LMFDB - Embedded newform 572.2.e.a.131.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(131,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("572.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.e (of order $2$, degree $1$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.342102016.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 $ x^8 + x^6 + 4x^4 + 4x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.2
Root			$-1.17915 - 0.780776i$ of defining polynomial
Character	$\chi$	$=$	572.131
Dual form			572.2.e.a.131.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17915 + 0.780776i) q^{2} +(0.780776 - 1.84130i) q^{4} -3.56155 q^{5} -4.05444 q^{7} +(0.516994 + 2.78078i) q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+(-1.17915 + 0.780776i) q^{2} +(0.780776 - 1.84130i) q^{4} -3.56155 q^{5} -4.05444 q^{7} +(0.516994 + 2.78078i) q^{8} +3.00000 q^{9} +(4.19960 - 2.78078i) q^{10} +(0.848071 - 3.20636i) q^{11} -1.00000i q^{13} +(4.78078 - 3.16561i) q^{14} +(-2.78078 - 2.87529i) q^{16} +5.12311i q^{17} +(-3.53744 + 2.34233i) q^{18} +4.34475 q^{19} +(-2.78078 + 6.55789i) q^{20} +(1.50345 + 4.44293i) q^{22} +2.35829i q^{23} +7.68466 q^{25} +(0.780776 + 1.17915i) q^{26} +(-3.16561 + 7.46543i) q^{28} +6.68466i q^{29} -0.371834i q^{31} +(5.52390 + 1.21922i) q^{32} +(-4.00000 - 6.04090i) q^{34} +14.4401 q^{35} +(2.34233 - 5.52390i) q^{36} +8.24621 q^{37} +(-5.12311 + 3.39228i) q^{38} +(-1.84130 - 9.90388i) q^{40} -4.43845i q^{41} +1.03399 q^{43} +(-5.24173 - 4.06501i) q^{44} -10.6847 q^{45} +(-1.84130 - 2.78078i) q^{46} +6.41273i q^{47} +9.43845 q^{49} +(-9.06134 + 6.00000i) q^{50} +(-1.84130 - 0.780776i) q^{52} +12.2462 q^{53} +(-3.02045 + 11.4196i) q^{55} +(-2.09612 - 11.2745i) q^{56} +(-5.21922 - 7.88220i) q^{58} -4.05444i q^{59} -12.6847i q^{61} +(0.290319 + 0.438447i) q^{62} -12.1633 q^{63} +(-7.46543 + 2.87529i) q^{64} +3.56155i q^{65} +14.0683i q^{67} +(9.43318 + 4.00000i) q^{68} +(-17.0270 + 11.2745i) q^{70} +13.7779i q^{71} +(1.55098 + 8.34233i) q^{72} -5.80776i q^{73} +(-9.72350 + 6.43845i) q^{74} +(3.39228 - 8.00000i) q^{76} +(-3.43845 + 13.0000i) q^{77} +1.32431 q^{79} +(9.90388 + 10.2405i) q^{80} +9.00000 q^{81} +(3.46543 + 5.23358i) q^{82} +1.69614 q^{83} -18.2462i q^{85} +(-1.21922 + 0.807313i) q^{86} +(9.35463 + 0.700624i) q^{88} -2.00000 q^{89} +(12.5988 - 8.34233i) q^{90} +4.05444i q^{91} +(4.34233 + 1.84130i) q^{92} +(-5.00691 - 7.56155i) q^{94} -15.4741 q^{95} -4.24621 q^{97} +(-11.1293 + 7.36932i) q^{98} +(2.54421 - 9.61909i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} - 12 q^{5} + 24 q^{9}+O(q^{10}) $ 8 * q - 2 * q^4 - 12 * q^5 + 24 * q^9	$ 8 q - 2 q^{4} - 12 q^{5} + 24 q^{9} + 30 q^{14} - 14 q^{16} - 14 q^{20} - 8 q^{22} + 12 q^{25} - 2 q^{26} - 32 q^{34} - 6 q^{36} - 8 q^{38} - 6 q^{44} - 36 q^{45} + 92 q^{49} + 32 q^{53} - 58 q^{56} - 50 q^{58} - 2 q^{64} - 62 q^{70} - 44 q^{77} + 38 q^{80} + 72 q^{81} - 30 q^{82} - 18 q^{86} + 20 q^{88} - 16 q^{89} + 10 q^{92} + 32 q^{97}+O(q^{100}) $ 8 * q - 2 * q^4 - 12 * q^5 + 24 * q^9 + 30 * q^14 - 14 * q^16 - 14 * q^20 - 8 * q^22 + 12 * q^25 - 2 * q^26 - 32 * q^34 - 6 * q^36 - 8 * q^38 - 6 * q^44 - 36 * q^45 + 92 * q^49 + 32 * q^53 - 58 * q^56 - 50 * q^58 - 2 * q^64 - 62 * q^70 - 44 * q^77 + 38 * q^80 + 72 * q^81 - 30 * q^82 - 18 * q^86 + 20 * q^88 - 16 * q^89 + 10 * q^92 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.17915	+	0.780776i	−0.833783	+	0.552092i
$2$	−1.17915	+	0.780776i	−0.833783	+	0.552092i
$3$		0			0		1.00000			$0$
$3$		0			0		−1.00000			$\pi$
$4$	0.780776	−	1.84130i	0.390388	−	0.920650i
$5$	−3.56155			−1.59277			−0.796387	−	0.604787i	$-0.793258\pi$
$5$	−3.56155			−1.59277			−0.796387	+	0.604787i	$0.793258\pi$
$6$		0			0
$7$	−4.05444			−1.53243			−0.766216	−	0.642583i	$-0.777863\pi$
$7$	−4.05444			−1.53243			−0.766216	+	0.642583i	$0.777863\pi$
$8$	0.516994	+	2.78078i	0.182785	+	0.983153i
$9$	3.00000			1.00000
$10$	4.19960	−	2.78078i	1.32803	−	0.879359i
$11$	0.848071	−	3.20636i	0.255703	−	0.966755i
$11$	0.848071	−	3.20636i	0.255703	−	0.966755i
$12$		0			0
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	4.78078	−	3.16561i	1.27772	−	0.846044i
$15$		0			0
$16$	−2.78078	−	2.87529i	−0.695194	−	0.718822i
$17$			5.12311i			1.24254i	0.783598	+	0.621268i	$0.213382\pi$
$17$			5.12311i			1.24254i	−0.783598	+	0.621268i	$0.786618\pi$
$18$	−3.53744	+	2.34233i	−0.833783	+	0.552092i
$19$	4.34475			0.996755			0.498378	−	0.866960i	$-0.333929\pi$
$19$	4.34475			0.996755			0.498378	+	0.866960i	$0.333929\pi$
$20$	−2.78078	+	6.55789i	−0.621801	+	1.46639i
$21$		0			0
$22$	1.50345	+	4.44293i	0.320537	+	0.947236i
$23$			2.35829i			0.491738i	0.969303	+	0.245869i	$0.0790734\pi$
$23$			2.35829i			0.491738i	−0.969303	+	0.245869i	$0.920927\pi$
$24$		0			0
$25$	7.68466			1.53693
$26$	0.780776	+	1.17915i	0.153123	+	0.231250i
$27$		0			0
$28$	−3.16561	+	7.46543i	−0.598244	+	1.41083i
$29$			6.68466i			1.24131i	0.784084	+	0.620655i	$0.213133\pi$
$29$			6.68466i			1.24131i	−0.784084	+	0.620655i	$0.786867\pi$
$30$		0			0
$31$		−	0.371834i		−	0.0667834i	−0.999442	−	0.0333917i	$-0.989369\pi$
$31$		−	0.371834i		−	0.0667834i	0.999442	−	0.0333917i	$-0.0106309\pi$
$32$	5.52390	+	1.21922i	0.976497	+	0.215530i
$33$		0			0
$34$	−4.00000	−	6.04090i	−0.685994	−	1.03601i
$35$	14.4401			2.44082
$36$	2.34233	−	5.52390i	0.390388	−	0.920650i
$37$	8.24621			1.35567			0.677834	−	0.735215i	$-0.262919\pi$
$37$	8.24621			1.35567			0.677834	+	0.735215i	$0.262919\pi$
$38$	−5.12311	+	3.39228i	−0.831077	+	0.550301i
$39$		0			0
$40$	−1.84130	−	9.90388i	−0.291135	−	1.56594i
$41$		−	4.43845i		−	0.693169i	−0.938019	−	0.346584i	$-0.887341\pi$
$41$		−	4.43845i		−	0.693169i	0.938019	−	0.346584i	$-0.112659\pi$
$42$		0			0
$43$	1.03399			0.157682			0.0788408	−	0.996887i	$-0.474878\pi$
$43$	1.03399			0.157682			0.0788408	+	0.996887i	$0.474878\pi$
$44$	−5.24173	−	4.06501i	−0.790220	−	0.612823i
$45$	−10.6847			−1.59277
$46$	−1.84130	−	2.78078i	−0.271485	−	0.410003i
$47$			6.41273i			0.935393i	0.883889	+	0.467696i	$0.154916\pi$
$47$			6.41273i			0.935393i	−0.883889	+	0.467696i	$0.845084\pi$
$48$		0			0
$49$	9.43845			1.34835
$50$	−9.06134	+	6.00000i	−1.28147	+	0.848528i
$51$		0			0
$52$	−1.84130	−	0.780776i	−0.255342	−	0.108274i
$53$	12.2462			1.68215			0.841073	−	0.540921i	$-0.181924\pi$
$53$	12.2462			1.68215			0.841073	+	0.540921i	$0.181924\pi$
$54$		0			0
$55$	−3.02045	+	11.4196i	−0.407277	+	1.53982i
$56$	−2.09612	−	11.2745i	−0.280106	−	1.50662i
$57$		0			0
$58$	−5.21922	−	7.88220i	−0.685318	−	1.03498i
$59$		−	4.05444i		−	0.527843i	−0.964544	−	0.263921i	$-0.914984\pi$
$59$		−	4.05444i		−	0.527843i	0.964544	−	0.263921i	$-0.0850159\pi$
$60$		0			0
$61$		−	12.6847i		−	1.62410i	−0.583585	−	0.812052i	$-0.698351\pi$
$61$		−	12.6847i		−	1.62410i	0.583585	−	0.812052i	$-0.301649\pi$
$62$	0.290319	+	0.438447i	0.0368706	+	0.0556828i
$63$	−12.1633			−1.53243
$64$	−7.46543	+	2.87529i	−0.933179	+	0.359411i
$65$			3.56155i			0.441756i
