LMFDB - Embedded newform 99.3.l.a.26.4

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			26.4
Character	$\chi$	$=$	99.26
Dual form			99.3.l.a.80.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.480038 + 0.660715i) q^{2} +(1.02996 + 3.16989i) q^{4} +(-0.615389 - 0.847011i) q^{5} +(2.11067 + 6.49597i) q^{7} +(-5.69568 - 1.85064i) q^{8} +O(q^{10})$	\(q+(-0.480038 + 0.660715i) q^{2} +(1.02996 + 3.16989i) q^{4} +(-0.615389 - 0.847011i) q^{5} +(2.11067 + 6.49597i) q^{7} +(-5.69568 - 1.85064i) q^{8} +0.855043 q^{10} +(-2.57144 + 10.6952i) q^{11} +(6.23315 + 4.52865i) q^{13} +(-5.30519 - 1.72376i) q^{14} +(-6.82898 + 4.96155i) q^{16} +(5.52104 + 7.59906i) q^{17} +(2.91103 - 8.95922i) q^{19} +(2.05110 - 2.82310i) q^{20} +(-5.83211 - 6.83310i) q^{22} -4.82409i q^{23} +(7.38670 - 22.7339i) q^{25} +(-5.98430 + 1.94442i) q^{26} +(-18.4176 + 13.3812i) q^{28} +(44.4675 - 14.4484i) q^{29} +(-15.3643 - 11.1628i) q^{31} -30.8489i q^{32} -7.67113 q^{34} +(4.20328 - 5.78531i) q^{35} +(-14.5803 - 44.8737i) q^{37} +(4.52209 + 6.22413i) q^{38} +(1.93755 + 5.96317i) q^{40} +(-7.22871 - 2.34875i) q^{41} +50.6851 q^{43} +(-36.5511 + 2.86447i) q^{44} +(3.18735 + 2.31575i) q^{46} +(62.9091 + 20.4404i) q^{47} +(1.89907 - 1.37976i) q^{49} +(11.4748 + 15.7937i) q^{50} +(-7.93542 + 24.4227i) q^{52} +(-22.5774 + 31.0751i) q^{53} +(10.6414 - 4.40369i) q^{55} -40.9051i q^{56} +(-11.7998 + 36.3161i) q^{58} +(-111.526 + 36.2371i) q^{59} +(-65.8779 + 47.8631i) q^{61} +(14.7509 - 4.79287i) q^{62} +(-6.93357 - 5.03753i) q^{64} -8.06643i q^{65} +70.1488 q^{67} +(-18.4017 + 25.3278i) q^{68} +(1.80471 + 5.55434i) q^{70} +(-25.4295 - 35.0007i) q^{71} +(14.1852 + 43.6575i) q^{73} +(36.6478 + 11.9076i) q^{74} +31.3980 q^{76} +(-74.9033 + 5.87008i) q^{77} +(69.3955 + 50.4188i) q^{79} +(8.40497 + 2.73094i) q^{80} +(5.02191 - 3.64863i) q^{82} +(93.5371 + 128.743i) q^{83} +(3.03890 - 9.35276i) q^{85} +(-24.3308 + 33.4884i) q^{86} +(34.4391 - 56.1578i) q^{88} -154.015i q^{89} +(-16.2619 + 50.0489i) q^{91} +(15.2918 - 4.96862i) q^{92} +(-43.7040 + 31.7528i) q^{94} +(-9.37997 + 3.04774i) q^{95} +(-124.151 - 90.2007i) q^{97} +1.91708i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.480038	+	0.660715i	−0.240019	+	0.330358i	−0.911984	−	0.410225i	$-0.865450\pi$
$2$	−0.480038	+	0.660715i	−0.240019	+	0.330358i	0.671966	+	0.740582i	$0.265450\pi$
$3$		0			0
$3$		0			0
$4$	1.02996	+	3.16989i	0.257490	+	0.792472i
$5$	−0.615389	−	0.847011i	−0.123078	−	0.169402i	0.743032	−	0.669256i	$-0.233387\pi$
$5$	−0.615389	−	0.847011i	−0.123078	−	0.169402i	−0.866110	+	0.499854i	$0.833387\pi$
$6$		0			0
$7$	2.11067	+	6.49597i	0.301524	+	0.927996i	0.980951	+	0.194253i	$0.0622284\pi$
$7$	2.11067	+	6.49597i	0.301524	+	0.927996i	−0.679427	+	0.733743i	$0.737772\pi$
$8$	−5.69568	−	1.85064i	−0.711961	−	0.231330i
$9$		0			0
$10$	0.855043			0.0855043
$11$	−2.57144	+	10.6952i	−0.233767	+	0.972293i
$11$	−2.57144	+	10.6952i	−0.233767	+	0.972293i
$12$		0			0
$13$	6.23315	+	4.52865i	0.479473	+	0.348358i	0.801122	−	0.598502i	$-0.204237\pi$
$13$	6.23315	+	4.52865i	0.479473	+	0.348358i	−0.321649	+	0.946859i	$0.604237\pi$
$14$	−5.30519	−	1.72376i	−0.378942	−	0.123126i
$15$		0			0
$16$	−6.82898	+	4.96155i	−0.426812	+	0.310097i
$17$	5.52104	+	7.59906i	0.324767	+	0.447004i	0.939915	−	0.341408i	$-0.110904\pi$
$17$	5.52104	+	7.59906i	0.324767	+	0.447004i	−0.615148	+	0.788412i	$0.710904\pi$
$18$		0			0
$19$	2.91103	−	8.95922i	0.153212	−	0.471538i	−0.844763	−	0.535140i	$-0.820259\pi$
$19$	2.91103	−	8.95922i	0.153212	−	0.471538i	0.997975	+	0.0636020i	$0.0202588\pi$
$20$	2.05110	−	2.82310i	0.102555	−	0.141155i
$21$		0			0
$22$	−5.83211	−	6.83310i	−0.265096	−	0.310595i
$23$		−	4.82409i		−	0.209743i	−0.994486	−	0.104872i	$-0.966557\pi$
$23$		−	4.82409i		−	0.209743i	0.994486	−	0.104872i	$-0.0334431\pi$
$24$		0			0
$25$	7.38670	−	22.7339i	0.295468	−	0.909357i
$26$	−5.98430	+	1.94442i	−0.230165	+	0.0747852i
$27$		0			0
$28$	−18.4176	+	13.3812i	−0.657772	+	0.477899i
$29$	44.4675	−	14.4484i	1.53336	−	0.498220i	0.583827	−	0.811878i	$-0.301555\pi$
$29$	44.4675	−	14.4484i	1.53336	−	0.498220i	0.949536	+	0.313658i	$0.101555\pi$
$30$		0			0
$31$	−15.3643	−	11.1628i	−0.495624	−	0.360092i	0.311719	−	0.950174i	$-0.399095\pi$
$31$	−15.3643	−	11.1628i	−0.495624	−	0.360092i	−0.807343	+	0.590082i	$0.799095\pi$
$32$		−	30.8489i		−	0.964029i
$33$		0			0
$34$	−7.67113			−0.225621
$35$	4.20328	−	5.78531i	0.120094	−	0.165295i
$36$		0			0
$37$	−14.5803	−	44.8737i	−0.394063	−	1.21280i	−0.929689	−	0.368346i	$-0.879924\pi$
$37$	−14.5803	−	44.8737i	−0.394063	−	1.21280i	0.535626	−	0.844455i	$-0.320076\pi$
$38$	4.52209	+	6.22413i	0.119002	+	0.163793i
$39$		0			0
$40$	1.93755	+	5.96317i	0.0484388	+	0.149079i
$41$	−7.22871	−	2.34875i	−0.176310	−	0.0572866i	0.219532	−	0.975605i	$-0.429547\pi$
$41$	−7.22871	−	2.34875i	−0.176310	−	0.0572866i	−0.395842	+	0.918319i	$0.629547\pi$
$42$		0			0
$43$	50.6851			1.17872			0.589362	−	0.807869i	$-0.299379\pi$
$43$	50.6851			1.17872			0.589362	+	0.807869i	$0.299379\pi$
$44$	−36.5511	+	2.86447i	−0.830708	+	0.0651015i
$45$		0			0
$46$	3.18735	+	2.31575i	0.0692903	+	0.0503423i
$47$	62.9091	+	20.4404i	1.33849	+	0.434902i	0.888805	−	0.458285i	$-0.151536\pi$
$47$	62.9091	+	20.4404i	1.33849	+	0.434902i	0.449686	+	0.893187i	$0.351536\pi$
$48$		0			0
$49$	1.89907	−	1.37976i	0.0387566	−	0.0281583i
$50$	11.4748	+	15.7937i	0.229495	+	0.315873i
$51$		0			0
$52$	−7.93542	+	24.4227i	−0.152604	+	0.469668i
$53$	−22.5774	+	31.0751i	−0.425988	+	0.586322i	−0.967026	−	0.254676i	$-0.918031\pi$
$53$	−22.5774	+	31.0751i	−0.425988	+	0.586322i	0.541039	+	0.840998i	$0.318031\pi$
$54$		0			0
$55$	10.6414	−	4.40369i	0.193480	−	0.0800671i
$56$		−	40.9051i		−	0.730448i
$57$		0			0
$58$	−11.7998	+	36.3161i	−0.203445	+	0.626140i
$59$	−111.526	+	36.2371i	−1.89028	+	0.614188i	−0.910720	+	0.413025i	$0.864472\pi$
$59$	−111.526	+	36.2371i	−1.89028	+	0.614188i	−0.979558	+	0.201164i	$0.935528\pi$
$60$		0			0
$61$	−65.8779	+	47.8631i	−1.07997	+	0.784641i	−0.977677	−	0.210114i	$-0.932616\pi$
$61$	−65.8779	+	47.8631i	−1.07997	+	0.784641i	−0.102288	+	0.994755i	$0.532616\pi$
$62$	14.7509	−	4.79287i	0.237918	−	0.0773043i
$63$		0			0
$64$	−6.93357	−	5.03753i	−0.108337	−	0.0787115i
$65$		−	8.06643i		−	0.124099i
$66$		0			0
$67$	70.1488			1.04700			0.523499	−	0.852027i	$-0.324627\pi$
$67$	70.1488			1.04700			0.523499	+	0.852027i	$0.324627\pi$
$68$	−18.4017	+	25.3278i	−0.270614	+	0.372468i
$69$		0			0
$70$	1.80471	+	5.55434i	0.0257816	+	0.0793477i
$71$	−25.4295	−	35.0007i	−0.358162	−	0.492968i	0.591473	−	0.806325i	$-0.298547\pi$
$71$	−25.4295	−	35.0007i	−0.358162	−	0.492968i	−0.949636	+	0.313356i	$0.898547\pi$
$72$		0			0
$73$	14.1852	+	43.6575i	0.194318	+	0.598048i	0.999984	+	0.00567825i	$0.00180745\pi$
$73$	14.1852	+	43.6575i	0.194318	+	0.598048i	−0.805666	+	0.592370i	$0.798193\pi$
$74$	36.6478	+	11.9076i	0.495241	+	0.160914i
$75$		0			0
$76$	31.3980			0.413131
$77$	−74.9033	+	5.87008i	−0.972771	+	0.0762348i
$78$		0			0
$79$	69.3955	+	50.4188i	0.878424	+	0.638212i	0.932834	−	0.360306i	$-0.117328\pi$
$79$	69.3955	+	50.4188i	0.878424	+	0.638212i	−0.0544101	+	0.998519i	$0.517328\pi$
$80$	8.40497	+	2.73094i	0.105062	+	0.0341367i
$81$		0			0
$82$	5.02191	−	3.64863i	0.0612428	−	0.0444955i
