LMFDB - Embedded newform 405.2.r.a.197.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,2,Mod(8,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.8"); S:= CuspForms(chi, 2); N := Newforms(S);

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

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

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			197.11
Character	$\chi$	$=$	405.197
Dual form			405.2.r.a.368.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.03355 - 0.0904240i) q^{2} +(-0.909563 + 0.160381i) q^{4} +(-1.76770 - 1.36939i) q^{5} +(-2.38295 + 1.66856i) q^{7} +(-2.92987 + 0.785057i) q^{8} +(-1.95083 - 1.25550i) q^{10} +(0.357163 + 0.981298i) q^{11} +(-0.102905 + 1.17621i) q^{13} +(-2.31203 + 1.94002i) q^{14} +(-1.22140 + 0.444552i) q^{16} +(-5.46688 - 1.46485i) q^{17} +(-3.77562 - 2.17985i) q^{19} +(1.82746 + 0.962045i) q^{20} +(0.457879 + 0.981926i) q^{22} +(-2.49254 + 3.55972i) q^{23} +(1.24952 + 4.84135i) q^{25} +1.22498i q^{26} +(1.89984 - 1.89984i) q^{28} +(5.99110 + 5.02713i) q^{29} +(-1.88318 - 10.6800i) q^{31} +(4.27590 - 1.99388i) q^{32} +(-5.78276 - 1.01966i) q^{34} +(6.49726 + 0.313684i) q^{35} +(1.84738 - 6.89452i) q^{37} +(-4.09941 - 1.91158i) q^{38} +(6.25419 + 2.62440i) q^{40} +(2.34606 + 2.79593i) q^{41} +(-0.986834 + 2.11627i) q^{43} +(-0.482244 - 0.835270i) q^{44} +(-2.25429 + 3.90454i) q^{46} +(0.209148 + 0.298694i) q^{47} +(0.500224 - 1.37435i) q^{49} +(1.72922 + 4.89080i) q^{50} +(-0.0950427 - 1.08634i) q^{52} +(-1.16516 - 1.16516i) q^{53} +(0.712425 - 2.22374i) q^{55} +(5.67183 - 6.75943i) q^{56} +(6.64669 + 4.65406i) q^{58} +(-9.77378 - 3.55737i) q^{59} +(-0.654019 + 3.70913i) q^{61} +(-2.91210 - 10.8681i) q^{62} +(6.49036 - 3.74721i) q^{64} +(1.79260 - 1.93827i) q^{65} +(0.570007 + 0.0498691i) q^{67} +(5.20741 + 0.455589i) q^{68} +(6.74362 - 0.263300i) q^{70} +(-2.83490 + 1.63673i) q^{71} +(3.56015 + 13.2867i) q^{73} +(1.28593 - 7.29289i) q^{74} +(3.78377 + 1.37718i) q^{76} +(-2.48846 - 1.74244i) q^{77} +(-2.43289 + 2.89941i) q^{79} +(2.76783 + 0.886738i) q^{80} +(2.67759 + 2.67759i) q^{82} +(0.416330 + 4.75867i) q^{83} +(7.65785 + 10.0757i) q^{85} +(-0.828582 + 2.27651i) q^{86} +(-1.81682 - 2.59468i) q^{88} +(1.62360 - 2.81215i) q^{89} +(-1.71736 - 2.97456i) q^{91} +(1.69622 - 3.63755i) q^{92} +(0.243174 + 0.289803i) q^{94} +(3.68908 + 9.02363i) q^{95} +(-10.8407 - 5.05512i) q^{97} +(0.392732 - 1.46570i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Character values

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

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	1.03355	−	0.0904240i	0.730831	−	0.0639395i	0.284335	−	0.958725i	$-0.408227\pi$
$2$	1.03355	−	0.0904240i	0.730831	−	0.0639395i	0.446496	+	0.894786i	$0.352672\pi$
$3$		0			0
$3$		0			0
$4$	−0.909563	+	0.160381i	−0.454782	+	0.0801903i
$5$	−1.76770	−	1.36939i	−0.790539	−	0.612411i
$5$	−1.76770	−	1.36939i	−0.790539	−	0.612411i
$6$		0			0
$7$	−2.38295	+	1.66856i	−0.900671	+	0.630657i	−0.929458	−	0.368929i	$-0.879725\pi$
$7$	−2.38295	+	1.66856i	−0.900671	+	0.630657i	0.0287865	+	0.999586i	$0.490836\pi$
$8$	−2.92987	+	0.785057i	−1.03587	+	0.277560i
$9$		0			0
$10$	−1.95083	−	1.25550i	−0.616908	−	0.397023i
$11$	0.357163	+	0.981298i	0.107689	+	0.295872i	0.981819	−	0.189819i	$-0.0607901\pi$
$11$	0.357163	+	0.981298i	0.107689	+	0.295872i	−0.874130	+	0.485691i	$0.838568\pi$
$12$		0			0
$13$	−0.102905	+	1.17621i	−0.0285408	+	0.326222i	0.968480	+	0.249091i	$0.0801317\pi$
$13$	−0.102905	+	1.17621i	−0.0285408	+	0.326222i	−0.997021	+	0.0771317i	$0.975424\pi$
$14$	−2.31203	+	1.94002i	−0.617915	+	0.518492i
$15$		0			0
$16$	−1.22140	+	0.444552i	−0.305349	+	0.111138i
$17$	−5.46688	−	1.46485i	−1.32591	−	0.355277i	−0.474723	−	0.880135i	$-0.657452\pi$
$17$	−5.46688	−	1.46485i	−1.32591	−	0.355277i	−0.851190	+	0.524858i	$0.824118\pi$
$18$		0			0
$19$	−3.77562	−	2.17985i	−0.866186	−	0.500093i	−0.000107079	−	1.00000i	$-0.500034\pi$
$19$	−3.77562	−	2.17985i	−0.866186	−	0.500093i	−0.866079	+	0.499907i	$0.833367\pi$
$20$	1.82746	+	0.962045i	0.408632	+	0.215120i
$21$		0			0
$22$	0.457879	+	0.981926i	0.0976202	+	0.209347i
$23$	−2.49254	+	3.55972i	−0.519731	+	0.742253i	−0.990123	−	0.140205i	$-0.955224\pi$
$23$	−2.49254	+	3.55972i	−0.519731	+	0.742253i	0.470391	+	0.882458i	$0.344113\pi$
$24$		0			0
$25$	1.24952	+	4.84135i	0.249905	+	0.968270i
$26$			1.22498i			0.240238i
$27$		0			0
$28$	1.89984	−	1.89984i	0.359036	−	0.359036i
$29$	5.99110	+	5.02713i	1.11252	+	0.933515i	0.998203	−	0.0599291i	$-0.0190875\pi$
$29$	5.99110	+	5.02713i	1.11252	+	0.933515i	0.114317	+	0.993444i	$0.463532\pi$
$30$		0			0
$31$	−1.88318	−	10.6800i	−0.338229	−	1.91819i	−0.392678	−	0.919676i	$-0.628451\pi$
$31$	−1.88318	−	10.6800i	−0.338229	−	1.91819i	0.0544490	−	0.998517i	$-0.482660\pi$
$32$	4.27590	−	1.99388i	0.755879	−	0.352472i
$33$		0			0
$34$	−5.78276	−	1.01966i	−0.991735	−	0.174870i
$35$	6.49726	+	0.313684i	1.09824	+	0.0530223i
$36$		0			0
$37$	1.84738	−	6.89452i	0.303708	−	1.13345i	−0.630344	−	0.776316i	$-0.717086\pi$
$37$	1.84738	−	6.89452i	0.303708	−	1.13345i	0.934052	−	0.357137i	$-0.116247\pi$
$38$	−4.09941	−	1.91158i	−0.665011	−	0.310100i
$39$		0			0
$40$	6.25419	+	2.62440i	0.988874	+	0.414955i
$41$	2.34606	+	2.79593i	0.366393	+	0.436650i	0.917471	−	0.397804i	$-0.130228\pi$
$41$	2.34606	+	2.79593i	0.366393	+	0.436650i	−0.551077	+	0.834454i	$0.685783\pi$
$42$		0			0
$43$	−0.986834	+	2.11627i	−0.150491	+	0.322729i	−0.967072	−	0.254501i	$-0.918089\pi$
$43$	−0.986834	+	2.11627i	−0.150491	+	0.322729i	0.816582	+	0.577230i	$0.195866\pi$
$44$	−0.482244	−	0.835270i	−0.0727010	−	0.125922i
$45$		0			0
$46$	−2.25429	+	3.90454i	−0.332377	+	0.575693i
$47$	0.209148	+	0.298694i	0.0305073	+	0.0435690i	0.834116	−	0.551589i	$-0.185978\pi$
$47$	0.209148	+	0.298694i	0.0305073	+	0.0435690i	−0.803609	+	0.595158i	$0.797089\pi$
$48$		0			0
$49$	0.500224	−	1.37435i	0.0714605	−	0.196336i
$50$	1.72922	+	4.89080i	0.244549	+	0.691664i
$51$		0			0
$52$	−0.0950427	−	1.08634i	−0.0131800	−	0.150649i
$53$	−1.16516	−	1.16516i	−0.160047	−	0.160047i	0.622540	−	0.782588i	$-0.286101\pi$
$53$	−1.16516	−	1.16516i	−0.160047	−	0.160047i	−0.782588	+	0.622540i	$0.786101\pi$
$54$		0			0
$55$	0.712425	−	2.22374i	0.0960634	−	0.299849i
$56$	5.67183	−	6.75943i	0.757930	−	0.903266i
$57$		0			0
$58$	6.64669	+	4.65406i	0.872753	+	0.611108i
$59$	−9.77378	−	3.55737i	−1.27244	−	0.463130i	−0.384514	−	0.923119i	$-0.625631\pi$
$59$	−9.77378	−	3.55737i	−1.27244	−	0.463130i	−0.887924	+	0.459990i	$0.847853\pi$
$60$		0			0
$61$	−0.654019	+	3.70913i	−0.0837385	+	0.474905i	0.913883	+	0.405977i	$0.133069\pi$
$61$	−0.654019	+	3.70913i	−0.0837385	+	0.474905i	−0.997622	+	0.0689275i	$0.978042\pi$
$62$	−2.91210	−	10.8681i	−0.369837	−	1.38025i
$63$		0			0
$64$	6.49036	−	3.74721i	0.811295	−	0.468401i
$65$	1.79260	−	1.93827i	0.222345	−	0.240413i
$66$		0			0
$67$	0.570007	+	0.0498691i	0.0696374	+	0.00609249i	0.121921	−	0.992540i	$-0.461094\pi$
$67$	0.570007	+	0.0498691i	0.0696374	+	0.00609249i	−0.0522838	+	0.998632i	$0.516650\pi$
$68$	5.20741	+	0.455589i	0.631491	+	0.0552483i
$69$		0			0
$70$	6.74362	−	0.263300i	0.806016	−	0.0314703i
$71$	−2.83490	+	1.63673i	−0.336441	+	0.194244i	−0.658697	−	0.752408i	$-0.728892\pi$
$71$	−2.83490	+	1.63673i	−0.336441	+	0.194244i	0.322256	+	0.946652i	$0.395559\pi$
$72$		0			0
$73$	3.56015	+	13.2867i	0.416684	+	1.55509i	0.781439	+	0.623982i	$0.214486\pi$
$73$	3.56015	+	13.2867i	0.416684	+	1.55509i	−0.364755	+	0.931104i	$0.618847\pi$
$74$	1.28593	−	7.29289i	0.149487	−	0.847782i
$75$		0			0
$76$	3.78377	+	1.37718i	0.434028	+	0.157973i
$77$	−2.48846	−	1.74244i	−0.283586	−	0.198569i
$78$		0			0
