LMFDB - Embedded newform 552.2.q.c.121.2

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			121.2
Character	$\chi$	$=$	552.121
Dual form			552.2.q.c.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 + 0.281733i) q^{3} +(-0.873450 + 0.561333i) q^{5} +(-0.322387 + 2.24225i) q^{7} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(0.959493 + 0.281733i) q^{3} +(-0.873450 + 0.561333i) q^{5} +(-0.322387 + 2.24225i) q^{7} +(0.841254 + 0.540641i) q^{9} +(-0.262635 - 0.575091i) q^{11} +(0.714374 + 4.96858i) q^{13} +(-0.996215 + 0.292515i) q^{15} +(0.0738723 - 0.0852532i) q^{17} +(-0.158083 - 0.182437i) q^{19} +(-0.941043 + 2.06060i) q^{21} +(1.69447 + 4.48651i) q^{23} +(-1.62925 + 3.56757i) q^{25} +(0.654861 + 0.755750i) q^{27} +(2.16270 - 2.49589i) q^{29} +(-2.03964 + 0.598893i) q^{31} +(-0.0899748 - 0.625788i) q^{33} +(-0.977059 - 2.13946i) q^{35} +(6.03509 + 3.87852i) q^{37} +(-0.714374 + 4.96858i) q^{39} +(7.75891 - 4.98635i) q^{41} +(-10.5247 - 3.09034i) q^{43} -1.03827 q^{45} -1.92999 q^{47} +(1.79270 + 0.526384i) q^{49} +(0.0948986 - 0.0609876i) q^{51} +(0.0970469 - 0.674976i) q^{53} +(0.552216 + 0.354888i) q^{55} +(-0.100281 - 0.219584i) q^{57} +(-1.10781 - 7.70497i) q^{59} +(5.42674 - 1.59344i) q^{61} +(-1.48346 + 1.71200i) q^{63} +(-3.41299 - 3.93881i) q^{65} +(0.326061 - 0.713975i) q^{67} +(0.361840 + 4.78216i) q^{69} +(2.29812 - 5.03218i) q^{71} +(6.60054 + 7.61743i) q^{73} +(-2.56836 + 2.96404i) q^{75} +(1.37417 - 0.403492i) q^{77} +(-0.352464 - 2.45144i) q^{79} +(0.415415 + 0.909632i) q^{81} +(-8.31306 - 5.34248i) q^{83} +(-0.0166684 + 0.115931i) q^{85} +(2.77827 - 1.78549i) q^{87} +(-9.87134 - 2.89849i) q^{89} -11.3711 q^{91} -2.12575 q^{93} +(0.240485 + 0.0706129i) q^{95} +(-2.68434 + 1.72512i) q^{97} +(0.0899748 - 0.625788i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−0.873450	+	0.561333i	−0.390619	+	0.251036i	−0.721178	−	0.692750i	$-0.756399\pi$
$5$	−0.873450	+	0.561333i	−0.390619	+	0.251036i	0.330559	+	0.943785i	$0.392763\pi$
$6$		0			0
$7$	−0.322387	+	2.24225i	−0.121851	+	0.847491i	0.833606	+	0.552360i	$0.186272\pi$
$7$	−0.322387	+	2.24225i	−0.121851	+	0.847491i	−0.955457	+	0.295131i	$0.904637\pi$
$8$		0			0
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$		0			0
$11$	−0.262635	−	0.575091i	−0.0791875	−	0.173396i	0.865897	−	0.500222i	$-0.166748\pi$
$11$	−0.262635	−	0.575091i	−0.0791875	−	0.173396i	−0.945085	+	0.326826i	$0.894021\pi$
$12$		0			0
$13$	0.714374	+	4.96858i	0.198132	+	1.37804i	0.809700	+	0.586844i	$0.199630\pi$
$13$	0.714374	+	4.96858i	0.198132	+	1.37804i	−0.611568	+	0.791192i	$0.709461\pi$
$14$		0			0
$15$	−0.996215	+	0.292515i	−0.257222	+	0.0755271i
$16$		0			0
$17$	0.0738723	−	0.0852532i	0.0179167	−	0.0206769i	−0.746721	−	0.665138i	$-0.768373\pi$
$17$	0.0738723	−	0.0852532i	0.0179167	−	0.0206769i	0.764637	+	0.644461i	$0.222918\pi$
$18$		0			0
$19$	−0.158083	−	0.182437i	−0.0362667	−	0.0418540i	0.737326	−	0.675537i	$-0.236088\pi$
$19$	−0.158083	−	0.182437i	−0.0362667	−	0.0418540i	−0.773593	+	0.633683i	$0.781543\pi$
$20$		0			0
$21$	−0.941043	+	2.06060i	−0.205352	+	0.449659i
$22$		0			0
$23$	1.69447	+	4.48651i	0.353322	+	0.935502i
$23$	1.69447	+	4.48651i	0.353322	+	0.935502i
$24$		0			0
$25$	−1.62925	+	3.56757i	−0.325851	+	0.713514i
$26$		0			0
$27$	0.654861	+	0.755750i	0.126028	+	0.145444i
$28$		0			0
$29$	2.16270	−	2.49589i	0.401603	−	0.463475i	−0.518542	−	0.855052i	$-0.673525\pi$
$29$	2.16270	−	2.49589i	0.401603	−	0.463475i	0.920145	+	0.391577i	$0.128070\pi$
$30$		0			0
$31$	−2.03964	+	0.598893i	−0.366331	+	0.107564i	−0.459717	−	0.888066i	$-0.652049\pi$
$31$	−2.03964	+	0.598893i	−0.366331	+	0.107564i	0.0933861	+	0.995630i	$0.470231\pi$
$32$		0			0
$33$	−0.0899748	−	0.625788i	−0.0156626	−	0.108936i
$34$		0			0
$35$	−0.977059	−	2.13946i	−0.165153	−	0.361635i
$36$		0			0
$37$	6.03509	+	3.87852i	0.992162	+	0.637624i	0.932718	−	0.360607i	$-0.117431\pi$
$37$	6.03509	+	3.87852i	0.992162	+	0.637624i	0.0594448	+	0.998232i	$0.481067\pi$
$38$		0			0
$39$	−0.714374	+	4.96858i	−0.114391	+	0.795609i
$40$		0			0
$41$	7.75891	−	4.98635i	1.21174	−	0.778737i	0.230789	−	0.973004i	$-0.425869\pi$
$41$	7.75891	−	4.98635i	1.21174	−	0.778737i	0.980949	+	0.194267i	$0.0622328\pi$
$42$		0			0
$43$	−10.5247	−	3.09034i	−1.60501	−	0.471272i	−0.648072	−	0.761579i	$-0.724424\pi$
$43$	−10.5247	−	3.09034i	−1.60501	−	0.471272i	−0.956934	+	0.290307i	$0.906243\pi$
$44$		0			0
$45$	−1.03827			−0.154777
$46$		0			0
$47$	−1.92999			−0.281518			−0.140759	−	0.990044i	$-0.544954\pi$
$47$	−1.92999			−0.281518			−0.140759	+	0.990044i	$0.544954\pi$
$48$		0			0
$49$	1.79270	+	0.526384i	0.256100	+	0.0751978i
$50$		0			0
$51$	0.0948986	−	0.0609876i	0.0132885	−	0.00853998i
$52$		0			0
$53$	0.0970469	−	0.674976i	0.0133304	−	0.0927151i	−0.982070	−	0.188516i	$-0.939632\pi$
$53$	0.0970469	−	0.674976i	0.0133304	−	0.0927151i	0.995400	+	0.0958011i	$0.0305413\pi$
$54$		0			0
$55$	0.552216	+	0.354888i	0.0744608	+	0.0478530i
$56$		0			0
$57$	−0.100281	−	0.219584i	−0.0132825	−	0.0290846i
$58$		0			0
$59$	−1.10781	−	7.70497i	−0.144224	−	1.00310i	−0.925455	−	0.378859i	$-0.876317\pi$
$59$	−1.10781	−	7.70497i	−0.144224	−	1.00310i	0.781230	−	0.624243i	$-0.214592\pi$
$60$		0			0
$61$	5.42674	−	1.59344i	0.694823	−	0.204019i	0.0847953	−	0.996398i	$-0.472976\pi$
$61$	5.42674	−	1.59344i	0.694823	−	0.204019i	0.610028	+	0.792380i	$0.291158\pi$
$62$		0			0
$63$	−1.48346	+	1.71200i	−0.186898	+	0.215692i
$64$		0			0
$65$	−3.41299	−	3.93881i	−0.423330	−	0.488549i
$66$		0			0
$67$	0.326061	−	0.713975i	0.0398347	−	0.0872259i	−0.888669	−	0.458550i	$-0.848369\pi$
$67$	0.326061	−	0.713975i	0.0398347	−	0.0872259i	0.928503	+	0.371324i	$0.121096\pi$
$68$		0			0
$69$	0.361840	+	4.78216i	0.0435605	+	0.575705i
$70$		0			0
$71$	2.29812	−	5.03218i	0.272737	−	0.597210i	−0.722855	−	0.691000i	$-0.757171\pi$
$71$	2.29812	−	5.03218i	0.272737	−	0.597210i	0.995592	+	0.0937891i	$0.0298979\pi$
$72$		0			0
$73$	6.60054	+	7.61743i	0.772535	+	0.891553i	0.996547	−	0.0830335i	$-0.0264608\pi$
$73$	6.60054	+	7.61743i	0.772535	+	0.891553i	−0.224012	+	0.974586i	$0.571915\pi$
$74$		0			0
$75$	−2.56836	+	2.96404i	−0.296568	+	0.342258i
$76$		0			0
$77$	1.37417	−	0.403492i	0.156601	−	0.0459822i
$78$		0			0
$79$	−0.352464	−	2.45144i	−0.0396553	−	0.275809i	0.960340	−	0.278831i	$-0.0899470\pi$
$79$	−0.352464	−	2.45144i	−0.0396553	−	0.275809i	−0.999995	+	0.00302249i	$0.999038\pi$
$80$		0			0
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$		0			0
$83$	−8.31306	−	5.34248i	−0.912477	−	0.586413i	−0.00201097	−	0.999998i	$-0.500640\pi$
$83$	−8.31306	−	5.34248i	−0.912477	−	0.586413i	−0.910466	+	0.413585i	$0.864276\pi$
$84$		0			0