$83$	93.5371	+	128.743i	1.12695	+	1.55112i	0.793731	+	0.608269i	$0.208136\pi$
$83$	93.5371	+	128.743i	1.12695	+	1.55112i	0.333222	+	0.942848i	$0.391864\pi$
$84$		0			0
$85$	3.03890	−	9.35276i	0.0357517	−	0.110033i
$86$	−24.3308	+	33.4884i	−0.282916	+	0.389400i
$87$		0			0
$88$	34.4391	−	56.1578i	0.391353	−	0.638157i
$89$		−	154.015i		−	1.73051i	−0.501335	−	0.865253i	$-0.667158\pi$
$89$		−	154.015i		−	1.73051i	0.501335	−	0.865253i	$-0.332842\pi$
$90$		0			0
$91$	−16.2619	+	50.0489i	−0.178702	+	0.549987i
$92$	15.2918	−	4.96862i	0.166216	−	0.0540067i
$93$		0			0
$94$	−43.7040	+	31.7528i	−0.464936	+	0.337796i
$95$	−9.37997	+	3.04774i	−0.0987366	+	0.0320815i
$96$		0			0
$97$	−124.151	−	90.2007i	−1.27990	−	0.929904i	−0.280353	−	0.959897i	$-0.590451\pi$
$97$	−124.151	−	90.2007i	−1.27990	−	0.929904i	−0.999550	+	0.0299934i	$0.990451\pi$
$98$			1.91708i			0.0195621i
$99$		0			0
$100$	79.6720			0.796720
$101$	92.2112	−	126.918i	0.912982	−	1.25661i	−0.0531554	−	0.998586i	$-0.516928\pi$
$101$	92.2112	−	126.918i	0.912982	−	1.25661i	0.966138	−	0.258026i	$-0.0830721\pi$
$102$		0			0
$103$	−19.5863	−	60.2804i	−0.190158	−	0.585246i	0.809841	−	0.586649i	$-0.199553\pi$
$103$	−19.5863	−	60.2804i	−0.190158	−	0.585246i	−0.999999	+	0.00140322i	$0.999553\pi$
$104$	−27.1212	−	37.3291i	−0.260780	−	0.358933i
$105$		0			0
$106$	−9.69379	−	29.8344i	−0.0914508	−	0.281457i
$107$	−48.9872	−	15.9169i	−0.457824	−	0.148756i	0.0710204	−	0.997475i	$-0.477374\pi$
$107$	−48.9872	−	15.9169i	−0.457824	−	0.148756i	−0.528844	+	0.848719i	$0.677374\pi$
$108$		0			0
$109$	−63.0507			−0.578446			−0.289223	−	0.957262i	$-0.593397\pi$
$109$	−63.0507			−0.578446			−0.289223	+	0.957262i	$0.593397\pi$
$110$	−2.19869	+	9.14487i	−0.0199881	+	0.0831352i
$111$		0			0
$112$	−46.6438	−	33.8887i	−0.416463	−	0.302578i
$113$	82.5291	+	26.8153i	0.730346	+	0.237304i	0.650503	−	0.759504i	$-0.274558\pi$
$113$	82.5291	+	26.8153i	0.730346	+	0.237304i	0.0798430	+	0.996807i	$0.474558\pi$
$114$		0			0
$115$	−4.08606	+	2.96869i	−0.0355309	+	0.0258147i
$116$	91.5995	+	126.076i	0.789651	+	1.08686i
$117$		0			0
$118$	29.5945	−	91.0824i	0.250801	−	0.771885i
$119$	−37.7102	+	51.9037i	−0.316893	+	0.436165i
$120$		0			0
$121$	−107.775	−	55.0042i	−0.890706	−	0.454580i
$122$		−	66.5026i		−	0.545103i
$123$		0			0
$124$	19.5603	−	60.2005i	0.157745	−	0.485488i
$125$	−48.6946	+	15.8218i	−0.389557	+	0.126575i
$126$		0			0
$127$	−61.2042	+	44.4675i	−0.481923	+	0.350138i	−0.802070	−	0.597230i	$-0.796268\pi$
$127$	−61.2042	+	44.4675i	−0.481923	+	0.350138i	0.320147	+	0.947368i	$0.396268\pi$
$128$	124.013	−	40.2943i	0.968852	−	0.314799i
$129$		0			0
$130$	5.32961	+	3.87219i	0.0409970	+	0.0297861i
$131$		−	124.201i		−	0.948097i	−0.880499	−	0.474049i	$-0.842792\pi$
$131$		−	124.201i		−	0.948097i	0.880499	−	0.474049i	$-0.157208\pi$
$132$		0			0
$133$	64.3431			0.483783
$134$	−33.6741	+	46.3484i	−0.251299	+	0.345884i
$135$		0			0
$136$	−17.3830	−	53.4993i	−0.127816	−	0.393377i
$137$	31.2464	+	43.0070i	0.228076	+	0.313920i	0.907683	−	0.419657i	$-0.137850\pi$
$137$	31.2464	+	43.0070i	0.228076	+	0.313920i	−0.679607	+	0.733577i	$0.737850\pi$
$138$		0			0
$139$	24.4299	+	75.1874i	0.175754	+	0.540917i	0.999667	−	0.0258002i	$-0.00821337\pi$
$139$	24.4299	+	75.1874i	0.175754	+	0.540917i	−0.823913	+	0.566717i	$0.808213\pi$
$140$	22.6680	+	7.36528i	0.161914	+	0.0526092i
$141$		0			0
$142$	35.3327			0.248822
$143$	−64.4630	+	55.0198i	−0.450790	+	0.384754i
$144$		0			0
$145$	−39.6028	−	28.7731i	−0.273123	−	0.198435i
$146$	−35.6546	−	11.5849i	−0.244210	−	0.0793485i
$147$		0			0
$148$	127.227	−	92.4361i	0.859644	−	0.624568i
$149$	−12.7700	−	17.5764i	−0.0857045	−	0.117962i	0.764012	−	0.645202i	$-0.223227\pi$
$149$	−12.7700	−	17.5764i	−0.0857045	−	0.117962i	−0.849716	+	0.527240i	$0.823227\pi$
$150$		0			0
$151$	−38.3457	+	118.016i	−0.253945	+	0.781563i	0.740091	+	0.672507i	$0.234783\pi$
$151$	−38.3457	+	118.016i	−0.253945	+	0.781563i	−0.994036	+	0.109055i	$0.965217\pi$
$152$	−33.1606	+	45.6416i	−0.218162	+	0.300274i
$153$		0			0
$154$	32.0780	−	52.3076i	0.208299	−	0.339660i
$155$			19.8833i			0.128279i
$156$		0			0
$157$	−55.9981	+	172.344i	−0.356676	+	1.09774i	0.598356	+	0.801231i	$0.295821\pi$
$157$	−55.9981	+	172.344i	−0.356676	+	1.09774i	−0.955031	+	0.296505i	$0.904179\pi$
$158$	−66.6249	+	21.6478i	−0.421677	+	0.137011i
$159$		0			0
$160$	−26.1294	+	18.9841i	−0.163309	+	0.118651i
$161$	31.3372	−	10.1821i	0.194641	−	0.0632426i
$162$		0			0
$163$	223.913	+	162.683i	1.37370	+	0.998053i	0.997438	+	0.0715405i	$0.0227915\pi$
$163$	223.913	+	162.683i	1.37370	+	0.998053i	0.376264	+	0.926512i	$0.377208\pi$
$164$		−	25.3333i		−	0.154472i
$165$		0			0
$166$	−129.964			−0.782914
$167$	32.0565	−	44.1220i	0.191955	−	0.264204i	−0.702181	−	0.711998i	$-0.747790\pi$
$167$	32.0565	−	44.1220i	0.191955	−	0.264204i	0.894136	+	0.447795i	$0.147790\pi$
$168$		0			0
$169$	−33.8804	−	104.273i	−0.200476	−	0.617000i
$170$	4.72073	+	6.49753i	0.0277690	+	0.0382208i
$171$		0			0
$172$	52.2036	+	160.666i	0.303509	+	0.934106i
$173$	−95.8015	−	31.1278i	−0.553766	−	0.179929i	0.0187484	−	0.999824i	$-0.494032\pi$
$173$	−95.8015	−	31.1278i	−0.553766	−	0.179929i	−0.572514	+	0.819895i	$0.694032\pi$
$174$		0			0
$175$	163.270			0.932971
$176$	−35.5045	−	85.7958i	−0.201730	−	0.487476i
$177$		0			0
$178$	101.760	+	73.9331i	0.571686	+	0.415354i
$179$	−77.8279	−	25.2878i	−0.434793	−	0.141273i	0.0834391	−	0.996513i	$-0.473410\pi$
$179$	−77.8279	−	25.2878i	−0.434793	−	0.141273i	−0.518232	+	0.855240i	$0.673410\pi$
$180$		0			0
$181$	−164.876	+	119.789i	−0.910915	+	0.661818i	−0.941246	−	0.337722i	$-0.890344\pi$
$181$	−164.876	+	119.789i	−0.910915	+	0.661818i	0.0303313	+	0.999540i	$0.490344\pi$
$182$	−25.2617	−	34.7698i	−0.138801	−	0.191043i
$183$		0			0
$184$	−8.92766	+	27.4765i	−0.0485199	+	0.149329i
$185$	−29.0359	+	39.9645i	−0.156951	+	0.216024i
$186$		0			0
$187$	−95.4707	+	39.5082i	−0.510538	+	0.211274i
$188$			220.468i			1.17270i
$189$		0			0
$190$	2.48905	−	7.66052i	0.0131003	−	0.0403185i
$191$	−191.865	+	62.3406i	−1.00453	+	0.326390i	−0.764673	−	0.644419i	$-0.777099\pi$
$191$	−191.865	+	62.3406i	−1.00453	+	0.326390i	−0.239854	+	0.970809i	$0.577099\pi$
$192$		0			0
$193$	184.461	−	134.019i	0.955755	−	0.694397i	0.00359389	−	0.999994i	$-0.498856\pi$
$193$	184.461	−	134.019i	0.955755	−	0.694397i	0.952161	+	0.305597i	$0.0988560\pi$
$194$	119.194	−	38.7285i	0.614402	−	0.199631i
$195$		0			0
$196$	6.32964	+	4.59875i	0.0322941	+	0.0234630i
$197$		−	170.096i		−	0.863429i	−0.902010	−	0.431715i	$-0.857909\pi$
$197$		−	170.096i		−	0.863429i	0.902010	−	0.431715i	$-0.142091\pi$
$198$		0			0
$199$	143.997			0.723602			0.361801	−	0.932255i	$-0.382162\pi$
$199$	143.997			0.723602			0.361801	+	0.932255i	$0.382162\pi$
$200$	−84.1446	+	115.815i	−0.420723	+	0.579076i
$201$		0			0
$202$	39.5917	+	121.851i	0.195999	+	0.603222i
$203$	187.713	+	258.364i	0.924692	+	1.27273i
$204$		0			0
$205$	2.45905	+	7.56819i	0.0119954	+	0.0369180i
$206$	49.2303	+	15.9959i	0.238982	+	0.0776500i
$207$		0			0
$208$	−65.0352			−0.312669
$209$	88.3353	+	54.1722i	0.422657	+	0.259197i
$210$		0			0
$211$	−97.3640	−	70.7391i	−0.461441	−	0.335256i	0.332655	−	0.943048i	$-0.392055\pi$
$211$	−97.3640	−	70.7391i	−0.461441	−	0.335256i	−0.794096	+	0.607792i	$0.792055\pi$
$212$	−121.758	−	39.5617i	−0.574331	−	0.186612i