$79$	−2.43289	+	2.89941i	−0.273722	+	0.326209i	−0.885340	−	0.464944i	$-0.846074\pi$
$79$	−2.43289	+	2.89941i	−0.273722	+	0.326209i	0.611618	+	0.791153i	$0.290519\pi$
$80$	2.76783	+	0.886738i	0.309453	+	0.0991403i
$81$		0			0
$82$	2.67759	+	2.67759i	0.295691	+	0.295691i
$83$	0.416330	+	4.75867i	0.0456981	+	0.522332i	0.984200	+	0.177059i	$0.0566583\pi$
$83$	0.416330	+	4.75867i	0.0456981	+	0.522332i	−0.938502	+	0.345273i	$0.887786\pi$
$84$		0			0
$85$	7.65785	+	10.0757i	0.830611	+	1.09286i
$86$	−0.828582	+	2.27651i	−0.0893483	+	0.245482i
$87$		0			0
$88$	−1.81682	−	2.59468i	−0.193673	−	0.276594i
$89$	1.62360	−	2.81215i	0.172101	−	0.298087i	−0.767053	−	0.641583i	$-0.778278\pi$
$89$	1.62360	−	2.81215i	0.172101	−	0.298087i	0.939154	+	0.343496i	$0.111611\pi$
$90$		0			0
$91$	−1.71736	−	2.97456i	−0.180029	−	0.311819i
$92$	1.69622	−	3.63755i	0.176843	−	0.379241i
$93$		0			0
$94$	0.243174	+	0.289803i	0.0250815	+	0.0298909i
$95$	3.68908	+	9.02363i	0.378492	+	0.925805i
$96$		0			0
$97$	−10.8407	−	5.05512i	−1.10071	−	0.513270i	−0.214581	−	0.976706i	$-0.568839\pi$
$97$	−10.8407	−	5.05512i	−1.10071	−	0.513270i	−0.886130	+	0.463436i	$0.846616\pi$
$98$	0.392732	−	1.46570i	0.0396719	−	0.148058i
$99$		0			0
$100$	−1.91298	−	4.20312i	−0.191298	−	0.420312i
$101$	−0.264044	−	0.0465580i	−0.0262733	−	0.00463269i	0.160496	−	0.987036i	$-0.448691\pi$
$101$	−0.264044	−	0.0465580i	−0.0262733	−	0.00463269i	−0.186769	+	0.982404i	$0.559802\pi$
$102$		0			0
$103$	−11.5058	+	5.36526i	−1.13370	+	0.528655i	−0.896606	−	0.442830i	$-0.853974\pi$
$103$	−11.5058	+	5.36526i	−1.13370	+	0.528655i	−0.237099	+	0.971485i	$0.576197\pi$
$104$	−0.621894	−	3.52694i	−0.0609817	−	0.345845i
$105$		0			0
$106$	−1.30961	−	1.09890i	−0.127201	−	0.106734i
$107$	−5.03532	+	5.03532i	−0.486782	+	0.486782i	−0.907289	−	0.420507i	$-0.861852\pi$
$107$	−5.03532	+	5.03532i	−0.486782	+	0.486782i	0.420507	+	0.907289i	$0.361852\pi$
$108$		0			0
$109$		−	8.81333i		−	0.844164i	−0.906558	−	0.422082i	$-0.861299\pi$
$109$		−	8.81333i		−	0.844164i	0.906558	−	0.422082i	$-0.138701\pi$
$110$	0.535249	−	2.36277i	0.0510340	−	0.225281i
$111$		0			0
$112$	2.16877	−	3.09732i	0.204929	−	0.292669i
$113$	−0.0274297	−	0.0588232i	−0.00258037	−	0.00553362i	0.905013	−	0.425383i	$-0.139861\pi$
$113$	−0.0274297	−	0.0588232i	−0.00258037	−	0.00553362i	−0.907594	+	0.419849i	$0.862083\pi$
$114$		0			0
$115$	9.28073	−	2.87925i	0.865433	−	0.268491i
$116$	−6.25554	−	3.61164i	−0.580813	−	0.335332i
$117$		0			0
$118$	−10.4234	−	2.79294i	−0.959550	−	0.257111i
$119$	15.4715	−	5.63116i	1.41827	−	0.516208i
$120$		0			0
$121$	7.59111	−	6.36970i	0.690101	−	0.579063i
$122$	−0.340568	+	3.89271i	−0.0308336	+	0.352430i
$123$		0			0
$124$	3.42574	+	9.41215i	0.307641	+	0.845236i
$125$	4.42093	−	10.2691i	0.395420	−	0.918500i
$126$		0			0
$127$	−16.2081	+	4.34294i	−1.43823	+	0.385374i	−0.891915	−	0.452203i	$-0.850638\pi$
$127$	−16.2081	+	4.34294i	−1.43823	+	0.385374i	−0.546320	+	0.837577i	$0.683972\pi$
$128$	−1.36013	+	0.952371i	−0.120219	+	0.0841785i
$129$		0			0
$130$	1.67748	−	2.16540i	0.147125	−	0.189918i
$131$	3.72744	−	0.657248i	0.325668	−	0.0574240i	−0.00842419	−	0.999965i	$-0.502682\pi$
$131$	3.72744	−	0.657248i	0.325668	−	0.0574240i	0.334092	+	0.942541i	$0.391570\pi$
$132$		0			0
$133$	12.6343	−	1.10536i	1.09554	−	0.0958470i
$134$	0.593641			0.0512828
$135$		0			0
$136$	17.1673			1.47208
$137$	−21.5441	+	1.88486i	−1.84064	+	0.161035i	−0.953681	−	0.300821i	$-0.902739\pi$
$137$	−21.5441	+	1.88486i	−1.84064	+	0.161035i	−0.886955	+	0.461856i	$0.847184\pi$
$138$		0			0
$139$	−11.0217	+	1.94342i	−0.934847	+	0.164839i	−0.620265	−	0.784392i	$-0.712975\pi$
$139$	−11.0217	+	1.94342i	−0.934847	+	0.164839i	−0.314581	+	0.949231i	$0.601864\pi$
$140$	−5.95998	+	0.756718i	−0.503710	+	0.0639544i
$141$		0			0
$142$	−2.78201	+	1.94799i	−0.233461	+	0.163471i
$143$	−1.19097	+	0.319119i	−0.0995937	+	0.0266861i
$144$		0			0
$145$	−3.70635	−	17.0906i	−0.307796	−	1.41930i
$146$	4.88103	+	13.4105i	0.403957	+	1.10986i
$147$		0			0
$148$	−0.574563	+	6.56729i	−0.0472288	+	0.539828i
$149$	10.1272	−	8.49772i	0.829651	−	0.696160i	−0.125560	−	0.992086i	$-0.540073\pi$
$149$	10.1272	−	8.49772i	0.829651	−	0.696160i	0.955211	+	0.295926i	$0.0956282\pi$
$150$		0			0
$151$	11.4353	−	4.16211i	0.930591	−	0.338708i	0.168147	−	0.985762i	$-0.446222\pi$
$151$	11.4353	−	4.16211i	0.930591	−	0.338708i	0.762444	+	0.647054i	$0.223999\pi$
$152$	12.7734	+	3.42262i	1.03606	+	0.277611i
$153$		0			0
$154$	−2.72951	−	1.57588i	−0.219950	−	0.126988i
$155$	−11.2963	+	21.4579i	−0.907339	+	1.72354i
$156$		0			0
$157$	5.01098	+	10.7461i	0.399920	+	0.857631i	0.998403	+	0.0564955i	$0.0179927\pi$
$157$	5.01098	+	10.7461i	0.399920	+	0.857631i	−0.598483	+	0.801136i	$0.704230\pi$
$158$	−2.25234	+	3.21668i	−0.179187	+	0.255905i
$159$		0			0
$160$	−10.2889	−	2.33080i	−0.813410	−	0.184266i
$161$		−	12.6416i		−	0.996298i
$162$		0			0
$163$	−10.1170	+	10.1170i	−0.792424	+	0.792424i	−0.981888	−	0.189463i	$-0.939325\pi$
$163$	−10.1170	+	10.1170i	−0.792424	+	0.792424i	0.189463	+	0.981888i	$0.439325\pi$
$164$	−2.58230	−	2.16681i	−0.201644	−	0.169199i
$165$		0			0
$166$	0.860597	+	4.88069i	0.0667953	+	0.378815i
$167$	19.2590	−	8.98064i	1.49031	−	0.694943i	0.504593	−	0.863357i	$-0.331643\pi$
$167$	19.2590	−	8.98064i	1.49031	−	0.694943i	0.985716	+	0.168415i	$0.0538648\pi$
$168$		0			0
$169$	11.4296	+	2.01535i	0.879201	+	0.155027i
$170$	8.82587	+	9.72132i	0.676913	+	0.745591i
$171$		0			0
$172$	0.558179	−	2.08315i	0.0425608	−	0.158839i
$173$	−7.68830	−	3.58511i	−0.584530	−	0.272571i	0.107775	−	0.994175i	$-0.465627\pi$
$173$	−7.68830	−	3.58511i	−0.584530	−	0.272571i	−0.692306	+	0.721604i	$0.743405\pi$
$174$		0			0
$175$	−11.0556	−	9.45180i	−0.835728	−	0.714489i
$176$	−0.872476	−	1.03978i	−0.0657653	−	0.0783761i
$177$		0			0
$178$	1.42378	−	3.05331i	0.106717	−	0.228856i
$179$	6.71299	+	11.6272i	0.501753	+	0.869061i	0.999998	+	0.00202486i	$0.000644535\pi$
$179$	6.71299	+	11.6272i	0.501753	+	0.869061i	−0.498245	+	0.867036i	$0.666022\pi$
$180$		0			0
$181$	−9.97071	+	17.2698i	−0.741117	+	1.28365i	0.210870	+	0.977514i	$0.432370\pi$
$181$	−9.97071	+	17.2698i	−0.741117	+	1.28365i	−0.951987	+	0.306138i	$0.900963\pi$
$182$	−2.04395	−	2.91907i	−0.151508	−	0.216376i
$183$		0			0
$184$	4.50825	−	12.3863i	0.332353	−	0.913132i
$185$	−12.7069	+	9.65765i	−0.934232	+	0.710045i
$186$		0			0
$187$	−0.515118	−	5.88783i	−0.0376692	−	0.430560i
$188$	−0.238138	−	0.238138i	−0.0173680	−	0.0173680i
$189$		0			0
$190$	4.62881	+	8.99281i	0.335809	+	0.652407i
$191$	−0.583207	+	0.695039i	−0.0421994	+	0.0502912i	−0.786731	−	0.617296i	$-0.788228\pi$
$191$	−0.583207	+	0.695039i	−0.0421994	+	0.0502912i	0.744532	+	0.667587i	$0.232673\pi$
$192$		0			0
$193$	−6.05638	−	4.24072i	−0.435948	−	0.305254i	0.334923	−	0.942245i	$-0.391290\pi$
$193$	−6.05638	−	4.24072i	−0.435948	−	0.305254i	−0.770871	+	0.636992i	$0.780179\pi$
$194$	−11.6616	−	4.24447i	−0.837252	−	0.304735i
$195$		0			0
$196$	−0.234566	+	1.33029i	−0.0167547	+	0.0950205i
$197$	4.43194	+	16.5402i	0.315763	+	1.17844i	0.923277	+	0.384134i	$0.125500\pi$
$197$	4.43194	+	16.5402i	0.315763	+	1.17844i	−0.607515	+	0.794309i	$0.707833\pi$
$198$		0			0
$199$	0.887783	−	0.512562i	0.0629332	−	0.0363345i	−0.468203	−	0.883621i	$-0.655098\pi$
$199$	0.887783	−	0.512562i	0.0629332	−	0.0363345i	0.531136	+	0.847286i	$0.321765\pi$
$200$	−7.46168	−	13.2036i	−0.527621	−	0.933636i
$201$		0			0
$202$	−0.277113	−	0.0242442i	−0.0194976	−	0.00170582i
$203$	−22.6646	−	1.98289i	−1.59074	−	0.139172i
$204$		0			0
$205$	−0.318408	−	8.15504i	−0.0222386	−	0.569573i
$206$	−11.4067	+	6.58568i	−0.794745	+	0.458846i
$207$		0			0
$208$	−0.397199	−	1.48237i	−0.0275408	−	0.102784i
