LMFDB - Embedded newform 99.3.l.a.80.1

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			80.1
Character	$\chi$	$=$	99.80
Dual form			99.3.l.a.26.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.91284 - 2.63279i) q^{2} +(-2.03659 + 6.26797i) q^{4} +(-0.936271 + 1.28867i) q^{5} +(-3.36204 + 10.3473i) q^{7} +(8.01778 - 2.60514i) q^{8} +O(q^{10})$	\(q+(-1.91284 - 2.63279i) q^{2} +(-2.03659 + 6.26797i) q^{4} +(-0.936271 + 1.28867i) q^{5} +(-3.36204 + 10.3473i) q^{7} +(8.01778 - 2.60514i) q^{8} +5.18373 q^{10} +(-5.25607 + 9.66301i) q^{11} +(7.47384 - 5.43007i) q^{13} +(33.6733 - 10.9411i) q^{14} +(-0.868063 - 0.630685i) q^{16} +(-2.83106 + 3.89662i) q^{17} +(-7.75281 - 23.8607i) q^{19} +(-6.17053 - 8.49300i) q^{20} +(35.4947 - 4.64560i) q^{22} +36.6892i q^{23} +(6.94137 + 21.3633i) q^{25} +(-28.5925 - 9.29026i) q^{26} +(-58.0094 - 42.1463i) q^{28} +(-23.2548 - 7.55594i) q^{29} +(-47.0703 + 34.1986i) q^{31} -30.2297i q^{32} +15.6743 q^{34} +(-10.1864 - 14.0204i) q^{35} +(3.95474 - 12.1714i) q^{37} +(-47.9904 + 66.0532i) q^{38} +(-4.14967 + 12.7714i) q^{40} +(-11.8089 + 3.83696i) q^{41} +19.6984 q^{43} +(-49.8630 - 52.6244i) q^{44} +(96.5949 - 70.1803i) q^{46} +(61.7676 - 20.0695i) q^{47} +(-56.1212 - 40.7744i) q^{49} +(42.9675 - 59.1397i) q^{50} +(18.8144 + 57.9046i) q^{52} +(29.0988 + 40.0511i) q^{53} +(-7.53129 - 15.8205i) q^{55} +91.7208i q^{56} +(24.5894 + 75.6782i) q^{58} +(22.9125 + 7.44473i) q^{59} +(-35.7910 - 26.0037i) q^{61} +(180.076 + 58.5101i) q^{62} +(-83.0609 + 60.3473i) q^{64} +14.7153i q^{65} +33.0898 q^{67} +(-18.6582 - 25.6808i) q^{68} +(-17.4279 + 53.6375i) q^{70} +(44.0480 - 60.6269i) q^{71} +(12.7859 - 39.3511i) q^{73} +(-39.6096 + 12.8700i) q^{74} +165.347 q^{76} +(-82.3148 - 86.8735i) q^{77} +(-51.7531 + 37.6008i) q^{79} +(1.62549 - 0.528152i) q^{80} +(32.6905 + 23.7510i) q^{82} +(-24.7962 + 34.1290i) q^{83} +(-2.37080 - 7.29658i) q^{85} +(-37.6797 - 51.8617i) q^{86} +(-16.9686 + 91.1687i) q^{88} -111.111i q^{89} +(31.0591 + 95.5901i) q^{91} +(-229.967 - 74.7207i) q^{92} +(-170.990 - 124.231i) q^{94} +(38.0072 + 12.3493i) q^{95} +(87.4573 - 63.5414i) q^{97} +225.750i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$-1$

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 $

$2$	−1.91284	−	2.63279i	−0.956418	−	1.31640i	−0.948617	−	0.316426i	$-0.897517\pi$
$2$	−1.91284	−	2.63279i	−0.956418	−	1.31640i	−0.00780058	−	0.999970i	$-0.502483\pi$
$3$		0			0
$3$		0			0
$4$	−2.03659	+	6.26797i	−0.509147	+	1.56699i
$5$	−0.936271	+	1.28867i	−0.187254	+	0.257733i	−0.892315	−	0.451414i	$-0.850920\pi$
$5$	−0.936271	+	1.28867i	−0.187254	+	0.257733i	0.705060	+	0.709147i	$0.250920\pi$
$6$		0			0
$7$	−3.36204	+	10.3473i	−0.480291	+	1.47818i	0.358396	+	0.933570i	$0.383324\pi$
$7$	−3.36204	+	10.3473i	−0.480291	+	1.47818i	−0.838687	+	0.544614i	$0.816676\pi$
$8$	8.01778	−	2.60514i	1.00222	−	0.325642i
$9$		0			0
$10$	5.18373			0.518373
$11$	−5.25607	+	9.66301i	−0.477825	+	0.878455i
$11$	−5.25607	+	9.66301i	−0.477825	+	0.878455i
$12$		0			0
$13$	7.47384	−	5.43007i	0.574911	−	0.417697i	−0.261975	−	0.965075i	$-0.584374\pi$
$13$	7.47384	−	5.43007i	0.574911	−	0.417697i	0.836886	+	0.547377i	$0.184374\pi$
$14$	33.6733	−	10.9411i	2.40523	−	0.781508i
$15$		0			0
$16$	−0.868063	−	0.630685i	−0.0542540	−	0.0394178i
$17$	−2.83106	+	3.89662i	−0.166533	+	0.229213i	−0.884125	−	0.467251i	$-0.845244\pi$
$17$	−2.83106	+	3.89662i	−0.166533	+	0.229213i	0.717592	+	0.696464i	$0.245244\pi$
$18$		0			0
$19$	−7.75281	−	23.8607i	−0.408043	−	1.25583i	−0.918328	−	0.395821i	$-0.870460\pi$
$19$	−7.75281	−	23.8607i	−0.408043	−	1.25583i	0.510285	−	0.860006i	$-0.329540\pi$
$20$	−6.17053	−	8.49300i	−0.308526	−	0.424650i
$21$		0			0
$22$	35.4947	−	4.64560i	1.61339	−	0.211163i
$23$			36.6892i			1.59518i	0.603199	+	0.797590i	$0.293892\pi$
$23$			36.6892i			1.59518i	−0.603199	+	0.797590i	$0.706108\pi$
$24$		0			0
$25$	6.94137	+	21.3633i	0.277655	+	0.854533i
$26$	−28.5925	−	9.29026i	−1.09971	−	0.357318i
$27$		0			0
$28$	−58.0094	−	42.1463i	−2.07176	−	1.50522i
$29$	−23.2548	−	7.55594i	−0.801889	−	0.260549i	−0.120730	−	0.992685i	$-0.538524\pi$
$29$	−23.2548	−	7.55594i	−0.801889	−	0.260549i	−0.681159	+	0.732136i	$0.738524\pi$
$30$		0			0
$31$	−47.0703	+	34.1986i	−1.51840	+	1.10318i	−0.556123	+	0.831100i	$0.687712\pi$
$31$	−47.0703	+	34.1986i	−1.51840	+	1.10318i	−0.962274	+	0.272081i	$0.912288\pi$
$32$		−	30.2297i		−	0.944680i
$33$		0			0
$34$	15.6743			0.461009
$35$	−10.1864	−	14.0204i	−0.291041	−	0.400583i
$36$		0			0
$37$	3.95474	−	12.1714i	0.106885	−	0.328958i	−0.883283	−	0.468840i	$-0.844672\pi$
$37$	3.95474	−	12.1714i	0.106885	−	0.328958i	0.990168	+	0.139882i	$0.0446722\pi$
$38$	−47.9904	+	66.0532i	−1.26291	+	1.73824i
$39$		0			0
$40$	−4.14967	+	12.7714i	−0.103742	+	0.319284i
$41$	−11.8089	+	3.83696i	−0.288023	+	0.0935843i	−0.449465	−	0.893298i	$-0.648385\pi$
$41$	−11.8089	+	3.83696i	−0.288023	+	0.0935843i	0.161442	+	0.986882i	$0.448385\pi$
$42$		0			0
$43$	19.6984			0.458102			0.229051	−	0.973414i	$-0.426438\pi$
$43$	19.6984			0.458102			0.229051	+	0.973414i	$0.426438\pi$
$44$	−49.8630	−	52.6244i	−1.13325	−	1.19601i
$45$		0			0
$46$	96.5949	−	70.1803i	2.09989	−	1.52566i
$47$	61.7676	−	20.0695i	1.31420	−	0.427011i	0.433703	−	0.901056i	$-0.357207\pi$
$47$	61.7676	−	20.0695i	1.31420	−	0.427011i	0.880500	+	0.474045i	$0.157207\pi$
$48$		0			0
$49$	−56.1212	−	40.7744i	−1.14533	−	0.832131i
$50$	42.9675	−	59.1397i	0.859350	−	1.18279i
$51$		0			0
$52$	18.8144	+	57.9046i	0.361814	+	1.11355i
$53$	29.0988	+	40.0511i	0.549034	+	0.755681i	0.989881	−	0.141901i	$-0.0453216\pi$
$53$	29.0988	+	40.0511i	0.549034	+	0.755681i	−0.440846	+	0.897583i	$0.645322\pi$
$54$		0			0
$55$	−7.53129	−	15.8205i	−0.136933	−	0.287646i
$56$			91.7208i			1.63787i
$57$		0			0
$58$	24.5894	+	75.6782i	0.423954	+	1.30480i
$59$	22.9125	+	7.44473i	0.388348	+	0.126182i	0.496682	−	0.867933i	$-0.334552\pi$
$59$	22.9125	+	7.44473i	0.388348	+	0.126182i	−0.108334	+	0.994115i	$0.534552\pi$
$60$		0			0
$61$	−35.7910	−	26.0037i	−0.586738	−	0.426290i	0.254409	−	0.967097i	$-0.418119\pi$
$61$	−35.7910	−	26.0037i	−0.586738	−	0.426290i	−0.841147	+	0.540807i	$0.818119\pi$
$62$	180.076	+	58.5101i	2.90444	+	0.943711i
$63$		0			0
$64$	−83.0609	+	60.3473i	−1.29783	+	0.942926i
$65$			14.7153i			0.226389i
$66$		0			0
$67$	33.0898			0.493878			0.246939	−	0.969031i	$-0.420575\pi$
$67$	33.0898			0.493878			0.246939	+	0.969031i	$0.420575\pi$
$68$	−18.6582	−	25.6808i	−0.274385	−	0.377658i
$69$		0			0
$70$	−17.4279	+	53.6375i	−0.248970	+	0.766250i
$71$	44.0480	−	60.6269i	0.620395	−	0.853900i	−0.376987	−	0.926219i	$-0.623040\pi$
$71$	44.0480	−	60.6269i	0.620395	−	0.853900i	0.997382	+	0.0723185i	$0.0230398\pi$
$72$		0			0
$73$	12.7859	−	39.3511i	0.175150	−	0.539056i	−0.824490	−	0.565876i	$-0.808538\pi$
$73$	12.7859	−	39.3511i	0.175150	−	0.539056i	0.999640	+	0.0268199i	$0.00853807\pi$
$74$	−39.6096	+	12.8700i	−0.535265	+	0.173918i
$75$		0			0
$76$	165.347			2.17562
$77$	−82.3148	−	86.8735i	−1.06902	−	1.12823i
$78$		0			0
$79$	−51.7531	+	37.6008i	−0.655102	+	0.475960i	−0.865005	−	0.501763i	$-0.832685\pi$
$79$	−51.7531	+	37.6008i	−0.655102	+	0.475960i	0.209903	+	0.977722i	$0.432685\pi$
$80$	1.62549	−	0.528152i	0.0203186	−	0.00660190i
$81$		0			0
