LMFDB - Embedded newform 731.2.d.d.560.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(560,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("731.560");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.d (of order $2$, degree $1$, 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:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			560.4
Character	$\chi$	$=$	731.560
Dual form			731.2.d.d.560.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.48305 q^{2} +0.676403i q^{3} +4.16556 q^{4} -3.88874i q^{5} -1.67955i q^{6} -2.90905i q^{7} -5.37720 q^{8} +2.54248 q^{9} +O(q^{10})$	\(q-2.48305 q^{2} +0.676403i q^{3} +4.16556 q^{4} -3.88874i q^{5} -1.67955i q^{6} -2.90905i q^{7} -5.37720 q^{8} +2.54248 q^{9} +9.65595i q^{10} -3.51296i q^{11} +2.81760i q^{12} +6.64252 q^{13} +7.22333i q^{14} +2.63036 q^{15} +5.02075 q^{16} +(0.886962 - 4.02657i) q^{17} -6.31311 q^{18} +1.34163 q^{19} -16.1988i q^{20} +1.96769 q^{21} +8.72288i q^{22} +0.0542671i q^{23} -3.63715i q^{24} -10.1223 q^{25} -16.4937 q^{26} +3.74895i q^{27} -12.1178i q^{28} +0.155313i q^{29} -6.53132 q^{30} +6.18665i q^{31} -1.71241 q^{32} +2.37618 q^{33} +(-2.20238 + 9.99820i) q^{34} -11.3125 q^{35} +10.5908 q^{36} -3.55503i q^{37} -3.33134 q^{38} +4.49302i q^{39} +20.9105i q^{40} +8.28090i q^{41} -4.88588 q^{42} -1.00000 q^{43} -14.6334i q^{44} -9.88704i q^{45} -0.134748i q^{46} +11.5638 q^{47} +3.39605i q^{48} -1.46257 q^{49} +25.1342 q^{50} +(2.72359 + 0.599944i) q^{51} +27.6698 q^{52} -13.3717 q^{53} -9.30885i q^{54} -13.6610 q^{55} +15.6425i q^{56} +0.907484i q^{57} -0.385650i q^{58} +0.329773 q^{59} +10.9569 q^{60} +7.36054i q^{61} -15.3618i q^{62} -7.39619i q^{63} -5.78950 q^{64} -25.8310i q^{65} -5.90018 q^{66} +7.69106 q^{67} +(3.69469 - 16.7729i) q^{68} -0.0367065 q^{69} +28.0896 q^{70} +0.947229i q^{71} -13.6714 q^{72} -8.32085i q^{73} +8.82733i q^{74} -6.84676i q^{75} +5.58864 q^{76} -10.2194 q^{77} -11.1564i q^{78} +12.9927i q^{79} -19.5244i q^{80} +5.09163 q^{81} -20.5619i q^{82} -12.7315 q^{83} +8.19653 q^{84} +(-15.6583 - 3.44917i) q^{85} +2.48305 q^{86} -0.105054 q^{87} +18.8899i q^{88} +12.7315 q^{89} +24.5500i q^{90} -19.3234i q^{91} +0.226053i q^{92} -4.18467 q^{93} -28.7135 q^{94} -5.21726i q^{95} -1.15828i q^{96} -3.66042i q^{97} +3.63163 q^{98} -8.93163i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 6 q^{2} + 34 q^{4} - 18 q^{8} - 48 q^{9}+O(q^{10}) $ 34 * q - 6 * q^2 + 34 * q^4 - 18 * q^8 - 48 * q^9	$ 34 q - 6 q^{2} + 34 q^{4} - 18 q^{8} - 48 q^{9} + 16 q^{13} - 8 q^{15} + 26 q^{16} + 14 q^{18} + 16 q^{19} + 20 q^{21} - 44 q^{25} - 26 q^{26} + 88 q^{30} - 42 q^{32} + 12 q^{33} - 42 q^{34} + 22 q^{35} + 34 q^{38} - 14 q^{42} - 34 q^{43} + 30 q^{47} - 62 q^{49} - 46 q^{50} - 10 q^{51} + 26 q^{52} - 46 q^{53} + 16 q^{55} - 20 q^{59} - 42 q^{60} + 102 q^{64} - 70 q^{66} - 32 q^{67} - 10 q^{68} + 74 q^{69} + 130 q^{70} + 22 q^{72} + 38 q^{76} - 78 q^{77} + 46 q^{81} - 60 q^{83} - 98 q^{84} - 38 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{89} + 14 q^{93} - 78 q^{94} + 78 q^{98}+O(q^{100}) $ 34 * q - 6 * q^2 + 34 * q^4 - 18 * q^8 - 48 * q^9 + 16 * q^13 - 8 * q^15 + 26 * q^16 + 14 * q^18 + 16 * q^19 + 20 * q^21 - 44 * q^25 - 26 * q^26 + 88 * q^30 - 42 * q^32 + 12 * q^33 - 42 * q^34 + 22 * q^35 + 34 * q^38 - 14 * q^42 - 34 * q^43 + 30 * q^47 - 62 * q^49 - 46 * q^50 - 10 * q^51 + 26 * q^52 - 46 * q^53 + 16 * q^55 - 20 * q^59 - 42 * q^60 + 102 * q^64 - 70 * q^66 - 32 * q^67 - 10 * q^68 + 74 * q^69 + 130 * q^70 + 22 * q^72 + 38 * q^76 - 78 * q^77 + 46 * q^81 - 60 * q^83 - 98 * q^84 - 38 * q^85 + 6 * q^86 + 16 * q^87 + 26 * q^89 + 14 * q^93 - 78 * q^94 + 78 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$173$	$562$
$\chi(n)$	$-1$	$1$

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 $

$2$	−2.48305			−1.75578			−0.877892	−	0.478858i	$-0.841051\pi$
$2$	−2.48305			−1.75578			−0.877892	+	0.478858i	$0.841051\pi$
$3$			0.676403i			0.390522i	0.980751	+	0.195261i	$0.0625553\pi$
$3$			0.676403i			0.390522i	−0.980751	+	0.195261i	$0.937445\pi$
$4$	4.16556			2.08278
$5$		−	3.88874i		−	1.73910i	−0.493847	−	0.869549i	$-0.664410\pi$
$5$		−	3.88874i		−	1.73910i	0.493847	−	0.869549i	$-0.335590\pi$
$6$		−	1.67955i		−	0.685672i
$7$		−	2.90905i		−	1.09952i	−0.835324	−	0.549759i	$-0.814720\pi$
$7$		−	2.90905i		−	1.09952i	0.835324	−	0.549759i	$-0.185280\pi$
$8$	−5.37720			−1.90113
$9$	2.54248			0.847493
$10$			9.65595i			3.05348i
$11$		−	3.51296i		−	1.05920i	−0.848248	−	0.529599i	$-0.822342\pi$
$11$		−	3.51296i		−	1.05920i	0.848248	−	0.529599i	$-0.177658\pi$
$12$			2.81760i			0.813370i
$13$	6.64252			1.84230			0.921152	−	0.389203i	$-0.127249\pi$
$13$	6.64252			1.84230			0.921152	+	0.389203i	$0.127249\pi$
$14$			7.22333i			1.93051i
$15$	2.63036			0.679155
$16$	5.02075			1.25519
$17$	0.886962	−	4.02657i	0.215120	−	0.976588i
$17$	0.886962	−	4.02657i	0.215120	−	0.976588i
$18$	−6.31311			−1.48801
$19$	1.34163			0.307791			0.153896	−	0.988087i	$-0.450818\pi$
$19$	1.34163			0.307791			0.153896	+	0.988087i	$0.450818\pi$
$20$		−	16.1988i		−	3.62215i
$21$	1.96769			0.429385
$22$			8.72288i			1.85972i
$23$			0.0542671i			0.0113155i	0.999984	+	0.00565774i	$0.00180092\pi$
$23$			0.0542671i			0.0113155i	−0.999984	+	0.00565774i	$0.998199\pi$
$24$		−	3.63715i		−	0.742431i
$25$	−10.1223			−2.02446
$26$	−16.4937			−3.23469
$27$			3.74895i			0.721486i
$28$		−	12.1178i		−	2.29005i
$29$			0.155313i			0.0288409i	0.999896	+	0.0144204i	$0.00459033\pi$
$29$			0.155313i			0.0288409i	−0.999896	+	0.0144204i	$0.995410\pi$
$30$	−6.53132			−1.19245
$31$			6.18665i			1.11116i	0.831464	+	0.555578i	$0.187503\pi$
$31$			6.18665i			1.11116i	−0.831464	+	0.555578i	$0.812497\pi$
$32$	−1.71241			−0.302714
$33$	2.37618			0.413640
$34$	−2.20238	+	9.99820i	−0.377704	+	1.71468i
$35$	−11.3125			−1.91217
$36$	10.5908			1.76514
$37$		−	3.55503i		−	0.584443i	−0.956351	−	0.292221i	$-0.905606\pi$
$37$		−	3.55503i		−	0.584443i	0.956351	−	0.292221i	$-0.0943944\pi$
$38$	−3.33134			−0.540415
$39$			4.49302i			0.719460i
$40$			20.9105i			3.30624i
$41$			8.28090i			1.29326i	0.762804	+	0.646630i	$0.223822\pi$
$41$			8.28090i			1.29326i	−0.762804	+	0.646630i	$0.776178\pi$
$42$	−4.88588			−0.753908
$43$	−1.00000			−0.152499
$43$	−1.00000			−0.152499
$44$		−	14.6334i		−	2.20608i
$45$		−	9.88704i		−	1.47387i
$46$		−	0.134748i		−	0.0198675i
$47$	11.5638			1.68675			0.843375	−	0.537325i	$-0.180565\pi$
$47$	11.5638			1.68675			0.843375	+	0.537325i	$0.180565\pi$
$48$			3.39605i			0.490178i
$49$	−1.46257			−0.208938
$50$	25.1342			3.55451
$51$	2.72359	+	0.599944i	0.381379	+	0.0840090i
$52$	27.6698			3.83711
$53$	−13.3717			−1.83674			−0.918369	−	0.395724i	$-0.870494\pi$
