LMFDB - Embedded newform 135.2.q.a.2.4

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			2.4
Character	$\chi$	$=$	135.2
Dual form			135.2.q.a.68.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.996232 - 1.42277i) q^{2} +(-1.44830 - 0.949962i) q^{3} +(-0.347747 + 0.955427i) q^{4} +(-1.86340 - 1.23602i) q^{5} +(0.0912678 + 3.00698i) q^{6} +(0.920112 + 0.429055i) q^{7} +(-1.64960 + 0.442010i) q^{8} +(1.19514 + 2.75166i) q^{9} +O(q^{10})$	\(q+(-0.996232 - 1.42277i) q^{2} +(-1.44830 - 0.949962i) q^{3} +(-0.347747 + 0.955427i) q^{4} +(-1.86340 - 1.23602i) q^{5} +(0.0912678 + 3.00698i) q^{6} +(0.920112 + 0.429055i) q^{7} +(-1.64960 + 0.442010i) q^{8} +(1.19514 + 2.75166i) q^{9} +(0.0978025 + 3.88255i) q^{10} +(-0.759141 + 0.904709i) q^{11} +(1.41126 - 1.05340i) q^{12} +(-3.16342 - 2.21505i) q^{13} +(-0.306200 - 1.73654i) q^{14} +(1.52458 + 3.56029i) q^{15} +(3.83001 + 3.21376i) q^{16} +(0.540727 + 0.144887i) q^{17} +(2.72433 - 4.44170i) q^{18} +(-3.83587 - 2.21464i) q^{19} +(1.82892 - 1.35052i) q^{20} +(-0.925012 - 1.49547i) q^{21} +(2.04347 + 0.178781i) q^{22} +(-1.96770 - 4.21975i) q^{23} +(2.80901 + 0.926898i) q^{24} +(1.94449 + 4.60640i) q^{25} +6.70752i q^{26} +(0.883047 - 5.12057i) q^{27} +(-0.729897 + 0.729897i) q^{28} +(1.44060 - 8.17007i) q^{29} +(3.54662 - 5.71600i) q^{30} +(-7.51688 - 2.73592i) q^{31} +(0.459164 - 5.24827i) q^{32} +(1.95890 - 0.589135i) q^{33} +(-0.332549 - 0.913671i) q^{34} +(-1.18421 - 1.93678i) q^{35} +(-3.04462 + 0.184991i) q^{36} +(1.42034 - 5.30076i) q^{37} +(0.670500 + 7.66385i) q^{38} +(2.47737 + 6.21319i) q^{39} +(3.62020 + 1.21531i) q^{40} +(5.46773 - 0.964109i) q^{41} +(-1.20618 + 2.80591i) q^{42} +(0.754568 - 0.0660161i) q^{43} +(-0.600395 - 1.03991i) q^{44} +(1.17409 - 6.60466i) q^{45} +(-4.04344 + 7.00343i) q^{46} +(-5.19301 + 11.1364i) q^{47} +(-2.49405 - 8.29285i) q^{48} +(-3.83700 - 4.57275i) q^{49} +(4.61667 - 7.35561i) q^{50} +(-0.645498 - 0.723511i) q^{51} +(3.21639 - 2.25214i) 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} +(3.45167 + 6.85140i) q^{57} +(-13.0593 + 6.08964i) q^{58} +(-6.20310 + 5.20502i) q^{59} +(-3.93177 + 0.218547i) q^{60} +(10.5365 - 3.83498i) q^{61} +(3.59598 + 13.4204i) q^{62} +(-0.0809482 + 3.04462i) q^{63} +(0.735277 - 0.424512i) q^{64} +(3.15685 + 8.03758i) q^{65} +(-2.78972 - 2.20015i) q^{66} +(0.906180 - 1.29416i) q^{67} +(-0.326466 + 0.466241i) q^{68} +(-1.15878 + 7.98071i) q^{69} +(-1.57584 + 3.61434i) q^{70} +(6.95937 - 4.01800i) q^{71} +(-3.18777 - 4.01088i) q^{72} +(1.36945 + 5.11087i) q^{73} +(-8.95674 + 3.25999i) q^{74} +(1.55970 - 8.51865i) q^{75} +(3.44984 - 2.89476i) q^{76} +(-1.08667 + 0.506721i) q^{77} +(6.37189 - 9.71449i) 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} +(0.245796 - 0.172108i) q^{83} +(1.75049 - 0.363735i) q^{84} +(-0.828505 - 0.938334i) q^{85} +(-0.845650 - 1.00781i) q^{86} +(-9.84768 + 10.4642i) q^{87} +(0.852391 - 1.82796i) q^{88} +(5.41601 - 9.38081i) q^{89} +(-10.5666 + 4.90932i) q^{90} +(-1.96032 - 3.39538i) q^{91} +(4.71593 - 0.412590i) q^{92} +(8.28768 + 11.1032i) q^{93} +(21.0180 - 3.70604i) q^{94} +(4.41040 + 8.86799i) q^{95} +(-5.65066 + 7.16487i) q^{96} +(-0.446362 - 5.10194i) q^{97} +(-2.68342 + 10.0147i) 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 $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.996232	−	1.42277i	−0.704443	−	1.00605i	−0.998733	−	0.0503320i	$-0.983972\pi$
$2$	−0.996232	−	1.42277i	−0.704443	−	1.00605i	0.294290	−	0.955716i	$-0.404917\pi$
$3$	−1.44830	−	0.949962i	−0.836176	−	0.548461i
$3$	−1.44830	−	0.949962i	−0.836176	−	0.548461i
$4$	−0.347747	+	0.955427i	−0.173874	+	0.477714i
$5$	−1.86340	−	1.23602i	−0.833336	−	0.552766i
$5$	−1.86340	−	1.23602i	−0.833336	−	0.552766i
$6$	0.0912678	+	3.00698i	0.0372599	+	1.22759i
$7$	0.920112	+	0.429055i	0.347770	+	0.162168i	0.588652	−	0.808387i	$-0.299659\pi$
$7$	0.920112	+	0.429055i	0.347770	+	0.162168i	−0.240882	+	0.970554i	$0.577437\pi$
$8$	−1.64960	+	0.442010i	−0.583223	+	0.156274i
$9$	1.19514	+	2.75166i	0.398381	+	0.917220i
$10$	0.0978025	+	3.88255i	0.0309279	+	1.22777i
$11$	−0.759141	+	0.904709i	−0.228890	+	0.272780i	−0.868250	−	0.496127i	$-0.834755\pi$
$11$	−0.759141	+	0.904709i	−0.228890	+	0.272780i	0.639360	+	0.768908i	$0.279199\pi$
$12$	1.41126	−	1.05340i	0.407396	−	0.304090i
$13$	−3.16342	−	2.21505i	−0.877375	−	0.614345i	0.0457040	−	0.998955i	$-0.485447\pi$
$13$	−3.16342	−	2.21505i	−0.877375	−	0.614345i	−0.923079	+	0.384610i	$0.874336\pi$
$14$	−0.306200	−	1.73654i	−0.0818353	−	0.464111i
$15$	1.52458	+	3.56029i	0.393645	+	0.919262i
$16$	3.83001	+	3.21376i	0.957502	+	0.803439i
$17$	0.540727	+	0.144887i	0.131146	+	0.0351404i	0.323795	−	0.946127i	$-0.395041\pi$
$17$	0.540727	+	0.144887i	0.131146	+	0.0351404i	−0.192649	+	0.981268i	$0.561708\pi$
$18$	2.72433	−	4.44170i	0.642131	−	1.04692i
$19$	−3.83587	−	2.21464i	−0.880010	−	0.508074i	−0.00934815	−	0.999956i	$-0.502976\pi$
$19$	−3.83587	−	2.21464i	−0.880010	−	0.508074i	−0.870662	+	0.491882i	$0.836309\pi$
$20$	1.82892	−	1.35052i	0.408959	−	0.301985i
$21$	−0.925012	−	1.49547i	−0.201854	−	0.326339i
$22$	2.04347	+	0.178781i	0.435670	+	0.0381162i
$23$	−1.96770	−	4.21975i	−0.410294	−	0.879879i	−0.997515	−	0.0704523i	$-0.977556\pi$
$23$	−1.96770	−	4.21975i	−0.410294	−	0.879879i	0.587221	−	0.809427i	$-0.300222\pi$
$24$	2.80901	+	0.926898i	0.573387	+	0.189202i
$25$	1.94449	+	4.60640i	0.388899	+	0.921281i
$26$			6.70752i			1.31545i
$27$	0.883047	−	5.12057i	0.169942	−	0.985454i
$28$	−0.729897	+	0.729897i	−0.137938	+	0.137938i
$29$	1.44060	−	8.17007i	0.267513	−	1.51714i	−0.494268	−	0.869309i	$-0.664564\pi$
$29$	1.44060	−	8.17007i	0.267513	−	1.51714i	0.761782	−	0.647834i	$-0.224325\pi$
$30$	3.54662	−	5.71600i	0.647522	−	1.04359i
$31$	−7.51688	−	2.73592i	−1.35007	−	0.491386i	−0.437102	−	0.899412i	$-0.643995\pi$
$31$	−7.51688	−	2.73592i	−1.35007	−	0.491386i	−0.912970	+	0.408026i	$0.866217\pi$
$32$	0.459164	−	5.24827i	0.0811694	−	0.927771i
$33$	1.95890	−	0.589135i	0.341001	−	0.102555i
$34$	−0.332549	−	0.913671i	−0.0570317	−	0.156693i
$35$	−1.18421	−	1.93678i	−0.200168	−	0.327376i
$36$	−3.04462	+	0.184991i	−0.507436	+	0.0308319i
$37$	1.42034	−	5.30076i	0.233502	−	0.871440i	−0.745317	−	0.666710i	$-0.767702\pi$
$37$	1.42034	−	5.30076i	0.233502	−	0.871440i	0.978819	−	0.204730i	$-0.0656316\pi$
$38$	0.670500	+	7.66385i	0.108770	+	1.24324i
$39$	2.47737	+	6.21319i	0.396696	+	0.994906i
$40$	3.62020	+	1.21531i	0.572404	+	0.192157i
$41$	5.46773	−	0.964109i	0.853917	−	0.150569i	0.270478	−	0.962726i	$-0.412818\pi$
$41$	5.46773	−	0.964109i	0.853917	−	0.150569i	0.583438	+	0.812157i	$0.301707\pi$
$42$	−1.20618	+	2.80591i	−0.186118	+	0.432962i
$43$	0.754568	−	0.0660161i	0.115070	−	0.0100674i	−0.0294750	−	0.999566i	$-0.509384\pi$
$43$	0.754568	−	0.0660161i	0.115070	−	0.0100674i	0.144546	+	0.989498i	$0.453828\pi$
$44$	−0.600395	−	1.03991i	−0.0905129	−	0.156773i
$45$	1.17409	−	6.60466i	0.175023	−	0.984564i
$46$	−4.04344	+	7.00343i	−0.596172	+	1.03260i
$47$	−5.19301	+	11.1364i	−0.757478	+	1.62442i	0.0233932	+	0.999726i	$0.492553\pi$
$47$	−5.19301	+	11.1364i	−0.757478	+	1.62442i	−0.780872	+	0.624691i	$0.785225\pi$
$48$	−2.49405	−	8.29285i	−0.359985	−	1.19697i
$49$	−3.83700	−	4.57275i	−0.548142	−	0.653250i
$50$	4.61667	−	7.35561i	0.652896	−	1.04024i
$51$	−0.645498	−	0.723511i	−0.0903877	−	0.101312i
$52$	3.21639	−	2.25214i	0.446033	−	0.312316i
$53$	5.40763	+	5.40763i	0.742795	+	0.742795i	0.973115	−	0.230320i	$-0.0739772\pi$
$53$	5.40763	+	5.40763i	0.742795	+	0.742795i	−0.230320	+	0.973115i	$0.573977\pi$
$54$	−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
$57$	3.45167	+	6.85140i	0.457185	+	0.907490i
$58$	−13.0593	+	6.08964i	−1.71477	+	0.799609i
$59$	−6.20310	+	5.20502i	−0.807575	+	0.677636i	−0.950028	−	0.312166i	$-0.898946\pi$
$59$	−6.20310	+	5.20502i	−0.807575	+	0.677636i	0.142453	+	0.989802i	$0.454501\pi$
$60$	−3.93177	+	0.218547i	−0.507589	+	0.0282142i
$61$	10.5365	−	3.83498i	1.34906	−	0.491018i	0.436407	−	0.899749i	$-0.356251\pi$
$61$	10.5365	−	3.83498i	1.34906	−	0.491018i	0.912655	+	0.408731i	$0.134029\pi$
$62$	3.59598	+	13.4204i	0.456690	+	1.70439i
$63$	−0.0809482	+	3.04462i	−0.0101985	+	0.383586i
$64$	0.735277	−	0.424512i	0.0919096	−	0.0530640i
$65$	3.15685	+	8.03758i	0.391559	+	0.996939i
$66$	−2.78972	−	2.20015i	−0.343391	−	0.270820i
$67$	0.906180	−	1.29416i	0.110707	−	0.158107i	−0.759975	−	0.649953i	$-0.774789\pi$
$67$	0.906180	−	1.29416i	0.110707	−	0.158107i	0.870682	+	0.491846i	$0.163678\pi$
$68$	−0.326466	+	0.466241i	−0.0395898	+	0.0565401i
$69$	−1.15878	+	7.98071i	−0.139501	+	0.960764i
$70$	−1.57584	+	3.61434i	−0.188349	+	0.431996i
$71$	6.95937	−	4.01800i	0.825926	−	0.476849i	−0.0265298	−	0.999648i	$-0.508446\pi$
$71$	6.95937	−	4.01800i	0.825926	−	0.476849i	0.852456	+	0.522800i	$0.175112\pi$
$72$	−3.18777	−	4.01088i	−0.375683	−	0.472687i
$73$	1.36945	+	5.11087i	0.160282	+	0.598182i	0.998595	+	0.0529922i	$0.0168758\pi$
$73$	1.36945	+	5.11087i	0.160282	+	0.598182i	−0.838312	+	0.545190i	$0.816457\pi$
$74$	−8.95674	+	3.25999i	−1.04120	+	0.378966i
