LMFDB - Embedded newform 369.2.ba.a.350.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [369,2,Mod(17,369)] 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("369.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(369, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([20, 33])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 369 = 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	369.ba (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [112,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.94647983459$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$7$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			350.6
Character	$\chi$	$=$	369.350
Dual form			369.2.ba.a.233.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.875527 + 1.71832i) q^{2} +(-1.01050 + 1.39084i) q^{4} +(-0.638617 - 4.03207i) q^{5} +(-2.63642 - 3.08685i) q^{7} +(0.534921 + 0.0847232i) q^{8} +(6.36925 - 4.62753i) q^{10} +(1.94834 - 3.17941i) q^{11} +(0.113432 + 1.44129i) q^{13} +(2.99594 - 7.23283i) q^{14} +(1.38526 + 4.26339i) q^{16} +(0.183896 + 0.765982i) q^{17} +(-0.404807 + 5.14355i) q^{19} +(6.25327 + 3.18620i) q^{20} +(7.16906 + 0.564217i) q^{22} +(0.857484 - 2.63907i) q^{23} +(-11.0945 + 3.60481i) q^{25} +(-2.37728 + 1.45680i) q^{26} +(6.95741 - 0.547560i) q^{28} +(1.75959 - 7.32921i) q^{29} +(-2.54909 - 3.50853i) q^{31} +(-5.34711 + 5.34711i) q^{32} +(-1.15520 + 0.986630i) q^{34} +(-10.7627 + 12.6015i) q^{35} +(6.42194 + 4.66581i) q^{37} +(-9.19269 + 3.80774i) q^{38} -2.21094i q^{40} +(-1.01566 + 6.32206i) q^{41} +(7.71558 - 3.93129i) q^{43} +(2.45323 + 5.92262i) q^{44} +(5.28551 - 0.837142i) q^{46} +(4.04102 + 3.45136i) q^{47} +(-1.48290 + 9.36266i) q^{49} +(-15.9077 - 15.9077i) q^{50} +(-2.11922 - 1.29866i) q^{52} +(6.53557 + 1.56905i) q^{53} +(-14.0638 - 5.82543i) q^{55} +(-1.14875 - 1.87459i) q^{56} +(14.1345 - 3.39339i) q^{58} +(9.78002 + 3.17772i) q^{59} +(-2.45194 + 4.81220i) q^{61} +(3.79697 - 7.45197i) q^{62} +(-5.34280 - 1.73598i) q^{64} +(5.73893 - 1.37780i) q^{65} +(-2.32815 - 3.79919i) q^{67} +(-1.25118 - 0.518257i) q^{68} +(-31.0766 - 7.46082i) q^{70} +(-5.35944 - 3.28427i) q^{71} +(5.83964 + 5.83964i) q^{73} +(-2.39477 + 15.1200i) q^{74} +(-6.74478 - 5.76059i) q^{76} +(-14.9510 + 2.36801i) q^{77} +(-3.90560 - 9.42896i) q^{79} +(16.3057 - 8.30814i) q^{80} +(-11.7526 + 3.78991i) q^{82} -1.50640i q^{83} +(2.97105 - 1.23065i) q^{85} +(13.5104 + 9.81589i) q^{86} +(1.31158 - 1.53566i) q^{88} +(5.47445 - 4.67562i) q^{89} +(4.14999 - 4.14999i) q^{91} +(2.80402 + 3.85940i) q^{92} +(-2.39251 + 9.96552i) q^{94} +(20.9977 - 1.65255i) q^{95} +(-10.7394 + 6.58113i) q^{97} +(-17.3864 + 5.64917i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 4 q^{5} + 24 q^{8} - 12 q^{11} - 4 q^{13} - 4 q^{14} + 28 q^{16} - 4 q^{17} + 88 q^{20} + 8 q^{22} + 24 q^{23} - 60 q^{26} + 8 q^{29} + 48 q^{32} - 152 q^{35} + 8 q^{37} - 56 q^{38} + 12 q^{41}+ \cdots + 60 q^{98}+O(q^{100}) $ 112 * q - 4 * q^5 + 24 * q^8 - 12 * q^11 - 4 * q^13 - 4 * q^14 + 28 * q^16 - 4 * q^17 + 88 * q^20 + 8 * q^22 + 24 * q^23 - 60 * q^26 + 8 * q^29 + 48 * q^32 - 152 * q^35 + 8 * q^37 - 56 * q^38 + 12 * q^41 - 24 * q^43 - 60 * q^44 - 56 * q^46 - 28 * q^47 + 64 * q^52 + 16 * q^53 - 8 * q^55 + 72 * q^56 - 16 * q^58 + 40 * q^59 + 28 * q^61 + 68 * q^62 + 172 * q^65 + 48 * q^67 - 36 * q^68 - 232 * q^70 - 32 * q^71 - 72 * q^73 - 4 * q^74 - 176 * q^76 - 60 * q^77 - 72 * q^79 - 128 * q^80 - 192 * q^82 + 16 * q^85 - 40 * q^86 - 112 * q^88 + 48 * q^89 - 80 * q^91 - 64 * q^94 + 20 * q^95 - 72 * q^97 + 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/369\mathbb{Z}\right)^\times$.

$n$	$83$	$334$
$\chi(n)$	$-1$	$e\left(\frac{29}{40}\right)$

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 $

$2$	0.875527	+	1.71832i	0.619091	+	1.21503i	0.961324	+	0.275420i	$0.0888168\pi$
$2$	0.875527	+	1.71832i	0.619091	+	1.21503i	−0.342233	+	0.939615i	$0.611183\pi$
$3$		0			0
$3$		0			0
$4$	−1.01050	+	1.39084i	−0.505251	+	0.695418i
$5$	−0.638617	−	4.03207i	−0.285598	−	1.80320i	−0.546097	−	0.837722i	$-0.683887\pi$
$5$	−0.638617	−	4.03207i	−0.285598	−	1.80320i	0.260498	−	0.965474i	$-0.416113\pi$
$6$		0			0
$7$	−2.63642	−	3.08685i	−0.996473	−	1.16672i	−0.985995	−	0.166775i	$-0.946665\pi$
$7$	−2.63642	−	3.08685i	−0.996473	−	1.16672i	−0.0104785	−	0.999945i	$-0.503335\pi$
$8$	0.534921	+	0.0847232i	0.189123	+	0.0299542i
$9$		0			0
$10$	6.36925	−	4.62753i	2.01414	−	1.46335i
$11$	1.94834	−	3.17941i	0.587447	−	0.958627i	−0.411439	−	0.911437i	$-0.634974\pi$
$11$	1.94834	−	3.17941i	0.587447	−	0.958627i	0.998886	−	0.0471893i	$-0.0150264\pi$
$12$		0			0
$13$	0.113432	+	1.44129i	0.0314603	+	0.399741i	0.992406	+	0.123005i	$0.0392530\pi$
$13$	0.113432	+	1.44129i	0.0314603	+	0.399741i	−0.960946	+	0.276737i	$0.910747\pi$
$14$	2.99594	−	7.23283i	0.800698	−	1.93306i
$15$		0			0
$16$	1.38526	+	4.26339i	0.346315	+	1.06585i
$17$	0.183896	+	0.765982i	0.0446013	+	0.185778i	0.990224	−	0.139489i	$-0.0445459\pi$
$17$	0.183896	+	0.765982i	0.0446013	+	0.185778i	−0.945622	+	0.325267i	$0.894546\pi$
$18$		0			0
$19$	−0.404807	+	5.14355i	−0.0928690	+	1.18001i	0.757143	+	0.653249i	$0.226595\pi$
$19$	−0.404807	+	5.14355i	−0.0928690	+	1.18001i	−0.850012	+	0.526763i	$0.823405\pi$
$20$	6.25327	+	3.18620i	1.39827	+	0.712456i
$21$		0			0
$22$	7.16906	+	0.564217i	1.52845	+	0.120292i
$23$	0.857484	−	2.63907i	0.178798	−	0.550283i	−0.820989	−	0.570944i	$-0.806577\pi$
$23$	0.857484	−	2.63907i	0.178798	−	0.550283i	0.999787	+	0.0206612i	$0.00657715\pi$
$24$		0			0
$25$	−11.0945	+	3.60481i	−2.21889	+	0.720962i
$26$	−2.37728	+	1.45680i	−0.466223	+	0.285702i
$27$		0			0
$28$	6.95741	−	0.547560i	1.31483	−	0.103479i
$29$	1.75959	−	7.32921i	0.326747	−	1.36100i	−0.531193	−	0.847251i	$-0.678256\pi$
$29$	1.75959	−	7.32921i	0.326747	−	1.36100i	0.857940	−	0.513749i	$-0.171744\pi$
$30$		0			0
$31$	−2.54909	−	3.50853i	−0.457831	−	0.630150i	0.516226	−	0.856452i	$-0.327336\pi$
$31$	−2.54909	−	3.50853i	−0.457831	−	0.630150i	−0.974057	+	0.226302i	$0.927336\pi$
$32$	−5.34711	+	5.34711i	−0.945245	+	0.945245i
$33$		0			0
$34$	−1.15520	+	0.986630i	−0.198114	+	0.169206i
$35$	−10.7627	+	12.6015i	−1.81924	+	2.13005i
$36$		0			0
$37$	6.42194	+	4.66581i	1.05576	+	0.767055i	0.973299	−	0.229540i	$-0.0737220\pi$
$37$	6.42194	+	4.66581i	1.05576	+	0.767055i	0.0824610	+	0.996594i	$0.473722\pi$
$38$	−9.19269	+	3.80774i	−1.49125	+	0.617696i
$39$		0			0
$40$		−	2.21094i		−	0.349581i
$41$	−1.01566	+	6.32206i	−0.158620	+	0.987340i
$41$	−1.01566	+	6.32206i	−0.158620	+	0.987340i
$42$		0			0
$43$	7.71558	−	3.93129i	1.17662	−	0.599516i	0.247349	−	0.968926i	$-0.420440\pi$
$43$	7.71558	−	3.93129i	1.17662	−	0.599516i	0.929266	+	0.369411i	$0.120440\pi$
$44$	2.45323	+	5.92262i	0.369838	+	0.892868i
$45$		0			0
$46$	5.28551	−	0.837142i	0.779306	−	0.123430i
$47$	4.04102	+	3.45136i	0.589443	+	0.503432i	0.893405	−	0.449252i	$-0.148309\pi$
$47$	4.04102	+	3.45136i	0.589443	+	0.503432i	−0.303962	+	0.952684i	$0.598309\pi$
$48$		0			0
$49$	−1.48290	+	9.36266i	−0.211843	+	1.33752i
$50$	−15.9077	−	15.9077i	−2.24969	−	2.24969i
$51$		0			0
$52$	−2.11922	−	1.29866i	−0.293883	−	0.180091i
$53$	6.53557	+	1.56905i	0.897730	+	0.215526i	0.655949	−	0.754805i	$-0.272269\pi$
$53$	6.53557	+	1.56905i	0.897730	+	0.215526i	0.241780	+	0.970331i	$0.422269\pi$
$54$		0			0
$55$	−14.0638	−	5.82543i	−1.89637	−	0.785501i
$56$	−1.14875	−	1.87459i	−0.153508	−	0.250502i
$57$		0			0
$58$	14.1345	−	3.39339i	1.85595	−	0.445574i
$59$	9.78002	+	3.17772i	1.27325	+	0.413704i	0.866198	−	0.499701i	$-0.166557\pi$
$59$	9.78002	+	3.17772i	1.27325	+	0.413704i	0.407052	+	0.913405i	$0.366557\pi$
$60$		0			0
$61$	−2.45194	+	4.81220i	−0.313939	+	0.616139i	−0.993023	−	0.117921i	$-0.962377\pi$
$61$	−2.45194	+	4.81220i	−0.313939	+	0.616139i	0.679084	+	0.734060i	$0.262377\pi$
