LMFDB - Embedded newform 405.2.r.a.233.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,2,Mod(8,405)] 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("405.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([2, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.r (of order $36$, degree $12$, not 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:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			233.15
Character	$\chi$	$=$	405.233
Dual form			405.2.r.a.332.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.48477 - 2.12047i) q^{2} +(-1.60780 - 4.41741i) q^{4} +(-1.13563 - 1.92622i) q^{5} +(-2.68394 + 1.25154i) q^{7} +(-6.75336 - 1.80956i) q^{8} +(-5.77064 - 0.451915i) q^{10} +(1.00437 + 1.19696i) q^{11} +(3.28227 - 2.29827i) q^{13} +(-1.33117 + 7.54945i) q^{14} +(-6.66205 + 5.59013i) q^{16} +(-1.82995 + 0.490334i) q^{17} +(2.41262 - 1.39293i) q^{19} +(-6.68303 + 8.11355i) q^{20} +(4.02936 - 0.352524i) q^{22} +(3.16476 - 6.78686i) q^{23} +(-2.42067 + 4.37497i) q^{25} -10.3723i q^{26} +(9.84382 + 9.84382i) q^{28} +(-0.683218 - 3.87472i) q^{29} +(5.45790 - 1.98651i) q^{31} +(0.743366 + 8.49672i) q^{32} +(-1.67731 + 4.60838i) q^{34} +(5.45873 + 3.74857i) q^{35} +(0.0847926 + 0.316450i) q^{37} +(0.628522 - 7.18404i) q^{38} +(4.18374 + 15.0635i) q^{40} +(-6.26389 - 1.10449i) q^{41} +(0.582670 + 0.0509770i) q^{43} +(3.67263 - 6.36118i) q^{44} +(-9.69236 - 16.7877i) q^{46} +(-0.321786 - 0.690071i) q^{47} +(1.13767 - 1.35582i) q^{49} +(5.68285 + 11.6287i) q^{50} +(-15.4296 - 10.8039i) q^{52} +(-5.57112 + 5.57112i) q^{53} +(1.16502 - 3.29395i) q^{55} +(20.3903 - 3.59537i) q^{56} +(-9.23063 - 4.30431i) q^{58} +(7.84000 + 6.57854i) q^{59} +(11.4160 + 4.15507i) q^{61} +(3.89137 - 14.5228i) q^{62} +(4.05760 + 2.34266i) q^{64} +(-8.15444 - 3.71239i) q^{65} +(1.14383 + 1.63356i) q^{67} +(5.10821 + 7.29527i) q^{68} +(16.0536 - 6.00929i) q^{70} +(6.11142 + 3.52843i) q^{71} +(-1.05397 + 3.93347i) q^{73} +(0.796919 + 0.290055i) q^{74} +(-10.0321 - 8.41796i) q^{76} +(-4.19371 - 1.95556i) q^{77} +(12.9467 - 2.28286i) q^{79} +(18.3335 + 6.48426i) q^{80} +(-11.6425 + 11.6425i) q^{82} +(3.33133 + 2.33262i) q^{83} +(3.02265 + 2.96805i) q^{85} +(0.973224 - 1.15984i) q^{86} +(-4.61689 - 9.90096i) q^{88} +(4.23520 + 7.33558i) q^{89} +(-5.93304 + 10.2763i) q^{91} +(-35.0686 - 3.06811i) q^{92} +(-1.94105 - 0.342259i) q^{94} +(-5.42294 - 3.06539i) q^{95} +(0.696015 - 7.95549i) q^{97} +(-1.18580 - 4.42546i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{17}{18}\right)$

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	$-0.437579\pi$
$2$	1.48477	−	2.12047i	1.04989	−	1.49940i	0.855040	−	0.518562i	$-0.173533\pi$
$3$		0			0
$3$		0			0
$4$	−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
$6$		0			0
$7$	−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
$9$		0			0
$10$	−5.77064	−	0.451915i	−1.82484	−	0.142908i
$11$	1.00437	+	1.19696i	0.302828	+	0.360897i	0.895902	−	0.444251i	$-0.146530\pi$
$11$	1.00437	+	1.19696i	0.302828	+	0.360897i	−0.593074	+	0.805148i	$0.702086\pi$
$12$		0			0
$13$	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
$15$		0			0
$16$	−6.66205	+	5.59013i	−1.66551	+	1.39753i
$17$	−1.82995	+	0.490334i	−0.443828	+	0.118923i	−0.473810	−	0.880627i	$-0.657122\pi$
$17$	−1.82995	+	0.490334i	−0.443828	+	0.118923i	0.0299818	+	0.999550i	$0.490455\pi$
$18$		0			0
$19$	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
$21$		0			0
$22$	4.02936	−	0.352524i	0.859063	−	0.0751583i
$23$	3.16476	−	6.78686i	0.659899	−	1.41516i	−0.236377	−	0.971661i	$-0.575960\pi$
$23$	3.16476	−	6.78686i	0.659899	−	1.41516i	0.896276	−	0.443496i	$-0.146262\pi$
$24$		0			0
$25$	−2.42067	+	4.37497i	−0.484133	+	0.874994i
$26$		−	10.3723i		−	2.03418i
$27$		0			0
$28$	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	$-0.174592\pi$
$30$		0			0
$31$	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
$33$		0			0
$34$	−1.67731	+	4.60838i	−0.287657	+	0.790331i
$35$	5.45873	+	3.74857i	0.922693	+	0.633624i
$36$		0			0
$37$	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
$39$		0			0
$40$	4.18374	+	15.0635i	0.661507	+	2.38174i
$41$	−6.26389	−	1.10449i	−0.978255	−	0.172493i	−0.338412	−	0.940998i	$-0.609890\pi$
$41$	−6.26389	−	1.10449i	−0.978255	−	0.172493i	−0.639843	+	0.768505i	$0.721001\pi$
$42$		0			0
$43$	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
$45$		0			0
$46$	−9.69236	−	16.7877i	−1.42906	−	2.47521i
$47$	−0.321786	−	0.690071i	−0.0469372	−	0.100657i	0.881441	−	0.472295i	$-0.156574\pi$
$47$	−0.321786	−	0.690071i	−0.0469372	−	0.100657i	−0.928378	+	0.371638i	$0.878796\pi$
$48$		0			0
$49$	1.13767	−	1.35582i	0.162524	−	0.193688i
$50$	5.68285	+	11.6287i	0.803676	+	1.64455i
$51$		0			0
$52$	−15.4296	−	10.8039i	−2.13971	−	1.49824i
$53$	−5.57112	+	5.57112i	−0.765253	+	0.765253i	−0.977267	−	0.212014i	$-0.931998\pi$
$53$	−5.57112	+	5.57112i	−0.765253	+	0.765253i	0.212014	+	0.977267i	$0.431998\pi$
$54$		0			0
$55$	1.16502	−	3.29395i	0.157091	−	0.444156i
$56$	20.3903	−	3.59537i	2.72477	−	0.480451i
$57$		0			0
$58$	−9.23063	−	4.30431i	−1.21204	−	0.565184i
$59$	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	$0.490141\pi$
$60$		0			0
$61$	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
$63$		0			0
$64$	4.05760	+	2.34266i	0.507201	+	0.292832i
$65$	−8.15444	−	3.71239i	−1.01143	−	0.460465i
$66$		0			0
$67$	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
$69$		0			0
$70$	16.0536	−	6.00929i	1.91878	−	0.718247i
$71$	6.11142	+	3.52843i	0.725292	+	0.418748i	0.816698	−	0.577066i	$-0.195802\pi$
$71$	6.11142	+	3.52843i	0.725292	+	0.418748i	−0.0914051	+	0.995814i	$0.529136\pi$
$72$		0			0
$73$	−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
$75$		0			0
$76$	−10.0321	−	8.41796i	−1.15076	−	0.965606i
$77$	−4.19371	−	1.95556i	−0.477918	−	0.222857i
$78$		0			0
