LMFDB - Embedded newform 403.2.r.a.218.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(218,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([5, 0]))

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

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

chi := DirichletCharacter("403.218");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			218.4
Character	$\chi$	$=$	403.218
Dual form			403.2.r.a.342.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.14952 + 1.24103i) q^{2} +(-0.331917 - 0.574896i) q^{3} +(2.08030 - 3.60319i) q^{4} -0.685218i q^{5} +(1.42693 + 0.823836i) q^{6} +(3.86933 + 2.23396i) q^{7} +5.36274i q^{8} +(1.27966 - 2.21644i) q^{9} +O(q^{10})$	\(q+(-2.14952 + 1.24103i) q^{2} +(-0.331917 - 0.574896i) q^{3} +(2.08030 - 3.60319i) q^{4} -0.685218i q^{5} +(1.42693 + 0.823836i) q^{6} +(3.86933 + 2.23396i) q^{7} +5.36274i q^{8} +(1.27966 - 2.21644i) q^{9} +(0.850375 + 1.47289i) q^{10} +(-4.37961 + 2.52857i) q^{11} -2.76195 q^{12} +(-1.71700 - 3.17047i) q^{13} -11.0896 q^{14} +(-0.393930 + 0.227435i) q^{15} +(-2.49471 - 4.32096i) q^{16} +(3.04608 - 5.27597i) q^{17} +6.35239i q^{18} +(1.93930 + 1.11966i) q^{19} +(-2.46897 - 1.42546i) q^{20} -2.96595i q^{21} +(6.27606 - 10.8704i) q^{22} +(-1.10680 - 1.91703i) q^{23} +(3.08302 - 1.77998i) q^{24} +4.53048 q^{25} +(7.62538 + 4.68416i) q^{26} -3.69046 q^{27} +(16.0987 - 9.29461i) q^{28} +(1.54278 + 2.67217i) q^{29} +(0.564507 - 0.977755i) q^{30} -1.00000i q^{31} +(1.43633 + 0.829266i) q^{32} +(2.90733 + 1.67855i) q^{33} +15.1211i q^{34} +(1.53075 - 2.65134i) q^{35} +(-5.32417 - 9.22173i) q^{36} +(-0.847004 + 0.489018i) q^{37} -5.55811 q^{38} +(-1.25279 + 2.03943i) q^{39} +3.67465 q^{40} +(8.98342 - 5.18658i) q^{41} +(3.68083 + 6.37538i) q^{42} +(-0.440878 + 0.763623i) q^{43} +21.0408i q^{44} +(-1.51875 - 0.876848i) q^{45} +(4.75817 + 2.74713i) q^{46} -4.67863i q^{47} +(-1.65607 + 2.86840i) q^{48} +(6.48114 + 11.2257i) q^{49} +(-9.73837 + 5.62245i) q^{50} -4.04418 q^{51} +(-14.9957 - 0.408864i) q^{52} +7.71717 q^{53} +(7.93274 - 4.57997i) q^{54} +(1.73262 + 3.00099i) q^{55} +(-11.9801 + 20.7502i) q^{56} -1.48653i q^{57} +(-6.63247 - 3.82926i) q^{58} +(0.266951 + 0.154124i) q^{59} +1.89254i q^{60} +(4.17977 - 7.23958i) q^{61} +(1.24103 + 2.14952i) q^{62} +(9.90287 - 5.71743i) q^{63} +5.86226 q^{64} +(-2.17247 + 1.17652i) q^{65} -8.33251 q^{66} +(4.20606 - 2.42837i) q^{67} +(-12.6735 - 21.9512i) q^{68} +(-0.734728 + 1.27259i) q^{69} +7.59881i q^{70} +(13.8281 + 7.98366i) q^{71} +(11.8862 + 6.86250i) q^{72} -14.0009i q^{73} +(1.21377 - 2.10231i) q^{74} +(-1.50374 - 2.60455i) q^{75} +(8.06868 - 4.65845i) q^{76} -22.5949 q^{77} +(0.161917 - 5.93856i) q^{78} -3.06698 q^{79} +(-2.96080 + 1.70942i) q^{80} +(-2.61406 - 4.52769i) q^{81} +(-12.8734 + 22.2973i) q^{82} +1.29185i q^{83} +(-10.6869 - 6.17007i) q^{84} +(-3.61519 - 2.08723i) q^{85} -2.18857i q^{86} +(1.02415 - 1.77387i) q^{87} +(-13.5601 - 23.4867i) q^{88} +(-15.8217 + 9.13464i) q^{89} +4.35277 q^{90} +(0.439064 - 16.1033i) q^{91} -9.20987 q^{92} +(-0.574896 + 0.331917i) q^{93} +(5.80632 + 10.0568i) q^{94} +(0.767210 - 1.32885i) q^{95} -1.10099i q^{96} +(6.07721 + 3.50868i) q^{97} +(-27.8627 - 16.0865i) q^{98} +12.9429i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 32 q^{4} - 34 q^{9}+O(q^{10}) $ 68 * q + 32 * q^4 - 34 * q^9	$ 68 q + 32 q^{4} - 34 q^{9} + 8 q^{10} - 12 q^{11} - 16 q^{12} + 6 q^{13} - 8 q^{14} - 36 q^{16} - 6 q^{17} + 12 q^{19} - 12 q^{20} - 20 q^{22} - 8 q^{23} + 48 q^{24} - 72 q^{25} - 12 q^{27} - 6 q^{28} + 32 q^{30} + 6 q^{33} + 30 q^{35} + 40 q^{36} - 42 q^{37} - 36 q^{38} - 14 q^{39} + 8 q^{40} + 18 q^{41} - 16 q^{42} + 12 q^{43} + 60 q^{45} + 30 q^{46} - 46 q^{48} + 22 q^{49} + 56 q^{51} + 20 q^{53} - 114 q^{54} - 6 q^{55} - 2 q^{56} - 12 q^{58} + 6 q^{59} + 6 q^{61} - 8 q^{62} - 30 q^{63} + 24 q^{64} + 24 q^{65} + 8 q^{66} - 48 q^{67} + 58 q^{68} - 28 q^{69} - 30 q^{71} + 72 q^{72} + 8 q^{74} - 4 q^{75} - 12 q^{76} - 20 q^{77} + 26 q^{78} + 16 q^{79} + 42 q^{80} - 58 q^{81} - 42 q^{82} - 72 q^{84} + 30 q^{85} - 20 q^{87} + 64 q^{88} + 18 q^{89} + 52 q^{90} - 22 q^{91} + 48 q^{92} + 8 q^{94} - 32 q^{95} - 168 q^{98}+O(q^{100}) $ 68 * q + 32 * q^4 - 34 * q^9 + 8 * q^10 - 12 * q^11 - 16 * q^12 + 6 * q^13 - 8 * q^14 - 36 * q^16 - 6 * q^17 + 12 * q^19 - 12 * q^20 - 20 * q^22 - 8 * q^23 + 48 * q^24 - 72 * q^25 - 12 * q^27 - 6 * q^28 + 32 * q^30 + 6 * q^33 + 30 * q^35 + 40 * q^36 - 42 * q^37 - 36 * q^38 - 14 * q^39 + 8 * q^40 + 18 * q^41 - 16 * q^42 + 12 * q^43 + 60 * q^45 + 30 * q^46 - 46 * q^48 + 22 * q^49 + 56 * q^51 + 20 * q^53 - 114 * q^54 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 6 * q^59 + 6 * q^61 - 8 * q^62 - 30 * q^63 + 24 * q^64 + 24 * q^65 + 8 * q^66 - 48 * q^67 + 58 * q^68 - 28 * q^69 - 30 * q^71 + 72 * q^72 + 8 * q^74 - 4 * q^75 - 12 * q^76 - 20 * q^77 + 26 * q^78 + 16 * q^79 + 42 * q^80 - 58 * q^81 - 42 * q^82 - 72 * q^84 + 30 * q^85 - 20 * q^87 + 64 * q^88 + 18 * q^89 + 52 * q^90 - 22 * q^91 + 48 * q^92 + 8 * q^94 - 32 * q^95 - 168 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.14952	+	1.24103i	−1.51994	+	0.877539i	−0.520219	+	0.854033i	$0.674150\pi$
$2$	−2.14952	+	1.24103i	−1.51994	+	0.877539i	−0.999724	+	0.0235067i	$0.992517\pi$
$3$	−0.331917	−	0.574896i	−0.191632	−	0.331917i	0.754159	−	0.656692i	$-0.228045\pi$
$3$	−0.331917	−	0.574896i	−0.191632	−	0.331917i	−0.945791	+	0.324775i	$0.894711\pi$
$4$	2.08030	−	3.60319i	1.04015	−	1.80159i
$5$		−	0.685218i		−	0.306439i	−0.988192	−	0.153219i	$-0.951036\pi$
$5$		−	0.685218i		−	0.306439i	0.988192	−	0.153219i	$-0.0489641\pi$
$6$	1.42693	+	0.823836i	0.582540	+	0.336330i
$7$	3.86933	+	2.23396i	1.46247	+	0.844357i	0.999125	−	0.0418218i	$-0.0133162\pi$
$7$	3.86933	+	2.23396i	1.46247	+	0.844357i	0.463344	+	0.886179i	$0.346650\pi$
$8$			5.36274i			1.89601i
$9$	1.27966	−	2.21644i	0.426554	−	0.738814i
$10$	0.850375	+	1.47289i	0.268912	+	0.465770i
$11$	−4.37961	+	2.52857i	−1.32050	+	0.762393i	−0.983809	−	0.179221i	$-0.942642\pi$
$11$	−4.37961	+	2.52857i	−1.32050	+	0.762393i	−0.336694	+	0.941614i	$0.609309\pi$
$12$	−2.76195			−0.797305
$13$	−1.71700	−	3.17047i	−0.476210	−	0.879331i
$13$	−1.71700	−	3.17047i	−0.476210	−	0.879331i
$14$	−11.0896			−2.96383
$15$	−0.393930	+	0.227435i	−0.101712	+	0.0587236i
$16$	−2.49471	−	4.32096i	−0.623677	−	1.08024i
$17$	3.04608	−	5.27597i	0.738783	−	1.27961i	−0.214261	−	0.976777i	$-0.568734\pi$
$17$	3.04608	−	5.27597i	0.738783	−	1.27961i	0.953044	−	0.302833i	$-0.0979325\pi$
$18$			6.35239i			1.49727i
$19$	1.93930	+	1.11966i	0.444907	+	0.256867i	0.705677	−	0.708534i	$-0.250643\pi$
$19$	1.93930	+	1.11966i	0.444907	+	0.256867i	−0.260770	+	0.965401i	$0.583976\pi$
$20$	−2.46897	−	1.42546i	−0.552079	−	0.318743i
$21$		−	2.96595i		−	0.647224i
$22$	6.27606	−	10.8704i	1.33806	−	2.31759i
$23$	−1.10680	−	1.91703i	−0.230783	−	0.399728i	0.727256	−	0.686366i	$-0.240795\pi$
$23$	−1.10680	−	1.91703i	−0.230783	−	0.399728i	−0.958039	+	0.286639i	$0.907462\pi$
$24$	3.08302	−	1.77998i	0.629319	−	0.363337i
$25$	4.53048			0.906095
$26$	7.62538	+	4.68416i	1.49546	+	0.918640i
$27$	−3.69046			−0.710230
$28$	16.0987	−	9.29461i	3.04238	−	1.75652i
$29$	1.54278	+	2.67217i	0.286486	+	0.496209i	0.972969	−	0.230938i	$-0.0741793\pi$
$29$	1.54278	+	2.67217i	0.286486	+	0.496209i	−0.686482	+	0.727147i	$0.740846\pi$
$30$	0.564507	−	0.977755i	0.103064	−	0.178513i
$31$		−	1.00000i		−	0.179605i
$31$		−	1.00000i		−	0.179605i
$32$	1.43633	+	0.829266i	0.253910	+	0.146595i
$33$	2.90733	+	1.67855i	0.506102	+	0.292198i
$34$			15.1211i			2.59325i
$35$	1.53075	−	2.65134i	0.258744	−	0.448157i
$36$	−5.32417	−	9.22173i	−0.887362	−	1.53696i
$37$	−0.847004	+	0.489018i	−0.139247	+	0.0803940i	−0.568005	−	0.823025i	$-0.692285\pi$
$37$	−0.847004	+	0.489018i	−0.139247	+	0.0803940i	0.428758	+	0.903419i	$0.358951\pi$
$38$	−5.55811			−0.901644
$39$	−1.25279	+	2.03943i	−0.200607	+	0.326570i
$40$	3.67465			0.581013
$41$	8.98342	−	5.18658i	1.40297	−	0.810007i	0.408277	−	0.912858i	$-0.366130\pi$
$41$	8.98342	−	5.18658i	1.40297	−	0.810007i	0.994697	+	0.102851i	$0.0327964\pi$
$42$	3.68083	+	6.37538i	0.567964	+	0.983743i
$43$	−0.440878	+	0.763623i	−0.0672333	+	0.116451i	−0.897682	−	0.440643i	$-0.854751\pi$
$43$	−0.440878	+	0.763623i	−0.0672333	+	0.116451i	0.830449	+	0.557094i	$0.188084\pi$
$44$			21.0408i			3.17201i
$45$	−1.51875	−	0.876848i	−0.226401	−	0.130713i
$46$	4.75817	+	2.74713i	0.701553	+	0.405042i
$47$		−	4.67863i		−	0.682449i	−0.939982	−	0.341224i	$-0.889158\pi$
$47$		−	4.67863i		−	0.682449i	0.939982	−	0.341224i	$-0.110842\pi$
$48$	−1.65607	+	2.86840i	−0.239033	+	0.414017i
$49$	6.48114	+	11.2257i	0.925877	+	1.60367i
$50$	−9.73837	+	5.62245i	−1.37721	+	0.795134i
$51$	−4.04418			−0.566298
$52$	−14.9957	−	0.408864i	−2.07953	−	0.0566992i
$53$	7.71717			1.06004			0.530018	−	0.847987i	$-0.322185\pi$
