LMFDB - Embedded newform 405.2.r.a.8.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(8,405)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			8.15
Character	$\chi$	$=$	405.8
Dual form			405.2.r.a.152.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.12047 - 1.48477i) q^{2} +(1.60780 - 4.41741i) q^{4} +(2.09416 - 0.783897i) q^{5} +(-1.25154 + 2.68394i) q^{7} +(-1.80956 - 6.75336i) q^{8} +O(q^{10})$	\(q+(2.12047 - 1.48477i) q^{2} +(1.60780 - 4.41741i) q^{4} +(2.09416 - 0.783897i) q^{5} +(-1.25154 + 2.68394i) q^{7} +(-1.80956 - 6.75336i) q^{8} +(3.27669 - 4.77156i) q^{10} +(1.00437 - 1.19696i) q^{11} +(-2.29827 + 3.28227i) q^{13} +(1.33117 + 7.54945i) q^{14} +(-6.66205 - 5.59013i) q^{16} +(-0.490334 + 1.82995i) q^{17} +(-2.41262 - 1.39293i) q^{19} +(-0.0957914 - 10.5111i) q^{20} +(0.352524 - 4.02936i) q^{22} +(-6.78686 + 3.16476i) q^{23} +(3.77101 - 3.28321i) q^{25} +10.3723i q^{26} +(9.84382 + 9.84382i) q^{28} +(0.683218 - 3.87472i) q^{29} +(5.45790 + 1.98651i) q^{31} +(-8.49672 - 0.743366i) q^{32} +(1.67731 + 4.60838i) q^{34} +(-0.516997 + 6.60168i) q^{35} +(-0.316450 - 0.0847926i) q^{37} +(-7.18404 + 0.628522i) q^{38} +(-9.08344 - 12.7241i) q^{40} +(-6.26389 + 1.10449i) q^{41} +(0.0509770 + 0.582670i) q^{43} +(-3.67263 - 6.36118i) q^{44} +(-9.69236 + 16.7877i) q^{46} +(0.690071 + 0.321786i) q^{47} +(-1.13767 - 1.35582i) q^{49} +(3.12150 - 12.5610i) q^{50} +(10.8039 + 15.4296i) q^{52} +(5.57112 - 5.57112i) q^{53} +(1.16502 - 3.29395i) q^{55} +(20.3903 + 3.59537i) q^{56} +(-4.30431 - 9.23063i) q^{58} +(-7.84000 + 6.57854i) q^{59} +(11.4160 - 4.15507i) q^{61} +(14.5228 - 3.89137i) q^{62} +(-4.05760 + 2.34266i) q^{64} +(-2.23998 + 8.67520i) q^{65} +(-1.63356 - 1.14383i) q^{67} +(7.29527 + 5.10821i) q^{68} +(8.70568 + 14.7663i) q^{70} +(6.11142 - 3.52843i) q^{71} +(3.93347 - 1.05397i) q^{73} +(-0.796919 + 0.290055i) q^{74} +(-10.0321 + 8.41796i) q^{76} +(1.95556 + 4.19371i) q^{77} +(-12.9467 - 2.28286i) q^{79} +(-18.3335 - 6.48426i) q^{80} +(-11.6425 + 11.6425i) q^{82} +(2.33262 + 3.33133i) q^{83} +(0.407655 + 4.21658i) q^{85} +(0.973224 + 1.15984i) q^{86} +(-9.90096 - 4.61689i) q^{88} +(-4.23520 + 7.33558i) q^{89} +(-5.93304 - 10.2763i) q^{91} +(3.06811 + 35.0686i) q^{92} +(1.94105 - 0.342259i) q^{94} +(-6.14432 - 1.02577i) q^{95} +(7.95549 - 0.696015i) q^{97} +(-4.42546 - 1.18580i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	2.12047	−	1.48477i	1.49940	−	1.04989i	0.518562	−	0.855040i	$-0.326467\pi$
$2$	2.12047	−	1.48477i	1.49940	−	1.04989i	0.980833	−	0.194848i	$-0.0624214\pi$
$3$		0			0
$3$		0			0
$4$	1.60780	−	4.41741i	0.803902	−	2.20870i
$5$	2.09416	−	0.783897i	0.936537	−	0.350569i
$5$	2.09416	−	0.783897i	0.936537	−	0.350569i
$6$		0			0
$7$	−1.25154	+	2.68394i	−0.473038	+	1.01443i	0.514563	+	0.857453i	$0.327954\pi$
$7$	−1.25154	+	2.68394i	−0.473038	+	1.01443i	−0.987602	+	0.156982i	$0.949824\pi$
$8$	−1.80956	−	6.75336i	−0.639775	−	2.38767i
$9$		0			0
$10$	3.27669	−	4.77156i	1.03618	−	1.50890i
$11$	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
$13$	−2.29827	+	3.28227i	−0.637425	+	0.910338i	−0.999764	−	0.0217086i	$-0.993089\pi$
$13$	−2.29827	+	3.28227i	−0.637425	+	0.910338i	0.362339	+	0.932046i	$0.381978\pi$
$14$	1.33117	+	7.54945i	0.355771	+	2.01768i
$15$		0			0
$16$	−6.66205	−	5.59013i	−1.66551	−	1.39753i
$17$	−0.490334	+	1.82995i	−0.118923	+	0.443828i	−0.999550	−	0.0299818i	$-0.990455\pi$
$17$	−0.490334	+	1.82995i	−0.118923	+	0.443828i	0.880627	+	0.473810i	$0.157122\pi$
$18$		0			0
$19$	−2.41262	−	1.39293i	−0.553493	−	0.319559i	0.197037	−	0.980396i	$-0.436868\pi$
$19$	−2.41262	−	1.39293i	−0.553493	−	0.319559i	−0.750529	+	0.660837i	$0.770201\pi$
$20$	−0.0957914	−	10.5111i	−0.0214196	−	2.35035i
$21$		0			0
$22$	0.352524	−	4.02936i	0.0751583	−	0.859063i
$23$	−6.78686	+	3.16476i	−1.41516	+	0.659899i	−0.971661	−	0.236377i	$-0.924040\pi$
$23$	−6.78686	+	3.16476i	−1.41516	+	0.659899i	−0.443496	+	0.896276i	$0.646262\pi$
$24$		0			0
$25$	3.77101	−	3.28321i	0.754202	−	0.656642i
$26$			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	$-0.825408\pi$
$29$	0.683218	−	3.87472i	0.126870	−	0.719518i	0.980179	−	0.198112i	$-0.0634810\pi$
$30$		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	$0.436450\pi$
$32$	−8.49672	−	0.743366i	−1.50202	−	0.131410i
$33$		0			0
$34$	1.67731	+	4.60838i	0.287657	+	0.790331i
$35$	−0.516997	+	6.60168i	−0.0873884	+	1.11589i
$36$		0			0
$37$	−0.316450	−	0.0847926i	−0.0520241	−	0.0139398i	0.232713	−	0.972545i	$-0.425240\pi$
$37$	−0.316450	−	0.0847926i	−0.0520241	−	0.0139398i	−0.284737	+	0.958606i	$0.591906\pi$
$38$	−7.18404	+	0.628522i	−1.16541	+	0.101960i
$39$		0			0
$40$	−9.08344	−	12.7241i	−1.43622	−	2.01186i
$41$	−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
$43$	0.0509770	+	0.582670i	0.00777393	+	0.0888564i	0.999090	−	0.0426408i	$-0.0135771\pi$
$43$	0.0509770	+	0.582670i	0.00777393	+	0.0888564i	−0.991317	+	0.131497i	$0.958022\pi$
$44$	−3.67263	−	6.36118i	−0.553670	−	0.958984i
$45$		0			0
$46$	−9.69236	+	16.7877i	−1.42906	+	2.47521i
$47$	0.690071	+	0.321786i	0.100657	+	0.0469372i	0.472295	−	0.881441i	$-0.343426\pi$
$47$	0.690071	+	0.321786i	0.100657	+	0.0469372i	−0.371638	+	0.928378i	$0.621204\pi$
$48$		0			0
$49$	−1.13767	−	1.35582i	−0.162524	−	0.193688i
$50$	3.12150	−	12.5610i	0.441447	−	1.77639i
$51$		0			0
$52$	10.8039	+	15.4296i	1.49824	+	2.13971i
$53$	5.57112	−	5.57112i	0.765253	−	0.765253i	−0.212014	−	0.977267i	$-0.568002\pi$
$53$	5.57112	−	5.57112i	0.765253	−	0.765253i	0.977267	+	0.212014i	$0.0680022\pi$
$54$		0			0
$55$	1.16502	−	3.29395i	0.157091	−	0.444156i
$56$	20.3903	+	3.59537i	2.72477	+	0.480451i
$57$		0			0
$58$	−4.30431	−	9.23063i	−0.565184	−	1.21204i
$59$	−7.84000	+	6.57854i	−1.02068	+	0.856453i	−0.989713	−	0.143067i	$-0.954303\pi$
$59$	−7.84000	+	6.57854i	−1.02068	+	0.856453i	−0.0309682	+	0.999520i	$0.509859\pi$
$60$		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	$0.105258\pi$
$62$	14.5228	−	3.89137i	1.84440	−	0.494205i
$63$		0			0
$64$	−4.05760	+	2.34266i	−0.507201	+	0.292832i
$65$	−2.23998	+	8.67520i	−0.277836	+	1.07603i
$66$		0			0
$67$	−1.63356	−	1.14383i	−0.199572	−	0.139742i	0.469519	−	0.882922i	$-0.344427\pi$
$67$	−1.63356	−	1.14383i	−0.199572	−	0.139742i	−0.669091	+	0.743181i	$0.733316\pi$
$68$	7.29527	+	5.10821i	0.884682	+	0.619461i
$69$		0			0
$70$	8.70568	+	14.7663i	1.04053	+	1.76491i
$71$	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
$73$	3.93347	−	1.05397i	0.460378	−	0.123358i	−0.0211733	−	0.999776i	$-0.506740\pi$
$73$	3.93347	−	1.05397i	0.460378	−	0.123358i	0.481551	+	0.876418i	$0.340074\pi$
$74$	−0.796919	+	0.290055i	−0.0926400	+	0.0337182i
$75$		0			0
