LMFDB - Embedded newform 405.2.r.a.332.15

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			332.15
Character	$\chi$	$=$	405.332
Dual form			405.2.r.a.233.15

$q$-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 $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{18}\right)$

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	0.855040	+	0.518562i	$0.173533\pi$
$2$	1.48477	+	2.12047i	1.04989	+	1.49940i	0.194848	+	0.980833i	$0.437579\pi$
$3$		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	−0.156982	−	0.987602i	$-0.550176\pi$
$7$	−2.68394	−	1.25154i	−1.01443	−	0.473038i	−0.857453	+	0.514563i	$0.827954\pi$
$8$	−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	−0.593074	−	0.805148i	$-0.702086\pi$
$11$	1.00437	−	1.19696i	0.302828	−	0.360897i	0.895902	+	0.444251i	$0.146530\pi$
$12$		0			0
$13$	3.28227	+	2.29827i	0.910338	+	0.637425i	0.932046	−	0.362339i	$-0.118022\pi$
$13$	3.28227	+	2.29827i	0.910338	+	0.637425i	−0.0217086	+	0.999764i	$0.506911\pi$
$14$	−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	0.0299818	−	0.999550i	$-0.490455\pi$
$17$	−1.82995	−	0.490334i	−0.443828	−	0.118923i	−0.473810	+	0.880627i	$0.657122\pi$
$18$		0			0
$19$	2.41262	+	1.39293i	0.553493	+	0.319559i	0.750529	−	0.660837i	$-0.229799\pi$
$19$	2.41262	+	1.39293i	0.553493	+	0.319559i	−0.197037	+	0.980396i	$0.563132\pi$
$20$	−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	0.896276	+	0.443496i	$0.146262\pi$
$23$	3.16476	+	6.78686i	0.659899	+	1.41516i	−0.236377	+	0.971661i	$0.575960\pi$
$24$		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	0.853309	+	0.521406i	$0.174592\pi$
$29$	−0.683218	+	3.87472i	−0.126870	+	0.719518i	−0.980179	+	0.198112i	$0.936519\pi$
$30$		0			0
$31$	5.45790	+	1.98651i	0.980267	+	0.356788i	0.781944	−	0.623348i	$-0.214228\pi$
$31$	5.45790	+	1.98651i	0.980267	+	0.356788i	0.198323	+	0.980137i	$0.436450\pi$
$32$	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	−0.958606	−	0.284737i	$-0.908094\pi$
$37$	0.0847926	−	0.316450i	0.0139398	−	0.0520241i	0.972545	+	0.232713i	$0.0747603\pi$
$38$	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	−0.639843	−	0.768505i	$-0.721001\pi$
$41$	−6.26389	+	1.10449i	−0.978255	+	0.172493i	−0.338412	+	0.940998i	$0.609890\pi$
$42$		0			0
$43$	0.582670	−	0.0509770i	0.0888564	−	0.00777393i	−0.0426408	−	0.999090i	$-0.513577\pi$
$43$	0.582670	−	0.0509770i	0.0888564	−	0.00777393i	0.131497	+	0.991317i	$0.458022\pi$
$44$	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	−0.928378	−	0.371638i	$-0.878796\pi$
$47$	−0.321786	+	0.690071i	−0.0469372	+	0.100657i	0.881441	+	0.472295i	$0.156574\pi$
$48$		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	0.212014	−	0.977267i	$-0.431998\pi$
$53$	−5.57112	−	5.57112i	−0.765253	−	0.765253i	−0.977267	+	0.212014i	$0.931998\pi$
$54$		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	0.0309682	−	0.999520i	$-0.490141\pi$
$59$	7.84000	−	6.57854i	1.02068	−	0.856453i	0.989713	+	0.143067i	$0.0456965\pi$
$60$		0			0
$61$	11.4160	−	4.15507i	1.46166	−	0.532002i	0.515840	−	0.856685i	$-0.327480\pi$
$61$	11.4160	−	4.15507i	1.46166	−	0.532002i	0.945823	+	0.324683i	$0.105258\pi$
$62$	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	−0.743181	−	0.669091i	$-0.766684\pi$
$67$	1.14383	−	1.63356i	0.139742	−	0.199572i	0.882922	+	0.469519i	$0.155573\pi$
$68$	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	−0.0914051	−	0.995814i	$-0.529136\pi$
$71$	6.11142	−	3.52843i	0.725292	−	0.418748i	0.816698	+	0.577066i	$0.195802\pi$
$72$		0			0
$73$	−1.05397	−	3.93347i	−0.123358	−	0.460378i	0.876418	−	0.481551i	$-0.159926\pi$
$73$	−1.05397	−	3.93347i	−0.123358	−	0.460378i	−0.999776	+	0.0211733i	$0.993260\pi$
$74$	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	0.845194	−	0.534460i	$-0.179485\pi$
