LMFDB - Embedded newform 1232.2.be.a.1167.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1232,2,Mod(815,1232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1232, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1, 0]))

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

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

chi := DirichletCharacter("1232.815");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1232.be (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.83756952902$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1167.5
Character	$\chi$	$=$	1232.1167
Dual form			1232.2.be.a.815.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.497233 - 0.861233i) q^{3} +(2.07786 + 1.19965i) q^{5} +(1.91531 + 1.82526i) q^{7} +(1.00552 - 1.74161i) q^{9} +O(q^{10})$	\(q+(-0.497233 - 0.861233i) q^{3} +(2.07786 + 1.19965i) q^{5} +(1.91531 + 1.82526i) q^{7} +(1.00552 - 1.74161i) q^{9} +(-0.866025 + 0.500000i) q^{11} -4.00796i q^{13} -2.38602i q^{15} +(2.89660 - 1.67235i) q^{17} +(-0.246716 + 0.427325i) q^{19} +(0.619619 - 2.55711i) q^{21} +(0.397082 + 0.229255i) q^{23} +(0.378327 + 0.655282i) q^{25} -4.98331 q^{27} +3.21462 q^{29} +(3.65614 + 6.33262i) q^{31} +(0.861233 + 0.497233i) q^{33} +(1.79007 + 6.09034i) q^{35} +(2.18098 - 3.77756i) q^{37} +(-3.45178 + 1.99289i) q^{39} +3.50462i q^{41} +1.21927i q^{43} +(4.17865 - 2.41254i) q^{45} +(3.58130 - 6.20300i) q^{47} +(0.336838 + 6.99189i) q^{49} +(-2.88057 - 1.66310i) q^{51} +(5.21128 + 9.02620i) q^{53} -2.39930 q^{55} +0.490702 q^{57} +(-1.89634 - 3.28455i) q^{59} +(-2.68828 - 1.55208i) q^{61} +(5.10478 - 1.50039i) q^{63} +(4.80815 - 8.32796i) q^{65} +(-3.39777 + 1.96170i) q^{67} -0.455973i q^{69} -8.57882i q^{71} +(2.79714 - 1.61493i) q^{73} +(0.376234 - 0.651656i) q^{75} +(-2.57134 - 0.623067i) q^{77} +(3.38345 + 1.95344i) q^{79} +(-0.538694 - 0.933045i) q^{81} -0.256697 q^{83} +8.02497 q^{85} +(-1.59841 - 2.76854i) q^{87} +(0.889581 + 0.513600i) q^{89} +(7.31557 - 7.67649i) q^{91} +(3.63590 - 6.29757i) q^{93} +(-1.02528 + 0.591948i) q^{95} +9.32648i q^{97} +2.01104i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{9}+O(q^{10}) $ 24 * q - 8 * q^9	$ 24 q - 8 q^{9} - 36 q^{17} - 4 q^{21} + 12 q^{25} + 16 q^{29} + 16 q^{37} + 12 q^{45} + 16 q^{49} + 4 q^{53} - 16 q^{57} + 24 q^{61} + 36 q^{65} + 12 q^{73} - 4 q^{77} - 20 q^{81} - 32 q^{85} + 60 q^{89} - 64 q^{93}+O(q^{100}) $ 24 * q - 8 * q^9 - 36 * q^17 - 4 * q^21 + 12 * q^25 + 16 * q^29 + 16 * q^37 + 12 * q^45 + 16 * q^49 + 4 * q^53 - 16 * q^57 + 24 * q^61 + 36 * q^65 + 12 * q^73 - 4 * q^77 - 20 * q^81 - 32 * q^85 + 60 * q^89 - 64 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times$.

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.497233	−	0.861233i	−0.287078	−	0.497233i	0.686033	−	0.727570i	$-0.259350\pi$
$3$	−0.497233	−	0.861233i	−0.287078	−	0.497233i	−0.973111	+	0.230337i	$0.926017\pi$
$4$		0			0
$5$	2.07786	+	1.19965i	0.929246	+	0.536500i	0.886573	−	0.462589i	$-0.153079\pi$
$5$	2.07786	+	1.19965i	0.929246	+	0.536500i	0.0426730	+	0.999089i	$0.486413\pi$
$6$		0			0
$7$	1.91531	+	1.82526i	0.723920	+	0.689884i
$7$	1.91531	+	1.82526i	0.723920	+	0.689884i
$8$		0			0
$9$	1.00552	−	1.74161i	0.335173	−	0.580537i
$10$		0			0
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$12$		0			0
$13$		−	4.00796i		−	1.11161i	−0.831314	−	0.555804i	$-0.812411\pi$
$13$		−	4.00796i		−	1.11161i	0.831314	−	0.555804i	$-0.187589\pi$
$14$		0			0
$15$		−	2.38602i		−	0.616069i
$16$		0			0
$17$	2.89660	−	1.67235i	0.702529	−	0.405605i	−0.105760	−	0.994392i	$-0.533727\pi$
$17$	2.89660	−	1.67235i	0.702529	−	0.405605i	0.808289	+	0.588786i	$0.200394\pi$
$18$		0			0
$19$	−0.246716	+	0.427325i	−0.0566006	+	0.0980352i	−0.892937	−	0.450181i	$-0.851360\pi$
$19$	−0.246716	+	0.427325i	−0.0566006	+	0.0980352i	0.836337	+	0.548216i	$0.184693\pi$
$20$		0			0
$21$	0.619619	−	2.55711i	0.135212	−	0.558007i
$22$		0			0
$23$	0.397082	+	0.229255i	0.0827972	+	0.0478030i	0.540827	−	0.841134i	$-0.318111\pi$
$23$	0.397082	+	0.229255i	0.0827972	+	0.0478030i	−0.458030	+	0.888937i	$0.651445\pi$
$24$		0			0
$25$	0.378327	+	0.655282i	0.0756655	+	0.131056i
$26$		0			0
$27$	−4.98331			−0.959038
$28$		0			0
$29$	3.21462			0.596940			0.298470	−	0.954419i	$-0.403524\pi$
$29$	3.21462			0.596940			0.298470	+	0.954419i	$0.403524\pi$
$30$		0			0
$31$	3.65614	+	6.33262i	0.656662	+	1.13737i	0.981474	+	0.191593i	$0.0613654\pi$
$31$	3.65614	+	6.33262i	0.656662	+	1.13737i	−0.324813	+	0.945778i	$0.605301\pi$
$32$		0			0
$33$	0.861233	+	0.497233i	0.149921	+	0.0865571i
$34$		0			0
$35$	1.79007	+	6.09034i	0.302576	+	1.02946i
$36$		0			0
$37$	2.18098	−	3.77756i	0.358550	−	0.621027i	−0.629169	−	0.777269i	$-0.716605\pi$
$37$	2.18098	−	3.77756i	0.358550	−	0.621027i	0.987719	+	0.156242i	$0.0499379\pi$
$38$		0			0
$39$	−3.45178	+	1.99289i	−0.552728	+	0.319118i
$40$		0			0
$41$			3.50462i			0.547330i	0.961825	+	0.273665i	$0.0882359\pi$
$41$			3.50462i			0.547330i	−0.961825	+	0.273665i	$0.911764\pi$
$42$		0			0
$43$			1.21927i			0.185937i	0.995669	+	0.0929686i	$0.0296356\pi$
$43$			1.21927i			0.185937i	−0.995669	+	0.0929686i	$0.970364\pi$
$44$		0			0
$45$	4.17865	−	2.41254i	0.622916	−	0.359641i
$46$		0			0
$47$	3.58130	−	6.20300i	0.522386	−	0.904800i	−0.477274	−	0.878754i	$-0.658375\pi$
$47$	3.58130	−	6.20300i	0.522386	−	0.904800i	0.999661	−	0.0260455i	$-0.00829148\pi$
$48$		0			0
$49$	0.336838	+	6.99189i	0.0481197	+	0.998842i
$50$		0			0
$51$	−2.88057	−	1.66310i	−0.403361	−	0.232880i
$52$		0			0
$53$	5.21128	+	9.02620i	0.715824	+	1.23984i	0.962641	+	0.270782i	$0.0872822\pi$
$53$	5.21128	+	9.02620i	0.715824	+	1.23984i	−0.246816	+	0.969062i	$0.579384\pi$
$54$		0			0
$55$	−2.39930			−0.323522
$56$		0			0
$57$	0.490702			0.0649951
$58$		0			0
$59$	−1.89634	−	3.28455i	−0.246882	−	0.427613i	0.715777	−	0.698329i	$-0.246073\pi$
$59$	−1.89634	−	3.28455i	−0.246882	−	0.427613i	−0.962659	+	0.270716i	$0.912739\pi$
$60$		0			0
$61$	−2.68828	−	1.55208i	−0.344198	−	0.198723i	0.317929	−	0.948115i	$-0.397013\pi$
$61$	−2.68828	−	1.55208i	−0.344198	−	0.198723i	−0.662127	+	0.749392i	$0.730346\pi$
$62$		0			0
$63$	5.10478	−	1.50039i	0.643141	−	0.189031i
$64$		0			0
$65$	4.80815	−	8.32796i	0.596378	−	1.03296i
$66$		0			0
$67$	−3.39777	+	1.96170i	−0.415104	+	0.239660i	−0.692980	−	0.720957i	$-0.743703\pi$
$67$	−3.39777	+	1.96170i	−0.415104	+	0.239660i	0.277877	+	0.960617i	$0.410369\pi$
$68$		0			0
$69$		−	0.455973i		−	0.0548927i
$70$		0			0
