LMFDB - Embedded newform 230.3.f.b.93.7

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			93.7
Character	$\chi$	$=$	230.93
Dual form			230.3.f.b.47.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} +(0.561611 + 0.561611i) q^{3} -2.00000i q^{4} +(-4.87730 + 1.10088i) q^{5} +1.12322 q^{6} +(-8.38816 + 8.38816i) q^{7} +(-2.00000 - 2.00000i) q^{8} -8.36919i q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} +(0.561611 + 0.561611i) q^{3} -2.00000i q^{4} +(-4.87730 + 1.10088i) q^{5} +1.12322 q^{6} +(-8.38816 + 8.38816i) q^{7} +(-2.00000 - 2.00000i) q^{8} -8.36919i q^{9} +(-3.77642 + 5.97818i) q^{10} -11.2203 q^{11} +(1.12322 - 1.12322i) q^{12} +(-15.9498 - 15.9498i) q^{13} +16.7763i q^{14} +(-3.35741 - 2.12088i) q^{15} -4.00000 q^{16} +(14.2936 - 14.2936i) q^{17} +(-8.36919 - 8.36919i) q^{18} +35.4325i q^{19} +(2.20176 + 9.75460i) q^{20} -9.42176 q^{21} +(-11.2203 + 11.2203i) q^{22} +(-3.39116 - 3.39116i) q^{23} -2.24644i q^{24} +(22.5761 - 10.7386i) q^{25} -31.8996 q^{26} +(9.75472 - 9.75472i) q^{27} +(16.7763 + 16.7763i) q^{28} +26.2015i q^{29} +(-5.47829 + 1.23653i) q^{30} +19.1987 q^{31} +(-4.00000 + 4.00000i) q^{32} +(-6.30145 - 6.30145i) q^{33} -28.5873i q^{34} +(31.6772 - 50.1459i) q^{35} -16.7384 q^{36} +(-26.7959 + 26.7959i) q^{37} +(35.4325 + 35.4325i) q^{38} -17.9152i q^{39} +(11.9564 + 7.55285i) q^{40} +19.3079 q^{41} +(-9.42176 + 9.42176i) q^{42} +(-44.0280 - 44.0280i) q^{43} +22.4406i q^{44} +(9.21345 + 40.8190i) q^{45} -6.78233 q^{46} +(-36.1558 + 36.1558i) q^{47} +(-2.24644 - 2.24644i) q^{48} -91.7225i q^{49} +(11.8375 - 33.3148i) q^{50} +16.0549 q^{51} +(-31.8996 + 31.8996i) q^{52} +(-0.502671 - 0.502671i) q^{53} -19.5094i q^{54} +(54.7249 - 12.3522i) q^{55} +33.5526 q^{56} +(-19.8993 + 19.8993i) q^{57} +(26.2015 + 26.2015i) q^{58} +5.81649i q^{59} +(-4.24176 + 6.71482i) q^{60} -0.344323 q^{61} +(19.1987 - 19.1987i) q^{62} +(70.2021 + 70.2021i) q^{63} +8.00000i q^{64} +(95.3508 + 60.2332i) q^{65} -12.6029 q^{66} +(-17.5051 + 17.5051i) q^{67} +(-28.5873 - 28.5873i) q^{68} -3.80903i q^{69} +(-18.4687 - 81.8232i) q^{70} -14.8564 q^{71} +(-16.7384 + 16.7384i) q^{72} +(-68.0071 - 68.0071i) q^{73} +53.5917i q^{74} +(18.7099 + 6.64807i) q^{75} +70.8650 q^{76} +(94.1179 - 94.1179i) q^{77} +(-17.9152 - 17.9152i) q^{78} -82.9910i q^{79} +(19.5092 - 4.40351i) q^{80} -64.3660 q^{81} +(19.3079 - 19.3079i) q^{82} +(-32.8277 - 32.8277i) q^{83} +18.8435i q^{84} +(-53.9788 + 85.4499i) q^{85} -88.0559 q^{86} +(-14.7150 + 14.7150i) q^{87} +(22.4406 + 22.4406i) q^{88} -59.4270i q^{89} +(50.0325 + 31.6056i) q^{90} +267.579 q^{91} +(-6.78233 + 6.78233i) q^{92} +(10.7822 + 10.7822i) q^{93} +72.3115i q^{94} +(-39.0068 - 172.815i) q^{95} -4.49289 q^{96} +(33.5713 - 33.5713i) q^{97} +(-91.7225 - 91.7225i) q^{98} +93.9050i 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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	0.561611	+	0.561611i	0.187204	+	0.187204i	0.794486	−	0.607282i	$-0.207740\pi$
$3$	0.561611	+	0.561611i	0.187204	+	0.187204i	−0.607282	+	0.794486i	$0.707740\pi$
$4$		−	2.00000i		−	0.500000i
$5$	−4.87730	+	1.10088i	−0.975460	+	0.220176i
$5$	−4.87730	+	1.10088i	−0.975460	+	0.220176i
$6$	1.12322			0.187204
$7$	−8.38816	+	8.38816i	−1.19831	+	1.19831i	−0.223636	+	0.974673i	$0.571793\pi$
$7$	−8.38816	+	8.38816i	−1.19831	+	1.19831i	−0.974673	+	0.223636i	$0.928207\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$		−	8.36919i		−	0.929910i
$10$	−3.77642	+	5.97818i	−0.377642	+	0.597818i
$11$	−11.2203			−1.02003			−0.510015	−	0.860166i	$-0.670360\pi$
$11$	−11.2203			−1.02003			−0.510015	+	0.860166i	$0.670360\pi$
$12$	1.12322	−	1.12322i	0.0936018	−	0.0936018i
$13$	−15.9498	−	15.9498i	−1.22691	−	1.22691i	−0.965127	−	0.261781i	$-0.915690\pi$
$13$	−15.9498	−	15.9498i	−1.22691	−	1.22691i	−0.261781	−	0.965127i	$-0.584310\pi$
$14$			16.7763i			1.19831i
$15$	−3.35741	−	2.12088i	−0.223827	−	0.141392i
$16$	−4.00000			−0.250000
$17$	14.2936	−	14.2936i	0.840802	−	0.840802i	−0.148161	−	0.988963i	$-0.547335\pi$
$17$	14.2936	−	14.2936i	0.840802	−	0.840802i	0.988963	+	0.148161i	$0.0473354\pi$
$18$	−8.36919	−	8.36919i	−0.464955	−	0.464955i
$19$			35.4325i			1.86487i	0.361340	+	0.932434i	$0.382319\pi$
$19$			35.4325i			1.86487i	−0.361340	+	0.932434i	$0.617681\pi$
$20$	2.20176	+	9.75460i	0.110088	+	0.487730i
$21$	−9.42176			−0.448655
$22$	−11.2203	+	11.2203i	−0.510015	+	0.510015i
$23$	−3.39116	−	3.39116i	−0.147442	−	0.147442i
$23$	−3.39116	−	3.39116i	−0.147442	−	0.147442i
$24$		−	2.24644i		−	0.0936018i
$25$	22.5761	−	10.7386i	0.903045	−	0.429545i
$26$	−31.8996			−1.22691
$27$	9.75472	−	9.75472i	0.361286	−	0.361286i
$28$	16.7763	+	16.7763i	0.599154	+	0.599154i
$29$			26.2015i			0.903499i	0.892145	+	0.451749i	$0.149200\pi$
$29$			26.2015i			0.903499i	−0.892145	+	0.451749i	$0.850800\pi$
$30$	−5.47829	+	1.23653i	−0.182610	+	0.0412176i
$31$	19.1987			0.619312			0.309656	−	0.950849i	$-0.399786\pi$
$31$	19.1987			0.619312			0.309656	+	0.950849i	$0.399786\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	−6.30145	−	6.30145i	−0.190953	−	0.190953i
$34$		−	28.5873i		−	0.840802i
$35$	31.6772	−	50.1459i	0.905064	−	1.43274i
$36$	−16.7384			−0.464955
$37$	−26.7959	+	26.7959i	−0.724212	+	0.724212i	−0.969460	−	0.245248i	$-0.921131\pi$
$37$	−26.7959	+	26.7959i	−0.724212	+	0.724212i	0.245248	+	0.969460i	$0.421131\pi$
$38$	35.4325	+	35.4325i	0.932434	+	0.932434i
$39$		−	17.9152i		−	0.459363i
$40$	11.9564	+	7.55285i	0.298909	+	0.188821i
$41$	19.3079			0.470924			0.235462	−	0.971883i	$-0.424340\pi$
$41$	19.3079			0.470924			0.235462	+	0.971883i	$0.424340\pi$
$42$	−9.42176	+	9.42176i	−0.224328	+	0.224328i
$43$	−44.0280	−	44.0280i	−1.02391	−	1.02391i	−0.999707	−	0.0241987i	$-0.992297\pi$
$43$	−44.0280	−	44.0280i	−1.02391	−	1.02391i	−0.0241987	−	0.999707i	$-0.507703\pi$
$44$			22.4406i			0.510015i
$45$	9.21345	+	40.8190i	0.204743	+	0.907090i
$46$	−6.78233			−0.147442
$47$	−36.1558	+	36.1558i	−0.769272	+	0.769272i	−0.977978	−	0.208707i	$-0.933075\pi$
$47$	−36.1558	+	36.1558i	−0.769272	+	0.769272i	0.208707	+	0.977978i	$0.433075\pi$
$48$	−2.24644	−	2.24644i	−0.0468009	−	0.0468009i
$49$		−	91.7225i		−	1.87189i
$50$	11.8375	−	33.3148i	0.236750	−	0.666295i
$51$	16.0549			0.314802
$52$	−31.8996	+	31.8996i	−0.613454	+	0.613454i
$53$	−0.502671	−	0.502671i	−0.00948435	−	0.00948435i	0.702349	−	0.711833i	$-0.252135\pi$
$53$	−0.502671	−	0.502671i	−0.00948435	−	0.00948435i	−0.711833	+	0.702349i	$0.752135\pi$
$54$		−	19.5094i		−	0.361286i
$55$	54.7249	−	12.3522i	0.994998	−	0.224586i
$56$	33.5526			0.599154
$57$	−19.8993	+	19.8993i	−0.349110	+	0.349110i
$58$	26.2015	+	26.2015i	0.451749	+	0.451749i
$59$			5.81649i			0.0985845i	0.998784	+	0.0492923i	$0.0156966\pi$
$59$			5.81649i			0.0985845i	−0.998784	+	0.0492923i	$0.984303\pi$
$60$	−4.24176	+	6.71482i	−0.0706960	+	0.111914i
$61$	−0.344323			−0.00564464			−0.00282232	−	0.999996i	$-0.500898\pi$
$61$	−0.344323			−0.00564464			−0.00282232	+	0.999996i	$0.500898\pi$
$62$	19.1987	−	19.1987i	0.309656	−	0.309656i
$63$	70.2021	+	70.2021i	1.11432	+	1.11432i
$64$			8.00000i			0.125000i
$65$	95.3508	+	60.2332i	1.46694	+	0.926665i
$66$	−12.6029			−0.190953
$67$	−17.5051	+	17.5051i	−0.261270	+	0.261270i	−0.825570	−	0.564300i	$-0.809146\pi$
$67$	−17.5051	+	17.5051i	−0.261270	+	0.261270i	0.564300	+	0.825570i	$0.309146\pi$
$68$	−28.5873	−	28.5873i	−0.420401	−	0.420401i
$69$		−	3.80903i		−	0.0552033i
$70$	−18.4687	−	81.8232i	−0.263838	−	1.16890i
$71$	−14.8564			−0.209245			−0.104623	−	0.994512i	$-0.533363\pi$
$71$	−14.8564			−0.209245			−0.104623	+	0.994512i	$0.533363\pi$
$72$	−16.7384	+	16.7384i	−0.232477	+	0.232477i
$73$	−68.0071	−	68.0071i	−0.931604	−	0.931604i	0.0662018	−	0.997806i	$-0.478912\pi$
$73$	−68.0071	−	68.0071i	−0.931604	−	0.931604i	−0.997806	+	0.0662018i	$0.978912\pi$
$74$			53.5917i			0.724212i
$75$	18.7099	+	6.64807i	0.249466	+	0.0886410i
$76$	70.8650			0.932434
$77$	94.1179	−	94.1179i	1.22231	−	1.22231i
$78$	−17.9152	−	17.9152i	−0.229682	−	0.229682i
$79$		−	82.9910i		−	1.05052i	−0.850942	−	0.525260i	$-0.823968\pi$