$79$	12.9467	+	2.28286i	1.45662	+	0.256842i	0.611427	+	0.791301i	$0.290596\pi$
$80$	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	−0.376277	−	0.926507i	$-0.622796\pi$
$83$	3.33133	−	2.33262i	0.365661	−	0.256038i	0.741938	+	0.670469i	$0.233907\pi$
$84$		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	−0.549386	−	0.835569i	$-0.685138\pi$
$89$	4.23520	−	7.33558i	0.448930	−	0.777570i	0.998317	+	0.0579982i	$0.0184718\pi$
$90$		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	0.945986	+	0.324207i	$0.105097\pi$
$97$	0.696015	+	7.95549i	0.0706696	+	0.807758i	−0.875317	+	0.483550i	$0.839347\pi$
$98$	−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	−0.859330	−	0.511422i	$-0.829119\pi$
$101$	−5.32423	−	14.6282i	−0.529781	−	1.45556i	0.329549	−	0.944139i	$-0.393103\pi$
$102$		0			0
$103$	−0.690517	+	7.89264i	−0.0680387	+	0.777685i	0.883153	+	0.469085i	$0.155416\pi$
$103$	−0.690517	+	7.89264i	−0.0680387	+	0.777685i	−0.951192	+	0.308601i	$0.900139\pi$
$104$	−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	−0.871903	−	0.489678i	$-0.837114\pi$
$107$	−3.95377	+	3.95377i	−0.382225	+	0.382225i	0.489678	+	0.871903i	$0.337114\pi$
$108$		0			0
$109$			6.56334i			0.628654i	0.949315	+	0.314327i	$0.101779\pi$
$109$			6.56334i			0.628654i	−0.949315	+	0.314327i	$0.898221\pi$
$110$	−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	0.193442	−	0.981112i	$-0.438035\pi$
$113$	2.27035	+	0.198630i	0.213577	+	0.0186855i	0.0201349	+	0.999797i	$0.493590\pi$
$114$		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	−0.350233	−	0.936662i	$-0.613898\pi$
$127$	−2.08725	+	0.559276i	−0.185213	+	0.0496277i	0.165020	+	0.986290i	$0.447231\pi$
$128$	−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	−0.953254	−	0.302169i	$-0.902289\pi$
$131$	−0.329501	+	0.905296i	−0.0287886	+	0.0790961i	0.924466	+	0.381265i	$0.124512\pi$
$132$		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	0.755098	−	0.655612i	$-0.227589\pi$
$137$	−1.39561	−	1.99313i	−0.119235	−	0.170285i	−0.874333	+	0.485327i	$0.838700\pi$
$138$		0			0
$139$	3.32712	−	9.14118i	0.282202	−	0.775345i	−0.714897	−	0.699230i	$-0.753526\pi$
$139$	3.32712	−	9.14118i	0.282202	−	0.775345i	0.997099	−	0.0761146i	$-0.0242515\pi$
$140$	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	0.905956	+	0.423373i	$0.139154\pi$
$149$	2.43445	+	13.8064i	0.199438	+	1.13107i	−0.706518	+	0.707695i	$0.749735\pi$
$150$		0			0
$151$	−13.9585	−	11.7126i	−1.13593	−	0.953156i	−0.136630	−	0.990622i	$-0.543627\pi$
$151$	−13.9585	−	11.7126i	−1.13593	−	0.953156i	−0.999298	+	0.0374659i	$0.988071\pi$
$152$	−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	−0.0345064	−	0.999404i	$-0.510986\pi$
$157$	−3.03267	−	0.265324i	−0.242033	−	0.0211752i	−0.207527	+	0.978229i	$0.566541\pi$
$158$	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	−0.300465	+	0.953793i	$0.597142\pi$
$163$	−16.0133	+	16.0133i	−1.25426	+	1.25426i	−0.953793	+	0.300465i	$0.902858\pi$
$164$	5.19212	−	29.4459i	0.405436	−	2.29934i
$165$		0			0
$166$	9.89249	+	3.60057i	0.767806	+	0.279459i
$167$	0.457294	−	5.22689i	0.0353865	−	0.404469i	−0.957758	−	0.287576i	$-0.907151\pi$
$167$	0.457294	−	5.22689i	0.0353865	−	0.404469i	0.993144	−	0.116894i	$-0.0372937\pi$
$168$		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	−0.973929	−	0.226854i	$-0.927156\pi$
$173$	−0.712745	−	8.14671i	−0.0541890	−	0.619383i	0.919740	−	0.392529i	$-0.128400\pi$
$174$		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	0.948000	−	0.318271i	$-0.103102\pi$
$179$	2.65400	+	4.59686i	0.198369	+	0.343585i	−0.749631	+	0.661856i	$0.769769\pi$
$180$		0			0
$181$	11.5435	−	19.9940i	0.858023	−	1.48614i	−0.0157880	−	0.999875i	$-0.505026\pi$
$181$	11.5435	−	19.9940i	0.858023	−	1.48614i	0.873811	−	0.486265i	$-0.161641\pi$
$182$	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	0.307377	−	0.951588i	$-0.400549\pi$
