LMFDB - Embedded newform 135.2.q.a.2.11

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			2.11
Character	$\chi$	$=$	135.2
Dual form			135.2.q.a.68.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.343150 + 0.490069i) q^{2} +(0.150104 + 1.72553i) q^{3} +(0.561625 - 1.54305i) q^{4} +(2.04155 - 0.912186i) q^{5} +(-0.794122 + 0.665679i) q^{6} +(-0.136472 - 0.0636379i) q^{7} +(2.10468 - 0.563947i) q^{8} +(-2.95494 + 0.518020i) q^{9} +O(q^{10})$	\(q+(0.343150 + 0.490069i) q^{2} +(0.150104 + 1.72553i) q^{3} +(0.561625 - 1.54305i) q^{4} +(2.04155 - 0.912186i) q^{5} +(-0.794122 + 0.665679i) q^{6} +(-0.136472 - 0.0636379i) q^{7} +(2.10468 - 0.563947i) q^{8} +(-2.95494 + 0.518020i) q^{9} +(1.14759 + 0.687482i) q^{10} +(-3.54970 + 4.23037i) q^{11} +(2.74689 + 0.737484i) q^{12} +(-1.54940 - 1.08490i) q^{13} +(-0.0156434 - 0.0887180i) q^{14} +(1.88045 + 3.38584i) q^{15} +(-1.51722 - 1.27310i) q^{16} +(4.40907 + 1.18141i) q^{17} +(-1.26785 - 1.27036i) q^{18} +(-6.55178 - 3.78267i) q^{19} +(-0.260967 - 3.66252i) q^{20} +(0.0893244 - 0.245039i) q^{21} +(-3.29125 - 0.287947i) q^{22} +(0.412075 + 0.883698i) q^{23} +(1.28903 + 3.54705i) q^{24} +(3.33583 - 3.72454i) q^{25} -1.13159i q^{26} +(-1.33741 - 5.02109i) q^{27} +(-0.174843 + 0.174843i) q^{28} +(0.486461 - 2.75886i) q^{29} +(-1.01402 + 2.08340i) q^{30} +(1.70974 + 0.622294i) q^{31} +(0.483084 - 5.52167i) q^{32} +(-7.83247 - 5.49013i) q^{33} +(0.934001 + 2.56615i) q^{34} +(-0.336664 - 0.00543199i) q^{35} +(-0.860234 + 4.85055i) q^{36} +(-1.53079 + 5.71298i) q^{37} +(-0.394473 - 4.50885i) q^{38} +(1.63946 - 2.83639i) q^{39} +(3.78238 - 3.07118i) q^{40} +(-0.682276 + 0.120304i) q^{41} +(0.150738 - 0.0403102i) q^{42} +(1.73456 - 0.151755i) q^{43} +(4.53407 + 7.85325i) q^{44} +(-5.56011 + 3.75302i) q^{45} +(-0.291669 + 0.505186i) q^{46} +(-4.70696 + 10.0941i) q^{47} +(1.96903 - 2.80911i) q^{48} +(-4.48494 - 5.34494i) q^{49} +(2.96997 + 0.356711i) q^{50} +(-1.37674 + 7.78533i) q^{51} +(-2.54423 + 1.78149i) q^{52} +(-0.204978 - 0.204978i) q^{53} +(2.00175 - 2.37841i) q^{54} +(-3.38800 + 11.8745i) q^{55} +(-0.323118 - 0.0569745i) q^{56} +(5.54368 - 11.8731i) q^{57} +(1.51896 - 0.708303i) q^{58} +(-0.796564 + 0.668396i) q^{59} +(6.28063 - 1.00007i) q^{60} +(9.12620 - 3.32167i) q^{61} +(0.281730 + 1.05143i) q^{62} +(0.436232 + 0.117351i) q^{63} +(-0.558711 + 0.322572i) q^{64} +(-4.15280 - 0.801535i) q^{65} +(0.00283170 - 5.72239i) q^{66} +(6.27537 - 8.96216i) q^{67} +(4.29921 - 6.13991i) q^{68} +(-1.46300 + 0.843697i) q^{69} +(-0.112864 - 0.166852i) q^{70} +(-2.53024 + 1.46084i) q^{71} +(-5.92706 + 2.75670i) q^{72} +(2.66706 + 9.95358i) q^{73} +(-3.32505 + 1.21022i) q^{74} +(6.92755 + 5.19702i) q^{75} +(-9.51649 + 7.98529i) q^{76} +(0.753647 - 0.351431i) q^{77} +(1.95261 - 0.169857i) q^{78} +(11.9179 + 2.10144i) q^{79} +(-4.25878 - 1.21510i) q^{80} +(8.46331 - 3.06144i) q^{81} +(-0.293080 - 0.293080i) q^{82} +(5.85978 - 4.10306i) q^{83} +(-0.327942 - 0.275452i) q^{84} +(10.0790 - 1.60999i) q^{85} +(0.669585 + 0.797981i) q^{86} +(4.83353 + 0.425289i) q^{87} +(-5.08528 + 10.9054i) q^{88} +(-6.74192 + 11.6773i) q^{89} +(-3.74719 - 1.43699i) q^{90} +(0.142409 + 0.246659i) q^{91} +(1.59502 - 0.139546i) q^{92} +(-0.817150 + 3.04362i) q^{93} +(-6.56201 + 1.15706i) q^{94} +(-16.8263 - 1.74606i) q^{95} +(9.60035 + 0.00475069i) q^{96} +(0.311872 + 3.56471i) q^{97} +(1.08038 - 4.03205i) q^{98} +(8.29773 - 14.3393i) 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 $

$2$	0.343150	+	0.490069i	0.242644	+	0.346531i	0.921940	−	0.387333i	$-0.126604\pi$
$2$	0.343150	+	0.490069i	0.242644	+	0.346531i	−0.679296	+	0.733864i	$0.737715\pi$
$3$	0.150104	+	1.72553i	0.0866628	+	0.996238i
$3$	0.150104	+	1.72553i	0.0866628	+	0.996238i
$4$	0.561625	−	1.54305i	0.280812	−	0.771525i
$5$	2.04155	−	0.912186i	0.913008	−	0.407942i
$5$	2.04155	−	0.912186i	0.913008	−	0.407942i
$6$	−0.794122	+	0.665679i	−0.324199	+	0.271762i
$7$	−0.136472	−	0.0636379i	−0.0515816	−	0.0240529i	0.396656	−	0.917967i	$-0.370170\pi$
$7$	−0.136472	−	0.0636379i	−0.0515816	−	0.0240529i	−0.448238	+	0.893914i	$0.647948\pi$
$8$	2.10468	−	0.563947i	0.744117	−	0.199385i
$9$	−2.95494	+	0.518020i	−0.984979	+	0.172673i
$10$	1.14759	+	0.687482i	0.362900	+	0.217401i
$11$	−3.54970	+	4.23037i	−1.07027	+	1.27550i	−0.110760	+	0.993847i	$0.535328\pi$
$11$	−3.54970	+	4.23037i	−1.07027	+	1.27550i	−0.959515	+	0.281657i	$0.909116\pi$
$12$	2.74689	+	0.737484i	0.792959	+	0.212893i
$13$	−1.54940	−	1.08490i	−0.429725	−	0.300897i	0.338631	−	0.940919i	$-0.390036\pi$
$13$	−1.54940	−	1.08490i	−0.429725	−	0.300897i	−0.768356	+	0.640022i	$0.778925\pi$
$14$	−0.0156434	−	0.0887180i	−0.00418087	−	0.0237109i
$15$	1.88045	+	3.38584i	0.485531	+	0.874219i
$16$	−1.51722	−	1.27310i	−0.379305	−	0.318275i
$17$	4.40907	+	1.18141i	1.06936	+	0.286533i	0.750228	−	0.661179i	$-0.229944\pi$
$17$	4.40907	+	1.18141i	1.06936	+	0.286533i	0.319127	+	0.947712i	$0.396610\pi$
$18$	−1.26785	−	1.27036i	−0.298836	−	0.299428i
$19$	−6.55178	−	3.78267i	−1.50308	−	0.867804i	−0.999994	−	0.00356839i	$-0.998864\pi$
$19$	−6.55178	−	3.78267i	−1.50308	−	0.867804i	−0.503087	−	0.864236i	$-0.667803\pi$
$20$	−0.260967	−	3.66252i	−0.0583539	−	0.818964i
$21$	0.0893244	−	0.245039i	0.0194922	−	0.0534720i
$22$	−3.29125	−	0.287947i	−0.701697	−	0.0613906i
$23$	0.412075	+	0.883698i	0.0859236	+	0.184264i	0.944575	−	0.328297i	$-0.106475\pi$
$23$	0.412075	+	0.883698i	0.0859236	+	0.184264i	−0.858651	+	0.512561i	$0.828697\pi$
$24$	1.28903	+	3.54705i	0.263122	+	0.724038i
$25$	3.33583	−	3.72454i	0.667166	−	0.744909i
$26$		−	1.13159i		−	0.221924i
$27$	−1.33741	−	5.02109i	−0.257385	−	0.966309i
$28$	−0.174843	+	0.174843i	−0.0330421	+	0.0330421i
$29$	0.486461	−	2.75886i	0.0903336	−	0.512307i	−0.905744	−	0.423825i	$-0.860687\pi$
$29$	0.486461	−	2.75886i	0.0903336	−	0.512307i	0.996078	−	0.0884824i	$-0.0282017\pi$
$30$	−1.01402	+	2.08340i	−0.185133	+	0.380375i
$31$	1.70974	+	0.622294i	0.307078	+	0.111767i	0.490963	−	0.871181i	$-0.336645\pi$
$31$	1.70974	+	0.622294i	0.307078	+	0.111767i	−0.183885	+	0.982948i	$0.558867\pi$
$32$	0.483084	−	5.52167i	0.0853979	−	0.976103i
$33$	−7.83247	−	5.49013i	−1.36346	−	0.955710i
$34$	0.934001	+	2.56615i	0.160180	+	0.440090i
$35$	−0.336664	−	0.00543199i	−0.0569065	−	0.000918174i
$36$	−0.860234	+	4.85055i	−0.143372	+	0.808425i
$37$	−1.53079	+	5.71298i	−0.251660	+	0.939209i	0.718258	+	0.695777i	$0.244940\pi$
$37$	−1.53079	+	5.71298i	−0.251660	+	0.939209i	−0.969918	+	0.243432i	$0.921727\pi$
$38$	−0.394473	−	4.50885i	−0.0639920	−	0.731431i
$39$	1.63946	−	2.83639i	0.262524	−	0.454185i
$40$	3.78238	−	3.07118i	0.598047	−	0.485597i
$41$	−0.682276	+	0.120304i	−0.106554	+	0.0187883i	−0.226671	−	0.973971i	$-0.572784\pi$
$41$	−0.682276	+	0.120304i	−0.106554	+	0.0187883i	0.120117	+	0.992760i	$0.461673\pi$
$42$	0.150738	−	0.0403102i	0.0232594	−	0.00621999i
$43$	1.73456	−	0.151755i	0.264518	−	0.0231424i	0.0458750	−	0.998947i	$-0.485392\pi$
$43$	1.73456	−	0.151755i	0.264518	−	0.0231424i	0.218643	+	0.975805i	$0.429837\pi$
$44$	4.53407	+	7.85325i	0.683537	+	1.18392i
$45$	−5.56011	+	3.75302i	−0.828853	+	0.559467i
$46$	−0.291669	+	0.505186i	−0.0430043	+	0.0744856i
$47$	−4.70696	+	10.0941i	−0.686581	+	1.47238i	0.185311	+	0.982680i	$0.440671\pi$
$47$	−4.70696	+	10.0941i	−0.686581	+	1.47238i	−0.871892	+	0.489698i	$0.837107\pi$
$48$	1.96903	−	2.80911i	0.284206	−	0.405460i
$49$	−4.48494	−	5.34494i	−0.640705	−	0.763563i
$50$	2.96997	+	0.356711i	0.420018	+	0.0504466i
$51$	−1.37674	+	7.78533i	−0.192782	+	1.09016i
$52$	−2.54423	+	1.78149i	−0.352822	+	0.247049i
$53$	−0.204978	−	0.204978i	−0.0281559	−	0.0281559i	0.692889	−	0.721045i	$-0.256338\pi$
$53$	−0.204978	−	0.204978i	−0.0281559	−	0.0281559i	−0.721045	+	0.692889i	$0.756338\pi$
$54$	2.00175	−	2.37841i	0.272403	−	0.323661i
$55$	−3.38800	+	11.8745i	−0.456838	+	1.60116i
$56$	−0.323118	−	0.0569745i	−0.0431785	−	0.00761353i
$57$	5.54368	−	11.8731i	0.734278	−	1.57263i
$58$	1.51896	−	0.708303i	0.199449	−	0.0930047i
$59$	−0.796564	+	0.668396i	−0.103704	+	0.0870178i	−0.693165	−	0.720779i	$-0.743784\pi$
$59$	−0.796564	+	0.668396i	−0.103704	+	0.0870178i	0.589462	+	0.807796i	$0.299340\pi$
$60$	6.28063	−	1.00007i	0.810826	−	0.129108i
$61$	9.12620	−	3.32167i	1.16849	−	0.425296i	0.316367	−	0.948637i	$-0.397537\pi$
$61$	9.12620	−	3.32167i	1.16849	−	0.425296i	0.852123	+	0.523341i	$0.175315\pi$
$62$	0.281730	+	1.05143i	0.0357797	+	0.133532i
$63$	0.436232	+	0.117351i	0.0549601	+	0.0147848i
$64$	−0.558711	+	0.322572i	−0.0698389	+	0.0403215i
$65$	−4.15280	−	0.801535i	−0.515091	−	0.0994182i
$66$	0.00283170	−	5.72239i	0.000348558	−	0.704378i
$67$	6.27537	−	8.96216i	0.766659	−	1.09490i	−0.226021	−	0.974122i	$-0.572572\pi$
$67$	6.27537	−	8.96216i	0.766659	−	1.09490i	0.992679	−	0.120780i	$-0.0385394\pi$
$68$	4.29921	−	6.13991i	0.521356	−	0.744573i
$69$	−1.46300	+	0.843697i	−0.176124	+	0.101569i
$70$	−0.112864	−	0.166852i	−0.0134898	−	0.0199427i
$71$	−2.53024	+	1.46084i	−0.300285	+	0.173369i	−0.642571	−	0.766226i	$-0.722132\pi$
$71$	−2.53024	+	1.46084i	−0.300285	+	0.173369i	0.342286	+	0.939596i	$0.388799\pi$
$72$	−5.92706	+	2.75670i	−0.698511	+	0.324880i
$73$	2.66706	+	9.95358i	0.312155	+	1.16498i	0.926609	+	0.376026i	$0.122710\pi$
$73$	2.66706	+	9.95358i	0.312155	+	1.16498i	−0.614454	+	0.788953i	$0.710624\pi$
$74$	−3.32505	+	1.21022i	−0.386529	+	0.140685i
$75$	6.92755	+	5.19702i	0.799925	+	0.600101i
$76$	−9.51649	+	7.98529i	−1.09162	+	0.915975i