$71$		−	8.57882i		−	1.01812i	−0.860731	−	0.509059i	$-0.829993\pi$
$71$		−	8.57882i		−	1.01812i	0.860731	−	0.509059i	$-0.170007\pi$
$72$		0			0
$73$	2.79714	−	1.61493i	0.327380	−	0.189013i	−0.327297	−	0.944921i	$-0.606138\pi$
$73$	2.79714	−	1.61493i	0.327380	−	0.189013i	0.654677	+	0.755908i	$0.272805\pi$
$74$		0			0
$75$	0.376234	−	0.651656i	0.0434437	−	0.0752467i
$76$		0			0
$77$	−2.57134	−	0.623067i	−0.293031	−	0.0710051i
$78$		0			0
$79$	3.38345	+	1.95344i	0.380668	+	0.219779i	0.678109	−	0.734961i	$-0.262800\pi$
$79$	3.38345	+	1.95344i	0.380668	+	0.219779i	−0.297441	+	0.954740i	$0.596133\pi$
$80$		0			0
$81$	−0.538694	−	0.933045i	−0.0598548	−	0.103672i
$82$		0			0
$83$	−0.256697			−0.0281761			−0.0140881	−	0.999901i	$-0.504485\pi$
$83$	−0.256697			−0.0281761			−0.0140881	+	0.999901i	$0.504485\pi$
$84$		0			0
$85$	8.02497			0.870430
$86$		0			0
$87$	−1.59841	−	2.76854i	−0.171368	−	0.296818i
$88$		0			0
$89$	0.889581	+	0.513600i	0.0942954	+	0.0544415i	0.546406	−	0.837520i	$-0.315995\pi$
$89$	0.889581	+	0.513600i	0.0942954	+	0.0544415i	−0.452111	+	0.891962i	$0.649329\pi$
$90$		0			0
$91$	7.31557	−	7.67649i	0.766880	−	0.804715i
$92$		0			0
$93$	3.63590	−	6.29757i	0.377026	−	0.653028i
$94$		0			0
$95$	−1.02528	+	0.591948i	−0.105192	+	0.0607325i
$96$		0			0
$97$			9.32648i			0.946961i	0.880804	+	0.473480i	$0.157002\pi$
$97$			9.32648i			0.946961i	−0.880804	+	0.473480i	$0.842998\pi$
$98$		0			0
$99$			2.01104i			0.202117i
$100$		0			0
$101$	2.59772	−	1.49979i	0.258483	−	0.149235i	−0.365160	−	0.930945i	$-0.618986\pi$
$101$	2.59772	−	1.49979i	0.258483	−	0.149235i	0.623642	+	0.781710i	$0.285652\pi$
$102$		0			0
$103$	9.60519	−	16.6367i	0.946428	−	1.63926i	0.193561	−	0.981088i	$-0.437996\pi$
$103$	9.60519	−	16.6367i	0.946428	−	1.63926i	0.752867	−	0.658173i	$-0.228670\pi$
$104$		0			0
$105$	4.35512	−	4.56998i	0.425016	−	0.445984i
$106$		0			0
$107$	−6.52004	−	3.76435i	−0.630316	−	0.363913i	0.150559	−	0.988601i	$-0.451893\pi$
$107$	−6.52004	−	3.76435i	−0.630316	−	0.363913i	−0.780874	+	0.624688i	$0.785226\pi$
$108$		0			0
$109$	−6.12625	−	10.6110i	−0.586788	−	1.01635i	−0.994650	−	0.103303i	$-0.967059\pi$
$109$	−6.12625	−	10.6110i	−0.586788	−	1.01635i	0.407862	−	0.913044i	$-0.366274\pi$
$110$		0			0
$111$	−4.33781			−0.411727
$112$		0			0
$113$	14.0464			1.32137			0.660686	−	0.750663i	$-0.270266\pi$
$113$	14.0464			1.32137			0.660686	+	0.750663i	$0.270266\pi$
$114$		0			0
$115$	0.550053	+	0.952719i	0.0512927	+	0.0888415i
$116$		0			0
$117$	−6.98030	−	4.03008i	−0.645329	−	0.372581i
$118$		0			0
$119$	8.60038	+	2.08398i	0.788395	+	0.191038i
$120$		0			0
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$		0			0
$123$	3.01829	−	1.74261i	0.272150	−	0.157126i
$124$		0			0
$125$		−	10.1811i		−	0.910623i
$126$		0			0
$127$			20.8086i			1.84646i	0.384244	+	0.923232i	$0.374462\pi$
$127$			20.8086i			1.84646i	−0.384244	+	0.923232i	$0.625538\pi$
$128$		0			0
$129$	1.05008	−	0.606262i	0.0924541	−	0.0533784i
$130$		0			0
$131$	−1.53704	+	2.66222i	−0.134291	+	0.232600i	−0.925327	−	0.379171i	$-0.876209\pi$
$131$	−1.53704	+	2.66222i	−0.134291	+	0.232600i	0.791035	+	0.611771i	$0.209543\pi$
$132$		0			0
$133$	−1.25252	+	0.368139i	−0.108607	+	0.0319217i
$134$		0			0
$135$	−10.3546	−	5.97823i	−0.891182	−	0.514524i
$136$		0			0
$137$	3.33684	+	5.77957i	0.285085	+	0.493782i	0.972630	−	0.232360i	$-0.0746447\pi$
$137$	3.33684	+	5.77957i	0.285085	+	0.493782i	−0.687545	+	0.726142i	$0.741311\pi$
$138$		0			0
$139$	2.17670			0.184626			0.0923128	−	0.995730i	$-0.470574\pi$
$139$	2.17670			0.184626			0.0923128	+	0.995730i	$0.470574\pi$
$140$		0			0
$141$	−7.12296			−0.599862
$142$		0			0
$143$	2.00398	+	3.47099i	0.167581	+	0.290259i
$144$		0			0
$145$	6.67952	+	3.85642i	0.554704	+	0.320259i
$146$		0			0
$147$	5.85416	−	3.76669i	0.482843	−	0.310672i
$148$		0			0
$149$	−4.57931	+	7.93160i	−0.375152	+	0.649782i	−0.990350	−	0.138591i	$-0.955743\pi$
$149$	−4.57931	+	7.93160i	−0.375152	+	0.649782i	0.615198	+	0.788373i	$0.289076\pi$
$150$		0			0
$151$	−17.6967	+	10.2172i	−1.44014	+	0.831462i	−0.997858	−	0.0654161i	$-0.979163\pi$
$151$	−17.6967	+	10.2172i	−1.44014	+	0.831462i	−0.442277	+	0.896878i	$0.645829\pi$
$152$		0			0
$153$		−	6.72633i		−	0.543792i
$154$		0			0
$155$			17.5444i			1.40920i
$156$		0			0
$157$	−11.6470	+	6.72440i	−0.929532	+	0.536666i	−0.886664	−	0.462415i	$-0.846983\pi$
$157$	−11.6470	+	6.72440i	−0.929532	+	0.536666i	−0.0428687	+	0.999081i	$0.513650\pi$
$158$		0			0
$159$	5.18244	−	8.97625i	0.410994	−	0.711863i
$160$		0			0
$161$	0.342084	+	1.16387i	0.0269600	+	0.0917261i
$162$		0			0
$163$	−0.587002	−	0.338906i	−0.0459776	−	0.0265452i	0.476835	−	0.878993i	$-0.341784\pi$
$163$	−0.587002	−	0.338906i	−0.0459776	−	0.0265452i	−0.522813	+	0.852448i	$0.675117\pi$
$164$		0			0
$165$	1.19301	+	2.06636i	0.0928759	+	0.160866i
$166$		0			0
$167$	−21.7395			−1.68225			−0.841127	−	0.540838i	$-0.818107\pi$
$167$	−21.7395			−1.68225			−0.841127	+	0.540838i	$0.818107\pi$
$168$		0			0
$169$	−3.06373			−0.235671
$170$		0			0
$171$	0.496156	+	0.859368i	0.0379420	+	0.0657175i
$172$		0			0
$173$	−15.6940	−	9.06094i	−1.19319	−	0.688891i	−0.234164	−	0.972197i	$-0.575235\pi$
$173$	−15.6940	−	9.06094i	−1.19319	−	0.688891i	−0.959029	+	0.283306i	$0.908569\pi$
$174$		0			0
$175$	−0.471447	+	1.94562i	−0.0356380	+	0.147075i
$176$		0			0
$177$	−1.88584	+	3.26638i	−0.141749	+	0.245516i
$178$		0			0
$179$	18.5166	−	10.6905i	1.38399	−	0.799049i	0.391364	−	0.920236i	$-0.372003\pi$
$179$	18.5166	−	10.6905i	1.38399	−	0.799049i	0.992630	+	0.121187i	$0.0386701\pi$
$180$		0			0
$181$			12.4356i			0.924329i	0.886794	+	0.462165i	$0.152927\pi$
$181$			12.4356i			0.924329i	−0.886794	+	0.462165i	$0.847073\pi$
$182$		0			0
$183$			3.08697i			0.228196i
$184$		0			0
$185$	9.06351	−	5.23282i	0.666363	−	0.384725i
$186$		0			0
$187$	−1.67235	+	2.89660i	−0.122295	+	0.211820i
$188$		0			0
$189$	−9.54458	−	9.09584i	−0.694266	−	0.661625i
$190$		0			0
$191$	5.04610	+	2.91337i	0.365123	+	0.210804i	0.671326	−	0.741162i	$-0.265725\pi$
$191$	5.04610	+	2.91337i	0.365123	+	0.210804i	−0.306203	+	0.951966i	$0.599059\pi$
$192$		0			0
$193$	9.29145	+	16.0933i	0.668814	+	1.15842i	0.978236	+	0.207494i	$0.0665309\pi$
$193$	9.29145	+	16.0933i	0.668814	+	1.15842i	−0.309423	+	0.950925i	$0.600136\pi$
$194$		0			0
$195$	−9.56309			−0.684827
$196$		0			0
$197$	−14.1293			−1.00667			−0.503334	−	0.864092i	$-0.667893\pi$
$197$	−14.1293			−1.00667			−0.503334	+	0.864092i	$0.667893\pi$
$198$		0			0
