LMFDB - Embedded newform 405.2.r.a.368.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 27]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("405.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			368.11
Character	$\chi$	$=$	405.368
Dual form			405.2.r.a.197.11

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

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{18}\right)$

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	0.446496	−	0.894786i	$-0.352672\pi$
$2$	1.03355	+	0.0904240i	0.730831	+	0.0639395i	0.284335	+	0.958725i	$0.408227\pi$
$3$		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	0.0287865	−	0.999586i	$-0.490836\pi$
$7$	−2.38295	−	1.66856i	−0.900671	−	0.630657i	−0.929458	+	0.368929i	$0.879725\pi$
$8$	−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	−0.874130	−	0.485691i	$-0.838568\pi$
$11$	0.357163	−	0.981298i	0.107689	−	0.295872i	0.981819	+	0.189819i	$0.0607901\pi$
$12$		0			0
$13$	−0.102905	−	1.17621i	−0.0285408	−	0.326222i	−0.997021	−	0.0771317i	$-0.975424\pi$
$13$	−0.102905	−	1.17621i	−0.0285408	−	0.326222i	0.968480	−	0.249091i	$-0.0801317\pi$
$14$	−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	−0.851190	−	0.524858i	$-0.824118\pi$
$17$	−5.46688	+	1.46485i	−1.32591	+	0.355277i	−0.474723	+	0.880135i	$0.657452\pi$
$18$		0			0
$19$	−3.77562	+	2.17985i	−0.866186	+	0.500093i	−0.866079	−	0.499907i	$-0.833367\pi$
$19$	−3.77562	+	2.17985i	−0.866186	+	0.500093i	−0.000107079		1.00000i	$0.500034\pi$
$20$	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	0.470391	−	0.882458i	$-0.344113\pi$
$23$	−2.49254	−	3.55972i	−0.519731	−	0.742253i	−0.990123	+	0.140205i	$0.955224\pi$
$24$		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	0.114317	−	0.993444i	$-0.463532\pi$
$29$	5.99110	−	5.02713i	1.11252	−	0.933515i	0.998203	+	0.0599291i	$0.0190875\pi$
$30$		0			0
$31$	−1.88318	+	10.6800i	−0.338229	+	1.91819i	0.0544490	+	0.998517i	$0.482660\pi$
$31$	−1.88318	+	10.6800i	−0.338229	+	1.91819i	−0.392678	+	0.919676i	$0.628451\pi$
$32$	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	0.934052	+	0.357137i	$0.116247\pi$
$37$	1.84738	+	6.89452i	0.303708	+	1.13345i	−0.630344	+	0.776316i	$0.717086\pi$
$38$	−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	−0.551077	−	0.834454i	$-0.685783\pi$
$41$	2.34606	−	2.79593i	0.366393	−	0.436650i	0.917471	+	0.397804i	$0.130228\pi$
$42$		0			0
$43$	−0.986834	−	2.11627i	−0.150491	−	0.322729i	0.816582	−	0.577230i	$-0.195866\pi$
$43$	−0.986834	−	2.11627i	−0.150491	−	0.322729i	−0.967072	+	0.254501i	$0.918089\pi$
$44$	−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	−0.803609	−	0.595158i	$-0.797089\pi$
$47$	0.209148	−	0.298694i	0.0305073	−	0.0435690i	0.834116	+	0.551589i	$0.185978\pi$
$48$		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	−0.782588	−	0.622540i	$-0.786101\pi$
$53$	−1.16516	+	1.16516i	−0.160047	+	0.160047i	0.622540	+	0.782588i	$0.286101\pi$
$54$		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	−0.887924	−	0.459990i	$-0.847853\pi$
$59$	−9.77378	+	3.55737i	−1.27244	+	0.463130i	−0.384514	+	0.923119i	$0.625631\pi$
