LMFDB - Embedded newform 403.2.h.b.222.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(118,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("403.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.h (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			222.15
Character	$\chi$	$=$	403.222
Dual form			403.2.h.b.118.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.35132 q^{2} +(1.34746 - 2.33387i) q^{3} +3.52869 q^{4} +(-0.0458962 - 0.0794945i) q^{5} +(3.16831 - 5.48767i) q^{6} +(-2.00349 + 3.47014i) q^{7} +3.59444 q^{8} +(-2.13130 - 3.69152i) q^{9} +O(q^{10})$	\(q+2.35132 q^{2} +(1.34746 - 2.33387i) q^{3} +3.52869 q^{4} +(-0.0458962 - 0.0794945i) q^{5} +(3.16831 - 5.48767i) q^{6} +(-2.00349 + 3.47014i) q^{7} +3.59444 q^{8} +(-2.13130 - 3.69152i) q^{9} +(-0.107916 - 0.186917i) q^{10} +(0.00492632 + 0.00853264i) q^{11} +(4.75477 - 8.23551i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-4.71083 + 8.15940i) q^{14} -0.247373 q^{15} +1.39429 q^{16} +(-1.21467 + 2.10386i) q^{17} +(-5.01136 - 8.67993i) q^{18} +(-2.38331 + 4.12801i) q^{19} +(-0.161953 - 0.280512i) q^{20} +(5.39924 + 9.35176i) q^{21} +(0.0115833 + 0.0200629i) q^{22} -0.809767 q^{23} +(4.84337 - 8.38896i) q^{24} +(2.49579 - 4.32283i) q^{25} +(-1.17566 - 2.03630i) q^{26} -3.40260 q^{27} +(-7.06969 + 12.2451i) q^{28} +2.84116 q^{29} -0.581652 q^{30} +(-0.597915 - 5.53557i) q^{31} -3.91047 q^{32} +0.0265521 q^{33} +(-2.85607 + 4.94685i) q^{34} +0.367810 q^{35} +(-7.52070 - 13.0262i) q^{36} +(-2.80734 + 4.86245i) q^{37} +(-5.60391 + 9.70626i) q^{38} -2.69492 q^{39} +(-0.164971 - 0.285738i) q^{40} +(-2.56912 - 4.44985i) q^{41} +(12.6953 + 21.9889i) q^{42} +(5.90557 - 10.2288i) q^{43} +(0.0173835 + 0.0301091i) q^{44} +(-0.195637 + 0.338853i) q^{45} -1.90402 q^{46} +7.29512 q^{47} +(1.87874 - 3.25408i) q^{48} +(-4.52792 - 7.84259i) q^{49} +(5.86839 - 10.1643i) q^{50} +(3.27343 + 5.66975i) q^{51} +(-1.76435 - 3.05594i) q^{52} +(1.42173 + 2.46251i) q^{53} -8.00058 q^{54} +(0.000452198 - 0.000783231i) q^{55} +(-7.20142 + 12.4732i) q^{56} +(6.42282 + 11.1247i) q^{57} +6.68046 q^{58} +(-7.22838 + 12.5199i) q^{59} -0.872903 q^{60} +11.7898 q^{61} +(-1.40589 - 13.0159i) q^{62} +17.0801 q^{63} -11.9833 q^{64} +(-0.0458962 + 0.0794945i) q^{65} +0.0624324 q^{66} +(-2.78471 - 4.82326i) q^{67} +(-4.28619 + 7.42389i) q^{68} +(-1.09113 + 1.88989i) q^{69} +0.864837 q^{70} +(-1.09821 - 1.90216i) q^{71} +(-7.66082 - 13.2689i) q^{72} +(1.50859 + 2.61295i) q^{73} +(-6.60094 + 11.4332i) q^{74} +(-6.72595 - 11.6497i) q^{75} +(-8.40996 + 14.5665i) q^{76} -0.0394793 q^{77} -6.33661 q^{78} +(-1.54226 + 2.67126i) q^{79} +(-0.0639924 - 0.110838i) q^{80} +(1.80903 - 3.13333i) q^{81} +(-6.04082 - 10.4630i) q^{82} +(4.24900 + 7.35949i) q^{83} +(19.0523 + 32.9995i) q^{84} +0.222994 q^{85} +(13.8859 - 24.0510i) q^{86} +(3.82835 - 6.63089i) q^{87} +(0.0177074 + 0.0306701i) q^{88} -2.36869 q^{89} +(-0.460004 + 0.796751i) q^{90} +4.00697 q^{91} -2.85742 q^{92} +(-13.7250 - 6.06350i) q^{93} +17.1531 q^{94} +0.437538 q^{95} +(-5.26921 + 9.12654i) q^{96} -10.0577 q^{97} +(-10.6466 - 18.4404i) q^{98} +(0.0209989 - 0.0363712i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) $ 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	2.35132			1.66263			0.831316	−	0.555800i	$-0.187588\pi$
$2$	2.35132			1.66263			0.831316	+	0.555800i	$0.187588\pi$
$3$	1.34746	−	2.33387i	0.777957	−	1.34746i	−0.155161	−	0.987889i	$-0.549590\pi$
$3$	1.34746	−	2.33387i	0.777957	−	1.34746i	0.933118	−	0.359571i	$-0.117077\pi$
$4$	3.52869			1.76435
$5$	−0.0458962	−	0.0794945i	−0.0205254	−	0.0355510i	0.855580	−	0.517670i	$-0.173201\pi$
$5$	−0.0458962	−	0.0794945i	−0.0205254	−	0.0355510i	−0.876106	+	0.482119i	$0.839867\pi$
$6$	3.16831	−	5.48767i	1.29346	−	2.24033i
$7$	−2.00349	+	3.47014i	−0.757247	+	1.31159i	0.187002	+	0.982359i	$0.440123\pi$
$7$	−2.00349	+	3.47014i	−0.757247	+	1.31159i	−0.944249	+	0.329231i	$0.893211\pi$
$8$	3.59444			1.27083
$9$	−2.13130	−	3.69152i	−0.710433	−	1.23051i
$10$	−0.107916	−	0.186917i	−0.0341262	−	0.0591083i
$11$	0.00492632	+	0.00853264i	0.00148534	+	0.00257269i	0.866767	−	0.498713i	$-0.166194\pi$
$11$	0.00492632	+	0.00853264i	0.00148534	+	0.00257269i	−0.865282	+	0.501286i	$0.832861\pi$
$12$	4.75477	−	8.23551i	1.37258	−	2.37739i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$14$	−4.71083	+	8.15940i	−1.25902	+	2.18069i
$15$	−0.247373			−0.0638714
$16$	1.39429			0.348571
$17$	−1.21467	+	2.10386i	−0.294600	+	0.510262i	−0.974892	−	0.222679i	$-0.928520\pi$
$17$	−1.21467	+	2.10386i	−0.294600	+	0.510262i	0.680292	+	0.732941i	$0.261853\pi$
$18$	−5.01136	−	8.67993i	−1.18119	−	2.04588i
$19$	−2.38331	+	4.12801i	−0.546768	+	0.947030i	0.451725	+	0.892157i	$0.350809\pi$
$19$	−2.38331	+	4.12801i	−0.546768	+	0.947030i	−0.998493	+	0.0548729i	$0.982525\pi$
$20$	−0.161953	−	0.280512i	−0.0362139	−	0.0627243i
$21$	5.39924	+	9.35176i	1.17821	+	2.04072i
$22$	0.0115833	+	0.0200629i	0.00246958	+	0.00427743i
$23$	−0.809767			−0.168848			−0.0844240	−	0.996430i	$-0.526905\pi$
$23$	−0.809767			−0.168848			−0.0844240	+	0.996430i	$0.526905\pi$
$24$	4.84337	−	8.38896i	0.988648	−	1.71239i
$25$	2.49579	−	4.32283i	0.499157	−	0.864566i
$26$	−1.17566	−	2.03630i	−0.230566	−	0.399351i
$27$	−3.40260			−0.654830
$28$	−7.06969	+	12.2451i	−1.33605	+	2.31410i
$29$	2.84116			0.527590			0.263795	−	0.964579i	$-0.415026\pi$
$29$	2.84116			0.527590			0.263795	+	0.964579i	$0.415026\pi$
$30$	−0.581652			−0.106195
$31$	−0.597915	−	5.53557i	−0.107389	−	0.994217i
$31$	−0.597915	−	5.53557i	−0.107389	−	0.994217i
$32$	−3.91047			−0.691281
$33$	0.0265521			0.00462212
$34$	−2.85607	+	4.94685i	−0.489811	+	0.848378i
$35$	0.367810			0.0621712
$36$	−7.52070	−	13.0262i	−1.25345	−	2.17104i
$37$	−2.80734	+	4.86245i	−0.461524	+	0.799382i	−0.999037	−	0.0438729i	$-0.986030\pi$
$37$	−2.80734	+	4.86245i	−0.461524	+	0.799382i	0.537514	+	0.843255i	$0.319364\pi$
$38$	−5.60391	+	9.70626i	−0.909074	+	1.57456i
$39$	−2.69492			−0.431533
$40$	−0.164971	−	0.285738i	−0.0260842	−	0.0451792i
$41$	−2.56912	−	4.44985i	−0.401229	−	0.694950i	0.592645	−	0.805464i	$-0.298084\pi$
$41$	−2.56912	−	4.44985i	−0.401229	−	0.694950i	−0.993875	+	0.110514i	$0.964750\pi$
$42$	12.6953	+	21.9889i	1.95893	+	3.39297i
$43$	5.90557	−	10.2288i	0.900592	−	1.55987i	0.0738639	−	0.997268i	$-0.476467\pi$
$43$	5.90557	−	10.2288i	0.900592	−	1.55987i	0.826728	−	0.562602i	$-0.190200\pi$
$44$	0.0173835	+	0.0301091i	0.00262066	+	0.00453911i
$45$	−0.195637	+	0.338853i	−0.0291638	+	0.0505132i
$46$	−1.90402			−0.280732
$47$	7.29512			1.06410			0.532051	−	0.846712i	$-0.321421\pi$
$47$	7.29512			1.06410			0.532051	+	0.846712i	$0.321421\pi$
$48$	1.87874	−	3.25408i	0.271173	−	0.469686i
$49$	−4.52792	−	7.84259i	−0.646846	−	1.12037i
$50$	5.86839	−	10.1643i	0.829915	−	1.43746i
$51$	3.27343	+	5.66975i	0.458372	+	0.793924i
$52$	−1.76435	−	3.05594i	−0.244671	−	0.423782i
$53$	1.42173	+	2.46251i	0.195290	+	0.338252i	0.946995	−	0.321247i	$-0.104102\pi$
$53$	1.42173	+	2.46251i	0.195290	+	0.338252i	−0.751706	+	0.659499i	$0.770769\pi$
$54$	−8.00058			−1.08874
$55$	0.000452198	0	0.000783231i	6.09744e−5	0	0.000105611i
$56$	−7.20142	+	12.4732i	−0.962330	+	1.66680i
$57$	6.42282	+	11.1247i	0.850723	+	1.47350i
$58$	6.68046			0.877188
$59$	−7.22838	+	12.5199i	−0.941055	+	1.62996i	−0.177591	+	0.984104i	$0.556830\pi$
$59$	−7.22838	+	12.5199i	−0.941055	+	1.62996i	−0.763464	+	0.645851i	$0.776503\pi$
$60$	−0.872903			−0.112691
$61$	11.7898			1.50953			0.754766	−	0.655995i	$-0.227751\pi$
$61$	11.7898			1.50953			0.754766	+	0.655995i	$0.227751\pi$
$62$	−1.40589	−	13.0159i	−0.178548	−	1.65302i
$63$	17.0801			2.15189
$64$	−11.9833			−1.49792
$65$	−0.0458962	+	0.0794945i	−0.00569272	+	0.00986008i
$66$	0.0624324			0.00768489
$67$	−2.78471	−	4.82326i	−0.340207	−	0.589255i	0.644264	−	0.764803i	$-0.277164\pi$
$67$	−2.78471	−	4.82326i	−0.340207	−	0.589255i	−0.984471	+	0.175548i	$0.943830\pi$
$68$	−4.28619	+	7.42389i	−0.519776	+	0.900279i
$69$	−1.09113	+	1.88989i	−0.131356	+	0.227516i
$70$	0.864837			0.103368
$71$	−1.09821	−	1.90216i	−0.130334	−	0.225745i	0.793471	−	0.608608i	$-0.208272\pi$
$71$	−1.09821	−	1.90216i	−0.130334	−	0.225745i	−0.923805	+	0.382862i	$0.874938\pi$
$72$	−7.66082	−	13.2689i	−0.902837	−	1.56376i
$73$	1.50859	+	2.61295i	0.176567	+	0.305823i	0.940702	−	0.339233i	$-0.110167\pi$
