LMFDB - Embedded newform 780.2.cc.b.121.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [780,2,Mod(121,780)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(780, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("780.121"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	780.cc (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$6.22833135766$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			121.3
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	780.121
Dual form			780.2.cc.b.361.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{3} +1.00000i q^{5} +(0.0590182 - 0.0340742i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-3.59077 - 2.07313i) q^{11} +(-1.86250 + 3.08725i) q^{13} +(-0.866025 - 0.500000i) q^{15} +(1.27646 + 2.21089i) q^{17} +(-6.89363 + 3.98004i) q^{19} +0.0681483i q^{21} +(2.96971 - 5.14368i) q^{23} -1.00000 q^{25} +1.00000 q^{27} +(-1.80701 + 3.12983i) q^{29} +1.42883i q^{31} +(3.59077 - 2.07313i) q^{33} +(0.0340742 + 0.0590182i) q^{35} +(-9.87127 - 5.69918i) q^{37} +(-1.74238 - 3.15660i) q^{39} +(-0.807007 - 0.465926i) q^{41} +(-1.23388 - 2.13713i) q^{43} +(0.866025 - 0.500000i) q^{45} -4.63859i q^{47} +(-3.49768 + 6.05816i) q^{49} -2.55291 q^{51} -6.36308 q^{53} +(2.07313 - 3.59077i) q^{55} -7.96008i q^{57} +(-0.0773604 + 0.0446641i) q^{59} +(3.41894 + 5.92178i) q^{61} +(-0.0590182 - 0.0340742i) q^{63} +(-3.08725 - 1.86250i) q^{65} +(-5.03699 - 2.90811i) q^{67} +(2.96971 + 5.14368i) q^{69} +(-5.41239 + 3.12484i) q^{71} +13.8812i q^{73} +(0.500000 - 0.866025i) q^{75} -0.282561 q^{77} +1.19615 q^{79} +(-0.500000 + 0.866025i) q^{81} +2.38234i q^{83} +(-2.21089 + 1.27646i) q^{85} +(-1.80701 - 3.12983i) q^{87} +(9.04758 + 5.22362i) q^{89} +(-0.00472611 + 0.245667i) q^{91} +(-1.23740 - 0.714413i) q^{93} +(-3.98004 - 6.89363i) q^{95} +(6.15111 - 3.55135i) q^{97} +4.14626i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 4 q^{9} - 12 q^{11} + 4 q^{17} + 12 q^{19} + 4 q^{23} - 8 q^{25} + 8 q^{27} - 8 q^{29} + 12 q^{33} + 8 q^{35} - 24 q^{37} - 16 q^{43} - 4 q^{49} - 8 q^{51} + 16 q^{53} + 4 q^{55} + 24 q^{59}+ \cdots + 48 q^{97}+O(q^{100}) $ 8 * q - 4 * q^3 - 4 * q^9 - 12 * q^11 + 4 * q^17 + 12 * q^19 + 4 * q^23 - 8 * q^25 + 8 * q^27 - 8 * q^29 + 12 * q^33 + 8 * q^35 - 24 * q^37 - 16 * q^43 - 4 * q^49 - 8 * q^51 + 16 * q^53 + 4 * q^55 + 24 * q^59 + 8 * q^61 + 24 * q^67 + 4 * q^69 - 12 * q^71 + 4 * q^75 - 8 * q^77 - 32 * q^79 - 4 * q^81 - 8 * q^87 - 12 * q^89 + 8 * q^91 - 24 * q^93 - 12 * q^95 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/780\mathbb{Z}\right)^\times$.

$n$	$157$	$301$	$391$	$521$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		0			0
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$	0.0590182	−	0.0340742i	0.0223068	−	0.0128788i	−0.488805	−	0.872393i	$-0.662567\pi$
$7$	0.0590182	−	0.0340742i	0.0223068	−	0.0128788i	0.511112	+	0.859514i	$0.329234\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−3.59077	−	2.07313i	−1.08266	−	0.625073i	−0.151046	−	0.988527i	$-0.548264\pi$
$11$	−3.59077	−	2.07313i	−1.08266	−	0.625073i	−0.931612	+	0.363454i	$0.881597\pi$
$12$		0			0
$13$	−1.86250	+	3.08725i	−0.516565	+	0.856248i
$13$	−1.86250	+	3.08725i	−0.516565	+	0.856248i
$14$		0			0
$15$	−0.866025	−	0.500000i	−0.223607	−	0.129099i
$16$		0			0
$17$	1.27646	+	2.21089i	0.309586	+	0.536219i	0.978272	−	0.207326i	$-0.0664761\pi$
$17$	1.27646	+	2.21089i	0.309586	+	0.536219i	−0.668686	+	0.743545i	$0.733143\pi$
$18$		0			0
$19$	−6.89363	+	3.98004i	−1.58151	+	0.913084i	−0.586868	+	0.809683i	$0.699639\pi$
$19$	−6.89363	+	3.98004i	−1.58151	+	0.913084i	−0.994640	+	0.103401i	$0.967028\pi$
$20$		0			0
$21$			0.0681483i			0.0148712i
$22$		0			0
$23$	2.96971	−	5.14368i	0.619227	−	1.07253i	−0.370400	−	0.928872i	$-0.620779\pi$
$23$	2.96971	−	5.14368i	0.619227	−	1.07253i	0.989627	−	0.143660i	$-0.0458872\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−1.80701	+	3.12983i	−0.335553	+	0.581195i	−0.983591	−	0.180413i	$-0.942256\pi$
$29$	−1.80701	+	3.12983i	−0.335553	+	0.581195i	0.648038	+	0.761608i	$0.275590\pi$
$30$		0			0
$31$			1.42883i			0.256625i	0.991734	+	0.128312i	$0.0409560\pi$
$31$			1.42883i			0.256625i	−0.991734	+	0.128312i	$0.959044\pi$
$32$		0			0
$33$	3.59077	−	2.07313i	0.625073	−	0.360886i
$34$		0			0
$35$	0.0340742	+	0.0590182i	0.00575959	+	0.00997590i
$36$		0			0
$37$	−9.87127	−	5.69918i	−1.62283	−	0.936939i	−0.986159	−	0.165800i	$-0.946979\pi$
$37$	−9.87127	−	5.69918i	−1.62283	−	0.936939i	−0.636667	−	0.771139i	$-0.719687\pi$
$38$		0			0
$39$	−1.74238	−	3.15660i	−0.279005	−	0.505460i
$40$		0			0
$41$	−0.807007	−	0.465926i	−0.126033	−	0.0727654i	0.435658	−	0.900112i	$-0.356516\pi$
$41$	−0.807007	−	0.465926i	−0.126033	−	0.0727654i	−0.561691	+	0.827347i	$0.689849\pi$
$42$		0			0
$43$	−1.23388	−	2.13713i	−0.188164	−	0.325910i	0.756474	−	0.654024i	$-0.226920\pi$
$43$	−1.23388	−	2.13713i	−0.188164	−	0.325910i	−0.944638	+	0.328114i	$0.893587\pi$
$44$		0			0
$45$	0.866025	−	0.500000i	0.129099	−	0.0745356i
$46$		0			0
$47$		−	4.63859i		−	0.676608i	−0.941037	−	0.338304i	$-0.890147\pi$
$47$		−	4.63859i		−	0.676608i	0.941037	−	0.338304i	$-0.109853\pi$
$48$		0			0
$49$	−3.49768	+	6.05816i	−0.499668	+	0.865451i
$50$		0			0
$51$	−2.55291			−0.357480
$52$		0			0
$53$	−6.36308			−0.874036			−0.437018	−	0.899453i	$-0.643965\pi$
$53$	−6.36308			−0.874036			−0.437018	+	0.899453i	$0.643965\pi$
$54$		0			0
$55$	2.07313	−	3.59077i	0.279541	−	0.484179i
$56$		0			0
$57$		−	7.96008i		−	1.05434i
$58$		0			0
$59$	−0.0773604	+	0.0446641i	−0.0100715	+	0.00581476i	−0.505027	−	0.863103i	$-0.668518\pi$
$59$	−0.0773604	+	0.0446641i	−0.0100715	+	0.00581476i	0.494956	+	0.868918i	$0.335184\pi$
$60$		0			0
$61$	3.41894	+	5.92178i	0.437750	+	0.758206i	0.997516	−	0.0704453i	$-0.0224420\pi$
$61$	3.41894	+	5.92178i	0.437750	+	0.758206i	−0.559765	+	0.828651i	$0.689109\pi$
$62$		0			0
$63$	−0.0590182	−	0.0340742i	−0.00743559	−	0.00429294i
$64$		0			0
$65$	−3.08725	−	1.86250i	−0.382926	−	0.231015i
$66$		0			0
$67$	−5.03699	−	2.90811i	−0.615367	−	0.355282i	0.159696	−	0.987166i	$-0.448949\pi$
$67$	−5.03699	−	2.90811i	−0.615367	−	0.355282i	−0.775063	+	0.631884i	$0.782282\pi$
$68$		0			0
$69$	2.96971	+	5.14368i	0.357511	+	0.619227i
$70$		0			0
$71$	−5.41239	+	3.12484i	−0.642332	+	0.370851i	−0.785512	−	0.618846i	$-0.787601\pi$
$71$	−5.41239	+	3.12484i	−0.642332	+	0.370851i	0.143180	+	0.989697i	$0.454267\pi$
$72$		0			0
$73$			13.8812i			1.62468i	0.583187	+	0.812338i	$0.301805\pi$
