LMFDB - Embedded newform 207.4.i.a.118.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,4,Mod(55,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("207.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	207.i (of order $11$, degree $10$, 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:	$12.2133953712$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	no (minimal twist has level 23)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			118.3
Character	$\chi$	$=$	207.118
Dual form			207.4.i.a.100.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0282746 - 0.196654i) q^{2} +(7.63807 - 2.24274i) q^{4} +(6.59261 - 7.60828i) q^{5} +(21.3237 - 13.7039i) q^{7} +(-1.31727 - 2.88443i) q^{8} +O(q^{10})$	\(q+(-0.0282746 - 0.196654i) q^{2} +(7.63807 - 2.24274i) q^{4} +(6.59261 - 7.60828i) q^{5} +(21.3237 - 13.7039i) q^{7} +(-1.31727 - 2.88443i) q^{8} +(-1.68261 - 1.08135i) q^{10} +(-2.01428 + 14.0097i) q^{11} +(-3.85568 - 2.47789i) q^{13} +(-3.29785 - 3.80592i) q^{14} +(53.0446 - 34.0897i) q^{16} +(-98.0272 - 28.7834i) q^{17} +(-66.4831 + 19.5212i) q^{19} +(33.2915 - 72.8981i) q^{20} +2.81201 q^{22} +(83.9685 + 71.5282i) q^{23} +(3.36596 + 23.4108i) q^{25} +(-0.378271 + 0.828297i) q^{26} +(132.137 - 152.495i) q^{28} +(202.341 + 59.4126i) q^{29} +(-117.310 - 256.874i) q^{31} +(-24.8161 - 28.6393i) q^{32} +(-2.88870 + 20.0913i) q^{34} +(36.3156 - 252.581i) q^{35} +(114.021 + 131.587i) q^{37} +(5.71872 + 12.5222i) q^{38} +(-30.6298 - 8.99373i) q^{40} +(66.9116 - 77.2201i) q^{41} +(53.4045 - 116.940i) q^{43} +(16.0348 + 111.524i) q^{44} +(11.6922 - 18.5352i) q^{46} -130.950 q^{47} +(124.415 - 272.430i) q^{49} +(4.50866 - 1.32386i) q^{50} +(-35.0072 - 10.2790i) q^{52} +(81.5152 - 52.3866i) q^{53} +(93.3100 + 107.685i) q^{55} +(-67.6170 - 43.4548i) q^{56} +(5.96264 - 41.4710i) q^{58} +(-232.487 - 149.411i) q^{59} +(190.268 + 416.628i) q^{61} +(-47.1985 + 30.3326i) q^{62} +(325.403 - 375.536i) q^{64} +(-44.2715 + 12.9993i) q^{65} +(49.8355 + 346.614i) q^{67} -813.292 q^{68} -50.6980 q^{70} +(109.006 + 758.154i) q^{71} +(-869.420 + 255.285i) q^{73} +(22.6533 - 26.1433i) q^{74} +(-464.022 + 298.209i) q^{76} +(149.035 + 326.341i) q^{77} +(377.358 + 242.513i) q^{79} +(90.3385 - 628.318i) q^{80} +(-17.0776 - 10.9751i) q^{82} +(281.892 + 325.321i) q^{83} +(-865.247 + 556.061i) q^{85} +(-24.5067 - 7.19581i) q^{86} +(43.0632 - 12.6445i) q^{88} +(138.980 - 304.324i) q^{89} -116.174 q^{91} +(801.777 + 358.018i) q^{92} +(3.70258 + 25.7520i) q^{94} +(-289.775 + 634.518i) q^{95} +(-557.372 + 643.241i) q^{97} +(-57.0924 - 16.7638i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 11 q^{2} - 27 q^{4} + 19 q^{5} - 19 q^{7} - 28 q^{8}+O(q^{10}) $ 50 * q + 11 * q^2 - 27 * q^4 + 19 * q^5 - 19 * q^7 - 28 * q^8	$ 50 q + 11 q^{2} - 27 q^{4} + 19 q^{5} - 19 q^{7} - 28 q^{8} + 47 q^{10} + 53 q^{11} - 65 q^{13} - 117 q^{14} - 499 q^{16} + 117 q^{17} + 73 q^{19} - 529 q^{20} + 310 q^{22} - 542 q^{23} + 246 q^{25} - 324 q^{26} - 677 q^{28} + 497 q^{29} - 471 q^{31} + 915 q^{32} - 2751 q^{34} + 737 q^{35} - 1071 q^{37} + 1504 q^{38} + 1479 q^{40} - 569 q^{41} + 1615 q^{43} - 2518 q^{44} + 4041 q^{46} - 2904 q^{47} + 1226 q^{49} - 1322 q^{50} - 2156 q^{52} - 391 q^{53} - 3323 q^{55} + 7028 q^{56} - 5639 q^{58} + 2445 q^{59} - 1059 q^{61} - 1468 q^{62} + 4570 q^{64} - 2641 q^{65} + 27 q^{67} - 8350 q^{68} + 9702 q^{70} - 3465 q^{71} + 435 q^{73} + 994 q^{74} - 3598 q^{76} + 5931 q^{77} - 2559 q^{79} + 14052 q^{80} - 3822 q^{82} + 3967 q^{83} + 299 q^{85} - 721 q^{86} + 5825 q^{88} - 3717 q^{89} + 7238 q^{91} - 9550 q^{92} + 6035 q^{94} - 4551 q^{95} - 2419 q^{97} + 5687 q^{98}+O(q^{100}) $ 50 * q + 11 * q^2 - 27 * q^4 + 19 * q^5 - 19 * q^7 - 28 * q^8 + 47 * q^10 + 53 * q^11 - 65 * q^13 - 117 * q^14 - 499 * q^16 + 117 * q^17 + 73 * q^19 - 529 * q^20 + 310 * q^22 - 542 * q^23 + 246 * q^25 - 324 * q^26 - 677 * q^28 + 497 * q^29 - 471 * q^31 + 915 * q^32 - 2751 * q^34 + 737 * q^35 - 1071 * q^37 + 1504 * q^38 + 1479 * q^40 - 569 * q^41 + 1615 * q^43 - 2518 * q^44 + 4041 * q^46 - 2904 * q^47 + 1226 * q^49 - 1322 * q^50 - 2156 * q^52 - 391 * q^53 - 3323 * q^55 + 7028 * q^56 - 5639 * q^58 + 2445 * q^59 - 1059 * q^61 - 1468 * q^62 + 4570 * q^64 - 2641 * q^65 + 27 * q^67 - 8350 * q^68 + 9702 * q^70 - 3465 * q^71 + 435 * q^73 + 994 * q^74 - 3598 * q^76 + 5931 * q^77 - 2559 * q^79 + 14052 * q^80 - 3822 * q^82 + 3967 * q^83 + 299 * q^85 - 721 * q^86 + 5825 * q^88 - 3717 * q^89 + 7238 * q^91 - 9550 * q^92 + 6035 * q^94 - 4551 * q^95 - 2419 * q^97 + 5687 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{8}{11}\right)$	$1$

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 $

$2$	−0.0282746	−	0.196654i	−0.00999659	−	0.0695278i	0.984212	−	0.176991i	$-0.0566363\pi$
$2$	−0.0282746	−	0.196654i	−0.00999659	−	0.0695278i	−0.994209	+	0.107463i	$0.965727\pi$
$3$		0			0
$3$		0			0
$4$	7.63807	−	2.24274i	0.954759	−	0.280342i
$5$	6.59261	−	7.60828i	0.589661	−	0.680505i	−0.379992	−	0.924990i	$-0.624073\pi$
$5$	6.59261	−	7.60828i	0.589661	−	0.680505i	0.969653	+	0.244484i	$0.0786187\pi$
$6$		0			0
$7$	21.3237	−	13.7039i	1.15137	−	0.739940i	0.181458	−	0.983399i	$-0.441918\pi$
$7$	21.3237	−	13.7039i	1.15137	−	0.739940i	0.969911	+	0.243458i	$0.0782819\pi$
$8$	−1.31727	−	2.88443i	−0.0582159	−	0.127475i
$9$		0			0
$10$	−1.68261	−	1.08135i	−0.0532087	−	0.0341951i
$11$	−2.01428	+	14.0097i	−0.0552118	+	0.384006i	0.943415	+	0.331615i	$0.107593\pi$
$11$	−2.01428	+	14.0097i	−0.0552118	+	0.384006i	−0.998627	+	0.0523914i	$0.983316\pi$
$12$		0			0
$13$	−3.85568	−	2.47789i	−0.0822594	−	0.0528649i	0.498865	−	0.866680i	$-0.333751\pi$
$13$	−3.85568	−	2.47789i	−0.0822594	−	0.0528649i	−0.581124	+	0.813815i	$0.697387\pi$
$14$	−3.29785	−	3.80592i	−0.0629562	−	0.0726553i
$15$		0			0
$16$	53.0446	−	34.0897i	0.828822	−	0.532651i
$17$	−98.0272	−	28.7834i	−1.39853	−	0.410647i	−0.506354	−	0.862326i	$-0.669007\pi$
$17$	−98.0272	−	28.7834i	−1.39853	−	0.410647i	−0.892180	+	0.451679i	$0.850825\pi$
$18$		0			0
$19$	−66.4831	+	19.5212i	−0.802751	+	0.235709i	−0.657273	−	0.753653i	$-0.728290\pi$
$19$	−66.4831	+	19.5212i	−0.802751	+	0.235709i	−0.145478	+	0.989361i	$0.546472\pi$
$20$	33.2915	−	72.8981i	0.372210	−	0.815026i
$21$		0			0
$22$	2.81201			0.0272511
$23$	83.9685	+	71.5282i	0.761246	+	0.648464i
$23$	83.9685	+	71.5282i	0.761246	+	0.648464i
$24$		0			0
$25$	3.36596	+	23.4108i	0.0269277	+	0.187286i
$26$	−0.378271	+	0.828297i	−0.00285327	+	0.00624779i
$27$		0			0
$28$	132.137	−	152.495i	0.891844	−	1.02924i
$29$	202.341	+	59.4126i	1.29565	+	0.380436i	0.855646	−	0.517562i	$-0.173160\pi$
$29$	202.341	+	59.4126i	1.29565	+	0.380436i	0.440000	+	0.897998i	$0.354979\pi$
$30$		0			0
$31$	−117.310	−	256.874i	−0.679664	−	1.48826i	−0.862999	−	0.505206i	$-0.831417\pi$
$31$	−117.310	−	256.874i	−0.679664	−	1.48826i	0.183335	−	0.983051i	$-0.441311\pi$
$32$	−24.8161	−	28.6393i	−0.137091	−	0.158211i
$33$		0			0
$34$	−2.88870	+	20.0913i	−0.0145708	+	0.101342i
$35$	36.3156	−	252.581i	0.175385	−	1.21983i
$36$		0			0
$37$	114.021	+	131.587i	0.506619	+	0.584669i	0.950230	−	0.311550i	$-0.100848\pi$
$37$	114.021	+	131.587i	0.506619	+	0.584669i	−0.443611	+	0.896219i	$0.646303\pi$
$38$	5.71872	+	12.5222i	0.0244131	+	0.0534572i
$39$		0			0
$40$	−30.6298	−	8.99373i	−0.121075	−	0.0355508i
$41$	66.9116	−	77.2201i	0.254874	−	0.294140i	−0.613864	−	0.789412i	$-0.710386\pi$
$41$	66.9116	−	77.2201i	0.254874	−	0.294140i	0.868738	+	0.495271i	$0.164931\pi$
$42$		0			0
$43$	53.4045	−	116.940i	0.189398	−	0.414724i	−0.790982	−	0.611839i	$-0.790430\pi$
$43$	53.4045	−	116.940i	0.189398	−	0.414724i	0.980380	+	0.197115i	$0.0631573\pi$
$44$	16.0348	+	111.524i	0.0549393	+	0.382112i
$45$		0			0
$46$	11.6922	−	18.5352i	0.0374764	−	0.0594102i
$47$	−130.950			−0.406406			−0.203203	−	0.979137i	$-0.565135\pi$
$47$	−130.950			−0.406406			−0.203203	+	0.979137i	$0.565135\pi$
$48$		0			0
$49$	124.415	−	272.430i	0.362725	−	0.794258i
$50$	4.50866	−	1.32386i	0.0127524	−	0.00374444i
$51$		0			0
$52$	−35.0072	−	10.2790i	−0.0933582	−	0.0274124i