$79$	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			0
$82$	−11.6425	+	11.6425i	−1.28569	+	1.28569i
$83$	3.33133	+	2.33262i	0.365661	+	0.256038i	0.741938	−	0.670469i	$-0.233907\pi$
$83$	3.33133	+	2.33262i	0.365661	+	0.256038i	−0.376277	+	0.926507i	$0.622796\pi$
$84$		0			0
$85$	3.02265	+	2.96805i	0.327852	+	0.321931i
$86$	0.973224	−	1.15984i	0.104945	−	0.125069i
$87$		0			0
$88$	−4.61689	−	9.90096i	−0.492162	−	1.05545i
$89$	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	$0.685138\pi$
$90$		0			0
$91$	−5.93304	+	10.2763i	−0.621951	+	1.07725i
$92$	−35.0686	−	3.06811i	−3.65616	−	0.319872i
$93$		0			0
$94$	−1.94105	−	0.342259i	−0.200204	−	0.0353013i
$95$	−5.42294	−	3.06539i	−0.556382	−	0.314502i
$96$		0			0
$97$	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
$99$		0			0
$100$	23.2180	+	3.65897i	2.32180	+	0.365897i
$101$	−5.32423	+	14.6282i	−0.529781	+	1.45556i	0.329549	+	0.944139i	$0.393103\pi$
$101$	−5.32423	+	14.6282i	−0.529781	+	1.45556i	−0.859330	+	0.511422i	$0.829119\pi$
$102$		0			0
$103$	−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
$105$		0			0
$106$	3.54156	+	20.0852i	0.343987	+	1.95085i
$107$	−3.95377	−	3.95377i	−0.382225	−	0.382225i	0.489678	−	0.871903i	$-0.337114\pi$
$107$	−3.95377	−	3.95377i	−0.382225	−	0.382225i	−0.871903	+	0.489678i	$0.837114\pi$
$108$		0			0
$109$		−	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			0
$112$	10.8843	−	23.3414i	1.02847	−	2.20556i
$113$	2.27035	−	0.198630i	0.213577	−	0.0186855i	0.0201349	−	0.999797i	$-0.493590\pi$
$113$	2.27035	−	0.198630i	0.213577	−	0.0186855i	0.193442	+	0.981112i	$0.438035\pi$
$114$		0			0
$115$	−16.6670	+	1.61135i	−1.55421	+	0.150259i
$116$	−16.0177	+	9.24784i	−1.48721	+	0.858641i
$117$		0			0
$118$	25.5901	−	6.85686i	2.35576	−	0.631225i
$119$	4.29781	−	3.60629i	0.393979	−	0.330588i
$120$		0			0
$121$	1.48617	−	8.42851i	0.135107	−	0.766228i
$122$	25.7607	−	18.0378i	2.33226	−	1.63307i
$123$		0			0
$124$	−17.5505	−	20.9158i	−1.57608	−	1.87830i
$125$	11.1762	−	0.305624i	0.999626	−	0.0273359i
$126$		0			0
$127$	−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			0
$130$	−19.9794	+	11.7792i	−1.75231	+	1.03310i
$131$	−0.329501	−	0.905296i	−0.0287886	−	0.0790961i	0.924466	−	0.381265i	$-0.124512\pi$
$131$	−0.329501	−	0.905296i	−0.0287886	−	0.0790961i	−0.953254	+	0.302169i	$0.902289\pi$
$132$		0			0
$133$	−4.73202	+	6.75802i	−0.410318	+	0.585995i
$134$	5.16224			0.445950
$135$		0			0
$136$	13.2456			1.13580
$137$	−1.39561	+	1.99313i	−0.119235	+	0.170285i	−0.874333	−	0.485327i	$-0.838700\pi$
$137$	−1.39561	+	1.99313i	−0.119235	+	0.170285i	0.755098	+	0.655612i	$0.227589\pi$
$138$		0			0
$139$	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			0
$142$	16.5560	−	7.72017i	1.38934	−	0.647862i
$143$	6.04754	+	1.62043i	0.505721	+	0.135508i
$144$		0			0
$145$	−6.68769	+	5.71630i	−0.555382	+	0.474713i
$146$	6.77589	+	8.07519i	0.560777	+	0.668308i
$147$		0			0
$148$	1.26156	−	0.883353i	0.103700	−	0.0726112i
$149$	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	$-0.139154\pi$
$150$		0			0
$151$	−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
$153$		0			0
$154$	−10.3734	+	5.98907i	−0.835910	+	0.482613i
$155$	−10.0246	−	8.25717i	−0.805199	−	0.663232i
$156$		0			0
$157$	−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
$159$		0			0
$160$	15.5224	−	11.0811i	1.22715	−	0.876034i
$161$			22.1764i			1.74774i
$162$		0			0
$163$	−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
$165$		0			0
$166$	9.89249	−	3.60057i	0.767806	−	0.279459i
$167$	0.457294	+	5.22689i	0.0353865	+	0.404469i	0.993144	+	0.116894i	$0.0372937\pi$
$167$	0.457294	+	5.22689i	0.0353865	+	0.404469i	−0.957758	+	0.287576i	$0.907151\pi$
$168$		0			0
$169$	1.04499	−	2.87108i	0.0803837	−	0.220852i
$170$	10.7816	−	2.00256i	0.826909	−	0.153589i
$171$		0			0
$172$	−0.711633	−	2.65585i	−0.0542615	−	0.202507i
$173$	−0.712745	+	8.14671i	−0.0541890	+	0.619383i	0.919740	+	0.392529i	$0.128400\pi$
$173$	−0.712745	+	8.14671i	−0.0541890	+	0.619383i	−0.973929	+	0.226854i	$0.927156\pi$
$174$		0			0
$175$	1.02147	−	14.7717i	0.0772157	−	1.11664i
$176$	−13.3823	−	2.35966i	−1.00873	−	0.177866i
$177$		0			0
$178$	21.8431	+	1.91103i	1.63721	+	0.143238i
$179$	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	$0.103102\pi$
$180$		0			0
$181$	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
$183$		0			0
$184$	−33.6540	+	40.1073i	−2.48100	+	2.95675i
$185$	0.513260	−	0.522701i	0.0377356	−	0.0384298i
$186$		0			0
$187$	−2.42486	−	1.69790i	−0.177323	−	0.124163i
$188$	−2.53096	+	2.53096i	−0.184589	+	0.184589i
$189$		0			0
$190$	−14.5518	+	6.94778i	−1.05570	+	0.504045i
$191$	3.74191	−	0.659800i	0.270755	−	0.0477414i	−0.0366221	−	0.999329i	$-0.511660\pi$
$191$	3.74191	−	0.659800i	0.270755	−	0.0477414i	0.307377	+	0.951588i	$0.400549\pi$
$192$		0			0
$193$	−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			0
$196$	−7.81835	−	2.84565i	−0.558453	−	0.203260i
$197$	−6.21326	+	23.1882i	−0.442676	+	1.65209i	0.279324	+	0.960197i	$0.409890\pi$
$197$	−6.21326	+	23.1882i	−0.442676	+	1.65209i	−0.722000	+	0.691893i	$0.756777\pi$
$198$		0			0
$199$	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
$201$		0			0
$202$	23.1134	+	33.0093i	1.62625	+	2.32253i
$203$	6.68309	+	9.54445i	0.469061	+	0.669889i
$204$		0			0
$205$	4.98599	+	13.3199i	0.348237	+	0.930305i
$206$	−17.7613	−	10.2545i	−1.23749	−	0.714466i
$207$		0			0
$208$	−9.01904	+	33.6595i	−0.625358	+	2.33387i
$209$	4.09043	+	1.48880i	0.282941	+	0.102982i
$210$		0			0
$211$	−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
$213$		0			0
$214$	−14.2542	+	2.51341i	−0.974400	+	0.171813i
$215$	−0.563508	−	1.18024i	−0.0384309	−	0.0804920i
$216$		0			0
$217$	−12.1625	+	12.1625i	−0.825642	+	0.825642i
$218$	−13.9173	−	9.74502i	−0.942601	−	0.660016i
$219$		0			0
