LMFDB - Embedded newform 275.2.bm.b.18.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,2,Mod(7,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.bm (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			18.1
Character	$\chi$	$=$	275.18
Dual form			275.2.bm.b.107.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.380541 - 2.40264i) q^{2} +(-0.532840 + 0.271495i) q^{3} +(-3.72576 + 1.21057i) q^{4} +(0.855073 + 1.17691i) q^{6} +(-1.17208 + 2.30033i) q^{7} +(2.11764 + 4.15610i) q^{8} +(-1.55315 + 2.13772i) q^{9} +(-2.55440 + 2.11543i) q^{11} +(1.65657 - 1.65657i) q^{12} +(-2.77422 + 0.439393i) q^{13} +(5.97289 + 1.94071i) q^{14} +(2.84111 - 2.06419i) q^{16} +(0.932684 + 0.147723i) q^{17} +(5.72722 + 2.91817i) q^{18} +(1.28236 - 3.94669i) q^{19} -1.54392i q^{21} +(6.05467 + 5.33231i) q^{22} +(-0.104710 - 0.104710i) q^{23} +(-2.25672 - 1.63960i) q^{24} +(2.11141 + 6.49824i) q^{26} +(0.527849 - 3.33271i) q^{27} +(1.58216 - 9.98937i) q^{28} +(2.14459 + 6.60038i) q^{29} +(-7.33171 - 5.32680i) q^{31} +(0.555921 + 0.555921i) q^{32} +(0.786759 - 1.82069i) q^{33} -2.29712i q^{34} +(3.19879 - 9.84486i) q^{36} +(-6.77002 - 3.44950i) q^{37} +(-9.97047 - 1.57917i) q^{38} +(1.35892 - 0.987312i) q^{39} +(3.27880 + 1.06535i) q^{41} +(-3.70949 + 0.587525i) q^{42} +(-3.91833 + 3.91833i) q^{43} +(6.95623 - 10.9739i) q^{44} +(-0.211733 + 0.291426i) q^{46} +(-0.479999 - 0.942051i) q^{47} +(-0.953440 + 1.87123i) q^{48} +(0.196744 + 0.270795i) q^{49} +(-0.537077 + 0.174507i) q^{51} +(9.80416 - 4.99547i) q^{52} +(0.644920 + 4.07187i) q^{53} -8.20817 q^{54} -12.0424 q^{56} +(0.388217 + 2.45111i) q^{57} +(15.0422 - 7.66441i) q^{58} +(-6.16460 + 2.00300i) q^{59} +(5.59880 + 7.70609i) q^{61} +(-10.0084 + 19.6426i) q^{62} +(-3.09706 - 6.07833i) q^{63} +(5.25251 - 7.22946i) q^{64} +(-4.67386 - 1.19745i) q^{66} +(-2.94509 + 2.94509i) q^{67} +(-3.65379 + 0.578703i) q^{68} +(0.0842215 + 0.0273652i) q^{69} +(-1.02426 + 0.744171i) q^{71} +(-12.1736 - 1.92811i) q^{72} +(-1.57831 - 0.804189i) q^{73} +(-5.71163 + 17.5786i) q^{74} +16.2568i q^{76} +(-1.87222 - 8.35541i) q^{77} +(-2.88928 - 2.88928i) q^{78} +(-3.51271 - 2.55214i) q^{79} +(-1.82606 - 5.62003i) q^{81} +(1.31193 - 8.28320i) q^{82} +(-1.29707 + 8.18939i) q^{83} +(1.86903 + 5.75228i) q^{84} +(10.9054 + 7.92326i) q^{86} +(-2.93470 - 2.93470i) q^{87} +(-14.2012 - 6.13664i) q^{88} -4.23092i q^{89} +(2.24084 - 6.89661i) q^{91} +(0.516882 + 0.263364i) q^{92} +(5.35283 + 0.847805i) q^{93} +(-2.08075 + 1.51175i) q^{94} +(-0.447147 - 0.145287i) q^{96} +(14.2460 - 2.25634i) q^{97} +(0.575755 - 0.575755i) q^{98} +(-0.554831 - 8.74618i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 10 q^{2} + 4 q^{3} - 20 q^{6} + 10 q^{8} - 24 q^{11} - 12 q^{12} + 10 q^{13} - 8 q^{16} + 10 q^{18} - 10 q^{22} + 24 q^{23} + 20 q^{26} + 16 q^{27} - 50 q^{28} - 28 q^{31} - 66 q^{33} + 24 q^{36}+ \cdots + 8 q^{97}+O(q^{100}) $ 32 * q + 10 * q^2 + 4 * q^3 - 20 * q^6 + 10 * q^8 - 24 * q^11 - 12 * q^12 + 10 * q^13 - 8 * q^16 + 10 * q^18 - 10 * q^22 + 24 * q^23 + 20 * q^26 + 16 * q^27 - 50 * q^28 - 28 * q^31 - 66 * q^33 + 24 * q^36 + 8 * q^37 - 10 * q^38 + 40 * q^41 + 10 * q^42 + 60 * q^46 + 28 * q^47 + 54 * q^48 + 20 * q^51 + 50 * q^52 + 24 * q^53 - 80 * q^56 - 30 * q^57 + 50 * q^58 - 60 * q^61 - 100 * q^62 + 30 * q^63 - 100 * q^66 + 8 * q^67 + 30 * q^68 + 24 * q^71 - 80 * q^72 - 50 * q^73 - 70 * q^77 - 60 * q^78 - 12 * q^81 + 10 * q^82 - 90 * q^83 + 100 * q^86 - 170 * q^88 + 20 * q^91 + 68 * q^92 + 8 * q^93 + 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.380541	−	2.40264i	−0.269083	−	1.69892i	−0.638468	−	0.769648i	$-0.720432\pi$
$2$	−0.380541	−	2.40264i	−0.269083	−	1.69892i	0.369385	−	0.929276i	$-0.379568\pi$
$3$	−0.532840	+	0.271495i	−0.307635	+	0.156748i	−0.600992	−	0.799255i	$-0.705228\pi$
$3$	−0.532840	+	0.271495i	−0.307635	+	0.156748i	0.293357	+	0.956003i	$0.405228\pi$
$4$	−3.72576	+	1.21057i	−1.86288	+	0.605287i
$5$		0			0
$5$		0			0
$6$	0.855073	+	1.17691i	0.349082	+	0.480470i
$7$	−1.17208	+	2.30033i	−0.443003	+	0.869443i	0.556258	+	0.831010i	$0.312237\pi$
$7$	−1.17208	+	2.30033i	−0.443003	+	0.869443i	−0.999261	+	0.0384331i	$0.987763\pi$
$8$	2.11764	+	4.15610i	0.748698	+	1.46940i
$9$	−1.55315	+	2.13772i	−0.517716	+	0.712575i
$10$		0			0
$11$	−2.55440	+	2.11543i	−0.770182	+	0.637825i
$11$	−2.55440	+	2.11543i	−0.770182	+	0.637825i
$12$	1.65657	−	1.65657i	0.478210	−	0.478210i
$13$	−2.77422	+	0.439393i	−0.769429	+	0.121866i	−0.528794	−	0.848750i	$-0.677356\pi$
$13$	−2.77422	+	0.439393i	−0.769429	+	0.121866i	−0.240635	+	0.970616i	$0.577356\pi$
$14$	5.97289	+	1.94071i	1.59632	+	0.518677i
$15$		0			0
$16$	2.84111	−	2.06419i	0.710279	−	0.516048i
$17$	0.932684	+	0.147723i	0.226209	+	0.0358280i	0.268510	−	0.963277i	$-0.413469\pi$
$17$	0.932684	+	0.147723i	0.226209	+	0.0358280i	−0.0423009	+	0.999105i	$0.513469\pi$
$18$	5.72722	+	2.91817i	1.34992	+	0.687818i
$19$	1.28236	−	3.94669i	0.294193	−	0.905433i	−0.689298	−	0.724478i	$-0.742081\pi$
$19$	1.28236	−	3.94669i	0.294193	−	0.905433i	0.983491	−	0.180955i	$-0.0579189\pi$
$20$		0			0
$21$		−	1.54392i		−	0.336911i
$22$	6.05467	+	5.33231i	1.29086	+	1.13685i
$23$	−0.104710	−	0.104710i	−0.0218334	−	0.0218334i	0.696106	−	0.717939i	$-0.254914\pi$
$23$	−0.104710	−	0.104710i	−0.0218334	−	0.0218334i	−0.717939	+	0.696106i	$0.754914\pi$
$24$	−2.25672	−	1.63960i	−0.460651	−	0.334683i
$25$		0			0
$26$	2.11141	+	6.49824i	0.414081	+	1.27441i
$27$	0.527849	−	3.33271i	0.101585	−	0.641380i
$28$	1.58216	−	9.98937i	0.299000	−	1.88781i
$29$	2.14459	+	6.60038i	0.398241	+	1.22566i	0.926409	+	0.376520i	$0.122879\pi$
$29$	2.14459	+	6.60038i	0.398241	+	1.22566i	−0.528168	+	0.849140i	$0.677121\pi$
$30$		0			0
$31$	−7.33171	−	5.32680i	−1.31681	−	0.956722i	−0.999966	−	0.00824590i	$-0.997375\pi$
$31$	−7.33171	−	5.32680i	−1.31681	−	0.956722i	−0.316849	−	0.948476i	$-0.602625\pi$
$32$	0.555921	+	0.555921i	0.0982739	+	0.0982739i
$33$	0.786759	−	1.82069i	0.136957	−	0.316942i
$34$		−	2.29712i		−	0.393953i
$35$		0			0
$36$	3.19879	−	9.84486i	0.533131	−	1.64081i
$37$	−6.77002	−	3.44950i	−1.11298	−	0.567094i	−0.201938	−	0.979398i	$-0.564724\pi$
$37$	−6.77002	−	3.44950i	−1.11298	−	0.567094i	−0.911046	+	0.412305i	$0.864724\pi$
$38$	−9.97047	−	1.57917i	−1.61742	−	0.256175i
$39$	1.35892	−	0.987312i	0.217601	−	0.158096i
$40$		0			0
$41$	3.27880	+	1.06535i	0.512063	+	0.166379i	0.553640	−	0.832756i	$-0.313238\pi$
$41$	3.27880	+	1.06535i	0.512063	+	0.166379i	−0.0415772	+	0.999135i	$0.513238\pi$
$42$	−3.70949	+	0.587525i	−0.572386	+	0.0906571i
$43$	−3.91833	+	3.91833i	−0.597540	+	0.597540i	−0.939657	−	0.342117i	$-0.888856\pi$
$43$	−3.91833	+	3.91833i	−0.597540	+	0.597540i	0.342117	+	0.939657i	$0.388856\pi$
$44$	6.95623	−	10.9739i	1.04869	−	1.65437i
$45$		0			0
$46$	−0.211733	+	0.291426i	−0.0312184	+	0.0429684i
$47$	−0.479999	−	0.942051i	−0.0700150	−	0.137412i	0.853346	−	0.521345i	$-0.174569\pi$
$47$	−0.479999	−	0.942051i	−0.0700150	−	0.137412i	−0.923361	+	0.383933i	$0.874569\pi$
$48$	−0.953440	+	1.87123i	−0.137617	+	0.270089i
$49$	0.196744	+	0.270795i	0.0281063	+	0.0386850i
$50$		0			0
$51$	−0.537077	+	0.174507i	−0.0752058	+	0.0244358i
$52$	9.80416	−	4.99547i	1.35959	−	0.692747i
$53$	0.644920	+	4.07187i	0.0885866	+	0.559314i	0.991563	+	0.129624i	$0.0413771\pi$
$53$	0.644920	+	4.07187i	0.0885866	+	0.559314i	−0.902977	+	0.429690i	$0.858623\pi$
$54$	−8.20817			−1.11699
$55$		0			0
$56$	−12.0424			−1.60924
$57$	0.388217	+	2.45111i	0.0514206	+	0.324657i
$58$	15.0422	−	7.66441i	1.97514	−	1.00639i
$59$	−6.16460	+	2.00300i	−0.802563	+	0.260768i	−0.681445	−	0.731870i	$-0.738648\pi$
$59$	−6.16460	+	2.00300i	−0.802563	+	0.260768i	−0.121118	+	0.992638i	$0.538648\pi$
$60$		0			0
$61$	5.59880	+	7.70609i	0.716853	+	0.986663i	0.999622	+	0.0274756i	$0.00874685\pi$
$61$	5.59880	+	7.70609i	0.716853	+	0.986663i	−0.282769	+	0.959188i	$0.591253\pi$
$62$	−10.0084	+	19.6426i	−1.27107	+	2.49461i
$63$	−3.09706	−	6.07833i	−0.390193	−	0.765797i
$64$	5.25251	−	7.22946i	0.656564	−	0.903682i
$65$		0			0
$66$	−4.67386	−	1.19745i	−0.575313	−	0.147396i
$67$	−2.94509	+	2.94509i	−0.359801	+	0.359801i	−0.863739	−	0.503939i	$-0.831884\pi$
$67$	−2.94509	+	2.94509i	−0.359801	+	0.359801i	0.503939	+	0.863739i	$0.331884\pi$
$68$	−3.65379	+	0.578703i	−0.443087	+	0.0701781i
$69$	0.0842215	+	0.0273652i	0.0101391	+	0.00329439i
$70$		0			0
$71$	−1.02426	+	0.744171i	−0.121558	+	0.0883168i	−0.646903	−	0.762572i	$-0.723936\pi$
$71$	−1.02426	+	0.744171i	−0.121558	+	0.0883168i	0.525345	+	0.850889i	$0.323936\pi$
$72$	−12.1736	−	1.92811i	−1.43467	−	0.227230i
