LMFDB - Embedded newform 210.3.f.a.181.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(181,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("210.181");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.f (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.3317760000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 7x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.4
Root			$1.72286 - 0.178197i$ of defining polynomial
Character	$\chi$	$=$	210.181
Dual form			210.3.f.a.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} +2.23607i q^{5} -2.44949i q^{6} +(-6.70141 + 2.02265i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} +2.23607i q^{5} -2.44949i q^{6} +(-6.70141 + 2.02265i) q^{7} -2.82843 q^{8} -3.00000 q^{9} -3.16228i q^{10} -5.00806 q^{11} +3.46410i q^{12} -9.06929i q^{13} +(9.47723 - 2.86045i) q^{14} -3.87298 q^{15} +4.00000 q^{16} +19.7410i q^{17} +4.24264 q^{18} -25.6863i q^{19} +4.47214i q^{20} +(-3.50333 - 11.6072i) q^{21} +7.08246 q^{22} -40.9686 q^{23} -4.89898i q^{24} -5.00000 q^{25} +12.8259i q^{26} -5.19615i q^{27} +(-13.4028 + 4.04529i) q^{28} -22.3071 q^{29} +5.47723 q^{30} -15.9015i q^{31} -5.65685 q^{32} -8.67421i q^{33} -27.9179i q^{34} +(-4.52277 - 14.9848i) q^{35} -6.00000 q^{36} -44.7506 q^{37} +36.3259i q^{38} +15.7085 q^{39} -6.32456i q^{40} +27.0829i q^{41} +(4.95445 + 16.4150i) q^{42} -30.6690 q^{43} -10.0161 q^{44} -6.70820i q^{45} +57.9383 q^{46} +58.1430i q^{47} +6.92820i q^{48} +(40.8178 - 27.1092i) q^{49} +7.07107 q^{50} -34.1924 q^{51} -18.1386i q^{52} +65.6199 q^{53} +7.34847i q^{54} -11.1984i q^{55} +(18.9545 - 5.72091i) q^{56} +44.4900 q^{57} +31.5469 q^{58} -32.5746i q^{59} -7.74597 q^{60} +83.5349i q^{61} +22.4881i q^{62} +(20.1042 - 6.06794i) q^{63} +8.00000 q^{64} +20.2796 q^{65} +12.2672i q^{66} +72.0585 q^{67} +39.4819i q^{68} -70.9597i q^{69} +(6.39617 + 21.1917i) q^{70} -24.8675 q^{71} +8.48528 q^{72} +67.8725i q^{73} +63.2870 q^{74} -8.66025i q^{75} -51.3726i q^{76} +(33.5610 - 10.1295i) q^{77} -22.2151 q^{78} +30.4452 q^{79} +8.94427i q^{80} +9.00000 q^{81} -38.3009i q^{82} +72.4623i q^{83} +(-7.00665 - 23.2144i) q^{84} -44.1421 q^{85} +43.3725 q^{86} -38.6370i q^{87} +14.1649 q^{88} -113.756i q^{89} +9.48683i q^{90} +(18.3440 + 60.7770i) q^{91} -81.9372 q^{92} +27.5422 q^{93} -82.2267i q^{94} +57.4363 q^{95} -9.79796i q^{96} +103.804i q^{97} +(-57.7251 + 38.3381i) q^{98} +15.0242 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{4} - 24 q^{9}+O(q^{10}) $ 8 * q + 16 * q^4 - 24 * q^9	$ 8 q + 16 q^{4} - 24 q^{9} - 16 q^{11} + 32 q^{14} + 32 q^{16} + 96 q^{22} - 40 q^{25} - 144 q^{29} - 80 q^{35} - 48 q^{36} - 48 q^{37} - 48 q^{39} - 48 q^{42} - 64 q^{43} - 32 q^{44} + 128 q^{46} - 24 q^{49} + 128 q^{53} + 64 q^{56} + 144 q^{57} + 224 q^{58} + 64 q^{64} + 80 q^{65} - 192 q^{67} + 176 q^{71} - 160 q^{74} + 192 q^{77} - 96 q^{78} - 288 q^{79} + 72 q^{81} - 240 q^{85} - 64 q^{86} + 192 q^{88} + 64 q^{91} + 336 q^{93} + 80 q^{95} + 48 q^{99}+O(q^{100}) $ 8 * q + 16 * q^4 - 24 * q^9 - 16 * q^11 + 32 * q^14 + 32 * q^16 + 96 * q^22 - 40 * q^25 - 144 * q^29 - 80 * q^35 - 48 * q^36 - 48 * q^37 - 48 * q^39 - 48 * q^42 - 64 * q^43 - 32 * q^44 + 128 * q^46 - 24 * q^49 + 128 * q^53 + 64 * q^56 + 144 * q^57 + 224 * q^58 + 64 * q^64 + 80 * q^65 - 192 * q^67 + 176 * q^71 - 160 * q^74 + 192 * q^77 - 96 * q^78 - 288 * q^79 + 72 * q^81 - 240 * q^85 - 64 * q^86 + 192 * q^88 + 64 * q^91 + 336 * q^93 + 80 * q^95 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	2.00000			0.500000
$5$			2.23607i			0.447214i
$5$			2.23607i			0.447214i
$6$		−	2.44949i		−	0.408248i
$7$	−6.70141	+	2.02265i	−0.957344	+	0.288949i
$7$	−6.70141	+	2.02265i	−0.957344	+	0.288949i
$8$	−2.82843			−0.353553
$9$	−3.00000			−0.333333
$10$		−	3.16228i		−	0.316228i
$11$	−5.00806			−0.455278			−0.227639	−	0.973746i	$-0.573101\pi$
$11$	−5.00806			−0.455278			−0.227639	+	0.973746i	$0.573101\pi$
$12$			3.46410i			0.288675i
$13$		−	9.06929i		−	0.697638i	−0.937190	−	0.348819i	$-0.886583\pi$
$13$		−	9.06929i		−	0.697638i	0.937190	−	0.348819i	$-0.113417\pi$
$14$	9.47723	−	2.86045i	0.676945	−	0.204318i
$15$	−3.87298			−0.258199
$16$	4.00000			0.250000
$17$			19.7410i			1.16123i	0.814177	+	0.580617i	$0.197188\pi$
$17$			19.7410i			1.16123i	−0.814177	+	0.580617i	$0.802812\pi$
$18$	4.24264			0.235702
$19$		−	25.6863i		−	1.35191i	−0.736942	−	0.675956i	$-0.763731\pi$
$19$		−	25.6863i		−	1.35191i	0.736942	−	0.675956i	$-0.236269\pi$
$20$			4.47214i			0.223607i
$21$	−3.50333	−	11.6072i	−0.166825	−	0.552723i
$22$	7.08246			0.321930
$23$	−40.9686			−1.78124			−0.890621	−	0.454746i	$-0.849730\pi$
$23$	−40.9686			−1.78124			−0.890621	+	0.454746i	$0.849730\pi$
$24$		−	4.89898i		−	0.204124i
$25$	−5.00000			−0.200000
$26$			12.8259i			0.493304i
$27$		−	5.19615i		−	0.192450i
$28$	−13.4028	+	4.04529i	−0.478672	+	0.144475i
$29$	−22.3071			−0.769209			−0.384604	−	0.923081i	$-0.625662\pi$
$29$	−22.3071			−0.769209			−0.384604	+	0.923081i	$0.625662\pi$
$30$	5.47723			0.182574
$31$		−	15.9015i		−	0.512952i	−0.966551	−	0.256476i	$-0.917439\pi$
$31$		−	15.9015i		−	0.512952i	0.966551	−	0.256476i	$-0.0825614\pi$
$32$	−5.65685			−0.176777
$33$		−	8.67421i		−	0.262855i
$34$		−	27.9179i		−	0.821116i
$35$	−4.52277	−	14.9848i	−0.129222	−	0.428137i
$36$	−6.00000			−0.166667
$37$	−44.7506			−1.20948			−0.604738	−	0.796424i	$-0.706722\pi$
$37$	−44.7506			−1.20948			−0.604738	+	0.796424i	$0.706722\pi$
$38$			36.3259i			0.955946i
$39$	15.7085			0.402781
$40$		−	6.32456i		−	0.158114i
$41$			27.0829i			0.660557i	0.943883	+	0.330279i	$0.107143\pi$
$41$			27.0829i			0.660557i	−0.943883	+	0.330279i	$0.892857\pi$
$42$	4.95445	+	16.4150i	0.117963	+	0.390834i
$43$	−30.6690			−0.713233			−0.356616	−	0.934251i	$-0.616070\pi$
$43$	−30.6690			−0.713233			−0.356616	+	0.934251i	$0.616070\pi$
$44$	−10.0161			−0.227639
$45$		−	6.70820i		−	0.149071i
$46$	57.9383			1.25953
$47$			58.1430i			1.23709i	0.785751	+	0.618543i	$0.212277\pi$
$47$			58.1430i			1.23709i	−0.785751	+	0.618543i	$0.787723\pi$
$48$			6.92820i			0.144338i
$49$	40.8178	−	27.1092i	0.833016	−	0.553248i
$50$	7.07107			0.141421
$51$	−34.1924			−0.670438
$52$		−	18.1386i		−	0.348819i
$53$	65.6199			1.23811			0.619055	−	0.785347i	$-0.287516\pi$
$53$	65.6199			1.23811			0.619055	+	0.785347i	$0.287516\pi$
$54$			7.34847i			0.136083i
$55$		−	11.1984i		−	0.203606i
$56$	18.9545	−	5.72091i	0.338472	−	0.102159i
$57$	44.4900			0.780526
$58$	31.5469			0.543913
$59$		−	32.5746i		−	0.552112i	−0.961142	−	0.276056i	$-0.910973\pi$
$59$		−	32.5746i		−	0.552112i	0.961142	−	0.276056i	$-0.0890275\pi$
$60$	−7.74597			−0.129099