$75$	1.55970	−	8.51865i	0.180099	−	0.983649i
$76$	3.44984	−	2.89476i	0.395724	−	0.332052i
$77$	−1.08667	+	0.506721i	−0.123837	+	0.0577462i
$78$	6.37189	−	9.71449i	0.721474	−	1.09995i
$79$	−6.62789	−	1.16868i	−0.745696	−	0.131486i	−0.212126	−	0.977242i	$-0.568039\pi$
$79$	−6.62789	−	1.16868i	−0.745696	−	0.131486i	−0.533570	+	0.845756i	$0.679150\pi$
$80$	−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
$83$	0.245796	−	0.172108i	0.0269796	−	0.0188913i	−0.560009	−	0.828487i	$-0.689202\pi$
$83$	0.245796	−	0.172108i	0.0269796	−	0.0188913i	0.586988	+	0.809595i	$0.300313\pi$
$84$	1.75049	−	0.363735i	0.190994	−	0.0396868i
$85$	−0.828505	−	0.938334i	−0.0898640	−	0.101777i
$86$	−0.845650	−	1.00781i	−0.0911888	−	0.108675i
$87$	−9.84768	+	10.4642i	−1.05578	+	1.12188i
$88$	0.852391	−	1.82796i	0.0908652	−	0.194861i
$89$	5.41601	−	9.38081i	0.574096	−	0.994364i	−0.422043	−	0.906576i	$-0.638687\pi$
$89$	5.41601	−	9.38081i	0.574096	−	0.994364i	0.996139	−	0.0877879i	$-0.0279798\pi$
$90$	−10.5666	+	4.90932i	−1.11381	+	0.517488i
$91$	−1.96032	−	3.39538i	−0.205498	−	0.355932i
$92$	4.71593	−	0.412590i	0.491670	−	0.0430155i
$93$	8.28768	+	11.1032i	0.859392	+	1.15135i
$94$	21.0180	−	3.70604i	2.16784	−	0.382249i
$95$	4.41040	+	8.86799i	0.452498	+	0.909836i
$96$	−5.65066	+	7.16487i	−0.576718	+	0.731262i
$97$	−0.446362	−	5.10194i	−0.0453212	−	0.518023i	−0.984595	−	0.174853i	$-0.944055\pi$
$97$	−0.446362	−	5.10194i	−0.0453212	−	0.518023i	0.939273	−	0.343170i	$-0.111501\pi$
$98$	−2.68342	+	10.0147i	−0.271067	+	1.01163i
$99$	−3.39674	−	1.00764i	−0.341385	−	0.101272i
$100$	−5.07727	+	0.255959i	−0.507727	+	0.0255959i
$101$	−6.63190	−	18.2210i	−0.659899	−	1.81306i	−0.577393	−	0.816467i	$-0.695930\pi$
$101$	−6.63190	−	18.2210i	−0.659899	−	1.81306i	−0.0825062	−	0.996591i	$-0.526292\pi$
$102$	−0.386322	+	1.63918i	−0.0382516	+	0.162303i
$103$	1.29943	−	14.8525i	0.128036	−	1.46346i	−0.611980	−	0.790873i	$-0.709627\pi$
$103$	1.29943	−	14.8525i	0.128036	−	1.46346i	0.740016	−	0.672589i	$-0.234818\pi$
$104$	6.19746	+	2.25569i	0.607711	+	0.221189i
$105$	−0.124775	+	3.92999i	−0.0121768	+	0.383528i
$106$	2.30654	−	13.0811i	0.224031	−	1.27054i
$107$	−3.20052	+	3.20052i	−0.309406	+	0.309406i	−0.844679	−	0.535273i	$-0.820209\pi$
$107$	−3.20052	+	3.20052i	−0.309406	+	0.309406i	0.535273	+	0.844679i	$0.320209\pi$
$108$	4.58525	+	2.62435i	0.441216	+	0.252528i
$109$			10.7258i			1.02735i	0.857986	+	0.513673i	$0.171716\pi$
$109$			10.7258i			1.02735i	−0.857986	+	0.513673i	$0.828284\pi$
$110$	−3.58682	−	2.85892i	−0.341990	−	0.272587i
$111$	−7.09260	+	6.32783i	−0.673200	+	0.600611i
$112$	2.14516	+	4.60030i	0.202698	+	0.434688i
$113$	12.5744	+	1.10011i	1.18290	+	0.103490i	0.661581	−	0.749874i	$-0.269886\pi$
$113$	12.5744	+	1.10011i	1.18290	+	0.103490i	0.521316	+	0.853364i	$0.325441\pi$
$114$	6.30929	−	11.7365i	0.590919	−	1.09922i
$115$	−1.54910	+	10.2952i	−0.144454	+	0.960032i
$116$	7.30494	+	4.21751i	0.678247	+	0.391586i
$117$	2.31432	−	11.3520i	0.213959	−	1.04949i
$118$	13.5853	+	3.64016i	1.25062	+	0.335104i
$119$	0.435365	+	0.365315i	0.0399099	+	0.0334883i
$120$	−4.08864	−	5.19918i	−0.373240	−	0.474618i
$121$	1.66793	+	9.45928i	0.151630	+	0.859935i
$122$	−15.9531	−	11.1705i	−1.44432	−	1.01133i
$123$	−8.83479	−	3.79782i	−0.796606	−	0.342438i
$124$	5.22795	−	6.23043i	0.469484	−	0.559509i
$125$	2.07026	−	10.9870i	0.185170	−	0.982707i
$126$	4.41243	−	2.91798i	0.393090	−	0.259954i
$127$	17.0449	−	4.56717i	1.51249	−	0.405270i	0.595229	−	0.803556i	$-0.297061\pi$
$127$	17.0449	−	4.56717i	1.51249	−	0.405270i	0.917261	+	0.398286i	$0.130395\pi$
$128$	−10.8859	−	5.07618i	−0.962188	−	0.448676i
$129$	−1.15555	−	0.621200i	−0.101741	−	0.0546936i
$130$	8.29064	−	12.4988i	0.727138	−	1.09621i
$131$	−0.988469	+	2.71580i	−0.0863629	+	0.237280i	−0.975355	−	0.220643i	$-0.929184\pi$
$131$	−0.988469	+	2.71580i	−0.0863629	+	0.237280i	0.888992	+	0.457923i	$0.151407\pi$
$132$	−0.118328	+	2.07646i	−0.0102991	+	0.180733i
$133$	−2.57923	−	3.68352i	−0.223648	−	0.319402i
$134$	−2.74405			−0.237050
$135$	−7.97461	+	8.45018i	−0.686345	+	0.727276i
$136$	−0.956027			−0.0819787
$137$	−4.83028	−	6.89836i	−0.412679	−	0.589367i	0.557972	−	0.829860i	$-0.311580\pi$
$137$	−4.83028	−	6.89836i	−0.412679	−	0.589367i	−0.970651	+	0.240493i	$0.922691\pi$
$138$	12.5091	−	6.30196i	1.06485	−	0.536459i
$139$	3.42050	−	9.39775i	0.290123	−	0.797107i	−0.705925	−	0.708287i	$-0.749468\pi$
$139$	3.42050	−	9.39775i	0.290123	−	0.797107i	0.996048	−	0.0888198i	$-0.0283095\pi$
$140$	2.26226	−	0.457918i	0.191196	−	0.0387011i
$141$	18.1002	−	11.1957i	1.52432	−	0.942852i
$142$	−12.6498	−	5.89871i	−1.06155	−	0.495009i
$143$	4.40546	−	1.18044i	0.368403	−	0.0987133i
$144$	−4.26576	+	14.3798i	−0.355480	+	1.19831i
$145$	−12.7828	+	13.4435i	−1.06155	+	1.11642i
$146$	5.90728	−	7.04003i	0.488890	−	0.582637i
$147$	1.21318	+	10.2677i	0.100061	+	0.846867i
$148$	4.57058	+	3.20035i	0.375699	+	0.263067i
$149$	2.48868	+	14.1140i	0.203881	+	1.15626i	0.899191	+	0.437555i	$0.144156\pi$
$149$	2.48868	+	14.1140i	0.203881	+	1.15626i	−0.695311	+	0.718709i	$0.744733\pi$
$150$	−13.6739	+	6.26746i	−1.11647	+	0.511736i
$151$	4.12708	+	3.46303i	0.335857	+	0.281818i	0.795081	−	0.606503i	$-0.207428\pi$
$151$	4.12708	+	3.46303i	0.335857	+	0.281818i	−0.459224	+	0.888320i	$0.651873\pi$
$152$	7.30656	+	1.95779i	0.592640	+	0.158798i
$153$	0.247566	+	1.66106i	0.0200145	+	0.134289i
$154$	1.80352	+	1.04126i	0.145332	+	0.0839072i
$155$	10.6253	+	14.3891i	0.853442	+	1.15576i
$156$	−6.79775	+	0.206325i	−0.544255	+	0.0165193i
$157$	−7.93317	−	0.694063i	−0.633136	−	0.0553922i	−0.233930	−	0.972253i	$-0.575159\pi$
$157$	−7.93317	−	0.694063i	−0.633136	−	0.0553922i	−0.399206	+	0.916861i	$0.630714\pi$
$158$	4.94016	+	10.5942i	0.393018	+	0.842831i
$159$	−2.69482	−	12.9689i	−0.213713	−	1.02850i
$160$	−7.34258	+	9.21206i	−0.580482	+	0.728277i
$161$		−	4.72690i		−	0.372532i
$162$	15.4780	+	2.18796i	1.21607	+	0.171902i
$163$	−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
$165$	−4.37840	−	1.32346i	−0.340858	−	0.103031i
$166$	−0.489740	−	0.178251i	−0.0380112	−	0.0138349i
$167$	0.0369225	−	0.422026i	0.00285715	−	0.0326574i	−0.994632	−	0.103473i	$-0.967005\pi$
$167$	0.0369225	−	0.422026i	0.00285715	−	0.0326574i	0.997489	+	0.0708153i	$0.0225601\pi$
$168$	2.18692	+	2.05807i	0.168724	+	0.158784i
$169$	0.654517	+	1.79827i	0.0503475	+	0.138329i
$170$	−0.509648	+	2.11357i	−0.0390882	+	0.162103i
$171$	1.50952	−	13.2018i	0.115436	−	1.00957i
$172$	−0.199325	+	0.743891i	−0.0151984	+	0.0567212i
$173$	0.704144	+	8.04840i	0.0535351	+	0.611909i	0.974816	+	0.223011i	$0.0715885\pi$
$173$	0.704144	+	8.04840i	0.0535351	+	0.611909i	−0.921281	+	0.388898i	$0.872856\pi$
$174$	24.6987	+	3.58619i	1.87240	+	0.271869i
$175$	−0.187250	+	5.07270i	−0.0141548	+	0.383460i
$176$	−5.81503	+	1.02535i	−0.438325	+	0.0772885i
$177$	13.9285	−	1.64572i	1.04693	−	0.123700i
$178$	−18.7423	+	1.63974i	−1.40480	+	0.122904i
$179$	−6.38218	−	11.0543i	−0.477026	−	0.826234i	0.522627	−	0.852561i	$-0.324952\pi$
$179$	−6.38218	−	11.0543i	−0.477026	−	0.826234i	−0.999653	+	0.0263277i	$0.991619\pi$
$180$	5.90198	+	3.41851i	0.439908	+	0.254800i
$181$	−9.24880	+	16.0194i	−0.687458	+	1.19071i	0.285199	+	0.958468i	$0.407940\pi$
$181$	−9.24880	+	16.0194i	−0.687458	+	1.19071i	−0.972657	+	0.232244i	$0.925393\pi$
$182$	−2.87790	+	6.17167i	−0.213324	+	0.457474i
$183$	−18.9031	−	4.45509i	−1.39736	−	0.329330i
$184$	5.11110	+	6.09117i	0.376795	+	0.449047i
$185$	−9.19852	+	8.12186i	−0.676288	+	0.597131i
$186$	7.54080	−	22.8528i	0.552918	−	1.67565i
$187$	−0.541570	+	0.379211i	−0.0396035	+	0.0277307i
$188$	−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	0.323642	−	0.946180i	$-0.395093\pi$
$191$	4.20349	+	0.741189i	0.304154	+	0.0536306i	−0.0194882	+	0.999810i	$0.506204\pi$
$192$	−1.46817	−	0.0836642i	−0.105956	−	0.00603794i
$193$	−9.18304	+	4.28212i	−0.661010	+	0.308234i	−0.724020	−	0.689779i	$-0.757708\pi$
$193$	−9.18304	+	4.28212i	−0.661010	+	0.308234i	0.0630104	+	0.998013i	$0.479930\pi$
$194$	−6.81419	+	5.71778i	−0.489230	+	0.410513i
$195$	3.06333	−	14.6397i	0.219370	−	1.04837i
$196$	5.70324	−	2.07581i	0.407374	−	0.148272i
$197$	−3.06853	−	11.4519i	−0.218624	−	0.815916i	−0.984859	−	0.173356i	$-0.944539\pi$
$197$	−3.06853	−	11.4519i	−0.218624	−	0.815916i	0.766235	−	0.642560i	$-0.222128\pi$
$198$	1.95030	+	5.83661i	0.138602	+	0.414790i
$199$	−5.06551	+	2.92457i	−0.359084	+	0.207317i	−0.668679	−	0.743551i	$-0.733140\pi$
$199$	−5.06551	+	2.92457i	−0.359084	+	0.207317i	0.309595	+	0.950869i	$0.399807\pi$
$200$	−5.24372	−	6.73925i	−0.370787	−	0.476537i
$201$	−2.54182	+	1.01349i	−0.179286	+	0.0714863i
$202$	−19.3173	+	27.5880i	−1.35916	+	1.94108i
$203$	4.83093	−	6.89928i	0.339065	−	0.484234i
$204$	0.915732	−	0.365127i	0.0641141	−	0.0255640i
$205$	−11.3802	−	4.96173i	−0.794829	−	0.346542i
$206$	−22.4262	+	12.9478i	−1.56251	+	0.902114i
$207$	9.25963	−	10.4577i	0.643589	−	0.726857i
$208$	−4.99729	−	18.6501i	−0.346500	−	1.29315i
$209$	4.91558	−	1.78912i	0.340018	−	0.123756i
$210$	5.71577	−	3.73766i	0.394426	−	0.257923i