$73$	−1.57831	−	0.804189i	−0.184727	−	0.0941232i	0.359181	−	0.933268i	$-0.383056\pi$
$73$	−1.57831	−	0.804189i	−0.184727	−	0.0941232i	−0.543908	+	0.839145i	$0.683056\pi$
$74$	−5.71163	+	17.5786i	−0.663964	+	2.04347i
$75$		0			0
$76$			16.2568i			1.86479i
$77$	−1.87222	−	8.35541i	−0.213359	−	0.952187i
$78$	−2.88928	−	2.88928i	−0.327147	−	0.327147i
$79$	−3.51271	−	2.55214i	−0.395211	−	0.287138i	0.372376	−	0.928082i	$-0.378543\pi$
$79$	−3.51271	−	2.55214i	−0.395211	−	0.287138i	−0.767588	+	0.640944i	$0.778543\pi$
$80$		0			0
$81$	−1.82606	−	5.62003i	−0.202895	−	0.624448i
$82$	1.31193	−	8.28320i	0.144878	−	0.914726i
$83$	−1.29707	+	8.18939i	−0.142372	+	0.898902i	0.808315	+	0.588750i	$0.200380\pi$
$83$	−1.29707	+	8.18939i	−0.142372	+	0.898902i	−0.950687	+	0.310152i	$0.899620\pi$
$84$	1.86903	+	5.75228i	0.203928	+	0.627625i
$85$		0			0
$86$	10.9054	+	7.92326i	1.17596	+	0.854388i
$87$	−2.93470	−	2.93470i	−0.314632	−	0.314632i
$88$	−14.2012	−	6.13664i	−1.51385	−	0.654168i
$89$		−	4.23092i		−	0.448477i	−0.974534	−	0.224238i	$-0.928011\pi$
$89$		−	4.23092i		−	0.448477i	0.974534	−	0.224238i	$-0.0719894\pi$
$90$		0			0
$91$	2.24084	−	6.89661i	0.234904	−	0.722961i
$92$	0.516882	+	0.263364i	0.0538886	+	0.0274576i
$93$	5.35283	+	0.847805i	0.555063	+	0.0879133i
$94$	−2.08075	+	1.51175i	−0.214613	+	0.155926i
$95$		0			0
$96$	−0.447147	−	0.145287i	−0.0456367	−	0.0148283i
$97$	14.2460	−	2.25634i	1.44646	−	0.229097i	0.616691	−	0.787205i	$-0.288473\pi$
$97$	14.2460	−	2.25634i	1.44646	−	0.229097i	0.829768	+	0.558109i	$0.188473\pi$
$98$	0.575755	−	0.575755i	0.0581600	−	0.0581600i
$99$	−0.554831	−	8.74618i	−0.0557626	−	0.879024i
$100$		0			0
$101$	1.13747	−	1.56559i	0.113182	−	0.155782i	−0.748668	−	0.662946i	$-0.769306\pi$
$101$	1.13747	−	1.56559i	0.113182	−	0.155782i	0.861850	+	0.507164i	$0.169306\pi$
$102$	0.623657	+	1.22400i	0.0617513	+	0.121194i
$103$	0.780525	−	1.53187i	0.0769075	−	0.150939i	−0.849351	−	0.527829i	$-0.823006\pi$
$103$	0.780525	−	1.53187i	0.0769075	−	0.150939i	0.926258	+	0.376889i	$0.123006\pi$
$104$	−7.70094	−	10.5994i	−0.755139	−	1.03936i
$105$		0			0
$106$	9.53782	−	3.09903i	0.926395	−	0.301004i
$107$	−3.70571	+	1.88816i	−0.358245	+	0.182535i	−0.623844	−	0.781549i	$-0.714430\pi$
$107$	−3.70571	+	1.88816i	−0.358245	+	0.182535i	0.265600	+	0.964083i	$0.414430\pi$
$108$	2.06785	+	13.0559i	0.198979	+	1.25630i
$109$	−3.22321			−0.308728			−0.154364	−	0.988014i	$-0.549333\pi$
$109$	−3.22321			−0.308728			−0.154364	+	0.988014i	$0.549333\pi$
$110$		0			0
$111$	4.54385			0.431284
$112$	1.41832	+	8.95489i	0.134018	+	0.846157i
$113$	9.93758	−	5.06345i	0.934849	−	0.476329i	0.0809210	−	0.996721i	$-0.474214\pi$
$113$	9.93758	−	5.06345i	0.934849	−	0.476329i	0.853928	+	0.520391i	$0.174214\pi$
$114$	5.74140	−	1.86549i	0.537731	−	0.174720i
$115$		0			0
$116$	−15.9805	−	21.9953i	−1.48375	−	2.04221i
$117$	3.36947	−	6.61295i	0.311507	−	0.611367i
$118$	7.15838	+	14.0491i	0.658982	+	1.29333i
$119$	−1.43299	+	1.97234i	−0.131362	+	0.180804i
$120$		0			0
$121$	2.04995	−	10.8073i	0.186359	−	0.982482i
$122$	16.3844	−	16.3844i	1.48337	−	1.48337i
$123$	−2.03631	+	0.322520i	−0.183608	+	0.0290807i
$124$	33.7647	+	10.9708i	3.03216	+	0.985209i
$125$		0			0
$126$	−13.4255	+	9.75419i	−1.19604	+	0.868972i
$127$	2.34580	+	0.371538i	0.208156	+	0.0329687i	0.259641	−	0.965705i	$-0.416396\pi$
$127$	2.34580	+	0.371538i	0.208156	+	0.0329687i	−0.0514856	+	0.998674i	$0.516396\pi$
$128$	−17.9676	−	9.15495i	−1.58813	−	0.809191i
$129$	1.02403	−	3.15165i	0.0901611	−	0.277487i
$130$		0			0
$131$		−	3.12466i		−	0.273003i	−0.990640	−	0.136501i	$-0.956414\pi$
$131$		−	3.12466i		−	0.273003i	0.990640	−	0.136501i	$-0.0435858\pi$
$132$	−0.727197	+	7.73590i	−0.0632944	+	0.673323i
$133$	7.57567	+	7.57567i	0.656894	+	0.656894i
$134$	8.19674	+	5.95528i	0.708090	+	0.514458i
$135$		0			0
$136$	1.36114	+	4.18915i	0.116716	+	0.359216i
$137$	−2.58679	+	16.3323i	−0.221004	+	1.39537i	0.588617	+	0.808412i	$0.299673\pi$
$137$	−2.58679	+	16.3323i	−0.221004	+	1.39537i	−0.809621	+	0.586953i	$0.800327\pi$
$138$	0.0336991	−	0.212768i	0.00286866	−	0.0181120i
$139$	1.33510	+	4.10901i	0.113242	+	0.348522i	0.991576	−	0.129524i	$-0.0413451\pi$
$139$	1.33510	+	4.10901i	0.113242	+	0.348522i	−0.878335	+	0.478046i	$0.841345\pi$
$140$		0			0
$141$	0.511525	+	0.371645i	0.0430782	+	0.0312981i
$142$	2.17775	+	2.17775i	0.182753	+	0.182753i
$143$	6.15696	−	6.99103i	0.514871	−	0.584619i
$144$			9.27951i			0.773293i
$145$		0			0
$146$	−1.33157	+	4.09814i	−0.110201	+	0.339164i
$147$	−0.178353	−	0.0908753i	−0.0147103	−	0.00749527i
$148$	29.3994	+	4.65640i	2.41661	+	0.382754i
$149$	6.83188	−	4.96365i	0.559689	−	0.406638i	−0.271656	−	0.962394i	$-0.587571\pi$
$149$	6.83188	−	4.96365i	0.559689	−	0.406638i	0.831345	+	0.555756i	$0.187571\pi$
$150$		0			0
$151$	11.3483	+	3.68729i	0.923513	+	0.300068i	0.731907	−	0.681404i	$-0.238630\pi$
$151$	11.3483	+	3.68729i	0.923513	+	0.300068i	0.191606	+	0.981472i	$0.438630\pi$
$152$	19.1184	−	3.02806i	1.55071	−	0.245608i
$153$	−1.76439	+	1.76439i	−0.142642	+	0.142642i
$154$	−19.3626	+	7.67785i	−1.56028	+	0.618699i
$155$		0			0
$156$	−3.86780	+	5.32357i	−0.309672	+	0.426226i
$157$	−0.618117	−	1.21312i	−0.0493311	−	0.0968177i	0.865025	−	0.501729i	$-0.167302\pi$
$157$	−0.618117	−	1.21312i	−0.0493311	−	0.0968177i	−0.914356	+	0.404911i	$0.867302\pi$
$158$	−4.79514	+	9.41098i	−0.381481	+	0.748698i
$159$	−1.44913	−	1.99456i	−0.114924	−	0.158179i
$160$		0			0
$161$	0.363594	−	0.118139i	0.0286552	−	0.00931064i
$162$	−12.8080	+	6.52602i	−1.00629	+	0.512732i
$163$	−3.58914	−	22.6610i	−0.281123	−	1.77494i	−0.574062	−	0.818812i	$-0.694633\pi$
$163$	−3.58914	−	22.6610i	−0.281123	−	1.77494i	0.292939	−	0.956131i	$-0.405367\pi$
$164$	−13.5057			−1.05462
$165$		0			0
$166$	20.1698			1.56548
$167$	2.24646	+	14.1836i	0.173836	+	1.09756i	0.908118	+	0.418714i	$0.137519\pi$
$167$	2.24646	+	14.1836i	0.173836	+	1.09756i	−0.734282	+	0.678845i	$0.762481\pi$
$168$	6.41668	−	3.26946i	0.495058	−	0.252244i
$169$	−4.86053	+	1.57928i	−0.373887	+	0.121483i
$170$		0			0
$171$	6.44525	+	8.87112i	0.492880	+	0.678391i
$172$	9.85535	−	19.3422i	0.751464	−	1.47483i
$173$	10.1247	+	19.8708i	0.769766	+	1.51075i	0.857430	+	0.514601i	$0.172060\pi$
$173$	10.1247	+	19.8708i	0.769766	+	1.51075i	−0.0876641	+	0.996150i	$0.527940\pi$
$174$	−5.93425	+	8.16780i	−0.449874	+	0.619199i
$175$		0			0
$176$	−2.89071	+	11.2829i	−0.217896	+	0.850484i
$177$	2.74094	−	2.74094i	0.206022	−	0.206022i
$178$	−10.1654	+	1.61004i	−0.761928	+	0.120678i
$179$	−4.15441	−	1.34985i	−0.310516	−	0.100893i	0.149614	−	0.988745i	$-0.452197\pi$
$179$	−4.15441	−	1.34985i	−0.310516	−	0.100893i	−0.460129	+	0.887852i	$0.652197\pi$
$180$		0			0
$181$	−7.63694	+	5.54857i	−0.567650	+	0.412422i	−0.834251	−	0.551385i	$-0.814099\pi$
$181$	−7.63694	+	5.54857i	−0.567650	+	0.412422i	0.266601	+	0.963807i	$0.414099\pi$
$182$	−17.4228	−	2.75950i	−1.29147	−	0.204548i
$183$	−5.07543	−	2.58606i	−0.375187	−	0.191167i
$184$	0.213446	−	0.656920i	0.0157355	−	0.0484287i
$185$		0			0
$186$		−	13.1836i		−	0.966665i
$187$	−2.69495	+	1.59568i	−0.197074	+	0.116688i
$188$	2.92879	+	2.92879i	0.213604	+	0.213604i
$189$	7.04765	+	5.12041i	0.512641	+	0.372455i
$190$		0			0
$191$	−2.00020	−	6.15597i	−0.144729	−	0.445430i	0.852247	−	0.523140i	$-0.175239\pi$
$191$	−2.00020	−	6.15597i	−0.144729	−	0.445430i	−0.996976	+	0.0777092i	$0.975239\pi$
$192$	−0.835981	+	5.27817i	−0.0603317	+	0.380919i
$193$	−0.157473	+	0.994245i	−0.0113352	+	0.0715674i	−0.992707	−	0.120548i	$-0.961535\pi$
$193$	−0.157473	+	0.994245i	−0.0113352	+	0.0715674i	0.981372	+	0.192115i	$0.0615348\pi$
$194$	−10.8424	−	33.3693i	−0.778436	−	2.39578i
$195$		0			0
$196$	−1.06084	−	0.770746i	−0.0757744	−	0.0550533i
$197$	−17.3425	−	17.3425i	−1.23560	−	1.23560i	−0.961781	−	0.273821i	$-0.911713\pi$
$197$	−17.3425	−	17.3425i	−1.23560	−	1.23560i	−0.273821	−	0.961781i	$-0.588287\pi$
$198$	−20.8028	+	4.66134i	−1.47839	+	0.331267i
$199$			3.25580i			0.230797i	0.993319	+	0.115399i	$0.0368146\pi$
$199$			3.25580i			0.230797i	−0.993319	+	0.115399i	$0.963185\pi$
$200$		0			0
$201$	0.769684	−	2.36884i	0.0542893	−	0.167085i
$202$	−4.19440	−	2.13715i	−0.295117	−	0.150370i
$203$	−17.6967	−	2.80288i	−1.24206	−	0.196723i
$204$	1.78977	−	1.30034i	0.125309	−	0.0910422i
$205$		0			0
$206$	−3.97755	−	1.29238i	−0.277129	−	0.0900447i
$207$	0.386469	−	0.0612107i	0.0268615	−	0.00425444i
$208$	−6.97487	+	6.97487i	−0.483621	+	0.483621i
$209$	5.07327	+	12.7942i	0.350926	+	0.884991i
$210$		0			0
$211$	−14.6014	+	20.0971i	−1.00520	+	1.38354i	−0.0831208	+	0.996539i	$0.526489\pi$
