LMFDB - Embedded newform 720.2.cu.b.353.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(113,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 10, 9]))

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

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

chi := DirichletCharacter("720.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.cu (of order $12$, degree $4$, not 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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			353.1
Root			$0.500000 - 0.410882i$ of defining polynomial
Character	$\chi$	$=$	720.353
Dual form			720.2.cu.b.257.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73022 - 0.0795432i) q^{3} +(-0.139908 + 2.23169i) q^{5} +(0.622279 + 2.32238i) q^{7} +(2.98735 + 0.275255i) q^{9} +O(q^{10})$	\(q+(-1.73022 - 0.0795432i) q^{3} +(-0.139908 + 2.23169i) q^{5} +(0.622279 + 2.32238i) q^{7} +(2.98735 + 0.275255i) q^{9} +(-0.991757 - 0.572591i) q^{11} +(-0.640322 + 2.38971i) q^{13} +(0.419588 - 3.85019i) q^{15} +(-4.99855 - 4.99855i) q^{17} +2.78390i q^{19} +(-0.891952 - 4.06773i) q^{21} +(5.95746 + 1.59630i) q^{23} +(-4.96085 - 0.624462i) q^{25} +(-5.14688 - 0.713876i) q^{27} +(0.672250 - 1.16437i) q^{29} +(-1.25223 - 2.16892i) q^{31} +(1.67042 + 1.06960i) q^{33} +(-5.26988 + 1.06381i) q^{35} +(-8.16761 + 8.16761i) q^{37} +(1.29799 - 4.08381i) q^{39} +(-1.70826 + 0.986264i) q^{41} +(-8.68498 + 2.32713i) q^{43} +(-1.03224 + 6.62831i) q^{45} +(-11.9118 + 3.19175i) q^{47} +(1.05598 - 0.609669i) q^{49} +(8.25101 + 9.04622i) q^{51} +(1.84828 - 1.84828i) q^{53} +(1.41660 - 2.13318i) q^{55} +(0.221441 - 4.81678i) q^{57} +(-1.31456 - 2.27688i) q^{59} +(-3.54275 + 6.13623i) q^{61} +(1.21972 + 7.10903i) q^{63} +(-5.24351 - 1.76334i) q^{65} +(-0.0545285 - 0.0146109i) q^{67} +(-10.1808 - 3.23582i) q^{69} -9.10005i q^{71} +(7.82779 + 7.82779i) q^{73} +(8.53371 + 1.47506i) q^{75} +(0.712623 - 2.65955i) q^{77} +(8.46375 + 4.88655i) q^{79} +(8.84847 + 1.64456i) q^{81} +(-0.724794 - 2.70497i) q^{83} +(11.8545 - 10.4559i) q^{85} +(-1.25576 + 1.96115i) q^{87} -4.87832 q^{89} -5.94827 q^{91} +(1.99411 + 3.85233i) q^{93} +(-6.21280 - 0.389491i) q^{95} +(2.08981 + 7.79929i) q^{97} +(-2.80511 - 1.98351i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{5} - 8 q^{7}+O(q^{10}) $ 16 * q - 12 * q^5 - 8 * q^7	$ 16 q - 12 q^{5} - 8 q^{7} + 24 q^{15} + 24 q^{21} + 24 q^{23} - 16 q^{25} + 8 q^{31} + 24 q^{41} + 36 q^{45} - 48 q^{47} + 48 q^{51} - 24 q^{55} + 24 q^{57} - 24 q^{61} + 48 q^{63} + 16 q^{67} + 16 q^{73} - 72 q^{77} + 24 q^{81} - 48 q^{83} - 4 q^{85} + 48 q^{87} + 72 q^{93} - 84 q^{95} - 48 q^{97}+O(q^{100}) $ 16 * q - 12 * q^5 - 8 * q^7 + 24 * q^15 + 24 * q^21 + 24 * q^23 - 16 * q^25 + 8 * q^31 + 24 * q^41 + 36 * q^45 - 48 * q^47 + 48 * q^51 - 24 * q^55 + 24 * q^57 - 24 * q^61 + 48 * q^63 + 16 * q^67 + 16 * q^73 - 72 * q^77 + 24 * q^81 - 48 * q^83 - 4 * q^85 + 48 * q^87 + 72 * q^93 - 84 * q^95 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.73022	−	0.0795432i	−0.998945	−	0.0459243i
$3$	−1.73022	−	0.0795432i	−0.998945	−	0.0459243i
$4$		0			0
$5$	−0.139908	+	2.23169i	−0.0625688	+	0.998041i
$5$	−0.139908	+	2.23169i	−0.0625688	+	0.998041i
$6$		0			0
$7$	0.622279	+	2.32238i	0.235199	+	0.877776i	0.978059	+	0.208328i	$0.0668023\pi$
$7$	0.622279	+	2.32238i	0.235199	+	0.877776i	−0.742860	+	0.669447i	$0.766531\pi$
$8$		0			0
$9$	2.98735	+	0.275255i	0.995782	+	0.0917517i
$10$		0			0
$11$	−0.991757	−	0.572591i	−0.299026	−	0.172643i	0.342979	−	0.939343i	$-0.388564\pi$
$11$	−0.991757	−	0.572591i	−0.299026	−	0.172643i	−0.642005	+	0.766700i	$0.721897\pi$
$12$		0			0
$13$	−0.640322	+	2.38971i	−0.177593	+	0.662788i	0.818502	+	0.574504i	$0.194805\pi$
$13$	−0.640322	+	2.38971i	−0.177593	+	0.662788i	−0.996095	+	0.0882838i	$0.971862\pi$
$14$		0			0
$15$	0.419588	−	3.85019i	0.108337	−	0.994114i
$16$		0			0
$17$	−4.99855	−	4.99855i	−1.21233	−	1.21233i	−0.970259	−	0.242068i	$-0.922174\pi$
$17$	−4.99855	−	4.99855i	−1.21233	−	1.21233i	−0.242068	−	0.970259i	$-0.577826\pi$
$18$		0			0
$19$			2.78390i			0.638671i	0.947642	+	0.319336i	$0.103460\pi$
$19$			2.78390i			0.638671i	−0.947642	+	0.319336i	$0.896540\pi$
$20$		0			0
$21$	−0.891952	−	4.06773i	−0.194640	−	0.887651i
$22$		0			0
$23$	5.95746	+	1.59630i	1.24222	+	0.332851i	0.819325	−	0.573330i	$-0.194349\pi$
$23$	5.95746	+	1.59630i	1.24222	+	0.332851i	0.422891	+	0.906181i	$0.361015\pi$
$24$		0			0
$25$	−4.96085	−	0.624462i	−0.992170	−	0.124892i
$26$		0			0
$27$	−5.14688	−	0.713876i	−0.990518	−	0.137386i
$28$		0			0
$29$	0.672250	−	1.16437i	0.124834	−	0.216218i	−0.796834	−	0.604198i	$-0.793494\pi$
$29$	0.672250	−	1.16437i	0.124834	−	0.216218i	0.921668	+	0.387980i	$0.126827\pi$
$30$		0			0
$31$	−1.25223	−	2.16892i	−0.224907	−	0.389550i	0.731385	−	0.681965i	$-0.238874\pi$
$31$	−1.25223	−	2.16892i	−0.224907	−	0.389550i	−0.956292	+	0.292415i	$0.905541\pi$
$32$		0			0
$33$	1.67042	+	1.06960i	0.290782	+	0.186193i
$34$		0			0
$35$	−5.26988	+	1.06381i	−0.890772	+	0.179817i
$36$		0			0
$37$	−8.16761	+	8.16761i	−1.34275	+	1.34275i	−0.449434	+	0.893314i	$0.648374\pi$
$37$	−8.16761	+	8.16761i	−1.34275	+	1.34275i	−0.893314	+	0.449434i	$0.851626\pi$
$38$		0			0
$39$	1.29799	−	4.08381i	0.207844	−	0.653932i
$40$		0			0
$41$	−1.70826	+	0.986264i	−0.266785	+	0.154029i	−0.627426	−	0.778676i	$-0.715891\pi$
$41$	−1.70826	+	0.986264i	−0.266785	+	0.154029i	0.360641	+	0.932705i	$0.382558\pi$
$42$		0			0
$43$	−8.68498	+	2.32713i	−1.32445	+	0.354885i	−0.850642	−	0.525745i	$-0.823787\pi$
$43$	−8.68498	+	2.32713i	−1.32445	+	0.354885i	−0.473805	+	0.880630i	$0.657120\pi$
$44$		0			0
$45$	−1.03224	+	6.62831i	−0.153877	+	0.988090i
$46$		0			0
$47$	−11.9118	+	3.19175i	−1.73751	+	0.465565i	−0.981891	−	0.189445i	$-0.939331\pi$
$47$	−11.9118	+	3.19175i	−1.73751	+	0.465565i	−0.755621	+	0.655010i	$0.772665\pi$
$48$		0			0
$49$	1.05598	−	0.609669i	0.150854	−	0.0870956i
$50$		0			0
$51$	8.25101	+	9.04622i	1.15537	+	1.26672i
$52$		0			0
$53$	1.84828	−	1.84828i	0.253881	−	0.253881i	−0.568679	−	0.822560i	$-0.692545\pi$
$53$	1.84828	−	1.84828i	0.253881	−	0.253881i	0.822560	+	0.568679i	$0.192545\pi$
$54$		0			0
$55$	1.41660	−	2.13318i	0.191014	−	0.287638i
$56$		0			0
$57$	0.221441	−	4.81678i	0.0293305	−	0.637998i
$58$		0			0
$59$	−1.31456	−	2.27688i	−0.171141	−	0.296424i	0.767678	−	0.640835i	$-0.221412\pi$
$59$	−1.31456	−	2.27688i	−0.171141	−	0.296424i	−0.938819	+	0.344411i	$0.888079\pi$
$60$		0			0
$61$	−3.54275	+	6.13623i	−0.453603	+	0.785664i	−0.998607	−	0.0527700i	$-0.983195\pi$
$61$	−3.54275	+	6.13623i	−0.453603	+	0.785664i	0.545004	+	0.838434i	$0.316528\pi$
$62$		0			0
$63$	1.21972	+	7.10903i	0.153670	+	0.895653i
$64$		0			0
$65$	−5.24351	−	1.76334i	−0.650377	−	0.218715i
$66$		0			0
$67$	−0.0545285	−	0.0146109i	−0.00666172	−	0.00178500i	0.255487	−	0.966813i	$-0.417764\pi$
$67$	−0.0545285	−	0.0146109i	−0.00666172	−	0.00178500i	−0.262148	+	0.965028i	$0.584431\pi$
$68$		0			0
$69$	−10.1808	−	3.23582i	−1.22562	−	0.389547i
$70$		0			0