$53$	7.71717			1.06004			0.530018	+	0.847987i	$0.322185\pi$
$54$	7.93274	−	4.57997i	1.07951	−	0.623255i
$55$	1.73262	+	3.00099i	0.233627	+	0.404654i
$56$	−11.9801	+	20.7502i	−1.60091	+	2.77286i
$57$		−	1.48653i		−	0.196896i
$58$	−6.63247	−	3.82926i	−0.870886	−	0.502806i
$59$	0.266951	+	0.154124i	0.0347540	+	0.0200652i	0.517276	−	0.855818i	$-0.326946\pi$
$59$	0.266951	+	0.154124i	0.0347540	+	0.0200652i	−0.482522	+	0.875884i	$0.660279\pi$
$60$			1.89254i			0.244325i
$61$	4.17977	−	7.23958i	0.535165	−	0.926933i	−0.463990	−	0.885840i	$-0.653583\pi$
$61$	4.17977	−	7.23958i	0.535165	−	0.926933i	0.999155	−	0.0410927i	$-0.0130839\pi$
$62$	1.24103	+	2.14952i	0.157611	+	0.272990i
$63$	9.90287	−	5.71743i	1.24764	−	0.720328i
$64$	5.86226			0.732783
$65$	−2.17247	+	1.17652i	−0.269461	+	0.145929i
$66$	−8.33251			−1.02566
$67$	4.20606	−	2.42837i	0.513852	−	0.296673i	−0.220563	−	0.975373i	$-0.570790\pi$
$67$	4.20606	−	2.42837i	0.513852	−	0.296673i	0.734416	+	0.678700i	$0.237456\pi$
$68$	−12.6735	−	21.9512i	−1.53689	−	2.66197i
$69$	−0.734728	+	1.27259i	−0.0884508	+	0.153201i
$70$			7.59881i			0.908232i
$71$	13.8281	+	7.98366i	1.64109	+	0.947486i	0.980446	+	0.196791i	$0.0630519\pi$
$71$	13.8281	+	7.98366i	1.64109	+	0.947486i	0.660648	+	0.750695i	$0.270281\pi$
$72$	11.8862	+	6.86250i	1.40080	+	0.808753i
$73$		−	14.0009i		−	1.63868i	−0.573310	−	0.819338i	$-0.694341\pi$
$73$		−	14.0009i		−	1.63868i	0.573310	−	0.819338i	$-0.305659\pi$
$74$	1.21377	−	2.10231i	0.141098	−	0.244389i
$75$	−1.50374	−	2.60455i	−0.173637	−	0.300748i
$76$	8.06868	−	4.65845i	0.925541	−	0.534361i
$77$	−22.5949			−2.57493
$78$	0.161917	−	5.93856i	0.0183335	−	0.672409i
$79$	−3.06698			−0.345063			−0.172531	−	0.985004i	$-0.555195\pi$
$79$	−3.06698			−0.345063			−0.172531	+	0.985004i	$0.555195\pi$
$80$	−2.96080	+	1.70942i	−0.331028	+	0.191119i
$81$	−2.61406	−	4.52769i	−0.290451	−	0.503076i
$82$	−12.8734	+	22.2973i	−1.42163	+	2.46233i
$83$			1.29185i			0.141799i	0.997483	+	0.0708994i	$0.0225869\pi$
$83$			1.29185i			0.141799i	−0.997483	+	0.0708994i	$0.977413\pi$
$84$	−10.6869	−	6.17007i	−1.16603	−	0.673210i
$85$	−3.61519	−	2.08723i	−0.392122	−	0.226392i
$86$		−	2.18857i		−	0.235999i
$87$	1.02415	−	1.77387i	0.109800	−	0.190179i
$88$	−13.5601	−	23.4867i	−1.44551	−	2.50369i
$89$	−15.8217	+	9.13464i	−1.67709	+	0.968269i	−0.713592	+	0.700562i	$0.752933\pi$
$89$	−15.8217	+	9.13464i	−1.67709	+	0.968269i	−0.963500	+	0.267707i	$0.913734\pi$
$90$	4.35277			0.458823
$91$	0.439064	−	16.1033i	0.0460264	−	1.68809i
$92$	−9.20987			−0.960196
$93$	−0.574896	+	0.331917i	−0.0596140	+	0.0344181i
$94$	5.80632	+	10.0568i	0.598876	+	1.03728i
$95$	0.767210	−	1.32885i	0.0787141	−	0.136337i
$96$		−	1.10099i		−	0.112369i
$97$	6.07721	+	3.50868i	0.617047	+	0.356252i	0.775718	−	0.631079i	$-0.217388\pi$
$97$	6.07721	+	3.50868i	0.617047	+	0.356252i	−0.158671	+	0.987331i	$0.550721\pi$
$98$	−27.8627	−	16.0865i	−2.81456	−	1.62499i
$99$			12.9429i			1.30081i
$100$	9.42476	−	16.3242i	0.942476	−	1.63242i
$101$	−5.59155	−	9.68485i	−0.556380	−	0.963678i	−0.997795	−	0.0663751i	$-0.978857\pi$
$101$	−5.59155	−	9.68485i	−0.556380	−	0.963678i	0.441415	−	0.897303i	$-0.354477\pi$
$102$	8.69306	−	5.01894i	0.860741	−	0.496949i
$103$	−11.0230			−1.08612			−0.543062	−	0.839693i	$-0.682735\pi$
$103$	−11.0230			−1.08612			−0.543062	+	0.839693i	$0.682735\pi$
$104$	17.0024	−	9.20783i	1.66723	−	0.902902i
$105$	−2.03232			−0.198335
$106$	−16.5882	+	9.57723i	−1.61119	+	0.930223i
$107$	−0.178690	−	0.309501i	−0.0172746	−	0.0299206i	0.857259	−	0.514886i	$-0.172166\pi$
$107$	−0.178690	−	0.309501i	−0.0172746	−	0.0299206i	−0.874534	+	0.484965i	$0.838832\pi$
$108$	−7.67728	+	13.2974i	−0.738747	+	1.27955i
$109$			6.37892i			0.610990i	0.952194	+	0.305495i	$0.0988219\pi$
$109$			6.37892i			0.610990i	−0.952194	+	0.305495i	$0.901178\pi$
$110$	−7.44863	−	4.30047i	−0.710199	−	0.410034i
$111$	0.562269	+	0.324626i	0.0533682	+	0.0308122i
$112$		−	22.2923i		−	2.10642i
$113$	−7.98870	+	13.8368i	−0.751514	+	1.30166i	0.195575	+	0.980689i	$0.437343\pi$
$113$	−7.98870	+	13.8368i	−0.751514	+	1.30166i	−0.947089	+	0.320971i	$0.895991\pi$
$114$	1.84483	+	3.19534i	0.172784	+	0.299271i
$115$	−1.31358	+	0.758397i	−0.122492	+	0.0707208i
$116$	12.8378			1.19196
$117$	−9.22435	−	0.251506i	−0.852792	−	0.0232517i
$118$	−0.765089			−0.0704321
$119$	23.5726	−	13.6096i	2.16089	−	1.24759i
$120$	−1.21968	−	2.11254i	−0.111341	−	0.192848i
$121$	7.28734	−	12.6220i	0.662486	−	1.14746i
$122$			20.7489i			1.87851i
$123$	−5.96349	−	3.44302i	−0.537710	−	0.310447i
$124$	−3.60319	−	2.08030i	−0.323576	−	0.186817i
$125$		−	6.53046i		−	0.584102i
$126$	−14.1910	+	24.5795i	−1.26423	+	2.18971i
$127$	−5.31957	−	9.21376i	−0.472035	−	0.817589i	0.527453	−	0.849584i	$-0.323147\pi$
$127$	−5.31957	−	9.21376i	−0.472035	−	0.817589i	−0.999488	+	0.0319955i	$0.989814\pi$
$128$	−15.4737	+	8.93377i	−1.36770	+	0.789641i
$129$	0.585339			0.0515362
$130$	3.20967	−	5.22505i	0.281507	−	0.458267i
$131$	6.35229			0.555002			0.277501	−	0.960725i	$-0.410494\pi$
$131$	6.35229			0.555002			0.277501	+	0.960725i	$0.410494\pi$
$132$	12.0963	−	6.98378i	1.05284	−	0.607860i
$133$	5.00254	+	8.66465i	0.433775	+	0.751321i
$134$	−6.02735	+	10.4397i	−0.520684	+	0.901851i
$135$			2.52877i			0.217642i
$136$	28.2936	+	16.3353i	2.42616	+	1.40074i
$137$	5.04176	+	2.91086i	0.430747	+	0.248692i	0.699665	−	0.714471i	$-0.253333\pi$
$137$	5.04176	+	2.91086i	0.430747	+	0.248692i	−0.268918	+	0.963163i	$0.586666\pi$
$138$		−	3.64727i		−	0.310476i
$139$	−9.67296	+	16.7541i	−0.820450	+	1.42106i	0.0848979	+	0.996390i	$0.472944\pi$
$139$	−9.67296	+	16.7541i	−0.820450	+	1.42106i	−0.905348	+	0.424671i	$0.860390\pi$
$140$	−6.36884	−	11.0312i	−0.538265	−	0.932303i
$141$	−2.68973	+	1.55292i	−0.226516	+	0.130779i
$142$	−39.6318			−3.32583
$143$	15.5366	+	9.54389i	1.29923	+	0.798100i
$144$	−12.7695			−1.06413
$145$	1.83102	−	1.05714i	0.152058	−	0.0877906i
$146$	17.3755	+	30.0952i	1.43800	+	2.49069i
$147$	4.30239	−	7.45197i	0.354856	−	0.614628i
$148$			4.06922i			0.334488i
$149$	−0.0448675	−	0.0259042i	−0.00367569	−	0.00212216i	0.498161	−	0.867085i	$-0.334009\pi$
$149$	−0.0448675	−	0.0259042i	−0.00367569	−	0.00212216i	−0.501837	+	0.864962i	$0.667342\pi$
$150$	6.46465	+	3.73237i	0.527837	+	0.304747i
$151$			7.55523i			0.614836i	0.951575	+	0.307418i	$0.0994650\pi$
$151$			7.55523i			0.614836i	−0.951575	+	0.307418i	$0.900535\pi$
$152$	−6.00444	+	10.4000i	−0.487024	+	0.843550i
$153$	−7.79591	−	13.5029i	−0.630262	−	1.09165i
$154$	48.5683	−	28.0409i	3.91374	−	2.25960i
$155$	−0.685218			−0.0550381
$156$	4.74227	+	8.75668i	0.379685	+	0.701096i
$157$	−1.80316			−0.143908			−0.0719538	−	0.997408i	$-0.522923\pi$
$157$	−1.80316			−0.143908			−0.0719538	+	0.997408i	$0.522923\pi$
$158$	6.59256	−	3.80621i	0.524476	−	0.302806i
$159$	−2.56146	−	4.43658i	−0.203137	−	0.351843i
$160$	0.568228	−	0.984200i	0.0449224	−	0.0778078i
$161$		−	9.89014i		−	0.779452i
$162$	11.2380	+	6.48825i	0.882939	+	0.509765i
$163$	−19.9561	−	11.5217i	−1.56309	−	0.902448i	−0.996942	−	0.0781415i	$-0.975101\pi$
$163$	−19.9561	−	11.5217i	−1.56309	−	0.902448i	−0.566144	−	0.824307i	$-0.691565\pi$
$164$		−	43.1586i		−	3.37012i
$165$	1.15017	−	1.99216i	0.0895408	−	0.155089i
$166$	−1.60322	−	2.77686i	−0.124434	−	0.215526i
$167$	8.59263	−	4.96096i	0.664917	−	0.383890i	−0.129231	−	0.991615i	$-0.541251\pi$
$167$	8.59263	−	4.96096i	0.664917	−	0.383890i	0.794148	+	0.607724i	$0.207917\pi$
$168$	15.9056			1.22715
$169$	−7.10381	+	10.8874i	−0.546447	+	0.837494i
$170$	10.3612			0.794671
$171$	4.96331	−	2.86557i	0.379554	−	0.219136i
$172$	1.83432	+	3.17713i	0.139866	+	0.242254i
$173$	−4.42442	+	7.66332i	−0.336382	+	0.582631i	−0.983749	−	0.179547i	$-0.942537\pi$
$173$	−4.42442	+	7.66332i	−0.336382	+	0.582631i	0.647367	+	0.762178i	$0.275870\pi$
$174$			5.08398i			0.385415i
$175$	17.5299	+	10.1209i	1.32514	+	0.765068i
$176$	21.8517	+	12.6161i	1.64713	+	0.950974i
$177$		−	0.204625i		−	0.0153806i
$178$	22.6727	−	39.2702i	1.69939	−	2.94343i
$179$	11.8253	+	20.4820i	0.883862	+	1.53089i	0.847013	+	0.531573i	$0.178399\pi$
$179$	11.8253	+	20.4820i	0.883862	+	1.53089i	0.0368494	+	0.999321i	$0.488268\pi$
$180$	−6.31890	+	3.64822i	−0.470983	+	0.271922i
$181$	7.13076			0.530025			0.265013	−	0.964245i	$-0.414624\pi$
$181$	7.13076			0.530025			0.265013	+	0.964245i	$0.414624\pi$
$182$	19.0409	+	35.1594i	1.41140	+	2.60618i
$183$	−5.54934			−0.410219
$184$	10.2805	−	5.93546i	0.757889	−	0.437568i
$185$	0.335084	+	0.580382i	0.0246359	+	0.0426706i
$186$	0.823836	−	1.42693i	0.0604066	−	0.104627i
$187$			30.8089i			2.25297i
$188$	−16.8580	−	9.73297i	−1.22950	−	0.709850i
$189$	−14.2796	−	8.24434i	−1.03869	−	0.599688i
$190$			3.80852i			0.276299i
$191$	−3.27449	+	5.67159i	−0.236934	+	0.410382i	−0.959833	−	0.280572i	$-0.909476\pi$
$191$	−3.27449	+	5.67159i	−0.236934	+	0.410382i	0.722899	+	0.690954i	$0.242809\pi$
