LMFDB - Embedded newform 135.2.q.a.122.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("135.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			122.2
Character	$\chi$	$=$	135.122
Dual form			135.2.q.a.83.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.12047 - 1.48477i) q^{2} +(1.59067 - 0.685393i) q^{3} +(1.60780 + 4.41741i) q^{4} +(-2.09416 - 0.783897i) q^{5} +(-4.39061 - 0.908422i) q^{6} +(-1.25154 - 2.68394i) q^{7} +(1.80956 - 6.75336i) q^{8} +(2.06047 - 2.18047i) q^{9} +O(q^{10})$	\(q+(-2.12047 - 1.48477i) q^{2} +(1.59067 - 0.685393i) q^{3} +(1.60780 + 4.41741i) q^{4} +(-2.09416 - 0.783897i) q^{5} +(-4.39061 - 0.908422i) q^{6} +(-1.25154 - 2.68394i) q^{7} +(1.80956 - 6.75336i) q^{8} +(2.06047 - 2.18047i) q^{9} +(3.27669 + 4.77156i) q^{10} +(-1.00437 - 1.19696i) q^{11} +(5.58515 + 5.92466i) q^{12} +(-2.29827 - 3.28227i) q^{13} +(-1.33117 + 7.54945i) q^{14} +(-3.86840 + 0.188401i) q^{15} +(-6.66205 + 5.59013i) q^{16} +(0.490334 + 1.82995i) q^{17} +(-7.60665 + 1.56430i) q^{18} +(-2.41262 + 1.39293i) q^{19} +(0.0957914 - 10.5111i) q^{20} +(-3.83035 - 3.41147i) q^{21} +(0.352524 + 4.02936i) q^{22} +(6.78686 + 3.16476i) q^{23} +(-1.75030 - 11.9826i) q^{24} +(3.77101 + 3.28321i) q^{25} +10.3723i q^{26} +(1.78305 - 4.88065i) q^{27} +(9.84382 - 9.84382i) q^{28} +(-0.683218 - 3.87472i) q^{29} +(8.48254 + 5.34417i) q^{30} +(5.45790 - 1.98651i) q^{31} +(8.49672 - 0.743366i) q^{32} +(-2.41801 - 1.21558i) q^{33} +(1.67731 - 4.60838i) q^{34} +(0.516997 + 6.60168i) q^{35} +(12.9449 + 5.59617i) q^{36} +(-0.316450 + 0.0847926i) q^{37} +(7.18404 + 0.628522i) q^{38} +(-5.90544 - 3.64579i) q^{39} +(-9.08344 + 12.7241i) q^{40} +(6.26389 + 1.10449i) q^{41} +(3.05689 + 12.9211i) q^{42} +(0.0509770 - 0.582670i) q^{43} +(3.67263 - 6.36118i) q^{44} +(-6.02422 + 2.95106i) q^{45} +(-9.69236 - 16.7877i) q^{46} +(-0.690071 + 0.321786i) q^{47} +(-6.76570 + 13.4582i) q^{48} +(-1.13767 + 1.35582i) q^{49} +(-3.12150 - 12.5610i) q^{50} +(2.03420 + 2.57478i) q^{51} +(10.8039 - 15.4296i) q^{52} +(-5.57112 - 5.57112i) q^{53} +(-11.0275 + 7.70183i) q^{54} +(1.16502 + 3.29395i) q^{55} +(-20.3903 + 3.59537i) q^{56} +(-2.88298 + 3.86928i) q^{57} +(-4.30431 + 9.23063i) q^{58} +(7.84000 + 6.57854i) q^{59} +(-7.05187 - 16.7854i) q^{60} +(11.4160 + 4.15507i) q^{61} +(-14.5228 - 3.89137i) q^{62} +(-8.43102 - 2.80123i) q^{63} +(-4.05760 - 2.34266i) q^{64} +(2.23998 + 8.67520i) q^{65} +(3.32245 + 6.16778i) q^{66} +(-1.63356 + 1.14383i) q^{67} +(-7.29527 + 5.10821i) q^{68} +(12.9648 + 0.382432i) q^{69} +(8.70568 - 14.7663i) q^{70} +(-6.11142 - 3.52843i) q^{71} +(-10.9970 - 17.8608i) q^{72} +(3.93347 + 1.05397i) q^{73} +(0.796919 + 0.290055i) q^{74} +(8.24873 + 2.63788i) q^{75} +(-10.0321 - 8.41796i) q^{76} +(-1.95556 + 4.19371i) q^{77} +(7.10913 + 16.4990i) q^{78} +(-12.9467 + 2.28286i) q^{79} +(18.3335 - 6.48426i) q^{80} +(-0.508912 - 8.98560i) q^{81} +(-11.6425 - 11.6425i) q^{82} +(-2.33262 + 3.33133i) q^{83} +(8.91139 - 22.4052i) q^{84} +(0.407655 - 4.21658i) q^{85} +(-0.973224 + 1.15984i) q^{86} +(-3.74248 - 5.69514i) q^{87} +(-9.90096 + 4.61689i) q^{88} +(4.23520 + 7.33558i) q^{89} +(17.1558 + 2.68694i) q^{90} +(-5.93304 + 10.2763i) q^{91} +(-3.06811 + 35.0686i) q^{92} +(7.32018 - 6.90070i) q^{93} +(1.94105 + 0.342259i) q^{94} +(6.14432 - 1.02577i) q^{95} +(13.0060 - 7.00604i) q^{96} +(7.95549 + 0.696015i) q^{97} +(4.42546 - 1.18580i) q^{98} +(-4.67941 - 0.276305i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−2.12047	−	1.48477i	−1.49940	−	1.04989i	−0.980833	−	0.194848i	$-0.937579\pi$
$2$	−2.12047	−	1.48477i	−1.49940	−	1.04989i	−0.518562	−	0.855040i	$-0.673533\pi$
$3$	1.59067	−	0.685393i	0.918375	−	0.395712i
$3$	1.59067	−	0.685393i	0.918375	−	0.395712i
$4$	1.60780	+	4.41741i	0.803902	+	2.20870i
$5$	−2.09416	−	0.783897i	−0.936537	−	0.350569i
$5$	−2.09416	−	0.783897i	−0.936537	−	0.350569i
$6$	−4.39061	−	0.908422i	−1.79246	−	0.370862i
$7$	−1.25154	−	2.68394i	−0.473038	−	1.01443i	−0.987602	−	0.156982i	$-0.949824\pi$
$7$	−1.25154	−	2.68394i	−0.473038	−	1.01443i	0.514563	−	0.857453i	$-0.327954\pi$
$8$	1.80956	−	6.75336i	0.639775	−	2.38767i
$9$	2.06047	−	2.18047i	0.686824	−	0.726824i
$10$	3.27669	+	4.77156i	1.03618	+	1.50890i
$11$	−1.00437	−	1.19696i	−0.302828	−	0.360897i	0.593074	−	0.805148i	$-0.297914\pi$
$11$	−1.00437	−	1.19696i	−0.302828	−	0.360897i	−0.895902	+	0.444251i	$0.853470\pi$
$12$	5.58515	+	5.92466i	1.61229	+	1.71030i
$13$	−2.29827	−	3.28227i	−0.637425	−	0.910338i	0.362339	−	0.932046i	$-0.381978\pi$
$13$	−2.29827	−	3.28227i	−0.637425	−	0.910338i	−0.999764	+	0.0217086i	$0.993089\pi$
$14$	−1.33117	+	7.54945i	−0.355771	+	2.01768i
$15$	−3.86840	+	0.188401i	−0.998816	+	0.0486449i
$16$	−6.66205	+	5.59013i	−1.66551	+	1.39753i
$17$	0.490334	+	1.82995i	0.118923	+	0.443828i	0.999550	−	0.0299818i	$-0.00954494\pi$
$17$	0.490334	+	1.82995i	0.118923	+	0.443828i	−0.880627	+	0.473810i	$0.842878\pi$
$18$	−7.60665	+	1.56430i	−1.79290	+	0.368708i
$19$	−2.41262	+	1.39293i	−0.553493	+	0.319559i	−0.750529	−	0.660837i	$-0.770201\pi$
$19$	−2.41262	+	1.39293i	−0.553493	+	0.319559i	0.197037	+	0.980396i	$0.436868\pi$
$20$	0.0957914	−	10.5111i	0.0214196	−	2.35035i
$21$	−3.83035	−	3.41147i	−0.835850	−	0.744444i
$22$	0.352524	+	4.02936i	0.0751583	+	0.859063i
$23$	6.78686	+	3.16476i	1.41516	+	0.659899i	0.971661	−	0.236377i	$-0.0759601\pi$
$23$	6.78686	+	3.16476i	1.41516	+	0.659899i	0.443496	+	0.896276i	$0.353738\pi$
$24$	−1.75030	−	11.9826i	−0.357278	−	2.44594i
$25$	3.77101	+	3.28321i	0.754202	+	0.656642i
$26$			10.3723i			2.03418i
$27$	1.78305	−	4.88065i	0.343149	−	0.939281i
$28$	9.84382	−	9.84382i	1.86031	−	1.86031i
$29$	−0.683218	−	3.87472i	−0.126870	−	0.719518i	−0.980179	−	0.198112i	$-0.936519\pi$
$29$	−0.683218	−	3.87472i	−0.126870	−	0.719518i	0.853309	−	0.521406i	$-0.174592\pi$
$30$	8.48254	+	5.34417i	1.54869	+	0.975707i
$31$	5.45790	−	1.98651i	0.980267	−	0.356788i	0.198323	−	0.980137i	$-0.436450\pi$
$31$	5.45790	−	1.98651i	0.980267	−	0.356788i	0.781944	+	0.623348i	$0.214228\pi$
$32$	8.49672	−	0.743366i	1.50202	−	0.131410i
$33$	−2.41801	−	1.21558i	−0.420921	−	0.211606i
$34$	1.67731	−	4.60838i	0.287657	−	0.790331i
$35$	0.516997	+	6.60168i	0.0873884	+	1.11589i
$36$	12.9449	+	5.59617i	2.15748	+	0.932695i
$37$	−0.316450	+	0.0847926i	−0.0520241	+	0.0139398i	−0.284737	−	0.958606i	$-0.591906\pi$
$37$	−0.316450	+	0.0847926i	−0.0520241	+	0.0139398i	0.232713	+	0.972545i	$0.425240\pi$
$38$	7.18404	+	0.628522i	1.16541	+	0.101960i
$39$	−5.90544	−	3.64579i	−0.945627	−	0.583794i
$40$	−9.08344	+	12.7241i	−1.43622	+	2.01186i
$41$	6.26389	+	1.10449i	0.978255	+	0.172493i	0.639843	−	0.768505i	$-0.278999\pi$
$41$	6.26389	+	1.10449i	0.978255	+	0.172493i	0.338412	+	0.940998i	$0.390110\pi$
$42$	3.05689	+	12.9211i	0.471688	+	1.99376i
$43$	0.0509770	−	0.582670i	0.00777393	−	0.0888564i	−0.991317	−	0.131497i	$-0.958022\pi$
$43$	0.0509770	−	0.582670i	0.00777393	−	0.0888564i	0.999090	+	0.0426408i	$0.0135771\pi$
$44$	3.67263	−	6.36118i	0.553670	−	0.958984i
$45$	−6.02422	+	2.95106i	−0.898038	+	0.439918i
$46$	−9.69236	−	16.7877i	−1.42906	−	2.47521i
$47$	−0.690071	+	0.321786i	−0.100657	+	0.0469372i	−0.472295	−	0.881441i	$-0.656574\pi$
$47$	−0.690071	+	0.321786i	−0.100657	+	0.0469372i	0.371638	+	0.928378i	$0.378796\pi$
$48$	−6.76570	+	13.4582i	−0.976545	+	1.94252i
$49$	−1.13767	+	1.35582i	−0.162524	+	0.193688i
$50$	−3.12150	−	12.5610i	−0.441447	−	1.77639i
$51$	2.03420	+	2.57478i	0.284845	+	0.360541i
$52$	10.8039	−	15.4296i	1.49824	−	2.13971i
$53$	−5.57112	−	5.57112i	−0.765253	−	0.765253i	0.212014	−	0.977267i	$-0.431998\pi$
$53$	−5.57112	−	5.57112i	−0.765253	−	0.765253i	−0.977267	+	0.212014i	$0.931998\pi$
$54$	−11.0275	+	7.70183i	−1.50066	+	1.04809i
$55$	1.16502	+	3.29395i	0.157091	+	0.444156i
$56$	−20.3903	+	3.59537i	−2.72477	+	0.480451i
$57$	−2.88298	+	3.86928i	−0.381860	+	0.512499i
$58$	−4.30431	+	9.23063i	−0.565184	+	1.21204i
$59$	7.84000	+	6.57854i	1.02068	+	0.856453i	0.989713	−	0.143067i	$-0.0456965\pi$
$59$	7.84000	+	6.57854i	1.02068	+	0.856453i	0.0309682	+	0.999520i	$0.490141\pi$
$60$	−7.05187	−	16.7854i	−0.910392	−	2.16698i
$61$	11.4160	+	4.15507i	1.46166	+	0.532002i	0.945823	−	0.324683i	$-0.105258\pi$
$61$	11.4160	+	4.15507i	1.46166	+	0.532002i	0.515840	+	0.856685i	$0.327480\pi$
$62$	−14.5228	−	3.89137i	−1.84440	−	0.494205i
$63$	−8.43102	−	2.80123i	−1.06221	−	0.352922i
$64$	−4.05760	−	2.34266i	−0.507201	−	0.292832i
$65$	2.23998	+	8.67520i	0.277836	+	1.07603i
$66$	3.32245	+	6.16778i	0.408965	+	0.759201i
$67$	−1.63356	+	1.14383i	−0.199572	+	0.139742i	−0.669091	−	0.743181i	$-0.733316\pi$
$67$	−1.63356	+	1.14383i	−0.199572	+	0.139742i	0.469519	+	0.882922i	$0.344427\pi$
$68$	−7.29527	+	5.10821i	−0.884682	+	0.619461i
$69$	12.9648	+	0.382432i	1.56077	+	0.0460394i
$70$	8.70568	−	14.7663i	1.04053	−	1.76491i
$71$	−6.11142	−	3.52843i	−0.725292	−	0.418748i	0.0914051	−	0.995814i	$-0.470864\pi$
$71$	−6.11142	−	3.52843i	−0.725292	−	0.418748i	−0.816698	+	0.577066i	$0.804198\pi$
$72$	−10.9970	−	17.8608i	−1.29600	−	2.10491i
$73$	3.93347	+	1.05397i	0.460378	+	0.123358i	0.481551	−	0.876418i	$-0.340074\pi$
$73$	3.93347	+	1.05397i	0.460378	+	0.123358i	−0.0211733	+	0.999776i	$0.506740\pi$
$74$	0.796919	+	0.290055i	0.0926400	+	0.0337182i
$75$	8.24873	+	2.63788i	0.952481	+	0.304597i