$79$		−	82.9910i		−	1.05052i	0.850942	−	0.525260i	$-0.176032\pi$
$80$	19.5092	−	4.40351i	0.243865	−	0.0550439i
$81$	−64.3660			−0.794642
$82$	19.3079	−	19.3079i	0.235462	−	0.235462i
$83$	−32.8277	−	32.8277i	−0.395514	−	0.395514i	0.481133	−	0.876647i	$-0.340225\pi$
$83$	−32.8277	−	32.8277i	−0.395514	−	0.395514i	−0.876647	+	0.481133i	$0.840225\pi$
$84$			18.8435i			0.224328i
$85$	−53.9788	+	85.4499i	−0.635045	+	1.00529i
$86$	−88.0559			−1.02391
$87$	−14.7150	+	14.7150i	−0.169138	+	0.169138i
$88$	22.4406	+	22.4406i	0.255007	+	0.255007i
$89$		−	59.4270i		−	0.667719i	−0.942623	−	0.333859i	$-0.891649\pi$
$89$		−	59.4270i		−	0.667719i	0.942623	−	0.333859i	$-0.108351\pi$
$90$	50.0325	+	31.6056i	0.555917	+	0.351173i
$91$	267.579			2.94043
$92$	−6.78233	+	6.78233i	−0.0737210	+	0.0737210i
$93$	10.7822	+	10.7822i	0.115937	+	0.115937i
$94$			72.3115i			0.769272i
$95$	−39.0068	−	172.815i	−0.410598	−	1.81910i
$96$	−4.49289			−0.0468009
$97$	33.5713	−	33.5713i	0.346096	−	0.346096i	−0.512557	−	0.858653i	$-0.671302\pi$
$97$	33.5713	−	33.5713i	0.346096	−	0.346096i	0.858653	+	0.512557i	$0.171302\pi$
$98$	−91.7225	−	91.7225i	−0.935944	−	0.935944i
$99$			93.9050i			0.948535i
$100$	−21.4772	−	45.1523i	−0.214772	−	0.451523i
$101$	−24.7403			−0.244953			−0.122477	−	0.992471i	$-0.539084\pi$
$101$	−24.7403			−0.244953			−0.122477	+	0.992471i	$0.539084\pi$
$102$	16.0549	−	16.0549i	0.157401	−	0.157401i
$103$	−75.8899	−	75.8899i	−0.736795	−	0.736795i	0.235161	−	0.971956i	$-0.424438\pi$
$103$	−75.8899	−	75.8899i	−0.736795	−	0.736795i	−0.971956	+	0.235161i	$0.924438\pi$
$104$			63.7992i			0.613454i
$105$	45.9528	−	10.3722i	0.437645	−	0.0987829i
$106$	−1.00534			−0.00948435
$107$	11.0949	−	11.0949i	0.103691	−	0.103691i	−0.653358	−	0.757049i	$-0.726640\pi$
$107$	11.0949	−	11.0949i	0.103691	−	0.103691i	0.757049	+	0.653358i	$0.226640\pi$
$108$	−19.5094	−	19.5094i	−0.180643	−	0.180643i
$109$			2.34795i			0.0215408i	0.999942	+	0.0107704i	$0.00342839\pi$
$109$			2.34795i			0.0215408i	−0.999942	+	0.0107704i	$0.996572\pi$
$110$	42.3727	−	67.0771i	0.385206	−	0.609792i
$111$	−30.0977			−0.271150
$112$	33.5526	−	33.5526i	0.299577	−	0.299577i
$113$	62.0808	+	62.0808i	0.549387	+	0.549387i	0.926264	−	0.376876i	$-0.123002\pi$
$113$	62.0808	+	62.0808i	0.549387	+	0.549387i	−0.376876	+	0.926264i	$0.623002\pi$
$114$			39.7985i			0.349110i
$115$	20.2730	+	12.8065i	0.176287	+	0.111361i
$116$	52.4029			0.451749
$117$	−133.487	+	133.487i	−1.14091	+	1.14091i
$118$	5.81649	+	5.81649i	0.0492923	+	0.0492923i
$119$			239.795i			2.01508i
$120$	2.47306	+	10.9566i	0.0206088	+	0.0913048i
$121$	4.89562			0.0404597
$122$	−0.344323	+	0.344323i	−0.00282232	+	0.00282232i
$123$	10.8435	+	10.8435i	0.0881587	+	0.0881587i
$124$		−	38.3973i		−	0.309656i
$125$	−98.2887	+	77.2291i	−0.786310	+	0.617833i
$126$	140.404			1.11432
$127$	−119.724	+	119.724i	−0.942709	+	0.942709i	−0.998445	−	0.0557367i	$-0.982249\pi$
$127$	−119.724	+	119.724i	−0.942709	+	0.942709i	0.0557367	+	0.998445i	$0.482249\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$		−	49.4531i		−	0.383358i
$130$	155.584	−	35.1176i	1.19680	−	0.270135i
$131$	210.891			1.60986			0.804929	−	0.593371i	$-0.202203\pi$
$131$	210.891			1.60986			0.804929	+	0.593371i	$0.202203\pi$
$132$	−12.6029	+	12.6029i	−0.0954766	+	0.0954766i
$133$	−297.213	−	297.213i	−2.23469	−	2.23469i
$134$			35.0101i			0.261270i
$135$	−36.8380	+	58.3155i	−0.272874	+	0.431966i
$136$	−57.1746			−0.420401
$137$	−176.740	+	176.740i	−1.29008	+	1.29008i	−0.355338	+	0.934738i	$0.615634\pi$
$137$	−176.740	+	176.740i	−1.29008	+	1.29008i	−0.934738	+	0.355338i	$0.884366\pi$
$138$	−3.80903	−	3.80903i	−0.0276017	−	0.0276017i
$139$			117.576i			0.845872i	0.906160	+	0.422936i	$0.139001\pi$
$139$			117.576i			0.845872i	−0.906160	+	0.422936i	$0.860999\pi$
$140$	−100.292	−	63.3545i	−0.716370	−	0.452532i
$141$	−40.6109			−0.288021
$142$	−14.8564	+	14.8564i	−0.104623	+	0.104623i
$143$	178.962	+	178.962i	1.25148	+	1.25148i
$144$			33.4767i			0.232477i
$145$	−28.8446	−	127.792i	−0.198928	−	0.881327i
$146$	−136.014			−0.931604
$147$	51.5123	−	51.5123i	0.350424	−	0.350424i
$148$	53.5917	+	53.5917i	0.362106	+	0.362106i
$149$		−	60.9513i		−	0.409069i	−0.978859	−	0.204535i	$-0.934432\pi$
$149$		−	60.9513i		−	0.409069i	0.978859	−	0.204535i	$-0.0655681\pi$
$150$	25.3580	−	12.0619i	0.169053	−	0.0804124i
$151$	−35.1827			−0.232998			−0.116499	−	0.993191i	$-0.537167\pi$
$151$	−35.1827			−0.232998			−0.116499	+	0.993191i	$0.537167\pi$
$152$	70.8650	−	70.8650i	0.466217	−	0.466217i
$153$	−119.626	−	119.626i	−0.781870	−	0.781870i
$154$		−	188.236i		−	1.22231i
$155$	−93.6377	+	21.1354i	−0.604114	+	0.136357i
$156$	−35.8303			−0.229682
$157$	12.1894	−	12.1894i	0.0776393	−	0.0776393i	−0.667221	−	0.744860i	$-0.732516\pi$
$157$	12.1894	−	12.1894i	0.0776393	−	0.0776393i	0.744860	+	0.667221i	$0.232516\pi$
$158$	−82.9910	−	82.9910i	−0.525260	−	0.525260i
$159$		−	0.564610i		−	0.00355101i
$160$	15.1057	−	23.9127i	0.0944106	−	0.149454i
$161$	56.8913			0.353362
$162$	−64.3660	+	64.3660i	−0.397321	+	0.397321i
$163$	19.4474	+	19.4474i	0.119309	+	0.119309i	0.764240	−	0.644931i	$-0.223114\pi$
$163$	19.4474	+	19.4474i	0.119309	+	0.119309i	−0.644931	+	0.764240i	$0.723114\pi$
$164$		−	38.6158i		−	0.235462i
$165$	37.6712	+	23.7970i	0.228310	+	0.144224i
$166$	−65.6553			−0.395514
$167$	54.5586	−	54.5586i	0.326698	−	0.326698i	−0.524631	−	0.851330i	$-0.675797\pi$
$167$	54.5586	−	54.5586i	0.326698	−	0.326698i	0.851330	+	0.524631i	$0.175797\pi$
$168$	18.8435	+	18.8435i	0.112164	+	0.112164i
$169$			339.793i			2.01061i
$170$	31.4711	+	139.429i	0.185124	+	0.820169i
$171$	296.541			1.73416
$172$	−88.0559	+	88.0559i	−0.511953	+	0.511953i
$173$	87.6542	+	87.6542i	0.506672	+	0.506672i	0.913503	−	0.406831i	$-0.133366\pi$
$173$	87.6542	+	87.6542i	0.506672	+	0.506672i	−0.406831	+	0.913503i	$0.633366\pi$
$174$			29.4300i			0.169138i
$175$	−99.2950	+	279.450i	−0.567400	+	1.59685i
$176$	44.8813			0.255007
$177$	−3.26660	+	3.26660i	−0.0184554	+	0.0184554i
$178$	−59.4270	−	59.4270i	−0.333859	−	0.333859i
$179$			94.3552i			0.527124i	0.964642	+	0.263562i	$0.0848974\pi$
$179$			94.3552i			0.527124i	−0.964642	+	0.263562i	$0.915103\pi$
$180$	81.6381	−	18.4269i	0.453545	−	0.102372i
$181$	−195.781			−1.08166			−0.540830	−	0.841132i	$-0.681890\pi$
$181$	−195.781			−1.08166			−0.540830	+	0.841132i	$0.681890\pi$
$182$	267.579	−	267.579i	1.47021	−	1.47021i
$183$	−0.193375	−	0.193375i	−0.00105670	−	0.00105670i
$184$			13.5647i			0.0737210i
$185$	101.192	−	160.190i	0.546986	−	0.865894i
$186$	21.5644			0.115937
$187$	−160.379	+	160.379i	−0.857643	+	0.857643i
$188$	72.3115	+	72.3115i	0.384636	+	0.384636i
$189$			163.648i			0.865864i
$190$	−211.822	−	133.808i	−1.11485	−	0.704253i
$191$	−149.478			−0.782605			−0.391302	−	0.920262i	$-0.627975\pi$
$191$	−149.478			−0.782605			−0.391302	+	0.920262i	$0.627975\pi$
$192$	−4.49289	+	4.49289i	−0.0234004	+	0.0234004i
$193$	−266.184	−	266.184i	−1.37919	−	1.37919i	−0.845989	−	0.533200i	$-0.820989\pi$
$193$	−266.184	−	266.184i	−1.37919	−	1.37919i	−0.533200	−	0.845989i	$-0.679011\pi$
$194$		−	67.1427i		−	0.346096i
$195$	19.7224	+	87.3776i	0.101141	+	0.448090i
$196$	−183.445			−0.935944
$197$	142.425	−	142.425i	0.722967	−	0.722967i	−0.246241	−	0.969209i	$-0.579196\pi$
$197$	142.425	−	142.425i	0.722967	−	0.722967i	0.969209	+	0.246241i	$0.0791956\pi$
$198$	93.9050	+	93.9050i	0.474268	+	0.474268i
$199$		−	253.594i		−	1.27434i	−0.770723	−	0.637170i	$-0.780105\pi$
$199$		−	253.594i		−	1.27434i	0.770723	−	0.637170i	$-0.219895\pi$
$200$	−66.6295	−	23.6750i	−0.333148	−	0.118375i
$201$	−19.6621			−0.0978212
$202$	−24.7403	+	24.7403i	−0.122477	+	0.122477i
$203$	−219.782	−	219.782i	−1.08267	−	1.08267i
$204$		−	32.1098i		−	0.157401i
$205$	−94.1705	+	21.2556i	−0.459368	+	0.103686i
$206$	−151.780			−0.736795
$207$	−28.3813	+	28.3813i	−0.137108	+	0.137108i
$208$	63.7992	+	63.7992i	0.306727	+	0.306727i
$209$		−	397.564i		−	1.90222i
$210$	35.5806	−	56.3250i	0.169431	−	0.268214i