$71$		−	9.10005i		−	1.07998i	−0.841672	−	0.539989i	$-0.818429\pi$
$71$		−	9.10005i		−	1.07998i	0.841672	−	0.539989i	$-0.181571\pi$
$72$		0			0
$73$	7.82779	+	7.82779i	0.916174	+	0.916174i	0.996749	−	0.0805747i	$-0.0256756\pi$
$73$	7.82779	+	7.82779i	0.916174	+	0.916174i	−0.0805747	+	0.996749i	$0.525676\pi$
$74$		0			0
$75$	8.53371	+	1.47506i	0.985388	+	0.170325i
$76$		0			0
$77$	0.712623	−	2.65955i	0.0812109	−	0.303083i
$78$		0			0
$79$	8.46375	+	4.88655i	0.952246	+	0.549779i	0.893778	−	0.448510i	$-0.148045\pi$
$79$	8.46375	+	4.88655i	0.952246	+	0.549779i	0.0584679	+	0.998289i	$0.481378\pi$
$80$		0			0
$81$	8.84847	+	1.64456i	0.983163	+	0.182729i
$82$		0			0
$83$	−0.724794	−	2.70497i	−0.0795565	−	0.296909i	0.914671	−	0.404198i	$-0.132449\pi$
$83$	−0.724794	−	2.70497i	−0.0795565	−	0.296909i	−0.994228	+	0.107290i	$0.965783\pi$
$84$		0			0
$85$	11.8545	−	10.4559i	1.28581	−	1.13410i
$86$		0			0
$87$	−1.25576	+	1.96115i	−0.134632	+	0.210257i
$88$		0			0
$89$	−4.87832			−0.517100			−0.258550	−	0.965998i	$-0.583245\pi$
$89$	−4.87832			−0.517100			−0.258550	+	0.965998i	$0.583245\pi$
$90$		0			0
$91$	−5.94827			−0.623549
$92$		0			0
$93$	1.99411	+	3.85233i	0.206780	+	0.399468i
$94$		0			0
$95$	−6.21280	−	0.389491i	−0.637420	−	0.0399609i
$96$		0			0
$97$	2.08981	+	7.79929i	0.212188	+	0.791898i	0.987137	+	0.159874i	$0.0511088\pi$
$97$	2.08981	+	7.79929i	0.212188	+	0.791898i	−0.774949	+	0.632024i	$0.782225\pi$
$98$		0			0
$99$	−2.80511	−	1.98351i	−0.281925	−	0.199351i
$100$		0			0
$101$	−0.631074	−	0.364351i	−0.0627942	−	0.0362543i	0.468274	−	0.883583i	$-0.344876\pi$
$101$	−0.631074	−	0.364351i	−0.0627942	−	0.0362543i	−0.531068	+	0.847329i	$0.678209\pi$
$102$		0			0
$103$	−0.353393	+	1.31888i	−0.0348209	+	0.129953i	−0.981148	−	0.193256i	$-0.938095\pi$
$103$	−0.353393	+	1.31888i	−0.0348209	+	0.129953i	0.946327	+	0.323209i	$0.104762\pi$
$104$		0			0
$105$	9.20268	−	1.42145i	0.898090	−	0.138719i
$106$		0			0
$107$	0.399208	+	0.399208i	0.0385929	+	0.0385929i	0.726140	−	0.687547i	$-0.241312\pi$
$107$	0.399208	+	0.399208i	0.0385929	+	0.0385929i	−0.687547	+	0.726140i	$0.741312\pi$
$108$		0			0
$109$		−	13.5974i		−	1.30239i	−0.758909	−	0.651196i	$-0.774268\pi$
$109$		−	13.5974i		−	1.30239i	0.758909	−	0.651196i	$-0.225732\pi$
$110$		0			0
$111$	14.7815	−	13.4821i	1.40300	−	1.27967i
$112$		0			0
$113$	4.94392	+	1.32472i	0.465084	+	0.124619i	0.483749	−	0.875207i	$-0.339275\pi$
$113$	4.94392	+	1.32472i	0.465084	+	0.124619i	−0.0186645	+	0.999826i	$0.505941\pi$
$114$		0			0
$115$	−4.39593	+	13.0718i	−0.409922	+	1.21896i
$116$		0			0
$117$	−2.57064	+	6.96265i	−0.237656	+	0.643697i
$118$		0			0
$119$	8.49803	−	14.7190i	0.779013	−	1.34929i
$120$		0			0
$121$	−4.84428	−	8.39054i	−0.440389	−	0.762776i
$122$		0			0
$123$	3.03412	−	1.57058i	0.273578	−	0.141614i
$124$		0			0
$125$	2.08767	−	10.9837i	0.186727	−	0.982412i
$126$		0			0
$127$	4.88817	−	4.88817i	0.433755	−	0.433755i	−0.456149	−	0.889904i	$-0.650772\pi$
$127$	4.88817	−	4.88817i	0.433755	−	0.433755i	0.889904	+	0.456149i	$0.150772\pi$
$128$		0			0
$129$	15.2121	−	3.33563i	1.33935	−	0.293686i
$130$		0			0
$131$	−4.98351	+	2.87723i	−0.435412	+	0.251385i	−0.701649	−	0.712522i	$-0.747553\pi$
$131$	−4.98351	+	2.87723i	−0.435412	+	0.251385i	0.266238	+	0.963907i	$0.414219\pi$
$132$		0			0
$133$	−6.46527	+	1.73236i	−0.560610	+	0.150215i
$134$		0			0
$135$	2.31324	−	11.3863i	0.199092	−	0.979981i
$136$		0			0
$137$	−10.0458	+	2.69177i	−0.858272	+	0.229973i	−0.661010	−	0.750377i	$-0.729872\pi$
$137$	−10.0458	+	2.69177i	−0.858272	+	0.229973i	−0.197262	+	0.980351i	$0.563205\pi$
$138$		0			0
$139$	2.19537	−	1.26750i	0.186209	−	0.107508i	−0.403998	−	0.914760i	$-0.632380\pi$
$139$	2.19537	−	1.26750i	0.186209	−	0.107508i	0.590207	+	0.807252i	$0.299046\pi$
$140$		0			0
$141$	20.8639	−	4.57494i	1.75706	−	0.385280i
$142$		0			0
$143$	2.00337	−	2.00337i	0.167531	−	0.167531i
$144$		0			0
$145$	2.50446	+	1.66316i	0.207984	+	0.138118i
$146$		0			0
$147$	−1.87557	+	0.970868i	−0.154695	+	0.0800759i
$148$		0			0
$149$	6.49294	+	11.2461i	0.531922	+	0.921316i	0.999306	+	0.0372613i	$0.0118634\pi$
$149$	6.49294	+	11.2461i	0.531922	+	0.921316i	−0.467384	+	0.884055i	$0.654803\pi$
$150$		0			0
$151$	−1.58502	+	2.74534i	−0.128987	+	0.223412i	−0.923284	−	0.384117i	$-0.874506\pi$
$151$	−1.58502	+	2.74534i	−0.128987	+	0.223412i	0.794297	+	0.607529i	$0.207839\pi$
$152$		0			0
$153$	−13.5565	−	16.3083i	−1.09598	−	1.31845i
$154$		0			0
$155$	5.01556	−	2.49113i	0.402859	−	0.200093i
$156$		0			0
$157$	10.3186	+	2.76487i	0.823515	+	0.220660i	0.645883	−	0.763437i	$-0.276489\pi$
$157$	10.3186	+	2.76487i	0.823515	+	0.220660i	0.177633	+	0.984097i	$0.443156\pi$
$158$		0			0
$159$	−3.34495	+	3.05092i	−0.265272	+	0.241953i
$160$		0			0
$161$			14.8288i			1.16867i
$162$		0			0
$163$	15.7354	+	15.7354i	1.23249	+	1.23249i	0.963003	+	0.269490i	$0.0868552\pi$
$163$	15.7354	+	15.7354i	1.23249	+	1.23249i	0.269490	+	0.963003i	$0.413145\pi$
$164$		0			0
$165$	−2.62071	+	3.57820i	−0.204022	+	0.278563i
$166$		0			0
$167$	1.05230	−	3.92724i	0.0814295	−	0.303899i	−0.913185	−	0.407546i	$-0.866385\pi$
$167$	1.05230	−	3.92724i	0.0814295	−	0.303899i	0.994614	+	0.103647i	$0.0330512\pi$
$168$		0			0
$169$	5.95761	+	3.43963i	0.458277	+	0.264587i
$170$		0			0
$171$	−0.766284	+	8.31648i	−0.0585992	+	0.635977i
$172$		0			0
$173$	−1.44105	−	5.37809i	−0.109561	−	0.408889i	0.889261	−	0.457400i	$-0.151219\pi$
$173$	−1.44105	−	5.37809i	−0.109561	−	0.408889i	−0.998823	+	0.0485110i	$0.984552\pi$
$174$		0			0
$175$	−1.63680	−	11.9096i	−0.123730	−	0.900278i
$176$		0			0
$177$	2.09336	+	4.04407i	0.157347	+	0.303971i
$178$		0			0
$179$	0.310192			0.0231848			0.0115924	−	0.999933i	$-0.496310\pi$
$179$	0.310192			0.0231848			0.0115924	+	0.999933i	$0.496310\pi$
$180$		0			0
$181$	3.07416			0.228501			0.114250	−	0.993452i	$-0.463553\pi$
$181$	3.07416			0.228501			0.114250	+	0.993452i	$0.463553\pi$
$182$		0			0
$183$	6.61785	−	10.3352i	0.489206	−	0.764003i
$184$		0			0
$185$	−17.0848	−	19.3703i	−1.25610	−	1.42413i
$186$		0			0
$187$	2.09522	+	7.81948i	0.153218	+	0.571817i
$188$		0			0
$189$	−1.54491	−	12.3972i	−0.112375	−	0.901765i
$190$		0			0
$191$	12.3541	+	7.13262i	0.893909	+	0.516098i	0.875219	−	0.483727i	$-0.160717\pi$
$191$	12.3541	+	7.13262i	0.893909	+	0.516098i	0.0186896	+	0.999825i	$0.494051\pi$
$192$		0			0
$193$	−2.48506	+	9.27437i	−0.178879	+	0.667584i	0.816980	+	0.576666i	$0.195647\pi$
$193$	−2.48506	+	9.27437i	−0.178879	+	0.667584i	−0.995858	+	0.0909176i	$0.971020\pi$
$194$		0			0
$195$	8.93218	+	3.46806i	0.639647	+	0.248353i
$196$		0			0
$197$	4.62495	+	4.62495i	0.329514	+	0.329514i	0.852402	−	0.522887i	$-0.175145\pi$
$197$	4.62495	+	4.62495i	0.329514	+	0.329514i	−0.522887	+	0.852402i	$0.675145\pi$
$198$		0			0
$199$			4.07227i			0.288675i	0.989528	+	0.144338i	$0.0461051\pi$
$199$			4.07227i			0.288675i	−0.989528	+	0.144338i	$0.953895\pi$
$200$		0			0
$201$	0.0931843	+	0.0296174i	0.00657271	+	0.00208905i
$202$		0			0
$203$	3.12243	+	0.836654i	0.219152	+	0.0587216i
$204$		0			0
