LMFDB - Embedded newform 135.2.q.a.68.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [135,2,Mod(2,135)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			68.2
Character	$\chi$	$=$	135.68
Dual form			135.2.q.a.2.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.48477 + 2.12047i) q^{2} +(0.685393 + 1.59067i) q^{3} +(-1.60780 - 4.41741i) q^{4} +(1.13563 + 1.92622i) q^{5} +(-4.39061 - 0.908422i) q^{6} +(-2.68394 + 1.25154i) q^{7} +(6.75336 + 1.80956i) q^{8} +(-2.06047 + 2.18047i) q^{9} +(-5.77064 - 0.451915i) q^{10} +(-1.00437 - 1.19696i) q^{11} +(5.92466 - 5.58515i) q^{12} +(3.28227 - 2.29827i) q^{13} +(1.33117 - 7.54945i) q^{14} +(-2.28563 + 3.12664i) q^{15} +(-6.66205 + 5.59013i) q^{16} +(1.82995 - 0.490334i) q^{17} +(-1.56430 - 7.60665i) q^{18} +(2.41262 - 1.39293i) q^{19} +(6.68303 - 8.11355i) q^{20} +(-3.83035 - 3.41147i) q^{21} +(4.02936 - 0.352524i) q^{22} +(-3.16476 + 6.78686i) q^{23} +(1.75030 + 11.9826i) q^{24} +(-2.42067 + 4.37497i) q^{25} +10.3723i q^{26} +(-4.88065 - 1.78305i) q^{27} +(9.84382 + 9.84382i) q^{28} +(0.683218 + 3.87472i) q^{29} +(-3.23631 - 9.48893i) q^{30} +(5.45790 - 1.98651i) q^{31} +(-0.743366 - 8.49672i) q^{32} +(1.21558 - 2.41801i) q^{33} +(-1.67731 + 4.60838i) q^{34} +(-5.45873 - 3.74857i) q^{35} +(12.9449 + 5.59617i) q^{36} +(0.0847926 + 0.316450i) q^{37} +(-0.628522 + 7.18404i) q^{38} +(5.90544 + 3.64579i) q^{39} +(4.18374 + 15.0635i) q^{40} +(6.26389 + 1.10449i) q^{41} +(12.9211 - 3.05689i) q^{42} +(0.582670 + 0.0509770i) q^{43} +(-3.67263 + 6.36118i) q^{44} +(-6.54002 - 1.49271i) q^{45} +(-9.69236 - 16.7877i) q^{46} +(0.321786 + 0.690071i) q^{47} +(-13.4582 - 6.76570i) q^{48} +(1.13767 - 1.35582i) q^{49} +(-5.68285 - 11.6287i) q^{50} +(2.03420 + 2.57478i) q^{51} +(-15.4296 - 10.8039i) 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} +(3.86928 + 2.88298i) q^{57} +(-9.23063 - 4.30431i) q^{58} +(-7.84000 - 6.57854i) q^{59} +(17.4865 + 5.06953i) q^{60} +(11.4160 + 4.15507i) q^{61} +(-3.89137 + 14.5228i) q^{62} +(2.80123 - 8.43102i) q^{63} +(4.05760 + 2.34266i) q^{64} +(8.15444 + 3.71239i) q^{65} +(3.32245 + 6.16778i) q^{66} +(1.14383 + 1.63356i) q^{67} +(-5.10821 - 7.29527i) q^{68} +(-12.9648 - 0.382432i) q^{69} +(16.0536 - 6.00929i) q^{70} +(-6.11142 - 3.52843i) q^{71} +(-17.8608 + 10.9970i) q^{72} +(-1.05397 + 3.93347i) q^{73} +(-0.796919 - 0.290055i) q^{74} +(-8.61825 - 0.851911i) q^{75} +(-10.0321 - 8.41796i) q^{76} +(4.19371 + 1.95556i) q^{77} +(-16.4990 + 7.10913i) 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} +(-3.33133 - 2.33262i) q^{83} +(-8.91139 + 22.4052i) q^{84} +(3.02265 + 2.96805i) q^{85} +(-0.973224 + 1.15984i) q^{86} +(-5.69514 + 3.74248i) q^{87} +(-4.61689 - 9.90096i) q^{88} +(-4.23520 - 7.33558i) q^{89} +(12.8756 - 11.6516i) q^{90} +(-5.93304 + 10.2763i) q^{91} +(35.0686 + 3.06811i) q^{92} +(6.90070 + 7.32018i) q^{93} +(-1.94105 - 0.342259i) q^{94} +(5.42294 + 3.06539i) q^{95} +(13.0060 - 7.00604i) q^{96} +(0.696015 - 7.95549i) q^{97} +(1.18580 + 4.42546i) 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} - 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}+ \cdots + 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

Character values

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

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.48477	+	2.12047i	−1.04989	+	1.49940i	−0.194848	+	0.980833i	$0.562421\pi$
$2$	−1.48477	+	2.12047i	−1.04989	+	1.49940i	−0.855040	+	0.518562i	$0.826467\pi$
$3$	0.685393	+	1.59067i	0.395712	+	0.918375i
$3$	0.685393	+	1.59067i	0.395712	+	0.918375i
$4$	−1.60780	−	4.41741i	−0.803902	−	2.20870i
$5$	1.13563	+	1.92622i	0.507871	+	0.861433i
$5$	1.13563	+	1.92622i	0.507871	+	0.861433i
$6$	−4.39061	−	0.908422i	−1.79246	−	0.370862i
$7$	−2.68394	+	1.25154i	−1.01443	+	0.473038i	−0.857453	−	0.514563i	$-0.827954\pi$
$7$	−2.68394	+	1.25154i	−1.01443	+	0.473038i	−0.156982	+	0.987602i	$0.550176\pi$
$8$	6.75336	+	1.80956i	2.38767	+	0.639775i
$9$	−2.06047	+	2.18047i	−0.686824	+	0.726824i
$10$	−5.77064	−	0.451915i	−1.82484	−	0.142908i
$11$	−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	$0.853470\pi$
$12$	5.92466	−	5.58515i	1.71030	−	1.61229i
$13$	3.28227	−	2.29827i	0.910338	−	0.637425i	−0.0217086	−	0.999764i	$-0.506911\pi$
$13$	3.28227	−	2.29827i	0.910338	−	0.637425i	0.932046	+	0.362339i	$0.118022\pi$
$14$	1.33117	−	7.54945i	0.355771	−	2.01768i
$15$	−2.28563	+	3.12664i	−0.590147	+	0.807296i
$16$	−6.66205	+	5.59013i	−1.66551	+	1.39753i
$17$	1.82995	−	0.490334i	0.443828	−	0.118923i	−0.0299818	−	0.999550i	$-0.509545\pi$
$17$	1.82995	−	0.490334i	0.443828	−	0.118923i	0.473810	+	0.880627i	$0.342878\pi$
$18$	−1.56430	−	7.60665i	−0.368708	−	1.79290i
$19$	2.41262	−	1.39293i	0.553493	−	0.319559i	−0.197037	−	0.980396i	$-0.563132\pi$
$19$	2.41262	−	1.39293i	0.553493	−	0.319559i	0.750529	+	0.660837i	$0.229799\pi$
$20$	6.68303	−	8.11355i	1.49437	−	1.81424i
$21$	−3.83035	−	3.41147i	−0.835850	−	0.744444i
$22$	4.02936	−	0.352524i	0.859063	−	0.0751583i
$23$	−3.16476	+	6.78686i	−0.659899	+	1.41516i	0.236377	+	0.971661i	$0.424040\pi$
$23$	−3.16476	+	6.78686i	−0.659899	+	1.41516i	−0.896276	+	0.443496i	$0.853738\pi$
$24$	1.75030	+	11.9826i	0.357278	+	2.44594i
$25$	−2.42067	+	4.37497i	−0.484133	+	0.874994i
$26$			10.3723i			2.03418i
$27$	−4.88065	−	1.78305i	−0.939281	−	0.343149i
$28$	9.84382	+	9.84382i	1.86031	+	1.86031i
$29$	0.683218	+	3.87472i	0.126870	+	0.719518i	0.980179	+	0.198112i	$0.0634810\pi$
$29$	0.683218	+	3.87472i	0.126870	+	0.719518i	−0.853309	+	0.521406i	$0.825408\pi$
$30$	−3.23631	−	9.48893i	−0.590867	−	1.73243i
$31$	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	$0.214228\pi$
$32$	−0.743366	−	8.49672i	−0.131410	−	1.50202i
$33$	1.21558	−	2.41801i	0.211606	−	0.420921i
$34$	−1.67731	+	4.60838i	−0.287657	+	0.790331i
$35$	−5.45873	−	3.74857i	−0.922693	−	0.633624i
$36$	12.9449	+	5.59617i	2.15748	+	0.932695i
$37$	0.0847926	+	0.316450i	0.0139398	+	0.0520241i	0.972545	−	0.232713i	$-0.0747603\pi$
$37$	0.0847926	+	0.316450i	0.0139398	+	0.0520241i	−0.958606	+	0.284737i	$0.908094\pi$
$38$	−0.628522	+	7.18404i	−0.101960	+	1.16541i
$39$	5.90544	+	3.64579i	0.945627	+	0.583794i
$40$	4.18374	+	15.0635i	0.661507	+	2.38174i
$41$	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	$0.390110\pi$
$42$	12.9211	−	3.05689i	1.99376	−	0.471688i
$43$	0.582670	+	0.0509770i	0.0888564	+	0.00777393i	0.131497	−	0.991317i	$-0.458022\pi$
$43$	0.582670	+	0.0509770i	0.0888564	+	0.00777393i	−0.0426408	+	0.999090i	$0.513577\pi$
$44$	−3.67263	+	6.36118i	−0.553670	+	0.958984i
$45$	−6.54002	−	1.49271i	−0.974928	−	0.222520i
$46$	−9.69236	−	16.7877i	−1.42906	−	2.47521i
$47$	0.321786	+	0.690071i	0.0469372	+	0.100657i	0.928378	−	0.371638i	$-0.121204\pi$
$47$	0.321786	+	0.690071i	0.0469372	+	0.100657i	−0.881441	+	0.472295i	$0.843426\pi$
$48$	−13.4582	−	6.76570i	−1.94252	−	0.976545i
$49$	1.13767	−	1.35582i	0.162524	−	0.193688i
$50$	−5.68285	−	11.6287i	−0.803676	−	1.64455i
$51$	2.03420	+	2.57478i	0.284845	+	0.360541i
$52$	−15.4296	−	10.8039i	−2.13971	−	1.49824i
$53$	5.57112	−	5.57112i	0.765253	−	0.765253i	−0.212014	−	0.977267i	$-0.568002\pi$
$53$	5.57112	−	5.57112i	0.765253	−	0.765253i	0.977267	+	0.212014i	$0.0680022\pi$
$54$	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
$57$	3.86928	+	2.88298i	0.512499	+	0.381860i
$58$	−9.23063	−	4.30431i	−1.21204	−	0.565184i
$59$	−7.84000	−	6.57854i	−1.02068	−	0.856453i	−0.0309682	−	0.999520i	$-0.509859\pi$
$59$	−7.84000	−	6.57854i	−1.02068	−	0.856453i	−0.989713	+	0.143067i	$0.954303\pi$
$60$	17.4865	+	5.06953i	2.25750	+	0.654474i
$61$	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	$0.327480\pi$
$62$	−3.89137	+	14.5228i	−0.494205	+	1.84440i
$63$	2.80123	−	8.43102i	0.352922	−	1.06221i
$64$	4.05760	+	2.34266i	0.507201	+	0.292832i
$65$	8.15444	+	3.71239i	1.01143	+	0.460465i
$66$	3.32245	+	6.16778i	0.408965	+	0.759201i
$67$	1.14383	+	1.63356i	0.139742	+	0.199572i	0.882922	−	0.469519i	$-0.155573\pi$
$67$	1.14383	+	1.63356i	0.139742	+	0.199572i	−0.743181	+	0.669091i	$0.766684\pi$
$68$	−5.10821	−	7.29527i	−0.619461	−	0.884682i
$69$	−12.9648	−	0.382432i	−1.56077	−	0.0460394i
$70$	16.0536	−	6.00929i	1.91878	−	0.718247i
$71$	−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	$0.804198\pi$
$72$	−17.8608	+	10.9970i	−2.10491	+	1.29600i
$73$	−1.05397	+	3.93347i	−0.123358	+	0.460378i	−0.999776	−	0.0211733i	$-0.993260\pi$
$73$	−1.05397	+	3.93347i	−0.123358	+	0.460378i	0.876418	+	0.481551i	$0.159926\pi$
$74$	−0.796919	−	0.290055i	−0.0926400	−	0.0337182i
$75$	−8.61825	−	0.851911i	−0.995150	−	0.0983702i
$76$	−10.0321	−	8.41796i	−1.15076	−	0.965606i
$77$	4.19371	+	1.95556i	0.477918	+	0.222857i
