LMFDB - Embedded newform 731.2.e.a.307.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(307,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("731.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			307.16
Character	$\chi$	$=$	731.307
Dual form			731.2.e.a.681.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.220069 q^{2} +(1.00430 - 1.73949i) q^{3} -1.95157 q^{4} +(-1.15229 + 1.99582i) q^{5} +(0.221015 - 0.382808i) q^{6} +(-1.47386 - 2.55280i) q^{7} -0.869618 q^{8} +(-0.517225 - 0.895859i) q^{9} +O(q^{10})$	\(q+0.220069 q^{2} +(1.00430 - 1.73949i) q^{3} -1.95157 q^{4} +(-1.15229 + 1.99582i) q^{5} +(0.221015 - 0.382808i) q^{6} +(-1.47386 - 2.55280i) q^{7} -0.869618 q^{8} +(-0.517225 - 0.895859i) q^{9} +(-0.253582 + 0.439217i) q^{10} -1.64230 q^{11} +(-1.95996 + 3.39474i) q^{12} +(0.208462 + 0.361068i) q^{13} +(-0.324350 - 0.561791i) q^{14} +(2.31447 + 4.00879i) q^{15} +3.71176 q^{16} +(0.500000 + 0.866025i) q^{17} +(-0.113825 - 0.197151i) q^{18} +(-3.05184 + 5.28595i) q^{19} +(2.24877 - 3.89498i) q^{20} -5.92076 q^{21} -0.361419 q^{22} +(-4.31162 + 7.46794i) q^{23} +(-0.873354 + 1.51269i) q^{24} +(-0.155524 - 0.269375i) q^{25} +(0.0458761 + 0.0794597i) q^{26} +3.94799 q^{27} +(2.87634 + 4.98196i) q^{28} +(-2.51609 - 4.35800i) q^{29} +(0.509344 + 0.882209i) q^{30} +(-4.45225 + 7.71152i) q^{31} +2.55608 q^{32} +(-1.64935 + 2.85676i) q^{33} +(0.110034 + 0.190585i) q^{34} +6.79322 q^{35} +(1.00940 + 1.74833i) q^{36} +(-0.989017 + 1.71303i) q^{37} +(-0.671616 + 1.16327i) q^{38} +0.837433 q^{39} +(1.00205 - 1.73560i) q^{40} -10.7766 q^{41} -1.30298 q^{42} +(-0.694915 - 6.52051i) q^{43} +3.20506 q^{44} +2.38396 q^{45} +(-0.948854 + 1.64346i) q^{46} -9.44409 q^{47} +(3.72771 - 6.45659i) q^{48} +(-0.844515 + 1.46274i) q^{49} +(-0.0342260 - 0.0592812i) q^{50} +2.00859 q^{51} +(-0.406829 - 0.704648i) q^{52} +(6.15840 - 10.6667i) q^{53} +0.868831 q^{54} +(1.89239 - 3.27772i) q^{55} +(1.28169 + 2.21996i) q^{56} +(6.12991 + 10.6173i) q^{57} +(-0.553714 - 0.959060i) q^{58} -0.141509 q^{59} +(-4.51686 - 7.82343i) q^{60} +(3.34872 + 5.80015i) q^{61} +(-0.979802 + 1.69707i) q^{62} +(-1.52463 + 2.64074i) q^{63} -6.86101 q^{64} -0.960833 q^{65} +(-0.362972 + 0.628685i) q^{66} +(-2.65555 + 4.59954i) q^{67} +(-0.975785 - 1.69011i) q^{68} +(8.66029 + 15.0001i) q^{69} +1.49498 q^{70} +(-5.73972 - 9.94149i) q^{71} +(0.449788 + 0.779055i) q^{72} +(7.34581 + 12.7233i) q^{73} +(-0.217652 + 0.376984i) q^{74} -0.624769 q^{75} +(5.95588 - 10.3159i) q^{76} +(2.42051 + 4.19245i) q^{77} +0.184293 q^{78} +(0.649518 + 1.12500i) q^{79} +(-4.27701 + 7.40800i) q^{80} +(5.51663 - 9.55509i) q^{81} -2.37160 q^{82} +(8.30770 - 14.3894i) q^{83} +11.5548 q^{84} -2.30457 q^{85} +(-0.152929 - 1.43496i) q^{86} -10.1076 q^{87} +1.42817 q^{88} +(1.61108 - 2.79048i) q^{89} +0.524636 q^{90} +(0.614488 - 1.06432i) q^{91} +(8.41443 - 14.5742i) q^{92} +(8.94276 + 15.4893i) q^{93} -2.07835 q^{94} +(-7.03319 - 12.1818i) q^{95} +(2.56706 - 4.44628i) q^{96} -2.99182 q^{97} +(-0.185852 + 0.321904i) q^{98} +(0.849436 + 1.47127i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9}+O(q^{10}) $ 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9} + 4 q^{10} + 16 q^{11} + 12 q^{12} + 2 q^{13} - 11 q^{14} + 7 q^{15} + 30 q^{16} + 29 q^{17} + 8 q^{18} + 8 q^{19} - 33 q^{20} - 26 q^{21} - 22 q^{22} - 5 q^{23} + 12 q^{24} - 36 q^{25} - 12 q^{27} + 15 q^{28} + 2 q^{29} + 11 q^{30} + 3 q^{31} - 40 q^{32} + 17 q^{33} - 3 q^{34} + 38 q^{35} - 7 q^{36} + 2 q^{37} + q^{38} - 54 q^{39} + 5 q^{40} + 14 q^{41} - 112 q^{42} + 31 q^{43} - 24 q^{44} - 46 q^{45} - 13 q^{46} - 28 q^{47} - 28 q^{49} - 13 q^{50} + 6 q^{51} + 85 q^{52} - 10 q^{53} + 34 q^{54} + 36 q^{55} - 54 q^{56} - 23 q^{57} + 3 q^{58} + 12 q^{59} + 2 q^{60} - q^{61} - q^{62} - 14 q^{63} + 28 q^{64} + 80 q^{65} - 74 q^{66} + 11 q^{67} + 27 q^{68} - 11 q^{69} + 2 q^{70} + 16 q^{71} + 21 q^{72} + 14 q^{73} + 21 q^{74} - 54 q^{75} + 44 q^{76} + 25 q^{77} + 88 q^{78} - 4 q^{79} - 112 q^{80} + 11 q^{81} - 176 q^{82} - 3 q^{83} + 100 q^{84} - 2 q^{85} + 44 q^{86} + 8 q^{87} - 106 q^{88} + 82 q^{89} + 54 q^{90} - 15 q^{91} + 42 q^{92} + 88 q^{94} + 29 q^{95} + 20 q^{96} + 20 q^{97} + 44 q^{98} - 54 q^{99}+O(q^{100}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9 + 4 * q^10 + 16 * q^11 + 12 * q^12 + 2 * q^13 - 11 * q^14 + 7 * q^15 + 30 * q^16 + 29 * q^17 + 8 * q^18 + 8 * q^19 - 33 * q^20 - 26 * q^21 - 22 * q^22 - 5 * q^23 + 12 * q^24 - 36 * q^25 - 12 * q^27 + 15 * q^28 + 2 * q^29 + 11 * q^30 + 3 * q^31 - 40 * q^32 + 17 * q^33 - 3 * q^34 + 38 * q^35 - 7 * q^36 + 2 * q^37 + q^38 - 54 * q^39 + 5 * q^40 + 14 * q^41 - 112 * q^42 + 31 * q^43 - 24 * q^44 - 46 * q^45 - 13 * q^46 - 28 * q^47 - 28 * q^49 - 13 * q^50 + 6 * q^51 + 85 * q^52 - 10 * q^53 + 34 * q^54 + 36 * q^55 - 54 * q^56 - 23 * q^57 + 3 * q^58 + 12 * q^59 + 2 * q^60 - q^61 - q^62 - 14 * q^63 + 28 * q^64 + 80 * q^65 - 74 * q^66 + 11 * q^67 + 27 * q^68 - 11 * q^69 + 2 * q^70 + 16 * q^71 + 21 * q^72 + 14 * q^73 + 21 * q^74 - 54 * q^75 + 44 * q^76 + 25 * q^77 + 88 * q^78 - 4 * q^79 - 112 * q^80 + 11 * q^81 - 176 * q^82 - 3 * q^83 + 100 * q^84 - 2 * q^85 + 44 * q^86 + 8 * q^87 - 106 * q^88 + 82 * q^89 + 54 * q^90 - 15 * q^91 + 42 * q^92 + 88 * q^94 + 29 * q^95 + 20 * q^96 + 20 * q^97 + 44 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.220069			0.155612			0.0778061	−	0.996969i	$-0.475208\pi$
$2$	0.220069			0.155612			0.0778061	+	0.996969i	$0.475208\pi$
$3$	1.00430	−	1.73949i	0.579831	−	1.00430i	−0.415667	−	0.909517i	$-0.636452\pi$
$3$	1.00430	−	1.73949i	0.579831	−	1.00430i	0.995498	−	0.0947801i	$-0.0302148\pi$
$4$	−1.95157			−0.975785
$5$	−1.15229	+	1.99582i	−0.515318	+	0.892557i	0.484524	+	0.874778i	$0.338993\pi$
$5$	−1.15229	+	1.99582i	−0.515318	+	0.892557i	−0.999842	+	0.0177787i	$0.994341\pi$
$6$	0.221015	−	0.382808i	0.0902288	−	0.156281i
$7$	−1.47386	−	2.55280i	−0.557066	−	0.964867i	−0.997740	−	0.0671992i	$-0.978594\pi$
$7$	−1.47386	−	2.55280i	−0.557066	−	0.964867i	0.440674	−	0.897667i	$-0.354740\pi$
$8$	−0.869618			−0.307456
$9$	−0.517225	−	0.895859i	−0.172408	−	0.298620i
$10$	−0.253582	+	0.439217i	−0.0801897	+	0.138893i
$11$	−1.64230			−0.495171			−0.247586	−	0.968866i	$-0.579637\pi$
$11$	−1.64230			−0.495171			−0.247586	+	0.968866i	$0.579637\pi$
$12$	−1.95996	+	3.39474i	−0.565790	+	0.979978i
$13$	0.208462	+	0.361068i	0.0578171	+	0.100142i	0.893485	−	0.449093i	$-0.148253\pi$
$13$	0.208462	+	0.361068i	0.0578171	+	0.100142i	−0.835668	+	0.549235i	$0.814919\pi$
$14$	−0.324350	−	0.561791i	−0.0866863	−	0.150145i
$15$	2.31447	+	4.00879i	0.597595	+	1.03506i
$16$	3.71176			0.927941
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i
$18$	−0.113825	−	0.197151i	−0.0268288	−	0.0464689i
$19$	−3.05184	+	5.28595i	−0.700141	+	1.21268i	0.268276	+	0.963342i	$0.413546\pi$
$19$	−3.05184	+	5.28595i	−0.700141	+	1.21268i	−0.968417	+	0.249337i	$0.919787\pi$
$20$	2.24877	−	3.89498i	0.502839	−	0.870943i
$21$	−5.92076			−1.29202
$22$	−0.361419			−0.0770547
$23$	−4.31162	+	7.46794i	−0.899035	+	1.55717i	−0.0703047	+	0.997526i	$0.522397\pi$
$23$	−4.31162	+	7.46794i	−0.899035	+	1.55717i	−0.828730	+	0.559648i	$0.810936\pi$
$24$	−0.873354	+	1.51269i	−0.178273	+	0.308777i
$25$	−0.155524	−	0.269375i	−0.0311048	−	0.0538751i
$26$	0.0458761	+	0.0794597i	0.00899704	+	0.0155833i
$27$	3.94799			0.759792
$28$	2.87634	+	4.98196i	0.543577	+	0.941502i
$29$	−2.51609	−	4.35800i	−0.467226	−	0.809260i	0.532072	−	0.846699i	$-0.321413\pi$
$29$	−2.51609	−	4.35800i	−0.467226	−	0.809260i	−0.999299	+	0.0374389i	$0.988080\pi$
$30$	0.509344	+	0.882209i	0.0929930	+	0.161069i
$31$	−4.45225	+	7.71152i	−0.799648	+	1.38503i	0.120198	+	0.992750i	$0.461647\pi$
$31$	−4.45225	+	7.71152i	−0.799648	+	1.38503i	−0.919846	+	0.392280i	$0.871686\pi$
$32$	2.55608			0.451855
$33$	−1.64935	+	2.85676i	−0.287116	+	0.497299i
$34$	0.110034	+	0.190585i	0.0188708	+	0.0326851i
$35$	6.79322			1.14826
$36$	1.00940	+	1.74833i	0.168233	+	0.291389i
$37$	−0.989017	+	1.71303i	−0.162593	+	0.281620i	−0.935798	−	0.352537i	$-0.885319\pi$
$37$	−0.989017	+	1.71303i	−0.162593	+	0.281620i	0.773205	+	0.634157i	$0.218653\pi$
$38$	−0.671616	+	1.16327i	−0.108950	+	0.188708i
$39$	0.837433			0.134097
$40$	1.00205	−	1.73560i	0.158438	−	0.274422i
$41$	−10.7766			−1.68302			−0.841512	−	0.540238i	$-0.818334\pi$
$41$	−10.7766			−1.68302			−0.841512	+	0.540238i	$0.818334\pi$
$42$	−1.30298			−0.201054
$43$	−0.694915	−	6.52051i	−0.105974	−	0.994369i
$43$	−0.694915	−	6.52051i	−0.105974	−	0.994369i
$44$	3.20506			0.483180
$45$	2.38396			0.355380
$46$	−0.948854	+	1.64346i	−0.139901	+	0.242315i
$47$	−9.44409			−1.37756			−0.688781	−	0.724969i	$-0.741854\pi$
$47$	−9.44409			−1.37756			−0.688781	+	0.724969i	$0.741854\pi$
$48$	3.72771	−	6.45659i	0.538049	−	0.931928i
$49$	−0.844515	+	1.46274i	−0.120645	+	0.208963i
$50$	−0.0342260	−	0.0592812i	−0.00484029	−	0.00838362i