$199$	0.170636	+	0.295550i	0.0120961	+	0.0209510i	0.872010	−	0.489488i	$-0.162816\pi$
$199$	0.170636	+	0.295550i	0.0120961	+	0.0209510i	−0.859914	+	0.510439i	$0.829483\pi$
$200$		0			0
$201$	3.37897	+	1.95085i	0.238334	+	0.137602i
$202$		0			0
$203$	6.15700	+	5.86752i	0.432137	+	0.411819i
$204$		0			0
$205$	−4.20432	+	7.28210i	−0.293643	+	0.508604i
$206$		0			0
$207$	0.798546	−	0.461041i	0.0555028	−	0.0320446i
$208$		0			0
$209$		−	0.493433i		−	0.0341315i
$210$		0			0
$211$			7.66121i			0.527420i	0.964602	+	0.263710i	$0.0849461\pi$
$211$			7.66121i			0.527420i	−0.964602	+	0.263710i	$0.915054\pi$
$212$		0			0
$213$	−7.38836	+	4.26567i	−0.506242	+	0.292279i
$214$		0			0
$215$	−1.46270	+	2.53347i	−0.0997554	+	0.172781i
$216$		0			0
$217$	−4.55604	+	18.8023i	−0.309284	+	1.27639i
$218$		0			0
$219$	−2.78166	−	1.60599i	−0.187967	−	0.108523i
$220$		0			0
$221$	−6.70272	−	11.6095i	−0.450874	−	0.780937i
$222$		0			0
$223$	−4.30362			−0.288191			−0.144096	−	0.989564i	$-0.546027\pi$
$223$	−4.30362			−0.288191			−0.144096	+	0.989564i	$0.546027\pi$
$224$		0			0
$225$	1.52166			0.101444
$226$		0			0
$227$	−5.63244	−	9.75568i	−0.373838	−	0.647507i	0.616314	−	0.787501i	$-0.288625\pi$
$227$	−5.63244	−	9.75568i	−0.373838	−	0.647507i	−0.990152	+	0.139993i	$0.955292\pi$
$228$		0			0
$229$	−19.3244	−	11.1570i	−1.27700	−	0.737273i	−0.300700	−	0.953719i	$-0.597220\pi$
$229$	−19.3244	−	11.1570i	−1.27700	−	0.737273i	−0.976295	+	0.216445i	$0.930554\pi$
$230$		0			0
$231$	0.741949	+	2.52433i	0.0488166	+	0.166089i
$232$		0			0
$233$	−5.65058	+	9.78709i	−0.370182	+	0.641173i	−0.989593	−	0.143893i	$-0.954038\pi$
$233$	−5.65058	+	9.78709i	−0.370182	+	0.641173i	0.619412	+	0.785066i	$0.287371\pi$
$234$		0			0
$235$	14.8829	−	8.59263i	0.970851	−	0.560521i
$236$		0			0
$237$		−	3.88525i		−	0.252374i
$238$		0			0
$239$			25.3205i			1.63784i	0.573905	+	0.818922i	$0.305428\pi$
$239$			25.3205i			1.63784i	−0.573905	+	0.818922i	$0.694572\pi$
$240$		0			0
$241$	−6.94676	+	4.01071i	−0.447480	+	0.258353i	−0.706765	−	0.707448i	$-0.749846\pi$
$241$	−6.94676	+	4.01071i	−0.447480	+	0.258353i	0.259285	+	0.965801i	$0.416513\pi$
$242$		0			0
$243$	−8.01067	+	13.8749i	−0.513885	+	0.890075i
$244$		0			0
$245$	−7.68793	+	14.9322i	−0.491164	+	0.953986i
$246$		0			0
$247$	1.71270	+	0.988829i	0.108977	+	0.0629177i
$248$		0			0
$249$	0.127638	+	0.221075i	0.00808873	+	0.0140101i
$250$		0			0
$251$	−15.0999			−0.953097			−0.476549	−	0.879148i	$-0.658112\pi$
$251$	−15.0999			−0.953097			−0.476549	+	0.879148i	$0.658112\pi$
$252$		0			0
$253$	−0.458510			−0.0288263
$254$		0			0
$255$	−3.99028	−	6.91136i	−0.249881	−	0.432806i
$256$		0			0
$257$	−4.08767	−	2.36002i	−0.254982	−	0.147214i	0.367061	−	0.930197i	$-0.380364\pi$
$257$	−4.08767	−	2.36002i	−0.254982	−	0.147214i	−0.622043	+	0.782983i	$0.713697\pi$
$258$		0			0
$259$	11.0723	−	3.25435i	0.687998	−	0.202216i
$260$		0			0
$261$	3.23236	−	5.59861i	0.200078	−	0.346546i
$262$		0			0
$263$	21.2073	−	12.2440i	1.30770	−	0.754999i	0.325985	−	0.945375i	$-0.394304\pi$
$263$	21.2073	−	12.2440i	1.30770	−	0.754999i	0.981711	+	0.190376i	$0.0609706\pi$
$264$		0			0
$265$			25.0069i			1.53616i
$266$		0			0
$267$		−	1.02152i		−	0.0625157i
$268$		0			0
$269$	−24.8114	+	14.3249i	−1.51278	+	0.873403i	−0.512891	+	0.858454i	$0.671425\pi$
$269$	−24.8114	+	14.3249i	−1.51278	+	0.873403i	−0.999888	+	0.0149494i	$0.995241\pi$
$270$		0			0
$271$	12.6853	−	21.9716i	0.770579	−	1.33468i	−0.166667	−	0.986013i	$-0.553301\pi$
$271$	12.6853	−	21.9716i	0.770579	−	1.33468i	0.937246	−	0.348669i	$-0.113366\pi$
$272$		0			0
$273$	−10.2488	−	2.48341i	−0.620285	−	0.150303i
$274$		0			0
$275$	−0.655282	−	0.378327i	−0.0395150	−	0.0228140i
$276$		0			0
$277$	2.24207	+	3.88337i	0.134713	+	0.233329i	0.925488	−	0.378778i	$-0.123656\pi$
$277$	2.24207	+	3.88337i	0.134713	+	0.233329i	−0.790775	+	0.612107i	$0.790322\pi$
$278$		0			0
$279$	14.7053			0.880381
$280$		0			0
$281$	−15.6070			−0.931034			−0.465517	−	0.885039i	$-0.654132\pi$
$281$	−15.6070			−0.931034			−0.465517	+	0.885039i	$0.654132\pi$
$282$		0			0
$283$	−0.887181	−	1.53664i	−0.0527374	−	0.0913439i	0.838452	−	0.544976i	$-0.183461\pi$
$283$	−0.887181	−	1.53664i	−0.0527374	−	0.0913439i	−0.891189	+	0.453632i	$0.850128\pi$
$284$		0			0
$285$	1.01961	+	0.588672i	0.0603964	+	0.0348699i
$286$		0			0
$287$	−6.39685	+	6.71244i	−0.377594	+	0.396223i
$288$		0			0
$289$	−2.90647	+	5.03415i	−0.170969	+	0.296126i
$290$		0			0
$291$	8.03227	−	4.63743i	0.470860	−	0.271851i
$292$		0			0
$293$			0.306885i			0.0179284i	0.999960	+	0.00896421i	$0.00285344\pi$
$293$			0.306885i			0.0179284i	−0.999960	+	0.00896421i	$0.997147\pi$
$294$		0			0
$295$		−	9.09978i		−	0.529810i
$296$		0			0
$297$	4.31567	−	2.49165i	0.250421	−	0.144580i
$298$		0			0
$299$	0.918845	−	1.59149i	0.0531382	−	0.0920380i
$300$		0			0
$301$	−2.22549	+	2.33529i	−0.128275	+	0.134604i
$302$		0			0
$303$	−2.58334	−	1.49149i	−0.148409	−	0.0856840i
$304$		0			0
$305$	−3.72390	−	6.44999i	−0.213230	−	0.369325i
$306$		0			0
$307$	−31.9193			−1.82173			−0.910864	−	0.412706i	$-0.864584\pi$
$307$	−31.9193			−1.82173			−0.910864	+	0.412706i	$0.864584\pi$
$308$		0			0
$309$	−19.1041			−1.08679
$310$		0			0
$311$	−3.66159	−	6.34206i	−0.207630	−	0.359625i	0.743338	−	0.668916i	$-0.233242\pi$
$311$	−3.66159	−	6.34206i	−0.207630	−	0.359625i	−0.950967	+	0.309291i	$0.899908\pi$
$312$		0			0
$313$	3.52880	+	2.03735i	0.199459	+	0.115158i	0.596403	−	0.802685i	$-0.296596\pi$
$313$	3.52880	+	2.03735i	0.199459	+	0.115158i	−0.396944	+	0.917843i	$0.629929\pi$
$314$		0			0
$315$	12.4069	+	3.00636i	0.699052	+	0.169389i
$316$		0			0
$317$	10.1404	−	17.5637i	0.569543	−	0.986477i	−0.427068	−	0.904219i	$-0.640454\pi$
$317$	10.1404	−	17.5637i	0.569543	−	0.986477i	0.996611	−	0.0822577i	$-0.0262131\pi$
$318$		0			0
$319$	−2.78394	+	1.60731i	−0.155871	+	0.0899921i
$320$		0			0
$321$			7.48702i			0.417885i
$322$		0			0
$323$			1.65039i			0.0918301i
$324$		0			0
$325$	2.62634	−	1.51632i	0.145683	−	0.0841103i
$326$		0			0
$327$	−6.09234	+	10.5522i	−0.336907	+	0.583541i
$328$		0			0
$329$	18.1814	−	5.34386i	1.00237	−	0.294616i
$330$		0			0
$331$	−10.3669	−	5.98531i	−0.569814	−	0.328982i	0.187261	−	0.982310i	$-0.440039\pi$
$331$	−10.3669	−	5.98531i	−0.569814	−	0.328982i	−0.757075	+	0.653328i	$0.773372\pi$
$332$		0			0
$333$	−4.38602	−	7.59682i	−0.240353	−	0.416303i
$334$		0			0
$335$	−9.41344			−0.514311
$336$		0			0
$337$	−14.4434			−0.786783			−0.393392	−	0.919371i	$-0.628698\pi$
