LMFDB - Embedded newform 99.3.l.a.71.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,3,Mod(26,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("99.26");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	99.l (of order $10$, degree $4$, 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:	$2.69755461717$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			71.8
Character	$\chi$	$=$	99.71
Dual form			99.3.l.a.53.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.44320 - 1.11876i) q^{2} +(7.36792 - 5.35311i) q^{4} +(0.157113 + 0.0510491i) q^{5} +(-8.33195 + 6.05352i) q^{7} +(10.8683 - 14.9589i) q^{8} +O(q^{10})$	\(q+(3.44320 - 1.11876i) q^{2} +(7.36792 - 5.35311i) q^{4} +(0.157113 + 0.0510491i) q^{5} +(-8.33195 + 6.05352i) q^{7} +(10.8683 - 14.9589i) q^{8} +0.598083 q^{10} +(-3.56713 + 10.4056i) q^{11} +(-6.29016 - 19.3591i) q^{13} +(-21.9161 + 30.1649i) q^{14} +(9.42903 - 29.0196i) q^{16} +(21.8883 + 7.11194i) q^{17} +(3.34849 + 2.43282i) q^{19} +(1.43087 - 0.464917i) q^{20} +(-0.641003 + 39.8192i) q^{22} +13.5095i q^{23} +(-20.2033 - 14.6786i) q^{25} +(-43.3165 - 59.6201i) q^{26} +(-28.9840 + 89.2036i) q^{28} +(-2.36082 - 3.24939i) q^{29} +(-6.33587 - 19.4998i) q^{31} -36.5080i q^{32} +83.3223 q^{34} +(-1.61808 + 0.525747i) q^{35} +(-35.2682 + 25.6238i) q^{37} +(14.2513 + 4.63052i) q^{38} +(2.47119 - 1.79542i) q^{40} +(30.6080 - 42.1283i) q^{41} +62.5698 q^{43} +(29.4197 + 95.7625i) q^{44} +(15.1139 + 46.5159i) q^{46} +(22.7504 - 31.3132i) q^{47} +(17.6345 - 54.2734i) q^{49} +(-85.9860 - 27.9385i) q^{50} +(-149.977 - 108.965i) q^{52} +(-33.6465 + 10.9324i) q^{53} +(-1.09164 + 1.45275i) q^{55} +190.428i q^{56} +(-11.7641 - 8.54709i) q^{58} +(-11.5725 - 15.9281i) q^{59} +(-1.98522 + 6.10989i) q^{61} +(-43.6314 - 60.0534i) q^{62} +(-3.12770 - 9.62606i) q^{64} -3.36267i q^{65} -3.98708 q^{67} +(199.342 - 64.7702i) q^{68} +(-4.98319 + 3.62050i) q^{70} +(52.0905 + 16.9252i) q^{71} +(18.4526 - 13.4066i) q^{73} +(-92.7684 + 127.685i) q^{74} +37.6946 q^{76} +(-33.2690 - 108.292i) q^{77} +(-17.6623 - 54.3588i) q^{79} +(2.96284 - 4.07801i) q^{80} +(58.2578 - 179.299i) q^{82} +(-54.0258 - 17.5540i) q^{83} +(3.07587 + 2.23475i) q^{85} +(215.440 - 70.0008i) q^{86} +(116.887 + 166.451i) q^{88} +28.1602i q^{89} +(169.600 + 123.222i) q^{91} +(72.3178 + 99.5369i) q^{92} +(43.3020 - 133.270i) q^{94} +(0.401898 + 0.553165i) q^{95} +(25.6275 + 78.8733i) q^{97} -206.603i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} - 16 q^{7}+O(q^{10}) $ 32 * q + 16 * q^4 - 16 * q^7	$ 32 q + 16 q^{4} - 16 q^{7} + 48 q^{10} + 8 q^{13} + 96 q^{16} - 40 q^{19} - 60 q^{22} - 188 q^{25} - 348 q^{28} - 164 q^{31} + 296 q^{34} - 36 q^{37} + 48 q^{40} + 544 q^{43} + 296 q^{46} + 196 q^{49} - 640 q^{52} - 440 q^{55} - 208 q^{58} - 432 q^{61} - 328 q^{64} + 48 q^{67} + 112 q^{70} + 712 q^{73} + 2104 q^{76} + 432 q^{79} + 676 q^{82} - 68 q^{85} - 176 q^{88} + 64 q^{91} - 1360 q^{94} + 132 q^{97}+O(q^{100}) $ 32 * q + 16 * q^4 - 16 * q^7 + 48 * q^10 + 8 * q^13 + 96 * q^16 - 40 * q^19 - 60 * q^22 - 188 * q^25 - 348 * q^28 - 164 * q^31 + 296 * q^34 - 36 * q^37 + 48 * q^40 + 544 * q^43 + 296 * q^46 + 196 * q^49 - 640 * q^52 - 440 * q^55 - 208 * q^58 - 432 * q^61 - 328 * q^64 + 48 * q^67 + 112 * q^70 + 712 * q^73 + 2104 * q^76 + 432 * q^79 + 676 * q^82 - 68 * q^85 - 176 * q^88 + 64 * q^91 - 1360 * q^94 + 132 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$

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 $

$2$	3.44320	−	1.11876i	1.72160	−	0.559382i	0.729405	−	0.684082i	$-0.239797\pi$
$2$	3.44320	−	1.11876i	1.72160	−	0.559382i	0.992194	+	0.124701i	$0.0397970\pi$
$3$		0			0
$3$		0			0
$4$	7.36792	−	5.35311i	1.84198	−	1.33828i
$5$	0.157113	+	0.0510491i	0.0314226	+	0.0102098i	0.324686	−	0.945822i	$-0.394741\pi$
$5$	0.157113	+	0.0510491i	0.0314226	+	0.0102098i	−0.293264	+	0.956032i	$0.594741\pi$
$6$		0			0
$7$	−8.33195	+	6.05352i	−1.19028	+	0.864788i	−0.993294	−	0.115619i	$-0.963115\pi$
$7$	−8.33195	+	6.05352i	−1.19028	+	0.864788i	−0.196985	+	0.980407i	$0.563115\pi$
$8$	10.8683	−	14.9589i	1.35854	−	1.86987i
$9$		0			0
$10$	0.598083			0.0598083
$11$	−3.56713	+	10.4056i	−0.324285	+	0.945959i
$11$	−3.56713	+	10.4056i	−0.324285	+	0.945959i
$12$		0			0
$13$	−6.29016	−	19.3591i	−0.483858	−	1.48916i	−0.833628	−	0.552327i	$-0.813740\pi$
$13$	−6.29016	−	19.3591i	−0.483858	−	1.48916i	0.349769	−	0.936836i	$-0.386260\pi$
$14$	−21.9161	+	30.1649i	−1.56544	+	2.15464i
$15$		0			0
$16$	9.42903	−	29.0196i	0.589314	−	1.81372i
$17$	21.8883	+	7.11194i	1.28755	+	0.418349i	0.871232	−	0.490871i	$-0.163321\pi$
$17$	21.8883	+	7.11194i	1.28755	+	0.418349i	0.416315	+	0.909221i	$0.363321\pi$
$18$		0			0
$19$	3.34849	+	2.43282i	0.176237	+	0.128043i	0.672406	−	0.740182i	$-0.265261\pi$
$19$	3.34849	+	2.43282i	0.176237	+	0.128043i	−0.496170	+	0.868225i	$0.665261\pi$
$20$	1.43087	−	0.464917i	0.0715433	−	0.0232458i
$21$		0			0
$22$	−0.641003	+	39.8192i	−0.0291365	+	1.80996i
$23$			13.5095i			0.587369i	0.955902	+	0.293685i	$0.0948816\pi$
$23$			13.5095i			0.587369i	−0.955902	+	0.293685i	$0.905118\pi$
$24$		0			0
$25$	−20.2033	−	14.6786i	−0.808134	−	0.587144i
$26$	−43.3165	−	59.6201i	−1.66602	−	2.29308i
$27$		0			0
$28$	−28.9840	+	89.2036i	−1.03514	+	3.18584i
$29$	−2.36082	−	3.24939i	−0.0814075	−	0.112048i	0.766371	−	0.642398i	$-0.222060\pi$
$29$	−2.36082	−	3.24939i	−0.0814075	−	0.112048i	−0.847779	+	0.530350i	$0.822060\pi$
$30$		0			0
$31$	−6.33587	−	19.4998i	−0.204383	−	0.629026i	−0.999738	−	0.0228826i	$-0.992716\pi$
$31$	−6.33587	−	19.4998i	−0.204383	−	0.629026i	0.795355	−	0.606144i	$-0.207284\pi$
$32$		−	36.5080i		−	1.14088i
$33$		0			0
$34$	83.3223			2.45066
$35$	−1.61808	+	0.525747i	−0.0462309	+	0.0150213i
$36$		0			0
$37$	−35.2682	+	25.6238i	−0.953195	+	0.692536i	−0.951560	−	0.307462i	$-0.900520\pi$
$37$	−35.2682	+	25.6238i	−0.953195	+	0.692536i	−0.00163432	+	0.999999i	$0.500520\pi$
$38$	14.2513	+	4.63052i	0.375034	+	0.121856i
$39$		0			0
$40$	2.47119	−	1.79542i	0.0617797	−	0.0448856i
$41$	30.6080	−	42.1283i	0.746536	−	1.02752i	−0.251679	−	0.967811i	$-0.580983\pi$
$41$	30.6080	−	42.1283i	0.746536	−	1.02752i	0.998216	−	0.0597086i	$-0.0190171\pi$
$42$		0			0
$43$	62.5698			1.45511			0.727556	−	0.686048i	$-0.240656\pi$
$43$	62.5698			1.45511			0.727556	+	0.686048i	$0.240656\pi$
$44$	29.4197	+	95.7625i	0.668629	+	2.17642i
$45$		0			0
$46$	15.1139	+	46.5159i	0.328564	+	1.01121i
$47$	22.7504	−	31.3132i	0.484050	−	0.666238i	−0.495227	−	0.868764i	$-0.664915\pi$
$47$	22.7504	−	31.3132i	0.484050	−	0.666238i	0.979277	+	0.202526i	$0.0649150\pi$
$48$		0			0
$49$	17.6345	−	54.2734i	0.359888	−	1.10762i
$50$	−85.9860	−	27.9385i	−1.71972	−	0.558771i
$51$		0			0
$52$	−149.977	−	108.965i	−2.88417	−	2.09547i
$53$	−33.6465	+	10.9324i	−0.634840	+	0.206272i	−0.608718	−	0.793387i	$-0.708316\pi$
$53$	−33.6465	+	10.9324i	−0.634840	+	0.206272i	−0.0261220	+	0.999659i	$0.508316\pi$
$54$		0			0
$55$	−1.09164	+	1.45275i	−0.0198479	+	0.0264136i
$56$			190.428i			3.40051i
$57$		0			0
$58$	−11.7641	−	8.54709i	−0.202829	−	0.147364i
$59$	−11.5725	−	15.9281i	−0.196143	−	0.269968i	0.699605	−	0.714530i	$-0.253359\pi$
$59$	−11.5725	−	15.9281i	−0.196143	−	0.269968i	−0.895748	+	0.444562i	$0.853359\pi$
$60$		0			0
$61$	−1.98522	+	6.10989i	−0.0325446	+	0.100162i	−0.966009	−	0.258507i	$-0.916769\pi$
$61$	−1.98522	+	6.10989i	−0.0325446	+	0.100162i	0.933465	+	0.358669i	$0.116769\pi$
$62$	−43.6314	−	60.0534i	−0.703731	−	0.968603i
$63$		0			0
$64$	−3.12770	−	9.62606i	−0.0488703	−	0.150407i
