LMFDB - Embedded newform 552.2.q.c.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(25,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("552.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.q (of order $11$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			121.3
Character	$\chi$	$=$	552.121
Dual form			552.2.q.c.73.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 + 0.281733i) q^{3} +(2.64512 - 1.69992i) q^{5} +(0.0583451 - 0.405799i) q^{7} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(0.959493 + 0.281733i) q^{3} +(2.64512 - 1.69992i) q^{5} +(0.0583451 - 0.405799i) q^{7} +(0.841254 + 0.540641i) q^{9} +(0.742783 + 1.62647i) q^{11} +(-0.395701 - 2.75216i) q^{13} +(3.01690 - 0.885841i) q^{15} +(1.07564 - 1.24136i) q^{17} +(0.916981 + 1.05825i) q^{19} +(0.170308 - 0.372923i) q^{21} +(-4.69916 + 0.958061i) q^{23} +(2.02987 - 4.44480i) q^{25} +(0.654861 + 0.755750i) q^{27} +(0.646092 - 0.745630i) q^{29} +(0.686370 - 0.201536i) q^{31} +(0.254466 + 1.76985i) q^{33} +(-0.535494 - 1.17257i) q^{35} +(-2.07448 - 1.33318i) q^{37} +(0.395701 - 2.75216i) q^{39} +(-6.15118 + 3.95312i) q^{41} +(7.39634 + 2.17176i) q^{43} +3.14426 q^{45} -2.85139 q^{47} +(6.55518 + 1.92478i) q^{49} +(1.38180 - 0.888030i) q^{51} +(0.372762 - 2.59262i) q^{53} +(4.72961 + 3.03954i) q^{55} +(0.581692 + 1.27373i) q^{57} +(1.19652 + 8.32198i) q^{59} +(7.71092 - 2.26413i) q^{61} +(0.268474 - 0.309836i) q^{63} +(-5.72512 - 6.60715i) q^{65} +(-4.60258 + 10.0782i) q^{67} +(-4.77873 - 0.404654i) q^{69} +(-0.0976848 + 0.213900i) q^{71} +(-4.37625 - 5.05046i) q^{73} +(3.19990 - 3.69288i) q^{75} +(0.703357 - 0.206524i) q^{77} +(1.17022 + 8.13904i) q^{79} +(0.415415 + 0.909632i) q^{81} +(-13.0290 - 8.37326i) q^{83} +(0.735001 - 5.11204i) q^{85} +(0.829989 - 0.533402i) q^{87} +(-12.6703 - 3.72034i) q^{89} -1.13991 q^{91} +0.715346 q^{93} +(4.22446 + 1.24041i) q^{95} +(6.89329 - 4.43005i) q^{97} +(-0.254466 + 1.76985i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9	$ 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9} + 13 q^{11} - 13 q^{13} + 2 q^{15} - 11 q^{17} + 11 q^{19} - 9 q^{21} - 12 q^{23} + 17 q^{25} + 3 q^{27} + 9 q^{29} + 33 q^{31} + 9 q^{33} + 62 q^{35} + 11 q^{37} + 13 q^{39} + 2 q^{41} - 40 q^{43} - 2 q^{45} - 38 q^{47} - 13 q^{49} + 11 q^{51} - 25 q^{53} + 62 q^{55} + 22 q^{57} + 73 q^{59} + 4 q^{61} - 2 q^{63} - 12 q^{65} - 29 q^{67} - 21 q^{69} - 19 q^{71} - 38 q^{73} + 27 q^{75} + 4 q^{77} - 12 q^{79} - 3 q^{81} - 65 q^{83} + 8 q^{85} + 2 q^{87} - 61 q^{89} - 150 q^{91} - 22 q^{93} - 9 q^{95} - 9 q^{97} - 9 q^{99}+O(q^{100}) $ 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9 + 13 * q^11 - 13 * q^13 + 2 * q^15 - 11 * q^17 + 11 * q^19 - 9 * q^21 - 12 * q^23 + 17 * q^25 + 3 * q^27 + 9 * q^29 + 33 * q^31 + 9 * q^33 + 62 * q^35 + 11 * q^37 + 13 * q^39 + 2 * q^41 - 40 * q^43 - 2 * q^45 - 38 * q^47 - 13 * q^49 + 11 * q^51 - 25 * q^53 + 62 * q^55 + 22 * q^57 + 73 * q^59 + 4 * q^61 - 2 * q^63 - 12 * q^65 - 29 * q^67 - 21 * q^69 - 19 * q^71 - 38 * q^73 + 27 * q^75 + 4 * q^77 - 12 * q^79 - 3 * q^81 - 65 * q^83 + 8 * q^85 + 2 * q^87 - 61 * q^89 - 150 * q^91 - 22 * q^93 - 9 * q^95 - 9 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{9}{11}\right)$	$1$	$1$	$1$

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
$3$	0.959493	+	0.281733i	0.553964	+	0.162658i
$3$	0.959493	+	0.281733i	0.553964	+	0.162658i
$4$		0			0
$5$	2.64512	−	1.69992i	1.18293	−	0.760225i	0.207010	−	0.978339i	$-0.433627\pi$
$5$	2.64512	−	1.69992i	1.18293	−	0.760225i	0.975923	+	0.218113i	$0.0699902\pi$
$6$		0			0
$7$	0.0583451	−	0.405799i	0.0220524	−	0.153378i	−0.975820	−	0.218576i	$-0.929859\pi$
$7$	0.0583451	−	0.405799i	0.0220524	−	0.153378i	0.997872	+	0.0651983i	$0.0207680\pi$
$8$		0			0
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$		0			0
$11$	0.742783	+	1.62647i	0.223958	+	0.490399i	0.987940	−	0.154839i	$-0.0494858\pi$
$11$	0.742783	+	1.62647i	0.223958	+	0.490399i	−0.763982	+	0.645237i	$0.776759\pi$
$12$		0			0
$13$	−0.395701	−	2.75216i	−0.109748	−	0.763313i	−0.968156	−	0.250346i	$-0.919456\pi$
$13$	−0.395701	−	2.75216i	−0.109748	−	0.763313i	0.858409	−	0.512967i	$-0.171454\pi$
$14$		0			0
$15$	3.01690	−	0.885841i	0.778959	−	0.228723i
$16$		0			0
$17$	1.07564	−	1.24136i	0.260882	−	0.301073i	−0.610164	−	0.792275i	$-0.708897\pi$
$17$	1.07564	−	1.24136i	0.260882	−	0.301073i	0.871046	+	0.491201i	$0.163442\pi$
$18$		0			0
$19$	0.916981	+	1.05825i	0.210370	+	0.242780i	0.851122	−	0.524968i	$-0.175923\pi$
$19$	0.916981	+	1.05825i	0.210370	+	0.242780i	−0.640752	+	0.767748i	$0.721377\pi$
$20$		0			0
$21$	0.170308	−	0.372923i	0.0371643	−	0.0813786i
$22$		0			0
$23$	−4.69916	+	0.958061i	−0.979843	+	0.199770i
$23$	−4.69916	+	0.958061i	−0.979843	+	0.199770i
$24$		0			0
$25$	2.02987	−	4.44480i	0.405975	−	0.888961i
$26$		0			0
$27$	0.654861	+	0.755750i	0.126028	+	0.145444i
$28$		0			0
$29$	0.646092	−	0.745630i	0.119976	−	0.138460i	−0.692584	−	0.721337i	$-0.743528\pi$
$29$	0.646092	−	0.745630i	0.119976	−	0.138460i	0.812560	+	0.582877i	$0.198073\pi$
$30$		0			0
$31$	0.686370	−	0.201536i	0.123276	−	0.0361970i	−0.219513	−	0.975610i	$-0.570447\pi$
$31$	0.686370	−	0.201536i	0.123276	−	0.0361970i	0.342788	+	0.939413i	$0.388629\pi$
$32$		0			0
$33$	0.254466	+	1.76985i	0.0442969	+	0.308092i
$34$		0			0
$35$	−0.535494	−	1.17257i	−0.0905150	−	0.198200i
$36$		0			0
$37$	−2.07448	−	1.33318i	−0.341042	−	0.219174i	0.358897	−	0.933377i	$-0.383153\pi$
$37$	−2.07448	−	1.33318i	−0.341042	−	0.219174i	−0.699939	+	0.714203i	$0.746789\pi$
$38$		0			0
$39$	0.395701	−	2.75216i	0.0633629	−	0.440699i
$40$		0			0
$41$	−6.15118	+	3.95312i	−0.960652	+	0.617374i	−0.924178	−	0.381961i	$-0.875249\pi$
$41$	−6.15118	+	3.95312i	−0.960652	+	0.617374i	−0.0364738	+	0.999335i	$0.511613\pi$
$42$		0			0
$43$	7.39634	+	2.17176i	1.12793	+	0.331190i	0.791894	−	0.610658i	$-0.209095\pi$
$43$	7.39634	+	2.17176i	1.12793	+	0.331190i	0.336037	+	0.941849i	$0.390913\pi$
$44$		0			0
$45$	3.14426			0.468719
$46$		0			0
$47$	−2.85139			−0.415918			−0.207959	−	0.978138i	$-0.566682\pi$
$47$	−2.85139			−0.415918			−0.207959	+	0.978138i	$0.566682\pi$
$48$		0			0
$49$	6.55518	+	1.92478i	0.936455	+	0.274968i
$50$		0			0
$51$	1.38180	−	0.888030i	0.193491	−	0.124349i
$52$		0			0
$53$	0.372762	−	2.59262i	0.0512028	−	0.356123i	−0.948072	−	0.318055i	$-0.896970\pi$
$53$	0.372762	−	2.59262i	0.0512028	−	0.356123i	0.999275	−	0.0380685i	$-0.0121205\pi$
$54$		0			0
$55$	4.72961	+	3.03954i	0.637740	+	0.409851i
$56$		0			0
$57$	0.581692	+	1.27373i	0.0770470	+	0.168709i
$58$		0			0
$59$	1.19652	+	8.32198i	0.155774	+	1.08343i	0.906314	+	0.422605i	$0.138884\pi$
$59$	1.19652	+	8.32198i	0.155774	+	1.08343i	−0.750540	+	0.660825i	$0.770207\pi$
$60$		0			0
$61$	7.71092	−	2.26413i	0.987283	−	0.289892i	0.252055	−	0.967713i	$-0.418894\pi$
$61$	7.71092	−	2.26413i	0.987283	−	0.289892i	0.735227	+	0.677821i	$0.237075\pi$
$62$		0			0
$63$	0.268474	−	0.309836i	0.0338246	−	0.0390357i