$51$	2.00859			0.281259
$52$	−0.406829	−	0.704648i	−0.0564170	−	0.0977172i
$53$	6.15840	−	10.6667i	0.845921	−	1.46518i	−0.0388975	−	0.999243i	$-0.512385\pi$
$53$	6.15840	−	10.6667i	0.845921	−	1.46518i	0.884819	−	0.465935i	$-0.154282\pi$
$54$	0.868831			0.118233
$55$	1.89239	−	3.27772i	0.255170	−	0.441968i
$56$	1.28169	+	2.21996i	0.171273	+	0.296654i
$57$	6.12991	+	10.6173i	0.811927	+	1.40630i
$58$	−0.553714	−	0.959060i	−0.0727061	−	0.125931i
$59$	−0.141509			−0.0184229			−0.00921144	−	0.999958i	$-0.502932\pi$
$59$	−0.141509			−0.0184229			−0.00921144	+	0.999958i	$0.502932\pi$
$60$	−4.51686	−	7.82343i	−0.583124	−	1.01000i
$61$	3.34872	+	5.80015i	0.428759	+	0.742633i	0.996763	−	0.0803928i	$-0.0256175\pi$
$61$	3.34872	+	5.80015i	0.428759	+	0.742633i	−0.568004	+	0.823026i	$0.692284\pi$
$62$	−0.979802	+	1.69707i	−0.124435	+	0.215528i
$63$	−1.52463	+	2.64074i	−0.192086	+	0.332702i
$64$	−6.86101			−0.857627
$65$	−0.960833			−0.119177
$66$	−0.362972	+	0.628685i	−0.0446787	+	0.0773858i
$67$	−2.65555	+	4.59954i	−0.324427	+	0.561923i	−0.981396	−	0.191994i	$-0.938505\pi$
$67$	−2.65555	+	4.59954i	−0.324427	+	0.561923i	0.656970	+	0.753917i	$0.271838\pi$
$68$	−0.975785	−	1.69011i	−0.118331	−	0.204956i
$69$	8.66029	+	15.0001i	1.04258	+	1.80580i
$70$	1.49498			0.178684
$71$	−5.73972	−	9.94149i	−0.681180	−	1.17984i	−0.974621	−	0.223861i	$-0.928134\pi$
$71$	−5.73972	−	9.94149i	−0.681180	−	1.17984i	0.293442	−	0.955977i	$-0.405199\pi$
$72$	0.449788	+	0.779055i	0.0530080	+	0.0918125i
$73$	7.34581	+	12.7233i	0.859762	+	1.48915i	0.872156	+	0.489229i	$0.162722\pi$
$73$	7.34581	+	12.7233i	0.859762	+	1.48915i	−0.0123933	+	0.999923i	$0.503945\pi$
$74$	−0.217652	+	0.376984i	−0.0253015	+	0.0438235i
$75$	−0.624769			−0.0721421
$76$	5.95588	−	10.3159i	0.683187	−	1.18331i
$77$	2.42051	+	4.19245i	0.275843	+	0.477774i
$78$	0.184293			0.0208671
$79$	0.649518	+	1.12500i	0.0730765	+	0.126572i	0.900248	−	0.435377i	$-0.143385\pi$
$79$	0.649518	+	1.12500i	0.0730765	+	0.126572i	−0.827172	+	0.561949i	$0.810052\pi$
$80$	−4.27701	+	7.40800i	−0.478184	+	0.828240i
$81$	5.51663	−	9.55509i	0.612959	−	1.06168i
$82$	−2.37160			−0.261899
$83$	8.30770	−	14.3894i	0.911888	−	1.57944i	0.100494	−	0.994938i	$-0.467958\pi$
$83$	8.30770	−	14.3894i	0.911888	−	1.57944i	0.811394	−	0.584499i	$-0.198709\pi$
$84$	11.5548			1.26073
$85$	−2.30457			−0.249966
$86$	−0.152929	−	1.43496i	−0.0164908	−	0.154736i
$87$	−10.1076			−1.08365
$88$	1.42817			0.152243
$89$	1.61108	−	2.79048i	0.170775	−	0.295790i	−0.767916	−	0.640550i	$-0.778706\pi$
$89$	1.61108	−	2.79048i	0.170775	−	0.295790i	0.938691	+	0.344760i	$0.112040\pi$
$90$	0.524636			0.0553015
$91$	0.614488	−	1.06432i	0.0644159	−	0.111572i
$92$	8.41443	−	14.5742i	0.877265	−	1.51947i
$93$	8.94276	+	15.4893i	0.927321	+	1.60617i
$94$	−2.07835			−0.214366
$95$	−7.03319	−	12.1818i	−0.721590	−	1.24983i
$96$	2.56706	−	4.44628i	0.262000	−	0.453797i
$97$	−2.99182			−0.303773			−0.151887	−	0.988398i	$-0.548535\pi$
$97$	−2.99182			−0.303773			−0.151887	+	0.988398i	$0.548535\pi$
$98$	−0.185852	+	0.321904i	−0.0187738	+	0.0325173i
$99$	0.849436	+	1.47127i	0.0853716	+	0.147868i
$100$	0.303516	+	0.525705i	0.0303516	+	0.0525705i
$101$	5.62081	+	9.73553i	0.559291	+	0.968721i	0.997556	+	0.0698750i	$0.0222600\pi$
$101$	5.62081	+	9.73553i	0.559291	+	0.968721i	−0.438264	+	0.898846i	$0.644407\pi$
$102$	0.442029			0.0437674
$103$	−0.547585	−	0.948445i	−0.0539552	−	0.0934531i	0.837786	−	0.545998i	$-0.183849\pi$
$103$	−0.547585	−	0.948445i	−0.0539552	−	0.0934531i	−0.891742	+	0.452545i	$0.850516\pi$
$104$	−0.181283	−	0.313991i	−0.0177762	−	0.0307893i
$105$	6.82241	−	11.8168i	0.665799	−	1.15320i
$106$	1.35527	−	2.34740i	0.131636	−	0.228000i
$107$	−11.5557			−1.11713			−0.558565	−	0.829461i	$-0.688648\pi$
$107$	−11.5557			−1.11713			−0.558565	+	0.829461i	$0.688648\pi$
$108$	−7.70478			−0.741393
$109$	2.73925	−	4.74452i	0.262372	−	0.454442i	−0.704499	−	0.709704i	$-0.748828\pi$
$109$	2.73925	−	4.74452i	0.262372	−	0.454442i	0.966872	+	0.255262i	$0.0821618\pi$
$110$	0.416457	−	0.721325i	0.0397076	−	0.0687757i
$111$	1.98653	+	3.44078i	0.188553	+	0.326584i
$112$	−5.47061	−	9.47538i	−0.516924	−	0.895339i
$113$	12.5300			1.17872			0.589360	−	0.807870i	$-0.299380\pi$
$113$	12.5300			1.17872			0.589360	+	0.807870i	$0.299380\pi$
$114$	1.34900	+	2.33654i	0.126346	+	0.218837i
$115$	−9.93643	−	17.2104i	−0.926577	−	1.60488i
$116$	4.91033	+	8.50494i	0.455912	+	0.789664i
$117$	0.215644	−	0.373506i	0.0199363	−	0.0345306i
$118$	−0.0311417			−0.00286682
$119$	1.47386	−	2.55280i	0.135108	−	0.234015i
$120$	−2.01271	−	3.48611i	−0.183734	−	0.318237i
$121$	−8.30286			−0.754806
$122$	0.736949	+	1.27643i	0.0667202	+	0.115563i
$123$	−10.8229	+	18.7459i	−0.975870	+	1.69026i
$124$	8.68887	−	15.0496i	0.780284	−	1.35149i
$125$	−10.8060			−0.966520
$126$	−0.335524	+	0.581145i	−0.0298909	+	0.0517725i
$127$	−12.1778			−1.08061			−0.540304	−	0.841470i	$-0.681691\pi$
$127$	−12.1778			−1.08061			−0.540304	+	0.841470i	$0.681691\pi$
$128$	−6.62205			−0.585312
$129$	−12.0403	−	5.33973i	−1.06009	−	0.470137i
$130$	−0.211450			−0.0185453
$131$	1.56016			0.136312			0.0681561	−	0.997675i	$-0.478288\pi$
$131$	1.56016			0.136312			0.0681561	+	0.997675i	$0.478288\pi$
$132$	3.21883	−	5.57517i	0.280163	−	0.485257i
$133$	17.9919			1.56010
$134$	−0.584403	+	1.01222i	−0.0504847	+	0.0874421i
$135$	−4.54922	+	7.87947i	−0.391534	+	0.678157i
$136$	−0.434809	−	0.753111i	−0.0372846	−	0.0645787i
$137$	−9.83288			−0.840080			−0.420040	−	0.907506i	$-0.637984\pi$
$137$	−9.83288			−0.840080			−0.420040	+	0.907506i	$0.637984\pi$
$138$	1.90586	+	3.30105i	0.162238	+	0.281004i
$139$	−3.76437	+	6.52007i	−0.319289	+	0.553025i	−0.980340	−	0.197316i	$-0.936778\pi$
$139$	−3.76437	+	6.52007i	−0.319289	+	0.553025i	0.661051	+	0.750341i	$0.270111\pi$
$140$	−13.2574			−1.12046
$141$	−9.48467	+	16.4279i	−0.798753	+	1.38348i
$142$	−1.26313	−	2.18781i	−0.106000	−	0.183597i
$143$	−0.342357	−	0.592980i	−0.0286293	−	0.0495875i
$144$	−1.91982	−	3.32522i	−0.159985	−	0.277102i
$145$	11.5970			0.963080
$146$	1.61658	+	2.80001i	0.133790	+	0.231730i
$147$	1.69629	+	2.93806i	0.139908	+	0.242327i
$148$	1.93013	−	3.34309i	0.158656	−	0.274800i
$149$	−9.63327	+	16.6853i	−0.789188	+	1.36691i	0.137277	+	0.990533i	$0.456165\pi$
$149$	−9.63327	+	16.6853i	−0.789188	+	1.36691i	−0.926465	+	0.376381i	$0.877168\pi$
$150$	−0.137492			−0.0112262
$151$	−1.93280			−0.157289			−0.0786447	−	0.996903i	$-0.525059\pi$
$151$	−1.93280			−0.157289			−0.0786447	+	0.996903i	$0.525059\pi$
$152$	2.65394	−	4.59675i	0.215263	−	0.372846i
$153$	0.517225	−	0.895859i	0.0418151	−	0.0724259i
$154$	0.532680	+	0.922628i	0.0429245	+	0.0743475i
$155$	−10.2605	−	17.7718i	−0.824145	−	1.42746i
$156$	−1.63431			−0.130849
$157$	−10.4277	−	18.0612i	−0.832217	−	1.44144i	−0.896276	−	0.443496i	$-0.853738\pi$
$157$	−10.4277	−	18.0612i	−0.832217	−	1.44144i	0.0640590	−	0.997946i	$-0.479595\pi$
$158$	0.142939	+	0.247577i	0.0113716	+	0.0196962i
$159$	−12.3697	−	21.4250i	−0.980983	−	1.69911i
$160$	−2.94533	+	5.10147i	−0.232849	+	0.403306i
$161$	25.4189			2.00329
$162$	1.21404	−	2.10278i	0.0953839	−	0.165210i
$163$	12.3348	+	21.3645i	0.966134	+	1.67339i	0.706536	+	0.707677i	$0.250257\pi$
$163$	12.3348	+	21.3645i	0.966134	+	1.67339i	0.259598	+	0.965717i	$0.416410\pi$
$164$	21.0313			1.64227
$165$	−3.80105	−	6.58362i	−0.295912	−	0.512534i
$166$	1.82827	−	3.16665i	0.141901	−	0.245780i
$167$	−1.15299	+	1.99704i	−0.0892213	+	0.154536i	−0.907182	−	0.420738i	$-0.861771\pi$
$167$	−1.15299	+	1.99704i	−0.0892213	+	0.154536i	0.817961	+	0.575274i	$0.195104\pi$
$168$	5.14880			0.397239
$169$	6.41309	−	11.1078i	0.493314	−	0.854446i
$170$	−0.507165			−0.0388977
$171$	6.31395			0.482840
$172$	1.35618	+	12.7252i	0.103407	+	0.970290i
$173$	−7.88055			−0.599147			−0.299574	−	0.954073i	$-0.596844\pi$
$173$	−7.88055			−0.599147			−0.299574	+	0.954073i	$0.596844\pi$
$174$	−2.22437			−0.168629
$175$	−0.458441	+	0.794042i	−0.0346549	+	0.0600240i
$176$	−6.09582			−0.459490
$177$	−0.142117	+	0.246154i	−0.0106822	+	0.0185020i
$178$	0.354550	−	0.614098i	0.0265746	−	0.0460286i
$179$	−10.1491	−	17.5788i	−0.758582	−	1.31390i	−0.943574	−	0.331162i	$-0.892559\pi$
$179$	−10.1491	−	17.5788i	−0.758582	−	1.31390i	0.184992	−	0.982740i	$-0.440774\pi$
$180$	−4.65247			−0.346774
$181$	−4.75480	−	8.23556i	−0.353422	−	0.612144i	0.633425	−	0.773804i	$-0.281649\pi$
$181$	−4.75480	−	8.23556i	−0.353422	−	0.612144i	−0.986847	+	0.161660i	$0.948315\pi$
$182$	0.135230	−	0.234225i	0.0100239	−	0.0173619i
$183$	13.4524			0.994432
$184$	3.74946	−	6.49426i	0.276414	−	0.478763i
$185$	−2.27926	−	3.94779i	−0.167574	−	0.290247i
$186$	1.96802	+	3.40872i	0.144303	+	0.249939i
$187$	−0.821148	−	1.42227i	−0.0600483	−	0.104007i
$188$	18.4308			1.34420
$189$	−5.81878	−	10.0784i	−0.423254	−	0.733098i
$190$	−1.54779	−	2.68084i	−0.112288	−	0.194489i