$220$	−16.4238	+	0.149676i	−1.10729	+	0.0100911i
$221$	−4.87947	+	5.81513i	−0.328229	+	0.391168i
$222$		0			0
$223$	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
$225$		0			0
$226$	2.94975	−	5.10912i	0.196215	−	0.339854i
$227$	7.40612	+	0.647951i	0.491561	+	0.0430060i	0.330242	−	0.943896i	$-0.392870\pi$
$227$	7.40612	+	0.647951i	0.491561	+	0.0430060i	0.161319	+	0.986902i	$0.448425\pi$
$228$		0			0
$229$	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			0
$232$	−2.39751	+	27.4037i	−0.157404	+	1.79914i
$233$	−3.69557	−	13.7921i	−0.242105	−	0.903549i	−0.974816	−	0.223009i	$-0.928412\pi$
$233$	−3.69557	−	13.7921i	−0.242105	−	0.903549i	0.732711	−	0.680540i	$-0.238255\pi$
$234$		0			0
$235$	−0.963800	+	1.40350i	−0.0628714	+	0.0915542i
$236$	16.4549	−	45.2095i	1.07112	−	2.94289i
$237$		0			0
$238$	−1.26577	−	14.4678i	−0.0820478	−	0.937811i
$239$	−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	$0.617805\pi$
$240$		0			0
$241$	−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
$243$		0			0
$244$		−	57.1094i		−	3.65606i
$245$	−3.90358	−	0.651685i	−0.249391	−	0.0416346i
$246$		0			0
$247$	4.71754	−	10.1168i	0.300170	−	0.643717i
$248$	−40.4538	+	3.53925i	−2.56882	+	0.224743i
$249$		0			0
$250$	15.9459	−	24.1524i	1.00851	−	1.52753i
$251$	8.96649	−	5.17681i	0.565960	−	0.326757i	−0.189574	−	0.981866i	$-0.560711\pi$
$251$	8.96649	−	5.17681i	0.565960	−	0.326757i	0.755534	+	0.655109i	$0.227377\pi$
$252$		0			0
$253$	11.3022	−	3.02841i	0.710562	−	0.190395i
$254$	−4.28500	+	3.59554i	−0.268865	+	0.225604i
$255$		0			0
$256$	−3.84321	+	21.7959i	−0.240201	+	1.36225i
$257$	−4.65492	+	3.25941i	−0.290366	+	0.203316i	−0.709679	−	0.704525i	$-0.751160\pi$
$257$	−4.65492	+	3.25941i	−0.290366	+	0.203316i	0.419313	+	0.907842i	$0.362271\pi$
$258$		0			0
$259$	−0.623629	−	0.743212i	−0.0387504	−	0.0461810i
$260$	−3.28838	+	41.9903i	−0.203937	+	2.60412i
$261$		0			0
$262$	−2.40888	−	0.645458i	−0.148821	−	0.0398765i
$263$	17.6574	−	8.23378i	1.08880	−	0.507717i	0.206522	−	0.978442i	$-0.433785\pi$
$263$	17.6574	−	8.23378i	1.08880	−	0.507717i	0.882280	+	0.470725i	$0.156008\pi$
$264$		0			0
$265$	17.0580	+	4.40446i	1.04786	+	0.270564i
$266$	7.30422	+	20.0682i	0.447850	+	1.23046i
$267$		0			0
$268$	5.37706	−	7.67923i	0.328456	−	0.469084i
$269$	−21.8628			−1.33300			−0.666501	−	0.745505i	$-0.732209\pi$
$269$	−21.8628			−1.33300			−0.666501	+	0.745505i	$0.732209\pi$
$270$		0			0
$271$	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
$273$		0			0
$274$	2.15422	+	5.91867i	0.130141	+	0.357560i
$275$	−7.66791	+	1.49664i	−0.462392	+	0.0902509i
$276$		0			0
$277$	−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
$279$		0			0
$280$	−30.0815	−	35.1933i	−1.79771	−	2.10320i
$281$	0.950287	+	1.13251i	0.0566894	+	0.0675598i	0.793644	−	0.608382i	$-0.208181\pi$
$281$	0.950287	+	1.13251i	0.0566894	+	0.0675598i	−0.736955	+	0.675942i	$0.763737\pi$
$282$		0			0
$283$	−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
$285$		0			0
$286$	12.4153	−	10.4176i	0.734130	−	0.616008i
$287$	18.1942	−	4.87513i	1.07397	−	0.287770i
$288$		0			0
$289$	−11.6141	+	6.70543i	−0.683185	+	0.394437i
$290$	2.19156	+	22.6684i	0.128693	+	1.33113i
$291$		0			0
$292$	19.0703	−	1.66844i	1.11601	−	0.0976379i
$293$	9.70762	−	20.8181i	0.567125	−	1.21620i	−0.388453	−	0.921468i	$-0.626991\pi$
$293$	9.70762	−	20.8181i	0.567125	−	1.21620i	0.955579	−	0.294736i	$-0.0952316\pi$
$294$		0			0
$295$	3.76836	−	22.5724i	0.219402	−	1.31422i
$296$		−	2.29054i		−	0.133135i
$297$		0			0
$298$	−25.6615	−	25.6615i	−1.48653	−	1.48653i
$299$	−5.21042	−	29.5498i	−0.301327	−	1.70891i
$300$		0			0
$301$	−1.62765	+	0.592417i	−0.0938163	+	0.0341464i
$302$	4.11100	+	46.9890i	0.236562	+	2.70391i
$303$		0			0
$304$	−8.28636	+	22.7666i	−0.475255	+	1.30575i
$305$	−4.96077	−	26.7083i	−0.284053	−	1.52931i
$306$		0			0
$307$	−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
$309$		0			0
$310$	−32.3933	+	8.99694i	−1.83982	+	0.510992i
$311$	−9.32616	−	1.64445i	−0.528838	−	0.0932485i	−0.0971473	−	0.995270i	$-0.530972\pi$
$311$	−9.32616	−	1.64445i	−0.528838	−	0.0932485i	−0.431691	+	0.902022i	$0.642083\pi$
$312$		0			0
$313$	−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
$315$		0			0
$316$	−30.9001	−	53.5206i	−1.73827	−	3.01077i
$317$	−8.89049	−	19.0657i	−0.499340	−	1.07084i	−0.980916	−	0.194433i	$-0.937713\pi$
$317$	−8.89049	−	19.0657i	−0.499340	−	1.07084i	0.481576	−	0.876404i	$-0.340064\pi$
$318$		0			0
$319$	3.95168	−	4.70943i	0.221252	−	0.263678i
$320$	−0.0954738	−	10.4763i	−0.00533715	−	0.585640i
$321$		0			0
$322$	47.0242	+	32.9267i	2.62056	+	1.83493i
$323$	−3.73198	+	3.73198i	−0.207653	+	0.207653i
$324$		0			0
$325$	2.10958	+	19.9232i	0.117018	+	1.10514i
$326$	−57.7316	+	10.1796i	−3.19746	+	0.563798i
$327$		0			0
$328$	40.3036	+	18.7939i	2.22540	+	1.03772i
$329$	1.72731	+	1.44938i	0.0952295	+	0.0799070i
$330$		0			0
$331$	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			0
$334$	11.7624	+	6.79104i	0.643611	+	0.371589i
$335$	1.84763	−	4.05841i	0.100947	−	0.221735i
$336$		0			0
$337$	−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
$339$		0			0
$340$	8.25127	−	18.1243i	0.447488	−	0.982929i
$341$	7.85952	+	4.53769i	0.425617	+	0.245730i
$342$		0			0
$343$	4.00870	−	14.9607i	0.216450	−	0.807801i
$344$	−3.84273	−	1.39864i	−0.207186	−	0.0754097i
$345$		0			0
$346$	16.2166	+	13.6073i	0.871808	+	0.731534i
$347$	−24.5967	−	11.4696i	−1.32042	−	0.615723i	−0.370681	−	0.928760i	$-0.620876\pi$
$347$	−24.5967	−	11.4696i	−1.32042	−	0.615723i	−0.949741	+	0.313038i	$0.898653\pi$
$348$		0			0
$349$	−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
$351$		0			0
$352$	−9.42361	+	9.42361i	−0.502280	+	0.502280i
$353$	24.9423	+	17.4648i	1.32755	+	0.929558i	0.999884	−	0.0152364i	$-0.00485008\pi$
$353$	24.9423	+	17.4648i	1.32755	+	0.929558i	0.327663	+	0.944795i	$0.393739\pi$
