LMFDB - Embedded newform 1890.2.bf.f.629.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(629,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1890.629");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.bf (of order $6$, 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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			629.7
Character	$\chi$	$=$	1890.629
Dual form			1890.2.bf.f.1259.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.452503 + 2.18980i) q^{5} +(2.02132 + 1.70712i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.452503 + 2.18980i) q^{5} +(2.02132 + 1.70712i) q^{7} -1.00000 q^{8} +(1.67017 + 1.48678i) q^{10} +(-5.48007 - 3.16392i) q^{11} +(-2.28203 - 3.95259i) q^{13} +(2.48907 - 0.896960i) q^{14} +(-0.500000 + 0.866025i) q^{16} +2.72847i q^{17} +4.11761i q^{19} +(2.12268 - 0.703023i) q^{20} +(-5.48007 + 3.16392i) q^{22} +(-1.15619 - 2.00258i) q^{23} +(-4.59048 - 1.98179i) q^{25} -4.56405 q^{26} +(0.467745 - 2.60408i) q^{28} +(0.173539 + 0.100193i) q^{29} +(2.10971 - 1.21804i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.36292 + 1.36423i) q^{34} +(-4.65291 + 3.65383i) q^{35} -10.4673i q^{37} +(3.56595 + 2.05880i) q^{38} +(0.452503 - 2.18980i) q^{40} +(1.03090 + 1.78558i) q^{41} +(-7.26144 - 4.19239i) q^{43} +6.32783i q^{44} -2.31238 q^{46} +(-7.86014 - 4.53806i) q^{47} +(1.17150 + 6.90127i) q^{49} +(-4.01152 + 2.98458i) q^{50} +(-2.28203 + 3.95259i) q^{52} -6.77638 q^{53} +(9.40810 - 10.5686i) q^{55} +(-2.02132 - 1.70712i) q^{56} +(0.173539 - 0.100193i) q^{58} +(0.616709 + 1.06817i) q^{59} +(1.66558 + 0.961623i) q^{61} -2.43609i q^{62} +1.00000 q^{64} +(9.68801 - 3.20863i) q^{65} +(-7.07376 + 4.08404i) q^{67} +(2.36292 - 1.36423i) q^{68} +(0.837855 + 5.85645i) q^{70} -8.31846i q^{71} -13.9450 q^{73} +(-9.06497 - 5.23366i) q^{74} +(3.56595 - 2.05880i) q^{76} +(-5.67581 - 15.7504i) q^{77} +(1.01691 - 1.76135i) q^{79} +(-1.67017 - 1.48678i) q^{80} +2.06181 q^{82} +(-3.64421 - 2.10398i) q^{83} +(-5.97481 - 1.23464i) q^{85} +(-7.26144 + 4.19239i) q^{86} +(5.48007 + 3.16392i) q^{88} -9.48716 q^{89} +(2.13481 - 11.8851i) q^{91} +(-1.15619 + 2.00258i) q^{92} +(-7.86014 + 4.53806i) q^{94} +(-9.01675 - 1.86323i) q^{95} +(2.42587 - 4.20173i) q^{97} +(6.56243 + 2.43609i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8}+O(q^{10}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 24 q^{11} - 16 q^{16} + 24 q^{22} + 24 q^{23} - 58 q^{25} + 36 q^{29} + 16 q^{32} + 48 q^{35} - 54 q^{43} + 48 q^{46} + 32 q^{49} - 50 q^{50} + 24 q^{53} + 36 q^{58} + 32 q^{64} + 90 q^{65} - 66 q^{67} + 36 q^{70} - 12 q^{74} - 18 q^{77} + 34 q^{79} + 4 q^{85} - 54 q^{86} - 24 q^{88} + 16 q^{91} + 24 q^{92} - 12 q^{95} + 64 q^{98}+O(q^{100}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 24 * q^11 - 16 * q^16 + 24 * q^22 + 24 * q^23 - 58 * q^25 + 36 * q^29 + 16 * q^32 + 48 * q^35 - 54 * q^43 + 48 * q^46 + 32 * q^49 - 50 * q^50 + 24 * q^53 + 36 * q^58 + 32 * q^64 + 90 * q^65 - 66 * q^67 + 36 * q^70 - 12 * q^74 - 18 * q^77 + 34 * q^79 + 4 * q^85 - 54 * q^86 - 24 * q^88 + 16 * q^91 + 24 * q^92 - 12 * q^95 + 64 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.452503	+	2.18980i	−0.202365	+	0.979310i
$5$	−0.452503	+	2.18980i	−0.202365	+	0.979310i
$6$		0			0
$7$	2.02132	+	1.70712i	0.763989	+	0.645230i
$7$	2.02132	+	1.70712i	0.763989	+	0.645230i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.67017	+	1.48678i	0.528155	+	0.470161i
$11$	−5.48007	−	3.16392i	−1.65230	−	0.953957i	−0.976123	−	0.217220i	$-0.930301\pi$
$11$	−5.48007	−	3.16392i	−1.65230	−	0.953957i	−0.676179	−	0.736737i	$-0.736366\pi$
$12$		0			0
$13$	−2.28203	−	3.95259i	−0.632920	−	1.09625i	−0.986952	−	0.161017i	$-0.948523\pi$
$13$	−2.28203	−	3.95259i	−0.632920	−	1.09625i	0.354031	−	0.935234i	$-0.384811\pi$
$14$	2.48907	−	0.896960i	0.665232	−	0.239723i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$			2.72847i			0.661751i	0.943674	+	0.330875i	$0.107344\pi$
$17$			2.72847i			0.661751i	−0.943674	+	0.330875i	$0.892656\pi$
$18$		0			0
$19$			4.11761i			0.944644i	0.881426	+	0.472322i	$0.156584\pi$
$19$			4.11761i			0.944644i	−0.881426	+	0.472322i	$0.843416\pi$
$20$	2.12268	−	0.703023i	0.474645	−	0.157201i
$21$		0			0
$22$	−5.48007	+	3.16392i	−1.16835	+	0.674549i
$23$	−1.15619	−	2.00258i	−0.241083	−	0.417568i	0.719940	−	0.694036i	$-0.244169\pi$
$23$	−1.15619	−	2.00258i	−0.241083	−	0.417568i	−0.961023	+	0.276468i	$0.910836\pi$
$24$		0			0
$25$	−4.59048	−	1.98179i	−0.918096	−	0.396357i
$26$	−4.56405			−0.895085
$27$		0			0
$28$	0.467745	−	2.60408i	0.0883954	−	0.492124i
$29$	0.173539	+	0.100193i	0.0322254	+	0.0186054i	0.516026	−	0.856573i	$-0.327411\pi$
$29$	0.173539	+	0.100193i	0.0322254	+	0.0186054i	−0.483801	+	0.875178i	$0.660744\pi$
$30$		0			0
$31$	2.10971	−	1.21804i	0.378915	−	0.218767i	−0.298431	−	0.954431i	$-0.596463\pi$
$31$	2.10971	−	1.21804i	0.378915	−	0.218767i	0.677346	+	0.735664i	$0.263130\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	2.36292	+	1.36423i	0.405238	+	0.233964i
$35$	−4.65291	+	3.65383i	−0.786485	+	0.617610i
$36$		0			0
$37$		−	10.4673i		−	1.72082i	−0.509605	−	0.860409i	$-0.670208\pi$
$37$		−	10.4673i		−	1.72082i	0.509605	−	0.860409i	$-0.329792\pi$
$38$	3.56595	+	2.05880i	0.578474	+	0.333982i
$39$		0			0
$40$	0.452503	−	2.18980i	0.0715470	−	0.346238i
$41$	1.03090	+	1.78558i	0.161000	+	0.278860i	0.935228	−	0.354047i	$-0.115195\pi$
$41$	1.03090	+	1.78558i	0.161000	+	0.278860i	−0.774228	+	0.632907i	$0.781861\pi$
$42$		0			0
$43$	−7.26144	−	4.19239i	−1.10736	−	0.639334i	−0.169215	−	0.985579i	$-0.554123\pi$
$43$	−7.26144	−	4.19239i	−1.10736	−	0.639334i	−0.938144	+	0.346245i	$0.887457\pi$
$44$			6.32783i			0.953957i
$45$		0			0
$46$	−2.31238			−0.340943
$47$	−7.86014	−	4.53806i	−1.14652	−	0.661943i	−0.198483	−	0.980104i	$-0.563601\pi$
$47$	−7.86014	−	4.53806i	−1.14652	−	0.661943i	−0.948037	+	0.318161i	$0.896935\pi$
$48$		0			0
$49$	1.17150	+	6.90127i	0.167358	+	0.985896i
$50$	−4.01152	+	2.98458i	−0.567314	+	0.422084i
$51$		0			0
$52$	−2.28203	+	3.95259i	−0.316460	+	0.548125i
$53$	−6.77638			−0.930808			−0.465404	−	0.885098i	$-0.654091\pi$
$53$	−6.77638			−0.930808			−0.465404	+	0.885098i	$0.654091\pi$
$54$		0			0
$55$	9.40810	−	10.5686i	1.26859	−	1.42507i
$56$	−2.02132	−	1.70712i	−0.270111	−	0.228123i
$57$		0			0
$58$	0.173539	−	0.100193i	0.0227868	−	0.0131560i
$59$	0.616709	+	1.06817i	0.0802887	+	0.139064i	0.903374	−	0.428854i	$-0.141082\pi$
$59$	0.616709	+	1.06817i	0.0802887	+	0.139064i	−0.823085	+	0.567918i	$0.807749\pi$
$60$		0			0
$61$	1.66558	+	0.961623i	0.213256	+	0.123123i	0.602824	−	0.797875i	$-0.294042\pi$
$61$	1.66558	+	0.961623i	0.213256	+	0.123123i	−0.389568	+	0.920998i	$0.627376\pi$
$62$		−	2.43609i		−	0.309383i
$63$		0			0
$64$	1.00000			0.125000
$65$	9.68801	−	3.20863i	1.20165	−	0.397982i
$66$		0			0
$67$	−7.07376	+	4.08404i	−0.864198	+	0.498945i	−0.865416	−	0.501054i	$-0.832946\pi$
$67$	−7.07376	+	4.08404i	−0.864198	+	0.498945i	0.00121797	+	0.999999i	$0.499612\pi$
$68$	2.36292	−	1.36423i	0.286546	−	0.165438i
$69$		0			0
$70$	0.837855	+	5.85645i	0.100143	+	0.699980i
$71$		−	8.31846i		−	0.987220i	−0.869684	−	0.493610i	$-0.835677\pi$
$71$		−	8.31846i		−	0.987220i	0.869684	−	0.493610i	$-0.164323\pi$
$72$		0			0
$73$	−13.9450			−1.63214			−0.816072	−	0.577951i	$-0.803852\pi$
$73$	−13.9450			−1.63214			−0.816072	+	0.577951i	$0.803852\pi$
$74$	−9.06497	−	5.23366i	−1.05378	−	0.608401i