$191$	1.67133	−	2.89483i	0.120933	−	0.209463i	−0.799203	−	0.601062i	$-0.794745\pi$
$191$	1.67133	−	2.89483i	0.120933	−	0.209463i	0.920136	+	0.391599i	$0.128078\pi$
$192$	−6.89049	+	11.9347i	−0.497279	+	0.861312i
$193$	18.4289			1.32654			0.663270	−	0.748380i	$-0.269168\pi$
$193$	18.4289			1.32654			0.663270	+	0.748380i	$0.269168\pi$
$194$	−0.658406			−0.0472708
$195$	−0.964962	+	1.67136i	−0.0691023	+	0.119689i
$196$	1.64813	−	2.85465i	0.117724	−	0.203903i
$197$	10.1812	+	17.6343i	0.725378	+	1.25639i	0.958818	+	0.284020i	$0.0916683\pi$
$197$	10.1812	+	17.6343i	0.725378	+	1.25639i	−0.233441	+	0.972371i	$0.574998\pi$
$198$	0.186935	+	0.323780i	0.0132849	+	0.0230101i
$199$	−10.6168			−0.752605			−0.376302	−	0.926497i	$-0.622805\pi$
$199$	−10.6168			−0.752605			−0.376302	+	0.926497i	$0.622805\pi$
$200$	0.135246	+	0.234254i	0.00956337	+	0.0165642i
$201$	5.33391	+	9.23861i	0.376225	+	0.651641i
$202$	1.23697	+	2.14249i	0.0870326	+	0.150745i
$203$	−7.41672	+	12.8461i	−0.520552	+	0.901622i
$204$	−3.91991			−0.274449
$205$	12.4177	−	21.5082i	0.867292	−	1.50219i
$206$	−0.120506	−	0.208723i	−0.00839609	−	0.0145424i
$207$	8.92030			0.620004
$208$	0.773763	+	1.34020i	0.0536508	+	0.0929260i
$209$	5.01203	−	8.68109i	0.346690	−	0.600484i
$210$	1.50140	−	2.60050i	0.103607	−	0.179452i
$211$	−4.25702			−0.293065			−0.146533	−	0.989206i	$-0.546811\pi$
$211$	−4.25702			−0.293065			−0.146533	+	0.989206i	$0.546811\pi$
$212$	−12.0185	+	20.8167i	−0.825437	+	1.42970i
$213$	−23.0575			−1.57988
$214$	−2.54305			−0.173839
$215$	13.8145	+	6.12657i	0.942141	+	0.417829i
$216$	−3.43324			−0.233603
$217$	26.2479			1.78183
$218$	0.602823	−	1.04412i	0.0408284	−	0.0707168i
$219$	29.5095			1.99407
$220$	−3.69314	+	6.39671i	−0.248991	+	0.431266i
$221$	−0.208462	+	0.361068i	−0.0140227	+	0.0242880i
$222$	0.437174	+	0.757208i	0.0293412	+	0.0508205i
$223$	14.4824			0.969812			0.484906	−	0.874566i	$-0.338854\pi$
$223$	14.4824			0.969812			0.484906	+	0.874566i	$0.338854\pi$
$224$	−3.76730	−	6.52515i	−0.251713	−	0.435980i
$225$	−0.160882	+	0.278655i	−0.0107254	+	0.0185770i
$226$	2.75746			0.183423
$227$	−12.3928	+	21.4649i	−0.822537	+	1.42468i	0.0812505	+	0.996694i	$0.474109\pi$
$227$	−12.3928	+	21.4649i	−0.822537	+	1.42468i	−0.903787	+	0.427982i	$0.859225\pi$
$228$	−11.9630	−	20.7204i	−0.792266	−	1.37224i
$229$	14.0392	+	24.3166i	0.927738	+	1.60689i	0.787098	+	0.616828i	$0.211583\pi$
$229$	14.0392	+	24.3166i	0.927738	+	1.60689i	0.140640	+	0.990061i	$0.455084\pi$
$230$	−2.18670	−	3.78748i	−0.144187	−	0.249739i
$231$	9.72365			0.639769
$232$	2.18804	+	3.78979i	0.143652	+	0.248812i
$233$	5.30708	+	9.19214i	0.347679	+	0.602197i	0.985837	−	0.167708i	$-0.0536367\pi$
$233$	5.30708	+	9.19214i	0.347679	+	0.602197i	−0.638158	+	0.769905i	$0.720303\pi$
$234$	0.0474565	−	0.0821971i	0.00310233	−	0.00537339i
$235$	10.8823	−	18.8487i	0.709882	−	1.22955i
$236$	0.276164			0.0179768
$237$	2.60924			0.169488
$238$	0.324350	−	0.561791i	0.0210245	−	0.0364155i
$239$	6.03257	−	10.4487i	0.390214	−	0.675871i	−0.602263	−	0.798298i	$-0.705734\pi$
$239$	6.03257	−	10.4487i	0.390214	−	0.675871i	0.992478	+	0.122427i	$0.0390676\pi$
$240$	8.59078	+	14.8797i	0.554532	+	0.960478i
$241$	10.5287	+	18.2362i	0.678211	+	1.17470i	0.975519	+	0.219915i	$0.0705779\pi$
$241$	10.5287	+	18.2362i	0.678211	+	1.17470i	−0.297308	+	0.954782i	$0.596089\pi$
$242$	−1.82720			−0.117457
$243$	−5.15868	−	8.93510i	−0.330930	−	0.573187i
$244$	−6.53526	−	11.3194i	−0.418377	−	0.724650i
$245$	−1.94625	−	3.37100i	−0.124341	−	0.215365i
$246$	−2.38179	+	4.12538i	−0.151857	+	0.263025i
$247$	−2.54478			−0.161920
$248$	3.87175	−	6.70608i	0.245857	−	0.425836i
$249$	−16.6868	−	28.9024i	−1.05748	−	1.83161i
$250$	−2.37807			−0.150402
$251$	−1.82652	−	3.16362i	−0.115289	−	0.199686i	0.802606	−	0.596509i	$-0.203446\pi$
$251$	−1.82652	−	3.16362i	−0.115289	−	0.199686i	−0.917895	+	0.396823i	$0.870113\pi$
$252$	2.97542	−	5.15359i	0.187434	−	0.324645i
$253$	7.08096	−	12.2646i	0.445176	−	0.771068i
$254$	−2.67996			−0.168156
$255$	−2.31447	+	4.00879i	−0.144938	+	0.251040i
$256$	12.2647			0.766545
$257$	−0.808273			−0.0504187			−0.0252093	−	0.999682i	$-0.508025\pi$
$257$	−0.808273			−0.0504187			−0.0252093	+	0.999682i	$0.508025\pi$
$258$	−2.64969	−	1.17511i	−0.164963	−	0.0731591i
$259$	5.83068			0.362301
$260$	1.87513			0.116291
$261$	−2.60277	+	4.50813i	−0.161107	+	0.279046i
$262$	0.343344			0.0212118
$263$	−1.16776	+	2.02262i	−0.0720072	+	0.124720i	−0.899781	−	0.436342i	$-0.856274\pi$
$263$	−1.16776	+	2.02262i	−0.0720072	+	0.124720i	0.827774	+	0.561062i	$0.189607\pi$
$264$	1.43431	−	2.48429i	0.0882755	−	0.152898i
$265$	14.1925	+	24.5821i	0.871837	+	1.51007i
$266$	3.95947			0.242770
$267$	−3.23601	−	5.60494i	−0.198041	−	0.343017i
$268$	5.18248	−	8.97632i	0.316571	−	0.548316i
$269$	−13.0837			−0.797726			−0.398863	−	0.917011i	$-0.630595\pi$
$269$	−13.0837			−0.797726			−0.398863	+	0.917011i	$0.630595\pi$
$270$	−1.00114	+	1.73403i	−0.0609275	+	0.105530i
$271$	−12.7245	−	22.0395i	−0.772958	−	1.33880i	−0.935935	−	0.352172i	$-0.885443\pi$
$271$	−12.7245	−	22.0395i	−0.772958	−	1.33880i	0.162978	−	0.986630i	$-0.447890\pi$
$272$	1.85588	+	3.21448i	0.112529	+	0.194907i
$273$	−1.23426	−	2.13780i	−0.0747006	−	0.129385i
$274$	−2.16391			−0.130727
$275$	0.255417	+	0.442394i	0.0154022	+	0.0266774i
$276$	−16.9012	−	29.2737i	−1.01733	−	1.76207i
$277$	3.40012	−	5.88917i	0.204293	−	0.353846i	−0.745614	−	0.666378i	$-0.767844\pi$
$277$	3.40012	−	5.88917i	0.204293	−	0.353846i	0.949907	+	0.312532i	$0.101177\pi$
$278$	−0.828420	+	1.43487i	−0.0496853	+	0.0860575i
$279$	9.21125			0.551463
$280$	−5.90751			−0.353041
$281$	−0.188053	+	0.325717i	−0.0112183	+	0.0194306i	−0.871580	−	0.490253i	$-0.836904\pi$
$281$	−0.188053	+	0.325717i	−0.0112183	+	0.0194306i	0.860362	+	0.509684i	$0.170238\pi$
$282$	−2.08728	+	3.61528i	−0.124296	+	0.215287i
$283$	15.0711	+	26.1039i	0.895883	+	1.55171i	0.832708	+	0.553712i	$0.186789\pi$
$283$	15.0711	+	26.1039i	0.895883	+	1.55171i	0.0631750	+	0.998002i	$0.479877\pi$
$284$	11.2015	+	19.4015i	0.664685	+	1.15127i
$285$	−28.2536			−1.67360
$286$	−0.0753422	−	0.130496i	−0.00445508	−	0.00771642i
$287$	15.8832	+	27.5105i	0.937556	+	1.62389i
$288$	−1.32207	−	2.28989i	−0.0779036	−	0.134933i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	2.55214			0.149867
$291$	−3.00467	+	5.20425i	−0.176137	+	0.305078i
$292$	−14.3359	−	24.8304i	−0.838943	−	1.45309i
$293$	−22.7806			−1.33086			−0.665429	−	0.746461i	$-0.731751\pi$
$293$	−22.7806			−1.33086			−0.665429	+	0.746461i	$0.731751\pi$
$294$	0.373300	+	0.646575i	0.0217713	+	0.0377090i
$295$	0.163058	−	0.282426i	0.00949363	−	0.0164435i
$296$	0.860066	−	1.48968i	0.0499903	−	0.0865858i
$297$	−6.48378			−0.376227
$298$	−2.11998	+	3.67192i	−0.122807	+	0.212708i
$299$	−3.59524			−0.207918
$300$	1.21928			0.0703952
$301$	−15.6213	+	11.3843i	−0.900399	+	0.656179i
$302$	−0.425350			−0.0244761
$303$	22.5798			1.29718
$304$	−11.3277	+	19.6202i	−0.649689	+	1.12529i
$305$	−15.4347			−0.883789
$306$	0.113825	−	0.197151i	0.00650695	−	0.0112704i
$307$	10.7818	−	18.6747i	0.615352	−	1.06582i	−0.374971	−	0.927036i	$-0.622347\pi$
$307$	10.7818	−	18.6747i	0.615352	−	1.06582i	0.990323	−	0.138784i	$-0.0443193\pi$
$308$	−4.72380	−	8.18186i	−0.269163	−	0.466205i
$309$	−2.19975			−0.125140
$310$	−2.25802	−	3.91101i	−0.128247	−	0.222130i
$311$	6.27978	−	10.8769i	0.356094	−	0.616772i	−0.631211	−	0.775611i	$-0.717442\pi$
$311$	6.27978	−	10.8769i	0.356094	−	0.616772i	0.987304	+	0.158839i	$0.0507751\pi$
$312$	−0.728246			−0.0412288
$313$	13.8469	−	23.9835i	0.782671	−	1.35563i	−0.147710	−	0.989031i	$-0.547190\pi$
$313$	13.8469	−	23.9835i	0.782671	−	1.35563i	0.930381	−	0.366595i	$-0.119476\pi$
$314$	−2.29480	−	3.97471i	−0.129503	−	0.224306i
$315$	−3.51362	−	6.08577i	−0.197970	−	0.342894i
$316$	−1.26758	−	2.19551i	−0.0713069	−	0.123507i
$317$	1.44487			0.0811523			0.0405761	−	0.999176i	$-0.487081\pi$
$317$	1.44487			0.0811523			0.0405761	+	0.999176i	$0.487081\pi$
$318$	−2.72219	−	4.71497i	−0.152653	−	0.264403i
$319$	4.13217	+	7.15713i	0.231357	+	0.400722i
$320$	7.90585	−	13.6933i	0.441950	−	0.765480i
$321$	−11.6053	+	20.1010i	−0.647746	+	1.12193i
$322$	5.59390			0.311736
$323$	−6.10369			−0.339618
$324$	−10.7661	+	18.6474i	−0.598116	+	1.03597i
$325$	0.0648418	−	0.112309i	0.00359678	−	0.00622980i
$326$	2.71450	+	4.70165i	0.150342	+	0.260400i
$327$	−5.50204	−	9.52981i	−0.304263	−	0.527000i
$328$	9.37154			0.517457
$329$	13.9193	+	24.1088i	0.767393	+	1.32916i
$330$	−0.836494	−	1.44885i	−0.0460475	−	0.0797565i
$331$	−2.38518	−	4.13126i	−0.131102	−	0.227074i	0.793000	−	0.609222i	$-0.208518\pi$
$331$	−2.38518	−	4.13126i	−0.131102	−	0.227074i	−0.924101	+	0.382147i	$0.875185\pi$
$332$	−16.2131	+	28.0818i	−0.889807	+	1.54119i
$333$	2.04618			0.112130
$334$	−0.253738	+	0.439487i	−0.0138839	+	0.0240477i
