LMFDB - Embedded newform 1288.2.q.a.737.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1288,2,Mod(737,1288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1288, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

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

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

chi := DirichletCharacter("1288.737");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1288 = 2^{3} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1288.q (of order $3$, 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:	$10.2847317803$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			737.5
Character	$\chi$	$=$	1288.737
Dual form			1288.2.q.a.921.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.328152 - 0.568377i) q^{3} +(1.04571 - 1.81122i) q^{5} +(-2.32073 - 1.27052i) q^{7} +(1.28463 - 2.22505i) q^{9} +O(q^{10})$	\(q+(-0.328152 - 0.568377i) q^{3} +(1.04571 - 1.81122i) q^{5} +(-2.32073 - 1.27052i) q^{7} +(1.28463 - 2.22505i) q^{9} +(0.921087 + 1.59537i) q^{11} +2.10767 q^{13} -1.37261 q^{15} +(2.30318 + 3.98922i) q^{17} +(4.22705 - 7.32146i) q^{19} +(0.0394175 + 1.73597i) q^{21} +(-0.500000 + 0.866025i) q^{23} +(0.312990 + 0.542115i) q^{25} -3.65513 q^{27} -2.24733 q^{29} +(-5.05693 - 8.75887i) q^{31} +(0.604513 - 1.04705i) q^{33} +(-4.72800 + 2.87475i) q^{35} +(3.13871 - 5.43641i) q^{37} +(-0.691638 - 1.19795i) q^{39} -0.725868 q^{41} -10.8164 q^{43} +(-2.68670 - 4.65350i) q^{45} +(-1.07447 + 1.86104i) q^{47} +(3.77155 + 5.89707i) q^{49} +(1.51159 - 2.61815i) q^{51} +(-6.41739 - 11.1152i) q^{53} +3.85275 q^{55} -5.54846 q^{57} +(0.687660 + 1.19106i) q^{59} +(-0.900671 + 1.56001i) q^{61} +(-5.80825 + 3.53158i) q^{63} +(2.20401 - 3.81746i) q^{65} +(2.91754 + 5.05333i) q^{67} +0.656305 q^{69} +4.43192 q^{71} +(-2.04432 - 3.54086i) q^{73} +(0.205417 - 0.355792i) q^{75} +(-0.110641 - 4.87268i) q^{77} +(-3.46381 + 5.99950i) q^{79} +(-2.65446 - 4.59765i) q^{81} -1.78309 q^{83} +9.63381 q^{85} +(0.737468 + 1.27733i) q^{87} +(1.84764 - 3.20021i) q^{89} +(-4.89134 - 2.67785i) q^{91} +(-3.31889 + 5.74848i) q^{93} +(-8.84051 - 15.3122i) q^{95} +3.34404 q^{97} +4.73303 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 4 q^{3} - q^{5} + q^{7} - 11 q^{9}+O(q^{10}) $ 22 * q - 4 * q^3 - q^5 + q^7 - 11 * q^9	$ 22 q - 4 q^{3} - q^{5} + q^{7} - 11 q^{9} - 6 q^{13} - 16 q^{15} - 5 q^{17} - 12 q^{19} + 3 q^{21} - 11 q^{23} - 22 q^{25} + 38 q^{27} - 30 q^{29} - 16 q^{31} - 4 q^{33} - 5 q^{35} - 3 q^{37} + q^{39} + 56 q^{41} - 18 q^{43} + 19 q^{45} - 31 q^{47} + 13 q^{49} + 15 q^{51} - 13 q^{53} + 70 q^{55} - 42 q^{57} - 11 q^{59} + 19 q^{61} - 23 q^{63} + 7 q^{65} - 19 q^{67} + 8 q^{69} - 10 q^{71} + 5 q^{73} - 28 q^{75} + 9 q^{77} + 13 q^{79} - 35 q^{81} + 34 q^{83} - 78 q^{85} - 4 q^{87} - 10 q^{89} - 30 q^{91} + 6 q^{93} - 33 q^{95} + 70 q^{97} + 26 q^{99}+O(q^{100}) $ 22 * q - 4 * q^3 - q^5 + q^7 - 11 * q^9 - 6 * q^13 - 16 * q^15 - 5 * q^17 - 12 * q^19 + 3 * q^21 - 11 * q^23 - 22 * q^25 + 38 * q^27 - 30 * q^29 - 16 * q^31 - 4 * q^33 - 5 * q^35 - 3 * q^37 + q^39 + 56 * q^41 - 18 * q^43 + 19 * q^45 - 31 * q^47 + 13 * q^49 + 15 * q^51 - 13 * q^53 + 70 * q^55 - 42 * q^57 - 11 * q^59 + 19 * q^61 - 23 * q^63 + 7 * q^65 - 19 * q^67 + 8 * q^69 - 10 * q^71 + 5 * q^73 - 28 * q^75 + 9 * q^77 + 13 * q^79 - 35 * q^81 + 34 * q^83 - 78 * q^85 - 4 * q^87 - 10 * q^89 - 30 * q^91 + 6 * q^93 - 33 * q^95 + 70 * q^97 + 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1288\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$645$	$967$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

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
$3$	−0.328152	−	0.568377i	−0.189459	−	0.328152i	0.755611	−	0.655021i	$-0.227340\pi$
$3$	−0.328152	−	0.568377i	−0.189459	−	0.328152i	−0.945070	+	0.326868i	$0.894007\pi$
$4$		0			0
$5$	1.04571	−	1.81122i	0.467655	−	0.810002i	−0.531662	−	0.846957i	$-0.678432\pi$
$5$	1.04571	−	1.81122i	0.467655	−	0.810002i	0.999317	+	0.0369547i	$0.0117657\pi$
$6$		0			0
$7$	−2.32073	−	1.27052i	−0.877152	−	0.480212i
$7$	−2.32073	−	1.27052i	−0.877152	−	0.480212i
$8$		0			0
$9$	1.28463	−	2.22505i	0.428211	−	0.741683i
$10$		0			0
$11$	0.921087	+	1.59537i	0.277718	+	0.481022i	0.970817	−	0.239820i	$-0.0770886\pi$
$11$	0.921087	+	1.59537i	0.277718	+	0.481022i	−0.693099	+	0.720842i	$0.743755\pi$
$12$		0			0
$13$	2.10767			0.584564			0.292282	−	0.956332i	$-0.405585\pi$
$13$	2.10767			0.584564			0.292282	+	0.956332i	$0.405585\pi$
$14$		0			0
$15$	−1.37261			−0.354405
$16$		0			0
$17$	2.30318	+	3.98922i	0.558603	+	0.967529i	0.997613	+	0.0690469i	$0.0219958\pi$
$17$	2.30318	+	3.98922i	0.558603	+	0.967529i	−0.439010	+	0.898482i	$0.644671\pi$
$18$		0			0
$19$	4.22705	−	7.32146i	0.969751	−	1.67966i	0.273482	−	0.961877i	$-0.411825\pi$
$19$	4.22705	−	7.32146i	0.969751	−	1.67966i	0.696269	−	0.717781i	$-0.254842\pi$
$20$		0			0
$21$	0.0394175	+	1.73597i	0.00860161	+	0.378820i
$22$		0			0
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$24$		0			0
$25$	0.312990	+	0.542115i	0.0625980	+	0.108423i
$26$		0			0
$27$	−3.65513			−0.703431
$28$		0			0
$29$	−2.24733			−0.417320			−0.208660	−	0.977988i	$-0.566910\pi$
$29$	−2.24733			−0.417320			−0.208660	+	0.977988i	$0.566910\pi$
$30$		0			0
$31$	−5.05693	−	8.75887i	−0.908252	−	1.57314i	−0.816491	−	0.577358i	$-0.804084\pi$
$31$	−5.05693	−	8.75887i	−0.908252	−	1.57314i	−0.0917606	−	0.995781i	$-0.529249\pi$
$32$		0			0
$33$	0.604513	−	1.04705i	0.105232	−	0.182268i
$34$		0			0
$35$	−4.72800	+	2.87475i	−0.799177	+	0.485922i
$36$		0			0
$37$	3.13871	−	5.43641i	0.516002	−	0.893741i	−0.483826	−	0.875164i	$-0.660753\pi$
$37$	3.13871	−	5.43641i	0.516002	−	0.893741i	0.999827	−	0.0185766i	$-0.00591346\pi$
$38$		0			0
$39$	−0.691638	−	1.19795i	−0.110751	−	0.191826i
$40$		0			0
$41$	−0.725868			−0.113361			−0.0566807	−	0.998392i	$-0.518052\pi$
$41$	−0.725868			−0.113361			−0.0566807	+	0.998392i	$0.518052\pi$
$42$		0			0
$43$	−10.8164			−1.64949			−0.824744	−	0.565506i	$-0.808681\pi$
$43$	−10.8164			−1.64949			−0.824744	+	0.565506i	$0.808681\pi$
$44$		0			0
$45$	−2.68670	−	4.65350i	−0.400510	−	0.693703i
$46$		0			0
$47$	−1.07447	+	1.86104i	−0.156728	+	0.271460i	−0.933687	−	0.358091i	$-0.883428\pi$
$47$	−1.07447	+	1.86104i	−0.156728	+	0.271460i	0.776959	+	0.629551i	$0.216761\pi$
$48$		0			0
$49$	3.77155	+	5.89707i	0.538793	+	0.842438i
$50$		0			0
$51$	1.51159	−	2.61815i	0.211665	−	0.366614i
$52$		0			0
$53$	−6.41739	−	11.1152i	−0.881496	−	1.52680i	−0.849678	−	0.527302i	$-0.823204\pi$
$53$	−6.41739	−	11.1152i	−0.881496	−	1.52680i	−0.0318178	−	0.999494i	$-0.510130\pi$
$54$		0			0
$55$	3.85275			0.519505
$56$		0			0
