LMFDB - Embedded newform 585.2.bu.a.316.1

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
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			316.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	585.316
Dual form			585.2.bu.a.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.633975 + 0.366025i) q^{2} +(-0.732051 - 1.26795i) q^{4} +1.00000i q^{5} +(-3.86603 + 2.23205i) q^{7} -2.53590i q^{8} +(-0.366025 + 0.633975i) q^{10} +(3.00000 + 1.73205i) q^{11} +(0.866025 + 3.50000i) q^{13} -3.26795 q^{14} +(-0.535898 + 0.928203i) q^{16} +(3.36603 + 5.83013i) q^{17} +(-4.73205 + 2.73205i) q^{19} +(1.26795 - 0.732051i) q^{20} +(1.26795 + 2.19615i) q^{22} +(0.267949 - 0.464102i) q^{23} -1.00000 q^{25} +(-0.732051 + 2.53590i) q^{26} +(5.66025 + 3.26795i) q^{28} +(-1.36603 + 2.36603i) q^{29} -3.19615i q^{31} +(-5.07180 + 2.92820i) q^{32} +4.92820i q^{34} +(-2.23205 - 3.86603i) q^{35} +(3.46410 + 2.00000i) q^{37} -4.00000 q^{38} +2.53590 q^{40} +(-4.56218 - 2.63397i) q^{41} +(-0.133975 - 0.232051i) q^{43} -5.07180i q^{44} +(0.339746 - 0.196152i) q^{46} -0.196152i q^{47} +(6.46410 - 11.1962i) q^{49} +(-0.633975 - 0.366025i) q^{50} +(3.80385 - 3.66025i) q^{52} +6.92820 q^{53} +(-1.73205 + 3.00000i) q^{55} +(5.66025 + 9.80385i) q^{56} +(-1.73205 + 1.00000i) q^{58} +(-6.29423 + 3.63397i) q^{59} +(-2.23205 - 3.86603i) q^{61} +(1.16987 - 2.02628i) q^{62} -2.14359 q^{64} +(-3.50000 + 0.866025i) q^{65} +(-10.7942 - 6.23205i) q^{67} +(4.92820 - 8.53590i) q^{68} -3.26795i q^{70} +(11.0263 - 6.36603i) q^{71} +15.3923i q^{73} +(1.46410 + 2.53590i) q^{74} +(6.92820 + 4.00000i) q^{76} -15.4641 q^{77} +1.92820 q^{79} +(-0.928203 - 0.535898i) q^{80} +(-1.92820 - 3.33975i) q^{82} +2.53590i q^{83} +(-5.83013 + 3.36603i) q^{85} -0.196152i q^{86} +(4.39230 - 7.60770i) q^{88} +(1.09808 + 0.633975i) q^{89} +(-11.1603 - 11.5981i) q^{91} -0.784610 q^{92} +(0.0717968 - 0.124356i) q^{94} +(-2.73205 - 4.73205i) q^{95} +(-14.2583 + 8.23205i) q^{97} +(8.19615 - 4.73205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{2} + 4 q^{4} - 12 q^{7} + 2 q^{10} + 12 q^{11} - 20 q^{14} - 16 q^{16} + 10 q^{17} - 12 q^{19} + 12 q^{20} + 12 q^{22} + 8 q^{23} - 4 q^{25} + 4 q^{26} - 12 q^{28} - 2 q^{29} - 48 q^{32} - 2 q^{35}+ \cdots + 12 q^{98}+O(q^{100}) $ 4 * q + 6 * q^2 + 4 * q^4 - 12 * q^7 + 2 * q^10 + 12 * q^11 - 20 * q^14 - 16 * q^16 + 10 * q^17 - 12 * q^19 + 12 * q^20 + 12 * q^22 + 8 * q^23 - 4 * q^25 + 4 * q^26 - 12 * q^28 - 2 * q^29 - 48 * q^32 - 2 * q^35 - 16 * q^38 + 24 * q^40 + 6 * q^41 - 4 * q^43 + 36 * q^46 + 12 * q^49 - 6 * q^50 + 36 * q^52 - 12 * q^56 + 6 * q^59 - 2 * q^61 + 22 * q^62 - 64 * q^64 - 14 * q^65 - 12 * q^67 - 8 * q^68 + 6 * q^71 - 8 * q^74 - 48 * q^77 - 20 * q^79 + 24 * q^80 + 20 * q^82 - 6 * q^85 - 24 * q^88 - 6 * q^89 - 10 * q^91 + 80 * q^92 + 28 * q^94 - 4 * q^95 - 12 * q^97 + 12 * q^98

Character values

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

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

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 $

$2$	0.633975	+	0.366025i	0.448288	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$2$	0.633975	+	0.366025i	0.448288	+	0.258819i	−0.258819	+	0.965926i	$0.583333\pi$
$3$		0			0
$3$		0			0
$4$	−0.732051	−	1.26795i	−0.366025	−	0.633975i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$	−3.86603	+	2.23205i	−1.46122	+	0.843636i	−0.999068	−	0.0431647i	$-0.986256\pi$
$7$	−3.86603	+	2.23205i	−1.46122	+	0.843636i	−0.462152	+	0.886801i	$0.652923\pi$
$8$		−	2.53590i		−	0.896575i
$9$		0			0
$10$	−0.366025	+	0.633975i	−0.115747	+	0.200480i
$11$	3.00000	+	1.73205i	0.904534	+	0.522233i	0.878668	−	0.477432i	$-0.158432\pi$
$11$	3.00000	+	1.73205i	0.904534	+	0.522233i	0.0258656	+	0.999665i	$0.491766\pi$
$12$		0			0
$13$	0.866025	+	3.50000i	0.240192	+	0.970725i
$13$	0.866025	+	3.50000i	0.240192	+	0.970725i
$14$	−3.26795			−0.873396
$15$		0			0
$16$	−0.535898	+	0.928203i	−0.133975	+	0.232051i
$17$	3.36603	+	5.83013i	0.816381	+	1.41401i	0.908332	+	0.418250i	$0.137356\pi$
$17$	3.36603	+	5.83013i	0.816381	+	1.41401i	−0.0919509	+	0.995764i	$0.529310\pi$
$18$		0			0
$19$	−4.73205	+	2.73205i	−1.08561	+	0.626775i	−0.932403	−	0.361419i	$-0.882292\pi$
$19$	−4.73205	+	2.73205i	−1.08561	+	0.626775i	−0.153203	+	0.988195i	$0.548959\pi$
$20$	1.26795	−	0.732051i	0.283522	−	0.163692i
$21$		0			0
$22$	1.26795	+	2.19615i	0.270328	+	0.468221i
$23$	0.267949	−	0.464102i	0.0558713	−	0.0967719i	−0.836737	−	0.547605i	$-0.815540\pi$
$23$	0.267949	−	0.464102i	0.0558713	−	0.0967719i	0.892608	+	0.450833i	$0.148873\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−0.732051	+	2.53590i	−0.143567	+	0.497331i
$27$		0			0
$28$	5.66025	+	3.26795i	1.06969	+	0.617584i
$29$	−1.36603	+	2.36603i	−0.253665	+	0.439360i	−0.964532	−	0.263966i	$-0.914969\pi$
$29$	−1.36603	+	2.36603i	−0.253665	+	0.439360i	0.710867	+	0.703326i	$0.248303\pi$
$30$		0			0
$31$		−	3.19615i		−	0.574046i	−0.957924	−	0.287023i	$-0.907334\pi$
$31$		−	3.19615i		−	0.574046i	0.957924	−	0.287023i	$-0.0926656\pi$
$32$	−5.07180	+	2.92820i	−0.896575	+	0.517638i
$33$		0			0
$34$			4.92820i			0.845180i
$35$	−2.23205	−	3.86603i	−0.377285	−	0.653478i
$36$		0			0
$37$	3.46410	+	2.00000i	0.569495	+	0.328798i	0.756948	−	0.653476i	$-0.226690\pi$
$37$	3.46410	+	2.00000i	0.569495	+	0.328798i	−0.187453	+	0.982274i	$0.560023\pi$
$38$	−4.00000			−0.648886
$39$		0			0
$40$	2.53590			0.400961
$41$	−4.56218	−	2.63397i	−0.712492	−	0.411358i	0.0994908	−	0.995038i	$-0.468279\pi$
$41$	−4.56218	−	2.63397i	−0.712492	−	0.411358i	−0.811983	+	0.583681i	$0.801612\pi$
$42$		0			0
$43$	−0.133975	−	0.232051i	−0.0204309	−	0.0353874i	0.855629	−	0.517589i	$-0.173170\pi$
$43$	−0.133975	−	0.232051i	−0.0204309	−	0.0353874i	−0.876060	+	0.482202i	$0.839837\pi$
$44$		−	5.07180i		−	0.764602i
$45$		0			0
$46$	0.339746	−	0.196152i	0.0500928	−	0.0289211i
$47$		−	0.196152i		−	0.0286118i	−0.999898	−	0.0143059i	$-0.995446\pi$
$47$		−	0.196152i		−	0.0286118i	0.999898	−	0.0143059i	$-0.00455386\pi$
$48$		0			0
$49$	6.46410	−	11.1962i	0.923443	−	1.59945i
$50$	−0.633975	−	0.366025i	−0.0896575	−	0.0517638i
$51$		0			0
$52$	3.80385	−	3.66025i	0.527499	−	0.507586i
$53$	6.92820			0.951662			0.475831	−	0.879537i	$-0.342147\pi$
$53$	6.92820			0.951662			0.475831	+	0.879537i	$0.342147\pi$
$54$		0			0
$55$	−1.73205	+	3.00000i	−0.233550	+	0.404520i
$56$	5.66025	+	9.80385i	0.756383	+	1.31009i
$57$		0			0
$58$	−1.73205	+	1.00000i	−0.227429	+	0.131306i
$59$	−6.29423	+	3.63397i	−0.819439	+	0.473103i	−0.850223	−	0.526423i	$-0.823533\pi$
$59$	−6.29423	+	3.63397i	−0.819439	+	0.473103i	0.0307841	+	0.999526i	$0.490200\pi$
$60$		0			0
$61$	−2.23205	−	3.86603i	−0.285785	−	0.494994i	0.687014	−	0.726644i	$-0.258921\pi$
$61$	−2.23205	−	3.86603i	−0.285785	−	0.494994i	−0.972799	+	0.231650i	$0.925588\pi$
$62$	1.16987	−	2.02628i	0.148574	−	0.257338i
$63$		0			0
$64$	−2.14359			−0.267949
$65$	−3.50000	+	0.866025i	−0.434122	+	0.107417i
$66$		0			0
$67$	−10.7942	−	6.23205i	−1.31872	−	0.761366i	−0.335201	−	0.942146i	$-0.608804\pi$
$67$	−10.7942	−	6.23205i	−1.31872	−	0.761366i	−0.983524	+	0.180780i	$0.942138\pi$
$68$	4.92820	−	8.53590i	0.597632	−	1.03513i
$69$		0			0
$70$		−	3.26795i		−	0.390595i
