LMFDB - Embedded newform 228.2.k.a.103.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [228,2,Mod(31,228)] 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("228.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(228, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.k (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,-1] 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:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 3 x^{18} - 2 x^{17} + x^{16} + 3 x^{14} - 12 x^{13} + 28 x^{12} - 24 x^{11} + \cdots + 1024 $ x^20 - 2x^19 + 3x^18 - 2x^17 + x^16 + 3x^14 - 12x^13 + 28x^12 - 24x^11 + 40x^10 - 48x^9 + 112x^8 - 96x^7 + 48x^6 + 64x^4 - 256x^3 + 768x^2 - 1024x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			103.5
Root			$1.34699 - 0.430844i$ of defining polynomial
Character	$\chi$	$=$	228.103
Dual form			228.2.k.a.31.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.300371 + 1.38195i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.81955 - 0.830194i) q^{4} +(1.45389 - 2.51821i) q^{5} +(-1.04662 - 0.951102i) q^{6} -5.22116i q^{7} +(1.69383 - 2.26516i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(3.04332 + 2.76559i) q^{10} -1.42673i q^{11} +(1.62875 - 1.16068i) q^{12} +(-3.35123 + 1.93483i) q^{13} +(7.21537 + 1.56829i) q^{14} +(1.45389 + 2.51821i) q^{15} +(2.62156 + 3.02117i) q^{16} +(-0.265735 + 0.460266i) q^{17} +(1.34699 - 0.430844i) q^{18} +(-3.74267 + 2.23437i) q^{19} +(-4.73603 + 3.37501i) q^{20} +(4.52166 + 2.61058i) q^{21} +(1.97166 + 0.428548i) q^{22} +(2.95664 - 1.70702i) q^{23} +(1.11477 + 2.59948i) q^{24} +(-1.72758 - 2.99225i) q^{25} +(-1.66723 - 5.21239i) q^{26} +1.00000 q^{27} +(-4.33457 + 9.50018i) q^{28} +(6.63731 - 3.83205i) q^{29} +(-3.91673 + 1.25280i) q^{30} -0.283986 q^{31} +(-4.96253 + 2.71538i) q^{32} +(1.23558 + 0.713364i) q^{33} +(-0.556244 - 0.505482i) q^{34} +(-13.1480 - 7.59098i) q^{35} +(0.190808 + 1.99088i) q^{36} +1.63314i q^{37} +(-1.96360 - 5.84331i) q^{38} -3.86967i q^{39} +(-3.24151 - 7.55869i) q^{40} +(5.69391 + 3.28738i) q^{41} +(-4.96586 + 5.46455i) q^{42} +(7.23299 + 4.17597i) q^{43} +(-1.18446 + 2.59601i) q^{44} -2.90777 q^{45} +(1.47092 + 4.59866i) q^{46} +(8.02928 - 4.63571i) q^{47} +(-3.92718 + 0.759752i) q^{48} -20.2605 q^{49} +(4.65404 - 1.48863i) q^{50} +(-0.265735 - 0.460266i) q^{51} +(7.70404 - 0.738365i) q^{52} +(1.86294 - 1.07557i) q^{53} +(-0.300371 + 1.38195i) q^{54} +(-3.59279 - 2.07430i) q^{55} +(-11.8268 - 8.84373i) q^{56} +(-0.0636895 - 4.35843i) q^{57} +(3.30204 + 10.3234i) q^{58} +(-2.94720 + 5.10469i) q^{59} +(-0.554827 - 5.78902i) q^{60} +(2.15156 + 3.72662i) q^{61} +(0.0853013 - 0.392454i) q^{62} +(-4.52166 + 2.61058i) q^{63} +(-2.26191 - 7.67358i) q^{64} +11.2521i q^{65} +(-1.35696 + 1.49324i) q^{66} +(-1.96866 - 3.40981i) q^{67} +(0.865629 - 0.616868i) q^{68} +3.41403i q^{69} +(14.4396 - 15.8897i) q^{70} +(-3.68578 + 6.38395i) q^{71} +(-2.80860 - 0.334315i) q^{72} +(5.78802 - 10.0251i) q^{73} +(-2.25691 - 0.490548i) q^{74} +3.45515 q^{75} +(8.66495 - 0.958423i) q^{76} -7.44917 q^{77} +(5.34768 + 1.16234i) q^{78} +(2.83681 - 4.91350i) q^{79} +(11.4194 - 2.20919i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-6.25327 + 6.88125i) q^{82} +4.49906i q^{83} +(-6.06011 - 8.50394i) q^{84} +(0.772697 + 1.33835i) q^{85} +(-7.94355 + 8.74127i) q^{86} +7.66410i q^{87} +(-3.23177 - 2.41663i) q^{88} +(-7.33193 + 4.23309i) q^{89} +(0.873411 - 4.01839i) q^{90} +(10.1021 + 17.4973i) q^{91} +(-6.79692 + 0.651426i) q^{92} +(0.141993 - 0.245939i) q^{93} +(3.99454 + 12.4885i) q^{94} +(0.185195 + 12.6733i) q^{95} +(0.129676 - 5.65537i) q^{96} +(-3.51925 - 2.03184i) q^{97} +(6.08567 - 27.9989i) q^{98} +(-1.23558 + 0.713364i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - q^{2} - 10 q^{3} + q^{4} - q^{6} - 4 q^{8} - 10 q^{9} + 6 q^{10} - 2 q^{12} + 6 q^{13} + 9 q^{14} + 13 q^{16} + 2 q^{18} - 12 q^{19} - 14 q^{20} + 6 q^{21} - 8 q^{22} - 7 q^{24} - 10 q^{25} + 20 q^{27}+ \cdots - 12 q^{98}+O(q^{100}) $ 20 * q - q^2 - 10 * q^3 + q^4 - q^6 - 4 * q^8 - 10 * q^9 + 6 * q^10 - 2 * q^12 + 6 * q^13 + 9 * q^14 + 13 * q^16 + 2 * q^18 - 12 * q^19 - 14 * q^20 + 6 * q^21 - 8 * q^22 - 7 * q^24 - 10 * q^25 + 20 * q^27 + 7 * q^28 - 12 * q^31 - 31 * q^32 - 30 * q^34 + q^36 - 11 * q^38 - 26 * q^40 + 12 * q^41 - 9 * q^42 + 18 * q^43 + 30 * q^44 + 32 * q^46 + 36 * q^47 - 11 * q^48 - 24 * q^49 + 34 * q^50 + 3 * q^52 - 12 * q^53 - q^54 - 38 * q^56 + 6 * q^57 + 16 * q^58 + 10 * q^60 + 10 * q^61 + 29 * q^62 - 6 * q^63 - 14 * q^64 - 8 * q^66 - 14 * q^67 + 40 * q^68 + 46 * q^70 - 8 * q^71 + 11 * q^72 - 6 * q^73 + 3 * q^74 + 20 * q^75 + 3 * q^76 - 32 * q^77 + 33 * q^78 + 6 * q^79 + 40 * q^80 - 10 * q^81 - 60 * q^82 - 14 * q^84 + 8 * q^85 - 25 * q^86 - 44 * q^88 - 24 * q^89 - 6 * q^90 - 26 * q^91 + 36 * q^92 + 6 * q^93 + 52 * q^94 - 4 * q^95 + 2 * q^96 - 12 * q^97 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.300371	+	1.38195i	−0.212394	+	0.977184i
$2$	−0.300371	+	1.38195i	−0.212394	+	0.977184i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−1.81955	−	0.830194i	−0.909777	−	0.415097i
$5$	1.45389	−	2.51821i	0.650198	−	1.12618i	−0.332877	−	0.942970i	$-0.608019\pi$
$5$	1.45389	−	2.51821i	0.650198	−	1.12618i	0.983075	−	0.183206i	$-0.0586474\pi$
$6$	−1.04662	−	0.951102i	−0.427279	−	0.388286i
$7$		−	5.22116i		−	1.97341i	−0.162513	−	0.986706i	$-0.551960\pi$
$7$		−	5.22116i		−	1.97341i	0.162513	−	0.986706i	$-0.448040\pi$
$8$	1.69383	−	2.26516i	0.598858	−	0.800855i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	3.04332	+	2.76559i	0.962383	+	0.874557i
$11$		−	1.42673i		−	0.430175i	−0.976595	−	0.215087i	$-0.930996\pi$
$11$		−	1.42673i		−	0.430175i	0.976595	−	0.215087i	$-0.0690036\pi$
$12$	1.62875	−	1.16068i	0.470179	−	0.335060i
$13$	−3.35123	+	1.93483i	−0.929464	+	0.536627i	−0.886642	−	0.462456i	$-0.846968\pi$
$13$	−3.35123	+	1.93483i	−0.929464	+	0.536627i	−0.0428222	+	0.999083i	$0.513635\pi$
$14$	7.21537	+	1.56829i	1.92839	+	0.419142i
$15$	1.45389	+	2.51821i	0.375392	+	0.650198i
$16$	2.62156	+	3.02117i	0.655389	+	0.755291i
$17$	−0.265735	+	0.460266i	−0.0644501	+	0.111631i	−0.896450	−	0.443145i	$-0.853863\pi$
$17$	−0.265735	+	0.460266i	−0.0644501	+	0.111631i	0.832000	+	0.554776i	$0.187196\pi$
$18$	1.34699	−	0.430844i	0.317488	−	0.101551i
$19$	−3.74267	+	2.23437i	−0.858627	+	0.512600i
$19$	−3.74267	+	2.23437i	−0.858627	+	0.512600i
$20$	−4.73603	+	3.37501i	−1.05901	+	0.754674i
$21$	4.52166	+	2.61058i	0.986706	+	0.569675i
$22$	1.97166	+	0.428548i	0.420360	+	0.0913667i
$23$	2.95664	−	1.70702i	0.616502	−	0.355938i	−0.159004	−	0.987278i	$-0.550828\pi$
$23$	2.95664	−	1.70702i	0.616502	−	0.355938i	0.775506	+	0.631340i	$0.217495\pi$
$24$	1.11477	+	2.59948i	0.227552	+	0.530616i
$25$	−1.72758	−	2.99225i	−0.345515	−	0.598450i
$26$	−1.66723	−	5.21239i	−0.326970	−	1.02223i
$27$	1.00000			0.192450
$28$	−4.33457	+	9.50018i	−0.819158	+	1.79537i
$29$	6.63731	−	3.83205i	1.23252	−	0.711594i	0.264963	−	0.964259i	$-0.414640\pi$
$29$	6.63731	−	3.83205i	1.23252	−	0.711594i	0.967554	+	0.252665i	$0.0813069\pi$
$30$	−3.91673	+	1.25280i	−0.715094	+	0.228729i
$31$	−0.283986			−0.0510055			−0.0255027	−	0.999675i	$-0.508119\pi$
$31$	−0.283986			−0.0510055			−0.0255027	+	0.999675i	$0.508119\pi$
$32$	−4.96253	+	2.71538i	−0.877260	+	0.480016i
$33$	1.23558	+	0.713364i	0.215087	+	0.124181i
$34$	−0.556244	−	0.505482i	−0.0953951	−	0.0866894i
$35$	−13.1480	−	7.59098i	−2.22241	−	1.28311i
$36$	0.190808	+	1.99088i	0.0318014	+	0.331813i
$37$			1.63314i			0.268486i	0.990948	+	0.134243i	$0.0428603\pi$
$37$			1.63314i			0.268486i	−0.990948	+	0.134243i	$0.957140\pi$
$38$	−1.96360	−	5.84331i	−0.318537	−	0.947910i
$39$		−	3.86967i		−	0.619643i
$40$	−3.24151	−	7.55869i	−0.512528	−	1.19513i
$41$	5.69391	+	3.28738i	0.889239	+	0.513402i	0.873694	−	0.486477i	$-0.161718\pi$
$41$	5.69391	+	3.28738i	0.889239	+	0.513402i	0.0155456	+	0.999879i	$0.495051\pi$
$42$	−4.96586	+	5.46455i	−0.766249	+	0.843198i
$43$	7.23299	+	4.17597i	1.10302	+	0.636829i	0.937013	−	0.349295i	$-0.113579\pi$
$43$	7.23299	+	4.17597i	1.10302	+	0.636829i	0.166008	+	0.986124i	$0.446912\pi$
$44$	−1.18446	+	2.59601i	−0.178564	+	0.391363i
$45$	−2.90777			−0.433465
$46$	1.47092	+	4.59866i	0.216875	+	0.678035i
$47$	8.02928	−	4.63571i	1.17119	−	0.676187i	0.217231	−	0.976120i	$-0.430298\pi$
$47$	8.02928	−	4.63571i	1.17119	−	0.676187i	0.953960	+	0.299933i	$0.0969643\pi$
$48$	−3.92718	+	0.759752i	−0.566840	+	0.109661i
$49$	−20.2605			−2.89436
$50$	4.65404	−	1.48863i	0.658181	−	0.210524i
$51$	−0.265735	−	0.460266i	−0.0372103	−	0.0644501i
$52$	7.70404	−	0.738365i	1.06836	−	0.102393i
$53$	1.86294	−	1.07557i	0.255895	−	0.147741i	−0.366566	−	0.930392i	$-0.619466\pi$
$53$	1.86294	−	1.07557i	0.255895	−	0.147741i	0.622460	+	0.782651i	$0.286133\pi$
$54$	−0.300371	+	1.38195i	−0.0408753	+	0.188059i
$55$	−3.59279	−	2.07430i	−0.484452	−	0.279699i
$56$	−11.8268	−	8.84373i	−1.58042	−	1.18179i
$57$	−0.0636895	−	4.35843i	−0.00843588	−	0.577289i
$58$	3.30204	+	10.3234i	0.433578	+	1.35553i
$59$	−2.94720	+	5.10469i	−0.383692	+	0.664575i	−0.991587	−	0.129443i	$-0.958681\pi$
$59$	−2.94720	+	5.10469i	−0.383692	+	0.664575i	0.607894	+	0.794018i	$0.292014\pi$
