LMFDB - Embedded newform 99.4.f.e.82.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,4,Mod(37,99)]

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([0, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("99.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	99.f (of order $5$, 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:	$5.84118909057$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			82.4
Character	$\chi$	$=$	99.82
Dual form			99.4.f.e.64.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0654439 + 0.201416i) q^{2} +(6.43585 - 4.67592i) q^{4} +(-5.73265 + 17.6433i) q^{5} +(-17.3440 + 12.6012i) q^{7} +(2.73367 + 1.98613i) q^{8} +O(q^{10})$	\(q+(0.0654439 + 0.201416i) q^{2} +(6.43585 - 4.67592i) q^{4} +(-5.73265 + 17.6433i) q^{5} +(-17.3440 + 12.6012i) q^{7} +(2.73367 + 1.98613i) q^{8} -3.92880 q^{10} +(29.4005 + 21.6012i) q^{11} +(1.29584 + 3.98820i) q^{13} +(-3.67313 - 2.66869i) q^{14} +(19.4451 - 59.8458i) q^{16} +(-26.8314 + 82.5787i) q^{17} +(85.7906 + 62.3305i) q^{19} +(45.6041 + 140.355i) q^{20} +(-2.42673 + 7.33539i) q^{22} -148.322 q^{23} +(-177.295 - 128.813i) q^{25} +(-0.718481 + 0.522007i) q^{26} +(-52.7014 + 162.198i) q^{28} +(211.201 - 153.447i) q^{29} +(14.4456 + 44.4590i) q^{31} +40.3584 q^{32} -18.3886 q^{34} +(-122.899 - 378.243i) q^{35} +(245.717 - 178.524i) q^{37} +(-6.93988 + 21.3587i) q^{38} +(-50.7129 + 36.8451i) q^{40} +(-116.323 - 84.5140i) q^{41} +174.897 q^{43} +(290.223 + 1.54754i) q^{44} +(-9.70676 - 29.8743i) q^{46} +(-300.564 - 218.373i) q^{47} +(36.0324 - 110.896i) q^{49} +(14.3420 - 44.1401i) q^{50} +(26.9884 + 19.6082i) q^{52} +(-44.9117 - 138.224i) q^{53} +(-549.659 + 394.890i) q^{55} -72.4402 q^{56} +(44.7284 + 32.4971i) q^{58} +(164.834 - 119.759i) q^{59} +(-56.4889 + 173.855i) q^{61} +(-8.00936 + 5.81914i) q^{62} +(-152.919 - 470.637i) q^{64} -77.7936 q^{65} -153.054 q^{67} +(213.448 + 656.925i) q^{68} +(68.1412 - 49.5075i) q^{70} +(48.7916 - 150.165i) q^{71} +(525.951 - 382.126i) q^{73} +(52.0381 + 37.8079i) q^{74} +843.588 q^{76} +(-782.122 - 4.17047i) q^{77} +(313.345 + 964.378i) q^{79} +(944.405 + 686.150i) q^{80} +(9.40977 - 28.9603i) q^{82} +(-94.2610 + 290.105i) q^{83} +(-1303.14 - 946.789i) q^{85} +(11.4459 + 35.2270i) q^{86} +(37.4685 + 117.443i) q^{88} +1345.51 q^{89} +(-72.7310 - 52.8422i) q^{91} +(-954.577 + 693.541i) q^{92} +(24.3136 - 74.8296i) q^{94} +(-1591.52 + 1156.31i) q^{95} +(320.534 + 986.501i) q^{97} +24.6944 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{4} - 28 q^{7}+O(q^{10}) $ 24 * q - 4 * q^4 - 28 * q^7	$ 24 q - 4 q^{4} - 28 q^{7} + 208 q^{10} + 20 q^{13} - 224 q^{16} - 40 q^{19} - 586 q^{22} + 362 q^{25} - 150 q^{28} + 670 q^{31} - 2520 q^{34} - 516 q^{37} + 2002 q^{40} + 4008 q^{43} + 2174 q^{46} + 342 q^{49} - 1894 q^{52} - 3300 q^{55} + 22 q^{58} - 2952 q^{61} - 3992 q^{64} - 1936 q^{67} - 1024 q^{70} + 2194 q^{73} + 15336 q^{76} + 1524 q^{79} + 2898 q^{82} - 7428 q^{85} - 3936 q^{88} - 6460 q^{91} - 16982 q^{94} - 1224 q^{97}+O(q^{100}) $ 24 * q - 4 * q^4 - 28 * q^7 + 208 * q^10 + 20 * q^13 - 224 * q^16 - 40 * q^19 - 586 * q^22 + 362 * q^25 - 150 * q^28 + 670 * q^31 - 2520 * q^34 - 516 * q^37 + 2002 * q^40 + 4008 * q^43 + 2174 * q^46 + 342 * q^49 - 1894 * q^52 - 3300 * q^55 + 22 * q^58 - 2952 * q^61 - 3992 * q^64 - 1936 * q^67 - 1024 * q^70 + 2194 * q^73 + 15336 * q^76 + 1524 * q^79 + 2898 * q^82 - 7428 * q^85 - 3936 * q^88 - 6460 * q^91 - 16982 * q^94 - 1224 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.0654439	+	0.201416i	0.0231379	+	0.0712112i	0.961959	−	0.273195i	$-0.0880803\pi$
$2$	0.0654439	+	0.201416i	0.0231379	+	0.0712112i	−0.938821	+	0.344406i	$0.888080\pi$
$3$		0			0
$3$		0			0
$4$	6.43585	−	4.67592i	0.804481	−	0.584490i
$5$	−5.73265	+	17.6433i	−0.512744	+	1.57806i	0.274605	+	0.961557i	$0.411453\pi$
$5$	−5.73265	+	17.6433i	−0.512744	+	1.57806i	−0.787350	+	0.616507i	$0.788547\pi$
$6$		0			0
$7$	−17.3440	+	12.6012i	−0.936488	+	0.680398i	−0.947573	−	0.319540i	$-0.896472\pi$
$7$	−17.3440	+	12.6012i	−0.936488	+	0.680398i	0.0110848	+	0.999939i	$0.496472\pi$
$8$	2.73367	+	1.98613i	0.120812	+	0.0877752i
$9$		0			0
$10$	−3.92880			−0.124240
$11$	29.4005	+	21.6012i	0.805871	+	0.592091i
$11$	29.4005	+	21.6012i	0.805871	+	0.592091i
$12$		0			0
$13$	1.29584	+	3.98820i	0.0276464	+	0.0850867i	0.963928	−	0.266164i	$-0.0857564\pi$
$13$	1.29584	+	3.98820i	0.0276464	+	0.0850867i	−0.936281	+	0.351251i	$0.885756\pi$
$14$	−3.67313	−	2.66869i	−0.0701204	−	0.0509454i
$15$		0			0
$16$	19.4451	−	59.8458i	0.303829	−	0.935090i
$17$	−26.8314	+	82.5787i	−0.382799	+	1.17813i	0.555266	+	0.831673i	$0.312616\pi$
$17$	−26.8314	+	82.5787i	−0.382799	+	1.17813i	−0.938065	+	0.346460i	$0.887384\pi$
$18$		0			0
$19$	85.7906	+	62.3305i	1.03588	+	0.752611i	0.969477	−	0.245182i	$-0.0788477\pi$
$19$	85.7906	+	62.3305i	1.03588	+	0.752611i	0.0664031	+	0.997793i	$0.478848\pi$
$20$	45.6041	+	140.355i	0.509869	+	1.56922i
$21$		0			0
$22$	−2.42673	+	7.33539i	−0.0235173	+	0.0710868i
$23$	−148.322			−1.34466			−0.672331	−	0.740251i	$-0.734707\pi$
$23$	−148.322			−1.34466			−0.672331	+	0.740251i	$0.734707\pi$
$24$		0			0
$25$	−177.295	−	128.813i	−1.41836	−	1.03050i
$26$	−0.718481	+	0.522007i	−0.00541945	+	0.00393746i
$27$		0			0
$28$	−52.7014	+	162.198i	−0.355701	+	1.09474i
$29$	211.201	−	153.447i	1.35238	−	0.982562i	0.353492	−	0.935438i	$-0.384994\pi$
$29$	211.201	−	153.447i	1.35238	−	0.982562i	0.998889	−	0.0471249i	$-0.0150059\pi$
$30$		0			0
$31$	14.4456	+	44.4590i	0.0836937	+	0.257583i	0.984143	−	0.177379i	$-0.0567619\pi$
$31$	14.4456	+	44.4590i	0.0836937	+	0.257583i	−0.900449	+	0.434962i	$0.856762\pi$
$32$	40.3584			0.222951
$33$		0			0
$34$	−18.3886			−0.0927535
$35$	−122.899	−	378.243i	−0.593533	−	1.82671i
$36$		0			0
$37$	245.717	−	178.524i	1.09177	−	0.793219i	0.112074	−	0.993700i	$-0.464251\pi$
$37$	245.717	−	178.524i	1.09177	−	0.793219i	0.979698	+	0.200481i	$0.0642505\pi$
$38$	−6.93988	+	21.3587i	−0.0296262	+	0.0911801i
$39$		0			0
$40$	−50.7129	+	36.8451i	−0.200461	+	0.145643i
$41$	−116.323	−	84.5140i	−0.443090	−	0.321923i	0.343772	−	0.939053i	$-0.388295\pi$
$41$	−116.323	−	84.5140i	−0.443090	−	0.321923i	−0.786861	+	0.617130i	$0.788295\pi$
$42$		0			0
$43$	174.897			0.620268			0.310134	−	0.950693i	$-0.399626\pi$
$43$	174.897			0.620268			0.310134	+	0.950693i	$0.399626\pi$
$44$	290.223	+	1.54754i	0.994379	+	0.00530228i
$45$		0			0
$46$	−9.70676	−	29.8743i	−0.0311127	−	0.0957550i
$47$	−300.564	−	218.373i	−0.932805	−	0.677722i	0.0138731	−	0.999904i	$-0.495584\pi$
$47$	−300.564	−	218.373i	−0.932805	−	0.677722i	−0.946678	+	0.322181i	$0.895584\pi$
$48$		0			0
$49$	36.0324	−	110.896i	0.105051	−	0.323313i
$50$	14.3420	−	44.1401i	0.0405652	−	0.124847i
$51$		0			0
$52$	26.9884	+	19.6082i	0.0719733	+	0.0522917i
$53$	−44.9117	−	138.224i	−0.116398	−	0.358237i	0.875838	−	0.482605i	$-0.160309\pi$
$53$	−44.9117	−	138.224i	−0.116398	−	0.358237i	−0.992236	+	0.124369i	$0.960309\pi$
$54$		0			0
$55$	−549.659	+	394.890i	−1.34756	+	0.968125i
$56$	−72.4402			−0.172861
$57$		0			0
$58$	44.7284	+	32.4971i	0.101261	+	0.0735702i
$59$	164.834	−	119.759i	0.363722	−	0.264259i	−0.390881	−	0.920441i	$-0.627830\pi$
$59$	164.834	−	119.759i	0.363722	−	0.264259i	0.754603	+	0.656182i	$0.227830\pi$
$60$		0			0
$61$	−56.4889	+	173.855i	−0.118568	+	0.364915i	−0.992675	−	0.120819i	$-0.961448\pi$
$61$	−56.4889	+	173.855i	−0.118568	+	0.364915i	0.874106	+	0.485735i	$0.161448\pi$
$62$	−8.00936	+	5.81914i	−0.0164063	+	0.0119199i
$63$		0			0
$64$	−152.919	−	470.637i	−0.298671	−	0.919214i