$77$	0.753647	−	0.351431i	0.0858860	−	0.0400493i
$78$	1.95261	−	0.169857i	0.221089	−	0.0192325i
$79$	11.9179	+	2.10144i	1.34086	+	0.236430i	0.797628	−	0.603150i	$-0.206088\pi$
$79$	11.9179	+	2.10144i	1.34086	+	0.236430i	0.543236	+	0.839580i	$0.317199\pi$
$80$	−4.25878	−	1.21510i	−0.476146	−	0.135853i
$81$	8.46331	−	3.06144i	0.940368	−	0.340159i
$82$	−0.293080	−	0.293080i	−0.0323653	−	0.0323653i
$83$	5.85978	−	4.10306i	0.643194	−	0.450370i	−0.205927	−	0.978567i	$-0.566021\pi$
$83$	5.85978	−	4.10306i	0.643194	−	0.450370i	0.849121	+	0.528198i	$0.177132\pi$
$84$	−0.327942	−	0.275452i	−0.0357814	−	0.0300543i
$85$	10.0790	−	1.60999i	1.09322	−	0.174628i
$86$	0.669585	+	0.797981i	0.0722033	+	0.0860485i
$87$	4.83353	+	0.425289i	0.518208	+	0.0455958i
$88$	−5.08528	+	10.9054i	−0.542092	+	1.16252i
$89$	−6.74192	+	11.6773i	−0.714642	+	1.23780i	0.248455	+	0.968643i	$0.420077\pi$
$89$	−6.74192	+	11.6773i	−0.714642	+	1.23780i	−0.963097	+	0.269153i	$0.913256\pi$
$90$	−3.74719	−	1.43699i	−0.394988	−	0.151472i
$91$	0.142409	+	0.246659i	0.0149285	+	0.0258569i
$92$	1.59502	−	0.139546i	0.166293	−	0.0145487i
$93$	−0.817150	+	3.04362i	−0.0847345	+	0.315609i
$94$	−6.56201	+	1.15706i	−0.676819	+	0.119341i
$95$	−16.8263	−	1.74606i	−1.72634	−	0.179142i
$96$	9.60035	+	0.00475069i	0.979831	+	0.000484865i
$97$	0.311872	+	3.56471i	0.0316658	+	0.361941i	0.995452	+	0.0952651i	$0.0303699\pi$
$97$	0.311872	+	3.56471i	0.0316658	+	0.361941i	−0.963786	+	0.266676i	$0.914075\pi$
$98$	1.08038	−	4.03205i	0.109135	−	0.407298i
$99$	8.29773	−	14.3393i	0.833953	−	1.44115i
$100$	−3.87367	−	7.23915i	−0.387367	−	0.723915i
$101$	−1.31720	−	3.61898i	−0.131067	−	0.360102i	0.856749	−	0.515734i	$-0.172481\pi$
$101$	−1.31720	−	3.61898i	−0.131067	−	0.360102i	−0.987815	+	0.155632i	$0.950259\pi$
$102$	−4.28777	+	1.99684i	−0.424553	+	0.197717i
$103$	−1.07356	+	12.2709i	−0.105781	+	1.20909i	0.738900	+	0.673816i	$0.235346\pi$
$103$	−1.07356	+	12.2709i	−0.105781	+	1.20909i	−0.844681	+	0.535270i	$0.820210\pi$
$104$	−3.87281	−	1.40959i	−0.379760	−	0.138221i
$105$	−0.0411616	−	0.581740i	−0.00401696	−	0.0567720i
$106$	0.0301151	−	0.170791i	0.00292504	−	0.0165887i
$107$	−0.874553	+	0.874553i	−0.0845462	+	0.0845462i	−0.748115	−	0.663569i	$-0.769041\pi$
$107$	−0.874553	+	0.874553i	−0.0845462	+	0.0845462i	0.663569	+	0.748115i	$0.269041\pi$
$108$	−8.49892	−	0.756274i	−0.817809	−	0.0727725i
$109$		−	8.22348i		−	0.787666i	−0.919182	−	0.393833i	$-0.871149\pi$
$109$		−	8.22348i		−	0.787666i	0.919182	−	0.393833i	$-0.128851\pi$
$110$	−6.98191	+	2.41438i	−0.665699	+	0.230202i
$111$	−10.0877	−	1.78389i	−0.957485	−	0.169319i
$112$	0.126041	+	0.270295i	0.0119097	+	0.0255405i
$113$	−1.98949	−	0.174058i	−0.187156	−	0.0163740i	−0.00680753	−	0.999977i	$-0.502167\pi$
$113$	−1.98949	−	0.174058i	−0.187156	−	0.0163740i	−0.180348	+	0.983603i	$0.557722\pi$
$114$	7.72096	−	1.35747i	0.723134	−	0.127139i
$115$	1.64737	+	1.42822i	0.153618	+	0.133182i
$116$	−3.98385	−	2.30008i	−0.369891	−	0.213557i
$117$	5.14037	+	2.40319i	0.475228	+	0.222175i
$118$	−0.600901	−	0.161011i	−0.0553174	−	0.0148223i
$119$	−0.526532	−	0.441813i	−0.0482671	−	0.0405009i
$120$	5.86719	+	6.06563i	0.535598	+	0.553713i
$121$	−3.38551	−	19.2002i	−0.307774	−	1.74547i
$122$	4.75950	+	3.33264i	0.430905	+	0.301723i
$123$	−0.310001	−	1.15923i	−0.0279518	−	0.104525i
$124$	1.92046	−	2.28872i	0.172463	−	0.205533i
$125$	3.41278	−	10.6467i	0.305249	−	0.952273i
$126$	0.0921830	+	0.254053i	0.00821231	+	0.0226328i
$127$	6.42494	−	1.72156i	0.570121	−	0.152764i	0.0377691	−	0.999286i	$-0.487975\pi$
$127$	6.42494	−	1.72156i	0.570121	−	0.152764i	0.532352	+	0.846523i	$0.321308\pi$
$128$	−10.3967	−	4.84806i	−0.918948	−	0.428512i
$129$	0.522223	+	2.97027i	0.0459792	+	0.261518i
$130$	−1.03223	−	2.31020i	−0.0905321	−	0.202618i
$131$	4.62535	−	12.7080i	0.404119	−	1.11031i	−0.556114	−	0.831106i	$-0.687708\pi$
$131$	4.62535	−	12.7080i	0.404119	−	1.11031i	0.960233	−	0.279201i	$-0.0900695\pi$
$132$	−12.8705	+	9.00251i	−1.12023	+	0.783568i
$133$	0.653413	+	0.933170i	0.0566581	+	0.0809161i
$134$	6.54547			0.565442
$135$	−7.31056	−	9.03082i	−0.629192	−	0.777250i
$136$	9.94592			0.852856
$137$	4.69542	+	6.70575i	0.401156	+	0.572911i	0.968011	−	0.250907i	$-0.0807288\pi$
$137$	4.69542	+	6.70575i	0.401156	+	0.572911i	−0.566855	+	0.823818i	$0.691840\pi$
$138$	−0.915497	−	0.427455i	−0.0779323	−	0.0363874i
$139$	−6.24384	+	17.1548i	−0.529596	+	1.45505i	0.329952	+	0.943998i	$0.392967\pi$
$139$	−6.24384	+	17.1548i	−0.529596	+	1.45505i	−0.859548	+	0.511055i	$0.829255\pi$
$140$	−0.197460	+	0.516438i	−0.0166885	+	0.0436470i
$141$	−18.1243	−	6.60686i	−1.52634	−	0.556398i
$142$	−1.58416	−	0.738707i	−0.132940	−	0.0619909i
$143$	10.0894	−	2.70345i	0.843720	−	0.226074i
$144$	5.14278	+	2.97598i	0.428565	+	0.247998i
$145$	−1.52346	−	6.07609i	−0.126516	−	0.504591i
$146$	−3.96274	+	4.72261i	−0.327959	+	0.390846i
$147$	8.54967	−	8.54121i	0.705165	−	0.704467i
$148$	7.95570	+	5.57064i	0.653954	+	0.457904i
$149$	0.725914	+	4.11686i	0.0594692	+	0.337266i	0.999997	−	0.00245028i	$-0.000779950\pi$
$149$	0.725914	+	4.11686i	0.0594692	+	0.337266i	−0.940528	+	0.339717i	$0.889669\pi$
$150$	−0.169711	+	5.17834i	−0.0138569	+	0.422809i
$151$	3.72470	+	3.12540i	0.303112	+	0.254341i	0.781638	−	0.623732i	$-0.214384\pi$
$151$	3.72470	+	3.12540i	0.303112	+	0.254341i	−0.478526	+	0.878073i	$0.658829\pi$
$152$	−15.9226	−	4.26645i	−1.29149	−	0.346055i
$153$	−13.6405	−	1.20699i	−1.10277	−	0.0975797i
$154$	0.430839	+	0.248745i	0.0347180	+	0.0200445i
$155$	4.05816	−	0.289157i	0.325959	−	0.0232257i
$156$	−3.45593	−	4.12275i	−0.276696	−	0.330085i
$157$	−17.3439	−	1.51739i	−1.38419	−	0.121101i	−0.629407	−	0.777075i	$-0.716702\pi$
$157$	−17.3439	−	1.51739i	−1.38419	−	0.121101i	−0.754783	+	0.655974i	$0.772258\pi$
$158$	3.05976	+	6.56168i	0.243422	+	0.522019i
$159$	0.322928	−	0.384464i	0.0256099	−	0.0304900i
$160$	−4.05056	−	11.7134i	−0.320225	−	0.926027i
$161$		−	0.146824i		−	0.0115713i
$162$	4.40450	+	3.09707i	0.346050	+	0.243329i
$163$	2.64439	−	2.64439i	0.207124	−	0.207124i	−0.595920	−	0.803044i	$-0.703212\pi$
$163$	2.64439	−	2.64439i	0.207124	−	0.207124i	0.803044	+	0.595920i	$0.203212\pi$
$164$	−0.197548	+	1.12035i	−0.0154259	+	0.0874848i
$165$	−20.9984	−	4.06370i	−1.63472	−	0.316358i
$166$	4.02157	+	1.46373i	0.312134	+	0.113608i
$167$	−0.0458006	+	0.523503i	−0.00354415	+	0.0405099i	−0.997761	−	0.0668828i	$-0.978695\pi$
$167$	−0.0458006	+	0.523503i	−0.00354415	+	0.0405099i	0.994217	+	0.107393i	$0.0342502\pi$
$168$	0.0498099	−	0.566104i	0.00384292	−	0.0436758i
$169$	−3.22264	−	8.85412i	−0.247895	−	0.681086i
$170$	4.24761	+	4.38693i	0.325777	+	0.336462i
$171$	21.3196	+	7.78360i	1.63035	+	0.595227i
$172$	0.740008	−	2.76175i	0.0564251	−	0.210581i
$173$	1.53373	+	17.5306i	0.116607	+	1.33282i	0.798776	+	0.601629i	$0.205481\pi$
$173$	1.53373	+	17.5306i	0.116607	+	1.33282i	−0.682169	+	0.731195i	$0.738963\pi$
$174$	1.45020	+	2.51470i	0.109940	+	0.190639i
$175$	−0.692270	+	0.296010i	−0.0523307	+	0.0223763i
$176$	10.7714	−	1.89928i	0.811921	−	0.143164i
$177$	−1.27291	−	1.27417i	−0.0956777	−	0.0957724i
$178$	−8.03619	+	0.703076i	−0.602338	+	0.0526978i
$179$	0.435152	+	0.753705i	0.0325248	+	0.0563346i	0.881830	−	0.471568i	$-0.156312\pi$
$179$	0.435152	+	0.753705i	0.0325248	+	0.0563346i	−0.849305	+	0.527903i	$0.822979\pi$
$180$	2.66840	+	10.6873i	0.198891	+	0.796586i
$181$	5.47447	−	9.48206i	0.406914	−	0.704796i	−0.587628	−	0.809131i	$-0.699938\pi$
$181$	5.47447	−	9.48206i	0.406914	−	0.704796i	0.994542	+	0.104335i	$0.0332715\pi$
$182$	−0.0720123	+	0.154431i	−0.00533791	+	0.0114472i
$183$	7.10153	+	15.2490i	0.524960	+	1.12724i
$184$	1.36565	+	1.62751i	0.100677	+	0.119982i
$185$	2.08613	+	13.0597i	0.153375	+	0.960168i
$186$	−1.77199	+	0.643958i	−0.129929	+	0.0472173i
$187$	−20.6486	+	14.4583i	−1.50998	+	1.05730i
$188$	12.9322	+	12.9322i	0.943177	+	0.943177i
$189$	−0.137013	+	0.770348i	−0.00996620	+	0.0560346i
$190$	−4.91824	−	8.84519i	−0.356807	−	0.641698i
$191$	14.0251	+	2.47300i	1.01482	+	0.178940i	0.656234	−	0.754557i	$-0.272148\pi$
$191$	14.0251	+	2.47300i	1.01482	+	0.178940i	0.358585	+	0.933497i	$0.383259\pi$
$192$	−0.640474	−	0.915656i	−0.0462223	−	0.0660818i
$193$	10.9821	−	5.12102i	0.790506	−	0.368619i	0.0149426	−	0.999888i	$-0.495243\pi$
$193$	10.9821	−	5.12102i	0.790506	−	0.368619i	0.775564	+	0.631269i	$0.217466\pi$
$194$	−1.63993	+	1.37607i	−0.117740	+	0.0987960i
$195$	0.759724	−	7.28611i	0.0544049	−	0.521769i
$196$	−10.7664	+	3.91864i	−0.769026	+	0.279903i
$197$	−2.87005	−	10.7112i	−0.204482	−	0.763138i	−0.989607	−	0.143800i	$-0.954068\pi$
$197$	−2.87005	−	10.7112i	−0.204482	−	0.763138i	0.785124	−	0.619338i	$-0.212599\pi$
$198$	9.87461	−	0.854069i	0.701758	−	0.0606961i
$199$	−3.29595	+	1.90292i	−0.233644	+	0.134894i	−0.612252	−	0.790663i	$-0.709736\pi$
$199$	−3.29595	+	1.90292i	−0.233644	+	0.134894i	0.378608	+	0.925557i	$0.376403\pi$
$200$	4.92041	−	9.72020i	0.347926	−	0.687322i
$201$	16.4065	+	9.48311i	1.15722	+	0.668887i
$202$	1.32155	−	1.88737i	0.0929842	−	0.132795i
$203$	−0.241956	+	0.345550i	−0.0169820	+	0.0242528i
$204$	11.2400	+	6.49681i	0.786954	+	0.454867i
$205$	−1.28316	+	0.867969i	−0.0896198	+	0.0606216i
$206$	−6.38197	+	3.68463i	−0.444653	+	0.256720i
$207$	−1.67543	−	2.39781i	−0.116450	−	0.166659i
$208$	0.969592	+	3.61857i	0.0672291	+	0.250902i
$209$	39.2589	−	14.2891i	2.71560	−	0.988397i
$210$	0.270968	−	0.219796i	0.0186986	−	0.0151674i
$211$	−0.117333	+	0.0984540i	−0.00807753	+	0.00677785i	−0.646817	−	0.762645i	$-0.723900\pi$
