LMFDB - Embedded newform 208.2.bm.b.63.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,2,Mod(15,208)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 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("208.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	208.bm (of order $12$, degree $4$, 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:	$1.66088836204$
Analytic rank:	$0$
Dimension:	$4$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			63.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	208.63
Dual form			208.2.bm.b.175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50000 + 0.866025i) q^{3} +(1.00000 + 1.00000i) q^{5} +(-0.866025 + 0.232051i) q^{7} +(-0.866025 + 3.23205i) q^{11} +(-1.00000 + 3.46410i) q^{13} +(-2.36603 - 0.633975i) q^{15} +(-1.96410 - 1.13397i) q^{17} +(0.866025 + 3.23205i) q^{19} +(1.09808 - 1.09808i) q^{21} +(1.50000 + 2.59808i) q^{23} -3.00000i q^{25} -5.19615i q^{27} +(3.96410 + 6.86603i) q^{29} +(5.19615 - 5.19615i) q^{31} +(-1.50000 - 5.59808i) q^{33} +(-1.09808 - 0.633975i) q^{35} +(-3.59808 - 0.964102i) q^{37} +(-1.50000 - 6.06218i) q^{39} +(2.13397 - 7.96410i) q^{41} +(4.50000 - 7.79423i) q^{43} +(4.26795 + 4.26795i) q^{47} +(-5.36603 + 3.09808i) q^{49} +3.92820 q^{51} +4.92820 q^{53} +(-4.09808 + 2.36603i) q^{55} +(-4.09808 - 4.09808i) q^{57} +(8.59808 - 2.30385i) q^{59} +(-3.50000 + 6.06218i) q^{61} +(-4.46410 + 2.46410i) q^{65} +(-12.0622 - 3.23205i) q^{67} +(-4.50000 - 2.59808i) q^{69} +(4.33013 + 16.1603i) q^{71} +(2.46410 - 2.46410i) q^{73} +(2.59808 + 4.50000i) q^{75} -3.00000i q^{77} -3.46410i q^{79} +(4.50000 + 7.79423i) q^{81} +(0.803848 - 0.803848i) q^{83} +(-0.830127 - 3.09808i) q^{85} +(-11.8923 - 6.86603i) q^{87} +(5.86603 + 1.57180i) q^{89} +(0.0621778 - 3.23205i) q^{91} +(-3.29423 + 12.2942i) q^{93} +(-2.36603 + 4.09808i) q^{95} +(11.3301 - 3.03590i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} + 4 q^{5} - 4 q^{13} - 6 q^{15} + 6 q^{17} - 6 q^{21} + 6 q^{23} + 2 q^{29} - 6 q^{33} + 6 q^{35} - 4 q^{37} - 6 q^{39} + 12 q^{41} + 18 q^{43} + 24 q^{47} - 18 q^{49} - 12 q^{51} - 8 q^{53}+ \cdots + 28 q^{97}+O(q^{100}) $ 4 * q - 6 * q^3 + 4 * q^5 - 4 * q^13 - 6 * q^15 + 6 * q^17 - 6 * q^21 + 6 * q^23 + 2 * q^29 - 6 * q^33 + 6 * q^35 - 4 * q^37 - 6 * q^39 + 12 * q^41 + 18 * q^43 + 24 * q^47 - 18 * q^49 - 12 * q^51 - 8 * q^53 - 6 * q^55 - 6 * q^57 + 24 * q^59 - 14 * q^61 - 4 * q^65 - 24 * q^67 - 18 * q^69 - 4 * q^73 + 18 * q^81 + 24 * q^83 + 14 * q^85 - 6 * q^87 + 20 * q^89 - 24 * q^91 + 18 * q^93 - 6 * q^95 + 28 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{12}\right)$

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			0
$2$		0			0
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$4$		0			0
$5$	1.00000	+	1.00000i	0.447214	+	0.447214i	0.894427	−	0.447214i	$-0.147584\pi$
$5$	1.00000	+	1.00000i	0.447214	+	0.447214i	−0.447214	+	0.894427i	$0.647584\pi$
$6$		0			0
$7$	−0.866025	+	0.232051i	−0.327327	+	0.0877070i	−0.418740	−	0.908106i	$-0.637528\pi$
$7$	−0.866025	+	0.232051i	−0.327327	+	0.0877070i	0.0914134	+	0.995813i	$0.470862\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.866025	+	3.23205i	−0.261116	+	0.974500i	0.703468	+	0.710727i	$0.251634\pi$
$11$	−0.866025	+	3.23205i	−0.261116	+	0.974500i	−0.964585	+	0.263773i	$0.915033\pi$
$12$		0			0
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$14$		0			0
$15$	−2.36603	−	0.633975i	−0.610905	−	0.163692i
$16$		0			0
$17$	−1.96410	−	1.13397i	−0.476365	−	0.275029i	0.242536	−	0.970143i	$-0.422021\pi$
$17$	−1.96410	−	1.13397i	−0.476365	−	0.275029i	−0.718900	+	0.695113i	$0.755354\pi$
$18$		0			0
$19$	0.866025	+	3.23205i	0.198680	+	0.741483i	0.991283	+	0.131746i	$0.0420584\pi$
$19$	0.866025	+	3.23205i	0.198680	+	0.741483i	−0.792604	+	0.609737i	$0.791275\pi$
$20$		0			0
$21$	1.09808	−	1.09808i	0.239620	−	0.239620i
$22$		0			0
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	0.978961	−	0.204046i	$-0.0654092\pi$
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	−0.666190	+	0.745782i	$0.732076\pi$
$24$		0			0
$25$		−	3.00000i		−	0.600000i
$26$		0			0
$27$		−	5.19615i		−	1.00000i
$28$		0			0
$29$	3.96410	+	6.86603i	0.736115	+	1.27499i	0.954232	+	0.299066i	$0.0966752\pi$
$29$	3.96410	+	6.86603i	0.736115	+	1.27499i	−0.218117	+	0.975923i	$0.569991\pi$
$30$		0			0
$31$	5.19615	−	5.19615i	0.933257	−	0.933257i	−0.0646514	−	0.997908i	$-0.520594\pi$
$31$	5.19615	−	5.19615i	0.933257	−	0.933257i	0.997908	+	0.0646514i	$0.0205935\pi$
$32$		0			0
$33$	−1.50000	−	5.59808i	−0.261116	−	0.974500i
$34$		0			0
$35$	−1.09808	−	0.633975i	−0.185609	−	0.107161i
$36$		0			0
$37$	−3.59808	−	0.964102i	−0.591520	−	0.158497i	−0.0493722	−	0.998780i	$-0.515722\pi$
$37$	−3.59808	−	0.964102i	−0.591520	−	0.158497i	−0.542148	+	0.840283i	$0.682389\pi$
$38$		0			0
$39$	−1.50000	−	6.06218i	−0.240192	−	0.970725i
$40$		0			0
$41$	2.13397	−	7.96410i	0.333271	−	1.24378i	−0.572461	−	0.819932i	$-0.694011\pi$
$41$	2.13397	−	7.96410i	0.333271	−	1.24378i	0.905732	−	0.423852i	$-0.139322\pi$
$42$		0			0
$43$	4.50000	−	7.79423i	0.686244	−	1.18861i	−0.286801	−	0.957990i	$-0.592592\pi$
$43$	4.50000	−	7.79423i	0.686244	−	1.18861i	0.973044	−	0.230618i	$-0.0740749\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.26795	+	4.26795i	0.622544	+	0.622544i	0.946181	−	0.323637i	$-0.104906\pi$
$47$	4.26795	+	4.26795i	0.622544	+	0.622544i	−0.323637	+	0.946181i	$0.604906\pi$
$48$		0			0
$49$	−5.36603	+	3.09808i	−0.766575	+	0.442582i
$50$		0			0
$51$	3.92820			0.550058
$52$		0			0
$53$	4.92820			0.676941			0.338470	−	0.940977i	$-0.390091\pi$
$53$	4.92820			0.676941			0.338470	+	0.940977i	$0.390091\pi$
$54$		0			0
$55$	−4.09808	+	2.36603i	−0.552584	+	0.319035i
$56$		0			0
$57$	−4.09808	−	4.09808i	−0.542803	−	0.542803i
$58$		0			0
$59$	8.59808	−	2.30385i	1.11937	−	0.299935i	0.348744	−	0.937218i	$-0.386608\pi$
$59$	8.59808	−	2.30385i	1.11937	−	0.299935i	0.770630	+	0.637283i	$0.219942\pi$
$60$		0			0
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	−0.998264	−	0.0588933i	$-0.981243\pi$
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	0.550135	+	0.835076i	$0.314576\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−4.46410	+	2.46410i	−0.553704	+	0.305634i
$66$		0			0
$67$	−12.0622	−	3.23205i	−1.47363	−	0.394858i	−0.569456	−	0.822022i	$-0.692846\pi$
$67$	−12.0622	−	3.23205i	−1.47363	−	0.394858i	−0.904174	+	0.427164i	$0.859513\pi$
$68$		0			0
$69$	−4.50000	−	2.59808i	−0.541736	−	0.312772i
$70$		0			0
$71$	4.33013	+	16.1603i	0.513892	+	1.91787i	0.372950	+	0.927851i	$0.378346\pi$