$192$	−1.94578	−	3.37019i	−0.140425	−	0.243223i
$193$	−14.8142	+	8.55296i	−1.06635	+	0.615656i	−0.927181	−	0.374613i	$-0.877775\pi$
$193$	−14.8142	+	8.55296i	−1.06635	+	0.615656i	−0.139166	+	0.990269i	$0.544442\pi$
$194$	−17.4175			−1.25050
$195$	1.39746	+	0.858437i	0.100074	+	0.0614739i
$196$	53.9309			3.85221
$197$	−2.59462	+	1.49801i	−0.184859	+	0.106729i	−0.589574	−	0.807715i	$-0.700704\pi$
$197$	−2.59462	+	1.49801i	−0.184859	+	0.106729i	0.404714	+	0.914443i	$0.367371\pi$
$198$	−16.0625	−	27.8210i	−1.14151	−	1.97715i
$199$	1.60128	−	2.77350i	0.113512	−	0.196608i	−0.803672	−	0.595072i	$-0.797123\pi$
$199$	1.60128	−	2.77350i	0.113512	−	0.196608i	0.917184	+	0.398464i	$0.130457\pi$
$200$			24.2958i			1.71797i
$201$	−2.79212	−	1.61203i	−0.196941	−	0.113704i
$202$	24.0383	+	13.8785i	1.69133	+	0.976491i
$203$			13.7860i			0.967587i
$204$	−8.41311	+	14.5719i	−0.589036	+	1.02024i
$205$	−3.55394	−	6.15560i	−0.248218	−	0.429926i
$206$	23.6941	−	13.6798i	1.65085	−	0.953117i
$207$	−5.66530			−0.393766
$208$	−9.41608	+	15.3285i	−0.652888	+	1.06284i
$209$	−11.3245			−0.783335
$210$	4.36853	−	2.52217i	0.301457	−	0.174046i
$211$	3.52299	+	6.10200i	0.242533	+	0.420079i	0.961435	−	0.275032i	$-0.0886885\pi$
$211$	3.52299	+	6.10200i	0.242533	+	0.420079i	−0.718902	+	0.695111i	$0.755355\pi$
$212$	16.0541	−	27.8064i	1.10260	−	1.90975i
$213$		−	10.5996i		−	0.726275i
$214$	0.768198	+	0.443519i	0.0525130	+	0.0303184i
$215$	0.523249	+	0.302098i	0.0356853	+	0.0206029i
$216$		−	19.7910i		−	1.34661i
$217$	2.23396	−	3.86933i	0.151651	−	0.262667i
$218$	−7.91642	−	13.7116i	−0.536167	−	0.928669i
$219$	−8.04904	+	4.64712i	−0.543904	+	0.314023i
$220$	14.4175			0.972029
$221$	−21.9574	−	0.598679i	−1.47702	−	0.0402715i
$222$	−1.61148			−0.108156
$223$	3.27605	−	1.89143i	0.219380	−	0.126659i	−0.386283	−	0.922380i	$-0.626241\pi$
$223$	3.27605	−	1.89143i	0.219380	−	0.126659i	0.605663	+	0.795721i	$0.292908\pi$
$224$	3.70509	+	6.41740i	0.247557	+	0.428781i
$225$	5.79748	−	10.0415i	0.386499	−	0.669435i
$226$		−	39.6568i		−	2.63793i
$227$	−22.4308	−	12.9504i	−1.48878	−	0.859550i	−0.488866	−	0.872359i	$-0.662589\pi$
$227$	−22.4308	−	12.9504i	−1.48878	−	0.859550i	−0.999918	+	0.0128095i	$0.995923\pi$
$228$	−5.35626	−	3.09244i	−0.354727	−	0.204802i
$229$			16.6868i			1.10269i	0.834277	+	0.551346i	$0.185886\pi$
$229$			16.6868i			1.10269i	−0.834277	+	0.551346i	$0.814114\pi$
$230$	1.88238	−	3.26038i	0.124121	−	0.214983i
$231$	7.49962	+	12.9897i	0.493439	+	0.854661i
$232$	−14.3301	+	8.27351i	−0.940820	+	0.543183i
$233$	21.1918			1.38832			0.694160	−	0.719821i	$-0.255776\pi$
$233$	21.1918			1.38832			0.694160	+	0.719821i	$0.255776\pi$
$234$	20.1401	−	10.9071i	1.31660	−	0.713017i
$235$	−3.20589			−0.209129
$236$	1.11068	−	0.641249i	0.0722988	−	0.0417417i
$237$	1.01798	+	1.76320i	0.0661251	+	0.114532i
$238$	−33.7799	+	58.5085i	−2.18962	+	3.79254i
$239$			8.01082i			0.518177i	0.965854	+	0.259088i	$0.0834221\pi$
$239$			8.01082i			0.518177i	−0.965854	+	0.259088i	$0.916578\pi$
$240$	1.96548	+	1.13477i	0.126871	+	0.0732491i
$241$	−20.2011	−	11.6631i	−1.30126	−	0.751285i	−0.320643	−	0.947200i	$-0.603899\pi$
$241$	−20.2011	−	11.6631i	−1.30126	−	0.751285i	−0.980621	+	0.195915i	$0.937232\pi$
$242$			36.1752i			2.32543i
$243$	−7.27100	+	12.5937i	−0.466435	+	0.807889i
$244$	−17.3904	−	30.1210i	−1.11330	−	1.92830i
$245$	7.69203	−	4.44099i	0.491426	−	0.283725i
$246$	17.0916			1.08972
$247$	0.220058	−	8.07097i	0.0140020	−	0.513544i
$248$	5.36274			0.340534
$249$	0.742679	−	0.428786i	0.0470654	−	0.0271732i
$250$	8.10448	+	14.0374i	0.512572	+	0.887801i
$251$	1.79136	−	3.10272i	0.113069	−	0.195842i	−0.803937	−	0.594715i	$-0.797265\pi$
$251$	1.79136	−	3.10272i	0.113069	−	0.195842i	0.917006	+	0.398873i	$0.130598\pi$
$252$		−	47.5759i		−	2.99700i
$253$	9.69467	+	5.59722i	0.609499	+	0.351894i
$254$	22.8691	+	13.2035i	1.43493	+	0.828459i
$255$			2.77115i			0.173536i
$256$	16.3118	−	28.2529i	1.01949	−	1.76581i
$257$	10.0223	+	17.3591i	0.625172	+	1.08283i	0.988508	+	0.151172i	$0.0483046\pi$
$257$	10.0223	+	17.3591i	0.625172	+	1.08283i	−0.363335	+	0.931658i	$0.618362\pi$
$258$	−1.25820	+	0.726422i	−0.0783321	+	0.0452251i
$259$	−4.36978			−0.271525
$260$	−0.280161	+	10.2753i	−0.0173749	+	0.637249i
$261$	7.89693			0.488808
$262$	−13.6544	+	7.88337i	−0.843571	+	0.487036i
$263$	−2.94258	−	5.09670i	−0.181447	−	0.314276i	0.760926	−	0.648838i	$-0.224745\pi$
$263$	−2.94258	−	5.09670i	−0.181447	−	0.314276i	−0.942374	+	0.334562i	$0.891412\pi$
$264$	−9.00162	+	15.5913i	−0.554012	+	0.959576i
$265$		−	5.28795i		−	0.324836i
$266$	−21.5062	−	12.4166i	−1.31863	−	0.761310i
$267$	10.5029	+	6.06387i	0.642769	+	0.371103i
$268$		−	20.2070i		−	1.23434i
$269$	5.23960	−	9.07526i	0.319464	−	0.553328i	−0.660912	−	0.750463i	$-0.729830\pi$
$269$	5.23960	−	9.07526i	0.319464	−	0.553328i	0.980376	+	0.197135i	$0.0631638\pi$
$270$	−3.13828	−	5.43566i	−0.190990	−	0.330804i
$271$	−1.43343	+	0.827590i	−0.0870745	+	0.0502725i	−0.542905	−	0.839794i	$-0.682676\pi$
$271$	−1.43343	+	0.827590i	−0.0870745	+	0.0502725i	0.455831	+	0.890067i	$0.349342\pi$
$272$	−30.3963			−1.84305
$273$	−9.40347	+	5.09254i	−0.569124	+	0.308215i
$274$	−14.4499			−0.872947
$275$	−19.8417	+	11.4556i	−1.19650	+	0.690800i
$276$	3.05691	+	5.29472i	0.184004	+	0.318705i
$277$	−4.33639	+	7.51085i	−0.260548	+	0.451283i	−0.966388	−	0.257089i	$-0.917237\pi$
$277$	−4.33639	+	7.51085i	−0.260548	+	0.451283i	0.705839	+	0.708372i	$0.250570\pi$
$278$		−	48.0177i		−	2.87991i
$279$	−2.21644	−	1.27966i	−0.132695	−	0.0766114i
$280$	14.2184	+	8.20901i	0.849713	+	0.490582i
$281$			13.9876i			0.834432i	0.908807	+	0.417216i	$0.136994\pi$
$281$			13.9876i			0.834432i	−0.908807	+	0.417216i	$0.863006\pi$
$282$	3.85443	−	6.67606i	0.229528	−	0.397554i
$283$	3.94999	+	6.84159i	0.234803	+	0.406690i	0.959215	−	0.282676i	$-0.0912222\pi$
$283$	3.94999	+	6.84159i	0.234803	+	0.406690i	−0.724413	+	0.689367i	$0.757889\pi$
$284$	57.5333	−	33.2168i	3.41397	−	1.97106i
$285$	−1.01860			−0.0603366
$286$	−45.2405	−	1.23350i	−2.67513	−	0.0729384i
$287$	46.3464			2.73574
$288$	3.67604	−	2.12236i	0.216613	−	0.125061i
$289$	−10.0572	−	17.4196i	−0.591601	−	1.02468i
$290$	−2.62388	+	4.54469i	−0.154079	+	0.266873i
$291$		−	4.65835i		−	0.273078i
$292$	−50.4477	−	29.1260i	−2.95223	−	1.70447i
$293$	−5.02448	−	2.90088i	−0.293533	−	0.169471i	0.346001	−	0.938234i	$-0.387539\pi$
$293$	−5.02448	−	2.90088i	−0.293533	−	0.169471i	−0.639534	+	0.768763i	$0.720873\pi$
$294$			21.3576i			1.24560i
$295$	0.105609	−	0.182919i	0.00614877	−	0.0106500i
$296$	−2.62247	−	4.54226i	−0.152428	−	0.264013i
$297$	16.1628	−	9.33160i	0.937861	−	0.541475i
$298$	0.128592			0.00744911
$299$	−4.17751	+	6.80060i	−0.241592	+	0.393289i
$300$	−12.5129			−0.722435
$301$	−3.41180	+	1.96981i	−0.196653	+	0.113538i
$302$	−9.37626	−	16.2402i	−0.539543	−	0.934516i
$303$	−3.71186	+	6.42912i	−0.213241	+	0.369343i
$304$		−	11.1729i		−	0.640809i
$305$	−4.96069	−	2.86406i	−0.284048	−	0.163995i
$306$	33.5150	+	19.3499i	1.91592	+	1.10616i
$307$			12.8293i			0.732204i	0.930575	+	0.366102i	$0.119308\pi$
$307$			12.8293i			0.732204i	−0.930575	+	0.366102i	$0.880692\pi$
$308$	−47.0042	+	81.4136i	−2.67831	+	4.63897i
$309$	3.65870	+	6.33706i	0.208136	+	0.360503i
$310$	1.47289	−	0.850375i	0.0836547	−	0.0482981i
$311$	−5.18056			−0.293762			−0.146881	−	0.989154i	$-0.546924\pi$
$311$	−5.18056			−0.293762			−0.146881	+	0.989154i	$0.546924\pi$
$312$	−10.9369	−	6.71840i	−0.619182	−	0.380355i
$313$	7.48834			0.423266			0.211633	−	0.977349i	$-0.432122\pi$
$313$	7.48834			0.423266			0.211633	+	0.977349i	$0.432122\pi$
$314$	3.87593	−	2.23777i	0.218731	−	0.126285i
$315$	−3.91769	−	6.78563i	−0.220737	−	0.382327i
$316$	−6.38025	+	11.0509i	−0.358917	+	0.621663i
$317$		−	22.8030i		−	1.28074i	−0.768065	−	0.640372i	$-0.778780\pi$
$317$		−	22.8030i		−	1.28074i	0.768065	−	0.640372i	$-0.221220\pi$
$318$	11.0118	+	6.35768i	0.617513	+	0.356521i
$319$	−13.5135	−	7.80204i	−0.756612	−	0.436830i
$320$		−	4.01693i		−	0.224553i
$321$	−0.118621	+	0.205457i	−0.00662075	+	0.0114675i
$322$	12.2739	+	21.2591i	0.684000	+	1.18472i
$323$	11.8146	−	6.82114i	0.657380	−	0.379538i
$324$	−21.7521			−1.20845
$325$	−7.77883	−	14.3638i	−0.431492	−	0.796758i
$326$	57.1949			3.16774
$327$	3.66722	−	2.11727i	0.202798	−	0.117085i
$328$	27.8143	+	48.1757i	1.53579	+	2.66006i
$329$	10.4519	−	18.1032i	0.576230	−	0.998060i
$330$			5.70959i			0.314302i
$331$	17.3013	+	9.98891i	0.950965	+	0.549040i	0.893381	−	0.449301i	$-0.148327\pi$
$331$	17.3013	+	9.98891i	0.950965	+	0.549040i	0.0575844	+	0.998341i	$0.481660\pi$
$332$	4.65478	+	2.68744i	0.255464	+	0.147492i
$333$			2.50311i			0.137170i
$334$	−12.3134	+	21.3274i	−0.673758	+	1.16698i
$335$	−1.66396	−	2.88207i	−0.0909121	−	0.157464i
$336$	−12.8158	+	7.39918i	−0.699157	+	0.403658i
$337$	−3.05650			−0.166498			−0.0832490	−	0.996529i	$-0.526530\pi$