$53$	81.5152	−	52.3866i	0.211264	−	0.135771i	−0.430730	−	0.902481i	$-0.641744\pi$
$53$	81.5152	−	52.3866i	0.211264	−	0.135771i	0.641994	+	0.766710i	$0.278108\pi$
$54$		0			0
$55$	93.3100	+	107.685i	0.228762	+	0.264006i
$56$	−67.6170	−	43.4548i	−0.161352	−	0.103695i
$57$		0			0
$58$	5.96264	−	41.4710i	0.0134988	−	0.0938865i
$59$	−232.487	−	149.411i	−0.513005	−	0.329688i	0.258395	−	0.966039i	$-0.416807\pi$
$59$	−232.487	−	149.411i	−0.513005	−	0.329688i	−0.771399	+	0.636351i	$0.780443\pi$
$60$		0			0
$61$	190.268	+	416.628i	0.399365	+	0.874487i	0.997334	+	0.0729682i	$0.0232472\pi$
$61$	190.268	+	416.628i	0.399365	+	0.874487i	−0.597969	+	0.801519i	$0.704026\pi$
$62$	−47.1985	+	30.3326i	−0.0966809	+	0.0621331i
$63$		0			0
$64$	325.403	−	375.536i	0.635554	−	0.733468i
$65$	−44.2715	+	12.9993i	−0.0844801	+	0.0248056i
$66$		0			0
$67$	49.8355	+	346.614i	0.0908713	+	0.632024i	0.983456	+	0.181145i	$0.0579803\pi$
$67$	49.8355	+	346.614i	0.0908713	+	0.632024i	−0.892585	+	0.450879i	$0.851111\pi$
$68$	−813.292			−1.45038
$69$		0			0
$70$	−50.6980			−0.0865652
$71$	109.006	+	758.154i	0.182206	+	1.26727i	0.851532	+	0.524303i	$0.175674\pi$
$71$	109.006	+	758.154i	0.182206	+	1.26727i	−0.669325	+	0.742969i	$0.733417\pi$
$72$		0			0
$73$	−869.420	+	255.285i	−1.39394	+	0.409299i	−0.890600	−	0.454787i	$-0.849715\pi$
$73$	−869.420	+	255.285i	−1.39394	+	0.409299i	−0.503344	+	0.864086i	$0.667897\pi$
$74$	22.6533	−	26.1433i	0.0355863	−	0.0410688i
$75$		0			0
$76$	−464.022	+	298.209i	−0.700354	+	0.450090i
$77$	149.035	+	326.341i	0.220573	+	0.482987i
$78$		0			0
$79$	377.358	+	242.513i	0.537419	+	0.345378i	0.781029	−	0.624495i	$-0.214695\pi$
$79$	377.358	+	242.513i	0.537419	+	0.345378i	−0.243609	+	0.969873i	$0.578332\pi$
$80$	90.3385	−	628.318i	0.126252	−	0.878101i
$81$		0			0
$82$	−17.0776	−	10.9751i	−0.0229988	−	0.0147804i
$83$	281.892	+	325.321i	0.372792	+	0.430225i	0.910885	−	0.412661i	$-0.135401\pi$
$83$	281.892	+	325.321i	0.372792	+	0.430225i	−0.538093	+	0.842885i	$0.680855\pi$
$84$		0			0
$85$	−865.247	+	556.061i	−1.10411	+	0.709568i
$86$	−24.5067	−	7.19581i	−0.0307282	−	0.00902261i
$87$		0			0
$88$	43.0632	−	12.6445i	0.0521654	−	0.0153171i
$89$	138.980	−	304.324i	0.165527	−	0.362453i	−0.808633	−	0.588314i	$-0.799792\pi$
$89$	138.980	−	304.324i	0.165527	−	0.362453i	0.974160	+	0.225860i	$0.0725193\pi$
$90$		0			0
$91$	−116.174			−0.133828
$92$	801.777	+	358.018i	0.908598	+	0.405717i
$93$		0			0
$94$	3.70258	+	25.7520i	0.00406268	+	0.0282565i
$95$	−289.775	+	634.518i	−0.312950	+	0.685265i
$96$		0			0
$97$	−557.372	+	643.241i	−0.583428	+	0.673312i	−0.968338	−	0.249642i	$-0.919687\pi$
$97$	−557.372	+	643.241i	−0.583428	+	0.673312i	0.384910	+	0.922954i	$0.374232\pi$
$98$	−57.0924	−	16.7638i	−0.0588490	−	0.0172796i
$99$		0			0
$100$	78.2137	+	171.264i	0.0782137	+	0.171264i
$101$	−94.5213	−	109.083i	−0.0931210	−	0.107467i	0.707276	−	0.706937i	$-0.249924\pi$
$101$	−94.5213	−	109.083i	−0.0931210	−	0.107467i	−0.800397	+	0.599470i	$0.795378\pi$
$102$		0			0
$103$	−69.9195	+	486.301i	−0.0668871	+	0.465210i	0.928659	+	0.370935i	$0.120963\pi$
$103$	−69.9195	+	486.301i	−0.0668871	+	0.465210i	−0.995546	+	0.0942756i	$0.969947\pi$
$104$	−2.06832	+	14.3855i	−0.00195015	+	0.0135636i
$105$		0			0
$106$	−12.6069	−	14.5491i	−0.0115518	−	0.0133315i
$107$	177.227	+	388.074i	0.160124	+	0.350622i	0.972640	−	0.232316i	$-0.0746304\pi$
$107$	177.227	+	388.074i	0.160124	+	0.350622i	−0.812517	+	0.582938i	$0.801903\pi$
$108$		0			0
$109$	−486.734	−	142.918i	−0.427713	−	0.125588i	0.0607892	−	0.998151i	$-0.480638\pi$
$109$	−486.734	−	142.918i	−0.427713	−	0.125588i	−0.488502	+	0.872563i	$0.662456\pi$
$110$	18.5385	−	21.3946i	0.0160689	−	0.0185445i
$111$		0			0
$112$	663.944	−	1453.83i	0.560150	−	1.22656i
$113$	−176.815	−	1229.77i	−0.147198	−	1.02378i	−0.920779	−	0.390085i	$-0.872446\pi$
$113$	−176.815	−	1229.77i	−0.147198	−	1.02378i	0.773581	−	0.633697i	$-0.218463\pi$
$114$		0			0
$115$	1097.78	−	167.299i	0.890160	−	0.135658i
$116$	1678.74			1.34368
$117$		0			0
$118$	−22.8087	+	49.9442i	−0.0177942	+	0.0389639i
$119$	−2484.74	+	729.586i	−1.91408	+	0.562026i
$120$		0			0
$121$	1084.87	+	318.547i	0.815081	+	0.239329i
$122$	76.5519	−	49.1969i	0.0568089	−	0.0365089i
$123$		0			0
$124$	−1472.13	−	1698.93i	−1.06614	−	1.23039i
$125$	1258.94	+	809.071i	0.900824	+	0.578924i
$126$		0			0
$127$	−232.988	+	1620.47i	−0.162790	+	1.13223i	0.730554	+	0.682855i	$0.239262\pi$
$127$	−232.988	+	1620.47i	−0.162790	+	1.13223i	−0.893344	+	0.449374i	$0.851647\pi$
$128$	−338.088	−	217.276i	−0.233461	−	0.150036i
$129$		0			0
$130$	3.80813	+	8.33863i	0.00256919	+	0.00562574i
$131$	−602.845	+	387.425i	−0.402067	+	0.258393i	−0.726010	−	0.687684i	$-0.758628\pi$
$131$	−602.845	+	387.425i	−0.402067	+	0.258393i	0.323943	+	0.946076i	$0.394991\pi$
$132$		0			0
$133$	−1150.15	+	1327.34i	−0.749853	+	0.865376i
$134$	66.7540	−	19.6008i	0.0430349	−	0.0126362i
$135$		0			0
$136$	46.1051	+	320.668i	0.0290697	+	0.202184i
$137$	−1582.55			−0.986905			−0.493452	−	0.869773i	$-0.664265\pi$
$137$	−1582.55			−0.986905			−0.493452	+	0.869773i	$0.664265\pi$
$138$		0			0
$139$	−1194.38			−0.728822			−0.364411	−	0.931238i	$-0.618730\pi$
$139$	−1194.38			−0.728822			−0.364411	+	0.931238i	$0.618730\pi$
$140$	−289.092	−	2010.68i	−0.174519	−	1.21381i
$141$		0			0
$142$	146.012	−	42.8731i	0.0862893	−	0.0253368i
$143$	42.4808	−	49.0255i	0.0248421	−	0.0286694i
$144$		0			0
$145$	1785.98	−	1147.78i	1.02288	−	0.657365i
$146$	74.7854	+	163.757i	0.0423924	+	0.0928264i
$147$		0			0
$148$	1166.01	+	749.351i	0.647606	+	0.416191i
$149$	−150.465	+	1046.50i	−0.0827284	+	0.575389i	0.905725	+	0.423865i	$0.139327\pi$
$149$	−150.465	+	1046.50i	−0.0827284	+	0.575389i	−0.988454	+	0.151524i	$0.951582\pi$
$150$		0			0
$151$	937.996	+	602.813i	0.505517	+	0.324876i	0.768419	−	0.639947i	$-0.221044\pi$
$151$	937.996	+	602.813i	0.505517	+	0.324876i	−0.262903	+	0.964822i	$0.584680\pi$
$152$	143.884	+	166.051i	0.0767798	+	0.0886086i
$153$		0			0
$154$	59.9624	−	38.5355i	0.0313760	−	0.0201642i
$155$	−2727.75	−	800.941i	−1.41354	−	0.415052i
$156$		0			0
$157$	1114.32	−	327.195i	0.566451	−	0.166325i	0.0140467	−	0.999901i	$-0.495529\pi$
$157$	1114.32	−	327.195i	0.566451	−	0.166325i	0.552404	+	0.833576i	$0.313710\pi$
$158$	37.0217	−	81.0662i	0.0186411	−	0.0408182i
$159$		0			0
$160$	−381.499			−0.188501
$161$	2770.73	+	374.548i	1.35630	+	0.183345i
$162$		0			0
$163$	−228.173	−	1586.98i	−0.109643	−	0.762586i	−0.968256	−	0.249961i	$-0.919582\pi$
$163$	−228.173	−	1586.98i	−0.109643	−	0.762586i	0.858613	−	0.512625i	$-0.171327\pi$
$164$	337.891	−	739.878i	0.160883	−	0.352285i
$165$		0			0
$166$	56.0054	−	64.6337i	0.0261859	−	0.0302202i
$167$	1271.62	+	373.381i	0.589227	+	0.173013i	0.562736	−	0.826636i	$-0.309749\pi$
$167$	1271.62	+	373.381i	0.589227	+	0.173013i	0.0264906	+	0.999649i	$0.491567\pi$
$168$		0			0
$169$	−903.940	−	1979.35i	−0.411443	−	0.900935i
$170$	133.816	+	154.432i	0.0603720	+	0.0696730i
$171$		0			0
$172$	145.642	−	1012.97i	0.0645647	−	0.449057i
$173$	161.341	−	1122.15i	0.0709049	−	0.493154i	−0.923164	−	0.384405i	$-0.874406\pi$
$173$	161.341	−	1122.15i	0.0709049	−	0.493154i	0.994069	−	0.108749i	$-0.0346844\pi$
$174$		0			0
$175$	392.593	+	453.076i	0.169584	+	0.195711i
$176$	370.738	+	811.802i	0.158781	+	0.347681i
$177$		0			0
$178$	−63.7764	−	18.7264i	−0.0268553	−	0.00788542i
$179$	2624.02	−	3028.28i	1.09569	−	1.26449i	0.133813	−	0.991007i	$-0.457278\pi$
$179$	2624.02	−	3028.28i	1.09569	−	1.26449i	0.961876	−	0.273485i	$-0.0881765\pi$
$180$		0			0
$181$	1159.55	−	2539.06i	0.476181	−	1.04269i	−0.507315	−	0.861761i	$-0.669362\pi$
$181$	1159.55	−	2539.06i	0.476181	−	1.04269i	0.983496	−	0.180930i	$-0.0579108\pi$
$182$	3.28478	+	22.8461i	0.00133782	+	0.00930476i
$183$		0			0
$184$	95.7084	−	336.424i	0.0383463	−	0.134791i
$185$	1752.85			0.696604
$186$		0			0
$187$	600.700	−	1315.35i	0.234906	−	0.514373i
$188$	−1000.21	+	293.688i	−0.388020	+	0.113933i
$189$		0			0
$190$	132.974	+	39.0447i	0.0507734	+	0.0149084i