$73$			13.8812i			1.62468i	−0.583187	+	0.812338i	$0.698195\pi$
$74$		0			0
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$		0			0
$77$	−0.282561			−0.0322008
$78$		0			0
$79$	1.19615			0.134578			0.0672888	−	0.997734i	$-0.478565\pi$
$79$	1.19615			0.134578			0.0672888	+	0.997734i	$0.478565\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			2.38234i			0.261495i	0.991416	+	0.130748i	$0.0417378\pi$
$83$			2.38234i			0.261495i	−0.991416	+	0.130748i	$0.958262\pi$
$84$		0			0
$85$	−2.21089	+	1.27646i	−0.239805	+	0.138451i
$86$		0			0
$87$	−1.80701	−	3.12983i	−0.193732	−	0.335553i
$88$		0			0
$89$	9.04758	+	5.22362i	0.959042	+	0.553703i	0.895878	−	0.444300i	$-0.146548\pi$
$89$	9.04758	+	5.22362i	0.959042	+	0.553703i	0.0631639	+	0.998003i	$0.479881\pi$
$90$		0			0
$91$	−0.00472611	+	0.245667i	−0.000495431	+	0.0257529i
$92$		0			0
$93$	−1.23740	−	0.714413i	−0.128312	−	0.0740811i
$94$		0			0
$95$	−3.98004	−	6.89363i	−0.408343	−	0.707272i
$96$		0			0
$97$	6.15111	−	3.55135i	0.624551	−	0.360585i	−0.154088	−	0.988057i	$-0.549244\pi$
$97$	6.15111	−	3.55135i	0.624551	−	0.360585i	0.778639	+	0.627472i	$0.215910\pi$
$98$		0			0
$99$			4.14626i			0.416715i
$100$		0			0
$101$	8.67593	−	15.0272i	0.863288	−	1.49526i	−0.00544959	−	0.999985i	$-0.501735\pi$
$101$	8.67593	−	15.0272i	0.863288	−	1.49526i	0.868737	−	0.495273i	$-0.164932\pi$
$102$		0			0
$103$	−3.56147			−0.350922			−0.175461	−	0.984486i	$-0.556142\pi$
$103$	−3.56147			−0.350922			−0.175461	+	0.984486i	$0.556142\pi$
$104$		0			0
$105$	−0.0681483			−0.00665060
$106$		0			0
$107$	9.47055	−	16.4035i	0.915552	−	1.58578i	0.109461	−	0.993991i	$-0.465087\pi$
$107$	9.47055	−	16.4035i	0.915552	−	1.58578i	0.806091	−	0.591792i	$-0.201579\pi$
$108$		0			0
$109$			16.6875i			1.59837i	0.601084	+	0.799186i	$0.294736\pi$
$109$			16.6875i			1.59837i	−0.601084	+	0.799186i	$0.705264\pi$
$110$		0			0
$111$	9.87127	−	5.69918i	0.936939	−	0.540942i
$112$		0			0
$113$	6.02458	+	10.4349i	0.566745	+	0.981631i	0.996885	+	0.0788687i	$0.0251308\pi$
$113$	6.02458	+	10.4349i	0.566745	+	0.981631i	−0.430140	+	0.902762i	$0.641536\pi$
$114$		0			0
$115$	5.14368	+	2.96971i	0.479651	+	0.276927i
$116$		0			0
$117$	3.60488	+	0.0693504i	0.333272	+	0.00641144i
$118$		0			0
$119$	0.150668	+	0.0869884i	0.0138118	+	0.00797422i
$120$		0			0
$121$	3.09575	+	5.36200i	0.281432	+	0.487455i
$122$		0			0
$123$	0.807007	−	0.465926i	0.0727654	−	0.0420111i
$124$		0			0
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	−5.92032	+	10.2543i	−0.525343	+	0.909921i	0.474221	+	0.880406i	$0.342730\pi$
$127$	−5.92032	+	10.2543i	−0.525343	+	0.909921i	−0.999564	+	0.0295154i	$0.990604\pi$
$128$		0			0
$129$	2.46775			0.217273
$130$		0			0
$131$	−8.87127			−0.775086			−0.387543	−	0.921852i	$-0.626676\pi$
$131$	−8.87127			−0.775086			−0.387543	+	0.921852i	$0.626676\pi$
$132$		0			0
$133$	−0.271233	+	0.469790i	−0.0235189	+	0.0407359i
$134$		0			0
$135$			1.00000i			0.0860663i
$136$		0			0
$137$	15.2938	−	8.82989i	1.30664	−	0.754388i	0.325105	−	0.945678i	$-0.394600\pi$
$137$	15.2938	−	8.82989i	1.30664	−	0.754388i	0.981534	+	0.191290i	$0.0612670\pi$
$138$		0			0
$139$	1.87894	+	3.25442i	0.159369	+	0.276036i	0.934641	−	0.355592i	$-0.115721\pi$
$139$	1.87894	+	3.25442i	0.159369	+	0.276036i	−0.775272	+	0.631627i	$0.782387\pi$
$140$		0			0
$141$	4.01714	+	2.31930i	0.338304	+	0.195320i
$142$		0			0
$143$	13.0881	−	7.22438i	1.09448	−	0.604133i
$144$		0			0
$145$	−3.12983	−	1.80701i	−0.259918	−	0.150064i
$146$		0			0
$147$	−3.49768	−	6.05816i	−0.288484	−	0.499668i
$148$		0			0
$149$	−11.9050	+	6.87333i	−0.975292	+	0.563085i	−0.900846	−	0.434140i	$-0.857052\pi$
$149$	−11.9050	+	6.87333i	−0.975292	+	0.563085i	−0.0744467	+	0.997225i	$0.523719\pi$
$150$		0			0
$151$			10.1669i			0.827373i	0.910419	+	0.413686i	$0.135759\pi$
$151$			10.1669i			0.827373i	−0.910419	+	0.413686i	$0.864241\pi$
$152$		0			0
$153$	1.27646	−	2.21089i	0.103195	−	0.178740i
$154$		0			0
$155$	−1.42883			−0.114766
$156$		0			0
$157$	9.13746			0.729248			0.364624	−	0.931155i	$-0.381197\pi$
$157$	9.13746			0.729248			0.364624	+	0.931155i	$0.381197\pi$
$158$		0			0
$159$	3.18154	−	5.51059i	0.252313	−	0.437018i
$160$		0			0
$161$		−	0.404761i		−	0.0318997i
$162$		0			0
$163$	15.0653	−	8.69798i	1.18001	−	0.681278i	0.223992	−	0.974591i	$-0.428091\pi$
$163$	15.0653	−	8.69798i	1.18001	−	0.681278i	0.956016	+	0.293313i	$0.0947578\pi$
$164$		0			0
$165$	2.07313	+	3.59077i	0.161393	+	0.279541i
$166$		0			0
$167$	−12.0063	−	6.93185i	−0.929077	−	0.536403i	−0.0425574	−	0.999094i	$-0.513551\pi$
$167$	−12.0063	−	6.93185i	−0.929077	−	0.536403i	−0.886519	+	0.462691i	$0.846884\pi$
$168$		0			0
$169$	−6.06218	−	11.5000i	−0.466321	−	0.884615i
$170$		0			0
$171$	6.89363	+	3.98004i	0.527169	+	0.304361i
$172$		0			0
$173$	8.21587	+	14.2303i	0.624641	+	1.08191i	0.988610	+	0.150499i	$0.0480881\pi$
$173$	8.21587	+	14.2303i	0.624641	+	1.08191i	−0.363969	+	0.931411i	$0.618579\pi$
$174$		0			0
$175$	−0.0590182	+	0.0340742i	−0.00446136	+	0.00257577i
$176$		0			0
$177$		−	0.0893281i		−	0.00671431i
$178$		0			0
$179$	−5.89716	+	10.2142i	−0.440774	+	0.763443i	−0.997747	−	0.0670875i	$-0.978629\pi$
$179$	−5.89716	+	10.2142i	−0.440774	+	0.763443i	0.556973	+	0.830531i	$0.311963\pi$
$180$		0			0
$181$	−5.88953			−0.437765			−0.218883	−	0.975751i	$-0.570241\pi$
$181$	−5.88953			−0.437765			−0.218883	+	0.975751i	$0.570241\pi$
$182$		0			0
$183$	−6.83788			−0.505471
$184$		0			0
$185$	5.69918	−	9.87127i	0.419012	−	0.725750i
$186$		0			0
$187$		−	10.5851i		−	0.774056i
$188$		0			0
$189$	0.0590182	−	0.0340742i	0.00429294	−	0.00247853i
$190$		0			0
$191$	9.10916	+	15.7775i	0.659116	+	1.14162i	0.980845	+	0.194791i	$0.0624027\pi$
$191$	9.10916	+	15.7775i	0.659116	+	1.14162i	−0.321729	+	0.946832i	$0.604264\pi$
$192$		0			0
$193$	−4.77886	−	2.75908i	−0.343990	−	0.198603i	0.318045	−	0.948076i	$-0.396974\pi$
$193$	−4.77886	−	2.75908i	−0.343990	−	0.198603i	−0.662035	+	0.749473i	$0.730307\pi$
$194$		0			0
$195$	3.15660	−	1.74238i	0.226049	−	0.124775i
$196$		0			0
$197$	21.9309	+	12.6618i	1.56252	+	0.902119i	0.997002	+	0.0773796i	$0.0246553\pi$
$197$	21.9309	+	12.6618i	1.56252	+	0.902119i	0.565514	+	0.824739i	$0.308678\pi$
$198$		0			0
$199$	11.9595	+	20.7144i	0.847783	+	1.46840i	0.883182	+	0.469031i	$0.155397\pi$
$199$	11.9595	+	20.7144i	0.847783	+	1.46840i	−0.0353984	+	0.999373i	$0.511270\pi$
$200$		0			0
$201$	5.03699	−	2.90811i	0.355282	−	0.205122i
$202$		0			0
$203$			0.246289i			0.0172861i
$204$		0			0
$205$	0.465926	−	0.807007i	0.0325417	−	0.0563638i