$337$	−3.05650			−0.166498			−0.0832490	+	0.996529i	$0.526530\pi$
$338$	1.75822	−	32.2188i	0.0956348	−	1.75247i
$339$	10.6063			0.576057
$340$	−15.0414	+	8.68414i	−0.815733	+	0.470963i
$341$	2.52857	+	4.37961i	0.136930	+	0.237169i
$342$	−7.11251	+	12.3192i	−0.384600	+	0.666147i
$343$			26.6389i			1.43837i
$344$	−4.09511	−	2.36431i	−0.220794	−	0.127475i
$345$	0.871999	+	0.503449i	0.0469468	+	0.0271048i
$346$		−	21.9633i		−	1.18075i
$347$	10.9654	−	18.9926i	0.588653	−	1.01958i	−0.405756	−	0.913982i	$-0.632992\pi$
$347$	10.9654	−	18.9926i	0.588653	−	1.01958i	0.994409	−	0.105596i	$-0.0336750\pi$
$348$	−4.26107	−	7.38038i	−0.228417	−	0.395630i
$349$	−28.3597	+	16.3735i	−1.51806	+	0.876452i	−0.518285	+	0.855208i	$0.673430\pi$
$349$	−28.3597	+	16.3735i	−1.51806	+	0.876452i	−0.999774	+	0.0212445i	$0.993237\pi$
$350$	−50.2413			−2.68551
$351$	6.33653	+	11.7005i	0.338219	+	0.624528i
$352$	−8.38743			−0.447051
$353$	4.33489	−	2.50275i	0.230723	−	0.133208i	−0.380183	−	0.924911i	$-0.624139\pi$
$353$	4.33489	−	2.50275i	0.230723	−	0.133208i	0.610905	+	0.791704i	$0.290806\pi$
$354$	0.253946	+	0.439847i	0.0134971	+	0.0233776i
$355$	5.47055	−	9.47527i	0.290347	−	0.502895i
$356$			76.0112i			4.02859i
$357$	−15.6483	−	9.03453i	−0.828194	−	0.478158i
$358$	−50.8374	−	29.3510i	−2.68684	−	1.55125i
$359$		−	14.8872i		−	0.785715i	−0.919599	−	0.392858i	$-0.871487\pi$
$359$		−	14.8872i		−	0.785715i	0.919599	−	0.392858i	$-0.128513\pi$
$360$	4.70231	−	8.14464i	0.247833	−	0.429260i
$361$	−6.99273	−	12.1118i	−0.368038	−	0.637461i
$362$	−15.3277	+	8.84948i	−0.805608	+	0.465118i
$363$	−9.67516			−0.507814
$364$	−57.1099	−	35.0818i	−2.99337	−	1.83879i
$365$	−9.59364			−0.502154
$366$	11.9284	−	6.88689i	0.623510	−	0.359984i
$367$	−4.61847	−	7.99943i	−0.241082	−	0.417567i	0.719941	−	0.694036i	$-0.244169\pi$
$367$	−4.61847	−	7.99943i	−0.241082	−	0.417567i	−0.961023	+	0.276469i	$0.910836\pi$
$368$	−5.52226	+	9.56484i	−0.287868	+	0.498602i
$369$		−	26.5483i		−	1.38205i
$370$	−1.44054	−	0.831697i	−0.0748902	−	0.0432379i
$371$	29.8603	+	17.2398i	1.55027	+	0.895048i
$372$			2.76195i			0.143200i
$373$	10.6526	−	18.4509i	0.551572	−	0.955351i	−0.446589	−	0.894739i	$-0.647362\pi$
$373$	10.6526	−	18.4509i	0.551572	−	0.955351i	0.998161	−	0.0606117i	$-0.0193051\pi$
$374$	−38.2347	−	66.2245i	−1.97707	−	3.42439i
$375$	−3.75434	+	2.16757i	−0.193873	+	0.111933i
$376$	25.0903			1.29393
$377$	5.82309	−	9.47945i	0.299904	−	0.488216i
$378$	40.9259			2.10500
$379$	−9.69065	+	5.59490i	−0.497775	+	0.287391i	−0.727794	−	0.685796i	$-0.759454\pi$
$379$	−9.69065	+	5.59490i	−0.497775	+	0.287391i	0.230019	+	0.973186i	$0.426121\pi$
$380$	−3.19206	−	5.52881i	−0.163749	−	0.283622i
$381$	−3.53130	+	6.11640i	−0.180914	+	0.313353i
$382$		−	16.2550i		−	0.831676i
$383$	−10.4938	−	6.05859i	−0.536207	−	0.309579i	0.207333	−	0.978270i	$-0.433522\pi$
$383$	−10.4938	−	6.05859i	−0.536207	−	0.309579i	−0.743540	+	0.668691i	$0.766855\pi$
$384$	10.2720	+	5.93053i	0.524190	+	0.302641i
$385$			15.4824i			0.789058i
$386$	21.2289	−	36.7696i	1.08052	−	1.87152i
$387$	1.12835	+	1.95436i	0.0573573	+	0.0993457i
$388$	25.2849	−	14.5982i	1.28364	−	0.741112i
$389$	−12.2084			−0.618988			−0.309494	−	0.950901i	$-0.600160\pi$
$389$	−12.2084			−0.618988			−0.309494	+	0.950901i	$0.600160\pi$
$390$	−4.06921	−	0.110949i	−0.206052	−	0.00561810i
$391$	−13.4856			−0.681994
$392$	−60.2003	+	34.7567i	−3.04057	+	1.75548i
$393$	−2.10843	−	3.65191i	−0.106356	−	0.184214i
$394$	3.71814	−	6.44001i	0.187317	−	0.324443i
$395$			2.10155i			0.105741i
$396$	46.6356	+	26.9251i	2.34353	+	1.35304i
$397$	14.7806	+	8.53356i	0.741815	+	0.428287i	0.822729	−	0.568434i	$-0.192451\pi$
$397$	14.7806	+	8.53356i	0.741815	+	0.428287i	−0.0809141	+	0.996721i	$0.525784\pi$
$398$			7.94893i			0.398444i
$399$	3.32085	−	5.75188i	0.166251	−	0.287954i
$400$	−11.3022	−	19.5760i	−0.565111	−	0.978800i
$401$	−21.4947	+	12.4100i	−1.07340	+	0.619725i	−0.929107	−	0.369811i	$-0.879423\pi$
$401$	−21.4947	+	12.4100i	−1.07340	+	0.619725i	−0.144288	+	0.989536i	$0.546089\pi$
$402$	8.00232			0.399119
$403$	−3.17047	+	1.71700i	−0.157933	+	0.0855299i
$404$	−46.5284			−2.31488
$405$	−3.10245	+	1.79120i	−0.154162	+	0.0890056i
$406$	−17.1088	−	29.6333i	−0.849096	−	1.47068i
$407$	2.47303	−	4.28342i	0.122584	−	0.212321i
$408$		−	21.6879i		−	1.07371i
$409$	5.06527	+	2.92444i	0.250462	+	0.144604i	0.619976	−	0.784621i	$-0.287142\pi$
$409$	5.06527	+	2.92444i	0.250462	+	0.144604i	−0.369514	+	0.929225i	$0.620476\pi$
$410$	15.2786	+	8.82108i	0.754554	+	0.435642i
$411$		−	3.86466i		−	0.190629i
$412$	−22.9311	+	39.7178i	−1.12973	+	1.95676i
$413$	0.688613	+	1.19271i	0.0338844	+	0.0586896i
$414$	12.1777	−	7.03080i	0.598501	−	0.345545i
$415$	0.885199			0.0434527
$416$	0.162984	−	5.97770i	0.00799097	−	0.293081i
$417$	12.8425			0.628898
$418$	24.3424	−	14.0541i	1.19062	−	0.687407i
$419$	−1.73464	−	3.00449i	−0.0847428	−	0.146779i	0.820539	−	0.571591i	$-0.193674\pi$
$419$	−1.73464	−	3.00449i	−0.0847428	−	0.146779i	−0.905282	+	0.424812i	$0.860340\pi$
$420$	−4.22785	+	7.32285i	−0.206298	+	0.357318i
$421$			35.4587i			1.72815i	0.503361	+	0.864076i	$0.332096\pi$
$421$			35.4587i			1.72815i	−0.503361	+	0.864076i	$0.667904\pi$
$422$	−15.1455	−	8.74426i	−0.737271	−	0.425664i
$423$	−10.3699	−	5.98707i	−0.504203	−	0.291101i
$424$			41.3852i			2.00984i
$425$	13.8002	−	23.9026i	0.669408	−	1.15945i
$426$	13.1544	+	22.7842i	0.637335	+	1.10390i
$427$	32.3458	−	18.6749i	1.56532	−	0.903740i
$428$	−1.48692			−0.0718730
$429$	0.329903	−	12.0997i	0.0159279	−	0.584179i
$430$	−1.49965			−0.0723194
$431$	−18.6402	+	10.7619i	−0.897867	+	0.518384i	−0.876508	−	0.481388i	$-0.840133\pi$
$431$	−18.6402	+	10.7619i	−0.897867	+	0.518384i	−0.0213598	+	0.999772i	$0.506800\pi$
$432$	9.20663	+	15.9464i	0.442954	+	0.767219i
$433$	−17.9459	+	31.0833i	−0.862426	+	1.49377i	0.00715398	+	0.999974i	$0.497723\pi$
$433$	−17.9459	+	31.0833i	−0.862426	+	1.49377i	−0.869580	+	0.493792i	$0.835611\pi$
$434$			11.0896i			0.532319i
$435$	−1.21549	−	0.701764i	−0.0582783	−	0.0336470i
$436$	22.9844	+	13.2701i	1.10076	+	0.635521i
$437$		−	4.95693i		−	0.237122i
$438$	11.5344	−	19.9782i	0.551135	−	0.954594i
$439$	3.84726	+	6.66365i	0.183620	+	0.318038i	0.943110	−	0.332479i	$-0.107885\pi$
$439$	3.84726	+	6.66365i	0.183620	+	0.318038i	−0.759491	+	0.650518i	$0.774552\pi$
$440$	−16.0935	+	9.29161i	−0.767229	+	0.442960i
$441$	33.1747			1.57975
$442$	47.9410	−	25.9629i	2.28032	−	1.23493i
$443$	15.8094			0.751126			0.375563	−	0.926797i	$-0.377449\pi$
$443$	15.8094			0.751126			0.375563	+	0.926797i	$0.377449\pi$
$444$	2.33938	−	1.35064i	0.111022	−	0.0640986i
$445$	6.25922	+	10.8413i	0.296715	+	0.513926i
$446$	−4.69463	+	8.13133i	−0.222297	+	0.385030i
$447$			0.0343922i			0.00162669i
$448$	22.6830	+	13.0961i	1.07167	+	0.618730i
$449$	15.5524	+	8.97919i	0.733964	+	0.423754i	0.819871	−	0.572549i	$-0.194045\pi$
$449$	15.5524	+	8.97919i	0.733964	+	0.423754i	−0.0859067	+	0.996303i	$0.527379\pi$
$450$			28.7793i			1.35667i
$451$	−26.2293	+	45.4304i	−1.23509	+	2.13923i
$452$	33.2378	+	57.5696i	1.56338	+	2.70785i
$453$	4.34348	−	2.50771i	0.204074	−	0.117822i
$454$	64.2873			3.01715
$455$	−11.0343	−	0.300854i	−0.517295	−	0.0141043i
$456$	7.97189			0.373318
$457$	15.4686	−	8.93082i	0.723592	−	0.417766i	−0.0924811	−	0.995714i	$-0.529480\pi$
$457$	15.4686	−	8.93082i	0.723592	−	0.417766i	0.816073	+	0.577948i	$0.196146\pi$
$458$	−20.7087	−	35.8686i	−0.967656	−	1.67603i
$459$	−11.2415	+	19.4708i	−0.524706	+	0.908818i
$460$			6.31077i			0.294241i
$461$	7.72407	+	4.45949i	0.359746	+	0.207699i	0.668969	−	0.743290i	$-0.266736\pi$
$461$	7.72407	+	4.45949i	0.359746	+	0.207699i	−0.309224	+	0.950989i	$0.600069\pi$
$462$	−32.2412	−	18.6145i	−1.50000	−	0.866024i
$463$			36.2749i			1.68584i	0.538042	+	0.842918i	$0.319164\pi$
$463$			36.2749i			1.68584i	−0.538042	+	0.842918i	$0.680836\pi$
$464$	7.69755	−	13.3326i	0.357350	−	0.618948i
$465$	0.227435	+	0.393930i	0.0105471	+	0.0182680i
$466$	−45.5522	+	26.2996i	−2.11017	+	1.21830i
$467$	3.40254			0.157451			0.0787253	−	0.996896i	$-0.474915\pi$
$467$	3.40254			0.157451			0.0787253	+	0.996896i	$0.474915\pi$
$468$	−20.0957	+	32.7139i	−0.928922	+	1.51220i
$469$	21.6995			1.00199
$470$	6.89113	−	3.97859i	0.317864	−	0.183519i
$471$	0.598498	+	1.03663i	0.0275773	+	0.0477653i
$472$	−0.826527	+	1.43159i	−0.0380440	+	0.0658941i
$473$		−	4.45917i		−	0.205033i
$474$	−4.37636	−	2.52669i	−0.201013	−	0.116055i
$475$	8.78597	+	5.07258i	0.403128	+	0.232746i
$476$		−	113.249i		−	5.19074i
$477$	9.87538	−	17.1047i	0.452163	−	0.783169i
$478$	−9.94165	−	17.2194i	−0.454721	−	0.787599i
$479$	−8.52791	+	4.92359i	−0.389650	+	0.224965i	−0.682009	−	0.731344i	$-0.738893\pi$
$479$	−8.52791	+	4.92359i	−0.389650	+	0.224965i	0.292358	+	0.956309i	$0.405560\pi$
$480$	−0.754417			−0.0344343