$71$	4.33013	+	16.1603i	0.513892	+	1.91787i	0.140941	+	0.990018i	$0.454987\pi$
$72$		0			0
$73$	2.46410	−	2.46410i	0.288401	−	0.288401i	−0.548047	−	0.836448i	$-0.684628\pi$
$73$	2.46410	−	2.46410i	0.288401	−	0.288401i	0.836448	+	0.548047i	$0.184628\pi$
$74$		0			0
$75$	2.59808	+	4.50000i	0.300000	+	0.519615i
$76$		0			0
$77$		−	3.00000i		−	0.341882i
$78$		0			0
$79$		−	3.46410i		−	0.389742i	−0.980829	−	0.194871i	$-0.937571\pi$
$79$		−	3.46410i		−	0.389742i	0.980829	−	0.194871i	$-0.0624288\pi$
$80$		0			0
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$		0			0
$83$	0.803848	−	0.803848i	0.0882337	−	0.0882337i	−0.661612	−	0.749846i	$-0.730128\pi$
$83$	0.803848	−	0.803848i	0.0882337	−	0.0882337i	0.749846	+	0.661612i	$0.230128\pi$
$84$		0			0
$85$	−0.830127	−	3.09808i	−0.0900399	−	0.336034i
$86$		0			0
$87$	−11.8923	−	6.86603i	−1.27499	−	0.736115i
$88$		0			0
$89$	5.86603	+	1.57180i	0.621797	+	0.166610i	0.555945	−	0.831219i	$-0.312357\pi$
$89$	5.86603	+	1.57180i	0.621797	+	0.166610i	0.0658527	+	0.997829i	$0.479023\pi$
$90$		0			0
$91$	0.0621778	−	3.23205i	0.00651801	−	0.338811i
$92$		0			0
$93$	−3.29423	+	12.2942i	−0.341596	+	1.27485i
$94$		0			0
$95$	−2.36603	+	4.09808i	−0.242749	+	0.420454i
$96$		0			0
$97$	11.3301	−	3.03590i	1.15040	−	0.308249i	0.367275	−	0.930113i	$-0.380291\pi$
$97$	11.3301	−	3.03590i	1.15040	−	0.308249i	0.783125	+	0.621864i	$0.213624\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	10.9641	−	6.33013i	1.09097	−	0.629871i	0.157135	−	0.987577i	$-0.449774\pi$
$101$	10.9641	−	6.33013i	1.09097	−	0.629871i	0.933834	+	0.357706i	$0.116441\pi$
$102$		0			0
$103$	−5.07180			−0.499739			−0.249869	−	0.968280i	$-0.580388\pi$
$103$	−5.07180			−0.499739			−0.249869	+	0.968280i	$0.580388\pi$
$104$		0			0
$105$	2.19615			0.214323
$106$		0			0
$107$	−17.8923	+	10.3301i	−1.72971	+	0.998651i	−0.838896	+	0.544292i	$0.816798\pi$
$107$	−17.8923	+	10.3301i	−1.72971	+	0.998651i	−0.890819	+	0.454359i	$0.849868\pi$
$108$		0			0
$109$	1.00000	+	1.00000i	0.0957826	+	0.0957826i	0.753374	−	0.657592i	$-0.228425\pi$
$109$	1.00000	+	1.00000i	0.0957826	+	0.0957826i	−0.657592	+	0.753374i	$0.728425\pi$
$110$		0			0
$111$	6.23205	−	1.66987i	0.591520	−	0.158497i
$112$		0			0
$113$	−4.42820	+	7.66987i	−0.416570	+	0.721521i	−0.995592	−	0.0937913i	$-0.970101\pi$
$113$	−4.42820	+	7.66987i	−0.416570	+	0.721521i	0.579022	+	0.815312i	$0.303435\pi$
$114$		0			0
$115$	−1.09808	+	4.09808i	−0.102396	+	0.382148i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.96410	+	0.526279i	0.180049	+	0.0482440i
$120$		0			0
$121$	−0.169873	−	0.0980762i	−0.0154430	−	0.00891602i
$122$		0			0
$123$	3.69615	+	13.7942i	0.333271	+	1.24378i
$124$		0			0
$125$	8.00000	−	8.00000i	0.715542	−	0.715542i
$126$		0			0
$127$	−1.96410	−	3.40192i	−0.174286	−	0.301872i	0.765628	−	0.643284i	$-0.222428\pi$
$127$	−1.96410	−	3.40192i	−0.174286	−	0.301872i	−0.939914	+	0.341412i	$0.889095\pi$
$128$		0			0
$129$			15.5885i			1.37249i
$130$		0			0
$131$			15.4641i			1.35110i	0.737312	+	0.675552i	$0.236095\pi$
$131$			15.4641i			1.35110i	−0.737312	+	0.675552i	$0.763905\pi$
$132$		0			0
$133$	−1.50000	−	2.59808i	−0.130066	−	0.225282i
$134$		0			0
$135$	5.19615	−	5.19615i	0.447214	−	0.447214i
$136$		0			0
$137$	−1.33013	−	4.96410i	−0.113640	−	0.424112i	0.885541	−	0.464561i	$-0.153788\pi$
$137$	−1.33013	−	4.96410i	−0.113640	−	0.424112i	−0.999182	+	0.0404491i	$0.987121\pi$
$138$		0			0
$139$	−14.8923	−	8.59808i	−1.26315	−	0.729279i	−0.289466	−	0.957188i	$-0.593478\pi$
$139$	−14.8923	−	8.59808i	−1.26315	−	0.729279i	−0.973682	+	0.227909i	$0.926811\pi$
$140$		0			0
$141$	−10.0981	−	2.70577i	−0.850411	−	0.227867i
$142$		0			0
$143$	−10.3301	−	6.23205i	−0.863849	−	0.521150i
$144$		0			0
$145$	−2.90192	+	10.8301i	−0.240992	+	0.899393i
$146$		0			0
$147$	5.36603	−	9.29423i	0.442582	−	0.766575i
$148$		0			0
$149$	7.33013	−	1.96410i	0.600507	−	0.160905i	0.0542564	−	0.998527i	$-0.482721\pi$
$149$	7.33013	−	1.96410i	0.600507	−	0.160905i	0.546251	+	0.837622i	$0.316054\pi$
$150$		0			0
$151$	13.7321	+	13.7321i	1.11750	+	1.11750i	0.992107	+	0.125391i	$0.0400186\pi$
$151$	13.7321	+	13.7321i	1.11750	+	1.11750i	0.125391	+	0.992107i	$0.459981\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	10.3923			0.834730
$156$		0			0
$157$	−19.8564			−1.58471			−0.792357	−	0.610058i	$-0.791146\pi$
$157$	−19.8564			−1.58471			−0.792357	+	0.610058i	$0.791146\pi$
$158$		0			0
$159$	−7.39230	+	4.26795i	−0.586248	+	0.338470i
$160$		0			0
$161$	−1.90192	−	1.90192i	−0.149893	−	0.149893i
$162$		0			0
$163$	12.0622	−	3.23205i	0.944783	−	0.253154i	0.246636	−	0.969108i	$-0.420675\pi$
$163$	12.0622	−	3.23205i	0.944783	−	0.253154i	0.698147	+	0.715954i	$0.254008\pi$
$164$		0			0
$165$	4.09808	−	7.09808i	0.319035	−	0.552584i
$166$		0			0
$167$	4.20577	−	15.6962i	0.325452	−	1.21460i	−0.588404	−	0.808567i	$-0.700244\pi$
$167$	4.20577	−	15.6962i	0.325452	−	1.21460i	0.913856	−	0.406038i	$-0.133090\pi$
$168$		0			0
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.03590	−	0.598076i	−0.0787579	−	0.0454709i	0.460104	−	0.887865i	$-0.347812\pi$
$173$	−1.03590	−	0.598076i	−0.0787579	−	0.0454709i	−0.538862	+	0.842394i	$0.681145\pi$
$174$		0			0
$175$	0.696152	+	2.59808i	0.0526242	+	0.196396i
$176$		0			0
$177$	−10.9019	+	10.9019i	−0.819439	+	0.819439i
$178$		0			0
$179$	−1.03590	−	1.79423i	−0.0774267	−	0.134107i	0.824712	−	0.565552i	$-0.191337\pi$
$179$	−1.03590	−	1.79423i	−0.0774267	−	0.134107i	−0.902139	+	0.431446i	$0.858004\pi$
$180$		0			0
$181$		−	18.9282i		−	1.40692i	−0.710734	−	0.703461i	$-0.751637\pi$
$181$		−	18.9282i		−	1.40692i	0.710734	−	0.703461i	$-0.248363\pi$
$182$		0			0
$183$		−	12.1244i		−	0.896258i
$184$		0			0
$185$	−2.63397	−	4.56218i	−0.193654	−	0.335418i
$186$		0			0
$187$	5.36603	−	5.36603i	0.392403	−	0.392403i
$188$		0			0
$189$	1.20577	+	4.50000i	0.0877070	+	0.327327i
$190$		0			0
$191$	5.89230	+	3.40192i	0.426352	+	0.246155i	0.697791	−	0.716301i	$-0.254166\pi$
$191$	5.89230	+	3.40192i	0.426352	+	0.246155i	−0.271439	+	0.962456i	$0.587500\pi$
$192$		0			0
$193$	25.7224	+	6.89230i	1.85154	+	0.496119i	0.999620	−	0.0275517i	$-0.00877110\pi$
$193$	25.7224	+	6.89230i	1.85154	+	0.496119i	0.851921	+	0.523671i	$0.175438\pi$
$194$		0			0
$195$	4.56218	−	7.56218i	0.326704	−	0.541539i
$196$		0			0
$197$	−1.86603	+	6.96410i	−0.132949	+	0.496172i	−0.999998	−	0.00205102i	$-0.999347\pi$
$197$	−1.86603	+	6.96410i	−0.132949	+	0.496172i	0.867049	+	0.498223i	$0.166014\pi$
$198$		0			0
$199$	4.50000	−	7.79423i	0.318997	−	0.552518i	−0.661282	−	0.750137i	$-0.729987\pi$
$199$	4.50000	−	7.79423i	0.318997	−	0.552518i	0.980279	+	0.197619i	$0.0633208\pi$