$60$		0			0
$61$	−0.654019	−	3.70913i	−0.0837385	−	0.474905i	−0.997622	−	0.0689275i	$-0.978042\pi$
$61$	−0.654019	−	3.70913i	−0.0837385	−	0.474905i	0.913883	−	0.405977i	$-0.133069\pi$
$62$	−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	−0.0522838	−	0.998632i	$-0.516650\pi$
$67$	0.570007	−	0.0498691i	0.0696374	−	0.00609249i	0.121921	+	0.992540i	$0.461094\pi$
$68$	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	0.322256	−	0.946652i	$-0.395559\pi$
$71$	−2.83490	−	1.63673i	−0.336441	−	0.194244i	−0.658697	+	0.752408i	$0.728892\pi$
$72$		0			0
$73$	3.56015	−	13.2867i	0.416684	−	1.55509i	−0.364755	−	0.931104i	$-0.618847\pi$
$73$	3.56015	−	13.2867i	0.416684	−	1.55509i	0.781439	−	0.623982i	$-0.214486\pi$
$74$	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	0.611618	−	0.791153i	$-0.290519\pi$
$79$	−2.43289	−	2.89941i	−0.273722	−	0.326209i	−0.885340	+	0.464944i	$0.846074\pi$
$80$	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	−0.938502	−	0.345273i	$-0.887786\pi$
$83$	0.416330	−	4.75867i	0.0456981	−	0.522332i	0.984200	−	0.177059i	$-0.0566583\pi$
$84$		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	0.939154	−	0.343496i	$-0.111611\pi$
$89$	1.62360	+	2.81215i	0.172101	+	0.298087i	−0.767053	+	0.641583i	$0.778278\pi$
$90$		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	−0.886130	−	0.463436i	$-0.846616\pi$
$97$	−10.8407	+	5.05512i	−1.10071	+	0.513270i	−0.214581	+	0.976706i	$0.568839\pi$
$98$	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	−0.186769	−	0.982404i	$-0.559802\pi$
$101$	−0.264044	+	0.0465580i	−0.0262733	+	0.00463269i	0.160496	+	0.987036i	$0.448691\pi$
$102$		0			0
$103$	−11.5058	−	5.36526i	−1.13370	−	0.528655i	−0.237099	−	0.971485i	$-0.576197\pi$
$103$	−11.5058	−	5.36526i	−1.13370	−	0.528655i	−0.896606	+	0.442830i	$0.853974\pi$
$104$	−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	0.420507	−	0.907289i	$-0.361852\pi$
$107$	−5.03532	−	5.03532i	−0.486782	−	0.486782i	−0.907289	+	0.420507i	$0.861852\pi$
$108$		0			0
$109$			8.81333i			0.844164i	0.906558	+	0.422082i	$0.138701\pi$
$109$			8.81333i			0.844164i	−0.906558	+	0.422082i	$0.861299\pi$
$110$	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	−0.907594	−	0.419849i	$-0.862083\pi$
$113$	−0.0274297	+	0.0588232i	−0.00258037	+	0.00553362i	0.905013	+	0.425383i	$0.139861\pi$
$114$		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	−0.546320	−	0.837577i	$-0.683972\pi$
$127$	−16.2081	−	4.34294i	−1.43823	−	0.385374i	−0.891915	+	0.452203i	$0.850638\pi$
$128$	−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	0.334092	−	0.942541i	$-0.391570\pi$
$131$	3.72744	+	0.657248i	0.325668	+	0.0574240i	−0.00842419	+	0.999965i	$0.502682\pi$
$132$		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	−0.886955	−	0.461856i	$-0.847184\pi$
$137$	−21.5441	−	1.88486i	−1.84064	−	0.161035i	−0.953681	+	0.300821i	$0.902739\pi$
$138$		0			0
$139$	−11.0217	−	1.94342i	−0.934847	−	0.164839i	−0.314581	−	0.949231i	$-0.601864\pi$
$139$	−11.0217	−	1.94342i	−0.934847	−	0.164839i	−0.620265	+	0.784392i	$0.712975\pi$
