LMFDB - Embedded newform 585.2.j.i.451.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(406,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("585.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.j (of order $3$, degree $2$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 10x^{8} - 8x^{7} + 50x^{6} - 42x^{5} + 124x^{4} - 12x^{3} + 96x^{2} - 36x + 36 $ x^10 - 2x^9 + 10x^8 - 8x^7 + 50x^6 - 42x^5 + 124x^4 - 12x^3 + 96x^2 - 36*x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.3
Root			$0.313396 + 0.542817i$ of defining polynomial
Character	$\chi$	$=$	585.451
Dual form			585.2.j.i.406.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.313396 - 0.542817i) q^{2} +(0.803566 + 1.39182i) q^{4} -1.00000 q^{5} +(-2.21563 - 3.83759i) q^{7} +2.26092 q^{8} +(-0.313396 + 0.542817i) q^{10} +(3.02903 - 5.24643i) q^{11} +(2.27075 + 2.80066i) q^{13} -2.77748 q^{14} +(-0.898570 + 1.55637i) q^{16} +(-2.92053 - 5.05850i) q^{17} +(1.80357 + 3.12387i) q^{19} +(-0.803566 - 1.39182i) q^{20} +(-1.89857 - 3.28842i) q^{22} +(1.13046 - 1.95801i) q^{23} +1.00000 q^{25} +(2.23189 - 0.354887i) q^{26} +(3.56082 - 6.16752i) q^{28} +(4.04253 - 7.00186i) q^{29} +6.45826 q^{31} +(2.82414 + 4.89155i) q^{32} -3.66112 q^{34} +(2.21563 + 3.83759i) q^{35} +(0.898570 - 1.55637i) q^{37} +2.26092 q^{38} -2.26092 q^{40} +(-3.99587 + 6.92106i) q^{41} +(-3.24375 - 5.61835i) q^{43} +9.73610 q^{44} +(-0.708563 - 1.22727i) q^{46} +3.22841 q^{47} +(-6.31807 + 10.9432i) q^{49} +(0.313396 - 0.542817i) q^{50} +(-2.07331 + 5.41098i) q^{52} -10.0768 q^{53} +(-3.02903 + 5.24643i) q^{55} +(-5.00937 - 8.67648i) q^{56} +(-2.53382 - 4.38871i) q^{58} +(1.56460 + 2.70997i) q^{59} +(1.22913 + 2.12892i) q^{61} +(2.02399 - 3.50566i) q^{62} -0.0539916 q^{64} +(-2.27075 - 2.80066i) q^{65} +(2.16932 - 3.75737i) q^{67} +(4.69368 - 8.12968i) q^{68} +2.77748 q^{70} +(4.24742 + 7.35675i) q^{71} -0.819388 q^{73} +(-0.563216 - 0.975519i) q^{74} +(-2.89857 + 5.02047i) q^{76} -26.8449 q^{77} -8.42187 q^{79} +(0.898570 - 1.55637i) q^{80} +(2.50458 + 4.33806i) q^{82} -2.35423 q^{83} +(2.92053 + 5.05850i) q^{85} -4.06631 q^{86} +(6.84839 - 11.8618i) q^{88} +(0.386706 - 0.669795i) q^{89} +(5.71664 - 14.9194i) q^{91} +3.63360 q^{92} +(1.01177 - 1.75244i) q^{94} +(-1.80357 - 3.12387i) q^{95} +(3.16052 + 5.47418i) q^{97} +(3.96011 + 6.85911i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} - 6 q^{4} - 10 q^{5} - q^{7} - 12 q^{8} - 2 q^{10} + 8 q^{11} + q^{13} + 8 q^{14} - 4 q^{16} + 4 q^{19} + 6 q^{20} - 14 q^{22} - 6 q^{23} + 10 q^{25} + 10 q^{26} + 2 q^{28} + 16 q^{29}+ \cdots + 30 q^{98}+O(q^{100}) $ 10 * q + 2 * q^2 - 6 * q^4 - 10 * q^5 - q^7 - 12 * q^8 - 2 * q^10 + 8 * q^11 + q^13 + 8 * q^14 - 4 * q^16 + 4 * q^19 + 6 * q^20 - 14 * q^22 - 6 * q^23 + 10 * q^25 + 10 * q^26 + 2 * q^28 + 16 * q^29 + 18 * q^31 + 14 * q^32 + q^35 + 4 * q^37 - 12 * q^38 + 12 * q^40 + 6 * q^41 - 15 * q^43 - 28 * q^44 + 16 * q^46 - 20 * q^47 - 10 * q^49 + 2 * q^50 - 22 * q^52 + 40 * q^53 - 8 * q^55 - 2 * q^56 + 4 * q^58 + 12 * q^59 - 11 * q^61 - 22 * q^62 + 8 * q^64 - q^65 - 5 * q^67 + 50 * q^68 - 8 * q^70 + 10 * q^71 + 2 * q^73 - 26 * q^74 - 24 * q^76 - 84 * q^77 - 34 * q^79 + 4 * q^80 - 16 * q^82 - 32 * q^83 - 88 * q^86 - 20 * q^88 + 4 * q^89 - q^91 + 68 * q^92 + 16 * q^94 - 4 * q^95 + 11 * q^97 + 30 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.313396	−	0.542817i	0.221604	−	0.383830i	−0.733691	−	0.679483i	$-0.762204\pi$
$2$	0.313396	−	0.542817i	0.221604	−	0.383830i	0.955295	+	0.295653i	$0.0955374\pi$
$3$		0			0
$3$		0			0
$4$	0.803566	+	1.39182i	0.401783	+	0.695909i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	−2.21563	−	3.83759i	−0.837431	−	1.45047i	−0.892036	−	0.451965i	$-0.850723\pi$
$7$	−2.21563	−	3.83759i	−0.837431	−	1.45047i	0.0546047	−	0.998508i	$-0.482610\pi$
$8$	2.26092			0.799356
$9$		0			0
$10$	−0.313396	+	0.542817i	−0.0991044	+	0.171654i
$11$	3.02903	−	5.24643i	0.913287	−	1.58186i	0.103897	−	0.994588i	$-0.466869\pi$
$11$	3.02903	−	5.24643i	0.913287	−	1.58186i	0.809390	−	0.587271i	$-0.199798\pi$
$12$		0			0
$13$	2.27075	+	2.80066i	0.629793	+	0.776763i
$13$	2.27075	+	2.80066i	0.629793	+	0.776763i
$14$	−2.77748			−0.742313
$15$		0			0
$16$	−0.898570	+	1.55637i	−0.224642	+	0.389092i
$17$	−2.92053	−	5.05850i	−0.708332	−	1.22687i	−0.965475	−	0.260494i	$-0.916115\pi$
$17$	−2.92053	−	5.05850i	−0.708332	−	1.22687i	0.257143	−	0.966373i	$-0.417219\pi$
$18$		0			0
$19$	1.80357	+	3.12387i	0.413766	+	0.716665i	0.995298	−	0.0968592i	$-0.0308797\pi$
$19$	1.80357	+	3.12387i	0.413766	+	0.716665i	−0.581532	+	0.813524i	$0.697546\pi$
$20$	−0.803566	−	1.39182i	−0.179683	−	0.311220i
$21$		0			0
$22$	−1.89857	−	3.28842i	−0.404776	−	0.701093i
$23$	1.13046	−	1.95801i	0.235717	−	0.408274i	−0.723764	−	0.690048i	$-0.757589\pi$
$23$	1.13046	−	1.95801i	0.235717	−	0.408274i	0.959481	+	0.281774i	$0.0909228\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	2.23189	−	0.354887i	0.437710	−	0.0695991i
$27$		0			0
$28$	3.56082	−	6.16752i	0.672931	−	1.16555i
$29$	4.04253	−	7.00186i	0.750679	−	1.30021i	−0.196816	−	0.980441i	$-0.563060\pi$
$29$	4.04253	−	7.00186i	0.750679	−	1.30021i	0.947494	−	0.319773i	$-0.103607\pi$
$30$		0			0
$31$	6.45826			1.15994			0.579969	−	0.814638i	$-0.303065\pi$
$31$	6.45826			1.15994			0.579969	+	0.814638i	$0.303065\pi$
$32$	2.82414	+	4.89155i	0.499241	+	0.864711i
$33$		0			0
$34$	−3.66112			−0.627878
$35$	2.21563	+	3.83759i	0.374511	+	0.648671i
$36$		0			0
$37$	0.898570	−	1.55637i	0.147724	−	0.255865i	−0.782662	−	0.622447i	$-0.786139\pi$
$37$	0.898570	−	1.55637i	0.147724	−	0.255865i	0.930386	+	0.366582i	$0.119472\pi$
$38$	2.26092			0.366770
$39$		0			0
$40$	−2.26092			−0.357483
$41$	−3.99587	+	6.92106i	−0.624051	+	1.08089i	0.364673	+	0.931136i	$0.381181\pi$
$41$	−3.99587	+	6.92106i	−0.624051	+	1.08089i	−0.988724	+	0.149752i	$0.952153\pi$
$42$		0			0
$43$	−3.24375	−	5.61835i	−0.494668	−	0.856790i	0.505313	−	0.862936i	$-0.331377\pi$
$43$	−3.24375	−	5.61835i	−0.494668	−	0.856790i	−0.999981	+	0.00614624i	$0.998044\pi$
$44$	9.73610			1.46777
$45$		0			0
$46$	−0.708563	−	1.22727i	−0.104472	−	0.180951i
$47$	3.22841			0.470912			0.235456	−	0.971885i	$-0.424342\pi$
$47$	3.22841			0.470912			0.235456	+	0.971885i	$0.424342\pi$
$48$		0			0
$49$	−6.31807	+	10.9432i	−0.902581	+	1.56332i
$50$	0.313396	−	0.542817i	0.0443208	−	0.0767660i
$51$		0			0
$52$	−2.07331	+	5.41098i	−0.287516	+	0.750369i
$53$	−10.0768			−1.38416			−0.692078	−	0.721823i	$-0.743304\pi$
$53$	−10.0768			−1.38416			−0.692078	+	0.721823i	$0.743304\pi$
$54$		0			0
$55$	−3.02903	+	5.24643i	−0.408434	+	0.707429i
$56$	−5.00937	−	8.67648i	−0.669405	−	1.15944i
$57$		0			0
$58$	−2.53382	−	4.38871i	−0.332707	−	0.576266i
$59$	1.56460	+	2.70997i	0.203694	+	0.352809i	0.949716	−	0.313113i	$-0.101372\pi$
$59$	1.56460	+	2.70997i	0.203694	+	0.352809i	−0.746022	+	0.665922i	$0.768039\pi$
$60$		0			0
$61$	1.22913	+	2.12892i	0.157374	+	0.272580i	0.933921	−	0.357479i	$-0.116364\pi$
$61$	1.22913	+	2.12892i	0.157374	+	0.272580i	−0.776547	+	0.630060i	$0.783030\pi$
$62$	2.02399	−	3.50566i	0.257047	−	0.445219i
$63$		0			0
$64$	−0.0539916			−0.00674895
$65$	−2.27075	−	2.80066i	−0.281652	−	0.347379i
$66$		0			0