$64$		0			0
$65$	−5.72512	−	6.60715i	−0.710114	−	0.819516i
$66$		0			0
$67$	−4.60258	+	10.0782i	−0.562294	+	1.23125i	0.388506	+	0.921446i	$0.372991\pi$
$67$	−4.60258	+	10.0782i	−0.562294	+	1.23125i	−0.950800	+	0.309806i	$0.899736\pi$
$68$		0			0
$69$	−4.77873	−	0.404654i	−0.575291	−	0.0487146i
$70$		0			0
$71$	−0.0976848	+	0.213900i	−0.0115930	+	0.0253852i	−0.915340	−	0.402682i	$-0.868078\pi$
$71$	−0.0976848	+	0.213900i	−0.0115930	+	0.0253852i	0.903747	+	0.428067i	$0.140805\pi$
$72$		0			0
$73$	−4.37625	−	5.05046i	−0.512201	−	0.591111i	0.439460	−	0.898262i	$-0.355170\pi$
$73$	−4.37625	−	5.05046i	−0.512201	−	0.591111i	−0.951661	+	0.307151i	$0.900624\pi$
$74$		0			0
$75$	3.19990	−	3.69288i	0.369492	−	0.426417i
$76$		0			0
$77$	0.703357	−	0.206524i	0.0801549	−	0.0235356i
$78$		0			0
$79$	1.17022	+	8.13904i	0.131660	+	0.915713i	0.943391	+	0.331682i	$0.107616\pi$
$79$	1.17022	+	8.13904i	0.131660	+	0.915713i	−0.811731	+	0.584031i	$0.801475\pi$
$80$		0			0
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$		0			0
$83$	−13.0290	−	8.37326i	−1.43012	−	0.919085i	−0.999866	−	0.0163789i	$-0.994786\pi$
$83$	−13.0290	−	8.37326i	−1.43012	−	0.919085i	−0.430258	−	0.902706i	$-0.641577\pi$
$84$		0			0
$85$	0.735001	−	5.11204i	0.0797220	−	0.554479i
$86$		0			0
$87$	0.829989	−	0.533402i	0.0889842	−	0.0571867i
$88$		0			0
$89$	−12.6703	−	3.72034i	−1.34305	−	0.394355i	−0.470293	−	0.882510i	$-0.655852\pi$
$89$	−12.6703	−	3.72034i	−1.34305	−	0.394355i	−0.872757	+	0.488155i	$0.837670\pi$
$90$		0			0
$91$	−1.13991			−0.119495
$92$		0			0
$93$	0.715346			0.0741779
$94$		0			0
$95$	4.22446	+	1.24041i	0.433421	+	0.127264i
$96$		0			0
$97$	6.89329	−	4.43005i	0.699907	−	0.449803i	−0.141688	−	0.989911i	$-0.545253\pi$
$97$	6.89329	−	4.43005i	0.699907	−	0.449803i	0.841596	+	0.540108i	$0.181617\pi$
$98$		0			0
$99$	−0.254466	+	1.76985i	−0.0255748	+	0.177877i
$100$		0			0
$101$	−6.64629	−	4.27131i	−0.661331	−	0.425011i	0.166460	−	0.986048i	$-0.446766\pi$
$101$	−6.64629	−	4.27131i	−0.661331	−	0.425011i	−0.827791	+	0.561037i	$0.810403\pi$
$102$		0			0
$103$	1.54878	+	3.39135i	0.152605	+	0.334159i	0.970459	−	0.241268i	$-0.0775632\pi$
$103$	1.54878	+	3.39135i	0.152605	+	0.334159i	−0.817853	+	0.575427i	$0.804836\pi$
$104$		0			0
$105$	−0.183452	−	1.27594i	−0.0179031	−	0.124519i
$106$		0			0
$107$	−11.4215	+	3.35365i	−1.10416	+	0.324210i	−0.782502	−	0.622648i	$-0.786057\pi$
$107$	−11.4215	+	3.35365i	−1.10416	+	0.324210i	−0.321654	+	0.946857i	$0.604239\pi$
$108$		0			0
$109$	−2.95416	+	3.40928i	−0.282957	+	0.326550i	−0.879380	−	0.476120i	$-0.842043\pi$
$109$	−2.95416	+	3.40928i	−0.282957	+	0.326550i	0.596423	+	0.802670i	$0.296588\pi$
$110$		0			0
$111$	−1.61484	−	1.86363i	−0.153274	−	0.176888i
$112$		0			0
$113$	−8.17894	+	17.9094i	−0.769410	+	1.68477i	−0.0414618	+	0.999140i	$0.513201\pi$
$113$	−8.17894	+	17.9094i	−0.769410	+	1.68477i	−0.727948	+	0.685632i	$0.759526\pi$
$114$		0			0
$115$	−10.8012	+	10.5224i	−1.00722	+	0.981216i
$116$		0			0
$117$	1.15505	−	2.52920i	0.106784	−	0.233825i
$118$		0			0
$119$	−0.440983	−	0.508922i	−0.0404249	−	0.0466528i
$120$		0			0
$121$	5.10980	−	5.89702i	0.464527	−	0.536093i
$122$		0			0
$123$	−7.01573	+	2.06001i	−0.632587	+	0.185744i
$124$		0			0
$125$	0.0508438	+	0.353627i	0.00454761	+	0.0316293i
$126$		0			0
$127$	−3.95458	−	8.65933i	−0.350913	−	0.768391i	−0.999971	−	0.00765257i	$-0.997564\pi$
$127$	−3.95458	−	8.65933i	−0.350913	−	0.768391i	0.649058	−	0.760739i	$-0.275163\pi$
$128$		0			0
$129$	6.48488	+	4.16758i	0.570962	+	0.366935i
$130$		0			0
$131$	0.0210243	−	0.146227i	0.00183690	−	0.0127759i	−0.988882	−	0.148700i	$-0.952491\pi$
$131$	0.0210243	−	0.146227i	0.00183690	−	0.0127759i	0.990719	+	0.135924i	$0.0434003\pi$
$132$		0			0
$133$	0.482939	−	0.310366i	0.0418761	−	0.0269121i
$134$		0			0
$135$	3.01690	+	0.885841i	0.259653	+	0.0762410i
$136$		0			0
$137$	−10.6025			−0.905834			−0.452917	−	0.891553i	$-0.649617\pi$
$137$	−10.6025			−0.905834			−0.452917	+	0.891553i	$0.649617\pi$
$138$		0			0
$139$	−19.6055			−1.66292			−0.831460	−	0.555584i	$-0.812495\pi$
$139$	−19.6055			−1.66292			−0.831460	+	0.555584i	$0.812495\pi$
$140$		0			0
$141$	−2.73589	−	0.803329i	−0.230403	−	0.0676525i
$142$		0			0
$143$	4.18239	−	2.68786i	0.349749	−	0.224770i
$144$		0			0
$145$	0.441483	−	3.07058i	0.0366632	−	0.254998i
$146$		0			0
$147$	5.74738	+	3.69362i	0.474036	+	0.304644i
$148$		0			0
$149$	9.46724	+	20.7304i	0.775586	+	1.69830i	0.713948	+	0.700199i	$0.246905\pi$
$149$	9.46724	+	20.7304i	0.775586	+	1.69830i	0.0616385	+	0.998099i	$0.480367\pi$
$150$		0			0
$151$	0.225555	+	1.56877i	0.0183554	+	0.127664i	0.996939	−	0.0781864i	$-0.0249129\pi$
$151$	0.225555	+	1.56877i	0.0183554	+	0.127664i	−0.978583	+	0.205851i	$0.934004\pi$
$152$		0			0
$153$	1.57602	−	0.462760i	0.127413	−	0.0374119i
$154$		0			0
$155$	1.47294	−	1.69986i	0.118309	−	0.136536i
$156$		0			0
$157$	−7.43802	−	8.58393i	−0.593618	−	0.685072i	0.376857	−	0.926271i	$-0.377005\pi$
$157$	−7.43802	−	8.58393i	−0.593618	−	0.685072i	−0.970476	+	0.241199i	$0.922459\pi$
$158$		0			0
$159$	1.08809	−	2.38258i	0.0862909	−	0.188951i
$160$		0			0
$161$	0.114607	+	1.96281i	0.00903231	+	0.154691i
$162$		0			0
$163$	−1.67765	+	3.67355i	−0.131404	+	0.287735i	−0.963885	−	0.266319i	$-0.914192\pi$
$163$	−1.67765	+	3.67355i	−0.131404	+	0.287735i	0.832481	+	0.554054i	$0.186920\pi$
$164$		0			0
$165$	3.68169	+	4.24890i	0.286619	+	0.330776i
$166$		0			0
$167$	14.0919	−	16.2629i	1.09046	−	1.25846i	0.126632	−	0.991950i	$-0.459583\pi$
$167$	14.0919	−	16.2629i	1.09046	−	1.25846i	0.963831	−	0.266513i	$-0.0858714\pi$
$168$		0			0
$169$	5.05558	−	1.48445i	0.388891	−	0.114189i
$170$		0			0
$171$	0.199279	+	1.38602i	0.0152392	+	0.105991i
$172$		0			0
$173$	5.50641	+	12.0574i	0.418645	+	0.916704i	0.995035	+	0.0995295i	$0.0317338\pi$
$173$	5.50641	+	12.0574i	0.418645	+	0.916704i	−0.576390	+	0.817175i	$0.695539\pi$
$174$		0			0
$175$	−1.68526	−	1.08305i	−0.127394	−	0.0818711i
$176$		0			0
$177$	−1.19652	+	8.32198i	−0.0899360	+	0.625518i
$178$		0			0
$179$	−4.33158	+	2.78374i	−0.323758	+	0.208066i	−0.692416	−	0.721499i	$-0.743454\pi$
$179$	−4.33158	+	2.78374i	−0.323758	+	0.208066i	0.368658	+	0.929565i	$0.379817\pi$
$180$		0			0
$181$	−23.9782	−	7.04063i	−1.78229	−	0.523326i	−0.786713	−	0.617319i	$-0.788219\pi$
$181$	−23.9782	−	7.04063i	−1.78229	−	0.523326i	−0.995573	+	0.0939930i	$0.970037\pi$
$182$		0			0
$183$	8.03646			0.594072
$184$		0			0
$185$	−7.75354			−0.570051
$186$		0			0
$187$	2.81800	+	0.827439i	0.206072	+	0.0605083i
$188$		0			0
$189$	0.344890	−	0.221647i	0.0250871	−	0.0161225i
$190$		0			0
$191$	2.57597	−	17.9163i	0.186391	−	1.29638i	−0.654868	−	0.755743i	$-0.727276\pi$
$191$	2.57597	−	17.9163i	0.186391	−	1.29638i	0.841259	−	0.540633i	$-0.181815\pi$
$192$		0			0
$193$	22.8182	+	14.6644i	1.64249	+	1.05556i	0.938456	+	0.345398i	$0.112256\pi$
$193$	22.8182	+	14.6644i	1.64249	+	1.05556i	0.704034	+	0.710166i	$0.251380\pi$
$194$		0			0
$195$	−3.63177	−	7.95246i	−0.260076	−	0.569488i