$85$	−0.0166684	+	0.115931i	−0.00180794	+	0.0125745i
$86$		0			0
$87$	2.77827	−	1.78549i	0.297862	−	0.191424i
$88$		0			0
$89$	−9.87134	−	2.89849i	−1.04636	−	0.307239i	−0.287014	−	0.957926i	$-0.592663\pi$
$89$	−9.87134	−	2.89849i	−1.04636	−	0.307239i	−0.759346	+	0.650688i	$0.774481\pi$
$90$		0			0
$91$	−11.3711			−1.19201
$92$		0			0
$93$	−2.12575			−0.220430
$94$		0			0
$95$	0.240485	+	0.0706129i	0.0246733	+	0.00724473i
$96$		0			0
$97$	−2.68434	+	1.72512i	−0.272554	+	0.175160i	−0.669777	−	0.742562i	$-0.733610\pi$
$97$	−2.68434	+	1.72512i	−0.272554	+	0.175160i	0.397223	+	0.917722i	$0.369974\pi$
$98$		0			0
$99$	0.0899748	−	0.625788i	0.00904280	−	0.0628941i
$100$		0			0
$101$	5.94538	+	3.82087i	0.591588	+	0.380190i	0.801913	−	0.597441i	$-0.203816\pi$
$101$	5.94538	+	3.82087i	0.591588	+	0.380190i	−0.210325	+	0.977632i	$0.567452\pi$
$102$		0			0
$103$	0.822788	+	1.80165i	0.0810717	+	0.177522i	0.945827	−	0.324671i	$-0.105254\pi$
$103$	0.822788	+	1.80165i	0.0810717	+	0.177522i	−0.864755	+	0.502194i	$0.832526\pi$
$104$		0			0
$105$	−0.334725	−	2.32807i	−0.0326659	−	0.227196i
$106$		0			0
$107$	10.9873	−	3.22616i	1.06218	−	0.311885i	0.296453	−	0.955048i	$-0.404196\pi$
$107$	10.9873	−	3.22616i	1.06218	−	0.311885i	0.765730	+	0.643163i	$0.222378\pi$
$108$		0			0
$109$	7.88296	−	9.09743i	0.755051	−	0.871375i	−0.239997	−	0.970774i	$-0.577146\pi$
$109$	7.88296	−	9.09743i	0.755051	−	0.871375i	0.995048	+	0.0993984i	$0.0316918\pi$
$110$		0			0
$111$	4.69792	+	5.42169i	0.445907	+	0.514604i
$112$		0			0
$113$	2.11910	−	4.64018i	0.199348	−	0.436511i	−0.783386	−	0.621536i	$-0.786509\pi$
$113$	2.11910	−	4.64018i	0.199348	−	0.436511i	0.982734	+	0.185024i	$0.0592364\pi$
$114$		0			0
$115$	−3.99846	−	2.96758i	−0.372859	−	0.276728i
$116$		0			0
$117$	−2.08525	+	4.56605i	−0.192781	+	0.422132i
$118$		0			0
$119$	0.167344	+	0.193125i	0.0153404	+	0.0177037i
$120$		0			0
$121$	6.94172	−	8.01117i	0.631065	−	0.728288i
$122$		0			0
$123$	8.84944	−	2.59843i	0.797927	−	0.234292i
$124$		0			0
$125$	−1.31833	−	9.16917i	−0.117915	−	0.820115i
$126$		0			0
$127$	−0.309806	−	0.678379i	−0.0274908	−	0.0601964i	0.895389	−	0.445286i	$-0.146898\pi$
$127$	−0.309806	−	0.678379i	−0.0274908	−	0.0601964i	−0.922879	+	0.385089i	$0.874171\pi$
$128$		0			0
$129$	−9.22775	−	5.93032i	−0.812458	−	0.522135i
$130$		0			0
$131$	1.03753	−	7.21618i	0.0906495	−	0.630481i	−0.892956	−	0.450145i	$-0.851372\pi$
$131$	1.03753	−	7.21618i	0.0906495	−	0.630481i	0.983605	−	0.180336i	$-0.0577185\pi$
$132$		0			0
$133$	0.460034	−	0.295646i	0.0398900	−	0.0256357i
$134$		0			0
$135$	−0.996215	−	0.292515i	−0.0857406	−	0.0251757i
$136$		0			0
$137$	−0.452146			−0.0386294			−0.0193147	−	0.999813i	$-0.506148\pi$
$137$	−0.452146			−0.0386294			−0.0193147	+	0.999813i	$0.506148\pi$
$138$		0			0
$139$	−10.6762			−0.905545			−0.452772	−	0.891626i	$-0.649565\pi$
$139$	−10.6762			−0.905545			−0.452772	+	0.891626i	$0.649565\pi$
$140$		0			0
$141$	−1.85181	−	0.543742i	−0.155951	−	0.0457913i
$142$		0			0
$143$	2.66976	−	1.71575i	0.223257	−	0.143478i
$144$		0			0
$145$	−0.487988	+	3.39403i	−0.0405252	+	0.281859i
$146$		0			0
$147$	1.57178	+	1.01012i	0.129639	+	0.0833137i
$148$		0			0
$149$	−9.02309	−	19.7578i	−0.739200	−	1.61862i	−0.784865	−	0.619666i	$-0.787268\pi$
$149$	−9.02309	−	19.7578i	−0.739200	−	1.61862i	0.0456650	−	0.998957i	$-0.485459\pi$
$150$		0			0
$151$	2.77899	+	19.3283i	0.226151	+	1.57292i	0.714099	+	0.700044i	$0.246836\pi$
$151$	2.77899	+	19.3283i	0.226151	+	1.57292i	−0.487948	+	0.872873i	$0.662254\pi$
$152$		0			0
$153$	0.108237	−	0.0317812i	0.00875042	−	0.00256936i
$154$		0			0
$155$	1.44535	−	1.66802i	0.116093	−	0.133979i
$156$		0			0
$157$	−6.25867	−	7.22289i	−0.499496	−	0.576450i	0.448882	−	0.893591i	$-0.351822\pi$
$157$	−6.25867	−	7.22289i	−0.499496	−	0.576450i	−0.948378	+	0.317142i	$0.897277\pi$
$158$		0			0
$159$	0.283279	−	0.620294i	0.0224655	−	0.0491925i
$160$		0			0
$161$	−10.6061	+	2.35304i	−0.835882	+	0.185446i
$162$		0			0
$163$	10.0327	−	21.9684i	0.785818	−	1.72070i	0.0975667	−	0.995229i	$-0.468894\pi$
$163$	10.0327	−	21.9684i	0.785818	−	1.72070i	0.688251	−	0.725472i	$-0.258379\pi$
$164$		0			0
$165$	0.429864	+	0.496089i	0.0334648	+	0.0386205i
$166$		0			0
$167$	−6.30456	+	7.27586i	−0.487862	+	0.563023i	−0.945293	−	0.326222i	$-0.894224\pi$
$167$	−6.30456	+	7.27586i	−0.487862	+	0.563023i	0.457431	+	0.889245i	$0.348770\pi$
$168$		0			0
$169$	−11.7030	+	3.43632i	−0.900233	+	0.264332i
$170$		0			0
$171$	−0.0343547	−	0.238942i	−0.00262717	−	0.0182723i
$172$		0			0
$173$	0.158530	+	0.347133i	0.0120528	+	0.0263920i	0.915563	−	0.402175i	$-0.131746\pi$
$173$	0.158530	+	0.347133i	0.0120528	+	0.0263920i	−0.903510	+	0.428567i	$0.859018\pi$
$174$		0			0
$175$	−7.47413	−	4.80333i	−0.564991	−	0.363098i
$176$		0			0
$177$	1.10781	−	7.70497i	0.0832679	−	0.579141i
$178$		0			0
$179$	5.34707	−	3.43635i	0.399659	−	0.256845i	−0.325338	−	0.945598i	$-0.605478\pi$
$179$	5.34707	−	3.43635i	0.399659	−	0.256845i	0.724996	+	0.688753i	$0.241842\pi$
$180$		0			0
$181$	0.00184102		0.000540571i	0.000136842		4.01803e-5i	0.281801	−	0.959473i	$-0.409068\pi$
$181$	0.00184102		0.000540571i	0.000136842		4.01803e-5i	−0.281664	+	0.959513i	$0.590886\pi$
$182$		0			0
$183$	5.65584			0.418092
$184$		0			0
$185$	−7.44849			−0.547624
$186$		0			0
$187$	−0.0684298	−	0.0200928i	−0.00500408	−	0.00146933i
$188$		0			0
$189$	−1.90570	+	1.22472i	−0.138619	+	0.0890851i
$190$		0			0
$191$	0.330968	−	2.30193i	0.0239480	−	0.166562i	−0.974338	−	0.225091i	$-0.927732\pi$
$191$	0.330968	−	2.30193i	0.0239480	−	0.166562i	0.998286	+	0.0585293i	$0.0186411\pi$
$192$		0			0
$193$	9.95148	+	6.39542i	0.716323	+	0.460353i	0.847356	−	0.531025i	$-0.178193\pi$
$193$	9.95148	+	6.39542i	0.716323	+	0.460353i	−0.131033	+	0.991378i	$0.541829\pi$
$194$		0			0
$195$	−2.16505	−	4.74081i	−0.155043	−	0.339496i
$196$		0			0
$197$	2.78628	+	19.3790i	0.198514	+	1.38070i	0.808599	+	0.588360i	$0.200226\pi$
$197$	2.78628	+	19.3790i	0.198514	+	1.38070i	−0.610085	+	0.792336i	$0.708865\pi$
$198$		0			0
$199$	10.8671	−	3.19087i	0.770349	−	0.226195i	0.127139	−	0.991885i	$-0.459421\pi$
$199$	10.8671	−	3.19087i	0.770349	−	0.226195i	0.643210	+	0.765690i	$0.277602\pi$
$200$		0			0
$201$	0.514003	−	0.593192i	0.0362550	−	0.0418405i
$202$		0			0
$203$	4.89918	+	5.65396i	0.343855	+	0.396830i
$204$		0			0
$205$	−3.97802	+	8.71066i	−0.277837	+	0.608379i
$206$		0			0
$207$	−1.00011	+	4.69039i	−0.0695123	+	0.326005i
$208$		0			0
$209$	−0.0633999	+	0.138826i	−0.00438546	+	0.00960282i
$210$		0			0
$211$	2.47744	+	2.85912i	0.170554	+	0.196830i	0.834591	−	0.550870i	$-0.185704\pi$
$211$	2.47744	+	2.85912i	0.170554	+	0.196830i	−0.664037	+	0.747699i	$0.731158\pi$
