LMFDB - Embedded newform 720.2.q.k.481.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(241,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))

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

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

chi := DirichletCharacter("720.241");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.q (of order $3$, degree $2$, 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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			481.2
Root			$0.403374 + 1.68443i$ of defining polynomial
Character	$\chi$	$=$	720.481
Dual form			720.2.q.k.241.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.403374 - 1.68443i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.91751 - 3.32123i) q^{7} +(-2.67458 - 1.35891i) q^{9} +O(q^{10})$	\(q+(0.403374 - 1.68443i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.91751 - 3.32123i) q^{7} +(-2.67458 - 1.35891i) q^{9} +(-0.853695 - 1.47864i) q^{11} +(-1.85369 + 3.21069i) q^{13} +(-1.25707 - 1.19154i) q^{15} +1.70739 q^{17} -0.292611 q^{19} +(-6.36783 + 1.89021i) q^{21} +(-2.91751 + 5.05328i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-3.36783 + 3.95698i) q^{27} +(-4.33502 - 7.50848i) q^{29} +(0.146305 - 0.253408i) q^{31} +(-2.83502 + 0.841540i) q^{33} -3.83502 q^{35} +11.9627 q^{37} +(4.66044 + 4.41752i) q^{39} +(3.48133 - 6.02983i) q^{41} +(1.85369 + 3.21069i) q^{43} +(-2.51414 + 1.63680i) q^{45} +(0.936184 + 1.62152i) q^{47} +(-3.85369 + 6.67479i) q^{49} +(0.688716 - 2.87597i) q^{51} -11.6700 q^{53} -1.70739 q^{55} +(-0.118031 + 0.492881i) q^{57} +(5.83502 - 10.1066i) q^{59} +(-7.48133 - 12.9580i) q^{61} +(0.615299 + 11.4886i) q^{63} +(1.85369 + 3.21069i) q^{65} +(4.77121 - 8.26397i) q^{67} +(7.33502 + 6.95269i) q^{69} -15.9627 q^{71} +8.00000 q^{73} +(-1.66044 + 0.492881i) q^{75} +(-3.27394 + 5.67063i) q^{77} +(1.00000 + 1.73205i) q^{79} +(5.30675 + 7.26900i) q^{81} +(-5.91751 - 10.2494i) q^{83} +(0.853695 - 1.47864i) q^{85} +(-14.3961 + 4.27330i) q^{87} -3.00000 q^{89} +14.2179 q^{91} +(-0.367832 - 0.348659i) q^{93} +(-0.146305 + 0.253408i) q^{95} +(1.83502 + 3.17835i) q^{97} +(0.273937 + 5.11484i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{3} + 3 q^{5} + 3 q^{7} + 5 q^{9}+O(q^{10}) $ 6 * q + q^3 + 3 * q^5 + 3 * q^7 + 5 * q^9	$ 6 q + q^{3} + 3 q^{5} + 3 q^{7} + 5 q^{9} - 6 q^{13} - q^{15} - 12 q^{19} - 20 q^{21} - 3 q^{23} - 3 q^{25} - 2 q^{27} + 3 q^{29} + 6 q^{31} + 12 q^{33} + 6 q^{35} + 24 q^{37} + 20 q^{39} - 3 q^{41} + 6 q^{43} - 2 q^{45} + 15 q^{47} - 18 q^{49} - 30 q^{51} - 12 q^{53} - 32 q^{57} + 6 q^{59} - 21 q^{61} + 29 q^{63} + 6 q^{65} + 9 q^{67} + 15 q^{69} - 48 q^{71} + 48 q^{73} - 2 q^{75} - 6 q^{77} + 6 q^{79} + 29 q^{81} - 21 q^{83} - 42 q^{87} - 18 q^{89} + 16 q^{93} - 6 q^{95} - 18 q^{97} - 12 q^{99}+O(q^{100}) $ 6 * q + q^3 + 3 * q^5 + 3 * q^7 + 5 * q^9 - 6 * q^13 - q^15 - 12 * q^19 - 20 * q^21 - 3 * q^23 - 3 * q^25 - 2 * q^27 + 3 * q^29 + 6 * q^31 + 12 * q^33 + 6 * q^35 + 24 * q^37 + 20 * q^39 - 3 * q^41 + 6 * q^43 - 2 * q^45 + 15 * q^47 - 18 * q^49 - 30 * q^51 - 12 * q^53 - 32 * q^57 + 6 * q^59 - 21 * q^61 + 29 * q^63 + 6 * q^65 + 9 * q^67 + 15 * q^69 - 48 * q^71 + 48 * q^73 - 2 * q^75 - 6 * q^77 + 6 * q^79 + 29 * q^81 - 21 * q^83 - 42 * q^87 - 18 * q^89 + 16 * q^93 - 6 * q^95 - 18 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	0.403374	−	1.68443i	0.232888	−	0.972504i
$3$	0.403374	−	1.68443i	0.232888	−	0.972504i
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−1.91751	−	3.32123i	−0.724751	−	1.25531i	−0.959076	−	0.283147i	$-0.908621\pi$
$7$	−1.91751	−	3.32123i	−0.724751	−	1.25531i	0.234326	−	0.972158i	$-0.424712\pi$
$8$		0			0
$9$	−2.67458	−	1.35891i	−0.891526	−	0.452969i
$10$		0			0
$11$	−0.853695	−	1.47864i	−0.257399	−	0.445828i	0.708146	−	0.706066i	$-0.249532\pi$
$11$	−0.853695	−	1.47864i	−0.257399	−	0.445828i	−0.965544	+	0.260239i	$0.916199\pi$
$12$		0			0
$13$	−1.85369	+	3.21069i	−0.514122	+	0.890486i	0.485743	+	0.874101i	$0.338549\pi$
$13$	−1.85369	+	3.21069i	−0.514122	+	0.890486i	−0.999866	+	0.0163846i	$0.994784\pi$
$14$		0			0
$15$	−1.25707	−	1.19154i	−0.324574	−	0.307656i
$16$		0			0
$17$	1.70739			0.414103			0.207051	−	0.978330i	$-0.433613\pi$
$17$	1.70739			0.414103			0.207051	+	0.978330i	$0.433613\pi$
$18$		0			0
$19$	−0.292611			−0.0671295			−0.0335647	−	0.999437i	$-0.510686\pi$
$19$	−0.292611			−0.0671295			−0.0335647	+	0.999437i	$0.510686\pi$
$20$		0			0
$21$	−6.36783	+	1.89021i	−1.38957	+	0.412477i
$22$		0			0
$23$	−2.91751	+	5.05328i	−0.608343	+	1.05368i	0.383171	+	0.923678i	$0.374832\pi$
$23$	−2.91751	+	5.05328i	−0.608343	+	1.05368i	−0.991514	+	0.130003i	$0.958501\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−3.36783	+	3.95698i	−0.648139	+	0.761522i
$28$		0			0
$29$	−4.33502	−	7.50848i	−0.804993	−	1.39429i	−0.916296	−	0.400503i	$-0.868836\pi$
$29$	−4.33502	−	7.50848i	−0.804993	−	1.39429i	0.111302	−	0.993787i	$-0.464498\pi$
$30$		0			0
$31$	0.146305	−	0.253408i	0.0262772	−	0.0455135i	−0.852588	−	0.522584i	$-0.824968\pi$
$31$	0.146305	−	0.253408i	0.0262772	−	0.0455135i	0.878865	+	0.477071i	$0.158301\pi$
$32$		0			0
$33$	−2.83502	+	0.841540i	−0.493514	+	0.146493i
$34$		0			0
$35$	−3.83502			−0.648237
$36$		0			0
$37$	11.9627			1.96665			0.983324	−	0.181862i	$-0.0582124\pi$
$37$	11.9627			1.96665			0.983324	+	0.181862i	$0.0582124\pi$
$38$		0			0
$39$	4.66044	+	4.41752i	0.746268	+	0.707369i
$40$		0			0
$41$	3.48133	−	6.02983i	0.543692	−	0.941702i	−0.454996	−	0.890493i	$-0.650359\pi$
$41$	3.48133	−	6.02983i	0.543692	−	0.941702i	0.998688	−	0.0512085i	$-0.0163073\pi$
$42$		0			0
$43$	1.85369	+	3.21069i	0.282686	+	0.489626i	0.972045	−	0.234793i	$-0.0754413\pi$
$43$	1.85369	+	3.21069i	0.282686	+	0.489626i	−0.689360	+	0.724419i	$0.742108\pi$
$44$		0			0
$45$	−2.51414	+	1.63680i	−0.374785	+	0.244000i
$46$		0			0
$47$	0.936184	+	1.62152i	0.136556	+	0.236523i	0.926191	−	0.377055i	$-0.123063\pi$
$47$	0.936184	+	1.62152i	0.136556	+	0.236523i	−0.789634	+	0.613578i	$0.789730\pi$
$48$		0			0
$49$	−3.85369	+	6.67479i	−0.550528	+	0.953542i
$50$		0			0
$51$	0.688716	−	2.87597i	0.0964395	−	0.402716i
$52$		0			0
$53$	−11.6700			−1.60300			−0.801502	−	0.597992i	$-0.795965\pi$
$53$	−11.6700			−1.60300			−0.801502	+	0.597992i	$0.795965\pi$
$54$		0			0
$55$	−1.70739			−0.230224
$56$		0			0
$57$	−0.118031	+	0.492881i	−0.0156336	+	0.0652837i
$58$		0			0
$59$	5.83502	−	10.1066i	0.759655	−	1.31576i	−0.183371	−	0.983044i	$-0.558701\pi$
$59$	5.83502	−	10.1066i	0.759655	−	1.31576i	0.943027	−	0.332718i	$-0.107966\pi$
$60$		0			0
$61$	−7.48133	−	12.9580i	−0.957886	−	1.65911i	−0.727622	−	0.685979i	$-0.759374\pi$
$61$	−7.48133	−	12.9580i	−0.957886	−	1.65911i	−0.230264	−	0.973128i	$-0.573959\pi$
$62$		0			0
$63$	0.615299	+	11.4886i	0.0775204	+	1.44743i
$64$		0			0
$65$	1.85369	+	3.21069i	0.229923	+	0.398237i
$66$		0			0