$196$		0			0
$197$	0.560525	+	3.89854i	0.0399357	+	0.277759i	0.999998	−	0.00202747i	$-0.000645365\pi$
$197$	0.560525	+	3.89854i	0.0399357	+	0.277759i	−0.960062	+	0.279787i	$0.909736\pi$
$198$		0			0
$199$	8.58410	−	2.52052i	0.608510	−	0.178675i	0.0370623	−	0.999313i	$-0.488200\pi$
$199$	8.58410	−	2.52052i	0.608510	−	0.178675i	0.571448	+	0.820638i	$0.306382\pi$
$200$		0			0
$201$	−7.25551	+	8.37330i	−0.511764	+	0.590607i
$202$		0			0
$203$	−0.264880	−	0.305687i	−0.0185909	−	0.0214550i
$204$		0			0
$205$	−9.55063	+	20.9130i	−0.667045	+	1.46062i
$206$		0			0
$207$	−4.47115	−	1.73459i	−0.310767	−	0.120562i
$208$		0			0
$209$	−1.04010	+	2.27749i	−0.0719449	+	0.157537i
$210$		0			0
$211$	−4.11476	−	4.74869i	−0.283272	−	0.326913i	0.596225	−	0.802817i	$-0.296666\pi$
$211$	−4.11476	−	4.74869i	−0.283272	−	0.326913i	−0.879497	+	0.475904i	$0.842121\pi$
$212$		0			0
$213$	−0.153990	+	0.177714i	−0.0105512	+	0.0121768i
$214$		0			0
$215$	23.2560	−	6.82858i	1.58605	−	0.465705i
$216$		0			0
$217$	−0.0417369	−	0.290287i	−0.00283329	−	0.0197059i
$218$		0			0
$219$	−2.77610	−	6.07881i	−0.187591	−	0.410768i
$220$		0			0
$221$	−3.84205	−	2.46914i	−0.258444	−	0.166092i
$222$		0			0
$223$	1.71882	−	11.9547i	0.115101	−	0.800544i	−0.847728	−	0.530431i	$-0.822030\pi$
$223$	1.71882	−	11.9547i	0.115101	−	0.800544i	0.962829	−	0.270113i	$-0.0870609\pi$
$224$		0			0
$225$	4.11068	−	2.64177i	0.274045	−	0.176118i
$226$		0			0
$227$	−6.55892	−	1.92587i	−0.435331	−	0.127825i	0.0567219	−	0.998390i	$-0.481935\pi$
$227$	−6.55892	−	1.92587i	−0.435331	−	0.127825i	−0.492053	+	0.870565i	$0.663753\pi$
$228$		0			0
$229$	−2.44693			−0.161698			−0.0808489	−	0.996726i	$-0.525763\pi$
$229$	−2.44693			−0.161698			−0.0808489	+	0.996726i	$0.525763\pi$
$230$		0			0
$231$	0.733050			0.0482312
$232$		0			0
$233$	−1.68535	−	0.494863i	−0.110411	−	0.0324195i	0.226060	−	0.974113i	$-0.427415\pi$
$233$	−1.68535	−	0.494863i	−0.110411	−	0.0324195i	−0.336471	+	0.941694i	$0.609233\pi$
$234$		0			0
$235$	−7.54226	+	4.84712i	−0.492003	+	0.316191i
$236$		0			0
$237$	−1.17022	+	8.13904i	−0.0760137	+	0.528687i
$238$		0			0
$239$	6.54515	+	4.20631i	0.423370	+	0.272084i	0.734930	−	0.678143i	$-0.237215\pi$
$239$	6.54515	+	4.20631i	0.423370	+	0.272084i	−0.311560	+	0.950227i	$0.600851\pi$
$240$		0			0
$241$	−2.48822	−	5.44845i	−0.160280	−	0.350965i	0.812405	−	0.583094i	$-0.198158\pi$
$241$	−2.48822	−	5.44845i	−0.160280	−	0.350965i	−0.972685	+	0.232129i	$0.925431\pi$
$242$		0			0
$243$	0.142315	+	0.989821i	0.00912950	+	0.0634971i
$244$		0			0
$245$	20.6112	−	6.05200i	1.31680	−	0.386648i
$246$		0			0
$247$	2.54963	−	2.94243i	0.162229	−	0.187222i
$248$		0			0
$249$	−10.1423	−	11.7048i	−0.642740	−	0.741761i
$250$		0			0
$251$	0.824494	−	1.80539i	0.0520416	−	0.113955i	−0.881825	−	0.471577i	$-0.843685\pi$
$251$	0.824494	−	1.80539i	0.0520416	−	0.113955i	0.933867	+	0.357622i	$0.116412\pi$
$252$		0			0
$253$	−5.04871	−	6.93141i	−0.317410	−	0.435774i
$254$		0			0
$255$	2.14546	−	4.69790i	0.134354	−	0.294194i
$256$		0			0
$257$	12.0654	+	13.9242i	0.752617	+	0.868566i	0.994819	−	0.101659i	$-0.0324152\pi$
$257$	12.0654	+	13.9242i	0.752617	+	0.868566i	−0.242202	+	0.970226i	$0.577870\pi$
$258$		0			0
$259$	−0.662040	+	0.764035i	−0.0411372	+	0.0474748i
$260$		0			0
$261$	0.946645	−	0.277960i	0.0585959	−	0.0172053i
$262$		0			0
$263$	−3.06518	−	21.3188i	−0.189007	−	1.31457i	−0.834586	−	0.550878i	$-0.814293\pi$
$263$	−3.06518	−	21.3188i	−0.189007	−	1.31457i	0.645579	−	0.763694i	$-0.276616\pi$
$264$		0			0
$265$	−3.42123	−	7.49145i	−0.210164	−	0.460196i
$266$		0			0
$267$	−11.1089	−	7.13928i	−0.679856	−	0.436917i
$268$		0			0
$269$	−2.71610	+	18.8909i	−0.165603	+	1.15180i	0.722237	+	0.691646i	$0.243114\pi$
$269$	−2.71610	+	18.8909i	−0.165603	+	1.15180i	−0.887841	+	0.460151i	$0.847795\pi$
$270$		0			0
$271$	21.1711	−	13.6058i	1.28605	−	0.826495i	0.294430	−	0.955673i	$-0.404870\pi$
$271$	21.1711	−	13.6058i	1.28605	−	0.826495i	0.991621	+	0.129178i	$0.0412339\pi$
$272$		0			0
$273$	−1.09374	−	0.321150i	−0.0661960	−	0.0194369i
$274$		0			0
$275$	8.73709			0.526866
$276$		0			0
$277$	25.7266			1.54576			0.772882	−	0.634550i	$-0.218815\pi$
$277$	25.7266			1.54576			0.772882	+	0.634550i	$0.218815\pi$
$278$		0			0
$279$	0.686370	+	0.201536i	0.0410919	+	0.0120657i
$280$		0			0
$281$	4.58284	−	2.94521i	0.273390	−	0.175697i	−0.396761	−	0.917922i	$-0.629866\pi$
$281$	4.58284	−	2.94521i	0.273390	−	0.175697i	0.670151	+	0.742225i	$0.266229\pi$
$282$		0			0
$283$	2.59233	−	18.0300i	0.154098	−	1.07177i	−0.755160	−	0.655541i	$-0.772441\pi$
$283$	2.59233	−	18.0300i	0.154098	−	1.07177i	0.909258	−	0.416234i	$-0.136650\pi$
$284$		0			0
$285$	3.70388	+	2.38034i	0.219399	+	0.140999i
$286$		0			0
$287$	1.24528	+	2.72679i	0.0735066	+	0.160957i
$288$		0			0
$289$	2.03539	+	14.1565i	0.119729	+	0.832732i
$290$		0			0
$291$	7.86215	−	2.30854i	0.460887	−	0.135329i
$292$		0			0
$293$	18.5619	−	21.4215i	1.08440	−	1.25146i	0.118382	−	0.992968i	$-0.462229\pi$
$293$	18.5619	−	21.4215i	1.08440	−	1.25146i	0.966014	−	0.258491i	$-0.0832253\pi$
$294$		0			0
$295$	17.3116	+	19.9787i	1.00792	+	1.16320i
$296$		0			0
$297$	−0.742783	+	1.62647i	−0.0431007	+	0.0943773i
$298$		0			0
$299$	4.49621	+	12.5538i	0.260022	+	0.726002i
$300$		0			0
$301$	1.31284	−	2.87471i	0.0756707	−	0.165696i
$302$		0			0
$303$	−5.17370	−	5.97077i	−0.297221	−	0.343012i
$304$		0			0
$305$	16.5475	−	19.0968i	0.947507	−	1.09348i
$306$		0			0
$307$	−17.8337	+	5.23645i	−1.01782	+	0.298860i	−0.747751	−	0.663980i	$-0.768866\pi$
$307$	−17.8337	+	5.23645i	−1.01782	+	0.298860i	−0.270073	+	0.962840i	$0.587048\pi$
$308$		0			0
$309$	0.530587	+	3.69031i	0.0301840	+	0.209935i
$310$		0			0
$311$	1.30390	+	2.85515i	0.0739375	+	0.161901i	0.942992	−	0.332817i	$-0.107999\pi$
$311$	1.30390	+	2.85515i	0.0739375	+	0.161901i	−0.869054	+	0.494717i	$0.835272\pi$
$312$		0			0
$313$	10.8712	+	6.98653i	0.614479	+	0.394902i	0.810534	−	0.585691i	$-0.199177\pi$
$313$	10.8712	+	6.98653i	0.614479	+	0.394902i	−0.196055	+	0.980593i	$0.562813\pi$
$314$		0			0
$315$	0.183452	−	1.27594i	0.0103364	−	0.0718909i
$316$		0			0
$317$	16.4628	−	10.5800i	0.924645	−	0.594233i	0.0106432	−	0.999943i	$-0.496612\pi$
$317$	16.4628	−	10.5800i	0.924645	−	0.594233i	0.914002	+	0.405710i	$0.132976\pi$
$318$		0			0
$319$	1.69265	+	0.497007i	0.0947702	+	0.0278270i
$320$		0			0
$321$	−11.9037			−0.664398
$322$		0			0
$323$	2.30001			0.127976
$324$		0			0
$325$	−13.0361	−	3.82773i	−0.723110	−	0.212324i
$326$		0			0
$327$	−3.79500	+	2.43890i	−0.209864	+	0.134871i
$328$		0			0
$329$	−0.166364	+	1.15709i	−0.00917197	+	0.0637924i
$330$		0			0
$331$	22.2408	+	14.2933i	1.22246	+	0.785630i	0.982701	−	0.185201i	$-0.0592936\pi$
$331$	22.2408	+	14.2933i	1.22246	+	0.785630i	0.239764	+	0.970831i	$0.422930\pi$
$332$		0			0
$333$	−1.02439	−	2.24309i	−0.0561360	−	0.122921i
$334$		0			0
$335$	4.95778	+	34.4821i	0.270873	+	1.88396i
$336$		0			0
$337$	17.5100	−	5.14139i	0.953829	−	0.280070i	0.232449	−	0.972609i	$-0.425326\pi$
