LMFDB - Embedded newform 552.2.q.b.265.1

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			265.1
Character	$\chi$	$=$	552.265
Dual form			552.2.q.b.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{3} +(-0.911030 + 0.267503i) q^{5} +(-1.46467 - 1.69032i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{3} +(-0.911030 + 0.267503i) q^{5} +(-1.46467 - 1.69032i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(-3.17727 - 2.04191i) q^{11} +(-0.129165 + 0.149064i) q^{13} +(-0.135127 - 0.939827i) q^{15} +(-1.19770 - 2.62260i) q^{17} +(1.90178 - 4.16431i) q^{19} +(1.88156 - 1.20920i) q^{21} +(-4.06339 - 2.54732i) q^{23} +(-3.44785 + 2.21580i) q^{25} +(0.415415 - 0.909632i) q^{27} +(0.572550 + 1.25371i) q^{29} +(-0.120729 - 0.839689i) q^{31} +(2.47329 - 2.85433i) q^{33} +(1.78652 + 1.14813i) q^{35} +(5.57420 + 1.63673i) q^{37} +(-0.129165 - 0.149064i) q^{39} +(1.39683 - 0.410145i) q^{41} +(1.75923 - 12.2357i) q^{43} +0.949491 q^{45} -13.0666 q^{47} +(0.284285 - 1.97724i) q^{49} +(2.76636 - 0.812276i) q^{51} +(-0.0705505 - 0.0814196i) q^{53} +(3.44080 + 1.01031i) q^{55} +(3.85127 + 2.47506i) q^{57} +(-3.66065 + 4.22462i) q^{59} +(1.04249 + 7.25071i) q^{61} +(0.929121 + 2.03449i) q^{63} +(0.0777980 - 0.170354i) q^{65} +(-4.74992 + 3.05259i) q^{67} +(3.09968 - 3.65951i) q^{69} +(-11.1779 + 7.18362i) q^{71} +(2.58219 - 5.65422i) q^{73} +(-1.70256 - 3.72810i) q^{75} +(1.20217 + 8.36130i) q^{77} +(-0.0200761 + 0.0231691i) q^{79} +(0.841254 + 0.540641i) q^{81} +(9.43824 + 2.77132i) q^{83} +(1.79270 + 2.06888i) q^{85} +(-1.32243 + 0.388301i) q^{87} +(0.111235 - 0.773655i) q^{89} +0.441150 q^{91} +0.848324 q^{93} +(-0.618612 + 4.30254i) q^{95} +(-2.46721 + 0.724439i) q^{97} +(2.47329 + 2.85433i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} - 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 - 3 * q^9	$ 30 q - 3 q^{3} - 3 q^{9} + 9 q^{11} + 13 q^{13} + 17 q^{17} - 9 q^{19} - 11 q^{21} - 12 q^{23} - 23 q^{25} - 3 q^{27} - q^{29} - 37 q^{31} + 9 q^{33} + 10 q^{35} + 7 q^{37} + 13 q^{39} + 16 q^{41} + 20 q^{43} - 22 q^{45} + 22 q^{47} + 19 q^{49} + 17 q^{51} + 25 q^{53} + 10 q^{55} + 24 q^{57} + 7 q^{59} + 8 q^{61} - 28 q^{65} - 23 q^{67} - q^{69} + 5 q^{71} + 34 q^{73} - 23 q^{75} + 62 q^{77} + 20 q^{79} - 3 q^{81} + 29 q^{83} - 46 q^{85} + 10 q^{87} - 67 q^{89} - 118 q^{91} - 26 q^{93} - 99 q^{95} - 41 q^{97} + 9 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 - 3 * q^9 + 9 * q^11 + 13 * q^13 + 17 * q^17 - 9 * q^19 - 11 * q^21 - 12 * q^23 - 23 * q^25 - 3 * q^27 - q^29 - 37 * q^31 + 9 * q^33 + 10 * q^35 + 7 * q^37 + 13 * q^39 + 16 * q^41 + 20 * q^43 - 22 * q^45 + 22 * q^47 + 19 * q^49 + 17 * q^51 + 25 * q^53 + 10 * q^55 + 24 * q^57 + 7 * q^59 + 8 * q^61 - 28 * q^65 - 23 * q^67 - q^69 + 5 * q^71 + 34 * q^73 - 23 * q^75 + 62 * q^77 + 20 * q^79 - 3 * q^81 + 29 * q^83 - 46 * q^85 + 10 * q^87 - 67 * q^89 - 118 * q^91 - 26 * q^93 - 99 * q^95 - 41 * q^97 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$1$	$1$	$1$

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
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$4$		0			0
$5$	−0.911030	+	0.267503i	−0.407425	+	0.119631i	−0.479022	−	0.877803i	$-0.659009\pi$
$5$	−0.911030	+	0.267503i	−0.407425	+	0.119631i	0.0715970	+	0.997434i	$0.477190\pi$
$6$		0			0
$7$	−1.46467	−	1.69032i	−0.553593	−	0.638880i	0.408124	−	0.912927i	$-0.366183\pi$
$7$	−1.46467	−	1.69032i	−0.553593	−	0.638880i	−0.961716	+	0.274047i	$0.911638\pi$
$8$		0			0
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$		0			0
$11$	−3.17727	−	2.04191i	−0.957982	−	0.615658i	−0.0345433	−	0.999403i	$-0.510998\pi$
$11$	−3.17727	−	2.04191i	−0.957982	−	0.615658i	−0.923439	+	0.383745i	$0.874634\pi$
$12$		0			0
$13$	−0.129165	+	0.149064i	−0.0358239	+	0.0413430i	−0.773379	−	0.633944i	$-0.781435\pi$
$13$	−0.129165	+	0.149064i	−0.0358239	+	0.0413430i	0.737555	+	0.675287i	$0.235980\pi$
$14$		0			0
$15$	−0.135127	−	0.939827i	−0.0348896	−	0.242662i
$16$		0			0
$17$	−1.19770	−	2.62260i	−0.290485	−	0.636074i	0.706979	−	0.707234i	$-0.250057\pi$
$17$	−1.19770	−	2.62260i	−0.290485	−	0.636074i	−0.997465	+	0.0711596i	$0.977330\pi$
$18$		0			0
$19$	1.90178	−	4.16431i	0.436297	−	0.955358i	−0.555966	−	0.831205i	$-0.687651\pi$
$19$	1.90178	−	4.16431i	0.436297	−	0.955358i	0.992263	−	0.124153i	$-0.0396213\pi$
$20$		0			0
$21$	1.88156	−	1.20920i	0.410589	−	0.263870i
$22$		0			0
$23$	−4.06339	−	2.54732i	−0.847275	−	0.531154i
$23$	−4.06339	−	2.54732i	−0.847275	−	0.531154i
$24$		0			0
$25$	−3.44785	+	2.21580i	−0.689570	+	0.443160i
$26$		0			0
$27$	0.415415	−	0.909632i	0.0799467	−	0.175059i
$28$		0			0
$29$	0.572550	+	1.25371i	0.106320	+	0.232808i	0.955313	−	0.295595i	$-0.0955180\pi$
$29$	0.572550	+	1.25371i	0.106320	+	0.232808i	−0.848993	+	0.528404i	$0.822791\pi$
$30$		0			0
$31$	−0.120729	−	0.839689i	−0.0216836	−	0.150813i	0.976103	−	0.217308i	$-0.0697275\pi$
$31$	−0.120729	−	0.839689i	−0.0216836	−	0.150813i	−0.997787	+	0.0664950i	$0.978818\pi$
$32$		0			0
$33$	2.47329	−	2.85433i	0.430545	−	0.496876i
$34$		0			0
$35$	1.78652	+	1.14813i	0.301977	+	0.194069i
$36$		0			0
$37$	5.57420	+	1.63673i	0.916392	+	0.269077i	0.705729	−	0.708482i	$-0.250619\pi$
$37$	5.57420	+	1.63673i	0.916392	+	0.269077i	0.210663	+	0.977559i	$0.432438\pi$
$38$		0			0
$39$	−0.129165	−	0.149064i	−0.0206829	−	0.0238694i
$40$		0			0
$41$	1.39683	−	0.410145i	0.218147	−	0.0640539i	−0.170833	−	0.985300i	$-0.554646\pi$
$41$	1.39683	−	0.410145i	0.218147	−	0.0640539i	0.388980	+	0.921246i	$0.372828\pi$
$42$		0			0
$43$	1.75923	−	12.2357i	0.268281	−	1.86593i	−0.196497	−	0.980504i	$-0.562957\pi$
$43$	1.75923	−	12.2357i	0.268281	−	1.86593i	0.464777	−	0.885428i	$-0.346134\pi$
$44$		0			0
$45$	0.949491			0.141542
$46$		0			0
$47$	−13.0666			−1.90595			−0.952976	−	0.303045i	$-0.901997\pi$
$47$	−13.0666			−1.90595			−0.952976	+	0.303045i	$0.901997\pi$
$48$		0			0
$49$	0.284285	−	1.97724i	0.0406121	−	0.282463i
$50$		0			0
$51$	2.76636	−	0.812276i	0.387368	−	0.113741i
$52$		0			0
$53$	−0.0705505	−	0.0814196i	−0.00969085	−	0.0111838i	0.750883	−	0.660435i	$-0.229628\pi$
$53$	−0.0705505	−	0.0814196i	−0.00969085	−	0.0111838i	−0.760574	+	0.649251i	$0.775083\pi$
$54$		0			0
$55$	3.44080	+	1.01031i	0.463958	+	0.136230i
$56$		0			0
$57$	3.85127	+	2.47506i	0.510113	+	0.327830i
$58$		0			0
$59$	−3.66065	+	4.22462i	−0.476576	+	0.549998i	−0.942229	−	0.334969i	$-0.891274\pi$
$59$	−3.66065	+	4.22462i	−0.476576	+	0.549998i	0.465653	+	0.884967i	$0.345820\pi$
$60$		0			0
$61$	1.04249	+	7.25071i	0.133478	+	0.928358i	0.940972	+	0.338483i	$0.109914\pi$
$61$	1.04249	+	7.25071i	0.133478	+	0.928358i	−0.807495	+	0.589875i	$0.799177\pi$
$62$		0			0
$63$	0.929121	+	2.03449i	0.117058	+	0.256322i
$64$		0			0
$65$	0.0777980	−	0.170354i	0.00964966	−	0.0211298i
$66$		0			0
$67$	−4.74992	+	3.05259i	−0.580295	+	0.372933i	−0.797614	−	0.603168i	$-0.793905\pi$
$67$	−4.74992	+	3.05259i	−0.580295	+	0.372933i	0.217320	+	0.976100i	$0.430269\pi$
$68$		0			0