$211$	−0.117333	+	0.0984540i	−0.00807753	+	0.00677785i	0.638740	+	0.769423i	$0.279456\pi$
$212$	−0.431412	+	0.201171i	−0.0296295	+	0.0138165i
$213$	−2.90052	−	4.14674i	−0.198741	−	0.284130i
$214$	−0.728694	−	0.128488i	−0.0498125	−	0.00878329i
$215$	3.40276	−	1.89206i	0.232067	−	0.129037i
$216$	−5.64645	−	9.81355i	−0.384192	−	0.667728i
$217$	−0.193730	−	0.193730i	−0.0131512	−	0.0131512i
$218$	4.03007	−	2.82189i	0.272951	−	0.191122i
$219$	−16.7749	+	6.09617i	−1.13354	+	0.411941i
$220$	16.4202	+	11.8969i	1.10705	+	0.802086i
$221$	−5.54969	−	6.61386i	−0.373312	−	0.444896i
$222$	−2.58738	−	5.55582i	−0.173653	−	0.372882i
$223$	11.2041	−	24.0272i	0.750281	−	1.60898i	−0.0422168	−	0.999108i	$-0.513442\pi$
$223$	11.2041	−	24.0272i	0.750281	−	1.60898i	0.792498	−	0.609875i	$-0.208780\pi$
$224$	−0.417315	+	0.722811i	−0.0278830	+	0.0482948i
$225$	−7.92779	+	12.7338i	−0.528519	+	0.848921i
$226$	−0.597394	−	1.03472i	−0.0397381	−	0.0688283i
$227$	16.1589	−	1.41372i	1.07250	−	0.0938320i	0.462802	−	0.886462i	$-0.346844\pi$
$227$	16.1589	−	1.41372i	1.07250	−	0.0938320i	0.609703	+	0.792630i	$0.291289\pi$
$228$	−15.2074	−	15.2224i	−1.00713	−	1.00813i
$229$	−2.26795	+	0.399901i	−0.149871	+	0.0264262i	−0.248080	−	0.968740i	$-0.579800\pi$
$229$	−2.26795	+	0.399901i	−0.149871	+	0.0264262i	0.0982095	+	0.995166i	$0.468688\pi$
$230$	−0.134633	+	1.29742i	−0.00887744	+	0.0855492i
$231$	0.719532	+	1.24769i	0.0473417	+	0.0820921i
$232$	−0.532006	−	6.08085i	−0.0349279	−	0.399228i
$233$	1.47008	−	5.48640i	0.0963080	−	0.359426i	−0.900907	−	0.434013i	$-0.857097\pi$
$233$	1.47008	−	5.48640i	0.0963080	−	0.359426i	0.997215	+	0.0745868i	$0.0237638\pi$
$234$	0.586189	+	3.34379i	0.0383204	+	0.218590i
$235$	−0.401776	+	24.9012i	−0.0262090	+	1.62438i
$236$	0.584000	+	1.60453i	0.0380152	+	0.104446i
$237$	−1.83718	+	20.8801i	−0.119338	+	1.35631i
$238$	0.0358393	−	0.409645i	0.00232312	−	0.0265533i
$239$	−27.4639	−	9.99603i	−1.77649	−	0.646589i	−0.999862	−	0.0166299i	$-0.994706\pi$
$239$	−27.4639	−	9.99603i	−1.77649	−	0.646589i	−0.776628	−	0.629960i	$-0.783071\pi$
$240$	1.45744	−	7.53106i	0.0940775	−	0.486128i
$241$	−1.09121	+	6.18855i	−0.0702909	+	0.398639i	0.929281	+	0.369374i	$0.120428\pi$
$241$	−1.09121	+	6.18855i	−0.0702909	+	0.398639i	−0.999572	+	0.0292653i	$0.990683\pi$
$242$	8.24768	−	8.24768i	0.530181	−	0.530181i
$243$	6.55299	+	14.1442i	0.420375	+	0.907351i
$244$		−	15.9477i		−	1.02095i
$245$	−14.0318	−	6.82085i	−0.896459	−	0.435768i
$246$	0.461727	−	0.549712i	0.0294387	−	0.0350484i
$247$	6.04749	+	12.9689i	0.384792	+	0.825190i
$248$	3.94939	+	0.345527i	0.250787	+	0.0219410i
$249$	7.95955	+	9.49536i	0.504416	+	0.601744i
$250$	6.38873	−	1.98093i	0.404059	−	0.125285i
$251$	−7.99676	−	4.61693i	−0.504751	−	0.291418i	0.225923	−	0.974145i	$-0.427460\pi$
$251$	−7.99676	−	4.61693i	−0.504751	−	0.291418i	−0.730673	+	0.682727i	$0.760794\pi$
$252$	0.426077	−	0.607221i	0.0268403	−	0.0382513i
$253$	−5.20111	−	1.39363i	−0.326991	−	0.0876170i
$254$	3.04840	+	2.55791i	0.191274	+	0.160498i
$255$	4.29100	+	17.1500i	0.268713	+	1.07397i
$256$	−0.967687	−	5.48803i	−0.0604805	−	0.343002i
$257$	13.4782	+	9.43754i	0.840747	+	0.588697i	0.912663	−	0.408713i	$-0.134022\pi$
$257$	13.4782	+	9.43754i	0.840747	+	0.588697i	−0.0719158	+	0.997411i	$0.522911\pi$
$258$	−1.27644	+	1.27517i	−0.0794674	+	0.0793888i
$259$	0.572472	−	0.682246i	0.0355717	−	0.0423927i
$260$	−3.56912	+	5.95782i	−0.221348	+	0.369488i
$261$	−0.00831761	+	8.40425i	−0.000514847	+	0.520210i
$262$	7.81501	−	2.09402i	0.482813	−	0.129369i
$263$	−11.1166	−	5.18376i	−0.685480	−	0.319644i	0.0484930	−	0.998824i	$-0.484558\pi$
$263$	−11.1166	−	5.18376i	−0.685480	−	0.319644i	−0.733973	+	0.679179i	$0.762336\pi$
$264$	−19.5810	−	7.13787i	−1.20513	−	0.439306i
$265$	−0.605450	−	0.231494i	−0.0371925	−	0.0142206i
$266$	−0.233099	+	0.640435i	−0.0142922	+	0.0392676i
$267$	−21.1617	−	9.88059i	−1.29507	−	0.604683i
$268$	−10.3047	−	14.7166i	−0.629458	−	0.898959i
$269$	−18.4528			−1.12509			−0.562544	−	0.826767i	$-0.690177\pi$
$269$	−18.4528			−1.12509			−0.562544	+	0.826767i	$0.690177\pi$
$270$	1.91711	−	6.68160i	0.116672	−	0.406629i
$271$	−13.3622			−0.811695			−0.405848	−	0.913941i	$-0.633024\pi$
$271$	−13.3622			−0.811695			−0.405848	+	0.913941i	$0.633024\pi$
$272$	−5.18548	−	7.40563i	−0.314416	−	0.449032i
$273$	−0.404242	+	0.282755i	−0.0244658	+	0.0171131i
$274$	−1.67505	+	4.60215i	−0.101193	+	0.278026i
$275$	3.91498	+	27.3328i	0.236082	+	1.64823i
$276$	0.480212	+	2.73132i	0.0289054	+	0.164406i
$277$	−19.4680	−	9.07810i	−1.16972	−	0.545450i	−0.262018	−	0.965063i	$-0.584388\pi$
$277$	−19.4680	−	9.07810i	−1.16972	−	0.545450i	−0.907703	+	0.419613i	$0.862166\pi$
$278$	−10.5496	+	2.82676i	−0.632724	+	0.169538i
$279$	−5.37453	−	0.953160i	−0.321765	−	0.0570642i
$280$	−0.711632	+	0.178428i	−0.0425282	+	0.0106631i
$281$	4.46928	−	5.32628i	0.266615	−	0.317739i	−0.616082	−	0.787682i	$-0.711281\pi$
$281$	4.46928	−	5.32628i	0.266615	−	0.317739i	0.882697	+	0.469943i	$0.155725\pi$
$282$	−2.98153	−	11.1493i	−0.177548	−	0.663930i
$283$	−19.7874	−	13.8553i	−1.17624	−	0.823612i	−0.188864	−	0.982003i	$-0.560480\pi$
$283$	−19.7874	−	13.8553i	−1.17624	−	0.823612i	−0.987376	+	0.158391i	$0.949369\pi$
$284$	0.833098	+	4.72473i	0.0494353	+	0.280361i
$285$	0.487192	−	29.2964i	0.0288587	−	1.73537i
$286$	4.78706	+	4.01682i	0.283065	+	0.237520i
$287$	0.100767	+	0.0270006i	0.00594811	+	0.00159379i
$288$	1.43286	+	16.5664i	0.0844319	+	0.976187i
$289$	3.32171	+	1.91779i	0.195395	+	0.112811i
$290$	2.45493	−	2.83161i	0.144158	−	0.166278i
$291$	−6.10421	+	1.07322i	−0.357835	+	0.0629135i
$292$	16.8568	+	1.47478i	0.986468	+	0.0863048i
$293$	6.80096	+	14.5847i	0.397316	+	0.852048i	0.998594	+	0.0530076i	$0.0168808\pi$
$293$	6.80096	+	14.5847i	0.397316	+	0.852048i	−0.601278	+	0.799040i	$0.705341\pi$
$294$	7.11960	+	1.25901i	0.415224	+	0.0734270i
$295$	−1.01652	+	2.09118i	−0.0591841	+	0.121753i
$296$			12.8873i			0.749058i
$297$	25.9885	+	12.1656i	1.50800	+	0.705921i
$298$	−1.76845	+	1.76845i	−0.102443	+	0.102443i
$299$	0.320256	−	1.81626i	0.0185209	−	0.105037i
$300$	11.9100	−	7.77079i	0.687622	−	0.448647i
$301$	−0.246377	−	0.0896737i	−0.0142009	−	0.00516871i
$302$	−0.253528	+	2.89784i	−0.0145889	+	0.166752i
$303$	6.04696	−	2.81610i	0.347389	−	0.161781i
$304$	5.12477	+	14.0802i	0.293926	+	0.807555i
$305$	15.6016	−	15.1061i	0.893345	−	0.864975i
$306$	−4.08923	−	7.09897i	−0.233766	−	0.405821i
$307$	8.29849	−	30.9704i	0.473620	−	1.76757i	−0.152978	−	0.988230i	$-0.548886\pi$
$307$	8.29849	−	30.9704i	0.473620	−	1.76757i	0.626598	−	0.779343i	$-0.284447\pi$
$308$	−0.119010	−	1.36029i	−0.00678121	−	0.0775096i
$309$	−21.3350	−	0.0105575i	−1.21370	−	0.000600596i
$310$	1.53426	+	1.88955i	0.0871404	+	0.107319i
$311$	−17.6839	+	3.11815i	−1.00276	+	0.176814i	−0.650840	−	0.759215i	$-0.725583\pi$
$311$	−17.6839	+	3.11815i	−1.00276	+	0.176814i	−0.351922	+	0.936029i	$0.614472\pi$
$312$	1.85097	−	6.89425i	0.104790	−	0.390310i
$313$	−0.534419	+	0.0467556i	−0.0302071	+	0.00264278i	−0.102249	−	0.994759i	$-0.532604\pi$
$313$	−0.534419	+	0.0467556i	−0.0302071	+	0.00264278i	0.0720422	+	0.997402i	$0.477048\pi$
$314$	−5.20792	−	9.02038i	−0.293900	−	0.509049i
$315$	0.997634	−	0.158347i	0.0562103	−	0.00892187i
$316$	9.93599	−	17.2096i	0.558943	−	0.968118i
$317$	−12.4989	+	26.8041i	−0.702011	+	1.50547i	0.153758	+	0.988109i	$0.450862\pi$
$317$	−12.4989	+	26.8041i	−0.702011	+	1.50547i	−0.855769	+	0.517358i	$0.826915\pi$
$318$	0.299227	+	0.0263282i	0.0167798	+	0.00147641i
$319$	9.94420	+	11.8510i	0.556768	+	0.663531i
$320$	−0.846390	+	1.16820i	−0.0473146	+	0.0653041i
$321$	−1.64034	−	1.37780i	−0.0915551	−	0.0769011i
$322$	0.0719537	−	0.0503825i	0.00400982	−	0.00280771i
$323$	−24.4183	−	24.4183i	−1.35867	−	1.35867i
$324$	0.0292527	−	14.7787i	0.00162515	−	0.821039i
$325$	−9.20928	+	2.15175i	−0.510839	+	0.119358i
$326$	2.20335	+	0.388511i	0.122032	+	0.0215176i
$327$	14.1899	−	1.23438i	0.784703	−	0.0682613i
$328$	−1.36813	+	0.637968i	−0.0755422	+	0.0352259i
$329$	1.28474	−	1.07802i	0.0708298	−	0.0594333i
$330$	−5.21410	−	11.6851i	−0.287027	−	0.643244i
$331$	−24.8454	+	9.04298i	−1.36563	+	0.497047i	−0.917789	−	0.397068i	$-0.870028\pi$
$331$	−24.8454	+	9.04298i	−1.36563	+	0.497047i	−0.447837	+	0.894115i	$0.647805\pi$
$332$	−3.04024	−	11.3463i	−0.166855	−	0.622710i
$333$	1.56394	−	17.6745i	0.0857037	−	0.968556i
$334$	−0.272269	+	0.157195i	−0.0148979	+	0.00860130i
$335$	4.63631	−	24.0210i	0.253309	−	1.31241i
$336$	−0.447484	+	0.258060i	−0.0244123	+	0.0140783i
$337$	9.94021	−	14.1961i	0.541478	−	0.773310i	−0.451416	−	0.892314i	$-0.649081\pi$
$337$	9.94021	−	14.1961i	0.541478	−	0.773310i	0.992894	+	0.119003i	$0.0379699\pi$
$338$	3.23328	−	4.61761i	0.175867	−	0.251165i
$339$	0.00171170	−	3.45907i	9.29669e−5	−	0.187871i
$340$	3.17630	−	16.4566i	0.172259	−	0.892484i
$341$	−8.70159	+	5.02387i	−0.471218	+	0.272058i
$342$	3.50132	+	13.1190i	0.189330	+	0.709395i
$343$	0.544739	+	2.03299i	0.0294131	+	0.109771i
$344$	3.56512	−	1.29760i	0.192218	−	0.0699617i
$345$	−2.21717	+	3.05697i	−0.119368	+	0.164582i
$346$	−8.06488	+	6.76724i	−0.433571	+	0.363809i
$347$	7.58241	−	3.53574i	0.407045	−	0.189808i	−0.208302	−	0.978065i	$-0.566794\pi$
$347$	7.58241	−	3.53574i	0.407045	−	0.189808i	0.615347	+	0.788256i	$0.289016\pi$
$348$	3.37087	−	7.21952i	0.180698	−	0.387007i
$349$	21.0838	+	3.71764i	1.12859	+	0.199000i	0.706608	−	0.707605i	$-0.250224\pi$