$337$	−14.4434			−0.786783			−0.393392	+	0.919371i	$0.628698\pi$
$338$		0			0
$339$	−6.98432	−	12.0972i	−0.379336	−	0.657029i
$340$		0			0
$341$	−6.33262	−	3.65614i	−0.342930	−	0.197991i
$342$		0			0
$343$	−12.1169	+	14.0065i	−0.654250	+	0.756278i
$344$		0			0
$345$	0.547009	−	0.947447i	0.0294499	−	0.0510088i
$346$		0			0
$347$	17.3161	−	9.99748i	0.929579	−	0.536693i	0.0429006	−	0.999079i	$-0.486340\pi$
$347$	17.3161	−	9.99748i	0.929579	−	0.536693i	0.886678	+	0.462387i	$0.153007\pi$
$348$		0			0
$349$		−	24.7629i		−	1.32553i	−0.748828	−	0.662765i	$-0.769383\pi$
$349$		−	24.7629i		−	1.32553i	0.748828	−	0.662765i	$-0.230617\pi$
$350$		0			0
$351$			19.9729i			1.06607i
$352$		0			0
$353$	4.89577	−	2.82658i	0.260576	−	0.150443i	−0.364021	−	0.931391i	$-0.618597\pi$
$353$	4.89577	−	2.82658i	0.260576	−	0.150443i	0.624597	+	0.780947i	$0.285263\pi$
$354$		0			0
$355$	10.2916	−	17.8256i	0.546221	−	0.946083i
$356$		0			0
$357$	−2.48160	−	8.44315i	−0.131340	−	0.446859i
$358$		0			0
$359$	15.3128	+	8.84088i	0.808181	+	0.466604i	0.846324	−	0.532669i	$-0.178811\pi$
$359$	15.3128	+	8.84088i	0.808181	+	0.466604i	−0.0381428	+	0.999272i	$0.512144\pi$
$360$		0			0
$361$	9.37826	+	16.2436i	0.493593	+	0.854928i
$362$		0			0
$363$	−0.994466			−0.0521959
$364$		0			0
$365$	7.74940			0.405622
$366$		0			0
$367$	−14.5571	−	25.2137i	−0.759877	−	1.31615i	−0.942913	−	0.333039i	$-0.891926\pi$
$367$	−14.5571	−	25.2137i	−0.759877	−	1.31615i	0.183036	−	0.983106i	$-0.441407\pi$
$368$		0			0
$369$	6.10368	+	3.52396i	0.317745	+	0.183450i
$370$		0			0
$371$	−6.49396	+	26.7999i	−0.337149	+	1.39138i
$372$		0			0
$373$	−17.2507	+	29.8791i	−0.893206	+	1.54708i	−0.0571973	+	0.998363i	$0.518216\pi$
$373$	−17.2507	+	29.8791i	−0.893206	+	1.54708i	−0.836009	+	0.548716i	$0.815117\pi$
$374$		0			0
$375$	−8.76827	+	5.06236i	−0.452792	+	0.261419i
$376$		0			0
$377$		−	12.8841i		−	0.663563i
$378$		0			0
$379$			31.0562i			1.59525i	0.603154	+	0.797625i	$0.293911\pi$
$379$			31.0562i			1.59525i	−0.603154	+	0.797625i	$0.706089\pi$
$380$		0			0
$381$	17.9210	−	10.3467i	0.918122	−	0.530078i
$382$		0			0
$383$	17.5617	−	30.4177i	0.897360	−	1.55427i	0.0665037	−	0.997786i	$-0.478816\pi$
$383$	17.5617	−	30.4177i	0.897360	−	1.55427i	0.830856	−	0.556487i	$-0.187851\pi$
$384$		0			0
$385$	−4.59541	−	4.37936i	−0.234204	−	0.223193i
$386$		0			0
$387$	2.12350	+	1.22600i	0.107943	+	0.0623211i
$388$		0			0
$389$	−12.9496	−	22.4294i	−0.656572	−	1.13722i	−0.981497	−	0.191477i	$-0.938672\pi$
$389$	−12.9496	−	22.4294i	−0.656572	−	1.13722i	0.324925	−	0.945740i	$-0.394661\pi$
$390$		0			0
$391$	1.53358			0.0775566
$392$		0			0
$393$	3.05706			0.154208
$394$		0			0
$395$	4.68689	+	8.11793i	0.235823	+	0.408457i
$396$		0			0
$397$	30.2317	+	17.4543i	1.51728	+	0.876005i	0.999794	+	0.0203164i	$0.00646736\pi$
$397$	30.2317	+	17.4543i	1.51728	+	0.876005i	0.517491	+	0.855688i	$0.326866\pi$
$398$		0			0
$399$	0.939848	+	0.895660i	0.0470512	+	0.0448391i
$400$		0			0
$401$	16.5512	−	28.6675i	0.826526	−	1.43159i	−0.0742209	−	0.997242i	$-0.523647\pi$
$401$	16.5512	−	28.6675i	0.826526	−	1.43159i	0.900747	−	0.434344i	$-0.143020\pi$
$402$		0			0
$403$	25.3809	−	14.6536i	1.26431	−	0.729950i
$404$		0			0
$405$		−	2.58498i		−	0.128449i
$406$		0			0
$407$			4.36195i			0.216214i
$408$		0			0
$409$	−30.1920	+	17.4313i	−1.49290	+	0.861924i	−0.999967	−	0.00814544i	$-0.997407\pi$
$409$	−30.1920	+	17.4313i	−1.49290	+	0.861924i	−0.492929	+	0.870069i	$0.664074\pi$
$410$		0			0
$411$	3.31837	−	5.74759i	0.163683	−	0.283508i
$412$		0			0
$413$	2.36309	−	9.75226i	0.116280	−	0.479877i
$414$		0			0
$415$	−0.533379	−	0.307946i	−0.0261825	−	0.0151165i
$416$		0			0
$417$	−1.08233	−	1.87465i	−0.0530018	−	0.0918019i
$418$		0			0
$419$	−30.7664			−1.50304			−0.751518	−	0.659713i	$-0.770678\pi$
$419$	−30.7664			−1.50304			−0.751518	+	0.659713i	$0.770678\pi$
$420$		0			0
$421$	5.26687			0.256692			0.128346	−	0.991729i	$-0.459033\pi$
$421$	5.26687			0.256692			0.128346	+	0.991729i	$0.459033\pi$
$422$		0			0
$423$	−7.20213	−	12.4745i	−0.350180	−	0.606529i
$424$		0			0
$425$	2.19173	+	1.26539i	0.106314	+	0.0613806i
$426$		0			0
$427$	−2.31594	−	7.87952i	−0.112076	−	0.381317i
$428$		0			0
$429$	1.99289	−	3.45178i	0.0962176	−	0.166654i
$430$		0			0
$431$	−20.6901	+	11.9455i	−0.996608	+	0.575392i	−0.907243	−	0.420607i	$-0.861817\pi$
$431$	−20.6901	+	11.9455i	−0.996608	+	0.575392i	−0.0893654	+	0.995999i	$0.528484\pi$
$432$		0			0
$433$			16.4377i			0.789946i	0.918693	+	0.394973i	$0.129246\pi$
$433$			16.4377i			0.789946i	−0.918693	+	0.394973i	$0.870754\pi$
$434$		0			0
$435$		−	7.67016i		−	0.367756i
$436$		0			0
$437$	−0.195933	+	0.113122i	−0.00937275	+	0.00541136i
$438$		0			0
$439$	6.32097	−	10.9482i	0.301683	−	0.522531i	−0.674834	−	0.737970i	$-0.735785\pi$
$439$	6.32097	−	10.9482i	0.301683	−	0.522531i	0.976517	+	0.215439i	$0.0691181\pi$
$440$		0			0
$441$	12.5158	+	6.44384i	0.595993	+	0.306849i
$442$		0			0
$443$	28.2851	+	16.3304i	1.34386	+	0.775881i	0.987372	−	0.158417i	$-0.0506392\pi$
$443$	28.2851	+	16.3304i	1.34386	+	0.775881i	0.356493	+	0.934298i	$0.383972\pi$
$444$		0			0
$445$	1.23228	+	2.13438i	0.0584158	+	0.101179i
$446$		0			0
$447$	9.10793			0.430790
$448$		0			0
$449$	−0.472314			−0.0222899			−0.0111449	−	0.999938i	$-0.503548\pi$
$449$	−0.472314			−0.0222899			−0.0111449	+	0.999938i	$0.503548\pi$
$450$		0			0
$451$	−1.75231	−	3.03509i	−0.0825131	−	0.142917i
$452$		0			0
$453$	17.5987	+	10.1606i	0.826861	+	0.477388i
$454$		0			0
$455$	24.4098	−	7.17451i	1.14435	−	0.336346i
$456$		0			0
$457$	−19.5311	+	33.8289i	−0.913628	+	1.58245i	−0.104731	+	0.994501i	$0.533398\pi$
$457$	−19.5311	+	33.8289i	−0.913628	+	1.58245i	−0.808897	+	0.587950i	$0.799935\pi$
$458$		0			0
$459$	−14.4347	+	8.33385i	−0.673752	+	0.388991i
$460$		0			0
$461$		−	2.32274i		−	0.108181i	−0.998536	−	0.0540904i	$-0.982774\pi$
$461$		−	2.32274i		−	0.108181i	0.998536	−	0.0540904i	$-0.0172259\pi$
$462$		0			0
$463$			36.7767i			1.70916i	0.519321	+	0.854579i	$0.326185\pi$
$463$			36.7767i			1.70916i	−0.519321	+	0.854579i	$0.673815\pi$
$464$		0			0
$465$	15.1098	−	8.72363i	0.700699	−	0.404549i
$466$		0			0
$467$	−4.56895	+	7.91366i	−0.211426	+	0.366201i	−0.952161	−	0.305597i	$-0.901144\pi$
$467$	−4.56895	+	7.91366i	−0.211426	+	0.366201i	0.740735	+	0.671797i	$0.234477\pi$
$468$		0			0
$469$	−10.0884	−	2.44455i	−0.465840	−	0.112879i
$470$		0			0
$471$	11.5825	+	6.68719i	0.533696	+	0.308129i
$472$		0			0
$473$	−0.609636	−	1.05592i	−0.0280311	−	0.0485513i