$209$	0.790574	−	4.48357i	0.0546852	−	0.310135i
$210$		0			0
$211$	−9.20369	−	3.34987i	−0.633608	−	0.230614i	0.00519293	−	0.999987i	$-0.498347\pi$
$211$	−9.20369	−	3.34987i	−0.633608	−	0.230614i	−0.638801	+	0.769372i	$0.720569\pi$
$212$	1.24666	+	0.872919i	0.0856208	+	0.0599523i
$213$		0			0
$214$	−4.74895	+	5.65957i	−0.324631	+	0.386880i
$215$	4.64244	−	2.38957i	0.316611	−	0.162967i
$216$		0			0
$217$	22.3078	+	22.3078i	1.51435	+	1.51435i
$218$	−0.796937	−	9.10903i	−0.0539754	−	0.616942i
$219$		0			0
$220$	−0.291352	+	2.13689i	−0.0196429	+	0.144069i
$221$	2.28554	−	6.27947i	0.153742	−	0.422403i
$222$		0			0
$223$	−5.62275	−	8.03011i	−0.376527	−	0.537736i	0.585507	−	0.810668i	$-0.300896\pi$
$223$	−5.62275	−	8.03011i	−0.376527	−	0.537736i	−0.962033	+	0.272932i	$0.912007\pi$
$224$	−6.86234	+	11.8859i	−0.458510	+	0.794162i
$225$		0			0
$226$	−0.0336690	−	0.0583165i	−0.00223963	−	0.00387916i
$227$	−7.23760	+	15.5211i	−0.480376	+	1.03017i	0.505520	+	0.862815i	$0.331301\pi$
$227$	−7.23760	+	15.5211i	−0.480376	+	1.03017i	−0.985897	+	0.167356i	$0.946477\pi$
$228$		0			0
$229$	−11.7568	−	14.0112i	−0.776912	−	0.925888i	0.221877	−	0.975075i	$-0.428782\pi$
$229$	−11.7568	−	14.0112i	−0.776912	−	0.925888i	−0.998790	+	0.0491866i	$0.984337\pi$
$230$	9.33176	−	3.81505i	0.615318	−	0.251557i
$231$		0			0
$232$	−21.4998	−	10.0255i	−1.41153	−	0.658207i
$233$	1.27701	−	4.76585i	0.0836594	−	0.312221i	−0.911398	−	0.411527i	$-0.864996\pi$
$233$	1.27701	−	4.76585i	0.0836594	−	0.312221i	0.995057	+	0.0993059i	$0.0316622\pi$
$234$		0			0
$235$	0.0393191	−	0.814406i	0.00256489	−	0.0531260i
$236$	9.46041	+	1.66812i	0.615820	+	0.108586i
$237$		0			0
$238$	15.4814	−	7.21909i	1.00351	−	0.467944i
$239$	−1.04890	−	5.94858i	−0.0678474	−	0.384782i	−0.999756	−	0.0220886i	$-0.992968\pi$
$239$	−1.04890	−	5.94858i	−0.0678474	−	0.384782i	0.931909	−	0.362693i	$-0.118143\pi$
$240$		0			0
$241$	−13.1764	−	11.0563i	−0.848766	−	0.712199i	0.110751	−	0.993848i	$-0.464674\pi$
$241$	−13.1764	−	11.0563i	−0.848766	−	0.712199i	−0.959518	+	0.281649i	$0.909119\pi$
$242$	7.26983	−	7.26983i	0.467322	−	0.467322i
$243$		0			0
$244$		−	3.47858i		−	0.222693i
$245$	−2.76627	+	1.74444i	−0.176731	+	0.111448i
$246$		0			0
$247$	2.95250	−	4.21661i	0.187863	−	0.268296i
$248$	13.9019	+	29.8128i	0.882773	+	1.89311i
$249$		0			0
$250$	3.64068	−	11.0134i	0.230257	−	0.696552i
$251$	0.245642	+	0.141822i	0.0155048	+	0.00895170i	0.507732	−	0.861515i	$-0.330484\pi$
$251$	0.245642	+	0.141822i	0.0155048	+	0.00895170i	−0.492228	+	0.870467i	$0.663817\pi$
$252$		0			0
$253$	−4.38339	−	1.17453i	−0.275582	−	0.0738419i
$254$	−16.3592	+	5.95426i	−1.02647	+	0.373603i
$255$		0			0
$256$	−12.8018	+	10.7420i	−0.800110	+	0.671372i
$257$	0.568503	−	6.49802i	0.0354623	−	0.405335i	−0.957630	−	0.288001i	$-0.907009\pi$
$257$	0.568503	−	6.49802i	0.0354623	−	0.405335i	0.993092	−	0.117335i	$-0.0374350\pi$
$258$		0			0
$259$	7.10171	+	19.5118i	0.441279	+	1.21240i
$260$	−1.31962	+	2.05048i	−0.0818396	+	0.127165i
$261$		0			0
$262$	3.79307	−	1.01635i	0.234336	−	0.0627903i
$263$	3.72625	−	2.60915i	0.229770	−	0.160887i	−0.453022	−	0.891499i	$-0.649654\pi$
$263$	3.72625	−	2.60915i	0.229770	−	0.160887i	0.682792	+	0.730612i	$0.260765\pi$
$264$		0			0
$265$	0.464091	+	3.65522i	0.0285089	+	0.224538i
$266$	12.9583	−	2.28489i	0.794523	−	0.140096i
$267$		0			0
$268$	−0.526455	+	0.0460589i	−0.0321584	+	0.00281349i
$269$	−7.68259			−0.468416			−0.234208	−	0.972187i	$-0.575250\pi$
$269$	−7.68259			−0.468416			−0.234208	+	0.972187i	$0.575250\pi$
$270$		0			0
$271$	18.8470			1.14487			0.572437	−	0.819949i	$-0.305998\pi$
$271$	18.8470			1.14487			0.572437	+	0.819949i	$0.305998\pi$
$272$	7.32843	−	0.641154i	0.444351	−	0.0388757i
$273$		0			0
$274$	−22.0965	+	3.89621i	−1.33490	+	0.235378i
$275$	−4.30452	+	2.95531i	−0.259573	+	0.178212i
$276$		0			0
$277$	8.10294	−	5.67374i	0.486858	−	0.340902i	−0.304235	−	0.952597i	$-0.598401\pi$
$277$	8.10294	−	5.67374i	0.486858	−	0.340902i	0.791094	+	0.611695i	$0.209512\pi$
$278$	−11.2157	+	3.00525i	−0.672675	+	0.180243i
$279$		0			0
$280$	−19.2824	+	4.18167i	−1.15234	+	0.249902i
$281$	1.61241	+	4.43006i	0.0961883	+	0.264275i	0.978450	−	0.206484i	$-0.0662022\pi$
$281$	1.61241	+	4.43006i	0.0961883	+	0.264275i	−0.882262	+	0.470759i	$0.843980\pi$
$282$		0			0
$283$	0.00130413	−	0.0149063i	7.75226e−5	−	0.000886087i	−0.996156	−	0.0875988i	$-0.972081\pi$
$283$	0.00130413	−	0.0149063i	7.75226e−5	−	0.000886087i	0.996233	+	0.0867127i	$0.0276362\pi$
$284$	2.31602	−	1.94337i	0.137431	−	0.115318i
$285$		0			0
$286$	−1.20207	+	0.437518i	−0.0710799	+	0.0258710i
$287$	−10.2557	−	2.74801i	−0.605376	−	0.162210i
$288$		0			0
$289$	13.0186	+	7.51627i	0.765798	+	0.442134i
$290$	−5.37611	−	17.3289i	−0.315696	−	1.01759i
$291$		0			0
$292$	−5.36910	−	11.5141i	−0.314203	−	0.673810i
$293$	13.1517	−	18.7826i	0.768330	−	1.09729i	−0.224110	−	0.974564i	$-0.571948\pi$
$293$	13.1517	−	18.7826i	0.768330	−	1.09729i	0.992441	−	0.122726i	$-0.0391636\pi$
$294$		0			0
$295$	12.4057	+	19.6725i	0.722286	+	1.14538i
$296$			21.6504i			1.25840i
$297$		0			0
$298$	9.69857	−	9.69857i	0.561823	−	0.561823i
$299$	−3.93049	−	3.29807i	−0.227306	−	0.190733i
$300$		0			0
$301$	−1.17955	−	6.68957i	−0.0679882	−	0.385580i
$302$	11.4426	−	5.33578i	0.658448	−	0.307040i
$303$		0			0
$304$	5.58058	+	0.984008i	0.320068	+	0.0564367i
$305$	6.23536	−	5.66101i	0.357036	−	0.324149i
$306$		0			0
$307$	−7.06051	+	26.3502i	−0.402965	+	1.50388i	0.404814	+	0.914399i	$0.367336\pi$
$307$	−7.06051	+	26.3502i	−0.402965	+	1.50388i	−0.807779	+	0.589486i	$0.799330\pi$
$308$	2.54286	+	1.18576i	0.144893	+	0.0675647i
$309$		0			0
$310$	−9.73498	+	23.1993i	−0.552910	+	1.31763i
$311$	−20.3862	−	24.2954i	−1.15600	−	1.37766i	−0.913162	−	0.407596i	$-0.866367\pi$
$311$	−20.3862	−	24.2954i	−1.15600	−	1.37766i	−0.242835	−	0.970068i	$-0.578077\pi$
$312$		0			0
$313$	4.83829	−	10.3757i	0.273476	−	0.586472i	−0.720820	−	0.693122i	$-0.756235\pi$
$313$	4.83829	−	10.3757i	0.273476	−	0.586472i	0.994297	+	0.106650i	$0.0340125\pi$
$314$	6.15081	+	10.6535i	0.347110	+	0.601213i
$315$		0			0
$316$	1.74786	−	3.02739i	0.0983249	−	0.170304i
$317$	7.17947	+	10.2533i	0.403239	+	0.575885i	0.968496	−	0.249030i	$-0.0801117\pi$
$317$	7.17947	+	10.2533i	0.403239	+	0.575885i	−0.565257	+	0.824915i	$0.691223\pi$
$318$		0			0
$319$	−2.79331	+	7.67456i	−0.156395	+	0.429693i
$320$	−16.6044	−	2.26391i	−0.928214	−	0.126556i
$321$		0			0
$322$	−1.14311	−	13.0658i	−0.0637028	−	0.728126i
$323$	17.4477	+	17.4477i	0.970816	+	0.970816i
$324$		0			0
$325$	−5.82304	+	0.971504i	−0.323004	+	0.0538893i
$326$	−9.54162	+	11.3713i	−0.528461	+	0.629796i
$327$		0			0
$328$	−9.06863	−	6.34992i	−0.500731	−	0.350616i
$329$	−0.996777	−	0.362797i	−0.0549541	−	0.0200017i
$330$		0			0
$331$	−4.38923	+	24.8926i	−0.241254	+	1.36822i	0.587780	+	0.809021i	$0.300002\pi$
$331$	−4.38923	+	24.8926i	−0.241254	+	1.36822i	−0.829034	+	0.559199i	$0.811109\pi$
$332$	−1.14188	−	4.26154i	−0.0626686	−	0.233883i
$333$		0			0
$334$	19.0931	−	11.0234i	1.04473	−	0.603175i
$335$	−0.939311	−	0.868717i	−0.0513200	−	0.0474631i
$336$		0			0
$337$	−1.72746	−	0.151133i	−0.0941006	−	0.00823274i	0.0400082	−	0.999199i	$-0.487262\pi$
$337$	−1.72746	−	0.151133i	−0.0941006	−	0.00823274i	−0.134109	+	0.990967i	$0.542817\pi$
$338$	11.9953	+	1.04946i	0.652460	+	0.0570829i
$339$		0			0
$340$	−8.58125	−	7.93633i	−0.465384	−	0.430408i
$341$	9.80770	−	5.66248i	0.531117	−	0.306640i
$342$		0			0
$343$	−4.16923	−	15.5598i	−0.225118	−	0.840150i
$344$	1.22990	−	6.97513i	0.0663120	−	0.376074i
$345$		0			0
$346$	−8.27043	−	3.01019i	−0.444621	−	0.161829i
$347$	−8.10639	−	5.67616i	−0.435174	−	0.304712i	0.335385	−	0.942081i	$-0.391134\pi$