$191$	3.74191	+	0.659800i	0.270755	+	0.0477414i	−0.0366221	+	0.999329i	$0.511660\pi$
$192$		0			0
$193$	−11.2015	+	5.22336i	−0.806305	+	0.375986i	−0.781656	−	0.623710i	$-0.785625\pi$
$193$	−11.2015	+	5.22336i	−0.806305	+	0.375986i	−0.0246489	+	0.999696i	$0.507847\pi$
$194$	−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	−0.722000	−	0.691893i	$-0.756777\pi$
$197$	−6.21326	−	23.1882i	−0.442676	−	1.65209i	0.279324	−	0.960197i	$-0.409890\pi$
$198$		0			0
$199$	5.73533	−	3.31129i	0.406566	−	0.234731i	−0.282747	−	0.959195i	$-0.591246\pi$
$199$	5.73533	−	3.31129i	0.406566	−	0.234731i	0.689313	+	0.724463i	$0.257912\pi$
$200$	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	−0.713253	−	0.700907i	$-0.752779\pi$
$211$	−2.13311	+	1.78989i	−0.146849	+	0.123221i	0.566404	+	0.824128i	$0.308334\pi$
$212$	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	−0.298923	−	0.954277i	$-0.596627\pi$
$223$	9.32189	−	19.9909i	0.624240	−	1.33869i	0.923163	−	0.384410i	$-0.125595\pi$
$224$	−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	0.161319	−	0.986902i	$-0.448425\pi$
$227$	7.40612	−	0.647951i	0.491561	−	0.0430060i	0.330242	+	0.943896i	$0.392870\pi$
$228$		0			0
$229$	4.57594	−	0.806861i	0.302386	−	0.0533189i	−0.0203963	−	0.999792i	$-0.506493\pi$
$229$	4.57594	−	0.806861i	0.302386	−	0.0533189i	0.322783	+	0.946473i	$0.395382\pi$
$230$	−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	0.732711	+	0.680540i	$0.238255\pi$
$233$	−3.69557	+	13.7921i	−0.242105	+	0.903549i	−0.974816	+	0.223009i	$0.928412\pi$
$234$		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	−0.361705	−	0.932293i	$-0.617805\pi$
$239$	−19.1398	−	6.96633i	−1.23805	−	0.450614i	−0.876348	+	0.481678i	$0.840027\pi$
$240$		0			0
$241$	−2.82578	+	16.0258i	−0.182024	+	1.03231i	0.747695	+	0.664043i	$0.231161\pi$
$241$	−2.82578	+	16.0258i	−0.182024	+	1.03231i	−0.929719	+	0.368269i	$0.879950\pi$
$242$	−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	0.755534	−	0.655109i	$-0.227377\pi$
$251$	8.96649	+	5.17681i	0.565960	+	0.326757i	−0.189574	+	0.981866i	$0.560711\pi$
$252$		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	0.419313	−	0.907842i	$-0.362271\pi$
$257$	−4.65492	−	3.25941i	−0.290366	−	0.203316i	−0.709679	+	0.704525i	$0.751160\pi$
$258$		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	0.882280	−	0.470725i	$-0.156008\pi$
$263$	17.6574	+	8.23378i	1.08880	+	0.507717i	0.206522	+	0.978442i	$0.433785\pi$
$264$		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	0.272798	−	0.962071i	$-0.412051\pi$
$277$	−4.80726	−	2.24166i	−0.288841	−	0.134689i	−0.561638	+	0.827383i	$0.689829\pi$
$278$	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	−0.736955	−	0.675942i	$-0.763737\pi$
$281$	0.950287	−	1.13251i	0.0566894	−	0.0675598i	0.793644	+	0.608382i	$0.208181\pi$
$282$		0			0
$283$	−4.14980	−	2.90572i	−0.246680	−	0.172727i	0.443697	−	0.896177i	$-0.353667\pi$
$283$	−4.14980	−	2.90572i	−0.246680	−	0.172727i	−0.690377	+	0.723449i	$0.742556\pi$
$284$	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	0.955579	+	0.294736i	$0.0952316\pi$
$293$	9.70762	+	20.8181i	0.567125	+	1.21620i	−0.388453	+	0.921468i	$0.626991\pi$
$294$		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	0.548801	+	0.835953i	$0.315084\pi$
$307$	−6.03527	+	22.5239i	−0.344451	+	1.28551i	−0.893252	+	0.449556i	$0.851582\pi$
$308$	−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	−0.431691	−	0.902022i	$-0.642083\pi$
$311$	−9.32616	+	1.64445i	−0.528838	+	0.0932485i	−0.0971473	+	0.995270i	$0.530972\pi$
$312$		0			0
$313$	−30.8225	+	2.69662i	−1.74219	+	0.152422i	−0.913380	−	0.407109i	$-0.866537\pi$
$313$	−30.8225	+	2.69662i	−1.74219	+	0.152422i	−0.828810	+	0.559530i	$0.810982\pi$
$314$	−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	0.481576	+	0.876404i	$0.340064\pi$