$67$	2.16932	−	3.75737i	0.265025	−	0.459036i	−0.702546	−	0.711639i	$-0.747953\pi$
$67$	2.16932	−	3.75737i	0.265025	−	0.459036i	0.967570	+	0.252603i	$0.0812866\pi$
$68$	4.69368	−	8.12968i	0.569192	−	0.985869i
$69$		0			0
$70$	2.77748			0.331972
$71$	4.24742	+	7.35675i	0.504076	+	0.873086i	0.999989	+	0.00471324i	$0.00150028\pi$
$71$	4.24742	+	7.35675i	0.504076	+	0.873086i	−0.495913	+	0.868372i	$0.665166\pi$
$72$		0			0
$73$	−0.819388			−0.0959021			−0.0479511	−	0.998850i	$-0.515269\pi$
$73$	−0.819388			−0.0959021			−0.0479511	+	0.998850i	$0.515269\pi$
$74$	−0.563216	−	0.975519i	−0.0654725	−	0.113402i
$75$		0			0
$76$	−2.89857	+	5.02047i	−0.332489	+	0.575887i
$77$	−26.8449			−3.05926
$78$		0			0
$79$	−8.42187			−0.947535			−0.473767	−	0.880650i	$-0.657106\pi$
$79$	−8.42187			−0.947535			−0.473767	+	0.880650i	$0.657106\pi$
$80$	0.898570	−	1.55637i	0.100463	−	0.174007i
$81$		0			0
$82$	2.50458	+	4.33806i	0.276584	+	0.479058i
$83$	−2.35423			−0.258410			−0.129205	−	0.991618i	$-0.541243\pi$
$83$	−2.35423			−0.258410			−0.129205	+	0.991618i	$0.541243\pi$
$84$		0			0
$85$	2.92053	+	5.05850i	0.316776	+	0.548672i
$86$	−4.06631			−0.438482
$87$		0			0
$88$	6.84839	−	11.8618i	0.730041	−	1.26447i
$89$	0.386706	−	0.669795i	0.0409908	−	0.0709982i	−0.844802	−	0.535079i	$-0.820282\pi$
$89$	0.386706	−	0.669795i	0.0409908	−	0.0709982i	0.885793	+	0.464081i	$0.153615\pi$
$90$		0			0
$91$	5.71664	−	14.9194i	0.599267	−	1.56398i
$92$	3.63360			0.378829
$93$		0			0
$94$	1.01177	−	1.75244i	0.104356	−	0.180750i
$95$	−1.80357	−	3.12387i	−0.185042	−	0.320502i
$96$		0			0
$97$	3.16052	+	5.47418i	0.320902	+	0.555819i	0.980674	−	0.195647i	$-0.0626806\pi$
$97$	3.16052	+	5.47418i	0.320902	+	0.555819i	−0.659772	+	0.751466i	$0.729347\pi$
$98$	3.96011	+	6.85911i	0.400032	+	0.692875i
$99$		0			0
$100$	0.803566	+	1.39182i	0.0803566	+	0.139182i
$101$	−4.45848	+	7.72231i	−0.443635	+	0.768398i	−0.997956	−	0.0639046i	$-0.979645\pi$
$101$	−4.45848	+	7.72231i	−0.443635	+	0.768398i	0.554321	+	0.832303i	$0.312978\pi$
$102$		0			0
$103$	0.112968			0.0111311			0.00556556	−	0.999985i	$-0.498228\pi$
$103$	0.112968			0.0111311			0.00556556	+	0.999985i	$0.498228\pi$
$104$	5.13398	+	6.33207i	0.503428	+	0.620910i
$105$		0			0
$106$	−3.15803	+	5.46986i	−0.306735	+	0.531280i
$107$	−3.87512	+	6.71191i	−0.374622	+	0.648865i	−0.990270	−	0.139156i	$-0.955561\pi$
$107$	−3.87512	+	6.71191i	−0.374622	+	0.648865i	0.615648	+	0.788021i	$0.288894\pi$
$108$		0			0
$109$	−11.4744			−1.09905			−0.549525	−	0.835477i	$-0.685191\pi$
$109$	−11.4744			−1.09905			−0.549525	+	0.835477i	$0.685191\pi$
$110$	1.89857	+	3.28842i	0.181022	+	0.313539i
$111$		0			0
$112$	7.96361			0.752490
$113$	3.12369	+	5.41040i	0.293852	+	0.508967i	0.974717	−	0.223442i	$-0.0717293\pi$
$113$	3.12369	+	5.41040i	0.293852	+	0.508967i	−0.680865	+	0.732409i	$0.738396\pi$
$114$		0			0
$115$	−1.13046	+	1.95801i	−0.105416	+	0.182586i
$116$	12.9938			1.20644
$117$		0			0
$118$	1.96136			0.180558
$119$	−12.9416	+	22.4156i	−1.18636	+	2.05483i
$120$		0			0
$121$	−12.8500	−	22.2569i	−1.16819	−	2.02336i
$122$	1.54082			0.139499
$123$		0			0
$124$	5.18964	+	8.98873i	0.466044	+	0.807211i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−5.60171	+	9.70245i	−0.497071	+	0.860953i	−0.999994	−	0.00337830i	$-0.998925\pi$
$127$	−5.60171	+	9.70245i	−0.497071	+	0.860953i	0.502923	+	0.864331i	$0.332258\pi$
$128$	−5.66519	+	9.81240i	−0.500737	+	0.867302i
$129$		0			0
$130$	−2.23189	+	0.354887i	−0.195750	+	0.0311257i
$131$	0.494893			0.0432390			0.0216195	−	0.999766i	$-0.493118\pi$
$131$	0.494893			0.0432390			0.0216195	+	0.999766i	$0.493118\pi$
$132$		0			0
$133$	7.99209	−	13.8427i	0.693002	−	1.20031i
$134$	−1.35971	−	2.35509i	−0.117461	−	0.203449i
$135$		0			0
$136$	−6.60308	−	11.4369i	−0.566209	−	0.980704i
$137$	11.5749	+	20.0483i	0.988909	+	1.71284i	0.623078	+	0.782160i	$0.285882\pi$
$137$	11.5749	+	20.0483i	0.988909	+	1.71284i	0.365832	+	0.930681i	$0.380785\pi$
$138$		0			0
$139$	5.97871	+	10.3554i	0.507107	+	0.878336i	0.999966	+	0.00822631i	$0.00261855\pi$
$139$	5.97871	+	10.3554i	0.507107	+	0.878336i	−0.492859	+	0.870109i	$0.664048\pi$
$140$	−3.56082	+	6.16752i	−0.300944	+	0.521250i
$141$		0			0
$142$	5.32450			0.446822
$143$	21.5716	−	3.43005i	1.80391	−	0.286835i
$144$		0			0
$145$	−4.04253	+	7.00186i	−0.335714	+	0.581473i
$146$	−0.256793	+	0.444778i	−0.0212523	+	0.0368101i
$147$		0			0
$148$	2.88824			0.237412
$149$	−10.6089	−	18.3752i	−0.869117	−	1.50536i	−0.862900	−	0.505375i	$-0.831354\pi$
$149$	−10.6089	−	18.3752i	−0.869117	−	1.50536i	−0.00621731	−	0.999981i	$-0.501979\pi$
$150$		0			0
$151$	19.4623			1.58382			0.791909	−	0.610639i	$-0.209087\pi$
$151$	19.4623			1.58382			0.791909	+	0.610639i	$0.209087\pi$
$152$	4.07772	+	7.06282i	0.330747	+	0.572870i
$153$		0			0
$154$	−8.41307	+	14.5719i	−0.677945	+	1.17423i
$155$	−6.45826			−0.518740
$156$		0			0
$157$	20.6547			1.64842			0.824212	−	0.566282i	$-0.191618\pi$
$157$	20.6547			1.64842			0.824212	+	0.566282i	$0.191618\pi$
$158$	−2.63938	+	4.57154i	−0.209978	+	0.363692i
$159$		0			0
$160$	−2.82414	−	4.89155i	−0.223268	−	0.386711i
$161$	−10.0187			−0.789587
$162$		0			0
$163$	2.42990	+	4.20871i	0.190324	+	0.329652i	0.945358	−	0.326035i	$-0.105713\pi$
$163$	2.42990	+	4.20871i	0.190324	+	0.329652i	−0.755033	+	0.655686i	$0.772379\pi$
$164$	−12.8438			−1.00293
$165$		0			0
$166$	−0.737805	+	1.27792i	−0.0572648	+	0.0991855i
$167$	1.28997	−	2.23430i	0.0998212	−	0.172895i	−0.811789	−	0.583950i	$-0.801506\pi$
$167$	1.28997	−	2.23430i	0.0998212	−	0.172895i	0.911611	+	0.411055i	$0.134840\pi$
$168$		0			0
$169$	−2.68740	+	12.7192i	−0.206723	+	0.978400i
$170$	3.66112			0.280795
$171$		0			0
$172$	5.21314	−	9.02943i	0.397498	−	0.688487i
$173$	−5.12339	−	8.87397i	−0.389524	−	0.674675i	0.602862	−	0.797846i	$-0.294027\pi$
$173$	−5.12339	−	8.87397i	−0.389524	−	0.674675i	−0.992386	+	0.123170i	$0.960694\pi$
$174$		0			0
$175$	−2.21563	−	3.83759i	−0.167486	−	0.290095i
$176$	5.44359	+	9.42857i	0.410326	+	0.710706i
$177$		0			0
$178$	−0.242384	−	0.419822i	−0.0181675	−	0.0314670i
$179$	−5.30141	+	9.18232i	−0.396246	+	0.686319i	−0.993259	−	0.115913i	$-0.963021\pi$
$179$	−5.30141	+	9.18232i	−0.396246	+	0.686319i	0.597013	+	0.802231i	$0.296354\pi$
$180$		0			0
$181$	16.8618			1.25333			0.626664	−	0.779289i	$-0.284420\pi$
$181$	16.8618			1.25333			0.626664	+	0.779289i	$0.284420\pi$
$182$	−6.30696	−	7.77878i	−0.467503	−	0.576602i
$183$		0			0
$184$	2.55588	−	4.42691i	0.188422	−	0.326356i
$185$	−0.898570	+	1.55637i	−0.0660642	+	0.114427i
$186$		0			0
$187$	−35.3855			−2.58764
$188$	2.59424	+	4.49336i	0.189204	+	0.327712i
$189$		0			0
$190$	−2.26092			−0.164024
$191$	−5.49549	−	9.51847i	−0.397640	−	0.688732i	0.595795	−	0.803137i	$-0.296837\pi$
$191$	−5.49549	−	9.51847i	−0.397640	−	0.688732i	−0.993434	+	0.114405i	$0.963504\pi$
$192$		0			0
$193$	3.32586	−	5.76057i	0.239401	−	0.414655i	−0.721142	−	0.692788i	$-0.756382\pi$
$193$	3.32586	−	5.76057i	0.239401	−	0.414655i	0.960543	+	0.278133i	$0.0897156\pi$
$194$	3.96197			0.284453
$195$		0			0
$196$	−20.3079			−1.45057
$197$	11.9930	−	20.7725i	0.854466	−	1.47998i	−0.0226743	−	0.999743i	$-0.507218\pi$
$197$	11.9930	−	20.7725i	0.854466	−	1.47998i	0.877140	−	0.480235i	$-0.159449\pi$