$75$		0			0
$76$	3.56595	−	2.05880i	0.409043	−	0.236161i
$77$	−5.67581	−	15.7504i	−0.646819	−	1.79493i
$78$		0			0
$79$	1.01691	−	1.76135i	0.114412	−	0.198167i	−0.803133	−	0.595800i	$-0.796835\pi$
$79$	1.01691	−	1.76135i	0.114412	−	0.198167i	0.917544	+	0.397633i	$0.130168\pi$
$80$	−1.67017	−	1.48678i	−0.186731	−	0.166227i
$81$		0			0
$82$	2.06181			0.227688
$83$	−3.64421	−	2.10398i	−0.400004	−	0.230942i	0.286482	−	0.958086i	$-0.407514\pi$
$83$	−3.64421	−	2.10398i	−0.400004	−	0.230942i	−0.686486	+	0.727143i	$0.740847\pi$
$84$		0			0
$85$	−5.97481	−	1.23464i	−0.648059	−	0.133915i
$86$	−7.26144	+	4.19239i	−0.783021	+	0.452078i
$87$		0			0
$88$	5.48007	+	3.16392i	0.584177	+	0.337275i
$89$	−9.48716			−1.00564			−0.502819	−	0.864392i	$-0.667704\pi$
$89$	−9.48716			−1.00564			−0.502819	+	0.864392i	$0.667704\pi$
$90$		0			0
$91$	2.13481	−	11.8851i	0.223789	−	1.24590i
$92$	−1.15619	+	2.00258i	−0.120541	+	0.208784i
$93$		0			0
$94$	−7.86014	+	4.53806i	−0.810712	+	0.468065i
$95$	−9.01675	−	1.86323i	−0.925099	−	0.191163i
$96$		0			0
$97$	2.42587	−	4.20173i	0.246310	−	0.426622i	−0.716189	−	0.697906i	$-0.754115\pi$
$97$	2.42587	−	4.20173i	0.246310	−	0.426622i	0.962499	+	0.271285i	$0.0874485\pi$
$98$	6.56243	+	2.43609i	0.662906	+	0.246082i
$99$		0			0
$100$	0.578965	+	4.96637i	0.0578965	+	0.496637i
$101$	8.61527	−	14.9221i	0.857252	−	1.48480i	−0.0172883	−	0.999851i	$-0.505503\pi$
$101$	8.61527	−	14.9221i	0.857252	−	1.48480i	0.874540	−	0.484953i	$-0.161163\pi$
$102$		0			0
$103$	9.19697	+	15.9296i	0.906204	+	1.56959i	0.819293	+	0.573375i	$0.194366\pi$
$103$	9.19697	+	15.9296i	0.906204	+	1.56959i	0.0869114	+	0.996216i	$0.472300\pi$
$104$	2.28203	+	3.95259i	0.223771	+	0.387583i
$105$		0			0
$106$	−3.38819	+	5.86852i	−0.329090	+	0.570001i
$107$	1.73454			0.167685			0.0838423	−	0.996479i	$-0.473281\pi$
$107$	1.73454			0.167685			0.0838423	+	0.996479i	$0.473281\pi$
$108$		0			0
$109$	0.400269			0.0383388			0.0191694	−	0.999816i	$-0.493898\pi$
$109$	0.400269			0.0383388			0.0191694	+	0.999816i	$0.493898\pi$
$110$	−4.44861	−	13.4320i	−0.424159	−	1.28069i
$111$		0			0
$112$	−2.48907	+	0.896960i	−0.235195	+	0.0847547i
$113$	−1.32959	−	2.30292i	−0.125077	−	0.216640i	0.796686	−	0.604394i	$-0.206585\pi$
$113$	−1.32959	−	2.30292i	−0.125077	−	0.216640i	−0.921763	+	0.387753i	$0.873251\pi$
$114$		0			0
$115$	4.90845	−	1.62566i	0.457715	−	0.151594i
$116$		−	0.200386i		−	0.0186054i
$117$		0			0
$118$	1.23342			0.113545
$119$	−4.65781	+	5.51512i	−0.426981	+	0.505570i
$120$		0			0
$121$	14.5207	+	25.1507i	1.32007	+	2.28642i
$122$	1.66558	−	0.961623i	0.150795	−	0.0870613i
$123$		0			0
$124$	−2.10971	−	1.21804i	−0.189458	−	0.109383i
$125$	6.41693	−	9.15549i	0.573948	−	0.818892i
$126$		0			0
$127$		−	0.955970i		−	0.0848287i	−0.999100	−	0.0424143i	$-0.986495\pi$
$127$		−	0.955970i		−	0.0848287i	0.999100	−	0.0424143i	$-0.0135050\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	2.06525	−	9.99438i	0.181134	−	0.876565i
$131$	5.64033	+	9.76935i	0.492798	+	0.853552i	0.999966	−	0.00829593i	$-0.00264071\pi$
$131$	5.64033	+	9.76935i	0.492798	+	0.853552i	−0.507167	+	0.861848i	$0.669307\pi$
$132$		0			0
$133$	−7.02924	+	8.32302i	−0.609512	+	0.721697i
$134$			8.16808i			0.705615i
$135$		0			0
$136$		−	2.72847i		−	0.233964i
$137$	−0.913329	+	1.58193i	−0.0780310	+	0.135154i	−0.902400	−	0.430899i	$-0.858197\pi$
$137$	−0.913329	+	1.58193i	−0.0780310	+	0.135154i	0.824369	+	0.566052i	$0.191530\pi$
$138$		0			0
$139$	−15.2206	+	8.78760i	−1.29099	+	0.745355i	−0.978830	−	0.204674i	$-0.934387\pi$
$139$	−15.2206	+	8.78760i	−1.29099	+	0.745355i	−0.312162	+	0.950029i	$0.601053\pi$
$140$	5.49076	+	2.20262i	0.464054	+	0.186155i
$141$		0			0
$142$	−7.20400	−	4.15923i	−0.604546	−	0.349035i
$143$			28.8806i			2.41512i
$144$		0			0
$145$	−0.297930	+	0.334679i	−0.0247417	+	0.0277936i
$146$	−6.97252	+	12.0768i	−0.577050	+	0.999479i
$147$		0			0
$148$	−9.06497	+	5.23366i	−0.745136	+	0.430204i
$149$	−5.26078	+	3.03731i	−0.430980	+	0.248826i	−0.699764	−	0.714374i	$-0.746712\pi$
$149$	−5.26078	+	3.03731i	−0.430980	+	0.248826i	0.268784	+	0.963200i	$0.413378\pi$
$150$		0			0
$151$	−8.97909	+	15.5522i	−0.730708	+	1.26562i	0.225873	+	0.974157i	$0.427477\pi$
$151$	−8.97909	+	15.5522i	−0.730708	+	1.26562i	−0.956581	+	0.291467i	$0.905857\pi$
$152$		−	4.11761i		−	0.333982i
$153$		0			0
$154$	−16.4782	−	2.95981i	−1.32785	−	0.238508i
$155$	1.71262	+	5.17102i	0.137561	+	0.415347i
$156$		0			0
$157$	−3.74566	−	6.48767i	−0.298936	−	0.517772i	0.676957	−	0.736023i	$-0.263298\pi$
$157$	−3.74566	−	6.48767i	−0.298936	−	0.517772i	−0.975893	+	0.218250i	$0.929965\pi$
$158$	−1.01691	−	1.76135i	−0.0809013	−	0.140125i
$159$		0			0
$160$	−2.12268	+	0.703023i	−0.167812	+	0.0555788i
$161$	1.08161	−	6.02163i	0.0852424	−	0.474571i
$162$		0			0
$163$		−	0.216711i		−	0.0169741i	−0.999964	−	0.00848704i	$-0.997298\pi$
$163$		−	0.216711i		−	0.0169741i	0.999964	−	0.00848704i	$-0.00270154\pi$
$164$	1.03090	−	1.78558i	0.0805000	−	0.139430i
$165$		0			0
$166$	−3.64421	+	2.10398i	−0.282845	+	0.163301i
$167$	6.59580	−	3.80809i	0.510398	−	0.294679i	−0.222599	−	0.974910i	$-0.571454\pi$
$167$	6.59580	−	3.80809i	0.510398	−	0.294679i	0.732997	+	0.680231i	$0.238121\pi$
$168$		0			0
$169$	−3.91530	+	6.78149i	−0.301177	+	0.521653i
$170$	−4.05663	+	4.55702i	−0.311130	+	0.349507i
$171$		0			0
$172$			8.38479i			0.639334i
$173$	6.39337	+	3.69121i	0.486079	+	0.280638i	0.722946	−	0.690904i	$-0.242787\pi$
$173$	6.39337	+	3.69121i	0.486079	+	0.280638i	−0.236868	+	0.971542i	$0.576121\pi$
$174$		0			0
$175$	−5.89571	−	11.8423i	−0.445674	−	0.895195i
$176$	5.48007	−	3.16392i	0.413075	−	0.238489i
$177$		0			0
$178$	−4.74358	+	8.21613i	−0.355547	+	0.615825i
$179$			8.41037i			0.628620i	0.949320	+	0.314310i	$0.101773\pi$
$179$			8.41037i			0.628620i	−0.949320	+	0.314310i	$0.898227\pi$
$180$		0			0
$181$			19.8492i			1.47538i	0.675138	+	0.737691i	$0.264084\pi$
$181$			19.8492i			1.47538i	−0.675138	+	0.737691i	$0.735916\pi$
$182$	−9.22543	−	7.79137i	−0.683835	−	0.577535i
$183$		0			0
$184$	1.15619	+	2.00258i	0.0852356	+	0.147632i
$185$	22.9214	+	4.73649i	1.68521	+	0.348234i
$186$		0			0
$187$	8.63265	−	14.9522i	0.631282	−	1.09341i
$188$			9.07611i			0.661943i
$189$		0			0
$190$	−6.12198	+	6.87712i	−0.444135	+	0.498919i
$191$	−2.20596	−	1.27361i	−0.159618	−	0.0921553i	0.418063	−	0.908418i	$-0.362709\pi$
$191$	−2.20596	−	1.27361i	−0.159618	−	0.0921553i	−0.577681	+	0.816262i	$0.696042\pi$
$192$		0			0
$193$	19.4328	−	11.2196i	1.39881	−	0.807601i	0.404539	−	0.914521i	$-0.367432\pi$
$193$	19.4328	−	11.2196i	1.39881	−	0.807601i	0.994268	+	0.106920i	$0.0340988\pi$
$194$	−2.42587	−	4.20173i	−0.174168	−	0.301667i
$195$		0			0
$196$	5.39093	−	4.46519i	0.385066	−	0.318942i
$197$	−10.3672			−0.738631			−0.369315	−	0.929304i	$-0.620408\pi$
$197$	−10.3672			−0.738631			−0.369315	+	0.929304i	$0.620408\pi$
$198$		0			0
$199$			11.5505i			0.818791i	0.912357	+	0.409395i	$0.134260\pi$
$199$			11.5505i			0.818791i	−0.912357	+	0.409395i	$0.865740\pi$
$200$	4.59048	+	1.98179i	0.324596	+	0.140133i
$201$		0			0
$202$	−8.61527	−	14.9221i	−0.606169	−	1.04991i
$203$	0.179738	+	0.498774i	0.0126151	+	0.0350071i
$204$		0			0
$205$	−4.37655	+	1.44950i	−0.305671	+	0.101237i
$206$	18.3939			1.28157
$207$		0			0
$208$	4.56405			0.316460
$209$	13.0278	−	22.5648i	0.901150	−	1.56084i
$210$		0			0