$65$	−77.7936			−0.148448
$66$		0			0
$67$	−153.054			−0.279083			−0.139542	−	0.990216i	$-0.544563\pi$
$67$	−153.054			−0.279083			−0.139542	+	0.990216i	$0.544563\pi$
$68$	213.448	+	656.925i	0.380653	+	1.17153i
$69$		0			0
$70$	68.1412	−	49.5075i	0.116349	−	0.0845325i
$71$	48.7916	−	150.165i	0.0815564	−	0.251005i	−0.901961	−	0.431817i	$-0.857873\pi$
$71$	48.7916	−	150.165i	0.0815564	−	0.251005i	0.983518	+	0.180812i	$0.0578726\pi$
$72$		0			0
$73$	525.951	−	382.126i	0.843260	−	0.612664i	−0.0800196	−	0.996793i	$-0.525498\pi$
$73$	525.951	−	382.126i	0.843260	−	0.612664i	0.923279	+	0.384129i	$0.125498\pi$
$74$	52.0381	+	37.8079i	0.0817474	+	0.0593930i
$75$		0			0
$76$	843.588			1.27324
$77$	−782.122	−	4.17047i	−1.15755	−	0.00617233i
$78$		0			0
$79$	313.345	+	964.378i	0.446255	+	1.37343i	0.881102	+	0.472926i	$0.156802\pi$
$79$	313.345	+	964.378i	0.446255	+	1.37343i	−0.434847	+	0.900504i	$0.643198\pi$
$80$	944.405	+	686.150i	1.31985	+	0.958924i
$81$		0			0
$82$	9.40977	−	28.9603i	0.0126724	−	0.0390016i
$83$	−94.2610	+	290.105i	−0.124656	+	0.383653i	−0.993838	−	0.110839i	$-0.964646\pi$
$83$	−94.2610	+	290.105i	−0.124656	+	0.383653i	0.869182	+	0.494493i	$0.164646\pi$
$84$		0			0
$85$	−1303.14	−	946.789i	−1.66289	−	1.20816i
$86$	11.4459	+	35.2270i	0.0143517	+	0.0441701i
$87$		0			0
$88$	37.4685	+	117.443i	0.0453882	+	0.142267i
$89$	1345.51			1.60252			0.801259	−	0.598318i	$-0.204164\pi$
$89$	1345.51			1.60252			0.801259	+	0.598318i	$0.204164\pi$
$90$		0			0
$91$	−72.7310	−	52.8422i	−0.0837833	−	0.0608722i
$92$	−954.577	+	693.541i	−1.08176	+	0.785941i
$93$		0			0
$94$	24.3136	−	74.8296i	0.0266783	−	0.0821073i
$95$	−1591.52	+	1156.31i	−1.71881	+	1.24879i
$96$		0			0
$97$	320.534	+	986.501i	0.335518	+	1.03262i	0.966466	+	0.256794i	$0.0826661\pi$
$97$	320.534	+	986.501i	0.335518	+	1.03262i	−0.630948	+	0.775825i	$0.717334\pi$
$98$	24.6944			0.0254542
$99$		0			0
$100$	−1743.36			−1.74336
$101$	225.488	+	693.982i	0.222148	+	0.683701i	0.998569	+	0.0534860i	$0.0170333\pi$
$101$	225.488	+	693.982i	0.222148	+	0.683701i	−0.776421	+	0.630215i	$0.782967\pi$
$102$		0			0
$103$	137.058	−	99.5783i	0.131114	−	0.0952596i	−0.520296	−	0.853986i	$-0.674178\pi$
$103$	137.058	−	99.5783i	0.131114	−	0.0952596i	0.651409	+	0.758727i	$0.274178\pi$
$104$	−4.37866	+	13.4761i	−0.00412849	+	0.0127062i
$105$		0			0
$106$	24.9013	−	18.0919i	0.0228173	−	0.0165777i
$107$	938.826	+	682.097i	0.848222	+	0.616269i	0.924655	−	0.380805i	$-0.124353\pi$
$107$	938.826	+	682.097i	0.848222	+	0.616269i	−0.0764332	+	0.997075i	$0.524353\pi$
$108$		0			0
$109$	963.937			0.847050			0.423525	−	0.905884i	$-0.360793\pi$
$109$	963.937			0.847050			0.423525	+	0.905884i	$0.360793\pi$
$110$	−115.509	−	84.8668i	−0.100121	−	0.0735612i
$111$		0			0
$112$	416.871	+	1283.00i	0.351701	+	1.08243i
$113$	−485.899	−	353.026i	−0.404509	−	0.293893i	0.366866	−	0.930274i	$-0.380431\pi$
$113$	−485.899	−	353.026i	−0.404509	−	0.293893i	−0.771375	+	0.636381i	$0.780431\pi$
$114$		0			0
$115$	850.277	−	2616.88i	0.689467	−	2.12196i
$116$	641.755	−	1975.12i	0.513668	−	1.58091i
$117$		0			0
$118$	34.9087	+	25.3627i	0.0272340	+	0.0197866i
$119$	−575.222	−	1770.35i	−0.443114	−	1.36376i
$120$		0			0
$121$	397.779	+	1270.17i	0.298857	+	0.954298i
$122$	−38.7139			−0.0287295
$123$		0			0
$124$	300.856	+	218.585i	0.217885	+	0.158302i
$125$	1413.01	−	1026.62i	1.01107	−	0.734586i
$126$		0			0
$127$	596.515	−	1835.88i	0.416789	−	1.28274i	−0.493853	−	0.869546i	$-0.664412\pi$
$127$	596.515	−	1835.88i	0.416789	−	1.28274i	0.910641	−	0.413198i	$-0.135588\pi$
$128$	345.991	−	251.377i	0.238919	−	0.173585i
$129$		0			0
$130$	−5.09112	−	15.6689i	−0.00343477	−	0.0105711i
$131$	50.4283			0.0336331			0.0168166	−	0.999859i	$-0.494647\pi$
$131$	50.4283			0.0336331			0.0168166	+	0.999859i	$0.494647\pi$
$132$		0			0
$133$	−2273.39			−1.48216
$134$	−10.0165	−	30.8276i	−0.00645741	−	0.0198739i
$135$		0			0
$136$	−237.360	+	172.452i	−0.149658	+	0.108733i
$137$	265.998	−	818.658i	0.165881	−	0.510531i	−0.833219	−	0.552944i	$-0.813505\pi$
$137$	265.998	−	818.658i	0.165881	−	0.510531i	0.999100	+	0.0424130i	$0.0135045\pi$
$138$		0			0
$139$	−991.138	+	720.104i	−0.604800	+	0.439413i	−0.847579	−	0.530669i	$-0.821941\pi$
$139$	−991.138	+	720.104i	−0.604800	+	0.439413i	0.242779	+	0.970082i	$0.421941\pi$
$140$	−2559.59	−	1859.65i	−1.54518	−	1.12264i
$141$		0			0
$142$	33.4388			0.0197614
$143$	−48.0513	+	145.247i	−0.0280997	+	0.0849381i
$144$		0			0
$145$	1496.56	+	4605.94i	0.857121	+	2.63795i
$146$	111.387	+	80.9271i	0.0631398	+	0.0458738i
$147$		0			0
$148$	746.634	−	2297.90i	0.414682	−	1.27626i
$149$	−667.923	+	2055.66i	−0.367237	+	1.13024i	0.581331	+	0.813667i	$0.302532\pi$
$149$	−667.923	+	2055.66i	−0.367237	+	1.13024i	−0.948568	+	0.316573i	$0.897468\pi$
$150$		0			0
$151$	−2079.02	−	1510.50i	−1.12045	−	0.814057i	−0.136176	−	0.990685i	$-0.543481\pi$
$151$	−2079.02	−	1510.50i	−1.12045	−	0.814057i	−0.984278	+	0.176627i	$0.943481\pi$
$152$	110.727	+	340.782i	0.0590863	+	0.181849i
$153$		0			0
$154$	−50.3451	−	157.805i	−0.0263437	−	0.0825731i
$155$	−867.214			−0.449396
$156$		0			0
$157$	−1889.81	−	1373.03i	−0.960658	−	0.697959i	−0.00735419	−	0.999973i	$-0.502341\pi$
$157$	−1889.81	−	1373.03i	−0.960658	−	0.697959i	−0.953303	+	0.302014i	$0.902341\pi$
$158$	−173.734	+	126.225i	−0.0874782	+	0.0635567i
$159$		0			0
$160$	−231.361	+	712.055i	−0.114317	+	0.351831i
$161$	2572.49	−	1869.03i	1.25926	−	0.914906i
$162$		0			0
$163$	477.263	+	1468.87i	0.229338	+	0.705831i	0.997822	+	0.0659615i	$0.0210115\pi$
$163$	477.263	+	1468.87i	0.229338	+	0.705831i	−0.768484	+	0.639869i	$0.778989\pi$
$164$	−1143.82			−0.544618
$165$		0			0
$166$	−64.6006			−0.0302047
$167$	−969.584	−	2984.07i	−0.449274	−	1.38272i	−0.877728	−	0.479159i	$-0.840942\pi$
$167$	−969.584	−	2984.07i	−0.449274	−	1.38272i	0.428455	−	0.903563i	$-0.359058\pi$
$168$		0			0
$169$	1763.18	−	1281.03i	0.802542	−	0.583081i
$170$	105.415	−	324.435i	0.0475588	−	0.146371i
$171$		0			0
$172$	1125.61	−	817.804i	0.498994	−	0.362541i
$173$	2411.39	+	1751.98i	1.05974	+	0.769944i	0.974040	−	0.226377i	$-0.0726883\pi$
$173$	2411.39	+	1751.98i	1.05974	+	0.769944i	0.0856971	+	0.996321i	$0.472688\pi$
$174$		0			0
$175$	4698.20			2.02943
$176$	1864.43	−	1339.46i	0.798506	−	0.573668i
$177$		0			0
$178$	88.0557	+	271.007i	0.0370789	+	0.114117i
$179$	−1045.40	−	759.528i	−0.436519	−	0.317150i	0.347731	−	0.937594i	$-0.386952\pi$
$179$	−1045.40	−	759.528i	−0.436519	−	0.317150i	−0.784250	+	0.620445i	$0.786952\pi$
$180$		0			0
$181$	357.508	−	1100.30i	0.146814	−	0.451847i	−0.850426	−	0.526095i	$-0.823656\pi$
$181$	357.508	−	1100.30i	0.146814	−	0.451847i	0.997240	+	0.0742478i	$0.0236556\pi$
$182$	5.88344	−	18.1074i	0.00239621	−	0.00737477i
$183$		0			0
$184$	−405.462	−	294.586i	−0.162451	−	0.118028i
$185$	1741.13	+	5358.66i	0.691950	+	2.12960i
$186$		0			0
$187$	−2572.65	+	1848.26i	−1.00605	+	0.722772i
$188$	−2955.48			−1.14655
$189$		0			0
$190$	−337.055	−	244.884i	−0.128697	−	0.0935041i
$191$	−1185.92	+	861.618i	−0.449266	+	0.326411i	−0.789306	−	0.614000i	$-0.789559\pi$
$191$	−1185.92	+	861.618i	−0.449266	+	0.326411i	0.340040	+	0.940411i	$0.389559\pi$
$192$		0			0
$193$	−800.582	+	2463.94i	−0.298586	+	0.918955i	0.683407	+	0.730038i	$0.260498\pi$
$193$	−800.582	+	2463.94i	−0.298586	+	0.918955i	−0.981993	+	0.188917i	$0.939502\pi$
$194$	−177.720	+	129.121i	−0.0657709	+	0.0477853i
$195$		0			0
$196$	−286.643	−	882.197i	−0.104462	−	0.321500i
$197$	2831.08			1.02389			0.511944	−	0.859019i	$-0.328926\pi$
