LMFDB - Embedded newform 230.3.f.b.47.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,3,Mod(47,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("230.47");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	230.f (of order $4$, 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:	$6.26704608029$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.10
Character	$\chi$	$=$	230.47
Dual form			230.3.f.b.93.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(2.20008 - 2.20008i) q^{3} +2.00000i q^{4} +(0.183624 - 4.99663i) q^{5} +4.40016 q^{6} +(-8.35722 - 8.35722i) q^{7} +(-2.00000 + 2.00000i) q^{8} -0.680698i q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(2.20008 - 2.20008i) q^{3} +2.00000i q^{4} +(0.183624 - 4.99663i) q^{5} +4.40016 q^{6} +(-8.35722 - 8.35722i) q^{7} +(-2.00000 + 2.00000i) q^{8} -0.680698i q^{9} +(5.18025 - 4.81300i) q^{10} +4.85484 q^{11} +(4.40016 + 4.40016i) q^{12} +(17.1820 - 17.1820i) q^{13} -16.7144i q^{14} +(-10.5890 - 11.3970i) q^{15} -4.00000 q^{16} +(-9.16287 - 9.16287i) q^{17} +(0.680698 - 0.680698i) q^{18} +28.3432i q^{19} +(9.99325 + 0.367249i) q^{20} -36.7731 q^{21} +(4.85484 + 4.85484i) q^{22} +(3.39116 - 3.39116i) q^{23} +8.80032i q^{24} +(-24.9326 - 1.83501i) q^{25} +34.3641 q^{26} +(18.3031 + 18.3031i) q^{27} +(16.7144 - 16.7144i) q^{28} +16.7951i q^{29} +(0.807977 - 21.9860i) q^{30} +49.9685 q^{31} +(-4.00000 - 4.00000i) q^{32} +(10.6810 - 10.6810i) q^{33} -18.3257i q^{34} +(-43.2925 + 40.2233i) q^{35} +1.36140 q^{36} +(-15.0634 - 15.0634i) q^{37} +(-28.3432 + 28.3432i) q^{38} -75.6037i q^{39} +(9.62601 + 10.3605i) q^{40} +43.9441 q^{41} +(-36.7731 - 36.7731i) q^{42} +(-5.23091 + 5.23091i) q^{43} +9.70969i q^{44} +(-3.40119 - 0.124993i) q^{45} +6.78233 q^{46} +(20.2706 + 20.2706i) q^{47} +(-8.80032 + 8.80032i) q^{48} +90.6862i q^{49} +(-23.0976 - 26.7676i) q^{50} -40.3181 q^{51} +(34.3641 + 34.3641i) q^{52} +(-34.0517 + 34.0517i) q^{53} +36.6062i q^{54} +(0.891468 - 24.2578i) q^{55} +33.4289 q^{56} +(62.3573 + 62.3573i) q^{57} +(-16.7951 + 16.7951i) q^{58} -67.5325i q^{59} +(22.7939 - 21.1780i) q^{60} -10.1955 q^{61} +(49.9685 + 49.9685i) q^{62} +(-5.68874 + 5.68874i) q^{63} -8.00000i q^{64} +(-82.6971 - 89.0072i) q^{65} +21.3621 q^{66} +(18.0435 + 18.0435i) q^{67} +(18.3257 - 18.3257i) q^{68} -14.9217i q^{69} +(-83.5158 - 3.06918i) q^{70} +21.4957 q^{71} +(1.36140 + 1.36140i) q^{72} +(-21.4816 + 21.4816i) q^{73} -30.1268i q^{74} +(-58.8908 + 50.8165i) q^{75} -56.6864 q^{76} +(-40.5730 - 40.5730i) q^{77} +(75.6037 - 75.6037i) q^{78} +113.271i q^{79} +(-0.734498 + 19.9865i) q^{80} +86.6629 q^{81} +(43.9441 + 43.9441i) q^{82} +(-45.6403 + 45.6403i) q^{83} -73.5462i q^{84} +(-47.4660 + 44.1009i) q^{85} -10.4618 q^{86} +(36.9505 + 36.9505i) q^{87} +(-9.70969 + 9.70969i) q^{88} +64.2133i q^{89} +(-3.27620 - 3.52619i) q^{90} -287.188 q^{91} +(6.78233 + 6.78233i) q^{92} +(109.935 - 109.935i) q^{93} +40.5412i q^{94} +(141.621 + 5.20451i) q^{95} -17.6006 q^{96} +(-98.3956 - 98.3956i) q^{97} +(-90.6862 + 90.6862i) q^{98} -3.30468i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8}+O(q^{10}) $ 24 * q + 24 * q^2 + 4 * q^5 + 8 * q^7 - 48 * q^8	$ 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8} + 16 q^{10} - 8 q^{11} - 24 q^{13} - 24 q^{15} - 96 q^{16} - 12 q^{17} + 88 q^{18} + 24 q^{20} - 24 q^{21} - 8 q^{22} - 48 q^{25} - 48 q^{26} + 60 q^{27} - 16 q^{28} + 12 q^{30} + 12 q^{31} - 96 q^{32} + 92 q^{33} + 48 q^{35} + 176 q^{36} - 100 q^{37} + 56 q^{38} + 16 q^{40} + 116 q^{41} - 24 q^{42} - 120 q^{43} - 204 q^{45} + 56 q^{47} - 104 q^{50} + 176 q^{51} - 48 q^{52} - 192 q^{53} + 180 q^{55} - 32 q^{56} + 28 q^{58} + 72 q^{60} - 152 q^{61} + 12 q^{62} + 364 q^{63} + 40 q^{65} + 184 q^{66} + 72 q^{67} + 24 q^{68} - 100 q^{70} - 28 q^{71} + 176 q^{72} - 364 q^{73} + 276 q^{75} + 112 q^{76} - 92 q^{77} - 32 q^{78} - 16 q^{80} - 440 q^{81} + 116 q^{82} + 360 q^{83} + 232 q^{85} - 240 q^{86} + 176 q^{87} + 16 q^{88} - 84 q^{90} - 432 q^{91} + 192 q^{93} + 144 q^{95} - 432 q^{97} - 484 q^{98}+O(q^{100}) $ 24 * q + 24 * q^2 + 4 * q^5 + 8 * q^7 - 48 * q^8 + 16 * q^10 - 8 * q^11 - 24 * q^13 - 24 * q^15 - 96 * q^16 - 12 * q^17 + 88 * q^18 + 24 * q^20 - 24 * q^21 - 8 * q^22 - 48 * q^25 - 48 * q^26 + 60 * q^27 - 16 * q^28 + 12 * q^30 + 12 * q^31 - 96 * q^32 + 92 * q^33 + 48 * q^35 + 176 * q^36 - 100 * q^37 + 56 * q^38 + 16 * q^40 + 116 * q^41 - 24 * q^42 - 120 * q^43 - 204 * q^45 + 56 * q^47 - 104 * q^50 + 176 * q^51 - 48 * q^52 - 192 * q^53 + 180 * q^55 - 32 * q^56 + 28 * q^58 + 72 * q^60 - 152 * q^61 + 12 * q^62 + 364 * q^63 + 40 * q^65 + 184 * q^66 + 72 * q^67 + 24 * q^68 - 100 * q^70 - 28 * q^71 + 176 * q^72 - 364 * q^73 + 276 * q^75 + 112 * q^76 - 92 * q^77 - 32 * q^78 - 16 * q^80 - 440 * q^81 + 116 * q^82 + 360 * q^83 + 232 * q^85 - 240 * q^86 + 176 * q^87 + 16 * q^88 - 84 * q^90 - 432 * q^91 + 192 * q^93 + 144 * q^95 - 432 * q^97 - 484 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$	2.20008	−	2.20008i	0.733360	−	0.733360i	−0.237924	−	0.971284i	$-0.576467\pi$
$3$	2.20008	−	2.20008i	0.733360	−	0.733360i	0.971284	+	0.237924i	$0.0764669\pi$
$4$			2.00000i			0.500000i
$5$	0.183624	−	4.99663i	0.0367249	−	0.999325i
$5$	0.183624	−	4.99663i	0.0367249	−	0.999325i
$6$	4.40016			0.733360
$7$	−8.35722	−	8.35722i	−1.19389	−	1.19389i	−0.975966	−	0.217922i	$-0.930072\pi$
$7$	−8.35722	−	8.35722i	−1.19389	−	1.19389i	−0.217922	−	0.975966i	$-0.569928\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		−	0.680698i		−	0.0756331i
$10$	5.18025	−	4.81300i	0.518025	−	0.481300i
$11$	4.85484			0.441349			0.220675	−	0.975347i	$-0.429174\pi$
$11$	4.85484			0.441349			0.220675	+	0.975347i	$0.429174\pi$
$12$	4.40016	+	4.40016i	0.366680	+	0.366680i
$13$	17.1820	−	17.1820i	1.32169	−	1.32169i	0.409290	−	0.912404i	$-0.365776\pi$
$13$	17.1820	−	17.1820i	1.32169	−	1.32169i	0.912404	−	0.409290i	$-0.134224\pi$
$14$		−	16.7144i		−	1.19389i
$15$	−10.5890	−	11.3970i	−0.705932	−	0.759798i
$16$	−4.00000			−0.250000
$17$	−9.16287	−	9.16287i	−0.538992	−	0.538992i	0.384241	−	0.923233i	$-0.374463\pi$
$17$	−9.16287	−	9.16287i	−0.538992	−	0.538992i	−0.923233	+	0.384241i	$0.874463\pi$
$18$	0.680698	−	0.680698i	0.0378166	−	0.0378166i
$19$			28.3432i			1.49175i	0.666087	+	0.745874i	$0.267968\pi$
$19$			28.3432i			1.49175i	−0.666087	+	0.745874i	$0.732032\pi$
$20$	9.99325	+	0.367249i	0.499663	+	0.0183624i
$21$	−36.7731			−1.75110
$22$	4.85484	+	4.85484i	0.220675	+	0.220675i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$24$			8.80032i			0.366680i
$25$	−24.9326	−	1.83501i	−0.997303	−	0.0734002i
$26$	34.3641			1.32169
$27$	18.3031	+	18.3031i	0.677893	+	0.677893i
$28$	16.7144	−	16.7144i	0.596944	−	0.596944i
$29$			16.7951i			0.579140i	0.957157	+	0.289570i	$0.0935124\pi$
$29$			16.7951i			0.579140i	−0.957157	+	0.289570i	$0.906488\pi$
$30$	0.807977	−	21.9860i	0.0269326	−	0.732865i
$31$	49.9685			1.61189			0.805944	−	0.591991i	$-0.201658\pi$
$31$	49.9685			1.61189			0.805944	+	0.591991i	$0.201658\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	10.6810	−	10.6810i	0.323668	−	0.323668i
$34$		−	18.3257i		−	0.538992i
$35$	−43.2925	+	40.2233i	−1.23693	+	1.14924i
$36$	1.36140			0.0378166
$37$	−15.0634	−	15.0634i	−0.407118	−	0.407118i	0.473614	−	0.880732i	$-0.342949\pi$
$37$	−15.0634	−	15.0634i	−0.407118	−	0.407118i	−0.880732	+	0.473614i	$0.842949\pi$
$38$	−28.3432	+	28.3432i	−0.745874	+	0.745874i
$39$		−	75.6037i		−	1.93856i
$40$	9.62601	+	10.3605i	0.240650	+	0.259013i
$41$	43.9441			1.07181			0.535903	−	0.844279i	$-0.319971\pi$
$41$	43.9441			1.07181			0.535903	+	0.844279i	$0.319971\pi$
$42$	−36.7731	−	36.7731i	−0.875550	−	0.875550i
$43$	−5.23091	+	5.23091i	−0.121649	+	0.121649i	−0.765310	−	0.643661i	$-0.777415\pi$
$43$	−5.23091	+	5.23091i	−0.121649	+	0.121649i	0.643661	+	0.765310i	$0.277415\pi$
$44$			9.70969i			0.220675i
$45$	−3.40119	−	0.124993i	−0.0755821	−	0.00277762i
$46$	6.78233			0.147442
$47$	20.2706	+	20.2706i	0.431289	+	0.431289i	0.889067	−	0.457778i	$-0.151354\pi$
$47$	20.2706	+	20.2706i	0.431289	+	0.431289i	−0.457778	+	0.889067i	$0.651354\pi$
$48$	−8.80032	+	8.80032i	−0.183340	+	0.183340i
$49$			90.6862i			1.85074i
$50$	−23.0976	−	26.7676i	−0.461951	−	0.535351i
$51$	−40.3181			−0.790550
$52$	34.3641	+	34.3641i	0.660847	+	0.660847i
$53$	−34.0517	+	34.0517i	−0.642484	+	0.642484i	−0.951165	−	0.308681i	$-0.900112\pi$
$53$	−34.0517	+	34.0517i	−0.642484	+	0.642484i	0.308681	+	0.951165i	$0.400112\pi$
$54$			36.6062i			0.677893i
$55$	0.891468	−	24.2578i	0.0162085	−	0.441052i