$200$		0			0
$201$	20.8923	−	5.59808i	1.47363	−	0.394858i
$202$		0			0
$203$	−5.02628	−	5.02628i	−0.352776	−	0.352776i
$204$		0			0
$205$	10.0981	−	5.83013i	0.705280	−	0.407194i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−11.1962			−0.774454
$210$		0			0
$211$	2.89230	−	1.66987i	0.199114	−	0.114959i	−0.397128	−	0.917763i	$-0.629993\pi$
$211$	2.89230	−	1.66987i	0.199114	−	0.114959i	0.596242	+	0.802804i	$0.296660\pi$
$212$		0			0
$213$	−20.4904	−	20.4904i	−1.40398	−	1.40398i
$214$		0			0
$215$	12.2942	−	3.29423i	0.838459	−	0.224665i
$216$		0			0
$217$	−3.29423	+	5.70577i	−0.223627	+	0.387333i
$218$		0			0
$219$	−1.56218	+	5.83013i	−0.105562	+	0.393963i
$220$		0			0
$221$	5.89230	−	5.66987i	0.396359	−	0.381397i
$222$		0			0
$223$	0.866025	+	0.232051i	0.0579934	+	0.0155393i	0.287699	−	0.957721i	$-0.407110\pi$
$223$	0.866025	+	0.232051i	0.0579934	+	0.0155393i	−0.229706	+	0.973260i	$0.573776\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.52628	−	13.1603i	−0.234047	−	0.873477i	−0.978576	−	0.205886i	$-0.933992\pi$
$227$	−3.52628	−	13.1603i	−0.234047	−	0.873477i	0.744529	−	0.667591i	$-0.232674\pi$
$228$		0			0
$229$	5.00000	−	5.00000i	0.330409	−	0.330409i	−0.522333	−	0.852742i	$-0.674938\pi$
$229$	5.00000	−	5.00000i	0.330409	−	0.330409i	0.852742	+	0.522333i	$0.174938\pi$
$230$		0			0
$231$	2.59808	+	4.50000i	0.170941	+	0.296078i
$232$		0			0
$233$			4.00000i			0.262049i	0.991379	+	0.131024i	$0.0418266\pi$
$233$			4.00000i			0.262049i	−0.991379	+	0.131024i	$0.958173\pi$
$234$		0			0
$235$			8.53590i			0.556821i
$236$		0			0
$237$	3.00000	+	5.19615i	0.194871	+	0.337526i
$238$		0			0
$239$	−1.73205	+	1.73205i	−0.112037	+	0.112037i	−0.760903	−	0.648866i	$-0.775244\pi$
$239$	−1.73205	+	1.73205i	−0.112037	+	0.112037i	0.648866	+	0.760903i	$0.275244\pi$
$240$		0			0
$241$	0.669873	+	2.50000i	0.0431503	+	0.161039i	0.984139	−	0.177399i	$-0.0567682\pi$
$241$	0.669873	+	2.50000i	0.0431503	+	0.161039i	−0.940989	+	0.338438i	$0.890102\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−8.46410	−	2.26795i	−0.540752	−	0.144894i
$246$		0			0
$247$	−12.0622	−	0.232051i	−0.767498	−	0.0147650i
$248$		0			0
$249$	−0.509619	+	1.90192i	−0.0322958	+	0.120530i
$250$		0			0
$251$	8.89230	−	15.4019i	0.561277	−	0.972161i	−0.436108	−	0.899894i	$-0.643643\pi$
$251$	8.89230	−	15.4019i	0.561277	−	0.972161i	0.997385	−	0.0722665i	$-0.0230232\pi$
$252$		0			0
$253$	−9.69615	+	2.59808i	−0.609592	+	0.163340i
$254$		0			0
$255$	3.92820	+	3.92820i	0.245994	+	0.245994i
$256$		0			0
$257$	−13.9641	+	8.06218i	−0.871057	+	0.502905i	−0.867699	−	0.497090i	$-0.834402\pi$
$257$	−13.9641	+	8.06218i	−0.871057	+	0.502905i	−0.00335747	+	0.999994i	$0.501069\pi$
$258$		0			0
$259$	3.33975			0.207522
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−17.8923	+	10.3301i	−1.10329	+	0.636983i	−0.937082	−	0.349108i	$-0.886484\pi$
$263$	−17.8923	+	10.3301i	−1.10329	+	0.636983i	−0.166204	+	0.986091i	$0.553151\pi$
$264$		0			0
$265$	4.92820	+	4.92820i	0.302737	+	0.302737i
$266$		0			0
$267$	−10.1603	+	2.72243i	−0.621797	+	0.166610i
$268$		0			0
$269$	−5.50000	+	9.52628i	−0.335341	+	0.580828i	−0.983550	−	0.180635i	$-0.942185\pi$
$269$	−5.50000	+	9.52628i	−0.335341	+	0.580828i	0.648209	+	0.761462i	$0.275518\pi$
$270$		0			0
$271$	−3.40192	+	12.6962i	−0.206652	+	0.771236i	0.782287	+	0.622918i	$0.214053\pi$
$271$	−3.40192	+	12.6962i	−0.206652	+	0.771236i	−0.988940	+	0.148319i	$0.952614\pi$
$272$		0			0
$273$	2.70577	+	4.90192i	0.163761	+	0.296678i
$274$		0			0
$275$	9.69615	+	2.59808i	0.584700	+	0.156670i
$276$		0			0
$277$	2.42820	+	1.40192i	0.145897	+	0.0842334i	0.571171	−	0.820831i	$-0.306489\pi$
$277$	2.42820	+	1.40192i	0.145897	+	0.0842334i	−0.425275	+	0.905064i	$0.639823\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.464102	+	0.464102i	−0.0276860	+	0.0276860i	−0.720814	−	0.693128i	$-0.756232\pi$
$281$	−0.464102	+	0.464102i	−0.0276860	+	0.0276860i	0.693128	+	0.720814i	$0.256232\pi$
$282$		0			0
$283$	4.03590	+	6.99038i	0.239909	+	0.415535i	0.960688	−	0.277630i	$-0.0895490\pi$
$283$	4.03590	+	6.99038i	0.239909	+	0.415535i	−0.720779	+	0.693165i	$0.756216\pi$
$284$		0			0
$285$		−	8.19615i		−	0.485498i
$286$		0			0
$287$			7.39230i			0.436354i
$288$		0			0
$289$	−5.92820	−	10.2679i	−0.348718	−	0.603997i
$290$		0			0
$291$	−14.3660	+	14.3660i	−0.842151	+	0.842151i
$292$		0			0
$293$	3.06218	+	11.4282i	0.178894	+	0.667643i	0.995855	+	0.0909500i	$0.0289903\pi$
$293$	3.06218	+	11.4282i	0.178894	+	0.667643i	−0.816961	+	0.576693i	$0.804343\pi$
$294$		0			0
$295$	10.9019	+	6.29423i	0.634735	+	0.366464i
$296$		0			0
$297$	16.7942	+	4.50000i	0.974500	+	0.261116i
$298$		0			0
$299$	−10.5000	+	2.59808i	−0.607231	+	0.150251i
$300$		0			0
$301$	−2.08846	+	7.79423i	−0.120377	+	0.449252i
$302$		0			0
$303$	−10.9641	+	18.9904i	−0.629871	+	1.09097i
$304$		0			0
$305$	−9.56218	+	2.56218i	−0.547529	+	0.146710i
$306$		0			0
$307$	−7.73205	−	7.73205i	−0.441291	−	0.441291i	0.451154	−	0.892446i	$-0.351012\pi$
$307$	−7.73205	−	7.73205i	−0.441291	−	0.441291i	−0.892446	+	0.451154i	$0.851012\pi$
$308$		0			0
$309$	7.60770	−	4.39230i	0.432787	−	0.249869i
$310$		0			0
$311$	−5.07180			−0.287595			−0.143798	−	0.989607i	$-0.545931\pi$
$311$	−5.07180			−0.287595			−0.143798	+	0.989607i	$0.545931\pi$
$312$		0			0
$313$	6.00000			0.339140			0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000			0.339140			0.169570	+	0.985518i	$0.445762\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	17.3923	+	17.3923i	0.976849	+	0.976849i	0.999738	−	0.0228889i	$-0.00728639\pi$
$317$	17.3923	+	17.3923i	0.976849	+	0.976849i	−0.0228889	+	0.999738i	$0.507286\pi$
$318$		0			0
$319$	−25.6244	+	6.86603i	−1.43469	+	0.384424i
$320$		0			0
$321$	17.8923	−	30.9904i	0.998651	−	1.72971i
$322$		0			0
$323$	1.96410	−	7.33013i	0.109286	−	0.407859i
$324$		0			0
$325$	10.3923	+	3.00000i	0.576461	+	0.166410i
$326$		0			0
$327$	−2.36603	−	0.633975i	−0.130842	−	0.0350589i
$328$		0			0
$329$	−4.68653	−	2.70577i	−0.258377	−	0.149174i
$330$		0			0
$331$	4.33013	+	16.1603i	0.238005	+	0.888248i	0.976771	+	0.214286i	$0.0687423\pi$
$331$	4.33013	+	16.1603i	0.238005	+	0.888248i	−0.738766	+	0.673962i	$0.764591\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−8.83013	−	15.2942i	−0.482441	−	0.835613i
$336$		0			0
$337$			30.9282i			1.68477i	0.538879	+	0.842383i	$0.318848\pi$
$337$			30.9282i			1.68477i	−0.538879	+	0.842383i	$0.681152\pi$
$338$		0			0
$339$		−	15.3397i		−	0.833141i
$340$		0			0
$341$	12.2942	+	21.2942i	0.665770	+	1.15315i
$342$		0			0
$343$	8.36603	−	8.36603i	0.451723	−	0.451723i
