LMFDB - Embedded newform 135.2.q.a.32.11

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			32.11
Character	$\chi$	$=$	135.32
Dual form			135.2.q.a.38.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0904240 - 1.03355i) q^{2} +(-0.538569 - 1.64619i) q^{3} +(0.909563 + 0.160381i) q^{4} +(-2.23437 + 0.0872392i) q^{5} +(-1.75012 + 0.407783i) q^{6} +(1.66856 - 2.38295i) q^{7} +(0.785057 - 2.92987i) q^{8} +(-2.41989 + 1.77317i) q^{9} +O(q^{10})$	\(q+(0.0904240 - 1.03355i) q^{2} +(-0.538569 - 1.64619i) q^{3} +(0.909563 + 0.160381i) q^{4} +(-2.23437 + 0.0872392i) q^{5} +(-1.75012 + 0.407783i) q^{6} +(1.66856 - 2.38295i) q^{7} +(0.785057 - 2.92987i) q^{8} +(-2.41989 + 1.77317i) q^{9} +(-0.111874 + 2.31722i) q^{10} +(-0.357163 + 0.981298i) q^{11} +(-0.225845 - 1.58369i) q^{12} +(-1.17621 + 0.102905i) q^{13} +(-2.31203 - 1.94002i) q^{14} +(1.34697 + 3.63121i) q^{15} +(-1.22140 - 0.444552i) q^{16} +(1.46485 + 5.46688i) q^{17} +(1.61385 + 2.66142i) q^{18} +(3.77562 - 2.17985i) q^{19} +(-2.04629 - 0.278999i) q^{20} +(-4.82143 - 1.46339i) q^{21} +(0.981926 + 0.457879i) q^{22} +(3.55972 - 2.49254i) q^{23} +(-5.24594 + 0.285584i) q^{24} +(4.98478 - 0.389849i) q^{25} +1.22498i q^{26} +(4.22226 + 3.02862i) q^{27} +(1.89984 - 1.89984i) q^{28} +(5.99110 - 5.02713i) q^{29} +(3.87484 - 1.06382i) q^{30} +(-1.88318 + 10.6800i) q^{31} +(1.99388 - 4.27590i) q^{32} +(1.80776 + 0.0594626i) q^{33} +(5.78276 - 1.01966i) q^{34} +(-3.52029 + 5.46995i) q^{35} +(-2.48542 + 1.22471i) q^{36} +(-6.89452 + 1.84738i) q^{37} +(-1.91158 - 4.09941i) q^{38} +(0.802872 + 1.88085i) q^{39} +(-1.49850 + 6.61490i) q^{40} +(-2.34606 + 2.79593i) q^{41} +(-1.94846 + 4.85087i) q^{42} +(-2.11627 + 0.986834i) q^{43} +(-0.482244 + 0.835270i) q^{44} +(5.25222 - 4.17303i) q^{45} +(-2.25429 - 3.90454i) q^{46} +(-0.298694 - 0.209148i) q^{47} +(-0.0740116 + 2.25007i) q^{48} +(-0.500224 - 1.37435i) q^{49} +(0.0478153 - 5.18728i) q^{50} +(8.21061 - 5.35571i) q^{51} +(-1.08634 - 0.0950427i) q^{52} +(-1.16516 - 1.16516i) q^{53} +(3.51203 - 4.09006i) q^{54} +(0.712425 - 2.22374i) q^{55} +(-5.67183 - 6.75943i) q^{56} +(-5.62188 - 5.04139i) q^{57} +(-4.65406 - 6.64669i) q^{58} +(-9.77378 + 3.55737i) q^{59} +(0.642781 + 3.51884i) q^{60} +(-0.654019 - 3.70913i) q^{61} +(10.8681 + 2.91210i) q^{62} +(0.187656 + 8.72512i) q^{63} +(-6.49036 - 3.74721i) q^{64} +(2.61911 - 0.332540i) q^{65} +(0.224923 - 1.86304i) q^{66} +(0.0498691 + 0.570007i) q^{67} +(0.455589 + 5.20741i) q^{68} +(-6.02036 - 4.51758i) q^{69} +(5.33516 + 4.13301i) q^{70} +(2.83490 + 1.63673i) q^{71} +(3.29542 + 8.48201i) q^{72} +(-13.2867 - 3.56015i) q^{73} +(1.28593 + 7.29289i) q^{74} +(-3.32641 - 7.99594i) q^{75} +(3.78377 - 1.37718i) q^{76} +(1.74244 + 2.48846i) q^{77} +(2.01655 - 0.659736i) q^{78} +(2.43289 + 2.89941i) q^{79} +(2.76783 + 0.886738i) q^{80} +(2.71171 - 8.58176i) q^{81} +(2.67759 + 2.67759i) q^{82} +(4.75867 + 0.416330i) q^{83} +(-4.15070 - 2.10431i) q^{84} +(-3.74993 - 12.0872i) q^{85} +(0.828582 + 2.27651i) q^{86} +(-11.5022 - 7.15504i) q^{87} +(2.59468 + 1.81682i) q^{88} +(1.62360 + 2.81215i) q^{89} +(-3.83811 - 5.80579i) q^{90} +(-1.71736 + 2.97456i) q^{91} +(3.63755 - 1.69622i) q^{92} +(18.5956 - 2.65186i) q^{93} +(-0.243174 + 0.289803i) q^{94} +(-8.24594 + 5.19997i) q^{95} +(-8.11279 - 0.979449i) q^{96} +(-5.05512 - 10.8407i) q^{97} +(-1.46570 + 0.392732i) q^{98} +(-0.875716 - 3.00794i) 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 $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.0904240	−	1.03355i	0.0639395	−	0.730831i	−0.894786	−	0.446496i	$-0.852672\pi$
$2$	0.0904240	−	1.03355i	0.0639395	−	0.730831i	0.958725	−	0.284335i	$-0.0917728\pi$
$3$	−0.538569	−	1.64619i	−0.310943	−	0.950429i
$3$	−0.538569	−	1.64619i	−0.310943	−	0.950429i
$4$	0.909563	+	0.160381i	0.454782	+	0.0801903i
$5$	−2.23437	+	0.0872392i	−0.999239	+	0.0390146i
$5$	−2.23437	+	0.0872392i	−0.999239	+	0.0390146i
$6$	−1.75012	+	0.407783i	−0.714484	+	0.166477i
$7$	1.66856	−	2.38295i	0.630657	−	0.900671i	−0.368929	−	0.929458i	$-0.620275\pi$
$7$	1.66856	−	2.38295i	0.630657	−	0.900671i	0.999586	+	0.0287865i	$0.00916428\pi$
$8$	0.785057	−	2.92987i	0.277560	−	1.03587i
$9$	−2.41989	+	1.77317i	−0.806629	+	0.591058i
$10$	−0.111874	+	2.31722i	−0.0353777	+	0.732769i
$11$	−0.357163	+	0.981298i	−0.107689	+	0.295872i	−0.981819	−	0.189819i	$-0.939210\pi$
$11$	−0.357163	+	0.981298i	−0.107689	+	0.295872i	0.874130	+	0.485691i	$0.161432\pi$
$12$	−0.225845	−	1.58369i	−0.0651959	−	0.457172i
$13$	−1.17621	+	0.102905i	−0.326222	+	0.0285408i	−0.249091	−	0.968480i	$-0.580132\pi$
$13$	−1.17621	+	0.102905i	−0.326222	+	0.0285408i	−0.0771317	+	0.997021i	$0.524576\pi$
$14$	−2.31203	−	1.94002i	−0.617915	−	0.518492i
$15$	1.34697	+	3.63121i	0.347787	+	0.937574i
$16$	−1.22140	−	0.444552i	−0.305349	−	0.111138i
$17$	1.46485	+	5.46688i	0.355277	+	1.32591i	0.880135	+	0.474723i	$0.157452\pi$
$17$	1.46485	+	5.46688i	0.355277	+	1.32591i	−0.524858	+	0.851190i	$0.675882\pi$
$18$	1.61385	+	2.66142i	0.380388	+	0.627302i
$19$	3.77562	−	2.17985i	0.866186	−	0.500093i	0.000107079	−	1.00000i	$-0.499966\pi$
$19$	3.77562	−	2.17985i	0.866186	−	0.500093i	0.866079	+	0.499907i	$0.166633\pi$
$20$	−2.04629	−	0.278999i	−0.457564	−	0.0623861i
$21$	−4.82143	−	1.46339i	−1.05212	−	0.319337i
$22$	0.981926	+	0.457879i	0.209347	+	0.0976202i
$23$	3.55972	−	2.49254i	0.742253	−	0.519731i	−0.140205	−	0.990123i	$-0.544776\pi$
$23$	3.55972	−	2.49254i	0.742253	−	0.519731i	0.882458	+	0.470391i	$0.155887\pi$
$24$	−5.24594	+	0.285584i	−1.07082	+	0.0582946i
$25$	4.98478	−	0.389849i	0.996956	−	0.0779697i
$26$			1.22498i			0.240238i
$27$	4.22226	+	3.02862i	0.812574	+	0.582858i
$28$	1.89984	−	1.89984i	0.359036	−	0.359036i
$29$	5.99110	−	5.02713i	1.11252	−	0.933515i	0.114317	−	0.993444i	$-0.463532\pi$
$29$	5.99110	−	5.02713i	1.11252	−	0.933515i	0.998203	+	0.0599291i	$0.0190875\pi$
$30$	3.87484	−	1.06382i	0.707445	−	0.194225i
$31$	−1.88318	+	10.6800i	−0.338229	+	1.91819i	0.0544490	+	0.998517i	$0.482660\pi$
$31$	−1.88318	+	10.6800i	−0.338229	+	1.91819i	−0.392678	+	0.919676i	$0.628451\pi$
$32$	1.99388	−	4.27590i	0.352472	−	0.755879i
$33$	1.80776	+	0.0594626i	0.314691	+	0.0103511i
$34$	5.78276	−	1.01966i	0.991735	−	0.174870i
$35$	−3.52029	+	5.46995i	−0.595037	+	0.924590i
$36$	−2.48542	+	1.22471i	−0.414237	+	0.204118i
$37$	−6.89452	+	1.84738i	−1.13345	+	0.303708i	−0.776316	−	0.630344i	$-0.782914\pi$
$37$	−6.89452	+	1.84738i	−1.13345	+	0.303708i	−0.357137	+	0.934052i	$0.616247\pi$
$38$	−1.91158	−	4.09941i	−0.310100	−	0.665011i
$39$	0.802872	+	1.88085i	0.128562	+	0.301177i
$40$	−1.49850	+	6.61490i	−0.236934	+	1.04591i
$41$	−2.34606	+	2.79593i	−0.366393	+	0.436650i	−0.917471	−	0.397804i	$-0.869772\pi$
$41$	−2.34606	+	2.79593i	−0.366393	+	0.436650i	0.551077	+	0.834454i	$0.314217\pi$
$42$	−1.94846	+	4.85087i	−0.300654	+	0.748505i
$43$	−2.11627	+	0.986834i	−0.322729	+	0.150491i	−0.577230	−	0.816582i	$-0.695866\pi$
$43$	−2.11627	+	0.986834i	−0.322729	+	0.150491i	0.254501	+	0.967072i	$0.418089\pi$
$44$	−0.482244	+	0.835270i	−0.0727010	+	0.125922i
$45$	5.25222	−	4.17303i	0.782955	−	0.622078i
$46$	−2.25429	−	3.90454i	−0.332377	−	0.575693i
$47$	−0.298694	−	0.209148i	−0.0435690	−	0.0305073i	0.551589	−	0.834116i	$-0.314022\pi$
$47$	−0.298694	−	0.209148i	−0.0435690	−	0.0305073i	−0.595158	+	0.803609i	$0.702911\pi$
$48$	−0.0740116	+	2.25007i	−0.0106826	+	0.324770i
$49$	−0.500224	−	1.37435i	−0.0714605	−	0.196336i
$50$	0.0478153	−	5.18728i	0.00676210	−	0.733592i
$51$	8.21061	−	5.35571i	1.14971	−	0.749949i
$52$	−1.08634	−	0.0950427i	−0.150649	−	0.0131800i
$53$	−1.16516	−	1.16516i	−0.160047	−	0.160047i	0.622540	−	0.782588i	$-0.286101\pi$
$53$	−1.16516	−	1.16516i	−0.160047	−	0.160047i	−0.782588	+	0.622540i	$0.786101\pi$
$54$	3.51203	−	4.09006i	0.477927	−	0.556587i
$55$	0.712425	−	2.22374i	0.0960634	−	0.299849i
$56$	−5.67183	−	6.75943i	−0.757930	−	0.903266i
$57$	−5.62188	−	5.04139i	−0.744637	−	0.667748i
$58$	−4.65406	−	6.64669i	−0.611108	−	0.872753i
$59$	−9.77378	+	3.55737i	−1.27244	+	0.463130i	−0.887924	−	0.459990i	$-0.847853\pi$
$59$	−9.77378	+	3.55737i	−1.27244	+	0.463130i	−0.384514	+	0.923119i	$0.625631\pi$
$60$	0.642781	+	3.51884i	0.0829826	+	0.454280i
$61$	−0.654019	−	3.70913i	−0.0837385	−	0.474905i	−0.997622	−	0.0689275i	$-0.978042\pi$
$61$	−0.654019	−	3.70913i	−0.0837385	−	0.474905i	0.913883	−	0.405977i	$-0.133069\pi$
$62$	10.8681	+	2.91210i	1.38025	+	0.369837i
$63$	0.187656	+	8.72512i	0.0236425	+	1.09926i
$64$	−6.49036	−	3.74721i	−0.811295	−	0.468401i
$65$	2.61911	−	0.332540i	0.324861	−	0.0412465i
$66$	0.224923	−	1.86304i	0.0276861	−	0.229324i
$67$	0.0498691	+	0.570007i	0.00609249	+	0.0696374i	0.998632	−	0.0522838i	$-0.0166500\pi$
$67$	0.0498691	+	0.570007i	0.00609249	+	0.0696374i	−0.992540	+	0.121921i	$0.961094\pi$
$68$	0.455589	+	5.20741i	0.0552483	+	0.631491i
$69$	−6.02036	−	4.51758i	−0.724766	−	0.543852i
$70$	5.33516	+	4.13301i	0.637673	+	0.493990i
$71$	2.83490	+	1.63673i	0.336441	+	0.194244i	0.658697	−	0.752408i	$-0.271108\pi$
$71$	2.83490	+	1.63673i	0.336441	+	0.194244i	−0.322256	+	0.946652i	$0.604441\pi$
$72$	3.29542	+	8.48201i	0.388369	+	0.999614i
$73$	−13.2867	−	3.56015i	−1.55509	−	0.416684i	−0.623982	−	0.781439i	$-0.714486\pi$
$73$	−13.2867	−	3.56015i	−1.55509	−	0.416684i	−0.931104	+	0.364755i	$0.881153\pi$
$74$	1.28593	+	7.29289i	0.149487	+	0.847782i
$75$	−3.32641	−	7.99594i	−0.384101	−	0.923291i