$71$	11.0263	−	6.36603i	1.30858	−	0.755508i	0.326720	−	0.945121i	$-0.394057\pi$
$71$	11.0263	−	6.36603i	1.30858	−	0.755508i	0.981859	+	0.189613i	$0.0607234\pi$
$72$		0			0
$73$			15.3923i			1.80153i	0.434304	+	0.900767i	$0.356994\pi$
$73$			15.3923i			1.80153i	−0.434304	+	0.900767i	$0.643006\pi$
$74$	1.46410	+	2.53590i	0.170198	+	0.294792i
$75$		0			0
$76$	6.92820	+	4.00000i	0.794719	+	0.458831i
$77$	−15.4641			−1.76230
$78$		0			0
$79$	1.92820			0.216940			0.108470	−	0.994100i	$-0.465405\pi$
$79$	1.92820			0.216940			0.108470	+	0.994100i	$0.465405\pi$
$80$	−0.928203	−	0.535898i	−0.103776	−	0.0599153i
$81$		0			0
$82$	−1.92820	−	3.33975i	−0.212934	−	0.368813i
$83$			2.53590i			0.278351i	0.990268	+	0.139176i	$0.0444452\pi$
$83$			2.53590i			0.278351i	−0.990268	+	0.139176i	$0.955555\pi$
$84$		0			0
$85$	−5.83013	+	3.36603i	−0.632366	+	0.365097i
$86$		−	0.196152i		−	0.0211517i
$87$		0			0
$88$	4.39230	−	7.60770i	0.468221	−	0.810983i
$89$	1.09808	+	0.633975i	0.116396	+	0.0672012i	0.557068	−	0.830467i	$-0.311926\pi$
$89$	1.09808	+	0.633975i	0.116396	+	0.0672012i	−0.440672	+	0.897668i	$0.645260\pi$
$90$		0			0
$91$	−11.1603	−	11.5981i	−1.16991	−	1.21581i
$92$	−0.784610			−0.0818012
$93$		0			0
$94$	0.0717968	−	0.124356i	0.00740527	−	0.0128263i
$95$	−2.73205	−	4.73205i	−0.280302	−	0.485498i
$96$		0			0
$97$	−14.2583	+	8.23205i	−1.44771	+	0.835838i	−0.998345	−	0.0575081i	$-0.981685\pi$
$97$	−14.2583	+	8.23205i	−1.44771	+	0.835838i	−0.449369	+	0.893346i	$0.648351\pi$
$98$	8.19615	−	4.73205i	0.827936	−	0.478009i
$99$		0			0
$100$	0.732051	+	1.26795i	0.0732051	+	0.126795i
$101$	2.46410	−	4.26795i	0.245187	−	0.424677i	−0.716997	−	0.697076i	$-0.754484\pi$
$101$	2.46410	−	4.26795i	0.245187	−	0.424677i	0.962184	+	0.272399i	$0.0878172\pi$
$102$		0			0
$103$	3.19615			0.314926			0.157463	−	0.987525i	$-0.449668\pi$
$103$	3.19615			0.314926			0.157463	+	0.987525i	$0.449668\pi$
$104$	8.87564	−	2.19615i	0.870329	−	0.215350i
$105$		0			0
$106$	4.39230	+	2.53590i	0.426618	+	0.246308i
$107$	8.56218	−	14.8301i	0.827737	−	1.43368i	−0.0720725	−	0.997399i	$-0.522961\pi$
$107$	8.56218	−	14.8301i	0.827737	−	1.43368i	0.899809	−	0.436283i	$-0.143705\pi$
$108$		0			0
$109$		−	8.26795i		−	0.791926i	−0.918266	−	0.395963i	$-0.870411\pi$
$109$		−	8.26795i		−	0.791926i	0.918266	−	0.395963i	$-0.129589\pi$
$110$	−2.19615	+	1.26795i	−0.209395	+	0.120894i
$111$		0			0
$112$		−	4.78461i		−	0.452103i
$113$	9.73205	+	16.8564i	0.915514	+	1.58572i	0.806147	+	0.591716i	$0.201549\pi$
$113$	9.73205	+	16.8564i	0.915514	+	1.58572i	0.109368	+	0.994001i	$0.465117\pi$
$114$		0			0
$115$	0.464102	+	0.267949i	0.0432777	+	0.0249864i
$116$	4.00000			0.371391
$117$		0			0
$118$	−5.32051			−0.489792
$119$	−26.0263	−	15.0263i	−2.38583	−	1.37746i
$120$		0			0
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$		−	3.26795i		−	0.295866i
$123$		0			0
$124$	−4.05256	+	2.33975i	−0.363931	+	0.210115i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	7.33013	−	12.6962i	0.650444	−	1.12660i	−0.332572	−	0.943078i	$-0.607916\pi$
$127$	7.33013	−	12.6962i	0.650444	−	1.12660i	0.983015	−	0.183523i	$-0.0587503\pi$
$128$	8.78461	+	5.07180i	0.776457	+	0.448288i
$129$		0			0
$130$	−2.53590	−	0.732051i	−0.222413	−	0.0642051i
$131$	−1.26795			−0.110781			−0.0553906	−	0.998465i	$-0.517640\pi$
$131$	−1.26795			−0.110781			−0.0553906	+	0.998465i	$0.517640\pi$
$132$		0			0
$133$	12.1962	−	21.1244i	1.05754	−	1.83171i
$134$	−4.56218	−	7.90192i	−0.394112	−	0.682622i
$135$		0			0
$136$	14.7846	−	8.53590i	1.26777	−	0.731947i
$137$	7.90192	−	4.56218i	0.675107	−	0.389773i	−0.122902	−	0.992419i	$-0.539220\pi$
$137$	7.90192	−	4.56218i	0.675107	−	0.389773i	0.798009	+	0.602646i	$0.205887\pi$
$138$		0			0
$139$	8.96410	+	15.5263i	0.760325	+	1.31692i	0.942683	+	0.333690i	$0.108294\pi$
$139$	8.96410	+	15.5263i	0.760325	+	1.31692i	−0.182358	+	0.983232i	$0.558373\pi$
$140$	−3.26795	+	5.66025i	−0.276192	+	0.478379i
$141$		0			0
$142$	9.32051			0.782160
$143$	−3.46410	+	12.0000i	−0.289683	+	1.00349i
$144$		0			0
$145$	−2.36603	−	1.36603i	−0.196488	−	0.113442i
$146$	−5.63397	+	9.75833i	−0.466271	+	0.807605i
$147$		0			0
$148$		−	5.85641i		−	0.481394i
$149$	3.46410	−	2.00000i	0.283790	−	0.163846i	−0.351348	−	0.936245i	$-0.614277\pi$
$149$	3.46410	−	2.00000i	0.283790	−	0.163846i	0.635138	+	0.772399i	$0.280943\pi$
$150$		0			0
$151$			17.8564i			1.45313i	0.687096	+	0.726567i	$0.258885\pi$
$151$			17.8564i			1.45313i	−0.687096	+	0.726567i	$0.741115\pi$
$152$	6.92820	+	12.0000i	0.561951	+	0.973329i
$153$		0			0
$154$	−9.80385	−	5.66025i	−0.790017	−	0.456116i
$155$	3.19615			0.256721
$156$		0			0
$157$	9.73205			0.776702			0.388351	−	0.921511i	$-0.373045\pi$
$157$	9.73205			0.776702			0.388351	+	0.921511i	$0.373045\pi$
$158$	1.22243	+	0.705771i	0.0972515	+	0.0561482i
$159$		0			0
$160$	−2.92820	−	5.07180i	−0.231495	−	0.400961i
$161$			2.39230i			0.188540i
$162$		0			0
$163$	4.79423	−	2.76795i	0.375513	−	0.216803i	−0.300351	−	0.953829i	$-0.597104\pi$
$163$	4.79423	−	2.76795i	0.375513	−	0.216803i	0.675864	+	0.737026i	$0.263771\pi$
$164$			7.71281i			0.602270i
$165$		0			0
$166$	−0.928203	+	1.60770i	−0.0720425	+	0.124781i
$167$	15.1244	+	8.73205i	1.17036	+	0.675706i	0.953764	−	0.300556i	$-0.0971721\pi$
$167$	15.1244	+	8.73205i	1.17036	+	0.675706i	0.216593	+	0.976262i	$0.430505\pi$
$168$		0			0
$169$	−11.5000	+	6.06218i	−0.884615	+	0.466321i
$170$	−4.92820			−0.377976
$171$		0			0
$172$	−0.196152	+	0.339746i	−0.0149565	+	0.0259054i
$173$	−1.63397	−	2.83013i	−0.124229	−	0.215171i	0.797202	−	0.603712i	$-0.206312\pi$
$173$	−1.63397	−	2.83013i	−0.124229	−	0.215171i	−0.921431	+	0.388542i	$0.872979\pi$
$174$		0			0
$175$	3.86603	−	2.23205i	0.292244	−	0.168727i
$176$	−3.21539	+	1.85641i	−0.242369	+	0.139932i
$177$		0			0
$178$	0.464102	+	0.803848i	0.0347859	+	0.0602509i
$179$	−4.56218	+	7.90192i	−0.340993	+	0.590618i	−0.984617	−	0.174724i	$-0.944097\pi$
$179$	−4.56218	+	7.90192i	−0.340993	+	0.590618i	0.643624	+	0.765342i	$0.277430\pi$
$180$		0			0
$181$	14.5359			1.08044			0.540222	−	0.841522i	$-0.318340\pi$
$181$	14.5359			1.08044			0.540222	+	0.841522i	$0.318340\pi$
$182$	−2.83013	−	11.4378i	−0.209783	−	0.847828i
$183$		0			0
$184$	−1.17691	−	0.679492i	−0.0867633	−	0.0500928i
$185$	−2.00000	+	3.46410i	−0.147043	+	0.254686i
$186$		0			0
$187$			23.3205i			1.70536i
$188$	−0.248711	+	0.143594i	−0.0181391	+	0.0104726i
$189$		0			0
$190$		−	4.00000i		−	0.290191i
$191$	−13.7583	−	23.8301i	−0.995518	−	1.72429i	−0.579662	−	0.814857i	$-0.696816\pi$
$191$	−13.7583	−	23.8301i	−0.995518	−	1.72429i	−0.415855	−	0.909431i	$-0.636518\pi$
$192$		0			0
$193$	5.25833	+	3.03590i	0.378503	+	0.218529i	0.677167	−	0.735830i	$-0.263208\pi$
$193$	5.25833	+	3.03590i	0.378503	+	0.218529i	−0.298664	+	0.954358i	$0.596541\pi$
$194$	−12.0526			−0.865323
$195$		0			0
$196$	−18.9282			−1.35201
$197$	2.53590	+	1.46410i	0.180675	+	0.104313i	0.587610	−	0.809144i	$-0.300069\pi$
$197$	2.53590	+	1.46410i	0.180675	+	0.104313i	−0.406935	+	0.913457i	$0.633402\pi$
$198$		0			0
$199$	−7.50000	−	12.9904i	−0.531661	−	0.920864i	−0.999317	−	0.0369532i	$-0.988235\pi$
$199$	−7.50000	−	12.9904i	−0.531661	−	0.920864i	0.467656	−	0.883911i	$-0.345099\pi$
$200$			2.53590i			0.179315i
$201$		0			0
$202$	3.12436	−	1.80385i	0.219829	−	0.126918i
