.166655	+	0.238008i
$554$	3.75221	−	21.2799i	0.159416	−	0.904094i
$555$	19.3087	−	8.88285i	0.819610	−	0.377056i
$556$	7.78940	−	6.53608i	0.330344	−	0.277192i
$557$	−9.87492	−	36.8537i	−0.418414	−	1.56154i	−0.777898	−	0.628391i	$-0.783714\pi$
$557$	−9.87492	−	36.8537i	−0.418414	−	1.56154i	0.359484	−	0.933151i	$-0.382953\pi$
$558$	−25.9342	+	32.6306i	−1.09788	+	1.38136i
$559$	2.53324	−	1.46257i	0.107145	−	0.0618601i
$560$	−8.50812	+	7.51227i	−0.359534	+	0.317451i
$561$	1.14459	+	0.0347407i	0.0483247	+	0.00146675i
$562$	−1.26983	−	14.5142i	−0.0535644	−	0.612244i
$563$	7.65616	+	3.57013i	0.322669	+	0.150463i	0.577203	−	0.816601i	$-0.304144\pi$
$563$	7.65616	+	3.57013i	0.322669	+	0.150463i	−0.254534	+	0.967064i	$0.581922\pi$
$564$	−4.40242	+	21.1868i	−0.185375	+	0.892123i
$565$	26.7571	+	8.98241i	1.12568	+	0.377893i
$566$			20.9575i			0.880909i
$567$	3.41601	−	8.47450i	0.143459	−	0.355895i
$568$	−9.70421	+	9.70421i	−0.407180	+	0.407180i
$569$	0.364320	+	2.06616i	0.0152731	+	0.0866180i	0.991492	−	0.130171i	$-0.0415527\pi$
$569$	0.364320	+	2.06616i	0.0152731	+	0.0866180i	−0.976218	+	0.216789i	$0.930442\pi$
$570$	29.6950	−	2.44371i	1.24379	−	0.102356i
$571$	39.5609	−	14.3990i	1.65557	−	0.602578i	0.665913	−	0.746029i	$-0.268042\pi$
$571$	39.5609	−	14.3990i	1.65557	−	0.602578i	0.989657	+	0.143451i	$0.0458200\pi$
$572$	4.61959	−	0.404162i	0.193155	−	0.0168989i
$573$	5.06662	+	5.38382i	0.211661	+	0.224912i
$574$	3.34844	−	9.19975i	0.139761	−	0.383990i
$575$	−7.14981	−	22.1548i	−0.298168	−	0.923918i
$576$	2.04687	−	1.51588i	0.0852864	−	0.0631616i
$577$	39.4191	−	10.5623i	1.64104	−	0.439715i	0.683955	−	0.729525i	$-0.260259\pi$
$577$	39.4191	−	10.5623i	1.64104	−	0.439715i	0.957084	+	0.289810i	$0.0935920\pi$
$578$	−28.8723	−	2.52600i	−1.20093	−	0.105068i
$579$	−17.3676	+	2.52174i	−0.721775	+	0.104800i
$580$	2.11651	+	18.7421i	0.0878833	+	0.778225i
$581$	0.300004	+	0.0528988i	0.0124463	+	0.00219461i
$582$	−1.80784	+	15.3007i	−0.0749374	+	0.634233i
$583$	−0.787178	+	8.99749i	−0.0326016	+	0.372638i
$584$	4.51811	−	7.82560i	0.186961	−	0.323825i
$585$	5.40119	−	25.3366i	0.223312	−	1.04754i
$586$	−18.6831	−	32.3600i	−0.771790	−	1.33678i
$587$	11.5098	−	5.36709i	0.475059	−	0.221524i	−0.170316	−	0.985389i	$-0.554479\pi$
$587$	11.5098	−	5.36709i	0.475059	−	0.221524i	0.645375	+	0.763866i	$0.276701\pi$
$588$	2.41147	+	10.2319i	0.0994472	+	0.421958i
$589$	−22.7747	+	27.1419i	−0.938416	+	1.11836i
$590$	31.0991	+	4.67943i	1.28033	+	0.192649i
$591$	−6.43474	−	19.5008i	−0.264690	−	0.802156i
$592$	−15.7374	+	22.4753i	−0.646801	+	0.923728i
$593$	−6.50749	−	6.50749i	−0.267230	−	0.267230i	0.560753	−	0.827983i	$-0.310512\pi$
$593$	−6.50749	−	6.50749i	−0.267230	−	0.267230i	−0.827983	+	0.560753i	$0.810512\pi$
$594$	−2.71994	−	10.3059i	−0.111600	−	0.422855i
$595$	−0.359720	−	1.21885i	−0.0147471	−	0.0499679i
$596$	−14.3503	+	2.53035i	−0.587813	+	0.103647i
$597$	0.576384	+	10.1146i	0.0235898	+	0.413963i
$598$	13.1984	−	28.3041i	0.539723	−	1.15744i
$599$	−7.62396	−	6.39726i	−0.311507	−	0.261385i	0.473608	−	0.880736i	$-0.342951\pi$
$599$	−7.62396	−	6.39726i	−0.311507	−	0.261385i	−0.785114	+	0.619351i	$0.787396\pi$
$600$	12.9540	+	7.13698i	0.528844	+	0.291366i
$601$	24.7845	+	9.02082i	1.01098	+	0.367967i	0.793809	−	0.608167i	$-0.208095\pi$
$601$	24.7845	+	9.02082i	1.01098	+	0.367967i	0.217171	+	0.976134i	$0.430317\pi$
$602$	−1.29013	−	0.345688i	−0.0525816	−	0.0140892i
$603$	−0.946793	−	4.64410i	−0.0385564	−	0.189122i
$604$	4.74386	+	2.73887i	0.193025	+	0.111443i
$605$	17.8983	+	11.8723i	0.727670	+	0.482676i
$606$	54.1848	+	21.6050i	2.20111	+	0.877641i
$607$	−5.73315	+	4.01440i	−0.232701	+	0.162939i	−0.684112	−	0.729377i	$-0.739810\pi$
$607$	−5.73315	+	4.01440i	−0.232701	+	0.162939i	0.451410	+	0.892316i	$0.350921\pi$
$608$	−19.1148	+	13.3843i	−0.775207	+	0.542806i
$609$	13.5507	+	5.40303i	0.549101	+	0.218942i
$610$	42.6821	−	8.63955i	1.72815	−	0.349805i
$611$	41.0955	+	23.7265i	1.66254	+	0.959871i
$612$	−0.341097	−	1.67311i	−0.0137880	−	0.0676315i
$613$	−3.76248	−	1.00815i	−0.151965	−	0.0407189i	0.182034	−	0.983292i	$-0.441732\pi$
$613$	−3.76248	−	1.00815i	−0.151965	−	0.0407189i	−0.334000	+	0.942573i	$0.608398\pi$