$344$		0			0
$345$	−1.90192	−	7.09808i	−0.102396	−	0.382148i
$346$		0			0
$347$	−0.107695	−	0.0621778i	−0.00578138	−	0.00333788i	0.497107	−	0.867690i	$-0.334396\pi$
$347$	−0.107695	−	0.0621778i	−0.00578138	−	0.00333788i	−0.502888	+	0.864352i	$0.667729\pi$
$348$		0			0
$349$	−5.06218	−	1.35641i	−0.270972	−	0.0726068i	0.120774	−	0.992680i	$-0.461462\pi$
$349$	−5.06218	−	1.35641i	−0.270972	−	0.0726068i	−0.391746	+	0.920073i	$0.628129\pi$
$350$		0			0
$351$	18.0000	+	5.19615i	0.960769	+	0.277350i
$352$		0			0
$353$	8.13397	−	30.3564i	0.432928	−	1.61571i	−0.313049	−	0.949737i	$-0.601351\pi$
$353$	8.13397	−	30.3564i	0.432928	−	1.61571i	0.745977	−	0.665972i	$-0.231983\pi$
$354$		0			0
$355$	−11.8301	+	20.4904i	−0.627878	+	1.08752i
$356$		0			0
$357$	−3.40192	+	0.911543i	−0.180049	+	0.0482440i
$358$		0			0
$359$	−5.19615	−	5.19615i	−0.274242	−	0.274242i	0.556563	−	0.830805i	$-0.312120\pi$
$359$	−5.19615	−	5.19615i	−0.274242	−	0.274242i	−0.830805	+	0.556563i	$0.812120\pi$
$360$		0			0
$361$	6.75833	−	3.90192i	0.355702	−	0.205364i
$362$		0			0
$363$	0.339746			0.0178320
$364$		0			0
$365$	4.92820			0.257954
$366$		0			0
$367$	26.8923	−	15.5263i	1.40377	−	0.810465i	0.408990	−	0.912539i	$-0.365881\pi$
$367$	26.8923	−	15.5263i	1.40377	−	0.810465i	0.994777	+	0.102074i	$0.0325477\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−4.26795	+	1.14359i	−0.221581	+	0.0593724i
$372$		0			0
$373$	−4.03590	+	6.99038i	−0.208971	+	0.361948i	−0.951391	−	0.307987i	$-0.900345\pi$
$373$	−4.03590	+	6.99038i	−0.208971	+	0.361948i	0.742420	+	0.669935i	$0.233678\pi$
$374$		0			0
$375$	−5.07180	+	18.9282i	−0.261906	+	0.977448i
$376$		0			0
$377$	−27.7487	+	6.86603i	−1.42913	+	0.353618i
$378$		0			0
$379$	−15.5263	−	4.16025i	−0.797531	−	0.213698i	−0.163032	−	0.986621i	$-0.552127\pi$
$379$	−15.5263	−	4.16025i	−0.797531	−	0.213698i	−0.634500	+	0.772923i	$0.718794\pi$
$380$		0			0
$381$	5.89230	+	3.40192i	0.301872	+	0.174286i
$382$		0			0
$383$	−8.59808	−	32.0885i	−0.439341	−	1.63964i	−0.730459	−	0.682956i	$-0.760694\pi$
$383$	−8.59808	−	32.0885i	−0.439341	−	1.63964i	0.291118	−	0.956687i	$-0.405973\pi$
$384$		0			0
$385$	3.00000	−	3.00000i	0.152894	−	0.152894i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	14.9282i		−	0.756890i	−0.925624	−	0.378445i	$-0.876459\pi$
$389$		−	14.9282i		−	0.756890i	0.925624	−	0.378445i	$-0.123541\pi$
$390$		0			0
$391$		−	6.80385i		−	0.344085i
$392$		0			0
$393$	−13.3923	−	23.1962i	−0.675552	−	1.17009i
$394$		0			0
$395$	3.46410	−	3.46410i	0.174298	−	0.174298i
$396$		0			0
$397$	2.52628	+	9.42820i	0.126790	+	0.473188i	0.999897	−	0.0143410i	$-0.00456503\pi$
$397$	2.52628	+	9.42820i	0.126790	+	0.473188i	−0.873107	+	0.487529i	$0.837898\pi$
$398$		0			0
$399$	4.50000	+	2.59808i	0.225282	+	0.130066i
$400$		0			0
$401$	−27.4545	−	7.35641i	−1.37101	−	0.367361i	−0.503163	−	0.864191i	$-0.667831\pi$
$401$	−27.4545	−	7.35641i	−1.37101	−	0.367361i	−0.867848	+	0.496830i	$0.834497\pi$
$402$		0			0
$403$	12.8038	+	23.1962i	0.637805	+	1.15548i
$404$		0			0
$405$	−3.29423	+	12.2942i	−0.163692	+	0.610905i
$406$		0			0
$407$	6.23205	−	10.7942i	0.308911	−	0.535050i
$408$		0			0
$409$	−17.9904	+	4.82051i	−0.889567	+	0.238359i	−0.674530	−	0.738247i	$-0.735654\pi$
$409$	−17.9904	+	4.82051i	−0.889567	+	0.238359i	−0.215037	+	0.976606i	$0.568987\pi$
$410$		0			0
$411$	6.29423	+	6.29423i	0.310471	+	0.310471i
$412$		0			0
$413$	−6.91154	+	3.99038i	−0.340095	+	0.196354i
$414$		0			0
$415$	1.60770			0.0789187
$416$		0			0
$417$	29.7846			1.45856
$418$		0			0
$419$	20.8923	−	12.0622i	1.02066	−	0.589276i	0.106362	−	0.994327i	$-0.466080\pi$
$419$	20.8923	−	12.0622i	1.02066	−	0.589276i	0.914294	+	0.405052i	$0.132746\pi$
$420$		0			0
$421$	−1.92820	−	1.92820i	−0.0939749	−	0.0939749i	0.658556	−	0.752531i	$-0.271167\pi$
$421$	−1.92820	−	1.92820i	−0.0939749	−	0.0939749i	−0.752531	+	0.658556i	$0.771167\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3.40192	+	5.89230i	−0.165018	+	0.285819i
$426$		0			0
$427$	1.62436	−	6.06218i	0.0786081	−	0.293369i
$428$		0			0
$429$	20.8923	+	0.401924i	1.00869	+	0.0194051i
$430$		0			0
$431$	25.7942	+	6.91154i	1.24246	+	0.332917i	0.819421	−	0.573192i	$-0.194295\pi$
$431$	25.7942	+	6.91154i	1.24246	+	0.332917i	0.423043	+	0.906109i	$0.360962\pi$
$432$		0			0
$433$	−8.89230	−	5.13397i	−0.427337	−	0.246723i	0.270875	−	0.962615i	$-0.412687\pi$
$433$	−8.89230	−	5.13397i	−0.427337	−	0.246723i	−0.698211	+	0.715892i	$0.746020\pi$
$434$		0			0
$435$	−5.02628	−	18.7583i	−0.240992	−	0.899393i
$436$		0			0
$437$	−7.09808	+	7.09808i	−0.339547	+	0.339547i
$438$		0			0
$439$	4.96410	+	8.59808i	0.236924	+	0.410364i	0.959830	−	0.280582i	$-0.0905275\pi$
$439$	4.96410	+	8.59808i	0.236924	+	0.410364i	−0.722906	+	0.690946i	$0.757194\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			1.60770i			0.0763839i	0.999270	+	0.0381920i	$0.0121598\pi$
$443$			1.60770i			0.0763839i	−0.999270	+	0.0381920i	$0.987840\pi$
$444$		0			0
$445$	4.29423	+	7.43782i	0.203566	+	0.352587i
$446$		0			0
$447$	−9.29423	+	9.29423i	−0.439602	+	0.439602i
$448$		0			0
$449$	−9.47372	−	35.3564i	−0.447093	−	1.66857i	−0.710352	−	0.703847i	$-0.751464\pi$
$449$	−9.47372	−	35.3564i	−0.447093	−	1.66857i	0.263259	−	0.964725i	$-0.415203\pi$
$450$		0			0
$451$	23.8923	+	13.7942i	1.12504	+	0.649545i
$452$		0			0
$453$	−32.4904	−	8.70577i	−1.52653	−	0.409033i
$454$		0			0
$455$	3.29423	−	3.16987i	0.154436	−	0.148606i
$456$		0			0
$457$	10.3827	−	38.7487i	0.485682	−	1.81259i	−0.0912904	−	0.995824i	$-0.529099\pi$
$457$	10.3827	−	38.7487i	0.485682	−	1.81259i	0.576972	−	0.816764i	$-0.304234\pi$
$458$		0			0
$459$	−5.89230	+	10.2058i	−0.275029	+	0.476365i
$460$		0			0
$461$	−39.4545	+	10.5718i	−1.83758	+	0.492378i	−0.998654	−	0.0518700i	$-0.983482\pi$
$461$	−39.4545	+	10.5718i	−1.83758	+	0.492378i	−0.838925	+	0.544248i	$0.816815\pi$
$462$		0			0
$463$	−22.2679	−	22.2679i	−1.03488	−	1.03488i	−0.999369	−	0.0355100i	$-0.988694\pi$
$463$	−22.2679	−	22.2679i	−1.03488	−	1.03488i	−0.0355100	−	0.999369i	$-0.511306\pi$
$464$		0			0
$465$	−15.5885	+	9.00000i	−0.722897	+	0.417365i
$466$		0			0
$467$	−13.8564			−0.641198			−0.320599	−	0.947215i	$-0.603884\pi$
$467$	−13.8564			−0.641198			−0.320599	+	0.947215i	$0.603884\pi$
$468$		0			0
$469$	11.1962			0.516990
$470$		0			0
$471$	29.7846	−	17.1962i	1.37240	−	0.792357i
$472$		0			0
$473$	21.2942	+	21.2942i	0.979110	+	0.979110i
$474$		0			0
$475$	9.69615	−	2.59808i	0.444890	−	0.119208i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	9.52628	−	35.5526i	0.435267	−	1.62444i	−0.305160	−	0.952301i	$-0.598710\pi$
