LMFDB - Embedded newform 99.3.l.a.26.2

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			26.2
Character	$\chi$	$=$	99.26
Dual form			99.3.l.a.80.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.75181 + 2.41117i) q^{2} +(-1.50880 - 4.64360i) q^{4} +(4.61811 + 6.35629i) q^{5} +(0.867699 + 2.67050i) q^{7} +(2.50164 + 0.812833i) q^{8} +O(q^{10})$	\(q+(-1.75181 + 2.41117i) q^{2} +(-1.50880 - 4.64360i) q^{4} +(4.61811 + 6.35629i) q^{5} +(0.867699 + 2.67050i) q^{7} +(2.50164 + 0.812833i) q^{8} -23.4161 q^{10} +(-8.89568 + 6.47047i) q^{11} +(1.22806 + 0.892235i) q^{13} +(-7.95907 - 2.58606i) q^{14} +(9.45804 - 6.87167i) q^{16} +(-15.5170 - 21.3573i) q^{17} +(-4.49342 + 13.8293i) q^{19} +(22.5483 - 31.0350i) q^{20} +(-0.0177905 - 32.7840i) q^{22} +25.0726i q^{23} +(-11.3500 + 34.9317i) q^{25} +(-4.30265 + 1.39802i) q^{26} +(11.0916 - 8.05850i) q^{28} +(48.2284 - 15.6704i) q^{29} +(41.7844 + 30.3581i) q^{31} +45.3643i q^{32} +78.6790 q^{34} +(-12.9674 + 17.8480i) q^{35} +(-6.04322 - 18.5991i) q^{37} +(-25.4731 - 35.0608i) q^{38} +(6.38627 + 19.6549i) q^{40} +(-29.4212 - 9.55953i) q^{41} +2.11848 q^{43} +(43.4680 + 31.5454i) q^{44} +(-60.4543 - 43.9226i) q^{46} +(38.2998 + 12.4444i) q^{47} +(33.2631 - 24.1671i) q^{49} +(-64.3430 - 88.5605i) q^{50} +(2.29029 - 7.04880i) q^{52} +(24.1836 - 33.2859i) q^{53} +(-82.2094 - 26.6621i) q^{55} +7.38594i q^{56} +(-46.7034 + 143.738i) q^{58} +(91.3627 - 29.6855i) q^{59} +(2.34234 - 1.70181i) q^{61} +(-146.397 + 47.5673i) q^{62} +(-71.5487 - 51.9832i) q^{64} +11.9263i q^{65} -88.2869 q^{67} +(-75.7629 + 104.279i) q^{68} +(-20.3182 - 62.5329i) q^{70} +(6.65733 + 9.16303i) q^{71} +(32.3776 + 99.6480i) q^{73} +(55.4322 + 18.0110i) q^{74} +70.9975 q^{76} +(-24.9982 - 18.1415i) q^{77} +(-13.5822 - 9.86808i) q^{79} +(87.3566 + 28.3839i) q^{80} +(74.5901 - 54.1929i) q^{82} +(-13.3848 - 18.4226i) q^{83} +(64.0940 - 197.261i) q^{85} +(-3.71118 + 5.10801i) q^{86} +(-27.5132 + 8.95610i) q^{88} +30.7523i q^{89} +(-1.31713 + 4.05372i) q^{91} +(116.427 - 37.8295i) q^{92} +(-97.0996 + 70.5470i) q^{94} +(-108.654 + 35.3039i) q^{95} +(23.0800 + 16.7686i) q^{97} +122.539i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.75181	+	2.41117i	−0.875907	+	1.20558i	0.101631	+	0.994822i	$0.467594\pi$
$2$	−1.75181	+	2.41117i	−0.875907	+	1.20558i	−0.977538	+	0.210760i	$0.932406\pi$
$3$		0			0
$3$		0			0
$4$	−1.50880	−	4.64360i	−0.377199	−	1.16090i
$5$	4.61811	+	6.35629i	0.923623	+	1.27126i	0.962296	+	0.272005i	$0.0876869\pi$
$5$	4.61811	+	6.35629i	0.923623	+	1.27126i	−0.0386732	+	0.999252i	$0.512313\pi$
$6$		0			0
$7$	0.867699	+	2.67050i	0.123957	+	0.381500i	0.993710	−	0.111988i	$-0.0357217\pi$
$7$	0.867699	+	2.67050i	0.123957	+	0.381500i	−0.869753	+	0.493488i	$0.835722\pi$
$8$	2.50164	+	0.812833i	0.312705	+	0.101604i
$9$		0			0
$10$	−23.4161			−2.34161
$11$	−8.89568	+	6.47047i	−0.808698	+	0.588224i
$11$	−8.89568	+	6.47047i	−0.808698	+	0.588224i
$12$		0			0
$13$	1.22806	+	0.892235i	0.0944658	+	0.0686334i	0.634016	−	0.773320i	$-0.281406\pi$
$13$	1.22806	+	0.892235i	0.0944658	+	0.0686334i	−0.539550	+	0.841954i	$0.681406\pi$
$14$	−7.95907	−	2.58606i	−0.568505	−	0.184719i
$15$		0			0
$16$	9.45804	−	6.87167i	0.591128	−	0.429479i
$17$	−15.5170	−	21.3573i	−0.912765	−	1.25631i	−0.966213	−	0.257743i	$-0.917021\pi$
$17$	−15.5170	−	21.3573i	−0.912765	−	1.25631i	0.0534480	−	0.998571i	$-0.482979\pi$
$18$		0			0
$19$	−4.49342	+	13.8293i	−0.236496	+	0.727859i	0.760424	+	0.649427i	$0.224991\pi$
$19$	−4.49342	+	13.8293i	−0.236496	+	0.727859i	−0.996919	+	0.0784318i	$0.975009\pi$
$20$	22.5483	−	31.0350i	1.12741	−	1.55175i
$21$		0			0
$22$	−0.0177905	−	32.7840i	−0.000808661	−	1.49018i
$23$			25.0726i			1.09011i	0.838399	+	0.545057i	$0.183492\pi$
$23$			25.0726i			1.09011i	−0.838399	+	0.545057i	$0.816508\pi$
$24$		0			0
$25$	−11.3500	+	34.9317i	−0.454000	+	1.39727i
$26$	−4.30265	+	1.39802i	−0.165487	+	0.0537698i
$27$		0			0
$28$	11.0916	−	8.05850i	0.396127	−	0.287803i
$29$	48.2284	−	15.6704i	1.66305	−	0.540358i	0.681542	−	0.731779i	$-0.261310\pi$
$29$	48.2284	−	15.6704i	1.66305	−	0.540358i	0.981508	+	0.191422i	$0.0613098\pi$
$30$		0			0
$31$	41.7844	+	30.3581i	1.34788	+	0.979295i	0.999114	+	0.0420867i	$0.0134006\pi$
$31$	41.7844	+	30.3581i	1.34788	+	0.979295i	0.348770	+	0.937208i	$0.386599\pi$
$32$			45.3643i			1.41764i
$33$		0			0
$34$	78.6790			2.31409
$35$	−12.9674	+	17.8480i	−0.370496	+	0.509944i
$36$		0			0
$37$	−6.04322	−	18.5991i	−0.163330	−	0.502679i	0.835579	−	0.549370i	$-0.185132\pi$
$37$	−6.04322	−	18.5991i	−0.163330	−	0.502679i	−0.998909	+	0.0466912i	$0.985132\pi$
$38$	−25.4731	−	35.0608i	−0.670346	−	0.922652i
$39$		0			0
$40$	6.38627	+	19.6549i	0.159657	+	0.491373i
$41$	−29.4212	−	9.55953i	−0.717591	−	0.233159i	−0.0726124	−	0.997360i	$-0.523134\pi$
$41$	−29.4212	−	9.55953i	−0.717591	−	0.233159i	−0.644978	+	0.764201i	$0.723134\pi$
$42$		0			0
$43$	2.11848			0.0492670			0.0246335	−	0.999697i	$-0.492158\pi$
$43$	2.11848			0.0492670			0.0246335	+	0.999697i	$0.492158\pi$
$44$	43.4680	+	31.5454i	0.987910	+	0.716940i
$45$		0			0
$46$	−60.4543	−	43.9226i	−1.31422	−	0.954839i
$47$	38.2998	+	12.4444i	0.814890	+	0.264774i	0.686667	−	0.726972i	$-0.259073\pi$
$47$	38.2998	+	12.4444i	0.814890	+	0.264774i	0.128222	+	0.991745i	$0.459073\pi$
$48$		0			0
$49$	33.2631	−	24.1671i	0.678840	−	0.493206i
$50$	−64.3430	−	88.5605i	−1.28686	−	1.77121i
$51$		0			0
$52$	2.29029	−	7.04880i	0.0440441	−	0.135554i
$53$	24.1836	−	33.2859i	0.456295	−	0.628036i	−0.517441	−	0.855719i	$-0.673115\pi$
$53$	24.1836	−	33.2859i	0.456295	−	0.628036i	0.973735	+	0.227683i	$0.0731151\pi$
$54$		0			0
$55$	−82.2094	−	26.6621i	−1.49472	−	0.484766i
$56$			7.38594i			0.131892i
$57$		0			0
$58$	−46.7034	+	143.738i	−0.805231	+	2.47825i
$59$	91.3627	−	29.6855i	1.54852	−	0.503145i	0.594808	−	0.803868i	$-0.297228\pi$
$59$	91.3627	−	29.6855i	1.54852	−	0.503145i	0.953712	+	0.300723i	$0.0972279\pi$
$60$		0			0
$61$	2.34234	−	1.70181i	0.0383990	−	0.0278985i	−0.568420	−	0.822738i	$-0.692445\pi$
$61$	2.34234	−	1.70181i	0.0383990	−	0.0278985i	0.606819	+	0.794840i	$0.292445\pi$
$62$	−146.397	+	47.5673i	−2.36124	+	0.767214i
$63$		0			0
$64$	−71.5487	−	51.9832i	−1.11795	−	0.812237i
$65$			11.9263i			0.183482i
$66$		0			0
$67$	−88.2869			−1.31772			−0.658858	−	0.752268i	$-0.728960\pi$
$67$	−88.2869			−1.31772			−0.658858	+	0.752268i	$0.728960\pi$
$68$	−75.7629	+	104.279i	−1.11416	+	1.53351i
$69$		0			0
$70$	−20.3182	−	62.5329i	−0.290259	−	0.893326i
$71$	6.65733	+	9.16303i	0.0937652	+	0.129057i	0.853322	−	0.521384i	$-0.174584\pi$
$71$	6.65733	+	9.16303i	0.0937652	+	0.129057i	−0.759557	+	0.650441i	$0.774584\pi$
$72$		0			0
$73$	32.3776	+	99.6480i	0.443529	+	1.36504i	0.884089	+	0.467318i	$0.154780\pi$
$73$	32.3776	+	99.6480i	0.443529	+	1.36504i	−0.440560	+	0.897723i	$0.645220\pi$
$74$	55.4322	+	18.0110i	0.749083	+	0.243392i
$75$		0			0
$76$	70.9975			0.934178
$77$	−24.9982	−	18.1415i	−0.324652	−	0.235604i
$78$		0			0
$79$	−13.5822	−	9.86808i	−0.171927	−	0.124912i	0.498494	−	0.866893i	$-0.333887\pi$
$79$	−13.5822	−	9.86808i	−0.171927	−	0.124912i	−0.670421	+	0.741981i	$0.733887\pi$
$80$	87.3566	+	28.3839i	1.09196	+	0.354799i
$81$		0			0
$82$	74.5901	−	54.1929i	0.909636	−	0.660889i