$481$	3.00472	+	1.84576i	0.137004	+	0.0841594i
$482$	57.8969			2.63713
$483$	−5.68581	+	3.28270i	−0.258713	+	0.149368i
$484$	−30.3197	−	52.5153i	−1.37817	−	2.38706i
$485$	2.40421	−	4.16421i	0.109170	−	0.189087i
$486$		−	36.0941i		−	1.63726i
$487$	−33.9772	−	19.6167i	−1.53965	−	0.888919i	−0.998859	−	0.0477645i	$-0.984790\pi$
$487$	−33.9772	−	19.6167i	−1.53965	−	0.888919i	−0.540795	−	0.841155i	$-0.681876\pi$
$488$	38.8240	+	22.4150i	1.75748	+	1.01468i
$489$			15.2970i			0.691752i
$490$	−11.0228	+	19.0920i	−0.497959	+	0.862491i
$491$	3.32215	+	5.75414i	0.149927	+	0.259681i	0.931200	−	0.364508i	$-0.118763\pi$
$491$	3.32215	+	5.75414i	0.149927	+	0.259681i	−0.781273	+	0.624189i	$0.785430\pi$
$492$	−24.8117	+	14.3251i	−1.11860	+	0.645823i
$493$	18.7977			0.846605
$494$	9.54328	+	17.6218i	0.429373	+	0.792844i
$495$	8.86869			0.398618
$496$	−4.32096	+	2.49471i	−0.194017	+	0.112016i
$497$	35.6703	+	61.7828i	1.60003	+	2.77134i
$498$	−1.06427	+	1.84337i	−0.0476911	+	0.0826035i
$499$		−	4.78984i		−	0.214422i	−0.994236	−	0.107211i	$-0.965808\pi$
$499$		−	4.78984i		−	0.214422i	0.994236	−	0.107211i	$-0.0341921\pi$
$500$	−23.5305	−	13.5853i	−1.05231	−	0.607554i
$501$	−5.70407	−	3.29325i	−0.254839	−	0.147131i
$502$			8.89250i			0.396892i
$503$	8.70064	−	15.0700i	0.387942	−	0.671936i	−0.604230	−	0.796810i	$-0.706519\pi$
$503$	8.70064	−	15.0700i	0.387942	−	0.671936i	0.992173	+	0.124874i	$0.0398526\pi$
$504$	30.6611	+	53.1065i	1.36575	+	2.36555i
$505$	−6.63623	+	3.83143i	−0.295309	+	0.170496i
$506$	−27.7852			−1.23520
$507$	8.61701	+	0.470242i	0.382695	+	0.0208842i
$508$	−44.2652			−1.96395
$509$	4.53756	−	2.61976i	0.201124	−	0.116119i	−0.396056	−	0.918226i	$-0.629621\pi$
$509$	4.53756	−	2.61976i	0.201124	−	0.116119i	0.597180	+	0.802108i	$0.296288\pi$
$510$	−3.43907	−	5.95664i	−0.152285	−	0.263765i
$511$	31.2773	−	54.1739i	1.38363	−	2.39651i
$512$			45.2388i			1.99929i
$513$	−7.15694	−	4.13206i	−0.315986	−	0.182435i
$514$	−43.0862	−	24.8758i	−1.90045	−	1.09723i
$515$			7.55313i			0.332831i
$516$	1.21768	−	2.10909i	0.0536055	−	0.0928474i
$517$	11.8303	+	20.4906i	0.520294	+	0.901176i
$518$	9.39295	−	5.42302i	0.412702	−	0.238274i
$519$	5.87415			0.257847
$520$	−6.30938	−	11.6504i	−0.276684	−	0.510903i
$521$	−19.3984			−0.849860			−0.424930	−	0.905226i	$-0.639701\pi$
$521$	−19.3984			−0.849860			−0.424930	+	0.905226i	$0.639701\pi$
$522$	−16.9746	+	9.80032i	−0.742960	+	0.428948i
$523$	6.78150	+	11.7459i	0.296534	+	0.513612i	0.975341	−	0.220705i	$-0.0708358\pi$
$523$	6.78150	+	11.7459i	0.296534	+	0.513612i	−0.678806	+	0.734317i	$0.737502\pi$
$524$	13.2147	−	22.8885i	0.577286	−	0.999888i
$525$		−	13.4372i		−	0.586446i
$526$	12.6503	+	7.30366i	0.551580	+	0.318455i
$527$	−5.27597	−	3.04608i	−0.229825	−	0.132689i
$528$		−	16.7500i		−	0.728949i
$529$	9.05001	−	15.6751i	0.393479	−	0.681525i
$530$	6.56249	+	11.3666i	0.285057	+	0.493732i
$531$	0.683213	−	0.394453i	0.0296489	−	0.0171178i
$532$	41.6272			1.80477
$533$	−31.8685	−	19.5763i	−1.38038	−	0.847945i
$534$	−30.1018			−1.30263
$535$	−0.212076	+	0.122442i	−0.00916883	+	0.00529362i
$536$	13.0227	+	22.5560i	0.562496	+	0.974272i
$537$	7.85000	−	13.5966i	0.338753	−	0.586737i
$538$			26.0100i			1.12137i
$539$	−56.7698	−	32.7760i	−2.44525	−	1.41176i
$540$	9.11165	+	5.26061i	0.392103	+	0.226381i
$541$		−	14.9396i		−	0.642303i	−0.947028	−	0.321151i	$-0.895930\pi$
$541$		−	14.9396i		−	0.642303i	0.947028	−	0.321151i	$-0.104070\pi$
$542$	2.05412	−	3.55785i	0.0882322	−	0.152823i
$543$	−2.36682	−	4.09945i	−0.101570	−	0.175924i
$544$	8.75035	−	5.05202i	0.375168	−	0.216604i
$545$	4.37095			0.187231
$546$	13.8930	−	22.6165i	0.594565	−	0.967897i
$547$	−21.5805			−0.922716			−0.461358	−	0.887214i	$-0.652638\pi$
$547$	−21.5805			−0.922716			−0.461358	+	0.887214i	$0.652638\pi$
$548$	20.9768	−	12.1109i	0.896083	−	0.517354i
$549$	−10.6974	−	18.5284i	−0.456554	−	0.790774i
$550$	28.4335	−	49.2483i	1.21241	−	2.09995i
$551$			6.90953i			0.294356i
$552$	−6.82455	−	3.94015i	−0.290472	−	0.167704i
$553$	−11.8672	−	6.85152i	−0.504644	−	0.291356i
$554$		−	21.5263i		−	0.914566i
$555$	0.222440	−	0.385277i	0.00944204	−	0.0163541i
$556$	40.2454	+	69.7070i	1.70678	+	2.95624i
$557$	−33.8008	+	19.5149i	−1.43218	+	0.826872i	−0.997287	−	0.0736077i	$-0.976549\pi$
$557$	−33.8008	+	19.5149i	−1.43218	+	0.826872i	−0.434898	+	0.900480i	$0.643215\pi$
$558$	6.35239			0.268918
$559$	3.17804	+	0.0866505i	0.134417	+	0.00366492i
$560$	−15.2751			−0.645490
$561$	17.7119	−	10.2260i	0.747799	−	0.431742i
$562$	−17.3590	−	30.0667i	−0.732247	−	1.26829i
$563$	16.3360	−	28.2947i	0.688479	−	1.19248i	−0.283851	−	0.958868i	$-0.591612\pi$
$563$	16.3360	−	28.2947i	0.688479	−	1.19248i	0.972330	−	0.233612i	$-0.0750545\pi$
$564$			12.9221i			0.544120i
$565$	9.48125	+	5.47400i	0.398879	+	0.230293i
$566$	−16.9812	−	9.80411i	−0.713774	−	0.412097i
$567$		−	23.3588i		−	0.980978i
$568$	−42.8143	+	74.1565i	−1.79645	+	3.11154i
$569$	14.4992	+	25.1133i	0.607837	+	1.05280i	0.991596	+	0.129372i	$0.0412960\pi$
$569$	14.4992	+	25.1133i	0.607837	+	1.05280i	−0.383759	+	0.923433i	$0.625371\pi$
$570$	2.18950	−	1.26411i	0.0917082	−	0.0529478i
$571$	29.3123			1.22668			0.613340	−	0.789819i	$-0.289825\pi$
$571$	29.3123			1.22668			0.613340	+	0.789819i	$0.289825\pi$
$572$	66.7092	−	36.1270i	2.78925	−	1.51055i
$573$	4.34743			0.181617
$574$	−99.6227	+	57.5172i	−4.15817	+	2.40072i
$575$	−5.01431	−	8.68504i	−0.209111	−	0.362191i
$576$	7.50172	−	12.9934i	0.312572	−	0.541390i
$577$			35.7272i			1.48734i	0.668544	+	0.743672i	$0.266918\pi$
$577$			35.7272i			1.48734i	−0.668544	+	0.743672i	$0.733082\pi$
$578$	43.2364	+	24.9626i	1.79840	+	1.03831i
$579$	9.83414	+	5.67774i	0.408693	+	0.235959i
$580$		−	8.79667i		−	0.365262i
$581$	−2.88594	+	4.99859i	−0.119729	+	0.207376i
$582$	5.78115	+	10.0132i	0.239636	+	0.415062i
$583$	−33.7982	+	19.5134i	−1.39978	+	0.808163i
$584$	75.0830			3.10696
$585$	−0.172336	+	6.32069i	−0.00712523	+	0.261329i
$586$	14.4003			0.594872
$587$	18.7973	−	10.8526i	0.775848	−	0.447936i	−0.0591086	−	0.998252i	$-0.518826\pi$
$587$	18.7973	−	10.8526i	0.775848	−	0.447936i	0.834957	+	0.550315i	$0.185492\pi$
$588$	−17.9006	−	31.0047i	−0.738207	−	1.27861i
$589$	1.11966	−	1.93930i	0.0461347	−	0.0799077i
$590$			0.524253i			0.0215832i
$591$	1.72240	+	0.994427i	0.0708500	+	0.0409053i
$592$	4.22605	+	2.43991i	0.173690	+	0.100280i
$593$		−	31.9930i		−	1.31379i	−0.753980	−	0.656897i	$-0.771869\pi$
$593$		−	31.9930i		−	1.31379i	0.753980	−	0.656897i	$-0.228131\pi$
$594$	−23.1616	+	40.1170i	−0.950330	+	1.64602i
$595$	−9.32557	−	16.1524i	−0.382311	−	0.662182i
$596$	−0.186676	+	0.107777i	−0.00764654	+	0.00441473i
$597$	−2.12596			−0.0870099
$598$	0.539923	−	19.8025i	0.0220791	−	0.809783i
$599$	−24.8048			−1.01350			−0.506748	−	0.862094i	$-0.669152\pi$
$599$	−24.8048			−1.01350			−0.506748	+	0.862094i	$0.669152\pi$
$600$	13.9675	−	8.06417i	0.570223	−	0.329218i
$601$	−7.72158	−	13.3742i	−0.314970	−	0.545543i	0.664461	−	0.747323i	$-0.268661\pi$
$601$	−7.72158	−	13.3742i	−0.314970	−	0.545543i	−0.979431	+	0.201779i	$0.935328\pi$
$602$	4.88917	−	8.46829i	0.199268	−	0.345142i
$603$		−	12.4300i		−	0.506188i
$604$	27.2229	+	15.7172i	1.10769	+	0.639523i
$605$	−8.64886	−	4.99342i	−0.351626	−	0.203011i
$606$		−	18.4261i		−	0.748508i
$607$	9.79608	−	16.9673i	0.397611	−	0.688682i	−0.595820	−	0.803118i	$-0.703173\pi$
$607$	9.79608	−	16.9673i	0.397611	−	0.688682i	0.993431	+	0.114436i	$0.0365062\pi$
$608$	1.85699	+	3.21640i	0.0753108	+	0.130442i
$609$	7.92552	−	4.57580i	0.321158	−	0.185421i
$610$	14.2175			0.575650
$611$	−14.8335	+	8.03322i	−0.600099	+	0.324989i
$612$	−64.8714			−2.62227
$613$	−14.3066	+	8.25989i	−0.577836	+	0.333614i	−0.760273	−	0.649604i	$-0.774935\pi$
$613$	−14.3066	+	8.25989i	−0.577836	+	0.333614i	0.182437	+	0.983218i	$0.441601\pi$
$614$	−15.9215	−	27.5768i	−0.642538	−	1.11291i
$615$	−2.35922	+	4.08629i	−0.0951330	+	0.164775i
$616$		−	121.171i		−	4.88210i
$617$	−17.2235	−	9.94398i	−0.693391	−	0.400330i	0.111490	−	0.993766i	$-0.464438\pi$
$617$	−17.2235	−	9.94398i	−0.693391	−	0.400330i	−0.804881	+	0.593436i	$0.797771\pi$
$618$	−15.7289	−	9.08111i	−0.632711	−	0.365296i
$619$		−	18.7081i		−	0.751942i	−0.926631	−	0.375971i	$-0.877309\pi$
$619$		−	18.7081i		−	0.751942i	0.926631	−	0.375971i	$-0.122691\pi$
$620$	−1.42546	+	2.46897i	−0.0572479	+	0.0991563i
$621$	4.08459	+	7.07472i	0.163909	+	0.283899i
$622$	11.1357	−	6.42922i	0.446502	−	0.257788i
$623$	−81.6256			−3.27026
$624$	11.9377	+	0.325485i	0.477889	+	0.0130298i
$625$	18.1776			0.727104
$626$	−16.0964	+	9.29324i	−0.643340	+	0.371433i
$627$	3.75880	+	6.51044i	0.150112	+	0.260002i
$628$	−3.75111	+	6.49711i	−0.149686	+	0.259263i
$629$			5.95835i			0.237575i
$630$	16.8423	+	9.72392i	0.671014	+	0.387410i
$631$	18.8353	+	10.8746i	0.749823	+	0.432911i	0.825630	−	0.564212i	$-0.190820\pi$
$631$	18.8353	+	10.8746i	0.749823	+	0.432911i	−0.0758068	+	0.997123i	$0.524153\pi$