$56$	33.4289			0.596944
$57$	62.3573	+	62.3573i	1.09399	+	1.09399i
$58$	−16.7951	+	16.7951i	−0.289570	+	0.289570i
$59$		−	67.5325i		−	1.14462i	−0.820038	−	0.572310i	$-0.806048\pi$
$59$		−	67.5325i		−	1.14462i	0.820038	−	0.572310i	$-0.193952\pi$
$60$	22.7939	−	21.1780i	0.379899	−	0.352966i
$61$	−10.1955			−0.167139			−0.0835697	−	0.996502i	$-0.526632\pi$
$61$	−10.1955			−0.167139			−0.0835697	+	0.996502i	$0.526632\pi$
$62$	49.9685	+	49.9685i	0.805944	+	0.805944i
$63$	−5.68874	+	5.68874i	−0.0902975	+	0.0902975i
$64$		−	8.00000i		−	0.125000i
$65$	−82.6971	−	89.0072i	−1.27226	−	1.36934i
$66$	21.3621			0.323668
$67$	18.0435	+	18.0435i	0.269305	+	0.269305i	0.828820	−	0.559515i	$-0.189013\pi$
$67$	18.0435	+	18.0435i	0.269305	+	0.269305i	−0.559515	+	0.828820i	$0.689013\pi$
$68$	18.3257	−	18.3257i	0.269496	−	0.269496i
$69$		−	14.9217i		−	0.216256i
$70$	−83.5158	−	3.06918i	−1.19308	−	0.0438454i
$71$	21.4957			0.302757			0.151378	−	0.988476i	$-0.451629\pi$
$71$	21.4957			0.302757			0.151378	+	0.988476i	$0.451629\pi$
$72$	1.36140	+	1.36140i	0.0189083	+	0.0189083i
$73$	−21.4816	+	21.4816i	−0.294269	+	0.294269i	−0.838764	−	0.544495i	$-0.816721\pi$
$73$	−21.4816	+	21.4816i	−0.294269	+	0.294269i	0.544495	+	0.838764i	$0.316721\pi$
$74$		−	30.1268i		−	0.407118i
$75$	−58.8908	+	50.8165i	−0.785210	+	0.677553i
$76$	−56.6864			−0.745874
$77$	−40.5730	−	40.5730i	−0.526922	−	0.526922i
$78$	75.6037	−	75.6037i	0.969278	−	0.969278i
$79$			113.271i			1.43381i	0.697172	+	0.716904i	$0.254442\pi$
$79$			113.271i			1.43381i	−0.697172	+	0.716904i	$0.745558\pi$
$80$	−0.734498	+	19.9865i	−0.00918122	+	0.249831i
$81$	86.6629			1.06991
$82$	43.9441	+	43.9441i	0.535903	+	0.535903i
$83$	−45.6403	+	45.6403i	−0.549883	+	0.549883i	−0.926407	−	0.376524i	$-0.877119\pi$
$83$	−45.6403	+	45.6403i	−0.549883	+	0.549883i	0.376524	+	0.926407i	$0.377119\pi$
$84$		−	73.5462i		−	0.875550i
$85$	−47.4660	+	44.1009i	−0.558423	+	0.518834i
$86$	−10.4618			−0.121649
$87$	36.9505	+	36.9505i	0.424718	+	0.424718i
$88$	−9.70969	+	9.70969i	−0.110337	+	0.110337i
$89$			64.2133i			0.721498i	0.932663	+	0.360749i	$0.117479\pi$
$89$			64.2133i			0.721498i	−0.932663	+	0.360749i	$0.882521\pi$
$90$	−3.27620	−	3.52619i	−0.0364022	−	0.0391799i
$91$	−287.188			−3.15591
$92$	6.78233	+	6.78233i	0.0737210	+	0.0737210i
$93$	109.935	−	109.935i	1.18209	−	1.18209i
$94$			40.5412i			0.431289i
$95$	141.621	+	5.20451i	1.49074	+	0.0547843i
$96$	−17.6006			−0.183340
$97$	−98.3956	−	98.3956i	−1.01439	−	1.01439i	−0.999895	−	0.0144922i	$-0.995387\pi$
$97$	−98.3956	−	98.3956i	−1.01439	−	1.01439i	−0.0144922	−	0.999895i	$-0.504613\pi$
$98$	−90.6862	+	90.6862i	−0.925370	+	0.925370i
$99$		−	3.30468i		−	0.0333806i
$100$	3.67001	−	49.8651i	0.0367001	−	0.498651i
$101$	−133.352			−1.32032			−0.660159	−	0.751126i	$-0.729511\pi$
$101$	−133.352			−1.32032			−0.660159	+	0.751126i	$0.729511\pi$
$102$	−40.3181	−	40.3181i	−0.395275	−	0.395275i
$103$	95.9912	−	95.9912i	0.931953	−	0.931953i	−0.0658749	−	0.997828i	$-0.520984\pi$
$103$	95.9912	−	95.9912i	0.931953	−	0.931953i	0.997828	+	0.0658749i	$0.0209838\pi$
$104$			68.7281i			0.660847i
$105$	−6.75244	+	183.741i	−0.0643089	+	1.74992i
$106$	−68.1033			−0.642484
$107$	93.8519	+	93.8519i	0.877120	+	0.877120i	0.993236	−	0.116116i	$-0.0370443\pi$
$107$	93.8519	+	93.8519i	0.877120	+	0.877120i	−0.116116	+	0.993236i	$0.537044\pi$
$108$	−36.6062	+	36.6062i	−0.338947	+	0.338947i
$109$		−	201.194i		−	1.84582i	−0.385021	−	0.922908i	$-0.625806\pi$
$109$		−	201.194i		−	1.84582i	0.385021	−	0.922908i	$-0.374194\pi$
$110$	25.1493	−	23.3664i	0.228630	−	0.212422i
$111$	−66.2812			−0.597128
$112$	33.4289	+	33.4289i	0.298472	+	0.298472i
$113$	52.4333	−	52.4333i	0.464012	−	0.464012i	−0.435956	−	0.899968i	$-0.643590\pi$
$113$	52.4333	−	52.4333i	0.464012	−	0.464012i	0.899968	+	0.435956i	$0.143590\pi$
$114$			124.715i			1.09399i
$115$	−16.3217	−	17.5671i	−0.141928	−	0.152757i
$116$	−33.5901			−0.289570
$117$	−11.6958	−	11.6958i	−0.0999639	−	0.0999639i
$118$	67.5325	−	67.5325i	0.572310	−	0.572310i
$119$			153.152i			1.28699i
$120$	43.9719	+	1.61595i	0.366433	+	0.0134663i
$121$	−97.4305			−0.805211
$122$	−10.1955	−	10.1955i	−0.0835697	−	0.0835697i
$123$	96.6804	−	96.6804i	0.786020	−	0.786020i
$124$			99.9371i			0.805944i
$125$	−13.7471	+	124.242i	−0.109977	+	0.993934i
$126$	−11.3775			−0.0902975
$127$	−41.9177	−	41.9177i	−0.330061	−	0.330061i	0.522549	−	0.852609i	$-0.324981\pi$
$127$	−41.9177	−	41.9177i	−0.330061	−	0.330061i	−0.852609	+	0.522549i	$0.824981\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$			23.0168i			0.178425i
$130$	6.31008	−	171.704i	0.0485391	−	1.32080i
$131$	222.893			1.70147			0.850737	−	0.525591i	$-0.176156\pi$
$131$	222.893			1.70147			0.850737	+	0.525591i	$0.176156\pi$
$132$	21.3621	+	21.3621i	0.161834	+	0.161834i
$133$	236.871	−	236.871i	1.78098	−	1.78098i
$134$			36.0869i			0.269305i
$135$	94.8148	−	88.0930i	0.702332	−	0.652541i
$136$	36.6515			0.269496
$137$	−0.0309506	−	0.0309506i	−0.000225917	−	0.000225917i	0.706994	−	0.707220i	$-0.250051\pi$
$137$	−0.0309506	−	0.0309506i	−0.000225917	−	0.000225917i	−0.707220	+	0.706994i	$0.750051\pi$
$138$	14.9217	−	14.9217i	0.108128	−	0.108128i
$139$		−	40.4927i		−	0.291314i	−0.989335	−	0.145657i	$-0.953470\pi$
$139$		−	40.4927i		−	0.291314i	0.989335	−	0.145657i	$-0.0465297\pi$
$140$	−80.4466	−	86.5850i	−0.574619	−	0.618464i
$141$	89.1938			0.632580
$142$	21.4957	+	21.4957i	0.151378	+	0.151378i
$143$	83.4161	−	83.4161i	0.583329	−	0.583329i
$144$			2.72279i			0.0189083i
$145$	83.9187	+	3.08399i	0.578750	+	0.0212689i
$146$	−42.9632			−0.294269
$147$	199.517	+	199.517i	1.35726	+	1.35726i
$148$	30.1268	−	30.1268i	0.203559	−	0.203559i
$149$		−	52.8325i		−	0.354581i	−0.984159	−	0.177290i	$-0.943267\pi$
$149$		−	52.8325i		−	0.354581i	0.984159	−	0.177290i	$-0.0567332\pi$
$150$	−109.707	−	8.07432i	−0.731382	−	0.0538288i
$151$	−180.168			−1.19317			−0.596583	−	0.802551i	$-0.703475\pi$
$151$	−180.168			−1.19317			−0.596583	+	0.802551i	$0.703475\pi$
$152$	−56.6864	−	56.6864i	−0.372937	−	0.372937i
$153$	−6.23715	+	6.23715i	−0.0407657	+	0.0407657i
$154$		−	81.1460i		−	0.526922i
$155$	9.17545	−	249.674i	0.0591964	−	1.61080i
$156$	151.207			0.969278
$157$	111.835	+	111.835i	0.712323	+	0.712323i	0.967021	−	0.254698i	$-0.0819759\pi$
$157$	111.835	+	111.835i	0.712323	+	0.712323i	−0.254698	+	0.967021i	$0.581976\pi$
$158$	−113.271	+	113.271i	−0.716904	+	0.716904i
$159$			149.833i			0.942344i
$160$	−20.7210	+	19.2520i	−0.129506	+	0.120325i
$161$	−56.6814			−0.352059
$162$	86.6629	+	86.6629i	0.534956	+	0.534956i
$163$	5.10164	−	5.10164i	0.0312984	−	0.0312984i	−0.691284	−	0.722583i	$-0.742955\pi$
$163$	5.10164	−	5.10164i	0.0312984	−	0.0312984i	0.722583	+	0.691284i	$0.242955\pi$
$164$			87.8881i			0.535903i
$165$	−51.4079	−	55.3305i	−0.311563	−	0.335336i
$166$	−91.2805			−0.549883
$167$	73.6717	+	73.6717i	0.441148	+	0.441148i	0.892398	−	0.451250i	$-0.149022\pi$
$167$	73.6717	+	73.6717i	0.441148	+	0.441148i	−0.451250	+	0.892398i	$0.649022\pi$
$168$	73.5462	−	73.5462i	0.437775	−	0.437775i
$169$		−	421.444i		−	2.49375i
$170$	−91.5669	−	3.36505i	−0.538629	−	0.0197944i
$171$	19.2932			0.112826
$172$	−10.4618	−	10.4618i	−0.0608245	−	0.0608245i
$173$	−88.0277	+	88.0277i	−0.508831	+	0.508831i	−0.914168	−	0.405337i	$-0.867154\pi$
$173$	−88.0277	+	88.0277i	−0.508831	+	0.508831i	0.405337	+	0.914168i	$0.367154\pi$
$174$			73.9010i			0.424718i
$175$	193.031	+	223.702i	1.10304	+	1.27830i
$176$	−19.4194			−0.110337
$177$	−148.577	−	148.577i	−0.839418	−	0.839418i
$178$	−64.2133	+	64.2133i	−0.360749	+	0.360749i
$179$			322.864i			1.80371i	0.432038	+	0.901856i	$0.357795\pi$
$179$			322.864i			1.80371i	−0.432038	+	0.901856i	$0.642205\pi$
$180$	0.249986	−	6.80239i	0.00138881	−	0.0377910i
$181$	114.556			0.632904			0.316452	−	0.948609i	$-0.397508\pi$
$181$	114.556			0.632904			0.316452	+	0.948609i	$0.397508\pi$
$182$	−287.188	−	287.188i	−1.57796	−	1.57796i
$183$	−22.4309	+	22.4309i	−0.122573	+	0.122573i
$184$			13.5647i			0.0737210i
$185$	−78.0321	+	72.5001i	−0.421795	+	0.391892i
$186$	219.870			1.18209
$187$	−44.4843	−	44.4843i	−0.237884	−	0.237884i
$188$	−40.5412	+	40.5412i	−0.215644	+	0.215644i
$189$		−	305.926i		−	1.61866i
$190$	136.416	+	146.825i	0.717979	+	0.772763i
$191$	228.537			1.19653			0.598265	−	0.801298i	$-0.295857\pi$
$191$	228.537			1.19653			0.598265	+	0.801298i	$0.295857\pi$
$192$	−17.6006	−	17.6006i	−0.0916700	−	0.0916700i
$193$	44.2681	−	44.2681i	0.229368	−	0.229368i	−0.583061	−	0.812429i	$-0.698145\pi$