$205$	−1.96203	−	3.95029i	−0.137034	−	0.275900i
$206$		0			0
$207$	17.3576	+	6.40851i	1.20644	+	0.445422i
$208$		0			0
$209$	1.59404	−	2.76096i	0.110262	−	0.190979i
$210$		0			0
$211$	7.58800	+	13.1428i	0.522379	+	0.904788i	0.999661	+	0.0260371i	$0.00828882\pi$
$211$	7.58800	+	13.1428i	0.522379	+	0.904788i	−0.477282	+	0.878750i	$0.658378\pi$
$212$		0			0
$213$	−0.723847	+	15.7451i	−0.0495972	+	1.07884i
$214$		0			0
$215$	−3.97833	−	19.7077i	−0.271320	−	1.34406i
$216$		0			0
$217$	4.25782	−	4.25782i	0.289040	−	0.289040i
$218$		0			0
$219$	−12.9212	−	14.1665i	−0.873133	−	0.957282i
$220$		0			0
$221$	15.1458	−	8.74443i	1.01882	−	0.588214i
$222$		0			0
$223$	−8.21978	+	2.20248i	−0.550437	+	0.147489i	−0.523309	−	0.852143i	$-0.675303\pi$
$223$	−8.21978	+	2.20248i	−0.550437	+	0.147489i	−0.0271279	+	0.999632i	$0.508636\pi$
$224$		0			0
$225$	−14.6479	−	3.23098i	−0.976526	−	0.215399i
$226$		0			0
$227$	−19.6687	+	5.27021i	−1.30546	+	0.349796i	−0.843511	−	0.537112i	$-0.819515\pi$
$227$	−19.6687	+	5.27021i	−1.30546	+	0.349796i	−0.461946	+	0.886908i	$0.652849\pi$
$228$		0			0
$229$	−12.2032	+	7.04551i	−0.806409	+	0.465580i	−0.845707	−	0.533647i	$-0.820821\pi$
$229$	−12.2032	+	7.04551i	−0.806409	+	0.465580i	0.0392983	+	0.999228i	$0.487488\pi$
$230$		0			0
$231$	−1.44455	+	4.54492i	−0.0950441	+	0.299034i
$232$		0			0
$233$	0.643009	−	0.643009i	0.0421249	−	0.0421249i	−0.685731	−	0.727855i	$-0.740517\pi$
$233$	0.643009	−	0.643009i	0.0421249	−	0.0421249i	0.727855	+	0.685731i	$0.240517\pi$
$234$		0			0
$235$	−5.45644	−	27.0299i	−0.355939	−	1.76324i
$236$		0			0
$237$	−14.2555	−	9.12805i	−0.925993	−	0.592931i
$238$		0			0
$239$	5.34131	+	9.25142i	0.345501	+	0.598425i	0.985445	−	0.169997i	$-0.0543758\pi$
$239$	5.34131	+	9.25142i	0.345501	+	0.598425i	−0.639944	+	0.768422i	$0.721042\pi$
$240$		0			0
$241$	−10.5666	+	18.3019i	−0.680654	+	1.17893i	0.294127	+	0.955766i	$0.404971\pi$
$241$	−10.5666	+	18.3019i	−0.680654	+	1.17893i	−0.974782	+	0.223161i	$0.928362\pi$
$242$		0			0
$243$	−15.1790	−	3.54930i	−0.973734	−	0.227688i
$244$		0			0
$245$	1.21285	+	2.44191i	0.0774862	+	0.156008i
$246$		0			0
$247$	−6.65274	−	1.78260i	−0.423303	−	0.113424i
$248$		0			0
$249$	1.03889	+	4.73785i	0.0658372	+	0.300249i
$250$		0			0
$251$			24.6952i			1.55874i	0.626561	+	0.779372i	$0.284462\pi$
$251$			24.6952i			1.55874i	−0.626561	+	0.779372i	$0.715538\pi$
$252$		0			0
$253$	−4.99433	−	4.99433i	−0.313991	−	0.313991i
$254$		0			0
$255$	−21.3427	+	17.1480i	−1.33653	+	1.07385i
$256$		0			0
$257$	−1.36020	+	5.07632i	−0.0848467	+	0.316652i	−0.995285	−	0.0969925i	$-0.969078\pi$
$257$	−1.36020	+	5.07632i	−0.0848467	+	0.316652i	0.910438	+	0.413645i	$0.135744\pi$
$258$		0			0
$259$	−24.0508	−	13.8857i	−1.49444	−	0.862818i
$260$		0			0
$261$	2.32874	−	3.29334i	0.144145	−	0.203852i
$262$		0			0
$263$	3.86551	+	14.4263i	0.238358	+	0.889563i	0.976606	+	0.215034i	$0.0689864\pi$
$263$	3.86551	+	14.4263i	0.238358	+	0.889563i	−0.738249	+	0.674529i	$0.764347\pi$
$264$		0			0
$265$	3.86619	+	4.38337i	0.237498	+	0.269268i
$266$		0			0
$267$	8.44057	+	0.388037i	0.516555	+	0.0237475i
$268$		0			0
$269$	20.0071			1.21985			0.609927	−	0.792457i	$-0.291199\pi$
$269$	20.0071			1.21985			0.609927	+	0.792457i	$0.291199\pi$
$270$		0			0
$271$	3.02714			0.183886			0.0919428	−	0.995764i	$-0.470692\pi$
$271$	3.02714			0.183886			0.0919428	+	0.995764i	$0.470692\pi$
$272$		0			0
$273$	10.2918	+	0.473145i	0.622891	+	0.0286360i
$274$		0			0
$275$	4.56240	+	3.45986i	0.275123	+	0.208637i
$276$		0			0
$277$	−0.723941	−	2.70178i	−0.0434974	−	0.162334i	0.940761	−	0.339071i	$-0.110113\pi$
$277$	−0.723941	−	2.70178i	−0.0434974	−	0.162334i	−0.984258	+	0.176736i	$0.943446\pi$
$278$		0			0
$279$	−3.14383	−	6.82401i	−0.188216	−	0.408543i
$280$		0			0
$281$	13.0998	+	7.56319i	0.781470	+	0.451182i	0.836951	−	0.547278i	$-0.184336\pi$
$281$	13.0998	+	7.56319i	0.781470	+	0.451182i	−0.0554808	+	0.998460i	$0.517669\pi$
$282$		0			0
$283$	6.22154	−	23.2191i	0.369832	−	1.38023i	−0.490918	−	0.871206i	$-0.663339\pi$
$283$	6.22154	−	23.2191i	0.369832	−	1.38023i	0.860750	−	0.509027i	$-0.169995\pi$
$284$		0			0
$285$	10.7186	+	1.16809i	0.634912	+	0.0691918i
$286$		0			0
$287$	−3.35349	−	3.35349i	−0.197950	−	0.197950i
$288$		0			0
$289$			32.9711i			1.93948i
$290$		0			0
$291$	−2.99546	−	13.6607i	−0.175597	−	0.800807i
$292$		0			0
$293$	14.5851	+	3.90805i	0.852068	+	0.228311i	0.658318	−	0.752740i	$-0.271268\pi$
$293$	14.5851	+	3.90805i	0.852068	+	0.228311i	0.193750	+	0.981051i	$0.437935\pi$
$294$		0			0
$295$	5.26519	−	2.61512i	0.306551	−	0.152258i
$296$		0			0
$297$	4.69570	+	3.65505i	0.272472	+	0.212088i
$298$		0			0
$299$	−7.62938	+	13.2145i	−0.441219	+	0.764213i
$300$		0			0
$301$	−10.8090	−	18.7217i	−0.623018	−	1.07910i
$302$		0			0
$303$	1.06292	+	0.680606i	0.0610630	+	0.0390998i
$304$		0			0
$305$	−13.1985	−	8.76483i	−0.755743	−	0.501872i
$306$		0			0
$307$	−8.29531	+	8.29531i	−0.473438	+	0.473438i	−0.903025	−	0.429587i	$-0.858659\pi$
$307$	−8.29531	+	8.29531i	−0.473438	+	0.473438i	0.429587	+	0.903025i	$0.358659\pi$
$308$		0			0
$309$	0.716358	−	2.25385i	0.0407522	−	0.128217i
$310$		0			0
$311$	−10.8857	+	6.28488i	−0.617274	+	0.356383i	−0.775807	−	0.630971i	$-0.782657\pi$
$311$	−10.8857	+	6.28488i	−0.617274	+	0.356383i	0.158533	+	0.987354i	$0.449324\pi$
$312$		0			0
$313$	11.5304	−	3.08956i	0.651737	−	0.174632i	0.0822229	−	0.996614i	$-0.473798\pi$
$313$	11.5304	−	3.08956i	0.651737	−	0.174632i	0.569514	+	0.821982i	$0.307131\pi$
$314$		0			0
$315$	−16.0358	+	1.72741i	−0.903513	+	0.0973288i
$316$		0			0
$317$	−1.87547	+	0.502531i	−0.105337	+	0.0282249i	−0.311102	−	0.950376i	$-0.600698\pi$
$317$	−1.87547	+	0.502531i	−0.105337	+	0.0282249i	0.205766	+	0.978601i	$0.434032\pi$
$318$		0			0
$319$	−1.33342	+	0.769849i	−0.0746570	+	0.0431033i
$320$		0			0
$321$	−0.658965	−	0.722473i	−0.0367798	−	0.0403245i
$322$		0			0
$323$	13.9155	−	13.9155i	0.774279	−	0.774279i
$324$		0			0
$325$	4.66883	−	11.4552i	0.258980	−	0.635418i
$326$		0			0
$327$	−1.08158	+	23.5265i	−0.0598115	+	1.30102i
$328$		0			0
$329$	−14.8249	−	25.6775i	−0.817323	−	1.41565i
$330$		0			0
$331$	10.9811	−	19.0198i	0.603575	−	1.04542i	−0.388700	−	0.921364i	$-0.627076\pi$
$331$	10.9811	−	19.0198i	0.603575	−	1.04542i	0.992275	−	0.124058i	$-0.0395909\pi$
$332$		0			0
$333$	−26.6477	+	22.1513i	−1.46028	+	1.21388i
$334$		0			0
$335$	0.0402359	−	0.119646i	0.00219832	−	0.00653698i
$336$		0			0
$337$	−25.8842	−	6.93565i	−1.41000	−	0.377809i	−0.528076	−	0.849197i	$-0.677086\pi$
$337$	−25.8842	−	6.93565i	−1.41000	−	0.377809i	−0.881926	+	0.471388i	$0.843753\pi$
$338$		0			0
$339$	−8.44871	−	2.68531i	−0.458871	−	0.145846i
$340$		0			0
$341$			2.86806i			0.155314i
$342$		0			0
$343$	13.9737	+	13.9737i	0.754508	+	0.754508i
$344$		0			0
$345$	8.64571	−	22.2675i	0.465470	−	1.19884i
$346$		0			0
$347$	7.78712	−	29.0619i	0.418035	−	1.56013i	−0.360644	−	0.932704i	$-0.617443\pi$
$347$	7.78712	−	29.0619i	0.418035	−	1.56013i	0.778679	−	0.627423i	$-0.215890\pi$
$348$		0			0
