LMFDB - Embedded newform 285.2.i.f.121.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,2,Mod(106,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("285.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	285.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.27573645761$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 9x^{8} - 2x^{7} + 56x^{6} - 18x^{5} + 125x^{4} + x^{3} + 189x^{2} - 52x + 16 $ x^10 - x^9 + 9x^8 - 2x^7 + 56x^6 - 18x^5 + 125x^4 + x^3 + 189x^2 - 52*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.4
Root			$0.823305 - 1.42601i$ of defining polynomial
Character	$\chi$	$=$	285.121
Dual form			285.2.i.f.106.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.823305 + 1.42601i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.355663 + 0.616027i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.823305 + 1.42601i) q^{6} +4.47988 q^{7} +2.12194 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.823305 - 1.42601i) q^{10} -3.44134 q^{11} -0.711327 q^{12} +(-1.23994 + 2.14764i) q^{13} +(3.68831 + 6.38834i) q^{14} +(0.500000 - 0.866025i) q^{15} +(2.45833 + 4.25796i) q^{16} +(-3.81400 - 6.60604i) q^{17} -1.64661 q^{18} +(-3.67522 + 2.34366i) q^{19} +0.711327 q^{20} +(2.23994 + 3.87969i) q^{21} +(-2.83327 - 4.90737i) q^{22} +(-1.93528 + 3.35201i) q^{23} +(1.06097 + 1.83766i) q^{24} +(-0.500000 + 0.866025i) q^{25} -4.08340 q^{26} -1.00000 q^{27} +(-1.59333 + 2.75973i) q^{28} +(4.36728 - 7.56435i) q^{29} +1.64661 q^{30} -0.422654 q^{31} +(-1.92598 + 3.33589i) q^{32} +(-1.72067 - 2.98028i) q^{33} +(6.28017 - 10.8776i) q^{34} +(-2.23994 - 3.87969i) q^{35} +(-0.355663 - 0.616027i) q^{36} +3.90253 q^{37} +(-6.36790 - 3.31135i) q^{38} -2.47988 q^{39} +(-1.06097 - 1.83766i) q^{40} +(-2.64661 - 4.58406i) q^{41} +(-3.68831 + 6.38834i) q^{42} +(-1.23994 - 2.14764i) q^{43} +(1.22396 - 2.11996i) q^{44} +1.00000 q^{45} -6.37332 q^{46} +(0.338665 - 0.586585i) q^{47} +(-2.45833 + 4.25796i) q^{48} +13.0693 q^{49} -1.64661 q^{50} +(3.81400 - 6.60604i) q^{51} +(-0.882003 - 1.52767i) q^{52} +(-5.74928 + 9.95805i) q^{53} +(-0.823305 - 1.42601i) q^{54} +(1.72067 + 2.98028i) q^{55} +9.50605 q^{56} +(-3.86728 - 2.01101i) q^{57} +14.3824 q^{58} +(4.26526 + 7.38765i) q^{59} +(0.355663 + 0.616027i) q^{60} +(-4.10117 + 7.10343i) q^{61} +(-0.347973 - 0.602707i) q^{62} +(-2.23994 + 3.87969i) q^{63} +3.49067 q^{64} +2.47988 q^{65} +(2.83327 - 4.90737i) q^{66} +(4.81729 - 8.34379i) q^{67} +5.42600 q^{68} -3.87057 q^{69} +(3.68831 - 6.38834i) q^{70} +(1.92594 + 3.33583i) q^{71} +(-1.06097 + 1.83766i) q^{72} +(-8.39260 - 14.5364i) q^{73} +(3.21298 + 5.56504i) q^{74} -1.00000 q^{75} +(-0.136613 - 3.09759i) q^{76} -15.4168 q^{77} +(-2.04170 - 3.53633i) q^{78} +(-6.06262 - 10.5008i) q^{79} +(2.45833 - 4.25796i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.35794 - 7.54817i) q^{82} -2.03855 q^{83} -3.18666 q^{84} +(-3.81400 + 6.60604i) q^{85} +(2.04170 - 3.53633i) q^{86} +8.73456 q^{87} -7.30232 q^{88} +(1.57255 - 2.72374i) q^{89} +(0.823305 + 1.42601i) q^{90} +(-5.55478 + 9.62117i) q^{91} +(-1.37662 - 2.38437i) q^{92} +(-0.211327 - 0.366029i) q^{93} +1.11530 q^{94} +(3.86728 + 2.01101i) q^{95} -3.85195 q^{96} +(-1.00000 - 1.73205i) q^{97} +(10.7600 + 18.6370i) q^{98} +(1.72067 - 2.98028i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} + 5 q^{3} - 7 q^{4} - 5 q^{5} - q^{6} + 4 q^{7} - 12 q^{8} - 5 q^{9} + q^{10} + 10 q^{11} - 14 q^{12} + 8 q^{13} + 4 q^{14} + 5 q^{15} - 7 q^{16} - 10 q^{17} - 2 q^{18} + 5 q^{19} + 14 q^{20}+ \cdots - 5 q^{99}+O(q^{100}) $ 10 * q + q^2 + 5 * q^3 - 7 * q^4 - 5 * q^5 - q^6 + 4 * q^7 - 12 * q^8 - 5 * q^9 + q^10 + 10 * q^11 - 14 * q^12 + 8 * q^13 + 4 * q^14 + 5 * q^15 - 7 * q^16 - 10 * q^17 - 2 * q^18 + 5 * q^19 + 14 * q^20 + 2 * q^21 - 2 * q^22 + 2 * q^23 - 6 * q^24 - 5 * q^25 - 4 * q^26 - 10 * q^27 - 10 * q^28 + 7 * q^29 + 2 * q^30 - 18 * q^31 + 23 * q^32 + 5 * q^33 - 25 * q^34 - 2 * q^35 - 7 * q^36 + 12 * q^37 - 37 * q^38 + 16 * q^39 + 6 * q^40 - 12 * q^41 - 4 * q^42 + 8 * q^43 - 16 * q^44 + 10 * q^45 - 40 * q^46 - 6 * q^47 + 7 * q^48 + 30 * q^49 - 2 * q^50 + 10 * q^51 + 4 * q^52 - 8 * q^53 - q^54 - 5 * q^55 + 72 * q^56 - 2 * q^57 + 76 * q^58 + q^59 + 7 * q^60 - 7 * q^61 - 15 * q^62 - 2 * q^63 + 28 * q^64 - 16 * q^65 + 2 * q^66 + 14 * q^67 - 2 * q^68 + 4 * q^69 + 4 * q^70 + 27 * q^71 + 6 * q^72 - 26 * q^73 + 18 * q^74 - 10 * q^75 - 56 * q^76 + 28 * q^77 - 2 * q^78 - 23 * q^79 - 7 * q^80 - 5 * q^81 + 36 * q^82 - 24 * q^83 - 20 * q^84 - 10 * q^85 + 2 * q^86 + 14 * q^87 + 9 * q^89 + q^90 - 46 * q^91 + 52 * q^92 - 9 * q^93 + 90 * q^94 + 2 * q^95 + 46 * q^96 - 10 * q^97 - 21 * q^98 - 5 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.823305	+	1.42601i	0.582165	+	1.00834i	0.995222	+	0.0976341i	$0.0311275\pi$
$2$	0.823305	+	1.42601i	0.582165	+	1.00834i	−0.413058	+	0.910705i	$0.635539\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.355663	+	0.616027i	−0.177832	+	0.308014i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−0.823305	+	1.42601i	−0.336113	+	0.582165i
$7$	4.47988			1.69324			0.846618	−	0.532201i	$-0.178635\pi$
$7$	4.47988			1.69324			0.846618	+	0.532201i	$0.178635\pi$
$8$	2.12194			0.750220
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.823305	−	1.42601i	0.260352	−	0.450943i
$11$	−3.44134			−1.03760			−0.518801	−	0.854895i	$-0.673621\pi$
$11$	−3.44134			−1.03760			−0.518801	+	0.854895i	$0.673621\pi$
$12$	−0.711327			−0.205342
$13$	−1.23994	+	2.14764i	−0.343898	+	0.595648i	−0.985153	−	0.171680i	$-0.945081\pi$
$13$	−1.23994	+	2.14764i	−0.343898	+	0.595648i	0.641255	+	0.767328i	$0.278414\pi$
$14$	3.68831	+	6.38834i	0.985742	+	1.70736i
$15$	0.500000	−	0.866025i	0.129099	−	0.223607i
$16$	2.45833	+	4.25796i	0.614583	+	1.06449i
$17$	−3.81400	−	6.60604i	−0.925030	−	1.60220i	−0.791513	−	0.611153i	$-0.790706\pi$
$17$	−3.81400	−	6.60604i	−0.925030	−	1.60220i	−0.133518	−	0.991046i	$-0.542627\pi$
$18$	−1.64661			−0.388110
$19$	−3.67522	+	2.34366i	−0.843154	+	0.537672i
$19$	−3.67522	+	2.34366i	−0.843154	+	0.537672i
$20$	0.711327			0.159058
$21$	2.23994	+	3.87969i	0.488795	+	0.846618i
$22$	−2.83327	−	4.90737i	−0.604055	−	1.04625i
$23$	−1.93528	+	3.35201i	−0.403535	+	0.698942i	−0.994150	−	0.108011i	$-0.965552\pi$
$23$	−1.93528	+	3.35201i	−0.403535	+	0.698942i	0.590615	+	0.806953i	$0.298885\pi$
$24$	1.06097	+	1.83766i	0.216570	+	0.375110i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−4.08340			−0.800820
$27$	−1.00000			−0.192450
$28$	−1.59333	+	2.75973i	−0.301111	+	0.521540i
$29$	4.36728	−	7.56435i	0.810983	−	1.40466i	−0.101193	−	0.994867i	$-0.532266\pi$
$29$	4.36728	−	7.56435i	0.810983	−	1.40466i	0.912177	−	0.409797i	$-0.134401\pi$
$30$	1.64661			0.300629
$31$	−0.422654			−0.0759108			−0.0379554	−	0.999279i	$-0.512084\pi$
$31$	−0.422654			−0.0759108			−0.0379554	+	0.999279i	$0.512084\pi$
$32$	−1.92598	+	3.33589i	−0.340468	+	0.589707i
$33$	−1.72067	−	2.98028i	−0.299530	−	0.518801i
$34$	6.28017	−	10.8776i	1.07704	−	1.86549i
$35$	−2.23994	−	3.87969i	−0.378619	−	0.655787i
$36$	−0.355663	−	0.616027i	−0.0592772	−	0.102671i
$37$	3.90253			0.641573			0.320786	−	0.947152i	$-0.396053\pi$
$37$	3.90253			0.641573			0.320786	+	0.947152i	$0.396053\pi$
$38$	−6.36790	−	3.31135i	−1.03301	−	0.537172i
$39$	−2.47988			−0.397099
$40$	−1.06097	−	1.83766i	−0.167754	−	0.290559i
$41$	−2.64661	−	4.58406i	−0.413331	−	0.715911i	0.581921	−	0.813246i	$-0.302301\pi$
$41$	−2.64661	−	4.58406i	−0.413331	−	0.715911i	−0.995252	+	0.0973351i	$0.968968\pi$
$42$	−3.68831	+	6.38834i	−0.569119	+	0.985742i
$43$	−1.23994	−	2.14764i	−0.189089	−	0.327512i	0.755858	−	0.654736i	$-0.227220\pi$
$43$	−1.23994	−	2.14764i	−0.189089	−	0.327512i	−0.944947	+	0.327224i	$0.893887\pi$
$44$	1.22396	−	2.11996i	0.184518	−	0.319595i
$45$	1.00000			0.149071
$46$	−6.37332			−0.939695
$47$	0.338665	−	0.586585i	0.0493994	−	0.0855622i	−0.840268	−	0.542171i	$-0.817603\pi$
$47$	0.338665	−	0.586585i	0.0493994	−	0.0855622i	0.889668	+	0.456608i	$0.150936\pi$
$48$	−2.45833	+	4.25796i	−0.354830	+	0.614583i
$49$	13.0693			1.86705
$50$	−1.64661			−0.232866
$51$	3.81400	−	6.60604i	0.534066	−	0.925030i
$52$	−0.882003	−	1.52767i	−0.122312	−	0.211850i
$53$	−5.74928	+	9.95805i	−0.789725	+	1.36784i	0.136411	+	0.990652i	$0.456443\pi$
$53$	−5.74928	+	9.95805i	−0.789725	+	1.36784i	−0.926136	+	0.377191i	$0.876890\pi$
$54$	−0.823305	−	1.42601i	−0.112038	−	0.194055i
$55$	1.72067	+	2.98028i	0.232015	+	0.401861i
$56$	9.50605			1.27030
$57$	−3.86728	−	2.01101i	−0.512234	−	0.266365i
$58$	14.3824			1.88850
$59$	4.26526	+	7.38765i	0.555290	+	0.961791i	0.997881	+	0.0650670i	$0.0207261\pi$