$337$	17.5100	−	5.14139i	0.953829	−	0.280070i	0.721380	+	0.692539i	$0.243508\pi$
$338$		0			0
$339$	−12.8933	+	14.8796i	−0.700267	+	0.808152i
$340$		0			0
$341$	0.837616	+	0.966661i	0.0453595	+	0.0523476i
$342$		0			0
$343$	2.35569	−	5.15825i	0.127195	−	0.278519i
$344$		0			0
$345$	−13.3282	+	7.05308i	−0.717566	+	0.379725i
$346$		0			0
$347$	10.4589	−	22.9019i	0.561465	−	1.22944i	−0.389754	−	0.920919i	$-0.627440\pi$
$347$	10.4589	−	22.9019i	0.561465	−	1.22944i	0.951219	−	0.308518i	$-0.0998329\pi$
$348$		0			0
$349$	3.60970	+	4.16581i	0.193223	+	0.222991i	0.844091	−	0.536200i	$-0.180141\pi$
$349$	3.60970	+	4.16581i	0.193223	+	0.222991i	−0.650869	+	0.759190i	$0.725595\pi$
$350$		0			0
$351$	1.82082	−	2.10134i	0.0971880	−	0.112161i
$352$		0			0
$353$	27.6735	−	8.12566i	1.47291	−	0.432485i	0.555866	−	0.831272i	$-0.312387\pi$
$353$	27.6735	−	8.12566i	1.47291	−	0.432485i	0.917044	+	0.398786i	$0.130568\pi$
$354$		0			0
$355$	0.105224	+	0.731847i	0.00558469	+	0.0388424i
$356$		0			0
$357$	−0.279740	−	0.612546i	−0.0148054	−	0.0324194i
$358$		0			0
$359$	−16.2496	−	10.4430i	−0.857619	−	0.551158i	0.0363234	−	0.999340i	$-0.488435\pi$
$359$	−16.2496	−	10.4430i	−0.857619	−	0.551158i	−0.893942	+	0.448182i	$0.852072\pi$
$360$		0			0
$361$	2.42494	−	16.8658i	0.127628	−	0.887674i
$362$		0			0
$363$	6.56420	−	4.21855i	0.344531	−	0.221417i
$364$		0			0
$365$	−20.1610	−	5.91982i	−1.05528	−	0.309857i
$366$		0			0
$367$	−9.48280			−0.494998			−0.247499	−	0.968888i	$-0.579609\pi$
$367$	−9.48280			−0.494998			−0.247499	+	0.968888i	$0.579609\pi$
$368$		0			0
$369$	−7.31192			−0.380643
$370$		0			0
$371$	−1.03033	−	0.302533i	−0.0534922	−	0.0157067i
$372$		0			0
$373$	−10.6592	+	6.85024i	−0.551911	+	0.354692i	−0.786682	−	0.617359i	$-0.788203\pi$
$373$	−10.6592	+	6.85024i	−0.551911	+	0.354692i	0.234770	+	0.972051i	$0.424566\pi$
$374$		0			0
$375$	−0.0508438	+	0.353627i	−0.00262556	+	0.0182612i
$376$		0			0
$377$	−2.30776	−	1.48310i	−0.118855	−	0.0763838i
$378$		0			0
$379$	2.33496	+	5.11285i	0.119939	+	0.262630i	0.960073	−	0.279749i	$-0.0902512\pi$
$379$	2.33496	+	5.11285i	0.119939	+	0.262630i	−0.840134	+	0.542378i	$0.817524\pi$
$380$		0			0
$381$	−1.35478	−	9.42270i	−0.0694075	−	0.482740i
$382$		0			0
$383$	7.17557	−	2.10694i	0.366654	−	0.107659i	−0.0932151	−	0.995646i	$-0.529714\pi$
$383$	7.17557	−	2.10694i	0.366654	−	0.107659i	0.459869	+	0.887987i	$0.347896\pi$
$384$		0			0
$385$	1.50939	−	1.74193i	0.0769256	−	0.0887769i
$386$		0			0
$387$	5.04805	+	5.82576i	0.256607	+	0.296140i
$388$		0			0
$389$	−3.67630	+	8.04997i	−0.186396	+	0.408150i	−0.979642	−	0.200751i	$-0.935662\pi$
$389$	−3.67630	+	8.04997i	−0.186396	+	0.408150i	0.793247	+	0.608901i	$0.208389\pi$
$390$		0			0
$391$	−3.86532	+	6.86387i	−0.195478	+	0.347121i
$392$		0			0
$393$	0.0613696	−	0.134381i	0.00309569	−	0.00677861i
$394$		0			0
$395$	16.9310	+	19.5395i	0.851893	+	0.983137i
$396$		0			0
$397$	−21.0462	+	24.2887i	−1.05628	+	1.21901i	−0.0813074	+	0.996689i	$0.525910\pi$
$397$	−21.0462	+	24.2887i	−1.05628	+	1.21901i	−0.974973	+	0.222323i	$0.928636\pi$
$398$		0			0
$399$	0.550817	−	0.161734i	0.0275753	−	0.00809684i
$400$		0			0
$401$	−1.89656	−	13.1909i	−0.0947098	−	0.658721i	−0.980772	−	0.195155i	$-0.937479\pi$
$401$	−1.89656	−	13.1909i	−0.0947098	−	0.658721i	0.886063	−	0.463566i	$-0.153430\pi$
$402$		0			0
$403$	−0.826258	−	1.80925i	−0.0411589	−	0.0901253i
$404$		0			0
$405$	2.64512	+	1.69992i	0.131437	+	0.0844695i
$406$		0			0
$407$	0.627497	−	4.36434i	0.0311039	−	0.216332i
$408$		0			0
$409$	6.34194	−	4.07572i	0.313589	−	0.201531i	−0.374373	−	0.927278i	$-0.622142\pi$
$409$	6.34194	−	4.07572i	0.313589	−	0.201531i	0.687962	+	0.725747i	$0.258506\pi$
$410$		0			0
$411$	−10.1730	−	2.98707i	−0.501799	−	0.147341i
$412$		0			0
$413$	3.44686			0.169609
$414$		0			0
$415$	−48.6972			−2.39045
$416$		0			0
$417$	−18.8114	−	5.52352i	−0.921198	−	0.270488i
$418$		0			0
$419$	−8.68815	+	5.58353i	−0.424444	+	0.272773i	−0.735377	−	0.677658i	$-0.762995\pi$
$419$	−8.68815	+	5.58353i	−0.424444	+	0.272773i	0.310933	+	0.950432i	$0.399358\pi$
$420$		0			0
$421$	−2.56880	+	17.8664i	−0.125196	+	0.870756i	0.826330	+	0.563186i	$0.190425\pi$
$421$	−2.56880	+	17.8664i	−0.125196	+	0.870756i	−0.951526	+	0.307569i	$0.900484\pi$
$422$		0			0
$423$	−2.39874	−	1.54158i	−0.116631	−	0.0749540i
$424$		0			0
$425$	−3.33417	−	7.30082i	−0.161731	−	0.354142i
$426$		0			0
$427$	−0.468888	−	3.26119i	−0.0226911	−	0.157820i
$428$		0			0
$429$	4.77023	−	1.40067i	0.230309	−	0.0676248i
$430$		0			0
$431$	−3.26048	+	3.76280i	−0.157052	+	0.181248i	−0.828822	−	0.559512i	$-0.810989\pi$
$431$	−3.26048	+	3.76280i	−0.157052	+	0.181248i	0.671771	+	0.740759i	$0.265534\pi$
$432$		0			0
$433$	−18.2737	−	21.0889i	−0.878176	−	1.01347i	−0.999782	−	0.0208906i	$-0.993350\pi$
$433$	−18.2737	−	21.0889i	−0.878176	−	1.01347i	0.121606	−	0.992578i	$-0.461196\pi$
$434$		0			0
$435$	1.28868	−	2.82182i	0.0617876	−	0.135296i
$436$		0			0
$437$	−5.32291	−	4.09437i	−0.254629	−	0.195860i
$438$		0			0
$439$	7.99122	−	17.4983i	0.381400	−	0.835149i	−0.617422	−	0.786632i	$-0.711823\pi$
$439$	7.99122	−	17.4983i	0.381400	−	0.835149i	0.998822	−	0.0485176i	$-0.0154497\pi$
$440$		0			0
$441$	4.47396	+	5.16322i	0.213046	+	0.245868i
$442$		0			0
$443$	−25.2157	+	29.1004i	−1.19803	+	1.38260i	−0.293633	+	0.955918i	$0.594864\pi$
$443$	−25.2157	+	29.1004i	−1.19803	+	1.38260i	−0.904400	+	0.426686i	$0.859681\pi$
$444$		0			0
$445$	−39.8388	+	11.6977i	−1.88854	+	0.554525i
$446$		0			0
$447$	3.24333	+	22.5579i	0.153404	+	1.06695i
$448$		0			0
$449$	12.7455	+	27.9087i	0.601496	+	1.31709i	0.928241	+	0.371979i	$0.121321\pi$
$449$	12.7455	+	27.9087i	0.601496	+	1.31709i	−0.326746	+	0.945112i	$0.605952\pi$
$450$		0			0
$451$	−10.9986	−	7.06838i	−0.517905	−	0.332837i
$452$		0			0
$453$	−0.225555	+	1.56877i	−0.0105975	+	0.0737071i
$454$		0			0
$455$	−3.01521	+	1.93775i	−0.141355	+	0.0908433i
$456$		0			0
$457$	−10.3508	−	3.03928i	−0.484192	−	0.142172i	0.0305209	−	0.999534i	$-0.490283\pi$
$457$	−10.3508	−	3.03928i	−0.484192	−	0.142172i	−0.514713	+	0.857362i	$0.672102\pi$
$458$		0			0
$459$	1.64255			0.0766677
$460$		0			0
$461$	3.84745			0.179194			0.0895968	−	0.995978i	$-0.471442\pi$
$461$	3.84745			0.179194			0.0895968	+	0.995978i	$0.471442\pi$
$462$		0			0
$463$	−28.2157	−	8.28488i	−1.31129	−	0.385031i	−0.449951	−	0.893053i	$-0.648558\pi$
$463$	−28.2157	−	8.28488i	−1.31129	−	0.385031i	−0.861344	+	0.508023i	$0.830377\pi$
$464$		0			0
$465$	1.89218	−	1.21603i	0.0877476	−	0.0563920i
$466$		0			0
$467$	3.36002	−	23.3695i	0.155483	−	1.08141i	−0.751345	−	0.659909i	$-0.770595\pi$
$467$	3.36002	−	23.3695i	0.155483	−	1.08141i	0.906828	−	0.421500i	$-0.138496\pi$
$468$		0			0
$469$	3.82120	+	2.45574i	0.176447	+	0.113395i
$470$		0			0
$471$	−4.71835	−	10.3317i	−0.217410	−	0.476062i
$472$		0			0
$473$	1.96158	+	13.6431i	0.0901933	+	0.627308i
$474$		0			0
$475$	6.56508	−	1.92768i	0.301226	−	0.0884481i
