LMFDB - Embedded newform 207.4.i.a.100.3

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			100.3
Character	$\chi$	$=$	207.100
Dual form			207.4.i.a.118.3

$q$-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 $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{3}{11}\right)$	$1$

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	−0.994209	−	0.107463i	$-0.965727\pi$
$2$	−0.0282746	+	0.196654i	−0.00999659	+	0.0695278i	0.984212	+	0.176991i	$0.0566363\pi$
$3$		0			0
$3$		0			0
$4$	7.63807	+	2.24274i	0.954759	+	0.280342i
$5$	6.59261	+	7.60828i	0.589661	+	0.680505i	0.969653	−	0.244484i	$-0.0786187\pi$
$5$	6.59261	+	7.60828i	0.589661	+	0.680505i	−0.379992	+	0.924990i	$0.624073\pi$
$6$		0			0
$7$	21.3237	+	13.7039i	1.15137	+	0.739940i	0.969911	−	0.243458i	$-0.0782819\pi$
$7$	21.3237	+	13.7039i	1.15137	+	0.739940i	0.181458	+	0.983399i	$0.441918\pi$
$8$	−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	−0.998627	−	0.0523914i	$-0.983316\pi$
$11$	−2.01428	−	14.0097i	−0.0552118	−	0.384006i	0.943415	−	0.331615i	$-0.107593\pi$
$12$		0			0
$13$	−3.85568	+	2.47789i	−0.0822594	+	0.0528649i	−0.581124	−	0.813815i	$-0.697387\pi$
$13$	−3.85568	+	2.47789i	−0.0822594	+	0.0528649i	0.498865	+	0.866680i	$0.333751\pi$
$14$	−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	−0.892180	−	0.451679i	$-0.850825\pi$
$17$	−98.0272	+	28.7834i	−1.39853	+	0.410647i	−0.506354	+	0.862326i	$0.669007\pi$
$18$		0			0
$19$	−66.4831	−	19.5212i	−0.802751	−	0.235709i	−0.145478	−	0.989361i	$-0.546472\pi$
$19$	−66.4831	−	19.5212i	−0.802751	−	0.235709i	−0.657273	+	0.753653i	$0.728290\pi$
$20$	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	0.440000	−	0.897998i	$-0.354979\pi$
$29$	202.341	−	59.4126i	1.29565	−	0.380436i	0.855646	+	0.517562i	$0.173160\pi$
$30$		0			0
$31$	−117.310	+	256.874i	−0.679664	+	1.48826i	0.183335	+	0.983051i	$0.441311\pi$
$31$	−117.310	+	256.874i	−0.679664	+	1.48826i	−0.862999	+	0.505206i	$0.831417\pi$
$32$	−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	−0.443611	−	0.896219i	$-0.646303\pi$
$37$	114.021	−	131.587i	0.506619	−	0.584669i	0.950230	+	0.311550i	$0.100848\pi$
$38$	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	0.868738	−	0.495271i	$-0.164931\pi$
$41$	66.9116	+	77.2201i	0.254874	+	0.294140i	−0.613864	+	0.789412i	$0.710386\pi$
$42$		0			0
$43$	53.4045	+	116.940i	0.189398	+	0.414724i	0.980380	−	0.197115i	$-0.0631573\pi$
$43$	53.4045	+	116.940i	0.189398	+	0.414724i	−0.790982	+	0.611839i	$0.790430\pi$
$44$	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	0.641994	−	0.766710i	$-0.278108\pi$
$53$	81.5152	+	52.3866i	0.211264	+	0.135771i	−0.430730	+	0.902481i	$0.641744\pi$
$54$		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	−0.771399	−	0.636351i	$-0.780443\pi$
$59$	−232.487	+	149.411i	−0.513005	+	0.329688i	0.258395	+	0.966039i	$0.416807\pi$
$60$		0			0
$61$	190.268	−	416.628i	0.399365	−	0.874487i	−0.597969	−	0.801519i	$-0.704026\pi$
$61$	190.268	−	416.628i	0.399365	−	0.874487i	0.997334	−	0.0729682i	$-0.0232472\pi$
$62$	−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	−0.892585	−	0.450879i	$-0.851111\pi$
$67$	49.8355	−	346.614i	0.0908713	−	0.632024i	0.983456	−	0.181145i	$-0.0579803\pi$
$68$	−813.292			−1.45038
$69$		0			0
$70$	−50.6980			−0.0865652
$71$	109.006	−	758.154i	0.182206	−	1.26727i	−0.669325	−	0.742969i	$-0.733417\pi$
$71$	109.006	−	758.154i	0.182206	−	1.26727i	0.851532	−	0.524303i	$-0.175674\pi$
$72$		0			0
$73$	−869.420	−	255.285i	−1.39394	−	0.409299i	−0.503344	−	0.864086i	$-0.667897\pi$