$354$		0			0
$355$	−0.143799	−	15.7790i	−0.00763207	−	0.837461i
$356$	25.5949	−	30.5028i	1.35653	−	1.61664i
$357$		0			0
$358$	−5.80691	−	12.4530i	−0.306905	−	0.658160i
$359$	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	$0.525010\pi$
$360$		0			0
$361$	−5.61951	+	9.73329i	−0.295764	+	0.512278i
$362$	59.5360	+	5.20872i	3.12914	+	0.273764i
$363$		0			0
$364$	54.9338	+	9.68632i	2.87931	+	0.507701i
$365$	8.77367	−	2.43681i	0.459235	−	0.127548i
$366$		0			0
$367$	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
$369$		0			0
$370$	−0.346299	−	1.86444i	−0.0180032	−	0.0969276i
$371$	7.98007	−	21.9251i	0.414305	−	1.13829i
$372$		0			0
$373$	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
$375$		0			0
$376$	0.924409	+	5.24259i	0.0476728	+	0.270366i
$377$	−11.1477	−	11.1477i	−0.574134	−	0.574134i
$378$		0			0
$379$			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			0
$382$	4.15678	−	8.91424i	0.212679	−	0.456092i
$383$	2.84641	−	0.249029i	0.145445	−	0.0127248i	−0.0142007	−	0.999899i	$-0.504520\pi$
$383$	2.84641	−	0.249029i	0.145445	−	0.0127248i	0.159646	+	0.987174i	$0.448965\pi$
$384$		0			0
$385$	0.995681	+	10.2988i	0.0507446	+	0.524877i
$386$	−27.7076	+	15.9970i	−1.41028	+	0.814226i
$387$		0			0
$388$	−36.2617	+	9.71629i	−1.84091	+	0.493270i
$389$	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	$0.173014\pi$
$390$		0			0
$391$	−2.46354	+	13.9714i	−0.124586	+	0.706565i
$392$	−10.1365	+	7.09766i	−0.511971	+	0.358486i
$393$		0			0
$394$	39.9445	+	47.6040i	2.01238	+	2.39826i
$395$	−19.1000	−	22.3458i	−0.961028	−	1.12434i
$396$		0			0
$397$	−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
$399$		0			0
$400$	−8.33002	−	42.6781i	−0.416501	−	2.13391i
$401$	7.04392	+	19.3530i	0.351756	+	0.966443i	0.981806	+	0.189888i	$0.0608124\pi$
$401$	7.04392	+	19.3530i	0.351756	+	0.966443i	−0.630049	+	0.776555i	$0.716965\pi$
$402$		0			0
$403$	13.3488	−	19.0640i	0.664949	−	0.949645i
$404$	73.1790			3.64079
$405$		0			0
$406$	30.1615			1.49689
$407$	−0.293615	+	0.419326i	−0.0145540	+	0.0207852i
$408$		0			0
$409$	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
$411$		0			0
$412$	−33.7548	+	15.7401i	−1.66298	+	0.775460i
$413$	−29.2754	−	7.84432i	−1.44055	−	0.385994i
$414$		0			0
$415$	0.709976	−	9.06589i	0.0348513	−	0.445027i
$416$	21.9677	+	26.1801i	1.07705	+	1.28358i
$417$		0			0
$418$	9.23028	−	6.46311i	0.451468	−	0.316121i
$419$	−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	$0.0597866\pi$
$420$		0			0
$421$	−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
$423$		0			0
$424$	47.7050	−	27.5425i	2.31676	−	1.33758i
$425$	2.28451	−	9.19292i	0.110815	−	0.445922i
$426$		0			0
$427$	−35.8400	+	3.13559i	−1.73442	+	0.151742i
$428$	−11.1085	+	23.8223i	−0.536950	+	1.15149i
$429$		0			0
$430$	−3.33934	−	0.557488i	−0.161037	−	0.0268845i
$431$		−	14.9683i		−	0.720998i	−0.932760	−	0.360499i	$-0.882606\pi$
$431$		−	14.9683i		−	0.720998i	0.932760	−	0.360499i	$-0.117394\pi$
$432$		0			0
$433$	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
$435$		0			0
$436$	−28.9929	+	10.5526i	−1.38851	+	0.505376i
$437$	−1.81822	−	20.7824i	−0.0869774	−	0.994156i
$438$		0			0
$439$	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			0
$442$	5.08591	+	18.9809i	0.241912	+	0.902828i
$443$	−2.49320	+	28.4974i	−0.118456	+	1.35395i	0.671597	+	0.740916i	$0.265608\pi$
$443$	−2.49320	+	28.4974i	−0.118456	+	1.35395i	−0.790053	+	0.613038i	$0.789947\pi$
$444$		0			0
$445$	9.32033	−	16.4885i	0.441826	−	0.781629i
$446$	56.2308	+	9.91500i	2.66260	+	0.469489i
$447$		0			0
$448$	−13.8223	−	1.20930i	−0.653043	−	0.0571338i
$449$	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	$-0.0331852\pi$
$450$		0			0
$451$	−4.96922	−	8.60694i	−0.233991	−	0.405285i
$452$	−4.52771	−	9.70971i	−0.212966	−	0.456706i
$453$		0			0
$454$	12.3703	−	14.7424i	0.580567	−	0.691893i
$455$	26.5322	−	0.241798i	1.24385	−	0.0113356i
$456$		0			0
$457$	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
$459$		0			0
$460$	33.9153	+	71.0342i	1.58131	+	3.31199i
$461$	15.0276	−	2.64977i	0.699905	−	0.123412i	0.187638	−	0.982238i	$-0.439917\pi$
$461$	15.0276	−	2.64977i	0.699905	−	0.123412i	0.512267	+	0.858826i	$0.328806\pi$
$462$		0			0
$463$	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
$465$		0			0
$466$	−34.7327	−	12.6417i	−1.60896	−	0.585614i
$467$	−4.51835	+	16.8627i	−0.209084	+	0.780313i	0.779082	+	0.626923i	$0.215686\pi$
$467$	−4.51835	+	16.8627i	−0.209084	+	0.780313i	−0.988166	+	0.153390i	$0.950981\pi$
$468$		0			0
$469$	−5.11446	−	2.95283i	−0.236164	−	0.136349i
$470$	1.54505	+	4.12757i	0.0712681	+	0.190391i
$471$		0			0
$472$	−41.0421	−	58.6142i	−1.88911	−	2.69794i
$473$	0.524198	+	0.748633i	0.0241027	+	0.0344222i
$474$		0			0
$475$	0.253863	+	13.9269i	0.0116480	+	0.639012i
$476$	−22.8405	−	13.1870i	−1.04689	−	0.604423i
$477$		0			0
$478$	−13.6463	+	50.9287i	−0.624168	+	2.32943i
$479$	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	$0.435875\pi$
$480$		0			0
$481$	1.00560	+	0.843799i	0.0458514	+	0.0384739i
$482$	−38.1778	−	17.8026i	−1.73895	−	0.810885i
$483$		0			0
$484$	−39.6216	+	6.98636i	−1.80098	+	0.317562i
$485$	−16.1145	+	7.69385i	−0.731720	+	0.349360i
$486$		0			0
$487$	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
$489$		0			0
$490$	−7.17778	+	7.30981i	−0.324259	+	0.330224i
$491$	8.85005	−	10.5471i	0.399397	−	0.475983i	−0.528439	−	0.848971i	$-0.677222\pi$
$491$	8.85005	−	10.5471i	0.399397	−	0.475983i	0.927836	+	0.372988i	$0.121667\pi$
$492$		0			0
$493$	3.15016	+	6.75555i	0.141876	+	0.304255i
$494$	−14.4479	−	25.0245i	−0.650041	−	1.12590i
$495$		0			0
$496$	−25.2560	+	43.7446i	−1.13403	+	1.96419i
$497$	−20.8187	−	1.82140i	−0.933845	−	0.0817009i
$498$		0			0
$499$	−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
$501$		0			0
$502$	2.33590	−	26.6995i	0.104256	−	1.19166i