$191$	−3157.98	+	2029.51i	−1.19635	+	0.768850i	−0.978322	−	0.207091i	$-0.933600\pi$
$191$	−3157.98	+	2029.51i	−1.19635	+	0.768850i	−0.218033	+	0.975941i	$0.569964\pi$
$192$		0			0
$193$	478.077	+	551.730i	0.178304	+	0.205774i	0.837865	−	0.545877i	$-0.183803\pi$
$193$	478.077	+	551.730i	0.178304	+	0.205774i	−0.659561	+	0.751651i	$0.729258\pi$
$194$	142.256	+	91.4222i	0.0526462	+	0.0338337i
$195$		0			0
$196$	339.298	−	2359.87i	0.123651	−	0.860012i
$197$	−1706.40	−	1096.63i	−0.617136	−	0.396609i	0.194391	−	0.980924i	$-0.437727\pi$
$197$	−1706.40	−	1096.63i	−0.617136	−	0.396609i	−0.811527	+	0.584315i	$0.801363\pi$
$198$		0			0
$199$	1620.58	+	3548.57i	0.577285	+	1.26408i	0.942827	+	0.333283i	$0.108156\pi$
$199$	1620.58	+	3548.57i	0.577285	+	1.26408i	−0.365542	+	0.930795i	$0.619116\pi$
$200$	63.0928	−	40.5473i	0.0223067	−	0.0143356i
$201$		0			0
$202$	−18.7792	+	21.6723i	−0.00654108	+	0.00754880i
$203$	5128.83	−	1505.96i	1.77327	−	0.520678i
$204$		0			0
$205$	−146.390	−	1018.16i	−0.0498747	−	0.346886i
$206$	97.6102			0.0330137
$207$		0			0
$208$	−288.993			−0.0963370
$209$	−139.569	−	970.726i	−0.0461924	−	0.321275i
$210$		0			0
$211$	−617.526	+	181.322i	−0.201480	+	0.0591598i	−0.380915	−	0.924610i	$-0.624391\pi$
$211$	−617.526	+	181.322i	−0.201480	+	0.0591598i	0.179436	+	0.983770i	$0.442573\pi$
$212$	505.129	−	582.950i	0.163644	−	0.188855i
$213$		0			0
$214$	71.3054	−	45.8252i	0.0227773	−	0.0146381i
$215$	−537.634	−	1177.25i	−0.170541	−	0.373433i
$216$		0			0
$217$	−6021.66	−	3869.89i	−1.88377	−	1.21062i
$218$	−14.3432	+	99.7594i	−0.00445618	+	0.0309934i
$219$		0			0
$220$	954.219	+	613.239i	0.292425	+	0.187930i
$221$	306.639	+	353.880i	0.0933338	+	0.107713i
$222$		0			0
$223$	23.7383	−	15.2557i	0.00712840	−	0.00458114i	−0.537072	−	0.843537i	$-0.680470\pi$
$223$	23.7383	−	15.2557i	0.00712840	−	0.00458114i	0.544200	+	0.838955i	$0.316833\pi$
$224$	−921.641	−	270.618i	−0.274909	−	0.0807207i
$225$		0			0
$226$	−236.841	+	69.5428i	−0.0697099	+	0.0204687i
$227$	−2822.88	+	6181.25i	−0.825380	+	1.80733i	−0.308673	+	0.951168i	$0.599885\pi$
$227$	−2822.88	+	6181.25i	−0.825380	+	1.80733i	−0.516707	+	0.856162i	$0.672842\pi$
$228$		0			0
$229$	281.246			0.0811583			0.0405791	−	0.999176i	$-0.487080\pi$
$229$	281.246			0.0811583			0.0405791	+	0.999176i	$0.487080\pi$
$230$	−63.9393	−	211.153i	−0.0183306	−	0.0605348i
$231$		0			0
$232$	−95.1668	−	661.900i	−0.0269311	−	0.187310i
$233$	825.179	−	1806.89i	0.232014	−	0.508040i	−0.757437	−	0.652908i	$-0.773549\pi$
$233$	825.179	−	1806.89i	0.232014	−	0.508040i	0.989451	+	0.144868i	$0.0462759\pi$
$234$		0			0
$235$	−863.306	+	996.308i	−0.239642	+	0.276562i
$236$	−2110.84	−	619.800i	−0.582221	−	0.170956i
$237$		0			0
$238$	213.732	+	468.007i	0.0582107	+	0.127464i
$239$	3220.98	+	3717.20i	0.871747	+	1.00605i	0.999898	+	0.0142954i	$0.00455053\pi$
$239$	3220.98	+	3717.20i	0.871747	+	1.00605i	−0.128150	+	0.991755i	$0.540904\pi$
$240$		0			0
$241$	−680.468	+	4732.76i	−0.181879	+	1.26500i	0.670436	+	0.741967i	$0.266107\pi$
$241$	−680.468	+	4732.76i	−0.181879	+	1.26500i	−0.852315	+	0.523029i	$0.824802\pi$
$242$	31.9693	−	222.352i	0.00849201	−	0.0590633i
$243$		0			0
$244$	2387.66	+	2755.51i	0.626453	+	0.722965i
$245$	−1252.51	−	2742.61i	−0.326612	−	0.715179i
$246$		0			0
$247$	304.709	+	89.4706i	0.0784946	+	0.0230481i
$248$	−586.405	+	676.747i	−0.150148	+	0.173280i
$249$		0			0
$250$	123.511	−	270.452i	0.0312462	−	0.0684196i
$251$	480.334	+	3340.80i	0.120790	+	0.840116i	0.956664	+	0.291194i	$0.0940525\pi$
$251$	480.334	+	3340.80i	0.120790	+	0.840116i	−0.835874	+	0.548922i	$0.815038\pi$
$252$		0			0
$253$	−1171.22	+	1032.29i	−0.291044	+	0.256520i
$254$	325.259			0.0803487
$255$		0			0
$256$	1618.20	−	3543.37i	0.395070	−	0.865082i
$257$	6743.49	−	1980.07i	1.63676	−	0.480596i	0.671308	−	0.741178i	$-0.265733\pi$
$257$	6743.49	−	1980.07i	1.63676	−	0.480596i	0.965452	+	0.260582i	$0.0839144\pi$
$258$		0			0
$259$	4234.59	+	1243.39i	1.01593	+	0.298303i
$260$	−308.995	+	198.579i	−0.0737040	+	0.0473667i
$261$		0			0
$262$	93.2340	+	107.598i	0.0219848	+	0.0253718i
$263$	−6668.41	−	4285.53i	−1.56347	−	1.00478i	−0.981476	−	0.191585i	$-0.938637\pi$
$263$	−6668.41	−	4285.53i	−1.56347	−	1.00478i	−0.581991	−	0.813195i	$-0.697726\pi$
$264$		0			0
$265$	138.826	−	965.556i	0.0321812	−	0.223825i
$266$	293.547	+	188.651i	0.0676637	+	0.0434848i
$267$		0			0
$268$	1158.01	+	2535.69i	0.263943	+	0.577955i
$269$	1461.34	−	939.148i	0.331225	−	0.212866i	−0.364448	−	0.931224i	$-0.618742\pi$
$269$	1461.34	−	939.148i	0.331225	−	0.212866i	0.695674	+	0.718358i	$0.255106\pi$
$270$		0			0
$271$	−650.787	+	751.048i	−0.145876	+	0.168350i	−0.823985	−	0.566611i	$-0.808254\pi$
$271$	−650.787	+	751.048i	−0.145876	+	0.168350i	0.678109	+	0.734961i	$0.262800\pi$
$272$	−6181.03	+	1814.91i	−1.37787	+	0.404578i
$273$		0			0
$274$	44.7459	+	311.214i	0.00986568	+	0.0686173i
$275$	−334.757			−0.0734057
$276$		0			0
$277$	71.1195			0.0154266			0.00771328	−	0.999970i	$-0.497545\pi$
$277$	71.1195			0.0154266			0.00771328	+	0.999970i	$0.497545\pi$
$278$	33.7707	+	234.881i	0.00728574	+	0.0506734i
$279$		0			0
$280$	−776.389	+	227.968i	−0.165708	+	0.0486561i
$281$	−2743.18	+	3165.79i	−0.582364	+	0.672084i	−0.968111	−	0.250521i	$-0.919398\pi$
$281$	−2743.18	+	3165.79i	−0.582364	+	0.672084i	0.385748	+	0.922604i	$0.373944\pi$
$282$		0			0
$283$	−4755.76	+	3056.34i	−0.998943	+	0.641981i	−0.934509	−	0.355941i	$-0.884161\pi$
$283$	−4755.76	+	3056.34i	−0.998943	+	0.641981i	−0.0644340	+	0.997922i	$0.520524\pi$
$284$	2532.94	+	5546.36i	0.529233	+	1.15886i
$285$		0			0
$286$	−10.8422	−	6.96787i	−0.00224166	−	0.00144062i
$287$	368.585	−	2563.57i	0.0758080	−	0.527256i
$288$		0			0
$289$	4647.77	+	2986.94i	0.946014	+	0.607966i
$290$	−276.214	−	318.768i	−0.0559305	−	0.0645472i
$291$		0			0
$292$	−6068.16	+	3899.77i	−1.21614	+	0.781564i
$293$	−8812.11	−	2587.47i	−1.75703	−	0.515910i	−0.765232	−	0.643754i	$-0.777376\pi$
$293$	−8812.11	−	2587.47i	−1.75703	−	0.515910i	−0.991794	+	0.127845i	$0.959194\pi$
$294$		0			0
$295$	−2669.46	+	783.823i	−0.526854	+	0.154698i
$296$	229.357	−	502.221i	0.0450374	−	0.0986182i
$297$		0			0
$298$	210.054			0.0408325
$299$	−146.516	−	483.855i	−0.0283387	−	0.0935854i
$300$		0			0
$301$	−463.747	−	3225.43i	−0.0888037	−	0.617644i
$302$	92.0244	−	201.505i	0.0175345	−	0.0383951i
$303$		0			0
$304$	−2861.10	+	3301.88i	−0.539787	+	0.622947i
$305$	4424.18	+	1299.06i	0.830583	+	0.243881i
$306$		0			0
$307$	−1489.72	−	3262.04i	−0.276948	−	0.606431i	0.719134	−	0.694872i	$-0.244539\pi$
$307$	−1489.72	−	3262.04i	−0.276948	−	0.606431i	−0.996081	+	0.0884410i	$0.971812\pi$
$308$	1870.24	+	2158.37i	0.345995	+	0.399300i
$309$		0			0
$310$	−80.3823	+	559.071i	−0.0147271	+	0.102429i
$311$	−677.976	+	4715.42i	−0.123616	+	0.859766i	0.829790	+	0.558075i	$0.188460\pi$
$311$	−677.976	+	4715.42i	−0.123616	+	0.859766i	−0.953406	+	0.301691i	$0.902449\pi$
$312$		0			0
$313$	−2183.58	−	2519.98i	−0.394323	−	0.455073i	0.523522	−	0.852012i	$-0.324618\pi$
$313$	−2183.58	−	2519.98i	−0.394323	−	0.455073i	−0.917845	+	0.396939i	$0.870072\pi$
$314$	−95.8515	−	209.886i	−0.0172268	−	0.0377214i
$315$		0			0
$316$	3426.18	+	1006.02i	0.609930	+	0.179092i
$317$	−2938.12	+	3390.77i	−0.520572	+	0.600772i	−0.953774	−	0.300525i	$-0.902838\pi$
$317$	−2938.12	+	3390.77i	−0.520572	+	0.600772i	0.433202	+	0.901297i	$0.357384\pi$
$318$		0			0
$319$	−1239.92	+	2715.05i	−0.217625	+	0.476531i
$320$	−711.921	−	4951.52i	−0.124368	−	0.864995i
$321$		0			0
$322$	−4.68493	−	555.467i	−0.000810811	−	0.0961334i
$323$	7079.04			1.21947
$324$		0			0
$325$	45.0313	−	98.6048i	0.00768581	−	0.0168296i
$326$	−305.634	+	89.7423i	−0.0519249	+	0.0152465i
$327$		0			0
$328$	−310.877	−	91.2817i	−0.0523332	−	0.0153664i
$329$	−2792.34	+	1794.53i	−0.467924	+	0.300716i
$330$		0			0
$331$	294.424	+	339.783i	0.0488912	+	0.0564235i	0.779668	−	0.626193i	$-0.215388\pi$
$331$	294.424	+	339.783i	0.0488912	+	0.0564235i	−0.730777	+	0.682616i	$0.760842\pi$
$332$	2882.72	+	1852.61i	0.476536	+	0.306251i
$333$		0			0