$76$	−10.0321	−	8.41796i	−1.15076	−	0.965606i
$77$	−1.95556	+	4.19371i	−0.222857	+	0.477918i
$78$	7.10913	+	16.4990i	0.804950	+	1.86814i
$79$	−12.9467	+	2.28286i	−1.45662	+	0.256842i	−0.845194	−	0.534460i	$-0.820515\pi$
$79$	−12.9467	+	2.28286i	−1.45662	+	0.256842i	−0.611427	+	0.791301i	$0.709404\pi$
$80$	18.3335	−	6.48426i	2.04975	−	0.724962i
$81$	−0.508912	−	8.98560i	−0.0565458	−	0.998400i
$82$	−11.6425	−	11.6425i	−1.28569	−	1.28569i
$83$	−2.33262	+	3.33133i	−0.256038	+	0.365661i	−0.926507	−	0.376277i	$-0.877204\pi$
$83$	−2.33262	+	3.33133i	−0.256038	+	0.365661i	0.670469	+	0.741938i	$0.266093\pi$
$84$	8.91139	−	22.4052i	0.972313	−	2.44460i
$85$	0.407655	−	4.21658i	0.0442164	−	0.457352i
$86$	−0.973224	+	1.15984i	−0.104945	+	0.125069i
$87$	−3.74248	−	5.69514i	−0.401236	−	0.610583i
$88$	−9.90096	+	4.61689i	−1.05545	+	0.492162i
$89$	4.23520	+	7.33558i	0.448930	+	0.777570i	0.998317	−	0.0579982i	$-0.0184718\pi$
$89$	4.23520	+	7.33558i	0.448930	+	0.777570i	−0.549386	+	0.835569i	$0.685138\pi$
$90$	17.1558	+	2.68694i	1.80838	+	0.283229i
$91$	−5.93304	+	10.2763i	−0.621951	+	1.07725i
$92$	−3.06811	+	35.0686i	−0.319872	+	3.65616i
$93$	7.32018	−	6.90070i	0.759067	−	0.715569i
$94$	1.94105	+	0.342259i	0.200204	+	0.0353013i
$95$	6.14432	−	1.02577i	0.630394	−	0.105241i
$96$	13.0060	−	7.00604i	1.32742	−	0.715051i
$97$	7.95549	+	0.696015i	0.807758	+	0.0706696i	0.483550	−	0.875317i	$-0.339347\pi$
$97$	7.95549	+	0.696015i	0.807758	+	0.0706696i	0.324207	+	0.945986i	$0.394903\pi$
$98$	4.42546	−	1.18580i	0.447039	−	0.119784i
$99$	−4.67941	−	0.276305i	−0.470298	−	0.0277697i
$100$	−8.44022	+	21.9368i	−0.844022	+	2.19368i
$101$	5.32423	−	14.6282i	0.529781	−	1.45556i	−0.329549	−	0.944139i	$-0.606897\pi$
$101$	5.32423	−	14.6282i	0.529781	−	1.45556i	0.859330	−	0.511422i	$-0.170881\pi$
$102$	−0.490499	−	8.48004i	−0.0485666	−	0.839649i
$103$	−7.89264	+	0.690517i	−0.777685	+	0.0680387i	−0.469085	−	0.883153i	$-0.655416\pi$
$103$	−7.89264	+	0.690517i	−0.777685	+	0.0680387i	−0.308601	+	0.951192i	$0.599861\pi$
$104$	−26.3252	+	9.58158i	−2.58140	+	0.939552i
$105$	5.34712	+	10.1468i	0.521826	+	0.990222i
$106$	3.54156	+	20.0852i	0.343987	+	1.95085i
$107$	−3.95377	+	3.95377i	−0.382225	+	0.382225i	−0.871903	−	0.489678i	$-0.837114\pi$
$107$	−3.95377	+	3.95377i	−0.382225	+	0.382225i	0.489678	+	0.871903i	$0.337114\pi$
$108$	24.4266	+	0.0293423i	2.35045	+	0.00282346i
$109$			6.56334i			0.628654i	0.949315	+	0.314327i	$0.101779\pi$
$109$			6.56334i			0.628654i	−0.949315	+	0.314327i	$0.898221\pi$
$110$	2.42036	−	8.71447i	0.230773	−	0.830893i
$111$	−0.445252	+	0.351770i	−0.0422615	+	0.0333885i
$112$	23.3414	+	10.8843i	2.20556	+	1.02847i
$113$	0.198630	+	2.27035i	0.0186855	+	0.213577i	0.999797	+	0.0201349i	$0.00640956\pi$
$113$	0.198630	+	2.27035i	0.0186855	+	0.213577i	−0.981112	+	0.193442i	$0.938035\pi$
$114$	11.8582	−	3.92412i	1.11063	−	0.367528i
$115$	−11.7319	−	11.9477i	−1.09401	−	1.11413i
$116$	16.0177	−	9.24784i	1.48721	−	0.858641i
$117$	−11.8924	−	1.75171i	−1.09945	−	0.161946i
$118$	−6.85686	−	25.5901i	−0.631225	−	2.35576i
$119$	4.29781	−	3.60629i	0.393979	−	0.330588i
$120$	−5.72775	+	26.4656i	−0.522869	+	2.41597i
$121$	1.48617	−	8.42851i	0.135107	−	0.766228i
$122$	−18.0378	−	25.7607i	−1.63307	−	2.33226i
$123$	10.7208	−	2.53634i	0.966662	−	0.228694i
$124$	17.5505	+	20.9158i	1.57608	+	1.87830i
$125$	−5.32340	−	9.83165i	−0.476140	−	0.879370i
$126$	13.7185	+	18.4580i	1.22214	+	1.64437i
$127$	0.559276	−	2.08725i	0.0496277	−	0.185213i	−0.936662	−	0.350233i	$-0.886102\pi$
$127$	0.559276	−	2.08725i	0.0496277	−	0.185213i	0.986290	+	0.165020i	$0.0527690\pi$
$128$	−2.08346	−	4.46799i	−0.184153	−	0.394918i
$129$	−0.318271	−	0.961776i	−0.0280222	−	0.0846797i
$130$	8.13084	−	21.7213i	0.713122	−	1.90509i
$131$	0.329501	+	0.905296i	0.0287886	+	0.0790961i	0.953254	−	0.302169i	$-0.0977107\pi$
$131$	0.329501	+	0.905296i	0.0287886	+	0.0790961i	−0.924466	+	0.381265i	$0.875488\pi$
$132$	1.48204	−	12.6357i	0.128995	−	1.09980i
$133$	6.75802	+	4.73202i	0.585995	+	0.410318i
$134$	5.16224			0.445950
$135$	−7.55992	+	8.82313i	−0.650655	+	0.759374i
$136$	13.2456			1.13580
$137$	1.99313	+	1.39561i	0.170285	+	0.119235i	0.655612	−	0.755098i	$-0.272411\pi$
$137$	1.99313	+	1.39561i	0.170285	+	0.119235i	−0.485327	+	0.874333i	$0.661300\pi$
$138$	−26.9235	−	20.0606i	−2.29188	−	1.70767i
$139$	−3.32712	−	9.14118i	−0.282202	−	0.775345i	−0.997099	−	0.0761146i	$-0.975749\pi$
$139$	−3.32712	−	9.14118i	−0.282202	−	0.775345i	0.714897	−	0.699230i	$-0.246474\pi$
$140$	−28.3311	+	12.8980i	−2.39441	+	1.09008i
$141$	−0.877127	+	0.984825i	−0.0738674	+	0.0829373i
$142$	7.72017	+	16.5560i	0.647862	+	1.38934i
$143$	−1.62043	+	6.04754i	−0.135508	+	0.505721i
$144$	−1.53786	+	26.0447i	−0.128155	+	2.17039i
$145$	−1.60661	+	8.64986i	−0.133422	+	0.718332i
$146$	−6.77589	−	8.07519i	−0.560777	−	0.668308i
$147$	−0.880385	+	2.93641i	−0.0726130	+	0.242191i
$148$	−0.883353	−	1.26156i	−0.0726112	−	0.103700i
$149$	2.43445	−	13.8064i	0.199438	−	1.13107i	−0.706518	−	0.707695i	$-0.749735\pi$
$149$	2.43445	−	13.8064i	0.199438	−	1.13107i	0.905956	−	0.423373i	$-0.139154\pi$
$150$	−13.5745	−	17.8410i	−1.10835	−	1.45671i
$151$	−13.9585	+	11.7126i	−1.13593	+	0.953156i	−0.999298	−	0.0374659i	$-0.988071\pi$
$151$	−13.9585	+	11.7126i	−1.13593	+	0.953156i	−0.136630	+	0.990622i	$0.543627\pi$
$152$	5.04116	+	18.8139i	0.408892	+	1.52600i
$153$	5.00048	+	2.70140i	0.404265	+	0.218396i
$154$	10.3734	−	5.98907i	0.835910	−	0.482613i
$155$	−12.9869	−	0.118354i	−1.04314	−	0.00950646i
$156$	6.61016	−	31.9484i	0.529236	−	2.55792i
$157$	−0.265324	−	3.03267i	−0.0211752	−	0.242033i	−0.999404	−	0.0345064i	$-0.989014\pi$
$157$	−0.265324	−	3.03267i	−0.0211752	−	0.242033i	0.978229	−	0.207527i	$-0.0665415\pi$
$158$	30.8426	+	14.3821i	2.45371	+	1.14418i
$159$	−12.6802	−	5.04342i	−1.00561	−	0.399969i
$160$	−18.3762	−	5.10382i	−1.45277	−	0.403492i
$161$		−	22.1764i		−	1.74774i
$162$	−12.2624	+	19.8093i	−0.963424	+	1.55636i
$163$	−16.0133	+	16.0133i	−1.25426	+	1.25426i	−0.300465	+	0.953793i	$0.597142\pi$
$163$	−16.0133	+	16.0133i	−1.25426	+	1.25426i	−0.953793	+	0.300465i	$0.902858\pi$
$164$	5.19212	+	29.4459i	0.405436	+	2.29934i
$165$	4.11081	+	4.44109i	0.320026	+	0.345739i
$166$	9.89249	−	3.60057i	0.767806	−	0.279459i
$167$	5.22689	−	0.457294i	0.404469	−	0.0353865i	0.116894	−	0.993144i	$-0.462706\pi$
$167$	5.22689	−	0.457294i	0.404469	−	0.0353865i	0.287576	+	0.957758i	$0.407151\pi$
$168$	−29.9701	+	19.6945i	−2.31224	+	1.51946i
$169$	−1.04499	+	2.87108i	−0.0803837	+	0.220852i
$170$	−7.12506	+	8.33584i	−0.546467	+	0.639330i
$171$	−1.93390	+	8.13073i	−0.147889	+	0.621772i
$172$	2.65585	−	0.711633i	0.202507	−	0.0542615i
$173$	−8.14671	−	0.712745i	−0.619383	−	0.0541890i	−0.226854	−	0.973929i	$-0.572844\pi$
$173$	−8.14671	−	0.712745i	−0.619383	−	0.0541890i	−0.392529	+	0.919740i	$0.628400\pi$
$174$	−0.520136	+	17.6331i	−0.0394314	+	1.33676i
$175$	4.09236	−	14.2302i	0.309354	−	1.07571i
$176$	13.3823	+	2.35966i	1.00873	+	0.177866i
$177$	16.9798	+	5.09081i	1.27628	+	0.382649i
$178$	1.91103	−	21.8431i	0.143238	−	1.63721i
$179$	2.65400	−	4.59686i	0.198369	−	0.343585i	−0.749631	−	0.661856i	$-0.769769\pi$
$179$	2.65400	−	4.59686i	0.198369	−	0.343585i	0.948000	+	0.318271i	$0.103102\pi$
$180$	−22.7218	−	21.8667i	−1.69358	−	1.62985i
$181$	11.5435	+	19.9940i	0.858023	+	1.48614i	0.873811	+	0.486265i	$0.161641\pi$
$181$	11.5435	+	19.9940i	0.858023	+	1.48614i	−0.0157880	+	0.999875i	$0.505026\pi$
$182$	27.8387	−	12.9814i	2.06354	−	0.962246i
$183$	21.0069	−	1.21507i	1.55287	−	0.0898207i
$184$	33.6540	−	40.1073i	2.48100	−	2.95675i
$185$	0.729166	+	0.0704951i	0.0536094	+	0.00518290i
$186$	−25.7681	+	3.76393i	−1.88941	+	0.275985i
$187$	1.69790	−	2.42486i	0.124163	−	0.177323i
$188$	−2.53096	−	2.53096i	−0.184589	−	0.184589i
$189$	−15.3309	+	1.32273i	−1.11516	+	0.0962143i
$190$	−14.5518	−	6.94778i	−1.05570	−	0.504045i
$191$	−3.74191	+	0.659800i	−0.270755	+	0.0477414i	−0.307377	−	0.951588i	$-0.599451\pi$
$191$	−3.74191	+	0.659800i	−0.270755	+	0.0477414i	0.0366221	+	0.999329i	$0.488340\pi$
$192$	−8.05996	−	0.945346i	−0.581677	−	0.0682245i
$193$	−5.22336	+	11.2015i	−0.375986	+	0.806305i	0.623710	+	0.781656i	$0.285625\pi$
$193$	−5.22336	+	11.2015i	−0.375986	+	0.806305i	−0.999696	+	0.0246489i	$0.992153\pi$
$194$	−15.8359	−	13.2879i	−1.13695	−	0.954017i
$195$	9.50901	+	12.2641i	0.680954	+	0.878253i
$196$	−7.81835	−	2.84565i	−0.558453	−	0.203260i
$197$	23.1882	+	6.21326i	1.65209	+	0.442676i	0.960197	−	0.279324i	$-0.0901104\pi$
$197$	23.1882	+	6.21326i	1.65209	+	0.442676i	0.691893	+	0.722000i	$0.256777\pi$
$198$	9.51228	+	7.53372i	0.676008	+	0.535398i
$199$	−5.73533	−	3.31129i	−0.406566	−	0.234731i	0.282747	−	0.959195i	$-0.408754\pi$
$199$	−5.73533	−	3.31129i	−0.406566	−	0.234731i	−0.689313	+	0.724463i	$0.742088\pi$
$200$	28.9966	−	19.5258i	2.05037	−	1.38068i
$201$	−1.81449	+	2.93910i	−0.127984	+	0.207308i
$202$	−33.0093	+	23.1134i	−2.32253	+	1.62625i
$203$	−9.54445	+	6.68309i	−0.669889	+	0.469061i
$204$	−8.10325	+	13.1256i	−0.567341	+	0.918977i
$205$	−12.2518	−	7.22323i	−0.855701	−	0.504492i
$206$	17.7613	+	10.2545i	1.23749	+	0.714466i
$207$	20.8848	−	8.27764i	1.45159	−	0.575336i
$208$	33.6595	+	9.01904i	2.33387	+	0.625358i
$209$	4.09043	+	1.48880i	0.282941	+	0.102982i
$210$	3.72718	−	29.4551i	0.257200	−	2.03259i