$335$	−6.11989	−	10.6000i	−0.334366	−	0.579138i
$336$	−21.9765			−1.19892
$337$	6.97749	+	12.0854i	0.380088	+	0.658332i	0.991075	−	0.133309i	$-0.0425603\pi$
$337$	6.97749	+	12.0854i	0.380088	+	0.658332i	−0.610986	+	0.791641i	$0.709227\pi$
$338$	1.41132	−	2.44448i	0.0767658	−	0.132962i
$339$	12.5838	−	21.7958i	0.683459	−	1.18379i
$340$	4.49753			0.243913
$341$	7.31192	−	12.6646i	0.395962	−	0.685827i
$342$	1.38951			0.0751358
$343$	−15.6552			−0.845303
$344$	0.604310	+	5.67035i	0.0325822	+	0.305725i
$345$	−39.9165			−2.14903
$346$	−1.73426			−0.0932347
$347$	−11.7649	+	20.3774i	−0.631574	+	1.09392i	0.355656	+	0.934617i	$0.384258\pi$
$347$	−11.7649	+	20.3774i	−0.631574	+	1.09392i	−0.987230	+	0.159302i	$0.949076\pi$
$348$	19.7257			1.05741
$349$	−16.9809	+	29.4118i	−0.908967	+	1.57438i	−0.0934640	+	0.995623i	$0.529794\pi$
$349$	−16.9809	+	29.4118i	−0.908967	+	1.57438i	−0.815502	+	0.578754i	$0.803539\pi$
$350$	−0.100889	+	0.174744i	−0.00539272	+	0.00934046i
$351$	0.823008	+	1.42549i	0.0439289	+	0.0760871i
$352$	−4.19784			−0.223746
$353$	4.82942	+	8.36480i	0.257044	+	0.445213i	0.965449	−	0.260593i	$-0.0839181\pi$
$353$	4.82942	+	8.36480i	0.257044	+	0.445213i	−0.708405	+	0.705807i	$0.750585\pi$
$354$	−0.0312755	+	0.0541707i	−0.00166227	+	0.00287914i
$355$	26.4552			1.40410
$356$	−3.14414	+	5.44582i	−0.166639	+	0.288628i
$357$	−2.96038	−	5.12753i	−0.156680	−	0.271378i
$358$	−2.23351	−	3.86855i	−0.118045	−	0.204459i
$359$	10.4061	+	18.0239i	0.549214	+	0.951266i	0.998329	+	0.0577921i	$0.0184060\pi$
$359$	10.4061	+	18.0239i	0.549214	+	0.951266i	−0.449115	+	0.893474i	$0.648261\pi$
$360$	−2.07314			−0.109264
$361$	−9.12749	−	15.8093i	−0.480394	−	0.832067i
$362$	−1.04638	−	1.81239i	−0.0549967	−	0.0952571i
$363$	−8.33854	+	14.4428i	−0.437660	+	0.758049i
$364$	−1.19922	+	2.07710i	−0.0628560	+	0.108870i
$365$	−33.8579			−1.77220
$366$	2.96046			0.154746
$367$	−5.70727	+	9.88529i	−0.297917	+	0.516008i	−0.975659	−	0.219292i	$-0.929625\pi$
$367$	−5.70727	+	9.88529i	−0.297917	+	0.516008i	0.677742	+	0.735300i	$0.262959\pi$
$368$	−16.0037	+	27.7192i	−0.834251	+	1.44497i
$369$	5.57393	+	9.65433i	0.290167	+	0.502584i
$370$	−0.501594	−	0.868786i	−0.0260766	−	0.0451661i
$371$	−36.3064			−1.88494
$372$	−17.4524	−	30.2285i	−0.904866	−	1.56727i
$373$	13.5678	+	23.5001i	0.702513	+	1.21679i	0.967582	+	0.252558i	$0.0812720\pi$
$373$	13.5678	+	23.5001i	0.702513	+	1.21679i	−0.265069	+	0.964229i	$0.585395\pi$
$374$	−0.180709	−	0.312998i	−0.00934425	−	0.0161847i
$375$	−10.8525	+	18.7970i	−0.560418	+	0.970673i
$376$	8.21275			0.423540
$377$	1.04902	−	1.81696i	0.0540273	−	0.0935781i
$378$	−1.28053	−	2.21795i	−0.0658635	−	0.114079i
$379$	−13.3847			−0.687527			−0.343764	−	0.939056i	$-0.611702\pi$
$379$	−13.3847			−0.687527			−0.343764	+	0.939056i	$0.611702\pi$
$380$	13.7258	+	23.7737i	0.704117	+	1.21957i
$381$	−12.2302	+	21.1832i	−0.626570	+	1.08525i
$382$	0.367808	−	0.637062i	0.0188187	−	0.0325950i
$383$	−3.67464			−0.187765			−0.0938826	−	0.995583i	$-0.529928\pi$
$383$	−3.67464			−0.187765			−0.0938826	+	0.995583i	$0.529928\pi$
$384$	−6.65051	+	11.5190i	−0.339382	+	0.587827i
$385$	−11.1565			−0.568587
$386$	4.05562			0.206426
$387$	−5.48204	+	3.99512i	−0.278668	+	0.203083i
$388$	5.83874			0.296417
$389$	8.54804			0.433403			0.216701	−	0.976238i	$-0.430470\pi$
$389$	8.54804			0.433403			0.216701	+	0.976238i	$0.430470\pi$
$390$	−0.212358	+	0.367815i	−0.0107532	+	0.0186250i
$391$	−8.62324			−0.436096
$392$	0.734406	−	1.27203i	0.0370931	−	0.0642471i
$393$	1.56687	−	2.71390i	0.0790380	−	0.136898i
$394$	2.24056	+	3.88076i	0.112878	+	0.195510i
$395$	−2.99372			−0.150630
$396$	−1.65773	−	2.87128i	−0.0833043	−	0.144287i
$397$	6.92612	−	11.9964i	0.347612	−	0.602082i	−0.638213	−	0.769860i	$-0.720326\pi$
$397$	6.92612	−	11.9964i	0.347612	−	0.602082i	0.985825	+	0.167778i	$0.0536593\pi$
$398$	−2.33643			−0.117114
$399$	18.0692	−	31.2968i	0.904594	−	1.56680i
$400$	−0.577268	−	0.999858i	−0.0288634	−	0.0499929i
$401$	−15.8727	−	27.4923i	−0.792645	−	1.37290i	−0.924324	−	0.381609i	$-0.875370\pi$
$401$	−15.8727	−	27.4923i	−0.792645	−	1.37290i	0.131678	−	0.991292i	$-0.457963\pi$
$402$	1.17383	+	2.03313i	0.0585452	+	0.101403i
$403$	−3.71251			−0.184933
$404$	−10.9694	−	18.9996i	−0.545748	−	0.945263i
$405$	12.7135	+	22.0204i	0.631737	+	1.09420i
$406$	−1.63219	+	2.82704i	−0.0810042	+	0.140303i
$407$	1.62426	−	2.81330i	0.0805115	−	0.139450i
$408$	−1.74671			−0.0864750
$409$	24.4235			1.20767			0.603833	−	0.797111i	$-0.293639\pi$
$409$	24.4235			1.20767			0.603833	+	0.797111i	$0.293639\pi$
$410$	2.73276	−	4.73328i	0.134961	−	0.233760i
$411$	−9.87513	+	17.1042i	−0.487104	+	0.843690i
$412$	1.06865	+	1.85096i	0.0526486	+	0.0911901i
$413$	0.208564	+	0.361243i	0.0102628	+	0.0177756i
$414$	1.96308			0.0964802
$415$	19.1457	+	33.1613i	0.939825	+	1.62782i
$416$	0.532847	+	0.922917i	0.0261250	+	0.0452497i
$417$	7.56108	+	13.0962i	0.370268	+	0.641323i
$418$	1.10299	−	1.91044i	0.0539491	−	0.0934426i
$419$	19.8652			0.970480			0.485240	−	0.874381i	$-0.338732\pi$
$419$	19.8652			0.970480			0.485240	+	0.874381i	$0.338732\pi$
$420$	−13.3144	+	23.0612i	−0.649677	+	1.12527i
$421$	13.3761	+	23.1680i	0.651910	+	1.12914i	0.982659	+	0.185422i	$0.0593652\pi$
$421$	13.3761	+	23.1680i	0.651910	+	1.12914i	−0.330749	+	0.943719i	$0.607301\pi$
$422$	−0.936837			−0.0456045
$423$	4.88472	+	8.46058i	0.237503	+	0.411367i
$424$	−5.35545	+	9.27592i	−0.260084	+	0.450478i
$425$	0.155524	−	0.269375i	0.00754402	−	0.0130666i
$426$	−5.07425			−0.245848
$427$	9.87107	−	17.0972i	0.477695	−	0.827391i
$428$	22.5517			1.09008
$429$	−1.37531			−0.0664007
$430$	3.04014	+	1.34827i	0.146609	+	0.0650192i
$431$	16.9822			0.818004			0.409002	−	0.912533i	$-0.365877\pi$
$431$	16.9822			0.818004			0.409002	+	0.912533i	$0.365877\pi$
$432$	14.6540			0.705042
$433$	3.59178	−	6.22114i	0.172610	−	0.298969i	−0.766722	−	0.641980i	$-0.778113\pi$
$433$	3.59178	−	6.22114i	0.172610	−	0.298969i	0.939331	+	0.343011i	$0.111447\pi$
$434$	5.77636			0.277274
$435$	11.6469	−	20.1729i	0.558424	−	0.967219i
$436$	−5.34583	+	9.25926i	−0.256019	+	0.443438i
$437$	−26.3168	−	45.5820i	−1.25890	−	2.18048i
$438$	6.49413			0.310301
$439$	−11.6415	−	20.1637i	−0.555621	−	0.962363i	−0.997855	−	0.0654636i	$-0.979147\pi$
$439$	−11.6415	−	20.1637i	−0.555621	−	0.962363i	0.442234	−	0.896900i	$-0.354186\pi$
$440$	−1.64566	+	2.85037i	−0.0784538	+	0.135886i
$441$	1.74722			0.0832008
$442$	−0.0458761	+	0.0794597i	−0.00218210	+	0.00377951i
$443$	−5.47968	−	9.49109i	−0.260348	−	0.450935i	0.705987	−	0.708225i	$-0.250504\pi$
$443$	−5.47968	−	9.49109i	−0.260348	−	0.450935i	−0.966334	+	0.257290i	$0.917170\pi$
$444$	−3.87686	−	6.71491i	−0.183987	−	0.318676i
$445$	3.71286	+	6.43086i	0.176006	+	0.304852i
$446$	3.18712			0.150915
$447$	19.3493	+	33.5140i	0.915191	+	1.58516i
$448$	10.1122	+	17.5148i	0.477755	+	0.827495i
$449$	4.62872	−	8.01717i	0.218443	−	0.378354i	−0.735889	−	0.677102i	$-0.763236\pi$
$449$	4.62872	−	8.01717i	0.218443	−	0.378354i	0.954332	+	0.298748i	$0.0965690\pi$
$450$	−0.0354051	+	0.0613234i	−0.00166901	+	0.00289081i
$451$	17.6984			0.833385
$452$	−24.4531			−1.15018
$453$	−1.94111	+	3.36210i	−0.0912012	+	0.157965i
$454$	−2.72726	+	4.72376i	−0.127997	+	0.221697i
$455$	1.41613	+	2.45281i	0.0663893	+	0.114990i
$456$	−5.33068	−	9.23301i	−0.249632	−	0.432375i
$457$	−2.50708			−0.117276			−0.0586381	−	0.998279i	$-0.518676\pi$
$457$	−2.50708			−0.117276			−0.0586381	+	0.998279i	$0.518676\pi$
$458$	3.08960	+	5.35134i	0.144367	+	0.250052i
$459$	1.97400	+	3.41906i	0.0921383	+	0.159588i
$460$	19.3916	+	33.5873i	0.904140	+	1.56602i
$461$	4.50785	−	7.80782i	0.209951	−	0.363646i	−0.741748	−	0.670679i	$-0.766003\pi$
$461$	4.50785	−	7.80782i	0.209951	−	0.363646i	0.951699	+	0.307033i	$0.0993361\pi$
$462$	2.13987			0.0995559
$463$	1.81301	−	3.14022i	0.0842576	−	0.145938i	−0.820817	−	0.571191i	$-0.806481\pi$
$463$	1.81301	−	3.14022i	0.0842576	−	0.145938i	0.905075	+	0.425253i	$0.139815\pi$
$464$	−9.33914	−	16.1759i	−0.433558	−	0.750945i
$465$	−41.2185			−1.91146
$466$	1.16792	+	2.02290i	0.0541031	+	0.0937092i
$467$	−4.29907	+	7.44620i	−0.198937	+	0.344569i	−0.948184	−	0.317722i	$-0.897082\pi$
$467$	−4.29907	+	7.44620i	−0.198937	+	0.344569i	0.749247	+	0.662291i	$0.230416\pi$
$468$	−0.420844	+	0.728923i	−0.0194535	+	0.0336945i
$469$	15.6556			0.722908
$470$	2.39485	−	4.14801i	0.110466	−	0.191333i
$471$	−41.8898			−1.93018
$472$	0.123059			0.00566423
$473$	1.14126	+	10.7086i	0.0524750	+	0.492383i
$474$	0.574212			0.0263744
$475$	1.89854			0.0871110
$476$	−2.87634	+	4.98196i	−0.131837	+	0.228348i
$477$	−12.7411			−0.583375
$478$	1.32758	−	2.29944i	0.0607221	−	0.105174i
$479$	−10.1942	+	17.6569i	−0.465785	+	0.806764i	−0.999237	−	0.0390668i	$-0.987561\pi$
$479$	−10.1942	+	17.6569i	−0.465785	+	0.806764i	0.533451	+	0.845831i	$0.320895\pi$
$480$	5.91598	+	10.2468i	0.270026	+	0.467699i