$334$	37.4725	−	260.627i	0.00613893	−	0.0426972i
$335$	2965.68	+	1905.93i	0.483679	+	0.310842i
$336$		0			0
$337$	−3948.39	−	8645.76i	−0.638226	−	1.39752i	−0.901491	−	0.432797i	$-0.857527\pi$
$337$	−3948.39	−	8645.76i	−0.638226	−	1.39752i	0.263265	−	0.964724i	$-0.415201\pi$
$338$	−363.690	+	233.729i	−0.0585270	+	0.0376130i
$339$		0			0
$340$	−5361.72	+	6187.76i	−0.855236	+	0.986995i
$341$	3835.01	−	1126.06i	0.609025	−	0.178826i
$342$		0			0
$343$	156.936	+	1091.51i	0.0247048	+	0.171826i
$344$	−407.652			−0.0638928
$345$		0			0
$346$	−225.238			−0.0349968
$347$	−1776.12	−	12353.2i	−0.274776	−	1.91111i	−0.395582	−	0.918431i	$-0.629457\pi$
$347$	−1776.12	−	12353.2i	−0.274776	−	1.91111i	0.120806	−	0.992676i	$-0.461452\pi$
$348$		0			0
$349$	6700.85	−	1967.55i	1.02776	−	0.301778i	0.275961	−	0.961169i	$-0.411004\pi$
$349$	6700.85	−	1967.55i	1.02776	−	0.301778i	0.751800	+	0.659391i	$0.229186\pi$
$350$	77.9990	−	90.0157i	0.0119121	−	0.0137473i
$351$		0			0
$352$	451.214	−	289.978i	0.0683232	−	0.0439087i
$353$	−985.333	−	2157.58i	−0.148567	−	0.325315i	0.820688	−	0.571377i	$-0.193591\pi$
$353$	−985.333	−	2157.58i	−0.148567	−	0.325315i	−0.969254	+	0.246062i	$0.920863\pi$
$354$		0			0
$355$	6486.89	+	4168.87i	0.969826	+	0.623269i
$356$	379.021	−	2636.15i	0.0564272	−	0.392459i
$357$		0			0
$358$	−669.717	−	430.401i	−0.0988705	−	0.0635402i
$359$	5305.83	+	6123.26i	0.780031	+	0.900203i	0.997112	−	0.0759502i	$-0.0241990\pi$
$359$	5305.83	+	6123.26i	0.780031	+	0.900203i	−0.217081	+	0.976154i	$0.569654\pi$
$360$		0			0
$361$	−1731.23	+	1112.60i	−0.252403	+	0.162210i
$362$	−532.104	−	156.240i	−0.0772562	−	0.0226845i
$363$		0			0
$364$	−887.345	+	260.548i	−0.127773	+	0.0375176i
$365$	−3789.47	+	8297.79i	−0.543425	+	1.18993i
$366$		0			0
$367$	3397.55			0.483244			0.241622	−	0.970370i	$-0.422321\pi$
$367$	3397.55			0.483244			0.241622	+	0.970370i	$0.422321\pi$
$368$	6892.45	+	931.722i	0.976342	+	0.131982i
$369$		0			0
$370$	−49.5611	−	344.705i	−0.00696367	−	0.0484334i
$371$	1020.30	−	2234.15i	0.142780	−	0.312645i
$372$		0			0
$373$	−73.1032	+	84.3656i	−0.0101478	+	0.0117112i	−0.760801	−	0.648985i	$-0.775194\pi$
$373$	−73.1032	+	84.3656i	−0.0101478	+	0.0117112i	0.750653	+	0.660697i	$0.229739\pi$
$374$	−275.654	−	80.9392i	−0.0381115	−	0.0111906i
$375$		0			0
$376$	172.498	+	377.717i	0.0236593	+	0.0518066i
$377$	−632.942	−	730.454i	−0.0864673	−	0.0997886i
$378$		0			0
$379$	572.266	−	3980.20i	0.0775603	−	0.539444i	−0.913584	−	0.406651i	$-0.866697\pi$
$379$	572.266	−	3980.20i	0.0775603	−	0.539444i	0.991144	−	0.132793i	$-0.0423944\pi$
$380$	−790.260	+	5496.38i	−0.106683	+	0.741996i
$381$		0			0
$382$	488.403	+	563.648i	0.0654160	+	0.0754940i
$383$	−2638.77	−	5778.09i	−0.352049	−	0.770879i	−0.999958	−	0.00916183i	$-0.997084\pi$
$383$	−2638.77	−	5778.09i	−0.352049	−	0.770879i	0.647909	−	0.761718i	$-0.275644\pi$
$384$		0			0
$385$	3465.42	+	1017.54i	0.458738	+	0.134698i
$386$	94.9827	−	109.616i	0.0125246	−	0.0144541i
$387$		0			0
$388$	−2814.62	+	6163.16i	−0.368275	+	0.806410i
$389$	−537.721	−	3739.93i	−0.0700862	−	0.487460i	−0.994388	−	0.105797i	$-0.966261\pi$
$389$	−537.721	−	3739.93i	−0.0700862	−	0.487460i	0.924302	−	0.381663i	$-0.124648\pi$
$390$		0			0
$391$	−6172.38	−	9428.61i	−0.798339	−	1.21950i
$392$	−949.694			−0.122364
$393$		0			0
$394$	−167.410	+	366.577i	−0.0214061	+	0.0468729i
$395$	4332.89	−	1272.25i	0.551927	−	0.162060i
$396$		0			0
$397$	−8482.77	−	2490.77i	−1.07239	−	0.314882i	−0.302558	−	0.953131i	$-0.597841\pi$
$397$	−8482.77	−	2490.77i	−1.07239	−	0.314882i	−0.769830	+	0.638249i	$0.779659\pi$
$398$	652.021	−	419.028i	0.0821177	−	0.0527738i
$399$		0			0
$400$	976.611	+	1127.07i	0.122076	+	0.140884i
$401$	−5337.82	−	3430.41i	−0.664733	−	0.427198i	0.164290	−	0.986412i	$-0.447467\pi$
$401$	−5337.82	−	3430.41i	−0.664733	−	0.427198i	−0.829023	+	0.559214i	$0.811103\pi$
$402$		0			0
$403$	−184.195	+	1281.11i	−0.0227678	+	0.158353i
$404$	−966.606	−	621.200i	−0.119036	−	0.0764996i
$405$		0			0
$406$	−441.169	−	966.026i	−0.0539282	−	0.118086i
$407$	−2073.16	+	1332.34i	−0.252488	+	0.162264i
$408$		0			0
$409$	8153.48	−	9409.62i	0.985730	−	1.13759i	−0.00475698	−	0.999989i	$-0.501514\pi$
$409$	8153.48	−	9409.62i	0.985730	−	1.13759i	0.990487	−	0.137605i	$-0.0439403\pi$
$410$	−196.087	+	57.5765i	−0.0236197	+	0.00693536i
$411$		0			0
$412$	556.596	+	3871.21i	0.0665571	+	0.462915i
$413$	−7004.99			−0.834607
$414$		0			0
$415$	4333.54			0.512591
$416$	24.7178	+	171.916i	0.00291319	+	0.0202617i
$417$		0			0
$418$	−186.951	+	54.8939i	−0.0218758	+	0.00642332i
$419$	−7220.58	+	8332.99i	−0.841881	+	0.971583i	−0.999874	−	0.0158574i	$-0.994952\pi$
$419$	−7220.58	+	8332.99i	−0.841881	+	0.971583i	0.157993	+	0.987440i	$0.449498\pi$
$420$		0			0
$421$	7865.76	−	5055.02i	0.910579	−	0.585194i	0.000669316	−	1.00000i	$-0.499787\pi$
$421$	7865.76	−	5055.02i	0.910579	−	0.585194i	0.909910	+	0.414806i	$0.136151\pi$
$422$	53.1180	+	116.312i	0.00612736	+	0.0134170i
$423$		0			0
$424$	−258.483	−	166.117i	−0.0296063	−	0.0190268i
$425$	343.885	−	2391.77i	0.0392491	−	0.272984i
$426$		0			0
$427$	9766.62	+	6276.63i	1.10688	+	0.711352i
$428$	2224.02	+	2566.66i	0.251174	+	0.289870i
$429$		0			0
$430$	−216.311	+	139.015i	−0.0242591	+	0.0155904i
$431$	9210.03	+	2704.31i	1.02931	+	0.302232i	0.752429	−	0.658673i	$-0.228882\pi$
$431$	9210.03	+	2704.31i	1.02931	+	0.302232i	0.276878	+	0.960905i	$0.410700\pi$
$432$		0			0
$433$	2726.13	−	800.465i	0.302562	−	0.0888404i	−0.126927	−	0.991912i	$-0.540512\pi$
$433$	2726.13	−	800.465i	0.302562	−	0.0888404i	0.429490	+	0.903072i	$0.358693\pi$
$434$	−590.770	+	1293.61i	−0.0653407	+	0.143076i
$435$		0			0
$436$	−4038.24			−0.443570
$437$	−6978.81	−	3116.25i	−0.763939	−	0.341122i
$438$		0			0
$439$	−967.153	−	6726.69i	−0.105147	−	0.731316i	−0.972378	−	0.233410i	$-0.925012\pi$
$439$	−967.153	−	6726.69i	−0.105147	−	0.731316i	0.867231	−	0.497906i	$-0.165897\pi$
$440$	187.696	−	410.997i	0.0203365	−	0.0445307i
$441$		0			0
$442$	60.9220	−	70.3077i	0.00655603	−	0.00756606i
$443$	−6945.43	−	2039.36i	−0.744893	−	0.218720i	−0.112805	−	0.993617i	$-0.535984\pi$
$443$	−6945.43	−	2039.36i	−0.744893	−	0.218720i	−0.632088	+	0.774897i	$0.717802\pi$
$444$		0			0
$445$	−1399.14	−	3063.69i	−0.149047	−	0.326366i
$446$	−3.67128	−	4.23689i	−0.000389777	−	0.000449826i
$447$		0			0
$448$	1792.50	−	12467.1i	0.189035	−	1.31476i
$449$	2046.96	−	14236.9i	0.215149	−	1.49640i	−0.540457	−	0.841372i	$-0.681749\pi$
$449$	2046.96	−	14236.9i	0.215149	−	1.49640i	0.755606	−	0.655026i	$-0.227342\pi$
$450$		0			0
$451$	947.048	+	1092.95i	0.0988797	+	0.114113i
$452$	−4108.59	−	8996.55i	−0.427548	−	0.936199i
$453$		0			0
$454$	1295.39	+	380.360i	0.133911	+	0.0393197i
$455$	−765.890	+	883.884i	−0.0789131	+	0.0910706i
$456$		0			0
$457$	3093.53	−	6773.89i	0.316650	−	0.693368i	−0.682651	−	0.730745i	$-0.739173\pi$
$457$	3093.53	−	6773.89i	0.316650	−	0.693368i	0.999301	+	0.0373770i	$0.0119003\pi$
$458$	−7.95212	−	55.3082i	−0.000811306	−	0.00564276i
$459$		0			0
$460$	8009.71	−	3739.87i	0.811857	−	0.379070i
$461$	10563.3			1.06720			0.533602	−	0.845735i	$-0.320838\pi$
$461$	10563.3			1.06720			0.533602	+	0.845735i	$0.320838\pi$
$462$		0			0
$463$	−495.167	+	1084.26i	−0.0497027	+	0.108834i	−0.932854	−	0.360254i	$-0.882690\pi$
$463$	−495.167	+	1084.26i	−0.0497027	+	0.108834i	0.883151	+	0.469088i	$0.155417\pi$
$464$	12758.4	−	3746.21i	1.27650	−	0.374814i
$465$		0			0
$466$	−378.665	−	111.186i	−0.0376423	−	0.0110528i
$467$	15865.5	−	10196.1i	1.57209	−	1.01032i	0.593422	−	0.804892i	$-0.297777\pi$
$467$	15865.5	−	10196.1i	1.57209	−	1.01032i	0.978672	−	0.205431i	$-0.0658597\pi$
$468$		0			0
$469$	5812.63	+	6708.13i	0.572287	+	0.660454i
$470$	220.338	+	141.603i	0.0216243	+	0.0138971i
$471$		0			0
$472$	−124.714	+	867.408i	−0.0121620	+	0.0845883i
$473$	1530.71	+	983.728i	0.148800	+	0.0956276i
$474$		0			0
$475$	−680.785	−	1490.71i	−0.0657612	−	0.143997i
$476$	−17342.4	+	11145.3i	−1.66993	+	1.07320i
$477$		0			0
$478$	639.933	−	738.522i	0.0612340	−	0.0706678i