$73$	1.50859	+	2.61295i	0.176567	+	0.305823i	−0.764135	+	0.645056i	$0.776834\pi$
$74$	−6.60094	+	11.4332i	−0.767344	+	1.32908i
$75$	−6.72595	−	11.6497i	−0.776646	−	1.34519i
$76$	−8.40996	+	14.5665i	−0.964688	+	1.67089i
$77$	−0.0394793			−0.00449908
$78$	−6.33661			−0.717480
$79$	−1.54226	+	2.67126i	−0.173517	+	0.300541i	−0.939647	−	0.342145i	$-0.888847\pi$
$79$	−1.54226	+	2.67126i	−0.173517	+	0.300541i	0.766130	+	0.642686i	$0.222180\pi$
$80$	−0.0639924	−	0.110838i	−0.00715456	−	0.0123921i
$81$	1.80903	−	3.13333i	0.201004	−	0.348148i
$82$	−6.04082	−	10.4630i	−0.667097	−	1.15545i
$83$	4.24900	+	7.35949i	0.466389	+	0.807809i	0.999263	−	0.0383856i	$-0.0122215\pi$
$83$	4.24900	+	7.35949i	0.466389	+	0.807809i	−0.532874	+	0.846194i	$0.678888\pi$
$84$	19.0523	+	32.9995i	2.07877	+	3.60054i
$85$	0.222994			0.0241871
$86$	13.8859	−	24.0510i	1.49735	−	2.59349i
$87$	3.82835	−	6.63089i	0.410442	−	0.710906i
$88$	0.0177074	+	0.0306701i	0.00188761	+	0.00326944i
$89$	−2.36869			−0.251081			−0.125540	−	0.992089i	$-0.540066\pi$
$89$	−2.36869			−0.251081			−0.125540	+	0.992089i	$0.540066\pi$
$90$	−0.460004	+	0.796751i	−0.0484887	+	0.0839849i
$91$	4.00697			0.420045
$92$	−2.85742			−0.297906
$93$	−13.7250	−	6.06350i	−1.42321	−	0.628756i
$94$	17.1531			1.76921
$95$	0.437538			0.0448905
$96$	−5.26921	+	9.12654i	−0.537786	+	0.931473i
$97$	−10.0577			−1.02121			−0.510604	−	0.859816i	$-0.670578\pi$
$97$	−10.0577			−1.02121			−0.510604	+	0.859816i	$0.670578\pi$
$98$	−10.6466	−	18.4404i	−1.07547	−	1.86276i
$99$	0.0209989	−	0.0363712i	0.00211047	−	0.00365544i
$100$	8.80687	−	15.2539i	0.880687	−	1.52539i
$101$	−12.0628			−1.20030			−0.600148	−	0.799889i	$-0.704892\pi$
$101$	−12.0628			−1.20030			−0.600148	+	0.799889i	$0.704892\pi$
$102$	7.69687	+	13.3314i	0.762104	+	1.32000i
$103$	5.54528	+	9.60470i	0.546392	+	0.946380i	0.998518	+	0.0544251i	$0.0173326\pi$
$103$	5.54528	+	9.60470i	0.546392	+	0.946380i	−0.452125	+	0.891954i	$0.649334\pi$
$104$	−1.79722	−	3.11288i	−0.176232	−	0.305243i
$105$	0.495609	−	0.858419i	0.0483665	−	0.0837732i
$106$	3.34294	+	5.79014i	0.324695	+	0.562388i
$107$	0.00698191	−	0.0120930i	0.000674967	−	0.00116908i	−0.865688	−	0.500584i	$-0.833118\pi$
$107$	0.00698191	−	0.0120930i	0.000674967	−	0.00116908i	0.866363	+	0.499415i	$0.166452\pi$
$108$	−12.0067			−1.15535
$109$	14.0232			1.34318			0.671591	−	0.740922i	$-0.265611\pi$
$109$	14.0232			1.34318			0.671591	+	0.740922i	$0.265611\pi$
$110$	0.00106326	−	0.00184162i	0.000101378	−	0.000175592i
$111$	7.56555	+	13.1039i	0.718090	+	1.24377i
$112$	−2.79343	+	4.83837i	−0.263955	+	0.457183i
$113$	−7.04991	−	12.2108i	−0.663200	−	1.14870i	−0.979770	−	0.200127i	$-0.935865\pi$
$113$	−7.04991	−	12.2108i	−0.663200	−	1.14870i	0.316570	−	0.948569i	$-0.397469\pi$
$114$	15.1021	+	26.1576i	1.41444	+	2.44988i
$115$	0.0371652	+	0.0643720i	0.00346567	+	0.00600272i
$116$	10.0256			0.930851
$117$	−2.13130	+	3.69152i	−0.197039	+	0.341281i
$118$	−16.9962	+	29.4383i	−1.56463	+	2.71002i
$119$	−4.86714	−	8.43013i	−0.446170	−	0.772789i
$120$	−0.889168			−0.0811695
$121$	5.49995	−	9.52620i	0.499996	−	0.866018i
$122$	27.7216			2.50980
$123$	−13.8472			−1.24856
$124$	−2.10986	−	19.5333i	−0.189471	−	1.75414i
$125$	−0.917150			−0.0820324
$126$	40.1608			3.57781
$127$	−4.95208	+	8.57726i	−0.439426	+	0.761109i	−0.997645	−	0.0685848i	$-0.978152\pi$
$127$	−4.95208	+	8.57726i	−0.439426	+	0.761109i	0.558219	+	0.829694i	$0.311485\pi$
$128$	−20.3557			−1.79920
$129$	−15.9151	−	27.5657i	−1.40124	−	2.42702i
$130$	−0.107916	+	0.186917i	−0.00946490	+	0.0163937i
$131$	0.234757	−	0.406610i	0.0205108	−	0.0355257i	−0.855588	−	0.517658i	$-0.826804\pi$
$131$	0.234757	−	0.406610i	0.0205108	−	0.0355257i	0.876099	+	0.482132i	$0.160137\pi$
$132$	0.0936941			0.00815503
$133$	−9.54985	−	16.5408i	−0.828077	−	1.43427i
$134$	−6.54774	−	11.3410i	−0.565638	−	0.979714i
$135$	0.156166	+	0.270488i	0.0134406	+	0.0232799i
$136$	−4.36605	+	7.56222i	−0.374386	+	0.648455i
$137$	−4.65019	−	8.05437i	−0.397293	−	0.688131i	0.596098	−	0.802911i	$-0.296717\pi$
$137$	−4.65019	−	8.05437i	−0.397293	−	0.688131i	−0.993391	+	0.114781i	$0.963384\pi$
$138$	−2.56559	+	4.44373i	−0.218397	+	0.378276i
$139$	−21.1823			−1.79666			−0.898329	−	0.439324i	$-0.855218\pi$
$139$	−21.1823			−1.79666			−0.898329	+	0.439324i	$0.855218\pi$
$140$	1.29789			0.109691
$141$	9.82988	−	17.0259i	0.827825	−	1.43384i
$142$	−2.58225	−	4.47259i	−0.216698	−	0.375331i
$143$	0.00492632	−	0.00853264i	0.000411960	−	0.000713535i
$144$	−2.97164	−	5.14703i	−0.247637	−	0.428919i
$145$	−0.130398	−	0.225856i	−0.0108290	−	0.0187563i
$146$	3.54717	+	6.14388i	0.293566	+	0.508471i
$147$	−24.4048			−2.01287
$148$	−9.90623	+	17.1581i	−0.814287	+	1.41039i
$149$	10.4589	−	18.1153i	0.856825	−	1.48406i	−0.0181170	−	0.999836i	$-0.505767\pi$
$149$	10.4589	−	18.1153i	0.856825	−	1.48406i	0.874942	−	0.484228i	$-0.160900\pi$
$150$	−15.8148	−	27.3921i	−1.29128	−	2.23656i
$151$	15.9637			1.29910			0.649552	−	0.760317i	$-0.274956\pi$
$151$	15.9637			1.29910			0.649552	+	0.760317i	$0.274956\pi$
$152$	−8.56665	+	14.8379i	−0.694847	+	1.20351i
$153$	10.3553			0.837174
$154$	−0.0928283			−0.00748032
$155$	−0.412605	+	0.301592i	−0.0331412	+	0.0242245i
$156$	−9.50955			−0.761373
$157$	−7.93608			−0.633368			−0.316684	−	0.948531i	$-0.602569\pi$
$157$	−7.93608			−0.633368			−0.316684	+	0.948531i	$0.602569\pi$
$158$	−3.62633	+	6.28099i	−0.288495	+	0.499689i
$159$	7.66290			0.607707
$160$	0.179476	+	0.310861i	0.0141888	+	0.0245757i
$161$	1.62236	−	2.81001i	0.127860	−	0.221459i
$162$	4.25361	−	7.36746i	0.334195	−	0.578843i
$163$	8.40425			0.658272			0.329136	−	0.944283i	$-0.393243\pi$
$163$	8.40425			0.658272			0.329136	+	0.944283i	$0.393243\pi$
$164$	−9.06564	−	15.7022i	−0.707908	−	1.22613i
$165$	−0.00121864	−	0.00211074i	−9.48709e−5	−	0.000164321i
$166$	9.99075	+	17.3045i	0.775433	+	1.34309i
$167$	−7.51405	+	13.0147i	−0.581454	+	1.00711i	0.413853	+	0.910344i	$0.364183\pi$
$167$	−7.51405	+	13.0147i	−0.581454	+	1.00711i	−0.995307	+	0.0967647i	$0.969151\pi$
$168$	19.4072	+	33.6143i	1.49730	+	2.59340i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	0.524330			0.0402143
$171$	20.3181			1.55377
$172$	20.8390	−	36.0941i	1.58896	−	2.75215i
$173$	2.07443	+	3.59301i	0.157716	+	0.273172i	0.934045	−	0.357156i	$-0.116254\pi$
$173$	2.07443	+	3.59301i	0.157716	+	0.273172i	−0.776329	+	0.630328i	$0.782920\pi$
$174$	9.00166	−	15.5913i	0.682414	−	1.18198i
$175$	10.0006	+	17.3215i	0.755971	+	1.30938i
$176$	0.00686870	+	0.0118969i	0.000517748	+	0.000896765i
$177$	19.4799	+	33.7402i	1.46420	+	2.53607i
$178$	−5.56954			−0.417455
$179$	−4.33620	+	7.51052i	−0.324103	+	0.561363i	−0.981330	−	0.192330i	$-0.938396\pi$
$179$	−4.33620	+	7.51052i	−0.324103	+	0.561363i	0.657227	+	0.753692i	$0.271729\pi$
$180$	−0.690342	+	1.19571i	−0.0514551	+	0.0891228i
$181$	1.07752	+	1.86632i	0.0800914	+	0.138722i	0.903289	−	0.429033i	$-0.141145\pi$
$181$	1.07752	+	1.86632i	0.0800914	+	0.138722i	−0.823198	+	0.567755i	$0.807812\pi$
$182$	9.42167			0.698381
$183$	15.8863	−	27.5159i	1.17435	−	2.03403i
$184$	−2.91066			−0.214577
$185$	0.515384			0.0378918
$186$	−32.2717	−	14.2572i	−2.36628	−	1.04539i
$187$	−0.0239354			−0.00175033
$188$	25.7422			1.87744
$189$	6.81706	−	11.8075i	0.495868	−	0.858868i
$190$	1.02879			0.0746364
$191$	11.7789	+	20.4017i	0.852293	+	1.47622i	0.879134	+	0.476575i	$0.158122\pi$
$191$	11.7789	+	20.4017i	0.852293	+	1.47622i	−0.0268403	+	0.999640i	$0.508545\pi$
$192$	−16.1471	+	27.9675i	−1.16531	+	2.01838i
$193$	−9.86758	+	17.0912i	−0.710284	+	1.23025i	0.254466	+	0.967082i	$0.418100\pi$
$193$	−9.86758	+	17.0912i	−0.710284	+	1.23025i	−0.964750	+	0.263167i	$0.915233\pi$
$194$	−23.6489			−1.69789
$195$	0.123686	+	0.214231i	0.00885737	+	0.0153414i
$196$	−15.9776	−	27.6741i	−1.14126	−	1.97672i
$197$	−10.5456	−	18.2655i	−0.751342	−	1.30136i	−0.947172	−	0.320725i	$-0.896073\pi$
$197$	−10.5456	−	18.2655i	−0.751342	−	1.30136i	0.195830	−	0.980638i	$-0.437260\pi$
$198$	0.0493751	−	0.0855202i	0.00350894	−	0.00607766i
$199$	−3.67166	−	6.35950i	−0.260277	−	0.450813i	0.706039	−	0.708173i	$-0.250481\pi$
$199$	−3.67166	−	6.35950i	−0.260277	−	0.450813i	−0.966315	+	0.257361i	$0.917147\pi$
$200$	8.97096	−	15.5382i	0.634343	−	1.09871i
$201$	−15.0091			−1.05866
$202$	−28.3635			−1.99565
$203$	−5.69222	+	9.85922i	−0.399516	+	0.691982i
$204$	11.5509	+	20.0068i	0.808727	+	1.40076i