$203$		−	12.1962i		−	0.856002i
$204$		0			0
$205$	2.63397	−	4.56218i	0.183965	−	0.318636i
$206$	2.02628	+	1.16987i	0.141178	+	0.0815089i
$207$		0			0
$208$	−3.71281	−	1.07180i	−0.257437	−	0.0743157i
$209$	−18.9282			−1.30929
$210$		0			0
$211$	−5.76795	+	9.99038i	−0.397082	+	0.687766i	−0.993365	−	0.115008i	$-0.963310\pi$
$211$	−5.76795	+	9.99038i	−0.397082	+	0.687766i	0.596283	+	0.802775i	$0.296644\pi$
$212$	−5.07180	−	8.78461i	−0.348332	−	0.603329i
$213$		0			0
$214$	10.8564	−	6.26795i	0.742129	−	0.428468i
$215$	0.232051	−	0.133975i	0.0158257	−	0.00913699i
$216$		0			0
$217$	7.13397	+	12.3564i	0.484286	+	0.838808i
$218$	3.02628	−	5.24167i	0.204966	−	0.355011i
$219$		0			0
$220$	5.07180			0.341940
$221$	−17.4904	+	16.8301i	−1.17653	+	1.13212i
$222$		0			0
$223$	−10.2679	−	5.92820i	−0.687593	−	0.396982i	0.115117	−	0.993352i	$-0.463276\pi$
$223$	−10.2679	−	5.92820i	−0.687593	−	0.396982i	−0.802710	+	0.596370i	$0.796609\pi$
$224$	13.0718	−	22.6410i	0.873396	−	1.51277i
$225$		0			0
$226$			14.2487i			0.947810i
$227$	−10.0981	+	5.83013i	−0.670233	+	0.386959i	−0.796165	−	0.605080i	$-0.793141\pi$
$227$	−10.0981	+	5.83013i	−0.670233	+	0.386959i	0.125932	+	0.992039i	$0.459808\pi$
$228$		0			0
$229$		−	18.3923i		−	1.21540i	−0.794168	−	0.607699i	$-0.792093\pi$
$229$		−	18.3923i		−	1.21540i	0.794168	−	0.607699i	$-0.207907\pi$
$230$	0.196152	+	0.339746i	0.0129339	+	0.0224022i
$231$		0			0
$232$	6.00000	+	3.46410i	0.393919	+	0.227429i
$233$	23.8564			1.56289			0.781443	−	0.623977i	$-0.214484\pi$
$233$	23.8564			1.56289			0.781443	+	0.623977i	$0.214484\pi$
$234$		0			0
$235$	0.196152			0.0127956
$236$	9.21539	+	5.32051i	0.599871	+	0.346336i
$237$		0			0
$238$	−11.0000	−	19.0526i	−0.713024	−	1.23499i
$239$			5.46410i			0.353443i	0.984261	+	0.176722i	$0.0565492\pi$
$239$			5.46410i			0.353443i	−0.984261	+	0.176722i	$0.943451\pi$
$240$		0			0
$241$	1.39230	−	0.803848i	0.0896862	−	0.0517804i	−0.454486	−	0.890754i	$-0.650177\pi$
$241$	1.39230	−	0.803848i	0.0896862	−	0.0517804i	0.544172	+	0.838973i	$0.316844\pi$
$242$			0.732051i			0.0470580i
$243$		0			0
$244$	−3.26795	+	5.66025i	−0.209209	+	0.362361i
$245$	11.1962	+	6.46410i	0.715296	+	0.412976i
$246$		0			0
$247$	−13.6603	−	14.1962i	−0.869181	−	0.903280i
$248$	−8.10512			−0.514675
$249$		0			0
$250$	0.366025	−	0.633975i	0.0231495	−	0.0400961i
$251$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$251$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$252$		0			0
$253$	1.60770	−	0.928203i	0.101075	−	0.0583556i
$254$	9.29423	−	5.36603i	0.583172	−	0.336694i
$255$		0			0
$256$	5.85641	+	10.1436i	0.366025	+	0.633975i
$257$	−5.36603	+	9.29423i	−0.334723	+	0.579758i	−0.983432	−	0.181279i	$-0.941976\pi$
$257$	−5.36603	+	9.29423i	−0.334723	+	0.579758i	0.648708	+	0.761037i	$0.275310\pi$
$258$		0			0
$259$	−17.8564			−1.10954
$260$	3.66025	+	3.80385i	0.226999	+	0.235905i
$261$		0			0
$262$	−0.803848	−	0.464102i	−0.0496619	−	0.0286723i
$263$	−3.16987	+	5.49038i	−0.195463	+	0.338551i	−0.947052	−	0.321080i	$-0.895954\pi$
$263$	−3.16987	+	5.49038i	−0.195463	+	0.338551i	0.751589	+	0.659631i	$0.229288\pi$
$264$		0			0
$265$			6.92820i			0.425596i
$266$	15.4641	−	8.92820i	0.948165	−	0.547423i
$267$		0			0
$268$			18.2487i			1.11472i
$269$	7.83013	+	13.5622i	0.477411	+	0.826901i	0.999665	−	0.0258897i	$-0.00824187\pi$
$269$	7.83013	+	13.5622i	0.477411	+	0.826901i	−0.522254	+	0.852790i	$0.674909\pi$
$270$		0			0
$271$	−3.23205	−	1.86603i	−0.196333	−	0.113353i	0.398611	−	0.917120i	$-0.369492\pi$
$271$	−3.23205	−	1.86603i	−0.196333	−	0.113353i	−0.594944	+	0.803767i	$0.702826\pi$
$272$	−7.21539			−0.437497
$273$		0			0
$274$	6.67949			0.403523
$275$	−3.00000	−	1.73205i	−0.180907	−	0.104447i
$276$		0			0
$277$	10.1244	+	17.5359i	0.608314	+	1.05363i	0.991518	+	0.129967i	$0.0414870\pi$
$277$	10.1244	+	17.5359i	0.608314	+	1.05363i	−0.383205	+	0.923663i	$0.625180\pi$
$278$			13.1244i			0.787147i
$279$		0			0
$280$	−9.80385	+	5.66025i	−0.585892	+	0.338265i
$281$		−	21.1244i		−	1.26017i	−0.776525	−	0.630087i	$-0.783019\pi$
$281$		−	21.1244i		−	1.26017i	0.776525	−	0.630087i	$-0.216981\pi$
$282$		0			0
$283$	−0.133975	+	0.232051i	−0.00796396	+	0.0137940i	−0.869980	−	0.493087i	$-0.835868\pi$
$283$	−0.133975	+	0.232051i	−0.00796396	+	0.0137940i	0.862016	+	0.506881i	$0.169202\pi$
$284$	−16.1436	−	9.32051i	−0.957946	−	0.553070i
$285$		0			0
$286$	−6.58846	+	6.33975i	−0.389584	+	0.374877i
$287$	23.5167			1.38814
$288$		0			0
$289$	−14.1603	+	24.5263i	−0.832956	+	1.44272i
$290$	−1.00000	−	1.73205i	−0.0587220	−	0.101710i
$291$		0			0
$292$	19.5167	−	11.2679i	1.14213	−	0.659407i
$293$	−21.2942	+	12.2942i	−1.24402	+	0.718237i	−0.969911	−	0.243461i	$-0.921717\pi$
$293$	−21.2942	+	12.2942i	−1.24402	+	0.718237i	−0.274112	+	0.961698i	$0.588384\pi$
$294$		0			0
$295$	−3.63397	−	6.29423i	−0.211578	−	0.366464i
$296$	5.07180	−	8.78461i	0.294792	−	0.510595i
$297$		0			0
$298$	2.92820			0.169626
$299$	1.85641	+	0.535898i	0.107359	+	0.0309918i
$300$		0			0
$301$	1.03590	+	0.598076i	0.0597082	+	0.0344725i
$302$	−6.53590	+	11.3205i	−0.376099	+	0.651422i
$303$		0			0
$304$		−	5.85641i		−	0.335888i
$305$	3.86603	−	2.23205i	0.221368	−	0.127807i
$306$		0			0
$307$			12.0718i			0.688974i	0.938791	+	0.344487i	$0.111947\pi$
$307$			12.0718i			0.688974i	−0.938791	+	0.344487i	$0.888053\pi$
$308$	11.3205	+	19.6077i	0.645046	+	1.11725i
$309$		0			0
$310$	2.02628	+	1.16987i	0.115085	+	0.0664443i
$311$	10.1962			0.578171			0.289085	−	0.957303i	$-0.406649\pi$
$311$	10.1962			0.578171			0.289085	+	0.957303i	$0.406649\pi$
$312$		0			0
$313$	−10.8038			−0.610670			−0.305335	−	0.952245i	$-0.598768\pi$
$313$	−10.8038			−0.610670			−0.305335	+	0.952245i	$0.598768\pi$
$314$	6.16987	+	3.56218i	0.348186	+	0.201025i
$315$		0			0
$316$	−1.41154	−	2.44486i	−0.0794055	−	0.137534i
$317$		−	17.4641i		−	0.980882i	−0.871474	−	0.490441i	$-0.836836\pi$
$317$		−	17.4641i		−	0.980882i	0.871474	−	0.490441i	$-0.163164\pi$
$318$		0			0
$319$	−8.19615	+	4.73205i	−0.458896	+	0.264944i
$320$		−	2.14359i		−	0.119831i
$321$		0			0
$322$	−0.875644	+	1.51666i	−0.0487978	+	0.0845202i
$323$	−31.8564	−	18.3923i	−1.77254	−	1.02338i
$324$		0			0
$325$	−0.866025	−	3.50000i	−0.0480384	−	0.194145i
$326$	4.05256			0.224450
$327$		0			0
$328$	−6.67949	+	11.5692i	−0.368813	+	0.638803i
$329$	0.437822	+	0.758330i	0.0241379	+	0.0418081i
$330$		0			0
$331$	7.03590	−	4.06218i	0.386728	−	0.223277i	−0.294013	−	0.955801i	$-0.594991\pi$
$331$	7.03590	−	4.06218i	0.386728	−	0.223277i	0.680741	+	0.732524i	$0.261658\pi$
$332$	3.21539	−	1.85641i	0.176467	−	0.101884i
$333$		0			0
$334$	6.39230	+	11.0718i	0.349771	+	0.605822i
$335$	6.23205	−	10.7942i	0.340493	−	0.589752i
$336$		0			0
$337$	−31.0526			−1.69154			−0.845770	−	0.533547i	$-0.820859\pi$
$337$	−31.0526			−1.69154			−0.845770	+	0.533547i	$0.820859\pi$
$338$	−9.50962	−	0.366025i	−0.517255	−	0.0199092i
$339$		0			0
$340$	8.53590	+	4.92820i	0.462924	+	0.267269i
$341$	5.53590	−	9.58846i	0.299786	−	0.519244i
$342$		0			0
$343$			26.4641i			1.42893i
$344$	−0.588457	+	0.339746i	−0.0317275	+	0.0183179i
$345$		0			0
$346$		−	2.39230i		−	0.128611i
$347$	3.26795	+	5.66025i	0.175433	+	0.303858i	0.940311	−	0.340317i	$-0.110534\pi$