$211$	−5.44373	+	4.56783i	−0.374762	+	0.314462i	−0.810642	−	0.585542i	$-0.800882\pi$
$211$	−5.44373	+	4.56783i	−0.374762	+	0.314462i	0.435880	+	0.900005i	$0.356437\pi$
$212$	−7.04709	+	3.28611i	−0.483996	+	0.225691i
$213$	−13.8962	−	0.791880i	−0.952152	−	0.0542587i
$214$	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
$218$	15.2603	−	10.6854i	1.03356	−	0.723707i
$219$	2.87176	−	8.70300i	0.194055	−	0.588094i
$220$	−0.166585	+	2.67988i	−0.0112311	+	0.180677i
$221$	−1.38961	−	1.65608i	−0.0934756	−	0.111400i
$222$	16.0689	+	3.78713i	1.07847	+	0.254175i
$223$	0.936774	−	2.00892i	0.0627310	−	0.134527i	−0.872443	−	0.488716i	$-0.837465\pi$
$223$	0.936774	−	2.00892i	0.0627310	−	0.134527i	0.935174	+	0.354189i	$0.115243\pi$
$224$	2.67428	−	4.63199i	0.178683	−	0.309488i
$225$	−10.3513	+	10.8559i	−0.690087	+	0.723726i
$226$	−10.9618	−	18.9864i	−0.729167	−	1.26295i
$227$	9.57526	−	0.837726i	0.635532	−	0.0556018i	0.235163	−	0.971956i	$-0.424438\pi$
$227$	9.57526	−	0.837726i	0.635532	−	0.0556018i	0.400369	+	0.916354i	$0.368882\pi$
$228$	−7.74632	+	0.915263i	−0.513013	+	0.0606147i
$229$	9.88832	−	1.74358i	0.653438	−	0.115219i	0.162906	−	0.986642i	$-0.447913\pi$
$229$	9.88832	−	1.74358i	0.653438	−	0.115219i	0.490533	+	0.871423i	$0.336802\pi$
$230$	16.1909	−	8.05240i	1.06760	−	0.530959i
$231$	2.05518	+	0.298408i	0.135221	+	0.0196338i
$232$	1.23483	+	14.1141i	0.0810703	+	0.926638i
$233$	−3.11576	+	11.6282i	−0.204120	+	0.761788i	0.785595	+	0.618741i	$0.212357\pi$
$233$	−3.11576	+	11.6282i	−0.204120	+	0.761788i	−0.989716	+	0.143047i	$0.954310\pi$
$234$	−18.4568	+	8.01644i	−1.20656	+	0.524051i
$235$	23.4415	−	14.3329i	1.52916	−	0.934978i
$236$	−2.81591	−	7.73664i	−0.183300	−	0.503613i
$237$	8.48897	+	7.98884i	0.551418	+	0.518931i
$238$	0.0860330	−	0.983361i	0.00557669	−	0.0637418i
$239$	1.69787	+	0.617976i	0.109826	+	0.0399735i	0.396349	−	0.918100i	$-0.370277\pi$
$239$	1.69787	+	0.617976i	0.109826	+	0.0399735i	−0.286522	+	0.958074i	$0.592499\pi$
$240$	−5.60275	+	18.5356i	−0.361656	+	1.19647i
$241$	−2.79425	+	15.8470i	−0.179994	+	1.02079i	0.752227	+	0.658904i	$0.228980\pi$
$241$	−2.79425	+	15.8470i	−0.179994	+	1.02079i	−0.932221	+	0.361890i	$0.882131\pi$
$242$	11.7967	−	11.7967i	0.758321	−	0.758321i
$243$	15.1454	−	3.68997i	0.971580	−	0.236712i
$244$			11.4005i			0.729840i
$245$	1.49781	+	13.2635i	0.0956919	+	0.847372i
$246$	3.39808	+	16.3534i	0.216654	+	1.04265i
$247$	7.22894	+	15.5025i	0.459966	+	0.986401i
$248$	13.6092	+	1.19065i	0.864184	+	0.0756063i
$249$	−0.519483	+	0.0157674i	−0.0329209	+	0.000999216i
$250$	−17.6944	+	8.00010i	−1.11909	+	0.505971i
$251$	−15.8224	−	9.13506i	−0.998700	−	0.576600i	−0.0908365	−	0.995866i	$-0.528954\pi$
$251$	−15.8224	−	9.13506i	−0.998700	−	0.576600i	−0.907863	+	0.419266i	$0.862287\pi$
$252$	−2.88076	−	1.13610i	−0.181471	−	0.0715674i
$253$	5.31141	+	1.42319i	0.333926	+	0.0894751i
$254$	−23.4787	−	19.7010i	−1.47318	−	1.23615i
$255$	0.308542	+	2.14604i	0.0193216	+	0.134390i
$256$	3.32781	+	18.8729i	0.207988	+	1.17956i
$257$	−11.6141	−	8.13228i	−0.724468	−	0.507278i	0.152215	−	0.988347i	$-0.451359\pi$
$257$	−11.6141	−	8.13228i	−0.724468	−	0.507278i	−0.876682	+	0.481070i	$0.840248\pi$
$258$	0.267377	+	2.26294i	0.0166461	+	0.140885i
$259$	3.58119	−	4.26790i	0.222524	−	0.265194i
$260$	−8.77711	+	0.221098i	−0.544333	+	0.0137119i
$261$	24.2030	−	5.80035i	1.49813	−	0.359033i
$262$	4.84869	−	1.29920i	0.299553	−	0.0802650i
$263$	3.32553	+	1.55072i	0.205061	+	0.0956215i	0.522436	−	0.852679i	$-0.325023\pi$
$263$	3.32553	+	1.55072i	0.205061	+	0.0956215i	−0.317375	+	0.948300i	$0.602801\pi$
$264$	−2.97101	+	1.83769i	−0.182853	+	0.113102i
$265$	−3.39260	−	16.7605i	−0.208406	−	1.02959i
$266$	−2.67128	+	7.33929i	−0.163787	+	0.450000i
$267$	−16.7554	+	8.44121i	−1.02542	+	0.516594i
$268$	0.921353	+	1.31583i	0.0562806	+	0.0803770i
$269$	11.1677			0.680904			0.340452	−	0.940262i	$-0.389420\pi$
$269$	11.1677			0.680904			0.340452	+	0.940262i	$0.389420\pi$
$270$	19.9672	+	2.92766i	1.21517	+	0.178172i
$271$	23.0328			1.39914			0.699572	−	0.714562i	$-0.253374\pi$
$271$	23.0328			1.39914			0.699572	+	0.714562i	$0.253374\pi$
$272$	1.60536	+	2.29269i	0.0973390	+	0.139015i
$273$	−0.386347	+	6.77976i	−0.0233828	+	0.410330i
$274$	−5.00267	+	13.7447i	−0.302223	+	0.830350i
$275$	−5.64360	−	1.73771i	−0.340322	−	0.104788i
$276$	−7.22202	−	3.88240i	−0.434715	−	0.233693i
$277$	11.2752	+	5.25770i	0.677460	+	0.315905i	0.730721	−	0.682676i	$-0.239184\pi$
$277$	11.2752	+	5.25770i	0.677460	+	0.315905i	−0.0532613	+	0.998581i	$0.516962\pi$
$278$	−16.7784	+	4.49577i	−1.00630	+	0.269638i
$279$	−1.45543	−	23.9537i	−0.0871343	−	1.43407i
$280$	2.80955	+	2.67149i	0.167903	+	0.159652i
$281$	5.39196	−	6.42589i	0.321657	−	0.383336i	−0.580850	−	0.814011i	$-0.697280\pi$
$281$	5.39196	−	6.42589i	0.321657	−	0.383336i	0.902507	+	0.430674i	$0.141724\pi$
$282$	−33.9610	−	14.5989i	−2.02235	−	0.869349i
$283$	9.88404	+	6.92088i	0.587545	+	0.411404i	0.829195	−	0.558960i	$-0.188799\pi$
$283$	9.88404	+	6.92088i	0.587545	+	0.411404i	−0.241649	+	0.970364i	$0.577688\pi$
$284$	1.41880	+	8.04642i	0.0841904	+	0.477467i
$285$	2.03667	−	17.0332i	0.120642	−	1.00896i
$286$	−6.06835	−	5.09195i	−0.358829	−	0.301093i
$287$	5.44459	+	1.45887i	0.321384	+	0.0861145i
$288$	14.9902	−	5.00897i	0.883306	−	0.295156i
$289$	−14.4510	−	8.34331i	−0.850061	−	0.490783i
$290$	31.8615	+	4.79415i	1.87097	+	0.281522i
$291$	−4.20018	+	7.81316i	−0.246219	+	0.458015i
$292$	−5.35929	−	0.468877i	−0.313629	−	0.0274390i
$293$	−9.09195	−	19.4978i	−0.531157	−	1.13907i	−0.970577	−	0.240789i	$-0.922594\pi$
$293$	−9.09195	−	19.4978i	−0.531157	−	1.13907i	0.439420	−	0.898282i	$-0.355184\pi$
$294$	13.4000	−	11.9551i	0.781502	−	0.697235i
$295$	17.9924	−	2.03184i	1.04756	−	0.118298i
$296$			9.37196i			0.544734i
$297$	3.96227	+	4.68614i	0.229914	+	0.271917i
$298$	17.6016	−	17.6016i	1.01964	−	1.01964i
$299$	−3.12229	+	17.7074i	−0.180567	+	1.02405i
$300$	7.59657	+	4.45251i	0.438588	+	0.257066i
$301$	0.722611	+	0.263009i	0.0416506	+	0.0151596i
$302$	0.815557	−	9.32186i	0.0469301	−	0.536413i
$303$	−7.70428	+	32.6895i	−0.442599	+	1.87796i
$304$	−7.57410	−	20.8097i	−0.434404	−	1.19352i
$305$	−24.3738	−	5.87729i	−1.39564	−	0.336533i
$306$	2.11667	−	2.00703i	0.121002	−	0.114734i
$307$	3.20074	−	11.9453i	0.182676	−	0.681757i	−0.812440	−	0.583045i	$-0.801861\pi$
$307$	3.20074	−	11.9453i	0.182676	−	0.681757i	0.995116	−	0.0987117i	$-0.0314722\pi$
$308$	−0.106250	−	1.21444i	−0.00605414	−	0.0691992i
$309$	−15.9913	+	20.2765i	−0.909713	+	1.15349i
$310$	9.88717	−	29.4522i	0.561553	−	1.67277i
$311$	−13.5294	+	2.38560i	−0.767181	+	0.135275i	−0.543524	−	0.839393i	$-0.682910\pi$
$311$	−13.5294	+	2.38560i	−0.767181	+	0.135275i	−0.223656	+	0.974668i	$0.571799\pi$
$312$	−6.83296	−	9.15427i	−0.386840	−	0.518259i
$313$	29.7347	−	2.60145i	1.68071	−	0.147043i	0.793548	−	0.608507i	$-0.208231\pi$
$313$	29.7347	−	2.60145i	1.68071	−	0.147043i	0.887159	+	0.461465i	$0.152676\pi$
$314$	6.91579	+	11.9785i	0.390281	+	0.675986i
$315$	3.91406	−	5.57328i	0.220532	−	0.314019i
$316$	3.42141	−	5.92606i	0.192470	−	0.333367i
$317$	9.04044	−	19.3873i	0.507762	−	1.08890i	−0.470666	−	0.882311i	$-0.655986\pi$
$317$	9.04044	−	19.3873i	0.507762	−	1.08890i	0.978428	−	0.206588i	$-0.0662358\pi$
$318$	−15.7671	+	16.7542i	−0.884173	+	0.939526i
$319$	6.29792	+	7.50556i	0.352616	+	0.420231i
$320$	−1.89482	−	0.117785i	−0.105924	−	0.00658435i
$321$	7.67568	−	1.59494i	0.428415	−	0.0890208i
$322$	−6.72527	+	4.70909i	−0.374785	+	0.262427i
$323$	−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
$327$	10.1891	−	15.5342i	0.563460	−	0.859043i
$328$	−8.59345	+	4.00719i	−0.474494	+	0.221260i
$329$	−9.55630	+	8.01869i	−0.526856	+	0.442085i
$330$	2.47893	+	7.54791i	0.136460	+	0.415499i
$331$	−24.1329	+	8.78365i	−1.32646	+	0.482793i	−0.905524	−	0.424296i	$-0.860522\pi$
$331$	−24.1329	+	8.78365i	−1.32646	+	0.482793i	−0.420939	+	0.907089i	$0.638299\pi$
$332$	0.0789621	+	0.294691i	0.00433361	+	0.0161732i
$333$	16.2834	−	2.42689i	0.892325	−	0.132993i
$334$	−0.637228	+	0.367904i	−0.0348676	+	0.0201308i
$335$	−3.28818	+	1.29147i	−0.179653	+	0.0705606i
$336$	1.26328	−	8.70043i	0.0689178	−	0.474648i
$337$	0.545344	−	0.778831i	0.0297068	−	0.0424256i	−0.804024	−	0.594597i	$-0.797312\pi$
$337$	0.545344	−	0.778831i	0.0297068	−	0.0424256i	0.833731	+	0.552171i	$0.186201\pi$
$338$	1.90647	−	2.72272i	0.103698	−	0.148096i
$339$	−17.1664	−	13.5385i	−0.932350	−	0.735309i
$340$	1.18462	−	0.465273i	0.0642451	−	0.0252330i
$341$	8.18159	−	4.72364i	0.443058	−	0.255800i
$342$	−20.2870	+	11.0044i	−1.09699	+	0.595049i
$343$	−3.40783	−	12.7182i	−0.184006	−	0.686718i
$344$	−1.21556	+	0.442427i	−0.0655385	+	0.0238540i
$345$	12.0236	−	13.4389i	0.647329	−	0.723528i
$346$	10.7495	−	9.01991i	0.577897	−	0.484913i
$347$	−1.84693	+	0.861237i	−0.0991483	+	0.0462336i	−0.471560	−	0.881834i	$-0.656309\pi$
$347$	−1.84693	+	0.861237i	−0.0991483	+	0.0462336i	0.372411	+	0.928068i	$0.378531\pi$
$348$	−6.57327	−	13.0476i	−0.352364	−	0.699426i
$349$	−13.3172	−	2.34817i	−0.712851	−	0.125695i	−0.194549	−	0.980893i	$-0.562324\pi$