$197$	2831.08			1.02389			0.511944	+	0.859019i	$0.328926\pi$
$198$		0			0
$199$	−4220.54			−1.50345			−0.751724	−	0.659478i	$-0.770777\pi$
$199$	−4220.54			−1.50345			−0.751724	+	0.659478i	$0.770777\pi$
$200$	−228.828	−	704.261i	−0.0809030	−	0.248994i
$201$		0			0
$202$	−125.022	+	90.8338i	−0.0435471	+	0.0316388i
$203$	−1729.47	+	5322.75i	−0.597955	+	1.84032i
$204$		0			0
$205$	2157.95	−	1567.84i	0.735207	−	0.534159i
$206$	29.0262	+	21.0888i	0.00981725	+	0.00713265i
$207$		0			0
$208$	263.875			0.0879635
$209$	1175.88	+	3685.73i	0.389172	+	1.21984i
$210$		0			0
$211$	−151.201	−	465.350i	−0.0493324	−	0.151829i	0.923356	−	0.383946i	$-0.125435\pi$
$211$	−151.201	−	465.350i	−0.0493324	−	0.151829i	−0.972688	+	0.232116i	$0.925435\pi$
$212$	−935.370	−	679.586i	−0.303026	−	0.220161i
$213$		0			0
$214$	−75.9446	+	233.734i	−0.0242592	+	0.0746621i
$215$	−1002.62	+	3085.76i	−0.318039	+	0.978823i
$216$		0			0
$217$	−810.779	−	589.065i	−0.253637	−	0.184278i
$218$	63.0838	+	194.152i	0.0195990	+	0.0603194i
$219$		0			0
$220$	−1691.05	+	5111.61i	−0.518229	+	1.56648i
$221$	−364.109			−0.110826
$222$		0			0
$223$	1142.63	+	830.169i	0.343122	+	0.249292i	0.745978	−	0.665971i	$-0.231982\pi$
$223$	1142.63	+	830.169i	0.343122	+	0.249292i	−0.402856	+	0.915263i	$0.631982\pi$
$224$	−699.977	+	508.563i	−0.208791	+	0.151695i
$225$		0			0
$226$	39.3059	−	120.971i	0.0115690	−	0.0356057i
$227$	1833.50	−	1332.11i	0.536095	−	0.389496i	−0.286538	−	0.958069i	$-0.592504\pi$
$227$	1833.50	−	1332.11i	0.536095	−	0.389496i	0.822633	+	0.568573i	$0.192504\pi$
$228$		0			0
$229$	−1068.63	−	3288.89i	−0.308370	−	0.949066i	−0.978398	−	0.206730i	$-0.933718\pi$
$229$	−1068.63	−	3288.89i	−0.308370	−	0.949066i	0.670028	−	0.742336i	$-0.266282\pi$
$230$	582.727			0.167060
$231$		0			0
$232$	882.117			0.249629
$233$	1012.89	+	3117.36i	0.284793	+	0.876503i	0.986461	+	0.163998i	$0.0524392\pi$
$233$	1012.89	+	3117.36i	0.284793	+	0.876503i	−0.701668	+	0.712504i	$0.747561\pi$
$234$		0			0
$235$	5575.85	−	4051.09i	1.54778	−	1.12453i
$236$	500.864	−	1541.50i	0.138150	−	0.425183i
$237$		0			0
$238$	318.932	−	231.717i	0.0868625	−	0.0631093i
$239$	−2911.30	−	2115.19i	−0.787935	−	0.572469i	0.119415	−	0.992844i	$-0.461898\pi$
$239$	−2911.30	−	2115.19i	−0.787935	−	0.572469i	−0.907350	+	0.420376i	$0.861898\pi$
$240$		0			0
$241$	3946.71			1.05490			0.527448	−	0.849587i	$-0.323149\pi$
$241$	3946.71			1.05490			0.527448	+	0.849587i	$0.323149\pi$
$242$	−229.800	+	163.244i	−0.0610418	+	0.0433625i
$243$		0			0
$244$	449.377	+	1383.04i	0.117903	+	0.362869i
$245$	1750.02	+	1271.46i	0.456344	+	0.331554i
$246$		0			0
$247$	−137.415	+	422.921i	−0.0353989	+	0.108947i
$248$	−48.8116	+	150.227i	−0.0124982	+	0.0384654i
$249$		0			0
$250$	299.250	+	217.418i	0.0757049	+	0.0550028i
$251$	−1212.75	−	3732.47i	−0.304973	−	0.938611i	−0.979687	−	0.200532i	$-0.935733\pi$
$251$	−1212.75	−	3732.47i	−0.304973	−	0.938611i	0.674714	−	0.738079i	$-0.264267\pi$
$252$		0			0
$253$	−4360.73	−	3203.92i	−1.08362	−	0.796162i
$254$	408.814			0.100989
$255$		0			0
$256$	−3129.51	−	2273.72i	−0.764041	−	0.555108i
$257$	4477.03	−	3252.75i	1.08665	−	0.789498i	0.107820	−	0.994170i	$-0.465613\pi$
$257$	4477.03	−	3252.75i	1.08665	−	0.789498i	0.978831	+	0.204672i	$0.0656129\pi$
$258$		0			0
$259$	−2012.11	+	6192.62i	−0.482726	+	1.48568i
$260$	−500.668	+	363.756i	−0.119423	+	0.0867662i
$261$		0			0
$262$	3.30022	+	10.1570i	0.000778200	+	0.00239505i
$263$	−6186.25			−1.45042			−0.725210	−	0.688528i	$-0.758257\pi$
$263$	−6186.25			−1.45042			−0.725210	+	0.688528i	$0.758257\pi$
$264$		0			0
$265$	2696.19			0.625003
$266$	−148.780	−	457.896i	−0.0342942	−	0.105547i
$267$		0			0
$268$	−985.035	+	715.670i	−0.224517	+	0.163121i
$269$	1464.92	−	4508.55i	0.332036	−	1.02190i	−0.636128	−	0.771583i	$-0.719465\pi$
$269$	1464.92	−	4508.55i	0.332036	−	1.02190i	0.968164	−	0.250317i	$-0.0805349\pi$
$270$		0			0
$271$	−4143.89	+	3010.71i	−0.928868	+	0.674862i	−0.945715	−	0.324996i	$-0.894637\pi$
$271$	−4143.89	+	3010.71i	−0.928868	+	0.674862i	0.0168471	+	0.999858i	$0.494637\pi$
$272$	4420.25	+	3211.50i	0.985356	+	0.715903i
$273$		0			0
$274$	182.299			0.0401936
$275$	−2430.07	−	7616.94i	−0.532868	−	1.67025i
$276$		0			0
$277$	341.958	+	1052.44i	0.0741742	+	0.228285i	0.981269	−	0.192641i	$-0.0617053\pi$
$277$	341.958	+	1052.44i	0.0741742	+	0.228285i	−0.907095	+	0.420926i	$0.861705\pi$
$278$	−209.904	−	152.504i	−0.0452850	−	0.0329014i
$279$		0			0
$280$	415.274	−	1278.08i	0.0886335	−	0.272786i
$281$	2718.17	−	8365.66i	0.577054	−	1.77599i	−0.0520205	−	0.998646i	$-0.516566\pi$
$281$	2718.17	−	8365.66i	0.577054	−	1.77599i	0.629075	−	0.777345i	$-0.283434\pi$
$282$		0			0
$283$	−166.756	−	121.155i	−0.0350269	−	0.0254485i	0.570134	−	0.821552i	$-0.306891\pi$
$283$	−166.756	−	121.155i	−0.0350269	−	0.0254485i	−0.605161	+	0.796103i	$0.706891\pi$
$284$	−388.145	−	1194.59i	−0.0810991	−	0.249597i
$285$		0			0
$286$	−32.3997	−	0.172763i	−0.00669871	−	3.57192e-5i
$287$	3082.49			0.633984
$288$		0			0
$289$	−2124.61	−	1543.62i	−0.432446	−	0.314191i
$290$	−829.767	+	602.861i	−0.168019	+	0.122073i
$291$		0			0
$292$	1598.15	−	4918.61i	0.320291	−	0.985754i
$293$	−6843.27	+	4971.93i	−1.36447	+	0.991342i	−0.366318	+	0.930490i	$0.619382\pi$
$293$	−6843.27	+	4971.93i	−1.36447	+	0.991342i	−0.998147	+	0.0608524i	$0.980618\pi$
$294$		0			0
$295$	1168.01	+	3594.75i	0.230522	+	0.709473i
$296$	1026.28			0.201524
$297$		0			0
$298$	−457.753			−0.0889829
$299$	−192.202	−	591.537i	−0.0371750	−	0.114413i
$300$		0			0
$301$	−3033.41	+	2203.90i	−0.580874	+	0.422030i
$302$	168.179	−	517.601i	0.0320450	−	0.0986245i
$303$		0			0
$304$	5398.43	−	3922.19i	1.01849	−	0.739976i
$305$	−2743.54	−	1993.30i	−0.515064	−	0.374216i
$306$		0			0
$307$	−847.003			−0.157463			−0.0787313	−	0.996896i	$-0.525087\pi$
$307$	−847.003			−0.157463			−0.0787313	+	0.996896i	$0.525087\pi$
$308$	−5053.12	+	3630.30i	−0.934832	+	0.671609i
$309$		0			0
$310$	−56.7539	−	174.671i	−0.0103981	−	0.0320020i
$311$	1728.52	+	1255.85i	0.315163	+	0.228979i	0.734109	−	0.679032i	$-0.237600\pi$
$311$	1728.52	+	1255.85i	0.315163	+	0.228979i	−0.418946	+	0.908011i	$0.637600\pi$
$312$		0			0
$313$	1210.83	−	3726.56i	0.218659	−	0.672964i	−0.780214	−	0.625512i	$-0.784890\pi$
$313$	1210.83	−	3726.56i	0.218659	−	0.672964i	0.998874	−	0.0474516i	$-0.0151100\pi$
$314$	152.873	−	470.494i	0.0274749	−	0.0845589i
$315$		0			0
$316$	6526.00	+	4741.41i	1.16176	+	0.844068i
$317$	−2669.87	−	8217.02i	−0.473044	−	1.45588i	−0.848578	−	0.529071i	$-0.822540\pi$
$317$	−2669.87	−	8217.02i	−0.473044	−	1.45588i	0.375533	−	0.926809i	$-0.377460\pi$
$318$		0			0
$319$	9524.04	+	50.7846i	1.67161	+	0.00891345i
$320$	9180.23			1.60372
$321$		0			0
$322$	544.805	+	395.824i	0.0942882	+	0.0685044i
$323$	−7449.06	+	5412.06i	−1.28321	+	0.932306i
$324$		0			0
$325$	283.983	−	874.010i	0.0484694	−	0.149173i
$326$	−264.619	+	192.257i	−0.0449566	+	0.0326629i
$327$		0			0
$328$	−150.134	−	462.066i	−0.0252737	−	0.0777845i
$329$	7964.74			1.33468
$330$		0			0
$331$	−3048.65			−0.506250			−0.253125	−	0.967434i	$-0.581458\pi$
$331$	−3048.65			−0.506250			−0.253125	+	0.967434i	$0.581458\pi$
$332$	749.860	+	2307.83i	0.123958	+	0.381502i
$333$		0			0
$334$	537.586	−	390.579i	0.0880701	−	0.0639866i
$335$	877.408	−	2700.38i	0.143098	−	0.440411i
$336$		0			0
$337$	−6783.37	+	4928.41i	−1.09648	+	0.796639i	−0.980482	−	0.196610i	$-0.937007\pi$
$337$	−6783.37	+	4928.41i	−1.09648	+	0.796639i	−0.115998	+	0.993249i	$0.537007\pi$
$338$	373.409	+	271.297i	0.0600910	+	0.0436587i
$339$		0			0
$340$	−12814.0			−2.04392