$503$	−3.19471	−	11.9228i	−0.142445	−	0.531612i	−0.999856	−	0.0169795i	$-0.994595\pi$
$503$	−3.19471	−	11.9228i	−0.142445	−	0.531612i	0.857411	−	0.514633i	$-0.172072\pi$
$504$		0			0
$505$	34.2236	−	6.35664i	1.52293	−	0.282867i
$506$	10.3595	−	28.4624i	0.460534	−	1.26531i
$507$		0			0
$508$	0.885334	+	10.1194i	0.0392803	+	0.448976i
$509$	−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	$0.397715\pi$
$510$		0			0
$511$	−2.09411	−	11.8763i	−0.0926380	−	0.525376i
$512$	33.5394	+	33.5394i	1.48224	+	1.48224i
$513$		0			0
$514$			14.7101i			0.648833i
$515$	−14.4188	+	10.2933i	−0.635369	+	0.453575i
$516$		0			0
$517$	0.502796	−	1.07825i	0.0221130	−	0.0474214i
$518$	−2.50190	+	0.218888i	−0.109927	+	0.00961738i
$519$		0			0
$520$	48.3521	+	39.8270i	2.12038	+	1.74653i
$521$	25.5030	−	14.7242i	1.11731	−	0.645078i	0.176595	−	0.984284i	$-0.443492\pi$
$521$	25.5030	−	14.7242i	1.11731	−	0.645078i	0.940712	+	0.339206i	$0.110158\pi$
$522$		0			0
$523$	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
$525$		0			0
$526$	8.75766	−	49.6671i	0.381852	−	2.16559i
$527$	−9.01363	+	6.31141i	−0.392640	+	0.274929i
$528$		0			0
$529$	−21.2616	−	25.3386i	−0.924417	−	1.10168i
$530$	34.6666	−	29.6313i	1.50582	−	1.28710i
$531$		0			0
$532$	37.4611	+	10.0377i	1.62414	+	0.435188i
$533$	−23.0982	+	10.7709i	−1.00049	+	0.466538i
$534$		0			0
$535$	−3.12580	+	12.1059i	−0.135140	+	0.523383i
$536$	−4.76869	−	13.1019i	−0.205976	−	0.565915i
$537$		0			0
$538$	−32.4612	+	46.3594i	−1.39950	+	1.99870i
$539$	2.76550			0.119118
$540$		0			0
$541$	−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
$543$		0			0
$544$	−5.52655	−	15.1841i	−0.236949	−	0.651012i
$545$	−12.6424	+	7.45355i	−0.541543	+	0.319275i
$546$		0			0
$547$	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
$549$		0			0
$550$	−8.21147	+	18.4817i	−0.350138	+	0.788062i
$551$	−7.04554	−	8.39655i	−0.300150	−	0.357705i
$552$		0			0
$553$	−31.8912	+	22.3304i	−1.35615	+	0.949586i
$554$	−2.38429	+	13.5220i	−0.101299	+	0.574494i
$555$		0			0
$556$	35.0309	−	29.3944i	1.48564	−	1.24660i
$557$	−19.0860	+	5.11407i	−0.808698	+	0.216690i	−0.639399	−	0.768875i	$-0.720817\pi$
$557$	−19.0860	+	5.11407i	−0.808698	+	0.216690i	−0.169299	+	0.985565i	$0.554150\pi$
$558$		0			0
$559$	2.02964	−	1.17181i	0.0858446	−	0.0495624i
$560$	−57.3213	+	5.54177i	−2.42227	+	0.234183i
$561$		0			0
$562$	3.81240	−	0.333542i	0.160816	−	0.0140696i
$563$	−11.2154	+	24.0516i	−0.472675	+	1.01365i	0.515008	+	0.857185i	$0.327789\pi$
$563$	−11.2154	+	24.0516i	−0.472675	+	1.01365i	−0.987683	+	0.156469i	$0.949989\pi$
$564$		0			0
$565$	−2.96090	−	4.14763i	−0.124566	−	0.174492i
$566$			13.1138i			0.551216i
$567$		0			0
$568$	−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	$0.590774\pi$
$570$		0			0
$571$	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
$573$		0			0
$574$	16.6766	−	45.8187i	0.696069	−	1.91243i
$575$	22.0315	+	30.2745i	0.918776	+	1.26253i
$576$		0			0
$577$	−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			0
$580$	36.0037	+	20.3516i	1.49497	+	0.845052i
$581$	−11.8605	−	2.09132i	−0.492055	−	0.0867626i
$582$		0			0
$583$	−12.2639	−	1.07295i	−0.507918	−	0.0444370i
$584$	14.2357	−	24.6569i	0.589077	−	1.02031i
$585$		0			0
$586$	−29.7304	−	51.4946i	−1.22815	−	2.12722i
$587$	1.70173	+	3.64938i	0.0702381	+	0.150626i	0.938292	−	0.345844i	$-0.112407\pi$
$587$	1.70173	+	3.64938i	0.0702381	+	0.150626i	−0.868054	+	0.496470i	$0.834629\pi$
$588$		0			0
$589$	10.4008	−	12.3951i	0.428556	−	0.510733i
$590$	−42.2689	−	41.5054i	−1.74018	−	1.70875i
$591$		0			0
$592$	−2.33389	−	1.63421i	−0.0959223	−	0.0671655i
$593$	−6.31053	+	6.31053i	−0.259142	+	0.259142i	−0.824705	−	0.565563i	$-0.808659\pi$
$593$	−6.31053	+	6.31053i	−0.259142	+	0.259142i	0.565563	+	0.824705i	$0.308659\pi$
$594$		0			0
$595$	−11.8273	−	4.18311i	−0.484870	−	0.171491i
$596$	−64.9028	+	11.4441i	−2.65852	+	0.468769i
$597$		0			0
$598$	−70.3955	−	32.8260i	−2.87869	−	1.34235i
$599$	−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	$0.960085\pi$
$600$		0			0
$601$	−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
$603$		0			0
$604$	74.1818	+	42.8289i	3.01841	+	1.74268i
$605$	−17.9229	+	6.70901i	−0.728671	+	0.272760i
$606$		0			0
$607$	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
$609$		0			0
$610$	−63.9996	−	29.1364i	−2.59127	−	1.17970i
$611$	−2.64216	−	1.52545i	−0.106890	−	0.0617131i
$612$		0			0
$613$	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
$615$		0			0
$616$	24.7829	+	20.7953i	0.998533	+	0.837868i
$617$	32.8468	+	15.3167i	1.32236	+	0.616628i	0.950229	−	0.311551i	$-0.100848\pi$
$617$	32.8468	+	15.3167i	1.32236	+	0.616628i	0.372134	+	0.928179i	$0.378626\pi$
$618$		0			0
$619$	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
$621$		0			0
$622$	−17.3342	+	17.3342i	−0.695037	+	0.695037i
$623$	−20.5478	−	14.3877i	−0.823231	−	0.576433i
$624$		0			0
$625$	−13.2807	−	21.1807i	−0.531230	−	0.847228i
$626$	−51.4823	+	61.3542i	−2.05764	+	2.45221i
$627$		0			0
$628$	6.04798	+	12.9699i	0.241341	+	0.517557i
$629$	−0.310333	−	0.537512i	−0.0123738	−	0.0214320i
$630$		0			0
$631$	−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
$633$		0			0
$634$	−53.6285	−	9.45615i	−2.12986	−	0.375552i
$635$	1.29306	+	4.65563i	0.0513135	+	0.184753i
$636$		0			0
$637$	0.618092	−	7.06483i	0.0244897	−	0.279919i
$638$	−4.11886	−	15.3718i	−0.163067	−	0.608576i
$639$		0			0
$640$	9.08721	+	6.24029i	0.359203	+	0.246669i
$641$	−1.87972	+	5.16450i	−0.0742446	+	0.203985i	−0.971263	−	0.238007i	$-0.923506\pi$
$641$	−1.87972	+	5.16450i	−0.0742446	+	0.203985i	0.897019	+	0.441992i	$0.145728\pi$
$642$		0			0
$643$	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
$645$		0			0
$646$	2.37242	+	13.4546i	0.0933414	+	0.529366i
$647$	18.1400	+	18.1400i	0.713158	+	0.713158i	0.967195	−	0.254037i	$-0.0817584\pi$