$140$	−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	0.955211	−	0.295926i	$-0.0956282\pi$
$149$	10.1272	+	8.49772i	0.829651	+	0.696160i	−0.125560	+	0.992086i	$0.540073\pi$
$150$		0			0
$151$	11.4353	+	4.16211i	0.930591	+	0.338708i	0.762444	−	0.647054i	$-0.223999\pi$
$151$	11.4353	+	4.16211i	0.930591	+	0.338708i	0.168147	+	0.985762i	$0.446222\pi$
$152$	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	−0.598483	−	0.801136i	$-0.704230\pi$
$157$	5.01098	−	10.7461i	0.399920	−	0.857631i	0.998403	−	0.0564955i	$-0.0179927\pi$
$158$	−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	0.189463	−	0.981888i	$-0.439325\pi$
$163$	−10.1170	−	10.1170i	−0.792424	−	0.792424i	−0.981888	+	0.189463i	$0.939325\pi$
$164$	−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	0.985716	−	0.168415i	$-0.0538648\pi$
$167$	19.2590	+	8.98064i	1.49031	+	0.694943i	0.504593	+	0.863357i	$0.331643\pi$
$168$		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	−0.692306	−	0.721604i	$-0.743405\pi$
$173$	−7.68830	+	3.58511i	−0.584530	+	0.272571i	0.107775	+	0.994175i	$0.465627\pi$
$174$		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	−0.498245	−	0.867036i	$-0.666022\pi$
$179$	6.71299	−	11.6272i	0.501753	−	0.869061i	0.999998	−	0.00202486i	$-0.000644535\pi$
$180$		0			0
$181$	−9.97071	−	17.2698i	−0.741117	−	1.28365i	−0.951987	−	0.306138i	$-0.900963\pi$
$181$	−9.97071	−	17.2698i	−0.741117	−	1.28365i	0.210870	−	0.977514i	$-0.432370\pi$
$182$	−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	0.744532	−	0.667587i	$-0.232673\pi$
$191$	−0.583207	−	0.695039i	−0.0421994	−	0.0502912i	−0.786731	+	0.617296i	$0.788228\pi$
$192$		0			0
$193$	−6.05638	+	4.24072i	−0.435948	+	0.305254i	−0.770871	−	0.636992i	$-0.780179\pi$
$193$	−6.05638	+	4.24072i	−0.435948	+	0.305254i	0.334923	+	0.942245i	$0.391290\pi$
$194$	−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	−0.607515	−	0.794309i	$-0.707833\pi$
$197$	4.43194	−	16.5402i	0.315763	−	1.17844i	0.923277	−	0.384134i	$-0.125500\pi$
$198$		0			0
$199$	0.887783	+	0.512562i	0.0629332	+	0.0363345i	0.531136	−	0.847286i	$-0.321765\pi$
$199$	0.887783	+	0.512562i	0.0629332	+	0.0363345i	−0.468203	+	0.883621i	$0.655098\pi$
$200$	−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	−0.638801	−	0.769372i	$-0.720569\pi$
$211$	−9.20369	+	3.34987i	−0.633608	+	0.230614i	0.00519293	+	0.999987i	$0.498347\pi$
$212$	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	−0.962033	−	0.272932i	$-0.912007\pi$
$223$	−5.62275	+	8.03011i	−0.376527	+	0.537736i	0.585507	+	0.810668i	$0.300896\pi$
$224$	−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	−0.985897	−	0.167356i	$-0.946477\pi$
$227$	−7.23760	−	15.5211i	−0.480376	−	1.03017i	0.505520	−	0.862815i	$-0.331301\pi$
$228$		0			0
$229$	−11.7568	+	14.0112i	−0.776912	+	0.925888i	−0.998790	−	0.0491866i	$-0.984337\pi$
$229$	−11.7568	+	14.0112i	−0.776912	+	0.925888i	0.221877	+	0.975075i	$0.428782\pi$
$230$	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	0.995057	−	0.0993059i	$-0.0316622\pi$