$78$	−16.4990	+	7.10913i	−1.86814	+	0.804950i
$79$	12.9467	−	2.28286i	1.45662	−	0.256842i	0.611427	−	0.791301i	$-0.290596\pi$
$79$	12.9467	−	2.28286i	1.45662	−	0.256842i	0.845194	+	0.534460i	$0.179485\pi$
$80$	−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
$83$	−3.33133	−	2.33262i	−0.365661	−	0.256038i	0.376277	−	0.926507i	$-0.377204\pi$
$83$	−3.33133	−	2.33262i	−0.365661	−	0.256038i	−0.741938	+	0.670469i	$0.766093\pi$
$84$	−8.91139	+	22.4052i	−0.972313	+	2.44460i
$85$	3.02265	+	2.96805i	0.327852	+	0.321931i
$86$	−0.973224	+	1.15984i	−0.104945	+	0.125069i
$87$	−5.69514	+	3.74248i	−0.610583	+	0.401236i
$88$	−4.61689	−	9.90096i	−0.492162	−	1.05545i
$89$	−4.23520	−	7.33558i	−0.448930	−	0.777570i	0.549386	−	0.835569i	$-0.314862\pi$
$89$	−4.23520	−	7.33558i	−0.448930	−	0.777570i	−0.998317	+	0.0579982i	$0.981528\pi$
$90$	12.8756	−	11.6516i	1.35721	−	1.22818i
$91$	−5.93304	+	10.2763i	−0.621951	+	1.07725i
$92$	35.0686	+	3.06811i	3.65616	+	0.319872i
$93$	6.90070	+	7.32018i	0.715569	+	0.759067i
$94$	−1.94105	−	0.342259i	−0.200204	−	0.0353013i
$95$	5.42294	+	3.06539i	0.556382	+	0.314502i
$96$	13.0060	−	7.00604i	1.32742	−	0.715051i
$97$	0.696015	−	7.95549i	0.0706696	−	0.807758i	−0.875317	−	0.483550i	$-0.839347\pi$
$97$	0.696015	−	7.95549i	0.0706696	−	0.807758i	0.945986	−	0.324207i	$-0.105097\pi$
$98$	1.18580	+	4.42546i	0.119784	+	0.447039i
$99$	4.67941	+	0.276305i	0.470298	+	0.0277697i
$100$	23.2180	+	3.65897i	2.32180	+	0.365897i
$101$	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	$-0.170881\pi$
$102$	−8.48004	+	0.490499i	−0.839649	+	0.0485666i
$103$	−0.690517	−	7.89264i	−0.0680387	−	0.777685i	−0.951192	−	0.308601i	$-0.900139\pi$
$103$	−0.690517	−	7.89264i	−0.0680387	−	0.777685i	0.883153	−	0.469085i	$-0.155416\pi$
$104$	26.3252	−	9.58158i	2.58140	−	0.939552i
$105$	2.22137	−	11.2523i	0.216784	−	1.09811i
$106$	3.54156	+	20.0852i	0.343987	+	1.95085i
$107$	3.95377	+	3.95377i	0.382225	+	0.382225i	0.871903	−	0.489678i	$-0.162886\pi$
$107$	3.95377	+	3.95377i	0.382225	+	0.382225i	−0.489678	+	0.871903i	$0.662886\pi$
$108$	−0.0293423	+	24.4266i	−0.00282346	+	2.35045i
$109$		−	6.56334i		−	0.628654i	−0.949315	−	0.314327i	$-0.898221\pi$
$109$		−	6.56334i		−	0.628654i	0.949315	−	0.314327i	$-0.101779\pi$
$110$	5.25492	+	7.36111i	0.501037	+	0.701855i
$111$	−0.445252	+	0.351770i	−0.0422615	+	0.0333885i
$112$	10.8843	−	23.3414i	1.02847	−	2.20556i
$113$	−2.27035	+	0.198630i	−0.213577	+	0.0186855i	−0.193442	−	0.981112i	$-0.561965\pi$
$113$	−2.27035	+	0.198630i	−0.213577	+	0.0186855i	−0.0201349	+	0.999797i	$0.506410\pi$
$114$	−11.8582	+	3.92412i	−1.11063	+	0.367528i
$115$	−16.6670	+	1.61135i	−1.55421	+	0.150259i
$116$	16.0177	−	9.24784i	1.48721	−	0.858641i
$117$	−1.75171	+	11.8924i	−0.161946	+	1.09945i
$118$	25.5901	−	6.85686i	2.35576	−	0.631225i
$119$	−4.29781	+	3.60629i	−0.393979	+	0.330588i
$120$	−21.0935	+	16.9794i	−1.92557	+	1.55000i
$121$	1.48617	−	8.42851i	0.135107	−	0.766228i
$122$	−25.7607	+	18.0378i	−2.33226	+	1.63307i
$123$	2.53634	+	10.7208i	0.228694	+	0.966662i
$124$	−17.5505	−	20.9158i	−1.57608	−	1.87830i
$125$	−11.1762	+	0.305624i	−0.999626	+	0.0273359i
$126$	13.7185	+	18.4580i	1.22214	+	1.64437i
$127$	−2.08725	−	0.559276i	−0.185213	−	0.0496277i	0.165020	−	0.986290i	$-0.447231\pi$
$127$	−2.08725	−	0.559276i	−0.185213	−	0.0496277i	−0.350233	+	0.936662i	$0.613898\pi$
$128$	4.46799	−	2.08346i	0.394918	−	0.184153i
$129$	0.318271	+	0.961776i	0.0280222	+	0.0846797i
$130$	−19.9794	+	11.7792i	−1.75231	+	1.03310i
$131$	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	$0.875488\pi$
$132$	−12.6357	−	1.48204i	−1.09980	−	0.128995i
$133$	−4.73202	+	6.75802i	−0.410318	+	0.585995i
$134$	−5.16224			−0.445950
$135$	−2.10808	−	11.4261i	−0.181434	−	0.983403i
$136$	13.2456			1.13580
$137$	1.39561	−	1.99313i	0.119235	−	0.170285i	−0.755098	−	0.655612i	$-0.772411\pi$
$137$	1.39561	−	1.99313i	0.119235	−	0.170285i	0.874333	+	0.485327i	$0.161300\pi$
$138$	20.0606	−	26.9235i	1.70767	−	2.29188i
$139$	3.32712	+	9.14118i	0.282202	+	0.775345i	0.997099	+	0.0761146i	$0.0242515\pi$
$139$	3.32712	+	9.14118i	0.282202	+	0.775345i	−0.714897	+	0.699230i	$0.753526\pi$
$140$	−7.78240	+	30.1404i	−0.657733	+	2.54733i
$141$	−0.877127	+	0.984825i	−0.0738674	+	0.0829373i
$142$	16.5560	−	7.72017i	1.38934	−	0.647862i
$143$	−6.04754	−	1.62043i	−0.505721	−	0.135508i
$144$	1.53786	−	26.0447i	0.128155	−	2.17039i
$145$	−6.68769	+	5.71630i	−0.555382	+	0.474713i
$146$	−6.77589	−	8.07519i	−0.560777	−	0.668308i
$147$	2.93641	+	0.880385i	0.242191	+	0.0726130i
$148$	1.26156	−	0.883353i	0.103700	−	0.0726112i
$149$	−2.43445	+	13.8064i	−0.199438	+	1.13107i	0.706518	+	0.707695i	$0.250265\pi$
$149$	−2.43445	+	13.8064i	−0.199438	+	1.13107i	−0.905956	+	0.423373i	$0.860846\pi$
$150$	14.6025	−	17.0098i	1.19229	−	1.38885i
$151$	−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	$0.543627\pi$
$152$	18.8139	−	5.04116i	1.52600	−	0.408892i
$153$	−2.70140	+	5.00048i	−0.218396	+	0.404265i
$154$	−10.3734	+	5.98907i	−0.835910	+	0.482613i
$155$	10.0246	+	8.25717i	0.805199	+	0.663232i
$156$	6.61016	−	31.9484i	0.529236	−	2.55792i
$157$	−3.03267	+	0.265324i	−0.242033	+	0.0211752i	−0.207527	−	0.978229i	$-0.566541\pi$
$157$	−3.03267	+	0.265324i	−0.242033	+	0.0211752i	−0.0345064	+	0.999404i	$0.510986\pi$
$158$	−14.3821	+	30.8426i	−1.14418	+	2.45371i
$159$	12.6802	+	5.04342i	1.00561	+	0.399969i
$160$	15.5224	−	11.0811i	1.22715	−	0.876034i
$161$		−	22.1764i		−	1.74774i
$162$	19.8093	+	12.2624i	1.55636	+	0.963424i
$163$	−16.0133	−	16.0133i	−1.25426	−	1.25426i	−0.953793	−	0.300465i	$-0.902858\pi$
$163$	−16.0133	−	16.0133i	−1.25426	−	1.25426i	−0.300465	−	0.953793i	$-0.597142\pi$
$164$	−5.19212	−	29.4459i	−0.405436	−	2.29934i
$165$	6.03808	−	0.404493i	0.470064	−	0.0314897i
$166$	9.89249	−	3.60057i	0.767806	−	0.279459i
$167$	−0.457294	−	5.22689i	−0.0353865	−	0.404469i	−0.993144	−	0.116894i	$-0.962706\pi$
$167$	−0.457294	−	5.22689i	−0.0353865	−	0.404469i	0.957758	−	0.287576i	$-0.0928492\pi$
$168$	−19.6945	−	29.9701i	−1.51946	−	2.31224i
$169$	1.04499	−	2.87108i	0.0803837	−	0.220852i
$170$	−10.7816	+	2.00256i	−0.826909	+	0.153589i
$171$	−1.93390	+	8.13073i	−0.147889	+	0.621772i
$172$	−0.711633	−	2.65585i	−0.0542615	−	0.202507i
$173$	0.712745	−	8.14671i	0.0541890	−	0.619383i	−0.919740	−	0.392529i	$-0.871600\pi$
$173$	0.712745	−	8.14671i	0.0541890	−	0.619383i	0.973929	−	0.226854i	$-0.0728441\pi$
$174$	0.520136	−	17.6331i	0.0394314	−	1.33676i
$175$	1.02147	−	14.7717i	0.0772157	−	1.11664i
$176$	13.3823	+	2.35966i	1.00873	+	0.177866i
$177$	5.09081	−	16.9798i	0.382649	−	1.27628i
$178$	21.8431	+	1.91103i	1.63721	+	0.143238i
$179$	−2.65400	+	4.59686i	−0.198369	+	0.343585i	−0.948000	−	0.318271i	$-0.896898\pi$
$179$	−2.65400	+	4.59686i	−0.198369	+	0.343585i	0.749631	+	0.661856i	$0.230231\pi$
$180$	3.92117	+	31.2899i	0.292267	+	2.33221i
$181$	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	$0.505026\pi$
$182$	−12.9814	−	27.8387i	−0.962246	−	2.06354i
$183$	1.21507	+	21.0069i	0.0898207	+	1.55287i
$184$	−33.6540	+	40.1073i	−2.48100	+	2.95675i
$185$	−0.513260	+	0.522701i	−0.0377356	+	0.0384298i
$186$	−25.7681	+	3.76393i	−1.88941	+	0.275985i
$187$	−2.42486	−	1.69790i	−0.177323	−	0.124163i
$188$	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	$0.488340\pi$
$192$	−0.945346	+	8.05996i	−0.0682245	+	0.581677i
$193$	−11.2015	−	5.22336i	−0.806305	−	0.375986i	−0.0246489	−	0.999696i	$-0.507847\pi$
$193$	−11.2015	−	5.22336i	−0.806305	−	0.375986i	−0.781656	+	0.623710i	$0.785625\pi$
$194$	15.8359	+	13.2879i	1.13695	+	0.954017i
$195$	−0.316189	+	15.5155i	−0.0226428	+	1.11109i
$196$	−7.81835	−	2.84565i	−0.558453	−	0.203260i
$197$	6.21326	−	23.1882i	0.442676	−	1.65209i	−0.279324	−	0.960197i	$-0.590110\pi$
$197$	6.21326	−	23.1882i	0.442676	−	1.65209i	0.722000	−	0.691893i	$-0.243223\pi$
$198$	−7.53372	+	9.51228i	−0.535398	+	0.676008i
$199$	5.73533	+	3.31129i	0.406566	+	0.234731i	0.689313	−	0.724463i	$-0.257912\pi$
$199$	5.73533	+	3.31129i	0.406566	+	0.234731i	−0.282747	+	0.959195i	$0.591246\pi$
$200$	−24.2644	+	25.1654i	−1.71575	+	1.77946i
$201$	−1.81449	+	2.93910i	−0.127984	+	0.207308i
$202$	23.1134	+	33.0093i	1.62625	+	2.32253i
$203$	−6.68309	−	9.54445i	−0.469061	−	0.669889i
$204$	8.10325	−	13.1256i	0.567341	−	0.918977i
$205$	4.98599	+	13.3199i	0.348237	+	0.930305i
$206$	17.7613	+	10.2545i	1.23749	+	0.714466i
$207$	−8.27764	−	20.8848i	−0.575336	−	1.45159i
$208$	−9.01904	+	33.6595i	−0.625358	+	2.33387i
$209$	−4.09043	−	1.48880i	−0.282941	−	0.102982i
$210$	20.5619	+	21.4174i	1.41890	+	1.47794i
$211$	−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	$0.752779\pi$