$62$	3.79697	−	7.45197i	0.482215	−	0.946401i
$63$		0			0
$64$	−5.34280	−	1.73598i	−0.667851	−	0.216998i
$65$	5.73893	−	1.37780i	0.711827	−	0.170895i
$66$		0			0
$67$	−2.32815	−	3.79919i	−0.284428	−	0.464145i	0.678235	−	0.734845i	$-0.262745\pi$
$67$	−2.32815	−	3.79919i	−0.284428	−	0.464145i	−0.962664	+	0.270700i	$0.912745\pi$
$68$	−1.25118	−	0.518257i	−0.151728	−	0.0628479i
$69$		0			0
$70$	−31.0766	−	7.46082i	−3.71436	−	0.891739i
$71$	−5.35944	−	3.28427i	−0.636048	−	0.389771i	0.166769	−	0.985996i	$-0.446667\pi$
$71$	−5.35944	−	3.28427i	−0.636048	−	0.389771i	−0.802817	+	0.596225i	$0.796667\pi$
$72$		0			0
$73$	5.83964	+	5.83964i	0.683479	+	0.683479i	0.960782	−	0.277304i	$-0.0894408\pi$
$73$	5.83964	+	5.83964i	0.683479	+	0.683479i	−0.277304	+	0.960782i	$0.589441\pi$
$74$	−2.39477	+	15.1200i	−0.278386	+	1.75766i
$75$		0			0
$76$	−6.74478	−	5.76059i	−0.773680	−	0.660785i
$77$	−14.9510	+	2.36801i	−1.70383	+	0.269859i
$78$		0			0
$79$	−3.90560	−	9.42896i	−0.439415	−	1.06084i	−0.976151	−	0.217091i	$-0.930343\pi$
$79$	−3.90560	−	9.42896i	−0.439415	−	1.06084i	0.536737	−	0.843750i	$-0.319657\pi$
$80$	16.3057	−	8.30814i	1.82303	−	0.928879i
$81$		0			0
$82$	−11.7526	+	3.78991i	−1.29785	+	0.418525i
$83$		−	1.50640i		−	0.165349i	−0.996577	−	0.0826743i	$-0.973654\pi$
$83$		−	1.50640i		−	0.165349i	0.996577	−	0.0826743i	$-0.0263461\pi$
$84$		0			0
$85$	2.97105	−	1.23065i	0.322256	−	0.133483i
$86$	13.5104	+	9.81589i	1.45686	+	1.05847i
$87$		0			0
$88$	1.31158	−	1.53566i	0.139815	−	0.163702i
$89$	5.47445	−	4.67562i	0.580291	−	0.495615i	−0.310166	−	0.950682i	$-0.600385\pi$
$89$	5.47445	−	4.67562i	0.580291	−	0.495615i	0.890457	+	0.455067i	$0.150385\pi$
$90$		0			0
$91$	4.14999	−	4.14999i	0.435037	−	0.435037i
$92$	2.80402	+	3.85940i	0.292339	+	0.402370i
$93$		0			0
$94$	−2.39251	+	9.96552i	−0.246768	+	1.02786i
$95$	20.9977	−	1.65255i	2.15432	−	0.169548i
$96$		0			0
$97$	−10.7394	+	6.58113i	−1.09042	+	0.668213i	−0.946930	−	0.321439i	$-0.895834\pi$
$97$	−10.7394	+	6.58113i	−1.09042	+	0.668213i	−0.143494	+	0.989651i	$0.545834\pi$
$98$	−17.3864	+	5.64917i	−1.75629	+	0.570653i
$99$		0			0
$100$	6.19728	−	19.0733i	0.619728	−	1.90733i
$101$	−15.7216	−	1.23731i	−1.56435	−	0.123117i	−0.733531	−	0.679656i	$-0.762129\pi$
$101$	−15.7216	−	1.23731i	−1.56435	−	0.123117i	−0.830822	+	0.556538i	$0.812129\pi$
$102$		0			0
$103$	7.13518	+	3.63556i	0.703051	+	0.358222i	0.768690	−	0.639621i	$-0.220909\pi$
$103$	7.13518	+	3.63556i	0.703051	+	0.358222i	−0.0656397	+	0.997843i	$0.520909\pi$
$104$	−0.0614334	+	0.780585i	−0.00602404	+	0.0765427i
$105$		0			0
$106$	3.02594	+	12.6039i	0.293905	+	1.22420i
$107$	0.747103	+	2.29935i	0.0722252	+	0.222286i	0.980653	−	0.195757i	$-0.0627162\pi$
$107$	0.747103	+	2.29935i	0.0722252	+	0.222286i	−0.908427	+	0.418043i	$0.862716\pi$
$108$		0			0
$109$	−0.494063	+	1.19277i	−0.0473227	+	0.114247i	−0.945773	−	0.324828i	$-0.894694\pi$
$109$	−0.494063	+	1.19277i	−0.0473227	+	0.114247i	0.898451	+	0.439075i	$0.144694\pi$
$110$	−2.30332	−	29.2665i	−0.219613	−	2.79045i
$111$		0			0
$112$	9.50834	−	15.5162i	0.898453	−	1.46614i
$113$	−0.0271475	+	0.0197238i	−0.00255382	+	0.00185546i	−0.589061	−	0.808088i	$-0.700502\pi$
$113$	−0.0271475	+	0.0197238i	−0.00255382	+	0.00185546i	0.586508	+	0.809944i	$0.300502\pi$
$114$		0			0
$115$	−11.1885	−	1.77208i	−1.04333	−	0.165248i
$116$	8.41566	+	9.85347i	0.781375	+	0.914872i
$117$		0			0
$118$	3.10233	+	19.5874i	0.285593	+	1.80316i
$119$	1.87965	−	2.58711i	0.172307	−	0.237160i
$120$		0			0
$121$	−1.31869	−	2.58807i	−0.119881	−	0.235279i
$122$	−10.4156			−0.942987
$123$		0			0
$124$	7.45565			0.669537
$125$	12.3533	+	24.2447i	1.10491	+	2.16851i
$126$		0			0
$127$	4.93402	−	6.79110i	0.437824	−	0.602612i	−0.531903	−	0.846805i	$-0.678523\pi$
$127$	4.93402	−	6.79110i	0.437824	−	0.602612i	0.969727	+	0.244193i	$0.0785230\pi$
$128$	0.671104	+	4.23718i	0.0593177	+	0.374517i
$129$		0			0
$130$	7.39208	+	8.65502i	0.648329	+	0.759095i
$131$	−19.7274	−	3.12451i	−1.72359	−	0.272990i	−0.785369	−	0.619028i	$-0.787527\pi$
$131$	−19.7274	−	3.12451i	−1.72359	−	0.272990i	−0.938220	+	0.346039i	$0.887527\pi$
$132$		0			0
$133$	16.9446	−	12.3110i	1.46929	−	1.06750i
$134$	4.48986	−	7.32679i	0.387865	−	0.632939i
$135$		0			0
$136$	0.0334734	+	0.425320i	0.00287032	+	0.0364709i
$137$	−3.42976	+	8.28018i	−0.293024	+	0.707423i	0.706976	+	0.707238i	$0.250059\pi$
$137$	−3.42976	+	8.28018i	−0.293024	+	0.707423i	−1.00000		0.000185484i	$0.999941\pi$
$138$		0			0
$139$	−2.07446	−	6.38453i	−0.175953	−	0.541529i	0.823722	−	0.566993i	$-0.191894\pi$
$139$	−2.07446	−	6.38453i	−0.175953	−	0.541529i	−0.999676	+	0.0254645i	$0.991894\pi$
$140$	−6.65092	−	27.7031i	−0.562106	−	2.34134i
$141$		0			0
$142$	0.951086	−	12.0847i	0.0798134	−	1.01412i
$143$	4.80344	+	2.44748i	0.401684	+	0.204668i
$144$		0			0
$145$	−30.6756	−	2.41422i	−2.54747	−	0.200490i
$146$	−4.92160	+	15.1471i	−0.407315	+	1.25359i
$147$		0			0
$148$	−12.9788	+	4.21705i	−1.06685	+	0.346640i
$149$	8.15422	−	4.99691i	0.668020	−	0.409363i	−0.146729	−	0.989177i	$-0.546875\pi$
$149$	8.15422	−	4.99691i	0.668020	−	0.409363i	0.814749	+	0.579814i	$0.196875\pi$
$150$		0			0
$151$	0.0972035	−	0.00765008i	0.00791031	−	0.000622555i	−0.0745033	−	0.997221i	$-0.523737\pi$
$151$	0.0972035	−	0.00765008i	0.00791031	−	0.000622555i	0.0824136	+	0.996598i	$0.473737\pi$
$152$	−0.652318	+	2.71710i	−0.0529100	+	0.220386i
$153$		0			0
$154$	−17.1590	−	23.6173i	−1.38271	−	1.90314i
$155$	−12.5187	+	12.5187i	−1.00553	+	1.00553i
$156$		0			0
$157$	−13.8516	+	11.8304i	−1.10548	+	0.944168i	−0.998743	−	0.0501199i	$-0.984040\pi$
$157$	−13.8516	+	11.8304i	−1.10548	+	0.944168i	−0.106735	+	0.994287i	$0.534040\pi$
$158$	12.7825	−	14.9664i	1.01692	−	1.19066i
$159$		0			0
$160$	24.9747	+	18.1452i	1.97442	+	1.43450i
$161$	−10.4071	+	4.31076i	−0.820194	+	0.339735i
$162$		0			0
$163$			12.8455i			1.00613i	0.864247	+	0.503067i	$0.167795\pi$
$163$			12.8455i			1.00613i	−0.864247	+	0.503067i	$0.832205\pi$
$164$	−7.76662	−	7.80107i	−0.606471	−	0.609161i
$165$		0			0
$166$	2.58847	−	1.31889i	0.200904	−	0.102366i
$167$	−4.43182	−	10.6994i	−0.342945	−	0.827942i	−0.997415	−	0.0718543i	$-0.977108\pi$
$167$	−4.43182	−	10.6994i	−0.342945	−	0.827942i	0.654470	−	0.756088i	$-0.272892\pi$
$168$		0			0
$169$	10.7755	−	1.70667i	0.828885	−	0.131282i
$170$	4.71589	+	4.02775i	0.361692	+	0.308914i
$171$		0			0
$172$	−2.32883	+	14.7037i	−0.177572	+	1.12115i
$173$	9.05474	+	9.05474i	0.688419	+	0.688419i	0.961882	−	0.273463i	$-0.0881692\pi$
$173$	9.05474	+	9.05474i	0.688419	+	0.688419i	−0.273463	+	0.961882i	$0.588169\pi$
$174$		0			0
$175$	40.3772	+	24.7432i	3.05223	+	1.87041i
$176$	16.2540	+	3.90224i	1.22519	+	0.294143i
$177$		0			0
$178$	12.8272	+	5.31322i	0.961442	+	0.398242i
$179$	−6.69658	−	10.9278i	−0.500526	−	0.816784i	0.498210	−	0.867056i	$-0.333991\pi$
$179$	−6.69658	−	10.9278i	−0.500526	−	0.816784i	−0.998736	+	0.0502728i	$0.983991\pi$
$180$		0			0
$181$	11.3268	−	2.71932i	0.841913	−	0.202125i	0.210521	−	0.977589i	$-0.432484\pi$
$181$	11.3268	−	2.71932i	0.841913	−	0.202125i	0.631392	+	0.775464i	$0.282484\pi$
$182$	10.7644	+	3.49757i	0.797912	+	0.259257i
$183$		0			0
$184$	0.682277	−	1.33904i	0.0502981	−	0.0987156i
$185$	14.7117	−	28.8734i	1.08163	−	2.12281i
$186$		0			0
$187$	2.79366	+	0.907715i	0.204293	+	0.0663787i
$188$	−8.88373	+	2.13279i	−0.647912	+	0.155550i
$189$		0			0
$190$	21.2237	+	34.6339i	1.53973	+	2.51260i
$191$	19.2551	+	7.97573i	1.39325	+	0.577103i	0.947991	−	0.318298i	$-0.103111\pi$
$191$	19.2551	+	7.97573i	1.39325	+	0.577103i	0.445260	+	0.895401i	$0.353111\pi$
$192$		0			0
$193$	−3.36942	−	0.808927i	−0.242536	−	0.0582279i	0.110355	−	0.993892i	$-0.464801\pi$
$193$	−3.36942	−	0.808927i	−0.242536	−	0.0582279i	−0.352891	+	0.935664i	$0.614801\pi$
$194$	−20.7111	−	12.6918i	−1.48697	−	0.911219i
