LMFDB - Embedded newform 585.2.bu.d.316.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(316,585)]

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, 1]))

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

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

chi := DirichletCharacter("585.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bu (of order $6$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.191102976.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 6x^{6} + 6x^{4} + 36x^{2} + 36 $ x^8 - 6x^6 + 6x^4 + 36*x^2 + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			316.3
Root			$2.10121 + 0.563016i$ of defining polynomial
Character	$\chi$	$=$	585.316
Dual form			585.2.bu.d.361.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.975173 + 0.563016i) q^{2} +(-0.366025 - 0.633975i) q^{4} +1.00000i q^{5} +(2.47517 - 1.42904i) q^{7} -3.07638i q^{8} +O(q^{10})$	\(q+(0.975173 + 0.563016i) q^{2} +(-0.366025 - 0.633975i) q^{4} +1.00000i q^{5} +(2.47517 - 1.42904i) q^{7} -3.07638i q^{8} +(-0.563016 + 0.975173i) q^{10} +(2.66422 + 1.53819i) q^{11} +(-3.55507 - 0.601205i) q^{13} +3.21829 q^{14} +(1.00000 - 1.73205i) q^{16} +(0.975173 + 1.68905i) q^{17} +(6.42652 - 3.71035i) q^{19} +(0.633975 - 0.366025i) q^{20} +(1.73205 + 3.00000i) q^{22} +(4.39627 - 7.61457i) q^{23} -1.00000 q^{25} +(-3.12832 - 2.58784i) q^{26} +(-1.81195 - 1.04613i) q^{28} +(-3.34120 + 5.78712i) q^{29} -3.15276i q^{31} +(-3.37810 + 1.95035i) q^{32} +2.19615i q^{34} +(1.42904 + 2.47517i) q^{35} +(7.14650 + 4.12603i) q^{37} +8.35596 q^{38} +3.07638 q^{40} +(-2.87710 - 1.66109i) q^{41} +(4.77337 + 8.26772i) q^{43} -2.25207i q^{44} +(8.57425 - 4.95035i) q^{46} +1.79759i q^{47} +(0.584320 - 1.01207i) q^{49} +(-0.975173 - 0.563016i) q^{50} +(0.920099 + 2.47388i) q^{52} -10.6569 q^{53} +(-1.53819 + 2.66422i) q^{55} +(-4.39627 - 7.61457i) q^{56} +(-6.51649 + 3.76230i) q^{58} +(-4.17256 + 2.40903i) q^{59} +(3.13397 + 5.42820i) q^{61} +(1.77505 - 3.07448i) q^{62} -8.39230 q^{64} +(0.601205 - 3.55507i) q^{65} +(-5.09097 - 2.93927i) q^{67} +(0.713876 - 1.23647i) q^{68} +3.21829i q^{70} +(-8.91942 + 5.14963i) q^{71} -11.1101i q^{73} +(4.64605 + 8.04719i) q^{74} +(-4.70454 - 2.71617i) q^{76} +8.79254 q^{77} -11.0968 q^{79} +(1.73205 + 1.00000i) q^{80} +(-1.87044 - 3.23970i) q^{82} -6.97707i q^{83} +(-1.68905 + 0.975173i) q^{85} +10.7499i q^{86} +(4.73205 - 8.19615i) q^{88} +(-0.0805845 - 0.0465255i) q^{89} +(-9.65857 + 3.59226i) q^{91} -6.43659 q^{92} +(-1.01207 + 1.75296i) q^{94} +(3.71035 + 6.42652i) q^{95} +(4.15483 - 2.39879i) q^{97} +(1.13963 - 0.657963i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 12 q^{7}+O(q^{10}) $ 8 * q + 4 * q^4 + 12 * q^7	$ 8 q + 4 q^{4} + 12 q^{7} - 8 q^{13} + 24 q^{14} + 8 q^{16} - 12 q^{19} + 12 q^{20} - 8 q^{25} + 24 q^{26} + 12 q^{28} - 12 q^{29} - 36 q^{41} + 16 q^{43} - 4 q^{49} + 20 q^{52} - 36 q^{58} - 36 q^{59} + 32 q^{61} + 16 q^{64} - 12 q^{65} - 48 q^{67} - 36 q^{71} + 24 q^{74} - 48 q^{76} - 16 q^{79} - 12 q^{82} + 24 q^{88} - 36 q^{89} - 48 q^{92} + 12 q^{94} + 12 q^{95} + 72 q^{98}+O(q^{100}) $ 8 * q + 4 * q^4 + 12 * q^7 - 8 * q^13 + 24 * q^14 + 8 * q^16 - 12 * q^19 + 12 * q^20 - 8 * q^25 + 24 * q^26 + 12 * q^28 - 12 * q^29 - 36 * q^41 + 16 * q^43 - 4 * q^49 + 20 * q^52 - 36 * q^58 - 36 * q^59 + 32 * q^61 + 16 * q^64 - 12 * q^65 - 48 * q^67 - 36 * q^71 + 24 * q^74 - 48 * q^76 - 16 * q^79 - 12 * q^82 + 24 * q^88 - 36 * q^89 - 48 * q^92 + 12 * q^94 + 12 * q^95 + 72 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.975173	+	0.563016i	0.689551	+	0.398113i	0.803444	−	0.595380i	$-0.202999\pi$
$2$	0.975173	+	0.563016i	0.689551	+	0.398113i	−0.113893	+	0.993493i	$0.536332\pi$
$3$		0			0
$3$		0			0
$4$	−0.366025	−	0.633975i	−0.183013	−	0.316987i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$	2.47517	−	1.42904i	0.935527	−	0.540127i	0.0469719	−	0.998896i	$-0.485043\pi$
$7$	2.47517	−	1.42904i	0.935527	−	0.540127i	0.888555	+	0.458769i	$0.151710\pi$
$8$		−	3.07638i		−	1.08766i
$9$		0			0
$10$	−0.563016	+	0.975173i	−0.178041	+	0.308377i
$11$	2.66422	+	1.53819i	0.803293	+	0.463781i	0.844621	−	0.535364i	$-0.179826\pi$
$11$	2.66422	+	1.53819i	0.803293	+	0.463781i	−0.0413283	+	0.999146i	$0.513159\pi$
$12$		0			0
$13$	−3.55507	−	0.601205i	−0.986000	−	0.166744i
$13$	−3.55507	−	0.601205i	−0.986000	−	0.166744i
$14$	3.21829			0.860125
$15$		0			0
$16$	1.00000	−	1.73205i	0.250000	−	0.433013i
$17$	0.975173	+	1.68905i	0.236514	+	0.409654i	0.959712	−	0.280987i	$-0.0906617\pi$
$17$	0.975173	+	1.68905i	0.236514	+	0.409654i	−0.723198	+	0.690641i	$0.757328\pi$
$18$		0			0
$19$	6.42652	−	3.71035i	1.47434	−	0.851213i	0.474762	−	0.880114i	$-0.342534\pi$
$19$	6.42652	−	3.71035i	1.47434	−	0.851213i	0.999582	+	0.0289008i	$0.00920068\pi$
$20$	0.633975	−	0.366025i	0.141761	−	0.0818458i
$21$		0			0
$22$	1.73205	+	3.00000i	0.369274	+	0.639602i
$23$	4.39627	−	7.61457i	0.916686	−	1.58775i	0.112272	−	0.993677i	$-0.464187\pi$
$23$	4.39627	−	7.61457i	0.916686	−	1.58775i	0.804414	−	0.594070i	$-0.202480\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−3.12832	−	2.58784i	−0.613515	−	0.507518i
$27$		0			0
$28$	−1.81195	−	1.04613i	−0.342427	−	0.197700i
$29$	−3.34120	+	5.78712i	−0.620445	+	1.07464i	0.368958	+	0.929446i	$0.379715\pi$
$29$	−3.34120	+	5.78712i	−0.620445	+	1.07464i	−0.989403	+	0.145196i	$0.953619\pi$
$30$		0			0
$31$		−	3.15276i		−	0.566252i	−0.959083	−	0.283126i	$-0.908629\pi$
$31$		−	3.15276i		−	0.566252i	0.959083	−	0.283126i	$-0.0913714\pi$
$32$	−3.37810	+	1.95035i	−0.597169	+	0.344776i
$33$		0			0
$34$			2.19615i			0.376637i
$35$	1.42904	+	2.47517i	0.241552	+	0.418381i
$36$		0			0
$37$	7.14650	+	4.12603i	1.17488	+	0.678316i	0.954824	−	0.297172i	$-0.0960436\pi$
$37$	7.14650	+	4.12603i	1.17488	+	0.678316i	0.220053	+	0.975488i	$0.429377\pi$
$38$	8.35596			1.35551
$39$		0			0
$40$	3.07638			0.486418
$41$	−2.87710	−	1.66109i	−0.449327	−	0.259419i	0.258219	−	0.966086i	$-0.416864\pi$
$41$	−2.87710	−	1.66109i	−0.449327	−	0.259419i	−0.707546	+	0.706667i	$0.750198\pi$
$42$		0			0
$43$	4.77337	+	8.26772i	0.727932	+	1.26082i	0.957756	+	0.287583i	$0.0928517\pi$
$43$	4.77337	+	8.26772i	0.727932	+	1.26082i	−0.229824	+	0.973232i	$0.573815\pi$
$44$		−	2.25207i		−	0.339512i
$45$		0			0
$46$	8.57425	−	4.95035i	1.26420	−	0.729889i
$47$			1.79759i			0.262205i	0.991369	+	0.131103i	$0.0418518\pi$
$47$			1.79759i			0.262205i	−0.991369	+	0.131103i	$0.958148\pi$
$48$		0			0
$49$	0.584320	−	1.01207i	0.0834743	−	0.144582i
$50$	−0.975173	−	0.563016i	−0.137910	−	0.0796225i
$51$		0			0
$52$	0.920099	+	2.47388i	0.127595	+	0.343066i
$53$	−10.6569			−1.46384			−0.731918	−	0.681393i	$-0.761375\pi$
$53$	−10.6569			−1.46384			−0.731918	+	0.681393i	$0.761375\pi$
$54$		0			0
$55$	−1.53819	+	2.66422i	−0.207409	+	0.359244i
$56$	−4.39627	−	7.61457i	−0.587477	−	1.01754i
$57$		0			0
$58$	−6.51649	+	3.76230i	−0.855657	+	0.494014i
$59$	−4.17256	+	2.40903i	−0.543221	+	0.313629i	−0.746383	−	0.665516i	$-0.768211\pi$
$59$	−4.17256	+	2.40903i	−0.543221	+	0.313629i	0.203162	+	0.979145i	$0.434878\pi$
$60$		0			0
$61$	3.13397	+	5.42820i	0.401264	+	0.695010i	0.993879	−	0.110476i	$-0.0352375\pi$
$61$	3.13397	+	5.42820i	0.401264	+	0.695010i	−0.592614	+	0.805486i	$0.701904\pi$
$62$	1.77505	−	3.07448i	0.225432	−	0.390460i
$63$		0			0
$64$	−8.39230			−1.04904
