LMFDB - Embedded newform 471.2.e.c.169.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(169,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, 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("471.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.e (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:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			169.10
Character	$\chi$	$=$	471.169
Dual form			471.2.e.c.301.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.10791 q^{2} +(-0.500000 - 0.866025i) q^{3} -0.772541 q^{4} +(1.74720 + 3.02624i) q^{5} +(-0.553954 - 0.959476i) q^{6} -4.63545 q^{7} -3.07172 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+1.10791 q^{2} +(-0.500000 - 0.866025i) q^{3} -0.772541 q^{4} +(1.74720 + 3.02624i) q^{5} +(-0.553954 - 0.959476i) q^{6} -4.63545 q^{7} -3.07172 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.93574 + 3.35280i) q^{10} +(-0.619790 - 1.07351i) q^{11} +(0.386270 + 0.669040i) q^{12} +(-3.04174 + 5.26845i) q^{13} -5.13565 q^{14} +(1.74720 - 3.02624i) q^{15} -1.85810 q^{16} +(1.45597 + 2.52182i) q^{17} +(-0.553954 + 0.959476i) q^{18} +(-3.53092 - 6.11573i) q^{19} +(-1.34978 - 2.33789i) q^{20} +(2.31773 + 4.01442i) q^{21} +(-0.686670 - 1.18935i) q^{22} +3.72787 q^{23} +(1.53586 + 2.66019i) q^{24} +(-3.60542 + 6.24477i) q^{25} +(-3.36997 + 5.83696i) q^{26} +1.00000 q^{27} +3.58108 q^{28} +3.49070 q^{29} +(1.93574 - 3.35280i) q^{30} +(-2.01285 + 3.48637i) q^{31} +4.08484 q^{32} +(-0.619790 + 1.07351i) q^{33} +(1.61308 + 2.79394i) q^{34} +(-8.09906 - 14.0280i) q^{35} +(0.386270 - 0.669040i) q^{36} +(0.339830 - 0.588602i) q^{37} +(-3.91193 - 6.77566i) q^{38} +6.08349 q^{39} +(-5.36691 - 9.29576i) q^{40} +2.45016 q^{41} +(2.56783 + 4.44760i) q^{42} +(-2.77096 + 4.79944i) q^{43} +(0.478813 + 0.829328i) q^{44} -3.49440 q^{45} +4.13014 q^{46} +(-4.11718 + 7.13116i) q^{47} +(0.929049 + 1.60916i) q^{48} +14.4874 q^{49} +(-3.99447 + 6.91863i) q^{50} +(1.45597 - 2.52182i) q^{51} +(2.34987 - 4.07010i) q^{52} +(-1.58207 + 2.74023i) q^{53} +1.10791 q^{54} +(2.16579 - 3.75127i) q^{55} +14.2388 q^{56} +(-3.53092 + 6.11573i) q^{57} +3.86738 q^{58} -8.51964 q^{59} +(-1.34978 + 2.33789i) q^{60} +(0.973816 + 1.68670i) q^{61} +(-2.23006 + 3.86257i) q^{62} +(2.31773 - 4.01442i) q^{63} +8.24182 q^{64} -21.2581 q^{65} +(-0.686670 + 1.18935i) q^{66} +11.1078 q^{67} +(-1.12480 - 1.94821i) q^{68} +(-1.86394 - 3.22843i) q^{69} +(-8.97301 - 15.5417i) q^{70} +(-5.39073 + 9.33702i) q^{71} +(1.53586 - 2.66019i) q^{72} +(-5.48381 - 9.49823i) q^{73} +(0.376500 - 0.652117i) q^{74} +7.21084 q^{75} +(2.72778 + 4.72465i) q^{76} +(2.87301 + 4.97619i) q^{77} +6.73994 q^{78} +5.38180 q^{79} +(-3.24647 - 5.62305i) q^{80} +(-0.500000 - 0.866025i) q^{81} +2.71456 q^{82} +(6.55772 - 11.3583i) q^{83} +(-1.79054 - 3.10130i) q^{84} +(-5.08775 + 8.81225i) q^{85} +(-3.06997 + 5.31734i) q^{86} +(-1.74535 - 3.02304i) q^{87} +(1.90382 + 3.29751i) q^{88} +(-9.26584 - 16.0489i) q^{89} -3.87147 q^{90} +(14.0999 - 24.4217i) q^{91} -2.87993 q^{92} +4.02571 q^{93} +(-4.56145 + 7.90067i) q^{94} +(12.3384 - 21.3708i) q^{95} +(-2.04242 - 3.53757i) q^{96} +(-3.36409 + 5.82677i) q^{97} +16.0507 q^{98} +1.23958 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9}+O(q^{10}) $ 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9} - q^{10} + 2 q^{11} - 13 q^{12} - 14 q^{14} - 2 q^{15} + 14 q^{16} + 3 q^{17} - q^{18} - 11 q^{19} + q^{20} - 2 q^{21} - 2 q^{22} - 6 q^{23} - 20 q^{25} + 12 q^{26} + 28 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 14 q^{31} + 12 q^{32} + 2 q^{33} - 15 q^{34} - 13 q^{35} - 13 q^{36} - q^{37} + 18 q^{38} - 8 q^{40} + 16 q^{41} + 7 q^{42} - 16 q^{43} + 12 q^{44} + 4 q^{45} + 16 q^{46} - 29 q^{47} - 7 q^{48} + 44 q^{49} - 29 q^{50} + 3 q^{51} + 27 q^{52} + 6 q^{53} + 2 q^{54} - 29 q^{55} - 26 q^{56} - 11 q^{57} + 62 q^{58} - 8 q^{59} + q^{60} + 14 q^{61} + 52 q^{62} - 2 q^{63} + 16 q^{64} - 52 q^{65} - 2 q^{66} + 36 q^{67} + 6 q^{68} + 3 q^{69} - 37 q^{70} - 27 q^{71} - 10 q^{73} - 5 q^{74} + 40 q^{75} - 43 q^{76} + 11 q^{77} - 24 q^{78} - 16 q^{79} - 26 q^{80} - 14 q^{81} - 24 q^{82} + 12 q^{83} - q^{84} + 12 q^{85} - 56 q^{86} + 5 q^{87} + 47 q^{88} - 13 q^{89} + 2 q^{90} + 13 q^{91} - 50 q^{92} + 28 q^{93} - 40 q^{94} - 7 q^{95} - 6 q^{96} + 6 q^{97} - 46 q^{98} - 4 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9 - q^10 + 2 * q^11 - 13 * q^12 - 14 * q^14 - 2 * q^15 + 14 * q^16 + 3 * q^17 - q^18 - 11 * q^19 + q^20 - 2 * q^21 - 2 * q^22 - 6 * q^23 - 20 * q^25 + 12 * q^26 + 28 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 14 * q^31 + 12 * q^32 + 2 * q^33 - 15 * q^34 - 13 * q^35 - 13 * q^36 - q^37 + 18 * q^38 - 8 * q^40 + 16 * q^41 + 7 * q^42 - 16 * q^43 + 12 * q^44 + 4 * q^45 + 16 * q^46 - 29 * q^47 - 7 * q^48 + 44 * q^49 - 29 * q^50 + 3 * q^51 + 27 * q^52 + 6 * q^53 + 2 * q^54 - 29 * q^55 - 26 * q^56 - 11 * q^57 + 62 * q^58 - 8 * q^59 + q^60 + 14 * q^61 + 52 * q^62 - 2 * q^63 + 16 * q^64 - 52 * q^65 - 2 * q^66 + 36 * q^67 + 6 * q^68 + 3 * q^69 - 37 * q^70 - 27 * q^71 - 10 * q^73 - 5 * q^74 + 40 * q^75 - 43 * q^76 + 11 * q^77 - 24 * q^78 - 16 * q^79 - 26 * q^80 - 14 * q^81 - 24 * q^82 + 12 * q^83 - q^84 + 12 * q^85 - 56 * q^86 + 5 * q^87 + 47 * q^88 - 13 * q^89 + 2 * q^90 + 13 * q^91 - 50 * q^92 + 28 * q^93 - 40 * q^94 - 7 * q^95 - 6 * q^96 + 6 * q^97 - 46 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.10791			0.783409			0.391704	−	0.920091i	$-0.371886\pi$
$2$	1.10791			0.783409			0.391704	+	0.920091i	$0.371886\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.772541			−0.386270
$5$	1.74720	+	3.02624i	0.781372	+	1.35338i	0.931143	+	0.364655i	$0.118813\pi$
$5$	1.74720	+	3.02624i	0.781372	+	1.35338i	−0.149771	+	0.988721i	$0.547854\pi$
$6$	−0.553954	−	0.959476i	−0.226151	−	0.391704i
$7$	−4.63545			−1.75204			−0.876018	−	0.482279i	$-0.839809\pi$
$7$	−4.63545			−1.75204			−0.876018	+	0.482279i	$0.839809\pi$
$8$	−3.07172			−1.08602
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.93574	+	3.35280i	0.612134	+	1.06025i
$11$	−0.619790	−	1.07351i	−0.186874	−	0.323675i	0.757333	−	0.653029i	$-0.226502\pi$
$11$	−0.619790	−	1.07351i	−0.186874	−	0.323675i	−0.944206	+	0.329355i	$0.893169\pi$
$12$	0.386270	+	0.669040i	0.111507	+	0.193135i
$13$	−3.04174	+	5.26845i	−0.843628	+	1.46121i	0.0431798	+	0.999067i	$0.486251\pi$
$13$	−3.04174	+	5.26845i	−0.843628	+	1.46121i	−0.886808	+	0.462139i	$0.847082\pi$
$14$	−5.13565			−1.37256
$15$	1.74720	−	3.02624i	0.451125	−	0.781372i
$16$	−1.85810			−0.464525
$17$	1.45597	+	2.52182i	0.353125	+	0.611631i	0.986795	−	0.161973i	$-0.0517857\pi$
$17$	1.45597	+	2.52182i	0.353125	+	0.611631i	−0.633670	+	0.773603i	$0.718452\pi$
$18$	−0.553954	+	0.959476i	−0.130568	+	0.226151i
$19$	−3.53092	−	6.11573i	−0.810048	−	1.40304i	−0.912830	−	0.408341i	$-0.866108\pi$
$19$	−3.53092	−	6.11573i	−0.810048	−	1.40304i	0.102781	−	0.994704i	$-0.467226\pi$
$20$	−1.34978	−	2.33789i	−0.301821	−	0.522769i
$21$	2.31773	+	4.01442i	0.505769	+	0.876018i
$22$	−0.686670	−	1.18935i	−0.146399	−	0.253570i
$23$	3.72787			0.777315			0.388658	−	0.921382i	$-0.372939\pi$
$23$	3.72787			0.777315			0.388658	+	0.921382i	$0.372939\pi$
$24$	1.53586	+	2.66019i	0.313506	+	0.543008i
$25$	−3.60542	+	6.24477i	−0.721084	+	1.24895i
$26$	−3.36997	+	5.83696i	−0.660906	+	1.14472i
$27$	1.00000			0.192450
$28$	3.58108			0.676760
$29$	3.49070			0.648207			0.324104	−	0.946022i	$-0.394937\pi$
$29$	3.49070			0.648207			0.324104	+	0.946022i	$0.394937\pi$
$30$	1.93574	−	3.35280i	0.353416	−	0.612134i
$31$	−2.01285	+	3.48637i	−0.361519	+	0.626170i	−0.988211	−	0.153098i	$-0.951075\pi$
$31$	−2.01285	+	3.48637i	−0.361519	+	0.626170i	0.626692	+	0.779267i	$0.284408\pi$
$32$	4.08484			0.722104
$33$	−0.619790	+	1.07351i	−0.107892	+	0.186874i
$34$	1.61308	+	2.79394i	0.276641	+	0.479157i
$35$	−8.09906	−	14.0280i	−1.36899	−	2.37116i
$36$	0.386270	−	0.669040i	0.0643784	−	0.111507i
$37$	0.339830	−	0.588602i	0.0558676	−	0.0967656i	−0.836739	−	0.547602i	$-0.815541\pi$
$37$	0.339830	−	0.588602i	0.0558676	−	0.0967656i	0.892607	+	0.450836i	$0.148874\pi$
$38$	−3.91193	−	6.77566i	−0.634599	−	1.09916i
$39$	6.08349			0.974137
$40$	−5.36691	−	9.29576i	−0.848583	−	1.46979i
$41$	2.45016			0.382651			0.191326	−	0.981527i	$-0.438721\pi$
$41$	2.45016			0.382651			0.191326	+	0.981527i	$0.438721\pi$
$42$	2.56783	+	4.44760i	0.396224	+	0.686280i
$43$	−2.77096	+	4.79944i	−0.422567	+	0.731908i	−0.996190	−	0.0872117i	$-0.972204\pi$
$43$	−2.77096	+	4.79944i	−0.422567	+	0.731908i	0.573622	+	0.819120i	$0.305538\pi$
$44$	0.478813	+	0.829328i	0.0721838	+	0.125026i
$45$	−3.49440			−0.520915
$46$	4.13014			0.608956
$47$	−4.11718	+	7.13116i	−0.600552	+	1.04019i	0.392186	+	0.919886i	$0.371719\pi$