$481$	−0.824691			−0.0376027
$482$	2.31703	+	4.01322i	0.105538	+	0.182797i
$483$	25.5281	−	44.2159i	1.16157	−	2.01189i
$484$	16.2036			0.736528
$485$	3.44743	−	5.97112i	0.156540	−	0.271135i
$486$	−1.13527	−	1.96634i	−0.0514967	−	0.0891949i
$487$	−3.71859	−	6.44079i	−0.168506	−	0.291860i	0.769389	−	0.638780i	$-0.220561\pi$
$487$	−3.71859	−	6.44079i	−0.168506	−	0.291860i	−0.937895	+	0.346920i	$0.887227\pi$
$488$	−2.91210	−	5.04391i	−0.131825	−	0.228327i
$489$	49.5511			2.24078
$490$	−0.428308	−	0.741852i	−0.0193490	−	0.0335134i
$491$	−1.03175	−	1.78704i	−0.0465622	−	0.0806480i	0.841805	−	0.539782i	$-0.181493\pi$
$491$	−1.03175	−	1.78704i	−0.0465622	−	0.0806480i	−0.888367	+	0.459134i	$0.848160\pi$
$492$	21.1217	−	36.5838i	0.952239	−	1.64933i
$493$	2.51609	−	4.35800i	0.113319	−	0.196274i
$494$	−0.560027			−0.0251968
$495$	−3.91517			−0.175974
$496$	−16.5257	+	28.6233i	−0.742026	+	1.28523i
$497$	−16.9191	+	29.3047i	−0.758924	+	1.31449i
$498$	−3.67224	−	6.36051i	−0.164557	−	0.285021i
$499$	−5.92150	−	10.2563i	−0.265083	−	0.459137i	0.702503	−	0.711681i	$-0.252066\pi$
$499$	−5.92150	−	10.2563i	−0.265083	−	0.459137i	−0.967585	+	0.252544i	$0.918733\pi$
$500$	21.0887			0.943116
$501$	2.31589	+	4.01125i	0.103467	+	0.179209i
$502$	−0.401960	−	0.696216i	−0.0179404	−	0.0310736i
$503$	−6.85454	−	11.8724i	−0.305629	−	0.529364i	0.671772	−	0.740758i	$-0.265533\pi$
$503$	−6.85454	−	11.8724i	−0.305629	−	0.529364i	−0.977401	+	0.211393i	$0.932200\pi$
$504$	1.32585	−	2.29643i	0.0590579	−	0.102291i
$505$	−25.9071			−1.15285
$506$	1.55830	−	2.69905i	0.0692748	−	0.119988i
$507$	−12.8813	−	22.3110i	−0.572078	−	0.990868i
$508$	23.7659			1.05444
$509$	−7.96559	−	13.7968i	−0.353068	−	0.611533i	0.633717	−	0.773565i	$-0.281528\pi$
$509$	−7.96559	−	13.7968i	−0.353068	−	0.611533i	−0.986785	+	0.162032i	$0.948195\pi$
$510$	−0.509344	+	0.882209i	−0.0225541	+	0.0390649i
$511$	21.6534	−	37.5047i	0.957889	−	1.65911i
$512$	15.9432			0.704596
$513$	−12.0487	+	20.8689i	−0.531961	+	0.921384i
$514$	−0.177876			−0.00784576
$515$	2.52390			0.111216
$516$	23.4975	+	10.4209i	1.03442	+	0.458753i
$517$	15.5100			0.682129
$518$	1.28315			0.0563784
$519$	−7.91442	+	13.7082i	−0.347404	+	0.601722i
$520$	0.835557			0.0366416
$521$	6.64470	−	11.5090i	0.291109	−	0.504216i	−0.682963	−	0.730453i	$-0.739309\pi$
$521$	6.64470	−	11.5090i	0.291109	−	0.504216i	0.974072	+	0.226237i	$0.0726423\pi$
$522$	−0.572789	+	0.992099i	−0.0250703	+	0.0434230i
$523$	10.0942	+	17.4837i	0.441388	+	0.764507i	0.997793	−	0.0664044i	$-0.0211528\pi$
$523$	10.0942	+	17.4837i	0.441388	+	0.764507i	−0.556404	+	0.830912i	$0.687819\pi$
$524$	−3.04477			−0.133011
$525$	0.920821	+	1.59491i	0.0401879	+	0.0696075i
$526$	−0.256988	+	0.445116i	−0.0112052	+	0.0194080i
$527$	−8.90450			−0.387886
$528$	−6.12201	+	10.6036i	−0.266426	+	0.461464i
$529$	−25.6801	−	44.4793i	−1.11653	−	1.93388i
$530$	3.12332	+	5.40975i	0.135668	+	0.234985i
$531$	0.0731918	+	0.126772i	0.00317625	+	0.00550143i
$532$	−35.1125			−1.52232
$533$	−2.24652	−	3.89109i	−0.0973076	−	0.168542i
$534$	−0.712146	−	1.23347i	−0.0308176	−	0.0533776i
$535$	13.3154	−	23.0630i	0.575677	−	0.997101i
$536$	2.30931	−	3.99984i	0.0997470	−	0.172767i
$537$	−40.7710			−1.75940
$538$	−2.87931			−0.124136
$539$	1.38695	−	2.40226i	0.0597400	−	0.103473i
$540$	8.87811	−	15.3773i	0.382053	−	0.661735i
$541$	12.0721	+	20.9095i	0.519020	+	0.898970i	0.999756	+	0.0221039i	$0.00703647\pi$
$541$	12.0721	+	20.9095i	0.519020	+	0.898970i	−0.480735	+	0.876866i	$0.659630\pi$
$542$	−2.80026	−	4.85020i	−0.120282	−	0.208334i
$543$	−19.1009			−0.819699
$544$	1.27804	+	2.21363i	0.0547955	+	0.0949086i
$545$	6.31279	+	10.9341i	0.270410	+	0.468364i
$546$	−0.271622	−	0.470462i	−0.0116243	−	0.0201339i
$547$	−3.21134	+	5.56220i	−0.137307	+	0.237822i	−0.926476	−	0.376353i	$-0.877178\pi$
$547$	−3.21134	+	5.56220i	−0.137307	+	0.237822i	0.789169	+	0.614176i	$0.210511\pi$
$548$	19.1896			0.819737
$549$	3.46408	−	5.99996i	0.147843	−	0.256072i
$550$	0.0562093	+	0.0973573i	0.00239677	+	0.00415133i
$551$	30.7149			1.30850
$552$	−7.53114	−	13.0443i	−0.320547	−	0.555203i
$553$	1.91459	−	3.31618i	0.0814169	−	0.141018i
$554$	0.748260	−	1.29602i	0.0317905	−	0.0550628i
$555$	−9.15621			−0.388660
$556$	7.34642	−	12.7244i	0.311558	−	0.539634i
$557$	29.5285			1.25116			0.625582	−	0.780158i	$-0.284862\pi$
$557$	29.5285			1.25116			0.625582	+	0.780158i	$0.284862\pi$
$558$	2.02711			0.0858144
$559$	2.20948	−	1.61019i	0.0934511	−	0.0681039i
$560$	25.2148			1.06552
$561$	−3.29871			−0.139272
$562$	−0.0413846	+	0.0716802i	−0.00174570	+	0.00302365i
$563$	25.7525			1.08534			0.542669	−	0.839946i	$-0.317414\pi$
$563$	25.7525			1.08534			0.542669	+	0.839946i	$0.317414\pi$
$564$	18.5100	−	32.0603i	0.779411	−	1.34998i
$565$	−14.4381	+	25.0075i	−0.607415	+	1.05207i
$566$	3.31668	+	5.74465i	0.139410	+	0.241466i
$567$	−32.5229			−1.36583
$568$	4.99136	+	8.64530i	0.209433	+	0.362749i
$569$	3.60245	−	6.23962i	0.151022	−	0.261578i	−0.780581	−	0.625054i	$-0.785077\pi$
$569$	3.60245	−	6.23962i	0.151022	−	0.261578i	0.931604	+	0.363476i	$0.118410\pi$
$570$	−6.21775			−0.260433
$571$	−2.63208	+	4.55890i	−0.110149	+	0.190784i	−0.915830	−	0.401566i	$-0.868466\pi$
$571$	−2.63208	+	4.55890i	−0.110149	+	0.190784i	0.805681	+	0.592349i	$0.201800\pi$
$572$	0.668134	+	1.15724i	0.0279361	+	0.0483867i
$573$	−3.35703	−	5.81454i	−0.140242	−	0.242906i
$574$	3.49540	+	6.05421i	0.145895	+	0.252698i
$575$	2.68224			0.111857
$576$	3.54869	+	6.14650i	0.147862	+	0.256104i
$577$	1.55886	+	2.70002i	0.0648962	+	0.112403i	0.896648	−	0.442744i	$-0.145995\pi$
$577$	1.55886	+	2.70002i	0.0648962	+	0.112403i	−0.831752	+	0.555148i	$0.812662\pi$
$578$	−0.110034	+	0.190585i	−0.00457683	+	0.00792730i
$579$	18.5081	−	32.0569i	0.769169	−	1.33224i
$580$	−22.6324			−0.939759
$581$	−48.9775			−2.03193
$582$	−0.661235	+	1.14529i	−0.0274091	+	0.0474739i
$583$	−10.1139	+	17.5178i	−0.418876	+	0.725514i
$584$	−6.38805	−	11.0644i	−0.264339	−	0.457849i
$585$	0.496967	+	0.860771i	0.0205470	+	0.0355885i
$586$	−5.01331			−0.207098
$587$	−4.71158	−	8.16070i	−0.194468	−	0.336828i	0.752258	−	0.658868i	$-0.228965\pi$
$587$	−4.71158	−	8.16070i	−0.194468	−	0.336828i	−0.946726	+	0.322040i	$0.895631\pi$
$588$	−3.31043	−	5.73382i	−0.136520	−	0.236459i
$589$	−27.1751	−	47.0687i	−1.11973	−	1.93943i
$590$	0.0358841	−	0.0621531i	0.00147733	−	0.00255880i
$591$	40.8996			1.68239
$592$	−3.67100	+	6.35835i	−0.150877	+	0.261327i
$593$	10.9182	+	18.9109i	0.448358	+	0.776579i	0.998279	−	0.0586377i	$-0.0186757\pi$
$593$	10.9182	+	18.9109i	0.448358	+	0.776579i	−0.549921	+	0.835216i	$0.685342\pi$
$594$	−1.42688			−0.0585455
$595$	3.39661	+	5.88310i	0.139247	+	0.241184i
$596$	18.8000	−	32.5625i	0.770078	−	1.33381i
$597$	−10.6624	+	18.4678i	−0.436384	+	0.755838i
$598$	−0.791201			−0.0323546
$599$	6.14432	−	10.6423i	0.251050	−	0.434831i	−0.712765	−	0.701403i	$-0.752558\pi$
$599$	6.14432	−	10.6423i	0.251050	−	0.434831i	0.963815	+	0.266571i	$0.0858908\pi$
$600$	0.543310			0.0221805
$601$	−0.142548			−0.00581465			−0.00290733	−	0.999996i	$-0.500925\pi$
$601$	−0.142548			−0.00581465			−0.00290733	+	0.999996i	$0.500925\pi$
$602$	−3.43777	+	2.50533i	−0.140113	+	0.102110i
$603$	5.49406			0.223735
$604$	3.77200			0.153481
$605$	9.56727	−	16.5710i	0.388965	−	0.673707i
$606$	4.96912			0.201857
$607$	−0.621706	+	1.07683i	−0.0252343	+	0.0437071i	−0.878367	−	0.477987i	$-0.841367\pi$
$607$	−0.621706	+	1.07683i	−0.0252343	+	0.0437071i	0.853132	+	0.521694i	$0.174700\pi$
$608$	−7.80075	+	13.5113i	−0.316362	+	0.547956i
$609$	14.8972	+	25.8027i	0.603664	+	1.04558i
$610$	−3.39670			−0.137528
$611$	−1.96874	−	3.40995i	−0.0796466	−	0.137952i
$612$	−1.00940	+	1.74833i	−0.0408026	+	0.0706721i
$613$	−40.3607			−1.63015			−0.815077	−	0.579352i	$-0.803306\pi$
$613$	−40.3607			−1.63015			−0.815077	+	0.579352i	$0.803306\pi$
$614$	2.37275	−	4.10972i	0.0957562	−	0.165855i
$615$	−24.9422	−	43.2011i	−1.00577	−	1.74204i
$616$	−2.10492	−	3.64583i	−0.0848097	−	0.146895i
$617$	4.08078	+	7.06812i	0.164286	+	0.284552i	0.936402	−	0.350931i	$-0.114135\pi$
$617$	4.08078	+	7.06812i	0.164286	+	0.284552i	−0.772115	+	0.635482i	$0.780801\pi$
$618$	−0.484097			−0.0194732
$619$	13.1827	+	22.8330i	0.529856	+	0.917738i	0.999393	+	0.0348250i	$0.0110874\pi$
$619$	13.1827	+	22.8330i	0.529856	+	0.917738i	−0.469537	+	0.882913i	$0.655579\pi$
$620$	20.0241	+	34.6828i	0.804188	+	1.39290i
$621$	−17.0222	+	29.4834i	−0.683079	+	1.18313i
$622$	1.38198	−	2.39367i	0.0554125	−	0.0959773i
$623$	−9.49804			−0.380531
$624$	3.10835			0.124434
$625$	13.2292	−	22.9137i	0.529170	−	0.916549i
$626$	3.04726	−	5.27801i	0.121793	−	0.210952i
$627$	−10.0671	−	17.4368i	−0.402043	−	0.696358i
$628$	20.3503	+	35.2477i	0.812065	+	1.40654i
$629$	−1.97803			−0.0788693
$630$	−0.773239	−	1.33929i	−0.0308066	−	0.0533586i
$631$	−6.64008	−	11.5010i	−0.264337	−	0.457846i	0.703052	−	0.711138i	$-0.251820\pi$