$53$	−13.3717			−1.83674			−0.918369	+	0.395724i	$0.870494\pi$
$54$		−	9.30885i		−	1.26677i
$55$	−13.6610			−1.84205
$56$			15.6425i			2.09032i
$57$			0.907484i			0.120199i
$58$		−	0.385650i		−	0.0506384i
$59$	0.329773			0.0429327			0.0214664	−	0.999770i	$-0.493167\pi$
$59$	0.329773			0.0429327			0.0214664	+	0.999770i	$0.493167\pi$
$60$	10.9569			1.41453
$61$			7.36054i			0.942421i	0.882021	+	0.471210i	$0.156183\pi$
$61$			7.36054i			0.942421i	−0.882021	+	0.471210i	$0.843817\pi$
$62$		−	15.3618i		−	1.95095i
$63$		−	7.39619i		−	0.931833i
$64$	−5.78950			−0.723688
$65$		−	25.8310i		−	3.20395i
$66$	−5.90018			−0.726262
$67$	7.69106			0.939613			0.469807	−	0.882769i	$-0.344324\pi$
$67$	7.69106			0.939613			0.469807	+	0.882769i	$0.344324\pi$
$68$	3.69469	−	16.7729i	0.448047	−	2.03402i
$69$	−0.0367065			−0.00441894
$70$	28.0896			3.35735
$71$			0.947229i			0.112415i	0.998419	+	0.0562077i	$0.0179009\pi$
$71$			0.947229i			0.112415i	−0.998419	+	0.0562077i	$0.982099\pi$
$72$	−13.6714			−1.61119
$73$		−	8.32085i		−	0.973882i	−0.873435	−	0.486941i	$-0.838113\pi$
$73$		−	8.32085i		−	0.973882i	0.873435	−	0.486941i	$-0.161887\pi$
$74$			8.82733i			1.02616i
$75$		−	6.84676i		−	0.790595i
$76$	5.58864			0.641061
$77$	−10.2194			−1.16461
$78$		−	11.1564i		−	1.26322i
$79$			12.9927i			1.46180i	0.682486	+	0.730898i	$0.260899\pi$
$79$			12.9927i			1.46180i	−0.682486	+	0.730898i	$0.739101\pi$
$80$		−	19.5244i		−	2.18289i
$81$	5.09163			0.565737
$82$		−	20.5619i		−	2.27068i
$83$	−12.7315			−1.39747			−0.698733	−	0.715382i	$-0.746253\pi$
$83$	−12.7315			−1.39747			−0.698733	+	0.715382i	$0.746253\pi$
$84$	8.19653			0.894314
$85$	−15.6583	−	3.44917i	−1.69838	−	0.374115i
$86$	2.48305			0.267755
$87$	−0.105054			−0.0112630
$88$			18.8899i			2.01367i
$89$	12.7315			1.34954			0.674770	−	0.738028i	$-0.264243\pi$
$89$	12.7315			1.34954			0.674770	+	0.738028i	$0.264243\pi$
$90$			24.5500i			2.58780i
$91$		−	19.3234i		−	2.02565i
$92$			0.226053i			0.0235676i
$93$	−4.18467			−0.433930
$94$	−28.7135			−2.96157
$95$		−	5.21726i		−	0.535279i
$96$		−	1.15828i		−	0.118216i
$97$		−	3.66042i		−	0.371659i	−0.982582	−	0.185829i	$-0.940503\pi$
$97$		−	3.66042i		−	0.371659i	0.982582	−	0.185829i	$-0.0594972\pi$
$98$	3.63163			0.366850
$99$		−	8.93163i		−	0.897663i
$100$	−42.1650			−4.21650
$101$	6.56770			0.653511			0.326756	−	0.945109i	$-0.394045\pi$
$101$	6.56770			0.653511			0.326756	+	0.945109i	$0.394045\pi$
$102$	−6.76282	−	1.48969i	−0.669619	−	0.147502i
$103$	−8.62009			−0.849363			−0.424681	−	0.905343i	$-0.639614\pi$
$103$	−8.62009			−0.849363			−0.424681	+	0.905343i	$0.639614\pi$
$104$	−35.7181			−3.50245
$105$		−	7.65184i		−	0.746743i
$106$	33.2026			3.22492
$107$			4.09685i			0.396058i	0.980196	+	0.198029i	$0.0634540\pi$
$107$			4.09685i			0.396058i	−0.980196	+	0.198029i	$0.936546\pi$
$108$			15.6165i			1.50270i
$109$		−	3.30427i		−	0.316492i	−0.987400	−	0.158246i	$-0.949416\pi$
$109$		−	3.30427i		−	0.316492i	0.987400	−	0.158246i	$-0.0505839\pi$
$110$	33.9210			3.23424
$111$	2.40463			0.228238
$112$		−	14.6056i		−	1.38010i
$113$		−	18.6358i		−	1.75311i	−0.481300	−	0.876556i	$-0.659835\pi$
$113$		−	18.6358i		−	1.75311i	0.481300	−	0.876556i	$-0.340165\pi$
$114$		−	2.25333i		−	0.211044i
$115$	0.211031			0.0196787
$116$			0.646965i			0.0600692i
$117$	16.8885			1.56134
$118$	−0.818843			−0.0753806
$119$	−11.7135	−	2.58022i	−1.07377	−	0.236528i
$120$	−14.1439			−1.29116
$121$	−1.34091			−0.121901
$122$		−	18.2766i		−	1.65469i
$123$	−5.60123			−0.505046
$124$			25.7709i			2.31429i
$125$			19.9193i			1.78163i
$126$			18.3652i			1.63610i
$127$	12.1362			1.07691			0.538457	−	0.842653i	$-0.319008\pi$
$127$	12.1362			1.07691			0.538457	+	0.842653i	$0.319008\pi$
$128$	17.8005			1.57335
$129$		−	0.676403i		−	0.0595540i
$130$			64.1399i			5.62544i
$131$			8.77596i			0.766759i	0.923591	+	0.383380i	$0.125240\pi$
$131$			8.77596i			0.766759i	−0.923591	+	0.383380i	$0.874760\pi$
$132$	9.89811			0.861520
$133$		−	3.90287i		−	0.338422i
$134$	−19.0973			−1.64976
$135$	14.5787			1.25473
$136$	−4.76937	+	21.6517i	−0.408970	+	1.85662i
$137$	−5.66290			−0.483814			−0.241907	−	0.970299i	$-0.577773\pi$
$137$	−5.66290			−0.483814			−0.241907	+	0.970299i	$0.577773\pi$
$138$	0.0911441			0.00775870
$139$			11.2843i			0.957125i	0.878053	+	0.478563i	$0.158842\pi$
$139$			11.2843i			0.957125i	−0.878053	+	0.478563i	$0.841158\pi$
$140$	−47.1230			−3.98262
$141$			7.82178i			0.658713i
$142$		−	2.35202i		−	0.197377i
$143$		−	23.3349i		−	1.95137i
$144$	12.7652			1.06376
$145$	0.603972			0.0501571
$146$			20.6611i			1.70993i
$147$		−	0.989284i		−	0.0815948i
$148$		−	14.8087i		−	1.21727i
$149$	−7.85499			−0.643506			−0.321753	−	0.946824i	$-0.604272\pi$
$149$	−7.85499			−0.643506			−0.321753	+	0.946824i	$0.604272\pi$
$150$			17.0009i			1.38811i
$151$	−21.8090			−1.77479			−0.887396	−	0.461007i	$-0.847488\pi$
$151$	−21.8090			−1.77479			−0.887396	+	0.461007i	$0.847488\pi$
$152$	−7.21421			−0.585150
$153$	2.25508	−	10.2375i	0.182313	−	0.827651i
$154$	25.3753			2.04480
$155$	24.0583			1.93241
$156$			18.7159i			1.49848i
$157$	−4.07100			−0.324901			−0.162451	−	0.986717i	$-0.551940\pi$
$157$	−4.07100			−0.324901			−0.162451	+	0.986717i	$0.551940\pi$
$158$		−	32.2617i		−	2.56660i
$159$		−	9.04463i		−	0.717286i
$160$			6.65911i			0.526449i
$161$	0.157866			0.0124416
$162$	−12.6428			−0.993312
$163$			16.3308i			1.27913i	0.768738	+	0.639564i	$0.220885\pi$
$163$			16.3308i			1.27913i	−0.768738	+	0.639564i	$0.779115\pi$
$164$			34.4946i			2.69357i
$165$		−	9.24034i		−	0.719360i
$166$	31.6131			2.45365
$167$			21.1547i			1.63700i	0.574505	+	0.818501i	$0.305195\pi$
$167$			21.1547i			1.63700i	−0.574505	+	0.818501i	$0.694805\pi$
$168$	−10.5807			−0.816315
$169$	31.1231			2.39409
$170$	38.8804	+	8.56446i	2.98199	+	0.656864i
$171$	3.41107			0.260851
$172$	−4.16556			−0.317621
$173$			7.13207i			0.542241i	0.962545	+	0.271121i	$0.0873943\pi$
$173$			7.13207i			0.542241i	−0.962545	+	0.271121i	$0.912606\pi$
$174$	0.260855			0.0197754
$175$			29.4463i			2.22593i
$176$		−	17.6377i		−	1.32949i
$177$			0.223059i			0.0167662i
$178$	−31.6131			−2.36950
$179$	−7.75298			−0.579485			−0.289742	−	0.957105i	$-0.593570\pi$
$179$	−7.75298			−0.579485			−0.289742	+	0.957105i	$0.593570\pi$
$180$		−	41.1850i		−	3.06975i
$181$			0.172835i			0.0128467i	0.999979	+	0.00642337i	$0.00204464\pi$
$181$			0.172835i			0.0128467i	−0.999979	+	0.00642337i	$0.997955\pi$
$182$			47.9811i			3.55660i
$183$	−4.97869			−0.368036
$184$		−	0.291805i		−	0.0215121i
$185$	−13.8246			−1.01640
$186$	10.3908			0.761888
$187$	−14.1452	−	3.11587i	−1.03440	−	0.227855i
$188$	48.1696			3.51313
$189$	10.9059			0.793286
$190$			12.9547i			0.939835i