$347$	−8.10639	−	5.67616i	−0.435174	−	0.304712i	−0.770559	+	0.637369i	$0.780023\pi$
$348$		0			0
$349$	19.9263	−	23.7472i	1.06663	−	1.27116i	0.105689	−	0.994399i	$-0.466295\pi$
$349$	19.9263	−	23.7472i	1.06663	−	1.27116i	0.960939	−	0.276759i	$-0.0892603\pi$
$350$	−12.2812	−	8.76923i	−0.656460	−	0.468735i
$351$		0			0
$352$	3.48379	+	3.48379i	0.185687	+	0.185687i
$353$	−0.319565	−	3.65264i	−0.0170087	−	0.194411i	−0.999945	−	0.0104654i	$-0.996669\pi$
$353$	−0.319565	−	3.65264i	−0.0170087	−	0.194411i	0.982937	−	0.183945i	$-0.0588869\pi$
$354$		0			0
$355$	7.25257	+	0.988845i	0.384927	+	0.0524825i
$356$	−1.02575	+	2.81822i	−0.0543646	+	0.149365i
$357$		0			0
$358$	7.98960	+	11.4103i	0.422264	+	0.603055i
$359$	−3.73590	+	6.47077i	−0.197173	+	0.341514i	−0.947611	−	0.319427i	$-0.896509\pi$
$359$	−3.73590	+	6.47077i	−0.197173	+	0.341514i	0.750438	+	0.660941i	$0.229843\pi$
$360$		0			0
$361$	0.00352408	+	0.00610389i	0.000185478	+	0.000321258i
$362$	−8.74364	+	18.7508i	−0.459555	+	0.985520i
$363$		0			0
$364$	2.03911	+	2.43012i	0.106878	+	0.127373i
$365$	11.9014	−	28.3621i	0.622947	−	1.48454i
$366$		0			0
$367$	15.3011	+	7.13502i	0.798711	+	0.372445i	0.778733	−	0.627356i	$-0.215863\pi$
$367$	15.3011	+	7.13502i	0.798711	+	0.372445i	0.0199776	+	0.999800i	$0.493640\pi$
$368$	1.46190	−	5.45590i	0.0762070	−	0.284408i
$369$		0			0
$370$	−12.2600	+	11.1307i	−0.637366	+	0.578657i
$371$	4.72067	+	0.832381i	0.245085	+	0.0432151i
$372$		0			0
$373$	−1.92488	+	0.897584i	−0.0996663	+	0.0464752i	−0.471812	−	0.881699i	$-0.656400\pi$
$373$	−1.92488	+	0.897584i	−0.0996663	+	0.0464752i	0.372146	+	0.928174i	$0.378622\pi$
$374$	−1.06480	−	6.03879i	−0.0550596	−	0.312259i
$375$		0			0
$376$	−0.847268	−	0.710942i	−0.0436945	−	0.0366640i
$377$	−6.52949	+	6.52949i	−0.336286	+	0.336286i
$378$		0			0
$379$			9.60506i			0.493379i	0.969095	+	0.246689i	$0.0793427\pi$
$379$			9.60506i			0.493379i	−0.969095	+	0.246689i	$0.920657\pi$
$380$	−4.80267	−	7.61591i	−0.246372	−	0.390688i
$381$		0			0
$382$	−0.539926	+	0.771094i	−0.0276250	+	0.0394526i
$383$	0.0510389	+	0.109453i	0.00260797	+	0.00559281i	0.907607	−	0.419820i	$-0.137907\pi$
$383$	0.0510389	+	0.109453i	0.00260797	+	0.00559281i	−0.904999	+	0.425413i	$0.860129\pi$
$384$		0			0
$385$	2.01276	+	6.48778i	0.102580	+	0.330648i
$386$	−6.64304	−	3.83536i	−0.338122	−	0.195215i
$387$		0			0
$388$	10.6711	+	2.85931i	0.541742	+	0.145159i
$389$	24.1005	−	8.77187i	1.22194	−	0.444752i	0.351113	−	0.936333i	$-0.385803\pi$
$389$	24.1005	−	8.77187i	1.22194	−	0.444752i	0.870832	+	0.491581i	$0.163581\pi$
$390$		0			0
$391$	18.8409	−	15.8094i	0.952825	−	0.799515i
$392$	−0.386646	+	4.41938i	−0.0195286	+	0.223213i
$393$		0			0
$394$	6.07627	+	16.6944i	0.306118	+	0.841053i
$395$	8.27106	−	1.79370i	0.416162	−	0.0902507i
$396$		0			0
$397$	25.5064	−	6.83441i	1.28013	−	0.343009i	0.446225	−	0.894921i	$-0.352768\pi$
$397$	25.5064	−	6.83441i	1.28013	−	0.343009i	0.833903	+	0.551911i	$0.186101\pi$
$398$	0.871221	−	0.610036i	0.0436704	−	0.0305783i
$399$		0			0
$400$	−3.67840	−	5.35773i	−0.183920	−	0.267887i
$401$	33.5008	−	5.90709i	1.67295	−	0.294986i	0.744826	−	0.667259i	$-0.232532\pi$
$401$	33.5008	−	5.90709i	1.67295	−	0.294986i	0.928124	+	0.372272i	$0.121421\pi$
$402$		0			0
$403$	12.7558	−	1.11599i	0.635411	−	0.0555912i
$404$	0.247631			0.0123201
$405$		0			0
$406$	−23.6043			−1.17146
$407$	7.42540	−	0.649638i	0.368063	−	0.0322014i
$408$		0			0
$409$	33.1027	−	5.83690i	1.63682	−	0.288616i	0.721826	−	0.692075i	$-0.243303\pi$
$409$	33.1027	−	5.83690i	1.63682	−	0.288616i	0.914998	+	0.403458i	$0.132192\pi$
$410$	−1.06650	−	8.39986i	−0.0526708	−	0.414840i
$411$		0			0
$412$	9.60481	−	6.72536i	0.473195	−	0.331335i
$413$	29.2261	−	7.83112i	1.43812	−	0.385344i
$414$		0			0
$415$	5.78055	−	8.98202i	0.283756	−	0.440910i
$416$	1.90522	+	5.23454i	0.0934110	+	0.256645i
$417$		0			0
$418$	0.411677	−	4.70549i	0.0201358	−	0.230153i
$419$	−23.6855	+	19.8745i	−1.15711	+	0.970932i	−0.999862	−	0.0166274i	$-0.994707\pi$
$419$	−23.6855	+	19.8745i	−1.15711	+	0.970932i	−0.157249	+	0.987559i	$0.550263\pi$
$420$		0			0
$421$	−13.7828	+	5.01653i	−0.671732	+	0.244490i	−0.655293	−	0.755374i	$-0.727455\pi$
$421$	−13.7828	+	5.01653i	−0.671732	+	0.244490i	−0.0164386	+	0.999865i	$0.505233\pi$
$422$	−9.81539	−	2.63003i	−0.477806	−	0.128028i
$423$		0			0
$424$	4.32849	+	2.49906i	0.210210	+	0.121365i
$425$	0.260840	−	28.2974i	0.0126526	−	1.37263i
$426$		0			0
$427$	−4.63041	−	9.92994i	−0.224081	−	0.480543i
$428$	3.77237	−	5.38751i	0.182345	−	0.260415i
$429$		0			0
$430$	4.58212	−	2.88953i	0.220970	−	0.139346i
$431$		−	30.3267i		−	1.46078i	−0.683028	−	0.730392i	$-0.739337\pi$
$431$		−	30.3267i		−	1.46078i	0.683028	−	0.730392i	$-0.260663\pi$
$432$		0			0
$433$	5.35178	−	5.35178i	0.257190	−	0.257190i	−0.566720	−	0.823910i	$-0.691788\pi$
$433$	5.35178	−	5.35178i	0.257190	−	0.257190i	0.823910	+	0.566720i	$0.191788\pi$
$434$	25.0735	+	21.0391i	1.20356	+	1.00991i
$435$		0			0
$436$	1.41349	+	8.01628i	0.0676938	+	0.383910i
$437$	17.1706	−	8.00677i	0.821380	−	0.383016i
$438$		0			0
$439$	−9.78003	−	1.72448i	−0.466775	−	0.0823051i	−0.0646863	−	0.997906i	$-0.520605\pi$
$439$	−9.78003	−	1.72448i	−0.466775	−	0.0823051i	−0.402089	+	0.915601i	$0.631716\pi$
$440$	−0.341556	+	7.07456i	−0.0162830	+	0.337266i
$441$		0			0
$442$	1.79441	−	6.69682i	0.0853513	−	0.318535i
$443$	−8.40263	−	3.91821i	−0.399221	−	0.186160i	0.212630	−	0.977133i	$-0.431797\pi$
$443$	−8.40263	−	3.91821i	−0.399221	−	0.186160i	−0.611851	+	0.790973i	$0.709575\pi$
$444$		0			0
$445$	−6.72097	+	2.74770i	−0.318605	+	0.130253i
$446$	−6.53751	−	7.79110i	−0.309560	−	0.368919i
$447$		0			0
$448$	−9.21376	+	19.7590i	−0.435309	+	0.933524i
$449$	15.0787	+	26.1171i	0.711609	+	1.23254i	0.964253	+	0.264984i	$0.0853667\pi$
$449$	15.0787	+	26.1171i	0.711609	+	1.23254i	−0.252644	+	0.967559i	$0.581300\pi$
$450$		0			0
$451$	−1.90571	+	3.30079i	−0.0897364	+	0.155428i
$452$	0.0343832	+	0.0491042i	0.00161725	+	0.00230967i
$453$		0			0
$454$	−6.07695	+	16.6963i	−0.285206	+	0.783596i
$455$	−1.03756	+	7.60987i	−0.0486416	+	0.356756i
$456$		0			0
$457$	2.64140	+	30.1913i	0.123559	+	1.41229i	0.764462	+	0.644669i	$0.223005\pi$
$457$	2.64140	+	30.1913i	0.123559	+	1.41229i	−0.640902	+	0.767622i	$0.721440\pi$
$458$	−13.4182	−	13.4182i	−0.626993	−	0.626993i
$459$		0			0
$460$	−7.97964	+	4.10731i	−0.372052	+	0.191504i
$461$	−8.35560	+	9.95782i	−0.389159	+	0.463782i	−0.924683	−	0.380738i	$-0.875670\pi$
$461$	−8.35560	+	9.95782i	−0.389159	+	0.463782i	0.535524	+	0.844520i	$0.320114\pi$
$462$		0			0
$463$	22.5069	+	15.7595i	1.04598	+	0.732405i	0.964450	−	0.264266i	$-0.0851295\pi$
$463$	22.5069	+	15.7595i	1.04598	+	0.732405i	0.0815330	+	0.996671i	$0.474018\pi$
$464$	−9.55234	−	3.47677i	−0.443456	−	0.161405i
$465$		0			0
$466$	0.888904	−	5.04122i	0.0411777	−	0.233530i
$467$	−7.76986	−	28.9975i	−0.359546	−	1.34184i	−0.874666	−	0.484727i	$-0.838919\pi$
$467$	−7.76986	−	28.9975i	−0.359546	−	1.34184i	0.515119	−	0.857118i	$-0.327748\pi$
$468$		0			0
$469$	−1.44151	+	0.832256i	−0.0665627	+	0.0384300i
$470$	−0.0330036	−	0.845286i	−0.00152234	−	0.0389901i
$471$		0			0
$472$	31.4287	+	2.74965i	1.44662	+	0.126563i
$473$	−2.42915	−	0.212523i	−0.111693	−	0.00977184i
$474$		0			0
$475$	5.83572	−	21.0029i	0.267761	−	0.963678i
$476$	−13.1692	+	7.60323i	−0.603608	+	0.348493i
$477$		0			0
$478$	−1.62198	−	6.05332i	−0.0741878	−	0.276872i
$479$	−1.81506	+	10.2937i	−0.0829324	+	0.470333i	0.914851	+	0.403791i	$0.132308\pi$
$479$	−1.81506	+	10.2937i	−0.0829324	+	0.470333i	−0.997784	+	0.0665419i	$0.978803\pi$
$480$		0			0
$481$	7.91931	+	2.88239i	0.361090	+	0.131426i
$482$	−14.6182	−	10.2358i	−0.665843	−	0.466228i
