LMFDB - Embedded newform 135.2.q.a.2.16

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			2.16
Character	$\chi$	$=$	135.2
Dual form			135.2.q.a.68.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.43892 + 2.05499i) q^{2} +(1.64201 - 0.551185i) q^{3} +(-1.46845 + 4.03452i) q^{4} +(-0.953539 - 2.02256i) q^{5} +(3.49539 + 2.58120i) q^{6} +(-2.44940 - 1.14217i) q^{7} +(-5.55747 + 1.48912i) q^{8} +(2.39239 - 1.81010i) q^{9} +O(q^{10})$	\(q+(1.43892 + 2.05499i) q^{2} +(1.64201 - 0.551185i) q^{3} +(-1.46845 + 4.03452i) q^{4} +(-0.953539 - 2.02256i) q^{5} +(3.49539 + 2.58120i) q^{6} +(-2.44940 - 1.14217i) q^{7} +(-5.55747 + 1.48912i) q^{8} +(2.39239 - 1.81010i) q^{9} +(2.78428 - 4.86981i) q^{10} +(-2.09979 + 2.50243i) q^{11} +(-0.187436 + 7.43411i) q^{12} +(-2.57758 - 1.80484i) q^{13} +(-1.17733 - 6.67697i) q^{14} +(-2.68053 - 2.79549i) q^{15} +(-4.47891 - 3.75825i) q^{16} +(5.88806 + 1.57770i) q^{17} +(7.16218 + 2.31175i) q^{18} +(-2.91796 - 1.68469i) q^{19} +(9.56030 - 0.877047i) q^{20} +(-4.65148 - 0.525389i) q^{21} +(-8.16389 - 0.714248i) q^{22} +(2.10003 + 4.50352i) q^{23} +(-8.30464 + 5.50834i) q^{24} +(-3.18153 + 3.85719i) q^{25} -7.89390i q^{26} +(2.93063 - 4.29085i) q^{27} +(8.20493 - 8.20493i) q^{28} +(-0.541940 + 3.07349i) q^{29} +(1.88765 - 9.53092i) q^{30} +(0.346096 + 0.125969i) q^{31} +(0.275472 - 3.14866i) q^{32} +(-2.06857 + 5.26639i) q^{33} +(5.23028 + 14.3701i) q^{34} +(0.0254777 + 6.04317i) q^{35} +(3.78979 + 12.3102i) q^{36} +(1.14721 - 4.28145i) q^{37} +(-0.736698 - 8.42050i) q^{38} +(-5.22721 - 1.54284i) q^{39} +(8.31110 + 9.82040i) q^{40} +(7.54663 - 1.33068i) q^{41} +(-5.61343 - 10.3147i) q^{42} +(4.42293 - 0.386956i) q^{43} +(-7.01269 - 12.1463i) q^{44} +(-5.94228 - 3.11276i) q^{45} +(-6.23291 + 10.7957i) q^{46} +(2.90859 - 6.23750i) q^{47} +(-9.42590 - 3.70238i) q^{48} +(0.195477 + 0.232960i) q^{49} +(-12.5044 - 0.987828i) q^{50} +(10.5379 - 0.654808i) q^{51} +(11.0667 - 7.74898i) q^{52} +(-3.48010 - 3.48010i) q^{53} +(13.0346 - 0.151776i) q^{54} +(7.06356 + 1.86079i) q^{55} +(15.3133 + 2.70014i) q^{56} +(-5.71990 - 1.15794i) q^{57} +(-7.09579 + 3.30882i) q^{58} +(-5.87095 + 4.92631i) q^{59} +(15.2147 - 6.70961i) q^{60} +(-6.73344 + 2.45077i) q^{61} +(0.239140 + 0.892481i) q^{62} +(-7.92737 + 1.70113i) q^{63} +(-3.26012 + 1.88223i) q^{64} +(-1.19258 + 6.93430i) q^{65} +(-13.7989 + 3.32701i) q^{66} +(0.221089 - 0.315748i) q^{67} +(-15.0116 + 21.4388i) q^{68} +(5.93054 + 6.23732i) q^{69} +(-12.3820 + 8.74797i) q^{70} +(-8.46099 + 4.88495i) q^{71} +(-10.6002 + 13.6221i) q^{72} +(0.00667095 + 0.0248963i) q^{73} +(10.4491 - 3.80315i) q^{74} +(-3.09808 + 8.08714i) q^{75} +(11.0818 - 9.29871i) q^{76} +(8.00143 - 3.73113i) q^{77} +(-4.35099 - 12.9619i) q^{78} +(-10.9549 - 1.93165i) q^{79} +(-3.33049 + 12.6425i) q^{80} +(2.44707 - 8.66094i) q^{81} +(13.5935 + 13.5935i) q^{82} +(-0.896484 + 0.627725i) q^{83} +(8.95014 - 17.9950i) q^{84} +(-2.42349 - 13.4134i) q^{85} +(7.15941 + 8.53226i) q^{86} +(0.804192 + 5.34541i) q^{87} +(7.94310 - 17.0340i) q^{88} +(3.93198 - 6.81039i) q^{89} +(-2.15376 - 16.6903i) q^{90} +(4.25207 + 7.36481i) q^{91} +(-21.2533 + 1.85943i) q^{92} +(0.637725 + 0.0160789i) q^{93} +(17.0032 - 2.99812i) q^{94} +(-0.624996 + 7.50818i) q^{95} +(-1.28317 - 5.32197i) q^{96} +(-0.446850 - 5.10752i) q^{97} +(-0.197455 + 0.736913i) q^{98} +(-0.493864 + 9.78763i) 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 $

$2$	1.43892	+	2.05499i	1.01747	+	1.45309i	0.887071	+	0.461633i	$0.152736\pi$
$2$	1.43892	+	2.05499i	1.01747	+	1.45309i	0.130396	+	0.991462i	$0.458375\pi$
$3$	1.64201	−	0.551185i	0.948015	−	0.318227i
$3$	1.64201	−	0.551185i	0.948015	−	0.318227i
$4$	−1.46845	+	4.03452i	−0.734223	+	2.01726i
$5$	−0.953539	−	2.02256i	−0.426435	−	0.904518i
$5$	−0.953539	−	2.02256i	−0.426435	−	0.904518i
$6$	3.49539	+	2.58120i	1.42699	+	1.05377i
$7$	−2.44940	−	1.14217i	−0.925785	−	0.431701i	−0.0995542	−	0.995032i	$-0.531742\pi$
$7$	−2.44940	−	1.14217i	−0.925785	−	0.431701i	−0.826231	+	0.563331i	$0.809519\pi$
$8$	−5.55747	+	1.48912i	−1.96486	+	0.526483i
$9$	2.39239	−	1.81010i	0.797464	−	0.603367i
$10$	2.78428	−	4.86981i	0.880466	−	1.53997i
$11$	−2.09979	+	2.50243i	−0.633111	+	0.754512i	−0.983265	−	0.182180i	$-0.941685\pi$
$11$	−2.09979	+	2.50243i	−0.633111	+	0.754512i	0.350155	+	0.936692i	$0.386129\pi$
$12$	−0.187436	+	7.43411i	−0.0541081	+	2.14604i
$13$	−2.57758	−	1.80484i	−0.714891	−	0.500572i	0.158642	−	0.987336i	$-0.449288\pi$
$13$	−2.57758	−	1.80484i	−0.714891	−	0.500572i	−0.873534	+	0.486764i	$0.838177\pi$
$14$	−1.17733	−	6.67697i	−0.314655	−	1.78450i
$15$	−2.68053	−	2.79549i	−0.692109	−	0.721793i
$16$	−4.47891	−	3.75825i	−1.11973	−	0.939563i
$17$	5.88806	+	1.57770i	1.42807	+	0.382649i	0.888338	−	0.459191i	$-0.151861\pi$
$17$	5.88806	+	1.57770i	1.42807	+	0.382649i	0.539728	+	0.841840i	$0.318527\pi$
$18$	7.16218	+	2.31175i	1.68814	+	0.544884i
$19$	−2.91796	−	1.68469i	−0.669427	−	0.386494i	0.126433	−	0.991975i	$-0.459647\pi$
$19$	−2.91796	−	1.68469i	−0.669427	−	0.386494i	−0.795859	+	0.605481i	$0.792981\pi$
$20$	9.56030	−	0.877047i	2.13775	−	0.196114i
$21$	−4.65148	−	0.525389i	−1.01504	−	0.114649i
$22$	−8.16389	−	0.714248i	−1.74055	−	0.152278i
$23$	2.10003	+	4.50352i	0.437886	+	0.939049i	0.994146	+	0.108041i	$0.0344579\pi$
$23$	2.10003	+	4.50352i	0.437886	+	0.939049i	−0.556261	+	0.831008i	$0.687764\pi$
$24$	−8.30464	+	5.50834i	−1.69518	+	1.12438i
$25$	−3.18153	+	3.85719i	−0.636306	+	0.771437i
$26$		−	7.89390i		−	1.54812i
$27$	2.93063	−	4.29085i	0.564000	−	0.825775i
$28$	8.20493	−	8.20493i	1.55059	−	1.55059i
$29$	−0.541940	+	3.07349i	−0.100636	+	0.570733i	0.892238	+	0.451565i	$0.149134\pi$
$29$	−0.541940	+	3.07349i	−0.100636	+	0.570733i	−0.992874	+	0.119169i	$0.961977\pi$
$30$	1.88765	−	9.53092i	0.344636	−	1.74010i
$31$	0.346096	+	0.125969i	0.0621607	+	0.0226246i	0.372913	−	0.927866i	$-0.378359\pi$
$31$	0.346096	+	0.125969i	0.0621607	+	0.0226246i	−0.310753	+	0.950491i	$0.600581\pi$
$32$	0.275472	−	3.14866i	0.0486971	−	0.556610i
$33$	−2.06857	+	5.26639i	−0.360092	+	0.916761i
$34$	5.23028	+	14.3701i	0.896985	+	2.46445i
$35$	0.0254777	+	6.04317i	0.00430652	+	1.02148i
$36$	3.78979	+	12.3102i	0.631632	+	2.05170i
$37$	1.14721	−	4.28145i	0.188600	−	0.703866i	−0.805231	−	0.592962i	$-0.797959\pi$
$37$	1.14721	−	4.28145i	0.188600	−	0.703866i	0.993831	−	0.110904i	$-0.0353747\pi$
$38$	−0.736698	−	8.42050i	−0.119508	−	1.36599i
$39$	−5.22721	−	1.54284i	−0.837023	−	0.247052i
$40$	8.31110	+	9.82040i	1.31410	+	1.55274i
$41$	7.54663	−	1.33068i	1.17859	−	0.207817i	0.450164	−	0.892946i	$-0.351365\pi$
$41$	7.54663	−	1.33068i	1.17859	−	0.207817i	0.728422	+	0.685129i	$0.240254\pi$
$42$	−5.61343	−	10.3147i	−0.866171	−	1.59160i
$43$	4.42293	−	0.386956i	0.674490	−	0.0590102i	0.255236	−	0.966879i	$-0.417847\pi$
$43$	4.42293	−	0.386956i	0.674490	−	0.0590102i	0.419255	+	0.907869i	$0.362291\pi$
$44$	−7.01269	−	12.1463i	−1.05720	−	1.83113i
$45$	−5.94228	−	3.11276i	−0.885823	−	0.464023i
$46$	−6.23291	+	10.7957i	−0.918992	+	1.59174i
$47$	2.90859	−	6.23750i	0.424262	−	0.909832i	−0.571735	−	0.820439i	$-0.693729\pi$
$47$	2.90859	−	6.23750i	0.424262	−	0.909832i	0.995996	−	0.0893938i	$-0.0284930\pi$
$48$	−9.42590	−	3.70238i	−1.36051	−	0.534392i
$49$	0.195477	+	0.232960i	0.0279253	+	0.0332800i
$50$	−12.5044	−	0.987828i	−1.76839	−	0.139700i
$51$	10.5379	−	0.654808i	1.47560	−	0.0916915i
$52$	11.0667	−	7.74898i	1.53467	−	1.07459i
$53$	−3.48010	−	3.48010i	−0.478029	−	0.478029i	0.426472	−	0.904501i	$-0.359756\pi$
$53$	−3.48010	−	3.48010i	−0.478029	−	0.478029i	−0.904501	+	0.426472i	$0.859756\pi$
$54$	13.0346	−	0.151776i	1.77378	−	0.0206542i
$55$	7.06356	+	1.86079i	0.952450	+	0.250909i
$56$	15.3133	+	2.70014i	2.04632	+	0.360822i
$57$	−5.71990	−	1.15794i	−0.757619	−	0.153372i
$58$	−7.09579	+	3.30882i	−0.931723	+	0.434470i
$59$	−5.87095	+	4.92631i	−0.764332	+	0.641351i	−0.939251	−	0.343232i	$-0.888478\pi$
$59$	−5.87095	+	4.92631i	−0.764332	+	0.641351i	0.174918	+	0.984583i	$0.444034\pi$
$60$	15.2147	−	6.70961i	1.96421	−	0.866207i
$61$	−6.73344	+	2.45077i	−0.862128	+	0.313789i	−0.734975	−	0.678094i	$-0.762806\pi$
$61$	−6.73344	+	2.45077i	−0.862128	+	0.313789i	−0.127153	+	0.991883i	$0.540584\pi$
$62$	0.239140	+	0.892481i	0.0303708	+	0.113345i
$63$	−7.92737	+	1.70113i	−0.998754	+	0.214323i
$64$	−3.26012	+	1.88223i	−0.407515	+	0.235279i
$65$	−1.19258	+	6.93430i	−0.147922	+	0.860094i
$66$	−13.7989	+	3.32701i	−1.69852	+	0.409526i
$67$	0.221089	−	0.315748i	0.0270103	−	0.0385747i	−0.805420	−	0.592705i	$-0.798060\pi$
$67$	0.221089	−	0.315748i	0.0270103	−	0.0385747i	0.832430	+	0.554130i	$0.186949\pi$
$68$	−15.0116	+	21.4388i	−1.82042	+	2.59983i
$69$	5.93054	+	6.23732i	0.713953	+	0.750885i
$70$	−12.3820	+	8.74797i	−1.47993	+	1.04558i
$71$	−8.46099	+	4.88495i	−1.00413	+	0.579737i	−0.909469	−	0.415772i	$-0.863511\pi$
$71$	−8.46099	+	4.88495i	−1.00413	+	0.579737i	−0.0946655	+	0.995509i	$0.530178\pi$
$72$	−10.6002	+	13.6221i	−1.24924	+	1.60538i
$73$	0.00667095	+	0.0248963i	0.000780776	+	0.00291389i	0.966315	−	0.257362i	$-0.0828532\pi$
$73$	0.00667095	+	0.0248963i	0.000780776	+	0.00291389i	−0.965534	+	0.260276i	$0.916187\pi$
$74$	10.4491	−	3.80315i	1.21468	−	0.442107i
$75$	−3.09808	+	8.08714i	−0.357735	+	0.933823i
$76$	11.0818	−	9.29871i	1.27117	−	1.06664i
$77$	8.00143	−	3.73113i	0.911848	−	0.425202i