$211$	−51.9224			−0.246078			−0.123039	−	0.992402i	$-0.539264\pi$
$211$	−51.9224			−0.246078			−0.123039	+	0.992402i	$0.539264\pi$
$212$	−1.00534	+	1.00534i	−0.00474218	+	0.00474218i
$213$	−8.34351	−	8.34351i	−0.0391714	−	0.0391714i
$214$		−	22.1898i		−	0.103691i
$215$	263.207	+	166.268i	1.22422	+	0.773340i
$216$	−39.0189			−0.180643
$217$	−161.042	+	161.042i	−0.742127	+	0.742127i
$218$	2.34795	+	2.34795i	0.0107704	+	0.0107704i
$219$		−	76.3871i		−	0.348799i
$220$	−24.7044	−	109.450i	−0.112293	−	0.497499i
$221$	−455.962			−2.06317
$222$	−30.0977	+	30.0977i	−0.135575	+	0.135575i
$223$	−30.5354	−	30.5354i	−0.136930	−	0.136930i	0.635319	−	0.772250i	$-0.280868\pi$
$223$	−30.5354	−	30.5354i	−0.136930	−	0.136930i	−0.772250	+	0.635319i	$0.780868\pi$
$224$		−	67.1053i		−	0.299577i
$225$	−89.8736	−	188.944i	−0.399438	−	0.839751i
$226$	124.162			0.549387
$227$	−76.8906	+	76.8906i	−0.338725	+	0.338725i	−0.855887	−	0.517162i	$-0.826988\pi$
$227$	−76.8906	+	76.8906i	−0.338725	+	0.338725i	0.517162	+	0.855887i	$0.326988\pi$
$228$	39.7985	+	39.7985i	0.174555	+	0.174555i
$229$			32.2750i			0.140939i	0.997514	+	0.0704693i	$0.0224497\pi$
$229$			32.2750i			0.140939i	−0.997514	+	0.0704693i	$0.977550\pi$
$230$	33.0795	−	7.46652i	0.143824	−	0.0324631i
$231$	105.715			0.457642
$232$	52.4029	−	52.4029i	0.225875	−	0.225875i
$233$	266.708	+	266.708i	1.14467	+	1.14467i	0.987585	+	0.157086i	$0.0502101\pi$
$233$	266.708	+	266.708i	1.14467	+	1.14467i	0.157086	+	0.987585i	$0.449790\pi$
$234$			266.974i			1.14091i
$235$	136.540	−	216.146i	0.581019	−	0.919769i
$236$	11.6330			0.0492923
$237$	46.6086	−	46.6086i	0.196661	−	0.196661i
$238$	239.795	+	239.795i	1.00754	+	1.00754i
$239$			336.743i			1.40897i	0.709720	+	0.704484i	$0.248821\pi$
$239$			336.743i			1.40897i	−0.709720	+	0.704484i	$0.751179\pi$
$240$	13.4296	+	8.48352i	0.0559568	+	0.0353480i
$241$	196.781			0.816517			0.408258	−	0.912866i	$-0.366136\pi$
$241$	196.781			0.816517			0.408258	+	0.912866i	$0.366136\pi$
$242$	4.89562	−	4.89562i	0.0202298	−	0.0202298i
$243$	−123.941	−	123.941i	−0.510046	−	0.510046i
$244$			0.688646i			0.00282232i
$245$	100.975	+	447.358i	0.412144	+	1.82595i
$246$	21.6870			0.0881587
$247$	565.141	−	565.141i	2.28802	−	2.28802i
$248$	−38.3973	−	38.3973i	−0.154828	−	0.154828i
$249$		−	36.8727i		−	0.148083i
$250$	−21.0596	+	175.518i	−0.0842385	+	0.702071i
$251$	156.618			0.623975			0.311988	−	0.950086i	$-0.399005\pi$
$251$	156.618			0.623975			0.311988	+	0.950086i	$0.399005\pi$
$252$	140.404	−	140.404i	0.557159	−	0.557159i
$253$	38.0500	+	38.0500i	0.150395	+	0.150395i
$254$			239.448i			0.942709i
$255$	−78.3047	+	17.6745i	−0.307077	+	0.0693118i
$256$	16.0000			0.0625000
$257$	133.914	−	133.914i	0.521068	−	0.521068i	−0.396826	−	0.917894i	$-0.629888\pi$
$257$	133.914	−	133.914i	0.521068	−	0.521068i	0.917894	+	0.396826i	$0.129888\pi$
$258$	−49.4531	−	49.4531i	−0.191679	−	0.191679i
$259$		−	449.536i		−	1.73566i
$260$	120.466	−	190.702i	0.463332	−	0.733468i
$261$	219.285			0.840172
$262$	210.891	−	210.891i	0.804929	−	0.804929i
$263$	215.159	+	215.159i	0.818095	+	0.818095i	0.985832	−	0.167737i	$-0.0536459\pi$
$263$	215.159	+	215.159i	0.818095	+	0.818095i	−0.167737	+	0.985832i	$0.553646\pi$
$264$			25.2058i			0.0954766i
$265$	3.00506	+	1.89830i	0.0113398	+	0.00716339i
$266$	−594.427			−2.23469
$267$	33.3748	−	33.3748i	0.124999	−	0.124999i
$268$	35.0101	+	35.0101i	0.130635	+	0.130635i
$269$			247.520i			0.920149i	0.887880	+	0.460075i	$0.152177\pi$
$269$			247.520i			0.920149i	−0.887880	+	0.460075i	$0.847823\pi$
$270$	21.4775	+	95.1534i	0.0795463	+	0.352420i
$271$	428.867			1.58253			0.791267	−	0.611470i	$-0.209422\pi$
$271$	428.867			1.58253			0.791267	+	0.611470i	$0.209422\pi$
$272$	−57.1746	+	57.1746i	−0.210201	+	0.210201i
$273$	150.275	+	150.275i	0.550459	+	0.550459i
$274$			353.481i			1.29008i
$275$	−253.312	+	120.491i	−0.921133	+	0.438148i
$276$	−7.61806			−0.0276017
$277$	92.4879	−	92.4879i	0.333891	−	0.333891i	−0.520171	−	0.854062i	$-0.674132\pi$
$277$	92.4879	−	92.4879i	0.333891	−	0.333891i	0.854062	+	0.520171i	$0.174132\pi$
$278$	117.576	+	117.576i	0.422936	+	0.422936i
$279$		−	160.677i		−	0.575904i
$280$	−163.646	+	36.9374i	−0.584451	+	0.131919i
$281$	473.576			1.68532			0.842662	−	0.538442i	$-0.180987\pi$
$281$	473.576			1.68532			0.842662	+	0.538442i	$0.180987\pi$
$282$	−40.6109	+	40.6109i	−0.144010	+	0.144010i
$283$	−264.849	−	264.849i	−0.935864	−	0.935864i	0.0622000	−	0.998064i	$-0.480188\pi$
$283$	−264.849	−	264.849i	−0.935864	−	0.935864i	−0.998064	+	0.0622000i	$0.980188\pi$
$284$			29.7128i			0.104623i
$285$	75.1481	−	118.961i	0.263677	−	0.417408i
$286$	357.924			1.25148
$287$	−161.958	+	161.958i	−0.564313	+	0.564313i
$288$	33.4767	+	33.4767i	0.116239	+	0.116239i
$289$		−	119.616i		−	0.413897i
$290$	−156.637	−	98.9478i	−0.540128	−	0.341199i
$291$	37.7080			0.129581
$292$	−136.014	+	136.014i	−0.465802	+	0.465802i
$293$	−128.536	−	128.536i	−0.438689	−	0.438689i	0.452882	−	0.891571i	$-0.350396\pi$
$293$	−128.536	−	128.536i	−0.438689	−	0.438689i	−0.891571	+	0.452882i	$0.850396\pi$
$294$		−	103.025i		−	0.350424i
$295$	−6.40324	−	28.3688i	−0.0217059	−	0.0961653i
$296$	107.183			0.362106
$297$	−109.451	+	109.451i	−0.368522	+	0.368522i
$298$	−60.9513	−	60.9513i	−0.204535	−	0.204535i
$299$			108.177i			0.361795i
$300$	13.2961	−	37.4199i	0.0443205	−	0.124733i
$301$	738.627			2.45391
$302$	−35.1827	+	35.1827i	−0.116499	+	0.116499i
$303$	−13.8944	−	13.8944i	−0.0458561	−	0.0458561i
$304$		−	141.730i		−	0.466217i
$305$	1.67937	−	0.379057i	0.00550612	−	0.00124281i
$306$	−239.252			−0.781870
$307$	228.266	−	228.266i	0.743537	−	0.743537i	−0.229720	−	0.973257i	$-0.573781\pi$
$307$	228.266	−	228.266i	0.743537	−	0.743537i	0.973257	+	0.229720i	$0.0737809\pi$
$308$	−188.236	−	188.236i	−0.611155	−	0.611155i
$309$		−	85.2412i		−	0.275861i
$310$	−72.5023	+	114.773i	−0.233878	+	0.370236i
$311$	−105.969			−0.340738			−0.170369	−	0.985380i	$-0.554496\pi$
$311$	−105.969			−0.340738			−0.170369	+	0.985380i	$0.554496\pi$
$312$	−35.8303	+	35.8303i	−0.114841	+	0.114841i
$313$	−51.0125	−	51.0125i	−0.162979	−	0.162979i	0.620906	−	0.783885i	$-0.286765\pi$
$313$	−51.0125	−	51.0125i	−0.162979	−	0.162979i	−0.783885	+	0.620906i	$0.786765\pi$
$314$		−	24.3787i		−	0.0776393i
$315$	−419.681	−	265.113i	−1.33232	−	0.841628i
$316$	−165.982			−0.525260
$317$	−345.566	+	345.566i	−1.09011	+	1.09011i	−0.0945988	+	0.995515i	$0.530157\pi$
$317$	−345.566	+	345.566i	−1.09011	+	1.09011i	−0.995515	+	0.0945988i	$0.969843\pi$
$318$	−0.564610	−	0.564610i	−0.00177550	−	0.00177550i
$319$		−	293.989i		−	0.921595i
$320$	−8.80702	−	39.0184i	−0.0275219	−	0.121933i
$321$	12.4620			0.0388226
$322$	56.8913	−	56.8913i	0.176681	−	0.176681i
$323$	506.459	+	506.459i	1.56799	+	1.56799i
$324$			128.732i			0.397321i
$325$	−531.364	−	188.806i	−1.63497	−	0.580942i
$326$	38.8948			0.119309
$327$	−1.31863	+	1.31863i	−0.00403251	+	0.00403251i
$328$	−38.6158	−	38.6158i	−0.117731	−	0.117731i
$329$		−	606.561i		−	1.84365i
$330$	61.4682	−	13.8743i	0.186267	−	0.0420432i
$331$	−386.634			−1.16808			−0.584039	−	0.811726i	$-0.698528\pi$
$331$	−386.634			−1.16808			−0.584039	+	0.811726i	$0.698528\pi$
$332$	−65.6553	+	65.6553i	−0.197757	+	0.197757i
$333$	224.260	+	224.260i	0.673452	+	0.673452i
$334$		−	109.117i		−	0.326698i
$335$	66.1065	−	104.648i	0.197333	−	0.312383i
$336$	37.6870			0.112164
$337$	122.880	−	122.880i	0.364629	−	0.364629i	−0.500885	−	0.865514i	$-0.666992\pi$
$337$	122.880	−	122.880i	0.364629	−	0.364629i	0.865514	+	0.500885i	$0.166992\pi$
$338$	339.793	+	339.793i	1.00530	+	1.00530i
$339$			69.7304i			0.205695i
$340$	170.900	+	107.958i	0.502647	+	0.317523i
$341$	−215.415			−0.631716
$342$	296.541	−	296.541i	0.867080	−	0.867080i
$343$	358.363	+	358.363i	1.04479	+	1.04479i
$344$			176.112i			0.511953i
$345$	4.19328	+	18.5778i	0.0121544	+	0.0538486i
$346$	175.308			0.506672
$347$	−71.2251	+	71.2251i	−0.205260	+	0.205260i	−0.802249	−	0.596989i	$-0.796363\pi$
$347$	−71.2251	+	71.2251i	−0.205260	+	0.205260i	0.596989	+	0.802249i	$0.296363\pi$