$83$	−13.3848	−	18.4226i	−0.161263	−	0.221959i	0.720738	−	0.693208i	$-0.243803\pi$
$83$	−13.3848	−	18.4226i	−0.161263	−	0.221959i	−0.882000	+	0.471249i	$0.843803\pi$
$84$		0			0
$85$	64.0940	−	197.261i	0.754048	−	2.32072i
$86$	−3.71118	+	5.10801i	−0.0431533	+	0.0593954i
$87$		0			0
$88$	−27.5132	+	8.95610i	−0.312650	+	0.101774i
$89$			30.7523i			0.345531i	0.984963	+	0.172766i	$0.0552703\pi$
$89$			30.7523i			0.345531i	−0.984963	+	0.172766i	$0.944730\pi$
$90$		0			0
$91$	−1.31713	+	4.05372i	−0.0144740	+	0.0445463i
$92$	116.427	−	37.8295i	1.26551	−	0.411191i
$93$		0			0
$94$	−97.0996	+	70.5470i	−1.03297	+	0.750500i
$95$	−108.654	+	35.3039i	−1.14373	+	0.371620i
$96$		0			0
$97$	23.0800	+	16.7686i	0.237939	+	0.172872i	0.700364	−	0.713785i	$-0.253021\pi$
$97$	23.0800	+	16.7686i	0.237939	+	0.172872i	−0.462426	+	0.886658i	$0.653021\pi$
$98$			122.539i			1.25040i
$99$		0			0
$100$	179.334			1.79334
$101$	−1.99764	+	2.74952i	−0.0197786	+	0.0272230i	−0.818792	−	0.574091i	$-0.805356\pi$
$101$	−1.99764	+	2.74952i	−0.0197786	+	0.0272230i	0.799013	+	0.601314i	$0.205356\pi$
$102$		0			0
$103$	6.89465	+	21.2195i	0.0669383	+	0.206015i	0.978931	−	0.204192i	$-0.0654566\pi$
$103$	6.89465	+	21.2195i	0.0669383	+	0.206015i	−0.911993	+	0.410207i	$0.865457\pi$
$104$	2.34692	+	3.23026i	0.0225665	+	0.0310602i
$105$		0			0
$106$	37.8926	+	116.621i	0.357477	+	1.10020i
$107$	−12.2413	−	3.97744i	−0.114405	−	0.0371724i	0.251255	−	0.967921i	$-0.419157\pi$
$107$	−12.2413	−	3.97744i	−0.114405	−	0.0371724i	−0.365660	+	0.930749i	$0.619157\pi$
$108$		0			0
$109$	109.301			1.00277			0.501383	−	0.865226i	$-0.332825\pi$
$109$	109.301			1.00277			0.501383	+	0.865226i	$0.332825\pi$
$110$	208.302	−	151.513i	1.89366	−	1.37739i
$111$		0			0
$112$	26.5575	+	19.2952i	0.237121	+	0.172278i
$113$	−87.5285	−	28.4397i	−0.774589	−	0.251679i	−0.105061	−	0.994466i	$-0.533504\pi$
$113$	−87.5285	−	28.4397i	−0.774589	−	0.251679i	−0.669528	+	0.742787i	$0.733504\pi$
$114$		0			0
$115$	−159.369	+	115.788i	−1.38582	+	1.00685i
$116$	−145.534	−	200.310i	−1.25460	−	1.72681i
$117$		0			0
$118$	−88.4737	+	272.294i	−0.749777	+	2.30758i
$119$	43.5707	−	59.9700i	0.366141	−	0.503949i
$120$		0			0
$121$	37.2661	−	115.118i	0.307985	−	0.951391i
$122$			8.62901i			0.0707296i
$123$		0			0
$124$	77.9269	−	239.834i	0.628443	−	1.93415i
$125$	−87.6447	+	28.4775i	−0.701158	+	0.227820i
$126$		0			0
$127$	6.70109	−	4.86862i	0.0527645	−	0.0383356i	−0.561090	−	0.827755i	$-0.689618\pi$
$127$	6.70109	−	4.86862i	0.0527645	−	0.0383356i	0.613855	+	0.789419i	$0.289618\pi$
$128$	78.1040	−	25.3775i	0.610187	−	0.198262i
$129$		0			0
$130$	−28.7563	−	20.8927i	−0.221202	−	0.160713i
$131$		−	1.63767i		−	0.0125013i	−0.999980	−	0.00625065i	$-0.998010\pi$
$131$		−	1.63767i		−	0.0125013i	0.999980	−	0.00625065i	$-0.00198966\pi$
$132$		0			0
$133$	−40.8302			−0.306994
$134$	154.662	−	212.874i	1.15420	−	1.58861i
$135$		0			0
$136$	−21.4581	−	66.0412i	−0.157780	−	0.485597i
$137$	−116.451	−	160.281i	−0.850008	−	1.16994i	−0.983861	−	0.178935i	$-0.942735\pi$
$137$	−116.451	−	160.281i	−0.850008	−	1.16994i	0.133853	−	0.991001i	$-0.457265\pi$
$138$		0			0
$139$	−57.9241	−	178.272i	−0.416720	−	1.28253i	−0.910703	−	0.413062i	$-0.864459\pi$
$139$	−57.9241	−	178.272i	−0.416720	−	1.28253i	0.493982	−	0.869472i	$-0.335541\pi$
$140$	102.444	+	33.2861i	0.731744	+	0.237758i
$141$		0			0
$142$	−33.7560			−0.237718
$143$	−16.6976	+	0.00906108i	−0.116766	+	6.33642e-5i
$144$		0			0
$145$	322.330	+	234.186i	2.22296	+	1.61508i
$146$	−296.987	−	96.4970i	−2.03416	−	0.660939i
$147$		0			0
$148$	−77.2489	+	56.1246i	−0.521952	+	0.379220i
$149$	140.590	+	193.505i	0.943555	+	1.29869i	0.954331	+	0.298750i	$0.0965696\pi$
$149$	140.590	+	193.505i	0.943555	+	1.29869i	−0.0107766	+	0.999942i	$0.503430\pi$
$150$		0			0
$151$	18.1318	−	55.8039i	0.120078	−	0.369562i	−0.872894	−	0.487909i	$-0.837760\pi$
$151$	18.1318	−	55.8039i	0.120078	−	0.369562i	0.992972	+	0.118347i	$0.0377596\pi$
$152$	−22.4819	+	30.9436i	−0.147907	+	0.203577i
$153$		0			0
$154$	87.5343	−	28.4942i	0.568405	−	0.185027i
$155$			405.791i			2.61801i
$156$		0			0
$157$	6.31024	−	19.4209i	0.0401926	−	0.123700i	−0.928947	−	0.370213i	$-0.879285\pi$
$157$	6.31024	−	19.4209i	0.0401926	−	0.123700i	0.969140	+	0.246513i	$0.0792847\pi$
$158$	47.5871	−	15.4620i	0.301184	−	0.0978607i
$159$		0			0
$160$	−288.349	+	209.498i	−1.80218	+	1.30936i
$161$	−66.9566	+	21.7555i	−0.415879	+	0.135127i
$162$		0			0
$163$	−84.5857	−	61.4551i	−0.518931	−	0.377025i	0.297270	−	0.954793i	$-0.403924\pi$
$163$	−84.5857	−	61.4551i	−0.518931	−	0.377025i	−0.816201	+	0.577768i	$0.803924\pi$
$164$			151.044i			0.920999i
$165$		0			0
$166$	67.8676			0.408841
$167$	−23.0472	+	31.7217i	−0.138007	+	0.189950i	−0.872426	−	0.488746i	$-0.837455\pi$
$167$	−23.0472	+	31.7217i	−0.138007	+	0.189950i	0.734419	+	0.678696i	$0.237455\pi$
$168$		0			0
$169$	−51.5118	−	158.537i	−0.304804	−	0.938089i
$170$	363.348	+	500.106i	2.13734	+	2.94180i
$171$		0			0
$172$	−3.19636	−	9.83738i	−0.0185835	−	0.0571940i
$173$	−86.9529	−	28.2527i	−0.502618	−	0.163310i	0.0467245	−	0.998908i	$-0.485122\pi$
$173$	−86.9529	−	28.2527i	−0.502618	−	0.163310i	−0.549342	+	0.835597i	$0.685122\pi$
$174$		0			0
$175$	−103.134			−0.589334
$176$	−39.6728	+	122.326i	−0.225414	+	0.695035i
$177$		0			0
$178$	−74.1488	−	53.8723i	−0.416566	−	0.302653i
$179$	−207.504	−	67.4220i	−1.15924	−	0.376659i	−0.334623	−	0.942352i	$-0.608609\pi$
$179$	−207.504	−	67.4220i	−1.15924	−	0.376659i	−0.824616	+	0.565693i	$0.808609\pi$
$180$		0			0
$181$	36.2608	−	26.3450i	0.200336	−	0.145553i	−0.483094	−	0.875568i	$-0.660487\pi$
$181$	36.2608	−	26.3450i	0.200336	−	0.145553i	0.683431	+	0.730016i	$0.260487\pi$
$182$	−7.46681	−	10.2772i	−0.0410264	−	0.0564680i
$183$		0			0
$184$	−20.3799	+	62.7228i	−0.110760	+	0.340885i
$185$	90.3131	−	124.305i	0.488179	−	0.671921i
$186$		0			0
$187$	276.226	+	89.5857i	1.47715	+	0.479068i
$188$		−	196.625i		−	1.04588i
$189$		0			0
$190$	105.219	−	323.829i	0.553782	−	1.70436i
$191$	141.682	−	46.0353i	0.741790	−	0.241022i	0.0863454	−	0.996265i	$-0.472481\pi$
$191$	141.682	−	46.0353i	0.741790	−	0.241022i	0.655445	+	0.755243i	$0.272481\pi$
$192$		0			0
$193$	−156.712	+	113.858i	−0.811978	+	0.589936i	−0.914403	−	0.404804i	$-0.867340\pi$
$193$	−156.712	+	113.858i	−0.811978	+	0.589936i	0.102426	+	0.994741i	$0.467340\pi$
$194$	−80.8639	+	26.2743i	−0.416824	+	0.135434i
$195$		0			0
$196$	−162.410	−	117.998i	−0.828621	−	0.602028i
$197$		−	331.307i		−	1.68176i	−0.541220	−	0.840881i	$-0.682037\pi$
$197$		−	331.307i		−	1.68176i	0.541220	−	0.840881i	$-0.317963\pi$
$198$		0			0
$199$	−294.829			−1.48155			−0.740775	−	0.671753i	$-0.765542\pi$
$199$	−294.829			−1.48155			−0.740775	+	0.671753i	$0.765542\pi$
$200$	−56.7873	+	78.1610i	−0.283936	+	0.390805i
$201$		0			0
$202$	−3.13005	−	9.63329i	−0.0154953	−	0.0476896i
$203$	83.6955	+	115.197i	0.412293	+	0.567473i
$204$		0			0
$205$	−75.1074	−	231.157i	−0.366377	−	1.12759i
$206$	−63.2420	−	20.5486i	−0.307000	−	0.0997503i
$207$		0			0
$208$	17.7461			0.0853180
$209$	−49.5102	−	152.096i	−0.236891	−	0.727731i
$210$		0			0
$211$	93.6252	+	68.0227i	0.443721	+	0.322382i	0.787112	−	0.616810i	$-0.211575\pi$
$211$	93.6252	+	68.0227i	0.443721	+	0.322382i	−0.343391	+	0.939193i	$0.611575\pi$