$60$	−0.554827	−	5.78902i	−0.0716279	−	0.747359i
$61$	2.15156	+	3.72662i	0.275479	+	0.477144i	0.970256	−	0.242081i	$-0.0778301\pi$
$61$	2.15156	+	3.72662i	0.275479	+	0.477144i	−0.694777	+	0.719226i	$0.744497\pi$
$62$	0.0853013	−	0.392454i	0.0108333	−	0.0498417i
$63$	−4.52166	+	2.61058i	−0.569675	+	0.328902i
$64$	−2.26191	−	7.67358i	−0.282739	−	0.959197i
$65$			11.2521i			1.39565i
$66$	−1.35696	+	1.49324i	−0.167031	+	0.183805i
$67$	−1.96866	−	3.40981i	−0.240510	−	0.416575i	0.720350	−	0.693611i	$-0.243981\pi$
$67$	−1.96866	−	3.40981i	−0.240510	−	0.416575i	−0.960860	+	0.277036i	$0.910648\pi$
$68$	0.865629	−	0.616868i	0.104973	−	0.0748062i
$69$			3.41403i			0.411001i
$70$	14.4396	−	15.8897i	1.72586	−	1.89918i
$71$	−3.68578	+	6.38395i	−0.437421	+	0.757636i	−0.997490	−	0.0708106i	$-0.977441\pi$
$71$	−3.68578	+	6.38395i	−0.437421	+	0.757636i	0.560069	+	0.828446i	$0.310775\pi$
$72$	−2.80860	−	0.334315i	−0.330997	−	0.0393994i
$73$	5.78802	−	10.0251i	0.677437	−	1.17335i	−0.298313	−	0.954468i	$-0.596424\pi$
$73$	5.78802	−	10.0251i	0.677437	−	1.17335i	0.975750	−	0.218887i	$-0.0702426\pi$
$74$	−2.25691	−	0.490548i	−0.262361	−	0.0570250i
$75$	3.45515			0.398966
$76$	8.66495	−	0.958423i	0.993938	−	0.109939i
$77$	−7.44917			−0.848912
$78$	5.34768	+	1.16234i	0.605505	+	0.131609i
$79$	2.83681	−	4.91350i	0.319166	−	0.552812i	−0.661148	−	0.750255i	$-0.729931\pi$
$79$	2.83681	−	4.91350i	0.319166	−	0.552812i	0.980314	+	0.197443i	$0.0632639\pi$
$80$	11.4194	−	2.20919i	1.27672	−	0.246994i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−6.25327	+	6.88125i	−0.690558	+	0.759906i
$83$			4.49906i			0.493836i	0.969036	+	0.246918i	$0.0794178\pi$
$83$			4.49906i			0.493836i	−0.969036	+	0.246918i	$0.920582\pi$
$84$	−6.06011	−	8.50394i	−0.661213	−	0.927856i
$85$	0.772697	+	1.33835i	0.0838107	+	0.145164i
$86$	−7.94355	+	8.74127i	−0.856575	+	0.942595i
$87$			7.66410i			0.821678i
$88$	−3.23177	−	2.41663i	−0.344508	−	0.257613i
$89$	−7.33193	+	4.23309i	−0.777183	+	0.448707i	−0.835431	−	0.549596i	$-0.814782\pi$
$89$	−7.33193	+	4.23309i	−0.777183	+	0.448707i	0.0582483	+	0.998302i	$0.481448\pi$
$90$	0.873411	−	4.01839i	0.0920656	−	0.423575i
$91$	10.1021	+	17.4973i	1.05899	+	1.83422i
$92$	−6.79692	+	0.651426i	−0.708628	+	0.0679158i
$93$	0.141993	−	0.245939i	0.0147240	−	0.0255027i
$94$	3.99454	+	12.4885i	0.412005	+	1.28809i
$95$	0.185195	+	12.6733i	0.0190006	+	1.30026i
$96$	0.129676	−	5.65537i	0.0132350	−	0.577199i
$97$	−3.51925	−	2.03184i	−0.357326	−	0.206302i	0.310581	−	0.950547i	$-0.399476\pi$
$97$	−3.51925	−	2.03184i	−0.357326	−	0.206302i	−0.667907	+	0.744245i	$0.732810\pi$
$98$	6.08567	−	27.9989i	0.614746	−	2.82832i
$99$	−1.23558	+	0.713364i	−0.124181	+	0.0716958i
$100$	0.659271	+	6.87878i	0.0659271	+	0.687878i
$101$	6.23562	+	10.8004i	0.620467	+	1.07468i	0.989399	+	0.145224i	$0.0463903\pi$
$101$	6.23562	+	10.8004i	0.620467	+	1.07468i	−0.368932	+	0.929457i	$0.620276\pi$
$102$	0.715882	−	0.228981i	0.0708829	−	0.0226725i
$103$	2.75643			0.271599			0.135800	−	0.990736i	$-0.456640\pi$
$103$	2.75643			0.271599			0.135800	+	0.990736i	$0.456640\pi$
$104$	−1.29369	+	10.8684i	−0.126857	+	1.06573i
$105$	13.1480	−	7.59098i	1.28311	−	0.740803i
$106$	0.926807	+	2.89756i	0.0900194	+	0.281436i
$107$	8.62681			0.833986			0.416993	−	0.908910i	$-0.363084\pi$
$107$	8.62681			0.833986			0.416993	+	0.908910i	$0.363084\pi$
$108$	−1.81955	−	0.830194i	−0.175087	−	0.0798854i
$109$	−10.8426	−	6.25996i	−1.03853	−	0.599596i	−0.119114	−	0.992881i	$-0.538005\pi$
$109$	−10.8426	−	6.25996i	−1.03853	−	0.599596i	−0.919417	+	0.393285i	$0.871339\pi$
$110$	3.94574	−	4.34199i	0.376212	−	0.413993i
$111$	−1.41434	−	0.816569i	−0.134243	−	0.0775053i
$112$	15.7740	−	13.6876i	1.49050	−	1.29335i
$113$		−	16.1398i		−	1.51830i	−0.650915	−	0.759151i	$-0.725615\pi$
$113$		−	16.1398i		−	1.51830i	0.650915	−	0.759151i	$-0.274385\pi$
$114$	6.04225	+	1.22113i	0.565909	+	0.114369i
$115$		−	9.92724i		−	0.925720i
$116$	−15.2583	+	1.46237i	−1.41670	+	0.135778i
$117$	3.35123	+	1.93483i	0.309821	+	0.178876i
$118$	−6.16916	−	5.60617i	−0.567918	−	0.516090i
$119$	2.40312	+	1.38744i	0.220294	+	0.127187i
$120$	8.16677	+	0.972113i	0.745521	+	0.0887414i
$121$	8.96445			0.814950
$122$	−5.79625	+	1.85398i	−0.524768	+	0.167851i
$123$	−5.69391	+	3.28738i	−0.513402	+	0.296413i
$124$	0.516729	+	0.235764i	0.0464036	+	0.0211722i
$125$	4.49207			0.401783
$126$	−2.24951	−	7.03283i	−0.200402	−	0.626535i
$127$	−1.05601	−	1.82906i	−0.0937055	−	0.162303i	0.815362	−	0.578951i	$-0.196538\pi$
$127$	−1.05601	−	1.82906i	−0.0937055	−	0.162303i	−0.909068	+	0.416649i	$0.863205\pi$
$128$	11.2839	−	0.820921i	0.997364	−	0.0725598i
$129$	−7.23299	+	4.17597i	−0.636829	+	0.367674i
$130$	−15.5498	−	3.37981i	−1.36381	−	0.296429i
$131$	17.2919	+	9.98348i	1.51080	+	0.872261i	0.999921	+	0.0126087i	$0.00401357\pi$
$131$	17.2919	+	9.98348i	1.51080	+	0.872261i	0.510880	+	0.859652i	$0.329320\pi$
$132$	−1.65598	−	2.32378i	−0.144134	−	0.202259i
$133$	11.6660	+	19.5411i	1.01157	+	1.69443i
$134$	5.30351	−	1.69637i	0.458153	−	0.146544i
$135$	1.45389	−	2.51821i	0.125131	−	0.216733i
$136$	0.592469	+	1.38154i	0.0508038	+	0.118466i
$137$	−8.00312	−	13.8618i	−0.683753	−	1.18429i	−0.973827	−	0.227290i	$-0.927013\pi$
$137$	−8.00312	−	13.8618i	−0.683753	−	1.18429i	0.290074	−	0.957004i	$-0.406320\pi$
$138$	−4.71801	−	1.02548i	−0.401624	−	0.0872944i
$139$	7.74680	−	4.47262i	0.657075	−	0.379363i	−0.134086	−	0.990970i	$-0.542810\pi$
$139$	7.74680	−	4.47262i	0.657075	−	0.379363i	0.791162	+	0.611607i	$0.209477\pi$
$140$	17.6214	+	24.7275i	1.48928	+	2.08986i
$141$			9.27141i			0.780794i
$142$	−7.71518	−	7.01110i	−0.647444	−	0.588359i
$143$	2.76048	+	4.78129i	0.230843	+	0.399832i
$144$	1.30563	−	3.78092i	0.108802	−	0.315076i
$145$		−	22.2855i		−	1.85071i
$146$	12.1157	+	11.0100i	1.00270	+	0.911194i
$147$	10.1303	−	17.5461i	0.835529	−	1.44718i
$148$	1.35582	−	2.97158i	0.111448	−	0.244263i
$149$	−0.0498162	+	0.0862842i	−0.00408110	+	0.00706868i	−0.868059	−	0.496461i	$-0.834632\pi$
$149$	−0.0498162	+	0.0862842i	−0.00408110	+	0.00706868i	0.863978	+	0.503530i	$0.167966\pi$
$150$	−1.03783	+	4.77483i	−0.0847382	+	0.389864i
$151$	−17.9903			−1.46403			−0.732016	−	0.681288i	$-0.761420\pi$
$151$	−17.9903			−1.46403			−0.732016	+	0.681288i	$0.761420\pi$
$152$	−1.27821	+	12.2624i	−0.103677	+	0.994611i
$153$	0.531469			0.0429668
$154$	2.23752	−	10.2944i	0.180304	−	0.829543i
$155$	−0.412884	+	0.715136i	−0.0331636	+	0.0574411i
$156$	−3.21258	+	7.04107i	−0.257212	+	0.563737i
$157$	−10.4761	+	18.1451i	−0.836084	+	1.44814i	0.0570610	+	0.998371i	$0.481827\pi$
$157$	−10.4761	+	18.1451i	−0.836084	+	1.44814i	−0.893145	+	0.449769i	$0.851506\pi$
$158$	5.93810	+	5.39620i	0.472410	+	0.429298i
$159$			2.15114i			0.170596i
$160$	−0.377070	+	16.4445i	−0.0298100	+	1.30005i
$161$	−8.91261	−	15.4371i	−0.702412	−	1.21661i
$162$	−1.04662	−	0.951102i	−0.0822299	−	0.0747257i
$163$		−	1.57730i		−	0.123544i	−0.998090	−	0.0617719i	$-0.980325\pi$
$163$		−	1.57730i		−	0.123544i	0.998090	−	0.0617719i	$-0.0196751\pi$
$164$	−7.63121	−	10.7086i	−0.595898	−	0.836202i
$165$	3.59279	−	2.07430i	0.279699	−	0.161484i
$166$	−6.21746	−	1.35139i	−0.482569	−	0.104888i
$167$	−1.82090	−	3.15389i	−0.140905	−	0.244055i	0.786932	−	0.617039i	$-0.211668\pi$
$167$	−1.82090	−	3.15389i	−0.140905	−	0.244055i	−0.927838	+	0.372984i	$0.878335\pi$
$168$	13.5723	−	5.82042i	1.04712	−	0.449055i
$169$	0.987168	−	1.70983i	0.0759360	−	0.131525i
$170$	−2.08162	+	0.665824i	−0.159653	+	0.0510664i
$171$	3.80636	+	2.12406i	0.291080	+	0.162431i
$172$	−9.69396	−	13.6032i	−0.739157	−	1.03723i
$173$	9.10847	+	5.25878i	0.692504	+	0.399817i	0.804549	−	0.593886i	$-0.202407\pi$
$173$	9.10847	+	5.25878i	0.692504	+	0.399817i	−0.112045	+	0.993703i	$0.535740\pi$
$174$	−10.5914	−	2.30207i	−0.802931	−	0.174520i
$175$	−15.6230	+	9.01995i	−1.18099	+	0.681844i
$176$	4.31038	−	3.74025i	0.324907	−	0.281932i
$177$	−2.94720	−	5.10469i	−0.221525	−	0.383692i
$178$	−3.64761	−	11.4038i	−0.273400	−	0.854753i
$179$	−10.2799			−0.768354			−0.384177	−	0.923260i	$-0.625515\pi$
$179$	−10.2799			−0.768354			−0.384177	+	0.923260i	$0.625515\pi$
$180$	5.29085	+	2.41402i	0.394357	+	0.179930i
$181$	−5.12517	+	2.95902i	−0.380951	+	0.219942i	−0.678232	−	0.734848i	$-0.737253\pi$
$181$	−5.12517	+	2.95902i	−0.380951	+	0.219942i	0.297281	+	0.954790i	$0.403920\pi$
$182$	−27.2147	+	8.70485i	−2.01729	+	0.645246i
$183$	−4.30313			−0.318096
$184$	1.14136	−	9.58866i	0.0841424	−	0.706885i
$185$	4.11258	+	2.37440i	0.302363	+	0.174569i
$186$	0.297225	+	0.270100i	0.0217936	+	0.0198047i
$187$	0.656674	+	0.379131i	0.0480208	+	0.0277248i
$188$	−18.4582	+	1.76906i	−1.34621	+	0.129022i
$189$		−	5.22116i		−	0.379784i
$190$	−17.5695	−	3.55078i	−1.27463	−	0.257600i
$191$			3.11717i			0.225550i	0.993621	+	0.112775i	$0.0359740\pi$
$191$			3.11717i			0.225550i	−0.993621	+	0.112775i	$0.964026\pi$
$192$	7.77647	+	1.87792i	0.561218	+	0.135527i
$193$	16.7723	+	9.68348i	1.20729	+	0.697032i	0.962167	−	0.272459i	$-0.0878370\pi$
$193$	16.7723	+	9.68348i	1.20729	+	0.697032i	0.245127	+	0.969491i	$0.421170\pi$
$194$	3.86498	−	4.25311i	0.277489	−	0.305356i