$476$		0			0
$477$	1.71526	−	1.97952i	0.0785364	−	0.0906359i
$478$		0			0
$479$	15.1162	+	17.4450i	0.690676	+	0.797083i	0.987461	−	0.157862i	$-0.0504600\pi$
$479$	15.1162	+	17.4450i	0.690676	+	0.797083i	−0.296785	+	0.954944i	$0.595915\pi$
$480$		0			0
$481$	−2.84827	+	6.23684i	−0.129870	+	0.284375i
$482$		0			0
$483$	−0.443023	+	1.91559i	−0.0201583	+	0.0871625i
$484$		0			0
$485$	10.7029	−	23.4360i	0.485992	−	1.06417i
$486$		0			0
$487$	9.22674	+	10.6482i	0.418103	+	0.482517i	0.925258	−	0.379338i	$-0.123848\pi$
$487$	9.22674	+	10.6482i	0.418103	+	0.482517i	−0.507155	+	0.861855i	$0.669303\pi$
$488$		0			0
$489$	−2.64465	+	3.05209i	−0.119595	+	0.138020i
$490$		0			0
$491$	28.9526	−	8.50125i	1.30661	−	0.383656i	0.446969	−	0.894550i	$-0.352503\pi$
$491$	28.9526	−	8.50125i	1.30661	−	0.383656i	0.859644	+	0.510893i	$0.170685\pi$
$492$		0			0
$493$	−0.230629	−	1.60406i	−0.0103870	−	0.0722434i
$494$		0			0
$495$	2.33550	+	5.11404i	0.104973	+	0.229859i
$496$		0			0
$497$	0.0811009	+	0.0521204i	0.00363787	+	0.00233792i
$498$		0			0
$499$	−0.953362	+	6.63078i	−0.0426783	+	0.296834i	0.957292	+	0.289123i	$0.0933637\pi$
$499$	−0.953362	+	6.63078i	−0.0426783	+	0.296834i	−0.999970	+	0.00771123i	$0.997545\pi$
$500$		0			0
$501$	18.1029	−	11.6340i	0.808777	−	0.519769i
$502$		0			0
$503$	−27.4488	−	8.05969i	−1.22388	−	0.359364i	−0.394944	−	0.918705i	$-0.629236\pi$
$503$	−27.4488	−	8.05969i	−1.22388	−	0.359364i	−0.828938	+	0.559341i	$0.811054\pi$
$504$		0			0
$505$	−24.8411			−1.10542
$506$		0			0
$507$	5.26901			0.234005
$508$		0			0
$509$	−30.2653	−	8.88670i	−1.34149	−	0.393896i	−0.469287	−	0.883046i	$-0.655489\pi$
$509$	−30.2653	−	8.88670i	−1.34149	−	0.393896i	−0.872200	+	0.489150i	$0.837307\pi$
$510$		0			0
$511$	−2.30480	+	1.48121i	−0.101958	+	0.0655247i
$512$		0			0
$513$	−0.199279	+	1.38602i	−0.00879838	+	0.0611941i
$514$		0			0
$515$	9.86170	+	6.33773i	0.434559	+	0.279274i
$516$		0			0
$517$	−2.11796	−	4.63769i	−0.0931479	−	0.203965i
$518$		0			0
$519$	1.88641	+	13.1203i	0.0828043	+	0.575917i
$520$		0			0
$521$	−2.11955	+	0.622355i	−0.0928590	+	0.0272659i	−0.327832	−	0.944736i	$-0.606318\pi$
$521$	−2.11955	+	0.622355i	−0.0928590	+	0.0272659i	0.234973	+	0.972002i	$0.424500\pi$
$522$		0			0
$523$	20.3345	−	23.4673i	0.889166	−	1.02615i	−0.110314	−	0.993897i	$-0.535186\pi$
$523$	20.3345	−	23.4673i	0.889166	−	1.02615i	0.999480	−	0.0322554i	$-0.0102690\pi$
$524$		0			0
$525$	−1.31187	−	1.51398i	−0.0572546	−	0.0660753i
$526$		0			0
$527$	0.488110	−	1.06881i	0.0212624	−	0.0465581i
$528$		0			0
$529$	21.1642	−	9.00417i	0.920184	−	0.391486i
$530$		0			0
$531$	−3.49263	+	7.64778i	−0.151567	+	0.331886i
$532$		0			0
$533$	13.3137	+	15.3648i	0.576679	+	0.665523i
$534$		0			0
$535$	−24.5103	+	28.2864i	−1.05967	+	1.22293i
$536$		0			0
$537$	−4.94039	+	1.45063i	−0.213194	+	0.0625993i
$538$		0			0
$539$	1.73849	+	12.0915i	0.0748822	+	0.520817i
$540$		0			0
$541$	−17.6667	−	38.6846i	−0.759549	−	1.66318i	−0.748404	−	0.663243i	$-0.769179\pi$
$541$	−17.6667	−	38.6846i	−0.759549	−	1.66318i	−0.0111455	−	0.999938i	$-0.503548\pi$
$542$		0			0
$543$	−21.0233	−	13.5109i	−0.902198	−	0.579807i
$544$		0			0
$545$	−2.01862	+	14.0398i	−0.0864680	+	0.601398i
$546$		0			0
$547$	21.0287	−	13.5143i	0.899123	−	0.577831i	−0.00740733	−	0.999973i	$-0.502358\pi$
$547$	21.0287	−	13.5143i	0.899123	−	0.577831i	0.906530	+	0.422142i	$0.138721\pi$
$548$		0			0
$549$	7.71092	+	2.26413i	0.329094	+	0.0966308i
$550$		0			0
$551$	1.38152			0.0588547
$552$		0			0
$553$	3.37109			0.143353
$554$		0			0
$555$	−7.43947	−	2.18442i	−0.315788	−	0.0927236i
$556$		0			0
$557$	1.11225	−	0.714799i	0.0471275	−	0.0302870i	−0.516865	−	0.856067i	$-0.672901\pi$
$557$	1.11225	−	0.714799i	0.0471275	−	0.0302870i	0.563992	+	0.825780i	$0.309265\pi$
$558$		0			0
$559$	3.05030	−	21.2153i	0.129014	−	0.897312i
$560$		0			0
$561$	2.47073	+	1.58784i	0.104314	+	0.0670388i
$562$		0			0
$563$	−5.76292	−	12.6190i	−0.242878	−	0.531829i	0.748457	−	0.663183i	$-0.230795\pi$
$563$	−5.76292	−	12.6190i	−0.242878	−	0.531829i	−0.991336	+	0.131354i	$0.958068\pi$
$564$		0			0
$565$	8.81015	+	61.2760i	0.370646	+	2.57790i
$566$		0			0
$567$	0.393365	−	0.115502i	0.0165198	−	0.00485064i
$568$		0			0
$569$	−9.11837	+	10.5232i	−0.382262	+	0.441154i	−0.913975	−	0.405771i	$-0.867003\pi$
$569$	−9.11837	+	10.5232i	−0.382262	+	0.441154i	0.531713	+	0.846925i	$0.321549\pi$
$570$		0			0
$571$	3.31562	+	3.82642i	0.138754	+	0.160131i	0.820874	−	0.571110i	$-0.193487\pi$
$571$	3.31562	+	3.82642i	0.138754	+	0.160131i	−0.682119	+	0.731241i	$0.738942\pi$
$572$		0			0
$573$	7.51923	−	16.4648i	0.314120	−	0.687827i
$574$		0			0
$575$	−5.28031	+	22.8316i	−0.220204	+	0.952143i
$576$		0			0
$577$	0.391494	−	0.857251i	0.0162981	−	0.0356878i	−0.901308	−	0.433179i	$-0.857392\pi$
$577$	0.391494	−	0.857251i	0.0162981	−	0.0356878i	0.917606	+	0.397491i	$0.130119\pi$
$578$		0			0
$579$	17.7625	+	20.4990i	0.738183	+	0.851909i
$580$		0			0
$581$	−4.15804	+	4.79863i	−0.172505	+	0.199081i
$582$		0			0
$583$	4.49369	−	1.31947i	0.186110	−	0.0546467i
$584$		0			0
$585$	−1.24419	−	8.65352i	−0.0514409	−	0.357779i
$586$		0			0
$587$	6.33288	+	13.8671i	0.261386	+	0.572355i	0.994135	−	0.108143i	$-0.0344906\pi$
$587$	6.33288	+	13.8671i	0.261386	+	0.572355i	−0.732749	+	0.680498i	$0.761763\pi$
$588$		0			0
$589$	0.842664	+	0.541547i	0.0347214	+	0.0223141i
$590$		0			0
$591$	−0.560525	+	3.89854i	−0.0230569	+	0.160364i
$592$		0			0
$593$	10.8708	−	6.98625i	0.446411	−	0.286891i	−0.298058	−	0.954548i	$-0.596339\pi$
$593$	10.8708	−	6.98625i	0.446411	−	0.286891i	0.744469	+	0.667657i	$0.232703\pi$
$594$		0			0
$595$	−2.03158	−	0.596525i	−0.0832866	−	0.0244551i
$596$		0			0
$597$	8.94649			0.366156
$598$		0			0
$599$	2.48728			0.101628			0.0508138	−	0.998708i	$-0.483818\pi$
$599$	2.48728			0.101628			0.0508138	+	0.998708i	$0.483818\pi$
$600$		0			0
$601$	−26.6806	−	7.83413i	−1.08832	−	0.319561i	−0.312120	−	0.950043i	$-0.601039\pi$
$601$	−26.6806	−	7.83413i	−1.08832	−	0.319561i	−0.776204	+	0.630482i	$0.782857\pi$
$602$		0			0
$603$	−9.32064	+	5.99001i	−0.379566	+	0.243932i
$604$		0			0
$605$	3.49159	−	24.2845i	0.141953	−	0.987307i
$606$		0			0
$607$	8.26559	+	5.31197i	0.335490	+	0.215606i	0.697529	−	0.716557i	$-0.254283\pi$
$607$	8.26559	+	5.31197i	0.335490	+	0.215606i	−0.362039	+	0.932163i	$0.617919\pi$
$608$		0			0
$609$	−0.168028	−	0.367930i	−0.00680884	−	0.0149093i
$610$		0			0
$611$	1.12830	+	7.84749i	0.0456461	+	0.317475i
$612$		0			0
$613$	29.0432	−	8.52784i	1.17304	−	0.344436i	0.363555	−	0.931573i	$-0.381563\pi$
$613$	29.0432	−	8.52784i	1.17304	−	0.344436i	0.809488	+	0.587136i	$0.199745\pi$
$614$		0			0
$615$	−15.0556	+	17.3751i	−0.607101	+	0.700632i
$616$		0			0
$617$	−18.7555	−	21.6450i	−0.755067	−	0.871394i	0.239982	−	0.970777i	$-0.422858\pi$
$617$	−18.7555	−	21.6450i	−0.755067	−	0.871394i	−0.995049	+	0.0993834i	$0.968313\pi$
$618$		0			0
$619$	−17.6733	+	38.6991i	−0.710349	+	1.55545i	0.116606	+	0.993178i	$0.462799\pi$