$198$		0			0
$199$	10.4552	+	18.1089i	0.741147	+	1.28370i	0.951973	+	0.306181i	$0.0990512\pi$
$199$	10.4552	+	18.1089i	0.741147	+	1.28370i	−0.210826	+	0.977524i	$0.567615\pi$
$200$	2.26092			0.159871
$201$		0			0
$202$	2.79454	+	4.84028i	0.196623	+	0.340561i
$203$	−35.8270			−2.51457
$204$		0			0
$205$	3.99587	−	6.92106i	0.279084	−	0.483387i
$206$	0.0354038	−	0.0613212i	0.00246670	−	0.00427245i
$207$		0			0
$208$	−6.39929	+	1.01753i	−0.443711	+	0.0705533i
$209$	21.8522			1.51155
$210$		0			0
$211$	−6.56540	+	11.3716i	−0.451981	+	0.782853i	−0.998509	−	0.0545873i	$-0.982616\pi$
$211$	−6.56540	+	11.3716i	−0.451981	+	0.782853i	0.546528	+	0.837441i	$0.315949\pi$
$212$	−8.09738	−	14.0251i	−0.556130	−	0.963246i
$213$		0			0
$214$	2.42889	+	4.20697i	0.166036	+	0.287582i
$215$	3.24375	+	5.61835i	0.221222	+	0.383168i
$216$		0			0
$217$	−14.3091	−	24.7842i	−0.971368	−	1.68246i
$218$	−3.59603	+	6.22851i	−0.243554	+	0.421848i
$219$		0			0
$220$	−9.73610			−0.656408
$221$	7.53536	−	19.6660i	0.506883	−	1.32288i
$222$		0			0
$223$	10.6003	−	18.3603i	0.709851	−	1.22950i	−0.255061	−	0.966925i	$-0.582095\pi$
$223$	10.6003	−	18.3603i	0.709851	−	1.22950i	0.964912	−	0.262574i	$-0.0845712\pi$
$224$	12.5145	−	21.6758i	0.836160	−	1.44827i
$225$		0			0
$226$	3.91581			0.260476
$227$	4.61972	+	8.00159i	0.306622	+	0.531084i	0.977621	−	0.210374i	$-0.0674681\pi$
$227$	4.61972	+	8.00159i	0.306622	+	0.531084i	−0.670999	+	0.741458i	$0.734135\pi$
$228$		0			0
$229$	3.16502			0.209150			0.104575	−	0.994517i	$-0.466652\pi$
$229$	3.16502			0.209150			0.104575	+	0.994517i	$0.466652\pi$
$230$	0.708563	+	1.22727i	0.0467212	+	0.0809235i
$231$		0			0
$232$	9.13983	−	15.8307i	0.600059	−	1.03933i
$233$	−2.83723			−0.185873			−0.0929364	−	0.995672i	$-0.529625\pi$
$233$	−2.83723			−0.185873			−0.0929364	+	0.995672i	$0.529625\pi$
$234$		0			0
$235$	−3.22841			−0.210598
$236$	−2.51453	+	4.35529i	−0.163682	+	0.283505i
$237$		0			0
$238$	8.11171	+	14.0499i	0.525804	+	0.910720i
$239$	−0.634366			−0.0410337			−0.0205169	−	0.999790i	$-0.506531\pi$
$239$	−0.634366			−0.0410337			−0.0205169	+	0.999790i	$0.506531\pi$
$240$		0			0
$241$	0.449233	+	0.778094i	0.0289376	+	0.0501215i	0.880132	−	0.474730i	$-0.157454\pi$
$241$	0.449233	+	0.778094i	0.0289376	+	0.0501215i	−0.851194	+	0.524851i	$0.824121\pi$
$242$	−16.1086			−1.03550
$243$		0			0
$244$	−1.97538	+	3.42146i	−0.126461	+	0.219036i
$245$	6.31807	−	10.9432i	0.403647	−	0.699136i
$246$		0			0
$247$	−4.65345	+	12.1447i	−0.296092	+	0.772749i
$248$	14.6016			0.927204
$249$		0			0
$250$	−0.313396	+	0.542817i	−0.0198209	+	0.0343308i
$251$	7.22838	+	12.5199i	0.456252	+	0.790251i	0.998759	−	0.0498000i	$-0.0158584\pi$
$251$	7.22838	+	12.5199i	0.456252	+	0.790251i	−0.542508	+	0.840051i	$0.682525\pi$
$252$		0			0
$253$	−6.84839	−	11.8618i	−0.430555	−	0.745743i
$254$	3.51110	+	6.08141i	0.220306	+	0.381582i
$255$		0			0
$256$	3.49690	+	6.05681i	0.218556	+	0.378551i
$257$	−0.209252	+	0.362435i	−0.0130528	+	0.0226081i	−0.872478	−	0.488653i	$-0.837488\pi$
$257$	−0.209252	+	0.362435i	−0.0130528	+	0.0226081i	0.859425	+	0.511261i	$0.170822\pi$
$258$		0			0
$259$	−7.96361			−0.494835
$260$	2.07331	−	5.41098i	0.128581	−	0.335575i
$261$		0			0
$262$	0.155097	−	0.268636i	0.00958194	−	0.0165964i
$263$	1.24526	−	2.15686i	0.0767861	−	0.132997i	−0.825075	−	0.565022i	$-0.808867\pi$
$263$	1.24526	−	2.15686i	0.0767861	−	0.132997i	0.901862	+	0.432025i	$0.142201\pi$
$264$		0			0
$265$	10.0768			0.619013
$266$	−5.00937	−	8.67648i	−0.307144	−	0.531989i
$267$		0			0
$268$	6.97277			0.425930
$269$	0.884288	+	1.53163i	0.0539160	+	0.0933853i	0.891724	−	0.452580i	$-0.149496\pi$
$269$	0.884288	+	1.53163i	0.0539160	+	0.0933853i	−0.837808	+	0.545965i	$0.816163\pi$
$270$		0			0
$271$	10.2018	−	17.6700i	0.619714	−	1.07338i	−0.369824	−	0.929102i	$-0.620582\pi$
$271$	10.2018	−	17.6700i	0.619714	−	1.07338i	0.989538	−	0.144274i	$-0.0460845\pi$
$272$	10.4972			0.636486
$273$		0			0
$274$	14.5101			0.876586
$275$	3.02903	−	5.24643i	0.182657	−	0.316372i
$276$		0			0
$277$	2.42247	+	4.19584i	0.145552	+	0.252103i	0.929579	−	0.368624i	$-0.120171\pi$
$277$	2.42247	+	4.19584i	0.145552	+	0.252103i	−0.784027	+	0.620727i	$0.786838\pi$
$278$	7.49480			0.449508
$279$		0			0
$280$	5.00937	+	8.67648i	0.299367	+	0.518519i
$281$	−5.20237			−0.310347			−0.155174	−	0.987887i	$-0.549594\pi$
$281$	−5.20237			−0.310347			−0.155174	+	0.987887i	$0.549594\pi$
$282$		0			0
$283$	−5.01017	+	8.67787i	−0.297824	+	0.515846i	−0.975638	−	0.219388i	$-0.929594\pi$
$283$	−5.01017	+	8.67787i	−0.297824	+	0.515846i	0.677814	+	0.735233i	$0.262927\pi$
$284$	−6.82617	+	11.8233i	−0.405059	+	0.701582i
$285$		0			0
$286$	4.89857	−	12.7844i	0.289659	−	0.755959i
$287$	35.4136			2.09040
$288$		0			0
$289$	−8.55897	+	14.8246i	−0.503469	+	0.872034i
$290$	2.53382	+	4.38871i	0.148791	+	0.257714i
$291$		0			0
$292$	−0.658433	−	1.14044i	−0.0385319	−	0.0667391i
$293$	3.75349	+	6.50123i	0.219281	+	0.379806i	0.954588	−	0.297928i	$-0.0962955\pi$
$293$	3.75349	+	6.50123i	0.219281	+	0.379806i	−0.735307	+	0.677734i	$0.762962\pi$
$294$		0			0
$295$	−1.56460	−	2.70997i	−0.0910948	−	0.157781i
$296$	2.03159	−	3.51882i	0.118084	−	0.204528i
$297$		0			0
$298$	−13.2992			−0.770400
$299$	8.05072	−	1.28012i	0.465585	−	0.0740315i
$300$		0			0
$301$	−14.3739	+	24.8964i	−0.828500	+	1.43500i
$302$	6.09940	−	10.5645i	0.350981	−	0.607917i
$303$		0			0
$304$	−6.48252			−0.371798
$305$	−1.22913	−	2.12892i	−0.0703799	−	0.121902i
$306$		0			0
$307$	−11.4404			−0.652940			−0.326470	−	0.945208i	$-0.605859\pi$
$307$	−11.4404			−0.652940			−0.326470	+	0.945208i	$0.605859\pi$
$308$	−21.5716	−	37.3632i	−1.22916	−	2.12897i
$309$		0			0
$310$	−2.02399	+	3.50566i	−0.114955	+	0.199108i
$311$	−24.2351			−1.37424			−0.687122	−	0.726542i	$-0.741126\pi$
$311$	−24.2351			−1.37424			−0.687122	+	0.726542i	$0.741126\pi$
$312$		0			0
$313$	−18.8796			−1.06714			−0.533570	−	0.845756i	$-0.679150\pi$
$313$	−18.8796			−1.06714			−0.533570	+	0.845756i	$0.679150\pi$
$314$	6.47309	−	11.2117i	0.365298	−	0.632714i
$315$		0			0
$316$	−6.76753	−	11.7217i	−0.380703	−	0.659398i
$317$	−22.3459			−1.25507			−0.627534	−	0.778589i	$-0.715936\pi$
$317$	−22.3459			−1.25507			−0.627534	+	0.778589i	$0.715936\pi$
$318$		0			0
$319$	−24.4899	−	42.4177i	−1.37117	−	2.37494i
$320$	0.0539916			0.00301822
$321$		0			0
$322$	−3.13983	+	5.43835i	−0.174976	+	0.303067i
$323$	10.5347	−	18.2467i	0.586168	−	1.01527i
$324$		0			0
$325$	2.27075	+	2.80066i	0.125959	+	0.155353i
$326$	3.04608			0.168707
$327$		0			0
$328$	−9.03435	+	15.6479i	−0.498838	+	0.864013i
$329$	−7.15297	−	12.3893i	−0.394356	−	0.683045i
$330$		0			0
$331$	11.3443	+	19.6490i	0.623541	+	1.08001i	0.988821	+	0.149107i	$0.0476400\pi$
$331$	11.3443	+	19.6490i	0.623541	+	1.08001i	−0.365280	+	0.930898i	$0.619027\pi$
$332$	−1.89178	−	3.27666i	−0.103825	−	0.179830i
$333$		0			0
$334$	−0.808545	−	1.40044i	−0.0442416	−	0.0766287i
$335$	−2.16932	+	3.75737i	−0.118523	+	0.205287i
$336$		0			0
$337$	−0.166960			−0.00909489			−0.00454745	−	0.999990i	$-0.501448\pi$
$337$	−0.166960			−0.00909489			−0.00454745	+	0.999990i	$0.501448\pi$
$338$	6.06198	+	5.44491i	0.329728	+	0.296164i
$339$		0			0