$483$		0			0
$484$	−5.88302	+	7.01111i	−0.267410	+	0.318687i
$485$	12.2407	+	23.7812i	0.555823	+	1.07985i
$486$		0			0
$487$	−13.7181	−	13.7181i	−0.621625	−	0.621625i	0.324322	−	0.945947i	$-0.394864\pi$
$487$	−13.7181	−	13.7181i	−0.621625	−	0.621625i	−0.945947	+	0.324322i	$0.894864\pi$
$488$	−0.995683	−	11.3807i	−0.0450725	−	0.515181i
$489$		0			0
$490$	−2.70135	+	2.05311i	−0.122034	+	0.0927499i
$491$	−14.3153	+	39.3310i	−0.646040	+	1.77498i	−0.0141799	+	0.999899i	$0.504514\pi$
$491$	−14.3153	+	39.3310i	−0.646040	+	1.77498i	−0.631861	+	0.775082i	$0.717708\pi$
$492$		0			0
$493$	−25.3887	−	36.2588i	−1.14345	−	1.63301i
$494$	2.67028	−	4.62506i	0.120141	−	0.208091i
$495$		0			0
$496$	7.04794	+	12.2074i	0.316462	+	0.548128i
$497$	4.02444	−	8.63045i	0.180521	−	0.387129i
$498$		0			0
$499$	−17.0051	−	20.2659i	−0.761253	−	0.907226i	0.236674	−	0.971589i	$-0.423943\pi$
$499$	−17.0051	−	20.2659i	−0.761253	−	0.907226i	−0.997927	+	0.0643635i	$0.979498\pi$
$500$	−2.37415	+	10.0495i	−0.106175	+	0.449426i
$501$		0			0
$502$	0.266708	+	0.124368i	0.0119038	+	0.00555082i
$503$	6.58100	−	24.5606i	0.293432	−	1.09510i	−0.649023	−	0.760769i	$-0.724822\pi$
$503$	6.58100	−	24.5606i	0.293432	−	1.09510i	0.942455	−	0.334334i	$-0.108511\pi$
$504$		0			0
$505$	0.402993	+	0.443880i	0.0179330	+	0.0197524i
$506$	−4.63667	−	0.817570i	−0.206125	−	0.0363454i
$507$		0			0
$508$	14.0458	−	6.54964i	0.623180	−	0.290593i
$509$	5.29524	+	30.0308i	0.234707	+	1.33109i	0.843229	+	0.537554i	$0.180652\pi$
$509$	5.29524	+	30.0308i	0.234707	+	1.33109i	−0.608522	+	0.793537i	$0.708237\pi$
$510$		0			0
$511$	−30.6533	−	25.7211i	−1.35602	−	1.13784i
$512$	−9.91177	+	9.91177i	−0.438043	+	0.438043i
$513$		0			0
$514$		−	6.76745i		−	0.298499i
$515$	27.6860	+	6.27185i	1.21999	+	0.276371i
$516$		0			0
$517$	−0.218408	+	0.311918i	−0.00960556	+	0.0137182i
$518$	9.10432	+	19.5243i	0.400021	+	0.857847i
$519$		0			0
$520$	−3.73044	+	7.08618i	−0.163591	+	0.310750i
$521$	1.09146	+	0.630155i	0.0478178	+	0.0276076i	0.523718	−	0.851892i	$-0.324544\pi$
$521$	1.09146	+	0.630155i	0.0478178	+	0.0276076i	−0.475901	+	0.879499i	$0.657878\pi$
$522$		0			0
$523$	−9.13037	−	2.44648i	−0.399243	−	0.106977i	0.0536101	−	0.998562i	$-0.482927\pi$
$523$	−9.13037	−	2.44648i	−0.399243	−	0.106977i	−0.452853	+	0.891585i	$0.649594\pi$
$524$	−3.28493	+	1.19562i	−0.143503	+	0.0522308i
$525$		0			0
$526$	3.61534	−	3.03363i	0.157636	−	0.132272i
$527$	−5.34950	+	61.1451i	−0.233028	+	2.66352i
$528$		0			0
$529$	1.40762	+	3.86740i	0.0612007	+	0.168148i
$530$	0.810182	+	3.73589i	0.0351920	+	0.162277i
$531$		0			0
$532$	−11.3144	+	3.03170i	−0.490544	+	0.131441i
$533$	−3.53002	+	2.47175i	−0.152902	+	0.107063i
$534$		0			0
$535$	15.7963	−	2.00560i	0.682932	−	0.0867096i
$536$	−1.70920	+	0.301378i	−0.0738261	+	0.0130175i
$537$		0			0
$538$	−7.94036	+	0.694691i	−0.342333	+	0.0299503i
$539$	1.52731			0.0657859
$540$		0			0
$541$	−14.5318			−0.624771			−0.312385	−	0.949955i	$-0.601128\pi$
$541$	−14.5318			−0.624771			−0.312385	+	0.949955i	$0.601128\pi$
$542$	19.4793	−	1.70422i	0.836710	−	0.0732026i
$543$		0			0
$544$	−26.2966	+	4.63679i	−1.12746	+	0.198801i
$545$	−12.0689	+	15.5793i	−0.516976	+	0.667345i
$546$		0			0
$547$	−11.9957	+	8.39950i	−0.512900	+	0.359136i	−0.801193	−	0.598406i	$-0.795801\pi$
$547$	−11.9957	+	8.39950i	−0.512900	+	0.359136i	0.288293	+	0.957542i	$0.406912\pi$
$548$	19.2934	−	5.16965i	0.824174	−	0.220837i
$549$		0			0
$550$	−4.18172	+	3.44369i	−0.178309	+	0.146840i
$551$	−11.6617	−	32.0403i	−0.496805	−	1.36496i
$552$		0			0
$553$	0.959627	−	10.9686i	0.0408075	−	0.466432i
$554$	7.86176	−	6.59680i	0.334014	−	0.280271i
$555$		0			0
$556$	9.71323	−	3.53533i	0.411933	−	0.149931i
$557$	−3.61631	−	0.968988i	−0.153228	−	0.0410573i	0.181390	−	0.983411i	$-0.441941\pi$
$557$	−3.61631	−	0.968988i	−0.153228	−	0.0410573i	−0.334618	+	0.942354i	$0.608607\pi$
$558$		0			0
$559$	−2.38763	−	1.37850i	−0.100986	−	0.0583044i
$560$	−8.07518	+	2.50524i	−0.341239	+	0.105866i
$561$		0			0
$562$	2.06709	+	4.43289i	0.0871950	+	0.186990i
$563$	5.55357	−	7.93132i	0.234055	−	0.334265i	−0.684893	−	0.728644i	$-0.740151\pi$
$563$	5.55357	−	7.93132i	0.234055	−	0.334265i	0.918948	+	0.394378i	$0.129040\pi$
$564$		0			0
$565$	−0.0320646	+	0.141544i	−0.00134897	+	0.00595479i
$566$		−	0.0155243i		−	0.000652537i
$567$		0			0
$568$	7.02097	−	7.02097i	0.294593	−	0.294593i
$569$	−29.7838	−	24.9915i	−1.24860	−	1.04770i	−0.996801	−	0.0799199i	$-0.974534\pi$
$569$	−29.7838	−	24.9915i	−1.24860	−	1.04770i	−0.251799	−	0.967780i	$-0.581022\pi$
$570$		0			0
$571$	−1.13871	−	6.45794i	−0.0476535	−	0.270256i	0.951666	−	0.307134i	$-0.0993700\pi$
$571$	−1.13871	−	6.45794i	−0.0476535	−	0.270256i	−0.999320	+	0.0368775i	$0.988259\pi$
$572$	1.03208	−	0.481267i	0.0431534	−	0.0201228i
$573$		0			0
$574$	−10.8483	−	1.91285i	−0.452800	−	0.0798408i
$575$	−20.3484	−	7.61933i	−0.848585	−	0.317748i
$576$		0			0
$577$	2.53716	−	9.46880i	0.105623	−	0.394191i	−0.892792	−	0.450469i	$-0.851257\pi$
$577$	2.53716	−	9.46880i	0.105623	−	0.394191i	0.998415	+	0.0562782i	$0.0179234\pi$
$578$	14.1350	+	6.59126i	0.587939	+	0.274160i
$579$		0			0
$580$	6.11217	+	14.9506i	0.253794	+	0.620790i
$581$	−8.93223	−	10.6450i	−0.370571	−	0.441630i
$582$		0			0
$583$	0.727218	−	1.55952i	0.0301183	−	0.0645888i
$584$	−20.8616	−	36.1333i	−0.863258	−	1.49521i
$585$		0			0
$586$	11.8946	−	20.6020i	0.491360	−	0.851060i
$587$	10.1521	+	14.4987i	0.419023	+	0.598427i	0.972061	−	0.234729i	$-0.0754204\pi$
$587$	10.1521	+	14.4987i	0.419023	+	0.598427i	−0.553038	+	0.833156i	$0.686531\pi$
$588$		0			0
$589$	−16.1708	+	44.4288i	−0.666305	+	1.83066i
$590$	14.6008	+	19.2108i	0.601104	+	0.790895i
$591$		0			0
$592$	0.808588	+	9.24221i	0.0332328	+	0.379852i
$593$	−3.34033	−	3.34033i	−0.137171	−	0.137171i	0.635187	−	0.772358i	$-0.280923\pi$
$593$	−3.34033	−	3.34033i	−0.137171	−	0.137171i	−0.772358	+	0.635187i	$0.780923\pi$
$594$		0			0
$595$	−35.0602	−	11.2324i	−1.43733	−	0.460482i
$596$	−7.84845	+	9.35341i	−0.321485	+	0.383131i
$597$		0			0
$598$	−4.36059	−	3.05332i	−0.178318	−	0.124859i
$599$	−18.0781	−	6.57991i	−0.738653	−	0.268848i	−0.0548301	−	0.998496i	$-0.517462\pi$
$599$	−18.0781	−	6.57991i	−0.738653	−	0.268848i	−0.683823	+	0.729648i	$0.739684\pi$
$600$		0			0
$601$	−1.93521	+	10.9751i	−0.0789387	+	0.447684i	0.919562	+	0.392945i	$0.128544\pi$
$601$	−1.93521	+	10.9751i	−0.0789387	+	0.447684i	−0.998501	+	0.0547387i	$0.982567\pi$
$602$	−1.82402	−	6.80735i	−0.0743417	−	0.277447i
$603$		0			0
$604$	−9.73361	+	5.61970i	−0.396055	+	0.228662i
$605$	−22.1414	+	0.864496i	−0.900177	+	0.0351468i
$606$		0			0
$607$	18.3352	+	1.60413i	0.744204	+	0.0651094i	0.452950	−	0.891536i	$-0.350372\pi$
$607$	18.3352	+	1.60413i	0.744204	+	0.0651094i	0.291255	+	0.956646i	$0.405927\pi$
$608$	−20.4905	−	1.79269i	−0.831001	−	0.0727032i
$609$		0			0
$610$	5.93268	−	6.41477i	0.240207	−	0.259727i
$611$	−0.372849	+	0.215265i	−0.0150839	+	0.00870868i
$612$		0			0
$613$	−2.08262	−	7.77243i	−0.0841161	−	0.313926i	0.911029	−	0.412342i	$-0.135289\pi$
$613$	−2.08262	−	7.77243i	−0.0841161	−	0.313926i	−0.995145	+	0.0984162i	$0.968622\pi$
$614$	−4.91471	+	27.8727i	−0.198342	+	1.12485i
$615$		0			0
$616$	8.65878	+	3.15154i	0.348872	+	0.126979i
$617$	−5.25082	−	3.67666i	−0.211390	−	0.148017i	0.463087	−	0.886313i	$-0.346742\pi$
$617$	−5.25082	−	3.67666i	−0.211390	−	0.148017i	−0.674477	+	0.738296i	$0.735631\pi$
$618$		0			0
$619$	−17.8281	+	21.2467i	−0.716573	+	0.853979i	−0.994293	−	0.106683i	$-0.965977\pi$
$619$	−17.8281	+	21.2467i	−0.716573	+	0.853979i	0.277720	+	0.960662i	$0.410421\pi$
$620$	6.83325	−	21.3290i	0.274430	−	0.856595i
$621$		0			0
$622$	−23.2671	−	23.2671i	−0.932926	−	0.932926i