$65$		−	3.36267i		−	0.0517334i
$66$		0			0
$67$	−3.98708			−0.0595087			−0.0297543	−	0.999557i	$-0.509472\pi$
$67$	−3.98708			−0.0595087			−0.0297543	+	0.999557i	$0.509472\pi$
$68$	199.342	−	64.7702i	2.93150	−	0.952503i
$69$		0			0
$70$	−4.98319	+	3.62050i	−0.0711885	+	0.0517215i
$71$	52.0905	+	16.9252i	0.733670	+	0.238384i	0.651940	−	0.758271i	$-0.273956\pi$
$71$	52.0905	+	16.9252i	0.733670	+	0.238384i	0.0817299	+	0.996655i	$0.473956\pi$
$72$		0			0
$73$	18.4526	−	13.4066i	0.252776	−	0.183652i	−0.454180	−	0.890910i	$-0.650068\pi$
$73$	18.4526	−	13.4066i	0.252776	−	0.183652i	0.706956	+	0.707257i	$0.250068\pi$
$74$	−92.7684	+	127.685i	−1.25363	+	1.72547i
$75$		0			0
$76$	37.6946			0.495981
$77$	−33.2690	−	108.292i	−0.432065	−	1.40639i
$78$		0			0
$79$	−17.6623	−	54.3588i	−0.223573	−	0.688086i	−0.998433	−	0.0559542i	$-0.982180\pi$
$79$	−17.6623	−	54.3588i	−0.223573	−	0.688086i	0.774861	−	0.632132i	$-0.217820\pi$
$80$	2.96284	−	4.07801i	0.0370356	−	0.0509751i
$81$		0			0
$82$	58.2578	−	179.299i	0.710461	−	2.18658i
$83$	−54.0258	−	17.5540i	−0.650913	−	0.211494i	−0.0350962	−	0.999384i	$-0.511174\pi$
$83$	−54.0258	−	17.5540i	−0.650913	−	0.211494i	−0.615817	+	0.787890i	$0.711174\pi$
$84$		0			0
$85$	3.07587	+	2.23475i	0.0361868	+	0.0262912i
$86$	215.440	−	70.0008i	2.50512	−	0.813963i
$87$		0			0
$88$	116.887	+	166.451i	1.32826	+	1.89149i
$89$			28.1602i			0.316407i	0.987407	+	0.158203i	$0.0505701\pi$
$89$			28.1602i			0.316407i	−0.987407	+	0.158203i	$0.949430\pi$
$90$		0			0
$91$	169.600	+	123.222i	1.86374	+	1.35408i
$92$	72.3178	+	99.5369i	0.786063	+	1.08192i
$93$		0			0
$94$	43.3020	−	133.270i	0.460659	−	1.41776i
$95$	0.401898	+	0.553165i	0.00423051	+	0.00582279i
$96$		0			0
$97$	25.6275	+	78.8733i	0.264201	+	0.813127i	0.991876	+	0.127205i	$0.0406007\pi$
$97$	25.6275	+	78.8733i	0.264201	+	0.813127i	−0.727676	+	0.685922i	$0.759399\pi$
$98$		−	206.603i		−	2.10819i
$99$		0			0
$100$	−227.433			−2.27433
$101$	145.555	−	47.2938i	1.44114	−	0.468255i	0.518888	−	0.854842i	$-0.326346\pi$
$101$	145.555	−	47.2938i	1.44114	−	0.468255i	0.922253	+	0.386587i	$0.126346\pi$
$102$		0			0
$103$	−85.0431	+	61.7875i	−0.825662	+	0.599878i	−0.918329	−	0.395819i	$-0.870461\pi$
$103$	−85.0431	+	61.7875i	−0.825662	+	0.599878i	0.0926670	+	0.995697i	$0.470461\pi$
$104$	−357.955	−	116.307i	−3.44187	−	1.11833i
$105$		0			0
$106$	−103.621	+	75.2850i	−0.977555	+	0.710235i
$107$	−66.2803	+	91.2270i	−0.619442	+	0.852588i	−0.997312	−	0.0732701i	$-0.976656\pi$
$107$	−66.2803	+	91.2270i	−0.619442	+	0.852588i	0.377870	+	0.925858i	$0.376656\pi$
$108$		0			0
$109$	−96.1530			−0.882137			−0.441069	−	0.897473i	$-0.645400\pi$
$109$	−96.1530			−0.882137			−0.441069	+	0.897473i	$0.645400\pi$
$110$	−2.13344	+	6.22338i	−0.0193949	+	0.0565762i
$111$		0			0
$112$	97.1082	+	298.868i	0.867038	+	2.66847i
$113$	−61.1891	+	84.2196i	−0.541497	+	0.745306i	−0.988828	−	0.149062i	$-0.952375\pi$
$113$	−61.1891	+	84.2196i	−0.541497	+	0.745306i	0.447331	+	0.894368i	$0.352375\pi$
$114$		0			0
$115$	−0.689647	+	2.12252i	−0.00599693	+	0.0184567i
$116$	−34.7886	−	11.3035i	−0.299902	−	0.0974441i
$117$		0			0
$118$	−57.6661	−	41.8969i	−0.488696	−	0.355058i
$119$	−225.424	+	73.2448i	−1.89432	+	0.615503i
$120$		0			0
$121$	−95.5511	−	74.2360i	−0.789679	−	0.613521i
$122$			23.2585i			0.190644i
$123$		0			0
$124$	−151.067	−	109.756i	−1.21828	−	0.885133i
$125$	−4.85240	−	6.67876i	−0.0388192	−	0.0534301i
$126$		0			0
$127$	−2.49011	+	7.66378i	−0.0196072	+	0.0603447i	−0.960381	−	0.278689i	$-0.910100\pi$
$127$	−2.49011	+	7.66378i	−0.0196072	+	0.0603447i	0.940774	+	0.339034i	$0.110100\pi$
$128$	64.2969	+	88.4971i	0.502320	+	0.691384i
$129$		0			0
$130$	−3.76203	−	11.5784i	−0.0289387	−	0.0890642i
$131$			240.588i			1.83655i	0.395947	+	0.918273i	$0.370416\pi$
$131$			240.588i			1.83655i	−0.395947	+	0.918273i	$0.629584\pi$
$132$		0			0
$133$	−42.6266			−0.320501
$134$	−13.7283	+	4.46060i	−0.102450	+	0.0332881i
$135$		0			0
$136$	344.275	−	250.131i	2.53144	−	1.83920i
$137$	−17.9446	−	5.83054i	−0.130982	−	0.0425587i	0.242792	−	0.970078i	$-0.421937\pi$
$137$	−17.9446	−	5.83054i	−0.130982	−	0.0425587i	−0.373775	+	0.927520i	$0.621937\pi$
$138$		0			0
$139$	27.0837	−	19.6775i	0.194847	−	0.141565i	−0.486084	−	0.873912i	$-0.661575\pi$
$139$	27.0837	−	19.6775i	0.194847	−	0.141565i	0.680931	+	0.732347i	$0.261575\pi$
$140$	−9.10752	+	12.5354i	−0.0650537	+	0.0895388i
$141$		0			0
$142$	198.293			1.39643
$143$	223.880	+	3.60399i	1.56560	+	0.0252027i
$144$		0			0
$145$	−0.205037	−	0.631038i	−0.00141405	−	0.00435199i
$146$	48.5373	−	66.8058i	0.332447	−	0.457574i
$147$		0			0
$148$	−122.686	+	377.589i	−0.828960	+	2.55128i
$149$	98.3588	+	31.9587i	0.660126	+	0.214488i	0.619874	−	0.784701i	$-0.287184\pi$
$149$	98.3588	+	31.9587i	0.660126	+	0.214488i	0.0402525	+	0.999190i	$0.487184\pi$
$150$		0			0
$151$	231.688	+	168.331i	1.53435	+	1.11477i	0.953755	+	0.300585i	$0.0971818\pi$
$151$	231.688	+	168.331i	1.53435	+	1.11477i	0.580600	+	0.814189i	$0.302818\pi$
$152$	72.7848	−	23.6492i	0.478848	−	0.155587i
$153$		0			0
$154$	−235.705	−	335.652i	−1.53055	−	2.17956i
$155$		−	3.38711i		−	0.0218523i
$156$		0			0
$157$	−211.399	−	153.591i	−1.34649	−	0.978285i	−0.999178	−	0.0405362i	$-0.987093\pi$
$157$	−211.399	−	153.591i	−1.34649	−	0.978285i	−0.347315	−	0.937748i	$-0.612907\pi$
$158$	−121.629	−	167.408i	−0.769806	−	1.05955i
$159$		0			0
$160$	1.86370	−	5.73588i	0.0116481	−	0.0358492i
$161$	−81.7800	−	112.560i	−0.507950	−	0.699133i
$162$		0			0
$163$	59.4847	+	183.075i	0.364937	+	1.12316i	0.950021	+	0.312187i	$0.101062\pi$
$163$	59.4847	+	183.075i	0.364937	+	1.12316i	−0.585084	+	0.810973i	$0.698938\pi$
$164$		−	474.246i		−	2.89174i
$165$		0			0
$166$	−205.660			−1.23892
$167$	−200.857	+	65.2624i	−1.20274	+	0.390793i	−0.840767	−	0.541397i	$-0.817896\pi$
$167$	−200.857	+	65.2624i	−1.20274	+	0.390793i	−0.361970	+	0.932190i	$0.617896\pi$
$168$		0			0
$169$	−198.485	+	144.208i	−1.17447	+	0.853303i
$170$	13.0910	+	4.25353i	0.0770059	+	0.0250207i
$171$		0			0
$172$	461.009	−	334.943i	2.68029	−	1.94734i
$173$	60.9963	−	83.9542i	0.352580	−	0.485284i	−0.595483	−	0.803368i	$-0.703039\pi$
$173$	60.9963	−	83.9542i	0.352580	−	0.485284i	0.948063	+	0.318084i	$0.103039\pi$
$174$		0			0
$175$	257.190			1.46966
$176$	268.330	+	201.631i	1.52460	+	1.14563i
$177$		0			0
$178$	31.5046	+	96.9611i	0.176992	+	0.544725i
$179$	6.49962	−	8.94596i	0.0363107	−	0.0499774i	−0.790476	−	0.612494i	$-0.790167\pi$
$179$	6.49962	−	8.94596i	0.0363107	−	0.0499774i	0.826786	+	0.562516i	$0.190167\pi$
$180$		0			0
$181$	38.4345	−	118.289i	0.212345	−	0.653532i	−0.786986	−	0.616971i	$-0.788360\pi$
$181$	38.4345	−	118.289i	0.212345	−	0.653532i	0.999331	−	0.0365609i	$-0.0116403\pi$
$182$	721.822	+	234.534i	3.96606	+	1.28865i
$183$		0			0
$184$	202.088	+	146.825i	1.09830	+	0.797963i
$185$	−6.84916	+	2.22543i	−0.0370225	+	0.0120293i
$186$		0			0
$187$	−152.082	+	202.391i	−0.813274	+	1.08230i
$188$		−	352.498i		−	1.87499i
$189$		0			0
$190$	2.00268	+	1.45503i	0.0105404	+	0.00765805i
$191$	−104.367	−	143.649i	−0.546425	−	0.752090i	0.443097	−	0.896474i	$-0.353880\pi$
$191$	−104.367	−	143.649i	−0.546425	−	0.752090i	−0.989522	+	0.144384i	$0.953880\pi$
$192$		0			0
$193$	75.1934	−	231.421i	0.389603	−	1.19907i	−0.543483	−	0.839420i	$-0.682895\pi$
$193$	75.1934	−	231.421i	0.389603	−	1.19907i	0.933086	−	0.359654i	$-0.117105\pi$
$194$	176.481	+	242.905i	0.909696	+	1.25209i
$195$		0			0
$196$	−160.602	−	494.282i	−0.819397	−	2.52184i
$197$			215.588i			1.09435i	0.837017	+	0.547177i	$0.184298\pi$