$340$	−4.69368	+	8.12968i	−0.254550	+	0.440894i
$341$	19.5623	−	33.8829i	1.05936	−	1.83486i
$342$		0			0
$343$	24.9752			1.34854
$344$	−7.33387	−	12.7026i	−0.395416	−	0.684880i
$345$		0			0
$346$	−6.42259			−0.345281
$347$	7.31716	+	12.6737i	0.392806	+	0.680359i	0.992818	−	0.119631i	$-0.0381712\pi$
$347$	7.31716	+	12.6737i	0.392806	+	0.680359i	−0.600013	+	0.799990i	$0.704838\pi$
$348$		0			0
$349$	−1.11356	+	1.92874i	−0.0596074	+	0.103243i	−0.894289	−	0.447489i	$-0.852318\pi$
$349$	−1.11356	+	1.92874i	−0.0596074	+	0.103243i	0.834682	+	0.550733i	$0.185652\pi$
$350$	−2.77748			−0.148463
$351$		0			0
$352$	34.2176			1.82380
$353$	2.96970	−	5.14366i	0.158061	−	0.273770i	−0.776108	−	0.630599i	$-0.782809\pi$
$353$	2.96970	−	5.14366i	0.158061	−	0.273770i	0.934169	+	0.356830i	$0.116142\pi$
$354$		0			0
$355$	−4.24742	−	7.35675i	−0.225430	−	0.390456i
$356$	1.24298			0.0658777
$357$		0			0
$358$	3.32288	+	5.75540i	0.175620	+	0.304182i
$359$	−10.9234			−0.576516			−0.288258	−	0.957553i	$-0.593076\pi$
$359$	−10.9234			−0.576516			−0.288258	+	0.957553i	$0.593076\pi$
$360$		0			0
$361$	2.99430	−	5.18628i	0.157595	−	0.272962i
$362$	5.28442	−	9.15288i	0.277743	−	0.481065i
$363$		0			0
$364$	25.3588	−	4.03224i	1.32916	−	0.211347i
$365$	0.819388			0.0428887
$366$		0			0
$367$	−4.32224	+	7.48634i	−0.225619	+	0.390784i	−0.956505	−	0.291716i	$-0.905774\pi$
$367$	−4.32224	+	7.48634i	−0.225619	+	0.390784i	0.730886	+	0.682500i	$0.239107\pi$
$368$	2.03159	+	3.51882i	0.105904	+	0.183431i
$369$		0			0
$370$	0.563216	+	0.975519i	0.0292802	+	0.0507148i
$371$	22.3265	+	38.6706i	1.15913	+	2.00768i
$372$		0			0
$373$	−9.15260	−	15.8528i	−0.473904	−	0.820826i	0.525650	−	0.850701i	$-0.323822\pi$
$373$	−9.15260	−	15.8528i	−0.473904	−	0.820826i	−0.999554	+	0.0298755i	$0.990489\pi$
$374$	−11.0897	+	19.2078i	−0.573432	+	0.993214i
$375$		0			0
$376$	7.29917			0.376426
$377$	28.7894	−	4.57773i	1.48273	−	0.235765i
$378$		0			0
$379$	15.0031	−	25.9861i	0.770657	−	1.33482i	−0.166546	−	0.986034i	$-0.553262\pi$
$379$	15.0031	−	25.9861i	0.770657	−	1.33482i	0.937203	−	0.348783i	$-0.113405\pi$
$380$	2.89857	−	5.02047i	0.148694	−	0.257545i
$381$		0			0
$382$	−6.88905			−0.352474
$383$	7.26799	+	12.5885i	0.371377	+	0.643244i	0.989778	−	0.142619i	$-0.0455524\pi$
$383$	7.26799	+	12.5885i	0.371377	+	0.643244i	−0.618401	+	0.785863i	$0.712219\pi$
$384$		0			0
$385$	26.8449			1.36814
$386$	−2.08462	−	3.61067i	−0.106105	−	0.183778i
$387$		0			0
$388$	−5.07937	+	8.79773i	−0.257866	+	0.446637i
$389$	−24.5259			−1.24351			−0.621756	−	0.783211i	$-0.713581\pi$
$389$	−24.5259			−1.24351			−0.621756	+	0.783211i	$0.713581\pi$
$390$		0			0
$391$	−13.2062			−0.667864
$392$	−14.2846	+	24.7417i	−0.721484	+	1.24965i
$393$		0			0
$394$	−7.51711	−	13.0200i	−0.378706	−	0.655939i
$395$	8.42187			0.423750
$396$		0			0
$397$	4.72045	+	8.17606i	0.236913	+	0.410345i	0.959827	−	0.280593i	$-0.0905312\pi$
$397$	4.72045	+	8.17606i	0.236913	+	0.410345i	−0.722914	+	0.690938i	$0.757198\pi$
$398$	13.1064			0.656965
$399$		0			0
$400$	−0.898570	+	1.55637i	−0.0449285	+	0.0778184i
$401$	0.244187	−	0.422945i	0.0121941	−	0.0211209i	−0.859864	−	0.510523i	$-0.829452\pi$
$401$	0.244187	−	0.422945i	0.0121941	−	0.0211209i	0.872058	+	0.489402i	$0.162785\pi$
$402$		0			0
$403$	14.6651	+	18.0874i	0.730521	+	0.900998i
$404$	−14.3307			−0.712980
$405$		0			0
$406$	−11.2280	+	19.4475i	−0.557238	+	0.965165i
$407$	−5.44359	−	9.42857i	−0.269829	−	0.467357i
$408$		0			0
$409$	−10.3602	−	17.9443i	−0.512277	−	0.887290i	−0.999899	−	0.0142348i	$-0.995469\pi$
$409$	−10.3602	−	17.9443i	−0.512277	−	0.887290i	0.487622	−	0.873055i	$-0.337865\pi$
$410$	−2.50458	−	4.33806i	−0.123692	−	0.214241i
$411$		0			0
$412$	0.0907776	+	0.157231i	0.00447229	+	0.00774624i
$413$	6.93318	−	12.0086i	0.341160	−	0.590906i
$414$		0			0
$415$	2.35423			0.115565
$416$	−7.28666	+	19.0169i	−0.357258	+	0.932381i
$417$		0			0
$418$	6.84839	−	11.8618i	0.334966	−	0.580178i
$419$	2.27374	−	3.93823i	0.111079	−	0.192395i	−0.805126	−	0.593103i	$-0.797903\pi$
$419$	2.27374	−	3.93823i	0.111079	−	0.192395i	0.916206	+	0.400708i	$0.131236\pi$
$420$		0			0
$421$	31.0991			1.51568			0.757840	−	0.652441i	$-0.226255\pi$
$421$	31.0991			1.51568			0.757840	+	0.652441i	$0.226255\pi$
$422$	4.11513	+	7.12762i	0.200322	+	0.346967i
$423$		0			0
$424$	−22.7828			−1.10643
$425$	−2.92053	−	5.05850i	−0.141666	−	0.245373i
$426$		0			0
$427$	5.44661	−	9.43381i	0.263580	−	0.456534i
$428$	−12.4557			−0.602068
$429$		0			0
$430$	4.06631			0.196095
$431$	17.1081	−	29.6321i	0.824067	−	1.42733i	−0.0785630	−	0.996909i	$-0.525033\pi$
$431$	17.1081	−	29.6321i	0.824067	−	1.42733i	0.902630	−	0.430417i	$-0.141633\pi$
$432$		0			0
$433$	2.78163	+	4.81792i	0.133676	+	0.231534i	0.925091	−	0.379745i	$-0.123988\pi$
$433$	2.78163	+	4.81792i	0.133676	+	0.231534i	−0.791415	+	0.611280i	$0.790655\pi$
$434$	−17.9377			−0.861037
$435$		0			0
$436$	−9.22045	−	15.9703i	−0.441580	−	0.764838i
$437$	8.15544			0.390127
$438$		0			0
$439$	1.40974	−	2.44175i	0.0672834	−	0.116538i	−0.830421	−	0.557136i	$-0.811900\pi$
$439$	1.40974	−	2.44175i	0.0672834	−	0.116538i	0.897705	+	0.440598i	$0.145234\pi$
$440$	−6.84839	+	11.8618i	−0.326484	+	0.565487i
$441$		0			0
$442$	−8.31349	−	10.2536i	−0.395433	−	0.487712i
$443$	15.0635			0.715686			0.357843	−	0.933782i	$-0.383512\pi$
$443$	15.0635			0.715686			0.357843	+	0.933782i	$0.383512\pi$
$444$		0			0
$445$	−0.386706	+	0.669795i	−0.0183316	+	0.0317513i
$446$	−6.64420	−	11.5081i	−0.314612	−	0.544924i
$447$		0			0
$448$	0.119626	+	0.207198i	0.00565178	+	0.00978918i
$449$	1.92228	+	3.32949i	0.0907181	+	0.157128i	0.907813	−	0.419374i	$-0.137750\pi$
$449$	1.92228	+	3.32949i	0.0907181	+	0.157128i	−0.817095	+	0.576502i	$0.804417\pi$
$450$		0			0
$451$	24.2072	+	41.9282i	1.13987	+	1.97432i
$452$	−5.02019	+	8.69522i	−0.236130	+	0.408989i
$453$		0			0
$454$	5.79120			0.271795
$455$	−5.71664	+	14.9194i	−0.268000	+	0.699434i
$456$		0			0
$457$	−15.2140	+	26.3515i	−0.711682	+	1.23267i	0.252544	+	0.967586i	$0.418733\pi$
$457$	−15.2140	+	26.3515i	−0.711682	+	1.23267i	−0.964225	+	0.265084i	$0.914600\pi$
$458$	0.991904	−	1.71803i	0.0463486	−	0.0802782i
$459$		0			0
$460$	−3.63360			−0.169417
$461$	15.3961	+	26.6667i	0.717066	+	1.24199i	0.962157	+	0.272494i	$0.0878486\pi$
$461$	15.3961	+	26.6667i	0.717066	+	1.24199i	−0.245092	+	0.969500i	$0.578818\pi$
$462$		0			0
$463$	−12.9034			−0.599674			−0.299837	−	0.953991i	$-0.596932\pi$
$463$	−12.9034			−0.599674			−0.299837	+	0.953991i	$0.596932\pi$
$464$	7.26499	+	12.5833i	0.337269	+	0.584166i
$465$		0			0
$466$	−0.889174	+	1.54010i	−0.0411902	+	0.0713435i
$467$	−10.2346			−0.473601			−0.236800	−	0.971558i	$-0.576099\pi$
$467$	−10.2346			−0.473601			−0.236800	+	0.971558i	$0.576099\pi$
$468$		0			0
$469$	−19.2257			−0.887759
$470$	−1.01177	+	1.75244i	−0.0466694	+	0.0808338i
$471$		0			0
$472$	3.53745	+	6.12704i	0.162824	+	0.282020i
$473$	−39.3017			−1.80709
$474$		0			0
$475$	1.80357	+	3.12387i	0.0827533	+	0.143333i
$476$	−41.5979			−1.90664
$477$		0			0
$478$	−0.198808	+	0.344345i	−0.00909325	+	0.0157500i
$479$	17.5021	−	30.3146i	0.799693	−	1.38511i	−0.120122	−	0.992759i	$-0.538329\pi$
$479$	17.5021	−	30.3146i	0.799693	−	1.38511i	0.919816	−	0.392351i	$-0.128338\pi$