$82$	32.6905	+	23.7510i	0.398664	+	0.289647i
$83$	−24.7962	+	34.1290i	−0.298749	+	0.411193i	−0.931831	−	0.362892i	$-0.881789\pi$
$83$	−24.7962	+	34.1290i	−0.298749	+	0.411193i	0.633082	+	0.774085i	$0.281789\pi$
$84$		0			0
$85$	−2.37080	−	7.29658i	−0.0278918	−	0.0858421i
$86$	−37.6797	−	51.8617i	−0.438137	−	0.603043i
$87$		0			0
$88$	−16.9686	+	91.1687i	−0.192825	+	1.03601i
$89$		−	111.111i		−	1.24844i	−0.781249	−	0.624220i	$-0.785417\pi$
$89$		−	111.111i		−	1.24844i	0.781249	−	0.624220i	$-0.214583\pi$
$90$		0			0
$91$	31.0591	+	95.5901i	0.341309	+	1.05044i
$92$	−229.967	−	74.7207i	−2.49964	−	0.812181i
$93$		0			0
$94$	−170.990	−	124.231i	−1.81904	−	1.32161i
$95$	38.0072	+	12.3493i	0.400076	+	0.129993i
$96$		0			0
$97$	87.4573	−	63.5414i	0.901622	−	0.655066i	−0.0372604	−	0.999306i	$-0.511863\pi$
$97$	87.4573	−	63.5414i	0.901622	−	0.655066i	0.938882	+	0.344239i	$0.111863\pi$
$98$			225.750i			2.30357i
$99$		0			0
$100$	−148.041			−1.48041
$101$	68.4285	+	94.1838i	0.677510	+	0.932513i	0.999901	−	0.0140942i	$-0.00448646\pi$
$101$	68.4285	+	94.1838i	0.677510	+	0.932513i	−0.322391	+	0.946607i	$0.604486\pi$
$102$		0			0
$103$	−33.7693	+	103.931i	−0.327857	+	1.00904i	0.642278	+	0.766472i	$0.277990\pi$
$103$	−33.7693	+	103.931i	−0.327857	+	1.00904i	−0.970134	+	0.242568i	$0.922010\pi$
$104$	45.7776	−	63.0075i	0.440169	−	0.605841i
$105$		0			0
$106$	49.7849	−	153.222i	0.469669	−	1.44549i
$107$	−41.0612	+	13.3416i	−0.383750	+	0.124688i	−0.494538	−	0.869156i	$-0.664663\pi$
$107$	−41.0612	+	13.3416i	−0.383750	+	0.124688i	0.110788	+	0.993844i	$0.464663\pi$
$108$		0			0
$109$	75.3063			0.690884			0.345442	−	0.938440i	$-0.387729\pi$
$109$	75.3063			0.690884			0.345442	+	0.938440i	$0.387729\pi$
$110$	−27.2460	+	50.0904i	−0.247691	+	0.455367i
$111$		0			0
$112$	9.44434	−	6.86171i	0.0843244	−	0.0612653i
$113$	−3.34964	+	1.08836i	−0.0296429	+	0.00963155i	−0.323801	−	0.946125i	$-0.604961\pi$
$113$	−3.34964	+	1.08836i	−0.0296429	+	0.00963155i	0.294158	+	0.955757i	$0.404961\pi$
$114$		0			0
$115$	−47.2801	−	34.3510i	−0.411131	−	0.298704i
$116$	94.7207	−	130.372i	0.816558	−	1.12390i
$117$		0			0
$118$	−24.2275	−	74.5644i	−0.205317	−	0.631902i
$119$	−30.8013	−	42.3943i	−0.258834	−	0.356255i
$120$		0			0
$121$	−65.7474	−	101.579i	−0.543367	−	0.839495i
$122$			143.971i			1.18009i
$123$		0			0
$124$	−118.493	−	364.684i	−0.955588	−	2.94100i
$125$	−71.9022	−	23.3624i	−0.575218	−	0.186900i
$126$		0			0
$127$	192.213	+	139.651i	1.51349	+	1.09961i	0.964601	+	0.263713i	$0.0849472\pi$
$127$	192.213	+	139.651i	1.51349	+	1.09961i	0.548884	+	0.835898i	$0.315053\pi$
$128$	202.763	+	65.8816i	1.58408	+	0.514700i
$129$		0			0
$130$	38.7424	−	28.1480i	0.298018	−	0.216523i
$131$			64.9832i			0.496055i	0.968753	+	0.248027i	$0.0797823\pi$
$131$			64.9832i			0.496055i	−0.968753	+	0.248027i	$0.920218\pi$
$132$		0			0
$133$	272.959			2.05232
$134$	−63.2954	−	87.1186i	−0.472354	−	0.650139i
$135$		0			0
$136$	−12.5476	+	38.6175i	−0.0922616	+	0.283952i
$137$	−73.7746	+	101.542i	−0.538501	+	0.741183i	−0.988396	−	0.151899i	$-0.951461\pi$
$137$	−73.7746	+	101.542i	−0.538501	+	0.741183i	0.449895	+	0.893081i	$0.351461\pi$
$138$		0			0
$139$	25.9426	−	79.8431i	0.186637	−	0.574411i	−0.813335	−	0.581795i	$-0.802351\pi$
$139$	25.9426	−	79.8431i	0.186637	−	0.574411i	0.999973	+	0.00738425i	$0.00235050\pi$
$140$	108.625	−	35.2944i	0.775893	−	0.252103i
$141$		0			0
$142$	−243.875			−1.71743
$143$	13.1877	+	100.761i	0.0922217	+	0.704620i
$144$		0			0
$145$	31.5099	−	22.8933i	0.217309	−	0.157885i
$146$	−128.061	+	41.6094i	−0.877128	+	0.284996i
$147$		0			0
$148$	68.2360	+	49.5764i	0.461054	+	0.334976i
$149$	122.754	−	168.957i	0.823854	−	1.13394i	−0.165182	−	0.986263i	$-0.552821\pi$
$149$	122.754	−	168.957i	0.823854	−	1.13394i	0.989036	−	0.147675i	$-0.0471789\pi$
$150$		0			0
$151$	19.1929	+	59.0698i	0.127106	+	0.391191i	0.994279	−	0.106816i	$-0.0340656\pi$
$151$	19.1929	+	59.0698i	0.127106	+	0.391191i	−0.867173	+	0.498007i	$0.834066\pi$
$152$	−124.321	−	171.113i	−0.817900	−	1.12574i
$153$		0			0
$154$	−71.2651	+	382.892i	−0.462761	+	2.48631i
$155$		−	92.6771i		−	0.597917i
$156$		0			0
$157$	−33.1773	−	102.109i	−0.211320	−	0.650377i	−0.999394	−	0.0347966i	$-0.988922\pi$
$157$	−33.1773	−	102.109i	−0.211320	−	0.650377i	0.788074	−	0.615580i	$-0.211078\pi$
$158$	197.990	+	64.3309i	1.25310	+	0.407158i
$159$		0			0
$160$	38.9561	+	28.3033i	0.243476	+	0.176895i
$161$	−379.633	−	123.350i	−2.35797	−	0.766151i
$162$		0			0
$163$	−164.551	+	119.554i	−1.00952	+	0.733457i	−0.964108	−	0.265511i	$-0.914459\pi$
$163$	−164.551	+	119.554i	−1.00952	+	0.733457i	−0.0454096	+	0.998968i	$0.514459\pi$
$164$		−	81.8324i		−	0.498978i
$165$		0			0
$166$	137.286			0.827021
$167$	185.782	+	255.707i	1.11247	+	1.53118i	0.817732	+	0.575600i	$0.195231\pi$
$167$	185.782	+	255.707i	1.11247	+	1.53118i	0.294735	+	0.955579i	$0.404769\pi$
$168$		0			0
$169$	−25.8511	+	79.5616i	−0.152965	+	0.470779i
$170$	−14.6754	+	20.1990i	−0.0863260	+	0.118818i
$171$		0			0
$172$	−40.1174	+	123.469i	−0.233241	+	0.717842i
$173$	−108.421	+	35.2281i	−0.626711	+	0.203631i	−0.605118	−	0.796136i	$-0.706874\pi$
$173$	−108.421	+	35.2281i	−0.626711	+	0.203631i	−0.0215935	+	0.999767i	$0.506874\pi$
$174$		0			0
$175$	−244.390			−1.39651
$176$	10.6569	−	5.07318i	0.0605507	−	0.0288249i
$177$		0			0
$178$	−292.532	+	212.537i	−1.64344	+	1.19403i
$179$	138.649	−	45.0498i	0.774575	−	0.251675i	0.105053	−	0.994467i	$-0.466499\pi$
$179$	138.649	−	45.0498i	0.774575	−	0.251675i	0.669522	+	0.742792i	$0.266499\pi$
$180$		0			0
$181$	281.220	+	204.318i	1.55370	+	1.12883i	0.940944	+	0.338562i	$0.109940\pi$
$181$	281.220	+	204.318i	1.55370	+	1.12883i	0.612759	+	0.790270i	$0.290060\pi$
$182$	192.258	−	264.620i	1.05636	−	1.45396i
$183$		0			0
$184$	95.5802	+	294.166i	0.519458	+	1.59873i
$185$	11.9822	+	16.4921i	0.0647688	+	0.0891466i
$186$		0			0
$187$	−22.7728	−	47.8374i	−0.121780	−	0.255815i
$188$			428.030i			2.27676i
$189$		0			0
$190$	−40.1885	−	123.687i	−0.211518	−	0.650986i
$191$	−71.2232	−	23.1418i	−0.372896	−	0.121161i	0.116572	−	0.993182i	$-0.462809\pi$
$191$	−71.2232	−	23.1418i	−0.372896	−	0.121161i	−0.489469	+	0.872021i	$0.662809\pi$
$192$		0			0
$193$	25.7429	+	18.7033i	0.133383	+	0.0969085i	0.652476	−	0.757809i	$-0.273730\pi$
$193$	25.7429	+	18.7033i	0.133383	+	0.0969085i	−0.519093	+	0.854718i	$0.673730\pi$
$194$	−334.583	−	108.713i	−1.72465	−	0.560374i
$195$		0			0
$196$	369.869	−	268.725i	1.88708	−	1.37105i
$197$		−	165.104i		−	0.838089i	−0.907966	−	0.419045i	$-0.862365\pi$
$197$		−	165.104i		−	0.838089i	0.907966	−	0.419045i	$-0.137635\pi$
$198$		0			0
$199$	195.093			0.980365			0.490182	−	0.871620i	$-0.336930\pi$
$199$	195.093			0.980365			0.490182	+	0.871620i	$0.336930\pi$
$200$	111.309	+	153.203i	0.556544	+	0.766016i
$201$		0			0
$202$	117.074	−	360.316i	0.579573	−	1.78374i
$203$	156.367	−	215.220i	0.770280	−	1.06020i
$204$		0			0
$205$	6.11181	−	18.8102i	0.0298137	−	0.0917572i
$206$	338.224	−	109.896i	1.64186	−	0.533474i
$207$		0			0
$208$	−9.91243			−0.0476559
$209$	271.316	+	50.4981i	1.29816	+	0.241618i
$210$		0			0
$211$	−147.480	+	107.151i	−0.698958	+	0.507823i	−0.879593	−	0.475728i	$-0.842185\pi$
$211$	−147.480	+	107.151i	−0.698958	+	0.507823i	0.180635	+	0.983550i	$0.442185\pi$