$197$			215.588i			1.09435i	−0.837017	+	0.547177i	$0.815702\pi$
$198$		0			0
$199$	−44.0830			−0.221523			−0.110761	−	0.993847i	$-0.535329\pi$
$199$	−44.0830			−0.221523			−0.110761	+	0.993847i	$0.535329\pi$
$200$	−439.152	+	142.689i	−2.19576	+	0.713446i
$201$		0			0
$202$	448.265	−	325.684i	2.21913	−	1.61230i
$203$	39.3404	+	12.7825i	0.193795	+	0.0629679i
$204$		0			0
$205$	6.95952	−	5.05639i	0.0339489	−	0.0246653i
$206$	−223.695	+	307.890i	−1.08590	+	1.49461i
$207$		0			0
$208$	−621.103			−2.98607
$209$	−37.2594	+	26.1647i	−0.178275	+	0.125190i
$210$		0			0
$211$	−81.6747	−	251.369i	−0.387084	−	1.19132i	−0.934957	−	0.354761i	$-0.884562\pi$
$211$	−81.6747	−	251.369i	−0.387084	−	1.19132i	0.547873	−	0.836562i	$-0.315438\pi$
$212$	−189.382	+	260.663i	−0.893313	+	1.22954i
$213$		0			0
$214$	−126.155	+	388.264i	−0.589508	+	1.81432i
$215$	9.83052	+	3.19413i	0.0457234	+	0.0148564i
$216$		0			0
$217$	170.833	+	124.117i	0.787247	+	0.571969i
$218$	−331.074	+	107.572i	−1.51869	+	0.493451i
$219$		0			0
$220$	−0.266377	+	16.5474i	−0.00121081	+	0.0752153i
$221$		−	468.473i		−	2.11979i
$222$		0			0
$223$	−11.7428	−	8.53162i	−0.0526581	−	0.0382584i	0.561145	−	0.827718i	$-0.310361\pi$
$223$	−11.7428	−	8.53162i	−0.0526581	−	0.0382584i	−0.613803	+	0.789459i	$0.710361\pi$
$224$	221.002	+	304.183i	0.986616	+	1.35796i
$225$		0			0
$226$	−116.465	+	358.441i	−0.515330	+	1.58602i
$227$	−72.0137	−	99.1183i	−0.317241	−	0.436645i	0.620381	−	0.784300i	$-0.286978\pi$
$227$	−72.0137	−	99.1183i	−0.317241	−	0.436645i	−0.937622	+	0.347656i	$0.886978\pi$
$228$		0			0
$229$	1.20322	+	3.70313i	0.00525423	+	0.0161709i	0.953649	−	0.300920i	$-0.0972938\pi$
$229$	1.20322	+	3.70313i	0.00525423	+	0.0161709i	−0.948395	+	0.317091i	$0.897294\pi$
$230$			8.07980i			0.0351295i
$231$		0			0
$232$	−74.2654			−0.320110
$233$	347.865	−	113.028i	1.49298	−	0.485100i	0.555022	−	0.831836i	$-0.312710\pi$
$233$	347.865	−	113.028i	1.49298	−	0.485100i	0.937963	+	0.346736i	$0.112710\pi$
$234$		0			0
$235$	5.17288	−	3.75832i	0.0220123	−	0.0159928i
$236$	−170.530	−	55.4085i	−0.722585	−	0.234782i
$237$		0			0
$238$	−694.237	+	504.393i	−2.91696	+	2.11930i
$239$	86.5794	−	119.166i	0.362257	−	0.498604i	−0.588519	−	0.808483i	$-0.700289\pi$
$239$	86.5794	−	119.166i	0.362257	−	0.498604i	0.950776	+	0.309880i	$0.100289\pi$
$240$		0			0
$241$	278.601			1.15602			0.578010	−	0.816029i	$-0.303829\pi$
$241$	278.601			1.15602			0.578010	+	0.816029i	$0.303829\pi$
$242$	−412.054	−	148.710i	−1.70270	−	0.614505i
$243$		0			0
$244$	18.0799	+	55.6442i	0.0740980	+	0.228050i
$245$	5.54121	−	7.62683i	0.0226172	−	0.0311299i
$246$		0			0
$247$	26.0348	−	80.1267i	0.105404	−	0.324400i
$248$	−360.556	−	117.152i	−1.45386	−	0.472387i
$249$		0			0
$250$	−24.1797	−	17.5676i	−0.0967190	−	0.0702705i
$251$	45.9565	−	14.9322i	0.183094	−	0.0594907i	−0.216035	−	0.976386i	$-0.569313\pi$
$251$	45.9565	−	14.9322i	0.183094	−	0.0594907i	0.399129	+	0.916895i	$0.369313\pi$
$252$		0			0
$253$	−140.574	−	48.1902i	−0.555628	−	0.190475i
$254$			29.1737i			0.114857i
$255$		0			0
$256$	353.148	+	256.577i	1.37948	+	1.00225i
$257$	117.102	+	161.176i	0.455648	+	0.627146i	0.973599	−	0.228265i	$-0.0733051\pi$
$257$	117.102	+	161.176i	0.455648	+	0.627146i	−0.517951	+	0.855410i	$0.673305\pi$
$258$		0			0
$259$	138.739	−	426.993i	0.535670	−	1.64862i
$260$	−18.0007	−	24.7759i	−0.0692336	−	0.0952919i
$261$		0			0
$262$	269.161	+	828.391i	1.02733	+	3.16180i
$263$		−	69.3106i		−	0.263538i	−0.991280	−	0.131769i	$-0.957934\pi$
$263$		−	69.3106i		−	0.263538i	0.991280	−	0.131769i	$-0.0420658\pi$
$264$		0			0
$265$	−5.84439			−0.0220543
$266$	−146.772	+	47.6891i	−0.551774	+	0.179282i
$267$		0			0
$268$	−29.3765	+	21.3433i	−0.109614	+	0.0796391i
$269$	−175.083	−	56.8880i	−0.650868	−	0.211480i	−0.0350710	−	0.999385i	$-0.511166\pi$
$269$	−175.083	−	56.8880i	−0.650868	−	0.211480i	−0.615797	+	0.787905i	$0.711166\pi$
$270$		0			0
$271$	70.9627	−	51.5574i	0.261855	−	0.190249i	−0.449109	−	0.893477i	$-0.648259\pi$
$271$	70.9627	−	51.5574i	0.261855	−	0.190249i	0.710964	+	0.703228i	$0.248259\pi$
$272$	412.771	−	568.130i	1.51754	−	2.08871i
$273$		0			0
$274$	−68.3096			−0.249305
$275$	224.807	−	157.867i	0.817480	−	0.574060i
$276$		0			0
$277$	−77.0171	−	237.034i	−0.278040	−	0.855719i	−0.988399	−	0.151880i	$-0.951467\pi$
$277$	−77.0171	−	237.034i	−0.278040	−	0.855719i	0.710359	−	0.703840i	$-0.248533\pi$
$278$	71.2402	−	98.0537i	0.256260	−	0.352711i
$279$		0			0
$280$	−9.72119	+	29.9188i	−0.0347185	+	0.106853i
$281$	16.0221	+	5.20589i	0.0570181	+	0.0185263i	0.337387	−	0.941366i	$-0.390457\pi$
$281$	16.0221	+	5.20589i	0.0570181	+	0.0185263i	−0.280369	+	0.959892i	$0.590457\pi$
$282$		0			0
$283$	−38.5194	−	27.9860i	−0.136111	−	0.0988904i	0.517646	−	0.855595i	$-0.326808\pi$
$283$	−38.5194	−	27.9860i	−0.136111	−	0.0988904i	−0.653757	+	0.756704i	$0.726808\pi$
$284$	474.402	−	154.142i	1.67043	−	0.542755i
$285$		0			0
$286$	774.896	−	238.060i	2.70943	−	0.832376i
$287$			536.297i			1.86863i
$288$		0			0
$289$	194.712	+	141.466i	0.673744	+	0.489503i
$290$	−1.41196	−	1.94340i	−0.00486884	−	0.00670139i
$291$		0			0
$292$	64.1905	−	197.558i	0.219830	−	0.676568i
$293$	−249.870	−	343.916i	−0.852797	−	1.17377i	−0.983239	−	0.182319i	$-0.941640\pi$
$293$	−249.870	−	343.916i	−0.852797	−	1.17377i	0.130442	−	0.991456i	$-0.458360\pi$
$294$		0			0
$295$	−1.00507	−	3.09328i	−0.00340701	−	0.0104857i
$296$			806.062i			2.72318i
$297$		0			0
$298$	374.423			1.25645
$299$	261.532	−	84.9769i	0.874689	−	0.284204i
$300$		0			0
$301$	−521.329	+	378.767i	−1.73199	+	1.25836i
$302$	986.069	+	320.393i	3.26513	+	1.06090i
$303$		0			0
$304$	102.173	−	74.2327i	0.336094	−	0.244187i
$305$	−0.623808	+	0.858598i	−0.00204527	+	0.00281507i
$306$		0			0
$307$	−463.469			−1.50967			−0.754836	−	0.655914i	$-0.772284\pi$
$307$	−463.469			−1.50967			−0.754836	+	0.655914i	$0.772284\pi$
$308$	−824.823	−	619.796i	−2.67800	−	2.01233i
$309$		0			0
$310$	−3.78938	−	11.6625i	−0.0122238	−	0.0376210i
$311$	84.1378	−	115.806i	0.270539	−	0.372366i	−0.652032	−	0.758191i	$-0.726083\pi$
$311$	84.1378	−	115.806i	0.270539	−	0.372366i	0.922572	+	0.385826i	$0.126083\pi$
$312$		0			0
$313$	73.4669	−	226.108i	0.234719	−	0.722390i	−0.762440	−	0.647059i	$-0.775999\pi$
$313$	73.4669	−	226.108i	0.234719	−	0.722390i	0.997159	−	0.0753307i	$-0.0240012\pi$
$314$	−899.722	−	292.337i	−2.86536	−	0.931011i
$315$		0			0
$316$	−421.123	−	305.964i	−1.33267	−	0.968239i
$317$	−298.545	+	97.0032i	−0.941783	+	0.306004i	−0.739372	−	0.673297i	$-0.764878\pi$
$317$	−298.545	+	97.0032i	−0.941783	+	0.306004i	−0.202411	+	0.979301i	$0.564878\pi$
$318$		0			0
$319$	42.2330	−	12.9746i	0.132392	−	0.0406728i
$320$		−	1.67204i		−	0.00522514i
$321$		0			0
$322$	−407.513	−	296.076i	−1.26557	−	0.919490i
$323$	55.9907	+	77.0646i	0.173346	+	0.238590i
$324$		0			0
$325$	−157.082	+	483.450i	−0.483330	+	1.48754i
$326$	409.635	+	563.814i	1.25655	+	1.72949i
$327$		0			0
$328$	−297.537	−	915.725i	−0.907126	−	2.79185i
$329$			398.620i			1.21161i
$330$		0			0
$331$	−52.4920			−0.158586			−0.0792931	−	0.996851i	$-0.525266\pi$
$331$	−52.4920			−0.158586			−0.0792931	+	0.996851i	$0.525266\pi$
$332$	−492.026	+	159.869i	−1.48201	+	0.481533i
$333$		0			0
$334$	−618.578	+	449.423i	−1.85203	+	1.34558i
$335$	−0.626422	−	0.203537i	−0.00186992	−	0.000607572i
$336$		0			0
$337$	399.526	−	290.273i	1.18554	−	0.861343i	0.192751	−	0.981248i	$-0.438259\pi$
$337$	399.526	−	290.273i	1.18554	−	0.861343i	0.992785	+	0.119905i	$0.0382589\pi$
$338$	−522.090	+	718.596i	−1.54465	+	2.12602i