$66$		0			0
$67$			14.0683i			1.71871i	0.511379	+	0.859355i	$0.329135\pi$
$67$			14.0683i			1.71871i	−0.511379	+	0.859355i	$0.670865\pi$
$68$	9.43318	+	4.00000i	1.14394	+	0.485071i
$69$		0			0
$70$	−17.0270	+	11.2745i	−2.03511	+	1.34756i
$71$			13.7779i			1.63514i	0.575829	+	0.817570i	$0.304679\pi$
$71$			13.7779i			1.63514i	−0.575829	+	0.817570i	$0.695321\pi$
$72$	1.55098	+	8.34233i	0.182785	+	0.983153i
$73$		−	5.80776i		−	0.679747i	−0.940471	−	0.339874i	$-0.889616\pi$
$73$		−	5.80776i		−	0.679747i	0.940471	−	0.339874i	$-0.110384\pi$
$74$	−9.72350	+	6.43845i	−1.13033	+	0.748454i
$75$		0			0
$76$	3.39228	−	8.00000i	0.389121	−	0.917663i
$77$	−3.43845	+	13.0000i	−0.391847	+	1.48149i
$78$		0			0
$79$	1.32431			0.148996			0.0744981	−	0.997221i	$-0.476265\pi$
$79$	1.32431			0.148996			0.0744981	+	0.997221i	$0.476265\pi$
$80$	9.90388	+	10.2405i	1.10729	+	1.14492i
$81$	9.00000			1.00000
$82$	3.46543	+	5.23358i	0.382693	+	0.577953i
$83$	1.69614			0.186176			0.0930878	−	0.995658i	$-0.470326\pi$
$83$	1.69614			0.186176			0.0930878	+	0.995658i	$0.470326\pi$
$84$		0			0
$85$		−	18.2462i		−	1.97908i
$86$	−1.21922	+	0.807313i	−0.131472	+	0.0870548i
$87$		0			0
$88$	9.35463	+	0.700624i	0.997207	+	0.0746867i
$89$	−2.00000			−0.212000			−0.106000	−	0.994366i	$-0.533804\pi$
$89$	−2.00000			−0.212000			−0.106000	+	0.994366i	$0.533804\pi$
$90$	12.5988	−	8.34233i	1.32803	−	0.879359i
$91$			4.05444i			0.425020i
$92$	4.34233	+	1.84130i	0.452719	+	0.191969i
$93$		0			0
$94$	−5.00691	−	7.56155i	−0.516423	−	0.779915i
$95$	−15.4741			−1.58761
$96$		0			0
$97$	−4.24621			−0.431137			−0.215569	−	0.976489i	$-0.569161\pi$
$97$	−4.24621			−0.431137			−0.215569	+	0.976489i	$0.569161\pi$
$98$	−11.1293	+	7.36932i	−1.12423	+	0.744413i
$99$	2.54421	−	9.61909i	0.255703	−	0.966755i
$100$	6.00000	−	14.1498i	0.600000	−	1.41498i
$101$			4.87689i			0.485269i	0.970118	+	0.242635i	$0.0780116\pi$
$101$			4.87689i			0.485269i	−0.970118	+	0.242635i	$0.921988\pi$
$102$		0			0
$103$		−	16.5081i		−	1.62659i	−0.581853	−	0.813294i	$-0.697672\pi$
$103$		−	16.5081i		−	1.62659i	0.581853	−	0.813294i	$-0.302328\pi$
$104$	2.78078	−	0.516994i	0.272678	−	0.0506954i
$105$		0			0
$106$	−14.4401	+	9.56155i	−1.40255	+	0.928700i
$107$	14.4401			1.39598			0.697988	−	0.716110i	$-0.254079\pi$
$107$	14.4401			1.39598			0.697988	+	0.716110i	$0.254079\pi$
$108$		0			0
$109$			2.00000i			0.191565i	0.995402	+	0.0957826i	$0.0305354\pi$
$109$			2.00000i			0.191565i	−0.995402	+	0.0957826i	$0.969465\pi$
$110$	−5.35463	−	15.8237i	−0.510544	−	1.50873i
$111$		0			0
$112$	11.2745	+	11.6577i	1.06534	+	1.10155i
$113$	−4.68466			−0.440696			−0.220348	−	0.975421i	$-0.570719\pi$
$113$	−4.68466			−0.440696			−0.220348	+	0.975421i	$0.570719\pi$
$114$		0			0
$115$		−	8.39919i		−	0.783229i
$116$	12.3085	+	5.21922i	1.14281	+	0.484593i
$117$		−	3.00000i		−	0.277350i
$118$	3.16561	+	4.78078i	0.291418	+	0.440106i
$119$		−	20.7713i		−	1.90410i
$120$		0			0
$121$	−9.56155	−	5.43845i	−0.869232	−	0.494404i
$122$	9.90388	+	14.9571i	0.896655	+	1.35415i
$123$		0			0
$124$	−0.684658	−	0.290319i	−0.0614841	−	0.0260714i
$125$	−9.56155			−0.855211
$126$	14.3423	−	9.49682i	1.27772	−	0.846044i
$127$	−19.4470			−1.72564			−0.862821	−	0.505510i	$-0.831304\pi$
$127$	−19.4470			−1.72564			−0.862821	+	0.505510i	$0.831304\pi$
$128$	6.55789	−	9.21922i	0.579641	−	0.814872i
$129$		0			0
$130$	−2.78078	−	4.19960i	−0.243890	−	0.368329i
$131$	−7.65552			−0.668866			−0.334433	−	0.942420i	$-0.608545\pi$
$131$	−7.65552			−0.668866			−0.334433	+	0.942420i	$0.608545\pi$
$132$		0			0
$133$	−17.6155			−1.52746
$134$	−10.9842	−	16.5885i	−0.948887	−	1.43303i
$135$		0			0
$136$	−14.2462	+	2.64861i	−1.22160	+	0.227117i
$137$	3.36932			0.287860			0.143930	−	0.989588i	$-0.454026\pi$
$137$	3.36932			0.287860			0.143930	+	0.989588i	$0.454026\pi$
$138$		0			0
$139$	5.46026			0.463133			0.231566	−	0.972819i	$-0.425615\pi$
$139$	5.46026			0.463133			0.231566	+	0.972819i	$0.425615\pi$
$140$	11.2745	−	26.5885i	0.952867	−	2.24714i
$141$		0			0
$142$	−10.7575	−	16.2462i	−0.902748	−	1.36335i
$143$	−3.20636	−	0.848071i	−0.268130	−	0.0709192i
$144$	−8.34233	−	8.62586i	−0.695194	−	0.718822i
$145$		−	23.8078i		−	1.97713i
$146$	4.53457	+	6.84821i	0.375283	+	0.566762i
$147$		0			0
$148$	6.43845	−	15.1838i	0.529237	−	1.24810i
$149$			14.4924i			1.18727i	0.804736	+	0.593633i	$0.202307\pi$
$149$			14.4924i			1.18727i	−0.804736	+	0.593633i	$0.797693\pi$
$150$		0			0
$151$	21.1431			1.72060			0.860302	−	0.509785i	$-0.170275\pi$
$151$	21.1431			1.72060			0.860302	+	0.509785i	$0.170275\pi$
$152$	2.24621	+	12.0818i	0.182192	+	0.979963i
$153$			15.3693i			1.24254i
$154$	−6.09566	−	18.0136i	−0.491202	−	1.45158i
$155$			1.32431i			0.106371i
$156$		0			0
$157$	8.00000			0.638470			0.319235	−	0.947676i	$-0.396574\pi$
$157$	8.00000			0.638470			0.319235	+	0.947676i	$0.396574\pi$
$158$	−1.56155	+	1.03399i	−0.124230	+	0.0822596i
$159$		0			0
$160$	−19.6737	−	4.34233i	−1.55534	−	0.343291i
$161$		−	9.56155i		−	0.753556i
$162$	−10.6123	+	7.02699i	−0.833783	+	0.552092i
$163$		−	1.98646i		−	0.155592i	−0.996969	−	0.0777958i	$-0.975212\pi$
$163$		−	1.98646i		−	0.155592i	0.996969	−	0.0777958i	$-0.0247882\pi$
$164$	−8.17252	−	3.46543i	−0.638166	−	0.270605i
$165$		0			0
$166$	−2.00000	+	1.32431i	−0.155230	+	0.102786i
$167$	5.37874			0.416220			0.208110	−	0.978105i	$-0.433269\pi$
$167$	5.37874			0.416220			0.208110	+	0.978105i	$0.433269\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	14.2462	+	21.5150i	1.09263	+	1.65012i
$171$	13.0343			0.996755
$172$	0.807313	−	1.90388i	0.0615570	−	0.145170i
$173$		−	3.80776i		−	0.289499i	−0.989468	−	0.144749i	$-0.953762\pi$
$173$		−	3.80776i		−	0.289499i	0.989468	−	0.144749i	$-0.0462376\pi$
$174$		0			0
$175$	−31.1570			−2.35524
$176$	−11.5775	+	6.47774i	−0.872688	+	0.488278i
$177$		0			0
$178$	2.35829	−	1.56155i	0.176762	−	0.117043i
$179$			20.7713i			1.55252i	0.630413	+	0.776260i	$0.282886\pi$
$179$			20.7713i			1.55252i	−0.630413	+	0.776260i	$0.717114\pi$
$180$	−8.34233	+	19.6737i	−0.621801	+	1.46639i
$181$	18.2462			1.35623			0.678115	−	0.734956i	$-0.262797\pi$
$181$	18.2462			1.35623			0.678115	+	0.734956i	$0.262797\pi$
$182$	−3.16561	−	4.78078i	−0.234650	−	0.354375i
$183$		0			0
$184$	−6.55789	+	1.21922i	−0.483454	+	0.0898824i
$185$	−29.3693			−2.15928
$186$		0			0
$187$	16.4265	+	4.34475i	1.20123	+	0.317720i
$188$	11.8078	+	5.00691i	0.861170	+	0.365166i
$189$		0			0
$190$	18.2462	−	12.0818i	1.32372	−	0.876505i
$191$		−	13.1158i		−	0.949024i	−0.880249	−	0.474512i	$-0.842624\pi$
$191$		−	13.1158i		−	0.949024i	0.880249	−	0.474512i	$-0.157376\pi$
$192$		0			0
$193$			12.2462i			0.881502i	0.897630	+	0.440751i	$0.145288\pi$
$193$			12.2462i			0.881502i	−0.897630	+	0.440751i	$0.854712\pi$
$194$	5.00691	−	3.31534i	0.359475	−	0.238028i
$195$		0			0
$196$	7.36932	−	17.3790i	0.526380	−	1.24136i
$197$		−	19.3693i		−	1.38001i	−0.723806	−	0.690003i	$-0.757609\pi$
$197$		−	19.3693i		−	1.38001i	0.723806	−	0.690003i	$-0.242391\pi$