$61$			83.5349i			1.36943i	0.728813	+	0.684713i	$0.240072\pi$
$61$			83.5349i			1.36943i	−0.728813	+	0.684713i	$0.759928\pi$
$62$			22.4881i			0.362712i
$63$	20.1042	−	6.06794i	0.319115	−	0.0963165i
$64$	8.00000			0.125000
$65$	20.2796			0.311993
$66$			12.2672i			0.185866i
$67$	72.0585			1.07550			0.537750	−	0.843104i	$-0.319274\pi$
$67$	72.0585			1.07550			0.537750	+	0.843104i	$0.319274\pi$
$68$			39.4819i			0.580617i
$69$		−	70.9597i		−	1.02840i
$70$	6.39617	+	21.1917i	0.0913738	+	0.302739i
$71$	−24.8675			−0.350246			−0.175123	−	0.984547i	$-0.556032\pi$
$71$	−24.8675			−0.350246			−0.175123	+	0.984547i	$0.556032\pi$
$72$	8.48528			0.117851
$73$			67.8725i			0.929760i	0.885374	+	0.464880i	$0.153902\pi$
$73$			67.8725i			0.929760i	−0.885374	+	0.464880i	$0.846098\pi$
$74$	63.2870			0.855229
$75$		−	8.66025i		−	0.115470i
$76$		−	51.3726i		−	0.675956i
$77$	33.5610	−	10.1295i	0.435858	−	0.131552i
$78$	−22.2151			−0.284809
$79$	30.4452			0.385383			0.192691	−	0.981259i	$-0.438278\pi$
$79$	30.4452			0.385383			0.192691	+	0.981259i	$0.438278\pi$
$80$			8.94427i			0.111803i
$81$	9.00000			0.111111
$82$		−	38.3009i		−	0.467085i
$83$			72.4623i			0.873040i	0.899695	+	0.436520i	$0.143789\pi$
$83$			72.4623i			0.873040i	−0.899695	+	0.436520i	$0.856211\pi$
$84$	−7.00665	−	23.2144i	−0.0834125	−	0.276362i
$85$	−44.1421			−0.519319
$86$	43.3725			0.504332
$87$		−	38.6370i		−	0.444103i
$88$	14.1649			0.160965
$89$		−	113.756i		−	1.27815i	−0.769143	−	0.639076i	$-0.779317\pi$
$89$		−	113.756i		−	1.27815i	0.769143	−	0.639076i	$-0.220683\pi$
$90$			9.48683i			0.105409i
$91$	18.3440	+	60.7770i	0.201582	+	0.667880i
$92$	−81.9372			−0.890621
$93$	27.5422			0.296153
$94$		−	82.2267i		−	0.874752i
$95$	57.4363			0.604593
$96$		−	9.79796i		−	0.102062i
$97$			103.804i			1.07014i	0.844806	+	0.535072i	$0.179716\pi$
$97$			103.804i			1.07014i	−0.844806	+	0.535072i	$0.820284\pi$
$98$	−57.7251	+	38.3381i	−0.589032	+	0.391206i
$99$	15.0242			0.151759
$100$	−10.0000			−0.100000
$101$			155.379i			1.53841i	0.639003	+	0.769204i	$0.279347\pi$
$101$			155.379i			1.53841i	−0.639003	+	0.769204i	$0.720653\pi$
$102$	48.3553			0.474071
$103$		−	65.9471i		−	0.640264i	−0.947373	−	0.320132i	$-0.896273\pi$
$103$		−	65.9471i		−	0.640264i	0.947373	−	0.320132i	$-0.103727\pi$
$104$			25.6518i			0.246652i
$105$	25.9545	−	7.83368i	0.247185	−	0.0746064i
$106$	−92.8005			−0.875476
$107$	−136.269			−1.27354			−0.636771	−	0.771053i	$-0.719730\pi$
$107$	−136.269			−1.27354			−0.636771	+	0.771053i	$0.719730\pi$
$108$		−	10.3923i		−	0.0962250i
$109$	166.003			1.52296			0.761482	−	0.648186i	$-0.224472\pi$
$109$	166.003			1.52296			0.761482	+	0.648186i	$0.224472\pi$
$110$			15.8369i			0.143971i
$111$		−	77.5104i		−	0.698292i
$112$	−26.8056	+	8.09058i	−0.239336	+	0.0722374i
$113$	−25.5037			−0.225696			−0.112848	−	0.993612i	$-0.535997\pi$
$113$	−25.5037			−0.225696			−0.112848	+	0.993612i	$0.535997\pi$
$114$	−62.9184			−0.551915
$115$		−	91.6085i		−	0.796596i
$116$	−44.6141			−0.384604
$117$			27.2079i			0.232546i
$118$			46.0674i			0.390402i
$119$	−39.9290	−	132.292i	−0.335538	−	1.11170i
$120$	10.9545			0.0912871
$121$	−95.9194			−0.792722
$122$		−	118.136i		−	0.968330i
$123$	−46.9089			−0.381373
$124$		−	31.8030i		−	0.256476i
$125$		−	11.1803i		−	0.0894427i
$126$	−28.4317	+	8.58136i	−0.225648	+	0.0681060i
$127$	−230.306			−1.81344			−0.906718	−	0.421738i	$-0.861420\pi$
$127$	−230.306			−1.81344			−0.906718	+	0.421738i	$0.861420\pi$
$128$	−11.3137			−0.0883883
$129$		−	53.1203i		−	0.411785i
$130$	−28.6796			−0.220612
$131$			40.9127i			0.312311i	0.987733	+	0.156155i	$0.0499101\pi$
$131$			40.9127i			0.312311i	−0.987733	+	0.156155i	$0.950090\pi$
$132$		−	17.3484i		−	0.131427i
$133$	51.9543	+	172.135i	0.390634	+	1.29424i
$134$	−101.906			−0.760493
$135$	11.6190			0.0860663
$136$		−	55.8359i		−	0.410558i
$137$	158.300			1.15547			0.577737	−	0.816223i	$-0.303936\pi$
$137$	158.300			1.15547			0.577737	+	0.816223i	$0.303936\pi$
$138$			100.352i			0.727189i
$139$			141.584i			1.01859i	0.860592	+	0.509296i	$0.170094\pi$
$139$			141.584i			1.01859i	−0.860592	+	0.509296i	$0.829906\pi$
$140$	−9.04555	−	29.9696i	−0.0646111	−	0.214069i
$141$	−100.707			−0.714232
$142$	35.1679			0.247661
$143$			45.4195i			0.317619i
$144$	−12.0000			−0.0833333
$145$		−	49.8801i		−	0.344001i
$146$		−	95.9861i		−	0.657439i
$147$	46.9545	+	70.6985i	0.319418	+	0.480942i
$148$	−89.5013			−0.604738
$149$	−121.456			−0.815139			−0.407569	−	0.913174i	$-0.633624\pi$
$149$	−121.456			−0.815139			−0.407569	+	0.913174i	$0.633624\pi$
$150$			12.2474i			0.0816497i
$151$	−219.093			−1.45094			−0.725472	−	0.688251i	$-0.758379\pi$
$151$	−219.093			−1.45094			−0.725472	+	0.688251i	$0.758379\pi$
$152$			72.6519i			0.477973i
$153$		−	59.2229i		−	0.387078i
$154$	−47.4625	+	14.3253i	−0.308198	+	0.0930215i
$155$	35.5569			0.229399
$156$	31.4169			0.201391
$157$		−	57.2815i		−	0.364850i	−0.983220	−	0.182425i	$-0.941605\pi$
$157$		−	57.2815i		−	0.364850i	0.983220	−	0.182425i	$-0.0583947\pi$
$158$	−43.0560			−0.272507
$159$			113.657i			0.714824i
$160$		−	12.6491i		−	0.0790569i
$161$	274.547	−	82.8649i	1.70526	−	0.514689i
$162$	−12.7279			−0.0785674
$163$	−8.52297			−0.0522882			−0.0261441	−	0.999658i	$-0.508323\pi$
$163$	−8.52297			−0.0522882			−0.0261441	+	0.999658i	$0.508323\pi$
$164$			54.1657i			0.330279i
$165$	19.3961			0.117552
$166$		−	102.477i		−	0.617333i
$167$		−	258.148i		−	1.54580i	−0.634529	−	0.772899i	$-0.718806\pi$
$167$		−	258.148i		−	1.54580i	0.634529	−	0.772899i	$-0.281194\pi$
$168$	9.90890	+	32.8301i	0.0589816	+	0.195417i
$169$	86.7480			0.513301
$170$	62.4264			0.367214
$171$			77.0589i			0.450637i
$172$	−61.3380			−0.356616
$173$		−	327.250i		−	1.89162i	−0.324725	−	0.945808i	$-0.605272\pi$
$173$		−	327.250i		−	1.89162i	0.324725	−	0.945808i	$-0.394728\pi$
$174$			54.6409i			0.314028i
$175$	33.5071	−	10.1132i	0.191469	−	0.0577899i
$176$	−20.0322			−0.113819
$177$	56.4208			0.318762
$178$			160.875i			0.903791i
$179$	−167.569			−0.936141			−0.468071	−	0.883691i	$-0.655051\pi$
$179$	−167.569			−0.936141			−0.468071	+	0.883691i	$0.655051\pi$
$180$		−	13.4164i		−	0.0745356i
$181$			147.957i			0.817442i	0.912659	+	0.408721i	$0.134025\pi$
$181$			147.957i			0.817442i	−0.912659	+	0.408721i	$0.865975\pi$
$182$	−25.9423	−	85.9517i	−0.142540	−	0.472262i
$183$	−144.687			−0.790638
$184$	115.877			0.629764
$185$		−	100.065i		−	0.540894i
$186$	−38.9506			−0.209412
$187$		−	98.8638i		−	0.528684i
$188$			116.286i			0.618543i
$189$	10.5100	+	34.8216i	0.0556083	+	0.184241i
$190$	−81.2273			−0.427512
$191$	49.4939			0.259130			0.129565	−	0.991571i	$-0.458642\pi$