$348$	29.4300	+	29.4300i	0.0845691	+	0.0845691i
$349$		−	53.6965i		−	0.153858i	−0.997037	−	0.0769291i	$-0.975488\pi$
$349$		−	53.6965i		−	0.153858i	0.997037	−	0.0769291i	$-0.0245115\pi$
$350$	180.155	+	378.745i	0.514728	+	1.08213i
$351$	−311.172			−0.886529
$352$	44.8813	−	44.8813i	0.127504	−	0.127504i
$353$	−242.586	−	242.586i	−0.687214	−	0.687214i	0.274402	−	0.961615i	$-0.411520\pi$
$353$	−242.586	−	242.586i	−0.687214	−	0.687214i	−0.961615	+	0.274402i	$0.911520\pi$
$354$			6.53320i			0.0184554i
$355$	72.4592	−	16.3551i	0.204110	−	0.0460707i
$356$	−118.854			−0.333859
$357$	−134.671	+	134.671i	−0.377230	+	0.377230i
$358$	94.3552	+	94.3552i	0.263562	+	0.263562i
$359$		−	308.225i		−	0.858566i	−0.903170	−	0.429283i	$-0.858766\pi$
$359$		−	308.225i		−	0.858566i	0.903170	−	0.429283i	$-0.141234\pi$
$360$	63.2112	−	100.065i	0.175587	−	0.277958i
$361$	−894.462			−2.47773
$362$	−195.781	+	195.781i	−0.540830	+	0.540830i
$363$	2.74943	+	2.74943i	0.00757420	+	0.00757420i
$364$		−	535.158i		−	1.47021i
$365$	406.559	+	256.824i	1.11386	+	0.703627i
$366$	−0.386751			−0.00105670
$367$	136.488	−	136.488i	0.371903	−	0.371903i	−0.496267	−	0.868170i	$-0.665296\pi$
$367$	136.488	−	136.488i	0.371903	−	0.371903i	0.868170	+	0.496267i	$0.165296\pi$
$368$	13.5647	+	13.5647i	0.0368605	+	0.0368605i
$369$		−	161.591i		−	0.437917i
$370$	−58.9979	−	261.383i	−0.159454	−	0.706440i
$371$	8.43297			0.0227304
$372$	21.5644	−	21.5644i	0.0579687	−	0.0579687i
$373$	403.664	+	403.664i	1.08221	+	1.08221i	0.996303	+	0.0859072i	$0.0273789\pi$
$373$	403.664	+	403.664i	1.08221	+	1.08221i	0.0859072	+	0.996303i	$0.472621\pi$
$374$			320.758i			0.857643i
$375$	−98.5727	−	11.8273i	−0.262860	−	0.0315395i
$376$	144.623			0.384636
$377$	417.908	−	417.908i	1.10851	−	1.10851i
$378$	163.648	+	163.648i	0.432932	+	0.432932i
$379$			148.502i			0.391826i	0.980621	+	0.195913i	$0.0627670\pi$
$379$			148.502i			0.391826i	−0.980621	+	0.195913i	$0.937233\pi$
$380$	−345.630	+	78.0137i	−0.909552	+	0.205299i
$381$	−134.477			−0.352957
$382$	−149.478	+	149.478i	−0.391302	+	0.391302i
$383$	−6.49326	−	6.49326i	−0.0169537	−	0.0169537i	0.698579	−	0.715533i	$-0.253816\pi$
$383$	−6.49326	−	6.49326i	−0.0169537	−	0.0169537i	−0.715533	+	0.698579i	$0.753816\pi$
$384$			8.98577i			0.0234004i
$385$	−355.429	+	562.653i	−0.923192	+	1.46144i
$386$	−532.367			−1.37919
$387$	−368.478	+	368.478i	−0.952140	+	0.952140i
$388$	−67.1427	−	67.1427i	−0.173048	−	0.173048i
$389$		−	275.558i		−	0.708376i	−0.935174	−	0.354188i	$-0.884757\pi$
$389$		−	275.558i		−	0.708376i	0.935174	−	0.354188i	$-0.115243\pi$
$390$	107.100	+	67.6552i	0.274616	+	0.173475i
$391$	−96.9442			−0.247939
$392$	−183.445	+	183.445i	−0.467972	+	0.467972i
$393$	118.439	+	118.439i	0.301371	+	0.301371i
$394$		−	284.849i		−	0.722967i
$395$	91.3630	+	404.772i	0.231299	+	1.02474i
$396$	187.810			0.474268
$397$	−163.172	+	163.172i	−0.411013	+	0.411013i	−0.882091	−	0.471078i	$-0.843865\pi$
$397$	−163.172	+	163.172i	−0.411013	+	0.411013i	0.471078	+	0.882091i	$0.343865\pi$
$398$	−253.594	−	253.594i	−0.637170	−	0.637170i
$399$		−	333.837i		−	0.836683i
$400$	−90.3045	+	42.9545i	−0.225761	+	0.107386i
$401$	13.1077			0.0326876			0.0163438	−	0.999866i	$-0.494797\pi$
$401$	13.1077			0.0326876			0.0163438	+	0.999866i	$0.494797\pi$
$402$	−19.6621	+	19.6621i	−0.0489106	+	0.0489106i
$403$	−306.215	−	306.215i	−0.759839	−	0.759839i
$404$			49.4805i			0.122477i
$405$	313.932	−	70.8591i	0.775141	−	0.174961i
$406$	−439.564			−1.08267
$407$	300.658	−	300.658i	0.738718	−	0.738718i
$408$	−32.1098	−	32.1098i	−0.0787006	−	0.0787006i
$409$		−	597.737i		−	1.46146i	−0.682667	−	0.730730i	$-0.739180\pi$
$409$		−	597.737i		−	1.46146i	0.682667	−	0.730730i	$-0.260820\pi$
$410$	−72.9148	+	115.426i	−0.177841	+	0.281527i
$411$	−198.519			−0.483014
$412$	−151.780	+	151.780i	−0.368398	+	0.368398i
$413$	−48.7896	−	48.7896i	−0.118135	−	0.118135i
$414$			56.7626i			0.137108i
$415$	196.250	+	123.971i	0.472891	+	0.298726i
$416$	127.598			0.306727
$417$	−66.0321	+	66.0321i	−0.158350	+	0.158350i
$418$	−397.564	−	397.564i	−0.951110	−	0.951110i
$419$			650.314i			1.55206i	0.630695	+	0.776031i	$0.282770\pi$
$419$			650.314i			1.55206i	−0.630695	+	0.776031i	$0.717230\pi$
$420$	−20.7444	−	91.9055i	−0.0493915	−	0.218823i
$421$	−719.579			−1.70921			−0.854607	−	0.519276i	$-0.826202\pi$
$421$	−719.579			−1.70921			−0.854607	+	0.519276i	$0.826202\pi$
$422$	−51.9224	+	51.9224i	−0.123039	+	0.123039i
$423$	302.594	+	302.594i	0.715353	+	0.715353i
$424$			2.01068i			0.00474218i
$425$	169.201	−	476.189i	0.398120	−	1.12045i
$426$	−16.6870			−0.0391714
$427$	2.88824	−	2.88824i	0.00676402	−	0.00676402i
$428$	−22.1898	−	22.1898i	−0.0518454	−	0.0518454i
$429$			201.014i			0.468564i
$430$	429.475	−	96.9388i	0.998780	−	0.225439i
$431$	−320.243			−0.743023			−0.371512	−	0.928428i	$-0.621160\pi$
$431$	−320.243			−0.743023			−0.371512	+	0.928428i	$0.621160\pi$
$432$	−39.0189	+	39.0189i	−0.0903215	+	0.0903215i
$433$	475.562	+	475.562i	1.09830	+	1.09830i	0.994610	+	0.103686i	$0.0330638\pi$
$433$	475.562	+	475.562i	1.09830	+	1.09830i	0.103686	+	0.994610i	$0.466936\pi$
$434$			322.083i			0.742127i
$435$	55.5702	−	87.9691i	0.127748	−	0.202228i
$436$	4.69589			0.0107704
$437$	120.157	−	120.157i	0.274960	−	0.274960i
$438$	−76.3871	−	76.3871i	−0.174400	−	0.174400i
$439$			188.615i			0.429647i	0.976653	+	0.214823i	$0.0689176\pi$
$439$			188.615i			0.429647i	−0.976653	+	0.214823i	$0.931082\pi$
$440$	−134.154	−	84.7454i	−0.304896	−	0.192603i
$441$	−767.643			−1.74069
$442$	−455.962	+	455.962i	−1.03159	+	1.03159i
$443$	−479.576	−	479.576i	−1.08256	−	1.08256i	−0.996270	−	0.0862935i	$-0.972498\pi$
$443$	−479.576	−	479.576i	−1.08256	−	1.08256i	−0.0862935	−	0.996270i	$-0.527502\pi$
$444$			60.1953i			0.135575i
$445$	65.4218	+	289.843i	0.147015	+	0.651333i
$446$	−61.0709			−0.136930
$447$	34.2309	−	34.2309i	0.0765793	−	0.0765793i
$448$	−67.1053	−	67.1053i	−0.149789	−	0.149789i
$449$		−	720.644i		−	1.60500i	−0.596653	−	0.802499i	$-0.703503\pi$
$449$		−	720.644i		−	1.60500i	0.596653	−	0.802499i	$-0.296497\pi$
$450$	−278.817	−	99.0703i	−0.619594	−	0.220156i
$451$	−216.641			−0.480357
$452$	124.162	−	124.162i	0.274694	−	0.274694i
$453$	−19.7590	−	19.7590i	−0.0436181	−	0.0436181i
$454$			153.781i			0.338725i
$455$	−1305.06	+	294.572i	−2.86827	+	0.647411i
$456$	79.5971			0.174555
$457$	−549.320	+	549.320i	−1.20201	+	1.20201i	−0.228461	+	0.973553i	$0.573369\pi$
$457$	−549.320	+	549.320i	−1.20201	+	1.20201i	−0.973553	+	0.228461i	$0.926631\pi$
$458$	32.2750	+	32.2750i	0.0704693	+	0.0704693i
$459$		−	278.861i		−	0.607540i
$460$	25.6130	−	40.5460i	0.0556803	−	0.0881434i
$461$	236.518			0.513054			0.256527	−	0.966537i	$-0.417422\pi$
$461$	236.518			0.513054			0.256527	+	0.966537i	$0.417422\pi$
$462$	105.715	−	105.715i	0.228821	−	0.228821i
$463$	−271.311	−	271.311i	−0.585985	−	0.585985i	0.350556	−	0.936542i	$-0.385993\pi$
$463$	−271.311	−	271.311i	−0.585985	−	0.585985i	−0.936542	+	0.350556i	$0.885993\pi$
$464$		−	104.806i		−	0.225875i
$465$	−64.4578	−	40.7181i	−0.138619	−	0.0875658i
$466$	533.417			1.14467
$467$	162.650	−	162.650i	0.348287	−	0.348287i	−0.511184	−	0.859471i	$-0.670793\pi$
$467$	162.650	−	162.650i	0.348287	−	0.348287i	0.859471	+	0.511184i	$0.170793\pi$
$468$	266.974	+	266.974i	0.570457	+	0.570457i
$469$		−	293.671i		−	0.626163i
$470$	−79.6062	−	352.685i	−0.169375	−	0.750394i
$471$	13.6914			0.0290687
$472$	11.6330	−	11.6330i	0.0246461	−	0.0246461i
$473$	494.008	+	494.008i	1.04441	+	1.04441i
$474$		−	93.2173i		−	0.196661i
$475$	380.496	+	799.929i	0.801045	+	1.68406i
$476$	479.589			1.00754
$477$	−4.20694	+	4.20694i	−0.00881959	+	0.00881959i
$478$	336.743	+	336.743i	0.704484	+	0.704484i
$479$			632.742i			1.32096i	0.750842	+	0.660482i	$0.229648\pi$
$479$			632.742i			1.32096i	−0.750842	+	0.660482i	$0.770352\pi$
$480$	21.9132	−	4.94612i	0.0456524	−	0.0103044i
$481$	854.777			1.77708
$482$	196.781	−	196.781i	0.408258	−	0.408258i
$483$	31.9507	+	31.9507i	0.0661506	+	0.0661506i
$484$		−	9.79125i		−	0.0202298i