$69$	3.09968	−	3.65951i	0.373157	−	0.440553i
$70$		0			0
$71$	−11.1779	+	7.18362i	−1.32658	+	0.852539i	−0.995834	−	0.0911822i	$-0.970935\pi$
$71$	−11.1779	+	7.18362i	−1.32658	+	0.852539i	−0.330742	+	0.943721i	$0.607299\pi$
$72$		0			0
$73$	2.58219	−	5.65422i	0.302223	−	0.661776i	−0.696204	−	0.717844i	$-0.745129\pi$
$73$	2.58219	−	5.65422i	0.302223	−	0.661776i	0.998427	+	0.0560679i	$0.0178563\pi$
$74$		0			0
$75$	−1.70256	−	3.72810i	−0.196595	−	0.430483i
$76$		0			0
$77$	1.20217	+	8.36130i	0.137000	+	0.952859i
$78$		0			0
$79$	−0.0200761	+	0.0231691i	−0.00225874	+	0.00260672i	−0.756878	−	0.653556i	$-0.773276\pi$
$79$	−0.0200761	+	0.0231691i	−0.00225874	+	0.00260672i	0.754619	+	0.656163i	$0.227822\pi$
$80$		0			0
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$		0			0
$83$	9.43824	+	2.77132i	1.03598	+	0.304192i	0.755141	−	0.655563i	$-0.227569\pi$
$83$	9.43824	+	2.77132i	1.03598	+	0.304192i	0.280841	+	0.959754i	$0.409387\pi$
$84$		0			0
$85$	1.79270	+	2.06888i	0.194445	+	0.224402i
$86$		0			0
$87$	−1.32243	+	0.388301i	−0.141780	+	0.0416302i
$88$		0			0
$89$	0.111235	−	0.773655i	0.0117909	−	0.0820072i	−0.983076	−	0.183196i	$-0.941356\pi$
$89$	0.111235	−	0.773655i	0.0117909	−	0.0820072i	0.994867	+	0.101189i	$0.0322647\pi$
$90$		0			0
$91$	0.441150			0.0462450
$92$		0			0
$93$	0.848324			0.0879671
$94$		0			0
$95$	−0.618612	+	4.30254i	−0.0634682	+	0.441431i
$96$		0			0
$97$	−2.46721	+	0.724439i	−0.250508	+	0.0735557i	−0.404576	−	0.914505i	$-0.632581\pi$
$97$	−2.46721	+	0.724439i	−0.250508	+	0.0735557i	0.154068	+	0.988060i	$0.450763\pi$
$98$		0			0
$99$	2.47329	+	2.85433i	0.248575	+	0.286871i
$100$		0			0
$101$	−6.47873	−	1.90233i	−0.644658	−	0.189289i	−0.0569692	−	0.998376i	$-0.518144\pi$
$101$	−6.47873	−	1.90233i	−0.644658	−	0.189289i	−0.587688	+	0.809087i	$0.699962\pi$
$102$		0			0
$103$	5.94569	+	3.82107i	0.585847	+	0.376501i	0.799731	−	0.600358i	$-0.204975\pi$
$103$	5.94569	+	3.82107i	0.585847	+	0.376501i	−0.213885	+	0.976859i	$0.568612\pi$
$104$		0			0
$105$	−1.39069	+	1.60494i	−0.135717	+	0.156626i
$106$		0			0
$107$	−0.634008	−	4.40962i	−0.0612918	−	0.426294i	−0.997246	−	0.0741710i	$-0.976369\pi$
$107$	−0.634008	−	4.40962i	−0.0612918	−	0.426294i	0.935954	−	0.352123i	$-0.114540\pi$
$108$		0			0
$109$	4.20391	+	9.20528i	0.402662	+	0.881706i	0.996993	+	0.0774859i	$0.0246893\pi$
$109$	4.20391	+	9.20528i	0.402662	+	0.881706i	−0.594332	+	0.804220i	$0.702583\pi$
$110$		0			0
$111$	−2.41336	+	5.28453i	−0.229066	+	0.501585i
$112$		0			0
$113$	−5.47929	+	3.52133i	−0.515449	+	0.331259i	−0.772369	−	0.635174i	$-0.780928\pi$
$113$	−5.47929	+	3.52133i	−0.515449	+	0.331259i	0.256921	+	0.966432i	$0.417292\pi$
$114$		0			0
$115$	4.38329	+	1.23372i	0.408744	+	0.115045i
$116$		0			0
$117$	0.165929	−	0.106636i	0.0153401	−	0.00985851i
$118$		0			0
$119$	−2.67879	+	5.86574i	−0.245565	+	0.537711i
$120$		0			0
$121$	1.35608	+	2.96941i	0.123280	+	0.269946i
$122$		0			0
$123$	0.207181	+	1.44098i	0.0186809	+	0.129929i
$124$		0			0
$125$	5.65729	−	6.52886i	0.506003	−	0.583959i
$126$		0			0
$127$	2.29317	+	1.47373i	0.203486	+	0.130773i	0.638415	−	0.769692i	$-0.279590\pi$
$127$	2.29317	+	1.47373i	0.203486	+	0.130773i	−0.434929	+	0.900465i	$0.643227\pi$
$128$		0			0
$129$	11.8608	+	3.48265i	1.04429	+	0.306631i
$130$		0			0
$131$	1.46589	+	1.69173i	0.128076	+	0.147807i	0.816165	−	0.577818i	$-0.196096\pi$
$131$	1.46589	+	1.69173i	0.128076	+	0.147807i	−0.688090	+	0.725626i	$0.741550\pi$
$132$		0			0
$133$	−9.82447	+	2.88473i	−0.851890	+	0.250137i
$134$		0			0
$135$	−0.135127	+	0.939827i	−0.0116299	+	0.0808874i
$136$		0			0
$137$	3.12399			0.266900			0.133450	−	0.991056i	$-0.457394\pi$
$137$	3.12399			0.266900			0.133450	+	0.991056i	$0.457394\pi$
$138$		0			0
$139$	10.7544			0.912179			0.456090	−	0.889934i	$-0.349250\pi$
$139$	10.7544			0.912179			0.456090	+	0.889934i	$0.349250\pi$
$140$		0			0
$141$	1.85956	−	12.9336i	0.156604	−	1.08920i
$142$		0			0
$143$	0.714767	−	0.209874i	0.0597718	−	0.0175506i
$144$		0			0
$145$	−0.856982	−	0.989010i	−0.0711685	−	0.0821328i
$146$		0			0
$147$	1.91666	+	0.562782i	0.158083	+	0.0464175i
$148$		0			0
$149$	0.764833	+	0.491529i	0.0626576	+	0.0402676i	0.571595	−	0.820536i	$-0.306325\pi$
$149$	0.764833	+	0.491529i	0.0626576	+	0.0402676i	−0.508937	+	0.860804i	$0.669961\pi$
$150$		0			0
$151$	−4.18615	+	4.83107i	−0.340664	+	0.393147i	−0.900069	−	0.435747i	$-0.856484\pi$
$151$	−4.18615	+	4.83107i	−0.340664	+	0.393147i	0.559405	+	0.828894i	$0.311030\pi$
$152$		0			0
$153$	0.410315	+	2.85380i	0.0331720	+	0.230716i
$154$		0			0
$155$	0.334607	+	0.732687i	0.0268763	+	0.0588508i
$156$		0			0
$157$	−6.42412	+	14.0669i	−0.512700	+	1.12266i	0.459430	+	0.888214i	$0.348054\pi$
$157$	−6.42412	+	14.0669i	−0.512700	+	1.12266i	−0.972130	+	0.234443i	$0.924673\pi$
$158$		0			0
$159$	0.0906312	−	0.0582452i	0.00718753	−	0.00461914i
$160$		0			0
$161$	1.64573	+	10.5994i	0.129702	+	0.835350i
$162$		0			0
$163$	13.7101	−	8.81094i	1.07386	−	0.690126i	0.120727	−	0.992686i	$-0.461478\pi$
$163$	13.7101	−	8.81094i	1.07386	−	0.690126i	0.953130	+	0.302560i	$0.0978411\pi$
$164$		0			0
$165$	−1.48970	+	3.26200i	−0.115973	+	0.253946i
$166$		0			0
$167$	−1.62935	−	3.56777i	−0.126083	−	0.276083i	0.836055	−	0.548645i	$-0.184856\pi$
$167$	−1.62935	−	3.56777i	−0.126083	−	0.276083i	−0.962138	+	0.272562i	$0.912129\pi$
$168$		0			0
$169$	1.84456	+	12.8292i	0.141889	+	0.986859i
$170$		0			0
$171$	−2.99796	+	3.45983i	−0.229260	+	0.264580i
$172$		0			0
$173$	−1.25443	−	0.806176i	−0.0953729	−	0.0612924i	0.492085	−	0.870547i	$-0.336235\pi$
$173$	−1.25443	−	0.806176i	−0.0953729	−	0.0612924i	−0.587458	+	0.809255i	$0.699871\pi$
$174$		0			0
$175$	8.79536	+	2.58255i	0.664866	+	0.195222i
$176$		0			0
$177$	−3.66065	−	4.22462i	−0.275151	−	0.317542i
$178$		0			0
$179$	12.8266	−	3.76624i	0.958708	−	0.281502i	0.235300	−	0.971923i	$-0.424393\pi$
$179$	12.8266	−	3.76624i	0.958708	−	0.281502i	0.723408	+	0.690421i	$0.242575\pi$
$180$		0			0
$181$	3.72928	−	25.9377i	0.277195	−	1.92794i	−0.0861527	−	0.996282i	$-0.527457\pi$
$181$	3.72928	−	25.9377i	0.277195	−	1.92794i	0.363348	−	0.931654i	$-0.381634\pi$
$182$		0			0
$183$	−7.32527			−0.541500
$184$		0			0
$185$	−5.51609			−0.405551
$186$		0			0
$187$	−1.54969	+	10.7783i	−0.113324	+	0.788188i
$188$		0			0
$189$	−2.14601	+	0.630126i	−0.156099	+	0.0458349i
$190$		0			0
$191$	1.18472	+	1.36725i	0.0857237	+	0.0989304i	0.796991	−	0.603991i	$-0.206424\pi$
$191$	1.18472	+	1.36725i	0.0857237	+	0.0989304i	−0.711267	+	0.702922i	$0.751878\pi$
$192$		0			0
$193$	−20.5982	−	6.04819i	−1.48269	−	0.435358i	−0.562492	−	0.826803i	$-0.690157\pi$
$193$	−20.5982	−	6.04819i	−1.48269	−	0.435358i	−0.920202	+	0.391445i	$0.871975\pi$
$194$		0			0
$195$	0.157548	+	0.101250i	0.0112823	+	0.00725067i
$196$		0			0
$197$	3.81799	−	4.40619i	0.272020	−	0.313928i	−0.603260	−	0.797545i	$-0.706132\pi$
$197$	3.81799	−	4.40619i	0.272020	−	0.313928i	0.875280	+	0.483617i	$0.160677\pi$
$198$		0			0