$614$	20.1841	+	7.34642i	0.814565	+	0.296477i
$615$	−21.5028	−	0.110907i	−0.867078	−	0.00447220i
$616$	1.56859	+	1.31620i	0.0632004	+	0.0530314i
$617$	−1.85144	+	3.97043i	−0.0745363	+	0.159844i	−0.940045	−	0.341050i	$-0.889217\pi$
$617$	−1.85144	+	3.97043i	−0.0745363	+	0.159844i	0.865509	+	0.500894i	$0.166995\pi$
$618$	−2.55179	−	44.7798i	−0.102648	−	1.80131i
$619$	33.2378	−	5.86071i	1.33594	−	0.235562i	0.540371	−	0.841427i	$-0.318284\pi$
$619$	33.2378	−	5.86071i	1.33594	−	0.235562i	0.795567	+	0.605865i	$0.207173\pi$
$620$	17.4427	−	5.14789i	0.700515	−	0.206744i
$621$	−23.3451	−	6.34952i	−0.936807	−	0.254797i
$622$	16.8726	+	16.8726i	0.676528	+	0.676528i
$623$	6.30763	−	9.00822i	0.252710	−	0.360907i
$624$	10.4793	+	31.7582i	0.419510	+	1.27135i
$625$	−1.84315	+	24.9320i	−0.0737261	+	0.997279i
$626$	−33.3240	+	39.7140i	−1.33189	+	1.58729i
$627$	−2.07843	−	8.81883i	−0.0830043	−	0.352190i
$628$	7.33821	−	3.42186i	0.292827	−	0.136547i
$629$	−1.53603	−	2.66048i	−0.0612455	−	0.106080i
$630$	−9.92429	+	6.43653i	−0.395393	+	0.256438i
$631$	−17.7304	+	30.7100i	−0.705837	+	1.22255i	0.260552	+	0.965460i	$0.416096\pi$
$631$	−17.7304	+	30.7100i	−0.705837	+	1.22255i	−0.966389	+	0.257086i	$0.917238\pi$
$632$	−1.00174	+	11.4500i	−0.0398471	+	0.455455i
$633$	1.44425	−	12.2234i	0.0574038	−	0.485837i
$634$	36.5900	+	6.45180i	1.45317	+	0.256234i
$635$	−30.8557	−	24.5939i	−1.22447	−	0.975980i
$636$	13.3280	−	1.93519i	0.528488	−	0.0767354i
$637$	22.9647	+	2.00915i	0.909894	+	0.0796054i
$638$	16.4377	−	4.40448i	0.650777	−	0.174375i
$639$	−19.3736	+	14.3477i	−0.766408	+	0.567588i
$640$	−26.8495	+	0.676347i	−1.06132	+	0.0267350i
$641$	−9.20207	+	25.2825i	−0.363460	+	0.998598i	0.614337	+	0.789044i	$0.289423\pi$
$641$	−9.20207	+	25.2825i	−0.363460	+	0.998598i	−0.977797	+	0.209554i	$0.932799\pi$
$642$	−9.33178	−	9.91599i	−0.368296	−	0.391353i
$643$	−16.3427	+	1.42980i	−0.644495	+	0.0563860i	−0.404717	−	0.914442i	$-0.632630\pi$
$643$	−16.3427	+	1.42980i	−0.644495	+	0.0563860i	−0.239778	+	0.970828i	$0.577075\pi$
$644$	−4.51621	+	1.64377i	−0.177964	+	0.0647734i
$645$	0.240603	+	2.92371i	0.00947373	+	0.115121i
$646$	−0.747838	−	4.24120i	−0.0294233	−	0.166868i
$647$	6.34739	−	6.34739i	0.249542	−	0.249542i	−0.571241	−	0.820783i	$-0.693538\pi$
$647$	6.34739	−	6.34739i	0.249542	−	0.249542i	0.820783	+	0.571241i	$0.193538\pi$
$648$	13.5652	−	7.22673i	0.532893	−	0.283893i
$649$		−	9.56335i		−	0.375394i
$650$	−24.5733	+	22.8237i	−0.963844	+	0.895220i
$651$	2.86171	−	13.7720i	0.112159	−	0.539769i
$652$	−14.7821	−	6.89302i	−0.578913	−	0.269951i
$653$	1.09427	+	12.5076i	0.0428222	+	0.489460i	0.987077	+	0.160245i	$0.0512284\pi$
$653$	1.09427	+	12.5076i	0.0428222	+	0.489460i	−0.944255	+	0.329215i	$0.893216\pi$
$654$	32.2523	+	0.978922i	1.26116	+	0.0382789i
$655$	6.44999	+	0.400940i	0.252022	+	0.0156660i
$656$	24.0399	−	13.8794i	0.938600	−	0.541901i
$657$	9.87650	−	12.4267i	0.385319	−	0.484811i
$658$	−5.60792	−	20.9290i	−0.218619	−	0.815898i
$659$	7.46847	−	6.26679i	0.290930	−	0.244120i	−0.485627	−	0.874166i	$-0.661409\pi$
$659$	7.46847	−	6.26679i	0.290930	−	0.244120i	0.776557	+	0.630047i	$0.216964\pi$
$660$	−1.61313	+	4.36191i	−0.0627910	+	0.169787i
$661$	−7.28597	+	41.3208i	−0.283391	+	1.60719i	0.427584	+	0.903976i	$0.359365\pi$
$661$	−7.28597	+	41.3208i	−0.283391	+	1.60719i	−0.710975	+	0.703217i	$0.751746\pi$
$662$	25.5849	+	36.5390i	0.994386	+	1.42013i
$663$	−3.71858	−	0.439367i	−0.144418	−	0.0170636i
$664$	0.329393	+	0.392555i	0.0127829	+	0.0152341i
$665$	−8.57855	+	5.24521i	−0.332662	+	0.203401i
$666$	−19.6750	+	20.7497i	−0.762389	+	0.804036i
$667$	9.99727	−	37.3103i	0.387096	−	1.44466i
$668$	−0.182035	−	0.390376i	−0.00704315	−	0.0151041i
$669$	3.26513	+	2.01962i	0.126237	+	0.0780828i
$670$	−2.45228	+	5.62454i	−0.0947397	+	0.217295i
$671$	−4.52916	−	12.4438i	−0.174846	−	0.480386i
$672$	4.16804	−	8.27337i	0.160786	−	0.319152i
$673$	7.99252	+	5.59642i	0.308089	+	0.215726i	0.717388	−	0.696674i	$-0.245338\pi$
$673$	7.99252	+	5.59642i	0.308089	+	0.215726i	−0.409299	+	0.912401i	$0.634227\pi$
$674$	1.65138			0.0636089
$675$	20.6589	+	15.7547i	0.795161	+	0.606398i
$676$	−1.94572			−0.0748355