$619$	−17.6733	+	38.6991i	−0.710349	+	1.55545i	−0.826955	+	0.562269i	$0.809929\pi$
$620$		0			0
$621$	−3.80135	−	2.92399i	−0.152543	−	0.117336i
$622$		0			0
$623$	−2.24896	+	4.92453i	−0.0901026	+	0.197297i
$624$		0			0
$625$	16.7351	+	19.3133i	0.669404	+	0.772534i
$626$		0			0
$627$	−1.63961	+	1.89221i	−0.0654796	+	0.0755675i
$628$		0			0
$629$	−3.88635	+	1.14114i	−0.154959	+	0.0455001i
$630$		0			0
$631$	−0.597900	−	4.15849i	−0.0238020	−	0.165547i	0.974453	−	0.224590i	$-0.0721042\pi$
$631$	−0.597900	−	4.15849i	−0.0238020	−	0.165547i	−0.998255	+	0.0590430i	$0.981195\pi$
$632$		0			0
$633$	−2.61023	−	5.71560i	−0.103747	−	0.227175i
$634$		0			0
$635$	−25.1805	−	16.1825i	−0.999257	−	0.642184i
$636$		0			0
$637$	2.70340	−	18.8026i	0.107113	−	0.744985i
$638$		0			0
$639$	−0.197821	+	0.127132i	−0.00782566	+	0.00502925i
$640$		0			0
$641$	−3.23281	−	0.949239i	−0.127688	−	0.0374927i	0.217264	−	0.976113i	$-0.430287\pi$
$641$	−3.23281	−	0.949239i	−0.127688	−	0.0374927i	−0.344952	+	0.938620i	$0.612105\pi$
$642$		0			0
$643$	−32.8938			−1.29720			−0.648602	−	0.761128i	$-0.724646\pi$
$643$	−32.8938			−1.29720			−0.648602	+	0.761128i	$0.724646\pi$
$644$		0			0
$645$	24.2378			0.954363
$646$		0			0
$647$	1.23052	+	0.361313i	0.0483766	+	0.0142047i	0.305831	−	0.952086i	$-0.401066\pi$
$647$	1.23052	+	0.361313i	0.0483766	+	0.0142047i	−0.257455	+	0.966290i	$0.582884\pi$
$648$		0			0
$649$	−12.6467	+	8.12753i	−0.496426	+	0.319033i
$650$		0			0
$651$	0.0417369	−	0.290287i	0.00163580	−	0.0113772i
$652$		0			0
$653$	−30.3802	−	19.5241i	−1.18887	−	0.764039i	−0.211872	−	0.977297i	$-0.567956\pi$
$653$	−30.3802	−	19.5241i	−1.18887	−	0.764039i	−0.976996	+	0.213258i	$0.931592\pi$
$654$		0			0
$655$	−0.192962	−	0.422528i	−0.00753966	−	0.0165095i
$656$		0			0
$657$	−0.951049	−	6.61469i	−0.0371040	−	0.258064i
$658$		0			0
$659$	−9.73106	+	2.85730i	−0.379068	+	0.111304i	−0.465715	−	0.884935i	$-0.654203\pi$
$659$	−9.73106	+	2.85730i	−0.379068	+	0.111304i	0.0866471	+	0.996239i	$0.472385\pi$
$660$		0			0
$661$	22.4899	−	25.9547i	0.874756	−	1.00952i	−0.125093	−	0.992145i	$-0.539923\pi$
$661$	22.4899	−	25.9547i	0.874756	−	1.00952i	0.999849	−	0.0173776i	$-0.00553174\pi$
$662$		0			0
$663$	−2.99079	−	3.45155i	−0.116153	−	0.134047i
$664$		0			0
$665$	0.749835	−	1.64191i	0.0290774	−	0.0636706i
$666$		0			0
$667$	−2.32173	+	4.12283i	−0.0898978	+	0.159637i
$668$		0			0
$669$	5.01722	−	10.9862i	0.193977	−	0.424750i
$670$		0			0
$671$	9.41008	+	10.8598i	0.363272	+	0.419238i
$672$		0			0
$673$	30.2554	−	34.9166i	1.16626	−	1.34594i	0.239226	−	0.970964i	$-0.423106\pi$
$673$	30.2554	−	34.9166i	1.16626	−	1.34594i	0.927036	−	0.374973i	$-0.122348\pi$
$674$		0			0
$675$	4.68844	−	1.37665i	0.180458	−	0.0529873i
$676$		0			0
$677$	−2.55762	−	17.7886i	−0.0982972	−	0.683672i	−0.978070	−	0.208277i	$-0.933214\pi$
$677$	−2.55762	−	17.7886i	−0.0982972	−	0.683672i	0.879773	−	0.475395i	$-0.157695\pi$
$678$		0			0
$679$	−1.39552	−	3.05576i	−0.0535551	−	0.117269i
$680$		0			0
$681$	−5.75066	−	3.69572i	−0.220366	−	0.141620i
$682$		0			0
$683$	2.55618	−	17.7786i	0.0978095	−	0.680280i	−0.880639	−	0.473788i	$-0.842886\pi$
$683$	2.55618	−	17.7786i	0.0978095	−	0.680280i	0.978448	−	0.206492i	$-0.0662047\pi$
$684$		0			0
$685$	−28.0449	+	18.0234i	−1.07154	+	0.688638i
$686$		0			0
$687$	−2.34781	−	0.689380i	−0.0895747	−	0.0263015i
$688$		0			0
$689$	−7.28281			−0.277453
$690$		0			0
$691$	26.5444			1.00979			0.504897	−	0.863179i	$-0.331530\pi$
$691$	26.5444			1.00979			0.504897	+	0.863179i	$0.331530\pi$
$692$		0			0
$693$	0.703357	+	0.206524i	0.0267183	+	0.00784520i
$694$		0			0
$695$	−51.8590	+	33.3278i	−1.96713	+	1.26419i
$696$		0			0
$697$	−1.70923	+	11.8880i	−0.0647417	+	0.450288i
$698$		0			0
$699$	−1.47766	−	0.949635i	−0.0558903	−	0.0359185i
$700$		0			0
$701$	−11.4647	−	25.1042i	−0.433015	−	0.948171i	−0.992828	−	0.119552i	$-0.961854\pi$
$701$	−11.4647	−	25.1042i	−0.433015	−	0.948171i	0.559813	−	0.828619i	$-0.310873\pi$
$702$		0			0
$703$	−0.491409	−	3.41782i	−0.0185338	−	0.128906i
$704$		0			0
$705$	−8.60234	+	2.52587i	−0.323983	+	0.0951300i
$706$		0			0
$707$	−2.12107	+	2.44785i	−0.0797711	+	0.0920608i
$708$		0			0
$709$	21.1025	+	24.3536i	0.792522	+	0.914619i	0.997946	−	0.0640537i	$-0.0204029\pi$
$709$	21.1025	+	24.3536i	0.792522	+	0.914619i	−0.205424	+	0.978673i	$0.565857\pi$
$710$		0			0
$711$	−3.41585	+	7.47966i	−0.128104	+	0.280509i
$712$		0			0
$713$	−3.03228	+	1.60464i	−0.113560	+	0.0600941i
$714$		0			0
$715$	6.49379	−	14.2194i	0.242854	−	0.531776i
$716$		0			0
$717$	5.09497	+	5.87991i	0.190275	+	0.219589i
$718$		0			0
$719$	−19.1880	+	22.1441i	−0.715591	+	0.825836i	−0.990770	−	0.135557i	$-0.956718\pi$
$719$	−19.1880	+	22.1441i	−0.715591	+	0.825836i	0.275178	+	0.961393i	$0.411263\pi$
$720$		0			0
$721$	1.46657	−	0.430623i	0.0546178	−	0.0160372i
$722$		0			0
$723$	−0.852427	−	5.92876i	−0.0317021	−	0.220493i
$724$		0			0
$725$	−2.00269	−	4.38529i	−0.0743782	−	0.162866i
$726$		0			0
$727$	28.0045	+	17.9974i	1.03863	+	0.667487i	0.944647	−	0.328087i	$-0.106404\pi$
$727$	28.0045	+	17.9974i	1.03863	+	0.667487i	0.0939819	+	0.995574i	$0.470040\pi$
$728$		0			0
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$		0			0
$731$	10.6517	−	6.84546i	0.393969	−	0.253189i
$732$		0			0
$733$	−16.4857	−	4.84063i	−0.608912	−	0.178793i	−0.0372829	−	0.999305i	$-0.511870\pi$
$733$	−16.4857	−	4.84063i	−0.608912	−	0.178793i	−0.571629	+	0.820512i	$0.693688\pi$
$734$		0			0
$735$	21.4813			0.792351
$736$		0			0
$737$	−19.8106			−0.729735
$738$		0			0
$739$	15.9438	+	4.68153i	0.586503	+	0.172213i	0.561503	−	0.827475i	$-0.310223\pi$
$739$	15.9438	+	4.68153i	0.586503	+	0.172213i	0.0249998	+	0.999687i	$0.492041\pi$
$740$		0			0
$741$	3.27533	−	2.10493i	0.120322	−	0.0773265i
$742$		0			0
$743$	3.44752	−	23.9780i	0.126477	−	0.879669i	−0.823492	−	0.567327i	$-0.807977\pi$
$743$	3.44752	−	23.9780i	0.126477	−	0.879669i	0.949970	−	0.312342i	$-0.101113\pi$
$744$		0			0
$745$	60.2819	+	38.7408i	2.20856	+	1.41935i
$746$		0			0
$747$	−6.43381	−	14.0881i	−0.235401	−	0.515456i
$748$		0			0
$749$	0.694520	+	4.83049i	0.0253772	+	0.176502i
$750$		0			0
$751$	16.7814	−	4.92746i	0.612362	−	0.179806i	0.0391778	−	0.999232i	$-0.487526\pi$
$751$	16.7814	−	4.92746i	0.612362	−	0.179806i	0.573184	+	0.819427i	$0.305708\pi$
$752$		0			0
$753$	1.29973	−	1.49997i	0.0473649	−	0.0546620i
$754$		0			0
$755$	3.26339	+	3.76615i	0.118767	+	0.137064i
$756$		0			0
$757$	−8.97013	+	19.6418i	−0.326025	+	0.713895i	−0.999684	−	0.0251476i	$-0.991994\pi$
$757$	−8.97013	+	19.6418i	−0.326025	+	0.713895i	0.673659	+	0.739042i	$0.264722\pi$
$758$		0			0
$759$	−2.89140	−	8.07302i	−0.104951	−	0.293032i
$760$		0			0
$761$	−1.61316	+	3.53233i	−0.0584770	+	0.128047i	−0.936615	−	0.350361i	$-0.886059\pi$
$761$	−1.61316	+	3.53233i	−0.0584770	+	0.128047i	0.878138	+	0.478408i	$0.158786\pi$
$762$		0			0
$763$	1.21112	+	1.39771i	0.0438455	+	0.0506005i
$764$		0			0
$765$	3.38210	−	3.90315i	0.122280	−	0.141119i
$766$		0			0