$317$	−8.89049	+	19.0657i	−0.499340	+	1.07084i	−0.980916	+	0.194433i	$0.937713\pi$
$318$		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	−0.335812	−	0.941929i	$-0.609011\pi$
$331$	0.225624	−	0.0821205i	0.0124014	−	0.00451375i	0.348213	+	0.937415i	$0.386788\pi$
$332$	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	−0.992142	−	0.125116i	$-0.960070\pi$
$337$	−9.82568	+	14.0325i	−0.535239	+	0.764400i	0.456903	+	0.889516i	$0.348959\pi$
$338$	−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	−0.949741	−	0.313038i	$-0.898653\pi$
$347$	−24.5967	+	11.4696i	−1.32042	+	0.615723i	−0.370681	+	0.928760i	$0.620876\pi$
$348$		0			0
$349$	−18.8404	−	3.32208i	−1.00851	−	0.177827i	−0.355095	−	0.934830i	$-0.615551\pi$
$349$	−18.8404	−	3.32208i	−1.00851	−	0.177827i	−0.653411	+	0.757003i	$0.726663\pi$
$350$	−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	0.327663	−	0.944795i	$-0.393739\pi$
$353$	24.9423	−	17.4648i	1.32755	−	0.929558i	0.999884	+	0.0152364i	$0.00485008\pi$
$354$		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	−0.0784904	−	0.996915i	$-0.525010\pi$
$359$	15.6146	−	27.0453i	0.824108	−	1.42740i	0.902599	−	0.430483i	$-0.141657\pi$
$360$		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	0.998745	−	0.0500864i	$-0.0159497\pi$
$367$	0.124058	+	1.41799i	0.00647576	+	0.0740183i	−0.992269	+	0.124105i	$0.960394\pi$
$368$	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	−0.941168	−	0.337940i	$-0.890270\pi$
$373$	0.857201	−	9.79785i	0.0443842	−	0.507313i	0.985552	−	0.169374i	$-0.0541745\pi$
$374$	−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	$-0.952697\pi$
$379$		−	5.76488i		−	0.296122i	0.988978	−	0.148061i	$-0.0473032\pi$
$380$	−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	0.159646	−	0.987174i	$-0.448965\pi$
$383$	2.84641	+	0.249029i	0.145445	+	0.0127248i	−0.0142007	+	0.999899i	$0.504520\pi$
$384$		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	0.855884	−	0.517168i	$-0.173014\pi$
$389$	9.76677	+	8.19530i	0.495195	+	0.415518i	−0.360689	+	0.932686i	$0.617458\pi$
$390$		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	−0.344828	−	0.938666i	$-0.612063\pi$
$397$	−3.46941	+	0.929625i	−0.174125	+	0.0466565i	0.170703	+	0.985322i	$0.445396\pi$
$398$	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	−0.630049	−	0.776555i	$-0.716965\pi$
$401$	7.04392	−	19.3530i	0.351756	−	0.966443i	0.981806	−	0.189888i	$-0.0608124\pi$
$402$		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	−0.712078	−	0.702101i	$-0.752246\pi$
$409$	5.75785	−	15.8196i	0.284707	−	0.782226i	0.996785	−	0.0801257i	$-0.0255322\pi$
$410$	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	0.982413	−	0.186723i	$-0.0597866\pi$
$419$	−0.0944911	−	0.535886i	−0.00461619	−	0.0261797i	−0.987029	+	0.160543i	$0.948675\pi$
$420$		0			0
$421$	−5.72762	−	4.80604i	−0.279147	−	0.234232i	0.492455	−	0.870338i	$-0.336100\pi$
$421$	−5.72762	−	4.80604i	−0.279147	−	0.234232i	−0.771602	+	0.636106i	$0.780544\pi$
$422$	−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	$0.117394\pi$
$431$			14.9683i			0.720998i	−0.932760	+	0.360499i	$0.882606\pi$
$432$		0			0
$433$	24.8822	−	24.8822i	1.19576	−	1.19576i	0.220337	−	0.975424i	$-0.429284\pi$
$433$	24.8822	−	24.8822i	1.19576	−	1.19576i	0.975424	−	0.220337i	$-0.0707157\pi$
$434$	7.73168	−	43.8485i	0.371132	−	2.10480i
$435$		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	0.703174	+	0.711017i	$0.251765\pi$
$439$	13.0228	+	35.7799i	0.621545	+	1.70768i	−0.0816297	+	0.996663i	$0.526012\pi$
$440$	−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	−0.790053	−	0.613038i	$-0.789947\pi$
$443$	−2.49320	−	28.4974i	−0.118456	−	1.35395i	0.671597	−	0.740916i	$-0.265608\pi$
$444$		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	0.994570	+	0.104066i	$0.0331852\pi$