$191$	−19.5815			−1.41687			−0.708435	−	0.705777i	$-0.750598\pi$
$191$	−19.5815			−1.41687			−0.708435	+	0.705777i	$0.750598\pi$
$192$		−	3.91604i		−	0.282616i
$193$		−	11.5262i		−	0.829676i	−0.909895	−	0.414838i	$-0.863838\pi$
$193$		−	11.5262i		−	0.829676i	0.909895	−	0.414838i	$-0.136162\pi$
$194$			9.08901i			0.652553i
$195$	17.4722			1.25121
$196$	−6.09240			−0.435171
$197$			11.3242i			0.806816i	0.915020	+	0.403408i	$0.132174\pi$
$197$			11.3242i			0.806816i	−0.915020	+	0.403408i	$0.867826\pi$
$198$			22.1777i			1.57610i
$199$			6.33673i			0.449199i	0.974451	+	0.224599i	$0.0721073\pi$
$199$			6.33673i			0.449199i	−0.974451	+	0.224599i	$0.927893\pi$
$200$	54.4296			3.84875
$201$			5.20226i			0.366939i
$202$	−16.3080			−1.14742
$203$	0.451813			0.0317110
$204$	11.3453	+	2.49910i	0.794327	+	0.174972i
$205$	32.2023			2.24910
$206$	21.4041			1.49130
$207$			0.137973i			0.00958979i
$208$	33.3505			2.31244
$209$		−	4.71310i		−	0.326012i
$210$			18.9999i			1.31112i
$211$		−	1.51205i		−	0.104094i	−0.998645	−	0.0520468i	$-0.983425\pi$
$211$		−	1.51205i		−	0.104094i	0.998645	−	0.0520468i	$-0.0165745\pi$
$212$	−55.7004			−3.82552
$213$	−0.640709			−0.0439006
$214$		−	10.1727i		−	0.695392i
$215$			3.88874i			0.265210i
$216$		−	20.1588i		−	1.37164i
$217$	17.9973			1.22173
$218$			8.20469i			0.555692i
$219$	5.62825			0.380322
$220$	−56.9057			−3.83658
$221$	5.89167	−	26.7466i	0.396316	−	1.79917i
$222$	−5.97083			−0.400736
$223$	−14.8840			−0.996706			−0.498353	−	0.866974i	$-0.666062\pi$
$223$	−14.8840			−0.996706			−0.498353	+	0.866974i	$0.666062\pi$
$224$			4.98148i			0.332839i
$225$	−25.7357			−1.71571
$226$			46.2738i			3.07809i
$227$		−	0.613843i		−	0.0407422i	−0.999792	−	0.0203711i	$-0.993515\pi$
$227$		−	0.613843i		−	0.0407422i	0.999792	−	0.0203711i	$-0.00648477\pi$
$228$			3.78018i			0.250348i
$229$	−0.427448			−0.0282466			−0.0141233	−	0.999900i	$-0.504496\pi$
$229$	−0.427448			−0.0282466			−0.0141233	+	0.999900i	$0.504496\pi$
$230$	−0.524001			−0.0345516
$231$		−	6.91242i		−	0.454804i
$232$		−	0.835148i		−	0.0548301i
$233$			24.1146i			1.57980i	0.613238	+	0.789898i	$0.289867\pi$
$233$			24.1146i			1.57980i	−0.613238	+	0.789898i	$0.710133\pi$
$234$	−41.9350			−2.74138
$235$		−	44.9685i		−	2.93342i
$236$	1.37369			0.0894194
$237$	−8.78833			−0.570863
$238$	29.0853	+	6.40682i	1.88532	+	0.415292i
$239$	−2.41288			−0.156076			−0.0780381	−	0.996950i	$-0.524866\pi$
$239$	−2.41288			−0.156076			−0.0780381	+	0.996950i	$0.524866\pi$
$240$	13.2064			0.852467
$241$			15.4766i			0.996935i	0.866908	+	0.498467i	$0.166104\pi$
$241$			15.4766i			0.996935i	−0.866908	+	0.498467i	$0.833896\pi$
$242$	3.32954			0.214031
$243$			14.6908i			0.942418i
$244$			30.6608i			1.96285i
$245$			5.68754i			0.363363i
$246$	13.9082			0.886751
$247$	8.91182			0.567045
$248$		−	33.2668i		−	2.11245i
$249$		−	8.61165i		−	0.545741i
$250$		−	49.4606i		−	3.12817i
$251$	−16.5173			−1.04256			−0.521282	−	0.853385i	$-0.674546\pi$
$251$	−16.5173			−1.04256			−0.521282	+	0.853385i	$0.674546\pi$
$252$		−	30.8093i		−	1.94080i
$253$	0.190638			0.0119853
$254$	−30.1348			−1.89083
$255$	2.33303	−	10.5913i	0.146100	−	0.663254i
$256$	−32.6205			−2.03878
$257$	0.703832			0.0439038			0.0219519	−	0.999759i	$-0.493012\pi$
$257$	0.703832			0.0439038			0.0219519	+	0.999759i	$0.493012\pi$
$258$			1.67955i			0.104564i
$259$	−10.3418			−0.642605
$260$		−	107.601i		−	6.67311i
$261$			0.394880i			0.0244424i
$262$		−	21.7912i		−	1.34626i
$263$	−15.2772			−0.942032			−0.471016	−	0.882125i	$-0.656113\pi$
$263$	−15.2772			−0.942032			−0.471016	+	0.882125i	$0.656113\pi$
$264$	−12.7772			−0.786381
$265$			51.9989i			3.19427i
$266$			9.69104i			0.594196i
$267$			8.61165i			0.527025i
$268$	32.0376			1.95701
$269$		−	3.36672i		−	0.205272i	−0.994719	−	0.102636i	$-0.967272\pi$
$269$		−	3.36672i		−	0.205272i	0.994719	−	0.102636i	$-0.0327277\pi$
$270$	−36.1997			−2.20304
$271$	−1.72492			−0.104781			−0.0523906	−	0.998627i	$-0.516684\pi$
$271$	−1.72492			−0.104781			−0.0523906	+	0.998627i	$0.516684\pi$
$272$	4.45322	−	20.2164i	0.270016	−	1.22580i
$273$	13.0704			0.791058
$274$	14.0613			0.849473
$275$			35.5593i			2.14430i
$276$	−0.152903			−0.00920367
$277$		−	13.7905i		−	0.828593i	−0.910142	−	0.414297i	$-0.864028\pi$
$277$		−	13.7905i		−	0.828593i	0.910142	−	0.414297i	$-0.135972\pi$
$278$		−	28.0196i		−	1.68051i
$279$			15.7294i			0.941697i
$280$	60.8297			3.63527
$281$	12.2554			0.731095			0.365547	−	0.930793i	$-0.380882\pi$
$281$	12.2554			0.731095			0.365547	+	0.930793i	$0.380882\pi$
$282$		−	19.4219i		−	1.15656i
$283$		−	10.4245i		−	0.619670i	−0.950790	−	0.309835i	$-0.899726\pi$
$283$		−	10.4245i		−	0.619670i	0.950790	−	0.309835i	$-0.100274\pi$
$284$			3.94574i			0.234136i
$285$	3.52897			0.209038
$286$			57.9419i			3.42618i
$287$	24.0895			1.42196
$288$	−4.35376			−0.256548
$289$	−15.4266	−	7.14284i	−0.907447	−	0.420167i
$290$	−1.49969			−0.0880651
$291$	2.47592			0.145141
$292$		−	34.6610i		−	2.02838i
$293$	5.76636			0.336874			0.168437	−	0.985712i	$-0.446128\pi$
$293$	5.76636			0.336874			0.168437	+	0.985712i	$0.446128\pi$
$294$			2.45645i			0.143263i
$295$		−	1.28240i		−	0.0746642i
$296$			19.1161i			1.11110i
$297$	13.1699			0.764196
$298$	19.5044			1.12986
$299$			0.360471i			0.0208466i
$300$		−	28.5205i		−	1.64663i
$301$			2.90905i			0.167675i
$302$	54.1530			3.11615
$303$			4.44242i			0.255210i
$304$	6.73600			0.386336
$305$	28.6232			1.63896
$306$	−5.59949	+	25.4202i	−0.320102	+	1.45318i
$307$	−8.49409			−0.484783			−0.242392	−	0.970178i	$-0.577932\pi$
$307$	−8.49409			−0.484783			−0.242392	+	0.970178i	$0.577932\pi$
$308$	−42.5694			−2.42562
$309$		−	5.83066i		−	0.331694i
$310$	−59.7380			−3.39289
$311$		−	18.8466i		−	1.06869i	−0.845265	−	0.534347i	$-0.820558\pi$
$311$		−	18.8466i		−	1.06869i	0.845265	−	0.534347i	$-0.179442\pi$
$312$		−	24.1599i		−	1.36778i
$313$		−	7.09159i		−	0.400840i	−0.979710	−	0.200420i	$-0.935769\pi$
$313$		−	7.09159i		−	0.400840i	0.979710	−	0.200420i	$-0.0642307\pi$
$314$	10.1085			0.570457
$315$	−28.7619			−1.62055
$316$			54.1220i			3.04460i
$317$		−	3.81984i		−	0.214543i	−0.994230	−	0.107272i	$-0.965789\pi$
$317$		−	3.81984i		−	0.214543i	0.994230	−	0.107272i	$-0.0342115\pi$
$318$			22.4583i			1.25940i
$319$	0.545608			0.0305482
$320$			22.5139i			1.25856i
$321$	−2.77112			−0.154669
$322$	−0.391989			−0.0218447
$323$	1.18998	−	5.40218i	0.0662121	−	0.300585i
$324$	21.2095			1.17830
$325$	−67.2376			−3.72967
$326$		−	40.5503i		−	2.24587i
$327$	2.23502			0.123597
$328$		−	44.5280i		−	2.45865i
$329$		−	33.6396i		−	1.85461i
$330$			22.9443i			1.26304i
$331$	12.6097			0.693093			0.346547	−	0.938033i	$-0.387354\pi$
$331$	12.6097			0.693093			0.346547	+	0.938033i	$0.387354\pi$