$211$	−2.13311	−	1.78989i	−0.146849	−	0.123221i	0.566404	−	0.824128i	$-0.308334\pi$
$211$	−2.13311	−	1.78989i	−0.146849	−	0.123221i	−0.713253	+	0.700907i	$0.752779\pi$
$212$	15.6526	−	33.5672i	1.07503	−	2.30540i
$213$	−12.1396	−	1.42385i	−0.831794	−	0.0975604i
$214$	14.2542	−	2.51341i	0.974400	−	0.171813i
$215$	−0.563508	+	1.18024i	−0.0384309	+	0.0804920i
$216$	−29.7342	−	20.8734i	−2.02316	−	1.42025i
$217$	−12.1625	−	12.1625i	−0.825642	−	0.825642i
$218$	9.74502	−	13.9173i	0.660016	−	0.942601i
$219$	6.97925	−	1.01945i	0.471614	−	0.0688884i
$220$	−12.6776	+	10.4424i	−0.854722	+	0.704024i
$221$	4.87947	−	5.81513i	0.328229	−	0.391168i
$222$	1.46644	−	0.0848211i	0.0984209	−	0.00569282i
$223$	19.9909	−	9.32189i	1.33869	−	0.624240i	0.384410	−	0.923163i	$-0.374405\pi$
$223$	19.9909	−	9.32189i	1.33869	−	0.624240i	0.954277	+	0.298923i	$0.0966273\pi$
$224$	−12.6291	−	21.8743i	−0.843821	−	1.46154i
$225$	14.9290	−	1.45762i	0.995267	−	0.0971747i
$226$	2.94975	−	5.10912i	0.196215	−	0.339854i
$227$	0.647951	−	7.40612i	0.0430060	−	0.491561i	−0.943896	−	0.330242i	$-0.892870\pi$
$227$	0.647951	−	7.40612i	0.0430060	−	0.491561i	0.986902	−	0.161319i	$-0.0515749\pi$
$228$	−21.7274	−	6.51425i	−1.43894	−	0.431417i
$229$	−4.57594	−	0.806861i	−0.302386	−	0.0533189i	0.0203963	−	0.999792i	$-0.493507\pi$
$229$	−4.57594	−	0.806861i	−0.302386	−	0.0533189i	−0.322783	+	0.946473i	$0.604618\pi$
$230$	7.13756	+	42.7539i	0.470637	+	2.81911i
$231$	−0.236311	+	8.01114i	−0.0155481	+	0.527095i
$232$	−27.4037	−	2.39751i	−1.79914	−	0.157404i
$233$	13.7921	−	3.69557i	0.903549	−	0.242105i	0.223009	−	0.974816i	$-0.428412\pi$
$233$	13.7921	−	3.69557i	0.903549	−	0.242105i	0.680540	+	0.732711i	$0.261745\pi$
$234$	22.6166	+	21.3719i	1.47849	+	1.39712i
$235$	1.69737	−	0.132926i	0.110724	−	0.00867111i
$236$	−16.4549	+	45.2095i	−1.07112	+	2.94289i
$237$	−19.0293	+	12.5049i	−1.23609	+	0.812279i
$238$	−14.4678	+	1.26577i	−0.937811	+	0.0820478i
$239$	−19.1398	+	6.96633i	−1.23805	+	0.450614i	−0.876348	−	0.481678i	$-0.840027\pi$
$239$	−19.1398	+	6.96633i	−1.23805	+	0.450614i	−0.361705	+	0.932293i	$0.617805\pi$
$240$	24.7183	−	22.8800i	1.59556	−	1.47690i
$241$	−2.82578	−	16.0258i	−0.182024	−	1.03231i	−0.929719	−	0.368269i	$-0.879950\pi$
$241$	−2.82578	−	16.0258i	−0.182024	−	1.03231i	0.747695	−	0.664043i	$-0.231161\pi$
$242$	−15.6657	+	15.6657i	−1.00703	+	1.00703i
$243$	−6.96818	−	13.9443i	−0.447009	−	0.894529i
$244$			57.1094i			3.65606i
$245$	3.44528	−	1.94749i	0.220111	−	0.124420i
$246$	−26.4990	−	10.5397i	−1.68951	−	0.671984i
$247$	10.1168	+	4.71754i	0.643717	+	0.300170i
$248$	−3.53925	−	40.4538i	−0.224743	−	2.56882i
$249$	−1.42716	+	6.89781i	−0.0904428	+	0.437131i
$250$	−3.30961	+	28.7517i	−0.209318	+	1.81842i
$251$	−8.96649	+	5.17681i	−0.565960	+	0.326757i	−0.755534	−	0.655109i	$-0.772623\pi$
$251$	−8.96649	+	5.17681i	−0.565960	+	0.326757i	0.189574	+	0.981866i	$0.439289\pi$
$252$	−1.18126	−	41.7471i	−0.0744121	−	2.62982i
$253$	−3.02841	−	11.3022i	−0.190395	−	0.710562i
$254$	−4.28500	+	3.59554i	−0.268865	+	0.225604i
$255$	−2.24157	−	6.98660i	−0.140373	−	0.437518i
$256$	−3.84321	+	21.7959i	−0.240201	+	1.36225i
$257$	3.25941	+	4.65492i	0.203316	+	0.290366i	0.907842	−	0.419313i	$-0.137729\pi$
$257$	3.25941	+	4.65492i	0.203316	+	0.290366i	−0.704525	+	0.709679i	$0.748840\pi$
$258$	−0.753131	+	2.51197i	−0.0468879	+	0.156388i
$259$	0.623629	+	0.743212i	0.0387504	+	0.0461810i
$260$	−34.7204	+	23.8429i	−2.15327	+	1.47868i
$261$	−9.85647	−	6.49402i	−0.610100	−	0.401970i
$262$	0.645458	−	2.40888i	0.0398765	−	0.148821i
$263$	8.23378	+	17.6574i	0.507717	+	1.08880i	0.978442	+	0.206522i	$0.0662145\pi$
$263$	8.23378	+	17.6574i	0.507717	+	1.08880i	−0.470725	+	0.882280i	$0.656008\pi$
$264$	−12.5848	+	14.1300i	−0.774540	+	0.869642i
$265$	7.29964	+	16.0340i	0.448413	+	0.984961i
$266$	−7.30422	−	20.0682i	−0.447850	−	1.23046i
$267$	11.7646	+	8.76573i	0.719980	+	0.536454i
$268$	−7.67923	−	5.37706i	−0.469084	−	0.328456i
$269$	−21.8628			−1.33300			−0.666501	−	0.745505i	$-0.732209\pi$
$269$	−21.8628			−1.33300			−0.666501	+	0.745505i	$0.732209\pi$
$270$	29.1308	−	7.48442i	1.77285	−	0.455487i
$271$	25.6697			1.55933			0.779663	−	0.626200i	$-0.215391\pi$
$271$	25.6697			1.55933			0.779663	+	0.626200i	$0.215391\pi$
$272$	−13.4963	−	9.45020i	−0.818333	−	0.573003i
$273$	−2.39419	+	20.4127i	−0.144903	+	1.23543i
$274$	−2.15422	−	5.91867i	−0.130141	−	0.357560i
$275$	0.142386	−	7.81130i	0.00858620	−	0.471039i
$276$	19.1555	+	57.8855i	1.15302	+	3.48430i
$277$	−2.24166	−	4.80726i	−0.134689	−	0.288841i	0.827383	−	0.561638i	$-0.189829\pi$
$277$	−2.24166	−	4.80726i	−0.134689	−	0.288841i	−0.962071	+	0.272798i	$0.912051\pi$
$278$	−6.51747	+	24.3235i	−0.390892	+	1.45883i
$279$	6.91431	−	15.9939i	0.413949	−	0.957532i
$280$	45.5190	+	8.45465i	2.72028	+	0.505262i
$281$	−0.950287	−	1.13251i	−0.0566894	−	0.0675598i	0.736955	−	0.675942i	$-0.236263\pi$
$281$	−0.950287	−	1.13251i	−0.0566894	−	0.0675598i	−0.793644	+	0.608382i	$0.791819\pi$
$282$	3.32215	−	0.785960i	0.197831	−	0.0468032i
$283$	2.90572	+	4.14980i	0.172727	+	0.246680i	0.896177	−	0.443697i	$-0.146333\pi$
$283$	2.90572	+	4.14980i	0.172727	+	0.246680i	−0.723449	+	0.690377i	$0.757444\pi$
$284$	5.76054	−	32.6697i	0.341825	−	1.93859i
$285$	9.07054	−	5.84293i	0.537292	−	0.346105i
$286$	12.4153	−	10.4176i	0.734130	−	0.616008i
$287$	−4.87513	−	18.1942i	−0.287770	−	1.07397i
$288$	15.8864	−	20.0585i	0.936112	−	1.18196i
$289$	11.6141	−	6.70543i	0.683185	−	0.394437i
$290$	16.2498	−	15.9563i	0.954220	−	0.936985i
$291$	13.1316	−	4.34551i	0.769789	−	0.254738i
$292$	1.66844	+	19.0703i	0.0976379	+	1.11601i
$293$	20.8181	+	9.70762i	1.21620	+	0.567125i	0.921468	−	0.388453i	$-0.126991\pi$
$293$	20.8181	+	9.70762i	1.21620	+	0.567125i	0.294736	+	0.955579i	$0.404768\pi$
$294$	6.22671	−	4.91939i	0.363149	−	0.286905i
$295$	−11.2613	−	19.9223i	−0.655659	−	1.15992i
$296$			2.29054i			0.133135i
$297$	−7.63278	+	2.76773i	−0.442899	+	0.160600i
$298$	−25.6615	+	25.6615i	−1.48653	+	1.48653i
$299$	−5.21042	−	29.5498i	−0.301327	−	1.70891i
$300$	1.60974	+	40.6792i	0.0929386	+	2.34861i
$301$	−1.62765	+	0.592417i	−0.0938163	+	0.0341464i
$302$	46.9890	−	4.11100i	2.70391	−	0.236562i
$303$	−1.55697	−	26.9179i	−0.0894457	−	1.54639i
$304$	8.28636	−	22.7666i	0.475255	−	1.30575i
$305$	−20.6497	−	17.6503i	−1.18240	−	1.01065i
$306$	−6.59238	−	13.1528i	−0.376862	−	0.751894i
$307$	22.5239	−	6.03527i	1.28551	−	0.344451i	0.449556	−	0.893252i	$-0.351582\pi$
$307$	22.5239	−	6.03527i	1.28551	−	0.344451i	0.835953	+	0.548801i	$0.184916\pi$
$308$	−21.6695	−	1.89583i	−1.23473	−	0.108025i
$309$	−12.0813	+	6.50795i	−0.687283	+	0.370224i
$310$	27.3626	+	19.5335i	1.55409	+	1.10943i
$311$	9.32616	+	1.64445i	0.528838	+	0.0932485i	0.431691	−	0.902022i	$-0.357917\pi$
$311$	9.32616	+	1.64445i	0.528838	+	0.0932485i	0.0971473	+	0.995270i	$0.469028\pi$
$312$	−35.3076	+	33.2843i	−1.99890	+	1.88435i
$313$	−2.69662	+	30.8225i	−0.152422	+	1.74219i	0.407109	+	0.913380i	$0.366537\pi$
$313$	−2.69662	+	30.8225i	−0.152422	+	1.74219i	−0.559530	+	0.828810i	$0.689018\pi$
$314$	−3.94019	+	6.82461i	−0.222358	+	0.385135i
$315$	15.4600	+	12.4753i	0.871074	+	0.702902i
$316$	−30.9001	−	53.5206i	−1.73827	−	3.01077i
$317$	−19.0657	+	8.89049i	−1.07084	+	0.499340i	−0.876404	−	0.481576i	$-0.840064\pi$
$317$	−19.0657	+	8.89049i	−1.07084	+	0.499340i	−0.194433	+	0.980916i	$0.562287\pi$
$318$	19.3997	+	29.5216i	1.08788	+	1.65549i
$319$	−3.95168	+	4.70943i	−0.221252	+	0.263678i
$320$	6.66087	+	8.08665i	0.372354	+	0.452057i
$321$	−3.57926	+	8.99903i	−0.199775	+	0.502277i
$322$	−32.9267	+	47.0242i	−1.83493	+	2.62056i
$323$	−3.73198	−	3.73198i	−0.207653	−	0.207653i
$324$	38.8748	−	16.6952i	2.15971	−	0.927509i
$325$	2.10958	−	19.9232i	0.117018	−	1.10514i
$326$	57.7316	−	10.1796i	3.19746	−	0.563798i
$327$	4.49847	+	10.4401i	0.248766	+	0.577340i
$328$	18.7939	−	40.3036i	1.03772	−	2.22540i
$329$	1.72731	+	1.44938i	0.0952295	+	0.0799070i
$330$	−2.12284	−	15.5208i	−0.116858	−	0.854390i
$331$	0.225624	+	0.0821205i	0.0124014	+	0.00451375i	0.348213	−	0.937415i	$-0.386788\pi$
$331$	0.225624	+	0.0821205i	0.0124014	+	0.00451375i	−0.335812	+	0.941929i	$0.609011\pi$
$332$	−18.4662	−	4.94801i	−1.01347	−	0.271557i
$333$	−0.467149	+	0.864723i	−0.0255996	+	0.0473866i
$334$	−11.7624	−	6.79104i	−0.643611	−	0.371589i
$335$	4.31759	−	1.11483i	0.235895	−	0.0609094i
$336$	44.5885	+	1.31526i	2.43250	+	0.0717535i
$337$	14.0325	−	9.82568i	0.764400	−	0.535239i	−0.125116	−	0.992142i	$-0.539930\pi$
$337$	14.0325	−	9.82568i	0.764400	−	0.535239i	0.889516	+	0.456903i	$0.151041\pi$
$338$	6.47874	−	4.53646i	0.352397	−	0.246751i
$339$	1.87204	+	3.47525i	0.101675	+	0.188749i
$340$	19.2818	−	4.97866i	1.04570	−	0.270006i
$341$	−7.85952	−	4.53769i	−0.425617	−	0.245730i
$342$	16.1730	−	14.3695i	0.874535	−	0.777016i
$343$	−14.9607	−	4.00870i	−0.807801	−	0.216450i
$344$	−3.84273	−	1.39864i	−0.207186	−	0.0754097i
$345$	−26.8505	−	10.9639i	−1.44558	−	0.590277i
$346$	16.2166	+	13.6073i	0.871808	+	0.731534i
$347$	−11.4696	+	24.5967i	−0.615723	+	1.32042i	0.313038	+	0.949741i	$0.398653\pi$
$347$	−11.4696	+	24.5967i	−0.615723	+	1.32042i	−0.928760	+	0.370681i	$0.879124\pi$
$348$	19.1405	−	25.6887i	1.02604	−	1.37706i
$349$	18.8404	−	3.32208i	1.00851	−	0.177827i	0.355095	−	0.934830i	$-0.384449\pi$