$449$	12.4470	+	21.5588i	0.587409	+	1.01742i	−0.407162	+	0.913356i	$0.633481\pi$
$450$		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	−0.500837	−	0.865542i	$-0.666974\pi$
$457$	3.01872	−	2.11373i	0.141210	−	0.0988761i	0.642047	+	0.766666i	$0.278086\pi$
$458$	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	0.512267	−	0.858826i	$-0.328806\pi$
$461$	15.0276	+	2.64977i	0.699905	+	0.123412i	0.187638	+	0.982238i	$0.439917\pi$
$462$		0			0
$463$	10.2029	−	4.75770i	0.474170	−	0.221109i	−0.170817	−	0.985303i	$-0.554641\pi$
$463$	10.2029	−	4.75770i	0.474170	−	0.221109i	0.644987	+	0.764194i	$0.276863\pi$
$464$	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	−0.988166	−	0.153390i	$-0.950981\pi$
$467$	−4.51835	−	16.8627i	−0.209084	−	0.780313i	0.779082	−	0.626923i	$-0.215686\pi$
$468$		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	0.200096	−	0.979776i	$-0.435875\pi$
$479$	21.5176	−	7.83178i	0.983166	−	0.357843i	0.783070	+	0.621933i	$0.213652\pi$
$480$		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	0.983896	+	0.178740i	$0.0572021\pi$
$487$	25.6571	+	25.6571i	1.16264	+	1.16264i	0.178740	+	0.983896i	$0.442798\pi$
$488$	−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	0.927836	−	0.372988i	$-0.121667\pi$
$491$	8.85005	+	10.5471i	0.399397	+	0.475983i	−0.528439	+	0.848971i	$0.677222\pi$
$492$		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	−0.534361	−	0.845256i	$-0.679448\pi$
$499$	−16.6957	+	2.94390i	−0.747401	+	0.131787i	−0.213040	+	0.977043i	$0.568337\pi$
$500$	−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	0.857411	+	0.514633i	$0.172072\pi$
$503$	−3.19471	+	11.9228i	−0.142445	+	0.531612i	−0.999856	+	0.0169795i	$0.994595\pi$
$504$		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	0.315835	−	0.948814i	$-0.397715\pi$
$509$	−1.17560	−	0.427885i	−0.0521077	−	0.0189657i	−0.367943	+	0.929849i	$0.619938\pi$
$510$		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	0.940712	−	0.339206i	$-0.110158\pi$
$521$	25.5030	+	14.7242i	1.11731	+	0.645078i	0.176595	+	0.984284i	$0.443492\pi$
$522$		0			0
$523$	10.8910	+	2.91822i	0.476228	+	0.127605i	0.488946	−	0.872314i	$-0.337382\pi$
$523$	10.8910	+	2.91822i	0.476228	+	0.127605i	−0.0127175	+	0.999919i	$0.504048\pi$
$524$	−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	0.502548	−	0.864549i	$-0.332396\pi$
$547$	3.81919	+	1.78092i	0.163297	+	0.0761465i	−0.339251	+	0.940696i	$0.610174\pi$
$548$	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	−0.169299	−	0.985565i	$-0.554150\pi$
$557$	−19.0860	−	5.11407i	−0.808698	−	0.216690i	−0.639399	+	0.768875i	$0.720817\pi$
$558$		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	−0.987683	−	0.156469i	$-0.949989\pi$
$563$	−11.2154	−	24.0516i	−0.472675	−	1.01365i	0.515008	−	0.857185i	$-0.327789\pi$
$564$		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	−0.281327	−	0.959612i	$-0.590774\pi$
$569$	7.42425	−	42.1050i	0.311241	−	1.76513i	0.592567	−	0.805521i	$-0.298114\pi$
$570$		0			0
$571$	9.01463	+	3.28106i	0.377251	+	0.137308i	0.523684	−	0.851912i	$-0.324557\pi$
$571$	9.01463	+	3.28106i	0.377251	+	0.137308i	−0.146433	+	0.989221i	$0.546779\pi$
$572$	−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	0.836958	+	0.547268i	$0.184332\pi$
$577$	−3.87943	+	14.4782i	−0.161503	+	0.602737i	−0.998460	+	0.0554690i	$0.982335\pi$
$578$	−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	−0.868054	−	0.496470i	$-0.834629\pi$
$587$	1.70173	−	3.64938i	0.0702381	−	0.150626i	0.938292	+	0.345844i	$0.112407\pi$
$588$		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	0.565563	−	0.824705i	$-0.308659\pi$
$593$	−6.31053	−	6.31053i	−0.259142	−	0.259142i	−0.824705	+	0.565563i	$0.808659\pi$
$594$		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	−0.992148	−	0.125067i	$-0.960085\pi$
