LMFDB - Embedded newform 140.2.u.a.33.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(17,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("140.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.u (of order $12$, degree $4$, 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:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 52 x^{14} - 224 x^{13} + 802 x^{12} - 2264 x^{11} + 5402 x^{10} - 10642 x^{9} + \cdots + 196 $ x^16 - 8x^15 + 52x^14 - 224x^13 + 802x^12 - 2264x^11 + 5402x^10 - 10642x^9 + 17766x^8 - 24680x^7 + 28682x^6 - 27248x^5 + 20861x^4 - 12338x^3 + 5322x^2 - 1484*x + 196
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			33.2
Root			$0.500000 - 0.105864i$ of defining polynomial
Character	$\chi$	$=$	140.33
Dual form			140.2.u.a.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.827625 - 0.221762i) q^{3} +(0.543268 - 2.16907i) q^{5} +(2.22829 - 1.42643i) q^{7} +(-1.96229 - 1.13293i) q^{9} +O(q^{10})$	\(q+(-0.827625 - 0.221762i) q^{3} +(0.543268 - 2.16907i) q^{5} +(2.22829 - 1.42643i) q^{7} +(-1.96229 - 1.13293i) q^{9} +(1.59116 + 2.75597i) q^{11} +(4.30021 - 4.30021i) q^{13} +(-0.930638 + 1.67470i) q^{15} +(0.0717406 - 0.267740i) q^{17} +(-2.95197 + 5.11295i) q^{19} +(-2.16052 + 0.686401i) q^{21} +(-5.64569 + 1.51276i) q^{23} +(-4.40972 - 2.35677i) q^{25} +(3.19039 + 3.19039i) q^{27} +9.49177i q^{29} +(3.16234 - 1.82578i) q^{31} +(-0.705715 - 2.63376i) q^{33} +(-1.88347 - 5.60826i) q^{35} +(0.175035 + 0.653239i) q^{37} +(-4.51258 + 2.60534i) q^{39} +1.09978i q^{41} +(4.70991 + 4.70991i) q^{43} +(-3.52345 + 3.64086i) q^{45} +(-0.443035 + 0.118711i) q^{47} +(2.93059 - 6.35702i) q^{49} +(-0.118749 + 0.205679i) q^{51} +(0.526437 - 1.96469i) q^{53} +(6.84231 - 1.95410i) q^{55} +(3.57698 - 3.57698i) q^{57} +(-4.29202 - 7.43399i) q^{59} +(8.23827 + 4.75637i) q^{61} +(-5.98861 + 0.274574i) q^{63} +(-6.99128 - 11.6636i) q^{65} +(-0.0674636 - 0.0180768i) q^{67} +5.00798 q^{69} -5.14237 q^{71} +(1.66692 + 0.446650i) q^{73} +(3.12695 + 2.92843i) q^{75} +(7.47676 + 3.87143i) q^{77} +(5.31629 + 3.06936i) q^{79} +(1.46584 + 2.53892i) q^{81} +(1.30581 - 1.30581i) q^{83} +(-0.541771 - 0.301065i) q^{85} +(2.10491 - 7.85563i) q^{87} +(-1.19035 + 2.06175i) q^{89} +(3.44817 - 15.7161i) q^{91} +(-3.02212 + 0.809775i) q^{93} +(9.48664 + 9.18072i) q^{95} +(-5.65663 - 5.65663i) q^{97} -7.21068i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{5} + 2 q^{7}+O(q^{10}) $ 16 * q + 6 * q^5 + 2 * q^7	$ 16 q + 6 q^{5} + 2 q^{7} - 20 q^{15} + 18 q^{17} - 4 q^{21} - 16 q^{23} + 6 q^{25} - 12 q^{31} - 42 q^{33} - 40 q^{35} - 14 q^{37} + 28 q^{43} - 66 q^{45} - 6 q^{47} + 20 q^{51} - 10 q^{53} + 44 q^{57} + 60 q^{61} + 48 q^{63} + 34 q^{65} + 8 q^{67} - 8 q^{71} + 78 q^{73} + 96 q^{75} + 10 q^{77} + 24 q^{81} + 30 q^{87} - 64 q^{91} - 62 q^{93} + 2 q^{95}+O(q^{100}) $ 16 * q + 6 * q^5 + 2 * q^7 - 20 * q^15 + 18 * q^17 - 4 * q^21 - 16 * q^23 + 6 * q^25 - 12 * q^31 - 42 * q^33 - 40 * q^35 - 14 * q^37 + 28 * q^43 - 66 * q^45 - 6 * q^47 + 20 * q^51 - 10 * q^53 + 44 * q^57 + 60 * q^61 + 48 * q^63 + 34 * q^65 + 8 * q^67 - 8 * q^71 + 78 * q^73 + 96 * q^75 + 10 * q^77 + 24 * q^81 + 30 * q^87 - 64 * q^91 - 62 * q^93 + 2 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−0.827625	−	0.221762i	−0.477830	−	0.128034i	0.0118622	−	0.999930i	$-0.496224\pi$
$3$	−0.827625	−	0.221762i	−0.477830	−	0.128034i	−0.489692	+	0.871896i	$0.662891\pi$
$4$		0			0
$5$	0.543268	−	2.16907i	0.242957	−	0.970037i
$5$	0.543268	−	2.16907i	0.242957	−	0.970037i
$6$		0			0
$7$	2.22829	−	1.42643i	0.842216	−	0.539140i
$7$	2.22829	−	1.42643i	0.842216	−	0.539140i
$8$		0			0
$9$	−1.96229	−	1.13293i	−0.654097	−	0.377643i
$10$		0			0
$11$	1.59116	+	2.75597i	0.479752	+	0.830955i	0.999730	−	0.0232245i	$-0.00739324\pi$
$11$	1.59116	+	2.75597i	0.479752	+	0.830955i	−0.519978	+	0.854180i	$0.674060\pi$
$12$		0			0
$13$	4.30021	−	4.30021i	1.19266	−	1.19266i	0.216346	−	0.976317i	$-0.430586\pi$
$13$	4.30021	−	4.30021i	1.19266	−	1.19266i	0.976317	−	0.216346i	$-0.0694138\pi$
$14$		0			0
$15$	−0.930638	+	1.67470i	−0.240290	+	0.432406i
$16$		0			0
$17$	0.0717406	−	0.267740i	0.0173997	−	0.0649364i	−0.956680	−	0.291141i	$-0.905965\pi$
$17$	0.0717406	−	0.267740i	0.0173997	−	0.0649364i	0.974080	+	0.226205i	$0.0726318\pi$
$18$		0			0
$19$	−2.95197	+	5.11295i	−0.677227	+	1.17299i	0.298585	+	0.954383i	$0.403485\pi$
$19$	−2.95197	+	5.11295i	−0.677227	+	1.17299i	−0.975813	+	0.218609i	$0.929848\pi$
$20$		0			0
$21$	−2.16052	+	0.686401i	−0.471464	+	0.149785i
$22$		0			0
$23$	−5.64569	+	1.51276i	−1.17721	+	0.315432i	−0.793818	−	0.608155i	$-0.791910\pi$
$23$	−5.64569	+	1.51276i	−1.17721	+	0.315432i	−0.383389	+	0.923587i	$0.625243\pi$
$24$		0			0
$25$	−4.40972	−	2.35677i	−0.881944	−	0.471354i
$26$		0			0
$27$	3.19039	+	3.19039i	0.613991	+	0.613991i
$28$		0			0
$29$			9.49177i			1.76258i	0.472579	+	0.881288i	$0.343323\pi$
$29$			9.49177i			1.76258i	−0.472579	+	0.881288i	$0.656677\pi$
$30$		0			0
$31$	3.16234	−	1.82578i	0.567973	−	0.327919i	−0.188366	−	0.982099i	$-0.560319\pi$
$31$	3.16234	−	1.82578i	0.567973	−	0.327919i	0.756339	+	0.654179i	$0.226986\pi$
$32$		0			0
$33$	−0.705715	−	2.63376i	−0.122849	−	0.458480i
$34$		0			0
$35$	−1.88347	−	5.60826i	−0.318364	−	0.947969i
$36$		0			0
$37$	0.175035	+	0.653239i	0.0287755	+	0.107392i	0.978820	−	0.204723i	$-0.0656293\pi$
$37$	0.175035	+	0.653239i	0.0287755	+	0.107392i	−0.950044	+	0.312115i	$0.898963\pi$
$38$		0			0
$39$	−4.51258	+	2.60534i	−0.722591	+	0.417188i
$40$		0			0
$41$			1.09978i			0.171756i	0.996306	+	0.0858781i	$0.0273696\pi$
$41$			1.09978i			0.171756i	−0.996306	+	0.0858781i	$0.972630\pi$
$42$		0			0
$43$	4.70991	+	4.70991i	0.718254	+	0.718254i	0.968248	−	0.249993i	$-0.0804285\pi$
$43$	4.70991	+	4.70991i	0.718254	+	0.718254i	−0.249993	+	0.968248i	$0.580428\pi$
$44$		0			0
$45$	−3.52345	+	3.64086i	−0.525245	+	0.542747i
$46$		0			0
$47$	−0.443035	+	0.118711i	−0.0646234	+	0.0173158i	−0.290986	−	0.956727i	$-0.593983\pi$
$47$	−0.443035	+	0.118711i	−0.0646234	+	0.0173158i	0.226363	+	0.974043i	$0.427317\pi$
$48$		0			0
$49$	2.93059	−	6.35702i	0.418655	−	0.908145i
$50$		0			0
$51$	−0.118749	+	0.205679i	−0.0166281	+	0.0288008i
$52$		0			0
$53$	0.526437	−	1.96469i	0.0723117	−	0.269871i	−0.920299	−	0.391217i	$-0.872054\pi$
$53$	0.526437	−	1.96469i	0.0723117	−	0.269871i	0.992610	+	0.121346i	$0.0387209\pi$
$54$		0			0
$55$	6.84231	−	1.95410i	0.922616	−	0.263491i
$56$		0			0
$57$	3.57698	−	3.57698i	0.473782	−	0.473782i
$58$		0			0
$59$	−4.29202	−	7.43399i	−0.558773	−	0.967824i	−0.997599	−	0.0692515i	$-0.977939\pi$
$59$	−4.29202	−	7.43399i	−0.558773	−	0.967824i	0.438826	−	0.898572i	$-0.355394\pi$
$60$		0			0
$61$	8.23827	+	4.75637i	1.05480	+	0.608990i	0.923990	−	0.382417i	$-0.124908\pi$
$61$	8.23827	+	4.75637i	1.05480	+	0.608990i	0.130812	+	0.991407i	$0.458242\pi$
$62$		0			0
$63$	−5.98861	+	0.274574i	−0.754493	+	0.0345931i
$64$		0			0
$65$	−6.99128	−	11.6636i	−0.867161	−	1.44669i
$66$		0			0
$67$	−0.0674636	−	0.0180768i	−0.00824199	−	0.00220843i	0.254696	−	0.967021i	$-0.418025\pi$