$47$	−4.11718	+	7.13116i	−0.600552	+	1.04019i	−0.992738	+	0.120300i	$0.961614\pi$
$48$	0.929049	+	1.60916i	0.134097	+	0.232262i
$49$	14.4874			2.06963
$50$	−3.99447	+	6.91863i	−0.564904	+	0.978442i
$51$	1.45597	−	2.52182i	0.203877	−	0.353125i
$52$	2.34987	−	4.07010i	0.325868	−	0.564421i
$53$	−1.58207	+	2.74023i	−0.217314	+	0.376399i	−0.953986	−	0.299851i	$-0.903063\pi$
$53$	−1.58207	+	2.74023i	−0.217314	+	0.376399i	0.736672	+	0.676251i	$0.236396\pi$
$54$	1.10791			0.150767
$55$	2.16579	−	3.75127i	0.292036	−	0.505821i
$56$	14.2388			1.90274
$57$	−3.53092	+	6.11573i	−0.467682	+	0.810048i
$58$	3.86738			0.507811
$59$	−8.51964			−1.10916			−0.554582	−	0.832129i	$-0.687122\pi$
$59$	−8.51964			−1.10916			−0.554582	+	0.832129i	$0.687122\pi$
$60$	−1.34978	+	2.33789i	−0.174256	+	0.301821i
$61$	0.973816	+	1.68670i	0.124684	+	0.215960i	0.921610	−	0.388118i	$-0.126875\pi$
$61$	0.973816	+	1.68670i	0.124684	+	0.215960i	−0.796925	+	0.604078i	$0.793542\pi$
$62$	−2.23006	+	3.86257i	−0.283217	+	0.490547i
$63$	2.31773	−	4.01442i	0.292006	−	0.505769i
$64$	8.24182			1.03023
$65$	−21.2581			−2.63675
$66$	−0.686670	+	1.18935i	−0.0845232	+	0.146399i
$67$	11.1078			1.35703			0.678516	−	0.734586i	$-0.262623\pi$
$67$	11.1078			1.35703			0.678516	+	0.734586i	$0.262623\pi$
$68$	−1.12480	−	1.94821i	−0.136402	−	0.236255i
$69$	−1.86394	−	3.22843i	−0.224392	−	0.388658i
$70$	−8.97301	−	15.5417i	−1.07248	−	1.85759i
$71$	−5.39073	+	9.33702i	−0.639762	+	1.10810i	0.345723	+	0.938337i	$0.387634\pi$
$71$	−5.39073	+	9.33702i	−0.639762	+	1.10810i	−0.985485	+	0.169763i	$0.945700\pi$
$72$	1.53586	−	2.66019i	0.181003	−	0.313506i
$73$	−5.48381	−	9.49823i	−0.641831	−	1.11168i	−0.985024	−	0.172419i	$-0.944842\pi$
$73$	−5.48381	−	9.49823i	−0.641831	−	1.11168i	0.343193	−	0.939265i	$-0.388492\pi$
$74$	0.376500	−	0.652117i	0.0437672	−	0.0758070i
$75$	7.21084			0.832637
$76$	2.72778	+	4.72465i	0.312898	+	0.541955i
$77$	2.87301	+	4.97619i	0.327409	+	0.567090i
$78$	6.73994			0.763148
$79$	5.38180			0.605500			0.302750	−	0.953070i	$-0.402095\pi$
$79$	5.38180			0.605500			0.302750	+	0.953070i	$0.402095\pi$
$80$	−3.24647	−	5.62305i	−0.362967	−	0.628677i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.71456			0.299772
$83$	6.55772	−	11.3583i	0.719803	−	1.24674i	−0.241274	−	0.970457i	$-0.577565\pi$
$83$	6.55772	−	11.3583i	0.719803	−	1.24674i	0.961078	−	0.276279i	$-0.0891013\pi$
$84$	−1.79054	−	3.10130i	−0.195364	−	0.338380i
$85$	−5.08775	+	8.81225i	−0.551844	+	0.955822i
$86$	−3.06997	+	5.31734i	−0.331043	+	0.573383i
$87$	−1.74535	−	3.02304i	−0.187121	−	0.324104i
$88$	1.90382	+	3.29751i	0.202948	+	0.351516i
$89$	−9.26584	−	16.0489i	−0.982177	−	1.70118i	−0.653866	−	0.756610i	$-0.726854\pi$
$89$	−9.26584	−	16.0489i	−0.982177	−	1.70118i	−0.328311	−	0.944570i	$-0.606479\pi$
$90$	−3.87147			−0.408089
$91$	14.0999	−	24.4217i	1.47807	−	2.56009i
$92$	−2.87993			−0.300254
$93$	4.02571			0.417446
$94$	−4.56145	+	7.90067i	−0.470478	+	0.814891i
$95$	12.3384	−	21.3708i	1.26590	−	2.19260i
$96$	−2.04242	−	3.53757i	−0.208453	−	0.361052i
$97$	−3.36409	+	5.82677i	−0.341571	+	0.591618i	−0.984725	−	0.174119i	$-0.944292\pi$
$97$	−3.36409	+	5.82677i	−0.341571	+	0.591618i	0.643154	+	0.765737i	$0.277626\pi$
$98$	16.0507			1.62137
$99$	1.23958			0.124582
$100$	2.78534	−	4.82434i	0.278534	−	0.482434i
$101$	0.664623			0.0661325			0.0330662	−	0.999453i	$-0.489473\pi$
$101$	0.664623			0.0661325			0.0330662	+	0.999453i	$0.489473\pi$
$102$	1.61308	−	2.79394i	0.159719	−	0.276641i
$103$	2.15404			0.212244			0.106122	−	0.994353i	$-0.466157\pi$
$103$	2.15404			0.212244			0.106122	+	0.994353i	$0.466157\pi$
$104$	9.34338	−	16.1832i	0.916194	−	1.58689i
$105$	−8.09906	+	14.0280i	−0.790388	+	1.36899i
$106$	−1.75279	+	3.03592i	−0.170246	+	0.294875i
$107$	−5.91937	+	10.2526i	−0.572247	+	0.991161i	0.424088	+	0.905621i	$0.360595\pi$
$107$	−5.91937	+	10.2526i	−0.572247	+	0.991161i	−0.996335	+	0.0855395i	$0.972739\pi$
$108$	−0.772541			−0.0743378
$109$	−6.71133	−	11.6244i	−0.642829	−	1.11341i	−0.984798	−	0.173702i	$-0.944427\pi$
$109$	−6.71133	−	11.6244i	−0.642829	−	1.11341i	0.341969	−	0.939711i	$-0.388906\pi$
$110$	2.39950	−	4.15606i	0.228783	−	0.396264i
$111$	−0.679659			−0.0645104
$112$	8.61313			0.813864
$113$	5.89365	+	10.2081i	0.554428	+	0.960297i	0.997948	+	0.0640327i	$0.0203962\pi$
$113$	5.89365	+	10.2081i	0.554428	+	0.960297i	−0.443520	+	0.896264i	$0.646270\pi$
$114$	−3.91193	+	6.77566i	−0.366386	+	0.634599i
$115$	6.51334	+	11.2814i	0.607373	+	1.05200i
$116$	−2.69671			−0.250383
$117$	−3.04174	−	5.26845i	−0.281209	−	0.487069i
$118$	−9.43898			−0.868928
$119$	−6.74909	−	11.6898i	−0.618688	−	1.07160i
$120$	−5.36691	+	9.29576i	−0.489930	+	0.848583i
$121$	4.73172	−	8.19558i	0.430156	−	0.745053i
$122$	1.07890	+	1.86871i	0.0976789	+	0.169185i
$123$	−1.22508	−	2.12190i	−0.110462	−	0.191326i
$124$	1.55501	−	2.69336i	0.139644	−	0.241871i
$125$	−7.72558			−0.690997
$126$	2.56783	−	4.44760i	0.228760	−	0.396224i
$127$	−6.99240	+	12.1112i	−0.620475	+	1.07469i	0.368923	+	0.929460i	$0.379727\pi$
$127$	−6.99240	+	12.1112i	−0.620475	+	1.07469i	−0.989397	+	0.145234i	$0.953607\pi$
$128$	0.961501			0.0849855
$129$	5.54192			0.487939
$130$	−23.5521			−2.06565
$131$	−9.88957	+	17.1292i	−0.864055	+	1.49659i	0.00392656	+	0.999992i	$0.498750\pi$
$131$	−9.88957	+	17.1292i	−0.864055	+	1.49659i	−0.867982	+	0.496596i	$0.834583\pi$
$132$	0.478813	−	0.829328i	0.0416753	−	0.0721838i
$133$	16.3674	+	28.3492i	1.41923	+	2.45818i
$134$	12.3064			1.06311
$135$	1.74720	+	3.02624i	0.150375	+	0.260457i
$136$	−4.47234	−	7.74632i	−0.383500	−	0.664241i
$137$	1.58106	+	2.73847i	0.135079	+	0.233963i	0.925628	−	0.378436i	$-0.123538\pi$
$137$	1.58106	+	2.73847i	0.135079	+	0.233963i	−0.790549	+	0.612399i	$0.790205\pi$
$138$	−2.06507	−	3.57681i	−0.175790	−	0.304478i
$139$	−8.15338	+	14.1221i	−0.691560	+	1.19782i	0.279766	+	0.960068i	$0.409743\pi$
$139$	−8.15338	+	14.1221i	−0.691560	+	1.19782i	−0.971326	+	0.237750i	$0.923590\pi$
$140$	6.25686	+	10.8372i	0.528801	+	0.915910i
$141$	8.23435			0.693458
$142$	−5.97243	+	10.3446i	−0.501195	+	0.868095i
$143$	7.54097			0.630607
$144$	0.929049	−	1.60916i	0.0774208	−	0.134097i
$145$	6.09896	+	10.5637i	0.506491	+	0.877268i
$146$	−6.07555	−	10.5232i	−0.502816	−	0.870903i
$147$	−7.24370	−	12.5465i	−0.597451	−	1.03481i
$148$	−0.262532	+	0.454719i	−0.0215800	+	0.0373777i
$149$	−1.19055			−0.0975336			−0.0487668	−	0.998810i	$-0.515529\pi$
$149$	−1.19055			−0.0975336			−0.0487668	+	0.998810i	$0.515529\pi$
$150$	7.98895			0.652295
$151$	4.29812	+	7.44457i	0.349776	+	0.605830i	0.986210	−	0.165502i	$-0.0529243\pi$
$151$	4.29812	+	7.44457i	0.349776	+	0.605830i	−0.636433	+	0.771332i	$0.719591\pi$
$152$	10.8460	+	18.7858i	0.879726	+	1.52373i
$153$	−2.91194			−0.235417
$154$	3.18302	+	5.51316i	0.256495	+	0.444263i
$155$	−14.0674			−1.12992
$156$	−4.69974			−0.376280
$157$	−12.4701	−	1.22310i	−0.995224	−	0.0976143i
$157$	−12.4701	−	1.22310i	−0.995224	−	0.0976143i
$158$	5.96254			0.474354
$159$	3.16414			0.250933
$160$	7.13703	+	12.3617i	0.564232	+	0.977278i
$161$	−17.2804			−1.36188
$162$	−0.553954	−	0.959476i	−0.0435227	−	0.0753836i
$163$	9.42288	+	16.3209i	0.738057	+	1.27835i	0.953369	+	0.301806i	$0.0975896\pi$
$163$	9.42288	+	16.3209i	0.738057	+	1.27835i	−0.215313	+	0.976545i	$0.569077\pi$
$164$	−1.89285			−0.147807
$165$	−4.33159			−0.337214
$166$	7.26535	−	12.5840i	0.563900	−	0.976704i
$167$	−1.34373	−	2.32742i	−0.103981	−	0.180101i	0.809340	−	0.587340i	$-0.199825\pi$
$167$	−1.34373	−	2.32742i	−0.103981	−	0.180101i	−0.913322	+	0.407239i	$0.866492\pi$
$168$	−7.11940	−	12.3312i	−0.549274	−	0.951370i
$169$	−12.0044	−	20.7922i	−0.923416	−	1.59940i
$170$	−5.63676	+	9.76315i	−0.432320	+	0.748800i
$171$	7.06184			0.540032
$172$	2.14068	−	3.70777i	0.163225	−	0.282714i
$173$	11.6117			0.882822			0.441411	−	0.897305i	$-0.354478\pi$
$173$	11.6117			0.882822			0.441411	+	0.897305i	$0.354478\pi$
$174$	−1.93369	−	3.34925i	−0.146592	−	0.253906i
$175$	16.7128	−	28.9473i	1.26337	−	2.18821i
$176$	1.15163	+	1.99468i	0.0868074	+	0.150355i
$177$	4.25982	+	7.37823i	0.320188	+	0.554582i
$178$	−10.2657	−	17.7807i	−0.769446	−	1.33272i
$179$	2.78619	+	4.82582i	0.208249	+	0.360698i	0.951163	−	0.308689i	$-0.0998901\pi$
$179$	2.78619	+	4.82582i	0.208249	+	0.360698i	−0.742914	+	0.669387i	$0.766557\pi$
$180$	2.69957			0.201214
$181$	11.1490	+	19.3106i	0.828698	+	1.43535i	0.899060	+	0.437825i	$0.144251\pi$
$181$	11.1490	+	19.3106i	0.828698	+	1.43535i	−0.0703624	+	0.997521i	$0.522416\pi$
$182$	15.6213	−	27.0569i	1.15793	−	2.00559i
$183$	0.973816	−	1.68670i	0.0719866	−	0.124684i
$184$	−11.4510			−0.844178
$185$	2.37500			0.174614
$186$	4.46011			0.327031
$187$	1.80479	−	3.12599i	0.131980	−	0.228595i
$188$	3.18069	−	5.50911i	0.231975	−	0.401793i
$189$	−4.63545			−0.337179