$78$	−4.35099	−	12.9619i	−0.492653	−	1.46764i
$79$	−10.9549	−	1.93165i	−1.23253	−	0.217327i	−0.480816	−	0.876822i	$-0.659659\pi$
$79$	−10.9549	−	1.93165i	−1.23253	−	0.217327i	−0.751710	+	0.659494i	$0.770770\pi$
$80$	−3.33049	+	12.6425i	−0.372360	+	1.41348i
$81$	2.44707	−	8.66094i	0.271897	−	0.962326i
$82$	13.5935	+	13.5935i	1.50115	+	1.50115i
$83$	−0.896484	+	0.627725i	−0.0984019	+	0.0689018i	−0.621742	−	0.783222i	$-0.713575\pi$
$83$	−0.896484	+	0.627725i	−0.0984019	+	0.0689018i	0.523340	+	0.852124i	$0.324686\pi$
$84$	8.95014	−	17.9950i	0.976540	−	1.96342i
$85$	−2.42349	−	13.4134i	−0.262865	−	1.45489i
$86$	7.15941	+	8.53226i	0.772019	+	0.920057i
$87$	0.804192	+	5.34541i	0.0862184	+	0.573089i
$88$	7.94310	−	17.0340i	0.846737	−	1.81583i
$89$	3.93198	−	6.81039i	0.416789	−	0.721900i	−0.578825	−	0.815452i	$-0.696489\pi$
$89$	3.93198	−	6.81039i	0.416789	−	0.721900i	0.995614	+	0.0935515i	$0.0298220\pi$
$90$	−2.15376	−	16.6903i	−0.227027	−	1.75931i
$91$	4.25207	+	7.36481i	0.445738	+	0.772042i
$92$	−21.2533	+	1.85943i	−2.21581	+	0.193858i
$93$	0.637725	+	0.0160789i	0.0661290	+	0.00166731i
$94$	17.0032	−	2.99812i	1.75375	−	0.309233i
$95$	−0.624996	+	7.50818i	−0.0641232	+	0.770323i
$96$	−1.28317	−	5.32197i	−0.130963	−	0.543171i
$97$	−0.446850	−	5.10752i	−0.0453707	−	0.518590i	−0.984543	−	0.175143i	$-0.943961\pi$
$97$	−0.446850	−	5.10752i	−0.0453707	−	0.518590i	0.939172	−	0.343447i	$-0.111594\pi$
$98$	−0.197455	+	0.736913i	−0.0199460	+	0.0744394i
$99$	−0.493864	+	9.78763i	−0.0496352	+	0.983694i
$100$	−10.8900	−	18.5000i	−1.08900	−	1.85000i
$101$	0.406707	+	1.11742i	0.0404688	+	0.111187i	0.958281	−	0.285827i	$-0.0922684\pi$
$101$	0.406707	+	1.11742i	0.0404688	+	0.111187i	−0.917812	+	0.397015i	$0.870046\pi$
$102$	16.5087	+	20.7129i	1.63461	+	2.05089i
$103$	0.0163965	−	0.187413i	0.00161560	−	0.0184664i	−0.995344	−	0.0963852i	$-0.969272\pi$
$103$	0.0163965	−	0.187413i	0.00161560	−	0.0184664i	0.996960	+	0.0779188i	$0.0248275\pi$
$104$	17.0124	+	6.19202i	1.66821	+	0.607177i
$105$	3.37274	+	9.90890i	0.329145	+	0.967009i
$106$	2.14398	−	12.1591i	0.208242	−	1.18100i
$107$	1.76707	−	1.76707i	0.170829	−	0.170829i	−0.616515	−	0.787344i	$-0.711456\pi$
$107$	1.76707	−	1.76707i	0.170829	−	0.170829i	0.787344	+	0.616515i	$0.211456\pi$
$108$	13.0081	+	18.1246i	1.25170	+	1.74404i
$109$		−	7.80745i		−	0.747818i	−0.927465	−	0.373909i	$-0.878017\pi$
$109$		−	7.80745i		−	0.747818i	0.927465	−	0.373909i	$-0.121983\pi$
$110$	6.33997	+	17.1930i	0.604492	+	1.63929i
$111$	−0.476138	−	7.66250i	−0.0451930	−	0.727293i
$112$	6.67806	+	14.3211i	0.631017	+	1.35322i
$113$	19.4214	+	1.69916i	1.82701	+	0.159843i	0.948273	−	0.317455i	$-0.102828\pi$
$113$	19.4214	+	1.69916i	1.82701	+	0.159843i	0.878741	+	0.477298i	$0.158384\pi$
$114$	−5.85091	−	13.4205i	−0.547988	−	1.25694i
$115$	7.10620	−	8.54172i	0.662657	−	0.796519i
$116$	−11.6043	−	6.69973i	−1.07743	−	0.622054i
$117$	−9.43351	+	0.347794i	−0.872129	+	0.0321536i
$118$	−18.5713	−	4.97617i	−1.70963	−	0.458093i
$119$	−12.6202	−	10.5896i	−1.15689	−	0.970748i
$120$	19.0598	+	11.5442i	1.73991	+	1.05384i
$121$	0.0570802	+	0.323718i	0.00518911	+	0.0294289i
$122$	−14.7252	−	10.3107i	−1.33315	−	0.933484i
$123$	11.6582	−	6.34457i	1.05118	−	0.572071i
$124$	−1.01645	+	1.21135i	−0.0912796	+	0.108783i
$125$	10.8351	+	2.75687i	0.969122	+	0.246582i
$126$	−14.9026	−	13.8428i	−1.32763	−	1.23322i
$127$	20.6263	−	5.52679i	1.83028	−	0.490423i	0.832326	−	0.554286i	$-0.187009\pi$
$127$	20.6263	−	5.52679i	1.83028	−	0.490423i	0.997959	+	0.0638628i	$0.0203420\pi$
$128$	−14.2881	−	6.66265i	−1.26290	−	0.588901i
$129$	7.04921	−	3.07324i	0.620648	−	0.270583i
$130$	−15.9659	+	7.52714i	−1.40030	+	0.660174i
$131$	−5.67190	+	15.5834i	−0.495556	+	1.36153i	0.399973	+	0.916527i	$0.369020\pi$
$131$	−5.67190	+	15.5834i	−0.495556	+	1.36153i	−0.895529	+	0.445003i	$0.853203\pi$
$132$	−18.2098	−	16.0791i	−1.58496	−	1.39951i
$133$	5.22305	+	7.45929i	0.452896	+	0.646802i
$134$	0.966985			0.0835348
$135$	−11.4730	−	1.83589i	−0.987438	−	0.158008i
$136$	−35.0721			−3.00741
$137$	−11.4989	−	16.4221i	−0.982418	−	1.40304i	−0.914152	−	0.405371i	$-0.867142\pi$
$137$	−11.4989	−	16.4221i	−0.982418	−	1.40304i	−0.0682654	−	0.997667i	$-0.521746\pi$
$138$	−4.28407	+	21.1622i	−0.364684	+	1.80144i
$139$	−6.07923	+	16.7026i	−0.515634	+	1.41669i	0.359652	+	0.933087i	$0.382895\pi$
$139$	−6.07923	+	16.7026i	−0.515634	+	1.41669i	−0.875286	+	0.483606i	$0.839327\pi$
$140$	−24.4187	−	8.77128i	−2.06376	−	0.741308i
$141$	1.33792	−	11.8452i	0.112674	−	0.997546i
$142$	−22.2132	−	10.3582i	−1.86409	−	0.869238i
$143$	9.92886	−	2.66043i	0.830293	−	0.222476i
$144$	−17.5181	−	0.883929i	−1.45984	−	0.0736607i
$145$	6.73310	−	1.83459i	0.559153	−	0.152354i
$146$	−0.0415627	+	0.0495324i	−0.00343975	+	0.00409933i
$147$	0.449379	+	0.274779i	0.0370642	+	0.0226634i
$148$	15.5890	+	10.9155i	1.28141	+	0.897250i
$149$	0.147586	+	0.837002i	0.0120907	+	0.0685699i	0.990256	−	0.139258i	$-0.0444717\pi$
$149$	0.147586	+	0.837002i	0.0120907	+	0.0685699i	−0.978165	+	0.207828i	$0.933361\pi$
$150$	−21.0768	+	5.27022i	−1.72092	+	0.430312i
$151$	11.3395	+	9.51495i	0.922794	+	0.774316i	0.974510	−	0.224346i	$-0.0720246\pi$
$151$	11.3395	+	9.51495i	0.922794	+	0.774316i	−0.0517160	+	0.998662i	$0.516469\pi$
$152$	18.7252	+	5.01740i	1.51881	+	0.406965i
$153$	16.9424	−	6.88351i	1.36971	−	0.556499i
$154$	19.1808	+	11.0740i	1.54563	+	0.892372i
$155$	−0.0752363	−	0.820118i	−0.00604313	−	0.0658734i
$156$	13.9005	−	18.8237i	1.11293	−	1.50710i
$157$	10.1875	+	0.891290i	0.813051	+	0.0711327i	0.486094	−	0.873907i	$-0.338421\pi$
$157$	10.1875	+	0.891290i	0.813051	+	0.0711327i	0.326957	+	0.945039i	$0.393977\pi$
$158$	−11.7937	−	25.2917i	−0.938257	−	2.01210i
$159$	−7.63254	−	3.79618i	−0.605300	−	0.301057i
$160$	−6.63104	+	2.44521i	−0.524230	+	0.193311i
$161$		−	13.4295i		−	1.05839i
$162$	21.3192	−	7.43367i	1.67500	−	0.584045i
$163$	−9.20802	+	9.20802i	−0.721228	+	0.721228i	−0.968855	−	0.247628i	$-0.920349\pi$
$163$	−9.20802	+	9.20802i	−0.721228	+	0.721228i	0.247628	+	0.968855i	$0.420349\pi$
$164$	−5.71318	+	32.4011i	−0.446125	+	2.53010i
$165$	12.6241	−	0.837885i	0.982783	−	0.0652292i
$166$	−2.57993	−	0.939019i	−0.200242	−	0.0728820i
$167$	−0.420214	+	4.80307i	−0.0325171	+	0.371672i	0.962449	+	0.271462i	$0.0875071\pi$
$167$	−0.420214	+	4.80307i	−0.0325171	+	0.371672i	−0.994966	+	0.100210i	$0.968048\pi$
$168$	26.6328	−	4.00678i	2.05477	−	0.309130i
$169$	−1.05980	−	2.91178i	−0.0815232	−	0.223983i
$170$	24.0771	−	24.2810i	1.84663	−	1.86227i
$171$	−10.0304	+	1.25138i	−0.767041	+	0.0956953i
$172$	−4.93365	+	18.4126i	−0.376187	+	1.40395i
$173$	−0.561923	−	6.42280i	−0.0427222	−	0.488317i	−0.987172	−	0.159661i	$-0.948960\pi$
$173$	−0.561923	−	6.42280i	−0.0427222	−	0.488317i	0.944450	−	0.328656i	$-0.106596\pi$
$174$	−9.82759	+	9.34421i	−0.745027	+	0.708383i
$175$	12.1984	−	5.81393i	0.922112	−	0.439491i
$176$	18.8095	−	3.31663i	1.41782	−	0.250000i
$177$	−6.92485	+	11.3250i	−0.520503	+	0.851241i
$178$	19.6531	−	1.71942i	1.47306	−	0.128876i
$179$	−1.30891	−	2.26710i	−0.0978327	−	0.169451i	0.812955	−	0.582327i	$-0.197858\pi$
$179$	−1.30891	−	2.26710i	−0.0978327	−	0.169451i	−0.910787	+	0.412876i	$0.864524\pi$
$180$	21.2844	−	19.4033i	1.58645	−	1.44624i
$181$	8.91293	−	15.4376i	0.662493	−	1.14747i	−0.317466	−	0.948270i	$-0.602832\pi$
$181$	8.91293	−	15.4376i	0.662493	−	1.14747i	0.979959	−	0.199202i	$-0.0638348\pi$
$182$	−9.01620	+	19.3353i	−0.668325	+	1.43323i
$183$	−9.70554	+	7.73556i	−0.717454	+	0.571829i
$184$	−18.3771	−	21.9010i	−1.35478	−	1.61456i
$185$	−9.75341	+	1.76222i	−0.717085	+	0.129561i
$186$	0.884591	+	1.33365i	0.0648614	+	0.0977881i
$187$	−16.3118	+	11.4216i	−1.19284	+	0.835233i
$188$	20.8942	+	20.8942i	1.52387	+	1.52387i
$189$	−12.0792	+	7.16272i	−0.878630	+	0.521011i
$190$	−16.3285	+	9.51929i	−1.18460	+	0.690602i
$191$	−8.64200	−	1.52382i	−0.625313	−	0.110260i	−0.147992	−	0.988989i	$-0.547281\pi$
$191$	−8.64200	−	1.52382i	−0.625313	−	0.110260i	−0.477321	+	0.878729i	$0.658392\pi$
$192$	−4.31569	+	4.88757i	−0.311458	+	0.352730i
$193$	1.10994	−	0.517574i	0.0798952	−	0.0372558i	−0.382260	−	0.924055i	$-0.624854\pi$
$193$	1.10994	−	0.517574i	0.0798952	−	0.0372558i	0.462155	+	0.886799i	$0.347076\pi$
$194$	9.85290	−	8.26756i	0.707397	−	0.593576i
$195$	1.86385	+	12.0435i	0.133473	+	0.862454i
$196$	−1.22693	+	0.446566i	−0.0876379	+	0.0318976i
$197$	3.63461	+	13.5645i	0.258955	+	0.966434i	0.965847	+	0.259112i	$0.0834300\pi$
$197$	3.63461	+	13.5645i	0.258955	+	0.966434i	−0.706892	+	0.707321i	$0.749903\pi$
$198$	−20.8241	+	13.0687i	−1.47990	+	0.928752i
$199$	11.1726	−	6.45050i	0.792004	−	0.457264i	−0.0486637	−	0.998815i	$-0.515496\pi$
$199$	11.1726	−	6.45050i	0.792004	−	0.457264i	0.840668	+	0.541552i	$0.182163\pi$
$200$	11.9374	−	26.1739i	0.844104	−	1.85077i
$201$	0.188995	−	0.640321i	0.0133307	−	0.0451648i
$202$	−1.71106	+	2.44365i	−0.120390	+	0.171934i
$203$	4.83789	−	6.90922i	0.339553	−	0.484932i
$204$	−12.8324	+	43.4768i	−0.898451	+	3.04398i
$205$	−9.88738	−	13.9947i	−0.690565	−	0.977432i
$206$	0.408725	−	0.235978i	0.0284772	−	0.0164413i
$207$	13.1759	+	6.97292i	0.915789	+	0.484652i
$208$	4.76170	+	17.7709i	0.330164	+	1.23219i
$209$	10.3429	−	3.76452i	0.715435	−	0.260397i
$210$	−15.5096	+	21.1890i	−1.07026	+	1.46218i