$341$	−535.658	+	1619.16i	−0.0850660	+	0.257133i
$342$		0			0
$343$	−1499.84	−	4616.02i	−0.236104	−	0.726652i
$344$	478.110	+	347.367i	0.0749360	+	0.0544442i
$345$		0			0
$346$	−195.065	+	600.348i	−0.0303085	+	0.0932800i
$347$	1998.22	−	6149.90i	0.309136	−	0.951423i	−0.668965	−	0.743294i	$-0.733263\pi$
$347$	1998.22	−	6149.90i	0.309136	−	0.951423i	0.978101	−	0.208129i	$-0.0667374\pi$
$348$		0			0
$349$	−3397.32	−	2468.30i	−0.521072	−	0.378581i	0.295935	−	0.955208i	$-0.404369\pi$
$349$	−3397.32	−	2468.30i	−0.521072	−	0.378581i	−0.817008	+	0.576627i	$0.804369\pi$
$350$	307.468	+	946.291i	0.0469568	+	0.144518i
$351$		0			0
$352$	1186.56	+	871.789i	0.179670	+	0.132007i
$353$	−6402.27			−0.965322			−0.482661	−	0.875807i	$-0.660330\pi$
$353$	−6402.27			−0.965322			−0.482661	+	0.875807i	$0.660330\pi$
$354$		0			0
$355$	2369.70	+	1721.69i	0.354284	+	0.257402i
$356$	8659.52	−	6291.51i	1.28920	−	0.936656i
$357$		0			0
$358$	84.5657	−	260.267i	0.0124845	−	0.0384232i
$359$	−3771.89	+	2740.44i	−0.554520	+	0.402882i	−0.829449	−	0.558582i	$-0.811346\pi$
$359$	−3771.89	+	2740.44i	−0.554520	+	0.402882i	0.274929	+	0.961464i	$0.411346\pi$
$360$		0			0
$361$	1355.39	+	4171.46i	0.197607	+	0.608173i
$362$	245.014			0.0355736
$363$		0			0
$364$	−715.172			−0.102981
$365$	3726.86	+	11470.1i	0.534447	+	1.64486i
$366$		0			0
$367$	−444.555	+	322.988i	−0.0632305	+	0.0459397i	−0.618952	−	0.785429i	$-0.712442\pi$
$367$	−444.555	+	322.988i	−0.0632305	+	0.0459397i	0.555721	+	0.831369i	$0.312442\pi$
$368$	−2884.13	+	8876.43i	−0.408548	+	1.25738i
$369$		0			0
$370$	−965.372	+	701.384i	−0.135641	+	0.0985492i
$371$	2520.73	+	1831.42i	0.352749	+	0.256287i
$372$		0			0
$373$	2727.49			0.378616			0.189308	−	0.981918i	$-0.439375\pi$
$373$	2727.49			0.378616			0.189308	+	0.981918i	$0.439375\pi$
$374$	−540.634	−	397.215i	−0.0747474	−	0.0549185i
$375$		0			0
$376$	−387.927	−	1193.92i	−0.0532070	−	0.163754i
$377$	885.659	+	643.469i	0.120991	+	0.0879054i
$378$		0			0
$379$	−3040.92	+	9358.98i	−0.412141	+	1.26844i	0.502643	+	0.864494i	$0.332361\pi$
$379$	−3040.92	+	9358.98i	−0.412141	+	1.26844i	−0.914783	+	0.403945i	$0.867639\pi$
$380$	−4836.00	+	14883.7i	−0.652846	+	2.00925i
$381$		0			0
$382$	−251.154	−	182.474i	−0.0336392	−	0.0244403i
$383$	3173.50	+	9767.01i	0.423389	+	1.30306i	0.904528	+	0.426413i	$0.140223\pi$
$383$	3173.50	+	9767.01i	0.423389	+	1.30306i	−0.481139	+	0.876644i	$0.659777\pi$
$384$		0			0
$385$	4557.21	−	13775.3i	0.603265	−	1.82352i
$386$	−548.669			−0.0723485
$387$		0			0
$388$	6675.71	+	4850.19i	0.873474	+	0.634616i
$389$	−5019.79	+	3647.09i	−0.654276	+	0.475360i	−0.864725	−	0.502245i	$-0.832507\pi$
$389$	−5019.79	+	3647.09i	−0.654276	+	0.475360i	0.210449	+	0.977605i	$0.432507\pi$
$390$		0			0
$391$	3979.69	−	12248.2i	0.514735	−	1.58419i
$392$	318.755	−	231.589i	0.0410703	−	0.0298393i
$393$		0			0
$394$	185.277	+	570.223i	0.0236906	+	0.0729123i
$395$	−18811.1			−2.39618
$396$		0			0
$397$	14388.1			1.81894			0.909471	−	0.415767i	$-0.136487\pi$
$397$	14388.1			1.81894			0.909471	+	0.415767i	$0.136487\pi$
$398$	−276.209	−	850.083i	−0.0347867	−	0.107062i
$399$		0			0
$400$	−11156.4	+	8105.61i	−1.39455	+	1.01320i
$401$	803.328	−	2472.39i	0.100041	−	0.307893i	−0.888494	−	0.458888i	$-0.848248\pi$
$401$	803.328	−	2472.39i	0.100041	−	0.307893i	0.988535	+	0.150995i	$0.0482478\pi$
$402$		0			0
$403$	−158.592	+	115.224i	−0.0196030	+	0.0142424i
$404$	4696.21	+	3412.00i	0.578330	+	0.420181i
$405$		0			0
$406$	−1185.27			−0.144887
$407$	11080.5	+	59.0840i	1.34948	+	0.00719579i
$408$		0			0
$409$	−1046.25	−	3220.02i	−0.126488	−	0.389290i	0.867681	−	0.497121i	$-0.165609\pi$
$409$	−1046.25	−	3220.02i	−0.126488	−	0.389290i	−0.994169	+	0.107831i	$0.965609\pi$
$410$	457.012	+	332.039i	0.0550493	+	0.0399957i
$411$		0			0
$412$	416.463	−	1281.74i	0.0498002	−	0.153269i
$413$	−1349.78	+	4154.20i	−0.160819	+	0.494951i
$414$		0			0
$415$	−4578.05	−	3326.15i	−0.541512	−	0.393432i
$416$	52.2982	+	160.957i	0.00616378	+	0.0189702i
$417$		0			0
$418$	−665.410	+	478.048i	−0.0778618	+	0.0559380i
$419$	627.249			0.0731339			0.0365670	−	0.999331i	$-0.488358\pi$
$419$	627.249			0.0731339			0.0365670	+	0.999331i	$0.488358\pi$
$420$		0			0
$421$	6662.59	+	4840.66i	0.771294	+	0.560378i	0.902354	−	0.430997i	$-0.141838\pi$
$421$	6662.59	+	4840.66i	0.771294	+	0.560378i	−0.131059	+	0.991375i	$0.541838\pi$
$422$	83.8336	−	60.9087i	0.00967051	−	0.00702604i
$423$		0			0
$424$	151.757	−	467.059i	0.0173820	−	0.0534962i
$425$	15394.3	−	11184.6i	1.75701	−	1.27655i
$426$		0			0
$427$	−1211.03	−	3727.16i	−0.137250	−	0.422412i
$428$	9231.58			1.04258
$429$		0			0
$430$	−687.136			−0.0770619
$431$	−5310.74	−	16344.8i	−0.593525	−	1.82668i	−0.561933	−	0.827183i	$-0.689942\pi$
$431$	−5310.74	−	16344.8i	−0.593525	−	1.82668i	−0.0315922	−	0.999501i	$-0.510058\pi$
$432$		0			0
$433$	−8105.23	+	5888.80i	−0.899568	+	0.653574i	−0.938355	−	0.345673i	$-0.887651\pi$
$433$	−8105.23	+	5888.80i	−0.899568	+	0.653574i	0.0387874	+	0.999247i	$0.487651\pi$
$434$	65.5864	−	201.854i	0.00725403	−	0.0223256i
$435$		0			0
$436$	6203.75	−	4507.29i	0.681436	−	0.495092i
$437$	−12724.6	−	9244.98i	−1.39291	−	1.01201i
$438$		0			0
$439$	−13539.5			−1.47199			−0.735995	−	0.676987i	$-0.763285\pi$
$439$	−13539.5			−1.47199			−0.735995	+	0.676987i	$0.763285\pi$
$440$	−2286.88	−	12.1942i	−0.247779	−	0.00132122i
$441$		0			0
$442$	−23.8288	−	73.3374i	−0.00256429	−	0.00789209i
$443$	−2196.39	−	1595.77i	−0.235561	−	0.171145i	0.463742	−	0.885970i	$-0.346506\pi$
$443$	−2196.39	−	1595.77i	−0.235561	−	0.171145i	−0.699304	+	0.714825i	$0.746506\pi$
$444$		0			0
$445$	−7713.36	+	23739.3i	−0.821682	+	2.52888i
$446$	−92.4309	+	284.473i	−0.00981330	+	0.0302022i
$447$		0			0
$448$	8582.81	+	6235.78i	0.905133	+	0.657618i
$449$	1659.48	+	5107.34i	0.174422	+	0.536816i	0.999607	−	0.0280473i	$-0.00892891\pi$
$449$	1659.48	+	5107.34i	0.174422	+	0.536816i	−0.825185	+	0.564863i	$0.808929\pi$
$450$		0			0
$451$	−1594.37	−	4997.48i	−0.166465	−	0.521778i
$452$	−4777.90			−0.497198
$453$		0			0
$454$	388.300	+	282.117i	0.0401406	+	0.0291639i
$455$	1349.25	−	980.289i	0.139020	−	0.101004i
$456$		0			0
$457$	−1616.02	+	4973.61i	−0.165415	+	0.509094i	−0.999067	−	0.0431964i	$-0.986246\pi$
$457$	−1616.02	+	4973.61i	−0.165415	+	0.509094i	0.833652	+	0.552290i	$0.186246\pi$
$458$	592.500	−	430.476i	0.0604491	−	0.0439188i
$459$		0			0
$460$	−6764.08	−	20817.7i	−0.685602	−	2.11007i
$461$	14846.7			1.49995			0.749976	−	0.661465i	$-0.230065\pi$
$461$	14846.7			1.49995			0.749976	+	0.661465i	$0.230065\pi$
$462$		0			0
$463$	10918.5			1.09595			0.547977	−	0.836494i	$-0.315398\pi$
$463$	10918.5			1.09595			0.547977	+	0.836494i	$0.315398\pi$
$464$	−5076.31	−	15623.3i	−0.507892	−	1.56313i
$465$		0			0
$466$	−561.598	+	408.025i	−0.0558273	+	0.0405609i
$467$	−2226.36	+	6852.03i	−0.220607	+	0.678960i	0.778100	+	0.628140i	$0.216183\pi$
$467$	−2226.36	+	6852.03i	−0.220607	+	0.678960i	−0.998708	+	0.0508198i	$0.983817\pi$
$468$		0			0
$469$	2654.58	−	1928.66i	0.261358	−	0.189888i
$470$	1180.86	+	857.944i	0.115891	+	0.0842000i
$471$		0			0
$472$	688.458			0.0671374
$473$	5142.06	+	3777.98i	0.499857	+	0.367255i
$474$		0			0
$475$	−7181.32	−	22101.8i	−0.693687	−	2.13495i
$476$	−11980.1	−	8704.02i	−1.15358	−	0.838127i
$477$		0			0
$478$	235.505	−	724.808i	0.0225350	−	0.0693556i
$479$	2880.68	−	8865.82i	0.274784	−	0.845699i	−0.714492	−	0.699643i	$-0.753342\pi$
$479$	2880.68	−	8865.82i	0.274784	−	0.845699i	0.989276	−	0.146055i	$-0.0466578\pi$
$480$		0			0
$481$	1030.40	+	748.628i	0.0976759	+	0.0709657i