$193$	44.2681	−	44.2681i	0.229368	−	0.229368i	0.812429	+	0.583061i	$0.198145\pi$
$194$		−	196.791i		−	1.01439i
$195$	−377.763	−	13.8827i	−1.93725	−	0.0711932i
$196$	−181.372			−0.925370
$197$	108.253	+	108.253i	0.549507	+	0.549507i	0.926298	−	0.376791i	$-0.122973\pi$
$197$	108.253	+	108.253i	0.549507	+	0.549507i	−0.376791	+	0.926298i	$0.622973\pi$
$198$	3.30468	−	3.30468i	0.0166903	−	0.0166903i
$199$		−	54.1132i		−	0.271925i	−0.990714	−	0.135963i	$-0.956587\pi$
$199$		−	54.1132i		−	0.271925i	0.990714	−	0.135963i	$-0.0434127\pi$
$200$	53.5351	−	46.1951i	0.267676	−	0.230976i
$201$	79.3941			0.394995
$202$	−133.352	−	133.352i	−0.660159	−	0.660159i
$203$	140.360	−	140.360i	0.691429	−	0.691429i
$204$		−	80.6361i		−	0.395275i
$205$	8.06921	−	219.572i	0.0393620	−	1.07108i
$206$	191.982			0.931953
$207$	−2.30836	−	2.30836i	−0.0111515	−	0.0111515i
$208$	−68.7281	+	68.7281i	−0.330424	+	0.330424i
$209$			137.602i			0.658382i
$210$	−190.494	+	176.989i	−0.907114	+	0.842805i
$211$	−318.790			−1.51085			−0.755426	−	0.655234i	$-0.772570\pi$
$211$	−318.790			−1.51085			−0.755426	+	0.655234i	$0.772570\pi$
$212$	−68.1033	−	68.1033i	−0.321242	−	0.321242i
$213$	47.2923	−	47.2923i	0.222029	−	0.222029i
$214$			187.704i			0.877120i
$215$	25.1764	+	27.0974i	0.117099	+	0.126035i
$216$	−73.2125			−0.338947
$217$	−417.598	−	417.598i	−1.92442	−	1.92442i
$218$	201.194	−	201.194i	0.922908	−	0.922908i
$219$			94.5225i			0.431610i
$220$	48.5157	+	1.78294i	0.220526	+	0.00810425i
$221$	−314.873			−1.42477
$222$	−66.2812	−	66.2812i	−0.298564	−	0.298564i
$223$	−115.343	+	115.343i	−0.517235	+	0.517235i	−0.916734	−	0.399499i	$-0.869184\pi$
$223$	−115.343	+	115.343i	−0.517235	+	0.517235i	0.399499	+	0.916734i	$0.369184\pi$
$224$			66.8578i			0.298472i
$225$	−1.24908	+	16.9715i	−0.00555149	+	0.0754291i
$226$	104.867			0.464012
$227$	57.9945	+	57.9945i	0.255482	+	0.255482i	0.823214	−	0.567732i	$-0.192179\pi$
$227$	57.9945	+	57.9945i	0.255482	+	0.255482i	−0.567732	+	0.823214i	$0.692179\pi$
$228$	−124.715	+	124.715i	−0.546994	+	0.546994i
$229$		−	320.751i		−	1.40066i	−0.713820	−	0.700329i	$-0.753037\pi$
$229$		−	320.751i		−	1.40066i	0.713820	−	0.700329i	$-0.246963\pi$
$230$	1.24540	−	33.8888i	0.00541479	−	0.147342i
$231$	−178.528			−0.772847
$232$	−33.5901	−	33.5901i	−0.144785	−	0.144785i
$233$	111.290	−	111.290i	0.477638	−	0.477638i	−0.426738	−	0.904375i	$-0.640337\pi$
$233$	111.290	−	111.290i	0.477638	−	0.477638i	0.904375	+	0.426738i	$0.140337\pi$
$234$		−	23.3915i		−	0.0999639i
$235$	105.007	−	97.5624i	0.446837	−	0.415159i
$236$	135.065			0.572310
$237$	249.205	+	249.205i	1.05150	+	1.05150i
$238$	−153.152	+	153.152i	−0.643497	+	0.643497i
$239$			249.659i			1.04460i	0.852762	+	0.522300i	$0.174926\pi$
$239$			249.659i			1.04460i	−0.852762	+	0.522300i	$0.825074\pi$
$240$	42.3559	+	45.5879i	0.176483	+	0.189949i
$241$	105.175			0.436411			0.218206	−	0.975903i	$-0.429980\pi$
$241$	105.175			0.436411			0.218206	+	0.975903i	$0.429980\pi$
$242$	−97.4305	−	97.4305i	−0.402605	−	0.402605i
$243$	25.9372	−	25.9372i	0.106737	−	0.106737i
$244$		−	20.3910i		−	0.0835697i
$245$	453.125	+	16.6522i	1.84949	+	0.0679682i
$246$	193.361			0.786020
$247$	486.994	+	486.994i	1.97164	+	1.97164i
$248$	−99.9371	+	99.9371i	−0.402972	+	0.402972i
$249$			200.824i			0.806524i
$250$	−137.989	+	110.495i	−0.551955	+	0.441979i
$251$	−114.474			−0.456071			−0.228036	−	0.973653i	$-0.573230\pi$
$251$	−114.474			−0.456071			−0.228036	+	0.973653i	$0.573230\pi$
$252$	−11.3775	−	11.3775i	−0.0451487	−	0.0451487i
$253$	16.4636	−	16.4636i	0.0650734	−	0.0650734i
$254$		−	83.8355i		−	0.330061i
$255$	−7.40339	+	201.454i	−0.0290329	+	0.790017i
$256$	16.0000			0.0625000
$257$	−159.057	−	159.057i	−0.618901	−	0.618901i	0.326349	−	0.945249i	$-0.394182\pi$
$257$	−159.057	−	159.057i	−0.618901	−	0.618901i	−0.945249	+	0.326349i	$0.894182\pi$
$258$	−23.0168	+	23.0168i	−0.0892126	+	0.0892126i
$259$			251.776i			0.972108i
$260$	178.014	−	165.394i	0.684671	−	0.636132i
$261$	11.4324			0.0438022
$262$	222.893	+	222.893i	0.850737	+	0.850737i
$263$	−41.8699	+	41.8699i	−0.159201	+	0.159201i	−0.782213	−	0.623012i	$-0.785909\pi$
$263$	−41.8699	+	41.8699i	−0.159201	+	0.159201i	0.623012	+	0.782213i	$0.285909\pi$
$264$			42.7242i			0.161834i
$265$	163.891	+	176.396i	0.618455	+	0.665646i
$266$	473.741			1.78098
$267$	141.274	+	141.274i	0.529117	+	0.529117i
$268$	−36.0869	+	36.0869i	−0.134653	+	0.134653i
$269$			354.532i			1.31796i	0.752160	+	0.658981i	$0.229012\pi$
$269$			354.532i			1.31796i	−0.752160	+	0.658981i	$0.770988\pi$
$270$	182.908	+	6.72180i	0.677436	+	0.0248956i
$271$	−179.845			−0.663636			−0.331818	−	0.943343i	$-0.607662\pi$
$271$	−179.845			−0.663636			−0.331818	+	0.943343i	$0.607662\pi$
$272$	36.6515	+	36.6515i	0.134748	+	0.134748i
$273$	−631.836	+	631.836i	−2.31442	+	2.31442i
$274$		−	0.0619011i		−	0.000225917i
$275$	−121.044	−	8.90867i	−0.440159	−	0.0323952i
$276$	29.8433			0.108128
$277$	−308.660	−	308.660i	−1.11429	−	1.11429i	−0.992563	−	0.121732i	$-0.961155\pi$
$277$	−308.660	−	308.660i	−1.11429	−	1.11429i	−0.121732	−	0.992563i	$-0.538845\pi$
$278$	40.4927	−	40.4927i	0.145657	−	0.145657i
$279$		−	34.0135i		−	0.121912i
$280$	6.13836	−	167.032i	0.0219227	−	0.596542i
$281$	156.370			0.556478			0.278239	−	0.960512i	$-0.410249\pi$
$281$	156.370			0.556478			0.278239	+	0.960512i	$0.410249\pi$
$282$	89.1938	+	89.1938i	0.316290	+	0.316290i
$283$	−125.940	+	125.940i	−0.445016	+	0.445016i	−0.893694	−	0.448678i	$-0.851895\pi$
$283$	−125.940	+	125.940i	−0.445016	+	0.445016i	0.448678	+	0.893694i	$0.351895\pi$
$284$			42.9914i			0.151378i
$285$	323.027	−	300.126i	1.13343	−	1.05307i
$286$	166.832			0.583329
$287$	−367.250	−	367.250i	−1.27962	−	1.27962i
$288$	−2.72279	+	2.72279i	−0.00945414	+	0.00945414i
$289$		−	121.084i		−	0.418975i
$290$	80.8347	+	87.0027i	0.278740	+	0.300009i
$291$	−432.956			−1.48782
$292$	−42.9632	−	42.9632i	−0.147134	−	0.147134i
$293$	−150.158	+	150.158i	−0.512485	+	0.512485i	−0.915287	−	0.402802i	$-0.868036\pi$
$293$	−150.158	+	150.158i	−0.512485	+	0.512485i	0.402802	+	0.915287i	$0.368036\pi$
$294$			399.034i			1.35726i
$295$	−337.435	−	12.4006i	−1.14385	−	0.0420360i
$296$	60.2535			0.203559
$297$	88.8588	+	88.8588i	0.299188	+	0.299188i
$298$	52.8325	−	52.8325i	0.177290	−	0.177290i
$299$		−	116.534i		−	0.389746i
$300$	−101.633	−	117.782i	−0.338776	−	0.392605i
$301$	87.4317			0.290471
$302$	−180.168	−	180.168i	−0.596583	−	0.596583i
$303$	−293.385	+	293.385i	−0.968268	+	0.968268i
$304$		−	113.373i		−	0.372937i
$305$	−1.87214	+	50.9431i	−0.00613818	+	0.167027i
$306$	−12.4743			−0.0407657
$307$	−159.257	−	159.257i	−0.518753	−	0.518753i	0.398441	−	0.917194i	$-0.369551\pi$
$307$	−159.257	−	159.257i	−0.518753	−	0.518753i	−0.917194	+	0.398441i	$0.869551\pi$
$308$	81.1460	−	81.1460i	0.263461	−	0.263461i
$309$		−	422.376i		−	1.36691i
$310$	258.850	−	240.499i	0.834999	−	0.775802i
$311$	−153.824			−0.494610			−0.247305	−	0.968938i	$-0.579545\pi$
$311$	−153.824			−0.494610			−0.247305	+	0.968938i	$0.579545\pi$
$312$	151.207	+	151.207i	0.484639	+	0.484639i
$313$	−330.942	+	330.942i	−1.05732	+	1.05732i	−0.0590683	+	0.998254i	$0.518813\pi$
$313$	−330.942	+	330.942i	−1.05732	+	1.05732i	−0.998254	+	0.0590683i	$0.981187\pi$
$314$			223.669i			0.712323i
$315$	27.3799	+	29.4691i	0.0869204	+	0.0935528i
$316$	−226.542			−0.716904
$317$	372.744	+	372.744i	1.17585	+	1.17585i	0.980792	+	0.195056i	$0.0624889\pi$
$317$	372.744	+	372.744i	1.17585	+	1.17585i	0.195056	+	0.980792i	$0.437511\pi$
$318$	−149.833	+	149.833i	−0.471172	+	0.471172i
$319$			81.5374i			0.255603i
$320$	−39.9730	−	1.46900i	−0.124916	−	0.00459061i
$321$	412.963			1.28649
$322$	−56.6814	−	56.6814i	−0.176029	−	0.176029i
$323$	259.705	−	259.705i	0.804041	−	0.804041i
$324$			173.326i			0.534956i
$325$	−459.921	+	396.863i	−1.41514	+	1.22112i
$326$	10.2033			0.0312984
$327$	−442.643	−	442.643i	−1.35365	−	1.35365i
$328$	−87.8881	+	87.8881i	−0.267952	+	0.267952i
$329$		−	338.811i		−	1.02982i
$330$	3.92260	−	106.738i	0.0118867	−	0.323450i
$331$	−286.269			−0.864861			−0.432430	−	0.901667i	$-0.642344\pi$
$331$	−286.269			−0.864861			−0.432430	+	0.901667i	$0.642344\pi$
$332$	−91.2805	−	91.2805i	−0.274941	−	0.274941i
$333$	−10.2536	+	10.2536i	−0.0307916	+	0.0307916i
$334$			147.343i			0.441148i
$335$	93.4697	−	86.8432i	0.279014	−	0.259234i
$336$	147.092			0.437775
$337$	−41.4913	−	41.4913i	−0.123120	−	0.123120i	0.642862	−	0.765982i	$-0.277747\pi$
$337$	−41.4913	−	41.4913i	−0.123120	−	0.123120i	−0.765982	+	0.642862i	$0.777747\pi$