$198$	4.51036	+	13.3288i	0.320537	+	0.947236i
$199$			11.7915i			0.835875i	0.908476	+	0.417938i	$0.137247\pi$
$199$			11.7915i			0.835875i	−0.908476	+	0.417938i	$0.862753\pi$
$200$	3.97292	+	21.3693i	0.280928	+	1.51104i
$201$		0			0
$202$	−3.80776	−	5.75058i	−0.267913	−	0.404609i
$203$		−	27.1025i		−	1.90222i
$204$		0			0
$205$			15.8078i			1.10406i
$206$	12.8891	+	19.4654i	0.898026	+	1.35622i
$207$			7.07488i			0.491738i
$208$	−2.87529	+	2.78078i	−0.199365	+	0.192812i
$209$	3.68466	−	13.9309i	0.254873	−	0.963618i
$210$		0			0
$211$	−5.46026			−0.375900			−0.187950	−	0.982179i	$-0.560184\pi$
$211$	−5.46026			−0.375900			−0.187950	+	0.982179i	$0.560184\pi$
$212$	9.56155	−	22.5490i	0.656690	−	1.54867i
$213$		0			0
$214$	−17.0270	+	11.2745i	−1.16394	+	0.770707i
$215$	−3.68260			−0.251151
$216$		0			0
$217$			1.50758i			0.102341i
$218$	−1.56155	−	2.35829i	−0.105762	−	0.159724i
$219$		0			0
$220$	18.6687	+	14.4777i	1.25864	+	0.976089i
$221$	5.12311			0.344617
$222$		0			0
$223$			11.8730i			0.795074i	0.917586	+	0.397537i	$0.130135\pi$
$223$			11.8730i			0.795074i	−0.917586	+	0.397537i	$0.869865\pi$
$224$	−22.3963	−	4.94326i	−1.49642	−	0.330286i
$225$	23.0540			1.53693
$226$	5.52390	−	3.65767i	0.367444	−	0.243305i
$227$	−13.0343			−0.865115			−0.432557	−	0.901606i	$-0.642389\pi$
$227$	−13.0343			−0.865115			−0.432557	+	0.901606i	$0.642389\pi$
$228$		0			0
$229$	25.8078			1.70543			0.852713	−	0.522380i	$-0.174956\pi$
$229$	25.8078			1.70543			0.852713	+	0.522380i	$0.174956\pi$
$230$	6.55789	+	9.90388i	0.432414	+	0.653043i
$231$		0			0
$232$	−18.5885	+	3.45593i	−1.22040	+	0.226893i
$233$			0.876894i			0.0574473i	0.999587	+	0.0287236i	$0.00914427\pi$
$233$			0.876894i			0.0574473i	−0.999587	+	0.0287236i	$0.990856\pi$
$234$	2.34233	+	3.53744i	0.153123	+	0.231250i
$235$		−	22.8393i		−	1.48987i
$236$	−7.46543	−	3.16561i	−0.485958	−	0.206064i
$237$		0			0
$238$	16.2177	+	24.4924i	1.05124	+	1.58761i
$239$	−0.662153			−0.0428311			−0.0214156	−	0.999771i	$-0.506817\pi$
$239$	−0.662153			−0.0428311			−0.0214156	+	0.999771i	$0.506817\pi$
$240$		0			0
$241$			30.4924i			1.96419i	0.188387	+	0.982095i	$0.439674\pi$
$241$			30.4924i			1.96419i	−0.188387	+	0.982095i	$0.560326\pi$
$242$	15.5207	−	1.05270i	0.997708	−	0.0676704i
$243$		0			0
$244$	−23.3563	−	9.90388i	−1.49523	−	0.634031i
$245$	−33.6155			−2.14762
$246$		0			0
$247$		−	4.34475i		−	0.276450i
$248$	1.03399	−	0.192236i	0.0656583	−	0.0122070i
$249$		0			0
$250$	11.2745	−	7.46543i	0.713061	−	0.472156i
$251$			14.8934i			0.940065i	0.882649	+	0.470033i	$0.155758\pi$
$251$			14.8934i			0.940065i	−0.882649	+	0.470033i	$0.844242\pi$
$252$	−9.49682	+	22.3963i	−0.598244	+	1.41083i
$253$	7.56155	+	2.00000i	0.475391	+	0.125739i
$254$	22.9309	−	15.1838i	1.43881	−	0.952713i
$255$		0			0
$256$	−0.534565	+	15.9911i	−0.0334103	+	0.999442i
$257$	−10.1922			−0.635774			−0.317887	−	0.948129i	$-0.602973\pi$
$257$	−10.1922			−0.635774			−0.317887	+	0.948129i	$0.602973\pi$
$258$		0			0
$259$	−33.4337			−2.07747
$260$	6.55789	+	2.78078i	0.406703	+	0.172456i
$261$			20.0540i			1.24131i
$262$	9.02699	−	5.97725i	0.557689	−	0.369276i
$263$	−2.81164			−0.173373			−0.0866867	−	0.996236i	$-0.527628\pi$
$263$	−2.81164			−0.173373			−0.0866867	+	0.996236i	$0.527628\pi$
$264$		0			0
$265$	−43.6155			−2.67928
$266$	20.7713	−	13.7538i	1.27357	−	0.843299i
$267$		0			0
$268$	25.9039	+	10.9842i	1.58233	+	0.670964i
$269$	−11.1231			−0.678188			−0.339094	−	0.940753i	$-0.610120\pi$
$269$	−11.1231			−0.678188			−0.339094	+	0.940753i	$0.610120\pi$
$270$		0			0
$271$	17.7509			1.07829			0.539144	−	0.842214i	$-0.318748\pi$
$271$	17.7509			1.07829			0.539144	+	0.842214i	$0.318748\pi$
$272$	14.7304	−	14.2462i	0.893162	−	0.863803i
$273$		0			0
$274$	−3.97292	+	2.63068i	−0.240013	+	0.158925i
$275$	6.51713	−	24.6398i	0.392998	−	1.48584i
$276$		0			0
$277$			5.56155i			0.334161i	0.985943	+	0.167081i	$0.0534340\pi$
$277$			5.56155i			0.334161i	−0.985943	+	0.167081i	$0.946566\pi$
$278$	−6.43845	+	4.26324i	−0.386152	+	0.255692i
$279$		−	1.11550i		−	0.0667834i
$280$	7.46543	+	40.1547i	0.446145	+	2.39970i
$281$			0.438447i			0.0261556i	0.999914	+	0.0130778i	$0.00416291\pi$
$281$			0.438447i			0.0261556i	−0.999914	+	0.0130778i	$0.995837\pi$
$282$		0			0
$283$	5.16994			0.307321			0.153660	−	0.988124i	$-0.450894\pi$
$283$	5.16994			0.307321			0.153660	+	0.988124i	$0.450894\pi$
$284$	25.3693	+	10.7575i	1.50539	+	0.638339i
$285$		0			0
$286$	4.44293	−	1.50345i	0.262716	−	0.0889011i
$287$			17.9954i			1.06223i
$288$	16.5717	+	3.65767i	0.976497	+	0.215530i
$289$	−9.24621			−0.543895
$290$	18.5885	+	28.0729i	1.09156	+	1.64850i
$291$		0			0
$292$	−10.6938	−	4.53457i	−0.625810	−	0.265365i
$293$		−	10.8769i		−	0.635435i	−0.948185	−	0.317717i	$-0.897084\pi$
$293$		−	10.8769i		−	0.635435i	0.948185	−	0.317717i	$-0.102916\pi$
$294$		0			0
$295$			14.4401i			0.840734i
$296$	4.26324	+	22.9309i	0.247796	+	1.33283i
$297$		0			0
$298$	−11.3153	−	17.0887i	−0.655480	−	0.989922i
$299$	2.35829			0.136384
$300$		0			0
$301$	−4.19224			−0.241636
$302$	−24.9309	+	16.5081i	−1.43461	+	0.949932i
$303$		0			0
$304$	−12.0818	−	12.4924i	−0.692938	−	0.716490i
$305$			45.1771i			2.58683i
$306$	−12.0000	−	18.1227i	−0.685994	−	1.03601i
$307$	15.1022			0.861930			0.430965	−	0.902369i	$-0.358173\pi$
$307$	15.1022			0.861930			0.430965	+	0.902369i	$0.358173\pi$
$308$	21.2523	+	16.4813i	1.21096	+	0.939110i
$309$		0			0
$310$	−1.03399	−	1.56155i	−0.0587265	−	0.0886902i
$311$			2.81164i			0.159434i	0.996818	+	0.0797168i	$0.0254016\pi$
$311$			2.81164i			0.159434i	−0.996818	+	0.0797168i	$0.974598\pi$
$312$		0			0
$313$	−19.3153			−1.09177			−0.545884	−	0.837861i	$-0.683806\pi$
$313$	−19.3153			−1.09177			−0.545884	+	0.837861i	$0.683806\pi$
$314$	−9.43318	+	6.24621i	−0.532345	+	0.352494i
$315$	43.3203			2.44082
$316$	1.03399	−	2.43845i	0.0581663	−	0.137173i
$317$	−11.1771			−0.627767			−0.313884	−	0.949461i	$-0.601630\pi$
$317$	−11.1771			−0.627767			−0.313884	+	0.949461i	$0.601630\pi$
$318$		0			0
$319$	21.4335	+	5.66906i	1.20004	+	0.317407i
$320$	26.5885	−	10.2405i	1.48634	−	0.572461i
$321$		0			0
$322$	7.46543	+	11.2745i	0.416032	+	0.628302i
$323$			22.2586i			1.23850i
$324$	7.02699	−	16.5717i	0.390388	−	0.920650i
$325$		−	7.68466i		−	0.426268i
$326$	1.55098	+	2.34233i	0.0859009	+	0.129730i
$327$		0			0
$328$	12.3423	−	2.29465i	0.681491	−	0.126701i
$329$		−	26.0000i		−	1.43343i
$330$		0			0
$331$		−	0.825183i		−	0.0453562i	−0.999743	−	0.0226781i	$-0.992781\pi$
$331$		−	0.825183i		−	0.0453562i	0.999743	−	0.0226781i	$-0.00721928\pi$
$332$	1.32431	−	3.12311i	0.0726808	−	0.171403i
$333$	24.7386			1.35567
$334$	−6.34233	+	4.19960i	−0.347037	+	0.229792i
$335$		−	50.1048i		−	2.73752i
$336$		0			0
$337$			20.2462i			1.10288i	0.834214	+	0.551441i	$0.185922\pi$
$337$			20.2462i			1.10288i	−0.834214	+	0.551441i	$0.814078\pi$
$338$	1.17915	−	0.780776i	0.0641372	−	0.0424686i
$339$		0			0