$212$	−310.301	+	100.823i	−1.46369	+	0.475580i
$213$		0			0
$214$	113.669	+	82.5854i	0.531164	+	0.385913i
$215$	−18.4430	+	25.3846i	−0.0857815	+	0.118068i
$216$		0			0
$217$	−195.610	−	602.027i	−0.901431	−	2.77432i
$218$	−144.049	−	198.266i	−0.660773	−	0.909477i
$219$		0			0
$220$	114.501	−	14.9860i	0.520458	−	0.0681182i
$221$			44.4955i			0.201337i
$222$		0			0
$223$	−35.4093	−	108.979i	−0.158786	−	0.488693i	0.839739	−	0.542991i	$-0.182708\pi$
$223$	−35.4093	−	108.979i	−0.158786	−	0.488693i	−0.998525	+	0.0542974i	$0.982708\pi$
$224$	312.796	+	101.634i	1.39641	+	0.453721i
$225$		0			0
$226$	9.27275	+	6.73705i	0.0410299	+	0.0298099i
$227$	222.208	+	72.1996i	0.978888	+	0.318060i	0.754399	−	0.656417i	$-0.227929\pi$
$227$	222.208	+	72.1996i	0.978888	+	0.318060i	0.224489	+	0.974477i	$0.427929\pi$
$228$		0			0
$229$	−112.679	+	81.8663i	−0.492049	+	0.357495i	−0.805972	−	0.591954i	$-0.798357\pi$
$229$	−112.679	+	81.8663i	−0.492049	+	0.357495i	0.313923	+	0.949449i	$0.398357\pi$
$230$			190.187i			0.826898i
$231$		0			0
$232$	−206.136			−0.888517
$233$	69.6784	+	95.9041i	0.299049	+	0.411606i	0.931927	−	0.362646i	$-0.118127\pi$
$233$	69.6784	+	95.9041i	0.299049	+	0.411606i	−0.632878	+	0.774251i	$0.718127\pi$
$234$		0			0
$235$	−31.9683	+	98.3883i	−0.136035	+	0.418674i
$236$	−93.3267	+	128.453i	−0.395452	+	0.544293i
$237$		0			0
$238$	−52.6976	+	162.187i	−0.221419	+	0.681457i
$239$	−274.203	+	89.0941i	−1.14729	+	0.372778i	−0.820123	−	0.572187i	$-0.806095\pi$
$239$	−274.203	+	89.0941i	−1.14729	+	0.372778i	−0.327171	+	0.944965i	$0.606095\pi$
$240$		0			0
$241$	−115.517			−0.479324			−0.239662	−	0.970856i	$-0.577037\pi$
$241$	−115.517			−0.479324			−0.239662	+	0.970856i	$0.577037\pi$
$242$	−141.672	+	367.403i	−0.585422	+	1.51819i
$243$		0			0
$244$	235.882	−	171.378i	0.966728	−	0.702369i
$245$	105.089	−	34.1456i	0.428936	−	0.139370i
$246$		0			0
$247$	−187.509	−	136.233i	−0.759144	−	0.551550i
$248$	−288.308	+	396.821i	−1.16253	+	1.60009i
$249$		0			0
$250$	76.0286	+	233.992i	0.304114	+	0.935968i
$251$	20.2429	+	27.8619i	0.0806489	+	0.111004i	0.847435	−	0.530899i	$-0.178145\pi$
$251$	20.2429	+	27.8619i	0.0806489	+	0.111004i	−0.766786	+	0.641902i	$0.778145\pi$
$252$		0			0
$253$	−354.528	−	192.841i	−1.40130	−	0.762217i
$254$		−	773.185i		−	3.04403i
$255$		0			0
$256$	−87.4935	−	269.277i	−0.341771	−	1.05186i
$257$	−198.210	−	64.4025i	−0.771247	−	0.250593i	−0.103148	−	0.994666i	$-0.532892\pi$
$257$	−198.210	−	64.4025i	−0.771247	−	0.250593i	−0.668099	+	0.744073i	$0.732892\pi$
$258$		0			0
$259$	112.645	+	81.8417i	0.434924	+	0.315991i
$260$	−92.2351	−	29.9690i	−0.354750	−	0.115265i
$261$		0			0
$262$	171.087	−	124.302i	0.653005	−	0.474436i
$263$		−	230.901i		−	0.877952i	−0.898499	−	0.438976i	$-0.855341\pi$
$263$		−	230.901i		−	0.877952i	0.898499	−	0.438976i	$-0.144659\pi$
$264$		0			0
$265$	−78.8569			−0.297573
$266$	−522.125	−	718.644i	−1.96288	−	2.70167i
$267$		0			0
$268$	−67.3903	+	207.406i	−0.251456	+	0.773903i
$269$	−6.51517	+	8.96736i	−0.0242200	+	0.0333359i	−0.820955	−	0.570993i	$-0.806559\pi$
$269$	−6.51517	+	8.96736i	−0.0242200	+	0.0333359i	0.796735	+	0.604328i	$0.206559\pi$
$270$		0			0
$271$	31.1472	−	95.8612i	0.114934	−	0.353731i	−0.876999	−	0.480492i	$-0.840458\pi$
$271$	31.1472	−	95.8612i	0.114934	−	0.353731i	0.991933	+	0.126761i	$0.0404581\pi$
$272$	4.91507	−	1.59700i	0.0180701	−	0.00587134i
$273$		0			0
$274$	408.458			1.49072
$275$	−242.918	−	45.2127i	−0.883339	−	0.164410i
$276$		0			0
$277$	43.2146	−	31.3972i	0.156009	−	0.113347i	−0.507042	−	0.861921i	$-0.669261\pi$
$277$	43.2146	−	31.3972i	0.156009	−	0.113347i	0.663051	+	0.748574i	$0.269261\pi$
$278$	−259.834	+	84.4253i	−0.934656	+	0.303688i
$279$		0			0
$280$	−118.198	−	85.8756i	−0.422134	−	0.306699i
$281$	−217.042	+	298.733i	−0.772392	+	1.06311i	0.223689	+	0.974661i	$0.428190\pi$
$281$	−217.042	+	298.733i	−0.772392	+	1.06311i	−0.996081	+	0.0884461i	$0.971810\pi$
$282$		0			0
$283$	74.4927	+	229.265i	0.263225	+	0.810123i	0.992097	+	0.125473i	$0.0400450\pi$
$283$	74.4927	+	229.265i	0.263225	+	0.810123i	−0.728872	+	0.684650i	$0.759955\pi$
$284$	290.300	+	399.564i	1.02218	+	1.40691i
$285$		0			0
$286$	240.056	−	227.459i	0.839356	−	0.795311i
$287$		−	135.090i		−	0.470699i
$288$		0			0
$289$	82.1372	+	252.792i	0.284212	+	0.874714i
$290$	−120.546	−	39.1679i	−0.415677	−	0.135062i
$291$		0			0
$292$	220.612	+	160.284i	0.755520	+	0.548917i
$293$	52.4316	+	17.0361i	0.178948	+	0.0581436i	0.397120	−	0.917767i	$-0.370010\pi$
$293$	52.4316	+	17.0361i	0.178948	+	0.0581436i	−0.218173	+	0.975910i	$0.570010\pi$
$294$		0			0
$295$	−31.0461	+	22.5563i	−0.105241	+	0.0764621i
$296$		−	107.891i		−	0.364495i
$297$		0			0
$298$	−679.637			−2.28066
$299$	199.225	+	274.209i	0.666303	+	0.917087i
$300$		0			0
$301$	−66.2267	+	203.825i	−0.220022	+	0.677158i
$302$	118.806	−	163.522i	0.393396	−	0.541463i
$303$		0			0
$304$	−8.31866	+	25.6022i	−0.0273640	+	0.0842177i
$305$	67.0202	−	21.7762i	0.219738	−	0.0713973i
$306$		0			0
$307$	−12.5104			−0.0407504			−0.0203752	−	0.999792i	$-0.506486\pi$
$307$	−12.5104			−0.0407504			−0.0203752	+	0.999792i	$0.506486\pi$
$308$	712.161	−	339.021i	2.31221	−	1.10072i
$309$		0			0
$310$	−244.000	+	177.276i	−0.787096	+	0.571858i
$311$	205.110	−	66.6443i	0.659518	−	0.214290i	0.0399116	−	0.999203i	$-0.487292\pi$
$311$	205.110	−	66.6443i	0.659518	−	0.214290i	0.619606	+	0.784913i	$0.287292\pi$
$312$		0			0
$313$	−352.445	−	256.066i	−1.12602	−	0.818102i	−0.140911	−	0.990022i	$-0.545003\pi$
$313$	−352.445	−	256.066i	−1.12602	−	0.818102i	−0.985111	+	0.171920i	$0.945003\pi$
$314$	−205.370	+	282.667i	−0.654043	+	0.900213i
$315$		0			0
$316$	−130.281	−	400.964i	−0.412282	−	1.26887i
$317$	184.456	+	253.883i	0.581882	+	0.800891i	0.993900	−	0.110284i	$-0.0351761\pi$
$317$	184.456	+	253.883i	0.581882	+	0.800891i	−0.412018	+	0.911175i	$0.635176\pi$
$318$		0			0
$319$	195.242	−	184.997i	0.612043	−	0.579926i
$320$		−	163.539i		−	0.511060i
$321$		0			0
$322$	401.420	+	1235.44i	1.24665	+	3.83678i
$323$	114.925	+	37.3413i	0.355804	+	0.115608i
$324$		0			0
$325$	167.883	+	121.974i	0.516563	+	0.375305i
$326$	629.519	+	204.543i	1.93104	+	0.627433i
$327$		0			0
$328$	−84.6857	+	61.5278i	−0.258188	+	0.187585i
$329$			706.601i			2.14772i
$330$		0			0
$331$	69.5045			0.209983			0.104992	−	0.994473i	$-0.466518\pi$
$331$	69.5045			0.209983			0.104992	+	0.994473i	$0.466518\pi$
$332$	−163.420	−	224.928i	−0.492229	−	0.677495i
$333$		0			0
$334$	317.853	−	978.250i	0.951655	−	2.92889i
$335$	−30.9811	+	42.6418i	−0.0924808	+	0.127289i
$336$		0			0
$337$	−33.6193	+	103.469i	−0.0997604	+	0.307031i	−0.988465	−	0.151449i	$-0.951606\pi$
$337$	−33.6193	+	103.469i	−0.0997604	+	0.307031i	0.888705	+	0.458480i	$0.151606\pi$
$338$	258.918	−	84.1276i	0.766030	−	0.248898i
$339$		0			0
$340$	50.5631			0.148715
$341$	−83.0562	−	634.591i	−0.243567	−	1.86097i
$342$		0			0
$343$	179.292	−	130.263i	0.522717	−	0.379776i
$344$	157.937	−	51.3169i	0.459120	−	0.149177i
$345$		0			0
$346$	300.140	+	218.064i	0.867456	+	0.630244i
$347$	−225.036	+	309.735i	−0.648518	+	0.892608i	−0.999034	−	0.0439485i	$-0.986006\pi$
$347$	−225.036	+	309.735i	−0.648518	+	0.892608i	0.350516	+	0.936557i	$0.386006\pi$
$348$		0			0