$213$		0			0
$214$	34.0322	−	24.7259i	0.159029	−	0.115541i
$215$	−31.1911	−	42.9308i	−0.145075	−	0.199678i
$216$		0			0
$217$	40.0845	−	123.367i	0.184721	−	0.568514i
$218$	30.2667	−	41.6585i	0.138838	−	0.191094i
$219$		0			0
$220$	24.9194	+	29.1964i	0.113270	+	0.132711i
$221$			72.3689i			0.327461i
$222$		0			0
$223$	33.5784	−	103.344i	0.150576	−	0.463424i	−0.847110	−	0.531417i	$-0.821660\pi$
$223$	33.5784	−	103.344i	0.150576	−	0.463424i	0.997686	+	0.0679933i	$0.0216597\pi$
$224$	200.394	−	65.1119i	0.894616	−	0.290678i
$225$		0			0
$226$	−57.3344	+	41.6559i	−0.253692	+	0.184318i
$227$	−201.524	+	65.4790i	−0.887770	+	0.288454i	−0.717180	−	0.696888i	$-0.754567\pi$
$227$	−201.524	+	65.4790i	−0.887770	+	0.288454i	−0.170590	+	0.985342i	$0.554567\pi$
$228$		0			0
$229$	−225.228	−	163.638i	−0.983528	−	0.714575i	−0.0250334	−	0.999687i	$-0.507969\pi$
$229$	−225.228	−	163.638i	−0.983528	−	0.714575i	−0.958494	+	0.285112i	$0.907969\pi$
$230$		−	4.12481i		−	0.0179339i
$231$		0			0
$232$	−280.012			−1.20695
$233$	111.143	−	152.976i	0.477010	−	0.656548i	−0.500917	−	0.865495i	$-0.667004\pi$
$233$	111.143	−	152.976i	0.477010	−	0.656548i	0.977927	+	0.208948i	$0.0670038\pi$
$234$		0			0
$235$	−21.4003	−	65.8635i	−0.0910653	−	0.280270i
$236$	−229.735	−	316.203i	−0.973455	−	1.33985i
$237$		0			0
$238$	−16.1912	−	49.8315i	−0.0680303	−	0.209376i
$239$	84.4525	+	27.4403i	0.353358	+	0.114813i	0.480317	−	0.877095i	$-0.340522\pi$
$239$	84.4525	+	27.4403i	0.353358	+	0.114813i	−0.126959	+	0.991908i	$0.540522\pi$
$240$		0			0
$241$	−155.144			−0.643750			−0.321875	−	0.946782i	$-0.604313\pi$
$241$	−155.144			−0.643750			−0.321875	+	0.946782i	$0.604313\pi$
$242$	88.0784	−	44.8048i	0.363960	−	0.185144i
$243$		0			0
$244$	−219.572	−	159.529i	−0.899886	−	0.653805i
$245$	−2.33734	−	0.759447i	−0.00954015	−	0.00309978i
$246$		0			0
$247$	58.7180	−	42.6611i	0.237725	−	0.172717i
$248$	66.8520	+	92.0139i	0.269565	+	0.371024i
$249$		0			0
$250$	12.9215	−	39.7684i	0.0516861	−	0.159073i
$251$	176.164	−	242.469i	0.701848	−	0.966011i	−0.298086	−	0.954539i	$-0.596348\pi$
$251$	176.164	−	242.469i	0.701848	−	0.966011i	0.999934	−	0.0114720i	$-0.00365174\pi$
$252$		0			0
$253$	51.5947	+	12.4049i	0.203932	+	0.0490310i
$254$		−	61.7847i		−	0.243247i
$255$		0			0
$256$	−22.3144	+	68.6765i	−0.0871655	+	0.268268i
$257$	352.243	−	114.451i	1.37060	−	0.445334i	0.471030	−	0.882117i	$-0.343882\pi$
$257$	352.243	−	114.451i	1.37060	−	0.445334i	0.899567	+	0.436784i	$0.143882\pi$
$258$		0			0
$259$	260.724	−	189.427i	1.00666	−	0.731378i
$260$	25.5697	−	8.30809i	0.0983449	−	0.0319542i
$261$		0			0
$262$	82.0613	+	59.6210i	0.313211	+	0.227561i
$263$			351.921i			1.33810i	0.743217	+	0.669050i	$0.233299\pi$
$263$			351.921i			1.33810i	−0.743217	+	0.669050i	$0.766701\pi$
$264$		0			0
$265$	40.2148			0.151754
$266$	−30.8871	+	42.5125i	−0.116117	+	0.159821i
$267$		0			0
$268$	72.2504	+	222.364i	0.269591	+	0.829716i
$269$	90.0689	+	123.969i	0.334828	+	0.460852i	0.942922	−	0.333013i	$-0.108065\pi$
$269$	90.0689	+	123.969i	0.334828	+	0.460852i	−0.608094	+	0.793865i	$0.708065\pi$
$270$		0			0
$271$	−112.596	−	346.534i	−0.415482	−	1.27872i	−0.911819	−	0.410592i	$-0.865322\pi$
$271$	−112.596	−	346.534i	−0.415482	−	1.27872i	0.496337	−	0.868130i	$-0.334678\pi$
$272$	−75.4062	−	24.5010i	−0.277229	−	0.0900771i
$273$		0			0
$274$	−43.4148			−0.158448
$275$	224.150	+	137.461i	0.815091	+	0.499859i
$276$		0			0
$277$	169.024	+	122.803i	0.610196	+	0.443333i	0.849483	−	0.527616i	$-0.176914\pi$
$277$	169.024	+	122.803i	0.610196	+	0.443333i	−0.239287	+	0.970949i	$0.576914\pi$
$278$	−61.4047	−	19.9516i	−0.220880	−	0.0717684i
$279$		0			0
$280$	−34.6471	+	25.1726i	−0.123740	+	0.0899020i
$281$	−278.880	−	383.845i	−0.992456	−	1.36600i	−0.929842	−	0.367960i	$-0.880056\pi$
$281$	−278.880	−	383.845i	−0.992456	−	1.36600i	−0.0626142	−	0.998038i	$-0.519944\pi$
$282$		0			0
$283$	53.4233	−	164.420i	0.188775	−	0.580989i	−0.811218	−	0.584744i	$-0.801195\pi$
$283$	53.4233	−	164.420i	0.188775	−	0.580989i	0.999993	+	0.00375459i	$0.00119513\pi$
$284$	84.7571	−	116.658i	0.298440	−	0.410768i
$285$		0			0
$286$	−5.40770	−	69.0033i	−0.0189081	−	0.241270i
$287$		−	51.9150i		−	0.180888i
$288$		0			0
$289$	62.0421	−	190.946i	0.214678	−	0.660712i
$290$	38.0217	−	12.3540i	0.131109	−	0.0425999i
$291$		0			0
$292$	−123.779	+	89.9309i	−0.423902	+	0.307983i
$293$	−361.681	+	117.517i	−1.23441	+	0.401083i	−0.852309	−	0.523039i	$-0.824798\pi$
$293$	−361.681	+	117.517i	−1.23441	+	0.401083i	−0.382098	+	0.924122i	$0.624798\pi$
$294$		0			0
$295$	99.3254	+	72.1641i	0.336696	+	0.244624i
$296$			282.569i			0.954625i
$297$		0			0
$298$	17.7430			0.0595404
$299$	21.8466	−	30.0693i	0.0730656	−	0.100566i
$300$		0			0
$301$	106.980	+	329.249i	0.355414	+	1.09385i
$302$	−59.5676	−	81.9877i	−0.197244	−	0.271483i
$303$		0			0
$304$	24.5722	+	75.6256i	0.0808298	+	0.248768i
$305$	81.0811	+	26.3448i	0.265840	+	0.0863765i
$306$		0			0
$307$	−343.458			−1.11876			−0.559378	−	0.828912i	$-0.688960\pi$
$307$	−343.458			−1.11876			−0.559378	+	0.828912i	$0.688960\pi$
$308$	−95.7549	−	231.389i	−0.310893	−	0.751264i
$309$		0			0
$310$	−13.1372	−	9.54472i	−0.0423780	−	0.0307894i
$311$	173.651	+	56.4225i	0.558362	+	0.181423i	0.574584	−	0.818446i	$-0.305164\pi$
$311$	173.651	+	56.4225i	0.558362	+	0.181423i	−0.0162221	+	0.999868i	$0.505164\pi$
$312$		0			0
$313$	50.5840	−	36.7514i	0.161610	−	0.117417i	−0.504041	−	0.863680i	$-0.668154\pi$
$313$	50.5840	−	36.7514i	0.161610	−	0.117417i	0.665651	+	0.746263i	$0.268154\pi$
$314$	−86.9894	−	119.731i	−0.277036	−	0.381308i
$315$		0			0
$316$	−88.3474	+	271.905i	−0.279580	+	0.860460i
$317$	−114.353	+	157.393i	−0.360734	+	0.496508i	−0.950353	−	0.311174i	$-0.899278\pi$
$317$	−114.353	+	157.393i	−0.360734	+	0.496508i	0.589619	+	0.807681i	$0.299278\pi$
$318$		0			0
$319$	40.1830	+	512.743i	0.125966	+	1.60734i
$320$			8.97285i			0.0280402i
$321$		0			0
$322$	−8.31558	+	25.5927i	−0.0258248	+	0.0794805i
$323$	84.1536	−	27.3432i	0.260537	−	0.0846538i
$324$		0			0
$325$	148.996	−	108.252i	0.458450	−	0.333084i
$326$	−214.974	+	69.8492i	−0.659429	+	0.214261i
$327$		0			0
$328$	36.8258	+	26.7555i	0.112274	+	0.0815716i
$329$			451.799i			1.37325i
$330$		0			0
$331$	−17.6498			−0.0533226			−0.0266613	−	0.999645i	$-0.508488\pi$
$331$	−17.6498			−0.0533226			−0.0266613	+	0.999645i	$0.508488\pi$
$332$	−311.761	+	429.102i	−0.939039	+	1.29248i
$333$		0			0
$334$	13.7637	+	42.3605i	0.0412088	+	0.126828i
$335$	−43.1688	−	59.4168i	−0.128862	−	0.177364i
$336$		0			0
$337$	−135.935	−	418.364i	−0.403367	−	1.24144i	−0.922251	−	0.386592i	$-0.873652\pi$
$337$	−135.935	−	418.364i	−0.403367	−	1.24144i	0.518884	−	0.854845i	$-0.326348\pi$
$338$	85.1587	+	27.6697i	0.251949	+	0.0818631i
$339$		0			0
$340$	32.7772			0.0964034
$341$	158.898	−	135.620i	0.465975	−	0.397714i
$342$		0			0
$343$	283.736	+	206.146i	0.827218	+	0.601009i
$344$	−288.686	−	93.7999i	−0.839205	−	0.272674i
$345$		0			0
$346$	66.5550	−	48.3550i	0.192355	−	0.139754i
$347$	−239.758	−	329.998i	−0.690944	−	0.951003i	0.309056	−	0.951044i	$-0.399987\pi$
$347$	−239.758	−	329.998i	−0.690944	−	0.951003i	−1.00000		4.11136e-5i	$0.999987\pi$
$348$		0			0
$349$	−147.852	+	455.042i	−0.423645	+	1.30385i	0.480640	+	0.876918i	$0.340404\pi$