$211$	−0.154076	−	0.266868i	−0.0106071	−	0.0183720i	0.860673	−	0.509158i	$-0.170043\pi$
$211$	−0.154076	−	0.266868i	−0.0106071	−	0.0183720i	−0.871280	+	0.490786i	$0.836710\pi$
$212$	3.38819	+	5.86852i	0.232702	+	0.403051i
$213$		0			0
$214$	0.867271	−	1.50216i	0.0592854	−	0.102685i
$215$	12.4663	−	14.0041i	0.850198	−	0.955069i
$216$		0			0
$217$	6.34375	+	1.13947i	0.430642	+	0.0773520i
$218$	0.200135	−	0.346643i	0.0135548	−	0.0234776i
$219$		0			0
$220$	−13.8567	−	2.86336i	−0.934220	−	0.193048i
$221$	10.7845	−	6.22644i	0.725444	−	0.418835i
$222$		0			0
$223$	−12.0678	+	20.9020i	−0.808118	+	1.39970i	0.106049	+	0.994361i	$0.466180\pi$
$223$	−12.0678	+	20.9020i	−0.808118	+	1.39970i	−0.914166	+	0.405340i	$0.867153\pi$
$224$	−0.467745	+	2.60408i	−0.0312525	+	0.173992i
$225$		0			0
$226$	−2.65918			−0.176886
$227$	−8.32843	−	4.80842i	−0.552777	−	0.319146i	0.197464	−	0.980310i	$-0.436729\pi$
$227$	−8.32843	−	4.80842i	−0.552777	−	0.319146i	−0.750241	+	0.661164i	$0.770063\pi$
$228$		0			0
$229$	19.7785	−	11.4191i	1.30700	−	0.754597i	0.325406	−	0.945574i	$-0.394499\pi$
$229$	19.7785	−	11.4191i	1.30700	−	0.754597i	0.981595	+	0.190977i	$0.0611656\pi$
$230$	1.04636	−	5.06367i	0.0689950	−	0.333888i
$231$		0			0
$232$	−0.173539	−	0.100193i	−0.0113934	−	0.00657799i
$233$	24.1221			1.58029			0.790147	−	0.612918i	$-0.210004\pi$
$233$	24.1221			1.58029			0.790147	+	0.612918i	$0.210004\pi$
$234$		0			0
$235$	13.4942	−	15.1587i	0.880264	−	0.988844i
$236$	0.616709	−	1.06817i	0.0401444	−	0.0695321i
$237$		0			0
$238$	2.44732	+	6.79134i	0.158637	+	0.440217i
$239$	13.7371	−	7.93114i	0.888582	−	0.513023i	0.0151034	−	0.999886i	$-0.495192\pi$
$239$	13.7371	−	7.93114i	0.888582	−	0.513023i	0.873478	+	0.486863i	$0.161859\pi$
$240$		0			0
$241$	−11.8605	−	6.84765i	−0.764000	−	0.441096i	0.0667298	−	0.997771i	$-0.478743\pi$
$241$	−11.8605	−	6.84765i	−0.764000	−	0.441096i	−0.830730	+	0.556675i	$0.812077\pi$
$242$	29.0415			1.86686
$243$		0			0
$244$		−	1.92325i		−	0.123123i
$245$	−15.6425	−	0.557485i	−0.999366	−	0.0356164i
$246$		0			0
$247$	16.2752	−	9.39649i	1.03557	−	0.597884i
$248$	−2.10971	+	1.21804i	−0.133967	+	0.0773458i
$249$		0			0
$250$	−4.72042	−	10.1350i	−0.298546	−	0.640992i
$251$	−24.1645			−1.52525			−0.762624	−	0.646842i	$-0.776089\pi$
$251$	−24.1645			−1.52525			−0.762624	+	0.646842i	$0.776089\pi$
$252$		0			0
$253$			14.6324i			0.919930i
$254$	−0.827895	−	0.477985i	−0.0519467	−	0.0299915i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.37439	+	4.25760i	−0.460002	+	0.265582i	−0.712045	−	0.702134i	$-0.752231\pi$
$257$	−7.37439	+	4.25760i	−0.460002	+	0.265582i	0.252043	+	0.967716i	$0.418897\pi$
$258$		0			0
$259$	17.8689	−	21.1579i	1.11032	−	1.31468i
$260$	−7.62277	−	6.78575i	−0.472744	−	0.420834i
$261$		0			0
$262$	11.2807			0.696922
$263$	9.99743	−	17.3161i	0.616468	−	1.06775i	−0.373657	−	0.927567i	$-0.621896\pi$
$263$	9.99743	−	17.3161i	0.616468	−	1.06775i	0.990125	−	0.140187i	$-0.0447704\pi$
$264$		0			0
$265$	3.06633	−	14.8389i	0.188363	−	0.911549i
$266$	3.69333	+	10.2490i	0.226452	+	0.628407i
$267$		0			0
$268$	7.07376	+	4.08404i	0.432099	+	0.249472i
$269$	−28.0807			−1.71211			−0.856055	−	0.516884i	$-0.827092\pi$
$269$	−28.0807			−1.71211			−0.856055	+	0.516884i	$0.827092\pi$
$270$		0			0
$271$		−	11.3996i		−	0.692475i	−0.938147	−	0.346237i	$-0.887459\pi$
$271$		−	11.3996i		−	0.692475i	0.938147	−	0.346237i	$-0.112541\pi$
$272$	−2.36292	−	1.36423i	−0.143273	−	0.0827188i
$273$		0			0
$274$	0.913329	+	1.58193i	0.0551762	+	0.0955681i
$275$	18.8859	+	25.3842i	1.13886	+	1.53073i
$276$		0			0
$277$	17.2040	+	9.93273i	1.03369	+	0.596800i	0.918039	−	0.396490i	$-0.129772\pi$
$277$	17.2040	+	9.93273i	1.03369	+	0.596800i	0.115649	+	0.993290i	$0.463105\pi$
$278$			17.5752i			1.05409i
$279$		0			0
$280$	4.65291	−	3.65383i	0.278064	−	0.218358i
$281$	9.44238	+	5.45156i	0.563285	+	0.325213i	0.754463	−	0.656343i	$-0.227897\pi$
$281$	9.44238	+	5.45156i	0.563285	+	0.325213i	−0.191178	+	0.981555i	$0.561231\pi$
$282$		0			0
$283$	−4.79927	−	8.31258i	−0.285287	−	0.494132i	0.687392	−	0.726287i	$-0.258756\pi$
$283$	−4.79927	−	8.31258i	−0.285287	−	0.494132i	−0.972679	+	0.232155i	$0.925422\pi$
$284$	−7.20400	+	4.15923i	−0.427479	+	0.246805i
$285$		0			0
$286$	25.0113	+	14.4403i	1.47895	+	0.853872i
$287$	−0.964399	+	5.36910i	−0.0569267	+	0.316928i
$288$		0			0
$289$	9.55547			0.562086
$290$	0.140876	+	0.425354i	0.00827251	+	0.0249777i
$291$		0			0
$292$	6.97252	+	12.0768i	0.408036	+	0.706739i
$293$	1.70013	−	0.981568i	0.0993224	−	0.0573438i	−0.449516	−	0.893272i	$-0.648404\pi$
$293$	1.70013	−	0.981568i	0.0993224	−	0.0573438i	0.548838	+	0.835928i	$0.315070\pi$
$294$		0			0
$295$	−2.61815	+	0.867122i	−0.152435	+	0.0504858i
$296$			10.4673i			0.608401i
$297$		0			0
$298$			6.07463i			0.351894i
$299$	−5.27692	+	9.13990i	−0.305172	+	0.528574i
$300$		0			0
$301$	−7.52082	−	20.8703i	−0.433493	−	1.20295i
$302$	8.97909	+	15.5522i	0.516689	+	0.894931i
$303$		0			0
$304$	−3.56595	−	2.05880i	−0.204521	−	0.118080i
$305$	−2.85945	+	3.21216i	−0.163731	+	0.183928i
$306$		0			0
$307$	3.13370			0.178850			0.0894248	−	0.995994i	$-0.471497\pi$
$307$	3.13370			0.178850			0.0894248	+	0.995994i	$0.471497\pi$
$308$	−10.8024	+	12.7906i	−0.615521	+	0.728812i
$309$		0			0
$310$	5.33455	+	1.10234i	0.302982	+	0.0626085i
$311$	−9.01232	−	15.6098i	−0.511042	−	0.885150i	−0.999918	−	0.0127972i	$-0.995926\pi$
$311$	−9.01232	−	15.6098i	−0.511042	−	0.885150i	0.488876	−	0.872353i	$-0.337407\pi$
$312$		0			0
$313$	−2.49357	+	4.31899i	−0.140945	+	0.244124i	−0.927853	−	0.372947i	$-0.878347\pi$
$313$	−2.49357	+	4.31899i	−0.140945	+	0.244124i	0.786908	+	0.617070i	$0.211681\pi$
$314$	−7.49132			−0.422759
$315$		0			0
$316$	−2.03383			−0.114412
$317$	−1.58024	+	2.73705i	−0.0887550	+	0.153728i	−0.906985	−	0.421163i	$-0.861622\pi$
$317$	−1.58024	+	2.73705i	−0.0887550	+	0.153728i	0.818230	+	0.574891i	$0.194955\pi$
$318$		0			0
$319$	−0.634004	−	1.09813i	−0.0354974	−	0.0614833i
$320$	−0.452503	+	2.18980i	−0.0252957	+	0.122414i
$321$		0			0
$322$	−4.67408	−	3.94751i	−0.260476	−	0.219986i
$323$	−11.2348			−0.625119
$324$		0			0
$325$	2.64243	+	22.6668i	0.146575	+	1.25733i
$326$	−0.187677	−	0.108355i	−0.0103945	−	0.00600124i
$327$		0			0
$328$	−1.03090	−	1.78558i	−0.0569221	−	0.0985920i
$329$	−8.14091	−	22.5911i	−0.448823	−	1.24549i
$330$		0			0
$331$	13.7475	−	23.8113i	0.755630	−	1.30879i	−0.189431	−	0.981894i	$-0.560664\pi$
$331$	13.7475	−	23.8113i	0.755630	−	1.30879i	0.945061	−	0.326895i	$-0.106002\pi$
$332$			4.20797i			0.230942i
$333$		0			0
$334$		−	7.61617i		−	0.416739i
$335$	−5.74235	−	17.3382i	−0.313738	−	0.947287i
$336$		0			0
$337$	1.95439	−	1.12837i	0.106462	−	0.0614661i	−0.445823	−	0.895121i	$-0.647089\pi$
$337$	1.95439	−	1.12837i	0.106462	−	0.0614661i	0.552286	+	0.833655i	$0.313756\pi$
$338$	3.91530	+	6.78149i	0.212964	+	0.368864i
$339$		0			0
$340$	1.91817	+	5.79166i	0.104028	+	0.314097i
$341$	−15.4151			−0.834777
$342$		0			0
$343$	−9.41329	+	15.9496i	−0.508270	+	0.861198i
$344$	7.26144	+	4.19239i	0.391511	+	0.226039i
$345$		0			0
$346$	6.39337	−	3.69121i	0.343709	−	0.198441i
$347$	−9.66391	−	16.7384i	−0.518786	−	0.898563i	−0.999762	−	0.0218295i	$-0.993051\pi$
$347$	−9.66391	−	16.7384i	−0.518786	−	0.898563i	0.480976	−	0.876734i	$-0.340282\pi$
$348$		0			0
$349$	−25.1498	−	14.5202i	−1.34624	−	0.777250i	−0.358523	−	0.933521i	$-0.616719\pi$
$349$	−25.1498	−	14.5202i	−1.34624	−	0.777250i	−0.987714	+	0.156271i	$0.950053\pi$