$67$	−0.0674636	−	0.0180768i	−0.00824199	−	0.00220843i	−0.262938	+	0.964813i	$0.584691\pi$
$68$		0			0
$69$	5.00798			0.602890
$70$		0			0
$71$	−5.14237			−0.610287			−0.305143	−	0.952306i	$-0.598704\pi$
$71$	−5.14237			−0.610287			−0.305143	+	0.952306i	$0.598704\pi$
$72$		0			0
$73$	1.66692	+	0.446650i	0.195098	+	0.0522765i	0.355045	−	0.934849i	$-0.384466\pi$
$73$	1.66692	+	0.446650i	0.195098	+	0.0522765i	−0.159947	+	0.987126i	$0.551132\pi$
$74$		0			0
$75$	3.12695	+	2.92843i	0.361070	+	0.338146i
$76$		0			0
$77$	7.47676	+	3.87143i	0.852056	+	0.441190i
$78$		0			0
$79$	5.31629	+	3.06936i	0.598129	+	0.345330i	0.768305	−	0.640084i	$-0.221100\pi$
$79$	5.31629	+	3.06936i	0.598129	+	0.345330i	−0.170176	+	0.985414i	$0.554434\pi$
$80$		0			0
$81$	1.46584	+	2.53892i	0.162872	+	0.282102i
$82$		0			0
$83$	1.30581	−	1.30581i	0.143331	−	0.143331i	−0.631800	−	0.775131i	$-0.717684\pi$
$83$	1.30581	−	1.30581i	0.143331	−	0.143331i	0.775131	+	0.631800i	$0.217684\pi$
$84$		0			0
$85$	−0.541771	−	0.301065i	−0.0587633	−	0.0326550i
$86$		0			0
$87$	2.10491	−	7.85563i	0.225670	−	0.842211i
$88$		0			0
$89$	−1.19035	+	2.06175i	−0.126177	+	0.218545i	−0.922192	−	0.386732i	$-0.873604\pi$
$89$	−1.19035	+	2.06175i	−0.126177	+	0.218545i	0.796016	+	0.605276i	$0.206937\pi$
$90$		0			0
$91$	3.44817	−	15.7161i	0.361467	−	1.64749i
$92$		0			0
$93$	−3.02212	+	0.809775i	−0.313379	+	0.0839697i
$94$		0			0
$95$	9.48664	+	9.18072i	0.973309	+	0.941922i
$96$		0			0
$97$	−5.65663	−	5.65663i	−0.574344	−	0.574344i	0.358995	−	0.933339i	$-0.383119\pi$
$97$	−5.65663	−	5.65663i	−0.574344	−	0.574344i	−0.933339	+	0.358995i	$0.883119\pi$
$98$		0			0
$99$		−	7.21068i		−	0.724700i
$100$		0			0
$101$	−11.9765	+	6.91466i	−1.19171	+	0.688034i	−0.958694	−	0.284439i	$-0.908193\pi$
$101$	−11.9765	+	6.91466i	−1.19171	+	0.688034i	−0.233016	+	0.972473i	$0.574859\pi$
$102$		0			0
$103$	−2.80463	−	10.4670i	−0.276348	−	1.03135i	−0.954932	−	0.296824i	$-0.904073\pi$
$103$	−2.80463	−	10.4670i	−0.276348	−	1.03135i	0.678584	−	0.734523i	$-0.262594\pi$
$104$		0			0
$105$	0.315110	+	5.05922i	0.0307516	+	0.493729i
$106$		0			0
$107$	1.04942	+	3.91649i	0.101451	+	0.378622i	0.997918	−	0.0644888i	$-0.0205417\pi$
$107$	1.04942	+	3.91649i	0.101451	+	0.378622i	−0.896467	+	0.443110i	$0.853875\pi$
$108$		0			0
$109$	0.855989	−	0.494205i	0.0819889	−	0.0473363i	−0.458445	−	0.888723i	$-0.651593\pi$
$109$	0.855989	−	0.494205i	0.0819889	−	0.0473363i	0.540434	+	0.841386i	$0.318260\pi$
$110$		0			0
$111$		−	0.579453i		−	0.0549992i
$112$		0			0
$113$	6.30945	+	6.30945i	0.593543	+	0.593543i	0.938587	−	0.345044i	$-0.112136\pi$
$113$	6.30945	+	6.30945i	0.593543	+	0.593543i	−0.345044	+	0.938587i	$0.612136\pi$
$114$		0			0
$115$	0.214155	+	13.0677i	0.0199701	+	1.21857i
$116$		0			0
$117$	−13.3101	+	3.56643i	−1.23052	+	0.329716i
$118$		0			0
$119$	−0.222053	−	0.698935i	−0.0203556	−	0.0640713i
$120$		0			0
$121$	0.436433	−	0.755924i	0.0396757	−	0.0687203i
$122$		0			0
$123$	0.243888	−	0.910203i	0.0219906	−	0.0820702i
$124$		0			0
$125$	−7.50766	+	8.28463i	−0.671505	+	0.741000i
$126$		0			0
$127$	−11.6305	+	11.6305i	−1.03204	+	1.03204i	−0.0325696	+	0.999469i	$0.510369\pi$
$127$	−11.6305	+	11.6305i	−1.03204	+	1.03204i	−0.999469	+	0.0325696i	$0.989631\pi$
$128$		0			0
$129$	−2.85356	−	4.94251i	−0.251242	−	0.435164i
$130$		0			0
$131$	−10.6389	−	6.14236i	−0.929523	−	0.536660i	−0.0428623	−	0.999081i	$-0.513648\pi$
$131$	−10.6389	−	6.14236i	−0.929523	−	0.536660i	−0.886661	+	0.462421i	$0.846981\pi$
$132$		0			0
$133$	0.715431	+	15.6039i	0.0620357	+	1.35303i
$134$		0			0
$135$	8.65342	−	5.18694i	0.744768	−	0.446421i
$136$		0			0
$137$	−14.6221	−	3.91798i	−1.24925	−	0.334735i	−0.427203	−	0.904156i	$-0.640501\pi$
$137$	−14.6221	−	3.91798i	−1.24925	−	0.334735i	−0.822046	+	0.569420i	$0.807168\pi$
$138$		0			0
$139$	−5.06783			−0.429847			−0.214924	−	0.976631i	$-0.568950\pi$
$139$	−5.06783			−0.429847			−0.214924	+	0.976631i	$0.568950\pi$
$140$		0			0
$141$	0.392993			0.0330960
$142$		0			0
$143$	18.6935	+	5.00892i	1.56323	+	0.418867i
$144$		0			0
$145$	20.5883	+	5.15657i	1.70976	+	0.428230i
$146$		0			0
$147$	−3.83517	+	4.61134i	−0.316319	+	0.380337i
$148$		0			0
$149$	18.8081	+	10.8588i	1.54082	+	0.889591i	0.998787	+	0.0492306i	$0.0156769\pi$
$149$	18.8081	+	10.8588i	1.54082	+	0.889591i	0.542029	+	0.840360i	$0.317656\pi$
$150$		0			0
$151$	−2.98002	−	5.16155i	−0.242511	−	0.420041i	0.718918	−	0.695095i	$-0.244638\pi$
$151$	−2.98002	−	5.16155i	−0.242511	−	0.420041i	−0.961429	+	0.275054i	$0.911304\pi$
$152$		0			0
$153$	−0.444106	+	0.444106i	−0.0359038	+	0.0359038i
$154$		0			0
$155$	−2.24224	−	7.85122i	−0.180101	−	0.630625i
$156$		0			0
$157$	−1.01175	+	3.77590i	−0.0807465	+	0.301350i	−0.994475	−	0.104976i	$-0.966523\pi$
$157$	−1.01175	+	3.77590i	−0.0807465	+	0.301350i	0.913728	+	0.406326i	$0.133190\pi$
$158$		0			0
$159$	−0.871386	+	1.50928i	−0.0691054	+	0.119694i
$160$		0			0
$161$	−10.4224	+	11.4241i	−0.821401	+	0.900341i
$162$		0			0
$163$	−21.8541	+	5.85580i	−1.71175	+	0.458661i	−0.975852	−	0.218434i	$-0.929905\pi$
$163$	−21.8541	+	5.85580i	−1.71175	+	0.458661i	−0.735896	+	0.677095i	$0.763239\pi$
$164$		0			0
$165$	−6.09621	+	0.0999054i	−0.474589	+	0.00777763i
$166$		0			0
$167$	−8.07859	−	8.07859i	−0.625140	−	0.625140i	0.321701	−	0.946841i	$-0.395745\pi$
$167$	−8.07859	−	8.07859i	−0.625140	−	0.625140i	−0.946841	+	0.321701i	$0.895745\pi$
$168$		0			0
$169$		−	23.9835i		−	1.84489i
$170$		0			0
$171$	11.5852	−	6.68874i	0.885945	−	0.511500i
$172$		0			0
$173$	−1.57711	−	5.88586i	−0.119906	−	0.447494i	0.879701	−	0.475526i	$-0.157742\pi$
$173$	−1.57711	−	5.88586i	−0.119906	−	0.447494i	−0.999607	+	0.0280327i	$0.991076\pi$
$174$		0			0
$175$	−13.1879	+	1.03859i	−0.996913	+	0.0785097i
$176$		0			0
$177$	1.90361	+	7.10437i	0.143084	+	0.533997i
$178$		0			0
$179$	19.2062	−	11.0887i	1.43554	−	0.828810i	0.438005	−	0.898973i	$-0.355685\pi$
$179$	19.2062	−	11.0887i	1.43554	−	0.828810i	0.997536	+	0.0701627i	$0.0223519\pi$
$180$		0			0
$181$			5.60751i			0.416803i	0.978043	+	0.208401i	$0.0668261\pi$
$181$			5.60751i			0.416803i	−0.978043	+	0.208401i	$0.933174\pi$
$182$		0			0
$183$	−5.76342	−	5.76342i	−0.426044	−	0.426044i
$184$		0			0
$185$	1.51201	−	0.0247790i	0.111165	−	0.00182179i
$186$		0			0
$187$	0.852032	−	0.228301i	0.0623067	−	0.0166950i
$188$		0			0
$189$	11.6600	+	2.55826i	0.848141	+	0.186086i
$190$		0			0
$191$	7.99574	−	13.8490i	0.578551	−	1.00208i	−0.417094	−	0.908863i	$-0.636952\pi$
$191$	7.99574	−	13.8490i	0.578551	−	1.00208i	0.995646	−	0.0932173i	$-0.0297151\pi$
$192$		0			0
$193$	3.99509	−	14.9099i	0.287573	−	1.07324i	−0.659366	−	0.751822i	$-0.729175\pi$
$193$	3.99509	−	14.9099i	0.287573	−	1.07324i	0.946939	−	0.321414i	$-0.104158\pi$
$194$		0			0
$195$	3.19962	+	11.2035i	0.229130	+	0.802299i
$196$		0			0
$197$	18.8412	−	18.8412i	1.34238	−	1.34238i	0.448690	−	0.893687i	$-0.351891\pi$
$197$	18.8412	−	18.8412i	1.34238	−	1.34238i	0.893687	−	0.448690i	$-0.148109\pi$
$198$		0			0
$199$	−3.04605	−	5.27591i	−0.215929	−	0.374000i	0.737631	−	0.675204i	$-0.235945\pi$