$76$	3.78377	−	1.37718i	0.434028	−	0.157973i
$77$	1.74244	+	2.48846i	0.198569	+	0.283586i
$78$	2.01655	−	0.659736i	0.228329	−	0.0747004i
$79$	2.43289	+	2.89941i	0.273722	+	0.326209i	0.885340	−	0.464944i	$-0.153926\pi$
$79$	2.43289	+	2.89941i	0.273722	+	0.326209i	−0.611618	+	0.791153i	$0.709481\pi$
$80$	2.76783	+	0.886738i	0.309453	+	0.0991403i
$81$	2.71171	−	8.58176i	0.301302	−	0.953529i
$82$	2.67759	+	2.67759i	0.295691	+	0.295691i
$83$	4.75867	+	0.416330i	0.522332	+	0.0456981i	0.345273	−	0.938502i	$-0.387786\pi$
$83$	4.75867	+	0.416330i	0.522332	+	0.0456981i	0.177059	+	0.984200i	$0.443342\pi$
$84$	−4.15070	−	2.10431i	−0.452878	−	0.229599i
$85$	−3.74993	−	12.0872i	−0.406737	−	1.31104i
$86$	0.828582	+	2.27651i	0.0893483	+	0.245482i
$87$	−11.5022	−	7.15504i	−1.23317	−	0.767101i
$88$	2.59468	+	1.81682i	0.276594	+	0.193673i
$89$	1.62360	+	2.81215i	0.172101	+	0.298087i	0.939154	−	0.343496i	$-0.111611\pi$
$89$	1.62360	+	2.81215i	0.172101	+	0.298087i	−0.767053	+	0.641583i	$0.778278\pi$
$90$	−3.83811	−	5.80579i	−0.404572	−	0.611984i
$91$	−1.71736	+	2.97456i	−0.180029	+	0.311819i
$92$	3.63755	−	1.69622i	0.379241	−	0.176843i
$93$	18.5956	−	2.65186i	1.92828	−	0.274985i
$94$	−0.243174	+	0.289803i	−0.0250815	+	0.0298909i
$95$	−8.24594	+	5.19997i	−0.846016	+	0.533506i
$96$	−8.11279	−	0.979449i	−0.828008	−	0.0999646i
$97$	−5.05512	−	10.8407i	−0.513270	−	1.10071i	−0.976706	−	0.214581i	$-0.931161\pi$
$97$	−5.05512	−	10.8407i	−0.513270	−	1.10071i	0.463436	−	0.886130i	$-0.346616\pi$
$98$	−1.46570	+	0.392732i	−0.148058	+	0.0396719i
$99$	−0.875716	−	3.00794i	−0.0880128	−	0.302310i
$100$	4.59650	+	0.444870i	0.459650	+	0.0444870i
$101$	0.264044	−	0.0465580i	0.0262733	−	0.00463269i	−0.160496	−	0.987036i	$-0.551309\pi$
$101$	0.264044	−	0.0465580i	0.0262733	−	0.00463269i	0.186769	+	0.982404i	$0.440198\pi$
$102$	−4.79296	−	8.97037i	−0.474574	−	0.888199i
$103$	−5.36526	+	11.5058i	−0.528655	+	1.13370i	0.442830	+	0.896606i	$0.353974\pi$
$103$	−5.36526	+	11.5058i	−0.528655	+	1.13370i	−0.971485	+	0.237099i	$0.923803\pi$
$104$	−0.621894	+	3.52694i	−0.0609817	+	0.345845i
$105$	10.9005	+	2.84912i	1.06378	+	0.278046i
$106$	−1.30961	+	1.09890i	−0.127201	+	0.106734i
$107$	−5.03532	+	5.03532i	−0.486782	+	0.486782i	−0.907289	−	0.420507i	$-0.861852\pi$
$107$	−5.03532	+	5.03532i	−0.486782	+	0.486782i	0.420507	+	0.907289i	$0.361852\pi$
$108$	3.35468	+	3.43189i	0.322804	+	0.330234i
$109$		−	8.81333i		−	0.844164i	−0.906558	−	0.422082i	$-0.861299\pi$
$109$		−	8.81333i		−	0.844164i	0.906558	−	0.422082i	$-0.138701\pi$
$110$	−2.23393	−	0.937408i	−0.212996	−	0.0893783i
$111$	6.75432	+	10.3548i	0.641091	+	0.982830i
$112$	−3.09732	+	2.16877i	−0.292669	+	0.204929i
$113$	−0.0588232	−	0.0274297i	−0.00553362	−	0.00258037i	0.419849	−	0.907594i	$-0.362083\pi$
$113$	−0.0588232	−	0.0274297i	−0.00553362	−	0.00258037i	−0.425383	+	0.905013i	$0.639861\pi$
$114$	−5.71888	+	5.35464i	−0.535623	+	0.501508i
$115$	−7.73627	+	5.87980i	−0.721411	+	0.548294i
$116$	6.25554	−	3.61164i	0.580813	−	0.335332i
$117$	2.66383	−	2.33465i	0.246271	−	0.215838i
$118$	2.79294	+	10.4234i	0.257111	+	0.959550i
$119$	15.4715	+	5.63116i	1.41827	+	0.516208i
$120$	11.6964	−	1.09575i	1.06773	−	0.100028i
$121$	7.59111	+	6.36970i	0.690101	+	0.579063i
$122$	−3.89271	+	0.340568i	−0.352430	+	0.0308336i
$123$	5.86614	+	2.35627i	0.528932	+	0.212457i
$124$	−3.42574	+	9.41215i	−0.307641	+	0.845236i
$125$	−11.1038	+	1.30593i	−0.993155	+	0.116806i
$126$	9.03483	+	0.595008i	0.804887	+	0.0530076i
$127$	4.34294	−	16.2081i	0.385374	−	1.43823i	−0.452203	−	0.891915i	$-0.649362\pi$
$127$	4.34294	−	16.2081i	0.385374	−	1.43823i	0.837577	−	0.546320i	$-0.183972\pi$
$128$	0.952371	−	1.36013i	0.0841785	−	0.120219i
$129$	2.76427	+	2.95231i	0.243381	+	0.259936i
$130$	−0.106866	−	2.73705i	−0.00937280	−	0.240056i
$131$	−3.72744	−	0.657248i	−0.325668	−	0.0574240i	0.00842419	−	0.999965i	$-0.497318\pi$
$131$	−3.72744	−	0.657248i	−0.325668	−	0.0574240i	−0.334092	+	0.942541i	$0.608430\pi$
$132$	1.63474	+	0.344015i	0.142285	+	0.0299426i
$133$	1.10536	−	12.6343i	0.0958470	−	1.09554i
$134$	0.593641			0.0512828
$135$	−9.69828	−	6.39870i	−0.834695	−	0.550712i
$136$	17.1673			1.47208
$137$	−1.88486	+	21.5441i	−0.161035	+	1.84064i	0.300821	+	0.953681i	$0.402739\pi$
$137$	−1.88486	+	21.5441i	−0.161035	+	1.84064i	−0.461856	+	0.886955i	$0.652816\pi$
$138$	−5.21353	+	5.81385i	−0.443805	+	0.494908i
$139$	11.0217	+	1.94342i	0.934847	+	0.164839i	0.620265	−	0.784392i	$-0.287025\pi$
$139$	11.0217	+	1.94342i	0.934847	+	0.164839i	0.314581	+	0.949231i	$0.398136\pi$
$140$	−4.07920	+	4.41068i	−0.344755	+	0.372770i
$141$	−0.183430	+	0.604347i	−0.0154476	+	0.0508952i
$142$	1.94799	−	2.78201i	0.163471	−	0.233461i
$143$	0.319119	−	1.19097i	0.0266861	−	0.0995937i
$144$	3.74391	−	1.08998i	0.311993	−	0.0908318i
$145$	−12.9478	+	11.7551i	−1.07525	+	0.976209i
$146$	−4.88103	+	13.4105i	−0.403957	+	1.10986i
$147$	−1.99304	+	1.56365i	−0.164383	+	0.128967i
$148$	−6.56729	+	0.574563i	−0.539828	+	0.0472288i
$149$	10.1272	+	8.49772i	0.829651	+	0.696160i	0.955211	−	0.295926i	$-0.0956282\pi$
$149$	10.1272	+	8.49772i	0.829651	+	0.696160i	−0.125560	+	0.992086i	$0.540073\pi$
$150$	−8.56500	+	2.71499i	−0.699329	+	0.221678i
$151$	11.4353	+	4.16211i	0.930591	+	0.338708i	0.762444	−	0.647054i	$-0.223999\pi$
$151$	11.4353	+	4.16211i	0.930591	+	0.338708i	0.168147	+	0.985762i	$0.446222\pi$
$152$	−3.42262	−	12.7734i	−0.277611	−	1.03606i
$153$	−13.2385	−	10.6318i	−1.07027	−	0.859531i
$154$	2.72951	−	1.57588i	0.219950	−	0.126988i
$155$	3.27599	−	24.0274i	0.263134	−	1.92993i
$156$	0.428612	+	1.83951i	0.0343164	+	0.147279i
$157$	10.7461	+	5.01098i	0.857631	+	0.399920i	0.801136	−	0.598483i	$-0.204230\pi$
$157$	10.7461	+	5.01098i	0.857631	+	0.399920i	0.0564955	+	0.998403i	$0.482007\pi$
$158$	3.21668	−	2.25234i	0.255905	−	0.179187i
$159$	−1.29056	+	2.54560i	−0.102348	+	0.201879i
$160$	−4.08204	+	9.72787i	−0.322714	+	0.769055i
$161$		−	12.6416i		−	0.996298i
$162$	−8.62449	−	3.57869i	−0.677604	−	0.281169i
$163$	−10.1170	+	10.1170i	−0.792424	+	0.792424i	−0.981888	−	0.189463i	$-0.939325\pi$
$163$	−10.1170	+	10.1170i	−0.792424	+	0.792424i	0.189463	+	0.981888i	$0.439325\pi$
$164$	−2.58230	+	2.16681i	−0.201644	+	0.169199i
$165$	−4.04438	+	0.0248464i	−0.314855	+	0.00193429i
$166$	0.860597	−	4.88069i	0.0667953	−	0.378815i
$167$	8.98064	−	19.2590i	0.694943	−	1.49031i	−0.168415	−	0.985716i	$-0.553865\pi$
$167$	8.98064	−	19.2590i	0.694943	−	1.49031i	0.863357	−	0.504593i	$-0.168357\pi$
$168$	−8.07263	+	12.9773i	−0.622817	+	1.00122i
$169$	−11.4296	+	2.01535i	−0.879201	+	0.155027i
$170$	−12.8318	+	2.78277i	−0.984157	+	0.213429i
$171$	−5.27131	+	11.9698i	−0.403107	+	0.915355i
$172$	−2.08315	+	0.558179i	−0.158839	+	0.0425608i
$173$	−3.58511	−	7.68830i	−0.272571	−	0.584530i	0.721604	−	0.692306i	$-0.243405\pi$
$173$	−3.58511	−	7.68830i	−0.272571	−	0.584530i	−0.994175	+	0.107775i	$0.965627\pi$
$174$	−8.43518	+	11.2412i	−0.639470	+	0.852191i
$175$	7.38842	−	12.5290i	0.558512	−	0.947101i
$176$	0.872476	−	1.03978i	0.0657653	−	0.0783761i
$177$	11.1200	+	14.1736i	0.835827	+	1.06535i
$178$	3.05331	−	1.42378i	0.228856	−	0.106717i
$179$	6.71299	−	11.6272i	0.501753	−	0.869061i	−0.498245	−	0.867036i	$-0.666022\pi$
$179$	6.71299	−	11.6272i	0.501753	−	0.869061i	0.999998	−	0.00202486i	$-0.000644535\pi$
$180$	5.44650	−	2.95328i	0.405958	−	0.220124i
$181$	−9.97071	−	17.2698i	−0.741117	−	1.28365i	−0.951987	−	0.306138i	$-0.900963\pi$
$181$	−9.97071	−	17.2698i	−0.741117	−	1.28365i	0.210870	−	0.977514i	$-0.432370\pi$
$182$	2.91907	+	2.04395i	0.216376	+	0.151508i
$183$	−5.75369	+	3.07426i	−0.425325	+	0.227256i
$184$	−4.50825	−	12.3863i	−0.332353	−	0.913132i
$185$	15.2437	−	4.72920i	1.12074	−	0.347698i
$186$	−1.05935	−	19.4593i	−0.0776751	−	1.42683i
$187$	−5.88783	−	0.515118i	−0.430560	−	0.0376692i
$188$	−0.238138	−	0.238138i	−0.0173680	−	0.0173680i
$189$	14.2622	−	5.00800i	1.03742	−	0.364278i
$190$	4.62881	+	8.99281i	0.335809	+	0.652407i
$191$	0.583207	+	0.695039i	0.0421994	+	0.0502912i	0.786731	−	0.617296i	$-0.211772\pi$
$191$	0.583207	+	0.695039i	0.0421994	+	0.0502912i	−0.744532	+	0.667587i	$0.767327\pi$
$192$	−2.67312	+	12.7025i	−0.192916	+	0.916724i
$193$	4.24072	+	6.05638i	0.305254	+	0.435948i	0.942245	−	0.334923i	$-0.108710\pi$
$193$	4.24072	+	6.05638i	0.305254	+	0.435948i	−0.636992	+	0.770871i	$0.719821\pi$
$194$	−11.6616	+	4.24447i	−0.837252	+	0.304735i
$195$	−1.95799	−	4.13246i	−0.140215	−	0.295931i
$196$	−0.234566	−	1.33029i	−0.0167547	−	0.0950205i
$197$	−16.5402	−	4.43194i	−1.17844	−	0.315763i	−0.384134	−	0.923277i	$-0.625500\pi$
$197$	−16.5402	−	4.43194i	−1.17844	−	0.315763i	−0.794309	+	0.607515i	$0.792167\pi$
$198$	−3.18805	+	0.633107i	−0.226565	+	0.0449930i
$199$	−0.887783	−	0.512562i	−0.0629332	−	0.0363345i	0.468203	−	0.883621i	$-0.344902\pi$
$199$	−0.887783	−	0.512562i	−0.0629332	−	0.0363345i	−0.531136	+	0.847286i	$0.678235\pi$
$200$	2.77113	−	14.9108i	0.195948	−	1.05435i
$201$	0.911482	−	0.389082i	0.0642910	−	0.0274437i
$202$	−0.0242442	−	0.277113i	−0.00170582	−	0.0194976i
$203$	−1.98289	−	22.6646i	−0.139172	−	1.59074i
$204$	8.32702	−	3.55453i	0.583008	−	0.248867i
$205$	4.99804	−	6.45179i	0.349079	−	0.450613i
$206$	11.4067	+	6.58568i	0.794745	+	0.458846i
$207$	−4.19442	+	12.3437i	−0.291532	+	0.857945i
$208$	1.48237	+	0.397199i	0.102784	+	0.0275408i
$209$	0.790574	+	4.48357i	0.0546852	+	0.310135i
$210$	3.93038	−	11.0086i	0.271222	−	0.759665i