$350$	−13.2036	−	0.815323i	−0.705763	−	0.0435809i
$351$		0			0
$352$		−	6.32783i		−	0.337275i
$353$	18.9251	+	10.9264i	1.00728	+	0.581554i	0.910394	−	0.413742i	$-0.135778\pi$
$353$	18.9251	+	10.9264i	1.00728	+	0.581554i	0.0968865	+	0.995295i	$0.469112\pi$
$354$		0			0
$355$	18.2158	+	3.76413i	0.966794	+	0.199779i
$356$	4.74358	+	8.21613i	0.251409	+	0.435454i
$357$		0			0
$358$	7.28359	+	4.20518i	0.384950	+	0.222251i
$359$			11.6743i			0.616144i	0.951363	+	0.308072i	$0.0996838\pi$
$359$			11.6743i			0.616144i	−0.951363	+	0.308072i	$0.900316\pi$
$360$		0			0
$361$	2.04531			0.107648
$362$	17.1900	+	9.92462i	0.903484	+	0.521627i
$363$		0			0
$364$	−11.3602	+	4.09377i	−0.595439	+	0.214572i
$365$	6.31017	−	30.5369i	0.330289	−	1.59837i
$366$		0			0
$367$	1.49120	−	2.58283i	0.0778398	−	0.134822i	−0.824478	−	0.565894i	$-0.808531\pi$
$367$	1.49120	−	2.58283i	0.0778398	−	0.134822i	0.902318	+	0.431072i	$0.141864\pi$
$368$	2.31238			0.120541
$369$		0			0
$370$	15.5626	−	17.4823i	0.809062	−	0.908859i
$371$	−13.6973	−	11.5681i	−0.711126	−	0.600585i
$372$		0			0
$373$	5.10400	−	2.94680i	0.264275	−	0.152579i	−0.362008	−	0.932175i	$-0.617909\pi$
$373$	5.10400	−	2.94680i	0.264275	−	0.152579i	0.626283	+	0.779596i	$0.284575\pi$
$374$	−8.63265	−	14.9522i	−0.446383	−	0.773159i
$375$		0			0
$376$	7.86014	+	4.53806i	0.405356	+	0.234032i
$377$		−	0.914572i		−	0.0471028i
$378$		0			0
$379$	−15.0087			−0.770948			−0.385474	−	0.922719i	$-0.625962\pi$
$379$	−15.0087			−0.770948			−0.385474	+	0.922719i	$0.625962\pi$
$380$	2.89477	+	8.74035i	0.148499	+	0.448371i
$381$		0			0
$382$	−2.20596	+	1.27361i	−0.112867	+	0.0651637i
$383$	−1.74800	+	1.00921i	−0.0893184	+	0.0515680i	−0.543994	−	0.839089i	$-0.683089\pi$
$383$	−1.74800	+	1.00921i	−0.0893184	+	0.0515680i	0.454676	+	0.890657i	$0.349755\pi$
$384$		0			0
$385$	37.0586	−	5.30181i	1.88868	−	0.270205i
$386$		−	22.4391i		−	1.14212i
$387$		0			0
$388$	−4.85175			−0.246310
$389$	17.3287	+	10.0047i	0.878601	+	0.507260i	0.870197	−	0.492704i	$-0.163992\pi$
$389$	17.3287	+	10.0047i	0.878601	+	0.507260i	0.00840401	+	0.999965i	$0.497325\pi$
$390$		0			0
$391$	5.46398	−	3.15463i	0.276326	−	0.159537i
$392$	−1.17150	−	6.90127i	−0.0591698	−	0.348567i
$393$		0			0
$394$	−5.18359	+	8.97824i	−0.261145	+	0.452317i
$395$	3.39685	+	3.02386i	0.170914	+	0.152147i
$396$		0			0
$397$	−15.3842			−0.772110			−0.386055	−	0.922476i	$-0.626163\pi$
$397$	−15.3842			−0.772110			−0.386055	+	0.922476i	$0.626163\pi$
$398$	10.0030	+	5.77523i	0.501405	+	0.289486i
$399$		0			0
$400$	4.01152	−	2.98458i	0.200576	−	0.149229i
$401$	−5.76625	+	3.32914i	−0.287953	+	0.166250i	−0.637018	−	0.770849i	$-0.719832\pi$
$401$	−5.76625	+	3.32914i	−0.287953	+	0.166250i	0.349066	+	0.937098i	$0.386499\pi$
$402$		0			0
$403$	−9.62884	−	5.55921i	−0.479647	−	0.276924i
$404$	−17.2305			−0.857252
$405$		0			0
$406$	0.521820	+	0.0937294i	0.0258975	+	0.00465171i
$407$	−33.1177	+	57.3616i	−1.64159	+	2.84331i
$408$		0			0
$409$	11.3648	−	6.56146i	0.561952	−	0.324443i	−0.191976	−	0.981400i	$-0.561490\pi$
$409$	11.3648	−	6.56146i	0.561952	−	0.324443i	0.753929	+	0.656956i	$0.228156\pi$
$410$	−0.932973	+	4.51495i	−0.0460763	+	0.222978i
$411$		0			0
$412$	9.19697	−	15.9296i	0.453102	−	0.784796i
$413$	−0.576925	+	3.21192i	−0.0283886	+	0.158048i
$414$		0			0
$415$	6.25632	−	7.02804i	0.307111	−	0.344993i
$416$	2.28203	−	3.95259i	0.111886	−	0.193792i
$417$		0			0
$418$	−13.0278	−	22.5648i	−0.637209	−	1.10368i
$419$	13.6846	+	23.7023i	0.668534	+	1.15794i	0.978314	+	0.207127i	$0.0664113\pi$
$419$	13.6846	+	23.7023i	0.668534	+	1.15794i	−0.309780	+	0.950808i	$0.600255\pi$
$420$		0			0
$421$	−0.808320	+	1.40005i	−0.0393951	+	0.0682343i	−0.885051	−	0.465495i	$-0.845876\pi$
$421$	−0.808320	+	1.40005i	−0.0393951	+	0.0682343i	0.845656	+	0.533729i	$0.179210\pi$
$422$	−0.308153			−0.0150006
$423$		0			0
$424$	6.77638			0.329090
$425$	5.40724	−	12.5250i	0.262290	−	0.607551i
$426$		0			0
$427$	1.72507	+	4.78709i	0.0834822	+	0.231664i
$428$	−0.867271	−	1.50216i	−0.0419211	−	0.0726095i
$429$		0			0
$430$	−5.89470	−	17.7982i	−0.284268	−	0.858306i
$431$			6.18722i			0.298028i	0.988835	+	0.149014i	$0.0476099\pi$
$431$			6.18722i			0.298028i	−0.988835	+	0.149014i	$0.952390\pi$
$432$		0			0
$433$	−21.5398			−1.03514			−0.517568	−	0.855642i	$-0.673162\pi$
$433$	−21.5398			−1.03514			−0.517568	+	0.855642i	$0.673162\pi$
$434$	4.15868	−	4.92412i	0.199623	−	0.236365i
$435$		0			0
$436$	−0.200135	−	0.346643i	−0.00958471	−	0.0166012i
$437$	8.24585	−	4.76075i	0.394453	−	0.227737i
$438$		0			0
$439$	12.8703	+	7.43067i	0.614266	+	0.354646i	0.774633	−	0.632411i	$-0.217935\pi$
$439$	12.8703	+	7.43067i	0.614266	+	0.354646i	−0.160367	+	0.987057i	$0.551268\pi$
$440$	−9.40810	+	10.5686i	−0.448514	+	0.503838i
$441$		0			0
$442$		−	12.4529i		−	0.592323i
$443$	−2.05313	+	3.55613i	−0.0975472	+	0.168957i	−0.910669	−	0.413137i	$-0.864433\pi$
$443$	−2.05313	+	3.55613i	−0.0975472	+	0.168957i	0.813122	+	0.582094i	$0.197766\pi$
$444$		0			0
$445$	4.29297	−	20.7750i	0.203506	−	0.984831i
$446$	12.0678	+	20.9020i	0.571425	+	0.989738i
$447$		0			0
$448$	2.02132	+	1.70712i	0.0954986	+	0.0806537i
$449$		−	23.7106i		−	1.11897i	−0.828839	−	0.559487i	$-0.810998\pi$
$449$		−	23.7106i		−	1.11897i	0.828839	−	0.559487i	$-0.189002\pi$
$450$		0			0
$451$		−	13.0468i		−	0.614348i
$452$	−1.32959	+	2.30292i	−0.0625387	+	0.108320i
$453$		0			0
$454$	−8.32843	+	4.80842i	−0.390872	+	0.225670i
$455$	25.0601	+	10.0529i	1.17484	+	0.471286i
$456$		0			0
$457$	19.1410	+	11.0510i	0.895377	+	0.516946i	0.875698	−	0.482860i	$-0.160402\pi$
$457$	19.1410	+	11.0510i	0.895377	+	0.516946i	0.0196797	+	0.999806i	$0.493735\pi$
$458$		−	22.8383i		−	1.06716i
$459$		0			0
$460$	−3.86209	−	3.43801i	−0.180071	−	0.160298i
$461$	9.53685	−	16.5183i	0.444175	−	0.769334i	−0.553819	−	0.832637i	$-0.686830\pi$
$461$	9.53685	−	16.5183i	0.444175	−	0.769334i	0.997994	+	0.0633028i	$0.0201634\pi$
$462$		0			0
$463$	−22.9165	+	13.2308i	−1.06502	+	0.614889i	−0.926816	−	0.375515i	$-0.877466\pi$
$463$	−22.9165	+	13.2308i	−1.06502	+	0.614889i	−0.138203	+	0.990404i	$0.544133\pi$
$464$	−0.173539	+	0.100193i	−0.00805635	+	0.00465134i
$465$		0			0
$466$	12.0611	−	20.8904i	0.558718	−	0.967728i
$467$		−	25.0308i		−	1.15829i	−0.815225	−	0.579144i	$-0.803387\pi$
$467$		−	25.0308i		−	1.15829i	0.815225	−	0.579144i	$-0.196613\pi$
$468$		0			0
$469$	−21.2703	−	3.82057i	−0.982171	−	0.176418i
$470$	−6.38071	−	19.2657i	−0.294320	−	0.888658i
$471$		0			0
$472$	−0.616709	−	1.06817i	−0.0283864	−	0.0491666i
$473$	26.5288	+	45.9492i	1.21979	+	2.11275i
$474$		0			0
$475$	8.16021	−	18.9018i	0.374416	−	0.867274i
$476$	7.10514	+	1.27623i	0.325663	+	0.0584957i
$477$		0			0
$478$		−	15.8623i		−	0.725524i
$479$	−3.86939	+	6.70198i	−0.176797	+	0.306221i	−0.940782	−	0.339013i	$-0.889907\pi$
$479$	−3.86939	+	6.70198i	−0.176797	+	0.306221i	0.763985	+	0.645234i	$0.223240\pi$
$480$		0			0
$481$	−41.3730	+	23.8867i	−1.88645	+	1.08914i
$482$	−11.8605	+	6.84765i	−0.540230	+	0.311902i
$483$		0			0
$484$	14.5207	−	25.1507i	0.660034	−	1.14321i
$485$	8.10326	+	7.21348i	0.367950	+	0.327547i
$486$		0			0
$487$			5.56297i			0.252082i	0.992025	+	0.126041i	$0.0402271\pi$
$487$			5.56297i			0.252082i	−0.992025	+	0.126041i	$0.959773\pi$
$488$	−1.66558	−	0.961623i	−0.0753973	−	0.0435306i
$489$		0			0
$490$	−8.30407	+	13.2681i	−0.375140	+	0.599392i