$339$		0			0
$340$	34.6257			0.101840
$341$	225.507	+	3.63018i	0.661312	+	0.0106457i
$342$		0			0
$343$	25.6717	+	79.0092i	0.0748445	+	0.230348i
$344$	680.027	−	935.978i	1.97682	−	2.72086i
$345$		0			0
$346$	116.098	−	357.311i	0.335542	−	1.03269i
$347$	−429.602	−	139.586i	−1.23805	−	0.402266i	−0.384424	−	0.923157i	$-0.625600\pi$
$347$	−429.602	−	139.586i	−1.23805	−	0.402266i	−0.853623	+	0.520891i	$0.825600\pi$
$348$		0			0
$349$	−143.320	−	104.128i	−0.410659	−	0.298362i	0.363209	−	0.931708i	$-0.381681\pi$
$349$	−143.320	−	104.128i	−0.410659	−	0.298362i	−0.773869	+	0.633346i	$0.781681\pi$
$350$	885.558	−	287.735i	2.53016	−	0.822100i
$351$		0			0
$352$	379.886	+	130.229i	1.07922	+	0.369969i
$353$			590.460i			1.67269i	0.548203	+	0.836346i	$0.315312\pi$
$353$			590.460i			1.67269i	−0.548203	+	0.836346i	$0.684688\pi$
$354$		0			0
$355$	7.32008	+	5.31835i	0.0206199	+	0.0149813i
$356$	150.745	+	207.482i	0.423440	+	0.582815i
$357$		0			0
$358$	12.3711	−	38.0742i	0.0345561	−	0.106353i
$359$	348.052	+	479.052i	0.969503	+	1.33441i	0.942297	+	0.334777i	$0.108661\pi$
$359$	348.052	+	479.052i	0.969503	+	1.33441i	0.0272060	+	0.999630i	$0.491339\pi$
$360$		0			0
$361$	−106.261	−	327.039i	−0.294353	−	0.905925i
$362$		−	450.292i		−	1.24390i
$363$		0			0
$364$	1909.22			5.24510
$365$	3.58354	−	1.16436i	0.00981793	−	0.00319004i
$366$		0			0
$367$	−183.454	+	133.287i	−0.499875	+	0.363181i	−0.808969	−	0.587851i	$-0.799974\pi$
$367$	−183.454	+	133.287i	−0.499875	+	0.363181i	0.309094	+	0.951031i	$0.399974\pi$
$368$	392.040	+	127.381i	1.06533	+	0.346145i
$369$		0			0
$370$	−21.0933	+	15.3252i	−0.0570089	+	0.0414194i
$371$	214.162	−	294.768i	0.577255	−	0.794523i
$372$		0			0
$373$	−76.5478			−0.205222			−0.102611	−	0.994722i	$-0.532720\pi$
$373$	−76.5478			−0.205222			−0.102611	+	0.994722i	$0.532720\pi$
$374$	−297.222	+	867.015i	−0.794711	+	2.31822i
$375$		0			0
$376$	−221.154	−	680.642i	−0.588176	−	1.81022i
$377$	−48.0553	+	66.1425i	−0.127468	+	0.175444i
$378$		0			0
$379$	108.644	−	334.371i	0.286659	−	0.882247i	−0.699237	−	0.714890i	$-0.746477\pi$
$379$	108.644	−	334.371i	0.286659	−	0.882247i	0.985896	−	0.167357i	$-0.0535232\pi$
$380$	5.92230	+	1.92427i	0.0155850	+	0.00506388i
$381$		0			0
$382$	−520.066	−	377.850i	−1.36143	−	0.989137i
$383$	−544.836	+	177.028i	−1.42255	+	0.462214i	−0.916411	−	0.400239i	$-0.868927\pi$
$383$	−544.836	+	177.028i	−1.42255	+	0.462214i	−0.506137	+	0.862453i	$0.668927\pi$
$384$		0			0
$385$	0.301230	−	18.7125i	0.000782417	−	0.0486038i
$386$		−	880.953i		−	2.28226i
$387$		0			0
$388$	611.038	+	443.945i	1.57484	+	1.14419i
$389$	115.310	+	158.711i	0.296427	+	0.407997i	0.931089	−	0.364793i	$-0.118860\pi$
$389$	115.310	+	158.711i	0.296427	+	0.407997i	−0.634661	+	0.772791i	$0.718860\pi$
$390$		0			0
$391$	−96.0787	+	295.700i	−0.245726	+	0.756266i
$392$	−620.215	−	853.653i	−1.58218	−	2.17769i
$393$		0			0
$394$	241.192	+	742.311i	0.612161	+	1.88404i
$395$		−	9.44211i		−	0.0239041i
$396$		0			0
$397$	−105.240			−0.265089			−0.132544	−	0.991177i	$-0.542315\pi$
$397$	−105.240			−0.265089			−0.132544	+	0.991177i	$0.542315\pi$
$398$	−151.787	+	49.3184i	−0.381373	+	0.123916i
$399$		0			0
$400$	−616.464	+	447.888i	−1.54116	+	1.11972i
$401$	466.038	+	151.425i	1.16219	+	0.377618i	0.825722	−	0.564077i	$-0.190768\pi$
$401$	466.038	+	151.425i	1.16219	+	0.377618i	0.336467	+	0.941695i	$0.390768\pi$
$402$		0			0
$403$	−337.646	+	245.314i	−0.837830	+	0.608719i
$404$	819.271	−	1127.63i	2.02790	−	2.79116i
$405$		0			0
$406$	149.757			0.368861
$407$	−140.824	−	458.389i	−0.346005	−	1.12626i
$408$		0			0
$409$	164.971	+	507.730i	0.403353	+	1.24139i	0.922263	+	0.386564i	$0.126338\pi$
$409$	164.971	+	507.730i	0.403353	+	1.24139i	−0.518910	+	0.854829i	$0.673662\pi$
$410$	18.3061	−	25.1962i	0.0446490	−	0.0614541i
$411$		0			0
$412$	−295.836	+	910.490i	−0.718049	+	2.20993i
$413$	192.842	+	62.6583i	0.466931	+	0.151715i
$414$		0			0
$415$	−7.59202	−	5.51593i	−0.0182940	−	0.0132914i
$416$	−706.763	+	229.641i	−1.69895	+	0.552022i
$417$		0			0
$418$	−99.0194	+	131.775i	−0.236888	+	0.315251i
$419$		−	344.904i		−	0.823160i	−0.911374	−	0.411580i	$-0.864977\pi$
$419$		−	344.904i		−	0.823160i	0.911374	−	0.411580i	$-0.135023\pi$
$420$		0			0
$421$	326.412	+	237.152i	0.775325	+	0.563307i	0.903572	−	0.428435i	$-0.140935\pi$
$421$	326.412	+	237.152i	0.775325	+	0.563307i	−0.128247	+	0.991742i	$0.540935\pi$
$422$	−562.445	−	774.139i	−1.33281	−	1.83445i
$423$		0			0
$424$	−202.143	+	622.132i	−0.476753	+	1.46729i
$425$	−337.824	−	464.974i	−0.794879	−	1.09406i
$426$		0			0
$427$	−20.4455	−	62.9248i	−0.0478818	−	0.147365i
$428$			1026.96i			2.39943i
$429$		0			0
$430$	37.4219			0.0870277
$431$	−126.197	+	41.0039i	−0.292800	+	0.0951366i	−0.451734	−	0.892153i	$-0.649194\pi$
$431$	−126.197	+	41.0039i	−0.292800	+	0.0951366i	0.158934	+	0.987289i	$0.449194\pi$
$432$		0			0
$433$	666.538	−	484.268i	1.53935	−	1.11840i	0.588608	−	0.808419i	$-0.299676\pi$
$433$	666.538	−	484.268i	1.53935	−	1.11840i	0.950742	−	0.309984i	$-0.100324\pi$
$434$	727.068	+	236.239i	1.67527	+	0.544329i
$435$		0			0
$436$	−708.447	+	514.717i	−1.62488	+	1.18054i
$437$	−32.8662	+	45.2365i	−0.0752087	+	0.103516i
$438$		0			0
$439$	109.320			0.249021			0.124511	−	0.992218i	$-0.460264\pi$
$439$	109.320			0.249021			0.124511	+	0.992218i	$0.460264\pi$
$440$	9.86731	+	32.1186i	0.0224257	+	0.0729968i
$441$		0			0
$442$	−524.111	−	1613.05i	−1.18577	−	3.64943i
$443$	−220.853	+	303.978i	−0.498540	+	0.686181i	−0.981934	−	0.189221i	$-0.939404\pi$
$443$	−220.853	+	303.978i	−0.498540	+	0.686181i	0.483395	+	0.875403i	$0.339404\pi$
$444$		0			0
$445$	−1.43755	+	4.42433i	−0.00323045	+	0.00994231i
$446$	−49.9775	−	16.2387i	−0.112057	−	0.0364096i
$447$		0			0
$448$	84.3313	+	61.2703i	0.188240	+	0.136764i
$449$	−358.602	+	116.517i	−0.798668	+	0.259503i	−0.679791	−	0.733406i	$-0.737930\pi$
$449$	−358.602	+	116.517i	−0.798668	+	0.259503i	−0.118877	+	0.992909i	$0.537930\pi$
$450$		0			0
$451$	329.185	+	468.770i	0.729901	+	1.03940i
$452$			948.075i			2.09751i
$453$		0			0
$454$	−358.847	−	260.718i	−0.790413	−	0.574268i
$455$	20.3560	+	28.0176i	0.0447385	+	0.0615772i
$456$		0			0
$457$	−122.907	+	378.268i	−0.268942	+	0.827719i	0.721817	+	0.692084i	$0.243307\pi$
$457$	−122.907	+	378.268i	−0.268942	+	0.827719i	−0.990759	+	0.135635i	$0.956693\pi$
$458$	8.28584	+	11.4045i	0.0180914	+	0.0249006i
$459$		0			0
$460$	6.28079	+	19.3303i	0.0136539	+	0.0420223i
$461$		−	452.581i		−	0.981737i	−0.871234	−	0.490869i	$-0.836680\pi$
$461$		−	452.581i		−	0.981737i	0.871234	−	0.490869i	$-0.163320\pi$
$462$		0			0
$463$	−125.818			−0.271745			−0.135873	−	0.990726i	$-0.543384\pi$
$463$	−125.818			−0.271745			−0.135873	+	0.990726i	$0.543384\pi$
$464$	−116.556	+	37.8714i	−0.251198	+	0.0816193i
$465$		0			0
$466$	1071.32	−	778.358i	2.29896	−	1.67030i
$467$	−263.442	−	85.5976i	−0.564117	−	0.183293i	0.0130560	−	0.999915i	$-0.495844\pi$
$467$	−263.442	−	85.5976i	−0.564117	−	0.183293i	−0.577173	+	0.816622i	$0.695844\pi$
$468$		0			0
$469$	33.2202	−	24.1359i	0.0708319	−	0.0514624i
$470$	13.6066	−	18.7279i	0.0289502	−	0.0398465i
$471$		0			0
$472$	−364.041			−0.771273
$473$	−223.195	+	651.074i	−0.471871	+	1.37648i
$474$		0			0
$475$	−31.9404	−	98.3023i	−0.0672429	−	0.206952i
$476$	−1268.82	+	1746.38i	−2.66559	+	3.66887i
$477$		0			0
$478$	164.791	−	507.175i	0.344751	−	1.06104i
$479$	476.471	+	154.815i	0.994721	+	0.323204i	0.760754	−	0.649040i	$-0.224829\pi$
$479$	476.471	+	154.815i	0.994721	+	0.323204i	0.233967	+	0.972245i	$0.424829\pi$
$480$		0			0