$57$	−5.54846			−0.734912
$58$		0			0
$59$	0.687660	+	1.19106i	0.0895258	+	0.155063i	0.907311	−	0.420461i	$-0.138132\pi$
$59$	0.687660	+	1.19106i	0.0895258	+	0.155063i	−0.817785	+	0.575524i	$0.804798\pi$
$60$		0			0
$61$	−0.900671	+	1.56001i	−0.115319	+	0.199738i	−0.917907	−	0.396795i	$-0.870122\pi$
$61$	−0.900671	+	1.56001i	−0.115319	+	0.199738i	0.802588	+	0.596533i	$0.203456\pi$
$62$		0			0
$63$	−5.80825	+	3.53158i	−0.731771	+	0.444937i
$64$		0			0
$65$	2.20401	−	3.81746i	0.273374	−	0.473498i
$66$		0			0
$67$	2.91754	+	5.05333i	0.356434	+	0.617362i	0.987362	−	0.158479i	$-0.0506590\pi$
$67$	2.91754	+	5.05333i	0.356434	+	0.617362i	−0.630928	+	0.775841i	$0.717326\pi$
$68$		0			0
$69$	0.656305			0.0790098
$70$		0			0
$71$	4.43192			0.525972			0.262986	−	0.964800i	$-0.415293\pi$
$71$	4.43192			0.525972			0.262986	+	0.964800i	$0.415293\pi$
$72$		0			0
$73$	−2.04432	−	3.54086i	−0.239269	−	0.414427i	0.721235	−	0.692690i	$-0.243575\pi$
$73$	−2.04432	−	3.54086i	−0.239269	−	0.414427i	−0.960505	+	0.278263i	$0.910241\pi$
$74$		0			0
$75$	0.205417	−	0.355792i	0.0237195	−	0.0410834i
$76$		0			0
$77$	−0.110641	−	4.87268i	−0.0126087	−	0.555293i
$78$		0			0
$79$	−3.46381	+	5.99950i	−0.389709	+	0.674997i	−0.992410	−	0.122971i	$-0.960758\pi$
$79$	−3.46381	+	5.99950i	−0.389709	+	0.674997i	0.602701	+	0.797967i	$0.294091\pi$
$80$		0			0
$81$	−2.65446	−	4.59765i	−0.294939	−	0.510850i
$82$		0			0
$83$	−1.78309			−0.195720			−0.0978599	−	0.995200i	$-0.531200\pi$
$83$	−1.78309			−0.195720			−0.0978599	+	0.995200i	$0.531200\pi$
$84$		0			0
$85$	9.63381			1.04493
$86$		0			0
$87$	0.737468	+	1.27733i	0.0790649	+	0.136944i
$88$		0			0
$89$	1.84764	−	3.20021i	0.195850	−	0.339222i	−0.751329	−	0.659928i	$-0.770587\pi$
$89$	1.84764	−	3.20021i	0.195850	−	0.339222i	0.947179	+	0.320706i	$0.103920\pi$
$90$		0			0
$91$	−4.89134	−	2.67785i	−0.512752	−	0.280715i
$92$		0			0
$93$	−3.31889	+	5.74848i	−0.344153	+	0.596090i
$94$		0			0
$95$	−8.84051	−	15.3122i	−0.907017	−	1.57100i
$96$		0			0
$97$	3.34404			0.339536			0.169768	−	0.985484i	$-0.445698\pi$
$97$	3.34404			0.339536			0.169768	+	0.985484i	$0.445698\pi$
$98$		0			0
$99$	4.73303			0.475687
$100$		0			0
$101$	1.16339	+	2.01505i	0.115762	+	0.200505i	0.918084	−	0.396386i	$-0.129736\pi$
$101$	1.16339	+	2.01505i	0.115762	+	0.200505i	−0.802322	+	0.596891i	$0.796402\pi$
$102$		0			0
$103$	−1.59477	+	2.76222i	−0.157137	+	0.272170i	−0.933835	−	0.357704i	$-0.883560\pi$
$103$	−1.59477	+	2.76222i	−0.157137	+	0.272170i	0.776698	+	0.629873i	$0.216893\pi$
$104$		0			0
$105$	3.18544	+	1.74393i	0.310868	+	0.170190i
$106$		0			0
$107$	5.18523	−	8.98108i	0.501275	−	0.868234i	−0.498724	−	0.866761i	$-0.666198\pi$
$107$	5.18523	−	8.98108i	0.501275	−	0.868234i	0.999999	−	0.00147288i	$-0.000468833\pi$
$108$		0			0
$109$	3.00340	+	5.20205i	0.287674	+	0.498266i	0.973254	−	0.229731i	$-0.0737848\pi$
$109$	3.00340	+	5.20205i	0.287674	+	0.498266i	−0.685580	+	0.727997i	$0.740451\pi$
$110$		0			0
$111$	−4.11991			−0.391044
$112$		0			0
$113$	3.85151			0.362320			0.181160	−	0.983454i	$-0.442015\pi$
$113$	3.85151			0.362320			0.181160	+	0.983454i	$0.442015\pi$
$114$		0			0
$115$	1.04571	+	1.81122i	0.0975128	+	0.168897i
$116$		0			0
$117$	2.70759	−	4.68968i	0.250316	−	0.433561i
$118$		0			0
$119$	−0.276657	−	12.1841i	−0.0253611	−	1.11692i
$120$		0			0
$121$	3.80320	−	6.58733i	0.345745	−	0.598849i
$122$		0			0
$123$	0.238195	+	0.412566i	0.0214773	+	0.0371998i
$124$		0			0
$125$	11.7663			1.05241
$126$		0			0
$127$	−9.28567			−0.823970			−0.411985	−	0.911191i	$-0.635164\pi$
$127$	−9.28567			−0.823970			−0.411985	+	0.911191i	$0.635164\pi$
$128$		0			0
$129$	3.54943	+	6.14780i	0.312510	+	0.541283i
$130$		0			0
$131$	−4.73616	+	8.20328i	−0.413801	+	0.716724i	−0.995302	−	0.0968219i	$-0.969132\pi$
$131$	−4.73616	+	8.20328i	−0.413801	+	0.716724i	0.581501	+	0.813546i	$0.302466\pi$
$132$		0			0
$133$	−19.1119	+	11.6206i	−1.65721	+	1.00763i
$134$		0			0
$135$	−3.82220	+	6.62025i	−0.328963	+	0.569780i
$136$		0			0
$137$	−5.21825	−	9.03828i	−0.445825	−	0.772192i	0.552284	−	0.833656i	$-0.313756\pi$
$137$	−5.21825	−	9.03828i	−0.445825	−	0.772192i	−0.998109	+	0.0614640i	$0.980423\pi$
$138$		0			0
$139$	22.3518			1.89585			0.947925	−	0.318492i	$-0.103177\pi$
$139$	22.3518			1.89585			0.947925	+	0.318492i	$0.103177\pi$
$140$		0			0
$141$	1.41036			0.118774
$142$		0			0
$143$	1.94135	+	3.36252i	0.162344	+	0.281188i
$144$		0			0
$145$	−2.35006	+	4.07042i	−0.195161	+	0.338030i
$146$		0			0
$147$	2.11411	−	4.07880i	0.174369	−	0.336414i
$148$		0			0
$149$	−6.96069	+	12.0563i	−0.570242	+	0.987688i	0.426299	+	0.904582i	$0.359817\pi$
$149$	−6.96069	+	12.0563i	−0.570242	+	0.987688i	−0.996541	+	0.0831054i	$0.973516\pi$
$150$		0			0
$151$	−7.61833	−	13.1953i	−0.619971	−	1.07382i	−0.989490	−	0.144599i	$-0.953811\pi$
$151$	−7.61833	−	13.1953i	−0.619971	−	1.07382i	0.369519	−	0.929223i	$-0.379522\pi$
$152$		0			0
$153$	11.8350			0.956799
$154$		0			0
$155$	−21.1523			−1.69899
$156$		0			0
$157$	4.35331	+	7.54015i	0.347432	+	0.601769i	0.985792	−	0.167968i	$-0.0537205\pi$
$157$	4.35331	+	7.54015i	0.347432	+	0.601769i	−0.638361	+	0.769737i	$0.720387\pi$
$158$		0			0
$159$	−4.21176	+	7.29498i	−0.334014	+	0.578530i
$160$		0			0
$161$	2.26067	−	1.37455i	0.178166	−	0.108330i
$162$		0			0
$163$	−1.70334	+	2.95028i	−0.133416	+	0.231084i	−0.924991	−	0.379988i	$-0.875928\pi$
$163$	−1.70334	+	2.95028i	−0.133416	+	0.231084i	0.791575	+	0.611072i	$0.209261\pi$
$164$		0			0
$165$	−1.26429	−	2.18981i	−0.0984248	−	0.170477i
$166$		0			0
$167$	10.4072			0.805331			0.402666	−	0.915347i	$-0.368084\pi$
$167$	10.4072			0.805331			0.402666	+	0.915347i	$0.368084\pi$
$168$		0			0
$169$	−8.55771			−0.658285
$170$		0			0
$171$	−10.8604	−	18.8108i	−0.830516	−	1.43850i
$172$		0			0
$173$	4.12230	−	7.14003i	0.313412	−	0.542846i	−0.665686	−	0.746232i	$-0.731861\pi$
$173$	4.12230	−	7.14003i	0.313412	−	0.542846i	0.979099	+	0.203385i	$0.0651945\pi$
$174$		0			0
$175$	−0.0375962	−	1.65576i	−0.00284201	−	0.125164i
$176$		0			0
$177$	0.451315	−	0.781700i	0.0339229	−	0.0587562i
$178$		0			0
$179$	9.59103	+	16.6122i	0.716867	+	1.24165i	0.962235	+	0.272221i	$0.0877581\pi$
$179$	9.59103	+	16.6122i	0.716867	+	1.24165i	−0.245367	+	0.969430i	$0.578909\pi$
$180$		0			0
$181$	10.1160			0.751916			0.375958	−	0.926637i	$-0.377314\pi$
$181$	10.1160			0.751916			0.375958	+	0.926637i	$0.377314\pi$
$182$		0			0
$183$	1.18223			0.0873929
$184$		0			0
$185$	−6.56436	−	11.3698i	−0.482621	−	0.835924i
$186$		0			0
$187$	−4.24285	+	7.34884i	−0.310268	+	0.537400i
$188$		0			0
$189$	8.48257	+	4.64393i	0.617016	+	0.337796i
$190$		0			0