$59$	4.26526	+	7.38765i	0.555290	+	0.961791i	−0.442591	+	0.896724i	$0.645941\pi$
$60$	0.355663	+	0.616027i	0.0459159	+	0.0795288i
$61$	−4.10117	+	7.10343i	−0.525101	+	0.909501i	0.474472	+	0.880271i	$0.342639\pi$
$61$	−4.10117	+	7.10343i	−0.525101	+	0.909501i	−0.999573	+	0.0292304i	$0.990694\pi$
$62$	−0.347973	−	0.602707i	−0.0441926	−	0.0765439i
$63$	−2.23994	+	3.87969i	−0.282206	+	0.488795i
$64$	3.49067			0.436334
$65$	2.47988			0.307591
$66$	2.83327	−	4.90737i	0.348751	−	0.604055i
$67$	4.81729	−	8.34379i	0.588525	−	1.01936i	−0.405901	−	0.913917i	$-0.633042\pi$
$67$	4.81729	−	8.34379i	0.588525	−	1.01936i	0.994426	−	0.105438i	$-0.0336246\pi$
$68$	5.42600			0.657999
$69$	−3.87057			−0.465962
$70$	3.68831	−	6.38834i	0.440837	−	0.763553i
$71$	1.92594	+	3.33583i	0.228567	+	0.395890i	0.957384	−	0.288819i	$-0.0932625\pi$
$71$	1.92594	+	3.33583i	0.228567	+	0.395890i	−0.728816	+	0.684709i	$0.759929\pi$
$72$	−1.06097	+	1.83766i	−0.125037	+	0.216570i
$73$	−8.39260	−	14.5364i	−0.982280	−	1.70136i	−0.653451	−	0.756969i	$-0.726679\pi$
$73$	−8.39260	−	14.5364i	−0.982280	−	1.70136i	−0.328829	−	0.944389i	$-0.606654\pi$
$74$	3.21298	+	5.56504i	0.373501	+	0.646923i
$75$	−1.00000			−0.115470
$76$	−0.136613	−	3.09759i	−0.0156706	−	0.355318i
$77$	−15.4168			−1.75690
$78$	−2.04170	−	3.53633i	−0.231177	−	0.400410i
$79$	−6.06262	−	10.5008i	−0.682098	−	1.18143i	−0.974339	−	0.225084i	$-0.927734\pi$
$79$	−6.06262	−	10.5008i	−0.682098	−	1.18143i	0.292241	−	0.956345i	$-0.405599\pi$
$80$	2.45833	−	4.25796i	0.274850	−	0.476054i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.35794	−	7.54817i	0.481254	−	0.833556i
$83$	−2.03855			−0.223759			−0.111880	−	0.993722i	$-0.535687\pi$
$83$	−2.03855			−0.223759			−0.111880	+	0.993722i	$0.535687\pi$
$84$	−3.18666			−0.347693
$85$	−3.81400	+	6.60604i	−0.413686	+	0.716525i
$86$	2.04170	−	3.53633i	0.220162	−	0.381332i
$87$	8.73456			0.936443
$88$	−7.30232			−0.778430
$89$	1.57255	−	2.72374i	0.166690	−	0.288716i	−0.770564	−	0.637363i	$-0.780025\pi$
$89$	1.57255	−	2.72374i	0.166690	−	0.288716i	0.937254	+	0.348647i	$0.113359\pi$
$90$	0.823305	+	1.42601i	0.0867840	+	0.150314i
$91$	−5.55478	+	9.62117i	−0.582300	+	1.00857i
$92$	−1.37662	−	2.38437i	−0.143522	−	0.248588i
$93$	−0.211327	−	0.366029i	−0.0219136	−	0.0379554i
$94$	1.11530			0.115034
$95$	3.86728	+	2.01101i	0.396774	+	0.206325i
$96$	−3.85195			−0.393138
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$	10.7600	+	18.6370i	1.08693	+	1.88262i
$99$	1.72067	−	2.98028i	0.172934	−	0.299530i
$100$	−0.355663	−	0.616027i	−0.0355663	−	0.0616027i
$101$	1.00934	−	1.74823i	0.100433	−	0.173955i	−0.811430	−	0.584450i	$-0.801310\pi$
$101$	1.00934	−	1.74823i	0.100433	−	0.173955i	0.911863	+	0.410494i	$0.134644\pi$
$102$	12.5603			1.24366
$103$	6.48898			0.639378			0.319689	−	0.947523i	$-0.396422\pi$
$103$	6.48898			0.639378			0.319689	+	0.947523i	$0.396422\pi$
$104$	−2.63108	+	4.55717i	−0.257999	+	0.446867i
$105$	2.23994	−	3.87969i	0.218596	−	0.378619i
$106$	−18.9337			−1.83900
$107$	3.96145			0.382968			0.191484	−	0.981496i	$-0.438670\pi$
$107$	3.96145			0.382968			0.191484	+	0.981496i	$0.438670\pi$
$108$	0.355663	−	0.616027i	0.0342237	−	0.0592772i
$109$	1.48402	+	2.57039i	0.142143	+	0.246199i	0.928303	−	0.371824i	$-0.121267\pi$
$109$	1.48402	+	2.57039i	0.142143	+	0.246199i	−0.786160	+	0.618023i	$0.787934\pi$
$110$	−2.83327	+	4.90737i	−0.270142	+	0.467899i
$111$	1.95127	+	3.37969i	0.185206	+	0.320786i
$112$	11.0130	+	19.0751i	1.04063	+	1.80243i
$113$	−8.71719			−0.820044			−0.410022	−	0.912076i	$-0.634479\pi$
$113$	−8.71719			−0.820044			−0.410022	+	0.912076i	$0.634479\pi$
$114$	−0.316239	−	7.17044i	−0.0296185	−	0.671573i
$115$	3.87057			0.360932
$116$	3.10656	+	5.38072i	0.288437	+	0.499588i
$117$	−1.23994	−	2.14764i	−0.114633	−	0.198549i
$118$	−7.02323	+	12.1646i	−0.646541	+	1.11984i
$119$	−17.0863	−	29.5943i	−1.56629	−	2.71290i
$120$	1.06097	−	1.83766i	0.0968530	−	0.167754i
$121$	0.842790			0.0766172
$122$	−13.5061			−1.22278
$123$	2.64661	−	4.58406i	0.238637	−	0.413331i
$124$	0.150322	−	0.260366i	0.0134994	−	0.0233816i
$125$	1.00000			0.0894427
$126$	−7.37662			−0.657161
$127$	2.28867	−	3.96410i	0.203087	−	0.351757i	−0.746435	−	0.665459i	$-0.768236\pi$
$127$	2.28867	−	3.96410i	0.203087	−	0.351757i	0.949522	+	0.313702i	$0.101569\pi$
$128$	6.72584	+	11.6495i	0.594486	+	1.02968i
$129$	1.23994	−	2.14764i	0.109171	−	0.189089i
$130$	2.04170	+	3.53633i	0.179069	+	0.310156i
$131$	10.3364	+	17.9031i	0.903094	+	1.56420i	0.823456	+	0.567380i	$0.192043\pi$
$131$	10.3364	+	17.9031i	0.903094	+	1.56420i	0.0796380	+	0.996824i	$0.474624\pi$
$132$	2.44791			0.213064
$133$	−16.4646	+	10.4993i	−1.42766	+	0.910405i
$134$	15.8644			1.37047
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$	−8.09309	−	14.0176i	−0.693976	−	1.20200i
$137$	−8.81400	+	15.2663i	−0.753031	+	1.30429i	0.193317	+	0.981136i	$0.438075\pi$
$137$	−8.81400	+	15.2663i	−0.753031	+	1.30429i	−0.946347	+	0.323151i	$0.895258\pi$
$138$	−3.18666	−	5.51946i	−0.271266	−	0.469847i
$139$	−5.86728	+	10.1624i	−0.497656	+	0.861966i	−0.999996	−	0.00270444i	$-0.999139\pi$
$139$	−5.86728	+	10.1624i	−0.497656	+	0.861966i	0.502340	+	0.864670i	$0.332472\pi$
$140$	3.18666			0.269322
$141$	0.677330			0.0570415
$142$	−3.17128	+	5.49282i	−0.266128	+	0.460947i
$143$	4.26705	−	7.39075i	0.356829	−	0.618045i
$144$	−4.91667			−0.409722
$145$	−8.73456			−0.725365
$146$	13.8193	−	23.9358i	1.14370	−	1.98094i
$147$	6.53467	+	11.3184i	0.538970	+	0.933524i
$148$	−1.38799	+	2.40407i	−0.114092	+	0.197613i
$149$	10.7824	+	18.6757i	0.883332	+	1.52998i	0.847613	+	0.530614i	$0.178039\pi$
$149$	10.7824	+	18.6757i	0.883332	+	1.52998i	0.0357187	+	0.999362i	$0.488628\pi$
$150$	−0.823305	−	1.42601i	−0.0672226	−	0.116433i
$151$	18.3102			1.49006			0.745032	−	0.667029i	$-0.232434\pi$
$151$	18.3102			1.49006			0.745032	+	0.667029i	$0.232434\pi$
$152$	−7.79862	+	4.97311i	−0.632551	+	0.403372i
$153$	7.62799			0.616687
$154$	−12.6927	−	21.9844i	−1.02281	−	1.77156i
$155$	0.211327	+	0.366029i	0.0169742	+	0.0294001i
$156$	0.882003	−	1.52767i	0.0706167	−	0.122312i
$157$	5.71527	+	9.89914i	0.456128	+	0.790038i	0.998752	−	0.0499382i	$-0.0159024\pi$
$157$	5.71527	+	9.89914i	0.456128	+	0.790038i	−0.542624	+	0.839976i	$0.682569\pi$
$158$	9.98278	−	17.2907i	0.794187	−	1.37557i
$159$	−11.4986			−0.911895
$160$	3.85195			0.304524
$161$	−8.66984	+	15.0166i	−0.683279	+	1.18347i
$162$	0.823305	−	1.42601i	0.0646850	−	0.112038i
$163$	−8.19876			−0.642177			−0.321088	−	0.947049i	$-0.604049\pi$
$163$	−8.19876			−0.642177			−0.321088	+	0.947049i	$0.604049\pi$
$164$	3.76521			0.294014
$165$	−1.72067	+	2.98028i	−0.133954	+	0.232015i
$166$	−1.67835	−	2.90698i	−0.130265	−	0.225625i
$167$	4.42206	−	7.65924i	0.342189	−	0.592690i	−0.642650	−	0.766160i	$-0.722165\pi$
$167$	4.42206	−	7.65924i	0.342189	−	0.592690i	0.984839	+	0.173471i	$0.0554982\pi$
$168$	4.75303	+	8.23248i	0.366704	+	0.635150i
$169$	3.42510	+	5.93244i	0.263469	+	0.456342i
$170$	−12.5603			−0.963334
$171$	−0.192054	−	4.35467i	−0.0146868	−	0.333010i
$172$	1.76401			0.134504
$173$	−8.77310	−	15.1955i	−0.667007	−	1.15529i	−0.978737	−	0.205119i	$-0.934242\pi$
$173$	−8.77310	−	15.1955i	−0.667007	−	1.15529i	0.311731	−	0.950171i	$-0.399091\pi$
$174$	7.19121	+	12.4555i	0.545164	+	0.944252i
$175$	−2.23994	+	3.87969i	−0.169324	+	0.293277i
$176$	−8.45995	−	14.6531i	−0.637693	−	1.10452i
$177$	−4.26526	+	7.38765i	−0.320597	+	0.555290i
$178$	5.17877			0.388165
$179$	4.30890			0.322062			0.161031	−	0.986949i	$-0.448518\pi$
$179$	4.30890			0.322062			0.161031	+	0.986949i	$0.448518\pi$
$180$	−0.355663	+	0.616027i	−0.0265096	+	0.0459159i
$181$	−3.17193	+	5.49395i	−0.235768	+	0.408362i	−0.959496	−	0.281724i	$-0.909094\pi$
$181$	−3.17193	+	5.49395i	−0.235768	+	0.408362i	0.723728	+	0.690086i	$0.242427\pi$
$182$	−18.2931			−1.35598
$183$	−8.20233			−0.606334
$184$	−4.10656	+	7.11277i	−0.302740	+	0.524361i
$185$	−1.95127	−	3.37969i	−0.143460	−	0.248480i
$186$	0.347973	−	0.602707i	0.0255146	−	0.0441926i
$187$	13.1252	+	22.7336i	0.959813	+	1.66244i
$188$	0.240901	+	0.417254i	0.0175695	+	0.0304313i
$189$	−4.47988			−0.325863
$190$	0.316239	+	7.17044i	0.0229424	+	0.520198i
$191$	0.845796			0.0611997			0.0305998	−	0.999532i	$-0.490258\pi$
$191$	0.845796			0.0611997			0.0305998	+	0.999532i	$0.490258\pi$
$192$	1.74534	+	3.02301i	0.125959	+	0.218167i
$193$	6.59039	+	11.4149i	0.474387	+	0.821662i	0.999570	−	0.0293275i	$-0.00933658\pi$
$193$	6.59039	+	11.4149i	0.474387	+	0.821662i	−0.525183	+	0.850989i	$0.676003\pi$
$194$	1.64661	−	2.85201i	0.118220	−	0.204763i
$195$	1.23994	+	2.14764i	0.0887940	+	0.153796i