$338$	421.444	−	421.444i	1.24688	−	1.24688i
$339$		−	230.715i		−	0.680575i
$340$	−88.2018	−	94.9319i	−0.259417	−	0.279212i
$341$	242.589			0.711406
$342$	19.2932	+	19.2932i	0.0564128	+	0.0564128i
$343$	348.381	−	348.381i	1.01569	−	1.01569i
$344$		−	20.9236i		−	0.0608245i
$345$	−74.5580	−	2.73998i	−0.216110	−	0.00794198i
$346$	−176.055			−0.508831
$347$	−393.288	−	393.288i	−1.13339	−	1.13339i	−0.989609	−	0.143785i	$-0.954073\pi$
$347$	−393.288	−	393.288i	−1.13339	−	1.13339i	−0.143785	−	0.989609i	$-0.545927\pi$
$348$	−73.9010	+	73.9010i	−0.212359	+	0.212359i
$349$			61.6981i			0.176785i	0.996086	+	0.0883927i	$0.0281730\pi$
$349$			61.6981i			0.176785i	−0.996086	+	0.0883927i	$0.971827\pi$
$350$	−30.6711	+	416.734i	−0.0876317	+	1.19067i
$351$	628.970			1.79194
$352$	−19.4194	−	19.4194i	−0.0551687	−	0.0551687i
$353$	−148.629	+	148.629i	−0.421045	+	0.421045i	−0.885563	−	0.464519i	$-0.846227\pi$
$353$	−148.629	+	148.629i	−0.421045	+	0.421045i	0.464519	+	0.885563i	$0.346227\pi$
$354$		−	297.154i		−	0.839418i
$355$	3.94714	−	107.406i	0.0111187	−	0.302552i
$356$	−128.427			−0.360749
$357$	336.947	+	336.947i	0.943829	+	0.943829i
$358$	−322.864	+	322.864i	−0.901856	+	0.901856i
$359$			133.489i			0.371836i	0.982565	+	0.185918i	$0.0595259\pi$
$359$			133.489i			0.371836i	−0.982565	+	0.185918i	$0.940474\pi$
$360$	7.05237	−	6.55240i	0.0195899	−	0.0182011i
$361$	−442.338			−1.22531
$362$	114.556	+	114.556i	0.316452	+	0.316452i
$363$	−214.355	+	214.355i	−0.590509	+	0.590509i
$364$		−	574.376i		−	1.57796i
$365$	103.391	+	111.280i	0.283263	+	0.304877i
$366$	−44.8618			−0.122573
$367$	159.240	+	159.240i	0.433895	+	0.433895i	0.889951	−	0.456056i	$-0.150738\pi$
$367$	159.240	+	159.240i	0.433895	+	0.433895i	−0.456056	+	0.889951i	$0.650738\pi$
$368$	−13.5647	+	13.5647i	−0.0368605	+	0.0368605i
$369$		−	29.9126i		−	0.0810641i
$370$	−150.532	−	5.53201i	−0.406844	−	0.0149514i
$371$	569.154			1.53411
$372$	219.870	+	219.870i	0.591047	+	0.591047i
$373$	−340.134	+	340.134i	−0.911888	+	0.911888i	−0.996421	−	0.0845323i	$-0.973060\pi$
$373$	−340.134	+	340.134i	−0.911888	+	0.911888i	0.0845323	+	0.996421i	$0.473060\pi$
$374$		−	88.9686i		−	0.237884i
$375$	243.097	+	303.586i	0.648259	+	0.809564i
$376$	−81.0823			−0.215644
$377$	288.573	+	288.573i	0.765447	+	0.765447i
$378$	305.926	−	305.926i	0.809329	−	0.809329i
$379$			578.294i			1.52584i	0.646492	+	0.762921i	$0.276235\pi$
$379$			578.294i			1.52584i	−0.646492	+	0.762921i	$0.723765\pi$
$380$	−10.4090	+	283.241i	−0.0273922	+	0.745371i
$381$	−184.445			−0.484107
$382$	228.537	+	228.537i	0.598265	+	0.598265i
$383$	41.1217	−	41.1217i	0.107367	−	0.107367i	−0.651382	−	0.758750i	$-0.725811\pi$
$383$	41.1217	−	41.1217i	0.107367	−	0.107367i	0.758750	+	0.651382i	$0.225811\pi$
$384$		−	35.2013i		−	0.0916700i
$385$	−210.178	+	195.278i	−0.545918	+	0.507215i
$386$	88.5361			0.229368
$387$	3.56067	+	3.56067i	0.00920070	+	0.00920070i
$388$	196.791	−	196.791i	0.507194	−	0.507194i
$389$		−	539.251i		−	1.38625i	−0.720818	−	0.693124i	$-0.756234\pi$
$389$		−	539.251i		−	1.38625i	0.720818	−	0.693124i	$-0.243766\pi$
$390$	−363.881	−	391.646i	−0.933027	−	1.00422i
$391$	−62.1456			−0.158940
$392$	−181.372	−	181.372i	−0.462685	−	0.462685i
$393$	490.383	−	490.383i	1.24779	−	1.24779i
$394$			216.506i			0.549507i
$395$	565.972	+	20.7993i	1.43284	+	0.0526565i
$396$	6.60936			0.0166903
$397$	−122.141	−	122.141i	−0.307659	−	0.307659i	0.536342	−	0.844001i	$-0.319806\pi$
$397$	−122.141	−	122.141i	−0.307659	−	0.307659i	−0.844001	+	0.536342i	$0.819806\pi$
$398$	54.1132	−	54.1132i	0.135963	−	0.135963i
$399$		−	1042.27i		−	2.61220i
$400$	99.7303	+	7.34002i	0.249326	+	0.0183501i
$401$	−190.196			−0.474305			−0.237152	−	0.971472i	$-0.576214\pi$
$401$	−190.196			−0.474305			−0.237152	+	0.971472i	$0.576214\pi$
$402$	79.3941	+	79.3941i	0.197498	+	0.197498i
$403$	858.561	−	858.561i	2.13042	−	2.13042i
$404$		−	266.704i		−	0.660159i
$405$	15.9134	−	433.022i	0.0392924	−	1.06919i
$406$	280.720			0.691429
$407$	−73.1303	−	73.1303i	−0.179681	−	0.179681i
$408$	80.6361	−	80.6361i	0.197638	−	0.197638i
$409$		−	350.710i		−	0.857482i	−0.903427	−	0.428741i	$-0.858957\pi$
$409$		−	350.710i		−	0.857482i	0.903427	−	0.428741i	$-0.141043\pi$
$410$	227.641	−	211.503i	0.555223	−	0.515861i
$411$	−0.136187			−0.000331356
$412$	191.982	+	191.982i	0.465976	+	0.465976i
$413$	−564.384	+	564.384i	−1.36655	+	1.36655i
$414$		−	4.61672i		−	0.0111515i
$415$	219.667	+	236.428i	0.529317	+	0.569706i
$416$	−137.456			−0.330424
$417$	−89.0872	−	89.0872i	−0.213638	−	0.213638i
$418$	−137.602	+	137.602i	−0.329191	+	0.329191i
$419$		−	747.433i		−	1.78385i	−0.452183	−	0.891925i	$-0.649355\pi$
$419$		−	747.433i		−	1.78385i	0.452183	−	0.891925i	$-0.350645\pi$
$420$	−367.483	−	13.5049i	−0.874959	−	0.0321545i
$421$	283.686			0.673839			0.336919	−	0.941534i	$-0.390615\pi$
$421$	283.686			0.673839			0.336919	+	0.941534i	$0.390615\pi$
$422$	−318.790	−	318.790i	−0.755426	−	0.755426i
$423$	13.7981	−	13.7981i	0.0326197	−	0.0326197i
$424$		−	136.207i		−	0.321242i
$425$	211.640	+	245.268i	0.497976	+	0.577101i
$426$	94.5845			0.222029
$427$	85.2060	+	85.2060i	0.199546	+	0.199546i
$428$	−187.704	+	187.704i	−0.438560	+	0.438560i
$429$		−	367.044i		−	0.855580i
$430$	−1.92105	+	52.2738i	−0.00446755	+	0.121567i
$431$	−47.3290			−0.109812			−0.0549061	−	0.998492i	$-0.517486\pi$
$431$	−47.3290			−0.109812			−0.0549061	+	0.998492i	$0.517486\pi$
$432$	−73.2125	−	73.2125i	−0.169473	−	0.169473i
$433$	−160.083	+	160.083i	−0.369706	+	0.369706i	−0.867370	−	0.497664i	$-0.834191\pi$
$433$	−160.083	+	160.083i	−0.369706	+	0.369706i	0.497664	+	0.867370i	$0.334191\pi$
$434$		−	835.196i		−	1.92442i
$435$	191.413	−	177.843i	0.440029	−	0.408834i
$436$	402.388			0.922908
$437$	96.1165	+	96.1165i	0.219946	+	0.219946i
$438$	−94.5225	+	94.5225i	−0.215805	+	0.215805i
$439$		−	298.531i		−	0.680026i	−0.940421	−	0.340013i	$-0.889569\pi$
$439$		−	298.531i		−	0.680026i	0.940421	−	0.340013i	$-0.110431\pi$
$440$	46.7327	+	50.2986i	0.106211	+	0.114315i
$441$	61.7299			0.139977
$442$	−314.873	−	314.873i	−0.712383	−	0.712383i
$443$	−215.423	+	215.423i	−0.486282	+	0.486282i	−0.907131	−	0.420849i	$-0.861732\pi$
$443$	−215.423	+	215.423i	−0.486282	+	0.486282i	0.420849	+	0.907131i	$0.361732\pi$
$444$		−	132.562i		−	0.298564i
$445$	320.850	+	11.7911i	0.721011	+	0.0264969i
$446$	−230.687			−0.517235
$447$	−116.236	−	116.236i	−0.260035	−	0.260035i
$448$	−66.8578	+	66.8578i	−0.149236	+	0.149236i
$449$		−	143.978i		−	0.320664i	−0.987063	−	0.160332i	$-0.948744\pi$
$449$		−	143.978i		−	0.320664i	0.987063	−	0.160332i	$-0.0512564\pi$
$450$	−18.2206	+	15.7225i	−0.0404903	+	0.0349388i
$451$	213.342			0.473041
$452$	104.867	+	104.867i	0.232006	+	0.232006i
$453$	−396.384	+	396.384i	−0.875020	+	0.875020i
$454$			115.989i			0.255482i
$455$	−52.7347	+	1434.97i	−0.115901	+	3.15378i
$456$	−249.429			−0.546994
$457$	275.771	+	275.771i	0.603437	+	0.603437i	0.941223	−	0.337786i	$-0.109678\pi$
$457$	275.771	+	275.771i	0.603437	+	0.603437i	−0.337786	+	0.941223i	$0.609678\pi$
$458$	320.751	−	320.751i	0.700329	−	0.700329i
$459$		−	335.418i		−	0.730759i
$460$	35.1342	−	32.6434i	0.0763786	−	0.0709639i
$461$	52.7338			0.114390			0.0571950	−	0.998363i	$-0.481784\pi$
$461$	52.7338			0.114390			0.0571950	+	0.998363i	$0.481784\pi$
$462$	−178.528	−	178.528i	−0.386423	−	0.386423i
$463$	−192.059	+	192.059i	−0.414814	+	0.414814i	−0.883412	−	0.468598i	$-0.844759\pi$
$463$	−192.059	+	192.059i	−0.414814	+	0.414814i	0.468598	+	0.883412i	$0.344759\pi$
$464$		−	67.1803i		−	0.144785i
$465$	−529.116	−	569.490i	−1.13788	−	1.22471i
$466$	222.579			0.477638
$467$	73.1687	+	73.1687i	0.156678	+	0.156678i	0.781093	−	0.624415i	$-0.214662\pi$
$467$	73.1687	+	73.1687i	0.156678	+	0.156678i	−0.624415	+	0.781093i	$0.714662\pi$
$468$	23.3915	−	23.3915i	0.0499819	−	0.0499819i
$469$		−	301.586i		−	0.643041i
$470$	202.569	+	7.44435i	0.430998	+	0.0158390i
$471$	492.091			1.04478
$472$	135.065	+	135.065i	0.286155	+	0.286155i
$473$	−25.3953	+	25.3953i	−0.0536898	+	0.0536898i
$474$			498.410i			1.05150i
$475$	52.0100	−	706.669i	0.109495	−	1.48772i
$476$	−306.304			−0.643497
$477$	23.1789	+	23.1789i	0.0485931	+	0.0485931i
$478$	−249.659	+	249.659i	−0.522300	+	0.522300i
$479$			99.9056i			0.208571i	0.994547	+	0.104286i	$0.0332556\pi$
$479$			99.9056i			0.208571i	−0.994547	+	0.104286i	$0.966744\pi$
$480$	−3.23191	+	87.9438i	−0.00673314	+	0.183216i
$481$	−517.639			−1.07617
$482$	105.175	+	105.175i	0.218206	+	0.218206i
$483$	−124.704	+	124.704i	−0.258186	+	0.258186i