$195$	−9.74462	−	5.62606i	−0.697827	−	0.402891i
$196$	36.8651	+	16.8202i	2.63322	+	1.20144i
$197$	−17.7374			−1.26373			−0.631867	−	0.775077i	$-0.717711\pi$
$197$	−17.7374			−1.26373			−0.631867	+	0.775077i	$0.717711\pi$
$198$	−0.614698	−	1.92178i	−0.0436847	−	0.136575i
$199$	−5.26542	+	3.03999i	−0.373256	+	0.215499i	−0.674880	−	0.737928i	$-0.735805\pi$
$199$	−5.26542	+	3.03999i	−0.373256	+	0.215499i	0.301624	+	0.953427i	$0.402471\pi$
$200$	−9.70413	−	1.15511i	−0.686186	−	0.0816785i
$201$	3.93731			0.277717
$202$	−16.7986	+	5.37316i	−1.18194	+	0.378054i
$203$	−20.0077	−	34.6544i	−1.40427	−	2.43226i
$204$	0.101409	+	1.05809i	0.00710003	+	0.0740812i
$205$	16.5566	−	9.55896i	1.15636	−	0.667627i
$206$	−0.827952	+	3.80924i	−0.0576862	+	0.265402i
$207$	−2.95664	−	1.70702i	−0.205501	−	0.118646i
$208$	−14.6309	−	5.05235i	−1.01447	−	0.350317i
$209$	3.18784	+	5.33977i	0.220508	+	0.369360i
$210$	6.54106	+	20.4499i	0.451376	+	1.41118i
$211$	−12.4711	+	21.6005i	−0.858543	+	1.48704i	0.0147752	+	0.999891i	$0.495297\pi$
$211$	−12.4711	+	21.6005i	−0.858543	+	1.48704i	−0.873318	+	0.487150i	$0.838037\pi$
$212$	−4.28266	+	0.410455i	−0.294134	+	0.0281902i
$213$	−3.68578	−	6.38395i	−0.252545	−	0.437421i
$214$	−2.59125	+	11.9218i	−0.177134	+	0.814957i
$215$	21.0319	−	12.1428i	1.43436	−	0.828130i
$216$	1.69383	−	2.26516i	0.115250	−	0.154125i
$217$			1.48274i			0.100655i
$218$	11.9077	−	13.1036i	0.806494	−	0.887485i
$219$	5.78802	+	10.0251i	0.391118	+	0.677437i
$220$	4.81521	+	6.75702i	0.324642	+	0.455558i
$221$		−	2.05661i		−	0.138343i
$222$	1.55328	−	1.70927i	0.104249	−	0.114719i
$223$	11.6648	−	20.2041i	0.781135	−	1.35297i	−0.150146	−	0.988664i	$-0.547974\pi$
$223$	11.6648	−	20.2041i	0.781135	−	1.35297i	0.931281	−	0.364302i	$-0.118692\pi$
$224$	14.1774	+	25.9102i	0.947270	+	1.73120i
$225$	−1.72758	+	2.99225i	−0.115172	+	0.199483i
$226$	22.3043	+	4.84792i	1.48366	+	0.322479i
$227$	−13.4269			−0.891177			−0.445588	−	0.895238i	$-0.647006\pi$
$227$	−13.4269			−0.891177			−0.445588	+	0.895238i	$0.647006\pi$
$228$	−3.50246	+	7.98328i	−0.231956	+	0.528706i
$229$	1.34084			0.0886052			0.0443026	−	0.999018i	$-0.485893\pi$
$229$	1.34084			0.0886052			0.0443026	+	0.999018i	$0.485893\pi$
$230$	13.7189	+	2.98186i	0.904599	+	0.196618i
$231$	3.72459	−	6.45117i	0.245060	−	0.424456i
$232$	2.56223	−	21.5254i	0.168218	−	1.41321i
$233$	−1.26876	+	2.19756i	−0.0831194	+	0.143967i	−0.904588	−	0.426286i	$-0.859822\pi$
$233$	−1.26876	+	2.19756i	−0.0831194	+	0.143967i	0.821469	+	0.570253i	$0.193155\pi$
$234$	−3.68045	+	4.05006i	−0.240599	+	0.264760i
$235$		−	26.9592i		−	1.75862i
$236$	9.60047	−	6.84152i	0.624937	−	0.445345i
$237$	2.83681	+	4.91350i	0.184271	+	0.319166i
$238$	−2.63920	+	2.90424i	−0.171074	+	0.188254i
$239$			13.2854i			0.859359i	0.902982	+	0.429679i	$0.141373\pi$
$239$			13.2854i			0.859359i	−0.902982	+	0.429679i	$0.858627\pi$
$240$	−3.79647	+	10.9941i	−0.245061	+	0.709663i
$241$	−15.8150	+	9.13080i	−1.01873	+	0.588167i	−0.913737	−	0.406306i	$-0.866817\pi$
$241$	−15.8150	+	9.13080i	−1.01873	+	0.588167i	−0.104997	+	0.994473i	$0.533483\pi$
$242$	−2.69266	+	12.3884i	−0.173091	+	0.796356i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−0.821072	−	8.56699i	−0.0525637	−	0.548446i
$245$	−29.4565	+	51.0201i	−1.88191	+	3.25956i
$246$	−2.83270	−	8.85611i	−0.180606	−	0.564645i
$247$	8.21941	−	14.7293i	0.522988	−	0.937206i
$248$	−0.481023	+	0.643275i	−0.0305450	+	0.0408480i
$249$	−3.89630	−	2.24953i	−0.246918	−	0.142558i
$250$	−1.34929	+	6.20781i	−0.0853366	+	0.392616i
$251$	−7.92106	+	4.57323i	−0.499973	+	0.288660i	−0.728702	−	0.684830i	$-0.759876\pi$
$251$	−7.92106	+	4.57323i	−0.499973	+	0.288660i	0.228729	+	0.973490i	$0.426543\pi$
$252$	10.3947	−	0.996240i	0.654804	−	0.0627572i
$253$	−2.43545	−	4.21832i	−0.153115	−	0.265204i
$254$	2.84486	−	0.909950i	0.178502	−	0.0570954i
$255$	−1.54539			−0.0967763
$256$	−2.25488	+	15.8403i	−0.140930	+	0.990020i
$257$	1.67063	−	0.964541i	0.104211	−	0.0601664i	−0.446989	−	0.894540i	$-0.647504\pi$
$257$	1.67063	−	0.964541i	0.104211	−	0.0601664i	0.551200	+	0.834373i	$0.314170\pi$
$258$	−3.59839	−	11.2499i	−0.224026	−	0.700391i
$259$	8.52688			0.529834
$260$	9.34144	−	20.4738i	0.579332	−	1.26973i
$261$	−6.63731	−	3.83205i	−0.410839	−	0.237198i
$262$	−18.9906	+	20.8977i	−1.17324	+	1.29107i
$263$	−0.864250	−	0.498975i	−0.0532919	−	0.0307681i	0.473117	−	0.880999i	$-0.343129\pi$
$263$	−0.864250	−	0.498975i	−0.0532919	−	0.0307681i	−0.526409	+	0.850231i	$0.676462\pi$
$264$	3.70874	−	1.59048i	0.228257	−	0.0978872i
$265$		−	6.25503i		−	0.384243i
$266$	−30.5089	+	10.2522i	−1.87062	+	0.628606i
$267$		−	8.46618i		−	0.518122i
$268$	0.751272	+	7.83870i	0.0458912	+	0.478825i
$269$	15.6268	+	9.02214i	0.952783	+	0.550090i	0.893944	−	0.448178i	$-0.147927\pi$
$269$	15.6268	+	9.02214i	0.952783	+	0.550090i	0.0588389	+	0.998267i	$0.481260\pi$
$270$	3.04332	+	2.76559i	0.185211	+	0.168309i
$271$	−3.15680	−	1.82258i	−0.191762	−	0.110714i	0.401045	−	0.916058i	$-0.368647\pi$
$271$	−3.15680	−	1.82258i	−0.191762	−	0.110714i	−0.592807	+	0.805345i	$0.701980\pi$
$272$	−2.08718	+	0.403785i	−0.126554	+	0.0244830i
$273$	−20.2042			−1.22281
$274$	21.5602	−	6.89620i	1.30250	−	0.416615i
$275$	−4.26912	+	2.46478i	−0.257438	+	0.148632i
$276$	2.83431	−	6.21202i	0.170605	−	0.373920i
$277$	23.1149			1.38884			0.694420	−	0.719570i	$-0.255661\pi$
$277$	23.1149			1.38884			0.694420	+	0.719570i	$0.255661\pi$
$278$	3.85401	+	12.0491i	0.231148	+	0.722658i
$279$	0.141993	+	0.245939i	0.00850091	+	0.0147240i
$280$	−39.4651	+	16.9245i	−2.35849	+	1.01143i
$281$	14.5165	−	8.38112i	0.865984	−	0.499976i	−2.78468e−5	−	1.00000i	$-0.500009\pi$
$281$	14.5165	−	8.38112i	0.865984	−	0.499976i	0.866011	+	0.500024i	$0.166676\pi$
$282$	−12.8126	−	2.78486i	−0.762979	−	0.165836i
$283$	−8.33961	−	4.81488i	−0.495738	−	0.286215i	0.231214	−	0.972903i	$-0.425730\pi$
$283$	−8.33961	−	4.81488i	−0.495738	−	0.286215i	−0.726952	+	0.686688i	$0.759064\pi$
$284$	12.0064	−	8.55604i	0.712448	−	0.507707i
$285$	−11.0680	−	6.17629i	−0.655614	−	0.365852i
$286$	−7.43666	+	2.37868i	−0.439739	+	0.140654i
$287$	17.1639	−	29.7288i	1.01316	−	1.75484i
$288$	4.83285	+	2.93999i	0.284779	+	0.173240i
$289$	8.35877	+	14.4778i	0.491692	+	0.851636i
$290$	30.7973	+	6.69391i	1.80848	+	0.393080i
$291$	3.51925	−	2.03184i	0.206302	−	0.119109i
$292$	−18.8544	+	13.4361i	−1.10337	+	0.786290i
$293$		−	8.50983i		−	0.497149i	−0.968613	−	0.248575i	$-0.920038\pi$
$293$		−	8.50983i		−	0.497149i	0.968613	−	0.248575i	$-0.0799622\pi$
$294$	21.2050	+	19.2698i	1.23670	+	1.12384i
$295$	8.56978	+	14.8433i	0.498952	+	0.864210i
$296$	3.69932	+	2.76625i	0.215019	+	0.160785i
$297$		−	1.42673i		−	0.0827871i
$298$	−0.104277	−	0.0947607i	−0.00604060	−	0.00548934i
$299$	−6.60559	+	11.4412i	−0.382011	+	0.661663i
$300$	−6.28683	−	2.86844i	−0.362971	−	0.165610i
$301$	21.8034	−	37.7646i	1.25673	−	2.17672i
$302$	5.40377	−	24.8617i	0.310952	−	1.43063i
$303$	−12.4712			−0.716454
$304$	−16.5620	−	5.44969i	−0.949898	−	0.312561i
$305$	12.5125			0.716465
$306$	−0.159638	+	0.734463i	−0.00912590	+	0.0419864i
$307$	−3.81054	+	6.60006i	−0.217479	+	0.376685i	−0.954037	−	0.299690i	$-0.903117\pi$
$307$	−3.81054	+	6.60006i	−0.217479	+	0.376685i	0.736557	+	0.676375i	$0.236450\pi$
$308$	13.5542	+	6.18426i	0.772321	+	0.352381i
$309$	−1.37822	+	2.38714i	−0.0784039	+	0.135800i
$310$	−0.864262	−	0.785390i	−0.0490868	−	0.0446072i
$311$		−	7.63504i		−	0.432943i	−0.976289	−	0.216472i	$-0.930545\pi$
$311$		−	7.63504i		−	0.432943i	0.976289	−	0.216472i	$-0.0694549\pi$
$312$	−8.76542	−	6.55454i	−0.496244	−	0.371078i
$313$	−2.08872	−	3.61778i	−0.118062	−	0.204489i	0.800938	−	0.598748i	$-0.204335\pi$
$313$	−2.08872	−	3.61778i	−0.118062	−	0.204489i	−0.918999	+	0.394259i	$0.871001\pi$
$314$	−21.9289	−	19.9277i	−1.23752	−	1.12458i
$315$			15.1820i			0.855406i
$316$	−9.24089	+	6.58528i	−0.519841	+	0.370451i
$317$	26.5322	−	15.3184i	1.49020	−	0.860365i	0.490259	−	0.871577i	$-0.336902\pi$
$317$	26.5322	−	15.3184i	1.49020	−	0.860365i	0.999937	+	0.0112112i	$0.00356870\pi$
$318$	−2.97276	−	0.646140i	−0.166704	−	0.0362337i
$319$	−5.46729	−	9.46963i	−0.306110	−	0.530197i
$320$	−22.6122	−	5.46055i	−1.26406	−	0.305254i
$321$	−4.31341	+	7.47104i	−0.240751	+	0.416993i
$322$	24.0103	−	7.67990i	1.33804	−	0.427984i
$323$	−0.0338490	−	2.31637i	−0.00188341	−	0.128887i
$324$	1.62875	−	1.16068i	0.0904859	−	0.0644824i
$325$	11.5790	+	6.68514i	0.642288	+	0.370825i
$326$	2.17975	+	0.473776i	0.120725	+	0.0262400i
$327$	10.8426	−	6.25996i	0.599596	−	0.346177i
$328$	17.0909	−	7.32937i	0.943689	−	0.404697i
$329$	−24.2038	−	41.9222i	−1.33440	−	2.31124i
$330$	1.78740	+	5.58811i	0.0983932	+	0.307615i
$331$	20.4935			1.12642			0.563212	−	0.826312i	$-0.309565\pi$
$331$	20.4935			1.12642			0.563212	+	0.826312i	$0.309565\pi$
$332$	3.73509	−	8.18628i	0.204990	−	0.449281i
$333$	1.41434	−	0.816569i	0.0775053	−	0.0447477i
$334$	4.90545	−	1.56905i	0.268414	−	0.0858545i
$335$	−11.4488			−0.625515
$336$	3.96678	+	20.5045i	0.216406	+	1.11861i
$337$	14.7866	+	8.53706i	0.805478	+	0.465043i	0.845383	−	0.534160i	$-0.179372\pi$
$337$	14.7866	+	8.53706i	0.805478	+	0.465043i	−0.0399048	+	0.999203i	$0.512705\pi$