$190$	13.6699	−	23.6769i	0.991716	−	1.71770i
$191$	0.935068	+	1.61959i	0.0676591	+	0.117189i	0.897870	−	0.440260i	$-0.145114\pi$
$191$	0.935068	+	1.61959i	0.0676591	+	0.117189i	−0.830211	+	0.557449i	$0.811780\pi$
$192$	−4.12091	−	7.13762i	−0.297401	−	0.515114i
$193$	1.57969	−	2.73611i	0.113709	−	0.196949i	−0.803554	−	0.595232i	$-0.797060\pi$
$193$	1.57969	−	2.73611i	0.113709	−	0.196949i	0.917263	+	0.398282i	$0.130394\pi$
$194$	−3.72710	+	6.45552i	−0.267590	+	0.463479i
$195$	10.6291	+	18.4101i	0.761164	+	1.31837i
$196$	−11.1921			−0.799437
$197$	5.99481	+	10.3833i	0.427112	+	0.739780i	0.996615	−	0.0822091i	$-0.0261975\pi$
$197$	5.99481	+	10.3833i	0.427112	+	0.739780i	−0.569503	+	0.821989i	$0.692864\pi$
$198$	1.37334			0.0975990
$199$	−2.78128	−	4.81732i	−0.197160	−	0.341491i	0.750447	−	0.660931i	$-0.229838\pi$
$199$	−2.78128	−	4.81732i	−0.197160	−	0.341491i	−0.947606	+	0.319440i	$0.896505\pi$
$200$	11.0748	−	19.1822i	0.783110	−	1.35639i
$201$	−5.55389	−	9.61962i	−0.391741	−	0.678516i
$202$	0.736341			0.0518088
$203$	−16.1810			−1.13568
$204$	−1.12480	+	1.94821i	−0.0787516	+	0.136402i
$205$	4.28093	+	7.41479i	0.298993	+	0.517871i
$206$	2.38648			0.166274
$207$	−1.86394	+	3.22843i	−0.129553	+	0.224392i
$208$	5.65186	−	9.78931i	0.391886	−	0.678766i
$209$	−4.37686	+	7.58094i	−0.302753	+	0.524384i
$210$	−8.97301	+	15.5417i	−0.619197	+	1.07248i
$211$	−1.98176			−0.136430			−0.0682150	−	0.997671i	$-0.521730\pi$
$211$	−1.98176			−0.136430			−0.0682150	+	0.997671i	$0.521730\pi$
$212$	1.22222	−	2.11694i	0.0839421	−	0.145392i
$213$	10.7815			0.738733
$214$	−6.55811	+	11.3590i	−0.448303	+	0.776484i
$215$	−19.3657			−1.32073
$216$	−3.07172			−0.209004
$217$	9.33049	−	16.1609i	0.633395	−	1.09707i
$218$	−7.43554	−	12.8787i	−0.503598	−	0.872258i
$219$	−5.48381	+	9.49823i	−0.370561	+	0.641831i
$220$	−1.67317	+	2.89801i	−0.112805	+	0.195384i
$221$	−17.7148			−1.19162
$222$	−0.753000			−0.0505380
$223$	−8.83158	+	15.2967i	−0.591406	+	1.02435i	0.402637	+	0.915360i	$0.368094\pi$
$223$	−8.83158	+	15.2967i	−0.591406	+	1.02435i	−0.994043	+	0.108986i	$0.965240\pi$
$224$	−18.9351			−1.26515
$225$	−3.60542	−	6.24477i	−0.240361	−	0.416318i
$226$	6.52962	+	11.3096i	0.434344	+	0.752305i
$227$	−11.7878	−	20.4170i	−0.782381	−	1.35512i	−0.930551	−	0.366162i	$-0.880671\pi$
$227$	−11.7878	−	20.4170i	−0.782381	−	1.35512i	0.148170	−	0.988962i	$-0.452662\pi$
$228$	2.72778	−	4.72465i	0.180652	−	0.312898i
$229$	−0.647264	+	1.12109i	−0.0427724	+	0.0740840i	−0.886619	−	0.462500i	$-0.846952\pi$
$229$	−0.647264	+	1.12109i	−0.0427724	+	0.0740840i	0.843847	+	0.536584i	$0.180286\pi$
$230$	7.21618	+	12.4988i	0.475821	+	0.824146i
$231$	2.87301	−	4.97619i	0.189030	−	0.327409i
$232$	−10.7225			−0.703964
$233$	4.06216	+	7.03586i	0.266121	+	0.460935i	0.967857	−	0.251503i	$-0.0809247\pi$
$233$	4.06216	+	7.03586i	0.266121	+	0.460935i	−0.701736	+	0.712437i	$0.747591\pi$
$234$	−3.36997	−	5.83696i	−0.220302	−	0.381574i
$235$	−28.7741			−1.87702
$236$	6.58177			0.428437
$237$	−2.69090	−	4.66077i	−0.174793	−	0.302750i
$238$	−7.47737	−	12.9512i	−0.484686	−	0.839500i
$239$	−6.84613			−0.442840			−0.221420	−	0.975179i	$-0.571069\pi$
$239$	−6.84613			−0.442840			−0.221420	+	0.975179i	$0.571069\pi$
$240$	−3.24647	+	5.62305i	−0.209559	+	0.362967i
$241$	1.82353	+	3.15845i	0.117464	+	0.203454i	0.918762	−	0.394812i	$-0.129190\pi$
$241$	1.82353	+	3.15845i	0.117464	+	0.203454i	−0.801298	+	0.598265i	$0.795857\pi$
$242$	5.24231	−	9.07995i	0.336988	−	0.583681i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−0.752313	−	1.30304i	−0.0481619	−	0.0834188i
$245$	25.3124	+	43.8424i	1.61715	+	2.80099i
$246$	−1.35728	−	2.35087i	−0.0865369	−	0.149886i
$247$	42.9606			2.73352
$248$	6.18292	−	10.7091i	0.392616	−	0.680031i
$249$	−13.1154			−0.831157
$250$	−8.55923			−0.541333
$251$	3.06641	−	5.31118i	0.193550	−	0.335239i	−0.752874	−	0.658165i	$-0.771333\pi$
$251$	3.06641	−	5.31118i	0.193550	−	0.335239i	0.946424	+	0.322926i	$0.104666\pi$
$252$	−1.79054	+	3.10130i	−0.112793	+	0.195364i
$253$	−2.31050	−	4.00190i	−0.145260	−	0.251597i
$254$	−7.74693	+	13.4181i	−0.486086	+	0.841925i
$255$	10.1755			0.637215
$256$	−15.4184			−0.963649
$257$	3.95298	−	6.84675i	0.246580	−	0.427089i	−0.715995	−	0.698106i	$-0.754027\pi$
$257$	3.95298	−	6.84675i	0.246580	−	0.427089i	0.962575	+	0.271017i	$0.0873599\pi$
$258$	6.13993			0.382256
$259$	−1.57526	+	2.72844i	−0.0978821	+	0.169537i
$260$	16.4228			1.01850
$261$	−1.74535	+	3.02304i	−0.108035	+	0.187121i
$262$	−10.9567	+	18.9776i	−0.676909	+	1.17244i
$263$	14.4242	−	24.9834i	0.889434	−	1.54054i	0.0488884	−	0.998804i	$-0.484432\pi$
$263$	14.4242	−	24.9834i	0.889434	−	1.54054i	0.840546	−	0.541741i	$-0.182235\pi$
$264$	1.90382	−	3.29751i	0.117172	−	0.202948i
$265$	−11.0568			−0.679213
$266$	18.1336	+	31.4083i	1.11184	+	1.92576i
$267$	−9.26584	+	16.0489i	−0.567060	+	0.982177i
$268$	−8.58122			−0.524181
$269$	9.78559			0.596638			0.298319	−	0.954466i	$-0.403574\pi$
$269$	9.78559			0.596638			0.298319	+	0.954466i	$0.403574\pi$
$270$	1.93574	+	3.35280i	0.117805	+	0.204045i
$271$	−4.91567	+	8.51418i	−0.298605	+	0.517200i	−0.975817	−	0.218588i	$-0.929855\pi$
$271$	−4.91567	+	8.51418i	−0.298605	+	0.517200i	0.677212	+	0.735788i	$0.263188\pi$
$272$	−2.70534	−	4.68579i	−0.164035	−	0.284118i
$273$	−28.1997			−1.70672
$274$	1.75166	+	3.03397i	0.105822	+	0.183289i
$275$	8.93842			0.539007
$276$	1.43997	+	2.49410i	0.0866759	+	0.150127i
$277$	15.5173	−	26.8768i	0.932347	−	1.61487i	0.153048	−	0.988219i	$-0.451091\pi$
$277$	15.5173	−	26.8768i	0.932347	−	1.61487i	0.779298	−	0.626653i	$-0.215576\pi$
$278$	−9.03319	+	15.6459i	−0.541775	+	0.938381i
$279$	−2.01285	−	3.48637i	−0.120506	−	0.208723i
$280$	24.8780	+	43.0900i	1.48675	+	2.57512i
$281$	−10.9497	+	18.9655i	−0.653206	+	1.13139i	0.329134	+	0.944283i	$0.393243\pi$
$281$	−10.9497	+	18.9655i	−0.653206	+	1.13139i	−0.982340	+	0.187103i	$0.940090\pi$
$282$	9.12290			0.543261
$283$	−8.76838	+	15.1873i	−0.521226	+	0.902790i	0.478469	+	0.878104i	$0.341192\pi$
$283$	−8.76838	+	15.1873i	−0.521226	+	0.902790i	−0.999695	+	0.0246857i	$0.992141\pi$
$284$	4.16456	−	7.21323i	0.247121	−	0.428026i
$285$	−24.6769			−1.46173
$286$	8.35469			0.494023
$287$	−11.3576			−0.670419
$288$	−2.04242	+	3.53757i	−0.120351	+	0.208453i
$289$	4.26029	−	7.37904i	0.250605	−	0.434061i
$290$	6.75708	+	11.7036i	0.396789	+	0.687260i
$291$	6.72817			0.394412
$292$	4.23646	+	7.33777i	0.247920	+	0.429411i
$293$	−6.05828	−	10.4932i	−0.353928	−	0.613022i	0.633006	−	0.774147i	$-0.281821\pi$
$293$	−6.05828	−	10.4932i	−0.353928	−	0.613022i	−0.986934	+	0.161125i	$0.948488\pi$
$294$	−8.02535	−	13.9003i	−0.468048	−	0.810683i
$295$	−14.8855	−	25.7825i	−0.866669	−	1.50111i
$296$	−1.04386	+	1.80802i	−0.0606732	+	0.105089i
$297$	−0.619790	−	1.07351i	−0.0359639	−	0.0622912i
$298$	−1.31902			−0.0764087
$299$	−11.3392	+	19.6401i	−0.655765	+	1.13582i
$300$	−5.57067			−0.321623
$301$	12.8446	−	22.2476i	0.740353	−	1.28233i
$302$	4.76192	+	8.24789i	0.274018	+	0.474613i
$303$	−0.332312	−	0.575580i	−0.0190908	−	0.0330662i
$304$	6.56080	+	11.3636i	0.376287	+	0.651749i
$305$	−3.40290	+	5.89400i	−0.194850	+	0.337490i
$306$	−3.22617			−0.184428
$307$	26.4016			1.50682			0.753409	−	0.657552i	$-0.228408\pi$
$307$	26.4016			1.50682			0.753409	+	0.657552i	$0.228408\pi$
$308$	−2.21951	−	3.84431i	−0.126469	−	0.219050i
$309$	−1.07702	−	1.86545i	−0.0612695	−	0.106122i
$310$	−15.5854			−0.885193
$311$	0.185200	+	0.320776i	0.0105017	+	0.0181895i	0.871229	−	0.490878i	$-0.163324\pi$
$311$	0.185200	+	0.320776i	0.0105017	+	0.0181895i	−0.860727	+	0.509067i	$0.829990\pi$
$312$	−18.6868			−1.05793
$313$	−8.32195			−0.470385			−0.235192	−	0.971949i	$-0.575572\pi$
$313$	−8.32195			−0.470385			−0.235192	+	0.971949i	$0.575572\pi$
$314$	−13.8157	−	1.35509i	−0.779668	−	0.0764719i
$315$	16.1981			0.912661
$316$	−4.15766			−0.233887
$317$	12.2447	+	21.2084i	0.687729	+	1.19118i	0.972571	+	0.232606i	$0.0747254\pi$
$317$	12.2447	+	21.2084i	0.687729	+	1.19118i	−0.284842	+	0.958574i	$0.591941\pi$
$318$	3.50558			0.196583
$319$	−2.16350	−	3.74730i	−0.121133	−	0.209808i
$320$	14.4001	+	24.9417i	0.804991	+	1.39428i
$321$	11.8387			0.660774
$322$	−19.1451			−1.06691
$323$	10.2818	−	17.8087i	0.572097	−	0.990901i
$324$	0.386270	+	0.669040i	0.0214595	+	0.0371689i
$325$	−21.9335	−	37.9900i	−1.21665	−	2.10731i
$326$	10.4397	+	18.0820i	0.578200	+	1.00147i
$327$	−6.71133	+	11.6244i	−0.371138	+	0.642829i
$328$	−7.52622			−0.415566
$329$	19.0850	−	33.0561i	1.05219	−	1.82244i
$330$	−4.79900			−0.264176
$331$	4.44442	+	7.69796i	0.244287	+	0.423118i	0.961931	−	0.273292i	$-0.0881126\pi$
$331$	4.44442	+	7.69796i	0.244287	+	0.423118i	−0.717644	+	0.696411i	$0.754779\pi$
$332$	−5.06611	+	8.77475i	−0.278039	+	0.481577i