$65$	0.601205	−	3.55507i	0.0745703	−	0.440953i
$66$		0			0
$67$	−5.09097	−	2.93927i	−0.621961	−	0.359090i	0.155671	−	0.987809i	$-0.450246\pi$
$67$	−5.09097	−	2.93927i	−0.621961	−	0.359090i	−0.777632	+	0.628719i	$0.783579\pi$
$68$	0.713876	−	1.23647i	0.0865702	−	0.149944i
$69$		0			0
$70$			3.21829i			0.384660i
$71$	−8.91942	+	5.14963i	−1.05854	+	0.611148i	−0.925028	−	0.379899i	$-0.875959\pi$
$71$	−8.91942	+	5.14963i	−1.05854	+	0.611148i	−0.133512	+	0.991047i	$0.542625\pi$
$72$		0			0
$73$		−	11.1101i		−	1.30034i	−0.759787	−	0.650172i	$-0.774697\pi$
$73$		−	11.1101i		−	1.30034i	0.759787	−	0.650172i	$-0.225303\pi$
$74$	4.64605	+	8.04719i	0.540092	+	0.935467i
$75$		0			0
$76$	−4.70454	−	2.71617i	−0.539648	−	0.311566i
$77$	8.79254			1.00200
$78$		0			0
$79$	−11.0968			−1.24849			−0.624246	−	0.781228i	$-0.714594\pi$
$79$	−11.0968			−1.24849			−0.624246	+	0.781228i	$0.714594\pi$
$80$	1.73205	+	1.00000i	0.193649	+	0.111803i
$81$		0			0
$82$	−1.87044	−	3.23970i	−0.206556	−	0.357765i
$83$		−	6.97707i		−	0.765833i	−0.923783	−	0.382916i	$-0.874920\pi$
$83$		−	6.97707i		−	0.765833i	0.923783	−	0.382916i	$-0.125080\pi$
$84$		0			0
$85$	−1.68905	+	0.975173i	−0.183203	+	0.105772i
$86$			10.7499i			1.15920i
$87$		0			0
$88$	4.73205	−	8.19615i	0.504438	−	0.873713i
$89$	−0.0805845	−	0.0465255i	−0.00854194	−	0.00493169i	0.495723	−	0.868481i	$-0.334903\pi$
$89$	−0.0805845	−	0.0465255i	−0.00854194	−	0.00493169i	−0.504265	+	0.863549i	$0.668236\pi$
$90$		0			0
$91$	−9.65857	+	3.59226i	−1.01249	+	0.376571i
$92$	−6.43659			−0.671061
$93$		0			0
$94$	−1.01207	+	1.75296i	−0.104387	+	0.180804i
$95$	3.71035	+	6.42652i	0.380674	+	0.659347i
$96$		0			0
$97$	4.15483	−	2.39879i	0.421860	−	0.243561i	−0.274013	−	0.961726i	$-0.588351\pi$
$97$	4.15483	−	2.39879i	0.421860	−	0.243561i	0.695873	+	0.718165i	$0.255018\pi$
$98$	1.13963	−	0.657963i	0.115120	−	0.0664643i
$99$		0			0
$100$	0.366025	+	0.633975i	0.0366025	+	0.0633975i
$101$	−1.39627	+	2.41841i	−0.138934	+	0.240641i	−0.927093	−	0.374830i	$-0.877701\pi$
$101$	−1.39627	+	2.41841i	−0.138934	+	0.240641i	0.788159	+	0.615471i	$0.211034\pi$
$102$		0			0
$103$	−8.35395			−0.823139			−0.411570	−	0.911378i	$-0.635019\pi$
$103$	−8.35395			−0.823139			−0.411570	+	0.911378i	$0.635019\pi$
$104$	−1.84953	+	10.9368i	−0.181362	+	1.07244i
$105$		0			0
$106$	−10.3923	−	6.00000i	−1.00939	−	0.582772i
$107$	3.17529	−	5.49977i	0.306967	−	0.531683i	−0.670730	−	0.741701i	$-0.734019\pi$
$107$	3.17529	−	5.49977i	0.306967	−	0.531683i	0.977697	+	0.210019i	$0.0673525\pi$
$108$		0			0
$109$			11.7996i			1.13020i	0.825024	+	0.565098i	$0.191162\pi$
$109$			11.7996i			1.13020i	−0.825024	+	0.565098i	$0.808838\pi$
$110$	−3.00000	+	1.73205i	−0.286039	+	0.165145i
$111$		0			0
$112$		−	5.71617i		−	0.540127i
$113$	1.73205	+	3.00000i	0.162938	+	0.282216i	0.935921	−	0.352210i	$-0.114570\pi$
$113$	1.73205	+	3.00000i	0.162938	+	0.282216i	−0.772983	+	0.634426i	$0.781236\pi$
$114$		0			0
$115$	7.61457	+	4.39627i	0.710062	+	0.409955i
$116$	4.89185			0.454197
$117$		0			0
$118$	−5.42529			−0.499438
$119$	4.82744	+	2.78712i	0.442531	+	0.255495i
$120$		0			0
$121$	−0.767949	−	1.33013i	−0.0698136	−	0.120921i
$122$			7.05791i			0.638994i
$123$		0			0
$124$	−1.99877	+	1.15399i	−0.179495	+	0.103631i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	−7.48601	+	12.9662i	−0.664276	+	1.15056i	0.315205	+	0.949024i	$0.397927\pi$
$127$	−7.48601	+	12.9662i	−0.664276	+	1.15056i	−0.979481	+	0.201536i	$0.935407\pi$
$128$	−1.42775	−	0.824313i	−0.126197	−	0.0728597i
$129$		0			0
$130$	2.58784	−	3.12832i	0.226969	−	0.274372i
$131$	10.5831			0.924649			0.462324	−	0.886711i	$-0.347016\pi$
$131$	10.5831			0.924649			0.462324	+	0.886711i	$0.347016\pi$
$132$		0			0
$133$	10.6045	−	18.3675i	0.919526	−	1.59267i
$134$	−3.30972	−	5.73260i	−0.285916	−	0.495221i
$135$		0			0
$136$	5.19615	−	3.00000i	0.445566	−	0.257248i
$137$	−7.54009	+	4.35327i	−0.644193	+	0.371925i	−0.786228	−	0.617937i	$-0.787969\pi$
$137$	−7.54009	+	4.35327i	−0.644193	+	0.371925i	0.142035	+	0.989862i	$0.454635\pi$
$138$		0			0
$139$	5.82844	+	10.0952i	0.494362	+	0.856260i	0.999979	−	0.00649792i	$-0.00206837\pi$
$139$	5.82844	+	10.0952i	0.494362	+	0.856260i	−0.505617	+	0.862758i	$0.668735\pi$
$140$	1.04613	−	1.81195i	0.0884142	−	0.153138i
$141$		0			0
$142$	−11.5973			−0.973223
$143$	−8.54674	−	7.07012i	−0.714714	−	0.591233i
$144$		0			0
$145$	−5.78712	−	3.34120i	−0.480595	−	0.277471i
$146$	6.25519	−	10.8343i	0.517684	−	0.896654i
$147$		0			0
$148$		−	6.04093i		−	0.496561i
$149$	−5.91003	+	3.41216i	−0.484168	+	0.279535i	−0.722152	−	0.691734i	$-0.756847\pi$
$149$	−5.91003	+	3.41216i	−0.484168	+	0.279535i	0.237984	+	0.971269i	$0.423514\pi$
$150$		0			0
$151$			12.6810i			1.03197i	0.856598	+	0.515984i	$0.172574\pi$
$151$			12.6810i			1.03197i	−0.856598	+	0.515984i	$0.827426\pi$
$152$	−11.4144	−	19.7704i	−0.925834	−	1.60359i
$153$		0			0
$154$	8.57425	+	4.95035i	0.690933	+	0.398910i
$155$	3.15276			0.253235
$156$		0			0
$157$	7.98333			0.637139			0.318569	−	0.947900i	$-0.396798\pi$
$157$	7.98333			0.637139			0.318569	+	0.947900i	$0.396798\pi$
$158$	−10.8213	−	6.24770i	−0.860900	−	0.497041i
$159$		0			0
$160$	−1.95035	−	3.37810i	−0.154188	−	0.267062i
$161$		−	25.1298i		−	1.98051i
$162$		0			0
$163$	−10.6713	+	6.16109i	−0.835843	+	0.482574i	−0.855849	−	0.517226i	$-0.826965\pi$
$163$	−10.6713	+	6.16109i	−0.835843	+	0.482574i	0.0200063	+	0.999800i	$0.493631\pi$
$164$			2.43201i			0.189908i
$165$		0			0
$166$	3.92820	−	6.80385i	0.304888	−	0.528081i
$167$	19.0020	+	10.9708i	1.47042	+	0.848947i	0.999449	−	0.0332022i	$-0.0105705\pi$
$167$	19.0020	+	10.9708i	1.47042	+	0.848947i	0.470970	+	0.882149i	$0.343904\pi$
$168$		0			0
$169$	12.2771	+	4.27466i	0.944393	+	0.328820i
$170$	−2.19615			−0.168437
$171$		0			0
$172$	3.49435	−	6.05239i	0.266442	−	0.461490i
$173$	−7.52528	−	13.0342i	−0.572136	−	0.990969i	−0.996346	−	0.0854053i	$-0.972781\pi$
$173$	−7.52528	−	13.0342i	−0.572136	−	0.990969i	0.424210	−	0.905564i	$-0.360552\pi$
$174$		0			0
$175$	−2.47517	+	1.42904i	−0.187105	+	0.108025i
$176$	5.32844	−	3.07638i	0.401647	−	0.231891i
$177$		0			0
$178$	−0.0523892	−	0.0907407i	−0.00392673	−	0.00680130i
$179$	0.240387	−	0.416363i	0.0179674	−	0.0311204i	−0.856902	−	0.515480i	$-0.827614\pi$
$179$	0.240387	−	0.416363i	0.0179674	−	0.0311204i	0.874869	+	0.484359i	$0.160947\pi$
$180$		0			0
$181$	−1.85887			−0.138169			−0.0690844	−	0.997611i	$-0.522008\pi$
$181$	−1.85887			−0.138169			−0.0690844	+	0.997611i	$0.522008\pi$
$182$	−11.4413	−	1.93486i	−0.848084	−	0.143421i
$183$		0			0
$184$	−23.4253	−	13.5246i	−1.72694	−	0.997046i
$185$	−4.12603	+	7.14650i	−0.303352	+	0.525421i
$186$		0			0
$187$			6.00000i			0.438763i
$188$	1.13963	−	0.657963i	0.0831158	−	0.0479869i
$189$		0			0
$190$			8.35596i			0.606205i
$191$	4.35937	+	7.55066i	0.315433	+	0.546346i	0.979529	−	0.201301i	$-0.0645169\pi$
$191$	4.35937	+	7.55066i	0.315433	+	0.546346i	−0.664096	+	0.747647i	$0.731184\pi$
$192$		0			0
$193$	5.58869	+	3.22663i	0.402283	+	0.232258i	0.687468	−	0.726214i	$-0.258722\pi$
$193$	5.58869	+	3.22663i	0.402283	+	0.232258i	−0.285186	+	0.958472i	$0.592055\pi$
$194$	5.40224			0.387858
$195$		0			0
$196$	−0.855504			−0.0611074
$197$	−10.0399	−	5.79651i	−0.715310	−	0.412984i	0.0977141	−	0.995215i	$-0.468847\pi$