$76$	−10.0321	+	8.41796i	−1.15076	+	0.965606i
$77$	1.95556	+	4.19371i	0.222857	+	0.477918i
$78$		0			0
$79$	−12.9467	−	2.28286i	−1.45662	−	0.256842i	−0.611427	−	0.791301i	$-0.709404\pi$
$79$	−12.9467	−	2.28286i	−1.45662	−	0.256842i	−0.845194	+	0.534460i	$0.820515\pi$
$80$	−18.3335	−	6.48426i	−2.04975	−	0.724962i
$81$		0			0
$82$	−11.6425	+	11.6425i	−1.28569	+	1.28569i
$83$	2.33262	+	3.33133i	0.256038	+	0.365661i	0.926507	−	0.376277i	$-0.122796\pi$
$83$	2.33262	+	3.33133i	0.256038	+	0.365661i	−0.670469	+	0.741938i	$0.733907\pi$
$84$		0			0
$85$	0.407655	+	4.21658i	0.0442164	+	0.457352i
$86$	0.973224	+	1.15984i	0.104945	+	0.125069i
$87$		0			0
$88$	−9.90096	−	4.61689i	−1.05545	−	0.492162i
$89$	−4.23520	+	7.33558i	−0.448930	+	0.777570i	−0.998317	−	0.0579982i	$-0.981528\pi$
$89$	−4.23520	+	7.33558i	−0.448930	+	0.777570i	0.549386	+	0.835569i	$0.314862\pi$
$90$		0			0
$91$	−5.93304	−	10.2763i	−0.621951	−	1.07725i
$92$	3.06811	+	35.0686i	0.319872	+	3.65616i
$93$		0			0
$94$	1.94105	−	0.342259i	0.200204	−	0.0353013i
$95$	−6.14432	−	1.02577i	−0.630394	−	0.105241i
$96$		0			0
$97$	7.95549	−	0.696015i	0.807758	−	0.0706696i	0.324207	−	0.945986i	$-0.394903\pi$
$97$	7.95549	−	0.696015i	0.807758	−	0.0706696i	0.483550	+	0.875317i	$0.339347\pi$
$98$	−4.42546	−	1.18580i	−0.447039	−	0.119784i
$99$		0			0
$100$	−8.44022	−	21.9368i	−0.844022	−	2.19368i
$101$	−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
$103$	−7.89264	−	0.690517i	−0.777685	−	0.0680387i	−0.308601	−	0.951192i	$-0.599861\pi$
$103$	−7.89264	−	0.690517i	−0.777685	−	0.0680387i	−0.469085	+	0.883153i	$0.655416\pi$
$104$	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	$-0.162886\pi$
$107$	3.95377	+	3.95377i	0.382225	+	0.382225i	−0.489678	+	0.871903i	$0.662886\pi$
$108$		0			0
$109$		−	6.56334i		−	0.628654i	−0.949315	−	0.314327i	$-0.898221\pi$
$109$		−	6.56334i		−	0.628654i	0.949315	−	0.314327i	$-0.101779\pi$
$110$	−2.42036	−	8.71447i	−0.230773	−	0.830893i
$111$		0			0
$112$	23.3414	−	10.8843i	2.20556	−	1.02847i
$113$	−0.198630	+	2.27035i	−0.0186855	+	0.213577i	0.981112	+	0.193442i	$0.0619651\pi$
$113$	−0.198630	+	2.27035i	−0.0186855	+	0.213577i	−0.999797	+	0.0201349i	$0.993590\pi$
$114$		0			0
$115$	−11.7319	+	11.9477i	−1.09401	+	1.11413i
$116$	−16.0177	−	9.24784i	−1.48721	−	0.858641i
$117$		0			0
$118$	−6.85686	+	25.5901i	−0.631225	+	2.35576i
$119$	−4.29781	−	3.60629i	−0.393979	−	0.330588i
$120$		0			0
$121$	1.48617	+	8.42851i	0.135107	+	0.766228i
$122$	18.0378	−	25.7607i	1.63307	−	2.33226i
$123$		0			0
$124$	17.5505	−	20.9158i	1.57608	−	1.87830i
$125$	5.32340	−	9.83165i	0.476140	−	0.879370i
$126$		0			0
$127$	0.559276	+	2.08725i	0.0496277	+	0.185213i	0.986290	−	0.165020i	$-0.0527690\pi$
$127$	0.559276	+	2.08725i	0.0496277	+	0.185213i	−0.936662	+	0.350233i	$0.886102\pi$
$128$	2.08346	−	4.46799i	0.184153	−	0.394918i
$129$		0			0
$130$	8.13084	+	21.7213i	0.713122	+	1.90509i
$131$	−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
$133$	6.75802	−	4.73202i	0.585995	−	0.410318i
$134$	−5.16224			−0.445950
$135$		0			0
$136$	13.2456			1.13580
$137$	−1.99313	+	1.39561i	−0.170285	+	0.119235i	−0.655612	−	0.755098i	$-0.727589\pi$
$137$	−1.99313	+	1.39561i	−0.170285	+	0.119235i	0.485327	+	0.874333i	$0.338700\pi$
$138$		0			0
$139$	−3.32712	+	9.14118i	−0.282202	+	0.775345i	0.714897	+	0.699230i	$0.246474\pi$
$139$	−3.32712	+	9.14118i	−0.282202	+	0.775345i	−0.997099	+	0.0761146i	$0.975749\pi$
$140$	28.3311	+	12.8980i	2.39441	+	1.09008i
$141$		0			0
$142$	7.72017	−	16.5560i	0.647862	−	1.38934i
$143$	1.62043	+	6.04754i	0.135508	+	0.505721i
$144$		0			0
$145$	−1.60661	−	8.64986i	−0.133422	−	0.718332i
$146$	6.77589	−	8.07519i	0.560777	−	0.668308i
$147$		0			0
$148$	−0.883353	+	1.26156i	−0.0726112	+	0.103700i
$149$	−2.43445	−	13.8064i	−0.199438	−	1.13107i	−0.905956	−	0.423373i	$-0.860846\pi$
$149$	−2.43445	−	13.8064i	−0.199438	−	1.13107i	0.706518	−	0.707695i	$-0.250265\pi$
$150$		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	$0.988071\pi$
$152$	−5.04116	+	18.8139i	−0.408892	+	1.52600i
$153$		0			0
$154$	10.3734	+	5.98907i	0.835910	+	0.482613i
$155$	12.9869	−	0.118354i	1.04314	−	0.00950646i
$156$		0			0
$157$	−0.265324	+	3.03267i	−0.0211752	+	0.242033i	0.978229	+	0.207527i	$0.0665415\pi$
$157$	−0.265324	+	3.03267i	−0.0211752	+	0.242033i	−0.999404	+	0.0345064i	$0.989014\pi$
$158$	−30.8426	+	14.3821i	−2.45371	+	1.14418i
$159$		0			0
$160$	−18.3762	+	5.10382i	−1.45277	+	0.403492i
$161$		−	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
$167$	−5.22689	−	0.457294i	−0.404469	−	0.0353865i	−0.116894	−	0.993144i	$-0.537294\pi$
$167$	−5.22689	−	0.457294i	−0.404469	−	0.0353865i	−0.287576	+	0.957758i	$0.592849\pi$
$168$		0			0
$169$	−1.04499	−	2.87108i	−0.0803837	−	0.220852i
$170$	7.12506	+	8.33584i	0.546467	+	0.639330i
$171$		0			0
$172$	2.65585	+	0.711633i	0.202507	+	0.0542615i
$173$	8.14671	−	0.712745i	0.619383	−	0.0541890i	0.226854	−	0.973929i	$-0.427156\pi$
$173$	8.14671	−	0.712745i	0.619383	−	0.0541890i	0.392529	+	0.919740i	$0.371600\pi$
$174$		0			0
$175$	4.09236	+	14.2302i	0.309354	+	1.07571i
$176$	−13.3823	+	2.35966i	−1.00873	+	0.177866i
$177$		0			0
$178$	1.91103	+	21.8431i	0.143238	+	1.63721i
$179$	−2.65400	−	4.59686i	−0.198369	−	0.343585i	0.749631	−	0.661856i	$-0.230231\pi$
$179$	−2.65400	−	4.59686i	−0.198369	−	0.343585i	−0.948000	+	0.318271i	$0.896898\pi$
$180$		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	$-0.161641\pi$
$182$	−27.8387	−	12.9814i	−2.06354	−	0.962246i
$183$		0			0
$184$	33.6540	+	40.1073i	2.48100	+	2.95675i
$185$	−0.729166	+	0.0704951i	−0.0536094	+	0.00518290i
$186$		0			0
$187$	1.69790	+	2.42486i	0.124163	+	0.177323i
$188$	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
$193$	−5.22336	−	11.2015i	−0.375986	−	0.806305i	−0.999696	−	0.0246489i	$-0.992153\pi$
$193$	−5.22336	−	11.2015i	−0.375986	−	0.806305i	0.623710	−	0.781656i	$-0.285625\pi$
$194$	15.8359	−	13.2879i	1.13695	−	0.954017i
$195$		0			0
$196$	−7.81835	+	2.84565i	−0.558453	+	0.203260i
$197$	−23.1882	+	6.21326i	−1.65209	+	0.442676i	−0.960197	−	0.279324i	$-0.909890\pi$
$197$	−23.1882	+	6.21326i	−1.65209	+	0.442676i	−0.691893	+	0.722000i	$0.743223\pi$
$198$		0			0
$199$	−5.73533	+	3.31129i	−0.406566	+	0.234731i	−0.689313	−	0.724463i	$-0.742088\pi$
$199$	−5.73533	+	3.31129i	−0.406566	+	0.234731i	0.282747	+	0.959195i	$0.408754\pi$
$200$	−28.9966	−	19.5258i	−2.05037	−	1.38068i
$201$		0			0
$202$	−33.0093	−	23.1134i	−2.32253	−	1.62625i
$203$	9.54445	+	6.68309i	0.669889	+	0.469061i
$204$		0			0
$205$	−12.2518	+	7.22323i	−0.855701	+	0.504492i
$206$	−17.7613	+	10.2545i	−1.23749	+	0.714466i
$207$		0			0
$208$	33.6595	−	9.01904i	2.33387	−	0.625358i