$333$	0.339830	+	0.588602i	0.0186225	+	0.0322552i
$334$	−1.48873	−	2.57856i	−0.0814599	−	0.141093i
$335$	19.4075	+	33.6148i	1.06035	+	1.83657i
$336$	−4.30656	−	7.45919i	−0.234942	−	0.406932i
$337$	6.89715			0.375712			0.187856	−	0.982197i	$-0.439846\pi$
$337$	6.89715			0.375712			0.187856	+	0.982197i	$0.439846\pi$
$338$	−13.2998	−	23.0359i	−0.723412	−	1.25299i
$339$	5.89365	−	10.2081i	0.320099	−	0.554428i
$340$	3.93050	−	6.80782i	0.213161	−	0.369206i
$341$	4.99019			0.270234
$342$	7.82386			0.423066
$343$	−34.7075			−1.87403
$344$	8.51161	−	14.7425i	0.458915	−	0.794864i
$345$	6.51334	−	11.2814i	0.350667	−	0.607373i
$346$	12.8647			0.691611
$347$	13.1364	−	22.7529i	0.705198	−	1.22144i	−0.261423	−	0.965224i	$-0.584192\pi$
$347$	13.1364	−	22.7529i	0.705198	−	1.22144i	0.966620	−	0.256214i	$-0.0824750\pi$
$348$	1.34835	+	2.33542i	0.0722794	+	0.125192i
$349$	−14.9262	−	25.8529i	−0.798981	−	1.38388i	−0.920280	−	0.391260i	$-0.872039\pi$
$349$	−14.9262	−	25.8529i	−0.798981	−	1.38388i	0.121299	−	0.992616i	$-0.461294\pi$
$350$	18.5162	−	32.0710i	0.989732	−	1.71427i
$351$	−3.04174	+	5.26845i	−0.162356	+	0.281209i
$352$	−2.53174	−	4.38510i	−0.134942	−	0.233727i
$353$	−6.15846			−0.327782			−0.163891	−	0.986478i	$-0.552404\pi$
$353$	−6.15846			−0.327782			−0.163891	+	0.986478i	$0.552404\pi$
$354$	4.71949	+	8.17440i	0.250838	+	0.434464i
$355$	−37.6747			−1.99957
$356$	7.15824	+	12.3984i	0.379386	+	0.657116i
$357$	−6.74909	+	11.6898i	−0.357200	+	0.618688i
$358$	3.08684	+	5.34656i	0.163144	+	0.282574i
$359$	16.7642			0.884783			0.442391	−	0.896822i	$-0.354130\pi$
$359$	16.7642			0.884783			0.442391	+	0.896822i	$0.354130\pi$
$360$	10.7338			0.565722
$361$	−15.4348	+	26.7338i	−0.812356	+	1.40704i
$362$	12.3520	+	21.3944i	0.649209	+	1.12446i
$363$	−9.46344			−0.496702
$364$	−10.8927	+	18.8667i	−0.570933	+	0.988885i
$365$	19.1626	−	33.1906i	1.00302	−	1.73728i
$366$	1.07890	−	1.86871i	0.0563949	−	0.0976789i
$367$	−9.85973	+	17.0776i	−0.514674	+	0.891441i	0.485181	+	0.874414i	$0.338754\pi$
$367$	−9.85973	+	17.0776i	−0.514674	+	0.891441i	−0.999855	+	0.0170274i	$0.994580\pi$
$368$	−6.92676			−0.361082
$369$	−1.22508	+	2.12190i	−0.0637752	+	0.110462i
$370$	2.63128			0.136794
$371$	7.33362	−	12.7022i	0.380742	−	0.659465i
$372$	−3.11002			−0.161247
$373$	2.73260			0.141489			0.0707444	−	0.997494i	$-0.477463\pi$
$373$	2.73260			0.141489			0.0707444	+	0.997494i	$0.477463\pi$
$374$	1.99954	−	3.46331i	0.103394	−	0.179084i
$375$	3.86279	+	6.69055i	0.199474	+	0.345498i
$376$	12.6468	−	21.9049i	0.652209	−	1.12966i
$377$	−10.6178	+	18.3906i	−0.546846	+	0.947164i
$378$	−5.13565			−0.264149
$379$	22.1498			1.13776			0.568879	−	0.822421i	$-0.307377\pi$
$379$	22.1498			1.13776			0.568879	+	0.822421i	$0.307377\pi$
$380$	−9.53196	+	16.5098i	−0.488979	+	0.846936i
$381$	13.9848			0.716463
$382$	1.03597	+	1.79435i	0.0530048	+	0.0918070i
$383$	−6.44052	−	11.1553i	−0.329095	−	0.570010i	0.653237	−	0.757153i	$-0.273410\pi$
$383$	−6.44052	−	11.1553i	−0.329095	−	0.570010i	−0.982333	+	0.187144i	$0.940077\pi$
$384$	−0.480751	−	0.832684i	−0.0245332	−	0.0424927i
$385$	−10.0394	+	17.3888i	−0.511657	+	0.886216i
$386$	1.75015	−	3.03135i	0.0890805	−	0.154292i
$387$	−2.77096	−	4.79944i	−0.140856	−	0.243969i
$388$	2.59889	−	4.50141i	0.131939	−	0.228525i
$389$	−8.95238			−0.453903			−0.226952	−	0.973906i	$-0.572876\pi$
$389$	−8.95238			−0.453903			−0.226952	+	0.973906i	$0.572876\pi$
$390$	11.7760	+	20.3967i	0.596302	+	1.03283i
$391$	5.42768	+	9.40102i	0.274490	+	0.475430i
$392$	−44.5012			−2.24765
$393$	19.7791			0.997725
$394$	6.64169	+	11.5037i	0.334604	+	0.579551i
$395$	9.40308	+	16.2866i	0.473120	+	0.819469i
$396$	−0.957626			−0.0481225
$397$	−6.14914	+	10.6506i	−0.308617	+	0.534540i	−0.978060	−	0.208323i	$-0.933199\pi$
$397$	−6.14914	+	10.6506i	−0.308617	+	0.534540i	0.669443	+	0.742863i	$0.266533\pi$
$398$	−3.08140	−	5.33715i	−0.154457	−	0.267527i
$399$	16.3674	−	28.3492i	0.819395	−	1.41923i
$400$	6.69923	−	11.6034i	0.334962	−	0.580170i
$401$	−10.9948	−	19.0436i	−0.549056	−	0.950993i	−0.998340	−	0.0576038i	$-0.981654\pi$
$401$	−10.9948	−	19.0436i	−0.549056	−	0.950993i	0.449283	−	0.893389i	$-0.351679\pi$
$402$	−6.15320	−	10.6577i	−0.306894	−	0.531555i
$403$	−12.2452	−	21.2093i	−0.609975	−	1.05651i
$404$	−0.513448			−0.0255450
$405$	1.74720	−	3.02624i	0.0868191	−	0.150375i
$406$	−17.9270			−0.889703
$407$	−0.842492			−0.0417608
$408$	−4.47234	+	7.74632i	−0.221414	+	0.383500i
$409$	7.88633	−	13.6595i	0.389954	−	0.675420i	−0.602489	−	0.798127i	$-0.705824\pi$
$409$	7.88633	−	13.6595i	0.389954	−	0.675420i	0.992443	+	0.122707i	$0.0391576\pi$
$410$	4.74287	+	8.21490i	0.234234	+	0.405705i
$411$	1.58106	−	2.73847i	0.0779877	−	0.135079i
$412$	−1.66408			−0.0819835
$413$	39.4924			1.94329
$414$	−2.06507	+	3.57681i	−0.101493	+	0.175790i
$415$	45.8306			2.24974
$416$	−12.4250	+	21.5208i	−0.609187	+	1.05514i
$417$	16.3068			0.798545
$418$	−4.84915	+	8.39898i	−0.237180	+	0.410807i
$419$	8.27796	−	14.3379i	0.404405	−	0.700450i	−0.589847	−	0.807515i	$-0.700812\pi$
$419$	8.27796	−	14.3379i	0.404405	−	0.700450i	0.994252	+	0.107065i	$0.0341453\pi$
$420$	6.25686	−	10.8372i	0.305303	−	0.528801i
$421$	−9.28534	+	16.0827i	−0.452540	+	0.783822i	−0.998543	−	0.0539611i	$-0.982815\pi$
$421$	−9.28534	+	16.0827i	−0.452540	+	0.783822i	0.546003	+	0.837783i	$0.316149\pi$
$422$	−2.19561			−0.106880
$423$	−4.11718	−	7.13116i	−0.200184	−	0.346729i
$424$	4.85968	−	8.41721i	0.236007	−	0.408776i
$425$	−20.9976			−1.01853
$426$	11.9449			0.578730
$427$	−4.51408	−	7.81861i	−0.218451	−	0.378369i
$428$	4.57295	−	7.92059i	0.221042	−	0.382856i
$429$	−3.77048	−	6.53067i	−0.182041	−	0.315304i
$430$	−21.4554			−1.03467
$431$	−15.4072	−	26.6860i	−0.742137	−	1.28542i	−0.951521	−	0.307585i	$-0.900479\pi$
$431$	−15.4072	−	26.6860i	−0.742137	−	1.28542i	0.209384	−	0.977833i	$-0.432854\pi$
$432$	−1.85810			−0.0893978
$433$	15.2594	+	26.4300i	0.733319	+	1.27015i	0.955457	+	0.295131i	$0.0953633\pi$
$433$	15.2594	+	26.4300i	0.733319	+	1.27015i	−0.222137	+	0.975015i	$0.571303\pi$
$434$	10.3373	−	17.9048i	0.496207	−	0.859456i
$435$	6.09896	−	10.5637i	0.292423	−	0.506491i
$436$	5.18478	+	8.98030i	0.248306	+	0.430078i
$437$	−13.1628	−	22.7987i	−0.629663	−	1.09061i
$438$	−6.07555	+	10.5232i	−0.290301	+	0.502816i
$439$	−34.9448			−1.66783			−0.833913	−	0.551896i	$-0.813904\pi$
$439$	−34.9448			−1.66783			−0.833913	+	0.551896i	$0.813904\pi$
$440$	−6.65271	+	11.5228i	−0.317156	+	0.549330i
$441$	−7.24370	+	12.5465i	−0.344938	+	0.597451i
$442$	−19.6263			−0.933529
$443$	−31.6116			−1.50191			−0.750955	−	0.660353i	$-0.770407\pi$
$443$	−31.6116			−1.50191			−0.750955	+	0.660353i	$0.770407\pi$
$444$	0.525064			0.0249185
$445$	32.3786	−	56.0813i	1.53489	−	2.65851i
$446$	−9.78457	+	16.9474i	−0.463313	+	0.802482i
$447$	0.595275	+	1.03105i	0.0281555	+	0.0487668i
$448$	−38.2045			−1.80500
$449$	−10.7060	−	18.5433i	−0.505246	−	0.875111i	−0.999982	−	0.00606767i	$-0.998069\pi$
$449$	−10.7060	−	18.5433i	−0.505246	−	0.875111i	0.494736	−	0.869043i	$-0.335265\pi$
$450$	−3.99447	−	6.91863i	−0.188301	−	0.326147i
$451$	−1.51859	−	2.63027i	−0.0715075	−	0.123855i
$452$	−4.55308	−	7.88617i	−0.214159	−	0.370934i
$453$	4.29812	−	7.44457i	0.201943	−	0.349776i
$454$	−13.0598	−	22.6202i	−0.612925	−	1.06162i
$455$	98.5411			4.61968
$456$	10.8460	−	18.7858i	0.507910	−	0.879726i
$457$	−20.6736			−0.967072			−0.483536	−	0.875324i	$-0.660648\pi$
$457$	−20.6736			−0.967072			−0.483536	+	0.875324i	$0.660648\pi$
$458$	−0.717109	+	1.24207i	−0.0335083	+	0.0580381i
$459$	1.45597	+	2.52182i	0.0679590	+	0.117708i
$460$	−5.03183	−	8.71538i	−0.234610	−	0.406357i
$461$	20.8494	+	36.1123i	0.971055	+	1.68192i	0.692382	+	0.721531i	$0.256561\pi$
$461$	20.8494	+	36.1123i	0.971055	+	1.68192i	0.278673	+	0.960386i	$0.410105\pi$
$462$	3.18302	−	5.51316i	0.148088	−	0.256495i
$463$	36.7321			1.70709			0.853543	−	0.521023i	$-0.174449\pi$
$463$	36.7321			1.70709			0.853543	+	0.521023i	$0.174449\pi$
$464$	−6.48607			−0.301108
$465$	7.03372	+	12.1828i	0.326181	+	0.564962i
$466$	4.50049	+	7.79508i	0.208481	+	0.361100i
$467$	22.3591			1.03465			0.517327	−	0.855788i	$-0.326927\pi$
$467$	22.3591			1.03465			0.517327	+	0.855788i	$0.326927\pi$
$468$	2.34987	+	4.07010i	0.108623	+	0.188140i
$469$	−51.4896			−2.37757
$470$	−31.8791			−1.47047
$471$	5.17582	+	11.4110i	0.238489	+	0.525791i
$472$	26.1700			1.20457
$473$	6.86965			0.315867
$474$	−2.98127	−	5.16371i	−0.136934	−	0.237177i
$475$	50.9218			2.33645
$476$	5.21395	+	9.03082i	0.238981	+	0.413927i
$477$	−1.58207	−	2.74023i	−0.0724381	−	0.125466i
$478$	−7.58488			−0.346925
$479$	−11.9253			−0.544880			−0.272440	−	0.962173i	$-0.587831\pi$
$479$	−11.9253			−0.544880			−0.272440	+	0.962173i	$0.587831\pi$
$480$	7.13703	−	12.3617i	0.325759	−	0.564232i