$195$		0			0
$196$	−11.5235	−	11.5235i	−0.823104	−	0.823104i
$197$	−0.663321	+	4.18804i	−0.0472596	+	0.298386i	−0.999985	−	0.00544669i	$-0.998266\pi$
$197$	−0.663321	+	4.18804i	−0.0472596	+	0.298386i	0.952726	+	0.303832i	$0.0982663\pi$
$198$		0			0
$199$	7.12004	+	6.08109i	0.504726	+	0.431077i	0.865002	−	0.501769i	$-0.167317\pi$
$199$	7.12004	+	6.08109i	0.504726	+	0.431077i	−0.360275	+	0.932846i	$0.617317\pi$
$200$	−6.24008	+	0.988331i	−0.441240	+	0.0698856i
$201$		0			0
$202$	−11.6386	−	28.0980i	−0.818886	−	1.97696i
$203$	−27.2632	+	13.8913i	−1.91350	+	0.974978i
$204$		0			0
$205$	26.1396	+	0.0578384i	1.82567	+	0.00403961i
$206$			15.4436i			1.07600i
$207$		0			0
$208$	−5.98764	+	2.48016i	−0.415168	+	0.171968i
$209$	15.5647	+	11.3084i	1.07664	+	0.782222i
$210$		0			0
$211$	−3.71497	+	4.34967i	−0.255749	+	0.299444i	−0.873395	−	0.487013i	$-0.838087\pi$
$211$	−3.71497	+	4.34967i	−0.255749	+	0.299444i	0.617646	+	0.786456i	$0.288087\pi$
$212$	−8.78650	+	7.50438i	−0.603459	+	0.515403i
$213$		0			0
$214$	−3.29690	+	3.29690i	−0.225372	+	0.225372i
$215$	−20.7785	−	28.5992i	−1.41708	−	1.95045i
$216$		0			0
$217$	−4.10982	+	17.1186i	−0.278993	+	1.16209i
$218$	−2.48213	+	0.195348i	−0.168111	+	0.0132306i
$219$		0			0
$220$	22.3137	−	13.6739i	1.50439	−	0.921892i
$221$	−1.08314	+	0.351934i	−0.0728599	+	0.0236736i
$222$		0			0
$223$	1.03403	−	3.18243i	0.0692440	−	0.213111i	−0.910446	−	0.413627i	$-0.864262\pi$
$223$	1.03403	−	3.18243i	0.0692440	−	0.213111i	0.979690	+	0.200516i	$0.0642618\pi$
$224$	30.6030	+	2.40851i	2.04475	+	0.160925i
$225$		0			0
$226$	−0.0576602	−	0.0293793i	−0.00383550	−	0.00195428i
$227$	−0.168994	+	2.14728i	−0.0112165	+	0.142520i	−0.999976	−	0.00699857i	$-0.997772\pi$
$227$	−0.168994	+	2.14728i	−0.0112165	+	0.142520i	0.988759	+	0.149518i	$0.0477723\pi$
$228$		0			0
$229$	3.25487	+	13.5575i	0.215088	+	0.895906i	0.970586	+	0.240755i	$0.0773949\pi$
$229$	3.25487	+	13.5575i	0.215088	+	0.895906i	−0.755498	+	0.655151i	$0.772605\pi$
$230$	−6.75083	−	20.7769i	−0.445137	−	1.36999i
$231$		0			0
$232$	1.56219	−	3.77147i	0.102563	−	0.247609i
$233$	0.552169	+	7.01597i	0.0361738	+	0.459632i	0.988153	+	0.153470i	$0.0490448\pi$
$233$	0.552169	+	7.01597i	0.0361738	+	0.459632i	−0.951980	+	0.306162i	$0.900955\pi$
$234$		0			0
$235$	11.3354	−	18.4978i	0.739443	−	1.20666i
$236$	−14.3024	+	10.3913i	−0.931007	+	0.676416i
$237$		0			0
$238$	6.09116	+	0.964745i	0.394831	+	0.0625352i
$239$	−10.6063	−	12.4183i	−0.686062	−	0.803275i	0.302651	−	0.953102i	$-0.402128\pi$
$239$	−10.6063	−	12.4183i	−0.686062	−	0.803275i	−0.988712	+	0.149827i	$0.952128\pi$
$240$		0			0
$241$	−1.10303	−	6.96427i	−0.0710526	−	0.448608i	−0.997408	−	0.0719571i	$-0.977076\pi$
$241$	−1.10303	−	6.96427i	−0.0710526	−	0.448608i	0.926355	−	0.376651i	$-0.122924\pi$
$242$	3.29258	−	4.53185i	0.211655	−	0.291318i
$243$		0			0
$244$	−4.21529	−	8.27298i	−0.269857	−	0.529623i
$245$	38.6979			2.47232
$246$		0			0
$247$	−7.45926			−0.474621
$248$	−1.06631	−	2.09275i	−0.0677108	−	0.132890i
$249$		0			0
$250$	−30.8445	+	42.4537i	−1.95077	+	2.68501i
$251$	−1.59177	−	10.0500i	−0.100472	−	0.634352i	−0.985611	−	0.169027i	$-0.945937\pi$
$251$	−1.59177	−	10.0500i	−0.100472	−	0.634352i	0.885140	−	0.465325i	$-0.154063\pi$
$252$		0			0
$253$	−6.71999	−	7.86809i	−0.422482	−	0.494663i
$254$	15.9891	+	2.53243i	1.00325	+	0.158899i
$255$		0			0
$256$	−15.7830	+	11.4670i	−0.986436	+	0.716688i
$257$	−9.10323	+	14.8551i	−0.567844	+	0.926637i	0.431851	+	0.901945i	$0.357860\pi$
$257$	−9.10323	+	14.8551i	−0.567844	+	0.926637i	−0.999695	+	0.0246919i	$0.992140\pi$
$258$		0			0
$259$	−2.52826	−	32.1246i	−0.157099	−	1.99613i
$260$	−3.88291	+	9.37418i	−0.240808	+	0.581362i
$261$		0			0
$262$	−11.9030	−	36.6335i	−0.735367	−	2.26323i
$263$	−2.92469	−	12.1822i	−0.180344	−	0.751186i	−0.987074	−	0.160266i	$-0.948765\pi$
$263$	−2.92469	−	12.1822i	−0.180344	−	0.751186i	0.806730	−	0.590920i	$-0.201235\pi$
$264$		0			0
$265$	2.15280	−	27.3539i	0.132245	−	1.68034i
$266$	35.9897	+	18.3377i	2.20667	+	1.12435i
$267$		0			0
$268$	7.63665	+	0.601017i	0.466482	+	0.0367130i
$269$	8.12133	−	24.9949i	0.495166	−	1.52396i	−0.321531	−	0.946899i	$-0.604198\pi$
$269$	8.12133	−	24.9949i	0.495166	−	1.52396i	0.816698	−	0.577066i	$-0.195802\pi$
$270$		0			0
$271$	−27.6408	+	8.98105i	−1.67906	+	0.545560i	−0.984729	−	0.174096i	$-0.944300\pi$
$271$	−27.6408	+	8.98105i	−1.67906	+	0.545560i	−0.694331	+	0.719655i	$0.744300\pi$
$272$	−3.01094	+	1.84511i	−0.182565	+	0.111876i
$273$		0			0
$274$	−17.2308	+	1.35610i	−1.04095	+	0.0819248i
$275$	−10.1547	+	42.2972i	−0.612349	+	2.55062i
$276$		0			0
$277$	18.8391	+	25.9298i	1.13193	+	1.55797i	0.784350	+	0.620318i	$0.212997\pi$
$277$	18.8391	+	25.9298i	1.13193	+	1.55797i	0.347580	+	0.937650i	$0.387003\pi$
$278$	9.15442	−	9.15442i	0.549045	−	0.549045i
$279$		0			0
$280$	−6.82486	+	5.82898i	−0.407863	+	0.348348i
$281$	−1.56547	+	1.83293i	−0.0933883	+	0.109344i	−0.805132	−	0.593095i	$-0.797906\pi$
$281$	−1.56547	+	1.83293i	−0.0933883	+	0.109344i	0.711744	+	0.702439i	$0.247906\pi$
$282$		0			0
$283$	13.5408	+	9.83794i	0.804914	+	0.584805i	0.912352	−	0.409407i	$-0.134264\pi$
$283$	13.5408	+	9.83794i	0.804914	+	0.584805i	−0.107437	+	0.994212i	$0.534264\pi$
$284$	9.98360	−	4.13534i	0.592418	−	0.245387i
$285$		0			0
$286$			10.3967i			0.614768i
$287$	22.1930	−	13.5324i	1.31001	−	0.798793i
$288$		0			0
$289$	14.5942	−	7.43612i	0.858482	−	0.437419i
$290$	−22.7089	−	54.8242i	−1.33351	−	3.21939i
$291$		0			0
$292$	−14.0230	+	2.22102i	−0.820631	+	0.129975i
$293$	−14.8214	−	12.6587i	−0.865877	−	0.739529i	0.100969	−	0.994890i	$-0.467806\pi$
$293$	−14.8214	−	12.6587i	−0.865877	−	0.739529i	−0.966846	+	0.255361i	$0.917806\pi$
$294$		0			0
$295$	6.56710	−	41.4631i	0.382351	−	2.41407i
$296$	3.03993	+	3.03993i	0.176692	+	0.176692i
$297$		0			0
$298$	15.7255	+	9.63662i	0.910956	+	0.558234i
$299$	3.90092	+	0.936528i	0.225596	+	0.0541608i
$300$		0			0
$301$	−32.4768	−	13.4523i	−1.87193	−	0.775380i
$302$	0.0982496	+	0.160329i	0.00565363	+	0.00922589i
$303$		0			0
$304$	−22.4898	+	5.39931i	−1.28988	+	0.309672i
$305$	20.9690	+	6.81324i	1.20068	+	0.390125i
$306$		0			0
$307$	4.39490	−	8.62549i	0.250830	−	0.492282i	−0.730918	−	0.682465i	$-0.760908\pi$
$307$	4.39490	−	8.62549i	0.250830	−	0.492282i	0.981749	+	0.190182i	$0.0609080\pi$
$308$	11.8145	−	23.1873i	0.673194	−	1.32122i
$309$		0			0
$310$	−32.4717	−	10.5507i	−1.84427	−	0.599239i
$311$	−4.64347	+	1.11480i	−0.263307	+	0.0632145i	−0.362949	−	0.931809i	$-0.618230\pi$
$311$	−4.64347	+	1.11480i	−0.263307	+	0.0632145i	0.0996421	+	0.995023i	$0.468230\pi$
$312$		0			0
$313$	2.44954	+	3.99729i	0.138456	+	0.225940i	0.914351	−	0.404922i	$-0.132701\pi$
$313$	2.44954	+	3.99729i	0.138456	+	0.225940i	−0.775895	+	0.630862i	$0.782701\pi$
$314$	−32.4558	−	13.4436i	−1.83159	−	0.758669i
$315$		0			0
$316$	17.0607	+	4.09592i	0.959742	+	0.230414i
$317$	8.56344	+	5.24768i	0.480971	+	0.294739i	0.741771	−	0.670654i	$-0.233986\pi$
$317$	8.56344	+	5.24768i	0.480971	+	0.294739i	−0.260800	+	0.965393i	$0.583986\pi$
$318$		0			0
$319$	−19.8742	−	19.8742i	−1.11274	−	1.11274i
$320$	−3.58760	+	22.6512i	−0.200553	+	1.26624i
$321$		0			0
$322$	−16.5190	−	14.1085i	−0.920565	−	0.786237i
$323$	−4.01431	+	0.635805i	−0.223362	+	0.0353771i
$324$		0			0
$325$	−6.45404	−	15.5814i	−0.358006	−	0.864302i
$326$	−22.0726	+	11.2465i	−1.22249	+	0.622889i
$327$		0			0
$328$	−1.07892	+	3.29575i	−0.0595736	+	0.181978i
$329$		−	21.5733i		−	1.18937i
$330$		0			0
$331$	−12.7580	+	5.28452i	−0.701240	+	0.290463i	−0.704674	−	0.709531i	$-0.748907\pi$
$331$	−12.7580	+	5.28452i	−0.701240	+	0.290463i	0.00343395	+	0.999994i	$0.498907\pi$
$332$	2.09515	+	1.52222i	0.114986	+	0.0835425i
$333$		0			0
$334$	14.5047	−	16.9829i	0.793664	−	0.929261i
$335$	−13.8318	+	11.8135i	−0.755712	+	0.645439i