$209$	−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	$0.308334\pi$
$212$	−15.6526	−	33.5672i	−1.07503	−	2.30540i
$213$		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
$218$	−9.74502	−	13.9173i	−0.660016	−	0.942601i
$219$		0			0
$220$	−12.6776	−	10.4424i	−0.854722	−	0.704024i
$221$	−4.87947	−	5.81513i	−0.328229	−	0.391168i
$222$		0			0
$223$	19.9909	+	9.32189i	1.33869	+	0.624240i	0.954277	−	0.298923i	$-0.0966273\pi$
$223$	19.9909	+	9.32189i	1.33869	+	0.624240i	0.384410	+	0.923163i	$0.374405\pi$
$224$	12.6291	−	21.8743i	0.843821	−	1.46154i
$225$		0			0
$226$	2.94975	+	5.10912i	0.196215	+	0.339854i
$227$	−0.647951	−	7.40612i	−0.0430060	−	0.491561i	−0.986902	−	0.161319i	$-0.948425\pi$
$227$	−0.647951	−	7.40612i	−0.0430060	−	0.491561i	0.943896	−	0.330242i	$-0.107130\pi$
$228$		0			0
$229$	−4.57594	+	0.806861i	−0.302386	+	0.0533189i	−0.322783	−	0.946473i	$-0.604618\pi$
$229$	−4.57594	+	0.806861i	−0.302386	+	0.0533189i	0.0203963	+	0.999792i	$0.493507\pi$
$230$	−7.13756	+	42.7539i	−0.470637	+	2.81911i
$231$		0			0
$232$	−27.4037	+	2.39751i	−1.79914	+	0.157404i
$233$	−13.7921	−	3.69557i	−0.903549	−	0.242105i	−0.223009	−	0.974816i	$-0.571588\pi$
$233$	−13.7921	−	3.69557i	−0.903549	−	0.242105i	−0.680540	+	0.732711i	$0.738255\pi$
$234$		0			0
$235$	1.69737	+	0.132926i	0.110724	+	0.00867111i
$236$	16.4549	+	45.2095i	1.07112	+	2.94289i
$237$		0			0
$238$	−14.4678	−	1.26577i	−0.937811	−	0.0820478i
$239$	19.1398	+	6.96633i	1.23805	+	0.450614i	0.876348	−	0.481678i	$-0.159973\pi$
$239$	19.1398	+	6.96633i	1.23805	+	0.450614i	0.361705	+	0.932293i	$0.382195\pi$
$240$		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
$245$	−3.44528	−	1.94749i	−0.220111	−	0.124420i
$246$		0			0
$247$	10.1168	−	4.71754i	0.643717	−	0.300170i
$248$	3.53925	−	40.4538i	0.224743	−	2.56882i
$249$		0			0
$250$	−3.30961	−	28.7517i	−0.209318	−	1.81842i
$251$	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
$253$	−3.02841	+	11.3022i	−0.190395	+	0.710562i
$254$	4.28500	+	3.59554i	0.268865	+	0.225604i
$255$		0			0
$256$	−3.84321	−	21.7959i	−0.240201	−	1.36225i
$257$	−3.25941	+	4.65492i	−0.203316	+	0.290366i	−0.907842	−	0.419313i	$-0.862271\pi$
$257$	−3.25941	+	4.65492i	−0.203316	+	0.290366i	0.704525	+	0.709679i	$0.251160\pi$
$258$		0			0
$259$	0.623629	−	0.743212i	0.0387504	−	0.0461810i
$260$	34.7204	+	23.8429i	2.15327	+	1.47868i
$261$		0			0
$262$	0.645458	+	2.40888i	0.0398765	+	0.148821i
$263$	−8.23378	+	17.6574i	−0.507717	+	1.08880i	0.470725	+	0.882280i	$0.343992\pi$
$263$	−8.23378	+	17.6574i	−0.507717	+	1.08880i	−0.978442	+	0.206522i	$0.933785\pi$
$264$		0			0
$265$	7.29964	−	16.0340i	0.448413	−	0.984961i
$266$	7.30422	−	20.0682i	0.447850	−	1.23046i
$267$		0			0
$268$	−7.67923	+	5.37706i	−0.469084	+	0.328456i
$269$	21.8628			1.33300			0.666501	−	0.745505i	$-0.267791\pi$
$269$	21.8628			1.33300			0.666501	+	0.745505i	$0.267791\pi$
$270$		0			0
$271$	25.6697			1.55933			0.779663	−	0.626200i	$-0.215391\pi$
$271$	25.6697			1.55933			0.779663	+	0.626200i	$0.215391\pi$
$272$	13.4963	−	9.45020i	0.818333	−	0.573003i
$273$		0			0
$274$	−2.15422	+	5.91867i	−0.130141	+	0.357560i
$275$	−0.142386	−	7.81130i	−0.00858620	−	0.471039i
$276$		0			0
$277$	−2.24166	+	4.80726i	−0.134689	+	0.288841i	−0.962071	−	0.272798i	$-0.912051\pi$
$277$	−2.24166	+	4.80726i	−0.134689	+	0.288841i	0.827383	+	0.561638i	$0.189829\pi$
$278$	6.51747	+	24.3235i	0.390892	+	1.45883i
$279$		0			0
$280$	45.5190	−	8.45465i	2.72028	−	0.505262i
$281$	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
$283$	2.90572	−	4.14980i	0.172727	−	0.246680i	−0.723449	−	0.690377i	$-0.757444\pi$
$283$	2.90572	−	4.14980i	0.172727	−	0.246680i	0.896177	+	0.443697i	$0.146333\pi$
$284$	−5.76054	−	32.6697i	−0.341825	−	1.93859i
$285$		0			0
$286$	12.4153	+	10.4176i	0.734130	+	0.616008i
$287$	4.87513	−	18.1942i	0.287770	−	1.07397i
$288$		0			0
$289$	11.6141	+	6.70543i	0.683185	+	0.394437i
$290$	−16.2498	−	15.9563i	−0.954220	−	0.936985i
$291$		0			0
$292$	1.66844	−	19.0703i	0.0976379	−	1.11601i
$293$	−20.8181	+	9.70762i	−1.21620	+	0.567125i	−0.921468	−	0.388453i	$-0.873009\pi$
$293$	−20.8181	+	9.70762i	−1.21620	+	0.567125i	−0.294736	+	0.955579i	$0.595232\pi$
$294$		0			0
$295$	−11.2613	+	19.9223i	−0.655659	+	1.15992i
$296$			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
$302$	−46.9890	−	4.11100i	−2.70391	−	0.236562i
$303$		0			0
$304$	8.28636	+	22.7666i	0.475255	+	1.30575i
$305$	20.6497	−	17.6503i	1.18240	−	1.01065i
$306$		0			0
$307$	22.5239	+	6.03527i	1.28551	+	0.344451i	0.835953	−	0.548801i	$-0.184916\pi$
$307$	22.5239	+	6.03527i	1.28551	+	0.344451i	0.449556	+	0.893252i	$0.351582\pi$
$308$	21.6695	−	1.89583i	1.23473	−	0.108025i
$309$		0			0
$310$	27.3626	−	19.5335i	1.55409	−	1.10943i
$311$	−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
$313$	−2.69662	−	30.8225i	−0.152422	−	1.74219i	−0.559530	−	0.828810i	$-0.689018\pi$
$313$	−2.69662	−	30.8225i	−0.152422	−	1.74219i	0.407109	−	0.913380i	$-0.366537\pi$
$314$	3.94019	+	6.82461i	0.222358	+	0.385135i
$315$		0			0
$316$	−30.9001	+	53.5206i	−1.73827	+	3.01077i
$317$	19.0657	+	8.89049i	1.07084	+	0.499340i	0.876404	−	0.481576i	$-0.159936\pi$
$317$	19.0657	+	8.89049i	1.07084	+	0.499340i	0.194433	+	0.980916i	$0.437713\pi$
$318$		0			0
$319$	−3.95168	−	4.70943i	−0.221252	−	0.263678i
$320$	−6.66087	+	8.08665i	−0.372354	+	0.452057i
$321$		0			0
$322$	−32.9267	−	47.0242i	−1.83493	−	2.62056i
$323$	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
$328$	18.7939	+	40.3036i	1.03772	+	2.22540i
$329$	−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	$0.386788\pi$
$332$	18.4662	−	4.94801i	1.01347	−	0.271557i
$333$		0			0
$334$	−11.7624	+	6.79104i	−0.643611	+	0.371589i
$335$	−4.31759	−	1.11483i	−0.235895	−	0.0609094i
$336$		0			0
$337$	14.0325	+	9.82568i	0.764400	+	0.535239i	0.889516	−	0.456903i	$-0.151041\pi$
$337$	14.0325	+	9.82568i	0.764400	+	0.535239i	−0.125116	+	0.992142i	$0.539930\pi$
$338$	−6.47874	−	4.53646i	−0.352397	−	0.246751i
$339$		0			0
$340$	19.2818	+	4.97866i	1.04570	+	0.270006i
$341$	7.85952	−	4.53769i	0.425617	−	0.245730i
$342$		0			0
$343$	−14.9607	+	4.00870i	−0.807801	+	0.216450i
$344$	3.84273	−	1.39864i	0.207186	−	0.0754097i
$345$		0			0
$346$	16.2166	−	13.6073i	0.871808	−	0.731534i
$347$	11.4696	+	24.5967i	0.615723	+	1.32042i	0.928760	+	0.370681i	$0.120876\pi$
$347$	11.4696	+	24.5967i	0.615723	+	1.32042i	−0.313038	+	0.949741i	$0.601347\pi$
$348$		0			0
$349$	18.8404	+	3.32208i	1.00851	+	0.177827i	0.653411	−	0.757003i	$-0.273337\pi$
$349$	18.8404	+	3.32208i	1.00851	+	0.177827i	0.355095	+	0.934830i	$0.384449\pi$
$350$	29.8063	+	24.0985i	1.59321	+	1.28812i
$351$		0			0
$352$	−9.42361	+	9.42361i	−0.502280	+	0.502280i