$481$	2.06735	+	3.58075i	0.0942630	+	0.163268i
$482$	2.02031	+	3.49927i	0.0920224	+	0.159387i
$483$	8.64019	+	14.9652i	0.393142	+	0.680942i
$484$	−3.65545	+	6.33142i	−0.166157	+	0.287792i
$485$	−23.5109			−1.06758
$486$	−0.553954	+	0.959476i	−0.0251279	+	0.0435227i
$487$	35.7139			1.61835			0.809175	−	0.587567i	$-0.199914\pi$
$487$	35.7139			1.61835			0.809175	+	0.587567i	$0.199914\pi$
$488$	−2.99129	−	5.18107i	−0.135409	−	0.234536i
$489$	9.42288	−	16.3209i	0.426117	−	0.738057i
$490$	28.0438	+	48.5733i	1.26689	+	2.19432i
$491$	2.19233	+	3.79723i	0.0989385	+	0.171367i	0.911246	−	0.411863i	$-0.135122\pi$
$491$	2.19233	+	3.79723i	0.0989385	+	0.171367i	−0.812307	+	0.583230i	$0.801789\pi$
$492$	0.946426	+	1.63926i	0.0426682	+	0.0739034i
$493$	5.08237	+	8.80291i	0.228898	+	0.396463i
$494$	47.5964			2.14146
$495$	2.16579	+	3.75127i	0.0973452	+	0.168607i
$496$	3.74008	−	6.47801i	0.167935	−	0.290871i
$497$	24.9885	−	43.2813i	1.12089	−	1.94143i
$498$	−14.5307			−0.651136
$499$	15.4652			0.692319			0.346159	−	0.938176i	$-0.387486\pi$
$499$	15.4652			0.692319			0.346159	+	0.938176i	$0.387486\pi$
$500$	5.96833			0.266912
$501$	−1.34373	+	2.32742i	−0.0600336	+	0.103981i
$502$	3.39730	−	5.88430i	0.151629	−	0.262629i
$503$	6.90721			0.307977			0.153989	−	0.988073i	$-0.450788\pi$
$503$	6.90721			0.307977			0.153989	+	0.988073i	$0.450788\pi$
$504$	−7.11940	+	12.3312i	−0.317123	+	0.549274i
$505$	1.16123	+	2.01131i	0.0516741	+	0.0895021i
$506$	−2.55982	−	4.43374i	−0.113798	−	0.197104i
$507$	−12.0044	+	20.7922i	−0.533134	+	0.923416i
$508$	5.40191	−	9.35639i	0.239671	−	0.415122i
$509$	−2.47358	−	4.28436i	−0.109639	−	0.189901i	0.805985	−	0.591936i	$-0.201636\pi$
$509$	−2.47358	−	4.28436i	−0.109639	−	0.189901i	−0.915624	+	0.402035i	$0.868303\pi$
$510$	11.2735			0.499200
$511$	25.4199	+	44.0286i	1.12451	+	1.94771i
$512$	−19.0051			−0.839917
$513$	−3.53092	−	6.11573i	−0.155894	−	0.270016i
$514$	4.37953	−	7.58557i	0.193173	−	0.334585i
$515$	3.76354	+	6.51864i	0.165841	+	0.287246i
$516$	−4.28136			−0.188476
$517$	10.2071			0.448909
$518$	−1.74525	+	3.02286i	−0.0766817	+	0.132817i
$519$	−5.80586	−	10.0560i	−0.254849	−	0.441411i
$520$	65.2991			2.86355
$521$	−5.37465	+	9.30917i	−0.235468	+	0.407842i	−0.959409	−	0.282020i	$-0.908996\pi$
$521$	−5.37465	+	9.30917i	−0.235468	+	0.407842i	0.723941	+	0.689862i	$0.242329\pi$
$522$	−1.93369	+	3.34925i	−0.0846352	+	0.146592i
$523$	4.03410	−	6.98726i	0.176399	−	0.305532i	−0.764246	−	0.644925i	$-0.776889\pi$
$523$	4.03410	−	6.98726i	0.176399	−	0.305532i	0.940644	+	0.339394i	$0.110222\pi$
$524$	7.64009	−	13.2330i	0.333759	−	0.578088i
$525$	−33.4255			−1.45881
$526$	15.9807	−	27.6793i	0.696791	−	1.20688i
$527$	−11.7226			−0.510646
$528$	1.15163	−	1.99468i	0.0501183	−	0.0868074i
$529$	−9.10296			−0.395781
$530$	−12.2499			−0.532102
$531$	4.25982	−	7.37823i	0.184861	−	0.320188i
$532$	−12.6445	−	21.9009i	−0.548208	−	0.949524i
$533$	−7.45277	+	12.9086i	−0.322815	+	0.559132i
$534$	−10.2657	+	17.7807i	−0.444240	+	0.769446i
$535$	−41.3693			−1.78855
$536$	−34.1200			−1.47376
$537$	2.78619	−	4.82582i	0.120233	−	0.208249i
$538$	10.8415			0.467412
$539$	−8.97915	−	15.5523i	−0.386759	−	0.669887i
$540$	−1.34978	−	2.33789i	−0.0580855	−	0.100607i
$541$	−5.22297	−	9.04645i	−0.224553	−	0.388937i	0.731632	−	0.681700i	$-0.238759\pi$
$541$	−5.22297	−	9.04645i	−0.224553	−	0.388937i	−0.956185	+	0.292762i	$0.905426\pi$
$542$	−5.44610	+	9.43293i	−0.233930	+	0.405179i
$543$	11.1490	−	19.3106i	0.478449	−	0.828698i
$544$	5.94741	+	10.3012i	0.254993	+	0.441661i
$545$	23.4521	−	40.6202i	1.00458	−	1.73998i
$546$	−31.2427			−1.33706
$547$	−15.2940	−	26.4900i	−0.653925	−	1.13263i	−0.982162	−	0.188036i	$-0.939788\pi$
$547$	−15.2940	−	26.4900i	−0.653925	−	1.13263i	0.328237	−	0.944596i	$-0.393546\pi$
$548$	−1.22143	−	2.11558i	−0.0521769	−	0.0903730i
$549$	−1.94763			−0.0831229
$550$	9.90294			0.422263
$551$	−12.3254	−	21.3482i	−0.525079	−	0.909464i
$552$	5.72549	+	9.91684i	0.243693	+	0.422089i
$553$	−24.9471			−1.06086
$554$	17.1918	−	29.7770i	0.730409	−	1.26511i
$555$	−1.18750	−	2.05681i	−0.0504066	−	0.0873068i
$556$	6.29882	−	10.9099i	0.267129	−	0.462682i
$557$	−2.46215	+	4.26458i	−0.104325	+	0.180696i	−0.913462	−	0.406924i	$-0.866601\pi$
$557$	−2.46215	+	4.26458i	−0.104325	+	0.180696i	0.809137	+	0.587620i	$0.199935\pi$
$558$	−2.23006	−	3.86257i	−0.0944058	−	0.163516i
$559$	−16.8571	−	29.1973i	−0.712979	−	1.23492i
$560$	15.0489	+	26.0654i	0.635931	+	1.10146i
$561$	−3.60959			−0.152397
$562$	−12.1313	+	21.0120i	−0.511728	+	0.886338i
$563$	−7.13061			−0.300519			−0.150260	−	0.988647i	$-0.548011\pi$
$563$	−7.13061			−0.300519			−0.150260	+	0.988647i	$0.548011\pi$
$564$	−6.36137			−0.267862
$565$	−20.5948	+	35.6712i	−0.866429	+	1.50070i
$566$	−9.71455	+	16.8261i	−0.408333	+	0.707254i
$567$	2.31773	+	4.01442i	0.0973353	+	0.168590i
$568$	16.5588	−	28.6807i	0.694792	−	1.20342i
$569$	9.17875			0.384793			0.192397	−	0.981317i	$-0.438374\pi$
$569$	9.17875			0.384793			0.192397	+	0.981317i	$0.438374\pi$
$570$	−27.3397			−1.14513
$571$	19.8278	−	34.3427i	0.829767	−	1.43720i	−0.0684548	−	0.997654i	$-0.521807\pi$
$571$	19.8278	−	34.3427i	0.829767	−	1.43720i	0.898221	−	0.439544i	$-0.144860\pi$
$572$	−5.82570			−0.243585
$573$	0.935068	−	1.61959i	0.0390630	−	0.0676591i
$574$	−12.5832			−0.525212
$575$	−13.4406	+	23.2797i	−0.560510	+	0.970832i
$576$	−4.12091	+	7.13762i	−0.171705	+	0.297401i
$577$	−10.9918	+	19.0383i	−0.457594	+	0.792576i	−0.998833	−	0.0482924i	$-0.984622\pi$
$577$	−10.9918	+	19.0383i	−0.457594	+	0.792576i	0.541239	+	0.840869i	$0.317955\pi$
$578$	4.72001	−	8.17529i	0.196326	−	0.340047i
$579$	−3.15939			−0.131300
$580$	−4.71169	−	8.16089i	−0.195642	−	0.338863i
$581$	−30.3980	+	52.6509i	−1.26112	+	2.18433i
$582$	7.45419			0.308986
$583$	3.92221			0.162441
$584$	16.8447	+	29.1759i	0.697039	+	1.20731i
$585$	10.6291	−	18.4101i	0.439458	−	0.761164i
$586$	−6.71201	−	11.6255i	−0.277271	−	0.480247i
$587$	−1.33519			−0.0551094			−0.0275547	−	0.999620i	$-0.508772\pi$
$587$	−1.33519			−0.0551094			−0.0275547	+	0.999620i	$0.508772\pi$
$588$	5.59606	+	9.69265i	0.230777	+	0.399718i
$589$	28.4289			1.17139
$590$	−16.4918	−	28.5646i	−0.678956	−	1.17599i
$591$	5.99481	−	10.3833i	0.246593	−	0.427112i
$592$	−0.631437	+	1.09368i	−0.0259519	+	0.0449500i
$593$	−3.60971	−	6.25220i	−0.148233	−	0.256747i	0.782341	−	0.622850i	$-0.214025\pi$
$593$	−3.60971	−	6.25220i	−0.148233	−	0.256747i	−0.930574	+	0.366103i	$0.880692\pi$
$594$	−0.686670	−	1.18935i	−0.0281744	−	0.0487995i
$595$	23.5840	−	40.8487i	0.966851	−	1.67463i
$596$	0.919748			0.0376743
$597$	−2.78128	+	4.81732i	−0.113830	+	0.197160i
$598$	−12.5628	+	21.7595i	−0.513732	+	0.889810i
$599$	−3.88137			−0.158588			−0.0792942	−	0.996851i	$-0.525267\pi$
$599$	−3.88137			−0.158588			−0.0792942	+	0.996851i	$0.525267\pi$
$600$	−22.1497			−0.904257
$601$	5.70342			0.232647			0.116324	−	0.993211i	$-0.462889\pi$
$601$	5.70342			0.232647			0.116324	+	0.993211i	$0.462889\pi$
$602$	14.2307	−	24.6483i	0.579999	−	1.00459i
$603$	−5.55389	+	9.61962i	−0.226172	+	0.391741i
$604$	−3.32048	−	5.75123i	−0.135108	−	0.234014i
$605$	33.0691			1.34445
$606$	−0.368170	−	0.637690i	−0.0149559	−	0.0259044i
$607$	5.73792	+	9.93837i	0.232895	+	0.403386i	0.958659	−	0.284558i	$-0.0918468\pi$
$607$	5.73792	+	9.93837i	0.232895	+	0.403386i	−0.725764	+	0.687944i	$0.758513\pi$
$608$	−14.4232	−	24.9818i	−0.584939	−	1.01314i
$609$	8.09049	+	14.0131i	0.327843	+	0.567841i
$610$	−3.77010	+	6.53001i	−0.152647	+	0.264392i
$611$	−25.0468	−	43.3823i	−1.01328	−	1.75506i
$612$	2.24960			0.0909345
$613$	0.622142	−	1.07758i	0.0251281	−	0.0435231i	−0.853188	−	0.521604i	$-0.825334\pi$
$613$	0.622142	−	1.07758i	0.0251281	−	0.0435231i	0.878316	+	0.478081i	$0.158667\pi$
$614$	29.2505			1.18046
$615$	4.28093	−	7.41479i	0.172624	−	0.298993i
$616$	−8.82507	−	15.2855i	−0.355572	−	0.615869i
$617$	10.1349	+	17.5541i	0.408015	+	0.706703i	0.994667	−	0.103136i	$-0.0328877\pi$
$617$	10.1349	+	17.5541i	0.408015	+	0.706703i	−0.586652	+	0.809839i	$0.699554\pi$
$618$	−1.19324	−	2.06675i	−0.0479991	−	0.0831369i
$619$	−7.33735	+	12.7087i	−0.294913	+	0.510804i	−0.974965	−	0.222360i	$-0.928624\pi$
$619$	−7.33735	+	12.7087i	−0.294913	+	0.510804i	0.680052	+	0.733164i	$0.261957\pi$
$620$	10.8677			0.436456
$621$	3.72787			0.149594
$622$	0.205184	+	0.355390i	0.00822715	+	0.0142498i
$623$	42.9513	+	74.3939i	1.72081	+	2.98053i
$624$	−11.3037			−0.452511
$625$	4.52897	+	7.84441i	0.181159	+	0.313776i
$626$	−9.21996			−0.368504
$627$	8.75371			0.349590
$628$	9.63368	+	0.944898i	0.384426	+	0.0377055i
$629$	1.97913			0.0789131
$630$	17.9460			0.714987
$631$	10.0523	+	17.4111i	0.400177	+	0.693126i	0.993747	−	0.111656i	$-0.0356155\pi$
$631$	10.0523	+	17.4111i	0.400177	+	0.693126i	−0.593570	+	0.804782i	$0.702282\pi$