$340$	−33.5968	−	14.2462i	−1.82204	−	0.772609i
$341$	−1.19224	−	0.315342i	−0.0645632	−	0.0170767i
$342$	−15.3693	+	10.1768i	−0.831077	+	0.550301i
$343$	−9.88653			−0.533822
$344$	0.534565	+	2.87529i	0.0288218	+	0.155025i
$345$		0			0
$346$	2.97301	+	4.48991i	0.159830	+	0.241379i
$347$	−6.62153			−0.355463			−0.177731	−	0.984079i	$-0.556876\pi$
$347$	−6.62153			−0.355463			−0.177731	+	0.984079i	$0.556876\pi$
$348$		0			0
$349$		−	18.0000i		−	0.963518i	−0.876304	−	0.481759i	$-0.839998\pi$
$349$		−	18.0000i		−	0.963518i	0.876304	−	0.481759i	$-0.160002\pi$
$350$	36.7386	−	24.3266i	1.96376	−	1.30031i
$351$		0			0
$352$	8.59393	−	16.6777i	0.458058	−	0.888922i
$353$	5.12311			0.272675			0.136338	−	0.990662i	$-0.456467\pi$
$353$	5.12311			0.272675			0.136338	+	0.990662i	$0.456467\pi$
$354$		0			0
$355$		−	49.0708i		−	2.60441i
$356$	−1.56155	+	3.68260i	−0.0827621	+	0.195177i
$357$		0			0
$358$	−16.2177	−	24.4924i	−0.857134	−	1.29446i
$359$	8.77102			0.462917			0.231458	−	0.972845i	$-0.425650\pi$
$359$	8.77102			0.462917			0.231458	+	0.972845i	$0.425650\pi$
$360$	−5.52390	−	29.7116i	−0.291135	−	1.56594i
$361$	−0.123106			−0.00647924
$362$	−21.5150	+	14.2462i	−1.13080	+	0.748764i
$363$		0			0
$364$	7.46543	+	3.16561i	0.391295	+	0.165923i
$365$			20.6847i			1.08268i
$366$		0			0
$367$		−	11.5012i		−	0.600355i	−0.953883	−	0.300178i	$-0.902954\pi$
$367$		−	11.5012i		−	0.600355i	0.953883	−	0.300178i	$-0.0970460\pi$
$368$	6.78078	−	6.55789i	0.353472	−	0.341854i
$369$		−	13.3153i		−	0.693169i
$370$	34.6307	−	22.9309i	1.80037	−	1.19212i
$371$	−49.6515			−2.57778
$372$		0			0
$373$			16.0540i			0.831243i	0.909538	+	0.415622i	$0.136436\pi$
$373$			16.0540i			0.831243i	−0.909538	+	0.415622i	$0.863564\pi$
$374$	−22.7616	+	7.70235i	−1.17697	+	0.398279i
$375$		0			0
$376$	−17.8324	+	3.31534i	−0.919634	+	0.170976i
$377$	6.68466			0.344277
$378$		0			0
$379$			13.6149i			0.699351i	0.936871	+	0.349675i	$0.113708\pi$
$379$			13.6149i			0.699351i	−0.936871	+	0.349675i	$0.886292\pi$
$380$	−12.0818	+	28.4924i	−0.619783	+	1.46163i
$381$		0			0
$382$	10.2405	+	15.4654i	0.523949	+	0.791280i
$383$			10.3857i			0.530682i	0.964155	+	0.265341i	$0.0854845\pi$
$383$			10.3857i			0.530682i	−0.964155	+	0.265341i	$0.914515\pi$
$384$		0			0
$385$	12.2462	−	46.3002i	0.624125	−	2.35968i
$386$	−9.56155	−	14.4401i	−0.486670	−	0.734981i
$387$	3.10196			0.157682
$388$	−3.31534	+	7.81855i	−0.168311	+	0.396927i
$389$	12.0000			0.608424			0.304212	−	0.952604i	$-0.401607\pi$
$389$	12.0000			0.608424			0.304212	+	0.952604i	$0.401607\pi$
$390$		0			0
$391$	−12.0818			−0.611002
$392$	4.87962	+	26.2462i	0.246458	+	1.32563i
$393$		0			0
$394$	15.1231	+	22.8393i	0.761891	+	1.15063i
$395$	−4.71659			−0.237317
$396$	−15.7252	−	12.1950i	−0.790220	−	0.612823i
$397$	−20.0540			−1.00648			−0.503240	−	0.864147i	$-0.667859\pi$
$397$	−20.0540			−1.00648			−0.503240	+	0.864147i	$0.667859\pi$
$398$	−9.20650	−	13.9039i	−0.461480	−	0.696939i
$399$		0			0
$400$	−21.3693	−	22.0956i	−1.06847	−	1.10478i
$401$	−9.61553			−0.480177			−0.240088	−	0.970751i	$-0.577176\pi$
$401$	−9.61553			−0.480177			−0.240088	+	0.970751i	$0.577176\pi$
$402$		0			0
$403$	−0.371834			−0.0185224
$404$	8.97983	+	3.80776i	0.446763	+	0.189443i
$405$	−32.0540			−1.59277
$406$	21.1610	+	31.9579i	1.05020	+	1.58604i
$407$	6.99337	−	26.4404i	0.346648	−	1.31060i
$408$		0			0
$409$			17.3153i			0.856189i	0.903734	+	0.428094i	$0.140815\pi$
$409$			17.3153i			0.856189i	−0.903734	+	0.428094i	$0.859185\pi$
$410$	−12.3423	−	18.6397i	−0.609544	−	0.920548i
$411$		0			0
$412$	−30.3963	−	12.8891i	−1.49752	−	0.635001i
$413$			16.4384i			0.808883i
$414$	−5.52390	−	8.34233i	−0.271485	−	0.410003i
$415$	−6.04090			−0.296536
$416$	1.21922	−	5.52390i	0.0597774	−	0.270832i
$417$		0			0
$418$	6.53214	+	19.3034i	0.319497	+	0.944162i
$419$		−	14.7304i		−	0.719627i	−0.933024	−	0.359814i	$-0.882840\pi$
$419$		−	14.7304i		−	0.719627i	0.933024	−	0.359814i	$-0.117160\pi$
$420$		0			0
$421$	30.6847			1.49548			0.747739	−	0.663992i	$-0.231139\pi$
$421$	30.6847			1.49548			0.747739	+	0.663992i	$0.231139\pi$
$422$	6.43845	−	4.26324i	0.313419	−	0.207531i
$423$			19.2382i			0.935393i
$424$	6.33122	+	34.0540i	0.307471	+	1.65381i
$425$			39.3693i			1.90969i
$426$		0			0
$427$			51.4291i			2.48883i
$428$	11.2745	−	26.5885i	0.544972	−	1.28521i
$429$		0			0
$430$	4.34233	−	2.87529i	0.209406	−	0.138659i
$431$	26.4404			1.27359			0.636794	−	0.771034i	$-0.280260\pi$
$431$	26.4404			1.27359			0.636794	+	0.771034i	$0.280260\pi$
$432$		0			0
$433$	24.0540			1.15596			0.577980	−	0.816051i	$-0.303841\pi$
$433$	24.0540			1.15596			0.577980	+	0.816051i	$0.303841\pi$
$434$	−1.17708	−	1.77766i	−0.0565017	−	0.0853302i
$435$		0			0
$436$	3.68260	+	1.56155i	0.176365	+	0.0747848i
$437$			10.2462i			0.490143i
$438$		0			0
$439$	−18.8664			−0.900442			−0.450221	−	0.892917i	$-0.648655\pi$
$439$	−18.8664			−0.900442			−0.450221	+	0.892917i	$0.648655\pi$
$440$	−33.3170	−	2.49531i	−1.58833	−	0.118959i
$441$	28.3153			1.34835
$442$	−6.04090	+	4.00000i	−0.287336	+	0.190261i
$443$		−	27.7189i		−	1.31696i	−0.752596	−	0.658482i	$-0.771199\pi$
$443$		−	27.7189i		−	1.31696i	0.752596	−	0.658482i	$-0.228801\pi$
$444$		0			0
$445$	7.12311			0.337668
$446$	−9.27015	−	14.0000i	−0.438954	−	0.662919i
$447$		0			0
$448$	30.2681	−	11.6577i	1.43003	−	0.550773i
$449$	−9.61553			−0.453785			−0.226892	−	0.973920i	$-0.572857\pi$
$449$	−9.61553			−0.453785			−0.226892	+	0.973920i	$0.572857\pi$
$450$	−27.1840	+	18.0000i	−1.28147	+	0.848528i
$451$	−14.2313	−	3.76412i	−0.670125	−	0.177245i
$452$	−3.65767	+	8.62586i	−0.172042	+	0.405727i
$453$		0			0
$454$	15.3693	−	10.1768i	0.721318	−	0.477623i
$455$		−	14.4401i		−	0.676962i
$456$		0			0
$457$			26.3002i			1.23027i	0.788421	+	0.615135i	$0.210899\pi$
$457$			26.3002i			1.23027i	−0.788421	+	0.615135i	$0.789101\pi$
$458$	−30.4312	+	20.1501i	−1.42195	+	0.941552i
$459$		0			0
$460$	−15.4654	−	6.55789i	−0.721080	−	0.305763i
$461$		−	17.6155i		−	0.820437i	−0.911987	−	0.410218i	$-0.865452\pi$
$461$		−	17.6155i		−	0.820437i	0.911987	−	0.410218i	$-0.134548\pi$
$462$		0			0
$463$		−	17.0072i		−	0.790391i	−0.918597	−	0.395195i	$-0.870677\pi$
$463$		−	17.0072i		−	0.790391i	0.918597	−	0.395195i	$-0.129323\pi$
$464$	19.2203	−	18.5885i	0.892281	−	0.862951i
$465$		0			0
$466$	−0.684658	−	1.03399i	−0.0317162	−	0.0478985i
$467$			23.4199i			1.08374i	0.840461	+	0.541872i	$0.182284\pi$
$467$			23.4199i			1.08374i	−0.840461	+	0.541872i	$0.817716\pi$
$468$	−5.52390	−	2.34233i	−0.255342	−	0.108274i
$469$		−	57.0388i		−	2.63381i
$470$	17.8324	+	26.9309i	0.822546	+	1.24223i
$471$		0			0
$472$	11.2745	−	2.09612i	0.518950	−	0.0964816i
$473$	0.876894	−	3.31534i	0.0403196	−	0.152440i
$474$		0			0
$475$	33.3880			1.53194
$476$	−38.2462	−	16.2177i	−1.75301	−	0.743339i
$477$	36.7386			1.68215
$478$	0.780776	−	0.516994i	0.0357119	−	0.0236467i
$479$	−14.0683			−0.642795			−0.321397	−	0.946944i	$-0.604153\pi$
$479$	−14.0683			−0.642795			−0.321397	+	0.946944i	$0.604153\pi$