$67$	4.77121	−	8.26397i	0.582896	−	1.00960i	−0.412239	−	0.911076i	$-0.635253\pi$
$67$	4.77121	−	8.26397i	0.582896	−	1.00960i	0.995134	−	0.0985288i	$-0.0314136\pi$
$68$		0			0
$69$	7.33502	+	6.95269i	0.883033	+	0.837005i
$70$		0			0
$71$	−15.9627			−1.89442			−0.947209	−	0.320616i	$-0.896110\pi$
$71$	−15.9627			−1.89442			−0.947209	+	0.320616i	$0.896110\pi$
$72$		0			0
$73$	8.00000			0.936329			0.468165	−	0.883641i	$-0.344915\pi$
$73$	8.00000			0.936329			0.468165	+	0.883641i	$0.344915\pi$
$74$		0			0
$75$	−1.66044	+	0.492881i	−0.191731	+	0.0569130i
$76$		0			0
$77$	−3.27394	+	5.67063i	−0.373100	+	0.646228i
$78$		0			0
$79$	1.00000	+	1.73205i	0.112509	+	0.194871i	0.916781	−	0.399390i	$-0.130778\pi$
$79$	1.00000	+	1.73205i	0.112509	+	0.194871i	−0.804272	+	0.594261i	$0.797445\pi$
$80$		0			0
$81$	5.30675	+	7.26900i	0.589639	+	0.807667i
$82$		0			0
$83$	−5.91751	−	10.2494i	−0.649531	−	1.12502i	−0.983235	−	0.182343i	$-0.941632\pi$
$83$	−5.91751	−	10.2494i	−0.649531	−	1.12502i	0.333704	−	0.942678i	$-0.391701\pi$
$84$		0			0
$85$	0.853695	−	1.47864i	0.0925962	−	0.160381i
$86$		0			0
$87$	−14.3961	+	4.27330i	−1.54342	+	0.458146i
$88$		0			0
$89$	−3.00000			−0.317999			−0.159000	−	0.987279i	$-0.550827\pi$
$89$	−3.00000			−0.317999			−0.159000	+	0.987279i	$0.550827\pi$
$90$		0			0
$91$	14.2179			1.49044
$92$		0			0
$93$	−0.367832	−	0.348659i	−0.0381424	−	0.0361542i
$94$		0			0
$95$	−0.146305	+	0.253408i	−0.0150106	+	0.0259991i
$96$		0			0
$97$	1.83502	+	3.17835i	0.186318	+	0.322713i	0.944020	−	0.329888i	$-0.107011\pi$
$97$	1.83502	+	3.17835i	0.186318	+	0.322713i	−0.757702	+	0.652601i	$0.773678\pi$
$98$		0			0
$99$	0.273937	+	5.11484i	0.0275317	+	0.514061i
$100$		0			0
$101$	−0.164979	−	0.285751i	−0.0164160	−	0.0284333i	0.857701	−	0.514149i	$-0.171892\pi$
$101$	−0.164979	−	0.285751i	−0.0164160	−	0.0284333i	−0.874117	+	0.485716i	$0.838559\pi$
$102$		0			0
$103$	−1.56108	+	2.70388i	−0.153818	+	0.266421i	−0.932628	−	0.360839i	$-0.882490\pi$
$103$	−1.56108	+	2.70388i	−0.153818	+	0.266421i	0.778810	+	0.627260i	$0.215824\pi$
$104$		0			0
$105$	−1.54695	+	6.45981i	−0.150967	+	0.630413i
$106$		0			0
$107$	14.9198			1.44236			0.721178	−	0.692750i	$-0.243601\pi$
$107$	14.9198			1.44236			0.721178	+	0.692750i	$0.243601\pi$
$108$		0			0
$109$	6.70739			0.642451			0.321226	−	0.947003i	$-0.395905\pi$
$109$	6.70739			0.642451			0.321226	+	0.947003i	$0.395905\pi$
$110$		0			0
$111$	4.82542	−	20.1502i	0.458009	−	1.91257i
$112$		0			0
$113$	−2.83502	+	4.91040i	−0.266696	+	0.461932i	−0.968007	−	0.250924i	$-0.919265\pi$
$113$	−2.83502	+	4.91040i	−0.266696	+	0.461932i	0.701310	+	0.712856i	$0.252599\pi$
$114$		0			0
$115$	2.91751	+	5.05328i	0.272059	+	0.471220i
$116$		0			0
$117$	9.32088	−	6.06826i	0.861716	−	0.561010i
$118$		0			0
$119$	−3.27394	−	5.67063i	−0.300121	−	0.519825i
$120$		0			0
$121$	4.04241	−	7.00166i	0.367492	−	0.636515i
$122$		0			0
$123$	−8.75253	−	8.29631i	−0.789189	−	0.748053i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	5.54241			0.491809			0.245905	−	0.969294i	$-0.420915\pi$
$127$	5.54241			0.491809			0.245905	+	0.969294i	$0.420915\pi$
$128$		0			0
$129$	6.15591	−	1.82730i	0.541997	−	0.160885i
$130$		0			0
$131$	6.41478	−	11.1107i	0.560462	−	0.970748i	−0.436994	−	0.899464i	$-0.643957\pi$
$131$	6.41478	−	11.1107i	0.560462	−	0.970748i	0.997456	−	0.0712840i	$-0.0227097\pi$
$132$		0			0
$133$	0.561084	+	0.971826i	0.0486522	+	0.0842680i
$134$		0			0
$135$	1.74293	+	4.89512i	0.150008	+	0.421305i
$136$		0			0
$137$	−4.54241	−	7.86769i	−0.388084	−	0.672182i	0.604108	−	0.796903i	$-0.293530\pi$
$137$	−4.54241	−	7.86769i	−0.388084	−	0.672182i	−0.992192	+	0.124721i	$0.960196\pi$
$138$		0			0
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	−0.938293	−	0.345843i	$-0.887593\pi$
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	0.768655	+	0.639664i	$0.220926\pi$
$140$		0			0
$141$	3.10896	−	0.922854i	0.261822	−	0.0777184i
$142$		0			0
$143$	6.32996			0.529338
$144$		0			0
$145$	−8.67004			−0.720008
$146$		0			0
$147$	9.68872	+	9.18370i	0.799112	+	0.757459i
$148$		0			0
$149$	4.06108	−	7.03400i	0.332697	−	0.576248i	−0.650343	−	0.759641i	$-0.725375\pi$
$149$	4.06108	−	7.03400i	0.332697	−	0.576248i	0.983040	+	0.183393i	$0.0587080\pi$
$150$		0			0
$151$	10.5237	+	18.2276i	0.856410	+	1.48334i	0.875331	+	0.483524i	$0.160643\pi$
$151$	10.5237	+	18.2276i	0.856410	+	1.48334i	−0.0189215	+	0.999821i	$0.506023\pi$
$152$		0			0
$153$	−4.56655	−	2.32018i	−0.369184	−	0.187576i
$154$		0			0
$155$	−0.146305	−	0.253408i	−0.0117515	−	0.0203542i
$156$		0			0
$157$	0.127632	−	0.221065i	0.0101861	−	0.0176429i	−0.860887	−	0.508796i	$-0.830091\pi$
$157$	0.127632	−	0.221065i	0.0101861	−	0.0176429i	0.871074	+	0.491153i	$0.163424\pi$
$158$		0			0
$159$	−4.70739	+	19.6573i	−0.373320	+	1.55893i
$160$		0			0
$161$	22.3774			1.76359
$162$		0			0
$163$	11.7074			0.916994			0.458497	−	0.888696i	$-0.348388\pi$
$163$	11.7074			0.916994			0.458497	+	0.888696i	$0.348388\pi$
$164$		0			0
$165$	−0.688716	+	2.87597i	−0.0536165	+	0.223894i
$166$		0			0
$167$	8.06382	−	13.9669i	0.623997	−	1.08079i	−0.364737	−	0.931111i	$-0.618841\pi$
$167$	8.06382	−	13.9669i	0.623997	−	1.08079i	0.988734	−	0.149684i	$-0.0478255\pi$
$168$		0			0
$169$	−0.372368	−	0.644960i	−0.0286437	−	0.0496123i
$170$		0			0
$171$	0.782610	+	0.397630i	0.0598477	+	0.0304076i
$172$		0			0
$173$	4.29261	+	7.43502i	0.326361	+	0.565274i	0.981787	−	0.189986i	$-0.0608441\pi$
$173$	4.29261	+	7.43502i	0.326361	+	0.565274i	−0.655426	+	0.755260i	$0.727511\pi$
$174$		0			0
$175$	−1.91751	+	3.32123i	−0.144950	+	0.251061i
$176$		0			0
$177$	−14.6700	−	13.9054i	−1.10267	−	1.04519i
$178$		0			0
$179$	7.37743			0.551415			0.275708	−	0.961242i	$-0.411088\pi$
$179$	7.37743			0.551415			0.275708	+	0.961242i	$0.411088\pi$
$180$		0			0
$181$	17.4996			1.30074			0.650368	−	0.759620i	$-0.274615\pi$
$181$	17.4996			1.30074			0.650368	+	0.759620i	$0.274615\pi$
$182$		0			0
$183$	−24.8446	+	7.37481i	−1.83657	+	0.545161i
$184$		0			0
$185$	5.98133	−	10.3600i	0.439756	−	0.761680i
$186$		0			0
$187$	−1.45759	−	2.52462i	−0.106589	−	0.184618i
$188$		0			0
$189$	19.5999	+	3.59777i	1.42568	+	0.261700i
$190$		0			0
$191$	3.27394	+	5.67063i	0.236894	+	0.410312i	0.959821	−	0.280612i	$-0.0905373\pi$
$191$	3.27394	+	5.67063i	0.236894	+	0.410312i	−0.722928	+	0.690924i	$0.757204\pi$
$192$		0			0
$193$	−3.56108	+	6.16798i	−0.256332	+	0.443981i	−0.965257	−	0.261304i	$-0.915848\pi$
$193$	−3.56108	+	6.16798i	−0.256332	+	0.443981i	0.708924	+	0.705285i	$0.249181\pi$
$194$		0			0
$195$	6.15591	−	1.82730i	0.440834	−	0.130856i
$196$		0			0
$197$	−17.6700			−1.25894			−0.629469	−	0.777025i	$-0.716728\pi$
$197$	−17.6700			−1.25894			−0.629469	+	0.777025i	$0.716728\pi$
$198$		0			0
$199$	−11.6327			−0.824620			−0.412310	−	0.911044i	$-0.635278\pi$
$199$	−11.6327			−0.824620			−0.412310	+	0.911044i	$0.635278\pi$
$200$		0			0