$212$		0			0
$213$	3.62276	−	4.18089i	0.248228	−	0.286470i
$214$		0			0
$215$	10.9275	−	3.20861i	0.745252	−	0.218826i
$216$		0			0
$217$	−0.685314	−	4.76646i	−0.0465221	−	0.323569i
$218$		0			0
$219$	4.18710	+	9.16846i	0.282938	+	0.619547i
$220$		0			0
$221$	0.476360	+	0.306138i	0.0320434	+	0.0205931i
$222$		0			0
$223$	0.469217	−	3.26347i	0.0314211	−	0.218538i	−0.968061	−	0.250714i	$-0.919335\pi$
$223$	0.469217	−	3.26347i	0.0314211	−	0.218538i	0.999482	+	0.0321758i	$0.0102436\pi$
$224$		0			0
$225$	−3.29939	+	2.12039i	−0.219959	+	0.141359i
$226$		0			0
$227$	0.771412	+	0.226507i	0.0512004	+	0.0150338i	0.307232	−	0.951634i	$-0.400597\pi$
$227$	0.771412	+	0.226507i	0.0512004	+	0.0150338i	−0.256032	+	0.966668i	$0.582415\pi$
$228$		0			0
$229$	−19.0074			−1.25605			−0.628023	−	0.778195i	$-0.716136\pi$
$229$	−19.0074			−1.25605			−0.628023	+	0.778195i	$0.716136\pi$
$230$		0			0
$231$	1.43218			0.0942305
$232$		0			0
$233$	−11.5454	−	3.39005i	−0.756367	−	0.222089i	−0.119258	−	0.992863i	$-0.538052\pi$
$233$	−11.5454	−	3.39005i	−0.756367	−	0.222089i	−0.637109	+	0.770774i	$0.719870\pi$
$234$		0			0
$235$	1.68575	−	1.08337i	0.109966	−	0.0706711i
$236$		0			0
$237$	0.352464	−	2.45144i	0.0228950	−	0.159238i
$238$		0			0
$239$	22.5755	+	14.5084i	1.46029	+	0.938470i	0.998679	+	0.0513870i	$0.0163642\pi$
$239$	22.5755	+	14.5084i	1.46029	+	0.938470i	0.461609	+	0.887083i	$0.347272\pi$
$240$		0			0
$241$	12.6178	+	27.6290i	0.812781	+	1.77974i	0.594964	+	0.803753i	$0.297166\pi$
$241$	12.6178	+	27.6290i	0.812781	+	1.77974i	0.217817	+	0.975990i	$0.430106\pi$
$242$		0			0
$243$	0.142315	+	0.989821i	0.00912950	+	0.0634971i
$244$		0			0
$245$	−1.86131	+	0.546531i	−0.118915	+	0.0349166i
$246$		0			0
$247$	0.793523	−	0.915775i	0.0504907	−	0.0582694i
$248$		0			0
$249$	−6.47117	−	7.46813i	−0.410094	−	0.473273i
$250$		0			0
$251$	−5.23194	+	11.4563i	−0.330237	+	0.723118i	−0.999807	−	0.0196306i	$-0.993751\pi$
$251$	−5.23194	+	11.4563i	−0.330237	+	0.723118i	0.669570	+	0.742749i	$0.266478\pi$
$252$		0			0
$253$	2.13512	−	2.15279i	0.134234	−	0.135345i
$254$		0			0
$255$	−0.0486549	+	0.106539i	−0.00304689	+	0.00667175i
$256$		0			0
$257$	11.0812	+	12.7884i	0.691226	+	0.797717i	0.987539	−	0.157374i	$-0.0503027\pi$
$257$	11.0812	+	12.7884i	0.691226	+	0.797717i	−0.296313	+	0.955091i	$0.595757\pi$
$258$		0			0
$259$	−10.6422	+	12.2818i	−0.661276	+	0.763153i
$260$		0			0
$261$	3.16876	−	0.930432i	0.196141	−	0.0575923i
$262$		0			0
$263$	3.71376	+	25.8297i	0.229000	+	1.59273i	0.702335	+	0.711847i	$0.252141\pi$
$263$	3.71376	+	25.8297i	0.229000	+	1.59273i	−0.473335	+	0.880883i	$0.656950\pi$
$264$		0			0
$265$	0.294120	+	0.644034i	0.0180677	+	0.0395627i
$266$		0			0
$267$	−8.65488	−	5.56215i	−0.529670	−	0.340398i
$268$		0			0
$269$	−1.89158	+	13.1562i	−0.115331	+	0.802148i	0.847258	+	0.531182i	$0.178252\pi$
$269$	−1.89158	+	13.1562i	−0.115331	+	0.802148i	−0.962589	+	0.270966i	$0.912657\pi$
$270$		0			0
$271$	10.9491	−	7.03658i	0.665113	−	0.427442i	−0.164048	−	0.986452i	$-0.552455\pi$
$271$	10.9491	−	7.03658i	0.665113	−	0.427442i	0.829161	+	0.559010i	$0.188819\pi$
$272$		0			0
$273$	−10.9105	−	3.20361i	−0.660333	−	0.193891i
$274$		0			0
$275$	2.47957			0.149524
$276$		0			0
$277$	−16.9944			−1.02109			−0.510546	−	0.859850i	$-0.670557\pi$
$277$	−16.9944			−1.02109			−0.510546	+	0.859850i	$0.670557\pi$
$278$		0			0
$279$	−2.03964	−	0.598893i	−0.122110	−	0.0358548i
$280$		0			0
$281$	12.5836	−	8.08697i	0.750673	−	0.482428i	−0.108511	−	0.994095i	$-0.534608\pi$
$281$	12.5836	−	8.08697i	0.750673	−	0.482428i	0.859184	+	0.511667i	$0.170972\pi$
$282$		0			0
$283$	2.45815	−	17.0968i	0.146122	−	1.01630i	−0.776369	−	0.630279i	$-0.782941\pi$
$283$	2.45815	−	17.0968i	0.146122	−	1.01630i	0.922491	−	0.386020i	$-0.126150\pi$
$284$		0			0
$285$	0.210850	+	0.135505i	0.0124897	+	0.00802663i
$286$		0			0
$287$	8.67927	+	19.0049i	0.512321	+	1.12183i
$288$		0			0
$289$	2.41754	+	16.8144i	0.142208	+	0.989081i
$290$		0			0
$291$	−3.06163	+	0.898977i	−0.179476	+	0.0526989i
$292$		0			0
$293$	−14.3689	+	16.5826i	−0.839442	+	0.968767i	−0.999833	−	0.0182862i	$-0.994179\pi$
$293$	−14.3689	+	16.5826i	−0.839442	+	0.968767i	0.160391	+	0.987054i	$0.448724\pi$
$294$		0			0
$295$	5.29266	+	6.10806i	0.308151	+	0.355625i
$296$		0			0
$297$	0.262635	−	0.575091i	0.0152396	−	0.0333701i
$298$		0			0
$299$	−21.0811	+	11.6242i	−1.21915	+	0.672243i
$300$		0			0
$301$	10.3223	−	22.6028i	0.594970	−	1.30280i
$302$		0			0
$303$	4.62809	+	5.34110i	0.265877	+	0.306838i
$304$		0			0
$305$	−3.84554	+	4.43799i	−0.220195	+	0.254119i
$306$		0			0
$307$	16.1266	−	4.73519i	0.920392	−	0.270251i	0.212983	−	0.977056i	$-0.431682\pi$
$307$	16.1266	−	4.73519i	0.920392	−	0.270251i	0.707409	+	0.706805i	$0.249864\pi$
$308$		0			0
$309$	0.281874	+	1.96048i	0.0160353	+	0.111528i
$310$		0			0
$311$	8.35825	+	18.3020i	0.473953	+	1.03781i	0.984082	+	0.177715i	$0.0568704\pi$
$311$	8.35825	+	18.3020i	0.473953	+	1.03781i	−0.510129	+	0.860098i	$0.670402\pi$
$312$		0			0
$313$	13.8050	+	8.87193i	0.780304	+	0.501471i	0.869135	−	0.494576i	$-0.164676\pi$
$313$	13.8050	+	8.87193i	0.780304	+	0.501471i	−0.0888302	+	0.996047i	$0.528313\pi$
$314$		0			0
$315$	0.334725	−	2.32807i	0.0188596	−	0.131172i
$316$		0			0
$317$	2.00417	−	1.28800i	0.112566	−	0.0723415i	−0.483147	−	0.875539i	$-0.660506\pi$
$317$	2.00417	−	1.28800i	0.112566	−	0.0723415i	0.595712	+	0.803198i	$0.296870\pi$
$318$		0			0
$319$	−2.00336	−	0.588241i	−0.112167	−	0.0329352i
$320$		0			0
$321$	11.4512			0.639141
$322$		0			0
$323$	−0.0272313			−0.00151519
$324$		0			0
$325$	−18.8896	−	5.54650i	−1.04781	−	0.307664i
$326$		0			0
$327$	10.1267	−	6.50803i	0.560007	−	0.359895i
$328$		0			0
$329$	0.622204	−	4.32752i	0.0343032	−	0.238584i
$330$		0			0
$331$	6.66212	+	4.28148i	0.366183	+	0.235332i	0.710773	−	0.703422i	$-0.248345\pi$
$331$	6.66212	+	4.28148i	0.366183	+	0.235332i	−0.344589	+	0.938754i	$0.611982\pi$
$332$		0			0
$333$	2.98016	+	6.52563i	0.163312	+	0.357602i
$334$		0			0
$335$	0.115979	+	0.806650i	0.00633660	+	0.0440720i
$336$		0			0
$337$	12.8684	−	3.77850i	0.700985	−	0.205828i	0.0882295	−	0.996100i	$-0.471879\pi$
$337$	12.8684	−	3.77850i	0.700985	−	0.205828i	0.612756	+	0.790272i	$0.290061\pi$
$338$		0			0
$339$	3.34055	−	3.85520i	0.181434	−	0.209386i
$340$		0			0
$341$	0.880100	+	1.01569i	0.0476601	+	0.0550026i
$342$		0			0
$343$	−8.34553	+	18.2742i	−0.450616	+	0.986712i
$344$		0			0
$345$	−3.00043	−	3.97387i	−0.161538	−	0.213946i
$346$		0			0
$347$	−1.98796	+	4.35302i	−0.106719	+	0.233683i	−0.955456	−	0.295132i	$-0.904636\pi$
$347$	−1.98796	+	4.35302i	−0.106719	+	0.233683i	0.848737	+	0.528815i	$0.177363\pi$
$348$		0			0