$211$	−0.0983096	+	0.0824916i	−0.00676791	+	0.00567895i	−0.646165	−	0.763197i	$-0.723628\pi$
$211$	−0.0983096	+	0.0824916i	−0.00676791	+	0.00567895i	0.639397	+	0.768876i	$0.279184\pi$
$212$	19.1509	−	8.93021i	1.31529	−	0.613329i
$213$	−11.2005	+	12.6847i	−0.767446	+	0.869142i
$214$	6.17397	+	1.08864i	0.422044	+	0.0744177i
$215$	−5.00008	−	8.57668i	−0.341002	−	0.584924i
$216$	−9.89729	+	28.2103i	−0.673425	+	1.91947i
$217$	−0.703849	−	0.703849i	−0.0477804	−	0.0477804i
$218$	16.0442	−	11.2343i	1.08665	−	0.760881i
$219$	0.0246762	+	0.0372031i	0.00166747	+	0.00251395i
$220$	−17.8799	+	25.7656i	−1.20546	+	1.73712i
$221$	−12.3294	−	14.6937i	−0.829368	−	0.988402i
$222$	15.0612	−	12.0042i	1.01084	−	0.805667i
$223$	−3.54033	+	7.59226i	−0.237078	+	0.508415i	−0.988466	−	0.151446i	$-0.951607\pi$
$223$	−3.54033	+	7.59226i	−0.237078	+	0.508415i	0.751388	+	0.659861i	$0.229385\pi$
$224$	−4.27106	+	7.39769i	−0.285372	+	0.494279i
$225$	−0.629566	+	14.9868i	−0.0419710	+	0.999119i
$226$	24.4541	+	42.3557i	1.62666	+	2.81746i
$227$	−3.59601	+	0.314610i	−0.238675	+	0.0208814i	−0.205866	−	0.978580i	$-0.566001\pi$
$227$	−3.59601	+	0.314610i	−0.238675	+	0.0208814i	−0.0328096	+	0.999462i	$0.510445\pi$
$228$	13.0711	−	21.3767i	0.865653	−	1.41571i
$229$	1.22130	−	0.215349i	0.0807059	−	0.0142306i	−0.133149	−	0.991096i	$-0.542509\pi$
$229$	1.22130	−	0.215349i	0.0807059	−	0.0142306i	0.213855	+	0.976865i	$0.431398\pi$
$230$	27.7783	+	2.31233i	1.83165	+	0.152470i
$231$	11.0819	−	10.5368i	0.729135	−	0.693272i
$232$	−1.56498	−	17.8879i	−0.102746	−	1.17440i
$233$	−5.37571	+	20.0624i	−0.352175	+	1.31433i	0.531828	+	0.846852i	$0.321505\pi$
$233$	−5.37571	+	20.0624i	−0.352175	+	1.31433i	−0.884003	+	0.467481i	$0.845161\pi$
$234$	−14.2888	−	18.8853i	−0.934085	−	1.23457i
$235$	−15.3892	+	0.0648800i	−1.00388	+	0.00423231i
$236$	−11.2541	−	30.9205i	−0.732582	−	2.01275i
$237$	−19.0528	+	2.86640i	−1.23761	+	0.186193i
$238$	3.60207	−	41.1719i	0.233488	−	2.66878i
$239$	11.3730	+	4.13943i	0.735658	+	0.267758i	0.682558	−	0.730831i	$-0.260867\pi$
$239$	11.3730	+	4.13943i	0.735658	+	0.267758i	0.0531004	+	0.998589i	$0.483090\pi$
$240$	1.49966	+	22.5948i	0.0968029	+	1.45849i
$241$	−1.19187	+	6.75943i	−0.0767751	+	0.435413i	0.922055	+	0.387059i	$0.126509\pi$
$241$	−1.19187	+	6.75943i	−0.0767751	+	0.435413i	−0.998830	+	0.0483548i	$0.984602\pi$
$242$	−0.583102	+	0.583102i	−0.0374832	+	0.0374832i
$243$	−0.755664	−	15.5701i	−0.0484759	−	0.998824i
$244$		−	30.7650i		−	1.96953i
$245$	0.284782	−	0.617501i	0.0181941	−	0.0394507i
$246$	29.8132	+	14.8281i	1.90082	+	0.945407i
$247$	4.48069	+	9.60887i	0.285099	+	0.611397i
$248$	−2.11100	−	0.184689i	−0.134049	−	0.0117277i
$249$	−1.12604	+	1.52486i	−0.0713601	+	0.0966340i
$250$	9.92550	+	26.2329i	0.627744	+	1.65911i
$251$	8.53784	+	4.92932i	0.538904	+	0.311136i	0.744634	−	0.667472i	$-0.232624\pi$
$251$	8.53784	+	4.92932i	0.538904	+	0.311136i	−0.205731	+	0.978609i	$0.565957\pi$
$252$	4.77765	−	34.4811i	0.300964	−	2.17211i
$253$	−15.6794	−	4.20128i	−0.985754	−	0.264132i
$254$	41.0369	+	34.4341i	2.57489	+	2.16059i
$255$	−11.3727	−	20.6891i	−0.712183	−	1.29560i
$256$	−5.56035	−	31.5343i	−0.347522	−	1.97090i
$257$	9.21372	+	6.45152i	0.574736	+	0.402435i	0.824491	−	0.565874i	$-0.191461\pi$
$257$	9.21372	+	6.45152i	0.574736	+	0.402435i	−0.249755	+	0.968309i	$0.580350\pi$
$258$	16.4587	+	10.0639i	1.02467	+	0.626550i
$259$	−7.70013	+	9.17666i	−0.478463	+	0.570210i
$260$	−26.2253	−	14.9941i	−1.62643	−	0.929897i
$261$	4.26680	+	8.33396i	0.264108	+	0.515859i
$262$	−40.1851	+	10.7676i	−2.48264	+	0.665222i
$263$	−7.46977	−	3.48321i	−0.460606	−	0.214784i	0.178443	−	0.983950i	$-0.442894\pi$
$263$	−7.46977	−	3.48321i	−0.460606	−	0.214784i	−0.639049	+	0.769166i	$0.720672\pi$
$264$	3.65375	−	32.3482i	0.224873	−	1.99089i
$265$	−3.72032	+	10.3571i	−0.228537	+	0.636234i
$266$	−7.81320	+	21.4666i	−0.479058	+	1.31620i
$267$	2.70257	−	13.3500i	0.165395	−	0.817005i
$268$	0.949234	+	1.35565i	0.0579837	+	0.0828093i
$269$	−21.3745			−1.30322			−0.651612	−	0.758553i	$-0.725907\pi$
$269$	−21.3745			−1.30322			−0.651612	+	0.758553i	$0.725907\pi$
$270$	−12.7359	−	26.2185i	−0.775085	−	1.59561i
$271$	−16.0063			−0.972313			−0.486157	−	0.873872i	$-0.661602\pi$
$271$	−16.0063			−0.972313			−0.486157	+	0.873872i	$0.661602\pi$
$272$	−20.4427	−	29.1952i	−1.23952	−	1.77022i
$273$	11.0413	+	9.74941i	0.668251	+	0.590061i
$274$	17.2013	−	47.2602i	1.03917	−	2.85509i
$275$	−2.97180	−	16.0608i	−0.179207	−	0.968505i
$276$	−33.8733	+	14.7677i	−2.03893	+	0.888911i
$277$	13.0267	+	6.07443i	0.782696	+	0.364977i	0.772536	−	0.634971i	$-0.218988\pi$
$277$	13.0267	+	6.07443i	0.782696	+	0.364977i	0.0101600	+	0.999948i	$0.496766\pi$
$278$	−43.0710	+	11.5408i	−2.58323	+	0.692174i
$279$	1.05601	−	0.325103i	0.0632219	−	0.0194634i
$280$	−9.14059	−	33.5468i	−0.546255	−	2.00480i
$281$	−6.85563	+	8.17022i	−0.408973	+	0.487395i	−0.930734	−	0.365697i	$-0.880831\pi$
$281$	−6.85563	+	8.17022i	−0.408973	+	0.487395i	0.521761	+	0.853091i	$0.325275\pi$
$282$	26.2669	−	14.2948i	1.56417	−	0.851245i
$283$	−20.1559	−	14.1133i	−1.19815	−	0.838951i	−0.207882	−	0.978154i	$-0.566657\pi$
$283$	−20.1559	−	14.1133i	−1.19815	−	0.838951i	−0.990264	+	0.139203i	$0.955546\pi$
$284$	−7.28395	−	41.3093i	−0.432223	−	2.45126i
$285$	3.11214	+	12.6730i	0.184348	+	0.750683i
$286$	19.7539	+	16.5755i	1.16808	+	0.980132i
$287$	−20.0046	−	5.36021i	−1.18083	−	0.316403i
$288$	−5.04036	−	8.03146i	−0.297006	−	0.473258i
$289$	17.4577	+	10.0792i	1.02692	+	0.592895i
$290$	13.4584	+	11.1966i	0.790305	+	0.657487i
$291$	−3.54892	−	8.14030i	−0.208041	−	0.477193i
$292$	−0.110241	−	0.00964481i	−0.00645135	−	0.000564420i
$293$	−10.1452	−	21.7565i	−0.592691	−	1.27103i	−0.942499	−	0.334208i	$-0.891531\pi$
$293$	−10.1452	−	21.7565i	−0.592691	−	1.27103i	0.349809	−	0.936821i	$-0.386247\pi$
$294$	0.0819517	+	1.31885i	0.00477952	+	0.0769170i
$295$	15.5620	+	7.17694i	0.906052	+	0.417858i
$296$			25.5023i			1.48229i
$297$	4.58386	+	16.3436i	0.265983	+	0.948351i
$298$	−1.50766	+	1.50766i	−0.0873366	+	0.0873366i
$299$	2.71515	−	15.3984i	0.157021	−	0.890512i
$300$	−28.0784	−	24.3748i	−1.62111	−	1.40728i
$301$	−11.2755	−	4.10394i	−0.649908	−	0.236547i
$302$	−3.23653	+	36.9937i	−0.186241	+	2.12875i
$303$	1.28372	+	1.61064i	0.0737478	+	0.0925289i
$304$	6.73782	+	18.5120i	0.386440	+	1.06174i
$305$	11.3774	+	11.2819i	0.651470	+	0.646000i
$306$	38.5241	+	24.9115i	2.20228	+	1.42410i
$307$	1.05256	−	3.92820i	0.0600726	−	0.224194i	−0.929363	−	0.369167i	$-0.879643\pi$
$307$	1.05256	−	3.92820i	0.0600726	−	0.224194i	0.989436	+	0.144973i	$0.0463096\pi$
$308$	3.30365	+	37.7609i	0.188243	+	2.15163i
$309$	−0.0763761	−	0.316772i	−0.00434488	−	0.0180205i
$310$	1.57707	−	1.33469i	0.0895716	−	0.0758053i
$311$	−9.98381	+	1.76041i	−0.566130	+	0.0998239i	−0.449385	−	0.893338i	$-0.648357\pi$
$311$	−9.98381	+	1.76041i	−0.566130	+	0.0998239i	−0.116744	+	0.993162i	$0.537246\pi$
$312$	31.3475	+	0.790363i	1.77470	+	0.0447455i
$313$	−29.3680	+	2.56936i	−1.65998	+	0.145229i	−0.878188	−	0.478316i	$-0.841247\pi$
$313$	−29.3680	+	2.56936i	−1.65998	+	0.145229i	−0.781787	+	0.623545i	$0.785692\pi$
$314$	12.8274	+	22.2177i	0.723890	+	1.25381i
$315$	10.9997	+	14.4115i	0.619763	+	0.811996i
$316$	23.8800	−	41.3614i	1.34335	−	2.32676i
$317$	−1.32127	+	2.83348i	−0.0742101	+	0.159144i	−0.939913	−	0.341414i	$-0.889094\pi$
$317$	−1.32127	+	2.83348i	−0.0742101	+	0.159144i	0.865703	+	0.500558i	$0.166872\pi$
$318$	−3.18149	−	21.1472i	−0.178409	−	1.18587i
$319$	−6.55325	−	7.80986i	−0.366912	−	0.437268i
$320$	6.91558	+	4.79902i	0.386593	+	0.268273i
$321$	1.92756	−	3.87553i	0.107586	−	0.216311i
$322$	27.5975	−	19.3239i	1.53795	−	1.07688i
$323$	−14.5232	−	14.5232i	−0.808094	−	0.808094i
$324$	31.3494	+	22.5909i	1.74163	+	1.25505i
$325$	15.1622	−	4.20005i	0.841049	−	0.232977i
$326$	−32.1719	−	5.67278i	−1.78184	−	0.314186i
$327$	−4.30335	−	12.8199i	−0.237976	−	0.708943i
$328$	−39.9586	+	18.6330i	−2.20635	+	1.02884i
$329$	−14.2486	+	11.9560i	−0.785551	+	0.659155i
$330$	19.8868	+	24.7367i	1.09473	+	1.36171i
$331$	27.5786	−	10.0378i	1.51586	−	0.551727i	0.555747	−	0.831351i	$-0.312432\pi$
$331$	27.5786	−	10.0378i	1.51586	−	0.551727i	0.960109	+	0.279624i	$0.0902099\pi$
$332$	−1.21613	−	4.53867i	−0.0667439	−	0.249092i
$333$	−5.00528	−	12.3195i	−0.274288	−	0.675103i
$334$	−10.4749	+	6.04768i	−0.573160	+	0.330914i
$335$	−0.849436	−	0.146089i	−0.0464097	−	0.00798168i
$336$	18.8590	+	19.8346i	1.02884	+	1.08207i
$337$	−9.18427	+	13.1165i	−0.500299	+	0.714501i	−0.987294	−	0.158904i	$-0.949204\pi$
$337$	−9.18427	+	13.1165i	−0.500299	+	0.714501i	0.486995	+	0.873405i	$0.338093\pi$
$338$	4.45870	−	6.36769i	0.242521	−	0.346356i
$339$	32.8267	−	7.91477i	1.78290	−	0.429871i
$340$	57.6754	+	9.91919i	3.12789	+	0.537944i
$341$	−1.04196	+	0.601574i	−0.0564252	+	0.0325771i
$342$	−17.0044	−	18.8116i	−0.919494	−	1.01722i
$343$	4.68369	+	17.4798i	0.252896	+	0.943819i
$344$	−24.0041	+	8.73676i	−1.29421	+	0.471055i
$345$	6.96039	−	17.9424i	0.374735	−	0.965987i
$346$	12.3902	−	10.3966i	0.666102	−	0.558926i
$347$	−1.87163	+	0.872755i	−0.100474	+	0.0468520i	−0.472206	−	0.881488i	$-0.656542\pi$
$347$	−1.87163	+	0.872755i	−0.100474	+	0.0468520i	0.371731	+	0.928340i	$0.378764\pi$
$348$	−22.7471	−	4.60492i	−1.21937	−	0.246850i
$349$	−0.561803	−	0.0990609i	−0.0300726	−	0.00530261i	0.158592	−	0.987344i	$-0.449305\pi$