$206$		0			0
$207$	−5.93942			−0.412818
$208$		0			0
$209$	33.0046			2.28298
$210$		0			0
$211$	8.59273	−	14.8830i	0.591548	−	1.02459i	−0.402476	−	0.915430i	$-0.631850\pi$
$211$	8.59273	−	14.8830i	0.591548	−	1.02459i	0.994024	−	0.109160i	$-0.0348162\pi$
$212$		0			0
$213$		−	6.24969i		−	0.428222i
$214$		0			0
$215$	2.13713	−	1.23388i	0.145751	−	0.0841496i
$216$		0			0
$217$	0.0486860	+	0.0843267i	0.00330502	+	0.00572447i
$218$		0			0
$219$	−12.0215	−	6.94062i	−0.812338	−	0.469003i
$220$		0			0
$221$	−9.20296	−	0.177046i	−0.619058	−	0.0119094i
$222$		0			0
$223$	6.28913	+	3.63103i	0.421151	+	0.243152i	0.695570	−	0.718459i	$-0.255152\pi$
$223$	6.28913	+	3.63103i	0.421151	+	0.243152i	−0.274419	+	0.961610i	$0.588485\pi$
$224$		0			0
$225$	0.500000	+	0.866025i	0.0333333	+	0.0577350i
$226$		0			0
$227$	−6.91347	+	3.99149i	−0.458863	+	0.264925i	−0.711566	−	0.702619i	$-0.752014\pi$
$227$	−6.91347	+	3.99149i	−0.458863	+	0.264925i	0.252703	+	0.967544i	$0.418680\pi$
$228$		0			0
$229$			0.146993i			0.00971359i	0.999988	+	0.00485680i	$0.00154597\pi$
$229$			0.146993i			0.00971359i	−0.999988	+	0.00485680i	$0.998454\pi$
$230$		0			0
$231$	0.141281	−	0.244705i	0.00929558	−	0.0161004i
$232$		0			0
$233$	−7.72424			−0.506032			−0.253016	−	0.967462i	$-0.581422\pi$
$233$	−7.72424			−0.506032			−0.253016	+	0.967462i	$0.581422\pi$
$234$		0			0
$235$	4.63859			0.302589
$236$		0			0
$237$	−0.598076	+	1.03590i	−0.0388492	+	0.0672888i
$238$		0			0
$239$		−	14.4529i		−	0.934880i	−0.884025	−	0.467440i	$-0.845176\pi$
$239$		−	14.4529i		−	0.934880i	0.884025	−	0.467440i	$-0.154824\pi$
$240$		0			0
$241$	−20.7437	+	11.9764i	−1.33622	+	0.771467i	−0.986245	−	0.165292i	$-0.947143\pi$
$241$	−20.7437	+	11.9764i	−1.33622	+	0.771467i	−0.349976	+	0.936759i	$0.613810\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	−6.05816	−	3.49768i	−0.387041	−	0.223458i
$246$		0			0
$247$	0.552034	−	28.6952i	0.0351251	−	1.82583i
$248$		0			0
$249$	−2.06316	−	1.19117i	−0.130748	−	0.0754872i
$250$		0			0
$251$	−12.9040	−	22.3503i	−0.814491	−	1.41074i	−0.909693	−	0.415282i	$-0.863683\pi$
$251$	−12.9040	−	22.3503i	−0.814491	−	1.41074i	0.0952019	−	0.995458i	$-0.469650\pi$
$252$		0			0
$253$	−21.3271	+	12.3132i	−1.34082	+	0.774124i
$254$		0			0
$255$		−	2.55291i		−	0.159870i
$256$		0			0
$257$	3.08920	−	5.35066i	0.192699	−	0.333765i	−0.753445	−	0.657511i	$-0.771609\pi$
$257$	3.08920	−	5.35066i	0.192699	−	0.333765i	0.946144	+	0.323746i	$0.104942\pi$
$258$		0			0
$259$	−0.776779			−0.0482667
$260$		0			0
$261$	3.61401			0.223702
$262$		0			0
$263$	−3.77244	+	6.53405i	−0.232618	+	0.402907i	−0.958578	−	0.284831i	$-0.908063\pi$
$263$	−3.77244	+	6.53405i	−0.232618	+	0.402907i	0.725960	+	0.687737i	$0.241396\pi$
$264$		0			0
$265$		−	6.36308i		−	0.390881i
$266$		0			0
$267$	−9.04758	+	5.22362i	−0.553703	+	0.319681i
$268$		0			0
$269$	7.56106	+	13.0961i	0.461006	+	0.798486i	0.999011	−	0.0444558i	$-0.0141554\pi$
$269$	7.56106	+	13.0961i	0.461006	+	0.798486i	−0.538006	+	0.842941i	$0.680822\pi$
$270$		0			0
$271$	17.6604	+	10.1962i	1.07279	+	0.619377i	0.928943	−	0.370222i	$-0.120719\pi$
$271$	17.6604	+	10.1962i	1.07279	+	0.619377i	0.143850	+	0.989600i	$0.454052\pi$
$272$		0			0
$273$	−0.210391	−	0.126926i	−0.0127334	−	0.00768193i
$274$		0			0
$275$	3.59077	+	2.07313i	0.216532	+	0.125015i
$276$		0			0
$277$	−2.38891	−	4.13770i	−0.143535	−	0.248611i	0.785290	−	0.619128i	$-0.212514\pi$
$277$	−2.38891	−	4.13770i	−0.143535	−	0.248611i	−0.928826	+	0.370517i	$0.879180\pi$
$278$		0			0
$279$	1.23740	−	0.714413i	0.0740811	−	0.0427708i
$280$		0			0
$281$		−	6.07274i		−	0.362269i	−0.983458	−	0.181135i	$-0.942023\pi$
$281$		−	6.07274i		−	0.362269i	0.983458	−	0.181135i	$-0.0579770\pi$
$282$		0			0
$283$	−10.0906	+	17.4775i	−0.599827	+	1.03893i	0.393020	+	0.919530i	$0.371430\pi$
$283$	−10.0906	+	17.4775i	−0.599827	+	1.03893i	−0.992846	+	0.119400i	$0.961903\pi$
$284$		0			0
$285$	7.96008			0.471514
$286$		0			0
$287$	−0.0635042			−0.00374853
$288$		0			0
$289$	5.24131	−	9.07822i	0.308313	−	0.534013i
$290$		0			0
$291$			7.10270i			0.416367i
$292$		0			0
$293$	−9.87380	+	5.70064i	−0.576833	+	0.333035i	−0.759874	−	0.650071i	$-0.774739\pi$
$293$	−9.87380	+	5.70064i	−0.576833	+	0.333035i	0.183041	+	0.983105i	$0.441406\pi$
$294$		0			0
$295$	−0.0446641	−	0.0773604i	−0.00260044	−	0.00450410i
$296$		0			0
$297$	−3.59077	−	2.07313i	−0.208358	−	0.120295i
$298$		0			0
$299$	10.3487	+	18.7483i	0.598483	+	1.08424i
$300$		0			0
$301$	−0.145642	−	0.0840865i	−0.00839467	−	0.00484667i
$302$		0			0
$303$	8.67593	+	15.0272i	0.498419	+	0.863288i
$304$		0			0
$305$	−5.92178	+	3.41894i	−0.339080	+	0.195768i
$306$		0			0
$307$		−	10.8374i		−	0.618523i	−0.950977	−	0.309262i	$-0.899918\pi$
$307$		−	10.8374i		−	0.618523i	0.950977	−	0.309262i	$-0.100082\pi$
$308$		0			0
$309$	1.78074	−	3.08433i	0.101303	−	0.175461i
$310$		0			0
$311$	−26.4772			−1.50138			−0.750691	−	0.660654i	$-0.770279\pi$
$311$	−26.4772			−1.50138			−0.750691	+	0.660654i	$0.770279\pi$
$312$		0			0
$313$	16.3534			0.924348			0.462174	−	0.886789i	$-0.347070\pi$
$313$	16.3534			0.924348			0.462174	+	0.886789i	$0.347070\pi$
$314$		0			0
$315$	0.0340742	−	0.0590182i	0.00191986	−	0.00332530i
$316$		0			0
$317$		−	22.0168i		−	1.23658i	−0.785948	−	0.618292i	$-0.787825\pi$
$317$		−	22.0168i		−	1.23658i	0.785948	−	0.618292i	$-0.212175\pi$
$318$		0			0
$319$	12.9771	−	7.49233i	0.726578	−	0.419490i
$320$		0			0
$321$	9.47055	+	16.4035i	0.528594	+	0.915552i
$322$		0			0
$323$	−17.5988	−	10.1607i	−0.979226	−	0.565356i
$324$		0			0
$325$	1.86250	−	3.08725i	0.103313	−	0.171250i
$326$		0			0
$327$	−14.4518	−	8.34374i	−0.799186	−	0.461410i
$328$		0			0
$329$	−0.158056	−	0.273761i	−0.00871392	−	0.0150930i
$330$		0			0
$331$	−21.1031	+	12.1839i	−1.15993	+	0.669686i	−0.951287	−	0.308306i	$-0.900238\pi$
$331$	−21.1031	+	12.1839i	−1.15993	+	0.669686i	−0.208642	+	0.977992i	$0.566904\pi$
$332$		0			0
$333$			11.3984i			0.624626i
$334$		0			0
$335$	2.90811	−	5.03699i	0.158887	−	0.275200i
$336$		0			0
$337$	−11.9178			−0.649201			−0.324601	−	0.945851i	$-0.605230\pi$
$337$	−11.9178			−0.649201			−0.324601	+	0.945851i	$0.605230\pi$
$338$		0			0
$339$	−12.0492			−0.654420
$340$		0			0
$341$	2.96214	−	5.13058i	0.160409	−	0.277837i
$342$		0			0
$343$			0.953760i			0.0514982i
$344$		0			0
$345$	−5.14368	+	2.96971i	−0.276927	+	0.159884i
$346$		0			0
$347$	3.57457	+	6.19134i	0.191893	+	0.332369i	0.945878	−	0.324524i	$-0.105204\pi$
$347$	3.57457	+	6.19134i	0.191893	+	0.332369i	−0.753984	+	0.656892i	$0.771871\pi$