$480$		0			0
$481$		−	8.24621i		−	0.375995i
$482$	−23.8078	−	35.9551i	−1.08441	−	1.63771i
$483$		0			0
$484$	−17.4793	+	13.3595i	−0.794511	+	0.607249i
$485$	15.1231			0.686705
$486$		0			0
$487$			19.2382i			0.871766i	0.900003	+	0.435883i	$0.143564\pi$
$487$			19.2382i			0.871766i	−0.900003	+	0.435883i	$0.856436\pi$
$488$	35.2732	−	6.55789i	1.59674	−	0.296862i
$489$		0			0
$490$	39.6377	−	26.2462i	1.79065	−	1.18568i
$491$	3.68260			0.166193			0.0830967	−	0.996541i	$-0.473519\pi$
$491$	3.68260			0.166193			0.0830967	+	0.996541i	$0.473519\pi$
$492$		0			0
$493$	−34.2462			−1.54237
$494$	3.39228	+	5.12311i	0.152626	+	0.230499i
$495$	−9.06134	+	34.2589i	−0.407277	+	1.53982i
$496$	−1.06913	+	1.03399i	−0.0480054	+	0.0464274i
$497$		−	55.8617i		−	2.50574i
$498$		0			0
$499$		−	3.31077i		−	0.148210i	−0.997250	−	0.0741051i	$-0.976390\pi$
$499$		−	3.31077i		−	0.148210i	0.997250	−	0.0741051i	$-0.0236100\pi$
$500$	−7.46543	+	17.6057i	−0.333864	+	0.787351i
$501$		0			0
$502$	−11.6284	−	17.5616i	−0.519003	−	0.783810i
$503$	−13.9867			−0.623638			−0.311819	−	0.950142i	$-0.600938\pi$
$503$	−13.9867			−0.623638			−0.311819	+	0.950142i	$0.600938\pi$
$504$	−6.28835	−	33.8234i	−0.280106	−	1.50662i
$505$		−	17.3693i		−	0.772924i
$506$	−10.4777	+	3.54559i	−0.465792	+	0.157621i
$507$		0			0
$508$	−15.1838	+	35.8078i	−0.673670	+	1.58871i
$509$	−14.0000			−0.620539			−0.310270	−	0.950649i	$-0.600419\pi$
$509$	−14.0000			−0.620539			−0.310270	+	0.950649i	$0.600419\pi$
$510$		0			0
$511$			23.5472i			1.04167i
$512$	−11.8551	−	19.2732i	−0.523927	−	0.851763i
$513$		0			0
$514$	12.0181	−	7.95786i	0.530098	−	0.351006i
$515$			58.7943i			2.59079i
$516$		0			0
$517$	20.5616	+	5.43845i	0.904296	+	0.239183i
$518$	39.4233	−	26.1043i	1.73216	−	1.14696i
$519$		0			0
$520$	−9.90388	+	1.84130i	−0.434314	+	0.0807464i
$521$	25.1771			1.10303			0.551514	−	0.834166i	$-0.314050\pi$
$521$	25.1771			1.10303			0.551514	+	0.834166i	$0.314050\pi$
$522$	−15.6577	−	23.6466i	−0.685318	−	1.03498i
$523$	−13.4061			−0.586208			−0.293104	−	0.956081i	$-0.594688\pi$
$523$	−13.4061			−0.586208			−0.293104	+	0.956081i	$0.594688\pi$
$524$	−5.97725	+	14.0961i	−0.261117	+	0.615792i
$525$		0			0
$526$	3.31534	−	2.19526i	0.144556	−	0.0957181i
$527$	1.90495			0.0829807
$528$		0			0
$529$	17.4384			0.758193
$530$	51.4291	−	34.0540i	2.23394	−	1.47921i
$531$		−	12.1633i		−	0.527843i
$532$	−13.7538	+	32.4355i	−0.596302	+	1.40626i
$533$	−4.43845			−0.192250
$534$		0			0
$535$	−51.4291			−2.22348
$536$	−39.1207	+	7.27320i	−1.68976	+	0.314154i
$537$		0			0
$538$	13.1158	−	8.68466i	0.565461	−	0.374422i
$539$	8.00447	−	30.2631i	0.344777	−	1.30352i
$540$		0			0
$541$		−	40.2462i		−	1.73032i	−0.501496	−	0.865160i	$-0.667217\pi$
$541$		−	40.2462i		−	1.73032i	0.501496	−	0.865160i	$-0.332783\pi$
$542$	−20.9309	+	13.8594i	−0.899058	+	0.595314i
$543$		0			0
$544$	−6.24621	+	28.2995i	−0.267804	+	1.21333i
$545$		−	7.12311i		−	0.305120i
$546$		0			0
$547$	36.5357			1.56215			0.781077	−	0.624435i	$-0.214671\pi$
$547$	36.5357			1.56215			0.781077	+	0.624435i	$0.214671\pi$
$548$	2.63068	−	6.20393i	0.112377	−	0.265019i
$549$		−	38.0540i		−	1.62410i
$550$	11.5535	+	34.1424i	0.492644	+	1.45584i
$551$			29.0432i			1.23728i
$552$		0			0
$553$	−5.36932			−0.228327
$554$	−4.34233	−	6.55789i	−0.184488	−	0.278618i
$555$		0			0
$556$	4.26324	−	10.0540i	0.180802	−	0.426384i
$557$		−	19.7538i		−	0.836995i	−0.908218	−	0.418497i	$-0.862557\pi$
$557$		−	19.7538i		−	0.836995i	0.908218	−	0.418497i	$-0.137443\pi$
$558$	0.870958	+	1.31534i	0.0368706	+	0.0556828i
$559$		−	1.03399i		−	0.0437330i
$560$	−40.1547	−	41.5194i	−1.69684	−	1.75452i
$561$		0			0
$562$	−0.342329	−	0.516994i	−0.0144403	−	0.0218081i
$563$	26.2316			1.10553			0.552764	−	0.833338i	$-0.313573\pi$
$563$	26.2316			1.10553			0.552764	+	0.833338i	$0.313573\pi$
$564$		0			0
$565$	16.6847			0.701929
$566$	−6.09612	+	4.03657i	−0.256239	+	0.169670i
$567$	−36.4899			−1.53243
$568$	−38.3134	+	7.12311i	−1.60759	+	0.298879i
$569$		−	20.9848i		−	0.879730i	−0.898064	−	0.439865i	$-0.855026\pi$
$569$		−	20.9848i		−	0.879730i	0.898064	−	0.439865i	$-0.144974\pi$
$570$		0			0
$571$	36.1181			1.51149			0.755747	−	0.654863i	$-0.227274\pi$
$571$	36.1181			1.51149			0.755747	+	0.654863i	$0.227274\pi$
$572$	−4.06501	+	5.24173i	−0.169966	+	0.219168i
$573$		0			0
$574$	−14.0504	−	21.2192i	−0.586452	−	0.885673i
$575$			18.1227i			0.755768i
$576$	−22.3963	+	8.62586i	−0.933179	+	0.359411i
$577$	−26.0000			−1.08239			−0.541197	−	0.840896i	$-0.682029\pi$
$577$	−26.0000			−1.08239			−0.541197	+	0.840896i	$0.682029\pi$
$578$	10.9026	−	7.21922i	0.453490	−	0.300280i
$579$		0			0
$580$	−43.8373	−	18.5885i	−1.82024	−	0.771847i
$581$	−6.87689			−0.285302
$582$		0			0
$583$	10.3857	−	39.2658i	0.430130	−	1.62622i
$584$	16.1501	−	3.00258i	0.668296	−	0.124248i
$585$			10.6847i			0.441756i
$586$	8.49242	+	12.8255i	0.350819	+	0.529815i
$587$		−	26.8937i		−	1.11002i	−0.831843	−	0.555011i	$-0.812714\pi$
$587$		−	26.8937i		−	1.11002i	0.831843	−	0.555011i	$-0.187286\pi$
$588$		0			0
$589$		−	1.61553i		−	0.0665667i
$590$	−11.2745	−	17.0270i	−0.464163	−	0.700990i
$591$		0			0
$592$	−22.9309	−	23.7102i	−0.942453	−	0.974485i
$593$			28.7386i			1.18015i	0.807347	+	0.590077i	$0.200903\pi$
$593$			28.7386i			1.18015i	−0.807347	+	0.590077i	$0.799097\pi$
$594$		0			0
$595$			73.9781i			3.03281i
$596$	26.6849	+	11.3153i	1.09306	+	0.463494i
$597$		0			0
$598$	−2.78078	+	1.84130i	−0.113714	+	0.0752964i
$599$		−	23.1296i		−	0.945050i	−0.881317	−	0.472525i	$-0.843343\pi$
$599$		−	23.1296i		−	0.945050i	0.881317	−	0.472525i	$-0.156657\pi$
$600$		0			0
$601$			8.73863i			0.356456i	0.983989	+	0.178228i	$0.0570365\pi$
$601$			8.73863i			0.356456i	−0.983989	+	0.178228i	$0.942963\pi$
$602$	4.94326	−	3.27320i	0.201472	−	0.133406i
$603$			42.2048i			1.71871i
$604$	16.5081	−	38.9309i	0.671703	−	1.58407i
$605$	34.0540	+	19.3693i	1.38449	+	0.787475i
$606$		0			0
$607$	−34.3404			−1.39384			−0.696918	−	0.717151i	$-0.745446\pi$
$607$	−34.3404			−1.39384			−0.696918	+	0.717151i	$0.745446\pi$
$608$	24.0000	+	5.29723i	0.973329	+	0.214831i
$609$		0			0
$610$	−35.2732	−	53.2704i	−1.42817	−	2.15686i
$611$	6.41273			0.259431
$612$	28.2995	+	12.0000i	1.14394	+	0.485071i
$613$			7.36932i			0.297644i	0.988864	+	0.148822i	$0.0475481\pi$
$613$			7.36932i			0.297644i	−0.988864	+	0.148822i	$0.952452\pi$
$614$	−17.8078	+	11.7915i	−0.718663	+	0.475865i
$615$		0			0
$616$	−37.9277	−	2.84063i	−1.52815	−	0.114452i
$617$	16.6307			0.669526			0.334763	−	0.942302i	$-0.391344\pi$
$617$	16.6307			0.669526			0.334763	+	0.942302i	$0.391344\pi$
$618$		0			0
$619$		−	13.4876i		−	0.542113i	−0.962563	−	0.271056i	$-0.912627\pi$
$619$		−	13.4876i		−	0.542113i	0.962563	−	0.271056i	$-0.0873730\pi$
$620$	2.43845	+	1.03399i	0.0979304	+	0.0415259i
$621$		0			0
$622$	−2.19526	−	3.31534i	−0.0880221	−	0.132933i
$623$	8.10887			0.324875
$624$		0			0
$625$	−4.36932			−0.174773