$349$	−0.561803	−	0.0990609i	−0.0300726	−	0.00530261i	−0.188664	+	0.982042i	$0.560416\pi$
$350$	29.5000	+	16.7018i	1.57684	+	0.892748i
$351$	−15.2982	+	5.77069i	−0.816559	+	0.308017i
$352$	7.30088	+	7.30088i	0.389138	+	0.389138i
$353$	6.18882	−	4.33346i	0.329398	−	0.230647i	−0.397165	−	0.917747i	$-0.630006\pi$
$353$	6.18882	−	4.33346i	0.329398	−	0.230647i	0.726562	+	0.687101i	$0.241117\pi$
$354$	−33.2370	+	2.06530i	−1.76653	+	0.109770i
$355$	17.9480	+	12.4549i	0.952581	+	0.661037i
$356$	21.7028	+	25.8644i	1.15024	+	1.37081i
$357$	−26.5593	−	10.4322i	−1.40567	−	0.552129i
$358$	2.77545	−	5.95197i	0.146687	−	0.314571i
$359$	−7.12655	+	12.3435i	−0.376125	+	0.651467i	−0.990495	−	0.137551i	$-0.956077\pi$
$359$	−7.12655	+	12.3435i	−0.376125	+	0.651467i	0.614370	+	0.789018i	$0.289410\pi$
$360$	37.6593	+	8.45031i	1.98482	+	0.445371i
$361$	−3.82366	−	6.62277i	−0.201245	−	0.348567i
$362$	44.5491	−	3.89754i	2.34145	−	0.204850i
$363$	0.272154	+	0.500086i	0.0142844	+	0.0262477i
$364$	−35.9574	+	6.34026i	−1.88468	+	0.332320i
$365$	0.0439934	−	0.0372320i	0.00230272	−	0.00194881i
$366$	−29.8619	−	8.81393i	−1.56091	−	0.460712i
$367$	−1.57285	−	17.9778i	−0.0821024	−	0.938434i	−0.919823	−	0.392335i	$-0.871668\pi$
$367$	−1.57285	−	17.9778i	−0.0821024	−	0.938434i	0.837720	−	0.546100i	$-0.183888\pi$
$368$	7.51954	−	28.0633i	0.391983	−	1.46290i
$369$	15.6458	−	16.8437i	0.814490	−	0.876846i
$370$	−17.6557	−	17.5074i	−0.917875	−	0.910168i
$371$	4.54928	+	12.4990i	0.236187	+	0.648918i
$372$	−1.00134	+	2.54930i	−0.0519168	+	0.132175i
$373$	−0.475246	+	5.43209i	−0.0246073	+	0.281263i	0.973915	+	0.226914i	$0.0728638\pi$
$373$	−0.475246	+	5.43209i	−0.0246073	+	0.281263i	−0.998522	+	0.0543485i	$0.982692\pi$
$374$	−46.9426	−	17.0857i	−2.42735	−	0.883481i
$375$	19.3109	−	1.44534i	0.997211	−	0.0746371i
$376$	−6.87604	+	38.9959i	−0.354604	+	2.01106i
$377$	6.94405	−	6.94405i	0.357637	−	0.357637i
$378$	−32.1002	−	14.5160i	−1.65106	−	0.746621i
$379$		−	4.04015i		−	0.207529i	−0.994602	−	0.103764i	$-0.966911\pi$
$379$		−	4.04015i		−	0.207529i	0.994602	−	0.103764i	$-0.0330888\pi$
$380$	−29.3741	−	13.5469i	−1.50686	−	0.694942i
$381$	30.8222	−	20.4439i	1.57907	−	1.04737i
$382$	−9.30369	−	19.9518i	−0.476018	−	1.02082i
$383$	30.5793	+	2.67534i	1.56253	+	0.136704i	0.835341	−	0.549732i	$-0.185270\pi$
$383$	30.5793	+	2.67534i	1.56253	+	0.136704i	0.727190	+	0.686436i	$0.240826\pi$
$384$	−27.1336	−	3.06476i	−1.38465	−	0.156398i
$385$	−15.1761	−	12.6256i	−0.773447	−	0.643462i
$386$	2.66072	+	1.53617i	0.135427	+	0.0781888i
$387$	9.88094	−	8.93170i	0.502277	−	0.454024i
$388$	21.2626	+	5.69729i	1.07944	+	0.289236i
$389$	23.0823	+	19.3684i	1.17032	+	0.982014i	0.999994	−	0.00337359i	$-0.00107385\pi$
$389$	23.0823	+	19.3684i	1.17032	+	0.982014i	0.170325	+	0.985388i	$0.445518\pi$
$390$	−22.0673	+	21.1598i	−1.11742	+	1.07147i
$391$	5.25988	+	29.8302i	0.266003	+	1.50858i
$392$	−1.43326	−	1.00358i	−0.0723907	−	0.0506885i
$393$	−0.723975	+	28.7144i	−0.0365197	+	1.44845i
$394$	−22.6451	+	26.9873i	−1.14084	+	1.35960i
$395$	6.53906	+	23.9989i	0.329016	+	1.20752i
$396$	−38.7632	−	16.3651i	−1.94792	−	0.822378i
$397$	−27.5321	+	7.37720i	−1.38180	+	0.370251i	−0.871773	−	0.489910i	$-0.837030\pi$
$397$	−27.5321	+	7.37720i	−1.38180	+	0.370251i	−0.510023	+	0.860161i	$0.670363\pi$
$398$	29.3321	+	13.6778i	1.47029	+	0.685605i
$399$	12.6877	+	9.36936i	0.635182	+	0.469055i
$400$	28.7460	−	5.31900i	1.43730	−	0.265950i
$401$	9.65646	−	26.5309i	0.482221	−	1.32489i	−0.425364	−	0.905022i	$-0.639854\pi$
$401$	9.65646	−	26.5309i	0.482221	−	1.32489i	0.907585	−	0.419868i	$-0.137924\pi$
$402$	1.58780	−	0.532987i	0.0791922	−	0.0265830i
$403$	−0.664736	−	0.949342i	−0.0331129	−	0.0472901i
$404$	−5.10547			−0.254007
$405$	−19.8507	+	3.30918i	−0.986388	+	0.164435i
$406$	21.1597			1.05014
$407$	8.30514	+	11.8610i	0.411670	+	0.587926i
$408$	−57.5888	+	19.3312i	−2.85107	+	0.957038i
$409$	−6.83310	+	18.7738i	−0.337875	+	0.928304i	0.648121	+	0.761537i	$0.275555\pi$
$409$	−6.83310	+	18.7738i	−0.337875	+	0.928304i	−0.985996	+	0.166767i	$0.946667\pi$
$410$	14.5318	−	40.4556i	0.717674	−	1.99796i
$411$	−27.9329	−	20.6273i	−1.37783	−	1.01747i
$412$	0.732046	+	0.341359i	0.0360653	+	0.0168175i
$413$	20.0070	−	5.36086i	0.984479	−	0.263790i
$414$	4.62978	+	37.1098i	0.227541	+	1.82385i
$415$	2.12445	+	1.21464i	0.104285	+	0.0596242i
$416$	−6.39288	+	7.61873i	−0.313437	+	0.373539i
$417$	−0.775968	+	30.7765i	−0.0379993	+	1.50713i
$418$	22.6186	+	15.8377i	1.10631	+	0.774649i
$419$	−1.26780	−	7.19003i	−0.0619359	−	0.351256i	−0.999989	−	0.00476336i	$-0.998484\pi$
$419$	−1.26780	−	7.19003i	−0.0619359	−	0.351256i	0.938053	−	0.346492i	$-0.112627\pi$
$420$	−44.9303	−	0.943302i	−2.19238	−	0.0460284i
$421$	−22.3147	−	18.7243i	−1.08755	−	0.912566i	−0.0910275	−	0.995848i	$-0.529015\pi$
$421$	−22.3147	−	18.7243i	−1.08755	−	0.912566i	−0.996526	+	0.0832827i	$0.973460\pi$
$422$	−0.310978	−	0.0833264i	−0.0151382	−	0.00405627i
$423$	−4.33201	−	20.1874i	−0.210629	−	0.981544i
$424$	24.5229	+	14.1583i	1.19094	+	0.687587i
$425$	−24.8185	+	17.6918i	−1.20388	+	0.858181i
$426$	−42.1835	−	4.76466i	−2.04380	−	0.230848i
$427$	19.2921	+	1.68784i	0.933609	+	0.0816802i
$428$	4.53443	+	9.72412i	0.219180	+	0.470033i
$429$	14.8369	−	9.84109i	0.716332	−	0.475132i
$430$	10.4303	−	22.6162i	0.502992	−	1.09065i
$431$			14.3391i			0.690690i	0.938476	+	0.345345i	$0.112238\pi$
$431$			14.3391i			0.690690i	−0.938476	+	0.345345i	$0.887762\pi$
$432$	−29.2521	+	8.20429i	−1.40739	+	0.394729i
$433$	16.2907	−	16.2907i	0.782881	−	0.782881i	−0.197435	−	0.980316i	$-0.563261\pi$
$433$	16.2907	−	16.2907i	0.782881	−	0.782881i	0.980316	+	0.197435i	$0.0632612\pi$
$434$	0.433620	−	2.45918i	0.0208144	−	0.118044i
$435$	10.0446	−	6.72359i	0.481602	−	0.322371i
$436$	31.4993	+	11.4648i	1.50854	+	0.549065i
$437$	1.45922	−	16.6790i	0.0698041	−	0.797865i
$438$	−0.0409448	+	0.104241i	−0.00195642	+	0.00498085i
$439$	−6.36027	−	17.4747i	−0.303559	−	0.834021i	−0.993875	−	0.110513i	$-0.964751\pi$
$439$	−6.36027	−	17.4747i	−0.303559	−	0.834021i	0.690316	−	0.723508i	$-0.257472\pi$
$440$	−42.0265	+	0.177181i	−2.00353	+	0.00844679i
$441$	0.889339	+	0.203499i	0.0423495	+	0.00969044i
$442$	12.4542	−	46.4798i	0.592387	−	2.21082i
$443$	−2.37273	−	27.1205i	−0.112732	−	1.28853i	−0.816185	−	0.577790i	$-0.803915\pi$
$443$	−2.37273	−	27.1205i	−0.112732	−	1.28853i	0.703453	−	0.710741i	$-0.251640\pi$
$444$	31.6137	+	9.33098i	1.50032	+	0.442829i
$445$	−17.5238	−	1.45871i	−0.830705	−	0.0691496i
$446$	−20.6962	+	3.64930i	−0.979994	+	0.172799i
$447$	0.703680	+	1.29302i	0.0332829	+	0.0611577i
$448$	10.1352	−	0.886712i	0.478841	−	0.0418932i
$449$	−15.3860	−	26.6493i	−0.726109	−	1.25766i	−0.958516	−	0.285039i	$-0.907994\pi$
$449$	−15.3860	−	26.6493i	−0.726109	−	1.25766i	0.232407	−	0.972619i	$-0.425340\pi$
$450$	−31.7035	+	20.2710i	−1.49452	+	0.955583i
$451$	−12.5164	+	21.6791i	−0.589375	+	1.02083i
$452$	−35.3746	+	75.8611i	−1.66388	+	3.56820i
$453$	23.8640	+	9.37350i	1.12123	+	0.440405i
$454$	−5.82087	−	6.93705i	−0.273187	−	0.325572i
$455$	10.8413	−	15.6227i	0.508247	−	0.732404i
$456$	33.5125	−	2.08242i	1.56936	−	0.0975182i
$457$	−19.1830	+	13.4321i	−0.897344	+	0.628327i	−0.928559	−	0.371185i	$-0.878951\pi$
$457$	−19.1830	+	13.4321i	−0.897344	+	0.628327i	0.0312144	+	0.999513i	$0.490063\pi$
$458$	2.19989	+	2.19989i	0.102794	+	0.102794i
$459$	24.0254	−	20.6412i	1.12141	−	0.963446i
$460$	24.0267	+	41.2132i	1.12025	+	1.92157i
$461$	31.1056	+	5.48476i	1.44873	+	0.255451i	0.842010	−	0.539462i	$-0.181372\pi$
$461$	31.1056	+	5.48476i	1.44873	+	0.255451i	0.606724	+	0.794913i	$0.292483\pi$
$462$	37.5989	+	7.61152i	1.74926	+	0.354120i
$463$	26.5805	−	12.3947i	1.23530	−	0.576030i	0.308371	−	0.951266i	$-0.400216\pi$
$463$	26.5805	−	12.3947i	1.23530	−	0.576030i	0.926929	+	0.375236i	$0.122438\pi$
$464$	13.9783	−	11.7292i	0.648924	−	0.544512i
$465$	−0.575575	−	1.30517i	−0.0266916	−	0.0605259i
$466$	−48.9632	+	17.8212i	−2.26818	+	0.825549i
$467$	−5.36199	−	20.0112i	−0.248123	−	0.926008i	−0.971788	−	0.235857i	$-0.924210\pi$
$467$	−5.36199	−	20.0112i	−0.248123	−	0.926008i	0.723665	−	0.690152i	$-0.242456\pi$
$468$	12.4494	−	38.5704i	0.575475	−	1.78292i
$469$	−0.902173	+	0.520870i	−0.0416585	+	0.0240515i
$470$	−22.2771	−	31.5312i	−1.02757	−	1.45443i
$471$	17.2192	−	4.15168i	0.793420	−	0.191299i
$472$	25.2917	−	36.1204i	1.16415	−	1.66257i
$473$	−8.31889	+	11.8806i	−0.382503	+	0.546271i
$474$	−33.3058	−	35.0287i	−1.52979	−	1.60892i
$475$	15.7817	−	5.89525i	0.724116	−	0.270492i
$476$	61.2561	−	35.3662i	2.80767	−	1.62101i
$477$	−14.6251	−	2.02643i	−0.669638	−	0.0927839i
$478$	7.85832	+	29.3277i	0.359431	+	1.34142i
$479$	−7.18880	+	2.61651i	−0.328465	+	0.119551i	−0.500988	−	0.865454i	$-0.667030\pi$
$479$	−7.18880	+	2.61651i	−0.328465	+	0.119551i	0.172524	+	0.985005i	$0.444808\pi$
$480$	−9.54047	+	7.66999i	−0.435461	+	0.350085i
$481$	−10.6843	+	8.96523i	−0.487164	+	0.408779i
$482$	−15.6055	+	7.27698i	−0.710813	+	0.331458i
$483$	−7.40214	−	22.0514i	−0.336809	−	1.00337i
$484$	−1.38986	−	0.245071i	−0.0631757	−	0.0111396i
$485$	−9.90419	+	5.77400i	−0.449726	+	0.262184i
$486$	30.9091	−	23.9570i	1.40206	−	1.08671i
$487$	8.90898	+	8.90898i	0.403704	+	0.403704i	0.879536	−	0.475832i	$-0.157853\pi$
$487$	8.90898	+	8.90898i	0.403704	+	0.403704i	−0.475832	+	0.879536i	$0.657853\pi$