$349$	136.469	+	420.008i	0.391029	+	1.20346i	0.932012	+	0.362429i	$0.118052\pi$
$349$	136.469	+	420.008i	0.391029	+	1.20346i	−0.540983	+	0.841034i	$0.681948\pi$
$350$	467.477	+	643.427i	1.33565	+	1.83836i
$351$		0			0
$352$	292.110	+	158.890i	0.829859	+	0.451391i
$353$		−	237.587i		−	0.673051i	−0.941674	−	0.336525i	$-0.890748\pi$
$353$		−	237.587i		−	0.673051i	0.941674	−	0.336525i	$-0.109252\pi$
$354$		0			0
$355$	36.8870	+	113.526i	0.103907	+	0.319793i
$356$	696.441	+	226.287i	1.95630	+	0.635639i
$357$		0			0
$358$	−383.819	−	278.861i	−1.07212	−	0.778941i
$359$	−366.865	−	119.202i	−1.02191	−	0.332038i	−0.250321	−	0.968163i	$-0.580536\pi$
$359$	−366.865	−	119.202i	−1.02191	−	0.332038i	−0.771586	+	0.636125i	$0.780536\pi$
$360$		0			0
$361$	−217.172	+	157.785i	−0.601585	+	0.437077i
$362$		−	1131.22i		−	3.12492i
$363$		0			0
$364$	−662.410			−1.81981
$365$	38.7393	+	53.3201i	0.106135	+	0.146083i
$366$		0			0
$367$	47.6728	−	146.722i	0.129899	−	0.399787i	−0.864863	−	0.502008i	$-0.832595\pi$
$367$	47.6728	−	146.722i	0.129899	−	0.399787i	0.994762	+	0.102221i	$0.0325949\pi$
$368$	23.1393	−	31.8485i	0.0628785	−	0.0865449i
$369$		0			0
$370$	20.5003	−	63.0934i	0.0554062	−	0.170523i
$371$	−512.251	+	166.441i	−1.38073	+	0.448627i
$372$		0			0
$373$	440.608			1.18125			0.590627	−	0.806944i	$-0.298880\pi$
$373$	440.608			1.18125			0.590627	+	0.806944i	$0.298880\pi$
$374$	−82.3854	+	151.461i	−0.220282	+	0.404976i
$375$		0			0
$376$	442.955	−	321.826i	1.17807	−	0.855919i
$377$	−214.832	+	69.8031i	−0.569846	+	0.185154i
$378$		0			0
$379$	−450.261	−	327.134i	−1.18802	−	0.863149i	−0.194969	−	0.980809i	$-0.562461\pi$
$379$	−450.261	−	327.134i	−1.18802	−	0.863149i	−0.993054	+	0.117660i	$0.962461\pi$
$380$	−154.810	+	213.078i	−0.407395	+	0.560731i
$381$		0			0
$382$	75.3106	+	231.782i	0.197148	+	0.606760i
$383$	−73.8657	−	101.667i	−0.192861	−	0.265450i	0.701625	−	0.712546i	$-0.252458\pi$
$383$	−73.8657	−	101.667i	−0.192861	−	0.265450i	−0.894486	+	0.447096i	$0.852458\pi$
$384$		0			0
$385$	189.020	−	24.7392i	0.490961	−	0.0642577i
$386$		−	103.552i		−	0.268270i
$387$		0			0
$388$	220.161	+	677.587i	0.567426	+	1.74636i
$389$	63.8640	+	20.7507i	0.164175	+	0.0533437i	0.389951	−	0.920835i	$-0.372492\pi$
$389$	63.8640	+	20.7507i	0.164175	+	0.0533437i	−0.225776	+	0.974179i	$0.572492\pi$
$390$		0			0
$391$	−142.964	−	103.869i	−0.365636	−	0.265650i
$392$	−556.190	−	180.717i	−1.41885	−	0.461013i
$393$		0			0
$394$	−434.683	+	315.816i	−1.10326	+	0.801563i
$395$		−	101.897i		−	0.257967i
$396$		0			0
$397$	342.588			0.862942			0.431471	−	0.902127i	$-0.357995\pi$
$397$	342.588			0.862942			0.431471	+	0.902127i	$0.357995\pi$
$398$	−373.180	−	513.638i	−0.937638	−	1.29055i
$399$		0			0
$400$	7.44798	−	22.9225i	0.0186200	−	0.0573063i
$401$	217.794	−	299.767i	0.543126	−	0.747549i	−0.445933	−	0.895066i	$-0.647128\pi$
$401$	217.794	−	299.767i	0.543126	−	0.747549i	0.989060	+	0.147517i	$0.0471281\pi$
$402$		0			0
$403$	−166.096	+	511.190i	−0.412148	+	1.26846i
$404$	−729.701	+	237.094i	−1.80619	+	0.586867i
$405$		0			0
$406$	−865.735			−2.13235
$407$	96.8263	+	102.189i	0.237902	+	0.251078i
$408$		0			0
$409$	259.018	−	188.188i	0.633296	−	0.460116i	−0.224245	−	0.974533i	$-0.571991\pi$
$409$	259.018	−	188.188i	0.633296	−	0.460116i	0.857540	+	0.514417i	$0.171991\pi$
$410$	−61.2143	+	19.8897i	−0.149303	+	0.0485115i
$411$		0			0
$412$	−582.663	−	423.329i	−1.41423	−	1.02750i
$413$	−154.065	+	212.053i	−0.373040	+	0.513445i
$414$		0			0
$415$	−20.7650	−	63.9080i	−0.0500361	−	0.153995i
$416$	−164.150	−	225.932i	−0.394590	−	0.543107i
$417$		0			0
$418$	−386.031	−	810.912i	−0.923519	−	1.93998i
$419$			574.973i			1.37225i	0.727483	+	0.686126i	$0.240690\pi$
$419$			574.973i			1.37225i	−0.727483	+	0.686126i	$0.759310\pi$
$420$		0			0
$421$	43.7992	+	134.800i	0.104036	+	0.320190i	0.989503	−	0.144512i	$-0.0461613\pi$
$421$	43.7992	+	134.800i	0.104036	+	0.320190i	−0.885467	+	0.464702i	$0.846161\pi$
$422$	564.210	+	183.323i	1.33699	+	0.434415i
$423$		0			0
$424$	337.647	+	245.315i	0.796336	+	0.578572i
$425$	−102.896	−	33.4330i	−0.242108	−	0.0786658i
$426$		0			0
$427$	389.398	−	282.914i	0.911940	−	0.662563i
$428$		−	284.542i		−	0.664817i
$429$		0			0
$430$	102.111			0.237467
$431$	−230.211	−	316.859i	−0.534133	−	0.735171i	0.453620	−	0.891195i	$-0.350132\pi$
$431$	−230.211	−	316.859i	−0.534133	−	0.735171i	−0.987753	+	0.156024i	$0.950132\pi$
$432$		0			0
$433$	−106.300	+	327.159i	−0.245497	+	0.755564i	0.750057	+	0.661373i	$0.230026\pi$
$433$	−106.300	+	327.159i	−0.245497	+	0.755564i	−0.995554	+	0.0941901i	$0.969974\pi$
$434$	−1210.84	+	1666.58i	−2.78996	+	3.84005i
$435$		0			0
$436$	−153.368	+	472.018i	−0.351761	+	1.08261i
$437$	875.429	−	284.444i	2.00327	−	0.650902i
$438$		0			0
$439$	36.1143			0.0822650			0.0411325	−	0.999154i	$-0.486903\pi$
$439$	36.1143			0.0822650			0.0411325	+	0.999154i	$0.486903\pi$
$440$	−101.599	−	107.225i	−0.230906	−	0.243694i
$441$		0			0
$442$	117.147	−	85.1126i	0.265039	−	0.192562i
$443$	363.367	−	118.065i	0.820241	−	0.266512i	0.131312	−	0.991341i	$-0.458081\pi$
$443$	363.367	−	118.065i	0.820241	−	0.266512i	0.688929	+	0.724829i	$0.258081\pi$
$444$		0			0
$445$	143.185	+	104.030i	0.321765	+	0.233776i
$446$	−219.186	+	301.683i	−0.491448	+	0.676420i
$447$		0			0
$448$	−345.177	−	1062.34i	−0.770484	−	2.37130i
$449$	−18.0511	−	24.8453i	−0.0402030	−	0.0553347i	0.788442	−	0.615109i	$-0.210888\pi$
$449$	−18.0511	−	24.8453i	−0.0402030	−	0.0553347i	−0.828645	+	0.559774i	$0.810888\pi$
$450$		0			0
$451$	24.9921	−	134.277i	0.0554149	−	0.297732i
$452$		−	23.2120i		−	0.0513540i
$453$		0			0
$454$	−234.960	−	723.132i	−0.517533	−	1.59280i
$455$	−152.264	−	49.4734i	−0.334645	−	0.108733i
$456$		0			0
$457$	−333.880	−	242.578i	−0.730592	−	0.530806i	0.159159	−	0.987253i	$-0.449122\pi$
$457$	−333.880	−	242.578i	−0.730592	−	0.530806i	−0.889751	+	0.456447i	$0.849122\pi$
$458$	431.074	+	140.064i	0.941209	+	0.305817i
$459$		0			0
$460$	311.601	−	226.391i	0.677394	−	0.492155i
$461$		−	765.072i		−	1.65959i	−0.558066	−	0.829797i	$-0.688456\pi$
$461$		−	765.072i		−	1.65959i	0.558066	−	0.829797i	$-0.311544\pi$
$462$		0			0
$463$	113.587			0.245328			0.122664	−	0.992448i	$-0.460856\pi$
$463$	113.587			0.245328			0.122664	+	0.992448i	$0.460856\pi$
$464$	15.4212	+	21.2255i	0.0332354	+	0.0457445i
$465$		0			0
$466$	119.212	−	366.897i	0.255820	−	0.787334i
$467$	444.846	−	612.278i	0.952561	−	1.31109i	0.00218113	−	0.999998i	$-0.499306\pi$
$467$	444.846	−	612.278i	0.952561	−	1.31109i	0.950380	−	0.311091i	$-0.100694\pi$
$468$		0			0
$469$	−111.249	+	342.390i	−0.237205	+	0.730042i
$470$	320.186	−	104.035i	0.681247	−	0.221351i
$471$		0			0
$472$	203.102			0.430301
$473$	−103.536	+	190.346i	−0.218892	+	0.402422i
$474$		0			0
$475$	455.929	−	331.252i	0.959851	−	0.697372i
$476$	328.456	−	106.722i	0.690033	−	0.224205i
$477$		0			0
$478$	759.072	+	551.498i	1.58802	+	1.15376i
$479$	214.285	−	294.937i	0.447358	−	0.615736i	−0.524469	−	0.851429i	$-0.675736\pi$
$479$	214.285	−	294.937i	0.447358	−	0.615736i	0.971827	+	0.235694i	$0.0757362\pi$
$480$		0			0
$481$	−36.5346	−	112.442i	−0.0759555	−	0.233767i
$482$	220.965	+	304.133i	0.458434	+	0.630981i
$483$		0			0
$484$	770.594	−	205.228i	1.59214	−	0.424026i
$485$			172.195i			0.355042i
$486$		0			0