$338$	2.06637	+	1.87780i	0.112396	+	0.102139i
$339$	13.9774	+	8.06988i	0.759151	+	0.438296i
$340$	−0.294874	−	3.07669i	−0.0159918	−	0.166857i
$341$			0.405171i			0.0219412i
$342$	−4.07866	+	4.62218i	−0.220549	+	0.249939i
$343$			69.2352i			3.73835i
$344$	21.7107	−	9.31053i	1.17056	−	0.501990i
$345$	8.59724	+	4.96362i	0.462860	+	0.267232i
$346$	−10.0033	+	11.0078i	−0.537779	+	0.591785i
$347$	9.57980	+	5.53090i	0.514271	+	0.296914i	0.734587	−	0.678514i	$-0.237376\pi$
$347$	9.57980	+	5.53090i	0.514271	+	0.296914i	−0.220317	+	0.975428i	$0.570709\pi$
$348$	6.36269	−	13.9452i	0.341076	−	0.747544i
$349$	2.92231			0.156428			0.0782139	−	0.996937i	$-0.475078\pi$
$349$	2.92231			0.156428			0.0782139	+	0.996937i	$0.475078\pi$
$350$	−7.77239	−	24.2995i	−0.415452	−	1.29886i
$351$	−3.35123	+	1.93483i	−0.178876	+	0.103274i
$352$	3.87411	+	7.08018i	0.206491	+	0.377375i
$353$	−4.00215			−0.213013			−0.106506	−	0.994312i	$-0.533966\pi$
$353$	−4.00215			−0.213013			−0.106506	+	0.994312i	$0.533966\pi$
$354$	7.93967	−	2.53957i	0.421989	−	0.134976i
$355$	10.7174	+	18.5631i	0.568821	+	0.985226i
$356$	16.8551	−	1.61542i	0.893320	−	0.0856169i
$357$	−2.40312	+	1.38744i	−0.127187	+	0.0734313i
$358$	3.08778	−	14.2062i	0.163194	−	0.750823i
$359$	2.02345	+	1.16824i	0.106794	+	0.0616574i	0.552446	−	0.833549i	$-0.313695\pi$
$359$	2.02345	+	1.16824i	0.106794	+	0.0616574i	−0.445652	+	0.895206i	$0.647028\pi$
$360$	−4.92526	+	6.58658i	−0.259584	+	0.347143i
$361$	9.01515	−	16.7250i	0.474482	−	0.880265i
$362$	−2.54975	−	7.97151i	−0.134012	−	0.418974i
$363$	−4.48222	+	7.76344i	−0.235256	+	0.407475i
$364$	−3.85512	−	40.2240i	−0.202063	−	2.10831i
$365$	−16.8303	−	29.1509i	−0.880936	−	1.52583i
$366$	1.29253	−	5.94669i	0.0675619	−	0.310838i
$367$	10.2342	−	5.90871i	0.534220	−	0.308432i	−0.208513	−	0.978020i	$-0.566862\pi$
$367$	10.2342	−	5.90871i	0.534220	−	0.308432i	0.742733	+	0.669587i	$0.233529\pi$
$368$	12.9082	+	4.45746i	0.672886	+	0.232361i
$369$		−	6.57476i		−	0.342268i
$370$	−4.51659	+	4.97017i	−0.234807	+	0.258387i
$371$	−5.61572	−	9.72672i	−0.291554	−	0.504986i
$372$	−0.462542	+	0.329618i	−0.0239817	+	0.0170899i
$373$		−	23.3883i		−	1.21100i	−0.795844	−	0.605501i	$-0.792973\pi$
$373$		−	23.3883i		−	1.21100i	0.795844	−	0.605501i	$-0.207027\pi$
$374$	−0.721185	+	0.793609i	−0.0372916	+	0.0410365i
$375$	−2.24604	+	3.89025i	−0.115985	+	0.200892i
$376$	3.09957	−	26.0397i	0.159848	−	1.34289i
$377$	−14.8288	+	25.6842i	−0.763720	+	1.32280i
$378$	7.21537	+	1.56829i	0.371118	+	0.0806639i
$379$	−20.1494			−1.03500			−0.517502	−	0.855682i	$-0.673138\pi$
$379$	−20.1494			−1.03500			−0.517502	+	0.855682i	$0.673138\pi$
$380$	10.1844	−	23.2136i	0.522447	−	1.19083i
$381$	2.11202			0.108202
$382$	−4.30776	−	0.936307i	−0.220404	−	0.0479056i
$383$	−6.01141	+	10.4121i	−0.307168	+	0.532031i	−0.977742	−	0.209812i	$-0.932715\pi$
$383$	−6.01141	+	10.4121i	−0.307168	+	0.532031i	0.670573	+	0.741843i	$0.266048\pi$
$384$	−4.93100	+	10.1826i	−0.251634	+	0.519628i
$385$	−10.8303	+	18.7586i	−0.551961	+	0.956024i
$386$	−18.4200	+	20.2698i	−0.937551	+	1.03170i
$387$		−	8.35194i		−	0.424553i
$388$	4.71665	+	6.61870i	0.239451	+	0.336014i
$389$	−5.25974	−	9.11013i	−0.266679	−	0.461902i	0.701323	−	0.712844i	$-0.252593\pi$
$389$	−5.25974	−	9.11013i	−0.266679	−	0.461902i	−0.968002	+	0.250942i	$0.919260\pi$
$390$	10.7019	−	11.7766i	0.541913	−	0.596334i
$391$			1.81446i			0.0917609i
$392$	−34.3178	+	45.8933i	−1.73331	+	2.31796i
$393$	−17.2919	+	9.98348i	−0.872261	+	0.503600i
$394$	5.32779	−	24.5121i	0.268410	−	1.23490i
$395$	−8.24881	−	14.2874i	−0.415042	−	0.718875i
$396$	2.84044	−	0.272231i	0.142737	−	0.0136801i
$397$	−15.3073	+	26.5130i	−0.768252	+	1.33065i	0.170259	+	0.985399i	$0.445540\pi$
$397$	−15.3073	+	26.5130i	−0.768252	+	1.33065i	−0.938510	+	0.345251i	$0.887794\pi$
$398$	−2.61953	−	8.18966i	−0.131305	−	0.410510i
$399$	−22.7561	+	0.332533i	−1.13923	+	0.0166475i
$400$	4.51114	−	13.0636i	0.225557	−	0.653182i
$401$	−9.62948	−	5.55959i	−0.480873	−	0.277632i	0.239907	−	0.970796i	$-0.422883\pi$
$401$	−9.62948	−	5.55959i	−0.480873	−	0.277632i	−0.720780	+	0.693163i	$0.756216\pi$
$402$	−1.18265	+	5.44116i	−0.0589855	+	0.271380i
$403$	0.951704	−	0.549467i	0.0474078	−	0.0273709i
$404$	−2.37961	−	24.8287i	−0.118390	−	1.23527i
$405$	1.45389	+	2.51821i	0.0722442	+	0.125131i
$406$	53.9003	−	17.2405i	2.67503	−	0.855629i
$407$	2.33004			0.115496
$408$	−1.49269	−	0.177678i	−0.0738989	−	0.00879639i
$409$	−0.183592	+	0.105997i	−0.00907804	+	0.00524121i	−0.504532	−	0.863393i	$-0.668335\pi$
$409$	−0.183592	+	0.105997i	−0.00907804	+	0.00524121i	0.495454	+	0.868634i	$0.335002\pi$
$410$	8.23685	+	25.7516i	0.406789	+	1.27178i
$411$	16.0062			0.789530
$412$	−5.01548	−	2.28837i	−0.247095	−	0.112740i
$413$	26.6524	+	15.3878i	1.31148	+	0.757183i
$414$	3.24710	−	3.57318i	0.159586	−	0.175612i
$415$	11.3296	+	6.54112i	0.556146	+	0.321091i
$416$	11.3768	−	18.7015i	0.557792	−	0.916919i
$417$			8.94524i			0.438050i
$418$	−8.33681	+	2.80152i	−0.407767	+	0.137027i
$419$		−	19.4441i		−	0.949905i	−0.880011	−	0.474953i	$-0.842465\pi$
$419$		−	19.4441i		−	0.949905i	0.880011	−	0.474953i	$-0.157535\pi$
$420$	−30.2254	+	2.89684i	−1.47485	+	0.141351i
$421$	1.17058	+	0.675837i	0.0570507	+	0.0329383i	0.528254	−	0.849086i	$-0.322847\pi$
$421$	1.17058	+	0.675837i	0.0570507	+	0.0329383i	−0.471203	+	0.882025i	$0.656180\pi$
$422$	−26.1048	−	23.7225i	−1.27076	−	1.15479i
$423$	−8.02928	−	4.63571i	−0.390397	−	0.225396i
$424$	0.719159	−	6.04169i	0.0349254	−	0.293410i
$425$	1.83631			0.0890740
$426$	9.92938	−	3.17599i	0.481080	−	0.153877i
$427$	19.4573	−	11.2337i	0.941603	−	0.543635i
$428$	−15.6970	−	7.16193i	−0.758741	−	0.346185i
$429$	−5.52096			−0.266555
$430$	10.4633	+	32.7123i	0.504585	+	1.57753i
$431$	5.57974	+	9.66439i	0.268766	+	0.465517i	0.968544	−	0.248844i	$-0.0800507\pi$
$431$	5.57974	+	9.66439i	0.268766	+	0.465517i	−0.699777	+	0.714361i	$0.746717\pi$
$432$	2.62156	+	3.02117i	0.126130	+	0.145356i
$433$	−34.6737	+	20.0189i	−1.66631	+	0.962046i	−0.696714	+	0.717349i	$0.745355\pi$
$433$	−34.6737	+	20.0189i	−1.66631	+	0.962046i	−0.969600	+	0.244697i	$0.921311\pi$
$434$	−2.04907	−	0.445372i	−0.0983583	−	0.0213785i
$435$	19.2998	+	11.1427i	0.925354	+	0.534253i
$436$	14.5317	+	20.3918i	0.695941	+	0.976589i
$437$	−7.25161	+	12.9950i	−0.346892	+	0.621637i
$438$	−15.5928	+	4.98747i	−0.745052	+	0.238311i
$439$	−7.99291	+	13.8441i	−0.381481	+	0.660744i	−0.991274	−	0.131816i	$-0.957919\pi$
$439$	−7.99291	+	13.8441i	−0.381481	+	0.660744i	0.609793	+	0.792560i	$0.291252\pi$
$440$	−10.7842	+	4.62475i	−0.514116	+	0.220477i
$441$	10.1303	+	17.5461i	0.482393	+	0.835529i
$442$	2.84213	+	0.617746i	0.135186	+	0.0293832i
$443$	−11.6594	+	6.73154i	−0.553953	+	0.319825i	−0.750715	−	0.660626i	$-0.770291\pi$
$443$	−11.6594	+	6.73154i	−0.553953	+	0.319825i	0.196762	+	0.980451i	$0.436957\pi$
$444$	1.89556	+	2.65997i	0.0899592	+	0.126237i
$445$			24.6177i			1.16699i
$446$	24.4172	+	22.1889i	1.15619	+	1.05068i
$447$	−0.0498162	−	0.0862842i	−0.00235623	−	0.00408110i
$448$	−40.0650	+	11.8098i	−1.89289	+	0.557961i
$449$		−	15.6819i		−	0.740076i	−0.929017	−	0.370038i	$-0.879345\pi$
$449$		−	15.6819i		−	0.740076i	0.929017	−	0.370038i	$-0.120655\pi$
$450$	−3.61621	−	3.28620i	−0.170470	−	0.154913i
$451$	4.69019	−	8.12366i	0.220853	−	0.382528i
$452$	−13.3991	+	29.3672i	−0.630242	+	1.38132i
$453$	8.99516	−	15.5801i	0.422629	−	0.732016i
$454$	4.03306	−	18.5553i	0.189281	−	0.870844i
$455$	58.7491			2.75420
$456$	−9.98043	−	7.23816i	−0.467377	−	0.338958i
$457$	8.93724			0.418066			0.209033	−	0.977909i	$-0.432968\pi$
$457$	8.93724			0.418066			0.209033	+	0.977909i	$0.432968\pi$
$458$	−0.402749	+	1.85297i	−0.0188192	+	0.0865836i
$459$	−0.265735	+	0.460266i	−0.0124034	+	0.0214834i
$460$	−8.24153	+	18.0632i	−0.384264	+	0.842199i
$461$	−10.3501	+	17.9269i	−0.482052	+	0.834939i	−0.999788	−	0.0206015i	$-0.993442\pi$
$461$	−10.3501	+	17.9269i	−0.482052	+	0.834939i	0.517735	+	0.855541i	$0.326775\pi$
$462$	7.79642	+	7.08493i	0.362722	+	0.329621i
$463$			20.0806i			0.933223i	0.884462	+	0.466612i	$0.154525\pi$
$463$			20.0806i			0.933223i	−0.884462	+	0.466612i	$0.845475\pi$
$464$	28.9773	+	10.0065i	1.34524	+	0.464539i
$465$	−0.412884	−	0.715136i	−0.0191470	−	0.0331636i
$466$	−2.65581	−	2.41345i	−0.123028	−	0.111801i
$467$			29.3355i			1.35748i	0.734377	+	0.678742i	$0.237475\pi$
$467$			29.3355i			1.35748i	−0.734377	+	0.678742i	$0.762525\pi$
$468$	−4.49146	−	6.30271i	−0.207618	−	0.291343i
$469$	−17.8032	+	10.2787i	−0.822074	+	0.474625i
$470$	37.2561	+	8.09776i	1.71850	+	0.373522i
$471$	−10.4761	−	18.1451i	−0.482713	−	0.836084i
$472$	6.57092	+	15.3223i	0.302451	+	0.705268i
$473$	5.95797	−	10.3195i	0.273948	−	0.474491i
$474$	−7.64229	+	2.44445i	−0.351022	+	0.112277i
$475$	13.1515	+	7.33895i	0.603434	+	0.336734i
$476$	−3.22077	−	4.51959i	−0.147624	−	0.207155i
$477$	−1.86294	−	1.07557i	−0.0852982	−	0.0492470i
$478$	−18.3597	−	3.99054i	−0.839752	−	0.182523i
$479$	−15.0547	+	8.69182i	−0.687866	+	0.397140i	−0.802812	−	0.596232i	$-0.796664\pi$
$479$	−15.0547	+	8.69182i	−0.687866	+	0.397140i	0.114946	+	0.993372i	$0.463330\pi$
$480$	−14.0528	−	8.54882i	−0.641422	−	0.390198i