$201$	−11.9955	−	11.3702i	−0.846095	−	0.801993i
$202$		0			0
$203$	−16.6249	+	28.7952i	−1.16684	+	2.02102i
$204$		0			0
$205$	−3.48133	−	6.02983i	−0.243146	−	0.421142i
$206$		0			0
$207$	14.6700	−	9.55077i	1.01964	−	0.663824i
$208$		0			0
$209$	0.249800	+	0.432667i	0.0172790	+	0.0299282i
$210$		0			0
$211$	2.81635	−	4.87806i	0.193885	−	0.335819i	−0.752649	−	0.658422i	$-0.771224\pi$
$211$	2.81635	−	4.87806i	0.193885	−	0.335819i	0.946535	+	0.322602i	$0.104558\pi$
$212$		0			0
$213$	−6.43892	+	26.8879i	−0.441187	+	1.84233i
$214$		0			0
$215$	3.70739			0.252842
$216$		0			0
$217$	−1.12217			−0.0761777
$218$		0			0
$219$	3.22699	−	13.4754i	0.218060	−	0.910583i
$220$		0			0
$221$	−3.16498	+	5.48190i	−0.212899	+	0.368753i
$222$		0			0
$223$	−4.06382	−	7.03874i	−0.272133	−	0.471349i	0.697275	−	0.716804i	$-0.254396\pi$
$223$	−4.06382	−	7.03874i	−0.272133	−	0.471349i	−0.969408	+	0.245455i	$0.921062\pi$
$224$		0			0
$225$	0.160442	+	2.99571i	0.0106961	+	0.199714i
$226$		0			0
$227$	4.98133	+	8.62791i	0.330622	+	0.572655i	0.982634	−	0.185554i	$-0.0594081\pi$
$227$	4.98133	+	8.62791i	0.330622	+	0.572655i	−0.652012	+	0.758209i	$0.726075\pi$
$228$		0			0
$229$	−0.627632	+	1.08709i	−0.0414751	+	0.0718370i	−0.886018	−	0.463651i	$-0.846539\pi$
$229$	−0.627632	+	1.08709i	−0.0414751	+	0.0718370i	0.844543	+	0.535488i	$0.179872\pi$
$230$		0			0
$231$	8.23113	+	7.80209i	0.541568	+	0.513340i
$232$		0			0
$233$	3.96265			0.259602			0.129801	−	0.991540i	$-0.458566\pi$
$233$	3.96265			0.259602			0.129801	+	0.991540i	$0.458566\pi$
$234$		0			0
$235$	1.87237			0.122140
$236$		0			0
$237$	3.32088	−	0.985762i	0.215715	−	0.0640321i
$238$		0			0
$239$	−2.83502	+	4.91040i	−0.183382	+	0.317627i	−0.943030	−	0.332707i	$-0.892038\pi$
$239$	−2.83502	+	4.91040i	−0.183382	+	0.317627i	0.759648	+	0.650335i	$0.225371\pi$
$240$		0			0
$241$	8.31635	+	14.4043i	0.535703	+	0.927865i	0.999129	+	0.0417293i	$0.0132867\pi$
$241$	8.31635	+	14.4043i	0.535703	+	0.927865i	−0.463426	+	0.886136i	$0.653380\pi$
$242$		0			0
$243$	14.3847	−	6.00670i	0.922779	−	0.385330i
$244$		0			0
$245$	3.85369	+	6.67479i	0.246204	+	0.426437i
$246$		0			0
$247$	0.542411	−	0.939483i	0.0345128	−	0.0597779i
$248$		0			0
$249$	−19.6514	+	5.83326i	−1.24535	+	0.369668i
$250$		0			0
$251$	−13.3774			−0.844376			−0.422188	−	0.906508i	$-0.638738\pi$
$251$	−13.3774			−0.844376			−0.422188	+	0.906508i	$0.638738\pi$
$252$		0			0
$253$	9.96265			0.626347
$254$		0			0
$255$	−2.14631	−	2.03443i	−0.134407	−	0.127401i
$256$		0			0
$257$	−0.414779	+	0.718418i	−0.0258732	+	0.0448137i	−0.878672	−	0.477426i	$-0.841570\pi$
$257$	−0.414779	+	0.718418i	−0.0258732	+	0.0448137i	0.852799	+	0.522239i	$0.174903\pi$
$258$		0			0
$259$	−22.9385	−	39.7307i	−1.42533	−	2.46874i
$260$		0			0
$261$	1.39104	+	25.9729i	0.0861033	+	1.60768i
$262$		0			0
$263$	6.10896	+	10.5810i	0.376695	+	0.652454i	0.990579	−	0.136942i	$-0.0437273\pi$
$263$	6.10896	+	10.5810i	0.376695	+	0.652454i	−0.613885	+	0.789396i	$0.710394\pi$
$264$		0			0
$265$	−5.83502	+	10.1066i	−0.358443	+	0.620841i
$266$		0			0
$267$	−1.21012	+	5.05328i	−0.0740582	+	0.309256i
$268$		0			0
$269$	17.5369			1.06925			0.534623	−	0.845091i	$-0.320454\pi$
$269$	17.5369			1.06925			0.534623	+	0.845091i	$0.320454\pi$
$270$		0			0
$271$	15.1222			0.918606			0.459303	−	0.888280i	$-0.348099\pi$
$271$	15.1222			0.918606			0.459303	+	0.888280i	$0.348099\pi$
$272$		0			0
$273$	5.73514	−	23.9490i	0.347106	−	1.44946i
$274$		0			0
$275$	−0.853695	+	1.47864i	−0.0514797	+	0.0891655i
$276$		0			0
$277$	2.85369	+	4.94274i	0.171462	+	0.296981i	0.938931	−	0.344105i	$-0.111818\pi$
$277$	2.85369	+	4.94274i	0.171462	+	0.296981i	−0.767469	+	0.641086i	$0.778484\pi$
$278$		0			0
$279$	−0.735663	+	0.478945i	−0.0440430	+	0.0286737i
$280$		0			0
$281$	−3.64631	−	6.31559i	−0.217520	−	0.376756i	0.736529	−	0.676406i	$-0.236464\pi$
$281$	−3.64631	−	6.31559i	−0.217520	−	0.376756i	−0.954049	+	0.299650i	$0.903130\pi$
$282$		0			0
$283$	−5.08249	+	8.80313i	−0.302123	+	0.523292i	−0.976617	−	0.214989i	$-0.931029\pi$
$283$	−5.08249	+	8.80313i	−0.302123	+	0.523292i	0.674494	+	0.738280i	$0.264362\pi$
$284$		0			0
$285$	0.367832	+	0.348659i	0.0217885	+	0.0206528i
$286$		0			0
$287$	−26.7019			−1.57616
$288$		0			0
$289$	−14.0848			−0.828519
$290$		0			0
$291$	6.09389	−	1.80889i	0.357230	−	0.106039i
$292$		0			0
$293$	−6.52374	+	11.2994i	−0.381121	+	0.660121i	−0.991223	−	0.132202i	$-0.957795\pi$
$293$	−6.52374	+	11.2994i	−0.381121	+	0.660121i	0.610102	+	0.792323i	$0.291128\pi$
$294$		0			0
$295$	−5.83502	−	10.1066i	−0.339728	−	0.588426i
$296$		0			0
$297$	8.72606	+	1.60176i	0.506338	+	0.0929438i
$298$		0			0
$299$	−10.8163	−	18.7345i	−0.625526	−	1.08344i
$300$		0			0
$301$	7.10896	−	12.3131i	0.409754	−	0.709714i
$302$		0			0
$303$	−0.547875	+	0.162630i	−0.0314746	+	0.00934282i
$304$		0			0
$305$	−14.9627			−0.856759
$306$		0			0
$307$	−1.50506			−0.0858986			−0.0429493	−	0.999077i	$-0.513675\pi$
$307$	−1.50506			−0.0858986			−0.0429493	+	0.999077i	$0.513675\pi$
$308$		0			0
$309$	3.92478	+	3.72020i	0.223273	+	0.211635i
$310$		0			0
$311$	−2.72606	+	4.72168i	−0.154581	+	0.267742i	−0.932906	−	0.360119i	$-0.882736\pi$
$311$	−2.72606	+	4.72168i	−0.154581	+	0.267742i	0.778325	+	0.627861i	$0.216069\pi$
$312$		0			0
$313$	5.27394	+	9.13473i	0.298101	+	0.516325i	0.975701	−	0.219105i	$-0.0703136\pi$
$313$	5.27394	+	9.13473i	0.298101	+	0.516325i	−0.677601	+	0.735430i	$0.736980\pi$
$314$		0			0
$315$	10.2571	+	5.21143i	0.577920	+	0.293631i
$316$		0			0
$317$	−12.6887	−	21.9775i	−0.712669	−	1.23438i	−0.963852	−	0.266440i	$-0.914153\pi$
$317$	−12.6887	−	21.9775i	−0.712669	−	1.23438i	0.251182	−	0.967940i	$-0.419181\pi$
$318$		0			0
$319$	−7.40157	+	12.8199i	−0.414408	+	0.717776i
$320$		0			0
$321$	6.01827	−	25.1314i	0.335907	−	1.40270i
$322$		0			0
$323$	−0.499600			−0.0277985
$324$		0			0
$325$	3.70739			0.205649
$326$		0			0
$327$	2.70559	−	11.2981i	0.149619	−	0.624786i
$328$		0			0
$329$	3.59029	−	6.21856i	0.197939	−	0.342840i
$330$		0			0
$331$	−15.5424	−	26.9202i	−0.854288	−	1.47967i	−0.877304	−	0.479935i	$-0.840660\pi$
$331$	−15.5424	−	26.9202i	−0.854288	−	1.47967i	0.0230157	−	0.999735i	$-0.492673\pi$
$332$		0			0
$333$	−31.9951	−	16.2561i	−1.75332	−	0.890830i
$334$		0			0
$335$	−4.77121	−	8.26397i	−0.260679	−	0.451509i
$336$		0			0
$337$	−5.12763	+	8.88132i	−0.279320	+	0.483796i	−0.971216	−	0.238201i	$-0.923442\pi$
$337$	−5.12763	+	8.88132i	−0.279320	+	0.483796i	0.691896	+	0.721997i	$0.256776\pi$
$338$		0			0
$339$	7.12763	+	6.75611i	0.387120	+	0.366942i
$340$		0			0
$341$	−0.499600			−0.0270549
$342$		0			0
$343$	2.71285			0.146480
$344$		0			0
$345$	9.68872	−	2.87597i	0.521623	−	0.154837i
$346$		0			0
$347$	−3.52374	+	6.10329i	−0.189164	+	0.327642i	−0.944972	−	0.327152i	$-0.893911\pi$
$347$	−3.52374	+	6.10329i	−0.189164	+	0.327642i	0.755808	+	0.654794i	$0.227244\pi$
$348$		0			0