$481$	717.898	+	521.583i	1.49251	+	1.08437i
$482$	959.279	−	311.689i	1.99020	−	0.646657i
$483$		0			0
$484$	−1101.41	−	35.4697i	−2.27563	−	0.0732846i
$485$			13.7003i			0.0282480i
$486$		0			0
$487$	−558.354	−	405.668i	−1.14652	−	0.832993i	−0.158503	−	0.987359i	$-0.550667\pi$
$487$	−558.354	−	405.668i	−1.14652	−	0.832993i	−0.988014	+	0.154366i	$0.950667\pi$
$488$	69.8213	+	96.1008i	0.143077	+	0.196928i
$489$		0			0
$490$	10.5469	−	32.4600i	0.0215243	−	0.0662449i
$491$	−209.152	−	287.873i	−0.425971	−	0.586299i	0.541051	−	0.840990i	$-0.318026\pi$
$491$	−209.152	−	287.873i	−0.425971	−	0.586299i	−0.967023	+	0.254690i	$0.918026\pi$
$492$		0			0
$493$	−28.5648	−	87.9135i	−0.0579408	−	0.178324i
$494$		−	305.019i		−	0.617447i
$495$		0			0
$496$	−625.618			−1.26133
$497$	−536.473	+	174.311i	−1.07942	+	0.350726i
$498$		0			0
$499$	−117.317	+	85.2357i	−0.235104	+	0.170813i	−0.699099	−	0.715025i	$-0.746415\pi$
$499$	−117.317	+	85.2357i	−0.235104	+	0.170813i	0.463995	+	0.885838i	$0.346415\pi$
$500$	−71.5042	−	23.2331i	−0.143008	−	0.0464663i
$501$		0			0
$502$	141.532	−	102.829i	0.281936	−	0.204838i
$503$	510.737	−	702.968i	1.01538	−	1.39755i	0.0999885	−	0.994989i	$-0.468119\pi$
$503$	510.737	−	702.968i	1.01538	−	1.39755i	0.915392	−	0.402563i	$-0.131881\pi$
$504$		0			0
$505$	25.2829			0.0500651
$506$	−537.937	−	8.65963i	−1.06312	−	0.0171139i
$507$		0			0
$508$	22.6781	+	69.7959i	0.0446419	+	0.137394i
$509$	296.308	−	407.833i	0.582137	−	0.801243i	−0.411791	−	0.911279i	$-0.635096\pi$
$509$	296.308	−	407.833i	0.582137	−	0.801243i	0.993928	+	0.110036i	$0.0350965\pi$
$510$		0			0
$511$	−72.5893	+	223.407i	−0.142053	+	0.437195i
$512$	1086.87	+	353.145i	2.12279	+	0.689737i
$513$		0			0
$514$	583.522	+	423.954i	1.13526	+	0.824813i
$515$	−16.5156	+	5.36623i	−0.0320691	+	0.0104199i
$516$		0			0
$517$	244.677	+	348.428i	0.473264	+	0.673943i
$518$		−	1625.44i		−	3.13791i
$519$		0			0
$520$	−50.3020	−	36.5465i	−0.0967346	−	0.0702818i
$521$	−152.184	−	209.464i	−0.292101	−	0.402042i	0.637594	−	0.770372i	$-0.279930\pi$
$521$	−152.184	−	209.464i	−0.292101	−	0.402042i	−0.929695	+	0.368330i	$0.879930\pi$
$522$		0			0
$523$	184.539	−	567.952i	0.352847	−	1.08595i	−0.604401	−	0.796680i	$-0.706587\pi$
$523$	184.539	−	567.952i	0.352847	−	1.08595i	0.957248	−	0.289270i	$-0.0934125\pi$
$524$	1287.89	+	1772.63i	2.45781	+	3.38288i
$525$		0			0
$526$	−77.5421	−	238.650i	−0.147418	−	0.453707i
$527$		−	471.878i		−	0.895404i
$528$		0			0
$529$	346.493			0.654997
$530$	−20.1234	+	6.53849i	−0.0379687	+	0.0123368i
$531$		0			0
$532$	−314.069	+	228.185i	−0.590356	+	0.428919i
$533$	−1008.10	−	327.550i	−1.89136	−	0.614541i
$534$		0			0
$535$	−15.0705	+	10.9494i	−0.0281692	+	0.0204661i
$536$	−43.3328	+	59.6425i	−0.0808447	+	0.111273i
$537$		0			0
$538$	−666.491			−1.23883
$539$	501.840	+	377.097i	0.931058	+	0.699624i
$540$		0			0
$541$	74.6911	+	229.876i	0.138061	+	0.424909i	0.996054	−	0.0887536i	$-0.0282884\pi$
$541$	74.6911	+	229.876i	0.138061	+	0.424909i	−0.857992	+	0.513662i	$0.828288\pi$
$542$	186.658	−	256.913i	0.344388	−	0.474009i
$543$		0			0
$544$	259.643	−	799.098i	0.477285	−	1.46893i
$545$	−15.1069	−	4.90852i	−0.0277190	−	0.00900646i
$546$		0			0
$547$	433.072	+	314.645i	0.791722	+	0.575220i	0.908474	−	0.417942i	$-0.137248\pi$
$547$	433.072	+	314.645i	0.791722	+	0.575220i	−0.116752	+	0.993161i	$0.537248\pi$
$548$	−163.425	+	53.1002i	−0.298222	+	0.0968981i
$549$		0			0
$550$	597.440	−	795.071i	1.08625	−	1.44558i
$551$		−	16.6240i		−	0.0301706i
$552$		0			0
$553$	476.223	+	345.996i	0.861163	+	0.625671i
$554$	−530.370	−	729.992i	−0.957347	−	1.31768i
$555$		0			0
$556$	94.2150	−	289.964i	0.169451	−	0.521518i
$557$	22.7200	+	31.2714i	0.0407900	+	0.0561426i	0.828925	−	0.559360i	$-0.188953\pi$
$557$	22.7200	+	31.2714i	0.0407900	+	0.0561426i	−0.788135	+	0.615503i	$0.788953\pi$
$558$		0			0
$559$	−393.574	−	1211.30i	−0.704068	−	2.16690i
$560$			51.9134i			0.0927024i
$561$		0			0
$562$	60.9914			0.108526
$563$	338.625	−	110.026i	0.601465	−	0.195428i	0.00757154	−	0.999971i	$-0.497590\pi$
$563$	338.625	−	110.026i	0.601465	−	0.195428i	0.593894	+	0.804543i	$0.297590\pi$
$564$		0			0
$565$	−13.9129	+	10.1083i	−0.0246247	+	0.0178909i
$566$	−163.940	−	53.2672i	−0.289646	−	0.0941117i
$567$		0			0
$568$	819.319	−	595.270i	1.44246	−	1.04801i
$569$	58.0232	−	79.8620i	0.101974	−	0.140355i	−0.754981	−	0.655747i	$-0.772354\pi$
$569$	58.0232	−	79.8620i	0.101974	−	0.140355i	0.856954	+	0.515392i	$0.172354\pi$
$570$		0			0
$571$	−37.7221			−0.0660633			−0.0330316	−	0.999454i	$-0.510516\pi$
$571$	−37.7221			−0.0660633			−0.0330316	+	0.999454i	$0.510516\pi$
$572$	1668.82	−	1171.90i	2.91752	−	2.04878i
$573$		0			0
$574$	599.989	+	1846.58i	1.04528	+	3.21703i
$575$	198.300	−	272.937i	0.344870	−	0.474673i
$576$		0			0
$577$	−302.325	+	930.462i	−0.523961	+	1.61259i	0.242400	+	0.970176i	$0.422065\pi$
$577$	−302.325	+	930.462i	−0.523961	+	1.61259i	−0.766361	+	0.642410i	$0.777935\pi$
$578$	828.699	+	269.261i	1.43374	+	0.465849i
$579$		0			0
$580$	−4.88871	−	3.55185i	−0.00842881	−	0.00612389i
$581$	556.403	−	180.786i	0.957665	−	0.311164i
$582$		0			0
$583$	6.26380	−	389.108i	0.0107441	−	0.667424i
$584$		−	421.739i		−	0.722156i
$585$		0			0
$586$	−1245.11	−	904.626i	−2.12476	−	1.54373i
$587$	655.577	+	902.324i	1.11683	+	1.53718i	0.810957	+	0.585105i	$0.198947\pi$
$587$	655.577	+	902.324i	1.11683	+	1.53718i	0.305868	+	0.952074i	$0.401053\pi$
$588$		0			0
$589$	26.2240	−	80.7091i	0.0445229	−	0.137027i
$590$	−6.92129	−	9.52634i	−0.0117310	−	0.0161463i
$591$		0			0
$592$	411.048	+	1265.08i	0.694338	+	2.13695i
$593$			1006.79i			1.69779i	0.528563	+	0.848894i	$0.322731\pi$
$593$			1006.79i			1.69779i	−0.528563	+	0.848894i	$0.677269\pi$
$594$		0			0
$595$	−39.1562			−0.0658087
$596$	895.778	−	291.056i	1.50298	−	0.488349i
$597$		0			0
$598$	805.438	−	585.185i	1.34689	−	0.978570i
$599$	−561.257	−	182.364i	−0.936991	−	0.304447i	−0.199572	−	0.979883i	$-0.563955\pi$
$599$	−561.257	−	182.364i	−0.936991	−	0.304447i	−0.737418	+	0.675436i	$0.763955\pi$
$600$		0			0
$601$	607.440	−	441.331i	1.01071	−	0.734327i	0.0463560	−	0.998925i	$-0.485239\pi$
$601$	607.440	−	441.331i	1.01071	−	0.734327i	0.964359	+	0.264598i	$0.0852391\pi$
$602$	−1371.29	+	1887.42i	−2.27789	+	3.13524i
$603$		0			0
$604$	2608.15			4.31813
$605$	−11.2226	−	16.5412i	−0.0185498	−	0.0273409i
$606$		0			0
$607$	54.4372	+	167.540i	0.0896823	+	0.276014i	0.985831	−	0.167739i	$-0.0536467\pi$
$607$	54.4372	+	167.540i	0.0896823	+	0.276014i	−0.896149	+	0.443753i	$0.853647\pi$
$608$	88.8175	−	122.247i	0.146081	−	0.201064i
$609$		0			0
$610$	−1.18733	+	3.65422i	−0.00194644	+	0.00599052i
$611$	−749.299	−	243.462i	−1.22635	−	0.398465i
$612$		0			0
$613$	−734.937	−	533.963i	−1.19892	−	0.871065i	−0.204741	−	0.978816i	$-0.565635\pi$
$613$	−734.937	−	533.963i	−1.19892	−	0.871065i	−0.994178	+	0.107751i	$0.965635\pi$
$614$	−1595.82	+	518.512i	−2.59905	+	0.844483i
$615$		0			0
$616$	−1981.51	−	679.284i	−3.21674	−	1.10273i
$617$			836.440i			1.35566i	0.735220	+	0.677828i	$0.237079\pi$
$617$			836.440i			1.35566i	−0.735220	+	0.677828i	$0.762921\pi$
$618$		0			0
$619$	−777.042	−	564.554i	−1.25532	−	0.912043i	−0.256801	−	0.966464i	$-0.582668\pi$
$619$	−777.042	−	564.554i	−1.25532	−	0.912043i	−0.998518	+	0.0544217i	$0.982668\pi$
$620$	−18.1316	−	24.9560i	−0.0292445	−	0.0402516i
$621$		0			0
$622$	160.144	−	492.872i	0.257466	−	0.792399i
$623$	−170.468	−	234.629i	−0.273625	−	0.376612i
$624$		0			0
$625$	192.503	+	592.464i	0.308005	+	0.947943i
$626$		−	860.727i		−	1.37496i