$212$	−191.055	−	62.0774i	−0.901201	−	0.292818i
$213$		0			0
$214$	31.0348	−	22.5481i	0.145022	−	0.105365i
$215$	9.78338	+	13.4657i	0.0455041	+	0.0626310i
$216$		0			0
$217$	−44.8152	+	137.927i	−0.206522	+	0.635609i
$218$	−191.476	+	263.544i	−0.878329	+	1.20892i
$219$		0			0
$220$	0.228989	+	421.975i	0.00104086	+	1.91807i
$221$		−	40.0728i		−	0.181325i
$222$		0			0
$223$	−75.4285	+	232.145i	−0.338245	+	1.04101i	0.626857	+	0.779134i	$0.284341\pi$
$223$	−75.4285	+	232.145i	−0.338245	+	1.04101i	−0.965102	+	0.261876i	$0.915659\pi$
$224$	−121.146	+	39.3626i	−0.540828	+	0.175726i
$225$		0			0
$226$	221.907	−	161.225i	0.981888	−	0.713383i
$227$	255.097	−	82.8861i	1.12378	−	0.365137i	0.312569	−	0.949895i	$-0.398811\pi$
$227$	255.097	−	82.8861i	1.12378	−	0.365137i	0.811208	+	0.584758i	$0.198811\pi$
$228$		0			0
$229$	−150.551	−	109.382i	−0.657430	−	0.477651i	0.208364	−	0.978051i	$-0.433186\pi$
$229$	−150.551	−	109.382i	−0.657430	−	0.477651i	−0.865794	+	0.500401i	$0.833186\pi$
$230$		−	587.104i		−	2.55263i
$231$		0			0
$232$	133.388			0.574947
$233$	95.3276	−	131.207i	0.409131	−	0.563121i	−0.553875	−	0.832600i	$-0.686851\pi$
$233$	95.3276	−	131.207i	0.409131	−	0.563121i	0.963006	+	0.269479i	$0.0868514\pi$
$234$		0			0
$235$	97.7729	+	300.914i	0.416055	+	1.28049i
$236$	−275.696	−	379.462i	−1.16820	−	1.60789i
$237$		0			0
$238$	68.2697	+	210.112i	0.286847	+	0.882826i
$239$	67.6141	+	21.9692i	0.282904	+	0.0919212i	0.447032	−	0.894518i	$-0.352481\pi$
$239$	67.6141	+	21.9692i	0.282904	+	0.0919212i	−0.164128	+	0.986439i	$0.552481\pi$
$240$		0			0
$241$	212.799			0.882984			0.441492	−	0.897265i	$-0.354449\pi$
$241$	212.799			0.882984			0.441492	+	0.897265i	$0.354449\pi$
$242$	212.286	+	291.521i	0.877215	+	1.20463i
$243$		0			0
$244$	−11.4366	−	8.30919i	−0.0468714	−	0.0340541i
$245$	307.226	+	99.8238i	1.25398	+	0.407444i
$246$		0			0
$247$	−17.8572	+	12.9740i	−0.0722962	+	0.0525263i
$248$	79.8536	+	109.909i	0.321990	+	0.443181i
$249$		0			0
$250$	84.8733	−	261.213i	0.339493	−	1.04485i
$251$	−110.272	+	151.777i	−0.439332	+	0.604689i	−0.970064	−	0.242851i	$-0.921917\pi$
$251$	−110.272	+	151.777i	−0.439332	+	0.604689i	0.530731	+	0.847540i	$0.321917\pi$
$252$		0			0
$253$	−162.232	−	223.038i	−0.641232	−	0.881573i
$254$			24.6864i			0.0971904i
$255$		0			0
$256$	33.6825	−	103.664i	0.131572	−	0.404937i
$257$	276.561	−	89.8603i	1.07611	−	0.349651i	0.283248	−	0.959047i	$-0.408588\pi$
$257$	276.561	−	89.8603i	1.07611	−	0.349651i	0.792866	+	0.609396i	$0.208588\pi$
$258$		0			0
$259$	44.4253	−	32.2769i	0.171526	−	0.124621i
$260$	55.3810	−	17.9944i	0.213004	−	0.0692092i
$261$		0			0
$262$	3.94869	+	2.86889i	0.0150714	+	0.0109500i
$263$			458.564i			1.74359i	0.489870	+	0.871795i	$0.337044\pi$
$263$			458.564i			1.74359i	−0.489870	+	0.871795i	$0.662956\pi$
$264$		0			0
$265$	323.257			1.21984
$266$	71.5269	−	98.4483i	0.268898	−	0.370106i
$267$		0			0
$268$	133.207	+	409.969i	0.497041	+	1.52974i
$269$	−122.701	−	168.884i	−0.456139	−	0.627822i	0.517563	−	0.855645i	$-0.326839\pi$
$269$	−122.701	−	168.884i	−0.456139	−	0.627822i	−0.973703	+	0.227823i	$0.926839\pi$
$270$		0			0
$271$	−142.441	−	438.388i	−0.525612	−	1.61767i	−0.763102	−	0.646279i	$-0.776324\pi$
$271$	−142.441	−	438.388i	−0.525612	−	1.61767i	0.237489	−	0.971390i	$-0.423676\pi$
$272$	−293.521	−	95.3708i	−1.07912	−	0.350628i
$273$		0			0
$274$	590.465			2.15498
$275$	−125.058	−	384.181i	−0.454758	−	1.39702i
$276$		0			0
$277$	85.4746	+	62.1009i	0.308573	+	0.224191i	0.731284	−	0.682073i	$-0.238922\pi$
$277$	85.4746	+	62.1009i	0.308573	+	0.224191i	−0.422711	+	0.906264i	$0.638922\pi$
$278$	531.316	+	172.635i	1.91121	+	0.620989i
$279$		0			0
$280$	−46.9472	+	34.1091i	−0.167668	+	0.121818i
$281$	253.323	+	348.669i	0.901506	+	1.24082i	0.969985	+	0.243164i	$0.0781853\pi$
$281$	253.323	+	348.669i	0.901506	+	1.24082i	−0.0684794	+	0.997653i	$0.521815\pi$
$282$		0			0
$283$	93.2355	−	286.949i	0.329454	−	1.01396i	−0.639935	−	0.768429i	$-0.721039\pi$
$283$	93.2355	−	286.949i	0.329454	−	1.01396i	0.969390	−	0.245527i	$-0.0789611\pi$
$284$	32.5049	−	44.7391i	0.114454	−	0.157532i
$285$		0			0
$286$	29.2292	−	40.2765i	0.102200	−	0.140827i
$287$		−	86.8643i		−	0.302663i
$288$		0			0
$289$	−126.052	+	387.949i	−0.436167	+	1.34238i
$290$	−1129.32	+	366.939i	−3.89422	+	1.26531i
$291$		0			0
$292$	413.874	−	300.697i	1.41738	−	1.02979i
$293$	−44.0479	+	14.3120i	−0.150334	+	0.0488465i	−0.383217	−	0.923658i	$-0.625184\pi$
$293$	−44.0479	+	14.3120i	−0.150334	+	0.0488465i	0.232883	+	0.972505i	$0.425184\pi$
$294$		0			0
$295$	610.613	+	443.636i	2.06987	+	1.50385i
$296$		−	51.4405i		−	0.173786i
$297$		0			0
$298$	−712.860			−2.39215
$299$	−22.3707	+	30.7906i	−0.0748183	+	0.102979i
$300$		0			0
$301$	1.83820	+	5.65741i	0.00610699	+	0.0187954i
$302$	102.789	+	141.477i	0.340360	+	0.468466i
$303$		0			0
$304$	52.5316	+	161.676i	0.172801	+	0.531828i
$305$	21.6343	+	7.02943i	0.0709323	+	0.0230473i
$306$		0			0
$307$	−448.259			−1.46013			−0.730063	−	0.683379i	$-0.760509\pi$
$307$	−448.259			−1.46013			−0.730063	+	0.683379i	$0.760509\pi$
$308$	−46.5248	+	143.453i	−0.151054	+	0.465758i
$309$		0			0
$310$	−978.429	−	710.870i	−3.15622	−	2.29313i
$311$	318.294	+	103.420i	1.02345	+	0.332540i	0.772199	−	0.635381i	$-0.219157\pi$
$311$	318.294	+	103.420i	1.02345	+	0.332540i	0.251255	+	0.967921i	$0.419157\pi$
$312$		0			0
$313$	−82.7752	+	60.1397i	−0.264458	+	0.192140i	−0.712110	−	0.702068i	$-0.752260\pi$
$313$	−82.7752	+	60.1397i	−0.264458	+	0.192140i	0.447652	+	0.894208i	$0.352260\pi$
$314$	35.7727	+	49.2369i	0.113926	+	0.156805i
$315$		0			0
$316$	−25.3306	+	77.9594i	−0.0801600	+	0.246707i
$317$	−222.110	+	305.708i	−0.700661	+	0.964377i	0.299287	+	0.954163i	$0.403251\pi$
$317$	−222.110	+	305.708i	−0.700661	+	0.964377i	−0.999948	+	0.0102140i	$0.996749\pi$
$318$		0			0
$319$	−327.630	+	451.459i	−1.02705	+	1.41523i
$320$		−	694.848i		−	2.17140i
$321$		0			0
$322$	64.8393	−	199.555i	0.201364	−	0.619736i
$323$	365.082	−	118.622i	1.13028	−	0.367252i
$324$		0			0
$325$	−45.1057	+	32.7712i	−0.138787	+	0.100834i
$326$	296.357	−	96.2922i	0.909070	−	0.295375i
$327$		0			0
$328$	−65.8311	−	47.8291i	−0.200705	−	0.145820i
$329$			113.078i			0.343701i
$330$		0			0
$331$	−170.972			−0.516533			−0.258266	−	0.966074i	$-0.583151\pi$
$331$	−170.972			−0.516533			−0.258266	+	0.966074i	$0.583151\pi$
$332$	−65.3522	+	89.9496i	−0.196844	+	0.270933i
$333$		0			0
$334$	−36.1119	−	111.141i	−0.108120	−	0.332758i
$335$	−407.719	−	561.177i	−1.21707	−	1.67516i
$336$		0			0
$337$	59.3115	+	182.542i	0.175999	+	0.541668i	0.999678	−	0.0253884i	$-0.00808224\pi$
$337$	59.3115	+	182.542i	0.175999	+	0.541668i	−0.823679	+	0.567056i	$0.808082\pi$
$338$	472.498	+	153.524i	1.39792	+	0.454213i
$339$		0			0
$340$	−1012.71			−2.97855
$341$	−568.132	+	0.308302i	−1.66608	+	0.000904111i
$342$		0			0
$343$	204.712	+	148.732i	0.596829	+	0.433622i
$344$	5.29968	+	1.72197i	0.0154061	+	0.00500573i
$345$		0			0
$346$	220.447	−	160.164i	0.637131	−	0.462903i
$347$	−109.245	−	150.363i	−0.314827	−	0.433322i	0.622052	−	0.782976i	$-0.286299\pi$
$347$	−109.245	−	150.363i	−0.314827	−	0.433322i	−0.936879	+	0.349654i	$0.886299\pi$
$348$		0			0
$349$	−54.5075	+	167.757i	−0.156182	+	0.480679i	−0.998279	−	0.0586476i	$-0.981321\pi$