$199$	−1.48217	−	10.3088i	−0.105069	−	0.730768i	−0.972448	−	0.233120i	$-0.925106\pi$
$199$	−1.48217	−	10.3088i	−0.105069	−	0.730768i	0.867379	−	0.497648i	$-0.165803\pi$
$200$		0			0
$201$	−2.34553	−	5.13600i	−0.165441	−	0.362265i
$202$		0			0
$203$	1.28057	−	2.80406i	0.0898785	−	0.196807i
$204$		0			0
$205$	−1.16284	+	0.747309i	−0.0812159	+	0.0521943i
$206$		0			0
$207$	3.18113	+	3.58893i	0.221104	+	0.249448i
$208$		0			0
$209$	−14.5456	+	9.34787i	−1.00614	+	0.646606i
$210$		0			0
$211$	5.77328	−	12.6417i	0.397449	−	0.870292i	−0.600073	−	0.799945i	$-0.704862\pi$
$211$	5.77328	−	12.6417i	0.397449	−	0.870292i	0.997523	−	0.0703474i	$-0.0224108\pi$
$212$		0			0
$213$	−5.51972	−	12.0865i	−0.378205	−	0.828153i
$214$		0			0
$215$	1.67038	+	11.6177i	0.113919	+	0.792322i
$216$		0			0
$217$	−1.24251	+	1.43394i	−0.0843472	+	0.0973419i
$218$		0			0
$219$	5.22918	+	3.36059i	0.353355	+	0.227088i
$220$		0			0
$221$	0.545637	+	0.160214i	0.0367035	+	0.0107771i
$222$		0			0
$223$	−8.44887	−	9.75052i	−0.565778	−	0.652943i	0.398707	−	0.917078i	$-0.369459\pi$
$223$	−8.44887	−	9.75052i	−0.565778	−	0.652943i	−0.964486	+	0.264135i	$0.914913\pi$
$224$		0			0
$225$	3.93245	−	1.15467i	0.262163	−	0.0769781i
$226$		0			0
$227$	2.55325	−	17.7582i	0.169465	−	1.17866i	−0.710528	−	0.703669i	$-0.751544\pi$
$227$	2.55325	−	17.7582i	0.169465	−	1.17866i	0.879993	−	0.474987i	$-0.157547\pi$
$228$		0			0
$229$	12.4890			0.825295			0.412647	−	0.910891i	$-0.364604\pi$
$229$	12.4890			0.825295			0.412647	+	0.910891i	$0.364604\pi$
$230$		0			0
$231$	−8.44729			−0.555791
$232$		0			0
$233$	1.05693	−	7.35110i	0.0692417	−	0.481587i	−0.925465	−	0.378833i	$-0.876326\pi$
$233$	1.05693	−	7.35110i	0.0692417	−	0.481587i	0.994707	−	0.102754i	$-0.0327654\pi$
$234$		0			0
$235$	11.9040	−	3.49534i	0.776533	−	0.228011i
$236$		0			0
$237$	−0.0200761	−	0.0231691i	−0.00130408	−	0.00150499i
$238$		0			0
$239$	17.8806	+	5.25021i	1.15660	+	0.339608i	0.803110	−	0.595831i	$-0.203177\pi$
$239$	17.8806	+	5.25021i	1.15660	+	0.339608i	0.353488	+	0.935439i	$0.384995\pi$
$240$		0			0
$241$	−7.45838	−	4.79321i	−0.480436	−	0.308758i	0.277913	−	0.960606i	$-0.410357\pi$
$241$	−7.45838	−	4.79321i	−0.480436	−	0.308758i	−0.758349	+	0.651849i	$0.773994\pi$
$242$		0			0
$243$	−0.654861	+	0.755750i	−0.0420093	+	0.0484814i
$244$		0			0
$245$	0.269926	+	1.87737i	0.0172449	+	0.119941i
$246$		0			0
$247$	0.375107	+	0.821369i	0.0238675	+	0.0522625i
$248$		0			0
$249$	−4.08631	+	8.94777i	−0.258959	+	0.567042i
$250$		0			0
$251$	−21.9529	+	14.1083i	−1.38566	+	0.890507i	−0.999490	−	0.0319217i	$-0.989837\pi$
$251$	−21.9529	+	14.1083i	−1.38566	+	0.890507i	−0.386166	+	0.922429i	$0.626201\pi$
$252$		0			0
$253$	7.70908	+	16.3906i	0.484666	+	1.03047i
$254$		0			0
$255$	−2.30295	+	1.48002i	−0.144216	+	0.0926822i
$256$		0			0
$257$	11.5048	−	25.1919i	0.717648	−	1.57143i	−0.0995227	−	0.995035i	$-0.531732\pi$
$257$	11.5048	−	25.1919i	0.717648	−	1.57143i	0.817171	−	0.576395i	$-0.195541\pi$
$258$		0			0
$259$	−5.39775	−	11.8194i	−0.335400	−	0.734424i
$260$		0			0
$261$	−0.196147	−	1.36423i	−0.0121412	−	0.0844439i
$262$		0			0
$263$	−7.44831	+	8.59581i	−0.459282	+	0.530040i	−0.937399	−	0.348256i	$-0.886774\pi$
$263$	−7.44831	+	8.59581i	−0.459282	+	0.530040i	0.478117	+	0.878296i	$0.341319\pi$
$264$		0			0
$265$	0.0860536	+	0.0553033i	0.00528623	+	0.00339725i
$266$		0			0
$267$	0.749950	+	0.220205i	0.0458962	+	0.0134763i
$268$		0			0
$269$	−17.3750	−	20.0518i	−1.05937	−	1.22258i	−0.974076	−	0.226222i	$-0.927363\pi$
$269$	−17.3750	−	20.0518i	−1.05937	−	1.22258i	−0.0852938	−	0.996356i	$-0.527183\pi$
$270$		0			0
$271$	−11.9492	+	3.50859i	−0.725860	+	0.213132i	−0.623731	−	0.781639i	$-0.714384\pi$
$271$	−11.9492	+	3.50859i	−0.725860	+	0.213132i	−0.102129	+	0.994771i	$0.532566\pi$
$272$		0			0
$273$	−0.0627821	+	0.436659i	−0.00379975	+	0.0264278i
$274$		0			0
$275$	15.4792			0.933430
$276$		0			0
$277$	−29.5480			−1.77537			−0.887683	−	0.460456i	$-0.847686\pi$
$277$	−29.5480			−1.77537			−0.887683	+	0.460456i	$0.847686\pi$
$278$		0			0
$279$	−0.120729	+	0.839689i	−0.00722786	+	0.0502709i
$280$		0			0
$281$	21.9865	−	6.45583i	1.31161	−	0.385123i	0.450150	−	0.892953i	$-0.351370\pi$
$281$	21.9865	−	6.45583i	1.31161	−	0.385123i	0.861457	+	0.507830i	$0.169552\pi$
$282$		0			0
$283$	−15.8311	−	18.2701i	−0.941062	−	1.08604i	−0.996159	−	0.0875620i	$-0.972092\pi$
$283$	−15.8311	−	18.2701i	−0.941062	−	1.08604i	0.0550975	−	0.998481i	$-0.482453\pi$
$284$		0			0
$285$	−4.17071	−	1.22463i	−0.247051	−	0.0725409i
$286$		0			0
$287$	−2.73916	−	1.76035i	−0.161688	−	0.103910i
$288$		0			0
$289$	5.68908	−	6.56555i	0.334652	−	0.386209i
$290$		0			0
$291$	−0.365944	−	2.54520i	−0.0214520	−	0.149202i
$292$		0			0
$293$	−13.5684	−	29.7106i	−0.792673	−	1.73571i	−0.668837	−	0.743409i	$-0.733208\pi$
$293$	−13.5684	−	29.7106i	−0.792673	−	1.73571i	−0.123835	−	0.992303i	$-0.539519\pi$
$294$		0			0
$295$	2.20487	−	4.82799i	0.128372	−	0.281096i
$296$		0			0
$297$	−3.17727	+	2.04191i	−0.184364	+	0.118483i
$298$		0			0
$299$	0.904562	−	0.276681i	0.0523122	−	0.0160009i
$300$		0			0
$301$	−23.2590	+	14.9476i	−1.34062	+	0.861567i
$302$		0			0
$303$	2.80498	−	6.14206i	0.161142	−	0.352852i
$304$		0			0
$305$	−2.88933	−	6.32675i	−0.165442	−	0.362268i
$306$		0			0
$307$	4.57366	+	31.8105i	0.261033	+	1.81552i	0.525124	+	0.851026i	$0.324019\pi$
$307$	4.57366	+	31.8105i	0.261033	+	1.81552i	−0.264091	+	0.964498i	$0.585072\pi$
$308$		0			0
$309$	−4.62833	+	5.34138i	−0.263297	+	0.303861i
$310$		0			0
$311$	9.81930	+	6.31048i	0.556801	+	0.357835i	0.788578	−	0.614934i	$-0.210818\pi$
$311$	9.81930	+	6.31048i	0.556801	+	0.357835i	−0.231777	+	0.972769i	$0.574454\pi$
$312$		0			0
$313$	−27.7204	−	8.13944i	−1.56685	−	0.460069i	−0.620767	−	0.783995i	$-0.713179\pi$
$313$	−27.7204	−	8.13944i	−1.56685	−	0.460069i	−0.946082	+	0.323926i	$0.894997\pi$
$314$		0			0
$315$	−1.39069	−	1.60494i	−0.0783565	−	0.0904282i
$316$		0			0
$317$	16.2603	−	4.77446i	0.913271	−	0.268161i	0.208854	−	0.977947i	$-0.433027\pi$
$317$	16.2603	−	4.77446i	0.913271	−	0.268161i	0.704417	+	0.709786i	$0.251208\pi$
$318$		0			0
$319$	0.740813	−	5.15247i	0.0414776	−	0.288483i
$320$		0			0
$321$	4.45497			0.248652
$322$		0			0
$323$	−13.1991			−0.734417
$324$		0			0
$325$	0.115045	−	0.800154i	0.00638154	−	0.0443846i
$326$		0			0
$327$	−9.70986	+	2.85107i	−0.536957	+	0.157665i
$328$		0			0
$329$	19.1382	+	22.0866i	1.05512	+	1.21767i
$330$		0			0
$331$	1.37230	+	0.402945i	0.0754287	+	0.0221479i	0.319229	−	0.947678i	$-0.396576\pi$
$331$	1.37230	+	0.402945i	0.0754287	+	0.0221479i	−0.243800	+	0.969825i	$0.578394\pi$
$332$		0			0
$333$	−4.88728	−	3.14087i	−0.267821	−	0.172118i
$334$		0			0
$335$	3.51074	−	4.05161i	0.191812	−	0.221363i
$336$		0			0
$337$	−2.57050	−	17.8782i	−0.140024	−	0.973889i	−0.931773	−	0.363042i	$-0.881738\pi$
$337$	−2.57050	−	17.8782i	−0.140024	−	0.973889i	0.791749	−	0.610847i	$-0.209171\pi$
$338$		0			0
$339$	−2.70570	−	5.92466i	−0.146954	−	0.321783i
$340$		0			0