$480$		0			0
$481$	6.39929	−	1.01753i	0.291782	−	0.0463956i
$482$	0.563151			0.0256508
$483$		0			0
$484$	20.6517	−	35.7698i	0.938715	−	1.62590i
$485$	−3.16052	−	5.47418i	−0.143512	−	0.248570i
$486$		0			0
$487$	0.765925	+	1.32662i	0.0347074	+	0.0601149i	0.882857	−	0.469641i	$-0.155617\pi$
$487$	0.765925	+	1.32662i	0.0347074	+	0.0601149i	−0.848150	+	0.529756i	$0.822283\pi$
$488$	2.77897	+	4.81332i	0.125798	+	0.217889i
$489$		0			0
$490$	−3.96011	−	6.85911i	−0.178900	−	0.309863i
$491$	−12.5124	+	21.6721i	−0.564676	+	0.978048i	0.432404	+	0.901680i	$0.357666\pi$
$491$	−12.5124	+	21.6721i	−0.564676	+	0.978048i	−0.997080	+	0.0763675i	$0.975668\pi$
$492$		0			0
$493$	−47.2253			−2.12692
$494$	5.13398	+	6.33207i	0.230989	+	0.284893i
$495$		0			0
$496$	−5.80320	+	10.0514i	−0.260571	+	0.451323i
$497$	18.8215	−	32.5997i	0.844258	−	1.46230i
$498$		0			0
$499$	27.7838			1.24377			0.621887	−	0.783107i	$-0.286366\pi$
$499$	27.7838			1.24377			0.621887	+	0.783107i	$0.286366\pi$
$500$	−0.803566	−	1.39182i	−0.0359366	−	0.0622440i
$501$		0			0
$502$	9.06138			0.404429
$503$	21.5069	+	37.2511i	0.958947	+	1.66094i	0.725067	+	0.688679i	$0.241809\pi$
$503$	21.5069	+	37.2511i	0.958947	+	1.66094i	0.233880	+	0.972266i	$0.424858\pi$
$504$		0			0
$505$	4.45848	−	7.72231i	0.198400	−	0.343638i
$506$	−8.58503			−0.381651
$507$		0			0
$508$	−18.0054			−0.798860
$509$	0.568519	−	0.984703i	0.0251992	−	0.0436462i	−0.853151	−	0.521664i	$-0.825311\pi$
$509$	0.568519	−	0.984703i	0.0251992	−	0.0436462i	0.878350	+	0.478018i	$0.158645\pi$
$510$		0			0
$511$	1.81546	+	3.14448i	0.0803114	+	0.139103i
$512$	−18.2771			−0.807742
$513$		0			0
$514$	0.131157	+	0.227171i	0.00578510	+	0.0100201i
$515$	−0.112968			−0.00497798
$516$		0			0
$517$	9.77894	−	16.9376i	0.430077	−	0.744916i
$518$	−2.49576	+	4.32278i	−0.109657	+	0.189932i
$519$		0			0
$520$	−5.13398	−	6.33207i	−0.225140	−	0.277680i
$521$	−30.7311			−1.34635			−0.673177	−	0.739481i	$-0.735071\pi$
$521$	−30.7311			−1.34635			−0.673177	+	0.739481i	$0.735071\pi$
$522$		0			0
$523$	8.63268	−	14.9522i	0.377481	−	0.653816i	−0.613214	−	0.789917i	$-0.710124\pi$
$523$	8.63268	−	14.9522i	0.377481	−	0.653816i	0.990695	+	0.136101i	$0.0434571\pi$
$524$	0.397679	+	0.688801i	0.0173727	+	0.0300904i
$525$		0			0
$526$	−0.780519	−	1.35190i	−0.0340322	−	0.0589456i
$527$	−18.8615	−	32.6691i	−0.821622	−	1.42309i
$528$		0			0
$529$	8.94412	+	15.4917i	0.388875	+	0.673551i
$530$	3.15803	−	5.46986i	0.137176	−	0.237596i
$531$		0			0
$532$	25.6887			1.11375
$533$	−28.4571	+	4.52490i	−1.23262	+	0.195995i
$534$		0			0
$535$	3.87512	−	6.71191i	0.167536	−	0.290181i
$536$	4.90466	−	8.49511i	0.211849	−	0.366933i
$537$		0			0
$538$	1.10853			0.0477921
$539$	38.2752	+	66.2947i	1.64863	+	2.85551i
$540$		0			0
$541$	−17.8625			−0.767970			−0.383985	−	0.923339i	$-0.625449\pi$
$541$	−17.8625			−0.767970			−0.383985	+	0.923339i	$0.625449\pi$
$542$	−6.39438	−	11.0754i	−0.274662	−	0.475729i
$543$		0			0
$544$	16.4959	−	28.5718i	0.707257	−	1.22501i
$545$	11.4744			0.491510
$546$		0			0
$547$	−4.97952			−0.212909			−0.106455	−	0.994318i	$-0.533950\pi$
$547$	−4.97952			−0.212909			−0.106455	+	0.994318i	$0.533950\pi$
$548$	−18.6024	+	32.2203i	−0.794654	+	1.37638i
$549$		0			0
$550$	−1.89857	−	3.28842i	−0.0809553	−	0.140219i
$551$	29.1639			1.24242
$552$		0			0
$553$	18.6598	+	32.3197i	0.793495	+	1.37437i
$554$	3.03676			0.129020
$555$		0			0
$556$	−9.60857	+	16.6425i	−0.407494	+	0.705801i
$557$	−18.4656	+	31.9833i	−0.782412	+	1.35518i	0.148121	+	0.988969i	$0.452678\pi$
$557$	−18.4656	+	31.9833i	−0.782412	+	1.35518i	−0.930533	+	0.366208i	$0.880656\pi$
$558$		0			0
$559$	8.36933	−	21.8425i	0.353985	−	0.923840i
$560$	−7.96361			−0.336524
$561$		0			0
$562$	−1.63040	+	2.82394i	−0.0687743	+	0.119121i
$563$	−4.68284	−	8.11092i	−0.197358	−	0.341835i	0.750313	−	0.661083i	$-0.229903\pi$
$563$	−4.68284	−	8.11092i	−0.197358	−	0.341835i	−0.947671	+	0.319248i	$0.896570\pi$
$564$		0			0
$565$	−3.12369	−	5.41040i	−0.131415	−	0.227617i
$566$	3.14033	+	5.43921i	0.131998	+	0.228627i
$567$		0			0
$568$	9.60308	+	16.6330i	0.402936	+	0.697906i
$569$	−0.218417	+	0.378309i	−0.00915650	+	0.0158595i	−0.870567	−	0.492049i	$-0.836248\pi$
$569$	−0.218417	+	0.378309i	−0.00915650	+	0.0158595i	0.861411	+	0.507909i	$0.169581\pi$
$570$		0			0
$571$	−4.69561			−0.196505			−0.0982525	−	0.995162i	$-0.531325\pi$
$571$	−4.69561			−0.196505			−0.0982525	+	0.995162i	$0.531325\pi$
$572$	22.1083	+	27.2675i	0.924392	+	1.14011i
$573$		0			0
$574$	11.0985	−	19.2231i	0.463241	−	0.802357i
$575$	1.13046	−	1.95801i	0.0471434	−	0.0816548i
$576$		0			0
$577$	−30.2121			−1.25775			−0.628873	−	0.777508i	$-0.716483\pi$
$577$	−30.2121			−1.25775			−0.628873	+	0.777508i	$0.716483\pi$
$578$	5.36469	+	9.29191i	0.223142	+	0.386493i
$579$		0			0
$580$	−12.9938			−0.539536
$581$	5.21611	+	9.03457i	0.216401	+	0.374817i
$582$		0			0
$583$	−30.5229	+	52.8673i	−1.26413	+	2.18954i
$584$	−1.85257			−0.0766599
$585$		0			0
$586$	4.70531			0.194375
$587$	−21.8769	+	37.8919i	−0.902956	+	1.56397i	−0.0793186	+	0.996849i	$0.525274\pi$
$587$	−21.8769	+	37.8919i	−0.902956	+	1.56397i	−0.823638	+	0.567117i	$0.808059\pi$
$588$		0			0
$589$	11.6479	+	20.1748i	0.479944	+	0.831287i
$590$	−1.96136			−0.0807480
$591$		0			0
$592$	1.61486	+	2.79701i	0.0663702	+	0.114957i
$593$	5.94151			0.243989			0.121994	−	0.992531i	$-0.461071\pi$
$593$	5.94151			0.243989			0.121994	+	0.992531i	$0.461071\pi$
$594$		0			0
$595$	12.9416	−	22.4156i	0.530556	−	0.918949i
$596$	17.0500	−	29.5314i	0.698393	−	1.20965i
$597$		0			0
$598$	1.82819	−	4.77126i	0.0747602	−	0.195111i
$599$	37.0505			1.51384			0.756922	−	0.653506i	$-0.226702\pi$
$599$	37.0505			1.51384			0.756922	+	0.653506i	$0.226702\pi$
$600$		0			0
$601$	18.6411	−	32.2874i	0.760387	−	1.31703i	−0.182264	−	0.983250i	$-0.558343\pi$
$601$	18.6411	−	32.2874i	0.760387	−	1.31703i	0.942651	−	0.333779i	$-0.108324\pi$
$602$	9.00946	+	15.6048i	0.367198	+	0.636006i
$603$		0			0
$604$	15.6392	+	27.0879i	0.636351	+	1.10219i
$605$	12.8500	+	22.2569i	0.522429	+	0.904873i
$606$		0			0
$607$	−12.2464	−	21.2115i	−0.497068	−	0.860946i	0.502927	−	0.864329i	$-0.332257\pi$
$607$	−12.2464	−	21.2115i	−0.497068	−	0.860946i	−0.999994	+	0.00338281i	$0.998923\pi$
$608$	−10.1870	+	17.6445i	−0.413139	+	0.715577i
$609$		0			0
$610$	−1.54082			−0.0623859
$611$	7.33091	+	9.04167i	0.296577	+	0.365787i
$612$		0			0
$613$	−4.73601	+	8.20301i	−0.191286	+	0.331316i	−0.945677	−	0.325109i	$-0.894599\pi$
$613$	−4.73601	+	8.20301i	−0.191286	+	0.331316i	0.754391	+	0.656425i	$0.227932\pi$
$614$	−3.58538	+	6.21006i	−0.144694	+	0.250618i
$615$		0			0
$616$	−60.6941			−2.44544
$617$	0.599037	+	1.03756i	0.0241163	+	0.0417707i	0.877832	−	0.478969i	$-0.158989\pi$
$617$	0.599037	+	1.03756i	0.0241163	+	0.0417707i	−0.853715	+	0.520740i	$0.825656\pi$
$618$		0			0
$619$	−19.2559			−0.773959			−0.386979	−	0.922088i	$-0.626482\pi$
$619$	−19.2559			−0.773959			−0.386979	+	0.922088i	$0.626482\pi$
$620$	−5.18964	−	8.98873i	−0.208421	−	0.360996i
$621$		0			0
$622$	−7.59517	+	13.1552i	−0.304538	+	0.527476i
$623$	−3.42720			−0.137308
$624$		0			0
$625$	1.00000			0.0400000
$626$	−5.91680	+	10.2482i	−0.236483	+	0.409600i
$627$		0			0