$488$	33.7714	−	23.6470i	1.52876	−	1.07045i
$489$	−10.0443	+	20.1950i	−0.454221	+	0.913248i
$490$	1.67873	−	0.303309i	0.0758375	−	0.0137021i
$491$	2.30460	+	2.74652i	0.104005	+	0.123949i	0.815536	−	0.578706i	$-0.196442\pi$
$491$	2.30460	+	2.74652i	0.104005	+	0.123949i	−0.711531	+	0.702655i	$0.751998\pi$
$492$	8.47787	+	56.3519i	0.382212	+	2.54054i
$493$	−8.04003	+	17.2419i	−0.362105	+	0.776536i
$494$	−13.2987	+	23.0341i	−0.598339	+	1.03635i
$495$	20.2670	−	8.33401i	0.910935	−	0.374586i
$496$	−1.07671	−	1.86492i	−0.0483458	−	0.0837373i
$497$	26.3038	−	2.30128i	1.17989	−	0.103227i
$498$	−4.75385	−	0.119859i	−0.213025	−	0.00537099i
$499$	0.621729	−	0.109628i	0.0278324	−	0.00490760i	−0.159715	−	0.987163i	$-0.551057\pi$
$499$	0.621729	−	0.109628i	0.0278324	−	0.00490760i	0.187547	+	0.982256i	$0.439946\pi$
$500$	−27.0334	+	39.6662i	−1.20897	+	1.77393i
$501$	1.95738	+	8.11829i	0.0874493	+	0.362699i
$502$	2.15555	+	24.6380i	0.0962068	+	1.09965i
$503$	−9.79612	+	36.5596i	−0.436788	+	1.63011i	0.299964	+	0.953950i	$0.403025\pi$
$503$	−9.79612	+	36.5596i	−0.436788	+	1.63011i	−0.736752	+	0.676163i	$0.763641\pi$
$504$	41.5229	−	21.2588i	1.84958	−	0.946941i
$505$	1.87224	−	1.88809i	0.0833135	−	0.0840190i
$506$	−13.9278	−	38.2662i	−0.619164	−	1.70114i
$507$	−3.34513	−	4.19702i	−0.148563	−	0.186396i
$508$	−7.99059	+	91.3329i	−0.354525	+	4.05224i
$509$	27.9791	+	10.1836i	1.24015	+	0.451378i	0.877063	−	0.480376i	$-0.159500\pi$
$509$	27.9791	+	10.1836i	1.24015	+	0.451378i	0.363089	+	0.931754i	$0.381722\pi$
$510$	26.1515	−	53.1405i	1.15801	−	2.35310i
$511$	0.0120961	−	0.0686004i	0.000535100	−	0.00303470i
$512$	34.5064	−	34.5064i	1.52498	−	1.52498i
$513$	−15.7802	+	7.58336i	−0.696713	+	0.334813i
$514$			28.2173i			1.24461i
$515$	−0.394690	+	0.145543i	−0.0173921	+	0.00641338i
$516$	2.04766	+	32.9531i	0.0901431	+	1.45068i
$517$	9.50148	+	20.3760i	0.417875	+	0.896135i
$518$	−29.9377	−	2.61921i	−1.31539	−	0.115082i
$519$	−4.46283	−	10.2366i	−0.195897	−	0.449336i
$520$	−3.69826	−	40.3130i	−0.162179	−	1.76784i
$521$	27.1230	+	15.6595i	1.18828	+	0.686054i	0.957915	−	0.287050i	$-0.0926747\pi$
$521$	27.1230	+	15.6595i	1.18828	+	0.686054i	0.230365	+	0.973104i	$0.426008\pi$
$522$	−10.9866	+	20.7601i	−0.480871	+	0.908645i
$523$	−31.8316	−	8.52925i	−1.39190	−	0.372958i	−0.516470	−	0.856305i	$-0.672754\pi$
$523$	−31.8316	−	8.52925i	−1.39190	−	0.372958i	−0.875429	+	0.483347i	$0.839421\pi$
$524$	−54.5428	−	45.7668i	−2.38271	−	1.99933i
$525$	16.8253	−	16.2701i	0.734318	−	0.710085i
$526$	−3.59043	−	20.3623i	−0.156550	−	0.887840i
$527$	1.83910	+	1.28775i	0.0801122	+	0.0560952i
$528$	29.0574	−	15.8135i	1.26456	−	0.688193i
$529$	−1.08748	+	1.29601i	−0.0472817	+	0.0563482i
$530$	−26.6370	+	7.25787i	−1.15704	+	0.315262i
$531$	−5.12848	+	22.4127i	−0.222557	+	0.972627i
$532$	−37.7644	+	10.1189i	−1.63730	+	0.438712i
$533$	−21.8537	−	10.1905i	−0.946588	−	0.441401i
$534$	31.3228	−	13.6558i	1.35547	−	0.590943i
$535$	−5.25898	−	1.88904i	−0.227365	−	0.0816704i
$536$	−0.758509	+	2.08399i	−0.0327626	+	0.0900144i
$537$	−3.39884	−	3.00115i	−0.146671	−	0.129509i
$538$	−30.7561	−	43.9242i	−1.32599	−	1.89371i
$539$	−0.993428			−0.0427900
$540$	24.2544	−	43.5921i	1.04374	−	1.87591i
$541$	−19.8436			−0.853142			−0.426571	−	0.904454i	$-0.640279\pi$
$541$	−19.8436			−0.853142			−0.426571	+	0.904454i	$0.640279\pi$
$542$	−23.0317	−	32.8927i	−0.989297	−	1.41286i
$543$	6.12612	−	30.2614i	0.262897	−	1.29864i
$544$	6.58965	−	18.1049i	0.282529	−	0.776241i
$545$	−15.7911	+	7.44471i	−0.676415	+	0.318896i
$546$	−4.14736	+	36.7183i	−0.177491	+	1.57140i
$547$	15.7916	+	7.36373i	0.675199	+	0.314851i	0.729803	−	0.683658i	$-0.239612\pi$
$547$	15.7916	+	7.36373i	0.675199	+	0.314851i	−0.0546038	+	0.998508i	$0.517390\pi$
$548$	83.1410	−	22.2776i	3.55161	−	0.951650i
$549$	−11.6729	+	18.0514i	−0.498186	+	0.770415i
$550$	28.7286	−	29.2172i	1.22499	−	1.24583i
$551$	6.75924	−	8.05534i	0.287953	−	0.343169i
$552$	−42.2469	−	25.8325i	−1.79815	−	1.09950i
$553$	24.6267	+	17.2438i	1.04723	+	0.733281i
$554$	6.26140	+	35.5102i	0.266022	+	1.50868i
$555$	−15.0439	+	8.26951i	−0.638578	+	0.351021i
$556$	−58.4598	−	49.0536i	−2.47925	−	2.08034i
$557$	−9.77513	−	2.61924i	−0.414185	−	0.110981i	0.0457078	−	0.998955i	$-0.485446\pi$
$557$	−9.77513	−	2.61924i	−0.414185	−	0.110981i	−0.459893	+	0.887974i	$0.652112\pi$
$558$	2.18760	+	1.70230i	0.0926083	+	0.0720640i
$559$	−12.0988	−	6.98526i	−0.511726	−	0.295445i
$560$	22.5976	−	27.1626i	0.954924	−	1.14783i
$561$	−20.4887	+	27.7453i	−0.865033	+	1.17141i
$562$	−26.6544	−	2.33196i	−1.12435	−	0.0983676i
$563$	15.7891	+	33.8599i	0.665432	+	1.42702i	0.891550	+	0.452923i	$0.149619\pi$
$563$	15.7891	+	33.8599i	0.665432	+	1.42702i	−0.226118	+	0.974100i	$0.572603\pi$
$564$	45.8251	+	22.7919i	1.92958	+	0.959713i
$565$	−15.0824	−	40.9013i	−0.634523	−	1.72073i
$566$		−	61.7281i		−	2.59462i
$567$	−15.8861	+	18.4191i	−0.667155	+	0.773530i
$568$	39.7474	−	39.7474i	1.66776	−	1.66776i
$569$	−0.949414	+	5.38439i	−0.0398015	+	0.225725i	−0.998220	−	0.0596413i	$-0.981004\pi$
$569$	−0.949414	+	5.38439i	−0.0398015	+	0.225725i	0.958418	+	0.285367i	$0.0921154\pi$
$570$	−21.5647	+	24.6308i	−0.903246	+	1.03167i
$571$	−27.1899	−	9.89631i	−1.13786	−	0.414148i	−0.296721	−	0.954964i	$-0.595893\pi$
$571$	−27.1899	−	9.89631i	−1.13786	−	0.414148i	−0.841141	+	0.540817i	$0.818115\pi$
$572$	−3.84643	+	43.9649i	−0.160827	+	1.83826i
$573$	−15.0302	+	2.26121i	−0.627894	+	0.0944636i
$574$	−17.7698	−	48.8220i	−0.741695	−	2.03779i
$575$	−24.0522	−	6.22789i	−1.00305	−	0.259721i
$576$	−4.39245	+	10.4042i	−0.183019	+	0.433507i
$577$	3.56601	−	13.3085i	0.148455	−	0.554041i	−0.851122	−	0.524967i	$-0.824078\pi$
$577$	3.56601	−	13.3085i	0.148455	−	0.554041i	0.999577	−	0.0290738i	$-0.00925578\pi$
$578$	4.40755	+	50.3785i	0.183330	+	2.09547i
$579$	1.53725	−	1.46164i	0.0638861	−	0.0607438i
$580$	−2.48551	+	29.8588i	−0.103205	+	1.23982i
$581$	2.91282	−	0.513608i	0.120844	−	0.0213081i
$582$	11.6216	−	19.0062i	0.481731	−	0.787832i
$583$	16.0162	−	1.40124i	0.663324	−	0.0580333i
$584$	−0.0741472	−	0.128427i	−0.00306823	−	0.00531433i
$585$	9.69865	+	18.7482i	0.400990	+	0.775145i
$586$	30.1112	−	52.1541i	1.24388	−	2.15447i
$587$	8.99405	−	19.2878i	0.371224	−	0.796093i	−0.628607	−	0.777723i	$-0.716375\pi$
$587$	8.99405	−	19.2878i	0.371224	−	0.796093i	0.999831	−	0.0183698i	$-0.00584763\pi$
$588$	−1.76849	+	1.40953i	−0.0729313	+	0.0581281i
$589$	−0.797678	−	0.950636i	−0.0328678	−	0.0391703i
$590$	7.64384	+	42.3066i	0.314692	+	1.74174i
$591$	13.4446	+	20.2698i	0.553038	+	0.833787i
$592$	−21.2290	+	14.8647i	−0.872507	+	0.610936i
$593$	9.84862	+	9.84862i	0.404434	+	0.404434i	0.879792	−	0.475358i	$-0.157681\pi$
$593$	9.84862	+	9.84862i	0.404434	+	0.404434i	−0.475358	+	0.879792i	$0.657681\pi$
$594$	−26.9901	+	32.9368i	−1.10742	+	1.35141i
$595$	−9.38431	+	35.6228i	−0.384719	+	1.46039i
$596$	−3.59362	−	0.633653i	−0.147201	−	0.0259554i
$597$	14.7901	−	16.7499i	0.605318	−	0.685529i
$598$	35.5503	−	16.5774i	1.45376	−	0.677900i
$599$	−7.79546	+	6.54117i	−0.318514	+	0.267265i	−0.788000	−	0.615675i	$-0.788884\pi$
$599$	−7.79546	+	6.54117i	−0.318514	+	0.267265i	0.469486	+	0.882940i	$0.344439\pi$
$600$	5.17475	−	49.5575i	0.211258	−	2.02317i
$601$	29.1191	−	10.5985i	1.18779	−	0.432321i	0.328845	−	0.944384i	$-0.393341\pi$
$601$	29.1191	−	10.5985i	1.18779	−	0.432321i	0.858948	+	0.512063i	$0.171119\pi$
$602$	−7.79094	−	29.0762i	−0.317535	−	1.18506i
$603$	−0.0426040	−	1.15558i	−0.00173497	−	0.0470591i
$604$	−55.0397	+	31.7772i	−2.23953	+	1.29299i
$605$	0.600311	−	0.424126i	0.0244061	−	0.0172432i
$606$	−1.46268	+	4.95560i	−0.0594172	+	0.201308i
$607$	17.4264	−	24.8874i	0.707315	−	1.01015i	−0.291253	−	0.956646i	$-0.594072\pi$
$607$	17.4264	−	24.8874i	0.707315	−	1.01015i	0.998568	−	0.0535038i	$-0.0170389\pi$
$608$	−6.10833	+	8.72359i	−0.247725	+	0.353788i
$609$	4.13560	−	14.0116i	0.167583	−	0.567778i
$610$	−6.81297	+	39.6142i	−0.275849	+	1.60393i
$611$	−18.7548	+	10.8281i	−0.758738	+	0.438058i
$612$	2.89274	+	78.4623i	0.116932	+	3.17165i
$613$	−0.956834	−	3.57095i	−0.0386462	−	0.144229i	0.943907	−	0.330211i	$-0.107120\pi$
$613$	−0.956834	−	3.57095i	−0.0386462	−	0.144229i	−0.982553	+	0.185982i	$0.940453\pi$
$614$	9.58694	−	3.48936i	0.386897	−	0.140819i
$615$	−23.9488	−	17.5297i	−0.965710	−	0.706864i
$616$	−38.9116	+	32.6507i	−1.56779	+	1.31553i
$617$	−14.6652	+	6.83850i	−0.590399	+	0.275308i	−0.694771	−	0.719231i	$-0.744494\pi$
$617$	−14.6652	+	6.83850i	−0.590399	+	0.275308i	0.104372	+	0.994538i	$0.466717\pi$
$618$	0.541063	−	0.612760i	0.0217648	−	0.0246488i
$619$	20.5670	+	3.62651i	0.826656	+	0.145762i	0.570942	−	0.820991i	$-0.306578\pi$
$619$	20.5670	+	3.62651i	0.826656	+	0.145762i	0.255714	+	0.966752i	$0.417689\pi$
$620$	3.41926	+	0.900756i	0.137321	+	0.0361752i
$621$	25.4783	+	4.18725i	1.02241	+	0.168029i
$622$	−17.9835	−	17.9835i	−0.721072	−	0.721072i
$623$	−17.4096	+	12.1904i	−0.697502	+	0.488396i
$624$	17.6138	+	26.5554i	0.705116	+	1.06307i
$625$	−4.75575	−	24.5435i	−0.190230	−	0.981740i
$626$	−47.5380	−	56.6536i	−1.90000	−	2.26433i
$627$	14.9082	−	11.8822i	0.595378	−	0.474531i
$628$	−18.5557	+	39.7929i	−0.740454	+	1.58791i
$629$	13.5097	−	23.3995i	0.538667	−	0.932999i
$630$	−13.7878	+	43.3412i	−0.549319	+	1.72675i
$631$	7.86152	+	13.6165i	0.312962	+	0.542066i	0.979002	−	0.203850i	$-0.0653454\pi$