$479$	9.52628	−	35.5526i	0.435267	−	1.62444i	0.740427	−	0.672137i	$-0.234623\pi$
$480$		0			0
$481$	6.93782	−	11.5000i	0.316337	−	0.524355i
$482$		0			0
$483$	4.50000	+	1.20577i	0.204757	+	0.0548645i
$484$		0			0
$485$	14.3660	+	8.29423i	0.652328	+	0.376622i
$486$		0			0
$487$	2.47372	+	9.23205i	0.112095	+	0.418344i	0.999053	−	0.0435055i	$-0.0138526\pi$
$487$	2.47372	+	9.23205i	0.112095	+	0.418344i	−0.886958	+	0.461850i	$0.847186\pi$
$488$		0			0
$489$	−15.2942	+	15.2942i	−0.691629	+	0.691629i
$490$		0			0
$491$	−13.9641	−	24.1865i	−0.630191	−	1.09152i	−0.987512	−	0.157541i	$-0.949643\pi$
$491$	−13.9641	−	24.1865i	−0.630191	−	1.09152i	0.357321	−	0.933982i	$-0.383690\pi$
$492$		0			0
$493$		−	17.9808i		−	0.809813i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−7.50000	−	12.9904i	−0.336421	−	0.582698i
$498$		0			0
$499$	−4.26795	+	4.26795i	−0.191060	+	0.191060i	−0.796154	−	0.605094i	$-0.793135\pi$
$499$	−4.26795	+	4.26795i	−0.191060	+	0.191060i	0.605094	+	0.796154i	$0.293135\pi$
$500$		0			0
$501$	7.28461	+	27.1865i	0.325452	+	1.21460i
$502$		0			0
$503$	−10.5000	−	6.06218i	−0.468172	−	0.270299i	0.247302	−	0.968938i	$-0.420456\pi$
$503$	−10.5000	−	6.06218i	−0.468172	−	0.270299i	−0.715474	+	0.698639i	$0.753789\pi$
$504$		0			0
$505$	17.2942	+	4.63397i	0.769583	+	0.206209i
$506$		0			0
$507$	22.5000	+	0.866025i	0.999260	+	0.0384615i
$508$		0			0
$509$	8.52628	−	31.8205i	0.377921	−	1.41042i	−0.471109	−	0.882075i	$-0.656146\pi$
$509$	8.52628	−	31.8205i	0.377921	−	1.41042i	0.849030	−	0.528344i	$-0.177187\pi$
$510$		0			0
$511$	−1.56218	+	2.70577i	−0.0691067	+	0.119696i
$512$		0			0
$513$	16.7942	−	4.50000i	0.741483	−	0.198680i
$514$		0			0
$515$	−5.07180	−	5.07180i	−0.223490	−	0.223490i
$516$		0			0
$517$	−17.4904	+	10.0981i	−0.769226	+	0.444113i
$518$		0			0
$519$	2.07180			0.0909418
$520$		0			0
$521$	8.14359			0.356777			0.178389	−	0.983960i	$-0.442912\pi$
$521$	8.14359			0.356777			0.178389	+	0.983960i	$0.442912\pi$
$522$		0			0
$523$	20.8923	−	12.0622i	0.913557	−	0.527442i	0.0319829	−	0.999488i	$-0.489818\pi$
$523$	20.8923	−	12.0622i	0.913557	−	0.527442i	0.881574	+	0.472046i	$0.156484\pi$
$524$		0			0
$525$	−3.29423	−	3.29423i	−0.143772	−	0.143772i
$526$		0			0
$527$	−16.0981	+	4.31347i	−0.701243	+	0.187898i
$528$		0			0
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	25.4545	+	15.3564i	1.10256	+	0.665160i
$534$		0			0
$535$	−28.2224	−	7.56218i	−1.22016	−	0.326941i
$536$		0			0
$537$	3.10770	+	1.79423i	0.134107	+	0.0774267i
$538$		0			0
$539$	−5.36603	−	20.0263i	−0.231131	−	0.862593i
$540$		0			0
$541$	19.5359	−	19.5359i	0.839914	−	0.839914i	−0.148933	−	0.988847i	$-0.547584\pi$
$541$	19.5359	−	19.5359i	0.839914	−	0.839914i	0.988847	+	0.148933i	$0.0475840\pi$
$542$		0			0
$543$	16.3923	+	28.3923i	0.703461	+	1.21843i
$544$		0			0
$545$			2.00000i			0.0856706i
$546$		0			0
$547$		−	13.6077i		−	0.581823i	−0.956750	−	0.290912i	$-0.906041\pi$
$547$		−	13.6077i		−	0.581823i	0.956750	−	0.290912i	$-0.0939585\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−18.7583	+	18.7583i	−0.799132	+	0.799132i
$552$		0			0
$553$	0.803848	+	3.00000i	0.0341831	+	0.127573i
$554$		0			0
$555$	7.90192	+	4.56218i	0.335418	+	0.193654i
$556$		0			0
$557$	3.86603	+	1.03590i	0.163809	+	0.0438924i	0.339791	−	0.940501i	$-0.389644\pi$
$557$	3.86603	+	1.03590i	0.163809	+	0.0438924i	−0.175983	+	0.984393i	$0.556310\pi$
$558$		0			0
$559$	22.5000	+	23.3827i	0.951649	+	0.988982i
$560$		0			0
$561$	−3.40192	+	12.6962i	−0.143629	+	0.536032i
$562$		0			0
$563$	−16.0359	+	27.7750i	−0.675833	+	1.17058i	0.300392	+	0.953816i	$0.402882\pi$
$563$	−16.0359	+	27.7750i	−0.675833	+	1.17058i	−0.976225	+	0.216761i	$0.930451\pi$
$564$		0			0
$565$	−12.0981	+	3.24167i	−0.508970	+	0.136378i
$566$		0			0
$567$	−5.70577	−	5.70577i	−0.239620	−	0.239620i
$568$		0			0
$569$	−29.4282	+	16.9904i	−1.23369	+	0.712274i	−0.967798	−	0.251728i	$-0.919001\pi$
$569$	−29.4282	+	16.9904i	−1.23369	+	0.712274i	−0.265896	+	0.964002i	$0.585668\pi$
$570$		0			0
$571$	−30.9282			−1.29431			−0.647153	−	0.762361i	$-0.724040\pi$
$571$	−30.9282			−1.29431			−0.647153	+	0.762361i	$0.724040\pi$
$572$		0			0
$573$	−11.7846			−0.492309
$574$		0			0
$575$	7.79423	−	4.50000i	0.325042	−	0.187663i
$576$		0			0
$577$	2.46410	+	2.46410i	0.102582	+	0.102582i	0.756535	−	0.653953i	$-0.226891\pi$
$577$	2.46410	+	2.46410i	0.102582	+	0.102582i	−0.653953	+	0.756535i	$0.726891\pi$
$578$		0			0
$579$	−44.5526	+	11.9378i	−1.85154	+	0.496119i
$580$		0			0
$581$	−0.509619	+	0.882686i	−0.0211426	+	0.0366200i
$582$		0			0
$583$	−4.26795	+	15.9282i	−0.176760	+	0.659679i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	20.7224	+	5.55256i	0.855306	+	0.229179i	0.659723	−	0.751509i	$-0.270673\pi$
$587$	20.7224	+	5.55256i	0.855306	+	0.229179i	0.195583	+	0.980687i	$0.437340\pi$
$588$		0			0
$589$	21.2942	+	12.2942i	0.877413	+	0.506575i
$590$		0			0
$591$	−3.23205	−	12.0622i	−0.132949	−	0.496172i
$592$		0			0
$593$	−6.60770	+	6.60770i	−0.271346	+	0.271346i	−0.829642	−	0.558296i	$-0.811455\pi$
$593$	−6.60770	+	6.60770i	−0.271346	+	0.271346i	0.558296	+	0.829642i	$0.311455\pi$
$594$		0			0
$595$	1.43782	+	2.49038i	0.0589450	+	0.102096i
$596$		0			0
$597$			15.5885i			0.637993i
$598$		0			0
$599$			48.2487i			1.97139i	0.168542	+	0.985694i	$0.446094\pi$
$599$			48.2487i			1.97139i	−0.168542	+	0.985694i	$0.553906\pi$
$600$		0			0
$601$	−4.03590	−	6.99038i	−0.164628	−	0.285144i	0.771895	−	0.635750i	$-0.219309\pi$
$601$	−4.03590	−	6.99038i	−0.164628	−	0.285144i	−0.936523	+	0.350606i	$0.885976\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.0717968	−	0.267949i	−0.00291895	−	0.0108937i
$606$		0			0
$607$	16.2846	+	9.40192i	0.660972	+	0.381612i	0.792647	−	0.609681i	$-0.208702\pi$
$607$	16.2846	+	9.40192i	0.660972	+	0.381612i	−0.131675	+	0.991293i	$0.542036\pi$
$608$		0			0
$609$	11.8923	+	3.18653i	0.481901	+	0.129125i
$610$		0			0
$611$	−19.0526	+	10.5167i	−0.770784	+	0.425459i
$612$		0			0
$613$	−2.79423	+	10.4282i	−0.112858	+	0.421191i	−0.999118	−	0.0419971i	$-0.986628\pi$
$613$	−2.79423	+	10.4282i	−0.112858	+	0.421191i	0.886260	+	0.463188i	$0.153295\pi$
$614$		0			0
$615$	−10.0981	+	17.4904i	−0.407194	+	0.705280i
$616$		0			0
$617$	−6.52628	+	1.74871i	−0.262738	+	0.0704005i	−0.387783	−	0.921751i	$-0.626759\pi$
$617$	−6.52628	+	1.74871i	−0.262738	+	0.0704005i	0.125045	+	0.992151i	$0.460092\pi$
$618$		0			0
$619$	11.1962	+	11.1962i	0.450011	+	0.450011i	0.895358	−	0.445347i	$-0.146920\pi$
$619$	11.1962	+	11.1962i	0.450011	+	0.450011i	−0.445347	+	0.895358i	$0.646920\pi$
$620$		0			0