$205$	−0.235826	+	0.408462i	−0.0164708	+	0.0285282i
$206$	13.0387	+	22.5837i	0.908450	+	1.57348i
$207$	1.72585	+	2.98927i	0.119955	+	0.207768i
$208$	−0.697143	−	1.20749i	−0.0483382	−	0.0837242i
$209$	−0.0469637			−0.00324855
$210$	1.16533	−	2.01842i	0.0804156	−	0.139284i
$211$	4.08007	−	7.06689i	0.280884	−	0.486505i	−0.690719	−	0.723123i	$-0.742706\pi$
$211$	4.08007	−	7.06689i	0.280884	−	0.486505i	0.971603	+	0.236619i	$0.0760392\pi$
$212$	5.01685	+	8.68944i	0.344559	+	0.596793i
$213$	−5.91920			−0.405577
$214$	0.0164167	−	0.0284346i	0.00112222	−	0.00194375i
$215$	−1.08417			−0.0739400
$216$	−12.2304			−0.832175
$217$	20.4071	+	9.01559i	1.38533	+	0.612018i
$218$	32.9731			2.23322
$219$	8.13105			0.549446
$220$	0.00159567	−	0.00276378i	0.000107580	−	0.000186334i
$221$	2.42933			0.163415
$222$	17.7890	+	30.8115i	1.19392	+	2.06793i
$223$	2.78123	−	4.81723i	0.186245	−	0.322586i	−0.757750	−	0.652545i	$-0.773702\pi$
$223$	2.78123	−	4.81723i	0.186245	−	0.322586i	0.943995	+	0.329959i	$0.107035\pi$
$224$	7.83458	−	13.5699i	0.523470	−	0.906677i
$225$	−21.2771			−1.41847
$226$	−16.5766	−	28.7115i	−1.10266	−	1.90986i
$227$	1.73060	+	2.99748i	0.114864	+	0.198950i	0.917725	−	0.397216i	$-0.130024\pi$
$227$	1.73060	+	2.99748i	0.114864	+	0.198950i	−0.802861	+	0.596166i	$0.796690\pi$
$228$	22.6642	+	39.2555i	1.50097	+	2.59976i
$229$	−9.14743	+	15.8438i	−0.604479	+	1.04699i	0.387654	+	0.921805i	$0.373285\pi$
$229$	−9.14743	+	15.8438i	−0.604479	+	1.04699i	−0.992134	+	0.125184i	$0.960048\pi$
$230$	0.0873871	+	0.151359i	0.00576214	+	0.00998032i
$231$	−0.0531968	+	0.0921395i	−0.00350009	+	0.00606233i
$232$	10.2124			0.670475
$233$	19.9647			1.30793			0.653967	−	0.756523i	$-0.273104\pi$
$233$	19.9647			1.30793			0.653967	+	0.756523i	$0.273104\pi$
$234$	−5.01136	+	8.67993i	−0.327603	+	0.567425i
$235$	−0.334818	−	0.579922i	−0.0218411	−	0.0378299i
$236$	−25.5067	+	44.1790i	−1.66035	+	2.87581i
$237$	4.15626	+	7.19884i	0.269978	+	0.467615i
$238$	−11.4442	−	19.8219i	−0.741817	−	1.28486i
$239$	10.3813	+	17.9809i	0.671508	+	1.16309i	0.977477	+	0.211044i	$0.0676862\pi$
$239$	10.3813	+	17.9809i	0.671508	+	1.16309i	−0.305969	+	0.952041i	$0.598980\pi$
$240$	−0.344909			−0.0222638
$241$	5.24411	−	9.08307i	0.337803	−	0.585092i	−0.646216	−	0.763154i	$-0.723650\pi$
$241$	5.24411	−	9.08307i	0.337803	−	0.585092i	0.984019	+	0.178062i	$0.0569829\pi$
$242$	12.9321	−	22.3991i	0.831309	−	1.43987i
$243$	−9.97909	−	17.2843i	−0.640159	−	1.10879i
$244$	41.6026			2.66334
$245$	−0.415629	+	0.719890i	−0.0265535	+	0.0459921i
$246$	−32.5591			−2.07589
$247$	4.76661			0.303292
$248$	−2.14917	−	19.8973i	−0.136472	−	1.26348i
$249$	22.9014			1.45132
$250$	−2.15651			−0.136390
$251$	−0.00476844	+	0.00825918i	−0.000300981	+	0.000521315i	−0.866176	−	0.499739i	$-0.833429\pi$
$251$	−0.00476844	+	0.00825918i	−0.000300981	+	0.000521315i	0.865875	+	0.500261i	$0.166762\pi$
$252$	60.2705			3.79668
$253$	−0.00398917	−	0.00690945i	−0.000250797	−	0.000434393i
$254$	−11.6439	+	20.1679i	−0.730605	+	1.26544i
$255$	0.300476	−	0.520439i	0.0188165	−	0.0325912i
$256$	−23.8960			−1.49350
$257$	−2.17387	−	3.76526i	−0.135602	−	0.234870i	0.790225	−	0.612817i	$-0.209964\pi$
$257$	−2.17387	−	3.76526i	−0.135602	−	0.234870i	−0.925827	+	0.377946i	$0.876630\pi$
$258$	−37.4213	−	64.8157i	−2.32975	−	4.03525i
$259$	−11.2489	−	19.4837i	−0.698975	−	1.21066i
$260$	−0.161953	+	0.280512i	−0.0100439	+	0.0173966i
$261$	−6.05535	−	10.4882i	−0.374817	−	0.649202i
$262$	0.551987	−	0.956070i	0.0341019	−	0.0590662i
$263$	15.8338			0.976352			0.488176	−	0.872745i	$-0.337662\pi$
$263$	15.8338			0.976352			0.488176	+	0.872745i	$0.337662\pi$
$264$	0.0954399			0.00587392
$265$	0.130504	−	0.226039i	0.00801679	−	0.0138855i
$266$	−22.4547	−	38.8927i	−1.37679	−	2.38467i
$267$	−3.19171	+	5.52821i	−0.195330	+	0.338321i
$268$	−9.82639	−	17.0198i	−0.600242	−	1.03965i
$269$	−11.0791	−	19.1896i	−0.675507	−	1.17001i	−0.976321	−	0.216329i	$-0.930592\pi$
$269$	−11.0791	−	19.1896i	−0.675507	−	1.17001i	0.300814	−	0.953683i	$-0.402742\pi$
$270$	0.367196	+	0.636002i	0.0223468	+	0.0387059i
$271$	22.5096			1.36736			0.683682	−	0.729780i	$-0.260378\pi$
$271$	22.5096			1.36736			0.683682	+	0.729780i	$0.260378\pi$
$272$	−1.69359	+	2.93339i	−0.102689	+	0.177863i
$273$	5.39924	−	9.35176i	0.326777	−	0.565994i
$274$	−10.9341	−	18.9384i	−0.660552	−	1.14411i
$275$	0.0491802			0.00296568
$276$	−3.85026	+	6.66884i	−0.231758	+	0.401417i
$277$	15.4592			0.928853			0.464427	−	0.885612i	$-0.346260\pi$
$277$	15.4592			0.928853			0.464427	+	0.885612i	$0.346260\pi$
$278$	−49.8063			−2.98718
$279$	−19.1603	+	14.0052i	−1.14710	+	0.838467i
$280$	1.32207			0.0790088
$281$	−32.1745			−1.91937			−0.959685	−	0.281076i	$-0.909309\pi$
$281$	−32.1745			−1.91937			−0.959685	+	0.281076i	$0.909309\pi$
$282$	23.1132	−	40.0332i	1.37637	−	2.38394i
$283$	−7.91393			−0.470434			−0.235217	−	0.971943i	$-0.575580\pi$
$283$	−7.91393			−0.470434			−0.235217	+	0.971943i	$0.575580\pi$
$284$	−3.87526	−	6.71215i	−0.229955	−	0.398293i
$285$	0.589566	−	1.02116i	0.0349229	−	0.0604882i
$286$	0.0115833	−	0.0200629i	0.000684937	−	0.00118635i
$287$	20.5888			1.21532
$288$	8.33438	+	14.4356i	0.491108	+	0.850625i
$289$	5.54917	+	9.61144i	0.326422	+	0.565379i
$290$	−0.306608	−	0.531060i	−0.0180046	−	0.0311849i
$291$	−13.5524	+	23.4734i	−0.794455	+	1.37604i
$292$	5.32335	+	9.22031i	0.311525	+	0.539578i
$293$	11.0773	−	19.1865i	0.647145	−	1.12089i	−0.336657	−	0.941627i	$-0.609296\pi$
$293$	11.0773	−	19.1865i	0.647145	−	1.12089i	0.983802	−	0.179261i	$-0.0573705\pi$
$294$	−57.3834			−3.34667
$295$	1.32702			0.0772621
$296$	−10.0908	+	17.4778i	−0.586516	+	1.01588i
$297$	−0.0167623	−	0.0290331i	−0.000972646	−	0.00168467i
$298$	24.5921	−	42.5948i	1.42458	−	2.46745i
$299$	0.404883	+	0.701279i	0.0234150	+	0.0405560i
$300$	−23.7338	−	41.1081i	−1.37027	−	2.37338i
$301$	23.6635	+	40.9864i	1.36394	+	2.36241i
$302$	37.5356			2.15993
$303$	−16.2542	+	28.1530i	−0.933778	+	1.61735i
$304$	−3.32301	+	5.75562i	−0.190588	+	0.330108i
$305$	−0.541107	−	0.937225i	−0.0309837	−	0.0536654i
$306$	24.3485			1.39191
$307$	1.77100	−	3.06746i	0.101076	−	0.175069i	−0.811052	−	0.584974i	$-0.801105\pi$
$307$	1.77100	−	3.06746i	0.101076	−	0.175069i	0.912128	+	0.409905i	$0.134438\pi$
$308$	−0.139310			−0.00793794
$309$	29.8882			1.70028
$310$	−0.970165	+	0.709139i	−0.0551017	+	0.0402764i
$311$	−24.2946			−1.37762			−0.688811	−	0.724941i	$-0.741867\pi$
$311$	−24.2946			−1.37762			−0.688811	+	0.724941i	$0.741867\pi$
$312$	−9.68673			−0.548403
$313$	−5.57726	+	9.66009i	−0.315245	+	0.546021i	−0.979490	−	0.201495i	$-0.935420\pi$
$313$	−5.57726	+	9.66009i	−0.315245	+	0.546021i	0.664244	+	0.747516i	$0.268753\pi$
$314$	−18.6602			−1.05306
$315$	−0.783912	−	1.35777i	−0.0441684	−	0.0765019i
$316$	−5.44214	+	9.42607i	−0.306145	+	0.530258i
$317$	−4.61381	+	7.99136i	−0.259138	+	0.448839i	−0.966011	−	0.258500i	$-0.916772\pi$
$317$	−4.61381	+	7.99136i	−0.259138	+	0.448839i	0.706874	+	0.707340i	$0.250105\pi$
$318$	18.0179			1.01039
$319$	0.0139965	+	0.0242426i	0.000783651	+	0.00135732i
$320$	0.549989	+	0.952609i	0.0307453	+	0.0532525i
$321$	−0.0188157	−	0.0325898i	−0.00105019	−	0.00181898i
$322$	3.81468	−	6.60721i	0.212584	−	0.368206i
$323$	−5.78985	−	10.0283i	−0.322156	−	0.557990i
$324$	6.38352	−	11.0566i	0.354640	−	0.614254i
$325$	−4.99157			−0.276883
$326$	19.7611			1.09446
$327$	18.8957	−	32.7284i	1.04494	−	1.80988i
$328$	−9.23456	−	15.9947i	−0.509893	−	0.883161i
$329$	−14.6157	+	25.3151i	−0.805788	+	1.39567i
$330$	−0.00286541	−	0.00496303i	−0.000157735	−	0.000273206i
$331$	−3.00281	−	5.20101i	−0.165049	−	0.285874i	0.771624	−	0.636079i	$-0.219445\pi$
$331$	−3.00281	−	5.20101i	−0.165049	−	0.285874i	−0.936673	+	0.350206i	$0.886112\pi$
$332$	14.9934	+	25.9694i	0.822871	+	1.42525i
$333$	23.9331			1.31153
$334$	−17.6679	+	30.6017i	−0.966745	+	1.67445i
$335$	−0.255615	+	0.442738i	−0.0139657	+	0.0241894i
$336$	7.52808	+	13.0390i	0.410691	+	0.711337i
$337$	24.3060			1.32403			0.662015	−	0.749490i	$-0.269701\pi$
$337$	24.3060			1.32403			0.662015	+	0.749490i	$0.269701\pi$
$338$	−1.17566	+	2.03630i	−0.0639474	+	0.110760i
$339$	−37.9979			−2.06376
$340$	0.786878			0.0426744
$341$	0.0442875	−	0.0323718i	0.00239830	−	0.00175303i
$342$	47.7744			2.58334
$343$	8.23772			0.444795
$344$	21.2272	−	36.7667i	1.14450	−	1.98233i