$196$	−4.64828	+	8.05106i	−0.332020	+	0.575076i
$197$	6.91212			0.492468			0.246234	−	0.969210i	$-0.420807\pi$
$197$	6.91212			0.492468			0.246234	+	0.969210i	$0.420807\pi$
$198$	5.66654			0.402703
$199$	6.69062	−	11.5885i	0.474285	−	0.821486i	−0.525281	−	0.850929i	$-0.676040\pi$
$199$	6.69062	−	11.5885i	0.474285	−	0.821486i	0.999566	+	0.0294426i	$0.00937321\pi$
$200$	−1.06097	+	1.83766i	−0.0750220	+	0.129942i
$201$	9.63457			0.679570
$202$	3.32398			0.233875
$203$	19.5649	−	33.8874i	1.37319	−	2.37843i
$204$	2.71300	+	4.69905i	0.189948	+	0.328999i
$205$	−2.64661	+	4.58406i	−0.184847	+	0.320165i
$206$	5.34241	+	9.25332i	0.372223	+	0.644710i
$207$	−1.93528	−	3.35201i	−0.134512	−	0.232981i
$208$	−12.1927			−0.845415
$209$	12.6477	−	8.06531i	0.874858	−	0.557889i
$210$	7.37662			0.509035
$211$	7.37512	+	12.7741i	0.507724	+	0.879404i	0.999960	+	0.00894190i	$0.00284633\pi$
$211$	7.37512	+	12.7741i	0.507724	+	0.879404i	−0.492236	+	0.870462i	$0.663820\pi$
$212$	−4.08962	−	7.08343i	−0.280876	−	0.486492i
$213$	−1.92594	+	3.33583i	−0.131963	+	0.228567i
$214$	3.26149	+	5.64906i	0.222951	+	0.386162i
$215$	−1.23994	+	2.14764i	−0.0845632	+	0.146468i
$216$	−2.12194			−0.144380
$217$	−1.89344			−0.128535
$218$	−2.44360	+	4.23244i	−0.165501	+	0.286657i
$219$	8.39260	−	14.5364i	0.567120	−	0.982280i
$220$	−2.44791			−0.165038
$221$	18.9165			1.27246
$222$	−3.21298	+	5.56504i	−0.215641	+	0.373501i
$223$	1.14417	+	1.98176i	0.0766192	+	0.132708i	0.901789	−	0.432176i	$-0.142254\pi$
$223$	1.14417	+	1.98176i	0.0766192	+	0.132708i	−0.825170	+	0.564884i	$0.808921\pi$
$224$	−8.62814	+	14.9444i	−0.576492	+	0.998513i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	−7.17691	−	12.4308i	−0.477401	−	0.826882i
$227$	−4.19493			−0.278427			−0.139214	−	0.990262i	$-0.544457\pi$
$227$	−4.19493			−0.278427			−0.139214	+	0.990262i	$0.544457\pi$
$228$	2.61429	−	1.66711i	0.173135	−	0.110407i
$229$	−26.2742			−1.73625			−0.868123	−	0.496348i	$-0.834674\pi$
$229$	−26.2742			−1.73625			−0.868123	+	0.496348i	$0.834674\pi$
$230$	3.18666	+	5.51946i	0.210122	+	0.363942i
$231$	−7.70839	−	13.3513i	−0.507175	−	0.878452i
$232$	9.26712	−	16.0511i	0.608416	−	1.05381i
$233$	2.78125	+	4.81726i	0.182206	+	0.315589i	0.942631	−	0.333836i	$-0.108343\pi$
$233$	2.78125	+	4.81726i	0.182206	+	0.315589i	−0.760426	+	0.649425i	$0.775010\pi$
$234$	2.04170	−	3.53633i	0.133470	−	0.231177i
$235$	−0.677330			−0.0441841
$236$	−6.06799			−0.394993
$237$	6.06262	−	10.5008i	0.393810	−	0.682098i
$238$	28.1344	−	48.7302i	1.82368	−	3.15871i
$239$	−6.84901			−0.443026			−0.221513	−	0.975157i	$-0.571099\pi$
$239$	−6.84901			−0.443026			−0.221513	+	0.975157i	$0.571099\pi$
$240$	4.91667			0.317370
$241$	−7.42122	+	12.8539i	−0.478043	+	0.827994i	−0.999683	−	0.0251714i	$-0.991987\pi$
$241$	−7.42122	+	12.8539i	−0.478043	+	0.827994i	0.521641	+	0.853165i	$0.325320\pi$
$242$	0.693873	+	1.20182i	0.0446039	+	0.0772561i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−2.91727	−	5.05286i	−0.186759	−	0.323476i
$245$	−6.53467	−	11.3184i	−0.417484	−	0.723104i
$246$	8.71588			0.555704
$247$	−0.476272	−	10.7991i	−0.0303044	−	0.687127i
$248$	−0.896847			−0.0569498
$249$	−1.01927	−	1.76543i	−0.0645938	−	0.111880i
$250$	0.823305	+	1.42601i	0.0520704	+	0.0901886i
$251$	2.40128	−	4.15913i	0.151567	−	0.262522i	−0.780237	−	0.625484i	$-0.784901\pi$
$251$	2.40128	−	4.15913i	0.151567	−	0.262522i	0.931804	+	0.362962i	$0.118235\pi$
$252$	−1.59333	−	2.75973i	−0.100370	−	0.173847i
$253$	6.65996	−	11.5354i	0.418708	−	0.725224i
$254$	7.53711			0.472920
$255$	−7.62799			−0.477684
$256$	−7.58417	+	13.1362i	−0.474011	+	0.821010i
$257$	−1.74862	+	3.02871i	−0.109076	+	0.188926i	−0.915396	−	0.402554i	$-0.868123\pi$
$257$	−1.74862	+	3.02871i	−0.109076	+	0.188926i	0.806320	+	0.591479i	$0.201456\pi$
$258$	4.08340			0.254221
$259$	17.4829			1.08633
$260$	−0.882003	+	1.52767i	−0.0546995	+	0.0947423i
$261$	4.36728	+	7.56435i	0.270328	+	0.468221i
$262$	−17.0200	+	29.4795i	−1.05150	+	1.82125i
$263$	2.61621	+	4.53141i	0.161322	+	0.279419i	0.935343	−	0.353741i	$-0.115091\pi$
$263$	2.61621	+	4.53141i	0.161322	+	0.279419i	−0.774021	+	0.633160i	$0.781757\pi$
$264$	−3.65116	−	6.32399i	−0.224713	−	0.389215i
$265$	11.4986			0.706351
$266$	−28.5274	−	14.8344i	−1.74913	−	0.909558i
$267$	3.14511			0.192477
$268$	3.42667	+	5.93516i	0.209317	+	0.362547i
$269$	7.94917	+	13.7684i	0.484670	+	0.839472i	0.999845	−	0.0176124i	$-0.00560650\pi$
$269$	7.94917	+	13.7684i	0.484670	+	0.839472i	−0.515175	+	0.857085i	$0.672273\pi$
$270$	−0.823305	+	1.42601i	−0.0501048	+	0.0867840i
$271$	−4.99789	−	8.65661i	−0.303600	−	0.525851i	0.673348	−	0.739325i	$-0.264855\pi$
$271$	−4.99789	−	8.65661i	−0.303600	−	0.525851i	−0.976949	+	0.213474i	$0.931522\pi$
$272$	18.7522	−	32.4797i	1.13702	−	1.96937i
$273$	−11.1096			−0.672382
$274$	−29.0264			−1.75355
$275$	1.72067	−	2.98028i	0.103760	−	0.179718i
$276$	1.37662	−	2.38437i	0.0828627	−	0.143522i
$277$	4.08619			0.245515			0.122758	−	0.992437i	$-0.460826\pi$
$277$	4.08619			0.245515			0.122758	+	0.992437i	$0.460826\pi$
$278$	−19.3222			−1.15887
$279$	0.211327	−	0.366029i	0.0126518	−	0.0219136i
$280$	−4.75303	−	8.23248i	−0.284048	−	0.491985i
$281$	5.81920	−	10.0792i	0.347144	−	0.601272i	−0.638596	−	0.769542i	$-0.720485\pi$
$281$	5.81920	−	10.0792i	0.347144	−	0.601272i	0.985741	+	0.168270i	$0.0538180\pi$
$282$	0.557649	+	0.965877i	0.0332075	+	0.0575171i
$283$	−2.17910	−	3.77432i	−0.129534	−	0.224360i	0.793962	−	0.607967i	$-0.208015\pi$
$283$	−2.17910	−	3.77432i	−0.129534	−	0.224360i	−0.923496	+	0.383607i	$0.874682\pi$
$284$	−2.73995			−0.162586
$285$	0.192054	+	4.35467i	0.0113763	+	0.257948i
$286$	14.0523			0.830932
$287$	−11.8565	−	20.5361i	−0.699867	−	1.21221i
$288$	−1.92598	−	3.33589i	−0.113489	−	0.196569i
$289$	−20.5932	+	35.6684i	−1.21136	+	2.09814i
$290$	−7.19121	−	12.4555i	−0.422282	−	0.731414i
$291$	1.00000	−	1.73205i	0.0586210	−	0.101535i
$292$	11.9398			0.698722
$293$	−7.20233			−0.420765			−0.210382	−	0.977619i	$-0.567471\pi$
$293$	−7.20233			−0.420765			−0.210382	+	0.977619i	$0.567471\pi$
$294$	−10.7600	+	18.6370i	−0.627539	+	1.08693i
$295$	4.26526	−	7.38765i	0.248333	−	0.430126i
$296$	8.28096			0.481321
$297$	3.44134			0.199687
$298$	−17.7545	+	30.7517i	−1.02849	+	1.78140i
$299$	−4.79927	−	8.31258i	−0.277549	−	0.480729i
$300$	0.355663	−	0.616027i	0.0205342	−	0.0355663i
$301$	−5.55478	−	9.62117i	−0.320172	−	0.554555i
$302$	15.0749	+	26.1105i	0.867463	+	1.50249i
$303$	2.01868			0.115970
$304$	−19.0141	−	9.88746i	−1.09053	−	0.567085i
$305$	8.20233			0.469664
$306$	6.28017	+	10.8776i	0.359013	+	0.621829i
$307$	−8.14056	−	14.0999i	−0.464606	−	0.804722i	0.534577	−	0.845120i	$-0.320471\pi$
$307$	−8.14056	−	14.0999i	−0.464606	−	0.804722i	−0.999184	+	0.0403979i	$0.987137\pi$
$308$	5.48318	−	9.49715i	0.312433	−	0.541150i
$309$	3.24449	+	5.61962i	0.184573	+	0.319689i
$310$	−0.347973	+	0.602707i	−0.0197635	+	0.0342315i
$311$	−4.07709			−0.231191			−0.115595	−	0.993296i	$-0.536878\pi$
$311$	−4.07709			−0.231191			−0.115595	+	0.993296i	$0.536878\pi$
$312$	−5.26217			−0.297911
$313$	10.7777	−	18.6674i	0.609189	−	1.05515i	−0.382186	−	0.924086i	$-0.624828\pi$
$313$	10.7777	−	18.6674i	0.609189	−	1.05515i	0.991374	−	0.131060i	$-0.0418382\pi$
$314$	−9.41083	+	16.3000i	−0.531084	+	0.919864i
$315$	4.47988			0.252413
$316$	8.62501			0.485195
$317$	7.13339	−	12.3554i	0.400651	−	0.693948i	−0.593154	−	0.805089i	$-0.702117\pi$
$317$	7.13339	−	12.3554i	0.400651	−	0.693948i	0.993805	+	0.111141i	$0.0354506\pi$
$318$	−9.46683	−	16.3970i	−0.530873	−	0.919500i
$319$	−15.0293	+	26.0315i	−0.841478	+	1.45748i
$320$	−1.74534	−	3.02301i	−0.0975672	−	0.168991i
$321$	1.98073	+	3.43072i	0.110553	+	0.191484i
$322$	−28.5517			−1.59112
$323$	29.4996	+	15.3400i	1.64140	+	0.853539i
$324$	0.711327			0.0395182
$325$	−1.23994	−	2.14764i	−0.0687795	−	0.119130i
$326$	−6.75008	−	11.6915i	−0.373853	−	0.647532i
$327$	−1.48402	+	2.57039i	−0.0820663	+	0.142143i
$328$	−5.61596	−	9.72712i	−0.310089	−	0.537091i
$329$	1.51718	−	2.62783i	0.0836448	−	0.144877i
$330$	−5.66654			−0.311933
$331$	23.9646			1.31722			0.658608	−	0.752486i	$-0.271146\pi$
$331$	23.9646			1.31722			0.658608	+	0.752486i	$0.271146\pi$
$332$	0.725036	−	1.25580i	0.0397915	−	0.0689209i
$333$	−1.95127	+	3.37969i	−0.106929	+	0.185206i
$334$	14.5628			0.796843
$335$	−9.63457			−0.526393
$336$	−11.0130	+	19.0751i	−0.600811	+	1.04063i
$337$	−16.3204	−	28.2678i	−0.889029	−	1.53984i	−0.841025	−	0.540996i	$-0.818048\pi$
$337$	−16.3204	−	28.2678i	−0.889029	−	1.53984i	−0.0480033	−	0.998847i	$-0.515286\pi$
$338$	−5.63980	+	9.76842i	−0.306765	+	0.531332i
$339$	−4.35859	−	7.54931i	−0.236726	−	0.410022i