$349$	−54.5075	+	167.757i	−0.156182	+	0.480679i	0.842097	+	0.539327i	$0.181321\pi$
$350$	180.671	−	248.672i	0.516202	−	0.710491i
$351$		0			0
$352$	−293.528	−	403.546i	−0.833887	−	1.14644i
$353$		−	232.825i		−	0.659561i	−0.944058	−	0.329780i	$-0.893025\pi$
$353$		−	232.825i		−	0.659561i	0.944058	−	0.329780i	$-0.106975\pi$
$354$		0			0
$355$	−27.4985	+	84.6318i	−0.0774606	+	0.238399i
$356$	142.801	−	46.3989i	0.401127	−	0.130334i
$357$		0			0
$358$	526.074	−	382.215i	1.46948	−	1.06764i
$359$	−383.394	+	124.572i	−1.06795	+	0.346998i	−0.789689	−	0.613508i	$-0.789758\pi$
$359$	−383.394	+	124.572i	−1.06795	+	0.346998i	−0.278261	+	0.960506i	$0.589758\pi$
$360$		0			0
$361$	120.996	+	87.9086i	0.335168	+	0.243514i
$362$			133.583i			0.369012i
$363$		0			0
$364$	20.8111			0.0571734
$365$	−483.868	+	665.987i	−1.32567	+	1.82462i
$366$		0			0
$367$	−167.337	−	515.010i	−0.455959	−	1.40330i	−0.870006	−	0.493041i	$-0.835885\pi$
$367$	−167.337	−	515.010i	−0.455959	−	1.40330i	0.414047	−	0.910255i	$-0.364115\pi$
$368$	172.291	+	237.138i	0.468182	+	0.644397i
$369$		0			0
$370$	141.509	+	435.520i	0.382456	+	1.17708i
$371$	109.874	+	35.7003i	0.296157	+	0.0962272i
$372$		0			0
$373$	−160.025			−0.429021			−0.214510	−	0.976722i	$-0.568816\pi$
$373$	−160.025			−0.429021			−0.214510	+	0.976722i	$0.568816\pi$
$374$	−699.903	+	509.090i	−1.87140	+	1.36120i
$375$		0			0
$376$	85.6973	+	62.2627i	0.227918	+	0.165592i
$377$	73.2089	+	23.7870i	0.194188	+	0.0630955i
$378$		0			0
$379$	306.310	−	222.547i	0.808206	−	0.587196i	−0.105104	−	0.994461i	$-0.533517\pi$
$379$	306.310	−	222.547i	0.808206	−	0.587196i	0.913310	+	0.407265i	$0.133517\pi$
$380$	327.875	+	451.281i	0.862828	+	1.18758i
$381$		0			0
$382$	−137.202	+	422.264i	−0.359167	+	1.10540i
$383$	140.814	−	193.814i	0.367661	−	0.506041i	−0.584603	−	0.811320i	$-0.698750\pi$
$383$	140.814	−	193.814i	0.367661	−	0.506041i	0.952263	+	0.305278i	$0.0987495\pi$
$384$		0			0
$385$	−0.131690	−	242.675i	−0.000342051	−	0.630325i
$386$		−	577.315i		−	1.49564i
$387$		0			0
$388$	43.0437	−	132.475i	0.110937	−	0.341430i
$389$	−478.020	+	155.318i	−1.22884	+	0.399276i	−0.850295	−	0.526306i	$-0.823577\pi$
$389$	−478.020	+	155.318i	−1.22884	+	0.399276i	−0.378549	+	0.925581i	$0.623577\pi$
$390$		0			0
$391$	535.485	−	389.052i	1.36953	−	0.995019i
$392$	102.856	−	33.4201i	0.262389	−	0.0852552i
$393$		0			0
$394$	798.836	+	580.389i	2.02750	+	1.47307i
$395$		−	131.905i		−	0.333935i
$396$		0			0
$397$	97.1039			0.244594			0.122297	−	0.992494i	$-0.460974\pi$
$397$	97.1039			0.244594			0.122297	+	0.992494i	$0.460974\pi$
$398$	516.485	−	710.880i	1.29770	−	1.78613i
$399$		0			0
$400$	132.690	+	408.379i	0.331726	+	1.02095i
$401$	386.262	+	531.644i	0.963247	+	1.32580i	0.945385	+	0.325955i	$0.105686\pi$
$401$	386.262	+	531.644i	0.963247	+	1.32580i	0.0178620	+	0.999840i	$0.494314\pi$
$402$		0			0
$403$	24.2270	+	74.5630i	0.0601166	+	0.185020i
$404$	15.7817	+	5.12779i	0.0390636	+	0.0126925i
$405$		0			0
$406$	−424.378			−1.04527
$407$	174.104	+	126.349i	0.427773	+	0.310441i
$408$		0			0
$409$	−82.1600	−	59.6928i	−0.200880	−	0.145948i	0.482798	−	0.875732i	$-0.339621\pi$
$409$	−82.1600	−	59.6928i	−0.200880	−	0.145948i	−0.683678	+	0.729784i	$0.739621\pi$
$410$	688.931	+	223.847i	1.68032	+	0.545969i
$411$		0			0
$412$	88.1325	−	64.0320i	0.213914	−	0.155417i
$413$	158.551	+	218.226i	0.383900	+	0.528393i
$414$		0			0
$415$	55.2868	−	170.155i	0.133221	−	0.410013i
$416$	−40.4756	+	55.7099i	−0.0972972	+	0.133918i
$417$		0			0
$418$	453.460	+	147.066i	1.08483	+	0.351833i
$419$			0.439819i			0.00104969i	1.00000		0.000524844i	$0.000167063\pi$
$419$			0.439819i			0.00104969i	−1.00000		0.000524844i	$0.999833\pi$
$420$		0			0
$421$	−129.343	+	398.076i	−0.307227	+	0.945548i	0.671610	+	0.740905i	$0.265603\pi$
$421$	−129.343	+	398.076i	−0.307227	+	0.945548i	−0.978837	+	0.204642i	$0.934397\pi$
$422$	−328.028	+	106.583i	−0.777317	+	0.252566i
$423$		0			0
$424$	87.5547	−	63.6122i	0.206497	−	0.150029i
$425$	922.166	−	299.630i	2.16980	−	0.705011i
$426$		0			0
$427$	6.57712	+	4.77856i	0.0154031	+	0.0111910i
$428$			62.8449i			0.146834i
$429$		0			0
$430$	−49.6066			−0.115364
$431$	−148.162	+	203.928i	−0.343764	+	0.473150i	−0.945536	−	0.325517i	$-0.894462\pi$
$431$	−148.162	+	203.928i	−0.343764	+	0.473150i	0.601772	+	0.798668i	$0.294462\pi$
$432$		0			0
$433$	−38.4570	−	118.359i	−0.0888153	−	0.273345i	0.896777	−	0.442482i	$-0.145902\pi$
$433$	−38.4570	−	118.359i	−0.0888153	−	0.273345i	−0.985593	+	0.169137i	$0.945902\pi$
$434$	−254.057	−	349.680i	−0.585385	−	0.805713i
$435$		0			0
$436$	−164.914	−	507.552i	−0.378243	−	1.16411i
$437$	−346.738	−	112.662i	−0.793450	−	0.257807i
$438$		0			0
$439$	−73.6933			−0.167866			−0.0839332	−	0.996471i	$-0.526748\pi$
$439$	−73.6933			−0.167866			−0.0839332	+	0.996471i	$0.526748\pi$
$440$	−183.987	−	133.522i	−0.418152	−	0.303458i
$441$		0			0
$442$	96.6222	+	70.2001i	0.218602	+	0.158824i
$443$	−351.831	−	114.317i	−0.794200	−	0.258051i	−0.116308	−	0.993213i	$-0.537106\pi$
$443$	−351.831	−	114.317i	−0.794200	−	0.258051i	−0.677892	+	0.735162i	$0.737106\pi$
$444$		0			0
$445$	−195.470	+	142.017i	−0.439259	+	0.319140i
$446$	−427.604	−	588.546i	−0.958753	−	1.31961i
$447$		0			0
$448$	76.7385	−	236.177i	0.171291	−	0.527180i
$449$	427.055	−	587.791i	0.951125	−	1.30911i	9.88759e−5	−	1.00000i	$-0.499969\pi$
$449$	427.055	−	587.791i	0.951125	−	1.30911i	0.951026	−	0.309111i	$-0.100031\pi$
$450$		0			0
$451$	323.576	−	105.330i	0.717464	−	0.233549i
$452$			449.357i			0.994153i
$453$		0			0
$454$	−247.031	+	760.283i	−0.544121	+	1.67463i
$455$	−31.8493	+	10.3485i	−0.0699984	+	0.0227438i
$456$		0			0
$457$	295.712	−	214.847i	0.647072	−	0.470125i	−0.215201	−	0.976570i	$-0.569041\pi$
$457$	295.712	−	214.847i	0.647072	−	0.470125i	0.862272	+	0.506445i	$0.169041\pi$
$458$	527.476	−	171.387i	1.15169	−	0.374208i
$459$		0			0
$460$	778.130	+	565.344i	1.69159	+	1.22901i
$461$			153.670i			0.333340i	0.986013	+	0.166670i	$0.0533014\pi$
$461$			153.670i			0.333340i	−0.986013	+	0.166670i	$0.946699\pi$
$462$		0			0
$463$	325.357			0.702714			0.351357	−	0.936242i	$-0.385720\pi$
$463$	325.357			0.702714			0.351357	+	0.936242i	$0.385720\pi$
$464$	348.465	−	479.621i	0.751002	−	1.03367i
$465$		0			0
$466$	149.366	+	459.701i	0.320528	+	0.986484i
$467$	−491.368	−	676.310i	−1.05218	−	1.44820i	−0.886904	−	0.461954i	$-0.847149\pi$
$467$	−491.368	−	676.310i	−1.05218	−	1.44820i	−0.165275	−	0.986247i	$-0.552851\pi$
$468$		0			0
$469$	−76.6065	−	235.771i	−0.163340	−	0.502709i
$470$	−896.834	−	291.399i	−1.90816	−	0.619998i
$471$		0			0
$472$	252.686			0.535352
$473$	−18.8453	+	13.7076i	−0.0398421	+	0.0289800i
$474$		0			0
$475$	−432.081	−	313.925i	−0.909645	−	0.660896i
$476$	−344.216	−	111.843i	−0.723143	−	0.234963i
$477$		0			0
$478$	−171.419	+	124.543i	−0.358616	+	0.260550i
$479$	−197.344	−	271.621i	−0.411992	−	0.567058i	0.551711	−	0.834035i	$-0.313975\pi$
$479$	−197.344	−	271.621i	−0.411992	−	0.567058i	−0.963703	+	0.266977i	$0.913975\pi$
$480$		0			0
$481$	9.17337	−	28.2327i	0.0190715	−	0.0586959i
$482$	−372.785	+	513.094i	−0.773412	+	1.06451i
$483$		0			0
$484$	−590.791	+	0.641196i	−1.22064	+	0.00132479i
$485$			224.143i			0.462150i
$486$		0			0
$487$	180.912	−	556.789i	0.371482	−	1.14330i	−0.574340	−	0.818617i	$-0.694741\pi$