$211$	−14.6014	+	20.0971i	−1.00520	+	1.38354i	−0.922080	+	0.387000i	$0.873511\pi$
$212$	−7.33212	−	14.3901i	−0.503572	−	0.988316i
$213$	0.343729	−	0.674606i	0.0235519	−	0.0462232i
$214$	5.94674	+	8.18498i	0.406511	+	0.559514i
$215$		0			0
$216$	14.9688	−	4.86367i	1.01850	−	0.330931i
$217$	20.8467	−	10.6219i	1.41517	−	0.721064i
$218$	1.22657	+	7.74423i	0.0830735	+	0.524505i
$219$	1.05932			0.0715822
$220$		0			0
$221$	−2.65237			−0.178418
$222$	−1.72912	−	10.9173i	−0.116051	−	0.732718i
$223$	−17.4548	+	8.89368i	−1.16886	+	0.595565i	−0.927116	−	0.374774i	$-0.877720\pi$
$223$	−17.4548	+	8.89368i	−1.16886	+	0.595565i	−0.241746	+	0.970339i	$0.577720\pi$
$224$	−1.93038	+	0.627220i	−0.128979	+	0.0419079i
$225$		0			0
$226$	−15.9473	−	21.9496i	−1.06080	−	1.46007i
$227$	−0.464395	+	0.911427i	−0.0308230	+	0.0604935i	−0.905904	−	0.423482i	$-0.860808\pi$
$227$	−0.464395	+	0.911427i	−0.0308230	+	0.0604935i	0.875081	+	0.483976i	$0.160808\pi$
$228$	−4.41365	−	8.66228i	−0.292301	−	0.573674i
$229$	0.0598653	−	0.0823975i	0.00395601	−	0.00544498i	−0.807034	−	0.590504i	$-0.798929\pi$
$229$	0.0598653	−	0.0823975i	0.00395601	−	0.00544498i	0.810990	+	0.585059i	$0.198929\pi$
$230$		0			0
$231$	3.26605	+	3.94379i	0.214890	+	0.259483i
$232$	−22.8903	+	22.8903i	−1.50282	+	1.50282i
$233$	21.1366	−	3.34771i	1.38470	−	0.219316i	0.580786	−	0.814056i	$-0.302745\pi$
$233$	21.1366	−	3.34771i	1.38470	−	0.219316i	0.803918	+	0.594740i	$0.202745\pi$
$234$	−17.1708	−	5.57912i	−1.12249	−	0.364719i
$235$		0			0
$236$	20.5431	−	14.9254i	1.33724	−	0.971562i
$237$	2.56461	+	0.406194i	0.166589	+	0.0263851i
$238$	5.28413	+	2.69240i	0.342519	+	0.174522i
$239$	−2.67723	+	8.23966i	−0.173175	+	0.532979i	−0.999545	−	0.0301483i	$-0.990402\pi$
$239$	−2.67723	+	8.23966i	−0.173175	+	0.532979i	0.826370	+	0.563128i	$0.190402\pi$
$240$		0			0
$241$			10.6492i			0.685976i	0.939340	+	0.342988i	$0.111439\pi$
$241$			10.6492i			0.685976i	−0.939340	+	0.342988i	$0.888561\pi$
$242$	−26.7462	−	0.812677i	−1.71931	−	0.0522408i
$243$	9.65667	+	9.65667i	0.619476	+	0.619476i
$244$	−30.1886	−	21.9333i	−1.93263	−	1.40414i
$245$		0			0
$246$	1.54980	+	4.76980i	0.0988118	+	0.304111i
$247$	−1.82339	+	11.5124i	−0.116020	+	0.732518i
$248$	6.61279	−	41.7515i	0.419913	−	2.65123i
$249$	−1.53225	−	4.71578i	−0.0971023	−	0.298850i
$250$		0			0
$251$	7.59915	+	5.52110i	0.479654	+	0.348489i	0.801192	−	0.598408i	$-0.204200\pi$
$251$	7.59915	+	5.52110i	0.479654	+	0.348489i	−0.321538	+	0.946897i	$0.604200\pi$
$252$	18.8972	+	18.8972i	1.19041	+	1.19041i
$253$	0.488975	+	0.0459651i	0.0307416	+	0.00288980i
$254$		−	5.77750i		−	0.362513i
$255$		0			0
$256$	−9.63584	+	29.6561i	−0.602240	+	1.85350i
$257$	16.4300	+	8.37149i	1.02487	+	0.522199i	0.883832	−	0.467804i	$-0.154955\pi$
$257$	16.4300	+	8.37149i	1.02487	+	0.522199i	0.141042	+	0.990004i	$0.454955\pi$
$258$	−7.96198	−	1.26105i	−0.495691	−	0.0785097i
$259$	15.8700	−	11.5302i	0.986111	−	0.716451i
$260$		0			0
$261$	−17.4407	−	5.66681i	−1.07955	−	0.350767i
$262$	−7.50744	+	1.18906i	−0.463811	+	0.0734605i
$263$	11.8928	−	11.8928i	0.733342	−	0.733342i	−0.237938	−	0.971280i	$-0.576472\pi$
$263$	11.8928	−	11.8928i	0.733342	−	0.733342i	0.971280	+	0.237938i	$0.0764717\pi$
$264$	9.23304	−	0.585716i	0.568254	−	0.0360483i
$265$		0			0
$266$	15.3188	−	21.0845i	0.939254	−	1.29277i
$267$	1.14868	+	2.25440i	0.0702978	+	0.137967i
$268$	7.40747	−	14.5380i	0.452483	−	0.888049i
$269$	16.7264	+	23.0219i	1.01983	+	1.40367i	0.912325	+	0.409467i	$0.134285\pi$
$269$	16.7264	+	23.0219i	1.01983	+	1.40367i	0.107502	+	0.994205i	$0.465715\pi$
$270$		0			0
$271$	−28.2295	+	9.17232i	−1.71482	+	0.557179i	−0.991124	−	0.132939i	$-0.957558\pi$
$271$	−28.2295	+	9.17232i	−1.71482	+	0.557179i	−0.723696	+	0.690118i	$0.757558\pi$
$272$	2.95479	−	1.50554i	0.179160	−	0.0912868i
$273$	0.678387	+	4.28317i	0.0410578	+	0.259229i
$274$	40.2251			2.43009
$275$		0			0
$276$	−0.346917			−0.0208820
$277$	1.94287	+	12.2668i	0.116736	+	0.737041i	0.974731	+	0.223383i	$0.0717099\pi$
$277$	1.94287	+	12.2668i	0.116736	+	0.737041i	−0.857995	+	0.513658i	$0.828290\pi$
$278$	9.36443	−	4.77141i	0.561641	−	0.286170i
$279$	22.7745	−	7.39987i	1.36347	−	0.443019i
$280$		0			0
$281$	12.8578	+	17.6972i	0.767032	+	1.05573i	0.996596	+	0.0824357i	$0.0262699\pi$
$281$	12.8578	+	17.6972i	0.767032	+	1.05573i	−0.229564	+	0.973294i	$0.573730\pi$
$282$	0.698273	−	1.37044i	0.0415815	−	0.0816083i
$283$	−12.3474	−	24.2332i	−0.733978	−	1.44051i	−0.891511	−	0.453000i	$-0.850354\pi$
$283$	−12.3474	−	24.2332i	−0.733978	−	1.44051i	0.157532	−	0.987514i	$-0.449646\pi$
$284$	2.91529	−	4.01255i	0.172991	−	0.238101i
$285$		0			0
$286$	−19.1399	−	12.1326i	−1.13177	−	0.717416i
$287$	−6.29366	+	6.29366i	−0.371503	+	0.371503i
$288$	−2.05183	+	0.324978i	−0.120905	+	0.0191495i
$289$	−15.3199	−	4.97773i	−0.901170	−	0.292808i
$290$		0			0
$291$	−6.97823	+	5.06998i	−0.409071	+	0.297207i
$292$	6.85394	+	1.08556i	0.401096	+	0.0635274i
$293$	−17.9201	−	9.13077i	−1.04691	−	0.533425i	−0.156068	−	0.987746i	$-0.549882\pi$
$293$	−17.9201	−	9.13077i	−1.04691	−	0.533425i	−0.890838	+	0.454321i	$0.849882\pi$
$294$	−0.150470	+	0.463100i	−0.00877560	+	0.0270085i
$295$		0			0
$296$		−	35.4416i		−	2.06000i
$297$	5.70176	+	9.62970i	0.330849	+	0.558772i
$298$	−14.5257	−	14.5257i	−0.841450	−	0.841450i
$299$	0.336495	+	0.244478i	0.0194600	+	0.0141385i
$300$		0			0
$301$	−4.42087	−	13.6060i	−0.254815	−	0.784239i
$302$	4.54074	−	28.6691i	0.261290	−	1.64972i
$303$	−0.181037	+	1.14302i	−0.0104003	+	0.0656650i
$304$	−4.50340	−	13.8600i	−0.258288	−	0.794927i
$305$		0			0
$306$	4.91061	+	3.56777i	0.280721	+	0.203956i
$307$	14.6921	+	14.6921i	0.838520	+	0.838520i	0.988664	−	0.150144i	$-0.0479738\pi$
$307$	14.6921	+	14.6921i	0.838520	+	0.838520i	−0.150144	+	0.988664i	$0.547974\pi$
$308$	17.0903	+	28.8638i	0.973810	+	1.64467i
$309$			1.02815i			0.0584893i
$310$		0			0
$311$	7.19358	−	22.1396i	0.407911	−	1.25542i	−0.510530	−	0.859860i	$-0.670551\pi$
$311$	7.19358	−	22.1396i	0.407911	−	1.25542i	0.918440	−	0.395560i	$-0.129449\pi$
$312$	6.98106	+	3.55703i	0.395225	+	0.201377i
$313$	−13.8454	−	2.19289i	−0.782587	−	0.123950i	−0.247659	−	0.968847i	$-0.579661\pi$
$313$	−13.8454	−	2.19289i	−0.782587	−	0.123950i	−0.534928	+	0.844898i	$0.679661\pi$
$314$	−2.67948	+	1.94676i	−0.151212	+	0.109862i
$315$		0			0
$316$	16.1771	+	5.25626i	0.910032	+	0.295687i
$317$	−29.1369	+	4.61482i	−1.63649	+	0.259194i	−0.905859	−	0.423580i	$-0.860773\pi$
$317$	−29.1369	+	4.61482i	−1.63649	+	0.259194i	−0.730630	+	0.682774i	$0.760773\pi$
$318$	−4.24076	+	4.24076i	−0.237810	+	0.237810i
$319$	−19.4408	−	12.3233i	−1.08847	−	0.689972i
$320$		0			0
$321$	1.46193	−	2.01217i	0.0815967	−	0.112308i
$322$	−0.422208	−	0.828629i	−0.0235287	−	0.0461777i
$323$	1.77905	−	3.49158i	0.0989889	−	0.194277i
$324$	13.6069	+	18.7283i	0.755940	+	1.04046i
$325$		0			0
$326$	−53.0803	+	17.2468i	−2.93985	+	0.955215i
$327$	1.71746	−	0.875087i	0.0949755	−	0.0483924i
$328$	2.51563	+	15.8830i	0.138902	+	0.876994i
$329$	2.72962			0.150489
$330$		0			0
$331$	2.18560			0.120131			0.0600657	−	0.998194i	$-0.480869\pi$
$331$	2.18560			0.120131			0.0600657	+	0.998194i	$0.480869\pi$
$332$	−5.08128	−	32.0819i	−0.278871	−	1.76072i
$333$	17.8889	−	9.11485i	0.980306	−	0.499491i
$334$	33.2232	−	10.7949i	1.81789	−	0.590670i
$335$		0			0
$336$	−3.18694	−	4.38645i	−0.173862	−	0.239301i
$337$	0.818095	−	1.60560i	0.0445645	−	0.0874627i	−0.867650	−	0.497175i	$-0.834371\pi$
$337$	0.818095	−	1.60560i	0.0445645	−	0.0874627i	0.912215	+	0.409712i	$0.134371\pi$
$338$	5.64408	+	11.0771i	0.306997	+	0.602516i
$339$	−3.92043	+	5.39601i	−0.212929	+	0.293071i
$340$		0			0
$341$	29.9966	−	1.90289i	1.62441	−	0.103047i
$342$	18.8614	−	18.8614i	1.01991	−	1.01991i
$343$	−18.7031	+	2.96227i	−1.00987	+	0.159948i
$344$	−24.5826	−	7.98736i	−1.32540	−	0.430650i
$345$		0			0
$346$	43.8896	−	31.8877i	2.35952	−	1.71429i
$347$	21.2079	+	3.35900i	1.13850	+	0.180321i	0.697090	−	0.716984i	$-0.254478\pi$
$347$	21.2079	+	3.35900i	1.13850	+	0.180321i	0.441411	+	0.897305i	$0.354478\pi$
$348$	14.4867	+	7.38132i	0.776566	+	0.395680i
$349$	3.29300	−	10.1348i	0.176270	−	0.542505i	−0.823419	−	0.567434i	$-0.807936\pi$
$349$	3.29300	−	10.1348i	0.176270	−	0.542505i	0.999689	+	0.0249295i	$0.00793612\pi$
$350$		0			0
$351$			9.47758i			0.505876i
$352$	−2.59606	−	0.244037i	−0.138370	−	0.0130072i
$353$	7.73857	+	7.73857i	0.411883	+	0.411883i	0.882394	−	0.470511i	$-0.155931\pi$
$353$	7.73857	+	7.73857i	0.411883	+	0.411883i	−0.470511	+	0.882394i	$0.655931\pi$