$353$	17.4648	+	24.9423i	0.929558	+	1.32755i	0.944795	+	0.327663i	$0.106261\pi$
$353$	17.4648	+	24.9423i	0.929558	+	1.32755i	−0.0152364	+	0.999884i	$0.504850\pi$
$354$		0			0
$355$	10.0324	−	12.1798i	0.532463	−	0.646438i
$356$	25.5949	+	30.5028i	1.35653	+	1.61664i
$357$		0			0
$358$	−12.4530	−	5.80691i	−0.658160	−	0.306905i
$359$	−15.6146	+	27.0453i	−0.824108	+	1.42740i	0.0784904	+	0.996915i	$0.474990\pi$
$359$	−15.6146	+	27.0453i	−0.824108	+	1.42740i	−0.902599	+	0.430483i	$0.858343\pi$
$360$		0			0
$361$	−5.61951	−	9.73329i	−0.295764	−	0.512278i
$362$	−5.20872	−	59.5360i	−0.273764	−	3.12914i
$363$		0			0
$364$	−54.9338	+	9.68632i	−2.87931	+	0.507701i
$365$	7.41111	−	5.29062i	0.387915	−	0.276924i
$366$		0			0
$367$	1.41799	−	0.124058i	0.0740183	−	0.00647576i	−0.0500864	−	0.998745i	$-0.515950\pi$
$367$	1.41799	−	0.124058i	0.0740183	−	0.00647576i	0.124105	+	0.992269i	$0.460394\pi$
$368$	62.9058	+	16.8556i	3.27919	+	0.878657i
$369$		0			0
$370$	−1.44150	+	1.23212i	−0.0749402	+	0.0640550i
$371$	7.98007	+	21.9251i	0.414305	+	1.13829i
$372$		0			0
$373$	9.79785	+	0.857201i	0.507313	+	0.0443842i	0.337940	−	0.941168i	$-0.390270\pi$
$373$	9.79785	+	0.857201i	0.507313	+	0.0443842i	0.169374	+	0.985552i	$0.445826\pi$
$374$	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	$0.952697\pi$
$380$	−14.4101	+	25.4927i	−0.739222	+	1.30775i
$381$		0			0
$382$	8.91424	−	4.15678i	0.456092	−	0.212679i
$383$	−0.249029	+	2.84641i	−0.0127248	+	0.145445i	−0.999899	−	0.0142007i	$-0.995480\pi$
$383$	−0.249029	+	2.84641i	−0.0127248	+	0.145445i	0.987174	+	0.159646i	$0.0510352\pi$
$384$		0			0
$385$	7.38269	+	7.24934i	0.376257	+	0.369461i
$386$	−27.7076	−	15.9970i	−1.41028	−	0.814226i
$387$		0			0
$388$	9.71629	−	36.2617i	0.493270	−	1.84091i
$389$	−9.76677	−	8.19530i	−0.495195	−	0.415518i	0.360689	−	0.932686i	$-0.382542\pi$
$389$	−9.76677	−	8.19530i	−0.495195	−	0.415518i	−0.855884	+	0.517168i	$0.826986\pi$
$390$		0			0
$391$	−2.46354	−	13.9714i	−0.124586	−	0.706565i
$392$	−7.09766	+	10.1365i	−0.358486	+	0.511971i
$393$		0			0
$394$	−39.9445	+	47.6040i	−2.01238	+	2.39826i
$395$	−28.9020	+	5.36823i	−1.45422	+	0.270105i
$396$		0			0
$397$	0.929625	+	3.46941i	0.0466565	+	0.174125i	0.985322	−	0.170703i	$-0.0546040\pi$
$397$	0.929625	+	3.46941i	0.0466565	+	0.174125i	−0.938666	+	0.344828i	$0.887937\pi$
$398$	−7.24507	+	15.5371i	−0.363162	+	0.778804i
$399$		0			0
$400$	−43.4762	+	0.792494i	−2.17381	+	0.0396247i
$401$	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
$403$	−19.0640	+	13.3488i	−0.949645	+	0.664949i
$404$	−73.1790			−3.64079
$405$		0			0
$406$	30.1615			1.49689
$407$	−0.419326	+	0.293615i	−0.0207852	+	0.0145540i
$408$		0			0
$409$	−5.75785	+	15.8196i	−0.284707	+	0.782226i	0.712078	+	0.702101i	$0.247754\pi$
$409$	−5.75785	+	15.8196i	−0.284707	+	0.782226i	−0.996785	+	0.0801257i	$0.974468\pi$
$410$	−15.2547	+	33.5076i	−0.753375	+	1.65482i
$411$		0			0
$412$	−15.7401	+	33.7548i	−0.775460	+	1.66298i
$413$	−7.84432	−	29.2754i	−0.385994	−	1.44055i
$414$		0			0
$415$	7.49630	+	5.14780i	0.367979	+	0.252696i
$416$	21.9677	−	26.1801i	1.07705	−	1.28358i
$417$		0			0
$418$	−6.46311	+	9.23028i	−0.316121	+	0.451468i
$419$	0.0944911	+	0.535886i	0.00461619	+	0.0261797i	0.987029	−	0.160543i	$-0.0513245\pi$
$419$	0.0944911	+	0.535886i	0.00461619	+	0.0261797i	−0.982413	+	0.186723i	$0.940213\pi$
$420$		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	$0.780544\pi$
$422$	−1.86561	+	6.96256i	−0.0908166	+	0.338932i
$423$		0			0
$424$	−47.7050	−	27.5425i	−2.31676	−	1.33758i
$425$	4.15906	+	8.51064i	0.201744	+	0.412827i
$426$		0			0
$427$	−3.13559	+	35.8400i	−0.151742	+	1.73442i
$428$	23.8223	−	11.1085i	1.15149	−	0.536950i
$429$		0			0
$430$	2.94728	+	1.66599i	0.142131	+	0.0803412i
$431$			14.9683i			0.720998i	0.932760	+	0.360499i	$0.117394\pi$
$431$			14.9683i			0.720998i	−0.932760	+	0.360499i	$0.882606\pi$
$432$		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
$437$	20.7824	+	1.81822i	0.994156	+	0.0869774i
$438$		0			0
$439$	−13.0228	−	35.7799i	−0.621545	−	1.70768i	−0.703174	−	0.711017i	$-0.748235\pi$
$439$	−13.0228	−	35.7799i	−0.621545	−	1.70768i	0.0816297	−	0.996663i	$-0.473988\pi$
$440$	−24.3534	−	1.90718i	−1.16100	−	0.0909213i
$441$		0			0
$442$	−18.9809	−	5.08591i	−0.902828	−	0.241912i
$443$	28.4974	−	2.49320i	1.35395	−	0.118456i	0.613038	−	0.790053i	$-0.289947\pi$
$443$	28.4974	−	2.49320i	1.35395	−	0.118456i	0.740916	+	0.671597i	$0.234392\pi$
$444$		0			0
$445$	−3.11885	+	18.6818i	−0.147848	+	0.885605i
$446$	56.2308	−	9.91500i	2.66260	−	0.469489i
$447$		0			0
$448$	−1.20930	−	13.8223i	−0.0571338	−	0.653043i
$449$	−12.4470	−	21.5588i	−0.587409	−	1.01742i	−0.994570	−	0.104066i	$-0.966815\pi$
$449$	−12.4470	−	21.5588i	−0.587409	−	1.01742i	0.407162	−	0.913356i	$-0.366519\pi$
$450$		0			0
$451$	−4.96922	+	8.60694i	−0.233991	+	0.405285i
$452$	9.70971	+	4.52771i	0.456706	+	0.212966i
$453$		0			0
$454$	−12.3703	−	14.7424i	−0.580567	−	0.691893i
$455$	−20.4803	−	16.8694i	−0.960131	−	0.790848i
$456$		0			0
$457$	−2.11373	−	3.01872i	−0.0988761	−	0.141210i	0.766666	−	0.642047i	$-0.221914\pi$
$457$	−2.11373	−	3.01872i	−0.0988761	−	0.141210i	−0.865542	+	0.500837i	$0.833026\pi$
$458$	−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
$463$	4.75770	+	10.2029i	0.221109	+	0.474170i	0.985303	−	0.170817i	$-0.0546406\pi$
$463$	4.75770	+	10.2029i	0.221109	+	0.474170i	−0.764194	+	0.644987i	$0.776863\pi$
$464$	−26.2118	+	21.9943i	−1.21685	+	1.02106i
$465$		0			0
$466$	−34.7327	+	12.6417i	−1.60896	+	0.585614i
$467$	−16.8627	+	4.51835i	−0.780313	+	0.209084i	−0.626923	−	0.779082i	$-0.715686\pi$
$467$	−16.8627	+	4.51835i	−0.780313	+	0.209084i	−0.153390	+	0.988166i	$0.549019\pi$
$468$		0			0
$469$	5.11446	−	2.95283i	0.236164	−	0.136349i
$470$	3.79657	−	2.23833i	0.175123	−	0.103246i
$471$		0			0
$472$	58.6142	+	41.0421i	2.69794	+	1.88911i
$473$	0.748633	+	0.524198i	0.0344222	+	0.0241027i
$474$		0			0
$475$	−13.6713	+	2.66840i	−0.627281	+	0.122434i
$476$	−22.8405	+	13.1870i	−1.04689	+	0.604423i
$477$		0			0
$478$	50.9287	−	13.6463i	2.32943	−	0.624168i
$479$	−21.5176	+	7.83178i	−0.983166	+	0.357843i	−0.783070	−	0.621933i	$-0.786348\pi$
$479$	−21.5176	+	7.83178i	−0.983166	+	0.357843i	−0.200096	+	0.979776i	$0.564125\pi$
$480$		0			0
$481$	1.00560	−	0.843799i	0.0458514	−	0.0384739i
$482$	17.8026	+	38.1778i	0.810885	+	1.73895i
$483$		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	$-0.0572021\pi$
$488$	−48.7185	−	69.5772i	−2.20538	−	3.14961i
$489$		0			0
$490$	−10.1972	+	0.985852i	−0.460661	+	0.0445363i
$491$	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
$493$	6.75555	+	3.15016i	0.304255	+	0.141876i