$487$	−74.1795	−	228.301i	−0.152319	−	0.468790i	0.845560	−	0.533880i	$-0.179267\pi$
$487$	−74.1795	−	228.301i	−0.152319	−	0.468790i	−0.997879	+	0.0650898i	$0.979267\pi$
$488$	−354.708	−	115.251i	−0.726860	−	0.236171i
$489$		0			0
$490$	−290.917	−	211.363i	−0.593708	−	0.431354i
$491$	−796.791	−	258.893i	−1.62279	−	0.527277i	−0.650194	−	0.759768i	$-0.725312\pi$
$491$	−796.791	−	258.893i	−1.62279	−	0.527277i	−0.972599	+	0.232491i	$0.925312\pi$
$492$		0			0
$493$	95.2782	−	69.2236i	0.193262	−	0.140413i
$494$			754.262i			1.52685i
$495$		0			0
$496$	62.4286			0.125864
$497$	479.233	+	659.607i	0.964251	+	1.32718i
$498$		0			0
$499$	199.212	−	613.111i	0.399222	−	1.22868i	−0.526403	−	0.850235i	$-0.676460\pi$
$499$	199.212	−	613.111i	0.399222	−	1.22868i	0.925624	−	0.378443i	$-0.123540\pi$
$500$	292.870	−	403.101i	0.585740	−	0.806202i
$501$		0			0
$502$	34.6334	−	106.591i	0.0689907	−	0.212332i
$503$	−9.99329	+	3.24702i	−0.0198674	+	0.00645530i	−0.318934	−	0.947777i	$-0.603325\pi$
$503$	−9.99329	+	3.24702i	−0.0198674	+	0.00645530i	0.299066	+	0.954232i	$0.403325\pi$
$504$		0			0
$505$	−185.439			−0.367206
$506$	170.443	+	1302.27i	0.336844	+	2.57366i
$507$		0			0
$508$	−1266.78	+	920.372i	−2.49367	+	1.81176i
$509$	870.887	−	282.968i	1.71098	−	0.555930i	0.720481	−	0.693475i	$-0.243921\pi$
$509$	870.887	−	282.968i	1.71098	−	0.555930i	0.990496	+	0.137545i	$0.0439211\pi$
$510$		0			0
$511$	364.190	+	264.600i	0.712701	+	0.517808i
$512$	−40.3331	+	55.5138i	−0.0787757	+	0.108425i
$513$		0			0
$514$	209.586	+	645.038i	0.407754	+	1.25494i
$515$	−102.315	−	140.825i	−0.198671	−	0.273447i
$516$		0			0
$517$	−130.723	+	702.347i	−0.252849	+	1.35851i
$518$		−	453.121i		−	0.874752i
$519$		0			0
$520$	38.3354	+	117.984i	0.0737219	+	0.226893i
$521$	−224.438	−	72.9245i	−0.430784	−	0.139970i	0.0855957	−	0.996330i	$-0.472721\pi$
$521$	−224.438	−	72.9245i	−0.430784	−	0.139970i	−0.516380	+	0.856360i	$0.672721\pi$
$522$		0			0
$523$	122.429	+	88.9499i	0.234090	+	0.170076i	0.698646	−	0.715467i	$-0.253786\pi$
$523$	122.429	+	88.9499i	0.234090	+	0.170076i	−0.464556	+	0.885544i	$0.653786\pi$
$524$	−407.313	−	132.344i	−0.777314	−	0.252565i
$525$		0			0
$526$	−607.916	+	441.677i	−1.15573	+	0.839689i
$527$		−	280.233i		−	0.531752i
$528$		0			0
$529$	−817.095			−1.54460
$530$	150.840	+	207.614i	0.284604	+	0.391724i
$531$		0			0
$532$	−555.904	+	1710.90i	−1.04493	+	3.21597i
$533$	−67.4233	+	92.8002i	−0.126498	+	0.174109i
$534$		0			0
$535$	21.2516	−	65.4056i	0.0397226	−	0.122253i
$536$	265.307	−	86.2035i	0.494976	−	0.160827i
$537$		0			0
$538$	36.0716			0.0670477
$539$	688.981	−	327.986i	1.27826	−	0.608509i
$540$		0			0
$541$	−243.056	+	176.591i	−0.449272	+	0.326415i	−0.789308	−	0.613997i	$-0.789561\pi$
$541$	−243.056	+	176.591i	−0.449272	+	0.326415i	0.340036	+	0.940412i	$0.389561\pi$
$542$	−311.962	+	101.363i	−0.575576	+	0.187016i
$543$		0			0
$544$	117.794	+	85.5821i	0.216533	+	0.157320i
$545$	−70.5072	+	97.0448i	−0.129371	+	0.178064i
$546$		0			0
$547$	−100.418	−	309.055i	−0.183580	−	0.565001i	0.816341	−	0.577570i	$-0.195999\pi$
$547$	−100.418	−	309.055i	−0.183580	−	0.565001i	−0.999921	+	0.0125693i	$0.995999\pi$
$548$	−486.214	−	669.216i	−0.887252	−	1.22120i
$549$		0			0
$550$	345.627	+	726.038i	0.628413	+	1.32007i
$551$			613.455i			1.11335i
$552$		0			0
$553$	−215.071	−	661.919i	−0.388916	−	1.19696i
$554$	−165.325	−	53.7173i	−0.298420	−	0.0969626i
$555$		0			0
$556$	447.620	+	325.215i	0.805072	+	0.584919i
$557$	−43.0763	−	13.9963i	−0.0773363	−	0.0251281i	0.270093	−	0.962834i	$-0.412945\pi$
$557$	−43.0763	−	13.9963i	−0.0773363	−	0.0251281i	−0.347430	+	0.937706i	$0.612945\pi$
$558$		0			0
$559$	147.223	−	106.963i	0.263368	−	0.191348i
$560$			18.5950i			0.0332054i
$561$		0			0
$562$	1201.67			2.13820
$563$	−428.403	−	589.646i	−0.760928	−	1.04733i	−0.997136	−	0.0756257i	$-0.975905\pi$
$563$	−428.403	−	589.646i	−0.760928	−	1.04733i	0.236208	−	0.971703i	$-0.424095\pi$
$564$		0			0
$565$	1.73363	−	5.33558i	0.00306838	−	0.00944350i
$566$	461.115	−	634.670i	0.814690	−	1.12132i
$567$		0			0
$568$	195.226	−	600.844i	0.343708	−	1.05782i
$569$	138.993	−	45.1615i	0.244276	−	0.0793700i	−0.184320	−	0.982866i	$-0.559008\pi$
$569$	138.993	−	45.1615i	0.244276	−	0.0793700i	0.428596	+	0.903496i	$0.359008\pi$
$570$		0			0
$571$	398.941			0.698672			0.349336	−	0.936998i	$-0.386407\pi$
$571$	398.941			0.698672			0.349336	+	0.936998i	$0.386407\pi$
$572$	−658.422	−	122.548i	−1.15109	−	0.214244i
$573$		0			0
$574$	−355.665	+	258.406i	−0.619626	+	0.450184i
$575$	−783.803	+	254.673i	−1.36314	+	0.442909i
$576$		0			0
$577$	−204.268	−	148.409i	−0.354017	−	0.257209i	0.396535	−	0.918020i	$-0.370212\pi$
$577$	−204.268	−	148.409i	−0.354017	−	0.257209i	−0.750552	+	0.660811i	$0.770212\pi$
$578$	508.435	−	699.800i	0.879644	−	1.21073i
$579$		0			0
$580$	79.3217	+	244.127i	0.136761	+	0.420909i
$581$	−269.777	−	371.316i	−0.464332	−	0.639098i
$582$		0			0
$583$	−539.960	+	70.6707i	−0.926174	+	0.121219i
$584$		−	348.818i		−	0.597290i
$585$		0			0
$586$	−55.4407	−	170.629i	−0.0946086	−	0.291175i
$587$	−937.333	−	304.558i	−1.59682	−	0.518838i	−0.630501	−	0.776188i	$-0.717151\pi$
$587$	−937.333	−	304.558i	−1.59682	−	0.518838i	−0.966318	+	0.257350i	$0.917151\pi$
$588$		0			0
$589$	1180.93	+	857.996i	2.00498	+	1.45670i
$590$	118.772	+	38.5914i	0.201309	+	0.0654092i
$591$		0			0
$592$	−11.1093	+	8.07139i	−0.0187657	+	0.0136341i
$593$			795.418i			1.34135i	0.741753	+	0.670673i	$0.233995\pi$
$593$			795.418i			1.34135i	−0.741753	+	0.670673i	$0.766005\pi$
$594$		0			0
$595$	83.4705			0.140287
$596$	809.016	+	1113.51i	1.35741	+	1.86831i
$597$		0			0
$598$	340.852	−	1049.03i	0.569986	−	1.75424i
$599$	67.5385	−	92.9587i	0.112752	−	0.155190i	−0.748911	−	0.662670i	$-0.769423\pi$
$599$	67.5385	−	92.9587i	0.112752	−	0.155190i	0.861663	+	0.507480i	$0.169423\pi$
$600$		0			0
$601$	−91.0388	+	280.189i	−0.151479	+	0.466204i	−0.997787	−	0.0664894i	$-0.978820\pi$
$601$	−91.0388	+	280.189i	−0.151479	+	0.466204i	0.846308	+	0.532694i	$0.178820\pi$
$602$	663.309	−	215.522i	1.10184	−	0.358010i
$603$		0			0
$604$	−409.336			−0.677708
$605$	192.459	+	10.3789i	0.318114	+	0.0171553i
$606$		0			0
$607$	352.020	−	255.758i	0.579934	−	0.421347i	−0.258766	−	0.965940i	$-0.583316\pi$
$607$	352.020	−	255.758i	0.579934	−	0.421347i	0.838700	+	0.544593i	$0.183316\pi$
$608$	−721.303	+	234.366i	−1.18635	+	0.385470i
$609$		0			0
$610$	−185.531	−	134.796i	−0.304149	−	0.220977i
$611$	352.662	−	485.398i	0.577189	−	0.794432i
$612$		0			0
$613$	194.113	+	597.417i	0.316660	+	0.974579i	0.975066	+	0.221916i	$0.0712310\pi$
$613$	194.113	+	597.417i	0.316660	+	0.974579i	−0.658406	+	0.752663i	$0.728769\pi$
$614$	23.9303	+	32.9372i	0.0389744	+	0.0536436i
$615$		0			0
$616$	−886.299	−	482.091i	−1.43880	−	0.782616i
$617$			215.080i			0.348590i	0.984694	+	0.174295i	$0.0557646\pi$
$617$			215.080i			0.348590i	−0.984694	+	0.174295i	$0.944235\pi$
$618$		0			0
$619$	−295.694	−	910.053i	−0.477697	−	1.47020i	−0.842286	−	0.539031i	$-0.818791\pi$
$619$	−295.694	−	910.053i	−0.477697	−	1.47020i	0.364589	−	0.931168i	$-0.381209\pi$
$620$	580.897	+	188.745i	0.936931	+	0.304427i
$621$		0			0
$622$	−567.802	−	412.532i	−0.912865	−	0.663235i
$623$	1149.70	+	373.560i	1.84542	+	0.599614i
$624$		0			0