$349$	18.8404	−	3.32208i	1.00851	−	0.177827i	0.653411	+	0.757003i	$0.273337\pi$
$350$	−29.8063	+	24.0985i	−1.59321	+	1.28812i
$351$	−20.1175	+	5.36459i	−1.07379	+	0.286340i
$352$	−9.42361	−	9.42361i	−0.502280	−	0.502280i
$353$	−17.4648	+	24.9423i	−0.929558	+	1.32755i	0.0152364	+	0.999884i	$0.495150\pi$
$353$	−17.4648	+	24.9423i	−0.929558	+	1.32755i	−0.944795	+	0.327663i	$0.893739\pi$
$354$	−28.4463	−	36.0059i	−1.51190	−	1.91369i
$355$	10.0324	+	12.1798i	0.532463	+	0.646438i
$356$	−25.5949	+	30.5028i	−1.35653	+	1.61664i
$357$	4.36467	−	8.68211i	0.231003	−	0.459506i
$358$	−12.4530	+	5.80691i	−0.658160	+	0.306905i
$359$	15.6146	+	27.0453i	0.824108	+	1.42740i	0.902599	+	0.430483i	$0.141657\pi$
$359$	15.6146	+	27.0453i	0.824108	+	1.42740i	−0.0784904	+	0.996915i	$0.525010\pi$
$360$	9.02838	+	46.0238i	0.475838	+	2.42567i
$361$	−5.61951	+	9.73329i	−0.295764	+	0.512278i
$362$	5.20872	−	59.5360i	0.273764	−	3.12914i
$363$	−3.41283	−	14.4256i	−0.179127	−	0.757148i
$364$	−54.9338	−	9.68632i	−2.87931	−	0.507701i
$365$	−7.41111	−	5.29062i	−0.387915	−	0.276924i
$366$	−46.3485	−	28.6138i	−2.42267	−	1.49567i
$367$	1.41799	+	0.124058i	0.0740183	+	0.00647576i	0.124105	−	0.992269i	$-0.460394\pi$
$367$	1.41799	+	0.124058i	0.0740183	+	0.00647576i	−0.0500864	+	0.998745i	$0.515950\pi$
$368$	−62.9058	+	16.8556i	−3.27919	+	0.878657i
$369$	15.3149	−	11.3825i	0.797261	−	0.592547i
$370$	−1.44150	−	1.23212i	−0.0749402	−	0.0640550i
$371$	−7.98007	+	21.9251i	−0.414305	+	1.13829i
$372$	42.2526	+	21.2412i	2.19069	+	1.10131i
$373$	9.79785	−	0.857201i	0.507313	−	0.0443842i	0.169374	−	0.985552i	$-0.445826\pi$
$373$	9.79785	−	0.857201i	0.507313	−	0.0443842i	0.337940	+	0.941168i	$0.390270\pi$
$374$	−7.20068	+	2.62083i	−0.372339	+	0.135520i
$375$	−15.2063	−	11.9903i	−0.785252	−	0.619177i
$376$	0.924409	+	5.24259i	0.0476728	+	0.270366i
$377$	−11.1477	+	11.1477i	−0.574134	+	0.574134i
$378$	34.4727	+	19.9581i	1.77308	+	1.02653i
$379$		−	5.76488i		−	0.296122i	−0.988978	−	0.148061i	$-0.952697\pi$
$379$		−	5.76488i		−	0.296122i	0.988978	−	0.148061i	$-0.0473032\pi$
$380$	14.4101	+	25.4927i	0.739222	+	1.30775i
$381$	−0.540960	−	3.70345i	−0.0277142	−	0.189733i
$382$	8.91424	+	4.15678i	0.456092	+	0.212679i
$383$	0.249029	+	2.84641i	0.0127248	+	0.145445i	0.999899	−	0.0142007i	$-0.00452038\pi$
$383$	0.249029	+	2.84641i	0.0127248	+	0.145445i	−0.987174	+	0.159646i	$0.948965\pi$
$384$	−6.37643	−	5.67911i	−0.325396	−	0.289811i
$385$	7.38269	−	7.24934i	0.376257	−	0.369461i
$386$	27.7076	−	15.9970i	1.41028	−	0.814226i
$387$	−1.16546	−	1.31173i	−0.0592436	−	0.0666790i
$388$	9.71629	+	36.2617i	0.493270	+	1.84091i
$389$	9.76677	−	8.19530i	0.495195	−	0.415518i	−0.360689	−	0.932686i	$-0.617458\pi$
$389$	9.76677	−	8.19530i	0.495195	−	0.415518i	0.855884	+	0.517168i	$0.173014\pi$
$390$	−1.95416	−	40.1243i	−0.0989526	−	2.03177i
$391$	−2.46354	+	13.9714i	−0.124586	+	0.706565i
$392$	7.09766	+	10.1365i	0.358486	+	0.511971i
$393$	1.14461	+	1.21419i	0.0577380	+	0.0612478i
$394$	−39.9445	−	47.6040i	−2.01238	−	2.39826i
$395$	28.9020	+	5.36823i	1.45422	+	0.270105i
$396$	−6.30302	−	21.1151i	−0.316739	−	1.06107i
$397$	0.929625	−	3.46941i	0.0466565	−	0.174125i	−0.938666	−	0.344828i	$-0.887937\pi$
$397$	0.929625	−	3.46941i	0.0466565	−	0.174125i	0.985322	+	0.170703i	$0.0546040\pi$
$398$	7.24507	+	15.5371i	0.363162	+	0.778804i
$399$	13.9931	+	2.89518i	0.700531	+	0.144940i
$400$	−43.4762	−	0.792494i	−2.17381	−	0.0396247i
$401$	−7.04392	−	19.3530i	−0.351756	−	0.966443i	−0.981806	−	0.189888i	$-0.939188\pi$
$401$	−7.04392	−	19.3530i	−0.351756	−	0.966443i	0.630049	−	0.776555i	$-0.283035\pi$
$402$	8.21143	−	3.53817i	0.409549	−	0.176468i
$403$	−19.0640	−	13.3488i	−0.949645	−	0.664949i
$404$	73.1790			3.64079
$405$	−5.97804	+	19.2162i	−0.297051	+	0.954862i
$406$	30.1615			1.49689
$407$	0.419326	+	0.293615i	0.0207852	+	0.0145540i
$408$	21.0694	−	9.07845i	1.04309	−	0.449450i
$409$	−5.75785	−	15.8196i	−0.284707	−	0.782226i	−0.996785	−	0.0801257i	$-0.974468\pi$
$409$	−5.75785	−	15.8196i	−0.284707	−	0.782226i	0.712078	−	0.702101i	$-0.247754\pi$
$410$	15.2547	+	33.5076i	0.753375	+	1.65482i
$411$	4.12696	+	0.853871i	0.203568	+	0.0421183i
$412$	−15.7401	−	33.7548i	−0.775460	−	1.66298i
$413$	7.84432	−	29.2754i	0.385994	−	1.44055i
$414$	−56.5759	−	13.4566i	−2.78055	−	0.661355i
$415$	7.49630	−	5.14780i	0.367979	−	0.252696i
$416$	−21.9677	−	26.1801i	−1.07705	−	1.28358i
$417$	−11.5577	−	12.2602i	−0.565981	−	0.600386i
$418$	−6.46311	−	9.23028i	−0.316121	−	0.451468i
$419$	−0.0944911	+	0.535886i	−0.00461619	+	0.0261797i	−0.987029	−	0.160543i	$-0.948675\pi$
$419$	−0.0944911	+	0.535886i	−0.00461619	+	0.0261797i	0.982413	+	0.186723i	$0.0597866\pi$
$420$	−36.2252	+	39.9344i	−1.76761	+	1.94860i
$421$	−5.72762	+	4.80604i	−0.279147	+	0.234232i	−0.771602	−	0.636106i	$-0.780544\pi$
$421$	−5.72762	+	4.80604i	−0.279147	+	0.234232i	0.492455	+	0.870338i	$0.336100\pi$
$422$	1.86561	+	6.96256i	0.0908166	+	0.338932i
$423$	−0.720228	+	2.16771i	−0.0350187	+	0.105398i
$424$	−47.7050	+	27.5425i	−2.31676	+	1.33758i
$425$	−4.15906	+	8.51064i	−0.201744	+	0.412827i
$426$	23.6276	+	21.0437i	1.14476	+	1.01957i
$427$	−3.13559	−	35.8400i	−0.151742	−	1.73442i
$428$	−23.8223	−	11.1085i	−1.15149	−	0.536950i
$429$	1.56737	+	10.7303i	0.0756732	+	0.518063i
$430$	2.94728	−	1.66599i	0.142131	−	0.0803412i
$431$			14.9683i			0.720998i	0.932760	+	0.360499i	$0.117394\pi$
$431$			14.9683i			0.720998i	−0.932760	+	0.360499i	$0.882606\pi$
$432$	15.4046	+	42.4826i	0.741156	+	2.04395i
$433$	24.8822	−	24.8822i	1.19576	−	1.19576i	0.220337	−	0.975424i	$-0.429284\pi$
$433$	24.8822	−	24.8822i	1.19576	−	1.19576i	0.975424	−	0.220337i	$-0.0707157\pi$
$434$	7.73168	+	43.8485i	0.371132	+	2.10480i
$435$	3.37296	+	14.8602i	0.161721	+	0.712494i
$436$	−28.9929	+	10.5526i	−1.38851	+	0.505376i
$437$	−20.7824	+	1.81822i	−0.994156	+	0.0869774i
$438$	−16.3129	−	8.20083i	−0.779461	−	0.391851i
$439$	−13.0228	+	35.7799i	−0.621545	+	1.70768i	0.0816297	+	0.996663i	$0.473988\pi$
$439$	−13.0228	+	35.7799i	−0.621545	+	1.70768i	−0.703174	+	0.711017i	$0.748235\pi$
$440$	24.3534	−	1.90718i	1.16100	−	0.0909213i
$441$	0.612193	+	5.27428i	0.0291521	+	0.251156i
$442$	−18.9809	+	5.08591i	−0.902828	+	0.241912i
$443$	−28.4974	−	2.49320i	−1.35395	−	0.118456i	−0.613038	−	0.790053i	$-0.710053\pi$
$443$	−28.4974	−	2.49320i	−1.35395	−	0.118456i	−0.740916	+	0.671597i	$0.765608\pi$
$444$	−2.26979	−	1.40128i	−0.107719	−	0.0665019i
$445$	−3.11885	−	18.6818i	−0.147848	−	0.885605i
$446$	−56.2308	−	9.91500i	−2.66260	−	0.469489i
$447$	−5.59044	−	23.6301i	−0.264419	−	1.11766i
$448$	−1.20930	+	13.8223i	−0.0571338	+	0.653043i
$449$	12.4470	−	21.5588i	0.587409	−	1.01742i	−0.407162	−	0.913356i	$-0.633481\pi$
$449$	12.4470	−	21.5588i	0.587409	−	1.01742i	0.994570	−	0.104066i	$-0.0331852\pi$
$450$	−33.8207	−	19.0753i	−1.59432	−	0.899216i
$451$	−4.96922	−	8.60694i	−0.233991	−	0.405285i
$452$	−9.70971	+	4.52771i	−0.456706	+	0.212966i
$453$	−14.1757	+	28.1979i	−0.666032	+	1.32485i
$454$	−12.3703	+	14.7424i	−0.580567	+	0.691893i
$455$	20.4803	−	16.8694i	0.960131	−	0.790848i
$456$	20.9137	+	26.4715i	0.979374	+	1.23964i
$457$	−2.11373	+	3.01872i	−0.0988761	+	0.141210i	−0.865542	−	0.500837i	$-0.833026\pi$
$457$	−2.11373	+	3.01872i	−0.0988761	+	0.141210i	0.766666	+	0.642047i	$0.221914\pi$
$458$	8.50512	+	8.50512i	0.397418	+	0.397418i
$459$	9.80564	+	0.869753i	0.457688	+	0.0405966i
$460$	33.9153	−	71.0342i	1.58131	−	3.31199i
$461$	−15.0276	+	2.64977i	−0.699905	+	0.123412i	−0.512267	−	0.858826i	$-0.671194\pi$
$461$	−15.0276	+	2.64977i	−0.699905	+	0.123412i	−0.187638	+	0.982238i	$0.560083\pi$
$462$	12.3958	−	16.6365i	0.576703	−	0.773999i
$463$	4.75770	−	10.2029i	0.221109	−	0.474170i	−0.764194	−	0.644987i	$-0.776863\pi$
$463$	4.75770	−	10.2029i	0.221109	−	0.474170i	0.985303	+	0.170817i	$0.0546406\pi$
$464$	26.2118	+	21.9943i	1.21685	+	1.02106i
$465$	−20.7391	+	8.71289i	−0.961751	+	0.404051i
$466$	−34.7327	−	12.6417i	−1.60896	−	0.585614i
$467$	16.8627	+	4.51835i	0.780313	+	0.209084i	0.626923	−	0.779082i	$-0.284314\pi$
$467$	16.8627	+	4.51835i	0.780313	+	0.209084i	0.153390	+	0.988166i	$0.450981\pi$
$468$	−11.3827	−	55.3500i	−0.526163	−	2.55856i
$469$	5.11446	+	2.95283i	0.236164	+	0.136349i
$470$	−3.79657	−	2.23833i	−0.175123	−	0.103246i
$471$	−2.50061	−	4.64213i	−0.115222	−	0.213898i
$472$	58.6142	−	41.0421i	2.69794	−	1.88911i
$473$	−0.748633	+	0.524198i	−0.0344222	+	0.0241027i
$474$	58.9179	+	1.73795i	2.70619	+	0.0798265i
$475$	−13.6713	−	2.66840i	−0.627281	−	0.122434i
$476$	22.8405	+	13.1870i	1.04689	+	0.604423i
$477$	−23.6268	+	0.668534i	−1.08180	+	0.0306101i
$478$	50.9287	+	13.6463i	2.32943	+	0.624168i
$479$	21.5176	+	7.83178i	0.983166	+	0.357843i	0.783070	−	0.621933i	$-0.213652\pi$
$479$	21.5176	+	7.83178i	0.983166	+	0.357843i	0.200096	+	0.979776i	$0.435875\pi$
$480$	−32.7286	+	4.47643i	−1.49385	+	0.204320i
$481$	1.00560	+	0.843799i	0.0458514	+	0.0384739i
$482$	−17.8026	+	38.1778i	−0.810885	+	1.73895i
$483$	−15.1995	−	35.2753i	−0.691603	−	1.60508i
$484$	39.6216	−	6.98636i	1.80098	−	0.317562i
$485$	−16.1145	−	7.69385i	−0.731720	−	0.349360i
$486$	−5.92828	+	39.9146i	−0.268912	+	1.81056i
$487$	25.6571	+	25.6571i	1.16264	+	1.16264i	0.983896	+	0.178740i	$0.0572021\pi$
$487$	25.6571	+	25.6571i	1.16264	+	1.16264i	0.178740	+	0.983896i	$0.442798\pi$