$485$	−126.780	+	200.695i	−0.261401	+	0.413805i
$486$	−247.882			−0.510046
$487$	16.0549	−	16.0549i	0.0329669	−	0.0329669i	−0.690431	−	0.723398i	$-0.742579\pi$
$487$	16.0549	−	16.0549i	0.0329669	−	0.0329669i	0.723398	+	0.690431i	$0.242579\pi$
$488$	0.688646	+	0.688646i	0.00141116	+	0.00141116i
$489$			21.8437i			0.0446702i
$490$	548.334	+	346.383i	1.11905	+	0.706904i
$491$	524.300			1.06782			0.533910	−	0.845541i	$-0.320722\pi$
$491$	524.300			1.06782			0.533910	+	0.845541i	$0.320722\pi$
$492$	21.6870	−	21.6870i	0.0440794	−	0.0440794i
$493$	374.514	+	374.514i	0.759664	+	0.759664i
$494$		−	1130.28i		−	2.28802i
$495$	−103.378	−	458.003i	−0.208844	−	0.925258i
$496$	−76.7947			−0.154828
$497$	124.618	−	124.618i	0.250740	−	0.250740i
$498$	−36.8727	−	36.8727i	−0.0740416	−	0.0740416i
$499$			252.276i			0.505562i	0.967523	+	0.252781i	$0.0813453\pi$
$499$			252.276i			0.505562i	−0.967523	+	0.252781i	$0.918655\pi$
$500$	154.458	+	196.577i	0.308916	+	0.393155i
$501$	61.2814			0.122318
$502$	156.618	−	156.618i	0.311988	−	0.311988i
$503$	−661.949	−	661.949i	−1.31600	−	1.31600i	−0.916912	−	0.399089i	$-0.869326\pi$
$503$	−661.949	−	661.949i	−1.31600	−	1.31600i	−0.399089	−	0.916912i	$-0.630674\pi$
$504$		−	280.808i		−	0.557159i
$505$	120.666	−	27.2360i	0.238942	−	0.0539327i
$506$	76.0999			0.150395
$507$	−190.831	+	190.831i	−0.376393	+	0.376393i
$508$	239.448	+	239.448i	0.471354	+	0.471354i
$509$		−	77.7088i		−	0.152670i	−0.997082	−	0.0763348i	$-0.975678\pi$
$509$		−	77.7088i		−	0.152670i	0.997082	−	0.0763348i	$-0.0243218\pi$
$510$	−60.6302	+	95.9792i	−0.118883	+	0.188195i
$511$	1140.91			2.23270
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	345.634	+	345.634i	0.673751	+	0.673751i
$514$		−	267.829i		−	0.521068i
$515$	453.684	+	286.593i	0.880939	+	0.556490i
$516$	−98.9063			−0.191679
$517$	405.679	−	405.679i	0.784680	−	0.784680i
$518$	−449.536	−	449.536i	−0.867830	−	0.867830i
$519$			98.4551i			0.189702i
$520$	−70.2351	−	311.168i	−0.135068	−	0.598400i
$521$	184.322			0.353784			0.176892	−	0.984230i	$-0.443396\pi$
$521$	184.322			0.353784			0.176892	+	0.984230i	$0.443396\pi$
$522$	219.285	−	219.285i	0.420086	−	0.420086i
$523$	−606.795	−	606.795i	−1.16022	−	1.16022i	−0.984427	−	0.175792i	$-0.943751\pi$
$523$	−606.795	−	606.795i	−1.16022	−	1.16022i	−0.175792	−	0.984427i	$-0.556249\pi$
$524$		−	421.783i		−	0.804929i
$525$	−212.707	+	101.177i	−0.405156	+	0.192718i
$526$	430.318			0.818095
$527$	274.419	−	274.419i	0.520719	−	0.520719i
$528$	25.2058	+	25.2058i	0.0477383	+	0.0477383i
$529$			23.0000i			0.0434783i
$530$	4.90335	−	1.10676i	0.00925161	−	0.00208822i
$531$	48.6793			0.0916747
$532$	−594.427	+	594.427i	−1.11734	+	1.11734i
$533$	−307.957	−	307.957i	−0.577781	−	0.577781i
$534$		−	66.7496i		−	0.124999i
$535$	−41.8991	+	66.3274i	−0.0783161	+	0.123976i
$536$	70.0202			0.130635
$537$	−52.9909	+	52.9909i	−0.0986795	+	0.0986795i
$538$	247.520	+	247.520i	0.460075	+	0.460075i
$539$			1029.16i			1.90938i
$540$	116.631	+	73.6759i	0.215983	+	0.136437i
$541$	−258.474			−0.477771			−0.238885	−	0.971048i	$-0.576782\pi$
$541$	−258.474			−0.477771			−0.238885	+	0.971048i	$0.576782\pi$
$542$	428.867	−	428.867i	0.791267	−	0.791267i
$543$	−109.952	−	109.952i	−0.202491	−	0.202491i
$544$			114.349i			0.210201i
$545$	−2.58480	−	11.4516i	−0.00474276	−	0.0210122i
$546$	300.551			0.550459
$547$	−185.276	+	185.276i	−0.338713	+	0.338713i	−0.855883	−	0.517170i	$-0.826985\pi$
$547$	−185.276	+	185.276i	−0.338713	+	0.338713i	0.517170	+	0.855883i	$0.326985\pi$
$548$	353.481	+	353.481i	0.645038	+	0.645038i
$549$			2.88170i			0.00524900i
$550$	−132.821	+	373.802i	−0.241492	+	0.679641i
$551$	−928.383			−1.68491
$552$	−7.61806	+	7.61806i	−0.0138008	+	0.0138008i
$553$	696.142	+	696.142i	1.25885	+	1.25885i
$554$		−	184.976i		−	0.333891i
$555$	146.795	−	33.1339i	0.264496	−	0.0597006i
$556$	235.152			0.422936
$557$	125.327	−	125.327i	0.225003	−	0.225003i	−0.585598	−	0.810601i	$-0.699140\pi$
$557$	125.327	−	125.327i	0.225003	−	0.225003i	0.810601	+	0.585598i	$0.199140\pi$
$558$	−160.677	−	160.677i	−0.287952	−	0.287952i
$559$			1404.47i			2.51248i
$560$	−126.709	+	200.584i	−0.226266	+	0.358185i
$561$	−180.141			−0.321108
$562$	473.576	−	473.576i	0.842662	−	0.842662i
$563$	−78.4316	−	78.4316i	−0.139310	−	0.139310i	0.634013	−	0.773323i	$-0.281407\pi$
$563$	−78.4316	−	78.4316i	−0.139310	−	0.139310i	−0.773323	+	0.634013i	$0.781407\pi$
$564$			81.2219i			0.144010i
$565$	−371.130	−	234.443i	−0.656867	−	0.414944i
$566$	−529.699			−0.935864
$567$	539.912	−	539.912i	0.952226	−	0.952226i
$568$	29.7128	+	29.7128i	0.0523113	+	0.0523113i
$569$			530.486i			0.932313i	0.884702	+	0.466156i	$0.154362\pi$
$569$			530.486i			0.932313i	−0.884702	+	0.466156i	$0.845638\pi$
$570$	−43.8133	−	194.109i	−0.0768655	−	0.340543i
$571$	−504.213			−0.883036			−0.441518	−	0.897252i	$-0.645560\pi$
$571$	−504.213			−0.883036			−0.441518	+	0.897252i	$0.645560\pi$
$572$	357.924	−	357.924i	0.625741	−	0.625741i
$573$	−83.9482	−	83.9482i	−0.146506	−	0.146506i
$574$			323.916i			0.564313i
$575$	−112.976	−	40.1430i	−0.196480	−	0.0698138i
$576$	66.9535			0.116239
$577$	−394.631	+	394.631i	−0.683937	+	0.683937i	−0.960885	−	0.276948i	$-0.910677\pi$
$577$	−394.631	+	394.631i	−0.683937	+	0.683937i	0.276948	+	0.960885i	$0.410677\pi$
$578$	−119.616	−	119.616i	−0.206949	−	0.206949i
$579$		−	298.983i		−	0.516378i
$580$	−255.585	+	57.6892i	−0.440664	+	0.0994642i
$581$	550.727			0.947896
$582$	37.7080	−	37.7080i	0.0647904	−	0.0647904i
$583$	5.64013	+	5.64013i	0.00967432	+	0.00967432i
$584$			272.028i			0.465802i
$585$	504.103	−	798.009i	0.861715	−	1.36412i
$586$	−257.072			−0.438689
$587$	−133.142	+	133.142i	−0.226817	+	0.226817i	−0.811362	−	0.584544i	$-0.801273\pi$
$587$	−133.142	+	133.142i	−0.226817	+	0.226817i	0.584544	+	0.811362i	$0.301273\pi$
$588$	−103.025	−	103.025i	−0.175212	−	0.175212i
$589$			680.257i			1.15494i
$590$	−34.7720	−	21.9655i	−0.0589356	−	0.0372297i
$591$	159.974			0.270684
$592$	107.183	−	107.183i	0.181053	−	0.181053i
$593$	−529.877	−	529.877i	−0.893553	−	0.893553i	0.101303	−	0.994856i	$-0.467699\pi$
$593$	−529.877	−	529.877i	−0.893553	−	0.893553i	−0.994856	+	0.101303i	$0.967699\pi$
$594$			218.902i			0.368522i
$595$	−263.985	−	1169.55i	−0.443672	−	1.96563i
$596$	−121.903			−0.204535
$597$	142.421	−	142.421i	0.238561	−	0.238561i
$598$	108.177	+	108.177i	0.180898	+	0.180898i
$599$		−	905.867i		−	1.51230i	−0.654399	−	0.756150i	$-0.727078\pi$
$599$		−	905.867i		−	1.51230i	0.654399	−	0.756150i	$-0.272922\pi$
$600$	−24.1237	−	50.7160i	−0.0402062	−	0.0845267i
$601$	166.228			0.276586			0.138293	−	0.990391i	$-0.455838\pi$
$601$	166.228			0.276586			0.138293	+	0.990391i	$0.455838\pi$
$602$	738.627	−	738.627i	1.22696	−	1.22696i
$603$	146.503	+	146.503i	0.242957	+	0.242957i
$604$			70.3654i			0.116499i
$605$	−23.8774	+	5.38948i	−0.0394668	+	0.00890824i
$606$	−27.7888			−0.0458561
$607$	132.189	−	132.189i	0.217774	−	0.217774i	−0.589786	−	0.807560i	$-0.700788\pi$
$607$	132.189	−	132.189i	0.217774	−	0.217774i	0.807560	+	0.589786i	$0.200788\pi$
$608$	−141.730	−	141.730i	−0.233109	−	0.233109i
$609$		−	246.864i		−	0.405360i
$610$	1.30031	−	2.05842i	0.00213165	−	0.00337447i
$611$	1153.36			1.88765
$612$	−239.252	+	239.252i	−0.390935	+	0.390935i
$613$	404.008	+	404.008i	0.659066	+	0.659066i	0.955159	−	0.296093i	$-0.0956837\pi$
$613$	404.008	+	404.008i	0.659066	+	0.659066i	−0.296093	+	0.955159i	$0.595684\pi$
$614$		−	456.532i		−	0.743537i
$615$	−64.8245	−	40.9497i	−0.105406	−	0.0665849i
$616$	−376.471			−0.611155
$617$	717.669	−	717.669i	1.16316	−	1.16316i	0.179379	−	0.983780i	$-0.442591\pi$
$617$	717.669	−	717.669i	1.16316	−	1.16316i	0.983780	−	0.179379i	$-0.0574089\pi$
$618$	−85.2412	−	85.2412i	−0.137931	−	0.137931i
$619$		−	623.796i		−	1.00775i	−0.863777	−	0.503874i	$-0.831908\pi$
$619$		−	623.796i		−	1.00775i	0.863777	−	0.503874i	$-0.168092\pi$
$620$	42.2708	+	187.275i	0.0681787	+	0.302057i
$621$	−66.1597			−0.106537
$622$	−105.969	+	105.969i	−0.170369	+	0.170369i
$623$	498.483	+	498.483i	0.800133	+	0.800133i