$349$	21.0838	+	3.71764i	1.12859	+	0.199000i	0.421979	+	0.906605i	$0.361335\pi$
$350$	−0.382618	−	0.237684i	−0.0204518	−	0.0127047i
$351$	−3.37520	+	9.23062i	−0.180155	+	0.492694i
$352$	21.6439	+	21.6439i	1.15362	+	1.15362i
$353$	−23.8257	+	16.6830i	−1.26812	+	0.887944i	−0.997209	−	0.0746612i	$-0.976212\pi$
$353$	−23.8257	+	16.6830i	−1.26812	+	0.887944i	−0.270907	+	0.962606i	$0.587324\pi$
$354$	0.187632	−	1.06104i	0.00997253	−	0.0563939i
$355$	−3.83306	+	5.29042i	−0.203437	+	0.280786i
$356$	14.2323	+	16.9614i	0.754311	+	0.898953i
$357$	0.683328	−	0.974867i	0.0361656	−	0.0515954i
$358$	−0.220045	+	0.471889i	−0.0116298	+	0.0249401i
$359$	5.32734	−	9.22723i	0.281166	−	0.486995i	−0.690506	−	0.723327i	$-0.742612\pi$
$359$	5.32734	−	9.22723i	0.281166	−	0.486995i	0.971672	+	0.236332i	$0.0759454\pi$
$360$	−9.58576	+	11.0345i	−0.505214	+	0.581570i
$361$	19.1172	+	33.1119i	1.00617	+	1.74273i
$362$	6.52543	−	0.570901i	0.342969	−	0.0300059i
$363$	32.6224	−	8.72385i	1.71223	−	0.457883i
$364$	0.460587	−	0.0812140i	0.0241413	−	0.00425677i
$365$	14.5244	+	17.8879i	0.760244	+	0.936294i
$366$	−5.03616	+	8.71293i	−0.263244	+	0.455432i
$367$	1.87406	+	21.4206i	0.0978249	+	1.11814i	0.873438	+	0.486935i	$0.161885\pi$
$367$	1.87406	+	21.4206i	0.0978249	+	1.11814i	−0.775613	+	0.631209i	$0.782559\pi$
$368$	0.499826	−	1.86538i	0.0260552	−	0.0972395i
$369$	1.95376	−	0.708923i	0.101709	−	0.0369050i
$370$	−5.68430	+	5.50378i	−0.295512	+	0.286128i
$371$	0.0149294	+	0.0410181i	0.000775094	+	0.00212955i
$372$	4.23753	+	2.97028i	0.219706	+	0.154002i
$373$	0.957189	−	10.9407i	0.0495614	−	0.566489i	−0.930299	−	0.366803i	$-0.880452\pi$
$373$	0.957189	−	10.9407i	0.0495614	−	0.566489i	0.979860	−	0.199686i	$-0.0639922\pi$
$374$	−14.1712	−	5.15788i	−0.732773	−	0.266708i
$375$	18.8836	+	4.29075i	0.975144	+	0.221574i
$376$	−4.21410	+	23.8994i	−0.217326	+	1.23252i
$377$	−3.74681	+	3.74681i	−0.192970	+	0.192970i
$378$	−0.424539	+	0.197199i	−0.0218360	+	0.0101428i
$379$		−	9.48980i		−	0.487458i	−0.969843	−	0.243729i	$-0.921629\pi$
$379$		−	9.48980i		−	0.487458i	0.969843	−	0.243729i	$-0.0783708\pi$
$380$	−12.1443	+	24.9832i	−0.622990	+	1.28161i
$381$	3.93502	+	10.8280i	0.201597	+	0.554737i
$382$	3.60077	+	7.72187i	0.184231	+	0.395085i
$383$	−26.0555	−	2.27956i	−1.33137	−	0.116480i	−0.600846	−	0.799364i	$-0.705170\pi$
$383$	−26.0555	−	2.27956i	−1.33137	−	0.116480i	−0.730526	+	0.682884i	$0.760725\pi$
$384$	6.80491	−	18.6676i	0.347262	−	0.952626i
$385$	1.21803	−	1.40493i	0.0620768	−	0.0716018i
$386$	6.27815	+	3.62469i	0.319549	+	0.184492i
$387$	−5.04691	+	1.34696i	−0.256549	+	0.0684700i
$388$	5.67568	+	1.52079i	0.288139	+	0.0772066i
$389$	−2.90227	−	2.43529i	−0.147151	−	0.123474i	0.566240	−	0.824240i	$-0.308397\pi$
$389$	−2.90227	−	2.43529i	−0.147151	−	0.123474i	−0.713391	+	0.700766i	$0.752842\pi$
$390$	3.83140	−	2.12791i	0.194010	−	0.107751i
$391$	0.772861	+	4.38311i	0.0390852	+	0.221663i
$392$	−12.4536	−	8.72012i	−0.629003	−	0.440433i
$393$	22.6224	+	6.07367i	1.14115	+	0.306376i
$394$	4.26435	−	5.08205i	0.214835	−	0.256030i
$395$	26.2478	−	6.58112i	1.32067	−	0.331132i
$396$	−17.4660	−	20.8571i	−0.877702	−	1.04811i
$397$	−17.7987	+	4.76915i	−0.893292	+	0.239357i	−0.676133	−	0.736779i	$-0.736346\pi$
$397$	−17.7987	+	4.76915i	−0.893292	+	0.239357i	−0.217159	+	0.976136i	$0.569679\pi$
$398$	−2.06357	−	0.962257i	−0.103437	−	0.0482336i
$399$	−1.51214	+	1.26756i	−0.0757015	+	0.0634573i
$400$	−9.80290	+	1.40411i	−0.490145	+	0.0702053i
$401$	3.20835	−	8.81488i	0.160217	−	0.440194i	−0.833445	−	0.552603i	$-0.813635\pi$
$401$	3.20835	−	8.81488i	0.160217	−	0.440194i	0.993662	+	0.112409i	$0.0358567\pi$
$402$	0.982503	+	11.2944i	0.0490028	+	0.563315i
$403$	−1.97394	−	2.81907i	−0.0983288	−	0.140428i
$404$	−6.32405			−0.314633
$405$	14.4857	−	13.9702i	0.719798	−	0.694184i
$406$	−0.252370			−0.0125249
$407$	−18.7342	−	26.7552i	−0.928619	−	1.32621i
$408$	1.49293	+	17.1620i	0.0739108	+	0.849647i
$409$	−6.70343	+	18.4175i	−0.331464	+	0.910689i	0.656268	+	0.754528i	$0.272134\pi$
$409$	−6.70343	+	18.4175i	−0.331464	+	0.910689i	−0.987732	+	0.156161i	$0.950088\pi$
$410$	−0.865681	−	0.330993i	−0.0427529	−	0.0163466i
$411$	−10.8662	+	9.10866i	−0.535990	+	0.449297i
$412$	18.3317	+	8.54819i	0.903136	+	0.421139i
$413$	0.151244	−	0.0405257i	0.00744223	−	0.00199414i
$414$	0.600168	−	1.64388i	0.0294967	−	0.0807925i
$415$	8.22026	−	13.7218i	0.403517	−	0.673577i
$416$	−6.73895	+	8.03117i	−0.330404	+	0.393760i
$417$	−30.5384	−	8.19895i	−1.49547	−	0.401504i
$418$	20.4743	+	14.3363i	1.00143	+	0.701211i
$419$	−4.78282	−	27.1247i	−0.233656	−	1.32513i	−0.845426	−	0.534092i	$-0.820653\pi$
$419$	−4.78282	−	27.1247i	−0.233656	−	1.32513i	0.611770	−	0.791035i	$-0.290458\pi$
$420$	−0.920772	−	0.263205i	−0.0449291	−	0.0128431i
$421$	−7.89176	−	6.62197i	−0.384621	−	0.322735i	0.429892	−	0.902880i	$-0.358551\pi$
$421$	−7.89176	−	6.62197i	−0.384621	−	0.322735i	−0.814513	+	0.580145i	$0.802996\pi$
$422$	−0.0885121	−	0.0237167i	−0.00430870	−	0.00115451i
$423$	8.67982	−	32.2658i	0.422027	−	1.56882i
$424$	−0.547009	−	0.315816i	−0.0265651	−	0.0153374i
$425$	19.1081	−	12.4808i	0.926879	−	0.605407i
$426$	1.03688	−	2.84441i	0.0502368	−	0.137812i
$427$	−1.45686	−	0.127458i	−0.0705022	−	0.00616814i
$428$	0.858309	+	1.84065i	0.0414879	+	0.0889712i
$429$	6.17936	+	17.0038i	0.298343	+	0.820953i
$430$	2.09490	+	1.01833i	0.101025	+	0.0491082i
$431$			0.427248i			0.0205798i	0.999947	+	0.0102899i	$0.00327543\pi$
$431$			0.427248i			0.0205798i	−0.999947	+	0.0102899i	$0.996725\pi$
$432$	−4.36319	+	9.32075i	−0.209924	+	0.448445i
$433$	−12.7271	+	12.7271i	−0.611625	+	0.611625i	−0.943369	−	0.331744i	$-0.892363\pi$
$433$	−12.7271	+	12.7271i	−0.611625	+	0.611625i	0.331744	+	0.943369i	$0.392363\pi$
$434$	0.0284626	−	0.161419i	0.00136625	−	0.00774838i
$435$	10.2558	−	3.54083i	0.491729	−	0.169770i
$436$	−12.6892	−	4.61851i	−0.607705	−	0.221186i
$437$	0.642914	−	7.34854i	0.0307547	−	0.351528i
$438$	−8.74386	−	6.12896i	−0.417798	−	0.292853i
$439$	2.87705	+	7.90463i	0.137314	+	0.377267i	0.989222	−	0.146425i	$-0.0467766\pi$
$439$	2.87705	+	7.90463i	0.137314	+	0.377267i	−0.851908	+	0.523692i	$0.824554\pi$
$440$	−0.434068	+	26.9026i	−0.0206934	+	1.28253i
$441$	16.0215	+	13.4707i	0.762929	+	0.641461i
$442$	1.33687	−	4.98928i	0.0635885	−	0.237316i
$443$	0.764452	+	8.73772i	0.0363202	+	0.415142i	0.992490	+	0.122328i	$0.0390360\pi$
$443$	0.764452	+	8.73772i	0.0363202	+	0.415142i	−0.956170	+	0.292814i	$0.905408\pi$
$444$	−8.41814	+	14.5640i	−0.399507	+	0.691177i
$445$	−3.11203	+	29.9897i	−0.147525	+	1.42165i
$446$	15.6197	−	2.75417i	0.739614	−	0.130414i
$447$	−6.99482	+	1.87055i	−0.330844	+	0.0884738i
$448$	0.0967763	−	0.00846683i	0.00457225	−	0.000400020i
$449$	12.5244	+	21.6930i	0.591065	+	1.02375i	0.994089	+	0.108565i	$0.0346255\pi$
$449$	12.5244	+	21.6930i	0.591065	+	1.02375i	−0.403025	+	0.915189i	$0.632041\pi$
$450$	−8.96087	+	0.484448i	−0.422419	+	0.0228371i
$451$	1.91295	−	3.31332i	0.0900772	−	0.156018i
$452$	−1.38593	+	2.97213i	−0.0651886	+	0.139797i
$453$	−4.83388	+	6.89624i	−0.227116	+	0.324013i
$454$	6.23775	+	7.43386i	0.292752	+	0.348888i
$455$	0.515733	+	0.373663i	0.0241779	+	0.0175176i
$456$	4.97186	−	28.1154i	0.232829	−	1.31663i
$457$	27.1956	−	19.0426i	1.27216	−	0.890775i	0.274666	−	0.961540i	$-0.411433\pi$
$457$	27.1956	−	19.0426i	1.27216	−	0.890775i	0.997493	+	0.0707647i	$0.0225439\pi$
$458$	−0.974227	−	0.974227i	−0.0455226	−	0.0455226i
$459$	0.0352107	−	23.7183i	0.00164350	−	1.10708i
$460$	3.12902	−	1.73985i	0.145891	−	0.0811208i
$461$	33.1856	+	5.85151i	1.54561	+	0.272532i	0.880438	−	0.474161i	$-0.157249\pi$
$461$	33.1856	+	5.85151i	1.54561	+	0.272532i	0.665169	+	0.746693i	$0.268360\pi$
$462$	−0.364547	+	0.780766i	−0.0169603	+	0.0363245i
$463$	9.25121	−	4.31391i	0.429940	−	0.200484i	−0.195588	−	0.980686i	$-0.562661\pi$
$463$	9.25121	−	4.31391i	0.429940	−	0.200484i	0.625528	+	0.780202i	$0.284884\pi$
$464$	−4.25037	+	3.56648i	−0.197318	+	0.165570i
$465$	1.10810	+	6.95909i	0.0513868	+	0.322720i
$466$	3.19317	−	1.16222i	0.147921	−	0.0538388i
$467$	−2.02342	−	7.55151i	−0.0936327	−	0.349442i	0.903176	−	0.429271i	$-0.141229\pi$
$467$	−2.02342	−	7.55151i	−0.0936327	−	0.349442i	−0.996809	+	0.0798287i	$0.974563\pi$
$468$	6.59521	−	6.58216i	0.304863	−	0.304261i
$469$	−1.42675	+	0.823732i	−0.0658810	+	0.0380364i
$470$	−12.3412	+	8.34796i	−0.569257	+	0.385063i
$471$	0.0149222	−	30.1552i	0.000687577	−	1.38948i
$472$	−1.29957	+	1.85598i	−0.0598176	+	0.0854284i
$473$	−5.51520	+	7.87652i	−0.253589	+	0.362163i
$474$	−10.8631	+	6.26466i	−0.498960	+	0.287745i
$475$	−35.9443	+	11.7840i	−1.64924	+	0.540688i
$476$	−0.977453	+	0.564332i	−0.0448015	+	0.0258661i
$477$	0.711879	+	0.499514i	0.0325947	+	0.0228712i
$478$	−4.52548	−	16.8893i	−0.206991	−	0.772500i
$479$	−12.4057	+	4.51531i	−0.566831	+	0.206310i	−0.609509	−	0.792779i	$-0.708633\pi$
$479$	−12.4057	+	4.51531i	−0.566831	+	0.206310i	0.0426779	+	0.999089i	$0.486411\pi$
$480$	19.6039	−	8.74761i	0.894792	−	0.399272i
$481$	8.56981	−	7.19093i	0.390750	−	0.327878i
$482$	−3.40726	+	1.58883i	−0.155197	+	0.0723693i
$483$	0.253349	−	0.0220389i	0.0115278	−	0.00100280i
$484$	−31.5283	−	5.55928i	−1.43310	−	0.252695i
$485$	3.88838	+	6.99304i	0.176562	+	0.317537i
$486$	−4.68297	+	8.06500i	−0.212424	+	0.365836i
$487$	12.1497	+	12.1497i	0.550553	+	0.550553i	0.926601	−	0.376047i	$-0.122717\pi$
$487$	12.1497	+	12.1497i	0.550553	+	0.550553i	−0.376047	+	0.926601i	$0.622717\pi$
$488$	17.3345	−	12.1377i	0.784696	−	0.549450i