$354$	−7.62853	−	5.54245i	−0.405452	−	0.294578i
$355$		0			0
$356$	5.12185	+	15.7634i	0.271457	+	0.835460i
$357$	0.228072	−	1.43999i	0.0120708	−	0.0762123i
$358$	−1.66228	+	10.4952i	−0.0878544	+	0.554691i
$359$	1.01178	+	3.11394i	0.0533997	+	0.164347i	0.974200	−	0.225688i	$-0.0724629\pi$
$359$	1.01178	+	3.11394i	0.0533997	+	0.164347i	−0.920800	+	0.390035i	$0.872463\pi$
$360$		0			0
$361$	1.43940	+	1.04578i	0.0757578	+	0.0550412i
$362$	16.2374	+	16.2374i	0.853418	+	0.853418i
$363$	1.84184	+	6.31511i	0.0966713	+	0.331457i
$364$			28.4079i			1.48898i
$365$		0			0
$366$	−4.28197	+	13.1785i	−0.223822	+	0.688853i
$367$	−16.2428	−	8.27615i	−0.847870	−	0.432011i	−0.0246243	−	0.999697i	$-0.507839\pi$
$367$	−16.2428	−	8.27615i	−0.847870	−	0.432011i	−0.823246	+	0.567686i	$0.807839\pi$
$368$	−0.513632	−	0.0813513i	−0.0267749	−	0.00424073i
$369$	−7.36989	+	5.35454i	−0.383661	+	0.278746i
$370$		0			0
$371$	−10.1225	−	3.28901i	−0.525536	−	0.170757i
$372$	−20.9697	+	3.32128i	−1.08723	+	0.172200i
$373$	−12.4917	+	12.4917i	−0.646795	+	0.646795i	−0.952217	−	0.305422i	$-0.901202\pi$
$373$	−12.4917	+	12.4917i	−0.646795	+	0.646795i	0.305422	+	0.952217i	$0.401202\pi$
$374$	4.85939	+	5.86777i	0.251273	+	0.303415i
$375$		0			0
$376$	2.89879	−	3.98984i	0.149494	−	0.205760i
$377$	−8.84972	−	17.3686i	−0.455784	−	0.894526i
$378$	9.62060	−	18.8815i	0.494831	−	0.971160i
$379$	−12.9685	−	17.8496i	−0.666146	−	0.916872i	0.333519	−	0.942743i	$-0.391764\pi$
$379$	−12.9685	−	17.8496i	−0.666146	−	0.916872i	−0.999665	+	0.0258717i	$0.991764\pi$
$380$		0			0
$381$	−1.35080	+	0.438903i	−0.0692038	+	0.0224857i
$382$	−14.0294	+	7.14836i	−0.717809	+	0.365742i
$383$	3.08015	+	19.4473i	0.157389	+	0.993712i	0.932311	+	0.361656i	$0.117789\pi$
$383$	3.08015	+	19.4473i	0.157389	+	0.993712i	−0.774923	+	0.632056i	$0.782211\pi$
$384$	12.0594			0.615402
$385$		0			0
$386$	2.44874			0.124638
$387$	−2.29057	−	14.4621i	−0.116436	−	0.735148i
$388$	−50.3457	+	25.6524i	−2.55591	+	1.30230i
$389$	−16.2827	+	5.29057i	−0.825565	+	0.268242i	−0.691176	−	0.722686i	$-0.742907\pi$
$389$	−16.2827	+	5.29057i	−0.825565	+	0.268242i	−0.134389	+	0.990929i	$0.542907\pi$
$390$		0			0
$391$	−0.0821929	−	0.113129i	−0.00415667	−	0.00572117i
$392$	−0.708818	+	1.39113i	−0.0358007	+	0.0702629i
$393$	0.848330	+	1.66494i	0.0427926	+	0.0839852i
$394$	−35.0683	+	48.2673i	−1.76671	+	2.43167i
$395$		0			0
$396$	12.6551	+	31.9145i	0.635941	+	1.60377i
$397$	−5.24887	+	5.24887i	−0.263433	+	0.263433i	−0.826447	−	0.563014i	$-0.809642\pi$
$397$	−5.24887	+	5.24887i	−0.263433	+	0.263433i	0.563014	+	0.826447i	$0.309642\pi$
$398$	7.82252	−	1.23896i	0.392107	−	0.0621037i
$399$	−6.09337	−	1.97986i	−0.305050	−	0.0991168i
$400$		0			0
$401$	−9.93091	+	7.21523i	−0.495926	+	0.360311i	−0.807459	−	0.589924i	$-0.799158\pi$
$401$	−9.93091	+	7.21523i	−0.495926	+	0.360311i	0.311533	+	0.950235i	$0.399158\pi$
$402$	−5.98438	−	0.947832i	−0.298474	−	0.0472736i
$403$	22.6803	+	11.5562i	1.12979	+	0.575655i
$404$	−2.34267	+	7.21000i	−0.116552	+	0.358711i
$405$		0			0
$406$			43.5854i			2.16311i
$407$	24.5905	−	5.51006i	1.21891	−	0.273124i
$408$	−1.86260	−	1.86260i	−0.0922125	−	0.0922125i
$409$	21.6485	+	15.7286i	1.07045	+	0.777727i	0.975993	−	0.217802i	$-0.0698887\pi$
$409$	21.6485	+	15.7286i	1.07045	+	0.777727i	0.0944563	+	0.995529i	$0.469889\pi$
$410$		0			0
$411$	−3.05581	−	9.40481i	−0.150732	−	0.463905i
$412$	−1.05361	+	6.65226i	−0.0519079	+	0.327733i
$413$	2.61782	−	16.5283i	0.128815	−	0.813304i
$414$	−0.294135	−	0.905254i	−0.0144559	−	0.0444908i
$415$		0			0
$416$	−1.78651	−	1.29798i	−0.0875910	−	0.0636386i
$417$	−1.82697	−	1.82697i	−0.0894672	−	0.0894672i
$418$	28.8092	−	17.0580i	1.40911	−	0.834332i
$419$			14.2401i			0.695676i	0.937555	+	0.347838i	$0.113084\pi$
$419$			14.2401i			0.695676i	−0.937555	+	0.347838i	$0.886916\pi$
$420$		0			0
$421$	−2.13413	+	6.56818i	−0.104011	+	0.320113i	−0.989497	−	0.144553i	$-0.953826\pi$
$421$	−2.13413	+	6.56818i	−0.104011	+	0.320113i	0.885486	+	0.464666i	$0.153826\pi$
$422$	53.8425	+	27.4341i	2.62101	+	1.33547i
$423$	2.75935	+	0.437039i	0.134164	+	0.0212496i
$424$	−15.5574	+	11.3031i	−0.755532	+	0.548926i
$425$		0			0
$426$	−1.75164	−	0.569142i	−0.0848672	−	0.0275750i
$427$	−24.2888	+	3.84696i	−1.17542	+	0.186168i
$428$	11.5209	−	11.5209i	0.556882	−	0.556882i
$429$	−1.38264	+	5.39668i	−0.0667545	+	0.260554i
$430$		0			0
$431$	−4.19638	+	5.77582i	−0.202132	+	0.278211i	−0.898034	−	0.439926i	$-0.855005\pi$
$431$	−4.19638	+	5.77582i	−0.202132	+	0.278211i	0.695902	+	0.718137i	$0.255005\pi$
$432$	−5.37966	−	10.5582i	−0.258829	−	0.507981i
$433$	7.62822	−	14.9712i	0.366589	−	0.719471i	−0.631864	−	0.775079i	$-0.717710\pi$
$433$	7.62822	−	14.9712i	0.366589	−	0.719471i	0.998453	+	0.0556084i	$0.0177098\pi$
$434$	−33.4538	−	46.0451i	−1.60583	−	2.21024i
$435$		0			0
$436$	12.0089	−	3.90194i	0.575124	−	0.186869i
$437$	−0.547531	+	0.278981i	−0.0261920	+	0.0133455i
$438$	−0.403114	−	2.54516i	−0.0192616	−	0.121613i
$439$	0.772934			0.0368901			0.0184451	−	0.999830i	$-0.494128\pi$
$439$	0.772934			0.0368901			0.0184451	+	0.999830i	$0.494128\pi$
$440$		0			0
$441$	−0.884459			−0.0421171
$442$	1.00934	+	6.37271i	0.0480093	+	0.303119i
$443$	−16.7419	+	8.53040i	−0.795430	+	0.405292i	−0.803968	−	0.594672i	$-0.797282\pi$
$443$	−16.7419	+	8.53040i	−0.795430	+	0.405292i	0.00853887	+	0.999964i	$0.497282\pi$
$444$	−16.9293	+	5.50067i	−0.803430	+	0.261050i
$445$		0			0
$446$	28.0106	+	38.5533i	1.32634	+	1.82555i
$447$	−2.29269	+	4.49965i	−0.108440	+	0.212826i
$448$	10.4738	+	20.5560i	0.494840	+	0.971179i
$449$	−0.419317	+	0.577140i	−0.0197888	+	0.0272369i	−0.818797	−	0.574084i	$-0.805358\pi$
$449$	−0.419317	+	0.577140i	−0.0197888	+	0.0272369i	0.799008	+	0.601320i	$0.205358\pi$
$450$		0			0
$451$	−10.6291	+	4.21474i	−0.500502	+	0.198464i
$452$	−30.8954	+	30.8954i	−1.45320	+	1.45320i
$453$	−7.04792	+	1.11628i	−0.331140	+	0.0524474i
$454$	2.36655	+	0.768940i	0.111068	+	0.0360882i
$455$		0			0
$456$	−9.36493	+	6.80402i	−0.438553	+	0.318628i
$457$	19.1068	+	3.02622i	0.893780	+	0.141561i	0.586396	−	0.810025i	$-0.300546\pi$
$457$	19.1068	+	3.02622i	0.893780	+	0.141561i	0.307384	+	0.951586i	$0.400546\pi$
$458$	−0.220753	−	0.112479i	−0.0103151	−	0.00525581i
$459$	0.984632	−	3.03039i	0.0459587	−	0.141446i
$460$		0			0
$461$		−	36.5277i		−	1.70126i	−0.525761	−	0.850632i	$-0.676219\pi$
$461$		−	36.5277i		−	1.70126i	0.525761	−	0.850632i	$-0.323781\pi$
$462$	8.23266	−	9.34792i	0.383018	−	0.434904i
$463$	17.1422	+	17.1422i	0.796664	+	0.796664i	0.982568	−	0.185904i	$-0.0595213\pi$
$463$	17.1422	+	17.1422i	0.796664	+	0.796664i	−0.185904	+	0.982568i	$0.559521\pi$
$464$	19.7175	+	14.3256i	0.915361	+	0.665049i
$465$		0			0
$466$	−16.0867	−	49.5097i	−0.745201	−	2.29349i
$467$	2.31832	−	14.6373i	0.107279	−	0.677333i	−0.874172	−	0.485617i	$-0.838595\pi$
$467$	2.31832	−	14.6373i	0.107279	−	0.677333i	0.981451	−	0.191715i	$-0.0614051\pi$
$468$	−4.54837	+	28.7173i	−0.210249	+	1.32746i
$469$	−3.32281	−	10.2266i	−0.153433	−	0.472219i
$470$		0			0
$471$	0.658714	+	0.478584i	0.0303519	+	0.0220520i
$472$	−21.3791	−	21.3791i	−0.984051	−	0.984051i
$473$	1.72006	−	18.2979i	0.0790885	−	0.841340i
$474$		−	6.31640i		−	0.290122i
$475$		0			0
$476$	2.95131	−	9.08320i	0.135273	−	0.416328i
$477$	−9.70618	−	4.94555i	−0.444416	−	0.226441i
$478$	20.8157	+	3.29689i	0.952090	+	0.150796i
$479$	22.3176	−	16.2146i	1.01971	−	0.740866i	0.0534905	−	0.998568i	$-0.482965\pi$
$479$	22.3176	−	16.2146i	1.01971	−	0.740866i	0.966224	+	0.257702i	$0.0829653\pi$
$480$		0			0
$481$	20.2972	+	6.59495i	0.925471	+	0.300704i
$482$	25.5862	−	4.05246i	1.16542	−	0.184585i
$483$	−0.161663	+	0.161663i	−0.00735592	+	0.00735592i
$484$	5.44540	+	42.7471i	0.247518	+	1.94305i
$485$		0			0
$486$	19.5268	−	26.8763i	0.885752	−	1.21913i
$487$	−17.6583	−	34.6563i	−0.800174	−	1.57043i	−0.821193	−	0.570650i	$-0.806691\pi$
$487$	−17.6583	−	34.6563i	−0.800174	−	1.57043i	0.0210198	−	0.999779i	$-0.493309\pi$
$488$	−20.1710	+	39.5879i	−0.913099	+	1.79206i
$489$	8.06478	+	11.1002i	0.364702	+	0.501969i
$490$		0			0
$491$	17.8811	−	5.80992i	0.806962	−	0.262198i	0.123652	−	0.992326i	$-0.460539\pi$
$491$	17.8811	−	5.80992i	0.806962	−	0.262198i	0.683311	+	0.730128i	$0.260539\pi$
$492$	7.19639	−	3.66674i	0.324438	−	0.165310i
$493$	1.02520	+	6.47287i	0.0461728	+	0.291523i
$494$	28.3541			1.27571
$495$		0			0
$496$	−31.8258			−1.42902
$497$	−0.511323	−	3.22837i	−0.0229360	−	0.144812i
$498$	−10.7472	+	5.47599i	−0.481595	+	0.245385i
$499$	−4.98327	+	1.61916i	−0.223082	+	0.0724837i	−0.418425	−	0.908251i	$-0.637418\pi$