$623$	0.823294	+	9.41029i	0.0329846	+	0.377015i
$624$		0			0
$625$	−21.8774	+	12.0988i	−0.875095	+	0.483951i
$626$	4.06240	−	11.1614i	0.162366	−	0.446098i
$627$		0			0
$628$	−6.28127	−	8.97058i	−0.250650	−	0.357965i
$629$	−20.1988	+	34.9854i	−0.805380	+	1.39496i
$630$		0			0
$631$	7.53540	+	13.0517i	0.299979	+	0.519580i	0.976131	−	0.217183i	$-0.0696868\pi$
$631$	7.53540	+	13.0517i	0.299979	+	0.519580i	−0.676151	+	0.736763i	$0.736353\pi$
$632$	4.85187	−	10.4049i	0.192997	−	0.413883i
$633$		0			0
$634$	8.34750	+	9.94816i	0.331522	+	0.395092i
$635$	34.5982	+	14.5182i	1.37299	+	0.576138i
$636$		0			0
$637$	1.56505	+	0.729797i	0.0620097	+	0.0289156i
$638$	−2.19307	+	8.18464i	−0.0868244	+	0.324033i
$639$		0			0
$640$	3.70847	+	0.179043i	0.146590	+	0.00707729i
$641$	−28.9474	−	5.10420i	−1.14335	−	0.201604i	−0.430281	−	0.902695i	$-0.641585\pi$
$641$	−28.9474	−	5.10420i	−1.14335	−	0.201604i	−0.713071	+	0.701091i	$0.752696\pi$
$642$		0			0
$643$	−19.6987	+	9.18567i	−0.776842	+	0.362248i	−0.770259	−	0.637731i	$-0.779873\pi$
$643$	−19.6987	+	9.18567i	−0.776842	+	0.362248i	−0.00658305	+	0.999978i	$0.502095\pi$
$644$	2.02747	+	11.4983i	0.0798935	+	0.453098i
$645$		0			0
$646$	19.6108	+	16.4554i	0.771576	+	0.647429i
$647$	16.4745	−	16.4745i	0.647680	−	0.647680i	−0.304752	−	0.952432i	$-0.598574\pi$
$647$	16.4745	−	16.4745i	0.647680	−	0.647680i	0.952432	+	0.304752i	$0.0985735\pi$
$648$		0			0
$649$		−	10.8616i		−	0.426353i
$650$	−5.93056	+	1.53064i	−0.232616	+	0.0600367i
$651$		0			0
$652$	7.57948	−	10.8246i	0.296835	−	0.423925i
$653$	−5.62864	−	12.0707i	−0.220266	−	0.472362i	0.764860	−	0.644197i	$-0.222808\pi$
$653$	−5.62864	−	12.0707i	−0.220266	−	0.472362i	−0.985126	+	0.171835i	$0.945030\pi$
$654$		0			0
$655$	−7.48902	−	3.94251i	−0.292620	−	0.154047i
$656$	−4.10841	−	2.37199i	−0.160406	−	0.0926106i
$657$		0			0
$658$	−1.06303	−	0.284837i	−0.0414411	−	0.0111041i
$659$	12.4761	−	4.54094i	0.486001	−	0.176890i	−0.0873859	−	0.996175i	$-0.527851\pi$
$659$	12.4761	−	4.54094i	0.486001	−	0.176890i	0.573387	+	0.819285i	$0.305629\pi$
$660$		0			0
$661$	−9.01628	+	7.56556i	−0.350693	+	0.294266i	−0.801068	−	0.598573i	$-0.795735\pi$
$661$	−9.01628	+	7.56556i	−0.350693	+	0.294266i	0.450375	+	0.892839i	$0.351290\pi$
$662$	−2.28561	+	26.1246i	−0.0888328	+	1.01536i
$663$		0			0
$664$	−4.95562	−	13.6155i	−0.192316	−	0.528383i
$665$	−23.8474	−	15.3474i	−0.924762	−	0.595148i
$666$		0			0
$667$	−32.8283	+	8.79631i	−1.27112	+	0.340595i
$668$	−16.0770	+	11.2572i	−0.622038	+	0.435555i
$669$		0			0
$670$	−1.04938	−	0.812928i	−0.0405410	−	0.0314061i
$671$	−3.87335	+	0.682976i	−0.149529	+	0.0263660i
$672$		0			0
$673$	11.5900	−	1.01400i	0.446763	−	0.0390867i	0.138445	−	0.990370i	$-0.455790\pi$
$673$	11.5900	−	1.01400i	0.446763	−	0.0390867i	0.308318	+	0.951283i	$0.400234\pi$
$674$	−1.79908			−0.0692981
$675$		0			0
$676$	−10.7192			−0.412276
$677$	−5.37998	+	0.470687i	−0.206769	+	0.0180900i	−0.190070	−	0.981771i	$-0.560871\pi$
$677$	−5.37998	+	0.470687i	−0.206769	+	0.0180900i	−0.0166995	+	0.999861i	$0.505316\pi$
$678$		0			0
$679$	34.2678	−	6.04233i	1.31508	−	0.231883i
$680$	−30.3465	−	23.5087i	−1.16374	−	0.901518i
$681$		0			0
$682$	9.62474	−	6.73932i	0.368550	−	0.258062i
$683$	−16.0348	+	4.29650i	−0.613553	+	0.164401i	−0.552195	−	0.833715i	$-0.686210\pi$
$683$	−16.0348	+	4.29650i	−0.613553	+	0.164401i	−0.0613579	+	0.998116i	$0.519543\pi$
$684$		0			0
$685$	40.6646	+	26.1705i	1.55371	+	0.999922i
$686$	−5.71610	−	15.7049i	−0.218242	−	0.599614i
$687$		0			0
$688$	0.264523	−	3.02351i	0.0100848	−	0.115270i
$689$	1.49038	−	1.25058i	0.0567789	−	0.0476431i
$690$		0			0
$691$	4.89099	−	1.78018i	0.186062	−	0.0677211i	−0.247309	−	0.968937i	$-0.579546\pi$
$691$	4.89099	−	1.78018i	0.186062	−	0.0677211i	0.433371	+	0.901216i	$0.357324\pi$
$692$	7.56797	+	2.02783i	0.287691	+	0.0770866i
$693$		0			0
$694$	−8.89164	−	5.13359i	−0.337522	−	0.194868i
$695$	22.1443	+	11.6576i	0.839982	+	0.442199i
$696$		0			0
$697$	−8.73003	−	18.7216i	−0.330674	−	0.709132i
$698$	18.4475	−	26.3458i	0.698248	−	0.997202i
$699$		0			0
$700$	11.5717	+	6.82390i	0.437369	+	0.257919i
$701$			30.8522i			1.16527i	0.812733	+	0.582636i	$0.197979\pi$
$701$			30.8522i			1.16527i	−0.812733	+	0.582636i	$0.802021\pi$
$702$		0			0
$703$	−22.0041	+	22.0041i	−0.829899	+	0.829899i
$704$	5.99524	+	5.03061i	0.225954	+	0.189598i
$705$		0			0
$706$	−0.660573	−	3.74630i	−0.0248610	−	0.140994i
$707$	0.706888	−	0.329627i	0.0265853	−	0.0123969i
$708$		0			0
$709$	−19.4630	−	3.43186i	−0.730949	−	0.128886i	−0.204227	−	0.978924i	$-0.565468\pi$
$709$	−19.4630	−	3.43186i	−0.730949	−	0.128886i	−0.526722	+	0.850038i	$0.676579\pi$
$710$	7.58533	+	0.366215i	0.284672	+	0.0137438i
$711$		0			0
$712$	−2.54923	+	9.51386i	−0.0955365	+	0.356547i
$713$	42.7119	+	19.9169i	1.59957	+	0.745893i
$714$		0			0
$715$	2.54227	+	1.06680i	0.0950756	+	0.0398959i
$716$	−7.97067	−	9.49908i	−0.297878	−	0.354997i
$717$		0			0
$718$	−3.27613	+	7.02568i	−0.122264	+	0.262196i
$719$	−3.29514	−	5.70736i	−0.122888	−	0.212849i	0.798017	−	0.602635i	$-0.205882\pi$
$719$	−3.29514	−	5.70736i	−0.122888	−	0.212849i	−0.920905	+	0.389786i	$0.872549\pi$
$720$		0			0
$721$	18.4656	−	31.9834i	0.687695	−	1.19112i
$722$	0.00419426	+	0.00599003i	0.000156094	+	0.000222926i
$723$		0			0
$724$	6.29925	−	17.3071i	0.234110	−	0.643212i
$725$	−16.8521	+	35.2866i	−0.625871	+	1.31051i
$726$		0			0
$727$	1.33493	+	15.2584i	0.0495099	+	0.565901i	0.979921	+	0.199384i	$0.0638942\pi$
$727$	1.33493	+	15.2584i	0.0495099	+	0.565901i	−0.930411	+	0.366517i	$0.880550\pi$
$728$	7.36685	+	7.36685i	0.273034	+	0.273034i
$729$		0			0
$730$	9.73608	−	30.3898i	0.360349	−	1.12478i
$731$	8.49492	−	10.1238i	0.314196	−	0.374444i
$732$		0			0
$733$	0.908462	+	0.636112i	0.0335548	+	0.0234953i	0.590234	−	0.807233i	$-0.299036\pi$
$733$	0.908462	+	0.636112i	0.0335548	+	0.0234953i	−0.556679	+	0.830728i	$0.687925\pi$
$734$	16.4596	+	5.99082i	0.607537	+	0.221125i
$735$		0			0
$736$	−3.56019	+	20.1909i	−0.131230	+	0.744245i
$737$	0.154649	+	0.577158i	0.00569657	+	0.0212599i
$738$		0			0
$739$	0.148882	−	0.0859569i	0.00547670	−	0.00316198i	−0.497259	−	0.867602i	$-0.665660\pi$
$739$	0.148882	−	0.0859569i	0.00547670	−	0.00316198i	0.502736	+	0.864440i	$0.332327\pi$
$740$	10.0089	−	10.8222i	0.367933	−	0.397832i
$741$		0			0
$742$	4.95432	+	0.433447i	0.181879	+	0.0159123i
$743$	−20.1450	−	1.76246i	−0.739048	−	0.0646584i	−0.288586	−	0.957454i	$-0.593185\pi$
$743$	−20.1450	−	1.76246i	−0.739048	−	0.0646584i	−0.450462	+	0.892796i	$0.648741\pi$
$744$		0			0
$745$	−29.5385	+	1.15331i	−1.08221	+	0.0422540i
$746$	−1.90830	+	1.10175i	−0.0698677	+	0.0403381i
$747$		0			0
$748$	1.41283	+	5.27274i	0.0516580	+	0.192790i
$749$	3.59719	−	20.4007i	0.131438	−	0.745424i
$750$		0			0
$751$	16.8648	+	6.13828i	0.615405	+	0.223989i	0.630867	−	0.775891i	$-0.282700\pi$
$751$	16.8648	+	6.13828i	0.615405	+	0.223989i	−0.0154616	+	0.999880i	$0.504922\pi$
$752$	−0.388237	−	0.271846i	−0.0141575	−	0.00991322i
$753$		0			0
$754$	−6.15814	+	7.33898i	−0.224266	+	0.267270i
$755$	−25.9137	−	8.30206i	−0.943097	−	0.302143i
$756$		0			0
$757$	−19.5487	−	19.5487i	−0.710508	−	0.710508i	0.256133	−	0.966641i	$-0.417551\pi$
$757$	−19.5487	−	19.5487i	−0.710508	−	0.710508i	−0.966641	+	0.256133i	$0.917551\pi$
$758$	0.868528	+	9.92732i	0.0315464	+	0.360577i
$759$		0			0
$760$	−17.8926	−	23.5420i	−0.649033	−	0.853957i
$761$	−0.210722	+	0.578955i	−0.00763868	+	0.0209871i	−0.943453	−	0.331505i	$-0.892444\pi$
$761$	−0.210722	+	0.578955i	−0.00763868	+	0.0209871i	0.935815	+	0.352492i	$0.114666\pi$
$762$		0			0
$763$	14.7056	+	21.0017i	0.532378	+	0.760314i
$764$	0.418993	−	0.725717i	0.0151586	−	0.0262555i