$211$	−9.20369	+	3.34987i	−0.633608	+	0.230614i	−0.638801	−	0.769372i	$-0.720569\pi$
$211$	−9.20369	+	3.34987i	−0.633608	+	0.230614i	0.00519293	+	0.999987i	$0.498347\pi$
$212$	−0.872919	−	1.24666i	−0.0599523	−	0.0856208i
$213$	1.16758	−	5.54827i	0.0800014	−	0.380161i
$214$	4.74895	+	5.65957i	0.324631	+	0.386880i
$215$	4.64244	−	2.38957i	0.316611	−	0.162967i
$216$	12.1882	−	9.99304i	0.829301	−	0.679940i
$217$	22.3078	+	22.3078i	1.51435	+	1.51435i
$218$	−9.10903	−	0.796937i	−0.616942	−	0.0539754i
$219$	1.29509	+	23.7898i	0.0875142	+	1.60756i
$220$	1.00464	−	1.90837i	0.0677328	−	0.128662i
$221$	−2.28554	−	6.27947i	−0.153742	−	0.422403i
$222$	11.3129	−	6.04462i	0.759274	−	0.405688i
$223$	8.03011	+	5.62275i	0.537736	+	0.376527i	0.810668	−	0.585507i	$-0.199104\pi$
$223$	8.03011	+	5.62275i	0.537736	+	0.376527i	−0.272932	+	0.962033i	$0.587993\pi$
$224$	−6.86234	−	11.8859i	−0.458510	−	0.794162i
$225$	−11.3713	+	9.78227i	−0.758089	+	0.652151i
$226$	−0.0336690	+	0.0583165i	−0.00223963	+	0.00387916i
$227$	−15.5211	+	7.23760i	−1.03017	+	0.480376i	−0.862815	−	0.505520i	$-0.831301\pi$
$227$	−15.5211	+	7.23760i	−1.03017	+	0.480376i	−0.167356	+	0.985897i	$0.553523\pi$
$228$	−4.30492	−	5.48710i	−0.285100	−	0.363392i
$229$	11.7568	−	14.0112i	0.776912	−	0.925888i	−0.221877	−	0.975075i	$-0.571218\pi$
$229$	11.7568	−	14.0112i	0.776912	−	0.925888i	0.998790	+	0.0491866i	$0.0156629\pi$
$230$	5.37753	+	8.52751i	0.354584	+	0.562288i
$231$	3.15805	−	4.20859i	0.207785	−	0.276905i
$232$	−10.0255	−	21.4998i	−0.658207	−	1.41153i
$233$	−4.76585	+	1.27701i	−0.312221	+	0.0836594i	−0.411527	−	0.911398i	$-0.635004\pi$
$233$	−4.76585	+	1.27701i	−0.312221	+	0.0836594i	0.0993059	+	0.995057i	$0.468338\pi$
$234$	−2.17210	−	2.96432i	−0.141995	−	0.193783i
$235$	0.685637	+	0.441254i	0.0447260	+	0.0287843i
$236$	−9.46041	+	1.66812i	−0.615820	+	0.108586i
$237$	3.46270	−	5.56654i	0.224927	−	0.361585i
$238$	7.21909	−	15.4814i	0.467944	−	1.00351i
$239$	−1.04890	+	5.94858i	−0.0678474	+	0.384782i	0.931909	+	0.362693i	$0.118143\pi$
$239$	−1.04890	+	5.94858i	−0.0678474	+	0.384782i	−0.999756	+	0.0220886i	$0.992968\pi$
$240$	−0.0309257	−	5.03394i	−0.00199625	−	0.324940i
$241$	−13.1764	+	11.0563i	−0.848766	+	0.712199i	−0.959518	−	0.281649i	$-0.909119\pi$
$241$	−13.1764	+	11.0563i	−0.848766	+	0.712199i	0.110751	+	0.993848i	$0.464674\pi$
$242$	7.26983	−	7.26983i	0.467322	−	0.467322i
$243$	−15.5877	+	0.157869i	−0.999949	+	0.0101273i
$244$		−	3.47858i		−	0.222693i
$245$	1.23758	+	3.02717i	0.0790661	+	0.193399i
$246$	2.96576	−	5.84990i	0.189090	−	0.372976i
$247$	−4.21661	+	2.95250i	−0.268296	+	0.187863i
$248$	29.8128	+	13.9019i	1.89311	+	0.882773i
$249$	−1.87751	−	8.05791i	−0.118983	−	0.510649i
$250$	0.345697	+	11.5944i	0.0218638	+	0.733297i
$251$	−0.245642	+	0.141822i	−0.0155048	+	0.00895170i	−0.507732	−	0.861515i	$-0.669516\pi$
$251$	−0.245642	+	0.141822i	−0.0155048	+	0.00895170i	0.492228	+	0.870467i	$0.336183\pi$
$252$	−1.22865	+	7.96615i	−0.0773980	+	0.501820i
$253$	1.17453	+	4.38339i	0.0738419	+	0.275582i
$254$	−16.3592	−	5.95426i	−1.02647	−	0.373603i
$255$	−17.8783	+	12.6829i	−1.11958	+	0.794233i
$256$	−12.8018	−	10.7420i	−0.800110	−	0.671372i
$257$	6.49802	−	0.568503i	0.405335	−	0.0354623i	0.117335	−	0.993092i	$-0.462565\pi$
$257$	6.49802	−	0.568503i	0.405335	−	0.0354623i	0.288001	+	0.957630i	$0.407009\pi$
$258$	3.30132	−	2.59006i	0.205531	−	0.161250i
$259$	−7.10171	+	19.5118i	−0.441279	+	1.21240i
$260$	2.43558	+	0.117588i	0.151048	+	0.00729252i
$261$	−5.58382	+	22.7884i	−0.345630	+	1.41056i
$262$	−1.01635	+	3.79307i	−0.0627903	+	0.234336i
$263$	−2.60915	+	3.72625i	−0.160887	+	0.229770i	−0.891499	−	0.453022i	$-0.850346\pi$
$263$	−2.60915	+	3.72625i	−0.160887	+	0.229770i	0.730612	+	0.682792i	$0.239235\pi$
$264$	1.59341	−	5.24983i	0.0980678	−	0.323104i
$265$	2.70504	+	2.50175i	0.166170	+	0.153681i
$266$	−12.9583	−	2.28489i	−0.794523	−	0.140096i
$267$	3.75492	−	4.18728i	0.229797	−	0.256258i
$268$	−0.0460589	+	0.526455i	−0.00281349	+	0.0321584i
$269$	−7.68259			−0.468416			−0.234208	−	0.972187i	$-0.575250\pi$
$269$	−7.68259			−0.468416			−0.234208	+	0.972187i	$0.575250\pi$
$270$	−7.49034	+	9.44507i	−0.455848	+	0.574809i
$271$	18.8470			1.14487			0.572437	−	0.819949i	$-0.305998\pi$
$271$	18.8470			1.14487			0.572437	+	0.819949i	$0.305998\pi$
$272$	0.641154	−	7.32843i	0.0388757	−	0.444351i
$273$	5.82161	+	1.22510i	0.352340	+	0.0741466i
$274$	22.0965	+	3.89621i	1.33490	+	0.235378i
$275$	−1.39782	+	5.03079i	−0.0842918	+	0.303368i
$276$	−4.75137	−	5.07457i	−0.285999	−	0.305453i
$277$	−5.67374	+	8.10294i	−0.340902	+	0.486858i	−0.952597	−	0.304235i	$-0.901599\pi$
$277$	−5.67374	+	8.10294i	−0.340902	+	0.486858i	0.611695	+	0.791094i	$0.290488\pi$
$278$	3.00525	−	11.2157i	0.180243	−	0.672675i
$279$	−14.3805	−	29.1837i	−0.860937	−	1.74718i
$280$	13.2626	+	14.6082i	0.792594	+	0.873008i
$281$	−1.61241	+	4.43006i	−0.0961883	+	0.264275i	−0.978450	−	0.206484i	$-0.933798\pi$
$281$	−1.61241	+	4.43006i	−0.0961883	+	0.264275i	0.882262	+	0.470759i	$0.156020\pi$
$282$	0.608037	+	0.244232i	0.0362081	+	0.0145438i
$283$	0.0149063	−	0.00130413i	0.000886087	−	7.75226e-5i	−0.0867127	−	0.996233i	$-0.527636\pi$
$283$	0.0149063	−	0.00130413i	0.000886087	−	7.75226e-5i	0.0875988	+	0.996156i	$0.472081\pi$
$284$	2.31602	+	1.94337i	0.137431	+	0.115318i
$285$	13.0011	+	10.7738i	0.770122	+	0.638188i
$286$	−1.20207	−	0.437518i	−0.0710799	−	0.0258710i
$287$	2.74801	+	10.2557i	0.162210	+	0.605376i
$288$	2.75693	+	13.8827i	0.162454	+	0.818046i
$289$	−13.0186	+	7.51627i	−0.765798	+	0.442134i
$290$	10.9787	+	14.4451i	0.644693	+	0.848246i
$291$	−15.1234	+	14.1602i	−0.886550	+	0.830085i
$292$	−11.5141	−	5.36910i	−0.673810	−	0.314203i
$293$	−18.7826	+	13.1517i	−1.09729	+	0.768330i	−0.974564	−	0.224110i	$-0.928052\pi$
$293$	−18.7826	+	13.1517i	−1.09729	+	0.768330i	−0.122726	+	0.992441i	$0.539164\pi$
$294$	1.43589	+	2.20130i	0.0837428	+	0.128383i
$295$	21.5279	−	8.80111i	1.25340	−	0.512421i
$296$			21.6504i			1.25840i
$297$	−4.48001	+	3.06158i	−0.259957	+	0.177651i
$298$	9.69857	−	9.69857i	0.561823	−	0.561823i
$299$	−3.93049	+	3.29807i	−0.227306	+	0.190733i
$300$	−1.74319	−	7.80630i	−0.100643	−	0.450697i
$301$	−1.17955	+	6.68957i	−0.0679882	+	0.385580i
$302$	5.33578	−	11.4426i	0.307040	−	0.658448i
$303$	−0.218849	−	0.409591i	−0.0125725	−	0.0235304i
$304$	−5.58058	+	0.984008i	−0.320068	+	0.0564367i
$305$	1.78490	+	8.23049i	0.102203	+	0.471276i
$306$	−12.1856	+	12.7213i	−0.696604	+	0.727228i
$307$	26.3502	−	7.06051i	1.50388	−	0.402965i	0.589486	−	0.807779i	$-0.299330\pi$
$307$	26.3502	−	7.06051i	1.50388	−	0.402965i	0.914399	+	0.404814i	$0.132664\pi$
$308$	1.18576	+	2.54286i	0.0675647	+	0.144893i
$309$	21.8304	+	2.63556i	1.24189	+	0.149932i
$310$	−24.5373	−	5.55856i	−1.39363	−	0.315705i
$311$	20.3862	−	24.2954i	1.15600	−	1.37766i	0.242835	−	0.970068i	$-0.421923\pi$
$311$	20.3862	−	24.2954i	1.15600	−	1.37766i	0.913162	−	0.407596i	$-0.133633\pi$
$312$	6.14094	−	0.875741i	0.347663	−	0.0495791i
$313$	10.3757	−	4.83829i	0.586472	−	0.273476i	−0.106650	−	0.994297i	$-0.534013\pi$
$313$	10.3757	−	4.83829i	0.586472	−	0.273476i	0.693122	+	0.720820i	$0.256235\pi$
$314$	6.15081	−	10.6535i	0.347110	−	0.601213i
$315$	−1.18047	−	19.4787i	−0.0665117	−	1.09750i
$316$	1.74786	+	3.02739i	0.0983249	+	0.170304i
$317$	−10.2533	−	7.17947i	−0.575885	−	0.403239i	0.249030	−	0.968496i	$-0.419888\pi$
$317$	−10.2533	−	7.17947i	−0.575885	−	0.403239i	−0.824915	+	0.565257i	$0.808777\pi$
$318$	2.51431	+	1.56404i	0.140995	+	0.0877071i
$319$	2.79331	+	7.67456i	0.156395	+	0.429693i
$320$	14.8287	+	7.80642i	0.828951	+	0.436392i
$321$	11.0010	+	5.57723i	0.614013	+	0.311291i
$322$	−13.0658	−	1.14311i	−0.728126	−	0.0637028i
$323$	17.4477	+	17.4477i	0.970816	+	0.970816i
$324$	3.84282	−	7.37075i	0.213490	−	0.409486i
$325$	−5.82304	+	0.971504i	−0.323004	+	0.0538893i
$326$	9.54162	+	11.3713i	0.528461	+	0.629796i
$327$	−14.5084	+	4.74658i	−0.802318	+	0.262487i
$328$	6.34992	+	9.06863i	0.350616	+	0.500731i
$329$	−0.996777	+	0.362797i	−0.0549541	+	0.0200017i
$330$	−0.340029	+	4.18233i	−0.0187180	+	0.230229i
$331$	−4.38923	−	24.8926i	−0.241254	−	1.36822i	−0.829034	−	0.559199i	$-0.811109\pi$
$331$	−4.38923	−	24.8926i	−0.241254	−	1.36822i	0.587780	−	0.809021i	$-0.300002\pi$
$332$	4.26154	+	1.14188i	0.233883	+	0.0626686i
$333$	13.4082	−	16.6956i	0.734767	−	0.914916i
$334$	−19.0931	−	11.0234i	−1.04473	−	0.603175i
$335$	−0.161153	−	1.26925i	−0.00880472	−	0.0693467i
$336$	5.23832	+	3.93075i	0.285774	+	0.214440i
$337$	−0.151133	−	1.72746i	−0.00823274	−	0.0941006i	0.990967	−	0.134109i	$-0.0428172\pi$
$337$	−0.151133	−	1.72746i	−0.00823274	−	0.0941006i	−0.999199	+	0.0400082i	$0.987262\pi$
$338$	1.04946	+	11.9953i	0.0570829	+	0.652460i
$339$	−0.0134742	+	0.111607i	−0.000731818	+	0.00606166i
$340$	−1.47224	−	11.5955i	−0.0798436	−	0.628854i
$341$	−9.80770	−	5.66248i	−0.531117	−	0.306640i
$342$	11.8948	+	6.53053i	0.643196	+	0.353131i
$343$	15.5598	+	4.16923i	0.840150	+	0.225118i
$344$	1.22990	+	6.97513i	0.0663120	+	0.376074i
$345$	13.8458	+	9.56870i	0.745432	+	0.515162i
$346$	−8.27043	+	3.01019i	−0.444621	+	0.161829i
$347$	5.67616	+	8.10639i	0.304712	+	0.435174i	0.942081	−	0.335385i	$-0.108866\pi$
$347$	5.67616	+	8.10639i	0.304712	+	0.435174i	−0.637369	+	0.770559i	$0.719977\pi$
$348$	−9.31449	−	8.35270i	−0.499309	−	0.447752i
$349$	−19.9263	−	23.7472i	−1.06663	−	1.27116i	−0.960939	−	0.276759i	$-0.910740\pi$