$349$	−14.5848	−	25.2617i	−0.780708	−	1.35223i	−0.931530	−	0.363664i	$-0.881526\pi$
$349$	−14.5848	−	25.2617i	−0.780708	−	1.35223i	0.150822	−	0.988561i	$-0.451808\pi$
$350$		0			0
$351$	−6.46173	−	18.1481i	−0.344901	−	0.968675i
$352$		0			0
$353$	12.0000	+	20.7846i	0.638696	+	1.10625i	0.985719	+	0.168397i	$0.0538590\pi$
$353$	12.0000	+	20.7846i	0.638696	+	1.10625i	−0.347024	+	0.937856i	$0.612808\pi$
$354$		0			0
$355$	−7.98133	+	13.8241i	−0.423605	+	0.733705i
$356$		0			0
$357$	−10.8724	+	3.22732i	−0.575427	+	0.170808i
$358$		0			0
$359$	28.7922			1.51959			0.759797	−	0.650160i	$-0.225298\pi$
$359$	28.7922			1.51959			0.759797	+	0.650160i	$0.225298\pi$
$360$		0			0
$361$	−18.9144			−0.995494
$362$		0			0
$363$	−10.1632	−	9.63343i	−0.533428	−	0.505624i
$364$		0			0
$365$	4.00000	−	6.92820i	0.209370	−	0.362639i
$366$		0			0
$367$	−5.52374	−	9.56739i	−0.288337	−	0.499414i	0.685076	−	0.728471i	$-0.259769\pi$
$367$	−5.52374	−	9.56739i	−0.288337	−	0.499414i	−0.973413	+	0.229058i	$0.926436\pi$
$368$		0			0
$369$	−17.5051	+	11.3965i	−0.911277	+	0.593277i
$370$		0			0
$371$	22.3774	+	38.7588i	1.16178	+	2.01226i
$372$		0			0
$373$	7.83502	−	13.5707i	0.405682	−	0.702662i	−0.588719	−	0.808338i	$-0.700367\pi$
$373$	7.83502	−	13.5707i	0.405682	−	0.702662i	0.994401	+	0.105676i	$0.0337007\pi$
$374$		0			0
$375$	−0.403374	+	1.68443i	−0.0208301	+	0.0869834i
$376$		0			0
$377$	32.1432			1.65546
$378$		0			0
$379$	6.58522			0.338260			0.169130	−	0.985594i	$-0.445904\pi$
$379$	6.58522			0.338260			0.169130	+	0.985594i	$0.445904\pi$
$380$		0			0
$381$	2.23566	−	9.33578i	0.114536	−	0.478286i
$382$		0			0
$383$	−6.10896	+	10.5810i	−0.312153	+	0.540665i	−0.978828	−	0.204683i	$-0.934384\pi$
$383$	−6.10896	+	10.5810i	−0.312153	+	0.540665i	0.666675	+	0.745348i	$0.267717\pi$
$384$		0			0
$385$	3.27394	+	5.67063i	0.166855	+	0.289002i
$386$		0			0
$387$	−0.594822	−	11.1063i	−0.0302365	−	0.564562i
$388$		0			0
$389$	−13.8588	−	24.0041i	−0.702667	−	1.21705i	−0.967527	−	0.252768i	$-0.918659\pi$
$389$	−13.8588	−	24.0041i	−0.702667	−	1.21705i	0.264860	−	0.964287i	$-0.414674\pi$
$390$		0			0
$391$	−4.98133	+	8.62791i	−0.251917	+	0.436332i
$392$		0			0
$393$	−16.1276	−	15.2870i	−0.813531	−	0.771127i
$394$		0			0
$395$	2.00000			0.100631
$396$		0			0
$397$	−26.5105			−1.33053			−0.665263	−	0.746609i	$-0.731680\pi$
$397$	−26.5105			−1.33053			−0.665263	+	0.746609i	$0.731680\pi$
$398$		0			0
$399$	1.86330	−	0.553095i	0.0932814	−	0.0276894i
$400$		0			0
$401$	−8.42024	+	14.5843i	−0.420487	+	0.728305i	−0.995987	−	0.0894970i	$-0.971474\pi$
$401$	−8.42024	+	14.5843i	−0.420487	+	0.728305i	0.575500	+	0.817802i	$0.304807\pi$
$402$		0			0
$403$	0.542411	+	0.939483i	0.0270194	+	0.0467990i
$404$		0			0
$405$	8.94852	−	0.961276i	0.444655	−	0.0477662i
$406$		0			0
$407$	−10.2125	−	17.6885i	−0.506213	−	0.876786i
$408$		0			0
$409$	−7.54787	+	13.0733i	−0.373218	+	0.646433i	−0.990059	−	0.140655i	$-0.955079\pi$
$409$	−7.54787	+	13.0733i	−0.373218	+	0.646433i	0.616840	+	0.787088i	$0.288412\pi$
$410$		0			0
$411$	−15.0848	+	4.47773i	−0.744079	+	0.220870i
$412$		0			0
$413$	−44.7549			−2.20224
$414$		0			0
$415$	−11.8350			−0.580958
$416$		0			0
$417$	5.02827	+	4.76618i	0.246236	+	0.233401i
$418$		0			0
$419$	−1.18365	+	2.05015i	−0.0578252	+	0.100156i	−0.893489	−	0.449085i	$-0.851750\pi$
$419$	−1.18365	+	2.05015i	−0.0578252	+	0.100156i	0.835664	+	0.549241i	$0.185083\pi$
$420$		0			0
$421$	−4.96265	−	8.59557i	−0.241865	−	0.418922i	0.719381	−	0.694616i	$-0.244426\pi$
$421$	−4.96265	−	8.59557i	−0.241865	−	0.418922i	−0.961246	+	0.275694i	$0.911092\pi$
$422$		0			0
$423$	−0.300407	−	5.60907i	−0.0146063	−	0.272722i
$424$		0			0
$425$	−0.853695	−	1.47864i	−0.0414103	−	0.0717247i
$426$		0			0
$427$	−28.6910	+	49.6944i	−1.38846	+	2.40488i
$428$		0			0
$429$	2.55334	−	10.6623i	0.123276	−	0.514783i
$430$		0			0
$431$	13.9253			0.670758			0.335379	−	0.942083i	$-0.391136\pi$
$431$	13.9253			0.670758			0.335379	+	0.942083i	$0.391136\pi$
$432$		0			0
$433$	−2.29261			−0.110176			−0.0550879	−	0.998482i	$-0.517544\pi$
$433$	−2.29261			−0.110176			−0.0550879	+	0.998482i	$0.517544\pi$
$434$		0			0
$435$	−3.49727	+	14.6040i	−0.167681	+	0.700210i
$436$		0			0
$437$	0.853695	−	1.47864i	0.0408378	−	0.0707331i
$438$		0			0
$439$	12.5051	+	21.6594i	0.596834	+	1.03375i	0.993285	+	0.115691i	$0.0369083\pi$
$439$	12.5051	+	21.6594i	0.596834	+	1.03375i	−0.396451	+	0.918056i	$0.629758\pi$
$440$		0			0
$441$	19.3774	−	12.6155i	0.922735	−	0.600736i
$442$		0			0
$443$	−9.93618	−	17.2100i	−0.472082	−	0.817671i	0.527407	−	0.849613i	$-0.323164\pi$
$443$	−9.93618	−	17.2100i	−0.472082	−	0.817671i	−0.999490	+	0.0319419i	$0.989831\pi$
$444$		0			0
$445$	−1.50000	+	2.59808i	−0.0711068	+	0.123161i
$446$		0			0
$447$	−10.2101	−	9.67793i	−0.482922	−	0.457750i
$448$		0			0
$449$	32.2553			1.52222			0.761110	−	0.648623i	$-0.224655\pi$
$449$	32.2553			1.52222			0.761110	+	0.648623i	$0.224655\pi$
$450$		0			0
$451$	−11.8880			−0.559782
$452$		0			0
$453$	34.9481	−	10.3739i	1.64201	−	0.487408i
$454$		0			0
$455$	7.10896	−	12.3131i	0.333273	−	0.577246i
$456$		0			0
$457$	−9.94398	−	17.2235i	−0.465160	−	0.805680i	0.534049	−	0.845454i	$-0.320670\pi$
$457$	−9.94398	−	17.2235i	−0.465160	−	0.805680i	−0.999209	+	0.0397732i	$0.987336\pi$
$458$		0			0
$459$	−5.75020	+	6.75611i	−0.268396	+	0.315348i
$460$		0			0
$461$	10.8829	+	18.8497i	0.506867	+	0.877919i	0.999968	+	0.00794757i	$0.00252982\pi$
$461$	10.8829	+	18.8497i	0.506867	+	0.877919i	−0.493101	+	0.869972i	$0.664137\pi$
$462$		0			0
$463$	8.98133	−	15.5561i	0.417398	−	0.722954i	−0.578279	−	0.815839i	$-0.696276\pi$
$463$	8.98133	−	15.5561i	0.417398	−	0.722954i	0.995677	+	0.0928850i	$0.0296089\pi$
$464$		0			0
$465$	−0.485863	+	0.144222i	−0.0225314	+	0.00668814i
$466$		0			0
$467$	−19.0475			−0.881412			−0.440706	−	0.897651i	$-0.645272\pi$
$467$	−19.0475			−0.881412			−0.440706	+	0.897651i	$0.645272\pi$
$468$		0			0
$469$	−36.5953			−1.68982
$470$		0			0
$471$	−0.320884	−	0.304159i	−0.0147856	−	0.0140149i
$472$		0			0
$473$	3.16498	−	5.48190i	0.145526	−	0.252058i
$474$		0			0
$475$	0.146305	+	0.253408i	0.00671295	+	0.0116272i
$476$		0			0
$477$	31.2125	+	15.8585i	1.42912	+	0.726111i
$478$		0			0
$479$	10.3774	+	17.9742i	0.474157	+	0.821264i	0.999562	−	0.0295882i	$-0.00941958\pi$
$479$	10.3774	+	17.9742i	0.474157	+	0.821264i	−0.525405	+	0.850852i	$0.676086\pi$
$480$		0			0
$481$	−22.1751	+	38.4084i	−1.01110	+	1.75127i
$482$		0			0
$483$	9.02647	−	37.6931i	0.410719	−	1.71510i
$484$		0			0
$485$	3.67004			0.166648
$486$		0			0
$487$	−4.86690			−0.220540			−0.110270	−	0.993902i	$-0.535172\pi$
$487$	−4.86690			−0.220540			−0.110270	+	0.993902i	$0.535172\pi$
$488$		0			0
$489$	4.72245	−	19.7202i	0.213557	−	0.891779i
$490$		0			0
$491$	19.1276	−	33.1300i	0.863218	−	1.49514i	−0.00558786	−	0.999984i	$-0.501779\pi$
$491$	19.1276	−	33.1300i	0.863218	−	1.49514i	0.868806	−	0.495153i	$-0.164888\pi$