$336$		0			0
$337$	23.6790	−	23.6790i	1.28987	−	1.28987i	0.355013	−	0.934861i	$-0.384476\pi$
$337$	23.6790	−	23.6790i	1.28987	−	1.28987i	0.934861	−	0.355013i	$-0.115524\pi$
$338$	12.3669	+	17.0215i	0.672668	+	0.925848i
$339$		0			0
$340$	−1.29062	+	5.37582i	−0.0699938	+	0.291545i
$341$	−16.1215	+	1.26879i	−0.873030	+	0.0687090i
$342$		0			0
$343$	8.58179	−	5.25893i	0.463373	−	0.283955i
$344$	4.46030	−	1.44924i	0.240483	−	0.0781377i
$345$		0			0
$346$	−7.63126	+	23.4866i	−0.410259	+	1.26265i
$347$	−18.0150	−	1.41781i	−0.967097	−	0.0761122i	−0.414937	−	0.909850i	$-0.636196\pi$
$347$	−18.0150	−	1.41781i	−0.967097	−	0.0761122i	−0.552160	+	0.833738i	$0.686196\pi$
$348$		0			0
$349$	6.09637	+	3.10626i	0.326331	+	0.166274i	0.609479	−	0.792802i	$-0.291379\pi$
$349$	6.09637	+	3.10626i	0.326331	+	0.166274i	−0.283148	+	0.959076i	$0.591379\pi$
$350$	−7.16534	+	91.0443i	−0.383004	+	4.86652i
$351$		0			0
$352$	6.58264	+	27.4187i	0.350856	+	1.46142i
$353$	6.47746	+	19.9356i	0.344761	+	1.06106i	0.961712	+	0.274062i	$0.0883675\pi$
$353$	6.47746	+	19.9356i	0.344761	+	1.06106i	−0.616951	+	0.787001i	$0.711632\pi$
$354$		0			0
$355$	−9.81977	+	23.7070i	−0.521179	+	1.25824i
$356$	0.971083	+	12.3388i	0.0514673	+	0.653954i
$357$		0			0
$358$	12.9144	−	21.0745i	0.682550	−	1.11382i
$359$	−17.9660	+	13.0531i	−0.948209	+	0.688914i	−0.950383	−	0.311084i	$-0.899308\pi$
$359$	−17.9660	+	13.0531i	−0.948209	+	0.688914i	0.00217363	+	0.999998i	$0.499308\pi$
$360$		0			0
$361$	−7.52621	−	1.19203i	−0.396116	−	0.0627386i
$362$	14.5896	+	17.0822i	0.766810	+	0.897819i
$363$		0			0
$364$	1.57838	+	9.96552i	0.0827298	+	0.522335i
$365$	19.8166	−	27.2751i	1.03725	−	1.42765i
$366$		0			0
$367$	15.5523	+	30.5231i	0.811822	+	1.59329i	0.804971	+	0.593314i	$0.202181\pi$
$367$	15.5523	+	30.5231i	0.811822	+	1.59329i	0.00685075	+	0.999977i	$0.497819\pi$
$368$	12.4392			0.648439
$369$		0			0
$370$	62.4942			3.24892
$371$	−12.3871	−	24.3110i	−0.643105	−	1.26217i
$372$		0			0
$373$	−11.9255	+	16.4140i	−0.617478	+	0.849886i	−0.997166	−	0.0752287i	$-0.976031\pi$
$373$	−11.9255	+	16.4140i	−0.617478	+	0.849886i	0.379688	+	0.925115i	$0.376031\pi$
$374$	0.886181	+	5.59513i	0.0458233	+	0.289317i
$375$		0			0
$376$	1.86922	+	2.18857i	0.0963975	+	0.112867i
$377$	10.7631	+	1.70471i	0.554327	+	0.0877968i
$378$		0			0
$379$	−23.4307	+	17.0234i	−1.20355	+	0.874433i	−0.994630	−	0.103499i	$-0.966996\pi$
$379$	−23.4307	+	17.0234i	−1.20355	+	0.874433i	−0.208924	+	0.977932i	$0.566996\pi$
$380$	−18.9198	+	30.8742i	−0.970563	+	1.58382i
$381$		0			0
$382$	3.15353	+	40.0694i	0.161349	+	2.05013i
$383$	1.62586	−	3.92517i	0.0830775	−	0.200567i	−0.876882	−	0.480706i	$-0.840381\pi$
$383$	1.62586	−	3.92517i	0.0830775	−	0.200567i	0.959959	+	0.280139i	$0.0903805\pi$
$384$		0			0
$385$	19.0959	+	58.7712i	0.973219	+	2.99526i
$386$	−1.56003	−	6.49798i	−0.0794033	−	0.330739i
$387$		0			0
$388$	1.69894	−	21.5870i	0.0862504	−	1.09592i
$389$	−17.6556	−	8.99596i	−0.895173	−	0.456114i	−0.0550341	−	0.998484i	$-0.517527\pi$
$389$	−17.6556	−	8.99596i	−0.895173	−	0.456114i	−0.840139	+	0.542371i	$0.817527\pi$
$390$		0			0
$391$	2.17917	+	0.171504i	0.110205	+	0.00867333i
$392$	−1.58647	+	4.88265i	−0.0801288	+	0.246611i
$393$		0			0
$394$	−7.77715	+	2.52695i	−0.391807	+	0.127306i
$395$	−35.5240	+	21.7692i	−1.78741	+	1.09532i
$396$		0			0
$397$	−32.6770	+	2.57174i	−1.64001	+	0.129072i	−0.864627	−	0.502415i	$-0.832445\pi$
$397$	−32.6770	+	2.57174i	−1.64001	+	0.129072i	−0.775387	+	0.631487i	$0.782445\pi$
$398$	−4.21546	+	17.5587i	−0.211302	+	0.880136i
$399$		0			0
$400$	−30.7375	−	42.3065i	−1.53687	−	2.11532i
$401$	−6.58967	+	6.58967i	−0.329072	+	0.329072i	−0.852234	−	0.523161i	$-0.824752\pi$
$401$	−6.58967	+	6.58967i	−0.329072	+	0.329072i	0.523161	+	0.852234i	$0.324752\pi$
$402$		0			0
$403$	4.76765	−	4.07196i	0.237493	−	0.202839i
$404$	17.6076	−	20.6158i	0.876009	−	1.02567i
$405$		0			0
$406$	−47.7393	−	34.6847i	−2.36926	−	1.72137i
$407$	27.3466	−	11.3273i	1.35552	−	0.561476i
$408$		0			0
$409$		−	29.5663i		−	1.46196i	−0.682399	−	0.730980i	$-0.739063\pi$
$409$		−	29.5663i		−	1.46196i	0.682399	−	0.730980i	$-0.260937\pi$
$410$	22.7865	+	44.9668i	1.12535	+	2.22075i
$411$		0			0
$412$	−12.2666	+	6.25013i	−0.604331	+	0.307922i
$413$	−15.9751	−	38.5673i	−0.786083	−	1.89777i
$414$		0			0
$415$	−6.07390	+	0.962011i	−0.298156	+	0.0472233i
$416$	−8.31326	−	7.10020i	−0.407591	−	0.348116i
$417$		0			0
$418$	−5.80416	+	36.6460i	−0.283891	+	1.79242i
$419$	−5.36794	−	5.36794i	−0.262241	−	0.262241i	0.563723	−	0.825964i	$-0.309369\pi$
$419$	−5.36794	−	5.36794i	−0.262241	−	0.262241i	−0.825964	+	0.563723i	$0.809369\pi$
$420$		0			0
$421$	16.8482	+	10.3246i	0.821132	+	0.503190i	0.868501	−	0.495687i	$-0.165084\pi$
$421$	16.8482	+	10.3246i	0.821132	+	0.503190i	−0.0473693	+	0.998877i	$0.515084\pi$
$422$	−10.7267	−	2.57525i	−0.522166	−	0.125361i
$423$		0			0
$424$	3.36308	+	1.39303i	0.163326	+	0.0676517i
$425$	−4.80145	−	7.83526i	−0.232905	−	0.380066i
$426$		0			0
$427$	21.3189	−	5.11821i	1.03169	−	0.247688i
$428$	−3.95296	−	1.28440i	−0.191074	−	0.0620836i
$429$		0			0
$430$	30.9504	−	60.7435i	1.49256	−	2.92931i
$431$	10.4239	−	20.4580i	0.502101	−	0.985428i	−0.491328	−	0.870975i	$-0.663488\pi$
$431$	10.4239	−	20.4580i	0.502101	−	0.985428i	0.993429	−	0.114454i	$-0.0365117\pi$
$432$		0			0
$433$	15.6137	+	5.07321i	0.750348	+	0.243803i	0.659131	−	0.752028i	$-0.270924\pi$
$433$	15.6137	+	5.07321i	0.750348	+	0.243803i	0.0912172	+	0.995831i	$0.470924\pi$
$434$	−33.0135	+	7.92585i	−1.58470	+	0.380453i
$435$		0			0
$436$	−1.15970	−	1.89246i	−0.0555396	−	0.0906324i
$437$	13.2271	+	5.47883i	0.632736	+	0.262088i
$438$		0			0
$439$	−13.6416	−	3.27507i	−0.651080	−	0.156310i	−0.105566	−	0.994412i	$-0.533665\pi$
$439$	−13.6416	−	3.27507i	−0.651080	−	0.156310i	−0.545514	+	0.838102i	$0.683665\pi$
$440$	−7.02949	−	4.30768i	−0.335118	−	0.205360i
$441$		0			0
$442$	−1.55305	−	1.55305i	−0.0738712	−	0.0738712i
$443$	0.212895	−	1.34417i	0.0101150	−	0.0638634i	−0.982115	−	0.188284i	$-0.939707\pi$
$443$	0.212895	−	1.34417i	0.0101150	−	0.0638634i	0.992230	+	0.124421i	$0.0397073\pi$
$444$		0			0
$445$	−22.3485	−	19.0874i	−1.05942	−	0.904831i
$446$	6.37375	−	1.00950i	0.301806	−	0.0478014i
$447$		0			0
$448$	8.72716	+	21.0692i	0.412320	+	0.995427i
$449$	−22.1959	+	11.3094i	−1.04749	+	0.533721i	−0.891021	−	0.453962i	$-0.850010\pi$
$449$	−22.1959	+	11.3094i	−1.04749	+	0.533721i	−0.156466	+	0.987683i	$0.550010\pi$
$450$		0			0
$451$	18.1215	+	15.5467i	0.853310	+	0.732067i
$452$		−	0.0576887i		−	0.00271345i
$453$		0			0
$454$	−3.83766	+	1.58961i	−0.180110	+	0.0746042i
$455$	−19.3833	−	14.0828i	−0.908703	−	0.660211i
$456$		0			0
$457$	−3.90751	+	4.57511i	−0.182786	+	0.214014i	−0.844232	−	0.535978i	$-0.819943\pi$
$457$	−3.90751	+	4.57511i	−0.182786	+	0.214014i	0.661446	+	0.749993i	$0.269943\pi$
$458$	−20.4464	+	17.4629i	−0.955397	+	0.815987i
$459$		0			0
$460$	13.7707	−	13.7707i	0.642061	−	0.642061i
$461$	−10.6494	−	14.6576i	−0.495991	−	0.682673i	0.485488	−	0.874243i	$-0.338642\pi$
$461$	−10.6494	−	14.6576i	−0.495991	−	0.682673i	−0.981479	+	0.191570i	$0.938642\pi$
$462$		0			0
$463$	6.45070	−	26.8691i	0.299789	−	1.24871i	−0.595546	−	0.803321i	$-0.703064\pi$
$463$	6.45070	−	26.8691i	0.299789	−	1.24871i	0.895336	−	0.445392i	$-0.146936\pi$
$464$	33.6848	−	2.65105i	1.56378	−	0.123072i
$465$		0			0
$466$	−11.5722	+	7.09148i	−0.536074	+	0.328506i
$467$	5.66892	−	1.84194i	0.262326	−	0.0852350i	−0.174901	−	0.984586i	$-0.555961\pi$
$467$	5.66892	−	1.84194i	0.262326	−	0.0852350i	0.437227	+	0.899351i	$0.355961\pi$
$468$		0			0
$469$	−5.58956	+	17.2029i	−0.258102	+	0.794357i
$470$	41.7096	+	3.28261i	1.92392	+	0.151416i
$471$		0			0
$472$	4.96231	+	2.52842i	0.228409	+	0.116380i
$473$	2.53344	−	32.1905i	0.116488	−	1.48012i
$474$		0			0