$233$	1.27701	+	4.76585i	0.0836594	+	0.312221i	−0.911398	+	0.411527i	$0.864996\pi$
$234$		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	0.931909	+	0.362693i	$0.118143\pi$
$239$	−1.04890	+	5.94858i	−0.0678474	+	0.384782i	−0.999756	+	0.0220886i	$0.992968\pi$
$240$		0			0
$241$	−13.1764	+	11.0563i	−0.848766	+	0.712199i	−0.959518	−	0.281649i	$-0.909119\pi$
$241$	−13.1764	+	11.0563i	−0.848766	+	0.712199i	0.110751	+	0.993848i	$0.464674\pi$
$242$	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	−0.492228	−	0.870467i	$-0.663817\pi$
$251$	0.245642	−	0.141822i	0.0155048	−	0.00895170i	0.507732	+	0.861515i	$0.330484\pi$
$252$		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	0.993092	+	0.117335i	$0.0374350\pi$
$257$	0.568503	+	6.49802i	0.0354623	+	0.405335i	−0.957630	+	0.288001i	$0.907009\pi$
$258$		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	0.682792	−	0.730612i	$-0.260765\pi$
$263$	3.72625	+	2.60915i	0.229770	+	0.160887i	−0.453022	+	0.891499i	$0.649654\pi$
$264$		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	0.791094	−	0.611695i	$-0.209512\pi$
$277$	8.10294	+	5.67374i	0.486858	+	0.340902i	−0.304235	+	0.952597i	$0.598401\pi$
$278$	−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	−0.882262	−	0.470759i	$-0.843980\pi$
$281$	1.61241	−	4.43006i	0.0961883	−	0.264275i	0.978450	+	0.206484i	$0.0662022\pi$
$282$		0			0
$283$	0.00130413	+	0.0149063i	7.75226e−5	+	0.000886087i	0.996233	−	0.0867127i	$-0.0276362\pi$
$283$	0.00130413	+	0.0149063i	7.75226e−5	+	0.000886087i	−0.996156	+	0.0875988i	$0.972081\pi$
$284$	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	0.992441	+	0.122726i	$0.0391636\pi$
$293$	13.1517	+	18.7826i	0.768330	+	1.09729i	−0.224110	+	0.974564i	$0.571948\pi$
$294$		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	−0.807779	−	0.589486i	$-0.799330\pi$
$307$	−7.06051	−	26.3502i	−0.402965	−	1.50388i	0.404814	−	0.914399i	$-0.367336\pi$
$308$	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	−0.242835	+	0.970068i	$0.578077\pi$
$311$	−20.3862	+	24.2954i	−1.15600	+	1.37766i	−0.913162	+	0.407596i	$0.866367\pi$
$312$		0			0
$313$	4.83829	+	10.3757i	0.273476	+	0.586472i	0.994297	−	0.106650i	$-0.0340125\pi$
$313$	4.83829	+	10.3757i	0.273476	+	0.586472i	−0.720820	+	0.693122i	$0.756235\pi$
$314$	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	−0.565257	−	0.824915i	$-0.691223\pi$
$317$	7.17947	−	10.2533i	0.403239	−	0.575885i	0.968496	+	0.249030i	$0.0801117\pi$
$318$		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	−0.829034	−	0.559199i	$-0.811109\pi$
$331$	−4.38923	−	24.8926i	−0.241254	−	1.36822i	0.587780	−	0.809021i	$-0.300002\pi$
$332$	−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	−0.134109	−	0.990967i	$-0.542817\pi$
$337$	−1.72746	+	0.151133i	−0.0941006	+	0.00823274i	0.0400082	+	0.999199i	$0.487262\pi$
$338$	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	−0.770559	−	0.637369i	$-0.780023\pi$
$347$	−8.10639	+	5.67616i	−0.435174	+	0.304712i	0.335385	+	0.942081i	$0.391134\pi$
$348$		0			0
$349$	19.9263	+	23.7472i	1.06663	+	1.27116i	0.960939	+	0.276759i	$0.0892603\pi$