$347$	3.26795	+	5.66025i	0.175433	+	0.303858i	−0.764878	+	0.644175i	$0.777201\pi$
$348$		0			0
$349$	25.9641	+	14.9904i	1.38983	+	0.802417i	0.993295	−	0.115605i	$-0.0368805\pi$
$349$	25.9641	+	14.9904i	1.38983	+	0.802417i	0.396531	+	0.918021i	$0.370214\pi$
$350$	3.26795			0.174679
$351$		0			0
$352$	−20.2872			−1.08131
$353$	31.9808	+	18.4641i	1.70216	+	0.982745i	0.943565	+	0.331187i	$0.107449\pi$
$353$	31.9808	+	18.4641i	1.70216	+	0.982745i	0.758599	+	0.651558i	$0.225884\pi$
$354$		0			0
$355$	6.36603	+	11.0263i	0.337874	+	0.585214i
$356$		−	1.85641i		−	0.0983893i
$357$		0			0
$358$	−5.78461	+	3.33975i	−0.305726	+	0.176511i
$359$			33.6603i			1.77652i	0.459341	+	0.888260i	$0.348086\pi$
$359$			33.6603i			1.77652i	−0.459341	+	0.888260i	$0.651914\pi$
$360$		0			0
$361$	5.42820	−	9.40192i	0.285695	−	0.494838i
$362$	9.21539	+	5.32051i	0.484350	+	0.279640i
$363$		0			0
$364$	−6.53590	+	22.6410i	−0.342574	+	1.18671i
$365$	−15.3923			−0.805670
$366$		0			0
$367$	9.06218	−	15.6962i	0.473042	−	0.819332i	−0.526482	−	0.850186i	$-0.676489\pi$
$367$	9.06218	−	15.6962i	0.473042	−	0.819332i	0.999524	+	0.0308537i	$0.00982261\pi$
$368$	0.287187	+	0.497423i	0.0149707	+	0.0259299i
$369$		0			0
$370$	−2.53590	+	1.46410i	−0.131835	+	0.0761150i
$371$	−26.7846	+	15.4641i	−1.39059	+	0.802856i
$372$		0			0
$373$	0.937822	+	1.62436i	0.0485586	+	0.0841059i	0.889283	−	0.457357i	$-0.151204\pi$
$373$	0.937822	+	1.62436i	0.0485586	+	0.0841059i	−0.840724	+	0.541463i	$0.817871\pi$
$374$	−8.53590	+	14.7846i	−0.441381	+	0.764494i
$375$		0			0
$376$	−0.497423			−0.0256526
$377$	−9.46410	−	2.73205i	−0.487426	−	0.140708i
$378$		0			0
$379$	−17.0885	−	9.86603i	−0.877775	−	0.506784i	−0.00785092	−	0.999969i	$-0.502499\pi$
$379$	−17.0885	−	9.86603i	−0.877775	−	0.506784i	−0.869924	+	0.493185i	$0.835832\pi$
$380$	−4.00000	+	6.92820i	−0.205196	+	0.355409i
$381$		0			0
$382$		−	20.1436i		−	1.03064i
$383$	−7.22243	+	4.16987i	−0.369049	+	0.213071i	−0.673043	−	0.739603i	$-0.735013\pi$
$383$	−7.22243	+	4.16987i	−0.369049	+	0.213071i	0.303994	+	0.952674i	$0.401680\pi$
$384$		0			0
$385$		−	15.4641i		−	0.788124i
$386$	2.22243	+	3.84936i	0.113119	+	0.195928i
$387$		0			0
$388$	20.8756	+	12.0526i	1.05980	+	0.611876i
$389$	17.4641			0.885465			0.442733	−	0.896654i	$-0.354009\pi$
$389$	17.4641			0.885465			0.442733	+	0.896654i	$0.354009\pi$
$390$		0			0
$391$	3.60770			0.182449
$392$	−28.3923	−	16.3923i	−1.43403	−	0.827936i
$393$		0			0
$394$	1.07180	+	1.85641i	0.0539963	+	0.0935244i
$395$			1.92820i			0.0970184i
$396$		0			0
$397$	21.0622	−	12.1603i	1.05708	−	0.610306i	0.132457	−	0.991189i	$-0.457713\pi$
$397$	21.0622	−	12.1603i	1.05708	−	0.610306i	0.924623	+	0.380883i	$0.124380\pi$
$398$		−	10.9808i		−	0.550416i
$399$		0			0
$400$	0.535898	−	0.928203i	0.0267949	−	0.0464102i
$401$	13.2679	+	7.66025i	0.662570	+	0.382535i	0.793255	−	0.608889i	$-0.208385\pi$
$401$	13.2679	+	7.66025i	0.662570	+	0.382535i	−0.130686	+	0.991424i	$0.541718\pi$
$402$		0			0
$403$	11.1865	−	2.76795i	0.557241	−	0.137881i
$404$	−7.21539			−0.358979
$405$		0			0
$406$	4.46410	−	7.73205i	0.221550	−	0.383735i
$407$	6.92820	+	12.0000i	0.343418	+	0.594818i
$408$		0			0
$409$	2.30385	−	1.33013i	0.113918	−	0.0657705i	−0.441958	−	0.897036i	$-0.645716\pi$
$409$	2.30385	−	1.33013i	0.113918	−	0.0657705i	0.555876	+	0.831265i	$0.312383\pi$
$410$	3.33975	−	1.92820i	0.164938	−	0.0952272i
$411$		0			0
$412$	−2.33975	−	4.05256i	−0.115271	−	0.199655i
$413$	16.2224	−	28.0981i	0.798254	−	1.38262i
$414$		0			0
$415$	−2.53590			−0.124482
$416$	−14.6410	−	15.2154i	−0.717835	−	0.745996i
$417$		0			0
$418$	−12.0000	−	6.92820i	−0.586939	−	0.338869i
$419$	10.2224	−	17.7058i	0.499398	−	0.864984i	−0.500601	−	0.865678i	$-0.666888\pi$
$419$	10.2224	−	17.7058i	0.499398	−	0.864984i	1.00000		0.000694440i	$0.000221047\pi$
$420$		0			0
$421$		−	23.5885i		−	1.14963i	−0.818283	−	0.574816i	$-0.805074\pi$
$421$		−	23.5885i		−	1.14963i	0.818283	−	0.574816i	$-0.194926\pi$
$422$	−7.31347	+	4.22243i	−0.356014	+	0.205545i
$423$		0			0
$424$		−	17.5692i		−	0.853237i
$425$	−3.36603	−	5.83013i	−0.163276	−	0.282803i
$426$		0			0
$427$	17.2583	+	9.96410i	0.835189	+	0.482197i
$428$	−25.0718			−1.21189
$429$		0			0
$430$	0.196152			0.00945931
$431$	20.1962	+	11.6603i	0.972814	+	0.561655i	0.900093	−	0.435698i	$-0.143498\pi$
$431$	20.1962	+	11.6603i	0.972814	+	0.561655i	0.0727213	+	0.997352i	$0.476832\pi$
$432$		0			0
$433$	2.40192	+	4.16025i	0.115429	+	0.199929i	0.917951	−	0.396693i	$-0.129842\pi$
$433$	2.40192	+	4.16025i	0.115429	+	0.199929i	−0.802522	+	0.596622i	$0.796509\pi$
$434$			10.4449i			0.501370i
$435$		0			0
$436$	−10.4833	+	6.05256i	−0.502061	+	0.289865i
$437$			2.92820i			0.140075i
$438$		0			0
$439$	7.69615	−	13.3301i	0.367317	−	0.636212i	−0.621828	−	0.783154i	$-0.713610\pi$
$439$	7.69615	−	13.3301i	0.367317	−	0.636212i	0.989145	+	0.146942i	$0.0469430\pi$
$440$	7.60770	+	4.39230i	0.362683	+	0.209395i
$441$		0			0
$442$	−17.2487	+	4.26795i	−0.820438	+	0.203006i
$443$	−3.12436			−0.148443			−0.0742213	−	0.997242i	$-0.523647\pi$
$443$	−3.12436			−0.148443			−0.0742213	+	0.997242i	$0.523647\pi$
$444$		0			0
$445$	−0.633975	+	1.09808i	−0.0300533	+	0.0520538i
$446$	−4.33975	−	7.51666i	−0.205493	−	0.355924i
$447$		0			0
$448$	8.28719	−	4.78461i	0.391533	−	0.226052i
$449$	−9.58846	+	5.53590i	−0.452507	+	0.261255i	−0.708889	−	0.705321i	$-0.750803\pi$
$449$	−9.58846	+	5.53590i	−0.452507	+	0.261255i	0.256381	+	0.966576i	$0.417470\pi$
$450$		0			0
$451$	−9.12436	−	15.8038i	−0.429649	−	0.744174i
$452$	14.2487	−	24.6795i	0.670203	−	1.16083i
$453$		0			0
$454$	−8.53590			−0.400610
$455$	11.5981	−	11.1603i	0.543726	−	0.523201i
$456$		0			0
$457$	−4.66987	−	2.69615i	−0.218447	−	0.126121i	0.386784	−	0.922170i	$-0.373586\pi$
$457$	−4.66987	−	2.69615i	−0.218447	−	0.126121i	−0.605231	+	0.796050i	$0.706919\pi$
$458$	6.73205	−	11.6603i	0.314568	−	0.544848i
$459$		0			0
$460$		−	0.784610i		−	0.0365826i
$461$	−9.97372	+	5.75833i	−0.464522	+	0.268192i	−0.713944	−	0.700203i	$-0.753093\pi$
$461$	−9.97372	+	5.75833i	−0.464522	+	0.268192i	0.249421	+	0.968395i	$0.419760\pi$
$462$		0			0
$463$		−	1.78461i		−	0.0829378i	−0.999140	−	0.0414689i	$-0.986796\pi$
$463$		−	1.78461i		−	0.0829378i	0.999140	−	0.0414689i	$-0.0132038\pi$
$464$	−1.46410	−	2.53590i	−0.0679692	−	0.117726i
$465$		0			0
$466$	15.1244	+	8.73205i	0.700622	+	0.404504i
$467$	−23.6603			−1.09487			−0.547433	−	0.836850i	$-0.684395\pi$
$467$	−23.6603			−1.09487			−0.547433	+	0.836850i	$0.684395\pi$
$468$		0			0
$469$	55.6410			2.56926
$470$	0.124356	+	0.0717968i	0.00573610	+	0.00331174i
$471$		0			0
$472$	9.21539	+	15.9615i	0.424173	+	0.734689i
$473$		−	0.928203i		−	0.0426788i
$474$		0			0
$475$	4.73205	−	2.73205i	0.217121	−	0.125355i
$476$			44.0000i			2.01674i
$477$		0			0
$478$	−2.00000	+	3.46410i	−0.0914779	+	0.158444i
$479$	31.0981	+	17.9545i	1.42091	+	0.820361i	0.996376	−	0.0850522i	$-0.0271057\pi$
$479$	31.0981	+	17.9545i	1.42091	+	0.820361i	0.424531	+	0.905413i	$0.360439\pi$
$480$		0			0
$481$	−4.00000	+	13.8564i	−0.182384	+	0.631798i
$482$	1.17691			0.0536070
$483$		0			0
$484$	0.732051	−	1.26795i	0.0332750	−	0.0576341i
$485$	−8.23205	−	14.2583i	−0.373798	−	0.647437i
$486$		0			0
$487$	18.0000	−	10.3923i	0.815658	−	0.470920i	−0.0332590	−	0.999447i	$-0.510589\pi$