$621$	13.5000	−	7.79423i	0.541736	−	0.312772i
$622$		0			0
$623$	−5.44486			−0.218144
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	16.7942	−	9.69615i	0.670697	−	0.387227i
$628$		0			0
$629$	5.97372	+	5.97372i	0.238188	+	0.238188i
$630$		0			0
$631$	−20.7224	+	5.55256i	−0.824947	+	0.221044i	−0.646508	−	0.762907i	$-0.723771\pi$
$631$	−20.7224	+	5.55256i	−0.824947	+	0.221044i	−0.178439	+	0.983951i	$0.557105\pi$
$632$		0			0
$633$	−2.89230	+	5.00962i	−0.114959	+	0.199114i
$634$		0			0
$635$	1.43782	−	5.36603i	0.0570582	−	0.212944i
$636$		0			0
$637$	−5.36603	−	21.6865i	−0.212610	−	0.859252i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	4.96410	+	2.86603i	0.196070	+	0.113201i	0.594821	−	0.803858i	$-0.297223\pi$
$641$	4.96410	+	2.86603i	0.196070	+	0.113201i	−0.398751	+	0.917059i	$0.630556\pi$
$642$		0			0
$643$	−7.66987	−	28.6244i	−0.302470	−	1.12883i	−0.935101	−	0.354381i	$-0.884692\pi$
$643$	−7.66987	−	28.6244i	−0.302470	−	1.12883i	0.632631	−	0.774453i	$-0.281975\pi$
$644$		0			0
$645$	−15.5885	+	15.5885i	−0.613795	+	0.613795i
$646$		0			0
$647$	−11.4282	−	19.7942i	−0.449289	−	0.778191i	0.549051	−	0.835789i	$-0.314989\pi$
$647$	−11.4282	−	19.7942i	−0.449289	−	0.778191i	−0.998340	+	0.0575975i	$0.981656\pi$
$648$		0			0
$649$			29.7846i			1.16915i
$650$		0			0
$651$		−	11.4115i		−	0.447254i
$652$		0			0
$653$	−3.50000	−	6.06218i	−0.136966	−	0.237231i	0.789381	−	0.613904i	$-0.210402\pi$
$653$	−3.50000	−	6.06218i	−0.136966	−	0.237231i	−0.926347	+	0.376672i	$0.877068\pi$
$654$		0			0
$655$	−15.4641	+	15.4641i	−0.604232	+	0.604232i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	16.2846	+	9.40192i	0.634358	+	0.366247i	0.782438	−	0.622728i	$-0.213976\pi$
$659$	16.2846	+	9.40192i	0.634358	+	0.366247i	−0.148080	+	0.988975i	$0.547309\pi$
$660$		0			0
$661$	−35.9904	−	9.64359i	−1.39986	−	0.375092i	−0.521568	−	0.853210i	$-0.674653\pi$
$661$	−35.9904	−	9.64359i	−1.39986	−	0.375092i	−0.878296	+	0.478118i	$0.841319\pi$
$662$		0			0
$663$	−3.92820	+	13.6077i	−0.152559	+	0.528479i
$664$		0			0
$665$	1.09808	−	4.09808i	0.0425816	−	0.158917i
$666$		0			0
$667$	−11.8923	+	20.5981i	−0.460472	+	0.797561i
$668$		0			0
$669$	−1.50000	+	0.401924i	−0.0579934	+	0.0155393i
$670$		0			0
$671$	−16.5622	−	16.5622i	−0.639376	−	0.639376i
$672$		0			0
$673$	27.3564	−	15.7942i	1.05451	−	0.608823i	0.130603	−	0.991435i	$-0.458309\pi$
$673$	27.3564	−	15.7942i	1.05451	−	0.608823i	0.923909	+	0.382612i	$0.124975\pi$
$674$		0			0
$675$	−15.5885			−0.600000
$676$		0			0
$677$	26.0000			0.999261			0.499631	−	0.866239i	$-0.333469\pi$
$677$	26.0000			0.999261			0.499631	+	0.866239i	$0.333469\pi$
$678$		0			0
$679$	−9.10770	+	5.25833i	−0.349521	+	0.201796i
$680$		0			0
$681$	16.6865	+	16.6865i	0.639429	+	0.639429i
$682$		0			0
$683$	22.4545	−	6.01666i	0.859197	−	0.230221i	0.197786	−	0.980245i	$-0.436625\pi$
$683$	22.4545	−	6.01666i	0.859197	−	0.230221i	0.661411	+	0.750024i	$0.269958\pi$
$684$		0			0
$685$	3.63397	−	6.29423i	0.138847	−	0.240490i
$686$		0			0
$687$	−3.16987	+	11.8301i	−0.120938	+	0.451347i
$688$		0			0
$689$	−4.92820	+	17.0718i	−0.187750	+	0.650384i
$690$		0			0
$691$	29.2583	+	7.83975i	1.11304	+	0.298238i	0.768064	−	0.640374i	$-0.221220\pi$
$691$	29.2583	+	7.83975i	1.11304	+	0.298238i	0.344976	+	0.938612i	$0.387887\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−6.29423	−	23.4904i	−0.238754	−	0.891041i
$696$		0			0
$697$	−13.2224	+	13.2224i	−0.500835	+	0.500835i
$698$		0			0
$699$	−3.46410	−	6.00000i	−0.131024	−	0.226941i
$700$		0			0
$701$		−	49.5692i		−	1.87220i	−0.351729	−	0.936102i	$-0.614406\pi$
$701$		−	49.5692i		−	1.87220i	0.351729	−	0.936102i	$-0.385594\pi$
$702$		0			0
$703$		−	12.4641i		−	0.470092i
$704$		0			0
$705$	−7.39230	−	12.8038i	−0.278410	−	0.482221i
$706$		0			0
$707$	−8.02628	+	8.02628i	−0.301859	+	0.301859i
$708$		0			0
$709$	6.13397	+	22.8923i	0.230366	+	0.859739i	0.980183	+	0.198093i	$0.0634749\pi$
$709$	6.13397	+	22.8923i	0.230366	+	0.859739i	−0.749817	+	0.661645i	$0.769858\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	21.2942	+	5.70577i	0.797475	+	0.213683i
$714$		0			0
$715$	−4.09808	−	16.5622i	−0.153259	−	0.619390i
$716$		0			0
$717$	1.09808	−	4.09808i	0.0410084	−	0.153045i
$718$		0			0
$719$	9.82051	−	17.0096i	0.366243	−	0.634352i	−0.622732	−	0.782435i	$-0.713977\pi$
$719$	9.82051	−	17.0096i	0.366243	−	0.634352i	0.988975	+	0.148084i	$0.0473105\pi$
$720$		0			0
$721$	4.39230	−	1.17691i	0.163578	−	0.0438306i
$722$		0			0
$723$	−3.16987	−	3.16987i	−0.117889	−	0.117889i
$724$		0			0
$725$	20.5981	−	11.8923i	0.764993	−	0.441669i
$726$		0			0
$727$	37.8564			1.40402			0.702008	−	0.712169i	$-0.252287\pi$
$727$	37.8564			1.40402			0.702008	+	0.712169i	$0.252287\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−17.6769	+	10.2058i	−0.653804	+	0.377474i
$732$		0			0
$733$	4.32051	+	4.32051i	0.159582	+	0.159582i	0.782381	−	0.622800i	$-0.214005\pi$
$733$	4.32051	+	4.32051i	0.159582	+	0.159582i	−0.622800	+	0.782381i	$0.714005\pi$
$734$		0			0
$735$	14.6603	−	3.92820i	0.540752	−	0.144894i
$736$		0			0
$737$	20.8923	−	36.1865i	0.769578	−	1.33295i
$738$		0			0
$739$	1.91858	−	7.16025i	0.0705763	−	0.263394i	−0.921618	−	0.388099i	$-0.873132\pi$
$739$	1.91858	−	7.16025i	0.0705763	−	0.263394i	0.992194	+	0.124705i	$0.0397985\pi$
$740$		0			0
$741$	18.2942	−	10.0981i	0.672055	−	0.370962i
$742$		0			0
$743$	32.7224	+	8.76795i	1.20047	+	0.321665i	0.803016	−	0.595957i	$-0.203227\pi$
$743$	32.7224	+	8.76795i	1.20047	+	0.321665i	0.397454	+	0.917622i	$0.369894\pi$
$744$		0			0
$745$	9.29423	+	5.36603i	0.340514	+	0.196596i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	13.0981	−	13.0981i	0.478593	−	0.478593i
$750$		0			0
$751$	−19.9641	−	34.5788i	−0.728500	−	1.26180i	−0.957517	−	0.288377i	$-0.906884\pi$
$751$	−19.9641	−	34.5788i	−0.728500	−	1.26180i	0.229016	−	0.973423i	$-0.426449\pi$
$752$		0			0
$753$			30.8038i			1.12255i
$754$		0			0
$755$			27.4641i			0.999521i
$756$		0			0
$757$	−16.2846	−	28.2058i	−0.591874	−	1.02516i	−0.993980	−	0.109563i	$-0.965055\pi$
$757$	−16.2846	−	28.2058i	−0.591874	−	1.02516i	0.402106	−	0.915593i	$-0.368278\pi$
$758$		0			0
$759$	12.2942	−	12.2942i	0.446252	−	0.446252i
$760$		0			0
$761$	11.5981	+	43.2846i	0.420430	+	1.56907i	0.773705	+	0.633546i	$0.218401\pi$
$761$	11.5981	+	43.2846i	0.420430	+	1.56907i	−0.353275	+	0.935520i	$0.614932\pi$
$762$		0			0
$763$	−1.09808	−	0.633975i	−0.0397530	−	0.0229514i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.617314	+	32.0885i	−0.0222899	+	1.15865i
$768$		0			0
$769$	−5.08142	+	18.9641i	−0.183241	+	0.683863i	0.811760	+	0.583991i	$0.198510\pi$