$632$		−	16.4474i		−	0.654244i
$633$	2.33868	−	4.05071i	0.0929541	−	0.161001i
$634$	28.2992	+	49.0156i	1.12390	+	1.94666i
$635$	−6.31344	+	3.64506i	−0.250541	+	0.144650i
$636$	−21.3144			−0.845172
$637$	24.4625	−	39.8228i	0.969241	−	1.57783i
$638$	38.7302			1.53334
$639$	35.3906	−	20.4328i	1.40003	−	0.808308i
$640$	6.12158	+	10.6029i	0.241977	+	0.419116i
$641$	−0.256953	+	0.445056i	−0.0101490	+	0.0175787i	−0.871055	−	0.491185i	$-0.836564\pi$
$641$	−0.256953	+	0.445056i	−0.0101490	+	0.0175787i	0.860906	+	0.508764i	$0.169897\pi$
$642$		−	0.588846i		−	0.0232399i
$643$	3.06714	+	1.77082i	0.120956	+	0.0698342i	0.559257	−	0.828994i	$-0.311086\pi$
$643$	3.06714	+	1.77082i	0.120956	+	0.0698342i	−0.438301	+	0.898828i	$0.644420\pi$
$644$	−35.6360	−	20.5745i	−1.40426	−	0.810748i
$645$		−	0.401085i		−	0.0157927i
$646$	−16.9304	+	29.3244i	−0.666120	+	1.15375i
$647$	14.2245	+	24.6375i	0.559222	+	0.968601i	0.997562	+	0.0697919i	$0.0222335\pi$
$647$	14.2245	+	24.6375i	0.559222	+	0.968601i	−0.438339	+	0.898810i	$0.644433\pi$
$648$	24.2808	−	14.0185i	0.953840	−	0.550700i
$649$	−1.55885			−0.0611904
$650$	34.5466	+	21.2215i	1.35503	+	0.832375i
$651$	−2.96595			−0.116245
$652$	−83.0296	+	47.9372i	−3.25169	+	1.87736i
$653$	11.2947	+	19.5630i	0.441995	+	0.765557i	0.997837	−	0.0657301i	$-0.0209376\pi$
$653$	11.2947	+	19.5630i	0.441995	+	0.765557i	−0.555843	+	0.831288i	$0.687604\pi$
$654$	−5.25518	+	9.10224i	−0.205494	+	0.355926i
$655$		−	4.35270i		−	0.170074i
$656$	−44.8220	−	25.8780i	−1.75001	−	1.01037i
$657$	−31.0321	−	17.9164i	−1.21068	−	0.698984i
$658$			51.8843i			2.02266i
$659$	2.71733	−	4.70655i	0.105852	−	0.183341i	−0.808234	−	0.588861i	$-0.799576\pi$
$659$	2.71733	−	4.70655i	0.105852	−	0.183341i	0.914086	+	0.405520i	$0.132910\pi$
$660$	−4.78541	−	8.28858i	−0.186272	−	0.322633i
$661$	−9.21692	+	5.32139i	−0.358497	+	0.206978i	−0.668421	−	0.743783i	$-0.733030\pi$
$661$	−9.21692	+	5.32139i	−0.358497	+	0.206978i	0.309924	+	0.950761i	$0.399696\pi$
$662$	−49.5861			−1.92722
$663$	6.94386	+	12.8220i	0.269677	+	0.497964i
$664$	−6.92785			−0.268853
$665$	5.93718	−	3.42783i	0.230234	−	0.132926i
$666$	−3.10643	−	5.38050i	−0.120372	−	0.208490i
$667$	3.41508	−	5.91509i	0.132232	−	0.229033i
$668$		−	41.2811i		−	1.59722i
$669$	−2.17475	−	1.25559i	−0.0840806	−	0.0485440i
$670$	7.15346	+	4.13005i	0.276362	+	0.159558i
$671$			42.2754i			1.63202i
$672$	2.45956	−	4.26009i	0.0948796	−	0.164336i
$673$	17.6983	+	30.6543i	0.682218	+	1.18164i	0.974302	+	0.225244i	$0.0723179\pi$
$673$	17.6983	+	30.6543i	0.682218	+	1.18164i	−0.292084	+	0.956393i	$0.594349\pi$
$674$	6.57001	−	3.79320i	0.253067	−	0.146108i
$675$	−16.7196			−0.643536
$676$	24.4513	+	48.2455i	0.940436	+	1.85560i
$677$	−33.5048			−1.28769			−0.643846	−	0.765155i	$-0.722662\pi$
$677$	−33.5048			−1.28769			−0.643846	+	0.765155i	$0.722662\pi$
$678$	−22.7986	+	13.1628i	−0.875573	+	0.505512i
$679$	15.6765	+	27.1525i	0.601608	+	1.04202i
$680$	11.1933	−	19.3873i	0.429242	−	0.743470i
$681$			17.1938i			0.658869i
$682$	−10.8704	−	6.27606i	−0.416251	−	0.240323i
$683$	7.00006	+	4.04149i	0.267850	+	0.154643i	0.627910	−	0.778286i	$-0.283911\pi$
$683$	7.00006	+	4.04149i	0.267850	+	0.154643i	−0.360060	+	0.932929i	$0.617244\pi$
$684$		−	23.8450i		−	0.911736i
$685$	1.99458	−	3.45471i	0.0762089	−	0.131998i
$686$	−33.0597	−	57.2611i	−1.26222	−	2.18624i
$687$	9.59316	−	5.53861i	0.366002	−	0.211311i
$688$	4.39945			0.167727
$689$	−13.2504	−	24.4671i	−0.504800	−	0.932122i
$690$	−2.49918			−0.0951420
$691$	39.9912	−	23.0889i	1.52134	−	0.878343i	0.521653	−	0.853158i	$-0.325316\pi$
$691$	39.9912	−	23.0889i	1.52134	−	0.878343i	0.999683	−	0.0251855i	$-0.00801763\pi$
$692$	18.4083	+	31.8840i	0.699777	+	1.21205i
$693$	−28.9138	+	50.0802i	−1.09835	+	1.90239i
$694$			54.4335i			2.06627i
$695$	11.4802	+	6.62809i	0.435468	+	0.251418i
$696$	9.51282	+	5.49223i	0.360583	+	0.208182i
$697$		−	63.1949i		−	2.39368i
$698$	40.6399	−	70.3904i	1.53824	−	2.66431i
$699$	−7.03390	−	12.1831i	−0.266047	−	0.460806i
$700$	72.9350	−	42.1090i	2.75668	−	1.59157i
$701$	−8.81532			−0.332950			−0.166475	−	0.986046i	$-0.553239\pi$
$701$	−8.81532			−0.332950			−0.166475	+	0.986046i	$0.553239\pi$
$702$	−28.1412	−	17.2867i	−1.06212	−	0.652446i
$703$	−2.19013			−0.0826023
$704$	−25.6745	+	14.8232i	−0.967642	+	0.558669i
$705$	1.06409	+	1.84305i	0.0400758	+	0.0694134i
$706$	−6.21196	+	10.7594i	−0.233790	+	0.404937i
$707$		−	49.9651i		−	1.87913i
$708$	−0.737303	−	0.425682i	−0.0277096	−	0.0159981i
$709$	36.2983	+	20.9568i	1.36321	+	0.787051i	0.990050	−	0.140715i	$-0.0449402\pi$
$709$	36.2983	+	20.9568i	1.36321	+	0.787051i	0.373162	+	0.927766i	$0.378274\pi$
$710$			27.1564i			1.01916i
$711$	−3.92471	+	6.79779i	−0.147188	+	0.254937i
$712$	−48.9867	−	84.8474i	−1.83585	−	3.17979i
$713$	−1.91703	+	1.10680i	−0.0717932	+	0.0414498i
$714$	44.8484			1.67841
$715$	6.53965	−	10.6459i	0.244569	−	0.398136i
$716$	98.4005			3.67740
$717$	4.60539	−	2.65892i	0.171991	−	0.0992993i
$718$	18.4754	+	32.0003i	0.689496	+	1.19424i
$719$	−19.6074	+	33.9610i	−0.731233	+	1.26653i	0.225123	+	0.974330i	$0.427722\pi$
$719$	−19.6074	+	33.9610i	−0.731233	+	1.26653i	−0.956356	+	0.292203i	$0.905612\pi$
$720$			8.74992i			0.326090i
$721$	−42.6514	−	24.6248i	−1.58842	−	0.917076i
$722$	30.0621	+	17.3564i	1.11879	+	0.645937i
$723$			15.4847i			0.575882i
$724$	14.8341	−	25.6935i	0.551306	−	0.954891i
$725$	6.98951	+	12.1062i	0.259584	+	0.449613i
$726$	20.7970	−	12.0071i	0.771849	−	0.445627i
$727$	−46.0809			−1.70904			−0.854522	−	0.519414i	$-0.826150\pi$
$727$	−46.0809			−1.70904			−0.854522	+	0.519414i	$0.826150\pi$
$728$	86.3579	+	2.35458i	3.20064	+	0.0872667i
$729$	−6.03091			−0.223367
$730$	20.6218	−	11.9060i	0.763246	−	0.440660i
$731$	2.68590	+	4.65212i	0.0993416	+	0.172065i
$732$	−11.5443	+	19.9953i	−0.426690	+	0.739049i
$733$			3.36439i			0.124267i	0.998068	+	0.0621333i	$0.0197904\pi$
$733$			3.36439i			0.124267i	−0.998068	+	0.0621333i	$0.980210\pi$
$734$	19.8550	+	11.4633i	0.732862	+	0.423118i
$735$	−5.10622	−	2.94808i	−0.188346	−	0.108742i
$736$		−	3.67131i		−	0.135326i
$737$	−12.2806	+	21.2707i	−0.452362	+	0.783515i
$738$	32.9472	+	57.0662i	1.21280	+	2.10063i
$739$	14.2658	−	8.23638i	0.524777	−	0.302980i	−0.214110	−	0.976810i	$-0.568685\pi$
$739$	14.2658	−	8.23638i	0.524777	−	0.302980i	0.738887	+	0.673829i	$0.235352\pi$
$740$	2.78830			0.102500
$741$	−4.71301	+	2.55238i	−0.173137	+	0.0937640i
$742$	−85.5805			−3.14176
$743$	21.9458	−	12.6704i	0.805113	−	0.464832i	−0.0401430	−	0.999194i	$-0.512781\pi$
$743$	21.9458	−	12.6704i	0.805113	−	0.464832i	0.845256	+	0.534362i	$0.179448\pi$
$744$	−1.77998	−	3.08302i	−0.0652573	−	0.113029i
$745$	−0.0177501	+	0.0307440i	−0.000650312	+	0.00112637i
$746$			52.8808i			1.93610i
$747$	2.86331	+	1.65313i	0.104763	+	0.0604849i
$748$	111.010	+	64.0919i	4.05894	+	2.34343i
$749$		−	1.59675i		−	0.0583439i
$750$	5.38002	−	9.31847i	0.196451	−	0.340263i
$751$	−10.1010	−	17.4954i	−0.368590	−	0.638416i	0.620755	−	0.784004i	$-0.286826\pi$
$751$	−10.1010	−	17.4954i	−0.368590	−	0.638416i	−0.989345	+	0.145588i	$0.953493\pi$
$752$	−20.2162	+	11.6718i	−0.737209	+	0.425628i
$753$	−2.37832			−0.0866710
$754$	−0.752605	+	27.6029i	−0.0274083	+	1.00524i
$755$	5.17699			0.188410
$756$	−59.4119	+	34.3014i	−2.16079	+	1.24753i
$757$	−3.64094	−	6.30630i	−0.132332	−	0.229206i	0.792243	−	0.610206i	$-0.208913\pi$
$757$	−3.64094	−	6.30630i	−0.132332	−	0.229206i	−0.924575	+	0.381000i	$0.875580\pi$
$758$	13.8869	−	24.0527i	0.504393	−	0.873635i
$759$		−	7.43124i		−	0.269737i
$760$	7.12626	+	4.11435i	0.258497	+	0.149243i
$761$	9.58010	+	5.53107i	0.347278	+	0.200501i	0.663486	−	0.748189i	$-0.269076\pi$
$761$	9.58010	+	5.53107i	0.347278	+	0.200501i	−0.316208	+	0.948690i	$0.602410\pi$
$762$		−	17.5298i		−	0.635037i
$763$	−14.2502	+	24.6821i	−0.515893	+	0.893553i
$764$	13.6239	+	23.5972i	0.492894	+	0.853718i
$765$	−9.25244	+	5.34190i	−0.334523	+	0.193137i
$766$	30.0755			1.08667
$767$	0.0302916	−	1.11099i	0.00109377	−	0.0401156i
$768$	−21.6567			−0.781469
$769$	25.2085	−	14.5541i	0.909040	−	0.524835i	0.0289180	−	0.999582i	$-0.490794\pi$
$769$	25.2085	−	14.5541i	0.909040	−	0.524835i	0.880122	+	0.474747i	$0.157460\pi$
$770$	−19.2141	−	33.2799i	−0.692429	−	1.19932i
$771$	6.65312	−	11.5235i	0.239606	−	0.415010i
$772$			71.1710i			2.56150i
$773$	36.9205	+	21.3161i	1.32794	+	0.766686i	0.984981	−	0.172665i	$-0.0552377\pi$
$773$	36.9205	+	21.3161i	1.32794	+	0.766686i	0.342958	+	0.939351i	$0.388571\pi$
$774$	−4.85083	−	2.80063i	−0.174360	−	0.100667i
$775$		−	4.53048i		−	0.162739i
$776$	−18.8161	+	32.5905i	−0.675460	+	1.16993i
$777$	1.45040	+	2.51217i	0.0520329	+	0.0901236i
$778$	26.2422	−	15.1509i	0.940827	−	0.543187i
$779$	23.2288			0.832257
$780$	6.00024	−	3.24949i	0.214843	−	0.116350i
$781$	−80.7490			−2.88943
$782$	28.9875	−	16.7360i	1.03659	−	0.598476i