$487$	18.0000	−	10.3923i	0.815658	−	0.470920i	0.848917	+	0.528526i	$0.177255\pi$
$488$	−9.80385	+	5.66025i	−0.443799	+	0.256228i
$489$		0			0
$490$	4.73205	+	8.19615i	0.213772	+	0.370264i
$491$	−3.56218	+	6.16987i	−0.160759	+	0.278442i	−0.935141	−	0.354276i	$-0.884727\pi$
$491$	−3.56218	+	6.16987i	−0.160759	+	0.278442i	0.774382	+	0.632718i	$0.218061\pi$
$492$		0			0
$493$	−18.3923			−0.828348
$494$	−3.46410	−	14.0000i	−0.155857	−	0.629890i
$495$		0			0
$496$	2.96668	+	1.71281i	0.133208	+	0.0769076i
$497$	−28.4186	+	49.2224i	−1.27475	+	2.20793i
$498$		0			0
$499$		−	0.392305i		−	0.0175620i	−0.999961	−	0.00878099i	$-0.997205\pi$
$499$		−	0.392305i		−	0.0175620i	0.999961	−	0.00878099i	$-0.00279511\pi$
$500$	−1.26795	+	0.732051i	−0.0567044	+	0.0327383i
$501$		0			0
$502$		0			0
$503$	−15.3923	−	26.6603i	−0.686309	−	1.18872i	−0.973024	−	0.230706i	$-0.925896\pi$
$503$	−15.3923	−	26.6603i	−0.686309	−	1.18872i	0.286715	−	0.958016i	$-0.407437\pi$
$504$		0			0
$505$	4.26795	+	2.46410i	0.189921	+	0.109651i
$506$	1.35898			0.0604142
$507$		0			0
$508$	−21.4641			−0.952316
$509$	−11.1962	−	6.46410i	−0.496261	−	0.286516i	0.230907	−	0.972976i	$-0.425831\pi$
$509$	−11.1962	−	6.46410i	−0.496261	−	0.286516i	−0.727168	+	0.686459i	$0.759164\pi$
$510$		0			0
$511$	−34.3564	−	59.5070i	−1.51984	−	2.63244i
$512$		−	11.7128i		−	0.517638i
$513$		0			0
$514$	−6.80385	+	3.92820i	−0.300105	+	0.173266i
$515$			3.19615i			0.140839i
$516$		0			0
$517$	0.339746	−	0.588457i	0.0149420	−	0.0258803i
$518$	−11.3205	−	6.53590i	−0.497395	−	0.287171i
$519$		0			0
$520$	2.19615	+	8.87564i	0.0963077	+	0.389223i
$521$	12.7321			0.557801			0.278901	−	0.960320i	$-0.410030\pi$
$521$	12.7321			0.557801			0.278901	+	0.960320i	$0.410030\pi$
$522$		0			0
$523$	18.7321	−	32.4449i	0.819095	−	1.41871i	−0.0872541	−	0.996186i	$-0.527809\pi$
$523$	18.7321	−	32.4449i	0.819095	−	1.41871i	0.906350	−	0.422529i	$-0.138857\pi$
$524$	0.928203	+	1.60770i	0.0405487	+	0.0702325i
$525$		0			0
$526$	−4.01924	+	2.32051i	−0.175247	+	0.101179i
$527$	18.6340	−	10.7583i	0.811709	−	0.468640i
$528$		0			0
$529$	11.3564	+	19.6699i	0.493757	+	0.855212i
$530$	−2.53590	+	4.39230i	−0.110152	+	0.190790i
$531$		0			0
$532$	−35.7128			−1.54835
$533$	5.26795	−	18.2487i	0.228180	−	0.790439i
$534$		0			0
$535$	14.8301	+	8.56218i	0.641162	+	0.370175i
$536$	−15.8038	+	27.3731i	−0.682622	+	1.18234i
$537$		0			0
$538$			11.4641i			0.494253i
$539$	38.7846	−	22.3923i	1.67057	−	0.964505i
$540$		0			0
$541$			17.5885i			0.756187i	0.925767	+	0.378093i	$0.123420\pi$
$541$			17.5885i			0.756187i	−0.925767	+	0.378093i	$0.876580\pi$
$542$	−1.36603	−	2.36603i	−0.0586758	−	0.101629i
$543$		0			0
$544$	−34.1436	−	19.7128i	−1.46389	−	0.845180i
$545$	8.26795			0.354160
$546$		0			0
$547$	−24.6603			−1.05440			−0.527198	−	0.849742i	$-0.676757\pi$
$547$	−24.6603			−1.05440			−0.527198	+	0.849742i	$0.676757\pi$
$548$	−11.5692	−	6.67949i	−0.494213	−	0.285334i
$549$		0			0
$550$	−1.26795	−	2.19615i	−0.0540655	−	0.0936443i
$551$		−	14.9282i		−	0.635963i
$552$		0			0
$553$	−7.45448	+	4.30385i	−0.316997	+	0.183018i
$554$			14.8231i			0.629773i
$555$		0			0
$556$	13.1244	−	22.7321i	0.556597	−	0.964054i
$557$	18.5885	+	10.7321i	0.787618	+	0.454732i	0.839123	−	0.543941i	$-0.183069\pi$
$557$	18.5885	+	10.7321i	0.787618	+	0.454732i	−0.0515052	+	0.998673i	$0.516402\pi$
$558$		0			0
$559$	0.696152	−	0.669873i	0.0294441	−	0.0283326i
$560$	4.78461			0.202187
$561$		0			0
$562$	7.73205	−	13.3923i	0.326157	−	0.564920i
$563$	1.73205	+	3.00000i	0.0729972	+	0.126435i	0.900214	−	0.435449i	$-0.143410\pi$
$563$	1.73205	+	3.00000i	0.0729972	+	0.126435i	−0.827216	+	0.561884i	$0.810077\pi$
$564$		0			0
$565$	−16.8564	+	9.73205i	−0.709154	+	0.409430i
$566$	−0.169873	+	0.0980762i	−0.00714029	+	0.00412245i
$567$		0			0
$568$	−16.1436	−	27.9615i	−0.677370	−	1.17324i
$569$	22.0981	−	38.2750i	0.926400	−	1.60457i	0.137105	−	0.990557i	$-0.456220\pi$
$569$	22.0981	−	38.2750i	0.926400	−	1.60457i	0.789295	−	0.614015i	$-0.210446\pi$
$570$		0			0
$571$	3.85641			0.161386			0.0806928	−	0.996739i	$-0.474287\pi$
$571$	3.85641			0.161386			0.0806928	+	0.996739i	$0.474287\pi$
$572$	17.7513	−	4.39230i	0.742219	−	0.183651i
$573$		0			0
$574$	14.9090	+	8.60770i	0.622288	+	0.359278i
$575$	−0.267949	+	0.464102i	−0.0111743	+	0.0193544i
$576$		0			0
$577$			11.7128i			0.487611i	0.969824	+	0.243805i	$0.0783958\pi$
$577$			11.7128i			0.487611i	−0.969824	+	0.243805i	$0.921604\pi$
$578$	−17.9545	+	10.3660i	−0.746808	+	0.431170i
$579$		0			0
$580$			4.00000i			0.166091i
$581$	−5.66025	−	9.80385i	−0.234827	−	0.406732i
$582$		0			0
$583$	20.7846	+	12.0000i	0.860811	+	0.496989i
$584$	39.0333			1.61521
$585$		0			0
$586$	−18.0000			−0.743573
$587$	22.2224	+	12.8301i	0.917218	+	0.529556i	0.882746	−	0.469850i	$-0.155692\pi$
$587$	22.2224	+	12.8301i	0.917218	+	0.529556i	0.0344715	+	0.999406i	$0.489025\pi$
$588$		0			0
$589$	8.73205	+	15.1244i	0.359798	+	0.623188i
$590$		−	5.32051i		−	0.219042i
$591$		0			0
$592$	−3.71281	+	2.14359i	−0.152596	+	0.0881012i
$593$		−	21.3205i		−	0.875528i	−0.899090	−	0.437764i	$-0.855770\pi$
$593$		−	21.3205i		−	0.875528i	0.899090	−	0.437764i	$-0.144230\pi$
$594$		0			0
$595$	15.0263	−	26.0263i	0.616017	−	1.06697i
$596$	−5.07180	−	2.92820i	−0.207749	−	0.119944i
$597$		0			0
$598$	0.980762	+	1.01924i	0.0401063	+	0.0416797i
$599$	23.1244			0.944836			0.472418	−	0.881375i	$-0.343381\pi$
$599$	23.1244			0.944836			0.472418	+	0.881375i	$0.343381\pi$
$600$		0			0
$601$	11.1244	−	19.2679i	0.453772	−	0.785956i	−0.544845	−	0.838537i	$-0.683411\pi$
$601$	11.1244	−	19.2679i	0.453772	−	0.785956i	0.998617	+	0.0525809i	$0.0167447\pi$
$602$	0.437822	+	0.758330i	0.0178443	+	0.0309072i
$603$		0			0
$604$	22.6410	−	13.0718i	0.921250	−	0.531884i
$605$	−0.866025	+	0.500000i	−0.0352089	+	0.0203279i
$606$		0			0
$607$	−8.80385	−	15.2487i	−0.357337	−	0.618926i	0.630178	−	0.776451i	$-0.282982\pi$
$607$	−8.80385	−	15.2487i	−0.357337	−	0.618926i	−0.987515	+	0.157525i	$0.949649\pi$
$608$	16.0000	−	27.7128i	0.648886	−	1.12390i
$609$		0			0
$610$	3.26795			0.132315
$611$	0.686533	−	0.169873i	0.0277742	−	0.00687233i
$612$		0			0
$613$	−1.91858	−	1.10770i	−0.0774909	−	0.0447394i	0.460754	−	0.887528i	$-0.347579\pi$
$613$	−1.91858	−	1.10770i	−0.0774909	−	0.0447394i	−0.538245	+	0.842789i	$0.680912\pi$
$614$	−4.41858	+	7.65321i	−0.178320	+	0.308859i
$615$		0			0
$616$			39.2154i			1.58003i
$617$	21.3397	−	12.3205i	0.859106	−	0.496005i	−0.00460693	−	0.999989i	$-0.501466\pi$
$617$	21.3397	−	12.3205i	0.859106	−	0.496005i	0.863713	+	0.503984i	$0.168133\pi$
$618$		0			0
$619$		−	11.5885i		−	0.465779i	−0.972503	−	0.232890i	$-0.925182\pi$
$619$		−	11.5885i		−	0.465779i	0.972503	−	0.232890i	$-0.0748181\pi$
$620$	−2.33975	−	4.05256i	−0.0939665	−	0.162755i
$621$		0			0
$622$	6.46410	+	3.73205i	0.259187	+	0.149642i
$623$	−5.66025			−0.226773
$624$		0			0
$625$	1.00000			0.0400000
$626$	−6.84936	−	3.95448i	−0.273756	−	0.158053i
$627$		0			0
$628$	−7.12436	−	12.3397i	−0.284293	−	0.492409i
$629$			26.9282i			1.07370i
$630$		0			0
$631$	−9.01666	+	5.20577i	−0.358948	+	0.207238i	−0.668619	−	0.743605i	$-0.733114\pi$
$631$	−9.01666	+	5.20577i	−0.358948	+	0.207238i	0.309671	+	0.950844i	$0.399781\pi$