$332$	−53.0339			−2.91061
$333$		−	9.03858i		−	0.495311i
$334$		−	52.5283i		−	2.87422i
$335$		−	29.9085i		−	1.63408i
$336$	9.87928			0.538959
$337$			2.65458i			0.144604i	0.997383	+	0.0723020i	$0.0230345\pi$
$337$			2.65458i			0.144604i	−0.997383	+	0.0723020i	$0.976965\pi$
$338$	−77.2804			−4.20350
$339$	12.6053			0.684628
$340$	−65.2255	−	14.3677i	−3.53735	−	0.779198i
$341$	21.7335			1.17693
$342$	−8.46987			−0.457998
$343$		−	16.1087i		−	0.869786i
$344$	5.37720			0.289919
$345$			0.142742i			0.00768496i
$346$		−	17.7093i		−	0.952059i
$347$			28.8666i			1.54964i	0.632181	+	0.774820i	$0.282160\pi$
$347$			28.8666i			1.54964i	−0.632181	+	0.774820i	$0.717840\pi$
$348$	−0.437609			−0.0234583
$349$	29.5550			1.58205			0.791023	−	0.611787i	$-0.209549\pi$
$349$	29.5550			1.58205			0.791023	+	0.611787i	$0.209549\pi$
$350$		−	73.1166i		−	3.90825i
$351$			24.9025i			1.32920i
$352$			6.01562i			0.320634i
$353$	11.0177			0.586414			0.293207	−	0.956049i	$-0.405277\pi$
$353$	11.0177			0.586414			0.293207	+	0.956049i	$0.405277\pi$
$354$		−	0.553868i		−	0.0294378i
$355$	3.68353			0.195501
$356$	53.0339			2.81079
$357$	1.74527	−	7.92305i	0.0923693	−	0.419332i
$358$	19.2511			1.01745
$359$	14.3049			0.754983			0.377491	−	0.926013i	$-0.376787\pi$
$359$	14.3049			0.754983			0.377491	+	0.926013i	$0.376787\pi$
$360$			53.1645i			2.80202i
$361$	−17.2000			−0.905264
$362$		−	0.429159i		−	0.0225561i
$363$		−	0.906993i		−	0.0476048i
$364$		−	80.4928i		−	4.21897i
$365$	−32.3576			−1.69368
$366$	12.3624			0.646191
$367$		−	22.5726i		−	1.17828i	−0.808032	−	0.589139i	$-0.799467\pi$
$367$		−	22.5726i		−	1.17828i	0.808032	−	0.589139i	$-0.200533\pi$
$368$			0.272462i			0.0142030i
$369$			21.0540i			1.09603i
$370$	34.3272			1.78458
$371$			38.8988i			2.01953i
$372$	−17.4315			−0.903781
$373$	4.24811			0.219959			0.109979	−	0.993934i	$-0.464922\pi$
$373$	4.24811			0.219959			0.109979	+	0.993934i	$0.464922\pi$
$374$	35.1233	+	7.73686i	1.81618	+	0.400064i
$375$	−13.4735			−0.695767
$376$	−62.1807			−3.20672
$377$			1.03167i			0.0531337i
$378$	−27.0799			−1.39284
$379$		−	9.44974i		−	0.485401i	−0.970101	−	0.242700i	$-0.921967\pi$
$379$		−	9.44974i		−	0.485401i	0.970101	−	0.242700i	$-0.0780332\pi$
$380$		−	21.7328i		−	1.11487i
$381$			8.20896i			0.420558i
$382$	48.6220			2.48772
$383$	15.8741			0.811127			0.405564	−	0.914067i	$-0.367075\pi$
$383$	15.8741			0.811127			0.405564	+	0.914067i	$0.367075\pi$
$384$			12.0403i			0.614429i
$385$			39.7405i			2.02536i
$386$			28.6202i			1.45673i
$387$	−2.54248			−0.129241
$388$		−	15.2477i		−	0.774083i
$389$	−18.8795			−0.957228			−0.478614	−	0.878025i	$-0.658861\pi$
$389$	−18.8795			−0.957228			−0.478614	+	0.878025i	$0.658861\pi$
$390$	−43.3844			−2.19686
$391$	0.218511	+	0.0481329i	0.0110506	+	0.00243418i
$392$	7.86450			0.397217
$393$	−5.93609			−0.299436
$394$		−	28.1186i		−	1.41659i
$395$	50.5254			2.54221
$396$		−	37.2052i		−	1.86963i
$397$		−	12.8864i		−	0.646752i	−0.946271	−	0.323376i	$-0.895182\pi$
$397$		−	12.8864i		−	0.646752i	0.946271	−	0.323376i	$-0.104818\pi$
$398$		−	15.7344i		−	0.788696i
$399$	2.63992			0.132161
$400$	−50.8215			−2.54108
$401$			37.3729i			1.86631i	0.359470	+	0.933157i	$0.382958\pi$
$401$			37.3729i			1.86631i	−0.359470	+	0.933157i	$0.617042\pi$
$402$		−	12.9175i		−	0.644266i
$403$			41.0950i			2.04709i
$404$	27.3581			1.36112
$405$		−	19.8000i		−	0.983872i
$406$	−1.12188			−0.0556778
$407$	−12.4887			−0.619041
$408$	−14.6453	−	3.22602i	−0.725049	−	0.159712i
$409$	8.51422			0.421001			0.210501	−	0.977594i	$-0.432491\pi$
$409$	8.51422			0.421001			0.210501	+	0.977594i	$0.432491\pi$
$410$	−79.9600			−3.94894
$411$		−	3.83040i		−	0.188940i
$412$	−35.9075			−1.76903
$413$		−	0.959325i		−	0.0472053i
$414$		−	0.342594i		−	0.0168376i
$415$			49.5096i			2.43033i
$416$	−11.3747			−0.557691
$417$	−7.63277			−0.373778
$418$			11.7029i			0.572407i
$419$		−	12.0204i		−	0.587237i	−0.955923	−	0.293618i	$-0.905140\pi$
$419$		−	12.0204i		−	0.587237i	0.955923	−	0.293618i	$-0.0948595\pi$
$420$		−	31.8742i		−	1.55530i
$421$	4.88938			0.238294			0.119147	−	0.992877i	$-0.461984\pi$
$421$	4.88938			0.238294			0.119147	+	0.992877i	$0.461984\pi$
$422$			3.75449i			0.182766i
$423$	29.4007			1.42951
$424$	71.9020			3.49187
$425$	−8.97810	+	40.7582i	−0.435502	+	1.97706i
$426$	1.59091			0.0770801
$427$	21.4122			1.03621
$428$			17.0657i			0.824900i
$429$	15.7838			0.762050
$430$		−	9.65595i		−	0.465651i
$431$			28.9867i			1.39624i	0.715980	+	0.698120i	$0.245980\pi$
$431$			28.9867i			1.39624i	−0.715980	+	0.698120i	$0.754020\pi$
$432$			18.8226i			0.905600i
$433$	26.0874			1.25368			0.626841	−	0.779147i	$-0.284347\pi$
$433$	26.0874			1.25368			0.626841	+	0.779147i	$0.284347\pi$
$434$	−44.6882			−2.14510
$435$			0.408528i			0.0195874i
$436$		−	13.7641i		−	0.659183i
$437$			0.0728065i			0.00348281i
$438$	−13.9752			−0.667763
$439$			11.0631i			0.528013i	0.964521	+	0.264007i	$0.0850441\pi$
$439$			11.0631i			0.528013i	−0.964521	+	0.264007i	$0.914956\pi$
$440$	73.4578			3.50197
$441$	−3.71854			−0.177073
$442$	−14.6293	+	66.4133i	−0.695846	+	3.15896i
$443$	14.8276			0.704481			0.352240	−	0.935910i	$-0.385420\pi$
$443$	14.8276			0.704481			0.352240	+	0.935910i	$0.385420\pi$
$444$	10.0166			0.475368
$445$		−	49.5096i		−	2.34698i
$446$	36.9578			1.75000
$447$		−	5.31314i		−	0.251303i
$448$			16.8419i			0.795707i
$449$		−	33.6508i		−	1.58808i	−0.607865	−	0.794040i	$-0.707974\pi$
$449$		−	33.6508i		−	1.58808i	0.607865	−	0.794040i	$-0.292026\pi$
$450$	63.9032			3.01243
$451$	29.0905			1.36982
$452$		−	77.6287i		−	3.65134i
$453$		−	14.7517i		−	0.693095i
$454$			1.52421i			0.0715345i
$455$	−75.1438			−3.52279
$456$		−	4.87972i		−	0.228514i
$457$	18.0624			0.844922			0.422461	−	0.906381i	$-0.361166\pi$
$457$	18.0624			0.844922			0.422461	+	0.906381i	$0.361166\pi$
$458$	1.06138			0.0495949
$459$	15.0954	+	3.32518i	0.704594	+	0.155206i
$460$	0.879060			0.0409864
$461$	−0.112551			−0.00524204			−0.00262102	−	0.999997i	$-0.500834\pi$
$461$	−0.112551			−0.00524204			−0.00262102	+	0.999997i	$0.500834\pi$
$462$			17.1639i			0.798538i
$463$	21.7945			1.01288			0.506439	−	0.862276i	$-0.330962\pi$
$463$	21.7945			1.01288			0.506439	+	0.862276i	$0.330962\pi$
$464$			0.779788i			0.0362007i
$465$			16.2731i			0.754647i
$466$		−	59.8777i		−	2.77378i
$467$	19.2311			0.889908			0.444954	−	0.895554i	$-0.353220\pi$
$467$	19.2311			0.889908			0.444954	+	0.895554i	$0.353220\pi$
$468$	70.3499			3.25192
$469$		−	22.3737i		−	1.03312i
$470$			111.659i			5.15046i
$471$		−	2.75364i		−	0.126881i
$472$	−1.77325			−0.0816205
$473$			3.51296i			0.161526i
$474$	21.8219			1.00231
$475$	−13.5804			−0.623111
$476$	−48.7933	−	10.7480i	−2.23644	−	0.492636i