$73$	−869.420	−	255.285i	−1.39394	−	0.409299i	−0.890600	+	0.454787i	$0.849715\pi$
$74$	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	−0.243609	−	0.969873i	$-0.578332\pi$
$79$	377.358	−	242.513i	0.537419	−	0.345378i	0.781029	+	0.624495i	$0.214695\pi$
$80$	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	−0.538093	−	0.842885i	$-0.680855\pi$
$83$	281.892	−	325.321i	0.372792	−	0.430225i	0.910885	+	0.412661i	$0.135401\pi$
$84$		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	0.974160	−	0.225860i	$-0.0725193\pi$
$89$	138.980	+	304.324i	0.165527	+	0.362453i	−0.808633	+	0.588314i	$0.799792\pi$
$90$		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	0.384910	−	0.922954i	$-0.374232\pi$
$97$	−557.372	−	643.241i	−0.583428	−	0.673312i	−0.968338	+	0.249642i	$0.919687\pi$
$98$	−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	−0.800397	−	0.599470i	$-0.795378\pi$
$101$	−94.5213	+	109.083i	−0.0931210	+	0.107467i	0.707276	+	0.706937i	$0.249924\pi$
$102$		0			0
$103$	−69.9195	−	486.301i	−0.0668871	−	0.465210i	−0.995546	−	0.0942756i	$-0.969947\pi$
$103$	−69.9195	−	486.301i	−0.0668871	−	0.465210i	0.928659	−	0.370935i	$-0.120963\pi$
$104$	−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	−0.812517	−	0.582938i	$-0.801903\pi$
$107$	177.227	−	388.074i	0.160124	−	0.350622i	0.972640	+	0.232316i	$0.0746304\pi$
$108$		0			0
$109$	−486.734	+	142.918i	−0.427713	+	0.125588i	−0.488502	−	0.872563i	$-0.662456\pi$
$109$	−486.734	+	142.918i	−0.427713	+	0.125588i	0.0607892	+	0.998151i	$0.480638\pi$
$110$	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	0.773581	+	0.633697i	$0.218463\pi$
$113$	−176.815	+	1229.77i	−0.147198	+	1.02378i	−0.920779	+	0.390085i	$0.872446\pi$
$114$		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	−0.893344	−	0.449374i	$-0.851647\pi$
$127$	−232.988	−	1620.47i	−0.162790	−	1.13223i	0.730554	−	0.682855i	$-0.239262\pi$
$128$	−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	0.323943	−	0.946076i	$-0.394991\pi$
$131$	−602.845	−	387.425i	−0.402067	−	0.258393i	−0.726010	+	0.687684i	$0.758628\pi$
$132$		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	−0.988454	−	0.151524i	$-0.951582\pi$
$149$	−150.465	−	1046.50i	−0.0827284	−	0.575389i	0.905725	−	0.423865i	$-0.139327\pi$
$150$		0			0
$151$	937.996	−	602.813i	0.505517	−	0.324876i	−0.262903	−	0.964822i	$-0.584680\pi$
$151$	937.996	−	602.813i	0.505517	−	0.324876i	0.768419	+	0.639947i	$0.221044\pi$
$152$	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	0.552404	−	0.833576i	$-0.313710\pi$
$157$	1114.32	+	327.195i	0.566451	+	0.166325i	0.0140467	+	0.999901i	$0.495529\pi$
$158$	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	0.858613	+	0.512625i	$0.171327\pi$
$163$	−228.173	+	1586.98i	−0.109643	+	0.762586i	−0.968256	+	0.249961i	$0.919582\pi$
$164$	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	0.0264906	−	0.999649i	$-0.491567\pi$
$167$	1271.62	−	373.381i	0.589227	−	0.173013i	0.562736	+	0.826636i	$0.309749\pi$
$168$		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	0.994069	+	0.108749i	$0.0346844\pi$
$173$	161.341	+	1122.15i	0.0709049	+	0.493154i	−0.923164	+	0.384405i	$0.874406\pi$
$174$		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	0.961876	+	0.273485i	$0.0881765\pi$
$179$	2624.02	+	3028.28i	1.09569	+	1.26449i	0.133813	+	0.991007i	$0.457278\pi$
$180$		0			0
$181$	1159.55	+	2539.06i	0.476181	+	1.04269i	0.983496	+	0.180930i	$0.0579108\pi$
$181$	1159.55	+	2539.06i	0.476181	+	1.04269i	−0.507315	+	0.861761i	$0.669362\pi$
$182$	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	−0.218033	−	0.975941i	$-0.569964\pi$