$474$		0			0
$475$	−0.373358			−0.0171309
$476$		0			0
$477$	20.9602			0.959700
$478$		0			0
$479$	−19.9130	−	34.4903i	−0.909849	−	1.57590i	−0.814273	−	0.580482i	$-0.802864\pi$
$479$	−19.9130	−	34.4903i	−0.909849	−	1.57590i	−0.0955753	−	0.995422i	$-0.530469\pi$
$480$		0			0
$481$	−15.1403	−	8.74126i	−0.690338	−	0.398567i
$482$		0			0
$483$	0.832270	−	0.873330i	0.0378696	−	0.0397379i
$484$		0			0
$485$	−11.1885	+	19.3791i	−0.508045	+	0.879959i
$486$		0			0
$487$	4.83193	−	2.78972i	0.218956	−	0.126414i	−0.386511	−	0.922285i	$-0.626320\pi$
$487$	4.83193	−	2.78972i	0.218956	−	0.126414i	0.605467	+	0.795871i	$0.292987\pi$
$488$		0			0
$489$			0.674061i			0.0304821i
$490$		0			0
$491$		−	23.1427i		−	1.04442i	−0.852818	−	0.522208i	$-0.825108\pi$
$491$		−	23.1427i		−	1.04442i	0.852818	−	0.522208i	$-0.174892\pi$
$492$		0			0
$493$	9.31147	−	5.37598i	0.419368	−	0.242122i
$494$		0			0
$495$	−2.41254	+	4.17865i	−0.108436	+	0.187816i
$496$		0			0
$497$	15.6586	−	16.4311i	0.702384	−	0.737036i
$498$		0			0
$499$	−31.7949	−	18.3568i	−1.42334	−	0.821763i	−0.426753	−	0.904368i	$-0.640343\pi$
$499$	−31.7949	−	18.3568i	−1.42334	−	0.821763i	−0.996582	+	0.0826047i	$0.973676\pi$
$500$		0			0
$501$	10.8096	+	18.7228i	0.482937	+	0.836472i
$502$		0			0
$503$	−30.5552			−1.36239			−0.681195	−	0.732102i	$-0.738539\pi$
$503$	−30.5552			−1.36239			−0.681195	+	0.732102i	$0.738539\pi$
$504$		0			0
$505$	7.19691			0.320259
$506$		0			0
$507$	1.52339	+	2.63858i	0.0676559	+	0.117184i
$508$		0			0
$509$	−8.22705	−	4.74989i	−0.364658	−	0.210535i	0.306464	−	0.951882i	$-0.400854\pi$
$509$	−8.22705	−	4.74989i	−0.364658	−	0.210535i	−0.671122	+	0.741347i	$0.734187\pi$
$510$		0			0
$511$	8.30505	+	2.01242i	0.367394	+	0.0890241i
$512$		0			0
$513$	1.22946	−	2.12949i	0.0542821	−	0.0940194i
$514$		0			0
$515$	39.9164	−	23.0458i	1.75893	−	1.01552i
$516$		0			0
$517$			7.16260i			0.315011i
$518$		0			0
$519$			18.0216i			0.791060i
$520$		0			0
$521$	−9.27580	+	5.35538i	−0.406380	+	0.234624i	−0.689233	−	0.724540i	$-0.742052\pi$
$521$	−9.27580	+	5.35538i	−0.406380	+	0.234624i	0.282853	+	0.959163i	$0.408719\pi$
$522$		0			0
$523$	15.2413	−	26.3986i	0.666454	−	1.15433i	−0.312435	−	0.949939i	$-0.601145\pi$
$523$	15.2413	−	26.3986i	0.666454	−	1.15433i	0.978889	−	0.204393i	$-0.0655219\pi$
$524$		0			0
$525$	1.91005	−	0.561399i	0.0833613	−	0.0245015i
$526$		0			0
$527$	21.1807	+	12.2287i	0.922648	+	0.532691i
$528$		0			0
$529$	−11.3949	−	19.7365i	−0.495430	−	0.858109i
$530$		0			0
$531$	−7.62722			−0.330993
$532$		0			0
$533$	14.0464			0.608416
$534$		0			0
$535$	−9.03180	−	15.6435i	−0.390479	−	0.676329i
$536$		0			0
$537$	−18.4141	−	10.6314i	−0.794627	−	0.458778i
$538$		0			0
$539$	−3.78766	−	5.88674i	−0.163146	−	0.253560i
$540$		0			0
$541$	0.0795126	−	0.137720i	0.00341851	−	0.00592104i	−0.864311	−	0.502958i	$-0.832245\pi$
$541$	0.0795126	−	0.137720i	0.00341851	−	0.00592104i	0.867730	+	0.497037i	$0.165579\pi$
$542$		0			0
$543$	10.7099	−	6.18338i	0.459607	−	0.265354i
$544$		0			0
$545$		−	29.3974i		−	1.25925i
$546$		0			0
$547$			36.3063i			1.55235i	0.630520	+	0.776173i	$0.282842\pi$
$547$			36.3063i			1.55235i	−0.630520	+	0.776173i	$0.717158\pi$
$548$		0			0
$549$	−5.40622	+	3.12129i	−0.230732	+	0.133213i
$550$		0			0
$551$	−0.793100	+	1.37369i	−0.0337872	+	0.0585211i
$552$		0			0
$553$	2.91483	+	9.91713i	0.123951	+	0.421719i
$554$		0			0
$555$	−9.01335	−	5.20386i	−0.382595	−	0.220892i
$556$		0			0
$557$	−4.29608	−	7.44102i	−0.182031	−	0.315286i	0.760541	−	0.649290i	$-0.224934\pi$
$557$	−4.29608	−	7.44102i	−0.182031	−	0.315286i	−0.942572	+	0.334003i	$0.891600\pi$
$558$		0			0
$559$	4.88679			0.206689
$560$		0			0
$561$	3.32620			0.140432
$562$		0			0
$563$	6.92628	+	11.9967i	0.291908	+	0.505599i	0.974261	−	0.225424i	$-0.0723766\pi$
$563$	6.92628	+	11.9967i	0.291908	+	0.505599i	−0.682353	+	0.731023i	$0.739043\pi$
$564$		0			0
$565$	29.1864	+	16.8507i	1.22788	+	0.708916i
$566$		0			0
$567$	0.671285	−	2.77033i	0.0281913	−	0.116343i
$568$		0			0
$569$	15.2458	−	26.4066i	0.639139	−	1.10702i	−0.346483	−	0.938056i	$-0.612624\pi$
$569$	15.2458	−	26.4066i	0.639139	−	1.10702i	0.985622	−	0.168965i	$-0.0540424\pi$
$570$		0			0
$571$	−28.9999	+	16.7431i	−1.21361	+	0.700676i	−0.963543	−	0.267553i	$-0.913785\pi$
$571$	−28.9999	+	16.7431i	−1.21361	+	0.700676i	−0.250064	+	0.968229i	$0.580452\pi$
$572$		0			0
$573$		−	5.79449i		−	0.242068i
$574$		0			0
$575$			0.346934i			0.0144681i
$576$		0			0
$577$	1.40478	−	0.811049i	0.0584817	−	0.0337644i	−0.470474	−	0.882414i	$-0.655917\pi$
$577$	1.40478	−	0.811049i	0.0584817	−	0.0337644i	0.528956	+	0.848649i	$0.322584\pi$
$578$		0			0
$579$	9.24003	−	16.0042i	0.384003	−	0.665112i
$580$		0			0
$581$	−0.491654	−	0.468539i	−0.0203972	−	0.0194383i
$582$		0			0
$583$	−9.02620	−	5.21128i	−0.373827	−	0.215829i
$584$		0			0
$585$	−9.66938	−	16.7479i	−0.399780	−	0.692438i
$586$		0			0
$587$	21.4139			0.883845			0.441923	−	0.897053i	$-0.354297\pi$
$587$	21.4139			0.883845			0.441923	+	0.897053i	$0.354297\pi$
$588$		0			0
$589$	−3.60812			−0.148670
$590$		0			0
$591$	7.02553	+	12.1686i	0.288992	+	0.500548i
$592$		0			0
$593$	28.3803	+	16.3854i	1.16544	+	0.672866i	0.952601	−	0.304222i	$-0.0983963\pi$
$593$	28.3803	+	16.3854i	1.16544	+	0.672866i	0.212837	+	0.977088i	$0.431730\pi$
$594$		0			0
$595$	15.3703	+	14.6477i	0.630121	+	0.600496i
$596$		0			0
$597$	0.169692	−	0.293915i	0.00694502	−	0.0120291i
$598$		0			0
$599$	−22.5468	+	13.0174i	−0.921236	+	0.531876i	−0.884029	−	0.467432i	$-0.845179\pi$
$599$	−22.5468	+	13.0174i	−0.921236	+	0.531876i	−0.0372069	+	0.999308i	$0.511846\pi$
$600$		0			0
$601$			30.0941i			1.22756i	0.789476	+	0.613782i	$0.210352\pi$
$601$			30.0941i			1.22756i	−0.789476	+	0.613782i	$0.789648\pi$
$602$		0			0
$603$			7.89012i			0.321311i
$604$		0			0
$605$	2.07786	−	1.19965i	0.0844769	−	0.0487728i
$606$		0			0
$607$	−2.39779	+	4.15309i	−0.0973233	+	0.168569i	−0.910576	−	0.413342i	$-0.864361\pi$
$607$	−2.39779	+	4.15309i	−0.0973233	+	0.168569i	0.813253	+	0.581911i	$0.197695\pi$
$608$		0			0
$609$	1.99184	−	8.22013i	0.0807134	−	0.333097i
$610$		0			0
$611$	−24.8613	−	14.3537i	−1.00578	−	0.580689i
$612$		0			0
$613$	21.3424	+	36.9661i	0.862012	+	1.49305i	0.869984	+	0.493080i	$0.164129\pi$
$613$	21.3424	+	36.9661i	0.862012	+	1.49305i	−0.00797261	+	0.999968i	$0.502538\pi$
$614$		0			0
$615$	8.36211			0.337193
$616$		0			0
$617$	14.6021			0.587858			0.293929	−	0.955827i	$-0.405037\pi$