$349$	19.9263	+	23.7472i	1.06663	+	1.27116i	0.105689	+	0.994399i	$0.466295\pi$
$350$	−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	0.982937	+	0.183945i	$0.0588869\pi$
$353$	−0.319565	+	3.65264i	−0.0170087	+	0.194411i	−0.999945	+	0.0104654i	$0.996669\pi$
$354$		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	0.750438	−	0.660941i	$-0.229843\pi$
$359$	−3.73590	−	6.47077i	−0.197173	−	0.341514i	−0.947611	+	0.319427i	$0.896509\pi$
$360$		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	0.0199776	−	0.999800i	$-0.493640\pi$
$367$	15.3011	−	7.13502i	0.798711	−	0.372445i	0.778733	+	0.627356i	$0.215863\pi$
$368$	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	0.372146	−	0.928174i	$-0.378622\pi$
$373$	−1.92488	−	0.897584i	−0.0996663	−	0.0464752i	−0.471812	+	0.881699i	$0.656400\pi$
$374$	−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	$-0.920657\pi$
$379$		−	9.60506i		−	0.493379i	0.969095	−	0.246689i	$-0.0793427\pi$
$380$	−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	−0.904999	−	0.425413i	$-0.860129\pi$
$383$	0.0510389	−	0.109453i	0.00260797	−	0.00559281i	0.907607	+	0.419820i	$0.137907\pi$
$384$		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	0.870832	−	0.491581i	$-0.163581\pi$
$389$	24.1005	+	8.77187i	1.22194	+	0.444752i	0.351113	+	0.936333i	$0.385803\pi$
$390$		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	0.833903	−	0.551911i	$-0.186101\pi$
$397$	25.5064	+	6.83441i	1.28013	+	0.343009i	0.446225	+	0.894921i	$0.352768\pi$
$398$	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	0.928124	−	0.372272i	$-0.121421\pi$
$401$	33.5008	+	5.90709i	1.67295	+	0.294986i	0.744826	+	0.667259i	$0.232532\pi$
$402$		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	0.914998	−	0.403458i	$-0.132192\pi$
$409$	33.1027	+	5.83690i	1.63682	+	0.288616i	0.721826	+	0.692075i	$0.243303\pi$
$410$	−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	−0.157249	−	0.987559i	$-0.550263\pi$
$419$	−23.6855	−	19.8745i	−1.15711	−	0.970932i	−0.999862	+	0.0166274i	$0.994707\pi$
$420$		0			0
$421$	−13.7828	−	5.01653i	−0.671732	−	0.244490i	−0.0164386	−	0.999865i	$-0.505233\pi$
$421$	−13.7828	−	5.01653i	−0.671732	−	0.244490i	−0.655293	+	0.755374i	$0.727455\pi$
$422$	−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	$0.260663\pi$
$431$			30.3267i			1.46078i	−0.683028	+	0.730392i	$0.739337\pi$
$432$		0			0
$433$	5.35178	+	5.35178i	0.257190	+	0.257190i	0.823910	−	0.566720i	$-0.191788\pi$
$433$	5.35178	+	5.35178i	0.257190	+	0.257190i	−0.566720	+	0.823910i	$0.691788\pi$
$434$	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	−0.402089	−	0.915601i	$-0.631716\pi$
$439$	−9.78003	+	1.72448i	−0.466775	+	0.0823051i	−0.0646863	+	0.997906i	$0.520605\pi$
$440$	−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	−0.611851	−	0.790973i	$-0.709575\pi$
$443$	−8.40263	+	3.91821i	−0.399221	+	0.186160i	0.212630	+	0.977133i	$0.431797\pi$
$444$		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	−0.252644	−	0.967559i	$-0.581300\pi$