$348$		0			0
$349$	−0.245478	−	0.141727i	−0.0131401	−	0.00758647i	0.493416	−	0.869794i	$-0.335748\pi$
$349$	−0.245478	−	0.141727i	−0.0131401	−	0.00758647i	−0.506556	+	0.862207i	$0.669082\pi$
$350$		0			0
$351$	−1.86250	+	3.08725i	−0.0994130	+	0.164785i
$352$		0			0
$353$	−11.9619	−	6.90620i	−0.636667	−	0.367580i	0.146662	−	0.989187i	$-0.453147\pi$
$353$	−11.9619	−	6.90620i	−0.636667	−	0.367580i	−0.783330	+	0.621607i	$0.786480\pi$
$354$		0			0
$355$	−3.12484	−	5.41239i	−0.165850	−	0.287260i
$356$		0			0
$357$	−0.150668	+	0.0869884i	−0.00797422	+	0.00460392i
$358$		0			0
$359$			24.0727i			1.27051i	0.772302	+	0.635255i	$0.219105\pi$
$359$			24.0727i			1.27051i	−0.772302	+	0.635255i	$0.780895\pi$
$360$		0			0
$361$	22.1814	−	38.4194i	1.16744	−	2.02207i
$362$		0			0
$363$	−6.19151			−0.324970
$364$		0			0
$365$	−13.8812			−0.726577
$366$		0			0
$367$	−0.0199778	+	0.0346025i	−0.00104283	+	0.00180623i	−0.866546	−	0.499097i	$-0.833665\pi$
$367$	−0.0199778	+	0.0346025i	−0.00104283	+	0.00180623i	0.865504	+	0.500903i	$0.166999\pi$
$368$		0			0
$369$			0.931852i			0.0485103i
$370$		0			0
$371$	−0.375538	+	0.216817i	−0.0194969	+	0.0112566i
$372$		0			0
$373$	1.59127	+	2.75616i	0.0823927	+	0.142708i	0.904277	−	0.426946i	$-0.140410\pi$
$373$	1.59127	+	2.75616i	0.0823927	+	0.142708i	−0.821884	+	0.569654i	$0.807077\pi$
$374$		0			0
$375$	0.866025	+	0.500000i	0.0447214	+	0.0258199i
$376$		0			0
$377$	−6.29700	−	11.4080i	−0.324312	−	0.587541i
$378$		0			0
$379$	−21.2413	−	12.2637i	−1.09109	−	0.629943i	−0.157226	−	0.987563i	$-0.550255\pi$
$379$	−21.2413	−	12.2637i	−1.09109	−	0.629943i	−0.933867	+	0.357620i	$0.883588\pi$
$380$		0			0
$381$	−5.92032	−	10.2543i	−0.303307	−	0.525343i
$382$		0			0
$383$	−0.238601	+	0.137756i	−0.0121919	+	0.00703902i	−0.506084	−	0.862484i	$-0.668907\pi$
$383$	−0.238601	+	0.137756i	−0.0121919	+	0.00703902i	0.493892	+	0.869523i	$0.335574\pi$
$384$		0			0
$385$		−	0.282561i		−	0.0144006i
$386$		0			0
$387$	−1.23388	+	2.13713i	−0.0627214	+	0.108637i
$388$		0			0
$389$	−0.575090			−0.0291582			−0.0145791	−	0.999894i	$-0.504641\pi$
$389$	−0.575090			−0.0291582			−0.0145791	+	0.999894i	$0.504641\pi$
$390$		0			0
$391$	15.1628			0.766817
$392$		0			0
$393$	4.43563	−	7.68274i	0.223748	−	0.387543i
$394$		0			0
$395$			1.19615i			0.0601850i
$396$		0			0
$397$	2.87663	−	1.66082i	0.144374	−	0.0833544i	−0.426073	−	0.904689i	$-0.640103\pi$
$397$	2.87663	−	1.66082i	0.144374	−	0.0833544i	0.570447	+	0.821334i	$0.306770\pi$
$398$		0			0
$399$	−0.271233	−	0.469790i	−0.0135786	−	0.0235189i
$400$		0			0
$401$	−9.70261	−	5.60181i	−0.484525	−	0.279741i	0.237775	−	0.971320i	$-0.423582\pi$
$401$	−9.70261	−	5.60181i	−0.484525	−	0.279741i	−0.722300	+	0.691579i	$0.756915\pi$
$402$		0			0
$403$	−4.41114	−	2.66119i	−0.219734	−	0.132563i
$404$		0			0
$405$	−0.866025	−	0.500000i	−0.0430331	−	0.0248452i
$406$		0			0
$407$	23.6303	+	40.9289i	1.17131	+	2.02877i
$408$		0			0
$409$	−21.3919	+	12.3506i	−1.05776	+	0.610698i	−0.924812	−	0.380425i	$-0.875778\pi$
$409$	−21.3919	+	12.3506i	−1.05776	+	0.610698i	−0.132948	+	0.991123i	$0.542444\pi$
$410$		0			0
$411$			17.6598i			0.871092i
$412$		0			0
$413$	−0.00304378	+	0.00527198i	−0.000149775	+	0.000259417i
$414$		0			0
$415$	−2.38234			−0.116944
$416$		0			0
$417$	−3.75787			−0.184024
$418$		0			0
$419$	−8.59633	+	14.8893i	−0.419958	+	0.727389i	−0.995935	−	0.0900770i	$-0.971289\pi$
$419$	−8.59633	+	14.8893i	−0.419958	+	0.727389i	0.575976	+	0.817466i	$0.304622\pi$
$420$		0			0
$421$			35.9492i			1.75206i	0.482261	+	0.876028i	$0.339816\pi$
$421$			35.9492i			1.75206i	−0.482261	+	0.876028i	$0.660184\pi$
$422$		0			0
$423$	−4.01714	+	2.31930i	−0.195320	+	0.112768i
$424$		0			0
$425$	−1.27646	−	2.21089i	−0.0619173	−	0.107244i
$426$		0			0
$427$	0.403559	+	0.232995i	0.0195296	+	0.0112754i
$428$		0			0
$429$	−0.287545	+	14.9468i	−0.0138828	+	0.721638i
$430$		0			0
$431$	−28.7200	−	16.5815i	−1.38339	−	0.798702i	−0.390833	−	0.920462i	$-0.627813\pi$
$431$	−28.7200	−	16.5815i	−1.38339	−	0.798702i	−0.992560	+	0.121760i	$0.961146\pi$
$432$		0			0
$433$	−14.4710	−	25.0645i	−0.695431	−	1.20452i	−0.970035	−	0.242965i	$-0.921880\pi$
$433$	−14.4710	−	25.0645i	−0.695431	−	1.20452i	0.274604	−	0.961558i	$-0.411453\pi$
$434$		0			0
$435$	3.12983	−	1.80701i	0.150064	−	0.0866394i
$436$		0			0
$437$			47.2782i			2.26162i
$438$		0			0
$439$	10.1317	−	17.5487i	0.483561	−	0.837553i	−0.516260	−	0.856432i	$-0.672676\pi$
$439$	10.1317	−	17.5487i	0.483561	−	0.837553i	0.999822	+	0.0188789i	$0.00600969\pi$
$440$		0			0
$441$	6.99536			0.333112
$442$		0			0
$443$	34.9067			1.65847			0.829234	−	0.558902i	$-0.188777\pi$
$443$	34.9067			1.65847			0.829234	+	0.558902i	$0.188777\pi$
$444$		0			0
$445$	−5.22362	+	9.04758i	−0.247624	+	0.428897i
$446$		0			0
$447$		−	13.7467i		−	0.650195i
$448$		0			0
$449$	12.9893	−	7.49938i	0.613003	−	0.353918i	−0.161137	−	0.986932i	$-0.551516\pi$
$449$	12.9893	−	7.49938i	0.613003	−	0.353918i	0.774140	+	0.633015i	$0.218183\pi$
$450$		0			0
$451$	1.93185	+	3.34607i	0.0909673	+	0.157560i
$452$		0			0
$453$	−8.80482	−	5.08346i	−0.413686	−	0.238842i
$454$		0			0
$455$	−0.245667	−	0.00472611i	−0.0115170	−	0.000221564i
$456$		0			0
$457$	−28.4511	−	16.4263i	−1.33089	−	0.768388i	−0.345452	−	0.938437i	$-0.612274\pi$
$457$	−28.4511	−	16.4263i	−1.33089	−	0.768388i	−0.985436	+	0.170048i	$0.945608\pi$
$458$		0			0
$459$	1.27646	+	2.21089i	0.0595799	+	0.103195i
$460$		0			0
$461$	−25.8488	+	14.9238i	−1.20390	+	0.695071i	−0.961420	−	0.275086i	$-0.911294\pi$
$461$	−25.8488	+	14.9238i	−1.20390	+	0.695071i	−0.242478	+	0.970157i	$0.577960\pi$
$462$		0			0
$463$		−	12.8467i		−	0.597036i	−0.954404	−	0.298518i	$-0.903508\pi$
$463$		−	12.8467i		−	0.597036i	0.954404	−	0.298518i	$-0.0964923\pi$
$464$		0			0
$465$	0.714413	−	1.23740i	0.0331301	−	0.0573830i
$466$		0			0
$467$	−11.9000			−0.550665			−0.275333	−	0.961349i	$-0.588788\pi$
$467$	−11.9000			−0.550665			−0.275333	+	0.961349i	$0.588788\pi$
$468$		0			0
$469$	−0.396366			−0.0183025
$470$		0			0
$471$	−4.56873	+	7.91327i	−0.210516	+	0.364624i
$472$		0			0
$473$			10.2319i			0.470465i
$474$		0			0
$475$	6.89363	−	3.98004i	0.316301	−	0.182617i
$476$		0			0
$477$	3.18154	+	5.51059i	0.145673	+	0.252313i
$478$		0			0
$479$	−26.7475	−	15.4427i	−1.22212	−	0.705594i	−0.256754	−	0.966477i	$-0.582653\pi$
$479$	−26.7475	−	15.4427i	−1.22212	−	0.705594i	−0.965371	+	0.260883i	$0.915986\pi$
$480$		0			0
$481$	35.9800	−	19.8603i	1.64055	−	0.905552i
$482$		0			0