$191$	8.45621	−	14.6466i	0.611870	−	1.05979i	−0.379055	−	0.925374i	$-0.623751\pi$
$191$	8.45621	−	14.6466i	0.611870	−	1.05979i	0.990925	−	0.134416i	$-0.0429157\pi$
$192$		0			0
$193$	−3.64707	−	6.31691i	−0.262522	−	0.454701i	0.704390	−	0.709814i	$-0.251221\pi$
$193$	−3.64707	−	6.31691i	−0.262522	−	0.454701i	−0.966911	+	0.255112i	$0.917887\pi$
$194$		0			0
$195$	−2.89301			−0.207173
$196$		0			0
$197$	4.20119			0.299322			0.149661	−	0.988737i	$-0.452182\pi$
$197$	4.20119			0.299322			0.149661	+	0.988737i	$0.452182\pi$
$198$		0			0
$199$	−1.65535	−	2.86715i	−0.117345	−	0.203247i	0.801370	−	0.598169i	$-0.204105\pi$
$199$	−1.65535	−	2.86715i	−0.117345	−	0.203247i	−0.918715	+	0.394922i	$0.870772\pi$
$200$		0			0
$201$	1.91480	−	3.31652i	0.135059	−	0.233930i
$202$		0			0
$203$	5.21545	+	2.85529i	0.366053	+	0.200402i
$204$		0			0
$205$	−0.759045	+	1.31471i	−0.0530140	+	0.0918230i
$206$		0			0
$207$	1.28463	+	2.22505i	0.0892881	+	0.154652i
$208$		0			0
$209$	15.5739			1.07727
$210$		0			0
$211$	−3.70533			−0.255085			−0.127543	−	0.991833i	$-0.540709\pi$
$211$	−3.70533			−0.255085			−0.127543	+	0.991833i	$0.540709\pi$
$212$		0			0
$213$	−1.45434	−	2.51900i	−0.0996500	−	0.172599i
$214$		0			0
$215$	−11.3108	+	19.5909i	−0.771391	+	1.33609i
$216$		0			0
$217$	0.607437	+	26.7519i	0.0412355	+	1.81604i
$218$		0			0
$219$	−1.34170	+	2.32389i	−0.0906634	+	0.157034i
$220$		0			0
$221$	4.85435	+	8.40799i	0.326539	+	0.565582i
$222$		0			0
$223$	0.499565			0.0334534			0.0167267	−	0.999860i	$-0.494675\pi$
$223$	0.499565			0.0334534			0.0167267	+	0.999860i	$0.494675\pi$
$224$		0			0
$225$	1.60831			0.107221
$226$		0			0
$227$	14.4186	+	24.9738i	0.956997	+	1.65757i	0.729730	+	0.683735i	$0.239646\pi$
$227$	14.4186	+	24.9738i	0.956997	+	1.65757i	0.227267	+	0.973833i	$0.427021\pi$
$228$		0			0
$229$	9.91744	−	17.1775i	0.655363	−	1.13512i	−0.326440	−	0.945218i	$-0.605849\pi$
$229$	9.91744	−	17.1775i	0.655363	−	1.13512i	0.981803	−	0.189903i	$-0.0608175\pi$
$230$		0			0
$231$	−2.73321	+	1.66187i	−0.179832	+	0.109343i
$232$		0			0
$233$	−4.82463	+	8.35650i	−0.316072	+	0.547452i	−0.979665	−	0.200642i	$-0.935697\pi$
$233$	−4.82463	+	8.35650i	−0.316072	+	0.547452i	0.663593	+	0.748094i	$0.269031\pi$
$234$		0			0
$235$	2.24717	+	3.89221i	0.146589	+	0.253900i
$236$		0			0
$237$	4.54663			0.295336
$238$		0			0
$239$	−4.66004			−0.301433			−0.150716	−	0.988577i	$-0.548158\pi$
$239$	−4.66004			−0.301433			−0.150716	+	0.988577i	$0.548158\pi$
$240$		0			0
$241$	4.93726	+	8.55159i	0.318037	+	0.550856i	0.980078	−	0.198611i	$-0.0636431\pi$
$241$	4.93726	+	8.55159i	0.318037	+	0.550856i	−0.662041	+	0.749467i	$0.730310\pi$
$242$		0			0
$243$	−7.22483	+	12.5138i	−0.463473	+	0.802759i
$244$		0			0
$245$	14.6248	−	0.664494i	0.934346	−	0.0424530i
$246$		0			0
$247$	8.90924	−	15.4313i	0.566881	−	0.981867i
$248$		0			0
$249$	0.585126	+	1.01347i	0.0370808	+	0.0642259i
$250$		0			0
$251$	28.2589			1.78368			0.891842	−	0.452348i	$-0.149413\pi$
$251$	28.2589			1.78368			0.891842	+	0.452348i	$0.149413\pi$
$252$		0			0
$253$	−1.84217			−0.115816
$254$		0			0
$255$	−3.16136	−	5.47563i	−0.197972	−	0.342897i
$256$		0			0
$257$	−11.4774	+	19.8794i	−0.715939	+	1.24004i	0.246657	+	0.969103i	$0.420668\pi$
$257$	−11.4774	+	19.8794i	−0.715939	+	1.24004i	−0.962596	+	0.270940i	$0.912666\pi$
$258$		0			0
$259$	−14.1912	+	8.62863i	−0.881797	+	0.536157i
$260$		0			0
$261$	−2.88700	+	5.00043i	−0.178701	+	0.309519i
$262$		0			0
$263$	9.40796	+	16.2951i	0.580120	+	1.00480i	0.995465	+	0.0951328i	$0.0303276\pi$
$263$	9.40796	+	16.2951i	0.580120	+	1.00480i	−0.415345	+	0.909664i	$0.636339\pi$
$264$		0			0
$265$	−26.8428			−1.64894
$266$		0			0
$267$	−2.42523			−0.148422
$268$		0			0
$269$	−8.31230	−	14.3973i	−0.506810	−	0.877820i	−0.999969	−	0.00788131i	$-0.997491\pi$
$269$	−8.31230	−	14.3973i	−0.506810	−	0.877820i	0.493159	−	0.869939i	$-0.335842\pi$
$270$		0			0
$271$	−2.82356	+	4.89054i	−0.171519	+	0.297079i	−0.938951	−	0.344051i	$-0.888201\pi$
$271$	−2.82356	+	4.89054i	−0.171519	+	0.297079i	0.767432	+	0.641130i	$0.221534\pi$
$272$		0			0
$273$	0.0830793	+	3.65886i	0.00502819	+	0.221444i
$274$		0			0
$275$	−0.576582	+	0.998669i	−0.0347692	+	0.0602220i
$276$		0			0
$277$	12.8374	+	22.2350i	0.771324	+	1.33597i	0.936837	+	0.349765i	$0.113739\pi$
$277$	12.8374	+	22.2350i	0.771324	+	1.33597i	−0.165513	+	0.986208i	$0.552928\pi$
$278$		0			0
$279$	−25.9852			−1.55569
$280$		0			0
$281$	23.7618			1.41751			0.708754	−	0.705456i	$-0.249258\pi$
$281$	23.7618			1.41751			0.708754	+	0.705456i	$0.249258\pi$
$282$		0			0
$283$	3.61957	+	6.26928i	0.215161	+	0.372670i	0.953322	−	0.301954i	$-0.0976390\pi$
$283$	3.61957	+	6.26928i	0.215161	+	0.372670i	−0.738161	+	0.674624i	$0.764306\pi$
$284$		0			0
$285$	−5.80207	+	10.0495i	−0.343685	+	0.595280i
$286$		0			0
$287$	1.68454	+	0.922230i	0.0994353	+	0.0544375i
$288$		0			0
$289$	−2.10927	+	3.65336i	−0.124075	+	0.214904i
$290$		0			0
$291$	−1.09735	−	1.90067i	−0.0643280	−	0.111419i
$292$		0			0
$293$	28.7605			1.68021			0.840103	−	0.542427i	$-0.182494\pi$
$293$	28.7605			1.68021			0.840103	+	0.542427i	$0.182494\pi$
$294$		0			0
$295$	2.87637			0.167469
$296$		0			0
$297$	−3.36669	−	5.83129i	−0.195355	−	0.338366i
$298$		0			0
$299$	−1.05384	+	1.82530i	−0.0609450	+	0.105560i
$300$		0			0
$301$	25.1020	+	13.7425i	1.44685	+	0.792104i
$302$		0			0
$303$	0.763539	−	1.32249i	0.0438641	−	0.0759749i
$304$		0			0
$305$	1.88368	+	3.26262i	0.107859	+	0.186817i
$306$		0			0
$307$	20.7093			1.18194			0.590970	−	0.806693i	$-0.298745\pi$
$307$	20.7093			1.18194			0.590970	+	0.806693i	$0.298745\pi$
$308$		0			0
$309$	2.09331			0.119084
$310$		0			0
$311$	−11.8237	−	20.4792i	−0.670458	−	1.16127i	−0.977774	−	0.209660i	$-0.932764\pi$
$311$	−11.8237	−	20.4792i	−0.670458	−	1.16127i	0.307317	−	0.951607i	$-0.400569\pi$
$312$		0			0
$313$	−17.4218	+	30.1754i	−0.984736	+	1.70561i	−0.341630	+	0.939835i	$0.610979\pi$
$313$	−17.4218	+	30.1754i	−0.984736	+	1.70561i	−0.643106	+	0.765777i	$0.722354\pi$
$314$		0			0
$315$	0.322725	+	14.2130i	0.0181835	+	0.800813i
$316$		0			0
$317$	−8.54761	+	14.8049i	−0.480082	+	0.831526i	−0.999739	−	0.0228490i	$-0.992726\pi$
$317$	−8.54761	+	14.8049i	−0.480082	+	0.831526i	0.519657	+	0.854375i	$0.326060\pi$
$318$		0			0
$319$	−2.06999	−	3.58533i	−0.115897	−	0.200740i
$320$		0			0
$321$	−6.80618			−0.379884
$322$		0			0
$323$	38.9426			2.16682
$324$		0			0
$325$	0.659681	+	1.14260i	0.0365925	+	0.0633801i
$326$		0			0
$327$	1.97115	−	3.41413i	0.109005	−	0.188802i
$328$		0			0
$329$	4.85805	−	2.95383i	0.267833	−	0.162850i
$330$		0			0
$331$	11.2433	−	19.4740i	0.617989	−	1.07039i	−0.371863	−	0.928288i	$-0.621281\pi$