$482$	258.288	+	794.930i	0.0244081	+	0.0751205i
$483$		0			0
$484$	8499.26	+	6314.65i	0.798202	+	0.593036i
$485$	−19242.6			−1.80157
$486$		0			0
$487$	7916.06	+	5751.36i	0.736573	+	0.535152i	0.891636	−	0.452753i	$-0.149558\pi$
$487$	7916.06	+	5751.36i	0.736573	+	0.535152i	−0.155063	+	0.987905i	$0.549558\pi$
$488$	−499.719	+	363.067i	−0.0463550	+	0.0336789i
$489$		0			0
$490$	−141.564	+	435.690i	−0.0130515	+	0.0401683i
$491$	5451.28	−	3960.59i	0.501045	−	0.364030i	−0.308371	−	0.951266i	$-0.599784\pi$
$491$	5451.28	−	3960.59i	0.501045	−	0.364030i	0.809416	+	0.587236i	$0.199784\pi$
$492$		0			0
$493$	7004.58	+	21557.9i	0.639900	+	1.96941i
$494$	−94.1759			−0.00857728
$495$		0			0
$496$	2941.58			0.266292
$497$	1046.01	+	3219.30i	0.0944066	+	0.290554i
$498$		0			0
$499$	14846.8	−	10786.9i	1.33194	−	0.967708i	0.332237	−	0.943196i	$-0.392197\pi$
$499$	14846.8	−	10786.9i	1.33194	−	0.967708i	0.999700	−	0.0245123i	$-0.00780328\pi$
$500$	4293.58	−	13214.3i	0.384030	−	1.18192i
$501$		0			0
$502$	672.410	−	488.535i	0.0597832	−	0.0434350i
$503$	995.261	+	723.099i	0.0882236	+	0.0640982i	0.631023	−	0.775764i	$-0.282635\pi$
$503$	995.261	+	723.099i	0.0882236	+	0.0640982i	−0.542799	+	0.839863i	$0.682635\pi$
$504$		0			0
$505$	−13536.8			−1.19283
$506$	359.937	−	1088.00i	0.0316228	−	0.0955877i
$507$		0			0
$508$	−4745.37	−	14604.7i	−0.414452	−	1.27555i
$509$	−895.023	−	650.272i	−0.0779395	−	0.0566263i	0.548133	−	0.836391i	$-0.315339\pi$
$509$	−895.023	−	650.272i	−0.0779395	−	0.0566263i	−0.626073	+	0.779765i	$0.715339\pi$
$510$		0			0
$511$	−4306.87	+	13255.2i	−0.372847	+	1.14750i
$512$	1310.41	−	4033.03i	0.113110	−	0.348118i
$513$		0			0
$514$	948.149	+	688.871i	0.0813640	+	0.0591144i
$515$	971.184	+	2989.00i	0.0830980	+	0.255749i
$516$		0			0
$517$	−4119.64	−	12912.8i	−0.350448	−	1.09846i
$518$	−1378.97			−0.116966
$519$		0			0
$520$	−212.662	−	154.508i	−0.0179343	−	0.0130300i
$521$	4770.34	−	3465.85i	0.401137	−	0.291443i	−0.368867	−	0.929482i	$-0.620254\pi$
$521$	4770.34	−	3465.85i	0.401137	−	0.291443i	0.770004	+	0.638039i	$0.220254\pi$
$522$		0			0
$523$	−231.034	+	711.048i	−0.0193162	+	0.0594493i	−0.960250	−	0.279141i	$-0.909950\pi$
$523$	−231.034	+	711.048i	−0.0193162	+	0.0594493i	0.940934	+	0.338591i	$0.109950\pi$
$524$	324.549	−	235.798i	0.0270572	−	0.0196582i
$525$		0			0
$526$	−404.853	−	1246.01i	−0.0335597	−	0.103286i
$527$	−4058.96			−0.335505
$528$		0			0
$529$	9832.34			0.808116
$530$	176.449	+	543.055i	0.0144613	+	0.0445072i
$531$		0			0
$532$	−14631.2	+	10630.2i	−1.19237	+	0.866310i
$533$	186.321	−	573.438i	0.0151416	−	0.0466011i
$534$		0			0
$535$	−17416.4	+	12653.8i	−1.40743	+	1.02256i
$536$	−418.400	−	303.985i	−0.0337166	−	0.0244966i
$537$		0			0
$538$	1003.96			0.0804534
$539$	3454.86	−	2482.07i	0.276088	−	0.198349i
$540$		0			0
$541$	−3280.34	−	10095.9i	−0.260690	−	0.802320i	−0.992655	−	0.120978i	$-0.961397\pi$
$541$	−3280.34	−	10095.9i	−0.260690	−	0.802320i	0.731966	−	0.681342i	$-0.238603\pi$
$542$	−877.597	−	637.612i	−0.0695499	−	0.0505309i
$543$		0			0
$544$	−1082.87	+	3332.74i	−0.0853453	+	0.262666i
$545$	−5525.92	+	17007.0i	−0.434320	+	1.33670i
$546$		0			0
$547$	8538.55	+	6203.62i	0.667426	+	0.484913i	0.869162	−	0.494527i	$-0.164659\pi$
$547$	8538.55	+	6203.62i	0.667426	+	0.484913i	−0.201737	+	0.979440i	$0.564659\pi$
$548$	−2116.05	−	6512.55i	−0.164951	−	0.507668i
$549$		0			0
$550$	1375.14	−	987.936i	0.106611	−	0.0765923i
$551$	27683.5			2.14039
$552$		0			0
$553$	−17586.9	−	12777.7i	−1.35239	−	0.982570i
$554$	−189.598	+	137.751i	−0.0145402	+	0.0105641i
$555$		0			0
$556$	−3011.67	+	9268.96i	−0.229718	+	0.706999i
$557$	−9481.81	+	6888.94i	−0.721287	+	0.524046i	−0.886795	−	0.462162i	$-0.847074\pi$
$557$	−9481.81	+	6888.94i	−0.721287	+	0.524046i	0.165508	+	0.986208i	$0.447074\pi$
$558$		0			0
$559$	226.639	+	697.524i	0.0171482	+	0.0527766i
$560$	−25026.0			−1.88847
$561$		0			0
$562$	1862.86			0.139822
$563$	2079.55	+	6400.21i	0.155671	+	0.479106i	0.998228	−	0.0595008i	$-0.0189509\pi$
$563$	2079.55	+	6400.21i	0.155671	+	0.479106i	−0.842557	+	0.538607i	$0.818951\pi$
$564$		0			0
$565$	9014.04	−	6549.08i	0.671192	−	0.487650i
$566$	13.4894	−	41.5162i	0.00100177	−	0.00308314i
$567$		0			0
$568$	431.627	−	313.595i	0.0318850	−	0.0231658i
$569$	−1059.77	−	769.965i	−0.0780804	−	0.0567287i	0.548060	−	0.836439i	$-0.315366\pi$
$569$	−1059.77	−	769.965i	−0.0780804	−	0.0567287i	−0.626141	+	0.779710i	$0.715366\pi$
$570$		0			0
$571$	−3206.49			−0.235005			−0.117502	−	0.993073i	$-0.537489\pi$
$571$	−3206.49			−0.235005			−0.117502	+	0.993073i	$0.537489\pi$
$572$	369.911	+	1159.47i	0.0270398	+	0.0847551i
$573$		0			0
$574$	201.730	+	620.861i	0.0146691	+	0.0451468i
$575$	26296.7	+	19105.7i	1.90722	+	1.38567i
$576$		0			0
$577$	3560.42	−	10957.9i	0.256884	−	0.790609i	−0.736568	−	0.676363i	$-0.763555\pi$
$577$	3560.42	−	10957.9i	0.256884	−	0.790609i	0.993453	−	0.114246i	$-0.0364451\pi$
$578$	171.866	−	528.950i	0.0123680	−	0.0380647i
$579$		0			0
$580$	31168.6	+	22645.3i	2.23139	+	1.62120i
$581$	−2020.80	−	6219.39i	−0.144298	−	0.444103i
$582$		0			0
$583$	1665.38	−	5034.01i	0.118307	−	0.357611i
$584$	2196.73			0.155653
$585$		0			0
$586$	−1449.28	−	1052.96i	−0.102166	−	0.0742276i
$587$	−1818.93	+	1321.53i	−0.127897	+	0.0929224i	−0.649894	−	0.760024i	$-0.725187\pi$
$587$	−1818.93	+	1321.53i	−0.127897	+	0.0929224i	0.521998	+	0.852947i	$0.325187\pi$
$588$		0			0
$589$	−1531.85	+	4714.56i	−0.107163	+	0.329814i
$590$	−647.601	+	470.510i	−0.0451886	+	0.0328315i
$591$		0			0
$592$	−5905.90	−	18176.5i	−0.410019	−	1.26191i
$593$	11998.0			0.830861			0.415431	−	0.909625i	$-0.363631\pi$
$593$	11998.0			0.830861			0.415431	+	0.909625i	$0.363631\pi$
$594$		0			0
$595$	34532.4			2.37931
$596$	5313.43	+	16353.0i	0.365179	+	1.12390i
$597$		0			0
$598$	106.566	−	77.4250i	0.00728733	−	0.00529455i
$599$	−6683.63	+	20570.1i	−0.455903	+	1.40312i	0.414169	+	0.910200i	$0.364072\pi$
$599$	−6683.63	+	20570.1i	−0.455903	+	1.40312i	−0.870072	+	0.492924i	$0.835928\pi$
$600$		0			0
$601$	2703.52	−	1964.22i	0.183492	−	0.133315i	−0.492247	−	0.870455i	$-0.663824\pi$
$601$	2703.52	−	1964.22i	0.183492	−	0.133315i	0.675739	+	0.737141i	$0.263824\pi$
$602$	−642.419	−	466.745i	−0.0434935	−	0.0315998i
$603$		0			0
$604$	−20443.3			−1.37719
$605$	−24690.3	−	263.317i	−1.65918	−	0.0176948i
$606$		0			0
$607$	1078.41	+	3318.99i	0.0721106	+	0.221934i	0.980616	−	0.195940i	$-0.0627756\pi$
$607$	1078.41	+	3318.99i	0.0721106	+	0.221934i	−0.908505	+	0.417873i	$0.862776\pi$
$608$	3462.38	+	2515.56i	0.230950	+	0.167795i
$609$		0			0
$610$	221.934	−	683.041i	0.0147309	−	0.0453370i
$611$	481.430	−	1481.69i	0.0318765	−	0.0981059i
$612$		0			0
$613$	2552.59	+	1854.56i	0.168186	+	0.122194i	0.668694	−	0.743537i	$-0.266854\pi$
$613$	2552.59	+	1854.56i	0.168186	+	0.122194i	−0.500508	+	0.865732i	$0.666854\pi$
$614$	−55.4312	−	170.600i	−0.00364336	−	0.0112131i
$615$		0			0
$616$	−2129.78	−	1564.79i	−0.139304	−	0.102349i
$617$	204.683			0.0133553			0.00667767	−	0.999978i	$-0.497874\pi$
$617$	204.683			0.0133553			0.00667767	+	0.999978i	$0.497874\pi$
$618$		0			0
$619$	−13999.8	−	10171.4i	−0.909044	−	0.660459i	0.0317289	−	0.999497i	$-0.489899\pi$
$619$	−13999.8	−	10171.4i	−0.909044	−	0.660459i	−0.940773	+	0.339037i	$0.889899\pi$
$620$	−5581.26	+	4055.02i	−0.361530	+	0.262667i
$621$		0			0
$622$	−139.826	+	430.339i	−0.00901367	+	0.0277412i
$623$	−23336.6	+	16955.0i	−1.50074	+	1.09035i
$624$		0			0
$625$	1547.45	+	4762.57i	0.0990370	+	0.304805i
$626$	829.830			0.0529819
$627$		0			0