$191$	−3157.98	−	2029.51i	−1.19635	−	0.768850i	−0.978322	+	0.207091i	$0.933600\pi$
$192$		0			0
$193$	478.077	−	551.730i	0.178304	−	0.205774i	−0.659561	−	0.751651i	$-0.729258\pi$
$193$	478.077	−	551.730i	0.178304	−	0.205774i	0.837865	+	0.545877i	$0.183803\pi$
$194$	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	−0.811527	−	0.584315i	$-0.801363\pi$
$197$	−1706.40	+	1096.63i	−0.617136	+	0.396609i	0.194391	+	0.980924i	$0.437727\pi$
$198$		0			0
$199$	1620.58	−	3548.57i	0.577285	−	1.26408i	−0.365542	−	0.930795i	$-0.619116\pi$
$199$	1620.58	−	3548.57i	0.577285	−	1.26408i	0.942827	−	0.333283i	$-0.108156\pi$
$200$	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	0.179436	−	0.983770i	$-0.442573\pi$
$211$	−617.526	−	181.322i	−0.201480	−	0.0591598i	−0.380915	+	0.924610i	$0.624391\pi$
$212$	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	0.544200	−	0.838955i	$-0.316833\pi$
$223$	23.7383	+	15.2557i	0.00712840	+	0.00458114i	−0.537072	+	0.843537i	$0.680470\pi$
$224$	−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	−0.516707	−	0.856162i	$-0.672842\pi$
$227$	−2822.88	−	6181.25i	−0.825380	−	1.80733i	−0.308673	−	0.951168i	$-0.599885\pi$
$228$		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	0.989451	−	0.144868i	$-0.0462759\pi$
$233$	825.179	+	1806.89i	0.232014	+	0.508040i	−0.757437	+	0.652908i	$0.773549\pi$
$234$		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	−0.128150	−	0.991755i	$-0.540904\pi$
$239$	3220.98	−	3717.20i	0.871747	−	1.00605i	0.999898	−	0.0142954i	$-0.00455053\pi$
$240$		0			0
$241$	−680.468	−	4732.76i	−0.181879	−	1.26500i	−0.852315	−	0.523029i	$-0.824802\pi$
$241$	−680.468	−	4732.76i	−0.181879	−	1.26500i	0.670436	−	0.741967i	$-0.266107\pi$
$242$	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	−0.835874	−	0.548922i	$-0.815038\pi$
$251$	480.334	−	3340.80i	0.120790	−	0.840116i	0.956664	−	0.291194i	$-0.0940525\pi$
$252$		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	0.965452	−	0.260582i	$-0.0839144\pi$
$257$	6743.49	+	1980.07i	1.63676	+	0.480596i	0.671308	+	0.741178i	$0.265733\pi$
$258$		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	−0.581991	+	0.813195i	$0.697726\pi$
$263$	−6668.41	+	4285.53i	−1.56347	+	1.00478i	−0.981476	+	0.191585i	$0.938637\pi$
$264$		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	0.695674	−	0.718358i	$-0.255106\pi$
$269$	1461.34	+	939.148i	0.331225	+	0.212866i	−0.364448	+	0.931224i	$0.618742\pi$
$270$		0			0
$271$	−650.787	−	751.048i	−0.145876	−	0.168350i	0.678109	−	0.734961i	$-0.262800\pi$
$271$	−650.787	−	751.048i	−0.145876	−	0.168350i	−0.823985	+	0.566611i	$0.808254\pi$
$272$	−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	0.385748	−	0.922604i	$-0.373944\pi$
$281$	−2743.18	−	3165.79i	−0.582364	−	0.672084i	−0.968111	+	0.250521i	$0.919398\pi$
$282$		0			0
$283$	−4755.76	−	3056.34i	−0.998943	−	0.641981i	−0.0644340	−	0.997922i	$-0.520524\pi$
$283$	−4755.76	−	3056.34i	−0.998943	−	0.641981i	−0.934509	+	0.355941i	$0.884161\pi$
$284$	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	−0.991794	−	0.127845i	$-0.959194\pi$
$293$	−8812.11	+	2587.47i	−1.75703	+	0.515910i	−0.765232	+	0.643754i	$0.777376\pi$
$294$		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	−0.996081	−	0.0884410i	$-0.971812\pi$
$307$	−1489.72	+	3262.04i	−0.276948	+	0.606431i	0.719134	+	0.694872i	$0.244539\pi$
$308$	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	−0.953406	−	0.301691i	$-0.902449\pi$
$311$	−677.976	−	4715.42i	−0.123616	−	0.859766i	0.829790	−	0.558075i	$-0.188460\pi$
$312$		0			0