$191$	49.4939			0.259130			0.129565	+	0.991571i	$0.458642\pi$
$192$			13.8564i			0.0721688i
$193$	172.674			0.894686			0.447343	−	0.894362i	$-0.352370\pi$
$193$	172.674			0.894686			0.447343	+	0.894362i	$0.352370\pi$
$194$		−	146.801i		−	0.756707i
$195$			35.1252i			0.180129i
$196$	81.6356	−	54.2183i	0.416508	−	0.276624i
$197$	75.6444			0.383982			0.191991	−	0.981397i	$-0.438506\pi$
$197$	75.6444			0.383982			0.191991	+	0.981397i	$0.438506\pi$
$198$	−21.2474			−0.107310
$199$			147.620i			0.741808i	0.928671	+	0.370904i	$0.120952\pi$
$199$			147.620i			0.741808i	−0.928671	+	0.370904i	$0.879048\pi$
$200$	14.1421			0.0707107
$201$			124.809i			0.620940i
$202$		−	219.739i		−	1.08782i
$203$	149.489	−	45.1193i	0.736398	−	0.222262i
$204$	−68.3847			−0.335219
$205$	−60.5591			−0.295410
$206$			93.2634i			0.452735i
$207$	122.906			0.593747
$208$		−	36.2772i		−	0.174409i
$209$			128.638i			0.615495i
$210$	−36.7051	+	11.0785i	−0.174786	+	0.0527547i
$211$	156.882			0.743518			0.371759	−	0.928329i	$-0.378755\pi$
$211$	156.882			0.743518			0.371759	+	0.928329i	$0.378755\pi$
$212$	131.240			0.619055
$213$		−	43.0717i		−	0.202215i
$214$	192.713			0.900530
$215$		−	68.5780i		−	0.318967i
$216$			14.6969i			0.0680414i
$217$	32.1631	+	106.563i	0.148217	+	0.491072i
$218$	−234.764			−1.07690
$219$	−117.559			−0.536797
$220$		−	22.3967i		−	0.101803i
$221$	179.037			0.810120
$222$			109.616i			0.493767i
$223$		−	60.4029i		−	0.270865i	−0.990787	−	0.135433i	$-0.956758\pi$
$223$		−	60.4029i		−	0.270865i	0.990787	−	0.135433i	$-0.0432424\pi$
$224$	37.9089	−	11.4418i	0.169236	−	0.0510795i
$225$	15.0000			0.0666667
$226$	36.0677			0.159592
$227$			313.611i			1.38155i	0.723071	+	0.690773i	$0.242730\pi$
$227$			313.611i			1.38155i	−0.723071	+	0.690773i	$0.757270\pi$
$228$	88.9800			0.390263
$229$			110.368i			0.481957i	0.970530	+	0.240979i	$0.0774684\pi$
$229$			110.368i			0.481957i	−0.970530	+	0.240979i	$0.922532\pi$
$230$			129.554i			0.563278i
$231$	17.5449	+	58.1294i	0.0759517	+	0.251643i
$232$	63.0939			0.271956
$233$	38.4067			0.164835			0.0824177	−	0.996598i	$-0.473736\pi$
$233$	38.4067			0.164835			0.0824177	+	0.996598i	$0.473736\pi$
$234$		−	38.4777i		−	0.164435i
$235$	−130.012			−0.553242
$236$		−	65.1492i		−	0.276056i
$237$			52.7327i			0.222501i
$238$	56.4681	+	187.090i	0.237261	+	0.786091i
$239$	−125.129			−0.523552			−0.261776	−	0.965129i	$-0.584308\pi$
$239$	−125.129			−0.523552			−0.261776	+	0.965129i	$0.584308\pi$
$240$	−15.4919			−0.0645497
$241$		−	154.625i		−	0.641598i	−0.947147	−	0.320799i	$-0.896049\pi$
$241$		−	154.625i		−	0.641598i	0.947147	−	0.320799i	$-0.103951\pi$
$242$	135.650			0.560539
$243$			15.5885i			0.0641500i
$244$			167.070i			0.684713i
$245$	60.6179	+	91.2714i	0.247420	+	0.372536i
$246$	66.3392			0.269671
$247$	−232.957			−0.943144
$248$			44.9763i			0.181356i
$249$	−125.508			−0.504050
$250$			15.8114i			0.0632456i
$251$		−	152.655i		−	0.608185i	−0.952642	−	0.304093i	$-0.901647\pi$
$251$		−	152.655i		−	0.608185i	0.952642	−	0.304093i	$-0.0983532\pi$
$252$	40.2085	−	12.1359i	0.159557	−	0.0481582i
$253$	205.173			0.810960
$254$	325.702			1.28229
$255$		−	76.4564i		−	0.299829i
$256$	16.0000			0.0625000
$257$		−	20.1517i		−	0.0784113i	−0.999231	−	0.0392057i	$-0.987517\pi$
$257$		−	20.1517i		−	0.0784113i	0.999231	−	0.0392057i	$-0.0124827\pi$
$258$			75.1234i			0.291176i
$259$	299.892	−	90.5147i	1.15789	−	0.349478i
$260$	40.5591			0.155997
$261$	66.9212			0.256403
$262$		−	57.8593i		−	0.220837i
$263$	−320.699			−1.21939			−0.609693	−	0.792637i	$-0.708707\pi$
$263$	−320.699			−1.21939			−0.609693	+	0.792637i	$0.708707\pi$
$264$			24.5344i			0.0929332i
$265$			146.730i			0.553700i
$266$	−73.4745	−	243.435i	−0.276220	−	0.915169i
$267$	197.030			0.737942
$268$	144.117			0.537750
$269$			39.2134i			0.145775i	0.997340	+	0.0728874i	$0.0232214\pi$
$269$			39.2134i			0.145775i	−0.997340	+	0.0728874i	$0.976779\pi$
$270$	−16.4317			−0.0608581
$271$			299.071i			1.10358i	0.833982	+	0.551792i	$0.186056\pi$
$271$			299.071i			1.10358i	−0.833982	+	0.551792i	$0.813944\pi$
$272$			78.9639i			0.290308i
$273$	−105.269	+	31.7727i	−0.385600	+	0.116383i
$274$	−223.870			−0.817044
$275$	25.0403			0.0910556
$276$		−	141.919i		−	0.514200i
$277$	−438.966			−1.58472			−0.792358	−	0.610056i	$-0.791147\pi$
$277$	−438.966			−1.58472			−0.792358	+	0.610056i	$0.791147\pi$
$278$		−	200.230i		−	0.720253i
$279$			47.7045i			0.170984i
$280$	12.7923	+	42.3834i	0.0456869	+	0.151369i
$281$	−199.479			−0.709889			−0.354944	−	0.934887i	$-0.615500\pi$
$281$	−199.479			−0.709889			−0.354944	+	0.934887i	$0.615500\pi$
$282$	142.421			0.505038
$283$		−	541.179i		−	1.91229i	−0.292889	−	0.956147i	$-0.594616\pi$
$283$		−	541.179i		−	1.91229i	0.292889	−	0.956147i	$-0.405384\pi$
$284$	−49.7349			−0.175123
$285$			99.4827i			0.349062i
$286$		−	64.2329i		−	0.224591i
$287$	−54.7790	−	181.493i	−0.190868	−	0.632381i
$288$	16.9706			0.0589256
$289$	−100.706			−0.348462
$290$			70.5411i			0.243245i
$291$	−179.794			−0.617848
$292$			135.745i			0.464880i
$293$		−	378.757i		−	1.29269i	−0.763047	−	0.646343i	$-0.776298\pi$
$293$		−	378.757i		−	1.29269i	0.763047	−	0.646343i	$-0.223702\pi$
$294$	−66.4036	−	99.9828i	−0.225863	−	0.340078i
$295$	72.8390			0.246912
$296$	126.574			0.427615
$297$			26.0226i			0.0876183i
$298$	171.764			0.576390
$299$			371.556i			1.24266i
$300$		−	17.3205i		−	0.0577350i
$301$	205.526	−	62.0326i	0.682810	−	0.206088i
$302$	309.844			1.02597
$303$	−269.125			−0.888200
$304$		−	102.745i		−	0.337978i
$305$	−186.790			−0.612426
$306$			83.7538i			0.273705i
$307$		−	140.210i		−	0.456710i	−0.973578	−	0.228355i	$-0.926665\pi$
$307$		−	140.210i		−	0.456710i	0.973578	−	0.228355i	$-0.0733346\pi$
$308$	67.1221	−	20.2591i	0.217929	−	0.0657761i
$309$	114.224			0.369656
$310$	−50.2850			−0.162210
$311$			249.886i			0.803491i	0.915751	+	0.401745i	$0.131596\pi$
$311$			249.886i			0.803491i	−0.915751	+	0.401745i	$0.868404\pi$
$312$	−44.4303			−0.142405
$313$		−	517.894i		−	1.65461i	−0.561750	−	0.827307i	$-0.689872\pi$
$313$		−	517.894i		−	1.65461i	0.561750	−	0.827307i	$-0.310128\pi$
$314$			81.0082i			0.257988i
$315$	13.5683	+	44.9544i	0.0430740	+	0.142712i
$316$	60.8904			0.192691
$317$	−180.043			−0.567959			−0.283980	−	0.958830i	$-0.591655\pi$
$317$	−180.043			−0.567959			−0.283980	+	0.958830i	$0.591655\pi$
$318$		−	160.735i		−	0.505457i
$319$	111.715			0.350204
$320$			17.8885i			0.0559017i
$321$		−	236.025i		−	0.735280i
$322$	−388.268	+	117.189i	−1.20580	+	0.363940i
$323$	507.073			1.56988
$324$	18.0000			0.0555556
$325$			45.3465i			0.139528i
$326$	12.0533			0.0369733