$197$	−10.0399	−	5.79651i	−0.715310	−	0.412984i	−0.813024	+	0.582230i	$0.802180\pi$
$198$		0			0
$199$	0.400691	+	0.694017i	0.0284042	+	0.0491976i	0.879878	−	0.475199i	$-0.157624\pi$
$199$	0.400691	+	0.694017i	0.0284042	+	0.0491976i	−0.851474	+	0.524397i	$0.824291\pi$
$200$			3.07638i			0.217533i
$201$		0			0
$202$	−2.72321	+	1.57225i	−0.191605	+	0.110623i
$203$			19.0988i			1.34048i
$204$		0			0
$205$	1.66109	−	2.87710i	0.116016	−	0.200945i
$206$	−8.14655	−	4.70341i	−0.567597	−	0.327702i
$207$		0			0
$208$	−4.59639	+	5.55636i	−0.318702	+	0.385265i
$209$	22.8289			1.57911
$210$		0			0
$211$	4.14605	−	7.18116i	0.285426	−	0.494372i	−0.687287	−	0.726386i	$-0.741198\pi$
$211$	4.14605	−	7.18116i	0.285426	−	0.494372i	0.972712	+	0.232015i	$0.0745317\pi$
$212$	3.90069	+	6.75620i	0.267901	+	0.464017i
$213$		0			0
$214$	6.19292	−	3.57548i	0.423339	−	0.244415i
$215$	−8.26772	+	4.77337i	−0.563854	+	0.325541i
$216$		0			0
$217$	−4.50542	−	7.80362i	−0.305848	−	0.529744i
$218$	−6.64336	+	11.5066i	−0.449945	+	0.779328i
$219$		0			0
$220$	2.25207			0.151834
$221$	−2.45135	−	6.59097i	−0.164895	−	0.443357i
$222$		0			0
$223$	11.0517	+	6.38068i	0.740074	+	0.427282i	0.822096	−	0.569349i	$-0.192805\pi$
$223$	11.0517	+	6.38068i	0.740074	+	0.427282i	−0.0820224	+	0.996630i	$0.526138\pi$
$224$	−5.57425	+	9.65488i	−0.372445	+	0.645094i
$225$		0			0
$226$			3.90069i			0.259470i
$227$	14.8189	−	8.55568i	0.983563	−	0.567860i	0.0802192	−	0.996777i	$-0.474438\pi$
$227$	14.8189	−	8.55568i	0.983563	−	0.567860i	0.903344	+	0.428917i	$0.141105\pi$
$228$		0			0
$229$			6.39993i			0.422919i	0.977387	+	0.211460i	$0.0678217\pi$
$229$			6.39993i			0.422919i	−0.977387	+	0.211460i	$0.932178\pi$
$230$	4.95035	+	8.57425i	0.326416	+	0.565369i
$231$		0			0
$232$	17.8034	+	10.2788i	1.16885	+	0.674836i
$233$	0.671557			0.0439952			0.0219976	−	0.999758i	$-0.492997\pi$
$233$	0.671557			0.0439952			0.0219976	+	0.999758i	$0.492997\pi$
$234$		0			0
$235$	−1.79759			−0.117262
$236$	3.05452	+	1.76353i	0.198833	+	0.114796i
$237$		0			0
$238$	3.13839	+	5.43586i	0.203432	+	0.352354i
$239$		−	7.12983i		−	0.461190i	−0.973050	−	0.230595i	$-0.925933\pi$
$239$		−	7.12983i		−	0.461190i	0.973050	−	0.230595i	$-0.0740673\pi$
$240$		0			0
$241$	−23.3292	+	13.4691i	−1.50277	+	0.867623i	−0.502772	+	0.864419i	$0.667686\pi$
$241$	−23.3292	+	13.4691i	−1.50277	+	0.867623i	−0.999995	+	0.00320355i	$0.998980\pi$
$242$		−	1.72947i		−	0.111175i
$243$		0			0
$244$	2.29423	−	3.97372i	0.146873	−	0.254391i
$245$	1.01207	+	0.584320i	0.0646589	+	0.0373308i
$246$		0			0
$247$	−25.0774	+	9.32692i	−1.59564	+	0.593458i
$248$	−9.69907			−0.615892
$249$		0			0
$250$	0.563016	−	0.975173i	0.0356083	−	0.0616753i
$251$	5.82402	+	10.0875i	0.367609	+	0.636718i	0.989191	−	0.146631i	$-0.0468431\pi$
$251$	5.82402	+	10.0875i	0.367609	+	0.636718i	−0.621582	+	0.783349i	$0.713510\pi$
$252$		0			0
$253$	23.4253	−	13.5246i	1.47274	−	0.850284i
$254$	−14.6003	+	8.42949i	−0.916105	+	0.528913i
$255$		0			0
$256$	7.46410	+	12.9282i	0.466506	+	0.808013i
$257$	3.63939	−	6.30362i	0.227019	−	0.393209i	−0.729904	−	0.683550i	$-0.760435\pi$
$257$	3.63939	−	6.30362i	0.227019	−	0.393209i	0.956923	+	0.290341i	$0.0937687\pi$
$258$		0			0
$259$	23.5851			1.46551
$260$	−2.47388	+	0.920099i	−0.153424	+	0.0570621i
$261$		0			0
$262$	10.3203	+	5.95845i	0.637593	+	0.368114i
$263$	11.9639	−	20.7220i	0.737724	−	1.27778i	−0.215794	−	0.976439i	$-0.569234\pi$
$263$	11.9639	−	20.7220i	0.737724	−	1.27778i	0.953518	−	0.301336i	$-0.0974327\pi$
$264$		0			0
$265$		−	10.6569i		−	0.654647i
$266$	20.6824	−	11.9410i	1.26812	−	0.732150i
$267$		0			0
$268$			4.30340i			0.262872i
$269$	2.19073	+	3.79446i	0.133571	+	0.231352i	0.925051	−	0.379843i	$-0.124022\pi$
$269$	2.19073	+	3.79446i	0.133571	+	0.231352i	−0.791479	+	0.611196i	$0.790689\pi$
$270$		0			0
$271$	−2.15488	−	1.24412i	−0.130900	−	0.0755751i	0.433120	−	0.901336i	$-0.357413\pi$
$271$	−2.15488	−	1.24412i	−0.130900	−	0.0755751i	−0.564020	+	0.825761i	$0.690746\pi$
$272$	3.90069			0.236514
$273$		0			0
$274$	−9.80385			−0.592272
$275$	−2.66422	−	1.53819i	−0.160659	−	0.0927563i
$276$		0			0
$277$	−10.8530	−	18.7980i	−0.652096	−	1.12946i	−0.982613	−	0.185663i	$-0.940557\pi$
$277$	−10.8530	−	18.7980i	−0.652096	−	1.12946i	0.330518	−	0.943800i	$-0.392777\pi$
$278$			13.1260i			0.787247i
$279$		0			0
$280$	7.61457	−	4.39627i	0.455057	−	0.262728i
$281$			29.7270i			1.77336i	0.462379	+	0.886682i	$0.346996\pi$
$281$			29.7270i			1.77336i	−0.462379	+	0.886682i	$0.653004\pi$
$282$		0			0
$283$	13.9998	−	24.2483i	0.832200	−	1.44141i	−0.0640902	−	0.997944i	$-0.520415\pi$
$283$	13.9998	−	24.2483i	0.832200	−	1.44141i	0.896290	−	0.443468i	$-0.146252\pi$
$284$	6.52947	+	3.76979i	0.387452	+	0.223696i
$285$		0			0
$286$	−4.35395	−	11.7065i	−0.257455	−	0.692222i
$287$	−9.49508			−0.560477
$288$		0			0
$289$	6.59808	−	11.4282i	0.388122	−	0.672247i
$290$	−3.76230	−	6.51649i	−0.220930	−	0.382662i
$291$		0			0
$292$	−7.04355	+	4.06660i	−0.412193	+	0.237980i
$293$	14.6866	−	8.47930i	0.857999	−	0.495366i	−0.00534246	−	0.999986i	$-0.501701\pi$
$293$	14.6866	−	8.47930i	0.857999	−	0.495366i	0.863342	+	0.504620i	$0.168367\pi$
$294$		0			0
$295$	−2.40903	−	4.17256i	−0.140259	−	0.242936i
$296$	12.6932	−	21.9853i	0.737779	−	1.27787i
$297$		0			0
$298$	−7.68440			−0.445145
$299$	−20.2070	+	24.4273i	−1.16860	+	1.41267i
$300$		0			0
$301$	23.6298	+	13.6427i	1.36200	+	0.786351i
$302$	−7.13963	+	12.3662i	−0.410839	+	0.711595i
$303$		0			0
$304$		−	14.8414i		−	0.851213i
$305$	−5.42820	+	3.13397i	−0.310818	+	0.179451i
$306$		0			0
$307$		−	15.6072i		−	0.890752i	−0.895344	−	0.445376i	$-0.853070\pi$
$307$		−	15.6072i		−	0.890752i	0.895344	−	0.445376i	$-0.146930\pi$
$308$	−3.21829	−	5.57425i	−0.183379	−	0.317622i
$309$		0			0
$310$	3.07448	+	1.77505i	0.174619	+	0.100816i
$311$	−24.9941			−1.41728			−0.708642	−	0.705568i	$-0.750692\pi$
$311$	−24.9941			−1.41728			−0.708642	+	0.705568i	$0.750692\pi$
$312$		0			0
$313$	1.16117			0.0656331			0.0328166	−	0.999461i	$-0.489552\pi$
$313$	1.16117			0.0656331			0.0328166	+	0.999461i	$0.489552\pi$
$314$	7.78512	+	4.49474i	0.439340	+	0.253653i
$315$		0			0
$316$	4.06173	+	7.03512i	0.228490	+	0.395756i
$317$		−	8.62570i		−	0.484467i	−0.970218	−	0.242234i	$-0.922120\pi$
$317$		−	8.62570i		−	0.484467i	0.970218	−	0.242234i	$-0.0778801\pi$
$318$		0			0
$319$	−17.8034	+	10.2788i	−0.996798	+	0.575502i
$320$		−	8.39230i		−	0.469144i
$321$		0			0
$322$	14.1485	−	24.5059i	0.788465	−	1.36566i
$323$	12.5339	+	7.23647i	0.697407	+	0.402648i
$324$		0			0
$325$	3.55507	+	0.601205i	0.197200	+	0.0333489i
$326$	−13.8752			−0.768475
$327$		0			0
$328$	−5.11015	+	8.85104i	−0.282161	+	0.488717i
$329$	2.56883	+	4.44934i	0.141624	+	0.245300i
$330$		0			0
$331$	−22.1899	+	12.8113i	−1.21967	+	0.704174i	−0.964846	−	0.262815i	$-0.915349\pi$
$331$	−22.1899	+	12.8113i	−1.21967	+	0.704174i	−0.254819	+	0.966989i	$0.582016\pi$
$332$	−4.42328	+	2.55378i	−0.242759	+	0.140157i
$333$		0			0
$334$	12.3535	+	21.3969i	0.675953	+	1.17078i
$335$	2.93927	−	5.09097i	0.160590	−	0.278150i
$336$		0			0
$337$	−20.1770			−1.09911			−0.549556	−	0.835457i	$-0.685203\pi$
$337$	−20.1770			−1.09911			−0.549556	+	0.835457i	$0.685203\pi$
$338$	9.56560	+	11.0807i	0.520300	+	0.602713i
$339$		0			0
$340$	1.23647	+	0.713876i	0.0670570	+	0.0387154i
$341$	4.84953	−	8.39964i	0.262617	−	0.454866i