$349$	−13.3172	−	2.34817i	−0.712851	−	0.125695i	−0.518302	+	0.855198i	$0.673436\pi$
$350$	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
$353$	−6.11610	+	4.28254i	−0.325527	+	0.227936i	−0.724903	−	0.688851i	$-0.758116\pi$
$353$	−6.11610	+	4.28254i	−0.325527	+	0.227936i	0.399376	+	0.916787i	$0.369227\pi$
$354$	−16.2175	−	18.1775i	−0.861951	−	0.966125i
$355$	−17.9344	−	1.11483i	−0.951860	−	0.0591689i
$356$	7.07928	+	8.43675i	0.375201	+	0.447147i
$357$	−0.283504	−	0.942665i	−0.0150046	−	0.0498911i
$358$	−9.36950	+	20.0930i	−0.495193	+	1.06195i
$359$	−4.40107	+	7.62287i	−0.232279	+	0.402320i	−0.958479	−	0.285165i	$-0.907952\pi$
$359$	−4.40107	+	7.62287i	−0.232279	+	0.402320i	0.726199	+	0.687484i	$0.241285\pi$
$360$	0.982543	+	11.4140i	0.0517846	+	0.601572i
$361$	0.309285	+	0.535697i	0.0162782	+	0.0281946i
$362$	32.0058	−	2.80015i	1.68219	−	0.147172i
$363$	6.57030	−	15.2843i	0.344851	−	0.802220i
$364$	3.92573	−	0.692213i	0.205764	−	0.0362818i
$365$	3.76532	−	11.2163i	0.197086	−	0.587086i
$366$	12.4933	+	31.3330i	0.653036	+	1.63780i
$367$	−2.37893	−	27.1913i	−0.124179	−	1.41938i	−0.761194	−	0.648524i	$-0.775387\pi$
$367$	−2.37893	−	27.1913i	−0.124179	−	1.41938i	0.637015	−	0.770852i	$-0.280169\pi$
$368$	6.02494	−	22.4854i	0.314072	−	1.17213i
$369$	9.18763	+	13.8931i	0.478289	+	0.723246i
$370$	20.7194	+	4.99609i	1.07715	+	0.259734i
$371$	2.65545	+	7.29580i	0.137864	+	0.378779i
$372$	−13.4903	+	4.05717i	−0.699440	+	0.210354i
$373$	1.05951	−	12.1103i	0.0548594	−	0.627046i	−0.918143	−	0.396250i	$-0.870311\pi$
$373$	1.05951	−	12.1103i	0.0548594	−	0.627046i	0.973002	−	0.230796i	$-0.0741331\pi$
$374$	1.07906	+	0.392745i	0.0557968	+	0.0203084i
$375$	−13.4356	+	13.9458i	−0.693811	+	0.720158i
$376$	3.64399	−	20.6661i	0.187924	−	1.06577i
$377$	−22.6543	+	22.6543i	−1.16676	+	1.16676i
$378$	−9.16248	+	0.0344665i	−0.471267	+	0.00177277i
$379$			22.6602i			1.16398i	0.813198	+	0.581988i	$0.197725\pi$
$379$			22.6602i			1.16398i	−0.813198	+	0.581988i	$0.802275\pi$
$380$	−10.0064	+	1.13000i	−0.513319	+	0.0579680i
$381$	−29.0248	−	9.57738i	−1.48698	−	0.490664i
$382$	−3.13312	−	6.71899i	−0.160304	−	0.343773i
$383$	−18.9950	−	1.66185i	−0.970601	−	0.0849166i	−0.409186	−	0.912451i	$-0.634187\pi$
$383$	−18.9950	−	1.66185i	−0.970601	−	0.0849166i	−0.561415	+	0.827534i	$0.689743\pi$
$384$	10.9439	+	17.6930i	0.558478	+	0.902894i
$385$	2.65121	+	0.398923i	0.135118	+	0.0203310i
$386$	15.2409	+	8.79934i	0.775741	+	0.447874i
$387$	1.08347	+	1.99741i	0.0550759	+	0.101534i
$388$	5.02975	+	1.34772i	0.255347	+	0.0684200i
$389$	−11.9485	−	10.0260i	−0.605814	−	0.508338i	0.287495	−	0.957782i	$-0.407178\pi$
$389$	−11.9485	−	10.0260i	−0.605814	−	0.508338i	−0.893309	+	0.449444i	$0.851622\pi$
$390$	−23.8807	+	10.2262i	−1.20925	+	0.517821i
$391$	−0.452602	−	2.56683i	−0.0228890	−	0.129810i
$392$	8.35072	+	5.84724i	0.421775	+	0.295330i
$393$	4.01150	−	2.99428i	0.202354	−	0.151041i
$394$	−13.2364	+	15.7746i	−0.666842	+	0.794712i
$395$	10.9059	+	10.3699i	0.548734	+	0.521768i
$396$	2.14393	−	2.89493i	0.107737	−	0.145476i
$397$	−8.59405	+	2.30277i	−0.431323	+	0.115573i	−0.467947	−	0.883756i	$-0.655006\pi$
$397$	−8.59405	+	2.30277i	−0.431323	+	0.115573i	0.0366240	+	0.999329i	$0.488340\pi$
$398$	9.20740	+	4.29348i	0.461525	+	0.215213i
$399$	0.236291	+	7.78501i	0.0118293	+	0.389738i
$400$	−7.35644	+	23.8917i	−0.367822	+	1.19458i
$401$	−0.377837	+	1.03810i	−0.0188683	+	0.0518401i	−0.948769	−	0.315970i	$-0.897670\pi$
$401$	−0.377837	+	1.03810i	−0.0188683	+	0.0518401i	0.929901	+	0.367810i	$0.119892\pi$
$402$	3.97421	+	2.60675i	0.198216	+	0.130013i
$403$	17.7189	+	25.3051i	0.882639	+	1.26054i
$404$	19.7151			0.980861
$405$	19.5770	−	4.66282i	0.972788	−	0.231697i
$406$	−14.6288			−0.726015
$407$	3.71742	+	5.30902i	0.184265	+	0.263158i
$408$	1.38461	+	0.908190i	0.0685486	+	0.0449621i
$409$	0.248916	−	0.683891i	0.0123081	−	0.0338162i	−0.933386	−	0.358873i	$-0.883161\pi$
$409$	0.248916	−	0.683891i	0.0123081	−	0.0338162i	0.945695	+	0.325057i	$0.105383\pi$
$410$	4.27796	+	21.1344i	0.211273	+	1.04376i
$411$	0.442517	+	14.5795i	0.0218277	+	0.719153i
$412$	13.7386	+	6.40643i	0.676854	+	0.315622i
$413$	−7.94079	+	2.12773i	−0.390741	+	0.104699i
$414$	−24.1036	−	2.75605i	−1.18463	−	0.135452i
$415$	−0.670746	+	0.0168963i	−0.0329256	+	0.000829406i
$416$	−13.0777	+	15.5854i	−0.641187	+	0.764137i
$417$	−13.8814	+	10.3614i	−0.679776	+	0.507401i
$418$	−7.44256	−	5.21134i	−0.364028	−	0.254895i
$419$	3.40845	+	19.3303i	0.166514	+	0.944347i	0.947490	+	0.319786i	$0.103611\pi$
$419$	3.40845	+	19.3303i	0.166514	+	0.944347i	−0.780976	+	0.624561i	$0.785278\pi$
$420$	−3.71143	−	1.48586i	−0.181099	−	0.0725024i
$421$	−8.09926	−	6.79608i	−0.394734	−	0.331221i	0.423720	−	0.905793i	$-0.360724\pi$
$421$	−8.09926	−	6.79608i	−0.394734	−	0.331221i	−0.818454	+	0.574572i	$0.805168\pi$
$422$	11.9222	+	3.19454i	0.580362	+	0.155508i
$423$	−36.8501	−	0.979745i	−1.79171	−	0.0476368i
$424$	−11.3107	−	6.53022i	−0.549295	−	0.317135i
$425$	0.384031	+	2.77254i	0.0186282	+	0.134488i
$426$	12.7172	+	20.5600i	0.616150	+	0.996133i
$427$	11.3402	+	0.992138i	0.548790	+	0.0480129i
$428$	−1.94489	−	4.17083i	−0.0940099	−	0.201605i
$429$	−7.50180	−	2.47539i	−0.362190	−	0.119513i
$430$	0.330109	+	2.92319i	0.0159193	+	0.140969i
$431$			16.6095i			0.800052i	0.916504	+	0.400026i	$0.130999\pi$
$431$			16.6095i			0.800052i	−0.916504	+	0.400026i	$0.869001\pi$
$432$	19.8383	−	16.7739i	0.954473	−	0.807036i
$433$	−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
$435$	31.2841	−	7.32697i	1.49996	−	0.351301i
$436$	−10.2477	−	3.72987i	−0.490778	−	0.178628i
$437$	−1.79738	+	20.5442i	−0.0859805	+	0.982762i
$438$	−15.2433	+	4.58437i	−0.728352	+	0.219050i
$439$	−4.05583	−	11.1433i	−0.193574	−	0.531840i	0.804495	−	0.593960i	$-0.202436\pi$
$439$	−4.05583	−	11.1433i	−0.193574	−	0.531840i	−0.998069	+	0.0621195i	$0.980214\pi$
$440$	−3.84774	+	2.35264i	−0.183434	+	0.112158i
$441$	7.99690	−	16.0232i	0.380805	−	0.763010i
$442$	−0.971835	+	3.62694i	−0.0462255	+	0.172516i
$443$	−1.94169	−	22.1937i	−0.0922527	−	1.05445i	−0.891369	−	0.453277i	$-0.850255\pi$
$443$	−1.94169	−	22.1937i	−0.0922527	−	1.05445i	0.799117	−	0.601176i	$-0.205301\pi$
$444$	−3.57935	−	8.97695i	−0.169868	−	0.426027i
$445$	−21.6871	+	10.7858i	−1.02807	+	0.511298i
$446$	−3.79147	+	0.668538i	−0.179531	+	0.0316562i
$447$	9.80342	−	22.8055i	0.463686	−	1.07866i
$448$	0.858676	−	0.0751244i	0.0405686	−	0.00354930i
$449$	−2.63657	−	4.56667i	−0.124427	−	0.215514i	0.797082	−	0.603872i	$-0.206376\pi$
$449$	−2.63657	−	4.56667i	−0.124427	−	0.215514i	−0.921509	+	0.388357i	$0.873043\pi$
$450$	25.7577	+	3.91250i	1.21423	+	0.184437i
$451$	−3.27855	+	5.67861i	−0.154381	+	0.267395i
$452$	−5.42378	+	11.6313i	−0.255113	+	0.547092i
$453$	−2.68750	−	8.93608i	−0.126270	−	0.419854i
$454$	−10.7311	−	12.7888i	−0.503634	−	0.600208i
$455$	−0.543908	+	8.74994i	−0.0254988	+	0.410203i
$456$	−8.72227	−	9.77642i	−0.408458	−	0.457823i
$457$	7.87211	−	5.51211i	0.368242	−	0.257846i	−0.374779	−	0.927114i	$-0.622281\pi$
$457$	7.87211	−	5.51211i	0.368242	−	0.257846i	0.743021	+	0.669269i	$0.233392\pi$
$458$	−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	0.414418	−	0.910087i	$-0.363985\pi$
$461$	10.5760	+	1.86484i	0.492575	+	0.0868543i	0.0781574	+	0.996941i	$0.475096\pi$
$462$	−1.62287	−	3.22133i	−0.0755029	−	0.149870i
$463$	32.4518	−	15.1325i	1.50816	−	0.703268i	0.519647	−	0.854381i	$-0.326064\pi$
$463$	32.4518	−	15.1325i	1.50816	−	0.703268i	0.988516	+	0.151113i	$0.0482859\pi$
$464$	31.7741	−	26.6617i	1.47508	−	1.23774i
$465$	−1.71943	−	30.9334i	−0.0797366	−	1.43450i
$466$	19.6482	−	7.15137i	0.910187	−	0.331281i
$467$	6.32261	+	23.5963i	0.292575	+	1.09191i	0.943124	+	0.332441i	$0.107872\pi$
$467$	6.32261	+	23.5963i	0.292575	+	1.09191i	−0.650549	+	0.759465i	$0.725461\pi$
$468$	10.0412	+	6.15878i	0.464153	+	0.284690i
$469$	1.38905	−	0.801970i	0.0641405	−	0.0370315i
$470$	−43.7456	−	19.0729i	−2.01784	−	0.879768i
$471$	10.8303	+	8.54143i	0.499033	+	0.393568i
$472$	7.93199	−	11.3280i	0.365099	−	0.521416i
$473$	−0.513098	+	0.732780i	−0.0235923	+	0.0336933i
$474$	2.90927	−	20.0366i	0.133627	−	0.920310i
$475$	2.74271	−	21.9759i	0.125844	−	1.00833i
$476$	−0.500429	+	0.288923i	−0.0229371	+	0.0132427i
$477$	−8.41706	+	21.3429i	−0.385391	+	0.977222i
$478$	−0.812242	−	3.03133i	−0.0371511	−	0.138650i
$479$	38.3549	−	13.9601i	1.75248	−	0.637851i	0.752692	−	0.658373i	$-0.228755\pi$
$479$	38.3549	−	13.9601i	1.75248	−	0.637851i	0.999789	+	0.0205215i	$0.00653265\pi$
$480$	19.3854	−	6.36665i	0.884817	−	0.290597i
$481$	−16.2346	+	13.6224i	−0.740233	+	0.621129i
$482$	25.3303	−	11.8117i	1.15376	−	0.538009i
$483$	−4.49037	+	6.84597i	−0.204319	+	0.311502i
$484$	−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	$-0.521757\pi$
$488$	−15.6860	+	10.9834i	−0.710070	+	0.497196i
$489$	27.2039	−	5.65273i	1.23020	−	0.255625i
$490$	17.3787	−	15.3445i	0.785087	−	0.693195i
$491$	−3.19936	−	3.81285i	−0.144385	−	0.172071i	0.689005	−	0.724756i	$-0.258048\pi$
$491$	−3.19936	−	3.81285i	−0.144385	−	0.172071i	−0.833390	+	0.552685i	$0.813603\pi$