$327$			287.526i			0.879283i
$328$		−	76.6019i		−	0.233542i
$329$	−117.603	−	389.640i	−0.357455	−	1.18432i
$330$	−27.4303			−0.0831220
$331$	81.0283			0.244799			0.122399	−	0.992481i	$-0.460941\pi$
$331$	81.0283			0.244799			0.122399	+	0.992481i	$0.460941\pi$
$332$			144.925i			0.436520i
$333$	134.252			0.403159
$334$			365.077i			1.09304i
$335$			161.128i			0.480978i
$336$	−14.0133	−	46.4287i	−0.0417063	−	0.138181i
$337$	−372.937			−1.10664			−0.553318	−	0.832970i	$-0.686639\pi$
$337$	−372.937			−1.10664			−0.553318	+	0.832970i	$0.686639\pi$
$338$	−122.680			−0.362959
$339$		−	44.1737i		−	0.130306i
$340$	−88.2843			−0.259660
$341$			79.6356i			0.233536i
$342$		−	108.978i		−	0.318649i
$343$	−218.705	+	264.230i	−0.637623	+	0.770349i
$344$	86.7451			0.252166
$345$	158.671			0.459915
$346$			462.801i			1.33758i
$347$	415.231			1.19663			0.598316	−	0.801260i	$-0.295837\pi$
$347$	415.231			1.19663			0.598316	+	0.801260i	$0.295837\pi$
$348$		−	77.2739i		−	0.222051i
$349$			536.207i			1.53641i	0.640203	+	0.768206i	$0.278850\pi$
$349$			536.207i			1.53641i	−0.640203	+	0.768206i	$0.721150\pi$
$350$	−47.3861	+	14.3023i	−0.135389	+	0.0408636i
$351$	−47.1254			−0.134260
$352$	28.3298			0.0804825
$353$			416.230i			1.17912i	0.807724	+	0.589560i	$0.200699\pi$
$353$			416.230i			1.17912i	−0.807724	+	0.589560i	$0.799301\pi$
$354$	−79.7911			−0.225399
$355$		−	55.6053i		−	0.156635i
$356$		−	227.511i		−	0.639076i
$357$	229.137	−	69.1590i	0.641840	−	0.193723i
$358$	236.979			0.661952
$359$	−270.563			−0.753659			−0.376829	−	0.926283i	$-0.622986\pi$
$359$	−270.563			−0.753659			−0.376829	+	0.926283i	$0.622986\pi$
$360$			18.9737i			0.0527046i
$361$	−298.787			−0.827664
$362$		−	209.243i		−	0.578019i
$363$		−	166.137i		−	0.457678i
$364$	36.6879	+	121.554i	0.100791	+	0.333940i
$365$	−151.767			−0.415801
$366$	204.618			0.559066
$367$		−	605.024i		−	1.64857i	−0.566178	−	0.824283i	$-0.691578\pi$
$367$		−	605.024i		−	1.64857i	0.566178	−	0.824283i	$-0.308422\pi$
$368$	−163.874			−0.445311
$369$		−	81.2486i		−	0.220186i
$370$			141.514i			0.382470i
$371$	−439.746	+	132.726i	−1.18530	+	0.357751i
$372$	55.0844			0.148076
$373$	−21.5124			−0.0576739			−0.0288370	−	0.999584i	$-0.509180\pi$
$373$	−21.5124			−0.0576739			−0.0288370	+	0.999584i	$0.509180\pi$
$374$			139.815i			0.373836i
$375$	19.3649			0.0516398
$376$		−	164.453i		−	0.437376i
$377$			202.309i			0.536629i
$378$	−14.8634	−	49.2451i	−0.0393210	−	0.130278i
$379$	449.862			1.18697			0.593486	−	0.804844i	$-0.297751\pi$
$379$	449.862			1.18697			0.593486	+	0.804844i	$0.297751\pi$
$380$	114.873			0.302297
$381$		−	398.902i		−	1.04699i
$382$	−69.9949			−0.183233
$383$		−	560.756i		−	1.46412i	−0.681242	−	0.732058i	$-0.738560\pi$
$383$		−	560.756i		−	1.46412i	0.681242	−	0.732058i	$-0.261440\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	22.6503	+	75.0448i	0.0588320	+	0.194921i
$386$	−244.199			−0.632639
$387$	92.0071			0.237744
$388$			207.608i			0.535072i
$389$	−582.222			−1.49671			−0.748357	−	0.663296i	$-0.769157\pi$
$389$	−582.222			−1.49671			−0.748357	+	0.663296i	$0.769157\pi$
$390$		−	49.6746i		−	0.127371i
$391$		−	808.759i		−	2.06844i
$392$	−115.450	+	76.6763i	−0.294516	+	0.195603i
$393$	−70.8629			−0.180313
$394$	−106.977			−0.271516
$395$			68.0776i			0.172348i
$396$	30.0483			0.0758796
$397$			726.563i			1.83013i	0.403304	+	0.915066i	$0.367862\pi$
$397$			726.563i			1.83013i	−0.403304	+	0.915066i	$0.632138\pi$
$398$		−	208.766i		−	0.524538i
$399$	−298.146	+	89.9875i	−0.747232	+	0.225533i
$400$	−20.0000			−0.0500000
$401$	−32.7962			−0.0817860			−0.0408930	−	0.999164i	$-0.513020\pi$
$401$	−32.7962			−0.0817860			−0.0408930	+	0.999164i	$0.513020\pi$
$402$		−	176.507i		−	0.439071i
$403$	−144.215			−0.357855
$404$			310.758i			0.769204i
$405$			20.1246i			0.0496904i
$406$	−211.409	+	63.8083i	−0.520712	+	0.157163i
$407$	224.114			0.550648
$408$	96.7106			0.237036
$409$		−	637.739i		−	1.55926i	−0.626238	−	0.779632i	$-0.715406\pi$
$409$		−	637.739i		−	1.55926i	0.626238	−	0.779632i	$-0.284594\pi$
$410$	85.6435			0.208887
$411$			274.184i			0.667114i
$412$		−	131.894i		−	0.320132i
$413$	65.8869	+	218.296i	0.159532	+	0.528561i
$414$	−173.815			−0.419843
$415$	−162.031			−0.390435
$416$			51.3037i			0.123326i
$417$	−245.231			−0.588084
$418$		−	181.922i		−	0.435221i
$419$			344.535i			0.822280i	0.911572	+	0.411140i	$0.134869\pi$
$419$			344.535i			0.822280i	−0.911572	+	0.411140i	$0.865131\pi$
$420$	51.9089	−	15.6674i	0.123593	−	0.0373032i
$421$	290.412			0.689814			0.344907	−	0.938637i	$-0.387910\pi$
$421$	290.412			0.689814			0.344907	+	0.938637i	$0.387910\pi$
$422$	−221.865			−0.525746
$423$		−	174.429i		−	0.412362i
$424$	−185.601			−0.437738
$425$		−	98.7048i		−	0.232247i
$426$			60.9126i			0.142987i
$427$	−168.962	−	559.802i	−0.395695	−	1.31101i
$428$	−272.538			−0.636771
$429$	−78.6689			−0.183377
$430$			96.9839i			0.225544i
$431$	−214.780			−0.498329			−0.249164	−	0.968461i	$-0.580156\pi$
$431$	−214.780			−0.498329			−0.249164	+	0.968461i	$0.580156\pi$
$432$		−	20.7846i		−	0.0481125i
$433$			425.041i			0.981619i	0.871267	+	0.490809i	$0.163299\pi$
$433$			425.041i			0.981619i	−0.871267	+	0.490809i	$0.836701\pi$
$434$	−45.4855	−	150.702i	−0.104805	−	0.347240i
$435$	86.3949			0.198609
$436$	332.006			0.761482
$437$			1052.33i			2.40808i
$438$	166.253			0.379573
$439$			204.200i			0.465149i	0.972579	+	0.232574i	$0.0747149\pi$
$439$			204.200i			0.465149i	−0.972579	+	0.232574i	$0.925285\pi$
$440$			31.6737i			0.0719857i
$441$	−122.453	+	81.3275i	−0.277672	+	0.184416i
$442$	−253.196			−0.572841
$443$	276.367			0.623854			0.311927	−	0.950106i	$-0.399026\pi$
$443$	276.367			0.623854			0.311927	+	0.950106i	$0.399026\pi$
$444$		−	155.021i		−	0.349146i
$445$	254.365			0.571607
$446$			85.4227i			0.191531i
$447$		−	210.367i		−	0.470620i
$448$	−53.6113	+	16.1812i	−0.119668	+	0.0361187i
$449$	195.290			0.434945			0.217472	−	0.976066i	$-0.430219\pi$
$449$	195.290			0.434945			0.217472	+	0.976066i	$0.430219\pi$
$450$	−21.2132			−0.0471405
$451$		−	135.632i		−	0.300737i
$452$	−51.0074			−0.112848
$453$		−	379.480i		−	0.837703i
$454$		−	443.513i		−	0.976901i
$455$	−135.902	+	41.0184i	−0.298685	+	0.0901502i
$456$	−125.837			−0.275958
$457$	10.3428			0.0226319			0.0113159	−	0.999936i	$-0.496398\pi$
$457$	10.3428			0.0226319			0.0113159	+	0.999936i	$0.496398\pi$
$458$		−	156.084i		−	0.340795i
$459$	102.577			0.223479
$460$		−	183.217i		−	0.398298i
$461$		−	527.572i		−	1.14441i	−0.820111	−	0.572204i	$-0.806088\pi$
$461$		−	527.572i		−	1.14441i	0.820111	−	0.572204i	$-0.193912\pi$
$462$	−24.8122	−	82.2074i	−0.0537060	−	0.177938i