$677$	−34.3309	−	24.0388i	−1.31944	−	0.923885i	−0.319724	−	0.947511i	$-0.603590\pi$
$677$	−34.3309	−	24.0388i	−1.31944	−	0.923885i	−0.999721	+	0.0236257i	$0.992479\pi$
$678$	−37.9112	+	2.16038i	−1.45597	+	0.0829690i
$679$	−1.77831	−	4.88587i	−0.0682453	−	0.187502i
$680$	0.854373	−	1.95959i	0.0327637	−	0.0751468i
$681$	−14.6636	+	7.88285i	−0.561912	+	0.302072i
$682$	−6.93465	−	14.8714i	−0.265542	−	0.569456i
$683$	5.59914	−	20.8963i	0.214245	−	0.799574i	−0.772186	−	0.635397i	$-0.780837\pi$
$683$	5.59914	−	20.8963i	0.214245	−	0.799574i	0.986431	−	0.164177i	$-0.0524968\pi$
$684$	−12.0885	+	6.03314i	−0.462214	+	0.230683i
$685$	16.0656	−	9.82303i	0.613835	−	0.375319i
$686$	−14.7000	−	17.5188i	−0.561250	−	0.668872i
$687$	−6.86830	−	15.9776i	−0.262042	−	0.609583i
$688$	−2.17216	−	3.10216i	−0.0828127	−	0.118269i
$689$	5.12843	−	29.0848i	0.195378	−	1.10804i
$690$	20.0083	+	24.0963i	0.761703	+	0.917329i
$691$	−19.0033	+	15.9457i	−0.722921	+	0.606603i	−0.928192	−	0.372102i	$-0.878637\pi$
$691$	−19.0033	+	15.9457i	−0.722921	+	0.606603i	0.205270	+	0.978705i	$0.434193\pi$
$692$	−2.12605	−	7.93453i	−0.0808203	−	0.301625i
$693$	2.38453	+	2.69304i	0.0905808	+	0.102300i
$694$	−3.06531	+	1.76976i	−0.116358	+	0.0671791i
$695$	22.3196	+	1.38741i	0.846629	+	0.0526276i
$696$	11.6195	+	21.6145i	0.440436	+	0.819296i
$697$	0.270886	+	3.09624i	0.0102605	+	0.117279i
$698$	−21.2865	−	9.92607i	−0.805707	−	0.375707i
$699$	−15.5589	−	13.8812i	−0.588492	−	0.525037i
$700$	5.15764	+	0.190385i	0.194941	+	0.00719589i
$701$			3.89640i			0.147165i	0.997289	+	0.0735825i	$0.0234432\pi$
$701$			3.89640i			0.147165i	−0.997289	+	0.0735825i	$0.976557\pi$
$702$	5.92305	+	34.3463i	0.223551	+	1.29632i
$703$	−17.1875	+	17.1875i	−0.648240	+	0.648240i
$704$	0.174119	+	0.987476i	0.00656235	+	0.0372169i
$705$	−39.1238	+	27.0951i	−1.47349	+	1.02046i
$706$	12.1861	−	4.43538i	0.458630	−	0.166928i
$707$	−19.6108	+	1.71572i	−0.737541	+	0.0645264i
$708$	−13.8800	+	3.27124i	−0.521642	+	0.122941i
$709$	−7.07809	+	19.4469i	−0.265823	+	0.730343i	0.732924	+	0.680310i	$0.238155\pi$
$709$	−7.07809	+	19.4469i	−0.265823	+	0.730343i	−0.998748	+	0.0500331i	$0.984067\pi$
$710$	31.2001	−	0.785940i	1.17092	−	0.0294958i
$711$	−4.70548	+	19.6344i	−0.176469	+	0.736349i
$712$	17.8685	−	4.78786i	0.669652	−	0.179433i
$713$	−37.1029	−	3.24608i	−1.38951	−	0.121567i
$714$	1.05876	+	1.34247i	0.0396230	+	0.0502408i
$715$	7.97504	+	6.35660i	0.298250	+	0.237723i
$716$	12.7809	+	2.25362i	0.477645	+	0.0842218i
$717$	−2.50793	−	1.87198i	−0.0936604	−	0.0699103i
$718$	1.33246	−	15.2301i	0.0497269	−	0.568381i
$719$	−23.2328	+	40.2403i	−0.866436	+	1.50071i	−0.000822468		1.00000i	$0.500262\pi$
$719$	−23.2328	+	40.2403i	−0.866436	+	1.50071i	−0.865614	+	0.500712i	$0.833072\pi$
$720$	−33.2867	−	4.10716i	−1.24052	−	0.153065i
$721$	7.56817	+	13.1085i	0.281853	+	0.488185i
$722$	−0.973719	+	0.454053i	−0.0362381	+	0.0168981i
$723$	20.2968	−	19.1010i	0.754844	−	0.710372i
$724$	12.0891	−	14.4073i	0.449289	−	0.535442i
$725$	−25.0295	+	33.0781i	−0.929571	+	1.22849i
$726$	−28.2916	−	5.87874i	−1.05000	−	0.218181i
$727$	14.7105	−	21.0088i	0.545584	−	0.779175i	−0.447785	−	0.894141i	$-0.647787\pi$
$727$	14.7105	−	21.0088i	0.545584	−	0.779175i	0.993369	+	0.114966i	$0.0366760\pi$
$728$	−4.73454	−	4.73454i	−0.175474	−	0.175474i
$729$	25.4405	−	9.04340i	0.942239	−	0.334941i
$730$	−19.7093	+	5.81682i	−0.729472	+	0.215290i
$731$	0.417580	−	0.0736307i	0.0154448	−	0.00272333i
$732$	−16.5113	+	10.8300i	−0.610275	+	0.400289i
$733$	1.12205	−	2.40624i	0.0414438	−	0.0888766i	−0.884496	−	0.466548i	$-0.845497\pi$
$733$	1.12205	−	2.40624i	0.0414438	−	0.0888766i	0.925940	+	0.377672i	$0.123275\pi$
$734$	36.3169	+	30.4735i	1.34048	+	1.12480i
$735$	−11.6626	+	19.9618i	−0.430182	+	0.736301i
$736$	−23.0499	−	8.38947i	−0.849630	−	0.309240i
$737$	1.80228	+	0.482919i	0.0663878	+	0.0177886i
$738$	26.9126	−	10.6136i	0.990667	−	0.390693i
$739$	−19.4519	−	11.2305i	−0.715548	−	0.413122i	0.0975639	−	0.995229i	$-0.468895\pi$
$739$	−19.4519	−	11.2305i	−0.715548	−	0.413122i	−0.813112	+	0.582107i	$0.802228\pi$
$740$	12.2285	−	2.47524i	0.449527	−	0.0909917i
$741$	4.25713	+	29.3195i	0.156389	+	1.07708i