$340$	−2.71300	−	4.69905i	−0.147133	−	0.254842i
$341$	1.45449			0.0787652
$342$	6.05166	−	3.85909i	0.327236	−	0.208676i
$343$	27.1899			1.46812
$344$	−2.63108	−	4.55717i	−0.141858	−	0.245706i
$345$	1.93528	+	3.35201i	0.104192	+	0.180466i
$346$	14.4459	−	25.0210i	0.776616	−	1.34514i
$347$	−8.41457	−	14.5745i	−0.451718	−	0.782398i	0.546775	−	0.837280i	$-0.315855\pi$
$347$	−8.41457	−	14.5745i	−0.451718	−	0.782398i	−0.998493	+	0.0548811i	$0.982522\pi$
$348$	−3.10656	+	5.38072i	−0.166529	+	0.288437i
$349$	2.46947			0.132188			0.0660939	−	0.997813i	$-0.478946\pi$
$349$	2.46947			0.132188			0.0660939	+	0.997813i	$0.478946\pi$
$350$	−7.37662			−0.394297
$351$	1.23994	−	2.14764i	0.0661831	−	0.114633i
$352$	6.62793	−	11.4799i	0.353270	−	0.611881i
$353$	27.7653			1.47780			0.738900	−	0.673815i	$-0.235346\pi$
$353$	27.7653			1.47780			0.738900	+	0.673815i	$0.235346\pi$
$354$	−14.0465			−0.746561
$355$	1.92594	−	3.33583i	0.102218	−	0.177048i
$356$	1.11860	+	1.93747i	0.0592857	+	0.102686i
$357$	17.0863	−	29.5943i	0.904300	−	1.56629i
$358$	3.54754	+	6.14452i	0.187493	+	0.324748i
$359$	10.0245	+	17.3629i	0.529072	+	0.916379i	0.999425	+	0.0339009i	$0.0107931\pi$
$359$	10.0245	+	17.3629i	0.529072	+	0.916379i	−0.470354	+	0.882478i	$0.655874\pi$
$360$	2.12194			0.111836
$361$	8.01455	−	17.2269i	0.421818	−	0.906680i
$362$	−10.4459			−0.549023
$363$	0.421395	+	0.729877i	0.0221175	+	0.0383086i
$364$	−3.95127	−	6.84380i	−0.207103	−	0.358712i
$365$	−8.39260	+	14.5364i	−0.439289	+	0.760871i
$366$	−6.75303	−	11.6966i	−0.352986	−	0.611390i
$367$	3.33741	−	5.78056i	0.174211	−	0.301743i	−0.765677	−	0.643225i	$-0.777596\pi$
$367$	3.33741	−	5.78056i	0.174211	−	0.301743i	0.939888	+	0.341483i	$0.110929\pi$
$368$	−19.0303			−0.992023
$369$	5.29322			0.275554
$370$	3.21298	−	5.56504i	0.167035	−	0.289313i
$371$	−25.7561	+	44.6109i	−1.33719	+	2.31608i
$372$	0.300645			0.0155877
$373$	−12.4380			−0.644014			−0.322007	−	0.946737i	$-0.604357\pi$
$373$	−12.4380			−0.644014			−0.322007	+	0.946737i	$0.604357\pi$
$374$	−21.6122	+	37.4334i	−1.11754	+	1.93563i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	0.718628	−	1.24470i	0.0370604	−	0.0641905i
$377$	10.8303	+	18.7587i	0.557790	+	0.966121i
$378$	−3.68831	−	6.38834i	−0.189706	−	0.328581i
$379$	21.3994			1.09921			0.549607	−	0.835423i	$-0.314777\pi$
$379$	21.3994			1.09921			0.549607	+	0.835423i	$0.314777\pi$
$380$	−2.61429	+	1.66711i	−0.134110	+	0.0855207i
$381$	4.57735			0.234505
$382$	0.696349	+	1.20611i	0.0356283	+	0.0617100i
$383$	−5.35405	−	9.27348i	−0.273579	−	0.473853i	0.696197	−	0.717851i	$-0.254874\pi$
$383$	−5.35405	−	9.27348i	−0.273579	−	0.473853i	−0.969776	+	0.243998i	$0.921541\pi$
$384$	−6.72584	+	11.6495i	−0.343227	+	0.594486i
$385$	7.70839	+	13.3513i	0.392856	+	0.680446i
$386$	−10.8518	+	18.7959i	−0.552342	+	0.956685i
$387$	2.47988			0.126059
$388$	1.42265			0.0722243
$389$	1.75466	−	3.03917i	0.0889650	−	0.154092i	−0.818109	−	0.575063i	$-0.804977\pi$
$389$	1.75466	−	3.03917i	0.0889650	−	0.154092i	0.907074	+	0.420971i	$0.138311\pi$
$390$	−2.04170	+	3.53633i	−0.103385	+	0.179069i
$391$	29.5247			1.49313
$392$	27.7324			1.40070
$393$	−10.3364	+	17.9031i	−0.521401	+	0.903094i
$394$	5.69079	+	9.85673i	0.286698	+	0.496575i
$395$	−6.06262	+	10.5008i	−0.305044	+	0.528351i
$396$	1.22396	+	2.11996i	0.0615062	+	0.106532i
$397$	−15.5995	−	27.0191i	−0.782916	−	1.35605i	−0.930236	−	0.366961i	$-0.880398\pi$
$397$	−15.5995	−	27.0191i	−0.782916	−	1.35605i	0.147321	−	0.989089i	$-0.452935\pi$
$398$	22.0337			1.10445
$399$	−17.3249	−	9.00908i	−0.867332	−	0.451018i
$400$	−4.91667			−0.245833
$401$	9.87661	+	17.1068i	0.493214	+	0.854272i	0.999969	−	0.00781786i	$-0.00248853\pi$
$401$	9.87661	+	17.1068i	0.493214	+	0.854272i	−0.506755	+	0.862090i	$0.669155\pi$
$402$	7.93220	+	13.7390i	0.395622	+	0.685237i
$403$	0.524065	−	0.907708i	0.0261055	−	0.0452161i
$404$	0.717971	+	1.24356i	0.0357204	+	0.0618696i
$405$	−0.500000	+	0.866025i	−0.0248452	+	0.0430331i
$406$	64.4315			3.19768
$407$	−13.4299			−0.665697
$408$	8.09309	−	14.0176i	0.400667	−	0.693976i
$409$	1.06951	−	1.85244i	0.0528838	−	0.0915974i	−0.838372	−	0.545099i	$-0.816492\pi$
$409$	1.06951	−	1.85244i	0.0528838	−	0.0915974i	0.891255	+	0.453502i	$0.149825\pi$
$410$	−8.71588			−0.430446
$411$	−17.6280			−0.869525
$412$	−2.30789	+	3.99739i	−0.113702	+	0.196937i
$413$	19.1079	+	33.0958i	0.940237	+	1.62854i
$414$	3.18666	−	5.51946i	0.156616	−	0.271266i
$415$	1.01927	+	1.76543i	0.0500341	+	0.0866616i
$416$	−4.77619	−	8.27260i	−0.234172	−	0.405598i
$417$	−11.7346			−0.574644
$418$	21.9141	+	11.3955i	1.07185	+	0.557370i
$419$	−5.70341			−0.278630			−0.139315	−	0.990248i	$-0.544490\pi$
$419$	−5.70341			−0.278630			−0.139315	+	0.990248i	$0.544490\pi$
$420$	1.59333	+	2.75973i	0.0777465	+	0.134661i
$421$	−19.5265	−	33.8209i	−0.951664	−	1.64833i	−0.741823	−	0.670595i	$-0.766039\pi$
$421$	−19.5265	−	33.8209i	−0.951664	−	1.64833i	−0.209841	−	0.977736i	$-0.567295\pi$
$422$	−12.1439	+	21.0339i	−0.591158	+	1.02392i
$423$	0.338665	+	0.586585i	0.0164665	+	0.0285207i
$424$	−12.1996	+	21.1304i	−0.592467	+	1.02618i
$425$	7.62799			0.370012
$426$	−6.34256			−0.307298
$427$	−18.3727	+	31.8225i	−0.889119	+	1.54000i
$428$	−1.40894	+	2.44036i	−0.0681039	+	0.117959i
$429$	8.53410			0.412030
$430$	−4.08340			−0.196919
$431$	−0.868782	+	1.50477i	−0.0418477	+	0.0724824i	−0.886191	−	0.463321i	$-0.846658\pi$
$431$	−0.868782	+	1.50477i	−0.0418477	+	0.0724824i	0.844343	+	0.535803i	$0.179991\pi$
$432$	−2.45833	−	4.25796i	−0.118277	−	0.204861i
$433$	−11.8156	+	20.4652i	−0.567821	+	0.983495i	0.428960	+	0.903324i	$0.358880\pi$
$433$	−11.8156	+	20.4652i	−0.567821	+	0.983495i	−0.996781	+	0.0801716i	$0.974453\pi$
$434$	−1.55888	−	2.70005i	−0.0748285	−	0.129607i
$435$	−4.36728	−	7.56435i	−0.209395	−	0.362683i
$436$	−2.11124			−0.101110
$437$	−0.743359	−	16.8550i	−0.0355597	−	0.806285i
$438$	27.6387			1.32063
$439$	1.58465	+	2.74469i	0.0756310	+	0.130997i	0.901360	−	0.433070i	$-0.142570\pi$
$439$	1.58465	+	2.74469i	0.0756310	+	0.130997i	−0.825730	+	0.564066i	$0.809236\pi$
$440$	3.65116	+	6.32399i	0.174062	+	0.301485i
$441$	−6.53467	+	11.3184i	−0.311175	+	0.538970i
$442$	15.5741	+	26.9751i	0.740783	+	1.28307i
$443$	−11.5916	+	20.0773i	−0.550736	+	0.953902i	0.447486	+	0.894291i	$0.352319\pi$
$443$	−11.5916	+	20.0773i	−0.550736	+	0.953902i	−0.998222	+	0.0596114i	$0.981014\pi$
$444$	−2.77598			−0.131742
$445$	−3.14511			−0.149092
$446$	−1.88400	+	3.26318i	−0.0892100	+	0.154516i
$447$	−10.7824	+	18.6757i	−0.509992	+	0.883332i
$448$	15.6378			0.738816
$449$	13.2505			0.625328			0.312664	−	0.949864i	$-0.398779\pi$
$449$	13.2505			0.625328			0.312664	+	0.949864i	$0.398779\pi$
$450$	0.823305	−	1.42601i	0.0388110	−	0.0672226i
$451$	9.10788	+	15.7753i	0.428873	+	0.742830i
$452$	3.10038	−	5.37002i	0.145830	−	0.252585i
$453$	9.15510	+	15.8571i	0.430144	+	0.745032i
$454$	−3.45371	−	5.98200i	−0.162091	−	0.280749i
$455$	11.1096			0.520825
$456$	−8.20614	−	4.26725i	−0.384288	−	0.199832i
$457$	4.13077			0.193229			0.0966146	−	0.995322i	$-0.469199\pi$
$457$	4.13077			0.193229			0.0966146	+	0.995322i	$0.469199\pi$
$458$	−21.6317	−	37.4672i	−1.01078	−	1.75073i
$459$	3.81400	+	6.60604i	0.178022	+	0.308343i
$460$	−1.37662	+	2.38437i	−0.0641852	+	0.111172i
$461$	−10.9292	−	18.9300i	−0.509026	−	0.881658i	−0.999945	−	0.0104535i	$-0.996673\pi$
$461$	−10.9292	−	18.9300i	−0.509026	−	0.881658i	0.490920	−	0.871205i	$-0.336661\pi$
$462$	12.6927	−	21.9844i	0.590518	−	1.02281i
$463$	30.9461			1.43819			0.719094	−	0.694913i	$-0.244557\pi$
$463$	30.9461			1.43819			0.719094	+	0.694913i	$0.244557\pi$
$464$	42.9449			1.99367
$465$	−0.211327	+	0.366029i	−0.00980005	+	0.0169742i
$466$	−4.57963	+	7.93216i	−0.212147	+	0.367450i
$467$	0.394259			0.0182441			0.00912207	−	0.999958i	$-0.497096\pi$
$467$	0.394259			0.0182441			0.00912207	+	0.999958i	$0.497096\pi$
$468$	1.76401			0.0815412
$469$	21.5809	−	37.3792i	0.996512	−	1.72601i
$470$	−0.557649	−	0.965877i	−0.0257224	−	0.0445526i
$471$	−5.71527	+	9.89914i	−0.263346	+	0.456128i
$472$	9.05065	+	15.6762i	0.416590	+	0.721555i
$473$	4.26705	+	7.39075i	0.196199	+	0.339827i
$474$	19.9656			0.917048
$475$	−0.192054	−	4.35467i	−0.00881205	−	0.199806i
$476$	24.3078			1.11415
$477$	−5.74928	−	9.95805i	−0.263242	−	0.455948i
$478$	−5.63883	−	9.76674i	−0.257914	−	0.446720i
$479$	3.52119	−	6.09888i	0.160887	−	0.278665i	−0.774300	−	0.632819i	$-0.781898\pi$
$479$	3.52119	−	6.09888i	0.160887	−	0.278665i	0.935187	+	0.354154i	$0.115231\pi$
$480$	1.92598	+	3.33589i	0.0879084	+	0.152262i
$481$	−4.83891	+	8.38124i	−0.220635	+	0.382152i
$482$	−24.4397			−1.11320