$463$	797.897			1.72332			0.861660	−	0.507486i	$-0.169425\pi$
$463$	797.897			1.72332			0.861660	+	0.507486i	$0.169425\pi$
$464$	−89.2282			−0.192302
$465$			61.5863i			0.132444i
$466$	−54.3152			−0.116556
$467$		−	169.651i		−	0.363278i	−0.983365	−	0.181639i	$-0.941860\pi$
$467$		−	169.651i		−	0.363278i	0.983365	−	0.181639i	$-0.0581403\pi$
$468$			54.4157i			0.116273i
$469$	−482.894	+	145.749i	−1.02962	+	0.310765i
$470$	183.864			0.391201
$471$	99.2144			0.210646
$472$			92.1348i			0.195201i
$473$	153.592			0.324719
$474$		−	74.5753i		−	0.157332i
$475$			128.432i			0.270382i
$476$	−79.8580	−	264.585i	−0.167769	−	0.555850i
$477$	−196.860			−0.412704
$478$	176.959			0.370207
$479$			704.272i			1.47030i	0.677906	+	0.735148i	$0.262887\pi$
$479$			704.272i			1.47030i	−0.677906	+	0.735148i	$0.737113\pi$
$480$	21.9089			0.0456435
$481$			405.857i			0.843777i
$482$			218.673i			0.453678i
$483$	143.526	+	475.530i	0.297156	+	0.984534i
$484$	−191.839			−0.396361
$485$	−232.113			−0.478583
$486$		−	22.0454i		−	0.0453609i
$487$	−66.7966			−0.137159			−0.0685797	−	0.997646i	$-0.521847\pi$
$487$	−66.7966			−0.137159			−0.0685797	+	0.997646i	$0.521847\pi$
$488$		−	236.273i		−	0.484165i
$489$		−	14.7622i		−	0.0301886i
$490$	−85.7267	−	129.077i	−0.174952	−	0.263423i
$491$	546.122			1.11227			0.556133	−	0.831094i	$-0.312285\pi$
$491$	546.122			1.11227			0.556133	+	0.831094i	$0.312285\pi$
$492$	−93.8178			−0.190687
$493$		−	440.363i		−	0.893231i
$494$	329.450			0.666904
$495$			33.5951i			0.0678688i
$496$		−	63.6060i		−	0.128238i
$497$	166.647	−	50.2981i	0.335306	−	0.101203i
$498$	177.496			0.356417
$499$	714.060			1.43098			0.715491	−	0.698622i	$-0.246203\pi$
$499$	714.060			1.43098			0.715491	+	0.698622i	$0.246203\pi$
$500$		−	22.3607i		−	0.0447214i
$501$	447.126			0.892467
$502$			215.886i			0.430052i
$503$			878.751i			1.74702i	0.486807	+	0.873510i	$0.338162\pi$
$503$			878.751i			1.74702i	−0.486807	+	0.873510i	$0.661838\pi$
$504$	−56.8634	+	17.1627i	−0.112824	+	0.0340530i
$505$	−347.438			−0.687997
$506$	−290.158			−0.573435
$507$			150.252i			0.296355i
$508$	−460.613			−0.906718
$509$		−	510.558i		−	1.00306i	−0.865140	−	0.501530i	$-0.832771\pi$
$509$		−	510.558i		−	1.00306i	0.865140	−	0.501530i	$-0.167229\pi$
$510$			108.126i			0.212011i
$511$	−137.282	−	454.841i	−0.268654	−	0.890100i
$512$	−22.6274			−0.0441942
$513$	−133.470			−0.260175
$514$			28.4988i			0.0554452i
$515$	147.462			0.286335
$516$		−	106.241i		−	0.205893i
$517$		−	291.184i		−	0.563218i
$518$	−424.112	+	128.007i	−0.818749	+	0.247118i
$519$	566.813			1.09213
$520$	−57.3592			−0.110306
$521$			17.2889i			0.0331841i	0.999862	+	0.0165921i	$0.00528166\pi$
$521$			17.2889i			0.0331841i	−0.999862	+	0.0165921i	$0.994718\pi$
$522$	−94.6408			−0.181304
$523$		−	287.840i		−	0.550364i	−0.961392	−	0.275182i	$-0.911262\pi$
$523$		−	287.840i		−	0.550364i	0.961392	−	0.275182i	$-0.0887381\pi$
$524$			81.8254i			0.156155i
$525$	17.5166	+	58.0359i	0.0333650	+	0.110545i
$526$	453.536			0.862237
$527$	313.911			0.595657
$528$		−	34.6968i		−	0.0657137i
$529$	1149.42			2.17282
$530$		−	207.508i		−	0.391525i
$531$			97.7238i			0.184037i
$532$	103.909	+	344.269i	0.195317	+	0.647122i
$533$	245.622			0.460830
$534$	−278.643			−0.521804
$535$		−	304.707i		−	0.569545i
$536$	−203.812			−0.380247
$537$		−	290.239i		−	0.540481i
$538$		−	55.4562i		−	0.103078i
$539$	−204.418	+	135.764i	−0.379254	+	0.251882i
$540$	23.2379			0.0430331
$541$	−228.274			−0.421949			−0.210974	−	0.977492i	$-0.567664\pi$
$541$	−228.274			−0.421949			−0.210974	+	0.977492i	$0.567664\pi$
$542$		−	422.950i		−	0.780351i
$543$	−256.269			−0.471950
$544$		−	111.672i		−	0.205279i
$545$			371.194i			0.681090i
$546$	148.873	−	44.9334i	0.272661	−	0.0822955i
$547$	876.996			1.60328			0.801642	−	0.597805i	$-0.203960\pi$
$547$	876.996			1.60328			0.801642	+	0.597805i	$0.203960\pi$
$548$	316.600			0.577737
$549$		−	250.605i		−	0.456475i
$550$	−35.4123			−0.0643860
$551$			572.986i			1.03990i
$552$			200.704i			0.363595i
$553$	−204.026	+	61.5799i	−0.368944	+	0.111356i
$554$	620.792			1.12056
$555$	173.318			0.312286
$556$			283.168i			0.509296i
$557$	561.224			1.00758			0.503792	−	0.863825i	$-0.331938\pi$
$557$	561.224			1.00758			0.503792	+	0.863825i	$0.331938\pi$
$558$		−	67.4644i		−	0.120904i
$559$			278.146i			0.497578i
$560$	−18.0911	−	59.9392i	−0.0323055	−	0.107034i
$561$	171.237			0.305236
$562$	282.105			0.501967
$563$			890.386i			1.58150i	0.612137	+	0.790752i	$0.290310\pi$
$563$			890.386i			1.58150i	−0.612137	+	0.790752i	$0.709690\pi$
$564$	−201.413			−0.357116
$565$		−	57.0280i		−	0.100935i
$566$			765.343i			1.35220i
$567$	−60.3127	+	18.2038i	−0.106372	+	0.0321055i
$568$	70.3358			0.123831
$569$	138.453			0.243327			0.121663	−	0.992571i	$-0.461177\pi$
$569$	138.453			0.243327			0.121663	+	0.992571i	$0.461177\pi$
$570$		−	140.690i		−	0.246824i
$571$	476.343			0.834225			0.417113	−	0.908855i	$-0.363042\pi$
$571$	476.343			0.834225			0.417113	+	0.908855i	$0.363042\pi$
$572$			90.8390i			0.158810i
$573$			85.7259i			0.149609i
$574$	77.4693	+	256.670i	0.134964	+	0.447161i
$575$	204.843			0.356248
$576$	−24.0000			−0.0416667
$577$			678.464i			1.17585i	0.808916	+	0.587924i	$0.200055\pi$
$577$			678.464i			1.17585i	−0.808916	+	0.587924i	$0.799945\pi$
$578$	142.419			0.246400
$579$			299.081i			0.516547i
$580$		−	99.7602i		−	0.172000i
$581$	−146.566	−	485.600i	−0.252264	−	0.835800i
$582$	254.267			0.436885
$583$	−328.628			−0.563684
$584$		−	191.972i		−	0.328720i
$585$	−60.8387			−0.103998
$586$			535.643i			0.914067i
$587$			48.9046i			0.0833128i	0.999132	+	0.0416564i	$0.0132635\pi$
$587$			48.9046i			0.0833128i	−0.999132	+	0.0416564i	$0.986737\pi$
$588$	93.9089	+	141.397i	0.159709	+	0.240471i
$589$	−408.451			−0.693465
$590$	−103.010			−0.174593
$591$			131.020i			0.221692i
$592$	−179.003			−0.302369
$593$		−	487.761i		−	0.822531i	−0.911516	−	0.411266i	$-0.865087\pi$
$593$		−	487.761i		−	0.822531i	0.911516	−	0.411266i	$-0.134913\pi$
$594$		−	36.8015i		−	0.0619555i
$595$	295.815	−	89.2839i	0.497167	−	0.150057i
$596$	−242.911			−0.407569
$597$	−255.685			−0.428283
$598$		−	525.459i		−	0.878695i
$599$	−1083.77			−1.80931			−0.904653	−	0.426149i	$-0.859870\pi$
$599$	−1083.77			−1.80931			−0.904653	+	0.426149i	$0.859870\pi$
$600$			24.4949i			0.0408248i
$601$		−	274.481i		−	0.456707i	−0.973578	−	0.228353i	$-0.926666\pi$
$601$		−	274.481i		−	0.456707i	0.973578	−	0.228353i	$-0.0733342\pi$
$602$	−290.657	+	87.7273i	−0.482819	+	0.145726i
$603$	−216.175			−0.358500
$604$	−438.185			−0.725472
$605$		−	214.482i		−	0.354516i
$606$	380.600			0.628052