$199$	−3.04605	−	5.27591i	−0.215929	−	0.374000i	−0.953559	+	0.301205i	$0.902611\pi$
$200$		0			0
$201$	0.0518258	+	0.0299216i	0.00365551	+	0.00211051i
$202$		0			0
$203$	13.5394	+	21.1504i	0.950276	+	1.48447i
$204$		0			0
$205$	2.38549	+	0.597473i	0.166610	+	0.0417293i
$206$		0			0
$207$	12.7923	+	3.42769i	0.889128	+	0.238241i
$208$		0			0
$209$	−18.7882			−1.29961
$210$		0			0
$211$	−7.58690			−0.522304			−0.261152	−	0.965298i	$-0.584102\pi$
$211$	−7.58690			−0.522304			−0.261152	+	0.965298i	$0.584102\pi$
$212$		0			0
$213$	4.25595	+	1.14038i	0.291613	+	0.0781375i
$214$		0			0
$215$	12.7749	−	7.65737i	0.871238	−	0.522228i
$216$		0			0
$217$	4.44228	−	8.57923i	0.301561	−	0.582396i
$218$		0			0
$219$	−1.28054	−	0.739318i	−0.0865307	−	0.0499585i
$220$		0			0
$221$	−0.842836	−	1.45983i	−0.0566953	−	0.0981991i
$222$		0			0
$223$	−11.9362	+	11.9362i	−0.799306	+	0.799306i	−0.982986	−	0.183680i	$-0.941199\pi$
$223$	−11.9362	+	11.9362i	−0.799306	+	0.799306i	0.183680	+	0.982986i	$0.441199\pi$
$224$		0			0
$225$	5.98310	+	9.62057i	0.398873	+	0.641371i
$226$		0			0
$227$	3.23562	−	12.0755i	0.214756	−	0.801479i	−0.771497	−	0.636233i	$-0.780492\pi$
$227$	3.23562	−	12.0755i	0.214756	−	0.801479i	0.986252	−	0.165246i	$-0.0528417\pi$
$228$		0			0
$229$	1.61341	−	2.79450i	0.106617	−	0.184666i	−0.807781	−	0.589483i	$-0.799332\pi$
$229$	1.61341	−	2.79450i	0.106617	−	0.184666i	0.914398	+	0.404817i	$0.132665\pi$
$230$		0			0
$231$	−5.32943	−	4.86215i	−0.350650	−	0.319906i
$232$		0			0
$233$	5.34770	−	1.43291i	0.350340	−	0.0938732i	−0.0793577	−	0.996846i	$-0.525287\pi$
$233$	5.34770	−	1.43291i	0.350340	−	0.0938732i	0.429697	+	0.902973i	$0.358620\pi$
$234$		0			0
$235$	0.0168055	+	1.02547i	0.00109627	+	0.0668940i
$236$		0			0
$237$	−3.71923	−	3.71923i	−0.241590	−	0.241590i
$238$		0			0
$239$		−	6.19755i		−	0.400886i	−0.979705	−	0.200443i	$-0.935762\pi$
$239$		−	6.19755i		−	0.400886i	0.979705	−	0.200443i	$-0.0642381\pi$
$240$		0			0
$241$	−7.61051	+	4.39393i	−0.490236	+	0.283038i	−0.724673	−	0.689093i	$-0.758009\pi$
$241$	−7.61051	+	4.39393i	−0.490236	+	0.283038i	0.234436	+	0.972132i	$0.424676\pi$
$242$		0			0
$243$	−4.15343	−	15.5008i	−0.266443	−	0.994378i
$244$		0			0
$245$	−12.1967	−	9.81021i	−0.779219	−	0.626751i
$246$		0			0
$247$	9.29269	+	34.6808i	0.591280	+	2.20669i
$248$		0			0
$249$	−1.37030	+	0.791144i	−0.0868393	+	0.0501367i
$250$		0			0
$251$			7.67945i			0.484723i	0.970186	+	0.242361i	$0.0779219\pi$
$251$			7.67945i			0.484723i	−0.970186	+	0.242361i	$0.922078\pi$
$252$		0			0
$253$	−13.1523	−	13.1523i	−0.826877	−	0.826877i
$254$		0			0
$255$	0.381619	+	0.369313i	0.0238979	+	0.0231273i
$256$		0			0
$257$	−16.1903	+	4.33818i	−1.00992	+	0.270608i	−0.725598	−	0.688119i	$-0.758437\pi$
$257$	−16.1903	+	4.33818i	−1.00992	+	0.270608i	−0.284327	+	0.958727i	$0.591770\pi$
$258$		0			0
$259$	1.32183	+	1.20593i	0.0821345	+	0.0749330i
$260$		0			0
$261$	10.7535	−	18.6256i	0.665625	−	1.15290i
$262$		0			0
$263$	−4.72385	+	17.6296i	−0.291285	+	1.08709i	0.652839	+	0.757497i	$0.273578\pi$
$263$	−4.72385	+	17.6296i	−0.291285	+	1.08709i	−0.944123	+	0.329592i	$0.893089\pi$
$264$		0			0
$265$	−3.97555	−	2.20923i	−0.244216	−	0.135712i
$266$		0			0
$267$	1.44238	−	1.44238i	0.0882722	−	0.0882722i
$268$		0			0
$269$	6.72717	+	11.6518i	0.410163	+	0.710423i	0.994907	−	0.100795i	$-0.0321385\pi$
$269$	6.72717	+	11.6518i	0.410163	+	0.710423i	−0.584744	+	0.811218i	$0.698805\pi$
$270$		0			0
$271$	20.9241	+	12.0805i	1.27105	+	0.733840i	0.975185	−	0.221391i	$-0.0710595\pi$
$271$	20.9241	+	12.0805i	1.27105	+	0.733840i	0.295863	+	0.955230i	$0.404393\pi$
$272$		0			0
$273$	−6.33902	+	12.2423i	−0.383655	+	0.740940i
$274$		0			0
$275$	−0.521382	−	15.9030i	−0.0314405	−	0.958989i
$276$		0			0
$277$	−1.07098	−	0.286969i	−0.0643490	−	0.0172423i	0.226501	−	0.974011i	$-0.427271\pi$
$277$	−1.07098	−	0.286969i	−0.0643490	−	0.0172423i	−0.290850	+	0.956769i	$0.593938\pi$
$278$		0			0
$279$	−8.27391			−0.495346
$280$		0			0
$281$	−10.3342			−0.616485			−0.308242	−	0.951308i	$-0.599741\pi$
$281$	−10.3342			−0.616485			−0.308242	+	0.951308i	$0.599741\pi$
$282$		0			0
$283$	3.75354	+	1.00576i	0.223125	+	0.0597860i	0.368649	−	0.929569i	$-0.379820\pi$
$283$	3.75354	+	1.00576i	0.223125	+	0.0597860i	−0.145525	+	0.989355i	$0.546487\pi$
$284$		0			0
$285$	−5.81545	−	9.70197i	−0.344478	−	0.574695i
$286$		0			0
$287$	1.56876	+	2.45062i	0.0926007	+	0.144656i
$288$		0			0
$289$	14.6559	+	8.46158i	0.862111	+	0.497740i
$290$		0			0
$291$	3.42715	+	5.93600i	0.200903	+	0.347974i
$292$		0			0
$293$	19.5722	−	19.5722i	1.14342	−	1.14342i	0.155598	−	0.987820i	$-0.450270\pi$
$293$	19.5722	−	19.5722i	1.14342	−	1.14342i	0.987820	−	0.155598i	$-0.0497304\pi$
$294$		0			0
$295$	−18.4566	+	5.27103i	−1.07458	+	0.306892i
$296$		0			0
$297$	−3.71620	+	13.8690i	−0.215636	+	0.804763i
$298$		0			0
$299$	−17.7724	+	30.7828i	−1.02781	+	1.78021i
$300$		0			0
$301$	17.2134	+	3.77670i	0.992165	+	0.217685i
$302$		0			0
$303$	11.4455	−	3.06681i	0.657526	−	0.176184i
$304$		0			0
$305$	14.7925	−	15.2854i	0.847014	−	0.875239i
$306$		0			0
$307$	−10.0944	−	10.0944i	−0.576117	−	0.576117i	0.357714	−	0.933831i	$-0.383556\pi$
$307$	−10.0944	−	10.0944i	−0.576117	−	0.576117i	−0.933831	+	0.357714i	$0.883556\pi$
$308$		0			0
$309$			9.28473i			0.528190i
$310$		0			0
$311$	−23.0982	+	13.3357i	−1.30978	+	0.756200i	−0.982059	−	0.188576i	$-0.939613\pi$
$311$	−23.0982	+	13.3357i	−1.30978	+	0.756200i	−0.327718	+	0.944776i	$0.606279\pi$
$312$		0			0
$313$	−1.18422	−	4.41958i	−0.0669362	−	0.249809i	0.924348	−	0.381551i	$-0.124610\pi$
$313$	−1.18422	−	4.41958i	−0.0669362	−	0.249809i	−0.991284	+	0.131741i	$0.957943\pi$
$314$		0			0
$315$	−2.65785	+	13.1389i	−0.149753	+	0.740291i
$316$		0			0
$317$	−4.76887	−	17.7977i	−0.267846	−	0.999616i	−0.960485	−	0.278332i	$-0.910219\pi$
$317$	−4.76887	−	17.7977i	−0.267846	−	0.999616i	0.692639	−	0.721285i	$-0.256448\pi$
$318$		0			0
$319$	−26.1590	+	15.1029i	−1.46462	+	0.845600i
$320$		0			0
$321$		−	3.47411i		−	0.193906i
$322$		0			0
$323$	1.15716	+	1.15716i	0.0643863	+	0.0643863i
$324$		0			0
$325$	−29.0973	+	8.82811i	−1.61403	+	0.489695i
$326$		0			0
$327$	−0.818034	+	0.219191i	−0.0452374	+	0.0121213i
$328$		0			0
$329$	−0.817880	+	0.896482i	−0.0450912	+	0.0494247i
$330$		0			0
$331$	−11.9163	+	20.6397i	−0.654980	+	1.13446i	0.326918	+	0.945053i	$0.393990\pi$
$331$	−11.9163	+	20.6397i	−0.654980	+	1.13446i	−0.981899	+	0.189407i	$0.939344\pi$
$332$		0			0
$333$	0.396604	−	1.48015i	0.0217338	−	0.0811115i
$334$		0			0
$335$	−0.0758606	+	0.136513i	−0.00414471	+	0.00745848i
$336$		0			0
$337$	0.802453	−	0.802453i	0.0437124	−	0.0437124i	−0.684913	−	0.728625i	$-0.740160\pi$
$337$	0.802453	−	0.802453i	0.0437124	−	0.0437124i	0.728625	+	0.684913i	$0.240160\pi$
$338$		0			0
$339$	−3.82267	−	6.62105i	−0.207619	−	0.359606i
$340$		0			0
$341$	10.0636	+	5.81020i	0.544973	+	0.314640i
$342$		0			0
$343$	−2.53764	−	18.3456i	−0.137019	−	0.990568i
$344$		0			0
$345$	2.72068	−	10.8627i	0.146476	−	0.584826i
$346$		0			0