$489$	4.95991	+	4.16605i	0.224295	+	0.188395i
$490$	−1.47232	−	9.21712i	−0.0665128	−	0.416387i
$491$	−11.2054	−	13.3541i	−0.505693	−	0.602661i	0.451443	−	0.892300i	$-0.350909\pi$
$491$	−11.2054	−	13.3541i	−0.505693	−	0.602661i	−0.957136	+	0.289639i	$0.906465\pi$
$492$	−1.96286	−	0.172707i	−0.0884925	−	0.00778622i
$493$	5.40417	−	11.5893i	0.243392	−	0.521955i
$494$	−4.28045	+	7.41396i	−0.192587	+	0.333570i
$495$	3.86010	−	36.8434i	0.173499	−	1.65599i
$496$	−1.80181	−	3.12082i	−0.0809035	−	0.140129i
$497$	0.438272	−	0.0383438i	0.0196592	−	0.00171995i
$498$	−1.92206	+	7.15906i	−0.0861297	+	0.320805i
$499$	3.01325	−	0.531318i	0.134892	−	0.0237851i	−0.105795	−	0.994388i	$-0.533739\pi$
$499$	3.01325	−	0.531318i	0.134892	−	0.0237851i	0.240686	+	0.970603i	$0.422627\pi$
$500$	−14.5117	−	11.2456i	−0.648985	−	0.502917i
$501$	−0.910197		0.000450407i	−0.0406646		2.01227e-5i
$502$	−0.481473	−	5.50326i	−0.0214892	−	0.245623i
$503$	−1.77923	+	6.64016i	−0.0793318	+	0.296070i	−0.994181	−	0.107726i	$-0.965643\pi$
$503$	−1.77923	+	6.64016i	−0.0793318	+	0.296070i	0.914849	+	0.403797i	$0.132310\pi$
$504$	0.984308		0.000974161i	0.0438446		4.33926e-5i
$505$	−5.99032	−	6.18679i	−0.266566	−	0.275309i
$506$	−1.10178	−	3.02713i	−0.0489803	−	0.134572i
$507$	14.7944	−	6.88981i	0.657041	−	0.305987i
$508$	0.951954	−	10.8809i	0.0422361	−	0.482761i
$509$	28.5486	+	10.3908i	1.26540	+	0.460566i	0.885576	−	0.464495i	$-0.153764\pi$
$509$	28.5486	+	10.3908i	1.26540	+	0.460566i	0.379819	+	0.925061i	$0.375986\pi$
$510$	−6.93221	+	7.98789i	−0.306963	+	0.353710i
$511$	0.269447	−	1.52811i	0.0119196	−	0.0675997i
$512$	−13.8657	+	13.8657i	−0.612783	+	0.612783i
$513$	−10.2307	+	37.9560i	−0.451697	+	1.67580i
$514$			9.84374i			0.434189i
$515$	9.00160	+	26.0309i	0.396658	+	1.14706i
$516$	4.87657	+	0.862359i	0.214679	+	0.0379632i
$517$	−25.9935	−	55.7433i	−1.14319	−	2.45159i
$518$	0.530791	+	0.0464382i	0.0233216	+	0.00204038i
$519$	−30.0194	+	5.27791i	−1.31770	+	0.231674i
$520$	−9.19233	+	0.654984i	−0.403110	+	0.0287230i
$521$	−1.31724	−	0.760511i	−0.0577095	−	0.0333186i	0.470868	−	0.882204i	$-0.343941\pi$
$521$	−1.31724	−	0.760511i	−0.0577095	−	0.0333186i	−0.528577	+	0.848885i	$0.677274\pi$
$522$	−4.12152	+	2.87984i	−0.180394	+	0.126047i
$523$	−13.3371	−	3.57368i	−0.583192	−	0.156266i	−0.0448523	−	0.998994i	$-0.514282\pi$
$523$	−13.3371	−	3.57368i	−0.583192	−	0.156266i	−0.538340	+	0.842728i	$0.680948\pi$
$524$	−17.0114	−	14.2743i	−0.743148	−	0.623576i
$525$	−0.614689	−	1.15010i	−0.0268272	−	0.0501946i
$526$	−1.27426	−	7.22671i	−0.0555606	−	0.315100i
$527$	6.80317	+	4.76363i	0.296351	+	0.207507i
$528$	4.89410	+	18.3012i	0.212988	+	0.796459i
$529$	14.1730	−	16.8907i	0.616217	−	0.734379i
$530$	−0.0943121	−	0.376149i	−0.00409666	−	0.0163389i
$531$	2.00755	−	2.38771i	0.0871204	−	0.103618i
$532$	1.80690	−	0.484158i	0.0783391	−	0.0209909i
$533$	1.18763	+	0.553803i	0.0514421	+	0.0239879i
$534$	−2.41945	−	13.7612i	−0.104700	−	0.595505i
$535$	−0.987686	+	2.58320i	−0.0427014	+	0.111681i
$536$	8.15346	−	22.4015i	0.352176	−	0.967595i
$537$	−1.23523	+	0.864004i	−0.0533040	+	0.0372845i
$538$	−6.33208	−	9.04315i	−0.272995	−	0.389878i
$539$	38.5313			1.65966
$540$	−18.0408	+	6.20863i	−0.776353	+	0.267177i
$541$	0.376014			0.0161661			0.00808305	−	0.999967i	$-0.497427\pi$
$541$	0.376014			0.0161661			0.00808305	+	0.999967i	$0.497427\pi$
$542$	−4.58523	−	6.54839i	−0.196953	−	0.281278i
$543$	17.1834	+	8.02309i	0.737408	+	0.344304i
$544$	8.65328	−	23.7747i	0.371006	−	1.01933i
$545$	−7.50134	−	16.7886i	−0.321322	−	0.719146i
$546$	−0.277285	−	0.101079i	−0.0118667	−	0.00432578i
$547$	11.9323	+	5.56415i	0.510190	+	0.237906i	0.660627	−	0.750714i	$-0.270290\pi$
$547$	11.9323	+	5.56415i	0.510190	+	0.237906i	−0.150437	+	0.988620i	$0.548068\pi$
$548$	12.9844	−	3.47915i	0.554665	−	0.148622i
$549$	−25.2467	+	14.5429i	−1.07750	+	0.620675i
$550$	−12.0515	+	11.2979i	−0.513879	+	0.481743i
$551$	−13.6230	+	16.2353i	−0.580361	+	0.691647i
$552$	−2.60334	+	2.60076i	−0.110805	+	0.110696i
$553$	−1.49272	−	1.04522i	−0.0634770	−	0.0444471i
$554$	−2.23156	−	12.6558i	−0.0948101	−	0.537695i
$555$	−22.2218	+	5.56000i	−0.943263	+	0.236009i
$556$	22.9641	+	19.2691i	0.973893	+	0.817193i
$557$	−28.3906	−	7.60724i	−1.20295	−	0.322329i	−0.398957	−	0.916970i	$-0.630628\pi$
$557$	−28.3906	−	7.60724i	−1.20295	−	0.322329i	−0.803991	+	0.594641i	$0.797294\pi$
$558$	−1.37716	−	2.96097i	−0.0582996	−	0.125348i
$559$	−2.85217	−	1.64670i	−0.120634	−	0.0696479i
$560$	0.503877	+	0.436847i	0.0212927	+	0.0184602i
$561$	−28.0478	−	33.4597i	−1.18418	−	1.41267i
$562$	4.14388	+	0.362542i	0.174799	+	0.0152929i
$563$	−3.69329	−	7.92028i	−0.155653	−	0.333800i	0.812981	−	0.582290i	$-0.197843\pi$
$563$	−3.69329	−	7.92028i	−0.155653	−	0.333800i	−0.968634	+	0.248490i	$0.920066\pi$
$564$	−20.3738	+	24.2561i	−0.857890	+	1.02137i
$565$	−4.22042	+	1.45944i	−0.177554	+	0.0613991i
$566$		−	14.4516i		−	0.607448i
$567$	−1.34983	−	0.120787i	−0.0566874	−	0.00507259i
$568$	−4.50151	+	4.50151i	−0.188879	+	0.188879i
$569$	0.230736	−	1.30857i	0.00967296	−	0.0548581i	−0.979589	−	0.201010i	$-0.935578\pi$
$569$	0.230736	−	1.30857i	0.00967296	−	0.0548581i	0.989262	+	0.146152i	$0.0466888\pi$
$570$	14.5244	−	9.81430i	0.608361	−	0.411076i
$571$	−14.3584	−	5.22603i	−0.600881	−	0.218703i	0.0236277	−	0.999721i	$-0.492478\pi$
$571$	−14.3584	−	5.22603i	−0.600881	−	0.218703i	−0.624508	+	0.781018i	$0.714701\pi$
$572$	1.49490	−	17.0868i	0.0625050	−	0.714436i
$573$	−2.16202	+	24.5720i	−0.0903197	+	1.02651i
$574$	0.0213462	+	0.0586482i	0.000890974	+	0.00244793i
$575$	4.66599	+	1.41308i	0.194585	+	0.0589294i
$576$	1.48386	−	1.24260i	0.0618274	−	0.0517752i
$577$	−9.05878	+	33.8078i	−0.377122	+	1.40744i	0.473098	+	0.881010i	$0.343136\pi$
$577$	−9.05878	+	33.8078i	−0.377122	+	1.40744i	−0.850220	+	0.526428i	$0.823531\pi$
$578$	0.199995	+	2.28596i	0.00831871	+	0.0950833i
$579$	10.4850	+	18.1812i	0.435740	+	0.755587i
$580$	−10.2313	−	1.06170i	−0.424833	−	0.0440848i
$581$	−1.06081	+	0.187049i	−0.0440097	+	0.00776009i
$582$	−2.62061	−	2.62321i	−0.108628	−	0.108736i
$583$	1.59474	−	0.139522i	0.0660475	−	0.00577840i
$584$	11.2266	+	19.4450i	0.464560	+	0.804641i
$585$	12.6865	+	0.217252i	0.524521	+	0.00898228i
$586$	−4.81376	+	8.33768i	−0.198855	+	0.344426i
$587$	−13.4481	+	28.8395i	−0.555061	+	1.19033i	0.405968	+	0.913887i	$0.366934\pi$
$587$	−13.4481	+	28.8395i	−0.555061	+	1.19033i	−0.961030	+	0.276446i	$0.910843\pi$
$588$	−8.37782	−	17.9895i	−0.345496	−	0.741876i
$589$	−8.84789	−	10.5445i	−0.364571	−	0.434479i
$590$	−1.37364	+	0.219422i	−0.0565519	+	0.00903347i
$591$	18.0517	−	6.56015i	0.742546	−	0.269849i
$592$	9.59573	−	6.71900i	0.394382	−	0.276149i
$593$	14.3845	+	14.3845i	0.590702	+	0.590702i	0.937821	−	0.347119i	$-0.112840\pi$
$593$	14.3845	+	14.3845i	0.590702	+	0.590702i	−0.347119	+	0.937821i	$0.612840\pi$
$594$	2.95595	+	16.9108i	0.121284	+	0.693857i
$595$	−1.47795	−	0.421686i	−0.0605902	−	0.0172875i
$596$	6.76022	+	1.19201i	0.276909	+	0.0488266i
$597$	−3.77829	−	5.40164i	−0.154635	−	0.221074i
$598$	0.999988	−	0.466302i	0.0408925	−	0.0190685i
$599$	30.6931	−	25.7546i	1.25409	−	1.05230i	0.257801	−	0.966198i	$-0.417002\pi$
$599$	30.6931	−	25.7546i	1.25409	−	1.05230i	0.996286	−	0.0861056i	$-0.0274423\pi$
$600$	17.5111	+	7.03130i	0.714888	+	0.287051i
$601$	30.8662	−	11.2344i	1.25906	−	0.458260i	0.375606	−	0.926779i	$-0.377435\pi$
$601$	30.8662	−	11.2344i	1.25906	−	0.458260i	0.883453	+	0.468519i	$0.155212\pi$
$602$	−0.0405978	−	0.151513i	−0.00165464	−	0.00617521i
$603$	−13.9007	+	29.7334i	−0.566082	+	1.21084i
$604$	6.91453	−	3.99211i	0.281348	−	0.162436i
$605$	−24.4258	−	36.1099i	−0.993052	−	1.46808i
$606$	3.45510	+	1.99708i	0.140354	+	0.0811259i
$607$	−13.8740	+	19.8141i	−0.563129	+	0.804231i	−0.995226	−	0.0975958i	$-0.968885\pi$
$607$	−13.8740	+	19.8141i	−0.563129	+	0.804231i	0.432097	+	0.901827i	$0.357774\pi$
$608$	−24.0517	+	34.3494i	−0.975426	+	1.39305i
$609$	−0.632576	−	0.365636i	−0.0256333	−	0.0148163i
$610$	12.7567	+	2.46219i	0.516505	+	0.0996911i
$611$	18.2441	−	10.5332i	0.738075	−	0.426128i
$612$	−9.52330	+	20.3701i	−0.384956	+	0.823413i
$613$	−5.74896	−	21.4554i	−0.232198	−	0.866575i	−0.979392	−	0.201969i	$-0.935266\pi$
$613$	−5.74896	−	21.4554i	−0.232198	−	0.866575i	0.747194	−	0.664606i	$-0.231401\pi$
$614$	18.0252	−	6.56065i	0.727440	−	0.264766i
$615$	−1.69032	−	2.08385i	−0.0681602	−	0.0840290i
$616$	1.38800	−	1.16467i	0.0559239	−	0.0469258i
$617$	10.6189	−	4.95167i	0.427500	−	0.199347i	−0.196946	−	0.980414i	$-0.563102\pi$
$617$	10.6189	−	4.95167i	0.427500	−	0.199347i	0.624446	+	0.781068i	$0.285325\pi$
$618$	−7.31592	−	10.4592i	−0.294289	−	0.420732i
$619$	28.3482	+	4.99855i	1.13941	+	0.200909i	0.711347	−	0.702841i	$-0.248085\pi$
$619$	28.3482	+	4.99855i	1.13941	+	0.200909i	0.428062	+	0.903749i	$0.359197\pi$
$620$	1.83298	−	6.42434i	0.0736142	−	0.258008i
$621$	3.88601	−	3.25093i	0.155940	−	0.130455i
$622$	−7.59634	−	7.59634i	−0.304585	−	0.304585i
$623$	1.66321	−	1.16459i	0.0666349	−	0.0466583i
$624$	−6.09842	+	2.21623i	−0.244132	+	0.0887201i
$625$	−2.74444	−	24.8489i	−0.109778	−	0.993956i
$626$	−0.206299	−	0.245858i	−0.00824538	−	0.00982646i
$627$	30.5492	+	65.5978i	1.22002	+	2.61972i
$628$	−12.0821	+	25.9103i	−0.482130	+	1.03393i
$629$	−13.4987	+	23.3804i	−0.538228	+	0.932239i
$630$	0.419939	+	0.434572i	0.0167308	+	0.0173138i
$631$	−8.26145	−	14.3093i	−0.328883	−	0.569643i	0.653407	−	0.757007i	$-0.273339\pi$