$341$	−1.33098	+	2.91443i	−0.0720765	+	0.157825i
$342$		0			0
$343$	−16.9294	+	10.8799i	−0.914104	+	0.587459i
$344$		0			0
$345$	−1.84497	+	4.16309i	−0.0993299	+	0.224133i
$346$		0			0
$347$	28.9748	−	18.6210i	1.55545	−	0.999626i	0.571619	−	0.820519i	$-0.306316\pi$
$347$	28.9748	−	18.6210i	1.55545	−	0.999626i	0.983830	−	0.179106i	$-0.0573206\pi$
$348$		0			0
$349$	−1.48766	+	3.25753i	−0.0796328	+	0.174371i	−0.945260	−	0.326317i	$-0.894192\pi$
$349$	−1.48766	+	3.25753i	−0.0796328	+	0.174371i	0.865628	+	0.500688i	$0.166920\pi$
$350$		0			0
$351$	0.0819366	+	0.179416i	0.00437345	+	0.00957652i
$352$		0			0
$353$	−1.60470	−	11.1610i	−0.0854098	−	0.594038i	−0.986912	−	0.161263i	$-0.948443\pi$
$353$	−1.60470	−	11.1610i	−0.0854098	−	0.594038i	0.901502	−	0.432775i	$-0.142466\pi$
$354$		0			0
$355$	8.26180	−	9.53462i	0.438491	−	0.506045i
$356$		0			0
$357$	−5.42480	−	3.48631i	−0.287111	−	0.184515i
$358$		0			0
$359$	31.1965	+	9.16011i	1.64649	+	0.483452i	0.967956	−	0.251120i	$-0.0807989\pi$
$359$	31.1965	+	9.16011i	1.64649	+	0.483452i	0.678531	+	0.734572i	$0.262617\pi$
$360$		0			0
$361$	−1.28236	−	1.47992i	−0.0674925	−	0.0778905i
$362$		0			0
$363$	−3.13218	+	0.919690i	−0.164397	+	0.0482712i
$364$		0			0
$365$	−0.839939	+	5.84191i	−0.0439644	+	0.305779i
$366$		0			0
$367$	−18.1256			−0.946151			−0.473075	−	0.881022i	$-0.656856\pi$
$367$	−18.1256			−0.946151			−0.473075	+	0.881022i	$0.656856\pi$
$368$		0			0
$369$	−1.45580			−0.0757857
$370$		0			0
$371$	−0.0342919	+	0.238505i	−0.00178035	+	0.0123826i
$372$		0			0
$373$	18.4445	−	5.41579i	0.955020	−	0.280419i	0.233144	−	0.972442i	$-0.425099\pi$
$373$	18.4445	−	5.41579i	0.955020	−	0.280419i	0.721875	+	0.692023i	$0.243280\pi$
$374$		0			0
$375$	5.65729	+	6.52886i	0.292141	+	0.337149i
$376$		0			0
$377$	−0.260837	−	0.0765886i	−0.0134338	−	0.00394451i
$378$		0			0
$379$	27.7644	+	17.8431i	1.42616	+	0.916540i	0.999929	+	0.0119275i	$0.00379672\pi$
$379$	27.7644	+	17.8431i	1.42616	+	0.916540i	0.426235	+	0.904612i	$0.359840\pi$
$380$		0			0
$381$	−1.78508	+	2.06010i	−0.0914527	+	0.105542i
$382$		0			0
$383$	−3.50446	−	24.3741i	−0.179070	−	1.24546i	−0.858922	−	0.512107i	$-0.828865\pi$
$383$	−3.50446	−	24.3741i	−0.179070	−	1.24546i	0.679852	−	0.733349i	$-0.262044\pi$
$384$		0			0
$385$	−3.33189	−	7.29582i	−0.169809	−	0.371829i
$386$		0			0
$387$	−5.13518	+	11.2445i	−0.261036	+	0.571588i
$388$		0			0
$389$	9.08619	−	5.83934i	0.460688	−	0.296066i	−0.289635	−	0.957137i	$-0.593534\pi$
$389$	9.08619	−	5.83934i	0.460688	−	0.296066i	0.750324	+	0.661071i	$0.229898\pi$
$390$		0			0
$391$	−1.81388	+	13.7076i	−0.0917321	+	0.693223i
$392$		0			0
$393$	−1.88313	+	1.21021i	−0.0949914	+	0.0610473i
$394$		0			0
$395$	0.0120922	−	0.0264781i	0.000608422	−	0.00133226i
$396$		0			0
$397$	10.5724	+	23.1502i	0.530611	+	1.16188i	0.965264	+	0.261278i	$0.0841439\pi$
$397$	10.5724	+	23.1502i	0.530611	+	1.16188i	−0.434653	+	0.900598i	$0.643129\pi$
$398$		0			0
$399$	−1.45719	−	10.1350i	−0.0729510	−	0.507385i
$400$		0			0
$401$	7.10594	−	8.20069i	0.354854	−	0.409523i	−0.550055	−	0.835128i	$-0.685393\pi$
$401$	7.10594	−	8.20069i	0.354854	−	0.409523i	0.904909	+	0.425605i	$0.139939\pi$
$402$		0			0
$403$	0.140762	+	0.0904619i	0.00701183	+	0.00450623i
$404$		0			0
$405$	−0.911030	−	0.267503i	−0.0452695	−	0.0132923i
$406$		0			0
$407$	−14.3687	−	16.5823i	−0.712228	−	0.821955i
$408$		0			0
$409$	9.20335	−	2.70235i	0.455076	−	0.133622i	−0.0461579	−	0.998934i	$-0.514698\pi$
$409$	9.20335	−	2.70235i	0.455076	−	0.133622i	0.501234	+	0.865312i	$0.332880\pi$
$410$		0			0
$411$	−0.444589	+	3.09219i	−0.0219300	+	0.152526i
$412$		0			0
$413$	12.5026			0.615212
$414$		0			0
$415$	−9.33986			−0.458475
$416$		0			0
$417$	−1.53052	+	10.6450i	−0.0749497	+	0.521287i
$418$		0			0
$419$	2.94326	−	0.864218i	0.143787	−	0.0422198i	−0.209047	−	0.977906i	$-0.567036\pi$
$419$	2.94326	−	0.864218i	0.143787	−	0.0422198i	0.352834	+	0.935686i	$0.385218\pi$
$420$		0			0
$421$	−3.28653	−	3.79286i	−0.160176	−	0.184853i	0.669989	−	0.742371i	$-0.266299\pi$
$421$	−3.28653	−	3.79286i	−0.160176	−	0.184853i	−0.830164	+	0.557519i	$0.811753\pi$
$422$		0			0
$423$	12.5373	+	3.68127i	0.609583	+	0.178990i
$424$		0			0
$425$	9.94065	+	6.38847i	0.482193	+	0.309886i
$426$		0			0
$427$	10.7291	−	12.3820i	0.519217	−	0.599209i
$428$		0			0
$429$	0.106016	+	0.737359i	0.00511851	+	0.0356001i
$430$		0			0
$431$	−0.348887	−	0.763955i	−0.0168053	−	0.0367984i	0.901043	−	0.433729i	$-0.142803\pi$
$431$	−0.348887	−	0.763955i	−0.0168053	−	0.0367984i	−0.917849	+	0.396931i	$0.870075\pi$
$432$		0			0
$433$	4.59573	−	10.0633i	0.220857	−	0.483609i	−0.766476	−	0.642273i	$-0.777991\pi$
$433$	4.59573	−	10.0633i	0.220857	−	0.483609i	0.987333	+	0.158664i	$0.0507187\pi$
$434$		0			0
$435$	1.10090	−	0.707508i	0.0527843	−	0.0339224i
$436$		0			0
$437$	−18.3355	+	12.0768i	−0.877106	+	0.577710i
$438$		0			0
$439$	−19.0317	+	12.2309i	−0.908334	+	0.583751i	−0.909251	−	0.416249i	$-0.863345\pi$
$439$	−19.0317	+	12.2309i	−0.908334	+	0.583751i	0.000916569		1.00000i	$0.499708\pi$
$440$		0			0
$441$	−0.829823	+	1.81706i	−0.0395154	+	0.0865266i
$442$		0			0
$443$	−0.260149	−	0.569646i	−0.0123600	−	0.0270647i	0.903351	−	0.428901i	$-0.141099\pi$
$443$	−0.260149	−	0.569646i	−0.0123600	−	0.0270647i	−0.915711	+	0.401837i	$0.868372\pi$
$444$		0			0
$445$	0.105616	+	0.734578i	0.00500670	+	0.0348224i
$446$		0			0
$447$	−0.595373	+	0.687097i	−0.0281602	+	0.0324986i
$448$		0			0
$449$	28.6791	+	18.4309i	1.35345	+	0.869809i	0.997895	−	0.0648468i	$-0.0206559\pi$
$449$	28.6791	+	18.4309i	1.35345	+	0.869809i	0.355554	+	0.934656i	$0.384292\pi$
$450$		0			0
$451$	−5.27556	−	1.54905i	−0.248417	−	0.0729417i
$452$		0			0
$453$	−4.18615	−	4.83107i	−0.196682	−	0.226984i
$454$		0			0
$455$	−0.401901	+	0.118009i	−0.0188414	+	0.00553233i
$456$		0			0
$457$	3.96204	−	27.5566i	0.185336	−	1.28904i	−0.658556	−	0.752531i	$-0.728833\pi$
$457$	3.96204	−	27.5566i	0.185336	−	1.28904i	0.843893	−	0.536512i	$-0.180258\pi$
$458$		0			0
$459$	−2.88315			−0.134574
$460$		0			0
$461$	9.85378			0.458936			0.229468	−	0.973316i	$-0.426301\pi$
$461$	9.85378			0.458936			0.229468	+	0.973316i	$0.426301\pi$
$462$		0			0
$463$	−4.30051	+	29.9107i	−0.199862	+	1.39007i	0.604820	+	0.796362i	$0.293245\pi$
$463$	−4.30051	+	29.9107i	−0.199862	+	1.39007i	−0.804682	+	0.593706i	$0.797664\pi$
$464$		0			0
$465$	−0.772848	+	0.226929i	−0.0358400	+	0.0105236i
$466$		0			0
$467$	−6.05410	−	6.98680i	−0.280150	−	0.323311i	0.598183	−	0.801360i	$-0.295890\pi$
$467$	−6.05410	−	6.98680i	−0.280150	−	0.323311i	−0.878333	+	0.478049i	$0.841344\pi$
$468$		0			0
$469$	12.1169	+	3.55784i	0.559506	+	0.164286i
$470$		0			0
$471$	−13.0094	−	8.36065i	−0.599443	−	0.385238i
$472$		0			0
$473$	−30.5738	+	35.2840i	−1.40578	+	1.62236i
$474$		0			0
$475$	2.67023	+	18.5719i	0.122519	+	0.852135i
$476$		0			0
$477$	0.0447541	+	0.0979979i	0.00204915	+	0.00448702i
$478$		0			0
$479$	−10.8542	+	23.7674i	−0.495941	+	1.08596i	0.481826	+	0.876267i	$0.339974\pi$