$349$	−19.9263	−	23.7472i	−1.06663	−	1.27116i	−0.105689	−	0.994399i	$-0.533705\pi$
$350$	−12.2812	−	8.76923i	−0.656460	−	0.468735i
$351$	−5.27793	−	3.12781i	−0.281715	−	0.166950i
$352$	3.48379	+	3.48379i	0.185687	+	0.185687i
$353$	−3.65264	−	0.319565i	−0.194411	−	0.0170087i	−0.0104654	−	0.999945i	$-0.503331\pi$
$353$	−3.65264	−	0.319565i	−0.194411	−	0.0170087i	−0.183945	+	0.982937i	$0.558887\pi$
$354$	15.6547	−	10.2114i	0.832037	−	0.542730i
$355$	−6.47699	−	3.40974i	−0.343763	−	0.180970i
$356$	1.02575	+	2.81822i	0.0543646	+	0.149365i
$357$	0.937508	−	28.5018i	0.0496182	−	1.50848i
$358$	−11.4103	−	7.98960i	−0.603055	−	0.422264i
$359$	−3.73590	−	6.47077i	−0.197173	−	0.341514i	0.750438	−	0.660941i	$-0.229843\pi$
$359$	−3.73590	−	6.47077i	−0.197173	−	0.341514i	−0.947611	+	0.319427i	$0.896509\pi$
$360$	−8.10314	−	18.6644i	−0.427073	−	0.983701i
$361$	0.00352408	−	0.00610389i	0.000185478	−	0.000321258i
$362$	−18.7508	+	8.74364i	−0.985520	+	0.459555i
$363$	6.39740	−	15.9269i	0.335777	−	0.835947i
$364$	−2.03911	+	2.43012i	−0.106878	+	0.127373i
$365$	29.9978	+	6.79556i	1.57016	+	0.355696i
$366$	2.65713	+	6.22473i	0.138891	+	0.325372i
$367$	7.13502	+	15.3011i	0.372445	+	0.798711i	0.999800	+	0.0199776i	$0.00635950\pi$
$367$	7.13502	+	15.3011i	0.372445	+	0.798711i	−0.627356	+	0.778733i	$0.715863\pi$
$368$	−5.45590	+	1.46190i	−0.284408	+	0.0762070i
$369$	0.719542	−	10.9258i	0.0374579	−	0.568775i
$370$	−3.50947	−	16.1828i	−0.182449	−	0.841304i
$371$	−4.72067	+	0.832381i	−0.245085	+	0.0432151i
$372$	17.3392	+	0.570337i	0.898995	+	0.0295706i
$373$	−0.897584	+	1.92488i	−0.0464752	+	0.0996663i	−0.928174	−	0.372146i	$-0.878622\pi$
$373$	−0.897584	+	1.92488i	−0.0464752	+	0.0996663i	0.881699	+	0.471812i	$0.156400\pi$
$374$	−1.06480	+	6.03879i	−0.0550596	+	0.312259i
$375$	8.12998	+	17.5757i	0.419830	+	0.907603i
$376$	−0.847268	+	0.710942i	−0.0436945	+	0.0366640i
$377$	−6.52949	+	6.52949i	−0.336286	+	0.336286i
$378$	−3.88638	−	15.1935i	−0.199894	−	0.781470i
$379$			9.60506i			0.493379i	0.969095	+	0.246689i	$0.0793427\pi$
$379$			9.60506i			0.493379i	−0.969095	+	0.246689i	$0.920657\pi$
$380$	−8.33418	+	3.40722i	−0.427534	+	0.174786i
$381$	−29.0206	+	1.57985i	−1.48677	+	0.0809383i
$382$	0.771094	−	0.539926i	0.0394526	−	0.0276250i
$383$	0.109453	+	0.0510389i	0.00559281	+	0.00260797i	0.425413	−	0.904999i	$-0.360129\pi$
$383$	0.109453	+	0.0510389i	0.00559281	+	0.00260797i	−0.419820	+	0.907607i	$0.637907\pi$
$384$	−2.75195	−	0.835263i	−0.140435	−	0.0426243i
$385$	−4.11033	−	5.40812i	−0.209482	−	0.275623i
$386$	6.64304	−	3.83536i	0.338122	−	0.195215i
$387$	3.37131	−	6.14055i	0.171374	−	0.312141i
$388$	−2.85931	−	10.6711i	−0.145159	−	0.541742i
$389$	24.1005	+	8.77187i	1.22194	+	0.444752i	0.870832	−	0.491581i	$-0.163581\pi$
$389$	24.1005	+	8.77187i	1.22194	+	0.444752i	0.351113	+	0.936333i	$0.385803\pi$
$390$	−4.44816	+	1.65001i	−0.225241	+	0.0835517i
$391$	18.8409	+	15.8094i	0.952825	+	0.799515i
$392$	−4.41938	+	0.386646i	−0.223213	+	0.0195286i
$393$	0.925525	+	6.49004i	0.0466866	+	0.327379i
$394$	−6.07627	+	16.6944i	−0.306118	+	0.841053i
$395$	−5.68892	−	6.26610i	−0.286240	−	0.315282i
$396$	−0.314104	−	2.87636i	−0.0157843	−	0.144543i
$397$	−6.83441	+	25.5064i	−0.343009	+	1.28013i	0.551911	+	0.833903i	$0.313899\pi$
$397$	−6.83441	+	25.5064i	−0.343009	+	1.28013i	−0.894921	+	0.446225i	$0.852768\pi$
$398$	−0.610036	+	0.871221i	−0.0305783	+	0.0436704i
$399$	−21.3938	+	4.98482i	−1.07103	+	0.249553i
$400$	−6.26170	−	1.73983i	−0.313085	−	0.0869917i
$401$	−33.5008	−	5.90709i	−1.67295	−	0.294986i	−0.744826	−	0.667259i	$-0.767468\pi$
$401$	−33.5008	−	5.90709i	−1.67295	−	0.294986i	−0.928124	+	0.372272i	$0.878579\pi$
$402$	−0.319716	−	0.977246i	−0.0159460	−	0.0487406i
$403$	1.11599	−	12.7558i	0.0555912	−	0.635411i
$404$	0.247631			0.0123201
$405$	−5.31029	+	19.4114i	−0.263871	+	0.964558i
$406$	−23.6043			−1.17146
$407$	0.649638	−	7.42540i	0.0322014	−	0.368063i
$408$	−9.24574	−	28.2606i	−0.457733	−	1.39911i
$409$	−33.1027	−	5.83690i	−1.63682	−	0.288616i	−0.721826	−	0.692075i	$-0.756697\pi$
$409$	−33.1027	−	5.83690i	−1.63682	−	0.288616i	−0.914998	+	0.403458i	$0.867808\pi$
$410$	−6.21632	−	5.74913i	−0.307002	−	0.283929i
$411$	36.4808	−	8.50012i	1.79947	−	0.419280i
$412$	−6.72536	+	9.60481i	−0.331335	+	0.473195i
$413$	−7.83112	+	29.2261i	−0.385344	+	1.43812i
$414$	12.3786	+	5.45131i	0.608373	+	0.267917i
$415$	−10.6689	−	0.515090i	−0.523717	−	0.0252848i
$416$	−1.90522	+	5.23454i	−0.0934110	+	0.256645i
$417$	−2.73669	−	19.1904i	−0.134016	−	0.939760i
$418$	4.70549	−	0.411677i	0.230153	−	0.0201358i
$419$	−23.6855	−	19.8745i	−1.15711	−	0.970932i	−0.157249	−	0.987559i	$-0.550263\pi$
$419$	−23.6855	−	19.8745i	−1.15711	−	0.970932i	−0.999862	+	0.0166274i	$0.994707\pi$
$420$	9.45775	+	4.33969i	0.461491	+	0.211755i
$421$	−13.7828	−	5.01653i	−0.671732	−	0.244490i	−0.0164386	−	0.999865i	$-0.505233\pi$
$421$	−13.7828	−	5.01653i	−0.671732	−	0.244490i	−0.655293	+	0.755374i	$0.727455\pi$
$422$	2.63003	+	9.81539i	0.128028	+	0.477806i
$423$	1.09366	−	0.0235220i	0.0531756	−	0.00114368i
$424$	−4.32849	+	2.49906i	−0.210210	+	0.121365i
$425$	9.43319	+	26.6801i	0.457577	+	1.29418i
$426$	−5.62885	−	1.70845i	−0.272719	−	0.0827748i
$427$	−9.92994	−	4.63041i	−0.480543	−	0.224081i
$428$	−5.38751	+	3.77237i	−0.260415	+	0.182345i
$429$	−2.13243	+	0.116087i	−0.102955	+	0.00560475i
$430$	−2.04996	−	5.01427i	−0.0988576	−	0.241810i
$431$		−	30.3267i		−	1.46078i	−0.683028	−	0.730392i	$-0.739337\pi$
$431$		−	30.3267i		−	1.46078i	0.683028	−	0.730392i	$-0.260663\pi$
$432$	−3.81067	−	5.57616i	−0.183341	−	0.268283i
$433$	5.35178	−	5.35178i	0.257190	−	0.257190i	−0.566720	−	0.823910i	$-0.691788\pi$
$433$	5.35178	−	5.35178i	0.257190	−	0.257190i	0.823910	+	0.566720i	$0.191788\pi$
$434$	25.0735	−	21.0391i	1.20356	−	1.00991i
$435$	26.3244	+	14.9835i	1.26216	+	0.718406i
$436$	1.41349	−	8.01628i	0.0676938	−	0.383910i
$437$	8.00677	−	17.1706i	0.383016	−	0.821380i
$438$	24.7050	+	0.812622i	1.18045	+	0.0388286i
$439$	9.78003	−	1.72448i	0.466775	−	0.0823051i	0.0646863	−	0.997906i	$-0.479395\pi$
$439$	9.78003	−	1.72448i	0.466775	−	0.0823051i	0.402089	+	0.915601i	$0.368284\pi$
$440$	−5.95597	−	3.83308i	−0.283940	−	0.182735i
$441$	3.64745	+	2.43880i	0.173688	+	0.116133i
$442$	−6.69682	+	1.79441i	−0.318535	+	0.0853513i
$443$	−3.91821	−	8.40263i	−0.186160	−	0.399221i	0.790973	−	0.611851i	$-0.209575\pi$
$443$	−3.91821	−	8.40263i	−0.186160	−	0.399221i	−0.977133	+	0.212630i	$0.931797\pi$
$444$	4.48278	+	10.5016i	0.212743	+	0.498382i
$445$	−3.87304	−	6.14173i	−0.183600	−	0.291146i
$446$	6.53751	−	7.79110i	0.309560	−	0.368919i
$447$	8.53468	−	21.2479i	0.403676	−	1.00499i
$448$	−19.7590	+	9.21376i	−0.933524	+	0.435309i
$449$	15.0787	−	26.1171i	0.711609	−	1.23254i	−0.252644	−	0.967559i	$-0.581300\pi$
$449$	15.0787	−	26.1171i	0.711609	−	1.23254i	0.964253	−	0.264984i	$-0.0853667\pi$
$450$	9.08223	+	12.6374i	0.428141	+	0.595733i
$451$	−1.90571	−	3.30079i	−0.0897364	−	0.155428i
$452$	−0.0491042	−	0.0343832i	−0.00230967	−	0.00161725i
$453$	0.692932	−	21.0663i	0.0325568	−	0.989779i
$454$	6.07695	+	16.6963i	0.285206	+	0.783596i
$455$	3.57772	−	6.79607i	0.167726	−	0.318605i
$456$	−19.1841	+	12.5136i	−0.898379	+	0.586004i
$457$	30.1913	+	2.64140i	1.41229	+	0.123559i	0.767622	−	0.640902i	$-0.221440\pi$
$457$	30.1913	+	2.64140i	1.41229	+	0.123559i	0.644669	+	0.764462i	$0.276995\pi$
$458$	−13.4182	−	13.4182i	−0.626993	−	0.626993i
$459$	−10.3722	+	27.5190i	−0.484131	+	1.28448i
$460$	−7.97964	+	4.10731i	−0.372052	+	0.191504i
$461$	8.35560	+	9.95782i	0.389159	+	0.463782i	0.924683	−	0.380738i	$-0.124330\pi$
$461$	8.35560	+	9.95782i	0.389159	+	0.463782i	−0.535524	+	0.844520i	$0.679886\pi$
$462$	−4.06423	−	3.64457i	−0.189085	−	0.169561i
$463$	−15.7595	−	22.5069i	−0.732405	−	1.04598i	−0.996671	−	0.0815330i	$-0.974018\pi$
$463$	−15.7595	−	22.5069i	−0.732405	−	1.04598i	0.264266	−	0.964450i	$-0.414870\pi$
$464$	−9.55234	+	3.47677i	−0.443456	+	0.161405i
$465$	−41.3180	+	7.54750i	−1.91608	+	0.350007i
$466$	0.888904	+	5.04122i	0.0411777	+	0.233530i
$467$	28.9975	+	7.76986i	1.34184	+	0.359546i	0.857118	−	0.515119i	$-0.172252\pi$
$467$	28.9975	+	7.76986i	1.34184	+	0.359546i	0.484727	+	0.874666i	$0.338919\pi$
$468$	2.79736	−	1.69628i	0.129308	−	0.0784106i
$469$	1.44151	+	0.832256i	0.0665627	+	0.0384300i
$470$	0.518057	−	0.668741i	0.0238962	−	0.0308467i
$471$	2.46153	−	20.3889i	0.113421	−	0.939469i
$472$	2.74965	+	31.4287i	0.126563	+	1.44662i
$473$	−0.212523	−	2.42915i	−0.00977184	−	0.111693i
$474$	−5.44019	−	4.08223i	−0.249876	−	0.187503i
$475$	17.9708	−	12.3380i	0.824557	−	0.566107i
$476$	13.1692	+	7.60323i	0.603608	+	0.348493i
$477$	4.88559	+	0.753527i	0.223696	+	0.0345016i
$478$	6.05332	+	1.62198i	0.276872	+	0.0741878i
$479$	−1.81506	−	10.2937i	−0.0829324	−	0.470333i	−0.997784	−	0.0665419i	$-0.978803\pi$
$479$	−1.81506	−	10.2937i	−0.0829324	−	0.470333i	0.914851	−	0.403791i	$-0.132308\pi$
$480$	18.2124	+	1.48069i	0.831278	+	0.0675841i
$481$	7.91931	−	2.88239i	0.361090	−	0.131426i
$482$	10.2358	+	14.6182i	0.466228	+	0.665843i
$483$	−20.8105	+	6.80837i	−0.946911	+	0.309792i
$484$	5.88302	+	7.01111i	0.267410	+	0.318687i
$485$	12.2407	+	23.7812i	0.555823	+	1.07985i
$486$	−1.24633	+	16.1249i	−0.0565348	+	0.731441i
$487$	−13.7181	−	13.7181i	−0.621625	−	0.621625i	0.324322	−	0.945947i	$-0.394864\pi$
$487$	−13.7181	−	13.7181i	−0.621625	−	0.621625i	−0.945947	+	0.324322i	$0.894864\pi$