$479$	3861.10	−	1133.72i	0.368305	−	0.108144i	−0.0923423	−	0.995727i	$-0.529435\pi$
$479$	3861.10	−	1133.72i	0.368305	−	0.108144i	0.460648	+	0.887583i	$0.347617\pi$
$480$		0			0
$481$	−113.569	−	789.888i	−0.0107657	−	0.0748769i
$482$	949.959			0.0897706
$483$		0			0
$484$	9000.75			0.845299
$485$	1219.42	+	8481.28i	0.114167	+	0.794052i
$486$		0			0
$487$	14333.1	−	4208.57i	1.33366	−	0.391599i	0.464258	−	0.885700i	$-0.346321\pi$
$487$	14333.1	−	4208.57i	1.33366	−	0.391599i	0.869404	+	0.494101i	$0.164503\pi$
$488$	951.098	−	1097.63i	0.0882258	−	0.101818i
$489$		0			0
$490$	−503.932	+	323.858i	−0.0464599	+	0.0298579i
$491$	−6476.08	−	14180.6i	−0.595237	−	1.30339i	−0.932225	−	0.361878i	$-0.882136\pi$
$491$	−6476.08	−	14180.6i	−0.595237	−	1.30339i	0.336989	−	0.941509i	$-0.390592\pi$
$492$		0			0
$493$	−18124.8	−	11648.1i	−1.65578	−	1.06410i
$494$	8.97925	−	62.4521i	0.000817805	−	0.00568796i
$495$		0			0
$496$	−14979.4	−	9626.70i	−1.35604	−	0.871475i
$497$	12714.1	+	14672.8i	1.14749	+	1.32428i
$498$		0			0
$499$	−3405.89	+	2188.83i	−0.305548	+	0.196364i	−0.684425	−	0.729083i	$-0.739947\pi$
$499$	−3405.89	+	2188.83i	−0.305548	+	0.196364i	0.378877	+	0.925447i	$0.376310\pi$
$500$	11430.4	+	3356.27i	1.02237	+	0.300194i
$501$		0			0
$502$	643.401	−	188.920i	0.0572040	−	0.0167966i
$503$	−1814.39	+	3972.96i	−0.160834	+	0.352178i	−0.972842	−	0.231468i	$-0.925647\pi$
$503$	−1814.39	+	3972.96i	−0.160834	+	0.352178i	0.812008	+	0.583646i	$0.198374\pi$
$504$		0			0
$505$	−1453.08			−0.128042
$506$	236.121	+	201.138i	0.0207447	+	0.0176713i
$507$		0			0
$508$	1854.71	+	12899.8i	0.161987	+	1.12664i
$509$	2562.65	−	5611.42i	0.223158	−	0.488648i	−0.764626	−	0.644474i	$-0.777076\pi$
$509$	2562.65	−	5611.42i	0.223158	−	0.488648i	0.987785	+	0.155825i	$0.0498037\pi$
$510$		0			0
$511$	−15040.8	+	17358.0i	−1.30209	+	1.50269i
$512$	−3827.43	−	1123.83i	−0.330371	−	0.0970057i
$513$		0			0
$514$	−580.059	−	1270.15i	−0.0497768	−	0.108996i
$515$	3238.96	+	3737.96i	0.277137	+	0.319834i
$516$		0			0
$517$	263.771	−	1834.57i	0.0224384	−	0.156062i
$518$	124.786	−	867.908i	0.0105845	−	0.0736171i
$519$		0			0
$520$	95.8132	+	110.574i	0.00808017	+	0.00932501i
$521$	−9069.37	−	19859.2i	−0.762642	−	1.66995i	−0.742216	−	0.670161i	$-0.766225\pi$
$521$	−9069.37	−	19859.2i	−0.762642	−	1.66995i	−0.0204262	−	0.999791i	$-0.506502\pi$
$522$		0			0
$523$	−12436.8	−	3651.79i	−1.03982	−	0.305318i	−0.283122	−	0.959084i	$-0.591370\pi$
$523$	−12436.8	−	3651.79i	−1.03982	−	0.305318i	−0.756697	+	0.653766i	$0.773188\pi$
$524$	−3735.68	+	4311.20i	−0.311439	+	0.359419i
$525$		0			0
$526$	−654.221	+	1432.54i	−0.0542308	+	0.118749i
$527$	4105.91	+	28557.2i	0.339386	+	2.36048i
$528$		0			0
$529$	1934.43	+	12012.2i	0.158990	+	0.987280i
$530$	−193.806			−0.0158838
$531$		0			0
$532$	−5808.02	+	12717.8i	−0.473327	+	1.03644i
$533$	−449.333	+	131.936i	−0.0365155	+	0.0107219i
$534$		0			0
$535$	4120.97	+	1210.03i	0.333019	+	0.0977831i
$536$	934.136	−	600.332i	0.0752771	−	0.0483776i
$537$		0			0
$538$	−226.007	−	260.825i	−0.0181112	−	0.0209015i
$539$	3566.05	+	2291.76i	0.284973	+	0.183141i
$540$		0			0
$541$	1217.02	−	8464.57i	0.0967169	−	0.672681i	−0.882567	−	0.470187i	$-0.844186\pi$
$541$	1217.02	−	8464.57i	0.0967169	−	0.672681i	0.979284	−	0.202494i	$-0.0649046\pi$
$542$	166.098	+	106.744i	0.0131633	+	0.00845954i
$543$		0			0
$544$	1608.32	+	3521.73i	0.126757	+	0.277560i
$545$	−4296.21	+	2761.01i	−0.337669	+	0.217007i
$546$		0			0
$547$	−6261.79	+	7226.49i	−0.489460	+	0.564867i	−0.945721	−	0.324979i	$-0.894643\pi$
$547$	−6261.79	+	7226.49i	−0.489460	+	0.564867i	0.456261	+	0.889846i	$0.349188\pi$
$548$	−12087.6	+	3549.24i	−0.942256	+	0.276671i
$549$		0			0
$550$	9.46512	+	65.8313i	0.000733807	+	0.00510374i
$551$	−14612.0			−1.12975
$552$		0			0
$553$	11370.0			0.874328
$554$	−2.01088	−	13.9860i	−0.000154213	−	0.00107258i
$555$		0			0
$556$	−9122.78	+	2678.69i	−0.695849	+	0.204320i
$557$	−1925.82	+	2222.51i	−0.146498	+	0.169068i	−0.824256	−	0.566217i	$-0.808406\pi$
$557$	−1925.82	+	2222.51i	−0.146498	+	0.169068i	0.677758	+	0.735285i	$0.262952\pi$
$558$		0			0
$559$	−495.674	+	318.551i	−0.0375041	+	0.0241024i
$560$	−6684.05	−	14636.0i	−0.504380	−	1.10444i
$561$		0			0
$562$	700.130	+	449.946i	0.0525502	+	0.0337719i
$563$	1757.94	−	12226.8i	0.131596	−	0.915269i	−0.811879	−	0.583826i	$-0.801555\pi$
$563$	1757.94	−	12226.8i	0.131596	−	0.915269i	0.943475	−	0.331444i	$-0.107536\pi$
$564$		0			0
$565$	−10522.1	−	6762.17i	−0.783486	−	0.503516i
$566$	735.511	+	848.825i	0.0546216	+	0.0630367i
$567$		0			0
$568$	2043.25	−	1313.12i	0.150938	−	0.0970021i
$569$	1796.91	+	527.620i	0.132391	+	0.0388735i	0.347257	−	0.937770i	$-0.387113\pi$
$569$	1796.91	+	527.620i	0.132391	+	0.0388735i	−0.214866	+	0.976644i	$0.568931\pi$
$570$		0			0
$571$	−19543.7	+	5738.55i	−1.43236	+	0.420580i	−0.903668	−	0.428233i	$-0.859136\pi$
$571$	−19543.7	+	5738.55i	−1.43236	+	0.420580i	−0.528694	+	0.848812i	$0.677318\pi$
$572$	214.520	−	469.734i	0.0156810	−	0.0343366i
$573$		0			0
$574$	−514.558			−0.0374168
$575$	−1391.89	+	2206.53i	−0.100950	+	0.160032i
$576$		0			0
$577$	637.099	+	4431.12i	0.0459667	+	0.319705i	0.999812	+	0.0194060i	$0.00617751\pi$
$577$	637.099	+	4431.12i	0.0459667	+	0.319705i	−0.953845	+	0.300299i	$0.902913\pi$
$578$	455.981	−	998.458i	0.0328137	−	0.0718519i
$579$		0			0
$580$	11067.3	−	12772.3i	0.792317	−	0.914382i
$581$	10469.1	+	3074.02i	0.747562	+	0.219504i
$582$		0			0
$583$	569.724	+	1247.52i	0.0404726	+	0.0886227i
$584$	1881.62	+	2171.50i	0.133325	+	0.153865i
$585$		0			0
$586$	−259.678	+	1806.10i	−0.0183058	+	0.127320i
$587$	−1185.74	+	8246.98i	−0.0833741	+	0.579880i	0.904717	+	0.426012i	$0.140082\pi$
$587$	−1185.74	+	8246.98i	−0.0833741	+	0.579880i	−0.988091	+	0.153867i	$0.950827\pi$
$588$		0			0
$589$	12813.7	+	14787.7i	0.896396	+	1.03450i
$590$	229.620	+	502.798i	0.0160226	+	0.0350845i
$591$		0			0
$592$	10533.9	+	3093.04i	0.731321	+	0.214735i
$593$	−11572.8	+	13355.7i	−0.801415	+	0.924882i	−0.998458	−	0.0555130i	$-0.982321\pi$
$593$	−11572.8	+	13355.7i	−0.801415	+	0.924882i	0.197043	+	0.980395i	$0.436866\pi$
$594$		0			0
$595$	−10830.1	+	23714.5i	−0.746200	+	1.63395i
$596$	1197.78	+	8330.72i	0.0823202	+	0.572550i
$597$		0			0
$598$	−91.0095	+	42.4939i	−0.00622350	+	0.00290586i
$599$	−6746.87			−0.460217			−0.230108	−	0.973165i	$-0.573908\pi$
$599$	−6746.87			−0.460217			−0.230108	+	0.973165i	$0.573908\pi$
$600$		0			0
$601$	8009.89	−	17539.2i	0.543644	−	1.19041i	−0.416043	−	0.909345i	$-0.636583\pi$
$601$	8009.89	−	17539.2i	0.543644	−	1.19041i	0.959687	−	0.281070i	$-0.0906892\pi$
$602$	−621.183	+	182.396i	−0.0420557	+	0.0123487i
$603$		0			0
$604$	8516.43	+	2500.65i	0.573723	+	0.168460i
$605$	9575.74	−	6153.95i	0.643486	−	0.413544i
$606$		0			0
$607$	6686.61	+	7716.76i	0.447119	+	0.516003i	0.933906	−	0.357518i	$-0.116377\pi$
$607$	6686.61	+	7716.76i	0.447119	+	0.516003i	−0.486788	+	0.873520i	$0.661831\pi$
$608$	2208.93	+	1419.59i	0.147342	+	0.0946908i
$609$		0			0
$610$	130.373	−	906.765i	0.00865353	−	0.0601866i
$611$	504.903	+	324.481i	0.0334307	+	0.0214846i
$612$		0			0
$613$	−10694.0	−	23416.7i	−0.704614	−	1.54289i	−0.834285	−	0.551333i	$-0.814119\pi$
$613$	−10694.0	−	23416.7i	−0.704614	−	1.54289i	0.129671	−	0.991557i	$-0.458608\pi$
$614$	−599.372	+	385.193i	−0.0393953	+	0.0253178i
$615$		0			0
$616$	744.986	−	859.760i	0.0487279	−	0.0562349i
$617$	−14446.5	+	4241.88i	−0.942618	+	0.276777i	−0.716710	−	0.697371i	$-0.754353\pi$
$617$	−14446.5	+	4241.88i	−0.942618	+	0.276777i	−0.225908	+	0.974149i	$0.572535\pi$
$618$		0			0
$619$	2614.42	+	18183.7i	0.169761	+	1.18072i	0.879377	+	0.476126i	$0.157960\pi$
$619$	2614.42	+	18183.7i	0.169761	+	1.18072i	−0.709616	+	0.704589i	$0.751131\pi$
$620$	−22631.1			−1.46594
$621$		0			0
$622$	946.479			0.0610134
$623$	−1206.86	−	8393.88i	−0.0776112	−	0.539797i
$624$		0			0
$625$	11618.7	−	3411.55i	0.743594	−	0.218339i
$626$	−433.826	+	500.661i	−0.0276983	+	0.0319656i
$627$		0			0
$628$	7777.48	−	4998.28i	0.494196	−	0.317601i
$629$	−7389.61	−	16181.0i	−0.468431	−	1.02572i
$630$		0			0