$742$	−11.0464	+	7.73477i	−0.405526	+	0.283952i
$743$	25.2126	−	17.6540i	0.924960	−	0.647664i	−0.0109359	−	0.999940i	$-0.503481\pi$
$743$	25.2126	−	17.6540i	0.924960	−	0.647664i	0.935896	+	0.352276i	$0.114592\pi$
$744$	18.5791	−	14.6526i	0.681143	−	0.537191i
$745$	−26.7057	−	17.7144i	−0.978422	−	0.649004i
$746$	−18.2856	−	10.5572i	−0.669484	−	0.386527i
$747$	0.470653	+	0.767345i	0.0172203	+	0.0280757i
$748$	0.649300	+	0.173979i	0.0237408	+	0.00636132i
$749$	4.31804	+	1.57164i	0.157778	+	0.0574264i
$750$	−10.1647	−	32.0618i	−0.371163	−	1.17073i
$751$	5.77858	+	4.84881i	0.210864	+	0.176936i	0.742102	−	0.670287i	$-0.233829\pi$
$751$	5.77858	+	4.84881i	0.210864	+	0.176936i	−0.531239	+	0.847222i	$0.678273\pi$
$752$	25.9636	−	55.6791i	0.946795	−	2.03041i
$753$	−28.2610	−	14.2376i	−1.02989	−	0.518847i
$754$	−54.8008	+	9.66287i	−1.99573	+	0.351901i
$755$	3.41000	+	11.5542i	0.124103	+	0.420499i
$756$	3.09296	−	4.38202i	0.112490	−	0.159373i
$757$	−18.1781	−	18.1781i	−0.660696	−	0.660696i	0.294848	−	0.955544i	$-0.404731\pi$
$757$	−18.1781	−	18.1781i	−0.660696	−	0.660696i	−0.955544	+	0.294848i	$0.904731\pi$
$758$	22.5748	−	32.2402i	0.819954	−	1.17102i
$759$	6.34054	−	7.10685i	0.230147	−	0.257962i
$760$	−16.7260	−	2.51674i	−0.606717	−	0.0912917i
$761$	19.2569	−	22.9494i	0.698061	−	0.831916i	−0.294245	−	0.955730i	$-0.595068\pi$
$761$	19.2569	−	22.9494i	0.698061	−	0.831916i	0.992305	+	0.123814i	$0.0395125\pi$
$762$	50.8368	+	15.2890i	1.84162	+	0.553862i
$763$	−9.86895	+	4.60197i	−0.357280	+	0.166602i
$764$	2.16991	+	3.75839i	0.0785044	+	0.135974i
$765$	1.99188	−	3.18346i	0.0720165	−	0.115098i
$766$	16.5590	−	28.6811i	0.598302	−	1.03629i
$767$	−2.72548	+	31.1524i	−0.0984115	+	1.12485i
$768$	30.4949	−	13.1089i	1.10039	−	0.473027i
$769$	4.02410	+	0.709557i	0.145113	+	0.0255873i	0.245733	−	0.969338i	$-0.420971\pi$
$769$	4.02410	+	0.709557i	0.145113	+	0.0255873i	−0.100620	+	0.994925i	$0.532083\pi$
$770$	−0.522545	−	4.62725i	−0.0188312	−	0.166754i
$771$	9.09534	−	22.8109i	0.327561	−	0.821516i
$772$	−10.2628	−	0.897880i	−0.369367	−	0.0323154i
$773$	−38.4073	+	10.2912i	−1.38141	+	0.370149i	−0.871635	−	0.490156i	$-0.836940\pi$
$773$	−38.4073	+	10.2912i	−1.38141	+	0.370149i	−0.509780	+	0.860305i	$0.670273\pi$
$774$	−1.76247	−	3.53142i	−0.0633506	−	0.126934i
$775$	35.6009	+	18.2289i	1.27882	+	0.654802i
$776$	2.99143	−	8.21887i	0.107386	−	0.295040i
$777$	2.77920	−	9.24097i	0.0997031	−	0.331518i
$778$	−26.9882	+	2.36116i	−0.967573	+	0.0846517i
$779$	23.1087	−	8.41088i	0.827955	−	0.301351i
$780$	6.49785	−	13.7491i	0.232660	−	0.492296i
$781$	−1.64803	−	9.34644i	−0.0589711	−	0.334442i
$782$	3.20111	−	3.20111i	0.114471	−	0.114471i
$783$	14.5913	+	40.5633i	0.521449	+	1.44961i
$784$		−	29.8449i		−	1.06589i
$785$	16.8811	+	5.66700i	0.602511	+	0.202264i
$786$	−8.25655	+	2.72444i	−0.294501	+	0.0971775i
$787$	4.88315	+	2.27705i	0.174066	+	0.0811681i	0.507698	−	0.861535i	$-0.330497\pi$
$787$	4.88315	+	2.27705i	0.174066	+	0.0811681i	−0.333632	+	0.942703i	$0.608274\pi$
$788$	−1.05061	−	12.0086i	−0.0374265	−	0.427787i
$789$	3.34324	−	5.40504i	0.119023	−	0.192424i
$790$	19.5937	−	17.3003i	0.697112	−	0.615517i
$791$	11.0978	−	6.40733i	0.394593	−	0.227818i
$792$	0.160817	+	6.04865i	0.00571439	+	0.214930i
$793$	11.2073	+	41.8261i	0.397982	+	1.48529i
$794$	−11.8380	+	9.93324i	−0.420114	+	0.352518i
$795$	24.1744	+	17.1136i	0.857376	+	0.606956i
$796$	−1.03270	+	5.85673i	−0.0366031	+	0.207586i
$797$	17.9597	+	25.6491i	0.636165	+	0.908538i	0.999735	−	0.0230287i	$-0.00733090\pi$
$797$	17.9597	+	25.6491i	0.636165	+	0.908538i	−0.363569	+	0.931567i	$0.618442\pi$
$798$	8.09187	−	10.8409i	0.286449	−	0.383762i
$799$	4.42153	+	5.26938i	0.156423	+	0.186417i
$800$	19.5405	+	17.6649i	0.690860	+	0.624547i
$801$	32.2857	−	3.69161i	1.14076	−	0.130437i
$802$	−0.496613	+	1.85338i	−0.0175360	+	0.0654453i
$803$	2.64092	+	5.66346i	0.0931959	+	0.199859i
$804$	0.0844079	−	2.78096i	0.00297684	−	0.0980771i
$805$	−9.68882	−	4.22429i	−0.341486	−	0.148887i
$806$	18.3512	+	50.4196i	0.646395	+	1.77595i
$807$	−10.6089	−	16.1741i	−0.373449	−	0.569356i
$808$	−27.1260	−	18.9939i	−0.954291	−	0.668202i
$809$	4.86947			0.171202			0.0856008	−	0.996330i	$-0.472719\pi$