$449$	15.0787	−	26.1171i	0.711609	−	1.23254i	0.964253	−	0.264984i	$-0.0853667\pi$
$450$		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	−0.640902	−	0.767622i	$-0.721440\pi$
$457$	2.64140	−	30.1913i	0.123559	−	1.41229i	0.764462	−	0.644669i	$-0.223005\pi$
$458$	−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	0.535524	−	0.844520i	$-0.320114\pi$
$461$	−8.35560	−	9.95782i	−0.389159	−	0.463782i	−0.924683	+	0.380738i	$0.875670\pi$
$462$		0			0
$463$	22.5069	−	15.7595i	1.04598	−	0.732405i	0.0815330	−	0.996671i	$-0.474018\pi$
$463$	22.5069	−	15.7595i	1.04598	−	0.732405i	0.964450	+	0.264266i	$0.0851295\pi$
$464$	−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	0.515119	+	0.857118i	$0.327748\pi$
$467$	−7.76986	+	28.9975i	−0.359546	+	1.34184i	−0.874666	+	0.484727i	$0.838919\pi$
$468$		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	−0.997784	−	0.0665419i	$-0.978803\pi$
$479$	−1.81506	−	10.2937i	−0.0829324	−	0.470333i	0.914851	−	0.403791i	$-0.132308\pi$
$480$		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	−0.945947	−	0.324322i	$-0.894864\pi$
$487$	−13.7181	+	13.7181i	−0.621625	+	0.621625i	0.324322	+	0.945947i	$0.394864\pi$
$488$	−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	−0.631861	−	0.775082i	$-0.717708\pi$
$491$	−14.3153	−	39.3310i	−0.646040	−	1.77498i	−0.0141799	−	0.999899i	$-0.504514\pi$
$492$		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	−0.997927	−	0.0643635i	$-0.979498\pi$
$499$	−17.0051	+	20.2659i	−0.761253	+	0.907226i	0.236674	+	0.971589i	$0.423943\pi$
$500$	−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	0.942455	+	0.334334i	$0.108511\pi$
$503$	6.58100	+	24.5606i	0.293432	+	1.09510i	−0.649023	+	0.760769i	$0.724822\pi$
$504$		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	−0.608522	−	0.793537i	$-0.708237\pi$
$509$	5.29524	−	30.0308i	0.234707	−	1.33109i	0.843229	−	0.537554i	$-0.180652\pi$
$510$		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	−0.475901	−	0.879499i	$-0.657878\pi$
$521$	1.09146	−	0.630155i	0.0478178	−	0.0276076i	0.523718	+	0.851892i	$0.324544\pi$
$522$		0			0
$523$	−9.13037	+	2.44648i	−0.399243	+	0.106977i	−0.452853	−	0.891585i	$-0.649594\pi$
$523$	−9.13037	+	2.44648i	−0.399243	+	0.106977i	0.0536101	+	0.998562i	$0.482927\pi$
$524$	−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	0.288293	−	0.957542i	$-0.406912\pi$
$547$	−11.9957	−	8.39950i	−0.512900	−	0.359136i	−0.801193	+	0.598406i	$0.795801\pi$
$548$	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	−0.334618	−	0.942354i	$-0.608607\pi$
$557$	−3.61631	+	0.968988i	−0.153228	+	0.0410573i	0.181390	+	0.983411i	$0.441941\pi$
$558$		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	0.918948	−	0.394378i	$-0.129040\pi$
$563$	5.55357	+	7.93132i	0.234055	+	0.334265i	−0.684893	+	0.728644i	$0.740151\pi$
$564$		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	−0.251799	+	0.967780i	$0.581022\pi$
$569$	−29.7838	+	24.9915i	−1.24860	+	1.04770i	−0.996801	+	0.0799199i	$0.974534\pi$
$570$		0			0
$571$	−1.13871	+	6.45794i	−0.0476535	+	0.270256i	−0.999320	−	0.0368775i	$-0.988259\pi$