$349$	−147.852	+	455.042i	−0.423645	+	1.30385i	−0.904286	+	0.426928i	$0.859596\pi$
$350$	−78.3757	+	107.875i	−0.223931	+	0.308214i
$351$		0			0
$352$	329.936	+	79.3261i	0.937318	+	0.225358i
$353$			551.674i			1.56282i	0.624020	+	0.781409i	$0.285498\pi$
$353$			551.674i			1.56282i	−0.624020	+	0.781409i	$0.714502\pi$
$354$		0			0
$355$	−13.9969	+	43.0782i	−0.0394280	+	0.121347i
$356$	488.211	−	158.629i	1.37138	−	0.445588i
$357$		0			0
$358$	54.0684	−	39.2830i	0.151029	−	0.109729i
$359$	−340.459	+	110.622i	−0.948354	+	0.308139i	−0.742047	−	0.670348i	$-0.766145\pi$
$359$	−340.459	+	110.622i	−0.948354	+	0.308139i	−0.206308	+	0.978487i	$0.566145\pi$
$360$		0			0
$361$	220.262	+	160.029i	0.610143	+	0.443295i
$362$		−	166.439i		−	0.459777i
$363$		0			0
$364$	−175.398			−0.481864
$365$	28.2490	−	38.8814i	0.0773944	−	0.106524i
$366$		0			0
$367$	−32.6507	−	100.489i	−0.0889666	−	0.273811i	0.896668	−	0.442704i	$-0.145981\pi$
$367$	−32.6507	−	100.489i	−0.0889666	−	0.273811i	−0.985634	+	0.168893i	$0.945981\pi$
$368$	23.9350	+	32.9436i	0.0650407	+	0.0895208i
$369$		0			0
$370$	−12.4668	−	38.3689i	−0.0336941	−	0.103700i
$371$	−249.516	−	81.0727i	−0.672550	−	0.218525i
$372$		0			0
$373$	483.127			1.29525			0.647623	−	0.761961i	$-0.275763\pi$
$373$	483.127			1.29525			0.647623	+	0.761961i	$0.275763\pi$
$374$	19.7258	−	82.0444i	0.0527429	−	0.219370i
$375$		0			0
$376$	−320.482	−	232.844i	−0.852347	−	0.619266i
$377$	342.604	+	111.319i	0.908765	+	0.295276i
$378$		0			0
$379$	−362.665	+	263.492i	−0.956901	+	0.695229i	−0.952429	−	0.304761i	$-0.901423\pi$
$379$	−362.665	+	263.492i	−0.956901	+	0.695229i	−0.00447174	+	0.999990i	$0.501423\pi$
$380$	−19.3220	−	26.5944i	−0.0508473	−	0.0699853i
$381$		0			0
$382$	50.9129	−	156.694i	0.133280	−	0.410193i
$383$	281.976	−	388.106i	0.736229	−	1.01333i	−0.262598	−	0.964905i	$-0.584579\pi$
$383$	281.976	−	388.106i	0.736229	−	1.01333i	0.998827	−	0.0484270i	$-0.0154208\pi$
$384$		0			0
$385$	51.0667	+	59.8315i	0.132641	+	0.155407i
$386$			186.210i			0.482409i
$387$		0			0
$388$	158.056	−	486.447i	0.407361	−	1.25373i
$389$	−289.807	+	94.1639i	−0.745005	+	0.242067i	−0.656830	−	0.754038i	$-0.728103\pi$
$389$	−289.807	+	94.1639i	−0.745005	+	0.242067i	−0.0881743	+	0.996105i	$0.528103\pi$
$390$		0			0
$391$	36.6586	−	26.6340i	0.0937560	−	0.0681177i
$392$	−13.3699	+	4.34416i	−0.0341070	+	0.0110820i
$393$		0			0
$394$	112.385	+	81.6523i	0.285241	+	0.207239i
$395$		−	89.8059i		−	0.227357i
$396$		0			0
$397$	−433.795			−1.09268			−0.546342	−	0.837562i	$-0.683980\pi$
$397$	−433.795			−1.09268			−0.546342	+	0.837562i	$0.683980\pi$
$398$	−69.1239	+	95.1409i	−0.173678	+	0.239048i
$399$		0			0
$400$	62.3518	+	191.899i	0.155880	+	0.479748i
$401$	31.3201	+	43.1084i	0.0781050	+	0.107502i	0.846282	−	0.532735i	$-0.178836\pi$
$401$	31.3201	+	43.1084i	0.0781050	+	0.107502i	−0.768177	+	0.640238i	$0.778836\pi$
$402$		0			0
$403$	−45.2156	−	139.159i	−0.112198	−	0.345309i
$404$	497.289	+	161.579i	1.23091	+	0.399948i
$405$		0			0
$406$	−260.814			−0.642400
$407$	517.426	−	40.5500i	1.27132	−	0.0996315i
$408$		0			0
$409$	96.8500	+	70.3657i	0.236797	+	0.172043i	0.699855	−	0.714285i	$-0.253248\pi$
$409$	96.8500	+	70.3657i	0.236797	+	0.172043i	−0.463058	+	0.886328i	$0.653248\pi$
$410$	−6.18086	−	2.00828i	−0.0150753	−	0.00489825i
$411$		0			0
$412$	170.909	−	124.173i	0.414828	−	0.301390i
$413$	−470.791	−	647.988i	−1.13993	−	1.56898i
$414$		0			0
$415$	51.4848	−	158.454i	0.124060	−	0.381816i
$416$	139.704	−	192.286i	0.335827	−	0.462226i
$417$		0			0
$418$	−78.1967	+	32.3598i	−0.187073	+	0.0774158i
$419$		−	165.561i		−	0.395133i	−0.980289	−	0.197566i	$-0.936696\pi$
$419$		−	165.561i		−	0.395133i	0.980289	−	0.197566i	$-0.0633038\pi$
$420$		0			0
$421$	−1.17216	+	3.60755i	−0.00278424	+	0.00856901i	−0.952439	−	0.304729i	$-0.901434\pi$
$421$	−1.17216	+	3.60755i	−0.00278424	+	0.00856901i	0.949655	+	0.313298i	$0.101434\pi$
$422$	93.4768	−	30.3725i	0.221509	−	0.0719726i
$423$		0			0
$424$	186.102	−	135.211i	0.438920	−	0.318894i
$425$	213.539	−	69.3830i	0.502444	−	0.163254i
$426$		0			0
$427$	−449.964	−	326.918i	−1.05378	−	0.765615i
$428$		−	171.678i		−	0.401116i
$429$		0			0
$430$	43.3380			0.100786
$431$	90.8780	−	125.083i	0.210854	−	0.290215i	−0.690470	−	0.723361i	$-0.742596\pi$
$431$	90.8780	−	125.083i	0.210854	−	0.290215i	0.901324	+	0.433145i	$0.142596\pi$
$432$		0			0
$433$	−82.0387	−	252.489i	−0.189466	−	0.583116i	0.810531	−	0.585696i	$-0.199179\pi$
$433$	−82.0387	−	252.489i	−0.189466	−	0.583116i	−0.999997	+	0.00258002i	$0.999179\pi$
$434$	62.2687	+	85.7055i	0.143476	+	0.197478i
$435$		0			0
$436$	−64.9396	−	199.864i	−0.148944	−	0.458403i
$437$	−43.2201	−	14.0431i	−0.0989019	−	0.0321352i
$438$		0			0
$439$	−716.385			−1.63186			−0.815928	−	0.578153i	$-0.803774\pi$
$439$	−716.385			−1.63186			−0.815928	+	0.578153i	$0.803774\pi$
$440$	−68.7597	+	5.38861i	−0.156272	+	0.0122469i
$441$		0			0
$442$	−47.8153	−	34.7398i	−0.108179	−	0.0785969i
$443$	−39.7219	−	12.9064i	−0.0896657	−	0.0291342i	0.263841	−	0.964566i	$-0.415011\pi$
$443$	−39.7219	−	12.9064i	−0.0896657	−	0.0291342i	−0.353506	+	0.935432i	$0.615011\pi$
$444$		0			0
$445$	−130.452	+	94.7793i	−0.293152	+	0.212987i
$446$	52.1618	+	71.7945i	0.116955	+	0.160974i
$447$		0			0
$448$	18.0892	−	55.6729i	0.0403777	−	0.124270i
$449$	156.198	−	214.988i	0.347880	−	0.478815i	−0.598843	−	0.800867i	$-0.704372\pi$
$449$	156.198	−	214.988i	0.347880	−	0.478815i	0.946722	+	0.322052i	$0.104372\pi$
$450$		0			0
$451$	43.7086	−	71.2730i	0.0969148	−	0.158033i
$452$			289.227i			0.639882i
$453$		0			0
$454$	53.4760	−	164.582i	0.117789	−	0.362516i
$455$	52.3993	−	17.0256i	0.115163	−	0.0374188i
$456$		0			0
$457$	346.228	−	251.549i	0.757609	−	0.550435i	−0.140567	−	0.990071i	$-0.544892\pi$
$457$	346.228	−	251.549i	0.757609	−	0.550435i	0.898176	+	0.439636i	$0.144892\pi$
$458$	216.236	−	70.2593i	0.472130	−	0.153404i
$459$		0			0
$460$	−13.6189	−	9.89471i	−0.0296063	−	0.0215102i
$461$			313.392i			0.679809i	0.940460	+	0.339904i	$0.110395\pi$
$461$			313.392i			0.679809i	−0.940460	+	0.339904i	$0.889605\pi$
$462$		0			0
$463$	−529.774			−1.14422			−0.572110	−	0.820177i	$-0.693875\pi$
$463$	−529.774			−1.14422			−0.572110	+	0.820177i	$0.693875\pi$
$464$	−231.982	+	319.295i	−0.499961	+	0.688137i
$465$		0			0
$466$	47.7204	+	146.868i	0.102404	+	0.315168i
$467$	40.7515	+	56.0896i	0.0872623	+	0.120106i	0.850416	−	0.526111i	$-0.176350\pi$
$467$	40.7515	+	56.0896i	0.0872623	+	0.120106i	−0.763154	+	0.646217i	$0.776350\pi$
$468$		0			0
$469$	148.061	+	455.685i	0.315695	+	0.971610i
$470$	53.7900	+	17.4774i	0.114447	+	0.0371860i
$471$		0			0
$472$	702.281			1.48788
$473$	−130.334	+	542.088i	−0.275547	+	1.14606i
$474$		0			0
$475$	−182.175	−	132.358i	−0.383527	−	0.278649i
$476$	−203.369	−	66.0786i	−0.427246	−	0.138820i
$477$		0			0
$478$	−58.6706	+	42.6267i	−0.122742	+	0.0891772i
$479$	−12.2496	−	16.8601i	−0.0255732	−	0.0351985i	0.796039	−	0.605245i	$-0.206925\pi$
$479$	−12.2496	−	16.8601i	−0.0255732	−	0.0351985i	−0.821612	+	0.570047i	$0.806925\pi$
$480$		0			0
$481$	112.336	−	345.733i	0.233546	−	0.718780i
$482$	74.4749	−	102.506i	0.154512	−	0.212668i
$483$		0			0
$484$	63.3529	−	398.288i	0.130894	−	0.822909i
$485$			160.665i			0.331269i
$486$		0			0
$487$	25.7159	−	79.1453i	0.0528047	−	0.162516i	−0.921176	−	0.389145i	$-0.872770\pi$