$599$	−25.4844	+	21.3840i	−1.04127	+	0.873726i	−0.0491180	+	0.998793i	$0.515641\pi$
$600$		0			0
$601$	−16.7184	+	6.08500i	−0.681958	+	0.248212i	−0.659688	−	0.751540i	$-0.729312\pi$
$601$	−16.7184	+	6.08500i	−0.681958	+	0.248212i	−0.0222700	+	0.999752i	$0.507089\pi$
$602$	−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	0.208966	−	0.977923i	$-0.432990\pi$
$607$	26.0280	−	37.1718i	1.05644	−	1.50876i	0.847477	−	0.530833i	$-0.178121\pi$
$608$	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	0.841427	+	0.540370i	$0.181716\pi$
$613$	9.48053	+	35.3818i	0.382915	+	1.42906i	−0.458512	+	0.888688i	$0.651617\pi$
$614$	−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	0.372134	−	0.928179i	$-0.378626\pi$
$617$	32.8468	−	15.3167i	1.32236	−	0.616628i	0.950229	+	0.311551i	$0.100848\pi$
$618$		0			0
$619$	33.7534	+	5.95163i	1.35666	+	0.239216i	0.804218	−	0.594334i	$-0.202584\pi$
$619$	33.7534	+	5.95163i	1.35666	+	0.239216i	0.552444	+	0.833550i	$0.313695\pi$
$620$	−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	−0.989002	−	0.147901i	$-0.952748\pi$
$631$	−15.6392	−	27.0879i	−0.622587	−	1.07835i	0.366415	−	0.930451i	$-0.380585\pi$
$632$	−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	0.897019	−	0.441992i	$-0.145728\pi$
$641$	−1.87972	−	5.16450i	−0.0742446	−	0.203985i	−0.971263	+	0.238007i	$0.923506\pi$
$642$		0			0
$643$	3.93539	−	44.9817i	0.155197	−	1.77390i	−0.375965	−	0.926634i	$-0.622689\pi$
$643$	3.93539	−	44.9817i	0.155197	−	1.77390i	0.531161	−	0.847271i	$-0.321756\pi$
$644$	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	−0.254037	−	0.967195i	$-0.581758\pi$
$647$	18.1400	−	18.1400i	0.713158	−	0.713158i	0.967195	+	0.254037i	$0.0817584\pi$
$648$		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	0.228292	−	0.973593i	$-0.426686\pi$
$653$	7.25864	+	0.635049i	0.284052	+	0.0248514i	0.0557608	+	0.998444i	$0.482242\pi$
$654$		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	0.947350	−	0.320200i	$-0.103750\pi$
$659$	20.4475	+	17.1575i	0.796520	+	0.668360i	−0.150830	+	0.988560i	$0.548195\pi$
$660$		0			0
$661$	−3.17425	−	18.0020i	−0.123464	−	0.700198i	−0.982208	−	0.187794i	$-0.939866\pi$
$661$	−3.17425	−	18.0020i	−0.123464	−	0.700198i	0.858745	−	0.512404i	$-0.171245\pi$
$662$	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	0.984284	−	0.176592i	$-0.0565074\pi$
$673$	12.4963	+	17.8466i	0.481697	+	0.687934i	−0.502587	+	0.864526i	$0.667618\pi$
$674$	−44.3443			−1.70808
$675$		0			0
$676$	−14.3629			−0.552418
$677$	6.04776	+	8.63710i	0.232434	+	0.331951i	0.918378	−	0.395704i	$-0.129499\pi$
$677$	6.04776	+	8.63710i	0.232434	+	0.331951i	−0.685944	+	0.727654i	$0.740610\pi$
$678$		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	−0.669746	−	0.742590i	$-0.733597\pi$
$683$	−22.9581	+	6.15162i	−0.878469	+	0.235385i	−0.208723	+	0.977975i	$0.566931\pi$
$684$		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	0.999228	−	0.0392778i	$-0.0125057\pi$
$691$	29.8109	+	25.0143i	1.13406	+	0.951591i	0.134833	+	0.990868i	$0.456950\pi$
$692$	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	$0.249804\pi$
$701$			37.4202i			1.41334i	−0.707542	+	0.706671i	$0.750196\pi$
$702$		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	−0.968648	−	0.248437i	$-0.920083\pi$
$709$	−10.2864	−	28.2616i	−0.386313	−	1.06139i	0.582335	−	0.812949i	$-0.302139\pi$
$710$	−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	0.830390	−	0.557183i	$-0.188118\pi$
$719$	−1.80566	−	3.12750i	−0.0673399	−	0.116636i	−0.897730	+	0.440547i	$0.854785\pi$
$720$		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	−0.0189200	−	0.999821i	$-0.506023\pi$
$727$	24.6477	−	17.2585i	0.914133	−	0.640083i	0.933053	+	0.359738i	$0.117134\pi$
$728$	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	−0.961780	−	0.273824i	$-0.911712\pi$