$475$	−14.0504	−	58.5243i	−0.644678	−	2.68528i
$476$	1.69886	+	5.22856i	0.0778672	+	0.239651i
$477$		0			0
$478$	12.0526	−	29.0975i	0.551272	−	1.33089i
$479$	−1.48202	−	18.8308i	−0.0677151	−	0.860402i	−0.933175	−	0.359423i	$-0.882973\pi$
$479$	−1.48202	−	18.8308i	−0.0677151	−	0.860402i	0.865460	−	0.500979i	$-0.167027\pi$
$480$		0			0
$481$	−5.99632	+	9.78511i	−0.273409	+	0.446163i
$482$	11.0011	−	7.99277i	0.501087	−	0.364061i
$483$		0			0
$484$	4.93211	+	0.781169i	0.224187	+	0.0355077i
$485$	33.3940	+	39.0993i	1.51634	+	1.77541i
$486$		0			0
$487$	−0.428035	−	2.70251i	−0.0193961	−	0.122462i	0.976090	−	0.217365i	$-0.0697461\pi$
$487$	−0.428035	−	2.70251i	−0.0193961	−	0.122462i	−0.995487	+	0.0949024i	$0.969746\pi$
$488$	−1.71930	+	2.36641i	−0.0778290	+	0.107122i
$489$		0			0
$490$	33.8811	+	66.4954i	1.53059	+	3.00395i
$491$	8.65222			0.390469			0.195235	−	0.980757i	$-0.437453\pi$
$491$	8.65222			0.390469			0.195235	+	0.980757i	$0.437453\pi$
$492$		0			0
$493$	5.93762			0.267417
$494$	−6.53078	−	12.8174i	−0.293834	−	0.576681i
$495$		0			0
$496$	11.4271	−	15.7280i	0.513091	−	0.706209i
$497$	3.99169	+	25.2025i	0.179052	+	1.13049i
$498$		0			0
$499$	−13.7968	−	16.1540i	−0.617631	−	0.723153i	0.360124	−	0.932905i	$-0.382734\pi$
$499$	−13.7968	−	16.1540i	−0.617631	−	0.723153i	−0.977755	+	0.209752i	$0.932734\pi$
$500$	−46.2034	−	7.31790i	−2.06628	−	0.327266i
$501$		0			0
$502$	15.8755	−	11.5342i	0.708559	−	0.514798i
$503$	1.86946	−	3.05068i	0.0833551	−	0.136023i	−0.808246	−	0.588845i	$-0.799583\pi$
$503$	1.86946	−	3.05068i	0.0833551	−	0.136023i	0.891601	+	0.452822i	$0.149583\pi$
$504$		0			0
$505$	5.05112	+	64.1806i	0.224772	+	2.85600i
$506$	7.63636	−	18.4358i	0.339478	−	0.819572i
$507$		0			0
$508$	4.45947	+	13.7248i	0.197857	+	0.608941i
$509$	3.10720	+	12.9424i	0.137724	+	0.573663i	0.997964	+	0.0637737i	$0.0203136\pi$
$509$	3.10720	+	12.9424i	0.137724	+	0.573663i	−0.860240	+	0.509889i	$0.829686\pi$
$510$		0			0
$511$	2.63036	−	33.4219i	0.116360	−	1.47850i
$512$	−25.8776	−	13.1853i	−1.14364	−	0.582713i
$513$		0			0
$514$	−33.4960	−	2.63619i	−1.47744	−	0.116277i
$515$	10.1022	−	31.0913i	0.445155	−	1.37005i
$516$		0			0
$517$	18.8466	−	6.12362i	0.828870	−	0.269316i
$518$	52.9868	−	32.4703i	2.32811	−	1.42666i
$519$		0			0
$520$	3.18661	−	0.250791i	0.139742	−	0.0109979i
$521$	4.37498	−	18.2231i	0.191671	−	0.798368i	−0.790818	−	0.612051i	$-0.790345\pi$
$521$	4.37498	−	18.2231i	0.191671	−	0.798368i	0.982490	−	0.186317i	$-0.0596553\pi$
$522$		0			0
$523$	4.48685	+	6.17563i	0.196196	+	0.270041i	0.895769	−	0.444521i	$-0.146626\pi$
$523$	4.48685	+	6.17563i	0.196196	+	0.270041i	−0.699572	+	0.714562i	$0.746626\pi$
$524$	24.2802	−	24.2802i	1.06069	−	1.06069i
$525$		0			0
$526$	18.3723	−	15.6914i	0.801068	−	0.684177i
$527$	2.21870	−	2.59776i	0.0966481	−	0.113160i
$528$		0			0
$529$	12.3780	+	8.99315i	0.538174	+	0.391006i
$530$	48.8875	−	20.2499i	2.12354	−	0.879599i
$531$		0			0
$532$			36.0075i			1.56112i
$533$	−9.22711	−	0.746736i	−0.399671	−	0.0323447i
$534$		0			0
$535$	8.79401	−	4.48077i	0.380198	−	0.193721i
$536$	−0.923495	−	2.22951i	−0.0398889	−	0.0963004i
$537$		0			0
$538$	50.0596	−	7.92866i	2.15822	−	0.341829i
$539$	26.8785	+	22.9564i	1.15774	+	0.988803i
$540$		0			0
$541$	−6.05368	+	38.2214i	−0.260268	+	1.64327i	0.417997	+	0.908449i	$0.362732\pi$
$541$	−6.05368	+	38.2214i	−0.260268	+	1.64327i	−0.678264	+	0.734818i	$0.737268\pi$
$542$	−39.6326	−	39.6326i	−1.70237	−	1.70237i
$543$		0			0
$544$	−5.07911	−	3.11248i	−0.217765	−	0.133447i
$545$	5.12486	+	1.23037i	0.219525	+	0.0527033i
$546$		0			0
$547$	−24.9293	−	10.3261i	−1.06590	−	0.441510i	−0.220358	−	0.975419i	$-0.570723\pi$
$547$	−24.9293	−	10.3261i	−1.06590	−	0.441510i	−0.845542	+	0.533909i	$0.820723\pi$
$548$	−8.05059	−	13.1374i	−0.343904	−	0.561201i
$549$		0			0
$550$	−81.5708	+	19.5834i	−3.47819	+	0.835040i
$551$	36.9859	+	12.0174i	1.57565	+	0.511960i
$552$		0			0
$553$	−18.8090	+	36.9147i	−0.799839	+	1.56977i
$554$	−28.0615	+	55.0738i	−1.19222	+	2.33986i
$555$		0			0
$556$	10.9761	+	3.56635i	0.465490	+	0.151247i
$557$	4.87587	−	1.17059i	0.206597	−	0.0495996i	−0.128826	−	0.991667i	$-0.541121\pi$
$557$	4.87587	−	1.17059i	0.206597	−	0.0495996i	0.335423	+	0.942068i	$0.391121\pi$
$558$		0			0
$559$	6.54131	+	10.6744i	0.276668	+	0.451481i
$560$	−68.6346	−	28.4294i	−2.90034	−	1.20136i
$561$		0			0
$562$	−4.52018	−	1.08520i	−0.190672	−	0.0457763i
$563$	28.6170	+	17.5365i	1.20606	+	0.739075i	0.972418	−	0.233247i	$-0.0749350\pi$
$563$	28.6170	+	17.5365i	1.20606	+	0.739075i	0.233644	+	0.972322i	$0.424935\pi$
$564$		0			0
$565$	0.0968647	+	0.0968647i	0.00407513	+	0.00407513i
$566$	−5.04941	+	31.8807i	−0.212243	+	1.34005i
$567$		0			0
$568$	−2.58862	−	2.21089i	−0.108616	−	0.0927670i
$569$	−26.7269	+	4.23313i	−1.12045	+	0.177462i	−0.689061	−	0.724703i	$-0.741977\pi$
$569$	−26.7269	+	4.23313i	−1.12045	+	0.177462i	−0.431391	+	0.902165i	$0.641977\pi$
$570$		0			0
$571$	−11.9136	−	28.7620i	−0.498569	−	1.20365i	−0.950255	−	0.311474i	$-0.899177\pi$
$571$	−11.9136	−	28.7620i	−0.498569	−	1.20365i	0.451686	−	0.892177i	$-0.350823\pi$
$572$	−8.25792	+	4.20762i	−0.345281	+	0.175929i
$573$		0			0
$574$	42.6836	+	26.2866i	1.78158	+	1.09718i
$575$			32.3701i			1.34993i
$576$		0			0
$577$	−17.0983	+	7.08237i	−0.711813	+	0.294843i	−0.709055	−	0.705153i	$-0.750878\pi$
$577$	−17.0983	+	7.08237i	−0.711813	+	0.294843i	−0.00275859	+	0.999996i	$0.500878\pi$
$578$	25.5552	+	18.5670i	1.06296	+	0.772284i
$579$		0			0
$580$	34.3555	−	40.2251i	1.42653	−	1.67026i
$581$	−4.65003	+	3.97150i	−0.192916	+	0.164765i
$582$		0			0
$583$	17.7222	−	17.7222i	0.733978	−	0.733978i
$584$	2.62900	+	3.61850i	0.108789	+	0.149735i
$585$		0			0
$586$	8.77511	−	36.5510i	0.362496	−	1.50991i
$587$	29.2557	−	2.30248i	1.20751	−	0.0950334i	0.541323	−	0.840815i	$-0.317924\pi$
$587$	29.2557	−	2.30248i	1.20751	−	0.0950334i	0.666191	+	0.745782i	$0.267924\pi$
$588$		0			0
$589$	19.0782	−	11.6911i	0.786103	−	0.481725i
$590$	76.9964	−	25.0177i	3.16989	−	1.02996i
$591$		0			0
$592$	−10.9961	+	33.8426i	−0.451938	+	1.39092i
$593$	6.42778	+	0.505877i	0.263957	+	0.0207739i	0.209747	−	0.977756i	$-0.432736\pi$
$593$	6.42778	+	0.505877i	0.263957	+	0.0207739i	0.0542102	+	0.998530i	$0.482736\pi$
$594$		0			0
$595$	−11.6318	−	5.92669i	−0.476857	−	0.242971i
$596$	−1.28997	+	16.3906i	−0.0528391	+	0.671384i
$597$		0			0
$598$	1.80611	+	7.52298i	0.0738572	+	0.307637i
$599$	9.31216	+	28.6599i	0.380485	+	1.17101i	0.939703	+	0.341991i	$0.111101\pi$
$599$	9.31216	+	28.6599i	0.380485	+	1.17101i	−0.559218	+	0.829020i	$0.688899\pi$
$600$		0			0
$601$	4.51679	−	10.9045i	0.184244	−	0.444803i	−0.804589	−	0.593832i	$-0.797615\pi$
$601$	4.51679	−	10.9045i	0.184244	−	0.444803i	0.988833	+	0.149028i	$0.0476145\pi$
$602$	−5.31893	−	67.5834i	−0.216783	−	2.75450i
$603$		0			0
$604$	−0.0875843	+	0.142925i	−0.00356375	+	0.00581552i
$605$	−9.59313	+	6.96982i	−0.390016	+	0.283363i
$606$		0			0
$607$	24.6902	+	3.91054i	1.00214	+	0.158724i	0.635881	−	0.771787i	$-0.280637\pi$
$607$	24.6902	+	3.91054i	1.00214	+	0.158724i	0.366263	+	0.930511i	$0.380637\pi$
$608$	−25.3386	−	29.6677i	−1.02762	−	1.20319i
$609$		0			0
$610$	6.65160	+	41.9966i	0.269316	+	1.70039i
$611$	−4.51602	+	6.21576i	−0.182698	+	0.251463i
$612$		0			0
$613$	−17.7323	−	34.8016i	−0.716202	−	1.40562i	−0.905775	−	0.423758i	$-0.860711\pi$
$613$	−17.7323	−	34.8016i	−0.716202	−	1.40562i	0.189574	−	0.981867i	$-0.439289\pi$
$614$	18.6692			0.753427
$615$		0			0
$616$	−8.19823			−0.330316
$617$	4.37096	+	8.57849i	0.175968	+	0.345357i	0.962098	−	0.272705i	$-0.0879182\pi$
$617$	4.37096	+	8.57849i	0.175968	+	0.345357i	−0.786130	+	0.618062i	$0.787918\pi$
$618$		0			0
$619$	−7.78254	+	10.7117i	−0.312807	+	0.430541i	−0.936254	−	0.351324i	$-0.885732\pi$
$619$	−7.78254	+	10.7117i	−0.312807	+	0.430541i	0.623447	+	0.781865i	$0.285732\pi$