$313$	−2183.58	+	2519.98i	−0.394323	+	0.455073i	−0.917845	−	0.396939i	$-0.870072\pi$
$313$	−2183.58	+	2519.98i	−0.394323	+	0.455073i	0.523522	+	0.852012i	$0.324618\pi$
$314$	−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	0.433202	−	0.901297i	$-0.357384\pi$
$317$	−2938.12	−	3390.77i	−0.520572	−	0.600772i	−0.953774	+	0.300525i	$0.902838\pi$
$318$		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	−0.730777	−	0.682616i	$-0.760842\pi$
$331$	294.424	−	339.783i	0.0488912	−	0.0564235i	0.779668	+	0.626193i	$0.215388\pi$
$332$	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	0.263265	+	0.964724i	$0.415201\pi$
$337$	−3948.39	+	8645.76i	−0.638226	+	1.39752i	−0.901491	+	0.432797i	$0.857527\pi$
$338$	−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	0.120806	+	0.992676i	$0.461452\pi$
$347$	−1776.12	+	12353.2i	−0.274776	+	1.91111i	−0.395582	+	0.918431i	$0.629457\pi$
$348$		0			0
$349$	6700.85	+	1967.55i	1.02776	+	0.301778i	0.751800	−	0.659391i	$-0.229186\pi$
$349$	6700.85	+	1967.55i	1.02776	+	0.301778i	0.275961	+	0.961169i	$0.411004\pi$
$350$	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	−0.969254	−	0.246062i	$-0.920863\pi$
$353$	−985.333	+	2157.58i	−0.148567	+	0.325315i	0.820688	+	0.571377i	$0.193591\pi$
$354$		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	−0.217081	−	0.976154i	$-0.569654\pi$
$359$	5305.83	−	6123.26i	0.780031	−	0.900203i	0.997112	+	0.0759502i	$0.0241990\pi$
$360$		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	0.750653	−	0.660697i	$-0.229739\pi$
$373$	−73.1032	−	84.3656i	−0.0101478	−	0.0117112i	−0.760801	+	0.648985i	$0.775194\pi$
$374$	−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	0.991144	+	0.132793i	$0.0423944\pi$
$379$	572.266	+	3980.20i	0.0775603	+	0.539444i	−0.913584	+	0.406651i	$0.866697\pi$
$380$	−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	0.647909	+	0.761718i	$0.275644\pi$
$383$	−2638.77	+	5778.09i	−0.352049	+	0.770879i	−0.999958	+	0.00916183i	$0.997084\pi$
$384$		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	0.924302	+	0.381663i	$0.124648\pi$
$389$	−537.721	+	3739.93i	−0.0700862	+	0.487460i	−0.994388	+	0.105797i	$0.966261\pi$
$390$		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	−0.769830	−	0.638249i	$-0.779659\pi$
$397$	−8482.77	+	2490.77i	−1.07239	+	0.314882i	−0.302558	+	0.953131i	$0.597841\pi$
$398$	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	−0.829023	−	0.559214i	$-0.811103\pi$
$401$	−5337.82	+	3430.41i	−0.664733	+	0.427198i	0.164290	+	0.986412i	$0.447467\pi$
$402$		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	0.990487	+	0.137605i	$0.0439403\pi$
$409$	8153.48	+	9409.62i	0.985730	+	1.13759i	−0.00475698	+	0.999989i	$0.501514\pi$
$410$	−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	0.157993	−	0.987440i	$-0.449498\pi$
$419$	−7220.58	−	8332.99i	−0.841881	−	0.971583i	−0.999874	+	0.0158574i	$0.994952\pi$
$420$		0			0
$421$	7865.76	+	5055.02i	0.910579	+	0.585194i	0.909910	−	0.414806i	$-0.136151\pi$
$421$	7865.76	+	5055.02i	0.910579	+	0.585194i	0.000669316		1.00000i	$0.499787\pi$
$422$	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	0.276878	−	0.960905i	$-0.410700\pi$
$431$	9210.03	−	2704.31i	1.02931	−	0.302232i	0.752429	+	0.658673i	$0.228882\pi$
$432$		0			0
$433$	2726.13	+	800.465i	0.302562	+	0.0888404i	0.429490	−	0.903072i	$-0.358693\pi$
$433$	2726.13	+	800.465i	0.302562	+	0.0888404i	−0.126927	+	0.991912i	$0.540512\pi$
$434$	−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	0.867231	+	0.497906i	$0.165897\pi$