$628$	−18582.7			−1.18078
$629$	8149.31	+	25081.0i	0.516588	+	1.58990i
$630$		0			0
$631$	−2010.05	+	1460.38i	−0.126813	+	0.0921347i	−0.649383	−	0.760461i	$-0.724973\pi$
$631$	−2010.05	+	1460.38i	−0.126813	+	0.0921347i	0.522571	+	0.852596i	$0.324973\pi$
$632$	−1058.79	+	3258.63i	−0.0666401	+	0.205097i
$633$		0			0
$634$	1480.31	−	1075.51i	0.0927297	−	0.0673721i
$635$	28971.4	+	21049.0i	1.81055	+	1.31544i
$636$		0			0
$637$	488.969			0.0304139
$638$	613.062	+	1921.62i	0.0380429	+	0.119244i
$639$		0			0
$640$	2451.68	+	7545.49i	0.151424	+	0.466034i
$641$	−13255.1	−	9630.41i	−0.816764	−	0.593414i	0.0990195	−	0.995085i	$-0.468429\pi$
$641$	−13255.1	−	9630.41i	−0.816764	−	0.593414i	−0.915784	+	0.401671i	$0.868429\pi$
$642$		0			0
$643$	−3764.00	+	11584.4i	−0.230852	+	0.710489i	0.766793	+	0.641895i	$0.221851\pi$
$643$	−3764.00	+	11584.4i	−0.230852	+	0.710489i	−0.997645	+	0.0685945i	$0.978149\pi$
$644$	7816.77	−	24057.5i	0.478298	−	1.47205i
$645$		0			0
$646$	−1577.57	−	1146.17i	−0.0960815	−	0.0698073i
$647$	−2292.65	−	7056.06i	−0.139310	−	0.428751i	0.856926	−	0.515440i	$-0.172371\pi$
$647$	−2292.65	−	7056.06i	−0.139310	−	0.428751i	−0.996235	+	0.0866885i	$0.972371\pi$
$648$		0			0
$649$	7433.14	+	39.6354i	0.449578	+	0.00239726i
$650$	194.624			0.0117443
$651$		0			0
$652$	9939.89	+	7221.75i	0.597049	+	0.433782i
$653$	−9933.63	+	7217.21i	−0.595303	+	0.432513i	−0.844209	−	0.536015i	$-0.819929\pi$
$653$	−9933.63	+	7217.21i	−0.595303	+	0.432513i	0.248905	+	0.968528i	$0.419929\pi$
$654$		0			0
$655$	−289.088	+	889.720i	−0.0172452	+	0.0530752i
$656$	−7319.72	+	5318.09i	−0.435651	+	0.316519i
$657$		0			0
$658$	521.244	+	1604.22i	0.0308818	+	0.0950443i
$659$	17155.7			1.01410			0.507049	−	0.861917i	$-0.330736\pi$
$659$	17155.7			1.01410			0.507049	+	0.861917i	$0.330736\pi$
$660$		0			0
$661$	−6971.48			−0.410226			−0.205113	−	0.978738i	$-0.565756\pi$
$661$	−6971.48			−0.410226			−0.205113	+	0.978738i	$0.565756\pi$
$662$	−199.515	−	614.045i	−0.0117136	−	0.0360507i
$663$		0			0
$664$	−833.864	+	605.837i	−0.0487352	+	0.0354082i
$665$	13032.6	−	40110.1i	0.759971	−	2.33895i
$666$		0			0
$667$	−31325.7	+	22759.5i	−1.81850	+	1.32121i
$668$	−20193.4	−	14671.4i	−1.16962	−	0.849778i
$669$		0			0
$670$	601.321			0.0346732
$671$	−5416.27	+	3891.19i	−0.311614	+	0.223872i
$672$		0			0
$673$	−8621.49	−	26534.2i	−0.493810	−	1.51979i	−0.818804	−	0.574074i	$-0.805362\pi$
$673$	−8621.49	−	26534.2i	−0.493810	−	1.51979i	0.324994	−	0.945716i	$-0.394638\pi$
$674$	−1436.59	−	1043.74i	−0.0820999	−	0.0596491i
$675$		0			0
$676$	5357.60	−	16489.0i	0.304825	−	0.938155i
$677$	2336.86	−	7192.12i	0.132663	−	0.408295i	−0.862556	−	0.505961i	$-0.831138\pi$
$677$	2336.86	−	7192.12i	0.132663	−	0.408295i	0.995219	+	0.0976664i	$0.0311378\pi$
$678$		0			0
$679$	−17990.4	−	13070.8i	−1.01680	−	0.738749i
$680$	−1681.92	−	5176.41i	−0.0948509	−	0.291921i
$681$		0			0
$682$	−361.179	−	1.92590i	−0.0202790	−	0.000108133i
$683$	28882.3			1.61809			0.809043	−	0.587750i	$-0.199986\pi$
$683$	28882.3			1.61809			0.809043	+	0.587750i	$0.199986\pi$
$684$		0			0
$685$	12918.9	+	9386.16i	0.720595	+	0.523543i
$686$	831.584	−	604.181i	0.0462829	−	0.0336265i
$687$		0			0
$688$	3400.89	−	10466.8i	0.188456	−	0.580007i
$689$	493.067	−	358.234i	0.0272632	−	0.0198079i
$690$		0			0
$691$	7893.89	+	24294.9i	0.434584	+	1.33751i	0.893512	+	0.449039i	$0.148234\pi$
$691$	7893.89	+	24294.9i	0.434584	+	1.33751i	−0.458928	+	0.888474i	$0.651766\pi$
$692$	23711.4			1.30256
$693$		0			0
$694$	1369.46			0.0749047
$695$	−7023.15	−	21615.0i	−0.383314	−	1.17972i
$696$		0			0
$697$	10100.2	−	7338.21i	0.548883	−	0.398787i
$698$	274.820	−	845.808i	0.0149027	−	0.0458658i
$699$		0			0
$700$	30236.9	−	21968.4i	1.63264	−	1.18618i
$701$	−5340.41	−	3880.03i	−0.287738	−	0.209054i	0.434547	−	0.900649i	$-0.356908\pi$
$701$	−5340.41	−	3880.03i	−0.287738	−	0.209054i	−0.722285	+	0.691595i	$0.756908\pi$
$702$		0			0
$703$	32207.7			1.72793
$704$	5670.41	−	17140.2i	0.303568	−	0.917608i
$705$		0			0
$706$	−418.990	−	1289.52i	−0.0223355	−	0.0687417i
$707$	−12655.8	−	9195.01i	−0.673228	−	0.489129i
$708$		0			0
$709$	−5952.67	+	18320.4i	−0.315314	+	0.970436i	0.660311	+	0.750992i	$0.270424\pi$
$709$	−5952.67	+	18320.4i	−0.315314	+	0.970436i	−0.975625	+	0.219444i	$0.929576\pi$
$710$	−191.693	+	589.970i	−0.0101325	+	0.0311847i
$711$		0			0
$712$	3678.18	+	2672.36i	0.193604	+	0.140661i
$713$	−2142.60	−	6594.23i	−0.112540	−	0.346362i
$714$		0			0
$715$	−2287.17	−	1680.43i	−0.119630	−	0.0878946i
$716$	−10279.5			−0.536542
$717$		0			0
$718$	−798.814	−	580.372i	−0.0415202	−	0.0301662i
$719$	21731.1	−	15788.5i	1.12717	−	0.818933i	0.141885	−	0.989883i	$-0.454684\pi$
$719$	21731.1	−	15788.5i	1.12717	−	0.818933i	0.985280	+	0.170950i	$0.0546835\pi$
$720$		0			0
$721$	−1122.33	+	3454.17i	−0.0579718	+	0.178419i
$722$	−751.495	+	545.993i	−0.0387365	+	0.0281437i
$723$		0			0
$724$	−2844.03	−	8753.02i	−0.145991	−	0.449314i
$725$	−57210.8			−2.93070
$726$		0			0
$727$	−17670.1			−0.901442			−0.450721	−	0.892665i	$-0.648833\pi$
$727$	−17670.1			−0.901442			−0.450721	+	0.892665i	$0.648833\pi$
$728$	−93.8712	−	288.906i	−0.00477898	−	0.0147082i
$729$		0			0
$730$	−2066.36	+	1501.30i	−0.104766	+	0.0761172i
$731$	−4692.74	+	14442.8i	−0.237438	+	0.730759i
$732$		0			0
$733$	12711.4	−	9235.38i	0.640528	−	0.465371i	−0.219504	−	0.975612i	$-0.570444\pi$
$733$	12711.4	−	9235.38i	0.640528	−	0.465371i	0.860031	+	0.510241i	$0.170444\pi$
$734$	−94.1484	−	68.4028i	−0.00473444	−	0.00343977i
$735$		0			0
$736$	−5986.03			−0.299794
$737$	−4499.88	−	3306.15i	−0.224905	−	0.165243i
$738$		0			0
$739$	5653.11	+	17398.5i	0.281398	+	0.866053i	0.987455	+	0.157899i	$0.0504720\pi$
$739$	5653.11	+	17398.5i	0.281398	+	0.866053i	−0.706058	+	0.708154i	$0.749528\pi$
$740$	36262.4	+	26346.1i	1.80139	+	1.30879i
$741$		0			0
$742$	−203.910	+	627.571i	−0.0100886	+	0.0310496i
$743$	−2963.38	+	9120.35i	−0.146320	+	0.450327i	−0.997178	−	0.0750681i	$-0.976083\pi$
$743$	−2963.38	+	9120.35i	−0.146320	+	0.450327i	0.850858	+	0.525395i	$0.176083\pi$
$744$		0			0
$745$	−32439.6	−	23568.7i	−1.59529	−	1.15905i
$746$	178.497	+	549.359i	0.00876040	+	0.0269617i
$747$		0			0
$748$	−7914.88	+	23924.7i	−0.386894	+	1.16948i
$749$	−24878.2			−1.21366
$750$		0			0
$751$	15875.4	+	11534.2i	0.771375	+	0.560437i	0.902378	−	0.430945i	$-0.141820\pi$
$751$	15875.4	+	11534.2i	0.771375	+	0.560437i	−0.131003	+	0.991382i	$0.541820\pi$
$752$	−18913.2	+	13741.2i	−0.917145	+	0.666345i
$753$		0			0
$754$	−71.6438	+	220.497i	−0.00346036	+	0.0106499i
$755$	38568.5	−	28021.6i	1.85914	−	1.35074i
$756$		0			0
$757$	−6612.31	−	20350.6i	−0.317475	−	0.977088i	−0.974724	−	0.223414i	$-0.928280\pi$
$757$	−6612.31	−	20350.6i	−0.317475	−	0.977088i	0.657249	−	0.753674i	$-0.271720\pi$
$758$	−2084.05			−0.0998632
$759$		0			0
$760$	−6647.27			−0.317266
$761$	−5366.23	−	16515.6i	−0.255618	−	0.786713i	−0.993707	−	0.112009i	$-0.964271\pi$
$761$	−5366.23	−	16515.6i	−0.255618	−	0.786713i	0.738089	−	0.674704i	$-0.235729\pi$
$762$		0			0
$763$	−16718.5	+	12146.7i	−0.793252	+	0.576331i
$764$	−3603.52	+	11090.5i	−0.170642	+	0.525183i
$765$		0			0
$766$	−1759.54	+	1278.38i	−0.0829960	+	0.0603001i
$767$	691.222	+	502.202i	0.0325405	+	0.0236421i
$768$		0			0
$769$	−7235.62			−0.339302			−0.169651	−	0.985504i	$-0.554264\pi$
$769$	−7235.62			−0.339302			−0.169651	+	0.985504i	$0.554264\pi$
$770$	3072.80	+	16.3850i	0.143813	+	0.000766848i
$771$		0			0
$772$	6368.75	+	19601.0i	0.296912	+	0.913803i
$773$	−29115.2	−	21153.4i	−1.35472	−	0.984263i	−0.998761	−	0.0497615i	$-0.984154\pi$