$349$	−1.78633	−	2.06153i	−0.0956198	−	0.110351i	0.705923	−	0.708289i	$-0.250533\pi$
$349$	−1.78633	−	2.06153i	−0.0956198	−	0.110351i	−0.801543	+	0.597938i	$0.795987\pi$
$350$		0			0
$351$	−3.28719	+	3.79361i	−0.175457	+	0.202488i
$352$		0			0
$353$	−19.9753	+	5.86528i	−1.06318	+	0.312177i	−0.766130	−	0.642686i	$-0.777820\pi$
$353$	−19.9753	+	5.86528i	−1.06318	+	0.312177i	−0.297048	+	0.954863i	$0.596002\pi$
$354$		0			0
$355$	0.817433	+	5.68537i	0.0433849	+	0.301748i
$356$		0			0
$357$	0.106155	+	0.232448i	0.00561834	+	0.0123025i
$358$		0			0
$359$	−28.5046	−	18.3188i	−1.50442	−	0.966830i	−0.994288	−	0.106733i	$-0.965961\pi$
$359$	−28.5046	−	18.3188i	−1.50442	−	0.966830i	−0.510129	−	0.860098i	$-0.670403\pi$
$360$		0			0
$361$	2.69569	−	18.7489i	0.141878	−	0.986786i
$362$		0			0
$363$	8.91753	−	5.73095i	0.468049	−	0.300797i
$364$		0			0
$365$	−10.0412	−	2.94835i	−0.525578	−	0.154324i
$366$		0			0
$367$	−16.9382			−0.884165			−0.442082	−	0.896974i	$-0.645760\pi$
$367$	−16.9382			−0.884165			−0.442082	+	0.896974i	$0.645760\pi$
$368$		0			0
$369$	9.22303			0.480132
$370$		0			0
$371$	1.48218	+	0.435207i	0.0769509	+	0.0225948i
$372$		0			0
$373$	1.21835	−	0.782984i	0.0630836	−	0.0405414i	−0.508719	−	0.860933i	$-0.669881\pi$
$373$	1.21835	−	0.782984i	0.0630836	−	0.0405414i	0.571802	+	0.820391i	$0.306244\pi$
$374$		0			0
$375$	1.31833	−	9.16917i	0.0680781	−	0.473494i
$376$		0			0
$377$	13.9460	+	8.96255i	0.718256	+	0.461595i
$378$		0			0
$379$	−8.17150	−	17.8931i	−0.419742	−	0.919106i	−0.994881	−	0.101051i	$-0.967780\pi$
$379$	−8.17150	−	17.8931i	−0.419742	−	0.919106i	0.575140	−	0.818055i	$-0.304948\pi$
$380$		0			0
$381$	−0.106135	−	0.738183i	−0.00543744	−	0.0378182i
$382$		0			0
$383$	14.8488	−	4.36000i	0.758738	−	0.222786i	0.120593	−	0.992702i	$-0.461520\pi$
$383$	14.8488	−	4.36000i	0.758738	−	0.222786i	0.638145	+	0.769916i	$0.279702\pi$
$384$		0			0
$385$	−0.973773	+	1.12379i	−0.0496281	+	0.0572739i
$386$		0			0
$387$	−7.18320	−	8.28985i	−0.365143	−	0.421397i
$388$		0			0
$389$	−14.9942	+	32.8328i	−0.760238	+	1.66469i	−0.0131958	+	0.999913i	$0.504200\pi$
$389$	−14.9942	+	32.8328i	−0.760238	+	1.66469i	−0.747042	+	0.664776i	$0.768527\pi$
$390$		0			0
$391$	0.507664	+	0.186970i	0.0256737	+	0.00945545i
$392$		0			0
$393$	3.02854	−	6.63157i	0.152769	−	0.334519i
$394$		0			0
$395$	1.68393	+	1.94336i	0.0847279	+	0.0977812i
$396$		0			0
$397$	23.8033	−	27.4705i	1.19465	−	1.37870i	0.287567	−	0.957760i	$-0.407153\pi$
$397$	23.8033	−	27.4705i	1.19465	−	1.37870i	0.907087	−	0.420944i	$-0.138301\pi$
$398$		0			0
$399$	0.524692	−	0.154063i	0.0262675	−	0.00771282i
$400$		0			0
$401$	−2.16691	−	15.0712i	−0.108210	−	0.752618i	−0.969604	−	0.244680i	$-0.921317\pi$
$401$	−2.16691	−	15.0712i	−0.108210	−	0.752618i	0.861394	−	0.507938i	$-0.169592\pi$
$402$		0			0
$403$	−4.43272	−	9.70629i	−0.220809	−	0.483505i
$404$		0			0
$405$	−0.873450	−	0.561333i	−0.0434021	−	0.0278928i
$406$		0			0
$407$	0.645472	−	4.48936i	0.0319949	−	0.222529i
$408$		0			0
$409$	0.996756	−	0.640576i	0.0492864	−	0.0316745i	−0.515766	−	0.856730i	$-0.672492\pi$
$409$	0.996756	−	0.640576i	0.0492864	−	0.0316745i	0.565052	+	0.825055i	$0.308856\pi$
$410$		0			0
$411$	−0.433831	−	0.127384i	−0.0213993	−	0.00628340i
$412$		0			0
$413$	17.6336			0.867693
$414$		0			0
$415$	10.2599			0.503641
$416$		0			0
$417$	−10.2438	−	3.00784i	−0.501639	−	0.147294i
$418$		0			0
$419$	−29.9970	+	19.2779i	−1.46545	+	0.941788i	−0.467110	+	0.884199i	$0.654705\pi$
$419$	−29.9970	+	19.2779i	−1.46545	+	0.941788i	−0.998340	+	0.0575886i	$0.981659\pi$
$420$		0			0
$421$	3.04856	−	21.2032i	0.148578	−	1.03338i	−0.769972	−	0.638077i	$-0.779730\pi$
$421$	3.04856	−	21.2032i	0.148578	−	1.03338i	0.918550	−	0.395304i	$-0.129361\pi$
$422$		0			0
$423$	−1.62361	−	1.04343i	−0.0789427	−	0.0507334i
$424$		0			0
$425$	0.183790	+	0.402444i	0.00891512	+	0.0195214i
$426$		0			0
$427$	1.82337	+	12.6818i	0.0882390	+	0.613716i
$428$		0			0
$429$	3.04500	−	0.894093i	0.147014	−	0.0431672i
$430$		0			0
$431$	−15.1181	+	17.4472i	−0.728211	+	0.840401i	−0.992269	−	0.124106i	$-0.960394\pi$
$431$	−15.1181	+	17.4472i	−0.728211	+	0.840401i	0.264058	+	0.964507i	$0.414939\pi$
$432$		0			0
$433$	3.68098	+	4.24808i	0.176897	+	0.204150i	0.837273	−	0.546785i	$-0.184149\pi$
$433$	3.68098	+	4.24808i	0.176897	+	0.204150i	−0.660376	+	0.750935i	$0.729603\pi$
$434$		0			0
$435$	−1.42443	+	3.11907i	−0.0682962	+	0.149548i
$436$		0			0
$437$	0.550639	−	1.01837i	0.0263406	−	0.0487155i
$438$		0			0
$439$	−7.64904	+	16.7491i	−0.365069	+	0.799389i	0.634579	+	0.772858i	$0.281173\pi$
$439$	−7.64904	+	16.7491i	−0.365069	+	0.799389i	−0.999648	+	0.0265315i	$0.991554\pi$
$440$		0			0
$441$	1.22353	+	1.41203i	0.0582634	+	0.0672395i
$442$		0			0
$443$	21.6831	−	25.0236i	1.03020	−	1.18891i	0.0484268	−	0.998827i	$-0.484579\pi$
$443$	21.6831	−	25.0236i	1.03020	−	1.18891i	0.981768	−	0.190082i	$-0.0608753\pi$
$444$		0			0
$445$	10.2491	−	3.00942i	0.485856	−	0.142660i
$446$		0			0
$447$	−3.09117	−	21.4996i	−0.146207	−	1.01690i
$448$		0			0
$449$	−1.32049	−	2.89147i	−0.0623177	−	0.136457i	0.875911	−	0.482473i	$-0.160261\pi$
$449$	−1.32049	−	2.89147i	−0.0623177	−	0.136457i	−0.938228	+	0.346016i	$0.887534\pi$
$450$		0			0
$451$	−4.90536	−	3.15249i	−0.230985	−	0.148445i
$452$		0			0
$453$	−2.77899	+	19.3283i	−0.130569	+	0.908124i
$454$		0			0
$455$	9.93209	−	6.38297i	0.465624	−	0.299238i
$456$		0			0
$457$	−30.7144	−	9.01856i	−1.43676	−	0.421870i	−0.531619	−	0.846984i	$-0.678416\pi$
$457$	−30.7144	−	9.01856i	−1.43676	−	0.421870i	−0.905140	+	0.425113i	$0.860234\pi$
$458$		0			0
$459$	0.112806			0.00526534
$460$		0			0
$461$	26.6551			1.24145			0.620726	−	0.784028i	$-0.286838\pi$
$461$	26.6551			1.24145			0.620726	+	0.784028i	$0.286838\pi$
$462$		0			0
$463$	14.9174	+	4.38013i	0.693269	+	0.203562i	0.609339	−	0.792910i	$-0.291435\pi$
$463$	14.9174	+	4.38013i	0.693269	+	0.203562i	0.0839294	+	0.996472i	$0.473253\pi$
$464$		0			0
$465$	1.85674	−	1.19325i	0.0861042	−	0.0553358i
$466$		0			0
$467$	1.25206	−	8.70828i	0.0579385	−	0.402971i	−0.940128	−	0.340821i	$-0.889295\pi$
$467$	1.25206	−	8.70828i	0.0579385	−	0.402971i	0.998067	−	0.0621504i	$-0.0197958\pi$
$468$		0			0
$469$	1.49579	+	0.961287i	0.0690692	+	0.0443881i
$470$		0			0
$471$	−3.97023	−	8.69359i	−0.182938	−	0.400579i
$472$		0			0
$473$	0.986938	+	6.86430i	0.0453794	+	0.315621i
$474$		0			0
$475$	0.908414	−	0.266734i	0.0416809	−	0.0122386i
$476$		0			0
$477$	0.446561	−	0.515359i	0.0204466	−	0.0235966i
$478$		0			0
$479$	−22.8038	−	26.3170i	−1.04193	−	1.20245i	−0.978879	−	0.204442i	$-0.934462\pi$
$479$	−22.8038	−	26.3170i	−1.04193	−	1.20245i	−0.0630522	−	0.998010i	$-0.520083\pi$