$212$	−33.5672	−	15.6526i	−2.30540	−	1.07503i
$213$	1.42385	−	12.1396i	0.0975604	−	0.831794i
$214$	−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
$218$	13.9173	+	9.74502i	0.942601	+	0.660016i
$219$	−6.97925	+	1.01945i	−0.471614	+	0.0688884i
$220$	−16.4238	+	0.149676i	−1.10729	+	0.0100911i
$221$	4.87947	−	5.81513i	0.328229	−	0.391168i
$222$	−0.0848211	−	1.46644i	−0.00569282	−	0.0984209i
$223$	9.32189	+	19.9909i	0.624240	+	1.33869i	0.923163	+	0.384410i	$0.125595\pi$
$223$	9.32189	+	19.9909i	0.624240	+	1.33869i	−0.298923	+	0.954277i	$0.596627\pi$
$224$	12.6291	+	21.8743i	0.843821	+	1.46154i
$225$	−4.55178	−	14.2927i	−0.303452	−	0.952847i
$226$	2.94975	−	5.10912i	0.196215	−	0.339854i
$227$	−7.40612	−	0.647951i	−0.491561	−	0.0430060i	−0.161319	−	0.986902i	$-0.551575\pi$
$227$	−7.40612	−	0.647951i	−0.491561	−	0.0430060i	−0.330242	+	0.943896i	$0.607130\pi$
$228$	6.51425	−	21.7274i	0.431417	−	1.43894i
$229$	4.57594	+	0.806861i	0.302386	+	0.0533189i	0.322783	−	0.946473i	$-0.395382\pi$
$229$	4.57594	+	0.806861i	0.302386	+	0.0533189i	−0.0203963	+	0.999792i	$0.506493\pi$
$230$	21.3298	−	37.7343i	1.40645	−	2.48813i
$231$	−0.236311	+	8.01114i	−0.0155481	+	0.527095i
$232$	−2.39751	+	27.4037i	−0.157404	+	1.79914i
$233$	3.69557	+	13.7921i	0.242105	+	0.903549i	0.974816	+	0.223009i	$0.0715879\pi$
$233$	3.69557	+	13.7921i	0.242105	+	0.903549i	−0.732711	+	0.680540i	$0.761745\pi$
$234$	−22.6166	−	21.3719i	−1.47849	−	1.39712i
$235$	−0.963800	+	1.40350i	−0.0628714	+	0.0915542i
$236$	−16.4549	+	45.2095i	−1.07112	+	2.94289i
$237$	12.5049	+	19.0293i	0.812279	+	1.23609i
$238$	−1.26577	−	14.4678i	−0.0820478	−	0.937811i
$239$	19.1398	−	6.96633i	1.23805	−	0.450614i	0.361705	−	0.932293i	$-0.382195\pi$
$239$	19.1398	−	6.96633i	1.23805	−	0.450614i	0.876348	+	0.481678i	$0.159973\pi$
$240$	−2.25133	−	33.6068i	−0.145323	−	2.16931i
$241$	−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
$243$	13.9443	−	6.96818i	0.894529	−	0.447009i
$244$		−	57.1094i		−	3.65606i
$245$	3.90358	+	0.651685i	0.249391	+	0.0416346i
$246$	−26.4990	−	10.5397i	−1.68951	−	0.671984i
$247$	4.71754	−	10.1168i	0.300170	−	0.643717i
$248$	40.4538	−	3.53925i	2.56882	−	0.224743i
$249$	1.42716	−	6.89781i	0.0904428	−	0.437131i
$250$	15.9459	−	24.1524i	1.00851	−	1.52753i
$251$	−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	$0.439289\pi$
$252$	−41.7471	+	1.18126i	−2.62982	+	0.0744121i
$253$	11.3022	−	3.02841i	0.710562	−	0.190395i
$254$	4.28500	−	3.59554i	0.268865	−	0.225604i
$255$	−2.64949	+	6.84232i	−0.165918	+	0.428483i
$256$	−3.84321	+	21.7959i	−0.240201	+	1.36225i
$257$	4.65492	−	3.25941i	0.290366	−	0.203316i	−0.419313	−	0.907842i	$-0.637729\pi$
$257$	4.65492	−	3.25941i	0.290366	−	0.203316i	0.709679	+	0.704525i	$0.248840\pi$
$258$	−2.51197	−	0.753131i	−0.156388	−	0.0468879i
$259$	−0.623629	−	0.743212i	−0.0387504	−	0.0461810i
$260$	3.28838	−	41.9903i	0.203937	−	2.60412i
$261$	−9.85647	−	6.49402i	−0.610100	−	0.401970i
$262$	−2.40888	−	0.645458i	−0.148821	−	0.0398765i
$263$	−17.6574	+	8.23378i	−1.08880	+	0.507717i	−0.882280	−	0.470725i	$-0.843992\pi$
$263$	−17.6574	+	8.23378i	−1.08880	+	0.507717i	−0.206522	+	0.978442i	$0.566215\pi$
$264$	12.5848	−	14.1300i	0.774540	−	0.869642i
$265$	17.0580	+	4.40446i	1.04786	+	0.270564i
$266$	−7.30422	−	20.0682i	−0.447850	−	1.23046i
$267$	8.76573	−	11.7646i	0.536454	−	0.719980i
$268$	5.37706	−	7.67923i	0.328456	−	0.469084i
$269$	21.8628			1.33300			0.666501	−	0.745505i	$-0.267791\pi$
$269$	21.8628			1.33300			0.666501	+	0.745505i	$0.267791\pi$
$270$	27.3587	+	12.4950i	1.66500	+	0.760421i
$271$	25.6697			1.55933			0.779663	−	0.626200i	$-0.215391\pi$
$271$	25.6697			1.55933			0.779663	+	0.626200i	$0.215391\pi$
$272$	−9.45020	+	13.4963i	−0.573003	+	0.818333i
$273$	−20.4127	−	2.39419i	−1.23543	−	0.144903i
$274$	2.15422	+	5.91867i	0.130141	+	0.357560i
$275$	7.66791	−	1.49664i	0.462392	−	0.0902509i
$276$	19.1555	+	57.8855i	1.15302	+	3.48430i
$277$	−4.80726	+	2.24166i	−0.288841	+	0.134689i	−0.561638	−	0.827383i	$-0.689829\pi$
$277$	−4.80726	+	2.24166i	−0.288841	+	0.134689i	0.272798	+	0.962071i	$0.412051\pi$
$278$	−24.3235	−	6.51747i	−1.45883	−	0.390892i
$279$	−6.91431	+	15.9939i	−0.413949	+	0.957532i
$280$	−30.0815	−	35.1933i	−1.79771	−	2.10320i
$281$	−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	$0.791819\pi$
$282$	−0.785960	−	3.32215i	−0.0468032	−	0.197831i
$283$	−4.14980	+	2.90572i	−0.246680	+	0.172727i	−0.690377	−	0.723449i	$-0.742556\pi$
$283$	−4.14980	+	2.90572i	−0.246680	+	0.172727i	0.443697	+	0.896177i	$0.353667\pi$
$284$	−5.76054	+	32.6697i	−0.341825	+	1.93859i
$285$	−1.15917	+	10.7271i	−0.0686636	+	0.635419i
$286$	12.4153	−	10.4176i	0.734130	−	0.616008i
$287$	−18.1942	+	4.87513i	−1.07397	+	0.287770i
$288$	20.0585	+	15.8864i	1.18196	+	0.936112i
$289$	−11.6141	+	6.70543i	−0.683185	+	0.394437i
$290$	−2.19156	−	22.6684i	−0.128693	−	1.33113i
$291$	13.1316	−	4.34551i	0.769789	−	0.254738i
$292$	19.0703	−	1.66844i	1.11601	−	0.0976379i
$293$	−9.70762	+	20.8181i	−0.567125	+	1.21620i	0.388453	+	0.921468i	$0.373009\pi$
$293$	−9.70762	+	20.8181i	−0.567125	+	1.21620i	−0.955579	+	0.294736i	$0.904768\pi$
$294$	−6.22671	+	4.91939i	−0.363149	+	0.286905i
$295$	3.76836	−	22.5724i	0.219402	−	1.31422i
$296$			2.29054i			0.133135i
$297$	2.76773	+	7.63278i	0.160600	+	0.442899i
$298$	−25.6615	−	25.6615i	−1.48653	−	1.48653i
$299$	5.21042	+	29.5498i	0.301327	+	1.70891i
$300$	10.0932	+	39.4400i	0.582733	+	2.27707i
$301$	−1.62765	+	0.592417i	−0.0938163	+	0.0341464i
$302$	−4.11100	−	46.9890i	−0.236562	−	2.70391i
$303$	26.9179	−	1.55697i	1.54639	−	0.0894457i
$304$	−8.28636	+	22.7666i	−0.475255	+	1.30575i
$305$	4.96077	+	26.7083i	0.284053	+	1.52931i
$306$	−6.59238	−	13.1528i	−0.376862	−	0.751894i
$307$	−6.03527	−	22.5239i	−0.344451	−	1.28551i	−0.893252	−	0.449556i	$-0.851582\pi$
$307$	−6.03527	−	22.5239i	−0.344451	−	1.28551i	0.548801	−	0.835953i	$-0.315084\pi$
$308$	1.89583	−	21.6695i	0.108025	−	1.23473i
$309$	12.0813	−	6.50795i	0.687283	−	0.370224i
$310$	−32.3933	+	8.99694i	−1.83982	+	0.510992i
$311$	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	$0.469028\pi$
$312$	33.2843	+	35.3076i	1.88435	+	1.99890i
$313$	−30.8225	−	2.69662i	−1.74219	−	0.152422i	−0.828810	−	0.559530i	$-0.810982\pi$
$313$	−30.8225	−	2.69662i	−1.74219	−	0.152422i	−0.913380	+	0.407109i	$0.866537\pi$
$314$	3.94019	−	6.82461i	0.222358	−	0.385135i
$315$	19.4212	−	4.17877i	1.09426	−	0.235447i
$316$	−30.9001	−	53.5206i	−1.73827	−	3.01077i
$317$	8.89049	+	19.0657i	0.499340	+	1.07084i	0.980916	+	0.194433i	$0.0622867\pi$
$317$	8.89049	+	19.0657i	0.499340	+	1.07084i	−0.481576	+	0.876404i	$0.659936\pi$
$318$	−29.5216	+	19.3997i	−1.65549	+	1.08788i
$319$	3.95168	−	4.70943i	0.221252	−	0.263678i
$320$	0.0954738	+	10.4763i	0.00533715	+	0.585640i
$321$	−3.57926	+	8.99903i	−0.199775	+	0.502277i
$322$	47.0242	+	32.9267i	2.62056	+	1.83493i
$323$	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
$327$	10.4401	−	4.49847i	0.577340	−	0.248766i
$328$	40.3036	+	18.7939i	2.22540	+	1.03772i
$329$	−1.72731	−	1.44938i	−0.0952295	−	0.0799070i
$330$	−8.10742	+	13.4041i	−0.446299	+	0.737872i
$331$	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	$0.609011\pi$
$332$	−4.94801	+	18.4662i	−0.271557	+	1.01347i
$333$	−0.864723	−	0.467149i	−0.0473866	−	0.0255996i
$334$	11.7624	+	6.79104i	0.643611	+	0.371589i
$335$	−1.84763	+	4.05841i	−0.100947	+	0.221735i
$336$	44.5885	+	1.31526i	2.43250	+	0.0717535i
$337$	−9.82568	−	14.0325i	−0.535239	−	0.764400i	0.456903	−	0.889516i	$-0.348959\pi$
$337$	−9.82568	−	14.0325i	−0.535239	−	0.764400i	−0.992142	+	0.125116i	$0.960070\pi$
$338$	4.53646	+	6.47874i	0.246751	+	0.352397i
$339$	−1.87204	−	3.47525i	−0.101675	−	0.188749i
$340$	8.25127	−	18.1243i	0.447488	−	0.982929i
$341$	−7.85952	−	4.53769i	−0.425617	−	0.245730i
$342$	−14.3695	−	16.1730i	−0.777016	−	0.874535i
$343$	4.00870	−	14.9607i	0.216450	−	0.807801i
$344$	3.84273	+	1.39864i	0.207186	+	0.0754097i
$345$	−13.9866	−	25.4073i	−0.753013	−	1.36788i
$346$	16.2166	+	13.6073i	0.871808	+	0.731534i
$347$	24.5967	+	11.4696i	1.32042	+	0.615723i	0.949741	−	0.313038i	$-0.101347\pi$
$347$	24.5967	+	11.4696i	1.32042	+	0.615723i	0.370681	+	0.928760i	$0.379124\pi$
$348$	25.6887	+	19.1405i	1.37706	+	1.02604i
$349$	−18.8404	+	3.32208i	−1.00851	+	0.177827i	−0.653411	−	0.757003i	$-0.726663\pi$
$349$	−18.8404	+	3.32208i	−1.00851	+	0.177827i	−0.355095	+	0.934830i	$0.615551\pi$
$350$	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
$353$	−24.9423	−	17.4648i	−1.32755	−	0.929558i	−0.327663	−	0.944795i	$-0.606261\pi$
$353$	−24.9423	−	17.4648i	−1.32755	−	0.929558i	−0.999884	+	0.0152364i	$0.995150\pi$
$354$	28.4463	+	36.0059i	1.51190	+	1.91369i