$492$	6.70081	−	7.12031i	0.302096	−	0.321009i
$493$	1.96271	−	4.20905i	0.0883962	−	0.189566i
$494$	14.8548	−	25.7292i	0.668347	−	1.15761i
$495$	5.08400	+	6.07608i	0.228509	+	0.273099i
$496$	−19.9971	−	34.6360i	−0.897897	−	1.55520i
$497$	8.12735	−	0.711051i	0.364561	−	0.0318950i
$498$	0.539959	+	0.723395i	0.0241961	+	0.0324161i
$499$	−6.36453	+	1.12224i	−0.284916	+	0.0502383i	−0.314280	−	0.949330i	$-0.601763\pi$
$499$	−6.36453	+	1.12224i	−0.284916	+	0.0502383i	0.0293640	+	0.999569i	$0.490652\pi$
$500$	9.77735	+	5.79868i	0.437256	+	0.259325i
$501$	−0.454384	+	0.576145i	−0.0203004	+	0.0257403i
$502$	2.76571	+	31.6122i	0.123440	+	1.41092i
$503$	6.62040	−	24.7077i	0.295189	−	1.10166i	−0.645878	−	0.763441i	$-0.723509\pi$
$503$	6.62040	−	24.7077i	0.295189	−	1.10166i	0.941067	−	0.338220i	$-0.109825\pi$
$504$	−1.21222	−	5.05819i	−0.0539965	−	0.225310i
$505$	−10.1637	+	42.1501i	−0.452279	+	1.87566i
$506$	−3.26654	−	8.97473i	−0.145215	−	0.398975i
$507$	0.760353	−	3.22620i	0.0337684	−	0.143281i
$508$	−1.56372	+	17.8734i	−0.0693788	+	0.793003i
$509$	22.5637	+	8.21250i	1.00012	+	0.364013i	0.789630	−	0.613584i	$-0.210273\pi$
$509$	22.5637	+	8.21250i	1.00012	+	0.364013i	0.210487	+	0.977597i	$0.432495\pi$
$510$	2.74593	−	2.57693i	0.121592	−	0.114109i
$511$	−0.932796	+	5.29015i	−0.0412644	+	0.234022i
$512$	6.55000	−	6.55000i	0.289472	−	0.289472i
$513$	−14.7275	+	17.6862i	−0.650234	+	0.780866i
$514$			24.6258i			1.08620i
$515$	−20.7794	+	26.0700i	−0.915650	+	1.14878i
$516$	0.995351	−	0.888026i	0.0438179	−	0.0390932i
$517$	−6.13302	−	13.1523i	−0.269730	−	0.578438i
$518$	−9.63992	−	0.843383i	−0.423554	−	0.0370561i
$519$	6.62587	−	12.3254i	0.290843	−	0.541025i
$520$	−8.76024	−	11.8635i	−0.384162	−	0.520247i
$521$	10.1059	+	5.83464i	0.442747	+	0.255620i	0.704762	−	0.709444i	$-0.251054\pi$
$521$	10.1059	+	5.83464i	0.442747	+	0.255620i	−0.262015	+	0.965064i	$0.584387\pi$
$522$	−32.3643	−	28.6567i	−1.41655	−	1.25427i
$523$	33.8581	+	9.07224i	1.48051	+	0.396701i	0.906521	−	0.422162i	$-0.138728\pi$
$523$	33.8581	+	9.07224i	1.48051	+	0.396701i	0.573989	+	0.818863i	$0.305395\pi$
$524$	−2.25101	−	1.88882i	−0.0983358	−	0.0825135i
$525$	5.09007	−	7.16891i	0.222149	−	0.312877i
$526$	−1.10669	−	6.27633i	−0.0482539	−	0.273661i
$527$	−3.66818	−	2.56849i	−0.159789	−	0.111885i
$528$	9.39595	+	4.03905i	0.408906	+	0.175777i
$529$	0.849663	−	1.01259i	0.0369419	−	0.0440256i
$530$	−20.4665	+	21.5242i	−0.889008	+	0.934954i
$531$	−21.7360	−	10.8481i	−0.943264	−	0.470767i
$532$	4.41626	−	1.18333i	0.191469	−	0.0513040i
$533$	−19.4323	−	9.06143i	−0.841706	−	0.392494i
$534$	28.7022	+	15.4297i	1.24206	+	0.667706i
$535$	9.91975	−	2.00792i	0.428868	−	0.0868100i
$536$	−0.922806	+	2.53539i	−0.0398591	+	0.109512i
$537$	−1.25782	+	22.0727i	−0.0542789	+	0.952507i
$538$	−11.1256	−	15.8890i	−0.479658	−	0.685022i
$539$	7.04983			0.303658
$540$	−5.30039	−	10.5577i	−0.228092	−	0.454330i
$541$	32.8530			1.41246			0.706230	−	0.707983i	$-0.250394\pi$
$541$	32.8530			1.41246			0.706230	+	0.707983i	$0.250394\pi$
$542$	−22.9460	−	32.7703i	−0.985617	−	1.40761i
$543$	28.6129	−	14.4149i	1.22790	−	0.618602i
$544$	1.00869	−	2.77135i	0.0432472	−	0.118821i
$545$	13.2574	−	19.9864i	0.567883	−	0.856125i
$546$	10.0309	−	6.20453i	0.429283	−	0.265529i
$547$	40.1294	+	18.7126i	1.71581	+	0.800094i	0.994170	+	0.107823i	$0.0343881\pi$
$547$	40.1294	+	18.7126i	1.71581	+	0.800094i	0.721638	+	0.692271i	$0.243390\pi$
$548$	8.27060	−	2.21610i	0.353302	−	0.0946671i
$549$	23.1452	+	24.4095i	0.987813	+	1.04177i
$550$	3.14998	+	9.76069i	0.134316	+	0.416197i
$551$	−23.6198	+	28.1489i	−1.00624	+	1.19918i
$552$	−1.61602	−	13.6772i	−0.0687824	−	0.582140i
$553$	−5.59698	−	3.91904i	−0.238008	−	0.166655i
$554$	−3.75221	−	21.2799i	−0.159416	−	0.904094i
$555$	21.0377	−	3.02464i	0.892999	−	0.128389i
$556$	7.78940	+	6.53608i	0.330344	+	0.277192i
$557$	−36.8537	−	9.87492i	−1.56154	−	0.418414i	−0.628391	−	0.777898i	$-0.716286\pi$
$557$	−36.8537	−	9.87492i	−1.56154	−	0.418414i	−0.933151	+	0.359484i	$0.882953\pi$
$558$	−32.6306	+	25.9342i	−1.38136	+	1.09788i
$559$	−2.53324	−	1.46257i	−0.107145	−	0.0618601i
$560$	1.68880	−	11.2237i	0.0713650	−	0.474286i
$561$	1.14459	−	0.0347407i	0.0483247	−	0.00146675i
$562$	−14.5142	−	1.26983i	−0.612244	−	0.0535644i
$563$	−3.57013	−	7.65616i	−0.150463	−	0.322669i	0.816601	−	0.577203i	$-0.195856\pi$
$563$	−3.57013	−	7.65616i	−0.150463	−	0.322669i	−0.967064	+	0.254534i	$0.918078\pi$
$564$	4.40242	+	21.1868i	0.185375	+	0.892123i
$565$	−22.0713	−	17.5922i	−0.928545	−	0.740108i
$566$		−	20.9575i		−	0.880909i
$567$	−8.47450	+	3.41601i	−0.355895	+	0.143459i
$568$	−9.70421	+	9.70421i	−0.407180	+	0.407180i
$569$	−0.364320	+	2.06616i	−0.0152731	+	0.0866180i	−0.991492	−	0.130171i	$-0.958447\pi$
$569$	−0.364320	+	2.06616i	−0.0152731	+	0.0866180i	0.976218	+	0.216789i	$0.0695584\pi$
$570$	−26.2633	+	14.0713i	−1.10005	+	0.589384i
$571$	39.5609	+	14.3990i	1.65557	+	0.602578i	0.989657	−	0.143451i	$-0.0458200\pi$
$571$	39.5609	+	14.3990i	1.65557	+	0.602578i	0.665913	+	0.746029i	$0.268042\pi$
$572$	−0.404162	+	4.61959i	−0.0168989	+	0.193155i
$573$	−5.38382	−	5.06662i	−0.224912	−	0.211661i
$574$	−3.34844	−	9.19975i	−0.139761	−	0.383990i
$575$	15.6117	−	17.2693i	0.651053	−	0.720180i
$576$	2.04687	+	1.51588i	0.0852864	+	0.0631616i
$577$	−10.5623	+	39.4191i	−0.439715	+	1.64104i	0.289810	+	0.957084i	$0.406408\pi$
$577$	−10.5623	+	39.4191i	−0.439715	+	1.64104i	−0.729525	+	0.683955i	$0.760259\pi$
$578$	2.52600	+	28.8723i	0.105068	+	1.20093i
$579$	17.3676	+	2.52174i	0.721775	+	0.104800i
$580$	−8.39906	−	16.8880i	−0.348752	−	0.701235i
$581$	0.300004	−	0.0528988i	0.0124463	−	0.00219461i
$582$	15.3007	−	1.80784i	0.634233	−	0.0749374i
$583$	−8.99749	+	0.787178i	−0.372638	+	0.0326016i
$584$	−4.51811	−	7.82560i	−0.186961	−	0.323825i
$585$	−18.3438	+	18.2926i	−0.758422	+	0.756308i
$586$	−18.6831	+	32.3600i	−0.771790	+	1.33678i
$587$	−5.36709	+	11.5098i	−0.221524	+	0.475059i	−0.985389	−	0.170316i	$-0.945521\pi$
$587$	−5.36709	+	11.5098i	−0.221524	+	0.475059i	0.763866	+	0.645375i	$0.223299\pi$
$588$	−10.2319	−	2.41147i	−0.421958	−	0.0994472i
$589$	22.7747	+	27.1419i	0.938416	+	1.11836i
$590$	−20.8154	−	23.5748i	−0.856957	−	0.970557i
$591$	−6.43474	+	19.5008i	−0.264690	+	0.802156i
$592$	22.4753	−	15.7374i	0.923728	−	0.646801i
$593$	6.50749	+	6.50749i	0.267230	+	0.267230i	0.827983	−	0.560753i	$-0.189488\pi$
$593$	6.50749	+	6.50749i	0.267230	+	0.267230i	−0.560753	+	0.827983i	$0.689488\pi$
$594$	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
$597$	10.1146	+	0.576384i	0.413963	+	0.0235898i
$598$	28.3041	−	13.1984i	1.15744	−	0.539723i
$599$	7.62396	−	6.39726i	0.311507	−	0.261385i	−0.473608	−	0.880736i	$-0.657049\pi$
$599$	7.62396	−	6.39726i	0.311507	−	0.261385i	0.785114	+	0.619351i	$0.212604\pi$
$600$	1.19244	+	14.7418i	0.0486811	+	0.601831i
$601$	24.7845	−	9.02082i	1.01098	−	0.367967i	0.217171	−	0.976134i	$-0.430317\pi$
$601$	24.7845	−	9.02082i	1.01098	−	0.367967i	0.793809	+	0.608167i	$0.208095\pi$
$602$	−0.345688	−	1.29013i	−0.0140892	−	0.0525816i
$603$	4.64410	+	0.946793i	0.189122	+	0.0385564i
$604$	−4.74386	+	2.73887i	−0.193025	+	0.111443i
$605$	8.58388	−	19.6880i	0.348984	−	0.800430i
$606$	54.1848	−	21.6050i	2.20111	−	0.877641i
$607$	4.01440	−	5.73315i	0.162939	−	0.232701i	−0.729377	−	0.684112i	$-0.760190\pi$
$607$	4.01440	−	5.73315i	0.162939	−	0.232701i	0.892316	+	0.451410i	$0.149079\pi$
$608$	−13.3843	+	19.1148i	−0.542806	+	0.775207i
$609$	−13.5507	+	5.40303i	−0.549101	+	0.218942i
$610$	15.9200	+	40.5334i	0.644580	+	1.64115i
$611$	41.0955	−	23.7265i	1.66254	−	0.959871i
$612$	−1.67311	−	0.341097i	−0.0676315	−	0.0137880i
$613$	1.00815	+	3.76248i	0.0407189	+	0.151965i	0.983292	−	0.182034i	$-0.0582683\pi$
$613$	1.00815	+	3.76248i	0.0407189	+	0.151965i	−0.942573	+	0.334000i	$0.891602\pi$
$614$	−20.1841	+	7.34642i	−0.814565	+	0.296477i
$615$	11.7685	+	17.9968i	0.474552	+	0.725703i
$616$	1.56859	−	1.31620i	0.0632004	−	0.0530314i
$617$	3.97043	−	1.85144i	0.159844	−	0.0745363i	−0.341050	−	0.940045i	$-0.610783\pi$
$617$	3.97043	−	1.85144i	0.159844	−	0.0745363i	0.500894	+	0.865509i	$0.333005\pi$
$618$	44.7798	+	2.55179i	1.80131	+	0.102648i
$619$	−33.2378	−	5.86071i	−1.33594	−	0.235562i	−0.540371	−	0.841427i	$-0.681716\pi$
$619$	−33.2378	−	5.86071i	−1.33594	−	0.235562i	−0.795567	+	0.605865i	$0.792827\pi$
$620$	−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
$623$	9.00822	−	6.30763i	0.360907	−	0.252710i
$624$	−10.4793	+	31.7582i	−0.419510	+	1.27135i
$625$	−17.4379	+	17.9142i	−0.697516	+	0.716569i
$626$	−33.3240	−	39.7140i	−1.33189	−	1.58729i
$627$	−8.81883	−	2.07843i	−0.352190	−	0.0830043i
$628$	3.42186	−	7.33821i	0.136547	−	0.292827i
$629$	1.53603	−	2.66048i	0.0612455	−	0.106080i
$630$	−11.8288	−	0.0165136i	−0.471270	−	0.000657919i
$631$	−17.7304	−	30.7100i	−0.705837	−	1.22255i	−0.966389	−	0.257086i	$-0.917238\pi$
$631$	−17.7304	−	30.7100i	−0.705837	−	1.22255i	0.260552	−	0.965460i	$-0.416096\pi$
$632$	11.4500	−	1.00174i	0.455455	−	0.0398471i
$633$	12.2234	−	1.44425i	0.485837	−	0.0574038i