$487$	25.7159	−	79.1453i	0.0528047	−	0.162516i	0.973981	+	0.226629i	$0.0727705\pi$
$488$	463.797	−	150.697i	0.950403	−	0.308805i
$489$		0			0
$490$	1.62379	−	1.17975i	0.00331385	−	0.00240766i
$491$	−92.5446	+	30.0696i	−0.188482	+	0.0612415i	−0.401737	−	0.915755i	$-0.631593\pi$
$491$	−92.5446	+	30.0696i	−0.188482	+	0.0612415i	0.213255	+	0.976997i	$0.431593\pi$
$492$		0			0
$493$	355.301	+	258.141i	0.720692	+	0.523613i
$494$			59.2749i			0.119990i
$495$		0			0
$496$	160.308			0.323201
$497$	173.691	−	239.065i	0.349478	−	0.481015i
$498$		0			0
$499$	94.0553	+	289.473i	0.188488	+	0.580105i	0.999991	−	0.00424242i	$-0.00135041\pi$
$499$	94.0553	+	289.473i	0.188488	+	0.580105i	−0.811503	+	0.584348i	$0.801350\pi$
$500$	−100.307	−	138.061i	−0.200614	−	0.276121i
$501$		0			0
$502$	75.6375	+	232.788i	0.150672	+	0.463722i
$503$	−675.460	−	219.470i	−1.34286	−	0.436323i	−0.452577	−	0.891725i	$-0.649495\pi$
$503$	−675.460	−	219.470i	−1.34286	−	0.436323i	−0.890286	+	0.455402i	$0.849495\pi$
$504$		0			0
$505$	−164.247			−0.325241
$506$	−32.9635	+	28.1346i	−0.0651452	+	0.0556020i
$507$		0			0
$508$	−203.995	−	148.211i	−0.401565	−	0.291754i
$509$	−720.939	−	234.247i	−1.41638	−	0.460211i	−0.501933	−	0.864907i	$-0.667377\pi$
$509$	−720.939	−	234.247i	−1.41638	−	0.460211i	−0.914451	+	0.404696i	$0.867377\pi$
$510$		0			0
$511$	−253.658	+	184.293i	−0.496395	+	0.360652i
$512$	271.913	+	374.257i	0.531081	+	0.730970i
$513$		0			0
$514$	−93.4707	+	287.673i	−0.181850	+	0.559676i
$515$	−39.0049	+	53.6857i	−0.0757377	+	0.104244i
$516$		0			0
$517$	−380.381	+	620.265i	−0.735747	+	1.19974i
$518$			263.196i			0.508101i
$519$		0			0
$520$	−14.9281	+	45.9438i	−0.0287078	+	0.0883535i
$521$	−257.644	+	83.7137i	−0.494519	+	0.160679i	−0.545650	−	0.838013i	$-0.683717\pi$
$521$	−257.644	+	83.7137i	−0.494519	+	0.160679i	0.0511313	+	0.998692i	$0.483717\pi$
$522$		0			0
$523$	−245.189	+	178.141i	−0.468814	+	0.340613i	−0.796979	−	0.604007i	$-0.793570\pi$
$523$	−245.189	+	178.141i	−0.468814	+	0.340613i	0.328165	+	0.944620i	$0.393570\pi$
$524$	393.702	−	127.922i	0.751341	−	0.244125i
$525$		0			0
$526$	−232.519	−	168.935i	−0.442052	−	0.321170i
$527$		−	178.385i		−	0.338492i
$528$		0			0
$529$	505.728			0.956008
$530$	−19.3046	+	26.5705i	−0.0364238	+	0.0501331i
$531$		0			0
$532$	66.2708	+	203.961i	0.124569	+	0.383384i
$533$	−34.4210	−	47.3764i	−0.0645797	−	0.0888863i
$534$		0			0
$535$	16.6644	+	51.2877i	0.0311484	+	0.0958649i
$536$	−399.545	−	129.820i	−0.745421	−	0.242202i
$537$		0			0
$538$	−125.145			−0.232611
$539$	9.87345	+	23.8589i	0.0183181	+	0.0442652i
$540$		0			0
$541$	840.309	+	610.520i	1.55325	+	1.12850i	0.941282	+	0.337622i	$0.109622\pi$
$541$	840.309	+	610.520i	1.55325	+	1.12850i	0.611969	+	0.790881i	$0.290378\pi$
$542$	283.010	+	91.9556i	0.522159	+	0.169660i
$543$		0			0
$544$	234.423	−	170.318i	0.430925	−	0.313085i
$545$	38.8007	+	53.4046i	0.0711939	+	0.0979901i
$546$		0			0
$547$	91.8203	−	282.594i	0.167862	−	0.516625i	−0.831374	−	0.555713i	$-0.812445\pi$
$547$	91.8203	−	282.594i	0.167862	−	0.516625i	0.999236	+	0.0390882i	$0.0124453\pi$
$548$	−104.145	+	143.343i	−0.190045	+	0.261575i
$549$		0			0
$550$	−198.423	+	82.1127i	−0.360770	+	0.149296i
$551$		−	440.454i		−	0.799372i
$552$		0			0
$553$	−181.048	+	557.209i	−0.327393	+	1.00761i
$554$	−162.276	+	52.7267i	−0.292917	+	0.0951745i
$555$		0			0
$556$	−213.174	+	154.880i	−0.383406	+	0.278561i
$557$	−507.507	+	164.899i	−0.911144	+	0.296049i	−0.726829	−	0.686819i	$-0.759007\pi$
$557$	−507.507	+	164.899i	−0.911144	+	0.296049i	−0.184315	+	0.982867i	$0.559007\pi$
$558$		0			0
$559$	315.928	+	229.535i	0.565166	+	0.410617i
$560$			60.3626i			0.107790i
$561$		0			0
$562$	387.486			0.689476
$563$	124.319	−	171.110i	0.220814	−	0.303925i	−0.684210	−	0.729285i	$-0.739853\pi$
$563$	124.319	−	171.110i	0.220814	−	0.303925i	0.905024	+	0.425360i	$0.139853\pi$
$564$		0			0
$565$	−28.0747	−	86.4049i	−0.0496897	−	0.152929i
$566$	82.9896	+	114.225i	0.146625	+	0.201812i
$567$		0			0
$568$	80.0648	+	246.414i	0.140959	+	0.433828i
$569$	686.408	+	223.027i	1.20634	+	0.391964i	0.842090	−	0.539337i	$-0.181325\pi$
$569$	686.408	+	223.027i	1.20634	+	0.391964i	0.364250	+	0.931301i	$0.381325\pi$
$570$		0			0
$571$	798.387			1.39823			0.699113	−	0.715011i	$-0.253578\pi$
$571$	798.387			1.39823			0.699113	+	0.715011i	$0.253578\pi$
$572$	−240.801	−	147.673i	−0.420980	−	0.258169i
$573$		0			0
$574$	34.3010	+	24.9211i	0.0597579	+	0.0434166i
$575$	−109.671	−	35.6341i	−0.190731	−	0.0619724i
$576$		0			0
$577$	476.899	−	346.488i	0.826515	−	0.600498i	−0.0920561	−	0.995754i	$-0.529344\pi$
$577$	476.899	−	346.488i	0.826515	−	0.600498i	0.918571	+	0.395255i	$0.129344\pi$
$578$	96.3783	+	132.653i	0.166745	+	0.229504i
$579$		0			0
$580$	50.4183	−	155.172i	0.0869281	−	0.267537i
$581$	−638.884	+	879.348i	−1.09963	+	1.51351i
$582$		0			0
$583$	−274.298	−	321.377i	−0.470494	−	0.551247i
$584$		−	274.911i		−	0.470738i
$585$		0			0
$586$	95.9752	−	295.381i	0.163780	−	0.504063i
$587$	−120.102	+	39.0236i	−0.204604	+	0.0664798i	−0.409526	−	0.912298i	$-0.634306\pi$
$587$	−120.102	+	39.0236i	−0.204604	+	0.0664798i	0.204922	+	0.978778i	$0.434306\pi$
$588$		0			0
$589$	−144.736	+	105.157i	−0.245733	+	0.178535i
$590$	−95.3599	+	30.9843i	−0.161627	+	0.0525158i
$591$		0			0
$592$	322.212	+	234.100i	0.544276	+	0.395440i
$593$		−	447.206i		−	0.754141i	−0.926185	−	0.377071i	$-0.876931\pi$
$593$		−	447.206i		−	0.754141i	0.926185	−	0.377071i	$-0.123069\pi$
$594$		0			0
$595$	67.1694			0.112890
$596$	42.5626	−	58.5823i	0.0714137	−	0.0982925i
$597$		0			0
$598$	9.38004	+	28.8688i	0.0156857	+	0.0482756i
$599$	385.750	+	530.940i	0.643990	+	0.886377i	0.998821	−	0.0485540i	$-0.0154613\pi$
$599$	385.750	+	530.940i	0.643990	+	0.886377i	−0.354830	+	0.934931i	$0.615461\pi$
$600$		0			0
$601$	−61.9808	−	190.757i	−0.103129	−	0.317400i	0.886157	−	0.463384i	$-0.153365\pi$
$601$	−61.9808	−	190.757i	−0.103129	−	0.317400i	−0.989287	+	0.145985i	$0.953365\pi$
$602$	−268.894	−	87.3690i	−0.446668	−	0.145131i
$603$		0			0
$604$	−413.592			−0.684755
$605$	19.7347	+	125.136i	0.0326193	+	0.206836i
$606$		0			0
$607$	−734.383	−	533.561i	−1.20986	−	0.879013i	−0.214640	−	0.976693i	$-0.568858\pi$
$607$	−734.383	−	533.561i	−1.20986	−	0.879013i	−0.995218	+	0.0976805i	$0.968858\pi$
$608$	−276.382	−	89.8021i	−0.454576	−	0.147701i
$609$		0			0
$610$	−56.3284	+	40.9250i	−0.0923417	+	0.0670902i
$611$	299.554	+	412.301i	0.490269	+	0.674797i
$612$		0			0
$613$	−240.068	+	738.852i	−0.391627	+	1.20531i	0.539930	+	0.841710i	$0.318451\pi$
$613$	−240.068	+	738.852i	−0.391627	+	1.20531i	−0.931557	+	0.363595i	$0.881549\pi$
$614$	164.873	−	226.928i	0.268523	−	0.369590i
$615$		0			0
$616$	437.489	+	105.185i	0.710210	+	0.170755i
$617$		−	490.222i		−	0.794525i	−0.917705	−	0.397263i	$-0.869960\pi$
$617$		−	490.222i		−	0.794525i	0.917705	−	0.397263i	$-0.130040\pi$
$618$		0			0
$619$	−92.4231	+	284.449i	−0.149310	+	0.459530i	−0.997540	−	0.0700985i	$-0.977669\pi$
$619$	−92.4231	+	284.449i	−0.149310	+	0.459530i	0.848230	+	0.529628i	$0.177669\pi$
$620$	−63.0277	+	20.4790i	−0.101658	+	0.0330306i
$621$		0			0
$622$	−120.638	+	87.6487i	−0.193952	+	0.140914i
$623$	1000.48	−	325.075i	1.60590	−	0.521790i
$624$		0			0
$625$	−440.098	−	319.750i	−0.704158	−	0.511600i
$626$			51.0637i			0.0815714i