$349$	−22.2846	−	12.8660i	−1.19287	−	0.688702i	−0.233911	−	0.972258i	$-0.575152\pi$
$349$	−22.2846	−	12.8660i	−1.19287	−	0.688702i	−0.958956	+	0.283556i	$0.908486\pi$
$350$		0			0
$351$	5.00162	−	11.8425i	0.266967	−	0.632104i
$352$		0			0
$353$	−4.03627	−	15.0636i	−0.214829	−	0.801752i	−0.986227	−	0.165399i	$-0.947109\pi$
$353$	−4.03627	−	15.0636i	−0.214829	−	0.801752i	0.771398	−	0.636353i	$-0.219558\pi$
$354$		0			0
$355$	20.3085	+	1.27317i	1.07786	+	0.0675728i
$356$		0			0
$357$	−15.8743	+	24.7912i	−0.840156	+	1.31209i
$358$		0			0
$359$	22.9830			1.21300			0.606498	−	0.795085i	$-0.292574\pi$
$359$	22.9830			1.21300			0.606498	+	0.795085i	$0.292574\pi$
$360$		0			0
$361$	11.2499			0.592099
$362$		0			0
$363$	7.71427	+	14.9028i	0.404894	+	0.782196i
$364$		0			0
$365$	−18.5644	+	16.3740i	−0.971703	+	0.857055i
$366$		0			0
$367$	0.901720	+	3.36526i	0.0470694	+	0.175665i	0.985459	−	0.169914i	$-0.0543490\pi$
$367$	0.901720	+	3.36526i	0.0470694	+	0.175665i	−0.938389	+	0.345580i	$0.887682\pi$
$368$		0			0
$369$	−5.37464	+	2.47611i	−0.279792	+	0.128901i
$370$		0			0
$371$	5.44254	+	3.14225i	0.282563	+	0.163138i
$372$		0			0
$373$	5.91894	−	22.0898i	0.306471	−	1.14377i	−0.625200	−	0.780464i	$-0.714983\pi$
$373$	5.91894	−	22.0898i	0.306471	−	1.14377i	0.931671	−	0.363302i	$-0.118351\pi$
$374$		0			0
$375$	−4.48581	+	18.8382i	−0.231646	+	0.972800i
$376$		0			0
$377$	2.35206	+	2.35206i	0.121137	+	0.121137i
$378$		0			0
$379$			36.3113i			1.86519i	0.360927	+	0.932594i	$0.382460\pi$
$379$			36.3113i			1.86519i	−0.360927	+	0.932594i	$0.617540\pi$
$380$		0			0
$381$	−8.84644	+	8.06880i	−0.453217	+	0.413377i
$382$		0			0
$383$	−16.0342	−	4.29635i	−0.819308	−	0.219533i	−0.175264	−	0.984521i	$-0.556078\pi$
$383$	−16.0342	−	4.29635i	−0.819308	−	0.219533i	−0.644044	+	0.764988i	$0.722745\pi$
$384$		0			0
$385$	5.83557	+	1.96244i	0.297408	+	0.100015i
$386$		0			0
$387$	−26.5856	+	4.56137i	−1.35142	+	0.231867i
$388$		0			0
$389$	−11.7878	+	20.4171i	−0.597667	+	1.03519i	0.395497	+	0.918467i	$0.370572\pi$
$389$	−11.7878	+	20.4171i	−0.597667	+	1.03519i	−0.993164	+	0.116723i	$0.962761\pi$
$390$		0			0
$391$	−21.7995	−	37.7578i	−1.10245	−	1.90950i
$392$		0			0
$393$	8.85146	−	4.58185i	0.446497	−	0.231124i
$394$		0			0
$395$	−12.0894	+	18.2048i	−0.608283	+	0.915981i
$396$		0			0
$397$	27.6509	−	27.6509i	1.38776	−	1.38776i	0.557748	−	0.830011i	$-0.311666\pi$
$397$	27.6509	−	27.6509i	1.38776	−	1.38776i	0.830011	−	0.557748i	$-0.188334\pi$
$398$		0			0
$399$	11.3242	−	2.48311i	0.566917	−	0.124311i
$400$		0			0
$401$	−26.4658	+	15.2801i	−1.32164	+	0.763050i	−0.983990	−	0.178222i	$-0.942966\pi$
$401$	−26.4658	+	15.2801i	−1.32164	+	0.763050i	−0.337651	+	0.941272i	$0.609632\pi$
$402$		0			0
$403$	5.98494	−	1.60366i	0.298131	−	0.0798840i
$404$		0			0
$405$	−4.90812	+	19.5169i	−0.243887	+	0.969804i
$406$		0			0
$407$	12.7770	−	3.42359i	0.633332	−	0.169701i
$408$		0			0
$409$	−2.43668	+	1.40682i	−0.120486	+	0.0695626i	−0.559032	−	0.829146i	$-0.688827\pi$
$409$	−2.43668	+	1.40682i	−0.120486	+	0.0695626i	0.438546	+	0.898709i	$0.355494\pi$
$410$		0			0
$411$	17.5956	−	3.85828i	0.867928	−	0.190315i
$412$		0			0
$413$	4.46974	−	4.46974i	0.219942	−	0.219942i
$414$		0			0
$415$	6.13805	−	1.23907i	0.301305	−	0.0608234i
$416$		0			0
$417$	−3.89931	+	2.01843i	−0.190950	+	0.0988429i
$418$		0			0
$419$	2.23812	+	3.87654i	0.109339	+	0.189381i	0.915503	−	0.402311i	$-0.131793\pi$
$419$	2.23812	+	3.87654i	0.109339	+	0.189381i	−0.806163	+	0.591693i	$0.798460\pi$
$420$		0			0
$421$	2.85177	−	4.93941i	0.138987	−	0.240732i	−0.788127	−	0.615513i	$-0.788949\pi$
$421$	2.85177	−	4.93941i	0.138987	−	0.240732i	0.927113	+	0.374781i	$0.122282\pi$
$422$		0			0
$423$	−36.4632	+	6.25609i	−1.77290	+	0.304181i
$424$		0			0
$425$	21.6757	+	27.9185i	1.05142	+	1.35425i
$426$		0			0
$427$	−16.4552	−	4.40916i	−0.796324	−	0.213374i
$428$		0			0
$429$	−3.62564	+	3.30693i	−0.175048	+	0.159660i
$430$		0			0
$431$			28.4120i			1.36856i	0.729221	+	0.684278i	$0.239883\pi$
$431$			28.4120i			1.36856i	−0.729221	+	0.684278i	$0.760117\pi$
$432$		0			0
$433$	20.2290	+	20.2290i	0.972142	+	0.972142i	0.999622	−	0.0274806i	$-0.00874844\pi$
$433$	20.2290	+	20.2290i	0.972142	+	0.972142i	−0.0274806	+	0.999622i	$0.508748\pi$
$434$		0			0
$435$	−4.20098	−	3.07684i	−0.201421	−	0.147523i
$436$		0			0
$437$	−4.44393	+	16.5850i	−0.212582	+	0.793368i
$438$		0			0
$439$	−12.4785	−	7.20447i	−0.595567	−	0.343851i	0.171729	−	0.985144i	$-0.445065\pi$
$439$	−12.4785	−	7.20447i	−0.595567	−	0.343851i	−0.767296	+	0.641293i	$0.778398\pi$
$440$		0			0
$441$	3.32239	−	1.53063i	0.158209	−	0.0728871i
$442$		0			0
$443$	−6.94511	−	25.9195i	−0.329972	−	1.23147i	−0.909218	−	0.416320i	$-0.863320\pi$
$443$	−6.94511	−	25.9195i	−0.329972	−	1.23147i	0.579246	−	0.815153i	$-0.303347\pi$
$444$		0			0
$445$	0.682516	−	10.8869i	0.0323543	−	0.516087i
$446$		0			0
$447$	−10.3397	−	19.9747i	−0.489050	−	0.944772i
$448$		0			0
$449$	−1.72288			−0.0813077			−0.0406538	−	0.999173i	$-0.512944\pi$
$449$	−1.72288			−0.0813077			−0.0406538	+	0.999173i	$0.512944\pi$
$450$		0			0
$451$	2.25891			0.106368
$452$		0			0
$453$	2.96081	−	4.62397i	0.139111	−	0.217253i
$454$		0			0
$455$	0.832211	−	13.2747i	0.0390147	−	0.622327i
$456$		0			0
$457$	−3.30155	−	12.3215i	−0.154440	−	0.576377i	−0.999153	−	0.0411576i	$-0.986895\pi$
$457$	−3.30155	−	12.3215i	−0.154440	−	0.576377i	0.844713	−	0.535220i	$-0.179771\pi$
$458$		0			0
$459$	22.1586	+	29.2953i	1.03428	+	1.36739i
$460$		0			0
$461$	8.72418	+	5.03691i	0.406326	+	0.234592i	0.689210	−	0.724562i	$-0.257958\pi$
$461$	8.72418	+	5.03691i	0.406326	+	0.234592i	−0.282884	+	0.959154i	$0.591291\pi$
$462$		0			0
$463$	−9.90706	+	36.9737i	−0.460420	+	1.71831i	0.211224	+	0.977438i	$0.432255\pi$
$463$	−9.90706	+	36.9737i	−0.460420	+	1.71831i	−0.671644	+	0.740874i	$0.734412\pi$
$464$		0			0
$465$	−8.87618	+	3.91126i	−0.411623	+	0.181380i
$466$		0			0
$467$	14.5094	+	14.5094i	0.671413	+	0.671413i	0.958042	−	0.286629i	$-0.0925347\pi$
$467$	14.5094	+	14.5094i	0.671413	+	0.671413i	−0.286629	+	0.958042i	$0.592535\pi$
$468$		0			0
$469$		−	0.135728i		−	0.00626733i
$470$		0			0
$471$	−17.6336	−	5.60461i	−0.812513	−	0.258247i
$472$		0			0
$473$	9.94589	+	2.66499i	0.457313	+	0.122537i
$474$		0			0
$475$	1.73844	−	13.8105i	0.0797652	−	0.633671i
$476$		0			0
$477$	6.03020	−	5.01270i	0.276104	−	0.229516i
$478$		0			0
$479$	−2.27813	+	3.94584i	−0.104091	+	0.180290i	−0.913366	−	0.407139i	$-0.866527\pi$
$479$	−2.27813	+	3.94584i	−0.104091	+	0.180290i	0.809276	+	0.587429i	$0.199860\pi$
$480$		0			0
$481$	−14.2884	−	24.7482i	−0.651493	−	1.12842i
$482$		0			0
$483$	1.17953	−	25.6571i	0.0536705	−	1.16744i
$484$		0			0
$485$	−17.6979	+	3.57262i	−0.803622	+	0.162225i
$486$		0			0
$487$	18.4889	−	18.4889i	0.837814	−	0.837814i	−0.150757	−	0.988571i	$-0.548171\pi$
$487$	18.4889	−	18.4889i	0.837814	−	0.837814i	0.988571	+	0.150757i	$0.0481710\pi$
$488$		0			0
$489$	−25.9741	−	28.4774i	−1.17459	−	1.28779i
$490$		0			0
$491$	0.730071	−	0.421507i	0.0329476	−	0.0190223i	−0.483436	−	0.875380i	$-0.660611\pi$