$483$	0.350534	+	0.202381i	0.0159498	+	0.00920864i
$484$		0			0
$485$	3.55135	+	6.15111i	0.161258	+	0.279308i
$486$		0			0
$487$	−6.17388	+	3.56449i	−0.279765	+	0.161522i	−0.633317	−	0.773892i	$-0.718307\pi$
$487$	−6.17388	+	3.56449i	−0.279765	+	0.161522i	0.353552	+	0.935415i	$0.384974\pi$
$488$		0			0
$489$			17.3960i			0.786672i
$490$		0			0
$491$	−13.0878	+	22.6688i	−0.590646	+	1.02303i	0.403499	+	0.914980i	$0.367794\pi$
$491$	−13.0878	+	22.6688i	−0.590646	+	1.02303i	−0.994146	+	0.108049i	$0.965540\pi$
$492$		0			0
$493$	−9.22627			−0.415530
$494$		0			0
$495$	−4.14626			−0.186361
$496$		0			0
$497$	−0.212953	+	0.368845i	−0.00955225	+	0.0165450i
$498$		0			0
$499$		−	16.8601i		−	0.754761i	−0.926058	−	0.377381i	$-0.876825\pi$
$499$		−	16.8601i		−	0.754761i	0.926058	−	0.377381i	$-0.123175\pi$
$500$		0			0
$501$	12.0063	−	6.93185i	0.536403	−	0.309692i
$502$		0			0
$503$	−3.82503	−	6.62514i	−0.170550	−	0.295400i	0.768063	−	0.640375i	$-0.221221\pi$
$503$	−3.82503	−	6.62514i	−0.170550	−	0.295400i	−0.938612	+	0.344974i	$0.887888\pi$
$504$		0			0
$505$	15.0272	+	8.67593i	0.668700	+	0.386074i
$506$		0			0
$507$	12.9904	+	0.500000i	0.576923	+	0.0222058i
$508$		0			0
$509$	−34.8439	−	20.1171i	−1.54443	−	0.891676i	−0.998551	−	0.0538111i	$-0.982863\pi$
$509$	−34.8439	−	20.1171i	−1.54443	−	0.891676i	−0.545877	−	0.837865i	$-0.683804\pi$
$510$		0			0
$511$	0.472992	+	0.819245i	0.0209239	+	0.0362413i
$512$		0			0
$513$	−6.89363	+	3.98004i	−0.304361	+	0.175723i
$514$		0			0
$515$		−	3.56147i		−	0.156937i
$516$		0			0
$517$	−9.61642	+	16.6561i	−0.422930	+	0.732536i
$518$		0			0
$519$	−16.4317			−0.721274
$520$		0			0
$521$	−21.8581			−0.957619			−0.478810	−	0.877919i	$-0.658932\pi$
$521$	−21.8581			−0.957619			−0.478810	+	0.877919i	$0.658932\pi$
$522$		0			0
$523$	20.5828	−	35.6505i	0.900024	−	1.55889i	0.0725626	−	0.997364i	$-0.476882\pi$
$523$	20.5828	−	35.6505i	0.900024	−	1.55889i	0.827461	−	0.561523i	$-0.189784\pi$
$524$		0			0
$525$		−	0.0681483i		−	0.00297424i
$526$		0			0
$527$	−3.15897	+	1.82383i	−0.137607	+	0.0794475i
$528$		0			0
$529$	−6.13833	−	10.6319i	−0.266884	−	0.462256i
$530$		0			0
$531$	0.0773604	+	0.0446641i	0.00335716	+	0.00193825i
$532$		0			0
$533$	2.94148	−	1.62364i	0.127410	−	0.0703278i
$534$		0			0
$535$	16.4035	+	9.47055i	0.709184	+	0.409447i
$536$		0			0
$537$	−5.89716	−	10.2142i	−0.254481	−	0.440774i
$538$		0			0
$539$	25.1187	−	14.5023i	1.08194	−	0.624658i
$540$		0			0
$541$		−	7.83663i		−	0.336923i	−0.985708	−	0.168462i	$-0.946120\pi$
$541$		−	7.83663i		−	0.336923i	0.985708	−	0.168462i	$-0.0538799\pi$
$542$		0			0
$543$	2.94476	−	5.10048i	0.126372	−	0.218883i
$544$		0			0
$545$	−16.6875			−0.714813
$546$		0			0
$547$	12.9185			0.552355			0.276178	−	0.961107i	$-0.410932\pi$
$547$	12.9185			0.552355			0.276178	+	0.961107i	$0.410932\pi$
$548$		0			0
$549$	3.41894	−	5.92178i	0.145917	−	0.252735i
$550$		0			0
$551$		−	28.7678i		−	1.22555i
$552$		0			0
$553$	0.0705948	−	0.0407579i	0.00300199	−	0.00173320i
$554$		0			0
$555$	5.69918	+	9.87127i	0.241917	+	0.419012i
$556$		0			0
$557$	25.4603	+	14.6995i	1.07879	+	0.622839i	0.930569	−	0.366116i	$-0.119313\pi$
$557$	25.4603	+	14.6995i	1.07879	+	0.622839i	0.148219	+	0.988955i	$0.452646\pi$
$558$		0			0
$559$	8.89595	+	0.171139i	0.376259	+	0.00723842i
$560$		0			0
$561$	9.16693	+	5.29253i	0.387028	+	0.223451i
$562$		0			0
$563$	2.49886	+	4.32816i	0.105314	+	0.182410i	0.913867	−	0.406014i	$-0.133082\pi$
$563$	2.49886	+	4.32816i	0.105314	+	0.182410i	−0.808552	+	0.588425i	$0.799748\pi$
$564$		0			0
$565$	−10.4349	+	6.02458i	−0.438999	+	0.253456i
$566$		0			0
$567$			0.0681483i			0.00286196i
$568$		0			0
$569$	16.1680	−	28.0038i	0.677799	−	1.17398i	−0.297844	−	0.954615i	$-0.596267\pi$
$569$	16.1680	−	28.0038i	0.677799	−	1.17398i	0.975642	−	0.219367i	$-0.0703993\pi$
$570$		0			0
$571$	27.8943			1.16734			0.583671	−	0.811990i	$-0.301616\pi$
$571$	27.8943			1.16734			0.583671	+	0.811990i	$0.301616\pi$
$572$		0			0
$573$	−18.2183			−0.761082
$574$		0			0
$575$	−2.96971	+	5.14368i	−0.123845	+	0.214506i
$576$		0			0
$577$		−	0.0715833i		−	0.00298005i	−0.999999	−	0.00149003i	$-0.999526\pi$
$577$		−	0.0715833i		−	0.00298005i	0.999999	−	0.00149003i	$-0.000474290\pi$
$578$		0			0
$579$	4.77886	−	2.75908i	0.198603	−	0.114663i
$580$		0			0
$581$	0.0811762	+	0.140601i	0.00336776	+	0.00583312i
$582$		0			0
$583$	22.8484	+	13.1915i	0.946282	+	0.546336i
$584$		0			0
$585$	−0.0693504	+	3.60488i	−0.00286728	+	0.149044i
$586$		0			0
$587$	28.7686	+	16.6096i	1.18741	+	0.685551i	0.957717	−	0.287712i	$-0.0928947\pi$
$587$	28.7686	+	16.6096i	1.18741	+	0.685551i	0.229692	+	0.973263i	$0.426228\pi$
$588$		0			0
$589$	−5.68678	−	9.84980i	−0.234320	−	0.405854i
$590$		0			0
$591$	−21.9309	+	12.6618i	−0.902119	+	0.520838i
$592$		0			0
$593$			12.0914i			0.496536i	0.968691	+	0.248268i	$0.0798614\pi$
$593$			12.0914i			0.496536i	−0.968691	+	0.248268i	$0.920139\pi$
$594$		0			0
$595$	−0.0869884	+	0.150668i	−0.00356618	+	0.00617680i
$596$		0			0
$597$	−23.9189			−0.978936
$598$		0			0
$599$	−17.7145			−0.723794			−0.361897	−	0.932218i	$-0.617871\pi$
$599$	−17.7145			−0.723794			−0.361897	+	0.932218i	$0.617871\pi$
$600$		0			0
$601$	21.0964	−	36.5400i	0.860538	−	1.49050i	−0.0108722	−	0.999941i	$-0.503461\pi$
$601$	21.0964	−	36.5400i	0.860538	−	1.49050i	0.871410	−	0.490555i	$-0.163206\pi$
$602$		0			0
$603$			5.81622i			0.236855i
$604$		0			0
$605$	−5.36200	+	3.09575i	−0.217996	+	0.125860i
$606$		0			0
$607$	7.00720	+	12.1368i	0.284413	+	0.492619i	0.972467	−	0.233042i	$-0.0748678\pi$
$607$	7.00720	+	12.1368i	0.284413	+	0.492619i	−0.688053	+	0.725660i	$0.741534\pi$
$608$		0			0
$609$	−0.213293	−	0.123145i	−0.00864305	−	0.00499007i
$610$		0			0
$611$	14.3205	+	8.63939i	0.579345	+	0.349512i
$612$		0			0
$613$	−37.1083	−	21.4245i	−1.49879	−	0.865328i	−0.498792	−	0.866722i	$-0.666223\pi$
$613$	−37.1083	−	21.4245i	−1.49879	−	0.865328i	−0.999999	+	0.00139405i	$0.999556\pi$
$614$		0			0
$615$	0.465926	+	0.807007i	0.0187879	+	0.0325417i
$616$		0			0
$617$	20.3603	−	11.7550i	0.819676	−	0.473240i	−0.0306285	−	0.999531i	$-0.509751\pi$
$617$	20.3603	−	11.7550i	0.819676	−	0.473240i	0.850305	+	0.526290i	$0.176418\pi$
$618$		0			0
$619$			1.39570i			0.0560981i	0.999607	+	0.0280491i	$0.00892946\pi$
$619$			1.39570i			0.0560981i	−0.999607	+	0.0280491i	$0.991071\pi$
$620$		0			0
$621$	2.96971	−	5.14368i	0.119170	−	0.206409i
$622$		0			0
$623$	0.711963			0.0285242
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−16.5023	+	28.5828i	−0.659038	+	1.14149i