$355$	−0.143799	−	15.7790i	−0.00763207	−	0.837461i
$356$	−25.5949	+	30.5028i	−1.35653	+	1.61664i
$357$	−8.68211	−	4.36467i	−0.459506	−	0.231003i
$358$	−5.80691	−	12.4530i	−0.306905	−	0.658160i
$359$	−15.6146	−	27.0453i	−0.824108	−	1.42740i	−0.902599	−	0.430483i	$-0.858343\pi$
$359$	−15.6146	−	27.0453i	−0.824108	−	1.42740i	0.0784904	−	0.996915i	$-0.474990\pi$
$360$	−41.4659	−	21.9153i	−2.18545	−	1.15504i
$361$	−5.61951	+	9.73329i	−0.295764	+	0.512278i
$362$	−59.5360	−	5.20872i	−3.12914	−	0.273764i
$363$	14.4256	−	3.41283i	0.757148	−	0.179127i
$364$	54.9338	+	9.68632i	2.87931	+	0.507701i
$365$	−8.77367	+	2.43681i	−0.459235	+	0.127548i
$366$	−46.3485	−	28.6138i	−2.42267	−	1.49567i
$367$	0.124058	−	1.41799i	0.00647576	−	0.0740183i	−0.992269	−	0.124105i	$-0.960394\pi$
$367$	0.124058	−	1.41799i	0.00647576	−	0.0740183i	0.998745	+	0.0500864i	$0.0159497\pi$
$368$	−16.8556	−	62.9058i	−0.878657	−	3.27919i
$369$	−15.3149	+	11.3825i	−0.797261	+	0.592547i
$370$	−0.346299	−	1.86444i	−0.0180032	−	0.0969276i
$371$	−7.98007	+	21.9251i	−0.414305	+	1.13829i
$372$	21.2412	−	42.2526i	1.10131	−	2.19069i
$373$	0.857201	+	9.79785i	0.0443842	+	0.507313i	0.985552	+	0.169374i	$0.0541745\pi$
$373$	0.857201	+	9.79785i	0.0443842	+	0.507313i	−0.941168	+	0.337940i	$0.890270\pi$
$374$	7.20068	−	2.62083i	0.372339	−	0.135520i
$375$	−8.14622	−	17.5681i	−0.420669	−	0.907214i
$376$	0.924409	+	5.24259i	0.0476728	+	0.270366i
$377$	11.1477	+	11.1477i	0.574134	+	0.574134i
$378$	−19.9581	+	34.4727i	−1.02653	+	1.77308i
$379$			5.76488i			0.296122i	0.988978	+	0.148061i	$0.0473032\pi$
$379$			5.76488i			0.296122i	−0.988978	+	0.148061i	$0.952697\pi$
$380$	4.82203	−	28.8839i	0.247365	−	1.48171i
$381$	−0.540960	−	3.70345i	−0.0277142	−	0.189733i
$382$	4.15678	−	8.91424i	0.212679	−	0.456092i
$383$	−2.84641	+	0.249029i	−0.145445	+	0.0127248i	−0.159646	−	0.987174i	$-0.551035\pi$
$383$	−2.84641	+	0.249029i	−0.145445	+	0.0127248i	0.0142007	+	0.999899i	$0.495480\pi$
$384$	6.37643	+	5.67911i	0.325396	+	0.289811i
$385$	0.995681	+	10.2988i	0.0507446	+	0.524877i
$386$	27.7076	−	15.9970i	1.41028	−	0.814226i
$387$	−1.31173	+	1.16546i	−0.0666790	+	0.0592436i
$388$	−36.2617	+	9.71629i	−1.84091	+	0.493270i
$389$	−9.76677	+	8.19530i	−0.495195	+	0.415518i	−0.855884	−	0.517168i	$-0.826986\pi$
$389$	−9.76677	+	8.19530i	−0.495195	+	0.415518i	0.360689	+	0.932686i	$0.382542\pi$
$390$	−32.4306	−	23.7073i	−1.64219	−	1.20047i
$391$	−2.46354	+	13.9714i	−0.124586	+	0.706565i
$392$	10.1365	−	7.09766i	0.511971	−	0.358486i
$393$	−1.21419	+	1.14461i	−0.0612478	+	0.0577380i
$394$	39.9445	+	47.6040i	2.01238	+	2.39826i
$395$	19.1000	+	22.3458i	0.961028	+	1.12434i
$396$	−6.30302	−	21.1151i	−0.316739	−	1.06107i
$397$	−3.46941	−	0.929625i	−0.174125	−	0.0466565i	0.170703	−	0.985322i	$-0.445396\pi$
$397$	−3.46941	−	0.929625i	−0.174125	−	0.0466565i	−0.344828	+	0.938666i	$0.612063\pi$
$398$	−15.5371	+	7.24507i	−0.778804	+	0.363162i
$399$	−13.9931	−	2.89518i	−0.700531	−	0.144940i
$400$	−8.33002	−	42.6781i	−0.416501	−	2.13391i
$401$	−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	$-0.283035\pi$
$402$	−3.53817	−	8.21143i	−0.176468	−	0.409549i
$403$	13.3488	−	19.0640i	0.664949	−	0.949645i
$404$	−73.1790			−3.64079
$405$	16.7303	−	11.1846i	0.831337	−	0.555769i
$406$	30.1615			1.49689
$407$	0.293615	−	0.419326i	0.0145540	−	0.0207852i
$408$	9.07845	+	21.0694i	0.449450	+	1.04309i
$409$	5.75785	+	15.8196i	0.284707	+	0.782226i	0.996785	+	0.0801257i	$0.0255322\pi$
$409$	5.75785	+	15.8196i	0.284707	+	0.782226i	−0.712078	+	0.702101i	$0.752246\pi$
$410$	−35.6475	−	9.20438i	−1.76051	−	0.454572i
$411$	4.12696	+	0.853871i	0.203568	+	0.0421183i
$412$	−33.7548	+	15.7401i	−1.66298	+	0.775460i
$413$	29.2754	+	7.84432i	1.44055	+	0.385994i
$414$	56.5759	+	13.4566i	2.78055	+	0.661355i
$415$	0.709976	−	9.06589i	0.0348513	−	0.445027i
$416$	−21.9677	−	26.1801i	−1.07705	−	1.28358i
$417$	−12.2602	+	11.5577i	−0.600386	+	0.565981i
$418$	9.23028	−	6.46311i	0.451468	−	0.316121i
$419$	0.0944911	−	0.535886i	0.00461619	−	0.0261797i	−0.982413	−	0.186723i	$-0.940213\pi$
$419$	0.0944911	−	0.535886i	0.00461619	−	0.0261797i	0.987029	+	0.160543i	$0.0513245\pi$
$420$	−53.2774	+	8.27876i	−2.59967	+	0.403962i
$421$	−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	$0.336100\pi$
$422$	6.96256	−	1.86561i	0.338932	−	0.0908166i
$423$	−2.16771	−	0.720228i	−0.105398	−	0.0350187i
$424$	47.7050	−	27.5425i	2.31676	−	1.33758i
$425$	−2.28451	+	9.19292i	−0.110815	+	0.445922i
$426$	23.6276	+	21.0437i	1.14476	+	1.01957i
$427$	−35.8400	+	3.13559i	−1.73442	+	0.151742i
$428$	11.1085	−	23.8223i	0.536950	−	1.15149i
$429$	−1.56737	−	10.7303i	−0.0756732	−	0.518063i
$430$	−3.33934	−	0.557488i	−0.161037	−	0.0268845i
$431$			14.9683i			0.720998i	0.932760	+	0.360499i	$0.117394\pi$
$431$			14.9683i			0.720998i	−0.932760	+	0.360499i	$0.882606\pi$
$432$	42.4826	−	15.4046i	2.04395	−	0.741156i
$433$	24.8822	+	24.8822i	1.19576	+	1.19576i	0.975424	+	0.220337i	$0.0707157\pi$
$433$	24.8822	+	24.8822i	1.19576	+	1.19576i	0.220337	+	0.975424i	$0.429284\pi$
$434$	−7.73168	−	43.8485i	−0.371132	−	2.10480i
$435$	−13.6765	−	6.72001i	−0.655736	−	0.322200i
$436$	−28.9929	+	10.5526i	−1.38851	+	0.505376i
$437$	1.81822	+	20.7824i	0.0869774	+	0.994156i
$438$	8.20083	−	16.3129i	0.391851	−	0.779461i
$439$	13.0228	−	35.7799i	0.621545	−	1.70768i	−0.0816297	−	0.996663i	$-0.526012\pi$
$439$	13.0228	−	35.7799i	0.621545	−	1.70768i	0.703174	−	0.711017i	$-0.251765\pi$
$440$	13.8283	−	20.1370i	0.659240	−	0.959995i
$441$	0.612193	+	5.27428i	0.0291521	+	0.251156i
$442$	5.08591	+	18.9809i	0.241912	+	0.902828i
$443$	2.49320	−	28.4974i	0.118456	−	1.35395i	−0.671597	−	0.740916i	$-0.734392\pi$
$443$	2.49320	−	28.4974i	0.118456	−	1.35395i	0.790053	−	0.613038i	$-0.210053\pi$
$444$	2.26979	+	1.40128i	0.107719	+	0.0665019i
$445$	9.32033	−	16.4885i	0.441826	−	0.781629i
$446$	−56.2308	−	9.91500i	−2.66260	−	0.469489i
$447$	−23.6301	+	5.59044i	−1.11766	+	0.264419i
$448$	−13.8223	−	1.20930i	−0.653043	−	0.0571338i
$449$	−12.4470	+	21.5588i	−0.587409	+	1.01742i	0.407162	+	0.913356i	$0.366519\pi$
$449$	−12.4470	+	21.5588i	−0.587409	+	1.01742i	−0.994570	+	0.104066i	$0.966815\pi$
$450$	37.0655	+	11.5694i	1.74728	+	0.545388i
$451$	−4.96922	−	8.60694i	−0.233991	−	0.405285i
$452$	4.52771	+	9.70971i	0.212966	+	0.456706i
$453$	−28.1979	−	14.1757i	−1.32485	−	0.666032i
$454$	12.3703	−	14.7424i	0.580567	−	0.691893i
$455$	−26.5322	+	0.241798i	−1.24385	+	0.0113356i
$456$	20.9137	+	26.4715i	0.979374	+	1.23964i
$457$	3.01872	+	2.11373i	0.141210	+	0.0988761i	0.642047	−	0.766666i	$-0.278086\pi$
$457$	3.01872	+	2.11373i	0.141210	+	0.0988761i	−0.500837	+	0.865542i	$0.666974\pi$
$458$	−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	$0.560083\pi$
$462$	−16.6365	−	12.3958i	−0.773999	−	0.576703i
$463$	10.2029	+	4.75770i	0.474170	+	0.221109i	0.644987	−	0.764194i	$-0.276863\pi$
$463$	10.2029	+	4.75770i	0.474170	+	0.221109i	−0.170817	+	0.985303i	$0.554641\pi$
$464$	−26.2118	−	21.9943i	−1.21685	−	1.02106i
$465$	−6.26363	+	21.6053i	−0.290469	+	1.00192i
$466$	−34.7327	−	12.6417i	−1.60896	−	0.585614i
$467$	4.51835	−	16.8627i	0.209084	−	0.780313i	−0.779082	−	0.626923i	$-0.784314\pi$
$467$	4.51835	−	16.8627i	0.209084	−	0.780313i	0.988166	−	0.153390i	$-0.0490191\pi$
$468$	55.3500	−	11.3827i	2.55856	−	0.526163i
$469$	−5.11446	−	2.95283i	−0.236164	−	0.136349i
$470$	−1.54505	−	4.12757i	−0.0712681	−	0.190391i
$471$	−2.50061	−	4.64213i	−0.115222	−	0.213898i
$472$	−41.0421	−	58.6142i	−1.88911	−	2.69794i
$473$	−0.524198	−	0.748633i	−0.0241027	−	0.0344222i
$474$	−58.9179	−	1.73795i	−2.70619	−	0.0798265i
$475$	0.253863	+	13.9269i	0.0116480	+	0.639012i
$476$	22.8405	+	13.1870i	1.04689	+	0.604423i
$477$	0.668534	+	23.6268i	0.0306101	+	1.08180i
$478$	−13.6463	+	50.9287i	−0.624168	+	2.32943i
$479$	−21.5176	−	7.83178i	−0.983166	−	0.357843i	−0.200096	−	0.979776i	$-0.564125\pi$
$479$	−21.5176	−	7.83178i	−0.983166	−	0.357843i	−0.783070	+	0.621933i	$0.786348\pi$
$480$	28.2653	+	17.0961i	1.29013	+	0.780327i
$481$	1.00560	+	0.843799i	0.0458514	+	0.0384739i
$482$	38.1778	+	17.8026i	1.73895	+	0.810885i
$483$	35.2753	−	15.1995i	1.60508	−	0.691603i
$484$	−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	0.178740	−	0.983896i	$-0.442798\pi$
$487$	25.6571	−	25.6571i	1.16264	−	1.16264i	0.983896	−	0.178740i	$-0.0572021\pi$
$488$	69.5772	+	48.7185i	3.14961	+	2.20538i
$489$	14.4965	−	36.4473i	0.655554	−	1.64820i
$490$	−7.17778	+	7.30981i	−0.324259	+	0.330224i
$491$	−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	$0.322778\pi$
$492$	43.2802	−	28.4410i	1.95122	−	1.28222i
$493$	3.15016	+	6.75555i	0.141876	+	0.304255i