$627$		0			0
$628$	−603.989			−0.961765
$629$	260.499	−	358.546i	0.414148	−	0.570026i
$630$		0			0
$631$	−260.825	−	802.738i	−0.413353	−	1.27217i	−0.913716	−	0.406353i	$-0.866800\pi$
$631$	−260.825	−	802.738i	−0.413353	−	1.27217i	0.500364	−	0.865815i	$-0.333200\pi$
$632$	−301.948	−	415.596i	−0.477766	−	0.657588i
$633$		0			0
$634$	−49.0983	−	151.109i	−0.0774421	−	0.238342i
$635$	75.3289	+	24.4758i	0.118628	+	0.0385446i
$636$		0			0
$637$	18.0856			0.0283919
$638$	−358.067	−	219.586i	−0.561233	−	0.344179i
$639$		0			0
$640$	−110.446	−	80.2437i	−0.172572	−	0.125381i
$641$	915.198	+	297.366i	1.42777	+	0.463909i	0.918061	−	0.396440i	$-0.129754\pi$
$641$	915.198	+	297.366i	1.42777	+	0.463909i	0.509705	+	0.860349i	$0.329754\pi$
$642$		0			0
$643$	−21.2668	+	15.4512i	−0.0330743	+	0.0240299i	−0.604200	−	0.796833i	$-0.706507\pi$
$643$	−21.2668	+	15.4512i	−0.0330743	+	0.0240299i	0.571125	+	0.820863i	$0.306507\pi$
$644$	64.5520	+	88.8483i	0.100236	+	0.137963i
$645$		0			0
$646$	−22.3309	+	68.7273i	−0.0345679	+	0.106389i
$647$	−172.665	+	237.653i	−0.266870	+	0.367315i	−0.921330	−	0.388781i	$-0.872896\pi$
$647$	−172.665	+	237.653i	−0.266870	+	0.367315i	0.654460	+	0.756097i	$0.272896\pi$
$648$		0			0
$649$	−100.781	−	1285.98i	−0.155286	−	1.98148i
$650$			150.409i			0.231399i
$651$		0			0
$652$	−285.064	+	877.337i	−0.437215	+	1.34561i
$653$	−570.706	+	185.433i	−0.873975	+	0.283972i	−0.711453	−	0.702733i	$-0.751963\pi$
$653$	−570.706	+	185.433i	−0.873975	+	0.283972i	−0.162522	+	0.986705i	$0.551963\pi$
$654$		0			0
$655$	−105.199	+	76.4318i	−0.160610	+	0.116690i
$656$	61.0182	−	19.8260i	0.0930155	−	0.0302226i
$657$		0			0
$658$	−298.510	−	216.880i	−0.453663	−	0.329606i
$659$			19.2417i			0.0291983i	0.999893	+	0.0145992i	$0.00464722\pi$
$659$			19.2417i			0.0291983i	−0.999893	+	0.0145992i	$0.995353\pi$
$660$		0			0
$661$	543.444			0.822154			0.411077	−	0.911601i	$-0.365153\pi$
$661$	543.444			0.822154			0.411077	+	0.911601i	$0.365153\pi$
$662$	8.47256	−	11.6615i	0.0127984	−	0.0176155i
$663$		0			0
$664$	−294.501	−	906.382i	−0.443526	−	1.36503i
$665$	−39.5961	−	54.4993i	−0.0595429	−	0.0819538i
$666$		0			0
$667$	−69.7003	−	214.515i	−0.104498	−	0.321612i
$668$	172.879	+	56.1717i	0.258801	+	0.0840894i
$669$		0			0
$670$	59.9803			0.0895228
$671$	−342.505	−	827.655i	−0.510440	−	1.23347i
$672$		0			0
$673$	−1.17118	−	0.850910i	−0.00174023	−	0.00126435i	0.586915	−	0.809649i	$-0.300342\pi$
$673$	−1.17118	−	0.850910i	−0.00174023	−	0.00126435i	−0.588655	+	0.808384i	$0.700342\pi$
$674$	341.673	+	111.016i	0.506934	+	0.164713i
$675$		0			0
$676$	295.639	−	214.794i	0.437335	−	0.317743i
$677$	616.765	+	848.904i	0.911026	+	1.25392i	0.966815	+	0.255477i	$0.0822326\pi$
$677$	616.765	+	848.904i	0.911026	+	1.25392i	−0.0557889	+	0.998443i	$0.517767\pi$
$678$		0			0
$679$	323.900	−	996.863i	0.477026	−	1.46813i
$680$	−34.6172	+	47.6465i	−0.0509077	+	0.0700684i
$681$		0			0
$682$	13.3297	+	170.089i	0.0195450	+	0.249397i
$683$		−	810.057i		−	1.18603i	−0.805192	−	0.593014i	$-0.797938\pi$
$683$		−	810.057i		−	1.18603i	0.805192	−	0.593014i	$-0.202062\pi$
$684$		0			0
$685$	17.1987	−	52.9321i	0.0251076	−	0.0772731i
$686$	−272.408	+	88.5106i	−0.397096	+	0.129024i
$687$		0			0
$688$	−346.128	+	251.477i	−0.503093	+	0.365518i
$689$	−281.456	+	91.4506i	−0.408499	+	0.132729i
$690$		0			0
$691$	86.1504	+	62.5919i	0.124675	+	0.0905817i	0.648375	−	0.761321i	$-0.275449\pi$
$691$	86.1504	+	62.5919i	0.124675	+	0.0905817i	−0.523700	+	0.851903i	$0.675449\pi$
$692$		−	335.740i		−	0.485174i
$693$		0			0
$694$	333.127			0.480011
$695$	48.6507	−	66.9619i	0.0700010	−	0.0963480i
$696$		0			0
$697$	−22.0617	−	67.8990i	−0.0316524	−	0.0974160i
$698$	−229.679	−	316.126i	−0.329053	−	0.452902i
$699$		0			0
$700$	168.161	+	517.548i	0.240231	+	0.739354i
$701$	1035.58	+	336.481i	1.47729	+	0.480002i	0.933303	−	0.359090i	$-0.116913\pi$
$701$	1035.58	+	336.481i	1.47729	+	0.480002i	0.543990	+	0.839092i	$0.316913\pi$
$702$		0			0
$703$	−444.477			−0.632257
$704$	71.7068	−	61.2023i	0.101856	−	0.0869351i
$705$		0			0
$706$	−364.500	−	264.825i	−0.516289	−	0.375106i
$707$	1019.08	+	331.120i	1.44142	+	0.468345i
$708$		0			0
$709$	−47.5479	+	34.5456i	−0.0670633	+	0.0487243i	−0.620812	−	0.783960i	$-0.713197\pi$
$709$	−47.5479	+	34.5456i	−0.0670633	+	0.0487243i	0.553749	+	0.832684i	$0.313197\pi$
$710$	−21.7433	−	29.9271i	−0.0306244	−	0.0421509i
$711$		0			0
$712$	−285.027	+	877.221i	−0.400318	+	1.23205i
$713$	−53.8506	+	74.1190i	−0.0755268	+	0.103954i
$714$		0			0
$715$	86.2722	+	20.7423i	0.120660	+	0.0290102i
$716$		−	272.751i		−	0.380938i
$717$		0			0
$718$	90.3437	−	278.049i	0.125827	−	0.387255i
$719$	−692.977	+	225.162i	−0.963806	+	0.313160i	−0.748313	−	0.663346i	$-0.769136\pi$
$719$	−692.977	+	225.162i	−0.963806	+	0.313160i	−0.215493	+	0.976505i	$0.569136\pi$
$720$		0			0
$721$	350.240	−	254.464i	0.485769	−	0.352932i
$722$	−211.468	+	68.7100i	−0.292892	+	0.0951663i
$723$		0			0
$724$	−549.533	−	399.259i	−0.759024	−	0.551463i
$725$		−	1117.65i		−	1.54158i
$726$		0			0
$727$	1161.64			1.59785			0.798925	−	0.601431i	$-0.205403\pi$
$727$	1161.64			1.59785			0.798925	+	0.601431i	$0.205403\pi$
$728$	185.245	−	254.968i	0.254457	−	0.350230i
$729$		0			0
$730$	12.1289	+	37.3290i	0.0166150	+	0.0511357i
$731$	279.835	+	385.159i	0.382811	+	0.526894i
$732$		0			0
$733$	72.2285	+	222.296i	0.0985382	+	0.303269i	0.988160	−	0.153429i	$-0.0490317\pi$
$733$	72.2285	+	222.296i	0.0985382	+	0.303269i	−0.889621	+	0.456699i	$0.849032\pi$
$734$	82.0680	+	26.6655i	0.111809	+	0.0363290i
$735$		0			0
$736$	−148.818			−0.202198
$737$	−180.383	+	750.257i	−0.244753	+	1.01799i
$738$		0			0
$739$	606.715	+	440.804i	0.820995	+	0.596487i	0.916997	−	0.398894i	$-0.130606\pi$
$739$	606.715	+	440.804i	0.820995	+	0.596487i	−0.0960026	+	0.995381i	$0.530606\pi$
$740$	−156.589	−	50.8788i	−0.211606	−	0.0687551i
$741$		0			0
$742$	173.343	−	125.941i	0.233616	−	0.169732i
$743$	313.977	+	432.152i	0.422580	+	0.581631i	0.966230	−	0.257680i	$-0.0829582\pi$
$743$	313.977	+	432.152i	0.422580	+	0.581631i	−0.543650	+	0.839312i	$0.682958\pi$
$744$		0			0
$745$	−7.02886	+	21.6326i	−0.00943471	+	0.0290371i
$746$	−231.919	+	319.209i	−0.310884	+	0.427895i
$747$		0			0
$748$	−223.568	−	261.940i	−0.298887	−	0.350187i
$749$		−	351.815i		−	0.469712i
$750$		0			0
$751$	−367.303	+	1130.44i	−0.489086	+	1.50525i	0.336889	+	0.941544i	$0.390625\pi$
$751$	−367.303	+	1130.44i	−0.489086	+	1.50525i	−0.825975	+	0.563707i	$0.809375\pi$
$752$	−531.021	+	172.539i	−0.706145	+	0.229440i
$753$		0			0
$754$	−238.013	+	172.927i	−0.315667	+	0.229346i
$755$	123.558	−	40.1465i	0.163653	−	0.0531742i
$756$		0			0
$757$	−120.025	−	87.2036i	−0.158554	−	0.115196i	0.505679	−	0.862722i	$-0.331242\pi$
$757$	−120.025	−	87.2036i	−0.158554	−	0.115196i	−0.664233	+	0.747525i	$0.731242\pi$
$758$		−	366.105i		−	0.482988i
$759$		0			0
$760$	59.0656			0.0777179
$761$	−115.997	+	159.657i	−0.152427	+	0.209798i	−0.878401	−	0.477924i	$-0.841389\pi$
$761$	−115.997	+	159.657i	−0.152427	+	0.209798i	0.725974	+	0.687722i	$0.241389\pi$
$762$		0			0
$763$	−133.079	−	409.575i	−0.174416	−	0.536796i
$764$	−395.225	−	543.981i	−0.517311	−	0.712017i
$765$		0			0
$766$	121.069	+	372.611i	0.158053	+	0.486438i
$767$	−859.266	−	279.192i	−1.12029	−	0.364006i
$768$		0			0