$347$	13.3758	+	3.58404i	0.718052	+	0.192401i	0.599302	−	0.800523i	$-0.295445\pi$
$347$	13.3758	+	3.58404i	0.718052	+	0.192401i	0.118749	+	0.992924i	$0.462111\pi$
$348$		0			0
$349$	−20.1282			−1.07744			−0.538720	−	0.842485i	$-0.681092\pi$
$349$	−20.1282			−1.07744			−0.538720	+	0.842485i	$0.681092\pi$
$350$		0			0
$351$	27.4387			1.46457
$352$		0			0
$353$	20.5124	+	5.49628i	1.09177	+	0.292538i	0.759407	−	0.650616i	$-0.225489\pi$
$353$	20.5124	+	5.49628i	1.09177	+	0.292538i	0.332358	+	0.943153i	$0.392156\pi$
$354$		0			0
$355$	−2.79368	+	11.1541i	−0.148273	+	0.592001i
$356$		0			0
$357$	0.0287796	+	0.627699i	0.00152318	+	0.0332214i
$358$		0			0
$359$	7.62630	+	4.40305i	0.402501	+	0.232384i	0.687562	−	0.726125i	$-0.258681\pi$
$359$	7.62630	+	4.40305i	0.402501	+	0.232384i	−0.285062	+	0.958509i	$0.592014\pi$
$360$		0			0
$361$	−7.92820	−	13.7320i	−0.417274	−	0.722739i
$362$		0			0
$363$	−0.528838	+	0.528838i	−0.0277568	+	0.0277568i
$364$		0			0
$365$	1.87440	−	3.37302i	0.0981106	−	0.176552i
$366$		0			0
$367$	5.97424	−	22.2962i	0.311853	−	1.16385i	−0.615031	−	0.788503i	$-0.710857\pi$
$367$	5.97424	−	22.2962i	0.311853	−	1.16385i	0.926884	−	0.375348i	$-0.122477\pi$
$368$		0			0
$369$	1.24597	−	2.15808i	0.0648625	−	0.112345i
$370$		0			0
$371$	−1.62944	−	5.12884i	−0.0845963	−	0.266276i
$372$		0			0
$373$	−34.8617	+	9.34117i	−1.80507	+	0.483668i	−0.994752	−	0.102319i	$-0.967374\pi$
$373$	−34.8617	+	9.34117i	−1.80507	+	0.483668i	−0.810321	+	0.585987i	$0.800707\pi$
$374$		0			0
$375$	8.05074	−	5.19166i	0.415738	−	0.268096i
$376$		0			0
$377$	40.8165	+	40.8165i	2.10216	+	2.10216i
$378$		0			0
$379$			11.6436i			0.598093i	0.954239	+	0.299046i	$0.0966685\pi$
$379$			11.6436i			0.598093i	−0.954239	+	0.299046i	$0.903331\pi$
$380$		0			0
$381$	12.2049	−	7.04649i	0.625275	−	0.361003i
$382$		0			0
$383$	−6.94215	−	25.9085i	−0.354727	−	1.32386i	−0.880827	−	0.473438i	$-0.843013\pi$
$383$	−6.94215	−	25.9085i	−0.354727	−	1.32386i	0.526100	−	0.850423i	$-0.323654\pi$
$384$		0			0
$385$	12.4593	−	14.1144i	0.634983	−	0.719336i
$386$		0			0
$387$	−3.90622	−	14.5782i	−0.198564	−	0.741051i
$388$		0			0
$389$	−21.9347	+	12.6640i	−1.11214	+	0.642092i	−0.939382	−	0.342873i	$-0.888600\pi$
$389$	−21.9347	+	12.6640i	−1.11214	+	0.642092i	−0.172754	+	0.984965i	$0.555266\pi$
$390$		0			0
$391$			1.62010i			0.0819320i
$392$		0			0
$393$	7.44286	+	7.44286i	0.375443	+	0.375443i
$394$		0			0
$395$	9.54583	−	9.86392i	0.480303	−	0.496307i
$396$		0			0
$397$	13.5896	−	3.64133i	0.682044	−	0.182753i	0.0988697	−	0.995100i	$-0.468477\pi$
$397$	13.5896	−	3.64133i	0.682044	−	0.182753i	0.583174	+	0.812347i	$0.301811\pi$
$398$		0			0
$399$	2.86824	−	13.0729i	0.143592	−	0.654462i
$400$		0			0
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	−0.901046	−	0.433724i	$-0.857199\pi$
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	0.826139	+	0.563466i	$0.190532\pi$
$402$		0			0
$403$	5.74749	−	21.4499i	0.286303	−	1.06850i
$404$		0			0
$405$	6.30343	−	1.80021i	0.313220	−	0.0894530i
$406$		0			0
$407$	−1.52180	+	1.52180i	−0.0754326	+	0.0754326i
$408$		0			0
$409$	−7.53689	−	13.0543i	−0.372675	−	0.645493i	0.617301	−	0.786727i	$-0.288226\pi$
$409$	−7.53689	−	13.0543i	−0.372675	−	0.645493i	−0.989976	+	0.141235i	$0.954893\pi$
$410$		0			0
$411$	11.2328	+	6.48523i	0.554071	+	0.319893i
$412$		0			0
$413$	−20.1680	−	10.4429i	−0.992400	−	0.513859i
$414$		0			0
$415$	−2.12299	−	3.54180i	−0.104214	−	0.173860i
$416$		0			0
$417$	4.19426	+	1.12385i	0.205394	+	0.0550351i
$418$		0			0
$419$	23.1211			1.12954			0.564770	−	0.825248i	$-0.308965\pi$
$419$	23.1211			1.12954			0.564770	+	0.825248i	$0.308965\pi$
$420$		0			0
$421$	6.71403			0.327222			0.163611	−	0.986525i	$-0.447686\pi$
$421$	6.71403			0.327222			0.163611	+	0.986525i	$0.447686\pi$
$422$		0			0
$423$	1.00386	+	0.268982i	0.0488091	+	0.0130784i
$424$		0			0
$425$	−0.947357	+	1.01158i	−0.0459535	+	0.0490689i
$426$		0			0
$427$	25.1419	−	1.15274i	1.21670	−	0.0557850i
$428$		0			0
$429$	−14.3605	−	8.29101i	−0.693329	−	0.400294i
$430$		0			0
$431$	7.40884	+	12.8325i	0.356871	+	0.618119i	0.987436	−	0.158017i	$-0.0505101\pi$
$431$	7.40884	+	12.8325i	0.356871	+	0.618119i	−0.630565	+	0.776136i	$0.717177\pi$
$432$		0			0
$433$	3.98442	−	3.98442i	0.191479	−	0.191479i	−0.604856	−	0.796335i	$-0.706769\pi$
$433$	3.98442	−	3.98442i	0.191479	−	0.191479i	0.796335	+	0.604856i	$0.206769\pi$
$434$		0			0
$435$	−15.8959	−	8.83340i	−0.762148	−	0.423529i
$436$		0			0
$437$	8.93121	−	33.3317i	0.427238	−	1.59447i
$438$		0			0
$439$	7.08258	−	12.2674i	0.338033	−	0.585491i	−0.646029	−	0.763312i	$-0.723572\pi$
$439$	7.08258	−	12.2674i	0.338033	−	0.585491i	0.984063	+	0.177822i	$0.0569050\pi$
$440$		0			0
$441$	−12.9527	+	9.15417i	−0.616796	+	0.435913i
$442$		0			0
$443$	−2.23023	+	0.597589i	−0.105962	+	0.0283923i	−0.311410	−	0.950276i	$-0.600801\pi$
$443$	−2.23023	+	0.597589i	−0.105962	+	0.0283923i	0.205449	+	0.978668i	$0.434135\pi$
$444$		0			0
$445$	3.82539	+	3.70203i	0.181341	+	0.175493i
$446$		0			0
$447$	−13.1580	−	13.1580i	−0.622350	−	0.622350i
$448$		0			0
$449$			9.87441i			0.466002i	0.972476	+	0.233001i	$0.0748545\pi$
$449$			9.87441i			0.466002i	−0.972476	+	0.233001i	$0.925145\pi$
$450$		0			0
$451$	−3.03095	+	1.74992i	−0.142722	+	0.0824004i
$452$		0			0
$453$	1.32171	+	4.93269i	0.0620993	+	0.231758i
$454$		0			0
$455$	−32.2160	−	16.0174i	−1.51031	−	0.750905i
$456$		0			0
$457$	5.10779	+	19.0625i	0.238932	+	0.891707i	0.976337	+	0.216256i	$0.0693846\pi$
$457$	5.10779	+	19.0625i	0.238932	+	0.891707i	−0.737404	+	0.675452i	$0.763949\pi$
$458$		0			0
$459$	1.08307	−	0.625314i	0.0505536	−	0.0291871i
$460$		0			0
$461$		−	16.9456i		−	0.789235i	−0.918845	−	0.394618i	$-0.870877\pi$
$461$		−	16.9456i		−	0.789235i	0.918845	−	0.394618i	$-0.129123\pi$
$462$		0			0
$463$	20.4791	+	20.4791i	0.951745	+	0.951745i	0.998888	−	0.0471427i	$-0.0150116\pi$
$463$	20.4791	+	20.4791i	0.951745	+	0.951745i	−0.0471427	+	0.998888i	$0.515012\pi$
$464$		0			0
$465$	0.114637	+	6.99511i	0.00531615	+	0.324391i
$466$		0			0
$467$	1.09744	−	0.294059i	0.0507837	−	0.0136074i	−0.233338	−	0.972396i	$-0.574965\pi$
$467$	1.09744	−	0.294059i	0.0507837	−	0.0136074i	0.284121	+	0.958788i	$0.408298\pi$
$468$		0			0
$469$	−0.176114	+	0.0559517i	−0.00813219	+	0.00258361i
$470$		0			0
$471$	1.67470	−	2.90067i	0.0771661	−	0.133656i
$472$		0			0
$473$	−5.48614	+	20.4745i	−0.252253	+	0.941421i
$474$		0			0
$475$	25.0674	−	15.5896i	1.15017	−	0.715300i
$476$		0			0
$477$	−3.25888	+	3.25888i	−0.149214	+	0.149214i
$478$		0			0
$479$	10.3749	+	17.9698i	0.474041	+	0.821063i	0.999558	−	0.0297200i	$-0.00946158\pi$
$479$	10.3749	+	17.9698i	0.474041	+	0.821063i	−0.525517	+	0.850783i	$0.676128\pi$
$480$		0			0
$481$	3.56175	+	2.05638i	0.162402	+	0.0937626i
$482$		0			0
$483$	11.1593	−	7.14354i	0.507764	−	0.325043i
$484$		0			0
$485$	−15.3427	+	9.19656i	−0.696676	+	0.417594i
$486$		0			0
$487$	−29.5118	−	7.90765i	−1.33731	−	0.358330i	−0.481871	−	0.876242i	$-0.660043\pi$
$487$	−29.5118	−	7.90765i	−1.33731	−	0.358330i	−0.855434	+	0.517912i	$0.826709\pi$
$488$		0			0
$489$	19.3856			0.876648