$484$		−	194.861i		−	0.402605i
$485$	−509.714	+	473.578i	−1.05096	+	0.976450i
$486$	51.8744			0.106737
$487$	186.182	+	186.182i	0.382304	+	0.382304i	0.871932	−	0.489628i	$-0.162867\pi$
$487$	186.182	+	186.182i	0.382304	+	0.382304i	−0.489628	+	0.871932i	$0.662867\pi$
$488$	20.3910	−	20.3910i	0.0417848	−	0.0417848i
$489$		−	22.4480i		−	0.0459060i
$490$	436.473	+	469.777i	0.890761	+	0.958730i
$491$	593.353			1.20846			0.604229	−	0.796811i	$-0.293481\pi$
$491$	593.353			1.20846			0.604229	+	0.796811i	$0.293481\pi$
$492$	193.361	+	193.361i	0.393010	+	0.393010i
$493$	153.891	−	153.891i	0.312152	−	0.312152i
$494$			973.988i			1.97164i
$495$	−16.5123	−	0.606820i	−0.0333581	−	0.00122590i
$496$	−199.874			−0.402972
$497$	−179.644	−	179.644i	−0.361458	−	0.361458i
$498$	−200.824	+	200.824i	−0.403262	+	0.403262i
$499$			757.209i			1.51745i	0.651410	+	0.758726i	$0.274178\pi$
$499$			757.209i			1.51745i	−0.651410	+	0.758726i	$0.725822\pi$
$500$	−248.484	−	27.4941i	−0.496967	−	0.0549883i
$501$	324.167			0.647041
$502$	−114.474	−	114.474i	−0.228036	−	0.228036i
$503$	243.599	−	243.599i	0.484293	−	0.484293i	−0.422207	−	0.906500i	$-0.638744\pi$
$503$	243.599	−	243.599i	0.484293	−	0.484293i	0.906500	+	0.422207i	$0.138744\pi$
$504$		−	22.7550i		−	0.0451487i
$505$	−24.4867	+	666.311i	−0.0484885	+	1.31943i
$506$	32.9271			0.0650734
$507$	−927.211	−	927.211i	−1.82882	−	1.82882i
$508$	83.8355	−	83.8355i	0.165030	−	0.165030i
$509$			955.807i			1.87781i	0.344172	+	0.938906i	$0.388160\pi$
$509$			955.807i			1.87781i	−0.344172	+	0.938906i	$0.611840\pi$
$510$	−208.858	+	194.051i	−0.409525	+	0.380492i
$511$	359.053			0.702648
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	−518.770	+	518.770i	−1.01125	+	1.01125i
$514$		−	318.115i		−	0.618901i
$515$	−462.006	−	497.258i	−0.897098	−	0.965550i
$516$	−46.0337			−0.0892126
$517$	98.4105	+	98.4105i	0.190349	+	0.190349i
$518$	−251.776	+	251.776i	−0.486054	+	0.486054i
$519$			387.336i			0.746312i
$520$	343.409	+	12.6202i	0.660401	+	0.0242695i
$521$	−383.665			−0.736402			−0.368201	−	0.929746i	$-0.620026\pi$
$521$	−383.665			−0.736402			−0.368201	+	0.929746i	$0.620026\pi$
$522$	11.4324	+	11.4324i	0.0219011	+	0.0219011i
$523$	233.552	−	233.552i	0.446563	−	0.446563i	−0.447647	−	0.894210i	$-0.647738\pi$
$523$	233.552	−	233.552i	0.446563	−	0.446563i	0.894210	+	0.447647i	$0.147738\pi$
$524$			445.786i			0.850737i
$525$	916.847	+	67.4788i	1.74638	+	0.128531i
$526$	−83.7398			−0.159201
$527$	−457.855	−	457.855i	−0.868796	−	0.868796i
$528$	−42.7242	+	42.7242i	−0.0809170	+	0.0809170i
$529$		−	23.0000i		−	0.0434783i
$530$	−12.5054	+	340.287i	−0.0235952	+	0.642051i
$531$	−45.9693			−0.0865711
$532$	473.741	+	473.741i	0.890491	+	0.890491i
$533$	755.048	−	755.048i	1.41660	−	1.41660i
$534$			282.549i			0.529117i
$535$	486.176	−	451.709i	0.908741	−	0.844316i
$536$	−72.1738			−0.134653
$537$	710.327	+	710.327i	1.32277	+	1.32277i
$538$	−354.532	+	354.532i	−0.658981	+	0.658981i
$539$			440.267i			0.816823i
$540$	176.186	+	189.630i	0.326270	+	0.351166i
$541$	99.6220			0.184144			0.0920721	−	0.995752i	$-0.470651\pi$
$541$	99.6220			0.184144			0.0920721	+	0.995752i	$0.470651\pi$
$542$	−179.845	−	179.845i	−0.331818	−	0.331818i
$543$	252.031	−	252.031i	0.464146	−	0.464146i
$544$			73.3029i			0.134748i
$545$	−1005.29	−	36.9441i	−1.84457	−	0.0677874i
$546$	−1263.67			−2.31442
$547$	−171.342	−	171.342i	−0.313240	−	0.313240i	0.532924	−	0.846163i	$-0.321093\pi$
$547$	−171.342	−	171.342i	−0.313240	−	0.313240i	−0.846163	+	0.532924i	$0.821093\pi$
$548$	0.0619011	−	0.0619011i	0.000112958	−	0.000112958i
$549$			6.94006i			0.0126413i
$550$	−112.135	−	129.952i	−0.203882	−	0.236277i
$551$	−476.026			−0.863932
$552$	29.8433	+	29.8433i	0.0540640	+	0.0540640i
$553$	946.629	−	946.629i	1.71181	−	1.71181i
$554$		−	617.319i		−	1.11429i
$555$	−12.1709	+	331.183i	−0.0219295	+	0.596726i
$556$	80.9854			0.145657
$557$	−236.687	−	236.687i	−0.424932	−	0.424932i	0.461966	−	0.886898i	$-0.347144\pi$
$557$	−236.687	−	236.687i	−0.424932	−	0.424932i	−0.886898	+	0.461966i	$0.847144\pi$
$558$	34.0135	−	34.0135i	0.0609561	−	0.0609561i
$559$			179.755i			0.321566i
$560$	173.170	−	160.893i	0.309232	−	0.287309i
$561$	−195.738			−0.348909
$562$	156.370	+	156.370i	0.278239	+	0.278239i
$563$	−627.002	+	627.002i	−1.11368	+	1.11368i	−0.121032	+	0.992649i	$0.538620\pi$
$563$	−627.002	+	627.002i	−1.11368	+	1.11368i	−0.992649	+	0.121032i	$0.961380\pi$
$564$			178.388i			0.316290i
$565$	−252.362	−	271.618i	−0.446658	−	0.480739i
$566$	−251.879			−0.445016
$567$	−724.261	−	724.261i	−1.27736	−	1.27736i
$568$	−42.9914	+	42.9914i	−0.0756891	+	0.0756891i
$569$			694.665i			1.22085i	0.792073	+	0.610426i	$0.209002\pi$
$569$			694.665i			1.22085i	−0.792073	+	0.610426i	$0.790998\pi$
$570$	623.153	+	22.9007i	1.09325	+	0.0401766i
$571$	−1107.18			−1.93902			−0.969512	−	0.245043i	$-0.921198\pi$
$571$	−1107.18			−1.93902			−0.969512	+	0.245043i	$0.921198\pi$
$572$	166.832	+	166.832i	0.291665	+	0.291665i
$573$	502.800	−	502.800i	0.877487	−	0.877487i
$574$		−	734.500i		−	1.27962i
$575$	−90.7732	+	78.3276i	−0.157867	+	0.136222i
$576$	−5.44558			−0.00945414
$577$	82.5531	+	82.5531i	0.143073	+	0.143073i	0.775015	−	0.631942i	$-0.217742\pi$
$577$	82.5531	+	82.5531i	0.143073	+	0.143073i	−0.631942	+	0.775015i	$0.717742\pi$
$578$	121.084	−	121.084i	0.209487	−	0.209487i
$579$		−	194.787i		−	0.336419i
$580$	−6.16797	+	167.837i	−0.0106344	+	0.289375i
$581$	762.851			1.31300
$582$	−432.956	−	432.956i	−0.743911	−	0.743911i
$583$	−165.315	+	165.315i	−0.283560	+	0.283560i
$584$		−	85.9265i		−	0.147134i
$585$	−60.5870	+	56.2918i	−0.103568	+	0.0962253i
$586$	−300.316			−0.512485
$587$	569.570	+	569.570i	0.970306	+	0.970306i	0.999572	−	0.0292653i	$-0.00931676\pi$
$587$	569.570	+	569.570i	0.970306	+	0.970306i	−0.0292653	+	0.999572i	$0.509317\pi$
$588$	−399.034	+	399.034i	−0.678629	+	0.678629i
$589$			1416.27i			2.40453i
$590$	−325.034	−	349.836i	−0.550906	−	0.592942i
$591$	476.330			0.805972
$592$	60.2535	+	60.2535i	0.101780	+	0.101780i
$593$	−713.467	+	713.467i	−1.20315	+	1.20315i	−0.229945	+	0.973204i	$0.573855\pi$
$593$	−713.467	+	713.467i	−1.20315	+	1.20315i	−0.973204	+	0.229945i	$0.926145\pi$
$594$			177.718i			0.299188i
$595$	765.244	+	28.1225i	1.28613	+	0.0472647i
$596$	105.665			0.177290
$597$	−119.053	−	119.053i	−0.199419	−	0.199419i
$598$	116.534	−	116.534i	0.194873	−	0.194873i
$599$		−	128.311i		−	0.214209i	−0.994248	−	0.107104i	$-0.965842\pi$
$599$		−	128.311i		−	0.214209i	0.994248	−	0.107104i	$-0.0341579\pi$
$600$	16.1486	−	219.414i	0.0269144	−	0.365691i
$601$	845.916			1.40751			0.703757	−	0.710440i	$-0.251504\pi$
$601$	845.916			1.40751			0.703757	+	0.710440i	$0.251504\pi$
$602$	87.4317	+	87.4317i	0.145235	+	0.145235i
$603$	12.2821	−	12.2821i	0.0203684	−	0.0203684i
$604$		−	360.336i		−	0.596583i
$605$	−17.8906	+	486.824i	−0.0295713	+	0.804668i
$606$	−586.771			−0.968268
$607$	−693.618	−	693.618i	−1.14270	−	1.14270i	−0.987955	−	0.154745i	$-0.950545\pi$
$607$	−693.618	−	693.618i	−1.14270	−	1.14270i	−0.154745	−	0.987955i	$-0.549455\pi$
$608$	113.373	−	113.373i	0.186469	−	0.186469i
$609$		−	617.607i		−	1.01413i
$610$	−52.8153	+	49.0710i	−0.0865824	+	0.0804442i
$611$	696.579			1.14006
$612$	−12.4743	−	12.4743i	−0.0203828	−	0.0203828i
$613$	83.2281	−	83.2281i	0.135772	−	0.135772i	−0.635955	−	0.771726i	$-0.719393\pi$
$613$	83.2281	−	83.2281i	0.135772	−	0.135772i	0.771726	+	0.635955i	$0.219393\pi$
$614$		−	318.514i		−	0.518753i
$615$	−465.323	−	500.829i	−0.756623	−	0.814356i
$616$	162.292			0.263461
$617$	−309.635	−	309.635i	−0.501840	−	0.501840i	0.410169	−	0.912009i	$-0.365470\pi$
$617$	−309.635	−	309.635i	−0.501840	−	0.501840i	−0.912009	+	0.410169i	$0.865470\pi$
$618$	422.376	−	422.376i	0.683457	−	0.683457i
$619$			965.745i			1.56017i	0.625674	+	0.780085i	$0.284824\pi$
$619$			965.745i			1.56017i	−0.625674	+	0.780085i	$0.715176\pi$
$620$	499.348	+	18.3509i	0.805401	+	0.0295982i
$621$	124.138			0.199900
$622$	−153.824	−	153.824i	−0.247305	−	0.247305i
$623$	536.645	−	536.645i	0.861388	−	0.861388i
$624$			302.415i			0.484639i
$625$	618.266	+	91.5028i	0.989225	+	0.146404i
$626$	−661.884			−1.05732
$627$	302.735	+	302.735i	0.482831	+	0.482831i
$628$	−223.669	+	223.669i	−0.356162	+	0.356162i
$629$			276.047i			0.438867i
$630$	−2.08918	+	56.8490i	−0.00331617	+	0.0902366i
$631$	−36.9891			−0.0586199			−0.0293099	−	0.999570i	$-0.509331\pi$
$631$	−36.9891			−0.0586199			−0.0293099	+	0.999570i	$0.509331\pi$
$632$	−226.542	−	226.542i	−0.358452	−	0.358452i