$624$			71.6606i			0.114841i
$625$	394.364	−	484.873i	0.630982	−	0.775797i
$626$	−102.025			−0.162979
$627$	223.276	−	223.276i	0.356102	−	0.356102i
$628$	−24.3787	−	24.3787i	−0.0388196	−	0.0388196i
$629$			766.021i			1.21784i
$630$	−684.793	+	154.568i	−1.08697	+	0.245346i
$631$	−486.238			−0.770584			−0.385292	−	0.922795i	$-0.625899\pi$
$631$	−486.238			−0.770584			−0.385292	+	0.922795i	$0.625899\pi$
$632$	−165.982	+	165.982i	−0.262630	+	0.262630i
$633$	−29.1602	−	29.1602i	−0.0460666	−	0.0460666i
$634$			691.132i			1.09011i
$635$	452.129	−	715.732i	0.712014	−	1.12714i
$636$	−1.12922			−0.00177550
$637$	−1462.96	+	1462.96i	−2.29663	+	2.29663i
$638$	−293.989	−	293.989i	−0.460798	−	0.460798i
$639$			124.336i			0.194579i
$640$	−47.8254	−	30.2114i	−0.0747272	−	0.0472053i
$641$	−679.444			−1.05998			−0.529988	−	0.848005i	$-0.677804\pi$
$641$	−679.444			−1.05998			−0.529988	+	0.848005i	$0.677804\pi$
$642$	12.4620	−	12.4620i	0.0194113	−	0.0194113i
$643$	−90.4151	−	90.4151i	−0.140614	−	0.140614i	0.633296	−	0.773910i	$-0.281702\pi$
$643$	−90.4151	−	90.4151i	−0.140614	−	0.140614i	−0.773910	+	0.633296i	$0.781702\pi$
$644$		−	113.783i		−	0.176681i
$645$	54.4419	+	241.198i	0.0844060	+	0.373950i
$646$	1012.92			1.56799
$647$	415.172	−	415.172i	0.641688	−	0.641688i	−0.309282	−	0.950970i	$-0.600089\pi$
$647$	415.172	−	415.172i	0.641688	−	0.641688i	0.950970	+	0.309282i	$0.100089\pi$
$648$	128.732	+	128.732i	0.198660	+	0.198660i
$649$		−	65.2629i		−	0.100559i
$650$	−720.170	+	342.558i	−1.10795	+	0.527012i
$651$	−180.885			−0.277858
$652$	38.8948	−	38.8948i	0.0596546	−	0.0596546i
$653$	655.560	+	655.560i	1.00392	+	1.00392i	0.999992	+	0.00392871i	$0.00125055\pi$
$653$	655.560	+	655.560i	1.00392	+	1.00392i	0.00392871	+	0.999992i	$0.498749\pi$
$654$			2.63726i			0.00403251i
$655$	−1028.58	+	232.166i	−1.57035	+	0.354451i
$656$	−77.2316			−0.117731
$657$	−569.164	+	569.164i	−0.866308	+	0.866308i
$658$	−606.561	−	606.561i	−0.921825	−	0.921825i
$659$			557.907i			0.846597i	0.905990	+	0.423298i	$0.139128\pi$
$659$			557.907i			0.846597i	−0.905990	+	0.423298i	$0.860872\pi$
$660$	47.5939	−	75.3424i	0.0721120	−	0.114155i
$661$	310.778			0.470163			0.235082	−	0.971976i	$-0.424464\pi$
$661$	310.778			0.470163			0.235082	+	0.971976i	$0.424464\pi$
$662$	−386.634	+	386.634i	−0.584039	+	0.584039i
$663$	−256.073	−	256.073i	−0.386234	−	0.386234i
$664$			131.311i			0.197757i
$665$	1776.80	+	1122.40i	2.67187	+	1.68783i
$666$	448.519			0.673452
$667$	88.8535	−	88.8535i	0.133214	−	0.133214i
$668$	−109.117	−	109.117i	−0.163349	−	0.163349i
$669$		−	34.2981i		−	0.0512677i
$670$	−38.5419	−	170.755i	−0.0575252	−	0.254858i
$671$	3.86341			0.00575770
$672$	37.6870	−	37.6870i	0.0560819	−	0.0560819i
$673$	53.9294	+	53.9294i	0.0801328	+	0.0801328i	0.746037	−	0.665904i	$-0.231954\pi$
$673$	53.9294	+	53.9294i	0.0801328	+	0.0801328i	−0.665904	+	0.746037i	$0.731954\pi$
$674$		−	245.760i		−	0.364629i
$675$	115.472	−	324.976i	0.171069	−	0.481446i
$676$	679.585			1.00530
$677$	−132.335	+	132.335i	−0.195472	+	0.195472i	−0.798056	−	0.602584i	$-0.794138\pi$
$677$	−132.335	+	132.335i	−0.195472	+	0.195472i	0.602584	+	0.798056i	$0.294138\pi$
$678$	69.7304	+	69.7304i	0.102847	+	0.102847i
$679$			563.204i			0.829460i
$680$	278.858	−	62.9422i	0.410085	−	0.0925621i
$681$	−86.3652			−0.126821
$682$	−215.415	+	215.415i	−0.315858	+	0.315858i
$683$	−633.830	−	633.830i	−0.928009	−	0.928009i	0.0695679	−	0.997577i	$-0.477838\pi$
$683$	−633.830	−	633.830i	−0.928009	−	0.928009i	−0.997577	+	0.0695679i	$0.977838\pi$
$684$		−	593.082i		−	0.867080i
$685$	667.447	−	1056.59i	0.974375	−	1.54246i
$686$	716.726			1.04479
$687$	−18.1260	+	18.1260i	−0.0263842	+	0.0263842i
$688$	176.112	+	176.112i	0.255976	+	0.255976i
$689$			16.0350i			0.0232729i
$690$	22.7711	+	14.3845i	0.0330015	+	0.0208471i
$691$	95.7685			0.138594			0.0692970	−	0.997596i	$-0.477924\pi$
$691$	95.7685			0.138594			0.0692970	+	0.997596i	$0.477924\pi$
$692$	175.308	−	175.308i	0.253336	−	0.253336i
$693$	−787.690	−	787.690i	−1.13664	−	1.13664i
$694$			142.450i			0.205260i
$695$	−129.437	−	573.455i	−0.186240	−	0.825115i
$696$	58.8601			0.0845691
$697$	275.980	−	275.980i	0.395954	−	0.395954i
$698$	−53.6965	−	53.6965i	−0.0769291	−	0.0769291i
$699$			299.573i			0.428573i
$700$	558.899	+	198.590i	0.798427	+	0.283700i
$701$	−467.837			−0.667386			−0.333693	−	0.942682i	$-0.608295\pi$
$701$	−467.837			−0.667386			−0.333693	+	0.942682i	$0.608295\pi$
$702$	−311.172	+	311.172i	−0.443265	+	0.443265i
$703$	−949.444	−	949.444i	−1.35056	−	1.35056i
$704$		−	89.7626i		−	0.127504i
$705$	198.072	−	44.7077i	0.280953	−	0.0634151i
$706$	−485.173			−0.687214
$707$	207.525	−	207.525i	0.293530	−	0.293530i
$708$	6.53320	+	6.53320i	0.00922769	+	0.00922769i
$709$		−	744.912i		−	1.05065i	−0.850901	−	0.525326i	$-0.823943\pi$
$709$		−	744.912i		−	1.05065i	0.850901	−	0.525326i	$-0.176057\pi$
$710$	56.1041	−	88.8142i	0.0790198	−	0.125090i
$711$	−694.567			−0.976888
$712$	−118.854	+	118.854i	−0.166930	+	0.166930i
$713$	−65.1059	−	65.1059i	−0.0913126	−	0.0913126i
$714$			269.343i			0.377230i
$715$	−1069.87	−	675.836i	−1.49632	−	0.945225i
$716$	188.710			0.263562
$717$	−189.119	+	189.119i	−0.263764	+	0.263764i
$718$	−308.225	−	308.225i	−0.429283	−	0.429283i
$719$		−	611.347i		−	0.850274i	−0.905129	−	0.425137i	$-0.860226\pi$
$719$		−	611.347i		−	0.850274i	0.905129	−	0.425137i	$-0.139774\pi$
$720$	−36.8538	−	163.276i	−0.0511858	−	0.226772i
$721$	1273.15			1.76582
$722$	−894.462	+	894.462i	−1.23887	+	1.23887i
$723$	110.514	+	110.514i	0.152855	+	0.152855i
$724$			391.561i			0.540830i
$725$	281.368	+	591.528i	0.388093	+	0.815901i
$726$	5.49887			0.00757420
$727$	−917.283	+	917.283i	−1.26174	+	1.26174i	−0.311488	+	0.950250i	$0.600827\pi$
$727$	−917.283	+	917.283i	−1.26174	+	1.26174i	−0.950250	+	0.311488i	$0.899173\pi$
$728$	−535.158	−	535.158i	−0.735107	−	0.735107i
$729$			440.080i			0.603677i
$730$	663.382	−	149.735i	0.908743	−	0.205117i
$731$	−1258.64			−1.72180
$732$	−0.386751	+	0.386751i	−0.000528348	+	0.000528348i
$733$	639.952	+	639.952i	0.873058	+	0.873058i	0.992805	−	0.119746i	$-0.0382081\pi$
$733$	639.952	+	639.952i	0.873058	+	0.873058i	−0.119746	+	0.992805i	$0.538208\pi$
$734$		−	272.977i		−	0.371903i
$735$	−194.532	+	307.950i	−0.264670	+	0.418980i
$736$	27.1293			0.0368605
$737$	196.412	−	196.412i	0.266503	−	0.266503i
$738$	−161.591	−	161.591i	−0.218959	−	0.218959i
$739$			115.163i			0.155836i	0.996960	+	0.0779181i	$0.0248273\pi$
$739$			115.163i			0.155836i	−0.996960	+	0.0779181i	$0.975173\pi$
$740$	−320.381	−	202.385i	−0.432947	−	0.273493i
$741$	634.779			0.856652
$742$	8.43297	−	8.43297i	0.0113652	−	0.0113652i
$743$	204.199	+	204.199i	0.274831	+	0.274831i	0.831041	−	0.556211i	$-0.187745\pi$
$743$	204.199	+	204.199i	0.274831	+	0.274831i	−0.556211	+	0.831041i	$0.687745\pi$
$744$		−	43.1287i		−	0.0579687i
$745$	67.1000	+	297.278i	0.0900671	+	0.399031i
$746$	807.329			1.08221
$747$	−274.741	+	274.741i	−0.367792	+	0.367792i
$748$	320.758	+	320.758i	0.428822	+	0.428822i
$749$			186.132i			0.248507i
$750$	−110.400	+	86.7453i	−0.147200	+	0.115660i
$751$	190.931			0.254236			0.127118	−	0.991888i	$-0.459427\pi$
$751$	190.931			0.254236			0.127118	+	0.991888i	$0.459427\pi$
$752$	144.623	−	144.623i	0.192318	−	0.192318i
$753$	87.9582	+	87.9582i	0.116810	+	0.116810i
$754$		−	835.817i		−	1.10851i
$755$	171.597	−	38.7319i	0.227280	−	0.0513005i
$756$	327.297			0.432932
$757$	−812.029	+	812.029i	−1.07269	+	1.07269i	−0.0755517	+	0.997142i	$0.524072\pi$
$757$	−812.029	+	812.029i	−1.07269	+	1.07269i	−0.997142	+	0.0755517i	$0.975928\pi$
$758$	148.502	+	148.502i	0.195913	+	0.195913i
$759$			42.7385i			0.0563090i
$760$	−267.616	+	423.644i	−0.352127	+	0.557426i
$761$	−847.042			−1.11306			−0.556532	−	0.830826i	$-0.687869\pi$
$761$	−847.042			−1.11306			−0.556532	+	0.830826i	$0.687869\pi$
$762$	−134.477	+	134.477i	−0.176478	+	0.176478i
$763$	−19.6950	−	19.6950i	−0.0258125	−	0.0258125i
$764$			298.955i			0.391302i
$765$	715.147	+	451.759i	0.934832	+	0.590535i
$766$	−12.9865			−0.0169537