$631$	−6.64008	−	11.5010i	−0.264337	−	0.457846i	−0.967390	+	0.253292i	$0.918487\pi$
$632$	−0.564832	−	0.978318i	−0.0224678	−	0.0389154i
$633$	−4.27531	+	7.40505i	−0.169928	+	0.294325i
$634$	0.317972			0.0126283
$635$	14.0323	−	24.3047i	0.556856	−	0.964503i
$636$	24.1404	+	41.8124i	0.957228	+	1.65797i
$637$	−0.704199			−0.0279014
$638$	0.909362	+	1.57506i	0.0360020	+	0.0623573i
$639$	−5.93745	+	10.2840i	−0.234882	+	0.406827i
$640$	7.63050	−	13.2164i	0.301622	−	0.522424i
$641$	−14.9672			−0.591170			−0.295585	−	0.955316i	$-0.595515\pi$
$641$	−14.9672			−0.591170			−0.295585	+	0.955316i	$0.595515\pi$
$642$	−2.55397	+	4.42361i	−0.100797	+	0.174586i
$643$	1.57563			0.0621369			0.0310684	−	0.999517i	$-0.490109\pi$
$643$	1.57563			0.0621369			0.0310684	+	0.999517i	$0.490109\pi$
$644$	−49.6067			−1.95478
$645$	24.5310	−	17.8773i	0.965906	−	0.703919i
$646$	−1.34323			−0.0528487
$647$	9.25001			0.363655			0.181828	−	0.983330i	$-0.441799\pi$
$647$	9.25001			0.363655			0.181828	+	0.983330i	$0.441799\pi$
$648$	−4.79736	+	8.30927i	−0.188458	+	0.326419i
$649$	0.232399			0.00912247
$650$	0.0142697	−	0.0247158i	0.000559703	−	0.000969433i
$651$	26.3607	−	45.6581i	1.03316	−	1.78948i
$652$	−24.0722	−	41.6942i	−0.942739	−	1.63287i
$653$	−1.44783			−0.0566579			−0.0283290	−	0.999599i	$-0.509019\pi$
$653$	−1.44783			−0.0566579			−0.0283290	+	0.999599i	$0.509019\pi$
$654$	−1.21083	−	2.09721i	−0.0473471	−	0.0820076i
$655$	−1.79775	+	3.11380i	−0.0702441	+	0.121666i
$656$	−40.0002			−1.56175
$657$	7.59887	−	13.1616i	0.296460	−	0.513484i
$658$	3.06319	+	5.30561i	0.119416	+	0.206834i
$659$	8.11526	+	14.0560i	0.316125	+	0.547545i	0.979676	−	0.200586i	$-0.0642846\pi$
$659$	8.11526	+	14.0560i	0.316125	+	0.547545i	−0.663551	+	0.748131i	$0.730951\pi$
$660$	7.41802	+	12.8484i	0.288746	+	0.500123i
$661$	43.8423			1.70527			0.852634	−	0.522508i	$-0.175004\pi$
$661$	43.8423			1.70527			0.852634	+	0.522508i	$0.175004\pi$
$662$	−0.524905	−	0.909161i	−0.0204010	−	0.0353356i
$663$	0.418716	+	0.725238i	0.0162616	+	0.0281659i
$664$	−7.22452	+	12.5132i	−0.280366	+	0.485608i
$665$	−20.7318	+	35.9086i	−0.803946	+	1.39248i
$666$	0.450300			0.0174488
$667$	43.3937			1.68021
$668$	2.25015	−	3.89737i	0.0870607	−	0.150794i
$669$	14.5446	−	25.1920i	0.562327	−	0.973979i
$670$	−1.34680	−	2.33272i	−0.0520314	−	0.0901210i
$671$	−5.49959	−	9.52557i	−0.212309	−	0.367730i
$672$	−15.1339			−0.583805
$673$	7.90166	+	13.6861i	0.304586	+	0.527559i	0.977169	−	0.212463i	$-0.0681484\pi$
$673$	7.90166	+	13.6861i	0.304586	+	0.527559i	−0.672583	+	0.740022i	$0.734815\pi$
$674$	1.53553	+	2.65961i	0.0591464	+	0.102445i
$675$	−0.614008	−	1.06349i	−0.0236332	−	0.0409338i
$676$	−12.5156	+	21.6776i	−0.481369	+	0.833755i
$677$	−35.8935			−1.37950			−0.689750	−	0.724048i	$-0.742279\pi$
$677$	−35.8935			−1.37950			−0.689750	+	0.724048i	$0.742279\pi$
$678$	2.76931	−	4.79658i	0.106355	−	0.184211i
$679$	4.40952	+	7.63750i	0.169222	+	0.293101i
$680$	2.00410			0.0768536
$681$	24.8920	+	43.1143i	0.953865	+	1.65214i
$682$	1.60913	−	2.78709i	0.0616166	−	0.106723i
$683$	−22.1662	+	38.3930i	−0.848166	+	1.46907i	0.0346775	+	0.999399i	$0.488960\pi$
$683$	−22.1662	+	38.3930i	−0.848166	+	1.46907i	−0.882843	+	0.469668i	$0.844374\pi$
$684$	−12.3221			−0.471148
$685$	11.3303	−	19.6246i	0.432908	−	0.749819i
$686$	−3.44523			−0.131539
$687$	56.3982			2.15172
$688$	−2.57936	−	24.2026i	−0.0983372	−	0.922716i
$689$	5.13518			0.195635
$690$	−8.78439			−0.334416
$691$	19.2588	−	33.3572i	0.732638	−	1.26897i	−0.223114	−	0.974792i	$-0.571622\pi$
$691$	19.2588	−	33.3572i	0.732638	−	1.26897i	0.955752	−	0.294174i	$-0.0950444\pi$
$692$	15.3794			0.584639
$693$	2.50390	−	4.33688i	0.0951152	−	0.164744i
$694$	−2.58909	+	4.48444i	−0.0982807	+	0.170227i
$695$	−8.67525	−	15.0260i	−0.329071	−	0.569968i
$696$	8.78976			0.333175
$697$	−5.38831	−	9.33282i	−0.204097	−	0.353506i
$698$	−3.73697	+	6.47262i	−0.141446	+	0.244992i
$699$	21.3196			0.806380
$700$	0.894679	−	1.54963i	0.0338157	−	0.0585705i
$701$	5.34283	+	9.25405i	0.201796	+	0.349520i	0.949107	−	0.314954i	$-0.101989\pi$
$701$	5.34283	+	9.25405i	0.201796	+	0.349520i	−0.747311	+	0.664474i	$0.768656\pi$
$702$	0.181119	+	0.313707i	0.00683588	+	0.0118401i
$703$	−6.03665	−	10.4558i	−0.227676	−	0.394347i
$704$	11.2678			0.424672
$705$	−21.8581	−	37.8593i	−0.823224	−	1.42587i
$706$	1.06281	+	1.84083i	0.0399992	+	0.0692806i
$707$	16.5685	−	28.6976i	0.623124	−	1.07928i
$708$	0.277351	−	0.480386i	0.0104235	−	0.0180540i
$709$	−26.6054			−0.999186			−0.499593	−	0.866260i	$-0.666517\pi$
$709$	−26.6054			−0.999186			−0.499593	+	0.866260i	$0.666517\pi$
$710$	5.82197			0.218494
$711$	0.671893	−	1.16375i	0.0251980	−	0.0436442i
$712$	−1.40103	+	2.42665i	−0.0525057	+	0.0909426i
$713$	−38.3928	−	66.4983i	−1.43782	−	2.49038i
$714$	−0.651488	−	1.12841i	−0.0243813	−	0.0422297i
$715$	1.57797			0.0590128
$716$	19.8067	+	34.3063i	0.740212	+	1.28209i
$717$	−12.1170	−	20.9872i	−0.452517	−	0.783782i
$718$	2.29006	+	3.96650i	0.0854644	+	0.148029i
$719$	−23.2094	+	40.1999i	−0.865566	+	1.49920i	0.000918687		1.00000i	$0.499708\pi$
$719$	−23.2094	+	40.1999i	−0.865566	+	1.49920i	−0.866484	+	0.499204i	$0.833626\pi$
$720$	8.84870			0.329772
$721$	−1.61413	+	2.79575i	−0.0601132	+	0.104119i
$722$	−2.00868	−	3.47913i	−0.0747552	−	0.129480i
$723$	42.2956			1.57299
$724$	9.27932	+	16.0723i	0.344863	+	0.597321i
$725$	−0.782625	+	1.35555i	−0.0290660	+	0.0503437i
$726$	−1.83505	+	3.17841i	−0.0681052	+	0.117962i
$727$	−6.30831			−0.233962			−0.116981	−	0.993134i	$-0.537322\pi$
$727$	−6.30831			−0.233962			−0.116981	+	0.993134i	$0.537322\pi$
$728$	−0.534370	+	0.925556i	−0.0198051	+	0.0343034i
$729$	12.3764			0.458385
$730$	−7.45107			−0.275776
$731$	5.29947	−	3.86207i	0.196008	−	0.142844i
$732$	−26.2534			−0.970352
$733$	10.1907			0.376401			0.188200	−	0.982131i	$-0.439735\pi$
$733$	10.1907			0.376401			0.188200	+	0.982131i	$0.439735\pi$
$734$	−1.25599	+	2.17544i	−0.0463596	+	0.0802971i
$735$	−7.81844			−0.288387
$736$	−11.0208	+	19.0887i	−0.406234	+	0.703617i
$737$	4.36119	−	7.55381i	0.160647	−	0.278248i
$738$	1.22665	+	2.12462i	0.0451536	+	0.0782083i
$739$	11.4077			0.419637			0.209819	−	0.977740i	$-0.432713\pi$
$739$	11.4077			0.419637			0.209819	+	0.977740i	$0.432713\pi$
$740$	4.44813	+	7.70439i	0.163517	+	0.283219i
$741$	−2.55571	+	4.42663i	−0.0938865	+	0.162616i
$742$	−7.98992			−0.293319
$743$	13.3183	−	23.0680i	0.488602	−	0.846283i	−0.511312	−	0.859395i	$-0.670840\pi$
$743$	13.3183	−	23.0680i	0.488602	−	0.846283i	0.999914	+	0.0131118i	$0.00417374\pi$
$744$	−7.77678	−	13.4698i	−0.285111	−	0.493826i
$745$	−22.2005	−	38.4525i	−0.813365	−	1.40879i
$746$	2.98585	+	5.17164i	0.109320	+	0.189347i
$747$	−17.1878			−0.628868
$748$	1.60253	+	2.77566i	0.0585942	+	0.101488i
$749$	17.0314	+	29.4993i	0.622315	+	1.07788i
$750$	−2.38829	+	4.13664i	−0.0872080	+	0.151049i
$751$	−12.7080	+	22.0109i	−0.463722	+	0.803190i	−0.999143	−	0.0413955i	$-0.986820\pi$
$751$	−12.7080	+	22.0109i	−0.463722	+	0.803190i	0.535421	+	0.844585i	$0.320153\pi$
$752$	−35.0542			−1.27830
$753$	−7.33747			−0.267392
$754$	0.230857	−	0.399856i	0.00840731	−	0.0145619i
$755$	2.22714	−	3.85752i	0.0810540	−	0.140390i
$756$	11.3558	+	19.6687i	0.413005	+	0.715346i
$757$	17.1555	+	29.7142i	0.623527	+	1.07998i	0.988824	+	0.149090i	$0.0476343\pi$
$757$	17.1555	+	29.7142i	0.623527	+	1.07998i	−0.365297	+	0.930891i	$0.619032\pi$
$758$	−2.94556			−0.106988
$759$	−14.2228	−	24.6346i	−0.516254	−	0.894178i
$760$	6.11619	+	10.5935i	0.221857	+	0.384268i
$761$	−9.75023	−	16.8879i	−0.353446	−	0.612186i	0.633405	−	0.773820i	$-0.281657\pi$
$761$	−9.75023	−	16.8879i	−0.353446	−	0.612186i	−0.986851	+	0.161635i	$0.948323\pi$
$762$	−2.69148	+	4.66178i	−0.0975019	+	0.168878i
$763$	−16.1491			−0.584635
$764$	−3.26172	+	5.64947i	−0.118005	+	0.204390i
$765$	1.19198	+	2.06457i	0.0430962	+	0.0746447i
$766$	−0.808674			−0.0292186
$767$	−0.0294993	−	0.0510942i	−0.00106516	−	0.00184491i
$768$	12.3174	−	21.3344i	0.444467	−	0.769839i
$769$	3.44806	−	5.97221i	0.124340	−	0.215363i	−0.797135	−	0.603802i	$-0.793652\pi$
$769$	3.44806	−	5.97221i	0.124340	−	0.215363i	0.921475	+	0.388438i	$0.126985\pi$
$770$	−2.45520			−0.0884791
$771$	−0.811746	+	1.40598i	−0.0292343	+	0.0506353i
$772$	−35.9653			−1.29442
$773$	−28.2206			−1.01502			−0.507512	−	0.861645i	$-0.669435\pi$
$773$	−28.2206			−1.01502			−0.507512	+	0.861645i	$0.669435\pi$
$774$	−1.20643	+	0.879201i	−0.0433641	+	0.0316022i
$775$	2.76973			0.0994915
$776$	2.60174			0.0933969
$777$	5.85573	−	10.1424i	0.210073	−	0.363858i
$778$	1.88116			0.0674428
$779$	32.8885	−	56.9646i	1.17835	−	2.04097i
$780$	1.88319	−	3.26178i	0.0674290	−	0.116790i
$781$	9.42633	+	16.3269i	0.337300	+	0.584222i
$782$	−1.89771			−0.0678619
$783$	−9.93351	−	17.2053i	−0.354995	−	0.614869i
$784$	−3.13464	+	5.42936i	−0.111951	+	0.193906i