$487$	180.912	−	556.789i	0.371482	−	1.14330i	0.945822	−	0.324686i	$-0.105259\pi$
$488$	7.24298	−	2.35339i	0.0148422	−	0.00482251i
$489$		0			0
$490$	−778.894	+	565.900i	−1.58958	+	1.15490i
$491$	309.648	−	100.611i	0.630647	−	0.204910i	0.0237854	−	0.999717i	$-0.492428\pi$
$491$	309.648	−	100.611i	0.630647	−	0.204910i	0.606862	+	0.794807i	$0.292428\pi$
$492$		0			0
$493$	−1083.04	−	786.874i	−2.19683	−	1.59609i
$494$		−	65.7846i		−	0.133167i
$495$		0			0
$496$	603.810			1.21736
$497$	−18.6933	+	25.7292i	−0.0376123	+	0.0517689i
$498$		0			0
$499$	124.634	+	383.583i	0.249767	+	0.768703i	0.994816	+	0.101693i	$0.0324261\pi$
$499$	124.634	+	383.583i	0.249767	+	0.768703i	−0.745049	+	0.667010i	$0.767574\pi$
$500$	264.476	+	364.020i	0.528953	+	0.728041i
$501$		0			0
$502$	−172.783	−	531.770i	−0.344188	−	1.05930i
$503$	643.433	+	209.064i	1.27919	+	0.415634i	0.868295	−	0.496048i	$-0.165216\pi$
$503$	643.433	+	209.064i	1.27919	+	0.415634i	0.410895	+	0.911683i	$0.365216\pi$
$504$		0			0
$505$	−26.7021			−0.0528754
$506$	821.981	−	0.446056i	1.62447	−	0.000881533i
$507$		0			0
$508$	−32.7185	−	23.7714i	−0.0644066	−	0.0467941i
$509$	−639.693	−	207.849i	−1.25677	−	0.408348i	−0.396425	−	0.918067i	$-0.629749\pi$
$509$	−639.693	−	207.849i	−1.25677	−	0.408348i	−0.860341	+	0.509720i	$0.829749\pi$
$510$		0			0
$511$	−238.016	+	172.929i	−0.465785	+	0.338413i
$512$	384.029	+	528.571i	0.750057	+	1.03236i
$513$		0			0
$514$	−267.816	+	824.254i	−0.521043	+	1.60361i
$515$	−103.037	+	141.819i	−0.200072	+	0.275376i
$516$		0			0
$517$	−421.224	+	137.117i	−0.814746	+	0.265216i
$518$			163.660i			0.315946i
$519$		0			0
$520$	−9.69410	+	29.8354i	−0.0186425	+	0.0573757i
$521$	70.0098	−	22.7476i	0.134376	−	0.0436613i	−0.241057	−	0.970511i	$-0.577494\pi$
$521$	70.0098	−	22.7476i	0.134376	−	0.0436613i	0.375433	+	0.926850i	$0.377494\pi$
$522$		0			0
$523$	432.771	−	314.426i	0.827478	−	0.601198i	−0.0913670	−	0.995817i	$-0.529124\pi$
$523$	432.771	−	314.426i	0.827478	−	0.601198i	0.918845	+	0.394620i	$0.129124\pi$
$524$	−7.60469	+	2.47091i	−0.0145128	+	0.00471548i
$525$		0			0
$526$	−1105.67	−	803.320i	−2.10204	−	1.52722i
$527$		−	1363.47i		−	2.58723i
$528$		0			0
$529$	−99.6371			−0.188350
$530$	−566.287	+	779.427i	−1.06847	+	1.47062i
$531$		0			0
$532$	61.6045	+	189.599i	0.115798	+	0.356389i
$533$	−27.6016	−	37.9903i	−0.0517853	−	0.0712763i
$534$		0			0
$535$	−31.2500	−	96.1775i	−0.0584112	−	0.179771i
$536$	−220.862	−	71.7626i	−0.412057	−	0.133885i
$537$		0			0
$538$	622.158			1.15643
$539$	−139.526	+	430.211i	−0.258861	+	0.798165i
$540$		0			0
$541$	−12.4454	−	9.04213i	−0.0230045	−	0.0167137i	0.576224	−	0.817292i	$-0.304526\pi$
$541$	−12.4454	−	9.04213i	−0.0230045	−	0.0167137i	−0.599228	+	0.800578i	$0.704526\pi$
$542$	1306.56	+	424.526i	2.41062	+	0.783258i
$543$		0			0
$544$	968.861	−	703.919i	1.78099	−	1.29397i
$545$	504.766	+	694.751i	0.926177	+	1.27477i
$546$		0			0
$547$	−56.2850	+	173.227i	−0.102898	+	0.316686i	−0.989231	−	0.146361i	$-0.953244\pi$
$547$	−56.2850	+	173.227i	−0.102898	+	0.316686i	0.886334	+	0.463047i	$0.153244\pi$
$548$	−568.581	+	782.584i	−1.03756	+	1.42807i
$549$		0			0
$550$	1145.40	+	371.477i	2.08255	+	0.675412i
$551$			737.380i			1.33826i
$552$		0			0
$553$	14.5674	−	44.8339i	0.0263425	−	0.0810740i
$554$	−299.471	+	97.3041i	−0.540562	+	0.175639i
$555$		0			0
$556$	−740.429	+	537.953i	−1.33171	+	0.967542i
$557$	−255.810	+	83.1179i	−0.459265	+	0.149224i	−0.529507	−	0.848306i	$-0.677623\pi$
$557$	−255.810	+	83.1179i	−0.459265	+	0.149224i	0.0702419	+	0.997530i	$0.477623\pi$
$558$		0			0
$559$	2.60161	+	1.89018i	0.00465405	+	0.00338136i
$560$			257.915i			0.460562i
$561$		0			0
$562$	−1284.47			−2.28554
$563$	−235.669	+	324.370i	−0.418594	+	0.576146i	−0.965288	−	0.261187i	$-0.915886\pi$
$563$	−235.669	+	324.370i	−0.418594	+	0.576146i	0.546694	+	0.837332i	$0.315886\pi$
$564$		0			0
$565$	−223.445	−	687.694i	−0.395479	−	1.21716i
$566$	528.551	+	727.489i	0.933836	+	1.28532i
$567$		0			0
$568$	9.20625	+	28.3339i	0.0162082	+	0.0498837i
$569$	174.429	+	56.6756i	0.306554	+	0.0996056i	0.458255	−	0.888821i	$-0.348475\pi$
$569$	174.429	+	56.6756i	0.306554	+	0.0996056i	−0.151700	+	0.988427i	$0.548475\pi$
$570$		0			0
$571$	693.995			1.21540			0.607701	−	0.794166i	$-0.292092\pi$
$571$	693.995			1.21540			0.607701	+	0.794166i	$0.292092\pi$
$572$	25.2353	+	77.5231i	0.0441177	+	0.135530i
$573$		0			0
$574$	209.444	+	152.170i	0.364885	+	0.265105i
$575$	−875.829	−	284.574i	−1.52318	−	0.494912i
$576$		0			0
$577$	−429.878	+	312.325i	−0.745023	+	0.541291i	−0.894280	−	0.447507i	$-0.852312\pi$
$577$	−429.878	+	312.325i	−0.745023	+	0.541291i	0.149257	+	0.988798i	$0.452312\pi$
$578$	−714.589	−	983.547i	−1.23631	−	1.70164i
$579$		0			0
$580$	601.137	−	1850.11i	1.03644	−	3.18985i
$581$	37.5836	−	51.7294i	0.0646878	−	0.0890351i
$582$		0			0
$583$	0.245596	+	452.580i	0.000421263	+	0.776295i
$584$			275.601i			0.471920i
$585$		0			0
$586$	42.6551	−	131.279i	0.0727902	−	0.224025i
$587$	510.666	−	165.925i	0.869958	−	0.282667i	0.160177	−	0.987088i	$-0.448794\pi$
$587$	510.666	−	165.925i	0.869958	−	0.282667i	0.709782	+	0.704422i	$0.248794\pi$
$588$		0			0
$589$	−607.587	+	441.438i	−1.03156	+	0.749470i
$590$	−2139.36	+	695.120i	−3.62603	+	1.17817i
$591$		0			0
$592$	−184.964	−	134.384i	−0.312439	−	0.227001i
$593$		−	228.398i		−	0.385156i	−0.981282	−	0.192578i	$-0.938315\pi$
$593$		−	228.398i		−	0.385156i	0.981282	−	0.192578i	$-0.0616849\pi$
$594$		0			0
$595$	582.401			0.978825
$596$	686.439	−	944.802i	1.15174	−	1.58524i
$597$		0			0
$598$	−35.0519	−	107.879i	−0.0586153	−	0.180399i
$599$	350.082	+	481.846i	0.584444	+	0.804418i	0.994174	−	0.107789i	$-0.0343771\pi$
$599$	350.082	+	481.846i	0.584444	+	0.804418i	−0.409730	+	0.912207i	$0.634377\pi$
$600$		0			0
$601$	245.022	+	754.101i	0.407691	+	1.25474i	0.918627	+	0.395125i	$0.129299\pi$
$601$	245.022	+	754.101i	0.407691	+	1.25474i	−0.510936	+	0.859619i	$0.670701\pi$
$602$	−16.8611	−	5.47851i	−0.0280085	−	0.00910052i
$603$		0			0
$604$	−286.488			−0.474318
$605$	903.824	−	294.755i	1.49392	−	0.487199i
$606$		0			0
$607$	706.476	+	513.285i	1.16388	+	0.845610i	0.990264	−	0.139203i	$-0.0444542\pi$
$607$	706.476	+	513.285i	1.16388	+	0.845610i	0.173618	+	0.984813i	$0.444454\pi$
$608$	−627.358	−	203.841i	−1.03184	−	0.335265i
$609$		0			0
$610$	−54.8485	+	39.8497i	−0.0899155	+	0.0653274i
$611$	35.9310	+	49.4548i	0.0588069	+	0.0809408i
$612$		0			0
$613$	97.3458	−	299.600i	0.158802	−	0.488743i	−0.839724	−	0.543014i	$-0.817283\pi$
$613$	97.3458	−	299.600i	0.158802	−	0.488743i	0.998526	+	0.0542702i	$0.0172832\pi$
$614$	785.266	−	1080.83i	1.27894	−	1.76030i
$615$		0			0
$616$	−47.7905	−	65.7029i	−0.0775819	−	0.106661i
$617$		−	738.239i		−	1.19650i	−0.801311	−	0.598249i	$-0.795864\pi$
$617$		−	738.239i		−	1.19650i	0.801311	−	0.598249i	$-0.204136\pi$
$618$		0			0
$619$	285.874	−	879.831i	0.461832	−	1.42137i	−0.401090	−	0.916038i	$-0.631369\pi$
$619$	285.874	−	879.831i	0.461832	−	1.42137i	0.862923	−	0.505336i	$-0.168631\pi$
$620$	1884.33	−	612.256i	3.03924	−	0.987510i
$621$		0			0
$622$	−806.955	+	586.287i	−1.29736	+	0.942584i
$623$	−82.1240	+	26.6837i	−0.131820	+	0.0428310i
$624$		0			0
$625$	157.102	+	114.141i	0.251363	+	0.182626i