$783$	−5.69356	−	9.86154i	−0.203471	−	0.352423i
$784$	32.3371	−	56.0095i	1.15490	−	2.00034i
$785$			1.23556i			0.0440989i
$786$	9.06424	+	5.23324i	0.323311	+	0.186664i
$787$	12.6077	+	7.27903i	0.449414	+	0.259469i	0.707583	−	0.706630i	$-0.249786\pi$
$787$	12.6077	+	7.27903i	0.449414	+	0.259469i	−0.258169	+	0.966100i	$0.583119\pi$
$788$			12.4652i			0.444055i
$789$	−1.95338	+	3.38336i	−0.0695423	+	0.120451i
$790$	−2.60809	−	4.51734i	−0.0927916	−	0.160720i
$791$	−61.8218	+	35.6928i	−2.19813	+	1.26909i
$792$	−69.4093			−2.46635
$793$	−30.1296	−	0.821495i	−1.06993	−	0.0291722i
$794$	−42.3615			−1.50335
$795$	−3.04002	+	1.75516i	−0.107819	+	0.0622490i
$796$	−6.66229	−	11.5394i	−0.236138	−	0.409004i
$797$	17.5659	−	30.4250i	0.622216	−	1.07771i	−0.366856	−	0.930278i	$-0.619566\pi$
$797$	17.5659	−	30.4250i	0.622216	−	1.07771i	0.989072	−	0.147432i	$-0.0471009\pi$
$798$			16.4851i			0.583566i
$799$	−24.6843	−	14.2515i	−0.873268	−	0.504182i
$800$	6.50726	+	3.75697i	0.230066	+	0.132829i
$801$			46.7570i			1.65208i
$802$	30.8023	−	53.3511i	1.08767	−	1.88389i
$803$	35.4022	+	61.3183i	1.24932	+	2.16388i
$804$	−11.6169	+	6.70703i	−0.409697	+	0.236539i
$805$	−6.77690			−0.238854
$806$	4.68416	−	7.62538i	0.164993	−	0.268593i
$807$	−6.95644			−0.244878
$808$	51.9373	−	29.9860i	1.82715	−	1.05490i
$809$	−2.59727	−	4.49861i	−0.0913152	−	0.158163i	0.816750	−	0.576992i	$-0.195774\pi$
$809$	−2.59727	−	4.49861i	−0.0913152	−	0.158163i	−0.908065	+	0.418830i	$0.862440\pi$
$810$	4.44587	−	7.70047i	0.156212	−	0.270567i
$811$			40.5456i			1.42375i	0.702307	+	0.711874i	$0.252153\pi$
$811$			40.5456i			1.42375i	−0.702307	+	0.711874i	$0.747847\pi$
$812$	49.6735	+	28.6790i	1.74320	+	1.00644i
$813$	0.951557	+	0.549382i	0.0333726	+	0.0192677i
$814$			12.2764i			0.430288i
$815$	−7.89487	+	13.6743i	−0.276545	+	0.478990i
$816$	10.0890	+	17.4747i	0.353187	+	0.611738i
$817$	−1.70999	+	0.987266i	−0.0598251	+	0.0345400i
$818$	−14.5172			−0.507583
$819$	−35.1302	−	21.5800i	−1.22755	−	0.754065i
$820$	−29.5731			−1.03274
$821$	−36.1476	+	20.8698i	−1.26156	+	0.728362i	−0.973376	−	0.229214i	$-0.926385\pi$
$821$	−36.1476	+	20.8698i	−1.26156	+	0.728362i	−0.288183	+	0.957575i	$0.593051\pi$
$822$	4.79615	+	8.30717i	0.167285	+	0.289746i
$823$	−7.18051	+	12.4370i	−0.250297	+	0.433527i	−0.963607	−	0.267321i	$-0.913862\pi$
$823$	−7.18051	+	12.4370i	−0.250297	+	0.433527i	0.713311	+	0.700848i	$0.247195\pi$
$824$		−	59.1133i		−	2.05931i
$825$	13.1716	+	7.60463i	0.458576	+	0.264759i
$826$	−2.96038	−	1.70918i	−0.103005	−	0.0594699i
$827$			26.2051i			0.911239i	0.890175	+	0.455619i	$0.150582\pi$
$827$			26.2051i			0.911239i	−0.890175	+	0.455619i	$0.849418\pi$
$828$	−11.7855	+	20.4131i	−0.409576	+	0.709406i
$829$	2.09433	+	3.62748i	0.0727390	+	0.125988i	0.900101	−	0.435682i	$-0.143493\pi$
$829$	2.09433	+	3.62748i	0.0727390	+	0.125988i	−0.827362	+	0.561669i	$0.810159\pi$
$830$	−1.90276	+	1.09856i	−0.0660456	+	0.0381315i
$831$	5.75728			0.199718
$832$	−10.0655	−	18.5862i	−0.348959	−	0.644359i
$833$	78.9683			2.73609
$834$	−27.6052	+	15.9379i	−0.955889	+	0.551883i
$835$	−3.39934	−	5.88783i	−0.117639	−	0.203757i
$836$	−23.5585	+	40.8045i	−0.814787	+	1.41125i
$837$			3.69046i			0.127561i
$838$	7.45731	+	4.30548i	0.257608	+	0.148730i
$839$	39.9260	+	23.0513i	1.37840	+	0.795819i	0.991967	−	0.126500i	$-0.0403742\pi$
$839$	39.9260	+	23.0513i	1.37840	+	0.795819i	0.386431	+	0.922318i	$0.373708\pi$
$840$		−	10.8988i		−	0.376045i
$841$	9.73968	−	16.8696i	0.335851	−	0.581711i
$842$	−44.0053	−	76.2194i	−1.51652	−	2.62669i
$843$	8.04144	−	4.64273i	0.276962	−	0.159904i
$844$	29.3155			1.00908
$845$	7.46026	+	4.86766i	0.256641	+	0.167453i
$846$	29.7205			1.02181
$847$	56.3943	−	32.5592i	1.93773	−	1.11875i
$848$	−19.2521	−	33.3456i	−0.661120	−	1.14509i
$849$	2.62214	−	4.54168i	0.0899915	−	0.155870i
$850$			68.5057i			2.34973i
$851$	1.87492	+	1.08249i	0.0642714	+	0.0371071i
$852$	−38.1925	−	22.0504i	−1.30845	−	0.755436i
$853$		−	22.1827i		−	0.759521i	−0.925085	−	0.379760i	$-0.876006\pi$
$853$		−	22.1827i		−	0.759521i	0.925085	−	0.379760i	$-0.123994\pi$
$854$	−46.3521	+	80.2842i	−1.58614	+	2.74727i
$855$	−1.96354	−	3.40095i	−0.0671517	−	0.116310i
$856$	1.65977	−	0.958270i	0.0567298	−	0.0327530i
$857$	40.7041			1.39043			0.695213	−	0.718804i	$-0.255310\pi$
$857$	40.7041			1.39043			0.695213	+	0.718804i	$0.255310\pi$
$858$	14.3069	+	26.4180i	0.488430	+	0.901896i
$859$	11.9687			0.408367			0.204183	−	0.978933i	$-0.434546\pi$
$859$	11.9687			0.408367			0.204183	+	0.978933i	$0.434546\pi$
$860$	2.17703	−	1.25691i	0.0742361	−	0.0428602i
$861$	−15.3831	−	26.6444i	−0.524256	−	0.908038i
$862$	26.7117	−	46.2661i	0.909805	−	1.57583i
$863$		−	53.1320i		−	1.80863i	−0.426863	−	0.904317i	$-0.640381\pi$
$863$		−	53.1320i		−	1.80863i	0.426863	−	0.904317i	$-0.359619\pi$
$864$	−5.30073	−	3.06038i	−0.180334	−	0.104116i
$865$	5.25105	+	3.03169i	0.178541	+	0.103081i
$866$		−	89.0856i		−	3.02725i
$867$	−6.67631	+	11.5637i	−0.226739	+	0.392724i
$868$	−9.29461	−	16.0987i	−0.315480	−	0.546427i
$869$	13.4322	−	7.75509i	0.455656	−	0.263073i
$870$	3.48363			0.118106
$871$	−14.9209	−	9.16570i	−0.505575	−	0.310568i
$872$	−34.2085			−1.15845
$873$	15.5536	−	8.97985i	0.526408	−	0.303922i
$874$	6.15169	+	10.6550i	0.208084	+	0.360412i
$875$	14.5888	−	25.2685i	0.493190	−	0.854231i
$876$			38.6696i			1.30653i
$877$	−34.0712	−	19.6710i	−1.15050	−	0.664243i	−0.201493	−	0.979490i	$-0.564579\pi$
$877$	−34.0712	−	19.6710i	−1.15050	−	0.664243i	−0.949010	+	0.315247i	$0.897913\pi$
$878$	−16.5395	−	9.54911i	−0.558183	−	0.322267i
$879$			3.85141i			0.129905i
$880$	8.64478	−	14.9732i	0.291415	−	0.504746i
$881$	−4.54502	−	7.87220i	−0.153126	−	0.265221i	0.779249	−	0.626714i	$-0.215601\pi$
$881$	−4.54502	−	7.87220i	−0.153126	−	0.265221i	−0.932375	+	0.361493i	$0.882267\pi$
$882$	−71.3098	+	41.1707i	−2.40112	+	1.38629i
$883$	32.6346			1.09824			0.549121	−	0.835743i	$-0.314962\pi$
$883$	32.6346			1.09824			0.549121	+	0.835743i	$0.314962\pi$
$884$	−47.8353	+	77.8714i	−1.60887	+	2.61910i
$885$	−0.140213			−0.00471321
$886$	−33.9826	+	19.6199i	−1.14167	+	0.659143i
$887$	18.3979	+	31.8662i	0.617742	+	1.06996i	0.989897	+	0.141790i	$0.0452859\pi$
$887$	18.3979	+	31.8662i	0.617742	+	1.06996i	−0.372154	+	0.928171i	$0.621381\pi$
$888$	−1.74089	+	3.01530i	−0.0584203	+	0.101187i
$889$		−	47.5347i		−	1.59426i
$890$	−26.9087	−	15.5357i	−0.901981	−	0.520759i
$891$	22.8972	+	13.2197i	0.767084	+	0.442876i
$892$		−	15.7389i		−	0.526979i
$893$	5.23847	−	9.07330i	0.175299	−	0.303626i
$894$	−0.0426817	−	0.0739268i	−0.00142749	−	0.00247248i
$895$	14.0346	−	8.10289i	0.469125	−	0.270850i
$896$	−79.8306			−2.66695
$897$	5.29623	+	0.144404i	0.176836	+	0.00482150i
$898$	−44.5737			−1.48744
$899$	2.67217	−	1.54278i	0.0891218	−	0.0514545i
$900$	−24.1210	−	41.7788i	−0.804034	−	1.39263i
$901$	23.5071	−	40.7155i	0.783136	−	1.35643i
$902$		−	130.205i		−	4.33535i
$903$	2.26487	+	1.30762i	0.0753701	+	0.0435150i
$904$	−74.2033	−	42.8413i	−2.46797	−	1.42488i
$905$		−	4.88613i		−	0.162420i
$906$	−6.22427	+	10.7808i	−0.206788	+	0.358167i
$907$	−23.5613	−	40.8094i	−0.782340	−	1.35505i	−0.930575	−	0.366101i	$-0.880693\pi$
$907$	−23.5613	−	40.8094i	−0.782340	−	1.35505i	0.148235	−	0.988952i	$-0.452641\pi$
$908$	−93.3256	+	53.8816i	−3.09712	+	1.78812i
$909$	−28.6212			−0.949305
$910$	24.0918	−	13.0472i	0.798637	−	0.432509i
$911$	−7.71151			−0.255494			−0.127747	−	0.991807i	$-0.540775\pi$
$911$	−7.71151			−0.255494			−0.127747	+	0.991807i	$0.540775\pi$
$912$	−6.42325	+	3.70846i	−0.212695	+	0.122800i
$913$	−3.26653	−	5.65780i	−0.108106	−	0.187246i
$914$	−22.1668	+	38.3940i	−0.733213	+	1.26996i
$915$			3.80251i			0.125707i
$916$	60.1256	+	34.7135i	1.98660	+	1.14697i
$917$	24.5791	+	14.1907i	0.811673	+	0.468620i
$918$		−	55.8038i		−	1.84180i
$919$	−18.2600	+	31.6272i	−0.602341	+	1.04329i	0.390125	+	0.920762i	$0.372432\pi$
$919$	−18.2600	+	31.6272i	−0.602341	+	1.04329i	−0.992466	+	0.122523i	$0.960901\pi$
$920$	−4.06708	−	7.04440i	−0.134088	−	0.232247i
$921$	7.37549	−	4.25824i	0.243031	−	0.140314i
$922$	−22.1374			−0.729057
$923$	1.56911	−	57.5496i	0.0516480	−	1.89427i
$924$	62.4059			2.05300
$925$	−3.83733	+	2.21548i	−0.126171	+	0.0728446i
$926$	−45.0181	−	77.9737i	−1.47939	−	2.56238i
$927$	−14.1057	+	24.4317i	−0.463291	+	0.802443i
$928$			5.11749i			0.167990i
$929$	14.7757	+	8.53073i	0.484774	+	0.279884i	0.722404	−	0.691471i	$-0.243037\pi$
$929$	14.7757	+	8.53073i	0.484774	+	0.279884i	−0.237630	+	0.971356i	$0.576371\pi$
$930$	−0.977755	−	0.564507i	−0.0320619	−	0.0185109i
$931$			29.0266i			0.951310i
$932$	44.0853	−	76.3580i	1.44406	−	2.50119i
$933$	1.71951	+	2.97828i	0.0562943	+	0.0975046i
$934$	−7.31384	+	4.22265i	−0.239316	+	0.138169i
$935$	21.1108			0.690398
$936$	1.34876	−	49.4678i	0.0440856	−	1.61691i
$937$	2.70547			0.0883839			0.0441920	−	0.999023i	$-0.485929\pi$