$767$	92.7719	−	92.7719i	0.120954	−	0.120954i
$768$	8.98577	+	8.98577i	0.0117002	+	0.0117002i
$769$			933.850i			1.21437i	0.794561	+	0.607185i	$0.207701\pi$
$769$			933.850i			1.21437i	−0.794561	+	0.607185i	$0.792299\pi$
$770$	207.225	+	918.082i	0.269123	+	1.19231i
$771$	150.416			0.195091
$772$	−532.367	+	532.367i	−0.689595	+	0.689595i
$773$	−731.065	−	731.065i	−0.945750	−	0.945750i	0.0528523	−	0.998602i	$-0.483169\pi$
$773$	−731.065	−	731.065i	−0.945750	−	0.945750i	−0.998602	+	0.0528523i	$0.983169\pi$
$774$			736.956i			0.952140i
$775$	433.432	−	206.167i	0.559267	−	0.266022i
$776$	−134.285			−0.173048
$777$	252.464	−	252.464i	0.324922	−	0.324922i
$778$	−275.558	−	275.558i	−0.354188	−	0.354188i
$779$			684.127i			0.878212i
$780$	174.755	−	39.4448i	0.224045	−	0.0505703i
$781$	166.694			0.213436
$782$	−96.9442	+	96.9442i	−0.123970	+	0.123970i
$783$	255.588	+	255.588i	0.326421	+	0.326421i
$784$			366.890i			0.467972i
$785$	−46.0322	+	72.8702i	−0.0586397	+	0.0928283i
$786$	236.878			0.301371
$787$	580.339	−	580.339i	0.737406	−	0.737406i	−0.234669	−	0.972075i	$-0.575401\pi$
$787$	580.339	−	580.339i	0.737406	−	0.737406i	0.972075	+	0.234669i	$0.0754007\pi$
$788$	−284.849	−	284.849i	−0.361484	−	0.361484i
$789$			241.671i			0.306301i
$790$	496.135	+	313.409i	0.628019	+	0.396721i
$791$	−1041.49			−1.31667
$792$	187.810	−	187.810i	0.237134	−	0.237134i
$793$	5.49188	+	5.49188i	0.00692545	+	0.00692545i
$794$			326.344i			0.411013i
$795$	0.621567	+	2.75378i	0.000781845	+	0.00346387i
$796$	−507.187			−0.637170
$797$	−77.1995	+	77.1995i	−0.0968626	+	0.0968626i	−0.753878	−	0.657015i	$-0.771819\pi$
$797$	−77.1995	+	77.1995i	−0.0968626	+	0.0968626i	0.657015	+	0.753878i	$0.271819\pi$
$798$	−333.837	−	333.837i	−0.418342	−	0.418342i
$799$			1033.60i			1.29361i
$800$	−47.3500	+	133.259i	−0.0591876	+	0.166574i
$801$	−497.355			−0.620918
$802$	13.1077	−	13.1077i	0.0163438	−	0.0163438i
$803$	763.062	+	763.062i	0.950264	+	0.950264i
$804$			39.3241i			0.0489106i
$805$	−277.476	+	62.6303i	−0.344691	+	0.0778017i
$806$	−612.430			−0.759839
$807$	−139.010	+	139.010i	−0.172255	+	0.172255i
$808$	49.4805	+	49.4805i	0.0612383	+	0.0612383i
$809$			135.639i			0.167663i	0.996480	+	0.0838314i	$0.0267157\pi$
$809$			135.639i			0.167663i	−0.996480	+	0.0838314i	$0.973284\pi$
$810$	243.073	−	384.791i	0.300090	−	0.475051i
$811$	−312.185			−0.384939			−0.192469	−	0.981303i	$-0.561650\pi$
$811$	−312.185			−0.384939			−0.192469	+	0.981303i	$0.561650\pi$
$812$	−439.564	+	439.564i	−0.541335	+	0.541335i
$813$	240.856	+	240.856i	0.296256	+	0.296256i
$814$		−	601.316i		−	0.738718i
$815$	−116.260	−	73.4416i	−0.142650	−	0.0901124i
$816$	−64.2197			−0.0787006
$817$	1560.02	−	1560.02i	1.90945	−	1.90945i
$818$	−597.737	−	597.737i	−0.730730	−	0.730730i
$819$		−	2239.42i		−	2.73433i
$820$	42.5113	+	188.341i	0.0518430	+	0.229684i
$821$	−6.29071			−0.00766226			−0.00383113	−	0.999993i	$-0.501219\pi$
$821$	−6.29071			−0.00766226			−0.00383113	+	0.999993i	$0.501219\pi$
$822$	−198.519	+	198.519i	−0.241507	+	0.241507i
$823$	462.893	+	462.893i	0.562446	+	0.562446i	0.930002	−	0.367555i	$-0.119805\pi$
$823$	462.893	+	462.893i	0.562446	+	0.562446i	−0.367555	+	0.930002i	$0.619805\pi$
$824$			303.560i			0.368398i
$825$	−209.931	−	74.5935i	−0.254462	−	0.0904164i
$826$	−97.5793			−0.118135
$827$	447.596	−	447.596i	0.541229	−	0.541229i	−0.382660	−	0.923889i	$-0.624992\pi$
$827$	447.596	−	447.596i	0.541229	−	0.541229i	0.923889	+	0.382660i	$0.124992\pi$
$828$	56.7626	+	56.7626i	0.0685538	+	0.0685538i
$829$		−	1416.66i		−	1.70887i	−0.519555	−	0.854437i	$-0.673902\pi$
$829$		−	1416.66i		−	1.70887i	0.519555	−	0.854437i	$-0.326098\pi$
$830$	320.221	−	72.2785i	0.385808	−	0.0870825i
$831$	103.884			0.125011
$832$	127.598	−	127.598i	0.153364	−	0.153364i
$833$	−1311.05	−	1311.05i	−1.57389	−	1.57389i
$834$			132.064i			0.158350i
$835$	−206.037	+	326.161i	−0.246750	+	0.390612i
$836$	−795.128			−0.951110
$837$	187.278	−	187.278i	0.223749	−	0.223749i
$838$	650.314	+	650.314i	0.776031	+	0.776031i
$839$			1348.70i			1.60751i	0.594960	+	0.803755i	$0.297168\pi$
$839$			1348.70i			1.60751i	−0.594960	+	0.803755i	$0.702832\pi$
$840$	−112.650	−	71.1611i	−0.134107	−	0.0847156i
$841$	154.483			0.183690
$842$	−719.579	+	719.579i	−0.854607	+	0.854607i
$843$	265.965	+	265.965i	0.315499	+	0.315499i
$844$			103.845i			0.123039i
$845$	−374.070	−	1657.27i	−0.442687	−	1.96127i
$846$	605.189			0.715353
$847$	−41.0653	+	41.0653i	−0.0484832	+	0.0484832i
$848$	2.01068	+	2.01068i	0.00237109	+	0.00237109i
$849$		−	297.485i		−	0.350394i
$850$	−306.988	−	645.390i	−0.361162	−	0.759283i
$851$	181.738			0.213559
$852$	−16.6870	+	16.6870i	−0.0195857	+	0.0195857i
$853$	−192.588	−	192.588i	−0.225777	−	0.225777i	0.585149	−	0.810926i	$-0.301036\pi$
$853$	−192.588	−	192.588i	−0.225777	−	0.225777i	−0.810926	+	0.585149i	$0.801036\pi$
$854$		−	5.77647i		−	0.00676402i
$855$	−1446.32	+	326.456i	−1.69160	+	0.381819i
$856$	−44.3797			−0.0518454
$857$	486.853	−	486.853i	0.568090	−	0.568090i	−0.363503	−	0.931593i	$-0.618419\pi$
$857$	486.853	−	486.853i	0.568090	−	0.568090i	0.931593	+	0.363503i	$0.118419\pi$
$858$	201.014	+	201.014i	0.234282	+	0.234282i
$859$			1464.52i			1.70491i	0.522797	+	0.852457i	$0.324888\pi$
$859$			1464.52i			1.70491i	−0.522797	+	0.852457i	$0.675112\pi$
$860$	332.536	−	526.414i	0.386670	−	0.612109i
$861$	−181.914			−0.211283
$862$	−320.243	+	320.243i	−0.371512	+	0.371512i
$863$	−232.450	−	232.450i	−0.269352	−	0.269352i	0.559487	−	0.828839i	$-0.310998\pi$
$863$	−232.450	−	232.450i	−0.269352	−	0.269352i	−0.828839	+	0.559487i	$0.810998\pi$
$864$			78.0378i			0.0903215i
$865$	−524.013	−	331.020i	−0.605795	−	0.382682i
$866$	951.125			1.09830
$867$	67.1778	−	67.1778i	0.0774830	−	0.0774830i
$868$	322.083	+	322.083i	0.371064	+	0.371064i
$869$			931.186i			1.07156i
$870$	−32.3989	−	143.539i	−0.0372401	−	0.164988i
$871$	558.405			0.641108
$872$	4.69589	−	4.69589i	0.00538520	−	0.00538520i
$873$	−280.965	−	280.965i	−0.321838	−	0.321838i
$874$		−	240.315i		−	0.274960i
$875$	176.652	−	1472.27i	0.201888	−	1.68260i
$876$	−152.774			−0.174400
$877$	−706.028	+	706.028i	−0.805049	+	0.805049i	−0.983880	−	0.178831i	$-0.942769\pi$
$877$	−706.028	+	706.028i	−0.805049	+	0.805049i	0.178831	+	0.983880i	$0.442769\pi$
$878$	188.615	+	188.615i	0.214823	+	0.214823i
$879$		−	144.374i		−	0.164248i
$880$	−218.900	+	49.4088i	−0.248750	+	0.0561464i
$881$	166.205			0.188655			0.0943276	−	0.995541i	$-0.469930\pi$
$881$	166.205			0.188655			0.0943276	+	0.995541i	$0.469930\pi$
$882$	−767.643	+	767.643i	−0.870343	+	0.870343i
$883$	699.075	+	699.075i	0.791704	+	0.791704i	0.981771	−	0.190067i	$-0.0608704\pi$
$883$	699.075	+	699.075i	0.791704	+	0.791704i	−0.190067	+	0.981771i	$0.560870\pi$
$884$			911.923i			1.03159i
$885$	12.3361	−	19.5283i	0.0139391	−	0.0220659i
$886$	−959.151			−1.08256
$887$	877.758	−	877.758i	0.989581	−	0.989581i	−0.0103652	−	0.999946i	$-0.503299\pi$
$887$	877.758	−	877.758i	0.989581	−	0.989581i	0.999946	+	0.0103652i	$0.00329942\pi$
$888$	60.1953	+	60.1953i	0.0677876	+	0.0677876i
$889$		−	2008.53i		−	2.25931i
$890$	355.265	+	224.421i	0.399174	+	0.252159i
$891$	722.207			0.810558
$892$	−61.0709	+	61.0709i	−0.0684651	+	0.0684651i
$893$	−1281.09	−	1281.09i	−1.43459	−	1.43459i
$894$		−	68.4619i		−	0.0765793i
$895$	−103.874	−	460.199i	−0.116060	−	0.514189i
$896$	−134.211			−0.149789
$897$	−60.7533	+	60.7533i	−0.0677294	+	0.0677294i
$898$	−720.644	−	720.644i	−0.802499	−	0.802499i
$899$			503.033i			0.559548i
$900$	−377.888	+	179.747i	−0.419875	+	0.199719i
$901$	−14.3700			−0.0159489
$902$	−216.641	+	216.641i	−0.240178	+	0.240178i
$903$	414.821	+	414.821i	0.459381	+	0.459381i
$904$		−	248.323i		−	0.274694i
$905$	954.881	−	215.530i	1.05512	−	0.238155i
$906$	−39.5180			−0.0436181
$907$	136.301	−	136.301i	0.150277	−	0.150277i	−0.627965	−	0.778242i	$-0.716112\pi$
$907$	136.301	−	136.301i	0.150277	−	0.150277i	0.778242	+	0.627965i	$0.216112\pi$
$908$	153.781	+	153.781i	0.169363	+	0.169363i
$909$			207.056i			0.227784i