$785$	48.0625			1.71543
$786$	0.344819	−	0.597244i	0.0122993	−	0.0213030i
$787$	−18.9572	−	32.8348i	−0.675750	−	1.17043i	−0.976249	−	0.216651i	$-0.930487\pi$
$787$	−18.9572	−	32.8348i	−0.675750	−	1.17043i	0.300499	−	0.953782i	$-0.402847\pi$
$788$	−19.8692	−	34.4145i	−0.707813	−	1.22597i
$789$	2.34556	+	4.06262i	0.0835040	+	0.144633i
$790$	−0.658825			−0.0234399
$791$	−18.4674	−	31.9865i	−0.656625	−	1.13731i
$792$	−0.738685	−	1.27944i	−0.0262480	−	0.0454629i
$793$	−1.39616	+	2.41823i	−0.0495792	+	0.0858738i
$794$	1.52422	−	2.64003i	0.0540927	−	0.0936913i
$795$	57.0138			2.02207
$796$	20.7194			0.734380
$797$	−20.8959	+	36.1928i	−0.740172	+	1.28202i	0.212244	+	0.977217i	$0.431923\pi$
$797$	−20.8959	+	36.1928i	−0.740172	+	1.28202i	−0.952417	+	0.304799i	$0.901411\pi$
$798$	3.97648	−	6.88746i	0.140766	−	0.243814i
$799$	−4.72205	−	8.17882i	−0.167054	−	0.289346i
$800$	−0.397532	−	0.688545i	−0.0140549	−	0.0243437i
$801$	−3.33317			−0.117772
$802$	−3.49309	−	6.05021i	−0.123345	−	0.213640i
$803$	−12.0640	−	20.8955i	−0.425729	−	0.737385i
$804$	−10.4095	−	18.0298i	−0.367115	−	0.635862i
$805$	−29.2898	+	50.7314i	−1.03233	+	1.78805i
$806$	−0.817007			−0.0287779
$807$	−13.1399	+	22.7590i	−0.462546	+	0.801154i
$808$	−4.88796	−	8.46619i	−0.171958	−	0.297839i
$809$	5.63262			0.198032			0.0990162	−	0.995086i	$-0.468430\pi$
$809$	5.63262			0.198032			0.0990162	+	0.995086i	$0.468430\pi$
$810$	2.79784	+	4.84600i	0.0983061	+	0.170271i
$811$	13.3879	−	23.1885i	0.470111	−	0.814257i	−0.529304	−	0.848432i	$-0.677547\pi$
$811$	13.3879	−	23.1885i	0.470111	−	0.814257i	0.999416	+	0.0341751i	$0.0108804\pi$
$812$	14.4743	−	25.0701i	0.507947	−	0.879789i
$813$	−51.1167			−1.79274
$814$	0.357449	−	0.619120i	0.0125286	−	0.0217001i
$815$	−56.8527			−1.99146
$816$	7.45543			0.260992
$817$	36.5879	+	16.2263i	1.28005	+	0.567686i
$818$	5.37486			0.187928
$819$	−1.27131			−0.0444233
$820$	−24.2341	+	41.9747i	−0.846291	+	1.46582i
$821$	−41.4868			−1.44790			−0.723950	−	0.689853i	$-0.757675\pi$
$821$	−41.4868			−1.44790			−0.723950	+	0.689853i	$0.757675\pi$
$822$	−2.17321	+	3.76411i	−0.0757994	+	0.131288i
$823$	4.81394	−	8.33799i	0.167803	−	0.290644i	−0.769844	−	0.638232i	$-0.779666\pi$
$823$	4.81394	−	8.33799i	0.167803	−	0.290644i	0.937647	+	0.347588i	$0.112999\pi$
$824$	0.476190	+	0.824785i	0.0165889	+	0.0287327i
$825$	1.02606			0.0357227
$826$	0.0458984	+	0.0794984i	0.00159701	+	0.00276610i
$827$	2.42675	−	4.20326i	0.0843865	−	0.146162i	−0.820743	−	0.571297i	$-0.806440\pi$
$827$	2.42675	−	4.20326i	0.0843865	−	0.146162i	0.905130	+	0.425136i	$0.139774\pi$
$828$	−17.4086			−0.604990
$829$	1.07387	−	1.85999i	0.0372969	−	0.0646001i	−0.846774	−	0.531952i	$-0.821459\pi$
$829$	1.07387	−	1.85999i	0.0372969	−	0.0646001i	0.884071	+	0.467352i	$0.154792\pi$
$830$	4.21337	+	7.29777i	0.146248	+	0.253309i
$831$	−6.82945	−	11.8290i	−0.236911	−	0.410342i
$832$	−1.43026	−	2.47729i	−0.0495855	−	0.0858846i
$833$	−1.68903			−0.0585215
$834$	1.66396	+	2.88206i	0.0576182	+	0.0997976i
$835$	−2.65715	−	4.60232i	−0.0919546	−	0.159270i
$836$	−9.78133	+	16.9418i	−0.338294	+	0.585943i
$837$	−17.5775	+	30.4450i	−0.607566	+	1.05233i
$838$	4.37172			0.151019
$839$	32.1328			1.10935			0.554673	−	0.832068i	$-0.312843\pi$
$839$	32.1328			1.10935			0.554673	+	0.832068i	$0.312843\pi$
$840$	−5.93289	+	10.2761i	−0.204704	+	0.354558i
$841$	1.83857	−	3.18450i	0.0633989	−	0.109810i
$842$	2.94366	+	5.09856i	0.101445	+	0.175708i
$843$	0.377722	+	0.654233i	0.0130094	+	0.0225330i
$844$	8.30787			0.285969
$845$	14.7794	+	25.5987i	0.508427	+	0.880622i
$846$	1.07497	+	1.86191i	0.0369584	+	0.0640138i
$847$	12.2372	+	21.1955i	0.420477	+	0.728287i
$848$	22.8585	−	39.5921i	0.784965	−	1.35960i
$849$	60.5434			2.07784
$850$	0.0342260	−	0.0592812i	0.00117394	−	0.00203333i
$851$	−8.52853	−	14.7718i	−0.292354	−	0.506372i
$852$	44.9984			1.54162
$853$	12.8845	+	22.3166i	0.441157	+	0.764106i	0.997776	−	0.0666623i	$-0.0212350\pi$
$853$	12.8845	+	22.3166i	0.441157	+	0.764106i	−0.556619	+	0.830768i	$0.687902\pi$
$854$	2.17232	−	3.76256i	0.0743351	−	0.128752i
$855$	−7.27548	+	12.6015i	−0.248816	+	0.430962i
$856$	10.0490			0.343468
$857$	18.9845	−	32.8822i	0.648499	−	1.12323i	−0.334982	−	0.942224i	$-0.608730\pi$
$857$	18.9845	−	32.8822i	0.648499	−	1.12323i	0.983481	−	0.181009i	$-0.0579363\pi$
$858$	−0.302664			−0.0103328
$859$	31.9108			1.08878			0.544391	−	0.838832i	$-0.316761\pi$
$859$	31.9108			1.08878			0.544391	+	0.838832i	$0.316761\pi$
$860$	−26.9599	−	11.9564i	−0.919326	−	0.407711i
$861$	63.8058			2.17450
$862$	3.73726			0.127292
$863$	−10.5246	+	18.2291i	−0.358262	+	0.620527i	−0.987671	−	0.156547i	$-0.949964\pi$
$863$	−10.5246	+	18.2291i	−0.358262	+	0.620527i	0.629409	+	0.777074i	$0.283297\pi$
$864$	10.0914			0.343316
$865$	9.08065	−	15.7281i	0.308751	−	0.534773i
$866$	0.790438	−	1.36908i	0.0268602	−	0.0465232i
$867$	1.00430	+	1.73949i	0.0341077	+	0.0590763i
$868$	−51.2247			−1.73868
$869$	−1.06670	−	1.84758i	−0.0361854	−	0.0626749i
$870$	2.56311	−	4.43944i	0.0868976	−	0.150511i
$871$	−2.21433			−0.0750296
$872$	−2.38210	+	4.12592i	−0.0806680	+	0.139721i
$873$	1.54744	+	2.68025i	0.0523730	+	0.0907127i
$874$	−5.79150	−	10.0312i	−0.195901	−	0.339310i
$875$	15.9265	+	27.5856i	0.538415	+	0.932563i
$876$	−57.5899			−1.94578
$877$	−9.44858	−	16.3654i	−0.319056	−	0.552621i	0.661235	−	0.750179i	$-0.270032\pi$
$877$	−9.44858	−	16.3654i	−0.319056	−	0.552621i	−0.980291	+	0.197557i	$0.936699\pi$
$878$	−2.56194	−	4.43741i	−0.0864614	−	0.149755i
$879$	−22.8785	+	39.6267i	−0.771673	+	1.33658i
$880$	7.02412	−	12.1661i	0.236783	−	0.410120i
$881$	38.0679			1.28254			0.641270	−	0.767316i	$-0.278408\pi$
$881$	38.0679			1.28254			0.641270	+	0.767316i	$0.278408\pi$
$882$	0.384508			0.0129471
$883$	5.83153	−	10.1005i	0.196247	−	0.339909i	−0.751062	−	0.660232i	$-0.770458\pi$
$883$	5.83153	−	10.1005i	0.196247	−	0.339909i	0.947308	+	0.320323i	$0.103791\pi$
$884$	0.406829	−	0.704648i	0.0136831	−	0.0236999i
$885$	−0.327518	−	0.567278i	−0.0110094	−	0.0190689i
$886$	−1.20591	−	2.08869i	−0.0405133	−	0.0701710i
$887$	11.7928			0.395963			0.197982	−	0.980206i	$-0.436561\pi$
$887$	11.7928			0.395963			0.197982	+	0.980206i	$0.436561\pi$
$888$	−1.72752	−	2.99216i	−0.0579719	−	0.100410i
$889$	17.9484	+	31.0875i	0.601970	+	1.04264i
$890$	0.817085	+	1.41523i	0.0273887	+	0.0474387i
$891$	−9.05995	+	15.6923i	−0.303520	+	0.525711i
$892$	−28.2634			−0.946328
$893$	28.8219	−	49.9210i	0.964488	−	1.67054i
$894$	4.25818	+	7.37539i	0.142415	+	0.246670i
$895$	46.7788			1.56364
$896$	9.75997	+	16.9048i	0.326058	+	0.564748i
$897$	−3.61069	+	6.25390i	−0.120557	+	0.208812i
$898$	1.01864	−	1.76433i	0.0339923	−	0.0588765i
$899$	44.8091			1.49447
$900$	0.313972	−	0.543815i	0.0104657	−	0.0181272i
$901$	12.3168			0.410332
$902$	3.89487			0.129685
$903$	4.11443	+	38.6064i	0.136920	+	1.28474i
$904$	−10.8963			−0.362405
$905$	21.9156			0.728498
$906$	−0.427178	+	0.739893i	−0.0141920	+	0.0245813i
$907$	−35.6950			−1.18523			−0.592616	−	0.805485i	$-0.701905\pi$
$907$	−35.6950			−1.18523			−0.592616	+	0.805485i	$0.701905\pi$
$908$	24.1853	−	41.8903i	0.802619	−	1.39018i
$909$	5.81444	−	10.0709i	0.192853	−	0.334031i
$910$	0.311647	+	0.539788i	0.0103310	+	0.0178938i
$911$	−14.2022			−0.470539			−0.235270	−	0.971930i	$-0.575597\pi$
$911$	−14.2022			−0.470539			−0.235270	+	0.971930i	$0.575597\pi$
$912$	22.7528	+	39.4090i	0.753420	+	1.30496i
$913$	−13.6437	+	23.6316i	−0.451541	+	0.782092i
$914$	−0.551730			−0.0182496
$915$	−15.5010	+	26.8486i	−0.512449	+	0.887587i
$916$	−27.3985	−	47.4556i	−0.905272	−	1.56798i
$917$	−2.29946	−	3.98278i	−0.0759349	−	0.131523i
$918$	0.434415	+	0.752429i	0.0143378	+	0.0248339i
$919$	2.33263			0.0769463			0.0384731	−	0.999260i	$-0.487751\pi$
$919$	2.33263			0.0769463			0.0384731	+	0.999260i	$0.487751\pi$
$920$	8.64090	+	14.9665i	0.284882	+	0.493430i
$921$	−21.6563	−	37.5098i	−0.713600	−	1.23599i
$922$	0.992037	−	1.71826i	0.0326710	−	0.0565878i
$923$	2.39303	−	4.14485i	0.0787676	−	0.136430i
$924$	−18.9764			−0.624277
$925$	0.615263			0.0202297
$926$	0.398986	−	0.691065i	0.0131115	−	0.0227098i
$927$	−0.566449	+	0.981119i	−0.0186046	+	0.0322242i
$928$	−6.43133	−	11.1394i	−0.211119	−	0.365668i
$929$	6.42294	+	11.1249i	0.210730	+	0.364995i	0.951943	−	0.306275i	$-0.0990826\pi$
$929$	6.42294	+	11.1249i	0.210730	+	0.364995i	−0.741213	+	0.671270i	$0.765749\pi$
$930$	−9.07090			−0.297447
$931$	−5.15466	−	8.92813i	−0.168937	−	0.292608i
$932$	−10.3571	−	17.9391i	−0.339260	−	0.587615i
$933$	−12.6135	−	21.8473i	−0.412948	−	0.715247i
$934$	−0.946091	+	1.63868i	−0.0309570	+	0.0536192i
$935$	3.78479			0.123776
$936$	−0.187528	+	0.324807i	−0.00612953	+	0.0106167i
$937$	−3.41722	−	5.91880i	−0.111636	−	0.193359i	0.804794	−	0.593554i	$-0.202276\pi$
$937$	−3.41722	−	5.91880i	−0.111636	−	0.193359i	−0.916430	+	0.400195i	$0.868942\pi$
$938$	3.44531			0.112493