$617$	14.6021			0.587858			0.293929	+	0.955827i	$0.405037\pi$
$618$		0			0
$619$	11.9589	+	20.7134i	0.480669	+	0.832543i	0.999754	−	0.0221796i	$-0.00706057\pi$
$619$	11.9589	+	20.7134i	0.480669	+	0.832543i	−0.519085	+	0.854723i	$0.673727\pi$
$620$		0			0
$621$	−1.97878	−	1.14245i	−0.0794057	−	0.0458449i
$622$		0			0
$623$	0.766371	+	2.60742i	0.0307040	+	0.104464i
$624$		0			0
$625$	14.1054	−	24.4312i	0.564215	−	0.977249i
$626$		0			0
$627$	−0.424961	+	0.245351i	−0.0169713	+	0.00979838i
$628$		0			0
$629$		−	14.5894i		−	0.581719i
$630$		0			0
$631$			13.7946i			0.549154i	0.961565	+	0.274577i	$0.0885379\pi$
$631$			13.7946i			0.549154i	−0.961565	+	0.274577i	$0.911462\pi$
$632$		0			0
$633$	6.59809	−	3.80941i	0.262250	−	0.151410i
$634$		0			0
$635$	−24.9630	+	43.2373i	−0.990628	+	1.71582i
$636$		0			0
$637$	28.0232	−	1.35003i	1.11032	−	0.0534902i
$638$		0			0
$639$	−14.9410	−	8.62616i	−0.591055	−	0.341246i
$640$		0			0
$641$	−14.7850	−	25.6083i	−0.583972	−	1.01147i	−0.995003	−	0.0998475i	$-0.968165\pi$
$641$	−14.7850	−	25.6083i	−0.583972	−	1.01147i	0.411031	−	0.911621i	$-0.365169\pi$
$642$		0			0
$643$	22.1928			0.875199			0.437600	−	0.899170i	$-0.355829\pi$
$643$	22.1928			0.875199			0.437600	+	0.899170i	$0.355829\pi$
$644$		0			0
$645$	2.90921			0.114550
$646$		0			0
$647$	−11.4054	−	19.7547i	−0.448393	−	0.776639i	0.549889	−	0.835238i	$-0.314670\pi$
$647$	−11.4054	−	19.7547i	−0.448393	−	0.776639i	−0.998282	+	0.0585989i	$0.981337\pi$
$648$		0			0
$649$	3.28455	+	1.89634i	0.128930	+	0.0744378i
$650$		0			0
$651$	18.4586	−	5.42533i	0.723450	−	0.212636i
$652$		0			0
$653$	5.16661	−	8.94883i	0.202185	−	0.350195i	−0.747047	−	0.664771i	$-0.768529\pi$
$653$	5.16661	−	8.94883i	0.202185	−	0.350195i	0.949232	+	0.314576i	$0.101862\pi$
$654$		0			0
$655$	−6.38748	+	3.68781i	−0.249580	+	0.144095i
$656$		0			0
$657$		−	6.49536i		−	0.253408i
$658$		0			0
$659$		−	5.05646i		−	0.196972i	−0.995138	−	0.0984858i	$-0.968600\pi$
$659$		−	5.05646i		−	0.196972i	0.995138	−	0.0984858i	$-0.0313999\pi$
$660$		0			0
$661$	19.8070	−	11.4356i	0.770402	−	0.444792i	−0.0626161	−	0.998038i	$-0.519944\pi$
$661$	19.8070	−	11.4356i	0.770402	−	0.444792i	0.833018	+	0.553246i	$0.186611\pi$
$662$		0			0
$663$	−6.66563	+	11.5452i	−0.258872	+	0.448379i
$664$		0			0
$665$	−3.04420	−	0.737646i	−0.118049	−	0.0286047i
$666$		0			0
$667$	1.27647	+	0.736968i	0.0494250	+	0.0285355i
$668$		0			0
$669$	2.13990	+	3.70641i	0.0827333	+	0.143298i
$670$		0			0
$671$	3.10415			0.119835
$672$		0			0
$673$	−23.6385			−0.911197			−0.455598	−	0.890185i	$-0.650575\pi$
$673$	−23.6385			−0.911197			−0.455598	+	0.890185i	$0.650575\pi$
$674$		0			0
$675$	−1.88532	−	3.26547i	−0.0725660	−	0.125688i
$676$		0			0
$677$	−1.72079	−	0.993500i	−0.0661354	−	0.0381833i	0.466568	−	0.884486i	$-0.345490\pi$
$677$	−1.72079	−	0.993500i	−0.0661354	−	0.0381833i	−0.532703	+	0.846302i	$0.678824\pi$
$678$		0			0
$679$	−17.0233	+	17.8631i	−0.653293	+	0.685523i
$680$		0			0
$681$	−5.60127	+	9.70169i	−0.214641	+	0.371770i
$682$		0			0
$683$	−32.3350	+	18.6686i	−1.23726	+	0.714334i	−0.968534	−	0.248882i	$-0.919937\pi$
$683$	−32.3350	+	18.6686i	−1.23726	+	0.714334i	−0.268729	+	0.963216i	$0.586604\pi$
$684$		0			0
$685$			16.0122i			0.611794i
$686$		0			0
$687$			22.1905i			0.846619i
$688$		0			0
$689$	36.1766	−	20.8866i	1.37822	−	0.795716i
$690$		0			0
$691$	11.8314	−	20.4925i	0.450087	−	0.779573i	−0.548304	−	0.836279i	$-0.684726\pi$
$691$	11.8314	−	20.4925i	0.450087	−	0.779573i	0.998391	+	0.0567058i	$0.0180597\pi$
$692$		0			0
$693$	−3.67067	+	3.85176i	−0.139437	+	0.146316i
$694$		0			0
$695$	4.52288	+	2.61128i	0.171563	+	0.0990517i
$696$		0			0
$697$	5.86096	+	10.1515i	0.222000	+	0.384515i
$698$		0			0
$699$	11.2386			0.425083
$700$		0			0
$701$	25.2358			0.953141			0.476571	−	0.879136i	$-0.341880\pi$
$701$	25.2358			0.953141			0.476571	+	0.879136i	$0.341880\pi$
$702$		0			0
$703$	1.07617	+	1.86397i	0.0405883	+	0.0703011i
$704$		0			0
$705$	−14.8005	−	8.54507i	−0.557419	−	0.321826i
$706$		0			0
$707$	7.71295	+	1.86894i	0.290075	+	0.0702889i
$708$		0			0
$709$	0.372838	−	0.645774i	0.0140022	−	0.0242525i	−0.858939	−	0.512077i	$-0.828876\pi$
$709$	0.372838	−	0.645774i	0.0140022	−	0.0242525i	0.872942	+	0.487825i	$0.162209\pi$
$710$		0			0
$711$	6.80425	−	3.92844i	0.255179	−	0.147328i
$712$		0			0
$713$			3.35275i			0.125562i
$714$		0			0
$715$			9.61631i			0.359629i
$716$		0			0
$717$	21.8068	−	12.5902i	0.814390	−	0.470188i
$718$		0			0
$719$	14.7163	−	25.4893i	0.548824	−	0.950592i	−0.449531	−	0.893265i	$-0.648409\pi$
$719$	14.7163	−	25.4893i	0.548824	−	0.950592i	0.998355	−	0.0573269i	$-0.0182577\pi$
$720$		0			0
$721$	48.7632	−	14.3324i	1.81604	−	0.533768i
$722$		0			0
$723$	6.90832	+	3.98852i	0.256923	+	0.148335i
$724$		0			0
$725$	1.21618	+	2.10648i	0.0451677	+	0.0782328i
$726$		0			0
$727$	0.327687			0.0121532			0.00607661	−	0.999982i	$-0.498066\pi$
$727$	0.327687			0.0121532			0.00607661	+	0.999982i	$0.498066\pi$
$728$		0			0
$729$	12.7005			0.470389
$730$		0			0
$731$	2.03905	+	3.53175i	0.0754171	+	0.130626i
$732$		0			0
$733$	23.9018	+	13.7997i	0.882831	+	0.509703i	0.871591	−	0.490234i	$-0.163089\pi$
$733$	23.9018	+	13.7997i	0.882831	+	0.509703i	0.0112405	+	0.999937i	$0.496422\pi$
$734$		0			0
$735$	16.6828	−	0.803703i	0.615355	−	0.0296450i
$736$		0			0
$737$	1.96170	−	3.39777i	0.0722603	−	0.125158i
$738$		0			0
$739$	6.56324	−	3.78929i	0.241433	−	0.139391i	−0.374402	−	0.927266i	$-0.622152\pi$
$739$	6.56324	−	3.78929i	0.241433	−	0.139391i	0.615835	+	0.787875i	$0.288819\pi$
$740$		0			0
$741$		−	1.96671i		−	0.0722490i
$742$		0			0
$743$		−	32.1380i		−	1.17903i	−0.807758	−	0.589514i	$-0.799319\pi$
$743$		−	32.1380i		−	1.17903i	0.807758	−	0.589514i	$-0.200681\pi$
$744$		0			0
$745$	−19.0303	+	10.9871i	−0.697216	+	0.402538i
$746$		0			0
$747$	−0.258113	+	0.447065i	−0.00944387	+	0.0163573i
$748$		0			0
$749$	−5.61699	−	19.1107i	−0.205240	−	0.698289i
$750$		0			0
$751$	−13.9294	−	8.04217i	−0.508292	−	0.293463i	0.223839	−	0.974626i	$-0.428141\pi$
$751$	−13.9294	−	8.04217i	−0.508292	−	0.293463i	−0.732131	+	0.681163i	$0.761474\pi$
$752$		0			0
$753$	7.50817	+	13.0045i	0.273613	+	0.473911i
$754$		0			0
$755$	−49.0282			−1.78432
$756$		0			0
$757$	33.9812			1.23507			0.617533	−	0.786545i	$-0.288132\pi$
$757$	33.9812			1.23507			0.617533	+	0.786545i	$0.288132\pi$
$758$		0			0
$759$	0.227986	+	0.394884i	0.00827538	+	0.0143334i
$760$		0			0
$761$	38.3289	+	22.1292i	1.38942	+	0.802183i	0.993250	−	0.115994i	$-0.0370054\pi$