$491$	7.49049	−	4.32464i	0.338041	−	0.195168i	−0.321364	−	0.946956i	$-0.604141\pi$
$491$	7.49049	−	4.32464i	0.338041	−	0.195168i	0.659405	+	0.751788i	$0.270808\pi$
$492$		0			0
$493$	−0.273373	+	0.473496i	−0.0123121	+	0.0213252i
$494$		−	18.7930i		−	0.845536i
$495$		0			0
$496$			2.43609i			0.109383i
$497$	14.2006	−	16.8143i	0.636983	−	0.754225i
$498$		0			0
$499$	9.61871	+	16.6601i	0.430592	+	0.745808i	0.996924	−	0.0783693i	$-0.0249713\pi$
$499$	9.61871	+	16.6601i	0.430592	+	0.745808i	−0.566332	+	0.824177i	$0.691638\pi$
$500$	−11.1374	−	0.979477i	−0.498078	−	0.0438035i
$501$		0			0
$502$	−12.0822	+	20.9270i	−0.539256	+	0.934019i
$503$			24.3743i			1.08680i	0.839475	+	0.543398i	$0.182863\pi$
$503$			24.3743i			1.08680i	−0.839475	+	0.543398i	$0.817137\pi$
$504$		0			0
$505$	28.7780	+	25.6181i	1.28061	+	1.13999i
$506$	12.6720	+	7.31619i	0.563340	+	0.325244i
$507$		0			0
$508$	−0.827895	+	0.477985i	−0.0367319	+	0.0212072i
$509$	11.0101	+	19.0700i	0.488013	+	0.845264i	0.999905	−	0.0137860i	$-0.00438835\pi$
$509$	11.0101	+	19.0700i	0.488013	+	0.845264i	−0.511891	+	0.859050i	$0.671055\pi$
$510$		0			0
$511$	−28.1874	−	23.8058i	−1.24694	−	1.05311i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$			8.51521i			0.375590i
$515$	−39.0444	+	12.9314i	−1.72050	+	0.569824i
$516$		0			0
$517$	28.7161	+	49.7377i	1.26293	+	2.18746i
$518$	−9.38877	−	26.0539i	−0.412519	−	1.14474i
$519$		0			0
$520$	−9.68801	+	3.20863i	−0.424848	+	0.140708i
$521$	23.9844			1.05078			0.525388	−	0.850863i	$-0.323920\pi$
$521$	23.9844			1.05078			0.525388	+	0.850863i	$0.323920\pi$
$522$		0			0
$523$	−23.3213			−1.01977			−0.509885	−	0.860242i	$-0.670312\pi$
$523$	−23.3213			−1.01977			−0.509885	+	0.860242i	$0.670312\pi$
$524$	5.64033	−	9.76935i	0.246399	−	0.426776i
$525$		0			0
$526$	−9.99743	−	17.3161i	−0.435909	−	0.755016i
$527$	3.32339	+	5.75628i	0.144769	+	0.250747i
$528$		0			0
$529$	8.82644	−	15.2878i	0.383758	−	0.664689i
$530$	−11.3177	−	10.0750i	−0.491611	−	0.437630i
$531$		0			0
$532$	10.7226	+	1.92599i	0.464882	+	0.0835022i
$533$	4.70510	−	8.14947i	0.203800	−	0.352993i
$534$		0			0
$535$	−0.784886	+	3.79831i	−0.0339336	+	0.164215i
$536$	7.07376	−	4.08404i	0.305540	−	0.176404i
$537$		0			0
$538$	−14.0404	+	24.3186i	−0.605323	+	1.04845i
$539$	15.4151	−	41.5260i	0.663977	−	1.78865i
$540$		0			0
$541$	29.4801			1.26745			0.633723	−	0.773560i	$-0.281526\pi$
$541$	29.4801			1.26745			0.633723	+	0.773560i	$0.281526\pi$
$542$	−9.87232	−	5.69979i	−0.424052	−	0.244827i
$543$		0			0
$544$	−2.36292	+	1.36423i	−0.101309	+	0.0584910i
$545$	−0.181123	+	0.876511i	−0.00775845	+	0.0375456i
$546$		0			0
$547$	−25.2017	−	14.5502i	−1.07755	−	0.622121i	−0.147313	−	0.989090i	$-0.547062\pi$
$547$	−25.2017	−	14.5502i	−1.07755	−	0.622121i	−0.930233	+	0.366969i	$0.880396\pi$
$548$	1.82666			0.0780310
$549$		0			0
$550$	31.4263	−	3.66359i	1.34002	−	0.156216i
$551$	−0.412555	+	0.714566i	−0.0175754	+	0.0304415i
$552$		0			0
$553$	5.06234	−	1.82426i	0.215272	−	0.0775755i
$554$	17.2040	−	9.93273i	0.730928	−	0.422001i
$555$		0			0
$556$	15.2206	+	8.78760i	0.645496	+	0.372677i
$557$	11.3404			0.480509			0.240255	−	0.970710i	$-0.422769\pi$
$557$	11.3404			0.480509			0.240255	+	0.970710i	$0.422769\pi$
$558$		0			0
$559$			38.2686i			1.61859i
$560$	−0.837855	−	5.85645i	−0.0354058	−	0.247480i
$561$		0			0
$562$	9.44238	−	5.45156i	0.398303	−	0.229960i
$563$	12.0632	−	6.96467i	0.508402	−	0.293526i	−0.223775	−	0.974641i	$-0.571838\pi$
$563$	12.0632	−	6.96467i	0.508402	−	0.293526i	0.732176	+	0.681115i	$0.238505\pi$
$564$		0			0
$565$	5.64459	−	1.86947i	0.237470	−	0.0786490i
$566$	−9.59854			−0.403457
$567$		0			0
$568$			8.31846i			0.349035i
$569$	24.0673	+	13.8953i	1.00895	+	0.582519i	0.910885	−	0.412660i	$-0.135400\pi$
$569$	24.0673	+	13.8953i	1.00895	+	0.582519i	0.0980680	+	0.995180i	$0.468734\pi$
$570$		0			0
$571$	−17.6064	−	30.4952i	−0.736806	−	1.27619i	−0.953926	−	0.300041i	$-0.903000\pi$
$571$	−17.6064	−	30.4952i	−0.736806	−	1.27619i	0.217120	−	0.976145i	$-0.430334\pi$
$572$	25.0113	−	14.4403i	1.04578	−	0.603779i
$573$		0			0
$574$	4.16758	+	3.51974i	0.173951	+	0.146911i
$575$	1.33879	+	11.4842i	0.0558313	+	0.478922i
$576$		0			0
$577$	−3.29407			−0.137134			−0.0685670	−	0.997647i	$-0.521843\pi$
$577$	−3.29407			−0.137134			−0.0685670	+	0.997647i	$0.521843\pi$
$578$	4.77773	−	8.27528i	0.198727	−	0.344206i
$579$		0			0
$580$	0.438806	+	0.0906752i	0.0182204	+	0.00376508i
$581$	−3.77438	−	10.4739i	−0.156588	−	0.434531i
$582$		0			0
$583$	37.1350	+	21.4399i	1.53798	+	0.887950i
$584$	13.9450			0.577050
$585$		0			0
$586$		−	1.96314i		−	0.0810964i
$587$	24.4065	+	14.0911i	1.00736	+	0.581602i	0.910419	−	0.413687i	$-0.135759\pi$
$587$	24.4065	+	14.0911i	1.00736	+	0.581602i	0.0969457	+	0.995290i	$0.469093\pi$
$588$		0			0
$589$	5.01542	+	8.68696i	0.206657	+	0.357940i
$590$	−0.558126	+	2.70095i	−0.0229777	+	0.111196i
$591$		0			0
$592$	9.06497	+	5.23366i	0.372568	+	0.215102i
$593$			36.9570i			1.51764i	0.651298	+	0.758822i	$0.274225\pi$
$593$			36.9570i			1.51764i	−0.651298	+	0.758822i	$0.725775\pi$
$594$		0			0
$595$	−9.96935	−	12.6953i	−0.408704	−	0.520457i
$596$	5.26078	+	3.03731i	0.215490	+	0.124413i
$597$		0			0
$598$	5.27692	+	9.13990i	0.215789	+	0.373758i
$599$	−31.2435	+	18.0385i	−1.27658	+	0.737032i	−0.976217	−	0.216794i	$-0.930440\pi$
$599$	−31.2435	+	18.0385i	−1.27658	+	0.737032i	−0.300359	+	0.953826i	$0.597107\pi$
$600$		0			0
$601$	−37.1333	−	21.4389i	−1.51470	−	0.874513i	−0.999852	−	0.0172319i	$-0.994515\pi$
$601$	−37.1333	−	21.4389i	−1.51470	−	0.874513i	−0.514849	−	0.857281i	$-0.672152\pi$
$602$	−21.8346	−	3.92194i	−0.889913	−	0.159846i
$603$		0			0
$604$	17.9582			0.730708
$605$	−61.6457	+	20.4168i	−2.50625	+	0.830062i
$606$		0			0
$607$	−9.71483	−	16.8266i	−0.394313	−	0.682970i	0.598700	−	0.800973i	$-0.295684\pi$
$607$	−9.71483	−	16.8266i	−0.394313	−	0.682970i	−0.993013	+	0.118003i	$0.962351\pi$
$608$	−3.56595	+	2.05880i	−0.144618	+	0.0834955i
$609$		0			0
$610$	1.35209	+	4.08243i	0.0547444	+	0.165293i
$611$			41.4239i			1.67583i
$612$		0			0
$613$		−	32.1273i		−	1.29761i	−0.760955	−	0.648805i	$-0.775269\pi$
$613$		−	32.1273i		−	1.29761i	0.760955	−	0.648805i	$-0.224731\pi$
$614$	1.56685	−	2.71386i	0.0632329	−	0.109523i
$615$		0			0
$616$	5.67581	+	15.7504i	0.228685	+	0.634602i
$617$	−8.54944	−	14.8081i	−0.344187	−	0.596150i	0.641018	−	0.767526i	$-0.278512\pi$
$617$	−8.54944	−	14.8081i	−0.344187	−	0.596150i	−0.985206	+	0.171375i	$0.945179\pi$
$618$		0			0
$619$	−16.4455	−	9.49482i	−0.661001	−	0.381629i	0.131657	−	0.991295i	$-0.457970\pi$
$619$	−16.4455	−	9.49482i	−0.661001	−	0.381629i	−0.792658	+	0.609666i	$0.791303\pi$
$620$	3.62193	−	4.06869i	0.145460	−	0.163402i
$621$		0			0
$622$	−18.0246			−0.722722
$623$	−19.1766	−	16.1957i	−0.768296	−	0.648867i
$624$		0			0
$625$	17.1451	+	18.1947i	0.685802	+	0.727788i
$626$	2.49357	+	4.31899i	0.0996630	+	0.172621i
$627$		0			0
$628$	−3.74566	+	6.48767i	−0.149468	+	0.258886i
$629$	28.5597			1.13875
$630$		0			0
$631$	−32.7042			−1.30193			−0.650967	−	0.759106i	$-0.725636\pi$
$631$	−32.7042			−1.30193			−0.650967	+	0.759106i	$0.725636\pi$
$632$	−1.01691	+	1.76135i	−0.0404507	+	0.0700626i
$633$		0			0
$634$	1.58024	+	2.73705i	0.0627593	+	0.108702i
$635$	2.09339	+	0.432579i	0.0830736	+	0.0171664i
$636$		0			0
$637$	24.6045	−	20.3794i	0.974865	−	0.807460i
$638$	−1.26801			−0.0502009
$639$		0			0
$640$	1.67017	+	1.48678i	0.0660194	+	0.0587702i