$627$		0			0
$628$	−2379.76			−3.78943
$629$	−954.196	+	310.037i	−1.51700	+	0.492905i
$630$		0			0
$631$	−186.323	+	135.371i	−0.295282	+	0.214535i	−0.725555	−	0.688164i	$-0.758417\pi$
$631$	−186.323	+	135.371i	−0.295282	+	0.214535i	0.430274	+	0.902698i	$0.358417\pi$
$632$	−1005.11	−	326.580i	−1.59036	−	0.516740i
$633$		0			0
$634$	−919.427	+	668.003i	−1.45020	+	1.05363i
$635$	−0.782457	+	1.07696i	−0.00123222	+	0.00169600i
$636$		0			0
$637$	−1161.61			−1.82356
$638$	130.901	−	91.9229i	0.205174	−	0.144080i
$639$		0			0
$640$	5.58418	+	17.1863i	0.00872528	+	0.0268537i
$641$	281.497	−	387.447i	0.439152	−	0.604441i	−0.530871	−	0.847453i	$-0.678135\pi$
$641$	281.497	−	387.447i	0.439152	−	0.604441i	0.970023	+	0.243011i	$0.0781352\pi$
$642$		0			0
$643$	−221.374	+	681.320i	−0.344284	+	1.05960i	0.617683	+	0.786428i	$0.288072\pi$
$643$	−221.374	+	681.320i	−0.344284	+	1.05960i	−0.961966	+	0.273169i	$0.911928\pi$
$644$	−1205.10	−	391.560i	−1.87127	−	0.608012i
$645$		0			0
$646$	279.004	+	202.708i	0.431895	+	0.313790i
$647$	929.344	−	301.962i	1.43639	−	0.466711i	0.515620	−	0.856817i	$-0.327562\pi$
$647$	929.344	−	301.962i	1.43639	−	0.466711i	0.920770	+	0.390106i	$0.127562\pi$
$648$		0			0
$649$	207.022	−	63.6001i	0.318985	−	0.0979971i
$650$			1840.35i			2.83131i
$651$		0			0
$652$	1418.30	+	1030.45i	2.17530	+	1.58045i
$653$	524.834	+	722.372i	0.803728	+	1.10624i	0.992261	+	0.124169i	$0.0396266\pi$
$653$	524.834	+	722.372i	0.803728	+	1.10624i	−0.188533	+	0.982067i	$0.560373\pi$
$654$		0			0
$655$	−12.2818	+	37.7994i	−0.0187508	+	0.0577090i
$656$	−933.941	−	1285.46i	−1.42369	−	1.95954i
$657$		0			0
$658$	445.961	+	1372.53i	0.677752	+	2.08591i
$659$		−	350.792i		−	0.532309i	−0.963930	−	0.266154i	$-0.914247\pi$
$659$		−	350.792i		−	0.532309i	0.963930	−	0.266154i	$-0.0857531\pi$
$660$		0			0
$661$	−285.033			−0.431215			−0.215607	−	0.976480i	$-0.569173\pi$
$661$	−285.033			−0.431215			−0.215607	+	0.976480i	$0.569173\pi$
$662$	−180.740	+	58.7261i	−0.273022	+	0.0887102i
$663$		0			0
$664$	−849.757	+	617.385i	−1.27976	+	0.929797i
$665$	−6.69719	−	2.17605i	−0.0100710	−	0.00327225i
$666$		0			0
$667$	43.8976	−	31.8935i	0.0658135	−	0.0478163i
$668$	−1130.54	+	1556.06i	−1.69243	+	2.32943i
$669$		0			0
$670$	−2.38460			−0.00355911
$671$	−56.4952	−	42.4521i	−0.0841955	−	0.0632669i
$672$		0			0
$673$	31.2838	+	96.2816i	0.0464841	+	0.143063i	0.971605	−	0.236610i	$-0.0760364\pi$
$673$	31.2838	+	96.2816i	0.0464841	+	0.143063i	−0.925121	+	0.379673i	$0.876036\pi$
$674$	1050.90	−	1446.44i	1.55920	−	2.14605i
$675$		0			0
$676$	−690.463	+	2125.03i	−1.02140	+	3.14353i
$677$	379.528	+	123.316i	0.560603	+	0.182151i	0.575592	−	0.817737i	$-0.304772\pi$
$677$	379.528	+	123.316i	0.560603	+	0.182151i	−0.0149896	+	0.999888i	$0.504772\pi$
$678$		0			0
$679$	−690.988	−	502.032i	−1.01765	−	0.739370i
$680$	66.8590	−	21.7238i	0.0983221	−	0.0319468i
$681$		0			0
$682$	780.528	−	239.790i	1.14447	−	0.351598i
$683$		−	781.537i		−	1.14427i	−0.820159	−	0.572135i	$-0.806115\pi$
$683$		−	781.537i		−	1.14427i	0.820159	−	0.572135i	$-0.193885\pi$
$684$		0			0
$685$	−2.52168	−	1.83210i	−0.00368128	−	0.00267461i
$686$	176.785	+	243.324i	0.257704	+	0.354700i
$687$		0			0
$688$	589.973	−	1815.75i	0.857519	−	2.63917i
$689$	423.284	+	582.600i	0.614345	+	0.845574i
$690$		0			0
$691$	−170.504	−	524.757i	−0.246749	−	0.759416i	−0.995344	−	0.0963881i	$-0.969271\pi$
$691$	−170.504	−	524.757i	−0.246749	−	0.759416i	0.748595	−	0.663028i	$-0.230729\pi$
$692$		−	945.087i		−	1.36573i
$693$		0			0
$694$	−1635.37			−2.35644
$695$	5.25972	−	1.70899i	0.00756794	−	0.00245897i
$696$		0			0
$697$	969.571	−	704.434i	1.39106	−	1.01067i
$698$	−609.975	−	198.193i	−0.873889	−	0.283944i
$699$		0			0
$700$	1894.96	−	1376.77i	2.70708	−	1.96681i
$701$	−192.537	+	265.005i	−0.274661	+	0.378038i	−0.923956	−	0.382498i	$-0.875064\pi$
$701$	−192.537	+	265.005i	−0.274661	+	0.378038i	0.649295	+	0.760536i	$0.275064\pi$
$702$		0			0
$703$	−180.434			−0.256662
$704$	111.321	+	1.79204i	0.158127	+	0.00254551i
$705$		0			0
$706$	660.585	+	2033.07i	0.935673	+	2.87970i
$707$	−926.465	+	1275.17i	−1.31042	+	1.80364i
$708$		0			0
$709$	321.304	−	988.873i	0.453179	−	1.39474i	−0.420080	−	0.907487i	$-0.637998\pi$
$709$	321.304	−	988.873i	0.453179	−	1.39474i	0.873259	−	0.487256i	$-0.162002\pi$
$710$	31.1544	+	10.1227i	0.0438795	+	0.0142573i
$711$		0			0
$712$	421.246	+	306.053i	0.591638	+	0.429850i
$713$	263.433	−	85.5945i	0.369471	−	0.120048i
$714$		0			0
$715$	34.9905	+	11.9951i	0.0489377	+	0.0167764i
$716$		−	100.706i		−	0.140651i
$717$		0			0
$718$	1734.36	+	1260.08i	2.41554	+	1.75499i
$719$	534.348	+	735.467i	0.743182	+	1.02290i	0.998429	+	0.0560264i	$0.0178431\pi$
$719$	534.348	+	735.467i	0.743182	+	1.02290i	−0.255247	+	0.966876i	$0.582157\pi$
$720$		0			0
$721$	334.544	−	1029.62i	0.464000	−	1.42804i
$722$	−731.758	−	1007.18i	−1.01352	−	1.39498i
$723$		0			0
$724$	−350.033	−	1077.29i	−0.483470	−	1.48797i
$725$			100.302i			0.138348i
$726$		0			0
$727$	−709.728			−0.976242			−0.488121	−	0.872776i	$-0.662318\pi$
$727$	−709.728			−0.976242			−0.488121	+	0.872776i	$0.662318\pi$
$728$	3686.53	−	1197.83i	5.06391	−	1.64536i
$729$		0			0
$730$	11.0362	−	8.01827i	0.0151181	−	0.0109839i
$731$	1369.55	+	444.993i	1.87353	+	0.608745i
$732$		0			0
$733$	−401.167	+	291.465i	−0.547294	+	0.397632i	−0.826787	−	0.562515i	$-0.809834\pi$
$733$	−401.167	+	291.465i	−0.547294	+	0.397632i	0.279493	+	0.960148i	$0.409834\pi$
$734$	−482.553	+	664.177i	−0.657428	+	0.904873i
$735$		0			0
$736$	493.205			0.670115
$737$	14.2225	−	41.4878i	0.0192978	−	0.0562928i
$738$		0			0
$739$	339.775	+	1045.72i	0.459776	+	1.41505i	0.865435	+	0.501022i	$0.167042\pi$
$739$	339.775	+	1045.72i	0.459776	+	1.41505i	−0.405658	+	0.914025i	$0.632958\pi$
$740$	−38.5511	+	53.0611i	−0.0520961	+	0.0717041i
$741$		0			0
$742$	407.625	−	1254.54i	0.549360	−	1.69076i
$743$	−688.259	−	223.629i	−0.926324	−	0.300981i	−0.193265	−	0.981147i	$-0.561908\pi$
$743$	−688.259	−	223.629i	−0.926324	−	0.300981i	−0.733058	+	0.680166i	$0.761908\pi$
$744$		0			0
$745$	13.8220	+	10.0423i	0.0185530	+	0.0134795i
$746$	−263.569	+	85.6389i	−0.353310	+	0.114797i
$747$		0			0
$748$	−37.1105	+	2305.31i	−0.0496130	+	3.08196i
$749$		−	1161.33i		−	1.55050i
$750$		0			0
$751$	439.525	+	319.333i	0.585253	+	0.425211i	0.840614	−	0.541635i	$-0.182194\pi$
$751$	439.525	+	319.333i	0.585253	+	0.425211i	−0.255361	+	0.966846i	$0.582194\pi$
$752$	−694.181	−	955.459i	−0.923114	−	1.27056i
$753$		0			0
$754$	−91.4663	+	281.504i	−0.121308	+	0.373348i
$755$	27.8080	+	38.2744i	0.0368317	+	0.0506945i
$756$		0			0
$757$	−107.305	−	330.251i	−0.141751	−	0.436263i	0.854828	−	0.518911i	$-0.173662\pi$
$757$	−107.305	−	330.251i	−0.141751	−	0.436263i	−0.996579	+	0.0826476i	$0.973662\pi$
$758$		−	1272.85i		−	1.67923i
$759$		0			0
$760$	12.6427			0.0166351
$761$	762.958	−	247.900i	1.00257	−	0.325756i	0.238680	−	0.971098i	$-0.423285\pi$
$761$	762.958	−	247.900i	1.00257	−	0.325756i	0.763893	+	0.645342i	$0.223285\pi$
$762$		0			0
$763$	801.142	−	582.064i	1.04999	−	0.762862i
$764$	−1537.94	−	499.706i	−2.01301	−	0.654066i
$765$		0			0
$766$	−1677.93	+	1219.08i	−2.19050	+	1.59149i
$767$	−235.562	+	324.223i	−0.307121	+	0.422716i
$768$		0			0
$769$	−1441.35			−1.87432			−0.937158	−	0.348905i	$-0.886554\pi$
$769$	−1441.35			−1.87432			−0.937158	+	0.348905i	$0.886554\pi$
$770$	−19.8976	−	64.7677i	−0.0258411	−	0.0841139i
$771$		0			0
$772$	−684.805	−	2107.61i	−0.887053	−	2.73007i
$773$	783.612	−	1078.55i	1.01373	−	1.39528i	0.0972200	−	0.995263i	$-0.469005\pi$