$761$	38.3289	+	22.1292i	1.38942	+	0.802183i	0.396171	+	0.918177i	$0.370339\pi$
$762$		0			0
$763$	7.63413	−	31.5053i	0.276374	−	1.14057i
$764$		0			0
$765$	8.06926	−	13.9764i	0.291745	−	0.505316i
$766$		0			0
$767$	−13.1644	+	7.60045i	−0.475337	+	0.274436i
$768$		0			0
$769$		−	25.4336i		−	0.917158i	−0.888654	−	0.458579i	$-0.848359\pi$
$769$		−	25.4336i		−	0.917158i	0.888654	−	0.458579i	$-0.151641\pi$
$770$		0			0
$771$			4.69391i			0.169047i
$772$		0			0
$773$	19.6950	−	11.3709i	0.708378	−	0.408982i	−0.102082	−	0.994776i	$-0.532550\pi$
$773$	19.6950	−	11.3709i	0.708378	−	0.408982i	0.810460	+	0.585794i	$0.199217\pi$
$774$		0			0
$775$	−2.76643	+	4.79160i	−0.0993732	+	0.172119i
$776$		0			0
$777$	−8.30826	−	7.91764i	−0.298057	−	0.284044i
$778$		0			0
$779$	−1.49761	−	0.864647i	−0.0536576	−	0.0309792i
$780$		0			0
$781$	4.28941	+	7.42947i	0.153487	+	0.265848i
$782$		0			0
$783$	−16.0194			−0.572488
$784$		0			0
$785$	−32.2678			−1.15169
$786$		0			0
$787$	21.0337	+	36.4314i	0.749770	+	1.29864i	0.947933	+	0.318470i	$0.103169\pi$
$787$	21.0337	+	36.4314i	0.749770	+	1.29864i	−0.198163	+	0.980169i	$0.563498\pi$
$788$		0			0
$789$	−21.0899	−	12.1763i	−0.750821	−	0.433487i
$790$		0			0
$791$	26.9032	+	25.6383i	0.956567	+	0.911593i
$792$		0			0
$793$	−6.22066	+	10.7745i	−0.220902	+	0.382614i
$794$		0			0
$795$	21.5367	−	12.4342i	0.763829	−	0.440997i
$796$		0			0
$797$		−	31.1150i		−	1.10215i	−0.834456	−	0.551074i	$-0.814218\pi$
$797$		−	31.1150i		−	1.10215i	0.834456	−	0.551074i	$-0.185782\pi$
$798$		0			0
$799$		−	23.9568i		−	0.847531i
$800$		0			0
$801$	1.78898	−	1.03287i	0.0632106	−	0.0364946i
$802$		0			0
$803$	−1.61493	+	2.79714i	−0.0569895	+	0.0987088i
$804$		0			0
$805$	−0.685440	+	2.82874i	−0.0241586	+	0.0997001i
$806$		0			0
$807$	24.6741	+	14.2456i	0.868570	+	0.501469i
$808$		0			0
$809$	−17.1068	−	29.6298i	−0.601442	−	1.04173i	−0.992603	−	0.121406i	$-0.961260\pi$
$809$	−17.1068	−	29.6298i	−0.601442	−	1.04173i	0.391161	−	0.920322i	$-0.372074\pi$
$810$		0			0
$811$	−46.4235			−1.63015			−0.815074	−	0.579357i	$-0.803304\pi$
$811$	−46.4235			−1.63015			−0.815074	+	0.579357i	$0.803304\pi$
$812$		0			0
$813$	−25.2303			−0.884864
$814$		0			0
$815$	−0.813138	−	1.40840i	−0.0284830	−	0.0493340i
$816$		0			0
$817$	−0.521026	−	0.300815i	−0.0182284	−	0.0105242i
$818$		0			0
$819$	−6.01350	−	20.4597i	−0.210129	−	0.714921i
$820$		0			0
$821$	−13.7019	+	23.7324i	−0.478201	+	0.828268i	−0.999688	−	0.0249916i	$-0.992044\pi$
$821$	−13.7019	+	23.7324i	−0.478201	+	0.828268i	0.521487	+	0.853259i	$0.325377\pi$
$822$		0			0
$823$	21.3225	−	12.3105i	0.743254	−	0.429118i	−0.0799972	−	0.996795i	$-0.525491\pi$
$823$	21.3225	−	12.3105i	0.743254	−	0.429118i	0.823251	+	0.567677i	$0.192158\pi$
$824$		0			0
$825$			0.752467i			0.0261975i
$826$		0			0
$827$		−	25.1364i		−	0.874080i	−0.899442	−	0.437040i	$-0.856027\pi$
$827$		−	25.1364i		−	0.874080i	0.899442	−	0.437040i	$-0.143973\pi$
$828$		0			0
$829$	7.23789	−	4.17880i	0.251382	−	0.145136i	−0.369015	−	0.929424i	$-0.620305\pi$
$829$	7.23789	−	4.17880i	0.251382	−	0.145136i	0.620397	+	0.784288i	$0.286971\pi$
$830$		0			0
$831$	2.22966	−	3.86188i	0.0773460	−	0.133967i
$832$		0			0
$833$	12.6686	+	19.6894i	0.438941	+	0.682198i
$834$		0			0
$835$	−45.1716	−	26.0798i	−1.56323	−	0.902530i
$836$		0			0
$837$	−18.2197	−	31.5574i	−0.629763	−	1.09078i
$838$		0			0
$839$	3.01785			0.104188			0.0520940	−	0.998642i	$-0.483410\pi$
$839$	3.01785			0.104188			0.0520940	+	0.998642i	$0.483410\pi$
$840$		0			0
$841$	−18.6662			−0.643663
$842$		0			0
$843$	7.76030	+	13.4412i	0.267279	+	0.462941i
$844$		0			0
$845$	−6.36599	−	3.67540i	−0.218997	−	0.126438i
$846$		0			0
$847$	2.53838	−	0.746078i	0.0872197	−	0.0256355i
$848$		0			0
$849$	−0.882271	+	1.52814i	−0.0302795	+	0.0524456i
$850$		0			0
$851$	1.73205	−	1.00000i	0.0593739	−	0.0342796i
$852$		0			0
$853$		−	9.28089i		−	0.317772i	−0.987297	−	0.158886i	$-0.949210\pi$
$853$		−	9.28089i		−	0.317772i	0.987297	−	0.158886i	$-0.0507902\pi$
$854$		0			0
$855$			2.38086i			0.0814236i
$856$		0			0
$857$	−21.3615	+	12.3331i	−0.729696	+	0.421290i	−0.818311	−	0.574776i	$-0.805089\pi$
$857$	−21.3615	+	12.3331i	−0.729696	+	0.421290i	0.0886147	+	0.996066i	$0.471756\pi$
$858$		0			0
$859$	−12.6369	+	21.8878i	−0.431166	+	0.746801i	−0.996974	−	0.0777361i	$-0.975231\pi$
$859$	−12.6369	+	21.8878i	−0.431166	+	0.746801i	0.565808	+	0.824537i	$0.308564\pi$
$860$		0			0
$861$	8.96170	+	2.17153i	0.305414	+	0.0740055i
$862$		0			0
$863$	−16.0382	−	9.25966i	−0.545947	−	0.315203i	0.201539	−	0.979481i	$-0.435406\pi$
$863$	−16.0382	−	9.25966i	−0.545947	−	0.315203i	−0.747486	+	0.664278i	$0.768739\pi$
$864$		0			0
$865$	−21.7399	−	37.6547i	−0.739180	−	1.28030i
$866$		0			0
$867$	5.78076			0.196325
$868$		0			0
$869$	−3.90688			−0.132532
$870$		0			0
$871$	7.86243	+	13.6181i	0.266408	+	0.461432i
$872$		0			0
$873$	16.2431	+	9.37795i	0.549745	+	0.317396i
$874$		0			0
$875$	18.5831	−	19.4999i	0.628224	−	0.659218i
$876$		0			0
$877$	−5.31690	+	9.20914i	−0.179539	+	0.310970i	−0.941723	−	0.336390i	$-0.890794\pi$
$877$	−5.31690	+	9.20914i	−0.179539	+	0.310970i	0.762184	+	0.647361i	$0.224127\pi$
$878$		0			0
$879$	0.264300	−	0.152593i	0.00891460	−	0.00514685i
$880$		0			0
$881$		−	17.9822i		−	0.605835i	−0.953017	−	0.302918i	$-0.902039\pi$
$881$		−	17.9822i		−	0.605835i	0.953017	−	0.302918i	$-0.0979607\pi$
$882$		0			0
$883$		−	16.4892i		−	0.554905i	−0.960739	−	0.277452i	$-0.910510\pi$
$883$		−	16.4892i		−	0.554905i	0.960739	−	0.277452i	$-0.0894901\pi$
$884$		0			0
$885$	−7.83703	+	4.52471i	−0.263439	+	0.152096i
$886$		0			0
$887$	21.1918	−	36.7052i	0.711550	−	1.23244i	−0.252725	−	0.967538i	$-0.581327\pi$
$887$	21.1918	−	36.7052i	0.711550	−	1.23244i	0.964275	−	0.264903i	$-0.0853399\pi$
$888$		0			0
$889$	−37.9811	+	39.8549i	−1.27385	+	1.33669i
$890$		0			0
$891$	0.933045	+	0.538694i	0.0312582	+	0.0180469i
$892$		0			0
$893$	1.76713	+	3.06076i	0.0591348	+	0.102425i
$894$		0			0
$895$	51.2997			1.71476
$896$		0			0
$897$	−1.82752			−0.0610191
$898$		0			0
$899$	11.7531	+	20.3570i	0.391988	+	0.678943i
$900$		0			0
$901$	30.1900	+	17.4302i	1.00577	+	0.580684i
$902$		0			0
$903$	3.11781	+	0.755484i	0.103754	+	0.0251409i
$904$		0			0
$905$	−14.9184	+	25.8394i	−0.495903	+	0.858929i
$906$		0			0
$907$	20.7690	−	11.9910i	0.689622	−	0.398153i	−0.113848	−	0.993498i	$-0.536318\pi$
$907$	20.7690	−	11.9910i	0.689622	−	0.398153i	0.803470	+	0.595345i	$0.202984\pi$
$908$		0			0
$909$		−	6.03228i		−	0.200078i