$733$	−37.0978	+	17.2990i	−1.37024	+	0.638953i	−0.408459	+	0.912777i	$0.633934\pi$
$734$	−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	−0.347927	−	0.937522i	$-0.613114\pi$
$739$	7.88425	−	4.55198i	0.290027	−	0.167447i	0.637954	+	0.770074i	$0.279781\pi$
$740$	−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	0.135449	−	0.990784i	$-0.456752\pi$
$743$	27.8074	−	39.7131i	1.02016	−	1.45693i	0.884706	−	0.466149i	$-0.154359\pi$
$744$		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	−0.999860	−	0.0167415i	$-0.994671\pi$
$751$	−31.7068	+	26.6051i	−1.15700	+	0.970835i	−0.157137	+	0.987577i	$0.550226\pi$
$752$	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	0.0165746	−	0.999863i	$-0.494724\pi$
$757$	−27.0538	−	27.0538i	−0.983288	−	0.983288i	−0.999863	+	0.0165746i	$0.994724\pi$
$758$	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	0.184281	−	0.982874i	$-0.441004\pi$
$761$	−22.5010	−	26.8156i	−0.815660	−	0.972066i	−0.999942	+	0.0108074i	$0.996560\pi$
$762$		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	−0.288781	−	0.957395i	$-0.593250\pi$
$769$	−6.45291	+	1.13782i	−0.232698	+	0.0410309i	0.0560832	+	0.998426i	$0.482139\pi$
$770$	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	−0.986949	−	0.161033i	$-0.948517\pi$
$773$	−1.43767	+	5.36547i	−0.0517095	+	0.192983i	0.935239	+	0.354016i	$0.115184\pi$
$774$		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	−0.988597	−	0.150582i	$-0.951885\pi$
$787$	−13.1429	−	28.1849i	−0.468492	−	1.00468i	0.520105	−	0.854102i	$-0.325893\pi$
$788$	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	0.641589	−	0.767049i	$-0.278275\pi$
$797$	3.95902	+	2.77214i	0.140236	+	0.0981941i	−0.501353	+	0.865243i	$0.667164\pi$
$798$		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	−0.0293416	−	0.999569i	$-0.509341\pi$
$821$	27.5109	−	32.7862i	0.960137	−	1.14425i	0.989479	−	0.144678i	$-0.0462145\pi$
$822$		0			0
$823$	−9.96073	−	6.97458i	−0.347209	−	0.243119i	0.386943	−	0.922104i	$-0.373531\pi$
$823$	−9.96073	−	6.97458i	−0.347209	−	0.243119i	−0.734152	+	0.678985i	$0.762420\pi$
$824$	−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	0.0245234	−	0.999699i	$-0.492193\pi$
$827$	−13.0585	−	3.49901i	−0.454088	−	0.121673i	−0.478612	+	0.878027i	$0.658860\pi$
$828$		0			0
$829$	−22.0957	−	12.7570i	−0.767415	−	0.443068i	0.0645364	−	0.997915i	$-0.479443\pi$
$829$	−22.0957	−	12.7570i	−0.767415	−	0.443068i	−0.831952	+	0.554848i	$0.812776\pi$
$830$	−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	0.659896	+	0.751357i	$0.270600\pi$
$839$	−6.29080	+	35.6769i	−0.217183	+	1.23170i	−0.877078	+	0.480347i	$0.840511\pi$
$840$		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	0.122409	−	0.992480i	$-0.460938\pi$
$853$	12.1293	−	1.06118i	0.415300	−	0.0363341i	0.292891	+	0.956146i	$0.405383\pi$
$854$	−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	−0.327232	−	0.944944i	$-0.606116\pi$
$857$	17.7690	−	38.1058i	0.606978	−	1.30167i	0.934210	−	0.356724i	$-0.116106\pi$
$858$		0			0
$859$	−16.1180	−	19.2086i	−0.549938	−	0.655390i	0.417447	−	0.908701i	$-0.362925\pi$
$859$	−16.1180	−	19.2086i	−0.549938	−	0.655390i	−0.967385	+	0.253311i	$0.918480\pi$
$860$	−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	0.374603	−	0.927185i	$-0.377779\pi$
$863$	−16.2331	−	16.2331i	−0.552582	−	0.552582i	−0.927185	+	0.374603i	$0.877779\pi$
$864$		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	0.254588	−	0.967049i	$-0.418060\pi$
$877$	31.8721	−	45.5180i	1.07624	−	1.53703i	0.821655	−	0.569985i	$-0.193051\pi$
$878$	−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	−0.805114	−	0.593121i	$-0.797896\pi$
$881$	−20.5994	+	11.8931i	−0.694013	+	0.400688i	0.111101	+	0.993809i	$0.464562\pi$
$882$		0			0
$883$	−6.72963	−	25.1153i	−0.226470	−	0.845198i	−0.981810	−	0.189865i	$-0.939195\pi$