$628$		0			0
$629$		−	29.0990i		−	1.16025i
$630$		0			0
$631$	1.70150	−	0.982362i	0.0677357	−	0.0391072i	−0.465750	−	0.884917i	$-0.654215\pi$
$631$	1.70150	−	0.982362i	0.0677357	−	0.0391072i	0.533485	+	0.845809i	$0.320882\pi$
$632$		0			0
$633$	8.59273	+	14.8830i	0.341530	+	0.591548i
$634$		0			0
$635$	−10.2543	−	5.92032i	−0.406929	−	0.234941i
$636$		0			0
$637$	−12.1886	−	22.0815i	−0.482929	−	0.874902i
$638$		0			0
$639$	5.41239	+	3.12484i	0.214111	+	0.123617i
$640$		0			0
$641$	−5.82684	−	10.0924i	−0.230146	−	0.398625i	0.727705	−	0.685891i	$-0.240587\pi$
$641$	−5.82684	−	10.0924i	−0.230146	−	0.398625i	−0.957851	+	0.287265i	$0.907254\pi$
$642$		0			0
$643$	−1.19971	+	0.692653i	−0.0473120	+	0.0273156i	−0.523469	−	0.852044i	$-0.675363\pi$
$643$	−1.19971	+	0.692653i	−0.0473120	+	0.0273156i	0.476157	+	0.879360i	$0.342029\pi$
$644$		0			0
$645$			2.46775i			0.0971676i
$646$		0			0
$647$	−16.4545	+	28.5000i	−0.646892	+	1.12045i	0.336969	+	0.941516i	$0.390598\pi$
$647$	−16.4545	+	28.5000i	−0.646892	+	1.12045i	−0.983861	+	0.178934i	$0.942735\pi$
$648$		0			0
$649$	0.370378			0.0145386
$650$		0			0
$651$	−0.0973721			−0.00381631
$652$		0			0
$653$	−12.4251	+	21.5209i	−0.486233	+	0.842180i	−0.999875	−	0.0158248i	$-0.994963\pi$
$653$	−12.4251	+	21.5209i	−0.486233	+	0.842180i	0.513642	+	0.858005i	$0.328296\pi$
$654$		0			0
$655$		−	8.87127i		−	0.346629i
$656$		0			0
$657$	12.0215	−	6.94062i	0.469003	−	0.270779i
$658$		0			0
$659$	22.4723	+	38.9232i	0.875398	+	1.51623i	0.856338	+	0.516416i	$0.172734\pi$
$659$	22.4723	+	38.9232i	0.875398	+	1.51623i	0.0190604	+	0.999818i	$0.493933\pi$
$660$		0			0
$661$	−22.3820	−	12.9222i	−0.870557	−	0.502617i	−0.00302403	−	0.999995i	$-0.500963\pi$
$661$	−22.3820	−	12.9222i	−0.870557	−	0.502617i	−0.867533	+	0.497379i	$0.834296\pi$
$662$		0			0
$663$	4.75481	−	7.88147i	0.184661	−	0.306091i
$664$		0			0
$665$	−0.469790	−	0.271233i	−0.0182177	−	0.0105180i
$666$		0			0
$667$	10.7326	+	18.5894i	0.415567	+	0.719783i
$668$		0			0
$669$	−6.28913	+	3.63103i	−0.243152	+	0.140384i
$670$		0			0
$671$		−	28.3517i		−	1.09450i
$672$		0			0
$673$	4.03736	−	6.99291i	0.155629	−	0.269557i	−0.777659	−	0.628686i	$-0.783593\pi$
$673$	4.03736	−	6.99291i	0.155629	−	0.269557i	0.933288	+	0.359129i	$0.116926\pi$
$674$		0			0
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	34.5084			1.32626			0.663132	−	0.748502i	$-0.269227\pi$
$677$	34.5084			1.32626			0.663132	+	0.748502i	$0.269227\pi$
$678$		0			0
$679$	0.242018	−	0.419188i	0.00928782	−	0.0160870i
$680$		0			0
$681$		−	7.98298i		−	0.305909i
$682$		0			0
$683$	14.7325	−	8.50582i	0.563724	−	0.325466i	−0.190915	−	0.981607i	$-0.561145\pi$
$683$	14.7325	−	8.50582i	0.563724	−	0.325466i	0.754639	+	0.656140i	$0.227812\pi$
$684$		0			0
$685$	8.82989	+	15.2938i	0.337373	+	0.584347i
$686$		0			0
$687$	−0.127300	−	0.0734967i	−0.00485680	−	0.00280407i
$688$		0			0
$689$	11.8512	−	19.6444i	0.451497	−	0.748392i
$690$		0			0
$691$	9.99871	+	5.77276i	0.380369	+	0.219606i	0.677979	−	0.735082i	$-0.262856\pi$
$691$	9.99871	+	5.77276i	0.380369	+	0.219606i	−0.297610	+	0.954688i	$0.596189\pi$
$692$		0			0
$693$	0.141281	+	0.244705i	0.00536680	+	0.00929558i
$694$		0			0
$695$	−3.25442	+	1.87894i	−0.123447	+	0.0712722i
$696$		0			0
$697$		−	2.37894i		−	0.0901087i
$698$		0			0
$699$	3.86212	−	6.68939i	0.146079	−	0.253016i
$700$		0			0
$701$	17.9804			0.679110			0.339555	−	0.940586i	$-0.389724\pi$
$701$	17.9804			0.679110			0.339555	+	0.940586i	$0.389724\pi$
$702$		0			0
$703$	90.7318			3.42202
$704$		0			0
$705$	−2.31930	+	4.01714i	−0.0873498	+	0.151294i
$706$		0			0
$707$		−	1.18250i		−	0.0444725i
$708$		0			0
$709$	2.78105	−	1.60564i	0.104445	−	0.0603011i	−0.446868	−	0.894600i	$-0.647461\pi$
$709$	2.78105	−	1.60564i	0.104445	−	0.0603011i	0.551312	+	0.834299i	$0.314127\pi$
$710$		0			0
$711$	−0.598076	−	1.03590i	−0.0224296	−	0.0388492i
$712$		0			0
$713$	7.34943	+	4.24319i	0.275238	+	0.158909i
$714$		0			0
$715$	7.22438	+	13.0881i	0.270177	+	0.489467i
$716$		0			0
$717$	12.5166	+	7.22644i	0.467440	+	0.269877i
$718$		0			0
$719$	21.5201	+	37.2739i	0.802563	+	1.39008i	0.917924	+	0.396756i	$0.129864\pi$
$719$	21.5201	+	37.2739i	0.802563	+	1.39008i	−0.115361	+	0.993324i	$0.536802\pi$
$720$		0			0
$721$	−0.210192	+	0.121354i	−0.00782795	+	0.00451947i
$722$		0			0
$723$		−	23.9528i		−	0.890814i
$724$		0			0
$725$	1.80701	−	3.12983i	0.0671106	−	0.116239i
$726$		0			0
$727$	−8.96129			−0.332356			−0.166178	−	0.986096i	$-0.553143\pi$
$727$	−8.96129			−0.332356			−0.166178	+	0.986096i	$0.553143\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	3.14998	−	5.45592i	0.116506	−	0.201795i
$732$		0			0
$733$		−	13.4176i		−	0.495592i	−0.968812	−	0.247796i	$-0.920294\pi$
$733$		−	13.4176i		−	0.495592i	0.968812	−	0.247796i	$-0.0797063\pi$
$734$		0			0
$735$	6.05816	−	3.49768i	0.223458	−	0.129014i
$736$		0			0
$737$	12.0578	+	20.8847i	0.444154	+	0.769298i
$738$		0			0
$739$	−18.0531	−	10.4229i	−0.664092	−	0.383414i	0.129742	−	0.991548i	$-0.458585\pi$
$739$	−18.0531	−	10.4229i	−0.664092	−	0.383414i	−0.793835	+	0.608134i	$0.791918\pi$
$740$		0			0
$741$	24.5747	+	14.8257i	0.902775	+	0.544634i
$742$		0			0
$743$	−4.78027	−	2.75989i	−0.175371	−	0.101250i	0.409745	−	0.912200i	$-0.365618\pi$
$743$	−4.78027	−	2.75989i	−0.175371	−	0.101250i	−0.585116	+	0.810950i	$0.698951\pi$
$744$		0			0
$745$	−6.87333	−	11.9050i	−0.251819	−	0.436164i
$746$		0			0
$747$	2.06316	−	1.19117i	0.0754872	−	0.0435826i
$748$		0			0
$749$		−	1.29080i		−	0.0471650i
$750$		0			0
$751$	−27.0426	+	46.8391i	−0.986797	+	1.70918i	−0.353137	+	0.935572i	$0.614885\pi$
$751$	−27.0426	+	46.8391i	−0.986797	+	1.70918i	−0.633660	+	0.773611i	$0.718448\pi$
$752$		0			0
$753$	25.8079			0.940493
$754$		0			0
$755$	−10.1669			−0.370012
$756$		0			0
$757$	−2.03564	+	3.52583i	−0.0739866	+	0.128149i	−0.900645	−	0.434555i	$-0.856906\pi$
$757$	−2.03564	+	3.52583i	−0.0739866	+	0.128149i	0.826659	+	0.562704i	$0.190239\pi$
$758$		0			0
$759$		−	24.6264i		−	0.893881i
$760$		0			0
$761$	5.34009	−	3.08310i	0.193578	−	0.111762i	−0.400079	−	0.916481i	$-0.631017\pi$
$761$	5.34009	−	3.08310i	0.193578	−	0.111762i	0.593656	+	0.804719i	$0.297684\pi$
$762$		0			0
$763$	0.568612	+	0.984865i	0.0205851	+	0.0356545i
$764$		0			0
$765$	2.21089	+	1.27646i	0.0799348	+	0.0461504i
$766$		0			0
$767$	0.00619494	−	0.322017i	0.000223686	−	0.0116274i
$768$		0			0
$769$	−0.266481	−	0.153853i	−0.00960955	−	0.00554808i	0.495188	−	0.868786i	$-0.335099\pi$