$494$	14.4479	+	25.0245i	0.650041	+	1.12590i
$495$	4.78187	+	9.32737i	0.214929	+	0.419234i
$496$	−25.2560	+	43.7446i	−1.13403	+	1.96419i
$497$	20.8187	+	1.82140i	0.933845	+	0.0817009i
$498$	12.5076	+	13.2679i	0.560478	+	0.594548i
$499$	−16.6957	−	2.94390i	−0.747401	−	0.131787i	−0.213040	−	0.977043i	$-0.568337\pi$
$499$	−16.6957	−	2.94390i	−0.747401	−	0.131787i	−0.534361	+	0.845256i	$0.679448\pi$
$500$	19.3191	+	48.8783i	0.863978	+	2.18590i
$501$	8.00085	−	4.30988i	0.357451	−	0.192551i
$502$	2.33590	−	26.6995i	0.104256	−	1.19166i
$503$	3.19471	+	11.9228i	0.142445	+	0.531612i	0.999856	+	0.0169795i	$0.00540500\pi$
$503$	3.19471	+	11.9228i	0.142445	+	0.531612i	−0.857411	+	0.514633i	$0.827928\pi$
$504$	34.1741	−	51.8687i	1.52224	−	2.31042i
$505$	34.2236	−	6.35664i	1.52293	−	0.282867i
$506$	−10.3595	+	28.4624i	−0.460534	+	1.26531i
$507$	5.28317	−	0.305587i	0.234634	−	0.0135716i
$508$	0.885334	+	10.1194i	0.0392803	+	0.448976i
$509$	1.17560	−	0.427885i	0.0521077	−	0.0189657i	−0.315835	−	0.948814i	$-0.602285\pi$
$509$	1.17560	−	0.427885i	0.0521077	−	0.0189657i	0.367943	+	0.929849i	$0.380062\pi$
$510$	−10.5750	−	15.7774i	−0.468270	−	0.698636i
$511$	−2.09411	−	11.8763i	−0.0926380	−	0.525376i
$512$	−33.5394	−	33.5394i	−1.48224	−	1.48224i
$513$	−14.2588	+	2.49655i	−0.629541	+	0.110226i
$514$			14.7101i			0.648833i
$515$	14.4188	−	10.2933i	0.635369	−	0.453575i
$516$	3.73684	−	2.95228i	0.164505	−	0.129967i
$517$	0.502796	−	1.07825i	0.0221130	−	0.0474214i
$518$	2.50190	−	0.218888i	0.109927	−	0.00961738i
$519$	13.4473	−	4.44996i	0.590269	−	0.195332i
$520$	48.3521	+	39.8270i	2.12038	+	1.74653i
$521$	−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	$0.556508\pi$
$522$	28.4049	−	11.2582i	1.24325	−	0.492759i
$523$	10.8910	−	2.91822i	0.476228	−	0.127605i	−0.0127175	−	0.999919i	$-0.504048\pi$
$523$	10.8910	−	2.91822i	0.476228	−	0.127605i	0.488946	+	0.872314i	$0.337382\pi$
$524$	3.46929	−	2.91108i	0.151556	−	0.127171i
$525$	24.1971	−	8.49963i	1.05605	−	0.370954i
$526$	8.75766	−	49.6671i	0.381852	−	2.16559i
$527$	9.01363	−	6.31141i	0.392640	−	0.274929i
$528$	5.41870	+	22.9042i	0.235819	+	0.996776i
$529$	−21.2616	−	25.3386i	−0.924417	−	1.10168i
$530$	−34.6666	+	29.6313i	−1.50582	+	1.28710i
$531$	30.4984	−	3.54000i	1.32352	−	0.153623i
$532$	37.4611	+	10.0377i	1.62414	+	0.435188i
$533$	23.0982	−	10.7709i	1.00049	−	0.466538i
$534$	11.9313	+	36.0551i	0.516319	+	1.56026i
$535$	−3.12580	+	12.1059i	−0.135140	+	0.523383i
$536$	4.76869	+	13.1019i	0.205976	+	0.565915i
$537$	−9.13112	−	1.07098i	−0.394037	−	0.0462163i
$538$	−32.4612	+	46.3594i	−1.39950	+	1.99870i
$539$	−2.76550			−0.119118
$540$	−47.0844	+	27.6832i	−2.02619	+	1.19129i
$541$	−2.55842			−0.109995			−0.0549975	−	0.998486i	$-0.517515\pi$
$541$	−2.55842			−0.109995			−0.0549975	+	0.998486i	$0.517515\pi$
$542$	−38.1136	+	54.4318i	−1.63712	+	2.33805i
$543$	−23.8920	+	32.0657i	−1.02530	+	1.37607i
$544$	−5.52655	−	15.1841i	−0.236949	−	0.651012i
$545$	12.6424	−	7.45355i	0.541543	−	0.319275i
$546$	35.3849	−	39.7296i	1.51433	−	1.70027i
$547$	3.81919	−	1.78092i	0.163297	−	0.0761465i	−0.339251	−	0.940696i	$-0.610174\pi$
$547$	3.81919	−	1.78092i	0.163297	−	0.0761465i	0.502548	+	0.864549i	$0.332396\pi$
$548$	−11.0483	−	2.96039i	−0.471961	−	0.126462i
$549$	−32.5823	+	16.3308i	−1.39058	+	0.696980i
$550$	−8.21147	+	18.4817i	−0.350138	+	0.788062i
$551$	7.04554	+	8.39655i	0.300150	+	0.357705i
$552$	−86.8637	−	26.0432i	−3.69716	−	1.10847i
$553$	−31.8912	+	22.3304i	−1.35615	+	0.949586i
$554$	2.38429	−	13.5220i	0.101299	−	0.574494i
$555$	−1.18323	−	0.458172i	−0.0502254	−	0.0194483i
$556$	35.0309	−	29.3944i	1.48564	−	1.24660i
$557$	19.0860	−	5.11407i	0.808698	−	0.216690i	0.169299	−	0.985565i	$-0.445850\pi$
$557$	19.0860	−	5.11407i	0.808698	−	0.216690i	0.639399	+	0.768875i	$0.279183\pi$
$558$	−23.6485	−	38.4088i	−1.00112	−	1.62598i
$559$	2.02964	−	1.17181i	0.0858446	−	0.0495624i
$560$	57.3213	−	5.54177i	2.42227	−	0.234183i
$561$	1.03882	−	5.02088i	0.0438592	−	0.211982i
$562$	3.81240	−	0.333542i	0.160816	−	0.0140696i
$563$	11.2154	−	24.0516i	0.472675	−	1.01365i	−0.515008	−	0.857185i	$-0.672211\pi$
$563$	11.2154	−	24.0516i	0.472675	−	1.01365i	0.987683	−	0.156469i	$-0.0500111\pi$
$564$	5.76062	+	2.29122i	0.242566	+	0.0964777i
$565$	−2.96090	−	4.14763i	−0.124566	−	0.174492i
$566$		−	13.1138i		−	0.551216i
$567$	12.6117	+	23.4799i	0.529644	+	0.986063i
$568$	−34.8877	−	34.8877i	−1.46386	−	1.46386i
$569$	−7.42425	−	42.1050i	−0.311241	−	1.76513i	−0.592567	−	0.805521i	$-0.701886\pi$
$569$	−7.42425	−	42.1050i	−0.311241	−	1.76513i	0.281327	−	0.959612i	$-0.409226\pi$
$570$	−21.0254	−	18.3852i	−0.880656	−	0.770073i
$571$	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	$0.324557\pi$
$572$	2.56515	+	29.3198i	0.107254	+	1.22592i
$573$	−3.61420	−	5.49993i	−0.150986	−	0.229763i
$574$	16.6766	−	45.8187i	0.696069	−	1.91243i
$575$	−22.0315	−	30.2745i	−0.918776	−	1.26253i
$576$	−13.4687	+	4.02051i	−0.561195	+	0.167521i
$577$	−3.87943	−	14.4782i	−0.161503	−	0.602737i	−0.998460	−	0.0554690i	$-0.982335\pi$
$577$	−3.87943	−	14.4782i	−0.161503	−	0.602737i	0.836958	−	0.547268i	$-0.184332\pi$
$578$	3.02565	−	34.5834i	0.125851	−	1.43848i
$579$	0.631195	−	21.3980i	0.0262316	−	0.889272i
$580$	36.0037	+	20.3516i	1.49497	+	0.845052i
$581$	11.8605	+	2.09132i	0.492055	+	0.0867626i
$582$	−10.2829	+	34.2972i	−0.426239	+	1.42166i
$583$	−12.2639	−	1.07295i	−0.507918	−	0.0444370i
$584$	−14.2357	+	24.6569i	−0.589077	+	1.02031i
$585$	−24.8967	+	10.1313i	−1.02935	+	0.418876i
$586$	−29.7304	−	51.4946i	−1.22815	−	2.12722i
$587$	−1.70173	−	3.64938i	−0.0702381	−	0.150626i	0.868054	−	0.496470i	$-0.165371\pi$
$587$	−1.70173	−	3.64938i	−0.0702381	−	0.150626i	−0.938292	+	0.345844i	$0.887593\pi$
$588$	−0.832156	−	14.3868i	−0.0343175	−	0.593302i
$589$	10.4008	−	12.3951i	0.428556	−	0.510733i
$590$	42.2689	+	41.5054i	1.74018	+	1.70875i
$591$	41.1433	−	6.00978i	1.69241	−	0.247209i
$592$	−2.33389	−	1.63421i	−0.0959223	−	0.0671655i
$593$	6.31053	−	6.31053i	0.259142	−	0.259142i	−0.565563	−	0.824705i	$-0.691341\pi$
$593$	6.31053	−	6.31053i	0.259142	−	0.259142i	0.824705	+	0.565563i	$0.191341\pi$
$594$	−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
$597$	−1.33622	+	11.3926i	−0.0546880	+	0.466266i
$598$	−70.3955	−	32.8260i	−2.87869	−	1.34235i
$599$	25.4844	+	21.3840i	1.04127	+	0.873726i	0.992148	−	0.125067i	$-0.0399145\pi$
$599$	25.4844	+	21.3840i	1.04127	+	0.873726i	0.0491180	+	0.998793i	$0.484359\pi$
$600$	−56.6605	−	21.3485i	−2.31316	−	0.871548i
$601$	−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	$0.729312\pi$
$602$	1.16048	−	4.33098i	0.0472978	−	0.176518i
$603$	−5.91878	−	0.871816i	−0.241031	−	0.0355031i
$604$	74.1818	+	42.8289i	3.01841	+	1.74268i
$605$	17.9229	−	6.70901i	0.728671	−	0.272760i
$606$	−36.6652	+	59.3901i	−1.48942	+	2.41256i
$607$	26.0280	+	37.1718i	1.05644	+	1.50876i	0.847477	+	0.530833i	$0.178121\pi$
$607$	26.0280	+	37.1718i	1.05644	+	1.50876i	0.208966	+	0.977923i	$0.432990\pi$
$608$	−13.6288	−	19.4639i	−0.552719	−	0.789365i
$609$	10.6015	−	17.1723i	0.429596	−	0.695857i
$610$	−63.9996	−	29.1364i	−2.59127	−	1.17970i
$611$	2.64216	+	1.52545i	0.106890	+	0.0617131i
$612$	26.4325	+	3.89341i	1.06847	+	0.157382i
$613$	9.48053	−	35.3818i	0.382915	−	1.42906i	−0.458512	−	0.888688i	$-0.651617\pi$
$613$	9.48053	−	35.3818i	0.382915	−	1.42906i	0.841427	−	0.540370i	$-0.181716\pi$
$614$	56.7222	+	20.6452i	2.28912	+	0.833172i
$615$	−17.7703	+	17.0605i	−0.716567	+	0.687945i
$616$	24.7829	+	20.7953i	0.998533	+	0.837868i
$617$	−32.8468	−	15.3167i	−1.32236	−	0.616628i	−0.372134	−	0.928179i	$-0.621374\pi$
$617$	−32.8468	−	15.3167i	−1.32236	−	0.616628i	−0.950229	+	0.311551i	$0.899152\pi$
$618$	−4.13806	+	35.2808i	−0.166457	+	1.41920i
$619$	33.7534	−	5.95163i	1.35666	−	0.239216i	0.552444	−	0.833550i	$-0.313695\pi$
$619$	33.7534	−	5.95163i	1.35666	−	0.239216i	0.804218	+	0.594334i	$0.202584\pi$
$620$	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
$623$	20.5478	+	14.3877i	0.823231	+	0.576433i
$624$	−59.7228	+	8.72368i	−2.39083	+	0.349227i
$625$	−13.2807	−	21.1807i	−0.531230	−	0.847228i
$626$	51.4823	−	61.3542i	2.05764	−	2.45221i
$627$	−0.435371	−	7.52695i	−0.0173870	−	0.300597i
$628$	6.04798	+	12.9699i	0.241341	+	0.517557i
$629$	0.310333	+	0.537512i	0.0123738	+	0.0214320i
$630$	−19.9750	+	47.3865i	−0.795824	+	1.88792i
$631$	−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	$0.952748\pi$
$632$	91.5648	+	8.01088i	3.64225	+	0.318656i
$633$	1.38511	−	4.61985i	0.0550531	−	0.183623i
$634$	−53.6285	−	9.45615i	−2.12986	−	0.375552i
$635$	−1.29306	−	4.65563i	−0.0513135	−	0.184753i
$636$	1.89147	−	64.1226i	0.0750018	−	2.54263i