$477$	−33.9972			−1.55662
$478$	5.99131			0.274036
$479$			33.4337i			1.52762i	0.645439	+	0.763812i	$0.276675\pi$
$479$			33.4337i			1.52762i	−0.645439	+	0.763812i	$0.723325\pi$
$480$	−4.50424			−0.205590
$481$		−	23.6144i		−	1.07672i
$482$		−	38.4292i		−	1.75040i
$483$			0.106781i			0.00485870i
$484$	−5.58562			−0.253892
$485$	−14.2344			−0.646351
$486$		−	36.4782i		−	1.65468i
$487$		−	4.21883i		−	0.191173i	−0.995421	−	0.0955867i	$-0.969527\pi$
$487$		−	4.21883i		−	0.191173i	0.995421	−	0.0955867i	$-0.0304727\pi$
$488$		−	39.5791i		−	1.79166i
$489$	−11.0462			−0.499527
$490$		−	14.1225i		−	0.637988i
$491$	4.33990			0.195857			0.0979284	−	0.995193i	$-0.468778\pi$
$491$	4.33990			0.195857			0.0979284	+	0.995193i	$0.468778\pi$
$492$	−23.3322			−1.05190
$493$	0.625379	+	0.137757i	0.0281657	+	0.00620425i
$494$	−22.1285			−0.995609
$495$	−34.7328			−1.56112
$496$			31.0617i			1.39471i
$497$	2.75554			0.123603
$498$			21.3832i			0.958203i
$499$		−	13.0407i		−	0.583782i	−0.956452	−	0.291891i	$-0.905715\pi$
$499$		−	13.0407i		−	0.583782i	0.956452	−	0.291891i	$-0.0942845\pi$
$500$			82.9749i			3.71075i
$501$	−14.3091			−0.639285
$502$	41.0134			1.83052
$503$			23.4274i			1.04457i	0.852770	+	0.522287i	$0.174921\pi$
$503$			23.4274i			1.04457i	−0.852770	+	0.522287i	$0.825079\pi$
$504$			39.7708i			1.77153i
$505$		−	25.5401i		−	1.13652i
$506$	−0.473365			−0.0210437
$507$			21.0518i			0.934942i
$508$	50.5540			2.24297
$509$	−38.7887			−1.71928			−0.859640	−	0.510901i	$-0.829312\pi$
$509$	−38.7887			−1.71928			−0.859640	+	0.510901i	$0.829312\pi$
$510$	−5.79303	+	26.2988i	−0.256520	+	1.16453i
$511$	−24.2058			−1.07080
$512$	45.3976			2.00631
$513$			5.02971i			0.222067i
$514$	−1.74765			−0.0770856
$515$			33.5213i			1.47712i
$516$		−	2.81760i		−	0.124038i
$517$		−	40.6231i		−	1.78660i
$518$	25.6791			1.12828
$519$	−4.82416			−0.211757
$520$			138.899i			6.09110i
$521$		−	27.2512i		−	1.19390i	−0.802280	−	0.596948i	$-0.796380\pi$
$521$		−	27.2512i		−	1.19390i	0.802280	−	0.596948i	$-0.203620\pi$
$522$		−	0.980508i		−	0.0429157i
$523$	−28.9776			−1.26710			−0.633552	−	0.773700i	$-0.718404\pi$
$523$	−28.9776			−1.26710			−0.633552	+	0.773700i	$0.718404\pi$
$524$			36.5568i			1.59699i
$525$	−19.9175			−0.869273
$526$	37.9341			1.65401
$527$	24.9110	+	5.48733i	1.08514	+	0.239032i
$528$	11.9302			0.519196
$529$	22.9971			0.999872
$530$		−	129.116i		−	5.60844i
$531$	0.838440			0.0363852
$532$		−	16.2576i		−	0.704858i
$533$			55.0061i			2.38258i
$534$		−	21.3832i		−	0.925341i
$535$	15.9316			0.688783
$536$	−41.3564			−1.78632
$537$		−	5.24414i		−	0.226301i
$538$			8.35974i			0.360414i
$539$			5.13794i			0.221307i
$540$	60.7284			2.61333
$541$		−	45.5380i		−	1.95783i	−0.204262	−	0.978916i	$-0.565480\pi$
$541$		−	45.5380i		−	1.95783i	0.204262	−	0.978916i	$-0.434520\pi$
$542$	4.28306			0.183973
$543$	−0.116906			−0.00501693
$544$	−1.51884	+	6.89514i	−0.0651198	+	0.295626i
$545$	−12.8495			−0.550411
$546$	−32.4546			−1.38893
$547$		−	26.6740i		−	1.14050i	−0.821471	−	0.570250i	$-0.806846\pi$
$547$		−	26.6740i		−	1.14050i	0.821471	−	0.570250i	$-0.193154\pi$
$548$	−23.5891			−1.00768
$549$			18.7140i			0.798695i
$550$		−	88.2955i		−	3.76493i
$551$			0.208373i			0.00887698i
$552$	0.197378			0.00840096
$553$	37.7965			1.60727
$554$			34.2427i			1.45483i
$555$		−	9.35099i		−	0.396927i
$556$			47.0056i			1.99348i
$557$	−36.0132			−1.52593			−0.762964	−	0.646441i	$-0.776257\pi$
$557$	−36.0132			−1.52593			−0.762964	+	0.646441i	$0.776257\pi$
$558$		−	39.0570i		−	1.65342i
$559$	−6.64252			−0.280949
$560$	−56.7974			−2.40013
$561$	2.10758	−	9.56786i	0.0889822	−	0.403955i
$562$	−30.4308			−1.28364
$563$	−2.12573			−0.0895888			−0.0447944	−	0.998996i	$-0.514263\pi$
$563$	−2.12573			−0.0895888			−0.0447944	+	0.998996i	$0.514263\pi$
$564$			32.5821i			1.37195i
$565$	−72.4699			−3.04883
$566$			25.8845i			1.08801i
$567$		−	14.8118i		−	0.622038i
$568$		−	5.09343i		−	0.213716i
$569$	7.33184			0.307367			0.153683	−	0.988120i	$-0.450886\pi$
$569$	7.33184			0.307367			0.153683	+	0.988120i	$0.450886\pi$
$570$	−8.76262			−0.367026
$571$			4.18622i			0.175188i	0.996156	+	0.0875940i	$0.0279178\pi$
$571$			4.18622i			0.175188i	−0.996156	+	0.0875940i	$0.972082\pi$
$572$		−	97.2030i		−	4.06426i
$573$		−	13.2450i		−	0.553318i
$574$	−59.8156			−2.49666
$575$		−	0.549308i		−	0.0229077i
$576$	−14.7197			−0.613320
$577$	−5.69278			−0.236994			−0.118497	−	0.992954i	$-0.537808\pi$
$577$	−5.69278			−0.236994			−0.118497	+	0.992954i	$0.537808\pi$
$578$	38.3051	+	17.7361i	1.59328	+	0.737723i
$579$	7.79638			0.324006
$580$	2.51588			0.104466
$581$			37.0366i			1.53654i
$582$	−6.14784			−0.254836
$583$			46.9741i			1.94547i
$584$			44.7428i			1.85147i
$585$		−	65.6749i		−	2.71532i
$586$	−14.3182			−0.591478
$587$	5.66022			0.233622			0.116811	−	0.993154i	$-0.462733\pi$
$587$	5.66022			0.233622			0.116811	+	0.993154i	$0.462733\pi$
$588$		−	4.12092i		−	0.169944i
$589$			8.30021i			0.342004i
$590$			3.18427i			0.131094i
$591$	−7.65973			−0.315079
$592$		−	17.8489i		−	0.733586i
$593$	−7.44412			−0.305693			−0.152847	−	0.988250i	$-0.548844\pi$
$593$	−7.44412			−0.305693			−0.152847	+	0.988250i	$0.548844\pi$
$594$	−32.7016			−1.34176
$595$	−10.0338	+	45.5508i	−0.411345	+	1.86740i
$596$	−32.7204			−1.34028
$597$	−4.28618			−0.175422
$598$		−	0.895068i		−	0.0366020i
$599$	38.4822			1.57234			0.786170	−	0.618010i	$-0.212061\pi$
$599$	38.4822			1.57234			0.786170	+	0.618010i	$0.212061\pi$
$600$			36.8163i			1.50302i
$601$			41.2507i			1.68265i	0.540530	+	0.841325i	$0.318224\pi$
$601$			41.2507i			1.68265i	−0.540530	+	0.841325i	$0.681776\pi$
$602$		−	7.22333i		−	0.294401i
$603$	19.5544			0.796315
$604$	−90.8467			−3.69650
$605$			5.21443i			0.211997i
$606$		−	11.0308i		−	0.448094i
$607$			27.6168i			1.12093i	0.828178	+	0.560465i	$0.189378\pi$
$607$			27.6168i			1.12093i	−0.828178	+	0.560465i	$0.810622\pi$
$608$	−2.29742			−0.0931727
$609$			0.305608i			0.0123839i
$610$	−71.0730			−2.87766
$611$	76.8127			3.10751
$612$	9.39368	−	42.6448i	0.379717	−	1.72381i
$613$	−15.7406			−0.635758			−0.317879	−	0.948131i	$-0.602971\pi$
$613$	−15.7406			−0.635758			−0.317879	+	0.948131i	$0.602971\pi$
$614$	21.0913			0.851175
$615$			21.7817i			0.878324i
$616$	54.9516			2.21406
$617$			38.4589i			1.54830i	0.633004	+	0.774148i	$0.281822\pi$
$617$			38.4589i			1.54830i	−0.633004	+	0.774148i	$0.718178\pi$
$618$			14.4778i			0.582384i
$619$		−	5.18953i		−	0.208585i	−0.994547	−	0.104292i	$-0.966742\pi$
$619$		−	5.18953i		−	0.208585i	0.994547	−	0.104292i	$-0.0332578\pi$
$620$	100.216			4.02478
$621$	−0.203445			−0.00816396
$622$			46.7972i			1.87640i
$623$		−	37.0367i		−	1.48384i
$624$			22.5584i			0.903057i
$625$	26.8494			1.07398