$488$	−11.3807	−	0.995683i	−0.515181	−	0.0450725i
$489$	22.1032	+	11.2058i	0.999541	+	0.506744i
$490$	3.24064	−	1.00537i	0.146397	−	0.0454181i
$491$	14.3153	+	39.3310i	0.646040	+	1.77498i	0.631861	+	0.775082i	$0.282292\pi$
$491$	14.3153	+	39.3310i	0.646040	+	1.77498i	0.0141799	+	0.999899i	$0.495486\pi$
$492$	4.95773	+	3.08399i	0.223512	+	0.139037i
$493$	36.2588	+	25.3887i	1.63301	+	1.14345i
$494$	2.67028	+	4.62506i	0.120141	+	0.208091i
$495$	2.21908	+	6.64445i	0.0997402	+	0.298646i
$496$	7.04794	−	12.2074i	0.316462	−	0.548128i
$497$	8.63045	−	4.02444i	0.387129	−	0.180521i
$498$	−8.49803	+	1.21188i	−0.380806	+	0.0543056i
$499$	17.0051	−	20.2659i	0.761253	−	0.907226i	−0.236674	−	0.971589i	$-0.576057\pi$
$499$	17.0051	−	20.2659i	0.761253	−	0.907226i	0.997927	+	0.0643635i	$0.0205017\pi$
$500$	−10.3091	−	0.593007i	−0.461035	−	0.0265201i
$501$	−36.5407	−	4.41153i	−1.63252	−	0.197093i
$502$	0.124368	+	0.266708i	0.00555082	+	0.0119038i
$503$	−24.5606	+	6.58100i	−1.09510	+	0.293432i	−0.760769	−	0.649023i	$-0.775178\pi$
$503$	−24.5606	+	6.58100i	−1.09510	+	0.293432i	−0.334334	+	0.942455i	$0.608511\pi$
$504$	25.7108	+	6.29991i	1.14525	+	0.280620i
$505$	−0.585908	+	0.127063i	−0.0260726	+	0.00565421i
$506$	4.63667	−	0.817570i	0.206125	−	0.0363454i
$507$	9.47328	+	17.7299i	0.420723	+	0.787414i
$508$	6.54964	−	14.0458i	0.290593	−	0.623180i
$509$	5.29524	−	30.0308i	0.234707	−	1.33109i	−0.608522	−	0.793537i	$-0.708237\pi$
$509$	5.29524	−	30.0308i	0.234707	−	1.33109i	0.843229	−	0.537554i	$-0.180652\pi$
$510$	11.4918	+	19.6250i	0.508865	+	0.869007i
$511$	−30.6533	+	25.7211i	−1.35602	+	1.13784i
$512$	−9.91177	+	9.91177i	−0.438043	+	0.438043i
$513$	22.5436	+	2.23101i	0.995323	+	0.0985017i
$514$		−	6.76745i		−	0.298499i
$515$	10.9842	−	26.1763i	0.484022	−	1.15347i
$516$	2.04079	+	3.12865i	0.0898408	+	0.137731i
$517$	0.311918	−	0.218408i	0.0137182	−	0.00960556i
$518$	19.5243	+	9.10432i	0.857847	+	0.400021i
$519$	−10.7256	+	10.0425i	−0.470800	+	0.440815i
$520$	1.08185	−	7.93472i	0.0474423	−	0.347961i
$521$	−1.09146	+	0.630155i	−0.0478178	+	0.0276076i	−0.523718	−	0.851892i	$-0.675456\pi$
$521$	−1.09146	+	0.630155i	−0.0478178	+	0.0276076i	0.475901	+	0.879499i	$0.342122\pi$
$522$	23.0480	+	7.83178i	1.00879	+	0.342788i
$523$	2.44648	+	9.13037i	0.106977	+	0.399243i	0.998562	−	0.0536101i	$-0.0170728\pi$
$523$	2.44648	+	9.13037i	0.106977	+	0.399243i	−0.891585	+	0.452853i	$0.850406\pi$
$524$	−3.28493	−	1.19562i	−0.143503	−	0.0522308i
$525$	−24.6043	−	5.41503i	−1.07382	−	0.236331i
$526$	3.61534	+	3.03363i	0.157636	+	0.132272i
$527$	−61.1451	+	5.34950i	−2.66352	+	0.233028i
$528$	−2.18156	−	0.876271i	−0.0949401	−	0.0381348i
$529$	−1.40762	+	3.86740i	−0.0612007	+	0.168148i
$530$	2.83029	−	2.56958i	0.122940	−	0.111616i
$531$	17.3436	−	25.9390i	0.752649	−	1.12566i
$532$	3.03170	−	11.3144i	0.131441	−	0.490544i
$533$	2.47175	−	3.53002i	0.107063	−	0.152902i
$534$	−3.98824	−	4.25953i	−0.172588	−	0.184328i
$535$	10.8115	−	11.6900i	0.467420	−	0.505403i
$536$	1.70920	+	0.301378i	0.0738261	+	0.0130175i
$537$	−22.7561	−	4.78880i	−0.981997	−	0.206652i
$538$	−0.694691	+	7.94036i	−0.0299503	+	0.342333i
$539$	1.52731			0.0657859
$540$	−7.79497	−	7.37544i	−0.335442	−	0.317388i
$541$	−14.5318			−0.624771			−0.312385	−	0.949955i	$-0.601128\pi$
$541$	−14.5318			−0.624771			−0.312385	+	0.949955i	$0.601128\pi$
$542$	1.70422	−	19.4793i	0.0732026	−	0.836710i
$543$	−23.0594	+	25.7146i	−0.989575	+	1.10352i
$544$	26.2966	+	4.63679i	1.12746	+	0.198801i
$545$	0.768868	+	19.6922i	0.0329347	+	0.843521i
$546$	1.79262	−	5.90615i	0.0767170	−	0.252760i
$547$	8.39950	−	11.9957i	0.359136	−	0.512900i	−0.598406	−	0.801193i	$-0.704199\pi$
$547$	8.39950	−	11.9957i	0.359136	−	0.512900i	0.957542	+	0.288293i	$0.0930878\pi$
$548$	−5.16965	+	19.2934i	−0.220837	+	0.824174i
$549$	8.15957	+	7.81598i	0.348242	+	0.333578i
$550$	5.07319	+	1.89963i	0.216321	+	0.0810003i
$551$	11.6617	−	32.0403i	0.496805	−	1.36496i
$552$	−17.9623	+	14.0923i	−0.764524	+	0.599809i
$553$	10.9686	−	0.959627i	0.466432	−	0.0408075i
$554$	7.86176	+	6.59680i	0.334014	+	0.280271i
$555$	−15.9950	−	22.5471i	−0.678948	−	0.957070i
$556$	9.71323	+	3.53533i	0.411933	+	0.149931i
$557$	0.968988	+	3.61631i	0.0410573	+	0.153228i	0.983411	−	0.181390i	$-0.0580595\pi$
$557$	0.968988	+	3.61631i	0.0410573	+	0.153228i	−0.942354	+	0.334618i	$0.891393\pi$
$558$	−31.4632	+	12.2241i	−1.33194	+	0.517486i
$559$	2.38763	−	1.37850i	0.100986	−	0.0583044i
$560$	6.73134	−	5.11603i	0.284451	−	0.216192i
$561$	2.32302	+	9.96991i	0.0980778	+	0.420930i
$562$	4.43289	+	2.06709i	0.186990	+	0.0871950i
$563$	−7.93132	+	5.55357i	−0.334265	+	0.234055i	−0.728644	−	0.684893i	$-0.759849\pi$
$563$	−7.93132	+	5.55357i	−0.334265	+	0.234055i	0.394378	+	0.918948i	$0.370960\pi$
$564$	−0.263767	+	0.520273i	−0.0111066	+	0.0219075i
$565$	0.133825	+	0.0561563i	0.00563008	+	0.00236251i
$566$		−	0.0155243i		−	0.000652537i
$567$	−15.9253	−	20.7811i	−0.668798	−	0.872723i
$568$	7.02097	−	7.02097i	0.294593	−	0.294593i
$569$	−29.7838	+	24.9915i	−1.24860	+	1.04770i	−0.251799	+	0.967780i	$0.581022\pi$
$569$	−29.7838	+	24.9915i	−1.24860	+	1.04770i	−0.996801	+	0.0799199i	$0.974534\pi$
$570$	12.3109	−	12.4631i	0.515649	−	0.522024i
$571$	−1.13871	+	6.45794i	−0.0476535	+	0.270256i	−0.999320	−	0.0368775i	$-0.988259\pi$
$571$	−1.13871	+	6.45794i	−0.0476535	+	0.270256i	0.951666	+	0.307134i	$0.0993700\pi$
$572$	0.481267	−	1.03208i	0.0201228	−	0.0431534i
$573$	0.830070	−	1.33440i	0.0346767	−	0.0557452i
$574$	10.8483	−	1.91285i	0.452800	−	0.0798408i
$575$	16.7727	−	13.8125i	0.699471	−	0.576023i
$576$	22.3504	−	2.44070i	0.931266	−	0.101696i
$577$	−9.46880	+	2.53716i	−0.394191	+	0.105623i	−0.450469	−	0.892792i	$-0.648743\pi$
$577$	−9.46880	+	2.53716i	−0.394191	+	0.105623i	0.0562782	+	0.998415i	$0.482077\pi$
$578$	6.59126	+	14.1350i	0.274160	+	0.587939i
$579$	7.68603	−	10.2428i	0.319421	−	0.425677i
$580$	−13.6621	+	8.61545i	−0.567287	+	0.357737i
$581$	8.93223	−	10.6450i	0.370571	−	0.441630i
$582$	13.2678	+	16.9112i	0.549966	+	0.700993i
$583$	1.55952	−	0.727218i	0.0645888	−	0.0301183i
$584$	−20.8616	+	36.1333i	−0.863258	+	1.49521i
$585$	−5.74830	+	5.44884i	−0.237663	+	0.225282i
$586$	11.8946	+	20.6020i	0.491360	+	0.851060i
$587$	−14.4987	−	10.1521i	−0.598427	−	0.419023i	0.234729	−	0.972061i	$-0.424580\pi$
$587$	−14.4987	−	10.1521i	−0.598427	−	0.419023i	−0.833156	+	0.553038i	$0.813469\pi$
$588$	−2.06358	+	1.10259i	−0.0851005	+	0.0454701i
$589$	16.1708	+	44.4288i	0.666305	+	1.83066i
$590$	−7.14977	−	23.0460i	−0.294351	−	0.948788i
$591$	1.61223	+	29.6153i	0.0663182	+	1.21821i
$592$	9.24221	+	0.808588i	0.379852	+	0.0332328i
$593$	−3.34033	−	3.34033i	−0.137171	−	0.137171i	0.635187	−	0.772358i	$-0.280923\pi$
$593$	−3.34033	−	3.34033i	−0.137171	−	0.137171i	−0.772358	+	0.635187i	$0.780923\pi$
$594$	2.75920	+	4.90717i	0.113211	+	0.201343i
$595$	−35.0602	−	11.2324i	−1.43733	−	0.460482i
$596$	7.84845	+	9.35341i	0.321485	+	0.383131i
$597$	−0.365642	+	1.73751i	−0.0149647	+	0.0711115i
$598$	3.05332	+	4.36059i	0.124859	+	0.178318i
$599$	−18.0781	+	6.57991i	−0.738653	+	0.268848i	−0.683823	−	0.729648i	$-0.739684\pi$
$599$	−18.0781	+	6.57991i	−0.738653	+	0.268848i	−0.0548301	+	0.998496i	$0.517462\pi$
$600$	−26.0385	+	3.46869i	−1.06302	+	0.141609i
$601$	−1.93521	−	10.9751i	−0.0789387	−	0.447684i	−0.998501	−	0.0547387i	$-0.982567\pi$
$601$	−1.93521	−	10.9751i	−0.0789387	−	0.447684i	0.919562	−	0.392945i	$-0.128544\pi$
$602$	6.80735	+	1.82402i	0.277447	+	0.0743417i
$603$	−1.13140	−	1.29093i	−0.0460741	−	0.0525706i
$604$	9.73361	+	5.61970i	0.396055	+	0.228662i
$605$	−17.5170	−	13.5700i	−0.712167	−	0.551698i
$606$	−0.443123	+	0.189155i	−0.0180006	+	0.00768388i
$607$	1.60413	+	18.3352i	0.0651094	+	0.744204i	0.956646	+	0.291255i	$0.0940727\pi$
$607$	1.60413	+	18.3352i	0.0651094	+	0.744204i	−0.891536	+	0.452950i	$0.850372\pi$
$608$	−1.79269	−	20.4905i	−0.0727032	−	0.831001i
$609$	−36.2423	+	15.4707i	−1.46861	+	0.626903i
$610$	8.66803	−	1.10055i	0.350958	−	0.0445600i
$611$	0.372849	+	0.215265i	0.0150839	+	0.00870868i
$612$	−10.3361	−	11.7935i	−0.417812	−	0.476724i
$613$	7.77243	+	2.08262i	0.313926	+	0.0841161i	0.412342	−	0.911029i	$-0.364711\pi$
$613$	7.77243	+	2.08262i	0.313926	+	0.0841161i	−0.0984162	+	0.995145i	$0.531378\pi$
$614$	−4.91471	−	27.8727i	−0.198342	−	1.12485i
$615$	−13.3127	−	4.75300i	−0.536819	−	0.191660i
$616$	8.65878	−	3.15154i	0.348872	−	0.126979i
$617$	3.67666	+	5.25082i	0.148017	+	0.211390i	0.886313	−	0.463087i	$-0.153258\pi$
$617$	3.67666	+	5.25082i	0.148017	+	0.211390i	−0.738296	+	0.674477i	$0.764369\pi$
$618$	4.69798	−	22.3245i	0.188980	−	0.898023i
$619$	17.8281	+	21.2467i	0.716573	+	0.853979i	0.994293	−	0.106683i	$-0.0340231\pi$
$619$	17.8281	+	21.2467i	0.716573	+	0.853979i	−0.277720	+	0.960662i	$0.589579\pi$
$620$	6.83325	−	21.3290i	0.274430	−	0.856595i
$621$	22.5790	+	0.256889i	0.906066	+	0.0103086i
$622$	−23.2671	−	23.2671i	−0.932926	−	0.932926i
$623$	9.41029	+	0.823294i	0.377015	+	0.0329846i
$624$	−0.144491	−	2.65418i	−0.00578427	−	0.106252i
$625$	24.6960	−	3.88662i	0.987841	−	0.155465i
$626$	−4.06240	−	11.1614i	−0.162366	−	0.446098i
$627$	6.95503	−	3.71614i	0.277757	−	0.148409i
$628$	8.97058	+	6.28127i	0.357965	+	0.250650i
$629$	−20.1988	−	34.9854i	−0.805380	−	1.39496i
$630$	−20.2390	−	0.541275i	−0.806342	−	0.0215649i
$631$	7.53540	−	13.0517i	0.299979	−	0.519580i	−0.676151	−	0.736763i	$-0.736353\pi$