$491$	0.730071	−	0.421507i	0.0329476	−	0.0190223i	0.516383	+	0.856358i	$0.327278\pi$
$492$		0			0
$493$	−9.18045	+	2.45989i	−0.413467	+	0.110788i
$494$		0			0
$495$	4.81904	−	5.98263i	0.216600	−	0.268899i
$496$		0			0
$497$	21.1337	−	5.66277i	0.947978	−	0.254010i
$498$		0			0
$499$	8.45869	−	4.88363i	0.378663	−	0.218621i	−0.298573	−	0.954387i	$-0.596511\pi$
$499$	8.45869	−	4.88363i	0.378663	−	0.218621i	0.677236	+	0.735765i	$0.263177\pi$
$500$		0			0
$501$	−2.13310	+	6.71130i	−0.0953000	+	0.299839i
$502$		0			0
$503$	−22.3161	+	22.3161i	−0.995025	+	0.995025i	−0.999988	−	0.00496279i	$-0.998420\pi$
$503$	−22.3161	+	22.3161i	−0.995025	+	0.995025i	0.00496279	+	0.999988i	$0.498420\pi$
$504$		0			0
$505$	0.901410	−	1.35738i	0.0401122	−	0.0604028i
$506$		0			0
$507$	−10.0344	−	6.42521i	−0.445643	−	0.285354i
$508$		0			0
$509$	3.83647	+	6.64497i	0.170049	+	0.294533i	0.938437	−	0.345451i	$-0.112274\pi$
$509$	3.83647	+	6.64497i	0.170049	+	0.294533i	−0.768388	+	0.639984i	$0.778941\pi$
$510$		0			0
$511$	−13.3080	+	23.0501i	−0.588712	+	1.01968i
$512$		0			0
$513$	1.98736	−	14.3284i	0.0877442	−	0.632615i
$514$		0			0
$515$	−2.89389	−	0.973185i	−0.127520	−	0.0428837i
$516$		0			0
$517$	13.6412	+	3.65514i	0.599938	+	0.160753i
$518$		0			0
$519$	2.06556	+	9.41992i	0.0906678	+	0.413489i
$520$		0			0
$521$			23.2333i			1.01787i	0.860805	+	0.508934i	$0.169960\pi$
$521$			23.2333i			1.01787i	−0.860805	+	0.508934i	$0.830040\pi$
$522$		0			0
$523$	3.86103	+	3.86103i	0.168831	+	0.168831i	0.786465	−	0.617634i	$-0.211909\pi$
$523$	3.86103	+	3.86103i	0.168831	+	0.168831i	−0.617634	+	0.786465i	$0.711909\pi$
$524$		0			0
$525$	1.88470	+	20.7364i	0.0822551	+	0.905010i
$526$		0			0
$527$	−4.58215	+	17.1008i	−0.199602	+	0.744923i
$528$		0			0
$529$	13.0246	+	7.51973i	0.566285	+	0.326945i
$530$		0			0
$531$	−3.30031	−	7.16366i	−0.143221	−	0.310876i
$532$		0			0
$533$	−1.26305	−	4.71378i	−0.0547089	−	0.204176i
$534$		0			0
$535$	−0.946759	+	0.835055i	−0.0409320	+	0.0361026i
$536$		0			0
$537$	−0.536701	−	0.0246737i	−0.0231604	−	0.00106475i
$538$		0			0
$539$	−1.39637			−0.0601457
$540$		0			0
$541$	−21.3692			−0.918732			−0.459366	−	0.888247i	$-0.651923\pi$
$541$	−21.3692			−0.918732			−0.459366	+	0.888247i	$0.651923\pi$
$542$		0			0
$543$	−5.31899	−	0.244529i	−0.228260	−	0.0104937i
$544$		0			0
$545$	30.3451	+	1.90238i	1.29984	+	0.0814891i
$546$		0			0
$547$	−7.10984	−	26.5343i	−0.303995	−	1.13452i	−0.933807	−	0.357777i	$-0.883535\pi$
$547$	−7.10984	−	26.5343i	−0.303995	−	1.13452i	0.629812	−	0.776747i	$-0.283132\pi$
$548$		0			0
$549$	−12.2725	+	17.3559i	−0.523776	+	0.740731i
$550$		0			0
$551$	3.24150	+	1.87148i	0.138092	+	0.0797277i
$552$		0			0
$553$	−6.08159	+	22.6968i	−0.258615	+	0.965166i
$554$		0			0
$555$	28.0198	+	34.8739i	1.18937	+	1.48031i
$556$		0			0
$557$	−13.7347	−	13.7347i	−0.581958	−	0.581958i	0.353483	−	0.935441i	$-0.384997\pi$
$557$	−13.7347	−	13.7347i	−0.581958	−	0.581958i	−0.935441	+	0.353483i	$0.884997\pi$
$558$		0			0
$559$		−	22.2447i		−	0.940852i
$560$		0			0
$561$	−3.00322	−	13.6961i	−0.126796	−	0.578250i
$562$		0			0
$563$	14.3759	+	3.85201i	0.605872	+	0.162343i	0.548697	−	0.836021i	$-0.315124\pi$
$563$	14.3759	+	3.85201i	0.605872	+	0.162343i	0.0571749	+	0.998364i	$0.481791\pi$
$564$		0			0
$565$	−3.64805	+	10.8479i	−0.153475	+	0.456376i
$566$		0			0
$567$	1.68692	+	21.5729i	0.0708439	+	0.905975i
$568$		0			0
$569$	14.7082	−	25.4753i	0.616599	−	1.06798i	−0.373503	−	0.927629i	$-0.621843\pi$
$569$	14.7082	−	25.4753i	0.616599	−	1.06798i	0.990102	−	0.140351i	$-0.0448232\pi$
$570$		0			0
$571$	−15.2909	−	26.4847i	−0.639906	−	1.10835i	−0.985453	−	0.169948i	$-0.945640\pi$
$571$	−15.2909	−	26.4847i	−0.639906	−	1.10835i	0.345548	−	0.938401i	$-0.387693\pi$
$572$		0			0
$573$	−20.8079	−	13.3237i	−0.869264	−	0.556606i
$574$		0			0
$575$	−28.5572	−	11.6392i	−1.19092	−	0.485388i
$576$		0			0
$577$	−2.75877	+	2.75877i	−0.114849	+	0.114849i	−0.762196	−	0.647347i	$-0.775879\pi$
$577$	−2.75877	+	2.75877i	−0.114849	+	0.114849i	0.647347	+	0.762196i	$0.275879\pi$
$578$		0			0
$579$	5.03742	−	15.8491i	0.209348	−	0.658665i
$580$		0			0
$581$	5.83093	−	3.36649i	0.241908	−	0.139665i
$582$		0			0
$583$	−2.89135	+	0.774736i	−0.119748	+	0.0320863i
$584$		0			0
$585$	−15.1788	−	6.71100i	−0.627566	−	0.277466i
$586$		0			0
$587$	15.5484	−	4.16617i	0.641750	−	0.171956i	0.0767539	−	0.997050i	$-0.475544\pi$
$587$	15.5484	−	4.16617i	0.641750	−	0.171956i	0.564996	+	0.825094i	$0.308878\pi$
$588$		0			0
$589$	6.03808	−	3.48608i	0.248795	−	0.143642i
$590$		0			0
$591$	−7.63432	−	8.37008i	−0.314034	−	0.344299i
$592$		0			0
$593$	−31.4829	+	31.4829i	−1.29285	+	1.29285i	−0.359830	+	0.933018i	$0.617165\pi$
$593$	−31.4829	+	31.4829i	−1.29285	+	1.29285i	−0.933018	+	0.359830i	$0.882835\pi$
$594$		0			0
$595$	31.6593	+	21.0242i	1.29790	+	0.861910i
$596$		0			0
$597$	0.323921	−	7.04593i	0.0132572	−	0.288371i
$598$		0			0
$599$	0.0708577	+	0.122729i	0.00289517	+	0.00501457i	0.867469	−	0.497491i	$-0.165745\pi$
$599$	0.0708577	+	0.122729i	0.00289517	+	0.00501457i	−0.864574	+	0.502505i	$0.832412\pi$
$600$		0			0
$601$	21.9425	−	38.0055i	0.895052	−	1.55028i	0.0613115	−	0.998119i	$-0.480472\pi$
$601$	21.9425	−	38.0055i	0.895052	−	1.55028i	0.833740	−	0.552157i	$-0.186195\pi$
$602$		0			0
$603$	−0.158874	−	0.0586570i	−0.00646984	−	0.00238870i
$604$		0			0
$605$	19.4028	−	9.63701i	0.788836	−	0.391800i
$606$		0			0
$607$	32.2841	+	8.65049i	1.31037	+	0.351113i	0.845362	−	0.534194i	$-0.179385\pi$
$607$	32.2841	+	8.65049i	1.31037	+	0.351113i	0.465008	+	0.885306i	$0.346051\pi$
$608$		0			0
$609$	−5.33596	−	1.69597i	−0.216224	−	0.0687240i
$610$		0			0
$611$		−	30.5095i		−	1.23428i
$612$		0			0
$613$	6.75021	+	6.75021i	0.272638	+	0.272638i	0.830161	−	0.557523i	$-0.188248\pi$
$613$	6.75021	+	6.75021i	0.272638	+	0.272638i	−0.557523	+	0.830161i	$0.688248\pi$
$614$		0			0
$615$	3.08054	+	6.99095i	0.124219	+	0.281902i
$616$		0			0
$617$	8.53953	−	31.8700i	0.343789	−	1.28304i	−0.550232	−	0.835012i	$-0.685461\pi$
$617$	8.53953	−	31.8700i	0.343789	−	1.28304i	0.894021	−	0.448025i	$-0.147872\pi$
$618$		0			0
$619$	−13.2360	−	7.64183i	−0.532001	−	0.307151i	0.209830	−	0.977738i	$-0.432709\pi$
$619$	−13.2360	−	7.64183i	−0.532001	−	0.307151i	−0.741831	+	0.670587i	$0.766042\pi$
$620$		0			0
$621$	−29.5228	−	12.4688i	−1.18471	−	0.500357i
$622$		0			0
$623$	−3.03567	−	11.3293i	−0.121622	−	0.453898i
$624$		0			0
$625$	24.2201	+	6.19573i	0.968804	+	0.247829i
$626$		0			0
$627$	−2.97766	+	4.65028i	−0.118916	+	0.185714i
$628$		0			0
$629$	81.6525			3.25570
$630$		0			0
$631$	−10.8347			−0.431321			−0.215660	−	0.976468i	$-0.569190\pi$
$631$	−10.8347			−0.431321			−0.215660	+	0.976468i	$0.569190\pi$
$632$		0			0
$633$	−12.0835	−	23.3435i	−0.480276	−	0.927823i
$634$		0			0
$635$	10.2250	+	11.5928i	0.405765	+	0.460044i
$636$		0			0
$637$	0.780770	+	2.91387i	0.0309352	+	0.115452i
$638$		0			0
$639$	2.50484	−	27.1850i	0.0990897	−	1.07542i
$640$		0			0
$641$	−23.0771	−	13.3236i	−0.911491	−	0.526250i	−0.0305804	−	0.999532i	$-0.509736\pi$