$634$	−36.5900	+	6.45180i	−1.45317	+	0.256234i
$635$	−37.4065	−	12.5574i	−1.48443	−	0.498327i
$636$	13.3280	+	1.93519i	0.528488	+	0.0767354i
$637$	2.00915	+	22.9647i	0.0796054	+	0.909894i
$638$	4.40448	−	16.4377i	0.174375	−	0.650777i
$639$	19.3736	+	14.3477i	0.766408	+	0.567588i
$640$	14.0105	+	22.9142i	0.553813	+	0.905763i
$641$	−9.20207	−	25.2825i	−0.363460	−	0.998598i	−0.977797	−	0.209554i	$-0.932799\pi$
$641$	−9.20207	−	25.2825i	−0.363460	−	0.998598i	0.614337	−	0.789044i	$-0.289423\pi$
$642$	−9.91599	−	9.33178i	−0.391353	−	0.368296i
$643$	−1.42980	+	16.3427i	−0.0563860	+	0.644495i	0.914442	+	0.404717i	$0.132630\pi$
$643$	−1.42980	+	16.3427i	−0.0563860	+	0.644495i	−0.970828	+	0.239778i	$0.922925\pi$
$644$	4.51621	+	1.64377i	0.177964	+	0.0647734i
$645$	1.38544	+	2.58583i	0.0545515	+	0.101817i
$646$	−0.747838	+	4.24120i	−0.0294233	+	0.166868i
$647$	−6.34739	+	6.34739i	−0.249542	+	0.249542i	−0.820783	−	0.571241i	$-0.806462\pi$
$647$	−6.34739	+	6.34739i	−0.249542	+	0.249542i	0.571241	+	0.820783i	$0.306462\pi$
$648$	7.22673	−	13.5652i	0.283893	−	0.532893i
$649$		−	9.56335i		−	0.375394i
$650$	−30.8975	+	13.0427i	−1.21190	+	0.511577i
$651$	2.86171	+	13.7720i	0.112159	+	0.539769i
$652$	−6.89302	−	14.7821i	−0.269951	−	0.578913i
$653$	−12.5076	−	1.09427i	−0.489460	−	0.0428222i	−0.160245	−	0.987077i	$-0.551228\pi$
$653$	−12.5076	−	1.09427i	−0.489460	−	0.0428222i	−0.329215	+	0.944255i	$0.606784\pi$
$654$	−32.2523	+	0.978922i	−1.26116	+	0.0382789i
$655$	5.19870	−	3.83883i	0.203130	−	0.149996i
$656$	24.0399	+	13.8794i	0.938600	+	0.541901i
$657$	−12.4267	+	9.87650i	−0.484811	+	0.385319i
$658$	20.9290	+	5.60792i	0.815898	+	0.218619i
$659$	−7.46847	−	6.26679i	−0.290930	−	0.244120i	0.485627	−	0.874166i	$-0.338591\pi$
$659$	−7.46847	−	6.26679i	−0.290930	−	0.244120i	−0.776557	+	0.630047i	$0.783036\pi$
$660$	2.78704	−	3.72301i	0.108486	−	0.144918i
$661$	−7.28597	−	41.3208i	−0.283391	−	1.60719i	−0.710975	−	0.703217i	$-0.751746\pi$
$661$	−7.28597	−	41.3208i	−0.283391	−	1.60719i	0.427584	−	0.903976i	$-0.359365\pi$
$662$	36.5390	+	25.5849i	1.42013	+	0.994386i
$663$	0.439367	+	3.71858i	0.0170636	+	0.144418i
$664$	−0.329393	+	0.392555i	−0.0127829	+	0.0152341i
$665$	0.253209	+	10.0518i	0.00981903	+	0.389794i
$666$	−19.6750	−	20.7497i	−0.762389	−	0.804036i
$667$	−37.3103	+	9.99727i	−1.44466	+	0.387096i
$668$	0.390376	+	0.182035i	0.0151041	+	0.00704315i
$669$	−3.26513	+	2.01962i	−0.126237	+	0.0780828i
$670$	5.11326	+	3.39171i	0.197542	+	0.131033i
$671$	−4.52916	+	12.4438i	−0.174846	+	0.480386i
$672$	−8.27337	+	4.16804i	−0.319152	+	0.160786i
$673$	−5.59642	−	7.99252i	−0.215726	−	0.308089i	0.696674	−	0.717388i	$-0.254662\pi$
$673$	−5.59642	−	7.99252i	−0.215726	−	0.308089i	−0.912401	+	0.409299i	$0.865773\pi$
$674$	−1.65138			−0.0636089
$675$	25.3045	−	5.88924i	0.973970	−	0.226677i
$676$	−1.94572			−0.0748355
$677$	−24.0388	−	34.3309i	−0.923885	−	1.31944i	−0.947511	−	0.319724i	$-0.896410\pi$
$677$	−24.0388	−	34.3309i	−0.923885	−	1.31944i	0.0236257	−	0.999721i	$-0.492479\pi$
$678$	−2.16038	+	37.9112i	−0.0829690	+	1.45597i
$679$	1.77831	−	4.88587i	0.0682453	−	0.187502i
$680$	1.78146	+	1.18167i	0.0683158	+	0.0453150i
$681$	−14.6636	−	7.88285i	−0.561912	−	0.302072i
$682$	−14.8714	−	6.93465i	−0.569456	−	0.265542i
$683$	20.8963	−	5.59914i	0.799574	−	0.214245i	0.164177	−	0.986431i	$-0.447503\pi$
$683$	20.8963	−	5.59914i	0.799574	−	0.214245i	0.635397	+	0.772186i	$0.280837\pi$
$684$	12.0885	+	6.03314i	0.462214	+	0.230683i
$685$	0.474200	+	18.8247i	0.0181183	+	0.719256i
$686$	−14.7000	+	17.5188i	−0.561250	+	0.668872i
$687$	−15.9776	−	6.86830i	−0.609583	−	0.262042i
$688$	3.10216	+	2.17216i	0.118269	+	0.0828127i
$689$	−5.12843	−	29.0848i	−0.195378	−	1.10804i
$690$	−31.0988	−	3.71849i	−1.18391	−	0.141560i
$691$	−19.0033	−	15.9457i	−0.722921	−	0.606603i	0.205270	−	0.978705i	$-0.434193\pi$
$691$	−19.0033	−	15.9457i	−0.722921	−	0.606603i	−0.928192	+	0.372102i	$0.878637\pi$
$692$	−7.93453	−	2.12605i	−0.301625	−	0.0808203i
$693$	−2.69304	−	2.38453i	−0.102300	−	0.0905808i
$694$	3.06531	+	1.76976i	0.116358	+	0.0671791i
$695$	−17.9896	+	13.2839i	−0.682384	+	0.503888i
$696$	11.6195	−	21.6145i	0.440436	−	0.819296i
$697$	3.09624	+	0.270886i	0.117279	+	0.0102605i
$698$	9.92607	+	21.2865i	0.375707	+	0.805707i
$699$	15.5589	−	13.8812i	0.588492	−	0.525037i
$700$	−4.78148	−	1.94292i	−0.180723	−	0.0734355i
$701$		−	3.89640i		−	0.147165i	−0.997289	−	0.0735825i	$-0.976557\pi$
$701$		−	3.89640i		−	0.147165i	0.997289	−	0.0735825i	$-0.0234432\pi$
$702$	34.3463	+	5.92305i	1.29632	+	0.223551i
$703$	−17.1875	+	17.1875i	−0.648240	+	0.648240i
$704$	−0.174119	+	0.987476i	−0.00656235	+	0.0372169i
$705$	−47.5661	−	1.51020i	−1.79144	−	0.0568773i
$706$	12.1861	+	4.43538i	0.458630	+	0.166928i
$707$	1.71572	−	19.6108i	0.0645264	−	0.737541i
$708$	−3.27124	+	13.8800i	−0.122941	+	0.521642i
$709$	7.07809	+	19.4469i	0.265823	+	0.730343i	0.998748	+	0.0500331i	$0.0159327\pi$
$709$	7.07809	+	19.4469i	0.265823	+	0.730343i	−0.732924	+	0.680310i	$0.761845\pi$
$710$	16.2807	+	26.6271i	0.611004	+	0.999298i
$711$	−4.70548	−	19.6344i	−0.176469	−	0.736349i
$712$	−4.78786	+	17.8685i	−0.179433	+	0.669652i
$713$	3.24608	+	37.1029i	0.121567	+	1.38951i
$714$	−1.05876	+	1.34247i	−0.0396230	+	0.0502408i
$715$	−9.66817	−	3.24562i	−0.361569	−	0.121379i
$716$	12.7809	−	2.25362i	0.477645	−	0.0842218i
$717$	−1.87198	−	2.50793i	−0.0699103	−	0.0936604i
$718$	15.2301	−	1.33246i	0.568381	−	0.0497269i
$719$	23.2328	+	40.2403i	0.866436	+	1.50071i	0.865614	+	0.500712i	$0.166928\pi$
$719$	23.2328	+	40.2403i	0.866436	+	1.50071i	0.000822468		1.00000i	$0.499738\pi$
$720$	25.7225	−	21.5227i	0.958623	−	0.802102i
$721$	7.56817	−	13.1085i	0.281853	−	0.488185i
$722$	0.454053	−	0.973719i	0.0168981	−	0.0362381i
$723$	19.1010	−	20.2968i	0.710372	−	0.754844i
$724$	−12.0891	−	14.4073i	−0.449289	−	0.535442i
$725$	40.4359	−	9.25064i	1.50175	−	0.343560i
$726$	−28.2916	+	5.87874i	−1.05000	+	0.218181i
$727$	−21.0088	+	14.7105i	−0.779175	+	0.545584i	−0.894141	−	0.447785i	$-0.852213\pi$
$727$	−21.0088	+	14.7105i	−0.779175	+	0.545584i	0.114966	+	0.993369i	$0.463324\pi$
$728$	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
$732$	10.8300	−	16.5113i	0.400289	−	0.610275i
$733$	2.40624	−	1.12205i	0.0888766	−	0.0414438i	−0.377672	−	0.925940i	$-0.623275\pi$
$733$	2.40624	−	1.12205i	0.0888766	−	0.0414438i	0.466548	+	0.884496i	$0.345497\pi$
$734$	−36.3169	+	30.4735i	−1.34048	+	1.12480i
$735$	10.4305	−	20.6323i	0.384735	−	0.761035i
$736$	−23.0499	+	8.38947i	−0.849630	+	0.309240i
$737$	0.482919	+	1.80228i	0.0177886	+	0.0663878i
$738$	10.6136	−	26.9126i	0.390693	−	0.990667i
$739$	19.4519	−	11.2305i	0.715548	−	0.413122i	−0.0975639	−	0.995229i	$-0.531105\pi$
$739$	19.4519	−	11.2305i	0.715548	−	0.413122i	0.813112	+	0.582107i	$0.197772\pi$
$740$	−4.56109	−	11.6129i	−0.167669	−	0.426897i
$741$	4.25713	−	29.3195i	0.156389	−	1.07708i
$742$	7.73477	−	11.0464i	0.283952	−	0.405526i
$743$	17.6540	−	25.2126i	0.647664	−	0.924960i	−0.352276	−	0.935896i	$-0.614592\pi$
$743$	17.6540	−	25.2126i	0.647664	−	0.924960i	0.999940	+	0.0109359i	$0.00348107\pi$
$744$	−18.5791	−	14.6526i	−0.681143	−	0.537191i
$745$	12.8078	−	29.3761i	0.469243	−	1.07626i
$746$	−18.2856	+	10.5572i	−0.669484	+	0.386527i
$747$	0.767345	+	0.470653i	0.0280757	+	0.0172203i
$748$	−0.173979	−	0.649300i	−0.00636132	−	0.0237408i
$749$	−4.31804	+	1.57164i	−0.157778	+	0.0574264i
$750$	33.2266	+	5.22246i	1.21326	+	0.190697i
$751$	5.77858	−	4.84881i	0.210864	−	0.176936i	−0.531239	−	0.847222i	$-0.678273\pi$
$751$	5.77858	−	4.84881i	0.210864	−	0.176936i	0.742102	+	0.670287i	$0.233829\pi$
$752$	−55.6791	+	25.9636i	−2.03041	+	0.946795i
$753$	14.2376	+	28.2610i	0.518847	+	1.02989i
$754$	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	$0.904731\pi$
$758$	32.2402	−	22.5748i	1.17102	−	0.819954i
$759$	−6.34054	−	7.10685i	−0.230147	−	0.257962i
$760$	−11.1952	−	12.6792i	−0.406091	−	0.459923i
$761$	19.2569	+	22.9494i	0.698061	+	0.831916i	0.992305	−	0.123814i	$-0.0395125\pi$
$761$	19.2569	+	22.9494i	0.698061	+	0.831916i	−0.294245	+	0.955730i	$0.595068\pi$
$762$	15.2890	+	50.8368i	0.553862	+	1.84162i
$763$	−4.60197	+	9.86895i	−0.166602	+	0.357280i
$764$	−2.16991	+	3.75839i	−0.0785044	+	0.135974i
$765$	1.59179	−	3.40121i	0.0575514	−	0.122971i
$766$	16.5590	+	28.6811i	0.598302	+	1.03629i
$767$	31.1524	−	2.72548i	1.12485	−	0.0984115i
$768$	13.1089	−	30.4949i	0.473027	−	1.10039i
$769$	−4.02410	+	0.709557i	−0.145113	+	0.0255873i	−0.245733	−	0.969338i	$-0.579029\pi$
$769$	−4.02410	+	0.709557i	−0.145113	+	0.0255873i	0.100620	+	0.994925i	$0.467917\pi$
$770$	−2.07364	−	4.16947i	−0.0747289	−	0.150257i
$771$	9.09534	+	22.8109i	0.327561	+	0.821516i
$772$	−0.897880	−	10.2628i	−0.0323154	−	0.369367i
$773$	−10.2912	+	38.4073i	−0.370149	+	1.38141i	0.490156	+	0.871635i	$0.336940\pi$
$773$	−10.2912	+	38.4073i	−0.370149	+	1.38141i	−0.860305	+	0.509780i	$0.829727\pi$
$774$	1.76247	−	3.53142i	0.0633506	−	0.126934i
$775$	−2.01377	−	39.9458i	−0.0723368	−	1.43489i
$776$	2.99143	+	8.21887i	0.107386	+	0.295040i