$939$	−27.8127	−	48.1730i	−0.907634	−	1.57207i
$940$	−21.2375	+	36.7845i	−0.692692	+	1.19978i
$941$	−6.73360	+	11.6629i	−0.219509	+	0.380201i	−0.954658	−	0.297705i	$-0.903779\pi$
$941$	−6.73360	+	11.6629i	−0.219509	+	0.380201i	0.735149	+	0.677906i	$0.237112\pi$
$942$	−9.21865			−0.300360
$943$	46.4647	−	80.4792i	1.51310	−	2.62076i
$944$	−0.525247			−0.0170953
$945$	26.8196			0.872441
$946$	0.251155	+	2.35663i	0.00816576	+	0.0766208i
$947$	−20.4735			−0.665300			−0.332650	−	0.943050i	$-0.607943\pi$
$947$	−20.4735			−0.665300			−0.332650	+	0.943050i	$0.607943\pi$
$948$	−5.09211			−0.165384
$949$	−3.06265	+	5.30467i	−0.0994179	+	0.172197i
$950$	0.417810			0.0135555
$951$	1.45108	−	2.51335i	0.0470546	−	0.0815010i
$952$	−1.28169	+	2.21996i	−0.0415399	+	0.0719492i
$953$	−1.62632	−	2.81687i	−0.0526816	−	0.0912473i	0.838482	−	0.544929i	$-0.183444\pi$
$953$	−1.62632	−	2.81687i	−0.0526816	−	0.0912473i	−0.891164	+	0.453682i	$0.850110\pi$
$954$	−2.80392			−0.0907803
$955$	3.85170	+	6.67134i	0.124638	+	0.215880i
$956$	−11.7730	+	20.3914i	−0.380765	+	0.659505i
$957$	16.5997			0.536592
$958$	−2.24343	+	3.88573i	−0.0724819	+	0.125542i
$959$	14.4923	+	25.1014i	0.467980	+	0.810565i
$960$	−15.8796	−	27.5043i	−0.512513	−	0.887699i
$961$	−24.1450	−	41.8205i	−0.778873	−	1.34905i
$962$	−0.181489			−0.00585144
$963$	5.97688	+	10.3523i	0.192602	+	0.333597i
$964$	−20.5474	−	35.5892i	−0.661788	−	1.14625i
$965$	−21.2353	+	36.7807i	−0.683590	+	1.18401i
$966$	5.61794	−	9.73055i	0.180754	−	0.313075i
$967$	−40.3088			−1.29625			−0.648123	−	0.761536i	$-0.724446\pi$
$967$	−40.3088			−1.29625			−0.648123	+	0.761536i	$0.724446\pi$
$968$	7.22032			0.232070
$969$	−6.12991	+	10.6173i	−0.196921	+	0.341077i
$970$	0.758672	−	1.31406i	0.0243595	−	0.0421919i
$971$	24.0984	+	41.7397i	0.773356	+	1.33949i	0.935714	+	0.352760i	$0.114757\pi$
$971$	24.0984	+	41.7397i	0.773356	+	1.33949i	−0.162358	+	0.986732i	$0.551910\pi$
$972$	10.0675	+	17.4375i	0.322916	+	0.559307i
$973$	22.1926			0.711461
$974$	−0.818347	−	1.41742i	−0.0262215	−	0.0454170i
$975$	−0.130241	−	0.225584i	−0.00417105	−	0.00722446i
$976$	12.4296	+	21.5288i	0.397863	+	0.689120i
$977$	3.54330	−	6.13718i	0.113360	−	0.196346i	−0.803763	−	0.594950i	$-0.797172\pi$
$977$	3.54330	−	6.13718i	0.113360	−	0.196346i	0.917123	+	0.398604i	$0.130505\pi$
$978$	10.9047			0.348693
$979$	−2.64588	+	4.58280i	−0.0845626	+	0.146467i
$980$	3.79823	+	6.57874i	0.121330	+	0.210150i
$981$	−5.66723			−0.180941
$982$	−0.227056	−	0.393272i	−0.00724564	−	0.0125498i
$983$	−23.3544	+	40.4509i	−0.744888	+	1.29018i	0.205359	+	0.978687i	$0.434164\pi$
$983$	−23.3544	+	40.4509i	−0.744888	+	1.29018i	−0.950247	+	0.311498i	$0.899169\pi$
$984$	9.41180	−	16.3017i	0.300037	−	0.519680i
$985$	−46.9264			−1.49520
$986$	0.553714	−	0.959060i	0.0176338	−	0.0305427i
$987$	55.9162			1.77983
$988$	4.96631			0.157999
$989$	51.6910	+	22.9244i	1.64368	+	0.728953i
$990$	−0.861608			−0.0273837
$991$	−55.2306			−1.75446			−0.877228	−	0.480073i	$-0.840610\pi$
$991$	−55.2306			−1.75446			−0.877228	+	0.480073i	$0.840610\pi$
$992$	−11.3803	+	19.7113i	−0.361325	+	0.625833i
$993$	−9.58173			−0.304067
$994$	−3.72336	+	6.44905i	−0.118098	+	0.204552i
$995$	12.2336	−	21.1892i	0.387830	−	0.671742i
$996$	32.5654	+	56.4050i	1.03188	+	1.78726i
$997$	−32.0413			−1.01476			−0.507380	−	0.861723i	$-0.669386\pi$
$997$	−32.0413			−1.01476			−0.507380	+	0.861723i	$0.669386\pi$
$998$	−1.30314	−	2.25710i	−0.0412501	−	0.0714473i
$999$	−3.90463	+	6.76302i	−0.123537	+	0.213972i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.e.a.307.16	✓	58
43.36	even	3	inner	731.2.e.a.681.16	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.e.a.307.16	✓	58	1.1	even	1	trivial
731.2.e.a.681.16	yes	58	43.36	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.220069 q^{2} +(1.00430 - 1.73949i) q^{3} -1.95157 q^{4} +(-1.15229 + 1.99582i) q^{5} +(0.221015 - 0.382808i) q^{6} +(-1.47386 - 2.55280i) q^{7} -0.869618 q^{8} +(-0.517225 - 0.895859i) q^{9} +O(q^{10})\)	\(q+0.220069 q^{2} +(1.00430 - 1.73949i) q^{3} -1.95157 q^{4} +(-1.15229 + 1.99582i) q^{5} +(0.221015 - 0.382808i) q^{6} +(-1.47386 - 2.55280i) q^{7} -0.869618 q^{8} +(-0.517225 - 0.895859i) q^{9} +(-0.253582 + 0.439217i) q^{10} -1.64230 q^{11} +(-1.95996 + 3.39474i) q^{12} +(0.208462 + 0.361068i) q^{13} +(-0.324350 - 0.561791i) q^{14} +(2.31447 + 4.00879i) q^{15} +3.71176 q^{16} +(0.500000 + 0.866025i) q^{17} +(-0.113825 - 0.197151i) q^{18} +(-3.05184 + 5.28595i) q^{19} +(2.24877 - 3.89498i) q^{20} -5.92076 q^{21} -0.361419 q^{22} +(-4.31162 + 7.46794i) q^{23} +(-0.873354 + 1.51269i) q^{24} +(-0.155524 - 0.269375i) q^{25} +(0.0458761 + 0.0794597i) q^{26} +3.94799 q^{27} +(2.87634 + 4.98196i) q^{28} +(-2.51609 - 4.35800i) q^{29} +(0.509344 + 0.882209i) q^{30} +(-4.45225 + 7.71152i) q^{31} +2.55608 q^{32} +(-1.64935 + 2.85676i) q^{33} +(0.110034 + 0.190585i) q^{34} +6.79322 q^{35} +(1.00940 + 1.74833i) q^{36} +(-0.989017 + 1.71303i) q^{37} +(-0.671616 + 1.16327i) q^{38} +0.837433 q^{39} +(1.00205 - 1.73560i) q^{40} -10.7766 q^{41} -1.30298 q^{42} +(-0.694915 - 6.52051i) q^{43} +3.20506 q^{44} +2.38396 q^{45} +(-0.948854 + 1.64346i) q^{46} -9.44409 q^{47} +(3.72771 - 6.45659i) q^{48} +(-0.844515 + 1.46274i) q^{49} +(-0.0342260 - 0.0592812i) q^{50} +2.00859 q^{51} +(-0.406829 - 0.704648i) q^{52} +(6.15840 - 10.6667i) q^{53} +0.868831 q^{54} +(1.89239 - 3.27772i) q^{55} +(1.28169 + 2.21996i) q^{56} +(6.12991 + 10.6173i) q^{57} +(-0.553714 - 0.959060i) q^{58} -0.141509 q^{59} +(-4.51686 - 7.82343i) q^{60} +(3.34872 + 5.80015i) q^{61} +(-0.979802 + 1.69707i) q^{62} +(-1.52463 + 2.64074i) q^{63} -6.86101 q^{64} -0.960833 q^{65} +(-0.362972 + 0.628685i) q^{66} +(-2.65555 + 4.59954i) q^{67} +(-0.975785 - 1.69011i) q^{68} +(8.66029 + 15.0001i) q^{69} +1.49498 q^{70} +(-5.73972 - 9.94149i) q^{71} +(0.449788 + 0.779055i) q^{72} +(7.34581 + 12.7233i) q^{73} +(-0.217652 + 0.376984i) q^{74} -0.624769 q^{75} +(5.95588 - 10.3159i) q^{76} +(2.42051 + 4.19245i) q^{77} +0.184293 q^{78} +(0.649518 + 1.12500i) q^{79} +(-4.27701 + 7.40800i) q^{80} +(5.51663 - 9.55509i) q^{81} -2.37160 q^{82} +(8.30770 - 14.3894i) q^{83} +11.5548 q^{84} -2.30457 q^{85} +(-0.152929 - 1.43496i) q^{86} -10.1076 q^{87} +1.42817 q^{88} +(1.61108 - 2.79048i) q^{89} +0.524636 q^{90} +(0.614488 - 1.06432i) q^{91} +(8.41443 - 14.5742i) q^{92} +(8.94276 + 15.4893i) q^{93} -2.07835 q^{94} +(-7.03319 - 12.1818i) q^{95} +(2.56706 - 4.44628i) q^{96} -2.99182 q^{97} +(-0.185852 + 0.321904i) q^{98} +(0.849436 + 1.47127i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9}+O(q^{10}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9} + 4 q^{10} + 16 q^{11} + 12 q^{12} + 2 q^{13} - 11 q^{14} + 7 q^{15} + 30 q^{16} + 29 q^{17} + 8 q^{18} + 8 q^{19} - 33 q^{20} - 26 q^{21} - 22 q^{22} - 5 q^{23} + 12 q^{24} - 36 q^{25} - 12 q^{27} + 15 q^{28} + 2 q^{29} + 11 q^{30} + 3 q^{31} - 40 q^{32} + 17 q^{33} - 3 q^{34} + 38 q^{35} - 7 q^{36} + 2 q^{37} + q^{38} - 54 q^{39} + 5 q^{40} + 14 q^{41} - 112 q^{42} + 31 q^{43} - 24 q^{44} - 46 q^{45} - 13 q^{46} - 28 q^{47} - 28 q^{49} - 13 q^{50} + 6 q^{51} + 85 q^{52} - 10 q^{53} + 34 q^{54} + 36 q^{55} - 54 q^{56} - 23 q^{57} + 3 q^{58} + 12 q^{59} + 2 q^{60} - q^{61} - q^{62} - 14 q^{63} + 28 q^{64} + 80 q^{65} - 74 q^{66} + 11 q^{67} + 27 q^{68} - 11 q^{69} + 2 q^{70} + 16 q^{71} + 21 q^{72} + 14 q^{73} + 21 q^{74} - 54 q^{75} + 44 q^{76} + 25 q^{77} + 88 q^{78} - 4 q^{79} - 112 q^{80} + 11 q^{81} - 176 q^{82} - 3 q^{83} + 100 q^{84} - 2 q^{85} + 44 q^{86} + 8 q^{87} - 106 q^{88} + 82 q^{89} + 54 q^{90} - 15 q^{91} + 42 q^{92} + 88 q^{94} + 29 q^{95} + 20 q^{96} + 20 q^{97} + 44 q^{98} - 54 q^{99}+O(q^{100}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9 + 4 * q^10 + 16 * q^11 + 12 * q^12 + 2 * q^13 - 11 * q^14 + 7 * q^15 + 30 * q^16 + 29 * q^17 + 8 * q^18 + 8 * q^19 - 33 * q^20 - 26 * q^21 - 22 * q^22 - 5 * q^23 + 12 * q^24 - 36 * q^25 - 12 * q^27 + 15 * q^28 + 2 * q^29 + 11 * q^30 + 3 * q^31 - 40 * q^32 + 17 * q^33 - 3 * q^34 + 38 * q^35 - 7 * q^36 + 2 * q^37 + q^38 - 54 * q^39 + 5 * q^40 + 14 * q^41 - 112 * q^42 + 31 * q^43 - 24 * q^44 - 46 * q^45 - 13 * q^46 - 28 * q^47 - 28 * q^49 - 13 * q^50 + 6 * q^51 + 85 * q^52 - 10 * q^53 + 34 * q^54 + 36 * q^55 - 54 * q^56 - 23 * q^57 + 3 * q^58 + 12 * q^59 + 2 * q^60 - q^61 - q^62 - 14 * q^63 + 28 * q^64 + 80 * q^65 - 74 * q^66 + 11 * q^67 + 27 * q^68 - 11 * q^69 + 2 * q^70 + 16 * q^71 + 21 * q^72 + 14 * q^73 + 21 * q^74 - 54 * q^75 + 44 * q^76 + 25 * q^77 + 88 * q^78 - 4 * q^79 - 112 * q^80 + 11 * q^81 - 176 * q^82 - 3 * q^83 + 100 * q^84 - 2 * q^85 + 44 * q^86 + 8 * q^87 - 106 * q^88 + 82 * q^89 + 54 * q^90 - 15 * q^91 + 42 * q^92 + 88 * q^94 + 29 * q^95 + 20 * q^96 + 20 * q^97 + 44 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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