$631$	−8.26145	−	14.3093i	−0.328883	−	0.569643i	−0.982291	+	0.187364i	$0.940006\pi$
$632$	26.2684	−	2.29819i	1.04490	−	0.0914169i
$633$	−0.187498	−	0.187684i	−0.00745238	−	0.00745975i
$634$	−17.4249	+	3.07247i	−0.692029	+	0.122023i
$635$	11.5464	−	9.37539i	0.458207	−	0.372051i
$636$	−0.411884	−	0.714219i	−0.0163322	−	0.0283206i
$637$	1.15023	+	13.1471i	0.0455736	+	0.520909i
$638$	−2.39547	+	8.94003i	−0.0948377	+	0.353939i
$639$	6.71996	−	5.62740i	0.265838	−	0.222616i
$640$	−25.6477	−	0.413820i	−1.01381	−	0.0163577i
$641$	−6.11791	−	16.8088i	−0.241643	−	0.663909i	−0.999928	−	0.0119858i	$-0.996185\pi$
$641$	−6.11791	−	16.8088i	−0.241643	−	0.663909i	0.758285	−	0.651923i	$-0.226038\pi$
$642$	0.112331	−	1.27667i	0.00443335	−	0.0503863i
$643$	1.84855	−	21.1290i	0.0728997	−	0.833247i	−0.868442	−	0.495791i	$-0.834878\pi$
$643$	1.84855	−	21.1290i	0.0728997	−	0.833247i	0.941341	−	0.337456i	$-0.109566\pi$
$644$	−0.226556	−	0.0824598i	−0.00892757	−	0.00324937i
$645$	3.77558	+	5.58758i	0.148663	+	0.220011i
$646$	3.58752	−	20.3458i	0.141149	−	0.800496i
$647$	7.44855	−	7.44855i	0.292833	−	0.292833i	−0.545366	−	0.838198i	$-0.683609\pi$
$647$	7.44855	−	7.44855i	0.292833	−	0.292833i	0.838198	+	0.545366i	$0.183609\pi$
$648$	16.0861	−	11.2162i	0.631920	−	0.440614i
$649$		−	5.74237i		−	0.225408i
$650$	−4.21467	−	3.77481i	−0.165313	−	0.148060i
$651$	0.305208	−	0.363367i	0.0119620	−	0.0142415i
$652$	−2.59527	−	5.56558i	−0.101639	−	0.217965i
$653$	45.7657	+	4.00398i	1.79095	+	0.156688i	0.933664	−	0.358150i	$-0.116592\pi$
$653$	45.7657	+	4.00398i	1.79095	+	0.156688i	0.857288	+	0.514838i	$0.172148\pi$
$654$	5.47419	+	6.53045i	0.214058	+	0.255361i
$655$	−2.14923	−	30.1633i	−0.0839774	−	1.17858i
$656$	1.18832	+	0.686078i	0.0463961	+	0.0267868i
$657$	−13.0371	−	28.0306i	−0.508627	−	1.09358i
$658$	0.969163	+	0.259686i	0.0377819	+	0.0101236i
$659$	3.34888	+	2.81004i	0.130454	+	0.109464i	0.705680	−	0.708531i	$-0.250642\pi$
$659$	3.34888	+	2.81004i	0.130454	+	0.109464i	−0.575226	+	0.817994i	$0.695086\pi$
$660$	−18.0637	+	30.1193i	−0.703129	+	1.17239i
$661$	6.57135	+	37.2680i	0.255596	+	1.44956i	0.794539	+	0.607214i	$0.207713\pi$
$661$	6.57135	+	37.2680i	0.255596	+	1.44956i	−0.538943	+	0.842342i	$0.681176\pi$
$662$	−12.9574	−	9.07285i	−0.503603	−	0.352626i
$663$	10.5794	−	10.5689i	0.410870	−	0.410464i
$664$	10.0190	−	11.9402i	0.388815	−	0.463371i
$665$	2.18520	+	1.30908i	0.0847383	+	0.0507638i
$666$	9.19839	−	5.29856i	0.356430	−	0.205315i
$667$	2.63846	−	0.706972i	0.102161	−	0.0273741i
$668$	0.782069	+	0.364685i	0.0302592	+	0.0141101i
$669$	43.1416	+	15.7264i	1.66795	+	0.608019i
$670$	13.3629	−	5.97069i	0.516253	−	0.230668i
$671$	−18.3434	+	50.3981i	−0.708140	+	1.94560i
$672$	−1.30988	−	0.611595i	−0.0505296	−	0.0235928i
$673$	24.7264	+	35.3130i	0.953134	+	1.36122i	0.932399	+	0.361431i	$0.117712\pi$
$673$	24.7264	+	35.3130i	0.953134	+	1.36122i	0.0207353	+	0.999785i	$0.493399\pi$
$674$	10.3680			0.399362
$675$	−23.1626	−	11.7683i	−0.891530	−	0.452961i
$676$	−15.4723			−0.595088
$677$	−22.6160	−	32.2989i	−0.869202	−	1.24135i	−0.969179	−	0.246359i	$-0.920766\pi$
$677$	−22.6160	−	32.2989i	−0.869202	−	1.24135i	0.0999769	−	0.994990i	$-0.468123\pi$
$678$	1.69577	−	1.18614i	0.0651256	−	0.0455534i
$679$	0.184289	−	0.506330i	0.00707236	−	0.0194312i
$680$	20.3051	−	9.07253i	0.778664	−	0.347916i
$681$	4.86495	+	27.6706i	0.186425	+	1.06034i
$682$	−5.44799	−	2.54044i	−0.208614	−	0.0972785i
$683$	−29.7818	+	7.98000i	−1.13957	+	0.305346i	−0.778777	−	0.627301i	$-0.784160\pi$
$683$	−29.7818	+	7.98000i	−1.13957	+	0.305346i	−0.360791	+	0.932647i	$0.617493\pi$
$684$	23.9841	−	28.5258i	0.917055	−	1.09071i
$685$	15.7028	+	9.40701i	0.599973	+	0.359423i
$686$	−0.809379	+	0.964580i	−0.0309022	+	0.0368279i
$687$	−1.03047	−	3.85340i	−0.0393150	−	0.147016i
$688$	−2.82491	−	1.97802i	−0.107699	−	0.0754115i
$689$	0.0952117	+	0.539972i	0.00362728	+	0.0205713i
$690$	−2.25895	−	0.0375658i	−0.0859967	−	0.00143010i
$691$	−14.5283	−	12.1907i	−0.552681	−	0.463755i	0.323166	−	0.946342i	$-0.395253\pi$
$691$	−14.5283	−	12.1907i	−0.552681	−	0.463755i	−0.875848	+	0.482587i	$0.839697\pi$
$692$	27.9119	+	7.47898i	1.06105	+	0.284308i
$693$	−2.04493	+	1.42886i	−0.0776805	+	0.0542779i
$694$	4.33466	+	2.50262i	0.164541	+	0.0949980i
$695$	2.90129	+	40.7179i	0.110052	+	1.54452i
$696$	10.4129	−	1.83076i	0.394699	−	0.0693946i
$697$	−3.15033	−	0.275618i	−0.119327	−	0.0104398i
$698$	5.41299	+	11.6082i	0.204885	+	0.439377i
$699$	9.68764	+	1.71314i	0.366420	+	0.0647968i
$700$	0.0679632	+	1.23445i	0.00256877	+	0.0466580i
$701$			10.8100i			0.408288i	0.978941	+	0.204144i	$0.0654410\pi$
$701$			10.8100i			0.408288i	−0.978941	+	0.204144i	$0.934559\pi$
$702$	−5.68184	+	1.51341i	−0.214447	+	0.0571199i
$703$	31.6397	−	31.6397i	1.19331	−	1.19331i
$704$	0.618659	−	3.50859i	0.0233166	−	0.132235i
$705$	−43.0283	+	3.04451i	−1.62054	+	0.114663i
$706$	−16.3516	−	5.95150i	−0.615401	−	0.223987i
$707$	−0.0505434	+	0.577714i	−0.00190088	+	0.0217272i
$708$	−2.68100	+	1.24856i	−0.100758	+	0.0469237i
$709$	11.3780	+	31.2608i	0.427310	+	1.17403i	0.947439	+	0.319937i	$0.103662\pi$
$709$	11.3780	+	31.2608i	0.427310	+	1.17403i	−0.520129	+	0.854088i	$0.674116\pi$
$710$	−3.90798	−	0.0630544i	−0.146664	−	0.00236639i
$711$	−36.3051	−	0.0359308i	−1.36155	−	0.00134751i
$712$	−7.60417	+	28.3792i	−0.284978	+	1.06355i
$713$	0.154621	+	1.76732i	0.00579060	+	0.0661868i
$714$	0.712236		0.000352447i	0.0266548		1.31900e-5i
$715$	18.1320	−	14.7227i	0.678098	−	0.550596i
$716$	1.40740	−	0.248162i	0.0525969	−	0.00927426i
$717$	13.1260	−	48.8903i	0.490201	−	1.82584i
$718$	6.35006	−	0.555558i	0.236982	−	0.0207332i
$719$	−20.7377	−	35.9188i	−0.773387	−	1.33955i	−0.935697	−	0.352806i	$-0.885228\pi$
$719$	−20.7377	−	35.9188i	−0.773387	−	1.33955i	0.162310	−	0.986740i	$-0.448106\pi$
$720$	13.2139	+	1.38442i	0.492452	+	0.0515944i
$721$	0.927405	−	1.60631i	0.0345384	−	0.0598222i
$722$	−9.66707	+	20.7311i	−0.359771	+	0.771532i
$723$	−10.8423	−	0.953989i	−0.403231	−	0.0354792i
$724$	−11.5567	−	13.7727i	−0.429501	−	0.511860i
$725$	−8.65274	−	11.0149i	−0.321355	−	0.409085i
$726$	15.4697	+	12.9936i	0.574133	+	0.482239i
$727$	−10.6642	+	7.46713i	−0.395512	+	0.276940i	−0.754367	−	0.656453i	$-0.772056\pi$
$727$	−10.6642	+	7.46713i	−0.395512	+	0.276940i	0.358855	+	0.933393i	$0.383167\pi$
$728$	0.438827	+	0.438827i	0.0162640	+	0.0162640i
$729$	−23.4227	+	13.4305i	−0.867506	+	0.497427i
$730$	−3.78223	+	13.2562i	−0.139986	+	0.490634i
$731$	7.82709	+	1.38013i	0.289495	+	0.0510458i
$732$	27.5184	−	2.39382i	1.01711	−	0.0884782i
$733$	−29.7979	+	13.8950i	−1.10061	+	0.513223i	−0.886098	−	0.463499i	$-0.846594\pi$
$733$	−29.7979	+	13.8950i	−1.10061	+	0.513223i	−0.214512	+	0.976721i	$0.568816\pi$
$734$	−9.85447	+	8.26888i	−0.363735	+	0.305210i
$735$	9.66338	−	25.2362i	0.356439	−	0.930851i
$736$	5.07856	−	1.84844i	0.187198	−	0.0681345i
$737$	15.6375	+	58.3601i	0.576016	+	2.14972i
$738$	1.01785	+	0.714212i	0.0374678	+	0.0262905i
$739$	−13.4399	+	7.75952i	−0.494394	+	0.285439i	−0.726396	−	0.687277i	$-0.758806\pi$
$739$	−13.4399	+	7.75952i	−0.494394	+	0.285439i	0.232001	+	0.972715i	$0.425473\pi$
$740$	21.3234	+	4.11565i	0.783863	+	0.151294i
$741$	−21.4705	+	12.3818i	−0.788738	+	0.454858i
$742$	−0.0149787	+	0.0213918i	−0.000549885	+	0.000785317i
$743$	17.7526	−	25.3533i	0.651279	−	0.930122i	−0.348696	−	0.937236i	$-0.613375\pi$
$743$	17.7526	−	25.3533i	0.651279	−	0.930122i	0.999975	+	0.00711360i	$0.00226435\pi$
$744$	−0.00339794	+	6.86668i	−0.000124575	+	0.251745i
$745$	5.23733	+	7.74260i	0.191881	+	0.283667i
$746$	5.69017	−	3.28522i	0.208332	−	0.120280i
$747$	−15.1898	+	15.1598i	−0.555766	+	0.554667i
$748$	10.7132	+	39.9821i	0.391712	+	1.46189i
$749$	0.175007	−	0.0636972i	0.00639460	−	0.00232745i
$750$	4.37713	+	10.7266i	0.159830	+	0.391681i
$751$	36.7847	−	30.8660i	1.34229	−	1.12632i	0.361263	−	0.932464i	$-0.382346\pi$
$751$	36.7847	−	30.8660i	1.34229	−	1.12632i	0.981030	−	0.193854i	$-0.0620989\pi$
$752$	19.9923	−	9.32256i	0.729044	−	0.339959i
$753$	6.76632	−	14.4917i	0.246578	−	0.528107i
$754$	−3.12191	−	0.550477i	−0.113693	−	0.0200472i
$755$	10.4551	+	2.98302i	0.380500	+	0.108563i
$756$	1.11174	+	0.644064i	0.0404335	+	0.0234244i
$757$	2.53936	+	2.53936i	0.0922948	+	0.0922948i	0.751747	−	0.659452i	$-0.229212\pi$
$757$	2.53936	+	2.53936i	0.0922948	+	0.0922948i	−0.659452	+	0.751747i	$0.729212\pi$
$758$	4.65066	−	3.25643i	0.168919	−	0.118279i
$759$	1.62405	−	9.18389i	0.0589494	−	0.333354i
$760$	−36.3986	+	5.81423i	−1.32032	+	0.210904i
$761$	−12.6924	−	15.1262i	−0.460099	−	0.548324i	0.485254	−	0.874373i	$-0.338727\pi$
$761$	−12.6924	−	15.1262i	−0.460099	−	0.548324i	−0.945353	+	0.326049i	$0.894283\pi$
$762$	−3.95619	+	5.64407i	−0.143318	+	0.204463i
$763$	−0.523325	+	1.12227i	−0.0189456	+	0.0406291i
$764$	11.6928	−	20.2525i	0.423030	−	0.732710i
$765$	−28.9487	+	9.97855i	−1.04664	+	0.360775i
$766$	−7.82380	−	13.5512i	−0.282685	−	0.489625i
$767$	1.95934	−	0.171420i	0.0707475	−	0.00618961i
$768$	9.32453	−	2.49355i	0.336470	−	0.0899784i
$769$	12.6400	−	2.22877i	0.455810	−	0.0803717i	0.0589709	−	0.998260i	$-0.481218\pi$
$769$	12.6400	−	2.22877i	0.455810	−	0.0803717i	0.396839	+	0.917888i	$0.370107\pi$
$770$	1.10648	+	0.114819i	0.0398748	+	0.00413780i
$771$	−14.2617	+	24.6737i	−0.513621	+	0.888602i
$772$	−1.73420	−	19.8220i	−0.0624152	−	0.713409i
$773$	−3.49320	+	13.0368i	−0.125642	+	0.468901i	−0.999862	−	0.0166290i	$-0.994707\pi$
$773$	−3.49320	+	13.0368i	−0.125642	+	0.468901i	0.874220	+	0.485530i	$0.161373\pi$