$607$		−	941.550i		−	1.55115i	−0.631253	−	0.775577i	$-0.717459\pi$
$607$		−	941.550i		−	1.55115i	0.631253	−	0.775577i	$-0.282541\pi$
$608$			145.304i			0.238986i
$609$	78.1489	+	258.922i	0.128323	+	0.425159i
$610$	264.161			0.433050
$611$	527.316			0.863038
$612$		−	118.446i		−	0.193539i
$613$	−658.706			−1.07456			−0.537281	−	0.843404i	$-0.680548\pi$
$613$	−658.706			−1.07456			−0.537281	+	0.843404i	$0.680548\pi$
$614$			198.287i			0.322942i
$615$		−	104.891i		−	0.170555i
$616$	−94.9249	+	28.6506i	−0.154099	+	0.0465108i
$617$	355.965			0.576929			0.288464	−	0.957491i	$-0.406855\pi$
$617$	355.965			0.576929			0.288464	+	0.957491i	$0.406855\pi$
$618$	−161.537			−0.261387
$619$		−	214.933i		−	0.347226i	−0.984814	−	0.173613i	$-0.944456\pi$
$619$		−	214.933i		−	0.347226i	0.984814	−	0.173613i	$-0.0555442\pi$
$620$	71.1137			0.114700
$621$			212.879i			0.342800i
$622$		−	353.392i		−	0.568154i
$623$	230.087	+	762.323i	0.369322	+	1.22363i
$624$	62.8339			0.100695
$625$	25.0000			0.0400000
$626$			732.413i			1.16999i
$627$	−222.808			−0.355356
$628$		−	114.563i		−	0.182425i
$629$		−	883.421i		−	1.40448i
$630$	−19.1885	−	63.5752i	−0.0304579	−	0.100913i
$631$	589.714			0.934570			0.467285	−	0.884107i	$-0.345232\pi$
$631$	589.714			0.934570			0.467285	+	0.884107i	$0.345232\pi$
$632$	−86.1121			−0.136253
$633$			271.728i			0.429270i
$634$	254.619			0.401608
$635$		−	514.980i		−	0.810993i
$636$			227.314i			0.357412i
$637$	−245.861	−	370.189i	−0.385967	−	0.581144i
$638$	−157.989			−0.247631
$639$	74.6024			0.116749
$640$		−	25.2982i		−	0.0395285i
$641$	−675.508			−1.05383			−0.526917	−	0.849917i	$-0.676652\pi$
$641$	−675.508			−1.05383			−0.526917	+	0.849917i	$0.676652\pi$
$642$			333.789i			0.519921i
$643$			733.747i			1.14113i	0.821252	+	0.570565i	$0.193276\pi$
$643$			733.747i			1.14113i	−0.821252	+	0.570565i	$0.806724\pi$
$644$	549.095	−	165.730i	0.852631	−	0.257345i
$645$	118.781			0.184156
$646$	−717.109			−1.11008
$647$		−	645.060i		−	0.997002i	−0.866889	−	0.498501i	$-0.833884\pi$
$647$		−	645.060i		−	0.997002i	0.866889	−	0.498501i	$-0.166116\pi$
$648$	−25.4558			−0.0392837
$649$			163.135i			0.251364i
$650$		−	64.1296i		−	0.0986609i
$651$	−184.572	+	55.7082i	−0.283520	+	0.0855732i
$652$	−17.0459			−0.0261441
$653$	−610.744			−0.935289			−0.467644	−	0.883917i	$-0.654897\pi$
$653$	−610.744			−0.935289			−0.467644	+	0.883917i	$0.654897\pi$
$654$		−	406.623i		−	0.621747i
$655$	−91.4836			−0.139670
$656$			108.331i			0.165139i
$657$		−	203.617i		−	0.309920i
$658$	166.315	+	551.035i	0.252759	+	0.837439i
$659$	220.888			0.335187			0.167594	−	0.985856i	$-0.446400\pi$
$659$	220.888			0.335187			0.167594	+	0.985856i	$0.446400\pi$
$660$	38.7922			0.0587761
$661$		−	306.043i		−	0.463000i	−0.972835	−	0.231500i	$-0.925637\pi$
$661$		−	306.043i		−	0.463000i	0.972835	−	0.231500i	$-0.0743634\pi$
$662$	−114.591			−0.173099
$663$			310.100i			0.467723i
$664$		−	204.954i		−	0.308666i
$665$	−384.905	+	116.173i	−0.578804	+	0.174697i
$666$	−189.861			−0.285076
$667$	913.888			1.37015
$668$		−	516.297i		−	0.772899i
$669$	104.621			0.156384
$670$		−	227.869i		−	0.340103i
$671$		−	418.348i		−	0.623469i
$672$	19.8178	+	65.6601i	0.0294908	+	0.0977085i
$673$	−1025.63			−1.52397			−0.761986	−	0.647594i	$-0.775775\pi$
$673$	−1025.63			−1.52397			−0.761986	+	0.647594i	$0.775775\pi$
$674$	527.412			0.782510
$675$			25.9808i			0.0384900i
$676$	173.496			0.256651
$677$		−	622.692i		−	0.919781i	−0.887976	−	0.459891i	$-0.847889\pi$
$677$		−	622.692i		−	0.919781i	0.887976	−	0.459891i	$-0.152111\pi$
$678$			62.4711i			0.0921402i
$679$	−209.959	−	695.634i	−0.309218	−	1.02450i
$680$	124.853			0.183607
$681$	−543.190			−0.797636
$682$		−	112.622i		−	0.165135i
$683$	170.676			0.249891			0.124946	−	0.992164i	$-0.460124\pi$
$683$	170.676			0.249891			0.124946	+	0.992164i	$0.460124\pi$
$684$			154.118i			0.225319i
$685$			353.970i			0.516744i
$686$	309.295	−	373.677i	0.450867	−	0.544719i
$687$	−191.163			−0.278258
$688$	−122.676			−0.178308
$689$		−	595.126i		−	0.863753i
$690$	−224.394			−0.325209
$691$			1353.09i			1.95816i	0.203481	+	0.979079i	$0.434774\pi$
$691$			1353.09i			1.95816i	−0.203481	+	0.979079i	$0.565226\pi$
$692$		−	654.499i		−	0.945808i
$693$	−100.683	+	30.3886i	−0.145286	+	0.0438508i
$694$	−587.226			−0.846147
$695$	−316.592			−0.455528
$696$			109.282i			0.157014i
$697$	−534.642			−0.767061
$698$		−	758.312i		−	1.08641i
$699$			66.5223i			0.0951678i
$700$	67.0141	−	20.2265i	0.0957344	−	0.0288949i
$701$	−631.426			−0.900750			−0.450375	−	0.892840i	$-0.648710\pi$
$701$	−631.426			−0.900750			−0.450375	+	0.892840i	$0.648710\pi$
$702$	66.6454			0.0949365
$703$			1149.48i			1.63510i
$704$	−40.0644			−0.0569097
$705$		−	225.187i		−	0.319414i
$706$		−	588.638i		−	0.833764i
$707$	−314.277	−	1041.26i	−0.444522	−	1.47279i
$708$	112.842			0.159381
$709$	−294.907			−0.415947			−0.207974	−	0.978134i	$-0.566687\pi$
$709$	−294.907			−0.415947			−0.207974	+	0.978134i	$0.566687\pi$
$710$			78.6378i			0.110757i
$711$	−91.3357			−0.128461
$712$			321.749i			0.451895i
$713$			651.462i			0.913692i
$714$	−324.049	+	97.8056i	−0.453850	+	0.136983i
$715$	−101.561			−0.142044
$716$	−335.139			−0.468071
$717$		−	216.730i		−	0.302273i
$718$	382.634			0.532917
$719$		−	884.788i		−	1.23058i	−0.788301	−	0.615290i	$-0.789039\pi$
$719$		−	884.788i		−	1.23058i	0.788301	−	0.615290i	$-0.210961\pi$
$720$		−	26.8328i		−	0.0372678i
$721$	133.388	+	441.939i	0.185004	+	0.612953i
$722$	422.548			0.585247
$723$	267.818			0.370427
$724$			295.914i			0.408721i
$725$	111.535			0.153842
$726$			234.954i			0.323627i
$727$			361.739i			0.497578i	0.968558	+	0.248789i	$0.0800325\pi$
$727$			361.739i			0.497578i	−0.968558	+	0.248789i	$0.919967\pi$
$728$	−51.8846	−	171.903i	−0.0712700	−	0.236131i
$729$	−27.0000			−0.0370370
$730$	214.632			0.294016
$731$		−	605.436i		−	0.828230i
$732$	−289.374			−0.395319
$733$			819.923i			1.11859i	0.828970	+	0.559293i	$0.188927\pi$
$733$			819.923i			1.11859i	−0.828970	+	0.559293i	$0.811073\pi$
$734$			855.633i			1.16571i
$735$	−158.087	+	104.993i	−0.215084	+	0.142848i
$736$	231.753			0.314882
$737$	−360.873			−0.489651
$738$			114.903i			0.155695i
$739$	−802.663			−1.08615			−0.543074	−	0.839685i	$-0.682740\pi$
$739$	−802.663			−1.08615			−0.543074	+	0.839685i	$0.682740\pi$
$740$		−	200.131i		−	0.270447i
$741$		−	403.493i		−	0.544525i
$742$	621.894	−	187.703i	0.838132	−	0.252968i
$743$	−1061.48			−1.42865			−0.714323	−	0.699816i	$-0.753265\pi$
$743$	−1061.48			−1.42865			−0.714323	+	0.699816i	$0.753265\pi$
$744$	−77.9012			−0.104706
$745$		−	271.583i		−	0.364541i
$746$	30.4231			0.0407816