$479$	−10.8542	+	23.7674i	−0.495941	+	1.08596i	−0.977767	+	0.209693i	$0.932754\pi$
$480$		0			0
$481$	−0.963969	+	0.619505i	−0.0439532	+	0.0282470i
$482$		0			0
$483$	−10.7257	+	0.120530i	−0.488038	+	0.00548432i
$484$		0			0
$485$	2.05392	−	1.31997i	0.0932636	−	0.0599368i
$486$		0			0
$487$	13.6113	−	29.8047i	0.616789	−	1.35058i	−0.301043	−	0.953610i	$-0.597335\pi$
$487$	13.6113	−	29.8047i	0.616789	−	1.35058i	0.917832	−	0.396969i	$-0.129938\pi$
$488$		0			0
$489$	6.77011	+	14.8245i	0.306155	+	0.670386i
$490$		0			0
$491$	−0.908362	−	6.31780i	−0.0409938	−	0.285118i	−0.999999	−	0.00172804i	$-0.999450\pi$
$491$	−0.908362	−	6.31780i	−0.0409938	−	0.285118i	0.959005	−	0.283390i	$-0.0914591\pi$
$492$		0			0
$493$	2.60224	−	3.00314i	0.117199	−	0.135255i
$494$		0			0
$495$	−3.01679	−	1.93877i	−0.135595	−	0.0871413i
$496$		0			0
$497$	28.5146	+	8.37263i	1.27905	+	0.375564i
$498$		0			0
$499$	−12.0492	−	13.9056i	−0.539398	−	0.622498i	0.418982	−	0.907994i	$-0.362387\pi$
$499$	−12.0492	−	13.9056i	−0.539398	−	0.622498i	−0.958380	+	0.285496i	$0.907842\pi$
$500$		0			0
$501$	3.76334	−	1.10502i	0.168134	−	0.0493685i
$502$		0			0
$503$	1.58403	−	11.0172i	0.0706286	−	0.491232i	−0.923549	−	0.383480i	$-0.874726\pi$
$503$	1.58403	−	11.0172i	0.0706286	−	0.491232i	0.994178	−	0.107752i	$-0.0343654\pi$
$504$		0			0
$505$	6.41119			0.285294
$506$		0			0
$507$	−12.9611			−0.575622
$508$		0			0
$509$	−3.64871	+	25.3773i	−0.161726	+	1.12483i	0.733652	+	0.679525i	$0.237814\pi$
$509$	−3.64871	+	25.3773i	−0.161726	+	1.12483i	−0.895379	+	0.445306i	$0.853095\pi$
$510$		0			0
$511$	−13.3395	+	3.91682i	−0.590104	+	0.173270i
$512$		0			0
$513$	−2.99796	−	3.45983i	−0.132363	−	0.152755i
$514$		0			0
$515$	−6.43885	−	1.89062i	−0.283730	−	0.0833106i
$516$		0			0
$517$	41.5159	+	26.6807i	1.82587	+	1.17341i
$518$		0			0
$519$	0.976495	−	1.12694i	0.0428634	−	0.0494670i
$520$		0			0
$521$	5.15812	+	35.8755i	0.225981	+	1.57174i	0.714787	+	0.699342i	$0.246524\pi$
$521$	5.15812	+	35.8755i	0.225981	+	1.57174i	−0.488805	+	0.872393i	$0.662567\pi$
$522$		0			0
$523$	0.153304	+	0.335688i	0.00670351	+	0.0146786i	0.912954	−	0.408062i	$-0.133795\pi$
$523$	0.153304	+	0.335688i	0.00670351	+	0.0146786i	−0.906251	+	0.422741i	$0.861068\pi$
$524$		0			0
$525$	−3.80797	+	8.33830i	−0.166194	+	0.363913i
$526$		0			0
$527$	−2.05757	+	1.32232i	−0.0896293	+	0.0576012i
$528$		0			0
$529$	10.0223	+	20.7015i	0.435751	+	0.900067i
$530$		0			0
$531$	4.70258	−	3.02217i	0.204075	−	0.131151i
$532$		0			0
$533$	−0.119283	+	0.261193i	−0.00516671	+	0.0113135i
$534$		0			0
$535$	1.75719	+	3.84770i	0.0759697	+	0.166351i
$536$		0			0
$537$	1.90248	+	13.2321i	0.0820983	+	0.571006i
$538$		0			0
$539$	−4.94059	+	5.70175i	−0.212806	+	0.245592i
$540$		0			0
$541$	10.7483	+	6.90753i	0.462107	+	0.296978i	0.750903	−	0.660413i	$-0.229619\pi$
$541$	10.7483	+	6.90753i	0.462107	+	0.296978i	−0.288796	+	0.957391i	$0.593255\pi$
$542$		0			0
$543$	25.1430	+	7.38264i	1.07899	+	0.316820i
$544$		0			0
$545$	−6.29232	−	7.26173i	−0.269534	−	0.311058i
$546$		0			0
$547$	−41.0643	+	12.0576i	−1.75578	+	0.515544i	−0.991587	−	0.129441i	$-0.958682\pi$
$547$	−41.0643	+	12.0576i	−1.75578	+	0.515544i	−0.764195	+	0.644986i	$0.776863\pi$
$548$		0			0
$549$	1.04249	−	7.25071i	0.0444926	−	0.309453i
$550$		0			0
$551$	6.30970			0.268802
$552$		0			0
$553$	0.0685679			0.00291580
$554$		0			0
$555$	0.785022	−	5.45995i	0.0333223	−	0.231762i
$556$		0			0
$557$	14.6198	−	4.29277i	0.619462	−	0.181891i	0.0430813	−	0.999072i	$-0.486283\pi$
$557$	14.6198	−	4.29277i	0.619462	−	0.181891i	0.576381	+	0.817181i	$0.304464\pi$
$558$		0			0
$559$	1.59668	+	1.84267i	0.0675323	+	0.0779365i
$560$		0			0
$561$	−10.4481	−	3.06783i	−0.441117	−	0.129524i
$562$		0			0
$563$	20.3184	+	13.0578i	0.856318	+	0.550322i	0.893539	−	0.448985i	$-0.148214\pi$
$563$	20.3184	+	13.0578i	0.856318	+	0.550322i	−0.0372217	+	0.999307i	$0.511851\pi$
$564$		0			0
$565$	4.04984	−	4.67376i	0.170378	−	0.196627i
$566$		0			0
$567$	−0.318303	−	2.21384i	−0.0133675	−	0.0929727i
$568$		0			0
$569$	−0.186316	−	0.407974i	−0.00781076	−	0.0171032i	0.905686	−	0.423948i	$-0.139356\pi$
$569$	−0.186316	−	0.407974i	−0.00781076	−	0.0171032i	−0.913497	+	0.406845i	$0.866629\pi$
$570$		0			0
$571$	−6.41181	+	14.0399i	−0.268326	+	0.587552i	−0.995050	−	0.0993779i	$-0.968315\pi$
$571$	−6.41181	+	14.0399i	−0.268326	+	0.587552i	0.726724	+	0.686930i	$0.241042\pi$
$572$		0			0
$573$	−1.52193	+	0.978087i	−0.0635796	+	0.0408602i
$574$		0			0
$575$	19.6543	−	0.220865i	0.819642	−	0.00921071i
$576$		0			0
$577$	−16.1566	+	10.3832i	−0.672609	+	0.432260i	−0.831865	−	0.554978i	$-0.812727\pi$
$577$	−16.1566	+	10.3832i	−0.672609	+	0.432260i	0.159256	+	0.987237i	$0.449090\pi$
$578$		0			0
$579$	8.91806	−	19.5278i	0.370622	−	0.811549i
$580$		0			0
$581$	−9.13948	−	20.0127i	−0.379170	−	0.830266i
$582$		0			0
$583$	0.0579066	+	0.402749i	0.00239825	+	0.0166802i
$584$		0			0
$585$	−0.122641	+	0.141535i	−0.00507058	+	0.00585176i
$586$		0			0
$587$	21.5879	+	13.8737i	0.891030	+	0.572630i	0.904117	−	0.427284i	$-0.140530\pi$
$587$	21.5879	+	13.8737i	0.891030	+	0.572630i	−0.0130874	+	0.999914i	$0.504166\pi$
$588$		0			0
$589$	−3.72632	−	1.09415i	−0.153540	−	0.0450835i
$590$		0			0
$591$	3.81799	+	4.40619i	0.157051	+	0.181246i
$592$		0			0
$593$	−34.7357	+	10.1993i	−1.42642	+	0.418835i	−0.901672	−	0.432421i	$-0.857659\pi$
$593$	−34.7357	+	10.1993i	−1.42642	+	0.418835i	−0.524750	+	0.851256i	$0.675841\pi$
$594$		0			0
$595$	0.871361	−	6.06045i	0.0357223	−	0.248454i
$596$		0			0
$597$	10.4148			0.426248
$598$		0			0
$599$	−41.4945			−1.69542			−0.847710	−	0.530460i	$-0.822019\pi$
$599$	−41.4945			−1.69542			−0.847710	+	0.530460i	$0.822019\pi$
$600$		0			0
$601$	0.549829	−	3.82414i	0.0224280	−	0.155990i	−0.975530	−	0.219867i	$-0.929438\pi$
$601$	0.549829	−	3.82414i	0.0224280	−	0.155990i	0.997958	+	0.0638773i	$0.0203466\pi$
$602$		0			0
$603$	5.41752	−	1.59073i	0.220619	−	0.0647795i
$604$		0			0
$605$	−2.02976	−	2.34247i	−0.0825214	−	0.0952348i
$606$		0			0
$607$	31.3526	+	9.20597i	1.27256	+	0.373659i	0.847157	−	0.531343i	$-0.178313\pi$
$607$	31.3526	+	9.20597i	1.27256	+	0.373659i	0.425408	+	0.905002i	$0.360131\pi$
$608$		0			0
$609$	2.59328	+	1.66660i	0.105085	+	0.0675339i
$610$		0			0
$611$	1.68774	−	1.94776i	0.0682787	−	0.0787978i
$612$		0			0
$613$	4.63550	+	32.2406i	0.187226	+	1.30218i	0.839150	+	0.543900i	$0.183053\pi$
$613$	4.63550	+	32.2406i	0.187226	+	1.30218i	−0.651924	+	0.758284i	$0.726038\pi$
$614$		0			0
$615$	−0.574214	−	1.25735i	−0.0231545	−	0.0507013i
$616$		0			0
$617$	−15.3343	+	33.5774i	−0.617335	+	1.35178i	0.300107	+	0.953906i	$0.402978\pi$
$617$	−15.3343	+	33.5774i	−0.617335	+	1.35178i	−0.917442	+	0.397870i	$0.869750\pi$
$618$		0			0
$619$	−27.3857	+	17.5997i	−1.10072	+	0.707393i	−0.959253	−	0.282550i	$-0.908820\pi$
$619$	−27.3857	+	17.5997i	−1.10072	+	0.707393i	−0.141472	+	0.989942i	$0.545183\pi$
$620$		0			0
$621$	−4.00512	+	2.63799i	−0.160720	+	0.105859i