$620$	−4.76131	−	30.0617i	−0.191219	−	1.20731i
$621$		0			0
$622$	−5.98107	−	7.00293i	−0.239819	−	0.280792i
$623$	−28.8659	−	4.57191i	−1.15649	−	0.183170i
$624$		0			0
$625$	42.6796	−	31.0085i	1.70718	−	1.24034i
$626$	−4.72398	+	7.70883i	−0.188808	+	0.308107i
$627$		0			0
$628$	−2.45706	−	31.2199i	−0.0980474	−	1.24581i
$629$	−2.39296	+	5.77711i	−0.0954135	+	0.230349i
$630$		0			0
$631$	3.12230	+	9.60946i	0.124297	+	0.382547i	0.993772	−	0.111430i	$-0.0355430\pi$
$631$	3.12230	+	9.60946i	0.124297	+	0.382547i	−0.869475	+	0.493976i	$0.835543\pi$
$632$	−1.29034	−	5.37464i	−0.0513269	−	0.213792i
$633$		0			0
$634$	−1.51967	+	19.3092i	−0.0603537	+	0.766866i
$635$	−30.5331	−	15.5574i	−1.21167	−	0.617377i
$636$		0			0
$637$	−13.6625	−	1.07526i	−0.541328	−	0.0426034i
$638$	16.7499	−	51.5507i	0.663133	−	2.04091i
$639$		0			0
$640$	16.6560	−	5.41187i	0.658387	−	0.213923i
$641$	13.4689	−	8.25377i	0.531991	−	0.326004i	−0.230427	−	0.973090i	$-0.574012\pi$
$641$	13.4689	−	8.25377i	0.531991	−	0.326004i	0.762418	+	0.647085i	$0.224012\pi$
$642$		0			0
$643$	−6.60119	+	0.519525i	−0.260326	+	0.0204881i	−0.207950	−	0.978139i	$-0.566679\pi$
$643$	−6.60119	+	0.519525i	−0.260326	+	0.0204881i	−0.0523754	+	0.998627i	$0.516679\pi$
$644$	4.52083	−	18.8306i	0.178145	−	0.742029i
$645$		0			0
$646$	−4.60716	−	6.34121i	−0.181266	−	0.249491i
$647$	26.4040	−	26.4040i	1.03805	−	1.03805i	0.0388000	−	0.999247i	$-0.487646\pi$
$647$	26.4040	−	26.4040i	1.03805	−	1.03805i	0.999247	−	0.0388000i	$-0.0123535\pi$
$648$		0			0
$649$	29.1581	−	24.9033i	1.14455	−	0.977542i
$650$	21.1232	−	24.7321i	0.828519	−	0.970071i
$651$		0			0
$652$	−17.8659	−	12.9804i	−0.699684	−	0.508350i
$653$	−43.5209	+	18.0270i	−1.70311	+	0.705450i	−0.999984	−	0.00561962i	$-0.998211\pi$
$653$	−43.5209	+	18.0270i	−1.70311	+	0.705450i	−0.703122	+	0.711069i	$0.748211\pi$
$654$		0			0
$655$			81.5375i			3.18593i
$656$	−28.3604	+	4.42754i	−1.10729	+	0.172866i
$657$		0			0
$658$	37.0697	−	18.8880i	1.44513	−	0.736330i
$659$	17.0670	+	41.2033i	0.664835	+	1.60505i	0.790134	+	0.612934i	$0.210011\pi$
$659$	17.0670	+	41.2033i	0.664835	+	1.60505i	−0.125299	+	0.992119i	$0.539989\pi$
$660$		0			0
$661$	−33.2403	+	5.26475i	−1.29290	+	0.204775i	−0.764723	−	0.644359i	$-0.777124\pi$
$661$	−33.2403	+	5.26475i	−1.29290	+	0.204775i	−0.528177	+	0.849135i	$0.677124\pi$
$662$	−20.2504	−	17.2955i	−0.787055	−	0.672208i
$663$		0			0
$664$	0.127627	−	0.805804i	0.00495288	−	0.0312712i
$665$	−60.4599	−	60.4599i	−2.34454	−	2.34454i
$666$		0			0
$667$	−17.8334	−	10.9284i	−0.690514	−	0.423147i
$668$	19.3594	+	4.64779i	0.749039	+	0.179828i
$669$		0			0
$670$	−32.4094	−	13.4244i	−1.25209	−	0.518631i
$671$	10.5227	+	17.1715i	0.406225	+	0.662899i
$672$		0			0
$673$	−14.3214	+	3.43825i	−0.552048	+	0.132535i	−0.499866	−	0.866103i	$-0.666617\pi$
$673$	−14.3214	+	3.43825i	−0.552048	+	0.132535i	−0.0521817	+	0.998638i	$0.516617\pi$
$674$	61.4196	+	19.9564i	2.36579	+	0.768693i
$675$		0			0
$676$	−8.51496	+	16.7116i	−0.327499	+	0.642752i
$677$	−7.47586	+	14.6722i	−0.287321	+	0.563898i	−0.988881	−	0.148712i	$-0.952487\pi$
$677$	−7.47586	+	14.6722i	−0.287321	+	0.563898i	0.701560	+	0.712610i	$0.252487\pi$
$678$		0			0
$679$	48.6286	+	15.8004i	1.86620	+	0.606364i
$680$	1.69354	−	0.406584i	0.0649445	−	0.0155918i
$681$		0			0
$682$	−16.2950	−	26.5911i	−0.623969	−	1.01823i
$683$	−7.82395	−	3.24079i	−0.299375	−	0.124005i	0.227940	−	0.973675i	$-0.426801\pi$
$683$	−7.82395	−	3.24079i	−0.299375	−	0.124005i	−0.527315	+	0.849670i	$0.676801\pi$
$684$		0			0
$685$	35.5766	+	8.54118i	1.35931	+	0.326342i
$686$	16.5501	+	10.1419i	0.631886	+	0.387220i
$687$		0			0
$688$	27.4487	+	27.4487i	1.04647	+	1.04647i
$689$	−1.52011	+	9.59761i	−0.0579117	+	0.365640i
$690$		0			0
$691$	2.80945	+	2.39949i	0.106876	+	0.0912810i	0.701281	−	0.712885i	$-0.252612\pi$
$691$	2.80945	+	2.39949i	0.106876	+	0.0912810i	−0.594404	+	0.804166i	$0.702612\pi$
$692$	−21.7435	+	3.44383i	−0.826563	+	0.130915i
$693$		0			0
$694$	−13.3364	−	32.1969i	−0.506242	−	1.22218i
$695$	−24.4181	+	12.4416i	−0.926231	+	0.471938i
$696$		0			0
$697$	−5.02936	+	0.384624i	−0.190501	+	0.0145687i
$698$			13.1951i			0.499443i
$699$		0			0
$700$	−75.2150	+	31.1551i	−2.84286	+	1.17755i
$701$	−12.6755	−	9.20926i	−0.478745	−	0.347829i	0.322094	−	0.946708i	$-0.395613\pi$
$701$	−12.6755	−	9.20926i	−0.478745	−	0.347829i	−0.800840	+	0.598879i	$0.795613\pi$
$702$		0			0
$703$	−26.5985	+	31.1428i	−1.00318	+	1.17457i
$704$	−15.9290	+	13.6047i	−0.600347	+	0.512745i
$705$		0			0
$706$	−28.5845	+	28.5845i	−1.07579	+	1.07579i
$707$	37.6292	+	51.7922i	1.41519	+	1.94785i
$708$		0			0
$709$	2.84446	−	11.8480i	0.106826	−	0.444963i	−0.893163	−	0.449734i	$-0.851519\pi$
$709$	2.84446	−	11.8480i	0.106826	−	0.444963i	0.999989	+	0.00477134i	$0.00151877\pi$
$710$	−49.3337	+	3.88265i	−1.85146	+	0.145713i
$711$		0			0
$712$	3.32453	−	2.03728i	0.124592	−	0.0763501i
$713$	−11.4450	+	3.71872i	−0.428620	+	0.139267i
$714$		0			0
$715$	6.80083	−	20.9308i	0.254337	−	0.782768i
$716$	21.9657	+	1.72874i	0.820897	+	0.0646060i
$717$		0			0
$718$	−38.1590	−	19.4430i	−1.42408	−	0.725606i
$719$	−1.43551	+	18.2399i	−0.0535354	+	0.680232i	0.910337	+	0.413868i	$0.135822\pi$
$719$	−1.43551	+	18.2399i	−0.0535354	+	0.680232i	−0.963872	+	0.266364i	$0.914178\pi$
$720$		0			0
$721$	−7.58892	−	31.6101i	−0.282626	−	1.17722i
$722$	−4.54110	−	13.9761i	−0.169002	−	0.520136i
$723$		0			0
$724$	−7.66360	+	18.5016i	−0.284815	+	0.687605i
$725$	6.89873	+	87.6567i	0.256212	+	3.25549i
$726$		0			0
$727$	8.85263	−	14.4462i	0.328326	−	0.535779i	−0.645300	−	0.763929i	$-0.723268\pi$
$727$	8.85263	−	14.4462i	0.328326	−	0.535779i	0.973626	+	0.228150i	$0.0732677\pi$
$728$	2.57152	−	1.86832i	0.0953067	−	0.0692444i
$729$		0			0
$730$	64.2173	+	10.1710i	2.37679	+	0.376447i
$731$	4.43016	+	5.18705i	0.163855	+	0.191850i
$732$		0			0
$733$	−1.91594	−	12.0968i	−0.0707670	−	0.446805i	−0.997475	−	0.0710223i	$-0.977374\pi$
$733$	−1.91594	−	12.0968i	−0.0707670	−	0.446805i	0.926708	−	0.375783i	$-0.122626\pi$
$734$	−38.8319	+	53.4475i	−1.43331	+	1.97278i
$735$		0			0
$736$	9.52632	+	18.6965i	0.351145	+	0.689160i
$737$	−16.6152			−0.612028
$738$		0			0
$739$	−4.00130			−0.147190			−0.0735951	−	0.997288i	$-0.523447\pi$
$739$	−4.00130			−0.147190			−0.0735951	+	0.997288i	$0.523447\pi$
$740$	25.2919	+	49.6382i	0.929749	+	1.82474i
$741$		0			0
$742$	30.9289	−	42.5699i	1.13543	−	1.56279i
$743$	−1.26831	−	8.00783i	−0.0465300	−	0.293779i	0.953440	−	0.301584i	$-0.0975154\pi$
$743$	−1.26831	−	8.00783i	−0.0465300	−	0.293779i	−0.999970	+	0.00780549i	$0.997515\pi$
$744$		0			0
$745$	−25.3553	−	29.6873i	−0.928947	−	1.08766i
$746$	−38.6456	−	6.12086i	−1.41492	−	0.224101i
$747$		0			0
$748$	−4.08548	+	2.96828i	−0.149380	+	0.108531i
$749$	5.12806	−	8.36824i	0.187375	−	0.305769i
$750$		0			0
$751$	2.15473	+	27.3784i	0.0786272	+	0.999054i	0.902052	+	0.431628i	$0.142061\pi$
$751$	2.15473	+	27.3784i	0.0786272	+	0.999054i	−0.823425	+	0.567426i	$0.807939\pi$
$752$	−9.11663	+	22.0095i	−0.332449	+	0.802603i
$753$		0			0
$754$	6.49415	+	19.9869i	0.236503	+	0.727881i
$755$	−0.0929215	−	0.387046i	−0.00338176	−	0.0140860i
$756$		0			0
$757$	0.567945	−	7.21643i	0.0206423	−	0.262285i	−0.977933	−	0.208920i	$-0.933005\pi$
$757$	0.567945	−	7.21643i	0.0206423	−	0.262285i	0.998575	−	0.0533655i	$-0.0169948\pi$
$758$	−49.7658	−	25.3570i	−1.80758	−	0.921006i
$759$		0			0
$760$	11.3721	+	0.895005i	0.412510	+	0.0324652i
$761$	0.958629	−	2.95036i	0.0347503	−	0.106950i	−0.932177	−	0.362003i	$-0.882093\pi$
$761$	0.958629	−	2.95036i	0.0347503	−	0.106950i	0.966927	+	0.255053i	$0.0820929\pi$
$762$		0			0
$763$	4.98447	−	1.61955i	0.180450	−	0.0586318i
$764$	−30.5503	+	18.7212i	−1.10527	+	0.677310i
$765$		0			0
$766$	8.16818	−	0.642850i	0.295128	−	0.0232271i
$767$	−3.47064	+	14.4563i	−0.125318	+	0.521986i