$628$	16.5974	+	28.7476i	0.662309	+	1.14715i
$629$	−10.4972			−0.418551
$630$		0			0
$631$	−3.12995	−	5.42123i	−0.124601	−	0.215816i	0.796976	−	0.604011i	$-0.206432\pi$
$631$	−3.12995	−	5.42123i	−0.124601	−	0.215816i	−0.921577	+	0.388196i	$0.873099\pi$
$632$	−19.0412			−0.757417
$633$		0			0
$634$	−7.00310	+	12.1297i	−0.278128	+	0.481733i
$635$	5.60171	−	9.70245i	0.222297	−	0.385030i
$636$		0			0
$637$	−44.9950	+	7.15454i	−1.78277	+	0.283473i
$638$	−30.7001			−1.21543
$639$		0			0
$640$	5.66519	−	9.81240i	0.223936	−	0.387869i
$641$	4.42209	+	7.65928i	0.174662	+	0.302523i	0.940044	−	0.341053i	$-0.110783\pi$
$641$	4.42209	+	7.65928i	0.174662	+	0.302523i	−0.765382	+	0.643576i	$0.777450\pi$
$642$		0			0
$643$	16.0506	+	27.8004i	0.632973	+	1.09634i	0.986941	+	0.161084i	$0.0514990\pi$
$643$	16.0506	+	27.8004i	0.632973	+	1.09634i	−0.353968	+	0.935258i	$0.615168\pi$
$644$	−8.05072	−	13.9443i	−0.317243	−	0.549481i
$645$		0			0
$646$	−6.60308	−	11.4369i	−0.259795	−	0.449978i
$647$	−7.37834	+	12.7797i	−0.290072	+	0.502420i	−0.973827	−	0.227292i	$-0.927013\pi$
$647$	−7.37834	+	12.7797i	−0.290072	+	0.502420i	0.683754	+	0.729712i	$0.260346\pi$
$648$		0			0
$649$	18.9569			0.744125
$650$	2.23189	−	0.354887i	0.0875419	−	0.0139198i
$651$		0			0
$652$	−3.90517	+	6.76395i	−0.152938	+	0.264897i
$653$	13.3246	−	23.0788i	0.521430	−	0.903144i	−0.478259	−	0.878219i	$-0.658732\pi$
$653$	13.3246	−	23.0788i	0.521430	−	0.903144i	0.999689	−	0.0249251i	$-0.00793473\pi$
$654$		0			0
$655$	−0.494893			−0.0193371
$656$	−7.18114	−	12.4381i	−0.280377	−	0.485626i
$657$		0			0
$658$	−8.96684			−0.349564
$659$	1.22477	+	2.12136i	0.0477101	+	0.0826363i	0.888894	−	0.458112i	$-0.151474\pi$
$659$	1.22477	+	2.12136i	0.0477101	+	0.0826363i	−0.841184	+	0.540749i	$0.818141\pi$
$660$		0			0
$661$	−8.23556	+	14.2644i	−0.320326	+	0.554821i	−0.980555	−	0.196243i	$-0.937126\pi$
$661$	−8.23556	+	14.2644i	−0.320326	+	0.554821i	0.660229	+	0.751064i	$0.270459\pi$
$662$	14.2211			0.552718
$663$		0			0
$664$	−5.32272			−0.206562
$665$	−7.99209	+	13.8427i	−0.309920	+	0.536797i
$666$		0			0
$667$	−9.13983	−	15.8307i	−0.353896	−	0.612965i
$668$	4.14632			0.160426
$669$		0			0
$670$	1.35971	+	2.35509i	0.0525302	+	0.0909850i
$671$	14.8923			0.574911
$672$		0			0
$673$	0.693745	−	1.20160i	0.0267419	−	0.0463184i	−0.852345	−	0.522980i	$-0.824820\pi$
$673$	0.693745	−	1.20160i	0.0267419	−	0.0463184i	0.879087	+	0.476662i	$0.158153\pi$
$674$	−0.0523246	+	0.0906288i	−0.00201547	+	0.00349089i
$675$		0			0
$676$	−19.8623	+	6.48035i	−0.763935	+	0.249244i
$677$	−23.0636			−0.886407			−0.443203	−	0.896421i	$-0.646158\pi$
$677$	−23.0636			−0.886407			−0.443203	+	0.896421i	$0.646158\pi$
$678$		0			0
$679$	14.0051	−	24.2576i	0.537467	−	0.930920i
$680$	6.60308	+	11.4369i	0.253217	+	0.438584i
$681$		0			0
$682$	−12.2615	−	21.2375i	−0.469516	−	0.813225i
$683$	10.5080	+	18.2004i	0.402078	+	0.696419i	0.993976	−	0.109593i	$-0.0349549\pi$
$683$	10.5080	+	18.2004i	0.402078	+	0.696419i	−0.591899	+	0.806012i	$0.701622\pi$
$684$		0			0
$685$	−11.5749	−	20.0483i	−0.442254	−	0.766006i
$686$	7.82713	−	13.5570i	0.298841	−	0.517608i
$687$		0			0
$688$	11.6590			0.444494
$689$	−22.8819	−	28.2217i	−0.871731	−	1.07516i
$690$		0			0
$691$	12.0289	−	20.8346i	0.457600	−	0.792587i	−0.541234	−	0.840872i	$-0.682043\pi$
$691$	12.0289	−	20.8346i	0.457600	−	0.792587i	0.998834	+	0.0482858i	$0.0153758\pi$
$692$	8.23396	−	14.2616i	0.313008	−	0.542146i
$693$		0			0
$694$	9.17266			0.348190
$695$	−5.97871	−	10.3554i	−0.226785	−	0.392804i
$696$		0			0
$697$	46.6802			1.76814
$698$	0.697969	+	1.20892i	0.0264185	+	0.0457582i
$699$		0			0
$700$	3.56082	−	6.16752i	0.134586	−	0.233110i
$701$	−20.0188			−0.756099			−0.378050	−	0.925785i	$-0.623405\pi$
$701$	−20.0188			−0.756099			−0.378050	+	0.925785i	$0.623405\pi$
$702$		0			0
$703$	6.48252			0.244493
$704$	−0.163542	+	0.283264i	−0.00616373	+	0.0106759i
$705$		0			0
$706$	−1.86138	−	3.22400i	−0.0700539	−	0.121337i
$707$	39.5134			1.48605
$708$		0			0
$709$	−8.52960	−	14.7737i	−0.320336	−	0.554838i	0.660221	−	0.751071i	$-0.270462\pi$
$709$	−8.52960	−	14.7737i	−0.320336	−	0.554838i	−0.980557	+	0.196233i	$0.937129\pi$
$710$	−5.32450			−0.199825
$711$		0			0
$712$	0.874312	−	1.51435i	0.0327662	−	0.0567528i
$713$	7.30081	−	12.6454i	0.273417	−	0.473573i
$714$		0			0
$715$	−21.5716	+	3.43005i	−0.806734	+	0.128277i
$716$	−17.0401			−0.636820
$717$		0			0
$718$	−3.42335	+	5.92942i	−0.127758	+	0.221284i
$719$	−21.0559	−	36.4700i	−0.785254	−	1.36010i	−0.928847	−	0.370463i	$-0.879199\pi$
$719$	−21.0559	−	36.4700i	−0.785254	−	1.36010i	0.143593	−	0.989637i	$-0.454134\pi$
$720$		0			0
$721$	−0.250297	−	0.433527i	−0.00932154	−	0.0161454i
$722$	−1.87680	−	3.25071i	−0.0698473	−	0.120979i
$723$		0			0
$724$	13.5496	+	23.4686i	0.503566	+	0.872202i
$725$	4.04253	−	7.00186i	0.150136	−	0.260043i
$726$		0			0
$727$	3.62167			0.134320			0.0671601	−	0.997742i	$-0.478606\pi$
$727$	3.62167			0.134320			0.0671601	+	0.997742i	$0.478606\pi$
$728$	12.9249	−	33.7317i	0.479027	−	1.25018i
$729$		0			0
$730$	0.256793	−	0.444778i	0.00950432	−	0.0164620i
$731$	−18.9469	+	32.8171i	−0.700778	+	1.21378i
$732$		0			0
$733$	−10.2438			−0.378362			−0.189181	−	0.981942i	$-0.560583\pi$
$733$	−10.2438			−0.378362			−0.189181	+	0.981942i	$0.560583\pi$
$734$	2.70914	+	4.69237i	0.0999963	+	0.173199i
$735$		0			0
$736$	12.7703			0.470719
$737$	−13.1419	−	22.7624i	−0.484087	−	0.838463i
$738$		0			0
$739$	−4.63472	+	8.02758i	−0.170491	+	0.295299i	−0.938592	−	0.345030i	$-0.887869\pi$
$739$	−4.63472	+	8.02758i	−0.170491	+	0.295299i	0.768101	+	0.640329i	$0.221202\pi$
$740$	−2.88824			−0.106174
$741$		0			0
$742$	27.9881			1.02748
$743$	22.3835	−	38.7694i	0.821172	−	1.42231i	−0.0836373	−	0.996496i	$-0.526654\pi$
$743$	22.3835	−	38.7694i	0.821172	−	1.42231i	0.904810	−	0.425816i	$-0.140013\pi$
$744$		0			0
$745$	10.6089	+	18.3752i	0.388681	+	0.673215i
$746$	−11.4735			−0.420076
$747$		0			0
$748$	−28.4346	−	49.2501i	−1.03967	−	1.80076i
$749$	34.3434			1.25488
$750$		0			0
$751$	−7.67016	+	13.2851i	−0.279888	+	0.484780i	−0.971357	−	0.237626i	$-0.923631\pi$
$751$	−7.67016	+	13.2851i	−0.279888	+	0.484780i	0.691469	+	0.722406i	$0.256964\pi$
$752$	−2.90095	+	5.02459i	−0.105787	+	0.183228i
$753$		0			0
$754$	6.53761	−	17.0620i	0.238086	−	0.621362i
$755$	−19.4623			−0.708305
$756$		0			0
$757$	−3.00148	+	5.19872i	−0.109091	+	0.188951i	−0.915402	−	0.402541i	$-0.868127\pi$
$757$	−3.00148	+	5.19872i	−0.109091	+	0.188951i	0.806311	+	0.591491i	$0.201461\pi$
$758$	−9.40381	−	16.2879i	−0.341562	−	0.591602i
$759$		0			0
$760$	−4.07772	−	7.06282i	−0.147914	−	0.256195i
$761$	−10.4825	−	18.1563i	−0.379992	−	0.658165i	0.611069	−	0.791578i	$-0.290740\pi$
$761$	−10.4825	−	18.1563i	−0.379992	−	0.658165i	−0.991061	+	0.133412i	$0.957407\pi$
$762$		0			0
$763$	25.4231	+	44.0341i	0.920378	+	1.59414i
$764$	8.83198	−	15.2974i	0.319530	−	0.553442i
$765$		0			0
$766$	9.11103			0.329195
$767$	−4.03689	+	10.5356i	−0.145764	+	0.380418i
$768$		0			0
$769$	21.9076	−	37.9451i	0.790008	−	1.36833i	−0.135953	−	0.990715i	$-0.543410\pi$
$769$	21.9076	−	37.9451i	0.790008	−	1.36833i	0.925961	−	0.377619i	$-0.123257\pi$
$770$	8.41307	−	14.5719i	0.303186	−	0.525134i