$480$		0			0
$481$	−14.9594	+	32.7565i	−0.682090	+	1.49357i
$482$		0			0
$483$	−10.8395	−	0.730369i	−0.493212	−	0.0332330i
$484$		0			0
$485$	1.37627	−	3.01362i	0.0624934	−	0.136841i
$486$		0			0
$487$	−20.9451	−	24.1720i	−0.949115	−	1.09534i	−0.995342	−	0.0964057i	$-0.969265\pi$
$487$	−20.9451	−	24.1720i	−0.949115	−	1.09534i	0.0462275	−	0.998931i	$-0.485280\pi$
$488$		0			0
$489$	15.8155	−	18.2520i	0.715201	−	0.825386i
$490$		0			0
$491$	9.40660	−	2.76203i	0.424514	−	0.124649i	−0.0624955	−	0.998045i	$-0.519906\pi$
$491$	9.40660	−	2.76203i	0.424514	−	0.124649i	0.487009	+	0.873397i	$0.338088\pi$
$492$		0			0
$493$	−0.0530189	−	0.368754i	−0.00238785	−	0.0166079i
$494$		0			0
$495$	0.272687	+	0.597101i	0.0122564	+	0.0268377i
$496$		0			0
$497$	10.5425	+	6.77527i	0.472897	+	0.303912i
$498$		0			0
$499$	5.44505	−	37.8711i	0.243754	−	1.69534i	−0.389199	−	0.921154i	$-0.627248\pi$
$499$	5.44505	−	37.8711i	0.243754	−	1.69534i	0.632953	−	0.774191i	$-0.281843\pi$
$500$		0			0
$501$	−8.09903	+	5.20493i	−0.361838	+	0.232539i
$502$		0			0
$503$	1.22035	+	0.358326i	0.0544125	+	0.0159770i	0.308826	−	0.951119i	$-0.400064\pi$
$503$	1.22035	+	0.358326i	0.0544125	+	0.0159770i	−0.254413	+	0.967096i	$0.581882\pi$
$504$		0			0
$505$	−7.33777			−0.326527
$506$		0			0
$507$	−12.1971			−0.541692
$508$		0			0
$509$	−42.4462	−	12.4633i	−1.88139	−	0.552427i	−0.996188	−	0.0872275i	$-0.972199\pi$
$509$	−42.4462	−	12.4633i	−1.88139	−	0.552427i	−0.885206	−	0.465200i	$-0.845983\pi$
$510$		0			0
$511$	−19.2081	+	12.3443i	−0.849717	+	0.546080i
$512$		0			0
$513$	0.0343547	−	0.238942i	0.00151680	−	0.0105495i
$514$		0			0
$515$	−1.72999	−	1.11180i	−0.0762325	−	0.0489917i
$516$		0			0
$517$	0.506884	+	1.10992i	0.0222927	+	0.0488142i
$518$		0			0
$519$	0.0543100	+	0.377735i	0.00238395	+	0.0165807i
$520$		0			0
$521$	27.9846	−	8.21702i	1.22603	−	0.359994i	0.396278	−	0.918131i	$-0.370302\pi$
$521$	27.9846	−	8.21702i	1.22603	−	0.359994i	0.829749	+	0.558137i	$0.188483\pi$
$522$		0			0
$523$	1.68540	−	1.94506i	0.0736976	−	0.0850516i	−0.717703	−	0.696349i	$-0.754807\pi$
$523$	1.68540	−	1.94506i	0.0736976	−	0.0850516i	0.791401	+	0.611297i	$0.209352\pi$
$524$		0			0
$525$	−5.81812	−	6.71447i	−0.253924	−	0.293043i
$526$		0			0
$527$	−0.0996156	+	0.218128i	−0.00433932	+	0.00950180i
$528$		0			0
$529$	−17.2575	+	15.2045i	−0.750327	+	0.661067i
$530$		0			0
$531$	3.23367	−	7.08076i	0.140329	−	0.307279i
$532$		0			0
$533$	30.3178	+	34.9886i	1.31321	+	1.51553i
$534$		0			0
$535$	−7.78591	+	8.98542i	−0.336614	+	0.388474i
$536$		0			0
$537$	6.09860	−	1.79071i	0.263174	−	0.0772749i
$538$		0			0
$539$	−0.168107	−	1.16921i	−0.00724090	−	0.0503615i
$540$		0			0
$541$	−19.0278	−	41.6650i	−0.818068	−	1.79132i	−0.567858	−	0.823127i	$-0.692228\pi$
$541$	−19.0278	−	41.6650i	−0.818068	−	1.79132i	−0.250210	−	0.968192i	$-0.580500\pi$
$542$		0			0
$543$	0.00161415	+	0.00103735i	6.92696e−5	+	4.45169e-5i
$544$		0			0
$545$	−1.77870	+	12.3711i	−0.0761910	+	0.529920i
$546$		0			0
$547$	10.2427	−	6.58256i	0.437945	−	0.281450i	−0.303032	−	0.952980i	$-0.597999\pi$
$547$	10.2427	−	6.58256i	0.437945	−	0.281450i	0.740977	+	0.671530i	$0.234363\pi$
$548$		0			0
$549$	5.42674	+	1.59344i	0.231608	+	0.0680062i
$550$		0			0
$551$	−0.797229			−0.0339631
$552$		0			0
$553$	5.61037			0.238577
$554$		0			0
$555$	−7.14677	−	2.09848i	−0.303364	−	0.0890756i
$556$		0			0
$557$	12.8218	−	8.24007i	0.543277	−	0.349143i	−0.240042	−	0.970762i	$-0.577161\pi$
$557$	12.8218	−	8.24007i	0.543277	−	0.349143i	0.783319	+	0.621619i	$0.213525\pi$
$558$		0			0
$559$	7.83600	−	54.5006i	0.331428	−	2.30513i
$560$		0			0
$561$	−0.0599971	−	0.0385578i	−0.00253308	−	0.00162791i
$562$		0			0
$563$	5.81773	+	12.7391i	0.245188	+	0.536887i	0.991713	−	0.128470i	$-0.0410065\pi$
$563$	5.81773	+	12.7391i	0.245188	+	0.536887i	−0.746525	+	0.665357i	$0.768279\pi$
$564$		0			0
$565$	0.753756	+	5.24249i	0.0317107	+	0.220553i
$566$		0			0
$567$	−2.17355	+	0.638211i	−0.0912804	+	0.0268023i
$568$		0			0
$569$	24.3459	−	28.0966i	1.02063	−	1.17787i	0.0366996	−	0.999326i	$-0.488316\pi$
$569$	24.3459	−	28.0966i	1.02063	−	1.17787i	0.983932	−	0.178545i	$-0.0571390\pi$
$570$		0			0
$571$	28.6529	+	33.0672i	1.19909	+	1.38382i	0.903546	+	0.428491i	$0.140955\pi$
$571$	28.6529	+	33.0672i	1.19909	+	1.38382i	0.295541	+	0.955330i	$0.404500\pi$
$572$		0			0
$573$	0.966090	−	2.11544i	0.0403590	−	0.0883739i
$574$		0			0
$575$	−18.7667	−	1.26451i	−0.782623	−	0.0527337i
$576$		0			0
$577$	5.93013	−	12.9852i	0.246875	−	0.540580i	−0.745110	−	0.666942i	$-0.767603\pi$
$577$	5.93013	−	12.9852i	0.246875	−	0.540580i	0.991984	+	0.126362i	$0.0403301\pi$
$578$		0			0
$579$	7.74657	+	8.94002i	0.321937	+	0.371535i
$580$		0			0
$581$	14.6592	−	16.9176i	0.608166	−	0.701860i
$582$		0			0
$583$	−0.413660	+	0.121462i	−0.0171321	+	0.00503043i
$584$		0			0
$585$	−0.741715	−	5.15874i	−0.0306661	−	0.213288i
$586$		0			0
$587$	−11.1953	−	24.5144i	−0.462082	−	1.01182i	−0.987008	−	0.160670i	$-0.948635\pi$
$587$	−11.1953	−	24.5144i	−0.462082	−	1.01182i	0.524927	−	0.851147i	$-0.324093\pi$
$588$		0			0
$589$	0.431693	+	0.277432i	0.0177876	+	0.0114314i
$590$		0			0
$591$	−2.78628	+	19.3790i	−0.114612	+	0.797145i
$592$		0			0
$593$	11.3332	−	7.28343i	0.465400	−	0.299095i	−0.286846	−	0.957977i	$-0.592607\pi$
$593$	11.3332	−	7.28343i	0.465400	−	0.299095i	0.752246	+	0.658882i	$0.228970\pi$
$594$		0			0
$595$	−0.254573	−	0.0747495i	−0.0104365	−	0.00306443i
$596$		0			0
$597$	11.3259			0.463538
$598$		0			0
$599$	−20.6190			−0.842470			−0.421235	−	0.906952i	$-0.638403\pi$
$599$	−20.6190			−0.842470			−0.421235	+	0.906952i	$0.638403\pi$
$600$		0			0
$601$	3.85884	+	1.13306i	0.157405	+	0.0462184i	0.359486	−	0.933151i	$-0.382952\pi$
$601$	3.85884	+	1.13306i	0.157405	+	0.0462184i	−0.202081	+	0.979369i	$0.564770\pi$
$602$		0			0
$603$	0.660304	−	0.424352i	0.0268897	−	0.0172809i
$604$		0			0
$605$	−1.56632	+	10.8940i	−0.0636798	+	0.442903i
$606$		0			0
$607$	23.7598	+	15.2695i	0.964379	+	0.619769i	0.925207	−	0.379463i	$-0.123891\pi$
$607$	23.7598	+	15.2695i	0.964379	+	0.619769i	0.0391727	+	0.999232i	$0.487528\pi$
$608$		0			0
$609$	3.10783	+	6.80519i	0.125935	+	0.275760i
$610$		0			0
$611$	−1.37874	−	9.58932i	−0.0557777	−	0.387942i
$612$		0			0
$613$	17.7731	−	5.21864i	0.717847	−	0.210779i	0.0976454	−	0.995221i	$-0.468869\pi$
$613$	17.7731	−	5.21864i	0.717847	−	0.210779i	0.620202	+	0.784442i	$0.287051\pi$
$614$		0			0
$615$	−6.27096	+	7.23708i	−0.252870	+	0.291827i
$616$		0			0
$617$	−10.8147	−	12.4808i	−0.435384	−	0.502460i	0.495078	−	0.868849i	$-0.335139\pi$
$617$	−10.8147	−	12.4808i	−0.435384	−	0.502460i	−0.930462	+	0.366389i	$0.880594\pi$
$618$		0			0