$769$	−5.08142	+	18.9641i	−0.183241	+	0.683863i	−0.995000	+	0.0998715i	$0.968157\pi$
$770$		0			0
$771$	13.9641	−	24.1865i	0.502905	−	0.871057i
$772$		0			0
$773$	−21.9904	+	5.89230i	−0.790939	+	0.211931i	−0.631602	−	0.775293i	$-0.717602\pi$
$773$	−21.9904	+	5.89230i	−0.790939	+	0.211931i	−0.159337	+	0.987224i	$0.550936\pi$
$774$		0			0
$775$	−15.5885	−	15.5885i	−0.559954	−	0.559954i
$776$		0			0
$777$	−5.00962	+	2.89230i	−0.179719	+	0.103761i
$778$		0			0
$779$	27.5885			0.988459
$780$		0			0
$781$	−55.9808			−2.00315
$782$		0			0
$783$	35.6769	−	20.5981i	1.27499	−	0.736115i
$784$		0			0
$785$	−19.8564	−	19.8564i	−0.708706	−	0.708706i
$786$		0			0
$787$	−42.1865	+	11.3038i	−1.50379	+	0.402939i	−0.914367	−	0.404887i	$-0.867311\pi$
$787$	−42.1865	+	11.3038i	−1.50379	+	0.402939i	−0.589421	+	0.807826i	$0.700644\pi$
$788$		0			0
$789$	17.8923	−	30.9904i	0.636983	−	1.10329i
$790$		0			0
$791$	2.05514	−	7.66987i	0.0730722	−	0.272709i
$792$		0			0
$793$	−17.5000	−	18.1865i	−0.621443	−	0.645823i
$794$		0			0
$795$	−11.6603	−	3.12436i	−0.413547	−	0.110809i
$796$		0			0
$797$	−29.4282	−	16.9904i	−1.04240	−	0.601830i	−0.121888	−	0.992544i	$-0.538895\pi$
$797$	−29.4282	−	16.9904i	−1.04240	−	0.601830i	−0.920512	+	0.390714i	$0.872228\pi$
$798$		0			0
$799$	−3.54294	−	13.2224i	−0.125340	−	0.467776i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	5.83013	+	10.0981i	0.205741	+	0.356353i
$804$		0			0
$805$		−	3.80385i		−	0.134068i
$806$		0			0
$807$		−	19.0526i		−	0.670682i
$808$		0			0
$809$	−4.42820	−	7.66987i	−0.155687	−	0.269658i	0.777622	−	0.628732i	$-0.216426\pi$
$809$	−4.42820	−	7.66987i	−0.155687	−	0.269658i	−0.933309	+	0.359074i	$0.883093\pi$
$810$		0			0
$811$	12.1244	−	12.1244i	0.425744	−	0.425744i	−0.461432	−	0.887176i	$-0.652664\pi$
$811$	12.1244	−	12.1244i	0.425744	−	0.425744i	0.887176	+	0.461432i	$0.152664\pi$
$812$		0			0
$813$	−5.89230	−	21.9904i	−0.206652	−	0.771236i
$814$		0			0
$815$	15.2942	+	8.83013i	0.535733	+	0.309306i
$816$		0			0
$817$	29.0885	+	7.79423i	1.01768	+	0.272686i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−9.18653	+	34.2846i	−0.320612	+	1.19654i	0.598037	+	0.801468i	$0.295947\pi$
$821$	−9.18653	+	34.2846i	−0.320612	+	1.19654i	−0.918650	+	0.395073i	$0.870719\pi$
$822$		0			0
$823$	8.89230	−	15.4019i	0.309966	−	0.536877i	−0.668388	−	0.743812i	$-0.733016\pi$
$823$	8.89230	−	15.4019i	0.309966	−	0.536877i	0.978355	+	0.206935i	$0.0663489\pi$
$824$		0			0
$825$	−16.7942	+	4.50000i	−0.584700	+	0.156670i
$826$		0			0
$827$	23.1962	+	23.1962i	0.806609	+	0.806609i	0.984119	−	0.177510i	$-0.0568041\pi$
$827$	23.1962	+	23.1962i	0.806609	+	0.806609i	−0.177510	+	0.984119i	$0.556804\pi$
$828$		0			0
$829$	16.9641	−	9.79423i	0.589188	−	0.340168i	−0.175589	−	0.984464i	$-0.556183\pi$
$829$	16.9641	−	9.79423i	0.589188	−	0.340168i	0.764776	+	0.644296i	$0.222850\pi$
$830$		0			0
$831$	−4.85641			−0.168467
$832$		0			0
$833$	14.0526			0.486892
$834$		0			0
$835$	19.9019	−	11.4904i	0.688734	−	0.397641i
$836$		0			0
$837$	−27.0000	−	27.0000i	−0.933257	−	0.933257i
$838$		0			0
$839$	37.9186	−	10.1603i	1.30909	−	0.350771i	0.464213	−	0.885724i	$-0.346337\pi$
$839$	37.9186	−	10.1603i	1.30909	−	0.350771i	0.844882	+	0.534953i	$0.179671\pi$
$840$		0			0
$841$	−16.9282	+	29.3205i	−0.583731	+	1.01105i
$842$		0			0
$843$	0.294229	−	1.09808i	0.0101338	−	0.0378198i
$844$		0			0
$845$	−4.07180	−	17.9282i	−0.140074	−	0.616749i
$846$		0			0
$847$	0.169873	+	0.0455173i	0.00583690	+	0.00156399i
$848$		0			0
$849$	−12.1077	−	6.99038i	−0.415535	−	0.239909i
$850$		0			0
$851$	−2.89230	−	10.7942i	−0.0991469	−	0.370021i
$852$		0			0
$853$	−20.8564	+	20.8564i	−0.714110	+	0.714110i	−0.967392	−	0.253283i	$-0.918490\pi$
$853$	−20.8564	+	20.8564i	−0.714110	+	0.714110i	0.253283	+	0.967392i	$0.418490\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			22.9282i			0.783213i	0.920133	+	0.391606i	$0.128080\pi$
$857$			22.9282i			0.783213i	−0.920133	+	0.391606i	$0.871920\pi$
$858$		0			0
$859$		−	22.3923i		−	0.764016i	−0.924159	−	0.382008i	$-0.875233\pi$
$859$		−	22.3923i		−	0.764016i	0.924159	−	0.382008i	$-0.124767\pi$
$860$		0			0
$861$	−6.40192	−	11.0885i	−0.218177	−	0.377894i
$862$		0			0
$863$	−22.5167	+	22.5167i	−0.766476	+	0.766476i	−0.977484	−	0.211008i	$-0.932325\pi$
$863$	−22.5167	+	22.5167i	−0.766476	+	0.766476i	0.211008	+	0.977484i	$0.432325\pi$
$864$		0			0
$865$	−0.437822	−	1.63397i	−0.0148864	−	0.0555568i
$866$		0			0
$867$	17.7846	+	10.2679i	0.603997	+	0.348718i
$868$		0			0
$869$	11.1962	+	3.00000i	0.379803	+	0.101768i
$870$		0			0
$871$	23.2583	−	38.5526i	0.788078	−	1.30630i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−5.07180	+	8.78461i	−0.171458	+	0.296974i
$876$		0			0
$877$	30.2583	−	8.10770i	1.02175	−	0.273777i	0.291220	−	0.956656i	$-0.405939\pi$
$877$	30.2583	−	8.10770i	1.02175	−	0.273777i	0.730532	+	0.682879i	$0.239272\pi$
$878$		0			0
$879$	−14.4904	−	14.4904i	−0.488748	−	0.488748i
$880$		0			0
$881$	−22.7487	+	13.1340i	−0.766424	+	0.442495i	−0.831597	−	0.555379i	$-0.812573\pi$
$881$	−22.7487	+	13.1340i	−0.766424	+	0.442495i	0.0651737	+	0.997874i	$0.479240\pi$
$882$		0			0
$883$	−6.92820			−0.233153			−0.116576	−	0.993182i	$-0.537192\pi$
$883$	−6.92820			−0.233153			−0.116576	+	0.993182i	$0.537192\pi$
$884$		0			0
$885$	−21.8038			−0.732928
$886$		0			0
$887$	−44.6769	+	25.7942i	−1.50010	+	0.866085i	−0.500104	+	0.865965i	$0.666705\pi$
$887$	−44.6769	+	25.7942i	−1.50010	+	0.866085i	−1.00000		0.000120075i	$0.999962\pi$
$888$		0			0
$889$	2.49038	+	2.49038i	0.0835247	+	0.0835247i
$890$		0			0
$891$	−29.0885	+	7.79423i	−0.974500	+	0.261116i
$892$		0			0
$893$	−10.0981	+	17.4904i	−0.337919	+	0.585293i
$894$		0			0
$895$	0.758330	−	2.83013i	0.0253482	−	0.0946007i
$896$		0			0
$897$	13.5000	−	12.9904i	0.450752	−	0.433736i
$898$		0			0
$899$	56.2750	+	15.0788i	1.87688	+	0.502907i
$900$		0			0
$901$	−9.67949	−	5.58846i	−0.322471	−	0.186179i
$902$		0			0
$903$	−3.61731	−	13.5000i	−0.120377	−	0.449252i
$904$		0			0
$905$	18.9282	−	18.9282i	0.629195	−	0.629195i
$906$		0			0
$907$	15.3564	+	26.5981i	0.509901	+	0.883175i	0.999934	+	0.0114708i	$0.00365135\pi$
$907$	15.3564	+	26.5981i	0.509901	+	0.883175i	−0.490033	+	0.871704i	$0.663015\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			45.0333i			1.49202i	0.665934	+	0.746010i	$0.268033\pi$
$911$			45.0333i			1.49202i	−0.665934	+	0.746010i	$0.731967\pi$
$912$		0			0
$913$	1.90192	+	3.29423i	0.0629445	+	0.109023i
$914$		0			0
$915$	12.1244	−	12.1244i	0.400819	−	0.400819i
$916$		0			0
$917$	−3.58846	−	13.3923i	−0.118501	−	0.442253i