$571$	−1.13871	+	6.45794i	−0.0476535	+	0.270256i	0.951666	+	0.307134i	$0.0993700\pi$
$572$	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	0.998415	−	0.0562782i	$-0.0179234\pi$
$577$	2.53716	+	9.46880i	0.105623	+	0.394191i	−0.892792	+	0.450469i	$0.851257\pi$
$578$	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	−0.553038	−	0.833156i	$-0.686531\pi$
$587$	10.1521	−	14.4987i	0.419023	−	0.598427i	0.972061	+	0.234729i	$0.0754204\pi$
$588$		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	−0.772358	−	0.635187i	$-0.780923\pi$
$593$	−3.34033	+	3.34033i	−0.137171	+	0.137171i	0.635187	+	0.772358i	$0.280923\pi$
$594$		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	−0.683823	−	0.729648i	$-0.739684\pi$
$599$	−18.0781	+	6.57991i	−0.738653	+	0.268848i	−0.0548301	+	0.998496i	$0.517462\pi$
$600$		0			0
$601$	−1.93521	−	10.9751i	−0.0789387	−	0.447684i	−0.998501	−	0.0547387i	$-0.982567\pi$
$601$	−1.93521	−	10.9751i	−0.0789387	−	0.447684i	0.919562	−	0.392945i	$-0.128544\pi$
$602$	−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	0.291255	−	0.956646i	$-0.405927\pi$
$607$	18.3352	−	1.60413i	0.744204	−	0.0651094i	0.452950	+	0.891536i	$0.350372\pi$
$608$	−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	−0.995145	−	0.0984162i	$-0.968622\pi$
$613$	−2.08262	+	7.77243i	−0.0841161	+	0.313926i	0.911029	+	0.412342i	$0.135289\pi$
$614$	−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	−0.674477	−	0.738296i	$-0.735631\pi$
$617$	−5.25082	+	3.67666i	−0.211390	+	0.148017i	0.463087	+	0.886313i	$0.346742\pi$
$618$		0			0
$619$	−17.8281	−	21.2467i	−0.716573	−	0.853979i	0.277720	−	0.960662i	$-0.410421\pi$
$619$	−17.8281	−	21.2467i	−0.716573	−	0.853979i	−0.994293	+	0.106683i	$0.965977\pi$
$620$	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	−0.676151	−	0.736763i	$-0.736353\pi$
$631$	7.53540	−	13.0517i	0.299979	−	0.519580i	0.976131	+	0.217183i	$0.0696868\pi$
$632$	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	−0.713071	−	0.701091i	$-0.752696\pi$
$641$	−28.9474	+	5.10420i	−1.14335	+	0.201604i	−0.430281	+	0.902695i	$0.641585\pi$
$642$		0			0
$643$	−19.6987	−	9.18567i	−0.776842	−	0.362248i	−0.00658305	−	0.999978i	$-0.502095\pi$
$643$	−19.6987	−	9.18567i	−0.776842	−	0.362248i	−0.770259	+	0.637731i	$0.779873\pi$
$644$	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	0.952432	−	0.304752i	$-0.0985735\pi$
$647$	16.4745	+	16.4745i	0.647680	+	0.647680i	−0.304752	+	0.952432i	$0.598574\pi$
$648$		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	−0.985126	−	0.171835i	$-0.945030\pi$
$653$	−5.62864	+	12.0707i	−0.220266	+	0.472362i	0.764860	+	0.644197i	$0.222808\pi$
$654$		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	0.573387	−	0.819285i	$-0.305629\pi$
$659$	12.4761	+	4.54094i	0.486001	+	0.176890i	−0.0873859	+	0.996175i	$0.527851\pi$
$660$		0			0
$661$	−9.01628	−	7.56556i	−0.350693	−	0.294266i	0.450375	−	0.892839i	$-0.351290\pi$
$661$	−9.01628	−	7.56556i	−0.350693	−	0.294266i	−0.801068	+	0.598573i	$0.795735\pi$
$662$	−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	0.308318	−	0.951283i	$-0.400234\pi$