$481$	−3.15985	−	5.47303i	−0.144077	−	0.249548i
$482$	−7.86791	−	24.5981i	−0.358373	−	1.12041i
$483$	17.8252			0.811076
$484$	−16.3113	−	7.44223i	−0.741423	−	0.338283i
$485$	−10.2332	+	5.90813i	−0.464665	+	0.268274i
$486$	1.34699	−	0.430844i	0.0611006	−	0.0195435i
$487$	−28.2262			−1.27905			−0.639525	−	0.768770i	$-0.720869\pi$
$487$	−28.2262			−1.27905			−0.639525	+	0.768770i	$0.720869\pi$
$488$	12.0858	+	1.43860i	0.547096	+	0.0651224i
$489$	1.36598	+	0.788650i	0.0617719	+	0.0356640i
$490$	−61.6593	−	56.0323i	−2.78548	−	2.53128i
$491$	−9.34445	−	5.39502i	−0.421709	−	0.243474i	0.274099	−	0.961701i	$-0.411620\pi$
$491$	−9.34445	−	5.39502i	−0.421709	−	0.243474i	−0.695808	+	0.718228i	$0.744954\pi$
$492$	13.0895	−	1.25452i	0.590122	−	0.0565581i
$493$			4.07324i			0.183449i
$494$	17.8863	+	15.7831i	0.804743	+	0.710113i
$495$			4.14860i			0.186466i
$496$	−0.744486	−	0.857970i	−0.0334284	−	0.0385240i
$497$	33.3316	+	19.2440i	1.49513	+	0.863213i
$498$	4.27907	−	4.70879i	0.191750	−	0.211006i
$499$	6.58971	+	3.80457i	0.294996	+	0.170316i	0.640193	−	0.768214i	$-0.278854\pi$
$499$	6.58971	+	3.80457i	0.294996	+	0.170316i	−0.345197	+	0.938530i	$0.612188\pi$
$500$	−8.17357	−	3.72929i	−0.365533	−	0.166779i
$501$	3.64180			0.162703
$502$	−3.94070	−	12.3202i	−0.175882	−	0.549875i
$503$	22.3387	−	12.8973i	0.996035	−	0.575061i	0.0889620	−	0.996035i	$-0.471645\pi$
$503$	22.3387	−	12.8973i	0.996035	−	0.575061i	0.907073	+	0.420974i	$0.138312\pi$
$504$	−1.74551	+	14.6641i	−0.0777513	+	0.653193i
$505$	36.2635			1.61371
$506$	6.56103	−	2.09860i	0.291674	−	0.0932941i
$507$	0.987168	+	1.70983i	0.0438417	+	0.0759360i
$508$	0.402990	+	4.20476i	0.0178798	+	0.186556i
$509$	16.4359	−	9.48924i	0.728506	−	0.420603i	−0.0893691	−	0.995999i	$-0.528485\pi$
$509$	16.4359	−	9.48924i	0.728506	−	0.420603i	0.817875	+	0.575395i	$0.195152\pi$
$510$	0.464191	−	2.13565i	0.0205547	−	0.0945682i
$511$	−52.3429	−	30.2202i	−2.31551	−	1.33686i
$512$	−21.2132	−	7.87410i	−0.937498	−	0.347989i
$513$	−3.74267	+	2.23437i	−0.165243	+	0.0986500i
$514$	0.831134	+	2.59845i	0.0366598	+	0.114613i
$515$	4.00754	−	6.94126i	0.176593	−	0.305869i
$516$	16.6277	−	1.59362i	0.731993	−	0.0701551i
$517$	−6.61389	−	11.4556i	−0.290879	−	0.503816i
$518$	−2.56123	+	11.7837i	−0.112534	+	0.517746i
$519$	−9.10847	+	5.25878i	−0.399817	+	0.230835i
$520$	25.4879	+	19.0591i	1.11772	+	0.835798i
$521$			8.55779i			0.374924i	0.982272	+	0.187462i	$0.0600261\pi$
$521$			8.55779i			0.374924i	−0.982272	+	0.187462i	$0.939974\pi$
$522$	7.28935	−	8.02137i	0.319046	−	0.351086i
$523$	−5.76078	−	9.97796i	−0.251901	−	0.436306i	0.712148	−	0.702029i	$-0.247722\pi$
$523$	−5.76078	−	9.97796i	−0.251901	−	0.436306i	−0.964049	+	0.265724i	$0.914389\pi$
$524$	−23.1753	−	32.5211i	−1.01242	−	1.42069i
$525$		−	18.0399i		−	0.787325i
$526$	0.949152	−	1.04447i	0.0413850	−	0.0455410i
$527$	0.0754650	−	0.130709i	0.00328731	−	0.00569379i
$528$	1.08396	+	5.60302i	0.0471732	+	0.243840i
$529$	−5.67218	+	9.82451i	−0.246617	+	0.427153i
$530$	8.64412	+	1.87883i	0.375476	+	0.0816112i
$531$	5.89439			0.255795
$532$	−5.00408	−	45.2411i	−0.216954	−	1.96145i
$533$	−25.4421			−1.10202
$534$	11.6998	+	2.54300i	0.506300	+	0.110046i
$535$	12.5424	−	21.7241i	0.542256	−	0.939215i
$536$	−11.0583	−	1.31630i	−0.477647	−	0.0568556i
$537$	5.13993	−	8.90263i	0.221805	−	0.384177i
$538$	−17.1620	+	18.8854i	−0.739905	+	0.814209i
$539$			28.9062i			1.24508i
$540$	−4.73603	+	3.37501i	−0.203806	+	0.145237i
$541$	−10.7837	−	18.6779i	−0.463627	−	0.803026i	0.535511	−	0.844528i	$-0.320119\pi$
$541$	−10.7837	−	18.6779i	−0.463627	−	0.803026i	−0.999138	+	0.0415023i	$0.986786\pi$
$542$	3.46692	−	3.81508i	0.148917	−	0.163872i
$543$		−	5.91804i		−	0.253967i
$544$	0.0689191	−	3.00566i	0.00295488	−	0.128866i
$545$	−31.5278	+	18.2026i	−1.35050	+	0.779712i
$546$	6.06875	−	27.9211i	0.259718	−	1.19491i
$547$	−1.36424	−	2.36294i	−0.0583308	−	0.101032i	0.835385	−	0.549665i	$-0.185244\pi$
$547$	−1.36424	−	2.36294i	−0.0583308	−	0.101032i	−0.893716	+	0.448633i	$0.851911\pi$
$548$	3.05412	+	31.8665i	0.130466	+	1.36127i
$549$	2.15156	−	3.72662i	0.0918265	−	0.159048i
$550$	−2.12387	−	6.64005i	−0.0905622	−	0.283133i
$551$	−16.2790	+	29.1723i	−0.693509	+	1.24278i
$552$	7.73334	+	5.78278i	0.329153	+	0.246131i
$553$	−25.6542	−	14.8114i	−1.09093	−	0.629847i
$554$	−6.94305	+	31.9436i	−0.294982	+	1.35715i
$555$	−4.11258	+	2.37440i	−0.174569	+	0.100788i
$556$	−17.8089	+	1.70683i	−0.755264	+	0.0723855i
$557$	−12.0879	−	20.9368i	−0.512179	−	0.887121i	−0.999900	−	0.0141210i	$-0.995505\pi$
$557$	−12.0879	−	20.9368i	−0.512179	−	0.887121i	0.487721	−	0.873000i	$-0.337828\pi$
$558$	−0.382526	+	0.122354i	−0.0161936	+	0.00517966i
$559$	−32.3192			−1.36696
$560$	−11.5345	−	59.6223i	−0.487422	−	2.51950i
$561$	−0.656674	+	0.379131i	−0.0277248	+	0.0160069i
$562$	7.22192	+	22.5785i	0.304638	+	0.952417i
$563$	12.7554			0.537577			0.268788	−	0.963199i	$-0.413377\pi$
$563$	12.7554			0.537577			0.268788	+	0.963199i	$0.413377\pi$
$564$	7.69707	−	16.8698i	0.324105	−	0.710348i
$565$	−40.6433	−	23.4654i	−1.70987	−	0.987197i
$566$	9.15888	−	10.0786i	0.384976	−	0.423637i
$567$	4.52166	+	2.61058i	0.189892	+	0.109634i
$568$	8.21762	+	19.1622i	0.344804	+	0.804027i
$569$			23.9344i			1.00338i	0.865047	+	0.501690i	$0.167288\pi$
$569$			23.9344i			1.00338i	−0.865047	+	0.501690i	$0.832712\pi$
$570$	11.8598	−	13.4403i	0.496753	−	0.562950i
$571$		−	13.1183i		−	0.548983i	−0.961590	−	0.274491i	$-0.911491\pi$
$571$		−	13.1183i		−	0.548983i	0.961590	−	0.274491i	$-0.0885095\pi$
$572$	−1.05345	−	10.9916i	−0.0440468	−	0.459580i
$573$	−2.69955	−	1.55858i	−0.112775	−	0.0651108i
$574$	35.9281	+	32.6493i	1.49961	+	1.36276i
$575$	−10.2156	−	5.89800i	−0.426022	−	0.245964i
$576$	−5.51456	+	5.79566i	−0.229773	+	0.241486i
$577$	1.39297			0.0579900			0.0289950	−	0.999580i	$-0.490769\pi$
$577$	1.39297			0.0579900			0.0289950	+	0.999580i	$0.490769\pi$
$578$	−22.5183	+	7.20266i	−0.936638	+	0.299591i
$579$	−16.7723	+	9.68348i	−0.697032	+	0.402432i
$580$	−18.5013	+	40.5496i	−0.768223	+	1.68373i
$581$	23.4903			0.974542
$582$	1.75081	+	5.47372i	0.0725736	+	0.226893i
$583$	−1.53455	−	2.65791i	−0.0635544	−	0.110079i
$584$	−12.9047	−	30.0917i	−0.533999	−	1.24520i
$585$	9.74462	−	5.62606i	0.402891	−	0.232609i
$586$	11.7601	+	2.55611i	0.485807	+	0.105592i
$587$	−31.4722	−	18.1705i	−1.29900	−	0.749976i	−0.318766	−	0.947834i	$-0.603268\pi$
$587$	−31.4722	−	18.1705i	−1.29900	−	0.749976i	−0.980231	+	0.197857i	$0.936602\pi$
$588$	−32.9992	+	23.5160i	−1.36087	+	0.969785i
$589$	1.06287	−	0.634532i	0.0437947	−	0.0261454i
$590$	−23.0868	+	7.38449i	−0.950467	+	0.304014i
$591$	8.86868	−	15.3610i	0.364809	−	0.631867i
$592$	−4.93398	+	4.28137i	−0.202785	+	0.175963i
$593$	19.8775	+	34.4289i	0.816271	+	1.41382i	0.908411	+	0.418078i	$0.137296\pi$
$593$	19.8775	+	34.4289i	0.816271	+	1.41382i	−0.0921398	+	0.995746i	$0.529371\pi$
$594$	1.97166	+	0.428548i	0.0808983	+	0.0175835i
$595$	6.98774	−	4.03437i	0.286469	−	0.165393i
$596$	0.162276	−	0.115642i	0.00664708	−	0.00473687i
$597$		−	6.07998i		−	0.248837i
$598$	−13.8270	−	12.5652i	−0.565429	−	0.513829i
$599$	−10.1236	−	17.5346i	−0.413640	−	0.716445i	0.581645	−	0.813443i	$-0.302409\pi$
$599$	−10.1236	−	17.5346i	−0.413640	−	0.716445i	−0.995285	+	0.0969977i	$0.969076\pi$
$600$	5.85242	−	7.82647i	0.238924	−	0.319514i
$601$			15.5662i			0.634960i	0.948265	+	0.317480i	$0.102837\pi$
$601$			15.5662i			0.634960i	−0.948265	+	0.317480i	$0.897163\pi$
$602$	45.6396	+	41.4745i	1.86013	+	1.69038i
$603$	−1.96866	+	3.40981i	−0.0801699	+	0.138858i
$604$	32.7344	+	14.9354i	1.33194	+	0.607715i
$605$	13.0333	−	22.5743i	0.529879	−	0.917777i
$606$	3.74600	−	17.2346i	0.152171	−	0.700107i
$607$	12.3785			0.502427			0.251214	−	0.967932i	$-0.419170\pi$
$607$	12.3785			0.502427			0.251214	+	0.967932i	$0.419170\pi$
$608$	12.5059	−	21.2509i	0.507183	−	0.861839i
$609$	40.0155			1.62151
$610$	−3.75840	+	17.2916i	−0.152173	+	0.700118i
$611$	−17.9386	+	31.0707i	−0.725720	+	1.25698i
$612$	−0.967038	−	0.441223i	−0.0390902	−	0.0178354i
$613$	−4.48088	+	7.76112i	−0.180981	+	0.313469i	−0.942215	−	0.335009i	$-0.891261\pi$
$613$	−4.48088	+	7.76112i	−0.180981	+	0.313469i	0.761234	+	0.648478i	$0.224594\pi$
$614$	−7.97635	−	7.24843i	−0.321899	−	0.292523i
$615$			19.1179i			0.770909i
$616$	−12.6176	+	16.8736i	−0.508377	+	0.679856i
$617$	−17.1115	−	29.6379i	−0.688882	−	1.19318i	−0.972200	−	0.234153i	$-0.924768\pi$
$617$	−17.1115	−	29.6379i	−0.688882	−	1.19318i	0.283318	−	0.959026i	$-0.408565\pi$
$618$	−2.88492	−	2.62165i	−0.116049	−	0.105458i
$619$		−	19.7496i		−	0.793804i	−0.917861	−	0.396902i	$-0.870085\pi$
$619$		−	19.7496i		−	0.793804i	0.917861	−	0.396902i	$-0.129915\pi$
$620$	1.34497	−	0.958455i	0.0540152	−	0.0384925i
$621$	2.95664	−	1.70702i	0.118646	−	0.0685002i
$622$	10.5512	+	2.29335i	0.423065	+	0.0919548i
$623$	22.1016	+	38.2812i	0.885483	+	1.53370i
$624$	11.6909	−	10.1446i	0.468011	−	0.406107i
$625$	15.1688	−	26.2732i	0.606754	−	1.05093i
$626$	5.62697	−	1.79983i	0.224899	−	0.0719357i
$627$	−6.21830	+	0.0908675i	−0.248335	+	0.00362890i
$628$	34.1258	−	24.3189i	1.36177	−	0.970429i