$619$	−18.2613	+	39.9866i	−0.733983	+	1.60720i	0.0592232	+	0.998245i	$0.481138\pi$
$619$	−18.2613	+	39.9866i	−0.733983	+	1.60720i	−0.793206	+	0.608953i	$0.791590\pi$
$620$		0			0
$621$	−2.28103	+	4.21864i	−0.0915347	+	0.169288i
$622$		0			0
$623$	9.68152	−	21.1996i	0.387882	−	0.849343i
$624$		0			0
$625$	−6.54334	−	7.55142i	−0.261734	−	0.302057i
$626$		0			0
$627$	−0.0999436	+	0.115341i	−0.00399136	+	0.00460628i
$628$		0			0
$629$	0.776482	−	0.227996i	0.0309604	−	0.00909078i
$630$		0			0
$631$	1.23319	+	8.57705i	0.0490927	+	0.341447i	0.999534	+	0.0305415i	$0.00972316\pi$
$631$	1.23319	+	8.57705i	0.0490927	+	0.341447i	−0.950441	+	0.310905i	$0.899368\pi$
$632$		0			0
$633$	1.57158	+	3.44128i	0.0624646	+	0.136779i
$634$		0			0
$635$	0.651396	+	0.418627i	0.0258499	+	0.0166127i
$636$		0			0
$637$	−1.33472	+	9.28321i	−0.0528837	+	0.367814i
$638$		0			0
$639$	4.65391	−	2.99088i	0.184106	−	0.118318i
$640$		0			0
$641$	−31.4550	−	9.23601i	−1.24240	−	0.364800i	−0.406481	−	0.913659i	$-0.633244\pi$
$641$	−31.4550	−	9.23601i	−1.24240	−	0.364800i	−0.835915	+	0.548859i	$0.815062\pi$
$642$		0			0
$643$	9.91288			0.390926			0.195463	−	0.980711i	$-0.437379\pi$
$643$	9.91288			0.390926			0.195463	+	0.980711i	$0.437379\pi$
$644$		0			0
$645$	11.3889			0.448436
$646$		0			0
$647$	−19.5390	−	5.73718i	−0.768159	−	0.225552i	−0.125904	−	0.992042i	$-0.540183\pi$
$647$	−19.5390	−	5.73718i	−0.768159	−	0.225552i	−0.642255	+	0.766491i	$0.722001\pi$
$648$		0			0
$649$	−4.14011	+	2.66068i	−0.162513	+	0.104441i
$650$		0			0
$651$	0.685314	−	4.76646i	0.0268596	−	0.186812i
$652$		0			0
$653$	−13.5339	−	8.69772i	−0.529623	−	0.340368i	0.248345	−	0.968672i	$-0.420113\pi$
$653$	−13.5339	−	8.69772i	−0.529623	−	0.340368i	−0.777968	+	0.628303i	$0.783750\pi$
$654$		0			0
$655$	3.14445	+	6.88538i	0.122864	+	0.269034i
$656$		0			0
$657$	1.43443	+	9.97671i	0.0559626	+	0.389229i
$658$		0			0
$659$	−27.5783	+	8.09773i	−1.07430	+	0.315443i	−0.770596	−	0.637324i	$-0.780041\pi$
$659$	−27.5783	+	8.09773i	−1.07430	+	0.315443i	−0.303703	+	0.952767i	$0.598223\pi$
$660$		0			0
$661$	21.3935	−	24.6894i	0.832110	−	0.960306i	−0.167564	−	0.985861i	$-0.553590\pi$
$661$	21.3935	−	24.6894i	0.832110	−	0.960306i	0.999673	+	0.0255556i	$0.00813550\pi$
$662$		0			0
$663$	0.370815	+	0.427943i	0.0144013	+	0.0166199i
$664$		0			0
$665$	−0.235861	+	0.516464i	−0.00914630	+	0.0200276i
$666$		0			0
$667$	14.8625	+	5.47376i	0.575477	+	0.211945i
$668$		0			0
$669$	1.36964	−	2.99909i	0.0529532	−	0.115951i
$670$		0			0
$671$	−2.34162	−	2.70238i	−0.0903973	−	0.104324i
$672$		0			0
$673$	−26.3135	+	30.3674i	−1.01431	+	1.17058i	−0.0290384	+	0.999578i	$0.509245\pi$
$673$	−26.3135	+	30.3674i	−1.01431	+	1.17058i	−0.985271	+	0.170998i	$0.945301\pi$
$674$		0			0
$675$	−3.76312	+	1.10495i	−0.144843	+	0.0425296i
$676$		0			0
$677$	5.27380	+	36.6801i	0.202688	+	1.40973i	0.796263	+	0.604950i	$0.206807\pi$
$677$	5.27380	+	36.6801i	0.202688	+	1.40973i	−0.593575	+	0.804779i	$0.702284\pi$
$678$		0			0
$679$	−3.00276	−	6.57513i	−0.115235	−	0.252330i
$680$		0			0
$681$	0.676350	+	0.434663i	0.0259178	+	0.0166563i
$682$		0			0
$683$	−1.31982	+	9.17955i	−0.0505015	+	0.351246i	0.948866	+	0.315680i	$0.102232\pi$
$683$	−1.31982	+	9.17955i	−0.0505015	+	0.351246i	−0.999367	+	0.0355660i	$0.988677\pi$
$684$		0			0
$685$	0.394927	−	0.253804i	0.0150894	−	0.00969736i
$686$		0			0
$687$	−18.2375	−	5.35501i	−0.695804	−	0.204306i
$688$		0			0
$689$	3.42300			0.130406
$690$		0			0
$691$	−25.6110			−0.974290			−0.487145	−	0.873321i	$-0.661962\pi$
$691$	−25.6110			−0.974290			−0.487145	+	0.873321i	$0.661962\pi$
$692$		0			0
$693$	1.37417	+	0.403492i	0.0522003	+	0.0153274i
$694$		0			0
$695$	9.32514	−	5.99291i	0.353723	−	0.227324i
$696$		0			0
$697$	0.148067	−	1.02983i	0.00560842	−	0.0390074i
$698$		0			0
$699$	−10.1227	−	6.50545i	−0.382875	−	0.246059i
$700$		0			0
$701$	−2.91911	−	6.39195i	−0.110253	−	0.241421i	0.846461	−	0.532451i	$-0.178729\pi$
$701$	−2.91911	−	6.39195i	−0.110253	−	0.241421i	−0.956714	+	0.291031i	$0.906002\pi$
$702$		0			0
$703$	−0.246458	−	1.71415i	−0.00929533	−	0.0646504i
$704$		0			0
$705$	1.92269	−	0.564552i	0.0724126	−	0.0212623i
$706$		0			0
$707$	−10.4840	+	12.0992i	−0.394293	+	0.455039i
$708$		0			0
$709$	−18.1783	−	20.9789i	−0.682700	−	0.787878i	0.303607	−	0.952797i	$-0.401809\pi$
$709$	−18.1783	−	20.9789i	−0.682700	−	0.787878i	−0.986307	+	0.164919i	$0.947264\pi$
$710$		0			0
$711$	1.02884	−	2.25284i	0.0385844	−	0.0844881i
$712$		0			0
$713$	−6.14306	−	8.13607i	−0.230059	−	0.304698i
$714$		0			0
$715$	−1.36880	+	2.99725i	−0.0511901	+	0.112091i
$716$		0			0
$717$	17.5736	+	20.2810i	0.656296	+	0.757406i
$718$		0			0
$719$	−14.0816	+	16.2511i	−0.525157	+	0.606063i	−0.954915	−	0.296881i	$-0.904054\pi$
$719$	−14.0816	+	16.2511i	−0.525157	+	0.606063i	0.429758	+	0.902944i	$0.358599\pi$
$720$		0			0
$721$	−4.30501	+	1.26407i	−0.160327	+	0.0470763i
$722$		0			0
$723$	4.32265	+	30.0647i	0.160761	+	1.11812i
$724$		0			0
$725$	5.38067	+	11.7820i	0.199833	+	0.437573i
$726$		0			0
$727$	−15.4521	−	9.93044i	−0.573085	−	0.368299i	0.221770	−	0.975099i	$-0.428817\pi$
$727$	−15.4521	−	9.93044i	−0.573085	−	0.368299i	−0.794855	+	0.606800i	$0.792453\pi$
$728$		0			0
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$		0			0
$731$	−1.04095	+	0.668976i	−0.0385008	+	0.0247430i
$732$		0			0
$733$	−5.23550	−	1.53728i	−0.193377	−	0.0567808i	0.183610	−	0.982999i	$-0.441222\pi$
$733$	−5.23550	−	1.53728i	−0.193377	−	0.0567808i	−0.376987	+	0.926218i	$0.623040\pi$
$734$		0			0
$735$	−1.93989			−0.0715540
$736$		0			0
$737$	−0.496235			−0.0182791
$738$		0			0
$739$	33.8647	+	9.94357i	1.24573	+	0.365780i	0.837166	−	0.546949i	$-0.184211\pi$
$739$	33.8647	+	9.94357i	1.24573	+	0.365780i	0.408566	+	0.912729i	$0.366029\pi$
$740$		0			0
$741$	1.01938	−	0.655118i	0.0374480	−	0.0240664i
$742$		0			0
$743$	7.18641	−	49.9826i	0.263644	−	1.83368i	−0.241203	−	0.970475i	$-0.577542\pi$
$743$	7.18641	−	49.9826i	0.263644	−	1.83368i	0.504847	−	0.863209i	$-0.331549\pi$
$744$		0			0
$745$	18.9719	+	12.1925i	0.695078	+	0.446699i
$746$		0			0
$747$	−4.10503	−	8.98876i	−0.150195	−	0.328881i
$748$		0			0
$749$	3.69170	+	25.6763i	0.134892	+	0.938193i
$750$		0			0
$751$	20.7485	−	6.09230i	0.757123	−	0.222311i	0.119684	−	0.992812i	$-0.461812\pi$
$751$	20.7485	−	6.09230i	0.757123	−	0.222311i	0.637439	+	0.770501i	$0.279994\pi$
$752$		0			0
$753$	−8.24763	+	9.51827i	−0.300560	+	0.346865i
$754$		0			0
$755$	−13.2769	−	15.3224i	−0.483197	−	0.557639i
$756$		0			0
$757$	−9.89582	+	21.6688i	−0.359670	+	0.787567i	0.640144	+	0.768255i	$0.278875\pi$
$757$	−9.89582	+	21.6688i	−0.359670	+	0.787567i	−0.999814	+	0.0193118i	$0.993852\pi$