$342$		0			0
$343$			16.6665i			0.899907i
$344$	25.4346	−	14.6847i	1.37134	−	0.791745i
$345$		0			0
$346$		−	16.9474i		−	0.911099i
$347$	12.0968	+	20.9523i	0.649393	+	1.12478i	0.983268	+	0.182164i	$0.0583101\pi$
$347$	12.0968	+	20.9523i	0.649393	+	1.12478i	−0.333876	+	0.942617i	$0.608357\pi$
$348$		0			0
$349$	22.2362	+	12.8381i	1.19028	+	0.687206i	0.958369	−	0.285532i	$-0.0921703\pi$
$349$	22.2362	+	12.8381i	1.19028	+	0.687206i	0.231907	+	0.972738i	$0.425504\pi$
$350$	−3.21829			−0.172025
$351$		0			0
$352$	−12.0000			−0.639602
$353$	6.79405	+	3.92254i	0.361611	+	0.208776i	0.669787	−	0.742553i	$-0.266385\pi$
$353$	6.79405	+	3.92254i	0.361611	+	0.208776i	−0.308176	+	0.951329i	$0.599719\pi$
$354$		0			0
$355$	−5.14963	−	8.91942i	−0.273314	−	0.473393i
$356$			0.0681180i			0.00361025i
$357$		0			0
$358$	0.468838	−	0.270684i	0.0247789	−	0.0143061i
$359$		−	19.7145i		−	1.04049i	−0.854017	−	0.520245i	$-0.825840\pi$
$359$		−	19.7145i		−	1.04049i	0.854017	−	0.520245i	$-0.174160\pi$
$360$		0			0
$361$	18.0334	−	31.2348i	0.949128	−	1.64394i
$362$	−1.81272	−	1.04658i	−0.0952745	−	0.0550068i
$363$		0			0
$364$	5.81268	+	4.80843i	0.304667	+	0.252030i
$365$	11.1101			0.581532
$366$		0			0
$367$	5.58806	−	9.67880i	0.291694	−	0.505229i	−0.682516	−	0.730870i	$-0.739114\pi$
$367$	5.58806	−	9.67880i	0.291694	−	0.505229i	0.974210	+	0.225641i	$0.0724477\pi$
$368$	−8.79254	−	15.2291i	−0.458343	−	0.793873i
$369$		0			0
$370$	−8.04719	+	4.64605i	−0.418353	+	0.241536i
$371$	−26.3776	+	15.2291i	−1.36946	+	0.790657i
$372$		0			0
$373$	4.37586	+	7.57922i	0.226574	+	0.392437i	0.956790	−	0.290778i	$-0.0939143\pi$
$373$	4.37586	+	7.57922i	0.226574	+	0.392437i	−0.730217	+	0.683216i	$0.760581\pi$
$374$	−3.37810	+	5.85104i	−0.174677	+	0.302550i
$375$		0			0
$376$	5.53006			0.285191
$377$	15.3575	−	18.5649i	0.790949	−	0.956142i
$378$		0			0
$379$	−16.2550	−	9.38481i	−0.834961	−	0.482065i	0.0205870	−	0.999788i	$-0.493446\pi$
$379$	−16.2550	−	9.38481i	−0.834961	−	0.482065i	−0.855548	+	0.517723i	$0.826780\pi$
$380$	2.71617	−	4.70454i	0.139336	−	0.241338i
$381$		0			0
$382$			9.81759i			0.502312i
$383$	−5.26083	+	3.03734i	−0.268816	+	0.155201i	−0.628349	−	0.777931i	$-0.716269\pi$
$383$	−5.26083	+	3.03734i	−0.268816	+	0.155201i	0.359533	+	0.933132i	$0.382936\pi$
$384$		0			0
$385$			8.79254i			0.448110i
$386$	3.63329	+	6.29305i	0.184930	+	0.320308i
$387$		0			0
$388$	−3.04155	−	1.75604i	−0.154411	−	0.0891494i
$389$	−9.66572			−0.490072			−0.245036	−	0.969514i	$-0.578800\pi$
$389$	−9.66572			−0.490072			−0.245036	+	0.969514i	$0.578800\pi$
$390$		0			0
$391$	17.1485			0.867237
$392$	−3.11352	−	1.79759i	−0.157256	−	0.0907920i
$393$		0			0
$394$	−6.52706	−	11.3052i	−0.328829	−	0.569548i
$395$		−	11.0968i		−	0.558343i
$396$		0			0
$397$	21.0718	−	12.1658i	1.05757	−	0.610585i	0.132807	−	0.991142i	$-0.457601\pi$
$397$	21.0718	−	12.1658i	1.05757	−	0.610585i	0.924758	+	0.380556i	$0.124268\pi$
$398$			0.902382i			0.0452323i
$399$		0			0
$400$	−1.00000	+	1.73205i	−0.0500000	+	0.0866025i
$401$	7.70454	+	4.44822i	0.384746	+	0.222133i	0.679881	−	0.733322i	$-0.262031\pi$
$401$	7.70454	+	4.44822i	0.384746	+	0.222133i	−0.295135	+	0.955456i	$0.595365\pi$
$402$		0			0
$403$	−1.89545	+	11.2083i	−0.0944193	+	0.558324i
$404$	2.04428			0.101707
$405$		0			0
$406$	−10.7530	+	18.6247i	−0.533660	+	0.924327i
$407$	12.6932	+	21.9853i	0.629180	+	1.08977i
$408$		0			0
$409$	24.4988	−	14.1444i	1.21139	−	0.699394i	0.248325	−	0.968677i	$-0.420120\pi$
$409$	24.4988	−	14.1444i	1.21139	−	0.699394i	0.963061	+	0.269283i	$0.0867866\pi$
$410$	3.23970	−	1.87044i	0.159998	−	0.0923746i
$411$		0			0
$412$	3.05776	+	5.29619i	0.150645	+	0.260925i
$413$	−6.88520	+	11.9255i	−0.338799	+	0.586816i
$414$		0			0
$415$	6.97707			0.342491
$416$	13.1819	−	4.90269i	0.646298	−	0.240374i
$417$		0			0
$418$	22.2621	+	12.8530i	1.08888	+	0.628663i
$419$	14.4474	−	25.0236i	0.705801	−	1.22248i	−0.260601	−	0.965447i	$-0.583921\pi$
$419$	14.4474	−	25.0236i	0.705801	−	1.22248i	0.966402	−	0.257036i	$-0.0827459\pi$
$420$		0			0
$421$			12.0134i			0.585498i	0.956189	+	0.292749i	$0.0945701\pi$
$421$			12.0134i			0.585498i	−0.956189	+	0.292749i	$0.905430\pi$
$422$	8.08622	−	4.66858i	0.393631	−	0.227263i
$423$		0			0
$424$			32.7846i			1.59216i
$425$	−0.975173	−	1.68905i	−0.0473028	−	0.0819309i
$426$		0			0
$427$	15.5143	+	8.95716i	0.750788	+	0.433467i
$428$	−4.64895			−0.224716
$429$		0			0
$430$	−10.7499			−0.518408
$431$	−19.9384	−	11.5115i	−0.960401	−	0.554488i	−0.0641046	−	0.997943i	$-0.520419\pi$
$431$	−19.9384	−	11.5115i	−0.960401	−	0.554488i	−0.896296	+	0.443455i	$0.853752\pi$
$432$		0			0
$433$	−13.4397	−	23.2783i	−0.645872	−	1.11868i	−0.984099	−	0.177619i	$-0.943161\pi$
$433$	−13.4397	−	23.2783i	−0.645872	−	1.11868i	0.338227	−	0.941064i	$-0.390173\pi$
$434$		−	10.1465i		−	0.487047i
$435$		0			0
$436$	7.48064	−	4.31895i	0.358258	−	0.206840i
$437$		−	65.2469i		−	3.12118i
$438$		0			0
$439$	−15.8272	+	27.4135i	−0.755392	+	1.30838i	0.189788	+	0.981825i	$0.439220\pi$
$439$	−15.8272	+	27.4135i	−0.755392	+	1.30838i	−0.945179	+	0.326551i	$0.894113\pi$
$440$	8.19615	+	4.73205i	0.390736	+	0.225592i
$441$		0			0
$442$	1.32034	−	7.80748i	0.0628021	−	0.371364i
$443$	9.89932			0.470331			0.235166	−	0.971955i	$-0.424437\pi$
$443$	9.89932			0.470331			0.235166	+	0.971955i	$0.424437\pi$
$444$		0			0
$445$	0.0465255	−	0.0805845i	0.00220552	−	0.00382007i
$446$	7.18485	+	12.4445i	0.340212	+	0.589265i
$447$		0			0
$448$	−20.7724	+	11.9930i	−0.981404	+	0.566614i
$449$	12.9975	−	7.50413i	0.613392	−	0.354142i	−0.160900	−	0.986971i	$-0.551440\pi$
$449$	12.9975	−	7.50413i	0.613392	−	0.354142i	0.774292	+	0.632829i	$0.218106\pi$
$450$		0			0
$451$	−5.11015	−	8.85104i	−0.240627	−	0.416779i
$452$	1.26795	−	2.19615i	0.0596393	−	0.103298i
$453$		0			0
$454$	19.2679			0.904290
$455$	−3.59226	−	9.65857i	−0.168408	−	0.452801i
$456$		0			0
$457$	−11.2847	−	6.51520i	−0.527874	−	0.304768i	0.212276	−	0.977210i	$-0.431912\pi$
$457$	−11.2847	−	6.51520i	−0.527874	−	0.304768i	−0.740150	+	0.672441i	$0.765246\pi$
$458$	−3.60326	+	6.24104i	−0.168369	+	0.291624i
$459$		0			0
$460$		−	6.43659i		−	0.300108i
$461$	−24.8693	+	14.3583i	−1.15828	+	0.668732i	−0.950891	−	0.309526i	$-0.899830\pi$
$461$	−24.8693	+	14.3583i	−1.15828	+	0.668732i	−0.207388	+	0.978259i	$0.566496\pi$
$462$		0			0
$463$		−	0.460309i		−	0.0213924i	−0.999943	−	0.0106962i	$-0.996595\pi$
$463$		−	0.460309i		−	0.0213924i	0.999943	−	0.0106962i	$-0.00340477\pi$
$464$	6.68240	+	11.5742i	0.310222	+	0.537321i
$465$		0			0
$466$	0.654884	+	0.378098i	0.0303369	+	0.0175150i
$467$	−34.0634			−1.57627			−0.788133	−	0.615505i	$-0.788952\pi$
$467$	−34.0634			−1.57627			−0.788133	+	0.615505i	$0.788952\pi$
$468$		0			0
$469$	−16.8014			−0.775816
$470$	−1.75296	−	1.01207i	−0.0808580	−	0.0466834i
$471$		0			0
$472$	7.41108	+	12.8364i	0.341123	+	0.590842i
$473$			29.3694i			1.35041i
$474$		0			0
$475$	−6.42652	+	3.71035i	−0.294869	+	0.170243i
$476$		−	4.08063i		−	0.187036i
$477$		0			0
$478$	4.01421	−	6.95281i	0.183606	−	0.318014i
$479$	−26.7871	−	15.4656i	−1.22393	−	0.706639i	−0.258180	−	0.966097i	$-0.583123\pi$
$479$	−26.7871	−	15.4656i	−1.22393	−	0.706639i	−0.965755	+	0.259458i	$0.916456\pi$
$480$		0			0
$481$	−22.9257	−	18.9649i	−1.04532	−	0.864723i
$482$	−30.3333			−1.38165
$483$		0			0