$629$	−0.751678	−	0.433982i	−0.0299714	−	0.0173040i
$630$	−20.9807	−	4.56022i	−0.835889	−	0.181684i
$631$	33.7208	−	19.4687i	1.34240	−	0.775037i	0.355243	−	0.934774i	$-0.384398\pi$
$631$	33.7208	−	19.4687i	1.34240	−	0.775037i	0.987160	+	0.159737i	$0.0510646\pi$
$632$	−6.32481	−	14.7484i	−0.251587	−	0.586662i
$633$	−12.4711	−	21.6005i	−0.495680	−	0.858543i
$634$	13.1997	+	41.2673i	0.524226	+	1.63893i
$635$	−6.14126			−0.243709
$636$	1.78586	−	3.91412i	0.0708141	−	0.155205i
$637$	67.8977	−	39.2007i	2.69020	−	1.55319i
$638$	14.7287	−	4.71110i	0.583116	−	0.186514i
$639$	7.37155			0.291614
$640$	14.3382	−	29.6087i	0.566769	−	1.17039i
$641$	0.268187	+	0.154838i	0.0105927	+	0.00611573i	0.505287	−	0.862951i	$-0.331387\pi$
$641$	0.268187	+	0.154838i	0.0105927	+	0.00611573i	−0.494694	+	0.869067i	$0.664720\pi$
$642$	−9.02896	−	8.20498i	−0.356345	−	0.323825i
$643$	−28.7893	−	16.6215i	−1.13534	−	0.655489i	−0.190068	−	0.981771i	$-0.560871\pi$
$643$	−28.7893	−	16.6215i	−1.13534	−	0.655489i	−0.945273	+	0.326282i	$0.894204\pi$
$644$	3.40120	+	35.4878i	0.134026	+	1.39842i
$645$			24.2855i			0.956243i
$646$	3.21127	+	0.648994i	0.126346	+	0.0255343i
$647$		−	26.6201i		−	1.04654i	−0.852166	−	0.523271i	$-0.824711\pi$
$647$		−	26.6201i		−	1.04654i	0.852166	−	0.523271i	$-0.175289\pi$
$648$	1.11477	+	2.59948i	0.0437925	+	0.102117i
$649$	7.28301	+	4.20485i	0.285883	+	0.165055i
$650$	−12.7165	+	13.9935i	−0.498783	+	0.548872i
$651$	−1.28409	−	0.741369i	−0.0503274	−	0.0290565i
$652$	−1.30947	+	2.86998i	−0.0512826	+	0.112397i
$653$	3.43319			0.134351			0.0671755	−	0.997741i	$-0.478601\pi$
$653$	3.43319			0.134351			0.0671755	+	0.997741i	$0.478601\pi$
$654$	5.39414	+	16.8642i	0.210928	+	0.659442i
$655$	50.2809	−	29.0297i	1.96464	−	1.13428i
$656$	4.99518	+	25.8203i	0.195029	+	1.00811i
$657$	−11.5760			−0.451625
$658$	65.2043	−	20.8561i	2.54193	−	0.813056i
$659$	5.76975	+	9.99351i	0.224758	+	0.389292i	0.956247	−	0.292561i	$-0.0945076\pi$
$659$	5.76975	+	9.99351i	0.224758	+	0.389292i	−0.731489	+	0.681853i	$0.761174\pi$
$660$	−8.25936	+	0.791587i	−0.321495	+	0.0308125i
$661$	−16.0474	+	9.26495i	−0.624170	+	0.360365i	−0.778491	−	0.627656i	$-0.784014\pi$
$661$	−16.0474	+	9.26495i	−0.624170	+	0.360365i	0.154321	+	0.988021i	$0.450681\pi$
$662$	−6.15565	+	28.3209i	−0.239246	+	1.10072i
$663$	1.78108	+	1.02831i	0.0691713	+	0.0399361i
$664$	10.1911	+	7.62062i	0.395491	+	0.295737i
$665$	66.1695	−	0.966931i	2.56594	−	0.0374960i
$666$	0.703629	+	2.19982i	0.0272651	+	0.0852411i
$667$	13.0828	−	22.6600i	0.506566	−	0.877398i
$668$	0.694885	+	7.25037i	0.0268859	+	0.280525i
$669$	11.6648	+	20.2041i	0.450989	+	0.781135i
$670$	3.43889	−	15.8217i	0.132856	−	0.611244i
$671$	5.31686	−	3.06969i	0.205255	−	0.118504i
$672$	−29.5276	−	0.677061i	−1.13905	−	0.0261182i
$673$			10.8678i			0.418924i	0.977817	+	0.209462i	$0.0671712\pi$
$673$			10.8678i			0.418924i	−0.977817	+	0.209462i	$0.932829\pi$
$674$	−16.2392	+	17.8700i	−0.625512	+	0.688328i
$675$	−1.72758	−	2.99225i	−0.0664944	−	0.115172i
$676$	−3.21569	+	2.29158i	−0.123680	+	0.0881377i
$677$			22.1612i			0.851725i	0.904788	+	0.425862i	$0.140029\pi$
$677$			22.1612i			0.851725i	−0.904788	+	0.425862i	$0.859971\pi$
$678$	−15.3506	+	16.8921i	−0.589535	+	0.648738i
$679$	−10.6086	+	18.3746i	−0.407119	+	0.705151i
$680$	4.34039	+	0.516648i	0.166446	+	0.0198126i
$681$	6.71347	−	11.6281i	0.257261	−	0.445588i
$682$	−0.559925	−	0.121702i	−0.0214406	−	0.00466020i
$683$	−12.3982			−0.474404			−0.237202	−	0.971460i	$-0.576230\pi$
$683$	−12.3982			−0.474404			−0.237202	+	0.971460i	$0.576230\pi$
$684$	−5.16250	−	7.02486i	−0.197393	−	0.268602i
$685$	−46.5425			−1.77830
$686$	−95.6794	−	20.7963i	−3.65306	−	0.794005i
$687$	−0.670420	+	1.16120i	−0.0255781	+	0.0443026i
$688$	6.34540	+	32.7996i	0.241916	+	1.25047i
$689$	−4.16210	+	7.20897i	−0.158563	+	0.274640i
$690$	−9.44182	+	10.3900i	−0.359444	+	0.395541i
$691$			0.525809i			0.0200027i	0.999950	+	0.0100014i	$0.00318358\pi$
$691$			0.525809i			0.0200027i	−0.999950	+	0.0100014i	$0.996816\pi$
$692$	−12.2076	−	17.1304i	−0.464062	−	0.651201i
$693$	3.72459	+	6.45117i	0.141485	+	0.245060i
$694$	−10.5209	+	11.5775i	−0.399368	+	0.439474i
$695$		−	26.0107i		−	0.986643i
$696$	17.3604	+	12.9816i	0.658045	+	0.492068i
$697$	−3.02614	+	1.74714i	−0.114623	+	0.0661777i
$698$	−0.877778	+	4.03848i	−0.0332244	+	0.152859i
$699$	−1.26876	−	2.19756i	−0.0479890	−	0.0831194i
$700$	35.9152	−	3.44216i	1.35747	−	0.130101i
$701$	7.56444	−	13.1020i	0.285705	−	0.494855i	−0.687075	−	0.726586i	$-0.741106\pi$
$701$	7.56444	−	13.1020i	0.285705	−	0.494855i	0.972780	+	0.231731i	$0.0744390\pi$
$702$	−1.66723	−	5.21239i	−0.0629254	−	0.196729i
$703$	−3.64904	−	6.11230i	−0.137626	−	0.230530i
$704$	−10.9481	+	3.22713i	−0.412622	+	0.121627i
$705$	23.3473	+	13.4796i	0.879311	+	0.507671i
$706$	1.20213	−	5.53075i	0.0452427	−	0.208153i
$707$	56.3907	−	32.5572i	2.12079	−	1.22444i
$708$	1.12470	+	11.7350i	0.0422688	+	0.441029i
$709$	−7.61629	−	13.1918i	−0.286036	−	0.495429i	0.686824	−	0.726824i	$-0.259004\pi$
$709$	−7.61629	−	13.1918i	−0.286036	−	0.495429i	−0.972860	+	0.231395i	$0.925671\pi$
$710$	−28.8724	+	9.23507i	−1.08356	+	0.346586i
$711$	−5.67362			−0.212777
$712$	−2.83037	+	23.7781i	−0.106073	+	0.891122i
$713$	−0.839646	+	0.484770i	−0.0314450	+	0.0181548i
$714$	−1.19554	−	3.73774i	−0.0447421	−	0.139881i
$715$	16.0537			0.600375
$716$	18.7048	+	8.53428i	0.699030	+	0.318941i
$717$	−11.5055	−	6.64268i	−0.429679	−	0.248076i
$718$	−2.22223	+	2.44540i	−0.0829330	+	0.0912614i
$719$	45.5456	+	26.2958i	1.69856	+	0.980667i	0.947125	+	0.320865i	$0.103974\pi$
$719$	45.5456	+	26.2958i	1.69856	+	0.980667i	0.751440	+	0.659801i	$0.229360\pi$
$720$	−7.62289	−	8.78487i	−0.284088	−	0.327393i
$721$		−	14.3918i		−	0.535977i
$722$	20.4052	+	17.4822i	0.759404	+	0.650619i
$723$		−	18.2616i		−	0.679156i
$724$	11.7821	−	1.12921i	0.437878	−	0.0419668i
$725$	−22.9329	−	13.2403i	−0.851706	−	0.491733i
$726$	−9.38233	−	8.52611i	−0.348211	−	0.316434i
$727$	10.2535	+	5.91983i	0.380279	+	0.219554i	0.677940	−	0.735117i	$-0.262873\pi$
$727$	10.2535	+	5.91983i	0.380279	+	0.219554i	−0.297660	+	0.954672i	$0.596206\pi$
$728$	56.7454	+	6.75456i	2.10312	+	0.250341i
$729$	1.00000			0.0370370
$730$	45.3403	−	14.5024i	1.67812	−	0.536760i
$731$	−3.84411	+	2.21940i	−0.142180	+	0.0820875i
$732$	7.82977	+	3.57243i	0.289397	+	0.132041i
$733$	16.5981			0.613064			0.306532	−	0.951860i	$-0.400831\pi$
$733$	16.5981			0.613064			0.306532	+	0.951860i	$0.400831\pi$
$734$	5.09147	+	15.9179i	0.187930	+	0.587541i
$735$	−29.4565	−	51.0201i	−1.08652	−	1.88191i
$736$	−10.0372	+	16.4995i	−0.369977	+	0.608181i
$737$	−4.86487	+	2.80874i	−0.179200	+	0.103461i
$738$	9.08597	+	1.97487i	0.334459	+	0.0726959i
$739$	−8.15606	−	4.70890i	−0.300026	−	0.173220i	0.342429	−	0.939544i	$-0.388750\pi$
$739$	−8.15606	−	4.70890i	−0.300026	−	0.173220i	−0.642454	+	0.766324i	$0.722084\pi$
$740$	−5.51185	−	7.73459i	−0.202620	−	0.284329i
$741$	8.64629	+	14.4829i	0.317629	+	0.532042i
$742$	15.1286	−	4.83901i	0.555389	−	0.177645i
$743$	10.2834	−	17.8114i	0.377262	−	0.653438i	−0.613400	−	0.789772i	$-0.710199\pi$
$743$	10.2834	−	17.8114i	0.377262	−	0.653438i	0.990663	+	0.136334i	$0.0435322\pi$
$744$	−0.316581	−	0.738216i	−0.0116064	−	0.0270643i
$745$	0.144854	+	0.250895i	0.00530705	+	0.00919208i
$746$	32.3215	+	7.02518i	1.18337	+	0.257210i
$747$	3.89630	−	2.24953i	0.142558	−	0.0823060i
$748$	−0.880102	−	1.23502i	−0.0321797	−	0.0451567i
$749$		−	45.0420i		−	1.64580i
$750$	−4.70148	−	4.27242i	−0.171674	−	0.156007i
$751$	2.82242	+	4.88858i	0.102992	+	0.178387i	0.912916	−	0.408148i	$-0.133825\pi$
$751$	2.82242	+	4.88858i	0.102992	+	0.178387i	−0.809924	+	0.586534i	$0.800492\pi$
$752$	35.0544	+	12.1050i	1.27830	+	0.441425i
$753$		−	9.14646i		−	0.333315i
$754$	−31.0400	−	28.2074i	−1.13041	−	1.02725i
$755$	−26.1559	+	45.3033i	−0.951910	+	1.64876i
$756$	−4.33457	+	9.50018i	−0.157647	+	0.345518i
$757$	−24.2417	+	41.9878i	−0.881079	+	1.52607i	−0.0309371	+	0.999521i	$0.509849\pi$
$757$	−24.2417	+	41.9878i	−0.881079	+	1.52607i	−0.850142	+	0.526553i	$0.823484\pi$
$758$	6.05230	−	27.8454i	0.219829	−	1.01139i
$759$	4.87090			0.176802
$760$	29.0208	+	21.0469i	1.05270	+	0.763452i
$761$	2.44466			0.0886189			0.0443095	−	0.999018i	$-0.485891\pi$
$761$	2.44466			0.0886189			0.0443095	+	0.999018i	$0.485891\pi$
$762$	−0.634389	+	2.91869i	−0.0229815	+	0.105733i
$763$	−32.6843	+	56.6108i	−1.18325	+	2.04945i
$764$	2.58785	−	5.67186i	0.0936252	−	0.205201i
$765$	0.772697	−	1.33835i	0.0279369	−	0.0483881i
$766$	−12.5833	−	11.4349i	−0.454652	−	0.413161i
$767$		−	22.8094i		−	0.823598i
$768$	−12.5907	−	9.87294i	−0.454327	−	0.356259i
$769$	9.99029	+	17.3037i	0.360259	+	0.623987i	0.988003	−	0.154433i	$-0.0493550\pi$
$769$	9.99029	+	17.3037i	0.360259	+	0.623987i	−0.627744	+	0.778420i	$0.716022\pi$
$770$	−22.6702	−	20.6014i	−0.816978	−	0.742422i
$771$			1.92908i			0.0694742i
$772$	−22.4789	−	31.5438i	−0.809033	−	1.13529i
$773$	−23.9506	+	13.8279i	−0.861444	+	0.497355i	−0.864496	−	0.502640i	$-0.832362\pi$
$773$	−23.9506	+	13.8279i	−0.861444	+	0.497355i	0.00305153	+	0.999995i	$0.499029\pi$
$774$	11.5419	+	2.50868i	0.414866	+	0.0901727i