$809$	4.86947			0.171202			0.0856008	+	0.996330i	$0.472719\pi$
$810$	−33.6809	−	9.34754i	−1.18343	−	0.328439i
$811$	−14.9764			−0.525893			−0.262947	−	0.964810i	$-0.584694\pi$
$811$	−14.9764			−0.525893			−0.262947	+	0.964810i	$0.584694\pi$
$812$	7.01480	+	4.91182i	0.246171	+	0.172371i
$813$	21.8803	+	33.3584i	0.767376	+	1.16993i
$814$	−3.85009	−	10.5780i	−0.134946	−	0.370760i
$815$	−13.1133	−	33.3874i	−0.459338	−	1.16951i
$816$	−0.147072	+	4.84553i	−0.00514853	+	0.169627i
$817$	−1.41787	−	3.04063i	−0.0496049	−	0.106378i
$818$	−0.327165	+	1.22100i	−0.0114391	+	0.0426911i
$819$	−7.00006	−	9.45210i	−0.244602	−	0.330283i
$820$	−12.2710	−	2.95893i	−0.428522	−	0.103330i
$821$	2.55907	+	3.04978i	0.0893122	+	0.106438i	0.808850	−	0.588015i	$-0.200091\pi$
$821$	2.55907	+	3.04978i	0.0893122	+	0.106438i	−0.719537	+	0.694454i	$0.755646\pi$
$822$	−15.1541	+	20.3024i	−0.528561	+	0.708126i
$823$	9.33088	+	13.3259i	0.325254	+	0.464511i	0.948163	−	0.317783i	$-0.102938\pi$
$823$	9.33088	+	13.3259i	0.325254	+	0.464511i	−0.622909	+	0.782294i	$0.714049\pi$
$824$	−4.42142	+	25.0751i	−0.154027	+	0.873533i
$825$	−9.18119	+	4.50726i	−0.319648	+	0.156923i
$826$	10.9381	−	9.17818i	0.380586	−	0.319350i
$827$	−5.10757	−	19.0617i	−0.177608	−	0.662841i	−0.996093	−	0.0883130i	$-0.971852\pi$
$827$	−5.10757	−	19.0617i	−0.177608	−	0.662841i	0.818485	−	0.574528i	$-0.194814\pi$
$828$	−12.4835	−	6.77152i	−0.433833	−	0.235327i
$829$	−32.1618	+	18.5687i	−1.11703	+	0.644916i	−0.940640	−	0.339405i	$-0.889774\pi$
$829$	−32.1618	+	18.5687i	−1.11703	+	0.644916i	−0.176387	+	0.984321i	$0.556441\pi$
$830$	0.0723016	−	1.16313i	0.00250963	−	0.0403727i
$831$	−11.3352	+	18.3257i	−0.393215	+	0.635713i
$832$	−0.285765	−	3.26630i	−0.00990711	−	0.113239i
$833$	3.02855	+	1.41223i	0.104933	+	0.0489310i
$834$	−28.5710	+	9.42765i	−0.989333	+	0.326453i
$835$	0.301471	−	0.898032i	0.0104328	−	0.0310777i
$836$		−	5.31864i		−	0.183949i
$837$	36.0748	−	20.6472i	1.24693	−	0.713673i
$838$	24.1069	−	24.1069i	0.832759	−	0.832759i
$839$	−6.68205	−	37.8958i	−0.230690	−	1.30831i	−0.851503	−	0.524349i	$-0.824309\pi$
$839$	−6.68205	−	37.8958i	−0.230690	−	1.30831i	0.620813	−	0.783958i	$-0.286802\pi$
$840$	6.32180	−	2.26409i	0.218123	−	0.0781186i
$841$	−37.4236	+	13.6211i	−1.29047	+	0.469692i
$842$	18.2938	−	1.60050i	0.630447	−	0.0551570i
$843$	−4.18445	+	13.9135i	−0.144120	+	0.479207i
$844$	2.47119	−	6.78953i	0.0850618	−	0.233705i
$845$	−3.10103	−	2.94864i	−0.106679	−	0.101436i
$846$	35.3173	−	53.4052i	1.21423	−	1.83611i
$847$	9.41923	−	2.52388i	0.323649	−	0.0867214i
$848$	−38.0901	−	3.33245i	−1.30802	−	0.114437i
$849$	7.74048	−	19.4130i	0.265653	−	0.666252i
$850$	−4.47884	+	1.89065i	−0.153623	+	0.0648486i
$851$	−25.1627	−	4.43686i	−0.862567	−	0.152094i
$852$	−13.0014	+	5.58895i	−0.445422	+	0.191474i
$853$	−3.27769	+	37.4642i	−0.112226	+	1.28275i	0.706148	+	0.708064i	$0.250431\pi$
$853$	−3.27769	+	37.4642i	−0.112226	+	1.28275i	−0.818374	+	0.574685i	$0.805124\pi$
$854$	9.88588	−	17.1228i	0.338288	−	0.585932i
$855$	−28.4091	−	8.70398i	−0.971570	−	0.297670i
$856$	3.86493	+	6.69425i	0.132100	+	0.228805i
$857$	17.6382	−	8.22482i	0.602509	−	0.280954i	−0.0973336	−	0.995252i	$-0.531031\pi$
$857$	17.6382	−	8.22482i	0.602509	−	0.280954i	0.699842	+	0.714297i	$0.253254\pi$
$858$	−13.1394	−	3.95163i	−0.448571	−	0.134906i
$859$	−13.2902	+	15.8386i	−0.453454	+	0.540406i	−0.943536	−	0.331271i	$-0.892523\pi$
$859$	−13.2902	+	15.8386i	−0.453454	+	0.540406i	0.490081	+	0.871677i	$0.336967\pi$
$860$	−0.256233	+	1.70290i	−0.00873746	+	0.0580684i
$861$	−6.49952	+	7.28503i	−0.221503	+	0.248273i
$862$	−16.5469	+	23.6315i	−0.563590	+	0.804891i
$863$	−1.02957	−	1.02957i	−0.0350471	−	0.0350471i	0.689366	−	0.724413i	$-0.257889\pi$
$863$	−1.02957	−	1.02957i	−0.0350471	−	0.0350471i	−0.724413	+	0.689366i	$0.757889\pi$
$864$	26.4686	−	6.98564i	0.900481	−	0.237656i
$865$	8.63591	−	15.8677i	0.293630	−	0.539518i
$866$	34.6408	−	6.10810i	1.17714	−	0.207562i
$867$	25.8116	+	13.0036i	0.876606	+	0.441626i
$868$	3.48961	−	7.48350i	0.118445	−	0.254006i
$869$	−6.08882	−	5.10913i	−0.206549	−	0.173315i
$870$	14.7218	−	53.8303i	0.499115	−	1.82502i
$871$	−5.73325	−	2.08673i	−0.194264	−	0.0707063i