$626$	22.7756	−	15.0810i	0.910297	−	0.602757i
$627$		0			0
$628$	6.24621	−	14.7304i	0.249251	−	0.587807i
$629$			42.2462i			1.68447i
$630$	−51.0810	+	33.8234i	−2.03511	+	1.34756i
$631$			19.6558i			0.782485i	0.920288	+	0.391242i	$0.127955\pi$
$631$			19.6558i			0.782485i	−0.920288	+	0.391242i	$0.872045\pi$
$632$	0.684658	+	3.68260i	0.0272343	+	0.146486i
$633$		0			0
$634$	13.1794	−	8.72680i	0.523422	−	0.346586i
$635$	69.2615			2.74856
$636$		0			0
$637$		−	9.43845i		−	0.373965i
$638$	−29.6995	+	10.0501i	−1.17581	+	0.397886i
$639$			41.3338i			1.63514i
$640$	−23.3563	+	32.8348i	−0.923238	+	1.29791i
$641$	−5.56155			−0.219668			−0.109834	−	0.993950i	$-0.535032\pi$
$641$	−5.56155			−0.219668			−0.109834	+	0.993950i	$0.535032\pi$
$642$		0			0
$643$		−	15.1022i		−	0.595574i	−0.954632	−	0.297787i	$-0.903751\pi$
$643$		−	15.1022i		−	0.595574i	0.954632	−	0.297787i	$-0.0962486\pi$
$644$	−17.6057	−	7.46543i	−0.693762	−	0.294179i
$645$		0			0
$646$	−17.3790	−	26.2462i	−0.683768	−	1.03264i
$647$		−	31.1112i		−	1.22311i	−0.791203	−	0.611553i	$-0.790545\pi$
$647$		−	31.1112i		−	1.22311i	0.791203	−	0.611553i	$-0.209455\pi$
$648$	4.65294	+	25.0270i	0.182785	+	0.983153i
$649$	−13.0000	−	3.43845i	−0.510295	−	0.134971i
$650$	6.00000	+	9.06134i	0.235339	+	0.355415i
$651$		0			0
$652$	−3.65767	−	1.55098i	−0.143245	−	0.0607411i
$653$	−46.2462			−1.80975			−0.904877	−	0.425673i	$-0.860037\pi$
$653$	−46.2462			−1.80975			−0.904877	+	0.425673i	$0.860037\pi$
$654$		0			0
$655$	27.2655			1.06535
$656$	−12.7618	+	12.3423i	−0.498265	+	0.481887i
$657$		−	17.4233i		−	0.679747i
$658$	20.3002	+	30.6578i	0.791384	+	1.19517i
$659$	−20.1907			−0.786517			−0.393258	−	0.919428i	$-0.628652\pi$
$659$	−20.1907			−0.786517			−0.393258	+	0.919428i	$0.628652\pi$
$660$		0			0
$661$	14.0000			0.544537			0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000			0.544537			0.272268	+	0.962221i	$0.412226\pi$
$662$	0.644283	+	0.973012i	0.0250408	+	0.0378172i
$663$		0			0
$664$	0.876894	+	4.71659i	0.0340301	+	0.183039i
$665$	62.7386			2.43290
$666$	−29.1705	+	19.3153i	−1.13033	+	0.748454i
$667$	−15.7644			−0.610400
$668$	4.19960	−	9.90388i	0.162487	−	0.383193i
$669$		0			0
$670$	39.1207	+	59.0810i	1.51136	+	2.28250i
$671$	−40.6716	−	10.7575i	−1.57011	−	0.415288i
$672$		0			0
$673$		−	27.7538i		−	1.06983i	−0.844906	−	0.534915i	$-0.820344\pi$
$673$		−	27.7538i		−	1.06983i	0.844906	−	0.534915i	$-0.179656\pi$
$674$	−15.8078	−	23.8733i	−0.608892	−	0.919564i
$675$		0			0
$676$	−0.780776	+	1.84130i	−0.0300299	+	0.0708193i
$677$		−	2.63068i		−	0.101105i	−0.998721	−	0.0505527i	$-0.983902\pi$
$677$		−	2.63068i		−	0.101105i	0.998721	−	0.0505527i	$-0.0160983\pi$
$678$		0			0
$679$	17.2160			0.660689
$680$	50.7386	−	9.43318i	1.94574	−	0.361746i
$681$		0			0
$682$	1.65203	−	0.559036i	0.0632596	−	0.0214066i
$683$		−	20.6898i		−	0.791673i	−0.918321	−	0.395836i	$-0.870455\pi$
$683$		−	20.6898i		−	0.791673i	0.918321	−	0.395836i	$-0.129545\pi$
$684$	10.1768	−	24.0000i	0.389121	−	0.917663i
$685$	−12.0000			−0.458496
$686$	11.6577	−	7.71917i	0.445092	−	0.294719i
$687$		0			0
$688$	−2.87529	−	2.97301i	−0.109619	−	0.113345i
$689$		−	12.2462i		−	0.466543i
$690$		0			0
$691$		−	28.3453i		−	1.07831i	−0.842208	−	0.539153i	$-0.818744\pi$
$691$		−	28.3453i		−	1.07831i	0.842208	−	0.539153i	$-0.181256\pi$
$692$	−7.01124	−	2.97301i	−0.266527	−	0.113017i
$693$	−10.3153	+	39.0000i	−0.391847	+	1.48149i
$694$	7.80776	−	5.16994i	0.296379	−	0.196248i
$695$	−19.4470			−0.737667
$696$		0			0
$697$	22.7386			0.861287
$698$	14.0540	+	21.2247i	0.531951	+	0.803365i
$699$		0			0
$700$	−24.3266	+	57.3693i	−0.919460	+	2.16836i
$701$			13.8078i			0.521512i	0.965405	+	0.260756i	$0.0839718\pi$
$701$			13.8078i			0.521512i	−0.965405	+	0.260756i	$0.916028\pi$
$702$		0			0
$703$	35.8278			1.35127
$704$	2.88801	+	26.3754i	0.108846	+	0.994059i
$705$		0			0
$706$	−6.04090	+	4.00000i	−0.227352	+	0.150542i
$707$		−	19.7731i		−	0.743642i
$708$		0			0
$709$	−28.9309			−1.08652			−0.543261	−	0.839564i	$-0.682811\pi$
$709$	−28.9309			−1.08652			−0.543261	+	0.839564i	$0.682811\pi$
$710$	38.3134	+	57.8617i	1.43787	+	2.17151i
$711$	3.97292			0.148996
$712$	−1.03399	−	5.56155i	−0.0387503	−	0.208428i
$713$	0.876894			0.0328400
$714$		0			0
$715$	11.4196	+	3.02045i	0.427070	+	0.112958i
$716$	38.2462	+	16.2177i	1.42933	+	0.606085i
$717$		0			0
$718$	−10.3423	+	6.84821i	−0.385972	+	0.255573i
$719$			38.0230i			1.41802i	0.705199	+	0.709010i	$0.250858\pi$
$719$			38.0230i			1.41802i	−0.705199	+	0.709010i	$0.749142\pi$
$720$	29.7116	+	30.7215i	1.10729	+	1.14492i
$721$			66.9309i			2.49264i
$722$	0.145160	−	0.0961180i	0.00540228	−	0.00357714i
$723$		0			0
$724$	14.2462	−	33.5968i	0.529456	−	1.24861i
$725$			51.3693i			1.90781i
$726$		0			0
$727$			24.0006i			0.890131i	0.895498	+	0.445066i	$0.146820\pi$
$727$			24.0006i			0.890131i	−0.895498	+	0.445066i	$0.853180\pi$
$728$	−11.2745	+	2.09612i	−0.417860	+	0.0776873i
$729$	27.0000			1.00000
$730$	−16.1501	−	24.3903i	−0.597742	−	0.902724i
$731$			5.29723i			0.195925i
$732$		0			0
$733$			43.8617i			1.62007i	0.586381	+	0.810035i	$0.300552\pi$
$733$			43.8617i			1.62007i	−0.586381	+	0.810035i	$0.699448\pi$
$734$	8.97983	+	13.5616i	0.331452	+	0.500566i
$735$		0			0
$736$	−2.87529	+	13.0270i	−0.105985	+	0.480181i
$737$	45.1080	+	11.9309i	1.66157	+	0.439479i
$738$	10.3963	+	15.7007i	0.382693	+	0.577953i
$739$	−22.6305			−0.832475			−0.416238	−	0.909256i	$-0.636652\pi$
$739$	−22.6305			−0.832475			−0.416238	+	0.909256i	$0.636652\pi$
$740$	−22.9309	+	54.0777i	−0.842956	+	1.98794i
$741$		0			0
$742$	58.5464	−	38.7667i	2.14931	−	1.42317i
$743$	32.7716			1.20227			0.601136	−	0.799147i	$-0.294715\pi$
$743$	32.7716			1.20227			0.601136	+	0.799147i	$0.294715\pi$
$744$		0			0
$745$		−	51.6155i		−	1.89105i
$746$	−12.5346	−	18.9300i	−0.458923	−	0.693077i
$747$	5.08842			0.186176
$748$	20.8255	−	26.8539i	0.761454	−	0.981877i
$749$	−58.5464			−2.13924
$750$		0			0
$751$			5.58755i			0.203892i	0.994790	+	0.101946i	$0.0325070\pi$
$751$			5.58755i			0.203892i	−0.994790	+	0.101946i	$0.967493\pi$
$752$	18.4384	−	17.8324i	0.672381	−	0.650280i
$753$		0			0
$754$	−7.88220	+	5.21922i	−0.287053	+	0.190073i
$755$	−75.3024			−2.74053
$756$		0			0
$757$	−0.246211			−0.00894870			−0.00447435	−	0.999990i	$-0.501424\pi$
$757$	−0.246211			−0.00894870			−0.00447435	+	0.999990i	$0.501424\pi$
$758$	−10.6302	−	16.0540i	−0.386106	−	0.583107i
$759$		0			0
$760$	−8.00000	−	43.0299i	−0.290191	−	1.56086i
$761$		−	1.31534i		−	0.0476811i	−0.999716	−	0.0238405i	$-0.992411\pi$
$761$		−	1.31534i		−	0.0476811i	0.999716	−	0.0238405i	$-0.00758940\pi$
$762$		0			0
$763$		−	8.10887i		−	0.293561i
$764$	−24.1501	−	10.2405i	−0.873720	−	0.370488i
$765$		−	54.7386i		−	1.97908i
$766$	−8.10887	−	12.2462i	−0.292985	−	0.442474i
$767$	−4.05444			−0.146397
$768$		0			0
$769$		−	28.0540i		−	1.01165i	−0.862635	−	0.505826i	$-0.831188\pi$
$769$		−	28.0540i		−	1.01165i	0.862635	−	0.505826i	$-0.168812\pi$