$883$	−6.72963	−	25.1153i	−0.226470	−	0.845198i	0.755340	−	0.655333i	$-0.227472\pi$
$884$	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	−0.611572	−	0.791189i	$-0.709463\pi$
$887$	−11.8712	+	5.53565i	−0.398597	+	0.185869i	0.212975	+	0.977058i	$0.431685\pi$
$888$		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	−0.775136	−	0.631795i	$-0.782319\pi$
$907$	−3.65873	−	41.8194i	−0.121486	−	1.38859i	0.653650	−	0.756797i	$-0.273237\pi$
$908$	−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	−0.701614	−	0.712557i	$-0.747537\pi$
$911$	−18.7788	−	51.5943i	−0.622169	−	1.70940i	0.0794445	−	0.996839i	$-0.474685\pi$
$912$		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	$0.218588\pi$
$919$			38.4394i			1.26800i	−0.773333	+	0.634000i	$0.781412\pi$
$920$	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	0.310645	−	0.950526i	$-0.399455\pi$
$929$	−17.4189	−	14.6162i	−0.571497	−	0.479543i	−0.882142	+	0.470983i	$0.843899\pi$
$930$		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	−0.224618	−	0.974447i	$-0.572113\pi$
$937$	2.08398	−	0.558400i	0.0680806	−	0.0182421i	0.292699	+	0.956205i	$0.405447\pi$
$938$	−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	0.387821	+	0.921735i	$0.373228\pi$
$941$	−15.3914	+	42.2876i	−0.501747	+	1.37854i	−0.889568	+	0.456803i	$0.848994\pi$
$942$		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	0.633030	−	0.774127i	$-0.281811\pi$
$947$	−9.56806	−	13.6646i	−0.310920	−	0.444040i	−0.943950	+	0.330087i	$0.892922\pi$
$948$		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	−0.531689	−	0.846940i	$-0.678443\pi$
$953$	−17.5554	+	4.70396i	−0.568676	+	0.152376i	−0.0369865	+	0.999316i	$0.511776\pi$
$954$		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	0.610763	−	0.791813i	$-0.290863\pi$
$967$	33.4211	+	2.92397i	1.07475	+	0.0940285i	0.463988	+	0.885842i	$0.346418\pi$
$968$	−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	$0.122768\pi$
$971$			23.4452i			0.752393i	−0.926540	+	0.376196i	$0.877232\pi$
$972$		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	−0.898949	−	0.438052i	$-0.855668\pi$
$977$	1.95075	−	22.2971i	0.0624099	−	0.713349i	0.961359	−	0.275297i	$-0.0887760\pi$
$978$		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	0.991910	−	0.126940i	$-0.0405155\pi$
$983$	−0.218640	−	2.49907i	−0.00697353	−	0.0797078i	−0.998884	+	0.0472321i	$0.984960\pi$
$984$		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	−0.990194	−	0.139697i	$-0.955387\pi$
$991$	−11.7772	+	20.3987i	−0.374116	+	0.647987i	0.616079	+	0.787685i	$0.288720\pi$
$992$	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	−0.758484	−	0.651691i	$-0.774060\pi$
$997$	−12.8042	+	8.96558i	−0.405512	+	0.283943i	0.352972	+	0.935634i	$0.385171\pi$
$998$	−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.332.15		192
3.2	odd	2		135.2.q.a.2.2	✓	192
5.3	odd	4	inner	405.2.r.a.8.15		192
15.2	even	4		675.2.ba.b.218.15		192
15.8	even	4		135.2.q.a.83.2	yes	192
15.14	odd	2		675.2.ba.b.407.15		192
27.13	even	9		135.2.q.a.122.2	yes	192
27.14	odd	18	inner	405.2.r.a.152.15		192
135.13	odd	36		135.2.q.a.68.2	yes	192
135.67	odd	36		675.2.ba.b.68.15		192
135.68	even	36	inner	405.2.r.a.233.15		192
135.94	even	18		675.2.ba.b.257.15		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.2	✓	192	3.2	odd	2
135.2.q.a.68.2	yes	192	135.13	odd	36
135.2.q.a.83.2	yes	192	15.8	even	4
135.2.q.a.122.2	yes	192	27.13	even	9
405.2.r.a.8.15		192	5.3	odd	4	inner
405.2.r.a.152.15		192	27.14	odd	18	inner
405.2.r.a.233.15		192	135.68	even	36	inner
405.2.r.a.332.15		192	1.1	even	1	trivial
675.2.ba.b.68.15		192	135.67	odd	36
675.2.ba.b.218.15		192	15.2	even	4
675.2.ba.b.257.15		192	135.94	even	18
675.2.ba.b.407.15		192	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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