$769$	1174.93			1.52787			0.763934	−	0.645294i	$-0.223265\pi$
$769$	1174.93			1.52787			0.763934	+	0.645294i	$0.223265\pi$
$770$	−64.0456	+	5.01917i	−0.0831761	+	0.00651841i
$771$		0			0
$772$	614.811	+	446.686i	0.796387	+	0.578609i
$773$	−681.055	−	221.288i	−0.881055	−	0.286272i	−0.166660	−	0.986014i	$-0.553298\pi$
$773$	−681.055	−	221.288i	−0.881055	−	0.286272i	−0.714395	+	0.699742i	$0.753298\pi$
$774$		0			0
$775$	−367.267	+	266.835i	−0.473893	+	0.344304i
$776$	540.193	+	743.512i	0.696126	+	0.958135i
$777$		0			0
$778$	76.9027	−	236.682i	0.0988466	−	0.304219i
$779$	−42.0860	+	57.9263i	−0.0540256	+	0.0743599i
$780$		0			0
$781$	439.731	−	181.972i	0.563036	−	0.232999i
$782$			37.0062i			0.0473225i
$783$		0			0
$784$	−6.12300	+	18.8447i	−0.00780996	+	0.0240366i
$785$	180.438	−	58.6279i	0.229858	−	0.0746853i
$786$		0			0
$787$	−529.623	+	384.793i	−0.672964	+	0.488937i	−0.871016	−	0.491255i	$-0.836538\pi$
$787$	−529.623	+	384.793i	−0.672964	+	0.488937i	0.198052	+	0.980192i	$0.436538\pi$
$788$	539.184	−	175.192i	0.684244	−	0.222324i
$789$		0			0
$790$	59.3361	+	43.1102i	0.0751090	+	0.0545699i
$791$			592.705i			0.749311i
$792$		0			0
$793$	−627.382			−0.791149
$794$	208.238	−	286.615i	0.262265	−	0.360976i
$795$		0			0
$796$	148.311	+	456.454i	0.186320	+	0.573435i
$797$	−305.358	−	420.289i	−0.383134	−	0.527338i	0.573278	−	0.819361i	$-0.305672\pi$
$797$	−305.358	−	420.289i	−0.383134	−	0.527338i	−0.956411	+	0.292023i	$0.905672\pi$
$798$		0			0
$799$	191.996	+	590.902i	0.240295	+	0.739552i
$800$	−701.318	−	227.872i	−0.876647	−	0.284840i
$801$		0			0
$802$	−43.5172			−0.0542609
$803$	−503.403	+	39.4511i	−0.626903	+	0.0491296i
$804$		0			0
$805$	−27.9089	−	20.2770i	−0.0346694	−	0.0251888i
$806$	113.650	+	36.9271i	0.141005	+	0.0458153i
$807$		0			0
$808$	−760.085	+	552.234i	−0.940700	+	0.683458i
$809$	561.893	+	773.379i	0.694552	+	0.955969i	0.999993	+	0.00375802i	$0.00119622\pi$
$809$	561.893	+	773.379i	0.694552	+	0.955969i	−0.305441	+	0.952211i	$0.598804\pi$
$810$		0			0
$811$	−93.2508	+	286.996i	−0.114982	+	0.353880i	−0.991943	−	0.126682i	$-0.959567\pi$
$811$	−93.2508	+	286.996i	−0.114982	+	0.353880i	0.876961	+	0.480562i	$0.159567\pi$
$812$	−625.649	+	861.133i	−0.770504	+	1.06051i
$813$		0			0
$814$	−221.592	+	361.337i	−0.272226	+	0.443903i
$815$		−	289.770i		−	0.355546i
$816$		0			0
$817$	147.546	−	454.099i	0.180595	−	0.555813i
$818$	−92.9834	+	30.2121i	−0.113672	+	0.0369341i
$819$		0			0
$820$	−21.4576	+	15.5899i	−0.0261678	+	0.0190120i
$821$	−219.376	+	71.2794i	−0.267205	+	0.0868203i	−0.439555	−	0.898215i	$-0.644864\pi$
$821$	−219.376	+	71.2794i	−0.267205	+	0.0868203i	0.172350	+	0.985036i	$0.444864\pi$
$822$		0			0
$823$	103.804	+	75.4178i	0.126128	+	0.0916376i	0.649061	−	0.760736i	$-0.275162\pi$
$823$	103.804	+	75.4178i	0.126128	+	0.0916376i	−0.522933	+	0.852374i	$0.675162\pi$
$824$			379.585i			0.460661i
$825$		0			0
$826$	654.133			0.791929
$827$	−387.612	+	533.503i	−0.468697	+	0.645106i	−0.976284	−	0.216495i	$-0.930538\pi$
$827$	−387.612	+	533.503i	−0.468697	+	0.645106i	0.507587	+	0.861601i	$0.330538\pi$
$828$		0			0
$829$	124.935	+	384.512i	0.150706	+	0.463826i	0.997701	−	0.0677757i	$-0.0215902\pi$
$829$	124.935	+	384.512i	0.150706	+	0.463826i	−0.846994	+	0.531602i	$0.821590\pi$
$830$	79.9783	+	110.081i	0.0963593	+	0.132627i
$831$		0			0
$832$	−20.4048	−	62.7994i	−0.0245250	−	0.0754800i
$833$	20.9697	+	6.81347i	0.0251737	+	0.00817944i
$834$		0			0
$835$	−57.0990			−0.0683821
$836$	−80.7380	+	335.808i	−0.0965765	+	0.401685i
$837$		0			0
$838$	109.389	+	79.4754i	0.130535	+	0.0948394i
$839$	−443.025	−	143.947i	−0.528039	−	0.171570i	0.0328515	−	0.999460i	$-0.489541\pi$
$839$	−443.025	−	143.947i	−0.528039	−	0.171570i	−0.560891	+	0.827890i	$0.689541\pi$
$840$		0			0
$841$	1088.22	−	790.639i	1.29396	−	0.940118i
$842$	−1.82088	−	2.50623i	−0.00216257	−	0.00297652i
$843$		0			0
$844$	123.954	−	381.491i	0.146865	−	0.452004i
$845$	−67.4708	+	92.8656i	−0.0798471	+	0.109900i
$846$		0			0
$847$	129.827	−	816.202i	0.153279	−	0.963639i
$848$		−	324.230i		−	0.382346i
$849$		0			0
$850$	−56.6643	+	174.395i	−0.0666639	+	0.205170i
$851$	−216.475	+	70.3369i	−0.254377	+	0.0826520i
$852$		0			0
$853$	−1188.83	+	863.733i	−1.39370	+	1.01258i	−0.398252	+	0.917276i	$0.630383\pi$
$853$	−1188.83	+	863.733i	−1.39370	+	1.01258i	−0.995448	+	0.0953067i	$0.969617\pi$
$854$	431.999	−	140.365i	0.505854	−	0.164362i
$855$		0			0
$856$	249.559	+	181.315i	0.291541	+	0.211817i
$857$		−	297.274i		−	0.346877i	−0.984845	−	0.173439i	$-0.944512\pi$
$857$		−	297.274i		−	0.346877i	0.984845	−	0.173439i	$-0.0554878\pi$
$858$		0			0
$859$	38.4367			0.0447459			0.0223729	−	0.999750i	$-0.492878\pi$
$859$	38.4367			0.0447459			0.0223729	+	0.999750i	$0.492878\pi$
$860$	103.960	−	143.089i	0.120884	−	0.166383i
$861$		0			0
$862$	39.0193	+	120.089i	0.0452660	+	0.139314i
$863$	585.706	+	806.155i	0.678686	+	0.934131i	0.999917	−	0.0128701i	$-0.00409680\pi$
$863$	585.706	+	806.155i	0.678686	+	0.934131i	−0.321232	+	0.947001i	$0.604097\pi$
$864$		0			0
$865$	32.5896	+	100.301i	0.0376759	+	0.115954i
$866$	206.205	+	67.0001i	0.238112	+	0.0773674i
$867$		0			0
$868$	432.347			0.498095
$869$	−717.686	+	612.551i	−0.825876	+	0.704892i
$870$		0			0
$871$	437.248	+	317.679i	0.502007	+	0.364729i
$872$	359.117	+	116.684i	0.411831	+	0.133812i
$873$		0			0
$874$	30.0258	−	21.8150i	0.0343544	−	0.0249599i
$875$	−205.556	−	282.924i	−0.234922	−	0.323342i
$876$		0			0
$877$	161.707	−	497.683i	0.184386	−	0.567483i	−0.815551	−	0.578685i	$-0.803566\pi$
$877$	161.707	−	497.683i	0.184386	−	0.567483i	0.999937	+	0.0112024i	$0.00356592\pi$
$878$	343.892	−	473.327i	0.391676	−	0.539096i
$879$		0			0
$880$	−50.8209	+	82.8705i	−0.0577510	+	0.0941711i
$881$		−	360.136i		−	0.408780i	−0.978889	−	0.204390i	$-0.934479\pi$
$881$		−	360.136i		−	0.408780i	0.978889	−	0.204390i	$-0.0655211\pi$
$882$		0			0
$883$	331.290	−	1019.61i	0.375187	−	1.15471i	−0.568166	−	0.822914i	$-0.692347\pi$
$883$	331.290	−	1019.61i	0.375187	−	1.15471i	0.943353	−	0.331792i	$-0.107653\pi$
$884$	−229.402	+	74.5371i	−0.259504	+	0.0843180i
$885$		0			0
$886$	27.5955	−	20.0493i	0.0311462	−	0.0226290i
$887$	1044.69	−	339.442i	1.17778	−	0.382685i	0.346240	−	0.938146i	$-0.387458\pi$
$887$	1044.69	−	339.442i	1.17778	−	0.382685i	0.831543	+	0.555461i	$0.187458\pi$
$888$		0			0
$889$	−418.042	−	303.725i	−0.470238	−	0.341648i
$890$		−	131.690i		−	0.147966i
$891$		0			0
$892$	362.172			0.406022
$893$	366.260	−	504.114i	0.410146	−	0.564517i
$894$		0			0
$895$	26.4754	+	81.4829i	0.0295815	+	0.0910424i
$896$	523.501	+	720.538i	0.584265	+	0.804172i
$897$		0			0
$898$	67.0650	+	206.405i	0.0746826	+	0.229849i
$899$	−844.499	−	274.394i	−0.939376	−	0.305222i
$900$		0			0
$901$	−360.792			−0.400435
$902$	26.1094	+	63.0927i	0.0289461	+	0.0699475i
$903$		0			0
$904$	−420.434	−	305.463i	−0.465082	−	0.337902i
$905$	202.925	+	65.9344i	0.224227	+	0.0728557i
$906$		0			0
$907$	−550.128	+	399.691i	−0.606536	+	0.440674i	−0.848193	−	0.529688i	$-0.822309\pi$
$907$	−550.128	+	399.691i	−0.606536	+	0.440674i	0.241657	+	0.970362i	$0.422309\pi$
$908$	−415.122	−	571.367i	−0.457183	−	0.629259i
$909$		0			0
$910$	−13.9046	+	42.7939i	−0.0152798	+	0.0470263i
$911$	18.2955	−	25.1817i	0.0200829	−	0.0276418i	−0.798857	−	0.601520i	$-0.794562\pi$