$626$		−	304.938i		−	0.487122i
$627$		0			0
$628$	−99.7039			−0.158764
$629$	−303.455	+	417.670i	−0.482440	+	0.664022i
$630$		0			0
$631$	−108.898	−	335.154i	−0.172580	−	0.531147i	0.826935	−	0.562298i	$-0.190083\pi$
$631$	−108.898	−	335.154i	−0.172580	−	0.531147i	−0.999515	+	0.0311513i	$0.990083\pi$
$632$	−25.9568	−	35.7265i	−0.0410709	−	0.0565293i
$633$		0			0
$634$	−348.017	−	1071.09i	−0.548922	−	1.68941i
$635$	61.8927	+	20.1102i	0.0974689	+	0.0316696i
$636$		0			0
$637$	62.4117			0.0979776
$638$	−514.595	−	1580.84i	−0.806576	−	2.47781i
$639$		0			0
$640$	522.000	+	379.255i	0.815625	+	0.592586i
$641$	−234.944	−	76.3379i	−0.366527	−	0.119092i	0.119962	−	0.992778i	$-0.461723\pi$
$641$	−234.944	−	76.3379i	−0.366527	−	0.119092i	−0.486489	+	0.873687i	$0.661723\pi$
$642$		0			0
$643$	−531.828	+	386.395i	−0.827104	+	0.600926i	−0.918738	−	0.394867i	$-0.870791\pi$
$643$	−531.828	+	386.395i	−0.827104	+	0.600926i	0.0916349	+	0.995793i	$0.470791\pi$
$644$	202.048	+	278.095i	0.313739	+	0.431824i
$645$		0			0
$646$	−353.538	+	1088.08i	−0.547272	+	1.68433i
$647$	−379.466	+	522.290i	−0.586500	+	0.807249i	−0.994389	−	0.105783i	$-0.966265\pi$
$647$	−379.466	+	522.290i	−0.586500	+	0.807249i	0.407889	+	0.913032i	$0.366265\pi$
$648$		0			0
$649$	−620.654	+	855.232i	−0.956323	+	1.31777i
$650$		−	166.166i		−	0.255640i
$651$		0			0
$652$	−157.750	+	485.506i	−0.241948	+	0.744640i
$653$	−33.8048	+	10.9839i	−0.0517685	+	0.0168206i	−0.334787	−	0.942294i	$-0.608664\pi$
$653$	−33.8048	+	10.9839i	−0.0517685	+	0.0168206i	0.283018	+	0.959115i	$0.408664\pi$
$654$		0			0
$655$	10.4095	−	7.56295i	0.0158924	−	0.0115465i
$656$	−343.957	+	111.758i	−0.524325	+	0.170363i
$657$		0			0
$658$	−272.649	−	198.091i	−0.414360	−	0.301050i
$659$			721.237i			1.09444i	0.836988	+	0.547221i	$0.184314\pi$
$659$			721.237i			1.09444i	−0.836988	+	0.547221i	$0.815686\pi$
$660$		0			0
$661$	−617.542			−0.934253			−0.467127	−	0.884190i	$-0.654711\pi$
$661$	−617.542			−0.934253			−0.467127	+	0.884190i	$0.654711\pi$
$662$	299.512	−	412.242i	0.452435	−	0.622723i
$663$		0			0
$664$	−18.5095	−	56.9664i	−0.0278757	−	0.0857927i
$665$	−188.558	−	259.528i	−0.283546	−	0.390268i
$666$		0			0
$667$	392.897	+	1209.21i	0.589052	+	1.81291i
$668$	182.077	+	59.1603i	0.272570	+	0.0885633i
$669$		0			0
$670$	2067.34			3.08558
$671$	−9.82518	+	30.2947i	−0.0146426	+	0.0451486i
$672$		0			0
$673$	679.954	+	494.016i	1.01033	+	0.734050i	0.964279	−	0.264889i	$-0.0853353\pi$
$673$	679.954	+	494.016i	1.01033	+	0.734050i	0.0460541	+	0.998939i	$0.485335\pi$
$674$	−544.042	−	176.770i	−0.807184	−	0.262270i
$675$		0			0
$676$	−658.462	+	478.401i	−0.974057	+	0.707694i
$677$	−227.212	−	312.730i	−0.335615	−	0.461935i	0.607539	−	0.794290i	$-0.292157\pi$
$677$	−227.212	−	312.730i	−0.335615	−	0.461935i	−0.943154	+	0.332355i	$0.892157\pi$
$678$		0			0
$679$	−24.7541	+	76.1854i	−0.0364568	+	0.112202i
$680$	320.681	−	441.379i	0.471589	−	0.649087i
$681$		0			0
$682$	994.518	−	1370.40i	1.45824	−	2.00938i
$683$		−	122.406i		−	0.179219i	−0.995977	−	0.0896094i	$-0.971438\pi$
$683$		−	122.406i		−	0.179219i	0.995977	−	0.0896094i	$-0.0285619\pi$
$684$		0			0
$685$	481.009	−	1480.39i	0.702203	−	2.16116i
$686$	−717.236	+	233.044i	−1.04553	+	0.339714i
$687$		0			0
$688$	20.0367	−	14.5575i	0.0291231	−	0.0211592i
$689$	59.3977	−	19.2995i	0.0862085	−	0.0280108i
$690$		0			0
$691$	−198.194	−	143.996i	−0.286822	−	0.208388i	0.435065	−	0.900399i	$-0.356725\pi$
$691$	−198.194	−	143.996i	−0.286822	−	0.208388i	−0.721888	+	0.692010i	$0.756725\pi$
$692$			446.402i			0.645090i
$693$		0			0
$694$	553.926			0.798165
$695$	865.649	−	1191.46i	1.24554	−	1.71434i
$696$		0			0
$697$	252.363	+	776.694i	0.362071	+	1.11434i
$698$	−309.003	−	425.306i	−0.442697	−	0.609320i
$699$		0			0
$700$	155.608	+	478.911i	0.222297	+	0.684159i
$701$	187.720	+	60.9938i	0.267788	+	0.0870097i	0.439833	−	0.898079i	$-0.355037\pi$
$701$	187.720	+	60.9938i	0.267788	+	0.0870097i	−0.172045	+	0.985089i	$0.555037\pi$
$702$		0			0
$703$	284.368			0.404506
$704$	972.830	−	0.527915i	1.38186	−	0.000749879i
$705$		0			0
$706$	561.379	+	407.866i	0.795155	+	0.577714i
$707$	−9.07595	−	2.94896i	−0.0128373	−	0.00417108i
$708$		0			0
$709$	425.433	−	309.095i	0.600046	−	0.435959i	−0.245849	−	0.969308i	$-0.579067\pi$
$709$	425.433	−	309.095i	0.600046	−	0.435959i	0.845895	+	0.533349i	$0.179067\pi$
$710$	−155.889	−	214.563i	−0.219562	−	0.302201i
$711$		0			0
$712$	−24.9965	+	76.9312i	−0.0351074	+	0.108049i
$713$	−761.159	+	1047.65i	−1.06754	+	1.46935i
$714$		0			0
$715$	−77.1688	−	106.093i	−0.107928	−	0.148381i
$716$			1065.29i			1.48784i
$717$		0			0
$718$	371.271	−	1142.65i	0.517090	−	1.59144i
$719$	−51.7903	+	16.8277i	−0.0720311	+	0.0234043i	−0.344811	−	0.938672i	$-0.612057\pi$
$719$	−51.7903	+	16.8277i	−0.0720311	+	0.0234043i	0.272780	+	0.962076i	$0.412057\pi$
$720$		0			0
$721$	−50.6844	+	36.8244i	−0.0702973	+	0.0510740i
$722$	−423.924	+	137.741i	−0.587153	+	0.190777i
$723$		0			0
$724$	−177.046	−	128.632i	−0.244539	−	0.177668i
$725$			1862.56i			2.56905i
$726$		0			0
$727$	1312.96			1.80600			0.902999	−	0.429642i	$-0.141360\pi$
$727$	1312.96			1.80600			0.902999	+	0.429642i	$0.141360\pi$
$728$	−6.58999	+	9.07035i	−0.00905219	+	0.0124593i
$729$		0			0
$730$	−758.158	−	2333.37i	−1.03857	−	3.19640i
$731$	−32.8725	−	45.2451i	−0.0449692	−	0.0618948i
$732$		0			0
$733$	122.245	+	376.231i	0.166774	+	0.513276i	0.999163	−	0.0409155i	$-0.0130275\pi$
$733$	122.245	+	376.231i	0.166774	+	0.513276i	−0.832389	+	0.554192i	$0.813027\pi$
$734$	1534.92	+	498.725i	2.09117	+	0.679461i
$735$		0			0
$736$	−1137.40			−1.54538
$737$	785.372	−	571.258i	1.06563	−	0.775112i
$738$		0			0
$739$	−1153.17	−	837.830i	−1.56045	−	1.13374i	−0.935637	−	0.352963i	$-0.885174\pi$
$739$	−1153.17	−	837.830i	−1.56045	−	1.13374i	−0.624816	−	0.780772i	$-0.714826\pi$
$740$	−713.488	−	231.826i	−0.964174	−	0.313279i
$741$		0			0
$742$	−278.558	+	202.385i	−0.375416	+	0.272755i
$743$	−381.078	−	524.508i	−0.512890	−	0.705933i	0.471513	−	0.881859i	$-0.343708\pi$
$743$	−381.078	−	524.508i	−0.512890	−	0.705933i	−0.984403	+	0.175926i	$0.943708\pi$
$744$		0			0
$745$	−580.715	+	1787.26i	−0.779483	+	2.39900i
$746$	280.334	−	385.846i	0.375783	−	0.517220i
$747$		0			0
$748$	−0.769410	−	1417.85i	−0.00102862	−	1.89552i
$749$		−	36.1417i		−	0.0482532i
$750$		0			0
$751$	−160.859	+	495.074i	−0.214193	+	0.659220i	0.785016	+	0.619475i	$0.212654\pi$
$751$	−160.859	+	495.074i	−0.214193	+	0.659220i	−0.999210	+	0.0397446i	$0.987346\pi$
$752$	447.755	−	145.484i	0.595419	−	0.193463i
$753$		0			0
$754$	−185.603	+	134.848i	−0.246157	+	0.178844i
$755$	438.440	−	142.458i	0.580715	−	0.188686i
$756$		0			0
$757$	442.250	+	321.314i	0.584214	+	0.424456i	0.840241	−	0.542213i	$-0.182414\pi$
$757$	442.250	+	321.314i	0.584214	+	0.424456i	−0.256027	+	0.966670i	$0.582414\pi$
$758$			1128.43i			1.48869i
$759$		0			0
$760$	−300.510			−0.395408
$761$	−485.510	+	668.247i	−0.637990	+	0.878118i	−0.998506	−	0.0546352i	$-0.982600\pi$
$761$	−485.510	+	668.247i	−0.637990	+	0.878118i	0.360517	+	0.932753i	$0.382600\pi$
$762$		0			0
$763$	94.8408	+	291.890i	0.124300	+	0.382555i
$764$	−427.539	−	588.457i	−0.559606	−	0.770231i
$765$		0			0
$766$	220.637	+	679.052i	0.288038	+	0.886491i
$767$	138.685	+	45.0615i	0.180815	+	0.0587503i