$345$	0.200314			0.0107846
$346$	4.87763	+	8.44831i	0.262223	+	0.454184i
$347$	−14.3936	+	24.9305i	−0.772689	+	1.33834i	0.163395	+	0.986561i	$0.447755\pi$
$347$	−14.3936	+	24.9305i	−0.772689	+	1.33834i	−0.936084	+	0.351776i	$0.885578\pi$
$348$	13.5091	−	23.3984i	0.724162	−	1.25428i
$349$	36.0861			1.93164			0.965821	−	0.259210i	$-0.0834622\pi$
$349$	36.0861			1.93164			0.965821	+	0.259210i	$0.0834622\pi$
$350$	23.5145	+	40.7283i	1.25690	+	2.17702i
$351$	1.70130	+	2.94673i	0.0908086	+	0.157285i
$352$	−0.0192642	−	0.0333667i	−0.00102679	−	0.00177845i
$353$	14.7115	−	25.4811i	0.783015	−	1.35622i	−0.147163	−	0.989112i	$-0.547014\pi$
$353$	14.7115	−	25.4811i	0.783015	−	1.35622i	0.930178	−	0.367109i	$-0.119653\pi$
$354$	45.8034	+	79.3339i	2.43443	+	4.21655i
$355$	−0.100808	+	0.174604i	−0.00535032	+	0.00926702i
$356$	−8.35838			−0.442993
$357$	−26.2331			−1.38840
$358$	−10.1958	+	17.6596i	−0.538864	+	0.933340i
$359$	−15.2472	−	26.4089i	−0.804714	−	1.39381i	−0.916484	−	0.400072i	$-0.868985\pi$
$359$	−15.2472	−	26.4089i	−0.804714	−	1.39381i	0.111770	−	0.993734i	$-0.464348\pi$
$360$	−0.703205	+	1.21799i	−0.0370622	+	0.0641935i
$361$	−1.86030	−	3.22213i	−0.0979104	−	0.169586i
$362$	2.53359	+	4.38830i	0.133162	+	0.230644i
$363$	−14.8219	−	25.6723i	−0.777950	−	1.34745i
$364$	14.1394			0.741105
$365$	0.138477	−	0.239849i	0.00724821	−	0.0125543i
$366$	37.3538	−	64.6986i	1.95251	−	3.38185i
$367$	17.6168	+	30.5131i	0.919587	+	1.59277i	0.800042	+	0.599943i	$0.204810\pi$
$367$	17.6168	+	30.5131i	0.919587	+	1.59277i	0.119545	+	0.992829i	$0.461856\pi$
$368$	−1.12905			−0.0588556
$369$	−10.9511	+	18.9679i	−0.570093	+	0.987430i
$370$	1.21183			0.0630001
$371$	−11.3937			−0.591530
$372$	−48.4312	−	21.3962i	−2.51104	−	1.10934i
$373$	19.1774			0.992967			0.496484	−	0.868046i	$-0.334624\pi$
$373$	19.1774			0.992967			0.496484	+	0.868046i	$0.334624\pi$
$374$	−0.0562796			−0.00291015
$375$	−1.23582	+	2.14051i	−0.0638176	+	0.110535i
$376$	26.2219			1.35229
$377$	−1.42058	−	2.46051i	−0.0731635	−	0.126723i
$378$	16.0291	−	27.7632i	0.824446	−	1.42798i
$379$	−10.7731	+	18.6596i	−0.553377	+	0.958478i	0.444650	+	0.895704i	$0.353328\pi$
$379$	−10.7731	+	18.6596i	−0.553377	+	0.958478i	−0.998028	+	0.0627736i	$0.980005\pi$
$380$	1.54394			0.0792024
$381$	13.3455	+	23.1150i	0.683709	+	1.18422i
$382$	27.6960	+	47.9709i	1.41705	+	2.45440i
$383$	2.56379	+	4.44061i	0.131003	+	0.226905i	0.924064	−	0.382239i	$-0.124847\pi$
$383$	2.56379	+	4.44061i	0.131003	+	0.226905i	−0.793060	+	0.609143i	$0.791513\pi$
$384$	−27.4285	+	47.5075i	−1.39970	+	2.42436i
$385$	0.00181195	+	0.00313838i	9.23454e−5	+	0.000159947i
$386$	−23.2018	+	40.1867i	−1.18094	+	2.04545i
$387$	−50.3462			−2.55924
$388$	−35.4906			−1.80176
$389$	−7.75954	+	13.4399i	−0.393424	+	0.681430i	−0.992899	−	0.118963i	$-0.962043\pi$
$389$	−7.75954	+	13.4399i	−0.393424	+	0.681430i	0.599475	+	0.800394i	$0.295376\pi$
$390$	0.290826	+	0.503726i	0.0147266	+	0.0255071i
$391$	0.983597	−	1.70364i	0.0497426	−	0.0861568i
$392$	−16.2754	−	28.1897i	−0.822029	−	1.42380i
$393$	−0.632651	−	1.09578i	−0.0319130	−	0.0552749i
$394$	−24.7960	−	42.9480i	−1.24921	−	2.16369i
$395$	0.283134			0.0142460
$396$	0.0740987	−	0.128343i	0.00372360	−	0.00644946i
$397$	−8.51031	+	14.7403i	−0.427120	+	0.739794i	−0.996616	−	0.0822006i	$-0.973805\pi$
$397$	−8.51031	+	14.7403i	−0.427120	+	0.739794i	0.569496	+	0.821994i	$0.307139\pi$
$398$	−8.63323	−	14.9532i	−0.432745	−	0.749536i
$399$	−51.4722			−2.57683
$400$	3.47984	−	6.02726i	0.173992	−	0.301363i
$401$	−38.3723			−1.91622			−0.958111	−	0.286396i	$-0.907543\pi$
$401$	−38.3723			−1.91622			−0.958111	+	0.286396i	$0.907543\pi$
$402$	−35.2913			−1.76017
$403$	−4.49498	+	3.28559i	−0.223911	+	0.163667i
$404$	−42.5660			−2.11774
$405$	−0.332110			−0.0165027
$406$	−13.3842	+	23.1822i	−0.664248	+	1.15051i
$407$	−0.0553194			−0.00274208
$408$	11.7662	+	20.3796i	0.582511	+	1.00894i
$409$	6.77574	−	11.7359i	0.335039	−	0.580304i	−0.648454	−	0.761254i	$-0.724584\pi$
$409$	6.77574	−	11.7359i	0.335039	−	0.580304i	0.983492	+	0.180950i	$0.0579173\pi$
$410$	−0.554501	+	0.960424i	−0.0273848	+	0.0474319i
$411$	−25.0638			−1.23631
$412$	19.5676	+	33.8920i	0.964025	+	1.66974i
$413$	−28.9639	−	50.1670i	−1.42522	−	2.46856i
$414$	4.05803	+	7.02872i	0.199441	+	0.345443i
$415$	0.390026	−	0.675545i	0.0191456	−	0.0331612i
$416$	1.95524	+	3.38657i	0.0958634	+	0.166040i
$417$	−28.5423	+	49.4367i	−1.39772	+	2.42092i
$418$	−0.110427			−0.00540114
$419$	−22.5265			−1.10049			−0.550245	−	0.835003i	$-0.685466\pi$
$419$	−22.5265			−1.10049			−0.550245	+	0.835003i	$0.685466\pi$
$420$	1.74885	−	3.02910i	0.0853352	−	0.147805i
$421$	−9.69923	−	16.7996i	−0.472711	−	0.818760i	0.526801	−	0.849989i	$-0.323391\pi$
$421$	−9.69923	−	16.7996i	−0.472711	−	0.818760i	−0.999512	+	0.0312287i	$0.990058\pi$
$422$	9.59354	−	16.6165i	0.467006	−	0.808879i
$423$	−15.5481	−	26.9300i	−0.755973	−	1.30938i
$424$	5.11032	+	8.85134i	0.248179	+	0.429859i
$425$	6.06310	+	10.5016i	0.294104	+	0.509402i
$426$	−13.9179			−0.674326
$427$	−23.6207	+	40.9123i	−1.14309	+	1.97989i
$428$	0.0246370	−	0.0426726i	0.00119088	−	0.00206266i
$429$	−0.0132760	−	0.0229948i	−0.000640973	−	0.00111020i
$430$	−2.54923			−0.122935
$431$	−7.68809	+	13.3162i	−0.370322	+	0.641417i	−0.989615	−	0.143743i	$-0.954086\pi$
$431$	−7.68809	+	13.3162i	−0.370322	+	0.641417i	0.619293	+	0.785160i	$0.287419\pi$
$432$	−4.74419			−0.228255
$433$	23.6632			1.13718			0.568590	−	0.822621i	$-0.307489\pi$
$433$	23.6632			1.13718			0.568590	+	0.822621i	$0.307489\pi$
$434$	47.9836	+	21.1985i	2.30329	+	1.01756i
$435$	−0.702826			−0.0336979
$436$	49.4837			2.36984
$437$	1.92992	−	3.34272i	0.0923207	−	0.159904i
$438$	19.1187			0.913526
$439$	2.49669	+	4.32440i	0.119161	+	0.206392i	0.919435	−	0.393241i	$-0.128646\pi$
$439$	2.49669	+	4.32440i	0.119161	+	0.206392i	−0.800275	+	0.599634i	$0.795313\pi$
$440$	0.00162540	−	0.00281528i	7.74879e−5	−	0.000134213i
$441$	−19.3007	+	33.4298i	−0.919081	+	1.59190i
$442$	5.71213			0.271699
$443$	5.47657	+	9.48570i	0.260200	+	0.450679i	0.966295	−	0.257438i	$-0.0828782\pi$
$443$	5.47657	+	9.48570i	0.260200	+	0.450679i	−0.706095	+	0.708117i	$0.749545\pi$
$444$	26.6965	+	46.2397i	1.26696	+	2.19444i
$445$	0.108714	+	0.188298i	0.00515353	+	0.00892617i
$446$	6.53955	−	11.3268i	0.309657	−	0.536341i
$447$	−28.1858	−	48.8193i	−1.33314	−	2.30907i
$448$	24.0085	−	41.5839i	1.13429	−	1.96465i
$449$	33.6121			1.58625			0.793126	−	0.609058i	$-0.208452\pi$
$449$	33.6121			1.58625			0.793126	+	0.609058i	$0.208452\pi$
$450$	−50.0291			−2.35840
$451$	0.0253126	−	0.0438428i	0.00119193	−	0.00206448i
$452$	−24.8770	−	43.0882i	−1.17011	−	2.02670i
$453$	21.5104	−	37.2571i	1.01065	−	1.75049i
$454$	4.06918	+	7.04803i	0.190976	+	0.330781i
$455$	−0.183905	−	0.318532i	−0.00862159	−	0.0149330i
$456$	23.0865	+	39.9869i	1.08112	+	1.87256i
$457$	−18.7472			−0.876959			−0.438479	−	0.898741i	$-0.644483\pi$
$457$	−18.7472			−0.876959			−0.438479	+	0.898741i	$0.644483\pi$
$458$	−21.5085	+	37.2538i	−1.00503	+	1.74076i
$459$	4.13302	−	7.15860i	0.192913	−	0.334135i
$460$	0.131145	+	0.227149i	0.00611464	+	0.0105909i
$461$	−35.8285			−1.66870			−0.834351	−	0.551234i	$-0.814157\pi$
$461$	−35.8285			−1.66870			−0.834351	+	0.551234i	$0.814157\pi$
$462$	−0.125082	+	0.216649i	−0.00581936	+	0.0100794i
$463$	28.5782			1.32814			0.664071	−	0.747670i	$-0.268827\pi$
$463$	28.5782			1.32814			0.664071	+	0.747670i	$0.268827\pi$
$464$	3.96139			0.183903
$465$	0.147908	+	1.36935i	0.00685907	+	0.0635021i
$466$	46.9435			2.17461
$467$	5.65039			0.261469			0.130735	−	0.991417i	$-0.458266\pi$
$467$	5.65039			0.261469			0.130735	+	0.991417i	$0.458266\pi$
$468$	−7.52070	+	13.0262i	−0.347644	+	0.602138i
$469$	22.3165			1.03048
$470$	−0.787263	−	1.36358i	−0.0363137	−	0.0628972i
$471$	−10.6935	+	18.5218i	−0.492733	+	0.853438i
$472$	−25.9820	+	45.0021i	−1.19592	+	2.07139i
$473$	0.116371			0.00535074
$474$	9.77267	+	16.9268i	0.448874	+	0.777472i
$475$	11.8965	+	20.6053i	0.545847	+	0.945434i
$476$	−17.1746	−	29.7473i	−0.787198	−	1.36347i
$477$	6.06026	−	10.4967i	0.277480	−	0.480610i
$478$	24.4096	+	42.2787i	1.11647	+	1.93378i
$479$	−16.6317	+	28.8070i	−0.759922	+	1.31622i	0.182968	+	0.983119i	$0.441430\pi$
$479$	−16.6317	+	28.8070i	−0.759922	+	1.31622i	−0.942890	+	0.333105i	$0.891904\pi$
$480$	0.967346			0.0441531
$481$	5.61468			0.256007