$632$		−	4.88973i		−	0.194503i
$633$		0			0
$634$	6.39230	−	11.0718i	0.253871	−	0.439717i
$635$	12.6962	+	7.33013i	0.503831	+	0.290887i
$636$		0			0
$637$	44.7846	+	12.9282i	1.77443	+	0.512234i
$638$	−6.92820			−0.274290
$639$		0			0
$640$	−5.07180	+	8.78461i	−0.200480	+	0.347242i
$641$	−19.3923	−	33.5885i	−0.765950	−	1.32666i	−0.939743	−	0.341882i	$-0.888936\pi$
$641$	−19.3923	−	33.5885i	−0.765950	−	1.32666i	0.173793	−	0.984782i	$-0.444398\pi$
$642$		0			0
$643$	−3.27757	+	1.89230i	−0.129255	+	0.0746252i	−0.563233	−	0.826298i	$-0.690443\pi$
$643$	−3.27757	+	1.89230i	−0.129255	+	0.0746252i	0.433978	+	0.900923i	$0.357109\pi$
$644$	3.03332	−	1.75129i	0.119530	−	0.0690104i
$645$		0			0
$646$	−13.4641	−	23.3205i	−0.529738	−	0.917533i
$647$	−1.00000	+	1.73205i	−0.0393141	+	0.0680939i	−0.885013	−	0.465566i	$-0.845851\pi$
$647$	−1.00000	+	1.73205i	−0.0393141	+	0.0680939i	0.845699	+	0.533660i	$0.179184\pi$
$648$		0			0
$649$	−25.1769			−0.988280
$650$	0.732051	−	2.53590i	0.0287134	−	0.0994661i
$651$		0			0
$652$	−7.01924	−	4.05256i	−0.274895	−	0.158710i
$653$	−0.241670	+	0.418584i	−0.00945727	+	0.0163805i	−0.870715	−	0.491787i	$-0.836344\pi$
$653$	−0.241670	+	0.418584i	−0.00945727	+	0.0163805i	0.861258	+	0.508168i	$0.169677\pi$
$654$		0			0
$655$		−	1.26795i		−	0.0495429i
$656$	4.88973	−	2.82309i	0.190912	−	0.110223i
$657$		0			0
$658$			0.641016i			0.0249894i
$659$	−18.5885	−	32.1962i	−0.724103	−	1.25418i	−0.959342	−	0.282246i	$-0.908920\pi$
$659$	−18.5885	−	32.1962i	−0.724103	−	1.25418i	0.235238	−	0.971938i	$-0.424413\pi$
$660$		0			0
$661$	18.2321	+	10.5263i	0.709145	+	0.409425i	0.810744	−	0.585401i	$-0.199063\pi$
$661$	18.2321	+	10.5263i	0.709145	+	0.409425i	−0.101600	+	0.994825i	$0.532396\pi$
$662$	5.94744			0.231154
$663$		0			0
$664$	6.43078			0.249563
$665$	21.1244	+	12.1962i	0.819167	+	0.472947i
$666$		0			0
$667$	0.732051	+	1.26795i	0.0283451	+	0.0490952i
$668$		−	25.5692i		−	0.989303i
$669$		0			0
$670$	7.90192	−	4.56218i	0.305278	−	0.176252i
$671$		−	15.4641i		−	0.596985i
$672$		0			0
$673$	−9.33013	+	16.1603i	−0.359650	+	0.622932i	−0.987902	−	0.155078i	$-0.950437\pi$
$673$	−9.33013	+	16.1603i	−0.359650	+	0.622932i	0.628252	+	0.778010i	$0.283771\pi$
$674$	−19.6865	−	11.3660i	−0.758297	−	0.437803i
$675$		0			0
$676$	16.1051	+	10.1436i	0.619428	+	0.390138i
$677$	−32.7846			−1.26001			−0.630007	−	0.776589i	$-0.716948\pi$
$677$	−32.7846			−1.26001			−0.630007	+	0.776589i	$0.716948\pi$
$678$		0			0
$679$	36.7487	−	63.6506i	1.41029	−	2.44269i
$680$	8.53590	+	14.7846i	0.327337	+	0.566964i
$681$		0			0
$682$	7.01924	−	4.05256i	0.268781	−	0.155180i
$683$	−35.7391	+	20.6340i	−1.36752	+	0.789537i	−0.990611	−	0.136714i	$-0.956346\pi$
$683$	−35.7391	+	20.6340i	−1.36752	+	0.789537i	−0.376908	+	0.926251i	$0.623013\pi$
$684$		0			0
$685$	4.56218	+	7.90192i	0.174312	+	0.301917i
$686$	−9.68653	+	16.7776i	−0.369834	+	0.640571i
$687$		0			0
$688$	0.287187			0.0109489
$689$	6.00000	+	24.2487i	0.228582	+	0.923802i
$690$		0			0
$691$	−37.7487	−	21.7942i	−1.43603	−	0.829092i	−0.438458	−	0.898752i	$-0.644475\pi$
$691$	−37.7487	−	21.7942i	−1.43603	−	0.829092i	−0.997571	+	0.0696602i	$0.977808\pi$
$692$	−2.39230	+	4.14359i	−0.0909418	+	0.157516i
$693$		0			0
$694$			4.78461i			0.181621i
$695$	−15.5263	+	8.96410i	−0.588945	+	0.340028i
$696$		0			0
$697$		−	35.4641i		−	1.34330i
$698$	10.9737	+	19.0070i	0.415361	+	0.719427i
$699$		0			0
$700$	−5.66025	−	3.26795i	−0.213937	−	0.123517i
$701$	−8.78461			−0.331790			−0.165895	−	0.986143i	$-0.553051\pi$
$701$	−8.78461			−0.331790			−0.165895	+	0.986143i	$0.553051\pi$
$702$		0			0
$703$	−21.8564			−0.824330
$704$	−6.43078	−	3.71281i	−0.242369	−	0.139932i
$705$		0			0
$706$	13.5167	+	23.4115i	0.508706	+	0.881105i
$707$			22.0000i			0.827395i
$708$		0			0
$709$	−26.5526	+	15.3301i	−0.997202	+	0.575735i	−0.907419	−	0.420226i	$-0.861951\pi$
$709$	−26.5526	+	15.3301i	−0.997202	+	0.575735i	−0.0897830	+	0.995961i	$0.528617\pi$
$710$			9.32051i			0.349792i
$711$		0			0
$712$	1.60770	−	2.78461i	0.0602509	−	0.104358i
$713$	−1.48334	−	0.856406i	−0.0555515	−	0.0320727i
$714$		0			0
$715$	−12.0000	−	3.46410i	−0.448775	−	0.129550i
$716$	13.3590			0.499249
$717$		0			0
$718$	−12.3205	+	21.3397i	−0.459797	+	0.796392i
$719$	−17.3660	−	30.0788i	−0.647643	−	1.12175i	−0.983684	−	0.179904i	$-0.942421\pi$
$719$	−17.3660	−	30.0788i	−0.647643	−	1.12175i	0.336041	−	0.941847i	$-0.390912\pi$
$720$		0			0
$721$	−12.3564	+	7.13397i	−0.460177	+	0.265683i
$722$	6.88269	−	3.97372i	0.256147	−	0.147887i
$723$		0			0
$724$	−10.6410	−	18.4308i	−0.395470	−	0.684975i
$725$	1.36603	−	2.36603i	0.0507329	−	0.0878720i
$726$		0			0
$727$	6.26795			0.232465			0.116233	−	0.993222i	$-0.462918\pi$
$727$	6.26795			0.232465			0.116233	+	0.993222i	$0.462918\pi$
$728$	−29.4115	+	28.3013i	−1.09006	+	1.04891i
$729$		0			0
$730$	−9.75833	−	5.63397i	−0.361172	−	0.208523i
$731$	0.901924	−	1.56218i	0.0333589	−	0.0577792i
$732$		0			0
$733$			2.32051i			0.0857099i	0.999081	+	0.0428550i	$0.0136453\pi$
$733$			2.32051i			0.0857099i	−0.999081	+	0.0428550i	$0.986355\pi$
$734$	11.4904	−	6.63397i	0.424118	−	0.244864i
$735$		0			0
$736$			3.13844i			0.115684i
$737$	−21.5885	−	37.3923i	−0.795221	−	1.37736i
$738$		0			0
$739$	9.00000	+	5.19615i	0.331070	+	0.191144i	0.656316	−	0.754486i	$-0.272114\pi$
$739$	9.00000	+	5.19615i	0.331070	+	0.191144i	−0.325246	+	0.945629i	$0.605447\pi$
$740$	5.85641			0.215286
$741$		0			0
$742$	−22.6410			−0.831178
$743$	−34.5622	−	19.9545i	−1.26796	−	0.732059i	−0.293361	−	0.956002i	$-0.594774\pi$
$743$	−34.5622	−	19.9545i	−1.26796	−	0.732059i	−0.974602	+	0.223943i	$0.928107\pi$
$744$		0			0
$745$	2.00000	+	3.46410i	0.0732743	+	0.126915i
$746$			1.37307i			0.0502716i
$747$		0			0
$748$	29.5692	−	17.0718i	1.08116	−	0.624207i
$749$			76.4449i			2.79323i
$750$		0			0
$751$	−10.6603	+	18.4641i	−0.388998	+	0.673765i	−0.992315	−	0.123737i	$-0.960512\pi$
$751$	−10.6603	+	18.4641i	−0.388998	+	0.673765i	0.603317	+	0.797502i	$0.293845\pi$
$752$	0.182069	+	0.105118i	0.00663938	+	0.00383325i
$753$		0			0
$754$	−5.00000	−	5.19615i	−0.182089	−	0.189233i
$755$	−17.8564			−0.649861
$756$		0			0
$757$	−13.4641	+	23.3205i	−0.489361	+	0.847598i	−0.999925	−	0.0122415i	$-0.996103\pi$
$757$	−13.4641	+	23.3205i	−0.489361	+	0.847598i	0.510564	+	0.859840i	$0.329437\pi$
$758$	−7.22243	−	12.5096i	−0.262331	−	0.454370i
$759$		0			0
$760$	−12.0000	+	6.92820i	−0.435286	+	0.251312i
$761$	5.07180	−	2.92820i	0.183852	−	0.106147i	−0.405249	−	0.914206i	$-0.632815\pi$
$761$	5.07180	−	2.92820i	0.183852	−	0.106147i	0.589101	+	0.808059i	$0.299482\pi$
$762$		0			0
$763$	18.4545	+	31.9641i	0.668097	+	1.15718i
$764$	−20.1436	+	34.8897i	−0.728770	+	1.26227i
$765$		0			0
$766$	−6.10512			−0.220587
$767$	−18.1699	−	18.8827i	−0.656076	−	0.681814i
$768$		0			0
$769$	43.6410	+	25.1962i	1.57374	+	0.908596i	0.995705	+	0.0925811i	$0.0295117\pi$
$769$	43.6410	+	25.1962i	1.57374	+	0.908596i	0.578030	+	0.816015i	$0.303822\pi$
$770$	5.66025	−	9.80385i	0.203981	−	0.353306i
$771$		0			0
$772$		−	8.88973i		−	0.319948i
$773$	−6.80385	+	3.92820i	−0.244717	+	0.141288i	−0.617343	−	0.786694i	$-0.711791\pi$
$773$	−6.80385	+	3.92820i	−0.244717	+	0.141288i	0.372626	+	0.927982i	$0.378458\pi$
$774$		0			0