$637$	0.618092	−	7.06483i	0.0244897	−	0.279919i
$638$	4.11886	+	15.3718i	0.163067	+	0.608576i
$639$	20.2861	−	6.05555i	0.802504	−	0.239554i
$640$	9.08721	+	6.24029i	0.359203	+	0.246669i
$641$	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	$0.0764941\pi$
$642$	−13.7678	−	20.9512i	−0.543371	−	0.826876i
$643$	3.93539	+	44.9817i	0.155197	+	1.77390i	0.531161	+	0.847271i	$0.321756\pi$
$643$	3.93539	+	44.9817i	0.155197	+	1.77390i	−0.375965	+	0.926634i	$0.622689\pi$
$644$	−97.9620	+	35.6552i	−3.86024	+	1.40501i
$645$	−1.49116	+	1.70529i	−0.0587142	+	0.0671456i
$646$	2.37242	+	13.4546i	0.0933414	+	0.529366i
$647$	−18.1400	−	18.1400i	−0.713158	−	0.713158i	0.254037	−	0.967195i	$-0.418242\pi$
$647$	−18.1400	−	18.1400i	−0.713158	−	0.713158i	−0.967195	+	0.254037i	$0.918242\pi$
$648$	12.8231	−	61.6039i	0.503738	−	2.42003i
$649$			15.9914i			0.627719i
$650$	−45.3787	−	25.1080i	−1.77990	−	0.984816i
$651$	−27.6826	−	11.0104i	−1.08497	−	0.431532i
$652$	−44.9910	+	96.4835i	−1.76198	+	3.77858i
$653$	−7.25864	+	0.635049i	−0.284052	+	0.0248514i	−0.228292	−	0.973593i	$-0.573314\pi$
$653$	−7.25864	+	0.635049i	−0.284052	+	0.0248514i	−0.0557608	+	0.998444i	$0.517758\pi$
$654$	−5.96228	+	28.8171i	−0.233144	+	1.12684i
$655$	−1.36961	+	1.66278i	−0.0535151	+	0.0649701i
$656$	−47.9046	+	27.6577i	−1.87036	+	1.07985i
$657$	−6.40515	−	10.4030i	−0.249889	−	0.405858i
$658$	5.63801	−	1.51070i	0.219793	−	0.0588932i
$659$	−20.4475	+	17.1575i	−0.796520	+	0.668360i	−0.947350	−	0.320200i	$-0.896250\pi$
$659$	−20.4475	+	17.1575i	−0.796520	+	0.668360i	0.150830	+	0.988560i	$0.451805\pi$
$660$	−11.4949	−	26.0223i	−0.447437	−	1.01292i
$661$	−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	$0.939866\pi$
$662$	−0.509133	+	0.356499i	−0.0197880	+	0.0138557i
$663$	12.5943	+	3.77599i	0.489123	+	0.146647i
$664$	−18.2766	−	21.7813i	−0.709271	−	0.845277i
$665$	−18.3913	−	1.44028i	−0.713184	−	0.0558515i
$666$	2.27449	−	1.14001i	0.0881345	−	0.0441745i
$667$	−28.4594	−	7.62568i	−1.10195	−	0.295267i
$668$	−22.3541	+	10.4239i	−0.864905	+	0.403312i
$669$	−25.4097	+	28.5297i	−0.982397	+	1.10302i
$670$	−5.86242	−	9.94363i	−0.226485	−	0.384156i
$671$	−6.49238	−	17.8377i	−0.250635	−	0.688615i
$672$	−26.1389	+	35.0813i	−1.00833	+	1.35329i
$673$	12.4963	−	17.8466i	0.481697	−	0.687934i	−0.502587	−	0.864526i	$-0.667618\pi$
$673$	12.4963	−	17.8466i	0.481697	−	0.687934i	0.984284	+	0.176592i	$0.0565074\pi$
$674$	44.3443			1.70808
$675$	19.6152	−	17.0365i	0.754991	−	0.655736i
$676$	−14.3629			−0.552418
$677$	−6.04776	+	8.63710i	−0.232434	+	0.331951i	−0.918378	−	0.395704i	$-0.870501\pi$
$677$	−6.04776	+	8.63710i	−0.232434	+	0.331951i	0.685944	+	0.727654i	$0.259390\pi$
$678$	10.1487	+	1.19033i	0.389758	+	0.0457143i
$679$	8.08857	+	22.2232i	0.310411	+	0.852846i
$680$	15.0422	+	25.5140i	0.576841	+	0.978416i
$681$	−4.04543	−	12.2248i	−0.155021	−	0.468455i
$682$	21.2916	−	9.92842i	0.815296	−	0.380179i
$683$	22.9581	+	6.15162i	0.878469	+	0.235385i	0.669746	−	0.742590i	$-0.266403\pi$
$683$	22.9581	+	6.15162i	0.878469	+	0.235385i	0.208723	+	0.977975i	$0.433069\pi$
$684$	39.0261	−	4.52981i	1.49220	−	0.173202i
$685$	5.42411	+	0.424778i	0.207245	+	0.0162299i
$686$	25.7716	+	30.7134i	0.983965	+	1.17264i
$687$	1.85287	+	7.83183i	0.0706912	+	0.298803i
$688$	−4.16675	+	2.91759i	−0.158856	+	0.111232i
$689$	5.48198	−	31.0899i	0.208847	−	1.18443i
$690$	74.6422	+	8.06586i	2.84158	+	0.307062i
$691$	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	$0.0125057\pi$
$692$	−37.1333	+	9.94983i	−1.41160	+	0.378236i
$693$	−12.9051	+	5.11489i	−0.490223	+	0.194299i
$694$	−60.8414	+	35.1268i	−2.30951	+	1.33339i
$695$	−13.8296	+	16.7898i	−0.524585	+	0.636874i
$696$	−45.2335	+	14.9687i	−1.71457	+	0.567386i
$697$	12.0042	−	1.05023i	0.454691	−	0.0397803i
$698$	20.9293	−	44.8830i	0.792185	−	1.69885i
$699$	−19.4057	+	15.3314i	−0.733992	+	0.579888i
$700$	−66.8950	+	19.2378i	−2.52839	+	0.727121i
$701$			37.4202i			1.41334i	0.707542	+	0.706671i	$0.249804\pi$
$701$			37.4202i			1.41334i	−0.707542	+	0.706671i	$0.750196\pi$
$702$	18.4944	−	50.6237i	0.698027	−	1.91067i
$703$	0.645364	+	0.645364i	0.0243404	+	0.0243404i
$704$	−1.27126	−	7.20968i	−0.0479125	−	0.271725i
$705$	−2.89309	−	0.571140i	−0.108960	−	0.0215104i
$706$	74.0671	−	26.9582i	2.78755	−	1.01459i
$707$	4.01789	+	45.9247i	0.151108	+	1.72718i
$708$	−83.1915	+	4.81193i	−3.12653	+	0.180843i
$709$	−10.2864	+	28.2616i	−0.386313	+	1.06139i	0.582335	+	0.812949i	$0.302139\pi$
$709$	−10.2864	+	28.2616i	−0.386313	+	1.06139i	−0.968648	+	0.248437i	$0.920083\pi$
$710$	33.6723	+	23.1232i	1.26370	+	0.867797i
$711$	−21.6987	+	32.9337i	−0.813763	+	1.23511i
$712$	−15.3277	−	57.2037i	−0.574429	−	2.14380i
$713$	−3.79078	+	43.3288i	−0.141966	+	1.62268i
$714$	22.1460	−	11.9296i	0.828795	−	0.446454i
$715$	−3.74648	−	13.4891i	−0.140111	−	0.504465i
$716$	24.5733	+	4.33293i	0.918347	+	0.161929i
$717$	24.1995	+	25.6705i	0.903745	+	0.958683i
$718$	80.5327	+	7.04570i	3.00546	+	0.262943i
$719$	1.80566	−	3.12750i	0.0673399	−	0.116636i	−0.830390	−	0.557183i	$-0.811882\pi$
$719$	1.80566	−	3.12750i	0.0673399	−	0.116636i	0.897730	+	0.440547i	$0.145215\pi$
$720$	51.9144	−	26.6150i	1.93473	−	0.991883i
$721$	11.7313	+	20.3192i	0.436896	+	0.756726i
$722$	−12.2954	−	26.3676i	−0.457589	−	0.981302i
$723$	23.5550	−	15.4789i	0.876020	−	0.575665i
$724$	69.7617	−	83.1388i	2.59268	−	3.08983i
$725$	−18.6056	−	6.39035i	−0.690996	−	0.237332i
$726$	−14.1819	+	35.6562i	−0.526338	+	1.32333i
$727$	24.6477	+	17.2585i	0.914133	+	0.640083i	0.933053	−	0.359738i	$-0.117134\pi$
$727$	24.6477	+	17.2585i	0.914133	+	0.640083i	−0.0189200	+	0.999821i	$0.506023\pi$
$728$	−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
$732$	90.8423	−	39.1424i	3.35763	−	1.44675i
$733$	−37.0978	−	17.2990i	−1.37024	−	0.638953i	−0.408459	−	0.912777i	$-0.633934\pi$
$733$	−37.0978	−	17.2990i	−1.37024	−	0.638953i	−0.961780	+	0.273824i	$0.911712\pi$
$734$	2.82259	+	2.36844i	0.104184	+	0.0874206i
$735$	1.63887	+	6.65598i	0.0604507	+	0.245509i
$736$	60.0186	+	21.8450i	2.21231	+	0.805217i
$737$	0.806480	−	3.00982i	0.0297071	−	0.110868i
$738$	−1.39709	−	49.3750i	−0.0514276	−	1.81752i
$739$	7.88425	+	4.55198i	0.290027	+	0.167447i	0.637954	−	0.770074i	$-0.279781\pi$
$739$	7.88425	+	4.55198i	0.290027	+	0.167447i	−0.347927	+	0.937522i	$0.613114\pi$
$740$	3.13421	+	1.42688i	0.115216	+	0.0524530i
$741$	19.3259	+	0.570071i	0.709954	+	0.0209421i
$742$	−34.6428	−	49.4750i	−1.27178	−	1.81629i
$743$	−27.8074	−	39.7131i	−1.02016	−	1.45693i	−0.884706	−	0.466149i	$-0.845641\pi$
$743$	−27.8074	−	39.7131i	−1.02016	−	1.45693i	−0.135449	−	0.990784i	$-0.543248\pi$
$744$	33.3566	+	61.9230i	1.22291	+	2.27021i
$745$	−29.3589	+	10.9898i	−1.07563	+	0.402635i
$746$	−22.0487	−	12.7298i	−0.807262	−	0.466073i
$747$	11.9503	−	2.45757i	0.437240	−	0.0899177i
$748$	−3.60163	+	13.4415i	−0.131689	+	0.491468i
$749$	−15.5600	−	5.66337i	−0.568550	−	0.206935i
$750$	49.3478	+	8.81079i	1.80193	+	0.321725i
$751$	−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	$0.994671\pi$
$752$	−6.00134	−	2.79847i	−0.218846	−	0.102050i
$753$	−14.3802	−	10.7146i	−0.524042	−	0.390461i
$754$	−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	−0.999863	−	0.0165746i	$-0.994724\pi$
$757$	−27.0538	+	27.0538i	−0.983288	+	0.983288i	0.0165746	+	0.999863i	$0.494724\pi$
$758$	−12.2242	−	8.55950i	−0.444004	−	0.310895i
$759$	12.5636	+	15.9024i	0.456032	+	0.577221i
$760$	31.0761	+	30.5148i	1.12725	+	1.10689i
$761$	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	$0.00344017\pi$
$762$	8.65623	+	4.35166i	0.313582	+	0.157644i
$763$	8.21429	+	17.6156i	0.297377	+	0.637728i
$764$	8.93086	+	15.4687i	0.323107	+	0.559638i
$765$	−12.6998	+	0.475209i	−0.459164	+	0.0171812i
$766$	3.69820	−	6.40547i	0.133621	−	0.231439i
$767$	−40.8523	−	3.57411i	−1.47509	−	0.129054i
$768$	−37.3043	+	8.82550i	−1.34610	+	0.318463i
$769$	−6.45291	−	1.13782i	−0.232698	−	0.0410309i	0.0560832	−	0.998426i	$-0.482139\pi$
$769$	−6.45291	−	1.13782i	−0.232698	−	0.0410309i	−0.288781	+	0.957395i	$0.593250\pi$
$770$	−23.3166	−	13.1800i	−0.840274	−	0.474975i
$771$	8.37510	+	5.17047i	0.301622	+	0.186210i
$772$	−5.06383	+	57.8799i	−0.182251	+	2.08314i
$773$	1.43767	+	5.36547i	0.0517095	+	0.192983i	0.986949	−	0.161033i	$-0.0514826\pi$
$773$	1.43767	+	5.36547i	0.0517095	+	0.192983i	−0.935239	+	0.354016i	$0.884816\pi$
$774$	−0.523705	−	4.51191i	−0.0188242	−	0.162177i
$775$	−4.52082	+	28.6868i	−0.162393	+	1.03046i
$776$	19.0963	−	52.4668i	0.685519	−	1.88345i
$777$	0.754775	−	1.50138i	0.0270774	−	0.0538618i
$778$	−2.87647	−	32.8782i	−0.103126	−	1.17874i
$779$	16.6509	−	6.06042i	0.596579	−	0.217137i