$484$	−0.562178	+	0.973721i	−0.0255535	+	0.0442600i
$485$	2.39879	+	4.15483i	0.108924	+	0.188661i
$486$		0			0
$487$	14.3223	−	8.26901i	0.649007	−	0.374704i	−0.139069	−	0.990283i	$-0.544411\pi$
$487$	14.3223	−	8.26901i	0.649007	−	0.374704i	0.788076	+	0.615578i	$0.211078\pi$
$488$	16.6992	−	9.64129i	0.755937	−	0.436441i
$489$		0			0
$490$	0.657963	+	1.13963i	0.0297238	+	0.0514831i
$491$	−9.34120	+	16.1794i	−0.421562	+	0.730167i	−0.996093	−	0.0883160i	$-0.971851\pi$
$491$	−9.34120	+	16.1794i	−0.421562	+	0.730167i	0.574530	+	0.818483i	$0.305185\pi$
$492$		0			0
$493$	−13.0330			−0.586976
$494$	−29.7060	−	5.02364i	−1.33654	−	0.226024i
$495$		0			0
$496$	−5.46073	−	3.15276i	−0.245194	−	0.141563i
$497$	−14.7181	+	25.4924i	−0.660195	+	1.14349i
$498$		0			0
$499$			10.9966i			0.492277i	0.969235	+	0.246138i	$0.0791618\pi$
$499$			10.9966i			0.492277i	−0.969235	+	0.246138i	$0.920838\pi$
$500$	−0.633975	+	0.366025i	−0.0283522	+	0.0163692i
$501$		0			0
$502$			13.1161i			0.585399i
$503$	−7.99663	−	13.8506i	−0.356552	−	0.617567i	0.630830	−	0.775921i	$-0.282714\pi$
$503$	−7.99663	−	13.8506i	−0.356552	−	0.617567i	−0.987382	+	0.158354i	$0.949381\pi$
$504$		0			0
$505$	−2.41841	−	1.39627i	−0.107618	−	0.0621333i
$506$	30.4583			1.35404
$507$		0			0
$508$	10.9603			0.486284
$509$	−1.23647	−	0.713876i	−0.0548055	−	0.0316420i	0.472347	−	0.881413i	$-0.343407\pi$
$509$	−1.23647	−	0.713876i	−0.0548055	−	0.0316420i	−0.527152	+	0.849771i	$0.676740\pi$
$510$		0			0
$511$	−15.8769	−	27.4995i	−0.702351	−	1.21651i
$512$			20.1069i			0.888608i
$513$		0			0
$514$	7.09808	−	4.09808i	0.313083	−	0.180758i
$515$		−	8.35395i		−	0.368119i
$516$		0			0
$517$	−2.76503	+	4.78918i	−0.121606	+	0.210628i
$518$	22.9995	+	13.2788i	1.01054	+	0.583436i
$519$		0			0
$520$	−10.9368	−	1.84953i	−0.479608	−	0.0811075i
$521$	−11.8172			−0.517719			−0.258859	−	0.965915i	$-0.583347\pi$
$521$	−11.8172			−0.517719			−0.258859	+	0.965915i	$0.583347\pi$
$522$		0			0
$523$	−14.3063	+	24.7792i	−0.625571	+	1.08352i	0.362859	+	0.931844i	$0.381801\pi$
$523$	−14.3063	+	24.7792i	−0.625571	+	1.08352i	−0.988430	+	0.151677i	$0.951533\pi$
$524$	−3.87368	−	6.70941i	−0.169222	−	0.293102i
$525$		0			0
$526$	23.3337	−	13.4717i	1.01740	−	0.587394i
$527$	5.32516	−	3.07448i	0.231968	−	0.133927i
$528$		0			0
$529$	−27.1544	−	47.0328i	−1.18063	−	2.04491i
$530$	6.00000	−	10.3923i	0.260623	−	0.451413i
$531$		0			0
$532$	−15.5261			−0.673140
$533$	9.22963	+	7.63503i	0.399780	+	0.330710i
$534$		0			0
$535$	5.49977	+	3.17529i	0.237776	+	0.137280i
$536$	−9.04232	+	15.6618i	−0.390569	+	0.676485i
$537$		0			0
$538$			4.93367i			0.212706i
$539$	3.11352	−	1.79759i	0.134109	−	0.0774277i
$540$		0			0
$541$			33.9315i			1.45883i	0.684072	+	0.729415i	$0.260208\pi$
$541$			33.9315i			1.45883i	−0.684072	+	0.729415i	$0.739792\pi$
$542$	−1.40092	−	2.42647i	−0.0601748	−	0.104226i
$543$		0			0
$544$	−6.58846	−	3.80385i	−0.282478	−	0.163089i
$545$	−11.7996			−0.505439
$546$		0			0
$547$	−0.0276116			−0.00118059			−0.000590294	−	1.00000i	$-0.500188\pi$
$547$	−0.0276116			−0.00118059			−0.000590294		1.00000i	$0.500188\pi$
$548$	5.51973	+	3.18682i	0.235791	+	0.136134i
$549$		0			0
$550$	−1.73205	−	3.00000i	−0.0738549	−	0.127920i
$551$			49.5881i			2.11252i
$552$		0			0
$553$	−27.4666	+	15.8579i	−1.16800	+	0.674344i
$554$		−	24.4417i		−	1.03843i
$555$		0			0
$556$	4.26672	−	7.39017i	0.180949	−	0.313413i
$557$	34.9572	+	20.1826i	1.48118	+	0.855162i	0.999772	−	0.0213318i	$-0.00679062\pi$
$557$	34.9572	+	20.1826i	1.48118	+	0.855162i	0.481412	+	0.876494i	$0.340124\pi$
$558$		0			0
$559$	−11.9991	−	32.2621i	−0.507507	−	1.36454i
$560$	5.71617			0.241552
$561$		0			0
$562$	−16.7368	+	28.9890i	−0.705999	+	1.22283i
$563$	−7.06049	−	12.2291i	−0.297564	−	0.515397i	0.678014	−	0.735049i	$-0.262841\pi$
$563$	−7.06049	−	12.2291i	−0.297564	−	0.515397i	−0.975578	+	0.219653i	$0.929508\pi$
$564$		0			0
$565$	−3.00000	+	1.73205i	−0.126211	+	0.0728679i
$566$	27.3044	−	15.7642i	1.14769	−	0.662618i
$567$		0			0
$568$	15.8422	+	27.4395i	0.664724	+	1.15134i
$569$	15.5158	−	26.8742i	0.650456	−	1.12662i	−0.332556	−	0.943084i	$-0.607911\pi$
$569$	15.5158	−	26.8742i	0.650456	−	1.12662i	0.983012	−	0.183540i	$-0.0587557\pi$
$570$		0			0
$571$	29.6336			1.24013			0.620065	−	0.784551i	$-0.287106\pi$
$571$	29.6336			1.24013			0.620065	+	0.784551i	$0.287106\pi$
$572$	−1.35395	+	8.00626i	−0.0566116	+	0.334758i
$573$		0			0
$574$	−9.25934	−	5.34589i	−0.386478	−	0.223133i
$575$	−4.39627	+	7.61457i	−0.183337	+	0.317549i
$576$		0			0
$577$		−	17.7788i		−	0.740140i	−0.929004	−	0.370070i	$-0.879334\pi$
$577$		−	17.7788i		−	0.740140i	0.929004	−	0.370070i	$-0.120666\pi$
$578$	12.8685	−	7.42965i	0.535260	−	0.309033i
$579$		0			0
$580$			4.89185i			0.203123i
$581$	−9.97052	−	17.2695i	−0.413647	−	0.716458i
$582$		0			0
$583$	−28.3923	−	16.3923i	−1.17589	−	0.678900i
$584$	−34.1790			−1.41434
$585$		0			0
$586$	19.0959			0.788846
$587$	−4.81687	−	2.78102i	−0.198814	−	0.114785i	0.397288	−	0.917694i	$-0.369951\pi$
$587$	−4.81687	−	2.78102i	−0.198814	−	0.114785i	−0.596102	+	0.802909i	$0.703285\pi$
$588$		0			0
$589$	−11.6978	−	20.2612i	−0.482001	−	0.834850i
$590$		−	5.42529i		−	0.223356i
$591$		0			0
$592$	14.2930	−	8.25207i	0.587439	−	0.339158i
$593$			33.4290i			1.37276i	0.727241	+	0.686382i	$0.240802\pi$
$593$			33.4290i			1.37276i	−0.727241	+	0.686382i	$0.759198\pi$
$594$		0			0
$595$	−2.78712	+	4.82744i	−0.114261	+	0.197906i
$596$	4.32644	+	2.49787i	0.177218	+	0.102317i
$597$		0			0
$598$	−33.4583	+	12.4440i	−1.36821	+	0.508871i
$599$	8.14349			0.332734			0.166367	−	0.986064i	$-0.446796\pi$
$599$	8.14349			0.332734			0.166367	+	0.986064i	$0.446796\pi$
$600$		0			0
$601$	−11.5588	+	20.0204i	−0.471494	+	0.816651i	−0.999468	−	0.0326092i	$-0.989618\pi$
$601$	−11.5588	+	20.0204i	−0.471494	+	0.816651i	0.527974	+	0.849260i	$0.322952\pi$
$602$	15.3621	+	26.6080i	0.626113	+	1.08446i
$603$		0			0
$604$	8.03945	−	4.64158i	0.327121	−	0.188863i
$605$	1.33013	−	0.767949i	0.0540774	−	0.0312216i
$606$		0			0
$607$	−3.48351	−	6.03361i	−0.141391	−	0.244897i	0.786629	−	0.617425i	$-0.211824\pi$
$607$	−3.48351	−	6.03361i	−0.141391	−	0.244897i	−0.928021	+	0.372528i	$0.878491\pi$
$608$	−14.4729	+	25.0679i	−0.586955	+	1.01664i
$609$		0			0
$610$	−7.05791			−0.285767
$611$	1.08072	−	6.39056i	0.0437213	−	0.258535i
$612$		0			0
$613$	−29.7784	−	17.1926i	−1.20274	−	0.694401i	−0.241574	−	0.970382i	$-0.577664\pi$
$613$	−29.7784	−	17.1926i	−1.20274	−	0.694401i	−0.961163	+	0.275982i	$0.910997\pi$
$614$	8.78712	−	15.2197i	0.354620	−	0.614219i
$615$		0			0
$616$		−	27.0492i		−	1.08984i
$617$	−13.5177	+	7.80446i	−0.544203	+	0.314196i	−0.746781	−	0.665070i	$-0.768402\pi$
$617$	−13.5177	+	7.80446i	−0.544203	+	0.314196i	0.202578	+	0.979266i	$0.435068\pi$
$618$		0			0
$619$		−	16.0626i		−	0.645610i	−0.946465	−	0.322805i	$-0.895374\pi$
$619$		−	16.0626i		−	0.645610i	0.946465	−	0.322805i	$-0.104626\pi$
$620$	−1.15399	−	1.99877i	−0.0463453	−	0.0802724i
$621$		0			0
$622$	−24.3735	−	14.0721i	−0.977290	−	0.564238i
$623$	−0.265947			−0.0106550
$624$		0			0
$625$	1.00000			0.0400000
$626$	1.13234	+	0.653757i	0.0452574	+	0.0261294i
$627$		0			0
$628$	−2.92210	−	5.06123i	−0.116605	−	0.201965i
$629$			16.0944i			0.641725i
$630$		0			0
$631$	−31.7588	+	18.3359i	−1.26430	+	0.729942i	−0.973903	−	0.226965i	$-0.927120\pi$