$483$	−17.3397			−0.788983
$484$	−0.299749	+	0.519181i	−0.0136250	+	0.0235991i
$485$	−1.00000	+	1.73205i	−0.0454077	+	0.0786484i
$486$	1.64661			0.0746918
$487$	0.689174			0.0312295			0.0156147	−	0.999878i	$-0.495029\pi$
$487$	0.689174			0.0312295			0.0156147	+	0.999878i	$0.495029\pi$
$488$	−8.70244	+	15.0731i	−0.393941	+	0.682326i
$489$	−4.09938	−	7.10034i	−0.185380	−	0.321088i
$490$	10.7600	−	18.6370i	0.486089	−	0.841932i
$491$	−4.54736	−	7.87626i	−0.205219	−	0.355450i	0.744983	−	0.667083i	$-0.232457\pi$
$491$	−4.54736	−	7.87626i	−0.205219	−	0.355450i	−0.950203	+	0.311633i	$0.899124\pi$
$492$	1.88261	+	3.26077i	0.0848744	+	0.147007i
$493$	−66.6272			−3.00074
$494$	15.0074	−	9.57008i	0.675215	−	0.430578i
$495$	−3.44134			−0.154677
$496$	−1.03902	−	1.79964i	−0.0466535	−	0.0808063i
$497$	8.62799	+	14.9441i	0.387018	+	0.670336i
$498$	1.67835	−	2.90698i	0.0752084	−	0.130265i
$499$	11.5404	+	19.9886i	0.516619	+	0.894811i	0.999814	+	0.0192976i	$0.00614300\pi$
$499$	11.5404	+	19.9886i	0.516619	+	0.894811i	−0.483195	+	0.875513i	$0.660524\pi$
$500$	−0.355663	+	0.616027i	−0.0159058	+	0.0275496i
$501$	8.84413			0.395126
$502$	7.90793			0.352948
$503$	10.5982	−	18.3567i	0.472552	−	0.818483i	−0.526955	−	0.849893i	$-0.676666\pi$
$503$	10.5982	−	18.3567i	0.472552	−	0.818483i	0.999507	+	0.0314099i	$0.00999972\pi$
$504$	−4.75303	+	8.23248i	−0.211717	+	0.366704i
$505$	−2.01868			−0.0898302
$506$	21.9327			0.975029
$507$	−3.42510	+	5.93244i	−0.152114	+	0.263469i
$508$	1.62799	+	2.81977i	0.0722306	+	0.125107i
$509$	−9.12649	+	15.8075i	−0.404525	+	0.700657i	−0.994266	−	0.106935i	$-0.965896\pi$
$509$	−9.12649	+	15.8075i	−0.404525	+	0.700657i	0.589741	+	0.807592i	$0.299230\pi$
$510$	−6.28017	−	10.8776i	−0.278091	−	0.481667i
$511$	−37.5979	−	65.1214i	−1.66323	−	2.88080i
$512$	1.92701			0.0851627
$513$	3.67522	−	2.34366i	0.162265	−	0.103475i
$514$	−5.75861			−0.254001
$515$	−3.24449	−	5.61962i	−0.142969	−	0.247630i
$516$	0.882003	+	1.52767i	0.0388280	+	0.0672521i
$517$	−1.16546	+	2.01864i	−0.0512569	+	0.0887795i
$518$	14.3938	+	24.9307i	0.632425	+	1.09539i
$519$	8.77310	−	15.1955i	0.385096	−	0.667007i
$520$	5.26217			0.230761
$521$	−34.4874			−1.51092			−0.755461	−	0.655194i	$-0.772587\pi$
$521$	−34.4874			−1.51092			−0.755461	+	0.655194i	$0.772587\pi$
$522$	−7.19121	+	12.4555i	−0.314751	+	0.545164i
$523$	−8.06993	+	13.9775i	−0.352874	+	0.611195i	−0.986752	−	0.162238i	$-0.948129\pi$
$523$	−8.06993	+	13.9775i	−0.352874	+	0.611195i	0.633878	+	0.773433i	$0.281462\pi$
$524$	−14.7051			−0.642395
$525$	−4.47988			−0.195518
$526$	−4.30788	+	7.46147i	−0.187833	+	0.325336i
$527$	1.61200	+	2.79207i	0.0702198	+	0.121624i
$528$	8.45995	−	14.6531i	0.368172	−	0.637693i
$529$	4.00935	+	6.94440i	0.174320	+	0.301931i
$530$	9.46683	+	16.3970i	0.411213	+	0.712241i
$531$	−8.53053			−0.370193
$532$	−0.612011	−	13.8768i	−0.0265341	−	0.601637i
$533$	13.1266			0.568574
$534$	2.58938	+	4.48494i	0.112054	+	0.194083i
$535$	−1.98073	−	3.43072i	−0.0856343	−	0.148323i
$536$	10.2220	−	17.7050i	0.441523	−	0.764741i
$537$	2.15445	+	3.73161i	0.0929713	+	0.161031i
$538$	−13.0892	+	22.6711i	−0.564315	+	0.977423i
$539$	−44.9759			−1.93725
$540$	−0.711327			−0.0306106
$541$	−8.46634	+	14.6641i	−0.363996	+	0.630460i	−0.988615	−	0.150470i	$-0.951921\pi$
$541$	−8.46634	+	14.6641i	−0.363996	+	0.630460i	0.624618	+	0.780930i	$0.285255\pi$
$542$	8.22959	−	14.2541i	0.353491	−	0.612264i
$543$	−6.34387			−0.272242
$544$	29.3827			1.25977
$545$	1.48402	−	2.57039i	0.0635683	−	0.110104i
$546$	−9.14657	−	15.8423i	−0.391437	−	0.677989i
$547$	14.6871	−	25.4389i	0.627977	−	1.08769i	−0.359981	−	0.932960i	$-0.617217\pi$
$547$	14.6871	−	25.4389i	0.627977	−	1.08769i	0.987957	−	0.154728i	$-0.0494500\pi$
$548$	−6.26963	−	10.8593i	−0.267825	−	0.463887i
$549$	−4.10117	−	7.10343i	−0.175034	−	0.303167i
$550$	5.66654			0.241622
$551$	1.67751	+	38.0361i	0.0714643	+	1.62039i
$552$	−8.21312			−0.349574
$553$	−27.1598	−	47.0422i	−1.15495	−	2.00044i
$554$	3.36418	+	5.82693i	0.142930	+	0.247563i
$555$	1.95127	−	3.37969i	0.0828267	−	0.143460i
$556$	−4.17355	−	7.22880i	−0.176998	−	0.306570i
$557$	−4.29322	+	7.43608i	−0.181910	+	0.315077i	−0.942531	−	0.334119i	$-0.891561\pi$
$557$	−4.29322	+	7.43608i	−0.181910	+	0.315077i	0.760621	+	0.649196i	$0.224895\pi$
$558$	0.695946			0.0294617
$559$	6.14981			0.260109
$560$	11.0130	−	19.0751i	0.465386	−	0.806072i
$561$	−13.1252	+	22.7336i	−0.554148	+	0.959813i
$562$	19.1639			0.808381
$563$	2.59685			0.109444			0.0547221	−	0.998502i	$-0.482573\pi$
$563$	2.59685			0.109444			0.0547221	+	0.998502i	$0.482573\pi$
$564$	−0.240901	+	0.417254i	−0.0101438	+	0.0175695i
$565$	4.35859	+	7.54931i	0.183367	+	0.317602i
$566$	3.58814	−	6.21483i	0.150821	−	0.261229i
$567$	−2.23994	−	3.87969i	−0.0940687	−	0.162932i
$568$	4.08674	+	7.07844i	0.171476	+	0.297005i
$569$	−33.8768			−1.42019			−0.710094	−	0.704107i	$-0.751348\pi$
$569$	−33.8768			−1.42019			−0.710094	+	0.704107i	$0.751348\pi$
$570$	−6.05166	+	3.85909i	−0.253476	+	0.161640i
$571$	−10.6731			−0.446657			−0.223329	−	0.974743i	$-0.571692\pi$
$571$	−10.6731			−0.446657			−0.223329	+	0.974743i	$0.571692\pi$
$572$	3.03527	+	5.25724i	0.126911	+	0.219816i
$573$	0.422898	+	0.732481i	0.0176668	+	0.0305998i
$574$	19.5230	−	33.8149i	0.814876	−	1.41141i
$575$	−1.93528	−	3.35201i	−0.0807069	−	0.139788i
$576$	−1.74534	+	3.02301i	−0.0727223	+	0.125959i
$577$	−11.6607			−0.485440			−0.242720	−	0.970096i	$-0.578040\pi$
$577$	−11.6607			−0.485440			−0.242720	+	0.970096i	$0.578040\pi$
$578$	−67.8178			−2.82085
$579$	−6.59039	+	11.4149i	−0.273887	+	0.474387i
$580$	3.10656	−	5.38072i	0.128993	−	0.223422i
$581$	−9.13244			−0.378877
$582$	3.29322			0.136508
$583$	19.7852	−	34.2690i	0.819419	−	1.41928i
$584$	−17.8086	−	30.8454i	−0.736926	−	1.27639i
$585$	−1.23994	+	2.14764i	−0.0512652	+	0.0887940i
$586$	−5.92972	−	10.2706i	−0.244954	−	0.424274i
$587$	−20.1362	−	34.8770i	−0.831112	−	1.43953i	−0.897157	−	0.441711i	$-0.854372\pi$
$587$	−20.1362	−	34.8770i	−0.831112	−	1.43953i	0.0660456	−	0.997817i	$-0.478962\pi$
$588$	−9.29656			−0.383384
$589$	1.55335	−	0.990555i	0.0640045	−	0.0408151i
$590$	14.0465			0.578284
$591$	3.45606	+	5.98607i	0.142163	+	0.246234i
$592$	9.59373	+	16.6168i	0.394300	+	0.682948i
$593$	7.05130	−	12.2132i	0.289562	−	0.501537i	−0.684143	−	0.729348i	$-0.739824\pi$
$593$	7.05130	−	12.2132i	0.289562	−	0.501537i	0.973705	+	0.227811i	$0.0731569\pi$
$594$	2.83327	+	4.90737i	0.116250	+	0.201352i
$595$	−17.0863	+	29.5943i	−0.700468	+	1.21325i
$596$	−15.3397			−0.628338
$597$	13.3812			0.547657
$598$	7.90253	−	13.6876i	0.323159	−	0.559727i
$599$	5.24355	−	9.08209i	0.214246	−	0.371084i	−0.738793	−	0.673932i	$-0.764604\pi$
$599$	5.24355	−	9.08209i	0.214246	−	0.371084i	0.953039	+	0.302848i	$0.0979374\pi$
$600$	−2.12194			−0.0866280
$601$	21.0718			0.859539			0.429769	−	0.902939i	$-0.358595\pi$
$601$	21.0718			0.859539			0.429769	+	0.902939i	$0.358595\pi$
$602$	9.14657	−	15.8423i	0.372786	−	0.645685i
$603$	4.81729	+	8.34379i	0.196175	+	0.339785i
$604$	−6.51227	+	11.2796i	−0.264981	+	0.458960i
$605$	−0.421395	−	0.729877i	−0.0171321	−	0.0296737i
$606$	1.66199	+	2.87865i	0.0675138	+	0.116937i
$607$	−22.2759			−0.904149			−0.452074	−	0.891980i	$-0.649316\pi$
$607$	−22.2759			−0.904149			−0.452074	+	0.891980i	$0.649316\pi$
$608$	−0.739784	−	16.7740i	−0.0300022	−	0.680274i
$609$	39.1298			1.58562
$610$	6.75303	+	11.6966i	0.273422	+	0.473581i
$611$	0.839849	+	1.45466i	0.0339766	+	0.0588493i
$612$	−2.71300	+	4.69905i	−0.109666	+	0.189948i
$613$	8.94766	+	15.4978i	0.361393	+	0.625950i	0.988190	−	0.153232i	$-0.0489681\pi$
$613$	8.94766	+	15.4978i	0.361393	+	0.625950i	−0.626798	+	0.779182i	$0.715635\pi$
$614$	13.4043	−	23.2170i	0.540955	−	0.936961i
$615$	−5.29322			−0.213443
$616$	−32.7135			−1.31806
$617$	−8.81560	+	15.2691i	−0.354903	+	0.614710i	−0.987101	−	0.160097i	$-0.948819\pi$
$617$	−8.81560	+	15.2691i	−0.354903	+	0.614710i	0.632198	+	0.774806i	$0.282153\pi$
$618$	−5.34241	+	9.25332i	−0.214903	+	0.372223i
$619$	−49.2003			−1.97753			−0.988763	−	0.149490i	$-0.952237\pi$
$619$	−49.2003			−1.97753			−0.988763	+	0.149490i	$0.952237\pi$
$620$	−0.300645			−0.0120742
$621$	1.93528	−	3.35201i	0.0776603	−	0.134512i
$622$	−3.35669	−	5.81396i	−0.134591	−	0.233118i
$623$	7.04485	−	12.2020i	0.282246	−	0.488865i
$624$	−6.09637	−	10.5592i	−0.244050	−	0.422708i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	35.4932			1.41859
$627$	13.3086	+	6.92056i	0.531494	+	0.276380i
$628$	−8.13085			−0.324456
$629$	−14.8843	−	25.7803i	−0.593474	−	1.02793i
$630$	3.68831	+	6.38834i	0.146946	+	0.254518i