$780$	69.0465	−	23.5491i	2.47226	−	0.843194i
$781$	1.91473	+	10.8590i	0.0685144	+	0.388565i
$782$	−25.9681	−	25.9681i	−0.928618	−	0.928618i
$783$	3.57429	−	20.1294i	0.127735	−	0.719365i
$784$			15.3922i			0.549723i
$785$	−3.95508	−	5.54028i	−0.141163	−	0.197741i
$786$	−0.624320	−	4.27413i	−0.0222687	−	0.152453i
$787$	−13.1429	+	28.1849i	−0.468492	+	1.00468i	0.520105	+	0.854102i	$0.325893\pi$
$787$	−13.1429	+	28.1849i	−0.468492	+	1.00468i	−0.988597	+	0.150582i	$0.951885\pi$
$788$	−112.421	+	9.83559i	−4.00484	+	0.350378i
$789$	−25.1995	−	22.4437i	−0.897126	−	0.799018i
$790$	−75.7426	+	7.32272i	−2.69480	+	0.260531i
$791$	5.84490	−	3.37455i	0.207821	−	0.119985i
$792$	31.1017	+	10.3336i	1.10515	+	0.367190i
$793$	47.0197	−	12.5989i	1.66972	−	0.447400i
$794$	7.12249	−	5.97648i	0.252768	−	0.212097i
$795$	4.68538	+	30.1524i	0.166173	+	1.06940i
$796$	5.40604	−	30.6592i	0.191612	−	1.08669i
$797$	−3.95902	+	2.77214i	−0.140236	+	0.0981941i	−0.641589	−	0.767049i	$-0.721725\pi$
$797$	−3.95902	+	2.77214i	−0.140236	+	0.0981941i	0.501353	+	0.865243i	$0.332836\pi$
$798$	26.9156	−	25.3732i	0.952802	−	0.898202i
$799$	0.927217	+	1.10501i	0.0328026	+	0.0390926i
$800$	38.9723	+	17.3155i	1.37788	+	0.612196i
$801$	24.7215	+	5.88003i	0.873493	+	0.207761i
$802$	51.4959	+	13.7983i	1.81838	+	0.487235i
$803$	5.76678	−	2.68909i	0.203505	−	0.0948961i
$804$	15.9005	+	3.28983i	0.560769	+	0.116024i
$805$	42.7166	−	25.1842i	1.50556	−	0.887628i
$806$	20.6048	+	56.6111i	0.725772	+	1.99404i
$807$	14.9846	+	34.7766i	0.527485	+	1.22419i
$808$	62.4270	−	89.1550i	2.19617	−	3.13646i
$809$	27.0458			0.950881			0.475440	−	0.879748i	$-0.342289\pi$
$809$	27.0458			0.950881			0.475440	+	0.879748i	$0.342289\pi$
$810$	−1.12398	+	52.0827i	−0.0394927	+	1.83000i
$811$	−47.9089			−1.68231			−0.841154	−	0.540795i	$-0.818123\pi$
$811$	−47.9089			−1.68231			−0.841154	+	0.540795i	$0.818123\pi$
$812$	−31.4166	+	44.8675i	−1.10251	+	1.57454i
$813$	17.5939	+	40.8321i	0.617044	+	1.43204i
$814$	0.453216	+	1.24520i	0.0158852	+	0.0436443i
$815$	12.6599	−	49.0304i	0.443458	−	1.71746i
$816$	−27.9453	−	5.78190i	−0.978280	−	0.202407i
$817$	1.47677	−	0.688628i	0.0516656	−	0.0240921i
$818$	−42.0939	−	11.2790i	−1.47178	−	0.394362i
$819$	−10.1824	−	34.1109i	−0.355801	−	1.19193i
$820$	50.8231	−	43.4410i	1.77482	−	1.51703i
$821$	−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	$-0.490659\pi$
$822$	−7.93817	+	7.48327i	−0.276875	+	0.261009i
$823$	−9.96073	+	6.97458i	−0.347209	+	0.243119i	−0.734152	−	0.678985i	$-0.762420\pi$
$823$	−9.96073	+	6.97458i	−0.347209	+	0.243119i	0.386943	+	0.922104i	$0.373531\pi$
$824$	9.61888	−	54.5514i	0.335090	−	1.90039i
$825$	7.63620	+	11.1713i	0.265858	+	0.388936i
$826$	−60.1008	+	50.4305i	−2.09117	+	1.75470i
$827$	13.0585	−	3.49901i	0.454088	−	0.121673i	−0.0245234	−	0.999699i	$-0.507807\pi$
$827$	13.0585	−	3.49901i	0.454088	−	0.121673i	0.478612	+	0.878027i	$0.341140\pi$
$828$	−78.9478	+	70.1444i	−2.74363	+	2.43769i
$829$	−22.0957	+	12.7570i	−0.767415	+	0.443068i	−0.831952	−	0.554848i	$-0.812776\pi$
$829$	−22.0957	+	12.7570i	−0.767415	+	0.443068i	0.0645364	+	0.997915i	$0.479443\pi$
$830$	18.1698	+	14.9662i	0.630681	+	0.519484i
$831$	−6.86062	−	6.11036i	−0.237992	−	0.211966i
$832$	18.7022	−	1.63623i	0.648383	−	0.0567261i
$833$	1.41707	−	3.03892i	0.0490986	−	0.105292i
$834$	−6.30404	−	43.1578i	−0.218291	−	1.49443i
$835$	9.54884	−	6.81669i	0.330451	−	0.235901i
$836$			20.4628i			0.707721i
$837$	−30.1801	−	0.0362537i	−1.04318	−	0.00125311i
$838$	0.996030	+	0.996030i	0.0344073	+	0.0344073i
$839$	6.29080	+	35.6769i	0.217183	+	1.23170i	0.877078	+	0.480347i	$0.159489\pi$
$839$	6.29080	+	35.6769i	0.217183	+	1.23170i	−0.659896	+	0.751357i	$0.729400\pi$
$840$	35.3634	−	71.9710i	1.22015	−	2.48324i
$841$	12.7044	−	4.62403i	0.438083	−	0.159449i
$842$	−1.68687	−	19.2811i	−0.0581335	−	0.664469i
$843$	1.15013	−	2.28781i	0.0396125	−	0.0787963i
$844$	−4.47705	+	12.3006i	−0.154106	+	0.423404i
$845$	6.71706	−	1.24762i	0.231074	−	0.0429194i
$846$	4.74576	−	3.52719i	0.163163	−	0.121267i
$847$	6.55983	+	24.4816i	0.225398	+	0.841199i
$848$	−5.97184	+	68.2584i	−0.205074	+	2.34400i
$849$	−7.46630	−	4.60941i	−0.256243	−	0.158195i
$850$	−16.1013	−	18.4935i	−0.552270	−	0.634324i
$851$	−2.41605	−	0.426015i	−0.0828212	−	0.0146036i
$852$	−55.9149	+	13.2284i	−1.91561	+	0.453199i
$853$	12.1293	+	1.06118i	0.415300	+	0.0363341i	0.292891	−	0.956146i	$-0.405383\pi$
$853$	12.1293	+	1.06118i	0.415300	+	0.0363341i	0.122409	+	0.992480i	$0.460938\pi$
$854$	46.5651	−	80.6531i	1.59342	−	2.75989i
$855$	−17.8578	+	5.50842i	−0.610724	+	0.188384i
$856$	19.5466	+	33.8558i	0.668090	+	1.15717i
$857$	−17.7690	−	38.1058i	−0.606978	−	1.30167i	−0.934210	−	0.356724i	$-0.883894\pi$
$857$	−17.7690	−	38.1058i	−0.606978	−	1.30167i	0.327232	−	0.944944i	$-0.393884\pi$
$858$	25.0804	+	12.6084i	0.856230	+	0.430444i
$859$	−16.1180	+	19.2086i	−0.549938	+	0.655390i	−0.967385	−	0.253311i	$-0.918480\pi$
$859$	−16.1180	+	19.2086i	−0.549938	+	0.655390i	0.417447	+	0.908701i	$0.362925\pi$
$860$	4.30761	−	4.38684i	0.146888	−	0.149590i
$861$	−20.2249	−	25.5997i	−0.689264	−	0.872434i
$862$	−31.7398	−	22.2244i	−1.08106	−	0.756967i
$863$	16.2331	−	16.2331i	0.552582	−	0.552582i	−0.374603	−	0.927185i	$-0.622221\pi$
$863$	16.2331	−	16.2331i	0.552582	−	0.552582i	0.927185	+	0.374603i	$0.122221\pi$
$864$	−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
$867$	−18.6264	−	13.8784i	−0.632585	−	0.471336i
$868$	73.2814	+	34.1717i	2.48733	+	1.15986i
$869$	−15.7358	−	13.2039i	−0.533800	−	0.447911i
$870$	34.5559	−	19.0228i	1.17155	−	0.644934i
$871$	7.50875	+	2.73296i	0.254424	+	0.0926028i
$872$	11.8767	−	44.3246i	0.402197	−	1.50102i
$873$	15.9126	+	17.9097i	0.538560	+	0.606152i
$874$	−46.7680	−	27.0015i	−1.58195	−	0.913339i
$875$	29.6137	−	14.8077i	1.00112	−	0.500592i
$876$	15.7246	+	29.1911i	0.531285	+	0.986275i
$877$	31.8721	+	45.5180i	1.07624	+	1.53703i	0.821655	+	0.569985i	$0.193051\pi$
$877$	31.8721	+	45.5180i	1.07624	+	1.53703i	0.254588	+	0.967049i	$0.418060\pi$
$878$	56.5342	+	80.7392i	1.90794	+	2.72481i
$879$	−39.7682	−	1.17307i	−1.34135	−	0.0395668i
$880$	10.6522	+	28.4570i	0.359085	+	0.959286i
$881$	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	$0.535438\pi$
$882$	−12.0929	−	6.53293i	−0.407189	−	0.219975i
$883$	−6.72963	+	25.1153i	−0.226470	+	0.845198i	0.755340	+	0.655333i	$0.227472\pi$
$883$	−6.72963	+	25.1153i	−0.226470	+	0.845198i	−0.981810	+	0.189865i	$0.939195\pi$
$884$	−33.5330	−	12.2050i	−1.12784	−	0.410499i
$885$	38.4881	−	9.47676i	1.29376	−	0.318558i
$886$	56.7260	+	47.5988i	1.90575	+	1.59911i
$887$	11.8712	+	5.53565i	0.398597	+	0.185869i	0.611572	−	0.791189i	$-0.290537\pi$
$887$	11.8712	+	5.53565i	0.398597	+	0.185869i	−0.212975	+	0.977058i	$0.568315\pi$
$888$	−3.64349	+	1.56992i	−0.122268	+	0.0526831i
$889$	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
$893$	1.73756	+	1.21666i	0.0581454	+	0.0407138i
$894$	23.2308	−	58.4073i	0.776954	−	1.95343i
$895$	−11.8685	+	0.108162i	−0.396722	+	0.00361546i
$896$	−9.38428	+	11.1838i	−0.313507	+	0.373623i
$897$	−43.4328	+	28.5413i	−1.45018	+	0.952966i
$898$	−27.2338	−	58.4031i	−0.908804	−	1.94894i
$899$	11.4261	+	19.7906i	0.381082	+	0.660054i
$900$	−55.8183	+	43.0869i	−1.86061	+	1.43623i
$901$	7.46317	−	12.9266i	0.248634	−	0.430647i
$902$	25.6289	+	2.24223i	0.853347	+	0.0746582i
$903$	−2.05792	−	2.18302i	−0.0684834	−	0.0726464i
$904$	−15.6919	−	2.76691i	−0.521906	−	0.0920261i
$905$	−25.4036	+	44.9412i	−0.844445	+	1.49390i
$906$	71.9264	−	38.7452i	2.38959	−	1.28722i
$907$	−3.65873	+	41.8194i	−0.121486	+	1.38859i	0.653650	+	0.756797i	$0.273237\pi$
$907$	−3.65873	+	41.8194i	−0.121486	+	1.38859i	−0.775136	+	0.631795i	$0.782319\pi$
$908$	9.04532	+	33.7576i	0.300180	+	1.12029i
$909$	20.9260	+	41.7503i	0.694070	+	1.38477i
$910$	38.8814	−	56.6197i	1.28891	−	1.87693i
$911$	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	$-0.252463\pi$
$912$	−41.8936	+	2.42319i	−1.38724	+	0.0802399i
$913$	0.553828	+	6.33028i	0.0183290	+	0.209502i
$914$	−8.96418	+	3.26269i	−0.296509	+	0.107920i
$915$	−39.0841	+	26.1967i	−1.29208	+	0.866035i
$916$	−3.79298	−	21.5110i	−0.125323	−	0.710745i
$917$	−2.01738	−	2.01738i	−0.0666196	−	0.0666196i
$918$	16.4034	−	19.5011i	0.541392	−	0.643634i
$919$		−	38.4394i		−	1.26800i	−0.773333	−	0.634000i	$-0.781412\pi$
$919$		−	38.4394i		−	1.26800i	0.773333	−	0.634000i	$-0.218588\pi$
$920$	−115.474	−	19.2779i	−3.80707	−	0.635573i
$921$	31.6916	−	25.0379i	1.04427	−	0.825026i
$922$	16.6937	−	35.7998i	0.549778	−	1.17900i
$923$	−28.1686	+	2.46444i	−0.927182	+	0.0811179i
$924$	35.7684	−	11.8365i	1.17669	−	0.389391i
$925$	−1.58972	−	0.395056i	−0.0522695	−	0.0129894i