$439$	−967.153	+	6726.69i	−0.105147	+	0.731316i	−0.972378	+	0.233410i	$0.925012\pi$
$440$	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	−0.632088	−	0.774897i	$-0.717802\pi$
$443$	−6945.43	+	2039.36i	−0.744893	+	0.218720i	−0.112805	+	0.993617i	$0.535984\pi$
$444$		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	0.755606	+	0.655026i	$0.227342\pi$
$449$	2046.96	+	14236.9i	0.215149	+	1.49640i	−0.540457	+	0.841372i	$0.681749\pi$
$450$		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	0.999301	−	0.0373770i	$-0.0119003\pi$
$457$	3093.53	+	6773.89i	0.316650	+	0.693368i	−0.682651	+	0.730745i	$0.739173\pi$
$458$	−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	0.883151	−	0.469088i	$-0.155417\pi$
$463$	−495.167	−	1084.26i	−0.0497027	−	0.108834i	−0.932854	+	0.360254i	$0.882690\pi$
$464$	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	0.978672	+	0.205431i	$0.0658597\pi$
$467$	15865.5	+	10196.1i	1.57209	+	1.01032i	0.593422	+	0.804892i	$0.297777\pi$
$468$		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	0.460648	−	0.887583i	$-0.347617\pi$
$479$	3861.10	+	1133.72i	0.368305	+	0.108144i	−0.0923423	+	0.995727i	$0.529435\pi$
$480$		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	0.869404	−	0.494101i	$-0.164503\pi$
$487$	14333.1	+	4208.57i	1.33366	+	0.391599i	0.464258	+	0.885700i	$0.346321\pi$
$488$	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	0.336989	+	0.941509i	$0.390592\pi$
$491$	−6476.08	+	14180.6i	−0.595237	+	1.30339i	−0.932225	+	0.361878i	$0.882136\pi$
$492$		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	0.378877	−	0.925447i	$-0.376310\pi$
$499$	−3405.89	−	2188.83i	−0.305548	−	0.196364i	−0.684425	+	0.729083i	$0.739947\pi$
$500$	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	0.812008	−	0.583646i	$-0.198374\pi$
$503$	−1814.39	−	3972.96i	−0.160834	−	0.352178i	−0.972842	+	0.231468i	$0.925647\pi$
$504$		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	0.987785	−	0.155825i	$-0.0498037\pi$
$509$	2562.65	+	5611.42i	0.223158	+	0.488648i	−0.764626	+	0.644474i	$0.777076\pi$
$510$		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	−0.0204262	+	0.999791i	$0.506502\pi$
$521$	−9069.37	+	19859.2i	−0.762642	+	1.66995i	−0.742216	+	0.670161i	$0.766225\pi$
$522$		0			0
$523$	−12436.8	+	3651.79i	−1.03982	+	0.305318i	−0.756697	−	0.653766i	$-0.773188\pi$
$523$	−12436.8	+	3651.79i	−1.03982	+	0.305318i	−0.283122	+	0.959084i	$0.591370\pi$
$524$	−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	0.979284	+	0.202494i	$0.0649046\pi$
$541$	1217.02	+	8464.57i	0.0967169	+	0.672681i	−0.882567	+	0.470187i	$0.844186\pi$
$542$	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	0.456261	−	0.889846i	$-0.349188\pi$
$547$	−6261.79	−	7226.49i	−0.489460	−	0.564867i	−0.945721	+	0.324979i	$0.894643\pi$
$548$	−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	0.677758	−	0.735285i	$-0.262952\pi$
$557$	−1925.82	−	2222.51i	−0.146498	−	0.169068i	−0.824256	+	0.566217i	$0.808406\pi$
$558$		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	0.943475	+	0.331444i	$0.107536\pi$
$563$	1757.94	+	12226.8i	0.131596	+	0.915269i	−0.811879	+	0.583826i	$0.801555\pi$
$564$		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	−0.214866	−	0.976644i	$-0.568931\pi$
$569$	1796.91	−	527.620i	0.132391	−	0.0388735i	0.347257	+	0.937770i	$0.387113\pi$
$570$		0			0
$571$	−19543.7	−	5738.55i	−1.43236	−	0.420580i	−0.528694	−	0.848812i	$-0.677318\pi$
$571$	−19543.7	−	5738.55i	−1.43236	−	0.420580i	−0.903668	+	0.428233i	$0.859136\pi$
$572$	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	−0.953845	−	0.300299i	$-0.902913\pi$