$331$	11.2433	−	19.4740i	0.617989	−	1.07039i	0.989852	−	0.142101i	$-0.0453859\pi$
$332$		0			0
$333$	−8.06419	−	13.9676i	−0.441915	−	0.765419i
$334$		0			0
$335$	12.2036			0.666753
$336$		0			0
$337$	−33.3104			−1.81453			−0.907265	−	0.420559i	$-0.861834\pi$
$337$	−33.3104			−1.81453			−0.907265	+	0.420559i	$0.861834\pi$
$338$		0			0
$339$	−1.26388	−	2.18911i	−0.0686447	−	0.118896i
$340$		0			0
$341$	9.31575	−	16.1353i	0.504476	−	0.873778i
$342$		0			0
$343$	−1.26039	−	18.4773i	−0.0680546	−	0.997682i
$344$		0			0
$345$	0.686303	−	1.18871i	0.0369493	−	0.0639981i
$346$		0			0
$347$	−4.57829	−	7.92983i	−0.245775	−	0.425695i	0.716574	−	0.697511i	$-0.245709\pi$
$347$	−4.57829	−	7.92983i	−0.245775	−	0.425695i	−0.962349	+	0.271816i	$0.912376\pi$
$348$		0			0
$349$	−14.4050			−0.771080			−0.385540	−	0.922691i	$-0.625985\pi$
$349$	−14.4050			−0.771080			−0.385540	+	0.922691i	$0.625985\pi$
$350$		0			0
$351$	−7.70383			−0.411200
$352$		0			0
$353$	16.2967	+	28.2267i	0.867387	+	1.50236i	0.864658	+	0.502362i	$0.167535\pi$
$353$	16.2967	+	28.2267i	0.867387	+	1.50236i	0.00272922	+	0.999996i	$0.499131\pi$
$354$		0			0
$355$	4.63449	−	8.02718i	0.245973	−	0.426038i
$356$		0			0
$357$	−6.83439	+	4.15550i	−0.361714	+	0.219932i
$358$		0			0
$359$	7.62207	−	13.2018i	0.402277	−	0.696765i	−0.591723	−	0.806141i	$-0.701552\pi$
$359$	7.62207	−	13.2018i	0.402277	−	0.696765i	0.994000	+	0.109377i	$0.0348854\pi$
$360$		0			0
$361$	−26.2359	−	45.4418i	−1.38083	−	2.39168i
$362$		0			0
$363$	−4.99211			−0.262018
$364$		0			0
$365$	−8.55104			−0.447582
$366$		0			0
$367$	8.59049	+	14.8792i	0.448420	+	0.776686i	0.998283	−	0.0585686i	$-0.0186536\pi$
$367$	8.59049	+	14.8792i	0.448420	+	0.776686i	−0.549864	+	0.835254i	$0.685320\pi$
$368$		0			0
$369$	−0.932473	+	1.61509i	−0.0485426	+	0.0840782i
$370$		0			0
$371$	0.770854	+	33.9489i	0.0400207	+	1.76254i
$372$		0			0
$373$	−8.27378	+	14.3306i	−0.428400	+	0.742010i	−0.996731	−	0.0807895i	$-0.974256\pi$
$373$	−8.27378	+	14.3306i	−0.428400	+	0.742010i	0.568331	+	0.822800i	$0.307589\pi$
$374$		0			0
$375$	−3.86113	−	6.68767i	−0.199388	−	0.345350i
$376$		0			0
$377$	−4.73665			−0.243950
$378$		0			0
$379$	−7.38165			−0.379170			−0.189585	−	0.981864i	$-0.560714\pi$
$379$	−7.38165			−0.379170			−0.189585	+	0.981864i	$0.560714\pi$
$380$		0			0
$381$	3.04712	+	5.27776i	0.156108	+	0.270388i
$382$		0			0
$383$	3.69331	−	6.39700i	0.188719	−	0.326871i	−0.756104	−	0.654451i	$-0.772900\pi$
$383$	3.69331	−	6.39700i	0.188719	−	0.326871i	0.944824	+	0.327580i	$0.106233\pi$
$384$		0			0
$385$	−8.94118	−	4.89500i	−0.455685	−	0.249472i
$386$		0			0
$387$	−13.8951	+	24.0670i	−0.706328	+	1.22340i
$388$		0			0
$389$	−8.80649	−	15.2533i	−0.446507	−	0.773373i	0.551649	−	0.834076i	$-0.313999\pi$
$389$	−8.80649	−	15.2533i	−0.446507	−	0.773373i	−0.998156	+	0.0607036i	$0.980666\pi$
$390$		0			0
$391$	−4.60636			−0.232954
$392$		0			0
$393$	6.21673			0.313593
$394$		0			0
$395$	7.24427	+	12.5474i	0.364499	+	0.631331i
$396$		0			0
$397$	−0.0294780	+	0.0510574i	−0.00147946	+	0.00256250i	−0.866764	−	0.498718i	$-0.833804\pi$
$397$	−0.0294780	+	0.0510574i	−0.00147946	+	0.00256250i	0.865285	+	0.501281i	$0.167138\pi$
$398$		0			0
$399$	12.8765	+	7.04944i	0.644630	+	0.352913i
$400$		0			0
$401$	12.4105	−	21.4956i	0.619750	−	1.07344i	−0.369781	−	0.929119i	$-0.620567\pi$
$401$	12.4105	−	21.4956i	0.619750	−	1.07344i	0.989531	−	0.144320i	$-0.0460994\pi$
$402$		0			0
$403$	−10.6584	−	18.4608i	−0.530931	−	0.919600i
$404$		0			0
$405$	−11.1031			−0.551719
$406$		0			0
$407$	11.5641			0.573212
$408$		0			0
$409$	−4.62548	−	8.01157i	−0.228715	−	0.396147i	0.728712	−	0.684820i	$-0.240119\pi$
$409$	−4.62548	−	8.01157i	−0.228715	−	0.396147i	−0.957428	+	0.288673i	$0.906786\pi$
$410$		0			0
$411$	−3.42476	+	5.93186i	−0.168931	+	0.292597i
$412$		0			0
$413$	−0.0826015	−	3.63782i	−0.00406455	−	0.179005i
$414$		0			0
$415$	−1.86459	+	3.22957i	−0.0915293	+	0.158533i
$416$		0			0
$417$	−7.33478	−	12.7042i	−0.359186	−	0.622128i
$418$		0			0
$419$	18.7225			0.914652			0.457326	−	0.889299i	$-0.348807\pi$
$419$	18.7225			0.914652			0.457326	+	0.889299i	$0.348807\pi$
$420$		0			0
$421$	−9.89925			−0.482460			−0.241230	−	0.970468i	$-0.577551\pi$
$421$	−9.89925			−0.482460			−0.241230	+	0.970468i	$0.577551\pi$
$422$		0			0
$423$	2.76060	+	4.78150i	0.134225	+	0.232485i
$424$		0			0
$425$	−1.44174	+	2.49718i	−0.0699349	+	0.121131i
$426$		0			0
$427$	4.07223	−	2.47603i	0.197069	−	0.119823i
$428$		0			0
$429$	1.27412	−	2.20684i	0.0615150	−	0.106547i
$430$		0			0
$431$	3.11685	+	5.39854i	0.150133	+	0.260039i	0.931276	−	0.364314i	$-0.118696\pi$
$431$	3.11685	+	5.39854i	0.150133	+	0.260039i	−0.781143	+	0.624352i	$0.785363\pi$
$432$		0			0
$433$	12.6098			0.605988			0.302994	−	0.952993i	$-0.402014\pi$
$433$	12.6098			0.605988			0.302994	+	0.952993i	$0.402014\pi$
$434$		0			0
$435$	3.08470			0.147900
$436$		0			0
$437$	4.22705	+	7.32146i	0.202207	+	0.350233i
$438$		0			0
$439$	−4.08272	+	7.07148i	−0.194858	+	0.337503i	−0.946854	−	0.321664i	$-0.895758\pi$
$439$	−4.08272	+	7.07148i	−0.194858	+	0.337503i	0.751996	+	0.659167i	$0.229091\pi$
$440$		0			0
$441$	17.9663	−	0.816319i	0.855539	−	0.0388723i
$442$		0			0
$443$	−0.734631	+	1.27242i	−0.0349034	+	0.0604544i	−0.882949	−	0.469468i	$-0.844446\pi$
$443$	−0.734631	+	1.27242i	−0.0349034	+	0.0604544i	0.848046	+	0.529923i	$0.177779\pi$
$444$		0			0
$445$	−3.86419	−	6.69297i	−0.183180	−	0.317277i
$446$		0			0
$447$	9.13666			0.432149
$448$		0			0
$449$	13.9254			0.657179			0.328589	−	0.944473i	$-0.393427\pi$
$449$	13.9254			0.657179			0.328589	+	0.944473i	$0.393427\pi$
$450$		0			0
$451$	−0.668587	−	1.15803i	−0.0314825	−	0.0545293i
$452$		0			0
$453$	−4.99995	+	8.66016i	−0.234918	+	0.406890i
$454$		0			0
$455$	−9.96508	+	6.05904i	−0.467170	+	0.284052i
$456$		0			0
$457$	16.1668	−	28.0018i	0.756253	−	1.30987i	−0.188496	−	0.982074i	$-0.560361\pi$
$457$	16.1668	−	28.0018i	0.756253	−	1.30987i	0.944749	−	0.327795i	$-0.106306\pi$
$458$		0			0
$459$	−8.41843	−	14.5811i	−0.392939	−	0.680590i
$460$		0			0
$461$	−12.6308			−0.588274			−0.294137	−	0.955763i	$-0.595032\pi$
$461$	−12.6308			−0.588274			−0.294137	+	0.955763i	$0.595032\pi$
$462$		0			0
$463$	35.5062			1.65011			0.825057	−	0.565050i	$-0.191143\pi$
$463$	35.5062			1.65011			0.825057	+	0.565050i	$0.191143\pi$
$464$		0			0
$465$	6.94118	+	12.0225i	0.321889	+	0.557529i
$466$		0			0
$467$	−21.1089	+	36.5617i	−0.976805	+	1.69188i	−0.302959	+	0.953004i	$0.597975\pi$
$467$	−21.1089	+	36.5617i	−0.976805	+	1.69188i	−0.673846	+	0.738872i	$0.735359\pi$
$468$		0			0
$469$	−0.350454	−	15.4342i	−0.0161825	−	0.712685i
$470$		0			0
$471$	2.85709	−	4.94863i	0.131648	−	0.228021i
$472$		0			0