$641$	−23.0771	−	13.3236i	−0.911491	−	0.526250i	−0.880911	+	0.473283i	$0.843069\pi$
$642$		0			0
$643$	3.67008	−	13.6969i	0.144734	−	0.540153i	−0.855033	−	0.518573i	$-0.826463\pi$
$643$	3.67008	−	13.6969i	0.144734	−	0.540153i	0.999767	−	0.0215806i	$-0.00686984\pi$
$644$		0			0
$645$	5.31579	+	34.4152i	0.209309	+	1.35510i
$646$		0			0
$647$	22.3507	+	22.3507i	0.878698	+	0.878698i	0.993400	−	0.114702i	$-0.0365912\pi$
$647$	22.3507	+	22.3507i	0.878698	+	0.878698i	−0.114702	+	0.993400i	$0.536591\pi$
$648$		0			0
$649$			3.01081i			0.118185i
$650$		0			0
$651$	−7.70566	+	7.02830i	−0.302009	+	0.275461i
$652$		0			0
$653$	24.6425	+	6.60293i	0.964334	+	0.258393i	0.706434	−	0.707779i	$-0.250303\pi$
$653$	24.6425	+	6.60293i	0.964334	+	0.258393i	0.257900	+	0.966172i	$0.416969\pi$
$654$		0			0
$655$	−5.72385	−	11.5242i	−0.223649	−	0.450287i
$656$		0			0
$657$	21.2297	+	25.5390i	0.828249	+	0.996370i
$658$		0			0
$659$	10.2346	−	17.7269i	0.398684	−	0.690540i	−0.594880	−	0.803814i	$-0.702800\pi$
$659$	10.2346	−	17.7269i	0.398684	−	0.690540i	0.993564	+	0.113274i	$0.0361338\pi$
$660$		0			0
$661$	−0.883223	−	1.52979i	−0.0343534	−	0.0595018i	0.848338	−	0.529456i	$-0.177604\pi$
$661$	−0.883223	−	1.52979i	−0.0343534	−	0.0595018i	−0.882691	+	0.469954i	$0.844271\pi$
$662$		0			0
$663$	−26.9012	+	13.9251i	−1.04476	+	0.540805i
$664$		0			0
$665$	−2.96155	−	14.6708i	−0.114844	−	0.568911i
$666$		0			0
$667$	5.86358	−	5.86358i	0.227039	−	0.227039i
$668$		0			0
$669$	14.3973	−	3.15696i	0.556630	−	0.122055i
$670$		0			0
$671$	7.02711	−	4.05710i	0.271278	−	0.156623i
$672$		0			0
$673$	−13.4819	+	3.61246i	−0.519688	+	0.139250i	−0.509122	−	0.860694i	$-0.670030\pi$
$673$	−13.4819	+	3.61246i	−0.519688	+	0.139250i	−0.0105656	+	0.999944i	$0.503363\pi$
$674$		0			0
$675$	25.0871	+	6.75546i	0.965604	+	0.260018i
$676$		0			0
$677$	−1.70954	+	0.458071i	−0.0657031	+	0.0176051i	−0.291521	−	0.956564i	$-0.594161\pi$
$677$	−1.70954	+	0.458071i	−0.0657031	+	0.0176051i	0.225818	+	0.974170i	$0.427495\pi$
$678$		0			0
$679$	−16.8124	+	9.70666i	−0.645202	+	0.372508i
$680$		0			0
$681$	34.4504	−	7.55413i	1.32014	−	0.289475i
$682$		0			0
$683$	22.8964	−	22.8964i	0.876105	−	0.876105i	−0.117024	−	0.993129i	$-0.537335\pi$
$683$	22.8964	−	22.8964i	0.876105	−	0.876105i	0.993129	+	0.117024i	$0.0373354\pi$
$684$		0			0
$685$	−4.60169	−	22.7957i	−0.175822	−	0.870980i
$686$		0			0
$687$	21.6747	−	11.2196i	0.826940	−	0.428055i
$688$		0			0
$689$	3.23336	+	5.60035i	0.123181	+	0.213356i
$690$		0			0
$691$	−11.3908	+	19.7295i	−0.433327	+	0.750545i	−0.997157	−	0.0753461i	$-0.975994\pi$
$691$	−11.3908	+	19.7295i	−0.433327	+	0.750545i	0.563830	+	0.825891i	$0.309327\pi$
$692$		0			0
$693$	2.86090	−	7.74883i	0.108677	−	0.294354i
$694$		0			0
$695$	2.52151	+	5.07672i	0.0956463	+	0.192571i
$696$		0			0
$697$	13.4687	+	3.60893i	0.510164	+	0.136698i
$698$		0			0
$699$	−1.16370	+	1.06140i	−0.0440150	+	0.0401459i
$700$		0			0
$701$			26.0321i			0.983220i	0.870816	+	0.491610i	$0.163591\pi$
$701$			26.0321i			0.983220i	−0.870816	+	0.491610i	$0.836409\pi$
$702$		0			0
$703$	−22.7379	−	22.7379i	−0.857574	−	0.857574i
$704$		0			0
$705$	7.29081	+	47.2018i	0.274588	+	1.77772i
$706$		0			0
$707$	0.453456	−	1.69232i	0.0170540	−	0.0636462i
$708$		0			0
$709$	−2.58254	−	1.49103i	−0.0969892	−	0.0559968i	0.450721	−	0.892665i	$-0.351167\pi$
$709$	−2.58254	−	1.49103i	−0.0969892	−	0.0559968i	−0.547710	+	0.836668i	$0.684500\pi$
$710$		0			0
$711$	23.9391	+	16.9275i	0.897786	+	0.634831i
$712$		0			0
$713$	−3.99786	−	14.9202i	−0.149721	−	0.558766i
$714$		0			0
$715$	4.19062	+	4.75119i	0.156720	+	0.177685i
$716$		0			0
$717$	−8.50577	−	16.4319i	−0.317654	−	0.613660i
$718$		0			0
$719$	7.38853			0.275546			0.137773	−	0.990464i	$-0.456006\pi$
$719$	7.38853			0.275546			0.137773	+	0.990464i	$0.456006\pi$
$720$		0			0
$721$	−3.28285			−0.122260
$722$		0			0
$723$	19.7384	−	30.8258i	0.734077	−	1.14643i
$724$		0			0
$725$	−4.06204	+	5.35648i	−0.150860	+	0.198935i
$726$		0			0
$727$	5.57881	+	20.8204i	0.206906	+	0.772185i	0.988860	+	0.148849i	$0.0475567\pi$
$727$	5.57881	+	20.8204i	0.206906	+	0.772185i	−0.781954	+	0.623337i	$0.785777\pi$
$728$		0			0
$729$	25.9808	+	7.34847i	0.962250	+	0.272166i
$730$		0			0
$731$	55.0446	+	31.7800i	2.03590	+	1.17543i
$732$		0			0
$733$	−1.74734	+	6.52116i	−0.0645395	+	0.240865i	−0.990658	−	0.136367i	$-0.956457\pi$
$733$	−1.74734	+	6.52116i	−0.0645395	+	0.240865i	0.926119	+	0.377232i	$0.123124\pi$
$734$		0			0
$735$	−1.90427	−	4.32152i	−0.0702399	−	0.159402i
$736$		0			0
$737$	0.0457130	+	0.0457130i	0.00168386	+	0.00168386i
$738$		0			0
$739$		−	12.8637i		−	0.473200i	−0.971607	−	0.236600i	$-0.923967\pi$
$739$		−	12.8637i		−	0.473200i	0.971607	−	0.236600i	$-0.0760331\pi$
$740$		0			0
$741$	11.3689	+	3.61347i	0.417648	+	0.132744i
$742$		0			0
$743$	32.7401	+	8.77270i	1.20112	+	0.321839i	0.803272	−	0.595613i	$-0.203091\pi$
$743$	32.7401	+	8.77270i	1.20112	+	0.321839i	0.397848	+	0.917452i	$0.369757\pi$
$744$		0			0
$745$	−26.0062	+	12.9168i	−0.952792	+	0.473234i
$746$		0			0
$747$	−1.42065	−	8.28018i	−0.0519790	−	0.302956i
$748$		0			0
$749$	−0.678692	+	1.17553i	−0.0247989	+	0.0429529i
$750$		0			0
$751$	−6.70415	−	11.6119i	−0.244638	−	0.423725i	0.717392	−	0.696670i	$-0.245336\pi$
$751$	−6.70415	−	11.6119i	−0.244638	−	0.423725i	−0.962030	+	0.272945i	$0.912002\pi$
$752$		0			0
$753$	1.96433	−	42.7281i	0.0715843	−	1.55710i
$754$		0			0
$755$	−5.90498	−	3.92137i	−0.214904	−	0.142713i
$756$		0			0
$757$	−1.11492	+	1.11492i	−0.0405223	+	0.0405223i	−0.727078	−	0.686555i	$-0.759122\pi$
$757$	−1.11492	+	1.11492i	−0.0405223	+	0.0405223i	0.686555	+	0.727078i	$0.259122\pi$
$758$		0			0
$759$	8.24404	+	9.03857i	0.299240	+	0.328079i
$760$		0			0
$761$	−29.7531	+	17.1780i	−1.07855	+	0.622702i	−0.930505	−	0.366279i	$-0.880632\pi$
$761$	−29.7531	+	17.1780i	−1.07855	+	0.622702i	−0.148046	+	0.988981i	$0.547298\pi$
$762$		0			0
$763$	31.5782	−	8.46136i	1.14321	−	0.306322i
$764$		0			0
$765$	38.2917	−	27.9723i	1.38444	−	1.01134i
$766$		0			0
$767$	6.28282	−	1.68348i	0.226860	−	0.0607869i
$768$		0			0
$769$	14.4890	−	8.36522i	0.522486	−	0.301658i	−0.215465	−	0.976512i	$-0.569127\pi$
$769$	14.4890	−	8.36522i	0.522486	−	0.301658i	0.737951	+	0.674854i	$0.235793\pi$
$770$		0			0
$771$	2.75723	−	8.67497i	0.0992992	−	0.312421i
$772$		0			0
$773$	5.20827	−	5.20827i	0.187328	−	0.187328i	−0.607212	−	0.794540i	$-0.707712\pi$
$773$	5.20827	−	5.20827i	0.187328	−	0.187328i	0.794540	+	0.607212i	$0.207712\pi$
$774$		0			0
$775$	4.85771	+	11.5417i	0.174494	+	0.414589i
$776$		0			0
$777$	40.5087	+	25.9385i	1.45324	+	0.930539i
$778$		0			0
$779$	−2.74567	−	4.75563i	−0.0983737	−	0.170388i
$780$		0			0
$781$	−5.21061	+	9.02504i	−0.186450	+	0.322941i
$782$		0			0
$783$	−4.29121	+	5.51297i	−0.153355	+	0.197018i
$784$		0			0
$785$	−7.61397	+	22.6411i	−0.271754	+	0.808095i
$786$		0			0
$787$	44.6815	+	11.9724i	1.59272	+	0.426769i	0.942834	−	0.333262i	$-0.108149\pi$