$631$	19578.6	+	12582.4i	1.23520	+	0.793817i	0.984693	−	0.174297i	$-0.0557653\pi$
$631$	19578.6	+	12582.4i	1.23520	+	0.793817i	0.250510	+	0.968114i	$0.419402\pi$
$632$	202.428	−	1407.92i	0.0127408	−	0.0886140i
$633$		0			0
$634$	749.884	+	481.921i	0.0469743	+	0.0301885i
$635$	10793.0	+	12455.7i	0.674497	+	0.778411i
$636$		0			0
$637$	−1154.76	+	742.117i	−0.0718259	+	0.0461597i
$638$	568.984	+	167.069i	0.0353077	+	0.0103673i
$639$		0			0
$640$	−3881.98	+	1139.85i	−0.239763	+	0.0704009i
$641$	7220.43	−	15810.5i	0.444914	−	0.974225i	−0.545756	−	0.837944i	$-0.683758\pi$
$641$	7220.43	−	15810.5i	0.444914	−	0.974225i	0.990670	−	0.136281i	$-0.0435151\pi$
$642$		0			0
$643$	−28080.8			−1.72224			−0.861119	−	0.508403i	$-0.830236\pi$
$643$	−28080.8			−1.72224			−0.861119	+	0.508403i	$0.830236\pi$
$644$	22003.1	−	3353.21i	1.34634	−	0.205178i
$645$		0			0
$646$	−200.157	−	1392.12i	−0.0121905	−	0.0847870i
$647$	2996.35	−	6561.09i	0.182069	−	0.398676i	−0.796487	−	0.604655i	$-0.793311\pi$
$647$	2996.35	−	6561.09i	0.182069	−	0.398676i	0.978556	+	0.205980i	$0.0660381\pi$
$648$		0			0
$649$	2561.49	−	2956.11i	0.154926	−	0.178794i
$650$	−20.6643	−	6.06759i	−0.00124696	−	0.000366139i
$651$		0			0
$652$	−5301.97	−	11609.7i	−0.318468	−	0.697348i
$653$	6706.04	+	7739.18i	0.401880	+	0.463794i	0.920232	−	0.391373i	$-0.128000\pi$
$653$	6706.04	+	7739.18i	0.401880	+	0.463794i	−0.518352	+	0.855167i	$0.673454\pi$
$654$		0			0
$655$	−1026.69	+	7140.75i	−0.0612457	+	0.425973i
$656$	916.889	−	6377.11i	0.0545709	−	0.379549i
$657$		0			0
$658$	431.855	+	498.387i	0.0255858	+	0.0295276i
$659$	9715.89	+	21274.8i	0.574321	+	1.25759i	0.944465	+	0.328613i	$0.106581\pi$
$659$	9715.89	+	21274.8i	0.574321	+	1.25759i	−0.370144	+	0.928974i	$0.620692\pi$
$660$		0			0
$661$	−13921.0	−	4087.59i	−0.819161	−	0.240527i	−0.154807	−	0.987945i	$-0.549475\pi$
$661$	−13921.0	−	4087.59i	−0.819161	−	0.240527i	−0.664355	+	0.747417i	$0.731294\pi$
$662$	58.4951	−	67.5070i	0.00343426	−	0.00396334i
$663$		0			0
$664$	567.036	−	1241.64i	0.0331405	−	0.0725675i
$665$	2516.30	+	17501.3i	0.146734	+	1.02056i
$666$		0			0
$667$	12740.6	+	19461.8i	0.739606	+	1.12978i
$668$	10550.1			0.611072
$669$		0			0
$670$	290.956	−	637.104i	0.0167770	−	0.0367365i
$671$	−6220.06	+	1826.38i	−0.357858	+	0.105077i
$672$		0			0
$673$	−16998.2	−	4991.13i	−0.973601	−	0.285875i	−0.244020	−	0.969770i	$-0.578466\pi$
$673$	−16998.2	−	4991.13i	−0.973601	−	0.285875i	−0.729580	+	0.683895i	$0.760285\pi$
$674$	−1588.59	+	1020.92i	−0.0907865	+	0.0583449i
$675$		0			0
$676$	−11343.5	−	13091.1i	−0.645399	−	0.744830i
$677$	−6108.28	−	3925.56i	−0.346766	−	0.222853i	0.355651	−	0.934619i	$-0.384259\pi$
$677$	−6108.28	−	3925.56i	−0.346766	−	0.222853i	−0.702417	+	0.711766i	$0.747896\pi$
$678$		0			0
$679$	−3070.30	+	21354.4i	−0.173531	+	1.20693i
$680$	2743.69	+	1763.26i	0.154729	+	0.0994381i
$681$		0			0
$682$	−329.879	−	722.333i	−0.0185216	−	0.0405566i
$683$	−25305.5	+	16262.8i	−1.41770	+	0.911098i	−0.417699	+	0.908586i	$0.637163\pi$
$683$	−25305.5	+	16262.8i	−1.41770	+	0.911098i	−0.999997	+	0.00251218i	$0.999200\pi$
$684$		0			0
$685$	−10433.1	+	12040.4i	−0.581940	+	0.671594i
$686$	210.214	−	61.7244i	0.0116997	−	0.00343535i
$687$		0			0
$688$	−1153.61	−	8023.56i	−0.0639260	−	0.444615i
$689$	−444.105			−0.0245559
$690$		0			0
$691$	−6377.88			−0.351123			−0.175562	−	0.984468i	$-0.556174\pi$
$691$	−6377.88			−0.351123			−0.175562	+	0.984468i	$0.556174\pi$
$692$	−1284.36	−	8932.93i	−0.0705550	−	0.490721i
$693$		0			0
$694$	−2379.09	+	698.564i	−0.130128	+	0.0382091i
$695$	−7874.11	+	9087.20i	−0.429758	+	0.495967i
$696$		0			0
$697$	−8781.81	+	5643.73i	−0.477238	+	0.306702i
$698$	−576.391	−	1262.12i	−0.0312561	−	0.0684412i
$699$		0			0
$700$	4014.78	+	2580.15i	0.216778	+	0.139315i
$701$	1097.12	−	7630.63i	0.0591122	−	0.411134i	−0.938684	−	0.344779i	$-0.887954\pi$
$701$	1097.12	−	7630.63i	0.0591122	−	0.411134i	0.997796	−	0.0663551i	$-0.0211370\pi$
$702$		0			0
$703$	−10149.2	−	6522.49i	−0.544500	−	0.349929i
$704$	4605.67	+	5315.22i	0.246566	+	0.284553i
$705$		0			0
$706$	−396.437	+	254.775i	−0.0211333	+	0.0135816i
$707$	−3510.41	−	1030.75i	−0.186736	−	0.0548306i
$708$		0			0
$709$	34408.5	−	10103.3i	1.82262	−	0.535170i	0.823155	−	0.567816i	$-0.192212\pi$
$709$	34408.5	−	10103.3i	1.82262	−	0.535170i	0.999467	+	0.0326459i	$0.0103933\pi$
$710$	636.412	−	1393.55i	0.0336396	−	0.0736605i
$711$		0			0
$712$	−1060.88			−0.0558400
$713$	8523.35	−	29960.4i	0.447689	−	1.57367i
$714$		0			0
$715$	−92.9401	−	646.412i	−0.00486121	−	0.0338104i
$716$	13250.8	−	29015.2i	0.691628	−	1.51445i
$717$		0			0
$718$	1054.14	−	1216.55i	0.0547915	−	0.0632328i
$719$	9588.78	+	2815.52i	0.497359	+	0.146038i	0.520785	−	0.853688i	$-0.325639\pi$
$719$	9588.78	+	2815.52i	0.497359	+	0.146038i	−0.0234260	+	0.999726i	$0.507457\pi$
$720$		0			0
$721$	5173.27	+	11327.9i	0.267216	+	0.585121i
$722$	267.747	+	308.996i	0.0138013	+	0.0159275i
$723$		0			0
$724$	3162.28	−	21994.1i	0.162327	−	1.12901i
$725$	−709.823	+	4936.93i	−0.0363616	+	0.252901i
$726$		0			0
$727$	3997.84	+	4613.76i	0.203950	+	0.235371i	0.848505	−	0.529187i	$-0.177503\pi$
$727$	3997.84	+	4613.76i	0.203950	+	0.235371i	−0.644555	+	0.764558i	$0.722957\pi$
$728$	153.033	+	335.095i	0.00779090	+	0.0170597i
$729$		0			0
$730$	1738.94	+	510.600i	0.0881660	+	0.0258879i
$731$	−8601.01	+	9926.10i	−0.435185	+	0.502230i
$732$		0			0
$733$	−3732.90	+	8173.91i	−0.188101	+	0.411883i	−0.980063	−	0.198687i	$-0.936332\pi$
$733$	−3732.90	+	8173.91i	−0.188101	+	0.411883i	0.791962	+	0.610570i	$0.209060\pi$
$734$	−96.0645	−	668.143i	−0.00483080	−	0.0335989i
$735$		0			0
$736$	−35.2539	−	4179.86i	−0.00176559	−	0.209336i
$737$	−4956.32			−0.247718
$738$		0			0
$739$	8281.43	−	18133.8i	0.412229	−	0.902656i	−0.583654	−	0.812003i	$-0.698377\pi$
$739$	8281.43	−	18133.8i	0.412229	−	0.902656i	0.995883	−	0.0906528i	$-0.0288954\pi$
$740$	13388.4	−	3931.18i	0.665089	−	0.195288i
$741$		0			0
$742$	−468.204	−	137.477i	−0.0231648	−	0.00680181i
$743$	1748.75	−	1123.85i	0.0863465	−	0.0554915i	−0.496755	−	0.867891i	$-0.665475\pi$
$743$	1748.75	−	1123.85i	0.0863465	−	0.0554915i	0.583102	+	0.812399i	$0.301839\pi$
$744$		0			0
$745$	6970.14	+	8043.97i	0.342773	+	0.395582i
$746$	18.6578	+	11.9907i	0.000915700	+	0.000588485i
$747$		0			0
$748$	1638.20	−	11393.9i	0.0800783	−	0.556957i
$749$	9097.26	+	5846.45i	0.443801	+	0.285213i
$750$		0			0
$751$	−11424.6	−	25016.4i	−0.555113	−	1.21553i	−0.954353	−	0.298681i	$-0.903453\pi$
$751$	−11424.6	−	25016.4i	−0.555113	−	1.21553i	0.399240	−	0.916847i	$-0.369274\pi$
$752$	−6946.21	+	4464.06i	−0.336838	+	0.216473i
$753$		0			0
$754$	−125.751	+	145.124i	−0.00607371	+	0.00700943i
$755$	10770.2	−	3162.42i	0.519163	−	0.152440i
$756$		0			0
$757$	−825.894	−	5744.22i	−0.0396534	−	0.275796i	0.960342	−	0.278825i	$-0.0899449\pi$
$757$	−825.894	−	5744.22i	−0.0396534	−	0.275796i	−0.999995	+	0.00302919i	$0.999036\pi$
$758$	−798.904			−0.0382817
$759$		0			0
$760$	2211.93			0.105573
$761$	−680.424	−	4732.45i	−0.0324118	−	0.225429i	0.967177	−	0.254103i	$-0.0817804\pi$
$761$	−680.424	−	4732.45i	−0.0324118	−	0.225429i	−0.999589	+	0.0286748i	$0.990871\pi$
$762$		0			0
$763$	−12337.5	+	3622.61i	−0.585383	+	0.171884i
$764$	−19569.2	+	22584.1i	−0.926688	+	1.06946i
$765$		0			0
$766$	−1061.68	+	682.299i	−0.0500783	+	0.0321834i
$767$	526.173	+	1152.16i	0.0247705	+	0.0542399i
$768$		0			0
$769$	−10288.7	−	6612.17i	−0.482472	−	0.310066i	0.276699	−	0.960957i	$-0.410759\pi$
$769$	−10288.7	−	6612.17i	−0.482472	−	0.310066i	−0.759172	+	0.650890i	$0.774396\pi$
$770$	102.120	−	710.261i	0.00477942	−	0.0332416i
$771$		0			0
$772$	4888.97	+	3141.95i	0.227925	+	0.146478i
$773$	18583.1	+	21446.0i	0.864667	+	0.997878i	0.999975	+	0.00707485i	$0.00225201\pi$
$773$	18583.1	+	21446.0i	0.864667	+	0.997878i	−0.135308	+	0.990804i	$0.543203\pi$
$774$		0			0
$775$	5618.75	−	3610.95i	0.260428	−	0.167367i
$776$	2589.59	+	760.374i	0.119795	+	0.0351750i
$777$		0			0
$778$	−720.270	+	211.490i	−0.0331914	+	0.00974588i