$773$	783.612	−	1078.55i	1.01373	−	1.39528i	0.916509	−	0.400015i	$-0.130995\pi$
$774$		0			0
$775$	−158.224	+	486.963i	−0.204160	+	0.628340i
$776$	1458.39	+	473.859i	1.87936	+	0.610643i
$777$		0			0
$778$	574.596	+	417.469i	0.738556	+	0.536592i
$779$	204.981	−	66.6025i	0.263134	−	0.0854974i
$780$		0			0
$781$	−361.931	+	481.656i	−0.463419	+	0.616717i
$782$			1125.64i			1.43944i
$783$		0			0
$784$	−1408.72	−	1023.49i	−1.79683	−	1.30547i
$785$	−25.3729	−	34.9228i	−0.0323222	−	0.0444877i
$786$		0			0
$787$	−136.617	+	420.465i	−0.173592	+	0.534263i	−0.999566	−	0.0294457i	$-0.990626\pi$
$787$	−136.617	+	420.465i	−0.173592	+	0.534263i	0.825974	+	0.563708i	$0.190626\pi$
$788$	1154.06	+	1588.43i	1.46455	+	2.01578i
$789$		0			0
$790$	−10.5635	−	32.5111i	−0.0133715	−	0.0411533i
$791$		−	1072.12i		−	1.35540i
$792$		0			0
$793$	130.769			0.164905
$794$	−362.363	+	117.739i	−0.456377	+	0.148286i
$795$		0			0
$796$	−324.800	+	235.981i	−0.408040	+	0.296459i
$797$	−1234.70	−	401.179i	−1.54919	−	0.503362i	−0.595295	−	0.803507i	$-0.702965\pi$
$797$	−1234.70	−	401.179i	−1.54919	−	0.503362i	−0.953893	+	0.300146i	$0.902965\pi$
$798$		0			0
$799$	720.664	−	523.593i	0.901958	−	0.655311i
$800$	−535.886	+	737.584i	−0.669858	+	0.921980i
$801$		0			0
$802$	1774.07			2.21206
$803$	73.6804	+	239.833i	0.0917564	+	0.298672i
$804$		0			0
$805$	−7.10258	−	21.8595i	−0.00882308	−	0.0271546i
$806$	−888.133	+	1222.41i	−1.10190	+	1.51664i
$807$		0			0
$808$	874.474	−	2691.35i	1.08227	−	3.33088i
$809$	−868.928	−	282.332i	−1.07408	−	0.348989i	−0.282002	−	0.959414i	$-0.590999\pi$
$809$	−868.928	−	282.332i	−1.07408	−	0.348989i	−0.792074	+	0.610425i	$0.790999\pi$
$810$		0			0
$811$	−277.542	−	201.646i	−0.342223	−	0.248639i	0.403376	−	0.915034i	$-0.367837\pi$
$811$	−277.542	−	201.646i	−0.342223	−	0.248639i	−0.745599	+	0.666395i	$0.767837\pi$
$812$	358.283	−	116.413i	0.441235	−	0.143366i
$813$		0			0
$814$	−997.713	−	1420.78i	−1.22569	−	1.74542i
$815$			31.8001i			0.0390185i
$816$		0			0
$817$	209.515	+	152.221i	0.256444	+	0.186317i
$818$	1136.06	+	1563.65i	1.38882	+	1.91155i
$819$		0			0
$820$	24.2098	−	74.5101i	0.0295241	−	0.0908660i
$821$	−9.61858	−	13.2388i	−0.0117157	−	0.0161253i	0.803119	−	0.595819i	$-0.203172\pi$
$821$	−9.61858	−	13.2388i	−0.0117157	−	0.0161253i	−0.814835	+	0.579693i	$0.803172\pi$
$822$		0			0
$823$	−19.6496	−	60.4751i	−0.0238755	−	0.0734813i	0.938409	−	0.345527i	$-0.112300\pi$
$823$	−19.6496	−	60.4751i	−0.0238755	−	0.0734813i	−0.962284	+	0.272046i	$0.912300\pi$
$824$			1943.68i			2.35883i
$825$		0			0
$826$	734.095			0.888734
$827$	−1117.38	+	363.059i	−1.35112	+	0.439007i	−0.893070	−	0.449917i	$-0.851453\pi$
$827$	−1117.38	+	363.059i	−1.35112	+	0.439007i	−0.458054	+	0.888924i	$0.651453\pi$
$828$		0			0
$829$	224.390	−	163.029i	0.270676	−	0.196657i	−0.444165	−	0.895945i	$-0.646499\pi$
$829$	224.390	−	163.029i	0.270676	−	0.196657i	0.714840	+	0.699288i	$0.246499\pi$
$830$	−32.3119	−	10.4988i	−0.0389300	−	0.0126491i
$831$		0			0
$832$	−166.678	+	121.099i	−0.200335	+	0.145552i
$833$	771.978	−	1062.54i	0.926745	−	1.27555i
$834$		0			0
$835$	−34.8888			−0.0417830
$836$	−134.462	+	392.233i	−0.160839	+	0.469178i
$837$		0			0
$838$	−385.866	−	1187.57i	−0.460460	−	1.41715i
$839$	−548.102	+	754.398i	−0.653280	+	0.899163i	−0.999236	−	0.0390878i	$-0.987555\pi$
$839$	−548.102	+	754.398i	−0.653280	+	0.899163i	0.345956	+	0.938251i	$0.387555\pi$
$840$		0			0
$841$	254.898	−	784.496i	0.303089	−	0.932813i
$842$	1389.22	+	451.384i	1.64990	+	0.536086i
$843$		0			0
$844$	−1947.38	−	1414.85i	−2.30732	−	1.67637i
$845$	−38.5463	+	12.5245i	−0.0456169	+	0.0148218i
$846$		0			0
$847$	1245.52	+	40.1107i	1.47050	+	0.0473562i
$848$			1079.49i			1.27298i
$849$		0			0
$850$	−1683.39	−	1223.05i	−1.98046	−	1.43889i
$851$	−346.165	−	476.456i	−0.406775	−	0.559877i
$852$		0			0
$853$	−475.586	+	1463.70i	−0.557545	+	1.71595i	0.131581	+	0.991305i	$0.457995\pi$
$853$	−475.586	+	1463.70i	−0.557545	+	1.71595i	−0.689126	+	0.724642i	$0.742005\pi$
$854$	−140.796	−	193.789i	−0.164866	−	0.226919i
$855$		0			0
$856$	644.304	+	1982.96i	0.752691	+	2.31655i
$857$			443.512i			0.517517i	0.965942	+	0.258758i	$0.0833133\pi$
$857$			443.512i			0.517517i	−0.965942	+	0.258758i	$0.916687\pi$
$858$		0			0
$859$	1399.85			1.62962			0.814812	−	0.579725i	$-0.196840\pi$
$859$	1399.85			1.62962			0.814812	+	0.579725i	$0.196840\pi$
$860$	89.5290	−	29.0897i	0.104104	−	0.0338253i
$861$		0			0
$862$	−388.647	+	282.369i	−0.450867	+	0.327574i
$863$	1376.77	+	447.341i	1.59534	+	0.518356i	0.965948	−	0.258735i	$-0.0833058\pi$
$863$	1376.77	+	447.341i	1.59534	+	0.518356i	0.629388	+	0.777091i	$0.283306\pi$
$864$		0			0
$865$	13.8691	−	10.0765i	0.0160336	−	0.0116491i
$866$	1753.24	−	2413.13i	2.02453	−	2.78653i
$867$		0			0
$868$	1923.09			2.21555
$869$	628.637	+	10.1197i	0.723403	+	0.0116452i
$870$		0			0
$871$	25.0794	+	77.1864i	0.0287938	+	0.0886181i
$872$	−1045.02	+	1438.35i	−1.19842	+	1.64948i
$873$		0			0
$874$	−62.5560	+	192.528i	−0.0715744	+	0.220283i
$875$	80.8600	+	26.2730i	0.0924114	+	0.0300263i
$876$		0			0
$877$	156.712	+	113.858i	0.178691	+	0.129826i	0.673535	−	0.739155i	$-0.264775\pi$
$877$	156.712	+	113.858i	0.178691	+	0.129826i	−0.494845	+	0.868981i	$0.664775\pi$
$878$	376.411	−	122.303i	0.428715	−	0.139298i
$879$		0			0
$880$	31.8650	+	45.3768i	0.0362103	+	0.0515646i
$881$			1111.18i			1.26127i	0.776079	+	0.630636i	$0.217206\pi$
$881$			1111.18i			1.26127i	−0.776079	+	0.630636i	$0.782794\pi$
$882$		0			0
$883$	−574.709	−	417.551i	−0.650860	−	0.472877i	0.212704	−	0.977117i	$-0.431773\pi$
$883$	−574.709	−	417.551i	−0.650860	−	0.472877i	−0.863564	+	0.504239i	$0.831773\pi$
$884$	−2507.79	−	3451.67i	−2.83686	−	3.90461i
$885$		0			0
$886$	−420.362	+	1293.74i	−0.474449	+	1.46020i
$887$	−666.596	−	917.490i	−0.751517	−	1.03437i	−0.997873	−	0.0651951i	$-0.979233\pi$
$887$	−666.596	−	917.490i	−0.751517	−	1.03437i	0.246355	−	0.969180i	$-0.420767\pi$
$888$		0			0
$889$	−25.6453	−	78.9281i	−0.0288474	−	0.0887830i
$890$			16.8421i			0.0189237i
$891$		0			0
$892$	−132.190			−0.148196
$893$	152.359	−	49.5044i	0.170615	−	0.0554361i
$894$		0			0
$895$	1.47786	−	1.07373i	0.00165124	−	0.00119969i
$896$	−1071.44	−	348.131i	−1.19580	−	0.388539i
$897$		0			0
$898$	−1104.38	+	802.382i	−1.22983	+	0.893521i
$899$	−48.4046	+	66.6232i	−0.0538427	+	0.0741081i
$900$		0			0
$901$	−814.215			−0.903680
$902$	1657.89	+	1245.79i	1.83802	+	1.38114i
$903$		0			0
$904$	594.813	+	1830.65i	0.657979	+	2.02505i
$905$	12.0771	−	16.6227i	0.0133449	−	0.0183676i
$906$		0			0
$907$	−305.093	+	938.981i	−0.336376	+	1.03526i	0.629664	+	0.776868i	$0.283193\pi$
$907$	−305.093	+	938.981i	−0.336376	+	1.03526i	−0.966040	+	0.258392i	$0.916807\pi$
$908$	−1061.18	−	344.799i	−1.16870	−	0.379735i
$909$		0			0
$910$	101.435	+	73.6967i	0.111467	+	0.0809854i
$911$	−979.272	+	318.185i	−1.07494	+	0.349270i	−0.792411	−	0.609988i	$-0.791174\pi$
$911$	−979.272	+	318.185i	−1.07494	+	0.349270i	−0.282532	+	0.959258i	$0.591174\pi$
$912$		0			0
$913$	375.377	−	499.550i	0.411146	−	0.547153i
$914$			1439.95i			1.57544i
$915$		0			0
$916$	28.6884	+	20.8434i	0.0313193	+	0.0227548i
$917$	−1456.40	−	2004.56i	−1.58822	−	2.18600i
$918$		0			0
$919$	−171.625	+	528.209i	−0.186752	+	0.574765i	−0.999974	−	0.00718921i	$-0.997712\pi$
$919$	−171.625	+	528.209i	−0.186752	+	0.574765i	0.813222	+	0.581954i	$0.197712\pi$
$920$	24.2553	+	33.3845i	0.0263644	+	0.0362875i
$921$		0			0
$922$	−506.331	−	1558.33i	−0.549166	−	1.69016i
$923$		−	1114.89i		−	1.20790i