$765$		0			0
$766$	0.0626486	+	0.108511i	0.00226359	+	0.00392064i
$767$	5.18999	−	11.1300i	0.187400	−	0.401880i
$768$		0			0
$769$	26.3803	+	31.4388i	0.951298	+	1.13371i	0.990914	+	0.134497i	$0.0429420\pi$
$769$	26.3803	+	31.4388i	0.951298	+	1.13371i	−0.0396163	+	0.999215i	$0.512614\pi$
$770$	2.66695	+	6.52346i	0.0961101	+	0.235089i
$771$		0			0
$772$	6.18879	+	2.88588i	0.222739	+	0.103865i
$773$	−8.41362	+	31.4000i	−0.302617	+	1.12938i	0.632361	+	0.774674i	$0.282086\pi$
$773$	−8.41362	+	31.4000i	−0.302617	+	1.12938i	−0.934977	+	0.354707i	$0.884581\pi$
$774$		0			0
$775$	49.3528	−	22.4621i	1.77280	−	0.806863i
$776$	35.7306	+	6.30026i	1.28265	+	0.226166i
$777$		0			0
$778$	24.1159	−	11.2454i	0.864598	−	0.403169i
$779$	−2.76312	−	15.6704i	−0.0989990	−	0.561451i
$780$		0			0
$781$	−2.61864	−	2.19730i	−0.0937023	−	0.0786256i
$782$	18.0435	−	18.0435i	0.645233	−	0.645233i
$783$		0			0
$784$			1.90101i			0.0678930i
$785$	5.85771	−	25.8579i	0.209071	−	0.922907i
$786$		0			0
$787$	14.4949	−	20.7009i	0.516689	−	0.737908i	−0.473012	−	0.881056i	$-0.656833\pi$
$787$	14.4949	−	20.7009i	0.516689	−	0.737908i	0.989701	+	0.143147i	$0.0457223\pi$
$788$	−6.68386	−	14.3336i	−0.238103	−	0.510613i
$789$		0			0
$790$	8.38637	−	2.60178i	0.298374	−	0.0925672i
$791$	0.163514	+	0.0944047i	0.00581388	+	0.00335665i
$792$		0			0
$793$	−4.29541	−	1.15095i	−0.152535	−	0.0408715i
$794$	25.7442	−	9.37011i	0.913626	−	0.332533i
$795$		0			0
$796$	−0.725290	+	0.608590i	−0.0257072	+	0.0215709i
$797$	−0.523838	+	5.98749i	−0.0185553	+	0.212088i	0.981257	+	0.192704i	$0.0617259\pi$
$797$	−0.523838	+	5.98749i	−0.0185553	+	0.212088i	−0.999812	+	0.0193834i	$0.993830\pi$
$798$		0			0
$799$	−0.705844	−	1.93929i	−0.0249710	−	0.0686072i
$800$	14.9959	+	18.2097i	0.530186	+	0.643811i
$801$		0			0
$802$	34.0906	−	9.13456i	1.20378	−	0.322553i
$803$	−11.7666	+	8.23907i	−0.415235	+	0.290750i
$804$		0			0
$805$	−17.3113	+	22.3466i	−0.610144	+	0.787613i
$806$	13.0828	−	2.30686i	0.460824	−	0.0812556i
$807$		0			0
$808$	0.810165	−	0.0708802i	0.0285015	−	0.00249356i
$809$	−0.987575			−0.0347213			−0.0173607	−	0.999849i	$-0.505526\pi$
$809$	−0.987575			−0.0347213			−0.0173607	+	0.999849i	$0.505526\pi$
$810$		0			0
$811$	−7.20371			−0.252957			−0.126478	−	0.991969i	$-0.540367\pi$
$811$	−7.20371			−0.252957			−0.126478	+	0.991969i	$0.540367\pi$
$812$	20.9329	−	1.83139i	0.734601	−	0.0642692i
$813$		0			0
$814$	7.61579	−	1.34287i	0.266933	−	0.0470675i
$815$	31.7380	−	4.02966i	1.11173	−	0.141153i
$816$		0			0
$817$	8.33907	−	5.83908i	0.291747	−	0.204284i
$818$	33.6856	−	9.02602i	1.17779	−	0.315587i
$819$		0			0
$820$	1.59752	+	7.36646i	0.0557879	+	0.257248i
$821$	3.24048	+	8.90315i	0.113094	+	0.310722i	0.983307	−	0.181952i	$-0.0582416\pi$
$821$	3.24048	+	8.90315i	0.113094	+	0.310722i	−0.870214	+	0.492674i	$0.836019\pi$
$822$		0			0
$823$	−3.23116	+	36.9323i	−0.112631	+	1.28738i	0.703992	+	0.710208i	$0.251399\pi$
$823$	−3.23116	+	36.9323i	−0.112631	+	1.28738i	−0.816623	+	0.577172i	$0.804156\pi$
$824$	29.4986	−	24.7523i	1.02763	−	0.862287i
$825$		0			0
$826$	29.4986	−	10.7366i	1.02639	−	0.373574i
$827$	−28.1808	−	7.55103i	−0.979943	−	0.262575i	−0.266923	−	0.963718i	$-0.586007\pi$
$827$	−28.1808	−	7.55103i	−0.979943	−	0.262575i	−0.713021	+	0.701143i	$0.752673\pi$
$828$		0			0
$829$	16.9573	+	9.79032i	0.588952	+	0.340032i	0.764683	−	0.644407i	$-0.222896\pi$
$829$	16.9573	+	9.79032i	0.588952	+	0.340032i	−0.175731	+	0.984438i	$0.556229\pi$
$830$	5.16230	−	9.80608i	0.179186	−	0.340374i
$831$		0			0
$832$	3.73962	+	8.01964i	0.129648	+	0.278031i
$833$	−4.74788	+	6.78067i	−0.164504	+	0.234936i
$834$		0			0
$835$	−46.3422	−	10.4981i	−1.60374	−	0.363303i
$836$			4.20488i			0.145429i
$837$		0			0
$838$	−22.6830	+	22.6830i	−0.783572	+	0.783572i
$839$	−1.00064	−	0.839639i	−0.0345460	−	0.0289876i	0.625351	−	0.780343i	$-0.284956\pi$
$839$	−1.00064	−	0.839639i	−0.0345460	−	0.0289876i	−0.659897	+	0.751356i	$0.729400\pi$
$840$		0			0
$841$	5.58546	+	31.6767i	0.192602	+	1.09230i
$842$	−13.7916	+	6.43113i	−0.475290	+	0.221631i
$843$		0			0
$844$	8.90859	+	1.57082i	0.306646	+	0.0540700i
$845$	−17.4443	−	19.2142i	−0.600103	−	0.660988i
$846$		0			0
$847$	−7.46102	+	27.8449i	−0.256364	+	0.956762i
$848$	1.94110	+	0.905149i	0.0666576	+	0.0310830i
$849$		0			0
$850$	−2.28918	−	29.2705i	−0.0785182	−	1.00397i
$851$	19.9379	+	23.7611i	0.683463	+	0.814519i
$852$		0			0
$853$	−0.525925	+	1.12785i	−0.0180073	+	0.0386168i	−0.915106	−	0.403214i	$-0.867893\pi$
$853$	−0.525925	+	1.12785i	−0.0180073	+	0.0386168i	0.897098	+	0.441831i	$0.145671\pi$
$854$	−5.68367	−	9.84440i	−0.194491	−	0.336869i
$855$		0			0
$856$	10.7998	−	18.7059i	0.369131	−	0.639353i
$857$	−3.01178	−	4.30127i	−0.102880	−	0.146928i	0.764411	−	0.644729i	$-0.223030\pi$
$857$	−3.01178	−	4.30127i	−0.102880	−	0.146928i	−0.867291	+	0.497801i	$0.834141\pi$
$858$		0			0
$859$	17.5440	−	48.2017i	0.598593	−	1.64462i	−0.155486	−	0.987838i	$-0.549694\pi$
$859$	17.5440	−	48.2017i	0.598593	−	1.64462i	0.754079	−	0.656783i	$-0.228083\pi$
$860$	−3.83935	+	2.91802i	−0.130921	+	0.0995037i
$861$		0			0
$862$	−2.74226	−	31.3442i	−0.0934018	−	1.06759i
$863$	4.17796	+	4.17796i	0.142219	+	0.142219i	0.774632	−	0.632412i	$-0.217935\pi$
$863$	4.17796	+	4.17796i	0.142219	+	0.142219i	−0.632412	+	0.774632i	$0.717935\pi$
$864$		0			0
$865$	8.68117	+	16.8657i	0.295169	+	0.573451i
$866$	5.04741	−	6.01526i	0.171518	−	0.204407i
$867$		0			0
$868$	−23.8681	−	16.7126i	−0.810137	−	0.567264i
$869$	−3.71412	−	1.35183i	−0.125993	−	0.0458577i
$870$		0			0
$871$	−0.117313	+	0.665317i	−0.00397501	+	0.0225434i
$872$	6.91897	+	25.8219i	0.234306	+	0.874442i
$873$		0			0
$874$	17.0227	−	9.82804i	0.575800	−	0.332438i
$875$	6.59982	+	31.8475i	0.223115	+	1.07664i
$876$		0			0
$877$	−50.0397	−	4.37791i	−1.68972	−	0.147832i	−0.798681	−	0.601754i	$-0.794469\pi$
$877$	−50.0397	−	4.37791i	−1.68972	−	0.147832i	−0.891041	+	0.453923i	$0.850024\pi$
$878$	−10.2641	−	0.897992i	−0.346397	−	0.0303058i
$879$		0			0
$880$	0.118412	+	3.03277i	0.00399168	+	0.102235i
$881$	11.9474	−	6.89781i	0.402517	−	0.232393i	−0.285053	−	0.958512i	$-0.592011\pi$
$881$	11.9474	−	6.89781i	0.402517	−	0.232393i	0.687569	+	0.726119i	$0.258678\pi$
$882$		0			0
$883$	−6.38476	−	23.8282i	−0.214864	−	0.801884i	−0.986214	−	0.165473i	$-0.947085\pi$
$883$	−6.38476	−	23.8282i	−0.214864	−	0.801884i	0.771350	−	0.636411i	$-0.219582\pi$
$884$	−1.07174	+	6.07813i	−0.0360465	+	0.204430i
$885$		0			0
$886$	−9.03886	−	3.28987i	−0.303666	−	0.110526i
$887$	−37.9805	−	26.5942i	−1.27526	−	0.892946i	−0.277558	−	0.960709i	$-0.589525\pi$
$887$	−37.9805	−	26.5942i	−1.27526	−	0.892946i	−0.997701	+	0.0677631i	$0.978414\pi$
$888$		0			0
$889$	31.3766	−	37.3932i	1.05234	−	1.25413i
$890$	−6.69801	+	3.44762i	−0.224518	+	0.115565i
$891$		0			0
$892$	6.40212	+	6.40212i	0.214359	+	0.214359i
$893$	−0.138553	−	1.58366i	−0.00463649	−	0.0529953i
$894$		0			0
$895$	4.05572	−	29.7462i	0.135568	−	0.994306i
$896$	1.65203	−	4.53891i	0.0551904	−	0.151634i
$897$		0			0
$898$	17.9463	+	25.6299i	0.598874	+	0.855281i
$899$	42.4077	−	73.4522i	1.41438	−	2.44977i
$900$		0			0
$901$	4.66302	+	8.07658i	0.155348	+	0.269070i
$902$	−1.67118	+	3.58386i	−0.0556442	+	0.119329i
$903$		0			0
$904$	0.126545	+	0.150811i	0.00420883	+	0.00501589i
$905$	41.2743	−	16.8739i	1.37200	−	0.560909i
$906$		0			0
$907$	12.3092	+	5.73988i	0.408721	+	0.190590i	0.616095	−	0.787672i	$-0.288714\pi$
$907$	12.3092	+	5.73988i	0.408721	+	0.190590i	−0.207374	+	0.978262i	$0.566492\pi$
$908$	4.09378	−	15.2782i	0.135857	−	0.507024i
$909$		0			0
$910$	−0.384257	+	7.95902i	−0.0127380	+	0.263839i
$911$	26.4310	+	4.66050i	0.875698	+	0.154409i	0.593391	−	0.804915i	$-0.297789\pi$