$631$	7.53540	−	13.0517i	0.299979	−	0.519580i	0.976131	+	0.217183i	$0.0696868\pi$
$632$	10.4049	−	4.85187i	0.413883	−	0.192997i
$633$	10.4713	+	13.3469i	0.416198	+	0.530491i
$634$	−8.34750	+	9.94816i	−0.331522	+	0.395092i
$635$	−8.28974	+	36.5937i	−0.328968	+	1.45218i
$636$	−1.58211	+	2.10840i	−0.0627347	+	0.0836036i
$637$	0.729797	+	1.56505i	0.0289156	+	0.0620097i
$638$	8.18464	−	2.19307i	0.324033	−	0.0868244i
$639$	−9.76234	+	1.06606i	−0.386192	+	0.0421729i
$640$	−2.00929	+	3.12211i	−0.0794241	+	0.123412i
$641$	28.9474	−	5.10420i	1.14335	−	0.201604i	0.430281	−	0.902695i	$-0.358415\pi$
$641$	28.9474	−	5.10420i	1.14335	−	0.201604i	0.713071	+	0.701091i	$0.247304\pi$
$642$	6.75910	−	10.8657i	0.266761	−	0.428836i
$643$	−9.18567	+	19.6987i	−0.362248	+	0.776842i	0.637731	+	0.770259i	$0.279873\pi$
$643$	−9.18567	+	19.6987i	−0.362248	+	0.776842i	−0.999978	+	0.00658305i	$0.997905\pi$
$644$	2.02747	−	11.4983i	0.0798935	−	0.453098i
$645$	−6.43396	−	6.35539i	−0.253337	−	0.250243i
$646$	19.6108	−	16.4554i	0.771576	−	0.647429i
$647$	16.4745	−	16.4745i	0.647680	−	0.647680i	−0.304752	−	0.952432i	$-0.598574\pi$
$647$	16.4745	−	16.4745i	0.647680	−	0.647680i	0.952432	+	0.304752i	$0.0985735\pi$
$648$	−23.0146	−	14.6822i	−0.904100	−	0.576769i
$649$		−	10.8616i		−	0.426353i
$650$	0.477557	+	6.10626i	0.0187313	+	0.239507i
$651$	24.7086	−	48.7372i	0.968408	−	1.91016i
$652$	−10.8246	+	7.57948i	−0.423925	+	0.296835i
$653$	−12.0707	−	5.62864i	−0.472362	−	0.220266i	0.171835	−	0.985126i	$-0.445030\pi$
$653$	−12.0707	−	5.62864i	−0.472362	−	0.220266i	−0.644197	+	0.764860i	$0.722808\pi$
$654$	3.59393	+	15.4244i	0.140534	+	0.603142i
$655$	8.38579	+	1.14335i	0.327660	+	0.0446745i
$656$	4.10841	−	2.37199i	0.160406	−	0.0926106i
$657$	38.4650	−	14.9444i	1.50066	−	0.583036i
$658$	0.284837	+	1.06303i	0.0111041	+	0.0414411i
$659$	12.4761	+	4.54094i	0.486001	+	0.176890i	0.573387	−	0.819285i	$-0.305629\pi$
$659$	12.4761	+	4.54094i	0.486001	+	0.176890i	−0.0873859	+	0.996175i	$0.527851\pi$
$660$	−3.68261	−	0.626041i	−0.143345	−	0.0243686i
$661$	−9.01628	−	7.56556i	−0.350693	−	0.294266i	0.450375	−	0.892839i	$-0.351290\pi$
$661$	−9.01628	−	7.56556i	−0.350693	−	0.294266i	−0.801068	+	0.598573i	$0.795735\pi$
$662$	−26.1246	+	2.28561i	−1.01536	+	0.0888328i
$663$	−9.10628	+	7.14436i	−0.353659	+	0.277464i
$664$	4.95562	−	13.6155i	0.192316	−	0.528383i
$665$	−1.36757	+	28.3262i	−0.0530321	+	1.09844i
$666$	−16.0434	−	15.3678i	−0.621668	−	0.595490i
$667$	8.79631	−	32.8283i	0.340595	−	1.27112i
$668$	11.2572	−	16.0770i	0.435555	−	0.622038i
$669$	4.93134	−	16.2473i	0.190657	−	0.628158i
$670$	−1.32641	+	0.0517888i	−0.0512437	+	0.00200077i
$671$	3.87335	+	0.682976i	0.149529	+	0.0263660i
$672$	−15.8707	+	17.6981i	−0.612224	+	0.682720i
$673$	1.01400	−	11.5900i	0.0390867	−	0.446763i	−0.951283	−	0.308318i	$-0.900234\pi$
$673$	1.01400	−	11.5900i	0.0390867	−	0.446763i	0.990370	−	0.138445i	$-0.0442105\pi$
$674$	−1.79908			−0.0692981
$675$	22.2277	+	13.4510i	0.855545	+	0.517728i
$676$	−10.7192			−0.412276
$677$	−0.470687	+	5.37998i	−0.0180900	+	0.206769i	0.981771	+	0.190070i	$0.0608714\pi$
$677$	−0.470687	+	5.37998i	−0.0180900	+	0.206769i	−0.999861	+	0.0166995i	$0.994684\pi$
$678$	0.114133	+	0.0240182i	0.00438326	+	0.000922415i
$679$	−34.2678	−	6.04233i	−1.31508	−	0.231883i
$680$	−38.3579	+	1.49766i	−1.47096	+	0.0574325i
$681$	20.2736	+	21.6527i	0.776888	+	0.829734i
$682$	−6.73932	+	9.62474i	−0.258062	+	0.368550i
$683$	4.29650	−	16.0348i	0.164401	−	0.613553i	−0.833715	−	0.552195i	$-0.813790\pi$
$683$	4.29650	−	16.0348i	0.164401	−	0.613553i	0.998116	−	0.0613579i	$-0.0195431\pi$
$684$	−6.71432	+	10.0419i	−0.256728	+	0.383962i
$685$	2.33198	−	48.3018i	0.0891006	−	1.84552i
$686$	5.71610	−	15.7049i	0.218242	−	0.599614i
$687$	−29.3970	−	11.8080i	−1.12157	−	0.450502i
$688$	3.02351	−	0.264523i	0.115270	−	0.0100848i
$689$	1.49038	+	1.25058i	0.0567789	+	0.0476431i
$690$	11.1417	−	13.4451i	0.424159	−	0.511846i
$691$	4.89099	+	1.78018i	0.186062	+	0.0677211i	0.433371	−	0.901216i	$-0.357324\pi$
$691$	4.89099	+	1.78018i	0.186062	+	0.0677211i	−0.247309	+	0.968937i	$0.579546\pi$
$692$	−2.02783	−	7.56797i	−0.0770866	−	0.287691i
$693$	−8.62897	−	2.93215i	−0.327787	−	0.111383i
$694$	8.89164	−	5.13359i	0.337522	−	0.194868i
$695$	−24.7960	−	3.38079i	−0.940566	−	0.128241i
$696$	−29.9933	+	28.0830i	−1.13689	+	1.06448i
$697$	−18.7216	−	8.73003i	−0.709132	−	0.330674i
$698$	−26.3458	+	18.4475i	−0.997202	+	0.698248i
$699$	4.66893	+	7.15774i	0.176595	+	0.270731i
$700$	8.72964	−	10.2109i	0.329949	−	0.385937i
$701$			30.8522i			1.16527i	0.812733	+	0.582636i	$0.197979\pi$
$701$			30.8522i			1.16527i	−0.812733	+	0.582636i	$0.802021\pi$
$702$	−3.71000	+	5.17218i	−0.140025	+	0.195211i
$703$	−22.0041	+	22.0041i	−0.829899	+	0.829899i
$704$	5.99524	−	5.03061i	0.225954	−	0.189598i
$705$	0.357126	−	1.36633i	0.0134502	−	0.0514591i
$706$	−0.660573	+	3.74630i	−0.0248610	+	0.140994i
$707$	0.329627	−	0.706888i	0.0123969	−	0.0265853i
$708$	7.84113	+	14.6752i	0.294688	+	0.551529i
$709$	19.4630	−	3.43186i	0.730949	−	0.128886i	0.204227	−	0.978924i	$-0.434532\pi$
$709$	19.4630	−	3.43186i	0.730949	−	0.128886i	0.526722	+	0.850038i	$0.323421\pi$
$710$	−4.10981	+	6.38598i	−0.154239	+	0.239661i
$711$	−11.0285	−	2.70230i	−0.413600	−	0.101344i
$712$	9.51386	−	2.54923i	0.356547	−	0.0955365i
$713$	19.9169	+	42.7119i	0.745893	+	1.59957i
$714$	−29.3733	−	3.54621i	−1.09927	−	0.132714i
$715$	−0.609129	+	2.68890i	−0.0227801	+	0.100559i
$716$	7.97067	−	9.49908i	0.297878	−	0.354997i
$717$	10.3574	−	1.47704i	0.386804	−	0.0551610i
$718$	−7.02568	+	3.27613i	−0.262196	+	0.122264i
$719$	−3.29514	+	5.70736i	−0.122888	+	0.212849i	−0.920905	−	0.389786i	$-0.872549\pi$
$719$	−3.29514	+	5.70736i	−0.122888	+	0.212849i	0.798017	+	0.602635i	$0.205882\pi$
$720$	−8.27017	+	2.76203i	−0.308211	+	0.102935i
$721$	18.4656	+	31.9834i	0.687695	+	1.19112i
$722$	−0.00599003	−	0.00419426i	−0.000222926	−	0.000156094i
$723$	25.2972	+	15.7363i	0.940813	+	0.585239i
$724$	−6.29925	−	17.3071i	−0.234110	−	0.643212i
$725$	27.9045	−	27.3948i	1.03635	−	1.01742i
$726$	−15.8828	−	8.05222i	−0.589467	−	0.298846i
$727$	15.2584	+	1.33493i	0.565901	+	0.0495099i	0.366517	−	0.930411i	$-0.380550\pi$
$727$	15.2584	+	1.33493i	0.565901	+	0.0495099i	0.199384	+	0.979921i	$0.436106\pi$
$728$	7.36685	+	7.36685i	0.273034	+	0.273034i
$729$	8.65490	+	25.5752i	0.320552	+	0.947231i
$730$	9.73608	−	30.3898i	0.360349	−	1.12478i
$731$	−8.49492	−	10.1238i	−0.314196	−	0.374444i
$732$	−5.72640	+	1.87345i	−0.211654	+	0.0692448i
$733$	−0.636112	−	0.908462i	−0.0234953	−	0.0335548i	0.807233	−	0.590234i	$-0.200964\pi$
$733$	−0.636112	−	0.908462i	−0.0234953	−	0.0335548i	−0.830728	+	0.556679i	$0.812075\pi$
$734$	16.4596	−	5.99082i	0.607537	−	0.221125i
$735$	4.31677	−	3.66763i	0.159227	−	0.135283i
$736$	−3.56019	−	20.1909i	−0.131230	−	0.744245i
$737$	−0.577158	−	0.154649i	−0.0212599	−	0.00569657i
$738$	−11.2273	−	1.73164i	−0.413283	−	0.0637425i
$739$	−0.148882	−	0.0859569i	−0.00547670	−	0.00316198i	0.497259	−	0.867602i	$-0.334340\pi$
$739$	−0.148882	−	0.0859569i	−0.00547670	−	0.00316198i	−0.502736	+	0.864440i	$0.667673\pi$
$740$	14.6236	−	1.85671i	0.537574	−	0.0682540i
$741$	7.13131	+	5.35122i	0.261975	+	0.196582i
$742$	0.433447	+	4.95432i	0.0159123	+	0.181879i
$743$	−1.76246	−	20.1450i	−0.0646584	−	0.739048i	−0.957454	−	0.288586i	$-0.906815\pi$
$743$	−1.76246	−	20.1450i	−0.0646584	−	0.739048i	0.892796	−	0.450462i	$-0.148741\pi$
$744$	6.82900	−	56.5646i	0.250363	−	2.07376i
$745$	−23.3692	−	18.1035i	−0.856180	−	0.663262i
$746$	1.90830	+	1.10175i	0.0698677	+	0.0403381i
$747$	−12.2537	+	7.43048i	−0.448339	+	0.271867i
$748$	−5.27274	−	1.41283i	−0.192790	−	0.0516580i
$749$	3.59719	+	20.4007i	0.131438	+	0.745424i
$750$	18.9005	−	6.81349i	0.690148	−	0.248793i
$751$	16.8648	−	6.13828i	0.615405	−	0.223989i	−0.0154616	−	0.999880i	$-0.504922\pi$
$751$	16.8648	−	6.13828i	0.615405	−	0.223989i	0.630867	+	0.775891i	$0.282700\pi$
$752$	0.271846	+	0.388237i	0.00991322	+	0.0141575i
$753$	0.365761	+	0.327993i	0.0133291	+	0.0119527i
$754$	6.15814	+	7.33898i	0.224266	+	0.267270i
$755$	−25.9137	−	8.30206i	−0.943097	−	0.302143i
$756$	13.7755	−	2.26772i	0.501011	−	0.0824761i
$757$	−19.5487	−	19.5487i	−0.710508	−	0.710508i	0.256133	−	0.966641i	$-0.417551\pi$
$757$	−19.5487	−	19.5487i	−0.710508	−	0.710508i	−0.966641	+	0.256133i	$0.917551\pi$
$758$	9.92732	+	0.868528i	0.360577	+	0.0315464i
$759$	6.58334	−	4.29425i	0.238960	−	0.155871i
$760$	8.76172	+	28.2418i	0.317821	+	1.02444i
$761$	0.210722	+	0.578955i	0.00763868	+	0.0209871i	0.943453	−	0.331505i	$-0.107556\pi$
$761$	0.210722	+	0.578955i	0.00763868	+	0.0209871i	−0.935815	+	0.352492i	$0.885334\pi$
$762$	−0.991298	+	30.1371i	−0.0359110	+	1.09175i
$763$	−21.0017	−	14.7056i	−0.760314	−	0.532378i
$764$	0.418993	+	0.725717i	0.0151586	+	0.0262555i
$765$	30.5071	+	22.6004i	1.10299	+	0.817120i
$766$	0.0626486	−	0.108511i	0.00226359	−	0.00392064i
$767$	11.1300	−	5.18999i	0.401880	−	0.187400i
$768$	−10.7887	+	26.8594i	−0.389303	+	0.969206i
$769$	−26.3803	+	31.4388i	−0.951298	+	1.13371i	0.0396163	+	0.999215i	$0.487386\pi$
$769$	−26.3803	+	31.4388i	−0.951298	+	1.13371i	−0.990914	+	0.134497i	$0.957058\pi$
$770$	−5.96124	+	3.75922i	−0.214828	+	0.135473i
$771$	−4.43549	−	10.3908i	−0.159740	−	0.374216i
$772$	2.88588	+	6.18879i	0.103865	+	0.222739i
$773$	31.4000	−	8.41362i	1.12938	−	0.302617i	0.354707	−	0.934977i	$-0.384581\pi$