$492$		0			0
$493$	−7.40157	−	12.8199i	−0.333350	−	0.577379i
$494$		0			0
$495$	4.56655	+	2.32018i	0.205251	+	0.104284i
$496$		0			0
$497$	30.6086	+	53.0156i	1.37298	+	2.37807i
$498$		0			0
$499$	−13.4202	+	23.2445i	−0.600773	+	1.04057i	0.391932	+	0.919994i	$0.371807\pi$
$499$	−13.4202	+	23.2445i	−0.600773	+	1.04057i	−0.992704	+	0.120574i	$0.961526\pi$
$500$		0			0
$501$	−20.2735	−	19.2168i	−0.905755	−	0.858543i
$502$		0			0
$503$	18.8825			0.841929			0.420964	−	0.907077i	$-0.361692\pi$
$503$	18.8825			0.841929			0.420964	+	0.907077i	$0.361692\pi$
$504$		0			0
$505$	−0.329957			−0.0146829
$506$		0			0
$507$	−1.23659	+	0.367066i	−0.0549189	+	0.0163020i
$508$		0			0
$509$	−16.5848	+	28.7258i	−0.735109	+	1.27325i	0.219566	+	0.975598i	$0.429536\pi$
$509$	−16.5848	+	28.7258i	−0.735109	+	1.27325i	−0.954675	+	0.297649i	$0.903797\pi$
$510$		0			0
$511$	−15.3401	−	26.5698i	−0.678605	−	1.17538i
$512$		0			0
$513$	0.985463	−	1.15786i	0.0435093	−	0.0511206i
$514$		0			0
$515$	1.56108	+	2.70388i	0.0687896	+	0.119147i
$516$		0			0
$517$	1.59843	−	2.76856i	0.0702989	−	0.121761i
$518$		0			0
$519$	14.2553	−	4.23149i	0.625737	−	0.185742i
$520$		0			0
$521$	−38.0101			−1.66525			−0.832627	−	0.553834i	$-0.813164\pi$
$521$	−38.0101			−1.66525			−0.832627	+	0.553834i	$0.813164\pi$
$522$		0			0
$523$	37.4677			1.63835			0.819174	−	0.573544i	$-0.194432\pi$
$523$	37.4677			1.63835			0.819174	+	0.573544i	$0.194432\pi$
$524$		0			0
$525$	4.82088	+	4.56960i	0.210401	+	0.199434i
$526$		0			0
$527$	0.249800	−	0.432667i	0.0108815	−	0.0188473i
$528$		0			0
$529$	−5.52374	−	9.56739i	−0.240163	−	0.415974i
$530$		0			0
$531$	−29.3401	+	19.1015i	−1.27325	+	0.828936i
$532$		0			0
$533$	12.9066	+	22.3549i	0.559048	+	0.968300i
$534$		0			0
$535$	7.45992	−	12.9210i	0.322521	−	0.558622i
$536$		0			0
$537$	2.97586	−	12.4267i	0.128418	−	0.536253i
$538$		0			0
$539$	13.1595			0.566820
$540$		0			0
$541$	31.7549			1.36525			0.682624	−	0.730770i	$-0.260839\pi$
$541$	31.7549			1.36525			0.682624	+	0.730770i	$0.260839\pi$
$542$		0			0
$543$	7.05888	−	29.4768i	0.302926	−	1.26497i
$544$		0			0
$545$	3.35369	−	5.80877i	0.143656	−	0.248820i
$546$		0			0
$547$	6.75253	+	11.6957i	0.288717	+	0.500073i	0.973504	−	0.228671i	$-0.0734379\pi$
$547$	6.75253	+	11.6957i	0.288717	+	0.500073i	−0.684786	+	0.728744i	$0.740105\pi$
$548$		0			0
$549$	2.40064	+	44.8237i	0.102457	+	1.91303i
$550$		0			0
$551$	1.26847	+	2.19706i	0.0540388	+	0.0935979i
$552$		0			0
$553$	3.83502	−	6.64245i	0.163082	−	0.282466i
$554$		0			0
$555$	−15.0379	−	14.2540i	−0.638322	−	0.605050i
$556$		0			0
$557$	6.00000			0.254228			0.127114	−	0.991888i	$-0.459429\pi$
$557$	6.00000			0.254228			0.127114	+	0.991888i	$0.459429\pi$
$558$		0			0
$559$	−13.7447			−0.581340
$560$		0			0
$561$	−4.84049	+	1.43684i	−0.204365	+	0.0606632i
$562$		0			0
$563$	−15.6062	+	27.0308i	−0.657724	+	1.13921i	0.323479	+	0.946235i	$0.395147\pi$
$563$	−15.6062	+	27.0308i	−0.657724	+	1.13921i	−0.981203	+	0.192976i	$0.938186\pi$
$564$		0			0
$565$	2.83502	+	4.91040i	0.119270	+	0.206582i
$566$		0			0
$567$	13.9663	−	31.5633i	0.586528	−	1.32553i
$568$		0			0
$569$	6.41478	+	11.1107i	0.268922	+	0.465786i	0.968584	−	0.248688i	$-0.0799994\pi$
$569$	6.41478	+	11.1107i	0.268922	+	0.465786i	−0.699662	+	0.714474i	$0.746666\pi$
$570$		0			0
$571$	−7.67004	+	13.2849i	−0.320981	+	0.555956i	−0.980691	−	0.195565i	$-0.937346\pi$
$571$	−7.67004	+	13.2849i	−0.320981	+	0.555956i	0.659709	+	0.751521i	$0.270679\pi$
$572$		0			0
$573$	10.8724	−	3.22732i	0.454200	−	0.134823i
$574$		0			0
$575$	5.83502			0.243337
$576$		0			0
$577$	33.3292			1.38751			0.693755	−	0.720211i	$-0.255955\pi$
$577$	33.3292			1.38751			0.693755	+	0.720211i	$0.255955\pi$
$578$		0			0
$579$	8.95305	+	8.48638i	0.372076	+	0.352682i
$580$		0			0
$581$	−22.6938	+	39.3068i	−0.941497	+	1.63072i
$582$		0			0
$583$	9.96265	+	17.2558i	0.412611	+	0.714663i
$584$		0			0
$585$	−0.594822	−	11.1063i	−0.0245929	−	0.459187i
$586$		0			0
$587$	20.7525	+	35.9444i	0.856549	+	1.48359i	0.875201	+	0.483760i	$0.160729\pi$
$587$	20.7525	+	35.9444i	0.856549	+	1.48359i	−0.0186522	+	0.999826i	$0.505938\pi$
$588$		0			0
$589$	−0.0428105	+	0.0741499i	−0.00176398	+	0.00305530i
$590$		0			0
$591$	−7.12763	+	29.7639i	−0.293192	+	1.22432i
$592$		0			0
$593$	17.0584			0.700505			0.350252	−	0.936655i	$-0.386096\pi$
$593$	17.0584			0.700505			0.350252	+	0.936655i	$0.386096\pi$
$594$		0			0
$595$	−6.54787			−0.268437
$596$		0			0
$597$	−4.69232	+	19.5944i	−0.192044	+	0.801946i
$598$		0			0
$599$	12.9627	−	22.4520i	0.529640	−	0.917363i	−0.469763	−	0.882793i	$-0.655660\pi$
$599$	12.9627	−	22.4520i	0.529640	−	0.917363i	0.999402	−	0.0345700i	$-0.0110062\pi$
$600$		0			0
$601$	5.54787	+	9.60920i	0.226303	+	0.391967i	0.956709	−	0.291045i	$-0.0940029\pi$
$601$	5.54787	+	9.60920i	0.226303	+	0.391967i	−0.730407	+	0.683012i	$0.760670\pi$
$602$		0			0
$603$	−23.9909	+	15.6190i	−0.976986	+	0.636056i
$604$		0			0
$605$	−4.04241	−	7.00166i	−0.164347	−	0.284658i
$606$		0			0
$607$	13.1914	−	22.8483i	0.535424	−	0.927382i	−0.463718	−	0.885983i	$-0.653485\pi$
$607$	13.1914	−	22.8483i	0.535424	−	0.927382i	0.999143	−	0.0413995i	$-0.0131816\pi$
$608$		0			0
$609$	41.7973	+	39.6186i	1.69371	+	1.60543i
$610$		0			0
$611$	−6.94160			−0.280827
$612$		0			0
$613$	2.87783			0.116235			0.0581173	−	0.998310i	$-0.481490\pi$
$613$	2.87783			0.116235			0.0581173	+	0.998310i	$0.481490\pi$
$614$		0			0
$615$	−11.5611	+	3.43176i	−0.466188	+	0.138382i
$616$		0			0
$617$	5.42024	−	9.38814i	0.218211	−	0.377952i	−0.736050	−	0.676927i	$-0.763311\pi$
$617$	5.42024	−	9.38814i	0.218211	−	0.377952i	0.954261	+	0.298975i	$0.0966446\pi$
$618$		0			0
$619$	4.43892	+	7.68843i	0.178415	+	0.309024i	0.941338	−	0.337466i	$-0.109570\pi$
$619$	4.43892	+	7.68843i	0.178415	+	0.309024i	−0.762923	+	0.646490i	$0.776236\pi$
$620$		0			0
$621$	−10.1700	−	28.5631i	−0.408110	−	1.14620i
$622$		0			0
$623$	5.75253	+	9.96368i	0.230470	+	0.399186i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	0.829557	−	0.246243i	0.0331293	−	0.00983401i
$628$		0			0
$629$	20.4249			0.814394
$630$		0			0
$631$	−14.3300			−0.570467			−0.285233	−	0.958458i	$-0.592071\pi$
$631$	−14.3300			−0.570467			−0.285233	+	0.958458i	$0.592071\pi$
$632$		0			0
$633$	−7.08068	−	6.71161i	−0.281432	−	0.266763i
$634$		0			0
$635$	2.77121	−	4.79987i	0.109972	−	0.190477i
$636$		0			0
$637$	−14.2871	−	24.7461i	−0.566077	−	0.980475i
$638$		0			0
$639$	42.6934	+	21.6917i	1.68892	+	0.858112i
$640$		0			0
$641$	−23.0237	−	39.8783i	−0.909383	−	1.57510i	−0.814923	−	0.579569i	$-0.803221\pi$
$641$	−23.0237	−	39.8783i	−0.909383	−	1.57510i	−0.0944596	−	0.995529i	$-0.530112\pi$
$642$		0			0
$643$	1.77121	−	3.06782i	0.0698495	−	0.120983i	−0.828985	−	0.559270i	$-0.811081\pi$
$643$	1.77121	−	3.06782i	0.0698495	−	0.120983i	0.898835	+	0.438287i	$0.144415\pi$
$644$		0			0