$768$		0			0
$769$	5.90303	+	8.12483i	0.212869	+	0.292989i	0.902077	−	0.431574i	$-0.142042\pi$
$769$	5.90303	+	8.12483i	0.212869	+	0.292989i	−0.689209	+	0.724563i	$0.742042\pi$
$770$	−84.2687	+	84.2687i	−3.03683	+	3.03683i
$771$		0			0
$772$	4.52989	−	3.86889i	0.163034	−	0.139245i
$773$	27.8064	−	32.5572i	1.00013	−	1.17100i	0.0148760	−	0.999889i	$-0.495265\pi$
$773$	27.8064	−	32.5572i	1.00013	−	1.17100i	0.985252	−	0.171110i	$-0.0547354\pi$
$774$		0			0
$775$	40.9284	+	29.7363i	1.47019	+	1.06816i
$776$	−6.30232	+	2.61051i	−0.226240	+	0.0937118i
$777$		0			0
$778$		−	38.2141i		−	1.37004i
$779$	−32.1067	−	7.78332i	−1.15034	−	0.278866i
$780$		0			0
$781$	−20.8840	+	10.6410i	−0.747290	+	0.380763i
$782$	1.61322	+	3.89466i	0.0576886	+	0.139273i
$783$		0			0
$784$	−41.9709	+	6.64754i	−1.49896	+	0.237412i
$785$	56.5468	+	48.2955i	2.01824	+	1.72374i
$786$		0			0
$787$	−6.18405	+	39.0446i	−0.220438	+	1.39179i	0.590680	+	0.806906i	$0.298860\pi$
$787$	−6.18405	+	39.0446i	−0.220438	+	1.39179i	−0.811118	+	0.584883i	$0.801140\pi$
$788$	−5.15459	−	5.15459i	−0.183625	−	0.183625i
$789$		0			0
$790$	−68.5086	−	41.9821i	−2.43743	−	1.49366i
$791$	0.132457	+	0.0318001i	0.00470962	+	0.00113068i
$792$		0			0
$793$	−7.21389	−	2.98809i	−0.256173	−	0.106110i
$794$	−33.0287	−	53.8979i	−1.17214	−	1.91277i
$795$		0			0
$796$	−15.6526	+	3.75786i	−0.554792	+	0.133194i
$797$	16.5643	+	5.38206i	0.586737	+	0.190643i	0.587317	−	0.809357i	$-0.300184\pi$
$797$	16.5643	+	5.38206i	0.586737	+	0.190643i	−0.000579223		1.00000i	$0.500184\pi$
$798$		0			0
$799$	−1.90055	+	3.73004i	−0.0672366	+	0.131959i
$800$	40.0481	−	78.5988i	1.41591	−	2.77889i
$801$		0			0
$802$	−17.0926	−	5.55372i	−0.603560	−	0.196109i
$803$	29.9442	−	7.18897i	1.05671	−	0.253693i
$804$		0			0
$805$	24.0274	+	39.2092i	0.846856	+	1.38194i
$806$	11.1711	+	4.62723i	0.393486	+	0.162987i
$807$		0			0
$808$	−8.30496	−	1.99385i	−0.292168	−	0.0701432i
$809$	31.6404	+	19.3893i	1.11242	+	0.681690i	0.952225	−	0.305396i	$-0.0987888\pi$
$809$	31.6404	+	19.3893i	1.11242	+	0.681690i	0.160191	+	0.987086i	$0.448789\pi$
$810$		0			0
$811$	−6.62574	−	6.62574i	−0.232661	−	0.232661i	0.581141	−	0.813803i	$-0.302606\pi$
$811$	−6.62574	−	6.62574i	−0.232661	−	0.232661i	−0.813803	+	0.581141i	$0.802606\pi$
$812$	8.22899	−	51.9558i	0.288781	−	1.82329i
$813$		0			0
$814$	43.4067	+	37.0728i	1.52141	+	1.29940i
$815$	51.7938	−	8.20333i	1.81426	−	0.287350i
$816$		0			0
$817$	17.0975	+	41.2769i	0.598165	+	1.44410i
$818$	50.8043	−	25.8861i	1.77633	−	0.905086i
$819$		0			0
$820$	−26.4946	+	36.2975i	−0.925230	+	1.26756i
$821$		−	0.148634i		−	0.00518735i	−0.999997	−	0.00259368i	$-0.999174\pi$
$821$		−	0.148634i		−	0.00518735i	0.999997	−	0.00259368i	$-0.000825594\pi$
$822$		0			0
$823$	31.6724	−	13.1191i	1.10403	−	0.457304i	0.245153	−	0.969485i	$-0.421162\pi$
$823$	31.6724	−	13.1191i	1.10403	−	0.457304i	0.858878	+	0.512180i	$0.171162\pi$
$824$	3.50874	+	2.54925i	0.122233	+	0.0888074i
$825$		0			0
$826$	52.2842	−	61.2170i	1.81920	−	2.13001i
$827$	−33.4348	+	28.5560i	−1.16264	+	0.992990i	−0.162662	+	0.986682i	$0.552008\pi$
$827$	−33.4348	+	28.5560i	−1.16264	+	0.992990i	−0.999980	+	0.00630870i	$0.997992\pi$
$828$		0			0
$829$	−31.2571	+	31.2571i	−1.08560	+	1.08560i	−0.0896281	+	0.995975i	$0.528568\pi$
$829$	−31.2571	+	31.2571i	−1.08560	+	1.08560i	−0.995975	+	0.0896281i	$0.971432\pi$
$830$	−6.97090	−	9.59463i	−0.241964	−	0.333034i
$831$		0			0
$832$	1.89601	−	7.89743i	0.0657322	−	0.273794i
$833$	−7.44433	+	0.585882i	−0.257931	+	0.0202996i
$834$		0			0
$835$	−40.3104	+	24.7022i	−1.39500	+	0.854856i
$836$	−31.4564	+	10.2208i	−1.08794	+	0.353494i
$837$		0			0
$838$	4.52405	−	13.9236i	0.156281	−	0.480983i
$839$	−2.80490	−	0.220750i	−0.0968359	−	0.00762115i	0.0299486	−	0.999551i	$-0.490466\pi$
$839$	−2.80490	−	0.220750i	−0.0968359	−	0.00762115i	−0.126784	+	0.991930i	$0.540466\pi$
$840$		0			0
$841$	−24.7820	−	12.6270i	−0.854551	−	0.435415i
$842$	−2.98988	+	37.9901i	−0.103038	+	1.30922i
$843$		0			0
$844$	−2.29570	−	9.56226i	−0.0790211	−	0.329147i
$845$	−13.7628	−	42.3577i	−0.473456	−	1.45715i
$846$		0			0
$847$	−4.51237	+	10.8938i	−0.155047	+	0.374316i
$848$	2.36398	+	30.0373i	0.0811795	+	1.03148i
$849$		0			0
$850$	9.25967	−	15.1104i	0.317604	−	0.518283i
$851$	17.8201	−	12.9471i	0.610865	−	0.443819i
$852$		0			0
$853$	−21.6098	−	3.42265i	−0.739904	−	0.117189i	−0.224906	−	0.974381i	$-0.572207\pi$
$853$	−21.6098	−	3.42265i	−0.739904	−	0.117189i	−0.514998	+	0.857191i	$0.672207\pi$
$854$	27.4600	+	32.1515i	0.939662	+	1.10020i
$855$		0			0
$856$	0.204833	+	1.29327i	0.00700105	+	0.0442029i
$857$	5.22450	−	7.19090i	0.178465	−	0.245637i	−0.710407	−	0.703791i	$-0.751489\pi$
$857$	5.22450	−	7.19090i	0.178465	−	0.245637i	0.888873	+	0.458154i	$0.151489\pi$
$858$		0			0
$859$	−15.7035	−	30.8200i	−0.535798	−	1.05156i	−0.987237	−	0.159261i	$-0.949089\pi$
$859$	−15.7035	−	30.8200i	−0.535798	−	1.05156i	0.451438	−	0.892302i	$-0.350911\pi$
$860$	60.7735			2.07236
$861$		0			0
$862$	44.2798			1.50818
$863$	−4.51695	−	8.86502i	−0.153759	−	0.301769i	0.801259	−	0.598318i	$-0.204164\pi$
$863$	−4.51695	−	8.86502i	−0.153759	−	0.301769i	−0.955018	+	0.296549i	$0.904164\pi$
$864$		0			0
$865$	30.7268	−	42.2919i	1.04474	−	1.43797i
$866$	4.95286	+	31.2711i	0.168305	+	1.06264i
$867$		0			0
$868$	−19.6562	−	23.0145i	−0.667176	−	0.781163i
$869$	−37.5879	−	5.95334i	−1.27508	−	0.201953i
$870$		0			0
$871$	5.21164	−	3.78648i	0.176590	−	0.128300i
$872$	−0.365340	+	0.596181i	−0.0123720	+	0.0201892i
$873$		0			0
$874$	2.16628	+	27.5252i	0.0732755	+	0.931053i
$875$	42.2713	−	102.052i	1.42903	−	3.44998i
$876$		0			0
$877$	−11.1052	−	34.1781i	−0.374994	−	1.15411i	−0.943482	−	0.331422i	$-0.892471\pi$
$877$	−11.1052	−	34.1781i	−0.374994	−	1.15411i	0.568488	−	0.822691i	$-0.307529\pi$
$878$	−6.31602	−	26.3081i	−0.213155	−	0.887855i
$879$		0			0
$880$	5.35403	−	68.0294i	0.180484	−	2.29327i
$881$	11.5624	+	5.89133i	0.389547	+	0.198484i	0.637784	−	0.770215i	$-0.279851\pi$
$881$	11.5624	+	5.89133i	0.389547	+	0.198484i	−0.248237	+	0.968699i	$0.579851\pi$
$882$		0			0
$883$	10.8501	+	0.853923i	0.365136	+	0.0287368i	0.259700	−	0.965689i	$-0.416376\pi$
$883$	10.8501	+	0.853923i	0.365136	+	0.0287368i	0.105436	+	0.994426i	$0.466376\pi$
$884$	0.605033	−	1.86210i	0.0203495	−	0.0626292i
$885$		0			0
$886$	2.49611	−	0.811034i	0.0838583	−	0.0272472i
$887$	−17.4967	+	10.7220i	−0.587483	+	0.360010i	−0.784254	−	0.620439i	$-0.786954\pi$
$887$	−17.4967	+	10.7220i	−0.587483	+	0.360010i	0.196772	+	0.980449i	$0.436954\pi$
$888$		0			0
$889$	−33.9713	+	2.67360i	−1.13936	+	0.0896696i
$890$	13.2316	−	55.1134i	0.443523	−	1.84741i
$891$		0			0
$892$	3.38134	+	4.65402i	0.113216	+	0.155828i
$893$	−19.3881	+	19.3881i	−0.648797	+	0.648797i
$894$		0			0
$895$	−39.7852	+	33.9798i	−1.32987	+	1.13582i
$896$	11.3102	−	13.2426i	0.377849	−	0.442404i
$897$		0			0
$898$	−38.8662	−	28.2379i	−1.29698	−	0.942311i
$899$	−30.2001	+	12.5093i	−1.00723	+	0.417208i
$900$		0			0
$901$			5.29467i			0.176391i
$902$	−10.8483	+	44.7502i	−0.361210	+	1.49002i
$903$		0			0
$904$	−0.0161928	+	0.00825066i	−0.000538566	+	0.000274413i
$905$	−18.1980	−	43.9337i	−0.604920	−	1.46041i
$906$		0			0
$907$	−33.5001	+	5.30589i	−1.11235	+	0.176179i	−0.685451	−	0.728119i	$-0.740395\pi$
$907$	−33.5001	+	5.30589i	−1.11235	+	0.176179i	−0.426902	+	0.904298i	$0.640395\pi$
$908$	−2.81574	−	2.40487i	−0.0934436	−	0.0798083i
$909$		0			0
$910$	7.22812	−	45.6365i	0.239610	−	1.51284i
$911$	−11.1519	−	11.1519i	−0.369478	−	0.369478i	0.497809	−	0.867287i	$-0.334138\pi$
$911$	−11.1519	−	11.1519i	−0.369478	−	0.369478i	−0.867287	+	0.497809i	$0.834138\pi$
$912$		0			0
$913$	−4.78945	−	2.93498i	−0.158508	−	0.0971336i
$914$	−11.2826	−	2.70872i	−0.373196	−	0.0895964i
$915$		0			0
$916$	−22.1453	−	9.17289i	−0.731702	−	0.303081i