$577$	637.099	−	4431.12i	0.0459667	−	0.319705i	0.999812	−	0.0194060i	$-0.00617751\pi$
$578$	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	−0.988091	−	0.153867i	$-0.950827\pi$
$587$	−1185.74	−	8246.98i	−0.0833741	−	0.579880i	0.904717	−	0.426012i	$-0.140082\pi$
$588$		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	0.197043	−	0.980395i	$-0.436866\pi$
$593$	−11572.8	−	13355.7i	−0.801415	−	0.924882i	−0.998458	+	0.0555130i	$0.982321\pi$
$594$		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	0.959687	+	0.281070i	$0.0906892\pi$
$601$	8009.89	+	17539.2i	0.543644	+	1.19041i	−0.416043	+	0.909345i	$0.636583\pi$
$602$	−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	−0.486788	−	0.873520i	$-0.661831\pi$
$607$	6686.61	−	7716.76i	0.447119	−	0.516003i	0.933906	+	0.357518i	$0.116377\pi$
$608$	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	0.129671	+	0.991557i	$0.458608\pi$
$613$	−10694.0	+	23416.7i	−0.704614	+	1.54289i	−0.834285	+	0.551333i	$0.814119\pi$
$614$	−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	−0.225908	−	0.974149i	$-0.572535\pi$
$617$	−14446.5	−	4241.88i	−0.942618	−	0.276777i	−0.716710	+	0.697371i	$0.754353\pi$
$618$		0			0
$619$	2614.42	−	18183.7i	0.169761	−	1.18072i	−0.709616	−	0.704589i	$-0.751131\pi$
$619$	2614.42	−	18183.7i	0.169761	−	1.18072i	0.879377	−	0.476126i	$-0.157960\pi$
$620$	−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	0.250510	−	0.968114i	$-0.419402\pi$
$631$	19578.6	−	12582.4i	1.23520	−	0.793817i	0.984693	+	0.174297i	$0.0557653\pi$
$632$	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	0.990670	+	0.136281i	$0.0435151\pi$
$641$	7220.43	+	15810.5i	0.444914	+	0.974225i	−0.545756	+	0.837944i	$0.683758\pi$
$642$		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	0.978556	−	0.205980i	$-0.0660381\pi$
$647$	2996.35	+	6561.09i	0.182069	+	0.398676i	−0.796487	+	0.604655i	$0.793311\pi$
$648$		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	−0.518352	−	0.855167i	$-0.673454\pi$
$653$	6706.04	−	7739.18i	0.401880	−	0.463794i	0.920232	+	0.391373i	$0.128000\pi$
$654$		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	−0.370144	−	0.928974i	$-0.620692\pi$
$659$	9715.89	−	21274.8i	0.574321	−	1.25759i	0.944465	−	0.328613i	$-0.106581\pi$
$660$		0			0
$661$	−13921.0	+	4087.59i	−0.819161	+	0.240527i	−0.664355	−	0.747417i	$-0.731294\pi$
$661$	−13921.0	+	4087.59i	−0.819161	+	0.240527i	−0.154807	+	0.987945i	$0.549475\pi$
$662$	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	−0.729580	−	0.683895i	$-0.760285\pi$
$673$	−16998.2	+	4991.13i	−0.973601	+	0.285875i	−0.244020	+	0.969770i	$0.578466\pi$
$674$	−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	−0.702417	−	0.711766i	$-0.747896\pi$
$677$	−6108.28	+	3925.56i	−0.346766	+	0.222853i	0.355651	+	0.934619i	$0.384259\pi$
$678$		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	−0.999997	−	0.00251218i	$-0.999200\pi$
$683$	−25305.5	−	16262.8i	−1.41770	−	0.911098i	−0.417699	−	0.908586i	$-0.637163\pi$
$684$		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	0.997796	+	0.0663551i	$0.0211370\pi$
$701$	1097.12	+	7630.63i	0.0591122	+	0.411134i	−0.938684	+	0.344779i	$0.887954\pi$
$702$		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	0.999467	−	0.0326459i	$-0.0103933\pi$
$709$	34408.5	+	10103.3i	1.82262	+	0.535170i	0.823155	+	0.567816i	$0.192212\pi$
$710$	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	−0.0234260	−	0.999726i	$-0.507457\pi$
$719$	9588.78	−	2815.52i	0.497359	−	0.146038i	0.520785	+	0.853688i	$0.325639\pi$