$626$			17.6088i			0.703789i
$627$	3.18796			0.127315
$628$	−16.9580			−0.676697
$629$	−14.3146	−	3.15318i	−0.570760	−	0.125725i
$630$	71.4173			2.84533
$631$	−18.6630			−0.742961			−0.371481	−	0.928441i	$-0.621150\pi$
$631$	−18.6630			−0.742961			−0.371481	+	0.928441i	$0.621150\pi$
$632$		−	69.8645i		−	2.77906i
$633$	1.02275			0.0406508
$634$			9.48486i			0.376692i
$635$		−	47.1945i		−	1.87286i
$636$		−	37.6759i		−	1.49395i
$637$	−9.71512			−0.384927
$638$	−1.35478			−0.0536361
$639$			2.40831i			0.0952712i
$640$		−	69.2214i		−	2.73622i
$641$		−	17.0492i		−	0.673404i	−0.941611	−	0.336702i	$-0.890688\pi$
$641$		−	17.0492i		−	0.673404i	0.941611	−	0.336702i	$-0.109312\pi$
$642$	6.88085			0.271566
$643$		−	45.7011i		−	1.80228i	−0.433533	−	0.901138i	$-0.642733\pi$
$643$		−	45.7011i		−	1.80228i	0.433533	−	0.901138i	$-0.357267\pi$
$644$	0.657599			0.0259130
$645$	−2.63036			−0.103570
$646$	−2.95478	+	13.4139i	−0.116254	+	0.527763i
$647$	−14.7823			−0.581153			−0.290576	−	0.956852i	$-0.593847\pi$
$647$	−14.7823			−0.581153			−0.290576	+	0.956852i	$0.593847\pi$
$648$	−27.3787			−1.07554
$649$		−	1.15848i		−	0.0454743i
$650$	166.955			6.54850
$651$			12.1734i			0.477114i
$652$			68.0269i			2.66414i
$653$			30.8685i			1.20798i	0.796992	+	0.603990i	$0.206423\pi$
$653$			30.8685i			1.20798i	−0.796992	+	0.603990i	$0.793577\pi$
$654$	−5.54968			−0.217010
$655$	34.1274			1.33347
$656$			41.5763i			1.62328i
$657$		−	21.1556i		−	0.825358i
$658$			83.5289i			3.25630i
$659$	27.0231			1.05267			0.526335	−	0.850277i	$-0.323566\pi$
$659$	27.0231			1.05267			0.526335	+	0.850277i	$0.323566\pi$
$660$		−	38.4912i		−	1.49827i
$661$	−32.1016			−1.24861			−0.624303	−	0.781182i	$-0.714617\pi$
$661$	−32.1016			−1.24861			−0.624303	+	0.781182i	$0.714617\pi$
$662$	−31.3106			−1.21692
$663$	18.0915	+	3.98514i	0.702615	+	0.154770i
$664$	68.4599			2.65676
$665$	−15.1773			−0.588549
$666$			22.4433i			0.869660i
$667$	−0.00842839			−0.000326348
$668$			88.1212i			3.40951i
$669$		−	10.0676i		−	0.389235i
$670$			74.2645i			2.86909i
$671$	25.8573			0.998210
$672$	−3.36949			−0.129981
$673$			39.6837i			1.52969i	0.644213	+	0.764846i	$0.277185\pi$
$673$			39.6837i			1.52969i	−0.644213	+	0.764846i	$0.722815\pi$
$674$		−	6.59146i		−	0.253894i
$675$		−	37.9480i		−	1.46062i
$676$	129.645			4.98635
$677$		−	5.96509i		−	0.229257i	−0.993408	−	0.114628i	$-0.963432\pi$
$677$		−	5.96509i		−	0.229257i	0.993408	−	0.114628i	$-0.0365678\pi$
$678$	−31.2997			−1.20206
$679$	−10.6483			−0.408645
$680$	84.1977	+	18.5468i	3.22884	+	0.711239i
$681$	0.415205			0.0159107
$682$	−53.9654			−2.06644
$683$			26.0243i			0.995791i	0.867237	+	0.497896i	$0.165894\pi$
$683$			26.0243i			0.995791i	−0.867237	+	0.497896i	$0.834106\pi$
$684$	14.2090			0.543295
$685$			22.0215i			0.841399i
$686$			39.9987i			1.52716i
$687$		−	0.289127i		−	0.0110309i
$688$	−5.02075			−0.191414
$689$	−88.8215			−3.38383
$690$		−	0.354436i		−	0.0134931i
$691$		−	24.1599i		−	0.919084i	−0.888156	−	0.459542i	$-0.848014\pi$
$691$		−	24.1599i		−	0.919084i	0.888156	−	0.459542i	$-0.151986\pi$
$692$			29.7091i			1.12937i
$693$	−25.9826			−0.986996
$694$		−	71.6774i		−	2.72084i
$695$	43.8819			1.66453
$696$	0.564897			0.0214124
$697$	33.3437	+	7.34485i	1.26298	+	0.278206i
$698$	−73.3868			−2.77773
$699$	−16.3112			−0.616945
$700$			122.660i			4.63611i
$701$	21.5076			0.812332			0.406166	−	0.913799i	$-0.366865\pi$
$701$	21.5076			0.812332			0.406166	+	0.913799i	$0.366865\pi$
$702$		−	61.8342i		−	2.33378i
$703$		−	4.76954i		−	0.179887i
$704$			20.3383i			0.766529i
$705$	30.4169			1.14557
$706$	−27.3576			−1.02962
$707$		−	19.1058i		−	0.718547i
$708$			0.929166i			0.0349202i
$709$		−	26.2523i		−	0.985925i	−0.870051	−	0.492962i	$-0.835914\pi$
$709$		−	26.2523i		−	0.985925i	0.870051	−	0.492962i	$-0.164086\pi$
$710$	−9.14640			−0.343258
$711$			33.0337i			1.23886i
$712$	−68.4599			−2.56564
$713$	−0.335732			−0.0125733
$714$	−4.33359	+	19.6734i	−0.162181	+	0.736257i
$715$	−90.7435			−3.39361
$716$	−32.2955			−1.20694
$717$		−	1.63208i		−	0.0609512i
$718$	−35.5198			−1.32559
$719$		−	37.9429i		−	1.41503i	−0.706697	−	0.707516i	$-0.749816\pi$
$719$		−	37.9429i		−	1.41503i	0.706697	−	0.707516i	$-0.250184\pi$
$720$		−	49.6404i		−	1.84999i
$721$			25.0763i			0.933889i
$722$	42.7086			1.58945
$723$	−10.4684			−0.389325
$724$			0.719955i			0.0267569i
$725$		−	1.57212i		−	0.0583872i
$726$			2.25211i			0.0835838i
$727$	4.27182			0.158433			0.0792165	−	0.996857i	$-0.474758\pi$
$727$	4.27182			0.158433			0.0792165	+	0.996857i	$0.474758\pi$
$728$			103.906i			3.85101i
$729$	5.33796			0.197702
$730$	80.3457			2.97373
$731$	−0.886962	+	4.02657i	−0.0328055	+	0.148928i
$732$	−20.7390			−0.766537
$733$	16.0441			0.592603			0.296301	−	0.955094i	$-0.404247\pi$
$733$	16.0441			0.592603			0.296301	+	0.955094i	$0.404247\pi$
$734$			56.0489i			2.06880i
$735$	−3.84707			−0.141901
$736$		−	0.0929274i		−	0.00342535i
$737$		−	27.0184i		−	0.995236i
$738$		−	52.2782i		−	1.92439i
$739$	17.3628			0.638702			0.319351	−	0.947636i	$-0.396535\pi$
$739$	17.3628			0.638702			0.319351	+	0.947636i	$0.396535\pi$
$740$	−57.5871			−2.11694
$741$			6.02798i			0.221443i
$742$		−	96.5878i		−	3.54585i
$743$			5.86873i			0.215303i	0.994189	+	0.107651i	$0.0343331\pi$
$743$			5.86873i			0.215303i	−0.994189	+	0.107651i	$0.965667\pi$
$744$	22.5018			0.824956
$745$			30.5460i			1.11912i
$746$	−10.5483			−0.386200
$747$	−32.3696			−1.18434
$748$	−58.9227	−	12.9793i	−2.15443	−	0.474571i
$749$	11.9179			0.435472
$750$	33.4553			1.22162
$751$			14.1694i			0.517050i	0.966005	+	0.258525i	$0.0832365\pi$
$751$			14.1694i			0.517050i	−0.966005	+	0.258525i	$0.916764\pi$
$752$	58.0589			2.11719
$753$		−	11.1724i		−	0.407143i
$754$		−	2.56169i		−	0.0932913i
$755$			84.8096i			3.08654i
$756$	45.4291			1.65224
$757$	40.5764			1.47478			0.737388	−	0.675470i	$-0.236059\pi$
$757$	40.5764			1.47478			0.737388	+	0.675470i	$0.236059\pi$
$758$			23.4642i			0.852259i
$759$			0.128948i			0.00468053i
$760$			28.0542i			1.01763i
$761$	24.5296			0.889196			0.444598	−	0.895730i	$-0.353347\pi$
$761$	24.5296			0.889196			0.444598	+	0.895730i	$0.353347\pi$
$762$		−	20.3833i		−	0.738409i
$763$	−9.61230			−0.347988
$764$	−81.5679			−2.95102
$765$	−39.8109	−	8.76943i	−1.43937	−	0.317059i
$766$	−39.4162			−1.42416
$767$	2.19052			0.0790952
$768$		−	22.0646i		−	0.796188i
$769$	21.8656			0.788493			0.394246	−	0.919005i	$-0.371006\pi$
$769$	21.8656			0.788493			0.394246	+	0.919005i	$0.371006\pi$
$770$		−	98.6778i		−	3.55610i
$771$			0.476074i			0.0171454i
$772$		−	48.0132i		−	1.72803i
$773$	−33.7377			−1.21346			−0.606730	−	0.794908i	$-0.707519\pi$
$773$	−33.7377			−1.21346			−0.606730	+	0.794908i	$0.707519\pi$