$490$		0			0
$491$	−1.92010			−0.0866529			−0.0433264	−	0.999061i	$-0.513796\pi$
$491$	−1.92010			−0.0866529			−0.0433264	+	0.999061i	$0.513796\pi$
$492$		0			0
$493$	2.54132	+	0.680945i	0.114455	+	0.0306682i
$494$		0			0
$495$	−15.6405	−	3.91733i	−0.702986	−	0.176071i
$496$		0			0
$497$	−11.4587	+	7.33523i	−0.513993	+	0.329030i
$498$		0			0
$499$	−18.3415	−	10.5895i	−0.821080	−	0.474051i	0.0297089	−	0.999559i	$-0.490542\pi$
$499$	−18.3415	−	10.5895i	−0.821080	−	0.474051i	−0.850789	+	0.525508i	$0.823875\pi$
$500$		0			0
$501$	4.89453	+	8.47757i	0.218671	+	0.378750i
$502$		0			0
$503$	5.68152	−	5.68152i	0.253326	−	0.253326i	−0.569007	−	0.822333i	$-0.692672\pi$
$503$	5.68152	−	5.68152i	0.253326	−	0.253326i	0.822333	+	0.569007i	$0.192672\pi$
$504$		0			0
$505$	8.49190	+	29.7344i	0.377885	+	1.32317i
$506$		0			0
$507$	−5.31862	+	19.8494i	−0.236208	+	0.881542i
$508$		0			0
$509$	−7.93038	+	13.7358i	−0.351508	+	0.608830i	−0.986514	−	0.163677i	$-0.947664\pi$
$509$	−7.93038	+	13.7358i	−0.351508	+	0.608830i	0.635006	+	0.772507i	$0.280998\pi$
$510$		0			0
$511$	4.35151	−	1.38248i	0.192499	−	0.0611574i
$512$		0			0
$513$	−25.7303	+	6.89440i	−1.13602	+	0.304395i
$514$		0			0
$515$	−24.2274	+	0.397041i	−1.06759	+	0.0174957i
$516$		0			0
$517$	−1.03210	−	1.03210i	−0.0453918	−	0.0453918i
$518$		0			0
$519$			5.22103i			0.229178i
$520$		0			0
$521$	−2.36477	+	1.36530i	−0.103602	+	0.0598148i	−0.550906	−	0.834567i	$-0.685718\pi$
$521$	−2.36477	+	1.36530i	−0.103602	+	0.0598148i	0.447304	+	0.894382i	$0.352384\pi$
$522$		0			0
$523$	6.66430	+	24.8715i	0.291409	+	1.08755i	0.944027	+	0.329867i	$0.107004\pi$
$523$	6.66430	+	24.8715i	0.291409	+	1.08755i	−0.652618	+	0.757687i	$0.726329\pi$
$524$		0			0
$525$	11.1450	+	2.06501i	0.486407	+	0.0901246i
$526$		0			0
$527$	−0.261965	−	0.977666i	−0.0114114	−	0.0425878i
$528$		0			0
$529$	9.66675	−	5.58110i	0.420294	−	0.242657i
$530$		0			0
$531$			19.4502i			0.844067i
$532$		0			0
$533$	4.72926	+	4.72926i	0.204847	+	0.204847i
$534$		0			0
$535$	9.06526	−	0.148563i	0.391925	−	0.00642292i
$536$		0			0
$537$	−18.3546	+	4.91810i	−0.792060	+	0.212232i
$538$		0			0
$539$	22.1828	−	2.03842i	0.955479	−	0.0878008i
$540$		0			0
$541$	7.82468	−	13.5527i	0.336409	−	0.582678i	−0.647345	−	0.762197i	$-0.724121\pi$
$541$	7.82468	−	13.5527i	0.336409	−	0.582678i	0.983755	+	0.179519i	$0.0574541\pi$
$542$		0			0
$543$	1.24353	−	4.64092i	0.0533650	−	0.199161i
$544$		0			0
$545$	−0.606934	−	2.12518i	−0.0259982	−	0.0910329i
$546$		0			0
$547$	−19.1465	+	19.1465i	−0.818645	+	0.818645i	−0.985912	−	0.167267i	$-0.946506\pi$
$547$	−19.1465	+	19.1465i	−0.818645	+	0.818645i	0.167267	+	0.985912i	$0.446506\pi$
$548$		0			0
$549$	−10.7773	−	18.6667i	−0.459962	−	0.796677i
$550$		0			0
$551$	−48.5310	−	28.0194i	−2.06749	−	1.19367i
$552$		0			0
$553$	16.2245	−	0.743883i	0.689936	−	0.0316331i
$554$		0			0
$555$	−1.25687	−	0.314798i	−0.0533513	−	0.0133624i
$556$		0			0
$557$	3.01546	+	0.807989i	0.127769	+	0.0342356i	0.322137	−	0.946693i	$-0.395599\pi$
$557$	3.01546	+	0.807989i	0.127769	+	0.0342356i	−0.194368	+	0.980929i	$0.562266\pi$
$558$		0			0
$559$	40.5071			1.71327
$560$		0			0
$561$	−0.755791			−0.0319095
$562$		0			0
$563$	−39.2089	−	10.5060i	−1.65246	−	0.442775i	−0.692160	−	0.721744i	$-0.743341\pi$
$563$	−39.2089	−	10.5060i	−1.65246	−	0.442775i	−0.960300	+	0.278969i	$0.910007\pi$
$564$		0			0
$565$	17.1134	−	10.2579i	0.719964	−	0.431554i
$566$		0			0
$567$	6.88792	+	3.56653i	0.289266	+	0.149780i
$568$		0			0
$569$	−27.5998	−	15.9348i	−1.15704	−	0.668020i	−0.206451	−	0.978457i	$-0.566191\pi$
$569$	−27.5998	−	15.9348i	−1.15704	−	0.668020i	−0.950594	+	0.310437i	$0.899525\pi$
$570$		0			0
$571$	−15.4723	−	26.7988i	−0.647495	−	1.12149i	−0.983719	−	0.179712i	$-0.942484\pi$
$571$	−15.4723	−	26.7988i	−0.647495	−	1.12149i	0.336225	−	0.941782i	$-0.390850\pi$
$572$		0			0
$573$	−9.68866	+	9.68866i	−0.404749	+	0.404749i
$574$		0			0
$575$	28.4611	+	6.63475i	1.18691	+	0.276688i
$576$		0			0
$577$	−8.45663	+	31.5606i	−0.352054	+	1.31388i	0.532097	+	0.846683i	$0.321404\pi$
$577$	−8.45663	+	31.5606i	−0.352054	+	1.31388i	−0.884151	+	0.467201i	$0.845263\pi$
$578$		0			0
$579$	−6.61287	+	11.4538i	−0.274822	+	0.476005i
$580$		0			0
$581$	1.04708	−	4.77238i	0.0434403	−	0.197992i
$582$		0			0
$583$	6.25227	−	1.67529i	0.258942	−	0.0693834i
$584$		0			0
$585$	0.504885	+	30.8080i	0.0208744	+	1.27375i
$586$		0			0
$587$	−18.6762	−	18.6762i	−0.770850	−	0.770850i	0.207405	−	0.978255i	$-0.433498\pi$
$587$	−18.6762	−	18.6762i	−0.770850	−	0.770850i	−0.978255	+	0.207405i	$0.933498\pi$
$588$		0			0
$589$			21.5585i			0.888304i
$590$		0			0
$591$	−19.7717	+	11.4152i	−0.813298	+	0.469558i
$592$		0			0
$593$	3.19807	+	11.9353i	0.131329	+	0.490126i	0.999986	−	0.00528774i	$-0.00168315\pi$
$593$	3.19807	+	11.9353i	0.131329	+	0.490126i	−0.868657	+	0.495414i	$0.835016\pi$
$594$		0			0
$595$	−1.63667	+	0.101939i	−0.0670971	+	0.00417909i
$596$		0			0
$597$	1.35099	+	5.04198i	0.0552925	+	0.206354i
$598$		0			0
$599$	13.6251	−	7.86645i	0.556706	−	0.321415i	−0.195116	−	0.980780i	$-0.562508\pi$
$599$	13.6251	−	7.86645i	0.556706	−	0.321415i	0.751822	+	0.659366i	$0.229175\pi$
$600$		0			0
$601$		−	23.7527i		−	0.968892i	−0.874821	−	0.484446i	$-0.839021\pi$
$601$		−	23.7527i		−	0.968892i	0.874821	−	0.484446i	$-0.160979\pi$
$602$		0			0
$603$	0.111903	+	0.111903i	0.00455706	+	0.00455706i
$604$		0			0
$605$	−1.40255	−	1.35732i	−0.0570218	−	0.0551830i
$606$		0			0
$607$	23.4617	−	6.28653i	0.952279	−	0.255162i	0.250950	−	0.968000i	$-0.419257\pi$
$607$	23.4617	−	6.28653i	0.952279	−	0.255162i	0.701329	+	0.712838i	$0.252590\pi$
$608$		0			0
$609$	−6.51515	−	20.5071i	−0.264007	−	0.830992i
$610$		0			0
$611$	−1.39466	+	2.41562i	−0.0564220	+	0.0977257i
$612$		0			0
$613$	−6.51764	+	24.3242i	−0.263245	+	0.982444i	0.700071	+	0.714073i	$0.253152\pi$
$613$	−6.51764	+	24.3242i	−0.263245	+	0.982444i	−0.963316	+	0.268370i	$0.913515\pi$
$614$		0			0
$615$	−1.84180	−	1.02349i	−0.0742684	−	0.0412712i
$616$		0			0
$617$	−9.80122	+	9.80122i	−0.394582	+	0.394582i	−0.876317	−	0.481735i	$-0.840007\pi$
$617$	−9.80122	+	9.80122i	−0.394582	+	0.394582i	0.481735	+	0.876317i	$0.340007\pi$
$618$		0			0
$619$	5.82024	+	10.0810i	0.233935	+	0.405188i	0.958963	−	0.283532i	$-0.0915063\pi$
$619$	5.82024	+	10.0810i	0.233935	+	0.405188i	−0.725028	+	0.688720i	$0.758173\pi$
$620$		0			0
$621$	−22.8382	−	13.1857i	−0.916467	−	0.529123i
$622$		0			0
$623$	0.288490	+	6.29213i	0.0115581	+	0.252089i
$624$		0			0
$625$	13.8913	+	20.7854i	0.555651	+	0.831416i
$626$		0			0
$627$	15.5496	+	4.16649i	0.620990	+	0.166394i
$628$		0			0
$629$	0.187455			0.00747432
$630$		0			0
$631$	9.30217			0.370313			0.185157	−	0.982709i	$-0.440721\pi$
$631$	9.30217			0.370313			0.185157	+	0.982709i	$0.440721\pi$
$632$		0			0
$633$	6.27911	+	1.68248i	0.249572	+	0.0668727i
$634$		0			0
$635$	18.9089	+	31.5458i	0.750375	+	1.25186i
$636$		0			0
$637$	−14.7343	−	39.9386i	−0.583796	−	1.58243i
$638$		0			0
$639$	10.0908	+	5.82594i	0.399187	+	0.230470i
$640$		0			0