$499$	−4.98327	+	1.61916i	−0.223082	+	0.0724837i	0.195343	+	0.980735i	$0.437418\pi$
$500$		0			0
$501$	−5.04778	−	6.94768i	−0.225518	−	0.310399i
$502$	10.3734	−	20.3590i	0.462990	−	0.908668i
$503$	−5.98921	−	11.7545i	−0.267046	−	0.524106i	0.718076	−	0.695965i	$-0.245023\pi$
$503$	−5.98921	−	11.7545i	−0.267046	−	0.524106i	−0.985122	+	0.171858i	$0.945023\pi$
$504$	18.7037	−	25.7434i	0.833127	−	1.14670i
$505$		0			0
$506$	−0.0756375	−	1.19232i	−0.00336250	−	0.0530053i
$507$	2.16111	−	2.16111i	0.0959784	−	0.0959784i
$508$	−9.18967	+	1.45550i	−0.407726	+	0.0645774i
$509$	−5.32193	−	1.72920i	−0.235890	−	0.0766454i	0.188686	−	0.982037i	$-0.439577\pi$
$509$	−5.32193	−	1.72920i	−0.235890	−	0.0766454i	−0.424577	+	0.905392i	$0.639577\pi$
$510$		0			0
$511$	3.69980	−	2.68806i	0.163669	−	0.118913i
$512$	35.0853	+	5.55696i	1.55056	+	0.245585i
$513$	−12.4763	−	6.35698i	−0.550841	−	0.280667i
$514$	13.8614	−	42.6611i	0.611401	−	1.88170i
$515$		0			0
$516$			12.9820i			0.571500i
$517$	3.21895	+	1.39098i	0.141569	+	0.0611751i
$518$	−33.7421	−	33.7421i	−1.48254	−	1.48254i
$519$	−10.7897	−	7.83915i	−0.473614	−	0.344101i
$520$		0			0
$521$	5.89515	+	18.1434i	0.258271	+	0.794877i	0.993168	+	0.116697i	$0.0372308\pi$
$521$	5.89515	+	18.1434i	0.258271	+	0.794877i	−0.734896	+	0.678179i	$0.762769\pi$
$522$	−6.97844	+	44.0601i	−0.305438	+	1.92846i
$523$	−5.49061	+	34.6664i	−0.240088	+	1.51585i	0.513261	+	0.858233i	$0.328437\pi$
$523$	−5.49061	+	34.6664i	−0.240088	+	1.51585i	−0.753349	+	0.657621i	$0.771563\pi$
$524$	3.78263	+	11.6417i	0.165245	+	0.508572i
$525$		0			0
$526$	−33.0999	−	24.0485i	−1.44322	−	1.04856i
$527$	−6.05128	−	6.05128i	−0.263598	−	0.263598i
$528$	−1.52298	−	6.79681i	−0.0662792	−	0.295793i
$529$		−	22.9781i		−	0.999047i
$530$		0			0
$531$	5.29267	−	16.2892i	0.229682	−	0.706890i
$532$	−37.3961	−	19.0542i	−1.62132	−	0.826106i
$533$	−9.56421	−	1.51482i	−0.414272	−	0.0656143i
$534$	4.97940	−	3.61775i	0.215480	−	0.156555i
$535$		0			0
$536$	−18.4767	−	6.00346i	−0.798074	−	0.259310i
$537$	2.58011	−	0.408650i	0.111340	−	0.0176345i
$538$	48.9484	−	48.9484i	2.11031	−	2.11031i
$539$	−1.07541	−	0.275523i	−0.0463213	−	0.0118676i
$540$		0			0
$541$	−1.49345	+	2.05556i	−0.0642084	+	0.0883752i	−0.839914	−	0.542720i	$-0.817394\pi$
$541$	−1.49345	+	2.05556i	−0.0642084	+	0.0883752i	0.775705	+	0.631095i	$0.217394\pi$
$542$	32.7803	+	64.3350i	1.40803	+	2.76342i
$543$	2.56286	−	5.02989i	0.109983	−	0.215853i
$544$	0.436376	+	0.600621i	0.0187095	+	0.0257514i
$545$		0			0
$546$	10.0328	−	3.25984i	0.429363	−	0.139508i
$547$	−13.2087	+	6.73017i	−0.564764	+	0.287761i	−0.712969	−	0.701195i	$-0.752650\pi$
$547$	−13.2087	+	6.73017i	−0.564764	+	0.287761i	0.148206	+	0.988957i	$0.452650\pi$
$548$	−10.1337	−	63.9819i	−0.432892	−	2.73317i
$549$	−25.1693			−1.07420
$550$		0			0
$551$	28.7998			1.22691
$552$	0.0646180	+	0.407982i	0.00275033	+	0.0173649i
$553$	9.98792	−	5.08910i	0.424730	−	0.216411i
$554$	28.7334	−	9.33604i	1.22076	−	0.396650i
$555$		0			0
$556$	−9.94853	−	13.6930i	−0.421912	−	0.580712i
$557$	−5.79353	+	11.3704i	−0.245480	+	0.481781i	−0.980565	−	0.196194i	$-0.937142\pi$
$557$	−5.79353	+	11.3704i	−0.245480	+	0.481781i	0.735086	+	0.677974i	$0.237142\pi$
$558$	−26.4459	−	51.9029i	−1.11954	−	2.19723i
$559$	9.14861	−	12.5920i	0.386945	−	0.532584i
$560$		0			0
$561$	1.00275	−	1.58191i	0.0423363	−	0.0667881i
$562$	37.6272	−	37.6272i	1.58721	−	1.58721i
$563$	33.1190	−	5.24553i	1.39580	−	0.221073i	0.587204	−	0.809439i	$-0.300229\pi$
$563$	33.1190	−	5.24553i	1.39580	−	0.221073i	0.808594	+	0.588367i	$0.200229\pi$
$564$	−2.35572	−	0.765421i	−0.0991939	−	0.0322300i
$565$		0			0
$566$	−53.5250	+	38.8882i	−2.24982	+	1.63459i
$567$	15.0682	+	2.38657i	0.632805	+	0.100226i
$568$	−5.26186	−	2.68105i	−0.220783	−	0.112494i
$569$	2.57065	−	7.91165i	0.107767	−	0.331674i	−0.882603	−	0.470120i	$-0.844211\pi$
$569$	2.57065	−	7.91165i	0.107767	−	0.331674i	0.990370	+	0.138446i	$0.0442107\pi$
$570$		0			0
$571$		−	45.2601i		−	1.89408i	−0.321118	−	0.947039i	$-0.604059\pi$
$571$		−	45.2601i		−	1.89408i	0.321118	−	0.947039i	$-0.395941\pi$
$572$	−14.4762	+	33.5004i	−0.605282	+	1.40072i
$573$	2.73710	+	2.73710i	0.114344	+	0.114344i
$574$	17.5164	+	12.7264i	0.731121	+	0.531190i
$575$		0			0
$576$	7.29667	+	22.4568i	0.304028	+	0.935701i
$577$	3.58768	−	22.6517i	0.149357	−	0.943005i	−0.793200	−	0.608961i	$-0.791587\pi$
$577$	3.58768	−	22.6517i	0.149357	−	0.943005i	0.942558	−	0.334044i	$-0.108413\pi$
$578$	−6.12986	+	38.7024i	−0.254969	+	1.60981i
$579$	−0.186025	−	0.572526i	−0.00773094	−	0.0237934i
$580$		0			0
$581$	−17.3180	−	12.5823i	−0.718472	−	0.522001i
$582$	14.8369	+	14.8369i	0.615007	+	0.615007i
$583$	−10.2611	−	9.03691i	−0.424972	−	0.374270i
$584$		−	8.26259i		−	0.341908i
$585$		0			0
$586$	−15.1186	+	46.5303i	−0.624545	+	1.92215i
$587$	−8.99622	−	4.58380i	−0.371314	−	0.189194i	0.258369	−	0.966046i	$-0.416815\pi$
$587$	−8.99622	−	4.58380i	−0.371314	−	0.189194i	−0.629683	+	0.776853i	$0.716815\pi$
$588$	0.774512	+	0.122671i	0.0319403	+	0.00505885i
$589$	−30.4251	+	22.1051i	−1.25365	+	0.910827i
$590$		0			0
$591$	13.9492	+	4.53236i	0.573792	+	0.186436i
$592$	−26.3548	+	4.17419i	−1.08318	+	0.171558i
$593$	−9.47168	+	9.47168i	−0.388955	+	0.388955i	−0.874315	−	0.485359i	$-0.838689\pi$
$593$	−9.47168	+	9.47168i	−0.388955	+	0.388955i	0.485359	+	0.874315i	$0.338689\pi$
$594$	20.9670	−	17.3638i	0.860286	−	0.712444i
$595$		0			0
$596$	−19.4451	+	26.7639i	−0.796503	+	1.09629i
$597$	−0.883934	−	1.73482i	−0.0361770	−	0.0710014i
$598$	0.459343	−	0.901512i	0.0187839	−	0.0368656i
$599$	23.5167	+	32.3680i	0.960866	+	1.32252i	0.946528	+	0.322622i	$0.104564\pi$
$599$	23.5167	+	32.3680i	0.960866	+	1.32252i	0.0143383	+	0.999897i	$0.495436\pi$
$600$		0			0
$601$	34.5805	−	11.2359i	1.41057	−	0.458322i	0.497976	−	0.867191i	$-0.334077\pi$
$601$	34.5805	−	11.2359i	1.41057	−	0.458322i	0.912593	+	0.408869i	$0.134077\pi$
$602$	−31.0081	+	15.7994i	−1.26380	+	0.643937i
$603$	−1.72163	−	10.8700i	−0.0701103	−	0.442659i
$604$	−46.7449			−1.90202
$605$		0			0
$606$	2.81517			0.114358
$607$	3.89991	+	24.6231i	0.158293	+	0.999420i	0.931096	+	0.364774i	$0.118854\pi$
$607$	3.89991	+	24.6231i	0.158293	+	0.999420i	−0.772803	+	0.634646i	$0.781146\pi$
$608$	2.90694	−	1.48116i	0.117892	−	0.0600689i
$609$	10.1905	−	3.31108i	0.412938	−	0.134172i
$610$		0			0
$611$	1.74555	+	2.40254i	0.0706174	+	0.0971965i
$612$	4.43777	−	8.70960i	0.179386	−	0.352065i
$613$	5.30759	+	10.4167i	0.214372	+	0.420728i	0.973003	−	0.230792i	$-0.0741317\pi$
$613$	5.30759	+	10.4167i	0.214372	+	0.420728i	−0.758632	+	0.651520i	$0.774132\pi$
$614$	29.7088	−	40.8907i	1.19895	−	1.65021i
$615$		0			0
$616$	30.7612	−	25.4748i	1.23940	−	1.02641i
$617$	−6.18386	+	6.18386i	−0.248953	+	0.248953i	−0.820541	−	0.571588i	$-0.806328\pi$
$617$	−6.18386	+	6.18386i	−0.248953	+	0.248953i	0.571588	+	0.820541i	$0.306328\pi$
$618$	2.47027	−	0.391253i	0.0993689	−	0.0157385i
$619$	−1.04489	−	0.339504i	−0.0419975	−	0.0136458i	0.287943	−	0.957648i	$-0.407029\pi$
$619$	−1.04489	−	0.339504i	−0.0419975	−	0.0136458i	−0.329940	+	0.944002i	$0.607029\pi$
$620$		0			0
$621$	−0.404237	+	0.293695i	−0.0162215	+	0.0117856i
$622$	−55.9309	−	8.85859i	−2.24263	−	0.355197i
$623$	9.73251	+	4.95896i	0.389925	+	0.198677i
$624$	1.82284	−	5.61013i	0.0729721	−	0.224585i
$625$		0			0
$626$			34.1000i			1.36291i
$627$	−6.17680	−	5.43987i	−0.246677	−	0.217247i
$628$	3.77153	+	3.77153i	0.150501	+	0.150501i
$629$	−5.80472	−	4.21737i	−0.231449	−	0.168158i
$630$		0			0
$631$	−1.00765	−	3.10124i	−0.0401140	−	0.123458i	0.928994	−	0.370095i	$-0.120675\pi$
$631$	−1.00765	−	3.10124i	−0.0401140	−	0.123458i	−0.969108	+	0.246636i	$0.920675\pi$
$632$	3.16827	−	20.0037i	0.126027	−	0.795703i
$633$	2.32393	−	14.6727i	0.0923680	−	0.583188i
$634$	22.1755	+	68.2493i	0.880703	+	2.71053i
$635$		0			0
$636$	7.81368	+	5.67697i	0.309833	+	0.225107i
$637$	−0.664797	−	0.664797i	−0.0263402	−	0.0263402i
$638$	−22.2105	+	51.3987i	−0.879321	+	2.03490i
$639$		−	3.34540i		−	0.132342i
$640$		0			0
$641$	−2.75407	+	8.47616i	−0.108779	+	0.334788i	−0.990599	−	0.136799i	$-0.956319\pi$
$641$	−2.75407	+	8.47616i	−0.108779	+	0.334788i	0.881820	+	0.471587i	$0.156319\pi$
$642$	−5.39084	−	2.74677i	−0.212760	−	0.108406i
$643$	36.6439	+	5.80382i	1.44509	+	0.228880i	0.829202	−	0.558950i	$-0.188796\pi$
$643$	36.6439	+	5.80382i	1.44509	+	0.228880i	0.615893	+	0.787830i	$0.288796\pi$
$644$	−1.21165	+	0.880315i	−0.0477457	+	0.0346893i
$645$		0			0
$646$	−9.06602	−	2.94573i	−0.356698	−	0.115898i