$779$	−2941.06	+	6440.03i	−0.135269	+	0.296198i
$780$		0			0
$781$	−10841.0			−0.496701
$782$	−1679.66	+	1480.42i	−0.0768086	+	0.0676976i
$783$		0			0
$784$	−2687.53	−	18692.2i	−0.122428	−	0.851504i
$785$	4856.92	−	10635.2i	0.220829	−	0.483548i
$786$		0			0
$787$	4391.55	−	5068.12i	0.198910	−	0.229554i	−0.647528	−	0.762041i	$-0.724197\pi$
$787$	4391.55	−	5068.12i	0.198910	−	0.229554i	0.846438	+	0.532488i	$0.178743\pi$
$788$	−15493.0	−	4549.17i	−0.700402	−	0.205657i
$789$		0			0
$790$	−372.705	−	816.109i	−0.0167851	−	0.0367543i
$791$	−20623.0	−	23800.2i	−0.927017	−	1.06983i
$792$		0			0
$793$	298.749	−	2077.84i	0.0133782	−	0.0930472i
$794$	−249.973	+	1738.60i	−0.0111728	+	0.0777085i
$795$		0			0
$796$	20336.6	+	23469.7i	0.905543	+	1.04505i
$797$	−10268.1	−	22484.0i	−0.456355	−	0.999279i	−0.988303	−	0.152502i	$-0.951267\pi$
$797$	−10268.1	−	22484.0i	−0.456355	−	0.999279i	0.531948	−	0.846777i	$-0.321460\pi$
$798$		0			0
$799$	12836.7	+	3769.20i	0.568373	+	0.166889i
$800$	586.939	−	677.363i	0.0259393	−	0.0299355i
$801$		0			0
$802$	−523.680	+	1146.70i	−0.0230571	+	0.0504880i
$803$	−1825.19	−	12694.5i	−0.0802113	−	0.557882i
$804$		0			0
$805$	21116.0	−	18611.3i	0.924524	−	0.814858i
$806$	257.143			0.0112376
$807$		0			0
$808$	−190.133	+	416.332i	−0.00827827	+	0.0181269i
$809$	23214.6	−	6816.43i	1.00888	−	0.296234i	0.264784	−	0.964308i	$-0.414699\pi$
$809$	23214.6	−	6816.43i	1.00888	−	0.296234i	0.744095	+	0.668074i	$0.232881\pi$
$810$		0			0
$811$	3566.64	+	1047.26i	0.154429	+	0.0453443i	0.358033	−	0.933709i	$-0.383447\pi$
$811$	3566.64	+	1047.26i	0.154429	+	0.0453443i	−0.203605	+	0.979053i	$0.565266\pi$
$812$	35796.9	−	23005.2i	1.54707	−	0.994244i
$813$		0			0
$814$	320.628	+	370.024i	0.0138059	+	0.0159328i
$815$	−13578.4	−	8726.31i	−0.583596	−	0.375055i
$816$		0			0
$817$	−1267.70	+	8817.03i	−0.0542853	+	0.377563i
$818$	−2080.98	−	1337.36i	−0.0889483	−	0.0571636i
$819$		0			0
$820$	−3401.62	−	7448.50i	−0.144865	−	0.317211i
$821$	−11689.2	+	7512.21i	−0.496902	+	0.319340i	−0.764976	−	0.644059i	$-0.777249\pi$
$821$	−11689.2	+	7512.21i	−0.496902	+	0.319340i	0.268074	+	0.963398i	$0.413613\pi$
$822$		0			0
$823$	29717.0	−	34295.3i	1.25865	−	1.45256i	0.420342	−	0.907366i	$-0.361910\pi$
$823$	29717.0	−	34295.3i	1.25865	−	1.45256i	0.838309	−	0.545195i	$-0.183544\pi$
$824$	1494.80	−	438.914i	0.0631965	−	0.0185562i
$825$		0			0
$826$	198.063	+	1377.56i	0.00834323	+	0.0580284i
$827$	26239.2			1.10330			0.551648	−	0.834077i	$-0.313999\pi$
$827$	26239.2			1.10330			0.551648	+	0.834077i	$0.313999\pi$
$828$		0			0
$829$	24569.3			1.02934			0.514672	−	0.857387i	$-0.327914\pi$
$829$	24569.3			1.02934			0.514672	+	0.857387i	$0.327914\pi$
$830$	−122.529	−	852.210i	−0.00512416	−	0.0356393i
$831$		0			0
$832$	−2185.19	+	641.629i	−0.0910550	+	0.0267362i
$833$	−20037.5	+	23124.5i	−0.833443	+	0.961845i
$834$		0			0
$835$	11224.1	−	7213.28i	0.465180	−	0.298953i
$836$	−3243.13	−	7101.46i	−0.134170	−	0.293791i
$837$		0			0
$838$	1842.88	+	1184.35i	0.0759680	+	0.0488217i
$839$	3303.81	−	22978.5i	0.135948	−	0.945538i	−0.801644	−	0.597801i	$-0.796041\pi$
$839$	3303.81	−	22978.5i	0.135948	−	0.945538i	0.937592	−	0.347737i	$-0.113050\pi$
$840$		0			0
$841$	16894.5	+	10857.5i	0.692711	+	0.445179i
$842$	−1216.49	−	1403.91i	−0.0497899	−	0.0574607i
$843$		0			0
$844$	−4310.05	+	2769.90i	−0.175779	+	0.112967i
$845$	−21018.8	−	6171.68i	−0.855703	−	0.251257i
$846$		0			0
$847$	27498.8	−	8074.37i	1.11555	−	0.327555i
$848$	2538.10	−	5557.66i	0.102781	−	0.225060i
$849$		0			0
$850$	−480.076			−0.0193723
$851$	161.978	+	19204.9i	0.00652473	+	0.773601i
$852$		0			0
$853$	−4989.85	−	34705.2i	−0.200292	−	1.39306i	−0.803417	−	0.595416i	$-0.796987\pi$
$853$	−4989.85	−	34705.2i	−0.200292	−	1.39306i	0.603125	−	0.797647i	$-0.293922\pi$
$854$	958.178	−	2098.12i	0.0383937	−	0.0840704i
$855$		0			0
$856$	885.915	−	1022.40i	0.0353738	−	0.0408235i
$857$	21687.7	+	6368.08i	0.864455	+	0.253827i	0.683755	−	0.729711i	$-0.260346\pi$
$857$	21687.7	+	6368.08i	0.864455	+	0.253827i	0.180700	+	0.983538i	$0.442164\pi$
$858$		0			0
$859$	11079.1	+	24259.8i	0.440062	+	0.963601i	0.991587	+	0.129443i	$0.0413188\pi$
$859$	11079.1	+	24259.8i	0.440062	+	0.963601i	−0.551525	+	0.834158i	$0.685954\pi$
$860$	−6746.76	−	7786.18i	−0.267515	−	0.308728i
$861$		0			0
$862$	271.404	−	1887.66i	0.0107240	−	0.0745868i
$863$	−3214.06	+	22354.2i	−0.126776	+	0.881747i	0.822827	+	0.568292i	$0.192396\pi$
$863$	−3214.06	+	22354.2i	−0.126776	+	0.881747i	−0.949603	+	0.313455i	$0.898514\pi$
$864$		0			0
$865$	−7473.99	−	8625.45i	−0.293784	−	0.339045i
$866$	−234.495	−	513.473i	−0.00920147	−	0.0201484i
$867$		0			0
$868$	−54673.0	−	16053.5i	−2.13793	−	0.627753i
$869$	−4157.64	+	4798.17i	−0.162299	+	0.187303i
$870$		0			0
$871$	666.722	−	1459.92i	0.0259369	−	0.0567938i
$872$	228.926	+	1592.21i	0.00889037	+	0.0618338i
$873$		0			0
$874$	−415.501	+	1460.52i	−0.0160807	+	0.0565251i
$875$	37932.6			1.46555
$876$		0			0
$877$	−14581.2	+	31928.4i	−0.561428	+	1.22936i	0.389810	+	0.920895i	$0.372541\pi$
$877$	−14581.2	+	31928.4i	−0.561428	+	1.22936i	−0.951237	+	0.308460i	$0.900186\pi$
$878$	−1295.49	+	380.390i	−0.0497957	+	0.0146213i
$879$		0			0
$880$	8620.55	+	2531.22i	0.330226	+	0.0969631i
$881$	−37797.3	+	24290.9i	−1.44543	+	0.928922i	−0.446005	+	0.895030i	$0.647154\pi$
$881$	−37797.3	+	24290.9i	−1.44543	+	0.928922i	−0.999426	+	0.0338914i	$0.989210\pi$
$882$		0			0
$883$	10339.9	+	11932.9i	0.394072	+	0.454784i	0.917765	−	0.397123i	$-0.129991\pi$
$883$	10339.9	+	11932.9i	0.394072	+	0.454784i	−0.523693	+	0.851907i	$0.675446\pi$
$884$	3135.79	+	2015.25i	0.119308	+	0.0766745i
$885$		0			0
$886$	−204.670	+	1423.51i	−0.00776076	+	0.0539772i
$887$	8123.03	+	5220.36i	0.307491	+	0.197613i	0.685281	−	0.728279i	$-0.259679\pi$
$887$	8123.03	+	5220.36i	0.307491	+	0.197613i	−0.377790	+	0.925891i	$0.623316\pi$
$888$		0			0
$889$	17238.5	+	37747.1i	0.650350	+	1.42407i
$890$	−562.929	+	361.772i	−0.0212016	+	0.0136254i
$891$		0			0
$892$	147.100	−	169.763i	0.00552161	−	0.00637228i
$893$	8705.99	−	2556.31i	0.326243	−	0.0957935i
$894$		0			0
$895$	−5740.86	−	39928.5i	−0.214409	−	1.49124i
$896$	−10186.8			−0.379818
$897$		0			0
$898$	−2857.63			−0.106192
$899$	−8475.12	−	58945.8i	−0.314417	−	2.18682i
$900$		0			0
$901$	−9498.57	+	2789.03i	−0.351213	+	0.103126i
$902$	188.156	−	217.144i	0.00694559	−	0.00801564i
$903$		0			0
$904$	−3314.28	+	2129.96i	−0.121937	+	0.0783644i
$905$	−11673.4	−	25561.2i	−0.428771	−	0.938878i
$906$		0			0
$907$	−17459.8	−	11220.7i	−0.639188	−	0.410781i	0.180513	−	0.983573i	$-0.442224\pi$
$907$	−17459.8	−	11220.7i	−0.639188	−	0.410781i	−0.819701	+	0.572792i	$0.805860\pi$
$908$	−7698.44	+	53543.8i	−0.281367	+	1.95695i
$909$		0			0
$910$	195.475	+	125.624i	0.00712080	+	0.00457626i
$911$	20082.5	+	23176.5i	0.730367	+	0.842889i	0.992513	−	0.122140i	$-0.0389756\pi$
$911$	20082.5	+	23176.5i	0.730367	+	0.842889i	−0.262146	+	0.965028i	$0.584430\pi$
$912$		0			0
$913$	−5125.45	+	3293.93i	−0.185791	+	0.119401i
$914$	−1419.58	−	416.827i	−0.0513738	−	0.0150847i
$915$		0			0
$916$	2148.17	−	630.761i	0.0774866	−	0.0227521i
$917$	−7545.63	+	16522.6i	−0.271733	+	0.595011i
$918$		0			0
$919$	−25701.9			−0.922555			−0.461277	−	0.887256i	$-0.652609\pi$
$919$	−25701.9			−0.922555			−0.461277	+	0.887256i	$0.652609\pi$
$920$	−1928.64	−	2946.09i	−0.0691144	−	0.105576i
$921$		0			0
$922$	−298.673	−	2077.32i	−0.0106684	−	0.0742004i
$923$	1458.33	−	3193.30i	0.0520061	−	0.113877i
$924$		0			0
$925$	−2696.76	+	3112.23i	−0.0958583	+	0.110626i
$926$	227.226	+	66.7196i	0.00806383	+	0.00236775i
$927$		0			0
$928$	−3319.77	−	7269.29i	−0.117432	−	0.257140i
$929$	31354.9	+	36185.5i	1.10734	+	1.27794i	0.957248	+	0.289268i	$0.0934119\pi$
$929$	31354.9	+	36185.5i	1.10734	+	1.27794i	0.150093	+	0.988672i	$0.452043\pi$
$930$		0			0
$931$	−2953.31	+	20540.7i	−0.103964	+	0.723089i
$932$	2250.39	−	15651.8i	0.0790923	−	0.550099i
$933$		0			0
$934$	−2453.71	−	2831.73i	−0.0859611	−	0.0992045i
$935$	−6047.36	−	13241.9i	−0.211519	−	0.463161i
$936$		0			0