$631$	7.86152	+	13.6165i	0.312962	+	0.542066i	−0.666040	+	0.745916i	$0.732012\pi$
$632$	63.7581	−	5.57811i	2.53616	−	0.221885i
$633$	−0.115957	+	0.189639i	−0.00460889	+	0.00753746i
$634$	−7.72396	+	1.36194i	−0.306758	+	0.0540897i
$635$	−30.8462	−	36.4479i	−1.22410	−	1.44639i
$636$	26.5238	−	25.2192i	1.05174	−	1.00001i
$637$	−0.0834010	−	0.953277i	−0.00330447	−	0.0377702i
$638$	6.61957	−	24.7046i	0.262071	−	0.978063i
$639$	−11.3997	+	27.0020i	−0.450966	+	1.06818i
$640$	0.148619	+	35.2517i	0.00587470	+	1.39345i
$641$	13.8355	+	38.0128i	0.546471	+	1.50142i	0.838443	+	0.544990i	$0.183467\pi$
$641$	13.8355	+	38.0128i	0.546471	+	1.50142i	−0.291971	+	0.956427i	$0.594311\pi$
$642$	10.7378	−	1.61544i	0.423785	−	0.0637565i
$643$	2.25900	−	25.8204i	0.0890861	−	1.01826i	−0.811723	−	0.584043i	$-0.801470\pi$
$643$	2.25900	−	25.8204i	0.0890861	−	1.01826i	0.900809	−	0.434216i	$-0.142974\pi$
$644$	54.1816	+	19.7205i	2.13506	+	0.777097i
$645$	−12.9375	−	11.3270i	−0.509414	−	0.446001i
$646$	8.94731	−	50.7427i	0.352027	−	1.99645i
$647$	−23.1817	+	23.1817i	−0.911366	+	0.911366i	−0.996380	−	0.0850141i	$-0.972906\pi$
$647$	−23.1817	+	23.1817i	−0.911366	+	0.911366i	0.0850141	+	0.996380i	$0.472906\pi$
$648$	−0.702344	+	51.7769i	−0.0275907	+	2.03399i
$649$		−	25.0359i		−	0.982744i
$650$	30.4482	+	25.1147i	1.19428	+	0.985078i
$651$	−1.54368	−	0.767776i	−0.0605015	−	0.0300915i
$652$	−23.6285	−	50.6714i	−0.925362	−	1.98445i
$653$	−32.8699	−	2.87574i	−1.28630	−	0.112537i	−0.576591	−	0.817033i	$-0.695617\pi$
$653$	−32.8699	−	2.87574i	−1.28630	−	0.112537i	−0.709708	+	0.704496i	$0.751173\pi$
$654$	20.1526	−	27.2901i	0.788028	−	1.06713i
$655$	36.9268	−	3.38761i	1.44285	−	0.132365i
$656$	−38.8017	−	22.4022i	−1.51495	−	0.874658i
$657$	0.0610244	+	0.0474867i	0.00238079	+	0.00185263i
$658$	−45.0720	−	12.0770i	−1.75709	−	0.470810i
$659$	−12.5302	−	10.5141i	−0.488108	−	0.409571i	0.365240	−	0.930914i	$-0.380987\pi$
$659$	−12.5302	−	10.5141i	−0.488108	−	0.409571i	−0.853348	+	0.521342i	$0.825432\pi$
$660$	−15.1573	+	52.1625i	−0.589997	+	2.03042i
$661$	4.84704	+	27.4889i	0.188528	+	1.06920i	0.921338	+	0.388762i	$0.127097\pi$
$661$	4.84704	+	27.4889i	0.188528	+	1.06920i	−0.732810	+	0.680433i	$0.761792\pi$
$662$	60.3108	+	42.2301i	2.34405	+	1.64132i
$663$	−28.3440	−	17.3313i	−1.10079	−	0.673093i
$664$	4.04743	−	4.82353i	0.157071	−	0.187189i
$665$	10.1065	−	17.6767i	0.391913	−	0.685472i
$666$	18.1142	−	28.0125i	0.701909	−	1.08546i
$667$	−14.9796	+	4.01378i	−0.580014	+	0.155414i
$668$	−18.7610	−	8.74840i	−0.725885	−	0.338486i
$669$	−1.62852	+	14.4179i	−0.0629621	+	0.557429i
$670$	−0.922058	−	1.95579i	−0.0356222	−	0.0755587i
$671$	8.00592	−	21.9961i	0.309065	−	0.849149i
$672$	−2.93562	+	14.5012i	−0.113244	+	0.559396i
$673$	20.3600	+	29.0771i	0.784821	+	1.12084i	0.989854	+	0.142085i	$0.0453807\pi$
$673$	20.3600	+	29.0771i	0.784821	+	1.12084i	−0.205034	+	0.978755i	$0.565730\pi$
$674$	−40.1696			−1.54728
$675$	7.22673	+	24.9554i	0.278157	+	0.960536i
$676$	13.3039			0.511688
$677$	−1.17325	−	1.67557i	−0.0450916	−	0.0643975i	0.795973	−	0.605332i	$-0.206960\pi$
$677$	−1.17325	−	1.67557i	−0.0450916	−	0.0643975i	−0.841065	+	0.540934i	$0.818071\pi$
$678$	63.4997	+	56.0698i	2.43869	+	2.15335i
$679$	−4.73916	+	13.0207i	−0.181872	+	0.499689i
$680$	33.4426	+	70.9356i	1.28247	+	2.72026i
$681$	−5.73127	+	2.49866i	−0.219623	+	0.0957487i
$682$	−2.73552	−	1.27559i	−0.104748	−	0.0488450i
$683$	8.66609	−	2.32207i	0.331599	−	0.0888516i	−0.0891783	−	0.996016i	$-0.528424\pi$
$683$	8.66609	−	2.32207i	0.331599	−	0.0888516i	0.420777	+	0.907164i	$0.361757\pi$
$684$	9.68033	−	42.3053i	0.370137	−	1.61758i
$685$	−22.2502	+	38.9164i	−0.850135	+	1.48692i
$686$	−29.1812	+	34.7769i	−1.11415	+	1.32779i
$687$	1.88669	−	1.02677i	0.0719819	−	0.0391736i
$688$	−21.2642	−	14.8893i	−0.810689	−	0.567650i
$689$	2.68921	+	15.2513i	0.102451	+	0.581027i
$690$	46.8868	−	11.5141i	1.78495	−	0.438336i
$691$	−22.2034	−	18.6309i	−0.844657	−	0.708752i	0.113949	−	0.993487i	$-0.463650\pi$
$691$	−22.2034	−	18.6309i	−0.844657	−	0.708752i	−0.958606	+	0.284735i	$0.908094\pi$
$692$	26.7381	+	7.16445i	1.01643	+	0.272352i
$693$	12.3888	−	23.4097i	0.470613	−	0.889262i
$694$	−4.48662	−	2.59035i	−0.170310	−	0.0983284i
$695$	39.5788	−	3.63090i	1.50131	−	0.137728i
$696$	−12.4292	−	28.5094i	−0.471129	−	1.08065i
$697$	46.5345	+	4.07124i	1.76262	+	0.154209i
$698$	−0.604818	−	1.29704i	−0.0228927	−	0.0490936i
$699$	2.23113	+	35.9057i	0.0843892	+	1.35808i
$700$	5.54372	+	57.7521i	0.209533	+	2.18283i
$701$			4.40189i			0.166257i	0.996539	+	0.0831285i	$0.0264912\pi$
$701$			4.40189i			0.166257i	−0.996539	+	0.0831285i	$0.973509\pi$
$702$	−33.8715	−	23.1341i	−1.27840	−	0.873140i
$703$	−10.5604	+	10.5604i	−0.398294	+	0.398294i
$704$	2.13541	−	12.1105i	0.0804813	−	0.456432i
$705$	−25.2334	+	8.58882i	−0.950346	+	0.323474i
$706$	17.8104	+	6.48245i	0.670303	+	0.243970i
$707$	0.280098	−	3.20153i	0.0105342	−	0.120406i
$708$	−35.5223	−	44.5686i	−1.33501	−	1.67499i
$709$	8.05475	+	22.1303i	0.302503	+	0.831119i	0.994064	+	0.108801i	$0.0347011\pi$
$709$	8.05475	+	22.1303i	0.302503	+	0.831119i	−0.691561	+	0.722318i	$0.743077\pi$
$710$	0.231053	+	54.8045i	0.00867125	+	2.05677i
$711$	−29.7049	+	15.2083i	−1.11402	+	0.570354i
$712$	−11.7104	+	43.7037i	−0.438865	+	1.63787i
$713$	0.159508	+	1.82319i	0.00597364	+	0.0682790i
$714$	−16.7787	−	69.5901i	−0.627926	−	2.60434i
$715$	−14.8484	−	17.5449i	−0.555300	−	0.656143i
$716$	11.0687	−	1.95172i	0.413658	−	0.0729391i
$717$	20.9562	+	0.528367i	0.782623	+	0.0197322i
$718$	−35.6203	+	3.11637i	−1.32934	+	0.116302i
$719$	3.55440	+	6.15640i	0.132557	+	0.229595i	0.924661	−	0.380790i	$-0.124348\pi$
$719$	3.55440	+	6.15640i	0.132557	+	0.229595i	−0.792105	+	0.610385i	$0.791015\pi$
$720$	14.9164	+	36.2744i	0.555901	+	1.35187i
$721$	−0.254220	+	0.440322i	−0.00946765	+	0.0163985i
$722$	8.10778	−	17.3872i	0.301740	−	0.647084i
$723$	1.76863	+	11.7560i	0.0657762	+	0.437210i
$724$	49.1954	+	58.6288i	1.82833	+	2.17892i
$725$	−10.1308	−	11.8688i	−0.376250	−	0.440795i
$726$	−0.636062	+	1.27886i	−0.0236065	+	0.0474628i
$727$	−15.9661	+	11.1796i	−0.592148	+	0.414627i	−0.830874	−	0.556460i	$-0.812159\pi$
$727$	−15.9661	+	11.1796i	−0.592148	+	0.414627i	0.238726	+	0.971087i	$0.423270\pi$
$728$	−34.5978	−	34.5978i	−1.28228	−	1.28228i
$729$	−9.82282	−	25.1498i	−0.363808	−	0.931474i
$730$	0.139814	+	0.0368320i	0.00517475	+	0.00136321i
$731$	26.6530	+	4.69964i	0.985796	+	0.173822i
$732$	−16.9572	−	50.5165i	−0.626756	−	1.86714i
$733$	33.2213	−	15.4914i	1.22706	−	0.572186i	0.302471	−	0.953159i	$-0.402188\pi$
$733$	33.2213	−	15.4914i	1.22706	−	0.572186i	0.924587	+	0.380972i	$0.124411\pi$
$734$	34.6809	−	29.1008i	1.28010	−	1.07413i
$735$	0.127258	−	1.17091i	0.00469399	−	0.0431897i
$736$	14.7586	−	5.37168i	0.544008	−	0.198003i
$737$	0.325897	+	1.21626i	0.0120046	+	0.0448017i
$738$	57.1266	+	7.91536i	2.10286	+	0.291368i
$739$	39.9362	−	23.0572i	1.46908	−	0.848172i	0.469678	−	0.882838i	$-0.344370\pi$
$739$	39.9362	−	23.0572i	1.46908	−	0.848172i	0.999399	+	0.0346657i	$0.0110366\pi$
$740$	7.21264	−	41.9381i	0.265142	−	1.54167i
$741$	12.6536	+	13.3082i	0.464841	+	0.488888i
$742$	−19.1393	+	27.3338i	−0.702626	+	1.00345i
$743$	4.00223	−	5.71577i	0.146828	−	0.209691i	−0.739001	−	0.673705i	$-0.764702\pi$
$743$	4.00223	−	5.71577i	0.146828	−	0.209691i	0.885828	+	0.464013i	$0.153591\pi$
$744$	−3.56808	+	0.860291i	−0.130812	+	0.0315398i
$745$	1.55216	−	1.09662i	0.0568668	−	0.0401769i
$746$	−11.8467	+	6.83970i	−0.433739	+	0.250419i
$747$	−1.00850	+	3.12449i	−0.0368989	+	0.114319i
$748$	−22.1279	−	82.5823i	−0.809075	−	3.01951i
$749$	−6.34655	+	2.30996i	−0.231898	+	0.0844040i
$750$	30.7569	+	37.6039i	1.12308	+	1.37310i
$751$	14.9900	−	12.5781i	0.546995	−	0.458983i	−0.326927	−	0.945050i	$-0.606013\pi$
$751$	14.9900	−	12.5781i	0.546995	−	0.458983i	0.873922	+	0.486067i	$0.161569\pi$
$752$	−36.4694	+	17.0060i	−1.32990	+	0.620144i
$753$	16.7362	+	3.38807i	0.609900	+	0.123468i
$754$	24.2618	+	4.27802i	0.883564	+	0.155796i
$755$	8.43197	−	32.0077i	0.306871	−	1.16488i
$756$	−11.1605	−	59.2517i	−0.405905	−	2.15496i
$757$	−13.8377	−	13.8377i	−0.502940	−	0.502940i	0.409411	−	0.912350i	$-0.365734\pi$
$757$	−13.8377	−	13.8377i	−0.502940	−	0.502940i	−0.912350	+	0.409411i	$0.865734\pi$
$758$	8.30245	−	5.81344i	0.301559	−	0.211154i
$759$	−28.0614	+	1.74369i	−1.01856	+	0.0632921i
$760$	−7.70718	−	42.6572i	−0.279569	−	1.54734i
$761$	−4.04597	−	4.82180i	−0.146666	−	0.174790i	0.687710	−	0.725986i	$-0.258616\pi$
$761$	−4.04597	−	4.82180i	−0.146666	−	0.174790i	−0.834376	+	0.551196i	$0.814172\pi$
$762$	86.3626	+	33.9222i	3.12859	+	1.22887i
$763$	−8.91746	+	19.1236i	−0.322834	+	0.692319i
$764$	18.8382	−	32.6287i	0.681542	−	1.18046i
$765$	−30.0775	−	27.7033i	−1.08746	−	1.00161i
$766$	38.5033	+	66.6897i	1.39118	+	2.40960i
$767$	24.0240	−	2.10183i	0.867457	−	0.0758927i
$768$	−26.5114	−	48.7149i	−0.956647	−	1.75785i
$769$	43.7099	−	7.70724i	1.57622	−	0.277930i	0.683983	−	0.729498i	$-0.260246\pi$
$769$	43.7099	−	7.70724i	1.57622	−	0.277930i	0.892237	+	0.451567i	$0.149135\pi$
$770$	4.10832	−	49.3539i	0.148054	−	1.77859i
$771$	18.6850	+	5.51499i	0.672924	+	0.198618i
$772$	0.458275	+	5.23811i	0.0164937	+	0.188524i
$773$	4.60315	−	17.1792i	0.165564	−	0.617893i	−0.832404	−	0.554170i	$-0.813036\pi$