$641$	14.6581	+	25.3885i	0.578959	+	1.00279i	0.995599	+	0.0937153i	$0.0298744\pi$
$641$	14.6581	+	25.3885i	0.578959	+	1.00279i	−0.416640	+	0.909072i	$0.636792\pi$
$642$		0			0
$643$	31.1484	−	31.1484i	1.22837	−	1.22837i	0.263793	−	0.964579i	$-0.415026\pi$
$643$	31.1484	−	31.1484i	1.22837	−	1.22837i	0.964579	−	0.263793i	$-0.0849737\pi$
$644$		0			0
$645$	−12.2709	+	3.50446i	−0.483166	+	0.137988i
$646$		0			0
$647$	2.48295	−	9.26648i	0.0976147	−	0.364303i	−0.899788	−	0.436327i	$-0.856279\pi$
$647$	2.48295	−	9.26648i	0.0976147	−	0.364303i	0.997403	+	0.0720240i	$0.0229458\pi$
$648$		0			0
$649$	13.6586	−	23.6573i	0.536145	−	0.928631i
$650$		0			0
$651$	−5.57908	+	6.11526i	−0.218662	+	0.239676i
$652$		0			0
$653$	25.8718	−	6.93234i	1.01244	−	0.271283i	0.285794	−	0.958291i	$-0.407743\pi$
$653$	25.8718	−	6.93234i	1.01244	−	0.271283i	0.726650	+	0.687008i	$0.241076\pi$
$654$		0			0
$655$	−19.1030	+	19.7395i	−0.746414	+	0.771287i
$656$		0			0
$657$	−2.76496	−	2.76496i	−0.107871	−	0.107871i
$658$		0			0
$659$		−	46.2930i		−	1.80332i	−0.432447	−	0.901659i	$-0.642350\pi$
$659$		−	46.2930i		−	1.80332i	0.432447	−	0.901659i	$-0.357650\pi$
$660$		0			0
$661$	39.8791	−	23.0242i	1.55112	−	0.895538i	0.553066	−	0.833137i	$-0.313458\pi$
$661$	39.8791	−	23.0242i	1.55112	−	0.895538i	0.998051	−	0.0624011i	$-0.0198758\pi$
$662$		0			0
$663$	0.373817	+	1.39510i	0.0145179	+	0.0541814i
$664$		0			0
$665$	34.2347	+	6.92530i	1.32756	+	0.268552i
$666$		0			0
$667$	−14.3587	−	53.5875i	−0.555972	−	2.07492i
$668$		0			0
$669$	12.5257	−	7.23170i	0.484271	−	0.279594i
$670$		0			0
$671$			30.2725i			1.16866i
$672$		0			0
$673$	−23.8326	−	23.8326i	−0.918681	−	0.918681i	0.0782525	−	0.996934i	$-0.475066\pi$
$673$	−23.8326	−	23.8326i	−0.918681	−	0.918681i	−0.996934	+	0.0782525i	$0.975066\pi$
$674$		0			0
$675$	−6.54972	−	21.5878i	−0.252099	−	0.830913i
$676$		0			0
$677$	−2.34476	+	0.628277i	−0.0901165	+	0.0241467i	−0.303596	−	0.952801i	$-0.598187\pi$
$677$	−2.34476	+	0.628277i	−0.0901165	+	0.0241467i	0.213479	+	0.976948i	$0.431520\pi$
$678$		0			0
$679$	−20.6734	−	4.53584i	−0.793374	−	0.174070i
$680$		0			0
$681$	−5.35576	+	9.27645i	−0.205233	+	0.355474i
$682$		0			0
$683$	−0.849224	+	3.16935i	−0.0324947	+	0.121272i	−0.980268	−	0.197673i	$-0.936662\pi$
$683$	−0.849224	+	3.16935i	−0.0324947	+	0.121272i	0.947773	+	0.318944i	$0.103328\pi$
$684$		0			0
$685$	−16.4421	+	29.5878i	−0.628219	+	1.13049i
$686$		0			0
$687$	−1.95501	+	1.95501i	−0.0745882	+	0.0745882i
$688$		0			0
$689$	−6.18479	−	10.7124i	−0.235622	−	0.408109i
$690$		0			0
$691$	22.6698	+	13.0884i	0.862401	+	0.497907i	0.864815	−	0.502090i	$-0.167435\pi$
$691$	22.6698	+	13.0884i	0.862401	+	0.497907i	−0.00241480	+	0.999997i	$0.500769\pi$
$692$		0			0
$693$	−10.2855	−	16.0675i	−0.390715	−	0.610354i
$694$		0			0
$695$	−2.75319	+	10.9925i	−0.104434	+	0.416968i
$696$		0			0
$697$	0.294454	+	0.0788986i	0.0111532	+	0.00298850i
$698$		0			0
$699$	−4.74366			−0.179422
$700$		0			0
$701$	−23.4738			−0.886592			−0.443296	−	0.896375i	$-0.646191\pi$
$701$	−23.4738			−0.886592			−0.443296	+	0.896375i	$0.646191\pi$
$702$		0			0
$703$	−3.85668	−	1.03339i	−0.145457	−	0.0389752i
$704$		0			0
$705$	0.213500	−	0.852428i	0.00804089	−	0.0321043i
$706$		0			0
$707$	−16.8240	+	32.4916i	−0.632730	+	1.22197i
$708$		0			0
$709$	17.1032	+	9.87455i	0.642325	+	0.370847i	0.785510	−	0.618849i	$-0.212401\pi$
$709$	17.1032	+	9.87455i	0.642325	+	0.370847i	−0.143184	+	0.989696i	$0.545734\pi$
$710$		0			0
$711$	−6.95474	−	12.0460i	−0.260823	−	0.451759i
$712$		0			0
$713$	−15.0916	+	15.0916i	−0.565186	+	0.565186i
$714$		0			0
$715$	21.0203	−	37.8264i	0.786114	−	1.41463i
$716$		0			0
$717$	−1.37438	+	5.12925i	−0.0513271	+	0.191555i
$718$		0			0
$719$	23.1884	−	40.1636i	0.864783	−	1.49785i	−0.00247948	−	0.999997i	$-0.500789\pi$
$719$	23.1884	−	40.1636i	0.864783	−	1.49785i	0.867262	−	0.497851i	$-0.165877\pi$
$720$		0			0
$721$	−21.1800	−	19.3230i	−0.788785	−	0.719626i
$722$		0			0
$723$	7.27306	−	1.94881i	0.270488	−	0.0724770i
$724$		0			0
$725$	22.3699	−	41.8560i	0.830798	−	1.55449i
$726$		0			0
$727$	16.4581	+	16.4581i	0.610397	+	0.610397i	0.943049	−	0.332653i	$-0.107944\pi$
$727$	16.4581	+	16.4581i	0.610397	+	0.610397i	−0.332653	+	0.943049i	$0.607944\pi$
$728$		0			0
$729$			4.95487i			0.183514i
$730$		0			0
$731$	1.59892	−	0.923137i	0.0591382	−	0.0341434i
$732$		0			0
$733$	8.41908	+	31.4204i	0.310966	+	1.16054i	0.927687	+	0.373358i	$0.121794\pi$
$733$	8.41908	+	31.4204i	0.310966	+	1.16054i	−0.616722	+	0.787181i	$0.711540\pi$
$734$		0			0
$735$	7.91878	+	10.8239i	0.292089	+	0.399247i
$736$		0			0
$737$	−0.0575261	−	0.214690i	−0.00211900	−	0.00790822i
$738$		0			0
$739$	26.6432	−	15.3825i	0.980086	−	0.565853i	0.0777897	−	0.996970i	$-0.475214\pi$
$739$	26.6432	−	15.3825i	0.980086	−	0.565853i	0.902296	+	0.431117i	$0.141880\pi$
$740$		0			0
$741$		−	30.7635i		−	1.13012i
$742$		0			0
$743$	23.8758	+	23.8758i	0.875917	+	0.875917i	0.993109	−	0.117193i	$-0.0373895\pi$
$743$	23.8758	+	23.8758i	0.875917	+	0.875917i	−0.117193	+	0.993109i	$0.537390\pi$
$744$		0			0
$745$	33.7714	−	34.8967i	1.23729	−	1.27852i
$746$		0			0
$747$	−4.04177	+	1.08299i	−0.147881	+	0.0396245i
$748$		0			0
$749$	7.92502	+	7.23017i	0.289574	+	0.264185i
$750$		0			0
$751$	−11.2895	+	19.5539i	−0.411959	+	0.713534i	−0.995104	−	0.0988344i	$-0.968489\pi$
$751$	−11.2895	+	19.5539i	−0.411959	+	0.713534i	0.583145	+	0.812368i	$0.301822\pi$
$752$		0			0
$753$	1.70301	−	6.35571i	0.0620610	−	0.231615i
$754$		0			0
$755$	−12.8147	+	3.65977i	−0.466375	+	0.133193i
$756$		0			0
$757$	20.3329	−	20.3329i	0.739013	−	0.739013i	−0.233374	−	0.972387i	$-0.574977\pi$
$757$	20.3329	−	20.3329i	0.739013	−	0.739013i	0.972387	+	0.233374i	$0.0749766\pi$
$758$		0			0
$759$	7.96849	+	13.8018i	0.289238	+	0.500975i
$760$		0			0
$761$	16.1822	+	9.34279i	0.586604	+	0.338676i	0.763753	−	0.645508i	$-0.223354\pi$
$761$	16.1822	+	9.34279i	0.586604	+	0.338676i	−0.177150	+	0.984184i	$0.556688\pi$
$762$		0			0
$763$	1.20244	−	2.32224i	0.0435314	−	0.0840709i
$764$		0			0
$765$	0.722028	+	1.20456i	0.0261050	+	0.0435511i
$766$		0			0
$767$	−50.4243	−	13.5111i	−1.82071	−	0.487859i
$768$		0			0
$769$	−22.1987			−0.800507			−0.400253	−	0.916404i	$-0.631078\pi$
$769$	−22.1987			−0.800507			−0.400253	+	0.916404i	$0.631078\pi$
$770$		0			0
$771$	14.3616			0.517219
$772$		0			0
$773$	−43.9750	−	11.7831i	−1.58167	−	0.423807i	−0.642228	−	0.766514i	$-0.721990\pi$
$773$	−43.9750	−	11.7831i	−1.58167	−	0.423807i	−0.939443	+	0.342706i	$0.888656\pi$
$774$		0			0
$775$	−18.2480	+	0.598261i	−0.655487	+	0.0214902i
$776$		0			0
$777$	−0.826550	−	1.29119i	−0.0296523	−	0.0463212i
$778$		0			0
$779$	−5.62311	−	3.24650i	−0.201469	−	0.116318i
$780$		0			0
$781$	−8.18232	−	14.1722i	−0.292786	−	0.507121i
$782$		0			0
$783$	−30.2825	+	30.2825i	−1.08221	+	1.08221i
$784$		0			0
$785$	7.64054	+	4.24588i	0.272703	+	0.151542i
$786$		0			0
$787$	−10.5000	+	39.1866i	−0.374285	+	1.39685i	0.480102	+	0.877213i	$0.340600\pi$
$787$	−10.5000	+	39.1866i	−0.374285	+	1.39685i	−0.854387	+	0.519638i	$0.826067\pi$