$872$	−17.6933	−	4.74092i	−0.599172	−	0.160548i
$873$	7.32578	−	13.5053i	0.247940	−	0.457086i
$874$	−31.0202	−	17.9095i	−1.04927	−	0.605799i
$875$	7.93156	+	8.11955i	0.268136	+	0.274491i
$876$	7.31644	−	5.77020i	0.247200	−	0.194957i
$877$	−47.3607	+	33.1623i	−1.59926	+	1.11981i	−0.675145	+	0.737685i	$0.735919\pi$
$877$	−47.3607	+	33.1623i	−1.59926	+	1.11981i	−0.924110	+	0.382126i	$0.875192\pi$
$878$	−16.8718	+	11.8138i	−0.569396	+	0.398695i
$879$	5.35426	+	36.8756i	0.180595	+	1.24378i
$880$	7.29840	−	11.0029i	0.246029	−	0.370907i
$881$	6.00946	+	3.46956i	0.202464	+	0.116893i	0.597804	−	0.801642i	$-0.296040\pi$
$881$	6.00946	+	3.46956i	0.202464	+	0.116893i	−0.395340	+	0.918535i	$0.629373\pi$
$882$	4.58510	−	30.7641i	0.154388	−	1.03588i
$883$	14.9527	+	4.00657i	0.503199	+	0.134832i	0.501484	−	0.865167i	$-0.332787\pi$
$883$	14.9527	+	4.00657i	0.503199	+	0.134832i	0.00171481	+	0.999999i	$0.499454\pi$
$884$	−2.06550	−	0.751779i	−0.0694702	−	0.0252851i
$885$	−27.0789	−	15.8208i	−0.910246	−	0.531809i
$886$	−29.6420	−	24.8726i	−0.995844	−	0.835612i
$887$	−16.6122	+	35.6250i	−0.557783	+	1.19617i	0.402055	+	0.915615i	$0.368296\pi$
$887$	−16.6122	+	35.6250i	−0.557783	+	1.19617i	−0.959838	+	0.280554i	$0.909482\pi$
$888$	13.5734	−	8.90301i	0.455494	−	0.298765i
$889$	−17.6428	+	3.11090i	−0.591720	+	0.104336i
$890$	−36.9511	−	20.1104i	−1.23860	−	0.674104i
$891$	−1.28690	+	10.5509i	−0.0431128	+	0.353470i
$892$	1.59361	+	1.59361i	0.0533582	+	0.0533582i
$893$	31.2173	−	44.5830i	1.04465	−	1.49191i
$894$	42.2134	+	8.77156i	1.41183	+	0.293365i
$895$	16.9546	+	22.9605i	0.566729	+	0.767486i
$896$	−7.83830	+	9.34132i	−0.261859	+	0.312072i
$897$	−22.6796	+	21.3434i	−0.757249	+	0.712635i
$898$	−8.30068	+	3.87067i	−0.276997	+	0.129166i
$899$	33.1815	+	57.4721i	1.10667	+	1.91680i
$900$	9.68223	+	11.7836i	0.322741	+	0.392786i
$901$	2.14056	−	3.70755i	0.0713123	−	0.123516i
$902$	−0.992605	+	11.3455i	−0.0330501	+	0.377765i
$903$	1.06737	+	0.796709i	0.0355198	+	0.0265128i
$904$	21.2290	+	3.74324i	0.706065	+	0.124498i
$905$	41.1007	−	4.64141i	1.36623	−	0.154286i
$906$	−10.0366	−	12.7261i	−0.333443	−	0.422796i
$907$	−16.6313	−	1.45505i	−0.552232	−	0.0483140i	−0.192375	−	0.981322i	$-0.561619\pi$
$907$	−16.6313	−	1.45505i	−0.552232	−	0.0483140i	−0.359857	+	0.933008i	$0.617174\pi$
$908$	−9.43978	+	2.52938i	−0.313270	+	0.0839404i
$909$	−42.2119	−	40.0254i	−1.40008	−	1.32756i
$910$	0.383449	+	15.2221i	0.0127112	+	0.504607i
$911$	15.5855	−	42.8207i	0.516369	−	1.41871i	−0.358124	−	0.933674i	$-0.616583\pi$
$911$	15.5855	−	42.8207i	0.516369	−	1.41871i	0.874493	−	0.485038i	$-0.161194\pi$
$912$	37.3337	−	8.79883i	1.23624	−	0.291358i
$913$	−0.353029	+	0.0308860i	−0.0116835	+	0.00102218i
$914$	15.6849	−	5.70884i	0.518810	−	0.188831i
$915$	−42.7275	−	7.76144i	−1.41253	−	0.256585i
$916$	−1.77277	−	10.0539i	−0.0585740	−	0.332190i
$917$	2.07473	−	2.07473i	0.0685136	−	0.0685136i
$918$	−0.896026	+	4.97217i	−0.0295733	+	0.164106i
$919$		−	3.56037i		−	0.117446i	−0.998274	−	0.0587228i	$-0.981297\pi$
$919$		−	3.56037i		−	0.117446i	0.998274	−	0.0587228i	$-0.0187028\pi$
$920$	−7.91756	−	15.9198i	−0.261034	−	0.524861i
$921$	−15.9833	−	14.2598i	−0.526666	−	0.469878i
$922$	−16.9051	−	7.88296i	−0.556738	−	0.259611i
$923$	2.70476	+	30.9155i	0.0890281	+	1.01760i
$924$	0.999791	+	1.85981i	0.0328907	+	0.0611832i
$925$	23.2404	+	14.5866i	0.764140	+	0.479605i
$926$	−53.8596	+	31.0958i	−1.76994	+	1.02187i
$927$	−14.1753	+	42.4221i	−0.465578	+	1.39332i
$928$	11.3121	+	42.2172i	0.371337	+	1.38585i
$929$	−9.72612	+	8.16118i	−0.319104	+	0.267760i	−0.788243	−	0.615365i	$-0.789009\pi$
$929$	−9.72612	+	8.16118i	−0.319104	+	0.267760i	0.469139	+	0.883124i	$0.344564\pi$
$930$	−53.5808	−	4.96631i	−1.75698	−	0.162852i
$931$	4.59122	−	26.0381i	0.150471	−	0.853364i
$932$	−7.02055	−	10.0264i	−0.229966	−	0.328425i
$933$	−9.39735	−	21.8608i	−0.307655	−	0.715691i
$934$	−27.2732	−	32.5030i	−0.892407	−	1.06353i
$935$	0.771177	+	1.26126i	0.0252202	+	0.0412477i
$936$	1.19996	−	19.7492i	0.0392220	−	0.645522i
$937$	−6.23661	+	23.2753i	−0.203741	+	0.760372i	0.786089	+	0.618114i	$0.212103\pi$
$937$	−6.23661	+	23.2753i	−0.203741	+	0.760372i	−0.989830	+	0.142258i	$0.954564\pi$