$910$	−1010.49	+	1599.64i	−1.11043	+	1.75784i
$911$	1011.37			1.11017			0.555087	−	0.831792i	$-0.312685\pi$
$911$	1011.37			1.11017			0.555087	+	0.831792i	$0.312685\pi$
$912$	79.5971	−	79.5971i	0.0872775	−	0.0872775i
$913$	368.337	+	368.337i	0.403436	+	0.403436i
$914$			1098.64i			1.20201i
$915$	1.15603	+	0.730267i	0.00126342	+	0.000798107i
$916$	64.5499			0.0704693
$917$	−1768.99	+	1768.99i	−1.92911	+	1.92911i
$918$	−278.861	−	278.861i	−0.303770	−	0.303770i
$919$			153.831i			0.167390i	0.996491	+	0.0836950i	$0.0266721\pi$
$919$			153.831i			0.167390i	−0.996491	+	0.0836950i	$0.973328\pi$
$920$	−14.9330	−	66.1589i	−0.0162316	−	0.0719119i
$921$	256.393			0.278386
$922$	236.518	−	236.518i	0.256527	−	0.256527i
$923$	236.957	+	236.957i	0.256725	+	0.256725i
$924$		−	211.430i		−	0.228821i
$925$	−317.196	+	892.697i	−0.342915	+	0.965078i
$926$	−542.622			−0.585985
$927$	−635.137	+	635.137i	−0.685153	+	0.685153i
$928$	−104.806	−	104.806i	−0.112937	−	0.112937i
$929$		−	506.995i		−	0.545743i	−0.962050	−	0.272872i	$-0.912027\pi$
$929$		−	506.995i		−	0.545743i	0.962050	−	0.272872i	$-0.0879734\pi$
$930$	−105.176	+	23.7397i	−0.113092	+	0.0255266i
$931$	3249.96			3.49082
$932$	533.417	−	533.417i	0.572336	−	0.572336i
$933$	−59.5135	−	59.5135i	−0.0637873	−	0.0637873i
$934$		−	325.300i		−	0.348287i
$935$	605.660	−	958.776i	0.647765	−	1.02543i
$936$	533.948			0.570457
$937$	111.119	−	111.119i	0.118590	−	0.118590i	−0.645321	−	0.763911i	$-0.723277\pi$
$937$	111.119	−	111.119i	0.118590	−	0.118590i	0.763911	+	0.645321i	$0.223277\pi$
$938$	−293.671	−	293.671i	−0.313082	−	0.313082i
$939$		−	57.2984i		−	0.0610206i
$940$	−432.291	−	273.079i	−0.459884	−	0.290510i
$941$	−485.679			−0.516131			−0.258066	−	0.966127i	$-0.583085\pi$
$941$	−485.679			−0.516131			−0.258066	+	0.966127i	$0.583085\pi$
$942$	13.6914	−	13.6914i	0.0145343	−	0.0145343i
$943$	−65.4763	−	65.4763i	−0.0694340	−	0.0694340i
$944$		−	23.2660i		−	0.0246461i
$945$	−180.157	−	798.162i	−0.190642	−	0.844616i
$946$	988.016			1.04441
$947$	−672.129	+	672.129i	−0.709746	+	0.709746i	−0.966482	−	0.256736i	$-0.917353\pi$
$947$	−672.129	+	672.129i	−0.709746	+	0.709746i	0.256736	+	0.966482i	$0.417353\pi$
$948$	−93.2173	−	93.2173i	−0.0983305	−	0.0983305i
$949$			2169.40i			2.28599i
$950$	1180.43	+	419.433i	1.24255	+	0.441508i
$951$	−388.147			−0.408147
$952$	479.589	−	479.589i	0.503770	−	0.503770i
$953$	−461.650	−	461.650i	−0.484418	−	0.484418i	0.422122	−	0.906539i	$-0.361286\pi$
$953$	−461.650	−	461.650i	−0.484418	−	0.484418i	−0.906539	+	0.422122i	$0.861286\pi$
$954$			8.41389i			0.00881959i
$955$	729.047	−	164.556i	0.763400	−	0.172310i
$956$	673.486			0.704484
$957$	165.107	−	165.107i	0.172526	−	0.172526i
$958$	632.742	+	632.742i	0.660482	+	0.660482i
$959$		−	2965.05i		−	3.09182i
$960$	16.9670	−	26.8593i	0.0176740	−	0.0279784i
$961$	−592.411			−0.616453
$962$	854.777	−	854.777i	0.888542	−	0.888542i
$963$	−92.8554	−	92.8554i	−0.0964231	−	0.0964231i
$964$		−	393.561i		−	0.408258i
$965$	1591.29	+	1005.22i	1.64901	+	1.04168i
$966$	63.9015			0.0661506
$967$	119.522	−	119.522i	0.123601	−	0.123601i	−0.642601	−	0.766201i	$-0.722145\pi$
$967$	119.522	−	119.522i	0.123601	−	0.123601i	0.766201	+	0.642601i	$0.222145\pi$
$968$	−9.79125	−	9.79125i	−0.0101149	−	0.0101149i
$969$			568.866i			0.587065i
$970$	73.9159	+	327.475i	0.0762019	+	0.337603i
$971$	−656.952			−0.676573			−0.338286	−	0.941043i	$-0.609847\pi$
$971$	−656.952			−0.676573			−0.338286	+	0.941043i	$0.609847\pi$
$972$	−247.882	+	247.882i	−0.255023	+	0.255023i
$973$	−986.248	−	986.248i	−1.01362	−	1.01362i
$974$		−	32.1097i		−	0.0329669i
$975$	−192.384	−	404.455i	−0.197317	−	0.414826i
$976$	1.37729			0.00141116
$977$	229.764	−	229.764i	0.235173	−	0.235173i	−0.579675	−	0.814848i	$-0.696820\pi$
$977$	229.764	−	229.764i	0.235173	−	0.235173i	0.814848	+	0.579675i	$0.196820\pi$
$978$	21.8437	+	21.8437i	0.0223351	+	0.0223351i
$979$			666.790i			0.681092i
$980$	894.716	−	201.951i	0.912976	−	0.206072i
$981$	19.6504			0.0200310
$982$	524.300	−	524.300i	0.533910	−	0.533910i
$983$	−47.7482	−	47.7482i	−0.0485739	−	0.0485739i	0.682403	−	0.730977i	$-0.260935\pi$
$983$	−47.7482	−	47.7482i	−0.0485739	−	0.0485739i	−0.730977	+	0.682403i	$0.760935\pi$
$984$		−	43.3741i		−	0.0440794i
$985$	−537.855	+	851.439i	−0.546046	+	0.864405i
$986$	749.029			0.759664
$987$	340.651	−	340.651i	0.345138	−	0.345138i
$988$	−1130.28	−	1130.28i	−1.14401	−	1.14401i
$989$			298.612i			0.301933i
$990$	−561.381	−	354.625i	−0.567051	−	0.358207i
$991$	−49.4964			−0.0499459			−0.0249730	−	0.999688i	$-0.507950\pi$
$991$	−49.4964			−0.0499459			−0.0249730	+	0.999688i	$0.507950\pi$
$992$	−76.7947	+	76.7947i	−0.0774140	+	0.0774140i
$993$	−217.138	−	217.138i	−0.218668	−	0.218668i
$994$		−	249.236i		−	0.250740i
$995$	279.176	+	1236.85i	0.280578	+	1.24307i
$996$	−73.7455			−0.0740416
$997$	52.4722	−	52.4722i	0.0526301	−	0.0526301i	−0.680302	−	0.732932i	$-0.738151\pi$
$997$	52.4722	−	52.4722i	0.0526301	−	0.0526301i	0.732932	+	0.680302i	$0.238151\pi$
$998$	252.276	+	252.276i	0.252781	+	0.252781i
$999$			522.772i			0.523295i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.f.b.93.7	yes	24
5.2	odd	4	inner	230.3.f.b.47.7	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.f.b.47.7	✓	24	5.2	odd	4	inner
230.3.f.b.93.7	yes	24	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} +(0.561611 + 0.561611i) q^{3} -2.00000i q^{4} +(-4.87730 + 1.10088i) q^{5} +1.12322 q^{6} +(-8.38816 + 8.38816i) q^{7} +(-2.00000 - 2.00000i) q^{8} -8.36919i q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} +(0.561611 + 0.561611i) q^{3} -2.00000i q^{4} +(-4.87730 + 1.10088i) q^{5} +1.12322 q^{6} +(-8.38816 + 8.38816i) q^{7} +(-2.00000 - 2.00000i) q^{8} -8.36919i q^{9} +(-3.77642 + 5.97818i) q^{10} -11.2203 q^{11} +(1.12322 - 1.12322i) q^{12} +(-15.9498 - 15.9498i) q^{13} +16.7763i q^{14} +(-3.35741 - 2.12088i) q^{15} -4.00000 q^{16} +(14.2936 - 14.2936i) q^{17} +(-8.36919 - 8.36919i) q^{18} +35.4325i q^{19} +(2.20176 + 9.75460i) q^{20} -9.42176 q^{21} +(-11.2203 + 11.2203i) q^{22} +(-3.39116 - 3.39116i) q^{23} -2.24644i q^{24} +(22.5761 - 10.7386i) q^{25} -31.8996 q^{26} +(9.75472 - 9.75472i) q^{27} +(16.7763 + 16.7763i) q^{28} +26.2015i q^{29} +(-5.47829 + 1.23653i) q^{30} +19.1987 q^{31} +(-4.00000 + 4.00000i) q^{32} +(-6.30145 - 6.30145i) q^{33} -28.5873i q^{34} +(31.6772 - 50.1459i) q^{35} -16.7384 q^{36} +(-26.7959 + 26.7959i) q^{37} +(35.4325 + 35.4325i) q^{38} -17.9152i q^{39} +(11.9564 + 7.55285i) q^{40} +19.3079 q^{41} +(-9.42176 + 9.42176i) q^{42} +(-44.0280 - 44.0280i) q^{43} +22.4406i q^{44} +(9.21345 + 40.8190i) q^{45} -6.78233 q^{46} +(-36.1558 + 36.1558i) q^{47} +(-2.24644 - 2.24644i) q^{48} -91.7225i q^{49} +(11.8375 - 33.3148i) q^{50} +16.0549 q^{51} +(-31.8996 + 31.8996i) q^{52} +(-0.502671 - 0.502671i) q^{53} -19.5094i q^{54} +(54.7249 - 12.3522i) q^{55} +33.5526 q^{56} +(-19.8993 + 19.8993i) q^{57} +(26.2015 + 26.2015i) q^{58} +5.81649i q^{59} +(-4.24176 + 6.71482i) q^{60} -0.344323 q^{61} +(19.1987 - 19.1987i) q^{62} +(70.2021 + 70.2021i) q^{63} +8.00000i q^{64} +(95.3508 + 60.2332i) q^{65} -12.6029 q^{66} +(-17.5051 + 17.5051i) q^{67} +(-28.5873 - 28.5873i) q^{68} -3.80903i q^{69} +(-18.4687 - 81.8232i) q^{70} -14.8564 q^{71} +(-16.7384 + 16.7384i) q^{72} +(-68.0071 - 68.0071i) q^{73} +53.5917i q^{74} +(18.7099 + 6.64807i) q^{75} +70.8650 q^{76} +(94.1179 - 94.1179i) q^{77} +(-17.9152 - 17.9152i) q^{78} -82.9910i q^{79} +(19.5092 - 4.40351i) q^{80} -64.3660 q^{81} +(19.3079 - 19.3079i) q^{82} +(-32.8277 - 32.8277i) q^{83} +18.8435i q^{84} +(-53.9788 + 85.4499i) q^{85} -88.0559 q^{86} +(-14.7150 + 14.7150i) q^{87} +(22.4406 + 22.4406i) q^{88} -59.4270i q^{89} +(50.0325 + 31.6056i) q^{90} +267.579 q^{91} +(-6.78233 + 6.78233i) q^{92} +(10.7822 + 10.7822i) q^{93} +72.3115i q^{94} +(-39.0068 - 172.815i) q^{95} -4.49289 q^{96} +(33.5713 - 33.5713i) q^{97} +(-91.7225 - 91.7225i) q^{98} +93.9050i 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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