$774$	−2.39195	−	2.01112i	−0.0859770	−	0.0722884i
$775$	8.02116	−	4.29213i	0.288129	−	0.154178i
$776$	2.66670	+	7.32669i	0.0957289	+	0.263013i
$777$	1.26317	+	0.885412i	0.0453159	+	0.0317640i
$778$	0.197548	−	2.25798i	0.00708244	−	0.0809526i
$779$	4.92519	+	1.79262i	0.176463	+	0.0642274i
$780$	−10.8162	−	5.26435i	−0.387281	−	0.188494i
$781$	2.80173	−	15.8894i	0.100254	−	0.568567i
$782$	−1.88282	+	1.88282i	−0.0673295	+	0.0673295i
$783$	−14.5031	+	1.24716i	−0.518298	+	0.0445699i
$784$			13.8192i			0.493544i
$785$	−36.7925	+	12.7230i	−1.31318	+	0.454103i
$786$	4.78638	+	13.1707i	0.170724	+	0.469785i
$787$	−5.40813	−	11.5978i	−0.192779	−	0.413416i	0.786031	−	0.618187i	$-0.212133\pi$
$787$	−5.40813	−	11.5978i	−0.192779	−	0.413416i	−0.978810	+	0.204771i	$0.934355\pi$
$788$	−18.1397	−	1.58702i	−0.646202	−	0.0565353i
$789$	7.27611	−	19.9602i	0.259036	−	0.710602i
$790$	12.2321	+	10.6049i	0.435200	+	0.377306i
$791$	0.260433	+	0.150361i	0.00925995	+	0.00534623i
$792$	9.37745	−	34.8591i	0.333213	−	1.23866i
$793$	−17.7438	−	4.75443i	−0.630100	−	0.168835i
$794$	−8.44484	−	7.08606i	−0.299696	−	0.251475i
$795$	0.308570	−	1.07947i	0.0109439	−	0.0382850i
$796$	1.08521	+	6.15455i	0.0384643	+	0.218142i
$797$	9.22231	+	6.45753i	0.326671	+	0.228738i	0.725394	−	0.688334i	$-0.241658\pi$
$797$	9.22231	+	6.45753i	0.326671	+	0.228738i	−0.398723	+	0.917071i	$0.630546\pi$
$798$	−1.14008	−	0.306089i	−0.0403584	−	0.0108354i
$799$	−32.6786	+	38.9448i	−1.15608	+	1.37777i
$800$	−18.9542	−	20.2186i	−0.670133	−	0.714837i
$801$	13.8728	−	37.9983i	0.490173	−	1.34260i
$802$	5.42084	−	1.45251i	0.191417	−	0.0512899i
$803$	−51.5746	−	24.0496i	−1.82003	−	0.848693i
$804$	23.8472	−	19.9901i	0.841026	−	0.704996i
$805$	−0.133930	−	0.299747i	−0.00472043	−	0.0105647i
$806$	0.704184	−	1.93473i	0.0248038	−	0.0681480i
$807$	−2.76985	−	31.8410i	−0.0975032	−	1.12085i
$808$	−4.81320	−	6.87397i	−0.169328	−	0.241825i
$809$	−28.7457			−1.01065			−0.505323	−	0.862930i	$-0.668627\pi$
$809$	−28.7457			−1.01065			−0.505323	+	0.862930i	$0.668627\pi$
$810$	11.8171	+	2.30510i	0.415211	+	0.0809930i
$811$	9.97816			0.350380			0.175190	−	0.984535i	$-0.443946\pi$
$811$	9.97816			0.350380			0.175190	+	0.984535i	$0.443946\pi$
$812$	0.397312	+	0.567420i	0.0139429	+	0.0199125i
$813$	−2.00572	−	23.0569i	−0.0703438	−	0.808641i
$814$	6.68325	−	18.3621i	0.234248	−	0.643591i
$815$	2.98647	−	7.81082i	0.104611	−	0.273601i
$816$	12.0003	−	10.0593i	0.420095	−	0.352147i
$817$	−11.9385	−	5.56702i	−0.417676	−	0.194765i
$818$	−11.3261	+	3.03483i	−0.396009	+	0.106110i
$819$	−0.548583	−	0.655091i	−0.0191690	−	0.0228907i
$820$	0.618666	+	2.46745i	0.0216047	+	0.0861672i
$821$	−18.8449	+	22.4584i	−0.657691	+	0.783805i	−0.987052	−	0.160399i	$-0.948722\pi$
$821$	−18.8449	+	22.4584i	−0.657691	+	0.783805i	0.329362	+	0.944204i	$0.393166\pi$
$822$	−8.19261	−	2.19955i	−0.285750	−	0.0767181i
$823$	11.6066	+	8.12702i	0.404580	+	0.283290i	0.758102	−	0.652136i	$-0.226127\pi$
$823$	11.6066	+	8.12702i	0.404580	+	0.283290i	−0.353522	+	0.935426i	$0.615016\pi$
$824$	4.66062	+	26.4317i	0.162360	+	0.920792i
$825$	−46.5761	+	10.8582i	−1.62157	+	0.378034i
$826$	0.0717598	+	0.0602136i	0.00249684	+	0.00209510i
$827$	23.3257	+	6.25009i	0.811113	+	0.217337i	0.640457	−	0.767994i	$-0.278745\pi$
$827$	23.3257	+	6.25009i	0.811113	+	0.217337i	0.170656	+	0.985331i	$0.445411\pi$
$828$	−4.64090	+	1.23861i	−0.161283	+	0.0430445i
$829$	−3.60048	−	2.07874i	−0.125050	−	0.0721976i	0.436170	−	0.899864i	$-0.356335\pi$
$829$	−3.60048	−	2.07874i	−0.125050	−	0.0721976i	−0.561220	+	0.827667i	$0.689668\pi$
$830$	9.54541	−	0.680142i	0.331326	−	0.0236081i
$831$	12.7423	−	34.9554i	0.442027	−	1.21259i
$832$	1.21562	+	0.106353i	0.0421442	+	0.00368714i
$833$	−13.4598	−	28.8647i	−0.466356	−	1.00010i
$834$	−6.46122	−	17.7794i	−0.223734	−	0.615651i
$835$	0.384028	+	1.11053i	0.0132898	+	0.0384316i
$836$		−	68.6036i		−	2.37271i
$837$	0.837970	−	9.41701i	0.0289645	−	0.325499i
$838$	11.6517	−	11.6517i	0.402503	−	0.402503i
$839$	−8.22992	+	46.6742i	−0.284128	+	1.61137i	0.424255	+	0.905543i	$0.360536\pi$
$839$	−8.22992	+	46.6742i	−0.284128	+	1.61137i	−0.708383	+	0.705828i	$0.750575\pi$
$840$	−0.414703	−	1.20116i	−0.0143086	−	0.0414441i
$841$	19.8764	+	7.23443i	0.685394	+	0.249463i
$842$	0.537166	−	6.13984i	0.0185120	−	0.211593i
$843$	9.86154	+	6.91240i	0.339649	+	0.238076i
$844$	0.0860225	+	0.236345i	0.00296102	+	0.00813533i
$845$	−14.6558	−	15.1365i	−0.504174	−	0.520710i
$846$	18.7909	−	6.81829i	0.646046	−	0.234418i
$847$	−0.759833	+	2.83574i	−0.0261082	+	0.0974370i
$848$	0.0500394	+	0.571953i	0.00171836	+	0.0196410i
$849$	20.9376	−	36.2236i	0.718577	−	1.24319i
$850$	12.6734	+	5.08151i	0.434694	+	0.174294i
$851$	−5.67935	+	1.00142i	−0.194686	+	0.0343283i
$852$	−8.02764	+	2.14674i	−0.275022	+	0.0735462i
$853$	−21.8701	+	1.91338i	−0.748817	+	0.0655130i	−0.455174	−	0.890402i	$-0.650423\pi$
$853$	−21.8701	+	1.91338i	−0.748817	+	0.0655130i	−0.293643	+	0.955915i	$0.594868\pi$
$854$	−0.437456	−	0.757697i	−0.0149695	−	0.0259279i
$855$	50.6251	−	3.55685i	1.73134	−	0.121642i
$856$	−1.34745	+	2.33385i	−0.0460550	+	0.0797695i
$857$	8.58498	−	18.4106i	0.293257	−	0.628893i	−0.703381	−	0.710813i	$-0.748327\pi$
$857$	8.58498	−	18.4106i	0.293257	−	0.628893i	0.996639	+	0.0819200i	$0.0261052\pi$
$858$	−6.21261	+	8.86318i	−0.212095	+	0.302584i
$859$	21.1435	+	25.1978i	0.721405	+	0.859737i	0.994767	−	0.102174i	$-0.0325798\pi$
$859$	21.1435	+	25.1978i	0.721405	+	0.859737i	−0.273361	+	0.961911i	$0.588135\pi$
$860$	−1.00847	−	6.31327i	−0.0343884	−	0.215281i
$861$	−0.0314648	+	0.177931i	−0.00107232	+	0.00606386i
$862$	−0.209381	+	0.146610i	−0.00713154	+	0.00499356i
$863$	8.90068	+	8.90068i	0.302983	+	0.302983i	0.842180	−	0.539197i	$-0.181272\pi$
$863$	8.90068	+	8.90068i	0.302983	+	0.302983i	−0.539197	+	0.842180i	$0.681272\pi$
$864$	−28.3709	+	4.95914i	−0.965197	+	0.168713i
$865$	19.1223	+	34.3904i	0.650178	+	1.16931i
$866$	−10.6045	−	1.86985i	−0.360354	−	0.0635402i
$867$	−2.81061	+	6.01960i	−0.0954534	+	0.204436i
$868$	−0.407738	+	0.190132i	−0.0138395	+	0.00645349i
$869$	−51.1947	+	42.9575i	−1.73666	+	1.45723i
$870$	5.25453	+	3.81102i	0.178145	+	0.129206i
$871$	−19.4461	+	7.07780i	−0.658905	+	0.239822i
$872$	−4.63761	−	17.3078i	−0.157049	−	0.586116i
$873$	−2.76815	−	10.3719i	−0.0936878	−	0.351037i
$874$	3.82191	−	2.20658i	0.129278	−	0.0746386i
$875$	−1.14329	+	1.23580i	−0.0386501	+	0.0417776i
$876$	−0.0145031	+	29.3083i	−0.000490014	+	0.990236i
$877$	−23.0489	+	32.9173i	−0.778307	+	1.11154i	0.212620	+	0.977135i	$0.431801\pi$
$877$	−23.0489	+	32.9173i	−0.778307	+	1.11154i	−0.990927	+	0.134403i	$0.957088\pi$
$878$	−2.88655	+	4.12243i	−0.0974165	+	0.139125i
$879$	−24.1456	+	13.9245i	−0.814410	+	0.469662i
$880$	20.2577	−	13.7029i	0.682888	−	0.461926i
$881$	5.14179	−	2.96862i	0.173231	−	0.100015i	−0.410877	−	0.911691i	$-0.634778\pi$
$881$	5.14179	−	2.96862i	0.173231	−	0.100015i	0.584109	+	0.811675i	$0.301444\pi$
$882$	−1.10378	+	12.4741i	−0.0371663	+	0.420025i
$883$	5.97531	+	22.3002i	0.201085	+	0.750460i	0.990607	+	0.136738i	$0.0436619\pi$
$883$	5.97531	+	22.3002i	0.201085	+	0.750460i	−0.789522	+	0.613722i	$0.789671\pi$
$884$	−13.3224	+	4.84894i	−0.448080	+	0.163088i
$885$	−3.76098	−	1.44015i	−0.126424	−	0.0484100i
$886$	−4.01977	+	3.37298i	−0.135047	+	0.113318i
$887$	−24.7531	+	11.5426i	−0.831127	+	0.387561i	−0.791137	−	0.611639i	$-0.790510\pi$
$887$	−24.7531	+	11.5426i	−0.831127	+	0.387561i	−0.0399903	+	0.999200i	$0.512733\pi$
$888$	−22.2374	+	1.93444i	−0.746240	+	0.0649155i
$889$	−0.986381	−	0.173926i	−0.0330822	−	0.00583328i
$890$	−15.7649	+	8.76587i	−0.528442	+	0.293833i
$891$	−17.0912	+	46.6701i	−0.572577	+	1.56351i
$892$	−30.7828	−	30.7828i	−1.03068	−	1.03068i
$893$	69.0217	−	48.3295i	2.30972	−	1.61728i
$894$	−3.31697	−	2.78607i	−0.110936	−	0.0931800i
$895$	1.57590	+	1.14179i	0.0526766	+	0.0381657i
$896$	1.11034	+	1.32325i	0.0370938	+	0.0442067i
$897$	3.18209	+	0.279984i	0.106247	+	0.00934838i
$898$	−6.33328	+	13.5818i	−0.211344	+	0.453230i
$899$	2.54854	−	4.41421i	0.0849987	−	0.147222i
$900$	15.1965	+	19.3846i	0.506550	+	0.646154i
$901$	−0.661599	−	1.14592i	−0.0220411	−	0.0381762i
$902$	2.28018	−	0.199490i	0.0759218	−	0.00664230i
$903$	0.117753	−	0.438592i	0.00391857	−	0.0145954i
$904$	−4.28541	+	0.755633i	−0.142530	+	0.0251320i
$905$	2.52698	−	24.3518i	0.0839998	−	0.809481i
$906$	−5.03838	−	0.00249322i	−0.167389	−	8.28316e-5i
$907$	−2.00584	−	22.9269i	−0.0666030	−	0.761275i	−0.953909	−	0.300095i	$-0.902982\pi$
$907$	−2.00584	−	22.9269i	−0.0666030	−	0.761275i	0.887306	−	0.461180i	$-0.152574\pi$
$908$	6.89380	−	25.7280i	0.228779	−	0.853814i
$909$	5.76696	+	10.0115i	0.191278	+	0.332062i
$910$	−0.00614681	+	0.380967i	−0.000203765	+	0.0126289i
$911$	−14.7689	−	40.5773i	−0.489316	−	1.34439i	−0.901301	−	0.433194i	$-0.857386\pi$
$911$	−14.7689	−	40.5773i	−0.489316	−	1.34439i	0.411984	−	0.911191i	$-0.364836\pi$
$912$	−23.5266	+	10.9565i	−0.779044	+	0.362805i
$913$	−3.44300	+	39.3537i	−0.113947	+	1.30242i
$914$	18.6644	+	6.79328i	0.617363	+	0.224702i
$915$	28.4080	+	24.6536i	0.939140	+	0.815023i
$916$	−0.656670	+	3.72416i	−0.0216970	+	0.123050i
$917$	−1.43994	+	1.43994i	−0.0475511	+	0.0475511i
$918$	11.6357	−	8.12169i	0.384035	−	0.268056i
$919$		−	4.18974i		−	0.138207i	−0.997609	−	0.0691034i	$-0.977986\pi$
$919$		−	4.18974i		−	0.138207i	0.997609	−	0.0691034i	$-0.0220139\pi$
$920$	4.27262	+	2.07692i	0.140864	+	0.0684741i