$488$	48.7185	−	69.5772i	2.20538	−	3.14961i
$489$	−14.4965	+	36.4473i	−0.655554	+	1.64820i
$490$	−10.1972	−	0.985852i	−0.460661	−	0.0445363i
$491$	−8.85005	+	10.5471i	−0.399397	+	0.475983i	−0.927836	−	0.372988i	$-0.878333\pi$
$491$	−8.85005	+	10.5471i	−0.399397	+	0.475983i	0.528439	+	0.848971i	$0.322778\pi$
$492$	28.4410	+	43.2802i	1.28222	+	1.95122i
$493$	6.75555	−	3.15016i	0.304255	−	0.141876i
$494$	−14.4479	−	25.0245i	−0.650041	−	1.12590i
$495$	9.58284	+	4.24680i	0.430716	+	0.190879i
$496$	−25.2560	+	43.7446i	−1.13403	+	1.96419i
$497$	−1.82140	+	20.8187i	−0.0817009	+	0.933845i
$498$	13.2679	−	12.5076i	0.594548	−	0.560478i
$499$	16.6957	+	2.94390i	0.747401	+	0.131787i	0.534361	−	0.845256i	$-0.320552\pi$
$499$	16.6957	+	2.94390i	0.747401	+	0.131787i	0.213040	+	0.977043i	$0.431663\pi$
$500$	34.8714	−	39.3230i	1.55950	−	1.75858i
$501$	8.00085	−	4.30988i	0.357451	−	0.192551i
$502$	26.6995	+	2.33590i	1.19166	+	0.104256i
$503$	11.9228	−	3.19471i	0.531612	−	0.142445i	0.0169795	−	0.999856i	$-0.494595\pi$
$503$	11.9228	−	3.19471i	0.531612	−	0.142445i	0.514633	+	0.857411i	$0.327928\pi$
$504$	−34.1741	+	51.8687i	−1.52224	+	2.31042i
$505$	−22.6168	+	26.4602i	−1.00643	+	1.17746i
$506$	−10.3595	+	28.4624i	−0.460534	+	1.26531i
$507$	0.305587	+	5.28317i	0.0135716	+	0.234634i
$508$	10.1194	−	0.885334i	0.448976	−	0.0392803i
$509$	−1.17560	+	0.427885i	−0.0521077	+	0.0189657i	−0.367943	−	0.929849i	$-0.619938\pi$
$509$	−1.17560	+	0.427885i	−0.0521077	+	0.0189657i	0.315835	+	0.948814i	$0.397715\pi$
$510$	−5.62029	+	18.1431i	−0.248871	+	0.803388i
$511$	−2.09411	−	11.8763i	−0.0926380	−	0.525376i
$512$	33.5394	−	33.5394i	1.48224	−	1.48224i
$513$	2.49655	+	14.2588i	0.110226	+	0.629541i
$514$		−	14.7101i		−	0.648833i
$515$	17.0698	+	4.74097i	0.752183	+	0.208912i
$516$	3.73684	−	2.95228i	0.164505	−	0.129967i
$517$	1.07825	+	0.502796i	0.0474214	+	0.0221130i
$518$	−0.218888	−	2.50190i	−0.00961738	−	0.109927i
$519$	−13.4473	+	4.44996i	−0.590269	+	0.195332i
$520$	62.6401	+	0.570861i	2.74695	+	0.0250339i
$521$	−25.5030	+	14.7242i	−1.11731	+	0.645078i	−0.940712	−	0.339206i	$-0.889842\pi$
$521$	−25.5030	+	14.7242i	−1.11731	+	0.645078i	−0.176595	+	0.984284i	$0.556508\pi$
$522$	11.2582	+	28.4049i	0.492759	+	1.24325i
$523$	−2.91822	−	10.8910i	−0.127605	−	0.476228i	0.872314	−	0.488946i	$-0.162618\pi$
$523$	−2.91822	−	10.8910i	−0.127605	−	0.476228i	−0.999919	+	0.0127175i	$0.995952\pi$
$524$	−3.46929	+	2.91108i	−0.151556	+	0.127171i
$525$	−3.24371	−	25.4405i	−0.141567	−	1.11032i
$526$	8.75766	−	49.6671i	0.381852	−	2.16559i
$527$	6.31141	+	9.01363i	0.274929	+	0.392640i
$528$	22.9042	−	5.41870i	0.996776	−	0.235819i
$529$	21.2616	+	25.3386i	0.924417	+	1.10168i
$530$	8.32812	−	44.8378i	0.361751	−	1.94763i
$531$	30.4984	−	3.54000i	1.32352	−	0.153623i
$532$	−10.0377	+	37.4611i	−0.435188	+	1.62414i
$533$	−10.7709	−	23.0982i	−0.466538	−	1.00049i
$534$	−11.9313	−	36.0551i	−0.516319	−	1.56026i
$535$	11.3792	−	5.18048i	0.491964	−	0.223972i
$536$	4.76869	+	13.1019i	0.205976	+	0.565915i
$537$	1.07098	−	9.13112i	0.0462163	−	0.394037i
$538$	46.3594	+	32.4612i	1.99870	+	1.39950i
$539$	2.76550			0.119118
$540$	−51.1302	−	19.2094i	−2.20029	−	0.826640i
$541$	−2.55842			−0.109995			−0.0549975	−	0.998486i	$-0.517515\pi$
$541$	−2.55842			−0.109995			−0.0549975	+	0.998486i	$0.517515\pi$
$542$	−54.4318	−	38.1136i	−2.33805	−	1.63712i
$543$	32.0657	+	23.8920i	1.37607	+	1.02530i
$544$	5.52655	+	15.1841i	0.236949	+	0.651012i
$545$	5.14498	−	13.7447i	0.220387	−	0.588757i
$546$	35.3849	−	39.7296i	1.51433	−	1.70027i
$547$	1.78092	+	3.81919i	0.0761465	+	0.163297i	0.940696	−	0.339251i	$-0.110174\pi$
$547$	1.78092	+	3.81919i	0.0761465	+	0.163297i	−0.864549	+	0.502548i	$0.832396\pi$
$548$	−2.96039	+	11.0483i	−0.126462	+	0.471961i
$549$	32.5823	−	16.3308i	1.39058	−	0.696980i
$550$	−11.8999	+	16.3522i	−0.507413	+	0.697260i
$551$	7.04554	+	8.39655i	0.300150	+	0.357705i
$552$	26.0432	−	86.8637i	1.10847	−	3.69716i
$553$	22.3304	+	31.8912i	0.949586	+	1.35615i
$554$	−2.38429	+	13.5220i	−0.101299	+	0.574494i
$555$	1.20818	−	0.387631i	0.0512844	−	0.0164540i
$556$	35.0309	−	29.3944i	1.48564	−	1.24660i
$557$	5.11407	+	19.0860i	0.216690	+	0.808698i	0.985565	+	0.169299i	$0.0541502\pi$
$557$	5.11407	+	19.0860i	0.216690	+	0.808698i	−0.768875	+	0.639399i	$0.779183\pi$
$558$	−38.4088	+	23.6485i	−1.62598	+	1.00112i
$559$	−2.02964	+	1.17181i	−0.0858446	+	0.0495624i
$560$	−40.3485	−	41.0907i	−1.70503	−	1.73640i
$561$	1.03882	−	5.02088i	0.0438592	−	0.211982i
$562$	0.333542	+	3.81240i	0.0140696	+	0.160816i
$563$	−24.0516	−	11.2154i	−1.01365	−	0.472675i	−0.156469	−	0.987683i	$-0.550011\pi$
$563$	−24.0516	−	11.2154i	−1.01365	−	0.472675i	−0.857185	+	0.515008i	$0.827789\pi$
$564$	−5.76062	−	2.29122i	−0.242566	−	0.0964777i
$565$	1.36376	−	4.91019i	0.0573738	−	0.206573i
$566$		−	13.1138i		−	0.551216i
$567$	−23.4799	+	12.6117i	−0.986063	+	0.529644i
$568$	−34.8877	+	34.8877i	−1.46386	+	1.46386i
$569$	7.42425	+	42.1050i	0.311241	+	1.76513i	0.592567	+	0.805521i	$0.298114\pi$
$569$	7.42425	+	42.1050i	0.311241	+	1.76513i	−0.281327	+	0.959612i	$0.590774\pi$
$570$	−27.9092	−	1.07789i	−1.16899	−	0.0451480i
$571$	9.01463	−	3.28106i	0.377251	−	0.137308i	−0.146433	−	0.989221i	$-0.546779\pi$
$571$	9.01463	−	3.28106i	0.377251	−	0.137308i	0.523684	+	0.851912i	$0.324557\pi$
$572$	−29.3198	+	2.56515i	−1.22592	+	0.107254i
$573$	−5.49993	+	3.61420i	−0.229763	+	0.150986i
$574$	−16.6766	+	45.8187i	−0.696069	+	1.91243i
$575$	15.2027	+	34.2170i	0.633998	+	1.42695i
$576$	−13.4687	+	4.02051i	−0.561195	+	0.167521i
$577$	14.4782	−	3.87943i	0.602737	−	0.161503i	0.0554690	−	0.998460i	$-0.482335\pi$
$577$	14.4782	−	3.87943i	0.602737	−	0.161503i	0.547268	+	0.836958i	$0.315668\pi$
$578$	−34.5834	−	3.02565i	−1.43848	−	0.125851i
$579$	−0.631195	+	21.3980i	−0.0262316	+	0.889272i
$580$	−40.7931	+	6.81021i	−1.69384	+	0.282779i
$581$	11.8605	+	2.09132i	0.492055	+	0.0867626i
$582$	−34.2972	−	10.2829i	−1.42166	−	0.426239i
$583$	−1.07295	+	12.2639i	−0.0444370	+	0.507918i
$584$	14.2357	−	24.6569i	0.589077	−	1.02031i
$585$	23.5315	+	12.9908i	0.972906	+	0.537103i
$586$	−29.7304	−	51.4946i	−1.22815	−	2.12722i
$587$	3.64938	−	1.70173i	0.150626	−	0.0702381i	−0.345844	−	0.938292i	$-0.612407\pi$
$587$	3.64938	−	1.70173i	0.150626	−	0.0702381i	0.496470	+	0.868054i	$0.334629\pi$
$588$	−14.3868	+	0.832156i	−0.593302	+	0.0343175i
$589$	−10.4008	+	12.3951i	−0.428556	+	0.510733i
$590$	−5.70067	+	58.9649i	−0.234693	+	2.42755i
$591$	41.1433	−	6.00978i	1.69241	−	0.247209i
$592$	1.63421	−	2.33389i	0.0671655	−	0.0959223i
$593$	−6.31053	−	6.31053i	−0.259142	−	0.259142i	0.565563	−	0.824705i	$-0.308659\pi$
$593$	−6.31053	−	6.31053i	−0.259142	−	0.259142i	−0.824705	+	0.565563i	$0.808659\pi$
$594$	20.2945	+	5.46402i	0.832692	+	0.224192i
$595$	−11.8273	+	4.18311i	−0.484870	+	0.171491i
$596$	64.9028	−	11.4441i	2.65852	−	0.468769i
$597$	−11.3926	−	1.33622i	−0.466266	−	0.0546880i
$598$	−32.8260	+	70.3955i	−1.34235	+	2.87869i
$599$	−25.4844	−	21.3840i	−1.04127	−	0.873726i	−0.0491180	−	0.998793i	$-0.515641\pi$
$599$	−25.4844	−	21.3840i	−1.04127	−	0.873726i	−0.992148	+	0.125067i	$0.960085\pi$
$600$	32.7411	−	50.9332i	1.33665	−	2.07934i
$601$	−16.7184	−	6.08500i	−0.681958	−	0.248212i	−0.0222700	−	0.999752i	$-0.507089\pi$
$601$	−16.7184	−	6.08500i	−0.681958	−	0.248212i	−0.659688	+	0.751540i	$0.729312\pi$
$602$	4.33098	+	1.16048i	0.176518	+	0.0472978i
$603$	−0.871816	+	5.91878i	−0.0355031	+	0.241031i
$604$	−74.1818	−	42.8289i	−3.01841	−	1.74268i
$605$	−9.71937	+	16.4856i	−0.395148	+	0.670236i
$606$	−36.6652	+	59.3901i	−1.48942	+	2.41256i
$607$	−37.1718	+	26.0280i	−1.50876	+	1.05644i	−0.530833	+	0.847477i	$0.678121\pi$
$607$	−37.1718	+	26.0280i	−1.50876	+	1.05644i	−0.977923	+	0.208966i	$0.932990\pi$
$608$	−19.4639	+	13.6288i	−0.789365	+	0.552719i
$609$	−10.6015	+	17.1723i	−0.429596	+	0.695857i
$610$	17.5804	+	68.0868i	0.711809	+	2.75675i
$611$	2.64216	+	1.52545i	0.106890	+	0.0617131i
$612$	−3.89341	+	26.4325i	−0.157382	+	1.06847i
$613$	−35.3818	−	9.48053i	−1.42906	−	0.382915i	−0.540370	−	0.841427i	$-0.681716\pi$
$613$	−35.3818	−	9.48053i	−1.42906	−	0.382915i	−0.888688	+	0.458512i	$0.848383\pi$
$614$	−56.7222	−	20.6452i	−2.28912	−	0.833172i
$615$	−24.4393	−	3.09250i	−0.985488	−	0.124701i
$616$	24.7829	+	20.7953i	0.998533	+	0.837868i
$617$	15.3167	−	32.8468i	0.616628	−	1.32236i	−0.311551	−	0.950229i	$-0.600848\pi$
$617$	15.3167	−	32.8468i	0.616628	−	1.32236i	0.928179	−	0.372134i	$-0.121374\pi$
$618$	35.2808	+	4.13806i	1.41920	+	0.166457i
$619$	−33.7534	+	5.95163i	−1.35666	+	0.239216i	−0.804218	−	0.594334i	$-0.797416\pi$
$619$	−33.7534	+	5.95163i	−1.35666	+	0.239216i	−0.552444	+	0.833550i	$0.686305\pi$
$620$	−20.3576	−	57.5588i	−0.817582	−	2.31162i
$621$	27.5474	−	27.4813i	1.10544	−	1.10279i
$622$	−17.3342	−	17.3342i	−0.695037	−	0.695037i
$623$	14.3877	−	20.5478i	0.576433	−	0.823231i
$624$	59.7228	−	8.72368i	2.39083	−	0.349227i
$625$	3.44105	+	24.7621i	0.137642	+	0.990482i
$626$	51.4823	−	61.3542i	2.05764	−	2.45221i
$627$	7.52695	−	0.435371i	0.300597	−	0.0173870i
$628$	12.9699	−	6.04798i	0.517557	−	0.241341i
$629$	−0.310333	−	0.537512i	−0.0123738	−	0.0214320i
$630$	−14.2596	−	49.4079i	−0.568116	−	1.96846i
$631$	−15.6392	+	27.0879i	−0.622587	+	1.07835i	0.366415	+	0.930451i	$0.380585\pi$