$770$	21.7100	+	64.1563i	0.782374	+	2.31203i
$771$		0			0
$772$	22.5490	+	9.56155i	0.811555	+	0.344128i
$773$	−40.7386			−1.46527			−0.732633	−	0.680623i	$-0.761709\pi$
$773$	−40.7386			−1.46527			−0.732633	+	0.680623i	$0.761709\pi$
$774$	−3.65767	+	2.42194i	−0.131472	+	0.0870548i
$775$		−	2.85742i		−	0.102641i
$776$	−2.19526	−	11.8078i	−0.0788054	−	0.423874i
$777$		0			0
$778$	−14.1498	+	9.36932i	−0.507294	+	0.335906i
$779$		−	19.2840i		−	0.690920i
$780$		0			0
$781$	44.1771	+	11.6847i	1.58078	+	0.418110i
$782$	14.2462	−	9.43318i	0.509443	−	0.337330i
$783$		0			0
$784$	−26.2462	−	27.1383i	−0.937365	−	0.969223i
$785$	−28.4924			−1.01694
$786$		0			0
$787$	38.5222			1.37317			0.686583	−	0.727051i	$-0.259110\pi$
$787$	38.5222			1.37317			0.686583	+	0.727051i	$0.259110\pi$
$788$	−35.6647	−	15.1231i	−1.27050	−	0.538738i
$789$		0			0
$790$	5.56155	−	3.68260i	0.197871	−	0.131021i
$791$	18.9936			0.675336
$792$	28.0639	+	2.10187i	0.997207	+	0.0746867i
$793$	−12.6847			−0.450445
$794$	23.6466	−	15.6577i	0.839186	−	0.555670i
$795$		0			0
$796$	21.7116	+	9.20650i	0.769549	+	0.326316i
$797$	28.0000			0.991811			0.495905	−	0.868377i	$-0.334836\pi$
$797$	28.0000			0.991811			0.495905	+	0.868377i	$0.334836\pi$
$798$		0			0
$799$	−32.8531			−1.16226
$800$	42.4493	+	9.36932i	1.50081	+	0.331255i
$801$	−6.00000			−0.212000
$802$	11.3381	−	7.50758i	0.400363	−	0.265102i
$803$	−18.6218	−	4.92539i	−0.657149	−	0.173813i
$804$		0			0
$805$			34.0540i			1.20024i
$806$	0.438447	−	0.290319i	0.0154436	−	0.0102261i
$807$		0			0
$808$	−13.5616	+	2.52132i	−0.477094	+	0.0886999i
$809$		−	26.8769i		−	0.944941i	−0.881346	−	0.472471i	$-0.843362\pi$
$809$		−	26.8769i		−	0.944941i	0.881346	−	0.472471i	$-0.156638\pi$
$810$	37.7964	−	25.0270i	1.32803	−	0.879359i
$811$	−27.3471			−0.960285			−0.480143	−	0.877190i	$-0.659415\pi$
$811$	−27.3471			−0.960285			−0.480143	+	0.877190i	$0.659415\pi$
$812$	−49.9039	−	21.1610i	−1.75128	−	0.742606i
$813$		0			0
$814$	12.3978	+	36.6373i	0.434543	+	1.28414i
$815$			7.07488i			0.247822i
$816$		0			0
$817$	4.49242			0.157170
$818$	−13.5194	−	20.4173i	−0.472695	−	0.713875i
$819$			12.1633i			0.425020i
$820$	29.1068	+	12.3423i	1.01646	+	0.431013i
$821$		−	45.2311i		−	1.57857i	−0.614024	−	0.789287i	$-0.710450\pi$
$821$		−	45.2311i		−	1.57857i	0.614024	−	0.789287i	$-0.289550\pi$
$822$		0			0
$823$		−	10.8848i		−	0.379419i	−0.981840	−	0.189710i	$-0.939245\pi$
$823$		−	10.8848i		−	0.379419i	0.981840	−	0.189710i	$-0.0607547\pi$
$824$	45.9052	−	8.53457i	1.59918	−	0.297316i
$825$		0			0
$826$	−12.8348	−	19.3833i	−0.446578	−	0.674433i
$827$	13.1973			0.458915			0.229457	−	0.973319i	$-0.426305\pi$
$827$	13.1973			0.458915			0.229457	+	0.973319i	$0.426305\pi$
$828$	13.0270	+	5.52390i	0.452719	+	0.191969i
$829$	−10.9848			−0.381519			−0.190760	−	0.981637i	$-0.561095\pi$
$829$	−10.9848			−0.381519			−0.190760	+	0.981637i	$0.561095\pi$
$830$	7.12311	−	4.71659i	0.247247	−	0.163715i
$831$		0			0
$832$	2.87529	+	7.46543i	0.0996827	+	0.258817i
$833$			48.3542i			1.67537i
$834$		0			0
$835$	−19.1567			−0.662944
$836$	−22.7740	−	17.6615i	−0.787656	−	0.610834i
$837$		0			0
$838$	11.5012	+	17.3693i	0.397301	+	0.600013i
$839$			33.3880i			1.15268i	0.817210	+	0.576340i	$0.195520\pi$
$839$			33.3880i			1.15268i	−0.817210	+	0.576340i	$0.804480\pi$
$840$		0			0
$841$	−15.6847			−0.540850
$842$	−36.1817	+	23.9579i	−1.24690	+	0.825642i
$843$		0			0
$844$	−4.26324	+	10.0540i	−0.146747	+	0.346072i
$845$	3.56155			0.122521
$846$	−15.0207	−	22.6847i	−0.516423	−	0.779915i
$847$	38.7667	+	22.0498i	1.33204	+	0.757641i
$848$	−34.0540	−	35.2114i	−1.16942	−	1.20916i
$849$		0			0
$850$	−30.7386	−	46.4222i	−1.05433	−	1.59227i
$851$			19.4470i			0.666634i
$852$		0			0
$853$		−	32.2462i		−	1.10409i	−0.833815	−	0.552045i	$-0.813848\pi$
$853$		−	32.2462i		−	1.10409i	0.833815	−	0.552045i	$-0.186152\pi$
$854$	−40.1547	−	60.6425i	−1.37406	−	2.07514i
$855$	−46.4222			−1.58761
$856$	7.46543	+	40.1547i	0.255163	+	1.37246i
$857$		−	12.0000i		−	0.409912i	−0.978771	−	0.204956i	$-0.934295\pi$
$857$		−	12.0000i		−	0.409912i	0.978771	−	0.204956i	$-0.0657052\pi$
$858$		0			0
$859$		−	56.2730i		−	1.92001i	−0.279982	−	0.960005i	$-0.590329\pi$
$859$		−	56.2730i		−	1.92001i	0.279982	−	0.960005i	$-0.409671\pi$
$860$	−2.87529	+	6.78078i	−0.0980465	+	0.231223i
$861$		0			0
$862$	−31.1771	+	20.6440i	−1.06190	+	0.703138i
$863$		−	55.3205i		−	1.88313i	−0.336827	−	0.941566i	$-0.609354\pi$
$863$		−	55.3205i		−	1.88313i	0.336827	−	0.941566i	$-0.390646\pi$
$864$		0			0
$865$			13.5616i			0.461107i
$866$	−28.3632	+	18.7808i	−0.963820	+	0.638197i
$867$		0			0
$868$	2.77590	+	1.17708i	0.0942203	+	0.0399527i
$869$	1.12311	−	4.24621i	0.0380987	−	0.144043i
$870$		0			0
$871$	14.0683			0.476685
$872$	−5.56155	+	1.03399i	−0.188338	+	0.0350152i
$873$	−12.7386			−0.431137
$874$	−8.00000	−	12.0818i	−0.270604	−	0.408673i
$875$	38.7667			1.31055
$876$		0			0
$877$		−	14.3845i		−	0.485729i	−0.970060	−	0.242865i	$-0.921913\pi$
$877$		−	14.3845i		−	0.485729i	0.970060	−	0.242865i	$-0.0780871\pi$
$878$	22.2462	−	14.7304i	0.750773	−	0.497127i
$879$		0			0
$880$	41.2339	−	23.0708i	1.39000	−	0.777717i
$881$	11.5616			0.389519			0.194759	−	0.980851i	$-0.437607\pi$
$881$	11.5616			0.389519			0.194759	+	0.980851i	$0.437607\pi$
$882$	−33.3880	+	22.1080i	−1.12423	+	0.744413i
$883$		−	12.8255i		−	0.431611i	−0.976436	−	0.215806i	$-0.930762\pi$
$883$		−	12.8255i		−	0.431611i	0.976436	−	0.215806i	$-0.0692377\pi$
$884$	4.00000	−	9.43318i	0.134535	−	0.317272i
$885$		0			0
$886$	21.6423	+	32.6847i	0.727086	+	1.09806i
$887$	42.8669			1.43933			0.719665	−	0.694321i	$-0.244295\pi$
$887$	42.8669			1.43933			0.719665	+	0.694321i	$0.244295\pi$
$888$		0			0
$889$	78.8466			2.64443
$890$	−8.39919	+	5.56155i	−0.281541	+	0.186424i
$891$	7.63263	−	28.8573i	0.255703	−	0.966755i
$892$	21.8617	+	9.27015i	0.731985	+	0.310388i
$893$			27.8617i			0.932358i
$894$		0			0
$895$		−	73.9781i		−	2.47281i
$896$	−26.5885	+	37.3787i	−0.888261	+	1.24874i
$897$		0			0
$898$	11.3381	−	7.50758i	0.378358	−	0.250531i
$899$	2.48558			0.0828989
$900$	18.0000	−	42.4493i	0.600000	−	1.41498i
$901$			62.7386i			2.09013i
$902$	19.7197	−	6.67300i	0.656595	−	0.222187i
$903$		0			0
$904$	−2.42194	−	13.0270i	−0.0805525	−	0.433271i
$905$	−64.9848			−2.16017
$906$		0			0
$907$			23.4199i			0.777646i	0.921313	+	0.388823i	$0.127118\pi$
$907$			23.4199i			0.777646i	−0.921313	+	0.388823i	$0.872882\pi$
$908$	−10.1768	+	24.0000i	−0.337731	+	0.796468i
$909$			14.6307i			0.485269i
$910$	11.2745	+	17.0270i	0.373745	+	0.564439i
$911$			1.74192i			0.0577122i	0.999584	+	0.0288561i	$0.00918646\pi$
$911$			1.74192i			0.0577122i	−0.999584	+	0.0288561i	$0.990814\pi$
$912$		0			0
$913$	1.43845	−	5.43845i	0.0476057	−	0.179986i
$914$	−20.5346	−	31.0118i	−0.679223	−	1.02578i
$915$		0			0
$916$	20.1501	−	47.5199i	0.665778	−	1.57010i
$917$	31.0388			1.02499
$918$		0			0
$919$	−47.0029			−1.55048			−0.775241	−	0.631666i	$-0.782371\pi$