$917$	42.3648	+	69.1330i	1.39901	+	2.28297i
$918$		0			0
$919$	−34.4509	+	8.27093i	−1.13643	+	0.272833i	−0.757655	−	0.652656i	$-0.773655\pi$
$919$	−34.4509	+	8.27093i	−1.13643	+	0.272833i	−0.378776	+	0.925489i	$0.623655\pi$
$920$	−5.83483	−	1.89585i	−0.192369	−	0.0625043i
$921$		0			0
$922$	15.8626	−	31.1322i	0.522408	−	1.02528i
$923$	4.12564	−	8.09703i	0.135797	−	0.266517i
$924$		0			0
$925$	−88.0674	−	28.6148i	−2.89564	−	0.940850i
$926$	51.8174	−	12.4403i	1.70283	−	0.408813i
$927$		0			0
$928$	29.7814	+	48.5988i	0.977623	+	1.59534i
$929$	−18.3719	−	7.60989i	−0.602762	−	0.249672i	0.0603682	−	0.998176i	$-0.480773\pi$
$929$	−18.3719	−	7.60989i	−0.602762	−	0.249672i	−0.663130	+	0.748504i	$0.730773\pi$
$930$		0			0
$931$	−47.5571	−	11.4174i	−1.55862	−	0.374192i
$932$	−10.3160	−	6.32167i	−0.337913	−	0.207073i
$933$		0			0
$934$	8.12834	+	8.12834i	0.265968	+	0.265968i
$935$	1.87589	−	11.8439i	0.0613482	−	0.387337i
$936$		0			0
$937$	−34.1493	−	29.1662i	−1.11561	−	0.952819i	−0.116423	−	0.993200i	$-0.537143\pi$
$937$	−34.1493	−	29.1662i	−1.11561	−	0.952819i	−0.999184	+	0.0403805i	$0.987143\pi$
$938$	−34.4539	+	5.45696i	−1.12496	+	0.178176i
$939$		0			0
$940$	14.2729	+	34.4578i	0.465530	+	1.12389i
$941$	−13.4796	+	6.86822i	−0.439424	+	0.223898i	−0.659683	−	0.751544i	$-0.729310\pi$
$941$	−13.4796	+	6.86822i	−0.439424	+	0.223898i	0.220260	+	0.975441i	$0.429310\pi$
$942$		0			0
$943$	15.8134	+	8.10146i	0.514956	+	0.263820i
$944$			46.0980i			1.50036i
$945$		0			0
$946$	57.5316	−	23.8304i	1.87051	−	0.774792i
$947$	−6.01499	−	4.37015i	−0.195461	−	0.142011i	0.485750	−	0.874098i	$-0.338546\pi$
$947$	−6.01499	−	4.37015i	−0.195461	−	0.142011i	−0.681211	+	0.732087i	$0.738546\pi$
$948$		0			0
$949$	−7.75420	+	9.07901i	−0.251712	+	0.294717i
$950$	88.2618	−	75.3827i	2.86359	−	2.44574i
$951$		0			0
$952$	1.22465	−	1.22465i	0.0396912	−	0.0396912i
$953$	22.6728	+	31.2065i	0.734445	+	1.01088i	0.998919	+	0.0464836i	$0.0148015\pi$
$953$	22.6728	+	31.2065i	0.734445	+	1.01088i	−0.264474	+	0.964393i	$0.585198\pi$
$954$		0			0
$955$	19.8621	−	82.7314i	0.642721	−	2.67713i
$956$	27.9895	−	2.20282i	0.905245	−	0.0712443i
$957$		0			0
$958$	31.0598	−	19.0335i	1.00350	−	0.614944i
$959$	34.6020	−	11.2429i	1.11736	−	0.363051i
$960$		0			0
$961$	3.76764	−	11.5956i	0.121537	−	0.374052i
$962$	−22.0639	−	1.73647i	−0.711368	−	0.0559859i
$963$		0			0
$964$	10.8008	+	5.50327i	0.347870	+	0.177248i
$965$	−1.10988	+	14.1024i	−0.0357283	+	0.453971i
$966$		0			0
$967$	9.29550	+	38.7185i	0.298923	+	1.24510i	0.896410	+	0.443226i	$0.146166\pi$
$967$	9.29550	+	38.7185i	0.298923	+	1.24510i	−0.597487	+	0.801879i	$0.703834\pi$
$968$	−0.486124	−	1.49613i	−0.0156246	−	0.0480876i
$969$		0			0
$970$	−37.9478	+	91.6140i	−1.21843	+	2.94155i
$971$	−1.03988	−	13.2129i	−0.0333714	−	0.424023i	−0.990798	−	0.135347i	$-0.956785\pi$
$971$	−1.03988	−	13.2129i	−0.0333714	−	0.424023i	0.957427	−	0.288676i	$-0.0932150\pi$
$972$		0			0
$973$	−14.2390	+	23.2359i	−0.456480	+	0.744908i
$974$	4.26901	−	3.10162i	0.136788	−	0.0993823i
$975$		0			0
$976$	−23.9129	−	3.78743i	−0.765433	−	0.121233i
$977$	−12.2797	−	14.3777i	−0.392864	−	0.459984i	0.528358	−	0.849021i	$-0.322808\pi$
$977$	−12.2797	−	14.3777i	−0.392864	−	0.459984i	−0.921222	+	0.389037i	$0.872808\pi$
$978$		0			0
$979$	−4.19960	−	26.5152i	−0.134220	−	0.847430i
$980$	−39.1043	+	53.8225i	−1.24914	+	1.71930i
$981$		0			0
$982$	7.57525	+	14.8673i	0.241736	+	0.474434i
$983$	−3.94890			−0.125950			−0.0629752	−	0.998015i	$-0.520059\pi$
$983$	−3.94890			−0.125950			−0.0629752	+	0.998015i	$0.520059\pi$
$984$		0			0
$985$	17.3101			0.551545
$986$	5.19855	+	10.2027i	0.165556	+	0.324921i
$987$		0			0
$988$	7.53759	−	10.3746i	0.239803	−	0.330060i
$989$	−3.75893	−	23.7329i	−0.119527	−	0.754664i
$990$		0			0
$991$	19.2113	+	22.4936i	0.610268	+	0.714532i	0.976385	−	0.216037i	$-0.0693131\pi$
$991$	19.2113	+	22.4936i	0.610268	+	0.714532i	−0.366117	+	0.930569i	$0.619313\pi$
$992$	32.3908	+	5.13020i	1.02841	+	0.162884i
$993$		0			0
$994$	−39.8111	+	28.9245i	−1.26273	+	0.917429i
$995$	19.9724	−	32.5920i	0.633167	−	1.03324i
$996$		0			0
$997$	−4.27936	−	54.3744i	−0.135529	−	1.72205i	−0.570235	−	0.821481i	$-0.693148\pi$
$997$	−4.27936	−	54.3744i	−0.135529	−	1.72205i	0.434707	−	0.900572i	$-0.356852\pi$
$998$	15.6782	−	37.8506i	0.496286	−	1.19814i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	369.2.ba.a.350.6	yes	112
3.2	odd	2		369.2.ba.b.350.2	yes	112
41.28	odd	40		369.2.ba.b.233.2	yes	112
123.110	even	40	inner	369.2.ba.a.233.6	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
369.2.ba.a.233.6	✓	112	123.110	even	40	inner
369.2.ba.a.350.6	yes	112	1.1	even	1	trivial
369.2.ba.b.233.2	yes	112	41.28	odd	40
369.2.ba.b.350.2	yes	112	3.2	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:	\( N \)	\(=\)	\( 369 = 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	369.ba (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.875527 + 1.71832i) q^{2} +(-1.01050 + 1.39084i) q^{4} +(-0.638617 - 4.03207i) q^{5} +(-2.63642 - 3.08685i) q^{7} +(0.534921 + 0.0847232i) q^{8} +(6.36925 - 4.62753i) q^{10} +(1.94834 - 3.17941i) q^{11} +(0.113432 + 1.44129i) q^{13} +(2.99594 - 7.23283i) q^{14} +(1.38526 + 4.26339i) q^{16} +(0.183896 + 0.765982i) q^{17} +(-0.404807 + 5.14355i) q^{19} +(6.25327 + 3.18620i) q^{20} +(7.16906 + 0.564217i) q^{22} +(0.857484 - 2.63907i) q^{23} +(-11.0945 + 3.60481i) q^{25} +(-2.37728 + 1.45680i) q^{26} +(6.95741 - 0.547560i) q^{28} +(1.75959 - 7.32921i) q^{29} +(-2.54909 - 3.50853i) q^{31} +(-5.34711 + 5.34711i) q^{32} +(-1.15520 + 0.986630i) q^{34} +(-10.7627 + 12.6015i) q^{35} +(6.42194 + 4.66581i) q^{37} +(-9.19269 + 3.80774i) q^{38} -2.21094i q^{40} +(-1.01566 + 6.32206i) q^{41} +(7.71558 - 3.93129i) q^{43} +(2.45323 + 5.92262i) q^{44} +(5.28551 - 0.837142i) q^{46} +(4.04102 + 3.45136i) q^{47} +(-1.48290 + 9.36266i) q^{49} +(-15.9077 - 15.9077i) q^{50} +(-2.11922 - 1.29866i) q^{52} +(6.53557 + 1.56905i) q^{53} +(-14.0638 - 5.82543i) q^{55} +(-1.14875 - 1.87459i) q^{56} +(14.1345 - 3.39339i) q^{58} +(9.78002 + 3.17772i) q^{59} +(-2.45194 + 4.81220i) q^{61} +(3.79697 - 7.45197i) q^{62} +(-5.34280 - 1.73598i) q^{64} +(5.73893 - 1.37780i) q^{65} +(-2.32815 - 3.79919i) q^{67} +(-1.25118 - 0.518257i) q^{68} +(-31.0766 - 7.46082i) q^{70} +(-5.35944 - 3.28427i) q^{71} +(5.83964 + 5.83964i) q^{73} +(-2.39477 + 15.1200i) q^{74} +(-6.74478 - 5.76059i) q^{76} +(-14.9510 + 2.36801i) q^{77} +(-3.90560 - 9.42896i) q^{79} +(16.3057 - 8.30814i) q^{80} +(-11.7526 + 3.78991i) q^{82} -1.50640i q^{83} +(2.97105 - 1.23065i) q^{85} +(13.5104 + 9.81589i) q^{86} +(1.31158 - 1.53566i) q^{88} +(5.47445 - 4.67562i) q^{89} +(4.14999 - 4.14999i) q^{91} +(2.80402 + 3.85940i) q^{92} +(-2.39251 + 9.96552i) q^{94} +(20.9977 - 1.65255i) q^{95} +(-10.7394 + 6.58113i) q^{97} +(-17.3864 + 5.64917i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 4 q^{5} + 24 q^{8} - 12 q^{11} - 4 q^{13} - 4 q^{14} + 28 q^{16} - 4 q^{17} + 88 q^{20} + 8 q^{22} + 24 q^{23} - 60 q^{26} + 8 q^{29} + 48 q^{32} - 152 q^{35} + 8 q^{37} - 56 q^{38} + 12 q^{41}+ \cdots + 60 q^{98}+O(q^{100}) \) 112 * q - 4 * q^5 + 24 * q^8 - 12 * q^11 - 4 * q^13 - 4 * q^14 + 28 * q^16 - 4 * q^17 + 88 * q^20 + 8 * q^22 + 24 * q^23 - 60 * q^26 + 8 * q^29 + 48 * q^32 - 152 * q^35 + 8 * q^37 - 56 * q^38 + 12 * q^41 - 24 * q^43 - 60 * q^44 - 56 * q^46 - 28 * q^47 + 64 * q^52 + 16 * q^53 - 8 * q^55 + 72 * q^56 - 16 * q^58 + 40 * q^59 + 28 * q^61 + 68 * q^62 + 172 * q^65 + 48 * q^67 - 36 * q^68 - 232 * q^70 - 32 * q^71 - 72 * q^73 - 4 * q^74 - 176 * q^76 - 60 * q^77 - 72 * q^79 - 128 * q^80 - 192 * q^82 + 16 * q^85 - 40 * q^86 - 112 * q^88 + 48 * q^89 - 80 * q^91 - 64 * q^94 + 20 * q^95 - 72 * q^97 + 60 * q^98

Introduction

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