$773$	4.60315	−	17.1792i	0.165564	−	0.617893i	0.997968	−	0.0637231i	$-0.0202974\pi$
$774$	32.5724	+	7.45323i	1.17079	+	0.267901i
$775$	−1.58700	+	0.934184i	−0.0570067	+	0.0335569i
$776$	10.0891	+	27.7195i	0.362176	+	0.995071i
$777$	−7.58565	+	19.3124i	−0.272134	+	0.692827i
$778$	−6.58818	+	75.3032i	−0.236198	+	2.69975i
$779$	−24.2626	−	8.83085i	−0.869297	−	0.316398i
$780$	−51.3268	−	10.1655i	−1.83779	−	0.363984i
$781$	5.54203	−	31.4304i	0.198310	−	1.12467i
$782$	−53.7322	+	53.7322i	−1.92146	+	1.92146i
$783$	11.5997	+	11.3327i	0.414539	+	0.404996i
$784$		−	1.77806i		−	0.0635021i
$785$	−7.91148	−	21.4547i	−0.282373	−	0.765752i
$786$	−60.0494	+	39.8299i	−2.14189	+	1.42068i
$787$	−12.6422	−	27.1112i	−0.450644	−	0.966410i	−0.992073	−	0.125663i	$-0.959894\pi$
$787$	−12.6422	−	27.1112i	−0.450644	−	0.966410i	0.541429	−	0.840747i	$-0.317884\pi$
$788$	−60.0637	−	5.25489i	−2.13968	−	0.187198i
$789$	−14.1853	−	1.60224i	−0.505011	−	0.0570414i
$790$	−39.9083	+	47.9701i	−1.41987	+	1.70670i
$791$	−45.6301	−	26.3445i	−1.62242	−	0.936704i
$792$	−11.8303	−	55.1299i	−0.420372	−	1.95895i
$793$	21.7792	+	5.83572i	0.773402	+	0.207232i
$794$	−54.7764	−	45.9629i	−1.94394	−	1.63116i
$795$	−0.400100	+	19.0571i	−0.0141901	+	0.675886i
$796$	9.61833	+	54.5483i	0.340913	+	1.93341i
$797$	−20.3795	−	14.2699i	−0.721880	−	0.505466i	0.153954	−	0.988078i	$-0.450799\pi$
$797$	−20.3795	−	14.2699i	−0.721880	−	0.505466i	−0.875834	+	0.482612i	$0.839688\pi$
$798$	−0.997295	+	39.5549i	−0.0353038	+	1.40023i
$799$	26.9669	−	32.1379i	0.954020	−	1.13696i
$800$	11.2685	+	11.0801i	0.398403	+	0.391741i
$801$	−2.92066	−	23.4104i	−0.103196	−	0.827166i
$802$	68.4155	−	18.3319i	2.41584	−	0.647321i
$803$	−0.0763090	−	0.0355835i	−0.00269289	−	0.00125571i
$804$	2.30586	+	1.70278i	0.0813215	+	0.0600525i
$805$	−27.1620	+	12.8056i	−0.957336	+	0.451337i
$806$	0.994384	−	2.73205i	0.0350257	−	0.0962323i
$807$	−35.0971	+	11.7813i	−1.23548	+	0.414720i
$808$	−3.92423	−	5.60438i	−0.138054	−	0.197161i
$809$	27.7036			0.974006			0.487003	−	0.873400i	$-0.338090\pi$
$809$	27.7036			0.974006			0.487003	+	0.873400i	$0.338090\pi$
$810$	−35.3638	−	36.0312i	−1.24256	−	1.26601i
$811$	−16.0245			−0.562695			−0.281347	−	0.959606i	$-0.590781\pi$
$811$	−16.0245			−0.562695			−0.281347	+	0.959606i	$0.590781\pi$
$812$	20.7712	+	29.6644i	0.728927	+	1.04102i
$813$	−26.2825	+	8.82242i	−0.921767	+	0.309416i
$814$	−12.4237	+	34.1339i	−0.435451	+	1.19639i
$815$	27.4040	+	9.84360i	0.959920	+	0.344806i
$816$	−49.6591	−	36.6711i	−1.73841	−	1.28375i
$817$	−13.5578	−	6.32213i	−0.474329	−	0.221183i
$818$	−48.4121	+	12.9720i	−1.69269	+	0.453555i
$819$	23.5037	+	9.92282i	0.821285	+	0.346731i
$820$	70.9810	−	19.3404i	2.47876	−	0.675396i
$821$	−36.5832	+	43.5982i	−1.27676	+	1.52159i	−0.548844	+	0.835925i	$0.684932\pi$
$821$	−36.5832	+	43.5982i	−1.27676	+	1.52159i	−0.727920	+	0.685663i	$0.759513\pi$
$822$	2.19561	−	87.0828i	0.0765808	−	3.03736i
$823$	−42.9536	−	30.0764i	−1.49727	−	1.04840i	−0.981454	−	0.191699i	$-0.938600\pi$
$823$	−42.9536	−	30.0764i	−1.49727	−	1.04840i	−0.515815	−	0.856700i	$-0.672511\pi$
$824$	0.187958	+	1.06596i	0.00654781	+	0.0371345i
$825$	−13.7322	−	24.7340i	−0.478094	−	0.861129i
$826$	39.8049	+	33.4002i	1.38499	+	1.16214i
$827$	−20.7603	−	5.56271i	−0.721907	−	0.193434i	−0.120885	−	0.992667i	$-0.538573\pi$
$827$	−20.7603	−	5.56271i	−0.721907	−	0.193434i	−0.601023	+	0.799232i	$0.705240\pi$
$828$	−47.4805	+	42.9191i	−1.65006	+	1.49154i
$829$	27.5695	+	15.9172i	0.957527	+	0.552828i	0.895411	−	0.445241i	$-0.146882\pi$
$829$	27.5695	+	15.9172i	0.957527	+	0.552828i	0.0621158	+	0.998069i	$0.480215\pi$
$830$	0.560840	+	6.11347i	0.0194670	+	0.212202i
$831$	24.7380	+	2.79418i	0.858152	+	0.0969290i
$832$	11.8003	+	1.03240i	0.409103	+	0.0357919i
$833$	0.783438	+	1.68009i	0.0271445	+	0.0582116i
$834$	−64.3619	+	42.6903i	−2.22867	+	1.47824i
$835$	10.1152	−	3.73000i	0.350051	−	0.129082i
$836$			47.2568i			1.63441i
$837$	1.55479	−	1.11588i	0.0537415	−	0.0385704i
$838$	12.9511	−	12.9511i	0.447390	−	0.447390i
$839$	−5.41257	+	30.6962i	−0.186863	+	1.05975i	0.736676	+	0.676246i	$0.236394\pi$
$839$	−5.41257	+	30.6962i	−0.186863	+	1.05975i	−0.923539	+	0.383505i	$0.874717\pi$
$840$	−33.4994	−	50.0460i	−1.15584	−	1.72675i
$841$	18.0984	+	6.58729i	0.624084	+	0.227148i
$842$	6.36910	−	72.7991i	0.219494	−	2.50882i
$843$	−6.75371	+	17.1943i	−0.232610	+	0.592203i
$844$	−0.188452	−	0.517767i	−0.00648677	−	0.0178223i
$845$	−4.87870	+	4.92001i	−0.167832	+	0.169254i
$846$	35.2514	−	37.9502i	1.21197	−	1.30475i
$847$	0.229930	−	0.858109i	0.00790047	−	0.0294850i
$848$	2.50796	+	28.6662i	0.0861239	+	0.984400i
$849$	−40.8753	−	12.0646i	−1.40284	−	0.414056i
$850$	−72.0683	−	25.5446i	−2.47192	−	0.876174i
$851$	21.6908	−	3.82467i	0.743550	−	0.131108i
$852$	−34.7294	−	63.8155i	−1.18981	−	2.18628i
$853$	34.9235	−	3.05541i	1.19576	−	0.104615i	0.528165	−	0.849142i	$-0.322880\pi$
$853$	34.9235	−	3.05541i	1.19576	−	0.104615i	0.667593	+	0.744526i	$0.267325\pi$
$854$	24.2912	+	42.0736i	0.831228	+	1.43973i
$855$	12.0953	+	19.0938i	0.413652	+	0.652995i
$856$	−7.18905	+	12.4518i	−0.245717	+	0.425594i
$857$	23.5835	−	50.5751i	0.805599	−	1.72761i	0.128512	−	0.991708i	$-0.458980\pi$
$857$	23.5835	−	50.5751i	0.805599	−	1.72761i	0.677086	−	0.735904i	$-0.263242\pi$
$858$	41.5723	+	16.3291i	1.41926	+	0.557467i
$859$	−18.4923	−	22.0383i	−0.630949	−	0.751936i	0.351962	−	0.936014i	$-0.385514\pi$
$859$	−18.4923	−	22.0383i	−0.630949	−	0.751936i	−0.982912	+	0.184078i	$0.941070\pi$
$860$	41.9451	−	7.57853i	1.43032	−	0.258426i
$861$	−35.8022	+	2.22470i	−1.22013	+	0.0758175i
$862$	−29.4666	+	20.6328i	−1.00364	+	0.702754i
$863$	20.3595	+	20.3595i	0.693044	+	0.693044i	0.962901	−	0.269856i	$-0.0869762\pi$
$863$	20.3595	+	20.3595i	0.693044	+	0.693044i	−0.269856	+	0.962901i	$0.586976\pi$
$864$	−12.7031	−	10.4096i	−0.432169	−	0.354141i
$865$	−12.4547	+	7.26092i	−0.423473	+	0.246879i
$866$	56.9181	+	10.0362i	1.93416	+	0.341044i
$867$	34.2213	+	6.92775i	1.16221	+	0.235279i
$868$	3.87326	−	1.80613i	0.131467	−	0.0613040i
$869$	27.8369	−	23.3579i	0.944301	−	0.792363i
$870$	28.2702	+	10.9669i	0.958451	+	0.371811i
$871$	−1.13975	+	0.414834i	−0.0386189	+	0.0140561i
$872$	11.6262	+	43.3897i	0.393714	+	1.46936i
$873$	−10.3142	−	11.4103i	−0.349082	−	0.386181i
$874$	36.3748	−	21.0010i	1.23040	−	0.710370i
$875$	−23.3907	−	19.1282i	−0.790749	−	0.646653i
$876$	−0.186332	+	0.0449261i	−0.00629559	+	0.00151791i
$877$	−24.2499	+	34.6324i	−0.818860	+	1.16945i	0.164247	+	0.986419i	$0.447481\pi$
$877$	−24.2499	+	34.6324i	−0.818860	+	1.16945i	−0.983107	+	0.183034i	$0.941408\pi$
$878$	26.7583	−	38.2149i	0.903050	−	1.28969i
$879$	−28.6504	−	30.1325i	−0.966355	−	1.01634i
$880$	−24.6437	−	34.8810i	−0.830739	−	1.17584i
$881$	17.8875	−	10.3273i	0.602644	−	0.347936i	−0.167437	−	0.985883i	$-0.553549\pi$
$881$	17.8875	−	10.3273i	0.602644	−	0.347936i	0.770081	+	0.637946i	$0.220216\pi$
$882$	0.861496	+	2.12040i	0.0290081	+	0.0713975i
$883$	−4.93007	−	18.3993i	−0.165910	−	0.619185i	−0.997922	−	0.0644275i	$-0.979478\pi$
$883$	−4.93007	−	18.3993i	−0.165910	−	0.619185i	0.832012	−	0.554757i	$-0.187189\pi$
$884$	77.3870	−	28.1666i	2.60281	−	0.947344i
$885$	29.5087	+	3.20710i	0.991924	+	0.107805i
$886$	52.3180	−	43.9000i	1.75766	−	1.47485i
$887$	−33.0811	+	15.4260i	−1.11076	+	0.517954i	−0.889350	−	0.457228i	$-0.848842\pi$
$887$	−33.0811	+	15.4260i	−1.11076	+	0.517954i	−0.221406	+	0.975182i	$0.571065\pi$
$888$	14.0565	+	41.8751i	0.471705	+	1.40524i
$889$	−56.8345	−	10.0215i	−1.90617	−	0.336109i
$890$	−22.2176	−	38.1100i	−0.744735	−	1.27745i
$891$	16.5351	+	24.3098i	0.553946	+	0.814408i
$892$	−25.4323	−	25.4323i	−0.851538	−	0.851538i
$893$	−18.9954	+	13.3007i	−0.635657	+	0.445092i
$894$	−1.64460	+	3.30660i	−0.0550035	+	0.110589i
$895$	−3.33726	+	4.80913i	−0.111552	+	0.160751i
$896$	27.3874	+	32.6390i	0.914947	+	1.09039i
$897$	−4.02905	−	26.7808i	−0.134526	−	0.894186i
$898$	32.6248	−	69.9640i	1.08870	−	2.33473i
$899$	−0.574727	+	0.995457i	−0.0191682	+	0.0332003i
$900$	−59.5400	−	24.5473i	−1.98467	−	0.818242i
$901$	−15.0005	−	25.9816i	−0.499739	−	0.865574i
$902$	−62.5603	+	5.47332i	−2.08303	+	0.182242i
$903$	−20.7765	−	0.523836i	−0.691398	−	0.0174322i
$904$	−110.464	+	19.4778i	−3.67399	+	0.647823i
$905$	−39.7224	−	3.30658i	−1.32042	−	0.109914i
$906$	15.0759	+	62.5279i	0.500865	+	2.07735i
$907$	3.14986	+	36.0031i	0.104589	+	1.19546i	0.849240	+	0.528008i	$0.177061\pi$
$907$	3.14986	+	36.0031i	0.104589	+	1.19546i	−0.744650	+	0.667455i	$0.767384\pi$
$908$	4.01124	−	14.9702i	0.133118	−	0.496802i
$909$	2.99564	+	1.93712i	0.0993591	+	0.0642502i
$910$	47.7042	−	0.201118i	1.58138	−	0.00666701i
$911$	−1.01321	−	2.78377i	−0.0335691	−	0.0922304i	0.921776	−	0.387723i	$-0.126738\pi$
$911$	−1.01321	−	2.78377i	−0.0335691	−	0.0922304i	−0.955345	+	0.295493i	$0.904516\pi$
$912$	21.2671	+	26.6831i	0.704224	+	0.883566i
$913$	0.311589	−	3.56148i	0.0103121	−	0.117868i
$914$	−55.2056	−	20.0932i	−1.82604	−	0.664623i
$915$	24.9003	+	12.2539i	0.823177	+	0.405102i
$916$	−0.924588	+	5.24360i	−0.0305492	+	0.173253i
$917$	31.6917	−	31.6917i	1.04655	−	1.04655i
$918$	76.9879	+	19.6710i	2.54098	+	0.649240i
$919$		−	31.4414i		−	1.03716i	−0.855030	−	0.518578i	$-0.826462\pi$
$919$		−	31.4414i		−	1.03716i	0.855030	−	0.518578i	$-0.173538\pi$
$920$	−26.7729	+	58.0523i	−0.882675	+	1.91393i