$641$	30.0032	+	17.3224i	1.18506	+	0.684193i	0.957179	−	0.289497i	$-0.0934881\pi$
$641$	30.0032	+	17.3224i	1.18506	+	0.684193i	0.227877	+	0.973690i	$0.426821\pi$
$642$		0			0
$643$	4.50753	+	7.80727i	0.177760	+	0.307889i	0.941113	−	0.338093i	$-0.109782\pi$
$643$	4.50753	+	7.80727i	0.177760	+	0.307889i	−0.763353	+	0.645981i	$0.776448\pi$
$644$	−5.75568	+	2.07412i	−0.226806	+	0.0817316i
$645$		0			0
$646$	−5.61738	+	9.72958i	−0.221013	+	0.382805i
$647$		−	19.3322i		−	0.760028i	−0.924981	−	0.380014i	$-0.875919\pi$
$647$		−	19.3322i		−	0.760028i	0.924981	−	0.380014i	$-0.124081\pi$
$648$		0			0
$649$		−	7.80487i		−	0.306368i
$650$	20.9512	+	9.04498i	0.821774	+	0.354773i
$651$		0			0
$652$	−0.187677	+	0.108355i	−0.00734999	+	0.00424352i
$653$	0.172113	+	0.298108i	0.00673529	+	0.0116659i	0.869373	−	0.494156i	$-0.164523\pi$
$653$	0.172113	+	0.298108i	0.00673529	+	0.0116659i	−0.862638	+	0.505822i	$0.831189\pi$
$654$		0			0
$655$	−23.9452	+	7.93057i	−0.935617	+	0.309873i
$656$	−2.06181			−0.0805000
$657$		0			0
$658$	−23.6349	−	4.24530i	−0.921384	−	0.165499i
$659$	−32.8621	−	18.9730i	−1.28013	−	0.739082i	−0.303256	−	0.952909i	$-0.598074\pi$
$659$	−32.8621	−	18.9730i	−1.28013	−	0.739082i	−0.976871	+	0.213828i	$0.931407\pi$
$660$		0			0
$661$	32.3820	−	18.6958i	1.25952	−	0.727182i	0.286535	−	0.958070i	$-0.407497\pi$
$661$	32.3820	−	18.6958i	1.25952	−	0.727182i	0.972980	+	0.230888i	$0.0741632\pi$
$662$	−13.7475	−	23.8113i	−0.534311	−	0.925454i
$663$		0			0
$664$	3.64421	+	2.10398i	0.141423	+	0.0816504i
$665$	−15.0450	−	19.1588i	−0.583421	−	0.742948i
$666$		0			0
$667$		−	0.463369i		−	0.0179417i
$668$	−6.59580	−	3.80809i	−0.255199	−	0.147339i
$669$		0			0
$670$	−17.8865	−	3.69608i	−0.691015	−	0.142792i
$671$	−6.08499	−	10.5395i	−0.234909	−	0.406873i
$672$		0			0
$673$	−7.53903	−	4.35266i	−0.290608	−	0.167783i	0.347608	−	0.937640i	$-0.386994\pi$
$673$	−7.53903	−	4.35266i	−0.290608	−	0.167783i	−0.638216	+	0.769857i	$0.720327\pi$
$674$		−	2.25674i		−	0.0869262i
$675$		0			0
$676$	7.83059			0.301177
$677$	−14.8248	−	8.55913i	−0.569765	−	0.328954i	0.187291	−	0.982305i	$-0.440029\pi$
$677$	−14.8248	−	8.55913i	−0.569765	−	0.328954i	−0.757055	+	0.653351i	$0.773363\pi$
$678$		0			0
$679$	12.0763	−	4.35182i	0.463447	−	0.167008i
$680$	5.97481	+	1.23464i	0.229123	+	0.0473463i
$681$		0			0
$682$	−7.70757	+	13.3499i	−0.295138	+	0.511194i
$683$	−42.3497			−1.62046			−0.810232	−	0.586109i	$-0.800659\pi$
$683$	−42.3497			−1.62046			−0.810232	+	0.586109i	$0.800659\pi$
$684$		0			0
$685$	−3.05084	−	2.71584i	−0.116567	−	0.103767i
$686$	9.10612	+	16.1270i	0.347673	+	0.615730i
$687$		0			0
$688$	7.26144	−	4.19239i	0.276840	−	0.159834i
$689$	15.4639	+	26.7842i	0.589127	+	1.02040i
$690$		0			0
$691$	−6.66895	−	3.85032i	−0.253699	−	0.146473i	0.367758	−	0.929922i	$-0.380125\pi$
$691$	−6.66895	−	3.85032i	−0.253699	−	0.146473i	−0.621457	+	0.783449i	$0.713459\pi$
$692$		−	7.38242i		−	0.280638i
$693$		0			0
$694$	−19.3278			−0.733674
$695$	−12.3558	−	37.3065i	−0.468681	−	1.41512i
$696$		0			0
$697$	−4.87189	+	2.81279i	−0.184536	+	0.106542i
$698$	−25.1498	+	14.5202i	−0.951933	+	0.549599i
$699$		0			0
$700$	−7.30789	+	11.0270i	−0.276212	+	0.416781i
$701$			28.9809i			1.09459i	0.836939	+	0.547297i	$0.184343\pi$
$701$			28.9809i			1.09459i	−0.836939	+	0.547297i	$0.815657\pi$
$702$		0			0
$703$	43.1003			1.62556
$704$	−5.48007	−	3.16392i	−0.206538	−	0.119245i
$705$		0			0
$706$	18.9251	−	10.9264i	0.712255	−	0.411221i
$707$	42.8880	−	15.4551i	1.61297	−	0.581249i
$708$		0			0
$709$	−3.82844	+	6.63105i	−0.143780	+	0.249034i	−0.928917	−	0.370288i	$-0.879259\pi$
$709$	−3.82844	+	6.63105i	−0.143780	+	0.249034i	0.785137	+	0.619322i	$0.212592\pi$
$710$	12.3677	−	13.8933i	0.464153	−	0.521405i
$711$		0			0
$712$	9.48716			0.355547
$713$	−4.87847	−	2.81658i	−0.182700	−	0.105482i
$714$		0			0
$715$	−63.2428	−	13.0685i	−2.36515	−	0.488736i
$716$	7.28359	−	4.20518i	0.272201	−	0.157155i
$717$		0			0
$718$	10.1102	+	5.83713i	0.377310	+	0.217840i
$719$	3.74789			0.139773			0.0698863	−	0.997555i	$-0.477736\pi$
$719$	3.74789			0.139773			0.0698863	+	0.997555i	$0.477736\pi$
$720$		0			0
$721$	−8.60366	+	47.8992i	−0.320417	+	1.78386i
$722$	1.02266	−	1.77129i	0.0380593	−	0.0659207i
$723$		0			0
$724$	17.1900	−	9.92462i	0.638860	−	0.368846i
$725$	−0.598068	−	0.803851i	−0.0222117	−	0.0298543i
$726$		0			0
$727$	−7.99237	+	13.8432i	−0.296420	+	0.513415i	−0.975314	−	0.220821i	$-0.929126\pi$
$727$	−7.99237	+	13.8432i	−0.296420	+	0.513415i	0.678894	+	0.734236i	$0.262460\pi$
$728$	−2.13481	+	11.8851i	−0.0791214	+	0.440493i
$729$		0			0
$730$	−23.2906	−	20.7332i	−0.862025	−	0.767371i
$731$	11.4388	−	19.8126i	0.423080	−	0.732796i
$732$		0			0
$733$	17.2764	+	29.9236i	0.638118	+	1.10525i	0.985845	+	0.167657i	$0.0536201\pi$
$733$	17.2764	+	29.9236i	0.638118	+	1.10525i	−0.347728	+	0.937596i	$0.613047\pi$
$734$	−1.49120	−	2.58283i	−0.0550410	−	0.0953339i
$735$		0			0
$736$	1.15619	−	2.00258i	0.0426178	−	0.0738162i
$737$	51.6863			1.90389
$738$		0			0
$739$	−2.42908			−0.0893552			−0.0446776	−	0.999001i	$-0.514226\pi$
$739$	−2.42908			−0.0893552			−0.0446776	+	0.999001i	$0.514226\pi$
$740$	−7.35877	−	22.2187i	−0.270514	−	0.816777i
$741$		0			0
$742$	−16.8669	+	6.07814i	−0.619203	+	0.223136i
$743$	7.44072	+	12.8877i	0.272973	+	0.472804i	0.969622	−	0.244609i	$-0.0786595\pi$
$743$	7.44072	+	12.8877i	0.272973	+	0.472804i	−0.696648	+	0.717413i	$0.745326\pi$
$744$		0			0
$745$	−4.27060	−	12.8945i	−0.156463	−	0.472417i
$746$		−	5.89359i		−	0.215780i
$747$		0			0
$748$	−17.2653			−0.631282
$749$	3.50607	+	2.96107i	0.128109	+	0.108195i
$750$		0			0
$751$	−2.50116	−	4.33213i	−0.0912685	−	0.158082i	0.816777	−	0.576954i	$-0.195759\pi$
$751$	−2.50116	−	4.33213i	−0.0912685	−	0.158082i	−0.908045	+	0.418872i	$0.862425\pi$
$752$	7.86014	−	4.53806i	0.286630	−	0.165486i
$753$		0			0
$754$	−0.792042	−	0.457286i	−0.0288445	−	0.0166534i
$755$	−29.9933	−	26.6999i	−1.09157	−	0.971708i
$756$		0			0
$757$		−	23.0241i		−	0.836826i	−0.908257	−	0.418413i	$-0.862586\pi$
$757$		−	23.0241i		−	0.836826i	0.908257	−	0.418413i	$-0.137414\pi$
$758$	−7.50437	+	12.9980i	−0.272571	+	0.472107i
$759$		0			0
$760$	9.01675	+	1.86323i	0.327072	+	0.0675864i
$761$	−10.4160	−	18.0411i	−0.377580	−	0.653988i	0.613129	−	0.789983i	$-0.289910\pi$
$761$	−10.4160	−	18.0411i	−0.377580	−	0.653988i	−0.990710	+	0.135994i	$0.956577\pi$
$762$		0			0
$763$	0.809074	+	0.683306i	0.0292904	+	0.0247373i
$764$			2.54722i			0.0921553i
$765$		0			0
$766$			2.01841i			0.0729282i
$767$	2.81470	−	4.87520i	0.101633	−	0.176033i
$768$		0			0
$769$	24.3363	−	14.0506i	0.877590	−	0.506677i	0.00772702	−	0.999970i	$-0.497540\pi$
$769$	24.3363	−	14.0506i	0.877590	−	0.506677i	0.869863	+	0.493293i	$0.164207\pi$
$770$	13.9378	−	34.7446i	0.502284	−	1.25211i
$771$		0			0
$772$	−19.4328	−	11.2196i	−0.699403	−	0.403801i
$773$			30.5269i			1.09798i	0.835830	+	0.548989i	$0.184987\pi$
$773$			30.5269i			1.09798i	−0.835830	+	0.548989i	$0.815013\pi$
$774$		0			0
$775$	−12.0985	+	1.41041i	−0.434591	+	0.0506633i
$776$	−2.42587	+	4.20173i	−0.0870838	+	0.150833i
$777$		0			0
$778$	17.3287	−	10.0047i	0.621265	−	0.358687i
$779$	−7.35230	+	4.24485i	−0.263424	+	0.152088i
$780$		0			0
$781$	−26.3189	+	45.5857i	−0.941765	+	1.63118i
$782$		−	6.30927i		−	0.225619i
$783$		0			0
$784$	−6.56243	−	2.43609i	−0.234373	−	0.0870031i
$785$	15.9016	−	5.26657i	0.567554	−	0.187972i