$494$	14.4479	−	25.0245i	0.650041	−	1.12590i
$495$		0			0
$496$	−25.2560	−	43.7446i	−1.13403	−	1.96419i
$497$	1.82140	+	20.8187i	0.0817009	+	0.933845i
$498$		0			0
$499$	16.6957	−	2.94390i	0.747401	−	0.131787i	0.213040	−	0.977043i	$-0.431663\pi$
$499$	16.6957	−	2.94390i	0.747401	−	0.131787i	0.534361	+	0.845256i	$0.320552\pi$
$500$	−34.8714	−	39.3230i	−1.55950	−	1.75858i
$501$		0			0
$502$	26.6995	−	2.33590i	1.19166	−	0.104256i
$503$	−11.9228	−	3.19471i	−0.531612	−	0.142445i	−0.0169795	−	0.999856i	$-0.505405\pi$
$503$	−11.9228	−	3.19471i	−0.531612	−	0.142445i	−0.514633	+	0.857411i	$0.672072\pi$
$504$		0			0
$505$	−22.6168	−	26.4602i	−1.00643	−	1.17746i
$506$	10.3595	+	28.4624i	0.460534	+	1.26531i
$507$		0			0
$508$	10.1194	+	0.885334i	0.448976	+	0.0392803i
$509$	1.17560	+	0.427885i	0.0521077	+	0.0189657i	0.367943	−	0.929849i	$-0.380062\pi$
$509$	1.17560	+	0.427885i	0.0521077	+	0.0189657i	−0.315835	+	0.948814i	$0.602285\pi$
$510$		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
$515$	−17.0698	+	4.74097i	−0.752183	+	0.208912i
$516$		0			0
$517$	1.07825	−	0.502796i	0.0474214	−	0.0221130i
$518$	0.218888	−	2.50190i	0.00961738	−	0.109927i
$519$		0			0
$520$	62.6401	−	0.570861i	2.74695	−	0.0250339i
$521$	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
$523$	−2.91822	+	10.8910i	−0.127605	+	0.476228i	−0.999919	−	0.0127175i	$-0.995952\pi$
$523$	−2.91822	+	10.8910i	−0.127605	+	0.476228i	0.872314	+	0.488946i	$0.162618\pi$
$524$	3.46929	+	2.91108i	0.151556	+	0.127171i
$525$		0			0
$526$	8.75766	+	49.6671i	0.381852	+	2.16559i
$527$	−6.31141	+	9.01363i	−0.274929	+	0.392640i
$528$		0			0
$529$	21.2616	−	25.3386i	0.924417	−	1.10168i
$530$	−8.32812	−	44.8378i	−0.361751	−	1.94763i
$531$		0			0
$532$	−10.0377	−	37.4611i	−0.435188	−	1.62414i
$533$	10.7709	−	23.0982i	0.466538	−	1.00049i
$534$		0			0
$535$	11.3792	+	5.18048i	0.491964	+	0.223972i
$536$	−4.76869	+	13.1019i	−0.205976	+	0.565915i
$537$		0			0
$538$	46.3594	−	32.4612i	1.99870	−	1.39950i
$539$	−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	$0.517515\pi$
$542$	54.4318	−	38.1136i	2.33805	−	1.63712i
$543$		0			0
$544$	5.52655	−	15.1841i	0.236949	−	0.651012i
$545$	−5.14498	−	13.7447i	−0.220387	−	0.588757i
$546$		0			0
$547$	1.78092	−	3.81919i	0.0761465	−	0.163297i	−0.864549	−	0.502548i	$-0.832396\pi$
$547$	1.78092	−	3.81919i	0.0761465	−	0.163297i	0.940696	+	0.339251i	$0.110174\pi$
$548$	2.96039	+	11.0483i	0.126462	+	0.471961i
$549$		0			0
$550$	−11.8999	−	16.3522i	−0.507413	−	0.697260i
$551$	−7.04554	+	8.39655i	−0.300150	+	0.357705i
$552$		0			0
$553$	22.3304	−	31.8912i	0.949586	−	1.35615i
$554$	2.38429	+	13.5220i	0.101299	+	0.574494i
$555$		0			0
$556$	35.0309	+	29.3944i	1.48564	+	1.24660i
$557$	−5.11407	+	19.0860i	−0.216690	+	0.808698i	0.768875	+	0.639399i	$0.220817\pi$
$557$	−5.11407	+	19.0860i	−0.216690	+	0.808698i	−0.985565	+	0.169299i	$0.945850\pi$
$558$		0			0
$559$	−2.02964	−	1.17181i	−0.0858446	−	0.0495624i
$560$	40.3485	−	41.0907i	1.70503	−	1.73640i
$561$		0			0
$562$	0.333542	−	3.81240i	0.0140696	−	0.160816i
$563$	24.0516	−	11.2154i	1.01365	−	0.472675i	0.156469	−	0.987683i	$-0.449989\pi$
$563$	24.0516	−	11.2154i	1.01365	−	0.472675i	0.857185	+	0.515008i	$0.172211\pi$
$564$		0			0
$565$	1.36376	+	4.91019i	0.0573738	+	0.206573i
$566$		−	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	$0.409226\pi$
$569$	−7.42425	+	42.1050i	−0.311241	+	1.76513i	−0.592567	+	0.805521i	$0.701886\pi$
$570$		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	$0.546779\pi$
$572$	29.3198	+	2.56515i	1.22592	+	0.107254i
$573$		0			0
$574$	−16.6766	−	45.8187i	−0.696069	−	1.91243i
$575$	−15.2027	+	34.2170i	−0.633998	+	1.42695i
$576$		0			0
$577$	14.4782	+	3.87943i	0.602737	+	0.161503i	0.547268	−	0.836958i	$-0.315668\pi$
$577$	14.4782	+	3.87943i	0.602737	+	0.161503i	0.0554690	+	0.998460i	$0.482335\pi$
$578$	34.5834	−	3.02565i	1.43848	−	0.125851i
$579$		0			0
$580$	−40.7931	−	6.81021i	−1.69384	−	0.282779i
$581$	−11.8605	+	2.09132i	−0.492055	+	0.0867626i
$582$		0			0
$583$	−1.07295	−	12.2639i	−0.0444370	−	0.507918i
$584$	−14.2357	−	24.6569i	−0.589077	−	1.02031i
$585$		0			0
$586$	−29.7304	+	51.4946i	−1.22815	+	2.12722i
$587$	−3.64938	−	1.70173i	−0.150626	−	0.0702381i	0.345844	−	0.938292i	$-0.387593\pi$
$587$	−3.64938	−	1.70173i	−0.150626	−	0.0702381i	−0.496470	+	0.868054i	$0.665371\pi$
$588$		0			0
$589$	−10.4008	−	12.3951i	−0.428556	−	0.510733i
$590$	5.70067	+	58.9649i	0.234693	+	2.42755i
$591$		0			0
$592$	1.63421	+	2.33389i	0.0671655	+	0.0959223i
$593$	6.31053	−	6.31053i	0.259142	−	0.259142i	−0.565563	−	0.824705i	$-0.691341\pi$
$593$	6.31053	−	6.31053i	0.259142	−	0.259142i	0.824705	+	0.565563i	$0.191341\pi$
$594$		0			0
$595$	−11.8273	−	4.18311i	−0.484870	−	0.171491i
$596$	−64.9028	−	11.4441i	−2.65852	−	0.468769i
$597$		0			0
$598$	−32.8260	−	70.3955i	−1.34235	−	2.87869i
$599$	25.4844	−	21.3840i	1.04127	−	0.873726i	0.0491180	−	0.998793i	$-0.484359\pi$
$599$	25.4844	−	21.3840i	1.04127	−	0.873726i	0.992148	+	0.125067i	$0.0399145\pi$
$600$		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	$0.507089\pi$
$602$	−4.33098	+	1.16048i	−0.176518	+	0.0472978i
$603$		0			0
$604$	−74.1818	+	42.8289i	−3.01841	+	1.74268i
$605$	9.71937	+	16.4856i	0.395148	+	0.670236i
$606$		0			0
$607$	−37.1718	−	26.0280i	−1.50876	−	1.05644i	−0.977923	−	0.208966i	$-0.932990\pi$
$607$	−37.1718	−	26.0280i	−1.50876	−	1.05644i	−0.530833	−	0.847477i	$-0.678121\pi$
$608$	19.4639	+	13.6288i	0.789365	+	0.552719i
$609$		0			0
$610$	17.5804	−	68.0868i	0.711809	−	2.75675i
$611$	−2.64216	+	1.52545i	−0.106890	+	0.0617131i
$612$		0			0
$613$	−35.3818	+	9.48053i	−1.42906	+	0.382915i	−0.888688	−	0.458512i	$-0.848383\pi$
$613$	−35.3818	+	9.48053i	−1.42906	+	0.382915i	−0.540370	+	0.841427i	$0.681716\pi$
$614$	56.7222	−	20.6452i	2.28912	−	0.833172i
$615$		0			0
$616$	24.7829	−	20.7953i	0.998533	−	0.837868i
$617$	−15.3167	−	32.8468i	−0.616628	−	1.32236i	−0.928179	−	0.372134i	$-0.878626\pi$
$617$	−15.3167	−	32.8468i	−0.616628	−	1.32236i	0.311551	−	0.950229i	$-0.399152\pi$
$618$		0			0
$619$	−33.7534	−	5.95163i	−1.35666	−	0.239216i	−0.552444	−	0.833550i	$-0.686305\pi$
$619$	−33.7534	−	5.95163i	−1.35666	−	0.239216i	−0.804218	+	0.594334i	$0.797416\pi$
$620$	20.3576	−	57.5588i	0.817582	−	2.31162i
$621$		0			0
$622$	−17.3342	+	17.3342i	−0.695037	+	0.695037i
$623$	−14.3877	−	20.5478i	−0.576433	−	0.823231i
$624$		0			0
$625$	3.44105	−	24.7621i	0.137642	−	0.990482i
$626$	−51.4823	−	61.3542i	−2.05764	−	2.45221i
$627$		0			0
$628$	12.9699	+	6.04798i	0.517557	+	0.241341i
$629$	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	$-0.380585\pi$
$632$	8.01088	+	91.5648i	0.318656	+	3.64225i