$758$		0			0
$759$	2.65514	−	1.46405i	0.0963756	−	0.0531418i
$760$		0			0
$761$	13.0279	−	28.5271i	0.472261	−	1.03411i	−0.512258	−	0.858832i	$-0.671191\pi$
$761$	13.0279	−	28.5271i	0.472261	−	1.03411i	0.984519	−	0.175276i	$-0.0560818\pi$
$762$		0			0
$763$	17.8573	+	20.6085i	0.646479	+	0.746076i
$764$		0			0
$765$	−0.0766996	+	0.0885161i	−0.00277308	+	0.00320031i
$766$		0			0
$767$	37.4914	−	11.0085i	1.35373	−	0.397492i
$768$		0			0
$769$	0.547276	+	3.80639i	0.0197353	+	0.137262i	0.997307	−	0.0733414i	$-0.0233663\pi$
$769$	0.547276	+	3.80639i	0.0197353	+	0.137262i	−0.977572	+	0.210603i	$0.932457\pi$
$770$		0			0
$771$	7.02942	+	15.3923i	0.253158	+	0.554340i
$772$		0			0
$773$	4.65926	+	2.99432i	0.167582	+	0.107698i	0.621743	−	0.783221i	$-0.286425\pi$
$773$	4.65926	+	2.99432i	0.167582	+	0.107698i	−0.454161	+	0.890919i	$0.650061\pi$
$774$		0			0
$775$	1.18650	−	8.25231i	0.0426205	−	0.296432i
$776$		0			0
$777$	−13.6713	+	8.78603i	−0.490456	+	0.315197i
$778$		0			0
$779$	−2.13625	−	0.627258i	−0.0765389	−	0.0224739i
$780$		0			0
$781$	−3.49753			−0.125151
$782$		0			0
$783$	3.30254			0.118023
$784$		0			0
$785$	9.52108	+	2.79564i	0.339822	+	0.0997807i
$786$		0			0
$787$	−26.6918	+	17.1538i	−0.951459	+	0.611466i	−0.921622	−	0.388089i	$-0.873135\pi$
$787$	−26.6918	+	17.1538i	−0.951459	+	0.611466i	−0.0298372	+	0.999555i	$0.509499\pi$
$788$		0			0
$789$	−3.71376	+	25.8297i	−0.132213	+	0.919563i
$790$		0			0
$791$	9.72127	+	6.24748i	0.345649	+	0.222135i
$792$		0			0
$793$	11.7938	+	25.8249i	0.418811	+	0.917069i
$794$		0			0
$795$	0.100761	+	0.700809i	0.00357363	+	0.0248551i
$796$		0			0
$797$	32.9765	−	9.68277i	1.16809	−	0.342981i	0.360517	−	0.932753i	$-0.382600\pi$
$797$	32.9765	−	9.68277i	1.16809	−	0.342981i	0.807570	+	0.589771i	$0.200782\pi$
$798$		0			0
$799$	−0.142573	+	0.164538i	−0.00504387	+	0.00582094i
$800$		0			0
$801$	−6.73726	−	7.77521i	−0.238049	−	0.274723i
$802$		0			0
$803$	2.64718	−	5.79651i	0.0934169	−	0.204555i
$804$		0			0
$805$	7.94311	−	8.00884i	0.279958	−	0.282275i
$806$		0			0
$807$	−5.52148	+	12.0904i	−0.194365	+	0.425601i
$808$		0			0
$809$	−6.60372	−	7.62110i	−0.232174	−	0.267944i	0.627693	−	0.778461i	$-0.283999\pi$
$809$	−6.60372	−	7.62110i	−0.232174	−	0.267944i	−0.859867	+	0.510517i	$0.829454\pi$
$810$		0			0
$811$	−22.3885	+	25.8377i	−0.786165	+	0.907283i	−0.997538	−	0.0701226i	$-0.977661\pi$
$811$	−22.3885	+	25.8377i	−0.786165	+	0.907283i	0.211373	+	0.977405i	$0.432206\pi$
$812$		0			0
$813$	12.4881	−	3.66682i	0.437975	−	0.128601i
$814$		0			0
$815$	3.56858	+	24.8200i	0.125002	+	0.869407i
$816$		0			0
$817$	1.09998	+	2.40863i	0.0384836	+	0.0842673i
$818$		0			0
$819$	−9.56598	−	6.14768i	−0.334262	−	0.214817i
$820$		0			0
$821$	−1.73958	+	12.0990i	−0.0607117	+	0.422259i	0.936686	+	0.350169i	$0.113876\pi$
$821$	−1.73958	+	12.0990i	−0.0607117	+	0.422259i	−0.997398	+	0.0720899i	$0.977033\pi$
$822$		0			0
$823$	12.7442	−	8.19020i	0.444235	−	0.285493i	−0.299338	−	0.954147i	$-0.596766\pi$
$823$	12.7442	−	8.19020i	0.444235	−	0.285493i	0.743573	+	0.668655i	$0.233129\pi$
$824$		0			0
$825$	2.37913	+	0.698577i	0.0828308	+	0.0243213i
$826$		0			0
$827$	25.2923			0.879500			0.439750	−	0.898120i	$-0.355067\pi$
$827$	25.2923			0.879500			0.439750	+	0.898120i	$0.355067\pi$
$828$		0			0
$829$	−2.35800			−0.0818966			−0.0409483	−	0.999161i	$-0.513038\pi$
$829$	−2.35800			−0.0818966			−0.0409483	+	0.999161i	$0.513038\pi$
$830$		0			0
$831$	−16.3060	−	4.78786i	−0.565648	−	0.166089i
$832$		0			0
$833$	0.177307	−	0.113948i	0.00614332	−	0.00394807i
$834$		0			0
$835$	1.42255	−	9.89406i	0.0492294	−	0.342398i
$836$		0			0
$837$	−1.78830	−	1.14927i	−0.0618125	−	0.0397245i
$838$		0			0
$839$	−14.2760	−	31.2601i	−0.492863	−	1.07922i	−0.978723	−	0.205184i	$-0.934221\pi$
$839$	−14.2760	−	31.2601i	−0.492863	−	1.07922i	0.485860	−	0.874037i	$-0.338506\pi$
$840$		0			0
$841$	2.57494	+	17.9091i	0.0887910	+	0.617555i
$842$		0			0
$843$	14.3522	−	4.21419i	0.494316	−	0.145144i
$844$		0			0
$845$	8.29310	−	9.57075i	0.285291	−	0.329244i
$846$		0			0
$847$	15.7251	+	18.1478i	0.540321	+	0.623564i
$848$		0			0
$849$	7.17529	−	15.7117i	0.246255	−	0.539224i
$850$		0			0
$851$	−7.17469	+	33.6485i	−0.245945	+	1.15346i
$852$		0			0
$853$	−8.52536	+	18.6679i	−0.291903	+	0.639178i	−0.997593	−	0.0693426i	$-0.977910\pi$
$853$	−8.52536	+	18.6679i	−0.291903	+	0.639178i	0.705690	+	0.708521i	$0.250637\pi$
$854$		0			0
$855$	0.164133	+	0.189420i	0.00561323	+	0.00647801i
$856$		0			0
$857$	16.5936	−	19.1500i	0.566826	−	0.654152i	−0.397894	−	0.917432i	$-0.630259\pi$
$857$	16.5936	−	19.1500i	0.566826	−	0.654152i	0.964720	+	0.263280i	$0.0848042\pi$
$858$		0			0
$859$	−8.63071	+	2.53421i	−0.294476	+	0.0864660i	−0.425634	−	0.904896i	$-0.639949\pi$
$859$	−8.63071	+	2.53421i	−0.294476	+	0.0864660i	0.131158	+	0.991362i	$0.458131\pi$
$860$		0			0
$861$	2.97338	+	20.6803i	0.101333	+	0.704784i
$862$		0			0
$863$	−18.0028	−	39.4207i	−0.612824	−	1.34190i	−0.920626	−	0.390446i	$-0.872321\pi$
$863$	−18.0028	−	39.4207i	−0.612824	−	1.34190i	0.307802	−	0.951450i	$-0.400407\pi$
$864$		0			0
$865$	−0.333325	−	0.214215i	−0.0113334	−	0.00728353i
$866$		0			0
$867$	−2.41754	+	16.8144i	−0.0821040	+	0.571046i
$868$		0			0
$869$	−1.31723	+	0.846533i	−0.0446840	+	0.0287167i
$870$		0			0
$871$	3.78037	+	1.11002i	0.128093	+	0.0376115i
$872$		0			0
$873$	−3.19089			−0.107995
$874$		0			0
$875$	20.9846			0.709408
$876$		0			0
$877$	−36.7828	−	10.8004i	−1.24207	−	0.364703i	−0.406275	−	0.913751i	$-0.633172\pi$
$877$	−36.7828	−	10.8004i	−1.24207	−	0.364703i	−0.835791	+	0.549048i	$0.814991\pi$
$878$		0			0
$879$	−18.4587	+	11.8627i	−0.622598	+	0.400120i
$880$		0			0
$881$	−5.68083	+	39.5110i	−0.191392	+	1.33116i	0.636936	+	0.770916i	$0.280201\pi$
$881$	−5.68083	+	39.5110i	−0.191392	+	1.33116i	−0.828328	+	0.560243i	$0.810708\pi$
$882$		0			0
$883$	39.9100	+	25.6486i	1.34308	+	0.863144i	0.997174	−	0.0751257i	$-0.0239358\pi$
$883$	39.9100	+	25.6486i	1.34308	+	0.863144i	0.345904	+	0.938270i	$0.387572\pi$
$884$		0			0
$885$	3.35743	+	7.35176i	0.112859	+	0.247127i
$886$		0			0
$887$	4.42422	+	30.7711i	0.148551	+	1.03319i	0.918594	+	0.395202i	$0.129325\pi$
$887$	4.42422	+	30.7711i	0.148551	+	1.03319i	−0.770043	+	0.637991i	$0.779766\pi$
$888$		0			0
$889$	1.62097	−	0.475961i	0.0543657	−	0.0159632i
$890$		0			0
$891$	0.414018	−	0.477803i	0.0138701	−	0.0160070i
$892$		0			0
$893$	0.305098	+	0.352102i	0.0102097	+	0.0117827i
$894$		0			0
$895$	−2.74146	+	6.00296i	−0.0916370	+	0.200657i
$896$		0			0
$897$	−23.5021	+	5.21408i	−0.784711	+	0.174093i
$898$		0			0
$899$	−2.91637	+	6.38595i	−0.0972663	+	0.212983i
$900$		0			0
$901$	−0.0503748	−	0.0581356i	−0.00167823	−	0.00193678i