$747$		−	217.387i		−	0.291013i
$748$		−	197.728i		−	0.264342i
$749$	913.194	−	275.624i	1.21922	−	0.367989i
$750$	−27.3861			−0.0365148
$751$	−1044.41			−1.39069			−0.695346	−	0.718675i	$-0.744749\pi$
$751$	−1044.41			−1.39069			−0.695346	+	0.718675i	$0.744749\pi$
$752$			232.572i			0.309272i
$753$	264.405			0.351136
$754$		−	286.108i		−	0.379454i
$755$		−	489.906i		−	0.648882i
$756$	21.0200	+	69.6431i	0.0278042	+	0.0921205i
$757$	−1267.83			−1.67481			−0.837406	−	0.546581i	$-0.815929\pi$
$757$	−1267.83			−1.67481			−0.837406	+	0.546581i	$0.815929\pi$
$758$	−636.202			−0.839316
$759$			355.370i			0.468208i
$760$	−162.455			−0.213756
$761$			257.020i			0.337740i	0.985638	+	0.168870i	$0.0540118\pi$
$761$			257.020i			0.337740i	−0.985638	+	0.168870i	$0.945988\pi$
$762$			564.133i			0.740332i
$763$	−1112.45	+	335.765i	−1.45800	+	0.440060i
$764$	98.9878			0.129565
$765$	132.426			0.173106
$766$			793.029i			1.03529i
$767$	−295.428			−0.385174
$768$			27.7128i			0.0360844i
$769$		−	1192.50i		−	1.55071i	−0.631524	−	0.775357i	$-0.717570\pi$
$769$		−	1192.50i		−	1.55071i	0.631524	−	0.775357i	$-0.282430\pi$
$770$	−32.0324	−	106.129i	−0.0416005	−	0.137830i
$771$	34.9038			0.0452708
$772$	345.349			0.447343
$773$		−	1121.01i		−	1.45021i	−0.688639	−	0.725104i	$-0.741792\pi$
$773$		−	1121.01i		−	1.45021i	0.688639	−	0.725104i	$-0.258208\pi$
$774$	−130.118			−0.168111
$775$			79.5075i			0.102590i
$776$		−	293.602i		−	0.378353i
$777$	156.776	+	519.429i	0.201771	+	0.668506i
$778$	823.386			1.05834
$779$	695.659			0.893015
$780$			70.2504i			0.0900647i
$781$	124.538			0.159459
$782$			1143.76i			1.46261i
$783$			115.911i			0.148034i
$784$	163.271	−	108.437i	0.208254	−	0.138312i
$785$	128.085			0.163166
$786$	100.215			0.127500
$787$			1207.04i			1.53372i	0.641813	+	0.766861i	$0.278183\pi$
$787$			1207.04i			1.53372i	−0.641813	+	0.766861i	$0.721817\pi$
$788$	151.289			0.191991
$789$		−	555.466i		−	0.704013i
$790$		−	96.2762i		−	0.121869i
$791$	170.911	−	51.5850i	0.216069	−	0.0652149i
$792$	−42.4948			−0.0536550
$793$	757.603			0.955363
$794$		−	1027.51i		−	1.29410i
$795$	−254.145			−0.319679
$796$			295.240i			0.370904i
$797$			378.901i			0.475409i	0.971338	+	0.237704i	$0.0763950\pi$
$797$			378.901i			0.475409i	−0.971338	+	0.237704i	$0.923605\pi$
$798$	421.642	−	127.262i	0.528373	−	0.159476i
$799$	−1147.80			−1.43655
$800$	28.2843			0.0353553
$801$			341.267i			0.426051i
$802$	46.3808			0.0578314
$803$		−	339.909i		−	0.423299i
$804$			249.618i			0.310470i
$805$	185.292	+	613.906i	0.230176	+	0.762617i
$806$	203.951			0.253041
$807$	−67.9196			−0.0841631
$808$		−	439.479i		−	0.543909i
$809$	−403.691			−0.499000			−0.249500	−	0.968375i	$-0.580266\pi$
$809$	−403.691			−0.499000			−0.249500	+	0.968375i	$0.580266\pi$
$810$		−	28.4605i		−	0.0351364i
$811$		−	109.713i		−	0.135281i	−0.997710	−	0.0676407i	$-0.978453\pi$
$811$		−	109.713i		−	0.135281i	0.997710	−	0.0676407i	$-0.0215471\pi$
$812$	298.977	−	90.2386i	0.368199	−	0.111131i
$813$	−518.006			−0.637154
$814$	−316.945			−0.389367
$815$		−	19.0579i		−	0.0233840i
$816$	−136.769			−0.167610
$817$			787.774i			0.964228i
$818$			901.899i			1.10257i
$819$	−55.0319	−	182.331i	−0.0671940	−	0.222627i
$820$	−121.118			−0.147705
$821$	426.293			0.519236			0.259618	−	0.965711i	$-0.416403\pi$
$821$	426.293			0.519236			0.259618	+	0.965711i	$0.416403\pi$
$822$		−	387.754i		−	0.471721i
$823$	−708.932			−0.861400			−0.430700	−	0.902495i	$-0.641733\pi$
$823$	−708.932			−0.861400			−0.430700	+	0.902495i	$0.641733\pi$
$824$			186.527i			0.226367i
$825$			43.3710i			0.0525710i
$826$	−93.1781	−	308.717i	−0.112806	−	0.373749i
$827$	−813.963			−0.984236			−0.492118	−	0.870528i	$-0.663777\pi$
$827$	−813.963			−0.984236			−0.492118	+	0.870528i	$0.663777\pi$
$828$	245.811			0.296874
$829$		−	92.7107i		−	0.111834i	−0.998435	−	0.0559172i	$-0.982192\pi$
$829$		−	92.7107i		−	0.111834i	0.998435	−	0.0559172i	$-0.0178083\pi$
$830$	229.146			0.276079
$831$		−	760.312i		−	0.914936i
$832$		−	72.5543i		−	0.0872047i
$833$	535.161	+	805.783i	0.642450	+	0.967326i
$834$	346.809			0.415838
$835$	577.237			0.691302
$836$			257.277i			0.307748i
$837$	−82.6267			−0.0987176
$838$		−	487.247i		−	0.581440i
$839$		−	852.206i		−	1.01574i	−0.861434	−	0.507870i	$-0.830433\pi$
$839$		−	852.206i		−	1.01574i	0.861434	−	0.507870i	$-0.169567\pi$
$840$	−73.4103	+	22.1570i	−0.0873932	+	0.0263774i
$841$	−343.395			−0.408318
$842$	−410.704			−0.487772
$843$		−	345.507i		−	0.409854i
$844$	313.764			0.371759
$845$			193.974i			0.229555i
$846$			246.680i			0.291584i
$847$	642.795	−	194.011i	0.758908	−	0.229057i
$848$	262.479			0.309528
$849$	937.349			1.10406
$850$			139.590i			0.164223i
$851$	1833.37			2.15437
$852$		−	86.1434i		−	0.101107i
$853$			1472.75i			1.72655i	0.504733	+	0.863275i	$0.331591\pi$
$853$			1472.75i			1.72655i	−0.504733	+	0.863275i	$0.668409\pi$
$854$	238.948	+	791.680i	0.279798	+	0.927025i
$855$	−172.309			−0.201531
$856$	385.427			0.450265
$857$			882.824i			1.03013i	0.857150	+	0.515066i	$0.172233\pi$
$857$			882.824i			1.03013i	−0.857150	+	0.515066i	$0.827767\pi$
$858$	111.255			0.129667
$859$			700.963i			0.816023i	0.912977	+	0.408011i	$0.133778\pi$
$859$			700.963i			0.816023i	−0.912977	+	0.408011i	$0.866222\pi$
$860$		−	137.156i		−	0.159484i
$861$	314.356	−	94.8801i	0.365105	−	0.110198i
$862$	303.744			0.352372
$863$	1246.07			1.44388			0.721938	−	0.691957i	$-0.243251\pi$
$863$	1246.07			1.44388			0.721938	+	0.691957i	$0.243251\pi$
$864$			29.3939i			0.0340207i
$865$	731.753			0.845957
$866$		−	601.099i		−	0.694109i
$867$		−	174.427i		−	0.201185i
$868$	64.3263	+	213.125i	0.0741086	+	0.245536i
$869$	−152.471			−0.175456
$870$	−122.181			−0.140438
$871$		−	653.519i		−	0.750309i
$872$	−469.527			−0.538449
$873$		−	311.412i		−	0.356715i
$874$		−	1488.22i		−	1.70277i
$875$	22.6139	+	74.9240i	0.0258444	+	0.0856275i
$876$	−235.117			−0.268399
$877$	957.986			1.09234			0.546172	−	0.837673i	$-0.316084\pi$
$877$	957.986			1.09234			0.546172	+	0.837673i	$0.316084\pi$
$878$		−	288.783i		−	0.328910i
$879$	656.026			0.746333
$880$		−	44.7934i		−	0.0509016i
$881$		−	865.707i		−	0.982642i	−0.870979	−	0.491321i	$-0.836514\pi$
$881$		−	865.707i		−	0.982642i	0.870979	−	0.491321i	$-0.163486\pi$
$882$	173.175	−	115.014i	0.196344	−	0.130402i
$883$	985.817			1.11644			0.558220	−	0.829693i	$-0.311484\pi$
$883$	985.817			1.11644			0.558220	+	0.829693i	$0.311484\pi$
$884$	358.073			0.405060
$885$			126.161i			0.142555i
$886$	−390.843			−0.441132
$887$			443.357i			0.499838i	0.968267	+	0.249919i	$0.0804040\pi$
$887$			443.357i			0.499838i	−0.968267	+	0.249919i	$0.919596\pi$