$769$	−0.266481	−	0.153853i	−0.00960955	−	0.00554808i	−0.504797	+	0.863238i	$0.668433\pi$
$770$		0			0
$771$	3.08920	+	5.35066i	0.111255	+	0.192699i
$772$		0			0
$773$	18.8391	−	10.8767i	0.677594	−	0.391209i	−0.121354	−	0.992609i	$-0.538724\pi$
$773$	18.8391	−	10.8767i	0.677594	−	0.391209i	0.798948	+	0.601400i	$0.205390\pi$
$774$		0			0
$775$		−	1.42883i		−	0.0513249i
$776$		0			0
$777$	0.388390	−	0.672711i	0.0139334	−	0.0241334i
$778$		0			0
$779$	7.41761			0.265764
$780$		0			0
$781$	25.9129			0.927235
$782$		0			0
$783$	−1.80701	+	3.12983i	−0.0645772	+	0.111851i
$784$		0			0
$785$			9.13746i			0.326130i
$786$		0			0
$787$	−26.0848	+	15.0601i	−0.929822	+	0.536833i	−0.886755	−	0.462239i	$-0.847046\pi$
$787$	−26.0848	+	15.0601i	−0.929822	+	0.536833i	−0.0430670	+	0.999072i	$0.513713\pi$
$788$		0			0
$789$	−3.77244	−	6.53405i	−0.134302	−	0.232618i
$790$		0			0
$791$	0.711120	+	0.410565i	0.0252845	+	0.0145980i
$792$		0			0
$793$	−24.6498	−	0.474209i	−0.875339	−	0.0168397i
$794$		0			0
$795$	5.51059	+	3.18154i	0.195440	+	0.112838i
$796$		0			0
$797$	6.58127	+	11.3991i	0.233120	+	0.403776i	0.958725	−	0.284336i	$-0.0917730\pi$
$797$	6.58127	+	11.3991i	0.233120	+	0.403776i	−0.725604	+	0.688112i	$0.758440\pi$
$798$		0			0
$799$	10.2554	−	5.92097i	0.362810	−	0.209469i
$800$		0			0
$801$		−	10.4472i		−	0.369135i
$802$		0			0
$803$	28.7776	−	49.8443i	1.01554	−	1.75897i
$804$		0			0
$805$	0.404761			0.0142660
$806$		0			0
$807$	−15.1221			−0.532324
$808$		0			0
$809$	−13.1402	+	22.7595i	−0.461985	+	0.800182i	−0.999060	−	0.0433528i	$-0.986196\pi$
$809$	−13.1402	+	22.7595i	−0.461985	+	0.800182i	0.537075	+	0.843535i	$0.319529\pi$
$810$		0			0
$811$			35.6658i			1.25240i	0.779664	+	0.626198i	$0.215390\pi$
$811$			35.6658i			1.25240i	−0.779664	+	0.626198i	$0.784610\pi$
$812$		0			0
$813$	−17.6604	+	10.1962i	−0.619377	+	0.357598i
$814$		0			0
$815$	8.69798	+	15.0653i	0.304677	+	0.527716i
$816$		0			0
$817$	17.0118	+	9.82174i	0.595166	+	0.343619i
$818$		0			0
$819$	0.215117	−	0.118741i	0.00751679	−	0.00414913i
$820$		0			0
$821$	21.3249	+	12.3119i	0.744245	+	0.429690i	0.823611	−	0.567156i	$-0.191956\pi$
$821$	21.3249	+	12.3119i	0.744245	+	0.429690i	−0.0793658	+	0.996846i	$0.525290\pi$
$822$		0			0
$823$	−1.57509	−	2.72814i	−0.0549042	−	0.0950968i	0.837267	−	0.546794i	$-0.184152\pi$
$823$	−1.57509	−	2.72814i	−0.0549042	−	0.0950968i	−0.892171	+	0.451697i	$0.850819\pi$
$824$		0			0
$825$	−3.59077	+	2.07313i	−0.125015	+	0.0721772i
$826$		0			0
$827$			26.3343i			0.915733i	0.889021	+	0.457866i	$0.151386\pi$
$827$			26.3343i			0.915733i	−0.889021	+	0.457866i	$0.848614\pi$
$828$		0			0
$829$	1.85189	−	3.20757i	0.0643189	−	0.111404i	−0.832073	−	0.554667i	$-0.812846\pi$
$829$	1.85189	−	3.20757i	0.0643189	−	0.111404i	0.896392	+	0.443263i	$0.146179\pi$
$830$		0			0
$831$	4.77781			0.165740
$832$		0			0
$833$	−17.8585			−0.618762
$834$		0			0
$835$	6.93185	−	12.0063i	0.239887	−	0.415496i
$836$		0			0
$837$			1.42883i			0.0493874i
$838$		0			0
$839$	−3.32218	+	1.91806i	−0.114694	+	0.0662188i	−0.556250	−	0.831015i	$-0.687760\pi$
$839$	−3.32218	+	1.91806i	−0.114694	+	0.0662188i	0.441555	+	0.897234i	$0.354427\pi$
$840$		0			0
$841$	7.96945	+	13.8035i	0.274809	+	0.475982i
$842$		0			0
$843$	5.25915	+	3.03637i	0.181135	+	0.104578i
$844$		0			0
$845$	11.5000	−	6.06218i	0.395612	−	0.208545i
$846$		0			0
$847$	0.365412	+	0.210971i	0.0125557	+	0.00724903i
$848$		0			0
$849$	−10.0906	−	17.4775i	−0.346310	−	0.599827i
$850$		0			0
$851$	−58.6296	+	33.8498i	−2.00980	+	1.16036i
$852$		0			0
$853$			18.6089i			0.637155i	0.947897	+	0.318578i	$0.103205\pi$
$853$			18.6089i			0.637155i	−0.947897	+	0.318578i	$0.896795\pi$
$854$		0			0
$855$	−3.98004	+	6.89363i	−0.136114	+	0.235757i
$856$		0			0
$857$	−25.1469			−0.859002			−0.429501	−	0.903066i	$-0.641311\pi$
$857$	−25.1469			−0.859002			−0.429501	+	0.903066i	$0.641311\pi$
$858$		0			0
$859$	51.8717			1.76984			0.884920	−	0.465744i	$-0.154213\pi$
$859$	51.8717			1.76984			0.884920	+	0.465744i	$0.154213\pi$
$860$		0			0
$861$	0.0317521	−	0.0549962i	0.00108211	−	0.00187427i
$862$		0			0
$863$		−	2.53391i		−	0.0862552i	−0.999070	−	0.0431276i	$-0.986268\pi$
$863$		−	2.53391i		−	0.0862552i	0.999070	−	0.0431276i	$-0.0137322\pi$
$864$		0			0
$865$	−14.2303	+	8.21587i	−0.483845	+	0.279348i
$866$		0			0
$867$	5.24131	+	9.07822i	0.178004	+	0.308313i
$868$		0			0
$869$	−4.29511	−	2.47978i	−0.145702	−	0.0841208i
$870$		0			0
$871$	18.3595	−	10.1341i	0.622086	−	0.343380i
$872$		0			0
$873$	−6.15111	−	3.55135i	−0.208184	−	0.120195i
$874$		0			0
$875$	−0.0340742	−	0.0590182i	−0.00115192	−	0.00199518i
$876$		0			0
$877$	32.7720	−	18.9209i	1.10663	−	0.638914i	0.168676	−	0.985672i	$-0.446051\pi$
$877$	32.7720	−	18.9209i	1.10663	−	0.638914i	0.937955	+	0.346758i	$0.112717\pi$
$878$		0			0
$879$		−	11.4013i		−	0.384556i
$880$		0			0
$881$	12.4488	−	21.5619i	0.419409	−	0.726438i	−0.576471	−	0.817118i	$-0.695571\pi$
$881$	12.4488	−	21.5619i	0.419409	−	0.726438i	0.995880	+	0.0906794i	$0.0289039\pi$
$882$		0			0
$883$	−3.54539			−0.119312			−0.0596559	−	0.998219i	$-0.519000\pi$
$883$	−3.54539			−0.119312			−0.0596559	+	0.998219i	$0.519000\pi$
$884$		0			0
$885$	0.0893281			0.00300273
$886$		0			0
$887$	−0.00386375	+	0.00669220i	−0.000129732	+	0.000224702i	−0.866090	−	0.499888i	$-0.833375\pi$
$887$	−0.00386375	+	0.00669220i	−0.000129732	+	0.000224702i	0.865961	+	0.500112i	$0.166708\pi$
$888$		0			0
$889$			0.806920i			0.0270632i
$890$		0			0
$891$	3.59077	−	2.07313i	0.120295	−	0.0694525i
$892$		0			0
$893$	18.4618	+	31.9768i	0.617800	+	1.07006i
$894$		0			0
$895$	−10.2142	−	5.89716i	−0.341422	−	0.197120i
$896$		0			0
$897$	−21.4109	−	0.411901i	−0.714889	−	0.0137530i
$898$		0			0
$899$	−4.47198	−	2.58190i	−0.149149	−	0.0861111i
$900$		0			0
$901$	−8.12220	−	14.0681i	−0.270590	−	0.468675i
$902$		0			0
$903$	0.145642	−	0.0840865i	0.00484667	−	0.00279822i
$904$		0			0
$905$		−	5.88953i		−	0.195775i
$906$		0			0
$907$	−15.1775	+	26.2882i	−0.503962	+	0.872887i	0.496028	+	0.868307i	$0.334791\pi$
$907$	−15.1775	+	26.2882i	−0.503962	+	0.872887i	−0.999990	+	0.00458044i	$0.998542\pi$
$908$		0			0
$909$	−17.3519			−0.575525
$910$		0			0
$911$	−17.1302			−0.567550			−0.283775	−	0.958891i	$-0.591587\pi$
$911$	−17.1302			−0.567550			−0.283775	+	0.958891i	$0.591587\pi$
$912$		0			0
$913$	4.93890	−	8.55443i	0.163454	−	0.283110i
$914$		0			0
$915$		−	6.83788i		−	0.226053i
$916$		0			0
$917$	−0.523566	+	0.302281i	−0.0172897	+	0.00998220i
$918$		0			0
$919$	−14.8453	−	25.7127i	−0.489700	−	0.848185i	0.510230	−	0.860038i	$-0.329560\pi$