$631$	−31.7588	+	18.3359i	−1.26430	+	0.729942i	−0.290394	+	0.956907i	$0.593786\pi$
$632$			34.1381i			1.35794i
$633$		0			0
$634$	4.85641	−	8.41154i	0.192873	−	0.334065i
$635$	−12.9662	−	7.48601i	−0.514546	−	0.297073i
$636$		0			0
$637$	−2.68576	+	3.24670i	−0.106414	+	0.128639i
$638$	−23.1485			−0.916458
$639$		0			0
$640$	0.824313	−	1.42775i	0.0325838	−	0.0564369i
$641$	−13.3211	−	23.0728i	−0.526152	−	0.911322i	−0.999536	−	0.0304659i	$-0.990301\pi$
$641$	−13.3211	−	23.0728i	−0.526152	−	0.911322i	0.473384	−	0.880856i	$-0.343032\pi$
$642$		0			0
$643$	−1.78484	+	1.03048i	−0.0703873	+	0.0406381i	−0.534781	−	0.844991i	$-0.679606\pi$
$643$	−1.78484	+	1.03048i	−0.0703873	+	0.0406381i	0.464393	+	0.885629i	$0.346272\pi$
$644$	−15.9317	+	9.19815i	−0.627796	+	0.362458i
$645$		0			0
$646$	8.14850	+	14.1136i	0.320598	+	0.555293i
$647$	7.76353	−	13.4468i	0.305216	−	0.528649i	−0.672093	−	0.740466i	$-0.734605\pi$
$647$	7.76353	−	13.4468i	0.305216	−	0.528649i	0.977309	+	0.211817i	$0.0679380\pi$
$648$		0			0
$649$	−14.8222			−0.581821
$650$	3.12832	+	2.58784i	0.122703	+	0.101504i
$651$		0			0
$652$	7.81195	+	4.51023i	0.305940	+	0.176634i
$653$	20.4368	−	35.3976i	0.799754	−	1.38521i	−0.120022	−	0.992771i	$-0.538297\pi$
$653$	20.4368	−	35.3976i	0.799754	−	1.38521i	0.919776	−	0.392444i	$-0.128370\pi$
$654$		0			0
$655$			10.5831i			0.413515i
$656$	−5.75419	+	3.32218i	−0.224663	+	0.129710i
$657$		0			0
$658$			5.78517i			0.225530i
$659$	0.917364	+	1.58892i	0.0357354	+	0.0618956i	0.883340	−	0.468733i	$-0.155289\pi$
$659$	0.917364	+	1.58892i	0.0357354	+	0.0618956i	−0.847605	+	0.530628i	$0.821956\pi$
$660$		0			0
$661$	15.0413	+	8.68408i	0.585038	+	0.337772i	0.763133	−	0.646242i	$-0.223660\pi$
$661$	15.0413	+	8.68408i	0.585038	+	0.337772i	−0.178095	+	0.984013i	$0.556994\pi$
$662$	−28.8519			−1.12136
$663$		0			0
$664$	−21.4641			−0.832969
$665$	18.3675	+	10.6045i	0.712262	+	0.411225i
$666$		0			0
$667$	29.3776	+	50.8836i	1.13751	+	1.97022i
$668$		−	16.0624i		−	0.621472i
$669$		0			0
$670$	5.73260	−	3.30972i	0.221470	−	0.127866i
$671$			19.2826i			0.744396i
$672$		0			0
$673$	−4.75396	+	8.23410i	−0.183252	+	0.317401i	−0.942986	−	0.332832i	$-0.891996\pi$
$673$	−4.75396	+	8.23410i	−0.183252	+	0.317401i	0.759734	+	0.650234i	$0.225329\pi$
$674$	−19.6761	−	11.3600i	−0.757894	−	0.437570i
$675$		0			0
$676$	−1.78371	−	9.34801i	−0.0686041	−	0.359539i
$677$	−20.7375			−0.797008			−0.398504	−	0.917167i	$-0.630470\pi$
$677$	−20.7375			−0.797008			−0.398504	+	0.917167i	$0.630470\pi$
$678$		0			0
$679$	6.85596	−	11.8749i	0.263107	−	0.455715i
$680$	3.00000	+	5.19615i	0.115045	+	0.199263i
$681$		0			0
$682$	9.45827	−	5.46073i	0.362176	−	0.209102i
$683$	−14.4521	+	8.34393i	−0.552995	+	0.319272i	−0.750329	−	0.661065i	$-0.770105\pi$
$683$	−14.4521	+	8.34393i	−0.552995	+	0.319272i	0.197334	+	0.980336i	$0.436772\pi$
$684$		0			0
$685$	−4.35327	−	7.54009i	−0.166330	−	0.288092i
$686$	−9.38352	+	16.2527i	−0.358264	+	0.620532i
$687$		0			0
$688$	19.0935			0.727932
$689$	37.8860	+	6.40698i	1.44334	+	0.244086i
$690$		0			0
$691$	19.6119	+	11.3229i	0.746073	+	0.430745i	0.824273	−	0.566192i	$-0.191584\pi$
$691$	19.6119	+	11.3229i	0.746073	+	0.430745i	−0.0782005	+	0.996938i	$0.524917\pi$
$692$	−5.50889	+	9.54167i	−0.209416	+	0.362720i
$693$		0			0
$694$			27.2429i			1.03413i
$695$	−10.0952	+	5.82844i	−0.382931	+	0.221085i
$696$		0			0
$697$		−	6.47941i		−	0.245425i
$698$	14.4561	+	25.0387i	0.547171	+	0.947728i
$699$		0			0
$700$	1.81195	+	1.04613i	0.0684854	+	0.0395400i
$701$	9.33818			0.352698			0.176349	−	0.984328i	$-0.443571\pi$
$701$	9.33818			0.352698			0.176349	+	0.984328i	$0.443571\pi$
$702$		0			0
$703$	61.2361			2.30956
$704$	−22.3590	−	12.9090i	−0.842685	−	0.486524i
$705$		0			0
$706$	4.41691	+	7.65032i	0.166233	+	0.287923i
$707$			7.98133i			0.300169i
$708$		0			0
$709$	24.6318	−	14.2212i	0.925068	−	0.534088i	0.0398194	−	0.999207i	$-0.487322\pi$
$709$	24.6318	−	14.2212i	0.925068	−	0.534088i	0.885248	+	0.465119i	$0.153988\pi$
$710$		−	11.5973i		−	0.435239i
$711$		0			0
$712$	−0.143130	+	0.247908i	−0.00536402	+	0.00929075i
$713$	−24.0069	−	13.8604i	−0.899064	−	0.519075i
$714$		0			0
$715$	7.07012	−	8.54674i	0.264407	−	0.319630i
$716$	−0.351951			−0.0131530
$717$		0			0
$718$	11.0996	−	19.2250i	0.414233	−	0.717472i
$719$	−15.9484	−	27.6235i	−0.594776	−	1.03018i	−0.993578	−	0.113145i	$-0.963907\pi$
$719$	−15.9484	−	27.6235i	−0.594776	−	1.03018i	0.398802	−	0.917037i	$-0.369426\pi$
$720$		0			0
$721$	−20.6775	+	11.9381i	−0.770070	+	0.444600i
$722$	35.1714	−	20.3062i	1.30894	−	0.755720i
$723$		0			0
$724$	0.680394	+	1.17848i	0.0252867	+	0.0437978i
$725$	3.34120	−	5.78712i	0.124089	−	0.214928i
$726$		0			0
$727$	4.68029			0.173583			0.0867913	−	0.996227i	$-0.472339\pi$
$727$	4.68029			0.173583			0.0867913	+	0.996227i	$0.472339\pi$
$728$	11.0512	+	29.7134i	0.409583	+	1.10125i
$729$		0			0
$730$	10.8343	+	6.25519i	0.400996	+	0.231515i
$731$	−9.30972	+	16.1249i	−0.344332	+	0.596401i
$732$		0			0
$733$			14.1306i			0.521926i	0.965349	+	0.260963i	$0.0840401\pi$
$733$			14.1306i			0.521926i	−0.965349	+	0.260963i	$0.915960\pi$
$734$	10.8986	−	6.29233i	0.402276	−	0.232254i
$735$		0			0
$736$			34.2970i			1.26420i
$737$	−9.04232	−	15.6618i	−0.333078	−	0.576908i
$738$		0			0
$739$	−10.2955	−	5.94409i	−0.378725	−	0.218657i	0.298539	−	0.954398i	$-0.403501\pi$
$739$	−10.2955	−	5.94409i	−0.378725	−	0.218657i	−0.677263	+	0.735741i	$0.736834\pi$
$740$	6.04093			0.222069
$741$		0			0
$742$	−34.2970			−1.25908
$743$	−20.7932	−	12.0050i	−0.762830	−	0.440420i	0.0674812	−	0.997721i	$-0.478504\pi$
$743$	−20.7932	−	12.0050i	−0.762830	−	0.440420i	−0.830311	+	0.557301i	$0.811837\pi$
$744$		0			0
$745$	−3.41216	−	5.91003i	−0.125012	−	0.216527i
$746$			9.85473i			0.360807i
$747$		0			0
$748$	3.80385	−	2.19615i	0.139082	−	0.0802993i
$749$		−	18.1505i		−	0.663205i
$750$		0			0
$751$	7.93491	−	13.7437i	0.289549	−	0.501513i	−0.684153	−	0.729338i	$-0.739828\pi$
$751$	7.93491	−	13.7437i	0.289549	−	0.501513i	0.973702	+	0.227825i	$0.0731614\pi$
$752$	3.11352	+	1.79759i	0.113538	+	0.0655513i
$753$		0			0
$754$	25.4285	−	9.45750i	0.926052	−	0.344422i
$755$	−12.6810			−0.461510
$756$		0			0
$757$	−18.0819	+	31.3188i	−0.657198	+	1.13830i	0.324140	+	0.946009i	$0.394925\pi$
$757$	−18.0819	+	31.3188i	−0.657198	+	1.13830i	−0.981338	+	0.192291i	$0.938408\pi$
$758$	−10.5676	−	18.3036i	−0.383832	−	0.664817i
$759$		0			0
$760$	19.7704	−	11.4144i	0.717148	−	0.414046i
$761$	12.6597	−	7.30905i	0.458912	−	0.264953i	−0.252675	−	0.967551i	$-0.581310\pi$
$761$	12.6597	−	7.30905i	0.458912	−	0.264953i	0.711587	+	0.702598i	$0.247977\pi$
$762$		0			0
$763$	16.8621	+	29.2060i	0.610449	+	1.05733i
$764$	3.19128	−	5.52746i	0.115457	−	0.199977i
$765$		0			0
$766$	−6.84029			−0.247150
$767$	16.2821	−	6.05571i	0.587912	−	0.218659i
$768$		0			0
$769$	−15.8994	−	9.17950i	−0.573346	−	0.331021i	0.185139	−	0.982712i	$-0.440727\pi$
$769$	−15.8994	−	9.17950i	−0.573346	−	0.331021i	−0.758484	+	0.651691i	$0.774060\pi$
$770$	−4.95035	+	8.57425i	−0.178398	+	0.308995i
$771$		0			0
$772$		−	4.72412i		−	0.170025i
$773$	7.38753	−	4.26519i	0.265711	−	0.153408i	−0.361226	−	0.932478i	$-0.617642\pi$
$773$	7.38753	−	4.26519i	0.265711	−	0.153408i	0.626937	+	0.779070i	$0.284308\pi$
$774$		0			0
$775$			3.15276i			0.113250i