$773$	−29115.2	−	21153.4i	−1.35472	−	0.984263i	−0.355960	−	0.934501i	$-0.615846\pi$
$774$		0			0
$775$	3165.74	−	9743.14i	0.146731	−	0.451592i
$776$	−1083.08	+	3333.39i	−0.0501036	+	0.154203i
$777$		0			0
$778$	−1063.10	−	772.385i	−0.0489895	−	0.0355930i
$779$	−4711.66	−	14501.0i	−0.216705	−	0.666948i
$780$		0			0
$781$	4678.24	−	3360.98i	0.214342	−	0.153989i
$782$	2727.43			0.124722
$783$		0			0
$784$	−5936.03	−	4312.78i	−0.270409	−	0.196464i
$785$	35058.3	−	25471.4i	1.59399	−	1.15810i
$786$		0			0
$787$	6781.01	−	20869.8i	0.307137	−	0.945271i	−0.671734	−	0.740792i	$-0.734450\pi$
$787$	6781.01	−	20869.8i	0.307137	−	0.945271i	0.978871	−	0.204478i	$-0.0655498\pi$
$788$	18220.4	−	13237.9i	0.823698	−	0.598452i
$789$		0			0
$790$	−1231.07	−	3788.85i	−0.0554425	−	0.170635i
$791$	12876.0			0.578783
$792$		0			0
$793$	−766.568			−0.0343274
$794$	941.617	+	2898.00i	0.0420865	+	0.129529i
$795$		0			0
$796$	−27162.8	+	19734.9i	−1.20950	+	0.878750i
$797$	435.879	−	1341.50i	0.0193722	−	0.0596214i	−0.940903	−	0.338676i	$-0.890021\pi$
$797$	435.879	−	1341.50i	0.0193722	−	0.0596214i	0.960275	+	0.279054i	$0.0900210\pi$
$798$		0			0
$799$	26097.5	−	18961.0i	1.15552	−	0.839537i
$800$	−7155.36	−	5198.67i	−0.316225	−	0.229751i
$801$		0			0
$802$	550.551			0.0242402
$803$	23717.6	+	126.468i	1.04231	+	0.00555787i
$804$		0			0
$805$	18228.5	+	56101.7i	0.798102	+	2.45630i
$806$	−33.5868	−	24.4022i	−0.00146780	−	0.00106642i
$807$		0			0
$808$	−761.925	+	2344.96i	−0.0331738	+	0.102098i
$809$	−4078.19	+	12551.4i	−0.177233	+	0.545467i	−0.999728	−	0.0233046i	$-0.992581\pi$
$809$	−4078.19	+	12551.4i	−0.177233	+	0.545467i	0.822495	+	0.568772i	$0.192581\pi$
$810$		0			0
$811$	−24529.0	−	17821.4i	−1.06206	−	0.771631i	−0.0875906	−	0.996157i	$-0.527917\pi$
$811$	−24529.0	−	17821.4i	−1.06206	−	0.771631i	−0.974468	+	0.224526i	$0.927917\pi$
$812$	13758.2	+	42343.3i	0.594602	+	1.83000i
$813$		0			0
$814$	713.252	+	2235.66i	0.0307119	+	0.0962650i
$815$	−28651.6			−1.23144
$816$		0			0
$817$	15004.5	+	10901.4i	0.642524	+	0.466821i
$818$	580.092	−	421.461i	0.0247951	−	0.0180147i
$819$		0			0
$820$	6557.13	−	20180.8i	0.279250	−	0.859443i
$821$	−18468.6	+	13418.3i	−0.785092	+	0.570403i	−0.906503	−	0.422200i	$-0.861258\pi$
$821$	−18468.6	+	13418.3i	−0.785092	+	0.570403i	0.121411	+	0.992602i	$0.461258\pi$
$822$		0			0
$823$	2612.94	+	8041.79i	0.110670	+	0.340607i	0.991019	−	0.133719i	$-0.0426919\pi$
$823$	2612.94	+	8041.79i	0.110670	+	0.340607i	−0.880349	+	0.474326i	$0.842692\pi$
$824$	572.445			0.0242015
$825$		0			0
$826$	−925.056			−0.0389671
$827$	−6279.59	−	19326.6i	−0.264042	−	0.812637i	−0.991913	−	0.126923i	$-0.959490\pi$
$827$	−6279.59	−	19326.6i	−0.264042	−	0.812637i	0.727871	−	0.685714i	$-0.240510\pi$
$828$		0			0
$829$	28127.5	−	20435.8i	1.17842	−	0.856171i	0.186426	−	0.982469i	$-0.440310\pi$
$829$	28127.5	−	20435.8i	1.17842	−	0.856171i	0.991992	+	0.126298i	$0.0403096\pi$
$830$	370.333	−	1139.77i	0.0154873	−	0.0476649i
$831$		0			0
$832$	1678.84	−	1219.75i	0.0699557	−	0.0508258i
$833$	8190.87	+	5951.02i	0.340693	+	0.247528i
$834$		0			0
$835$	58207.2			2.41239
$836$	24801.9	+	18222.5i	1.02607	+	0.753873i
$837$		0			0
$838$	41.0496	+	126.338i	0.00169217	+	0.00520795i
$839$	−20046.1	−	14564.3i	−0.824872	−	0.599305i	0.0932319	−	0.995644i	$-0.470280\pi$
$839$	−20046.1	−	14564.3i	−0.824872	−	0.599305i	−0.918104	+	0.396340i	$0.870280\pi$
$840$		0			0
$841$	13523.4	−	41620.8i	0.554489	−	1.70654i
$842$	−538.958	+	1658.74i	−0.0220590	+	0.0678908i
$843$		0			0
$844$	−3149.05	−	2287.92i	−0.128430	−	0.0933097i
$845$	12493.8	+	38452.1i	0.508640	+	1.56543i
$846$		0			0
$847$	−22904.7	−	17017.4i	−0.929179	−	0.690346i
$848$	−9145.44			−0.370349
$849$		0			0
$850$	3260.21	+	2368.68i	0.131558	+	0.0955825i
$851$	−36445.1	+	26478.9i	−1.46806	+	1.06661i
$852$		0			0
$853$	−4036.24	+	12422.3i	−0.162014	+	0.498628i	−0.998804	−	0.0488960i	$-0.984430\pi$
$853$	−4036.24	+	12422.3i	−0.162014	+	0.498628i	0.836790	+	0.547524i	$0.184430\pi$
$854$	671.455	−	487.840i	0.0269048	−	0.0195475i
$855$		0			0
$856$	1211.71	+	3729.25i	0.0483824	+	0.148906i
$857$	40272.1			1.60521			0.802607	−	0.596508i	$-0.203446\pi$
$857$	40272.1			1.60521			0.802607	+	0.596508i	$0.203446\pi$
$858$		0			0
$859$	−44537.4			−1.76903			−0.884515	−	0.466512i	$-0.845510\pi$
$859$	−44537.4			−1.76903			−0.884515	+	0.466512i	$0.845510\pi$
$860$	7976.02	+	24547.7i	0.316256	+	0.973335i
$861$		0			0
$862$	2944.54	−	2139.33i	0.116347	−	0.0845313i
$863$	−4560.22	+	14034.9i	−0.179874	+	0.553597i	−0.999822	−	0.0188413i	$-0.994002\pi$
$863$	−4560.22	+	14034.9i	−0.179874	+	0.553597i	0.819948	+	0.572438i	$0.194002\pi$
$864$		0			0
$865$	−44734.3	+	32501.4i	−1.75839	+	1.27755i
$866$	−1716.53	−	1247.14i	−0.0673559	−	0.0489369i
$867$		0			0
$868$	−7972.47			−0.311755
$869$	−11619.2	+	35121.8i	−0.453572	+	1.37103i
$870$		0			0
$871$	−198.335	−	610.412i	−0.00771563	−	0.0237463i
$872$	2635.08	+	1914.50i	0.102334	+	0.0743499i
$873$		0			0
$874$	1029.33	−	3167.97i	0.0398373	−	0.122606i
$875$	−11570.8	+	35611.2i	−0.447045	+	1.37586i
$876$		0			0
$877$	−11771.8	−	8552.74i	−0.453258	−	0.329311i	0.337623	−	0.941281i	$-0.390377\pi$
$877$	−11771.8	−	8552.74i	−0.453258	−	0.329311i	−0.790881	+	0.611971i	$0.790377\pi$
$878$	−886.076	−	2727.06i	−0.0340588	−	0.104822i
$879$		0			0
$880$	12944.3	+	40573.4i	0.495856	+	1.55424i
$881$	−13139.5			−0.502476			−0.251238	−	0.967925i	$-0.580838\pi$
$881$	−13139.5			−0.502476			−0.251238	+	0.967925i	$0.580838\pi$
$882$		0			0
$883$	−25815.2	−	18755.8i	−0.983861	−	0.714817i	−0.0252930	−	0.999680i	$-0.508052\pi$
$883$	−25815.2	−	18755.8i	−0.983861	−	0.714817i	−0.958568	+	0.284863i	$0.908052\pi$
$884$	−2343.35	+	1702.55i	−0.0891578	+	0.0647770i
$885$		0			0
$886$	177.673	−	546.821i	0.00673707	−	0.0207346i
$887$	6871.20	−	4992.22i	0.260104	−	0.188977i	−0.450089	−	0.892984i	$-0.648608\pi$
$887$	6871.20	−	4992.22i	0.260104	−	0.188977i	0.710193	+	0.704007i	$0.248608\pi$
$888$		0			0
$889$	12788.3	+	39358.4i	0.482459	+	1.48486i
$890$	−5286.26			−0.199096
$891$		0			0
$892$	11235.6			0.421744
$893$	−12174.3	−	37468.7i	−0.456213	−	1.40408i
$894$		0			0
$895$	19393.5	−	14090.2i	0.724305	−	0.526238i
$896$	−2833.23	+	8719.78i	−0.105638	+	0.325120i
$897$		0			0
$898$	−920.096	+	668.489i	−0.0341916	+	0.0248416i
$899$	9873.00	+	7173.15i	0.366277	+	0.266116i
$900$		0			0
$901$	12619.4			0.466608
$902$	902.228	−	648.185i	0.0333048	−	0.0239271i
$903$		0			0
$904$	−627.132	−	1930.11i	−0.0230731	−	0.0710117i
$905$	17363.4	+	12615.2i	0.637766	+	0.463364i
$906$		0			0
$907$	4266.48	−	13130.9i	0.156192	−	0.480710i	−0.842088	−	0.539341i	$-0.818674\pi$
$907$	4266.48	−	13130.9i	0.156192	−	0.480710i	0.998280	+	0.0586309i	$0.0186735\pi$
$908$	5571.26	−	17146.6i	0.203622	−	0.626684i
$909$		0			0
$910$	285.746	+	207.607i	0.0104092	+	0.00756274i
$911$	6457.15	+	19873.1i	0.234835	+	0.722748i	0.997143	+	0.0755340i	$0.0240661\pi$
$911$	6457.15	+	19873.1i	0.234835	+	0.722748i	−0.762308	+	0.647214i	$0.775934\pi$
$912$		0			0
$913$	−9037.94	+	6493.10i	−0.327615	+	0.235367i
$914$	−1107.52			−0.0400805
$915$		0			0
$916$	−22256.1	−	16170.0i	−0.802798	−	0.583267i
$917$	−874.628	+	635.454i	−0.0314970	+	0.0228839i
$918$		0			0
$919$	−3616.18	+	11129.4i	−0.129800	+	0.399485i	−0.994745	−	0.102383i	$-0.967353\pi$
$919$	−3616.18	+	11129.4i	−0.129800	+	0.399485i	0.864945	+	0.501867i	$0.167353\pi$
$920$	7521.83	−	5464.93i	0.269552	−	0.195841i
$921$		0			0
$922$	971.624	+	2990.35i	0.0347058	+	0.106813i
$923$	662.115			0.0236119
$924$		0			0