$938$	1.17735	+	2.52484i	0.0384418	+	0.0824388i
$939$	45.5361	−	24.4792i	1.48601	−	0.798848i
$940$	−26.0025	+	10.2128i	−0.848109	+	0.333105i
$941$	−2.96478	−	8.14566i	−0.0966490	−	0.265541i	0.881941	−	0.471359i	$-0.156237\pi$
$941$	−2.96478	−	8.14566i	−0.0966490	−	0.265541i	−0.978590	+	0.205819i	$0.934014\pi$
$942$	−23.9182	+	1.36299i	−0.779297	+	0.0444085i
$943$	21.1754	+	14.8272i	0.689566	+	0.482839i
$944$	40.4856			1.31769
$945$	11.5702	−	2.29672i	0.376378	−	0.0747123i
$946$	1.55374			0.0505165
$947$	−23.3157	−	16.3258i	−0.757658	−	0.530518i	0.129726	−	0.991550i	$-0.458590\pi$
$947$	−23.3157	−	16.3258i	−0.757658	−	0.530518i	−0.887383	+	0.461032i	$0.847479\pi$
$948$	−5.33250	+	10.5848i	−0.173192	+	0.343777i
$949$	−6.98868	−	19.2012i	−0.226862	−	0.623299i
$950$	23.6214	+	30.3584i	0.766381	+	0.984957i
$951$	−31.5105	−	19.4905i	−1.02180	−	0.632024i
$952$	−0.410189	−	0.879652i	−0.0132943	−	0.0285097i
$953$	−3.74136	+	13.9629i	−0.121194	+	0.452304i	−0.999675	−	0.0254735i	$-0.991891\pi$
$953$	−3.74136	+	13.9629i	−0.121194	+	0.452304i	0.878481	+	0.477777i	$0.158557\pi$
$954$	−38.7513	−	9.28692i	−1.25462	−	0.300675i
$955$	−2.23730	+	9.27837i	−0.0723975	+	0.300241i
$956$	−1.18086	−	1.40730i	−0.0381918	−	0.0455152i
$957$	−16.8531	−	1.99127i	−0.544783	−	0.0643685i
$958$	40.6627	+	58.0723i	1.31375	+	1.87623i
$959$	1.48462	−	8.41972i	0.0479410	−	0.271887i
$960$	3.08411	+	1.14057i	0.0995392	+	0.0368118i
$961$	25.2709	−	21.2048i	0.815190	−	0.684025i
$962$	9.52692	+	35.5550i	0.307160	+	1.14634i
$963$	4.98166	+	12.6318i	0.160532	+	0.407055i
$964$	14.1690	−	8.18045i	0.456351	−	0.263474i
$965$	−14.9959	−	16.9838i	−0.482734	−	0.546726i
$966$	14.2137	+	0.431414i	0.457317	+	0.0138805i
$967$	−2.08098	−	23.7858i	−0.0669199	−	0.764898i	−0.953317	−	0.301972i	$-0.902355\pi$
$967$	−2.08098	−	23.7858i	−0.0669199	−	0.764898i	0.886397	−	0.462926i	$-0.153201\pi$
$968$	14.8668	+	6.93251i	0.477838	+	0.222819i
$969$	−0.873729	+	4.20484i	−0.0280682	+	0.135079i
$970$	−17.8095	+	8.85737i	−0.571828	+	0.284393i
$971$			55.0723i			1.76735i	0.468098	+	0.883676i	$0.344939\pi$
$971$			55.0723i			1.76735i	−0.468098	+	0.883676i	$0.655061\pi$
$972$	15.7535	−	1.74128i	0.505295	−	0.0558516i
$973$	7.17940	−	7.17940i	0.230161	−	0.230161i
$974$	10.0337	+	56.9040i	0.321501	+	1.82332i
$975$	31.1921	−	12.0657i	0.998945	−	0.386412i
$976$	52.6796	−	19.1738i	1.68623	−	0.613738i
$977$	−12.7178	+	1.11266i	−0.406878	+	0.0355972i	−0.288758	−	0.957402i	$-0.593242\pi$
$977$	−12.7178	+	1.11266i	−0.406878	+	0.0355972i	−0.118120	+	0.992999i	$0.537687\pi$
$978$	33.0734	+	35.1439i	1.05757	+	1.12378i
$979$	−4.37539	+	12.0213i	−0.139838	+	0.384202i
$980$	−9.35164	+	9.83495i	−0.298727	+	0.314166i
$981$	−29.5138	−	12.8189i	−0.942303	−	0.409276i
$982$	8.35043	−	2.23749i	0.266473	−	0.0714012i
$983$	7.16081	+	0.626489i	0.228394	+	0.0199819i	0.200778	−	0.979637i	$-0.435653\pi$
$983$	7.16081	+	0.626489i	0.228394	+	0.0199819i	0.0276159	+	0.999619i	$0.491208\pi$
$984$	−16.2526	+	2.35984i	−0.518113	+	0.0752289i
$985$	16.5239	−	20.7310i	0.526494	−	0.660544i
$986$	−7.94382	−	1.40071i	−0.252983	−	0.0446077i
$987$	−2.53534	+	21.4578i	−0.0807008	+	0.683011i
$988$	−1.51577	+	17.3254i	−0.0482231	+	0.551193i
$989$	1.76334	−	3.05419i	0.0560708	−	0.0971175i
$990$	9.21357	−	10.2205i	0.292826	−	0.324829i
$991$	18.6356	+	32.2778i	0.591979	+	1.02534i	0.993966	+	0.109692i	$0.0349863\pi$
$991$	18.6356	+	32.2778i	0.591979	+	1.02534i	−0.401987	+	0.915645i	$0.631680\pi$
$992$	38.1944	−	17.8103i	1.21267	−	0.565478i
$993$	−10.2040	−	43.2958i	−0.323813	−	1.37395i
$994$	9.10839	−	10.8550i	0.288900	−	0.344298i
$995$	−10.5214	+	7.76927i	−0.333552	+	0.246302i
$996$	0.165584	+	0.501811i	0.00524673	+	0.0159005i
$997$	18.5746	−	26.5272i	0.588262	−	0.840126i	−0.409116	−	0.912482i	$-0.634163\pi$
$997$	18.5746	−	26.5272i	0.588262	−	0.840126i	0.997379	+	0.0723564i	$0.0230519\pi$
$998$	−7.93723	−	7.93723i	−0.251249	−	0.251249i
$999$	25.8887	−	11.9537i	0.819082	−	0.378200i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.122.4	yes	192
3.2	odd	2		405.2.r.a.152.13		192
5.2	odd	4		675.2.ba.b.68.13		192
5.3	odd	4	inner	135.2.q.a.68.4	yes	192