$647$	18.1400	+	18.1400i	0.713158	+	0.713158i	−0.254037	+	0.967195i	$0.581758\pi$
$648$		0			0
$649$			15.9914i			0.627719i
$650$	45.3787	+	25.1080i	1.77990	+	0.984816i
$651$		0			0
$652$	−44.9910	+	96.4835i	−1.76198	+	3.77858i
$653$	7.25864	−	0.635049i	0.284052	−	0.0248514i	0.0557608	−	0.998444i	$-0.482242\pi$
$653$	7.25864	−	0.635049i	0.284052	−	0.0248514i	0.228292	+	0.973593i	$0.426686\pi$
$654$		0			0
$655$	−1.36961	+	1.66278i	−0.0535151	+	0.0649701i
$656$	47.9046	−	27.6577i	1.87036	−	1.07985i
$657$		0			0
$658$	5.63801	−	1.51070i	0.219793	−	0.0588932i
$659$	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	$0.103750\pi$
$660$		0			0
$661$	−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
$663$		0			0
$664$	−18.2766	−	21.7813i	−0.709271	−	0.845277i
$665$	18.3913	+	1.44028i	0.713184	+	0.0558515i
$666$		0			0
$667$	−28.4594	−	7.62568i	−1.10195	−	0.295267i
$668$	22.3541	−	10.4239i	0.864905	−	0.403312i
$669$		0			0
$670$	−5.86242	−	9.94363i	−0.226485	−	0.384156i
$671$	6.49238	+	17.8377i	0.250635	+	0.688615i
$672$		0			0
$673$	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
$675$		0			0
$676$	−14.3629			−0.552418
$677$	6.04776	−	8.63710i	0.232434	−	0.331951i	−0.685944	−	0.727654i	$-0.740610\pi$
$677$	6.04776	−	8.63710i	0.232434	−	0.331951i	0.918378	+	0.395704i	$0.129499\pi$
$678$		0			0
$679$	8.08857	+	22.2232i	0.310411	+	0.852846i
$680$	−15.0422	−	25.5140i	−0.576841	−	0.978416i
$681$		0			0
$682$	21.2916	−	9.92842i	0.815296	−	0.380179i
$683$	−22.9581	−	6.15162i	−0.878469	−	0.235385i	−0.208723	−	0.977975i	$-0.566931\pi$
$683$	−22.9581	−	6.15162i	−0.878469	−	0.235385i	−0.669746	+	0.742590i	$0.733597\pi$
$684$		0			0
$685$	5.42411	+	0.424778i	0.207245	+	0.0162299i
$686$	−25.7716	−	30.7134i	−0.983965	−	1.17264i
$687$		0			0
$688$	−4.16675	+	2.91759i	−0.158856	+	0.111232i
$689$	−5.48198	+	31.0899i	−0.208847	+	1.18443i
$690$		0			0
$691$	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
$693$		0			0
$694$	−60.8414	+	35.1268i	−2.30951	+	1.33339i
$695$	13.8296	−	16.7898i	0.524585	−	0.636874i
$696$		0			0
$697$	12.0042	−	1.05023i	0.454691	−	0.0397803i
$698$	−20.9293	+	44.8830i	−0.792185	+	1.69885i
$699$		0			0
$700$	−66.8950	+	19.2378i	−2.52839	+	0.727121i
$701$		−	37.4202i		−	1.41334i	−0.707542	−	0.706671i	$-0.750196\pi$
$701$		−	37.4202i		−	1.41334i	0.707542	−	0.706671i	$-0.249804\pi$
$702$		0			0
$703$	0.645364	+	0.645364i	0.0243404	+	0.0243404i
$704$	1.27126	+	7.20968i	0.0479125	+	0.271725i
$705$		0			0
$706$	74.0671	−	26.9582i	2.78755	−	1.01459i
$707$	−4.01789	−	45.9247i	−0.151108	−	1.72718i
$708$		0			0
$709$	−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
$711$		0			0
$712$	−15.3277	−	57.2037i	−0.574429	−	2.14380i
$713$	3.79078	−	43.3288i	0.141966	−	1.62268i
$714$		0			0
$715$	−3.74648	−	13.4891i	−0.140111	−	0.504465i
$716$	−24.5733	−	4.33293i	−0.918347	−	0.161929i
$717$		0			0
$718$	80.5327	+	7.04570i	3.00546	+	0.262943i
$719$	−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	$0.188118\pi$
$720$		0			0
$721$	11.7313	+	20.3192i	0.436896	+	0.756726i
$722$	12.2954	+	26.3676i	0.457589	+	0.981302i
$723$		0			0
$724$	69.7617	−	83.1388i	2.59268	−	3.08983i
$725$	18.6056	+	6.39035i	0.690996	+	0.237332i
$726$		0			0
$727$	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
$729$		0			0
$730$	7.85968	−	22.2223i	0.290900	−	0.822486i
$731$	−1.09125	+	0.192418i	−0.0403615	+	0.00711682i
$732$		0			0
$733$	−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
$735$		0			0
$736$	60.0186	+	21.8450i	2.21231	+	0.805217i
$737$	−0.806480	+	3.00982i	−0.0297071	+	0.110868i
$738$		0			0
$739$	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
$741$		0			0
$742$	−34.6428	−	49.4750i	−1.27178	−	1.81629i
$743$	27.8074	+	39.7131i	1.02016	+	1.45693i	0.884706	+	0.466149i	$0.154359\pi$
$743$	27.8074	+	39.7131i	1.02016	+	1.45693i	0.135449	+	0.990784i	$0.456752\pi$
$744$		0			0
$745$	−29.3589	+	10.9898i	−1.07563	+	0.402635i
$746$	22.0487	+	12.7298i	0.807262	+	0.466073i
$747$		0			0
$748$	−3.60163	+	13.4415i	−0.131689	+	0.491468i
$749$	15.5600	+	5.66337i	0.568550	+	0.206935i
$750$		0			0
$751$	−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
$753$		0			0
$754$	−40.1899	+	7.08656i	−1.46363	+	0.258077i
$755$	38.4128	+	13.5860i	1.39799	+	0.494445i
$756$		0			0
$757$	−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
$759$		0			0
$760$	31.0761	+	30.5148i	1.12725	+	1.10689i
$761$	−22.5010	+	26.8156i	−0.815660	+	0.972066i	−0.999942	−	0.0108074i	$-0.996560\pi$
$761$	−22.5010	+	26.8156i	−0.815660	+	0.972066i	0.184281	+	0.982874i	$0.441004\pi$
$762$		0			0
$763$	8.21429	+	17.6156i	0.297377	+	0.637728i
$764$	−8.93086	−	15.4687i	−0.323107	−	0.559638i
$765$		0			0
$766$	3.69820	−	6.40547i	0.133621	−	0.231439i
$767$	40.8523	+	3.57411i	1.47509	+	0.129054i
$768$		0			0
$769$	−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
$771$		0			0
$772$	−5.06383	+	57.8799i	−0.182251	+	2.08314i
$773$	−1.43767	−	5.36547i	−0.0517095	−	0.192983i	0.935239	−	0.354016i	$-0.115184\pi$
$773$	−1.43767	−	5.36547i	−0.0517095	−	0.192983i	−0.986949	+	0.161033i	$0.948517\pi$
$774$		0			0
$775$	−4.52082	+	28.6868i	−0.162393	+	1.03046i
$776$	−19.0963	+	52.4668i	−0.685519	+	1.88345i
$777$		0			0
$778$	−2.87647	−	32.8782i	−0.103126	−	1.17874i
$779$	−16.6509	+	6.06042i	−0.596579	+	0.217137i
$780$		0			0
$781$	1.91473	+	10.8590i	0.0685144	+	0.388565i
$782$	25.9681	+	25.9681i	0.928618	+	0.928618i
$783$		0			0
$784$			15.3922i			0.549723i
$785$	3.95508	+	5.54028i	0.141163	+	0.197741i
$786$		0			0
$787$	−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
$789$		0			0
$790$	−75.7426	+	7.32272i	−2.69480	+	0.260531i
$791$	−5.84490	+	3.37455i	−0.207821	+	0.119985i
$792$		0			0
$793$	47.0197	−	12.5989i	1.66972	−	0.447400i
$794$	−7.12249	+	5.97648i	−0.252768	+	0.212097i
$795$		0			0