$473$	−9.96286	−	17.2562i	−0.458093	−	0.793440i
$474$		0			0
$475$	5.29210			0.242818
$476$		0			0
$477$	−32.9759			−1.50986
$478$		0			0
$479$	−18.6414	−	32.2879i	−0.851748	−	1.47527i	−0.879629	−	0.475660i	$-0.842209\pi$
$479$	−18.6414	−	32.2879i	−0.851748	−	1.47527i	0.0278812	−	0.999611i	$-0.491124\pi$
$480$		0			0
$481$	6.61539	−	11.4582i	0.301636	−	0.522449i
$482$		0			0
$483$	−1.52310	−	0.833849i	−0.0693036	−	0.0379415i
$484$		0			0
$485$	3.49689	−	6.05679i	0.158785	−	0.275025i
$486$		0			0
$487$	−16.1747	−	28.0155i	−0.732948	−	1.26950i	−0.955618	−	0.294609i	$-0.904811\pi$
$487$	−16.1747	−	28.0155i	−0.732948	−	1.26950i	0.222670	−	0.974894i	$-0.428523\pi$
$488$		0			0
$489$	2.23583			0.101108
$490$		0			0
$491$	27.3117			1.23256			0.616281	−	0.787526i	$-0.288639\pi$
$491$	27.3117			1.23256			0.616281	+	0.787526i	$0.288639\pi$
$492$		0			0
$493$	−5.17602	−	8.96512i	−0.233116	−	0.403769i
$494$		0			0
$495$	4.94937	−	8.57255i	0.222457	−	0.385308i
$496$		0			0
$497$	−10.2853	−	5.63085i	−0.461358	−	0.252578i
$498$		0			0
$499$	−14.2581	+	24.6958i	−0.638281	+	1.10553i	0.347529	+	0.937669i	$0.387021\pi$
$499$	−14.2581	+	24.6958i	−0.638281	+	1.10553i	−0.985810	+	0.167865i	$0.946313\pi$
$500$		0			0
$501$	−3.41514	−	5.91519i	−0.152577	−	0.264271i
$502$		0			0
$503$	30.0184			1.33846			0.669228	−	0.743057i	$-0.266625\pi$
$503$	30.0184			1.33846			0.669228	+	0.743057i	$0.266625\pi$
$504$		0			0
$505$	4.86627			0.216546
$506$		0			0
$507$	2.80823	+	4.86400i	0.124718	+	0.216018i
$508$		0			0
$509$	−12.7119	+	22.0176i	−0.563445	+	0.975915i	0.433748	+	0.901034i	$0.357191\pi$
$509$	−12.7119	+	22.0176i	−0.563445	+	0.975915i	−0.997192	+	0.0748808i	$0.976142\pi$
$510$		0			0
$511$	0.245563	+	10.8147i	0.0108631	+	0.478416i
$512$		0			0
$513$	−15.4504	+	26.7609i	−0.682153	+	1.18152i
$514$		0			0
$515$	3.33532	+	5.77695i	0.146972	+	0.254563i
$516$		0			0
$517$	−3.95873			−0.174105
$518$		0			0
$519$	−5.41096			−0.237515
$520$		0			0
$521$	9.92233	+	17.1860i	0.434705	+	0.752932i	0.997272	−	0.0738205i	$-0.0235192\pi$
$521$	9.92233	+	17.1860i	0.434705	+	0.752932i	−0.562566	+	0.826752i	$0.690186\pi$
$522$		0			0
$523$	−8.90771	+	15.4286i	−0.389507	+	0.674646i	−0.992383	−	0.123189i	$-0.960688\pi$
$523$	−8.90771	+	15.4286i	−0.389507	+	0.674646i	0.602876	+	0.797835i	$0.294021\pi$
$524$		0			0
$525$	−0.928758	+	0.564711i	−0.0405343	+	0.0246460i
$526$		0			0
$527$	23.2940	−	40.3465i	1.01470	−	1.75752i
$528$		0			0
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$		0			0
$531$	3.53356			0.153344
$532$		0			0
$533$	−1.52989			−0.0662670
$534$		0			0
$535$	−10.8445	−	18.7832i	−0.468847	−	0.812067i
$536$		0			0
$537$	6.29464	−	10.9026i	0.271634	−	0.470483i
$538$		0			0
$539$	−5.93407	+	11.4487i	−0.255599	+	0.493131i
$540$		0			0
$541$	3.02649	−	5.24203i	0.130119	−	0.225373i	−0.793603	−	0.608436i	$-0.791797\pi$
$541$	3.02649	−	5.24203i	0.130119	−	0.225373i	0.923722	+	0.383063i	$0.125131\pi$
$542$		0			0
$543$	−3.31959	−	5.74969i	−0.142457	−	0.246743i
$544$		0			0
$545$	12.5627			0.538128
$546$		0			0
$547$	−30.0674			−1.28559			−0.642794	−	0.766039i	$-0.722225\pi$
$547$	−30.0674			−1.28559			−0.642794	+	0.766039i	$0.722225\pi$
$548$		0			0
$549$	2.31406	+	4.00807i	0.0987617	+	0.171060i
$550$		0			0
$551$	−9.49959	+	16.4538i	−0.404696	+	0.700954i
$552$		0			0
$553$	15.6611	−	9.52236i	0.665976	−	0.404932i
$554$		0			0
$555$	−4.30822	+	7.46205i	−0.182874	+	0.316747i
$556$		0			0
$557$	4.42715	+	7.66805i	0.187584	+	0.324906i	0.944444	−	0.328671i	$-0.106601\pi$
$557$	4.42715	+	7.66805i	0.187584	+	0.324906i	−0.756860	+	0.653577i	$0.773268\pi$
$558$		0			0
$559$	−22.7975			−0.964231
$560$		0			0
$561$	5.56921			0.235132
$562$		0			0
$563$	−3.13547	−	5.43079i	−0.132144	−	0.228881i	0.792359	−	0.610056i	$-0.208853\pi$
$563$	−3.13547	−	5.43079i	−0.132144	−	0.228881i	−0.924503	+	0.381175i	$0.875520\pi$
$564$		0			0
$565$	4.02756	−	6.97594i	0.169441	−	0.293480i
$566$		0			0
$567$	0.318852	+	14.0424i	0.0133905	+	0.589727i
$568$		0			0
$569$	−6.48991	+	11.2409i	−0.272071	+	0.471241i	−0.969392	−	0.245518i	$-0.921042\pi$
$569$	−6.48991	+	11.2409i	−0.272071	+	0.471241i	0.697321	+	0.716759i	$0.254375\pi$
$570$		0			0
$571$	7.52736	+	13.0378i	0.315010	+	0.545614i	0.979440	−	0.201737i	$-0.0646587\pi$
$571$	7.52736	+	13.0378i	0.315010	+	0.545614i	−0.664429	+	0.747351i	$0.731325\pi$
$572$		0			0
$573$	−11.0997			−0.463697
$574$		0			0
$575$	−0.625980			−0.0261052
$576$		0			0
$577$	11.9819	+	20.7533i	0.498813	+	0.863970i	0.999999	−	0.00136978i	$-0.000436016\pi$
$577$	11.9819	+	20.7533i	0.498813	+	0.863970i	−0.501186	+	0.865340i	$0.667103\pi$
$578$		0			0
$579$	−2.39359	+	4.14582i	−0.0994741	+	0.172294i
$580$		0			0
$581$	4.13807	+	2.26546i	0.171676	+	0.0939870i
$582$		0			0
$583$	11.8219	−	20.4762i	0.489615	−	0.848037i
$584$		0			0
$585$	−5.66269	−	9.80807i	−0.234123	−	0.405514i
$586$		0			0
$587$	12.1473			0.501374			0.250687	−	0.968068i	$-0.419343\pi$
$587$	12.1473			0.501374			0.250687	+	0.968068i	$0.419343\pi$
$588$		0			0
$589$	−85.5036			−3.52311
$590$		0			0
$591$	−1.37863	−	2.38786i	−0.0567093	−	0.0982233i
$592$		0			0
$593$	14.6831	−	25.4319i	0.602963	−	1.04436i	−0.389407	−	0.921066i	$-0.627320\pi$
$593$	14.6831	−	25.4319i	0.602963	−	1.04436i	0.992370	−	0.123296i	$-0.0393466\pi$
$594$		0			0
$595$	−22.3574	−	12.2400i	−0.916566	−	0.501790i
$596$		0			0
$597$	−1.08641	+	1.88172i	−0.0444639	+	0.0770138i
$598$		0			0
$599$	3.11333	+	5.39244i	0.127207	+	0.220329i	0.922594	−	0.385773i	$-0.126065\pi$
$599$	3.11333	+	5.39244i	0.127207	+	0.220329i	−0.795386	+	0.606103i	$0.792732\pi$
$600$		0			0
$601$	−25.7823			−1.05168			−0.525842	−	0.850582i	$-0.676250\pi$
$601$	−25.7823			−1.05168			−0.525842	+	0.850582i	$0.676250\pi$
$602$		0			0
$603$	14.9919			0.610516
$604$		0			0
$605$	−7.95407	−	13.7769i	−0.323379	−	0.560109i
$606$		0			0
$607$	−12.0490	+	20.8695i	−0.489053	+	0.847065i	−0.999921	−	0.0125944i	$-0.995991\pi$
$607$	−12.0490	+	20.8695i	−0.489053	+	0.847065i	0.510867	+	0.859660i	$0.329324\pi$
$608$		0			0
$609$	−0.0885844	−	3.90131i	−0.00358962	−	0.158089i
$610$		0			0
$611$	−2.26464	+	3.92247i	−0.0916174	+	0.158686i
$612$		0			0
$613$	2.21263	+	3.83238i	0.0893672	+	0.154789i	0.907244	−	0.420605i	$-0.138182\pi$
$613$	2.21263	+	3.83238i	0.0893672	+	0.154789i	−0.817877	+	0.575394i	$0.804849\pi$
$614$		0			0
$615$	0.996330			0.0401759
$616$		0			0
$617$	−38.6078			−1.55429			−0.777145	−	0.629321i	$-0.783333\pi$
$617$	−38.6078			−1.55429			−0.777145	+	0.629321i	$0.783333\pi$
$618$		0			0
$619$	19.5214	+	33.8121i	0.784632	+	1.35902i	0.929219	+	0.369530i	$0.120481\pi$
$619$	19.5214	+	33.8121i	0.784632	+	1.35902i	−0.144587	+	0.989492i	$0.546185\pi$