$767$	22.4300	−	6.58604i	0.809900	−	0.237808i
$768$		0			0
$769$	0.656132	+	4.56350i	0.0236607	+	0.164564i	0.998226	−	0.0595403i	$-0.0189635\pi$
$769$	0.656132	+	4.56350i	0.0236607	+	0.164564i	−0.974565	+	0.224104i	$0.928054\pi$
$770$		0			0
$771$	7.65374	+	16.7594i	0.275643	+	0.603574i
$772$		0			0
$773$	13.8120	+	8.87645i	0.496784	+	0.319264i	0.764929	−	0.644115i	$-0.222774\pi$
$773$	13.8120	+	8.87645i	0.496784	+	0.319264i	−0.268145	+	0.963379i	$0.586410\pi$
$774$		0			0
$775$	0.497454	−	3.45987i	0.0178691	−	0.124282i
$776$		0			0
$777$	−0.850476	+	0.546568i	−0.0305107	+	0.0196080i
$778$		0			0
$779$	−9.82391	−	2.88456i	−0.351978	−	0.103350i
$780$		0			0
$781$	−0.420460			−0.0150452
$782$		0			0
$783$	0.986610			0.0352586
$784$		0			0
$785$	−34.2664	−	10.0615i	−1.22302	−	0.359111i
$786$		0			0
$787$	20.6595	−	13.2771i	0.736433	−	0.473277i	−0.117885	−	0.993027i	$-0.537611\pi$
$787$	20.6595	−	13.2771i	0.736433	−	0.473277i	0.854318	+	0.519750i	$0.173975\pi$
$788$		0			0
$789$	3.06518	−	21.3188i	0.109123	−	0.758969i
$790$		0			0
$791$	6.79040	+	4.36393i	0.241439	+	0.155163i
$792$		0			0
$793$	−9.28248	−	20.3258i	−0.329631	−	0.721791i
$794$		0			0
$795$	−1.17206	−	8.15186i	−0.0415687	−	0.289117i
$796$		0			0
$797$	23.8944	−	7.01603i	0.846383	−	0.248521i	0.170343	−	0.985385i	$-0.445513\pi$
$797$	23.8944	−	7.01603i	0.846383	−	0.248521i	0.676041	+	0.736864i	$0.263694\pi$
$798$		0			0
$799$	−3.06707	+	3.53959i	−0.108505	+	0.125222i
$800$		0			0
$801$	−8.64757	−	9.97983i	−0.305547	−	0.352620i
$802$		0			0
$803$	4.96381	−	10.8692i	0.175169	−	0.383566i
$804$		0			0
$805$	3.63977	+	4.99705i	0.128285	+	0.176123i
$806$		0			0
$807$	−7.92825	+	17.3604i	−0.279088	+	0.611117i
$808$		0			0
$809$	26.0288	+	30.0389i	0.915124	+	1.05611i	0.998224	+	0.0595685i	$0.0189725\pi$
$809$	26.0288	+	30.0389i	0.915124	+	1.05611i	−0.0830999	+	0.996541i	$0.526482\pi$
$810$		0			0
$811$	2.47577	−	2.85719i	0.0869361	−	0.100330i	−0.710615	−	0.703581i	$-0.751583\pi$
$811$	2.47577	−	2.85719i	0.0869361	−	0.100330i	0.797551	+	0.603252i	$0.206129\pi$
$812$		0			0
$813$	24.1467	−	7.09011i	0.846862	−	0.248661i
$814$		0			0
$815$	1.80713	+	12.5688i	0.0633009	+	0.440268i
$816$		0			0
$817$	4.48403	+	9.81865i	0.156876	+	0.343511i
$818$		0			0
$819$	−0.958955	−	0.616283i	−0.0335086	−	0.0215347i
$820$		0			0
$821$	−6.03202	+	41.9536i	−0.210519	+	1.46419i	0.560910	+	0.827877i	$0.310451\pi$
$821$	−6.03202	+	41.9536i	−0.210519	+	1.46419i	−0.771429	+	0.636315i	$0.780458\pi$
$822$		0			0
$823$	46.6960	−	30.0097i	1.62772	−	1.04607i	0.677021	−	0.735964i	$-0.263271\pi$
$823$	46.6960	−	30.0097i	1.62772	−	1.04607i	0.950701	−	0.310110i	$-0.100366\pi$
$824$		0			0
$825$	8.38318	+	2.46152i	0.291865	+	0.0856992i
$826$		0			0
$827$	−6.45170			−0.224348			−0.112174	−	0.993689i	$-0.535781\pi$
$827$	−6.45170			−0.224348			−0.112174	+	0.993689i	$0.535781\pi$
$828$		0			0
$829$	8.70197			0.302232			0.151116	−	0.988516i	$-0.451713\pi$
$829$	8.70197			0.302232			0.151116	+	0.988516i	$0.451713\pi$
$830$		0			0
$831$	24.6845	+	7.24803i	0.856297	+	0.251431i
$832$		0			0
$833$	9.44037	−	6.06696i	0.327089	−	0.210208i
$834$		0			0
$835$	9.62918	−	66.9724i	0.333231	−	2.31768i
$836$		0			0
$837$	0.601787	+	0.386745i	0.0208008	+	0.0133679i
$838$		0			0
$839$	12.8189	+	28.0694i	0.442556	+	0.969063i	0.991122	+	0.132955i	$0.0424467\pi$
$839$	12.8189	+	28.0694i	0.442556	+	0.969063i	−0.548566	+	0.836107i	$0.684826\pi$
$840$		0			0
$841$	3.98860	+	27.7413i	0.137538	+	0.956598i
$842$		0			0
$843$	5.22697	−	1.53478i	0.180026	−	0.0528605i
$844$		0			0
$845$	10.8492	−	12.5206i	0.373223	−	0.430722i
$846$		0			0
$847$	−2.09487	−	2.41761i	−0.0719807	−	0.0830701i
$848$		0			0
$849$	7.56697	−	16.5694i	0.259698	−	0.568659i
$850$		0			0
$851$	11.0256	+	4.27737i	0.377952	+	0.146627i
$852$		0			0
$853$	6.87274	−	15.0492i	0.235318	−	0.515275i	−0.754725	−	0.656042i	$-0.772230\pi$
$853$	6.87274	−	15.0492i	0.235318	−	0.515275i	0.990043	+	0.140767i	$0.0449568\pi$
$854$		0			0
$855$	2.88323	+	3.32742i	0.0986042	+	0.113795i
$856$		0			0
$857$	34.9901	−	40.3807i	1.19524	−	1.37938i	0.288612	−	0.957446i	$-0.406806\pi$
$857$	34.9901	−	40.3807i	1.19524	−	1.37938i	0.906627	−	0.421933i	$-0.138648\pi$
$858$		0			0
$859$	42.4626	−	12.4682i	1.44881	−	0.425408i	0.539659	−	0.841883i	$-0.318553\pi$
$859$	42.4626	−	12.4682i	1.44881	−	0.425408i	0.909147	+	0.416475i	$0.136735\pi$
$860$		0			0
$861$	0.426614	+	2.96717i	0.0145390	+	0.101121i
$862$		0			0
$863$	−9.10560	−	19.9385i	−0.309958	−	0.678714i	0.688980	−	0.724780i	$-0.258059\pi$
$863$	−9.10560	−	19.9385i	−0.309958	−	0.678714i	−0.998938	+	0.0460664i	$0.985331\pi$
$864$		0			0
$865$	35.0616	+	22.5327i	1.19213	+	0.766136i
$866$		0			0
$867$	−2.03539	+	14.1565i	−0.0691255	+	0.480778i
$868$		0			0
$869$	−12.3687	+	7.94886i	−0.419578	+	0.269647i
$870$		0			0
$871$	29.5582	+	8.67907i	1.00154	+	0.294079i
$872$		0			0
$873$	8.19407			0.277327
$874$		0			0
$875$	0.146468			0.00495151
$876$		0			0
$877$	−37.3713	−	10.9732i	−1.26194	−	0.370539i	−0.418724	−	0.908114i	$-0.637522\pi$
$877$	−37.3713	−	10.9732i	−1.26194	−	0.370539i	−0.843216	+	0.537575i	$0.819341\pi$
$878$		0			0
$879$	23.8451	−	15.3243i	0.804276	−	0.516877i
$880$		0			0
$881$	3.84941	−	26.7733i	0.129690	−	0.902014i	−0.816256	−	0.577690i	$-0.803954\pi$
$881$	3.84941	−	26.7733i	0.129690	−	0.902014i	0.945946	−	0.324324i	$-0.105137\pi$
$882$		0			0
$883$	−20.5109	−	13.1816i	−0.690247	−	0.443595i	0.147926	−	0.988998i	$-0.452740\pi$
$883$	−20.5109	−	13.1816i	−0.690247	−	0.443595i	−0.838174	+	0.545403i	$0.816377\pi$
$884$		0			0
$885$	10.9817	+	24.0466i	0.369147	+	0.808319i
$886$		0			0
$887$	−4.35384	−	30.2816i	−0.146188	−	1.01676i	−0.922386	−	0.386269i	$-0.873764\pi$
$887$	−4.35384	−	30.2816i	−0.146188	−	1.01676i	0.776199	−	0.630488i	$-0.217145\pi$
$888$		0			0
$889$	−3.74468	+	1.09954i	−0.125592	+	0.0368773i
$890$		0			0
$891$	−1.17092	+	1.35132i	−0.0392274	+	0.0452709i
$892$		0			0
$893$	−2.61467	−	3.01749i	−0.0874965	−	0.100976i
$894$		0			0
$895$	−6.72544	+	14.7266i	−0.224807	+	0.492258i
$896$		0			0
$897$	0.777276	+	13.3120i	0.0259525	+	0.444474i
$898$		0			0
$899$	0.293186	−	0.641989i	0.00977832	−	0.0214115i
$900$		0			0
$901$	−2.81741	−	3.25146i	−0.0938614	−	0.108322i
$902$		0			0
$903$	2.06956	−	2.38840i	0.0688706	−	0.0794809i
$904$		0			0
$905$	−75.3937	+	22.1376i	−2.50617	+	0.735878i
$906$		0			0
$907$	3.84914	+	26.7713i	0.127808	+	0.888928i	0.948324	+	0.317303i	$0.102777\pi$
$907$	3.84914	+	26.7713i	0.127808	+	0.888928i	−0.820516	+	0.571624i	$0.806314\pi$
$908$		0			0
$909$	−3.28197	−	7.18651i	−0.108856	−	0.238362i
$910$		0			0
$911$	−27.9210	−	17.9438i	−0.925065	−	0.594503i	−0.0109423	−	0.999940i	$-0.503483\pi$
$911$	−27.9210	−	17.9438i	−0.925065	−	0.594503i	−0.914123	+	0.405437i	$0.867119\pi$
$912$		0			0
$913$	3.94109	−	27.4109i	0.130431	−	0.907167i
$914$		0			0
$915$	21.2574	−	13.6613i	0.702748	−	0.451629i
$916$		0			0
$917$	−0.0581122	−	0.0170633i	−0.00191903	−	0.000563479i