$796$	5.40604	−	30.6592i	0.191612	−	1.08669i
$797$	3.95902	−	2.77214i	0.140236	−	0.0981941i	−0.501353	−	0.865243i	$-0.667164\pi$
$797$	3.95902	−	2.77214i	0.140236	−	0.0981941i	0.641589	+	0.767049i	$0.278275\pi$
$798$		0			0
$799$	0.927217	+	1.10501i	0.0328026	+	0.0390926i
$800$	−38.9723	−	17.3155i	−1.37788	−	0.612196i
$801$		0			0
$802$	51.4959	+	13.7983i	1.81838	+	0.487235i
$803$	−5.76678	+	2.68909i	−0.203505	+	0.0948961i
$804$		0			0
$805$	42.7166	−	25.1842i	1.50556	−	0.887628i
$806$	−20.6048	−	56.6111i	−0.725772	−	1.99404i
$807$		0			0
$808$	62.4270	−	89.1550i	2.19617	−	3.13646i
$809$	−27.0458			−0.950881			−0.475440	−	0.879748i	$-0.657711\pi$
$809$	−27.0458			−0.950881			−0.475440	+	0.879748i	$0.657711\pi$
$810$		0			0
$811$	−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
$813$		0			0
$814$	0.453216	+	1.24520i	0.0158852	+	0.0436443i
$815$	−12.6599	+	49.0304i	−0.443458	+	1.71746i
$816$		0			0
$817$	1.47677	−	0.688628i	0.0516656	−	0.0240921i
$818$	42.0939	+	11.2790i	1.47178	+	0.394362i
$819$		0			0
$820$	50.8231	−	43.4410i	1.77482	−	1.51703i
$821$	27.5109	+	32.7862i	0.960137	+	1.14425i	0.989479	+	0.144678i	$0.0462145\pi$
$821$	27.5109	+	32.7862i	0.960137	+	1.14425i	−0.0293416	+	0.999569i	$0.509341\pi$
$822$		0			0
$823$	−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
$825$		0			0
$826$	−60.1008	+	50.4305i	−2.09117	+	1.75470i
$827$	−13.0585	+	3.49901i	−0.454088	+	0.121673i	−0.478612	−	0.878027i	$-0.658860\pi$
$827$	−13.0585	+	3.49901i	−0.454088	+	0.121673i	0.0245234	+	0.999699i	$0.492193\pi$
$828$		0			0
$829$	−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
$831$		0			0
$832$	18.7022	−	1.63623i	0.648383	−	0.0567261i
$833$	−1.41707	+	3.03892i	−0.0490986	+	0.105292i
$834$		0			0
$835$	9.54884	−	6.81669i	0.330451	−	0.235901i
$836$		−	20.4628i		−	0.707721i
$837$		0			0
$838$	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	$-0.270600\pi$
$840$		0			0
$841$	12.7044	−	4.62403i	0.438083	−	0.159449i
$842$	1.68687	+	19.2811i	0.0581335	+	0.664469i
$843$		0			0
$844$	−4.47705	+	12.3006i	−0.154106	+	0.423404i
$845$	−6.71706	+	1.24762i	−0.231074	+	0.0429194i
$846$		0			0
$847$	6.55983	+	24.4816i	0.225398	+	0.841199i
$848$	5.97184	−	68.2584i	0.205074	−	2.34400i
$849$		0			0
$850$	−16.1013	−	18.4935i	−0.552270	−	0.634324i
$851$	2.41605	+	0.426015i	0.0828212	+	0.0146036i
$852$		0			0
$853$	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
$855$		0			0
$856$	19.5466	+	33.8558i	0.668090	+	1.15717i
$857$	17.7690	+	38.1058i	0.606978	+	1.30167i	0.934210	+	0.356724i	$0.116106\pi$
$857$	17.7690	+	38.1058i	0.606978	+	1.30167i	−0.327232	+	0.944944i	$0.606116\pi$
$858$		0			0
$859$	−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
$861$		0			0
$862$	−31.7398	−	22.2244i	−1.08106	−	0.756967i
$863$	−16.2331	+	16.2331i	−0.552582	+	0.552582i	−0.927185	−	0.374603i	$-0.877779\pi$
$863$	−16.2331	+	16.2331i	−0.552582	+	0.552582i	0.374603	+	0.927185i	$0.377779\pi$
$864$		0			0
$865$	16.5018	−	7.87879i	0.561078	−	0.267887i
$866$	89.7060	−	15.8176i	3.04833	−	0.537503i
$867$		0			0
$868$	73.2814	+	34.1717i	2.48733	+	1.15986i
$869$	15.7358	+	13.2039i	0.533800	+	0.447911i
$870$		0			0
$871$	7.50875	+	2.73296i	0.254424	+	0.0926028i
$872$	−11.8767	+	44.3246i	−0.402197	+	1.50102i
$873$		0			0
$874$	−46.7680	−	27.0015i	−1.58195	−	0.913339i
$875$	−29.6137	+	14.8077i	−1.00112	+	0.500592i
$876$		0			0
$877$	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
$879$		0			0
$880$	10.6522	+	28.4570i	0.359085	+	0.959286i
$881$	−20.5994	−	11.8931i	−0.694013	−	0.400688i	0.111101	−	0.993809i	$-0.464562\pi$
$881$	−20.5994	−	11.8931i	−0.694013	−	0.400688i	−0.805114	+	0.593121i	$0.797896\pi$
$882$		0			0
$883$	−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
$885$		0			0
$886$	56.7260	+	47.5988i	1.90575	+	1.59911i
$887$	−11.8712	−	5.53565i	−0.398597	−	0.185869i	0.212975	−	0.977058i	$-0.431685\pi$
$887$	−11.8712	−	5.53565i	−0.398597	−	0.185869i	−0.611572	+	0.791189i	$0.709463\pi$
$888$		0			0
$889$	6.30200	−	1.11121i	0.211362	−	0.0372689i
$890$	−21.1248	−	44.2450i	−0.708104	−	1.48309i
$891$		0			0
$892$	73.3199	−	73.3199i	2.45493	−	2.45493i
$893$	−1.73756	−	1.21666i	−0.0581454	−	0.0407138i
$894$		0			0
$895$	−11.8685	+	0.108162i	−0.396722	+	0.00361546i
$896$	9.38428	−	11.1838i	0.313507	−	0.373623i
$897$		0			0
$898$	−27.2338	−	58.4031i	−0.908804	−	1.94894i
$899$	−11.4261	−	19.7906i	−0.381082	−	0.660054i
$900$		0			0
$901$	7.46317	−	12.9266i	0.248634	−	0.430647i
$902$	−25.6289	−	2.24223i	−0.853347	−	0.0746582i
$903$		0			0
$904$	−15.6919	−	2.76691i	−0.521906	−	0.0920261i
$905$	25.4036	−	44.9412i	0.844445	−	1.49390i
$906$		0			0
$907$	−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
$909$		0			0
$910$	38.8814	−	56.6197i	1.28891	−	1.87693i
$911$	−18.7788	+	51.5943i	−0.622169	+	1.70940i	0.0794445	+	0.996839i	$0.474685\pi$
$911$	−18.7788	+	51.5943i	−0.622169	+	1.70940i	−0.701614	+	0.712557i	$0.747537\pi$
$912$		0			0
$913$	0.553828	+	6.33028i	0.0183290	+	0.209502i
$914$	8.96418	−	3.26269i	0.296509	−	0.107920i
$915$		0			0
$916$	−3.79298	−	21.5110i	−0.125323	−	0.710745i
$917$	2.01738	+	2.01738i	0.0666196	+	0.0666196i
$918$		0			0
$919$		−	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
$921$		0			0
$922$	16.6937	−	35.7998i	0.549778	−	1.17900i
$923$	28.1686	−	2.46444i	0.927182	−	0.0811179i
$924$		0			0
$925$	−1.58972	−	0.395056i	−0.0522695	−	0.0129894i
$926$	25.2375	−	14.5709i	0.829356	−	0.478829i
$927$		0			0
$928$	32.4145	−	8.68545i	1.06406	−	0.285114i
$929$	−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	$0.399455\pi$
$930$		0			0
$931$	0.856201	−	4.85576i	0.0280609	−	0.159141i
$932$	−54.9834	+	38.4998i	−1.80104	+	1.26110i
$933$		0			0
$934$	29.0481	+	34.6182i	0.950482	+	1.13274i
$935$	−0.516787	+	6.59901i	−0.0169007	+	0.215811i
$936$		0			0