$774$	6.31311			0.226920
$775$		−	62.6231i		−	2.24949i
$776$			19.6828i			0.706570i
$777$		−	6.99519i		−	0.250951i
$778$	46.8788			1.68069
$779$			11.1099i			0.398054i
$780$	72.7815			2.60599
$781$	3.32758			0.119070
$782$	−0.542574	−	0.119517i	−0.0194024	−	0.00427390i
$783$	−0.582261			−0.0208083
$784$	−7.34318			−0.262256
$785$			15.8311i			0.565035i
$786$	14.7396			0.525745
$787$		−	23.3610i		−	0.832729i	−0.909198	−	0.416364i	$-0.863304\pi$
$787$		−	23.3610i		−	0.832729i	0.909198	−	0.416364i	$-0.136696\pi$
$788$			47.1716i			1.68042i
$789$		−	10.3335i		−	0.367884i
$790$	−125.457			−4.46357
$791$	−54.2126			−1.92758
$792$			48.0271i			1.70657i
$793$			48.8926i			1.73623i
$794$			31.9977i			1.13556i
$795$	−35.1722			−1.24743
$796$			26.3960i			0.935581i
$797$	−33.8889			−1.20041			−0.600203	−	0.799848i	$-0.704914\pi$
$797$	−33.8889			−1.20041			−0.600203	+	0.799848i	$0.704914\pi$
$798$	−6.55505			−0.232046
$799$	10.2566	−	46.5624i	0.362854	−	1.64726i
$800$	17.3335			0.612832
$801$	32.3697			1.14373
$802$		−	92.7989i		−	3.27684i
$803$	−29.2308			−1.03153
$804$			21.6703i			0.764253i
$805$		−	0.613899i		−	0.0216371i
$806$		−	102.041i		−	3.59424i
$807$	2.27726			0.0801633
$808$	−35.3158			−1.24241
$809$		−	26.6350i		−	0.936437i	−0.883613	−	0.468218i	$-0.844896\pi$
$809$		−	26.6350i		−	0.936437i	0.883613	−	0.468218i	$-0.155104\pi$
$810$			49.1646i			1.72747i
$811$		−	38.1937i		−	1.34116i	−0.741836	−	0.670582i	$-0.766045\pi$
$811$		−	38.1937i		−	1.34116i	0.741836	−	0.670582i	$-0.233955\pi$
$812$	1.88205			0.0660471
$813$		−	1.16674i		−	0.0409194i
$814$	31.0101			1.08690
$815$	63.5062			2.22453
$816$	13.6745	+	3.01217i	0.478702	+	0.105447i
$817$	−1.34163			−0.0469377
$818$	−21.1413			−0.739187
$819$		−	49.1294i		−	1.71672i
$820$	134.140			4.68439
$821$		−	36.2586i		−	1.26543i	−0.774383	−	0.632717i	$-0.781940\pi$
$821$		−	36.2586i		−	1.26543i	0.774383	−	0.632717i	$-0.218060\pi$
$822$			9.51109i			0.331738i
$823$			4.69315i			0.163593i	0.996649	+	0.0817964i	$0.0260657\pi$
$823$			4.69315i			0.163593i	−0.996649	+	0.0817964i	$0.973934\pi$
$824$	46.3519			1.61475
$825$	−24.0524			−0.837397
$826$			2.38206i			0.0828823i
$827$		−	4.01089i		−	0.139472i	−0.997565	−	0.0697361i	$-0.977784\pi$
$827$		−	4.01089i		−	0.139472i	0.997565	−	0.0697361i	$-0.0222157\pi$
$828$			0.574734i			0.0199734i
$829$	−13.1443			−0.456520			−0.228260	−	0.973600i	$-0.573304\pi$
$829$	−13.1443			−0.456520			−0.228260	+	0.973600i	$0.573304\pi$
$830$		−	122.935i		−	4.26714i
$831$	9.32797			0.323584
$832$	−38.4569			−1.33325
$833$	−1.29724	+	5.88913i	−0.0449467	+	0.204046i
$834$	18.9526			0.656274
$835$	82.2652			2.84691
$836$		−	19.6327i		−	0.679011i
$837$	−23.1935			−0.801683
$838$			29.8474i			1.03106i
$839$			11.8226i			0.408162i	0.978954	+	0.204081i	$0.0654206\pi$
$839$			11.8226i			0.408162i	−0.978954	+	0.204081i	$0.934579\pi$
$840$			41.1454i			1.41965i
$841$	28.9759			0.999168
$842$	−12.1406			−0.418393
$843$			8.28958i			0.285508i
$844$		−	6.29852i		−	0.216804i
$845$		−	121.030i		−	4.16355i
$846$	−73.0034			−2.50991
$847$			3.90076i			0.134032i
$848$	−67.1358			−2.30545
$849$	7.05114			0.241994
$850$	22.2931	−	101.205i	0.764647	−	3.47129i
$851$	0.192921			0.00661325
$852$	−2.66891			−0.0914353
$853$		−	27.9139i		−	0.955753i	−0.878427	−	0.477877i	$-0.841407\pi$
$853$		−	27.9139i		−	0.955753i	0.878427	−	0.477877i	$-0.158593\pi$
$854$	−53.1676			−1.81936
$855$		−	13.2648i		−	0.453645i
$856$		−	22.0296i		−	0.752955i
$857$			22.4400i			0.766534i	0.923638	+	0.383267i	$0.125201\pi$
$857$			22.4400i			0.766534i	−0.923638	+	0.383267i	$0.874799\pi$
$858$	−39.1921			−1.33800
$859$	−28.5481			−0.974050			−0.487025	−	0.873388i	$-0.661918\pi$
$859$	−28.5481			−0.974050			−0.487025	+	0.873388i	$0.661918\pi$
$860$			16.1988i			0.552373i
$861$			16.2942i			0.555306i
$862$		−	71.9756i		−	2.45150i
$863$	5.27819			0.179672			0.0898359	−	0.995957i	$-0.471366\pi$
$863$	5.27819			0.179672			0.0898359	+	0.995957i	$0.471366\pi$
$864$		−	6.41973i		−	0.218404i
$865$	27.7348			0.943011
$866$	−64.7765			−2.20120
$867$	4.83144	−	10.4346i	0.164084	−	0.354378i
$868$	74.9687			2.54460
$869$	45.6430			1.54833
$870$		−	1.01440i		−	0.0343913i
$871$	51.0881			1.73105
$872$			17.7677i			0.601691i
$873$		−	9.30653i		−	0.314978i
$874$		−	0.180782i		−	0.00611506i
$875$	57.9462			1.95894
$876$	23.4448			0.792126
$877$			7.38896i			0.249507i	0.992188	+	0.124754i	$0.0398141\pi$
$877$			7.38896i			0.249507i	−0.992188	+	0.124754i	$0.960186\pi$
$878$		−	27.4703i		−	0.927077i
$879$			3.90038i			0.131557i
$880$	−68.5885			−2.31212
$881$			28.1254i			0.947569i	0.880641	+	0.473784i	$0.157112\pi$
$881$			28.1254i			0.947569i	−0.880641	+	0.473784i	$0.842888\pi$
$882$	9.23334			0.310903
$883$	38.8850			1.30858			0.654292	−	0.756242i	$-0.272967\pi$
$883$	38.8850			1.30858			0.654292	+	0.756242i	$0.272967\pi$
$884$	24.5421	−	111.415i	0.825439	−	3.74728i
$885$	0.867420			0.0291580
$886$	−36.8177			−1.23692
$887$		−	39.3701i		−	1.32192i	−0.750421	−	0.660960i	$-0.770149\pi$
$887$		−	39.3701i		−	1.32192i	0.750421	−	0.660960i	$-0.229851\pi$
$888$	−12.9302			−0.433908
$889$		−	35.3048i		−	1.18408i
$890$			122.935i			4.12079i
$891$		−	17.8867i		−	0.599228i
$892$	−62.0001			−2.07592
$893$	15.5143			0.519167
$894$			13.1928i			0.441234i
$895$			30.1493i			1.00778i
$896$		−	51.7824i		−	1.72993i
$897$	−0.243823			−0.00814103
$898$			83.5568i			2.78833i
$899$	−0.960867			−0.0320467
$900$	−107.204			−3.57345
$901$	−11.8602	+	53.8420i	−0.395119	+	1.79374i
$902$	−72.2333			−2.40510
$903$	−1.96769			−0.0654806
$904$			100.209i			3.33289i
$905$	0.672112			0.0223417
$906$			36.6292i			1.21693i
$907$		−	13.0730i		−	0.434080i	−0.976163	−	0.217040i	$-0.930360\pi$
$907$		−	13.0730i		−	0.434080i	0.976163	−	0.217040i	$-0.0696403\pi$
$908$		−	2.55700i		−	0.0848570i
$909$	16.6982			0.553846
$910$	186.586			6.18527
$911$			46.7044i			1.54739i	0.633561	+	0.773693i	$0.281593\pi$
$911$			46.7044i			1.54739i	−0.633561	+	0.773693i	$0.718407\pi$
$912$			4.55625i			0.150873i
$913$			44.7254i			1.48019i
$914$	−44.8498			−1.48350
$915$			19.3608i			0.640050i
$916$	−1.78056			−0.0588313
$917$	25.5297			0.843065
$918$	−37.4828	−	8.25660i	−1.23712	−	0.272508i
$919$	−33.4588			−1.10370			−0.551852	−	0.833942i	$-0.686079\pi$
$919$	−33.4588			−1.10370			−0.551852	+	0.833942i	$0.686079\pi$
$920$	−1.13475			−0.0374117
$921$		−	5.74543i		−	0.189318i
$922$	0.279471			0.00920389
$923$			6.29199i			0.207103i
$924$		−	28.7941i		−	0.947256i
$925$			35.9850i			1.18318i
$926$	−54.1170			−1.77839
$927$	−21.9164			−0.719829
$928$		−	0.265959i		−	0.00873053i
$929$			2.67942i			0.0879090i	0.999034	+	0.0439545i	$0.0139957\pi$