$777$	−9.24097	+	2.77920i	−0.331518	+	0.0997031i
$778$	−2.36116	+	26.9882i	−0.0846517	+	0.967573i
$779$	−23.1087	−	8.41088i	−0.827955	−	0.301351i
$780$	12.9219	+	8.01771i	0.462679	+	0.287080i
$781$	−1.64803	+	9.34644i	−0.0589711	+	0.334442i
$782$	−3.20111	+	3.20111i	−0.114471	+	0.114471i
$783$	−40.5633	−	14.5913i	−1.44961	−	0.521449i
$784$		−	29.8449i		−	1.06589i
$785$	13.9248	+	11.0989i	0.496996	+	0.396137i
$786$	−8.25655	−	2.72444i	−0.294501	−	0.0971775i
$787$	2.27705	+	4.88315i	0.0811681	+	0.174066i	0.942703	−	0.333632i	$-0.108274\pi$
$787$	2.27705	+	4.88315i	0.0811681	+	0.174066i	−0.861535	+	0.507698i	$0.830497\pi$
$788$	12.0086	+	1.05061i	0.427787	+	0.0374265i
$789$	−3.34324	−	5.40504i	−0.119023	−	0.192424i
$790$	3.88921	−	25.8474i	0.138372	−	0.919609i
$791$	11.0978	+	6.40733i	0.394593	+	0.227818i
$792$	6.04865	+	0.160817i	0.214930	+	0.00571439i
$793$	−41.8261	−	11.2073i	−1.48529	−	0.397982i
$794$	11.8380	+	9.93324i	0.420114	+	0.352518i
$795$	−11.0084	+	27.4971i	−0.390426	+	0.975221i
$796$	−1.03270	−	5.85673i	−0.0366031	−	0.207586i
$797$	25.6491	+	17.9597i	0.908538	+	0.636165i	0.931567	−	0.363569i	$-0.118442\pi$
$797$	25.6491	+	17.9597i	0.908538	+	0.636165i	−0.0230287	+	0.999735i	$0.507331\pi$
$798$	10.8409	−	8.09187i	0.383762	−	0.286449i
$799$	−4.42153	+	5.26938i	−0.156423	+	0.186417i
$800$	25.0685	−	8.09012i	0.886304	−	0.286029i
$801$	32.2857	+	3.69161i	1.14076	+	0.130437i
$802$	1.85338	−	0.496613i	0.0654453	−	0.0175360i
$803$	−5.66346	−	2.64092i	−0.199859	−	0.0931959i
$804$	−0.0844079	−	2.78096i	−0.00297684	−	0.0980771i
$805$	−5.84256	+	8.80809i	−0.205923	+	0.310444i
$806$	18.3512	−	50.4196i	0.646395	−	1.77595i
$807$	−16.1741	−	10.6089i	−0.569356	−	0.373449i
$808$	18.9939	+	27.1260i	0.668202	+	0.954291i
$809$	−4.86947			−0.171202			−0.0856008	−	0.996330i	$-0.527281\pi$
$809$	−4.86947			−0.171202			−0.0856008	+	0.996330i	$0.527281\pi$
$810$	−26.1373	−	23.2082i	−0.918372	−	0.815454i
$811$	−14.9764			−0.525893			−0.262947	−	0.964810i	$-0.584694\pi$
$811$	−14.9764			−0.525893			−0.262947	+	0.964810i	$0.584694\pi$
$812$	4.91182	+	7.01480i	0.172371	+	0.246171i
$813$	−33.3584	−	21.8803i	−1.16993	−	0.767376i
$814$	3.85009	−	10.5780i	0.134946	−	0.370760i
$815$	35.1572	−	7.11640i	1.23150	−	0.249277i
$816$	−0.147072	−	4.84553i	−0.00514853	−	0.169627i
$817$	−3.04063	−	1.41787i	−0.106378	−	0.0496049i
$818$	−1.22100	+	0.327165i	−0.0426911	+	0.0114391i
$819$	7.00006	−	9.45210i	0.244602	−	0.330283i
$820$	8.69801	−	9.14755i	0.303748	−	0.319446i
$821$	2.55907	−	3.04978i	0.0893122	−	0.106438i	−0.719537	−	0.694454i	$-0.755646\pi$
$821$	2.55907	−	3.04978i	0.0893122	−	0.106438i	0.808850	+	0.588015i	$0.200091\pi$
$822$	20.3024	−	15.1541i	0.708126	−	0.528561i
$823$	−13.3259	−	9.33088i	−0.464511	−	0.325254i	0.317783	−	0.948163i	$-0.397062\pi$
$823$	−13.3259	−	9.33088i	−0.464511	−	0.325254i	−0.782294	+	0.622909i	$0.785951\pi$
$824$	4.42142	+	25.0751i	0.154027	+	0.873533i
$825$	6.52287	+	7.87793i	0.227097	+	0.274274i
$826$	10.9381	+	9.17818i	0.380586	+	0.319350i
$827$	−19.0617	−	5.10757i	−0.662841	−	0.177608i	−0.0883130	−	0.996093i	$-0.528148\pi$
$827$	−19.0617	−	5.10757i	−0.662841	−	0.177608i	−0.574528	+	0.818485i	$0.694814\pi$
$828$	6.77152	+	12.4835i	0.235327	+	0.433833i
$829$	32.1618	+	18.5687i	1.11703	+	0.644916i	0.940640	−	0.339405i	$-0.110226\pi$
$829$	32.1618	+	18.5687i	1.11703	+	0.644916i	0.176387	+	0.984321i	$0.443559\pi$
$830$	0.692258	+	0.937482i	0.0240286	+	0.0325405i
$831$	−11.3352	−	18.3257i	−0.393215	−	0.635713i
$832$	−3.26630	−	0.285765i	−0.113239	−	0.00990711i
$833$	−1.41223	−	3.02855i	−0.0489310	−	0.104933i
$834$	28.5710	+	9.42765i	0.989333	+	0.326453i
$835$	−0.590436	+	0.740765i	−0.0204329	+	0.0256352i
$836$			5.31864i			0.183949i
$837$	−20.6472	+	36.0748i	−0.713673	+	1.24693i
$838$	24.1069	−	24.1069i	0.832759	−	0.832759i
$839$	6.68205	−	37.8958i	0.230690	−	1.30831i	−0.620813	−	0.783958i	$-0.713198\pi$
$839$	6.68205	−	37.8958i	0.230690	−	1.30831i	0.851503	−	0.524349i	$-0.175691\pi$
$840$	−1.53127	−	6.53808i	−0.0528337	−	0.225585i
$841$	−37.4236	−	13.6211i	−1.29047	−	0.469692i
$842$	−1.60050	+	18.2938i	−0.0551570	+	0.630447i
$843$	−13.9135	+	4.18445i	−0.479207	+	0.144120i
$844$	−2.47119	−	6.78953i	−0.0850618	−	0.233705i
$845$	1.00308	−	4.15989i	0.0345070	−	0.143105i
$846$	35.3173	+	53.4052i	1.21423	+	1.83611i
$847$	−2.52388	+	9.41923i	−0.0867214	+	0.323649i
$848$	3.33245	+	38.0901i	0.114437	+	1.30802i
$849$	−7.74048	−	19.4130i	−0.265653	−	0.666252i
$850$	3.56210	−	3.30848i	0.122179	−	0.113480i
$851$	−25.1627	+	4.43686i	−0.862567	+	0.152094i
$852$	5.58895	−	13.0014i	0.191474	−	0.445422i
$853$	−37.4642	+	3.27769i	−1.28275	+	0.112226i	−0.708064	−	0.706148i	$-0.750431\pi$
$853$	−37.4642	+	3.27769i	−1.28275	+	0.112226i	−0.574685	+	0.818374i	$0.694876\pi$
$854$	−9.88588	−	17.1228i	−0.338288	−	0.585932i
$855$	−19.1306	+	22.7344i	−0.654253	+	0.777502i
$856$	3.86493	−	6.69425i	0.132100	−	0.228805i
$857$	−8.22482	+	17.6382i	−0.280954	+	0.602509i	−0.995252	−	0.0973336i	$-0.968969\pi$
$857$	−8.22482	+	17.6382i	−0.280954	+	0.602509i	0.714297	+	0.699842i	$0.246746\pi$
$858$	3.95163	+	13.1394i	0.134906	+	0.448571i
$859$	13.2902	+	15.8386i	0.453454	+	0.540406i	0.943536	−	0.331271i	$-0.107477\pi$
$859$	13.2902	+	15.8386i	0.453454	+	0.540406i	−0.490081	+	0.871677i	$0.663033\pi$
$860$	1.29089	−	1.13979i	0.0440189	−	0.0388667i
$861$	−6.49952	−	7.28503i	−0.221503	−	0.248273i
$862$	23.6315	−	16.5469i	0.804891	−	0.563590i
$863$	1.02957	+	1.02957i	0.0350471	+	0.0350471i	0.724413	−	0.689366i	$-0.242111\pi$
$863$	1.02957	+	1.02957i	0.0350471	+	0.0350471i	−0.689366	+	0.724413i	$0.742111\pi$
$864$	−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
$867$	13.0036	+	25.8116i	0.441626	+	0.876606i
$868$	7.48350	−	3.48961i	0.254006	−	0.118445i
$869$	6.08882	−	5.10913i	0.206549	−	0.173315i
$870$	−41.5908	−	37.2106i	−1.41006	−	1.26156i
$871$	−5.73325	+	2.08673i	−0.194264	+	0.0707063i
$872$	−4.74092	−	17.6933i	−0.160548	−	0.599172i
$873$	13.5053	−	7.32578i	0.457086	−	0.247940i
$874$	31.0202	−	17.9095i	1.04927	−	0.605799i
$875$	6.61890	−	9.22101i	0.223760	−	0.311727i
$876$	7.31644	+	5.77020i	0.247200	+	0.194957i
$877$	33.1623	−	47.3607i	1.11981	−	1.59926i	0.382126	−	0.924110i	$-0.375192\pi$
$877$	33.1623	−	47.3607i	1.11981	−	1.59926i	0.737685	−	0.675145i	$-0.235919\pi$
$878$	−11.8138	+	16.8718i	−0.398695	+	0.569396i
$879$	−5.35426	+	36.8756i	−0.180595	+	1.24378i
$880$	12.1031	+	5.27689i	0.407994	+	0.177884i
$881$	6.00946	−	3.46956i	0.202464	−	0.116893i	−0.395340	−	0.918535i	$-0.629373\pi$
$881$	6.00946	−	3.46956i	0.202464	−	0.116893i	0.597804	+	0.801642i	$0.296040\pi$
$882$	−30.7641	+	4.58510i	−1.03588	+	0.154388i
$883$	−4.00657	−	14.9527i	−0.134832	−	0.503199i	−0.999999	−	0.00171481i	$-0.999454\pi$
$883$	−4.00657	−	14.9527i	−0.134832	−	0.503199i	0.865167	−	0.501484i	$-0.167213\pi$
$884$	2.06550	−	0.751779i	0.0694702	−	0.0252851i
$885$	−27.9885	−	14.1494i	−0.940823	−	0.475625i
$886$	−29.6420	+	24.8726i	−0.995844	+	0.835612i
$887$	35.6250	−	16.6122i	1.19617	−	0.557783i	0.280554	−	0.959838i	$-0.409482\pi$
$887$	35.6250	−	16.6122i	1.19617	−	0.557783i	0.915615	+	0.402055i	$0.131704\pi$
$888$	8.90301	−	13.5734i	0.298765	−	0.455494i
$889$	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
$893$	44.5830	−	31.2173i	1.49191	−	1.04465i
$894$	−42.2134	+	8.77156i	−1.41183	+	0.293365i
$895$	−1.77079	+	28.4870i	−0.0591909	+	0.952214i
$896$	−7.83830	−	9.34132i	−0.261859	−	0.312072i
$897$	21.3434	−	22.6796i	0.712635	−	0.757249i
$898$	−3.87067	+	8.30068i	−0.129166	+	0.276997i
$899$	−33.1815	+	57.4721i	−1.10667	+	1.91680i
$900$	−6.77238	−	13.6650i	−0.225746	−	0.455501i
$901$	2.14056	+	3.70755i	0.0713123	+	0.123516i
$902$	11.3455	−	0.992605i	0.377765	−	0.0330501i
$903$	−0.796709	−	1.06737i	−0.0265128	−	0.0355198i
$904$	−21.2290	+	3.74324i	−0.706065	+	0.124498i
$905$	37.0345	−	18.4188i	1.23107	−	0.612260i
$906$	−10.0366	+	12.7261i	−0.333443	+	0.422796i
$907$	−1.45505	−	16.6313i	−0.0483140	−	0.552232i	−0.981322	−	0.192375i	$-0.938381\pi$
$907$	−1.45505	−	16.6313i	−0.0483140	−	0.552232i	0.933008	−	0.359857i	$-0.117174\pi$
$908$	−2.52938	+	9.43978i	−0.0839404	+	0.313270i
$909$	42.2119	−	40.0254i	1.40008	−	1.32756i
$910$	12.9910	−	7.94312i	0.430647	−	0.263312i
$911$	15.5855	+	42.8207i	0.516369	+	1.41871i	0.874493	+	0.485038i	$0.161194\pi$
$911$	15.5855	+	42.8207i	0.516369	+	1.41871i	−0.358124	+	0.933674i	$0.616583\pi$
$912$	−8.79883	+	37.3337i	−0.291358	+	1.23624i
$913$	−0.0308860	+	0.353029i	−0.00102218	+	0.0116835i
$914$	−15.6849	−	5.70884i	−0.518810	−	0.188831i
$915$	29.7174	+	31.6663i	0.982426	+	1.04685i
$916$	−1.77277	+	10.0539i	−0.0585740	+	0.332190i
$917$	−2.07473	+	2.07473i	−0.0685136	+	0.0685136i
$918$	−4.97217	+	0.896026i	−0.164106	+	0.0295733i
$919$		−	3.56037i		−	0.117446i	−0.998274	−	0.0587228i	$-0.981297\pi$
$919$		−	3.56037i		−	0.117446i	0.998274	−	0.0587228i	$-0.0187028\pi$
$920$	−1.99518	−	17.6677i	−0.0657790	−	0.582487i
$921$	−15.9833	+	14.2598i	−0.526666	+	0.469878i
$922$	−7.88296	−	16.9051i	−0.259611	−	0.556738i