$482$	12.3306	−	21.3572i	0.561642	−	0.972793i
$483$	−4.37212	−	7.57274i	−0.198939	−	0.344572i
$484$	19.4076	−	33.6150i	0.882165	−	1.52796i
$485$	0.461611	+	0.799534i	0.0209607	+	0.0363050i
$486$	−23.4640	−	40.6409i	−1.06435	−	1.84351i
$487$	11.3599	+	19.6760i	0.514768	+	0.891604i	0.999853	+	0.0171370i	$0.00545516\pi$
$487$	11.3599	+	19.6760i	0.514768	+	0.891604i	−0.485085	+	0.874467i	$0.661212\pi$
$488$	42.3778			1.91835
$489$	11.3244	−	19.6144i	0.512107	−	0.886995i
$490$	−0.977275	+	1.69269i	−0.0441488	+	0.0764679i
$491$	−20.2603	−	35.0919i	−0.914335	−	1.58367i	−0.807872	−	0.589358i	$-0.799381\pi$
$491$	−20.2603	−	35.0919i	−0.914335	−	1.58367i	−0.106463	−	0.994317i	$-0.533953\pi$
$492$	−48.8624			−2.20289
$493$	−3.45106	+	5.97741i	−0.155428	+	0.269209i
$494$	11.2078			0.504264
$495$	−0.00385508			−0.000173273
$496$	−0.833664	−	7.71816i	−0.0374326	−	0.346556i
$497$	8.80104			0.394781
$498$	53.8486			2.41301
$499$	8.01287	−	13.8787i	0.358705	−	0.621296i	−0.629039	−	0.777373i	$-0.716552\pi$
$499$	8.01287	−	13.8787i	0.358705	−	0.621296i	0.987745	+	0.156078i	$0.0498850\pi$
$500$	−3.23634			−0.144734
$501$	20.2498	+	35.0736i	0.904692	+	1.56697i
$502$	−0.0112121	+	0.0194199i	−0.000500421	+	0.000866755i
$503$	−11.0824	+	19.1953i	−0.494140	+	0.855875i	−0.999977	−	0.00675382i	$-0.997850\pi$
$503$	−11.0824	+	19.1953i	−0.494140	+	0.855875i	0.505838	+	0.862629i	$0.331184\pi$
$504$	61.3935			2.73468
$505$	0.553637	+	0.958928i	0.0246365	+	0.0426717i
$506$	−0.00937981	−	0.0162463i	−0.000416983	−	0.000722236i
$507$	1.34746	+	2.33387i	0.0598428	+	0.103651i
$508$	−17.4744	+	30.2665i	−0.775300	+	1.34286i
$509$	5.78924	+	10.0273i	0.256603	+	0.444450i	0.965330	−	0.261033i	$-0.0840633\pi$
$509$	5.78924	+	10.0273i	0.256603	+	0.444450i	−0.708726	+	0.705483i	$0.750730\pi$
$510$	0.706514	−	1.22372i	0.0312850	−	0.0541871i
$511$	−12.0898			−0.534819
$512$	−15.4757			−0.683935
$513$	8.10943	−	14.0459i	0.358040	−	0.620143i
$514$	−5.11147	−	8.85332i	−0.225457	−	0.390503i
$515$	0.509014	−	0.881638i	0.0224298	−	0.0388496i
$516$	−56.1593	−	97.2708i	−2.47228	−	4.28211i
$517$	0.0359381	+	0.0622466i	0.00158055	+	0.00273760i
$518$	−26.4498	−	45.8124i	−1.16214	−	2.01288i
$519$	11.1808			0.490784
$520$	−0.164971	+	0.285738i	−0.00723446	+	0.0125305i
$521$	−18.5385	+	32.1096i	−0.812187	+	1.40675i	0.0991433	+	0.995073i	$0.468390\pi$
$521$	−18.5385	+	32.1096i	−0.812187	+	1.40675i	−0.911330	+	0.411676i	$0.864944\pi$
$522$	−14.2381	−	24.6610i	−0.623183	−	1.07938i
$523$	4.03873			0.176601			0.0883007	−	0.996094i	$-0.471856\pi$
$523$	4.03873			0.176601			0.0883007	+	0.996094i	$0.471856\pi$
$524$	0.828384	−	1.43480i	0.0361881	−	0.0626797i
$525$	53.9014			2.35245
$526$	37.2302			1.62331
$527$	12.3724	+	5.46594i	0.538948	+	0.238100i
$528$	0.0370212			0.00161114
$529$	−22.3443			−0.971490
$530$	0.306856	−	0.531490i	0.0133290	−	0.0230865i
$531$	61.6233			2.67422
$532$	−33.6985	−	58.3675i	−1.46101	−	2.53055i
$533$	−2.56912	+	4.44985i	−0.111281	+	0.192744i
$534$	−7.50473	+	12.9986i	−0.324762	+	0.562504i
$535$	−0.00128177			−5.54158e−5
$536$	−10.0095	−	17.3369i	−0.432344	−	0.748841i
$537$	11.6857	+	20.2403i	0.504276	+	0.873432i
$538$	−26.0506	−	45.1209i	−1.12312	−	1.94530i
$539$	0.0446120	−	0.0772702i	0.00192157	−	0.00332826i
$540$	0.551062	+	0.954467i	0.0237139	+	0.0410737i
$541$	11.3543	−	19.6663i	0.488162	−	0.845521i	−0.511746	−	0.859137i	$-0.671001\pi$
$541$	11.3543	−	19.6663i	0.488162	−	0.845521i	0.999907	+	0.0136163i	$0.00433435\pi$
$542$	52.9273			2.27342
$543$	5.80766			0.249230
$544$	4.74992	−	8.22711i	0.203651	−	0.352734i
$545$	−0.643612	−	1.11477i	−0.0275693	−	0.0477515i
$546$	12.6953	−	21.9889i	0.543310	−	0.941040i
$547$	−16.9118	−	29.2920i	−0.723095	−	1.25244i	−0.959753	−	0.280844i	$-0.909386\pi$
$547$	−16.9118	−	29.2920i	−0.723095	−	1.25244i	0.236658	−	0.971593i	$-0.423948\pi$
$548$	−16.4091	−	28.4214i	−0.700962	−	1.21410i
$549$	−25.1276	−	43.5223i	−1.07242	−	1.85749i
$550$	0.115638			0.00493083
$551$	−6.77135	+	11.7283i	−0.288469	+	0.499643i
$552$	−3.92200	+	6.79310i	−0.166931	+	0.289133i
$553$	−6.17978	−	10.7037i	−0.262791	−	0.455167i
$554$	36.3495			1.54434
$555$	0.694460	−	1.20284i	0.0294782	−	0.0510577i
$556$	−74.7457			−3.16993
$557$	26.3971			1.11848			0.559241	−	0.829005i	$-0.311093\pi$
$557$	26.3971			1.11848			0.559241	+	0.829005i	$0.311093\pi$
$558$	−45.0519	+	32.9306i	−1.90720	+	1.39406i
$559$	−11.8111			−0.499558
$560$	0.512832			0.0216711
$561$	−0.0322519	+	0.0558620i	−0.00136168	+	0.00235850i
$562$	−75.6525			−3.19121
$563$	−2.39000	−	4.13960i	−0.100727	−	0.174464i	0.811258	−	0.584689i	$-0.198783\pi$
$563$	−2.39000	−	4.13960i	−0.100727	−	0.174464i	−0.911984	+	0.410225i	$0.865450\pi$
$564$	34.6866	−	60.0790i	1.46057	−	2.52978i
$565$	−0.647128	+	1.12086i	−0.0272249	+	0.0471548i
$566$	−18.6082			−0.782159
$567$	7.24874	+	12.5552i	0.304419	+	0.527269i
$568$	−3.94747	−	6.83722i	−0.165632	−	0.286883i
$569$	7.22055	+	12.5064i	0.302701	+	0.524294i	0.976747	−	0.214396i	$-0.0687782\pi$
$569$	7.22055	+	12.5064i	0.302701	+	0.524294i	−0.674046	+	0.738690i	$0.735445\pi$
$570$	1.38626	−	2.40107i	0.0580639	−	0.100570i
$571$	0.262156	+	0.454067i	0.0109709	+	0.0190021i	0.871459	−	0.490469i	$-0.163174\pi$
$571$	0.262156	+	0.454067i	0.0109709	+	0.0190021i	−0.860488	+	0.509471i	$0.829841\pi$
$572$	0.0173835	−	0.0301091i	0.000726839	−	0.00125892i
$573$	63.4865			2.65219
$574$	48.4108			2.02063
$575$	−2.02101	+	3.50048i	−0.0842818	+	0.145980i
$576$	25.5401	+	44.2367i	1.06417	+	1.84319i
$577$	16.9655	−	29.3851i	0.706283	−	1.22332i	−0.259944	−	0.965624i	$-0.583704\pi$
$577$	16.9655	−	29.3851i	0.706283	−	1.22332i	0.966227	−	0.257694i	$-0.0829625\pi$
$578$	13.0479	+	22.5995i	0.542719	+	0.940017i
$579$	26.5923	+	46.0593i	1.10514	+	1.91416i
$580$	−0.460135	−	0.796978i	−0.0191061	−	0.0330927i
$581$	−34.0513			−1.41269
$582$	−31.8660	+	55.1935i	−1.32089	+	2.28784i
$583$	−0.0140078	+	0.0242622i	−0.000580144	+	0.00100484i
$584$	5.42253	+	9.39210i	0.224386	+	0.388648i
$585$	0.391274			0.0161772
$586$	26.0463	−	45.1136i	1.07596	−	1.86362i
$587$	9.04716			0.373416			0.186708	−	0.982415i	$-0.440218\pi$
$587$	9.04716			0.373416			0.186708	+	0.982415i	$0.440218\pi$
$588$	−86.1170			−3.55140
$589$	24.2759	+	10.7248i	1.00027	+	0.441906i
$590$	3.12024			0.128458
$591$	−56.8391			−2.33805
$592$	−3.91423	+	6.77965i	−0.160874	+	0.278642i
$593$	10.7119			0.439884			0.219942	−	0.975513i	$-0.429413\pi$
$593$	10.7119			0.439884			0.219942	+	0.975513i	$0.429413\pi$
$594$	−0.0394134	−	0.0682661i	−0.00161715	−	0.00280099i
$595$	−0.446766	+	0.773821i	−0.0183156	+	0.0317236i
$596$	36.9062	−	63.9234i	1.51174	−	2.61840i
$597$	−19.7897			−0.809937
$598$	0.952009	+	1.64893i	0.0389306	+	0.0674297i
$599$	−16.4028	−	28.4105i	−0.670200	−	1.16082i	−0.977847	−	0.209320i	$-0.932875\pi$
$599$	−16.4028	−	28.4105i	−0.670200	−	1.16082i	0.307647	−	0.951501i	$-0.400458\pi$
$600$	−24.1760	−	41.8741i	−0.986982	−	1.70950i
$601$	10.5817	−	18.3280i	0.431635	−	0.747614i	−0.565379	−	0.824831i	$-0.691270\pi$
$601$	10.5817	−	18.3280i	0.431635	−	0.747614i	0.997014	+	0.0772169i	$0.0246034\pi$
$602$	55.6404	+	96.3719i	2.26773	+	3.92783i
$603$	−11.8701	+	20.5596i	−0.483388	+	0.837252i
$604$	56.3309			2.29207
$605$	−1.00971			−0.0410504
$606$	−38.2187	+	66.1967i	−1.55253	+	2.68906i
$607$	−6.76080	−	11.7100i	−0.274412	−	0.475296i	0.695574	−	0.718454i	$-0.255150\pi$
$607$	−6.76080	−	11.7100i	−0.274412	−	0.475296i	−0.969987	+	0.243158i	$0.921817\pi$
$608$	9.31986	−	16.1425i	0.377970	−	0.654663i
$609$	15.3401	+	26.5698i	0.621612	+	1.07666i
$610$	−1.27231	−	2.20371i	−0.0515145	−	0.0892258i
$611$	−3.64756	−	6.31776i	−0.147564	−	0.255589i
$612$	36.5406			1.47706
$613$	−6.33371	+	10.9703i	−0.255816	+	0.443087i	−0.965117	−	0.261819i	$-0.915678\pi$
$613$	−6.33371	+	10.9703i	−0.255816	+	0.443087i	0.709301	+	0.704906i	$0.249011\pi$
$614$	4.16418	−	7.21258i	0.168053	−	0.291076i
$615$	0.635531	+	1.10077i	0.0256271	+	0.0443874i
$616$	−0.141906			−0.00571755
$617$	10.4563	−	18.1109i	0.420956	−	0.729116i	−0.575078	−	0.818099i	$-0.695028\pi$
$617$	10.4563	−	18.1109i	0.420956	−	0.729116i	0.996033	+	0.0889825i	$0.0283615\pi$
$618$	70.2766			2.82694
$619$	1.86008			0.0747628			0.0373814	−	0.999301i	$-0.488098\pi$
$619$	1.86008			0.0747628			0.0373814	+	0.999301i	$0.488098\pi$
$620$	−1.45596	+	1.06423i	−0.0584726	+	0.0427403i