$647$	21.7803	−	3.44966i	0.856273	−	0.135620i	0.287163	−	0.957882i	$-0.407288\pi$
$647$	21.7803	−	3.44966i	0.856273	−	0.135620i	0.569110	+	0.822262i	$0.307288\pi$
$648$	19.4905	−	19.4905i	0.765657	−	0.765657i
$649$	11.5097	−	18.1572i	0.451794	−	0.712734i
$650$		0			0
$651$	−8.22416	+	11.3196i	−0.322330	+	0.443649i
$652$	40.8051	+	80.0844i	1.59805	+	3.13635i
$653$	−22.0554	+	43.2861i	−0.863093	+	1.69392i	−0.154861	+	0.987936i	$0.549493\pi$
$653$	−22.0554	+	43.2861i	−0.863093	+	1.69392i	−0.708232	+	0.705980i	$0.750507\pi$
$654$	−2.75608	−	3.79342i	−0.107771	−	0.148335i
$655$		0			0
$656$	11.5145	−	3.74130i	0.449567	−	0.146073i
$657$	4.17048	−	2.12497i	0.162706	−	0.0829028i
$658$	−1.03873	−	6.55831i	−0.0404941	−	0.255669i
$659$	−47.3029			−1.84266			−0.921329	−	0.388783i	$-0.872896\pi$
$659$	−47.3029			−1.84266			−0.921329	+	0.388783i	$0.872896\pi$
$660$		0			0
$661$	−26.7159			−1.03913			−0.519564	−	0.854432i	$-0.673906\pi$
$661$	−26.7159			−1.03913			−0.519564	+	0.854432i	$0.673906\pi$
$662$	−0.831711	−	5.25121i	−0.0323254	−	0.204094i
$663$	1.41329	−	0.720107i	0.0548876	−	0.0279666i
$664$	−36.7826	+	11.9514i	−1.42744	+	0.463804i
$665$		0			0
$666$	−28.7072	−	39.5121i	−1.11238	−	1.53106i
$667$	0.466563	−	0.915682i	0.0180654	−	0.0354553i
$668$	−25.5401	−	50.1252i	−0.988175	−	1.93940i
$669$	6.88603	−	9.47781i	0.266229	−	0.366433i
$670$		0			0
$671$	−30.6032	−	7.84061i	−1.18143	−	0.302683i
$672$	0.858297	−	0.858297i	0.0331095	−	0.0331095i
$673$	−13.0723	+	2.07046i	−0.503902	+	0.0798102i	−0.403210	−	0.915107i	$-0.632106\pi$
$673$	−13.0723	+	2.07046i	−0.503902	+	0.0798102i	−0.100692	+	0.994918i	$0.532106\pi$
$674$	−4.16900	−	1.35459i	−0.160584	−	0.0521769i
$675$		0			0
$676$	16.1973	−	11.7681i	0.622975	−	0.452618i
$677$	−33.9668	−	5.37982i	−1.30545	−	0.206763i	−0.535321	−	0.844649i	$-0.679809\pi$
$677$	−33.9668	−	5.37982i	−1.30545	−	0.206763i	−0.770131	+	0.637885i	$0.779809\pi$
$678$	14.4566	+	7.36599i	0.555201	+	0.282889i
$679$	−11.5070	+	35.4150i	−0.441600	+	1.35910i
$680$		0			0
$681$		−	0.611726i		−	0.0234414i
$682$	−15.9869	−	71.3470i	−0.612171	−	2.73202i
$683$	−27.9495	−	27.9495i	−1.06946	−	1.06946i	−0.997401	−	0.0720555i	$-0.977044\pi$
$683$	−27.9495	−	27.9495i	−1.06946	−	1.06946i	−0.0720555	−	0.997401i	$-0.522956\pi$
$684$	−34.7526	−	25.2493i	−1.32880	−	0.965429i
$685$		0			0
$686$	14.2346	+	43.8095i	0.543478	+	1.67265i
$687$	−0.00952805	+	0.0601578i	−0.000363518	+	0.00229516i
$688$	−3.04425	+	19.2206i	−0.116061	+	0.732779i
$689$	−3.57830	−	11.0129i	−0.136322	−	0.419557i
$690$		0			0
$691$	−2.64892	−	1.92455i	−0.100770	−	0.0732134i	0.536259	−	0.844053i	$-0.319837\pi$
$691$	−2.64892	−	1.92455i	−0.100770	−	0.0732134i	−0.637029	+	0.770840i	$0.719837\pi$
$692$	−61.7773	−	61.7773i	−2.34842	−	2.34842i
$693$	20.7694	+	8.97489i	0.788964	+	0.340928i
$694$		−	52.2333i		−	1.98275i
$695$		0			0
$696$	5.98226	−	18.4115i	0.226757	−	0.697886i
$697$	2.90071	+	1.47799i	0.109872	+	0.0559827i
$698$	−25.6035	−	4.05519i	−0.969106	−	0.153491i
$699$	−10.3535	+	7.52228i	−0.391606	+	0.284519i
$700$		0			0
$701$	−5.55696	−	1.80557i	−0.209883	−	0.0681953i	0.202188	−	0.979347i	$-0.435195\pi$
$701$	−5.55696	−	1.80557i	−0.209883	−	0.0681953i	−0.412072	+	0.911151i	$0.635195\pi$
$702$	22.7712	−	3.60661i	0.859445	−	0.136123i
$703$	−22.2957	+	22.2957i	−0.840897	+	0.840897i
$704$	1.87635	+	29.5782i	0.0707178	+	1.11477i
$705$		0			0
$706$	15.6482	−	21.5379i	0.588927	−	0.810588i
$707$	2.26817	+	4.45154i	0.0853034	+	0.167417i
$708$	−6.89398	+	13.5302i	−0.259092	+	0.508496i
$709$	−23.5016	−	32.3472i	−0.882623	−	1.21483i	−0.975688	−	0.219166i	$-0.929666\pi$
$709$	−23.5016	−	32.3472i	−0.882623	−	1.21483i	0.0930647	−	0.995660i	$-0.470334\pi$
$710$		0			0
$711$	10.9115	−	3.54537i	0.409214	−	0.132962i
$712$	17.5841	−	8.95956i	0.658993	−	0.335774i
$713$	0.209933	+	1.32547i	0.00786207	+	0.0496391i
$714$	−3.54657			−0.132727
$715$		0			0
$716$	17.1125			0.639523
$717$	−0.810496	−	5.11727i	−0.0302685	−	0.191108i
$718$	7.09665	−	3.61592i	0.264845	−	0.134945i
$719$	−19.2106	+	6.24190i	−0.716434	+	0.232784i	−0.644477	−	0.764624i	$-0.722925\pi$
$719$	−19.2106	+	6.24190i	−0.716434	+	0.232784i	−0.0719577	+	0.997408i	$0.522925\pi$
$720$		0			0
$721$	2.60896	+	3.59093i	0.0971629	+	0.133733i
$722$	1.96489	−	3.85632i	0.0731258	−	0.143517i
$723$	−2.89121	−	5.67432i	−0.107525	−	0.211030i
$724$	21.7365	−	29.9177i	0.807831	−	1.11188i
$725$		0			0
$726$	14.4720	−	6.82843i	0.537108	−	0.253427i
$727$	−26.5141	+	26.5141i	−0.983354	+	0.983354i	−0.999864	−	0.0165102i	$-0.994744\pi$
$727$	−26.5141	+	26.5141i	−0.983354	+	0.983354i	0.0165102	+	0.999864i	$0.494744\pi$
$728$	33.4083	−	5.29135i	1.23819	−	0.196111i
$729$	9.09289	+	2.95446i	0.336774	+	0.109424i
$730$		0			0
$731$	−4.23339	+	3.07574i	−0.156578	+	0.113760i
$732$	22.0405	+	3.49087i	0.814639	+	0.129026i
$733$	−28.4208	−	14.4811i	−1.04975	−	0.534873i	−0.158015	−	0.987437i	$-0.550510\pi$
$733$	−28.4208	−	14.4811i	−1.04975	−	0.534873i	−0.891732	+	0.452563i	$0.850510\pi$
$734$	−13.7035	+	42.1752i	−0.505807	+	1.55671i
$735$		0			0
$736$		−	0.116420i		−	0.00429131i
$737$	1.29283	−	13.7531i	0.0476220	−	0.506601i
$738$	15.6696	+	15.6696i	0.576805	+	0.576805i
$739$	31.6871	+	23.0220i	1.16563	+	0.846879i	0.990479	−	0.137662i	$-0.0439589\pi$
$739$	31.6871	+	23.0220i	1.16563	+	0.846879i	0.175150	+	0.984542i	$0.443959\pi$
$740$		0			0
$741$	−2.15400	−	6.62932i	−0.0791290	−	0.243534i
$742$	−4.05027	+	25.5724i	−0.148690	+	0.938793i
$743$	−1.06140	+	6.70139i	−0.0389389	+	0.245850i	−0.999478	−	0.0322930i	$-0.989719\pi$
$743$	−1.06140	+	6.70139i	−0.0389389	+	0.245850i	0.960540	+	0.278143i	$0.0897190\pi$
$744$	7.81179	+	24.0422i	0.286394	+	0.881430i
$745$		0			0
$746$	34.7666	+	25.2594i	1.27290	+	0.924814i
$747$	−15.4921	−	15.4921i	−0.566826	−	0.566826i
$748$	8.10905	−	9.20756i	0.296496	−	0.336662i
$749$		−	10.7374i		−	0.392337i
$750$		0			0
$751$	−6.82703	+	21.0114i	−0.249122	+	0.766718i	0.745809	+	0.666160i	$0.232063\pi$
$751$	−6.82703	+	21.0114i	−0.249122	+	0.766718i	−0.994931	+	0.100559i	$0.967937\pi$
$752$	−3.30830	−	1.68567i	−0.120641	−	0.0614699i
$753$	−5.54808	−	0.878729i	−0.202183	−	0.0320227i
$754$	−38.3627	+	27.8722i	−1.39709	+	1.01504i
$755$		0			0
$756$	−32.4565	−	10.5458i	−1.18043	−	0.383546i
$757$	33.0425	−	5.23341i	1.20095	−	0.190212i	0.476271	−	0.879299i	$-0.341988\pi$
$757$	33.0425	−	5.23341i	1.20095	−	0.190212i	0.724678	+	0.689087i	$0.241988\pi$
$758$	−37.9511	+	37.9511i	−1.37845	+	1.37845i
$759$	−0.273025	+	0.108262i	−0.00991017	+	0.00392968i
$760$		0			0
$761$	−15.3149	+	21.0791i	−0.555163	+	0.764117i	−0.990701	−	0.136054i	$-0.956558\pi$
$761$	−15.3149	+	21.0791i	−0.555163	+	0.764117i	0.435538	+	0.900170i	$0.356558\pi$
$762$	1.56856	+	3.07848i	0.0568231	+	0.111522i
$763$	3.77785	−	7.41445i	0.136767	−	0.268421i
$764$	14.9045	+	20.5143i	0.539227	+	0.742182i
$765$		0			0
$766$	45.5528	−	14.8010i	1.64589	−	0.534782i
$767$	16.2218	−	8.26544i	0.585736	−	0.298448i
$768$	−2.91713	−	18.4180i	−0.105263	−	0.664603i
$769$	51.2907			1.84959			0.924794	−	0.380468i	$-0.124237\pi$
$769$	51.2907			1.84959			0.924794	+	0.380468i	$0.124237\pi$
$770$		0			0
$771$	−11.0274			−0.397141
$772$	−0.616901	−	3.89496i	−0.0222027	−	0.140183i
$773$	−14.7145	+	7.49740i	−0.529243	+	0.269663i	−0.698128	−	0.715973i	$-0.745983\pi$
$773$	−14.7145	+	7.49740i	−0.529243	+	0.269663i	0.168885	+	0.985636i	$0.445983\pi$
$774$	−33.8755	+	11.0068i	−1.21763	+	0.395632i
$775$		0			0
$776$	39.5453	+	54.4295i	1.41960	+	1.95391i
$777$	−5.32574	+	10.4524i	−0.191060	+	0.374976i
$778$	18.9076	+	37.1082i	0.677869	+	1.33039i
$779$	8.40920	−	11.5743i	0.301291	−	0.414691i
$780$		0			0
$781$	1.04214	−	4.06766i	0.0372908	−	0.145552i
$782$	−0.240530	+	0.240530i	−0.00860135	+	0.00860135i
$783$	23.1292	−	3.66330i	0.826569	−	0.130916i
$784$	1.11795	+	0.363243i	0.0399267	+	0.0129730i
$785$		0			0
$786$	3.67744	−	2.67181i	0.131170	−	0.0953004i
$787$	−4.37316	−	0.692641i	−0.155886	−	0.0246900i	0.0780034	−	0.996953i	$-0.475146\pi$
$787$	−4.37316	−	0.692641i	−0.155886	−	0.0246900i	−0.233890	+	0.972263i	$0.575146\pi$
$788$	85.6084	+	43.6197i	3.04967	+	1.55389i
$789$	−3.10812	+	9.56580i	−0.110652	+	0.340551i
$790$		0			0
$791$			28.7945i			1.02381i
$792$	35.1750	−	20.8272i	1.24989	−	0.740061i
$793$	−18.9183	−	18.9183i	−0.671808	−	0.671808i
$794$	14.6086	+	10.6137i	0.518438	+	0.376667i
$795$		0			0
$796$	−3.94138	−	12.1303i	−0.139699	−	0.429948i
$797$	−3.00692	+	18.9850i	−0.106511	+	0.672482i	0.875437	+	0.483331i	$0.160573\pi$
$797$	−3.00692	+	18.9850i	−0.106511	+	0.672482i	−0.981948	+	0.189150i	$0.939427\pi$