$631$	−15.6392	+	27.0879i	−0.622587	+	1.07835i	−0.989002	+	0.147901i	$0.952748\pi$
$632$	−8.01088	+	91.5648i	−0.318656	+	3.64225i
$633$	−4.61985	−	1.38511i	−0.183623	−	0.0550531i
$634$	53.6285	+	9.45615i	2.12986	+	0.375552i
$635$	−2.80740	+	3.93261i	−0.111408	+	0.156061i
$636$	1.89147	−	64.1226i	0.0750018	−	2.54263i
$637$	7.06483	+	0.618092i	0.279919	+	0.0244897i
$638$	15.3718	−	4.11886i	0.608576	−	0.163067i
$639$	−20.2861	+	6.05555i	−0.802504	+	0.239554i
$640$	0.860650	+	10.9899i	0.0340202	+	0.434414i
$641$	1.87972	−	5.16450i	0.0742446	−	0.203985i	−0.897019	−	0.441992i	$-0.854272\pi$
$641$	1.87972	−	5.16450i	0.0742446	−	0.203985i	0.971263	+	0.238007i	$0.0764941\pi$
$642$	20.9512	−	13.7678i	0.826876	−	0.543371i
$643$	44.9817	−	3.93539i	1.77390	−	0.155197i	0.847271	−	0.531161i	$-0.178244\pi$
$643$	44.9817	−	3.93539i	1.77390	−	0.155197i	0.926634	+	0.375965i	$0.122689\pi$
$644$	97.9620	−	35.6552i	3.86024	−	1.40501i
$645$	−0.0874239	+	2.26360i	−0.00344231	+	0.0891294i
$646$	2.37242	+	13.4546i	0.0933414	+	0.529366i
$647$	18.1400	−	18.1400i	0.713158	−	0.713158i	−0.254037	−	0.967195i	$-0.581758\pi$
$647$	18.1400	−	18.1400i	0.713158	−	0.713158i	0.967195	+	0.254037i	$0.0817584\pi$
$648$	−61.6039	−	12.8231i	−2.42003	−	0.503738i
$649$		−	15.9914i		−	0.627719i
$650$	−34.0546	+	39.1142i	−1.33573	+	1.53418i
$651$	−27.6826	−	11.0104i	−1.08497	−	0.431532i
$652$	−96.4835	−	44.9910i	−3.77858	−	1.76198i
$653$	0.635049	+	7.25864i	0.0248514	+	0.284052i	0.998444	+	0.0557608i	$0.0177584\pi$
$653$	0.635049	+	7.25864i	0.0248514	+	0.284052i	−0.973593	+	0.228292i	$0.926686\pi$
$654$	5.96228	−	28.8171i	0.233144	−	1.12684i
$655$	0.0196313	−	2.15413i	0.000767060	−	0.0841688i
$656$	−47.9046	+	27.6577i	−1.87036	+	1.07985i
$657$	10.4030	−	6.40515i	0.405858	−	0.249889i
$658$	−1.51070	−	5.63801i	−0.0588932	−	0.219793i
$659$	20.4475	−	17.1575i	0.796520	−	0.668360i	−0.150830	−	0.988560i	$-0.548195\pi$
$659$	20.4475	−	17.1575i	0.796520	−	0.668360i	0.947350	+	0.320200i	$0.103750\pi$
$660$	−13.0087	+	25.2995i	−0.506364	+	0.984782i
$661$	−3.17425	+	18.0020i	−0.123464	+	0.700198i	0.858745	+	0.512404i	$0.171245\pi$
$661$	−3.17425	+	18.0020i	−0.123464	+	0.700198i	−0.982208	+	0.187794i	$0.939866\pi$
$662$	−0.356499	−	0.509133i	−0.0138557	−	0.0197880i
$663$	3.77599	−	12.5943i	0.146647	−	0.489123i
$664$	18.2766	+	21.7813i	0.709271	+	0.845277i
$665$	−10.4430	−	15.2072i	−0.404961	−	0.589710i
$666$	2.27449	−	1.14001i	0.0881345	−	0.0441745i
$667$	7.62568	−	28.4594i	0.295267	−	1.10195i
$668$	10.4239	+	22.3541i	0.403312	+	0.864905i
$669$	25.4097	−	28.5297i	0.982397	−	1.10302i
$670$	−10.8106	−	4.04667i	−0.417649	−	0.156336i
$671$	−6.49238	−	17.8377i	−0.250635	−	0.688615i
$672$	−35.0813	−	26.1389i	−1.35329	−	1.00833i
$673$	−17.8466	−	12.4963i	−0.687934	−	0.481697i	0.176592	−	0.984284i	$-0.443493\pi$
$673$	−17.8466	−	12.4963i	−0.687934	−	0.481697i	−0.864526	+	0.502587i	$0.832382\pi$
$674$	−44.3443			−1.70808
$675$	22.7481	−	12.5508i	0.875575	−	0.483082i
$676$	−14.3629			−0.552418
$677$	−8.63710	−	6.04776i	−0.331951	−	0.232434i	0.395704	−	0.918378i	$-0.370501\pi$
$677$	−8.63710	−	6.04776i	−0.331951	−	0.232434i	−0.727654	+	0.685944i	$0.759390\pi$
$678$	1.19033	−	10.1487i	0.0457143	−	0.389758i
$679$	−8.08857	−	22.2232i	−0.310411	−	0.852846i
$680$	−27.7384	−	10.3832i	−1.06372	−	0.398177i
$681$	−4.04543	−	12.2248i	−0.155021	−	0.468455i
$682$	9.92842	+	21.2916i	0.380179	+	0.815296i
$683$	6.15162	−	22.9581i	0.235385	−	0.878469i	−0.742590	−	0.669746i	$-0.766403\pi$
$683$	6.15162	−	22.9581i	0.235385	−	0.878469i	0.977975	−	0.208723i	$-0.0669306\pi$
$684$	−39.0261	+	4.52981i	−1.49220	+	0.173202i
$685$	−3.07992	−	4.48503i	−0.117678	−	0.171364i
$686$	25.7716	+	30.7134i	0.983965	+	1.17264i
$687$	−7.83183	+	1.85287i	−0.298803	+	0.0706912i
$688$	2.91759	+	4.16675i	0.111232	+	0.158856i
$689$	−5.48198	+	31.0899i	−0.208847	+	1.18443i
$690$	40.6567	+	63.1153i	1.54778	+	2.40276i
$691$	29.8109	−	25.0143i	1.13406	−	0.951591i	0.134833	−	0.990868i	$-0.456950\pi$
$691$	29.8109	−	25.0143i	1.13406	−	0.951591i	0.999228	+	0.0392778i	$0.0125057\pi$
$692$	−9.94983	−	37.1333i	−0.378236	−	1.41160i
$693$	5.11489	+	12.9051i	0.194299	+	0.490223i
$694$	60.8414	−	35.1268i	2.30951	−	1.33339i
$695$	−0.198226	+	21.7512i	−0.00751915	+	0.825070i
$696$	−45.2335	+	14.9687i	−1.71457	+	0.567386i
$697$	1.05023	+	12.0042i	0.0397803	+	0.454691i
$698$	−44.8830	−	20.9293i	−1.69885	−	0.792185i
$699$	19.4057	−	15.3314i	0.733992	−	0.579888i
$700$	69.4405	−	4.80182i	2.62460	−	0.181492i
$701$			37.4202i			1.41334i	0.707542	+	0.706671i	$0.249804\pi$
$701$			37.4202i			1.41334i	−0.707542	+	0.706671i	$0.750196\pi$
$702$	50.6237	+	18.4944i	1.91067	+	0.698027i
$703$	0.645364	−	0.645364i	0.0243404	−	0.0243404i
$704$	1.27126	+	7.20968i	0.0479125	+	0.271725i
$705$	2.60885	−	1.37480i	0.0982548	−	0.0517781i
$706$	74.0671	−	26.9582i	2.78755	−	1.01459i
$707$	−45.9247	+	4.01789i	−1.72718	+	0.151108i
$708$	4.81193	+	83.1915i	0.180843	+	3.12653i
$709$	10.2864	−	28.2616i	0.386313	−	1.06139i	−0.582335	−	0.812949i	$-0.697861\pi$
$709$	10.2864	−	28.2616i	0.386313	−	1.06139i	0.968648	−	0.248437i	$-0.0799168\pi$
$710$	−3.18911	−	40.7226i	−0.119685	−	1.52829i
$711$	−21.6987	+	32.9337i	−0.813763	+	1.23511i
$712$	57.2037	−	15.3277i	2.14380	−	0.574429i
$713$	43.3288	+	3.79078i	1.62268	+	0.141966i
$714$	−22.1460	+	11.9296i	−0.828795	+	0.446454i
$715$	8.13410	−	11.3943i	0.304198	−	0.426122i
$716$	24.5733	+	4.33293i	0.918347	+	0.161929i
$717$	−25.6705	+	24.1995i	−0.958683	+	0.903745i
$718$	7.04570	−	80.5327i	0.262943	−	3.00546i
$719$	−1.80566	+	3.12750i	−0.0673399	+	0.116636i	−0.897730	−	0.440547i	$-0.854785\pi$
$719$	−1.80566	+	3.12750i	−0.0673399	+	0.116636i	0.830390	+	0.557183i	$0.188118\pi$
$720$	23.6369	−	53.3363i	0.880895	−	1.98773i
$721$	11.7313	+	20.3192i	0.436896	+	0.756726i
$722$	26.3676	−	12.2954i	0.981302	−	0.457589i
$723$	−15.4789	−	23.5550i	−0.575665	−	0.876020i
$724$	−69.7617	+	83.1388i	−2.59268	+	3.08983i
$725$	10.1451	−	16.8548i	0.376780	−	0.625970i
$726$	−14.1819	+	35.6562i	−0.526338	+	1.32333i
$727$	−17.2585	+	24.6477i	−0.640083	+	0.914133i	−0.999821	−	0.0189200i	$-0.993977\pi$
$727$	−17.2585	+	24.6477i	−0.640083	+	0.914133i	0.359738	+	0.933053i	$0.382866\pi$
$728$	58.6635	+	58.6635i	2.17421	+	2.17421i
$729$	−20.6414	−	17.4049i	−0.764498	−	0.644626i
$730$	7.85968	+	22.2223i	0.290900	+	0.822486i
$731$	1.09125	−	0.192418i	0.0403615	−	0.00711682i
$732$	39.1424	+	90.8423i	1.44675	+	3.35763i
$733$	−17.2990	+	37.0978i	−0.638953	+	1.37024i	0.273824	+	0.961780i	$0.411712\pi$
$733$	−17.2990	+	37.0978i	−0.638953	+	1.37024i	−0.912777	+	0.408459i	$0.866066\pi$
$734$	−2.82259	−	2.36844i	−0.104184	−	0.0874206i
$735$	4.14551	−	5.45918i	0.152910	−	0.201365i
$736$	60.0186	+	21.8450i	2.21231	+	0.805217i
$737$	3.00982	+	0.806480i	0.110868	+	0.0297071i
$738$	−49.3750	+	1.39709i	−1.81752	+	0.0514276i
$739$	−7.88425	−	4.55198i	−0.290027	−	0.167447i	0.347927	−	0.937522i	$-0.386886\pi$
$739$	−7.88425	−	4.55198i	−0.290027	−	0.167447i	−0.637954	+	0.770074i	$0.720219\pi$
$740$	0.860951	+	3.33436i	0.0316492	+	0.122574i
$741$	19.3259	+	0.570071i	0.709954	+	0.0209421i
$742$	49.4750	−	34.6428i	1.81629	−	1.27178i
$743$	−39.7131	+	27.8074i	−1.45693	+	1.02016i	−0.466149	+	0.884706i	$0.654359\pi$
$743$	−39.7131	+	27.8074i	−1.45693	+	1.02016i	−0.990784	+	0.135449i	$0.956752\pi$
$744$	−33.3566	−	61.9230i	−1.22291	−	2.27021i
$745$	−15.9210	+	27.0045i	−0.583299	+	0.989370i
$746$	−22.0487	−	12.7298i	−0.807262	−	0.466073i
$747$	2.45757	+	11.9503i	0.0899177	+	0.437240i
$748$	13.4415	+	3.60163i	0.491468	+	0.131689i
$749$	15.5600	+	5.66337i	0.568550	+	0.206935i
$750$	14.4417	+	48.0029i	0.527337	+	1.75282i
$751$	−31.7068	−	26.6051i	−1.15700	−	0.970835i	−0.157137	−	0.987577i	$-0.550226\pi$
$751$	−31.7068	−	26.6051i	−1.15700	−	0.970835i	−0.999860	+	0.0167415i	$0.994671\pi$
$752$	2.79847	−	6.00134i	0.102050	−	0.218846i
$753$	−10.7146	+	14.3802i	−0.390461	+	0.524042i
$754$	40.1899	−	7.08656i	1.46363	−	0.258077i
$755$	38.4128	−	13.5860i	1.39799	−	0.494445i
$756$	−30.4922	−	65.5963i	−1.10899	−	2.38571i
$757$	−27.0538	−	27.0538i	−0.983288	−	0.983288i	0.0165746	−	0.999863i	$-0.494724\pi$
$757$	−27.0538	−	27.0538i	−0.983288	−	0.983288i	−0.999863	+	0.0165746i	$0.994724\pi$
$758$	−8.55950	+	12.2242i	−0.310895	+	0.444004i
$759$	−12.5636	−	15.9024i	−0.456032	−	0.577221i
$760$	4.19113	−	43.3510i	0.152028	−	1.57250i
$761$	22.5010	−	26.8156i	0.815660	−	0.972066i	−0.184281	−	0.982874i	$-0.558996\pi$
$761$	22.5010	−	26.8156i	0.815660	−	0.972066i	0.999942	+	0.0108074i	$0.00344017\pi$
$762$	−4.35166	+	8.65623i	−0.157644	+	0.313582i
$763$	17.6156	−	8.21429i	0.637728	−	0.297377i
$764$	−8.93086	−	15.4687i	−0.323107	−	0.559638i
$765$	−8.35417	−	9.57703i	−0.302046	−	0.346258i
$766$	3.69820	−	6.40547i	0.133621	−	0.231439i
$767$	3.57411	−	40.8523i	0.129054	−	1.47509i
$768$	8.82550	+	37.3043i	0.318463	+	1.34610i
$769$	6.45291	+	1.13782i	0.232698	+	0.0410309i	0.288781	−	0.957395i	$-0.406750\pi$
$769$	6.45291	+	1.13782i	0.232698	+	0.0410309i	−0.0560832	+	0.998426i	$0.517861\pi$
$770$	−26.4183	+	4.41042i	−0.952050	+	0.158940i
$771$	8.37510	+	5.17047i	0.301622	+	0.186210i
$772$	−57.8799	−	5.06383i	−2.08314	−	0.182251i
$773$	5.36547	−	1.43767i	0.192983	−	0.0517095i	−0.161033	−	0.986949i	$-0.551483\pi$