$633$		0			0
$634$	53.6285	−	9.45615i	2.12986	−	0.375552i
$635$	2.80740	+	3.93261i	0.111408	+	0.156061i
$636$		0			0
$637$	7.06483	−	0.618092i	0.279919	−	0.0244897i
$638$	−15.3718	−	4.11886i	−0.608576	−	0.163067i
$639$		0			0
$640$	0.860650	−	10.9899i	0.0340202	−	0.434414i
$641$	−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
$643$	44.9817	+	3.93539i	1.77390	+	0.155197i	0.926634	−	0.375965i	$-0.122689\pi$
$643$	44.9817	+	3.93539i	1.77390	+	0.155197i	0.847271	+	0.531161i	$0.178244\pi$
$644$	−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	$-0.418242\pi$
$647$	−18.1400	−	18.1400i	−0.713158	−	0.713158i	−0.967195	+	0.254037i	$0.918242\pi$
$648$		0			0
$649$			15.9914i			0.627719i
$650$	34.0546	+	39.1142i	1.33573	+	1.53418i
$651$		0			0
$652$	−96.4835	+	44.9910i	−3.77858	+	1.76198i
$653$	−0.635049	+	7.25864i	−0.0248514	+	0.284052i	0.973593	+	0.228292i	$0.0733140\pi$
$653$	−0.635049	+	7.25864i	−0.0248514	+	0.284052i	−0.998444	+	0.0557608i	$0.982242\pi$
$654$		0			0
$655$	0.0196313	+	2.15413i	0.000767060	+	0.0841688i
$656$	47.9046	+	27.6577i	1.87036	+	1.07985i
$657$		0			0
$658$	−1.51070	+	5.63801i	−0.0588932	+	0.219793i
$659$	−20.4475	−	17.1575i	−0.796520	−	0.668360i	0.150830	−	0.988560i	$-0.451805\pi$
$659$	−20.4475	−	17.1575i	−0.796520	−	0.668360i	−0.947350	+	0.320200i	$0.896250\pi$
$660$		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	$-0.171245\pi$
$662$	0.356499	−	0.509133i	0.0138557	−	0.0197880i
$663$		0			0
$664$	18.2766	−	21.7813i	0.709271	−	0.845277i
$665$	10.4430	−	15.2072i	0.404961	−	0.589710i
$666$		0			0
$667$	7.62568	+	28.4594i	0.295267	+	1.10195i
$668$	−10.4239	+	22.3541i	−0.403312	+	0.864905i
$669$		0			0
$670$	−10.8106	+	4.04667i	−0.417649	+	0.156336i
$671$	6.49238	−	17.8377i	0.250635	−	0.688615i
$672$		0			0
$673$	−17.8466	+	12.4963i	−0.687934	+	0.481697i	−0.864526	−	0.502587i	$-0.832382\pi$
$673$	−17.8466	+	12.4963i	−0.687934	+	0.481697i	0.176592	+	0.984284i	$0.443493\pi$
$674$	44.3443			1.70808
$675$		0			0
$676$	−14.3629			−0.552418
$677$	8.63710	−	6.04776i	0.331951	−	0.232434i	−0.395704	−	0.918378i	$-0.629499\pi$
$677$	8.63710	−	6.04776i	0.331951	−	0.232434i	0.727654	+	0.685944i	$0.240610\pi$
$678$		0			0
$679$	−8.08857	+	22.2232i	−0.310411	+	0.852846i
$680$	27.7384	−	10.3832i	1.06372	−	0.398177i
$681$		0			0
$682$	9.92842	−	21.2916i	0.380179	−	0.815296i
$683$	−6.15162	−	22.9581i	−0.235385	−	0.878469i	−0.977975	−	0.208723i	$-0.933069\pi$
$683$	−6.15162	−	22.9581i	−0.235385	−	0.878469i	0.742590	−	0.669746i	$-0.233597\pi$
$684$		0			0
$685$	−3.07992	+	4.48503i	−0.117678	+	0.171364i
$686$	−25.7716	+	30.7134i	−0.983965	+	1.17264i
$687$		0			0
$688$	2.91759	−	4.16675i	0.111232	−	0.158856i
$689$	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	$0.456950\pi$
$692$	9.94983	−	37.1333i	0.378236	−	1.41160i
$693$		0			0
$694$	60.8414	+	35.1268i	2.30951	+	1.33339i
$695$	0.198226	+	21.7512i	0.00751915	+	0.825070i
$696$		0			0
$697$	1.05023	−	12.0042i	0.0397803	−	0.454691i
$698$	44.8830	−	20.9293i	1.69885	−	0.792185i
$699$		0			0
$700$	69.4405	+	4.80182i	2.62460	+	0.181492i
$701$			37.4202i			1.41334i	0.707542	+	0.706671i	$0.249804\pi$
$701$			37.4202i			1.41334i	−0.707542	+	0.706671i	$0.750196\pi$
$702$		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
$707$	45.9247	+	4.01789i	1.72718	+	0.151108i
$708$		0			0
$709$	10.2864	+	28.2616i	0.386313	+	1.06139i	0.968648	+	0.248437i	$0.0799168\pi$
$709$	10.2864	+	28.2616i	0.386313	+	1.06139i	−0.582335	+	0.812949i	$0.697861\pi$
$710$	3.18911	−	40.7226i	0.119685	−	1.52829i
$711$		0			0
$712$	57.2037	+	15.3277i	2.14380	+	0.574429i
$713$	−43.3288	+	3.79078i	−1.62268	+	0.141966i
$714$		0			0
$715$	8.13410	+	11.3943i	0.304198	+	0.426122i
$716$	−24.5733	+	4.33293i	−0.918347	+	0.161929i
$717$		0			0
$718$	7.04570	+	80.5327i	0.262943	+	3.00546i
$719$	1.80566	+	3.12750i	0.0673399	+	0.116636i	0.897730	−	0.440547i	$-0.145215\pi$
$719$	1.80566	+	3.12750i	0.0673399	+	0.116636i	−0.830390	+	0.557183i	$0.811882\pi$
$720$		0			0
$721$	11.7313	−	20.3192i	0.436896	−	0.756726i
$722$	−26.3676	−	12.2954i	−0.981302	−	0.457589i
$723$		0			0
$724$	−69.7617	−	83.1388i	−2.59268	−	3.08983i
$725$	−10.1451	−	16.8548i	−0.376780	−	0.625970i
$726$		0			0
$727$	−17.2585	−	24.6477i	−0.640083	−	0.914133i	0.359738	−	0.933053i	$-0.382866\pi$
$727$	−17.2585	−	24.6477i	−0.640083	−	0.914133i	−0.999821	+	0.0189200i	$0.993977\pi$
$728$	−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
$733$	−17.2990	−	37.0978i	−0.638953	−	1.37024i	−0.912777	−	0.408459i	$-0.866066\pi$
$733$	−17.2990	−	37.0978i	−0.638953	−	1.37024i	0.273824	−	0.961780i	$-0.411712\pi$
$734$	2.82259	−	2.36844i	0.104184	−	0.0874206i
$735$		0			0
$736$	60.0186	−	21.8450i	2.21231	−	0.805217i
$737$	−3.00982	+	0.806480i	−0.110868	+	0.0297071i
$738$		0			0
$739$	−7.88425	+	4.55198i	−0.290027	+	0.167447i	−0.637954	−	0.770074i	$-0.720219\pi$
$739$	−7.88425	+	4.55198i	−0.290027	+	0.167447i	0.347927	+	0.937522i	$0.386886\pi$
$740$	−0.860951	+	3.33436i	−0.0316492	+	0.122574i
$741$		0			0
$742$	49.4750	+	34.6428i	1.81629	+	1.27178i
$743$	39.7131	+	27.8074i	1.45693	+	1.02016i	0.990784	+	0.135449i	$0.0432478\pi$
$743$	39.7131	+	27.8074i	1.45693	+	1.02016i	0.466149	+	0.884706i	$0.345641\pi$
$744$		0			0
$745$	−15.9210	−	27.0045i	−0.583299	−	0.989370i
$746$	22.0487	−	12.7298i	0.807262	−	0.466073i
$747$		0			0
$748$	13.4415	−	3.60163i	0.491468	−	0.131689i
$749$	−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	$0.550226\pi$
$752$	−2.79847	−	6.00134i	−0.102050	−	0.218846i
$753$		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	$0.494724\pi$
$758$	8.55950	+	12.2242i	0.310895	+	0.444004i
$759$		0			0
$760$	4.19113	+	43.3510i	0.152028	+	1.57250i
$761$	−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
$763$	17.6156	+	8.21429i	0.637728	+	0.297377i
$764$	8.93086	−	15.4687i	0.323107	−	0.559638i
$765$		0			0
$766$	3.69820	+	6.40547i	0.133621	+	0.231439i
$767$	−3.57411	−	40.8523i	−0.129054	−	1.47509i
$768$		0			0
$769$	6.45291	−	1.13782i	0.232698	−	0.0410309i	−0.0560832	−	0.998426i	$-0.517861\pi$
$769$	6.45291	−	1.13782i	0.232698	−	0.0410309i	0.288781	+	0.957395i	$0.406750\pi$
$770$	26.4183	+	4.41042i	0.952050	+	0.158940i
$771$		0			0
$772$	−57.8799	+	5.06383i	−2.08314	+	0.182251i
$773$	−5.36547	−	1.43767i	−0.192983	−	0.0517095i	0.161033	−	0.986949i	$-0.448517\pi$
$773$	−5.36547	−	1.43767i	−0.192983	−	0.0517095i	−0.354016	+	0.935239i	$0.615184\pi$
$774$		0			0
$775$	27.1039	−	10.4283i	0.973602	−	0.374594i
$776$	−19.0963	−	52.4668i	−0.685519	−	1.88345i
$777$		0			0
$778$	−32.8782	−	2.87647i	−1.17874	−	0.103126i
$779$	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