$632$	−16.5314			−0.657583
$633$	0.990880	+	1.71625i	0.0393839	+	0.0682150i
$634$	13.5659	+	23.4969i	0.538773	+	0.933182i
$635$	−48.8685			−1.93929
$636$	−2.44443			−0.0969280
$637$	−44.0670	+	76.3262i	−1.74600	+	3.02416i
$638$	−2.39696	−	4.15166i	−0.0948966	−	0.164366i
$639$	−5.39073	−	9.33702i	−0.213254	−	0.369367i
$640$	1.67994	+	2.90973i	0.0664053	+	0.115017i
$641$	−4.72570	+	8.18515i	−0.186654	+	0.323294i	−0.944133	−	0.329566i	$-0.893098\pi$
$641$	−4.72570	+	8.18515i	−0.186654	+	0.323294i	0.757479	+	0.652860i	$0.226431\pi$
$642$	13.1162			0.517656
$643$	−5.10632	+	8.84441i	−0.201374	+	0.348789i	−0.948971	−	0.315363i	$-0.897874\pi$
$643$	−5.10632	+	8.84441i	−0.201374	+	0.348789i	0.747598	+	0.664152i	$0.231207\pi$
$644$	13.3498			0.526056
$645$	9.68285	+	16.7712i	0.381262	+	0.660365i
$646$	11.3913	−	19.7304i	0.448186	−	0.776281i
$647$	22.7328	+	39.3743i	0.893718	+	1.54797i	0.835383	+	0.549668i	$0.185246\pi$
$647$	22.7328	+	39.3743i	0.893718	+	1.54797i	0.0583351	+	0.998297i	$0.481421\pi$
$648$	1.53586	+	2.66019i	0.0603343	+	0.104502i
$649$	5.28039	+	9.14590i	0.207273	+	0.359008i
$650$	−24.3003	−	42.0894i	−0.953137	−	1.65088i
$651$	−18.6610			−0.731381
$652$	−7.27956	−	12.6086i	−0.285089	−	0.493789i
$653$	−2.21584	+	3.83794i	−0.0867124	+	0.150190i	−0.906120	−	0.423022i	$-0.860969\pi$
$653$	−2.21584	+	3.83794i	−0.0867124	+	0.150190i	0.819407	+	0.573212i	$0.194303\pi$
$654$	−7.43554	+	12.8787i	−0.290753	+	0.503598i
$655$	−69.1162			−2.70059
$656$	−4.55265			−0.177751
$657$	10.9676			0.427887
$658$	21.1444	−	36.6231i	0.824294	−	1.42772i
$659$	−13.4318	+	23.2646i	−0.523229	+	0.906260i	0.476405	+	0.879226i	$0.341940\pi$
$659$	−13.4318	+	23.2646i	−0.523229	+	0.906260i	−0.999635	+	0.0270341i	$0.991394\pi$
$660$	3.34633			0.130256
$661$	7.45725	−	12.9163i	0.290053	−	0.502387i	−0.683769	−	0.729699i	$-0.739660\pi$
$661$	7.45725	−	12.9163i	0.290053	−	0.502387i	0.973822	+	0.227312i	$0.0729936\pi$
$662$	4.92401	+	8.52863i	0.191377	+	0.331475i
$663$	8.85739	+	15.3414i	0.343992	+	0.595812i
$664$	−20.1435	+	34.8895i	−0.781718	+	1.35398i
$665$	−57.1943	+	99.0634i	−2.21790	+	3.84151i
$666$	0.376500	+	0.652117i	0.0145891	+	0.0252690i
$667$	13.0129			0.503861
$668$	1.03809	+	1.79802i	0.0401649	+	0.0695677i
$669$	17.6632			0.682897
$670$	21.5017	+	37.2421i	0.830685	+	1.43879i
$671$	1.20712	−	2.09080i	0.0466005	−	0.0807144i
$672$	9.46753	+	16.3982i	0.365218	+	0.632576i
$673$	−6.79395			−0.261888			−0.130944	−	0.991390i	$-0.541801\pi$
$673$	−6.79395			−0.261888			−0.130944	+	0.991390i	$0.541801\pi$
$674$	7.64140			0.294336
$675$	−3.60542	+	6.24477i	−0.138773	+	0.240361i
$676$	9.27389	+	16.0629i	0.356688	+	0.617802i
$677$	−1.04695			−0.0402374			−0.0201187	−	0.999798i	$-0.506404\pi$
$677$	−1.04695			−0.0402374			−0.0201187	+	0.999798i	$0.506404\pi$
$678$	6.52962	−	11.3096i	0.250768	−	0.434344i
$679$	15.5941	−	27.0097i	0.598445	−	1.03654i
$680$	15.6281	−	27.0687i	0.599312	−	1.03804i
$681$	−11.7878	+	20.4170i	−0.451708	+	0.782381i
$682$	5.52866			0.211704
$683$	11.8368	−	20.5019i	0.452921	−	0.784482i	−0.545645	−	0.838016i	$-0.683715\pi$
$683$	11.8368	−	20.5019i	0.452921	−	0.784482i	0.998566	+	0.0535343i	$0.0170486\pi$
$684$	−5.45556			−0.208598
$685$	−5.52484	+	9.56931i	−0.211093	+	0.365625i
$686$	−38.4527			−1.46813
$687$	1.29453			0.0493894
$688$	5.14872	−	8.91784i	0.196293	−	0.339989i
$689$	−9.62451	−	16.6701i	−0.366665	−	0.635082i
$690$	7.21618	−	12.4988i	0.274715	−	0.475821i
$691$	23.8453	−	41.3013i	0.907120	−	1.57118i	0.0890731	−	0.996025i	$-0.471610\pi$
$691$	23.8453	−	41.3013i	0.907120	−	1.57118i	0.818046	−	0.575152i	$-0.195057\pi$
$692$	−8.97052			−0.341008
$693$	−5.74601			−0.218273
$694$	14.5539	−	25.2081i	0.552458	−	0.956885i
$695$	−56.9824			−2.16146
$696$	5.36123	+	9.28592i	0.203217	+	0.351982i
$697$	3.56737	+	6.17887i	0.135124	+	0.234041i
$698$	−16.5369	−	28.6427i	−0.625929	−	1.08414i
$699$	4.06216	−	7.03586i	0.153645	−	0.266121i
$700$	−12.9113	+	22.3630i	−0.488001	+	0.845242i
$701$	−13.3521	−	23.1265i	−0.504301	−	0.873474i	−0.999988	−	0.00497296i	$-0.998417\pi$
$701$	−13.3521	−	23.1265i	−0.504301	−	0.873474i	0.495687	−	0.868501i	$-0.334916\pi$
$702$	−3.36997	+	5.83696i	−0.127191	+	0.220302i
$703$	−4.79964			−0.181022
$704$	−5.10820	−	8.84765i	−0.192522	−	0.333459i
$705$	14.3871	+	24.9191i	0.541848	+	0.938509i
$706$	−6.82300			−0.256787
$707$	−3.08083			−0.115866
$708$	−3.29089	−	5.69998i	−0.123679	−	0.214218i
$709$	7.57362	+	13.1179i	0.284433	+	0.492653i	0.972472	−	0.233021i	$-0.0748612\pi$
$709$	7.57362	+	13.1179i	0.284433	+	0.492653i	−0.688038	+	0.725674i	$0.741528\pi$
$710$	−41.7401			−1.56648
$711$	−2.69090	+	4.66077i	−0.100917	+	0.174793i
$712$	28.4620	+	49.2977i	1.06666	+	1.84751i
$713$	−7.50367	+	12.9967i	−0.281014	+	0.486731i
$714$	−7.47737	+	12.9512i	−0.279833	+	0.484686i
$715$	13.1756	+	22.8208i	0.492739	+	0.853449i
$716$	−2.15244	−	3.72814i	−0.0804405	−	0.139327i
$717$	3.42307	+	5.92893i	0.127837	+	0.221420i
$718$	18.5732			0.693147
$719$	−4.88790	+	8.46609i	−0.182288	+	0.315732i	−0.942659	−	0.333757i	$-0.891684\pi$
$719$	−4.88790	+	8.46609i	−0.182288	+	0.315732i	0.760371	+	0.649488i	$0.225017\pi$
$720$	6.49294			0.241978
$721$	−9.98494			−0.371859
$722$	−17.1003	+	29.6186i	−0.636407	+	1.10229i
$723$	1.82353	−	3.15845i	0.0678179	−	0.117464i
$724$	−8.61305	−	14.9182i	−0.320101	−	0.554432i
$725$	−12.5855	+	21.7986i	−0.467412	+	0.809581i
$726$	−10.4846			−0.389121
$727$	12.3955			0.459723			0.229862	−	0.973223i	$-0.426173\pi$
$727$	12.3955			0.459723			0.229862	+	0.973223i	$0.426173\pi$
$728$	−43.3108	+	75.0165i	−1.60520	+	2.78030i
$729$	1.00000			0.0370370
$730$	21.2304	−	36.7722i	0.785773	−	1.36100i
$731$	−16.1378			−0.596877
$732$	−0.752313	+	1.30304i	−0.0278063	+	0.0481619i
$733$	−22.4447	+	38.8754i	−0.829014	+	1.43590i	0.0697977	+	0.997561i	$0.477765\pi$
$733$	−22.4447	+	38.8754i	−0.829014	+	1.43590i	−0.898812	+	0.438334i	$0.855569\pi$
$734$	−10.9237	+	18.9203i	−0.403200	+	0.698363i
$735$	25.3124	−	43.8424i	0.933662	−	1.61715i
$736$	15.2278			0.561302
$737$	−6.88449	−	11.9243i	−0.253594	−	0.439237i
$738$	−1.35728	+	2.35087i	−0.0499621	+	0.0865369i
$739$	38.7714			1.42623			0.713114	−	0.701048i	$-0.247284\pi$
$739$	38.7714			1.42623			0.713114	+	0.701048i	$0.247284\pi$
$740$	−1.83479			−0.0674481
$741$	−21.4803	−	37.2050i	−0.789098	−	1.36676i
$742$	8.12497	−	14.0729i	0.298277	−	0.516631i
$743$	1.85434	+	3.21180i	0.0680290	+	0.117830i	0.898034	−	0.439927i	$-0.144996\pi$
$743$	1.85434	+	3.21180i	0.0680290	+	0.117830i	−0.830005	+	0.557757i	$0.811662\pi$
$744$	−12.3658			−0.453354
$745$	−2.08013	−	3.60289i	−0.0762100	−	0.132000i
$746$	3.02747			0.110844
$747$	6.55772	+	11.3583i	0.239934	+	0.415579i
$748$	−1.39428	+	2.41496i	−0.0509798	+	0.0882996i
$749$	27.4389	−	47.5256i	1.00260	−	1.73655i
$750$	4.27961	+	7.41251i	0.156269	+	0.270667i
$751$	−14.9608	−	25.9128i	−0.545926	−	0.945571i	−0.998548	−	0.0538690i	$-0.982845\pi$
$751$	−14.9608	−	25.9128i	−0.545926	−	0.945571i	0.452622	−	0.891702i	$-0.350489\pi$
$752$	7.65012	−	13.2504i	0.278971	−	0.483192i
$753$	−6.13283			−0.223493
$754$	−11.7636	+	20.3751i	−0.428404	+	0.742017i
$755$	−15.0194	+	26.0143i	−0.546611	+	0.946758i
$756$	3.58108			0.130242
$757$	12.6693			0.460474			0.230237	−	0.973135i	$-0.426050\pi$
$757$	12.6693			0.460474			0.230237	+	0.973135i	$0.426050\pi$
$758$	24.5399			0.891330
$759$	−2.31050	+	4.00190i	−0.0838658	+	0.145260i
$760$	−37.9002	+	65.6452i	−1.37479	+	2.38120i
$761$	18.3785	+	31.8324i	0.666218	+	1.15392i	0.978953	+	0.204084i	$0.0654215\pi$
$761$	18.3785	+	31.8324i	0.666218	+	1.15392i	−0.312735	+	0.949840i	$0.601245\pi$
$762$	15.4939			0.561283
$763$	31.1101	+	53.8842i	1.12626	+	1.95074i
$764$	−0.722378	−	1.25120i	−0.0261347	−	0.0452667i
$765$	−5.08775	−	8.81225i	−0.183948	−	0.318607i
$766$	−7.13550	−	12.3590i	−0.257816	−	0.446551i
$767$	25.9146	−	44.8854i	0.935721	−	1.62072i
$768$	7.70919	+	13.3527i	0.278181	+	0.481824i
$769$	−7.40494			−0.267029			−0.133514	−	0.991047i	$-0.542626\pi$
$769$	−7.40494			−0.267029			−0.133514	+	0.991047i	$0.542626\pi$
$770$	−11.1228	+	19.2652i	−0.400837	+	0.694270i
$771$	−7.90595			−0.284726
$772$	−1.22038	+	2.11375i	−0.0439223	+	0.0760757i
$773$	−13.3709	−	23.1591i	−0.480918	−	0.832975i	0.518842	−	0.854870i	$-0.326363\pi$
$773$	−13.3709	−	23.1591i	−0.480918	−	0.832975i	−0.999760	+	0.0218954i	$0.993030\pi$
$774$	−3.06997	−	5.31734i	−0.110348	−	0.191128i
$775$	−14.5144	−	25.1396i	−0.521372	−	0.903042i
$776$	10.3335	−	17.8982i	0.370952	−	0.642508i
$777$	3.15053			0.113025
$778$	−9.91840			−0.355592
$779$	−8.65133	−	14.9845i	−0.309966	−	0.536877i
$780$	−8.21139	−	14.2226i	−0.294015	−	0.509249i
$781$	13.3645			0.478219
$782$	6.01337	+	10.4155i	0.215038	+	0.372456i
$783$	3.49070			0.124748