$621$	2.75531			0.110567
$622$	−57.1243			−2.29048
$623$	4.74564	−	8.21969i	0.190130	−	0.329315i
$624$	−3.75749			−0.150420
$625$	−12.4368	−	21.5412i	−0.497474	−	0.861650i
$626$	−13.1139	+	22.7139i	−0.524137	+	0.907832i
$627$	−0.0632817	+	0.109607i	−0.00252723	+	0.00437729i
$628$	−28.0040			−1.11748
$629$	−6.81996	−	11.8125i	−0.271930	−	0.470996i
$630$	−1.84322	−	3.19256i	−0.0734358	−	0.127195i
$631$	−9.95353	−	17.2400i	−0.396244	−	0.686314i	0.597015	−	0.802230i	$-0.296353\pi$
$631$	−9.95353	−	17.2400i	−0.396244	−	0.686314i	−0.993259	+	0.115916i	$0.963020\pi$
$632$	−5.54355	+	9.60170i	−0.220510	+	0.381935i
$633$	−10.9955	−	19.0447i	−0.437031	−	0.756959i
$634$	−10.8485	+	18.7902i	−0.430851	+	0.746255i
$635$	0.909127			0.0360776
$636$	27.0400			1.07221
$637$	−4.52792	+	7.84259i	−0.179403	+	0.310735i
$638$	0.0329101	+	0.0570020i	0.00130292	+	0.00225673i
$639$	−4.68125	+	8.10816i	−0.185187	+	0.320754i
$640$	0.934247	+	1.61816i	0.0369294	+	0.0639635i
$641$	1.53767	+	2.66333i	0.0607345	+	0.105195i	0.894794	−	0.446479i	$-0.147322\pi$
$641$	1.53767	+	2.66333i	0.0607345	+	0.105195i	−0.834059	+	0.551675i	$0.813989\pi$
$642$	−0.0442417	−	0.0766289i	−0.00174608	−	0.00302430i
$643$	5.02770			0.198273			0.0991365	−	0.995074i	$-0.468392\pi$
$643$	5.02770			0.198273			0.0991365	+	0.995074i	$0.468392\pi$
$644$	5.72480	−	9.91565i	0.225589	−	0.390731i
$645$	−1.46088	+	2.53032i	−0.0575221	+	0.0996312i
$646$	−13.6138	−	23.5797i	−0.535626	−	0.927732i
$647$	0.153149			0.00602091			0.00301045	−	0.999995i	$-0.499042\pi$
$647$	0.153149			0.00602091			0.00301045	+	0.999995i	$0.499042\pi$
$648$	6.50246	−	11.2626i	0.255441	−	0.442436i
$649$	−0.142437			−0.00559115
$650$	−11.7368			−0.460354
$651$	48.5390	−	35.4794i	1.90239	−	1.39055i
$652$	29.6560			1.16142
$653$	−48.0459			−1.88018			−0.940091	−	0.340922i	$-0.889261\pi$
$653$	−48.0459			−1.88018			−0.940091	+	0.340922i	$0.889261\pi$
$654$	44.4299	−	76.9548i	1.73735	−	3.00917i
$655$	−0.0430977			−0.00168397
$656$	−3.58209	−	6.20436i	−0.139857	−	0.242240i
$657$	6.43051	−	11.1380i	0.250878	−	0.434533i
$658$	−34.3661	+	59.5238i	−1.33973	+	2.32048i
$659$	10.4959			0.408862			0.204431	−	0.978881i	$-0.434466\pi$
$659$	10.4959			0.408862			0.204431	+	0.978881i	$0.434466\pi$
$660$	−0.00430020	−	0.00744817i	−0.000167385	−	0.000289919i
$661$	−15.7391	−	27.2609i	−0.612179	−	1.06032i	−0.990872	−	0.134803i	$-0.956960\pi$
$661$	−15.7391	−	27.2609i	−0.612179	−	1.06032i	0.378694	−	0.925522i	$-0.376373\pi$
$662$	−7.06055	−	12.2292i	−0.274416	−	0.475303i
$663$	3.27343	−	5.66975i	0.127130	−	0.220195i
$664$	15.2728	+	26.4532i	0.592699	+	1.02659i
$665$	−0.876603	+	1.51832i	−0.0339932	+	0.0588779i
$666$	56.2743			2.18058
$667$	−2.30068			−0.0890825
$668$	−26.5148	+	45.9249i	−1.02589	+	1.77689i
$669$	−7.49519	−	12.9821i	−0.289781	−	0.501915i
$670$	−0.601032	+	1.04102i	−0.0232199	+	0.0402180i
$671$	0.0580804	+	0.100598i	0.00224217	+	0.00388355i
$672$	−21.1136	−	36.5698i	−0.814474	−	1.41071i
$673$	25.1738	+	43.6023i	0.970379	+	1.68075i	0.694411	+	0.719579i	$0.255665\pi$
$673$	25.1738	+	43.6023i	0.970379	+	1.68075i	0.275968	+	0.961167i	$0.411002\pi$
$674$	57.1510			2.20138
$675$	−8.49215	+	14.7088i	−0.326863	+	0.566144i
$676$	−1.76435	+	3.05594i	−0.0678595	+	0.117536i
$677$	8.65338	+	14.9881i	0.332576	+	0.576039i	0.983016	−	0.183519i	$-0.0587488\pi$
$677$	8.65338	+	14.9881i	0.332576	+	0.576039i	−0.650440	+	0.759558i	$0.725415\pi$
$678$	−89.3451			−3.43128
$679$	20.1505	−	34.9017i	0.773306	−	1.33941i
$680$	0.801539			0.0307376
$681$	9.32765			0.357436
$682$	0.104134	−	0.0761163i	0.00398749	−	0.00291464i
$683$	−6.70441			−0.256537			−0.128269	−	0.991739i	$-0.540942\pi$
$683$	−6.70441			−0.256537			−0.128269	+	0.991739i	$0.540942\pi$
$684$	71.6965			2.74138
$685$	−0.426852	+	0.739329i	−0.0163092	+	0.0282483i
$686$	19.3695			0.739531
$687$	24.6516	+	42.6978i	0.940517	+	1.62902i
$688$	8.23406	−	14.2618i	0.313921	−	0.543726i
$689$	1.42173	−	2.46251i	0.0541636	−	0.0938141i
$690$	0.471003			0.0179308
$691$	1.90995	+	3.30813i	0.0726578	+	0.125847i	0.900065	−	0.435755i	$-0.143519\pi$
$691$	1.90995	+	3.30813i	0.0726578	+	0.125847i	−0.827408	+	0.561602i	$0.810185\pi$
$692$	7.32001	+	12.6786i	0.278265	+	0.481969i
$693$	0.0841421	+	0.145738i	0.00319629	+	0.00553614i
$694$	−33.8439	+	58.6194i	−1.28470	+	2.22516i
$695$	0.972185	+	1.68387i	0.0368771	+	0.0638730i
$696$	13.7608	−	23.8343i	0.521600	−	0.903439i
$697$	12.4825			0.472809
$698$	84.8497			3.21161
$699$	26.9017	−	46.5951i	1.01752	−	1.76239i
$700$	35.2889	+	61.1221i	1.33379	+	2.31020i
$701$	1.24702	−	2.15991i	0.0470994	−	0.0815785i	−0.841515	−	0.540234i	$-0.818336\pi$
$701$	1.24702	−	2.15991i	0.0470994	−	0.0815785i	0.888614	+	0.458656i	$0.151669\pi$
$702$	4.00029	+	6.92871i	0.150981	+	0.261507i
$703$	−13.3815	−	23.1774i	−0.504693	−	0.874153i
$704$	−0.0590337	−	0.102249i	−0.00222492	−	0.00385367i
$705$	−1.80461			−0.0679657
$706$	34.5914	−	59.9141i	1.30187	−	2.25490i
$707$	24.1677	−	41.8597i	0.908920	−	1.57430i
$708$	68.7386	+	119.059i	2.58336	+	4.47450i
$709$	0.997071			0.0374458			0.0187229	−	0.999825i	$-0.494040\pi$
$709$	0.997071			0.0374458			0.0187229	+	0.999825i	$0.494040\pi$
$710$	−0.237031	+	0.410549i	−0.00889561	+	0.0154076i
$711$	13.1480			0.493089
$712$	−8.51411			−0.319080
$713$	0.484172	+	4.48252i	0.0181324	+	0.167872i
$714$	−61.6824			−2.30840
$715$	−0.000904397	0		−3.38225e−5	0
$716$	−15.3011	+	26.5023i	−0.571830	+	0.990438i
$717$	55.9533			2.08961
$718$	−35.8509	−	62.0956i	−1.33794	−	2.31739i
$719$	14.8305	−	25.6872i	0.553085	−	0.957971i	−0.444965	−	0.895548i	$-0.646784\pi$
$719$	14.8305	−	25.6872i	0.553085	−	0.957971i	0.998050	−	0.0624232i	$-0.0198828\pi$
$720$	−0.272774	+	0.472458i	−0.0101657	+	0.0176075i
$721$	−44.4396			−1.65502
$722$	−4.37415	−	7.57625i	−0.162789	−	0.281959i
$723$	−14.1325	−	24.4781i	−0.525592	−	0.910352i
$724$	3.80223	+	6.58566i	0.141309	+	0.244754i
$725$	7.09092	−	12.2818i	0.263350	−	0.456136i
$726$	−34.8511	−	60.3638i	−1.29344	−	2.24031i
$727$	−5.46012	+	9.45720i	−0.202504	+	0.350748i	−0.949335	−	0.314267i	$-0.898241\pi$
$727$	−5.46012	+	9.45720i	−0.202504	+	0.350748i	0.746830	+	0.665015i	$0.231575\pi$
$728$	14.4028			0.533805
$729$	−42.9315			−1.59006
$730$	0.325603	−	0.563961i	0.0120511	−	0.0208731i
$731$	14.3466	+	24.8491i	0.530629	+	0.919076i
$732$	56.0579	−	97.0951i	2.07196	−	3.58874i
$733$	2.44544	+	4.23563i	0.0903244	+	0.156446i	0.907648	−	0.419733i	$-0.137876\pi$
$733$	2.44544	+	4.23563i	0.0903244	+	0.156446i	−0.817323	+	0.576179i	$0.804543\pi$
$734$	41.4226	+	71.7460i	1.52894	+	2.64819i
$735$	1.12009	+	1.94005i	0.0413150	+	0.0715597i
$736$	3.16657			0.116721
$737$	0.0274367	−	0.0475218i	0.00101065	−	0.00175049i
$738$	−25.7496	+	44.5996i	−0.947855	+	1.64173i
$739$	10.5630	+	18.2957i	0.388566	+	0.673016i	0.992257	−	0.124202i	$-0.0396371\pi$
$739$	10.5630	+	18.2957i	0.388566	+	0.673016i	−0.603691	+	0.797219i	$0.706304\pi$
$740$	1.81863			0.0668542
$741$	6.42282	−	11.1247i	0.235948	−	0.408674i
$742$	−26.7901			−0.983497
$743$	−0.609608			−0.0223643			−0.0111822	−	0.999937i	$-0.503559\pi$
$743$	−0.609608			−0.0223643			−0.0111822	+	0.999937i	$0.503559\pi$
$744$	−49.3335	−	21.7949i	−1.80866	−	0.799040i
$745$	−1.92009			−0.0703466
$746$	45.0921			1.65094
$747$	18.1118	−	31.3705i	0.662675	−	1.14779i
$748$	−0.0844605			−0.00308818
$749$	0.0279764	+	0.0484565i	0.00102223	+	0.00177056i
$750$	−2.90581	+	5.03301i	−0.106105	+	0.183780i
$751$	−1.76865	+	3.06340i	−0.0645391	+	0.111785i	−0.896489	−	0.443065i	$-0.853891\pi$
$751$	−1.76865	+	3.06340i	−0.0645391	+	0.111785i	0.831950	+	0.554850i	$0.187224\pi$
$752$	10.1715			0.370916
$753$	0.0128506	+	0.0222578i	0.000468300	+	0.000811120i
$754$	−3.34023	−	5.78545i	−0.121644	−	0.210694i
$755$	−0.732671	−	1.26902i	−0.0266646	−	0.0461845i
$756$	24.0553	−	41.6650i	0.874883	−	1.51534i
$757$	−6.27342	−	10.8659i	−0.228011	−	0.394927i	0.729207	−	0.684293i	$-0.239889\pi$
$757$	−6.27342	−	10.8659i	−0.228011	−	0.394927i	−0.957219	+	0.289366i	$0.906556\pi$
$758$	−25.3310	+	43.8746i	−0.920063	+	1.59360i
$759$	−0.0215010			−0.000780437
$760$	1.57271			0.0570480
$761$	9.74494	−	16.8787i	0.353254	−	0.611854i	−0.633564	−	0.773691i	$-0.718409\pi$
$761$	9.74494	−	16.8787i	0.353254	−	0.611854i	0.986818	+	0.161837i	$0.0517419\pi$
$762$	31.3794	+	54.3508i	1.13676	+	1.96892i