$911$	26.4310	+	4.66050i	0.875698	+	0.154409i	0.282308	+	0.959324i	$0.408900\pi$
$912$		0			0
$913$	−4.52098	+	2.10817i	−0.149623	+	0.0697701i
$914$	5.46005	+	30.9655i	0.180602	+	1.02425i
$915$		0			0
$916$	12.9407	+	10.8585i	0.427573	+	0.358776i
$917$	−7.78565	+	7.78565i	−0.257105	+	0.257105i
$918$		0			0
$919$		−	29.6273i		−	0.977314i	−0.872476	−	0.488657i	$-0.837487\pi$
$919$		−	29.6273i		−	0.977314i	0.872476	−	0.488657i	$-0.162513\pi$
$920$	−24.9310	+	15.7217i	−0.821950	+	0.518330i
$921$		0			0
$922$	−7.73552	+	11.0475i	−0.254756	+	0.363829i
$923$	−1.63341	−	3.50287i	−0.0537645	−	0.115298i
$924$		0			0
$925$	35.6872	+	0.328957i	1.17339	+	0.0108160i
$926$	24.6870	+	14.2531i	0.811267	+	0.468385i
$927$		0			0
$928$	35.6409	+	9.54994i	1.16997	+	0.313492i
$929$	−52.3804	+	19.0649i	−1.71854	+	0.625499i	−0.997712	−	0.0676108i	$-0.978462\pi$
$929$	−52.3804	+	19.0649i	−1.71854	+	0.625499i	−0.720832	+	0.693110i	$0.756240\pi$
$930$		0			0
$931$	−4.88454	+	4.09862i	−0.160084	+	0.134327i
$932$	−0.397168	+	4.53965i	−0.0130097	+	0.148701i
$933$		0			0
$934$	−10.6526	−	29.2678i	−0.348564	−	0.957673i
$935$	−7.15218	+	11.1133i	−0.233901	+	0.363444i
$936$		0			0
$937$	13.0469	−	3.49591i	0.426224	−	0.114206i	−0.0393290	−	0.999226i	$-0.512522\pi$
$937$	13.0469	−	3.49591i	0.426224	−	0.114206i	0.465553	+	0.885020i	$0.345855\pi$
$938$	−1.41462	+	0.990526i	−0.0461889	+	0.0323418i
$939$		0			0
$940$	0.0948517	+	0.747060i	0.00309372	+	0.0243664i
$941$	−14.9533	+	2.63667i	−0.487463	+	0.0859529i	−0.411977	−	0.911194i	$-0.635162\pi$
$941$	−14.9533	+	2.63667i	−0.487463	+	0.0859529i	−0.0754855	+	0.997147i	$0.524051\pi$
$942$		0			0
$943$	−15.8004	+	1.38235i	−0.514531	+	0.0450157i
$944$	13.5191			0.440009
$945$		0			0
$946$	−2.52987			−0.0822533
$947$	−5.42282	+	0.474435i	−0.176218	+	0.0154171i	−0.174923	−	0.984582i	$-0.555968\pi$
$947$	−5.42282	+	0.474435i	−0.176218	+	0.0154171i	−0.00129474	+	0.999999i	$0.500412\pi$
$948$		0			0
$949$	−15.9943	+	2.82022i	−0.519196	+	0.0915483i
$950$	4.13235	−	22.2352i	0.134071	−	0.721406i
$951$		0			0
$952$	−40.9087	+	28.6446i	−1.32586	+	0.928377i
$953$	−45.1915	+	12.1090i	−1.46390	+	0.392250i	−0.900834	−	0.434164i	$-0.857044\pi$
$953$	−45.1915	+	12.1090i	−1.46390	+	0.392250i	−0.563063	+	0.826414i	$0.690377\pi$
$954$		0			0
$955$	1.98272	−	0.429980i	0.0641592	−	0.0139138i
$956$	1.90807	+	5.24239i	0.0617115	+	0.169551i
$957$		0			0
$958$	−0.945161	+	10.8032i	−0.0305367	+	0.349037i
$959$	48.1935	−	40.4392i	1.55625	−	1.30585i
$960$		0			0
$961$	−81.3865	+	29.6223i	−2.62537	+	0.955557i
$962$	8.44566	+	2.26301i	0.272299	+	0.0729623i
$963$		0			0
$964$	13.7580	+	7.94318i	0.443115	+	0.255832i
$965$	4.89864	+	15.7899i	0.157693	+	0.508294i
$966$		0			0
$967$	10.4693	+	22.4516i	0.336671	+	0.721994i	0.999645	−	0.0266490i	$-0.00848366\pi$
$967$	10.4693	+	22.4516i	0.336671	+	0.721994i	−0.662974	+	0.748643i	$0.730706\pi$
$968$	−17.2404	+	24.6219i	−0.554128	+	0.791377i
$969$		0			0
$970$	14.8018	+	23.4722i	0.475258	+	0.753648i
$971$			39.1684i			1.25697i	0.777821	+	0.628486i	$0.216325\pi$
$971$			39.1684i			1.25697i	−0.777821	+	0.628486i	$0.783675\pi$
$972$		0			0
$973$	23.0214	−	23.0214i	0.738033	−	0.738033i
$974$	−15.4188	−	12.9379i	−0.494050	−	0.414557i
$975$		0			0
$976$	−0.850083	−	4.82106i	−0.0272105	−	0.154318i
$977$	27.2371	−	12.7009i	0.871393	−	0.406337i	0.0651176	−	0.997878i	$-0.479258\pi$
$977$	27.2371	−	12.7009i	0.871393	−	0.406337i	0.806275	+	0.591540i	$0.201480\pi$
$978$		0			0
$979$	3.33945	+	0.588834i	0.106729	+	0.0188192i
$980$	2.23633	−	2.03034i	0.0714369	−	0.0648567i
$981$		0			0
$982$	−11.2391	+	41.9450i	−0.358655	+	1.33852i
$983$	−53.0117	−	24.7198i	−1.69081	−	0.788438i	−0.997713	−	0.0675941i	$-0.978468\pi$
$983$	−53.0117	−	24.7198i	−1.69081	−	0.788438i	−0.693098	−	0.720844i	$-0.743755\pi$
$984$		0			0
$985$	14.8157	−	35.3072i	0.472069	−	1.12498i
$986$	−29.5192	−	35.1796i	−0.940082	−	1.12035i
$987$		0			0
$988$	−2.00922	+	4.30879i	−0.0639219	+	0.137081i
$989$	−5.07361	−	8.78776i	−0.161332	−	0.279434i
$990$		0			0
$991$	−6.16723	+	10.6820i	−0.195909	+	0.339324i	−0.947198	−	0.320649i	$-0.896099\pi$
$991$	−6.16723	+	10.6820i	−0.195909	+	0.339324i	0.751289	+	0.659973i	$0.229432\pi$
$992$	−29.3471	−	41.9119i	−0.931770	−	1.33071i
$993$		0			0
$994$	3.37907	−	9.28392i	0.107178	−	0.294468i
$995$	−2.27123	−	0.309669i	−0.0720029	−	0.00981716i
$996$		0			0
$997$	2.51324	+	28.7265i	0.0795952	+	0.909777i	0.926071	+	0.377350i	$0.123165\pi$
$997$	2.51324	+	28.7265i	0.0795952	+	0.909777i	−0.846476	+	0.532427i	$0.821280\pi$
$998$	−19.4082	−	19.4082i	−0.614355	−	0.614355i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.197.11		192
3.2	odd	2		135.2.q.a.92.6	yes	192
5.3	odd	4	inner	405.2.r.a.278.6		192
15.2	even	4		675.2.ba.b.443.6		192
15.8	even	4		135.2.q.a.38.11	yes	192
15.14	odd	2		675.2.ba.b.632.11		192
27.5	odd	18	inner	405.2.r.a.287.6		192
27.22	even	9		135.2.q.a.32.11	✓	192
135.22	odd	36		675.2.ba.b.518.11		192
135.49	even	18		675.2.ba.b.32.6		192
135.103	odd	36		135.2.q.a.113.6	yes	192
135.113	even	36	inner	405.2.r.a.368.11		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.11	✓	192	27.22	even	9
135.2.q.a.38.11	yes	192	15.8	even	4
135.2.q.a.92.6	yes	192	3.2	odd	2
135.2.q.a.113.6	yes	192	135.103	odd	36
405.2.r.a.197.11		192	1.1	even	1	trivial
405.2.r.a.278.6		192	5.3	odd	4	inner
405.2.r.a.287.6		192	27.5	odd	18	inner
405.2.r.a.368.11		192	135.113	even	36	inner
675.2.ba.b.32.6		192	135.49	even	18
675.2.ba.b.443.6		192	15.2	even	4
675.2.ba.b.518.11		192	135.22	odd	36
675.2.ba.b.632.11		192	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.03355 - 0.0904240i) q^{2} +(-0.909563 + 0.160381i) q^{4} +(-1.76770 - 1.36939i) q^{5} +(-2.38295 + 1.66856i) q^{7} +(-2.92987 + 0.785057i) q^{8} +(-1.95083 - 1.25550i) q^{10} +(0.357163 + 0.981298i) q^{11} +(-0.102905 + 1.17621i) q^{13} +(-2.31203 + 1.94002i) q^{14} +(-1.22140 + 0.444552i) q^{16} +(-5.46688 - 1.46485i) q^{17} +(-3.77562 - 2.17985i) q^{19} +(1.82746 + 0.962045i) q^{20} +(0.457879 + 0.981926i) q^{22} +(-2.49254 + 3.55972i) q^{23} +(1.24952 + 4.84135i) q^{25} +1.22498i q^{26} +(1.89984 - 1.89984i) q^{28} +(5.99110 + 5.02713i) q^{29} +(-1.88318 - 10.6800i) q^{31} +(4.27590 - 1.99388i) q^{32} +(-5.78276 - 1.01966i) q^{34} +(6.49726 + 0.313684i) q^{35} +(1.84738 - 6.89452i) q^{37} +(-4.09941 - 1.91158i) q^{38} +(6.25419 + 2.62440i) q^{40} +(2.34606 + 2.79593i) q^{41} +(-0.986834 + 2.11627i) q^{43} +(-0.482244 - 0.835270i) q^{44} +(-2.25429 + 3.90454i) q^{46} +(0.209148 + 0.298694i) q^{47} +(0.500224 - 1.37435i) q^{49} +(1.72922 + 4.89080i) q^{50} +(-0.0950427 - 1.08634i) q^{52} +(-1.16516 - 1.16516i) q^{53} +(0.712425 - 2.22374i) q^{55} +(5.67183 - 6.75943i) q^{56} +(6.64669 + 4.65406i) q^{58} +(-9.77378 - 3.55737i) q^{59} +(-0.654019 + 3.70913i) q^{61} +(-2.91210 - 10.8681i) q^{62} +(6.49036 - 3.74721i) q^{64} +(1.79260 - 1.93827i) q^{65} +(0.570007 + 0.0498691i) q^{67} +(5.20741 + 0.455589i) q^{68} +(6.74362 - 0.263300i) q^{70} +(-2.83490 + 1.63673i) q^{71} +(3.56015 + 13.2867i) q^{73} +(1.28593 - 7.29289i) q^{74} +(3.78377 + 1.37718i) q^{76} +(-2.48846 - 1.74244i) q^{77} +(-2.43289 + 2.89941i) q^{79} +(2.76783 + 0.886738i) q^{80} +(2.67759 + 2.67759i) q^{82} +(0.416330 + 4.75867i) q^{83} +(7.65785 + 10.0757i) q^{85} +(-0.828582 + 2.27651i) q^{86} +(-1.81682 - 2.59468i) q^{88} +(1.62360 - 2.81215i) q^{89} +(-1.71736 - 2.97456i) q^{91} +(1.69622 - 3.63755i) q^{92} +(0.243174 + 0.289803i) q^{94} +(3.68908 + 9.02363i) q^{95} +(-10.8407 - 5.05512i) q^{97} +(0.392732 - 1.46570i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

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