$622$		0			0
$623$	−1.47064	+	0.945125i	−0.0589201	+	0.0378656i
$624$		0			0
$625$	5.10535	−	11.1792i	0.204214	−	0.447166i
$626$		0			0
$627$	−7.18267	−	15.7279i	−0.286848	−	0.628110i
$628$		0			0
$629$	−2.38373	−	16.5792i	−0.0950456	−	0.661057i
$630$		0			0
$631$	10.7823	−	12.4434i	0.429236	−	0.495365i	−0.499392	−	0.866376i	$-0.666443\pi$
$631$	10.7823	−	12.4434i	0.429236	−	0.495365i	0.928629	+	0.371011i	$0.120989\pi$
$632$		0			0
$633$	11.6914	+	7.51362i	0.464693	+	0.298640i
$634$		0			0
$635$	−2.48338	−	0.729185i	−0.0985498	−	0.0289368i
$636$		0			0
$637$	0.258017	+	0.297767i	0.0102230	+	0.0117980i
$638$		0			0
$639$	12.7490	−	3.74345i	0.504343	−	0.148088i
$640$		0			0
$641$	3.64171	−	25.3286i	0.143839	−	1.00042i	−0.782209	−	0.623016i	$-0.785907\pi$
$641$	3.64171	−	25.3286i	0.143839	−	1.00042i	0.926048	−	0.377405i	$-0.123184\pi$
$642$		0			0
$643$	6.87598			0.271162			0.135581	−	0.990766i	$-0.456710\pi$
$643$	6.87598			0.271162			0.135581	+	0.990766i	$0.456710\pi$
$644$		0			0
$645$	−11.7372			−0.462151
$646$		0			0
$647$	4.38755	−	30.5161i	0.172492	−	1.19971i	−0.701104	−	0.713059i	$-0.747309\pi$
$647$	4.38755	−	30.5161i	0.172492	−	1.19971i	0.873596	−	0.486652i	$-0.161782\pi$
$648$		0			0
$649$	20.2571	−	5.94803i	0.795162	−	0.233481i
$650$		0			0
$651$	−1.24251	−	1.43394i	−0.0486979	−	0.0562004i
$652$		0			0
$653$	0.0904584	+	0.0265610i	0.00353991	+	0.00103941i	0.283502	−	0.958972i	$-0.408504\pi$
$653$	0.0904584	+	0.0265610i	0.00353991	+	0.00103941i	−0.279962	+	0.960011i	$0.590322\pi$
$654$		0			0
$655$	−1.78802	−	1.14909i	−0.0698636	−	0.0448986i
$656$		0			0
$657$	−4.07058	+	4.69769i	−0.158808	+	0.183275i
$658$		0			0
$659$	1.98168	+	13.7829i	0.0771952	+	0.536904i	0.991320	+	0.131471i	$0.0419701\pi$
$659$	1.98168	+	13.7829i	0.0771952	+	0.536904i	−0.914125	+	0.405433i	$0.867121\pi$
$660$		0			0
$661$	−4.14914	−	9.08535i	−0.161383	−	0.353379i	0.811615	−	0.584192i	$-0.198589\pi$
$661$	−4.14914	−	9.08535i	−0.161383	−	0.353379i	−0.972998	+	0.230813i	$0.925861\pi$
$662$		0			0
$663$	−0.236235	+	0.517283i	−0.00917461	+	0.0200896i
$664$		0			0
$665$	8.17872	−	5.25614i	0.317157	−	0.203824i
$666$		0			0
$667$	0.867111	−	6.55279i	0.0335747	−	0.253725i
$668$		0			0
$669$	10.8537	−	6.97523i	0.419627	−	0.269678i
$670$		0			0
$671$	11.4930	−	25.1661i	0.443682	−	0.971528i
$672$		0			0
$673$	−5.75470	−	12.6010i	−0.221827	−	0.485734i	0.765697	−	0.643202i	$-0.222394\pi$
$673$	−5.75470	−	12.6010i	−0.221827	−	0.485734i	−0.987524	+	0.157468i	$0.949667\pi$
$674$		0			0
$675$	0.583273	+	4.05675i	0.0224502	+	0.156144i
$676$		0			0
$677$	3.72303	−	4.29661i	0.143088	−	0.165132i	−0.679682	−	0.733507i	$-0.737882\pi$
$677$	3.72303	−	4.29661i	0.143088	−	0.165132i	0.822770	+	0.568375i	$0.192428\pi$
$678$		0			0
$679$	4.83818	+	3.10931i	0.185672	+	0.119324i
$680$		0			0
$681$	17.2141	+	5.05452i	0.659647	+	0.193690i
$682$		0			0
$683$	−16.7624	−	19.3448i	−0.641394	−	0.740208i	0.338227	−	0.941065i	$-0.390173\pi$
$683$	−16.7624	−	19.3448i	−0.641394	−	0.740208i	−0.979621	+	0.200857i	$0.935627\pi$
$684$		0			0
$685$	−2.84604	+	0.835674i	−0.108742	+	0.0319295i
$686$		0			0
$687$	−1.77737	+	12.3619i	−0.0678108	+	0.471634i
$688$		0			0
$689$	0.0212494			0.000809537
$690$		0			0
$691$	−40.7131			−1.54880			−0.774399	−	0.632698i	$-0.781948\pi$
$691$	−40.7131			−1.54880			−0.774399	+	0.632698i	$0.781948\pi$
$692$		0			0
$693$	1.20217	−	8.36130i	0.0456668	−	0.317620i
$694$		0			0
$695$	−9.79762	+	2.87684i	−0.371645	+	0.109125i
$696$		0			0
$697$	−2.74863	−	3.17209i	−0.104112	−	0.120151i
$698$		0			0
$699$	7.12586	+	2.09234i	0.269525	+	0.0791396i
$700$		0			0
$701$	−2.19786	−	1.41248i	−0.0830119	−	0.0533485i	0.498476	−	0.866903i	$-0.333893\pi$
$701$	−2.19786	−	1.41248i	−0.0830119	−	0.0533485i	−0.581488	+	0.813555i	$0.697529\pi$
$702$		0			0
$703$	17.4167	−	20.1000i	0.656884	−	0.758085i
$704$		0			0
$705$	1.76564	+	12.2803i	0.0664979	+	0.462503i
$706$		0			0
$707$	6.27365	+	13.7374i	0.235945	+	0.516647i
$708$		0			0
$709$	0.138623	−	0.303542i	0.00520610	−	0.0113998i	−0.907011	−	0.421107i	$-0.861642\pi$
$709$	0.138623	−	0.303542i	0.00520610	−	0.0113998i	0.912217	+	0.409707i	$0.134369\pi$
$710$		0			0
$711$	0.0257904	−	0.0165745i	0.000967214	−	0.000621591i
$712$		0			0
$713$	−1.64839	+	3.71952i	−0.0617327	+	0.139297i
$714$		0			0
$715$	−0.595032	+	0.382404i	−0.0222529	+	0.0143011i
$716$		0			0
$717$	−7.74144	+	16.9514i	−0.289109	+	0.633061i
$718$		0			0
$719$	−0.553313	−	1.21159i	−0.0206351	−	0.0451846i	0.899034	−	0.437879i	$-0.144270\pi$
$719$	−0.553313	−	1.21159i	−0.0206351	−	0.0451846i	−0.919669	+	0.392695i	$0.871543\pi$
$720$		0			0
$721$	−2.24966	−	15.6467i	−0.0837816	−	0.582714i
$722$		0			0
$723$	5.80586	−	6.70032i	0.215922	−	0.249188i
$724$		0			0
$725$	−4.75204	−	3.05395i	−0.176486	−	0.113421i
$726$		0			0
$727$	−8.06361	−	2.36769i	−0.299063	−	0.0878127i	0.128759	−	0.991676i	$-0.458901\pi$
$727$	−8.06361	−	2.36769i	−0.299063	−	0.0878127i	−0.427822	+	0.903863i	$0.640719\pi$
$728$		0			0
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$		0			0
$731$	−34.1965	+	10.0410i	−1.26480	+	0.371380i
$732$		0			0
$733$	2.91554	−	20.2781i	0.107688	−	0.748987i	−0.862399	−	0.506229i	$-0.831039\pi$
$733$	2.91554	−	20.2781i	0.107688	−	0.748987i	0.970087	−	0.242758i	$-0.0780520\pi$
$734$		0			0
$735$	−1.89668			−0.0699601
$736$		0			0
$737$	21.3248			0.785511
$738$		0			0
$739$	−3.60427	+	25.0683i	−0.132585	+	0.922151i	0.809582	+	0.587007i	$0.199694\pi$
$739$	−3.60427	+	25.0683i	−0.132585	+	0.922151i	−0.942167	+	0.335144i	$0.891215\pi$
$740$		0			0
$741$	−0.866392	+	0.254396i	−0.0318277	+	0.00934546i
$742$		0			0
$743$	−18.3731	−	21.2037i	−0.674043	−	0.777887i	0.310960	−	0.950423i	$-0.399349\pi$
$743$	−18.3731	−	21.2037i	−0.674043	−	0.777887i	−0.985003	+	0.172536i	$0.944804\pi$
$744$		0			0
$745$	−0.828272	−	0.243202i	−0.0303455	−	0.00891025i
$746$		0			0
$747$	−8.27515	−	5.31812i	−0.302772	−	0.194580i
$748$		0			0
$749$	−6.52505	+	7.53031i	−0.238420	+	0.275151i
$750$		0			0
$751$	−7.73725	−	53.8137i	−0.282336	−	1.96369i	−0.266572	−	0.963815i	$-0.585891\pi$
$751$	−7.73725	−	53.8137i	−0.282336	−	1.96369i	−0.0157638	−	0.999876i	$-0.505018\pi$
$752$		0			0
$753$	−10.8405	−	23.7373i	−0.395048	−	0.865035i
$754$		0			0
$755$	2.52138	−	5.52106i	0.0917625	−	0.200932i
$756$		0			0
$757$	35.7864	−	22.9985i	1.30068	−	0.835895i	0.307392	−	0.951583i	$-0.400544\pi$
$757$	35.7864	−	22.9985i	1.30068	−	0.835895i	0.993286	+	0.115688i	$0.0369072\pi$
$758$		0			0
$759$	−17.3209	+	5.29799i	−0.628708	+	0.192305i
$760$		0			0
$761$	−30.7309	+	19.7495i	−1.11399	+	0.715920i	−0.962160	−	0.272486i	$-0.912154\pi$
$761$	−30.7309	+	19.7495i	−1.11399	+	0.715920i	−0.151834	+	0.988406i	$0.548518\pi$
$762$		0			0
$763$	9.40251	−	20.5886i	0.340394	−	0.745358i
$764$		0			0
$765$	−1.13721	−	2.49014i	−0.0411158	−	0.0900311i
$766$		0			0
$767$	−0.156912	−	1.09134i	−0.00566575	−	0.0394062i
$768$		0			0
$769$	28.9659	−	33.4284i	1.04454	−	1.20546i	0.0663369	−	0.997797i	$-0.478869\pi$