$788$		0			0
$789$	7.81915	−	13.5432i	0.278369	−	0.482149i
$790$		0			0
$791$	23.0593	+	5.05931i	0.819895	+	0.179888i
$792$		0			0
$793$	55.8796	−	14.9729i	1.98434	−	0.531703i
$794$		0			0
$795$	2.80035	+	2.71004i	0.0993180	+	0.0961153i
$796$		0			0
$797$	20.2379	+	20.2379i	0.716863	+	0.716863i	0.967962	−	0.251098i	$-0.0807917\pi$
$797$	20.2379	+	20.2379i	0.716863	+	0.716863i	−0.251098	+	0.967962i	$0.580792\pi$
$798$		0			0
$799$			0.127134i			0.00449769i
$800$		0			0
$801$	4.67163	−	2.69716i	0.165064	−	0.0952996i
$802$		0			0
$803$	1.42138	+	5.30467i	0.0501595	+	0.187198i
$804$		0			0
$805$	19.1174	+	28.8132i	0.673800	+	1.01553i
$806$		0			0
$807$	−2.98366	−	11.1352i	−0.105030	−	0.391976i
$808$		0			0
$809$	−0.231574	+	0.133699i	−0.00814172	+	0.00470062i	−0.504065	−	0.863666i	$-0.668163\pi$
$809$	−0.231574	+	0.133699i	−0.00814172	+	0.00470062i	0.495924	+	0.868366i	$0.334830\pi$
$810$		0			0
$811$			0.751247i			0.0263799i	0.999913	+	0.0131899i	$0.00419861\pi$
$811$			0.751247i			0.0263799i	−0.999913	+	0.0131899i	$0.995801\pi$
$812$		0			0
$813$	−14.6383	−	14.6383i	−0.513388	−	0.513388i
$814$		0			0
$815$	0.828983	+	50.5844i	0.0290380	+	1.77189i
$816$		0			0
$817$	−37.9850	+	10.1781i	−1.32893	+	0.356085i
$818$		0			0
$819$	−24.5715	+	26.9330i	−0.858598	+	0.941114i
$820$		0			0
$821$	−5.63523	+	9.76051i	−0.196671	+	0.340644i	−0.947447	−	0.319913i	$-0.896346\pi$
$821$	−5.63523	+	9.76051i	−0.196671	+	0.340644i	0.750776	+	0.660557i	$0.229680\pi$
$822$		0			0
$823$	1.82320	−	6.80428i	0.0635528	−	0.237182i	−0.926842	−	0.375452i	$-0.877487\pi$
$823$	1.82320	−	6.80428i	0.0635528	−	0.237182i	0.990395	+	0.138270i	$0.0441541\pi$
$824$		0			0
$825$	−3.09517	+	13.2774i	−0.107760	+	0.462259i
$826$		0			0
$827$	−6.45564	+	6.45564i	−0.224485	+	0.224485i	−0.810384	−	0.585899i	$-0.800741\pi$
$827$	−6.45564	+	6.45564i	−0.224485	+	0.224485i	0.585899	+	0.810384i	$0.300741\pi$
$828$		0			0
$829$	5.45878	+	9.45489i	0.189591	+	0.328382i	0.945114	−	0.326741i	$-0.105950\pi$
$829$	5.45878	+	9.45489i	0.189591	+	0.328382i	−0.755523	+	0.655123i	$0.772617\pi$
$830$		0			0
$831$	0.822732	+	0.475005i	0.0285403	+	0.0164777i
$832$		0			0
$833$	−1.49178	−	1.24069i	−0.0516872	−	0.0429874i
$834$		0			0
$835$	−21.9119	+	13.1342i	−0.758291	+	0.454527i
$836$		0			0
$837$	15.9141	+	4.26416i	0.550070	+	0.147391i
$838$		0			0
$839$	−41.6035			−1.43631			−0.718157	−	0.695882i	$-0.755014\pi$
$839$	−41.6035			−1.43631			−0.718157	+	0.695882i	$0.755014\pi$
$840$		0			0
$841$	−61.0936			−2.10668
$842$		0			0
$843$	8.55282	+	2.29172i	0.294575	+	0.0789311i
$844$		0			0
$845$	−52.0219	−	13.0295i	−1.78961	−	0.448228i
$846$		0			0
$847$	−0.105773	−	2.30696i	−0.00363439	−	0.0792681i
$848$		0			0
$849$	−2.88348	−	1.66478i	−0.0989609	−	0.0571351i
$850$		0			0
$851$	−1.97638	−	3.42320i	−0.0677495	−	0.117346i
$852$		0			0
$853$	−15.7425	+	15.7425i	−0.539013	+	0.539013i	−0.923239	−	0.384226i	$-0.874468\pi$
$853$	−15.7425	+	15.7425i	−0.539013	+	0.539013i	0.384226	+	0.923239i	$0.374468\pi$
$854$		0			0
$855$	−8.21445	−	28.7629i	−0.280928	−	0.983672i
$856$		0			0
$857$	6.22812	−	23.2437i	0.212749	−	0.793988i	−0.774198	−	0.632943i	$-0.781847\pi$
$857$	6.22812	−	23.2437i	0.212749	−	0.793988i	0.986947	−	0.161045i	$-0.0514866\pi$
$858$		0			0
$859$	−6.61840	+	11.4634i	−0.225817	+	0.391127i	−0.956564	−	0.291522i	$-0.905838\pi$
$859$	−6.61840	+	11.4634i	−0.225817	+	0.391127i	0.730747	+	0.682648i	$0.239172\pi$
$860$		0			0
$861$	−0.754887	−	2.37609i	−0.0257265	−	0.0809769i
$862$		0			0
$863$	37.4574	−	10.0367i	1.27507	−	0.341653i	0.443096	−	0.896474i	$-0.353880\pi$
$863$	37.4574	−	10.0367i	1.27507	−	0.341653i	0.831969	+	0.554822i	$0.187213\pi$
$864$		0			0
$865$	−13.6236	+	0.223266i	−0.463217	+	0.00759126i
$866$		0			0
$867$	−10.2531	−	10.2531i	−0.348215	−	0.348215i
$868$		0			0
$869$			19.5354i			0.662692i
$870$		0			0
$871$	−0.367841	+	0.212373i	−0.0124638	+	0.00719599i
$872$		0			0
$873$	4.69139	+	17.5085i	0.158780	+	0.592574i
$874$		0			0
$875$	−4.91181	+	29.1697i	−0.166049	+	0.986117i
$876$		0			0
$877$	6.55124	+	24.4496i	0.221220	+	0.825603i	0.983884	+	0.178808i	$0.0572242\pi$
$877$	6.55124	+	24.4496i	0.221220	+	0.825603i	−0.762664	+	0.646795i	$0.776109\pi$
$878$		0			0
$879$	−20.5388	+	11.8581i	−0.692756	+	0.399963i
$880$		0			0
$881$		−	32.6516i		−	1.10006i	−0.835145	−	0.550030i	$-0.814616\pi$
$881$		−	32.6516i		−	1.10006i	0.835145	−	0.550030i	$-0.185384\pi$
$882$		0			0
$883$	−9.26586	−	9.26586i	−0.311821	−	0.311821i	0.533794	−	0.845615i	$-0.320766\pi$
$883$	−9.26586	−	9.26586i	−0.311821	−	0.311821i	−0.845615	+	0.533794i	$0.820766\pi$
$884$		0			0
$885$	16.4440	−	0.269487i	0.552760	−	0.00905870i
$886$		0			0
$887$	49.8736	−	13.3636i	1.67459	−	0.448705i	0.708248	−	0.705963i	$-0.249486\pi$
$887$	49.8736	−	13.3636i	1.67459	−	0.448705i	0.966343	+	0.257258i	$0.0828190\pi$
$888$		0			0
$889$	−9.32606	+	42.5062i	−0.312786	+	1.42561i
$890$		0			0
$891$	−4.66478	+	8.07964i	−0.156276	+	0.270678i
$892$		0			0
$893$	0.700861	−	2.61565i	0.0234534	−	0.0875294i
$894$		0			0
$895$	−13.6181	−	47.6838i	−0.455202	−	1.59389i
$896$		0			0
$897$	21.5354	−	21.5354i	0.719045	−	0.719045i
$898$		0			0
$899$	17.3299	+	30.0162i	0.577983	+	1.00110i
$900$		0			0
$901$	−0.488259	−	0.281896i	−0.0162663	−	0.00939132i
$902$		0			0
$903$	−13.4087	−	6.94296i	−0.446215	−	0.231047i
$904$		0			0
$905$	12.1631	+	3.04638i	0.404314	+	0.101265i
$906$		0			0
$907$	31.4156	+	8.41780i	1.04314	+	0.279508i	0.739414	−	0.673251i	$-0.235103\pi$
$907$	31.4156	+	8.41780i	1.04314	+	0.279508i	0.303726	+	0.952760i	$0.401769\pi$
$908$		0			0
$909$	31.3353			1.03932
$910$		0			0
$911$	1.25581			0.0416068			0.0208034	−	0.999784i	$-0.493378\pi$
$911$	1.25581			0.0416068			0.0208034	+	0.999784i	$0.493378\pi$
$912$		0			0
$913$	5.67653	+	1.52102i	0.187866	+	0.0503384i
$914$		0			0
$915$	−15.6323	+	9.37017i	−0.516789	+	0.309768i
$916$		0			0
$917$	−32.4682	+	1.48865i	−1.07219	+	0.0491594i
$918$		0			0
$919$	28.5463	+	16.4812i	0.941656	+	0.543666i	0.890479	−	0.455024i	$-0.150369\pi$
$919$	28.5463	+	16.4812i	0.941656	+	0.543666i	0.0511772	+	0.998690i	$0.483703\pi$
$920$		0			0
$921$	6.11583	+	10.5929i	0.201523	+	0.349049i
$922$		0			0
$923$	−22.1132	+	22.1132i	−0.727866	+	0.727866i
$924$		0			0
$925$	0.767679	−	3.29312i	0.0252411	−	0.108277i
$926$		0			0
$927$	−6.35489	+	23.7168i	−0.208722	+	0.778962i
$928$		0			0
$929$	17.3855	−	30.1125i	0.570399	−	0.987960i	−0.426126	−	0.904664i	$-0.640122\pi$
$929$	17.3855	−	30.1125i	0.570399	−	0.987960i	0.996525	−	0.0832962i	$-0.0265448\pi$
$930$		0			0
$931$	23.8521	+	33.7497i	0.781722	+	1.10610i
$932$		0			0
$933$	22.0740	−	5.91470i	0.722669	−	0.193639i
$934$		0			0
$935$	−0.0323197	−	1.97214i	−0.00105697	−	0.0644960i
$936$		0			0
$937$	−12.4528	−	12.4528i	−0.406816	−	0.406816i	0.473811	−	0.880627i	$-0.342878\pi$
$937$	−12.4528	−	12.4528i	−0.406816	−	0.406816i	−0.880627	+	0.473811i	$0.842878\pi$
$938$		0			0
$939$			3.92037i			0.127936i
$940$		0			0
$941$	33.8968	−	19.5703i	1.10500	−	0.637974i	0.167473	−	0.985877i	$-0.446439\pi$