$776$	−7.37960	−	12.7818i	−0.264912	−	0.458841i
$777$		0			0
$778$	−9.42575	−	5.44196i	−0.337930	−	0.195104i
$779$	−24.6530			−0.883284
$780$		0			0
$781$	−31.6844			−1.13376
$782$	16.7227	+	9.65488i	0.598004	+	0.345258i
$783$		0			0
$784$	−1.16864	−	2.02414i	−0.0417371	−	0.0722909i
$785$			7.98333i			0.284937i
$786$		0			0
$787$	−2.96679	+	1.71288i	−0.105755	+	0.0610574i	−0.551944	−	0.833881i	$-0.686114\pi$
$787$	−2.96679	+	1.71288i	−0.105755	+	0.0610574i	0.446190	+	0.894938i	$0.352781\pi$
$788$			8.48668i			0.302326i
$789$		0			0
$790$	6.24770	−	10.8213i	0.222283	−	0.385006i
$791$	8.57425	+	4.95035i	0.304865	+	0.176014i
$792$		0			0
$793$	−7.87805	−	21.1818i	−0.279758	−	0.752189i
$794$	27.3982			0.972327
$795$		0			0
$796$	0.293326	−	0.508056i	0.0103967	−	0.0180076i
$797$	−14.0505	−	24.3361i	−0.497693	−	0.862030i	0.502303	−	0.864692i	$-0.332486\pi$
$797$	−14.0505	−	24.3361i	−0.497693	−	0.862030i	−0.999996	+	0.00266150i	$0.999153\pi$
$798$		0			0
$799$	−3.03622	+	1.75296i	−0.107414	+	0.0620153i
$800$	3.37810	−	1.95035i	0.119434	−	0.0689551i
$801$		0			0
$802$	5.00884	+	8.67556i	0.176868	+	0.306345i
$803$	17.0895	−	29.5999i	0.603076	−	1.04456i
$804$		0			0
$805$	25.1298			0.885710
$806$	−8.15884	+	9.86284i	−0.287383	+	0.347404i
$807$		0			0
$808$	7.43996	+	4.29546i	0.261737	+	0.151114i
$809$	18.0846	−	31.3235i	0.635822	−	1.10128i	−0.350518	−	0.936556i	$-0.613995\pi$
$809$	18.0846	−	31.3235i	0.635822	−	1.10128i	0.986340	−	0.164720i	$-0.0526721\pi$
$810$		0			0
$811$		−	13.9825i		−	0.490993i	−0.969397	−	0.245497i	$-0.921049\pi$
$811$		−	13.9825i		−	0.490993i	0.969397	−	0.245497i	$-0.0789510\pi$
$812$	12.1082	−	6.99066i	0.424914	−	0.245324i
$813$		0			0
$814$			28.5860i			1.00194i
$815$	−6.16109	−	10.6713i	−0.215814	−	0.373800i
$816$		0			0
$817$	61.3523	+	35.4218i	2.14645	+	1.23925i
$818$	31.8540			1.11375
$819$		0			0
$820$	−2.43201			−0.0849294
$821$	−3.67156	−	2.11977i	−0.128138	−	0.0739806i	0.434561	−	0.900643i	$-0.356904\pi$
$821$	−3.67156	−	2.11977i	−0.128138	−	0.0739806i	−0.562699	+	0.826662i	$0.690237\pi$
$822$		0			0
$823$	16.8201	+	29.1332i	0.586310	+	1.01552i	0.994711	+	0.102716i	$0.0327534\pi$
$823$	16.8201	+	29.1332i	0.586310	+	1.01552i	−0.408400	+	0.912803i	$0.633913\pi$
$824$			25.6999i			0.895299i
$825$		0			0
$826$	−13.4285	+	7.75296i	−0.467238	+	0.269760i
$827$			6.94609i			0.241539i	0.992681	+	0.120770i	$0.0385362\pi$
$827$			6.94609i			0.241539i	−0.992681	+	0.120770i	$0.961464\pi$
$828$		0			0
$829$	6.68271	−	11.5748i	0.232100	−	0.402009i	−0.726326	−	0.687351i	$-0.758774\pi$
$829$	6.68271	−	11.5748i	0.232100	−	0.402009i	0.958426	+	0.285341i	$0.0921069\pi$
$830$	6.80385	+	3.92820i	0.236165	+	0.136350i
$831$		0			0
$832$	29.8353	+	5.04550i	1.03435	+	0.174921i
$833$	2.27925			0.0789714
$834$		0			0
$835$	−10.9708	+	19.0020i	−0.379661	+	0.657591i
$836$	−8.35596	−	14.4729i	−0.288997	−	0.500557i
$837$		0			0
$838$	28.1774	−	16.2682i	0.973371	−	0.561976i
$839$	−17.3830	+	10.0361i	−0.600127	+	0.346483i	−0.769091	−	0.639139i	$-0.779291\pi$
$839$	−17.3830	+	10.0361i	−0.600127	+	0.346483i	0.168965	+	0.985622i	$0.445958\pi$
$840$		0			0
$841$	−7.82721	−	13.5571i	−0.269904	−	0.467487i
$842$	−6.76375	+	11.7152i	−0.233094	+	0.403731i
$843$		0			0
$844$	−6.07023			−0.208946
$845$	−4.27466	+	12.2771i	−0.147053	+	0.422345i
$846$		0			0
$847$	−3.80161	−	2.19486i	−0.130625	−	0.0754164i
$848$	−10.6569	+	18.4583i	−0.365959	+	0.633860i
$849$		0			0
$850$		−	2.19615i		−	0.0753274i
$851$	62.8359	−	36.2783i	2.15399	−	1.24360i
$852$		0			0
$853$		−	54.6353i		−	1.87068i	−0.353755	−	0.935338i	$-0.615095\pi$
$853$		−	54.6353i		−	1.87068i	0.353755	−	0.935338i	$-0.384905\pi$
$854$	10.0861	+	17.4696i	0.345138	+	0.597796i
$855$		0			0
$856$	−16.9194	−	9.76840i	−0.578292	−	0.333877i
$857$	−3.66436			−0.125172			−0.0625860	−	0.998040i	$-0.519935\pi$
$857$	−3.66436			−0.125172			−0.0625860	+	0.998040i	$0.519935\pi$
$858$		0			0
$859$	28.1460			0.960330			0.480165	−	0.877178i	$-0.340577\pi$
$859$	28.1460			0.960330			0.480165	+	0.877178i	$0.340577\pi$
$860$	6.05239	+	3.49435i	0.206385	+	0.119156i
$861$		0			0
$862$	−12.9623	−	22.4513i	−0.441497	−	0.764696i
$863$			50.4623i			1.71776i	0.512180	+	0.858878i	$0.328838\pi$
$863$			50.4623i			1.71776i	−0.512180	+	0.858878i	$0.671162\pi$
$864$		0			0
$865$	13.0342	−	7.52528i	0.443175	−	0.255867i
$866$		−	30.2671i		−	1.02852i
$867$		0			0
$868$	−3.29820	+	5.71264i	−0.111948	+	0.193900i
$869$	−29.5644	−	17.0690i	−1.00291	−	0.579028i
$870$		0			0
$871$	16.3317	+	13.5101i	0.553378	+	0.457771i
$872$	36.3000			1.22927
$873$		0			0
$874$	36.7351	−	63.6270i	1.24258	−	2.15221i
$875$	−1.42904	−	2.47517i	−0.0483104	−	0.0836761i
$876$		0			0
$877$	−20.0993	+	11.6043i	−0.678705	+	0.391851i	−0.799367	−	0.600843i	$-0.794832\pi$
$877$	−20.0993	+	11.6043i	−0.678705	+	0.391851i	0.120662	+	0.992694i	$0.461498\pi$
$878$	−30.8685	+	17.8220i	−1.04176	+	0.601462i
$879$		0			0
$880$	3.07638	+	5.32844i	0.103705	+	0.179622i
$881$	8.55758	−	14.8222i	0.288312	−	0.499371i	−0.685095	−	0.728454i	$-0.740239\pi$
$881$	8.55758	−	14.8222i	0.288312	−	0.499371i	0.973407	+	0.229083i	$0.0735726\pi$
$882$		0			0
$883$	21.3589			0.718783			0.359391	−	0.933187i	$-0.382984\pi$
$883$	21.3589			0.718783			0.359391	+	0.933187i	$0.382984\pi$
$884$	−3.28125	+	3.96655i	−0.110361	+	0.133410i
$885$		0			0
$886$	9.65355	+	5.57348i	0.324317	+	0.187245i
$887$	17.1600	−	29.7220i	0.576177	−	0.997968i	−0.419735	−	0.907646i	$-0.637877\pi$
$887$	17.1600	−	29.7220i	0.576177	−	0.997968i	0.995913	−	0.0903216i	$-0.0287895\pi$
$888$		0			0
$889$			42.7913i			1.43517i
$890$	0.0907407	−	0.0523892i	0.00304164	−	0.00175609i
$891$		0			0
$892$		−	9.34196i		−	0.312792i
$893$	6.66969	+	11.5522i	0.223193	+	0.386581i
$894$		0			0
$895$	0.416363	+	0.240387i	0.0139175	+	0.00803526i
$896$	−4.71191			−0.157414
$897$		0			0
$898$	16.8998			0.563953
$899$	18.2454	+	10.5340i	0.608518	+	0.351328i
$900$		0			0
$901$	−10.3923	−	18.0000i	−0.346218	−	0.599667i
$902$		−	11.5084i		−	0.383187i
$903$		0			0
$904$	9.22913	−	5.32844i	0.306956	−	0.177221i
$905$		−	1.85887i		−	0.0617910i
$906$		0			0
$907$	29.4542	−	51.0161i	0.978010	−	1.69396i	0.308387	−	0.951261i	$-0.400211\pi$
$907$	29.4542	−	51.0161i	0.978010	−	1.69396i	0.669623	−	0.742701i	$-0.266456\pi$
$908$	−10.8482	−	6.26319i	−0.360009	−	0.207851i
$909$		0			0
$910$	1.93486	−	11.4413i	0.0641398	−	0.379275i
$911$	55.5007			1.83882			0.919410	−	0.393299i	$-0.128666\pi$
$911$	55.5007			1.83882			0.919410	+	0.393299i	$0.128666\pi$
$912$		0			0
$913$	10.7321	−	18.5885i	0.355179	−	0.615188i
$914$	−7.33633	−	12.7069i	−0.242664	−	0.420307i
$915$		0			0
$916$	4.05739	−	2.34254i	0.134060	−	0.0773996i
$917$	26.1950	−	15.1237i	0.865034	−	0.499428i
$918$		0			0
$919$	−27.3656	−	47.3985i	−0.902707	−	1.56353i	−0.823967	−	0.566638i	$-0.808244\pi$
$919$	−27.3656	−	47.3985i	−0.902707	−	1.56353i	−0.0787401	−	0.996895i	$-0.525090\pi$
$920$	13.5246	−	23.4253i	0.445893	−	0.772309i
$921$		0			0
$922$	−32.3358			−1.06492
$923$	34.8052	−	12.9449i	1.14563	−	0.426087i
$924$		0			0
$925$	−7.14650	−	4.12603i	−0.234975	−	0.135663i
$926$	0.259162	−	0.448881i	0.00851658	−	0.0147511i
$927$		0			0
$928$		−	26.0660i		−	0.855657i
$929$	−14.8799	+	8.59092i	−0.488194	+	0.281859i	−0.723825	−	0.689984i	$-0.757618\pi$