$923$	−30.9155	−	2.70476i	−1.01760	−	0.0890281i
$924$	−0.999791	+	1.85981i	−0.0328907	+	0.0611832i
$925$	27.1793	−	3.76466i	0.893650	−	0.123781i
$926$	−53.8596	−	31.0958i	−1.76994	−	1.02187i
$927$	42.4221	−	14.1753i	1.39332	−	0.465578i
$928$	−42.2172	−	11.3121i	−1.38585	−	0.371337i
$929$	9.72612	+	8.16118i	0.319104	+	0.267760i	0.788243	−	0.615365i	$-0.210991\pi$
$929$	9.72612	+	8.16118i	0.319104	+	0.267760i	−0.469139	+	0.883124i	$0.655436\pi$
$930$	−42.2981	+	33.2632i	−1.38701	+	1.09074i
$931$	4.59122	+	26.0381i	0.150471	+	0.853364i
$932$	−10.0264	−	7.02055i	−0.328425	−	0.229966i
$933$	21.8608	+	9.39735i	0.715691	+	0.307655i
$934$	27.2732	−	32.5030i	0.892407	−	1.06353i
$935$	1.47787	−	0.0372281i	0.0483316	−	0.00121749i
$936$	1.19996	+	19.7492i	0.0392220	+	0.645522i
$937$	23.2753	−	6.23661i	0.760372	−	0.203741i	0.142258	−	0.989830i	$-0.454564\pi$
$937$	23.2753	−	6.23661i	0.760372	−	0.203741i	0.618114	+	0.786089i	$0.287897\pi$
$938$	−2.52484	−	1.17735i	−0.0824388	−	0.0384418i
$939$	−45.5361	−	24.4792i	−1.48601	−	0.798848i
$940$	5.54235	+	27.3809i	0.180771	+	0.893067i
$941$	−2.96478	+	8.14566i	−0.0966490	+	0.265541i	−0.978590	−	0.205819i	$-0.934014\pi$
$941$	−2.96478	+	8.14566i	−0.0966490	+	0.265541i	0.881941	+	0.471359i	$0.156237\pi$
$942$	1.36299	−	23.9182i	0.0444085	−	0.779297i
$943$	−14.8272	−	21.1754i	−0.482839	−	0.689566i
$944$	−40.4856			−1.31769
$945$	−10.9631	+	4.35357i	−0.356631	+	0.141622i
$946$	1.55374			0.0505165
$947$	−16.3258	−	23.3157i	−0.530518	−	0.757658i	0.461032	−	0.887383i	$-0.347479\pi$
$947$	−16.3258	−	23.3157i	−0.530518	−	0.757658i	−0.991550	+	0.129726i	$0.958590\pi$
$948$	−10.5848	+	5.33250i	−0.343777	+	0.173192i
$949$	6.98868	−	19.2012i	0.226862	−	0.623299i
$950$	−33.9990	+	17.9909i	−1.10307	+	0.583702i
$951$	−31.5105	+	19.4905i	−1.02180	+	0.632024i
$952$	−0.879652	−	0.410189i	−0.0285097	−	0.0132943i
$953$	−13.9629	+	3.74136i	−0.452304	+	0.121194i	−0.477777	−	0.878481i	$-0.658557\pi$
$953$	−13.9629	+	3.74136i	−0.452304	+	0.121194i	0.0254735	+	0.999675i	$0.491891\pi$
$954$	38.7513	−	9.28692i	1.25462	−	0.300675i
$955$	−6.91665	−	6.57675i	−0.223817	−	0.212819i
$956$	−1.18086	+	1.40730i	−0.0381918	+	0.0455152i
$957$	−1.99127	−	16.8531i	−0.0643685	−	0.544783i
$958$	−58.0723	−	40.6627i	−1.87623	−	1.31375i
$959$	−1.48462	−	8.41972i	−0.0479410	−	0.271887i
$960$	2.63237	+	1.97059i	0.0849595	+	0.0636006i
$961$	25.2709	+	21.2048i	0.815190	+	0.684025i
$962$	35.5550	+	9.52692i	1.14634	+	0.307160i
$963$	−12.6318	−	4.98166i	−0.407055	−	0.160532i
$964$	−14.1690	−	8.18045i	−0.456351	−	0.263474i
$965$	22.4044	+	3.37116i	0.721225	+	0.108521i
$966$	14.2137	−	0.431414i	0.457317	−	0.0138805i
$967$	−23.7858	−	2.08098i	−0.764898	−	0.0669199i	−0.301972	−	0.953317i	$-0.597645\pi$
$967$	−23.7858	−	2.08098i	−0.764898	−	0.0669199i	−0.462926	+	0.886397i	$0.653201\pi$
$968$	−6.93251	−	14.8668i	−0.222819	−	0.477838i
$969$	0.873729	+	4.20484i	0.0280682	+	0.135079i
$970$	19.7648	−	2.23200i	0.634611	−	0.0716652i
$971$		−	55.0723i		−	1.76735i	−0.468098	−	0.883676i	$-0.655061\pi$
$971$		−	55.0723i		−	1.76735i	0.468098	−	0.883676i	$-0.344939\pi$
$972$	−1.74128	+	15.7535i	−0.0558516	+	0.505295i
$973$	7.17940	−	7.17940i	0.230161	−	0.230161i
$974$	−10.0337	+	56.9040i	−0.321501	+	1.82332i
$975$	−23.8032	+	23.4932i	−0.762313	+	0.752386i
$976$	52.6796	+	19.1738i	1.68623	+	0.613738i
$977$	1.11266	−	12.7178i	0.0355972	−	0.406878i	−0.957402	−	0.288758i	$-0.906758\pi$
$977$	1.11266	−	12.7178i	0.0355972	−	0.406878i	0.992999	−	0.118120i	$-0.0376868\pi$
$978$	−35.1439	−	33.0734i	−1.12378	−	1.05757i
$979$	4.37539	+	12.0213i	0.139838	+	0.384202i
$980$	−13.1931	−	3.18128i	−0.421439	−	0.101622i
$981$	−29.5138	+	12.8189i	−0.942303	+	0.409276i
$982$	−2.23749	+	8.35043i	−0.0714012	+	0.266473i
$983$	−0.626489	−	7.16081i	−0.0199819	−	0.228394i	−0.999619	−	0.0276159i	$-0.991208\pi$
$983$	−0.626489	−	7.16081i	−0.0199819	−	0.228394i	0.979637	−	0.200778i	$-0.0643471\pi$
$984$	16.2526	+	2.35984i	0.518113	+	0.0752289i
$985$	−8.43695	+	25.1322i	−0.268823	+	0.800780i
$986$	−7.94382	+	1.40071i	−0.252983	+	0.0446077i
$987$	21.4578	−	2.53534i	0.683011	−	0.0807008i
$988$	−17.3254	+	1.51577i	−0.551193	+	0.0482231i
$989$	−1.76334	−	3.05419i	−0.0560708	−	0.0971175i
$990$	3.58000	−	13.2865i	0.113780	−	0.422274i
$991$	18.6356	−	32.2778i	0.591979	−	1.02534i	−0.401987	−	0.915645i	$-0.631680\pi$
$991$	18.6356	−	32.2778i	0.591979	−	1.02534i	0.993966	−	0.109692i	$-0.0349863\pi$
$992$	−17.8103	+	38.1944i	−0.565478	+	1.21267i
$993$	43.2958	+	10.2040i	1.37395	+	0.323813i
$994$	−9.10839	−	10.8550i	−0.288900	−	0.344298i
$995$	13.0539	+	0.811447i	0.413836	+	0.0257246i
$996$	0.165584	−	0.501811i	0.00524673	−	0.0159005i
$997$	−26.5272	+	18.5746i	−0.840126	+	0.588262i	−0.912482	−	0.409116i	$-0.865837\pi$
$997$	−26.5272	+	18.5746i	−0.840126	+	0.588262i	0.0723564	+	0.997379i	$0.476948\pi$
$998$	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.2.4	✓	192
3.2	odd	2		405.2.r.a.332.13		192
5.2	odd	4		675.2.ba.b.218.13		192
5.3	odd	4	inner	135.2.q.a.83.4	yes	192
5.4	even	2		675.2.ba.b.407.13		192
15.8	even	4		405.2.r.a.8.13		192
27.13	even	9		405.2.r.a.152.13		192
27.14	odd	18	inner	135.2.q.a.122.4	yes	192
135.13	odd	36		405.2.r.a.233.13		192
135.14	odd	18		675.2.ba.b.257.13		192
135.68	even	36	inner	135.2.q.a.68.4	yes	192
135.122	even	36		675.2.ba.b.68.13		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.4	✓	192	1.1	even	1	trivial
135.2.q.a.68.4	yes	192	135.68	even	36	inner
135.2.q.a.83.4	yes	192	5.3	odd	4	inner
135.2.q.a.122.4	yes	192	27.14	odd	18	inner
405.2.r.a.8.13		192	15.8	even	4
405.2.r.a.152.13		192	27.13	even	9
405.2.r.a.233.13		192	135.13	odd	36
405.2.r.a.332.13		192	3.2	odd	2
675.2.ba.b.68.13		192	135.122	even	36
675.2.ba.b.218.13		192	5.2	odd	4
675.2.ba.b.257.13		192	135.14	odd	18
675.2.ba.b.407.13		192	5.4	even	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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.996232 - 1.42277i) q^{2} +(-1.44830 - 0.949962i) q^{3} +(-0.347747 + 0.955427i) q^{4} +(-1.86340 - 1.23602i) q^{5} +(0.0912678 + 3.00698i) q^{6} +(0.920112 + 0.429055i) q^{7} +(-1.64960 + 0.442010i) q^{8} +(1.19514 + 2.75166i) q^{9} +O(q^{10})\)	\(q+(-0.996232 - 1.42277i) q^{2} +(-1.44830 - 0.949962i) q^{3} +(-0.347747 + 0.955427i) q^{4} +(-1.86340 - 1.23602i) q^{5} +(0.0912678 + 3.00698i) q^{6} +(0.920112 + 0.429055i) q^{7} +(-1.64960 + 0.442010i) q^{8} +(1.19514 + 2.75166i) q^{9} +(0.0978025 + 3.88255i) q^{10} +(-0.759141 + 0.904709i) q^{11} +(1.41126 - 1.05340i) q^{12} +(-3.16342 - 2.21505i) q^{13} +(-0.306200 - 1.73654i) q^{14} +(1.52458 + 3.56029i) q^{15} +(3.83001 + 3.21376i) q^{16} +(0.540727 + 0.144887i) q^{17} +(2.72433 - 4.44170i) q^{18} +(-3.83587 - 2.21464i) q^{19} +(1.82892 - 1.35052i) q^{20} +(-0.925012 - 1.49547i) q^{21} +(2.04347 + 0.178781i) q^{22} +(-1.96770 - 4.21975i) q^{23} +(2.80901 + 0.926898i) q^{24} +(1.94449 + 4.60640i) q^{25} +6.70752i q^{26} +(0.883047 - 5.12057i) q^{27} +(-0.729897 + 0.729897i) q^{28} +(1.44060 - 8.17007i) q^{29} +(3.54662 - 5.71600i) q^{30} +(-7.51688 - 2.73592i) q^{31} +(0.459164 - 5.24827i) q^{32} +(1.95890 - 0.589135i) q^{33} +(-0.332549 - 0.913671i) q^{34} +(-1.18421 - 1.93678i) q^{35} +(-3.04462 + 0.184991i) q^{36} +(1.42034 - 5.30076i) q^{37} +(0.670500 + 7.66385i) q^{38} +(2.47737 + 6.21319i) q^{39} +(3.62020 + 1.21531i) q^{40} +(5.46773 - 0.964109i) q^{41} +(-1.20618 + 2.80591i) q^{42} +(0.754568 - 0.0660161i) q^{43} +(-0.600395 - 1.03991i) q^{44} +(1.17409 - 6.60466i) q^{45} +(-4.04344 + 7.00343i) q^{46} +(-5.19301 + 11.1364i) q^{47} +(-2.49405 - 8.29285i) q^{48} +(-3.83700 - 4.57275i) q^{49} +(4.61667 - 7.35561i) q^{50} +(-0.645498 - 0.723511i) q^{51} +(3.21639 - 2.25214i) 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} +(3.45167 + 6.85140i) q^{57} +(-13.0593 + 6.08964i) q^{58} +(-6.20310 + 5.20502i) q^{59} +(-3.93177 + 0.218547i) q^{60} +(10.5365 - 3.83498i) q^{61} +(3.59598 + 13.4204i) q^{62} +(-0.0809482 + 3.04462i) q^{63} +(0.735277 - 0.424512i) q^{64} +(3.15685 + 8.03758i) q^{65} +(-2.78972 - 2.20015i) q^{66} +(0.906180 - 1.29416i) q^{67} +(-0.326466 + 0.466241i) q^{68} +(-1.15878 + 7.98071i) q^{69} +(-1.57584 + 3.61434i) q^{70} +(6.95937 - 4.01800i) q^{71} +(-3.18777 - 4.01088i) q^{72} +(1.36945 + 5.11087i) q^{73} +(-8.95674 + 3.25999i) q^{74} +(1.55970 - 8.51865i) q^{75} +(3.44984 - 2.89476i) q^{76} +(-1.08667 + 0.506721i) q^{77} +(6.37189 - 9.71449i) 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} +(0.245796 - 0.172108i) q^{83} +(1.75049 - 0.363735i) q^{84} +(-0.828505 - 0.938334i) q^{85} +(-0.845650 - 1.00781i) q^{86} +(-9.84768 + 10.4642i) q^{87} +(0.852391 - 1.82796i) q^{88} +(5.41601 - 9.38081i) q^{89} +(-10.5666 + 4.90932i) q^{90} +(-1.96032 - 3.39538i) q^{91} +(4.71593 - 0.412590i) q^{92} +(8.28768 + 11.1032i) q^{93} +(21.0180 - 3.70604i) q^{94} +(4.41040 + 8.86799i) q^{95} +(-5.65066 + 7.16487i) q^{96} +(-0.446362 - 5.10194i) q^{97} +(-2.68342 + 10.0147i) 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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