$625$	−356.892	+	259.297i	−0.571027	+	0.414875i
$626$			1417.73i			2.26474i
$627$		0			0
$628$	707.585			1.12673
$629$	36.2313	+	49.8681i	0.0576015	+	0.0792816i
$630$		0			0
$631$	−197.152	+	606.771i	−0.312443	+	0.961602i	0.664351	+	0.747421i	$0.268708\pi$
$631$	−197.152	+	606.771i	−0.312443	+	0.961602i	−0.976794	+	0.214181i	$0.931292\pi$
$632$	−316.990	+	436.299i	−0.501566	+	0.690346i
$633$		0			0
$634$	315.585	−	971.271i	0.497768	−	1.53197i
$635$	−359.926	+	116.947i	−0.566813	+	0.184169i
$636$		0			0
$637$	−640.849			−1.00604
$638$	−860.523	−	160.163i	−1.34878	−	0.251040i
$639$		0			0
$640$	−274.741	+	199.611i	−0.429282	+	0.311892i
$641$	−911.311	+	296.103i	−1.42170	+	0.461939i	−0.916143	−	0.400853i	$-0.868714\pi$
$641$	−911.311	+	296.103i	−1.42170	+	0.461939i	−0.505560	+	0.862792i	$0.668714\pi$
$642$		0			0
$643$	238.550	+	173.317i	0.370995	+	0.269544i	0.757623	−	0.652692i	$-0.226360\pi$
$643$	238.550	+	173.317i	0.370995	+	0.269544i	−0.386628	+	0.922236i	$0.626360\pi$
$644$	1546.31	−	2128.32i	2.40111	−	3.30484i
$645$		0			0
$646$	−121.520	−	374.000i	−0.188112	−	0.578948i
$647$	590.791	+	813.155i	0.913124	+	1.25681i	0.966088	+	0.258211i	$0.0831331\pi$
$647$	590.791	+	813.155i	0.913124	+	1.25681i	−0.0529642	+	0.998596i	$0.516867\pi$
$648$		0			0
$649$	−192.368	+	182.274i	−0.296407	+	0.280853i
$650$		−	675.317i		−	1.03895i
$651$		0			0
$652$	−414.235	−	1274.88i	−0.635329	−	1.95534i
$653$	984.939	+	320.026i	1.50833	+	0.490086i	0.942434	−	0.334392i	$-0.108531\pi$
$653$	984.939	+	320.026i	1.50833	+	0.490086i	0.565895	+	0.824477i	$0.308531\pi$
$654$		0			0
$655$	−83.7417	−	60.8419i	−0.127850	−	0.0928884i
$656$	12.6708	+	4.11700i	0.0193153	+	0.00627591i
$657$		0			0
$658$	1860.33	−	1351.61i	2.82725	−	2.05412i
$659$			572.524i			0.868777i	0.900726	+	0.434388i	$0.143035\pi$
$659$			572.524i			0.868777i	−0.900726	+	0.434388i	$0.856965\pi$
$660$		0			0
$661$	−717.443			−1.08539			−0.542695	−	0.839930i	$-0.682596\pi$
$661$	−717.443			−1.08539			−0.542695	+	0.839930i	$0.682596\pi$
$662$	−132.951	−	182.991i	−0.200832	−	0.276421i
$663$		0			0
$664$	−109.900	+	338.236i	−0.165511	+	0.509392i
$665$	−255.564	+	351.753i	−0.384306	+	0.528952i
$666$		0			0
$667$	277.221	−	853.198i	0.415624	−	1.27916i
$668$	−1981.12	+	643.706i	−2.96575	+	0.963632i
$669$		0			0
$670$	171.529			0.256013
$671$	439.394	−	209.171i	0.654834	−	0.311731i
$672$		0			0
$673$	705.491	−	512.569i	1.04828	−	0.761619i	0.0763941	−	0.997078i	$-0.475659\pi$
$673$	705.491	−	512.569i	1.04828	−	0.761619i	0.971884	+	0.235459i	$0.0756593\pi$
$674$	336.722	−	109.408i	0.499587	−	0.162326i
$675$		0			0
$676$	−446.042	−	324.068i	−0.659825	−	0.479391i
$677$	−750.046	+	1032.35i	−1.10790	+	1.52489i	−0.283418	+	0.958997i	$0.591468\pi$
$677$	−750.046	+	1032.35i	−1.10790	+	1.52489i	−0.824479	+	0.565893i	$0.808532\pi$
$678$		0			0
$679$	363.447	+	1118.57i	0.535268	+	1.64738i
$680$	−38.0171	−	52.3261i	−0.0559076	−	0.0769502i
$681$		0			0
$682$	−1511.87	+	1432.54i	−2.21682	+	2.10050i
$683$			411.727i			0.602822i	0.953494	+	0.301411i	$0.0974575\pi$
$683$			411.727i			0.602822i	−0.953494	+	0.301411i	$0.902542\pi$
$684$		0			0
$685$	−61.7808	−	190.142i	−0.0901910	−	0.277579i
$686$	−685.911	−	222.866i	−0.999871	−	0.324878i
$687$		0			0
$688$	−17.0994	−	12.4235i	−0.0248538	−	0.0180574i
$689$	434.960	+	141.327i	0.631292	+	0.205119i
$690$		0			0
$691$	673.521	−	489.342i	0.974705	−	0.708165i	0.0181860	−	0.999835i	$-0.494211\pi$
$691$	673.521	−	489.342i	0.974705	−	0.708165i	0.956519	+	0.291670i	$0.0942109\pi$
$692$		−	751.325i		−	1.08573i
$693$		0			0
$694$	1245.92			1.79528
$695$	78.6019	+	108.186i	0.113096	+	0.155664i
$696$		0			0
$697$	18.4806	−	56.8775i	0.0265145	−	0.0816034i
$698$	844.752	−	1162.70i	1.21025	−	1.66576i
$699$		0			0
$700$	497.721	−	1531.83i	0.711029	−	2.18832i
$701$	−86.3690	+	28.0630i	−0.123208	+	0.0400328i	−0.369972	−	0.929043i	$-0.620633\pi$
$701$	−86.3690	+	28.0630i	−0.123208	+	0.0400328i	0.246764	+	0.969076i	$0.420633\pi$
$702$		0			0
$703$	−321.080			−0.456728
$704$	−146.562	−	1119.81i	−0.208185	−	1.59064i
$705$		0			0
$706$	−625.517	+	454.465i	−0.886001	+	0.643718i
$707$	−1204.61	+	391.400i	−1.70383	+	0.553607i
$708$		0			0
$709$	553.750	+	402.323i	0.781030	+	0.567451i	0.905288	−	0.424799i	$-0.139655\pi$
$709$	553.750	+	402.323i	0.781030	+	0.567451i	−0.124258	+	0.992250i	$0.539655\pi$
$710$	228.333	−	314.273i	0.321596	−	0.442638i
$711$		0			0
$712$	−289.459	−	890.865i	−0.406544	−	1.25121i
$713$	−1254.72	−	1726.97i	−1.75977	−	2.42212i
$714$		0			0
$715$	−142.194	−	77.3447i	−0.198873	−	0.108174i
$716$			960.795i			1.34189i
$717$		0			0
$718$	387.919	+	1193.89i	0.540277	+	1.66280i
$719$	−1185.83	−	385.298i	−1.64927	−	0.535880i	−0.670689	−	0.741739i	$-0.734001\pi$
$719$	−1185.83	−	385.298i	−1.64927	−	0.535880i	−0.978582	+	0.205859i	$0.934001\pi$
$720$		0			0
$721$	−961.871	−	698.840i	−1.33408	−	0.969266i
$722$	830.829	+	269.953i	1.15073	+	0.373896i
$723$		0			0
$724$	−1853.39	+	1346.57i	−2.55993	+	1.85990i
$725$		−	549.248i		−	0.757583i
$726$		0			0
$727$	−837.811			−1.15242			−0.576211	−	0.817301i	$-0.695469\pi$
$727$	−837.811			−1.15242			−0.576211	+	0.817301i	$0.695469\pi$
$728$	498.050	+	685.507i	0.684135	+	0.941631i
$729$		0			0
$730$	66.2788	−	203.985i	0.0907929	−	0.279432i
$731$	−55.7672	+	76.7570i	−0.0762889	+	0.105003i
$732$		0			0
$733$	−19.4439	+	59.8422i	−0.0265265	+	0.0816401i	−0.963443	−	0.267912i	$-0.913666\pi$
$733$	−19.4439	+	59.8422i	−0.0265265	+	0.0816401i	0.936917	+	0.349552i	$0.113666\pi$
$734$	−477.478	+	155.142i	−0.650515	+	0.211365i
$735$		0			0
$736$	1109.10			1.50694
$737$	−173.922	+	319.747i	−0.235987	+	0.433850i
$738$		0			0
$739$	−954.793	+	693.698i	−1.29201	+	0.938698i	−0.999844	−	0.0176705i	$-0.994375\pi$
$739$	−954.793	+	693.698i	−1.29201	+	0.938698i	−0.292163	+	0.956369i	$0.594375\pi$
$740$	−127.775	+	41.5166i	−0.172669	+	0.0561035i
$741$		0			0
$742$	1418.06	+	1030.28i	1.91113	+	1.38852i
$743$	−291.584	+	401.331i	−0.392441	+	0.540149i	−0.958827	−	0.283991i	$-0.908341\pi$
$743$	−291.584	+	401.331i	−0.392441	+	0.540149i	0.566386	+	0.824140i	$0.308341\pi$
$744$		0			0
$745$	102.798	+	316.379i	0.137983	+	0.424669i
$746$	−842.811	−	1160.03i	−1.12977	−	1.55500i
$747$		0			0
$748$	346.222	−	45.3141i	0.462864	−	0.0605803i
$749$		−	469.727i		−	0.627139i
$750$		0			0
$751$	126.227	+	388.487i	0.168079	+	0.517293i	0.999250	−	0.0387234i	$-0.0123291\pi$
$751$	126.227	+	388.487i	0.168079	+	0.517293i	−0.831171	+	0.556017i	$0.812329\pi$
$752$	−66.2757	−	21.5343i	−0.0881326	−	0.0286360i
$753$		0			0
$754$	594.715	+	432.086i	0.788747	+	0.573058i
$755$	−94.0911	−	30.5720i	−0.124624	−	0.0404928i
$756$		0			0
$757$	613.228	−	445.536i	0.810077	−	0.588555i	−0.103776	−	0.994601i	$-0.533093\pi$
$757$	613.228	−	445.536i	0.810077	−	0.588555i	0.913853	+	0.406045i	$0.133093\pi$
$758$			1811.20i			2.38944i
$759$		0			0
$760$	336.905			0.443297
$761$	795.597	+	1095.05i	1.04546	+	1.43896i	0.892677	+	0.450697i	$0.148825\pi$
$761$	795.597	+	1095.05i	1.04546	+	1.43896i	0.152786	+	0.988259i	$0.451175\pi$
$762$		0			0
$763$	−253.183	+	779.216i	−0.331825	+	1.02125i
$764$	290.104	−	399.294i	0.379718	−	0.522637i
$765$		0			0
$766$	−126.376	+	388.946i	−0.164982	+	0.507763i
$767$	211.670	−	68.7757i	0.275971	−	0.0896685i