$787$	44.6815	+	11.9724i	1.59272	+	0.426769i	0.649888	+	0.760030i	$0.274816\pi$
$788$		0			0
$789$	−5.54069	−	25.2682i	−0.197254	−	0.899571i
$790$		0			0
$791$			12.3060i			0.437550i
$792$		0			0
$793$	−12.3953	−	12.3953i	−0.440171	−	0.440171i
$794$		0			0
$795$	−6.34070	−	7.89173i	−0.224882	−	0.279891i
$796$		0			0
$797$	13.3339	−	49.7628i	0.472311	−	1.76269i	−0.159123	−	0.987259i	$-0.550866\pi$
$797$	13.3339	−	49.7628i	0.472311	−	1.76269i	0.631434	−	0.775430i	$-0.282467\pi$
$798$		0			0
$799$	75.4958	+	43.5875i	2.67085	+	1.54202i
$800$		0			0
$801$	−14.5732	−	1.34278i	−0.514919	−	0.0474448i
$802$		0			0
$803$	−3.28114	−	12.2454i	−0.115789	−	0.432131i
$804$		0			0
$805$	−33.0932	−	2.07467i	−1.16638	−	0.0731224i
$806$		0			0
$807$	−34.6168	−	1.59143i	−1.21857	−	0.0560210i
$808$		0			0
$809$	−18.0260			−0.633762			−0.316881	−	0.948465i	$-0.602636\pi$
$809$	−18.0260			−0.633762			−0.316881	+	0.948465i	$0.602636\pi$
$810$		0			0
$811$	−46.7969			−1.64326			−0.821630	−	0.570021i	$-0.806935\pi$
$811$	−46.7969			−1.64326			−0.821630	+	0.570021i	$0.806935\pi$
$812$		0			0
$813$	−5.23762	−	0.240788i	−0.183691	−	0.00844481i
$814$		0			0
$815$	−37.3180	+	32.9150i	−1.30719	+	1.15296i
$816$		0			0
$817$	−6.47852	−	24.1782i	−0.226655	−	0.845886i
$818$		0			0
$819$	−17.7696	−	1.63729i	−0.620918	−	0.0572117i
$820$		0			0
$821$	5.91006	+	3.41218i	0.206263	+	0.119086i	0.599573	−	0.800320i	$-0.295337\pi$
$821$	5.91006	+	3.41218i	0.206263	+	0.119086i	−0.393311	+	0.919406i	$0.628670\pi$
$822$		0			0
$823$	−5.27529	+	19.6876i	−0.183885	+	0.686268i	0.810982	+	0.585072i	$0.198934\pi$
$823$	−5.27529	+	19.6876i	−0.183885	+	0.686268i	−0.994866	+	0.101196i	$0.967733\pi$
$824$		0			0
$825$	−7.61876	−	6.34923i	−0.265251	−	0.221052i
$826$		0			0
$827$	−29.8425	−	29.8425i	−1.03773	−	1.03773i	−0.999260	−	0.0384654i	$-0.987753\pi$
$827$	−29.8425	−	29.8425i	−1.03773	−	1.03773i	−0.0384654	−	0.999260i	$-0.512247\pi$
$828$		0			0
$829$			20.4152i			0.709050i	0.935047	+	0.354525i	$0.115357\pi$
$829$			20.4152i			0.709050i	−0.935047	+	0.354525i	$0.884643\pi$
$830$		0			0
$831$	1.03767	+	4.73227i	0.0359964	+	0.164161i
$832$		0			0
$833$	−8.32583	−	2.23090i	−0.288473	−	0.0772961i
$834$		0			0
$835$	8.61715	+	2.89786i	0.298209	+	0.100285i
$836$		0			0
$837$	4.89673	+	12.0571i	0.169256	+	0.416755i
$838$		0			0
$839$	−9.70261	+	16.8054i	−0.334971	+	0.580187i	−0.983479	−	0.181021i	$-0.942060\pi$
$839$	−9.70261	+	16.8054i	−0.334971	+	0.580187i	0.648508	+	0.761208i	$0.275393\pi$
$840$		0			0
$841$	13.5962	+	23.5492i	0.468833	+	0.812043i
$842$		0			0
$843$	−22.0640	−	14.1280i	−0.759926	−	0.486595i
$844$		0			0
$845$	−8.50968	+	12.8143i	−0.292742	+	0.440825i
$846$		0			0
$847$	16.4715	−	16.4715i	0.565967	−	0.565967i
$848$		0			0
$849$	−12.6116	+	39.6794i	−0.432828	+	1.36179i
$850$		0			0
$851$	−61.6961	+	35.6203i	−2.11492	+	1.22105i
$852$		0			0
$853$	−0.496213	+	0.132960i	−0.0169900	+	0.00455246i	−0.267304	−	0.963612i	$-0.586133\pi$
$853$	−0.496213	+	0.132960i	−0.0169900	+	0.00455246i	0.250314	+	0.968165i	$0.419466\pi$
$854$		0			0
$855$	−18.4526	−	2.87365i	−0.631065	−	0.0982767i
$856$		0			0
$857$	−43.0427	+	11.5332i	−1.47031	+	0.393968i	−0.903037	−	0.429562i	$-0.858668\pi$
$857$	−43.0427	+	11.5332i	−1.47031	+	0.393968i	−0.567272	+	0.823530i	$0.692001\pi$
$858$		0			0
$859$	−25.5432	+	14.7474i	−0.871522	+	0.503174i	−0.867854	−	0.496820i	$-0.834501\pi$
$859$	−25.5432	+	14.7474i	−0.871522	+	0.503174i	−0.00366859	+	0.999993i	$0.501168\pi$
$860$		0			0
$861$	5.53554	+	6.06903i	0.188651	+	0.206832i
$862$		0			0
$863$	6.17951	−	6.17951i	0.210353	−	0.210353i	−0.594064	−	0.804417i	$-0.702478\pi$
$863$	6.17951	−	6.17951i	0.210353	−	0.210353i	0.804417	+	0.594064i	$0.202478\pi$
$864$		0			0
$865$	12.2038	−	2.46354i	0.414943	−	0.0837630i
$866$		0			0
$867$	2.62263	−	57.0473i	0.0890691	−	1.93743i
$868$		0			0
$869$	−5.59599	−	9.69254i	−0.189831	−	0.328797i
$870$		0			0
$871$	0.0698316	−	0.120952i	0.00236615	−	0.00409830i
$872$		0			0
$873$	4.09620	+	23.8744i	0.138635	+	0.808026i
$874$		0			0
$875$	26.8074	−	1.98658i	0.906255	−	0.0671586i
$876$		0			0
$877$	20.0896	+	5.38298i	0.678376	+	0.181770i	0.581525	−	0.813528i	$-0.302456\pi$
$877$	20.0896	+	5.38298i	0.678376	+	0.181770i	0.0968513	+	0.995299i	$0.469123\pi$
$878$		0			0
$879$	−24.9245	−	7.92195i	−0.840684	−	0.267201i
$880$		0			0
$881$		−	28.3087i		−	0.953745i	−0.878972	−	0.476873i	$-0.841770\pi$
$881$		−	28.3087i		−	0.953745i	0.878972	−	0.476873i	$-0.158230\pi$
$882$		0			0
$883$	−15.1647	−	15.1647i	−0.510333	−	0.510333i	0.404295	−	0.914629i	$-0.367517\pi$
$883$	−15.1647	−	15.1647i	−0.510333	−	0.510333i	−0.914629	+	0.404295i	$0.867517\pi$
$884$		0			0
$885$	−9.31797	+	4.10594i	−0.313220	+	0.138019i
$886$		0			0
$887$	12.4339	−	46.4040i	0.417490	−	1.55809i	−0.362306	−	0.932059i	$-0.618011\pi$
$887$	12.4339	−	46.4040i	0.417490	−	1.55809i	0.779796	−	0.626034i	$-0.215323\pi$
$888$		0			0
$889$	14.3940	+	8.31036i	0.482758	+	0.278721i
$890$		0			0
$891$	−7.83387	−	6.69757i	−0.262445	−	0.224377i
$892$		0			0
$893$	−8.88553	−	33.1613i	−0.297343	−	1.10970i
$894$		0			0
$895$	−0.0433983	+	0.692251i	−0.00145065	+	0.0231394i
$896$		0			0
$897$	14.2517	−	22.2571i	0.475849	−	0.743144i
$898$		0			0
$899$	−3.36724			−0.112304
$900$		0			0
$901$	−18.4774			−0.615573
$902$		0			0
$903$	17.2127	+	33.2524i	0.572804	+	1.10657i
$904$		0			0
$905$	−0.430100	+	6.86057i	−0.0142970	+	0.228053i
$906$		0			0
$907$	−9.66001	−	36.0516i	−0.320755	−	1.19707i	−0.918511	−	0.395396i	$-0.870607\pi$
$907$	−9.66001	−	36.0516i	−0.320755	−	1.19707i	0.597755	−	0.801679i	$-0.296059\pi$
$908$		0			0
$909$	−1.78495	−	1.26215i	−0.0592030	−	0.0418628i
$910$		0			0
$911$	−46.5957	−	26.9020i	−1.54378	−	0.891304i	−0.998595	−	0.0529906i	$-0.983125\pi$
$911$	−46.5957	−	26.9020i	−1.54378	−	0.891304i	−0.545189	−	0.838313i	$-0.683542\pi$
$912$		0			0
$913$	−0.830022	+	3.09768i	−0.0274697	+	0.102518i
$914$		0			0
$915$	22.1391	+	16.2150i	0.731897	+	0.536050i
$916$		0			0
$917$	−9.78315	−	9.78315i	−0.323068	−	0.323068i
$918$		0			0
$919$		−	23.1668i		−	0.764203i	−0.924120	−	0.382101i	$-0.875201\pi$
$919$		−	23.1668i		−	0.764203i	0.924120	−	0.382101i	$-0.124799\pi$
$920$		0			0
$921$	15.0126	−	13.6929i	0.494681	−	0.451196i
$922$		0			0
$923$	21.7465	+	5.82696i	0.715795	+	0.191797i
$924$		0			0
$925$	45.6187	−	35.4180i	1.49993	−	1.16454i
$926$		0			0
$927$	−1.41874	+	3.84268i	−0.0465974	+	0.126210i
$928$		0			0
$929$	−6.78350	+	11.7494i	−0.222559	+	0.385484i	−0.955584	−	0.294717i	$-0.904774\pi$
$929$	−6.78350	+	11.7494i	−0.222559	+	0.385484i	0.733025	+	0.680202i	$0.238108\pi$
$930$		0			0
$931$	1.69726	+	2.93974i	0.0556255	+	0.0963462i
$932$		0			0
$933$	19.3347	−	10.0084i	0.632989	−	0.327659i
$934$		0			0
$935$	−17.7438	+	3.58188i	−0.580283	+	0.117140i
$936$		0			0
$937$	−6.94086	+	6.94086i	−0.226748	+	0.226748i	−0.811333	−	0.584585i	$-0.801258\pi$
$937$	−6.94086	+	6.94086i	−0.226748	+	0.226748i	0.584585	+	0.811333i	$0.301258\pi$
$938$		0			0
$939$	−20.1959	+	4.42847i	−0.659069	+	0.144518i
$940$		0			0