$919$	−47.0029			−1.55048			−0.775241	+	0.631666i	$0.782371\pi$
$920$	23.3563	−	4.34233i	0.770033	−	0.143162i
$921$		0			0
$922$	13.7538	+	20.7713i	0.452957	+	0.684066i
$923$	13.7779			0.453506
$924$		0			0
$925$	63.3693			2.08357
$926$	13.2788	+	20.0540i	0.436369	+	0.659015i
$927$		−	49.5242i		−	1.62659i
$928$	−8.15009	+	36.9254i	−0.267540	+	1.21214i
$929$	−14.8769			−0.488095			−0.244048	−	0.969763i	$-0.578475\pi$
$929$	−14.8769			−0.488095			−0.244048	+	0.969763i	$0.578475\pi$
$930$		0			0
$931$	41.0077			1.34397
$932$	1.61463	+	0.684658i	0.0528888	+	0.0224267i
$933$		0			0
$934$	−18.2857	−	27.6155i	−0.598327	−	0.903608i
$935$	−58.5040	−	15.4741i	−1.91329	−	0.506056i
$936$	8.34233	−	1.55098i	0.272678	−	0.0506954i
$937$		−	3.12311i		−	0.102027i	−0.998698	−	0.0510137i	$-0.983755\pi$
$937$		−	3.12311i		−	0.102027i	0.998698	−	0.0510137i	$-0.0162452\pi$
$938$	44.5346	+	67.2572i	1.45411	+	2.19602i
$939$		0			0
$940$	−42.0540	−	17.8324i	−1.37165	−	0.581628i
$941$		−	30.4924i		−	0.994025i	−0.867744	−	0.497012i	$-0.834430\pi$
$941$		−	30.4924i		−	0.994025i	0.867744	−	0.497012i	$-0.165570\pi$
$942$		0			0
$943$	10.4672			0.340858
$944$	−11.6577	+	11.2745i	−0.379425	+	0.366953i
$945$		0			0
$946$	1.55455	+	4.59393i	0.0505429	+	0.149362i
$947$			30.5763i			0.993597i	0.867866	+	0.496798i	$0.165491\pi$
$947$			30.5763i			0.993597i	−0.867866	+	0.496798i	$0.834509\pi$
$948$		0			0
$949$	−5.80776			−0.188528
$950$	−39.3693	+	26.0685i	−1.27731	+	0.845775i
$951$		0			0
$952$	57.7603	−	10.7386i	1.87202	−	0.348041i
$953$		−	5.75379i		−	0.186383i	−0.995648	−	0.0931917i	$-0.970293\pi$
$953$		−	5.75379i		−	0.186383i	0.995648	−	0.0931917i	$-0.0297070\pi$
$954$	−43.3203	+	28.6847i	−1.40255	+	0.928700i
$955$			46.7125i			1.51158i
$956$	−0.516994	+	1.21922i	−0.0167208	+	0.0394325i
$957$		0			0
$958$	16.5885	−	10.9842i	0.535951	−	0.354882i
$959$	−13.6607			−0.441126
$960$		0			0
$961$	30.8617			0.995540
$962$	6.43845	+	9.72350i	0.207584	+	0.313498i
$963$	43.3203			1.39598
$964$	56.1457	+	23.8078i	1.80833	+	0.766796i
$965$		−	43.6155i		−	1.40403i
$966$		0			0
$967$	−46.9213			−1.50889			−0.754444	−	0.656364i	$-0.772094\pi$
$967$	−46.9213			−1.50889			−0.754444	+	0.656364i	$0.772094\pi$
$968$	10.1798	−	29.4002i	0.327193	−	0.944958i
$969$		0			0
$970$	−17.8324	+	11.8078i	−0.572563	+	0.379124i
$971$			25.6509i			0.823177i	0.911370	+	0.411589i	$0.135026\pi$
$971$			25.6509i			0.823177i	−0.911370	+	0.411589i	$0.864974\pi$
$972$		0			0
$973$	−22.1383			−0.709720
$974$	−15.0207	−	22.6847i	−0.481295	−	0.726863i
$975$		0			0
$976$	−36.4720	+	35.2732i	−1.16744	+	1.12907i
$977$	−57.1231			−1.82753			−0.913765	−	0.406243i	$-0.866839\pi$
$977$	−57.1231			−1.82753			−0.913765	+	0.406243i	$0.866839\pi$
$978$		0			0
$979$	−1.69614	+	6.41273i	−0.0542089	+	0.204952i
$980$	−26.2462	+	61.8963i	−0.838404	+	1.97720i
$981$			6.00000i			0.191565i
$982$	−4.34233	+	2.87529i	−0.138569	+	0.0917541i
$983$			20.5625i			0.655842i	0.944705	+	0.327921i	$0.106348\pi$
$983$			20.5625i			0.655842i	−0.944705	+	0.327921i	$0.893652\pi$
$984$		0			0
$985$			68.9848i			2.19804i
$986$	40.3813	−	26.7386i	1.28600	−	0.851532i
$987$		0			0
$988$	−8.00000	−	3.39228i	−0.254514	−	0.107923i
$989$			2.43845i			0.0775381i
$990$	−16.0639	−	47.4712i	−0.510544	−	1.50873i
$991$			40.8347i			1.29716i	0.761148	+	0.648578i	$0.224636\pi$
$991$			40.8347i			1.29716i	−0.761148	+	0.648578i	$0.775364\pi$
$992$	0.453349	−	2.05398i	0.0143938	−	0.0652138i
$993$		0			0
$994$	43.6155	+	65.8692i	1.38340	+	2.08924i
$995$		−	41.9960i		−	1.33136i
$996$		0			0
$997$			23.4233i			0.741823i	0.928668	+	0.370912i	$0.120955\pi$
$997$			23.4233i			0.741823i	−0.928668	+	0.370912i	$0.879045\pi$
$998$	2.58497	+	3.90388i	0.0818258	+	0.123575i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.e.a.131.2	yes	8
4.3	odd	2	inner	572.2.e.a.131.8	yes	8
11.10	odd	2	inner	572.2.e.a.131.7	yes	8
44.43	even	2	inner	572.2.e.a.131.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.e.a.131.1	✓	8	44.43	even	2	inner
572.2.e.a.131.2	yes	8	1.1	even	1	trivial
572.2.e.a.131.7	yes	8	11.10	odd	2	inner
572.2.e.a.131.8	yes	8	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17915 + 0.780776i) q^{2} +(0.780776 - 1.84130i) q^{4} -3.56155 q^{5} -4.05444 q^{7} +(0.516994 + 2.78078i) q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+(-1.17915 + 0.780776i) q^{2} +(0.780776 - 1.84130i) q^{4} -3.56155 q^{5} -4.05444 q^{7} +(0.516994 + 2.78078i) q^{8} +3.00000 q^{9} +(4.19960 - 2.78078i) q^{10} +(0.848071 - 3.20636i) q^{11} -1.00000i q^{13} +(4.78078 - 3.16561i) q^{14} +(-2.78078 - 2.87529i) q^{16} +5.12311i q^{17} +(-3.53744 + 2.34233i) q^{18} +4.34475 q^{19} +(-2.78078 + 6.55789i) q^{20} +(1.50345 + 4.44293i) q^{22} +2.35829i q^{23} +7.68466 q^{25} +(0.780776 + 1.17915i) q^{26} +(-3.16561 + 7.46543i) q^{28} +6.68466i q^{29} -0.371834i q^{31} +(5.52390 + 1.21922i) q^{32} +(-4.00000 - 6.04090i) q^{34} +14.4401 q^{35} +(2.34233 - 5.52390i) q^{36} +8.24621 q^{37} +(-5.12311 + 3.39228i) q^{38} +(-1.84130 - 9.90388i) q^{40} -4.43845i q^{41} +1.03399 q^{43} +(-5.24173 - 4.06501i) q^{44} -10.6847 q^{45} +(-1.84130 - 2.78078i) q^{46} +6.41273i q^{47} +9.43845 q^{49} +(-9.06134 + 6.00000i) q^{50} +(-1.84130 - 0.780776i) q^{52} +12.2462 q^{53} +(-3.02045 + 11.4196i) q^{55} +(-2.09612 - 11.2745i) q^{56} +(-5.21922 - 7.88220i) q^{58} -4.05444i q^{59} -12.6847i q^{61} +(0.290319 + 0.438447i) q^{62} -12.1633 q^{63} +(-7.46543 + 2.87529i) q^{64} +3.56155i q^{65} +14.0683i q^{67} +(9.43318 + 4.00000i) q^{68} +(-17.0270 + 11.2745i) q^{70} +13.7779i q^{71} +(1.55098 + 8.34233i) q^{72} -5.80776i q^{73} +(-9.72350 + 6.43845i) q^{74} +(3.39228 - 8.00000i) q^{76} +(-3.43845 + 13.0000i) q^{77} +1.32431 q^{79} +(9.90388 + 10.2405i) q^{80} +9.00000 q^{81} +(3.46543 + 5.23358i) q^{82} +1.69614 q^{83} -18.2462i q^{85} +(-1.21922 + 0.807313i) q^{86} +(9.35463 + 0.700624i) q^{88} -2.00000 q^{89} +(12.5988 - 8.34233i) q^{90} +4.05444i q^{91} +(4.34233 + 1.84130i) q^{92} +(-5.00691 - 7.56155i) q^{94} -15.4741 q^{95} -4.24621 q^{97} +(-11.1293 + 7.36932i) q^{98} +(2.54421 - 9.61909i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} - 12 q^{5} + 24 q^{9}+O(q^{10}) \) 8 * q - 2 * q^4 - 12 * q^5 + 24 * q^9	\( 8 q - 2 q^{4} - 12 q^{5} + 24 q^{9} + 30 q^{14} - 14 q^{16} - 14 q^{20} - 8 q^{22} + 12 q^{25} - 2 q^{26} - 32 q^{34} - 6 q^{36} - 8 q^{38} - 6 q^{44} - 36 q^{45} + 92 q^{49} + 32 q^{53} - 58 q^{56} - 50 q^{58} - 2 q^{64} - 62 q^{70} - 44 q^{77} + 38 q^{80} + 72 q^{81} - 30 q^{82} - 18 q^{86} + 20 q^{88} - 16 q^{89} + 10 q^{92} + 32 q^{97}+O(q^{100}) \) 8 * q - 2 * q^4 - 12 * q^5 + 24 * q^9 + 30 * q^14 - 14 * q^16 - 14 * q^20 - 8 * q^22 + 12 * q^25 - 2 * q^26 - 32 * q^34 - 6 * q^36 - 8 * q^38 - 6 * q^44 - 36 * q^45 + 92 * q^49 + 32 * q^53 - 58 * q^56 - 50 * q^58 - 2 * q^64 - 62 * q^70 - 44 * q^77 + 38 * q^80 + 72 * q^81 - 30 * q^82 - 18 * q^86 + 20 * q^88 - 16 * q^89 + 10 * q^92 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more