$773$	5.36547	−	1.43767i	0.192983	−	0.0517095i	0.354016	+	0.935239i	$0.384816\pi$
$774$	0.523705	+	4.51191i	0.0188242	+	0.162177i
$775$	27.1039	+	10.4283i	0.973602	+	0.374594i
$776$	19.0963	−	52.4668i	0.685519	−	1.88345i
$777$	1.50138	+	0.754775i	0.0538618	+	0.0270774i
$778$	−32.8782	+	2.87647i	−1.17874	+	0.103126i
$779$	−16.6509	+	6.06042i	−0.596579	+	0.217137i
$780$	−38.8870	+	61.7235i	−1.39238	+	2.21005i
$781$	1.91473	+	10.8590i	0.0685144	+	0.388565i
$782$	25.9681	−	25.9681i	0.928618	−	0.928618i
$783$	−20.1294	−	3.57429i	−0.719365	−	0.127735i
$784$		−	15.3922i		−	0.549723i
$785$	−1.82167	+	6.55888i	−0.0650181	+	0.234096i
$786$	−0.624320	−	4.27413i	−0.0222687	−	0.152453i
$787$	−28.1849	−	13.1429i	−1.00468	−	0.468492i	−0.150582	−	0.988597i	$-0.548115\pi$
$787$	−28.1849	−	13.1429i	−1.00468	−	0.468492i	−0.854102	+	0.520105i	$0.825893\pi$
$788$	9.83559	+	112.421i	0.350378	+	4.00484i
$789$	25.1995	+	22.4437i	0.897126	+	0.799018i
$790$	−53.3152	−	54.2959i	−1.89687	−	1.93176i
$791$	5.84490	−	3.37455i	0.207821	−	0.119985i
$792$	−10.3336	+	31.1017i	−0.367190	+	1.10515i
$793$	−12.5989	−	47.0197i	−0.447400	−	1.66972i
$794$	−7.12249	+	5.97648i	−0.252768	+	0.212097i
$795$	22.6009	+	20.5017i	0.801572	+	0.727121i
$796$	5.40604	−	30.6592i	0.191612	−	1.08669i
$797$	−2.77214	−	3.95902i	−0.0981941	−	0.140236i	0.767049	−	0.641589i	$-0.221725\pi$
$797$	−2.77214	−	3.95902i	−0.0981941	−	0.140236i	−0.865243	+	0.501353i	$0.832836\pi$
$798$	−25.3732	−	26.9156i	−0.898202	−	0.952802i
$799$	−0.927217	−	1.10501i	−0.0328026	−	0.0390926i
$800$	34.4818	+	25.0933i	1.21912	+	0.887181i
$801$	24.7215	+	5.88003i	0.873493	+	0.207761i
$802$	−13.7983	+	51.4959i	−0.487235	+	1.81838i
$803$	−2.68909	−	5.76678i	−0.0948961	−	0.203505i
$804$	−15.9005	−	3.28983i	−0.560769	−	0.116024i
$805$	−17.3840	+	46.4408i	−0.612705	+	1.63682i
$806$	20.6048	+	56.6111i	0.725772	+	1.99404i
$807$	−34.7766	+	14.9846i	−1.22419	+	0.527485i
$808$	−89.1550	−	62.4270i	−3.13646	−	2.19617i
$809$	−27.0458			−0.950881			−0.475440	−	0.879748i	$-0.657711\pi$
$809$	−27.0458			−0.950881			−0.475440	+	0.879748i	$0.657711\pi$
$810$	41.2078	−	31.8713i	1.44790	−	1.11984i
$811$	−47.9089			−1.68231			−0.841154	−	0.540795i	$-0.818123\pi$
$811$	−47.9089			−1.68231			−0.841154	+	0.540795i	$0.818123\pi$
$812$	−44.8675	−	31.4166i	−1.57454	−	1.10251i
$813$	40.8321	−	17.5939i	1.43204	−	0.617044i
$814$	−0.453216	−	1.24520i	−0.0158852	−	0.0436443i
$815$	46.0872	−	20.9816i	1.61436	−	0.734954i
$816$	−27.9453	−	5.78190i	−0.978280	−	0.202407i
$817$	0.688628	+	1.47677i	0.0240921	+	0.0516656i
$818$	−11.2790	+	42.0939i	−0.394362	+	1.47178i
$819$	10.1824	+	34.1109i	0.355801	+	1.19193i
$820$	12.2095	−	65.7346i	0.426373	−	2.29555i
$821$	−27.5109	−	32.7862i	−0.960137	−	1.14425i	−0.989479	−	0.144678i	$-0.953786\pi$
$821$	−27.5109	−	32.7862i	−0.960137	−	1.14425i	0.0293416	−	0.999569i	$-0.490659\pi$
$822$	−7.48327	−	7.93817i	−0.261009	−	0.276875i
$823$	6.97458	+	9.96073i	0.243119	+	0.347209i	0.922104	−	0.386943i	$-0.126469\pi$
$823$	6.97458	+	9.96073i	0.243119	+	0.347209i	−0.678985	+	0.734152i	$0.737580\pi$
$824$	−9.61888	+	54.5514i	−0.335090	+	1.90039i
$825$	−5.12733	−	12.5228i	−0.178511	−	0.435988i
$826$	−60.1008	+	50.4305i	−2.09117	+	1.75470i
$827$	3.49901	+	13.0585i	0.121673	+	0.454088i	0.999699	−	0.0245234i	$-0.00780681\pi$
$827$	3.49901	+	13.0585i	0.121673	+	0.454088i	−0.878027	+	0.478612i	$0.841140\pi$
$828$	70.1444	+	78.9478i	2.43769	+	2.74363i
$829$	22.0957	−	12.7570i	0.767415	−	0.443068i	−0.0645364	−	0.997915i	$-0.520557\pi$
$829$	22.0957	−	12.7570i	0.767415	−	0.443068i	0.831952	+	0.554848i	$0.187224\pi$
$830$	−23.5389	−	0.214518i	−0.817048	−	0.00744605i
$831$	−6.86062	−	6.11036i	−0.237992	−	0.211966i
$832$	1.63623	+	18.7022i	0.0567261	+	0.648383i
$833$	−3.03892	−	1.41707i	−0.105292	−	0.0490986i
$834$	6.30404	+	43.1578i	0.218291	+	1.49443i
$835$	−11.3044	−	3.13970i	−0.391206	−	0.108654i
$836$			20.4628i			0.707721i
$837$	0.0362537	−	30.1801i	0.00125311	−	1.04318i
$838$	0.996030	−	0.996030i	0.0344073	−	0.0344073i
$839$	−6.29080	−	35.6769i	−0.217183	−	1.23170i	−0.877078	−	0.480347i	$-0.840511\pi$
$839$	−6.29080	−	35.6769i	−0.217183	−	1.23170i	0.659896	−	0.751357i	$-0.270600\pi$
$840$	78.2006	−	17.7499i	2.69818	−	0.612429i
$841$	12.7044	−	4.62403i	0.438083	−	0.159449i
$842$	19.2811	−	1.68687i	0.664469	−	0.0581335i
$843$	−2.28781	−	1.15013i	−0.0787963	−	0.0396125i
$844$	4.47705	−	12.3006i	0.154106	−	0.423404i
$845$	4.43900	−	5.19334i	0.152706	−	0.178656i
$846$	4.74576	−	3.52719i	0.163163	−	0.121267i
$847$	−24.4816	+	6.55983i	−0.841199	+	0.225398i
$848$	68.2584	+	5.97184i	2.34400	+	0.205074i
$849$	7.46630	+	4.60941i	0.256243	+	0.158195i
$850$	21.4554	−	11.8713i	0.735916	−	0.407182i
$851$	−2.41605	−	0.426015i	−0.0828212	−	0.0146036i
$852$	−13.2284	−	55.9149i	−0.453199	−	1.91561i
$853$	1.06118	−	12.1293i	0.0363341	−	0.415300i	−0.956146	−	0.292891i	$-0.905383\pi$
$853$	1.06118	−	12.1293i	0.0363341	−	0.415300i	0.992480	−	0.122409i	$-0.0390619\pi$
$854$	−46.5651	+	80.6531i	−1.59342	+	2.75989i
$855$	10.4235	−	15.5111i	0.356478	−	0.530468i
$856$	19.5466	+	33.8558i	0.668090	+	1.15717i
$857$	38.1058	−	17.7690i	1.30167	−	0.606978i	0.356724	−	0.934210i	$-0.383894\pi$
$857$	38.1058	−	17.7690i	1.30167	−	0.606978i	0.944944	+	0.327232i	$0.106116\pi$
$858$	12.6084	−	25.0804i	0.430444	−	0.856230i
$859$	16.1180	−	19.2086i	0.549938	−	0.655390i	−0.417447	−	0.908701i	$-0.637075\pi$
$859$	16.1180	−	19.2086i	0.549938	−	0.655390i	0.967385	+	0.253311i	$0.0815195\pi$
$860$	−6.11963	−	0.591640i	−0.208678	−	0.0201748i
$861$	−20.2249	−	25.5997i	−0.689264	−	0.872434i
$862$	22.2244	−	31.7398i	0.756967	−	1.08106i
$863$	−16.2331	−	16.2331i	−0.552582	−	0.552582i	0.374603	−	0.927185i	$-0.377779\pi$
$863$	−16.2331	−	16.2331i	−0.552582	−	0.552582i	−0.927185	+	0.374603i	$0.877779\pi$
$864$	11.5220	−	42.7949i	0.391986	−	1.45591i
$865$	16.5018	+	7.87879i	0.561078	+	0.267887i
$866$	−89.7060	+	15.8176i	−3.04833	+	0.537503i
$867$	13.8784	−	18.6264i	0.471336	−	0.632585i
$868$	34.1717	−	73.2814i	1.15986	−	2.48733i
$869$	15.7358	+	13.2039i	0.533800	+	0.447911i
$870$	14.9117	−	36.5187i	0.505555	−	1.23810i
$871$	7.50875	+	2.73296i	0.254424	+	0.0926028i
$872$	44.3246	+	11.8767i	1.50102	+	0.402197i
$873$	17.9097	−	15.9126i	0.606152	−	0.538560i
$874$	46.7680	+	27.0015i	1.58195	+	0.913339i
$875$	−19.7251	+	26.5924i	−0.666830	+	0.898988i
$876$	15.7246	+	29.1911i	0.531285	+	0.986275i
$877$	−45.5180	+	31.8721i	−1.53703	+	1.07624i	−0.569985	+	0.821655i	$0.693051\pi$
$877$	−45.5180	+	31.8721i	−1.53703	+	1.07624i	−0.967049	+	0.254588i	$0.918060\pi$
$878$	80.7392	−	56.5342i	2.72481	−	1.90794i
$879$	39.7682	+	1.17307i	1.34135	+	0.0395668i
$880$	−26.1750	−	15.4319i	−0.882358	−	0.520208i
$881$	20.5994	+	11.8931i	0.694013	+	0.400688i	0.805114	−	0.593121i	$-0.202104\pi$
$881$	20.5994	+	11.8931i	0.694013	+	0.400688i	−0.111101	+	0.993809i	$0.535438\pi$
$882$	6.53293	−	12.0929i	0.219975	−	0.407189i
$883$	25.1153	+	6.72963i	0.845198	+	0.226470i	0.655333	−	0.755340i	$-0.272528\pi$
$883$	25.1153	+	6.72963i	0.845198	+	0.226470i	0.189865	+	0.981810i	$0.439195\pi$
$884$	33.5330	+	12.2050i	1.12784	+	0.410499i
$885$	−31.5676	−	23.9714i	−1.06113	−	0.805788i
$886$	56.7260	+	47.5988i	1.90575	+	1.59911i
$887$	−5.53565	+	11.8712i	−0.185869	+	0.398597i	−0.977058	−	0.212975i	$-0.931685\pi$
$887$	−5.53565	+	11.8712i	−0.185869	+	0.398597i	0.791189	+	0.611572i	$0.209463\pi$
$888$	1.56992	+	3.64349i	0.0526831	+	0.122268i
$889$	−6.30200	+	1.11121i	−0.211362	+	0.0372689i
$890$	−21.1248	+	44.2450i	−0.708104	+	1.48309i
$891$	−10.2443	+	9.63400i	−0.343196	+	0.322751i
$892$	73.3199	+	73.3199i	2.45493	+	2.45493i
$893$	1.21666	−	1.73756i	0.0407138	−	0.0581454i
$894$	−23.2308	+	58.4073i	−0.776954	+	1.95343i
$895$	−9.16135	+	7.54609i	−0.306230	+	0.252238i
$896$	−9.38428	+	11.1838i	−0.313507	+	0.373623i
$897$	−28.5413	−	43.4328i	−0.952966	−	1.45018i
$898$	−58.4031	+	27.2338i	−1.94894	+	0.908804i
$899$	−11.4261	−	19.7906i	−0.381082	−	0.660054i
$900$	30.4418	+	63.6039i	1.01473	+	2.12013i
$901$	7.46317	−	12.9266i	0.248634	−	0.430647i
$902$	−2.24223	+	25.6289i	−0.0746582	+	0.853347i
$903$	−2.18302	+	2.05792i	−0.0726464	+	0.0684834i
$904$	15.6919	+	2.76691i	0.521906	+	0.0920261i
$905$	−8.50078	−	50.9195i	−0.282575	−	1.69262i
$906$	71.9264	−	38.7452i	2.38959	−	1.28722i
$907$	−41.8194	−	3.65873i	−1.38859	−	0.121486i	−0.631795	−	0.775136i	$-0.717681\pi$
$907$	−41.8194	−	3.65873i	−1.38859	−	0.121486i	−0.756797	+	0.653650i	$0.773237\pi$
$908$	33.7576	−	9.04532i	1.12029	−	0.300180i
$909$	−20.9260	−	41.7503i	−0.694070	−	1.38477i
$910$	−68.4748	+	5.36246i	−2.26992	+	0.177764i
$911$	18.7788	−	51.5943i	0.622169	−	1.70940i	−0.0794445	−	0.996839i	$-0.525315\pi$
$911$	18.7788	−	51.5943i	0.622169	−	1.70940i	0.701614	−	0.712557i	$-0.252463\pi$
$912$	−2.42319	−	41.8936i	−0.0802399	−	1.38724i
$913$	6.33028	−	0.553828i	0.209502	−	0.0183290i
$914$	8.96418	−	3.26269i	0.296509	−	0.107920i
$915$	−44.9443	−	13.9227i	−1.48581	−	0.460270i
$916$	−3.79298	−	21.5110i	−0.125323	−	0.710745i
$917$	2.01738	−	2.01738i	0.0666196	−	0.0666196i
$918$	−19.5011	−	16.4034i	−0.643634	−	0.541392i
$919$			38.4394i			1.26800i	0.773333	+	0.634000i	$0.218588\pi$
$919$			38.4394i			1.26800i	−0.773333	+	0.634000i	$0.781412\pi$
$920$	−101.917	+	57.6098i	−3.36010	+	1.89934i