$925$	−66560.5			−2.36594
$926$	714.550	+	2199.16i	0.0253581	+	0.0780441i
$927$		0			0
$928$	8523.74	−	6192.86i	0.301515	−	0.219063i
$929$	−9323.94	+	28696.1i	−0.329288	+	1.01344i	0.640180	+	0.768225i	$0.278860\pi$
$929$	−9323.94	+	28696.1i	−0.329288	+	1.01344i	−0.969468	+	0.245219i	$0.921140\pi$
$930$		0			0
$931$	10003.5	−	7267.95i	0.352149	−	0.255851i
$932$	21095.4	+	15326.7i	0.741418	+	0.538671i
$933$		0			0
$934$	−1525.81			−0.0534539
$935$	−17861.3	−	55985.5i	−0.624736	−	1.95821i
$936$		0			0
$937$	16674.1	+	51317.7i	0.581345	+	1.78919i	0.613479	+	0.789711i	$0.289770\pi$
$937$	16674.1	+	51317.7i	0.581345	+	1.78919i	−0.0321342	+	0.999484i	$0.510230\pi$
$938$	562.189	+	408.454i	0.0195694	+	0.0142180i
$939$		0			0
$940$	16942.8	−	52144.4i	0.587885	−	1.80932i
$941$	2538.21	−	7811.81i	0.0879313	−	0.270625i	−0.897416	−	0.441186i	$-0.854558\pi$
$941$	2538.21	−	7811.81i	0.0879313	−	0.270625i	0.985347	+	0.170561i	$0.0545580\pi$
$942$		0			0
$943$	17253.3	+	12535.3i	0.595806	+	0.432878i
$944$	−3961.86	−	12193.3i	−0.136597	−	0.420402i
$945$		0			0
$946$	−424.428	+	1282.94i	−0.0145870	+	0.0440929i
$947$	16429.1			0.563752			0.281876	−	0.959451i	$-0.409043\pi$
$947$	16429.1			0.563752			0.281876	+	0.959451i	$0.409043\pi$
$948$		0			0
$949$	2205.55	+	1602.42i	0.0754426	+	0.0548123i
$950$	3981.68	−	2892.86i	0.135982	−	0.0987966i
$951$		0			0
$952$	1943.67	−	5982.01i	0.0661710	−	0.203654i
$953$	9432.80	−	6853.33i	0.320628	−	0.232950i	−0.415816	−	0.909449i	$-0.636504\pi$
$953$	9432.80	−	6853.33i	0.320628	−	0.232950i	0.736443	+	0.676499i	$0.236504\pi$
$954$		0			0
$955$	−8403.34	−	25862.8i	−0.284739	−	0.876336i
$956$	−28627.2			−0.968482
$957$		0			0
$958$	1974.24			0.0665812
$959$	5702.56	+	17550.7i	0.192018	+	0.590971i
$960$		0			0
$961$	22333.5	−	16226.2i	0.749673	−	0.544669i
$962$	−83.3521	+	256.531i	−0.00279353	+	0.00859762i
$963$		0			0
$964$	25400.4	−	18454.5i	0.848644	−	0.616576i
$965$	−38882.5	−	28249.8i	−1.29707	−	0.942377i
$966$		0			0
$967$	15270.1			0.507809			0.253905	−	0.967229i	$-0.418285\pi$
$967$	15270.1			0.507809			0.253905	+	0.967229i	$0.418285\pi$
$968$	−1435.32	+	4262.26i	−0.0476581	+	0.141523i
$969$		0			0
$970$	−1259.31	−	3875.77i	−0.0416847	−	0.128292i
$971$	24556.6	+	17841.4i	0.811594	+	0.589658i	0.914292	−	0.405055i	$-0.132748\pi$
$971$	24556.6	+	17841.4i	0.811594	+	0.589658i	−0.102698	+	0.994713i	$0.532748\pi$
$972$		0			0
$973$	8116.16	−	24979.0i	0.267412	−	0.823010i
$974$	−640.355	+	1970.81i	−0.0210660	+	0.0648346i
$975$		0			0
$976$	9306.05	+	6761.24i	0.305204	+	0.221744i
$977$	−16241.9	−	49987.4i	−0.531857	−	1.63689i	−0.750344	−	0.661047i	$-0.770112\pi$
$977$	−16241.9	−	49987.4i	−0.531857	−	1.63689i	0.218488	−	0.975840i	$-0.429888\pi$
$978$		0			0
$979$	39558.8	+	29064.7i	1.29142	+	0.948836i
$980$	17208.1			0.560910
$981$		0			0
$982$	1154.48	+	838.778i	0.0375162	+	0.0272571i
$983$	27337.5	−	19861.9i	0.887012	−	0.644452i	−0.0480855	−	0.998843i	$-0.515312\pi$
$983$	27337.5	−	19861.9i	0.887012	−	0.644452i	0.935097	+	0.354392i	$0.115312\pi$
$984$		0			0
$985$	−16229.6	+	49949.5i	−0.524992	+	1.61576i
$986$	−3883.69	+	2821.67i	−0.125438	+	0.0911361i
$987$		0			0
$988$	1093.16	+	3364.40i	0.0352004	+	0.108336i
$989$	−25941.0			−0.834051
$990$		0			0
$991$	5221.81			0.167383			0.0836914	−	0.996492i	$-0.473329\pi$
$991$	5221.81			0.167383			0.0836914	+	0.996492i	$0.473329\pi$
$992$	583.001	+	1794.29i	0.0186596	+	0.0574283i
$993$		0			0
$994$	−579.962	+	421.367i	−0.0185063	+	0.0134456i
$995$	24194.9	−	74464.2i	0.770884	−	2.37254i
$996$		0			0
$997$	−11623.6	+	8445.03i	−0.369230	+	0.268262i	−0.756892	−	0.653540i	$-0.773283\pi$
$997$	−11623.6	+	8445.03i	−0.369230	+	0.268262i	0.387661	+	0.921802i	$0.373283\pi$
$998$	3144.28	+	2284.45i	0.0997299	+	0.0724580i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.4.f.e.82.4	yes	24
3.2	odd	2	inner	99.4.f.e.82.3	yes	24
11.3	even	5		1089.4.a.bm.1.7		12
11.8	odd	10		1089.4.a.bl.1.6		12
11.9	even	5	inner	99.4.f.e.64.4	yes	24
33.8	even	10		1089.4.a.bl.1.7		12
33.14	odd	10		1089.4.a.bm.1.6		12
33.20	odd	10	inner	99.4.f.e.64.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.4.f.e.64.3	✓	24	33.20	odd	10	inner
99.4.f.e.64.4	yes	24	11.9	even	5	inner
99.4.f.e.82.3	yes	24	3.2	odd	2	inner
99.4.f.e.82.4	yes	24	1.1	even	1	trivial
1089.4.a.bl.1.6		12	11.8	odd	10
1089.4.a.bl.1.7		12	33.8	even	10
1089.4.a.bm.1.6		12	33.14	odd	10
1089.4.a.bm.1.7		12	11.3	even	5

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	99.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0654439 + 0.201416i) q^{2} +(6.43585 - 4.67592i) q^{4} +(-5.73265 + 17.6433i) q^{5} +(-17.3440 + 12.6012i) q^{7} +(2.73367 + 1.98613i) q^{8} +O(q^{10})\)	\(q+(0.0654439 + 0.201416i) q^{2} +(6.43585 - 4.67592i) q^{4} +(-5.73265 + 17.6433i) q^{5} +(-17.3440 + 12.6012i) q^{7} +(2.73367 + 1.98613i) q^{8} -3.92880 q^{10} +(29.4005 + 21.6012i) q^{11} +(1.29584 + 3.98820i) q^{13} +(-3.67313 - 2.66869i) q^{14} +(19.4451 - 59.8458i) q^{16} +(-26.8314 + 82.5787i) q^{17} +(85.7906 + 62.3305i) q^{19} +(45.6041 + 140.355i) q^{20} +(-2.42673 + 7.33539i) q^{22} -148.322 q^{23} +(-177.295 - 128.813i) q^{25} +(-0.718481 + 0.522007i) q^{26} +(-52.7014 + 162.198i) q^{28} +(211.201 - 153.447i) q^{29} +(14.4456 + 44.4590i) q^{31} +40.3584 q^{32} -18.3886 q^{34} +(-122.899 - 378.243i) q^{35} +(245.717 - 178.524i) q^{37} +(-6.93988 + 21.3587i) q^{38} +(-50.7129 + 36.8451i) q^{40} +(-116.323 - 84.5140i) q^{41} +174.897 q^{43} +(290.223 + 1.54754i) q^{44} +(-9.70676 - 29.8743i) q^{46} +(-300.564 - 218.373i) q^{47} +(36.0324 - 110.896i) q^{49} +(14.3420 - 44.1401i) q^{50} +(26.9884 + 19.6082i) q^{52} +(-44.9117 - 138.224i) q^{53} +(-549.659 + 394.890i) q^{55} -72.4402 q^{56} +(44.7284 + 32.4971i) q^{58} +(164.834 - 119.759i) q^{59} +(-56.4889 + 173.855i) q^{61} +(-8.00936 + 5.81914i) q^{62} +(-152.919 - 470.637i) q^{64} -77.7936 q^{65} -153.054 q^{67} +(213.448 + 656.925i) q^{68} +(68.1412 - 49.5075i) q^{70} +(48.7916 - 150.165i) q^{71} +(525.951 - 382.126i) q^{73} +(52.0381 + 37.8079i) q^{74} +843.588 q^{76} +(-782.122 - 4.17047i) q^{77} +(313.345 + 964.378i) q^{79} +(944.405 + 686.150i) q^{80} +(9.40977 - 28.9603i) q^{82} +(-94.2610 + 290.105i) q^{83} +(-1303.14 - 946.789i) q^{85} +(11.4459 + 35.2270i) q^{86} +(37.4685 + 117.443i) q^{88} +1345.51 q^{89} +(-72.7310 - 52.8422i) q^{91} +(-954.577 + 693.541i) q^{92} +(24.3136 - 74.8296i) q^{94} +(-1591.52 + 1156.31i) q^{95} +(320.534 + 986.501i) q^{97} +24.6944 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{4} - 28 q^{7}+O(q^{10}) \) 24 * q - 4 * q^4 - 28 * q^7	\( 24 q - 4 q^{4} - 28 q^{7} + 208 q^{10} + 20 q^{13} - 224 q^{16} - 40 q^{19} - 586 q^{22} + 362 q^{25} - 150 q^{28} + 670 q^{31} - 2520 q^{34} - 516 q^{37} + 2002 q^{40} + 4008 q^{43} + 2174 q^{46} + 342 q^{49} - 1894 q^{52} - 3300 q^{55} + 22 q^{58} - 2952 q^{61} - 3992 q^{64} - 1936 q^{67} - 1024 q^{70} + 2194 q^{73} + 15336 q^{76} + 1524 q^{79} + 2898 q^{82} - 7428 q^{85} - 3936 q^{88} - 6460 q^{91} - 16982 q^{94} - 1224 q^{97}+O(q^{100}) \) 24 * q - 4 * q^4 - 28 * q^7 + 208 * q^10 + 20 * q^13 - 224 * q^16 - 40 * q^19 - 586 * q^22 + 362 * q^25 - 150 * q^28 + 670 * q^31 - 2520 * q^34 - 516 * q^37 + 2002 * q^40 + 4008 * q^43 + 2174 * q^46 + 342 * q^49 - 1894 * q^52 - 3300 * q^55 + 22 * q^58 - 2952 * q^61 - 3992 * q^64 - 1936 * q^67 - 1024 * q^70 + 2194 * q^73 + 15336 * q^76 + 1524 * q^79 + 2898 * q^82 - 7428 * q^85 - 3936 * q^88 - 6460 * q^91 - 16982 * q^94 - 1224 * q^97

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