$921$	54.6861	+	9.67053i	1.80197	+	0.318655i
$922$	8.51999	+	18.2712i	0.280591	+	0.601729i
$923$	5.50521	+	0.481644i	0.181206	+	0.0158535i
$924$	2.32936	−	0.409540i	0.0766303	−	0.0134729i
$925$	16.1718	+	24.7590i	0.531725	+	0.814072i
$926$	5.28866	+	3.05341i	0.173796	+	0.100341i
$927$	−3.18425	−	36.8158i	−0.104585	−	1.20919i
$928$	−14.9985	−	4.01884i	−0.492350	−	0.131925i
$929$	−30.3026	−	25.4269i	−0.994196	−	0.834229i	−0.00802588	−	0.999968i	$-0.502555\pi$
$929$	−30.3026	−	25.4269i	−0.994196	−	0.834229i	−0.986170	+	0.165739i	$0.946999\pi$
$930$	−3.03019	+	2.93106i	−0.0993638	+	0.0961131i
$931$	9.16617	+	51.9839i	0.300409	+	1.70370i
$932$	−7.64017	−	5.34970i	−0.250262	−	0.175235i
$933$	−8.03490	−	30.0461i	−0.263051	−	0.983666i
$934$	3.00642	−	3.58291i	0.0983731	−	0.117237i
$935$	−28.9665	+	48.3528i	−0.947306	+	1.58131i
$936$	12.1741	+	2.15905i	0.397923	+	0.0705707i
$937$	15.6076	−	4.18203i	0.509877	−	0.136621i	0.00529663	−	0.999986i	$-0.498314\pi$
$937$	15.6076	−	4.18203i	0.509877	−	0.136621i	0.504580	+	0.863365i	$0.331647\pi$
$938$	−0.893273	−	0.416540i	−0.0291664	−	0.0136005i
$939$	−0.160897	−	0.915140i	−0.00525067	−	0.0298645i
$940$	38.1982	+	14.6051i	1.24589	+	0.476366i
$941$	−1.64321	+	4.51470i	−0.0535673	+	0.147175i	−0.963591	−	0.267382i	$-0.913841\pi$
$941$	−1.64321	+	4.51470i	−0.0535673	+	0.147175i	0.910023	+	0.414557i	$0.136064\pi$
$942$	14.7832	−	10.3404i	0.481664	−	0.336910i
$943$	−0.387461	−	0.553352i	−0.0126175	−	0.0180196i
$944$	2.05950			0.0670309
$945$	0.422983	+	1.69768i	0.0137596	+	0.0552256i
$946$	−5.75258			−0.187033
$947$	4.77585	+	6.82062i	0.155194	+	0.221640i	0.889218	−	0.457483i	$-0.151249\pi$
$947$	4.77585	+	6.82062i	0.155194	+	0.221640i	−0.734024	+	0.679124i	$0.762360\pi$
$948$	31.1873	+	14.5617i	1.01292	+	0.472941i
$949$	6.66631	−	18.3155i	0.216398	−	0.594548i
$950$	−18.1093	−	13.5715i	−0.587543	−	0.440318i
$951$	−48.1275	−	17.5440i	−1.56064	−	0.568902i
$952$	−1.35734	−	0.632938i	−0.0439916	−	0.0205136i
$953$	48.7769	−	13.0697i	1.58004	−	0.423370i	0.641101	−	0.767456i	$-0.278478\pi$
$953$	48.7769	−	13.0697i	1.58004	−	0.423370i	0.938938	+	0.344086i	$0.111811\pi$
$954$	−0.000514915		0.520278i	−1.66710e−5		0.0168446i
$955$	30.8887	−	7.74474i	0.999535	−	0.250614i
$956$	−30.8488	+	36.7641i	−0.997720	+	1.18904i
$957$	−18.9567	+	18.9379i	−0.612783	+	0.612177i
$958$	−6.46983	−	4.53022i	−0.209031	−	0.146365i
$959$	−0.214053	−	1.21395i	−0.00691212	−	0.0392006i
$960$	−2.14281	−	1.28512i	−0.0691588	−	0.0414772i
$961$	−21.2114	−	17.7985i	−0.684239	−	0.574145i
$962$	6.46478	+	1.73223i	0.208433	+	0.0558494i
$963$	2.13121	−	3.03728i	0.0686774	−	0.0978751i
$964$	8.93639	+	5.15943i	0.287822	+	0.166174i
$965$	17.7491	−	20.4725i	0.571363	−	0.659033i
$966$	0.0977373	+	0.116596i	0.00314465	+	0.00375141i
$967$	48.8782	+	4.27628i	1.57182	+	0.137516i	0.839466	−	0.543413i	$-0.182868\pi$
$967$	48.8782	+	4.27628i	1.57182	+	0.137516i	0.732350	+	0.680929i	$0.238424\pi$
$968$	−17.9533	−	38.5010i	−0.577041	−	1.23747i
$969$	38.4694	−	45.8000i	1.23582	−	1.47131i
$970$	−2.09277	+	4.30523i	−0.0671949	+	0.138233i
$971$			49.8235i			1.59891i	0.600725	+	0.799456i	$0.294879\pi$
$971$			49.8235i			1.59891i	−0.600725	+	0.799456i	$0.705121\pi$
$972$	25.5055	−	2.16787i	0.818091	−	0.0695344i
$973$	1.94381	−	1.94381i	0.0623156	−	0.0623156i
$974$	−1.78501	+	10.1233i	−0.0571956	+	0.324372i
$975$	−5.09528	−	15.5679i	−0.163179	−	0.498573i
$976$	−18.0753	−	6.57886i	−0.578575	−	0.210584i
$977$	−4.83254	+	55.2362i	−0.154607	+	1.76716i	0.382793	+	0.923834i	$0.374962\pi$
$977$	−4.83254	+	55.2362i	−0.154607	+	1.76716i	−0.537400	+	0.843328i	$0.680593\pi$
$978$	−0.339656	+	3.86028i	−0.0108610	+	0.123438i
$979$	−25.4677	−	69.9719i	−0.813951	−	2.23631i
$980$	−18.4055	+	17.8210i	−0.587943	+	0.569272i
$981$	4.25993	+	24.2999i	0.136009	+	0.775835i
$982$	2.69929	−	10.0739i	0.0861377	−	0.321470i
$983$	5.35195	+	61.1731i	0.170701	+	1.95112i	0.287061	+	0.957912i	$0.407322\pi$
$983$	5.35195	+	61.1731i	0.170701	+	1.95112i	−0.116360	+	0.993207i	$0.537123\pi$
$984$	−1.30620	−	2.26499i	−0.0416401	−	0.0722052i
$985$	−15.6299	−	19.2493i	−0.498010	−	0.613334i
$986$	7.53399	−	1.32845i	0.239931	−	0.0423063i
$987$	2.05301	+	2.05504i	0.0653480	+	0.0654127i
$988$	23.4081	−	2.04794i	0.744710	−	0.0651536i
$989$	0.848876	+	1.47030i	0.0269927	+	0.0467527i
$990$	19.3804	−	10.7511i	0.615950	−	0.341692i
$991$	−23.2830	+	40.3274i	−0.739609	+	1.28104i	0.213062	+	0.977039i	$0.431656\pi$
$991$	−23.2830	+	40.3274i	−0.739609	+	1.28104i	−0.952671	+	0.304002i	$0.901677\pi$
$992$	4.26205	−	9.13999i	0.135320	−	0.290195i
$993$	−19.3334	−	41.5142i	−0.613526	−	1.31741i
$994$	0.169184	+	0.201626i	0.00536619	+	0.00639518i
$995$	−4.99303	+	6.89142i	−0.158290	+	0.218473i
$996$	19.1221	−	6.94917i	0.605907	−	0.220193i
$997$	15.2890	−	10.7055i	0.484208	−	0.339046i	−0.305848	−	0.952080i	$-0.598940\pi$
$997$	15.2890	−	10.7055i	0.484208	−	0.339046i	0.790056	+	0.613034i	$0.210051\pi$
$998$	1.29438	+	1.29438i	0.0409729	+	0.0409729i
$999$	30.7327	+	0.0456238i	0.972339	+	0.00144347i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.2.11	✓	192
3.2	odd	2		405.2.r.a.332.6		192
5.2	odd	4		675.2.ba.b.218.6		192
5.3	odd	4	inner	135.2.q.a.83.11	yes	192
5.4	even	2		675.2.ba.b.407.6		192
15.8	even	4		405.2.r.a.8.6		192
27.13	even	9		405.2.r.a.152.6		192
27.14	odd	18	inner	135.2.q.a.122.11	yes	192
135.13	odd	36		405.2.r.a.233.6		192
135.14	odd	18		675.2.ba.b.257.6		192
135.68	even	36	inner	135.2.q.a.68.11	yes	192
135.122	even	36		675.2.ba.b.68.6		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.11	✓	192	1.1	even	1	trivial
135.2.q.a.68.11	yes	192	135.68	even	36	inner
135.2.q.a.83.11	yes	192	5.3	odd	4	inner
135.2.q.a.122.11	yes	192	27.14	odd	18	inner
405.2.r.a.8.6		192	15.8	even	4
405.2.r.a.152.6		192	27.13	even	9
405.2.r.a.233.6		192	135.13	odd	36
405.2.r.a.332.6		192	3.2	odd	2
675.2.ba.b.68.6		192	135.122	even	36
675.2.ba.b.218.6		192	5.2	odd	4
675.2.ba.b.257.6		192	135.14	odd	18
675.2.ba.b.407.6		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)

\(f(q)\)	\(=\)	\(q+(0.343150 + 0.490069i) q^{2} +(0.150104 + 1.72553i) q^{3} +(0.561625 - 1.54305i) q^{4} +(2.04155 - 0.912186i) q^{5} +(-0.794122 + 0.665679i) q^{6} +(-0.136472 - 0.0636379i) q^{7} +(2.10468 - 0.563947i) q^{8} +(-2.95494 + 0.518020i) q^{9} +O(q^{10})\)	\(q+(0.343150 + 0.490069i) q^{2} +(0.150104 + 1.72553i) q^{3} +(0.561625 - 1.54305i) q^{4} +(2.04155 - 0.912186i) q^{5} +(-0.794122 + 0.665679i) q^{6} +(-0.136472 - 0.0636379i) q^{7} +(2.10468 - 0.563947i) q^{8} +(-2.95494 + 0.518020i) q^{9} +(1.14759 + 0.687482i) q^{10} +(-3.54970 + 4.23037i) q^{11} +(2.74689 + 0.737484i) q^{12} +(-1.54940 - 1.08490i) q^{13} +(-0.0156434 - 0.0887180i) q^{14} +(1.88045 + 3.38584i) q^{15} +(-1.51722 - 1.27310i) q^{16} +(4.40907 + 1.18141i) q^{17} +(-1.26785 - 1.27036i) q^{18} +(-6.55178 - 3.78267i) q^{19} +(-0.260967 - 3.66252i) q^{20} +(0.0893244 - 0.245039i) q^{21} +(-3.29125 - 0.287947i) q^{22} +(0.412075 + 0.883698i) q^{23} +(1.28903 + 3.54705i) q^{24} +(3.33583 - 3.72454i) q^{25} -1.13159i q^{26} +(-1.33741 - 5.02109i) q^{27} +(-0.174843 + 0.174843i) q^{28} +(0.486461 - 2.75886i) q^{29} +(-1.01402 + 2.08340i) q^{30} +(1.70974 + 0.622294i) q^{31} +(0.483084 - 5.52167i) q^{32} +(-7.83247 - 5.49013i) q^{33} +(0.934001 + 2.56615i) q^{34} +(-0.336664 - 0.00543199i) q^{35} +(-0.860234 + 4.85055i) q^{36} +(-1.53079 + 5.71298i) q^{37} +(-0.394473 - 4.50885i) q^{38} +(1.63946 - 2.83639i) q^{39} +(3.78238 - 3.07118i) q^{40} +(-0.682276 + 0.120304i) q^{41} +(0.150738 - 0.0403102i) q^{42} +(1.73456 - 0.151755i) q^{43} +(4.53407 + 7.85325i) q^{44} +(-5.56011 + 3.75302i) q^{45} +(-0.291669 + 0.505186i) q^{46} +(-4.70696 + 10.0941i) q^{47} +(1.96903 - 2.80911i) q^{48} +(-4.48494 - 5.34494i) q^{49} +(2.96997 + 0.356711i) q^{50} +(-1.37674 + 7.78533i) q^{51} +(-2.54423 + 1.78149i) q^{52} +(-0.204978 - 0.204978i) q^{53} +(2.00175 - 2.37841i) q^{54} +(-3.38800 + 11.8745i) q^{55} +(-0.323118 - 0.0569745i) q^{56} +(5.54368 - 11.8731i) q^{57} +(1.51896 - 0.708303i) q^{58} +(-0.796564 + 0.668396i) q^{59} +(6.28063 - 1.00007i) q^{60} +(9.12620 - 3.32167i) q^{61} +(0.281730 + 1.05143i) q^{62} +(0.436232 + 0.117351i) q^{63} +(-0.558711 + 0.322572i) q^{64} +(-4.15280 - 0.801535i) q^{65} +(0.00283170 - 5.72239i) q^{66} +(6.27537 - 8.96216i) q^{67} +(4.29921 - 6.13991i) q^{68} +(-1.46300 + 0.843697i) q^{69} +(-0.112864 - 0.166852i) q^{70} +(-2.53024 + 1.46084i) q^{71} +(-5.92706 + 2.75670i) q^{72} +(2.66706 + 9.95358i) q^{73} +(-3.32505 + 1.21022i) q^{74} +(6.92755 + 5.19702i) q^{75} +(-9.51649 + 7.98529i) q^{76} +(0.753647 - 0.351431i) q^{77} +(1.95261 - 0.169857i) q^{78} +(11.9179 + 2.10144i) q^{79} +(-4.25878 - 1.21510i) q^{80} +(8.46331 - 3.06144i) q^{81} +(-0.293080 - 0.293080i) q^{82} +(5.85978 - 4.10306i) q^{83} +(-0.327942 - 0.275452i) q^{84} +(10.0790 - 1.60999i) q^{85} +(0.669585 + 0.797981i) q^{86} +(4.83353 + 0.425289i) q^{87} +(-5.08528 + 10.9054i) q^{88} +(-6.74192 + 11.6773i) q^{89} +(-3.74719 - 1.43699i) q^{90} +(0.142409 + 0.246659i) q^{91} +(1.59502 - 0.139546i) q^{92} +(-0.817150 + 3.04362i) q^{93} +(-6.56201 + 1.15706i) q^{94} +(-16.8263 - 1.74606i) q^{95} +(9.60035 + 0.00475069i) q^{96} +(0.311872 + 3.56471i) q^{97} +(1.08038 - 4.03205i) q^{98} +(8.29773 - 14.3393i) 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

Varieties

Fields

Representations

Groups

Database

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