$786$		0			0
$787$	−10.7974	−	18.7017i	−0.384887	−	0.666644i	0.606867	−	0.794804i	$-0.292426\pi$
$787$	−10.7974	−	18.7017i	−0.384887	−	0.666644i	−0.991754	+	0.128160i	$0.959093\pi$
$788$	5.18359	+	8.97824i	0.184658	+	0.319837i
$789$		0			0
$790$	4.31716	−	1.42983i	0.153598	−	0.0508710i
$791$	1.24382	−	6.92471i	0.0442251	−	0.246215i
$792$		0			0
$793$		−	8.77780i		−	0.311709i
$794$	−7.69209	+	13.3231i	−0.272982	+	0.472819i
$795$		0			0
$796$	10.0030	−	5.77523i	0.354547	−	0.204698i
$797$	−34.2994	+	19.8028i	−1.21495	+	0.701450i	−0.963833	−	0.266507i	$-0.914130\pi$
$797$	−34.2994	+	19.8028i	−1.21495	+	0.701450i	−0.251114	+	0.967957i	$0.580797\pi$
$798$		0			0
$799$	12.3819	−	21.4461i	0.438041	−	0.758710i
$800$	−0.578965	−	4.96637i	−0.0204695	−	0.175588i
$801$		0			0
$802$			6.65829i			0.235112i
$803$	76.4197	+	44.1209i	2.69679	+	1.55699i
$804$		0			0
$805$	12.6968	+	5.09331i	0.447502	+	0.179516i
$806$	−9.62884	+	5.55921i	−0.339161	+	0.195815i
$807$		0			0
$808$	−8.61527	+	14.9221i	−0.303084	+	0.524957i
$809$			7.18884i			0.252746i	0.991983	+	0.126373i	$0.0403337\pi$
$809$			7.18884i			0.252746i	−0.991983	+	0.126373i	$0.959666\pi$
$810$		0			0
$811$			0.343005i			0.0120445i	0.999982	+	0.00602227i	$0.00191696\pi$
$811$			0.343005i			0.0120445i	−0.999982	+	0.00602227i	$0.998083\pi$
$812$	0.342082	−	0.405045i	0.0120047	−	0.0142143i
$813$		0			0
$814$	33.1177	+	57.3616i	1.16078	+	2.01052i
$815$	0.474554	+	0.0980622i	0.0166229	+	0.00343497i
$816$		0			0
$817$	17.2626	−	29.8998i	0.603943	−	1.04606i
$818$		−	13.1229i		−	0.458832i
$819$		0			0
$820$	3.44358	+	3.06545i	0.120255	+	0.107050i
$821$	−33.2366	−	19.1892i	−1.15997	−	0.669707i	−0.208670	−	0.977986i	$-0.566913\pi$
$821$	−33.2366	−	19.1892i	−1.15997	−	0.669707i	−0.951296	+	0.308279i	$0.900247\pi$
$822$		0			0
$823$	−16.0577	+	9.27092i	−0.559737	+	0.323164i	−0.753040	−	0.657975i	$-0.771413\pi$
$823$	−16.0577	+	9.27092i	−0.559737	+	0.323164i	0.193303	+	0.981139i	$0.438080\pi$
$824$	−9.19697	−	15.9296i	−0.320392	−	0.554934i
$825$		0			0
$826$	2.49314	+	2.10559i	0.0867474	+	0.0732629i
$827$	26.9688			0.937797			0.468899	−	0.883252i	$-0.344651\pi$
$827$	26.9688			0.937797			0.468899	+	0.883252i	$0.344651\pi$
$828$		0			0
$829$		−	12.5804i		−	0.436937i	−0.975844	−	0.218468i	$-0.929894\pi$
$829$		−	12.5804i		−	0.436937i	0.975844	−	0.218468i	$-0.0701061\pi$
$830$	−2.95830	−	8.93215i	−0.102684	−	0.310040i
$831$		0			0
$832$	−2.28203	−	3.95259i	−0.0791151	−	0.137031i
$833$	−18.8299	+	3.19641i	−0.652417	+	0.110749i
$834$		0			0
$835$	5.35435	+	16.1667i	0.185295	+	0.559471i
$836$	−26.0555			−0.901150
$837$		0			0
$838$	27.3691			0.945450
$839$	−24.8006	+	42.9559i	−0.856213	+	1.48300i	0.0193027	+	0.999814i	$0.493855\pi$
$839$	−24.8006	+	42.9559i	−0.856213	+	1.48300i	−0.875515	+	0.483190i	$0.839478\pi$
$840$		0			0
$841$	−14.4799	−	25.0800i	−0.499308	−	0.864826i
$842$	0.808320	+	1.40005i	0.0278565	+	0.0482489i
$843$		0			0
$844$	−0.154076	+	0.266868i	−0.00530353	+	0.00918598i
$845$	−13.0785	−	11.6424i	−0.449912	−	0.400510i
$846$		0			0
$847$	−13.5840	+	75.6263i	−0.466752	+	2.59855i
$848$	3.38819	−	5.86852i	0.116351	−	0.201526i
$849$		0			0
$850$	−8.14333	−	10.9453i	−0.279314	−	0.375421i
$851$	−20.9617	+	12.1022i	−0.718558	+	0.414859i
$852$		0			0
$853$	9.04430	−	15.6652i	0.309671	−	0.536366i	−0.668619	−	0.743605i	$-0.733114\pi$
$853$	9.04430	−	15.6652i	0.309671	−	0.536366i	0.978290	+	0.207239i	$0.0664478\pi$
$854$	5.00828	+	0.899588i	0.171380	+	0.0307833i
$855$		0			0
$856$	−1.73454			−0.0592854
$857$	−18.2726	−	10.5497i	−0.624179	−	0.360370i	0.154315	−	0.988022i	$-0.450683\pi$
$857$	−18.2726	−	10.5497i	−0.624179	−	0.360370i	−0.778494	+	0.627652i	$0.784016\pi$
$858$		0			0
$859$	−21.7021	+	12.5297i	−0.740466	+	0.427508i	−0.822239	−	0.569143i	$-0.807275\pi$
$859$	−21.7021	+	12.5297i	−0.740466	+	0.427508i	0.0817725	+	0.996651i	$0.473942\pi$
$860$	−18.3610	−	3.79414i	−0.626106	−	0.129379i
$861$		0			0
$862$	5.35829	+	3.09361i	0.182504	+	0.105369i
$863$	36.1751			1.23141			0.615707	−	0.787975i	$-0.288870\pi$
$863$	36.1751			1.23141			0.615707	+	0.787975i	$0.288870\pi$
$864$		0			0
$865$	−10.9760	+	12.3299i	−0.373197	+	0.419230i
$866$	−10.7699	+	18.6540i	−0.365976	+	0.633889i
$867$		0			0
$868$	−2.18507	−	6.06358i	−0.0741661	−	0.205811i
$869$	−11.1455	+	6.43486i	−0.378085	+	0.218288i
$870$		0			0
$871$	32.2850	+	18.6398i	1.09394	+	0.631585i
$872$	−0.400269			−0.0135548
$873$		0			0
$874$		−	9.52149i		−	0.322069i
$875$	28.6002	−	7.55177i	0.966863	−	0.255296i
$876$		0			0
$877$	24.8553	−	14.3502i	0.839302	−	0.484571i	−0.0177247	−	0.999843i	$-0.505642\pi$
$877$	24.8553	−	14.3502i	0.839302	−	0.484571i	0.857027	+	0.515271i	$0.172309\pi$
$878$	12.8703	−	7.43067i	0.434351	−	0.250773i
$879$		0			0
$880$	4.44861	+	13.4320i	0.149963	+	0.452791i
$881$	13.5132			0.455271			0.227636	−	0.973746i	$-0.426901\pi$
$881$	13.5132			0.455271			0.227636	+	0.973746i	$0.426901\pi$
$882$		0			0
$883$			28.0874i			0.945218i	0.881272	+	0.472609i	$0.156688\pi$
$883$			28.0874i			0.945218i	−0.881272	+	0.472609i	$0.843312\pi$
$884$	−10.7845	−	6.22644i	−0.362722	−	0.209418i
$885$		0			0
$886$	2.05313	+	3.55613i	0.0689763	+	0.119470i
$887$	−25.4215	+	14.6771i	−0.853569	+	0.492809i	−0.861854	−	0.507157i	$-0.830696\pi$
$887$	−25.4215	+	14.6771i	−0.853569	+	0.492809i	0.00828416	+	0.999966i	$0.497363\pi$
$888$		0			0
$889$	1.63195	−	1.93233i	0.0547340	−	0.0648081i
$890$	−15.8452	−	14.1053i	−0.531133	−	0.472812i
$891$		0			0
$892$	24.1355			0.808118
$893$	18.6859	−	32.3650i	0.625301	−	1.08305i
$894$		0			0
$895$	−18.4171	−	3.80572i	−0.615614	−	0.127211i
$896$	2.48907	−	0.896960i	0.0831540	−	0.0299653i
$897$		0			0
$898$	−20.5340	−	11.8553i	−0.685229	−	0.395617i
$899$	0.488157			0.0162809
$900$		0			0
$901$		−	18.4891i		−	0.615962i
$902$	−11.2988	−	6.52338i	−0.376210	−	0.217205i
$903$		0			0
$904$	1.32959	+	2.30292i	0.0442215	+	0.0765940i
$905$	−43.4660	−	8.98184i	−1.44486	−	0.298567i
$906$		0			0
$907$	−39.8069	−	22.9825i	−1.32177	−	0.763122i	−0.337756	−	0.941234i	$-0.609668\pi$
$907$	−39.8069	−	22.9825i	−1.32177	−	0.763122i	−0.984010	+	0.178112i	$0.943001\pi$
$908$			9.61684i			0.319146i
$909$		0			0
$910$	21.2361	−	16.6763i	0.703970	−	0.552813i
$911$	11.3878	+	6.57475i	0.377295	+	0.217831i	0.676641	−	0.736314i	$-0.263435\pi$
$911$	11.3878	+	6.57475i	0.377295	+	0.217831i	−0.299346	+	0.954145i	$0.596768\pi$
$912$		0			0
$913$	13.3137	+	23.0599i	0.440618	+	0.763172i
$914$	19.1410	−	11.0510i	0.633127	−	0.365536i
$915$		0			0
$916$	−19.7785	−	11.4191i	−0.653500	−	0.377299i
$917$	−5.27647	+	29.3757i	−0.174244	+	0.970072i
$918$		0			0
$919$	−53.8086			−1.77498			−0.887492	−	0.460824i	$-0.847554\pi$
$919$	−53.8086			−1.77498			−0.887492	+	0.460824i	$0.847554\pi$
$920$	−4.90845	+	1.62566i	−0.161827	+	0.0535964i
$921$		0			0
$922$	−9.53685	−	16.5183i	−0.314079	−	0.544001i
$923$	−32.8794	+	18.9830i	−1.08224	+	0.624831i
$924$		0			0
$925$	−20.7440	+	48.0501i	−0.682058	+	1.57988i
$926$			26.4617i			0.869585i
$927$		0			0
$928$			0.200386i			0.00657799i
$929$	25.6490	−	44.4253i	0.841515	−	1.45755i	−0.0470989	−	0.998890i	$-0.514998\pi$
$929$	25.6490	−	44.4253i	0.841515	−	1.45755i	0.888614	−	0.458656i	$-0.151669\pi$
$930$		0			0
$931$	−28.4167	+	4.82379i	−0.931321	+	0.158093i
$932$	−12.0611	−	20.8904i	−0.395073	−	0.684287i
$933$		0			0
$934$	−21.6773	−	12.5154i	−0.709303	−	0.409516i