$620$		0			0
$621$	1.82757	−	3.16544i	0.0733377	−	0.127025i
$622$		0			0
$623$	−8.35381	+	5.07935i	−0.334688	+	0.203500i
$624$		0			0
$625$	10.7391	−	18.6007i	0.429565	−	0.744028i
$626$		0			0
$627$	−5.11061	−	8.85184i	−0.204098	−	0.353508i
$628$		0			0
$629$	28.9161			1.15296
$630$		0			0
$631$	39.0520			1.55463			0.777317	−	0.629109i	$-0.216580\pi$
$631$	39.0520			1.55463			0.777317	+	0.629109i	$0.216580\pi$
$632$		0			0
$633$	1.21591	+	2.10602i	0.0483281	+	0.0837068i
$634$		0			0
$635$	−9.71010	+	16.8184i	−0.385334	+	0.667418i
$636$		0			0
$637$	7.94920	+	12.4291i	0.314959	+	0.492459i
$638$		0			0
$639$	5.69338	−	9.86123i	0.225227	−	0.390104i
$640$		0			0
$641$	−16.1132	−	27.9089i	−0.636434	−	1.10234i	−0.986209	−	0.165502i	$-0.947075\pi$
$641$	−16.1132	−	27.9089i	−0.636434	−	1.10234i	0.349776	−	0.936834i	$-0.386258\pi$
$642$		0			0
$643$	5.83718			0.230196			0.115098	−	0.993354i	$-0.463282\pi$
$643$	5.83718			0.230196			0.115098	+	0.993354i	$0.463282\pi$
$644$		0			0
$645$	14.8467			0.584587
$646$		0			0
$647$	−16.6367	−	28.8156i	−0.654056	−	1.13286i	−0.982130	−	0.188205i	$-0.939733\pi$
$647$	−16.6367	−	28.8156i	−0.654056	−	1.13286i	0.328074	−	0.944652i	$-0.393600\pi$
$648$		0			0
$649$	−1.26679	+	2.19414i	−0.0497258	+	0.0861277i
$650$		0			0
$651$	15.0058	−	9.12394i	0.588124	−	0.357596i
$652$		0			0
$653$	8.92627	−	15.4608i	0.349312	−	0.605026i	−0.636815	−	0.771016i	$-0.719749\pi$
$653$	8.92627	−	15.4608i	0.349312	−	0.605026i	0.986127	+	0.165990i	$0.0530820\pi$
$654$		0			0
$655$	9.90529	+	17.1565i	0.387032	+	0.670359i
$656$		0			0
$657$	−10.5048			−0.409831
$658$		0			0
$659$	39.3673			1.53353			0.766765	−	0.641927i	$-0.221865\pi$
$659$	39.3673			1.53353			0.766765	+	0.641927i	$0.221865\pi$
$660$		0			0
$661$	−3.00734	−	5.20886i	−0.116972	−	0.202601i	0.801594	−	0.597868i	$-0.203985\pi$
$661$	−3.00734	−	5.20886i	−0.116972	−	0.202601i	−0.918566	+	0.395267i	$0.870652\pi$
$662$		0			0
$663$	3.18593	−	5.51820i	0.123731	−	0.214309i
$664$		0			0
$665$	1.06192	+	46.7675i	0.0411794	+	1.81357i
$666$		0			0
$667$	1.12367	−	1.94625i	0.0435086	−	0.0753591i
$668$		0			0
$669$	−0.163934	−	0.283941i	−0.00633804	−	0.0109778i
$670$		0			0
$671$	−3.31838			−0.128105
$672$		0			0
$673$	−51.3147			−1.97804			−0.989018	−	0.147792i	$-0.952783\pi$
$673$	−51.3147			−1.97804			−0.989018	+	0.147792i	$0.952783\pi$
$674$		0			0
$675$	−1.14402	−	1.98150i	−0.0440334	−	0.0762681i
$676$		0			0
$677$	22.6925	−	39.3045i	0.872143	−	1.51060i	0.0123673	−	0.999924i	$-0.496063\pi$
$677$	22.6925	−	39.3045i	0.872143	−	1.51060i	0.859776	−	0.510672i	$-0.170603\pi$
$678$		0			0
$679$	−7.76060	−	4.24867i	−0.297825	−	0.163049i
$680$		0			0
$681$	9.46301	−	16.3904i	0.362623	−	0.628082i
$682$		0			0
$683$	12.4451	+	21.5555i	0.476197	+	0.824797i	0.999628	−	0.0272708i	$-0.00868166\pi$
$683$	12.4451	+	21.5555i	0.476197	+	0.824797i	−0.523431	+	0.852068i	$0.675348\pi$
$684$		0			0
$685$	−21.8271			−0.833969
$686$		0			0
$687$	−13.0177			−0.496657
$688$		0			0
$689$	−13.5258	−	23.4273i	−0.515291	−	0.892509i
$690$		0			0
$691$	14.4445	−	25.0186i	0.549495	−	0.951754i	−0.448814	−	0.893625i	$-0.648153\pi$
$691$	14.4445	−	25.0186i	0.549495	−	0.951754i	0.998309	−	0.0581285i	$-0.0185133\pi$
$692$		0			0
$693$	−10.9841	−	6.01342i	−0.417250	−	0.228431i
$694$		0			0
$695$	23.3734	−	40.4839i	0.886604	−	1.53564i
$696$		0			0
$697$	−1.67180	−	2.89565i	−0.0633241	−	0.109680i
$698$		0			0
$699$	6.33285			0.239530
$700$		0			0
$701$	5.88167			0.222148			0.111074	−	0.993812i	$-0.464571\pi$
$701$	5.88167			0.222148			0.111074	+	0.993812i	$0.464571\pi$
$702$		0			0
$703$	−26.5350	−	45.9600i	−1.00079	−	1.73341i
$704$		0			0
$705$	1.47483	−	2.55447i	0.0555452	−	0.0962070i
$706$		0			0
$707$	−0.139746	−	6.15450i	−0.00525569	−	0.231464i
$708$		0			0
$709$	20.2687	−	35.1065i	0.761208	−	1.31845i	−0.181020	−	0.983479i	$-0.557940\pi$
$709$	20.2687	−	35.1065i	0.761208	−	1.31845i	0.942228	−	0.334971i	$-0.108727\pi$
$710$		0			0
$711$	8.89945	+	15.4143i	0.333755	+	0.578081i
$712$		0			0
$713$	10.1139			0.378767
$714$		0			0
$715$	8.12034			0.303684
$716$		0			0
$717$	1.52920	+	2.64865i	0.0571091	+	0.0989158i
$718$		0			0
$719$	23.0654	−	39.9505i	0.860194	−	1.48990i	−0.0115465	−	0.999933i	$-0.503675\pi$
$719$	23.0654	−	39.9505i	0.860194	−	1.48990i	0.871741	−	0.489967i	$-0.162991\pi$
$720$		0			0
$721$	7.21048	−	4.38417i	0.268532	−	0.163275i
$722$		0			0
$723$	3.24035	−	5.61245i	0.120510	−	0.208729i
$724$		0			0
$725$	−0.703394	−	1.21831i	−0.0261234	−	0.0452470i
$726$		0			0
$727$	38.2028			1.41686			0.708431	−	0.705780i	$-0.249403\pi$
$727$	38.2028			1.41686			0.708431	+	0.705780i	$0.249403\pi$
$728$		0			0
$729$	−6.44335			−0.238643
$730$		0			0
$731$	−24.9122	−	43.1491i	−0.921409	−	1.59593i
$732$		0			0
$733$	−7.56920	+	13.1102i	−0.279575	+	0.484238i	−0.971279	−	0.237943i	$-0.923527\pi$
$733$	−7.56920	+	13.1102i	−0.279575	+	0.484238i	0.691704	+	0.722181i	$0.256860\pi$
$734$		0			0
$735$	−5.17685	−	8.09435i	−0.190951	−	0.298565i
$736$		0			0
$737$	−5.37462	+	9.30911i	−0.197976	+	0.342905i
$738$		0			0
$739$	−8.27240	−	14.3282i	−0.304305	−	0.527072i	0.672801	−	0.739823i	$-0.265091\pi$
$739$	−8.27240	−	14.3282i	−0.304305	−	0.527072i	−0.977106	+	0.212751i	$0.931758\pi$
$740$		0			0
$741$	−11.6944			−0.429603
$742$		0			0
$743$	−40.6663			−1.49190			−0.745951	−	0.666000i	$-0.768005\pi$
$743$	−40.6663			−1.49190			−0.745951	+	0.666000i	$0.768005\pi$
$744$		0			0
$745$	14.5577	+	25.2147i	0.533353	+	0.923794i
$746$		0			0
$747$	−2.29062	+	3.96747i	−0.0838093	+	0.145162i
$748$		0			0
$749$	−23.4442	+	14.2547i	−0.856631	+	0.520855i
$750$		0			0
$751$	17.4919	−	30.2968i	0.638287	−	1.10555i	−0.347521	−	0.937672i	$-0.612977\pi$
$751$	17.4919	−	30.2968i	0.638287	−	1.10555i	0.985809	−	0.167874i	$-0.0536901\pi$
$752$		0			0
$753$	−9.27321	−	16.0617i	−0.337935	−	0.585320i
$754$		0			0
$755$	−31.8662			−1.15973
$756$		0			0
$757$	−4.88371			−0.177502			−0.0887508	−	0.996054i	$-0.528287\pi$
$757$	−4.88371			−0.177502			−0.0887508	+	0.996054i	$0.528287\pi$
$758$		0			0
$759$	0.604513	+	1.04705i	0.0219424	+	0.0380054i
$760$		0			0
$761$	5.23713	−	9.07098i	0.189846	−	0.328823i	−0.755353	−	0.655318i	$-0.772534\pi$
$761$	5.23713	−	9.07098i	0.189846	−	0.328823i	0.945199	+	0.326496i	$0.105868\pi$
$762$		0			0
$763$	−0.360768	−	15.8884i	−0.0130607	−	0.575199i
$764$		0			0
$765$	12.3759	−	21.4357i	0.447452	−	0.775009i
$766$		0			0
$767$	1.44936	+	2.51037i	0.0523335	+	0.0906443i
$768$		0			0
$769$	20.0464			0.722891			0.361446	−	0.932393i	$-0.382283\pi$
$769$	20.0464			0.722891			0.361446	+	0.932393i	$0.382283\pi$
$770$		0			0