$773$	31.4000	−	8.41362i	1.12938	−	0.302617i	0.774674	+	0.632361i	$0.217914\pi$
$774$	−6.04172	−	4.03968i	−0.217165	−	0.145203i
$775$	−5.22364	+	53.9718i	−0.187639	+	1.93872i
$776$	−35.7306	+	6.30026i	−1.28265	+	0.226166i
$777$	35.9449	+	1.18233i	1.28952	+	0.0424160i
$778$	11.2454	−	24.1159i	0.403169	−	0.864598i
$779$	−2.76312	+	15.6704i	−0.0989990	+	0.561451i
$780$	−1.11815	−	4.07276i	−0.0400363	−	0.145828i
$781$	−2.61864	+	2.19730i	−0.0937023	+	0.0786256i
$782$	18.0435	−	18.0435i	0.645233	−	0.645233i
$783$	40.5213	−	3.08106i	1.44811	−	0.110108i
$784$			1.90101i			0.0678930i
$785$	−24.4478	−	10.2589i	−0.872581	−	0.366155i
$786$	6.79149	−	0.369722i	0.242244	−	0.0131875i
$787$	−20.7009	+	14.4949i	−0.737908	+	0.516689i	−0.881056	−	0.473012i	$-0.843167\pi$
$787$	−20.7009	+	14.4949i	−0.737908	+	0.516689i	0.143147	+	0.989701i	$0.454278\pi$
$788$	−14.3336	−	6.68386i	−0.510613	−	0.238103i
$789$	7.53931	+	2.28831i	0.268407	+	0.0814661i
$790$	−6.99075	+	5.31318i	−0.248720	+	0.189035i
$791$	−0.163514	+	0.0944047i	−0.00581388	+	0.00335665i
$792$	−9.50038	+	0.204330i	−0.337581	+	0.00726056i
$793$	1.15095	+	4.29541i	0.0408715	+	0.152535i
$794$	25.7442	+	9.37011i	0.913626	+	0.332533i
$795$	2.66150	−	5.80038i	0.0943938	−	0.205718i
$796$	−0.725290	−	0.608590i	−0.0257072	−	0.0215709i
$797$	−5.98749	+	0.523838i	−0.212088	+	0.0185553i	−0.192704	−	0.981257i	$-0.561726\pi$
$797$	−5.98749	+	0.523838i	−0.212088	+	0.0185553i	−0.0193834	+	0.999812i	$0.506170\pi$
$798$	3.21755	+	22.5624i	0.113900	+	0.798700i
$799$	0.705844	−	1.93929i	0.0249710	−	0.0686072i
$800$	8.27212	−	22.0917i	0.292464	−	0.781060i
$801$	−8.91535	−	3.92617i	−0.315008	−	0.138724i
$802$	−9.13456	+	34.0906i	−0.322553	+	1.20378i
$803$	8.23907	−	11.7666i	0.290750	−	0.415235i
$804$	0.891452	−	0.207711i	0.0314391	−	0.00732539i
$805$	1.10284	+	28.2460i	0.0388701	+	0.995540i
$806$	−13.0828	−	2.30686i	−0.460824	−	0.0812556i
$807$	4.13760	+	12.6470i	0.145651	+	0.445196i
$808$	0.0708802	−	0.810165i	0.00249356	−	0.0285015i
$809$	−0.987575			−0.0347213			−0.0173607	−	0.999849i	$-0.505526\pi$
$809$	−0.987575			−0.0347213			−0.0173607	+	0.999849i	$0.505526\pi$
$810$	19.5825	+	7.24372i	0.688057	+	0.254518i
$811$	−7.20371			−0.252957			−0.126478	−	0.991969i	$-0.540367\pi$
$811$	−7.20371			−0.252957			−0.126478	+	0.991969i	$0.540367\pi$
$812$	1.83139	−	20.9329i	0.0642692	−	0.734601i
$813$	−10.1504	−	31.0258i	−0.355990	−	1.08812i
$814$	−7.61579	−	1.34287i	−0.266933	−	0.0470675i
$815$	21.7225	−	23.4877i	0.760905	−	0.822737i
$816$	−12.4093	+	2.89140i	−0.434412	+	0.101219i
$817$	−5.83908	+	8.33907i	−0.204284	+	0.291747i
$818$	−9.02602	+	33.6856i	−0.315587	+	1.17779i
$819$	−1.11858	−	10.2433i	−0.0390865	−	0.357929i
$820$	5.58078	−	5.06672i	0.194889	−	0.176938i
$821$	−3.24048	+	8.90315i	−0.113094	+	0.310722i	−0.983307	−	0.181952i	$-0.941758\pi$
$821$	−3.24048	+	8.90315i	−0.113094	+	0.310722i	0.870214	+	0.492674i	$0.163981\pi$
$822$	−5.48657	−	38.4734i	−0.191366	−	1.34191i
$823$	−36.9323	+	3.23116i	−1.28738	+	0.112631i	−0.710208	−	0.703992i	$-0.751399\pi$
$823$	−36.9323	+	3.23116i	−1.28738	+	0.112631i	−0.577172	+	0.816623i	$0.695844\pi$
$824$	29.4986	+	24.7523i	1.02763	+	0.862287i
$825$	9.03447	−	0.408345i	0.314540	−	0.0142167i
$826$	29.4986	+	10.7366i	1.02639	+	0.373574i
$827$	7.55103	+	28.1808i	0.262575	+	0.979943i	0.963718	+	0.266923i	$0.0860068\pi$
$827$	7.55103	+	28.1808i	0.262575	+	0.979943i	−0.701143	+	0.713021i	$0.747327\pi$
$828$	−5.79477	+	10.5547i	−0.201382	+	0.366800i
$829$	−16.9573	+	9.79032i	−0.588952	+	0.340032i	−0.764683	−	0.644407i	$-0.777104\pi$
$829$	−16.9573	+	9.79032i	−0.588952	+	0.340032i	0.175731	+	0.984438i	$0.443771\pi$
$830$	−1.49710	+	10.9803i	−0.0519651	+	0.381132i
$831$	16.3947	+	4.97607i	0.568725	+	0.172618i
$832$	8.01964	+	3.73962i	0.278031	+	0.129648i
$833$	6.78067	−	4.74788i	0.234936	−	0.164504i
$834$	−20.0818	+	1.09323i	−0.695375	+	0.0378556i
$835$	−18.3859	+	43.8152i	−0.636270	+	1.51629i
$836$			4.20488i			0.145429i
$837$	−40.2971	+	39.3904i	−1.39287	+	1.36153i
$838$	−22.6830	+	22.6830i	−0.783572	+	0.783572i
$839$	−1.00064	+	0.839639i	−0.0345460	+	0.0289876i	−0.659897	−	0.751356i	$-0.729400\pi$
$839$	−1.00064	+	0.839639i	−0.0345460	+	0.0289876i	0.625351	+	0.780343i	$0.284956\pi$
$840$	16.9051	−	29.7004i	0.583281	−	1.02476i
$841$	5.58546	−	31.6767i	0.192602	−	1.09230i
$842$	−6.43113	+	13.7916i	−0.221631	+	0.475290i
$843$	8.16111	+	0.268443i	0.281084	+	0.00924567i
$844$	−8.90859	+	1.57082i	−0.306646	+	0.0540700i
$845$	25.3621	−	5.50014i	0.872484	−	0.189211i
$846$	0.0745820	−	1.13248i	0.00256418	−	0.0389355i
$847$	27.8449	−	7.46102i	0.956762	−	0.256364i
$848$	0.905149	+	1.94110i	0.0310830	+	0.0666576i
$849$	−0.0101749	−	0.0238362i	−0.000349202	−	0.000818057i
$850$	28.4283	−	7.33716i	0.975081	−	0.251663i
$851$	−19.9379	+	23.7611i	−0.683463	+	0.814519i
$852$	1.95182	−	4.85925i	0.0668684	−	0.166475i
$853$	−1.12785	+	0.525925i	−0.0386168	+	0.0180073i	−0.441831	−	0.897098i	$-0.645671\pi$
$853$	−1.12785	+	0.525925i	−0.0386168	+	0.0180073i	0.403214	+	0.915106i	$0.367893\pi$
$854$	−5.68367	+	9.84440i	−0.194491	+	0.336869i
$855$	10.7338	−	27.2048i	0.367088	−	0.930386i
$856$	10.7998	+	18.7059i	0.369131	+	0.639353i
$857$	4.30127	+	3.01178i	0.146928	+	0.102880i	0.644729	−	0.764411i	$-0.276970\pi$
$857$	4.30127	+	3.01178i	0.146928	+	0.102880i	−0.497801	+	0.867291i	$0.665859\pi$
$858$	−0.0728405	+	2.21447i	−0.00248673	+	0.0756008i
$859$	−17.5440	−	48.2017i	−0.598593	−	1.64462i	−0.754079	−	0.656783i	$-0.771917\pi$
$859$	−17.5440	−	48.2017i	−0.598593	−	1.64462i	0.155486	−	0.987838i	$-0.450306\pi$
$860$	4.60583	−	1.42891i	0.157057	−	0.0487254i
$861$	15.4029	−	10.0472i	0.524929	−	0.342407i
$862$	−31.3442	−	2.74226i	−1.06759	−	0.0934018i
$863$	4.17796	+	4.17796i	0.142219	+	0.142219i	0.774632	−	0.632412i	$-0.217935\pi$
$863$	4.17796	+	4.17796i	0.142219	+	0.142219i	−0.632412	+	0.774632i	$0.717935\pi$
$864$	21.3688	−	12.0152i	0.726980	−	0.408766i
$865$	8.68117	+	16.8657i	0.295169	+	0.573451i
$866$	−5.04741	−	6.01526i	−0.171518	−	0.204407i
$867$	19.3846	+	17.3830i	0.658336	+	0.590358i
$868$	16.7126	+	23.8681i	0.567264	+	0.810137i
$869$	−3.71412	+	1.35183i	−0.125993	+	0.0458577i
$870$	17.8666	−	25.8528i	0.605735	−	0.876491i
$871$	−0.117313	−	0.665317i	−0.00397501	−	0.0225434i
$872$	−25.8219	−	6.91897i	−0.874442	−	0.234306i
$873$	31.4554	+	17.2698i	1.06460	+	0.584494i
$874$	−17.0227	−	9.82804i	−0.575800	−	0.332438i
$875$	−15.4154	+	28.6389i	−0.521136	+	0.968170i
$876$	−2.63745	+	21.8460i	−0.0891110	+	0.738108i
$877$	−4.37791	−	50.0397i	−0.147832	−	1.68972i	−0.601754	−	0.798681i	$-0.705531\pi$
$877$	−4.37791	−	50.0397i	−0.147832	−	1.68972i	0.453923	−	0.891041i	$-0.350024\pi$
$878$	−0.897992	−	10.2641i	−0.0303058	−	0.346397i
$879$	31.7659	+	23.8366i	1.07144	+	0.803989i
$880$	−1.85872	+	2.39935i	−0.0626575	+	0.0808822i
$881$	−11.9474	−	6.89781i	−0.402517	−	0.232393i	0.285053	−	0.958512i	$-0.407989\pi$
$881$	−11.9474	−	6.89781i	−0.402517	−	0.232393i	−0.687569	+	0.726119i	$0.741322\pi$
$882$	2.85044	−	3.54930i	0.0959793	−	0.119511i
$883$	23.8282	+	6.38476i	0.801884	+	0.214864i	0.636411	−	0.771350i	$-0.280418\pi$
$883$	23.8282	+	6.38476i	0.801884	+	0.214864i	0.165473	+	0.986214i	$0.447085\pi$
$884$	−1.07174	−	6.07813i	−0.0360465	−	0.204430i
$885$	−26.0825	−	30.6990i	−0.876755	−	1.03193i
$886$	−9.03886	+	3.28987i	−0.303666	+	0.110526i
$887$	26.5942	+	37.9805i	0.892946	+	1.27526i	0.960709	+	0.277558i	$0.0895249\pi$
$887$	26.5942	+	37.9805i	0.892946	+	1.27526i	−0.0677631	+	0.997701i	$0.521586\pi$
$888$	35.6407	−	11.6602i	1.19602	−	0.391291i
$889$	−31.3766	−	37.3932i	−1.05234	−	1.25413i
$890$	−6.69801	+	3.44762i	−0.224518	+	0.115565i
$891$	7.45274	+	5.72609i	0.249676	+	0.191831i
$892$	6.40212	+	6.40212i	0.214359	+	0.214359i
$893$	−1.58366	−	0.138553i	−0.0529953	−	0.00463649i
$894$	−21.1890	−	10.7423i	−0.708667	−	0.359278i
$895$	−13.9849	+	26.5651i	−0.467465	+	0.887975i
$896$	−1.65203	−	4.53891i	−0.0551904	−	0.151634i
$897$	7.54610	+	4.69410i	0.251957	+	0.156731i
$898$	−25.6299	−	17.9463i	−0.855281	−	0.598874i
$899$	42.4077	+	73.4522i	1.41438	+	2.44977i
$900$	−11.9118	+	7.07385i	−0.397061	+	0.235795i
$901$	4.66302	−	8.07658i	0.155348	−	0.269070i
$902$	−3.58386	+	1.67118i	−0.119329	+	0.0556442i
$903$	11.6476	−	1.66102i	0.387607	−	0.0552754i
$904$	−0.126545	+	0.150811i	−0.00420883	+	0.00501589i
$905$	23.7848	+	37.7171i	0.790634	+	1.25376i
$906$	−21.7104	−	2.62108i	−0.721280	−	0.0870794i
$907$	5.73988	+	12.3092i	0.190590	+	0.408721i	0.978262	−	0.207374i	$-0.0664917\pi$
$907$	5.73988	+	12.3092i	0.190590	+	0.408721i	−0.787672	+	0.616095i	$0.788714\pi$
$908$	−15.2782	+	4.09378i	−0.507024	+	0.135857i
$909$	−0.556400	+	0.580860i	−0.0184546	+	0.0192659i
$910$	−6.70058	−	4.31228i	−0.222122	−	0.142951i
$911$	−26.4310	+	4.66050i	−0.875698	+	0.154409i	−0.593391	−	0.804915i	$-0.702211\pi$
$911$	−26.4310	+	4.66050i	−0.875698	+	0.154409i	−0.282308	+	0.959324i	$0.591100\pi$
$912$	4.62539	+	8.65675i	0.153162	+	0.286654i
$913$	−2.10817	+	4.52098i	−0.0697701	+	0.149623i
$914$	5.46005	−	30.9655i	0.180602	−	1.02425i
$915$	12.5877	−	7.37096i	0.416135	−	0.243677i
$916$	12.9407	−	10.8585i	0.427573	−	0.358776i
$917$	−7.78565	+	7.78565i	−0.257105	+	0.257105i
$918$	27.5044	+	13.2085i	0.907782	+	0.435947i
$919$		−	29.6273i		−	0.977314i	−0.872476	−	0.488657i	$-0.837487\pi$
$919$		−	29.6273i		−	0.977314i	0.872476	−	0.488657i	$-0.162513\pi$