$935$	28.8360	+	25.6697i	0.943039	+	0.839489i
$936$		0			0
$937$	26.4979			0.865650			0.432825	−	0.901478i	$-0.357517\pi$
$937$	26.4979			0.865650			0.432825	+	0.901478i	$0.357517\pi$
$938$	−13.9439	+	16.5103i	−0.455283	+	0.539082i
$939$		0			0
$940$	−19.8749	−	4.10697i	−0.648248	−	0.133954i
$941$	−27.4639	−	47.5689i	−0.895298	−	1.55070i	−0.833435	−	0.552617i	$-0.813629\pi$
$941$	−27.4639	−	47.5689i	−0.895298	−	1.55070i	−0.0618625	−	0.998085i	$-0.519704\pi$
$942$		0			0
$943$	2.38384	−	4.12894i	0.0776287	−	0.134457i
$944$	−1.23342			−0.0401444
$945$		0			0
$946$	53.0576			1.72505
$947$	−6.38577	+	11.0605i	−0.207510	+	0.359417i	−0.950929	−	0.309408i	$-0.899869\pi$
$947$	−6.38577	+	11.0605i	−0.207510	+	0.359417i	0.743420	+	0.668825i	$0.233203\pi$
$948$		0			0
$949$	31.8230	+	55.1190i	1.03302	+	1.78924i
$950$	−12.2893	−	16.5179i	−0.398719	−	0.535910i
$951$		0			0
$952$	4.65781	−	5.51512i	0.150961	−	0.178746i
$953$	−27.4326			−0.888629			−0.444315	−	0.895871i	$-0.646553\pi$
$953$	−27.4326			−0.888629			−0.444315	+	0.895871i	$0.646553\pi$
$954$		0			0
$955$	3.78716	−	4.25431i	0.122550	−	0.137666i
$956$	−13.7371	−	7.93114i	−0.444291	−	0.256511i
$957$		0			0
$958$	3.86939	+	6.70198i	0.125014	+	0.216531i
$959$	−4.54668	+	1.63844i	−0.146820	+	0.0529080i
$960$		0			0
$961$	−12.5327	+	21.7073i	−0.404282	+	0.700237i
$962$			47.7734i			1.54028i
$963$		0			0
$964$			13.6953i			0.441096i
$965$	15.7752	+	47.6310i	0.507822	+	1.53330i
$966$		0			0
$967$	3.69352	−	2.13245i	0.118776	−	0.0685751i	−0.439435	−	0.898274i	$-0.644821\pi$
$967$	3.69352	−	2.13245i	0.118776	−	0.0685751i	0.558211	+	0.829699i	$0.311488\pi$
$968$	−14.5207	−	25.1507i	−0.466714	−	0.808373i
$969$		0			0
$970$	10.2987	−	3.41089i	0.330671	−	0.109517i
$971$	21.6336			0.694255			0.347127	−	0.937818i	$-0.387157\pi$
$971$	21.6336			0.694255			0.347127	+	0.937818i	$0.387157\pi$
$972$		0			0
$973$	−45.7672	−	8.22071i	−1.46723	−	0.263544i
$974$	4.81767	+	2.78148i	0.154368	+	0.0891245i
$975$		0			0
$976$	−1.66558	+	0.961623i	−0.0533139	+	0.0307808i
$977$	−20.6630	−	35.7893i	−0.661067	−	1.14500i	−0.980336	−	0.197337i	$-0.936771\pi$
$977$	−20.6630	−	35.7893i	−0.661067	−	1.14500i	0.319269	−	0.947664i	$-0.396563\pi$
$978$		0			0
$979$	51.9903	+	30.0166i	1.66162	+	0.959335i
$980$	7.33848	+	13.8256i	0.234419	+	0.441642i
$981$		0			0
$982$		−	8.64927i		−	0.276009i
$983$	−32.8450	−	18.9631i	−1.04759	−	0.604828i	−0.125619	−	0.992079i	$-0.540092\pi$
$983$	−32.8450	−	18.9631i	−1.04759	−	0.604828i	−0.921975	+	0.387250i	$0.873425\pi$
$984$		0			0
$985$	4.69118	−	22.7021i	0.149473	−	0.723349i
$986$	0.273373	+	0.473496i	0.00870597	+	0.0150792i
$987$		0			0
$988$	−16.2752	−	9.39649i	−0.517783	−	0.298942i
$989$			19.3889i			0.616530i
$990$		0			0
$991$	−10.0234			−0.318404			−0.159202	−	0.987246i	$-0.550892\pi$
$991$	−10.0234			−0.318404			−0.159202	+	0.987246i	$0.550892\pi$
$992$	2.10971	+	1.21804i	0.0669834	+	0.0386729i
$993$		0			0
$994$	−7.46132	−	20.7052i	−0.236659	−	0.656730i
$995$	−25.2933	−	5.22662i	−0.801850	−	0.165695i
$996$		0			0
$997$	−11.8913	+	20.5963i	−0.376601	+	0.652292i	−0.990565	−	0.137042i	$-0.956241\pi$
$997$	−11.8913	+	20.5963i	−0.376601	+	0.652292i	0.613964	+	0.789334i	$0.289574\pi$
$998$	19.2374			0.608950
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.bf.f.629.7		32
3.2	odd	2		630.2.bf.e.209.12	yes	32
5.4	even	2		1890.2.bf.e.629.13		32
7.6	odd	2	inner	1890.2.bf.f.629.10		32
9.4	even	3		630.2.bf.f.419.12	yes	32
9.5	odd	6		1890.2.bf.e.1259.4		32
15.14	odd	2		630.2.bf.f.209.5	yes	32
21.20	even	2		630.2.bf.e.209.5	✓	32
35.34	odd	2		1890.2.bf.e.629.4		32
45.4	even	6		630.2.bf.e.419.5	yes	32
45.14	odd	6	inner	1890.2.bf.f.1259.10		32
63.13	odd	6		630.2.bf.f.419.5	yes	32
63.41	even	6		1890.2.bf.e.1259.13		32
105.104	even	2		630.2.bf.f.209.12	yes	32
315.104	even	6	inner	1890.2.bf.f.1259.7		32
315.139	odd	6		630.2.bf.e.419.12	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bf.e.209.5	✓	32	21.20	even	2
630.2.bf.e.209.12	yes	32	3.2	odd	2
630.2.bf.e.419.5	yes	32	45.4	even	6
630.2.bf.e.419.12	yes	32	315.139	odd	6
630.2.bf.f.209.5	yes	32	15.14	odd	2
630.2.bf.f.209.12	yes	32	105.104	even	2
630.2.bf.f.419.5	yes	32	63.13	odd	6
630.2.bf.f.419.12	yes	32	9.4	even	3
1890.2.bf.e.629.4		32	35.34	odd	2
1890.2.bf.e.629.13		32	5.4	even	2
1890.2.bf.e.1259.4		32	9.5	odd	6
1890.2.bf.e.1259.13		32	63.41	even	6
1890.2.bf.f.629.7		32	1.1	even	1	trivial
1890.2.bf.f.629.10		32	7.6	odd	2	inner
1890.2.bf.f.1259.7		32	315.104	even	6	inner
1890.2.bf.f.1259.10		32	45.14	odd	6	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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.bf (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.452503 + 2.18980i) q^{5} +(2.02132 + 1.70712i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.452503 + 2.18980i) q^{5} +(2.02132 + 1.70712i) q^{7} -1.00000 q^{8} +(1.67017 + 1.48678i) q^{10} +(-5.48007 - 3.16392i) q^{11} +(-2.28203 - 3.95259i) q^{13} +(2.48907 - 0.896960i) q^{14} +(-0.500000 + 0.866025i) q^{16} +2.72847i q^{17} +4.11761i q^{19} +(2.12268 - 0.703023i) q^{20} +(-5.48007 + 3.16392i) q^{22} +(-1.15619 - 2.00258i) q^{23} +(-4.59048 - 1.98179i) q^{25} -4.56405 q^{26} +(0.467745 - 2.60408i) q^{28} +(0.173539 + 0.100193i) q^{29} +(2.10971 - 1.21804i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.36292 + 1.36423i) q^{34} +(-4.65291 + 3.65383i) q^{35} -10.4673i q^{37} +(3.56595 + 2.05880i) q^{38} +(0.452503 - 2.18980i) q^{40} +(1.03090 + 1.78558i) q^{41} +(-7.26144 - 4.19239i) q^{43} +6.32783i q^{44} -2.31238 q^{46} +(-7.86014 - 4.53806i) q^{47} +(1.17150 + 6.90127i) q^{49} +(-4.01152 + 2.98458i) q^{50} +(-2.28203 + 3.95259i) q^{52} -6.77638 q^{53} +(9.40810 - 10.5686i) q^{55} +(-2.02132 - 1.70712i) q^{56} +(0.173539 - 0.100193i) q^{58} +(0.616709 + 1.06817i) q^{59} +(1.66558 + 0.961623i) q^{61} -2.43609i q^{62} +1.00000 q^{64} +(9.68801 - 3.20863i) q^{65} +(-7.07376 + 4.08404i) q^{67} +(2.36292 - 1.36423i) q^{68} +(0.837855 + 5.85645i) q^{70} -8.31846i q^{71} -13.9450 q^{73} +(-9.06497 - 5.23366i) q^{74} +(3.56595 - 2.05880i) q^{76} +(-5.67581 - 15.7504i) q^{77} +(1.01691 - 1.76135i) q^{79} +(-1.67017 - 1.48678i) q^{80} +2.06181 q^{82} +(-3.64421 - 2.10398i) q^{83} +(-5.97481 - 1.23464i) q^{85} +(-7.26144 + 4.19239i) q^{86} +(5.48007 + 3.16392i) q^{88} -9.48716 q^{89} +(2.13481 - 11.8851i) q^{91} +(-1.15619 + 2.00258i) q^{92} +(-7.86014 + 4.53806i) q^{94} +(-9.01675 - 1.86323i) q^{95} +(2.42587 - 4.20173i) q^{97} +(6.56243 + 2.43609i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8}+O(q^{10}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 24 q^{11} - 16 q^{16} + 24 q^{22} + 24 q^{23} - 58 q^{25} + 36 q^{29} + 16 q^{32} + 48 q^{35} - 54 q^{43} + 48 q^{46} + 32 q^{49} - 50 q^{50} + 24 q^{53} + 36 q^{58} + 32 q^{64} + 90 q^{65} - 66 q^{67} + 36 q^{70} - 12 q^{74} - 18 q^{77} + 34 q^{79} + 4 q^{85} - 54 q^{86} - 24 q^{88} + 16 q^{91} + 24 q^{92} - 12 q^{95} + 64 q^{98}+O(q^{100}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 24 * q^11 - 16 * q^16 + 24 * q^22 + 24 * q^23 - 58 * q^25 + 36 * q^29 + 16 * q^32 + 48 * q^35 - 54 * q^43 + 48 * q^46 + 32 * q^49 - 50 * q^50 + 24 * q^53 + 36 * q^58 + 32 * q^64 + 90 * q^65 - 66 * q^67 + 36 * q^70 - 12 * q^74 - 18 * q^77 + 34 * q^79 + 4 * q^85 - 54 * q^86 - 24 * q^88 + 16 * q^91 + 24 * q^92 - 12 * q^95 + 64 * q^98

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