$763$	−28.0954	+	48.6626i	−1.01712	+	1.76170i
$764$	41.5642	+	71.9913i	1.50374	+	2.60455i
$765$	−0.475267	−	0.823187i	−0.0171833	−	0.0297624i
$766$	6.02828	+	10.4413i	0.217811	+	0.377259i
$767$	14.4568			0.522003
$768$	−32.1989	+	55.7701i	−1.16188	+	2.01243i
$769$	−3.88838	+	6.73488i	−0.140219	+	0.242866i	−0.927579	−	0.373627i	$-0.878114\pi$
$769$	−3.88838	+	6.73488i	−0.140219	+	0.242866i	0.787360	+	0.616493i	$0.211447\pi$
$770$	0.00426046	+	0.00737934i	0.000153536	+	0.000265933i
$771$	−11.7168			−0.421971
$772$	−34.8197	+	60.3094i	−1.25319	+	2.17058i
$773$	−27.5806			−0.992004			−0.496002	−	0.868321i	$-0.665199\pi$
$773$	−27.5806			−0.992004			−0.496002	+	0.868321i	$0.665199\pi$
$774$	−118.380			−4.25507
$775$	−25.4216	−	11.2309i	−0.913170	−	0.403426i
$776$	−36.1519			−1.29778
$777$	−60.6300			−2.17509
$778$	−18.2451	+	31.6015i	−0.654120	+	1.13297i
$779$	24.4920			0.877518
$780$	0.436452	+	0.755956i	0.0156275	+	0.0270676i
$781$	0.0108203	−	0.0187413i	0.000387181	−	0.000670618i
$782$	2.31275	−	4.00580i	0.0827037	−	0.143247i
$783$	−9.66731			−0.345481
$784$	−6.31322	−	10.9348i	−0.225472	−	0.390529i
$785$	0.364235	+	0.630874i	0.0130001	+	0.0225169i
$786$	−1.48756	−	2.57653i	−0.0530596	−	0.0919019i
$787$	6.82762	−	11.8258i	0.243378	−	0.421544i	−0.718296	−	0.695738i	$-0.755078\pi$
$787$	6.82762	−	11.8258i	0.243378	−	0.421544i	0.961674	+	0.274194i	$0.0884110\pi$
$788$	−37.2122	−	64.4533i	−1.32563	−	2.29606i
$789$	21.3354	−	36.9540i	0.759560	−	1.31560i
$790$	0.665739			0.0236859
$791$	56.4976			2.00882
$792$	0.0754794	−	0.130734i	0.00268204	−	0.00464543i
$793$	−5.89491	−	10.2103i	−0.209334	−	0.362578i
$794$	−20.0104	+	34.6591i	−0.710144	+	1.23001i
$795$	−0.351698	−	0.609158i	−0.0124734	−	0.0216046i
$796$	−12.9562	−	22.4407i	−0.459219	−	0.795390i
$797$	−11.5745	−	20.0476i	−0.409990	−	0.710123i	0.584898	−	0.811107i	$-0.301134\pi$
$797$	−11.5745	−	20.0476i	−0.409990	−	0.710123i	−0.994888	+	0.100983i	$0.967801\pi$
$798$	−121.027			−4.28432
$799$	−8.86114	+	15.3479i	−0.313484	+	0.542971i
$800$	−9.75971	+	16.9043i	−0.345058	+	0.597658i
$801$	5.04838	+	8.74406i	0.178376	+	0.308956i
$802$	−90.2255			−3.18597
$803$	−0.0148636	+	0.0257445i	−0.000524525	+	0.000908503i
$804$	−52.9627			−1.86785
$805$	−0.297840			−0.0104975
$806$	−10.5691	+	7.72547i	−0.372282	+	0.272118i
$807$	−59.7148			−2.10206
$808$	−43.3591			−1.52537
$809$	12.0064	−	20.7956i	0.422121	−	0.731135i	−0.574026	−	0.818837i	$-0.694619\pi$
$809$	12.0064	−	20.7956i	0.422121	−	0.731135i	0.996147	+	0.0877022i	$0.0279524\pi$
$810$	−0.780897			−0.0274379
$811$	14.5872	+	25.2657i	0.512225	+	0.887200i	0.999900	+	0.0141742i	$0.00451194\pi$
$811$	14.5872	+	25.2657i	0.512225	+	0.887200i	−0.487675	+	0.873026i	$0.662155\pi$
$812$	−20.0861	+	34.7902i	−0.704884	+	1.22090i
$813$	30.3308	−	52.5346i	1.06375	−	1.84247i
$814$	−0.130073			−0.00455907
$815$	−0.385723	−	0.668092i	−0.0135113	−	0.0234022i
$816$	4.56410	+	7.90525i	0.159775	+	0.276739i
$817$	28.1496	+	48.7565i	0.984829	+	1.70577i
$818$	15.9319	−	27.5949i	0.557046	−	0.964832i
$819$	−8.54006	−	14.7918i	−0.298414	−	0.516868i
$820$	−0.832156	+	1.44134i	−0.0290602	+	0.0503337i
$821$	−0.728860			−0.0254374			−0.0127187	−	0.999919i	$-0.504049\pi$
$821$	−0.728860			−0.0254374			−0.0127187	+	0.999919i	$0.504049\pi$
$822$	−58.9329			−2.05552
$823$	10.1179	−	17.5248i	0.352689	−	0.610875i	−0.634031	−	0.773308i	$-0.718601\pi$
$823$	10.1179	−	17.5248i	0.352689	−	0.610875i	0.986720	+	0.162433i	$0.0519340\pi$
$824$	19.9322	+	34.5235i	0.694370	+	1.20268i
$825$	0.0662683	−	0.114780i	0.00230717	−	0.00399613i
$826$	−68.1034	−	117.959i	−2.36962	−	4.10430i
$827$	3.55806	+	6.16275i	0.123726	+	0.214300i	0.921234	−	0.389008i	$-0.127182\pi$
$827$	3.55806	+	6.16275i	0.123726	+	0.214300i	−0.797508	+	0.603308i	$0.793849\pi$
$828$	6.09001	+	10.5482i	0.211642	+	0.366576i
$829$	−23.3707			−0.811697			−0.405848	−	0.913940i	$-0.633024\pi$
$829$	−23.3707			−0.811697			−0.405848	+	0.913940i	$0.633024\pi$
$830$	0.917074	−	1.58842i	0.0318321	−	0.0551348i
$831$	20.8307	−	36.0798i	0.722607	−	1.25159i
$832$	5.99167	+	10.3779i	0.207724	+	0.359788i
$833$	21.9997			0.762244
$834$	−67.1119	+	116.241i	−2.32390	+	4.02511i
$835$	1.37946			0.0477383
$836$	−0.165721			−0.00573156
$837$	2.03446	+	18.8353i	0.0703213	+	0.651043i
$838$	−52.9669			−1.82971
$839$	19.1966			0.662741			0.331371	−	0.943501i	$-0.392489\pi$
$839$	19.1966			0.662741			0.331371	+	0.943501i	$0.392489\pi$
$840$	1.78144	−	3.08554i	0.0614654	−	0.106461i
$841$	−20.9278			−0.721649
$842$	−22.8060	−	39.5011i	−0.785945	−	1.36130i
$843$	−43.3539	+	75.0911i	−1.49319	+	2.58628i
$844$	14.3973	−	24.9369i	0.495576	−	0.858363i
$845$	0.0917923			0.00315775
$846$	−36.5584	−	63.3211i	−1.25691	−	2.17702i
$847$	22.0382	+	38.1712i	0.757240	+	1.31158i
$848$	1.98230	+	3.43344i	0.0680724	+	0.117905i
$849$	−10.6637	+	18.4701i	−0.365977	+	0.633891i
$850$	14.2563	+	24.6926i	0.488986	+	0.846949i
$851$	2.27329	−	3.93745i	0.0779274	−	0.134974i
$852$	−20.8870			−0.715578
$853$	−15.4548			−0.529162			−0.264581	−	0.964364i	$-0.585234\pi$
$853$	−15.4548			−0.529162			−0.264581	+	0.964364i	$0.585234\pi$
$854$	−55.5399	+	96.1979i	−1.90054	+	3.29182i
$855$	−0.932525	−	1.61518i	−0.0318917	−	0.0552380i
$856$	0.0250961	−	0.0434677i	0.000857766	−	0.00148569i
$857$	20.7902	+	36.0097i	0.710179	+	1.23007i	0.964790	+	0.263023i	$0.0847194\pi$
$857$	20.7902	+	36.0097i	0.710179	+	1.23007i	−0.254610	+	0.967044i	$0.581947\pi$
$858$	−0.0312162	−	0.0540680i	−0.00106570	−	0.00184585i
$859$	3.41633	+	5.91725i	0.116564	+	0.201894i	0.918404	−	0.395645i	$-0.129479\pi$
$859$	3.41633	+	5.91725i	0.116564	+	0.201894i	−0.801840	+	0.597539i	$0.796145\pi$
$860$	−3.82571			−0.130456
$861$	27.7426	−	48.0516i	0.945465	−	1.63759i
$862$	−18.0771	+	31.3105i	−0.615710	+	1.06644i
$863$	3.96322	+	6.86449i	0.134909	+	0.233670i	0.925563	−	0.378594i	$-0.123592\pi$
$863$	3.96322	+	6.86449i	0.134909	+	0.233670i	−0.790653	+	0.612264i	$0.790259\pi$
$864$	13.3058			0.452671
$865$	0.190416	−	0.329811i	0.00647435	−	0.0112139i
$866$	55.6397			1.89071
$867$	29.9091			1.01577
$868$	72.0104	+	31.8132i	2.44419	+	1.07981i
$869$	−0.0303906			−0.00103093
$870$	−1.65257			−0.0560272
$871$	−2.78471	+	4.82326i	−0.0943563	+	0.163430i
$872$	50.4057			1.70695
$873$	21.4360	+	37.1283i	0.725499	+	1.25660i
$874$	4.53786	−	7.85980i	0.153495	−	0.265862i
$875$	1.83750	−	3.18264i	0.0621188	−	0.107593i
$876$	28.6920			0.969413
$877$	−7.11708	−	12.3272i	−0.240327	−	0.416258i	0.720481	−	0.693475i	$-0.243921\pi$
$877$	−7.11708	−	12.3272i	−0.240327	−	0.416258i	−0.960807	+	0.277217i	$0.910588\pi$
$878$	5.87052	+	10.1680i	0.198120	+	0.343154i
$879$	−29.8525	−	51.7061i	−1.00690	−	1.74400i
$880$	0.000630494	−	0.00109205i	2.12539e−5	−	3.68129e-5i
$881$	−2.51538	−	4.35677i	−0.0847453	−	0.146783i	0.820537	−	0.571593i	$-0.193674\pi$
$881$	−2.51538	−	4.35677i	−0.0847453	−	0.146783i	−0.905283	+	0.424810i	$0.860341\pi$
$882$	−45.3821	+	78.6041i	−1.52809	+	2.64674i
$883$	53.4135			1.79751			0.898754	−	0.438453i	$-0.144474\pi$
$883$	53.4135			1.79751			0.898754	+	0.438453i	$0.144474\pi$
$884$	8.57237			0.288320
$885$	1.78811	−	3.09709i	0.0601065	−	0.104108i
$886$	12.8772	+	22.3039i	0.432617	+	0.749314i
$887$	−18.5776	+	32.1773i	−0.623774	+	1.08041i	0.365002	+	0.931007i	$0.381068\pi$
$887$	−18.5776	+	32.1773i	−0.623774	+	1.08041i	−0.988776	+	0.149402i	$0.952265\pi$
$888$	27.1939	+	47.1013i	0.912569	+	1.58062i
$889$	−19.8429	−	34.3689i	−0.665509	−	1.15269i
$890$	0.255620	+	0.442748i	0.00856842	+	0.0148409i
$891$	0.0356475			0.00119424
$892$	9.81411	−	16.9985i	0.328601	−	0.569153i
$893$	−17.3865	+	30.1143i	−0.581817	+	1.00774i
$894$	−66.2739	−	114.790i	−2.21653	−	3.83914i
$895$	0.796060			0.0266094
$896$	40.7823	−	70.6371i	1.36244	−	2.35982i
$897$	2.18226			0.0728634
$898$	79.0326			2.63735
$899$	−1.69877	−	15.7274i	−0.0566572	−	0.524539i
$900$	−75.0802			−2.50267
$901$	−6.90771			−0.230129
$902$	0.0595180	−	0.103088i	0.00198173	−	0.00343246i
$903$	127.542			4.24435
$904$	−25.3405	−	43.8910i	−0.842812	−	1.45979i
$905$	0.0989080	−	0.171314i	0.00328781	−	0.00569466i
$906$	50.5778	−	87.6033i	1.68033	−	2.91042i
$907$	−14.8956			−0.494600			−0.247300	−	0.968939i	$-0.579543\pi$
$907$	−14.8956			−0.494600			−0.247300	+	0.968939i	$0.579543\pi$
$908$	6.10675	+	10.5772i	0.202660	+	0.351017i
$909$	25.7095	+	44.5301i	0.852729	+	1.47697i