$918$		0			0
$919$	5.89230	+	3.40192i	0.194369	+	0.112219i	0.594026	−	0.804446i	$-0.297537\pi$
$919$	5.89230	+	3.40192i	0.194369	+	0.112219i	−0.399657	+	0.916665i	$0.630871\pi$
$920$		0			0
$921$	18.2942	+	4.90192i	0.602815	+	0.161524i
$922$		0			0
$923$	−60.3109	−	1.16025i	−1.98516	−	0.0381902i
$924$		0			0
$925$	−2.89230	+	10.7942i	−0.0950984	+	0.354912i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	29.7224	−	7.96410i	0.975161	−	0.261294i	0.264156	−	0.964480i	$-0.414907\pi$
$929$	29.7224	−	7.96410i	0.975161	−	0.261294i	0.711006	+	0.703186i	$0.248240\pi$
$930$		0			0
$931$	−14.6603	−	14.6603i	−0.480470	−	0.480470i
$932$		0			0
$933$	7.60770	−	4.39230i	0.249065	−	0.143798i
$934$		0			0
$935$	10.7321			0.350976
$936$		0			0
$937$	−18.7846			−0.613666			−0.306833	−	0.951763i	$-0.599269\pi$
$937$	−18.7846			−0.613666			−0.306833	+	0.951763i	$0.599269\pi$
$938$		0			0
$939$	−9.00000	+	5.19615i	−0.293704	+	0.169570i
$940$		0			0
$941$	4.60770	+	4.60770i	0.150207	+	0.150207i	0.778210	−	0.628004i	$-0.216128\pi$
$941$	4.60770	+	4.60770i	0.150207	+	0.150207i	−0.628004	+	0.778210i	$0.716128\pi$
$942$		0			0
$943$	23.8923	−	6.40192i	0.778040	−	0.208475i
$944$		0			0
$945$	−3.29423	+	5.70577i	−0.107161	+	0.185609i
$946$		0			0
$947$	6.74167	−	25.1603i	0.219075	−	0.817598i	−0.765617	−	0.643296i	$-0.777566\pi$
$947$	6.74167	−	25.1603i	0.219075	−	0.817598i	0.984692	−	0.174302i	$-0.0557670\pi$
$948$		0			0
$949$	6.07180	+	11.0000i	0.197099	+	0.357075i
$950$		0			0
$951$	−41.1506	−	11.0263i	−1.33440	−	0.357552i
$952$		0			0
$953$	48.8205	+	28.1865i	1.58145	+	0.913051i	0.994648	+	0.103322i	$0.0329472\pi$
$953$	48.8205	+	28.1865i	1.58145	+	0.913051i	0.586803	+	0.809729i	$0.300386\pi$
$954$		0			0
$955$	2.49038	+	9.29423i	0.0805868	+	0.300754i
$956$		0			0
$957$	32.4904	−	32.4904i	1.05026	−	1.05026i
$958$		0			0
$959$	2.30385	+	3.99038i	0.0743951	+	0.128856i
$960$		0			0
$961$		−	23.0000i		−	0.741935i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	18.8301	+	32.6147i	0.606163	+	1.04991i
$966$		0			0
$967$	−13.7321	+	13.7321i	−0.441593	+	0.441593i	−0.892547	−	0.450954i	$-0.851084\pi$
$967$	−13.7321	+	13.7321i	−0.441593	+	0.441593i	0.450954	+	0.892547i	$0.351084\pi$
$968$		0			0
$969$	3.40192	+	12.6962i	0.109286	+	0.407859i
$970$		0			0
$971$	−13.2846	−	7.66987i	−0.426323	−	0.246138i	0.271456	−	0.962451i	$-0.412495\pi$
$971$	−13.2846	−	7.66987i	−0.426323	−	0.246138i	−0.697779	+	0.716313i	$0.745828\pi$
$972$		0			0
$973$	14.8923	+	3.99038i	0.477425	+	0.127926i
$974$		0			0
$975$	−18.1865	+	4.50000i	−0.582435	+	0.144115i
$976$		0			0
$977$	7.06218	−	26.3564i	0.225939	−	0.843216i	−0.756087	−	0.654471i	$-0.772891\pi$
$977$	7.06218	−	26.3564i	0.225939	−	0.843216i	0.982026	−	0.188745i	$-0.0604420\pi$
$978$		0			0
$979$	−10.1603	+	17.5981i	−0.324723	+	0.562437i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	32.6603	+	32.6603i	1.04170	+	1.04170i	0.999092	+	0.0426085i	$0.0135668\pi$
$983$	32.6603	+	32.6603i	1.04170	+	1.04170i	0.0426085	+	0.999092i	$0.486433\pi$
$984$		0			0
$985$	−8.83013	+	5.09808i	−0.281351	+	0.162438i
$986$		0			0
$987$	9.37307			0.298348
$988$		0			0
$989$	27.0000			0.858550
$990$		0			0
$991$	−19.5000	+	11.2583i	−0.619438	+	0.357633i	−0.776650	−	0.629932i	$-0.783083\pi$
$991$	−19.5000	+	11.2583i	−0.619438	+	0.357633i	0.157212	+	0.987565i	$0.449749\pi$
$992$		0			0
$993$	−20.4904	−	20.4904i	−0.650243	−	0.650243i
$994$		0			0
$995$	12.2942	−	3.29423i	0.389753	−	0.104434i
$996$		0			0
$997$	12.5000	−	21.6506i	0.395879	−	0.685682i	−0.597334	−	0.801993i	$-0.703773\pi$
$997$	12.5000	−	21.6506i	0.395879	−	0.685682i	0.993213	+	0.116310i	$0.0371066\pi$
$998$		0			0
$999$	−5.00962	+	18.6962i	−0.158497	+	0.591520i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.2.bm.b.63.1	✓	4
4.3	odd	2		208.2.bm.e.63.1	yes	4
8.3	odd	2		832.2.bu.a.63.1		4
8.5	even	2		832.2.bu.f.63.1		4
13.6	odd	12		208.2.bm.e.175.1	yes	4
52.19	even	12	inner	208.2.bm.b.175.1	yes	4
104.19	even	12		832.2.bu.f.383.1		4
104.45	odd	12		832.2.bu.a.383.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
208.2.bm.b.63.1	✓	4	1.1	even	1	trivial
208.2.bm.b.175.1	yes	4	52.19	even	12	inner
208.2.bm.e.63.1	yes	4	4.3	odd	2
208.2.bm.e.175.1	yes	4	13.6	odd	12
832.2.bu.a.63.1		4	8.3	odd	2
832.2.bu.a.383.1		4	104.45	odd	12
832.2.bu.f.63.1		4	8.5	even	2
832.2.bu.f.383.1		4	104.19	even	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:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	208.bm (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{3} +(1.00000 + 1.00000i) q^{5} +(-0.866025 + 0.232051i) q^{7} +(-0.866025 + 3.23205i) q^{11} +(-1.00000 + 3.46410i) q^{13} +(-2.36603 - 0.633975i) q^{15} +(-1.96410 - 1.13397i) q^{17} +(0.866025 + 3.23205i) q^{19} +(1.09808 - 1.09808i) q^{21} +(1.50000 + 2.59808i) q^{23} -3.00000i q^{25} -5.19615i q^{27} +(3.96410 + 6.86603i) q^{29} +(5.19615 - 5.19615i) q^{31} +(-1.50000 - 5.59808i) q^{33} +(-1.09808 - 0.633975i) q^{35} +(-3.59808 - 0.964102i) q^{37} +(-1.50000 - 6.06218i) q^{39} +(2.13397 - 7.96410i) q^{41} +(4.50000 - 7.79423i) q^{43} +(4.26795 + 4.26795i) q^{47} +(-5.36603 + 3.09808i) q^{49} +3.92820 q^{51} +4.92820 q^{53} +(-4.09808 + 2.36603i) q^{55} +(-4.09808 - 4.09808i) q^{57} +(8.59808 - 2.30385i) q^{59} +(-3.50000 + 6.06218i) q^{61} +(-4.46410 + 2.46410i) q^{65} +(-12.0622 - 3.23205i) q^{67} +(-4.50000 - 2.59808i) q^{69} +(4.33013 + 16.1603i) q^{71} +(2.46410 - 2.46410i) q^{73} +(2.59808 + 4.50000i) q^{75} -3.00000i q^{77} -3.46410i q^{79} +(4.50000 + 7.79423i) q^{81} +(0.803848 - 0.803848i) q^{83} +(-0.830127 - 3.09808i) q^{85} +(-11.8923 - 6.86603i) q^{87} +(5.86603 + 1.57180i) q^{89} +(0.0621778 - 3.23205i) q^{91} +(-3.29423 + 12.2942i) q^{93} +(-2.36603 + 4.09808i) q^{95} +(11.3301 - 3.03590i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} + 4 q^{5} - 4 q^{13} - 6 q^{15} + 6 q^{17} - 6 q^{21} + 6 q^{23} + 2 q^{29} - 6 q^{33} + 6 q^{35} - 4 q^{37} - 6 q^{39} + 12 q^{41} + 18 q^{43} + 24 q^{47} - 18 q^{49} - 12 q^{51} - 8 q^{53}+ \cdots + 28 q^{97}+O(q^{100}) \) 4 * q - 6 * q^3 + 4 * q^5 - 4 * q^13 - 6 * q^15 + 6 * q^17 - 6 * q^21 + 6 * q^23 + 2 * q^29 - 6 * q^33 + 6 * q^35 - 4 * q^37 - 6 * q^39 + 12 * q^41 + 18 * q^43 + 24 * q^47 - 18 * q^49 - 12 * q^51 - 8 * q^53 - 6 * q^55 - 6 * q^57 + 24 * q^59 - 14 * q^61 - 4 * q^65 - 24 * q^67 - 18 * q^69 - 4 * q^73 + 18 * q^81 + 24 * q^83 + 14 * q^85 - 6 * q^87 + 20 * q^89 - 24 * q^91 + 18 * q^93 - 6 * q^95 + 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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