$769$	28.9659	−	33.4284i	1.04454	−	1.20546i	0.978200	−	0.207663i	$-0.0665858\pi$
$770$		0			0
$771$	23.2982	+	14.9729i	0.839065	+	0.539235i
$772$		0			0
$773$	−23.1433	−	6.79548i	−0.832406	−	0.244416i	−0.162356	−	0.986732i	$-0.551909\pi$
$773$	−23.1433	−	6.79548i	−0.832406	−	0.244416i	−0.670050	+	0.742316i	$0.733727\pi$
$774$		0			0
$775$	2.27684	+	2.62761i	0.0817864	+	0.0943865i
$776$		0			0
$777$	12.4673	−	3.66073i	0.447262	−	0.131328i
$778$		0			0
$779$	0.948479	−	6.59681i	0.0339828	−	0.236355i
$780$		0			0
$781$	50.1836			1.79571
$782$		0			0
$783$	1.37826			0.0492550
$784$		0			0
$785$	2.08964	−	14.5338i	0.0745826	−	0.518733i
$786$		0			0
$787$	−50.2896	+	14.7664i	−1.79263	+	0.526364i	−0.996856	−	0.0792286i	$-0.974754\pi$
$787$	−50.2896	+	14.7664i	−1.79263	+	0.526364i	−0.795775	+	0.605593i	$0.792936\pi$
$788$		0			0
$789$	−7.44831	−	8.59581i	−0.265167	−	0.306019i
$790$		0			0
$791$	13.9775	+	4.10417i	0.496983	+	0.145927i
$792$		0			0
$793$	−1.21548	−	0.781139i	−0.0431628	−	0.0277390i
$794$		0			0
$795$	−0.0669871	+	0.0773072i	−0.00237579	+	0.00274180i
$796$		0			0
$797$	0.103820	+	0.722087i	0.00367751	+	0.0255776i	0.991578	−	0.129514i	$-0.0413418\pi$
$797$	0.103820	+	0.722087i	0.00367751	+	0.0255776i	−0.987900	+	0.155092i	$0.950433\pi$
$798$		0			0
$799$	15.6498	+	34.2684i	0.553652	+	1.21233i
$800$		0			0
$801$	−0.324693	+	0.710978i	−0.0114725	+	0.0251212i
$802$		0			0
$803$	−19.7497	+	12.6924i	−0.696952	+	0.447904i
$804$		0			0
$805$	−4.33468	−	9.21614i	−0.152777	−	0.324826i
$806$		0			0
$807$	22.3204	−	14.3444i	0.785715	−	0.504948i
$808$		0			0
$809$	−7.39762	+	16.1985i	−0.260087	+	0.569510i	−0.993956	−	0.109781i	$-0.964985\pi$
$809$	−7.39762	+	16.1985i	−0.260087	+	0.569510i	0.733869	+	0.679291i	$0.237712\pi$
$810$		0			0
$811$	1.50702	+	3.29992i	0.0529187	+	0.115876i	0.934244	−	0.356634i	$-0.116076\pi$
$811$	1.50702	+	3.29992i	0.0529187	+	0.115876i	−0.881326	+	0.472509i	$0.843348\pi$
$812$		0			0
$813$	−1.77234	−	12.3269i	−0.0621585	−	0.432322i
$814$		0			0
$815$	−10.1334	+	11.6945i	−0.354956	+	0.409641i
$816$		0			0
$817$	−47.6077	−	30.5956i	−1.66558	−	1.07040i
$818$		0			0
$819$	−0.423280	−	0.124286i	−0.0147906	−	0.00434291i
$820$		0			0
$821$	−2.96774	−	3.42496i	−0.103575	−	0.119532i	0.701595	−	0.712576i	$-0.252472\pi$
$821$	−2.96774	−	3.42496i	−0.103575	−	0.119532i	−0.805170	+	0.593044i	$0.797926\pi$
$822$		0			0
$823$	−4.19701	+	1.23235i	−0.146298	+	0.0429571i	−0.354062	−	0.935222i	$-0.615200\pi$
$823$	−4.19701	+	1.23235i	−0.146298	+	0.0429571i	0.207763	+	0.978179i	$0.433382\pi$
$824$		0			0
$825$	−2.20292	+	15.3216i	−0.0766958	+	0.533431i
$826$		0			0
$827$	−31.3421			−1.08987			−0.544936	−	0.838478i	$-0.683446\pi$
$827$	−31.3421			−1.08987			−0.544936	+	0.838478i	$0.683446\pi$
$828$		0			0
$829$	27.3700			0.950599			0.475299	−	0.879824i	$-0.342340\pi$
$829$	27.3700			0.950599			0.475299	+	0.879824i	$0.342340\pi$
$830$		0			0
$831$	4.20511	−	29.2472i	0.145874	−	1.01457i
$832$		0			0
$833$	−5.52601	+	1.62258i	−0.191465	+	0.0562192i
$834$		0			0
$835$	2.43877	+	2.81450i	0.0843973	+	0.0973996i
$836$		0			0
$837$	−0.813961	−	0.239000i	−0.0281346	−	0.00826106i
$838$		0			0
$839$	10.9321	+	7.02564i	0.377418	+	0.242552i	0.715572	−	0.698539i	$-0.246166\pi$
$839$	10.9321	+	7.02564i	0.377418	+	0.242552i	−0.338154	+	0.941091i	$0.609802\pi$
$840$		0			0
$841$	17.7470	−	20.4811i	0.611965	−	0.706245i
$842$		0			0
$843$	3.26111	+	22.6815i	0.112319	+	0.781193i
$844$		0			0
$845$	−5.11228	−	11.1943i	−0.175868	−	0.385097i
$846$		0			0
$847$	3.03303	−	6.64141i	0.104216	−	0.228202i
$848$		0			0
$849$	20.3371	−	13.0699i	0.697968	−	0.448557i
$850$		0			0
$851$	−18.4809	−	20.8500i	−0.633516	−	0.714728i
$852$		0			0
$853$	−37.3041	+	23.9739i	−1.27727	+	0.820850i	−0.990548	−	0.137164i	$-0.956201\pi$
$853$	−37.3041	+	23.9739i	−1.27727	+	0.820850i	−0.286720	+	0.958014i	$0.592565\pi$
$854$		0			0
$855$	1.80572	−	3.95397i	0.0617543	−	0.135223i
$856$		0			0
$857$	−22.6490	−	49.5943i	−0.773674	−	1.69411i	−0.718392	−	0.695639i	$-0.755121\pi$
$857$	−22.6490	−	49.5943i	−0.773674	−	1.69411i	−0.0552821	−	0.998471i	$-0.517606\pi$
$858$		0			0
$859$	4.15609	+	28.9062i	0.141804	+	0.986268i	0.929136	+	0.369739i	$0.120553\pi$
$859$	4.15609	+	28.9062i	0.141804	+	0.986268i	−0.787332	+	0.616529i	$0.788538\pi$
$860$		0			0
$861$	2.13226	−	2.46076i	0.0726671	−	0.0838623i
$862$		0			0
$863$	28.4386	+	18.2764i	0.968060	+	0.622134i	0.926217	−	0.376990i	$-0.123041\pi$
$863$	28.4386	+	18.2764i	0.968060	+	0.622134i	0.0418425	+	0.999124i	$0.486677\pi$
$864$		0			0
$865$	1.35848	+	0.398886i	0.0461898	+	0.0135625i
$866$		0			0
$867$	5.68908	+	6.56555i	0.193211	+	0.222978i
$868$		0			0
$869$	0.111096	−	0.0326208i	0.00376868	−	0.00110658i
$870$		0			0
$871$	0.158491	−	1.10233i	0.00537026	−	0.0373510i
$872$		0			0
$873$	2.57137			0.0870278
$874$		0			0
$875$	−19.3219			−0.653199
$876$		0			0
$877$	−7.67085	+	53.3519i	−0.259026	+	1.80157i	0.280775	+	0.959774i	$0.409408\pi$
$877$	−7.67085	+	53.3519i	−0.259026	+	1.80157i	−0.539801	+	0.841793i	$0.681501\pi$
$878$		0			0
$879$	31.3392	−	9.20201i	1.05704	−	0.310376i
$880$		0			0
$881$	−10.1317	−	11.6927i	−0.341347	−	0.393936i	0.558957	−	0.829196i	$-0.311202\pi$
$881$	−10.1317	−	11.6927i	−0.341347	−	0.393936i	−0.900304	+	0.435261i	$0.856656\pi$
$882$		0			0
$883$	0.324679	+	0.0953343i	0.0109263	+	0.00320826i	0.287191	−	0.957873i	$-0.407279\pi$
$883$	0.324679	+	0.0953343i	0.0109263	+	0.00320826i	−0.276265	+	0.961082i	$0.589097\pi$
$884$		0			0
$885$	4.46506	+	2.86952i	0.150091	+	0.0964578i
$886$		0			0
$887$	21.9394	−	25.3195i	0.736654	−	0.850145i	−0.256550	−	0.966531i	$-0.582586\pi$
$887$	21.9394	−	25.3195i	0.736654	−	0.850145i	0.993204	+	0.116387i	$0.0371311\pi$
$888$		0			0
$889$	−0.867662	−	6.03472i	−0.0291004	−	0.202398i
$890$		0			0
$891$	−1.56895	−	3.43552i	−0.0525618	−	0.115094i
$892$		0			0
$893$	−24.8497	+	54.4132i	−0.831562	+	1.82087i
$894$		0			0
$895$	−10.6780	+	6.86232i	−0.356925	+	0.229382i
$896$		0			0
$897$	0.145133	+	0.934731i	0.00484583	+	0.0312098i
$898$		0			0
$899$	0.983603	−	0.632124i	0.0328050	−	0.0210825i
$900$		0			0
$901$	−0.129033	+	0.282542i	−0.00429870	+	0.00941285i
$902$		0			0
$903$	−11.4854	−	25.1495i	−0.382210	−	0.836923i
$904$		0			0
$905$	3.54092	+	24.6276i	0.117704	+	0.818650i
$906$		0			0
$907$	10.4812	−	12.0960i	0.348023	−	0.401640i	−0.554568	−	0.832138i	$-0.687117\pi$
$907$	10.4812	−	12.0960i	0.348023	−	0.401640i	0.902592	+	0.430498i	$0.141662\pi$
$908$		0			0
$909$	5.68035	+	3.65054i	0.188405	+	0.121081i
$910$		0			0
$911$	−3.43321	−	1.00808i	−0.113747	−	0.0333992i	0.224364	−	0.974506i	$-0.427970\pi$
$911$	−3.43321	−	1.00808i	−0.113747	−	0.0333992i	−0.338111	+	0.941106i	$0.609788\pi$
$912$		0			0
$913$	−24.3290	−	28.0772i	−0.805174	−	0.929220i
$914$		0			0
$915$	6.67354	−	1.95953i	0.220621	−	0.0647800i
$916$		0			0
$917$	0.712515	−	4.95565i	0.0235293	−	0.163650i
$918$		0			0