$768$		0			0
$769$	550.877			0.716355			0.358178	−	0.933654i	$-0.383398\pi$
$769$	550.877			0.716355			0.358178	+	0.933654i	$0.383398\pi$
$770$	−426.697	−	450.328i	−0.554152	−	0.584842i
$771$		0			0
$772$	−169.660	+	123.265i	−0.219766	+	0.159670i
$773$	841.817	−	273.523i	1.08903	−	0.353846i	0.291156	−	0.956676i	$-0.405960\pi$
$773$	841.817	−	273.523i	1.08903	−	0.353846i	0.797870	+	0.602830i	$0.205960\pi$
$774$		0			0
$775$	−1057.33	−	768.194i	−1.36429	−	0.991218i
$776$	535.679	−	737.299i	0.690309	−	0.950128i
$777$		0			0
$778$	−67.5292	−	207.833i	−0.0867984	−	0.267138i
$779$	183.105	+	252.023i	0.235051	+	0.323521i
$780$		0			0
$781$	354.319	+	744.296i	0.453673	+	0.953004i
$782$			575.078i			0.735394i
$783$		0			0
$784$	23.0009	+	70.7896i	0.0293379	+	0.0902928i
$785$	162.648	+	52.8474i	0.207194	+	0.0673216i
$786$		0			0
$787$	−1198.79	−	870.971i	−1.52324	−	1.10670i	−0.959853	−	0.280504i	$-0.909498\pi$
$787$	−1198.79	−	870.971i	−1.52324	−	1.10670i	−0.563386	−	0.826194i	$-0.690502\pi$
$788$	1034.86	+	336.248i	1.31328	+	0.426710i
$789$		0			0
$790$	−268.274	+	194.912i	−0.339587	+	0.246724i
$791$		−	38.3188i		−	0.0484435i
$792$		0			0
$793$	−408.698			−0.515382
$794$	−655.314	−	901.963i	−0.825333	−	1.13597i
$795$		0			0
$796$	−397.323	+	1222.83i	−0.499149	+	1.53622i
$797$	40.8253	−	56.1913i	0.0512238	−	0.0705035i	−0.782637	−	0.622479i	$-0.786126\pi$
$797$	40.8253	−	56.1913i	0.0512238	−	0.0705035i	0.833860	+	0.551975i	$0.186126\pi$
$798$		0			0
$799$	−96.6644	+	297.502i	−0.120982	+	0.372343i
$800$	645.808	−	209.836i	0.807260	−	0.262295i
$801$		0			0
$802$	−1205.83			−1.50353
$803$	313.046	+	330.383i	0.389846	+	0.411436i
$804$		0			0
$805$	514.397	−	373.731i	0.639003	−	0.464263i
$806$	1663.57	−	540.527i	2.06398	−	0.670629i
$807$		0			0
$808$	794.006	+	576.879i	0.982681	+	0.713960i
$809$	518.029	−	713.006i	0.640333	−	0.881343i	−0.358300	−	0.933606i	$-0.616644\pi$
$809$	518.029	−	713.006i	0.640333	−	0.881343i	0.998633	+	0.0522635i	$0.0166436\pi$
$810$		0			0
$811$	324.072	+	997.392i	0.399596	+	1.22983i	0.925324	+	0.379177i	$0.123793\pi$
$811$	324.072	+	997.392i	0.399596	+	1.22983i	−0.525728	+	0.850653i	$0.676207\pi$
$812$	1030.54	+	1418.42i	1.26914	+	1.74682i
$813$		0			0
$814$	83.8287	−	450.394i	0.102984	−	0.553309i
$815$		−	323.986i		−	0.397529i
$816$		0			0
$817$	−152.718	−	470.017i	−0.186925	−	0.575296i
$818$	−990.917	−	321.969i	−1.21139	−	0.393605i
$819$		0			0
$820$	105.455	+	76.6173i	0.128603	+	0.0934357i
$821$	935.538	+	303.975i	1.13951	+	0.370249i	0.817182	−	0.576379i	$-0.195535\pi$
$821$	935.538	+	303.975i	1.13951	+	0.370249i	0.322327	+	0.946628i	$0.395535\pi$
$822$		0			0
$823$	790.703	−	574.479i	0.960757	−	0.698030i	0.00743019	−	0.999972i	$-0.497635\pi$
$823$	790.703	−	574.479i	0.960757	−	0.698030i	0.953326	+	0.301942i	$0.0976349\pi$
$824$			921.270i			1.11805i
$825$		0			0
$826$	852.993			1.03268
$827$	−13.9507	−	19.2015i	−0.0168690	−	0.0232182i	0.800499	−	0.599334i	$-0.204568\pi$
$827$	−13.9507	−	19.2015i	−0.0168690	−	0.0232182i	−0.817368	+	0.576116i	$0.804568\pi$
$828$		0			0
$829$	280.708	−	863.929i	0.338610	−	1.04213i	−0.626306	−	0.779577i	$-0.715434\pi$
$829$	280.708	−	863.929i	0.338610	−	1.04213i	0.964916	−	0.262557i	$-0.0845659\pi$
$830$	−128.537	+	176.915i	−0.154863	+	0.213151i
$831$		0			0
$832$	−293.095	+	902.052i	−0.352277	+	1.08420i
$833$	317.765	−	103.248i	0.381470	−	0.123947i
$834$		0			0
$835$	−503.463			−0.602950
$836$	−869.078	+	1597.75i	−1.03957	+	1.91119i
$837$		0			0
$838$	1513.79	−	1099.83i	1.80643	−	1.31245i
$839$	741.834	−	241.036i	0.884188	−	0.287290i	0.168493	−	0.985703i	$-0.446110\pi$
$839$	741.834	−	241.036i	0.884188	−	0.287290i	0.715695	+	0.698413i	$0.246110\pi$
$840$		0			0
$841$	−196.691	−	142.904i	−0.233877	−	0.169922i
$842$	271.120	−	373.164i	0.321995	−	0.443188i
$843$		0			0
$844$	−371.260	−	1142.62i	−0.439882	−	1.35382i
$845$	−78.3248	−	107.805i	−0.0926920	−	0.127580i
$846$		0			0
$847$	1272.11	−	338.795i	1.50190	−	0.399994i
$848$		−	53.1191i		−	0.0626404i
$849$		0			0
$850$	108.801	+	334.856i	0.128001	+	0.393948i
$851$	446.560	+	145.096i	0.524747	+	0.170501i
$852$		0			0
$853$	519.837	+	377.684i	0.609422	+	0.442771i	0.849211	−	0.528054i	$-0.177078\pi$
$853$	519.837	+	377.684i	0.609422	+	0.442771i	−0.239789	+	0.970825i	$0.577078\pi$
$854$	−1489.71	−	484.036i	−1.74439	−	0.566787i
$855$		0			0
$856$	−294.463	+	213.940i	−0.343999	+	0.249930i
$857$		−	442.968i		−	0.516883i	−0.966027	−	0.258441i	$-0.916791\pi$
$857$		−	442.968i		−	0.516883i	0.966027	−	0.258441i	$-0.0832088\pi$
$858$		0			0
$859$	−95.7522			−0.111469			−0.0557347	−	0.998446i	$-0.517750\pi$
$859$	−95.7522			−0.111469			−0.0557347	+	0.998446i	$0.517750\pi$
$860$	−121.549	−	167.298i	−0.141336	−	0.194533i
$861$		0			0
$862$	−393.867	+	1212.20i	−0.456922	+	1.40626i
$863$	−338.902	+	466.459i	−0.392702	+	0.540508i	−0.958894	−	0.283765i	$-0.908416\pi$
$863$	−338.902	+	466.459i	−0.392702	+	0.540508i	0.566191	+	0.824274i	$0.308416\pi$
$864$		0			0
$865$	56.1142	−	172.702i	0.0648719	−	0.199655i
$866$	1064.68	−	345.934i	1.22942	−	0.399462i
$867$		0			0
$868$	4171.86			4.80630
$869$	−91.3190	−	697.723i	−0.105085	−	0.802903i
$870$		0			0
$871$	247.308	−	179.680i	0.283936	−	0.206292i
$872$	603.790	−	196.183i	0.692419	−	0.224981i
$873$		0			0
$874$	−2423.43	−	1760.73i	−2.77281	−	2.01456i
$875$	483.476	−	665.447i	0.552544	−	0.760511i
$876$		0			0
$877$	−280.986	−	864.787i	−0.320395	−	0.986074i	−0.973477	−	0.228786i	$-0.926524\pi$
$877$	−280.986	−	864.787i	−0.320395	−	0.986074i	0.653082	−	0.757287i	$-0.273476\pi$
$878$	−69.0807	−	95.0815i	−0.0786797	−	0.108293i
$879$		0			0
$880$	−3.44013	+	18.4831i	−0.00390924	+	0.0210035i
$881$			864.536i			0.981312i	0.871353	+	0.490656i	$0.163243\pi$
$881$			864.536i			0.981312i	−0.871353	+	0.490656i	$0.836757\pi$
$882$		0			0
$883$	−0.597361	−	1.83849i	−0.000676513	−	0.00208209i	0.950718	−	0.310058i	$-0.100348\pi$
$883$	−0.597361	−	1.83849i	−0.000676513	−	0.00208209i	−0.951394	+	0.307976i	$0.900348\pi$
$884$	−278.897	−	90.6190i	−0.315494	−	0.102510i
$885$		0			0
$886$	−1005.90	−	730.830i	−1.13533	−	0.824865i
$887$	−706.932	−	229.696i	−0.796992	−	0.258958i	−0.117913	−	0.993024i	$-0.537621\pi$
$887$	−706.932	−	229.696i	−0.796992	−	0.258958i	−0.679079	+	0.734065i	$0.737621\pi$
$888$		0			0
$889$	−2091.23	+	1519.37i	−2.35234	+	1.70908i
$890$		−	575.970i		−	0.647157i
$891$		0			0
$892$	755.189			0.846624
$893$	−957.745	−	1318.22i	−1.07250	−	1.47617i
$894$		0			0
$895$	−71.7589	+	220.851i	−0.0801775	+	0.246761i
$896$	−1363.39	+	1876.55i	−1.52164	+	2.09436i
$897$		0			0
$898$	−30.8835	+	95.0498i	−0.0343915	+	0.105846i
$899$	1353.01	−	439.620i	1.50502	−	0.489010i
$900$		0			0
$901$	−238.444			−0.264644
$902$	−401.330	+	191.051i	−0.444933	+	0.211808i
$903$		0			0
$904$	−24.0214	+	17.4525i	−0.0265723	+	0.0193059i
$905$	−526.597	+	171.102i	−0.581875	+	0.189063i
$906$		0			0
$907$	578.547	+	420.339i	0.637869	+	0.463439i	0.859117	−	0.511779i	$-0.171013\pi$
$907$	578.547	+	420.339i	0.637869	+	0.463439i	−0.221249	+	0.975217i	$0.571013\pi$
$908$	−905.090	+	1245.75i	−0.996795	+	1.37197i
$909$		0			0
$910$	161.002	+	495.513i	0.176925	+	0.544519i
$911$	224.917	+	309.572i	0.246891	+	0.339816i	0.914419	−	0.404768i	$-0.132648\pi$