$720$		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	−0.644555	−	0.764558i	$-0.722957\pi$
$727$	3997.84	−	4613.76i	0.203950	−	0.235371i	0.848505	+	0.529187i	$0.177503\pi$
$728$	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	0.791962	−	0.610570i	$-0.209060\pi$
$733$	−3732.90	−	8173.91i	−0.188101	−	0.411883i	−0.980063	+	0.198687i	$0.936332\pi$
$734$	−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	0.995883	+	0.0906528i	$0.0288954\pi$
$739$	8281.43	+	18133.8i	0.412229	+	0.902656i	−0.583654	+	0.812003i	$0.698377\pi$
$740$	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	0.583102	−	0.812399i	$-0.301839\pi$
$743$	1748.75	+	1123.85i	0.0863465	+	0.0554915i	−0.496755	+	0.867891i	$0.665475\pi$
$744$		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	0.399240	+	0.916847i	$0.369274\pi$
$751$	−11424.6	+	25016.4i	−0.555113	+	1.21553i	−0.954353	+	0.298681i	$0.903453\pi$
$752$	−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	−0.999995	−	0.00302919i	$-0.999036\pi$
$757$	−825.894	+	5744.22i	−0.0396534	+	0.275796i	0.960342	+	0.278825i	$0.0899449\pi$
$758$	−798.904			−0.0382817
$759$		0			0
$760$	2211.93			0.105573
$761$	−680.424	+	4732.45i	−0.0324118	+	0.225429i	−0.999589	−	0.0286748i	$-0.990871\pi$
$761$	−680.424	+	4732.45i	−0.0324118	+	0.225429i	0.967177	+	0.254103i	$0.0817804\pi$
$762$		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	−0.759172	−	0.650890i	$-0.774396\pi$
$769$	−10288.7	+	6612.17i	−0.482472	+	0.310066i	0.276699	+	0.960957i	$0.410759\pi$
$770$	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	−0.135308	−	0.990804i	$-0.543203\pi$
$773$	18583.1	−	21446.0i	0.864667	−	0.997878i	0.999975	−	0.00707485i	$-0.00225201\pi$
$774$		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	0.846438	−	0.532488i	$-0.178743\pi$
$787$	4391.55	+	5068.12i	0.198910	+	0.229554i	−0.647528	+	0.762041i	$0.724197\pi$
$788$	−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	0.531948	+	0.846777i	$0.321460\pi$
$797$	−10268.1	+	22484.0i	−0.456355	+	0.999279i	−0.988303	+	0.152502i	$0.951267\pi$
$798$		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	0.744095	−	0.668074i	$-0.232881\pi$
$809$	23214.6	+	6816.43i	1.00888	+	0.296234i	0.264784	+	0.964308i	$0.414699\pi$
$810$		0			0
$811$	3566.64	−	1047.26i	0.154429	−	0.0453443i	−0.203605	−	0.979053i	$-0.565266\pi$
$811$	3566.64	−	1047.26i	0.154429	−	0.0453443i	0.358033	+	0.933709i	$0.383447\pi$
$812$	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	0.268074	−	0.963398i	$-0.413613\pi$
$821$	−11689.2	−	7512.21i	−0.496902	−	0.319340i	−0.764976	+	0.644059i	$0.777249\pi$
$822$		0			0
$823$	29717.0	+	34295.3i	1.25865	+	1.45256i	0.838309	+	0.545195i	$0.183544\pi$
$823$	29717.0	+	34295.3i	1.25865	+	1.45256i	0.420342	+	0.907366i	$0.361910\pi$
$824$	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	0.937592	+	0.347737i	$0.113050\pi$
$839$	3303.81	+	22978.5i	0.135948	+	0.945538i	−0.801644	+	0.597801i	$0.796041\pi$
$840$		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	0.603125	+	0.797647i	$0.293922\pi$
$853$	−4989.85	+	34705.2i	−0.200292	+	1.39306i	−0.803417	+	0.595416i	$0.796987\pi$
$854$	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	0.180700	−	0.983538i	$-0.442164\pi$
$857$	21687.7	−	6368.08i	0.864455	−	0.253827i	0.683755	+	0.729711i	$0.260346\pi$
$858$		0			0
$859$	11079.1	−	24259.8i	0.440062	−	0.963601i	−0.551525	−	0.834158i	$-0.685954\pi$
$859$	11079.1	−	24259.8i	0.440062	−	0.963601i	0.991587	−	0.129443i	$-0.0413188\pi$
$860$	−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	−0.949603	−	0.313455i	$-0.898514\pi$