$919$	59.1588			1.95147			0.975734	−	0.218960i	$-0.0702664\pi$
$919$	59.1588			1.95147			0.975734	+	0.218960i	$0.0702664\pi$
$920$		0			0
$921$	−32.1377			−1.05897
$922$		0			0
$923$	0.372975	−	2.59410i	0.0122766	−	0.0853859i
$924$		0			0
$925$	−22.8457	+	6.70809i	−0.751161	+	0.220561i
$926$		0			0
$927$	−4.62833	−	5.34138i	−0.152014	−	0.175434i
$928$		0			0
$929$	−32.7118	−	9.60505i	−1.07324	−	0.315131i	−0.303068	−	0.952969i	$-0.598011\pi$
$929$	−32.7118	−	9.60505i	−1.07324	−	0.315131i	−0.770171	+	0.637837i	$0.779829\pi$
$930$		0			0
$931$	−7.69320	−	4.94412i	−0.252135	−	0.162037i
$932$		0			0
$933$	−7.64368	+	8.82128i	−0.250243	+	0.288796i
$934$		0			0
$935$	−1.47141	−	10.2339i	−0.0481204	−	0.334685i
$936$		0			0
$937$	−8.72351	−	19.1018i	−0.284985	−	0.624029i	0.711953	−	0.702227i	$-0.247811\pi$
$937$	−8.72351	−	19.1018i	−0.284985	−	0.624029i	−0.996938	+	0.0781976i	$0.975083\pi$
$938$		0			0
$939$	12.0016	−	26.2799i	0.391658	−	0.857612i
$940$		0			0
$941$	−20.9625	+	13.4718i	−0.683359	+	0.439168i	−0.835719	−	0.549157i	$-0.814949\pi$
$941$	−20.9625	+	13.4718i	−0.683359	+	0.439168i	0.152360	+	0.988325i	$0.451313\pi$
$942$		0			0
$943$	−6.72062	−	1.89159i	−0.218853	−	0.0615985i
$944$		0			0
$945$	1.78652	−	1.14813i	0.0581155	−	0.0373486i
$946$		0			0
$947$	−6.99165	+	15.3096i	−0.227198	+	0.497494i	−0.988559	−	0.150834i	$-0.951804\pi$
$947$	−6.99165	+	15.3096i	−0.227198	+	0.497494i	0.761361	+	0.648328i	$0.224531\pi$
$948$		0			0
$949$	0.509313	+	1.11524i	0.0165330	+	0.0362022i
$950$		0			0
$951$	2.41178	+	16.7743i	0.0782073	+	0.543944i
$952$		0			0
$953$	10.7819	−	12.4430i	0.349260	−	0.403067i	−0.553753	−	0.832681i	$-0.686805\pi$
$953$	10.7819	−	12.4430i	0.349260	−	0.403067i	0.903013	+	0.429614i	$0.141350\pi$
$954$		0			0
$955$	−1.44506	−	0.928685i	−0.0467611	−	0.0300515i
$956$		0			0
$957$	4.99460	+	1.46655i	0.161452	+	0.0474067i
$958$		0			0
$959$	−4.57560	−	5.28053i	−0.147754	−	0.170517i
$960$		0			0
$961$	29.0538	−	8.53096i	0.937219	−	0.275192i
$962$		0			0
$963$	−0.634008	+	4.40962i	−0.0204306	+	0.142098i
$964$		0			0
$965$	20.3835			0.656169
$966$		0			0
$967$	19.7075			0.633750			0.316875	−	0.948467i	$-0.397366\pi$
$967$	19.7075			0.633750			0.316875	+	0.948467i	$0.397366\pi$
$968$		0			0
$969$	1.87843	−	13.0647i	0.0603437	−	0.419700i
$970$		0			0
$971$	−21.2253	+	6.23230i	−0.681151	+	0.200004i	−0.603963	−	0.797012i	$-0.706412\pi$
$971$	−21.2253	+	6.23230i	−0.681151	+	0.200004i	−0.0771884	+	0.997017i	$0.524594\pi$
$972$		0			0
$973$	−15.7517	−	18.1784i	−0.504976	−	0.582773i
$974$		0			0
$975$	0.775637	+	0.227748i	0.0248403	+	0.00729376i
$976$		0			0
$977$	−42.1878	−	27.1124i	−1.34971	−	0.867404i	−0.352060	−	0.935977i	$-0.614519\pi$
$977$	−42.1878	−	27.1124i	−1.34971	−	0.867404i	−0.997646	+	0.0685737i	$0.978155\pi$
$978$		0			0
$979$	−1.93315	+	2.23098i	−0.0617838	+	0.0713023i
$980$		0			0
$981$	−1.44020	−	10.0168i	−0.0459819	−	0.319811i
$982$		0			0
$983$	7.57118	+	16.5786i	0.241483	+	0.528774i	0.991103	−	0.133094i	$-0.0424912\pi$
$983$	7.57118	+	16.5786i	0.241483	+	0.528774i	−0.749620	+	0.661868i	$0.769764\pi$
$984$		0			0
$985$	−2.29963	+	5.03549i	−0.0732724	+	0.160444i
$986$		0			0
$987$	−24.5855	+	15.8001i	−0.782564	+	0.502923i
$988$		0			0
$989$	−38.3168	+	45.2372i	−1.21840	+	1.43846i
$990$		0			0
$991$	−4.39499	+	2.82449i	−0.139612	+	0.0897229i	−0.608582	−	0.793491i	$-0.708261\pi$
$991$	−4.39499	+	2.82449i	−0.139612	+	0.0897229i	0.468971	+	0.883214i	$0.344625\pi$
$992$		0			0
$993$	−0.594143	+	1.30099i	−0.0188546	+	0.0412857i
$994$		0			0
$995$	4.10792	+	8.99510i	0.130230	+	0.285164i
$996$		0			0
$997$	−5.14370	−	35.7752i	−0.162903	−	1.13301i	−0.893127	−	0.449805i	$-0.851494\pi$
$997$	−5.14370	−	35.7752i	−0.162903	−	1.13301i	0.730225	−	0.683207i	$-0.239415\pi$
$998$		0			0
$999$	3.80443	−	4.39055i	0.120367	−	0.138911i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.b.265.1	yes	30
23.2	even	11	inner	552.2.q.b.25.1	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.b.25.1	✓	30	23.2	even	11	inner
552.2.q.b.265.1	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)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{3} +(-0.911030 + 0.267503i) q^{5} +(-1.46467 - 1.69032i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{3} +(-0.911030 + 0.267503i) q^{5} +(-1.46467 - 1.69032i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(-3.17727 - 2.04191i) q^{11} +(-0.129165 + 0.149064i) q^{13} +(-0.135127 - 0.939827i) q^{15} +(-1.19770 - 2.62260i) q^{17} +(1.90178 - 4.16431i) q^{19} +(1.88156 - 1.20920i) q^{21} +(-4.06339 - 2.54732i) q^{23} +(-3.44785 + 2.21580i) q^{25} +(0.415415 - 0.909632i) q^{27} +(0.572550 + 1.25371i) q^{29} +(-0.120729 - 0.839689i) q^{31} +(2.47329 - 2.85433i) q^{33} +(1.78652 + 1.14813i) q^{35} +(5.57420 + 1.63673i) q^{37} +(-0.129165 - 0.149064i) q^{39} +(1.39683 - 0.410145i) q^{41} +(1.75923 - 12.2357i) q^{43} +0.949491 q^{45} -13.0666 q^{47} +(0.284285 - 1.97724i) q^{49} +(2.76636 - 0.812276i) q^{51} +(-0.0705505 - 0.0814196i) q^{53} +(3.44080 + 1.01031i) q^{55} +(3.85127 + 2.47506i) q^{57} +(-3.66065 + 4.22462i) q^{59} +(1.04249 + 7.25071i) q^{61} +(0.929121 + 2.03449i) q^{63} +(0.0777980 - 0.170354i) q^{65} +(-4.74992 + 3.05259i) q^{67} +(3.09968 - 3.65951i) q^{69} +(-11.1779 + 7.18362i) q^{71} +(2.58219 - 5.65422i) q^{73} +(-1.70256 - 3.72810i) q^{75} +(1.20217 + 8.36130i) q^{77} +(-0.0200761 + 0.0231691i) q^{79} +(0.841254 + 0.540641i) q^{81} +(9.43824 + 2.77132i) q^{83} +(1.79270 + 2.06888i) q^{85} +(-1.32243 + 0.388301i) q^{87} +(0.111235 - 0.773655i) q^{89} +0.441150 q^{91} +0.848324 q^{93} +(-0.618612 + 4.30254i) q^{95} +(-2.46721 + 0.724439i) q^{97} +(2.47329 + 2.85433i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} - 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 - 3 * q^9	\( 30 q - 3 q^{3} - 3 q^{9} + 9 q^{11} + 13 q^{13} + 17 q^{17} - 9 q^{19} - 11 q^{21} - 12 q^{23} - 23 q^{25} - 3 q^{27} - q^{29} - 37 q^{31} + 9 q^{33} + 10 q^{35} + 7 q^{37} + 13 q^{39} + 16 q^{41} + 20 q^{43} - 22 q^{45} + 22 q^{47} + 19 q^{49} + 17 q^{51} + 25 q^{53} + 10 q^{55} + 24 q^{57} + 7 q^{59} + 8 q^{61} - 28 q^{65} - 23 q^{67} - q^{69} + 5 q^{71} + 34 q^{73} - 23 q^{75} + 62 q^{77} + 20 q^{79} - 3 q^{81} + 29 q^{83} - 46 q^{85} + 10 q^{87} - 67 q^{89} - 118 q^{91} - 26 q^{93} - 99 q^{95} - 41 q^{97} + 9 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 - 3 * q^9 + 9 * q^11 + 13 * q^13 + 17 * q^17 - 9 * q^19 - 11 * q^21 - 12 * q^23 - 23 * q^25 - 3 * q^27 - q^29 - 37 * q^31 + 9 * q^33 + 10 * q^35 + 7 * q^37 + 13 * q^39 + 16 * q^41 + 20 * q^43 - 22 * q^45 + 22 * q^47 + 19 * q^49 + 17 * q^51 + 25 * q^53 + 10 * q^55 + 24 * q^57 + 7 * q^59 + 8 * q^61 - 28 * q^65 - 23 * q^67 - q^69 + 5 * q^71 + 34 * q^73 - 23 * q^75 + 62 * q^77 + 20 * q^79 - 3 * q^81 + 29 * q^83 - 46 * q^85 + 10 * q^87 - 67 * q^89 - 118 * q^91 - 26 * q^93 - 99 * q^95 - 41 * q^97 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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