$785$	1.82167	+	6.55888i	0.0650181	+	0.234096i
$786$		0			0
$787$	−28.1849	+	13.1429i	−1.00468	+	0.468492i	−0.854102	−	0.520105i	$-0.825893\pi$
$787$	−28.1849	+	13.1429i	−1.00468	+	0.468492i	−0.150582	+	0.988597i	$0.548115\pi$
$788$	−9.83559	+	112.421i	−0.350378	+	4.00484i
$789$		0			0
$790$	−53.3152	+	54.2959i	−1.89687	+	1.93176i
$791$	−5.84490	−	3.37455i	−0.207821	−	0.119985i
$792$		0			0
$793$	−12.5989	+	47.0197i	−0.447400	+	1.66972i
$794$	7.12249	+	5.97648i	0.252768	+	0.212097i
$795$		0			0
$796$	5.40604	+	30.6592i	0.191612	+	1.08669i
$797$	2.77214	−	3.95902i	0.0981941	−	0.140236i	−0.767049	−	0.641589i	$-0.778275\pi$
$797$	2.77214	−	3.95902i	0.0981941	−	0.140236i	0.865243	+	0.501353i	$0.167164\pi$
$798$		0			0
$799$	−0.927217	+	1.10501i	−0.0328026	+	0.0390926i
$800$	−34.4818	+	25.0933i	−1.21912	+	0.887181i
$801$		0			0
$802$	−13.7983	−	51.4959i	−0.487235	−	1.81838i
$803$	2.68909	−	5.76678i	0.0948961	−	0.203505i
$804$		0			0
$805$	−17.3840	−	46.4408i	−0.612705	−	1.63682i
$806$	−20.6048	+	56.6111i	−0.725772	+	1.99404i
$807$		0			0
$808$	−89.1550	+	62.4270i	−3.13646	+	2.19617i
$809$	27.0458			0.950881			0.475440	−	0.879748i	$-0.342289\pi$
$809$	27.0458			0.950881			0.475440	+	0.879748i	$0.342289\pi$
$810$		0			0
$811$	−47.9089			−1.68231			−0.841154	−	0.540795i	$-0.818123\pi$
$811$	−47.9089			−1.68231			−0.841154	+	0.540795i	$0.818123\pi$
$812$	44.8675	−	31.4166i	1.57454	−	1.10251i
$813$		0			0
$814$	−0.453216	+	1.24520i	−0.0158852	+	0.0436443i
$815$	−46.0872	−	20.9816i	−1.61436	−	0.734954i
$816$		0			0
$817$	0.688628	−	1.47677i	0.0240921	−	0.0516656i
$818$	11.2790	+	42.0939i	0.394362	+	1.47178i
$819$		0			0
$820$	12.2095	+	65.7346i	0.426373	+	2.29555i
$821$	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
$823$	6.97458	−	9.96073i	0.243119	−	0.347209i	−0.678985	−	0.734152i	$-0.737580\pi$
$823$	6.97458	−	9.96073i	0.243119	−	0.347209i	0.922104	+	0.386943i	$0.126469\pi$
$824$	9.61888	+	54.5514i	0.335090	+	1.90039i
$825$		0			0
$826$	−60.1008	−	50.4305i	−2.09117	−	1.75470i
$827$	−3.49901	+	13.0585i	−0.121673	+	0.454088i	−0.999699	−	0.0245234i	$-0.992193\pi$
$827$	−3.49901	+	13.0585i	−0.121673	+	0.454088i	0.878027	+	0.478612i	$0.158860\pi$
$828$		0			0
$829$	22.0957	+	12.7570i	0.767415	+	0.443068i	0.831952	−	0.554848i	$-0.187224\pi$
$829$	22.0957	+	12.7570i	0.767415	+	0.443068i	−0.0645364	+	0.997915i	$0.520557\pi$
$830$	23.5389	−	0.214518i	0.817048	−	0.00744605i
$831$		0			0
$832$	1.63623	−	18.7022i	0.0567261	−	0.648383i
$833$	3.03892	−	1.41707i	0.105292	−	0.0490986i
$834$		0			0
$835$	−11.3044	+	3.13970i	−0.391206	+	0.108654i
$836$			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	$-0.729400\pi$
$839$	6.29080	−	35.6769i	0.217183	−	1.23170i	0.877078	−	0.480347i	$-0.159489\pi$
$840$		0			0
$841$	12.7044	+	4.62403i	0.438083	+	0.159449i
$842$	−19.2811	−	1.68687i	−0.664469	−	0.0581335i
$843$		0			0
$844$	4.47705	+	12.3006i	0.154106	+	0.423404i
$845$	−4.43900	−	5.19334i	−0.152706	−	0.178656i
$846$		0			0
$847$	−24.4816	−	6.55983i	−0.841199	−	0.225398i
$848$	−68.2584	+	5.97184i	−2.34400	+	0.205074i
$849$		0			0
$850$	21.4554	+	11.8713i	0.735916	+	0.407182i
$851$	2.41605	−	0.426015i	0.0828212	−	0.0146036i
$852$		0			0
$853$	1.06118	+	12.1293i	0.0363341	+	0.415300i	0.992480	+	0.122409i	$0.0390619\pi$
$853$	1.06118	+	12.1293i	0.0363341	+	0.415300i	−0.956146	+	0.292891i	$0.905383\pi$
$854$	46.5651	+	80.6531i	1.59342	+	2.75989i
$855$		0			0
$856$	19.5466	−	33.8558i	0.668090	−	1.15717i
$857$	−38.1058	−	17.7690i	−1.30167	−	0.606978i	−0.356724	−	0.934210i	$-0.616106\pi$
$857$	−38.1058	−	17.7690i	−1.30167	−	0.606978i	−0.944944	+	0.327232i	$0.893884\pi$
$858$		0			0
$859$	16.1180	+	19.2086i	0.549938	+	0.655390i	0.967385	−	0.253311i	$-0.0815195\pi$
$859$	16.1180	+	19.2086i	0.549938	+	0.655390i	−0.417447	+	0.908701i	$0.637075\pi$
$860$	6.11963	−	0.591640i	0.208678	−	0.0201748i
$861$		0			0
$862$	22.2244	+	31.7398i	0.756967	+	1.08106i
$863$	16.2331	−	16.2331i	0.552582	−	0.552582i	−0.374603	−	0.927185i	$-0.622221\pi$
$863$	16.2331	−	16.2331i	0.552582	−	0.552582i	0.927185	+	0.374603i	$0.122221\pi$
$864$		0			0
$865$	16.5018	−	7.87879i	0.561078	−	0.267887i
$866$	89.7060	+	15.8176i	3.04833	+	0.537503i
$867$		0			0
$868$	34.1717	+	73.2814i	1.15986	+	2.48733i
$869$	−15.7358	+	13.2039i	−0.533800	+	0.447911i
$870$		0			0
$871$	7.50875	−	2.73296i	0.254424	−	0.0926028i
$872$	−44.3246	+	11.8767i	−1.50102	+	0.402197i
$873$		0			0
$874$	46.7680	−	27.0015i	1.58195	−	0.913339i
$875$	19.7251	+	26.5924i	0.666830	+	0.898988i
$876$		0			0
$877$	−45.5180	−	31.8721i	−1.53703	−	1.07624i	−0.967049	−	0.254588i	$-0.918060\pi$
$877$	−45.5180	−	31.8721i	−1.53703	−	1.07624i	−0.569985	−	0.821655i	$-0.693051\pi$
$878$	−80.7392	−	56.5342i	−2.72481	−	1.90794i
$879$		0			0
$880$	−26.1750	+	15.4319i	−0.882358	+	0.520208i
$881$	−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
$883$	25.1153	−	6.72963i	0.845198	−	0.226470i	0.189865	−	0.981810i	$-0.439195\pi$
$883$	25.1153	−	6.72963i	0.845198	−	0.226470i	0.655333	+	0.755340i	$0.272528\pi$
$884$	−33.5330	+	12.2050i	−1.12784	+	0.410499i
$885$		0			0
$886$	56.7260	−	47.5988i	1.90575	−	1.59911i
$887$	5.53565	+	11.8712i	0.185869	+	0.398597i	0.977058	−	0.212975i	$-0.0683152\pi$
$887$	5.53565	+	11.8712i	0.185869	+	0.398597i	−0.791189	+	0.611572i	$0.790537\pi$
$888$		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
$893$	−1.21666	−	1.73756i	−0.0407138	−	0.0581454i
$894$		0			0
$895$	−9.16135	−	7.54609i	−0.306230	−	0.252238i
$896$	9.38428	+	11.1838i	0.313507	+	0.373623i
$897$		0			0
$898$	−58.4031	−	27.2338i	−1.94894	−	0.908804i
$899$	11.4261	−	19.7906i	0.381082	−	0.660054i
$900$		0			0
$901$	7.46317	+	12.9266i	0.248634	+	0.430647i
$902$	2.24223	+	25.6289i	0.0746582	+	0.853347i
$903$		0			0
$904$	15.6919	−	2.76691i	0.521906	−	0.0920261i
$905$	8.50078	−	50.9195i	0.282575	−	1.69262i
$906$		0			0
$907$	−41.8194	+	3.65873i	−1.38859	+	0.121486i	−0.756797	−	0.653650i	$-0.773237\pi$
$907$	−41.8194	+	3.65873i	−1.38859	+	0.121486i	−0.631795	+	0.775136i	$0.717681\pi$
$908$	−33.7576	−	9.04532i	−1.12029	−	0.300180i
$909$		0			0
$910$	−68.4748	−	5.36246i	−2.26992	−	0.177764i
$911$	−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
$913$	6.33028	+	0.553828i	0.209502	+	0.0183290i
$914$	−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	$-0.218588\pi$
$920$	101.917	+	57.6098i	3.36010	+	1.89934i
$921$		0			0
$922$	35.7998	−	16.6937i	1.17900	−	0.549778i
$923$	−2.46444	+	28.1686i	−0.0811179	+	0.927182i
$924$		0			0
$925$	−1.47173	+	0.719219i	−0.0483902	+	0.0236478i
$926$	25.2375	+	14.5709i	0.829356	+	0.478829i
$927$		0			0
$928$	−8.68545	+	32.4145i	−0.285114	+	1.06406i