$920$	11.1537	+	27.2823i	0.367725	+	0.899470i
$921$	−25.8143	−	39.5749i	−0.850611	−	1.30404i
$922$	11.0475	−	7.73552i	0.363829	−	0.254756i
$923$	−3.50287	−	1.63341i	−0.115298	−	0.0537645i
$924$	3.54743	−	3.32149i	0.116702	−	0.109269i
$925$	−33.6475	+	11.8966i	−1.10632	+	0.391158i
$926$	−24.6870	+	14.2531i	−0.811267	+	0.468385i
$927$	−7.41852	−	37.3564i	−0.243656	−	1.22695i
$928$	−9.54994	−	35.6409i	−0.313492	−	1.16997i
$929$	−52.3804	−	19.0649i	−1.71854	−	0.625499i	−0.720832	−	0.693110i	$-0.756240\pi$
$929$	−52.3804	−	19.0649i	−1.71854	−	0.625499i	−0.997712	+	0.0676108i	$0.978462\pi$
$930$	4.06458	+	43.3868i	0.133283	+	1.42271i
$931$	−4.88454	−	4.09862i	−0.160084	−	0.134327i
$932$	−4.53965	+	0.397168i	−0.148701	+	0.0130097i
$933$	−50.9742	−	20.4749i	−1.66882	−	0.670318i
$934$	10.6526	−	29.2678i	0.348564	−	0.957673i
$935$	13.2005	+	0.637313i	0.431702	+	0.0208424i
$936$	−4.74896	−	9.63752i	−0.155225	−	0.315012i
$937$	−3.49591	+	13.0469i	−0.114206	+	0.426224i	−0.999226	−	0.0393290i	$-0.987478\pi$
$937$	−3.49591	+	13.0469i	−0.114206	+	0.426224i	0.885020	+	0.465553i	$0.154145\pi$
$938$	0.990526	−	1.41462i	0.0323418	−	0.0461889i
$939$	−13.5528	−	14.4747i	−0.442279	−	0.472364i
$940$	0.552861	+	0.511312i	0.0180324	+	0.0166771i
$941$	14.9533	+	2.63667i	0.487463	+	0.0859529i	0.411977	−	0.911194i	$-0.364838\pi$
$941$	14.9533	+	2.63667i	0.487463	+	0.0859529i	0.0754855	+	0.997147i	$0.475949\pi$
$942$	−20.8504	−	4.38776i	−0.679341	−	0.142961i
$943$	−1.38235	+	15.8004i	−0.0450157	+	0.514531i
$944$	13.5191			0.440009
$945$	−31.4300	+	12.4339i	−1.02242	+	0.404475i
$946$	−2.52987			−0.0822533
$947$	−0.474435	+	5.42282i	−0.0154171	+	0.176218i	0.984582	+	0.174923i	$0.0559677\pi$
$947$	−0.474435	+	5.42282i	−0.0154171	+	0.176218i	−0.999999	+	0.00129474i	$0.999588\pi$
$948$	4.04231	−	4.50777i	0.131288	−	0.146406i
$949$	15.9943	+	2.82022i	0.519196	+	0.0915483i
$950$	−11.1270	−	19.6894i	−0.361007	−	0.638809i
$951$	−6.29665	+	20.7456i	−0.204183	+	0.672722i
$952$	28.6446	−	40.9087i	0.928377	−	1.32586i
$953$	12.1090	−	45.1915i	0.392250	−	1.46390i	−0.434164	−	0.900834i	$-0.642956\pi$
$953$	12.1090	−	45.1915i	0.392250	−	1.46390i	0.826414	−	0.563063i	$-0.190377\pi$
$954$	1.22058	−	4.98137i	0.0395179	−	0.161278i
$955$	−1.36373	−	1.50209i	−0.0441293	−	0.0486066i
$956$	−1.90807	+	5.24239i	−0.0617115	+	0.169551i
$957$	11.1294	−	8.73160i	0.359763	−	0.282253i
$958$	−10.8032	+	0.945161i	−0.349037	+	0.0305367i
$959$	48.1935	+	40.4392i	1.55625	+	1.30585i
$960$	4.86457	−	28.6152i	0.157003	−	0.923552i
$961$	−81.3865	−	29.6223i	−2.62537	−	0.955557i
$962$	−2.26301	−	8.44566i	−0.0729623	−	0.272299i
$963$	3.25641	−	21.1134i	0.104936	−	0.680370i
$964$	−13.7580	+	7.94318i	−0.443115	+	0.255832i
$965$	−10.0037	−	13.1622i	−0.322030	−	0.423706i
$966$	5.15504	+	22.1244i	0.165861	+	0.711840i
$967$	22.4516	+	10.4693i	0.721994	+	0.336671i	0.748643	−	0.662974i	$-0.230706\pi$
$967$	22.4516	+	10.4693i	0.721994	+	0.336671i	−0.0266490	+	0.999645i	$0.508484\pi$
$968$	24.6219	−	17.2404i	0.791377	−	0.554128i
$969$	19.3255	−	38.1190i	0.620823	−	1.22456i
$970$	25.6859	−	10.5010i	0.824726	−	0.337168i
$971$			39.1684i			1.25697i	0.777821	+	0.628486i	$0.216325\pi$
$971$			39.1684i			1.25697i	−0.777821	+	0.628486i	$0.783675\pi$
$972$	−14.2033	−	2.35637i	−0.455570	−	0.0755805i
$973$	23.0214	−	23.0214i	0.738033	−	0.738033i
$974$	−15.4188	+	12.9379i	−0.494050	+	0.414557i
$975$	4.73539	+	9.06261i	0.151654	+	0.290236i
$976$	−0.850083	+	4.82106i	−0.0272105	+	0.154318i
$977$	12.7009	−	27.2371i	0.406337	−	0.871393i	−0.591540	−	0.806275i	$-0.701480\pi$
$977$	12.7009	−	27.2371i	0.406337	−	0.871393i	0.997878	−	0.0651176i	$-0.0207422\pi$
$978$	13.5804	−	21.8315i	0.434255	−	0.698095i
$979$	−3.33945	+	0.588834i	−0.106729	+	0.0188192i
$980$	0.640158	+	2.95188i	0.0204491	+	0.0942945i
$981$	15.6276	+	21.3273i	0.498950	+	0.680928i
$982$	41.9450	−	11.2391i	1.33852	−	0.358655i
$983$	−24.7198	−	53.0117i	−0.788438	−	1.69081i	−0.720844	−	0.693098i	$-0.756245\pi$
$983$	−24.7198	−	53.0117i	−0.788438	−	1.69081i	−0.0675941	−	0.997713i	$-0.521532\pi$
$984$	11.5088	−	15.3373i	0.366888	−	0.488934i
$985$	37.3436	+	8.45962i	1.18986	+	0.269546i
$986$	29.5192	−	35.1796i	0.940082	−	1.12035i
$987$	1.13407	+	1.44549i	0.0360977	+	0.0460106i
$988$	−4.30879	+	2.00922i	−0.137081	+	0.0639219i
$989$	−5.07361	+	8.78776i	−0.161332	+	0.279434i
$990$	7.06804	−	1.69272i	0.224637	−	0.0537980i
$991$	−6.16723	−	10.6820i	−0.195909	−	0.339324i	0.751289	−	0.659973i	$-0.229432\pi$
$991$	−6.16723	−	10.6820i	−0.195909	−	0.339324i	−0.947198	+	0.320649i	$0.896099\pi$
$992$	41.9119	+	29.3471i	1.33071	+	0.931770i
$993$	−38.6140	+	20.6319i	−1.22538	+	0.654733i
$994$	−3.37907	−	9.28392i	−0.107178	−	0.294468i
$995$	2.02835	+	1.06780i	0.0643029	+	0.0338515i
$996$	−0.415386	−	7.63029i	−0.0131620	−	0.241775i
$997$	28.7265	+	2.51324i	0.909777	+	0.0795952i	0.532427	−	0.846476i	$-0.321280\pi$
$997$	28.7265	+	2.51324i	0.909777	+	0.0795952i	0.377350	+	0.926071i	$0.376835\pi$
$998$	−19.4082	−	19.4082i	−0.614355	−	0.614355i
$999$	−34.7055	−	13.0808i	−1.09803	−	0.413858i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.32.11	✓	192
3.2	odd	2		405.2.r.a.287.6		192
5.2	odd	4		675.2.ba.b.518.11		192
5.3	odd	4	inner	135.2.q.a.113.6	yes	192
5.4	even	2		675.2.ba.b.32.6		192
15.8	even	4		405.2.r.a.368.11		192
27.11	odd	18	inner	135.2.q.a.92.6	yes	192
27.16	even	9		405.2.r.a.197.11		192
135.38	even	36	inner	135.2.q.a.38.11	yes	192
135.43	odd	36		405.2.r.a.278.6		192
135.92	even	36		675.2.ba.b.443.6		192
135.119	odd	18		675.2.ba.b.632.11		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.11	✓	192	1.1	even	1	trivial
135.2.q.a.38.11	yes	192	135.38	even	36	inner
135.2.q.a.92.6	yes	192	27.11	odd	18	inner
135.2.q.a.113.6	yes	192	5.3	odd	4	inner
405.2.r.a.197.11		192	27.16	even	9
405.2.r.a.278.6		192	135.43	odd	36
405.2.r.a.287.6		192	3.2	odd	2
405.2.r.a.368.11		192	15.8	even	4
675.2.ba.b.32.6		192	5.4	even	2
675.2.ba.b.443.6		192	135.92	even	36
675.2.ba.b.518.11		192	5.2	odd	4
675.2.ba.b.632.11		192	135.119	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.0904240 - 1.03355i) q^{2} +(-0.538569 - 1.64619i) q^{3} +(0.909563 + 0.160381i) q^{4} +(-2.23437 + 0.0872392i) q^{5} +(-1.75012 + 0.407783i) q^{6} +(1.66856 - 2.38295i) q^{7} +(0.785057 - 2.92987i) q^{8} +(-2.41989 + 1.77317i) q^{9} +O(q^{10})\)	\(q+(0.0904240 - 1.03355i) q^{2} +(-0.538569 - 1.64619i) q^{3} +(0.909563 + 0.160381i) q^{4} +(-2.23437 + 0.0872392i) q^{5} +(-1.75012 + 0.407783i) q^{6} +(1.66856 - 2.38295i) q^{7} +(0.785057 - 2.92987i) q^{8} +(-2.41989 + 1.77317i) q^{9} +(-0.111874 + 2.31722i) q^{10} +(-0.357163 + 0.981298i) q^{11} +(-0.225845 - 1.58369i) q^{12} +(-1.17621 + 0.102905i) q^{13} +(-2.31203 - 1.94002i) q^{14} +(1.34697 + 3.63121i) q^{15} +(-1.22140 - 0.444552i) q^{16} +(1.46485 + 5.46688i) q^{17} +(1.61385 + 2.66142i) q^{18} +(3.77562 - 2.17985i) q^{19} +(-2.04629 - 0.278999i) q^{20} +(-4.82143 - 1.46339i) q^{21} +(0.981926 + 0.457879i) q^{22} +(3.55972 - 2.49254i) q^{23} +(-5.24594 + 0.285584i) q^{24} +(4.98478 - 0.389849i) q^{25} +1.22498i q^{26} +(4.22226 + 3.02862i) q^{27} +(1.89984 - 1.89984i) q^{28} +(5.99110 - 5.02713i) q^{29} +(3.87484 - 1.06382i) q^{30} +(-1.88318 + 10.6800i) q^{31} +(1.99388 - 4.27590i) q^{32} +(1.80776 + 0.0594626i) q^{33} +(5.78276 - 1.01966i) q^{34} +(-3.52029 + 5.46995i) q^{35} +(-2.48542 + 1.22471i) q^{36} +(-6.89452 + 1.84738i) q^{37} +(-1.91158 - 4.09941i) q^{38} +(0.802872 + 1.88085i) q^{39} +(-1.49850 + 6.61490i) q^{40} +(-2.34606 + 2.79593i) q^{41} +(-1.94846 + 4.85087i) q^{42} +(-2.11627 + 0.986834i) q^{43} +(-0.482244 + 0.835270i) q^{44} +(5.25222 - 4.17303i) q^{45} +(-2.25429 - 3.90454i) q^{46} +(-0.298694 - 0.209148i) q^{47} +(-0.0740116 + 2.25007i) q^{48} +(-0.500224 - 1.37435i) q^{49} +(0.0478153 - 5.18728i) q^{50} +(8.21061 - 5.35571i) q^{51} +(-1.08634 - 0.0950427i) q^{52} +(-1.16516 - 1.16516i) q^{53} +(3.51203 - 4.09006i) q^{54} +(0.712425 - 2.22374i) q^{55} +(-5.67183 - 6.75943i) q^{56} +(-5.62188 - 5.04139i) q^{57} +(-4.65406 - 6.64669i) q^{58} +(-9.77378 + 3.55737i) q^{59} +(0.642781 + 3.51884i) q^{60} +(-0.654019 - 3.70913i) q^{61} +(10.8681 + 2.91210i) q^{62} +(0.187656 + 8.72512i) q^{63} +(-6.49036 - 3.74721i) q^{64} +(2.61911 - 0.332540i) q^{65} +(0.224923 - 1.86304i) q^{66} +(0.0498691 + 0.570007i) q^{67} +(0.455589 + 5.20741i) q^{68} +(-6.02036 - 4.51758i) q^{69} +(5.33516 + 4.13301i) q^{70} +(2.83490 + 1.63673i) q^{71} +(3.29542 + 8.48201i) q^{72} +(-13.2867 - 3.56015i) q^{73} +(1.28593 + 7.29289i) q^{74} +(-3.32641 - 7.99594i) q^{75} +(3.78377 - 1.37718i) q^{76} +(1.74244 + 2.48846i) q^{77} +(2.01655 - 0.659736i) q^{78} +(2.43289 + 2.89941i) q^{79} +(2.76783 + 0.886738i) q^{80} +(2.71171 - 8.58176i) q^{81} +(2.67759 + 2.67759i) q^{82} +(4.75867 + 0.416330i) q^{83} +(-4.15070 - 2.10431i) q^{84} +(-3.74993 - 12.0872i) q^{85} +(0.828582 + 2.27651i) q^{86} +(-11.5022 - 7.15504i) q^{87} +(2.59468 + 1.81682i) q^{88} +(1.62360 + 2.81215i) q^{89} +(-3.83811 - 5.80579i) q^{90} +(-1.71736 + 2.97456i) q^{91} +(3.63755 - 1.69622i) q^{92} +(18.5956 - 2.65186i) q^{93} +(-0.243174 + 0.289803i) q^{94} +(-8.24594 + 5.19997i) q^{95} +(-8.11279 - 0.979449i) q^{96} +(-5.05512 - 10.8407i) q^{97} +(-1.46570 + 0.392732i) q^{98} +(-0.875716 - 3.00794i) 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

Properties

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