$911$	18.2955	−	25.1817i	0.0200829	−	0.0276418i	0.818940	+	0.573879i	$0.194562\pi$
$912$		0			0
$913$	−1617.46	+	669.346i	−1.77158	+	0.733128i
$914$			349.511i			0.382397i
$915$		0			0
$916$	286.738	−	882.487i	0.313032	−	0.963414i
$917$	806.805	−	262.147i	0.879831	−	0.285874i
$918$		0			0
$919$	51.8578	−	37.6769i	0.0564285	−	0.0409977i	−0.559213	−	0.829024i	$-0.688897\pi$
$919$	51.8578	−	37.6769i	0.0564285	−	0.0409977i	0.615642	+	0.788026i	$0.288897\pi$
$920$	28.7669	−	9.34693i	0.0312683	−	0.0101597i
$921$		0			0
$922$	−207.063	−	150.440i	−0.224580	−	0.163167i
$923$		−	333.326i		−	0.361133i
$924$		0			0
$925$	−1127.86			−1.21930
$926$	254.312	−	350.030i	0.274634	−	0.378002i
$927$		0			0
$928$	−445.717	−	1371.78i	−0.480298	−	1.47821i
$929$	−924.026	−	1271.81i	−0.994646	−	1.36901i	−0.928553	−	0.371199i	$-0.878947\pi$
$929$	−924.026	−	1271.81i	−0.994646	−	1.36901i	−0.0660924	−	0.997814i	$-0.521053\pi$
$930$		0			0
$931$	−6.83329	−	21.0307i	−0.00733974	−	0.0225894i
$932$	599.389	+	194.753i	0.643121	+	0.208963i
$933$		0			0
$934$	−56.6215			−0.0606226
$935$	92.2155	+	56.5517i	0.0986262	+	0.0604831i
$936$		0			0
$937$	−158.579	−	115.214i	−0.169241	−	0.122961i	0.499941	−	0.866060i	$-0.333355\pi$
$937$	−158.579	−	115.214i	−0.169241	−	0.122961i	−0.669182	+	0.743099i	$0.733355\pi$
$938$	−372.153	−	120.920i	−0.396751	−	0.128912i
$939$		0			0
$940$	186.738	−	135.673i	0.198658	−	0.144333i
$941$	−280.415	−	385.958i	−0.297997	−	0.410157i	0.633594	−	0.773665i	$-0.281579\pi$
$941$	−280.415	−	385.958i	−0.297997	−	0.410157i	−0.931591	+	0.363508i	$0.881579\pi$
$942$		0			0
$943$	−11.3306	+	34.8720i	−0.0120155	+	0.0369798i
$944$	581.820	−	800.806i	0.616334	−	0.848312i
$945$		0			0
$946$	−295.601	−	346.336i	−0.312475	−	0.366106i
$947$		−	151.161i		−	0.159621i	−0.996810	−	0.0798106i	$-0.974568\pi$
$947$		−	151.161i		−	0.159621i	0.996810	−	0.0798106i	$-0.0254316\pi$
$948$		0			0
$949$	−109.291	+	336.363i	−0.115164	+	0.354440i
$950$	174.902	−	56.8292i	0.184108	−	0.0598202i
$951$		0			0
$952$	310.841	−	225.839i	0.326513	−	0.237226i
$953$	1728.32	−	561.565i	1.81356	−	0.589260i	0.813586	−	0.581445i	$-0.197512\pi$
$953$	1728.32	−	561.565i	1.81356	−	0.589260i	0.999969	−	0.00781532i	$-0.00248772\pi$
$954$		0			0
$955$	170.875	+	124.148i	0.178926	+	0.129998i
$956$			295.967i			0.309589i
$957$		0			0
$958$	17.0200			0.0177662
$959$	−213.421	+	293.749i	−0.222546	+	0.306308i
$960$		0			0
$961$	−185.512	−	570.946i	−0.193040	−	0.594116i
$962$	174.506	+	240.187i	0.181399	+	0.249675i
$963$		0			0
$964$	−159.792	−	491.789i	−0.165759	−	0.510154i
$965$	−227.030	−	73.7666i	−0.235265	−	0.0764421i
$966$		0			0
$967$	1457.23			1.50696			0.753480	−	0.657471i	$-0.228374\pi$
$967$	1457.23			1.50696			0.753480	+	0.657471i	$0.228374\pi$
$968$	512.062	+	512.740i	0.528989	+	0.529690i
$969$		0			0
$970$	−106.154	−	77.1255i	−0.109437	−	0.0795108i
$971$	476.422	+	154.799i	0.490651	+	0.159422i	0.543885	−	0.839160i	$-0.316953\pi$
$971$	476.422	+	154.799i	0.490651	+	0.159422i	−0.0532339	+	0.998582i	$0.516953\pi$
$972$		0			0
$973$	−436.852	+	317.392i	−0.448974	+	0.326199i
$974$	39.9479	+	54.9836i	0.0410143	+	0.0564514i
$975$		0			0
$976$	212.404	−	653.712i	0.217627	−	0.669787i
$977$	149.082	−	205.194i	0.152592	−	0.210025i	−0.725877	−	0.687825i	$-0.758566\pi$
$977$	149.082	−	205.194i	0.152592	−	0.210025i	0.878469	+	0.477800i	$0.158566\pi$
$978$		0			0
$979$	1647.23	+	396.040i	1.68256	+	0.404536i
$980$		−	8.19130i		−	0.00835847i
$981$		0			0
$982$	24.5575	−	75.5802i	0.0250076	−	0.0769656i
$983$	−627.861	+	204.005i	−0.638720	+	0.207533i	−0.610434	−	0.792067i	$-0.709005\pi$
$983$	−627.861	+	204.005i	−0.638720	+	0.207533i	−0.0282858	+	0.999600i	$0.509005\pi$
$984$		0			0
$985$	−144.073	+	104.675i	−0.146267	+	0.106269i
$986$	−341.116	+	110.835i	−0.345959	+	0.112409i
$987$		0			0
$988$	195.708	+	142.190i	0.198085	+	0.143917i
$989$		−	244.510i		−	0.247229i
$990$		0			0
$991$	33.5854			0.0338905			0.0169452	−	0.999856i	$-0.494606\pi$
$991$	33.5854			0.0338905			0.0169452	+	0.999856i	$0.494606\pi$
$992$	−344.362	+	473.974i	−0.347139	+	0.477796i
$993$		0			0
$994$	74.5756	+	229.520i	0.0750257	+	0.230906i
$995$	−88.6141	−	121.967i	−0.0890594	−	0.122580i
$996$		0			0
$997$	−369.277	−	1136.52i	−0.370388	−	1.13994i	−0.946538	−	0.322593i	$-0.895445\pi$
$997$	−369.277	−	1136.52i	−0.370388	−	1.13994i	0.576149	−	0.817344i	$-0.304555\pi$
$998$	−236.409	−	76.8140i	−0.236883	−	0.0769679i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.3.l.a.26.4	✓	32
3.2	odd	2	inner	99.3.l.a.26.5	yes	32
11.3	even	5	inner	99.3.l.a.80.5	yes	32
11.5	even	5		1089.3.b.i.485.7		16
11.6	odd	10		1089.3.b.j.485.10		16
33.5	odd	10		1089.3.b.i.485.10		16
33.14	odd	10	inner	99.3.l.a.80.4	yes	32
33.17	even	10		1089.3.b.j.485.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.3.l.a.26.4	✓	32	1.1	even	1	trivial
99.3.l.a.26.5	yes	32	3.2	odd	2	inner
99.3.l.a.80.4	yes	32	33.14	odd	10	inner
99.3.l.a.80.5	yes	32	11.3	even	5	inner
1089.3.b.i.485.7		16	11.5	even	5
1089.3.b.i.485.10		16	33.5	odd	10
1089.3.b.j.485.7		16	33.17	even	10
1089.3.b.j.485.10		16	11.6	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)

\(f(q)\)	\(=\)	\(q+(-0.480038 + 0.660715i) q^{2} +(1.02996 + 3.16989i) q^{4} +(-0.615389 - 0.847011i) q^{5} +(2.11067 + 6.49597i) q^{7} +(-5.69568 - 1.85064i) q^{8} +O(q^{10})\)	\(q+(-0.480038 + 0.660715i) q^{2} +(1.02996 + 3.16989i) q^{4} +(-0.615389 - 0.847011i) q^{5} +(2.11067 + 6.49597i) q^{7} +(-5.69568 - 1.85064i) q^{8} +0.855043 q^{10} +(-2.57144 + 10.6952i) q^{11} +(6.23315 + 4.52865i) q^{13} +(-5.30519 - 1.72376i) q^{14} +(-6.82898 + 4.96155i) q^{16} +(5.52104 + 7.59906i) q^{17} +(2.91103 - 8.95922i) q^{19} +(2.05110 - 2.82310i) q^{20} +(-5.83211 - 6.83310i) q^{22} -4.82409i q^{23} +(7.38670 - 22.7339i) q^{25} +(-5.98430 + 1.94442i) q^{26} +(-18.4176 + 13.3812i) q^{28} +(44.4675 - 14.4484i) q^{29} +(-15.3643 - 11.1628i) q^{31} -30.8489i q^{32} -7.67113 q^{34} +(4.20328 - 5.78531i) q^{35} +(-14.5803 - 44.8737i) q^{37} +(4.52209 + 6.22413i) q^{38} +(1.93755 + 5.96317i) q^{40} +(-7.22871 - 2.34875i) q^{41} +50.6851 q^{43} +(-36.5511 + 2.86447i) q^{44} +(3.18735 + 2.31575i) q^{46} +(62.9091 + 20.4404i) q^{47} +(1.89907 - 1.37976i) q^{49} +(11.4748 + 15.7937i) q^{50} +(-7.93542 + 24.4227i) q^{52} +(-22.5774 + 31.0751i) q^{53} +(10.6414 - 4.40369i) q^{55} -40.9051i q^{56} +(-11.7998 + 36.3161i) q^{58} +(-111.526 + 36.2371i) q^{59} +(-65.8779 + 47.8631i) q^{61} +(14.7509 - 4.79287i) q^{62} +(-6.93357 - 5.03753i) q^{64} -8.06643i q^{65} +70.1488 q^{67} +(-18.4017 + 25.3278i) q^{68} +(1.80471 + 5.55434i) q^{70} +(-25.4295 - 35.0007i) q^{71} +(14.1852 + 43.6575i) q^{73} +(36.6478 + 11.9076i) q^{74} +31.3980 q^{76} +(-74.9033 + 5.87008i) q^{77} +(69.3955 + 50.4188i) q^{79} +(8.40497 + 2.73094i) q^{80} +(5.02191 - 3.64863i) q^{82} +(93.5371 + 128.743i) q^{83} +(3.03890 - 9.35276i) q^{85} +(-24.3308 + 33.4884i) q^{86} +(34.4391 - 56.1578i) q^{88} -154.015i q^{89} +(-16.2619 + 50.0489i) q^{91} +(15.2918 - 4.96862i) q^{92} +(-43.7040 + 31.7528i) q^{94} +(-9.37997 + 3.04774i) q^{95} +(-124.151 - 90.2007i) q^{97} +1.91708i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 16 q^{7}+O(q^{10}) \) 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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