$771$	15.0653			0.542564
$772$		0			0
$773$	−20.6260	−	35.7252i	−0.741864	−	1.28495i	−0.951646	−	0.307198i	$-0.900609\pi$
$773$	−20.6260	−	35.7252i	−0.741864	−	1.28495i	0.209781	−	0.977748i	$-0.432725\pi$
$774$		0			0
$775$	3.16554	−	5.48288i	0.113710	−	0.196951i
$776$		0			0
$777$	9.56118	+	5.23443i	0.343005	+	0.187784i
$778$		0			0
$779$	−3.06828	+	5.31441i	−0.109932	+	0.190409i
$780$		0			0
$781$	4.08218	+	7.07054i	0.146072	+	0.253004i
$782$		0			0
$783$	8.21431			0.293555
$784$		0			0
$785$	18.2091			0.649912
$786$		0			0
$787$	−8.69694	−	15.0635i	−0.310012	−	0.536957i	0.668352	−	0.743845i	$-0.267000\pi$
$787$	−8.69694	−	15.0635i	−0.310012	−	0.536957i	−0.978365	+	0.206888i	$0.933667\pi$
$788$		0			0
$789$	6.17449	−	10.6945i	0.219818	−	0.380735i
$790$		0			0
$791$	−8.93832	−	4.89343i	−0.317810	−	0.173990i
$792$		0			0
$793$	−1.89832	+	3.28799i	−0.0674113	+	0.116760i
$794$		0			0
$795$	8.80854	+	15.2568i	0.312407	+	0.541104i
$796$		0			0
$797$	−2.80365			−0.0993105			−0.0496553	−	0.998766i	$-0.515812\pi$
$797$	−2.80365			−0.0993105			−0.0496553	+	0.998766i	$0.515812\pi$
$798$		0			0
$799$	−9.89880			−0.350194
$800$		0			0
$801$	−4.74708	−	8.22218i	−0.167730	−	0.290517i
$802$		0			0
$803$	3.76599	−	6.52289i	0.132899	−	0.230188i
$804$		0			0
$805$	−0.125610	−	5.53194i	−0.00442717	−	0.194975i
$806$		0			0
$807$	−5.45540	+	9.44903i	−0.192039	+	0.332622i
$808$		0			0
$809$	17.6880	+	30.6366i	0.621879	+	1.07713i	0.989136	+	0.147006i	$0.0469636\pi$
$809$	17.6880	+	30.6366i	0.621879	+	1.07713i	−0.367257	+	0.930119i	$0.619703\pi$
$810$		0			0
$811$	−5.70149			−0.200207			−0.100103	−	0.994977i	$-0.531917\pi$
$811$	−5.70149			−0.200207			−0.100103	+	0.994977i	$0.531917\pi$
$812$		0			0
$813$	3.70623			0.129983
$814$		0			0
$815$	3.56240	+	6.17026i	0.124786	+	0.216135i
$816$		0			0
$817$	−45.7215	+	79.1920i	−1.59959	+	2.77058i
$818$		0			0
$819$	−12.2419	+	7.44342i	−0.427767	+	0.260094i
$820$		0			0
$821$	−22.4193	+	38.8314i	−0.782440	+	1.35523i	0.148077	+	0.988976i	$0.452692\pi$
$821$	−22.4193	+	38.8314i	−0.782440	+	1.35523i	−0.930517	+	0.366250i	$0.880642\pi$
$822$		0			0
$823$	0.255416	+	0.442394i	0.00890325	+	0.0154209i	0.870443	−	0.492270i	$-0.163833\pi$
$823$	0.255416	+	0.442394i	0.00890325	+	0.0154209i	−0.861539	+	0.507691i	$0.830499\pi$
$824$		0			0
$825$	0.756827			0.0263493
$826$		0			0
$827$	24.9250			0.866726			0.433363	−	0.901219i	$-0.357327\pi$
$827$	24.9250			0.866726			0.433363	+	0.901219i	$0.357327\pi$
$828$		0			0
$829$	−5.49253	−	9.51334i	−0.190763	−	0.330412i	0.754740	−	0.656024i	$-0.227763\pi$
$829$	−5.49253	−	9.51334i	−0.190763	−	0.330412i	−0.945503	+	0.325612i	$0.894430\pi$
$830$		0			0
$831$	8.42524	−	14.5929i	0.292268	−	0.506224i
$832$		0			0
$833$	−14.8382	+	28.6276i	−0.514112	+	0.991886i
$834$		0			0
$835$	10.8829	−	18.8497i	0.376617	−	0.652320i
$836$		0			0
$837$	18.4838	+	32.0148i	0.638893	+	1.10659i
$838$		0			0
$839$	−7.42486			−0.256335			−0.128167	−	0.991753i	$-0.540909\pi$
$839$	−7.42486			−0.256335			−0.128167	+	0.991753i	$0.540909\pi$
$840$		0			0
$841$	−23.9495			−0.825844
$842$		0			0
$843$	−7.79748	−	13.5056i	−0.268559	−	0.465159i
$844$		0			0
$845$	−8.94886	+	15.4999i	−0.307850	+	0.533212i
$846$		0			0
$847$	−17.1955	+	10.4554i	−0.590846	+	0.359250i
$848$		0			0
$849$	2.37554	−	4.11456i	0.0815283	−	0.141211i
$850$		0			0
$851$	3.13871	+	5.43641i	0.107594	+	0.186358i
$852$		0			0
$853$	−18.4615			−0.632111			−0.316055	−	0.948741i	$-0.602359\pi$
$853$	−18.4615			−0.632111			−0.316055	+	0.948741i	$0.602359\pi$
$854$		0			0
$855$	−45.4272			−1.55358
$856$		0			0
$857$	2.44368	+	4.23258i	0.0834745	+	0.144582i	0.904740	−	0.425964i	$-0.140065\pi$
$857$	2.44368	+	4.23258i	0.0834745	+	0.144582i	−0.821266	+	0.570546i	$0.806732\pi$
$858$		0			0
$859$	−7.03392	+	12.1831i	−0.239994	+	0.415682i	−0.960712	−	0.277546i	$-0.910479\pi$
$859$	−7.03392	+	12.1831i	−0.239994	+	0.415682i	0.720718	+	0.693228i	$0.243812\pi$
$860$		0			0
$861$	−0.0286119	−	1.26009i	−0.000975091	−	0.0429436i
$862$		0			0
$863$	−11.7900	+	20.4209i	−0.401337	+	0.695136i	−0.993888	−	0.110397i	$-0.964788\pi$
$863$	−11.7900	+	20.4209i	−0.401337	+	0.695136i	0.592551	+	0.805533i	$0.298121\pi$
$864$		0			0
$865$	−8.62143	−	14.9328i	−0.293138	−	0.507729i
$866$		0			0
$867$	2.76865			0.0940282
$868$		0			0
$869$	−12.7619			−0.432917
$870$		0			0
$871$	6.14923	+	10.6508i	0.208359	+	0.360888i
$872$		0			0
$873$	4.29586	−	7.44065i	0.145393	−	0.251828i
$874$		0			0
$875$	−27.3063	−	14.9493i	−0.923121	−	0.505378i
$876$		0			0
$877$	−6.70700	+	11.6169i	−0.226479	+	0.392274i	−0.956762	−	0.290871i	$-0.906055\pi$
$877$	−6.70700	+	11.6169i	−0.226479	+	0.392274i	0.730283	+	0.683145i	$0.239388\pi$
$878$		0			0
$879$	−9.43782	−	16.3468i	−0.318330	−	0.551364i
$880$		0			0
$881$	21.8130			0.734898			0.367449	−	0.930044i	$-0.380231\pi$
$881$	21.8130			0.734898			0.367449	+	0.930044i	$0.380231\pi$
$882$		0			0
$883$	16.6473			0.560226			0.280113	−	0.959967i	$-0.409628\pi$
$883$	16.6473			0.560226			0.280113	+	0.959967i	$0.409628\pi$
$884$		0			0
$885$	−0.943887	−	1.63486i	−0.0317284	−	0.0549552i
$886$		0			0
$887$	−13.5409	+	23.4536i	−0.454660	+	0.787495i	−0.998669	−	0.0515852i	$-0.983573\pi$
$887$	−13.5409	+	23.4536i	−0.454660	+	0.787495i	0.544008	+	0.839080i	$0.316906\pi$
$888$		0			0
$889$	21.5495	+	11.7976i	0.722748	+	0.395680i
$890$		0			0
$891$	4.88997	−	8.46967i	0.163820	−	0.283745i
$892$		0			0
$893$	9.08368	+	15.7334i	0.303974	+	0.526498i
$894$		0			0
$895$	40.1177			1.34099
$896$		0			0
$897$	1.38328			0.0461863
$898$		0			0
$899$	11.3646	+	19.6841i	0.379031	+	0.656502i
$900$		0			0
$901$	29.5608	−	51.2008i	0.984812	−	1.70575i
$902$		0			0
$903$	−0.426356	−	18.7770i	−0.0141883	−	0.624859i
$904$		0			0
$905$	10.5784	−	18.3223i	0.351637	−	0.609053i
$906$		0			0
$907$	0.860049	+	1.48965i	0.0285575	+	0.0494630i	0.879951	−	0.475065i	$-0.157575\pi$
$907$	0.860049	+	1.48965i	0.0285575	+	0.0494630i	−0.851393	+	0.524528i	$0.824242\pi$
$908$		0			0
$909$	5.97811			0.198282
$910$		0			0
$911$	−21.1481			−0.700669			−0.350335	−	0.936625i	$-0.613932\pi$
$911$	−21.1481			−0.700669			−0.350335	+	0.936625i	$0.613932\pi$
$912$		0			0
$913$	−1.64238	−	2.84469i	−0.0543549	−	0.0941455i
$914$		0			0
$915$	1.23627	−	2.14128i	0.0408697	−	0.0707884i
$916$		0			0
$917$	21.4138	−	13.0202i	0.707146	−	0.429964i
$918$		0			0
$919$	−19.3664	+	33.5435i	−0.638838	+	1.10650i	0.346850	+	0.937920i	$0.387251\pi$
$919$	−19.3664	+	33.5435i	−0.638838	+	1.10650i	−0.985688	+	0.168579i	$0.946082\pi$
$920$		0			0
$921$	−6.79579	−	11.7707i	−0.223929	−	0.387856i
$922$		0			0
$923$	9.34104			0.307464
$924$		0			0
$925$	3.92955			0.129203