$937$	−29358.4	−	8620.40i	−1.02358	−	0.300551i	−0.273484	−	0.961877i	$-0.588176\pi$
$937$	−29358.4	−	8620.40i	−1.02358	−	0.300551i	−0.750099	+	0.661326i	$0.769994\pi$
$938$	1154.83	−	1332.75i	0.0401990	−	0.0463921i
$939$		0			0
$940$	−4359.53	+	9546.04i	−0.151268	+	0.331231i
$941$	−2682.59	−	18657.8i	−0.0929331	−	0.646364i	−0.982041	−	0.188666i	$-0.939583\pi$
$941$	−2682.59	−	18657.8i	−0.0929331	−	0.646364i	0.889108	−	0.457697i	$-0.151326\pi$
$942$		0			0
$943$	11141.9	−	1697.99i	0.384761	−	0.0586366i
$944$	−17425.6			−0.600798
$945$		0			0
$946$	150.174	−	328.836i	0.00516129	−	0.0113017i
$947$	5824.75	−	1710.30i	0.199872	−	0.0586878i	−0.180264	−	0.983618i	$-0.557695\pi$
$947$	5824.75	−	1710.30i	0.199872	−	0.0586878i	0.380136	+	0.924930i	$0.375877\pi$
$948$		0			0
$949$	3984.77	+	1170.03i	0.136303	+	0.0400221i
$950$	−273.906	+	176.029i	−0.00935441	+	0.00601171i
$951$		0			0
$952$	5377.53	+	6206.00i	0.183074	+	0.211279i
$953$	−22046.5	−	14168.4i	−0.749378	−	0.481596i	0.109365	−	0.994002i	$-0.465118\pi$
$953$	−22046.5	−	14168.4i	−0.749378	−	0.481596i	−0.858744	+	0.512406i	$0.828754\pi$
$954$		0			0
$955$	−5378.26	+	37406.6i	−0.182237	+	1.26749i
$956$	32938.8	+	21168.5i	1.11435	+	0.716147i
$957$		0			0
$958$	−332.123	−	727.247i	−0.0112008	−	0.0245264i
$959$	−33745.7	+	21687.0i	−1.13629	+	0.730251i
$960$		0			0
$961$	−32713.6	+	37753.5i	−1.09810	+	1.26728i
$962$	−152.124	+	44.6676i	−0.00509841	+	0.00149703i
$963$		0			0
$964$	5416.89	+	37675.3i	0.180982	+	1.25875i
$965$	7349.49			0.245169
$966$		0			0
$967$	−42074.3			−1.39919			−0.699595	−	0.714539i	$-0.746636\pi$
$967$	−42074.3			−1.39919			−0.699595	+	0.714539i	$0.746636\pi$
$968$	−510.248	−	3548.85i	−0.0169421	−	0.117835i
$969$		0			0
$970$	1633.40	−	479.610i	0.0540674	−	0.0158756i
$971$	−10756.7	+	12413.9i	−0.355508	+	0.410278i	−0.905130	−	0.425136i	$-0.860226\pi$
$971$	−10756.7	+	12413.9i	−0.355508	+	0.410278i	0.549622	+	0.835414i	$0.314772\pi$
$972$		0			0
$973$	−25468.6	+	16367.7i	−0.839143	+	0.539285i
$974$	−1232.90	−	2699.67i	−0.0405591	−	0.0888120i
$975$		0			0
$976$	24295.4	+	15613.7i	0.796799	+	0.512072i
$977$	−2486.26	+	17292.3i	−0.0814150	+	0.566254i	0.907757	+	0.419496i	$0.137793\pi$
$977$	−2486.26	+	17292.3i	−0.0814150	+	0.566254i	−0.989172	+	0.146758i	$0.953116\pi$
$978$		0			0
$979$	3983.53	+	2560.06i	0.130045	+	0.0835750i
$980$	−15717.7	−	18139.2i	−0.512330	−	0.591261i
$981$		0			0
$982$	−2605.57	+	1674.50i	−0.0846713	+	0.0544149i
$983$	−16710.1	−	4906.53i	−0.542187	−	0.159200i	−0.000839647	−	1.00000i	$-0.500267\pi$
$983$	−16710.1	−	4906.53i	−0.542187	−	0.159200i	−0.541347	+	0.840799i	$0.682085\pi$
$984$		0			0
$985$	−19593.1	+	5753.06i	−0.633796	+	0.186099i
$986$	−1778.18	+	3893.66i	−0.0574327	+	0.125760i
$987$		0			0
$988$	2528.05			0.0814047
$989$	12848.8	−	5999.32i	0.413112	−	0.192889i
$990$		0			0
$991$	−1496.28	−	10406.9i	−0.0479627	−	0.333588i	−0.999648	−	0.0265143i	$-0.991559\pi$
$991$	−1496.28	−	10406.9i	−0.0479627	−	0.333588i	0.951686	−	0.307074i	$-0.0993498\pi$
$992$	−4445.51	+	9734.31i	−0.142283	+	0.311557i
$993$		0			0
$994$	2525.99	−	2915.15i	0.0806031	−	0.0930210i
$995$	37682.4	+	11064.5i	1.20061	+	0.352532i
$996$		0			0
$997$	−21647.6	−	47401.6i	−0.687649	−	1.50574i	−0.854331	−	0.519730i	$-0.826033\pi$
$997$	−21647.6	−	47401.6i	−0.687649	−	1.50574i	0.166682	−	0.986011i	$-0.446695\pi$
$998$	526.744	+	607.895i	0.0167072	+	0.0192811i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.4.i.a.118.3		50
3.2	odd	2		23.4.c.a.3.3	✓	50
23.8	even	11	inner	207.4.i.a.100.3		50
69.8	odd	22		23.4.c.a.8.3	yes	50
69.56	even	22		529.4.a.m.1.13		25
69.59	odd	22		529.4.a.n.1.13		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.c.a.3.3	✓	50	3.2	odd	2
23.4.c.a.8.3	yes	50	69.8	odd	22
207.4.i.a.100.3		50	23.8	even	11	inner
207.4.i.a.118.3		50	1.1	even	1	trivial
529.4.a.m.1.13		25	69.56	even	22
529.4.a.n.1.13		25	69.59	odd	22

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	207.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0282746 - 0.196654i) q^{2} +(7.63807 - 2.24274i) q^{4} +(6.59261 - 7.60828i) q^{5} +(21.3237 - 13.7039i) q^{7} +(-1.31727 - 2.88443i) q^{8} +O(q^{10})\)	\(q+(-0.0282746 - 0.196654i) q^{2} +(7.63807 - 2.24274i) q^{4} +(6.59261 - 7.60828i) q^{5} +(21.3237 - 13.7039i) q^{7} +(-1.31727 - 2.88443i) q^{8} +(-1.68261 - 1.08135i) q^{10} +(-2.01428 + 14.0097i) q^{11} +(-3.85568 - 2.47789i) q^{13} +(-3.29785 - 3.80592i) q^{14} +(53.0446 - 34.0897i) q^{16} +(-98.0272 - 28.7834i) q^{17} +(-66.4831 + 19.5212i) q^{19} +(33.2915 - 72.8981i) q^{20} +2.81201 q^{22} +(83.9685 + 71.5282i) q^{23} +(3.36596 + 23.4108i) q^{25} +(-0.378271 + 0.828297i) q^{26} +(132.137 - 152.495i) q^{28} +(202.341 + 59.4126i) q^{29} +(-117.310 - 256.874i) q^{31} +(-24.8161 - 28.6393i) q^{32} +(-2.88870 + 20.0913i) q^{34} +(36.3156 - 252.581i) q^{35} +(114.021 + 131.587i) q^{37} +(5.71872 + 12.5222i) q^{38} +(-30.6298 - 8.99373i) q^{40} +(66.9116 - 77.2201i) q^{41} +(53.4045 - 116.940i) q^{43} +(16.0348 + 111.524i) q^{44} +(11.6922 - 18.5352i) q^{46} -130.950 q^{47} +(124.415 - 272.430i) q^{49} +(4.50866 - 1.32386i) q^{50} +(-35.0072 - 10.2790i) q^{52} +(81.5152 - 52.3866i) q^{53} +(93.3100 + 107.685i) q^{55} +(-67.6170 - 43.4548i) q^{56} +(5.96264 - 41.4710i) q^{58} +(-232.487 - 149.411i) q^{59} +(190.268 + 416.628i) q^{61} +(-47.1985 + 30.3326i) q^{62} +(325.403 - 375.536i) q^{64} +(-44.2715 + 12.9993i) q^{65} +(49.8355 + 346.614i) q^{67} -813.292 q^{68} -50.6980 q^{70} +(109.006 + 758.154i) q^{71} +(-869.420 + 255.285i) q^{73} +(22.6533 - 26.1433i) q^{74} +(-464.022 + 298.209i) q^{76} +(149.035 + 326.341i) q^{77} +(377.358 + 242.513i) q^{79} +(90.3385 - 628.318i) q^{80} +(-17.0776 - 10.9751i) q^{82} +(281.892 + 325.321i) q^{83} +(-865.247 + 556.061i) q^{85} +(-24.5067 - 7.19581i) q^{86} +(43.0632 - 12.6445i) q^{88} +(138.980 - 304.324i) q^{89} -116.174 q^{91} +(801.777 + 358.018i) q^{92} +(3.70258 + 25.7520i) q^{94} +(-289.775 + 634.518i) q^{95} +(-557.372 + 643.241i) q^{97} +(-57.0924 - 16.7638i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 11 q^{2} - 27 q^{4} + 19 q^{5} - 19 q^{7} - 28 q^{8}+O(q^{10}) \) 50 * q + 11 * q^2 - 27 * q^4 + 19 * q^5 - 19 * q^7 - 28 * q^8	\( 50 q + 11 q^{2} - 27 q^{4} + 19 q^{5} - 19 q^{7} - 28 q^{8} + 47 q^{10} + 53 q^{11} - 65 q^{13} - 117 q^{14} - 499 q^{16} + 117 q^{17} + 73 q^{19} - 529 q^{20} + 310 q^{22} - 542 q^{23} + 246 q^{25} - 324 q^{26} - 677 q^{28} + 497 q^{29} - 471 q^{31} + 915 q^{32} - 2751 q^{34} + 737 q^{35} - 1071 q^{37} + 1504 q^{38} + 1479 q^{40} - 569 q^{41} + 1615 q^{43} - 2518 q^{44} + 4041 q^{46} - 2904 q^{47} + 1226 q^{49} - 1322 q^{50} - 2156 q^{52} - 391 q^{53} - 3323 q^{55} + 7028 q^{56} - 5639 q^{58} + 2445 q^{59} - 1059 q^{61} - 1468 q^{62} + 4570 q^{64} - 2641 q^{65} + 27 q^{67} - 8350 q^{68} + 9702 q^{70} - 3465 q^{71} + 435 q^{73} + 994 q^{74} - 3598 q^{76} + 5931 q^{77} - 2559 q^{79} + 14052 q^{80} - 3822 q^{82} + 3967 q^{83} + 299 q^{85} - 721 q^{86} + 5825 q^{88} - 3717 q^{89} + 7238 q^{91} - 9550 q^{92} + 6035 q^{94} - 4551 q^{95} - 2419 q^{97} + 5687 q^{98}+O(q^{100}) \) 50 * q + 11 * q^2 - 27 * q^4 + 19 * q^5 - 19 * q^7 - 28 * q^8 + 47 * q^10 + 53 * q^11 - 65 * q^13 - 117 * q^14 - 499 * q^16 + 117 * q^17 + 73 * q^19 - 529 * q^20 + 310 * q^22 - 542 * q^23 + 246 * q^25 - 324 * q^26 - 677 * q^28 + 497 * q^29 - 471 * q^31 + 915 * q^32 - 2751 * q^34 + 737 * q^35 - 1071 * q^37 + 1504 * q^38 + 1479 * q^40 - 569 * q^41 + 1615 * q^43 - 2518 * q^44 + 4041 * q^46 - 2904 * q^47 + 1226 * q^49 - 1322 * q^50 - 2156 * q^52 - 391 * q^53 - 3323 * q^55 + 7028 * q^56 - 5639 * q^58 + 2445 * q^59 - 1059 * q^61 - 1468 * q^62 + 4570 * q^64 - 2641 * q^65 + 27 * q^67 - 8350 * q^68 + 9702 * q^70 - 3465 * q^71 + 435 * q^73 + 994 * q^74 - 3598 * q^76 + 5931 * q^77 - 2559 * q^79 + 14052 * q^80 - 3822 * q^82 + 3967 * q^83 + 299 * q^85 - 721 * q^86 + 5825 * q^88 - 3717 * q^89 + 7238 * q^91 - 9550 * q^92 + 6035 * q^94 - 4551 * q^95 - 2419 * q^97 + 5687 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more