$929$	17.4189	+	14.6162i	0.571497	+	0.479543i	0.882142	−	0.470983i	$-0.156101\pi$
$929$	17.4189	+	14.6162i	0.571497	+	0.479543i	−0.310645	+	0.950526i	$0.600545\pi$
$930$		0			0
$931$	0.856201	+	4.85576i	0.0280609	+	0.159141i
$932$	−38.4998	+	54.9834i	−1.26110	+	1.80104i
$933$		0			0
$934$	−29.0481	+	34.6182i	−0.950482	+	1.13274i
$935$	5.45651	+	3.74705i	0.178447	+	0.122542i
$936$		0			0
$937$	−0.558400	−	2.08398i	−0.0182421	−	0.0680806i	0.956205	−	0.292699i	$-0.0945532\pi$
$937$	−0.558400	−	2.08398i	−0.0182421	−	0.0680806i	−0.974447	+	0.224618i	$0.927887\pi$
$938$	6.46077	−	13.8552i	0.210951	−	0.452387i
$939$		0			0
$940$	3.31622	−	7.28424i	0.108163	−	0.237586i
$941$	−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
$943$	39.0167	−	27.3198i	1.27056	−	0.889654i
$944$	89.0054			2.89688
$945$		0			0
$946$	2.36576			0.0769175
$947$	−13.6646	+	9.56806i	−0.444040	+	0.310920i	−0.774127	−	0.633030i	$-0.781811\pi$
$947$	−13.6646	+	9.56806i	−0.444040	+	0.310920i	0.330087	+	0.943950i	$0.392922\pi$
$948$		0			0
$949$	−5.58076	+	15.3330i	−0.181159	+	0.497731i
$950$	−25.0275	+	25.9569i	−0.812001	+	0.842153i
$951$		0			0
$952$	−16.5774	+	35.5504i	−0.537277	+	1.15220i
$953$	−4.70396	−	17.5554i	−0.152376	−	0.568676i	−0.999316	−	0.0369865i	$-0.988224\pi$
$953$	−4.70396	−	17.5554i	−0.152376	−	0.568676i	0.846940	−	0.531689i	$-0.178443\pi$
$954$		0			0
$955$	8.35337	−	1.55155i	0.270309	−	0.0502068i
$956$	61.5462	−	73.3479i	1.99055	−	2.37224i
$957$		0			0
$958$	−33.9991	+	48.5557i	−1.09846	+	1.56876i
$959$	−1.25123	−	7.09611i	−0.0404045	−	0.229145i
$960$		0			0
$961$	2.09504	+	1.75795i	0.0675821	+	0.0567081i
$962$	0.879497	−	3.28233i	0.0283561	−	0.105826i
$963$		0			0
$964$	66.2491	+	38.2489i	2.13374	+	1.23192i
$965$	−19.7194	−	19.3632i	−0.634790	−	0.623325i
$966$		0			0
$967$	2.92397	−	33.4211i	0.0940285	−	1.07475i	−0.791813	−	0.610763i	$-0.790863\pi$
$967$	2.92397	−	33.4211i	0.0940285	−	1.07475i	0.885842	−	0.463988i	$-0.153582\pi$
$968$	54.2314	−	25.2885i	1.74306	−	0.812804i
$969$		0			0
$970$	22.7466	−	40.2407i	0.730349	−	1.29205i
$971$			23.4452i			0.752393i	0.926540	+	0.376196i	$0.122768\pi$
$971$			23.4452i			0.752393i	−0.926540	+	0.376196i	$0.877232\pi$
$972$		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
$977$	−22.2971	−	1.95075i	−0.713349	−	0.0624099i	−0.275297	−	0.961359i	$-0.588776\pi$
$977$	−22.2971	−	1.95075i	−0.713349	−	0.0624099i	−0.438052	+	0.898949i	$0.644332\pi$
$978$		0			0
$979$	4.52670	+	12.4370i	0.144674	+	0.397488i
$980$	−14.1422	+	12.0880i	−0.451755	+	0.386137i
$981$		0			0
$982$	34.4262	+	9.22446i	1.09858	+	0.294365i
$983$	2.49907	−	0.218640i	0.0797078	−	0.00697353i	−0.0472321	−	0.998884i	$-0.515040\pi$
$983$	2.49907	−	0.218640i	0.0797078	−	0.00697353i	0.126940	+	0.991910i	$0.459484\pi$
$984$		0			0
$985$	−43.6892	+	31.1887i	−1.39205	+	0.993754i
$986$	19.0022	−	3.35059i	0.605152	−	0.106705i
$987$		0			0
$988$	−4.57346	−	52.2749i	−0.145501	−	1.66309i
$989$	−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	$0.288720\pi$
$992$	−44.8975	−	20.9361i	−1.42550	−	0.664720i
$993$		0			0
$994$	34.7731	+	41.4409i	1.10294	+	1.31443i
$995$	−9.41498	+	11.4303i	−0.298475	+	0.362364i
$996$		0			0
$997$	8.96558	+	12.8042i	0.283943	+	0.405512i	0.935634	−	0.352972i	$-0.114829\pi$
$997$	8.96558	+	12.8042i	0.283943	+	0.405512i	−0.651691	+	0.758484i	$0.725940\pi$
$998$	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.8.15		192
3.2	odd	2		135.2.q.a.83.2	yes	192
5.2	odd	4	inner	405.2.r.a.332.15		192
15.2	even	4		135.2.q.a.2.2	✓	192
15.8	even	4		675.2.ba.b.407.15		192
15.14	odd	2		675.2.ba.b.218.15		192
27.13	even	9		135.2.q.a.68.2	yes	192
27.14	odd	18	inner	405.2.r.a.233.15		192
135.13	odd	36		675.2.ba.b.257.15		192
135.67	odd	36		135.2.q.a.122.2	yes	192
135.94	even	18		675.2.ba.b.68.15		192
135.122	even	36	inner	405.2.r.a.152.15		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.2	✓	192	15.2	even	4
135.2.q.a.68.2	yes	192	27.13	even	9
135.2.q.a.83.2	yes	192	3.2	odd	2
135.2.q.a.122.2	yes	192	135.67	odd	36
405.2.r.a.8.15		192	1.1	even	1	trivial
405.2.r.a.152.15		192	135.122	even	36	inner
405.2.r.a.233.15		192	27.14	odd	18	inner
405.2.r.a.332.15		192	5.2	odd	4	inner
675.2.ba.b.68.15		192	135.94	even	18
675.2.ba.b.218.15		192	15.14	odd	2
675.2.ba.b.257.15		192	135.13	odd	36
675.2.ba.b.407.15		192	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.r (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.12047 - 1.48477i) q^{2} +(1.60780 - 4.41741i) q^{4} +(2.09416 - 0.783897i) q^{5} +(-1.25154 + 2.68394i) q^{7} +(-1.80956 - 6.75336i) q^{8} +O(q^{10})\)	\(q+(2.12047 - 1.48477i) q^{2} +(1.60780 - 4.41741i) q^{4} +(2.09416 - 0.783897i) q^{5} +(-1.25154 + 2.68394i) q^{7} +(-1.80956 - 6.75336i) q^{8} +(3.27669 - 4.77156i) q^{10} +(1.00437 - 1.19696i) q^{11} +(-2.29827 + 3.28227i) q^{13} +(1.33117 + 7.54945i) q^{14} +(-6.66205 - 5.59013i) q^{16} +(-0.490334 + 1.82995i) q^{17} +(-2.41262 - 1.39293i) q^{19} +(-0.0957914 - 10.5111i) q^{20} +(0.352524 - 4.02936i) q^{22} +(-6.78686 + 3.16476i) q^{23} +(3.77101 - 3.28321i) q^{25} +10.3723i q^{26} +(9.84382 + 9.84382i) q^{28} +(0.683218 - 3.87472i) q^{29} +(5.45790 + 1.98651i) q^{31} +(-8.49672 - 0.743366i) q^{32} +(1.67731 + 4.60838i) q^{34} +(-0.516997 + 6.60168i) q^{35} +(-0.316450 - 0.0847926i) q^{37} +(-7.18404 + 0.628522i) q^{38} +(-9.08344 - 12.7241i) q^{40} +(-6.26389 + 1.10449i) q^{41} +(0.0509770 + 0.582670i) q^{43} +(-3.67263 - 6.36118i) q^{44} +(-9.69236 + 16.7877i) q^{46} +(0.690071 + 0.321786i) q^{47} +(-1.13767 - 1.35582i) q^{49} +(3.12150 - 12.5610i) q^{50} +(10.8039 + 15.4296i) q^{52} +(5.57112 - 5.57112i) q^{53} +(1.16502 - 3.29395i) q^{55} +(20.3903 + 3.59537i) q^{56} +(-4.30431 - 9.23063i) q^{58} +(-7.84000 + 6.57854i) q^{59} +(11.4160 - 4.15507i) q^{61} +(14.5228 - 3.89137i) q^{62} +(-4.05760 + 2.34266i) q^{64} +(-2.23998 + 8.67520i) q^{65} +(-1.63356 - 1.14383i) q^{67} +(7.29527 + 5.10821i) q^{68} +(8.70568 + 14.7663i) q^{70} +(6.11142 - 3.52843i) q^{71} +(3.93347 - 1.05397i) q^{73} +(-0.796919 + 0.290055i) q^{74} +(-10.0321 + 8.41796i) q^{76} +(1.95556 + 4.19371i) q^{77} +(-12.9467 - 2.28286i) q^{79} +(-18.3335 - 6.48426i) q^{80} +(-11.6425 + 11.6425i) q^{82} +(2.33262 + 3.33133i) q^{83} +(0.407655 + 4.21658i) q^{85} +(0.973224 + 1.15984i) q^{86} +(-9.90096 - 4.61689i) q^{88} +(-4.23520 + 7.33558i) q^{89} +(-5.93304 - 10.2763i) q^{91} +(3.06811 + 35.0686i) q^{92} +(1.94105 - 0.342259i) q^{94} +(-6.14432 - 1.02577i) q^{95} +(7.95549 - 0.696015i) q^{97} +(-4.42546 - 1.18580i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) 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

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