$631$	16.6592	−	28.8547i	0.663194	−	1.14869i	−0.316578	−	0.948567i	$-0.602534\pi$
$631$	16.6592	−	28.8547i	0.663194	−	1.14869i	0.979772	−	0.200119i	$-0.0641329\pi$
$632$	−12.8645	−	22.2820i	−0.511724	−	0.886332i
$633$	−7.37512	+	12.7741i	−0.293135	+	0.507724i
$634$	23.4918			0.932980
$635$	−4.57735			−0.181646
$636$	4.08962	−	7.08343i	0.162164	−	0.280876i
$637$	−16.2052	+	28.0682i	−0.642073	+	1.11210i
$638$	−49.4947			−1.95951
$639$	−3.85189			−0.152378
$640$	6.72584	−	11.6495i	0.265862	−	0.460487i
$641$	−6.61110	−	11.4508i	−0.261123	−	0.452278i	0.705418	−	0.708792i	$-0.250759\pi$
$641$	−6.61110	−	11.4508i	−0.261123	−	0.452278i	−0.966541	+	0.256514i	$0.917426\pi$
$642$	−3.26149	+	5.64906i	−0.128721	+	0.222951i
$643$	0.951267	+	1.64764i	0.0375143	+	0.0649767i	0.884173	−	0.467160i	$-0.154723\pi$
$643$	0.951267	+	1.64764i	0.0375143	+	0.0649767i	−0.846659	+	0.532136i	$0.821389\pi$
$644$	−6.16709	−	10.6817i	−0.243017	−	0.420918i
$645$	−2.47988			−0.0976452
$646$	2.41227	+	54.6961i	0.0949093	+	2.15199i
$647$	27.2141			1.06989			0.534947	−	0.844885i	$-0.320331\pi$
$647$	27.2141			1.06989			0.534947	+	0.844885i	$0.320331\pi$
$648$	−1.06097	−	1.83766i	−0.0416789	−	0.0721900i
$649$	−14.6782	−	25.4234i	−0.576170	−	0.997956i
$650$	2.04170	−	3.53633i	0.0800820	−	0.138706i
$651$	−0.946719	−	1.63977i	−0.0371048	−	0.0642675i
$652$	2.91600	−	5.05066i	0.114199	−	0.197799i
$653$	−43.6980			−1.71004			−0.855018	−	0.518599i	$-0.826454\pi$
$653$	−43.6980			−1.71004			−0.855018	+	0.518599i	$0.826454\pi$
$654$	−4.88720			−0.191104
$655$	10.3364	−	17.9031i	0.403876	−	0.699533i
$656$	13.0125	−	22.5383i	0.508053	−	0.879974i
$657$	16.7852			0.654853
$658$	4.99640			0.194780
$659$	3.43672	−	5.95258i	0.133876	−	0.231879i	−0.791292	−	0.611439i	$-0.790591\pi$
$659$	3.43672	−	5.95258i	0.133876	−	0.231879i	0.925167	+	0.379559i	$0.123924\pi$
$660$	−1.22396	−	2.11996i	−0.0476425	−	0.0825192i
$661$	−18.6491	+	32.3012i	−0.725367	+	1.25637i	0.233456	+	0.972367i	$0.424996\pi$
$661$	−18.6491	+	32.3012i	−0.725367	+	1.25637i	−0.958823	+	0.284005i	$0.908337\pi$
$662$	19.7302	+	34.1737i	0.766837	+	1.32820i
$663$	9.45826	+	16.3822i	0.367328	+	0.636231i
$664$	−4.32568			−0.167869
$665$	17.3249	+	9.00908i	0.671833	+	0.349357i
$666$	−6.42595			−0.249001
$667$	16.9038	+	29.2783i	0.654520	+	1.13366i
$668$	3.14553	+	5.44822i	0.121704	+	0.210798i
$669$	−1.14417	+	1.98176i	−0.0442361	+	0.0766192i
$670$	−7.93220	−	13.7390i	−0.306447	−	0.530783i
$671$	14.1135	−	24.4453i	0.544845	−	0.943700i
$672$	−17.2563			−0.665676
$673$	50.6185			1.95120			0.975601	−	0.219553i	$-0.0704597\pi$
$673$	50.6185			1.95120			0.975601	+	0.219553i	$0.0704597\pi$
$674$	26.8733	−	46.5460i	1.03512	−	1.79288i
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	−4.87273			−0.187413
$677$	33.8725			1.30182			0.650912	−	0.759153i	$-0.274387\pi$
$677$	33.8725			1.30182			0.650912	+	0.759153i	$0.274387\pi$
$678$	7.17691	−	12.4308i	0.275627	−	0.477401i
$679$	−4.47988	−	7.75938i	−0.171922	−	0.297778i
$680$	−8.09309	+	14.0176i	−0.310356	+	0.537552i
$681$	−2.09747	−	3.63292i	−0.0803751	−	0.139214i
$682$	1.19749	+	2.07412i	0.0458543	+	0.0794220i
$683$	47.0846			1.80164			0.900822	−	0.434190i	$-0.142965\pi$
$683$	47.0846			1.80164			0.900822	+	0.434190i	$0.142965\pi$
$684$	2.75090	+	1.43048i	0.105183	+	0.0546959i
$685$	17.6280			0.673531
$686$	22.3856	+	38.7729i	0.854685	+	1.48036i
$687$	−13.1371	−	22.7541i	−0.501211	−	0.868123i
$688$	6.09637	−	10.5592i	0.232422	−	0.402567i
$689$	−14.2575	−	24.6948i	−0.543169	−	0.940796i
$690$	−3.18666	+	5.51946i	−0.121314	+	0.210122i
$691$	3.91269			0.148846			0.0744228	−	0.997227i	$-0.476289\pi$
$691$	3.91269			0.148846			0.0744228	+	0.997227i	$0.476289\pi$
$692$	12.4811			0.474460
$693$	7.70839	−	13.3513i	0.292817	−	0.507175i
$694$	13.8555	−	23.9985i	0.525949	−	0.910970i
$695$	11.7346			0.445117
$696$	18.5342			0.702538
$697$	−20.1883	+	34.9672i	−0.764688	+	1.32448i
$698$	2.03313	+	3.52148i	0.0769551	+	0.133290i
$699$	−2.78125	+	4.81726i	−0.105196	+	0.182206i
$700$	−1.59333	−	2.75973i	−0.0602222	−	0.104308i
$701$	−6.60352	−	11.4376i	−0.249411	−	0.431993i	0.713951	−	0.700195i	$-0.246904\pi$
$701$	−6.60352	−	11.4376i	−0.249411	−	0.431993i	−0.963363	+	0.268202i	$0.913570\pi$
$702$	4.08340			0.154118
$703$	−14.3427	+	9.14620i	−0.540945	+	0.344955i
$704$	−12.0126			−0.452741
$705$	−0.338665	−	0.586585i	−0.0127549	−	0.0220921i
$706$	22.8594	+	39.5936i	0.860323	+	1.49012i
$707$	4.52173	−	7.83186i	0.170057	−	0.294547i
$708$	−3.03400	−	5.25504i	−0.114025	−	0.197496i
$709$	8.99856	−	15.5860i	0.337948	−	0.585343i	−0.646099	−	0.763254i	$-0.723600\pi$
$709$	8.99856	−	15.5860i	0.337948	−	0.585343i	0.984047	+	0.177911i	$0.0569338\pi$
$710$	6.34256			0.238032
$711$	12.1252			0.454732
$712$	3.33687	−	5.77963i	0.125054	−	0.216601i
$713$	0.817955	−	1.41674i	0.0306326	−	0.0530573i
$714$	56.2688			2.10581
$715$	−8.53410			−0.319157
$716$	−1.53252	+	2.65440i	−0.0572728	+	0.0991995i
$717$	−3.42451	−	5.93142i	−0.127890	−	0.221513i
$718$	−16.5064	+	28.5899i	−0.616014	+	1.06697i
$719$	6.23909	+	10.8064i	0.232679	+	0.403012i	0.958596	−	0.284771i	$-0.0919175\pi$
$719$	6.23909	+	10.8064i	0.232679	+	0.403012i	−0.725917	+	0.687783i	$0.758584\pi$
$720$	2.45833	+	4.25796i	0.0916167	+	0.158685i
$721$	29.0698			1.08262
$722$	31.1641	−	2.75423i	1.15981	−	0.102502i
$723$	−14.8424			−0.551996
$724$	−2.25628	−	3.90800i	−0.0838541	−	0.145240i
$725$	4.36728	+	7.56435i	0.162197	+	0.280933i
$726$	−0.693873	+	1.20182i	−0.0257520	+	0.0446039i
$727$	21.7065	+	37.5968i	0.805051	+	1.39439i	0.916257	+	0.400592i	$0.131195\pi$
$727$	21.7065	+	37.5968i	0.805051	+	1.39439i	−0.111206	+	0.993797i	$0.535471\pi$
$728$	−11.7869	+	20.4156i	−0.436853	+	0.756651i
$729$	1.00000			0.0370370
$730$	−27.6387			−1.02295
$731$	−9.45826	+	16.3822i	−0.349826	+	0.605917i
$732$	2.91727	−	5.05286i	0.107825	−	0.186759i
$733$	−28.5740			−1.05540			−0.527702	−	0.849430i	$-0.676946\pi$
$733$	−28.5740			−1.05540			−0.527702	+	0.849430i	$0.676946\pi$
$734$	10.9908			0.405678
$735$	6.53467	−	11.3184i	0.241035	−	0.417484i
$736$	−7.45462	−	12.9118i	−0.274781	−	0.475935i
$737$	−16.5779	+	28.7138i	−0.610655	+	1.05769i
$738$	4.35794	+	7.54817i	0.160418	+	0.277852i
$739$	4.61769	+	7.99807i	0.169864	+	0.294214i	0.938372	−	0.345627i	$-0.112334\pi$
$739$	4.61769	+	7.99807i	0.169864	+	0.294214i	−0.768508	+	0.639841i	$0.779000\pi$
$740$	2.77598			0.102047
$741$	9.11412	−	5.81199i	0.334815	−	0.213509i
$742$	−84.8205			−3.11386
$743$	2.51875	+	4.36259i	0.0924038	+	0.160048i	0.908522	−	0.417837i	$-0.137212\pi$
$743$	2.51875	+	4.36259i	0.0924038	+	0.160048i	−0.816118	+	0.577885i	$0.803878\pi$
$744$	−0.448423	−	0.776692i	−0.0164400	−	0.0284749i
$745$	10.7824	−	18.6757i	0.395038	−	0.684226i
$746$	−10.2402	−	17.7366i	−0.374922	−	0.649384i
$747$	1.01927	−	1.76543i	0.0372932	−	0.0645938i
$748$	−18.6727			−0.682741
$749$	17.7468			0.648456
$750$	−0.823305	+	1.42601i	−0.0300629	+	0.0520704i
$751$	−6.41366	+	11.1088i	−0.234038	+	0.405365i	−0.958993	−	0.283431i	$-0.908527\pi$
$751$	−6.41366	+	11.1088i	−0.234038	+	0.405365i	0.724955	+	0.688796i	$0.241861\pi$
$752$	3.33021			0.121440
$753$	4.80255			0.175015
$754$	−17.8333	+	30.8882i	−0.649452	+	1.12488i
$755$	−9.15510	−	15.8571i	−0.333188	−	0.577099i
$756$	1.59333	−	2.75973i	0.0579488	−	0.100370i
$757$	−12.9425	−	22.4171i	−0.470404	−	0.814764i	0.529023	−	0.848608i	$-0.322559\pi$
$757$	−12.9425	−	22.4171i	−0.470404	−	0.814764i	−0.999427	+	0.0338435i	$0.989225\pi$
$758$	17.6183	+	30.5157i	0.639924	+	1.10838i
$759$	13.3199			0.483483
$760$	8.20614	+	4.26725i	0.297668	+	0.154789i
$761$	−28.9722			−1.05024			−0.525121	−	0.851028i	$-0.675980\pi$
$761$	−28.9722			−1.05024			−0.525121	+	0.851028i	$0.675980\pi$
$762$	3.76855	+	6.52733i	0.136520	+	0.236460i
$763$	6.64822	+	11.5151i	0.240682	+	0.416873i
$764$	−0.300819	+	0.521033i	−0.0108832	+	0.0188503i
$765$	−3.81400	−	6.60604i	−0.137895	−	0.238842i
$766$	8.81603	−	15.2698i	0.318536	−	0.551721i
$767$	−21.1547			−0.763852
$768$	−15.1683			−0.547340
$769$	−2.72690	+	4.72313i	−0.0983345	+	0.170320i	−0.910995	−	0.412417i	$-0.864685\pi$
$769$	−2.72690	+	4.72313i	−0.0983345	+	0.170320i	0.812661	+	0.582737i	$0.198018\pi$
$770$	−12.6927	+	21.9844i	−0.457414	+	0.792263i
$771$	−3.49725			−0.125950
$772$	−9.37584			−0.337444
$773$	23.5060	−	40.7135i	0.845451	−	1.46436i	−0.0397783	−	0.999209i	$-0.512665\pi$
$773$	23.5060	−	40.7135i	0.845451	−	1.46436i	0.885229	−	0.465155i	$-0.154001\pi$
$774$	2.04170	+	3.53633i	0.0733874	+	0.127111i
$775$	0.211327	−	0.366029i	0.00759108	−	0.0131481i
$776$	−2.12194	−	3.67531i	−0.0761733	−	0.131936i
$777$	8.74144	+	15.1406i	0.313598	+	0.543167i