$921$	31.6916	−	25.0379i	1.04427	−	0.825026i
$922$	35.7998	+	16.6937i	1.17900	+	0.549778i
$923$	2.46444	+	28.1686i	0.0811179	+	0.927182i
$924$	−35.7684	+	11.8365i	−1.17669	+	0.389391i
$925$	−1.47173	−	0.719219i	−0.0483902	−	0.0236478i
$926$	−25.2375	+	14.5709i	−0.829356	+	0.478829i
$927$	−14.7569	+	18.6325i	−0.484681	+	0.611971i
$928$	−8.68545	−	32.4145i	−0.285114	−	1.06406i
$929$	−17.4189	+	14.6162i	−0.571497	+	0.479543i	−0.882142	−	0.470983i	$-0.843899\pi$
$929$	−17.4189	+	14.6162i	−0.571497	+	0.479543i	0.310645	+	0.950526i	$0.399455\pi$
$930$	56.9131	+	12.3173i	1.86625	+	0.403899i
$931$	0.856201	−	4.85576i	0.0280609	−	0.159141i
$932$	38.4998	+	54.9834i	1.26110	+	1.80104i
$933$	15.9620	−	3.77630i	0.522571	−	0.123631i
$934$	−29.0481	−	34.6182i	−0.950482	−	1.13274i
$935$	−5.45651	+	3.74705i	−0.178447	+	0.122542i
$936$	−33.3499	+	77.1439i	−1.09008	+	2.52153i
$937$	−0.558400	+	2.08398i	−0.0182421	+	0.0680806i	−0.974447	−	0.224618i	$-0.927887\pi$
$937$	−0.558400	+	2.08398i	−0.0182421	+	0.0680806i	0.956205	+	0.292699i	$0.0945532\pi$
$938$	−6.46077	−	13.8552i	−0.210951	−	0.452387i
$939$	16.8361	+	50.8767i	0.549425	+	1.66030i
$940$	3.31622	+	7.28424i	0.108163	+	0.237586i
$941$	15.3914	+	42.2876i	0.501747	+	1.37854i	0.889568	+	0.456803i	$0.151006\pi$
$941$	15.3914	+	42.2876i	0.501747	+	1.37854i	−0.387821	+	0.921735i	$0.626772\pi$
$942$	−1.59001	+	13.5563i	−0.0518052	+	0.441688i
$943$	39.0167	+	27.3198i	1.27056	+	0.889654i
$944$	−89.0054			−2.89688
$945$	33.1423	+	9.24787i	1.07812	+	0.300833i
$946$	2.36576			0.0769175
$947$	13.6646	+	9.56806i	0.444040	+	0.310920i	0.774127	−	0.633030i	$-0.218189\pi$
$947$	13.6646	+	9.56806i	0.444040	+	0.310920i	−0.330087	+	0.943950i	$0.607078\pi$
$948$	−85.8346	−	63.9549i	−2.78778	−	2.07716i
$949$	−5.58076	−	15.3330i	−0.181159	−	0.497731i
$950$	25.0275	+	25.9569i	0.812001	+	0.842153i
$951$	−24.2338	+	27.2094i	−0.785835	+	0.882324i
$952$	−16.5774	−	35.5504i	−0.537277	−	1.15220i
$953$	4.70396	−	17.5554i	0.152376	−	0.568676i	−0.846940	−	0.531689i	$-0.821557\pi$
$953$	4.70396	−	17.5554i	0.152376	−	0.568676i	0.999316	−	0.0369865i	$-0.0117759\pi$
$954$	51.0925	+	33.6627i	1.65418	+	1.08987i
$955$	8.35337	+	1.55155i	0.270309	+	0.0502068i
$956$	−61.5462	−	73.3479i	−1.99055	−	2.37224i
$957$	−3.05802	+	10.1996i	−0.0988516	+	0.329707i
$958$	−33.9991	−	48.5557i	−1.09846	−	1.56876i
$959$	1.25123	−	7.09611i	0.0404045	−	0.229145i
$960$	16.1378	+	8.29788i	0.520845	+	0.267813i
$961$	2.09504	−	1.75795i	0.0675821	−	0.0567081i
$962$	−0.879497	−	3.28233i	−0.0283561	−	0.105826i
$963$	0.474451	+	16.7677i	0.0152890	+	0.540332i
$964$	66.2491	−	38.2489i	2.13374	−	1.23192i
$965$	19.7194	−	19.3632i	0.634790	−	0.623325i
$966$	−20.1455	+	97.3678i	−0.648170	+	3.13276i
$967$	2.92397	+	33.4211i	0.0940285	+	1.07475i	0.885842	+	0.463988i	$0.153582\pi$
$967$	2.92397	+	33.4211i	0.0940285	+	1.07475i	−0.791813	+	0.610763i	$0.790863\pi$
$968$	−54.2314	−	25.2885i	−1.74306	−	0.812804i
$969$	−8.49422	−	3.37848i	−0.272874	−	0.108532i
$970$	22.7466	+	40.2407i	0.730349	+	1.29205i
$971$			23.4452i			0.752393i	0.926540	+	0.376196i	$0.122768\pi$
$971$			23.4452i			0.752393i	−0.926540	+	0.376196i	$0.877232\pi$
$972$	50.3943	−	53.2010i	1.61640	−	1.70642i
$973$	−20.3704	+	20.3704i	−0.653044	+	0.653044i
$974$	−16.3102	−	92.5000i	−0.522614	−	2.96389i
$975$	−10.2996	−	33.1371i	−0.329850	−	1.06124i
$976$	−99.2811	+	36.1353i	−3.17791	+	1.15666i
$977$	22.2971	−	1.95075i	0.713349	−	0.0624099i	0.275297	−	0.961359i	$-0.411224\pi$
$977$	22.2971	−	1.95075i	0.713349	−	0.0624099i	0.438052	+	0.898949i	$0.355668\pi$
$978$	84.8550	−	55.7614i	2.71336	−	1.78305i
$979$	4.52670	−	12.4370i	0.144674	−	0.397488i
$980$	14.1422	+	12.0880i	0.451755	+	0.386137i
$981$	14.3112	+	13.5236i	0.456921	+	0.431774i
$982$	34.4262	−	9.22446i	1.09858	−	0.294365i
$983$	−2.49907	−	0.218640i	−0.0797078	−	0.00697353i	0.0472321	−	0.998884i	$-0.484960\pi$
$983$	−2.49907	−	0.218640i	−0.0797078	−	0.00697353i	−0.126940	+	0.991910i	$0.540516\pi$
$984$	2.27107	−	76.9911i	0.0723989	−	2.45439i
$985$	−43.6892	−	31.1887i	−1.39205	−	0.993754i
$986$	−19.0022	−	3.35059i	−0.605152	−	0.106705i
$987$	3.74097	+	1.12161i	0.119077	+	0.0357011i
$988$	−4.57346	+	52.2749i	−0.145501	+	1.66309i
$989$	2.18999	−	3.79317i	0.0696376	−	0.120616i
$990$	−14.0146	−	23.2335i	−0.445412	−	0.738408i
$991$	−11.7772	−	20.3987i	−0.374116	−	0.647987i	0.616079	−	0.787685i	$-0.288720\pi$
$991$	−11.7772	−	20.3987i	−0.374116	−	0.647987i	−0.990194	+	0.139697i	$0.955387\pi$
$992$	44.8975	−	20.9361i	1.42550	−	0.664720i
$993$	0.415179	−	0.0240146i	0.0131753	−	0.000762081i
$994$	34.7731	−	41.4409i	1.10294	−	1.31443i
$995$	9.41498	+	11.4303i	0.298475	+	0.362364i
$996$	−32.7650	+	4.78597i	−1.03820	+	0.151649i
$997$	8.96558	−	12.8042i	0.283943	−	0.405512i	−0.651691	−	0.758484i	$-0.725940\pi$
$997$	8.96558	−	12.8042i	0.283943	−	0.405512i	0.935634	+	0.352972i	$0.114829\pi$
$998$	−31.0316	−	31.0316i	−0.982289	−	0.982289i
$999$	−0.150405	+	1.69567i	−0.00475860	+	0.0536487i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.122.2	yes	192
3.2	odd	2		405.2.r.a.152.15		192
5.2	odd	4		675.2.ba.b.68.15		192
5.3	odd	4	inner	135.2.q.a.68.2	yes	192
5.4	even	2		675.2.ba.b.257.15		192
15.8	even	4		405.2.r.a.233.15		192
27.2	odd	18	inner	135.2.q.a.2.2	✓	192
27.25	even	9		405.2.r.a.332.15		192
135.2	even	36		675.2.ba.b.218.15		192
135.29	odd	18		675.2.ba.b.407.15		192
135.83	even	36	inner	135.2.q.a.83.2	yes	192
135.133	odd	36		405.2.r.a.8.15		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.2	✓	192	27.2	odd	18	inner
135.2.q.a.68.2	yes	192	5.3	odd	4	inner
135.2.q.a.83.2	yes	192	135.83	even	36	inner
135.2.q.a.122.2	yes	192	1.1	even	1	trivial
405.2.r.a.8.15		192	135.133	odd	36
405.2.r.a.152.15		192	3.2	odd	2
405.2.r.a.233.15		192	15.8	even	4
405.2.r.a.332.15		192	27.25	even	9
675.2.ba.b.68.15		192	5.2	odd	4
675.2.ba.b.218.15		192	135.2	even	36
675.2.ba.b.257.15		192	5.4	even	2
675.2.ba.b.407.15		192	135.29	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.12047 - 1.48477i) q^{2} +(1.59067 - 0.685393i) q^{3} +(1.60780 + 4.41741i) q^{4} +(-2.09416 - 0.783897i) q^{5} +(-4.39061 - 0.908422i) q^{6} +(-1.25154 - 2.68394i) q^{7} +(1.80956 - 6.75336i) q^{8} +(2.06047 - 2.18047i) q^{9} +O(q^{10})\)	\(q+(-2.12047 - 1.48477i) q^{2} +(1.59067 - 0.685393i) q^{3} +(1.60780 + 4.41741i) q^{4} +(-2.09416 - 0.783897i) q^{5} +(-4.39061 - 0.908422i) q^{6} +(-1.25154 - 2.68394i) q^{7} +(1.80956 - 6.75336i) q^{8} +(2.06047 - 2.18047i) q^{9} +(3.27669 + 4.77156i) q^{10} +(-1.00437 - 1.19696i) q^{11} +(5.58515 + 5.92466i) q^{12} +(-2.29827 - 3.28227i) q^{13} +(-1.33117 + 7.54945i) q^{14} +(-3.86840 + 0.188401i) q^{15} +(-6.66205 + 5.59013i) q^{16} +(0.490334 + 1.82995i) q^{17} +(-7.60665 + 1.56430i) q^{18} +(-2.41262 + 1.39293i) q^{19} +(0.0957914 - 10.5111i) q^{20} +(-3.83035 - 3.41147i) q^{21} +(0.352524 + 4.02936i) q^{22} +(6.78686 + 3.16476i) q^{23} +(-1.75030 - 11.9826i) q^{24} +(3.77101 + 3.28321i) q^{25} +10.3723i q^{26} +(1.78305 - 4.88065i) q^{27} +(9.84382 - 9.84382i) q^{28} +(-0.683218 - 3.87472i) q^{29} +(8.48254 + 5.34417i) q^{30} +(5.45790 - 1.98651i) q^{31} +(8.49672 - 0.743366i) q^{32} +(-2.41801 - 1.21558i) q^{33} +(1.67731 - 4.60838i) q^{34} +(0.516997 + 6.60168i) q^{35} +(12.9449 + 5.59617i) q^{36} +(-0.316450 + 0.0847926i) q^{37} +(7.18404 + 0.628522i) q^{38} +(-5.90544 - 3.64579i) q^{39} +(-9.08344 + 12.7241i) q^{40} +(6.26389 + 1.10449i) q^{41} +(3.05689 + 12.9211i) q^{42} +(0.0509770 - 0.582670i) q^{43} +(3.67263 - 6.36118i) q^{44} +(-6.02422 + 2.95106i) q^{45} +(-9.69236 - 16.7877i) q^{46} +(-0.690071 + 0.321786i) q^{47} +(-6.76570 + 13.4582i) q^{48} +(-1.13767 + 1.35582i) q^{49} +(-3.12150 - 12.5610i) q^{50} +(2.03420 + 2.57478i) q^{51} +(10.8039 - 15.4296i) q^{52} +(-5.57112 - 5.57112i) q^{53} +(-11.0275 + 7.70183i) q^{54} +(1.16502 + 3.29395i) q^{55} +(-20.3903 + 3.59537i) q^{56} +(-2.88298 + 3.86928i) q^{57} +(-4.30431 + 9.23063i) q^{58} +(7.84000 + 6.57854i) q^{59} +(-7.05187 - 16.7854i) q^{60} +(11.4160 + 4.15507i) q^{61} +(-14.5228 - 3.89137i) q^{62} +(-8.43102 - 2.80123i) q^{63} +(-4.05760 - 2.34266i) q^{64} +(2.23998 + 8.67520i) q^{65} +(3.32245 + 6.16778i) q^{66} +(-1.63356 + 1.14383i) q^{67} +(-7.29527 + 5.10821i) q^{68} +(12.9648 + 0.382432i) q^{69} +(8.70568 - 14.7663i) q^{70} +(-6.11142 - 3.52843i) q^{71} +(-10.9970 - 17.8608i) q^{72} +(3.93347 + 1.05397i) q^{73} +(0.796919 + 0.290055i) q^{74} +(8.24873 + 2.63788i) q^{75} +(-10.0321 - 8.41796i) q^{76} +(-1.95556 + 4.19371i) q^{77} +(7.10913 + 16.4990i) q^{78} +(-12.9467 + 2.28286i) q^{79} +(18.3335 - 6.48426i) q^{80} +(-0.508912 - 8.98560i) q^{81} +(-11.6425 - 11.6425i) q^{82} +(-2.33262 + 3.33133i) q^{83} +(8.91139 - 22.4052i) q^{84} +(0.407655 - 4.21658i) q^{85} +(-0.973224 + 1.15984i) q^{86} +(-3.74248 - 5.69514i) q^{87} +(-9.90096 + 4.61689i) q^{88} +(4.23520 + 7.33558i) q^{89} +(17.1558 + 2.68694i) q^{90} +(-5.93304 + 10.2763i) q^{91} +(-3.06811 + 35.0686i) q^{92} +(7.32018 - 6.90070i) q^{93} +(1.94105 + 0.342259i) q^{94} +(6.14432 - 1.02577i) q^{95} +(13.0060 - 7.00604i) q^{96} +(7.95549 + 0.696015i) q^{97} +(4.42546 - 1.18580i) q^{98} +(-4.67941 - 0.276305i) 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

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