$863$	−3214.06	−	22354.2i	−0.126776	−	0.881747i	0.822827	−	0.568292i	$-0.192396\pi$
$864$		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	−0.951237	−	0.308460i	$-0.900186\pi$
$877$	−14581.2	−	31928.4i	−0.561428	−	1.22936i	0.389810	−	0.920895i	$-0.372541\pi$
$878$	−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	−0.999426	−	0.0338914i	$-0.989210\pi$
$881$	−37797.3	−	24290.9i	−1.44543	−	0.928922i	−0.446005	−	0.895030i	$-0.647154\pi$
$882$		0			0
$883$	10339.9	−	11932.9i	0.394072	−	0.454784i	−0.523693	−	0.851907i	$-0.675446\pi$
$883$	10339.9	−	11932.9i	0.394072	−	0.454784i	0.917765	+	0.397123i	$0.129991\pi$
$884$	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	−0.377790	−	0.925891i	$-0.623316\pi$
$887$	8123.03	−	5220.36i	0.307491	−	0.197613i	0.685281	+	0.728279i	$0.259679\pi$
$888$		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	−0.819701	−	0.572792i	$-0.805860\pi$
$907$	−17459.8	+	11220.7i	−0.639188	+	0.410781i	0.180513	+	0.983573i	$0.442224\pi$
$908$	−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	−0.262146	−	0.965028i	$-0.584430\pi$
$911$	20082.5	−	23176.5i	0.730367	−	0.842889i	0.992513	+	0.122140i	$0.0389756\pi$
$912$		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	0.150093	−	0.988672i	$-0.452043\pi$
$929$	31354.9	−	36185.5i	1.10734	−	1.27794i	0.957248	−	0.289268i	$-0.0934119\pi$
$930$		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	−0.750099	−	0.661326i	$-0.769994\pi$
$937$	−29358.4	+	8620.40i	−1.02358	+	0.300551i	−0.273484	+	0.961877i	$0.588176\pi$
$938$	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	0.889108	+	0.457697i	$0.151326\pi$
$941$	−2682.59	+	18657.8i	−0.0929331	+	0.646364i	−0.982041	+	0.188666i	$0.939583\pi$
$942$		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	0.380136	−	0.924930i	$-0.375877\pi$
$947$	5824.75	+	1710.30i	0.199872	+	0.0586878i	−0.180264	+	0.983618i	$0.557695\pi$
$948$		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	−0.858744	−	0.512406i	$-0.828754\pi$
$953$	−22046.5	+	14168.4i	−0.749378	+	0.481596i	0.109365	+	0.994002i	$0.465118\pi$
$954$		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	0.549622	−	0.835414i	$-0.314772\pi$
$971$	−10756.7	−	12413.9i	−0.355508	−	0.410278i	−0.905130	+	0.425136i	$0.860226\pi$
$972$		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	−0.989172	−	0.146758i	$-0.953116\pi$
$977$	−2486.26	−	17292.3i	−0.0814150	−	0.566254i	0.907757	−	0.419496i	$-0.137793\pi$
$978$		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	−0.541347	−	0.840799i	$-0.682085\pi$
$983$	−16710.1	+	4906.53i	−0.542187	+	0.159200i	−0.000839647		1.00000i	$0.500267\pi$
$984$		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	0.951686	+	0.307074i	$0.0993498\pi$
$991$	−1496.28	+	10406.9i	−0.0479627	+	0.333588i	−0.999648	+	0.0265143i	$0.991559\pi$
$992$	−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	0.166682	+	0.986011i	$0.446695\pi$
$997$	−21647.6	+	47401.6i	−0.687649	+	1.50574i	−0.854331	+	0.519730i	$0.826033\pi$
$998$	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.100.3		50
3.2	odd	2		23.4.c.a.8.3	yes	50
23.3	even	11	inner	207.4.i.a.118.3		50
69.26	odd	22		23.4.c.a.3.3	✓	50
69.53	even	22		529.4.a.m.1.13		25
69.62	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	69.26	odd	22
23.4.c.a.8.3	yes	50	3.2	odd	2
207.4.i.a.100.3		50	1.1	even	1	trivial
207.4.i.a.118.3		50	23.3	even	11	inner
529.4.a.m.1.13		25	69.53	even	22
529.4.a.n.1.13		25	69.62	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

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