$910$		0			0
$911$		−	48.9874i		−	1.62303i	−0.584335	−	0.811513i	$-0.698645\pi$
$911$		−	48.9874i		−	1.62303i	0.584335	−	0.811513i	$-0.301355\pi$
$912$		0			0
$913$	0.222306	−	0.128348i	0.00735725	−	0.00424771i
$914$		0			0
$915$	−3.70329	+	6.41429i	−0.122427	+	0.212050i
$916$		0			0
$917$	−7.80316	+	2.29350i	−0.257683	+	0.0757379i
$918$		0			0
$919$	5.93753	+	3.42804i	0.195861	+	0.113080i	0.594723	−	0.803930i	$-0.297262\pi$
$919$	5.93753	+	3.42804i	0.195861	+	0.113080i	−0.398862	+	0.917011i	$0.630595\pi$
$920$		0			0
$921$	15.8713	+	27.4899i	0.522977	+	0.905823i
$922$		0			0
$923$	−34.3835			−1.13175
$924$		0			0
$925$	3.30049			0.108519
$926$		0			0
$927$	−19.3164	−	33.4570i	−0.634434	−	1.09887i
$928$		0			0
$929$	−31.9329	−	18.4365i	−1.04768	−	0.604881i	−0.125685	−	0.992070i	$-0.540113\pi$
$929$	−31.9329	−	18.4365i	−1.04768	−	0.604881i	−0.922000	+	0.387189i	$0.873446\pi$
$930$		0			0
$931$	−3.07092	−	1.58108i	−0.100645	−	0.0518177i
$932$		0			0
$933$	−3.64132	+	6.30696i	−0.119212	+	0.206481i
$934$		0			0
$935$	−6.94982	+	4.01248i	−0.227284	+	0.131222i
$936$		0			0
$937$			1.09951i			0.0359194i	0.999839	+	0.0179597i	$0.00571707\pi$
$937$			1.09951i			0.0359194i	−0.999839	+	0.0179597i	$0.994283\pi$
$938$		0			0
$939$		−	4.05215i		−	0.132237i
$940$		0			0
$941$	−47.1443	+	27.2188i	−1.53686	+	0.887306i	−0.537839	+	0.843048i	$0.680759\pi$
$941$	−47.1443	+	27.2188i	−1.53686	+	0.887306i	−0.999020	+	0.0442583i	$0.985908\pi$
$942$		0			0
$943$	−0.803452	+	1.39162i	−0.0261640	+	0.0453174i
$944$		0			0
$945$	−8.92045	−	30.3500i	−0.290182	−	0.987286i
$946$		0			0
$947$	23.3038	+	13.4545i	0.757273	+	0.437212i	0.828316	−	0.560261i	$-0.189299\pi$
$947$	23.3038	+	13.4545i	0.757273	+	0.437212i	−0.0710427	+	0.997473i	$0.522633\pi$
$948$		0			0
$949$	−6.47256	−	11.2108i	−0.210108	−	0.363918i
$950$		0			0
$951$	−20.1686			−0.654012
$952$		0			0
$953$	25.9977			0.842149			0.421074	−	0.907026i	$-0.361653\pi$
$953$	25.9977			0.842149			0.421074	+	0.907026i	$0.361653\pi$
$954$		0			0
$955$	6.99005	+	12.1071i	0.226193	+	0.391777i
$956$		0			0
$957$	2.76854	+	1.59841i	0.0894941	+	0.0516694i
$958$		0			0
$959$	−4.15815	+	17.1603i	−0.134274	+	0.554135i
$960$		0			0
$961$	−11.2347	+	19.4590i	−0.362409	+	0.627711i
$962$		0			0
$963$	−13.1120	+	7.57024i	−0.422530	+	0.243948i
$964$		0			0
$965$			44.5860i			1.43528i
$966$		0			0
$967$		−	43.9234i		−	1.41248i	−0.707971	−	0.706241i	$-0.750389\pi$
$967$		−	43.9234i		−	1.41248i	0.707971	−	0.706241i	$-0.249611\pi$
$968$		0			0
$969$	1.42137	−	0.820628i	0.0456609	−	0.0263624i
$970$		0			0
$971$	14.6114	−	25.3077i	0.468903	−	0.812163i	−0.530466	−	0.847706i	$-0.677983\pi$
$971$	14.6114	−	25.3077i	0.468903	−	0.812163i	0.999368	+	0.0355434i	$0.0113162\pi$
$972$		0			0
$973$	4.16906	+	3.97305i	0.133654	+	0.127370i
$974$		0			0
$975$	−2.61181	−	1.50793i	−0.0836448	−	0.0482923i
$976$		0			0
$977$	27.4613	+	47.5644i	0.878565	+	1.52172i	0.852916	+	0.522048i	$0.174832\pi$
$977$	27.4613	+	47.5644i	0.878565	+	1.52172i	0.0256487	+	0.999671i	$0.491835\pi$
$978$		0			0
$979$	−1.02720			−0.0328295
$980$		0			0
$981$	−24.6402			−0.786702
$982$		0			0
$983$	18.1859	+	31.4989i	0.580040	+	1.00466i	0.995474	+	0.0950349i	$0.0302963\pi$
$983$	18.1859	+	31.4989i	0.580040	+	1.00466i	−0.415434	+	0.909623i	$0.636370\pi$
$984$		0			0
$985$	−29.3586	−	16.9502i	−0.935442	−	0.540077i
$986$		0			0
$987$	−13.6427	−	13.0013i	−0.434252	−	0.413835i
$988$		0			0
$989$	−0.279524	+	0.484151i	−0.00888836	+	0.0153951i
$990$		0			0
$991$	−18.7747	+	10.8396i	−0.596399	+	0.344331i	−0.767624	−	0.640901i	$-0.778561\pi$
$991$	−18.7747	+	10.8396i	−0.596399	+	0.344331i	0.171225	+	0.985232i	$0.445228\pi$
$992$		0			0
$993$			11.9044i			0.377774i
$994$		0			0
$995$			0.818815i			0.0259582i
$996$		0			0
$997$	−28.7086	+	16.5749i	−0.909211	+	0.524933i	−0.880177	−	0.474645i	$-0.842576\pi$
$997$	−28.7086	+	16.5749i	−0.909211	+	0.524933i	−0.0290338	+	0.999578i	$0.509243\pi$
$998$		0			0
$999$	−10.8685	+	18.8247i	−0.343863	+	0.595588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.be.a.1167.5	yes	24
4.3	odd	2	inner	1232.2.be.a.1167.8	yes	24
7.3	odd	6	inner	1232.2.be.a.815.8	yes	24
28.3	even	6	inner	1232.2.be.a.815.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1232.2.be.a.815.5	✓	24	28.3	even	6	inner
1232.2.be.a.815.8	yes	24	7.3	odd	6	inner
1232.2.be.a.1167.5	yes	24	1.1	even	1	trivial
1232.2.be.a.1167.8	yes	24	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.497233 - 0.861233i) q^{3} +(2.07786 + 1.19965i) q^{5} +(1.91531 + 1.82526i) q^{7} +(1.00552 - 1.74161i) q^{9} +O(q^{10})\)	\(q+(-0.497233 - 0.861233i) q^{3} +(2.07786 + 1.19965i) q^{5} +(1.91531 + 1.82526i) q^{7} +(1.00552 - 1.74161i) q^{9} +(-0.866025 + 0.500000i) q^{11} -4.00796i q^{13} -2.38602i q^{15} +(2.89660 - 1.67235i) q^{17} +(-0.246716 + 0.427325i) q^{19} +(0.619619 - 2.55711i) q^{21} +(0.397082 + 0.229255i) q^{23} +(0.378327 + 0.655282i) q^{25} -4.98331 q^{27} +3.21462 q^{29} +(3.65614 + 6.33262i) q^{31} +(0.861233 + 0.497233i) q^{33} +(1.79007 + 6.09034i) q^{35} +(2.18098 - 3.77756i) q^{37} +(-3.45178 + 1.99289i) q^{39} +3.50462i q^{41} +1.21927i q^{43} +(4.17865 - 2.41254i) q^{45} +(3.58130 - 6.20300i) q^{47} +(0.336838 + 6.99189i) q^{49} +(-2.88057 - 1.66310i) q^{51} +(5.21128 + 9.02620i) q^{53} -2.39930 q^{55} +0.490702 q^{57} +(-1.89634 - 3.28455i) q^{59} +(-2.68828 - 1.55208i) q^{61} +(5.10478 - 1.50039i) q^{63} +(4.80815 - 8.32796i) q^{65} +(-3.39777 + 1.96170i) q^{67} -0.455973i q^{69} -8.57882i q^{71} +(2.79714 - 1.61493i) q^{73} +(0.376234 - 0.651656i) q^{75} +(-2.57134 - 0.623067i) q^{77} +(3.38345 + 1.95344i) q^{79} +(-0.538694 - 0.933045i) q^{81} -0.256697 q^{83} +8.02497 q^{85} +(-1.59841 - 2.76854i) q^{87} +(0.889581 + 0.513600i) q^{89} +(7.31557 - 7.67649i) q^{91} +(3.63590 - 6.29757i) q^{93} +(-1.02528 + 0.591948i) q^{95} +9.32648i q^{97} +2.01104i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{9}+O(q^{10}) \) 24 * q - 8 * q^9	\( 24 q - 8 q^{9} - 36 q^{17} - 4 q^{21} + 12 q^{25} + 16 q^{29} + 16 q^{37} + 12 q^{45} + 16 q^{49} + 4 q^{53} - 16 q^{57} + 24 q^{61} + 36 q^{65} + 12 q^{73} - 4 q^{77} - 20 q^{81} - 32 q^{85} + 60 q^{89} - 64 q^{93}+O(q^{100}) \) 24 * q - 8 * q^9 - 36 * q^17 - 4 * q^21 + 12 * q^25 + 16 * q^29 + 16 * q^37 + 12 * q^45 + 16 * q^49 + 4 * q^53 - 16 * q^57 + 24 * q^61 + 36 * q^65 + 12 * q^73 - 4 * q^77 - 20 * q^81 - 32 * q^85 + 60 * q^89 - 64 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more