$926$		0			0
$927$	4.09738	+	7.09687i	0.134576	+	0.233092i
$928$		0			0
$929$	−1.96997	+	3.41210i	−0.0646328	+	0.111947i	−0.896531	−	0.442981i	$-0.853921\pi$
$929$	−1.96997	+	3.41210i	−0.0646328	+	0.111947i	0.831898	+	0.554928i	$0.187254\pi$
$930$		0			0
$931$	59.1177	−	2.68607i	1.93750	−	0.0880325i
$932$		0			0
$933$	−7.75992	+	13.4406i	−0.254048	+	0.440025i
$934$		0			0
$935$	8.87357	+	15.3695i	0.290197	+	0.502636i
$936$		0			0
$937$	35.6176			1.16358			0.581788	−	0.813340i	$-0.302353\pi$
$937$	35.6176			1.16358			0.581788	+	0.813340i	$0.302353\pi$
$938$		0			0
$939$	22.8680			0.746267
$940$		0			0
$941$	18.2282	+	31.5722i	0.594223	+	1.02923i	0.993656	+	0.112463i	$0.0358739\pi$
$941$	18.2282	+	31.5722i	0.594223	+	1.02923i	−0.399433	+	0.916763i	$0.630793\pi$
$942$		0			0
$943$	0.362934	−	0.628620i	0.0118187	−	0.0204707i
$944$		0			0
$945$	17.2815	−	10.5076i	0.562166	−	0.341812i
$946$		0			0
$947$	−14.5362	+	25.1775i	−0.472365	+	0.818159i	−0.999500	−	0.0316219i	$-0.989933\pi$
$947$	−14.5362	+	25.1775i	−0.472365	+	0.818159i	0.527135	+	0.849781i	$0.323266\pi$
$948$		0			0
$949$	−4.30876	−	7.46299i	−0.139868	−	0.242259i
$950$		0			0
$951$	11.2197			0.363823
$952$		0			0
$953$	56.7993			1.83991			0.919955	−	0.392025i	$-0.128225\pi$
$953$	56.7993			1.83991			0.919955	+	0.392025i	$0.128225\pi$
$954$		0			0
$955$	−17.6855	−	30.6321i	−0.572288	−	0.991231i
$956$		0			0
$957$	−1.35854	+	2.35307i	−0.0439155	+	0.0760639i
$958$		0			0
$959$	0.626814	+	27.6053i	0.0202409	+	0.891421i
$960$		0			0
$961$	−35.6451	+	61.7392i	−1.14984	+	1.99159i
$962$		0			0
$963$	−13.3222	−	23.0748i	−0.429303	−	0.743574i
$964$		0			0
$965$	−15.2551			−0.491078
$966$		0			0
$967$	24.5018			0.787924			0.393962	−	0.919127i	$-0.371104\pi$
$967$	24.5018			0.787924			0.393962	+	0.919127i	$0.371104\pi$
$968$		0			0
$969$	−12.7791	−	22.1341i	−0.410524	−	0.711048i
$970$		0			0
$971$	4.56449	−	7.90593i	0.146482	−	0.253713i	−0.783443	−	0.621463i	$-0.786538\pi$
$971$	4.56449	−	7.90593i	0.146482	−	0.253713i	0.929925	+	0.367750i	$0.119872\pi$
$972$		0			0
$973$	−51.8723	−	28.3984i	−1.66295	−	0.910410i
$974$		0			0
$975$	0.432952	−	0.749895i	0.0138656	−	0.0240159i
$976$		0			0
$977$	11.1087	+	19.2408i	0.355397	+	0.615566i	0.987186	−	0.159574i	$-0.0510122\pi$
$977$	11.1087	+	19.2408i	0.355397	+	0.615566i	−0.631788	+	0.775141i	$0.717679\pi$
$978$		0			0
$979$	6.80735			0.217564
$980$		0			0
$981$	15.4331			0.492740
$982$		0			0
$983$	−1.03604	−	1.79447i	−0.0330445	−	0.0572347i	0.849030	−	0.528344i	$-0.177187\pi$
$983$	−1.03604	−	1.79447i	−0.0330445	−	0.0572347i	−0.882075	+	0.471110i	$0.843854\pi$
$984$		0			0
$985$	4.39322	−	7.60927i	0.139980	−	0.242452i
$986$		0			0
$987$	−3.27306	−	1.79189i	−0.104183	−	0.0570366i
$988$		0			0
$989$	5.40821	−	9.36729i	0.171971	−	0.297863i
$990$		0			0
$991$	3.03400	+	5.25505i	0.0963782	+	0.166932i	0.910183	−	0.414206i	$-0.135941\pi$
$991$	3.03400	+	5.25505i	0.0963782	+	0.166932i	−0.813805	+	0.581138i	$0.802607\pi$
$992$		0			0
$993$	−14.7581			−0.468334
$994$		0			0
$995$	−6.92405			−0.219507
$996$		0			0
$997$	23.2442	+	40.2602i	0.736153	+	1.27505i	0.954216	+	0.299119i	$0.0966927\pi$
$997$	23.2442	+	40.2602i	0.736153	+	1.27505i	−0.218063	+	0.975935i	$0.569974\pi$
$998$		0			0
$999$	−11.4724	+	19.8708i	−0.362971	+	0.628685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1288.2.q.a.737.5	✓	22
7.2	even	3		9016.2.a.bq.1.7		11
7.4	even	3	inner	1288.2.q.a.921.5	yes	22
7.5	odd	6		9016.2.a.bl.1.5		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1288.2.q.a.737.5	✓	22	1.1	even	1	trivial
1288.2.q.a.921.5	yes	22	7.4	even	3	inner
9016.2.a.bl.1.5		11	7.5	odd	6
9016.2.a.bq.1.7		11	7.2	even	3

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:	\( N \)	\(=\)	\( 1288 = 2^{3} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1288.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.328152 - 0.568377i) q^{3} +(1.04571 - 1.81122i) q^{5} +(-2.32073 - 1.27052i) q^{7} +(1.28463 - 2.22505i) q^{9} +O(q^{10})\)	\(q+(-0.328152 - 0.568377i) q^{3} +(1.04571 - 1.81122i) q^{5} +(-2.32073 - 1.27052i) q^{7} +(1.28463 - 2.22505i) q^{9} +(0.921087 + 1.59537i) q^{11} +2.10767 q^{13} -1.37261 q^{15} +(2.30318 + 3.98922i) q^{17} +(4.22705 - 7.32146i) q^{19} +(0.0394175 + 1.73597i) q^{21} +(-0.500000 + 0.866025i) q^{23} +(0.312990 + 0.542115i) q^{25} -3.65513 q^{27} -2.24733 q^{29} +(-5.05693 - 8.75887i) q^{31} +(0.604513 - 1.04705i) q^{33} +(-4.72800 + 2.87475i) q^{35} +(3.13871 - 5.43641i) q^{37} +(-0.691638 - 1.19795i) q^{39} -0.725868 q^{41} -10.8164 q^{43} +(-2.68670 - 4.65350i) q^{45} +(-1.07447 + 1.86104i) q^{47} +(3.77155 + 5.89707i) q^{49} +(1.51159 - 2.61815i) q^{51} +(-6.41739 - 11.1152i) q^{53} +3.85275 q^{55} -5.54846 q^{57} +(0.687660 + 1.19106i) q^{59} +(-0.900671 + 1.56001i) q^{61} +(-5.80825 + 3.53158i) q^{63} +(2.20401 - 3.81746i) q^{65} +(2.91754 + 5.05333i) q^{67} +0.656305 q^{69} +4.43192 q^{71} +(-2.04432 - 3.54086i) q^{73} +(0.205417 - 0.355792i) q^{75} +(-0.110641 - 4.87268i) q^{77} +(-3.46381 + 5.99950i) q^{79} +(-2.65446 - 4.59765i) q^{81} -1.78309 q^{83} +9.63381 q^{85} +(0.737468 + 1.27733i) q^{87} +(1.84764 - 3.20021i) q^{89} +(-4.89134 - 2.67785i) q^{91} +(-3.31889 + 5.74848i) q^{93} +(-8.84051 - 15.3122i) q^{95} +3.34404 q^{97} +4.73303 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 4 q^{3} - q^{5} + q^{7} - 11 q^{9}+O(q^{10}) \) 22 * q - 4 * q^3 - q^5 + q^7 - 11 * q^9	\( 22 q - 4 q^{3} - q^{5} + q^{7} - 11 q^{9} - 6 q^{13} - 16 q^{15} - 5 q^{17} - 12 q^{19} + 3 q^{21} - 11 q^{23} - 22 q^{25} + 38 q^{27} - 30 q^{29} - 16 q^{31} - 4 q^{33} - 5 q^{35} - 3 q^{37} + q^{39} + 56 q^{41} - 18 q^{43} + 19 q^{45} - 31 q^{47} + 13 q^{49} + 15 q^{51} - 13 q^{53} + 70 q^{55} - 42 q^{57} - 11 q^{59} + 19 q^{61} - 23 q^{63} + 7 q^{65} - 19 q^{67} + 8 q^{69} - 10 q^{71} + 5 q^{73} - 28 q^{75} + 9 q^{77} + 13 q^{79} - 35 q^{81} + 34 q^{83} - 78 q^{85} - 4 q^{87} - 10 q^{89} - 30 q^{91} + 6 q^{93} - 33 q^{95} + 70 q^{97} + 26 q^{99}+O(q^{100}) \) 22 * q - 4 * q^3 - q^5 + q^7 - 11 * q^9 - 6 * q^13 - 16 * q^15 - 5 * q^17 - 12 * q^19 + 3 * q^21 - 11 * q^23 - 22 * q^25 + 38 * q^27 - 30 * q^29 - 16 * q^31 - 4 * q^33 - 5 * q^35 - 3 * q^37 + q^39 + 56 * q^41 - 18 * q^43 + 19 * q^45 - 31 * q^47 + 13 * q^49 + 15 * q^51 - 13 * q^53 + 70 * q^55 - 42 * q^57 - 11 * q^59 + 19 * q^61 - 23 * q^63 + 7 * q^65 - 19 * q^67 + 8 * q^69 - 10 * q^71 + 5 * q^73 - 28 * q^75 + 9 * q^77 + 13 * q^79 - 35 * q^81 + 34 * q^83 - 78 * q^85 - 4 * q^87 - 10 * q^89 - 30 * q^91 + 6 * q^93 - 33 * q^95 + 70 * q^97 + 26 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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