$924$		0			0
$925$	1088.66			1.17693
$926$	−433.217	+	140.761i	−0.467837	+	0.152009i
$927$		0			0
$928$	−118.629	+	86.1888i	−0.127833	+	0.0928758i
$929$	−593.479	−	192.833i	−0.638837	−	0.207571i	−0.0283513	−	0.999598i	$-0.509026\pi$
$929$	−593.479	−	192.833i	−0.638837	−	0.207571i	−0.610486	+	0.792027i	$0.709026\pi$
$930$		0			0
$931$	191.087	−	138.833i	0.205249	−	0.149122i
$932$	1957.99	−	2694.94i	2.10085	−	2.89157i
$933$		0			0
$934$	−1002.85			−1.07371
$935$	−34.2259	+	24.0345i	−0.0366053	+	0.0257054i
$936$		0			0
$937$	83.5018	+	256.992i	0.0891161	+	0.274271i	0.985676	−	0.168652i	$-0.0539414\pi$
$937$	83.5018	+	256.992i	0.0891161	+	0.274271i	−0.896560	+	0.442923i	$0.853941\pi$
$938$	87.3813	−	120.270i	0.0931570	−	0.128220i
$939$		0			0
$940$	17.9947	−	55.3820i	0.0191433	−	0.0589170i
$941$	1575.36	+	511.866i	1.67414	+	0.543960i	0.983760	−	0.179490i	$-0.0574446\pi$
$941$	1575.36	+	511.866i	1.67414	+	0.543960i	0.690377	+	0.723450i	$0.257445\pi$
$942$		0			0
$943$	569.132	+	413.499i	0.603533	+	0.438493i
$944$	−571.345	+	185.641i	−0.605238	+	0.196654i
$945$		0			0
$946$	−40.1075	+	2491.48i	−0.0423969	+	2.63370i
$947$		−	771.207i		−	0.814368i	−0.913346	−	0.407184i	$-0.866511\pi$
$947$		−	771.207i		−	0.814368i	0.913346	−	0.407184i	$-0.133489\pi$
$948$		0			0
$949$	−375.611	−	272.897i	−0.395796	−	0.287563i
$950$	−219.954	−	302.741i	−0.231531	−	0.318674i
$951$		0			0
$952$	−1354.32	+	4168.15i	−1.42260	+	4.37831i
$953$	174.881	+	240.703i	0.183506	+	0.252574i	0.890852	−	0.454293i	$-0.150108\pi$
$953$	174.881	+	240.703i	0.183506	+	0.252574i	−0.707347	+	0.706867i	$0.750108\pi$
$954$		0			0
$955$	−9.06428	−	27.8970i	−0.00949139	−	0.0292115i
$956$		−	1341.48i		−	1.40322i
$957$		0			0
$958$	1813.79			1.89331
$959$	184.808	−	60.0479i	0.192709	−	0.0626151i
$960$		0			0
$961$	437.366	−	317.765i	0.455115	−	0.330661i
$962$	3055.39	+	992.757i	3.17608	+	1.03197i
$963$		0			0
$964$	2052.71	−	1491.38i	2.12937	−	1.54708i
$965$	23.6277	−	32.5207i	0.0244847	−	0.0337002i
$966$		0			0
$967$	1078.20			1.11499			0.557497	−	0.830179i	$-0.311762\pi$
$967$	1078.20			1.11499			0.557497	+	0.830179i	$0.311762\pi$
$968$	−2148.97	+	622.523i	−2.22001	+	0.643102i
$969$		0			0
$970$	15.3274	+	47.1727i	0.0158014	+	0.0486317i
$971$	404.079	−	556.167i	0.416147	−	0.572777i	−0.548557	−	0.836113i	$-0.684823\pi$
$971$	404.079	−	556.167i	0.416147	−	0.572777i	0.964704	+	0.263336i	$0.0848227\pi$
$972$		0			0
$973$	−106.542	+	327.903i	−0.109499	+	0.337002i
$974$	−2376.37	−	772.129i	−2.43980	−	0.792740i
$975$		0			0
$976$	158.588	+	115.221i	0.162487	+	0.118054i
$977$	1519.46	−	493.703i	1.55523	−	0.505326i	0.599703	−	0.800223i	$-0.295285\pi$
$977$	1519.46	−	493.703i	1.55523	−	0.505326i	0.955529	+	0.294897i	$0.0952853\pi$
$978$		0			0
$979$	−293.022	−	100.451i	−0.299308	−	0.102606i
$980$		−	85.8566i		−	0.0876087i
$981$		0			0
$982$	−1042.21	−	757.212i	−1.06132	−	0.771092i
$983$	737.578	+	1015.19i	0.750333	+	1.03275i	0.997957	+	0.0638890i	$0.0203504\pi$
$983$	737.578	+	1015.19i	0.750333	+	1.03275i	−0.247624	+	0.968856i	$0.579650\pi$
$984$		0			0
$985$	−11.0056	+	33.8716i	−0.0111731	+	0.0343874i
$986$	−196.709	−	270.746i	−0.199502	−	0.274591i
$987$		0			0
$988$	−237.105	−	729.734i	−0.239985	−	0.738597i
$989$			845.287i			0.854689i
$990$		0			0
$991$	973.882			0.982727			0.491363	−	0.870955i	$-0.336499\pi$
$991$	973.882			0.982727			0.491363	+	0.870955i	$0.336499\pi$
$992$	−711.900	+	231.310i	−0.717641	+	0.233176i
$993$		0			0
$994$	−1652.17	+	1200.37i	−1.66214	+	1.20762i
$995$	−6.92601	−	2.25040i	−0.00696081	−	0.00226170i
$996$		0			0
$997$	−1295.26	+	941.061i	−1.29916	+	0.943893i	−0.999947	−	0.0102948i	$-0.996723\pi$
$997$	−1295.26	+	941.061i	−1.29916	+	0.943893i	−0.299210	+	0.954187i	$0.596723\pi$
$998$	−308.587	+	424.733i	−0.309205	+	0.425584i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.3.l.a.71.8	yes	32
3.2	odd	2	inner	99.3.l.a.71.1	yes	32
11.3	even	5		1089.3.b.i.485.1		16
11.8	odd	10		1089.3.b.j.485.16		16
11.9	even	5	inner	99.3.l.a.53.1	✓	32
33.8	even	10		1089.3.b.j.485.1		16
33.14	odd	10		1089.3.b.i.485.16		16
33.20	odd	10	inner	99.3.l.a.53.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.3.l.a.53.1	✓	32	11.9	even	5	inner
99.3.l.a.53.8	yes	32	33.20	odd	10	inner
99.3.l.a.71.1	yes	32	3.2	odd	2	inner
99.3.l.a.71.8	yes	32	1.1	even	1	trivial
1089.3.b.i.485.1		16	11.3	even	5
1089.3.b.i.485.16		16	33.14	odd	10
1089.3.b.j.485.1		16	33.8	even	10
1089.3.b.j.485.16		16	11.8	odd	10

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	99.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.44320 - 1.11876i) q^{2} +(7.36792 - 5.35311i) q^{4} +(0.157113 + 0.0510491i) q^{5} +(-8.33195 + 6.05352i) q^{7} +(10.8683 - 14.9589i) q^{8} +O(q^{10})\)	\(q+(3.44320 - 1.11876i) q^{2} +(7.36792 - 5.35311i) q^{4} +(0.157113 + 0.0510491i) q^{5} +(-8.33195 + 6.05352i) q^{7} +(10.8683 - 14.9589i) q^{8} +0.598083 q^{10} +(-3.56713 + 10.4056i) q^{11} +(-6.29016 - 19.3591i) q^{13} +(-21.9161 + 30.1649i) q^{14} +(9.42903 - 29.0196i) q^{16} +(21.8883 + 7.11194i) q^{17} +(3.34849 + 2.43282i) q^{19} +(1.43087 - 0.464917i) q^{20} +(-0.641003 + 39.8192i) q^{22} +13.5095i q^{23} +(-20.2033 - 14.6786i) q^{25} +(-43.3165 - 59.6201i) q^{26} +(-28.9840 + 89.2036i) q^{28} +(-2.36082 - 3.24939i) q^{29} +(-6.33587 - 19.4998i) q^{31} -36.5080i q^{32} +83.3223 q^{34} +(-1.61808 + 0.525747i) q^{35} +(-35.2682 + 25.6238i) q^{37} +(14.2513 + 4.63052i) q^{38} +(2.47119 - 1.79542i) q^{40} +(30.6080 - 42.1283i) q^{41} +62.5698 q^{43} +(29.4197 + 95.7625i) q^{44} +(15.1139 + 46.5159i) q^{46} +(22.7504 - 31.3132i) q^{47} +(17.6345 - 54.2734i) q^{49} +(-85.9860 - 27.9385i) q^{50} +(-149.977 - 108.965i) q^{52} +(-33.6465 + 10.9324i) q^{53} +(-1.09164 + 1.45275i) q^{55} +190.428i q^{56} +(-11.7641 - 8.54709i) q^{58} +(-11.5725 - 15.9281i) q^{59} +(-1.98522 + 6.10989i) q^{61} +(-43.6314 - 60.0534i) q^{62} +(-3.12770 - 9.62606i) q^{64} -3.36267i q^{65} -3.98708 q^{67} +(199.342 - 64.7702i) q^{68} +(-4.98319 + 3.62050i) q^{70} +(52.0905 + 16.9252i) q^{71} +(18.4526 - 13.4066i) q^{73} +(-92.7684 + 127.685i) q^{74} +37.6946 q^{76} +(-33.2690 - 108.292i) q^{77} +(-17.6623 - 54.3588i) q^{79} +(2.96284 - 4.07801i) q^{80} +(58.2578 - 179.299i) q^{82} +(-54.0258 - 17.5540i) q^{83} +(3.07587 + 2.23475i) q^{85} +(215.440 - 70.0008i) q^{86} +(116.887 + 166.451i) q^{88} +28.1602i q^{89} +(169.600 + 123.222i) q^{91} +(72.3178 + 99.5369i) q^{92} +(43.3020 - 133.270i) q^{94} +(0.401898 + 0.553165i) q^{95} +(25.6275 + 78.8733i) q^{97} -206.603i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 16 q^{7}+O(q^{10}) \) 32 * q + 16 * q^4 - 16 * q^7	\( 32 q + 16 q^{4} - 16 q^{7} + 48 q^{10} + 8 q^{13} + 96 q^{16} - 40 q^{19} - 60 q^{22} - 188 q^{25} - 348 q^{28} - 164 q^{31} + 296 q^{34} - 36 q^{37} + 48 q^{40} + 544 q^{43} + 296 q^{46} + 196 q^{49} - 640 q^{52} - 440 q^{55} - 208 q^{58} - 432 q^{61} - 328 q^{64} + 48 q^{67} + 112 q^{70} + 712 q^{73} + 2104 q^{76} + 432 q^{79} + 676 q^{82} - 68 q^{85} - 176 q^{88} + 64 q^{91} - 1360 q^{94} + 132 q^{97}+O(q^{100}) \) 32 * q + 16 * q^4 - 16 * q^7 + 48 * q^10 + 8 * q^13 + 96 * q^16 - 40 * q^19 - 60 * q^22 - 188 * q^25 - 348 * q^28 - 164 * q^31 + 296 * q^34 - 36 * q^37 + 48 * q^40 + 544 * q^43 + 296 * q^46 + 196 * q^49 - 640 * q^52 - 440 * q^55 - 208 * q^58 - 432 * q^61 - 328 * q^64 + 48 * q^67 + 112 * q^70 + 712 * q^73 + 2104 * q^76 + 432 * q^79 + 676 * q^82 - 68 * q^85 - 176 * q^88 + 64 * q^91 - 1360 * q^94 + 132 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more