$937$	2.70547			0.0883839			0.0441920	+	0.999023i	$0.485929\pi$
$938$	−46.6436	+	26.9297i	−1.52297	+	0.879286i
$939$	−2.48550	−	4.30502i	−0.0811114	−	0.140489i
$940$	−6.66921	+	11.5514i	−0.217526	+	0.376765i
$941$		−	49.6009i		−	1.61694i	−0.588534	−	0.808472i	$-0.700295\pi$
$941$		−	49.6009i		−	1.61694i	0.588534	−	0.808472i	$-0.299705\pi$
$942$	−2.57297	−	1.48550i	−0.0838319	−	0.0484004i
$943$	−19.8856	−	11.4810i	−0.647565	−	0.373872i
$944$		−	1.53798i		−	0.0500569i
$945$	−5.64918	+	9.78466i	−0.183768	+	0.318295i
$946$	5.53395	+	9.58508i	0.179924	+	0.311638i
$947$	−12.9129	+	7.45525i	−0.419612	+	0.242263i	−0.694911	−	0.719095i	$-0.744556\pi$
$947$	−12.9129	+	7.45525i	−0.419612	+	0.242263i	0.275299	+	0.961359i	$0.411223\pi$
$948$	8.47085			0.275120
$949$	−44.3894	+	24.0395i	−1.44094	+	0.780355i
$950$	−25.1809			−0.816976
$951$	−13.1094	+	7.56870i	−0.425100	+	0.245432i
$952$	72.9849	+	126.414i	2.36546	+	4.09709i
$953$	−27.7670	+	48.0938i	−0.899461	+	1.55791i	−0.0712760	+	0.997457i	$0.522707\pi$
$953$	−27.7670	+	48.0938i	−0.899461	+	1.55791i	−0.828185	+	0.560455i	$0.810626\pi$
$954$			49.0225i			1.58716i
$955$	3.88628	+	2.24374i	0.125757	+	0.0726058i
$956$	28.8645	+	16.6649i	0.933544	+	0.538982i
$957$			10.3585i			0.334843i
$958$	12.2206	−	21.1668i	0.394831	−	0.683867i
$959$	13.0055	+	22.5262i	0.419969	+	0.727408i
$960$	−2.30932	+	1.33329i	−0.0745330	+	0.0430316i
$961$	−1.00000			−0.0322581
$962$	−8.74936	−	0.238555i	−0.282091	−	0.00769132i
$963$	−0.914653			−0.0294743
$964$	−84.0486	+	48.5255i	−2.70702	+	1.56290i
$965$	5.86065	+	10.1509i	0.188661	+	0.326770i
$966$	8.14785	−	14.1125i	0.262153	−	0.454062i
$967$		−	25.0836i		−	0.806633i	−0.915060	−	0.403317i	$-0.867857\pi$
$967$		−	25.0836i		−	0.806633i	0.915060	−	0.403317i	$-0.132143\pi$
$968$	67.6888	+	39.0801i	2.17560	+	1.25608i
$969$	−7.84290	−	4.52810i	−0.251950	−	0.145463i
$970$			11.9348i			0.383202i
$971$	0.109605	−	0.189841i	0.00351738	−	0.00609228i	−0.864261	−	0.503043i	$-0.832214\pi$
$971$	0.109605	−	0.189841i	0.00351738	−	0.00609228i	0.867779	+	0.496951i	$0.165547\pi$
$972$	30.2517	+	52.3976i	0.970325	+	1.68065i
$973$	−74.8557	+	43.2180i	−2.39976	+	1.38550i
$974$	97.3797			3.12025
$975$	−5.67575	+	9.23959i	−0.181769	+	0.295904i
$976$	−41.7092			−1.33508
$977$	5.32208	−	3.07271i	0.170269	−	0.0983046i	−0.412444	−	0.910983i	$-0.635325\pi$
$977$	5.32208	−	3.07271i	0.170269	−	0.0983046i	0.582712	+	0.812678i	$0.301991\pi$
$978$	−18.9840	−	32.8812i	−0.607040	−	1.05142i
$979$	46.1951	−	80.0123i	1.47640	−	2.55721i
$980$		−	36.9544i		−	1.18047i
$981$	14.1385	+	8.16286i	0.451407	+	0.260620i
$982$	−14.2821	−	8.24577i	−0.455760	−	0.263133i
$983$			12.2385i			0.390348i	0.980769	+	0.195174i	$0.0625272\pi$
$983$			12.2385i			0.390348i	−0.980769	+	0.195174i	$0.937473\pi$
$984$	18.4640	−	31.9806i	0.588612	−	1.01951i
$985$	1.02646	+	1.77788i	0.0327058	+	0.0566481i
$986$	−40.4061	+	23.3285i	−1.28679	+	0.742929i
$987$	−13.8766			−0.441697
$988$	−28.6234	−	17.5830i	−0.910633	−	0.559389i
$989$	1.95185			0.0620651
$990$	−19.0635	+	11.0063i	−0.605877	+	0.349803i
$991$	−26.7461	−	46.3256i	−0.849618	−	1.47158i	−0.881550	−	0.472091i	$-0.843499\pi$
$991$	−26.7461	−	46.3256i	−0.849618	−	1.47158i	0.0319317	−	0.999490i	$-0.489834\pi$
$992$	0.829266	−	1.43633i	0.0263292	−	0.0456035i
$993$		−	13.2619i		−	0.420855i
$994$	−153.348	−	88.5357i	−4.86392	−	2.80818i
$995$	−1.90045	−	1.09723i	−0.0602483	−	0.0347844i
$996$		−	3.56802i		−	0.113057i
$997$	−16.5026	+	28.5833i	−0.522642	+	0.905242i	0.477011	+	0.878897i	$0.341720\pi$
$997$	−16.5026	+	28.5833i	−0.522642	+	0.905242i	−0.999653	+	0.0263448i	$0.991613\pi$
$998$	5.94432	+	10.2959i	0.188164	+	0.325910i
$999$	3.12584	−	1.80470i	0.0988971	−	0.0570983i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.r.a.218.4	✓	68
13.2	odd	12		5239.2.a.r.1.2		34
13.4	even	6	inner	403.2.r.a.342.4	yes	68
13.11	odd	12		5239.2.a.q.1.33		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.r.a.218.4	✓	68	1.1	even	1	trivial
403.2.r.a.342.4	yes	68	13.4	even	6	inner
5239.2.a.q.1.33		34	13.11	odd	12
5239.2.a.r.1.2		34	13.2	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.14952 + 1.24103i) q^{2} +(-0.331917 - 0.574896i) q^{3} +(2.08030 - 3.60319i) q^{4} -0.685218i q^{5} +(1.42693 + 0.823836i) q^{6} +(3.86933 + 2.23396i) q^{7} +5.36274i q^{8} +(1.27966 - 2.21644i) q^{9} +O(q^{10})\)	\(q+(-2.14952 + 1.24103i) q^{2} +(-0.331917 - 0.574896i) q^{3} +(2.08030 - 3.60319i) q^{4} -0.685218i q^{5} +(1.42693 + 0.823836i) q^{6} +(3.86933 + 2.23396i) q^{7} +5.36274i q^{8} +(1.27966 - 2.21644i) q^{9} +(0.850375 + 1.47289i) q^{10} +(-4.37961 + 2.52857i) q^{11} -2.76195 q^{12} +(-1.71700 - 3.17047i) q^{13} -11.0896 q^{14} +(-0.393930 + 0.227435i) q^{15} +(-2.49471 - 4.32096i) q^{16} +(3.04608 - 5.27597i) q^{17} +6.35239i q^{18} +(1.93930 + 1.11966i) q^{19} +(-2.46897 - 1.42546i) q^{20} -2.96595i q^{21} +(6.27606 - 10.8704i) q^{22} +(-1.10680 - 1.91703i) q^{23} +(3.08302 - 1.77998i) q^{24} +4.53048 q^{25} +(7.62538 + 4.68416i) q^{26} -3.69046 q^{27} +(16.0987 - 9.29461i) q^{28} +(1.54278 + 2.67217i) q^{29} +(0.564507 - 0.977755i) q^{30} -1.00000i q^{31} +(1.43633 + 0.829266i) q^{32} +(2.90733 + 1.67855i) q^{33} +15.1211i q^{34} +(1.53075 - 2.65134i) q^{35} +(-5.32417 - 9.22173i) q^{36} +(-0.847004 + 0.489018i) q^{37} -5.55811 q^{38} +(-1.25279 + 2.03943i) q^{39} +3.67465 q^{40} +(8.98342 - 5.18658i) q^{41} +(3.68083 + 6.37538i) q^{42} +(-0.440878 + 0.763623i) q^{43} +21.0408i q^{44} +(-1.51875 - 0.876848i) q^{45} +(4.75817 + 2.74713i) q^{46} -4.67863i q^{47} +(-1.65607 + 2.86840i) q^{48} +(6.48114 + 11.2257i) q^{49} +(-9.73837 + 5.62245i) q^{50} -4.04418 q^{51} +(-14.9957 - 0.408864i) q^{52} +7.71717 q^{53} +(7.93274 - 4.57997i) q^{54} +(1.73262 + 3.00099i) q^{55} +(-11.9801 + 20.7502i) q^{56} -1.48653i q^{57} +(-6.63247 - 3.82926i) q^{58} +(0.266951 + 0.154124i) q^{59} +1.89254i q^{60} +(4.17977 - 7.23958i) q^{61} +(1.24103 + 2.14952i) q^{62} +(9.90287 - 5.71743i) q^{63} +5.86226 q^{64} +(-2.17247 + 1.17652i) q^{65} -8.33251 q^{66} +(4.20606 - 2.42837i) q^{67} +(-12.6735 - 21.9512i) q^{68} +(-0.734728 + 1.27259i) q^{69} +7.59881i q^{70} +(13.8281 + 7.98366i) q^{71} +(11.8862 + 6.86250i) q^{72} -14.0009i q^{73} +(1.21377 - 2.10231i) q^{74} +(-1.50374 - 2.60455i) q^{75} +(8.06868 - 4.65845i) q^{76} -22.5949 q^{77} +(0.161917 - 5.93856i) q^{78} -3.06698 q^{79} +(-2.96080 + 1.70942i) q^{80} +(-2.61406 - 4.52769i) q^{81} +(-12.8734 + 22.2973i) q^{82} +1.29185i q^{83} +(-10.6869 - 6.17007i) q^{84} +(-3.61519 - 2.08723i) q^{85} -2.18857i q^{86} +(1.02415 - 1.77387i) q^{87} +(-13.5601 - 23.4867i) q^{88} +(-15.8217 + 9.13464i) q^{89} +4.35277 q^{90} +(0.439064 - 16.1033i) q^{91} -9.20987 q^{92} +(-0.574896 + 0.331917i) q^{93} +(5.80632 + 10.0568i) q^{94} +(0.767210 - 1.32885i) q^{95} -1.10099i q^{96} +(6.07721 + 3.50868i) q^{97} +(-27.8627 - 16.0865i) q^{98} +12.9429i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 32 q^{4} - 34 q^{9}+O(q^{10}) \) 68 * q + 32 * q^4 - 34 * q^9	\( 68 q + 32 q^{4} - 34 q^{9} + 8 q^{10} - 12 q^{11} - 16 q^{12} + 6 q^{13} - 8 q^{14} - 36 q^{16} - 6 q^{17} + 12 q^{19} - 12 q^{20} - 20 q^{22} - 8 q^{23} + 48 q^{24} - 72 q^{25} - 12 q^{27} - 6 q^{28} + 32 q^{30} + 6 q^{33} + 30 q^{35} + 40 q^{36} - 42 q^{37} - 36 q^{38} - 14 q^{39} + 8 q^{40} + 18 q^{41} - 16 q^{42} + 12 q^{43} + 60 q^{45} + 30 q^{46} - 46 q^{48} + 22 q^{49} + 56 q^{51} + 20 q^{53} - 114 q^{54} - 6 q^{55} - 2 q^{56} - 12 q^{58} + 6 q^{59} + 6 q^{61} - 8 q^{62} - 30 q^{63} + 24 q^{64} + 24 q^{65} + 8 q^{66} - 48 q^{67} + 58 q^{68} - 28 q^{69} - 30 q^{71} + 72 q^{72} + 8 q^{74} - 4 q^{75} - 12 q^{76} - 20 q^{77} + 26 q^{78} + 16 q^{79} + 42 q^{80} - 58 q^{81} - 42 q^{82} - 72 q^{84} + 30 q^{85} - 20 q^{87} + 64 q^{88} + 18 q^{89} + 52 q^{90} - 22 q^{91} + 48 q^{92} + 8 q^{94} - 32 q^{95} - 168 q^{98}+O(q^{100}) \) 68 * q + 32 * q^4 - 34 * q^9 + 8 * q^10 - 12 * q^11 - 16 * q^12 + 6 * q^13 - 8 * q^14 - 36 * q^16 - 6 * q^17 + 12 * q^19 - 12 * q^20 - 20 * q^22 - 8 * q^23 + 48 * q^24 - 72 * q^25 - 12 * q^27 - 6 * q^28 + 32 * q^30 + 6 * q^33 + 30 * q^35 + 40 * q^36 - 42 * q^37 - 36 * q^38 - 14 * q^39 + 8 * q^40 + 18 * q^41 - 16 * q^42 + 12 * q^43 + 60 * q^45 + 30 * q^46 - 46 * q^48 + 22 * q^49 + 56 * q^51 + 20 * q^53 - 114 * q^54 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 6 * q^59 + 6 * q^61 - 8 * q^62 - 30 * q^63 + 24 * q^64 + 24 * q^65 + 8 * q^66 - 48 * q^67 + 58 * q^68 - 28 * q^69 - 30 * q^71 + 72 * q^72 + 8 * q^74 - 4 * q^75 - 12 * q^76 - 20 * q^77 + 26 * q^78 + 16 * q^79 + 42 * q^80 - 58 * q^81 - 42 * q^82 - 72 * q^84 + 30 * q^85 - 20 * q^87 + 64 * q^88 + 18 * q^89 + 52 * q^90 - 22 * q^91 + 48 * q^92 + 8 * q^94 - 32 * q^95 - 168 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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