$633$	−701.363	+	701.363i	−1.10800	+	1.10800i
$634$			745.488i			1.17585i
$635$	−217.144	+	201.750i	−0.341960	+	0.317717i
$636$	−299.665			−0.471172
$637$	1558.17	+	1558.17i	2.44611	+	2.44611i
$638$	−81.5374	+	81.5374i	−0.127802	+	0.127802i
$639$		−	14.6321i		−	0.0228984i
$640$	−38.5040	−	41.4420i	−0.0601625	−	0.0647531i
$641$	−343.983			−0.536635			−0.268317	−	0.963331i	$-0.586468\pi$
$641$	−343.983			−0.536635			−0.268317	+	0.963331i	$0.586468\pi$
$642$	412.963	+	412.963i	0.643245	+	0.643245i
$643$	307.618	−	307.618i	0.478411	−	0.478411i	−0.426212	−	0.904623i	$-0.640152\pi$
$643$	307.618	−	307.618i	0.478411	−	0.478411i	0.904623	+	0.426212i	$0.140152\pi$
$644$		−	113.363i		−	0.176029i
$645$	115.007	+	4.22645i	0.178305	+	0.00655264i
$646$	519.410			0.804041
$647$	−169.670	−	169.670i	−0.262241	−	0.262241i	0.563723	−	0.825964i	$-0.309369\pi$
$647$	−169.670	−	169.670i	−0.262241	−	0.262241i	−0.825964	+	0.563723i	$0.809369\pi$
$648$	−173.326	+	173.326i	−0.267478	+	0.267478i
$649$		−	327.860i		−	0.505177i
$650$	−856.784	−	63.0583i	−1.31813	−	0.0970127i
$651$	−1837.50			−2.82258
$652$	10.2033	+	10.2033i	0.0156492	+	0.0156492i
$653$	417.861	−	417.861i	0.639909	−	0.639909i	−0.310624	−	0.950533i	$-0.600538\pi$
$653$	417.861	−	417.861i	0.639909	−	0.639909i	0.950533	+	0.310624i	$0.100538\pi$
$654$		−	885.285i		−	1.35365i
$655$	40.9286	−	1113.71i	0.0624865	−	1.70033i
$656$	−175.776			−0.267952
$657$	14.6225	+	14.6225i	0.0222565	+	0.0222565i
$658$	338.811	−	338.811i	0.514911	−	0.514911i
$659$			483.607i			0.733849i	0.930251	+	0.366925i	$0.119589\pi$
$659$			483.607i			0.733849i	−0.930251	+	0.366925i	$0.880411\pi$
$660$	110.661	−	102.816i	0.167668	−	0.155781i
$661$	692.421			1.04754			0.523768	−	0.851861i	$-0.324526\pi$
$661$	692.421			1.04754			0.523768	+	0.851861i	$0.324526\pi$
$662$	−286.269	−	286.269i	−0.432430	−	0.432430i
$663$	−692.746	+	692.746i	−1.04487	+	1.04487i
$664$		−	182.561i		−	0.274941i
$665$	−1140.06	−	1227.05i	−1.71437	−	1.84519i
$666$	−20.5072			−0.0307916
$667$	56.9549	+	56.9549i	0.0853896	+	0.0853896i
$668$	−147.343	+	147.343i	−0.220574	+	0.220574i
$669$			507.529i			0.758639i
$670$	180.313	+	6.62644i	0.269124	+	0.00989021i
$671$	−49.4976			−0.0737669
$672$	147.092	+	147.092i	0.218887	+	0.218887i
$673$	−225.899	+	225.899i	−0.335660	+	0.335660i	−0.854731	−	0.519071i	$-0.826278\pi$
$673$	−225.899	+	225.899i	−0.335660	+	0.335660i	0.519071	+	0.854731i	$0.326278\pi$
$674$		−	82.9826i		−	0.123120i
$675$	−422.757	−	489.930i	−0.626307	−	0.725822i
$676$	842.888			1.24688
$677$	−384.203	−	384.203i	−0.567508	−	0.567508i	0.363922	−	0.931429i	$-0.381437\pi$
$677$	−384.203	−	384.203i	−0.567508	−	0.567508i	−0.931429	+	0.363922i	$0.881437\pi$
$678$	230.715	−	230.715i	0.340288	−	0.340288i
$679$			1644.63i			2.42213i
$680$	6.73011	−	183.134i	0.00989722	−	0.269314i
$681$	255.185			0.374721
$682$	242.589	+	242.589i	0.355703	+	0.355703i
$683$	902.944	−	902.944i	1.32203	−	1.32203i	0.409893	−	0.912133i	$-0.365566\pi$
$683$	902.944	−	902.944i	1.32203	−	1.32203i	0.912133	−	0.409893i	$-0.134434\pi$
$684$			38.5864i			0.0564128i
$685$	−0.160332	+	0.148965i	−0.000234061	+	0.000217467i
$686$	696.762			1.01569
$687$	−705.677	−	705.677i	−1.02719	−	1.02719i
$688$	20.9236	−	20.9236i	0.0304123	−	0.0304123i
$689$			1170.15i			1.69834i
$690$	−71.8180	−	77.2980i	−0.104084	−	0.112026i
$691$	621.287			0.899113			0.449557	−	0.893252i	$-0.351582\pi$
$691$	621.287			0.899113			0.449557	+	0.893252i	$0.351582\pi$
$692$	−176.055	−	176.055i	−0.254415	−	0.254415i
$693$	−27.6180	+	27.6180i	−0.0398527	+	0.0398527i
$694$		−	786.575i		−	1.13339i
$695$	−202.327	−	7.43545i	−0.291118	−	0.0106985i
$696$	−147.802			−0.212359
$697$	−402.654	−	402.654i	−0.577695	−	0.577695i
$698$	−61.6981	+	61.6981i	−0.0883927	+	0.0883927i
$699$		−	489.692i		−	0.700561i
$700$	−447.405	+	386.063i	−0.639150	+	0.551518i
$701$	754.563			1.07641			0.538205	−	0.842814i	$-0.319103\pi$
$701$	754.563			1.07641			0.538205	+	0.842814i	$0.319103\pi$
$702$	628.970	+	628.970i	0.895968	+	0.895968i
$703$	426.945	−	426.945i	0.607318	−	0.607318i
$704$		−	38.8387i		−	0.0551687i
$705$	16.3782	−	445.668i	0.0232314	−	0.632153i
$706$	−297.258			−0.421045
$707$	1114.45	+	1114.45i	1.57631	+	1.57631i
$708$	297.154	−	297.154i	0.419709	−	0.419709i
$709$		−	789.221i		−	1.11315i	−0.830798	−	0.556574i	$-0.812116\pi$
$709$		−	789.221i		−	1.11315i	0.830798	−	0.556574i	$-0.187884\pi$
$710$	111.353	−	103.459i	0.156835	−	0.145717i
$711$	77.1033			0.108443
$712$	−128.427	−	128.427i	−0.180374	−	0.180374i
$713$	169.452	−	169.452i	0.237660	−	0.237660i
$714$			673.894i			0.943829i
$715$	−401.482	−	432.116i	−0.561513	−	0.604358i
$716$	−645.729			−0.901856
$717$	549.270	+	549.270i	0.766067	+	0.766067i
$718$	−133.489	+	133.489i	−0.185918	+	0.185918i
$719$		−	904.423i		−	1.25789i	−0.777450	−	0.628945i	$-0.783487\pi$
$719$		−	904.423i		−	1.25789i	0.777450	−	0.628945i	$-0.216513\pi$
$720$	13.6048	+	0.499971i	0.0188955	+	0.000694404i
$721$	−1604.44			−2.22530
$722$	−442.338	−	442.338i	−0.612657	−	0.612657i
$723$	231.394	−	231.394i	0.320046	−	0.320046i
$724$			229.111i			0.316452i
$725$	30.8191	−	418.744i	0.0425090	−	0.577578i
$726$	−428.710			−0.590509
$727$	−80.8538	−	80.8538i	−0.111216	−	0.111216i	0.649309	−	0.760525i	$-0.275058\pi$
$727$	−80.8538	−	80.8538i	−0.111216	−	0.111216i	−0.760525	+	0.649309i	$0.775058\pi$
$728$	574.376	−	574.376i	0.788978	−	0.788978i
$729$			665.839i			0.913359i
$730$	−7.88910	+	214.671i	−0.0108070	+	0.294070i
$731$	95.8603			0.131136
$732$	−44.8618	−	44.8618i	−0.0612866	−	0.0612866i
$733$	3.67038	−	3.67038i	0.00500735	−	0.00500735i	−0.704599	−	0.709606i	$-0.748873\pi$
$733$	3.67038	−	3.67038i	0.00500735	−	0.00500735i	0.709606	+	0.704599i	$0.248873\pi$
$734$			318.479i			0.433895i
$735$	1033.55	−	960.275i	1.40619	−	1.30650i
$736$	−27.1293			−0.0368605
$737$	87.5982	+	87.5982i	0.118858	+	0.118858i
$738$	29.9126	−	29.9126i	0.0405320	−	0.0405320i
$739$			13.1697i			0.0178209i	0.999960	+	0.00891047i	$0.00283633\pi$
$739$			13.1697i			0.0178209i	−0.999960	+	0.00891047i	$0.997164\pi$
$740$	−145.000	−	156.064i	−0.195946	−	0.210898i
$741$	2142.85			2.89184
$742$	569.154	+	569.154i	0.767054	+	0.767054i
$743$	−519.149	+	519.149i	−0.698720	+	0.698720i	−0.964134	−	0.265414i	$-0.914491\pi$
$743$	−519.149	+	519.149i	−0.698720	+	0.698720i	0.265414	+	0.964134i	$0.414491\pi$
$744$			439.739i			0.591047i
$745$	−263.985	−	9.70135i	−0.354342	−	0.0130219i
$746$	−680.269			−0.911888
$747$	31.0672	+	31.0672i	0.0415893	+	0.0415893i
$748$	88.9686	−	88.9686i	0.118942	−	0.118942i
$749$		−	1568.68i		−	2.09437i
$750$	−60.4893	+	546.684i	−0.0806524	+	0.728911i
$751$	1.54655			0.00205932			0.00102966	−	0.999999i	$-0.499672\pi$
$751$	1.54655			0.00205932			0.00102966	+	0.999999i	$0.499672\pi$
$752$	−81.0823	−	81.0823i	−0.107822	−	0.107822i
$753$	−251.852	+	251.852i	−0.334464	+	0.334464i
$754$			577.147i			0.765447i
$755$	−33.0833	+	900.233i	−0.0438189	+	1.19236i
$756$	611.853			0.809329
$757$	−354.268	−	354.268i	−0.467989	−	0.467989i	0.433273	−	0.901263i	$-0.357358\pi$
$757$	−354.268	−	354.268i	−0.467989	−	0.467989i	−0.901263	+	0.433273i	$0.857358\pi$
$758$	−578.294	+	578.294i	−0.762921	+	0.762921i
$759$		−	72.4423i		−	0.0954445i
$760$	−293.650	+	272.832i	−0.386382	+	0.358990i
$761$	409.762			0.538452			0.269226	−	0.963077i	$-0.413232\pi$
$761$	409.762			0.538452			0.269226	+	0.963077i	$0.413232\pi$
$762$	−184.445	−	184.445i	−0.242053	−	0.242053i
$763$	−1681.42	+	1681.42i	−2.20370	+	2.20370i
$764$			457.075i			0.598265i
$765$	30.0194	+	32.3100i	0.0392410	+	0.0422353i
$766$	82.2434			0.107367
$767$	−1160.35	−	1160.35i	−1.51284	−	1.51284i
$768$	35.2013	−	35.2013i	0.0458350	−	0.0458350i
$769$		−	386.028i		−	0.501987i	−0.967989	−	0.250994i	$-0.919243\pi$
$769$		−	386.028i		−	0.501987i	0.967989	−	0.250994i	$-0.0807573\pi$
$770$	−405.456	−	14.9004i	−0.526566	−	0.0193512i
$771$	−699.878			−0.907753
$772$	88.5361	+	88.5361i	0.114684	+	0.114684i
$773$	1008.36	−	1008.36i	1.30448	−	1.30448i	0.379135	−	0.925341i	$-0.376222\pi$
$773$	1008.36	−	1008.36i	1.30448	−	1.30448i	0.925341	−	0.379135i	$-0.123778\pi$
$774$			7.12134i			0.00920070i
$775$	−1245.84	−	91.6926i	−1.60754	−	0.118313i
$776$	393.582			0.507194
$777$	553.927	+	553.927i	0.712905	+	0.712905i
$778$	539.251	−	539.251i	0.693124	−	0.693124i
$779$			1245.52i			1.59887i
$780$	27.7654	−	755.526i	0.0355966	−	0.968624i
$781$	104.358			0.133621
$782$	−62.1456	−	62.1456i	−0.0794701	−	0.0794701i
$783$	−307.402	+	307.402i	−0.392595	+	0.392595i