$798$	−2.43811	+	15.3936i	−0.0863081	+	0.544928i
$799$	−0.308525	−	0.949542i	−0.0109148	−	0.0335924i
$800$		0			0
$801$	9.04454	+	6.57125i	0.319573	+	0.232184i
$802$	21.1147	+	21.1147i	0.745587	+	0.745587i
$803$	5.73284	−	1.28457i	0.202308	−	0.0453316i
$804$			9.75751i			0.344121i
$805$		0			0
$806$	19.1346	−	58.8903i	0.673988	−	2.07432i
$807$	−15.1628	−	7.72585i	−0.533757	−	0.271963i
$808$	8.91548	+	1.41207i	0.313645	+	0.0496765i
$809$	24.9923	−	18.1580i	0.878683	−	0.638401i	−0.0542197	−	0.998529i	$-0.517267\pi$
$809$	24.9923	−	18.1580i	0.878683	−	0.638401i	0.932903	+	0.360128i	$0.117267\pi$
$810$		0			0
$811$	23.8090	+	7.73601i	0.836047	+	0.271648i	0.695590	−	0.718439i	$-0.255143\pi$
$811$	23.8090	+	7.73601i	0.836047	+	0.271648i	0.140456	+	0.990087i	$0.455143\pi$
$812$	69.3267	−	10.9803i	2.43289	−	0.385332i
$813$	12.5516	−	12.5516i	0.440202	−	0.440202i
$814$	−22.5964	−	56.9854i	−0.792004	−	1.99734i
$815$		0			0
$816$	−1.16568	+	1.60442i	−0.0408070	+	0.0561660i
$817$	10.4397	+	20.4891i	0.365240	+	0.716825i
$818$	29.5519	−	57.9990i	1.03326	−	2.02789i
$819$	11.2627	+	15.5018i	0.393550	+	0.541675i
$820$		0			0
$821$	−21.6750	+	7.04264i	−0.756463	+	0.245790i	−0.661760	−	0.749716i	$-0.730190\pi$
$821$	−21.6750	+	7.04264i	−0.756463	+	0.245790i	−0.0947032	+	0.995506i	$0.530190\pi$
$822$	−21.4335	+	10.9209i	−0.747580	+	0.380911i
$823$	−2.76029	−	17.4278i	−0.0962177	−	0.607495i	−0.987931	−	0.154894i	$-0.950496\pi$
$823$	−2.76029	−	17.4278i	−0.0962177	−	0.607495i	0.891713	−	0.452601i	$-0.149504\pi$
$824$	8.01946			0.279371
$825$		0			0
$826$	−40.7077			−1.41640
$827$	2.60613	+	16.4544i	0.0906239	+	0.572177i	0.990659	+	0.136360i	$0.0435404\pi$
$827$	2.60613	+	16.4544i	0.0906239	+	0.572177i	−0.900035	+	0.435817i	$0.856460\pi$
$828$	−1.36579	+	0.695907i	−0.0474646	+	0.0241844i
$829$	−39.7855	+	12.9271i	−1.38181	+	0.448976i	−0.903263	−	0.429087i	$-0.858835\pi$
$829$	−39.7855	+	12.9271i	−1.38181	+	0.448976i	−0.478544	+	0.878064i	$0.658835\pi$
$830$		0			0
$831$	−4.36562	−	6.00876i	−0.151442	−	0.208441i
$832$	−11.3950	+	22.3640i	−0.395051	+	0.775332i
$833$	0.143498	+	0.281630i	0.00497190	+	0.00975790i
$834$	−3.69432	+	5.08480i	−0.127924	+	0.176072i
$835$		0			0
$836$	−34.3901	−	41.5265i	−1.18941	−	1.43622i
$837$	−21.6227	+	21.6227i	−0.747390	+	0.747390i
$838$	34.2139	−	5.41895i	1.18190	−	0.187195i
$839$	49.3818	+	16.0451i	1.70485	+	0.553939i	0.989463	−	0.144788i	$-0.0462501\pi$
$839$	49.3818	+	16.0451i	1.70485	+	0.553939i	0.715388	+	0.698728i	$0.246250\pi$
$840$		0			0
$841$	−15.5042	+	11.2645i	−0.534629	+	0.388431i
$842$	16.5931	+	2.62809i	0.571836	+	0.0905699i
$843$	−11.6559	−	5.93896i	−0.401449	−	0.204549i
$844$	30.0723	−	92.5530i	1.03513	−	3.18581i
$845$		0			0
$846$		−	6.79605i		−	0.233653i
$847$	22.4576	+	17.3825i	0.771654	+	0.597271i
$848$	10.2374	+	10.2374i	0.351554	+	0.351554i
$849$	13.1584	+	9.56013i	0.451595	+	0.328103i
$850$		0			0
$851$	0.347690	+	1.07008i	0.0119187	+	0.0366819i
$852$	−0.463992	+	2.92953i	−0.0158961	+	0.100364i
$853$	2.19089	−	13.8327i	0.0750145	−	0.473623i	−0.921372	−	0.388683i	$-0.872930\pi$
$853$	2.19089	−	13.8327i	0.0750145	−	0.473623i	0.996386	−	0.0849401i	$-0.0270699\pi$
$854$	18.4857	+	56.8933i	0.632569	+	1.94685i
$855$		0			0
$856$	−15.6947	−	11.4029i	−0.536434	−	0.389742i
$857$	10.2364	+	10.2364i	0.349669	+	0.349669i	0.859986	−	0.510317i	$-0.170472\pi$
$857$	10.2364	+	10.2364i	0.349669	+	0.349669i	−0.510317	+	0.859986i	$0.670472\pi$
$858$	13.4925	+	1.26833i	0.460625	+	0.0433001i
$859$			56.0426i			1.91215i	0.293125	+	0.956074i	$0.405305\pi$
$859$			56.0426i			1.91215i	−0.293125	+	0.956074i	$0.594695\pi$
$860$		0			0
$861$	1.64481	−	5.06221i	0.0560550	−	0.172520i
$862$	15.4741	+	7.88446i	0.527050	+	0.268546i
$863$	17.0244	+	2.69640i	0.579518	+	0.0917867i	0.439310	−	0.898335i	$-0.355223\pi$
$863$	17.0244	+	2.69640i	0.579518	+	0.0917867i	0.140208	+	0.990122i	$0.455223\pi$
$864$	2.14616	−	1.55928i	0.0730140	−	0.0530478i
$865$		0			0
$866$	−38.8733	−	12.6307i	−1.32097	−	0.429209i
$867$	9.51447	−	1.50694i	0.323128	−	0.0511785i
$868$	−64.8114	+	64.8114i	−2.19984	+	2.19984i
$869$	14.3717	−	0.911700i	0.487528	−	0.0309273i
$870$		0			0
$871$	6.87628	−	9.46438i	0.232994	−	0.320688i
$872$	−6.82560	−	13.3960i	−0.231144	−	0.453645i
$873$	−17.3027	+	33.9584i	−0.585606	+	1.14932i
$874$	0.878650	+	1.20936i	0.0297208	+	0.0409071i
$875$		0			0
$876$	−3.94677	+	1.28238i	−0.133349	+	0.0433278i
$877$	−6.28165	+	3.20066i	−0.212116	+	0.108079i	−0.556821	−	0.830633i	$-0.687979\pi$
$877$	−6.28165	+	3.20066i	−0.212116	+	0.108079i	0.344705	+	0.938711i	$0.387979\pi$
$878$	−0.294133	−	1.85708i	−0.00992651	−	0.0626735i
$879$	12.0275			0.405678
$880$		0			0
$881$	−46.6330			−1.57111			−0.785553	−	0.618794i	$-0.787622\pi$
$881$	−46.6330			−1.57111			−0.785553	+	0.618794i	$0.787622\pi$
$882$	0.336573	+	2.12504i	0.0113330	+	0.0715537i
$883$	−9.80743	+	4.99714i	−0.330046	+	0.168167i	−0.611159	−	0.791508i	$-0.709296\pi$
$883$	−9.80743	+	4.99714i	−0.330046	+	0.168167i	0.281113	+	0.959675i	$0.409296\pi$
$884$	9.88212	−	3.21090i	0.332372	−	0.107994i
$885$		0			0
$886$	26.8665	+	36.9785i	0.902597	+	1.24232i
$887$	17.6954	−	34.7292i	0.594154	−	1.16609i	−0.376680	−	0.926343i	$-0.622934\pi$
$887$	17.6954	−	34.7292i	0.594154	−	1.16609i	0.970835	−	0.239750i	$-0.0770655\pi$
$888$	9.62223	+	18.8847i	0.322901	+	0.633729i
$889$	−3.60411	+	4.96064i	−0.120878	+	0.166374i
$890$		0			0
$891$	16.5532	+	10.4929i	0.554554	+	0.351526i
$892$	54.2662	−	54.2662i	1.81697	−	1.81697i
$893$	−4.33351	+	0.686361i	−0.145016	+	0.0229682i
$894$	11.6835	+	3.79620i	0.390755	+	0.126964i
$895$		0			0
$896$	42.1188	−	30.6011i	1.40709	−	1.02231i
$897$	−0.245673	−	0.0389107i	−0.00820277	−	0.00129919i
$898$	1.54623	+	0.787843i	0.0515983	+	0.0262906i
$899$	19.4354	−	59.8159i	0.648206	−	1.99497i
$900$		0			0
$901$			3.89303i			0.129696i
$902$	14.1713	+	23.9339i	0.471852	+	0.796912i
$903$	6.04959	+	6.04959i	0.201318	+	0.201318i
$904$	42.0884	+	30.5790i	1.39984	+	1.01704i
$905$		0			0
$906$	5.36404	+	16.5088i	0.178208	+	0.548469i
$907$	4.39815	−	27.7688i	0.146038	−	0.922049i	−0.800471	−	0.599372i	$-0.795417\pi$
$907$	4.39815	−	27.7688i	0.146038	−	0.922049i	0.946509	−	0.322677i	$-0.104583\pi$
$908$	0.626877	−	3.95795i	0.0208037	−	0.131349i
$909$	1.58014	+	4.86318i	0.0524100	+	0.161301i
$910$		0			0
$911$	23.8530	+	17.3302i	0.790285	+	0.574175i	0.908048	−	0.418866i	$-0.137572\pi$
$911$	23.8530	+	17.3302i	0.790285	+	0.574175i	−0.117763	+	0.993042i	$0.537572\pi$
$912$	6.16252	+	6.16252i	0.204061	+	0.204061i
$913$	−14.0108	−	23.6628i	−0.463689	−	0.783126i
$914$		−	47.0585i		−	1.55656i
$915$		0			0
$916$	−0.123296	+	0.379465i	−0.00407380	+	0.0125379i
$917$	7.18775	+	3.66234i	0.237360	+	0.120941i
$918$	−7.65563	−	1.21253i	−0.252673	−	0.0400195i
$919$	−32.9943	+	23.9718i	−1.08838	+	0.790755i	−0.979125	−	0.203258i	$-0.934847\pi$
$919$	−32.9943	+	23.9718i	−1.08838	+	0.790755i	−0.109256	+	0.994014i	$0.534847\pi$
$920$		0			0
$921$	−11.8173	−	3.83968i	−0.389394	−	0.126522i
$922$	−87.7630	+	13.9003i	−2.89032	+	0.457782i
$923$	2.51454	−	2.51454i	0.0827672	−	0.0827672i
$924$	−16.9428	−	10.7399i	−0.557376	−	0.353315i
$925$		0			0
$926$	34.6632	−	47.7098i	1.13910	−	1.56784i
$927$	2.06244	+	4.04776i	0.0677394	+	0.132946i
$928$	−2.47706	+	4.86151i	−0.0813136	+	0.159587i
$929$	−30.1380	−	41.4814i	−0.988795	−	1.36096i	−0.931954	−	0.362577i	$-0.881897\pi$
$929$	−30.1380	−	41.4814i	−0.988795	−	1.36096i	−0.0568413	−	0.998383i	$-0.518103\pi$
$930$		0			0
$931$	1.32104	−	0.429233i	0.0432954	−	0.0140675i
$932$	−74.6973	+	38.0602i	−2.44679	+	1.24670i
$933$	2.17776	+	13.7499i	0.0712968	+	0.450150i
$934$	−36.0504			−1.17960
$935$		0			0
$936$	34.6194			1.13157
$937$	−0.481891	−	3.04254i	−0.0157427	−	0.0993955i	0.978566	−	0.205934i	$-0.0660232\pi$
$937$	−0.481891	−	3.04254i	−0.0157427	−	0.0993955i	−0.994309	+	0.106539i	$0.966023\pi$
$938$	−23.3063	+	11.8752i	−0.760978	+	0.387738i
$939$	7.97272	−	2.59049i	0.260180	−	0.0845376i
$940$		0			0
$941$	−16.7138	−	23.0045i	−0.544854	−	0.749927i	0.444449	−	0.895804i	$-0.353399\pi$
$941$	−16.7138	−	23.0045i	−0.544854	−	0.749927i	−0.989303	+	0.145877i	$0.953399\pi$
$942$	0.899198	−	1.76477i	0.0292974	−	0.0574995i
$943$	−0.231770	−	0.454874i	−0.00754747	−	0.0148127i
$944$	−13.3798	+	18.4157i	−0.435474	+	0.599379i
$945$		0			0
$946$	−44.6180	+	2.83043i	−1.45065	+	0.0920252i
$947$	40.6526	−	40.6526i	1.32103	−	1.32103i	0.408091	−	0.912941i	$-0.366195\pi$
$947$	40.6526	−	40.6526i	1.32103	−	1.32103i	0.912941	−	0.408091i	$-0.133805\pi$
$948$	−10.0468	+	1.59126i	−0.326306	+	0.0516818i