$921$	−0.436853	−	7.03029i	−0.0143948	−	0.231656i
$922$	33.4873	+	71.8138i	1.10285	+	2.36506i
$923$	30.6254	+	2.67938i	1.00805	+	0.0881927i
$924$	26.2379	+	60.1829i	0.863162	+	1.97987i
$925$	12.8645	+	18.0466i	0.422981	+	0.593367i
$926$	63.7180	+	36.7876i	2.09390	+	1.20892i
$927$	−0.300010	−	0.478045i	−0.00985362	−	0.0157011i
$928$	9.52810	+	2.55305i	0.312775	+	0.0838079i
$929$	35.9403	+	30.1575i	1.17916	+	0.989435i	0.999984	+	0.00561833i	$0.00178838\pi$
$929$	35.9403	+	30.1575i	1.17916	+	0.989435i	0.179178	+	0.983817i	$0.442656\pi$
$930$	1.85391	−	3.06083i	0.0607919	−	0.100369i
$931$	−0.177929	−	1.00909i	−0.00583140	−	0.0330715i
$932$	−73.0484	−	51.1490i	−2.39278	−	1.67544i
$933$	−15.4232	+	8.39354i	−0.504933	+	0.274792i
$934$	33.4073	−	39.8133i	1.09312	−	1.30273i
$935$	38.6549	+	22.1007i	1.26415	+	0.722769i
$936$	51.9085	−	15.9805i	1.69668	−	0.522338i
$937$	45.8184	−	12.2770i	1.49682	−	0.401072i	0.584788	−	0.811186i	$-0.301178\pi$
$937$	45.8184	−	12.2770i	1.49682	−	0.401072i	0.912034	+	0.410114i	$0.134511\pi$
$938$	−2.36853	−	1.10446i	−0.0773353	−	0.0360620i
$939$	−46.8063	+	20.4061i	−1.52747	+	0.665927i
$940$	22.3364	−	62.1833i	0.728534	−	2.02820i
$941$	3.46508	−	9.52023i	0.112958	−	0.310351i	−0.870313	−	0.492500i	$-0.836083\pi$
$941$	3.46508	−	9.52023i	0.112958	−	0.310351i	0.983271	+	0.182149i	$0.0583054\pi$
$942$	33.3087	+	29.4113i	1.08526	+	0.958274i
$943$	21.8409	+	31.1920i	0.711236	+	1.01575i
$944$	44.8097			1.45843
$945$	26.0050	+	17.6010i	0.845943	+	0.572560i
$946$	−36.3847			−1.18297
$947$	16.1599	+	23.0787i	0.525126	+	0.749958i	0.990849	−	0.134973i	$-0.0430946\pi$
$947$	16.1599	+	23.0787i	0.525126	+	0.749958i	−0.465723	+	0.884930i	$0.654206\pi$
$948$	16.4134	−	81.0780i	0.533083	−	2.63329i
$949$	0.0277390	−	0.0762122i	0.000900445	−	0.00247395i
$950$	34.8232	+	23.9485i	1.12982	+	0.776991i
$951$	−0.607773	+	5.38087i	−0.0197084	+	0.174487i
$952$	85.9056	+	40.0584i	2.78422	+	1.29830i
$953$	0.146858	−	0.0393504i	0.00475719	−	0.00127468i	−0.256440	−	0.966560i	$-0.582549\pi$
$953$	0.146858	−	0.0393504i	0.00475719	−	0.00127468i	0.261197	+	0.965286i	$0.415883\pi$
$954$	−16.8800	−	32.9703i	−0.546511	−	1.06745i
$955$	5.15846	+	18.9320i	0.166924	+	0.612626i
$956$	−33.4013	+	39.8061i	−1.08027	+	1.28742i
$957$	−15.0652	−	9.21181i	−0.486988	−	0.297776i
$958$	−15.7210	−	11.0079i	−0.507922	−	0.355651i
$959$	9.40847	+	53.3581i	0.303815	+	1.72302i
$960$	14.0006	+	4.06827i	0.451867	+	0.131303i
$961$	−23.6435	−	19.8392i	−0.762692	−	0.639975i
$962$	−33.7973	−	9.05596i	−1.08967	−	0.291976i
$963$	1.02895	−	7.42609i	0.0331573	−	0.239302i
$964$	−25.5209	−	14.7345i	−0.821972	−	0.474566i
$965$	−2.10520	−	1.75140i	−0.0677687	−	0.0563795i
$966$	34.6642	−	46.9414i	1.11530	−	1.51031i
$967$	−39.1584	−	3.42592i	−1.25925	−	0.110170i	−0.562084	−	0.827080i	$-0.690000\pi$
$967$	−39.1584	−	3.42592i	−1.25925	−	0.110170i	−0.697165	+	0.716910i	$0.745556\pi$
$968$	−0.799275	−	1.71405i	−0.0256897	−	0.0550917i
$969$	−31.8522	−	15.8423i	−1.02324	−	0.508928i
$970$	−26.1168	−	12.0447i	−0.838560	−	0.386731i
$971$		−	16.2895i		−	0.522755i	−0.965237	−	0.261378i	$-0.915823\pi$
$971$		−	16.2895i		−	0.522755i	0.965237	−	0.261378i	$-0.0841768\pi$
$972$	63.9277	+	19.8151i	2.05048	+	0.635571i
$973$	33.9677	−	33.9677i	1.08895	−	1.08895i
$974$	−5.48855	+	31.1271i	−0.175864	+	0.997376i
$975$	22.5815	−	15.2537i	0.723188	−	0.488510i
$976$	39.3691	+	14.3292i	1.26017	+	0.458665i
$977$	−3.90528	+	44.6375i	−0.124941	+	1.42808i	0.632188	+	0.774815i	$0.282157\pi$
$977$	−3.90528	+	44.6375i	−0.124941	+	1.42808i	−0.757129	+	0.653266i	$0.773398\pi$
$978$	−55.9533	+	8.41791i	−1.78919	+	0.269175i
$979$	8.78621	+	24.1399i	0.280809	+	0.771515i
$980$	2.07313	+	2.05573i	0.0662238	+	0.0656678i
$981$	−14.1323	−	18.6785i	−0.451209	−	0.596358i
$982$	−2.32792	+	8.68793i	−0.0742871	+	0.277243i
$983$	0.145188	+	1.65951i	0.00463078	+	0.0529300i	0.998158	−	0.0606600i	$-0.0193205\pi$
$983$	0.145188	+	1.65951i	0.00463078	+	0.0529300i	−0.993528	+	0.113590i	$0.963765\pi$
$984$	−55.3422	+	52.6202i	−1.76425	+	1.67747i
$985$	23.9694	−	20.2855i	0.763729	−	0.646351i
$986$	−47.0008	+	8.28751i	−1.49681	+	0.263928i
$987$	−16.8064	+	27.4855i	−0.534953	+	0.874872i
$988$	−45.3468	+	3.96733i	−1.44267	+	0.126218i
$989$	11.0309	+	19.1061i	0.350763	+	0.607540i
$990$	46.2888	+	29.6565i	1.47116	+	0.942545i
$991$	20.3962	−	35.3273i	0.647908	−	1.12221i	−0.335714	−	0.941964i	$-0.608977\pi$
$991$	20.3962	−	35.3273i	0.647908	−	1.12221i	0.983622	−	0.180246i	$-0.0576892\pi$
$992$	0.491973	−	1.05504i	0.0156201	−	0.0334975i
$993$	39.7517	−	31.6830i	1.26148	−	1.00543i
$994$	42.5781	+	50.7425i	1.35049	+	1.60946i
$995$	−23.7000	−	16.4465i	−0.751342	−	0.521388i
$996$	−4.49854	−	6.78222i	−0.142542	−	0.214903i
$997$	46.5404	−	32.5879i	1.47395	−	1.03207i	0.486578	−	0.873637i	$-0.338245\pi$
$997$	46.5404	−	32.5879i	1.47395	−	1.03207i	0.987370	−	0.158432i	$-0.0506439\pi$
$998$	1.11990	+	1.11990i	0.0354498	+	0.0354498i
$999$	−15.0090	−	17.4699i	−0.474864	−	0.552722i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.2.16	✓	192
3.2	odd	2		405.2.r.a.332.1		192
5.2	odd	4		675.2.ba.b.218.1		192
5.3	odd	4	inner	135.2.q.a.83.16	yes	192
5.4	even	2		675.2.ba.b.407.1		192
15.8	even	4		405.2.r.a.8.1		192
27.13	even	9		405.2.r.a.152.1		192
27.14	odd	18	inner	135.2.q.a.122.16	yes	192
135.13	odd	36		405.2.r.a.233.1		192
135.14	odd	18		675.2.ba.b.257.1		192
135.68	even	36	inner	135.2.q.a.68.16	yes	192
135.122	even	36		675.2.ba.b.68.1		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.16	✓	192	1.1	even	1	trivial
135.2.q.a.68.16	yes	192	135.68	even	36	inner
135.2.q.a.83.16	yes	192	5.3	odd	4	inner
135.2.q.a.122.16	yes	192	27.14	odd	18	inner
405.2.r.a.8.1		192	15.8	even	4
405.2.r.a.152.1		192	27.13	even	9
405.2.r.a.233.1		192	135.13	odd	36
405.2.r.a.332.1		192	3.2	odd	2
675.2.ba.b.68.1		192	135.122	even	36
675.2.ba.b.218.1		192	5.2	odd	4
675.2.ba.b.257.1		192	135.14	odd	18
675.2.ba.b.407.1		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)

\(f(q)\)	\(=\)	\(q+(1.43892 + 2.05499i) q^{2} +(1.64201 - 0.551185i) q^{3} +(-1.46845 + 4.03452i) q^{4} +(-0.953539 - 2.02256i) q^{5} +(3.49539 + 2.58120i) q^{6} +(-2.44940 - 1.14217i) q^{7} +(-5.55747 + 1.48912i) q^{8} +(2.39239 - 1.81010i) q^{9} +O(q^{10})\)	\(q+(1.43892 + 2.05499i) q^{2} +(1.64201 - 0.551185i) q^{3} +(-1.46845 + 4.03452i) q^{4} +(-0.953539 - 2.02256i) q^{5} +(3.49539 + 2.58120i) q^{6} +(-2.44940 - 1.14217i) q^{7} +(-5.55747 + 1.48912i) q^{8} +(2.39239 - 1.81010i) q^{9} +(2.78428 - 4.86981i) q^{10} +(-2.09979 + 2.50243i) q^{11} +(-0.187436 + 7.43411i) q^{12} +(-2.57758 - 1.80484i) q^{13} +(-1.17733 - 6.67697i) q^{14} +(-2.68053 - 2.79549i) q^{15} +(-4.47891 - 3.75825i) q^{16} +(5.88806 + 1.57770i) q^{17} +(7.16218 + 2.31175i) q^{18} +(-2.91796 - 1.68469i) q^{19} +(9.56030 - 0.877047i) q^{20} +(-4.65148 - 0.525389i) q^{21} +(-8.16389 - 0.714248i) q^{22} +(2.10003 + 4.50352i) q^{23} +(-8.30464 + 5.50834i) q^{24} +(-3.18153 + 3.85719i) q^{25} -7.89390i q^{26} +(2.93063 - 4.29085i) q^{27} +(8.20493 - 8.20493i) q^{28} +(-0.541940 + 3.07349i) q^{29} +(1.88765 - 9.53092i) q^{30} +(0.346096 + 0.125969i) q^{31} +(0.275472 - 3.14866i) q^{32} +(-2.06857 + 5.26639i) q^{33} +(5.23028 + 14.3701i) q^{34} +(0.0254777 + 6.04317i) q^{35} +(3.78979 + 12.3102i) q^{36} +(1.14721 - 4.28145i) q^{37} +(-0.736698 - 8.42050i) q^{38} +(-5.22721 - 1.54284i) q^{39} +(8.31110 + 9.82040i) q^{40} +(7.54663 - 1.33068i) q^{41} +(-5.61343 - 10.3147i) q^{42} +(4.42293 - 0.386956i) q^{43} +(-7.01269 - 12.1463i) q^{44} +(-5.94228 - 3.11276i) q^{45} +(-6.23291 + 10.7957i) q^{46} +(2.90859 - 6.23750i) q^{47} +(-9.42590 - 3.70238i) q^{48} +(0.195477 + 0.232960i) q^{49} +(-12.5044 - 0.987828i) q^{50} +(10.5379 - 0.654808i) q^{51} +(11.0667 - 7.74898i) q^{52} +(-3.48010 - 3.48010i) q^{53} +(13.0346 - 0.151776i) q^{54} +(7.06356 + 1.86079i) q^{55} +(15.3133 + 2.70014i) q^{56} +(-5.71990 - 1.15794i) q^{57} +(-7.09579 + 3.30882i) q^{58} +(-5.87095 + 4.92631i) q^{59} +(15.2147 - 6.70961i) q^{60} +(-6.73344 + 2.45077i) q^{61} +(0.239140 + 0.892481i) q^{62} +(-7.92737 + 1.70113i) q^{63} +(-3.26012 + 1.88223i) q^{64} +(-1.19258 + 6.93430i) q^{65} +(-13.7989 + 3.32701i) q^{66} +(0.221089 - 0.315748i) q^{67} +(-15.0116 + 21.4388i) q^{68} +(5.93054 + 6.23732i) q^{69} +(-12.3820 + 8.74797i) q^{70} +(-8.46099 + 4.88495i) q^{71} +(-10.6002 + 13.6221i) q^{72} +(0.00667095 + 0.0248963i) q^{73} +(10.4491 - 3.80315i) q^{74} +(-3.09808 + 8.08714i) q^{75} +(11.0818 - 9.29871i) q^{76} +(8.00143 - 3.73113i) q^{77} +(-4.35099 - 12.9619i) q^{78} +(-10.9549 - 1.93165i) q^{79} +(-3.33049 + 12.6425i) q^{80} +(2.44707 - 8.66094i) q^{81} +(13.5935 + 13.5935i) q^{82} +(-0.896484 + 0.627725i) q^{83} +(8.95014 - 17.9950i) q^{84} +(-2.42349 - 13.4134i) q^{85} +(7.15941 + 8.53226i) q^{86} +(0.804192 + 5.34541i) q^{87} +(7.94310 - 17.0340i) q^{88} +(3.93198 - 6.81039i) q^{89} +(-2.15376 - 16.6903i) q^{90} +(4.25207 + 7.36481i) q^{91} +(-21.2533 + 1.85943i) q^{92} +(0.637725 + 0.0160789i) q^{93} +(17.0032 - 2.99812i) q^{94} +(-0.624996 + 7.50818i) q^{95} +(-1.28317 - 5.32197i) q^{96} +(-0.446850 - 5.10752i) q^{97} +(-0.197455 + 0.736913i) q^{98} +(-0.493864 + 9.78763i) 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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