$771$		0			0
$772$	10.6902			0.384749
$773$	−1.68610	−	2.92041i	−0.0606449	−	0.105040i	0.834109	−	0.551600i	$-0.185982\pi$
$773$	−1.68610	−	2.92041i	−0.0606449	−	0.105040i	−0.894754	+	0.446560i	$0.852649\pi$
$774$		0			0
$775$	6.45826			0.231988
$776$	7.14568	+	12.3767i	0.256515	+	0.444297i
$777$		0			0
$778$	−7.68631	+	13.3131i	−0.275568	+	0.477297i
$779$	−28.8273			−1.03284
$780$		0			0
$781$	51.4623			1.84146
$782$	−4.13875	+	7.16853i	−0.148002	+	0.256346i
$783$		0			0
$784$	−11.3545	−	19.6665i	−0.405516	−	0.702375i
$785$	−20.6547			−0.737198
$786$		0			0
$787$	17.8922	+	30.9902i	0.637789	+	1.10468i	0.985917	+	0.167235i	$0.0534840\pi$
$787$	17.8922	+	30.9902i	0.637789	+	1.10468i	−0.348128	+	0.937447i	$0.613183\pi$
$788$	38.5487			1.37324
$789$		0			0
$790$	2.63938	−	4.57154i	0.0939049	−	0.162648i
$791$	13.8419	−	23.9749i	0.492162	−	0.852450i
$792$		0			0
$793$	−3.17133	+	8.27662i	−0.112617	+	0.293911i
$794$	5.91748			0.210003
$795$		0			0
$796$	−16.8028	+	29.1034i	−0.595561	+	1.03154i
$797$	−14.1625	−	24.5303i	−0.501663	−	0.868906i	−0.999998	−	0.00192156i	$-0.999388\pi$
$797$	−14.1625	−	24.5303i	−0.501663	−	0.868906i	0.498335	−	0.866985i	$-0.333945\pi$
$798$		0			0
$799$	−9.42866	−	16.3309i	−0.333562	−	0.577746i
$800$	2.82414	+	4.89155i	0.0998483	+	0.172942i
$801$		0			0
$802$	−0.153055	−	0.265098i	−0.00540455	−	0.00936095i
$803$	−2.48195	+	4.29887i	−0.0875861	+	0.151704i
$804$		0			0
$805$	10.0187			0.353114
$806$	14.4141	−	2.29195i	0.507716	−	0.0807306i
$807$		0			0
$808$	−10.0803	+	17.4595i	−0.354622	+	0.614224i
$809$	−14.5698	+	25.2357i	−0.512248	+	0.887239i	0.487651	+	0.873038i	$0.337854\pi$
$809$	−14.5698	+	25.2357i	−0.512248	+	0.887239i	−0.999899	+	0.0142007i	$0.995480\pi$
$810$		0			0
$811$	−16.3733			−0.574946			−0.287473	−	0.957789i	$-0.592815\pi$
$811$	−16.3733			−0.574946			−0.287473	+	0.957789i	$0.592815\pi$
$812$	−28.7894	−	49.8647i	−1.01031	−	1.74991i
$813$		0			0
$814$	−6.82399			−0.239181
$815$	−2.42990	−	4.20871i	−0.0851157	−	0.147425i
$816$		0			0
$817$	11.7006	−	20.2661i	0.409354	−	0.709022i
$818$	−12.9873			−0.454091
$819$		0			0
$820$	12.8438			0.448525
$821$	17.5806	−	30.4505i	0.613566	−	1.06273i	−0.377068	−	0.926186i	$-0.623068\pi$
$821$	17.5806	−	30.4505i	0.613566	−	1.06273i	0.990634	−	0.136543i	$-0.0435990\pi$
$822$		0			0
$823$	−9.84233	−	17.0474i	−0.343082	−	0.594236i	0.641921	−	0.766771i	$-0.278138\pi$
$823$	−9.84233	−	17.0474i	−0.343082	−	0.594236i	−0.985003	+	0.172535i	$0.944804\pi$
$824$	0.255413			0.00889772
$825$		0			0
$826$	−4.34566	−	7.52690i	−0.151205	−	0.261894i
$827$	−11.6881			−0.406436			−0.203218	−	0.979134i	$-0.565140\pi$
$827$	−11.6881			−0.406436			−0.203218	+	0.979134i	$0.565140\pi$
$828$		0			0
$829$	22.7601	−	39.4217i	0.790493	−	1.36917i	−0.135170	−	0.990822i	$-0.543158\pi$
$829$	22.7601	−	39.4217i	0.790493	−	1.36917i	0.925662	−	0.378351i	$-0.123509\pi$
$830$	0.737805	−	1.27792i	0.0256096	−	0.0443571i
$831$		0			0
$832$	−0.122601	−	0.151212i	−0.00425044	−	0.00524234i
$833$	73.8084			2.55731
$834$		0			0
$835$	−1.28997	+	2.23430i	−0.0446414	+	0.0773212i
$836$	17.5597	+	30.4143i	0.607315	+	1.05190i
$837$		0			0
$838$	−1.42516	−	2.46845i	−0.0492313	−	0.0852711i
$839$	14.5239	+	25.1561i	0.501420	+	0.868485i	0.999999	+	0.00164022i	$0.000522098\pi$
$839$	14.5239	+	25.1561i	0.501420	+	0.868485i	−0.498579	+	0.866844i	$0.666145\pi$
$840$		0			0
$841$	−18.1841	−	31.4957i	−0.627037	−	1.08606i
$842$	9.74634	−	16.8812i	0.335881	−	0.581763i
$843$		0			0
$844$	−21.1029			−0.726393
$845$	2.68740	−	12.7192i	0.0924492	−	0.437554i
$846$		0			0
$847$	−56.9420	+	98.6264i	−1.95655	+	3.38884i
$848$	9.05471	−	15.6832i	0.310940	−	0.538564i
$849$		0			0
$850$	−3.66112			−0.125576
$851$	−2.03159	−	3.51882i	−0.0696422	−	0.120624i
$852$		0			0
$853$	−48.3320			−1.65486			−0.827429	−	0.561571i	$-0.810197\pi$
$853$	−48.3320			−1.65486			−0.827429	+	0.561571i	$0.810197\pi$
$854$	−3.41389	−	5.91303i	−0.116821	−	0.202340i
$855$		0			0
$856$	−8.76134	+	15.1751i	−0.299457	+	0.518674i
$857$	41.2151			1.40788			0.703940	−	0.710260i	$-0.251422\pi$
$857$	41.2151			1.40788			0.703940	+	0.710260i	$0.251422\pi$
$858$		0			0
$859$	−52.5448			−1.79280			−0.896402	−	0.443242i	$-0.853828\pi$
$859$	−52.5448			−1.79280			−0.896402	+	0.443242i	$0.853828\pi$
$860$	−5.21314	+	9.02943i	−0.177767	+	0.307901i
$861$		0			0
$862$	−10.7232	−	18.5731i	−0.365234	−	0.632603i
$863$	22.9888			0.782549			0.391275	−	0.920274i	$-0.372034\pi$
$863$	22.9888			0.782549			0.391275	+	0.920274i	$0.372034\pi$
$864$		0			0
$865$	5.12339	+	8.87397i	0.174200	+	0.301724i
$866$	3.48700			0.118493
$867$		0			0
$868$	22.9967	−	39.8315i	0.780559	−	1.35197i
$869$	−25.5101	+	44.1848i	−0.865371	+	1.49887i
$870$		0			0
$871$	15.4491	−	2.45652i	0.523473	−	0.0832360i
$872$	−25.9427			−0.878532
$873$		0			0
$874$	2.55588	−	4.42691i	0.0864539	−	0.149743i
$875$	2.21563	+	3.83759i	0.0749021	+	0.129734i
$876$		0			0
$877$	26.1492	+	45.2917i	0.882995	+	1.52939i	0.847994	+	0.530006i	$0.177810\pi$
$877$	26.1492	+	45.2917i	0.882995	+	1.52939i	0.0350015	+	0.999387i	$0.488856\pi$
$878$	−0.883615	−	1.53047i	−0.0298206	−	0.0516508i
$879$		0			0
$880$	−5.44359	−	9.42857i	−0.183503	−	0.317837i
$881$	−16.8483	+	29.1821i	−0.567634	+	0.983171i	0.429165	+	0.903226i	$0.358808\pi$
$881$	−16.8483	+	29.1821i	−0.567634	+	0.983171i	−0.996799	+	0.0799447i	$0.974526\pi$
$882$		0			0
$883$	−20.4392			−0.687835			−0.343917	−	0.939000i	$-0.611754\pi$
$883$	−20.4392			−0.687835			−0.343917	+	0.939000i	$0.611754\pi$
$884$	33.4266	−	5.31508i	1.12426	−	0.178766i
$885$		0			0
$886$	4.72082	−	8.17671i	0.158599	−	0.274702i
$887$	−10.1003	+	17.4942i	−0.339134	+	0.587397i	−0.984270	−	0.176670i	$-0.943467\pi$
$887$	−10.1003	+	17.4942i	−0.339134	+	0.587397i	0.645136	+	0.764068i	$0.276801\pi$
$888$		0			0
$889$	49.6454			1.66505
$890$	0.242384	+	0.419822i	0.00812474	+	0.0140725i
$891$		0			0
$892$	34.0723			1.14083
$893$	5.82265	+	10.0851i	0.194847	+	0.337486i
$894$		0			0
$895$	5.30141	−	9.18232i	0.177207	−	0.306931i
$896$	50.2080			1.67733
$897$		0			0
$898$	2.40974			0.0804140
$899$	26.1077	−	45.2199i	0.870741	−	1.50817i
$900$		0			0
$901$	29.4296	+	50.9735i	0.980442	+	1.69817i
$902$	30.3458			1.01040
$903$		0			0
$904$	7.06242	+	12.2325i	0.234893	+	0.406846i
$905$	−16.8618			−0.560505
$906$		0			0
$907$	20.9015	−	36.2024i	0.694022	−	1.20208i	−0.276488	−	0.961017i	$-0.589170\pi$
$907$	20.9015	−	36.2024i	0.694022	−	1.20208i	0.970509	−	0.241063i	$-0.0774962\pi$
$908$	−7.42450	+	12.8596i	−0.246391	+	0.426761i
$909$		0			0
$910$	6.30696	+	7.77878i	0.209074	+	0.257864i
$911$	3.42332			0.113420			0.0567098	−	0.998391i	$-0.481939\pi$
$911$	3.42332			0.113420			0.0567098	+	0.998391i	$0.481939\pi$
$912$		0			0
$913$	−7.13103	+	12.3513i	−0.236003	+	0.408769i
$914$	9.53602	+	16.5169i	0.315423	+	0.546329i
$915$		0			0
$916$	2.54330	+	4.40513i	0.0840331	+	0.145550i
$917$	−1.09650	−	1.89920i	−0.0362097	−	0.0627170i
$918$		0			0
$919$	−3.52603	−	6.10727i	−0.116313	−	0.201460i	0.801991	−	0.597336i	$-0.203774\pi$
$919$	−3.52603	−	6.10727i	−0.116313	−	0.201460i	−0.918304	+	0.395876i	$0.870441\pi$
$920$	−2.55588	+	4.42691i	−0.0842648	+	0.145951i
$921$		0			0
$922$	19.3002			0.635619