$778$	5.77850			0.207169
$779$	20.4704	+	10.6447i	0.733427	+	0.381387i
$780$	−1.76401			−0.0631615
$781$	−6.62782	−	11.4797i	−0.237162	−	0.410776i
$782$	24.3078	+	42.1024i	0.869246	+	1.50558i
$783$	−4.36728	+	7.56435i	−0.156074	+	0.270328i
$784$	32.1288	+	55.6487i	1.14746	+	1.98745i
$785$	5.71527	−	9.89914i	0.203987	−	0.353316i
$786$	−34.0400			−1.21417
$787$	3.86923			0.137923			0.0689616	−	0.997619i	$-0.478031\pi$
$787$	3.86923			0.137923			0.0689616	+	0.997619i	$0.478031\pi$
$788$	−2.45839	+	4.25805i	−0.0875764	+	0.151687i
$789$	−2.61621	+	4.53141i	−0.0931396	+	0.161322i
$790$	−19.9656			−0.710343
$791$	−39.0520			−1.38853
$792$	3.65116	−	6.32399i	0.129738	−	0.224713i
$793$	−10.1704	−	17.6157i	−0.361162	−	0.625550i
$794$	25.6863	−	44.4899i	0.911572	−	1.57889i
$795$	5.74928	+	9.95805i	0.203906	+	0.353176i
$796$	4.75921	+	8.24320i	0.168686	+	0.292173i
$797$	−12.6814			−0.449198			−0.224599	−	0.974451i	$-0.572107\pi$
$797$	−12.6814			−0.449198			−0.224599	+	0.974451i	$0.572107\pi$
$798$	−1.41671	−	32.1227i	−0.0501510	−	1.13713i
$799$	−5.16667			−0.182784
$800$	−1.92598	−	3.33589i	−0.0680935	−	0.117941i
$801$	1.57255	+	2.72374i	0.0555635	+	0.0962387i
$802$	−16.2629	+	28.1682i	−0.574264	+	0.994654i
$803$	28.8818	+	50.0247i	1.01922	+	1.76533i
$804$	−3.42667	+	5.93516i	−0.120849	+	0.209317i
$805$	17.3397			0.611143
$806$	1.72586			0.0607909
$807$	−7.94917	+	13.7684i	−0.279824	+	0.484670i
$808$	2.14176	−	3.70964i	0.0753470	−	0.130505i
$809$	33.2439			1.16879			0.584397	−	0.811468i	$-0.301331\pi$
$809$	33.2439			1.16879			0.584397	+	0.811468i	$0.301331\pi$
$810$	−1.64661			−0.0578560
$811$	1.43265	−	2.48142i	0.0503072	−	0.0871346i	−0.839775	−	0.542934i	$-0.817313\pi$
$811$	1.43265	−	2.48142i	0.0503072	−	0.0871346i	0.890082	+	0.455800i	$0.150647\pi$
$812$	13.9170	+	24.1050i	0.488392	+	0.845920i
$813$	4.99789	−	8.65661i	0.175284	−	0.303600i
$814$	−11.0569	−	19.1512i	−0.387545	−	0.671248i
$815$	4.09938	+	7.10034i	0.143595	+	0.248714i
$816$	37.5043			1.31291
$817$	9.59039	+	4.98706i	0.335525	+	0.174475i
$818$	3.52213			0.123148
$819$	−5.55478	−	9.62117i	−0.194100	−	0.336191i
$820$	−1.88261	−	3.26077i	−0.0657434	−	0.113871i
$821$	7.18851	−	12.4509i	0.250881	−	0.434538i	−0.712888	−	0.701278i	$-0.752613\pi$
$821$	7.18851	−	12.4509i	0.250881	−	0.434538i	0.963769	+	0.266740i	$0.0859465\pi$
$822$	−14.5132	−	25.1376i	−0.506207	−	0.876776i
$823$	−28.3639	+	49.1277i	−0.988702	+	1.71248i	−0.364540	+	0.931188i	$0.618774\pi$
$823$	−28.3639	+	49.1277i	−0.988702	+	1.71248i	−0.624163	+	0.781294i	$0.714560\pi$
$824$	13.7692			0.479674
$825$	3.44134			0.119812
$826$	−31.4632	+	54.4959i	−1.09475	+	1.89616i
$827$	−10.0977	+	17.4897i	−0.351131	+	0.608177i	−0.986448	−	0.164074i	$-0.947536\pi$
$827$	−10.0977	+	17.4897i	−0.351131	+	0.608177i	0.635317	+	0.772252i	$0.280870\pi$
$828$	2.75324			0.0956817
$829$	38.0954			1.32311			0.661554	−	0.749898i	$-0.269897\pi$
$829$	38.0954			1.32311			0.661554	+	0.749898i	$0.269897\pi$
$830$	−1.67835	+	2.90698i	−0.0582562	+	0.100903i
$831$	2.04309	+	3.53874i	0.0708741	+	0.122758i
$832$	−4.32822	+	7.49670i	−0.150054	+	0.259901i
$833$	−49.8464	−	86.3365i	−1.72708	−	2.99138i
$834$	−9.66112	−	16.7336i	−0.334537	−	0.579436i
$835$	−8.84413			−0.306064
$836$	0.470132	+	10.6598i	0.0162599	+	0.368679i
$837$	0.422654			0.0146090
$838$	−4.69565	−	8.13311i	−0.162209	−	0.280954i
$839$	−19.1320	−	33.1376i	−0.660511	−	1.14404i	−0.980482	−	0.196611i	$-0.937007\pi$
$839$	−19.1320	−	33.1376i	−0.660511	−	1.14404i	0.319971	−	0.947427i	$-0.396327\pi$
$840$	4.75303	−	8.23248i	0.163995	−	0.284048i
$841$	−23.6462	−	40.9565i	−0.815388	−	1.41229i
$842$	32.1526	−	55.6899i	1.10805	−	1.91920i
$843$	11.6384			0.400848
$844$	−10.4922			−0.361158
$845$	3.42510	−	5.93244i	0.117827	−	0.204082i
$846$	−0.557649	+	0.965877i	−0.0191724	+	0.0332075i
$847$	3.77560			0.129731
$848$	−56.5346			−1.94141
$849$	2.17910	−	3.77432i	0.0747867	−	0.129534i
$850$	6.28017	+	10.8776i	0.215408	+	0.373098i
$851$	−7.55251	+	13.0813i	−0.258897	+	0.448422i
$852$	−1.36997	−	2.37287i	−0.0469346	−	0.0812931i
$853$	−1.71697	−	2.97387i	−0.0587878	−	0.101823i	0.835134	−	0.550047i	$-0.185390\pi$
$853$	−1.71697	−	2.97387i	−0.0587878	−	0.101823i	−0.893922	+	0.448224i	$0.852057\pi$
$854$	−60.5055			−2.07046
$855$	−3.67522	+	2.34366i	−0.125690	+	0.0801514i
$856$	8.40598			0.287311
$857$	13.6630	+	23.6650i	0.466719	+	0.808382i	0.999277	−	0.0380118i	$-0.0121024\pi$
$857$	13.6630	+	23.6650i	0.466719	+	0.808382i	−0.532558	+	0.846394i	$0.678769\pi$
$858$	7.02617	+	12.1697i	0.239870	+	0.415466i
$859$	22.0603	−	38.2096i	0.752689	−	1.30370i	−0.193826	−	0.981036i	$-0.562090\pi$
$859$	22.0603	−	38.2096i	0.752689	−	1.30370i	0.946515	−	0.322660i	$-0.104577\pi$
$860$	−0.882003	−	1.52767i	−0.0300760	−	0.0520932i
$861$	11.8565	−	20.5361i	0.404068	−	0.699867i
$862$	−2.86109			−0.0974491
$863$	−41.3721			−1.40832			−0.704161	−	0.710040i	$-0.748677\pi$
$863$	−41.3721			−1.40832			−0.704161	+	0.710040i	$0.748677\pi$
$864$	1.92598	−	3.33589i	0.0655230	−	0.113489i
$865$	−8.77310	+	15.1955i	−0.298294	+	0.516661i
$866$	−38.9114			−1.32226
$867$	−41.1863			−1.39876
$868$	0.673427	−	1.16641i	0.0228576	−	0.0395905i
$869$	20.8635	+	36.1367i	0.707746	+	1.22585i
$870$	7.19121	−	12.4555i	0.243805	−	0.422282i
$871$	11.9463	+	20.6916i	0.404785	+	0.701108i
$872$	3.14900	+	5.45423i	0.106639	+	0.184703i
$873$	2.00000			0.0676897
$874$	23.4234	−	14.9369i	0.792307	−	0.505247i
$875$	4.47988			0.151448
$876$	5.96988	+	10.3401i	0.201704	+	0.349361i
$877$	−28.3151	−	49.0432i	−0.956134	−	1.65607i	−0.731751	−	0.681572i	$-0.761297\pi$
$877$	−28.3151	−	49.0432i	−0.956134	−	1.65607i	−0.224383	−	0.974501i	$-0.572037\pi$
$878$	−2.60929	+	4.51943i	−0.0880594	+	0.152523i
$879$	−3.60117	−	6.23740i	−0.121464	−	0.210382i
$880$	−8.45995	+	14.6531i	−0.285185	+	0.493955i
$881$	−1.34253			−0.0452311			−0.0226156	−	0.999744i	$-0.507199\pi$
$881$	−1.34253			−0.0452311			−0.0226156	+	0.999744i	$0.507199\pi$
$882$	−21.5201			−0.724619
$883$	−13.3420	+	23.1089i	−0.448993	+	0.777678i	−0.998321	−	0.0579288i	$-0.981550\pi$
$883$	−13.3420	+	23.1089i	−0.448993	+	0.777678i	0.549328	+	0.835607i	$0.314884\pi$
$884$	−6.72791	+	11.6531i	−0.226284	+	0.391936i
$885$	8.53053			0.286751
$886$	−38.1739			−1.28248
$887$	−13.8879	+	24.0545i	−0.466309	+	0.807671i	−0.999260	−	0.0384753i	$-0.987750\pi$
$887$	−13.8879	+	24.0545i	−0.466309	+	0.807671i	0.532950	+	0.846147i	$0.321083\pi$
$888$	4.14048	+	7.17152i	0.138945	+	0.240660i
$889$	10.2530	−	17.7587i	0.343874	−	0.595607i
$890$	−2.58938	−	4.48494i	−0.0867963	−	0.150336i
$891$	1.72067	+	2.98028i	0.0576445	+	0.0998433i
$892$	−1.62776			−0.0545013
$893$	0.130084	+	2.94955i	0.00435310	+	0.0987028i
$894$	−35.5090			−1.18760
$895$	−2.15445	−	3.73161i	−0.0720153	−	0.124734i
$896$	30.1310	+	52.1884i	1.00660	+	1.74349i
$897$	4.79927	−	8.31258i	0.160243	−	0.277549i
$898$	10.9092	+	18.8953i	0.364044	+	0.630543i
$899$	−1.84585	+	3.19710i	−0.0615624	+	0.106629i
$900$	0.711327			0.0237109
$901$	87.7110			2.92208
$902$	−14.9971	+	25.9758i	−0.499350	+	0.864899i
$903$	5.55478	−	9.62117i	0.184852	−	0.320172i
$904$	−18.4974			−0.615214
$905$	6.34387			0.210877
$906$	−15.0749	+	26.1105i	−0.500830	+	0.867463i
$907$	−3.69599	−	6.40164i	−0.122723	−	0.212563i	0.798117	−	0.602502i	$-0.205829\pi$
$907$	−3.69599	−	6.40164i	−0.122723	−	0.212563i	−0.920841	+	0.389939i	$0.872496\pi$
$908$	1.49198	−	2.58419i	0.0495132	−	0.0857594i
$909$	1.00934	+	1.74823i	0.0334777	+	0.0579851i
$910$	9.14657	+	15.8423i	0.303206	+	0.525168i
$911$	13.3084			0.440926			0.220463	−	0.975395i	$-0.429243\pi$
$911$	13.3084			0.440926			0.220463	+	0.975395i	$0.429243\pi$
$912$	−0.944267	−	21.4104i	−0.0312678	−	0.708971i
$913$	7.01532			0.232173
$914$	3.40088	+	5.89050i	0.112491	+	0.194841i
$915$	4.10117	+	7.10343i	0.135580	+	0.234832i
$916$	9.34477	−	16.1856i	0.308760	−	0.534788i
$917$	46.3058	+	80.2039i	1.52915	+	2.64857i
$918$	−6.28017	+	10.8776i	−0.207276	+	0.359013i
$919$	−27.8298			−0.918022			−0.459011	−	0.888431i	$-0.651796\pi$
$919$	−27.8298			−0.918022			−0.459011	+	0.888431i	$0.651796\pi$
$920$	8.21312			0.270779
$921$	8.14056	−	14.0999i	0.268241	−	0.464606i
$922$	17.9962	−	31.1704i	0.592674	−	1.02654i
$923$	−9.55222			−0.314415
$924$	10.9664			0.360767
$925$	−1.95127	+	3.37969i	−0.0641573	+	0.111124i
$926$	25.4781	+	44.1294i	0.837262	+	1.45018i
$927$	−3.24449	+	5.61962i	−0.106563	+	0.184573i
$928$	16.8225	+	29.1375i	0.552227	+	0.956485i
$929$	−3.17108	−	5.49247i	−0.104040	−	0.180202i	0.809306	−	0.587388i	$-0.199844\pi$
$929$	−3.17108	−	5.49247i	−0.104040	−	0.180202i	−0.913345	+	0.407186i	$0.866510\pi$