$918$		0			0
$919$	−32.0883			−1.05850			−0.529248	−	0.848467i	$-0.677526\pi$
$919$	−32.0883			−1.05850			−0.529248	+	0.848467i	$0.677526\pi$
$920$		0			0
$921$	−18.5866			−0.612449
$922$		0			0
$923$	0.627341	+	0.184204i	0.0206492	+	0.00606315i
$924$		0			0
$925$	−10.1367	+	6.51444i	−0.333292	+	0.214193i
$926$		0			0
$927$	−0.530587	+	3.69031i	−0.0174268	+	0.121206i
$928$		0			0
$929$	12.8286	+	8.24447i	0.420894	+	0.270492i	0.733898	−	0.679260i	$-0.237699\pi$
$929$	12.8286	+	8.24447i	0.420894	+	0.270492i	−0.313004	+	0.949752i	$0.601335\pi$
$930$		0			0
$931$	3.97408	+	8.70202i	0.130245	+	0.285197i
$932$		0			0
$933$	0.446697	+	3.10684i	0.0146242	+	0.101714i
$934$		0			0
$935$	8.86052	−	2.60168i	0.289770	−	0.0850842i
$936$		0			0
$937$	15.7812	−	18.2125i	0.515550	−	0.594977i	−0.436961	−	0.899480i	$-0.643945\pi$
$937$	15.7812	−	18.2125i	0.515550	−	0.594977i	0.952511	+	0.304504i	$0.0984907\pi$
$938$		0			0
$939$	8.46255	+	9.76631i	0.276165	+	0.318711i
$940$		0			0
$941$	−7.37524	+	16.1495i	−0.240426	+	0.526459i	−0.990926	−	0.134412i	$-0.957086\pi$
$941$	−7.37524	+	16.1495i	−0.240426	+	0.526459i	0.750500	+	0.660871i	$0.229813\pi$
$942$		0			0
$943$	25.1180	−	24.4696i	0.817956	−	0.796838i
$944$		0			0
$945$	0.535494	−	1.17257i	0.0174196	−	0.0381437i
$946$		0			0
$947$	−20.9960	−	24.2307i	−0.682279	−	0.787391i	0.303966	−	0.952683i	$-0.401689\pi$
$947$	−20.9960	−	24.2307i	−0.682279	−	0.787391i	−0.986245	+	0.165291i	$0.947144\pi$
$948$		0			0
$949$	−12.1680	+	14.0426i	−0.394990	+	0.455843i
$950$		0			0
$951$	18.7767	−	5.51334i	0.608877	−	0.178782i
$952$		0			0
$953$	0.993681	+	6.91120i	0.0321885	+	0.223876i	0.999566	−	0.0294640i	$-0.00938003\pi$
$953$	0.993681	+	6.91120i	0.0321885	+	0.223876i	−0.967377	+	0.253340i	$0.918471\pi$
$954$		0			0
$955$	−23.6424	−	51.7696i	−0.765050	−	1.67523i
$956$		0			0
$957$	1.48406	+	0.953749i	0.0479729	+	0.0308303i
$958$		0			0
$959$	−0.618604	+	4.30249i	−0.0199758	+	0.138935i
$960$		0			0
$961$	−25.6484	+	16.4832i	−0.827367	+	0.531716i
$962$		0			0
$963$	−11.4215	−	3.35365i	−0.368052	−	0.108070i
$964$		0			0
$965$	85.2851			2.74542
$966$		0			0
$967$	−8.64923			−0.278141			−0.139070	−	0.990283i	$-0.544411\pi$
$967$	−8.64923			−0.278141			−0.139070	+	0.990283i	$0.544411\pi$
$968$		0			0
$969$	2.20685	+	0.647988i	0.0708941	+	0.0208164i
$970$		0			0
$971$	−20.5078	+	13.1796i	−0.658128	+	0.422953i	−0.826628	−	0.562748i	$-0.809744\pi$
$971$	−20.5078	+	13.1796i	−0.658128	+	0.422953i	0.168500	+	0.985702i	$0.446108\pi$
$972$		0			0
$973$	−1.14389	+	7.95591i	−0.0366713	+	0.255055i
$974$		0			0
$975$	−11.4296	−	7.34536i	−0.366040	−	0.235240i
$976$		0			0
$977$	−0.866836	−	1.89811i	−0.0277325	−	0.0607258i	0.895259	−	0.445546i	$-0.146991\pi$
$977$	−0.866836	−	1.89811i	−0.0277325	−	0.0607258i	−0.922991	+	0.384821i	$0.874263\pi$
$978$		0			0
$979$	−3.36028	−	23.3713i	−0.107395	−	0.746949i
$980$		0			0
$981$	−4.32839	+	1.27093i	−0.138195	+	0.0405777i
$982$		0			0
$983$	−39.8815	+	46.0257i	−1.27202	+	1.46799i	−0.455988	+	0.889986i	$0.650714\pi$
$983$	−39.8815	+	46.0257i	−1.27202	+	1.46799i	−0.816033	+	0.578005i	$0.803831\pi$
$984$		0			0
$985$	8.10984	+	9.35925i	0.258401	+	0.298211i
$986$		0			0
$987$	−0.485615	+	1.06335i	−0.0154573	+	0.0338468i
$988$		0			0
$989$	−36.8373	−	3.11931i	−1.17136	−	0.0991883i
$990$		0			0
$991$	−1.49697	+	3.27790i	−0.0475527	+	0.104126i	−0.931917	−	0.362671i	$-0.881865\pi$
$991$	−1.49697	+	3.27790i	−0.0475527	+	0.104126i	0.884365	+	0.466797i	$0.154592\pi$
$992$		0			0
$993$	17.3130	+	19.9803i	0.549411	+	0.634055i
$994$		0			0
$995$	18.4213	−	21.2593i	0.583995	−	0.673966i
$996$		0			0
$997$	−4.68467	+	1.37554i	−0.148365	+	0.0435639i	−0.355072	−	0.934839i	$-0.615544\pi$
$997$	−4.68467	+	1.37554i	−0.148365	+	0.0435639i	0.206707	+	0.978403i	$0.433725\pi$
$998$		0			0
$999$	−0.350939	−	2.44083i	−0.0111032	−	0.0772246i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.c.121.3	yes	30
23.4	even	11	inner	552.2.q.c.73.3	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.c.73.3	✓	30	23.4	even	11	inner
552.2.q.c.121.3	yes	30	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.959493 + 0.281733i) q^{3} +(2.64512 - 1.69992i) q^{5} +(0.0583451 - 0.405799i) q^{7} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(0.959493 + 0.281733i) q^{3} +(2.64512 - 1.69992i) q^{5} +(0.0583451 - 0.405799i) q^{7} +(0.841254 + 0.540641i) q^{9} +(0.742783 + 1.62647i) q^{11} +(-0.395701 - 2.75216i) q^{13} +(3.01690 - 0.885841i) q^{15} +(1.07564 - 1.24136i) q^{17} +(0.916981 + 1.05825i) q^{19} +(0.170308 - 0.372923i) q^{21} +(-4.69916 + 0.958061i) q^{23} +(2.02987 - 4.44480i) q^{25} +(0.654861 + 0.755750i) q^{27} +(0.646092 - 0.745630i) q^{29} +(0.686370 - 0.201536i) q^{31} +(0.254466 + 1.76985i) q^{33} +(-0.535494 - 1.17257i) q^{35} +(-2.07448 - 1.33318i) q^{37} +(0.395701 - 2.75216i) q^{39} +(-6.15118 + 3.95312i) q^{41} +(7.39634 + 2.17176i) q^{43} +3.14426 q^{45} -2.85139 q^{47} +(6.55518 + 1.92478i) q^{49} +(1.38180 - 0.888030i) q^{51} +(0.372762 - 2.59262i) q^{53} +(4.72961 + 3.03954i) q^{55} +(0.581692 + 1.27373i) q^{57} +(1.19652 + 8.32198i) q^{59} +(7.71092 - 2.26413i) q^{61} +(0.268474 - 0.309836i) q^{63} +(-5.72512 - 6.60715i) q^{65} +(-4.60258 + 10.0782i) q^{67} +(-4.77873 - 0.404654i) q^{69} +(-0.0976848 + 0.213900i) q^{71} +(-4.37625 - 5.05046i) q^{73} +(3.19990 - 3.69288i) q^{75} +(0.703357 - 0.206524i) q^{77} +(1.17022 + 8.13904i) q^{79} +(0.415415 + 0.909632i) q^{81} +(-13.0290 - 8.37326i) q^{83} +(0.735001 - 5.11204i) q^{85} +(0.829989 - 0.533402i) q^{87} +(-12.6703 - 3.72034i) q^{89} -1.13991 q^{91} +0.715346 q^{93} +(4.22446 + 1.24041i) q^{95} +(6.89329 - 4.43005i) q^{97} +(-0.254466 + 1.76985i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9	\( 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9} + 13 q^{11} - 13 q^{13} + 2 q^{15} - 11 q^{17} + 11 q^{19} - 9 q^{21} - 12 q^{23} + 17 q^{25} + 3 q^{27} + 9 q^{29} + 33 q^{31} + 9 q^{33} + 62 q^{35} + 11 q^{37} + 13 q^{39} + 2 q^{41} - 40 q^{43} - 2 q^{45} - 38 q^{47} - 13 q^{49} + 11 q^{51} - 25 q^{53} + 62 q^{55} + 22 q^{57} + 73 q^{59} + 4 q^{61} - 2 q^{63} - 12 q^{65} - 29 q^{67} - 21 q^{69} - 19 q^{71} - 38 q^{73} + 27 q^{75} + 4 q^{77} - 12 q^{79} - 3 q^{81} - 65 q^{83} + 8 q^{85} + 2 q^{87} - 61 q^{89} - 150 q^{91} - 22 q^{93} - 9 q^{95} - 9 q^{97} - 9 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9 + 13 * q^11 - 13 * q^13 + 2 * q^15 - 11 * q^17 + 11 * q^19 - 9 * q^21 - 12 * q^23 + 17 * q^25 + 3 * q^27 + 9 * q^29 + 33 * q^31 + 9 * q^33 + 62 * q^35 + 11 * q^37 + 13 * q^39 + 2 * q^41 - 40 * q^43 - 2 * q^45 - 38 * q^47 - 13 * q^49 + 11 * q^51 - 25 * q^53 + 62 * q^55 + 22 * q^57 + 73 * q^59 + 4 * q^61 - 2 * q^63 - 12 * q^65 - 29 * q^67 - 21 * q^69 - 19 * q^71 - 38 * q^73 + 27 * q^75 + 4 * q^77 - 12 * q^79 - 3 * q^81 - 65 * q^83 + 8 * q^85 + 2 * q^87 - 61 * q^89 - 150 * q^91 - 22 * q^93 - 9 * q^95 - 9 * q^97 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more