$784$	−26.9190			−0.961394
$785$	−18.0864	−	39.8746i	−0.645532	−	1.42319i
$786$	21.9135			0.781627
$787$	3.73603			0.133175			0.0665875	−	0.997781i	$-0.478789\pi$
$787$	3.73603			0.133175			0.0665875	+	0.997781i	$0.478789\pi$
$788$	−4.63123	−	8.02153i	−0.164981	−	0.285755i
$789$	−28.8484			−1.02703
$790$	10.4177	+	18.0441i	0.370647	+	0.641979i
$791$	−27.3197	−	47.3191i	−0.971377	−	1.68247i
$792$	−3.80764			−0.135299
$793$	−11.8484			−0.420749
$794$	−6.81268	+	11.7999i	−0.241773	+	0.418763i
$795$	5.52839	+	9.57546i	0.196072	+	0.339607i
$796$	2.14865	+	3.72158i	0.0761570	+	0.131908i
$797$	−17.6521	−	30.5743i	−0.625269	−	1.08300i	−0.988489	−	0.151294i	$-0.951656\pi$
$797$	−17.6521	−	30.5743i	−0.625269	−	1.08300i	0.363220	−	0.931704i	$-0.381677\pi$
$798$	18.1336	−	31.4083i	0.641921	−	1.11184i
$799$	−23.9780			−0.848280
$800$	−14.7276	+	25.5089i	−0.520698	+	0.901875i
$801$	18.5317			0.654785
$802$	−12.1813	−	21.0986i	−0.430135	−	0.745017i
$803$	−6.79762	+	11.7738i	−0.239883	+	0.415489i
$804$	4.29061	+	7.43155i	0.151318	+	0.262091i
$805$	−30.1923	−	52.2946i	−1.06414	−	1.84314i
$806$	−13.5665	−	23.4979i	−0.477860	−	0.827678i
$807$	−4.89280	−	8.47457i	−0.172235	−	0.298319i
$808$	−2.04154			−0.0718210
$809$	−12.8890	−	22.3245i	−0.453154	−	0.784886i	0.545426	−	0.838159i	$-0.316368\pi$
$809$	−12.8890	−	22.3245i	−0.453154	−	0.784886i	−0.998580	+	0.0532731i	$0.983035\pi$
$810$	1.93574	−	3.35280i	0.0680149	−	0.117805i
$811$	16.1703	−	28.0079i	0.567818	−	0.983489i	−0.428964	−	0.903322i	$-0.641121\pi$
$811$	16.1703	−	28.0079i	0.567818	−	0.983489i	0.996781	−	0.0801672i	$-0.0255454\pi$
$812$	12.5005			0.438680
$813$	9.83133			0.344800
$814$	−0.933403			−0.0327158
$815$	−32.9273	+	57.0318i	−1.15339	+	1.99774i
$816$	−2.70534	+	4.68579i	−0.0947059	+	0.164035i
$817$	39.1361			1.36920
$818$	8.73732	−	15.1335i	0.305493	−	0.529130i
$819$	14.0999	+	24.4217i	0.492689	+	0.853362i
$820$	−3.30719	−	5.72823i	−0.115492	−	0.200038i
$821$	20.2481	−	35.0707i	0.706663	−	1.22398i	−0.259424	−	0.965763i	$-0.583533\pi$
$821$	20.2481	−	35.0707i	0.706663	−	1.22398i	0.966088	−	0.258214i	$-0.0831338\pi$
$822$	1.75166	−	3.03397i	0.0610963	−	0.105822i
$823$	1.56821	+	2.71622i	0.0546644	+	0.0946816i	0.892063	−	0.451912i	$-0.149258\pi$
$823$	1.56821	+	2.71622i	0.0546644	+	0.0946816i	−0.837398	+	0.546593i	$0.815924\pi$
$824$	−6.61660			−0.230500
$825$	−4.46921	−	7.74090i	−0.155598	−	0.269503i
$826$	43.7539			1.52239
$827$	−3.91511	−	6.78117i	−0.136142	−	0.235804i	0.789891	−	0.613247i	$-0.210137\pi$
$827$	−3.91511	−	6.78117i	−0.136142	−	0.235804i	−0.926033	+	0.377442i	$0.876804\pi$
$828$	1.43997	−	2.49410i	0.0500423	−	0.0866759i
$829$	19.9300	+	34.5198i	0.692198	+	1.19892i	0.971116	+	0.238607i	$0.0766907\pi$
$829$	19.9300	+	34.5198i	0.692198	+	1.19892i	−0.278919	+	0.960315i	$0.589976\pi$
$830$	50.7761			1.76246
$831$	−31.0347			−1.07658
$832$	−25.0695	+	43.4216i	−0.869128	+	1.50537i
$833$	21.0933	+	36.5346i	0.730838	+	1.26585i
$834$	18.0664			0.625588
$835$	4.69555	−	8.13293i	0.162496	−	0.281452i
$836$	3.38130	−	5.85658i	0.116945	−	0.202554i
$837$	−2.01285	+	3.48637i	−0.0695744	+	0.120506i
$838$	9.17122	−	15.8850i	0.316814	−	0.548739i
$839$	−36.5665			−1.26241			−0.631207	−	0.775614i	$-0.717440\pi$
$839$	−36.5665			−1.26241			−0.631207	+	0.775614i	$0.717440\pi$
$840$	24.8780	−	43.0900i	0.858374	−	1.48675i
$841$	−16.8150			−0.579828
$842$	−10.2873	+	17.8181i	−0.354524	+	0.614053i
$843$	21.8995			0.754258
$844$	1.53099			0.0526989
$845$	41.9482	−	72.6564i	1.44306	−	2.49946i
$846$	−4.56145	−	7.90067i	−0.156826	−	0.271630i
$847$	−21.9337	+	37.9902i	−0.753650	+	1.30536i
$848$	2.93965	−	5.09162i	0.100948	−	0.174847i
$849$	17.5368			0.601860
$850$	−23.2634			−0.797927
$851$	1.26684	−	2.19423i	0.0434268	−	0.0752174i
$852$	−8.32912			−0.285351
$853$	−18.8534	−	32.6550i	−0.645527	−	1.11808i	−0.984180	−	0.177174i	$-0.943305\pi$
$853$	−18.8534	−	32.6550i	−0.645527	−	1.11808i	0.338653	−	0.940911i	$-0.390029\pi$
$854$	−5.00118	−	8.66230i	−0.171137	−	0.296418i
$855$	12.3384	+	21.3708i	0.421966	+	0.730867i
$856$	18.1826	−	31.4932i	0.621470	−	1.07642i
$857$	−25.1844	+	43.6207i	−0.860284	+	1.49006i	0.0113715	+	0.999935i	$0.496380\pi$
$857$	−25.1844	+	43.6207i	−0.860284	+	1.49006i	−0.871655	+	0.490120i	$0.836953\pi$
$858$	−4.17735	−	7.23538i	−0.142612	−	0.247012i
$859$	−13.5449	+	23.4604i	−0.462145	+	0.800459i	−0.999068	−	0.0431724i	$-0.986254\pi$
$859$	−13.5449	+	23.4604i	−0.462145	+	0.800459i	0.536922	+	0.843632i	$0.319587\pi$
$860$	14.9608			0.510159
$861$	5.67881	+	9.83598i	0.193533	+	0.335209i
$862$	−17.0697	−	29.5656i	−0.581396	−	1.00701i
$863$	−21.5933			−0.735043			−0.367522	−	0.930015i	$-0.619794\pi$
$863$	−21.5933			−0.735043			−0.367522	+	0.930015i	$0.619794\pi$
$864$	4.08484			0.138969
$865$	20.2880	+	35.1398i	0.689813	+	1.19479i
$866$	16.9060	+	29.2820i	0.574489	+	0.995044i
$867$	−8.52058			−0.289374
$868$	−7.20818	+	12.4849i	−0.244662	+	0.423766i
$869$	−3.33558	−	5.77740i	−0.113152	−	0.195985i
$870$	6.75708	−	11.7036i	0.229087	−	0.396789i
$871$	−33.7870	+	58.5208i	−1.14483	+	1.98290i
$872$	20.6153	+	35.7068i	0.698123	+	1.20918i
$873$	−3.36409	−	5.82677i	−0.113857	−	0.197206i
$874$	−14.5832	−	25.2588i	−0.493284	−	0.854392i
$875$	35.8115			1.21065
$876$	4.23646	−	7.33777i	0.143137	−	0.247920i
$877$	11.4128			0.385384			0.192692	−	0.981259i	$-0.438278\pi$
$877$	11.4128			0.385384			0.192692	+	0.981259i	$0.438278\pi$
$878$	−38.7156			−1.30659
$879$	−6.05828	+	10.4932i	−0.204341	+	0.353928i
$880$	−4.02426	+	6.97023i	−0.135658	+	0.234966i
$881$	−13.6240	−	23.5975i	−0.459005	−	0.795020i	0.539903	−	0.841727i	$-0.318461\pi$
$881$	−13.6240	−	23.5975i	−0.459005	−	0.795020i	−0.998909	+	0.0467066i	$0.985127\pi$
$882$	−8.02535	+	13.9003i	−0.270228	+	0.468048i
$883$	24.2372			0.815646			0.407823	−	0.913061i	$-0.366288\pi$
$883$	24.2372			0.815646			0.407823	+	0.913061i	$0.366288\pi$
$884$	13.6854			0.460289
$885$	−14.8855	+	25.7825i	−0.500372	+	0.866669i
$886$	−35.0227			−1.17661
$887$	2.34984	−	4.07005i	0.0789000	−	0.136659i	−0.823876	−	0.566771i	$-0.808193\pi$
$887$	2.34984	−	4.07005i	0.0789000	−	0.136659i	0.902776	+	0.430112i	$0.141526\pi$
$888$	2.08772			0.0700594
$889$	32.4129	−	56.1408i	1.08709	−	1.88290i
$890$	35.8724	−	62.1329i	1.20245	−	2.08270i
$891$	−0.619790	+	1.07351i	−0.0207637	+	0.0359639i
$892$	6.82276	−	11.8174i	0.228443	−	0.395674i
$893$	58.1497			1.94590
$894$	0.659509	+	1.14230i	0.0220573	+	0.0382043i
$895$	−9.73605	+	16.8633i	−0.325440	+	0.563679i
$896$	−4.45699			−0.148898
$897$	22.6785			0.757212
$898$	−11.8612	−	20.5442i	−0.395814	−	0.685570i
$899$	−7.02627	+	12.1699i	−0.234339	+	0.405888i
$900$	2.78534	+	4.82434i	0.0928445	+	0.160811i
$901$	−9.21381			−0.306957
$902$	−1.68245	−	2.91410i	−0.0560196	−	0.0970288i
$903$	−25.6893			−0.854886
$904$	−18.1036	−	31.3564i	−0.602118	−	1.04290i
$905$	−38.9590	+	67.4790i	−1.29504	+	2.24308i
$906$	4.76192	−	8.24789i	0.158204	−	0.274018i
$907$	−1.48389	−	2.57017i	−0.0492717	−	0.0853411i	0.840338	−	0.542063i	$-0.182357\pi$
$907$	−1.48389	−	2.57017i	−0.0492717	−	0.0853411i	−0.889609	+	0.456722i	$0.849023\pi$
$908$	9.10653	+	15.7730i	0.302211	+	0.523444i
$909$	−0.332312	+	0.575580i	−0.0110221	+	0.0190908i
$910$	109.174			3.61910
$911$	2.60217	−	4.50709i	0.0862138	−	0.149327i	−0.819694	−	0.572802i	$-0.805857\pi$
$911$	2.60217	−	4.50709i	0.0862138	−	0.149327i	0.905908	+	0.423475i	$0.139190\pi$
$912$	6.56080	−	11.3636i	0.217250	−	0.376287i
$913$	−16.2576			−0.538049
$914$	−22.9045			−0.757613
$915$	6.80581			0.224993
$916$	0.500038	−	0.866092i	0.0165217	−	0.0286165i
$917$	45.8426	−	79.4017i	1.51386	−	2.62208i
$918$	1.61308	+	2.79394i	0.0532397	+	0.0922138i
$919$	−28.7524			−0.948453			−0.474227	−	0.880403i	$-0.657272\pi$
$919$	−28.7524			−0.948453			−0.474227	+	0.880403i	$0.657272\pi$
$920$	−20.0072	−	34.6534i	−0.659617	−	1.14249i
$921$	−13.2008	−	22.8645i	−0.434981	−	0.753409i
$922$	23.0993	+	40.0091i	0.760733	+	1.31763i
$923$	−32.7944	−	56.8016i	−1.07944	−	1.86965i
$924$	−2.21951	+	3.84431i	−0.0730167	+	0.126469i
$925$	2.45046	+	4.24432i	0.0805706	+	0.139552i
$926$	40.6958			1.33735
$927$	−1.07702	+	1.86545i	−0.0353740	+	0.0612695i
$928$	14.2589			0.468073
$929$	7.88177	−	13.6516i	0.258593	−	0.447896i	−0.707272	−	0.706941i	$-0.750075\pi$
$929$	7.88177	−	13.6516i	0.258593	−	0.447896i	0.965865	+	0.259045i	$0.0834079\pi$
$930$	7.79271	+	13.4974i	0.255533	+	0.442596i
$931$	−51.1539	−	88.6011i	−1.67650	−	2.90378i
$932$	−3.13818	−	5.43549i	−0.102795	−	0.178045i
$933$	0.185200	−	0.320776i	0.00606317	−	0.0105017i
$934$	24.7718			0.810558
$935$	12.6133			0.412501
$936$	9.34338	+	16.1832i	0.305398	+	0.528965i
$937$	4.94450	+	8.56413i	0.161530	+	0.279778i	0.935418	−	0.353545i	$-0.115024\pi$