$930$	−0.695946			−0.0228210
$931$	−48.0327	+	30.6300i	−1.57421	+	1.00386i
$932$	−3.95675			−0.129608
$933$	−2.03855	−	3.53086i	−0.0667390	−	0.115595i
$934$	0.324596	+	0.562216i	0.0106211	+	0.0183963i
$935$	13.1252	−	22.7336i	0.429241	−	0.743468i
$936$	−2.63108	−	4.55717i	−0.0859996	−	0.148956i
$937$	21.9869	−	38.0825i	0.718282	−	1.24410i	−0.243398	−	0.969926i	$-0.578262\pi$
$937$	21.9869	−	38.0825i	0.718282	−	1.24410i	0.961680	−	0.274174i	$-0.0884045\pi$
$938$	71.0706			2.32054
$939$	21.5553			0.703431
$940$	0.240901	−	0.417254i	0.00785734	−	0.0136093i
$941$	−7.97283	+	13.8093i	−0.259907	+	0.450172i	−0.966217	−	0.257731i	$-0.917025\pi$
$941$	−7.97283	+	13.8093i	−0.259907	+	0.450172i	0.706310	+	0.707903i	$0.250358\pi$
$942$	−18.8217			−0.613243
$943$	20.4878			0.667174
$944$	−20.9709	+	36.3226i	−0.682544	+	1.18220i
$945$	2.23994	+	3.87969i	0.0728653	+	0.126206i
$946$	−7.02617	+	12.1697i	−0.228441	+	0.395671i
$947$	1.55287	+	2.68965i	0.0504615	+	0.0874018i	0.890153	−	0.455662i	$-0.150597\pi$
$947$	1.55287	+	2.68965i	0.0504615	+	0.0874018i	−0.839691	+	0.543064i	$0.817264\pi$
$948$	4.31251	+	7.46948i	0.140064	+	0.242597i
$949$	41.6253			1.35121
$950$	6.05166	−	3.85909i	0.196342	−	0.125205i
$951$	14.2668			0.462632
$952$	−36.2561	−	62.7973i	−1.17507	−	2.03527i
$953$	10.2628	+	17.7757i	0.332445	+	0.575812i	0.982991	−	0.183655i	$-0.0587929\pi$
$953$	10.2628	+	17.7757i	0.332445	+	0.575812i	−0.650545	+	0.759467i	$0.725460\pi$
$954$	9.46683	−	16.3970i	0.306500	−	0.530873i
$955$	−0.422898	−	0.732481i	−0.0136847	−	0.0237025i
$956$	2.43594	−	4.21918i	0.0787840	−	0.136458i
$957$	−30.0585			−0.971655
$958$	11.5961			0.374651
$959$	−39.4857	+	68.3912i	−1.27506	+	2.20847i
$960$	1.74534	−	3.02301i	0.0563305	−	0.0975672i
$961$	−30.8214			−0.994238
$962$	−15.9356			−0.513784
$963$	−1.98073	+	3.43072i	−0.0638280	+	0.110553i
$964$	−5.27891	−	9.14334i	−0.170022	−	0.294487i
$965$	6.59039	−	11.4149i	0.212152	−	0.367458i
$966$	−14.2759	−	24.7265i	−0.459318	−	0.795562i
$967$	−12.4113	−	21.4970i	−0.399120	−	0.691296i	0.594498	−	0.804097i	$-0.297351\pi$
$967$	−12.4113	−	21.4970i	−0.399120	−	0.691296i	−0.993618	+	0.112801i	$0.964018\pi$
$968$	1.78835			0.0574798
$969$	1.46499	+	33.2174i	0.0470622	+	1.06710i
$970$	−3.29322			−0.105739
$971$	18.2999	+	31.6963i	0.587271	+	1.01718i	0.994588	+	0.103896i	$0.0331309\pi$
$971$	18.2999	+	31.6963i	0.587271	+	1.01718i	−0.407318	+	0.913287i	$0.633536\pi$
$972$	0.355663	+	0.616027i	0.0114079	+	0.0197591i
$973$	−26.2847	+	45.5264i	−0.842649	+	1.45951i
$974$	0.567401	+	0.982767i	0.0181807	+	0.0314899i
$975$	1.23994	−	2.14764i	0.0397099	−	0.0687795i
$976$	−40.3282			−1.29087
$977$	31.6228			1.01170			0.505851	−	0.862621i	$-0.331178\pi$
$977$	31.6228			1.01170			0.505851	+	0.862621i	$0.331178\pi$
$978$	6.75008	−	11.6915i	0.215844	−	0.373853i
$979$	−5.41168	+	9.37331i	−0.172958	+	0.299572i
$980$	9.29656			0.296968
$981$	−2.96803			−0.0947620
$982$	7.48773	−	12.9691i	0.238943	−	0.413862i
$983$	−22.8804	−	39.6300i	−0.729771	−	1.26400i	−0.956980	−	0.290154i	$-0.906293\pi$
$983$	−22.8804	−	39.6300i	−0.729771	−	1.26400i	0.227209	−	0.973846i	$-0.427040\pi$
$984$	5.61596	−	9.72712i	0.179030	−	0.310089i
$985$	−3.45606	−	5.98607i	−0.110119	−	0.190732i
$986$	−54.8545	−	95.0108i	−1.74692	−	3.02576i
$987$	3.03436			0.0965846
$988$	6.82190	+	3.54743i	0.217034	+	0.112859i
$989$	9.59855			0.305216
$990$	−2.83327	−	4.90737i	−0.0900472	−	0.155966i
$991$	−13.2056	−	22.8728i	−0.419490	−	0.726579i	0.576398	−	0.817169i	$-0.304458\pi$
$991$	−13.2056	−	22.8728i	−0.419490	−	0.726579i	−0.995888	+	0.0905905i	$0.971125\pi$
$992$	0.814021	−	1.40993i	0.0258452	−	0.0447652i
$993$	11.9823	+	20.7540i	0.380248	+	0.658608i
$994$	−14.2069	+	24.6072i	−0.450617	+	0.780492i
$995$	−13.3812			−0.424214
$996$	1.45007			0.0459473
$997$	20.5781	−	35.6423i	0.651714	−	1.12880i	−0.330992	−	0.943633i	$-0.607383\pi$
$997$	20.5781	−	35.6423i	0.651714	−	1.12880i	0.982707	−	0.185169i	$-0.0592832\pi$
$998$	−19.0025	+	32.9134i	−0.601515	+	1.04185i
$999$	−3.90253			−0.123471

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.2.i.f.121.4	yes	10
3.2	odd	2		855.2.k.i.406.2		10
19.7	even	3		5415.2.a.y.1.2		5
19.11	even	3	inner	285.2.i.f.106.4	✓	10
19.12	odd	6		5415.2.a.z.1.4		5
57.11	odd	6		855.2.k.i.676.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.i.f.106.4	✓	10	19.11	even	3	inner
285.2.i.f.121.4	yes	10	1.1	even	1	trivial
855.2.k.i.406.2		10	3.2	odd	2
855.2.k.i.676.2		10	57.11	odd	6
5415.2.a.y.1.2		5	19.7	even	3
5415.2.a.z.1.4		5	19.12	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.823305 + 1.42601i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.355663 + 0.616027i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.823305 + 1.42601i) q^{6} +4.47988 q^{7} +2.12194 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.823305 - 1.42601i) q^{10} -3.44134 q^{11} -0.711327 q^{12} +(-1.23994 + 2.14764i) q^{13} +(3.68831 + 6.38834i) q^{14} +(0.500000 - 0.866025i) q^{15} +(2.45833 + 4.25796i) q^{16} +(-3.81400 - 6.60604i) q^{17} -1.64661 q^{18} +(-3.67522 + 2.34366i) q^{19} +0.711327 q^{20} +(2.23994 + 3.87969i) q^{21} +(-2.83327 - 4.90737i) q^{22} +(-1.93528 + 3.35201i) q^{23} +(1.06097 + 1.83766i) q^{24} +(-0.500000 + 0.866025i) q^{25} -4.08340 q^{26} -1.00000 q^{27} +(-1.59333 + 2.75973i) q^{28} +(4.36728 - 7.56435i) q^{29} +1.64661 q^{30} -0.422654 q^{31} +(-1.92598 + 3.33589i) q^{32} +(-1.72067 - 2.98028i) q^{33} +(6.28017 - 10.8776i) q^{34} +(-2.23994 - 3.87969i) q^{35} +(-0.355663 - 0.616027i) q^{36} +3.90253 q^{37} +(-6.36790 - 3.31135i) q^{38} -2.47988 q^{39} +(-1.06097 - 1.83766i) q^{40} +(-2.64661 - 4.58406i) q^{41} +(-3.68831 + 6.38834i) q^{42} +(-1.23994 - 2.14764i) q^{43} +(1.22396 - 2.11996i) q^{44} +1.00000 q^{45} -6.37332 q^{46} +(0.338665 - 0.586585i) q^{47} +(-2.45833 + 4.25796i) q^{48} +13.0693 q^{49} -1.64661 q^{50} +(3.81400 - 6.60604i) q^{51} +(-0.882003 - 1.52767i) q^{52} +(-5.74928 + 9.95805i) q^{53} +(-0.823305 - 1.42601i) q^{54} +(1.72067 + 2.98028i) q^{55} +9.50605 q^{56} +(-3.86728 - 2.01101i) q^{57} +14.3824 q^{58} +(4.26526 + 7.38765i) q^{59} +(0.355663 + 0.616027i) q^{60} +(-4.10117 + 7.10343i) q^{61} +(-0.347973 - 0.602707i) q^{62} +(-2.23994 + 3.87969i) q^{63} +3.49067 q^{64} +2.47988 q^{65} +(2.83327 - 4.90737i) q^{66} +(4.81729 - 8.34379i) q^{67} +5.42600 q^{68} -3.87057 q^{69} +(3.68831 - 6.38834i) q^{70} +(1.92594 + 3.33583i) q^{71} +(-1.06097 + 1.83766i) q^{72} +(-8.39260 - 14.5364i) q^{73} +(3.21298 + 5.56504i) q^{74} -1.00000 q^{75} +(-0.136613 - 3.09759i) q^{76} -15.4168 q^{77} +(-2.04170 - 3.53633i) q^{78} +(-6.06262 - 10.5008i) q^{79} +(2.45833 - 4.25796i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.35794 - 7.54817i) q^{82} -2.03855 q^{83} -3.18666 q^{84} +(-3.81400 + 6.60604i) q^{85} +(2.04170 - 3.53633i) q^{86} +8.73456 q^{87} -7.30232 q^{88} +(1.57255 - 2.72374i) q^{89} +(0.823305 + 1.42601i) q^{90} +(-5.55478 + 9.62117i) q^{91} +(-1.37662 - 2.38437i) q^{92} +(-0.211327 - 0.366029i) q^{93} +1.11530 q^{94} +(3.86728 + 2.01101i) q^{95} -3.85195 q^{96} +(-1.00000 - 1.73205i) q^{97} +(10.7600 + 18.6370i) q^{98} +(1.72067 - 2.98028i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} + 5 q^{3} - 7 q^{4} - 5 q^{5} - q^{6} + 4 q^{7} - 12 q^{8} - 5 q^{9} + q^{10} + 10 q^{11} - 14 q^{12} + 8 q^{13} + 4 q^{14} + 5 q^{15} - 7 q^{16} - 10 q^{17} - 2 q^{18} + 5 q^{19} + 14 q^{20}+ \cdots - 5 q^{99}+O(q^{100}) \) 10 * q + q^2 + 5 * q^3 - 7 * q^4 - 5 * q^5 - q^6 + 4 * q^7 - 12 * q^8 - 5 * q^9 + q^10 + 10 * q^11 - 14 * q^12 + 8 * q^13 + 4 * q^14 + 5 * q^15 - 7 * q^16 - 10 * q^17 - 2 * q^18 + 5 * q^19 + 14 * q^20 + 2 * q^21 - 2 * q^22 + 2 * q^23 - 6 * q^24 - 5 * q^25 - 4 * q^26 - 10 * q^27 - 10 * q^28 + 7 * q^29 + 2 * q^30 - 18 * q^31 + 23 * q^32 + 5 * q^33 - 25 * q^34 - 2 * q^35 - 7 * q^36 + 12 * q^37 - 37 * q^38 + 16 * q^39 + 6 * q^40 - 12 * q^41 - 4 * q^42 + 8 * q^43 - 16 * q^44 + 10 * q^45 - 40 * q^46 - 6 * q^47 + 7 * q^48 + 30 * q^49 - 2 * q^50 + 10 * q^51 + 4 * q^52 - 8 * q^53 - q^54 - 5 * q^55 + 72 * q^56 - 2 * q^57 + 76 * q^58 + q^59 + 7 * q^60 - 7 * q^61 - 15 * q^62 - 2 * q^63 + 28 * q^64 - 16 * q^65 + 2 * q^66 + 14 * q^67 - 2 * q^68 + 4 * q^69 + 4 * q^70 + 27 * q^71 + 6 * q^72 - 26 * q^73 + 18 * q^74 - 10 * q^75 - 56 * q^76 + 28 * q^77 - 2 * q^78 - 23 * q^79 - 7 * q^80 - 5 * q^81 + 36 * q^82 - 24 * q^83 - 20 * q^84 - 10 * q^85 + 2 * q^86 + 14 * q^87 + 9 * q^89 + q^90 - 46 * q^91 + 52 * q^92 - 9 * q^93 + 90 * q^94 + 2 * q^95 + 46 * q^96 - 10 * q^97 - 21 * q^98 - 5 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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