$768$		0			0
$769$	712.096			0.926003			0.463001	−	0.886358i	$-0.346772\pi$
$769$	712.096			0.926003			0.463001	+	0.886358i	$0.346772\pi$
$770$	585.360	+	424.804i	0.760208	+	0.551694i
$771$		0			0
$772$	765.156	+	555.918i	0.991135	+	0.720102i
$773$	262.790	+	85.3856i	0.339961	+	0.110460i	0.474022	−	0.880513i	$-0.342802\pi$
$773$	262.790	+	85.3856i	0.339961	+	0.110460i	−0.134061	+	0.990973i	$0.542802\pi$
$774$		0			0
$775$	−1534.71	+	1115.03i	−1.98028	+	1.43875i
$776$	44.1079	+	60.7094i	0.0568401	+	0.0782337i
$777$		0			0
$778$	462.905	−	1424.67i	0.594993	−	1.83120i
$779$	264.404	−	363.921i	0.339414	−	0.467164i
$780$		0			0
$781$	−118.510	−	38.4353i	−0.151742	−	0.0492129i
$782$			1972.69i			2.52262i
$783$		0			0
$784$	148.536	−	457.147i	0.189459	−	0.583095i
$785$	152.586	−	49.5783i	0.194377	−	0.0631571i
$786$		0			0
$787$	−773.348	+	561.870i	−0.982653	+	0.713939i	−0.958300	−	0.285764i	$-0.907753\pi$
$787$	−773.348	+	561.870i	−0.982653	+	0.713939i	−0.0243534	+	0.999703i	$0.507753\pi$
$788$	−1538.46	+	499.875i	−1.95236	+	0.634360i
$789$		0			0
$790$	318.044	+	231.072i	0.402587	+	0.292496i
$791$		−	258.422i		−	0.326703i
$792$		0			0
$793$	4.39493			0.00554216
$794$	−170.108	+	234.134i	−0.214242	+	0.294879i
$795$		0			0
$796$	444.837	+	1369.07i	0.558840	+	1.71993i
$797$	623.281	+	857.873i	0.782034	+	1.07638i	0.995055	+	0.0993298i	$0.0316699\pi$
$797$	623.281	+	857.873i	0.782034	+	1.07638i	−0.213021	+	0.977048i	$0.568330\pi$
$798$		0			0
$799$	−328.520	−	1011.08i	−0.411164	−	1.26543i
$800$	−1584.65	−	514.885i	−1.98082	−	0.643606i
$801$		0			0
$802$	−1958.54			−2.44207
$803$	−932.790	−	676.938i	−1.16163	−	0.843012i
$804$		0			0
$805$	−447.497	−	325.126i	−0.555897	−	0.403883i
$806$	−222.225	−	72.2052i	−0.275713	−	0.0895847i
$807$		0			0
$808$	−7.23229	+	5.25457i	−0.00895085	+	0.00650318i
$809$	−215.410	−	296.487i	−0.266268	−	0.366486i	0.654858	−	0.755752i	$-0.272729\pi$
$809$	−215.410	−	296.487i	−0.266268	−	0.366486i	−0.921125	+	0.389266i	$0.872729\pi$
$810$		0			0
$811$	185.554	−	571.077i	0.228797	−	0.704164i	−0.769087	−	0.639144i	$-0.779289\pi$
$811$	185.554	−	571.077i	0.228797	−	0.704164i	0.997884	−	0.0650200i	$-0.0207111\pi$
$812$	408.649	−	562.458i	0.503263	−	0.692682i
$813$		0			0
$814$	−609.646	+	198.452i	−0.748951	+	0.243798i
$815$		−	821.458i		−	1.00792i
$816$		0			0
$817$	−9.51922	+	29.2971i	−0.0116514	+	0.0358594i
$818$	287.858	−	93.5308i	0.351905	−	0.114341i
$819$		0			0
$820$	−960.078	+	697.537i	−1.17083	+	0.850655i
$821$	757.896	−	246.255i	0.923138	−	0.299946i	0.191384	−	0.981515i	$-0.438702\pi$
$821$	757.896	−	246.255i	0.923138	−	0.299946i	0.731753	+	0.681569i	$0.238702\pi$
$822$		0			0
$823$	−665.312	−	483.377i	−0.808398	−	0.587336i	0.104968	−	0.994476i	$-0.466526\pi$
$823$	−665.312	−	483.377i	−0.808398	−	0.587336i	−0.913366	+	0.407140i	$0.866526\pi$
$824$			58.6879i			0.0712232i
$825$		0			0
$826$	−803.931			−0.973282
$827$	−537.163	+	739.341i	−0.649532	+	0.894003i	−0.999079	−	0.0429153i	$-0.986335\pi$
$827$	−537.163	+	739.341i	−0.649532	+	0.894003i	0.349547	+	0.936919i	$0.386335\pi$
$828$		0			0
$829$	−401.217	−	1234.82i	−0.483977	−	1.48953i	−0.833458	−	0.552583i	$-0.813642\pi$
$829$	−401.217	−	1234.82i	−0.483977	−	1.48953i	0.349481	−	0.936943i	$-0.386358\pi$
$830$	313.420	+	431.386i	0.377615	+	0.519742i
$831$		0			0
$832$	−41.4846	−	127.677i	−0.0498613	−	0.153457i
$833$	−1032.29	−	335.411i	−1.23924	−	0.402654i
$834$		0			0
$835$	−308.067			−0.368942
$836$	−631.571	+	459.387i	−0.755468	+	0.549506i
$837$		0			0
$838$	−1.06048	−	0.770482i	−0.00126549	−	0.000919429i
$839$	55.7860	+	18.1260i	0.0664910	+	0.0216042i	0.342074	−	0.939673i	$-0.388871\pi$
$839$	55.7860	+	18.1260i	0.0664910	+	0.0216042i	−0.275583	+	0.961277i	$0.588871\pi$
$840$		0			0
$841$	1400.04	−	1017.19i	1.66473	−	1.20950i
$842$	−733.242	−	1009.22i	−0.870833	−	1.19860i
$843$		0			0
$844$	174.609	−	537.390i	0.206882	−	0.636718i
$845$	769.820	−	1059.57i	0.911030	−	1.25392i
$846$		0			0
$847$	339.760	−	0.368747i	0.401133	−	0.000435357i
$848$		−	481.001i		−	0.567218i
$849$		0			0
$850$	−893.006	+	2748.39i	−1.05060	+	3.23340i
$851$	466.329	−	151.520i	0.547978	−	0.178049i
$852$		0			0
$853$	925.786	−	672.623i	1.08533	−	0.788538i	0.106725	−	0.994289i	$-0.465964\pi$
$853$	925.786	−	672.623i	1.08533	−	0.788538i	0.978605	+	0.205750i	$0.0659635\pi$
$854$	−23.0438	+	7.48738i	−0.0269834	+	0.00876743i
$855$		0			0
$856$	−27.3904	−	19.9003i	−0.0319981	−	0.0232480i
$857$		−	1380.38i		−	1.61071i	−0.592790	−	0.805357i	$-0.701973\pi$
$857$		−	1380.38i		−	1.61071i	0.592790	−	0.805357i	$-0.298027\pi$
$858$		0			0
$859$	210.196			0.244698			0.122349	−	0.992487i	$-0.460957\pi$
$859$	210.196			0.244698			0.122349	+	0.992487i	$0.460957\pi$
$860$	47.7680	−	65.7471i	0.0555442	−	0.0764501i
$861$		0			0
$862$	−232.151	−	714.487i	−0.269317	−	0.828872i
$863$	118.360	+	162.909i	0.137150	+	0.188771i	0.872067	−	0.489386i	$-0.162779\pi$
$863$	118.360	+	162.909i	0.137150	+	0.188771i	−0.734917	+	0.678157i	$0.762779\pi$
$864$		0			0
$865$	−221.976	−	683.172i	−0.256620	−	0.789794i
$866$	352.752	+	114.616i	0.407334	+	0.132351i
$867$		0			0
$868$	708.096			0.815778
$869$	184.674	−	0.100215i	0.212514	−	0.000115322i
$870$		0			0
$871$	−108.421	−	78.7727i	−0.124479	−	0.0904393i
$872$	273.433	+	88.8438i	0.313570	+	0.101885i
$873$		0			0
$874$	879.066	−	638.679i	1.00580	−	0.730754i
$875$	−152.099	−	209.346i	−0.173827	−	0.239252i
$876$		0			0
$877$	−327.015	+	1006.45i	−0.372879	+	1.14760i	0.572019	+	0.820241i	$0.306160\pi$
$877$	−327.015	+	1006.45i	−0.372879	+	1.14760i	−0.944898	+	0.327364i	$0.893840\pi$
$878$	129.097	−	177.687i	0.147035	−	0.202377i
$879$		0			0
$880$	−960.753	+	312.744i	−1.09176	+	0.355391i
$881$			402.743i			0.457144i	0.973527	+	0.228572i	$0.0734056\pi$
$881$			402.743i			0.457144i	−0.973527	+	0.228572i	$0.926594\pi$
$882$		0			0
$883$	−359.028	+	1104.98i	−0.406600	+	1.25139i	0.512951	+	0.858418i	$0.328552\pi$
$883$	−359.028	+	1104.98i	−0.406600	+	1.25139i	−0.919552	+	0.392970i	$0.871448\pi$
$884$	−186.082	+	60.4618i	−0.210500	+	0.0683957i
$885$		0			0
$886$	891.978	−	648.060i	1.00675	−	0.731445i
$887$	464.536	−	150.937i	0.523716	−	0.170166i	−0.0352149	−	0.999380i	$-0.511212\pi$
$887$	464.536	−	150.937i	0.523716	−	0.170166i	0.558931	+	0.829214i	$0.311212\pi$
$888$		0			0
$889$	18.8162	+	13.6708i	0.0211656	+	0.0153777i
$890$		−	720.099i		−	0.809100i
$891$		0			0
$892$	1191.80			1.33609
$893$	−344.194	+	473.743i	−0.385436	+	0.530507i
$894$		0			0
$895$	−529.722	−	1630.32i	−0.591868	−	1.82158i
$896$	135.541	+	186.557i	0.151274	+	0.208211i
$897$		0			0
$898$	669.140	+	2059.40i	0.745145	+	2.29332i
$899$	2490.92	+	809.349i	2.77077	+	0.900277i
$900$		0			0
$901$	−1086.16			−1.20550
$902$	−312.876	+	964.715i	−0.346870	+	1.06953i
$903$		0			0
$904$	−195.848	−	142.292i	−0.216646	−	0.157403i
$905$	334.913	+	108.820i	0.370070	+	0.120243i
$906$		0			0
$907$	1365.03	−	991.753i	1.50500	−	1.09344i	0.536657	−	0.843800i	$-0.319687\pi$
$907$	1365.03	−	991.753i	1.50500	−	1.09344i	0.968338	−	0.249643i	$-0.0803131\pi$
$908$	−769.780	−	1059.51i	−0.847776	−	1.16686i
$909$		0			0
$910$	30.8422	−	94.9224i	0.0338925	−	0.104310i
$911$	−642.283	+	884.026i	−0.705030	+	0.970391i	0.294859	+	0.955541i	$0.404727\pi$