$941$	33.8968	−	19.5703i	1.10500	−	0.637974i	0.937531	+	0.347903i	$0.113106\pi$
$942$		0			0
$943$	−1.66369	−	6.20899i	−0.0541773	−	0.202193i
$944$		0			0
$945$	11.8835	−	23.9015i	0.386572	−	0.777517i
$946$		0			0
$947$	3.27748	+	12.2317i	0.106504	+	0.397478i	0.998511	−	0.0545424i	$-0.0173700\pi$
$947$	3.27748	+	12.2317i	0.106504	+	0.397478i	−0.892008	+	0.452021i	$0.850703\pi$
$948$		0			0
$949$	9.08879	−	5.24742i	0.295035	−	0.170338i
$950$		0			0
$951$			15.7873i			0.511940i
$952$		0			0
$953$	−34.9436	−	34.9436i	−1.13193	−	1.13193i	−0.989855	−	0.142078i	$-0.954622\pi$
$953$	−34.9436	−	34.9436i	−1.13193	−	1.13193i	−0.142078	−	0.989855i	$-0.545378\pi$
$954$		0			0
$955$	−25.6957	−	24.8670i	−0.831492	−	0.804679i
$956$		0			0
$957$	24.9991	−	6.69848i	0.808106	−	0.216531i
$958$		0			0
$959$	−38.1710	+	12.1270i	−1.23261	+	0.391601i
$960$		0			0
$961$	−8.83307	+	15.2993i	−0.284938	+	0.493526i
$962$		0			0
$963$	2.37784	−	8.87422i	0.0766248	−	0.285968i
$964$		0			0
$965$	−30.1702	−	16.7657i	−0.971212	−	0.539706i
$966$		0			0
$967$	17.3593	−	17.3593i	0.558236	−	0.558236i	−0.370569	−	0.928805i	$-0.620837\pi$
$967$	17.3593	−	17.3593i	0.558236	−	0.558236i	0.928805	+	0.370569i	$0.120837\pi$
$968$		0			0
$969$	−0.701084	−	1.21431i	−0.0225221	−	0.0390093i
$970$		0			0
$971$	−30.4870	−	17.6017i	−0.978375	−	0.564865i	−0.0765959	−	0.997062i	$-0.524405\pi$
$971$	−30.4870	−	17.6017i	−0.978375	−	0.564865i	−0.901779	+	0.432197i	$0.857738\pi$
$972$		0			0
$973$	−11.2926	+	7.22891i	−0.362024	+	0.231748i
$974$		0			0
$975$	26.0394	−	0.853703i	0.833928	−	0.0273404i
$976$		0			0
$977$	21.3931	+	5.73226i	0.684425	+	0.183391i	0.584244	−	0.811578i	$-0.301391\pi$
$977$	21.3931	+	5.73226i	0.684425	+	0.183391i	0.100181	+	0.994969i	$0.468058\pi$
$978$		0			0
$979$	−7.57614			−0.242134
$980$		0			0
$981$	−2.23960			−0.0715049
$982$		0			0
$983$	−14.7987	−	3.96530i	−0.472005	−	0.126473i	0.0149724	−	0.999888i	$-0.495234\pi$
$983$	−14.7987	−	3.96530i	−0.472005	−	0.126473i	−0.486977	+	0.873415i	$0.661901\pi$
$984$		0			0
$985$	−30.6320	−	51.1036i	−0.976016	−	1.62830i
$986$		0			0
$987$	0.875703	−	0.560577i	0.0278739	−	0.0178434i
$988$		0			0
$989$	−33.7156	−	19.4657i	−1.07209	−	0.618974i
$990$		0			0
$991$	12.1139	+	20.9818i	0.384810	+	0.666510i	0.991743	−	0.128243i	$-0.0409337\pi$
$991$	12.1139	+	20.9818i	0.384810	+	0.666510i	−0.606933	+	0.794753i	$0.707600\pi$
$992$		0			0
$993$	14.4393	−	14.4393i	0.458218	−	0.458218i
$994$		0			0
$995$	−13.0986	+	3.74086i	−0.415255	+	0.118593i
$996$		0			0
$997$	−8.35755	+	31.1908i	−0.264686	+	0.987823i	0.697756	+	0.716336i	$0.254182\pi$
$997$	−8.35755	+	31.1908i	−0.264686	+	0.987823i	−0.962442	+	0.271487i	$0.912485\pi$
$998$		0			0
$999$	−1.52566	+	2.64252i	−0.0482697	+	0.0836056i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.u.a.33.2	yes	16
3.2	odd	2		1260.2.dq.a.1153.3		16
4.3	odd	2		560.2.ci.d.33.3		16
5.2	odd	4	inner	140.2.u.a.117.2	yes	16
5.3	odd	4		700.2.bc.b.257.3		16
5.4	even	2		700.2.bc.b.593.3		16
7.2	even	3		980.2.m.a.293.5		16
7.3	odd	6	inner	140.2.u.a.73.2	yes	16
7.4	even	3		980.2.v.a.913.3		16
7.5	odd	6		980.2.m.a.293.4		16
7.6	odd	2		980.2.v.a.313.3		16
15.2	even	4		1260.2.dq.a.397.4		16
20.7	even	4		560.2.ci.d.257.3		16
21.17	even	6		1260.2.dq.a.73.4		16
28.3	even	6		560.2.ci.d.353.3		16
35.2	odd	12		980.2.m.a.97.4		16
35.3	even	12		700.2.bc.b.157.3		16
35.12	even	12		980.2.m.a.97.5		16
35.17	even	12	inner	140.2.u.a.17.2	✓	16
35.24	odd	6		700.2.bc.b.493.3		16
35.27	even	4		980.2.v.a.117.3		16
35.32	odd	12		980.2.v.a.717.3		16
105.17	odd	12		1260.2.dq.a.577.3		16
140.87	odd	12		560.2.ci.d.17.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.u.a.17.2	✓	16	35.17	even	12	inner
140.2.u.a.33.2	yes	16	1.1	even	1	trivial
140.2.u.a.73.2	yes	16	7.3	odd	6	inner
140.2.u.a.117.2	yes	16	5.2	odd	4	inner
560.2.ci.d.17.3		16	140.87	odd	12
560.2.ci.d.33.3		16	4.3	odd	2
560.2.ci.d.257.3		16	20.7	even	4
560.2.ci.d.353.3		16	28.3	even	6
700.2.bc.b.157.3		16	35.3	even	12
700.2.bc.b.257.3		16	5.3	odd	4
700.2.bc.b.493.3		16	35.24	odd	6
700.2.bc.b.593.3		16	5.4	even	2
980.2.m.a.97.4		16	35.2	odd	12
980.2.m.a.97.5		16	35.12	even	12
980.2.m.a.293.4		16	7.5	odd	6
980.2.m.a.293.5		16	7.2	even	3
980.2.v.a.117.3		16	35.27	even	4
980.2.v.a.313.3		16	7.6	odd	2
980.2.v.a.717.3		16	35.32	odd	12
980.2.v.a.913.3		16	7.4	even	3
1260.2.dq.a.73.4		16	21.17	even	6
1260.2.dq.a.397.4		16	15.2	even	4
1260.2.dq.a.577.3		16	105.17	odd	12
1260.2.dq.a.1153.3		16	3.2	odd	2

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:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.827625 - 0.221762i) q^{3} +(0.543268 - 2.16907i) q^{5} +(2.22829 - 1.42643i) q^{7} +(-1.96229 - 1.13293i) q^{9} +O(q^{10})\)	\(q+(-0.827625 - 0.221762i) q^{3} +(0.543268 - 2.16907i) q^{5} +(2.22829 - 1.42643i) q^{7} +(-1.96229 - 1.13293i) q^{9} +(1.59116 + 2.75597i) q^{11} +(4.30021 - 4.30021i) q^{13} +(-0.930638 + 1.67470i) q^{15} +(0.0717406 - 0.267740i) q^{17} +(-2.95197 + 5.11295i) q^{19} +(-2.16052 + 0.686401i) q^{21} +(-5.64569 + 1.51276i) q^{23} +(-4.40972 - 2.35677i) q^{25} +(3.19039 + 3.19039i) q^{27} +9.49177i q^{29} +(3.16234 - 1.82578i) q^{31} +(-0.705715 - 2.63376i) q^{33} +(-1.88347 - 5.60826i) q^{35} +(0.175035 + 0.653239i) q^{37} +(-4.51258 + 2.60534i) q^{39} +1.09978i q^{41} +(4.70991 + 4.70991i) q^{43} +(-3.52345 + 3.64086i) q^{45} +(-0.443035 + 0.118711i) q^{47} +(2.93059 - 6.35702i) q^{49} +(-0.118749 + 0.205679i) q^{51} +(0.526437 - 1.96469i) q^{53} +(6.84231 - 1.95410i) q^{55} +(3.57698 - 3.57698i) q^{57} +(-4.29202 - 7.43399i) q^{59} +(8.23827 + 4.75637i) q^{61} +(-5.98861 + 0.274574i) q^{63} +(-6.99128 - 11.6636i) q^{65} +(-0.0674636 - 0.0180768i) q^{67} +5.00798 q^{69} -5.14237 q^{71} +(1.66692 + 0.446650i) q^{73} +(3.12695 + 2.92843i) q^{75} +(7.47676 + 3.87143i) q^{77} +(5.31629 + 3.06936i) q^{79} +(1.46584 + 2.53892i) q^{81} +(1.30581 - 1.30581i) q^{83} +(-0.541771 - 0.301065i) q^{85} +(2.10491 - 7.85563i) q^{87} +(-1.19035 + 2.06175i) q^{89} +(3.44817 - 15.7161i) q^{91} +(-3.02212 + 0.809775i) q^{93} +(9.48664 + 9.18072i) q^{95} +(-5.65663 - 5.65663i) q^{97} -7.21068i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{5} + 2 q^{7}+O(q^{10}) \) 16 * q + 6 * q^5 + 2 * q^7	\( 16 q + 6 q^{5} + 2 q^{7} - 20 q^{15} + 18 q^{17} - 4 q^{21} - 16 q^{23} + 6 q^{25} - 12 q^{31} - 42 q^{33} - 40 q^{35} - 14 q^{37} + 28 q^{43} - 66 q^{45} - 6 q^{47} + 20 q^{51} - 10 q^{53} + 44 q^{57} + 60 q^{61} + 48 q^{63} + 34 q^{65} + 8 q^{67} - 8 q^{71} + 78 q^{73} + 96 q^{75} + 10 q^{77} + 24 q^{81} + 30 q^{87} - 64 q^{91} - 62 q^{93} + 2 q^{95}+O(q^{100}) \) 16 * q + 6 * q^5 + 2 * q^7 - 20 * q^15 + 18 * q^17 - 4 * q^21 - 16 * q^23 + 6 * q^25 - 12 * q^31 - 42 * q^33 - 40 * q^35 - 14 * q^37 + 28 * q^43 - 66 * q^45 - 6 * q^47 + 20 * q^51 - 10 * q^53 + 44 * q^57 + 60 * q^61 + 48 * q^63 + 34 * q^65 + 8 * q^67 - 8 * q^71 + 78 * q^73 + 96 * q^75 + 10 * q^77 + 24 * q^81 + 30 * q^87 - 64 * q^91 - 62 * q^93 + 2 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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