$923$	−10.9589	+	28.6009i	−0.360718	+	0.941411i
$924$		0			0
$925$	0.898570	−	1.55637i	0.0295448	−	0.0511731i
$926$	−4.04388	+	7.00421i	−0.132890	+	0.230173i
$927$		0			0
$928$	45.6666			1.49908
$929$	−5.02099	−	8.69661i	−0.164733	−	0.285326i	0.771827	−	0.635832i	$-0.219343\pi$
$929$	−5.02099	−	8.69661i	−0.164733	−	0.285326i	−0.936561	+	0.350506i	$0.886010\pi$
$930$		0			0
$931$	−45.5802			−1.49383
$932$	−2.27990	−	3.94890i	−0.0746806	−	0.129351i
$933$		0			0
$934$	−3.20748	+	5.55552i	−0.104952	+	0.181782i
$935$	35.3855			1.15723
$936$		0			0
$937$	5.84613			0.190985			0.0954924	−	0.995430i	$-0.469557\pi$
$937$	5.84613			0.190985			0.0954924	+	0.995430i	$0.469557\pi$
$938$	−6.02524	+	10.4360i	−0.196731	+	0.340748i
$939$		0			0
$940$	−2.59424	−	4.49336i	−0.0846148	−	0.146557i
$941$	46.1640			1.50490			0.752452	−	0.658647i	$-0.228871\pi$
$941$	46.1640			1.50490			0.752452	+	0.658647i	$0.228871\pi$
$942$		0			0
$943$	9.03435	+	15.6479i	0.294199	+	0.509567i
$944$	−5.62363			−0.183033
$945$		0			0
$946$	−12.3170	+	21.3336i	−0.400460	+	0.693617i
$947$	−7.24152	+	12.5427i	−0.235318	+	0.407582i	−0.959365	−	0.282168i	$-0.908946\pi$
$947$	−7.24152	+	12.5427i	−0.235318	+	0.407582i	0.724047	+	0.689750i	$0.242280\pi$
$948$		0			0
$949$	−1.86062	−	2.29483i	−0.0603984	−	0.0744933i
$950$	2.26092			0.0733539
$951$		0			0
$952$	−29.2600	+	50.6798i	−0.948323	+	1.64254i
$953$	−19.2212	−	33.2920i	−0.622635	−	1.07843i	−0.988993	−	0.147961i	$-0.952729\pi$
$953$	−19.2212	−	33.2920i	−0.622635	−	1.07843i	0.366359	−	0.930474i	$-0.380604\pi$
$954$		0			0
$955$	5.49549	+	9.51847i	0.177830	+	0.308010i
$956$	−0.509755	−	0.882922i	−0.0164867	−	0.0285557i
$957$		0			0
$958$	−10.9702	−	19.0009i	−0.354431	−	0.613892i
$959$	51.2914	−	88.8394i	1.65629	−	2.86877i
$960$		0			0
$961$	10.7092			0.345457
$962$	1.45317	−	3.79253i	0.0468522	−	0.122276i
$963$		0			0
$964$	−0.721977	+	1.25050i	−0.0232533	+	0.0402759i
$965$	−3.32586	+	5.76057i	−0.107063	+	0.185439i
$966$		0			0
$967$	44.2627			1.42339			0.711696	−	0.702487i	$-0.247927\pi$
$967$	44.2627			1.42339			0.711696	+	0.702487i	$0.247927\pi$
$968$	−29.0529	−	50.3211i	−0.933796	−	1.61738i
$969$		0			0
$970$	−3.96197			−0.127211
$971$	−22.2030	−	38.4567i	−0.712527	−	1.23413i	−0.963906	−	0.266244i	$-0.914217\pi$
$971$	−22.2030	−	38.4567i	−0.712527	−	1.23413i	0.251378	−	0.967889i	$-0.419116\pi$
$972$		0			0
$973$	26.4933	−	45.8877i	0.849335	−	1.47109i
$974$	0.960150			0.0307652
$975$		0			0
$976$	−4.41784			−0.141412
$977$	−1.69219	+	2.93096i	−0.0541379	+	0.0937696i	−0.891824	−	0.452382i	$-0.850574\pi$
$977$	−1.69219	+	2.93096i	−0.0541379	+	0.0937696i	0.837686	+	0.546152i	$0.183908\pi$
$978$		0			0
$979$	−2.34269	−	4.05766i	−0.0748727	−	0.129683i
$980$	20.3079			0.648714
$981$		0			0
$982$	7.84266	+	13.5839i	0.250269	+	0.433479i
$983$	−39.6424			−1.26440			−0.632198	−	0.774807i	$-0.717847\pi$
$983$	−39.6424			−1.26440			−0.632198	+	0.774807i	$0.717847\pi$
$984$		0			0
$985$	−11.9930	+	20.7725i	−0.382129	+	0.661866i
$986$	−14.8002	+	25.6347i	−0.471334	+	0.816375i
$987$		0			0
$988$	−20.6426	+	3.28232i	−0.656727	+	0.104424i
$989$	−14.6677			−0.466407
$990$		0			0
$991$	22.6722	−	39.2693i	0.720205	−	1.24743i	−0.240712	−	0.970596i	$-0.577381\pi$
$991$	22.6722	−	39.2693i	0.720205	−	1.24743i	0.960917	−	0.276835i	$-0.0892856\pi$
$992$	18.2390	+	31.5909i	0.579089	+	1.00301i
$993$		0			0
$994$	−11.7971	−	20.4332i	−0.374182	−	0.648103i
$995$	−10.4552	−	18.1089i	−0.331451	−	0.574090i
$996$		0			0
$997$	−26.9984	−	46.7626i	−0.855048	−	1.48099i	−0.876601	−	0.481218i	$-0.840194\pi$
$997$	−26.9984	−	46.7626i	−0.855048	−	1.48099i	0.0215531	−	0.999768i	$-0.493139\pi$
$998$	8.70733	−	15.0815i	0.275626	−	0.477398i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.j.i.451.3	yes	10
3.2	odd	2		585.2.j.h.451.3	yes	10
13.3	even	3	inner	585.2.j.i.406.3	yes	10
13.4	even	6		7605.2.a.cn.1.3		5
13.9	even	3		7605.2.a.cm.1.3		5
39.17	odd	6		7605.2.a.cl.1.3		5
39.29	odd	6		585.2.j.h.406.3	✓	10
39.35	odd	6		7605.2.a.co.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.j.h.406.3	✓	10	39.29	odd	6
585.2.j.h.451.3	yes	10	3.2	odd	2
585.2.j.i.406.3	yes	10	13.3	even	3	inner
585.2.j.i.451.3	yes	10	1.1	even	1	trivial
7605.2.a.cl.1.3		5	39.17	odd	6
7605.2.a.cm.1.3		5	13.9	even	3
7605.2.a.cn.1.3		5	13.4	even	6
7605.2.a.co.1.3		5	39.35	odd	6

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.313396 - 0.542817i) q^{2} +(0.803566 + 1.39182i) q^{4} -1.00000 q^{5} +(-2.21563 - 3.83759i) q^{7} +2.26092 q^{8} +(-0.313396 + 0.542817i) q^{10} +(3.02903 - 5.24643i) q^{11} +(2.27075 + 2.80066i) q^{13} -2.77748 q^{14} +(-0.898570 + 1.55637i) q^{16} +(-2.92053 - 5.05850i) q^{17} +(1.80357 + 3.12387i) q^{19} +(-0.803566 - 1.39182i) q^{20} +(-1.89857 - 3.28842i) q^{22} +(1.13046 - 1.95801i) q^{23} +1.00000 q^{25} +(2.23189 - 0.354887i) q^{26} +(3.56082 - 6.16752i) q^{28} +(4.04253 - 7.00186i) q^{29} +6.45826 q^{31} +(2.82414 + 4.89155i) q^{32} -3.66112 q^{34} +(2.21563 + 3.83759i) q^{35} +(0.898570 - 1.55637i) q^{37} +2.26092 q^{38} -2.26092 q^{40} +(-3.99587 + 6.92106i) q^{41} +(-3.24375 - 5.61835i) q^{43} +9.73610 q^{44} +(-0.708563 - 1.22727i) q^{46} +3.22841 q^{47} +(-6.31807 + 10.9432i) q^{49} +(0.313396 - 0.542817i) q^{50} +(-2.07331 + 5.41098i) q^{52} -10.0768 q^{53} +(-3.02903 + 5.24643i) q^{55} +(-5.00937 - 8.67648i) q^{56} +(-2.53382 - 4.38871i) q^{58} +(1.56460 + 2.70997i) q^{59} +(1.22913 + 2.12892i) q^{61} +(2.02399 - 3.50566i) q^{62} -0.0539916 q^{64} +(-2.27075 - 2.80066i) q^{65} +(2.16932 - 3.75737i) q^{67} +(4.69368 - 8.12968i) q^{68} +2.77748 q^{70} +(4.24742 + 7.35675i) q^{71} -0.819388 q^{73} +(-0.563216 - 0.975519i) q^{74} +(-2.89857 + 5.02047i) q^{76} -26.8449 q^{77} -8.42187 q^{79} +(0.898570 - 1.55637i) q^{80} +(2.50458 + 4.33806i) q^{82} -2.35423 q^{83} +(2.92053 + 5.05850i) q^{85} -4.06631 q^{86} +(6.84839 - 11.8618i) q^{88} +(0.386706 - 0.669795i) q^{89} +(5.71664 - 14.9194i) q^{91} +3.63360 q^{92} +(1.01177 - 1.75244i) q^{94} +(-1.80357 - 3.12387i) q^{95} +(3.16052 + 5.47418i) q^{97} +(3.96011 + 6.85911i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} - 6 q^{4} - 10 q^{5} - q^{7} - 12 q^{8} - 2 q^{10} + 8 q^{11} + q^{13} + 8 q^{14} - 4 q^{16} + 4 q^{19} + 6 q^{20} - 14 q^{22} - 6 q^{23} + 10 q^{25} + 10 q^{26} + 2 q^{28} + 16 q^{29}+ \cdots + 30 q^{98}+O(q^{100}) \) 10 * q + 2 * q^2 - 6 * q^4 - 10 * q^5 - q^7 - 12 * q^8 - 2 * q^10 + 8 * q^11 + q^13 + 8 * q^14 - 4 * q^16 + 4 * q^19 + 6 * q^20 - 14 * q^22 - 6 * q^23 + 10 * q^25 + 10 * q^26 + 2 * q^28 + 16 * q^29 + 18 * q^31 + 14 * q^32 + q^35 + 4 * q^37 - 12 * q^38 + 12 * q^40 + 6 * q^41 - 15 * q^43 - 28 * q^44 + 16 * q^46 - 20 * q^47 - 10 * q^49 + 2 * q^50 - 22 * q^52 + 40 * q^53 - 8 * q^55 - 2 * q^56 + 4 * q^58 + 12 * q^59 - 11 * q^61 - 22 * q^62 + 8 * q^64 - q^65 - 5 * q^67 + 50 * q^68 - 8 * q^70 + 10 * q^71 + 2 * q^73 - 26 * q^74 - 24 * q^76 - 84 * q^77 - 34 * q^79 + 4 * q^80 - 16 * q^82 - 32 * q^83 - 88 * q^86 - 20 * q^88 + 4 * q^89 - q^91 + 68 * q^92 + 16 * q^94 - 4 * q^95 + 11 * q^97 + 30 * q^98

Introduction

L-functions

Modular forms

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Database

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