$645$	1.49546	−	6.24482i	0.0588838	−	0.245890i
$646$		0			0
$647$	−16.1276			−0.634043			−0.317021	−	0.948418i	$-0.602683\pi$
$647$	−16.1276			−0.634043			−0.317021	+	0.948418i	$0.602683\pi$
$648$		0			0
$649$	−19.9253			−0.782137
$650$		0			0
$651$	−0.452653	+	1.89021i	−0.0177409	+	0.0740831i
$652$		0			0
$653$	12.7735	−	22.1244i	0.499867	−	0.865795i	−0.500133	−	0.865949i	$-0.666715\pi$
$653$	12.7735	−	22.1244i	0.499867	−	0.865795i	1.00000		0.000153387i	$4.88247e-5\pi$
$654$		0			0
$655$	−6.41478	−	11.1107i	−0.250646	−	0.434132i
$656$		0			0
$657$	−21.3966	−	10.8713i	−0.834762	−	0.424128i
$658$		0			0
$659$	−18.2498	−	31.6096i	−0.710911	−	1.23133i	−0.964515	−	0.264026i	$-0.914949\pi$
$659$	−18.2498	−	31.6096i	−0.710911	−	1.23133i	0.253604	−	0.967308i	$-0.418384\pi$
$660$		0			0
$661$	3.84049	−	6.65192i	0.149378	−	0.258730i	−0.781620	−	0.623755i	$-0.785606\pi$
$661$	3.84049	−	6.65192i	0.149378	−	0.258730i	0.930998	+	0.365025i	$0.118940\pi$
$662$		0			0
$663$	7.95719	+	7.54243i	0.309032	+	0.292924i
$664$		0			0
$665$	1.12217			0.0435158
$666$		0			0
$667$	50.5899			1.95885
$668$		0			0
$669$	−13.4955	+	4.00595i	−0.521765	+	0.154879i
$670$		0			0
$671$	−12.7735	+	22.1244i	−0.493117	+	0.854104i
$672$		0			0
$673$	−5.01867	−	8.69260i	−0.193456	−	0.335075i	0.752938	−	0.658092i	$-0.228636\pi$
$673$	−5.01867	−	8.69260i	−0.193456	−	0.335075i	−0.946393	+	0.323017i	$0.895303\pi$
$674$		0			0
$675$	5.11076	+	0.938136i	0.196713	+	0.0361089i
$676$		0			0
$677$	14.7261	+	25.5063i	0.565969	+	0.980286i	0.996959	+	0.0779297i	$0.0248310\pi$
$677$	14.7261	+	25.5063i	0.565969	+	0.980286i	−0.430990	+	0.902357i	$0.641836\pi$
$678$		0			0
$679$	7.03735	−	12.1890i	0.270069	−	0.467772i
$680$		0			0
$681$	16.5424	−	4.91040i	0.633907	−	0.188167i
$682$		0			0
$683$	24.2179			0.926673			0.463336	−	0.886182i	$-0.346652\pi$
$683$	24.2179			0.926673			0.463336	+	0.886182i	$0.346652\pi$
$684$		0			0
$685$	−9.08482			−0.347113
$686$		0			0
$687$	1.57795	+	1.49570i	0.0602027	+	0.0570646i
$688$		0			0
$689$	21.6327	−	37.4689i	0.824140	−	1.42745i
$690$		0			0
$691$	0.122168	+	0.211601i	0.00464749	+	0.00804969i	0.868340	−	0.495970i	$-0.165187\pi$
$691$	0.122168	+	0.211601i	0.00464749	+	0.00804969i	−0.863692	+	0.504019i	$0.831854\pi$
$692$		0			0
$693$	16.4623	−	10.7176i	0.625349	−	0.407127i
$694$		0			0
$695$	2.00000	+	3.46410i	0.0758643	+	0.131401i
$696$		0			0
$697$	5.94398	−	10.2953i	0.225144	−	0.389961i
$698$		0			0
$699$	1.59843	−	6.67479i	0.0604582	−	0.252464i
$700$		0			0
$701$	−7.79221			−0.294308			−0.147154	−	0.989114i	$-0.547011\pi$
$701$	−7.79221			−0.294308			−0.147154	+	0.989114i	$0.547011\pi$
$702$		0			0
$703$	−3.50040			−0.132020
$704$		0			0
$705$	0.755264	−	3.15386i	0.0284449	−	0.118781i
$706$		0			0
$707$	−0.632696	+	1.09586i	−0.0237950	+	0.0412141i
$708$		0			0
$709$	12.4198	+	21.5118i	0.466437	+	0.807893i	0.999265	−	0.0383309i	$-0.0122041\pi$
$709$	12.4198	+	21.5118i	0.466437	+	0.807893i	−0.532828	+	0.846223i	$0.678871\pi$
$710$		0			0
$711$	−0.320884	−	5.99141i	−0.0120341	−	0.224696i
$712$		0			0
$713$	0.853695	+	1.47864i	0.0319711	+	0.0553756i
$714$		0			0
$715$	3.16498	−	5.48190i	0.118363	−	0.205012i
$716$		0			0
$717$	7.12763	+	6.75611i	0.266186	+	0.252312i
$718$		0			0
$719$	−35.0101			−1.30566			−0.652829	−	0.757506i	$-0.726418\pi$
$719$	−35.0101			−1.30566			−0.652829	+	0.757506i	$0.726418\pi$
$720$		0			0
$721$	11.9736			0.445919
$722$		0			0
$723$	27.6176	−	8.19794i	1.02711	−	0.304885i
$724$		0			0
$725$	−4.33502	+	7.50848i	−0.160999	+	0.278858i
$726$		0			0
$727$	11.1541	+	19.3195i	0.413683	+	0.716520i	0.995289	−	0.0969508i	$-0.0309089\pi$
$727$	11.1541	+	19.3195i	0.413683	+	0.716520i	−0.581606	+	0.813470i	$0.697576\pi$
$728$		0			0
$729$	−4.31542	−	26.6529i	−0.159830	−	0.987144i
$730$		0			0
$731$	3.16498	+	5.48190i	0.117061	+	0.202756i
$732$		0			0
$733$	8.08482	−	14.0033i	0.298620	−	0.517224i	−0.677201	−	0.735798i	$-0.736807\pi$
$733$	8.08482	−	14.0033i	0.298620	−	0.517224i	0.975820	+	0.218574i	$0.0701405\pi$
$734$		0			0
$735$	12.7977	−	3.79882i	0.472049	−	0.140122i
$736$		0			0
$737$	−16.2926			−0.600146
$738$		0			0
$739$	−38.9354			−1.43226			−0.716132	−	0.697965i	$-0.754089\pi$
$739$	−38.9354			−1.43226			−0.716132	+	0.697965i	$0.754089\pi$
$740$		0			0
$741$	−1.36369	−	1.29261i	−0.0500966	−	0.0474853i
$742$		0			0
$743$	−2.66771	+	4.62061i	−0.0978688	+	0.169514i	−0.910802	−	0.412843i	$-0.864536\pi$
$743$	−2.66771	+	4.62061i	−0.0978688	+	0.169514i	0.812933	+	0.582357i	$0.197869\pi$
$744$		0			0
$745$	−4.06108	−	7.03400i	−0.148787	−	0.257706i
$746$		0			0
$747$	1.89884	+	35.4543i	0.0694748	+	1.29720i
$748$		0			0
$749$	−28.6090	−	49.5522i	−1.04535	−	1.81060i
$750$		0			0
$751$	17.1035	−	29.6241i	0.624115	−	1.08100i	−0.364596	−	0.931166i	$-0.618793\pi$
$751$	17.1035	−	29.6241i	0.624115	−	1.08100i	0.988711	−	0.149834i	$-0.0478738\pi$
$752$		0			0
$753$	−5.39611	+	22.5333i	−0.196645	+	0.821159i
$754$		0			0
$755$	21.0475			0.765996
$756$		0			0
$757$	0.952525			0.0346201			0.0173101	−	0.999850i	$-0.494490\pi$
$757$	0.952525			0.0346201			0.0173101	+	0.999850i	$0.494490\pi$
$758$		0			0
$759$	4.01867	−	16.7813i	0.145869	−	0.609124i
$760$		0			0
$761$	−8.29767	+	14.3720i	−0.300790	+	0.520984i	−0.976315	−	0.216353i	$-0.930584\pi$
$761$	−8.29767	+	14.3720i	−0.300790	+	0.520984i	0.675525	+	0.737337i	$0.263917\pi$
$762$		0			0
$763$	−12.8615	−	22.2768i	−0.465617	−	0.806473i
$764$		0			0
$765$	−4.29261	+	2.79466i	−0.155200	+	0.101041i
$766$		0			0
$767$	21.6327	+	37.4689i	0.781111	+	1.35292i
$768$		0			0
$769$	−3.29767	+	5.71174i	−0.118917	+	0.205971i	−0.919339	−	0.393467i	$-0.871276\pi$
$769$	−3.29767	+	5.71174i	−0.118917	+	0.205971i	0.800422	+	0.599437i	$0.204609\pi$
$770$		0			0
$771$	1.04281	+	0.988455i	0.0375559	+	0.0355983i
$772$		0			0
$773$	18.8296			0.677252			0.338626	−	0.940921i	$-0.390038\pi$
$773$	18.8296			0.677252			0.338626	+	0.940921i	$0.390038\pi$
$774$		0			0
$775$	−0.292611			−0.0105109
$776$		0			0
$777$	−76.1762	+	22.6119i	−2.73280	+	0.811198i
$778$		0			0
$779$	−1.01867	+	1.76439i	−0.0364978	+	0.0632160i
$780$		0			0
$781$	13.6272	+	23.6031i	0.487621	+	0.844584i
$782$		0			0
$783$	44.3105	+	8.13368i	1.58353	+	0.290674i
$784$		0			0
$785$	−0.127632	−	0.221065i	−0.00455538	−	0.00789016i
$786$		0			0
$787$	3.56108	−	6.16798i	0.126939	−	0.219865i	−0.795550	−	0.605888i	$-0.792818\pi$
$787$	3.56108	−	6.16798i	0.126939	−	0.219865i	0.922489	+	0.386023i	$0.126151\pi$
$788$		0			0
$789$	20.2871	−	6.02198i	0.722242	−	0.214388i
$790$		0			0
$791$	21.7447			0.773154
$792$		0			0
$793$	55.4724			1.96988
$794$		0			0
$795$	14.6700	+	13.9054i	0.520293	+	0.493173i
$796$		0			0
$797$	24.3588	−	42.1906i	0.862832	−	1.49447i	−0.00635283	−	0.999980i	$-0.502022\pi$
$797$	24.3588	−	42.1906i	0.862832	−	1.49447i	0.869184	−	0.494488i	$-0.164644\pi$
$798$		0			0
$799$	1.59843	+	2.76856i	0.0565484	+	0.0979447i
$800$		0			0