$775$			3.19615i			0.114809i
$776$	20.8756	+	36.1577i	0.749392	+	1.29798i
$777$		0			0
$778$	11.0718	+	6.39230i	0.396943	+	0.229175i
$779$	28.7846			1.03132
$780$		0			0
$781$	44.1051			1.57821
$782$	2.28719	+	1.32051i	0.0817896	+	0.0472213i
$783$		0			0
$784$	6.92820	+	12.0000i	0.247436	+	0.428571i
$785$			9.73205i			0.347352i
$786$		0			0
$787$	−18.6506	+	10.7679i	−0.664823	+	0.383836i	−0.794112	−	0.607771i	$-0.792064\pi$
$787$	−18.6506	+	10.7679i	−0.664823	+	0.383836i	0.129289	+	0.991607i	$0.458731\pi$
$788$		−	4.28719i		−	0.152725i
$789$		0			0
$790$	−0.705771	+	1.22243i	−0.0251102	+	0.0434922i
$791$	−75.2487	−	43.4449i	−2.67554	−	1.54472i
$792$		0			0
$793$	11.5981	−	11.1603i	0.411860	−	0.396312i
$794$	17.8038			0.631835
$795$		0			0
$796$	−10.9808	+	19.0192i	−0.389203	+	0.674119i
$797$	15.2224	+	26.3660i	0.539206	+	0.933933i	0.998947	+	0.0458794i	$0.0146090\pi$
$797$	15.2224	+	26.3660i	0.539206	+	0.933933i	−0.459741	+	0.888053i	$0.652058\pi$
$798$		0			0
$799$	1.14359	−	0.660254i	0.0404574	−	0.0233581i
$800$	5.07180	−	2.92820i	0.179315	−	0.103528i
$801$		0			0
$802$	5.60770	+	9.71281i	0.198015	+	0.342971i
$803$	−26.6603	+	46.1769i	−0.940820	+	1.62955i
$804$		0			0
$805$	−2.39230			−0.0843177
$806$	8.10512	+	2.33975i	0.285491	+	0.0824140i
$807$		0			0
$808$	−10.8231	−	6.24871i	−0.380755	−	0.219829i
$809$	18.0000	−	31.1769i	0.632846	−	1.09612i	−0.354121	−	0.935200i	$-0.615220\pi$
$809$	18.0000	−	31.1769i	0.632846	−	1.09612i	0.986967	−	0.160922i	$-0.0514468\pi$
$810$		0			0
$811$			0.947441i			0.0332692i	0.999862	+	0.0166346i	$0.00529520\pi$
$811$			0.947441i			0.0332692i	−0.999862	+	0.0166346i	$0.994705\pi$
$812$	−15.4641	+	8.92820i	−0.542684	+	0.313319i
$813$		0			0
$814$			10.1436i			0.355533i
$815$	2.76795	+	4.79423i	0.0969570	+	0.167935i
$816$		0			0
$817$	1.26795	+	0.732051i	0.0443599	+	0.0256112i
$818$	1.94744			0.0680907
$819$		0			0
$820$	−7.71281			−0.269343
$821$	0.803848	+	0.464102i	0.0280545	+	0.0161973i	0.513962	−	0.857813i	$-0.328177\pi$
$821$	0.803848	+	0.464102i	0.0280545	+	0.0161973i	−0.485907	+	0.874010i	$0.661511\pi$
$822$		0			0
$823$	−6.58846	−	11.4115i	−0.229659	−	0.397781i	0.728048	−	0.685526i	$-0.240428\pi$
$823$	−6.58846	−	11.4115i	−0.229659	−	0.397781i	−0.957707	+	0.287745i	$0.907094\pi$
$824$		−	8.10512i		−	0.282355i
$825$		0			0
$826$	20.5692	−	11.8756i	0.715695	−	0.413207i
$827$			2.58846i			0.0900095i	0.998987	+	0.0450047i	$0.0143303\pi$
$827$			2.58846i			0.0900095i	−0.998987	+	0.0450047i	$0.985670\pi$
$828$		0			0
$829$	−19.0885	+	33.0622i	−0.662970	+	1.14830i	0.316862	+	0.948472i	$0.397371\pi$
$829$	−19.0885	+	33.0622i	−0.662970	+	1.14830i	−0.979832	+	0.199825i	$0.935963\pi$
$830$	−1.60770	−	0.928203i	−0.0558039	−	0.0322184i
$831$		0			0
$832$	−1.85641	−	7.50258i	−0.0643593	−	0.260105i
$833$	87.0333			3.01553
$834$		0			0
$835$	−8.73205	+	15.1244i	−0.302185	+	0.523400i
$836$	13.8564	+	24.0000i	0.479234	+	0.830057i
$837$		0			0
$838$	12.9615	−	7.48334i	0.447748	−	0.258508i
$839$	17.7846	−	10.2679i	0.613993	−	0.354489i	−0.160534	−	0.987030i	$-0.551322\pi$
$839$	17.7846	−	10.2679i	0.613993	−	0.354489i	0.774527	+	0.632541i	$0.217988\pi$
$840$		0			0
$841$	10.7679	+	18.6506i	0.371309	+	0.643125i
$842$	8.63397	−	14.9545i	0.297546	−	0.515366i
$843$		0			0
$844$	16.8897			0.581368
$845$	−6.06218	−	11.5000i	−0.208545	−	0.395612i
$846$		0			0
$847$	−3.86603	−	2.23205i	−0.132838	−	0.0766942i
$848$	−3.71281	+	6.43078i	−0.127499	+	0.220834i
$849$		0			0
$850$		−	4.92820i		−	0.169036i
$851$	1.85641	−	1.07180i	0.0636368	−	0.0367407i
$852$		0			0
$853$		−	16.6077i		−	0.568637i	−0.958730	−	0.284318i	$-0.908233\pi$
$853$		−	16.6077i		−	0.568637i	0.958730	−	0.284318i	$-0.0917673\pi$
$854$	7.29423	+	12.6340i	0.249603	+	0.432326i
$855$		0			0
$856$	−37.6077	−	21.7128i	−1.28540	−	0.742129i
$857$	−17.1244			−0.584957			−0.292478	−	0.956272i	$-0.594480\pi$
$857$	−17.1244			−0.584957			−0.292478	+	0.956272i	$0.594480\pi$
$858$		0			0
$859$	7.78461			0.265607			0.132804	−	0.991142i	$-0.457602\pi$
$859$	7.78461			0.265607			0.132804	+	0.991142i	$0.457602\pi$
$860$	−0.339746	−	0.196152i	−0.0115852	−	0.00668874i
$861$		0			0
$862$	8.53590	+	14.7846i	0.290734	+	0.503566i
$863$			34.3923i			1.17073i	0.810771	+	0.585364i	$0.199048\pi$
$863$			34.3923i			1.17073i	−0.810771	+	0.585364i	$0.800952\pi$
$864$		0			0
$865$	2.83013	−	1.63397i	0.0962272	−	0.0555568i
$866$			3.51666i			0.119501i
$867$		0			0
$868$	10.4449	−	18.0910i	0.354522	−	0.614050i
$869$	5.78461	+	3.33975i	0.196229	+	0.113293i
$870$		0			0
$871$	12.4641	−	43.1769i	0.422330	−	1.46299i
$872$	−20.9667			−0.710021
$873$		0			0
$874$	−1.07180	+	1.85641i	−0.0362541	+	0.0627939i
$875$	2.23205	+	3.86603i	0.0754571	+	0.130696i
$876$		0			0
$877$	−16.1436	+	9.32051i	−0.545130	+	0.314731i	−0.747156	−	0.664649i	$-0.768581\pi$
$877$	−16.1436	+	9.32051i	−0.545130	+	0.314731i	0.202025	+	0.979380i	$0.435248\pi$
$878$	9.75833	−	5.63397i	0.329328	−	0.190137i
$879$		0			0
$880$	−1.85641	−	3.21539i	−0.0625794	−	0.108391i
$881$	12.5885	−	21.8038i	0.424116	−	0.734590i	−0.572222	−	0.820099i	$-0.693918\pi$
$881$	12.5885	−	21.8038i	0.424116	−	0.734590i	0.996337	+	0.0855088i	$0.0272516\pi$
$882$		0			0
$883$	0.660254			0.0222193			0.0111097	−	0.999938i	$-0.496464\pi$
$883$	0.660254			0.0222193			0.0111097	+	0.999938i	$0.496464\pi$
$884$	34.1436	+	9.85641i	1.14837	+	0.331507i
$885$		0			0
$886$	−1.98076	−	1.14359i	−0.0665450	−	0.0384198i
$887$	−1.49038	+	2.58142i	−0.0500421	+	0.0866755i	−0.889961	−	0.456036i	$-0.849269\pi$
$887$	−1.49038	+	2.58142i	−0.0500421	+	0.0866755i	0.839919	+	0.542711i	$0.182602\pi$
$888$		0			0
$889$			65.4449i			2.19495i
$890$	−0.803848	+	0.464102i	−0.0269450	+	0.0155567i
$891$		0			0
$892$			17.3590i			0.581222i
$893$	0.535898	+	0.928203i	0.0179332	+	0.0310611i
$894$		0			0
$895$	−7.90192	−	4.56218i	−0.264132	−	0.152497i
$896$	−45.2820			−1.51277
$897$		0			0
$898$	−8.10512			−0.270471
$899$	7.56218	+	4.36603i	0.252213	+	0.145615i
$900$		0			0
$901$	23.3205	+	40.3923i	0.776919	+	1.34566i
$902$		−	13.3590i		−	0.444806i
$903$		0			0
$904$	42.7461	−	24.6795i	1.42172	−	0.820828i
$905$			14.5359i			0.483190i
$906$		0			0
$907$	−12.2679	+	21.2487i	−0.407351	+	0.705552i	−0.994592	−	0.103860i	$-0.966881\pi$
$907$	−12.2679	+	21.2487i	−0.407351	+	0.705552i	0.587241	+	0.809412i	$0.300214\pi$
$908$	14.7846	+	8.53590i	0.490645	+	0.283274i
$909$		0			0
$910$	11.4378	−	2.83013i	0.379160	−	0.0938178i
$911$	7.71281			0.255537			0.127768	−	0.991804i	$-0.459219\pi$
$911$	7.71281			0.255537			0.127768	+	0.991804i	$0.459219\pi$
$912$		0			0
$913$	−4.39230	+	7.60770i	−0.145364	+	0.251778i
$914$	−1.97372	−	3.41858i	−0.0652849	−	0.113077i
$915$		0			0
$916$	−23.3205	+	13.4641i	−0.770531	+	0.444866i
$917$	4.90192	−	2.83013i	0.161876	−	0.0934590i
$918$		0			0
$919$	9.53590	+	16.5167i	0.314560	+	0.544834i	0.979344	−	0.202202i	$-0.0648096\pi$
$919$	9.53590	+	16.5167i	0.314560	+	0.544834i	−0.664784	+	0.747036i	$0.731476\pi$
$920$	0.679492	−	1.17691i	0.0224022	−	0.0388017i
$921$		0			0
$922$	−8.43078			−0.277653
$923$	31.8301	+	33.0788i	1.04770	+	1.08880i
$924$		0			0
$925$	−3.46410	−	2.00000i	−0.113899	−	0.0657596i
$926$	0.653212	−	1.13140i	0.0214659	−	0.0371800i
$927$		0			0
$928$		−	16.0000i		−	0.525226i