$941$	−14.5976	+	8.42791i	−0.475867	+	0.274742i	−0.718693	−	0.695328i	$-0.755259\pi$
$941$	−14.5976	+	8.42791i	−0.475867	+	0.274742i	0.242825	+	0.970070i	$0.421926\pi$
$942$		0			0
$943$	−11.7513	+	3.14874i	−0.382673	+	0.102537i
$944$		0			0
$945$	27.8829	−	1.71328i	0.907030	−	0.0557329i
$946$		0			0
$947$	−37.0498	+	9.92745i	−1.20396	+	0.322599i	−0.804388	−	0.594105i	$-0.797506\pi$
$947$	−37.0498	+	9.92745i	−1.20396	+	0.322599i	−0.399568	+	0.916704i	$0.630840\pi$
$948$		0			0
$949$	−23.7185	+	13.6939i	−0.769935	+	0.444522i
$950$		0			0
$951$	3.28496	−	0.720309i	0.106522	−	0.0233576i
$952$		0			0
$953$	18.8861	−	18.8861i	0.611780	−	0.611780i	−0.331630	−	0.943410i	$-0.607598\pi$
$953$	18.8861	−	18.8861i	0.611780	−	0.611780i	0.943410	+	0.331630i	$0.107598\pi$
$954$		0			0
$955$	−17.6462	+	26.5725i	−0.571018	+	0.859865i
$956$		0			0
$957$	2.36835	−	1.22595i	0.0765578	−	0.0396292i
$958$		0			0
$959$	−12.5026	−	21.6551i	−0.403730	−	0.699281i
$960$		0			0
$961$	12.3638	−	21.4148i	0.398834	−	0.690800i
$962$		0			0
$963$	1.08269	+	1.30246i	0.0348891	+	0.0419711i
$964$		0			0
$965$	−20.3498	−	6.84343i	−0.655084	−	0.220298i
$966$		0			0
$967$	−30.9494	−	8.29288i	−0.995267	−	0.266681i	−0.275805	−	0.961213i	$-0.588945\pi$
$967$	−30.9494	−	8.29288i	−0.995267	−	0.266681i	−0.719461	+	0.694533i	$0.755611\pi$
$968$		0			0
$969$	−25.1838	+	22.9700i	−0.809020	+	0.737904i
$970$		0			0
$971$		−	29.2201i		−	0.937716i	−0.883274	−	0.468858i	$-0.844666\pi$
$971$		−	29.2201i		−	0.937716i	0.883274	−	0.468858i	$-0.155334\pi$
$972$		0			0
$973$	4.30974	+	4.30974i	0.138164	+	0.138164i
$974$		0			0
$975$	−8.98930	+	19.4486i	−0.287888	+	0.622854i
$976$		0			0
$977$	−10.1124	+	37.7399i	−0.323523	+	1.20741i	0.592265	+	0.805743i	$0.298234\pi$
$977$	−10.1124	+	37.7399i	−0.323523	+	1.20741i	−0.915788	+	0.401662i	$0.868433\pi$
$978$		0			0
$979$	4.83811	+	2.79328i	0.154627	+	0.0892737i
$980$		0			0
$981$	3.74275	−	40.6201i	0.119497	−	1.29690i
$982$		0			0
$983$	−2.96514	−	11.0660i	−0.0945732	−	0.352952i	0.902381	−	0.430939i	$-0.141818\pi$
$983$	−2.96514	−	11.0660i	−0.0945732	−	0.352952i	−0.996954	+	0.0779867i	$0.975151\pi$
$984$		0			0
$985$	−10.9685	+	9.67438i	−0.349486	+	0.308251i
$986$		0			0
$987$	23.6079	+	45.6070i	0.751448	+	1.45169i
$988$		0			0
$989$	−55.4552			−1.76337
$990$		0			0
$991$	26.7986			0.851286			0.425643	−	0.904891i	$-0.360048\pi$
$991$	26.7986			0.851286			0.425643	+	0.904891i	$0.360048\pi$
$992$		0			0
$993$	−20.5126	+	32.0350i	−0.650949	+	1.01660i
$994$		0			0
$995$	−9.08802	−	0.569743i	−0.288110	−	0.0180621i
$996$		0			0
$997$	14.2233	+	53.0819i	0.450455	+	1.68112i	0.701116	+	0.713047i	$0.252685\pi$
$997$	14.2233	+	53.0819i	0.450455	+	1.68112i	−0.250661	+	0.968075i	$0.580648\pi$
$998$		0			0
$999$	47.8684	−	36.2071i	1.51449	−	1.14554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.cu.b.353.1		16
4.3	odd	2		90.2.l.b.83.2	yes	16
5.2	odd	4	inner	720.2.cu.b.497.2		16
9.5	odd	6	inner	720.2.cu.b.113.2		16
12.11	even	2		270.2.m.b.143.3		16
20.3	even	4		450.2.p.h.407.3		16
20.7	even	4		90.2.l.b.47.2	yes	16
20.19	odd	2		450.2.p.h.443.3		16
36.7	odd	6		810.2.f.c.323.6		16
36.11	even	6		810.2.f.c.323.3		16
36.23	even	6		90.2.l.b.23.2	✓	16
36.31	odd	6		270.2.m.b.233.4		16
45.32	even	12	inner	720.2.cu.b.257.1		16
60.23	odd	4		1350.2.q.h.1007.2		16
60.47	odd	4		270.2.m.b.197.4		16
60.59	even	2		1350.2.q.h.143.1		16
180.7	even	12		810.2.f.c.647.3		16
180.23	odd	12		450.2.p.h.257.3		16
180.47	odd	12		810.2.f.c.647.6		16
180.59	even	6		450.2.p.h.293.3		16
180.67	even	12		270.2.m.b.17.3		16
180.103	even	12		1350.2.q.h.557.1		16
180.139	odd	6		1350.2.q.h.1043.2		16
180.167	odd	12		90.2.l.b.77.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.2	✓	16	36.23	even	6
90.2.l.b.47.2	yes	16	20.7	even	4
90.2.l.b.77.2	yes	16	180.167	odd	12
90.2.l.b.83.2	yes	16	4.3	odd	2
270.2.m.b.17.3		16	180.67	even	12
270.2.m.b.143.3		16	12.11	even	2
270.2.m.b.197.4		16	60.47	odd	4
270.2.m.b.233.4		16	36.31	odd	6
450.2.p.h.257.3		16	180.23	odd	12
450.2.p.h.293.3		16	180.59	even	6
450.2.p.h.407.3		16	20.3	even	4
450.2.p.h.443.3		16	20.19	odd	2
720.2.cu.b.113.2		16	9.5	odd	6	inner
720.2.cu.b.257.1		16	45.32	even	12	inner
720.2.cu.b.353.1		16	1.1	even	1	trivial
720.2.cu.b.497.2		16	5.2	odd	4	inner
810.2.f.c.323.3		16	36.11	even	6
810.2.f.c.323.6		16	36.7	odd	6
810.2.f.c.647.3		16	180.7	even	12
810.2.f.c.647.6		16	180.47	odd	12
1350.2.q.h.143.1		16	60.59	even	2
1350.2.q.h.557.1		16	180.103	even	12
1350.2.q.h.1007.2		16	60.23	odd	4
1350.2.q.h.1043.2		16	180.139	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.cu (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.73022 - 0.0795432i) q^{3} +(-0.139908 + 2.23169i) q^{5} +(0.622279 + 2.32238i) q^{7} +(2.98735 + 0.275255i) q^{9} +O(q^{10})\)	\(q+(-1.73022 - 0.0795432i) q^{3} +(-0.139908 + 2.23169i) q^{5} +(0.622279 + 2.32238i) q^{7} +(2.98735 + 0.275255i) q^{9} +(-0.991757 - 0.572591i) q^{11} +(-0.640322 + 2.38971i) q^{13} +(0.419588 - 3.85019i) q^{15} +(-4.99855 - 4.99855i) q^{17} +2.78390i q^{19} +(-0.891952 - 4.06773i) q^{21} +(5.95746 + 1.59630i) q^{23} +(-4.96085 - 0.624462i) q^{25} +(-5.14688 - 0.713876i) q^{27} +(0.672250 - 1.16437i) q^{29} +(-1.25223 - 2.16892i) q^{31} +(1.67042 + 1.06960i) q^{33} +(-5.26988 + 1.06381i) q^{35} +(-8.16761 + 8.16761i) q^{37} +(1.29799 - 4.08381i) q^{39} +(-1.70826 + 0.986264i) q^{41} +(-8.68498 + 2.32713i) q^{43} +(-1.03224 + 6.62831i) q^{45} +(-11.9118 + 3.19175i) q^{47} +(1.05598 - 0.609669i) q^{49} +(8.25101 + 9.04622i) q^{51} +(1.84828 - 1.84828i) q^{53} +(1.41660 - 2.13318i) q^{55} +(0.221441 - 4.81678i) q^{57} +(-1.31456 - 2.27688i) q^{59} +(-3.54275 + 6.13623i) q^{61} +(1.21972 + 7.10903i) q^{63} +(-5.24351 - 1.76334i) q^{65} +(-0.0545285 - 0.0146109i) q^{67} +(-10.1808 - 3.23582i) q^{69} -9.10005i q^{71} +(7.82779 + 7.82779i) q^{73} +(8.53371 + 1.47506i) q^{75} +(0.712623 - 2.65955i) q^{77} +(8.46375 + 4.88655i) q^{79} +(8.84847 + 1.64456i) q^{81} +(-0.724794 - 2.70497i) q^{83} +(11.8545 - 10.4559i) q^{85} +(-1.25576 + 1.96115i) q^{87} -4.87832 q^{89} -5.94827 q^{91} +(1.99411 + 3.85233i) q^{93} +(-6.21280 - 0.389491i) q^{95} +(2.08981 + 7.79929i) q^{97} +(-2.80511 - 1.98351i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{5} - 8 q^{7}+O(q^{10}) \) 16 * q - 12 * q^5 - 8 * q^7	\( 16 q - 12 q^{5} - 8 q^{7} + 24 q^{15} + 24 q^{21} + 24 q^{23} - 16 q^{25} + 8 q^{31} + 24 q^{41} + 36 q^{45} - 48 q^{47} + 48 q^{51} - 24 q^{55} + 24 q^{57} - 24 q^{61} + 48 q^{63} + 16 q^{67} + 16 q^{73} - 72 q^{77} + 24 q^{81} - 48 q^{83} - 4 q^{85} + 48 q^{87} + 72 q^{93} - 84 q^{95} - 48 q^{97}+O(q^{100}) \) 16 * q - 12 * q^5 - 8 * q^7 + 24 * q^15 + 24 * q^21 + 24 * q^23 - 16 * q^25 + 8 * q^31 + 24 * q^41 + 36 * q^45 - 48 * q^47 + 48 * q^51 - 24 * q^55 + 24 * q^57 - 24 * q^61 + 48 * q^63 + 16 * q^67 + 16 * q^73 - 72 * q^77 + 24 * q^81 - 48 * q^83 - 4 * q^85 + 48 * q^87 + 72 * q^93 - 84 * q^95 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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