$911$	−642.283	+	884.026i	−0.705030	+	0.970391i	−0.999890	+	0.0148504i	$0.995273\pi$
$912$		0			0
$913$	238.270	+	77.2756i	0.260974	+	0.0846392i
$914$			1089.38i			1.19188i
$915$		0			0
$916$	−280.775	+	864.136i	−0.306523	+	0.943380i
$917$	4.37340	−	1.42101i	0.00476925	−	0.00154962i
$918$		0			0
$919$	−974.396	+	707.940i	−1.06028	+	0.770338i	−0.974140	−	0.225946i	$-0.927453\pi$
$919$	−974.396	+	707.940i	−1.06028	+	0.770338i	−0.0861388	+	0.996283i	$0.527453\pi$
$920$	−492.801	+	160.121i	−0.535653	+	0.174044i
$921$		0			0
$922$	−370.523	−	269.201i	−0.401869	−	0.291975i
$923$			17.1926i			0.0186269i
$924$		0			0
$925$	718.289			0.776529
$926$	−569.965	+	784.489i	−0.615512	+	0.847180i
$927$		0			0
$928$	710.876	+	2187.85i	0.766030	+	2.35760i
$929$	133.527	+	183.784i	0.143732	+	0.197830i	0.874813	−	0.484460i	$-0.160984\pi$
$929$	133.527	+	183.784i	0.143732	+	0.197830i	−0.731081	+	0.682290i	$0.760984\pi$
$930$		0			0
$931$	184.749	+	568.600i	0.198442	+	0.610741i
$932$	−753.104	−	244.698i	−0.808052	−	0.262552i
$933$		0			0
$934$	2491.48			2.66754
$935$	706.212	+	2169.49i	0.755307	+	2.32031i
$936$		0			0
$937$	−287.786	−	209.089i	−0.307135	−	0.223147i	0.423531	−	0.905882i	$-0.360791\pi$
$937$	−287.786	−	209.089i	−0.307135	−	0.223147i	−0.730666	+	0.682735i	$0.760791\pi$
$938$	702.682	+	228.315i	0.749128	+	0.243406i
$939$		0			0
$940$	1249.81	−	908.037i	1.32958	−	0.965997i
$941$	−801.260	−	1102.84i	−0.851498	−	1.17199i	−0.983531	−	0.180741i	$-0.942150\pi$
$941$	−801.260	−	1102.84i	−0.851498	−	1.17199i	0.132032	−	0.991245i	$-0.457850\pi$
$942$		0			0
$943$	239.683	−	737.668i	0.254170	−	0.782256i
$944$	660.123	−	908.581i	0.699283	−	0.962480i
$945$		0			0
$946$	−0.0376889	−	69.4523i	−3.98403e−5	−	0.0734168i
$947$			90.3298i			0.0953852i	0.998862	+	0.0476926i	$0.0151868\pi$
$947$			90.3298i			0.0953852i	−0.998862	+	0.0476926i	$0.984813\pi$
$948$		0			0
$949$	−49.1479	+	151.262i	−0.0517892	+	0.159391i
$950$	1513.85	−	491.880i	1.59353	−	0.517769i
$951$		0			0
$952$	157.744	−	114.608i	0.165697	−	0.120386i
$953$	−582.669	+	189.321i	−0.611405	+	0.198657i	−0.598320	−	0.801257i	$-0.704165\pi$
$953$	−582.669	+	189.321i	−0.611405	+	0.198657i	−0.0130843	+	0.999914i	$0.504165\pi$
$954$		0			0
$955$	946.916	+	687.975i	0.991535	+	0.720393i
$956$		−	347.120i		−	0.363096i
$957$		0			0
$958$	1000.63			1.04450
$959$	326.987	−	450.059i	0.340967	−	0.469300i
$960$		0			0
$961$	527.354	+	1623.03i	0.548755	+	1.68890i
$962$	52.0038	+	71.5770i	0.0540580	+	0.0744044i
$963$		0			0
$964$	−321.071	−	988.154i	−0.333061	−	1.02506i
$965$	−1447.42	−	470.297i	−1.49992	−	0.487354i
$966$		0			0
$967$	−446.224			−0.461452			−0.230726	−	0.973019i	$-0.574110\pi$
$967$	−446.224			−0.461452			−0.230726	+	0.973019i	$0.574110\pi$
$968$	186.799	−	257.694i	0.192974	−	0.266213i
$969$		0			0
$970$	−540.445	−	392.656i	−0.557160	−	0.404800i
$971$	145.304	+	47.2121i	0.149644	+	0.0486221i	0.382881	−	0.923798i	$-0.374932\pi$
$971$	145.304	+	47.2121i	0.149644	+	0.0486221i	−0.233237	+	0.972420i	$0.574932\pi$
$972$		0			0
$973$	425.816	−	309.373i	0.437632	−	0.317958i
$974$	1025.59	+	1411.60i	1.05296	+	1.44928i
$975$		0			0
$976$	10.4597	−	32.1915i	0.0107169	−	0.0329831i
$977$	331.987	−	456.941i	0.339803	−	0.467698i	−0.604581	−	0.796544i	$-0.706659\pi$
$977$	331.987	−	456.941i	0.339803	−	0.467698i	0.944384	+	0.328845i	$0.106659\pi$
$978$		0			0
$979$	−198.982	−	273.562i	−0.203250	−	0.279430i
$980$		−	1577.25i		−	1.60944i
$981$		0			0
$982$	−299.856	+	922.863i	−0.305353	+	0.939779i
$983$	−899.158	+	292.154i	−0.914708	+	0.297207i	−0.728294	−	0.685265i	$-0.759687\pi$
$983$	−899.158	+	292.154i	−0.914708	+	0.297207i	−0.186414	+	0.982471i	$0.559687\pi$
$984$		0			0
$985$	2105.88	−	1530.01i	2.13795	−	1.55331i
$986$	3794.56	−	1232.93i	3.84844	−	1.25043i
$987$		0			0
$988$	87.1889	+	63.3465i	0.0882479	+	0.0641158i
$989$			53.1159i			0.0537067i
$990$		0			0
$991$	1225.61			1.23674			0.618371	−	0.785886i	$-0.287793\pi$
$991$	1225.61			1.23674			0.618371	+	0.785886i	$0.287793\pi$
$992$	−1377.18	+	1895.52i	−1.38828	+	1.91081i
$993$		0			0
$994$	−29.2900	−	90.1454i	−0.0294668	−	0.0906896i
$995$	−1361.55	−	1874.01i	−1.36839	−	1.88343i
$996$		0			0
$997$	−394.466	−	1214.04i	−0.395653	−	1.21770i	−0.928452	−	0.371453i	$-0.878860\pi$
$997$	−394.466	−	1214.04i	−0.395653	−	1.21770i	0.532798	−	0.846242i	$-0.321140\pi$
$998$	−1143.22	−	371.454i	−1.14551	−	0.372198i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.3.l.a.26.2	✓	32
3.2	odd	2	inner	99.3.l.a.26.7	yes	32
11.3	even	5	inner	99.3.l.a.80.7	yes	32
11.5	even	5		1089.3.b.i.485.4		16
11.6	odd	10		1089.3.b.j.485.13		16
33.5	odd	10		1089.3.b.i.485.13		16
33.14	odd	10	inner	99.3.l.a.80.2	yes	32
33.17	even	10		1089.3.b.j.485.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.3.l.a.26.2	✓	32	1.1	even	1	trivial
99.3.l.a.26.7	yes	32	3.2	odd	2	inner
99.3.l.a.80.2	yes	32	33.14	odd	10	inner
99.3.l.a.80.7	yes	32	11.3	even	5	inner
1089.3.b.i.485.4		16	11.5	even	5
1089.3.b.i.485.13		16	33.5	odd	10
1089.3.b.j.485.4		16	33.17	even	10
1089.3.b.j.485.13		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)

\(f(q)\)	\(=\)	\(q+(-1.75181 + 2.41117i) q^{2} +(-1.50880 - 4.64360i) q^{4} +(4.61811 + 6.35629i) q^{5} +(0.867699 + 2.67050i) q^{7} +(2.50164 + 0.812833i) q^{8} +O(q^{10})\)	\(q+(-1.75181 + 2.41117i) q^{2} +(-1.50880 - 4.64360i) q^{4} +(4.61811 + 6.35629i) q^{5} +(0.867699 + 2.67050i) q^{7} +(2.50164 + 0.812833i) q^{8} -23.4161 q^{10} +(-8.89568 + 6.47047i) q^{11} +(1.22806 + 0.892235i) q^{13} +(-7.95907 - 2.58606i) q^{14} +(9.45804 - 6.87167i) q^{16} +(-15.5170 - 21.3573i) q^{17} +(-4.49342 + 13.8293i) q^{19} +(22.5483 - 31.0350i) q^{20} +(-0.0177905 - 32.7840i) q^{22} +25.0726i q^{23} +(-11.3500 + 34.9317i) q^{25} +(-4.30265 + 1.39802i) q^{26} +(11.0916 - 8.05850i) q^{28} +(48.2284 - 15.6704i) q^{29} +(41.7844 + 30.3581i) q^{31} +45.3643i q^{32} +78.6790 q^{34} +(-12.9674 + 17.8480i) q^{35} +(-6.04322 - 18.5991i) q^{37} +(-25.4731 - 35.0608i) q^{38} +(6.38627 + 19.6549i) q^{40} +(-29.4212 - 9.55953i) q^{41} +2.11848 q^{43} +(43.4680 + 31.5454i) q^{44} +(-60.4543 - 43.9226i) q^{46} +(38.2998 + 12.4444i) q^{47} +(33.2631 - 24.1671i) q^{49} +(-64.3430 - 88.5605i) q^{50} +(2.29029 - 7.04880i) q^{52} +(24.1836 - 33.2859i) q^{53} +(-82.2094 - 26.6621i) q^{55} +7.38594i q^{56} +(-46.7034 + 143.738i) q^{58} +(91.3627 - 29.6855i) q^{59} +(2.34234 - 1.70181i) q^{61} +(-146.397 + 47.5673i) q^{62} +(-71.5487 - 51.9832i) q^{64} +11.9263i q^{65} -88.2869 q^{67} +(-75.7629 + 104.279i) q^{68} +(-20.3182 - 62.5329i) q^{70} +(6.65733 + 9.16303i) q^{71} +(32.3776 + 99.6480i) q^{73} +(55.4322 + 18.0110i) q^{74} +70.9975 q^{76} +(-24.9982 - 18.1415i) q^{77} +(-13.5822 - 9.86808i) q^{79} +(87.3566 + 28.3839i) q^{80} +(74.5901 - 54.1929i) q^{82} +(-13.3848 - 18.4226i) q^{83} +(64.0940 - 197.261i) q^{85} +(-3.71118 + 5.10801i) q^{86} +(-27.5132 + 8.95610i) q^{88} +30.7523i q^{89} +(-1.31713 + 4.05372i) q^{91} +(116.427 - 37.8295i) q^{92} +(-97.0996 + 70.5470i) q^{94} +(-108.654 + 35.3039i) q^{95} +(23.0800 + 16.7686i) q^{97} +122.539i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 16 q^{7}+O(q^{10}) \) 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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