$929$	13.2679	−	7.66025i	0.435307	−	0.251325i	−0.266298	−	0.963891i	$-0.585800\pi$
$929$	13.2679	−	7.66025i	0.435307	−	0.251325i	0.701605	+	0.712566i	$0.252467\pi$
$930$		0			0
$931$			70.6410i			2.31517i
$932$	−17.4641	−	30.2487i	−0.572056	−	0.990829i
$933$		0			0
$934$	−15.0000	−	8.66025i	−0.490815	−	0.283372i
$935$	−23.3205			−0.762662
$936$		0			0
$937$	32.2487			1.05352			0.526760	−	0.850014i	$-0.323407\pi$
$937$	32.2487			1.05352			0.526760	+	0.850014i	$0.323407\pi$
$938$	35.2750	+	20.3660i	1.15177	+	0.664974i
$939$		0			0
$940$	−0.143594	−	0.248711i	−0.00468350	−	0.00811207i
$941$		−	9.41154i		−	0.306808i	−0.988164	−	0.153404i	$-0.950976\pi$
$941$		−	9.41154i		−	0.306808i	0.988164	−	0.153404i	$-0.0490235\pi$
$942$		0			0
$943$	−2.44486	+	1.41154i	−0.0796157	+	0.0459662i
$944$		−	7.78976i		−	0.253535i
$945$		0			0
$946$	0.339746	−	0.588457i	0.0110461	−	0.0191324i
$947$	4.68653	+	2.70577i	0.152292	+	0.0879258i	0.574209	−	0.818708i	$-0.305310\pi$
$947$	4.68653	+	2.70577i	0.152292	+	0.0879258i	−0.421918	+	0.906634i	$0.638643\pi$
$948$		0			0
$949$	−53.8731	+	13.3301i	−1.74879	+	0.432714i
$950$	4.00000			0.129777
$951$		0			0
$952$	−38.1051	+	66.0000i	−1.23499	+	2.13907i
$953$	−12.1244	−	21.0000i	−0.392746	−	0.680257i	0.600064	−	0.799952i	$-0.295142\pi$
$953$	−12.1244	−	21.0000i	−0.392746	−	0.680257i	−0.992811	+	0.119695i	$0.961808\pi$
$954$		0			0
$955$	23.8301	−	13.7583i	0.771125	−	0.445209i
$956$	6.92820	−	4.00000i	0.224074	−	0.129369i
$957$		0			0
$958$	13.1436	+	22.7654i	0.424650	+	0.735516i
$959$	−20.3660	+	35.2750i	−0.657653	+	1.13909i
$960$		0			0
$961$	20.7846			0.670471
$962$	−7.60770	+	7.32051i	−0.245282	+	0.236023i
$963$		0			0
$964$	−2.03848	−	1.17691i	−0.0656549	−	0.0379059i
$965$	−3.03590	+	5.25833i	−0.0977290	+	0.169272i
$966$		0			0
$967$		−	16.2487i		−	0.522523i	−0.965268	−	0.261262i	$-0.915861\pi$
$967$		−	16.2487i		−	0.522523i	0.965268	−	0.261262i	$-0.0841385\pi$
$968$	2.19615	−	1.26795i	0.0705870	−	0.0407534i
$969$		0			0
$970$		−	12.0526i		−	0.386984i
$971$	30.5885	+	52.9808i	0.981630	+	1.70023i	0.656047	+	0.754720i	$0.272227\pi$
$971$	30.5885	+	52.9808i	0.981630	+	1.70023i	0.325584	+	0.945513i	$0.394439\pi$
$972$		0			0
$973$	−69.3109	−	40.0167i	−2.22201	−	1.28288i
$974$	15.2154			0.487533
$975$		0			0
$976$	4.78461			0.153152
$977$	12.9282	+	7.46410i	0.413610	+	0.238798i	0.692340	−	0.721572i	$-0.256580\pi$
$977$	12.9282	+	7.46410i	0.413610	+	0.238798i	−0.278730	+	0.960370i	$0.589913\pi$
$978$		0			0
$979$	2.19615	+	3.80385i	0.0701893	+	0.121571i
$980$		−	18.9282i		−	0.604639i
$981$		0			0
$982$	−4.51666	+	2.60770i	−0.144132	+	0.0832149i
$983$			3.85641i			0.123000i	0.998107	+	0.0615001i	$0.0195885\pi$
$983$			3.85641i			0.123000i	−0.998107	+	0.0615001i	$0.980412\pi$
$984$		0			0
$985$	−1.46410	+	2.53590i	−0.0466502	+	0.0808004i
$986$	−11.6603	−	6.73205i	−0.371338	−	0.214392i
$987$		0			0
$988$	−8.00000	+	27.7128i	−0.254514	+	0.881662i
$989$	−0.143594			−0.00456601
$990$		0			0
$991$	−7.53590	+	13.0526i	−0.239386	+	0.414628i	−0.960538	−	0.278148i	$-0.910279\pi$
$991$	−7.53590	+	13.0526i	−0.239386	+	0.414628i	0.721152	+	0.692776i	$0.243613\pi$
$992$	9.35898	+	16.2102i	0.297148	+	0.514675i
$993$		0			0
$994$	−36.0333	+	20.8038i	−1.14291	+	0.659858i
$995$	12.9904	−	7.50000i	0.411823	−	0.237766i
$996$		0			0
$997$	13.2058	+	22.8731i	0.418231	+	0.724397i	0.995762	−	0.0919717i	$-0.0293169\pi$
$997$	13.2058	+	22.8731i	0.418231	+	0.724397i	−0.577531	+	0.816369i	$0.695984\pi$
$998$	0.143594	−	0.248711i	0.00454537	−	0.00787282i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bu.a.316.1		4
3.2	odd	2		195.2.bb.a.121.2	✓	4
13.6	odd	12		7605.2.a.bk.1.1		2
13.7	odd	12		7605.2.a.y.1.2		2
13.10	even	6	inner	585.2.bu.a.361.1		4
15.2	even	4		975.2.w.a.199.2		4
15.8	even	4		975.2.w.f.199.1		4
15.14	odd	2		975.2.bc.h.901.1		4
39.20	even	12		2535.2.a.s.1.1		2
39.23	odd	6		195.2.bb.a.166.2	yes	4
39.32	even	12		2535.2.a.n.1.2		2
195.23	even	12		975.2.w.a.49.2		4
195.62	even	12		975.2.w.f.49.1		4
195.179	odd	6		975.2.bc.h.751.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bb.a.121.2	✓	4	3.2	odd	2
195.2.bb.a.166.2	yes	4	39.23	odd	6
585.2.bu.a.316.1		4	1.1	even	1	trivial
585.2.bu.a.361.1		4	13.10	even	6	inner
975.2.w.a.49.2		4	195.23	even	12
975.2.w.a.199.2		4	15.2	even	4
975.2.w.f.49.1		4	195.62	even	12
975.2.w.f.199.1		4	15.8	even	4
975.2.bc.h.751.1		4	195.179	odd	6
975.2.bc.h.901.1		4	15.14	odd	2
2535.2.a.n.1.2		2	39.32	even	12
2535.2.a.s.1.1		2	39.20	even	12
7605.2.a.y.1.2		2	13.7	odd	12
7605.2.a.bk.1.1		2	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)

\(f(q)\)	\(=\)	\(q+(0.633975 + 0.366025i) q^{2} +(-0.732051 - 1.26795i) q^{4} +1.00000i q^{5} +(-3.86603 + 2.23205i) q^{7} -2.53590i q^{8} +(-0.366025 + 0.633975i) q^{10} +(3.00000 + 1.73205i) q^{11} +(0.866025 + 3.50000i) q^{13} -3.26795 q^{14} +(-0.535898 + 0.928203i) q^{16} +(3.36603 + 5.83013i) q^{17} +(-4.73205 + 2.73205i) q^{19} +(1.26795 - 0.732051i) q^{20} +(1.26795 + 2.19615i) q^{22} +(0.267949 - 0.464102i) q^{23} -1.00000 q^{25} +(-0.732051 + 2.53590i) q^{26} +(5.66025 + 3.26795i) q^{28} +(-1.36603 + 2.36603i) q^{29} -3.19615i q^{31} +(-5.07180 + 2.92820i) q^{32} +4.92820i q^{34} +(-2.23205 - 3.86603i) q^{35} +(3.46410 + 2.00000i) q^{37} -4.00000 q^{38} +2.53590 q^{40} +(-4.56218 - 2.63397i) q^{41} +(-0.133975 - 0.232051i) q^{43} -5.07180i q^{44} +(0.339746 - 0.196152i) q^{46} -0.196152i q^{47} +(6.46410 - 11.1962i) q^{49} +(-0.633975 - 0.366025i) q^{50} +(3.80385 - 3.66025i) q^{52} +6.92820 q^{53} +(-1.73205 + 3.00000i) q^{55} +(5.66025 + 9.80385i) q^{56} +(-1.73205 + 1.00000i) q^{58} +(-6.29423 + 3.63397i) q^{59} +(-2.23205 - 3.86603i) q^{61} +(1.16987 - 2.02628i) q^{62} -2.14359 q^{64} +(-3.50000 + 0.866025i) q^{65} +(-10.7942 - 6.23205i) q^{67} +(4.92820 - 8.53590i) q^{68} -3.26795i q^{70} +(11.0263 - 6.36603i) q^{71} +15.3923i q^{73} +(1.46410 + 2.53590i) q^{74} +(6.92820 + 4.00000i) q^{76} -15.4641 q^{77} +1.92820 q^{79} +(-0.928203 - 0.535898i) q^{80} +(-1.92820 - 3.33975i) q^{82} +2.53590i q^{83} +(-5.83013 + 3.36603i) q^{85} -0.196152i q^{86} +(4.39230 - 7.60770i) q^{88} +(1.09808 + 0.633975i) q^{89} +(-11.1603 - 11.5981i) q^{91} -0.784610 q^{92} +(0.0717968 - 0.124356i) q^{94} +(-2.73205 - 4.73205i) q^{95} +(-14.2583 + 8.23205i) q^{97} +(8.19615 - 4.73205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{2} + 4 q^{4} - 12 q^{7} + 2 q^{10} + 12 q^{11} - 20 q^{14} - 16 q^{16} + 10 q^{17} - 12 q^{19} + 12 q^{20} + 12 q^{22} + 8 q^{23} - 4 q^{25} + 4 q^{26} - 12 q^{28} - 2 q^{29} - 48 q^{32} - 2 q^{35}+ \cdots + 12 q^{98}+O(q^{100}) \) 4 * q + 6 * q^2 + 4 * q^4 - 12 * q^7 + 2 * q^10 + 12 * q^11 - 20 * q^14 - 16 * q^16 + 10 * q^17 - 12 * q^19 + 12 * q^20 + 12 * q^22 + 8 * q^23 - 4 * q^25 + 4 * q^26 - 12 * q^28 - 2 * q^29 - 48 * q^32 - 2 * q^35 - 16 * q^38 + 24 * q^40 + 6 * q^41 - 4 * q^43 + 36 * q^46 + 12 * q^49 - 6 * q^50 + 36 * q^52 - 12 * q^56 + 6 * q^59 - 2 * q^61 + 22 * q^62 - 64 * q^64 - 14 * q^65 - 12 * q^67 - 8 * q^68 + 6 * q^71 - 8 * q^74 - 48 * q^77 - 20 * q^79 + 24 * q^80 + 20 * q^82 - 6 * q^85 - 24 * q^88 - 6 * q^89 - 10 * q^91 + 80 * q^92 + 28 * q^94 - 4 * q^95 - 12 * q^97 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more