$784$		−	362.745i		−	0.462685i
$785$	579.332	−	538.261i	0.738003	−	0.685683i
$786$	980.765			1.24779
$787$	358.581	+	358.581i	0.455630	+	0.455630i	0.897218	−	0.441588i	$-0.145585\pi$
$787$	358.581	+	358.581i	0.455630	+	0.455630i	−0.441588	+	0.897218i	$0.645585\pi$
$788$	−216.506	+	216.506i	−0.274753	+	0.274753i
$789$			184.234i			0.233503i
$790$	545.173	+	586.772i	0.690092	+	0.742749i
$791$	−876.394			−1.10796
$792$	6.60936	+	6.60936i	0.00834516	+	0.00834516i
$793$	−175.179	+	175.179i	−0.220907	+	0.220907i
$794$		−	244.281i		−	0.307659i
$795$	748.658	+	27.5129i	0.941708	+	0.0346075i
$796$	108.226			0.135963
$797$	−362.026	−	362.026i	−0.454236	−	0.454236i	0.442522	−	0.896758i	$-0.354084\pi$
$797$	−362.026	−	362.026i	−0.454236	−	0.454236i	−0.896758	+	0.442522i	$0.854084\pi$
$798$	1042.27	−	1042.27i	1.30610	−	1.30610i
$799$		−	371.473i		−	0.464923i
$800$	92.3902	+	107.070i	0.115488	+	0.133838i
$801$	43.7099			0.0545691
$802$	−190.196	−	190.196i	−0.237152	−	0.237152i
$803$	−104.290	+	104.290i	−0.129875	+	0.129875i
$804$			158.788i			0.197498i
$805$	−10.4081	+	283.216i	−0.0129293	+	0.351821i
$806$	1717.12			2.13042
$807$	779.997	+	779.997i	0.966540	+	0.966540i
$808$	266.704	−	266.704i	0.330080	−	0.330080i
$809$		−	676.712i		−	0.836479i	−0.908337	−	0.418240i	$-0.862647\pi$
$809$		−	676.712i		−	0.836479i	0.908337	−	0.418240i	$-0.137353\pi$
$810$	448.936	−	417.109i	0.554242	−	0.514949i
$811$	−597.480			−0.736720			−0.368360	−	0.929683i	$-0.620081\pi$
$811$	−597.480			−0.736720			−0.368360	+	0.929683i	$0.620081\pi$
$812$	280.720	+	280.720i	0.345714	+	0.345714i
$813$	−395.674	+	395.674i	−0.486684	+	0.486684i
$814$		−	146.261i		−	0.179681i
$815$	−24.5542	−	26.4278i	−0.0301278	−	0.0324267i
$816$	161.272			0.197638
$817$	−148.261	−	148.261i	−0.181470	−	0.181470i
$818$	350.710	−	350.710i	0.428741	−	0.428741i
$819$			195.488i			0.238691i
$820$	439.144	+	16.1384i	0.535542	+	0.0196810i
$821$	−731.016			−0.890397			−0.445199	−	0.895432i	$-0.646867\pi$
$821$	−731.016			−0.890397			−0.445199	+	0.895432i	$0.646867\pi$
$822$	−0.136187	−	0.136187i	−0.000165678	−	0.000165678i
$823$	−346.050	+	346.050i	−0.420474	+	0.420474i	−0.885367	−	0.464893i	$-0.846093\pi$
$823$	−346.050	+	346.050i	−0.420474	+	0.420474i	0.464893	+	0.885367i	$0.346093\pi$
$824$			383.965i			0.465976i
$825$	−285.905	+	246.706i	−0.346552	+	0.299038i
$826$	−1128.77			−1.36655
$827$	209.168	+	209.168i	0.252924	+	0.252924i	0.822168	−	0.569245i	$-0.192764\pi$
$827$	209.168	+	209.168i	0.252924	+	0.252924i	−0.569245	+	0.822168i	$0.692764\pi$
$828$	4.61672	−	4.61672i	0.00557575	−	0.00557575i
$829$		−	1158.20i		−	1.39710i	−0.715561	−	0.698550i	$-0.753829\pi$
$829$		−	1158.20i		−	1.39710i	0.715561	−	0.698550i	$-0.246171\pi$
$830$	−16.7613	+	456.095i	−0.0201944	+	0.549512i
$831$	−1358.15			−1.63436
$832$	−137.456	−	137.456i	−0.165212	−	0.165212i
$833$	830.946	−	830.946i	0.997534	−	0.997534i
$834$		−	178.174i		−	0.213638i
$835$	381.638	−	354.582i	0.457052	−	0.424649i
$836$	−275.204			−0.329191
$837$	914.581	+	914.581i	1.09269	+	1.09269i
$838$	747.433	−	747.433i	0.891925	−	0.891925i
$839$		−	150.216i		−	0.179042i	−0.995985	−	0.0895210i	$-0.971466\pi$
$839$		−	150.216i		−	0.179042i	0.995985	−	0.0895210i	$-0.0285336\pi$
$840$	−353.978	−	380.988i	−0.421402	−	0.453557i
$841$	558.926			0.664596
$842$	283.686	+	283.686i	0.336919	+	0.336919i
$843$	344.027	−	344.027i	0.408099	−	0.408099i
$844$		−	637.579i		−	0.755426i
$845$	−2105.80	−	77.3875i	−2.49207	−	0.0915828i
$846$	27.5963			0.0326197
$847$	814.248	+	814.248i	0.961332	+	0.961332i
$848$	136.207	−	136.207i	0.160621	−	0.160621i
$849$			554.154i			0.652714i
$850$	−33.6278	+	456.908i	−0.0395622	+	0.537538i
$851$	−102.165			−0.120053
$852$	94.5845	+	94.5845i	0.111015	+	0.111015i
$853$	−16.8839	+	16.8839i	−0.0197936	+	0.0197936i	−0.716934	−	0.697141i	$-0.754455\pi$
$853$	−16.8839	+	16.8839i	−0.0197936	+	0.0197936i	0.697141	+	0.716934i	$0.254455\pi$
$854$			170.412i			0.199546i
$855$	3.54270	−	96.4008i	0.00414351	−	0.112749i
$856$	−375.407			−0.438560
$857$	−943.212	−	943.212i	−1.10060	−	1.10060i	−0.994338	−	0.106259i	$-0.966113\pi$
$857$	−943.212	−	943.212i	−1.10060	−	1.10060i	−0.106259	−	0.994338i	$-0.533887\pi$
$858$	367.044	−	367.044i	0.427790	−	0.427790i
$859$		−	1298.04i		−	1.51110i	−0.655088	−	0.755552i	$-0.727369\pi$
$859$		−	1298.04i		−	1.51110i	0.655088	−	0.755552i	$-0.272631\pi$
$860$	−54.1949	+	50.3528i	−0.0630173	+	0.0585497i
$861$	−1615.96			−1.87684
$862$	−47.3290	−	47.3290i	−0.0549061	−	0.0549061i
$863$	512.914	−	512.914i	0.594338	−	0.594338i	−0.344462	−	0.938800i	$-0.611939\pi$
$863$	512.914	−	512.914i	0.594338	−	0.594338i	0.938800	+	0.344462i	$0.111939\pi$
$864$		−	146.425i		−	0.169473i
$865$	423.678	+	456.006i	0.489801	+	0.527174i
$866$	−320.166			−0.369706
$867$	−266.394	−	266.394i	−0.307259	−	0.307259i
$868$	835.196	−	835.196i	0.962208	−	0.962208i
$869$			549.912i			0.632810i
$870$	369.256	+	13.5700i	0.424432	+	0.0155977i
$871$	620.047			0.711879
$872$	402.388	+	402.388i	0.461454	+	0.461454i
$873$	−66.9777	+	66.9777i	−0.0767213	+	0.0767213i
$874$			192.233i			0.219946i
$875$	1153.20	−	923.428i	1.31795	−	1.05535i
$876$	−189.045			−0.215805
$877$	−172.303	−	172.303i	−0.196469	−	0.196469i	0.602015	−	0.798484i	$-0.294365\pi$
$877$	−172.303	−	172.303i	−0.196469	−	0.196469i	−0.798484	+	0.602015i	$0.794365\pi$
$878$	298.531	−	298.531i	0.340013	−	0.340013i
$879$			660.719i			0.751671i
$880$	−3.56587	+	97.0314i	−0.00405213	+	0.110263i
$881$	723.223			0.820911			0.410456	−	0.911881i	$-0.365370\pi$
$881$	723.223			0.820911			0.410456	+	0.911881i	$0.365370\pi$
$882$	61.7299	+	61.7299i	0.0699886	+	0.0699886i
$883$	1050.94	−	1050.94i	1.19020	−	1.19020i	0.213186	−	0.977012i	$-0.431616\pi$
$883$	1050.94	−	1050.94i	1.19020	−	1.19020i	0.977012	−	0.213186i	$-0.0683841\pi$
$884$		−	629.747i		−	0.712383i
$885$	−769.666	+	715.101i	−0.869679	+	0.808024i
$886$	−430.846			−0.486282
$887$	−379.967	−	379.967i	−0.428373	−	0.428373i	0.459701	−	0.888074i	$-0.347957\pi$
$887$	−379.967	−	379.967i	−0.428373	−	0.428373i	−0.888074	+	0.459701i	$0.847957\pi$
$888$	132.562	−	132.562i	0.149282	−	0.149282i
$889$			700.631i			0.788112i
$890$	309.059	+	332.641i	0.347257	+	0.373754i
$891$	420.735			0.472205
$892$	−230.687	−	230.687i	−0.258617	−	0.258617i
$893$	−574.534	+	574.534i	−0.643375	+	0.643375i
$894$		−	232.472i		−	0.260035i
$895$	1613.23	+	59.2858i	1.80249	+	0.0662411i
$896$	−133.716			−0.149236
$897$	−256.384	−	256.384i	−0.285824	−	0.285824i
$898$	143.978	−	143.978i	0.160332	−	0.160332i
$899$			839.225i			0.933510i
$900$	−33.9431	−	2.49817i	−0.0377145	−	0.00277574i
$901$	624.022			0.692588
$902$	213.342	+	213.342i	0.236521	+	0.236521i
$903$	192.357	−	192.357i	0.213020	−	0.213020i
$904$			209.733i			0.232006i
$905$	21.0352	−	572.392i	0.0232433	−	0.632477i
$906$	−792.768			−0.875020
$907$	651.343	+	651.343i	0.718129	+	0.718129i	0.968222	−	0.250093i	$-0.0804612\pi$
$907$	651.343	+	651.343i	0.718129	+	0.718129i	−0.250093	+	0.968222i	$0.580461\pi$
$908$	−115.989	+	115.989i	−0.127741	+	0.127741i
$909$			90.7725i			0.0998598i
$910$	−1487.71	+	1382.24i	−1.63484	+	1.51894i
$911$	1182.01			1.29749			0.648744	−	0.761007i	$-0.275295\pi$
$911$	1182.01			1.29749			0.648744	+	0.761007i	$0.275295\pi$
$912$	−249.429	−	249.429i	−0.273497	−	0.273497i
$913$	−221.576	+	221.576i	−0.242690	+	0.242690i
$914$			551.542i			0.603437i
$915$	107.960	+	116.198i	0.117989	+	0.126992i
$916$	641.502			0.700329
$917$	−1862.77	−	1862.77i	−2.03137	−	2.03137i
$918$	335.418	−	335.418i	0.365379	−	0.365379i
$919$		−	1262.29i		−	1.37355i	−0.726871	−	0.686774i	$-0.759026\pi$
$919$		−	1262.29i		−	1.37355i	0.726871	−	0.686774i	$-0.240974\pi$
$920$	67.7775	+	2.49080i	0.0736712	+	0.00270740i
$921$	−700.757			−0.760865
$922$	52.7338	+	52.7338i	0.0571950	+	0.0571950i
$923$	369.340	−	369.340i	0.400152	−	0.400152i
$924$		−	357.055i		−	0.386423i
$925$	347.927	+	403.210i	0.376138	+	0.435903i
$926$	−384.118			−0.414814
$927$	−65.3410	−	65.3410i	−0.0704865	−	0.0704865i
$928$	67.1803	−	67.1803i	0.0723925	−	0.0723925i
$929$			1396.75i			1.50350i	0.659448	+	0.751750i	$0.270790\pi$
$929$			1396.75i			1.50350i	−0.659448	+	0.751750i	$0.729210\pi$
$930$	40.3734	−	1098.61i	0.0434123	−	1.18130i
$931$	−2570.34			−2.76084
$932$	222.579	+	222.579i	0.238819	+	0.238819i
$933$	−338.424	+	338.424i	−0.362727	+	0.362727i
$934$			146.337i			0.156678i
$935$	−230.440	+	214.103i	−0.246460	+	0.228987i
$936$	46.7831			0.0499819
$937$	326.849	+	326.849i	0.348825	+	0.348825i	0.859672	−	0.510847i	$-0.170668\pi$