$937$	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
$939$		0			0
$940$	7.74943	+	2.00094i	0.252758	+	0.0652636i
$941$	−15.3914	−	42.2876i	−0.501747	−	1.37854i	−0.889568	−	0.456803i	$-0.848994\pi$
$941$	−15.3914	−	42.2876i	−0.501747	−	1.37854i	0.387821	−	0.921735i	$-0.373228\pi$
$942$		0			0
$943$	−27.3198	+	39.0167i	−0.889654	+	1.27056i
$944$	−89.0054			−2.89688
$945$		0			0
$946$	2.36576			0.0769175
$947$	−9.56806	+	13.6646i	−0.310920	+	0.444040i	−0.943950	−	0.330087i	$-0.892922\pi$
$947$	−9.56806	+	13.6646i	−0.310920	+	0.444040i	0.633030	+	0.774127i	$0.281811\pi$
$948$		0			0
$949$	5.58076	+	15.3330i	0.181159	+	0.497731i
$950$	29.9085	+	20.1399i	0.970361	+	0.653426i
$951$		0			0
$952$	−35.5504	+	16.5774i	−1.15220	+	0.537277i
$953$	−17.5554	−	4.70396i	−0.568676	−	0.152376i	−0.0369865	−	0.999316i	$-0.511776\pi$
$953$	−17.5554	−	4.70396i	−0.568676	−	0.152376i	−0.531689	+	0.846940i	$0.678443\pi$
$954$		0			0
$955$	−5.52036	−	6.45846i	−0.178635	−	0.208991i
$956$	61.5462	+	73.3479i	1.99055	+	2.37224i
$957$		0			0
$958$	48.5557	−	33.9991i	1.56876	−	1.09846i
$959$	1.25123	−	7.09611i	0.0404045	−	0.229145i
$960$		0			0
$961$	2.09504	−	1.75795i	0.0675821	−	0.0567081i
$962$	3.28233	−	0.879497i	0.105826	−	0.0283561i
$963$		0			0
$964$	−66.2491	+	38.2489i	−2.13374	+	1.23192i
$965$	2.65950	+	27.5085i	0.0856122	+	0.885530i
$966$		0			0
$967$	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
$969$		0			0
$970$	−7.61166	+	45.5937i	−0.244396	+	1.46393i
$971$		−	23.4452i		−	0.752393i	−0.926540	−	0.376196i	$-0.877232\pi$
$971$		−	23.4452i		−	0.752393i	0.926540	−	0.376196i	$-0.122768\pi$
$972$		0			0
$973$	−20.3704	−	20.3704i	−0.653044	−	0.653044i
$974$	−16.3102	−	92.5000i	−0.522614	−	2.96389i
$975$		0			0
$976$	−99.2811	+	36.1353i	−3.17791	+	1.15666i
$977$	1.95075	+	22.2971i	0.0624099	+	0.713349i	0.961359	+	0.275297i	$0.0887760\pi$
$977$	1.95075	+	22.2971i	0.0624099	+	0.713349i	−0.898949	+	0.438052i	$0.855668\pi$
$978$		0			0
$979$	−4.52670	+	12.4370i	−0.144674	+	0.397488i
$980$	3.39744	+	18.2915i	0.108527	+	0.584300i
$981$		0			0
$982$	−9.22446	−	34.4262i	−0.294365	−	1.09858i
$983$	−0.218640	+	2.49907i	−0.00697353	+	0.0797078i	−0.998884	−	0.0472321i	$-0.984960\pi$
$983$	−0.218640	+	2.49907i	−0.00697353	+	0.0797078i	0.991910	+	0.126940i	$0.0405155\pi$
$984$		0			0
$985$	51.7216	−	14.3652i	1.64799	−	0.457713i
$986$	19.0022	+	3.35059i	0.605152	+	0.106705i
$987$		0			0
$988$	−52.2749	−	4.57346i	−1.66309	−	0.145501i
$989$	2.18999	−	3.79317i	0.0696376	−	0.120616i
$990$		0			0
$991$	−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			0
$994$	−34.7731	+	41.4409i	−1.10294	+	1.31443i
$995$	−0.134950	−	14.8079i	−0.00427820	−	0.469443i
$996$		0			0
$997$	−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			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.233.15		192
3.2	odd	2		135.2.q.a.68.2	yes	192
5.2	odd	4	inner	405.2.r.a.152.15		192
15.2	even	4		135.2.q.a.122.2	yes	192
15.8	even	4		675.2.ba.b.257.15		192
15.14	odd	2		675.2.ba.b.68.15		192
27.2	odd	18	inner	405.2.r.a.8.15		192
27.25	even	9		135.2.q.a.83.2	yes	192
135.2	even	36	inner	405.2.r.a.332.15		192
135.52	odd	36		135.2.q.a.2.2	✓	192
135.79	even	18		675.2.ba.b.218.15		192
135.133	odd	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	135.52	odd	36
135.2.q.a.68.2	yes	192	3.2	odd	2
135.2.q.a.83.2	yes	192	27.25	even	9
135.2.q.a.122.2	yes	192	15.2	even	4
405.2.r.a.8.15		192	27.2	odd	18	inner
405.2.r.a.152.15		192	5.2	odd	4	inner
405.2.r.a.233.15		192	1.1	even	1	trivial
405.2.r.a.332.15		192	135.2	even	36	inner
675.2.ba.b.68.15		192	15.14	odd	2
675.2.ba.b.218.15		192	135.79	even	18
675.2.ba.b.257.15		192	15.8	even	4
675.2.ba.b.407.15		192	135.133	odd	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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.r (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.48477 - 2.12047i) q^{2} +(-1.60780 - 4.41741i) q^{4} +(-1.13563 - 1.92622i) q^{5} +(-2.68394 + 1.25154i) q^{7} +(-6.75336 - 1.80956i) q^{8} +(-5.77064 - 0.451915i) q^{10} +(1.00437 + 1.19696i) q^{11} +(3.28227 - 2.29827i) q^{13} +(-1.33117 + 7.54945i) q^{14} +(-6.66205 + 5.59013i) q^{16} +(-1.82995 + 0.490334i) q^{17} +(2.41262 - 1.39293i) q^{19} +(-6.68303 + 8.11355i) q^{20} +(4.02936 - 0.352524i) q^{22} +(3.16476 - 6.78686i) q^{23} +(-2.42067 + 4.37497i) q^{25} -10.3723i q^{26} +(9.84382 + 9.84382i) q^{28} +(-0.683218 - 3.87472i) q^{29} +(5.45790 - 1.98651i) q^{31} +(0.743366 + 8.49672i) q^{32} +(-1.67731 + 4.60838i) q^{34} +(5.45873 + 3.74857i) q^{35} +(0.0847926 + 0.316450i) q^{37} +(0.628522 - 7.18404i) q^{38} +(4.18374 + 15.0635i) q^{40} +(-6.26389 - 1.10449i) q^{41} +(0.582670 + 0.0509770i) q^{43} +(3.67263 - 6.36118i) q^{44} +(-9.69236 - 16.7877i) q^{46} +(-0.321786 - 0.690071i) q^{47} +(1.13767 - 1.35582i) q^{49} +(5.68285 + 11.6287i) q^{50} +(-15.4296 - 10.8039i) q^{52} +(-5.57112 + 5.57112i) q^{53} +(1.16502 - 3.29395i) q^{55} +(20.3903 - 3.59537i) q^{56} +(-9.23063 - 4.30431i) q^{58} +(7.84000 + 6.57854i) q^{59} +(11.4160 + 4.15507i) q^{61} +(3.89137 - 14.5228i) q^{62} +(4.05760 + 2.34266i) q^{64} +(-8.15444 - 3.71239i) q^{65} +(1.14383 + 1.63356i) q^{67} +(5.10821 + 7.29527i) q^{68} +(16.0536 - 6.00929i) q^{70} +(6.11142 + 3.52843i) q^{71} +(-1.05397 + 3.93347i) q^{73} +(0.796919 + 0.290055i) q^{74} +(-10.0321 - 8.41796i) q^{76} +(-4.19371 - 1.95556i) q^{77} +(12.9467 - 2.28286i) q^{79} +(18.3335 + 6.48426i) q^{80} +(-11.6425 + 11.6425i) q^{82} +(3.33133 + 2.33262i) q^{83} +(3.02265 + 2.96805i) q^{85} +(0.973224 - 1.15984i) q^{86} +(-4.61689 - 9.90096i) q^{88} +(4.23520 + 7.33558i) q^{89} +(-5.93304 + 10.2763i) q^{91} +(-35.0686 - 3.06811i) q^{92} +(-1.94105 - 0.342259i) q^{94} +(-5.42294 - 3.06539i) q^{95} +(0.696015 - 7.95549i) q^{97} +(-1.18580 - 4.42546i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more