$919$	−14.8453	−	25.7127i	−0.489700	−	0.848185i	−0.999930	+	0.0118531i	$0.996227\pi$
$920$		0			0
$921$	9.38546	+	5.41870i	0.309262	+	0.178552i
$922$		0			0
$923$	0.433418	−	22.5294i	0.0142661	−	0.741564i
$924$		0			0
$925$	9.87127	+	5.69918i	0.324565	+	0.187388i
$926$		0			0
$927$	1.78074	+	3.08433i	0.0584871	+	0.101303i
$928$		0			0
$929$	39.2752	−	22.6755i	1.28858	−	0.743961i	0.310177	−	0.950679i	$-0.399612\pi$
$929$	39.2752	−	22.6755i	1.28858	−	0.743961i	0.978400	+	0.206718i	$0.0662784\pi$
$930$		0			0
$931$		−	55.6836i		−	1.82496i
$932$		0			0
$933$	13.2386	−	22.9299i	0.433412	−	0.750691i
$934$		0			0
$935$	10.5851			0.346168
$936$		0			0
$937$	11.4107			0.372770			0.186385	−	0.982477i	$-0.440323\pi$
$937$	11.4107			0.372770			0.186385	+	0.982477i	$0.440323\pi$
$938$		0			0
$939$	−8.17669	+	14.1624i	−0.266836	+	0.462174i
$940$		0			0
$941$		−	44.7284i		−	1.45810i	−0.684459	−	0.729051i	$-0.739962\pi$
$941$		−	44.7284i		−	1.45810i	0.684459	−	0.729051i	$-0.260038\pi$
$942$		0			0
$943$	−4.79315	+	2.76733i	−0.156086	+	0.0901166i
$944$		0			0
$945$	0.0340742	+	0.0590182i	0.00110843	+	0.00191986i
$946$		0			0
$947$	13.6568	+	7.88476i	0.443786	+	0.256220i	0.705202	−	0.709006i	$-0.250856\pi$
$947$	13.6568	+	7.88476i	0.443786	+	0.256220i	−0.261416	+	0.965226i	$0.584189\pi$
$948$		0			0
$949$	−42.8548	−	25.8538i	−1.39113	−	0.839250i
$950$		0			0
$951$	19.0671	+	11.0084i	0.618292	+	0.356971i
$952$		0			0
$953$	−15.8843	−	27.5124i	−0.514543	−	0.891214i	−0.999858	−	0.0168748i	$-0.994628\pi$
$953$	−15.8843	−	27.5124i	−0.514543	−	0.891214i	0.485315	−	0.874339i	$-0.338705\pi$
$954$		0			0
$955$	−15.7775	+	9.10916i	−0.510549	+	0.294766i
$956$		0			0
$957$			14.9847i			0.484385i
$958$		0			0
$959$	0.601742	−	1.04225i	0.0194313	−	0.0336559i
$960$		0			0
$961$	28.9585			0.934144
$962$		0			0
$963$	−18.9411			−0.610368
$964$		0			0
$965$	2.75908	−	4.77886i	0.0888178	−	0.153837i
$966$		0			0
$967$			45.9318i			1.47707i	0.674216	+	0.738534i	$0.264482\pi$
$967$			45.9318i			1.47707i	−0.674216	+	0.738534i	$0.735518\pi$
$968$		0			0
$969$	17.5988	−	10.1607i	0.565356	−	0.326409i
$970$		0			0
$971$	−7.07794	−	12.2594i	−0.227142	−	0.393421i	0.729818	−	0.683642i	$-0.239605\pi$
$971$	−7.07794	−	12.2594i	−0.227142	−	0.393421i	−0.956960	+	0.290220i	$0.906271\pi$
$972$		0			0
$973$	0.221783	+	0.128046i	0.00711004	+	0.00410498i
$974$		0			0
$975$	1.74238	+	3.15660i	0.0558009	+	0.101092i
$976$		0			0
$977$	−33.4755	−	19.3271i	−1.07098	−	0.618328i	−0.142528	−	0.989791i	$-0.545523\pi$
$977$	−33.4755	−	19.3271i	−1.07098	−	0.618328i	−0.928448	+	0.371463i	$0.878856\pi$
$978$		0			0
$979$	−21.6585	−	37.5137i	−0.692210	−	1.19894i
$980$		0			0
$981$	14.4518	−	8.34374i	0.461410	−	0.266395i
$982$		0			0
$983$		−	8.18510i		−	0.261064i	−0.991444	−	0.130532i	$-0.958331\pi$
$983$		−	8.18510i		−	0.261064i	0.991444	−	0.130532i	$-0.0416686\pi$
$984$		0			0
$985$	−12.6618	+	21.9309i	−0.403440	+	0.698778i
$986$		0			0
$987$	0.316113			0.0100620
$988$		0			0
$989$	−14.6570			−0.466065
$990$		0			0
$991$	−14.7104	+	25.4791i	−0.467290	+	0.809370i	−0.999302	−	0.0373668i	$-0.988103\pi$
$991$	−14.7104	+	25.4791i	−0.467290	+	0.809370i	0.532011	+	0.846737i	$0.321436\pi$
$992$		0			0
$993$		−	24.3677i		−	0.773286i
$994$		0			0
$995$	−20.7144	+	11.9595i	−0.656690	+	0.379140i
$996$		0			0
$997$	17.7596	+	30.7605i	0.562452	+	0.974196i	0.997282	+	0.0736832i	$0.0234754\pi$
$997$	17.7596	+	30.7605i	0.562452	+	0.974196i	−0.434829	+	0.900513i	$0.643191\pi$
$998$		0			0
$999$	−9.87127	−	5.69918i	−0.312313	−	0.180314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	780.2.cc.b.121.3	✓	8
3.2	odd	2		2340.2.dj.c.901.1		8
5.2	odd	4		3900.2.bw.l.2149.3		8
5.3	odd	4		3900.2.bw.g.2149.2		8
5.4	even	2		3900.2.cd.l.901.2		8
13.10	even	6	inner	780.2.cc.b.361.1	yes	8
39.23	odd	6		2340.2.dj.c.361.3		8
65.23	odd	12		3900.2.bw.l.49.3		8
65.49	even	6		3900.2.cd.l.2701.2		8
65.62	odd	12		3900.2.bw.g.49.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
780.2.cc.b.121.3	✓	8	1.1	even	1	trivial
780.2.cc.b.361.1	yes	8	13.10	even	6	inner
2340.2.dj.c.361.3		8	39.23	odd	6
2340.2.dj.c.901.1		8	3.2	odd	2
3900.2.bw.g.49.2		8	65.62	odd	12
3900.2.bw.g.2149.2		8	5.3	odd	4
3900.2.bw.l.49.3		8	65.23	odd	12
3900.2.bw.l.2149.3		8	5.2	odd	4
3900.2.cd.l.901.2		8	5.4	even	2
3900.2.cd.l.2701.2		8	65.49	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	780.cc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +1.00000i q^{5} +(0.0590182 - 0.0340742i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-3.59077 - 2.07313i) q^{11} +(-1.86250 + 3.08725i) q^{13} +(-0.866025 - 0.500000i) q^{15} +(1.27646 + 2.21089i) q^{17} +(-6.89363 + 3.98004i) q^{19} +0.0681483i q^{21} +(2.96971 - 5.14368i) q^{23} -1.00000 q^{25} +1.00000 q^{27} +(-1.80701 + 3.12983i) q^{29} +1.42883i q^{31} +(3.59077 - 2.07313i) q^{33} +(0.0340742 + 0.0590182i) q^{35} +(-9.87127 - 5.69918i) q^{37} +(-1.74238 - 3.15660i) q^{39} +(-0.807007 - 0.465926i) q^{41} +(-1.23388 - 2.13713i) q^{43} +(0.866025 - 0.500000i) q^{45} -4.63859i q^{47} +(-3.49768 + 6.05816i) q^{49} -2.55291 q^{51} -6.36308 q^{53} +(2.07313 - 3.59077i) q^{55} -7.96008i q^{57} +(-0.0773604 + 0.0446641i) q^{59} +(3.41894 + 5.92178i) q^{61} +(-0.0590182 - 0.0340742i) q^{63} +(-3.08725 - 1.86250i) q^{65} +(-5.03699 - 2.90811i) q^{67} +(2.96971 + 5.14368i) q^{69} +(-5.41239 + 3.12484i) q^{71} +13.8812i q^{73} +(0.500000 - 0.866025i) q^{75} -0.282561 q^{77} +1.19615 q^{79} +(-0.500000 + 0.866025i) q^{81} +2.38234i q^{83} +(-2.21089 + 1.27646i) q^{85} +(-1.80701 - 3.12983i) q^{87} +(9.04758 + 5.22362i) q^{89} +(-0.00472611 + 0.245667i) q^{91} +(-1.23740 - 0.714413i) q^{93} +(-3.98004 - 6.89363i) q^{95} +(6.15111 - 3.55135i) q^{97} +4.14626i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 4 q^{9} - 12 q^{11} + 4 q^{17} + 12 q^{19} + 4 q^{23} - 8 q^{25} + 8 q^{27} - 8 q^{29} + 12 q^{33} + 8 q^{35} - 24 q^{37} - 16 q^{43} - 4 q^{49} - 8 q^{51} + 16 q^{53} + 4 q^{55} + 24 q^{59}+ \cdots + 48 q^{97}+O(q^{100}) \) 8 * q - 4 * q^3 - 4 * q^9 - 12 * q^11 + 4 * q^17 + 12 * q^19 + 4 * q^23 - 8 * q^25 + 8 * q^27 - 8 * q^29 + 12 * q^33 + 8 * q^35 - 24 * q^37 - 16 * q^43 - 4 * q^49 - 8 * q^51 + 16 * q^53 + 4 * q^55 + 24 * q^59 + 8 * q^61 + 24 * q^67 + 4 * q^69 - 12 * q^71 + 4 * q^75 - 8 * q^77 - 32 * q^79 - 4 * q^81 - 8 * q^87 - 12 * q^89 + 8 * q^91 - 24 * q^93 - 12 * q^95 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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