$937$	4.94450	+	8.56413i	0.161530	+	0.279778i	−0.773888	+	0.633323i	$0.781691\pi$
$938$	−57.0457			−1.86261
$939$	4.16098	+	7.20702i	0.135788	+	0.235192i
$940$	22.2292			0.725037
$941$	17.7798			0.579604			0.289802	−	0.957087i	$-0.406411\pi$
$941$	17.7798			0.579604			0.289802	+	0.957087i	$0.406411\pi$
$942$	5.73433	+	12.6423i	0.186835	+	0.411909i
$943$	9.13390			0.297441
$944$	15.8303			0.515234
$945$	−8.09906	−	14.0280i	−0.263463	−	0.456331i
$946$	7.61094			0.247453
$947$	−7.35467	−	12.7387i	−0.238995	−	0.413951i	0.721431	−	0.692486i	$-0.243485\pi$
$947$	−7.35467	−	12.7387i	−0.238995	−	0.413951i	−0.960426	+	0.278535i	$0.910151\pi$
$948$	2.07883	+	3.60064i	0.0675172	+	0.116943i
$949$	66.7213			2.16587
$950$	56.4167			1.83040
$951$	12.2447	−	21.2084i	0.397060	−	0.687729i
$952$	20.7313	+	35.9077i	0.671905	+	1.16377i
$953$	16.8003	+	29.0990i	0.544215	+	0.942608i	0.998656	+	0.0518312i	$0.0165058\pi$
$953$	16.8003	+	29.0990i	0.544215	+	0.942608i	−0.454441	+	0.890777i	$0.650161\pi$
$954$	−1.75279	−	3.03592i	−0.0567487	−	0.0982915i
$955$	−3.26750	+	5.65948i	−0.105734	+	0.183137i
$956$	5.28892			0.171056
$957$	−2.16350	+	3.74730i	−0.0699361	+	0.121133i
$958$	−13.2121			−0.426864
$959$	−7.32891	−	12.6940i	−0.236663	−	0.409912i
$960$	14.4001	−	24.9417i	0.464762	−	0.804991i
$961$	7.39684	+	12.8117i	0.238608	+	0.413281i
$962$	2.29043	+	3.96714i	0.0738465	+	0.127906i
$963$	−5.91937	−	10.2526i	−0.190749	−	0.330387i
$964$	−1.40875	−	2.44003i	−0.0453729	−	0.0785882i
$965$	11.0402			0.355395
$966$	9.57253	+	16.5801i	0.307991	+	0.533456i
$967$	−29.5485	+	51.1795i	−0.950215	+	1.64582i	−0.205259	+	0.978708i	$0.565804\pi$
$967$	−29.5485	+	51.1795i	−0.950215	+	1.64582i	−0.744956	+	0.667113i	$0.767530\pi$
$968$	−14.5345	+	25.1745i	−0.467157	+	0.809140i
$969$	−20.5637			−0.660601
$970$	−26.0479			−0.836349
$971$	27.5479			0.884055			0.442027	−	0.897001i	$-0.354259\pi$
$971$	27.5479			0.884055			0.442027	+	0.897001i	$0.354259\pi$
$972$	0.386270	−	0.669040i	0.0123896	−	0.0214595i
$973$	37.7946	−	65.4621i	1.21164	−	2.09862i
$974$	39.5677			1.26783
$975$	−21.9335	+	37.9900i	−0.702435	+	1.21665i
$976$	−1.80945	−	3.13405i	−0.0579190	−	0.100319i
$977$	18.1344	+	31.4096i	0.580169	+	1.00488i	0.995459	+	0.0951934i	$0.0303470\pi$
$977$	18.1344	+	31.4096i	0.580169	+	1.00488i	−0.415289	+	0.909689i	$0.636320\pi$
$978$	10.4397	−	18.0820i	0.333824	−	0.578200i
$979$	−11.4857	+	19.8939i	−0.367086	+	0.635812i
$980$	−19.5549	−	33.8700i	−0.624657	−	1.08194i
$981$	13.4227			0.428553
$982$	2.42890	+	4.20698i	0.0775093	+	0.134250i
$983$	58.6858			1.87179			0.935893	−	0.352284i	$-0.114595\pi$
$983$	58.6858			1.87179			0.935893	+	0.352284i	$0.114595\pi$
$984$	3.76311	+	6.51789i	0.119963	+	0.207783i
$985$	−20.9483	+	36.2835i	−0.667467	+	1.15609i
$986$	5.63079	+	9.75282i	0.179321	+	0.310593i
$987$	−38.1699			−1.21496
$988$	−33.1888			−1.05588
$989$	−10.3298	+	17.8917i	−0.328468	+	0.568923i
$990$	2.39950	+	4.15606i	0.0762611	+	0.132088i
$991$	−9.00904			−0.286182			−0.143091	−	0.989710i	$-0.545704\pi$
$991$	−9.00904			−0.286182			−0.143091	+	0.989710i	$0.545704\pi$
$992$	−8.22218	+	14.2412i	−0.261054	+	0.452159i
$993$	4.44442	−	7.69796i	0.141039	−	0.244287i
$994$	27.6849	−	47.9517i	0.878112	−	1.52093i
$995$	9.71892	−	16.8337i	0.308110	−	0.533663i
$996$	10.1322			0.321051
$997$	3.66305	−	6.34459i	0.116010	−	0.200935i	−0.802173	−	0.597092i	$-0.796323\pi$
$997$	3.66305	−	6.34459i	0.116010	−	0.200935i	0.918183	+	0.396156i	$0.129656\pi$
$998$	17.1340			0.542369
$999$	0.339830	−	0.588602i	0.0107517	−	0.0186225i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.e.c.169.10	✓	28
157.144	even	3	inner	471.2.e.c.301.10	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.e.c.169.10	✓	28	1.1	even	1	trivial
471.2.e.c.301.10	yes	28	157.144	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.10791 q^{2} +(-0.500000 - 0.866025i) q^{3} -0.772541 q^{4} +(1.74720 + 3.02624i) q^{5} +(-0.553954 - 0.959476i) q^{6} -4.63545 q^{7} -3.07172 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+1.10791 q^{2} +(-0.500000 - 0.866025i) q^{3} -0.772541 q^{4} +(1.74720 + 3.02624i) q^{5} +(-0.553954 - 0.959476i) q^{6} -4.63545 q^{7} -3.07172 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.93574 + 3.35280i) q^{10} +(-0.619790 - 1.07351i) q^{11} +(0.386270 + 0.669040i) q^{12} +(-3.04174 + 5.26845i) q^{13} -5.13565 q^{14} +(1.74720 - 3.02624i) q^{15} -1.85810 q^{16} +(1.45597 + 2.52182i) q^{17} +(-0.553954 + 0.959476i) q^{18} +(-3.53092 - 6.11573i) q^{19} +(-1.34978 - 2.33789i) q^{20} +(2.31773 + 4.01442i) q^{21} +(-0.686670 - 1.18935i) q^{22} +3.72787 q^{23} +(1.53586 + 2.66019i) q^{24} +(-3.60542 + 6.24477i) q^{25} +(-3.36997 + 5.83696i) q^{26} +1.00000 q^{27} +3.58108 q^{28} +3.49070 q^{29} +(1.93574 - 3.35280i) q^{30} +(-2.01285 + 3.48637i) q^{31} +4.08484 q^{32} +(-0.619790 + 1.07351i) q^{33} +(1.61308 + 2.79394i) q^{34} +(-8.09906 - 14.0280i) q^{35} +(0.386270 - 0.669040i) q^{36} +(0.339830 - 0.588602i) q^{37} +(-3.91193 - 6.77566i) q^{38} +6.08349 q^{39} +(-5.36691 - 9.29576i) q^{40} +2.45016 q^{41} +(2.56783 + 4.44760i) q^{42} +(-2.77096 + 4.79944i) q^{43} +(0.478813 + 0.829328i) q^{44} -3.49440 q^{45} +4.13014 q^{46} +(-4.11718 + 7.13116i) q^{47} +(0.929049 + 1.60916i) q^{48} +14.4874 q^{49} +(-3.99447 + 6.91863i) q^{50} +(1.45597 - 2.52182i) q^{51} +(2.34987 - 4.07010i) q^{52} +(-1.58207 + 2.74023i) q^{53} +1.10791 q^{54} +(2.16579 - 3.75127i) q^{55} +14.2388 q^{56} +(-3.53092 + 6.11573i) q^{57} +3.86738 q^{58} -8.51964 q^{59} +(-1.34978 + 2.33789i) q^{60} +(0.973816 + 1.68670i) q^{61} +(-2.23006 + 3.86257i) q^{62} +(2.31773 - 4.01442i) q^{63} +8.24182 q^{64} -21.2581 q^{65} +(-0.686670 + 1.18935i) q^{66} +11.1078 q^{67} +(-1.12480 - 1.94821i) q^{68} +(-1.86394 - 3.22843i) q^{69} +(-8.97301 - 15.5417i) q^{70} +(-5.39073 + 9.33702i) q^{71} +(1.53586 - 2.66019i) q^{72} +(-5.48381 - 9.49823i) q^{73} +(0.376500 - 0.652117i) q^{74} +7.21084 q^{75} +(2.72778 + 4.72465i) q^{76} +(2.87301 + 4.97619i) q^{77} +6.73994 q^{78} +5.38180 q^{79} +(-3.24647 - 5.62305i) q^{80} +(-0.500000 - 0.866025i) q^{81} +2.71456 q^{82} +(6.55772 - 11.3583i) q^{83} +(-1.79054 - 3.10130i) q^{84} +(-5.08775 + 8.81225i) q^{85} +(-3.06997 + 5.31734i) q^{86} +(-1.74535 - 3.02304i) q^{87} +(1.90382 + 3.29751i) q^{88} +(-9.26584 - 16.0489i) q^{89} -3.87147 q^{90} +(14.0999 - 24.4217i) q^{91} -2.87993 q^{92} +4.02571 q^{93} +(-4.56145 + 7.90067i) q^{94} +(12.3384 - 21.3708i) q^{95} +(-2.04242 - 3.53757i) q^{96} +(-3.36409 + 5.82677i) q^{97} +16.0507 q^{98} +1.23958 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9}+O(q^{10}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9} - q^{10} + 2 q^{11} - 13 q^{12} - 14 q^{14} - 2 q^{15} + 14 q^{16} + 3 q^{17} - q^{18} - 11 q^{19} + q^{20} - 2 q^{21} - 2 q^{22} - 6 q^{23} - 20 q^{25} + 12 q^{26} + 28 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 14 q^{31} + 12 q^{32} + 2 q^{33} - 15 q^{34} - 13 q^{35} - 13 q^{36} - q^{37} + 18 q^{38} - 8 q^{40} + 16 q^{41} + 7 q^{42} - 16 q^{43} + 12 q^{44} + 4 q^{45} + 16 q^{46} - 29 q^{47} - 7 q^{48} + 44 q^{49} - 29 q^{50} + 3 q^{51} + 27 q^{52} + 6 q^{53} + 2 q^{54} - 29 q^{55} - 26 q^{56} - 11 q^{57} + 62 q^{58} - 8 q^{59} + q^{60} + 14 q^{61} + 52 q^{62} - 2 q^{63} + 16 q^{64} - 52 q^{65} - 2 q^{66} + 36 q^{67} + 6 q^{68} + 3 q^{69} - 37 q^{70} - 27 q^{71} - 10 q^{73} - 5 q^{74} + 40 q^{75} - 43 q^{76} + 11 q^{77} - 24 q^{78} - 16 q^{79} - 26 q^{80} - 14 q^{81} - 24 q^{82} + 12 q^{83} - q^{84} + 12 q^{85} - 56 q^{86} + 5 q^{87} + 47 q^{88} - 13 q^{89} + 2 q^{90} + 13 q^{91} - 50 q^{92} + 28 q^{93} - 40 q^{94} - 7 q^{95} - 6 q^{96} + 6 q^{97} - 46 q^{98} - 4 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9 - q^10 + 2 * q^11 - 13 * q^12 - 14 * q^14 - 2 * q^15 + 14 * q^16 + 3 * q^17 - q^18 - 11 * q^19 + q^20 - 2 * q^21 - 2 * q^22 - 6 * q^23 - 20 * q^25 + 12 * q^26 + 28 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 14 * q^31 + 12 * q^32 + 2 * q^33 - 15 * q^34 - 13 * q^35 - 13 * q^36 - q^37 + 18 * q^38 - 8 * q^40 + 16 * q^41 + 7 * q^42 - 16 * q^43 + 12 * q^44 + 4 * q^45 + 16 * q^46 - 29 * q^47 - 7 * q^48 + 44 * q^49 - 29 * q^50 + 3 * q^51 + 27 * q^52 + 6 * q^53 + 2 * q^54 - 29 * q^55 - 26 * q^56 - 11 * q^57 + 62 * q^58 - 8 * q^59 + q^60 + 14 * q^61 + 52 * q^62 - 2 * q^63 + 16 * q^64 - 52 * q^65 - 2 * q^66 + 36 * q^67 + 6 * q^68 + 3 * q^69 - 37 * q^70 - 27 * q^71 - 10 * q^73 - 5 * q^74 + 40 * q^75 - 43 * q^76 + 11 * q^77 - 24 * q^78 - 16 * q^79 - 26 * q^80 - 14 * q^81 - 24 * q^82 + 12 * q^83 - q^84 + 12 * q^85 - 56 * q^86 + 5 * q^87 + 47 * q^88 - 13 * q^89 + 2 * q^90 + 13 * q^91 - 50 * q^92 + 28 * q^93 - 40 * q^94 - 7 * q^95 - 6 * q^96 + 6 * q^97 - 46 * q^98 - 4 * q^99

Introduction

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