$801$	8.02374	+	4.07672i	0.283505	+	0.144044i
$802$		0			0
$803$	−6.82956	−	11.8291i	−0.241010	−	0.417441i
$804$		0			0
$805$	11.1887	−	19.3794i	0.394350	−	0.683035i
$806$		0			0
$807$	7.07394	−	29.5397i	0.249015	−	1.03985i
$808$		0			0
$809$	19.1595			0.673613			0.336806	−	0.941574i	$-0.390653\pi$
$809$	19.1595			0.673613			0.336806	+	0.941574i	$0.390653\pi$
$810$		0			0
$811$	−13.3401			−0.468434			−0.234217	−	0.972184i	$-0.575253\pi$
$811$	−13.3401			−0.468434			−0.234217	+	0.972184i	$0.575253\pi$
$812$		0			0
$813$	6.09989	−	25.4722i	0.213932	−	0.893348i
$814$		0			0
$815$	5.85369	−	10.1389i	0.205046	−	0.355150i
$816$		0			0
$817$	−0.542411	−	0.939483i	−0.0189766	−	0.0328684i
$818$		0			0
$819$	−38.0269	−	19.3208i	−1.32877	−	0.675124i
$820$		0			0
$821$	0.811284	+	1.40518i	0.0283140	+	0.0490413i	0.879835	−	0.475279i	$-0.157653\pi$
$821$	0.811284	+	1.40518i	0.0283140	+	0.0490413i	−0.851521	+	0.524320i	$0.824320\pi$
$822$		0			0
$823$	13.0265	−	22.5625i	0.454074	−	0.786480i	−0.544560	−	0.838722i	$-0.683303\pi$
$823$	13.0265	−	22.5625i	0.454074	−	0.786480i	0.998634	+	0.0522422i	$0.0166368\pi$
$824$		0			0
$825$	2.14631	+	2.03443i	0.0747248	+	0.0708298i
$826$		0			0
$827$	−37.4786			−1.30326			−0.651630	−	0.758537i	$-0.725915\pi$
$827$	−37.4786			−1.30326			−0.651630	+	0.758537i	$0.725915\pi$
$828$		0			0
$829$	32.9627			1.14484			0.572420	−	0.819960i	$-0.306005\pi$
$829$	32.9627			1.14484			0.572420	+	0.819960i	$0.306005\pi$
$830$		0			0
$831$	9.47679	−	2.81306i	0.328746	−	0.0975841i
$832$		0			0
$833$	−6.57976	+	11.3965i	−0.227975	+	0.394864i
$834$		0			0
$835$	−8.06382	−	13.9669i	−0.279060	−	0.483346i
$836$		0			0
$837$	0.510000	+	1.43236i	0.0176282	+	0.0495097i
$838$		0			0
$839$	−6.43892	−	11.1525i	−0.222296	−	0.385028i	0.733209	−	0.680004i	$-0.238022\pi$
$839$	−6.43892	−	11.1525i	−0.222296	−	0.385028i	−0.955505	+	0.294976i	$0.904688\pi$
$840$		0			0
$841$	−23.0848	+	39.9841i	−0.796028	+	1.37876i
$842$		0			0
$843$	−12.1090	+	3.59439i	−0.417055	+	0.123797i
$844$		0			0
$845$	−0.744736			−0.0256197
$846$		0			0
$847$	−31.0055			−1.06536
$848$		0			0
$849$	12.7781	+	12.1120i	0.438542	+	0.415684i
$850$		0			0
$851$	−34.9012	+	60.4506i	−1.19640	+	2.07222i
$852$		0			0
$853$	22.0661	+	38.2197i	0.755531	+	1.30862i	0.945110	+	0.326752i	$0.105954\pi$
$853$	22.0661	+	38.2197i	0.755531	+	1.30862i	−0.189580	+	0.981865i	$0.560713\pi$
$854$		0			0
$855$	0.735663	−	0.478945i	0.0251592	−	0.0163796i
$856$		0			0
$857$	7.81635	+	13.5383i	0.267001	+	0.462460i	0.968086	−	0.250618i	$-0.0806338\pi$
$857$	7.81635	+	13.5383i	0.267001	+	0.462460i	−0.701085	+	0.713078i	$0.747301\pi$
$858$		0			0
$859$	3.94398	−	6.83117i	0.134567	−	0.233077i	−0.790865	−	0.611991i	$-0.790369\pi$
$859$	3.94398	−	6.83117i	0.134567	−	0.233077i	0.925432	+	0.378914i	$0.123702\pi$
$860$		0			0
$861$	−10.7709	+	44.9774i	−0.367070	+	1.53283i
$862$		0			0
$863$	−9.53148			−0.324455			−0.162228	−	0.986753i	$-0.551868\pi$
$863$	−9.53148			−0.324455			−0.162228	+	0.986753i	$0.551868\pi$
$864$		0			0
$865$	8.58522			0.291906
$866$		0			0
$867$	−5.68145	+	23.7248i	−0.192952	+	0.805738i
$868$		0			0
$869$	1.70739	−	2.95729i	0.0579192	−	0.100319i
$870$		0			0
$871$	17.6887	+	30.6378i	0.599359	+	1.03812i
$872$		0			0
$873$	−0.588830	−	10.9944i	−0.0199289	−	0.372103i
$874$		0			0
$875$	1.91751	+	3.32123i	0.0648237	+	0.112278i
$876$		0			0
$877$	−18.9759	+	32.8672i	−0.640769	+	1.10985i	0.344492	+	0.938789i	$0.388051\pi$
$877$	−18.9759	+	32.8672i	−0.640769	+	1.10985i	−0.985261	+	0.171056i	$0.945282\pi$
$878$		0			0
$879$	16.4016	+	15.5467i	0.553211	+	0.524376i
$880$		0			0
$881$	23.2070			0.781863			0.390932	−	0.920420i	$-0.372153\pi$
$881$	23.2070			0.781863			0.390932	+	0.920420i	$0.372153\pi$
$882$		0			0
$883$	−30.9572			−1.04179			−0.520896	−	0.853620i	$-0.674402\pi$
$883$	−30.9572			−1.04179			−0.520896	+	0.853620i	$0.674402\pi$
$884$		0			0
$885$	−19.3774	+	5.75194i	−0.651365	+	0.193349i
$886$		0			0
$887$	18.9385	−	32.8025i	0.635893	−	1.10140i	−0.350432	−	0.936588i	$-0.613965\pi$
$887$	18.9385	−	32.8025i	0.635893	−	1.10140i	0.986325	−	0.164811i	$-0.0527014\pi$
$888$		0			0
$889$	−10.6276	−	18.4076i	−0.356439	−	0.617371i
$890$		0			0
$891$	6.21792	−	14.0523i	0.208308	−	0.470770i
$892$		0			0
$893$	−0.273937	−	0.474473i	−0.00916697	−	0.0158776i
$894$		0			0
$895$	3.68872	−	6.38904i	0.123300	−	0.213562i
$896$		0			0
$897$	−35.9198	+	10.6623i	−1.19933	+	0.356005i
$898$		0			0
$899$	−2.53695			−0.0846119
$900$		0			0
$901$	−19.9253			−0.663808
$902$		0			0
$903$	−17.8729	−	16.9413i	−0.594773	−	0.563771i
$904$		0			0
$905$	8.74980	−	15.1551i	0.290853	−	0.503773i
$906$		0			0
$907$	16.1914	+	28.0444i	0.537628	+	0.931199i	0.999031	+	0.0440087i	$0.0140129\pi$
$907$	16.1914	+	28.0444i	0.537628	+	0.931199i	−0.461403	+	0.887191i	$0.652654\pi$
$908$		0			0
$909$	0.0529391	+	0.988455i	0.00175588	+	0.0327850i
$910$		0			0
$911$	−22.6272	−	39.1915i	−0.749674	−	1.29847i	−0.947979	−	0.318333i	$-0.896877\pi$
$911$	−22.6272	−	39.1915i	−0.749674	−	1.29847i	0.198305	−	0.980140i	$-0.436456\pi$
$912$		0			0
$913$	−10.1035	+	17.4998i	−0.334377	+	0.579158i
$914$		0			0
$915$	−6.03554	+	25.2035i	−0.199529	+	0.833201i
$916$		0			0
$917$	−49.2016			−1.62478
$918$		0			0
$919$	−21.9253			−0.723249			−0.361625	−	0.932324i	$-0.617778\pi$
$919$	−21.9253			−0.723249			−0.361625	+	0.932324i	$0.617778\pi$
$920$		0			0
$921$	−0.607103	+	2.53517i	−0.0200047	+	0.0835367i
$922$		0			0
$923$	29.5899	−	51.2512i	0.973963	−	1.68695i
$924$		0			0
$925$	−5.98133	−	10.3600i	−0.196665	−	0.340633i
$926$		0			0
$927$	7.84956	−	5.11037i	0.257813	−	0.167846i
$928$		0			0
$929$	6.63270	+	11.4882i	0.217612	+	0.376915i	0.954077	−	0.299560i	$-0.0968400\pi$
$929$	6.63270	+	11.4882i	0.217612	+	0.376915i	−0.736466	+	0.676475i	$0.763507\pi$
$930$		0			0
$931$	1.12763	−	1.95312i	0.0369566	−	0.0640108i
$932$		0			0
$933$	6.85369	+	6.49645i	0.224380	+	0.212684i
$934$		0			0
$935$	−2.91518			−0.0953365
$936$		0			0
$937$	−40.4996			−1.32306			−0.661532	−	0.749917i	$-0.730093\pi$
$937$	−40.4996			−1.32306			−0.661532	+	0.749917i	$0.730093\pi$
$938$		0			0
$939$	17.5141	−	5.19885i	0.571552	−	0.169658i
$940$		0			0
$941$	−1.33502	+	2.31232i	−0.0435205	+	0.0753796i	−0.886965	−	0.461836i	$-0.847191\pi$
$941$	−1.33502	+	2.31232i	−0.0435205	+	0.0753796i	0.843445	+	0.537216i	$0.180524\pi$
$942$		0			0
$943$	20.3136	+	35.1842i	0.661502	+	1.14576i
$944$		0			0
$945$	12.9157	−	15.1751i	0.420148	−	0.493646i
$946$		0			0
$947$	18.4412	+	31.9412i	0.599260	+	1.03795i	0.992930	+	0.118697i	$0.0378718\pi$
$947$	18.4412	+	31.9412i	0.599260	+	1.03795i	−0.393670	+	0.919252i	$0.628795\pi$
$948$		0			0
$949$	−14.8296	+	25.6855i	−0.481388	+	0.833788i
$950$		0			0
$951$	−42.1378	+	12.5081i	−1.36641	+	0.405601i
$952$		0			0
$953$	12.7175			0.411961			0.205980	−	0.978556i	$-0.433962\pi$
$953$	12.7175			0.411961			0.205980	+	0.978556i	$0.433962\pi$