$775$	0.490608	+	0.849757i	0.0176231	+	0.0305242i
$776$	−10.5634	+	4.53009i	−0.379205	+	0.162621i
$777$	−4.26344	+	7.38449i	−0.152950	+	0.264917i
$778$	14.1696	−	4.53226i	0.508005	−	0.162489i
$779$	−28.6557	+	0.418743i	−1.02670	+	0.0150030i
$780$	13.0602	+	18.3269i	0.467628	+	0.656207i
$781$	9.10816	+	5.25860i	0.325916	+	0.188167i
$782$	−2.50748	−	0.545010i	−0.0896673	−	0.0194895i
$783$	6.63731	−	3.83205i	0.237198	−	0.136946i
$784$	−53.1141	−	61.2104i	−1.89693	−	2.18608i
$785$	30.4621	+	52.7620i	1.08724	+	1.88316i
$786$	−8.60266	−	26.8952i	−0.306847	−	0.959321i
$787$	−24.8066			−0.884258			−0.442129	−	0.896951i	$-0.645777\pi$
$787$	−24.8066			−0.884258			−0.442129	+	0.896951i	$0.645777\pi$
$788$	32.2741	+	14.7254i	1.14972	+	0.524572i
$789$	0.864250	−	0.498975i	0.0307681	−	0.0177640i
$790$	22.2221	−	7.10790i	0.790625	−	0.252888i
$791$	−84.2683			−2.99624
$792$	−0.476977	+	4.00711i	−0.0169486	+	0.142386i
$793$	−14.4208	−	8.32583i	−0.512096	−	0.295659i
$794$	−32.0417	−	29.1176i	−1.13712	−	1.03335i
$795$	5.41701	+	3.12751i	0.192122	+	0.110922i
$796$	12.1045	−	1.16011i	0.429033	−	0.0411190i
$797$		−	34.9670i		−	1.23860i	−0.785156	−	0.619298i	$-0.787417\pi$
$797$		−	34.9670i		−	1.23860i	0.785156	−	0.619298i	$-0.212583\pi$
$798$	6.37573	−	31.5476i	0.225698	−	1.11677i
$799$			4.92747i			0.174321i
$800$	16.6982	+	10.1581i	0.590372	+	0.359143i
$801$	7.33193	+	4.23309i	0.259061	+	0.149569i
$802$	10.5755	−	11.6375i	0.373433	−	0.410934i
$803$	−14.3032	−	8.25793i	−0.504747	−	0.291416i
$804$	−7.16415	−	3.26873i	−0.252660	−	0.115279i
$805$	−51.8317			−1.82683
$806$	0.473469	+	1.48025i	0.0166772	+	0.0521395i
$807$	−15.6268	+	9.02214i	−0.550090	+	0.317594i
$808$	35.0267	+	4.16932i	1.23224	+	0.146676i
$809$	−38.2652			−1.34533			−0.672667	−	0.739945i	$-0.734851\pi$
$809$	−38.2652			−1.34533			−0.672667	+	0.739945i	$0.734851\pi$
$810$	−3.91673	+	1.25280i	−0.137620	+	0.0440188i
$811$	17.3524	+	30.0552i	0.609324	+	1.05538i	0.991352	+	0.131229i	$0.0418924\pi$
$811$	17.3524	+	30.0552i	0.609324	+	1.05538i	−0.382028	+	0.924151i	$0.624774\pi$
$812$	7.63529	+	79.6659i	0.267946	+	2.79573i
$813$	3.15680	−	1.82258i	0.110714	−	0.0639206i
$814$	−0.699878	+	3.22000i	−0.0245307	+	0.112861i
$815$	−3.97197	−	2.29322i	−0.139132	−	0.0803279i
$816$	0.693901	−	2.00944i	0.0242914	−	0.0703445i
$817$	−36.4014	+	0.531930i	−1.27352	+	0.0186099i
$818$	−0.0913364	−	0.285553i	−0.00319350	−	0.00998412i
$819$	10.1021	−	17.4973i	0.352995	−	0.611406i
$820$	−38.0614	+	3.64786i	−1.32916	+	0.127389i
$821$	4.69701	+	8.13547i	0.163927	+	0.283930i	0.936274	−	0.351271i	$-0.114251\pi$
$821$	4.69701	+	8.13547i	0.163927	+	0.283930i	−0.772347	+	0.635201i	$0.780917\pi$
$822$	−4.80781	+	22.1198i	−0.167692	+	0.771516i
$823$	−23.4401	+	13.5332i	−0.817072	+	0.471736i	−0.849406	−	0.527741i	$-0.823039\pi$
$823$	−23.4401	+	13.5332i	−0.817072	+	0.471736i	0.0323340	+	0.999477i	$0.489706\pi$
$824$	4.66891	−	6.24376i	0.162649	−	0.217512i
$825$		−	4.92956i		−	0.171625i
$826$	−29.2707	+	32.2102i	−1.01846	+	1.12074i
$827$	−4.21550	−	7.30146i	−0.146587	−	0.253897i	0.783377	−	0.621547i	$-0.213496\pi$
$827$	−4.21550	−	7.30146i	−0.146587	−	0.253897i	−0.929964	+	0.367651i	$0.880162\pi$
$828$	3.96261	+	5.56060i	0.137710	+	0.193244i
$829$		−	18.8618i		−	0.655097i	−0.944834	−	0.327549i	$-0.893777\pi$
$829$		−	18.8618i		−	0.655097i	0.944834	−	0.327549i	$-0.106223\pi$
$830$	−12.4426	+	13.6921i	−0.431887	+	0.475259i
$831$	−11.5574	+	20.0181i	−0.400923	+	0.694420i
$832$	22.4273	+	21.3395i	0.777526	+	0.739814i
$833$	5.38392	−	9.32523i	0.186542	−	0.323100i
$834$	−12.3618	−	2.68689i	−0.428056	−	0.0930394i
$835$	−10.5895			−0.366465
$836$	−1.36741	−	12.3625i	−0.0472928	−	0.427567i
$837$	−0.283986			−0.00981600
$838$	26.8707	+	5.84044i	0.928232	+	0.201755i
$839$	17.1706	−	29.7403i	0.592795	−	1.02675i	−0.401059	−	0.916052i	$-0.631358\pi$
$839$	17.1706	−	29.7403i	0.592795	−	1.02675i	0.993854	−	0.110699i	$-0.0353088\pi$
$840$	5.07556	−	42.6400i	0.175123	−	1.47122i
$841$	14.8692	−	25.7543i	0.512732	−	0.888078i
$842$	−1.28558	+	1.41468i	−0.0443040	+	0.0487532i
$843$			16.7622i			0.577322i
$844$	40.6244	−	28.9499i	1.39835	−	0.996497i
$845$	−2.87046	−	4.97179i	−0.0987469	−	0.171035i
$846$	8.81806	−	9.70361i	0.303171	−	0.333617i
$847$		−	46.8048i		−	1.60823i
$848$	8.13328	+	2.80859i	0.279298	+	0.0964473i
$849$	8.33961	−	4.81488i	0.286215	−	0.165246i
$850$	−0.551574	+	2.53768i	−0.0189188	+	0.0870417i
$851$	2.78780	+	4.82860i	0.0955644	+	0.165522i
$852$	1.40655	+	14.6759i	0.0481877	+	0.502787i
$853$	2.68574	−	4.65185i	0.0919581	−	0.159276i	−0.816377	−	0.577520i	$-0.804021\pi$
$853$	2.68574	−	4.65185i	0.0919581	−	0.159276i	0.908335	+	0.418243i	$0.137354\pi$
$854$	9.67991	+	30.2632i	0.331240	+	1.03558i
$855$	10.8828	−	6.49705i	0.372185	−	0.222195i
$856$	14.6123	−	19.5411i	0.499439	−	0.667902i
$857$	16.2292	+	9.36992i	0.554378	+	0.320070i	0.750886	−	0.660432i	$-0.229627\pi$
$857$	16.2292	+	9.36992i	0.554378	+	0.320070i	−0.196508	+	0.980502i	$0.562960\pi$
$858$	1.65834	−	7.62968i	0.0566147	−	0.260473i
$859$	−39.3619	+	22.7256i	−1.34301	+	0.775388i	−0.987248	−	0.159188i	$-0.949112\pi$
$859$	−39.3619	+	22.7256i	−1.34301	+	0.775388i	−0.355764	+	0.934576i	$0.615779\pi$
$860$	−48.3495	+	4.63388i	−1.64871	+	0.158014i
$861$	17.1639	+	29.7288i	0.584945	+	1.01316i
$862$	−15.0317	+	4.80800i	−0.511980	+	0.163761i
$863$	52.6923			1.79367			0.896833	−	0.442369i	$-0.145862\pi$
$863$	52.6923			1.79367			0.896833	+	0.442369i	$0.145862\pi$
$864$	−4.96253	+	2.71538i	−0.168829	+	0.0923791i
$865$	26.4854	−	15.2913i	0.900530	−	0.519921i
$866$	−17.2501	−	53.9304i	−0.586181	−	1.83263i
$867$	−16.7175			−0.567757
$868$	1.23096	−	2.69792i	0.0417815	−	0.0915735i
$869$	−7.01023	−	4.04736i	−0.237806	−	0.137297i
$870$	−21.1958	+	23.3243i	−0.718604	+	0.790769i
$871$	13.1948	+	7.61805i	0.447090	+	0.258128i
$872$	−32.5453	+	13.9569i	−1.10212	+	0.472640i
$873$			4.06368i			0.137535i
$874$	−15.7803	−	13.9247i	−0.533776	−	0.471009i
$875$		−	23.4538i		−	0.792884i
$876$	−2.20880	−	23.0465i	−0.0746286	−	0.778669i
$877$	8.36103	+	4.82724i	0.282332	+	0.163004i	0.634479	−	0.772940i	$-0.281215\pi$
$877$	8.36103	+	4.82724i	0.282332	+	0.163004i	−0.352147	+	0.935945i	$0.614548\pi$
$878$	−16.7310	−	15.2042i	−0.564644	−	0.513115i
$879$	7.36973	+	4.25491i	0.248575	+	0.143515i
$880$	−3.15191	−	16.2923i	−0.106251	−	0.549214i
$881$	−2.09300			−0.0705150			−0.0352575	−	0.999378i	$-0.511225\pi$
$881$	−2.09300			−0.0705150			−0.0352575	+	0.999378i	$0.511225\pi$
$882$	−27.2906	+	8.72913i	−0.918924	+	0.293925i
$883$	0.0695276	−	0.0401418i	0.00233979	−	0.00135088i	−0.498830	−	0.866700i	$-0.666237\pi$
$883$	0.0695276	−	0.0401418i	0.00233979	−	0.00135088i	0.501169	+	0.865349i	$0.332903\pi$
$884$	−1.70739	+	3.74212i	−0.0574256	+	0.125861i
$885$	−17.1396			−0.576140
$886$	−5.80049	−	18.1346i	−0.194871	−	0.609243i
$887$	28.4945	+	49.3539i	0.956752	+	1.65714i	0.730307	+	0.683119i	$0.239377\pi$
$887$	28.4945	+	49.3539i	0.956752	+	1.65714i	0.226445	+	0.974024i	$0.427289\pi$
$888$	−4.24531	+	1.82058i	−0.142463	+	0.0610947i
$889$	−9.54981	+	5.51359i	−0.320290	+	0.184920i
$890$	−34.0204	−	7.39446i	−1.14037	−	0.247863i
$891$	1.23558	+	0.713364i	0.0413936	+	0.0238986i
$892$	−37.9981	+	27.0784i	−1.27227	+	0.906651i
$893$	−19.6930	+	35.2903i	−0.659002	+	1.18095i
$894$	0.134204	−	0.0429261i	0.00448844	−	0.00143566i
$895$	−14.9458	+	25.8868i	−0.499582	+	0.865301i
$896$	−4.28616	−	58.9150i	−0.143191	−	1.96821i
$897$	−6.60559	−	11.4412i	−0.220554	−	0.382011i
$898$	21.6716	+	4.71040i	0.723190	+	0.157188i
$899$	−1.88490	+	1.08825i	−0.0628651	+	0.0362952i
$900$	5.62756	−	4.01034i	0.187585	−	0.133678i
$901$			1.14327i			0.0380877i
$902$	9.81766	+	8.92171i	0.326892	+	0.297060i
$903$	21.8034	+	37.7646i	0.725572	+	1.25673i
$904$	−36.5592	−	27.3379i	−1.21594	−	0.909247i
$905$			17.2083i			0.572024i
$906$	18.8289	+	17.1106i	0.625550	+	0.568463i
$907$	10.0210	−	17.3570i	0.332743	−	0.576329i	−0.650305	−	0.759673i	$-0.725359\pi$
$907$	10.0210	−	17.3570i	0.332743	−	0.576329i	0.983049	+	0.183344i	$0.0586924\pi$
$908$	24.4310	+	11.1470i	0.810772	+	0.369925i
$909$	6.23562	−	10.8004i	0.206822	−	0.358227i
$910$	−17.6465	+	81.1882i	−0.584977	+	2.69136i
$911$	46.9598			1.55585			0.777924	−	0.628358i	$-0.216273\pi$
$911$	46.9598			1.55585			0.777924	+	0.628358i	$0.216273\pi$
$912$	13.0006	−	11.6183i	0.430492	−	0.384720i
$913$	6.41893			0.212436
$914$	−2.68449	+	12.3508i	−0.0887950	+	0.408528i
$915$	−6.25626	+	10.8362i	−0.206826	+	0.358232i
$916$	−2.43973	−	1.11316i	−0.0806110	−	0.0367797i
$917$	52.1254	−	90.2838i	1.72133	−	2.98143i
$918$	−0.556244	−	0.505482i	−0.0183588	−	0.0166834i
$919$		−	32.0041i		−	1.05572i	−0.849332	−	0.527859i	$-0.822995\pi$
$919$		−	32.0041i		−	1.05572i	0.849332	−	0.527859i	$-0.177005\pi$
$920$	−22.4868	−	16.8150i	−0.741368	−	0.554375i
$921$	−3.81054	−	6.60006i	−0.125562	−	0.217479i
$922$	−21.6652	−	19.6880i	−0.713504	−	0.648390i
$923$		−	28.5255i		−	0.938927i
$924$	−12.1328	+	8.64613i	−0.399140	+	0.284437i
$925$	4.88676	−	2.82137i	0.160676	−	0.0927661i
$926$	−27.7503	−	6.03162i	−0.911931	−	0.198211i
$927$	−1.37822	−	2.38714i	−0.0452665	−	0.0784039i
$928$	−22.5324	+	37.0395i	−0.739661	+	1.21588i