$910$	−0.432418	−	0.748971i	−0.0143345	−	0.0248281i
$911$	3.56535	−	6.17537i	0.118125	−	0.204599i	−0.800899	−	0.598799i	$-0.795645\pi$
$911$	3.56535	−	6.17537i	0.118125	−	0.204599i	0.919025	+	0.394200i	$0.128978\pi$
$912$	8.95525	+	15.5109i	0.296538	+	0.513619i
$913$	−0.0418639	+	0.0725104i	−0.00138549	+	0.00239974i
$914$	−44.0807			−1.45806
$915$	−2.91648			−0.0964159
$916$	−32.2785	+	55.9080i	−1.06651	+	1.84725i
$917$	0.940664	+	1.62928i	0.0310635	+	0.0538035i
$918$	9.71804	−	16.8321i	0.320743	−	0.555543i
$919$	5.77376	+	10.0004i	0.190459	+	0.329884i	0.945402	−	0.325906i	$-0.105669\pi$
$919$	5.77376	+	10.0004i	0.190459	+	0.329884i	−0.754944	+	0.655790i	$0.772336\pi$
$920$	0.133588	+	0.231381i	0.00440427	+	0.00762842i
$921$	−4.77271	−	8.26657i	−0.157266	−	0.272393i
$922$	−84.2443			−2.77444
$923$	−1.09821	+	1.90216i	−0.0361482	+	0.0626105i
$924$	−0.187715	+	0.325132i	−0.00617537	+	0.0106961i
$925$	14.0130	+	24.2713i	0.460746	+	0.798035i
$926$	67.1964			2.20821
$927$	23.6373	−	40.9410i	0.776350	−	1.34468i
$928$	−11.1103			−0.364713
$929$	−50.9257			−1.67082			−0.835408	−	0.549630i	$-0.814769\pi$
$929$	−50.9257			−1.67082			−0.835408	+	0.549630i	$0.814769\pi$
$930$	0.347779	+	3.21978i	0.0114041	+	0.105581i
$931$	43.1657			1.41470
$932$	70.4495			2.30765
$933$	−32.7360	+	56.7005i	−1.07173	+	1.85629i
$934$	13.2859			0.434727
$935$	0.00109854	+	0.00190273i	3.59261e−5	+	6.22259e-5i
$936$	−7.66082	+	13.2689i	−0.250402	+	0.433709i
$937$	19.6145	−	33.9733i	0.640778	−	1.10986i	−0.344482	−	0.938793i	$-0.611945\pi$
$937$	19.6145	−	33.9733i	0.640778	−	1.10986i	0.985260	−	0.171066i	$-0.0547213\pi$
$938$	52.4732			1.71331
$939$	15.0303	+	26.0332i	0.490494	+	0.849561i
$940$	−1.18147	−	2.04636i	−0.0385353	−	0.0667451i
$941$	−8.87993	−	15.3805i	−0.289477	−	0.501390i	0.684208	−	0.729287i	$-0.260148\pi$
$941$	−8.87993	−	15.3805i	−0.289477	−	0.501390i	−0.973685	+	0.227898i	$0.926815\pi$
$942$	−25.1439	+	43.5505i	−0.819233	+	1.41895i
$943$	2.08039	+	3.60334i	0.0677468	+	0.117341i
$944$	−10.0784	+	17.4564i	−0.328025	+	0.568156i
$945$	−1.25151			−0.0407115
$946$	0.273625			0.00889632
$947$	24.4175	−	42.2923i	0.793461	−	1.37431i	−0.130351	−	0.991468i	$-0.541610\pi$
$947$	24.4175	−	42.2923i	0.793461	−	1.37431i	0.923812	−	0.382846i	$-0.125056\pi$
$948$	14.6661	+	25.4025i	0.476334	+	0.825035i
$949$	1.50859	−	2.61295i	0.0489709	−	0.0848200i
$950$	27.9723	+	48.4495i	0.907542	+	1.57191i
$951$	12.4339	+	21.5361i	0.403196	+	0.698355i
$952$	−17.4946	−	30.3016i	−0.567005	−	0.982081i
$953$	−3.48680			−0.112948			−0.0564742	−	0.998404i	$-0.517986\pi$
$953$	−3.48680			−0.112948			−0.0564742	+	0.998404i	$0.517986\pi$
$954$	14.2496	−	24.6810i	0.461348	−	0.799078i
$955$	1.08122	−	1.87272i	0.0349873	−	0.0605998i
$956$	36.6323	+	63.4489i	1.18477	+	2.05209i
$957$	0.0754386			0.00243858
$958$	−39.1064	+	67.7343i	−1.26347	+	2.18840i
$959$	37.2664			1.20339
$960$	2.96435			0.0956741
$961$	−30.2850	+	6.61959i	−0.976935	+	0.213535i
$962$	13.2019			0.425646
$963$	−0.0595222			−0.00191807
$964$	18.5049	−	32.0514i	0.596001	−	1.03230i
$965$	1.81154			0.0583154
$966$	−10.2803	−	17.8059i	−0.330762	−	0.572896i
$967$	3.19039	−	5.52592i	0.102596	−	0.177702i	−0.810157	−	0.586212i	$-0.800618\pi$
$967$	3.19039	−	5.52592i	0.102596	−	0.177702i	0.912754	+	0.408511i	$0.133952\pi$
$968$	19.7693	−	34.2413i	0.635408	−	1.10056i
$969$	−31.2064			−1.00249
$970$	1.08539	+	1.87996i	0.0348499	+	0.0603618i
$971$	−12.2079	−	21.1447i	−0.391770	−	0.678566i	0.600913	−	0.799315i	$-0.294804\pi$
$971$	−12.2079	−	21.1447i	−0.391770	−	0.678566i	−0.992683	+	0.120748i	$0.961471\pi$
$972$	−35.2131	−	60.9909i	−1.12946	−	1.95629i
$973$	42.4384	−	73.5055i	1.36051	−	2.35648i
$974$	26.7108	+	46.2645i	0.855869	+	1.48241i
$975$	−6.72595	+	11.6497i	−0.215403	+	0.373088i
$976$	16.4384			0.526180
$977$	38.9117			1.24490			0.622448	−	0.782661i	$-0.286138\pi$
$977$	38.9117			1.24490			0.622448	+	0.782661i	$0.286138\pi$
$978$	26.6272	−	46.1197i	0.851445	−	1.47475i
$979$	−0.0116689	−	0.0202112i	−0.000372940	−	0.000645952i
$980$	−1.46663	+	2.54027i	−0.0468496	+	0.0811459i
$981$	−29.8877	−	51.7670i	−0.954240	−	1.65279i
$982$	−47.6384	−	82.5122i	−1.52020	−	2.63307i
$983$	3.97304	+	6.88150i	0.126720	+	0.219486i	0.922404	−	0.386226i	$-0.126222\pi$
$983$	3.97304	+	6.88150i	0.126720	+	0.219486i	−0.795684	+	0.605712i	$0.792888\pi$
$984$	−49.7728			−1.58670
$985$	−0.968004	+	1.67663i	−0.0308432	+	0.0534220i
$986$	−8.11454	+	14.0548i	−0.258419	+	0.447596i
$987$	39.3881	+	68.2222i	1.25374	+	2.17154i
$988$	16.8199			0.535113
$989$	−4.78214	+	8.28291i	−0.152063	+	0.263381i
$990$	−0.00906451			−0.000288089
$991$	−55.8077			−1.77279			−0.886395	−	0.462930i	$-0.846798\pi$
$991$	−55.8077			−1.77279			−0.886395	+	0.462930i	$0.846798\pi$
$992$	2.33813	+	21.6467i	0.0742357	+	0.687283i
$993$	−16.1847			−0.513604
$994$	20.6940			0.656375
$995$	−0.337030	+	0.583753i	−0.0106846	+	0.0185062i
$996$	80.8122			2.56063
$997$	−16.9787	−	29.4080i	−0.537722	−	0.931361i	−0.999026	−	0.0441194i	$-0.985952\pi$
$997$	−16.9787	−	29.4080i	−0.537722	−	0.931361i	0.461305	−	0.887242i	$-0.347382\pi$
$998$	18.8408	−	32.6332i	0.596395	−	1.03299i
$999$	9.55224	−	16.5450i	0.302219	−	0.523459i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.h.b.222.15	yes	34
31.25	even	3	inner	403.2.h.b.118.15	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.h.b.118.15	✓	34	31.25	even	3	inner
403.2.h.b.222.15	yes	34	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.35132 q^{2} +(1.34746 - 2.33387i) q^{3} +3.52869 q^{4} +(-0.0458962 - 0.0794945i) q^{5} +(3.16831 - 5.48767i) q^{6} +(-2.00349 + 3.47014i) q^{7} +3.59444 q^{8} +(-2.13130 - 3.69152i) q^{9} +O(q^{10})\)	\(q+2.35132 q^{2} +(1.34746 - 2.33387i) q^{3} +3.52869 q^{4} +(-0.0458962 - 0.0794945i) q^{5} +(3.16831 - 5.48767i) q^{6} +(-2.00349 + 3.47014i) q^{7} +3.59444 q^{8} +(-2.13130 - 3.69152i) q^{9} +(-0.107916 - 0.186917i) q^{10} +(0.00492632 + 0.00853264i) q^{11} +(4.75477 - 8.23551i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-4.71083 + 8.15940i) q^{14} -0.247373 q^{15} +1.39429 q^{16} +(-1.21467 + 2.10386i) q^{17} +(-5.01136 - 8.67993i) q^{18} +(-2.38331 + 4.12801i) q^{19} +(-0.161953 - 0.280512i) q^{20} +(5.39924 + 9.35176i) q^{21} +(0.0115833 + 0.0200629i) q^{22} -0.809767 q^{23} +(4.84337 - 8.38896i) q^{24} +(2.49579 - 4.32283i) q^{25} +(-1.17566 - 2.03630i) q^{26} -3.40260 q^{27} +(-7.06969 + 12.2451i) q^{28} +2.84116 q^{29} -0.581652 q^{30} +(-0.597915 - 5.53557i) q^{31} -3.91047 q^{32} +0.0265521 q^{33} +(-2.85607 + 4.94685i) q^{34} +0.367810 q^{35} +(-7.52070 - 13.0262i) q^{36} +(-2.80734 + 4.86245i) q^{37} +(-5.60391 + 9.70626i) q^{38} -2.69492 q^{39} +(-0.164971 - 0.285738i) q^{40} +(-2.56912 - 4.44985i) q^{41} +(12.6953 + 21.9889i) q^{42} +(5.90557 - 10.2288i) q^{43} +(0.0173835 + 0.0301091i) q^{44} +(-0.195637 + 0.338853i) q^{45} -1.90402 q^{46} +7.29512 q^{47} +(1.87874 - 3.25408i) q^{48} +(-4.52792 - 7.84259i) q^{49} +(5.86839 - 10.1643i) q^{50} +(3.27343 + 5.66975i) q^{51} +(-1.76435 - 3.05594i) q^{52} +(1.42173 + 2.46251i) q^{53} -8.00058 q^{54} +(0.000452198 - 0.000783231i) q^{55} +(-7.20142 + 12.4732i) q^{56} +(6.42282 + 11.1247i) q^{57} +6.68046 q^{58} +(-7.22838 + 12.5199i) q^{59} -0.872903 q^{60} +11.7898 q^{61} +(-1.40589 - 13.0159i) q^{62} +17.0801 q^{63} -11.9833 q^{64} +(-0.0458962 + 0.0794945i) q^{65} +0.0624324 q^{66} +(-2.78471 - 4.82326i) q^{67} +(-4.28619 + 7.42389i) q^{68} +(-1.09113 + 1.88989i) q^{69} +0.864837 q^{70} +(-1.09821 - 1.90216i) q^{71} +(-7.66082 - 13.2689i) q^{72} +(1.50859 + 2.61295i) q^{73} +(-6.60094 + 11.4332i) q^{74} +(-6.72595 - 11.6497i) q^{75} +(-8.40996 + 14.5665i) q^{76} -0.0394793 q^{77} -6.33661 q^{78} +(-1.54226 + 2.67126i) q^{79} +(-0.0639924 - 0.110838i) q^{80} +(1.80903 - 3.13333i) q^{81} +(-6.04082 - 10.4630i) q^{82} +(4.24900 + 7.35949i) q^{83} +(19.0523 + 32.9995i) q^{84} +0.222994 q^{85} +(13.8859 - 24.0510i) q^{86} +(3.82835 - 6.63089i) q^{87} +(0.0177074 + 0.0306701i) q^{88} -2.36869 q^{89} +(-0.460004 + 0.796751i) q^{90} +4.00697 q^{91} -2.85742 q^{92} +(-13.7250 - 6.06350i) q^{93} +17.1531 q^{94} +0.437538 q^{95} +(-5.26921 + 9.12654i) q^{96} -10.0577 q^{97} +(-10.6466 - 18.4404i) q^{98} +(0.0209989 - 0.0363712i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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