$937$	326.849	+	326.849i	0.348825	+	0.348825i	−0.510847	+	0.859672i	$0.670668\pi$
$938$	301.586	−	301.586i	0.321521	−	0.321521i
$939$			1456.20i			1.55080i
$940$	195.125	+	210.013i	0.207580	+	0.223419i
$941$	−415.375			−0.441418			−0.220709	−	0.975340i	$-0.570837\pi$
$941$	−415.375			−0.441418			−0.220709	+	0.975340i	$0.570837\pi$
$942$	492.091	+	492.091i	0.522389	+	0.522389i
$943$	149.022	−	149.022i	0.158029	−	0.158029i
$944$			270.130i			0.286155i
$945$	−1528.60	−	56.1756i	−1.61757	−	0.0594451i
$946$	−50.7905			−0.0536898
$947$	368.863	+	368.863i	0.389507	+	0.389507i	0.874512	−	0.485005i	$-0.161182\pi$
$947$	368.863	+	368.863i	0.389507	+	0.389507i	−0.485005	+	0.874512i	$0.661182\pi$
$948$	−498.410	+	498.410i	−0.525749	+	0.525749i
$949$			738.196i			0.777867i
$950$	758.679	−	654.659i	0.798610	−	0.689115i
$951$	1640.13			1.72464
$952$	−306.304	−	306.304i	−0.321748	−	0.321748i
$953$	−1064.52	+	1064.52i	−1.11702	+	1.11702i	−0.124847	+	0.992176i	$0.539844\pi$
$953$	−1064.52	+	1064.52i	−1.11702	+	1.11702i	−0.992176	+	0.124847i	$0.960156\pi$
$954$			46.3578i			0.0485931i
$955$	41.9651	−	1141.92i	0.0439425	−	1.19572i
$956$	−499.319			−0.522300
$957$	179.389	+	179.389i	0.187449	+	0.187449i
$958$	−99.9056	+	99.9056i	−0.104286	+	0.104286i
$959$			0.517321i			0.000539438i
$960$	−91.1757	+	84.7119i	−0.0949747	+	0.0882416i
$961$	1535.86			1.59819
$962$	−517.639	−	517.639i	−0.538086	−	0.538086i
$963$	63.8848	−	63.8848i	0.0663393	−	0.0663393i
$964$			210.350i			0.218206i
$965$	−213.062	−	229.320i	−0.220790	−	0.237637i
$966$	−249.407			−0.258186
$967$	−55.8496	−	55.8496i	−0.0577555	−	0.0577555i	0.677639	−	0.735395i	$-0.263003\pi$
$967$	−55.8496	−	55.8496i	−0.0577555	−	0.0577555i	−0.735395	+	0.677639i	$0.763003\pi$
$968$	194.861	−	194.861i	0.201303	−	0.201303i
$969$		−	1142.74i		−	1.17930i
$970$	−983.292	−	36.1357i	−1.01370	−	0.0372533i
$971$	−50.5920			−0.0521030			−0.0260515	−	0.999661i	$-0.508293\pi$
$971$	−50.5920			−0.0521030			−0.0260515	+	0.999661i	$0.508293\pi$
$972$	51.8744	+	51.8744i	0.0533687	+	0.0533687i
$973$	−338.406	+	338.406i	−0.347797	+	0.347797i
$974$			372.364i			0.382304i
$975$	−138.733	+	1884.99i	−0.142290	+	1.93333i
$976$	40.7820			0.0417848
$977$	1144.04	+	1144.04i	1.17097	+	1.17097i	0.981979	+	0.188992i	$0.0605220\pi$
$977$	1144.04	+	1144.04i	1.17097	+	1.17097i	0.188992	+	0.981979i	$0.439478\pi$
$978$	22.4480	−	22.4480i	0.0229530	−	0.0229530i
$979$			311.746i			0.318433i
$980$	−33.3044	+	906.251i	−0.0339841	+	0.924745i
$981$	−136.952			−0.139605
$982$	593.353	+	593.353i	0.604229	+	0.604229i
$983$	−525.511	+	525.511i	−0.534599	+	0.534599i	−0.921938	−	0.387339i	$-0.873394\pi$
$983$	−525.511	+	525.511i	−0.534599	+	0.534599i	0.387339	+	0.921938i	$0.373394\pi$
$984$			386.722i			0.393010i
$985$	560.777	−	521.021i	0.569317	−	0.528955i
$986$	307.782			0.312152
$987$	−745.412	−	745.412i	−0.755230	−	0.755230i
$988$	−973.988	+	973.988i	−0.985818	+	0.985818i
$989$			35.4778i			0.0358724i
$990$	−15.9054	−	17.1191i	−0.0160661	−	0.0172920i
$991$	−584.279			−0.589585			−0.294793	−	0.955561i	$-0.595251\pi$
$991$	−584.279			−0.589585			−0.294793	+	0.955561i	$0.595251\pi$
$992$	−199.874	−	199.874i	−0.201486	−	0.201486i
$993$	−629.814	+	629.814i	−0.634254	+	0.634254i
$994$		−	359.289i		−	0.361458i
$995$	−270.383	−	9.93650i	−0.271742	−	0.00998643i
$996$	−401.649			−0.403262
$997$	−730.044	−	730.044i	−0.732240	−	0.732240i	0.238823	−	0.971063i	$-0.423238\pi$
$997$	−730.044	−	730.044i	−0.732240	−	0.732240i	−0.971063	+	0.238823i	$0.923238\pi$
$998$	−757.209	+	757.209i	−0.758726	+	0.758726i
$999$		−	551.414i		−	0.551966i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.f.b.47.10	✓	24
5.3	odd	4	inner	230.3.f.b.93.10	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.f.b.47.10	✓	24	1.1	even	1	trivial
230.3.f.b.93.10	yes	24	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	230.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(2.20008 - 2.20008i) q^{3} +2.00000i q^{4} +(0.183624 - 4.99663i) q^{5} +4.40016 q^{6} +(-8.35722 - 8.35722i) q^{7} +(-2.00000 + 2.00000i) q^{8} -0.680698i q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(2.20008 - 2.20008i) q^{3} +2.00000i q^{4} +(0.183624 - 4.99663i) q^{5} +4.40016 q^{6} +(-8.35722 - 8.35722i) q^{7} +(-2.00000 + 2.00000i) q^{8} -0.680698i q^{9} +(5.18025 - 4.81300i) q^{10} +4.85484 q^{11} +(4.40016 + 4.40016i) q^{12} +(17.1820 - 17.1820i) q^{13} -16.7144i q^{14} +(-10.5890 - 11.3970i) q^{15} -4.00000 q^{16} +(-9.16287 - 9.16287i) q^{17} +(0.680698 - 0.680698i) q^{18} +28.3432i q^{19} +(9.99325 + 0.367249i) q^{20} -36.7731 q^{21} +(4.85484 + 4.85484i) q^{22} +(3.39116 - 3.39116i) q^{23} +8.80032i q^{24} +(-24.9326 - 1.83501i) q^{25} +34.3641 q^{26} +(18.3031 + 18.3031i) q^{27} +(16.7144 - 16.7144i) q^{28} +16.7951i q^{29} +(0.807977 - 21.9860i) q^{30} +49.9685 q^{31} +(-4.00000 - 4.00000i) q^{32} +(10.6810 - 10.6810i) q^{33} -18.3257i q^{34} +(-43.2925 + 40.2233i) q^{35} +1.36140 q^{36} +(-15.0634 - 15.0634i) q^{37} +(-28.3432 + 28.3432i) q^{38} -75.6037i q^{39} +(9.62601 + 10.3605i) q^{40} +43.9441 q^{41} +(-36.7731 - 36.7731i) q^{42} +(-5.23091 + 5.23091i) q^{43} +9.70969i q^{44} +(-3.40119 - 0.124993i) q^{45} +6.78233 q^{46} +(20.2706 + 20.2706i) q^{47} +(-8.80032 + 8.80032i) q^{48} +90.6862i q^{49} +(-23.0976 - 26.7676i) q^{50} -40.3181 q^{51} +(34.3641 + 34.3641i) q^{52} +(-34.0517 + 34.0517i) q^{53} +36.6062i q^{54} +(0.891468 - 24.2578i) q^{55} +33.4289 q^{56} +(62.3573 + 62.3573i) q^{57} +(-16.7951 + 16.7951i) q^{58} -67.5325i q^{59} +(22.7939 - 21.1780i) q^{60} -10.1955 q^{61} +(49.9685 + 49.9685i) q^{62} +(-5.68874 + 5.68874i) q^{63} -8.00000i q^{64} +(-82.6971 - 89.0072i) q^{65} +21.3621 q^{66} +(18.0435 + 18.0435i) q^{67} +(18.3257 - 18.3257i) q^{68} -14.9217i q^{69} +(-83.5158 - 3.06918i) q^{70} +21.4957 q^{71} +(1.36140 + 1.36140i) q^{72} +(-21.4816 + 21.4816i) q^{73} -30.1268i q^{74} +(-58.8908 + 50.8165i) q^{75} -56.6864 q^{76} +(-40.5730 - 40.5730i) q^{77} +(75.6037 - 75.6037i) q^{78} +113.271i q^{79} +(-0.734498 + 19.9865i) q^{80} +86.6629 q^{81} +(43.9441 + 43.9441i) q^{82} +(-45.6403 + 45.6403i) q^{83} -73.5462i q^{84} +(-47.4660 + 44.1009i) q^{85} -10.4618 q^{86} +(36.9505 + 36.9505i) q^{87} +(-9.70969 + 9.70969i) q^{88} +64.2133i q^{89} +(-3.27620 - 3.52619i) q^{90} -287.188 q^{91} +(6.78233 + 6.78233i) q^{92} +(109.935 - 109.935i) q^{93} +40.5412i q^{94} +(141.621 + 5.20451i) q^{95} -17.6006 q^{96} +(-98.3956 - 98.3956i) q^{97} +(-90.6862 + 90.6862i) q^{98} -3.30468i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8}+O(q^{10}) \) 24 * q + 24 * q^2 + 4 * q^5 + 8 * q^7 - 48 * q^8	\( 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8} + 16 q^{10} - 8 q^{11} - 24 q^{13} - 24 q^{15} - 96 q^{16} - 12 q^{17} + 88 q^{18} + 24 q^{20} - 24 q^{21} - 8 q^{22} - 48 q^{25} - 48 q^{26} + 60 q^{27} - 16 q^{28} + 12 q^{30} + 12 q^{31} - 96 q^{32} + 92 q^{33} + 48 q^{35} + 176 q^{36} - 100 q^{37} + 56 q^{38} + 16 q^{40} + 116 q^{41} - 24 q^{42} - 120 q^{43} - 204 q^{45} + 56 q^{47} - 104 q^{50} + 176 q^{51} - 48 q^{52} - 192 q^{53} + 180 q^{55} - 32 q^{56} + 28 q^{58} + 72 q^{60} - 152 q^{61} + 12 q^{62} + 364 q^{63} + 40 q^{65} + 184 q^{66} + 72 q^{67} + 24 q^{68} - 100 q^{70} - 28 q^{71} + 176 q^{72} - 364 q^{73} + 276 q^{75} + 112 q^{76} - 92 q^{77} - 32 q^{78} - 16 q^{80} - 440 q^{81} + 116 q^{82} + 360 q^{83} + 232 q^{85} - 240 q^{86} + 176 q^{87} + 16 q^{88} - 84 q^{90} - 432 q^{91} + 192 q^{93} + 144 q^{95} - 432 q^{97} - 484 q^{98}+O(q^{100}) \) 24 * q + 24 * q^2 + 4 * q^5 + 8 * q^7 - 48 * q^8 + 16 * q^10 - 8 * q^11 - 24 * q^13 - 24 * q^15 - 96 * q^16 - 12 * q^17 + 88 * q^18 + 24 * q^20 - 24 * q^21 - 8 * q^22 - 48 * q^25 - 48 * q^26 + 60 * q^27 - 16 * q^28 + 12 * q^30 + 12 * q^31 - 96 * q^32 + 92 * q^33 + 48 * q^35 + 176 * q^36 - 100 * q^37 + 56 * q^38 + 16 * q^40 + 116 * q^41 - 24 * q^42 - 120 * q^43 - 204 * q^45 + 56 * q^47 - 104 * q^50 + 176 * q^51 - 48 * q^52 - 192 * q^53 + 180 * q^55 - 32 * q^56 + 28 * q^58 + 72 * q^60 - 152 * q^61 + 12 * q^62 + 364 * q^63 + 40 * q^65 + 184 * q^66 + 72 * q^67 + 24 * q^68 - 100 * q^70 - 28 * q^71 + 176 * q^72 - 364 * q^73 + 276 * q^75 + 112 * q^76 - 92 * q^77 - 32 * q^78 - 16 * q^80 - 440 * q^81 + 116 * q^82 + 360 * q^83 + 232 * q^85 - 240 * q^86 + 176 * q^87 + 16 * q^88 - 84 * q^90 - 432 * q^91 + 192 * q^93 + 144 * q^95 - 432 * q^97 - 484 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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