$929$	−28.9749	+	50.1860i	−0.950635	+	1.64655i	−0.206580	+	0.978430i	$0.566234\pi$
$929$	−28.9749	+	50.1860i	−0.950635	+	1.64655i	−0.744055	+	0.668119i	$0.767100\pi$
$930$	1.11230	−	0.355778i	0.0364737	−	0.0116664i
$931$	75.8284	−	45.2695i	2.48518	−	1.48365i
$932$	4.13298	−	2.94526i	0.135380	−	0.0964753i
$933$	6.61214	+	3.81752i	0.216472	+	0.124980i
$934$	−40.5401	−	8.81153i	−1.32651	−	0.288322i
$935$	1.90946	−	1.10243i	0.0624460	−	0.0360532i
$936$	10.0591	−	4.31381i	0.328792	−	0.141001i
$937$	11.6344	+	20.1514i	0.380080	+	0.658317i	0.991073	−	0.133318i	$-0.0425632\pi$
$937$	11.6344	+	20.1514i	0.380080	+	0.658317i	−0.610994	+	0.791635i	$0.709230\pi$
$938$	−8.85701	−	27.6905i	−0.289192	−	0.904125i
$939$	4.17745			0.136326
$940$	−22.3813	+	49.0537i	−0.729999	+	1.59995i
$941$	−38.7801	+	22.3897i	−1.26419	+	0.729883i	−0.973883	−	0.227049i	$-0.927092\pi$
$941$	−38.7801	+	22.3897i	−1.26419	+	0.729883i	−0.290311	+	0.956932i	$0.593759\pi$
$942$	28.2223	−	9.02714i	0.919533	−	0.294120i
$943$	22.4465			0.730957
$944$	−23.1484	+	4.47827i	−0.753415	+	0.145755i
$945$	−13.1480	−	7.59098i	−0.427703	−	0.246934i
$946$	12.4714	+	11.3333i	0.405480	+	0.368477i
$947$	−21.0121	−	12.1313i	−0.682800	−	0.394215i	0.118109	−	0.993001i	$-0.462317\pi$
$947$	−21.0121	−	12.1313i	−0.682800	−	0.394215i	−0.800909	+	0.598786i	$0.795650\pi$
$948$	−1.08257	−	11.2955i	−0.0351604	−	0.366860i
$949$			44.7955i			1.45412i
$950$	−14.0924	+	15.9703i	−0.457217	+	0.518146i
$951$			30.6367i			0.993464i
$952$	7.21325	−	3.09337i	0.233783	−	0.100257i
$953$	5.79186	+	3.34393i	0.187617	+	0.108321i	0.590866	−	0.806769i	$-0.298786\pi$
$953$	5.79186	+	3.34393i	0.187617	+	0.108321i	−0.403250	+	0.915090i	$0.632119\pi$
$954$	2.04595	−	2.25142i	0.0662402	−	0.0728923i
$955$	7.84967	+	4.53201i	0.254009	+	0.146652i
$956$	11.0294	−	24.1734i	0.356717	−	0.781825i
$957$	10.9346			0.353465
$958$	−7.48965	−	23.4155i	−0.241980	−	0.756522i
$959$	−72.3747	+	41.7856i	−2.33710	+	1.34933i
$960$	16.0351	−	16.8525i	0.517530	−	0.543911i
$961$	−30.9194			−0.997398
$962$	8.51256	−	2.72281i	0.274456	−	0.0877869i
$963$	−4.31341	−	7.47104i	−0.138998	−	0.240751i
$964$	36.3566	−	3.48446i	1.17097	−	0.112227i
$965$	48.7700	−	28.1574i	1.56996	−	0.906417i
$966$	−5.35418	+	24.6335i	−0.172268	+	0.792570i
$967$	37.2806	+	21.5240i	1.19886	+	0.692164i	0.960302	−	0.278963i	$-0.0899907\pi$
$967$	37.2806	+	21.5240i	1.19886	+	0.692164i	0.238562	+	0.971127i	$0.423324\pi$
$968$	15.1842	−	20.3059i	0.488039	−	0.652657i
$969$	2.02296	+	1.12887i	0.0649870	+	0.0362646i
$970$	−5.09097	−	15.9164i	−0.163461	−	0.511043i
$971$	−25.8736	+	44.8144i	−0.830324	+	1.43816i	0.0674572	+	0.997722i	$0.478511\pi$
$971$	−25.8736	+	44.8144i	−0.830324	+	1.43816i	−0.897781	+	0.440441i	$0.854822\pi$
$972$	0.190808	+	1.99088i	0.00612018	+	0.0638574i
$973$	−23.3523	−	40.4473i	−0.748639	−	1.29668i
$974$	8.47833	−	39.0071i	0.271663	−	1.24987i
$975$	−11.5790	+	6.68514i	−0.370825	+	0.214096i
$976$	−5.61828	+	16.2698i	−0.179837	+	0.520782i
$977$			31.1225i			0.995698i	0.867264	+	0.497849i	$0.165877\pi$
$977$			31.1225i			0.995698i	−0.867264	+	0.497849i	$0.834123\pi$
$978$	−1.50017	+	1.65083i	−0.0479703	+	0.0527876i
$979$	6.03946	+	10.4607i	0.193022	+	0.334324i
$980$	95.9543	−	68.3793i	3.06515	−	2.18430i
$981$			12.5199i			0.399731i
$982$	10.2624	−	11.2930i	0.327487	−	0.360375i
$983$	19.0646	−	33.0209i	0.608066	−	1.05320i	−0.383493	−	0.923544i	$-0.625279\pi$
$983$	19.0646	−	33.0209i	0.608066	−	1.05320i	0.991559	−	0.129658i	$-0.0413878\pi$
$984$	−2.19804	+	18.4659i	−0.0700710	+	0.588670i
$985$	−25.7881	+	44.6663i	−0.821678	+	1.42319i
$986$	−5.62900	−	1.22348i	−0.179264	−	0.0389636i
$987$	48.4075			1.54083
$988$	−27.1839	+	19.9771i	−0.864834	+	0.635558i
$989$	28.5138			0.906686
$990$	−5.73315	−	1.24612i	−0.182211	−	0.0396043i
$991$	16.7801	−	29.0639i	0.533037	−	0.923246i	−0.466219	−	0.884669i	$-0.654384\pi$
$991$	16.7801	−	29.0639i	0.533037	−	0.923246i	0.999256	−	0.0385771i	$-0.0122825\pi$
$992$	1.40929	−	0.771131i	0.0447450	−	0.0244834i
$993$	−10.2467	+	17.7479i	−0.325171	+	0.563212i
$994$	−36.6061	+	40.2822i	−1.16107	+	1.27767i
$995$			17.6792i			0.560469i
$996$	5.22198	+	7.32783i	0.165465	+	0.232191i
$997$	1.29261	+	2.23886i	0.0409373	+	0.0709056i	0.885768	−	0.464128i	$-0.153632\pi$
$997$	1.29261	+	2.23886i	0.0409373	+	0.0709056i	−0.844831	+	0.535034i	$0.820299\pi$
$998$	−7.23708	+	7.96385i	−0.229086	+	0.252091i
$999$			1.63314i			0.0516702i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.k.a.103.5	yes	20
3.2	odd	2		684.2.r.c.559.6		20
4.3	odd	2		228.2.k.b.103.7	yes	20
12.11	even	2		684.2.r.b.559.4		20
19.12	odd	6		228.2.k.b.31.7	yes	20
57.50	even	6		684.2.r.b.487.4		20
76.31	even	6	inner	228.2.k.a.31.5	✓	20
228.107	odd	6		684.2.r.c.487.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.k.a.31.5	✓	20	76.31	even	6	inner
228.2.k.a.103.5	yes	20	1.1	even	1	trivial
228.2.k.b.31.7	yes	20	19.12	odd	6
228.2.k.b.103.7	yes	20	4.3	odd	2
684.2.r.b.487.4		20	57.50	even	6
684.2.r.b.559.4		20	12.11	even	2
684.2.r.c.487.6		20	228.107	odd	6
684.2.r.c.559.6		20	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.300371 + 1.38195i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.81955 - 0.830194i) q^{4} +(1.45389 - 2.51821i) q^{5} +(-1.04662 - 0.951102i) q^{6} -5.22116i q^{7} +(1.69383 - 2.26516i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(3.04332 + 2.76559i) q^{10} -1.42673i q^{11} +(1.62875 - 1.16068i) q^{12} +(-3.35123 + 1.93483i) q^{13} +(7.21537 + 1.56829i) q^{14} +(1.45389 + 2.51821i) q^{15} +(2.62156 + 3.02117i) q^{16} +(-0.265735 + 0.460266i) q^{17} +(1.34699 - 0.430844i) q^{18} +(-3.74267 + 2.23437i) q^{19} +(-4.73603 + 3.37501i) q^{20} +(4.52166 + 2.61058i) q^{21} +(1.97166 + 0.428548i) q^{22} +(2.95664 - 1.70702i) q^{23} +(1.11477 + 2.59948i) q^{24} +(-1.72758 - 2.99225i) q^{25} +(-1.66723 - 5.21239i) q^{26} +1.00000 q^{27} +(-4.33457 + 9.50018i) q^{28} +(6.63731 - 3.83205i) q^{29} +(-3.91673 + 1.25280i) q^{30} -0.283986 q^{31} +(-4.96253 + 2.71538i) q^{32} +(1.23558 + 0.713364i) q^{33} +(-0.556244 - 0.505482i) q^{34} +(-13.1480 - 7.59098i) q^{35} +(0.190808 + 1.99088i) q^{36} +1.63314i q^{37} +(-1.96360 - 5.84331i) q^{38} -3.86967i q^{39} +(-3.24151 - 7.55869i) q^{40} +(5.69391 + 3.28738i) q^{41} +(-4.96586 + 5.46455i) q^{42} +(7.23299 + 4.17597i) q^{43} +(-1.18446 + 2.59601i) q^{44} -2.90777 q^{45} +(1.47092 + 4.59866i) q^{46} +(8.02928 - 4.63571i) q^{47} +(-3.92718 + 0.759752i) q^{48} -20.2605 q^{49} +(4.65404 - 1.48863i) q^{50} +(-0.265735 - 0.460266i) q^{51} +(7.70404 - 0.738365i) q^{52} +(1.86294 - 1.07557i) q^{53} +(-0.300371 + 1.38195i) q^{54} +(-3.59279 - 2.07430i) q^{55} +(-11.8268 - 8.84373i) q^{56} +(-0.0636895 - 4.35843i) q^{57} +(3.30204 + 10.3234i) q^{58} +(-2.94720 + 5.10469i) q^{59} +(-0.554827 - 5.78902i) q^{60} +(2.15156 + 3.72662i) q^{61} +(0.0853013 - 0.392454i) q^{62} +(-4.52166 + 2.61058i) q^{63} +(-2.26191 - 7.67358i) q^{64} +11.2521i q^{65} +(-1.35696 + 1.49324i) q^{66} +(-1.96866 - 3.40981i) q^{67} +(0.865629 - 0.616868i) q^{68} +3.41403i q^{69} +(14.4396 - 15.8897i) q^{70} +(-3.68578 + 6.38395i) q^{71} +(-2.80860 - 0.334315i) q^{72} +(5.78802 - 10.0251i) q^{73} +(-2.25691 - 0.490548i) q^{74} +3.45515 q^{75} +(8.66495 - 0.958423i) q^{76} -7.44917 q^{77} +(5.34768 + 1.16234i) q^{78} +(2.83681 - 4.91350i) q^{79} +(11.4194 - 2.20919i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-6.25327 + 6.88125i) q^{82} +4.49906i q^{83} +(-6.06011 - 8.50394i) q^{84} +(0.772697 + 1.33835i) q^{85} +(-7.94355 + 8.74127i) q^{86} +7.66410i q^{87} +(-3.23177 - 2.41663i) q^{88} +(-7.33193 + 4.23309i) q^{89} +(0.873411 - 4.01839i) q^{90} +(10.1021 + 17.4973i) q^{91} +(-6.79692 + 0.651426i) q^{92} +(0.141993 - 0.245939i) q^{93} +(3.99454 + 12.4885i) q^{94} +(0.185195 + 12.6733i) q^{95} +(0.129676 - 5.65537i) q^{96} +(-3.51925 - 2.03184i) q^{97} +(6.08567 - 27.9989i) q^{98} +(-1.23558 + 0.713364i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{2} - 10 q^{3} + q^{4} - q^{6} - 4 q^{8} - 10 q^{9} + 6 q^{10} - 2 q^{12} + 6 q^{13} + 9 q^{14} + 13 q^{16} + 2 q^{18} - 12 q^{19} - 14 q^{20} + 6 q^{21} - 8 q^{22} - 7 q^{24} - 10 q^{25} + 20 q^{27}+ \cdots - 12 q^{98}+O(q^{100}) \) 20 * q - q^2 - 10 * q^3 + q^4 - q^6 - 4 * q^8 - 10 * q^9 + 6 * q^10 - 2 * q^12 + 6 * q^13 + 9 * q^14 + 13 * q^16 + 2 * q^18 - 12 * q^19 - 14 * q^20 + 6 * q^21 - 8 * q^22 - 7 * q^24 - 10 * q^25 + 20 * q^27 + 7 * q^28 - 12 * q^31 - 31 * q^32 - 30 * q^34 + q^36 - 11 * q^38 - 26 * q^40 + 12 * q^41 - 9 * q^42 + 18 * q^43 + 30 * q^44 + 32 * q^46 + 36 * q^47 - 11 * q^48 - 24 * q^49 + 34 * q^50 + 3 * q^52 - 12 * q^53 - q^54 - 38 * q^56 + 6 * q^57 + 16 * q^58 + 10 * q^60 + 10 * q^61 + 29 * q^62 - 6 * q^63 - 14 * q^64 - 8 * q^66 - 14 * q^67 + 40 * q^68 + 46 * q^70 - 8 * q^71 + 11 * q^72 - 6 * q^73 + 3 * q^74 + 20 * q^75 + 3 * q^76 - 32 * q^77 + 33 * q^78 + 6 * q^79 + 40 * q^80 - 10 * q^81 - 60 * q^82 - 14 * q^84 + 8 * q^85 - 25 * q^86 - 44 * q^88 - 24 * q^89 - 6 * q^90 - 26 * q^91 + 36 * q^92 + 6 * q^93 + 52 * q^94 - 4 * q^95 + 2 * q^96 - 12 * q^97 - 12 * q^98

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