$902$		0			0
$903$	16.2722	−	18.7791i	0.541503	−	0.624928i
$904$		0			0
$905$	−0.00191148		0.000561260i	−6.35396e−5		1.86569e-5i
$906$		0			0
$907$	5.84227	+	40.6339i	0.193990	+	1.34923i	0.821317	+	0.570472i	$0.193240\pi$
$907$	5.84227	+	40.6339i	0.193990	+	1.34923i	−0.627328	+	0.778755i	$0.715851\pi$
$908$		0			0
$909$	2.93586	+	6.42863i	0.0973763	+	0.213224i
$910$		0			0
$911$	−44.7334	−	28.7484i	−1.48209	−	0.952478i	−0.996950	−	0.0780389i	$-0.975134\pi$
$911$	−44.7334	−	28.7484i	−1.48209	−	0.952478i	−0.485135	−	0.874439i	$-0.661229\pi$
$912$		0			0
$913$	−0.889108	+	6.18388i	−0.0294252	+	0.204657i
$914$		0			0
$915$	−4.94010	+	3.17481i	−0.163315	+	0.104956i
$916$		0			0
$917$	15.8460	+	4.65281i	0.523281	+	0.153649i
$918$		0			0
$919$	4.17260			0.137641			0.0688206	−	0.997629i	$-0.478076\pi$
$919$	4.17260			0.137641			0.0688206	+	0.997629i	$0.478076\pi$
$920$		0			0
$921$	16.8074			0.553822
$922$		0			0
$923$	26.6445	+	7.82354i	0.877015	+	0.257515i
$924$		0			0
$925$	−23.6696	+	15.2115i	−0.778250	+	0.500151i
$926$		0			0
$927$	−0.281874	+	1.96048i	−0.00925797	+	0.0643906i
$928$		0			0
$929$	−26.9869	−	17.3434i	−0.885411	−	0.569019i	0.0170189	−	0.999855i	$-0.494582\pi$
$929$	−26.9869	−	17.3434i	−0.885411	−	0.569019i	−0.902430	+	0.430836i	$0.858219\pi$
$930$		0			0
$931$	−0.187363	−	0.410268i	−0.00614057	−	0.0134460i
$932$		0			0
$933$	2.86341	+	19.9155i	0.0937438	+	0.652003i
$934$		0			0
$935$	0.0710488	−	0.0208618i	0.00232354	−	0.000682254i
$936$		0			0
$937$	38.1778	−	44.0596i	1.24722	−	1.43936i	0.392923	−	0.919572i	$-0.371464\pi$
$937$	38.1778	−	44.0596i	1.24722	−	1.43936i	0.854293	−	0.519792i	$-0.173991\pi$
$938$		0			0
$939$	10.7463	+	12.4019i	0.350692	+	0.404720i
$940$		0			0
$941$	5.60369	−	12.2704i	0.182675	−	0.400003i	−0.796035	−	0.605251i	$-0.793073\pi$
$941$	5.60369	−	12.2704i	0.182675	−	0.400003i	0.978710	+	0.205248i	$0.0658001\pi$
$942$		0			0
$943$	35.5186	+	26.3612i	1.15664	+	0.858438i
$944$		0			0
$945$	0.977059	−	2.13946i	0.0317837	−	0.0695966i
$946$		0			0
$947$	34.3865	+	39.6842i	1.11741	+	1.28956i	0.952933	+	0.303182i	$0.0980489\pi$
$947$	34.3865	+	39.6842i	1.11741	+	1.28956i	0.164479	+	0.986381i	$0.447406\pi$
$948$		0			0
$949$	−33.1326	+	38.2370i	−1.07553	+	1.24123i
$950$		0			0
$951$	2.28586	−	0.671190i	0.0741242	−	0.0217648i
$952$		0			0
$953$	−3.54837	−	24.6795i	−0.114943	−	0.799446i	−0.962992	−	0.269529i	$-0.913132\pi$
$953$	−3.54837	−	24.6795i	−0.114943	−	0.799446i	0.848049	−	0.529917i	$-0.177777\pi$
$954$		0			0
$955$	1.00306	+	2.19641i	0.0324584	+	0.0710740i
$956$		0			0
$957$	−1.75649	−	1.12883i	−0.0567792	−	0.0364898i
$958$		0			0
$959$	0.145766	−	1.01382i	0.00470702	−	0.0327381i
$960$		0			0
$961$	−22.2774	+	14.3168i	−0.718625	+	0.461833i
$962$		0			0
$963$	10.9873	+	3.22616i	0.354061	+	0.103962i
$964$		0			0
$965$	−12.2821			−0.395374
$966$		0			0
$967$	−37.7705			−1.21462			−0.607309	−	0.794466i	$-0.707751\pi$
$967$	−37.7705			−1.21462			−0.607309	+	0.794466i	$0.707751\pi$
$968$		0			0
$969$	−0.0261282	−	0.00767194i	−0.000839360	−	0.000246458i
$970$		0			0
$971$	1.13064	−	0.726615i	0.0362838	−	0.0233182i	−0.522373	−	0.852717i	$-0.674953\pi$
$971$	1.13064	−	0.726615i	0.0362838	−	0.0233182i	0.558657	+	0.829399i	$0.311317\pi$
$972$		0			0
$973$	3.44187	−	23.9387i	0.110341	−	0.767441i
$974$		0			0
$975$	−16.5618	−	10.6437i	−0.530404	−	0.340870i
$976$		0			0
$977$	−12.2390	−	26.7996i	−0.391559	−	0.857396i	−0.998057	−	0.0623101i	$-0.980153\pi$
$977$	−12.2390	−	26.7996i	−0.391559	−	0.857396i	0.606497	−	0.795085i	$-0.292574\pi$
$978$		0			0
$979$	0.925667	+	6.43816i	0.0295845	+	0.205764i
$980$		0			0
$981$	11.5500	−	3.39139i	0.368763	−	0.108279i
$982$		0			0
$983$	1.90681	−	2.20057i	0.0608177	−	0.0701874i	−0.724525	−	0.689248i	$-0.757941\pi$
$983$	1.90681	−	2.20057i	0.0608177	−	0.0701874i	0.785343	+	0.619061i	$0.212486\pi$
$984$		0			0
$985$	−13.3117	−	15.3626i	−0.424147	−	0.489492i
$986$		0			0
$987$	1.81620	−	3.97693i	0.0578104	−	0.126587i
$988$		0			0
$989$	−3.96905	−	52.4558i	−0.126208	−	1.66800i
$990$		0			0
$991$	−0.796678	+	1.74448i	−0.0253073	+	0.0554153i	−0.921864	−	0.387515i	$-0.873334\pi$
$991$	−0.796678	+	1.74448i	−0.0253073	+	0.0554153i	0.896556	+	0.442930i	$0.146061\pi$
$992$		0			0
$993$	5.18602	+	5.98499i	0.164573	+	0.189928i
$994$		0			0
$995$	−7.70074	+	8.88713i	−0.244130	+	0.281741i
$996$		0			0
$997$	−40.5948	+	11.9197i	−1.28565	+	0.377501i	−0.851982	−	0.523571i	$-0.824600\pi$
$997$	−40.5948	+	11.9197i	−1.28565	+	0.377501i	−0.433669	+	0.901072i	$0.642781\pi$
$998$		0			0
$999$	1.02096	+	7.10090i	0.0323016	+	0.224663i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.c.121.2	yes	30
23.4	even	11	inner	552.2.q.c.73.2	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.c.73.2	✓	30	23.4	even	11	inner
552.2.q.c.121.2	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)

\(f(q)\)	\(=\)	\(q+(0.959493 + 0.281733i) q^{3} +(-0.873450 + 0.561333i) q^{5} +(-0.322387 + 2.24225i) q^{7} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(0.959493 + 0.281733i) q^{3} +(-0.873450 + 0.561333i) q^{5} +(-0.322387 + 2.24225i) q^{7} +(0.841254 + 0.540641i) q^{9} +(-0.262635 - 0.575091i) q^{11} +(0.714374 + 4.96858i) q^{13} +(-0.996215 + 0.292515i) q^{15} +(0.0738723 - 0.0852532i) q^{17} +(-0.158083 - 0.182437i) q^{19} +(-0.941043 + 2.06060i) q^{21} +(1.69447 + 4.48651i) q^{23} +(-1.62925 + 3.56757i) q^{25} +(0.654861 + 0.755750i) q^{27} +(2.16270 - 2.49589i) q^{29} +(-2.03964 + 0.598893i) q^{31} +(-0.0899748 - 0.625788i) q^{33} +(-0.977059 - 2.13946i) q^{35} +(6.03509 + 3.87852i) q^{37} +(-0.714374 + 4.96858i) q^{39} +(7.75891 - 4.98635i) q^{41} +(-10.5247 - 3.09034i) q^{43} -1.03827 q^{45} -1.92999 q^{47} +(1.79270 + 0.526384i) q^{49} +(0.0948986 - 0.0609876i) q^{51} +(0.0970469 - 0.674976i) q^{53} +(0.552216 + 0.354888i) q^{55} +(-0.100281 - 0.219584i) q^{57} +(-1.10781 - 7.70497i) q^{59} +(5.42674 - 1.59344i) q^{61} +(-1.48346 + 1.71200i) q^{63} +(-3.41299 - 3.93881i) q^{65} +(0.326061 - 0.713975i) q^{67} +(0.361840 + 4.78216i) q^{69} +(2.29812 - 5.03218i) q^{71} +(6.60054 + 7.61743i) q^{73} +(-2.56836 + 2.96404i) q^{75} +(1.37417 - 0.403492i) q^{77} +(-0.352464 - 2.45144i) q^{79} +(0.415415 + 0.909632i) q^{81} +(-8.31306 - 5.34248i) q^{83} +(-0.0166684 + 0.115931i) q^{85} +(2.77827 - 1.78549i) q^{87} +(-9.87134 - 2.89849i) q^{89} -11.3711 q^{91} -2.12575 q^{93} +(0.240485 + 0.0706129i) q^{95} +(-2.68434 + 1.72512i) q^{97} +(0.0899748 - 0.625788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9}+O(q^{10}) \) 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

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