$926$	−25.2375	+	14.5709i	−0.829356	+	0.478829i
$927$	18.6325	+	14.7569i	0.611971	+	0.484681i
$928$	32.4145	−	8.68545i	1.06406	−	0.285114i
$929$	17.4189	−	14.6162i	0.571497	−	0.479543i	−0.310645	−	0.950526i	$-0.600545\pi$
$929$	17.4189	−	14.6162i	0.571497	−	0.479543i	0.882142	+	0.470983i	$0.156101\pi$
$930$	−36.5133	−	45.3607i	−1.19732	−	1.48743i
$931$	0.856201	−	4.85576i	0.0280609	−	0.159141i
$932$	54.9834	−	38.4998i	1.80104	−	1.26110i
$933$	3.77630	+	15.9620i	0.123631	+	0.522571i
$934$	29.0481	+	34.6182i	0.950482	+	1.13274i
$935$	0.516787	−	6.59901i	0.0169007	−	0.215811i
$936$	−33.3499	+	77.1439i	−1.09008	+	2.52153i
$937$	2.08398	+	0.558400i	0.0680806	+	0.0182421i	0.292699	−	0.956205i	$-0.405447\pi$
$937$	2.08398	+	0.558400i	0.0680806	+	0.0182421i	−0.224618	+	0.974447i	$0.572113\pi$
$938$	13.8552	−	6.46077i	0.452387	−	0.210951i
$939$	−16.8361	−	50.8767i	−0.549425	−	1.66030i
$940$	7.74943	+	2.00094i	0.252758	+	0.0652636i
$941$	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	$0.626772\pi$
$942$	13.5563	+	1.59001i	0.441688	+	0.0518052i
$943$	−27.3198	+	39.0167i	−0.889654	+	1.27056i
$944$	89.0054			2.89688
$945$	19.9582	+	28.0287i	0.649241	+	0.911772i
$946$	2.36576			0.0769175
$947$	9.56806	−	13.6646i	0.310920	−	0.444040i	−0.633030	−	0.774127i	$-0.718189\pi$
$947$	9.56806	−	13.6646i	0.310920	−	0.444040i	0.943950	+	0.330087i	$0.107078\pi$
$948$	63.9549	−	85.8346i	2.07716	−	2.78778i
$949$	5.58076	+	15.3330i	0.181159	+	0.497731i
$950$	−29.9085	−	20.1399i	−0.970361	−	0.653426i
$951$	−24.2338	+	27.2094i	−0.785835	+	0.882324i
$952$	−35.5504	+	16.5774i	−1.15220	+	0.537277i
$953$	17.5554	+	4.70396i	0.568676	+	0.152376i	0.531689	−	0.846940i	$-0.321557\pi$
$953$	17.5554	+	4.70396i	0.568676	+	0.152376i	0.0369865	+	0.999316i	$0.488224\pi$
$954$	−51.0925	−	33.6627i	−1.65418	−	1.08987i
$955$	−5.52036	−	6.45846i	−0.178635	−	0.208991i
$956$	−61.5462	−	73.3479i	−1.99055	−	2.37224i
$957$	10.1996	+	3.05802i	0.329707	+	0.0988516i
$958$	48.5557	−	33.9991i	1.56876	−	1.09846i
$959$	−1.25123	+	7.09611i	−0.0404045	+	0.229145i
$960$	−16.5988	+	7.33222i	−0.535725	+	0.236647i
$961$	2.09504	−	1.75795i	0.0675821	−	0.0567081i
$962$	−3.28233	+	0.879497i	−0.105826	+	0.0283561i
$963$	−16.7677	+	0.474451i	−0.540332	+	0.0152890i
$964$	−66.2491	+	38.2489i	−2.13374	+	1.23192i
$965$	−2.65950	−	27.5085i	−0.0856122	−	0.885530i
$966$	−20.1455	+	97.3678i	−0.648170	+	3.13276i
$967$	33.4211	−	2.92397i	1.07475	−	0.0940285i	0.463988	−	0.885842i	$-0.346418\pi$
$967$	33.4211	−	2.92397i	1.07475	−	0.0940285i	0.610763	+	0.791813i	$0.290863\pi$
$968$	25.2885	−	54.2314i	0.812804	−	1.74306i
$969$	8.49422	+	3.37848i	0.272874	+	0.108532i
$970$	−7.61166	+	45.5937i	−0.244396	+	1.46393i
$971$			23.4452i			0.752393i	0.926540	+	0.376196i	$0.122768\pi$
$971$			23.4452i			0.752393i	−0.926540	+	0.376196i	$0.877232\pi$
$972$	−53.2010	−	50.3943i	−1.70642	−	1.61640i
$973$	−20.3704	−	20.3704i	−0.653044	−	0.653044i
$974$	16.3102	+	92.5000i	0.522614	+	2.96389i
$975$	−30.2453	+	17.0109i	−0.968626	+	0.544784i
$976$	−99.2811	+	36.1353i	−3.17791	+	1.15666i
$977$	−1.95075	−	22.2971i	−0.0624099	−	0.713349i	−0.961359	−	0.275297i	$-0.911224\pi$
$977$	−1.95075	−	22.2971i	−0.0624099	−	0.713349i	0.898949	−	0.438052i	$-0.144332\pi$
$978$	55.7614	+	84.8550i	1.78305	+	2.71336i
$979$	−4.52670	+	12.4370i	−0.144674	+	0.397488i
$980$	−3.39744	−	18.2915i	−0.108527	−	0.584300i
$981$	14.3112	+	13.5236i	0.456921	+	0.431774i
$982$	−9.22446	−	34.4262i	−0.294365	−	1.09858i
$983$	0.218640	−	2.49907i	0.00697353	−	0.0797078i	−0.991910	−	0.126940i	$-0.959484\pi$
$983$	0.218640	−	2.49907i	0.00697353	−	0.0797078i	0.998884	+	0.0472321i	$0.0150400\pi$
$984$	−2.27107	+	76.9911i	−0.0723989	+	2.45439i
$985$	51.7216	−	14.3652i	1.64799	−	0.457713i
$986$	−19.0022	−	3.35059i	−0.605152	−	0.106705i
$987$	1.12161	−	3.74097i	0.0357011	−	0.119077i
$988$	−52.2749	−	4.57346i	−1.66309	−	0.145501i
$989$	−2.18999	+	3.79317i	−0.0696376	+	0.120616i
$990$	−26.8783	−	3.70915i	−0.854249	−	0.117885i
$991$	−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	$0.955387\pi$
$992$	−20.9361	−	44.8975i	−0.664720	−	1.42550i
$993$	0.0240146	+	0.415179i	0.000762081	+	0.0131753i
$994$	−34.7731	+	41.4409i	−1.10294	+	1.31443i
$995$	0.134950	+	14.8079i	0.00427820	+	0.469443i
$996$	−32.7650	+	4.78597i	−1.03820	+	0.151649i
$997$	−12.8042	−	8.96558i	−0.405512	−	0.283943i	0.352972	−	0.935634i	$-0.385171\pi$
$997$	−12.8042	−	8.96558i	−0.405512	−	0.283943i	−0.758484	+	0.651691i	$0.774060\pi$
$998$	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.68.2	yes	192
3.2	odd	2		405.2.r.a.233.15		192
5.2	odd	4	inner	135.2.q.a.122.2	yes	192
5.3	odd	4		675.2.ba.b.257.15		192
5.4	even	2		675.2.ba.b.68.15		192
15.2	even	4		405.2.r.a.152.15		192
27.2	odd	18	inner	135.2.q.a.83.2	yes	192
27.25	even	9		405.2.r.a.8.15		192
135.2	even	36	inner	135.2.q.a.2.2	✓	192
135.29	odd	18		675.2.ba.b.218.15		192
135.52	odd	36		405.2.r.a.332.15		192
135.83	even	36		675.2.ba.b.407.15		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.2	✓	192	135.2	even	36	inner
135.2.q.a.68.2	yes	192	1.1	even	1	trivial
135.2.q.a.83.2	yes	192	27.2	odd	18	inner
135.2.q.a.122.2	yes	192	5.2	odd	4	inner
405.2.r.a.8.15		192	27.25	even	9
405.2.r.a.152.15		192	15.2	even	4
405.2.r.a.233.15		192	3.2	odd	2
405.2.r.a.332.15		192	135.52	odd	36
675.2.ba.b.68.15		192	5.4	even	2
675.2.ba.b.218.15		192	135.29	odd	18
675.2.ba.b.257.15		192	5.3	odd	4
675.2.ba.b.407.15		192	135.83	even	36

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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-1.48477 + 2.12047i) q^{2} +(0.685393 + 1.59067i) q^{3} +(-1.60780 - 4.41741i) q^{4} +(1.13563 + 1.92622i) q^{5} +(-4.39061 - 0.908422i) q^{6} +(-2.68394 + 1.25154i) q^{7} +(6.75336 + 1.80956i) q^{8} +(-2.06047 + 2.18047i) q^{9} +(-5.77064 - 0.451915i) q^{10} +(-1.00437 - 1.19696i) q^{11} +(5.92466 - 5.58515i) q^{12} +(3.28227 - 2.29827i) q^{13} +(1.33117 - 7.54945i) q^{14} +(-2.28563 + 3.12664i) q^{15} +(-6.66205 + 5.59013i) q^{16} +(1.82995 - 0.490334i) q^{17} +(-1.56430 - 7.60665i) q^{18} +(2.41262 - 1.39293i) q^{19} +(6.68303 - 8.11355i) q^{20} +(-3.83035 - 3.41147i) q^{21} +(4.02936 - 0.352524i) q^{22} +(-3.16476 + 6.78686i) q^{23} +(1.75030 + 11.9826i) q^{24} +(-2.42067 + 4.37497i) q^{25} +10.3723i q^{26} +(-4.88065 - 1.78305i) q^{27} +(9.84382 + 9.84382i) q^{28} +(0.683218 + 3.87472i) q^{29} +(-3.23631 - 9.48893i) q^{30} +(5.45790 - 1.98651i) q^{31} +(-0.743366 - 8.49672i) q^{32} +(1.21558 - 2.41801i) q^{33} +(-1.67731 + 4.60838i) q^{34} +(-5.45873 - 3.74857i) q^{35} +(12.9449 + 5.59617i) q^{36} +(0.0847926 + 0.316450i) q^{37} +(-0.628522 + 7.18404i) q^{38} +(5.90544 + 3.64579i) q^{39} +(4.18374 + 15.0635i) q^{40} +(6.26389 + 1.10449i) q^{41} +(12.9211 - 3.05689i) q^{42} +(0.582670 + 0.0509770i) q^{43} +(-3.67263 + 6.36118i) q^{44} +(-6.54002 - 1.49271i) q^{45} +(-9.69236 - 16.7877i) q^{46} +(0.321786 + 0.690071i) q^{47} +(-13.4582 - 6.76570i) q^{48} +(1.13767 - 1.35582i) q^{49} +(-5.68285 - 11.6287i) q^{50} +(2.03420 + 2.57478i) q^{51} +(-15.4296 - 10.8039i) 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} +(3.86928 + 2.88298i) q^{57} +(-9.23063 - 4.30431i) q^{58} +(-7.84000 - 6.57854i) q^{59} +(17.4865 + 5.06953i) q^{60} +(11.4160 + 4.15507i) q^{61} +(-3.89137 + 14.5228i) q^{62} +(2.80123 - 8.43102i) q^{63} +(4.05760 + 2.34266i) q^{64} +(8.15444 + 3.71239i) q^{65} +(3.32245 + 6.16778i) q^{66} +(1.14383 + 1.63356i) q^{67} +(-5.10821 - 7.29527i) q^{68} +(-12.9648 - 0.382432i) q^{69} +(16.0536 - 6.00929i) q^{70} +(-6.11142 - 3.52843i) q^{71} +(-17.8608 + 10.9970i) q^{72} +(-1.05397 + 3.93347i) q^{73} +(-0.796919 - 0.290055i) q^{74} +(-8.61825 - 0.851911i) q^{75} +(-10.0321 - 8.41796i) q^{76} +(4.19371 + 1.95556i) q^{77} +(-16.4990 + 7.10913i) 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} +(-3.33133 - 2.33262i) q^{83} +(-8.91139 + 22.4052i) q^{84} +(3.02265 + 2.96805i) q^{85} +(-0.973224 + 1.15984i) q^{86} +(-5.69514 + 3.74248i) q^{87} +(-4.61689 - 9.90096i) q^{88} +(-4.23520 - 7.33558i) q^{89} +(12.8756 - 11.6516i) q^{90} +(-5.93304 + 10.2763i) q^{91} +(35.0686 + 3.06811i) q^{92} +(6.90070 + 7.32018i) q^{93} +(-1.94105 - 0.342259i) q^{94} +(5.42294 + 3.06539i) q^{95} +(13.0060 - 7.00604i) q^{96} +(0.696015 - 7.95549i) q^{97} +(1.18580 + 4.42546i) q^{98} +(4.67941 + 0.276305i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22}+ \cdots + 324 q^{98}+O(q^{100}) \) 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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Representations

Groups

Database

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