$949$	4.73193	+	1.53750i	0.153605	+	0.0499092i
$950$		0			0
$951$	14.2724	−	10.3695i	0.462813	−	0.336253i
$952$	−11.2318	−	1.77894i	−0.364024	−	0.0576557i
$953$	17.0501	+	8.68746i	0.552307	+	0.281414i	0.707788	−	0.706424i	$-0.249693\pi$
$953$	17.0501	+	8.68746i	0.552307	+	0.281414i	−0.155482	+	0.987839i	$0.549693\pi$
$954$	−8.18878	+	25.2025i	−0.265122	+	0.815960i
$955$		0			0
$956$		−	33.9400i		−	1.09770i
$957$	13.7045	+	1.28827i	0.443004	+	0.0416437i
$958$	−47.4507	−	47.4507i	−1.53306	−	1.53306i
$959$	−34.5378	−	25.0932i	−1.11528	−	0.810302i
$960$		0			0
$961$	15.7997	+	48.6264i	0.509667	+	1.56859i
$962$	8.12140	−	51.2765i	0.261844	−	1.65322i
$963$	1.71916	−	10.8544i	0.0553993	−	0.349777i
$964$	−12.8917	−	39.6764i	−0.415212	−	1.27789i
$965$		0			0
$966$	0.449938	+	0.326899i	0.0144765	+	0.0105178i
$967$	−12.6930	−	12.6930i	−0.408178	−	0.408178i	0.472925	−	0.881103i	$-0.343198\pi$
$967$	−12.6930	−	12.6930i	−0.408178	−	0.408178i	−0.881103	+	0.472925i	$0.843198\pi$
$968$	49.2572	−	14.3661i	1.58319	−	0.461745i
$969$			2.34346i			0.0752826i
$970$		0			0
$971$	−1.07721	+	3.31533i	−0.0345695	+	0.106394i	−0.966852	−	0.255336i	$-0.917814\pi$
$971$	−1.07721	+	3.31533i	−0.0345695	+	0.106394i	0.932283	+	0.361730i	$0.117814\pi$
$972$	−47.6686	−	24.2884i	−1.52897	−	0.779050i
$973$	−11.0169	−	1.74491i	−0.353186	−	0.0559392i
$974$	−76.5471	+	55.6147i	−2.45273	+	1.78201i
$975$		0			0
$976$	31.8137	+	10.3369i	1.01833	+	0.330876i
$977$	−25.5183	+	4.04170i	−0.816402	+	0.129305i	−0.550650	−	0.834736i	$-0.685620\pi$
$977$	−25.5183	+	4.04170i	−0.816402	+	0.129305i	−0.265752	+	0.964042i	$0.585620\pi$
$978$	23.6009	−	23.6009i	0.754672	−	0.754672i
$979$	8.95020	+	10.8075i	0.286050	+	0.345409i
$980$		0			0
$981$	5.00613	−	6.89034i	0.159833	−	0.219992i
$982$	−20.7636	−	40.7509i	−0.662595	−	1.30042i
$983$	14.1764	−	27.8228i	0.452158	−	0.887409i	−0.546591	−	0.837400i	$-0.684075\pi$
$983$	14.1764	−	27.8228i	0.452158	−	0.887409i	0.998749	−	0.0500096i	$-0.0159252\pi$
$984$	−5.65260	−	7.78013i	−0.180198	−	0.248022i
$985$		0			0
$986$	15.1619	−	4.92639i	0.482852	−	0.156888i
$987$	−1.45445	+	0.741080i	−0.0462957	+	0.0235888i
$988$	−7.14313	−	45.1000i	−0.227253	−	1.43482i
$989$	0.820573			0.0260927
$990$		0			0
$991$	−19.5868			−0.622196			−0.311098	−	0.950378i	$-0.600697\pi$
$991$	−19.5868			−0.622196			−0.311098	+	0.950378i	$0.600697\pi$
$992$	−1.11457	−	7.03714i	−0.0353877	−	0.223429i
$993$	−1.16457	+	0.593380i	−0.0369566	+	0.0188303i
$994$	−7.56203	+	2.45705i	−0.239853	+	0.0779330i
$995$		0			0
$996$	11.4176	+	15.7150i	0.361780	+	0.497948i
$997$	−12.8543	+	25.2279i	−0.407098	+	0.798976i	−0.999980	−	0.00631392i	$-0.997990\pi$
$997$	−12.8543	+	25.2279i	−0.407098	+	0.798976i	0.592882	+	0.805290i	$0.297990\pi$
$998$	5.78661	+	11.3569i	0.183172	+	0.359495i
$999$	−15.0697	+	20.7417i	−0.476784	+	0.656237i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.bm.b.18.1		32
5.2	odd	4	inner	275.2.bm.b.7.4		32
5.3	odd	4		55.2.l.a.7.1	✓	32
5.4	even	2		55.2.l.a.18.4	yes	32
11.8	odd	10	inner	275.2.bm.b.118.4		32
15.8	even	4		495.2.bj.a.172.4		32
15.14	odd	2		495.2.bj.a.73.1		32
20.3	even	4		880.2.cm.a.337.3		32
20.19	odd	2		880.2.cm.a.513.2		32
55.3	odd	20		605.2.m.e.602.1		32
55.4	even	10		605.2.m.c.233.1		32
55.8	even	20		55.2.l.a.52.4	yes	32
55.9	even	10		605.2.m.d.578.4		32
55.13	even	20		605.2.m.c.457.1		32
55.14	even	10		605.2.m.e.118.4		32
55.18	even	20		605.2.m.d.112.4		32
55.19	odd	10		55.2.l.a.8.1	yes	32
55.24	odd	10		605.2.m.c.578.1		32
55.28	even	20		605.2.e.b.362.2		32
55.29	odd	10		605.2.m.d.233.4		32
55.38	odd	20		605.2.e.b.362.15		32
55.39	odd	10		605.2.e.b.483.15		32
55.43	even	4		605.2.m.e.282.4		32
55.48	odd	20		605.2.m.c.112.1		32
55.49	even	10		605.2.e.b.483.2		32
55.52	even	20	inner	275.2.bm.b.107.1		32
55.53	odd	20		605.2.m.d.457.4		32
55.54	odd	2		605.2.m.e.403.1		32
165.8	odd	20		495.2.bj.a.217.1		32
165.74	even	10		495.2.bj.a.118.4		32
220.19	even	10		880.2.cm.a.833.3		32
220.63	odd	20		880.2.cm.a.657.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.7.1	✓	32	5.3	odd	4
55.2.l.a.8.1	yes	32	55.19	odd	10
55.2.l.a.18.4	yes	32	5.4	even	2
55.2.l.a.52.4	yes	32	55.8	even	20
275.2.bm.b.7.4		32	5.2	odd	4	inner
275.2.bm.b.18.1		32	1.1	even	1	trivial
275.2.bm.b.107.1		32	55.52	even	20	inner
275.2.bm.b.118.4		32	11.8	odd	10	inner
495.2.bj.a.73.1		32	15.14	odd	2
495.2.bj.a.118.4		32	165.74	even	10
495.2.bj.a.172.4		32	15.8	even	4
495.2.bj.a.217.1		32	165.8	odd	20
605.2.e.b.362.2		32	55.28	even	20
605.2.e.b.362.15		32	55.38	odd	20
605.2.e.b.483.2		32	55.49	even	10
605.2.e.b.483.15		32	55.39	odd	10
605.2.m.c.112.1		32	55.48	odd	20
605.2.m.c.233.1		32	55.4	even	10
605.2.m.c.457.1		32	55.13	even	20
605.2.m.c.578.1		32	55.24	odd	10
605.2.m.d.112.4		32	55.18	even	20
605.2.m.d.233.4		32	55.29	odd	10
605.2.m.d.457.4		32	55.53	odd	20
605.2.m.d.578.4		32	55.9	even	10
605.2.m.e.118.4		32	55.14	even	10
605.2.m.e.282.4		32	55.43	even	4
605.2.m.e.403.1		32	55.54	odd	2
605.2.m.e.602.1		32	55.3	odd	20
880.2.cm.a.337.3		32	20.3	even	4
880.2.cm.a.513.2		32	20.19	odd	2
880.2.cm.a.657.2		32	220.63	odd	20
880.2.cm.a.833.3		32	220.19	even	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.bm (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.380541 - 2.40264i) q^{2} +(-0.532840 + 0.271495i) q^{3} +(-3.72576 + 1.21057i) q^{4} +(0.855073 + 1.17691i) q^{6} +(-1.17208 + 2.30033i) q^{7} +(2.11764 + 4.15610i) q^{8} +(-1.55315 + 2.13772i) q^{9} +(-2.55440 + 2.11543i) q^{11} +(1.65657 - 1.65657i) q^{12} +(-2.77422 + 0.439393i) q^{13} +(5.97289 + 1.94071i) q^{14} +(2.84111 - 2.06419i) q^{16} +(0.932684 + 0.147723i) q^{17} +(5.72722 + 2.91817i) q^{18} +(1.28236 - 3.94669i) q^{19} -1.54392i q^{21} +(6.05467 + 5.33231i) q^{22} +(-0.104710 - 0.104710i) q^{23} +(-2.25672 - 1.63960i) q^{24} +(2.11141 + 6.49824i) q^{26} +(0.527849 - 3.33271i) q^{27} +(1.58216 - 9.98937i) q^{28} +(2.14459 + 6.60038i) q^{29} +(-7.33171 - 5.32680i) q^{31} +(0.555921 + 0.555921i) q^{32} +(0.786759 - 1.82069i) q^{33} -2.29712i q^{34} +(3.19879 - 9.84486i) q^{36} +(-6.77002 - 3.44950i) q^{37} +(-9.97047 - 1.57917i) q^{38} +(1.35892 - 0.987312i) q^{39} +(3.27880 + 1.06535i) q^{41} +(-3.70949 + 0.587525i) q^{42} +(-3.91833 + 3.91833i) q^{43} +(6.95623 - 10.9739i) q^{44} +(-0.211733 + 0.291426i) q^{46} +(-0.479999 - 0.942051i) q^{47} +(-0.953440 + 1.87123i) q^{48} +(0.196744 + 0.270795i) q^{49} +(-0.537077 + 0.174507i) q^{51} +(9.80416 - 4.99547i) q^{52} +(0.644920 + 4.07187i) q^{53} -8.20817 q^{54} -12.0424 q^{56} +(0.388217 + 2.45111i) q^{57} +(15.0422 - 7.66441i) q^{58} +(-6.16460 + 2.00300i) q^{59} +(5.59880 + 7.70609i) q^{61} +(-10.0084 + 19.6426i) q^{62} +(-3.09706 - 6.07833i) q^{63} +(5.25251 - 7.22946i) q^{64} +(-4.67386 - 1.19745i) q^{66} +(-2.94509 + 2.94509i) q^{67} +(-3.65379 + 0.578703i) q^{68} +(0.0842215 + 0.0273652i) q^{69} +(-1.02426 + 0.744171i) q^{71} +(-12.1736 - 1.92811i) q^{72} +(-1.57831 - 0.804189i) q^{73} +(-5.71163 + 17.5786i) q^{74} +16.2568i q^{76} +(-1.87222 - 8.35541i) q^{77} +(-2.88928 - 2.88928i) q^{78} +(-3.51271 - 2.55214i) q^{79} +(-1.82606 - 5.62003i) q^{81} +(1.31193 - 8.28320i) q^{82} +(-1.29707 + 8.18939i) q^{83} +(1.86903 + 5.75228i) q^{84} +(10.9054 + 7.92326i) q^{86} +(-2.93470 - 2.93470i) q^{87} +(-14.2012 - 6.13664i) q^{88} -4.23092i q^{89} +(2.24084 - 6.89661i) q^{91} +(0.516882 + 0.263364i) q^{92} +(5.35283 + 0.847805i) q^{93} +(-2.08075 + 1.51175i) q^{94} +(-0.447147 - 0.145287i) q^{96} +(14.2460 - 2.25634i) q^{97} +(0.575755 - 0.575755i) q^{98} +(-0.554831 - 8.74618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 10 q^{2} + 4 q^{3} - 20 q^{6} + 10 q^{8} - 24 q^{11} - 12 q^{12} + 10 q^{13} - 8 q^{16} + 10 q^{18} - 10 q^{22} + 24 q^{23} + 20 q^{26} + 16 q^{27} - 50 q^{28} - 28 q^{31} - 66 q^{33} + 24 q^{36}+ \cdots + 8 q^{97}+O(q^{100}) \) 32 * q + 10 * q^2 + 4 * q^3 - 20 * q^6 + 10 * q^8 - 24 * q^11 - 12 * q^12 + 10 * q^13 - 8 * q^16 + 10 * q^18 - 10 * q^22 + 24 * q^23 + 20 * q^26 + 16 * q^27 - 50 * q^28 - 28 * q^31 - 66 * q^33 + 24 * q^36 + 8 * q^37 - 10 * q^38 + 40 * q^41 + 10 * q^42 + 60 * q^46 + 28 * q^47 + 54 * q^48 + 20 * q^51 + 50 * q^52 + 24 * q^53 - 80 * q^56 - 30 * q^57 + 50 * q^58 - 60 * q^61 - 100 * q^62 + 30 * q^63 - 100 * q^66 + 8 * q^67 + 30 * q^68 + 24 * q^71 - 80 * q^72 - 50 * q^73 - 70 * q^77 - 60 * q^78 - 12 * q^81 + 10 * q^82 - 90 * q^83 + 100 * q^86 - 170 * q^88 + 20 * q^91 + 68 * q^92 + 8 * q^93 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

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