$929$			2.67942i			0.0879090i	−0.999034	+	0.0439545i	$0.986004\pi$
$930$		−	40.4070i		−	1.32500i
$931$	−1.96222			−0.0643093
$932$			100.451i			3.29037i
$933$	12.7479			0.417348
$934$	−47.7518			−1.56249
$935$	−12.1168	+	55.0070i	−0.396261	+	1.79892i
$936$	−90.8126			−2.96830
$937$	2.72784			0.0891147			0.0445574	−	0.999007i	$-0.485812\pi$
$937$	2.72784			0.0891147			0.0445574	+	0.999007i	$0.485812\pi$
$938$			55.5551i			1.81394i
$939$	4.79677			0.156537
$940$		−	187.319i		−	6.10967i
$941$		−	25.6274i		−	0.835430i	−0.908578	−	0.417715i	$-0.862831\pi$
$941$		−	25.6274i		−	0.835430i	0.908578	−	0.417715i	$-0.137169\pi$
$942$			6.83743i			0.222776i
$943$	−0.449381			−0.0146338
$944$	1.65571			0.0538887
$945$		−	42.4101i		−	1.37960i
$946$		−	8.72288i		−	0.283605i
$947$		−	3.39492i		−	0.110320i	−0.998478	−	0.0551600i	$-0.982433\pi$
$947$		−	3.39492i		−	0.110320i	0.998478	−	0.0551600i	$-0.0175669\pi$
$948$	−36.6083			−1.18898
$949$		−	55.2714i		−	1.79419i
$950$	33.7208			1.09405
$951$	2.58375			0.0837839
$952$	62.9858	+	13.8743i	2.04138	+	0.449670i
$953$	−52.9839			−1.71632			−0.858158	−	0.513385i	$-0.828391\pi$
$953$	−52.9839			−1.71632			−0.858158	+	0.513385i	$0.828391\pi$
$954$	84.4168			2.73309
$955$			76.1474i			2.46407i
$956$	−10.0510			−0.325072
$957$			0.369051i			0.0119297i
$958$		−	83.0177i		−	2.68218i
$959$			16.4736i			0.531962i
$960$	−15.2285			−0.491496
$961$	−7.27469			−0.234667
$962$			58.6357i			1.89049i
$963$			10.4162i			0.335656i
$964$			64.4686i			2.07639i
$965$	−44.8225			−1.44289
$966$		−	0.265143i		−	0.00853083i
$967$	−22.2489			−0.715476			−0.357738	−	0.933822i	$-0.616452\pi$
$967$	−22.2489			−0.715476			−0.357738	+	0.933822i	$0.616452\pi$
$968$	7.21031			0.231748
$969$	3.65405	+	0.804904i	0.117385	+	0.0258572i
$970$	35.3448			1.13485
$971$	−0.0503171			−0.00161475			−0.000807376	−	1.00000i	$-0.500257\pi$
$971$	−0.0503171			−0.00161475			−0.000807376		1.00000i	$0.500257\pi$
$972$			61.1956i			1.96285i
$973$	32.8267			1.05238
$974$			10.4756i			0.335659i
$975$		−	45.4797i		−	1.45652i
$976$			36.9554i			1.18291i
$977$	7.70543			0.246518			0.123259	−	0.992375i	$-0.460665\pi$
$977$	7.70543			0.246518			0.123259	+	0.992375i	$0.460665\pi$
$978$	27.4283			0.877061
$979$		−	44.7254i		−	1.42943i
$980$			23.6918i			0.756805i
$981$		−	8.40105i		−	0.268225i
$982$	−10.7762			−0.343882
$983$			12.4037i			0.395617i	0.980241	+	0.197808i	$0.0633824\pi$
$983$			12.4037i			0.395617i	−0.980241	+	0.197808i	$0.936618\pi$
$984$	30.1189			0.960155
$985$	44.0369			1.40313
$986$	−1.55285	−	0.342057i	−0.0494528	−	0.0108933i
$987$	22.7539			0.724266
$988$	37.1227			1.18103
$989$		−	0.0542671i		−	0.00172559i
$990$	86.2434			2.74100
$991$		−	23.6020i		−	0.749741i	−0.927077	−	0.374871i	$-0.877687\pi$
$991$		−	23.6020i		−	0.749741i	0.927077	−	0.374871i	$-0.122313\pi$
$992$		−	10.5941i		−	0.336362i
$993$			8.52926i			0.270668i
$994$	−6.84214			−0.217020
$995$	24.6419			0.781200
$996$		−	35.8723i		−	1.13666i
$997$		−	6.58641i		−	0.208594i	−0.994546	−	0.104297i	$-0.966741\pi$
$997$		−	6.58641i		−	0.208594i	0.994546	−	0.104297i	$-0.0332592\pi$
$998$			32.3808i			1.02500i
$999$	13.3276			0.421667

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.d.d.560.4	yes	34
17.16	even	2	inner	731.2.d.d.560.3	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.d.d.560.3	✓	34	17.16	even	2	inner
731.2.d.d.560.4	yes	34	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.48305 q^{2} +0.676403i q^{3} +4.16556 q^{4} -3.88874i q^{5} -1.67955i q^{6} -2.90905i q^{7} -5.37720 q^{8} +2.54248 q^{9} +O(q^{10})\)	\(q-2.48305 q^{2} +0.676403i q^{3} +4.16556 q^{4} -3.88874i q^{5} -1.67955i q^{6} -2.90905i q^{7} -5.37720 q^{8} +2.54248 q^{9} +9.65595i q^{10} -3.51296i q^{11} +2.81760i q^{12} +6.64252 q^{13} +7.22333i q^{14} +2.63036 q^{15} +5.02075 q^{16} +(0.886962 - 4.02657i) q^{17} -6.31311 q^{18} +1.34163 q^{19} -16.1988i q^{20} +1.96769 q^{21} +8.72288i q^{22} +0.0542671i q^{23} -3.63715i q^{24} -10.1223 q^{25} -16.4937 q^{26} +3.74895i q^{27} -12.1178i q^{28} +0.155313i q^{29} -6.53132 q^{30} +6.18665i q^{31} -1.71241 q^{32} +2.37618 q^{33} +(-2.20238 + 9.99820i) q^{34} -11.3125 q^{35} +10.5908 q^{36} -3.55503i q^{37} -3.33134 q^{38} +4.49302i q^{39} +20.9105i q^{40} +8.28090i q^{41} -4.88588 q^{42} -1.00000 q^{43} -14.6334i q^{44} -9.88704i q^{45} -0.134748i q^{46} +11.5638 q^{47} +3.39605i q^{48} -1.46257 q^{49} +25.1342 q^{50} +(2.72359 + 0.599944i) q^{51} +27.6698 q^{52} -13.3717 q^{53} -9.30885i q^{54} -13.6610 q^{55} +15.6425i q^{56} +0.907484i q^{57} -0.385650i q^{58} +0.329773 q^{59} +10.9569 q^{60} +7.36054i q^{61} -15.3618i q^{62} -7.39619i q^{63} -5.78950 q^{64} -25.8310i q^{65} -5.90018 q^{66} +7.69106 q^{67} +(3.69469 - 16.7729i) q^{68} -0.0367065 q^{69} +28.0896 q^{70} +0.947229i q^{71} -13.6714 q^{72} -8.32085i q^{73} +8.82733i q^{74} -6.84676i q^{75} +5.58864 q^{76} -10.2194 q^{77} -11.1564i q^{78} +12.9927i q^{79} -19.5244i q^{80} +5.09163 q^{81} -20.5619i q^{82} -12.7315 q^{83} +8.19653 q^{84} +(-15.6583 - 3.44917i) q^{85} +2.48305 q^{86} -0.105054 q^{87} +18.8899i q^{88} +12.7315 q^{89} +24.5500i q^{90} -19.3234i q^{91} +0.226053i q^{92} -4.18467 q^{93} -28.7135 q^{94} -5.21726i q^{95} -1.15828i q^{96} -3.66042i q^{97} +3.63163 q^{98} -8.93163i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 6 q^{2} + 34 q^{4} - 18 q^{8} - 48 q^{9}+O(q^{10}) \) 34 * q - 6 * q^2 + 34 * q^4 - 18 * q^8 - 48 * q^9	\( 34 q - 6 q^{2} + 34 q^{4} - 18 q^{8} - 48 q^{9} + 16 q^{13} - 8 q^{15} + 26 q^{16} + 14 q^{18} + 16 q^{19} + 20 q^{21} - 44 q^{25} - 26 q^{26} + 88 q^{30} - 42 q^{32} + 12 q^{33} - 42 q^{34} + 22 q^{35} + 34 q^{38} - 14 q^{42} - 34 q^{43} + 30 q^{47} - 62 q^{49} - 46 q^{50} - 10 q^{51} + 26 q^{52} - 46 q^{53} + 16 q^{55} - 20 q^{59} - 42 q^{60} + 102 q^{64} - 70 q^{66} - 32 q^{67} - 10 q^{68} + 74 q^{69} + 130 q^{70} + 22 q^{72} + 38 q^{76} - 78 q^{77} + 46 q^{81} - 60 q^{83} - 98 q^{84} - 38 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{89} + 14 q^{93} - 78 q^{94} + 78 q^{98}+O(q^{100}) \) 34 * q - 6 * q^2 + 34 * q^4 - 18 * q^8 - 48 * q^9 + 16 * q^13 - 8 * q^15 + 26 * q^16 + 14 * q^18 + 16 * q^19 + 20 * q^21 - 44 * q^25 - 26 * q^26 + 88 * q^30 - 42 * q^32 + 12 * q^33 - 42 * q^34 + 22 * q^35 + 34 * q^38 - 14 * q^42 - 34 * q^43 + 30 * q^47 - 62 * q^49 - 46 * q^50 - 10 * q^51 + 26 * q^52 - 46 * q^53 + 16 * q^55 - 20 * q^59 - 42 * q^60 + 102 * q^64 - 70 * q^66 - 32 * q^67 - 10 * q^68 + 74 * q^69 + 130 * q^70 + 22 * q^72 + 38 * q^76 - 78 * q^77 + 46 * q^81 - 60 * q^83 - 98 * q^84 - 38 * q^85 + 6 * q^86 + 16 * q^87 + 26 * q^89 + 14 * q^93 - 78 * q^94 + 78 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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