$673$	11.5900	+	1.01400i	0.446763	+	0.0390867i	0.138445	+	0.990370i	$0.455790\pi$
$674$	−1.79908			−0.0692981
$675$		0			0
$676$	−10.7192			−0.412276
$677$	−5.37998	−	0.470687i	−0.206769	−	0.0180900i	−0.0166995	−	0.999861i	$-0.505316\pi$
$677$	−5.37998	−	0.470687i	−0.206769	−	0.0180900i	−0.190070	+	0.981771i	$0.560871\pi$
$678$		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	−0.0613579	−	0.998116i	$-0.519543\pi$
$683$	−16.0348	−	4.29650i	−0.613553	−	0.164401i	−0.552195	+	0.833715i	$0.686210\pi$
$684$		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	0.433371	−	0.901216i	$-0.357324\pi$
$691$	4.89099	+	1.78018i	0.186062	+	0.0677211i	−0.247309	+	0.968937i	$0.579546\pi$
$692$	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	$-0.802021\pi$
$701$		−	30.8522i		−	1.16527i	0.812733	−	0.582636i	$-0.197979\pi$
$702$		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	−0.526722	−	0.850038i	$-0.676579\pi$
$709$	−19.4630	+	3.43186i	−0.730949	+	0.128886i	−0.204227	+	0.978924i	$0.565468\pi$
$710$	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	−0.920905	−	0.389786i	$-0.872549\pi$
$719$	−3.29514	+	5.70736i	−0.122888	+	0.212849i	0.798017	+	0.602635i	$0.205882\pi$
$720$		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	−0.930411	−	0.366517i	$-0.880550\pi$
$727$	1.33493	−	15.2584i	0.0495099	−	0.565901i	0.979921	−	0.199384i	$-0.0638942\pi$
$728$	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	−0.556679	−	0.830728i	$-0.687925\pi$
$733$	0.908462	−	0.636112i	0.0335548	−	0.0234953i	0.590234	+	0.807233i	$0.299036\pi$
$734$	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	0.502736	−	0.864440i	$-0.332327\pi$
$739$	0.148882	+	0.0859569i	0.00547670	+	0.00316198i	−0.497259	+	0.867602i	$0.665660\pi$
$740$	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	−0.450462	−	0.892796i	$-0.648741\pi$
$743$	−20.1450	+	1.76246i	−0.739048	+	0.0646584i	−0.288586	+	0.957454i	$0.593185\pi$
$744$		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	−0.0154616	−	0.999880i	$-0.504922\pi$
$751$	16.8648	−	6.13828i	0.615405	−	0.223989i	0.630867	+	0.775891i	$0.282700\pi$
$752$	−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	−0.966641	−	0.256133i	$-0.917551\pi$
$757$	−19.5487	+	19.5487i	−0.710508	+	0.710508i	0.256133	+	0.966641i	$0.417551\pi$
$758$	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	0.935815	−	0.352492i	$-0.114666\pi$
$761$	−0.210722	−	0.578955i	−0.00763868	−	0.0209871i	−0.943453	+	0.331505i	$0.892444\pi$
$762$		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	−0.0396163	−	0.999215i	$-0.512614\pi$
$769$	26.3803	−	31.4388i	0.951298	−	1.13371i	0.990914	−	0.134497i	$-0.0429420\pi$
$770$	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	−0.934977	−	0.354707i	$-0.884581\pi$
$773$	−8.41362	−	31.4000i	−0.302617	−	1.12938i	0.632361	−	0.774674i	$-0.282086\pi$
$774$		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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

L-functions

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