$954$		0			0
$955$	6.54787			0.211884
$956$		0			0
$957$	18.6086	+	17.6386i	0.601529	+	0.570175i
$958$		0			0
$959$	−17.4202	+	30.1727i	−0.562529	+	0.974329i
$960$		0			0
$961$	15.4572	+	26.7726i	0.498619	+	0.863633i
$962$		0			0
$963$	−39.9043	−	20.2747i	−1.28590	−	0.653342i
$964$		0			0
$965$	3.56108	+	6.16798i	0.114635	+	0.198554i
$966$		0			0
$967$	21.1728	−	36.6723i	0.680871	−	1.17930i	−0.293845	−	0.955853i	$-0.594935\pi$
$967$	21.1728	−	36.6723i	0.680871	−	1.17930i	0.974716	−	0.223449i	$-0.0717317\pi$
$968$		0			0
$969$	−0.201526	+	0.841540i	−0.00647394	+	0.0270341i
$970$		0			0
$971$	−5.38836			−0.172921			−0.0864604	−	0.996255i	$-0.527556\pi$
$971$	−5.38836			−0.172921			−0.0864604	+	0.996255i	$0.527556\pi$
$972$		0			0
$973$	15.3401			0.491781
$974$		0			0
$975$	1.49546	−	6.24482i	0.0478932	−	0.199994i
$976$		0			0
$977$	−14.0661	+	24.3633i	−0.450016	+	0.779450i	−0.998386	−	0.0567850i	$-0.981915\pi$
$977$	−14.0661	+	24.3633i	−0.450016	+	0.779450i	0.548370	+	0.836236i	$0.315248\pi$
$978$		0			0
$979$	2.56108	+	4.43593i	0.0818526	+	0.141773i
$980$		0			0
$981$	−17.9394	−	9.11471i	−0.572762	−	0.291010i
$982$		0			0
$983$	−12.8802	−	22.3091i	−0.410813	−	0.711550i	0.584165	−	0.811635i	$-0.301422\pi$
$983$	−12.8802	−	22.3091i	−0.410813	−	0.711550i	−0.994979	+	0.100085i	$0.968089\pi$
$984$		0			0
$985$	−8.83502	+	15.3027i	−0.281507	+	0.487585i
$986$		0			0
$987$	−9.02647	−	8.55597i	−0.287316	−	0.272340i
$988$		0			0
$989$	−21.6327			−0.687880
$990$		0			0
$991$	−23.0848			−0.733314			−0.366657	−	0.930356i	$-0.619498\pi$
$991$	−23.0848			−0.733314			−0.366657	+	0.930356i	$0.619498\pi$
$992$		0			0
$993$	−51.6146	+	15.3211i	−1.63794	+	0.486201i
$994$		0			0
$995$	−5.81635	+	10.0742i	−0.184391	+	0.319374i
$996$		0			0
$997$	16.4202	+	28.4407i	0.520034	+	0.900726i	0.999729	+	0.0232902i	$0.00741418\pi$
$997$	16.4202	+	28.4407i	0.520034	+	0.900726i	−0.479694	+	0.877436i	$0.659252\pi$
$998$		0			0
$999$	−40.2882	+	47.3360i	−1.27466	+	1.49765i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.q.k.481.2		6
3.2	odd	2		2160.2.q.i.1441.1		6
4.3	odd	2		180.2.i.b.121.2	yes	6
9.2	odd	6		2160.2.q.i.721.1		6
9.4	even	3		6480.2.a.bt.1.3		3
9.5	odd	6		6480.2.a.bw.1.3		3
9.7	even	3	inner	720.2.q.k.241.2		6
12.11	even	2		540.2.i.b.361.3		6
20.3	even	4		900.2.s.c.49.1		12
20.7	even	4		900.2.s.c.49.6		12
20.19	odd	2		900.2.i.c.301.2		6
36.7	odd	6		180.2.i.b.61.2	✓	6
36.11	even	6		540.2.i.b.181.3		6
36.23	even	6		1620.2.a.j.1.1		3
36.31	odd	6		1620.2.a.i.1.1		3
60.23	odd	4		2700.2.s.c.1549.5		12
60.47	odd	4		2700.2.s.c.1549.2		12
60.59	even	2		2700.2.i.c.901.1		6
180.7	even	12		900.2.s.c.349.1		12
180.23	odd	12		8100.2.d.o.649.5		6
180.43	even	12		900.2.s.c.349.6		12
180.47	odd	12		2700.2.s.c.2449.5		12
180.59	even	6		8100.2.a.u.1.3		3
180.67	even	12		8100.2.d.p.649.2		6
180.79	odd	6		900.2.i.c.601.2		6
180.83	odd	12		2700.2.s.c.2449.2		12
180.103	even	12		8100.2.d.p.649.5		6
180.119	even	6		2700.2.i.c.1801.1		6
180.139	odd	6		8100.2.a.v.1.3		3
180.167	odd	12		8100.2.d.o.649.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.i.b.61.2	✓	6	36.7	odd	6
180.2.i.b.121.2	yes	6	4.3	odd	2
540.2.i.b.181.3		6	36.11	even	6
540.2.i.b.361.3		6	12.11	even	2
720.2.q.k.241.2		6	9.7	even	3	inner
720.2.q.k.481.2		6	1.1	even	1	trivial
900.2.i.c.301.2		6	20.19	odd	2
900.2.i.c.601.2		6	180.79	odd	6
900.2.s.c.49.1		12	20.3	even	4
900.2.s.c.49.6		12	20.7	even	4
900.2.s.c.349.1		12	180.7	even	12
900.2.s.c.349.6		12	180.43	even	12
1620.2.a.i.1.1		3	36.31	odd	6
1620.2.a.j.1.1		3	36.23	even	6
2160.2.q.i.721.1		6	9.2	odd	6
2160.2.q.i.1441.1		6	3.2	odd	2
2700.2.i.c.901.1		6	60.59	even	2
2700.2.i.c.1801.1		6	180.119	even	6
2700.2.s.c.1549.2		12	60.47	odd	4
2700.2.s.c.1549.5		12	60.23	odd	4
2700.2.s.c.2449.2		12	180.83	odd	12
2700.2.s.c.2449.5		12	180.47	odd	12
6480.2.a.bt.1.3		3	9.4	even	3
6480.2.a.bw.1.3		3	9.5	odd	6
8100.2.a.u.1.3		3	180.59	even	6
8100.2.a.v.1.3		3	180.139	odd	6
8100.2.d.o.649.2		6	180.167	odd	12
8100.2.d.o.649.5		6	180.23	odd	12
8100.2.d.p.649.2		6	180.67	even	12
8100.2.d.p.649.5		6	180.103	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.403374 - 1.68443i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.91751 - 3.32123i) q^{7} +(-2.67458 - 1.35891i) q^{9} +O(q^{10})\)	\(q+(0.403374 - 1.68443i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.91751 - 3.32123i) q^{7} +(-2.67458 - 1.35891i) q^{9} +(-0.853695 - 1.47864i) q^{11} +(-1.85369 + 3.21069i) q^{13} +(-1.25707 - 1.19154i) q^{15} +1.70739 q^{17} -0.292611 q^{19} +(-6.36783 + 1.89021i) q^{21} +(-2.91751 + 5.05328i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-3.36783 + 3.95698i) q^{27} +(-4.33502 - 7.50848i) q^{29} +(0.146305 - 0.253408i) q^{31} +(-2.83502 + 0.841540i) q^{33} -3.83502 q^{35} +11.9627 q^{37} +(4.66044 + 4.41752i) q^{39} +(3.48133 - 6.02983i) q^{41} +(1.85369 + 3.21069i) q^{43} +(-2.51414 + 1.63680i) q^{45} +(0.936184 + 1.62152i) q^{47} +(-3.85369 + 6.67479i) q^{49} +(0.688716 - 2.87597i) q^{51} -11.6700 q^{53} -1.70739 q^{55} +(-0.118031 + 0.492881i) q^{57} +(5.83502 - 10.1066i) q^{59} +(-7.48133 - 12.9580i) q^{61} +(0.615299 + 11.4886i) q^{63} +(1.85369 + 3.21069i) q^{65} +(4.77121 - 8.26397i) q^{67} +(7.33502 + 6.95269i) q^{69} -15.9627 q^{71} +8.00000 q^{73} +(-1.66044 + 0.492881i) q^{75} +(-3.27394 + 5.67063i) q^{77} +(1.00000 + 1.73205i) q^{79} +(5.30675 + 7.26900i) q^{81} +(-5.91751 - 10.2494i) q^{83} +(0.853695 - 1.47864i) q^{85} +(-14.3961 + 4.27330i) q^{87} -3.00000 q^{89} +14.2179 q^{91} +(-0.367832 - 0.348659i) q^{93} +(-0.146305 + 0.253408i) q^{95} +(1.83502 + 3.17835i) q^{97} +(0.273937 + 5.11484i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{3} + 3 q^{5} + 3 q^{7} + 5 q^{9}+O(q^{10}) \) 6 * q + q^3 + 3 * q^5 + 3 * q^7 + 5 * q^9	\( 6 q + q^{3} + 3 q^{5} + 3 q^{7} + 5 q^{9} - 6 q^{13} - q^{15} - 12 q^{19} - 20 q^{21} - 3 q^{23} - 3 q^{25} - 2 q^{27} + 3 q^{29} + 6 q^{31} + 12 q^{33} + 6 q^{35} + 24 q^{37} + 20 q^{39} - 3 q^{41} + 6 q^{43} - 2 q^{45} + 15 q^{47} - 18 q^{49} - 30 q^{51} - 12 q^{53} - 32 q^{57} + 6 q^{59} - 21 q^{61} + 29 q^{63} + 6 q^{65} + 9 q^{67} + 15 q^{69} - 48 q^{71} + 48 q^{73} - 2 q^{75} - 6 q^{77} + 6 q^{79} + 29 q^{81} - 21 q^{83} - 42 q^{87} - 18 q^{89} + 16 q^{93} - 6 q^{95} - 18 q^{97} - 12 q^{99}+O(q^{100}) \) 6 * q + q^3 + 3 * q^5 + 3 * q^7 + 5 * q^9 - 6 * q^13 - q^15 - 12 * q^19 - 20 * q^21 - 3 * q^23 - 3 * q^25 - 2 * q^27 + 3 * q^29 + 6 * q^31 + 12 * q^33 + 6 * q^35 + 24 * q^37 + 20 * q^39 - 3 * q^41 + 6 * q^43 - 2 * q^45 + 15 * q^47 - 18 * q^49 - 30 * q^51 - 12 * q^53 - 32 * q^57 + 6 * q^59 - 21 * q^61 + 29 * q^63 + 6 * q^65 + 9 * q^67 + 15 * q^69 - 48 * q^71 + 48 * q^73 - 2 * q^75 - 6 * q^77 + 6 * q^79 + 29 * q^81 - 21 * q^83 - 42 * q^87 - 18 * q^89 + 16 * q^93 - 6 * q^95 - 18 * q^97 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more