5.4	even	2		675.2.ba.b.257.13		192
15.8	even	4		405.2.r.a.233.13		192
27.2	odd	18	inner	135.2.q.a.2.4	✓	192
27.25	even	9		405.2.r.a.332.13		192
135.2	even	36		675.2.ba.b.218.13		192
135.29	odd	18		675.2.ba.b.407.13		192
135.83	even	36	inner	135.2.q.a.83.4	yes	192
135.133	odd	36		405.2.r.a.8.13		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.4	✓	192	27.2	odd	18	inner
135.2.q.a.68.4	yes	192	5.3	odd	4	inner
135.2.q.a.83.4	yes	192	135.83	even	36	inner
135.2.q.a.122.4	yes	192	1.1	even	1	trivial
405.2.r.a.8.13		192	135.133	odd	36
405.2.r.a.152.13		192	3.2	odd	2
405.2.r.a.233.13		192	15.8	even	4
405.2.r.a.332.13		192	27.25	even	9
675.2.ba.b.68.13		192	5.2	odd	4
675.2.ba.b.218.13		192	135.2	even	36
675.2.ba.b.257.13		192	5.4	even	2
675.2.ba.b.407.13		192	135.29	odd	18

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.42277 - 0.996232i) q^{2} +(0.949962 + 1.44830i) q^{3} +(0.347747 + 0.955427i) q^{4} +(-0.893670 + 2.04972i) q^{5} +(0.0912678 - 3.00698i) q^{6} +(0.429055 + 0.920112i) q^{7} +(-0.442010 + 1.64960i) q^{8} +(-1.19514 + 2.75166i) q^{9} +O(q^{10})\)	\(q+(-1.42277 - 0.996232i) q^{2} +(0.949962 + 1.44830i) q^{3} +(0.347747 + 0.955427i) q^{4} +(-0.893670 + 2.04972i) q^{5} +(0.0912678 - 3.00698i) q^{6} +(0.429055 + 0.920112i) q^{7} +(-0.442010 + 1.64960i) q^{8} +(-1.19514 + 2.75166i) q^{9} +(3.31348 - 2.02597i) q^{10} +(-0.759141 - 0.904709i) q^{11} +(-1.05340 + 1.41126i) q^{12} +(2.21505 + 3.16342i) q^{13} +(0.306200 - 1.73654i) q^{14} +(-3.81756 + 0.652855i) q^{15} +(3.83001 - 3.21376i) q^{16} +(0.144887 + 0.540727i) q^{17} +(4.44170 - 2.72433i) q^{18} +(3.83587 - 2.21464i) q^{19} +(-2.26913 - 0.141052i) q^{20} +(-0.925012 + 1.49547i) q^{21} +(0.178781 + 2.04347i) q^{22} +(4.21975 + 1.96770i) q^{23} +(-2.80901 + 0.926898i) q^{24} +(-3.40271 - 3.66355i) q^{25} -6.70752i q^{26} +(-5.12057 + 0.883047i) q^{27} +(-0.729897 + 0.729897i) q^{28} +(-1.44060 - 8.17007i) q^{29} +(6.08190 + 2.87432i) q^{30} +(-7.51688 + 2.73592i) q^{31} +(-5.24827 + 0.459164i) q^{32} +(0.589135 - 1.95890i) q^{33} +(0.332549 - 0.913671i) q^{34} +(-2.26941 + 0.0571670i) q^{35} +(-3.04462 - 0.184991i) q^{36} +(-5.30076 + 1.42034i) q^{37} +(-7.66385 - 0.670500i) q^{38} +(-2.47737 + 6.21319i) q^{39} +(-2.98621 - 2.38020i) q^{40} +(5.46773 + 0.964109i) q^{41} +(2.80591 - 1.20618i) q^{42} +(0.0660161 - 0.754568i) q^{43} +(0.600395 - 1.03991i) q^{44} +(-4.57207 - 4.90879i) q^{45} +(-4.04344 - 7.00343i) q^{46} +(11.1364 - 5.19301i) q^{47} +(8.29285 + 2.49405i) q^{48} +(3.83700 - 4.57275i) q^{49} +(1.19152 + 8.60226i) q^{50} +(-0.645498 + 0.723511i) q^{51} +(-2.25214 + 3.21639i) q^{52} +(-5.40763 - 5.40763i) q^{53} +(8.16510 + 3.84491i) q^{54} +(2.53282 - 0.747516i) q^{55} +(-1.70747 + 0.301072i) q^{56} +(6.85140 + 3.45167i) q^{57} +(-6.08964 + 13.0593i) q^{58} +(6.20310 + 5.20502i) q^{59} +(-1.95130 - 3.42037i) q^{60} +(10.5365 + 3.83498i) q^{61} +(13.4204 + 3.59598i) q^{62} +(-3.04462 + 0.0809482i) q^{63} +(-0.735277 - 0.424512i) q^{64} +(-8.46365 + 1.71318i) q^{65} +(-2.78972 + 2.20015i) q^{66} +(-1.29416 + 0.906180i) q^{67} +(-0.466241 + 0.326466i) q^{68} +(1.15878 + 7.98071i) q^{69} +(3.28579 + 2.17952i) q^{70} +(6.95937 + 4.01800i) q^{71} +(-4.01088 - 3.18777i) q^{72} +(-5.11087 - 1.36945i) q^{73} +(8.95674 + 3.25999i) q^{74} +(2.07347 - 8.40837i) q^{75} +(3.44984 + 2.89476i) q^{76} +(0.506721 - 1.08667i) q^{77} +(9.71449 - 6.37189i) q^{78} +(6.62789 - 1.16868i) q^{79} +(3.16454 + 10.7225i) q^{80} +(-6.14326 - 6.57726i) q^{81} +(-6.81884 - 6.81884i) q^{82} +(0.172108 - 0.245796i) q^{83} +(-1.75049 - 0.363735i) q^{84} +(-1.23782 - 0.186253i) q^{85} +(-0.845650 + 1.00781i) q^{86} +(10.4642 - 9.84768i) q^{87} +(1.82796 - 0.852391i) q^{88} +(-5.41601 - 9.38081i) q^{89} +(1.61470 + 11.5389i) q^{90} +(-1.96032 + 3.39538i) q^{91} +(-0.412590 + 4.71593i) q^{92} +(-11.1032 - 8.28768i) q^{93} +(-21.0180 - 3.70604i) q^{94} +(1.11139 + 9.84163i) q^{95} +(-5.65066 - 7.16487i) q^{96} +(-5.10194 - 0.446362i) q^{97} +(-10.0147 + 2.68342i) q^{98} +(3.39674 - 1.00764i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Introduction

L-functions

Modular forms

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