$929$	−14.8799	+	8.59092i	−0.488194	+	0.281859i	0.235631	+	0.971843i	$0.424284\pi$
$930$		0			0
$931$		−	8.67213i		−	0.284218i
$932$	−0.245807	−	0.425750i	−0.00805167	−	0.0139459i
$933$		0			0
$934$	−33.2177	−	19.1782i	−1.08692	−	0.627531i
$935$	−6.00000			−0.196221
$936$		0			0
$937$	39.6401			1.29499			0.647493	−	0.762071i	$-0.275817\pi$
$937$	39.6401			1.29499			0.647493	+	0.762071i	$0.275817\pi$
$938$	−16.3842	−	9.45945i	−0.534965	−	0.308862i
$939$		0			0
$940$	0.657963	+	1.13963i	0.0214604	+	0.0371705i
$941$		−	33.3796i		−	1.08815i	−0.839038	−	0.544073i	$-0.816882\pi$
$941$		−	33.3796i		−	1.08815i	0.839038	−	0.544073i	$-0.183118\pi$
$942$		0			0
$943$	−25.2970	+	14.6052i	−0.823784	+	0.475612i
$944$			9.63611i			0.313629i
$945$		0			0
$946$	−16.5354	+	28.6402i	−0.537613	+	0.931174i
$947$	17.8054	+	10.2800i	0.578599	+	0.334054i	0.760576	−	0.649249i	$-0.224916\pi$
$947$	17.8054	+	10.2800i	0.578599	+	0.334054i	−0.181978	+	0.983303i	$0.558250\pi$
$948$		0			0
$949$	−6.67948	+	39.4974i	−0.216825	+	1.28214i
$950$	−8.35596			−0.271103
$951$		0			0
$952$	8.57425	−	14.8510i	0.277893	−	0.481325i
$953$	27.4376	+	47.5234i	0.888792	+	1.53943i	0.841305	+	0.540561i	$0.181788\pi$
$953$	27.4376	+	47.5234i	0.888792	+	1.53943i	0.0474871	+	0.998872i	$0.484879\pi$
$954$		0			0
$955$	−7.55066	+	4.35937i	−0.244333	+	0.141066i
$956$	−4.52013	+	2.60970i	−0.146191	+	0.0844036i
$957$		0			0
$958$	−17.4147	−	30.1632i	−0.562644	−	0.974528i
$959$	−12.4420	+	21.5502i	−0.401773	+	0.695892i
$960$		0			0
$961$	21.0601			0.679359
$962$	−11.6790	−	31.4016i	−0.376547	−	1.01243i
$963$		0			0
$964$	17.0782	+	9.86009i	0.550051	+	0.317572i
$965$	−3.22663	+	5.58869i	−0.103869	+	0.179906i
$966$		0			0
$967$			10.9215i			0.351211i	0.984461	+	0.175605i	$0.0561883\pi$
$967$			10.9215i			0.351211i	−0.984461	+	0.175605i	$0.943812\pi$
$968$	−4.09197	+	2.36250i	−0.131521	+	0.0759337i
$969$		0			0
$970$			5.40224i			0.173456i
$971$	15.7356	+	27.2548i	0.504978	+	0.874648i	0.999983	+	0.00575765i	$0.00183273\pi$
$971$	15.7356	+	27.2548i	0.504978	+	0.874648i	−0.495005	+	0.868890i	$0.664834\pi$
$972$		0			0
$973$	28.8528	+	16.6582i	0.924979	+	0.534037i
$974$	18.6223			0.596698
$975$		0			0
$976$	12.5359			0.401264
$977$	27.3260	+	15.7767i	0.874235	+	0.504740i	0.868753	−	0.495245i	$-0.164922\pi$
$977$	27.3260	+	15.7767i	0.874235	+	0.504740i	0.00548205	+	0.999985i	$0.498255\pi$
$978$		0			0
$979$	−0.143130	−	0.247908i	−0.00457445	−	0.00792318i
$980$		−	0.855504i		−	0.0273281i
$981$		0			0
$982$	−18.2186	+	10.5185i	−0.581378	+	0.335659i
$983$			43.6214i			1.39131i	0.718377	+	0.695654i	$0.244885\pi$
$983$			43.6214i			1.39131i	−0.718377	+	0.695654i	$0.755115\pi$
$984$		0			0
$985$	5.79651	−	10.0399i	0.184692	−	0.319896i
$986$	−12.7094	−	7.33778i	−0.404750	−	0.233683i
$987$		0			0
$988$	15.0920	+	12.4846i	0.480141	+	0.397187i
$989$	83.9401			2.66914
$990$		0			0
$991$	−8.99740	+	15.5840i	−0.285812	+	0.495041i	−0.972806	−	0.231623i	$-0.925597\pi$
$991$	−8.99740	+	15.5840i	−0.285812	+	0.495041i	0.686994	+	0.726663i	$0.258930\pi$
$992$	6.14896	+	10.6503i	0.195230	+	0.338148i
$993$		0			0
$994$	−28.7053	+	16.5730i	−0.910477	+	0.525664i
$995$	−0.694017	+	0.400691i	−0.0220018	+	0.0127028i
$996$		0			0
$997$	12.1045	+	20.9657i	0.383355	+	0.663990i	0.991539	−	0.129806i	$-0.0414353\pi$
$997$	12.1045	+	20.9657i	0.383355	+	0.663990i	−0.608185	+	0.793796i	$0.708102\pi$
$998$	−6.19128	+	10.7236i	−0.195982	+	0.339450i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bu.d.316.3		8
3.2	odd	2		195.2.bb.b.121.2	✓	8
13.6	odd	12		7605.2.a.ci.1.2		4
13.7	odd	12		7605.2.a.ch.1.3		4
13.10	even	6	inner	585.2.bu.d.361.3		8
15.2	even	4		975.2.w.i.199.3		8
15.8	even	4		975.2.w.h.199.2		8
15.14	odd	2		975.2.bc.j.901.3		8
39.20	even	12		2535.2.a.bk.1.2		4
39.23	odd	6		195.2.bb.b.166.2	yes	8
39.32	even	12		2535.2.a.bj.1.3		4
195.23	even	12		975.2.w.i.49.3		8
195.62	even	12		975.2.w.h.49.2		8
195.179	odd	6		975.2.bc.j.751.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bb.b.121.2	✓	8	3.2	odd	2
195.2.bb.b.166.2	yes	8	39.23	odd	6
585.2.bu.d.316.3		8	1.1	even	1	trivial
585.2.bu.d.361.3		8	13.10	even	6	inner
975.2.w.h.49.2		8	195.62	even	12
975.2.w.h.199.2		8	15.8	even	4
975.2.w.i.49.3		8	195.23	even	12
975.2.w.i.199.3		8	15.2	even	4
975.2.bc.j.751.3		8	195.179	odd	6
975.2.bc.j.901.3		8	15.14	odd	2
2535.2.a.bj.1.3		4	39.32	even	12
2535.2.a.bk.1.2		4	39.20	even	12
7605.2.a.ch.1.3		4	13.7	odd	12
7605.2.a.ci.1.2		4	13.6	odd	12

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.bu (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.975173 + 0.563016i) q^{2} +(-0.366025 - 0.633975i) q^{4} +1.00000i q^{5} +(2.47517 - 1.42904i) q^{7} -3.07638i q^{8} +O(q^{10})\)	\(q+(0.975173 + 0.563016i) q^{2} +(-0.366025 - 0.633975i) q^{4} +1.00000i q^{5} +(2.47517 - 1.42904i) q^{7} -3.07638i q^{8} +(-0.563016 + 0.975173i) q^{10} +(2.66422 + 1.53819i) q^{11} +(-3.55507 - 0.601205i) q^{13} +3.21829 q^{14} +(1.00000 - 1.73205i) q^{16} +(0.975173 + 1.68905i) q^{17} +(6.42652 - 3.71035i) q^{19} +(0.633975 - 0.366025i) q^{20} +(1.73205 + 3.00000i) q^{22} +(4.39627 - 7.61457i) q^{23} -1.00000 q^{25} +(-3.12832 - 2.58784i) q^{26} +(-1.81195 - 1.04613i) q^{28} +(-3.34120 + 5.78712i) q^{29} -3.15276i q^{31} +(-3.37810 + 1.95035i) q^{32} +2.19615i q^{34} +(1.42904 + 2.47517i) q^{35} +(7.14650 + 4.12603i) q^{37} +8.35596 q^{38} +3.07638 q^{40} +(-2.87710 - 1.66109i) q^{41} +(4.77337 + 8.26772i) q^{43} -2.25207i q^{44} +(8.57425 - 4.95035i) q^{46} +1.79759i q^{47} +(0.584320 - 1.01207i) q^{49} +(-0.975173 - 0.563016i) q^{50} +(0.920099 + 2.47388i) q^{52} -10.6569 q^{53} +(-1.53819 + 2.66422i) q^{55} +(-4.39627 - 7.61457i) q^{56} +(-6.51649 + 3.76230i) q^{58} +(-4.17256 + 2.40903i) q^{59} +(3.13397 + 5.42820i) q^{61} +(1.77505 - 3.07448i) q^{62} -8.39230 q^{64} +(0.601205 - 3.55507i) q^{65} +(-5.09097 - 2.93927i) q^{67} +(0.713876 - 1.23647i) q^{68} +3.21829i q^{70} +(-8.91942 + 5.14963i) q^{71} -11.1101i q^{73} +(4.64605 + 8.04719i) q^{74} +(-4.70454 - 2.71617i) q^{76} +8.79254 q^{77} -11.0968 q^{79} +(1.73205 + 1.00000i) q^{80} +(-1.87044 - 3.23970i) q^{82} -6.97707i q^{83} +(-1.68905 + 0.975173i) q^{85} +10.7499i q^{86} +(4.73205 - 8.19615i) q^{88} +(-0.0805845 - 0.0465255i) q^{89} +(-9.65857 + 3.59226i) q^{91} -6.43659 q^{92} +(-1.01207 + 1.75296i) q^{94} +(3.71035 + 6.42652i) q^{95} +(4.15483 - 2.39879i) q^{97} +(1.13963 - 0.657963i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 12 q^{7}+O(q^{10}) \) 8 * q + 4 * q^4 + 12 * q^7	\( 8 q + 4 q^{4} + 12 q^{7} - 8 q^{13} + 24 q^{14} + 8 q^{16} - 12 q^{19} + 12 q^{20} - 8 q^{25} + 24 q^{26} + 12 q^{28} - 12 q^{29} - 36 q^{41} + 16 q^{43} - 4 q^{49} + 20 q^{52} - 36 q^{58} - 36 q^{59} + 32 q^{61} + 16 q^{64} - 12 q^{65} - 48 q^{67} - 36 q^{71} + 24 q^{74} - 48 q^{76} - 16 q^{79} - 12 q^{82} + 24 q^{88} - 36 q^{89} - 48 q^{92} + 12 q^{94} + 12 q^{95} + 72 q^{98}+O(q^{100}) \) 8 * q + 4 * q^4 + 12 * q^7 - 8 * q^13 + 24 * q^14 + 8 * q^16 - 12 * q^19 + 12 * q^20 - 8 * q^25 + 24 * q^26 + 12 * q^28 - 12 * q^29 - 36 * q^41 + 16 * q^43 - 4 * q^49 + 20 * q^52 - 36 * q^58 - 36 * q^59 + 32 * q^61 + 16 * q^64 - 12 * q^65 - 48 * q^67 - 36 * q^71 + 24 * q^74 - 48 * q^76 - 16 * q^79 - 12 * q^82 + 24 * q^88 - 36 * q^89 - 48 * q^92 + 12 * q^94 + 12 * q^95 + 72 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more