$911$	224.917	+	309.572i	0.246891	+	0.339816i	−0.667529	+	0.744584i	$0.732648\pi$
$912$		0			0
$913$	−199.458	−	418.990i	−0.218465	−	0.458916i
$914$			1343.05i			1.46942i
$915$		0			0
$916$	−283.654	−	872.998i	−0.309666	−	0.953054i
$917$	−672.400	−	218.476i	−0.733260	−	0.238251i
$918$		0			0
$919$	−310.138	−	225.328i	−0.337473	−	0.245189i	0.406122	−	0.913819i	$-0.366881\pi$
$919$	−310.138	−	225.328i	−0.337473	−	0.245189i	−0.743595	+	0.668630i	$0.766881\pi$
$920$	−468.571	−	152.248i	−0.509316	−	0.165487i
$921$		0			0
$922$	−2014.28	+	1463.46i	−2.18468	+	1.58726i
$923$		−	692.300i		−	0.750054i
$924$		0			0
$925$	287.474			0.310782
$926$	−217.273	−	299.050i	−0.234636	−	0.322948i
$927$		0			0
$928$	−228.414	+	702.986i	−0.246136	+	0.757528i
$929$	127.290	−	175.200i	0.137019	−	0.188590i	−0.734994	−	0.678074i	$-0.762815\pi$
$929$	127.290	−	175.200i	0.137019	−	0.188590i	0.872012	+	0.489484i	$0.162815\pi$
$930$		0			0
$931$	−537.810	+	1655.21i	−0.577669	+	1.77788i
$932$	−743.030	+	241.425i	−0.797242	+	0.259040i
$933$		0			0
$934$	−2462.92			−2.63696
$935$	82.9680	+	15.4423i	0.0887358	+	0.0165158i
$936$		0			0
$937$	753.282	−	547.292i	0.803930	−	0.584089i	−0.108135	−	0.994136i	$-0.534488\pi$
$937$	753.282	−	547.292i	0.803930	−	0.584089i	0.912064	+	0.410047i	$0.134488\pi$
$938$	1114.24	−	362.039i	1.18789	−	0.385969i
$939$		0			0
$940$	−551.589	−	400.753i	−0.586796	−	0.426333i
$941$	−802.242	+	1104.19i	−0.852542	+	1.17342i	0.130755	+	0.991415i	$0.458260\pi$
$941$	−802.242	+	1104.19i	−0.852542	+	1.17342i	−0.983297	+	0.182008i	$0.941740\pi$
$942$		0			0
$943$	−140.775	−	433.260i	−0.149284	−	0.459449i
$944$	−15.1942	−	20.9131i	−0.0160956	−	0.0221537i
$945$		0			0
$946$	699.188	−	91.5107i	0.739099	−	0.0967343i
$947$			564.949i			0.596567i	0.954477	+	0.298283i	$0.0964141\pi$
$947$			564.949i			0.596567i	−0.954477	+	0.298283i	$0.903586\pi$
$948$		0			0
$949$	−118.119	−	363.533i	−0.124467	−	0.383069i
$950$	−1744.23	−	566.736i	−1.83604	−	0.596564i
$951$		0			0
$952$	−357.401	−	259.667i	−0.375421	−	0.272759i
$953$	−190.034	−	61.7458i	−0.199406	−	0.0647910i	0.207611	−	0.978211i	$-0.433431\pi$
$953$	−190.034	−	61.7458i	−0.199406	−	0.0647910i	−0.407017	+	0.913420i	$0.633431\pi$
$954$		0			0
$955$	96.5063	−	70.1159i	0.101054	−	0.0734198i
$956$		−	1900.15i		−	1.98760i
$957$		0			0
$958$	−1186.40			−1.23841
$959$	−802.651	−	1104.75i	−0.836967	−	1.15199i
$960$		0			0
$961$	749.107	−	2305.51i	0.779507	−	2.39908i
$962$	−226.152	+	311.271i	−0.235085	+	0.323566i
$963$		0			0
$964$	235.261	−	724.058i	0.244046	−	0.751097i
$965$	−48.2047	+	15.6627i	−0.0499531	+	0.0162307i
$966$		0			0
$967$	267.827			0.276967			0.138483	−	0.990365i	$-0.455777\pi$
$967$	267.827			0.276967			0.138483	+	0.990365i	$0.455777\pi$
$968$	−791.775	−	643.157i	−0.817950	−	0.664418i
$969$		0			0
$970$	453.355	−	329.381i	0.467376	−	0.339568i
$971$	1663.28	−	540.432i	1.71296	−	0.556573i	0.722134	−	0.691753i	$-0.243161\pi$
$971$	1663.28	−	540.432i	1.71296	−	0.556573i	0.990821	+	0.135180i	$0.0431613\pi$
$972$		0			0
$973$	738.940	+	536.871i	0.759445	+	0.551769i
$974$	−459.176	+	632.001i	−0.471433	+	0.648872i
$975$		0			0
$976$	14.6687	+	45.1457i	0.0150294	+	0.0462558i
$977$	−539.551	−	742.629i	−0.552253	−	0.760111i	0.438063	−	0.898944i	$-0.355665\pi$
$977$	−539.551	−	742.629i	−0.552253	−	0.760111i	−0.990316	+	0.138833i	$0.955665\pi$
$978$		0			0
$979$	1073.67	+	584.008i	1.09670	+	0.596535i
$980$			728.237i			0.743099i
$981$		0			0
$982$	842.518	+	2593.01i	0.857962	+	2.64053i
$983$	620.362	+	201.568i	0.631090	+	0.205054i	0.607058	−	0.794657i	$-0.292350\pi$
$983$	620.362	+	201.568i	0.631090	+	0.205054i	0.0240324	+	0.999711i	$0.492350\pi$
$984$		0			0
$985$	212.763	+	154.582i	0.216004	+	0.156936i
$986$	−364.503	−	118.434i	−0.369678	−	0.120116i
$987$		0			0
$988$	1235.78	−	897.848i	1.25079	−	0.908753i
$989$			722.717i			0.730755i
$990$		0			0
$991$	573.705			0.578915			0.289458	−	0.957191i	$-0.406525\pi$
$991$	573.705			0.578915			0.289458	+	0.957191i	$0.406525\pi$
$992$	1033.81	+	1422.92i	1.04215	+	1.43440i
$993$		0			0
$994$	819.916	−	2523.44i	0.824865	−	2.53867i
$995$	−182.660	+	251.409i	−0.183577	+	0.252673i
$996$		0			0
$997$	102.911	−	316.727i	0.103220	−	0.317680i	−0.886088	−	0.463517i	$-0.846587\pi$
$997$	102.911	−	316.727i	0.103220	−	0.317680i	0.989309	+	0.145837i	$0.0465875\pi$
$998$	−1995.25	+	648.297i	−1.99925	+	0.649596i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.3.l.a.80.1	yes	32
3.2	odd	2	inner	99.3.l.a.80.8	yes	32
11.2	odd	10		1089.3.b.j.485.2		16
11.4	even	5	inner	99.3.l.a.26.8	yes	32
11.9	even	5		1089.3.b.i.485.15		16
33.2	even	10		1089.3.b.j.485.15		16
33.20	odd	10		1089.3.b.i.485.2		16
33.26	odd	10	inner	99.3.l.a.26.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.3.l.a.26.1	✓	32	33.26	odd	10	inner
99.3.l.a.26.8	yes	32	11.4	even	5	inner
99.3.l.a.80.1	yes	32	1.1	even	1	trivial
99.3.l.a.80.8	yes	32	3.2	odd	2	inner
1089.3.b.i.485.2		16	33.20	odd	10
1089.3.b.i.485.15		16	11.9	even	5
1089.3.b.j.485.2		16	11.2	odd	10
1089.3.b.j.485.15		16	33.2	even	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)

\(f(q)\)	\(=\)	\(q+(-1.91284 - 2.63279i) q^{2} +(-2.03659 + 6.26797i) q^{4} +(-0.936271 + 1.28867i) q^{5} +(-3.36204 + 10.3473i) q^{7} +(8.01778 - 2.60514i) q^{8} +O(q^{10})\)	\(q+(-1.91284 - 2.63279i) q^{2} +(-2.03659 + 6.26797i) q^{4} +(-0.936271 + 1.28867i) q^{5} +(-3.36204 + 10.3473i) q^{7} +(8.01778 - 2.60514i) q^{8} +5.18373 q^{10} +(-5.25607 + 9.66301i) q^{11} +(7.47384 - 5.43007i) q^{13} +(33.6733 - 10.9411i) q^{14} +(-0.868063 - 0.630685i) q^{16} +(-2.83106 + 3.89662i) q^{17} +(-7.75281 - 23.8607i) q^{19} +(-6.17053 - 8.49300i) q^{20} +(35.4947 - 4.64560i) q^{22} +36.6892i q^{23} +(6.94137 + 21.3633i) q^{25} +(-28.5925 - 9.29026i) q^{26} +(-58.0094 - 42.1463i) q^{28} +(-23.2548 - 7.55594i) q^{29} +(-47.0703 + 34.1986i) q^{31} -30.2297i q^{32} +15.6743 q^{34} +(-10.1864 - 14.0204i) q^{35} +(3.95474 - 12.1714i) q^{37} +(-47.9904 + 66.0532i) q^{38} +(-4.14967 + 12.7714i) q^{40} +(-11.8089 + 3.83696i) q^{41} +19.6984 q^{43} +(-49.8630 - 52.6244i) q^{44} +(96.5949 - 70.1803i) q^{46} +(61.7676 - 20.0695i) q^{47} +(-56.1212 - 40.7744i) q^{49} +(42.9675 - 59.1397i) q^{50} +(18.8144 + 57.9046i) q^{52} +(29.0988 + 40.0511i) q^{53} +(-7.53129 - 15.8205i) q^{55} +91.7208i q^{56} +(24.5894 + 75.6782i) q^{58} +(22.9125 + 7.44473i) q^{59} +(-35.7910 - 26.0037i) q^{61} +(180.076 + 58.5101i) q^{62} +(-83.0609 + 60.3473i) q^{64} +14.7153i q^{65} +33.0898 q^{67} +(-18.6582 - 25.6808i) q^{68} +(-17.4279 + 53.6375i) q^{70} +(44.0480 - 60.6269i) q^{71} +(12.7859 - 39.3511i) q^{73} +(-39.6096 + 12.8700i) q^{74} +165.347 q^{76} +(-82.3148 - 86.8735i) q^{77} +(-51.7531 + 37.6008i) q^{79} +(1.62549 - 0.528152i) q^{80} +(32.6905 + 23.7510i) q^{82} +(-24.7962 + 34.1290i) q^{83} +(-2.37080 - 7.29658i) q^{85} +(-37.6797 - 51.8617i) q^{86} +(-16.9686 + 91.1687i) q^{88} -111.111i q^{89} +(31.0591 + 95.5901i) q^{91} +(-229.967 - 74.7207i) q^{92} +(-170.990 - 124.231i) q^{94} +(38.0072 + 12.3493i) q^{95} +(87.4573 - 63.5414i) q^{97} +225.750i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 16 q^{7}+O(q^{10}) \) 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

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