$888$			219.232i			0.246883i
$889$	1543.38	−	465.828i	1.73608	−	0.523991i
$890$	−359.727			−0.404187
$891$	−45.0725			−0.0505864
$892$		−	120.806i		−	0.135433i
$893$	1493.48			1.67243
$894$			297.504i			0.332779i
$895$		−	374.696i		−	0.418655i
$896$	75.8178	−	22.8836i	0.0846181	−	0.0255398i
$897$	−643.554			−0.717451
$898$	−276.182			−0.307552
$899$			354.716i			0.394567i
$900$	30.0000			0.0333333
$901$			1295.40i			1.43774i
$902$			191.813i			0.212653i
$903$	107.444	+	355.981i	0.118985	+	0.394220i
$904$	72.1354			0.0797958
$905$	−330.842			−0.365571
$906$			536.665i			0.592346i
$907$	49.0514			0.0540810			0.0270405	−	0.999634i	$-0.491392\pi$
$907$	49.0514			0.0540810			0.0270405	+	0.999634i	$0.491392\pi$
$908$			627.222i			0.690773i
$909$		−	466.138i		−	0.512803i
$910$	192.194	−	58.0087i	0.211202	−	0.0637458i
$911$	−290.836			−0.319249			−0.159624	−	0.987178i	$-0.551028\pi$
$911$	−290.836			−0.319249			−0.159624	+	0.987178i	$0.551028\pi$
$912$	177.960			0.195132
$913$		−	362.895i		−	0.397476i
$914$	−14.6269			−0.0160032
$915$		−	323.529i		−	0.353584i
$916$			220.736i			0.240979i
$917$	−82.7519	−	274.173i	−0.0902420	−	0.298989i
$918$	−145.066			−0.158024
$919$	−721.872			−0.785498			−0.392749	−	0.919646i	$-0.628476\pi$
$919$	−721.872			−0.785498			−0.392749	+	0.919646i	$0.628476\pi$
$920$			259.108i			0.281639i
$921$	242.851			0.263681
$922$			746.100i			0.809219i
$923$			225.530i			0.244345i
$924$	35.0897	+	116.259i	0.0379759	+	0.125821i
$925$	223.753			0.241895
$926$	−1128.40			−1.21857
$927$			197.841i			0.213421i
$928$	126.188			0.135978
$929$		−	617.161i		−	0.664329i	−0.943222	−	0.332164i	$-0.892221\pi$
$929$		−	617.161i		−	0.664329i	0.943222	−	0.332164i	$-0.107779\pi$
$930$		−	87.0962i		−	0.0936518i
$931$	−696.335	−	1048.46i	−0.747943	−	1.12616i
$932$	76.8133			0.0824177
$933$	−432.815			−0.463896
$934$			239.923i			0.256877i
$935$	221.066			0.236435
$936$		−	76.9555i		−	0.0822174i
$937$			224.045i			0.239108i	0.992828	+	0.119554i	$0.0381465\pi$
$937$			224.045i			0.239108i	−0.992828	+	0.119554i	$0.961853\pi$
$938$	682.915	−	206.120i	0.728054	−	0.219744i
$939$	897.019			0.955292
$940$	−260.024			−0.276621
$941$			522.371i			0.555124i	0.960708	+	0.277562i	$0.0895264\pi$
$941$			522.371i			0.555124i	−0.960708	+	0.277562i	$0.910474\pi$
$942$	−140.310			−0.148949
$943$		−	1109.55i		−	1.17661i
$944$		−	130.298i		−	0.138028i
$945$	−77.8634	+	23.5010i	−0.0823951	+	0.0248688i
$946$	−217.212			−0.229611
$947$	−728.427			−0.769194			−0.384597	−	0.923084i	$-0.625660\pi$
$947$	−728.427			−0.769194			−0.384597	+	0.923084i	$0.625660\pi$
$948$			105.465i			0.111250i
$949$	615.555			0.648636
$950$		−	181.630i		−	0.191189i
$951$		−	311.844i		−	0.327911i
$952$	112.936	+	374.179i	0.118630	+	0.393045i
$953$	−1169.38			−1.22705			−0.613527	−	0.789674i	$-0.710250\pi$
$953$	−1169.38			−1.22705			−0.613527	+	0.789674i	$0.710250\pi$
$954$	278.402			0.291825
$955$			110.672i			0.115887i
$956$	−250.258			−0.261776
$957$			193.496i			0.202190i
$958$		−	995.991i		−	1.03966i
$959$	−1060.83	+	320.185i	−1.10619	+	0.333874i
$960$	−30.9839			−0.0322749
$961$	708.142			0.736880
$962$		−	573.968i		−	0.596640i
$963$	408.807			0.424514
$964$		−	309.250i		−	0.320799i
$965$			386.112i			0.400116i
$966$	−202.977	−	672.501i	−0.210121	−	0.696170i
$967$	771.440			0.797767			0.398883	−	0.917002i	$-0.369398\pi$
$967$	771.440			0.797767			0.398883	+	0.917002i	$0.369398\pi$
$968$	271.301			0.280270
$969$			878.275i			0.906373i
$970$	328.257			0.338410
$971$			1380.71i			1.42195i	0.703220	+	0.710973i	$0.251745\pi$
$971$			1380.71i			1.42195i	−0.703220	+	0.710973i	$0.748255\pi$
$972$			31.1769i			0.0320750i
$973$	−286.375	−	948.814i	−0.294321	−	0.975143i
$974$	94.4647			0.0969864
$975$	−78.5424			−0.0805563
$976$			334.140i			0.342356i
$977$	974.771			0.997718			0.498859	−	0.866683i	$-0.333752\pi$
$977$	974.771			0.997718			0.498859	+	0.866683i	$0.333752\pi$
$978$			20.8769i			0.0213466i
$979$			569.694i			0.581915i
$980$	121.236	+	182.543i	0.123710	+	0.186268i
$981$	−498.009			−0.507655
$982$	−772.333			−0.786490
$983$			206.961i			0.210540i	0.994444	+	0.105270i	$0.0335708\pi$
$983$			206.961i			0.210540i	−0.994444	+	0.105270i	$0.966429\pi$
$984$	132.678			0.134836
$985$			169.146i			0.171722i
$986$			622.767i			0.631610i
$987$	674.877	−	203.694i	0.683766	−	0.206377i
$988$	−465.913			−0.471572
$989$	1256.47			1.27044
$990$		−	47.5106i		−	0.0479905i
$991$	−413.701			−0.417459			−0.208729	−	0.977973i	$-0.566933\pi$
$991$	−413.701			−0.417459			−0.208729	+	0.977973i	$0.566933\pi$
$992$			89.9525i			0.0906779i
$993$			140.345i			0.141335i
$994$	−235.675	+	71.1322i	−0.237097	+	0.0715616i
$995$	−330.088			−0.331747
$996$	−251.017			−0.252025
$997$			542.511i			0.544143i	0.962277	+	0.272072i	$0.0877088\pi$
$997$			542.511i			0.544143i	−0.962277	+	0.272072i	$0.912291\pi$
$998$	−1009.83			−1.01186
$999$			232.531i			0.232764i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.f.a.181.4	yes	8
3.2	odd	2		630.3.f.c.181.5		8
4.3	odd	2		1680.3.s.a.1441.4		8
5.2	odd	4		1050.3.h.b.349.6		16
5.3	odd	4		1050.3.h.b.349.11		16
5.4	even	2		1050.3.f.b.601.6		8
7.6	odd	2	inner	210.3.f.a.181.1	✓	8
21.20	even	2		630.3.f.c.181.7		8
28.27	even	2		1680.3.s.a.1441.6		8
35.13	even	4		1050.3.h.b.349.14		16
35.27	even	4		1050.3.h.b.349.3		16
35.34	odd	2		1050.3.f.b.601.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.f.a.181.1	✓	8	7.6	odd	2	inner
210.3.f.a.181.4	yes	8	1.1	even	1	trivial
630.3.f.c.181.5		8	3.2	odd	2
630.3.f.c.181.7		8	21.20	even	2
1050.3.f.b.601.6		8	5.4	even	2
1050.3.f.b.601.8		8	35.34	odd	2
1050.3.h.b.349.3		16	35.27	even	4
1050.3.h.b.349.6		16	5.2	odd	4
1050.3.h.b.349.11		16	5.3	odd	4
1050.3.h.b.349.14		16	35.13	even	4
1680.3.s.a.1441.4		8	4.3	odd	2
1680.3.s.a.1441.6		8	28.27	even	2

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} +2.23607i q^{5} -2.44949i q^{6} +(-6.70141 + 2.02265i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} +2.23607i q^{5} -2.44949i q^{6} +(-6.70141 + 2.02265i) q^{7} -2.82843 q^{8} -3.00000 q^{9} -3.16228i q^{10} -5.00806 q^{11} +3.46410i q^{12} -9.06929i q^{13} +(9.47723 - 2.86045i) q^{14} -3.87298 q^{15} +4.00000 q^{16} +19.7410i q^{17} +4.24264 q^{18} -25.6863i q^{19} +4.47214i q^{20} +(-3.50333 - 11.6072i) q^{21} +7.08246 q^{22} -40.9686 q^{23} -4.89898i q^{24} -5.00000 q^{25} +12.8259i q^{26} -5.19615i q^{27} +(-13.4028 + 4.04529i) q^{28} -22.3071 q^{29} +5.47723 q^{30} -15.9015i q^{31} -5.65685 q^{32} -8.67421i q^{33} -27.9179i q^{34} +(-4.52277 - 14.9848i) q^{35} -6.00000 q^{36} -44.7506 q^{37} +36.3259i q^{38} +15.7085 q^{39} -6.32456i q^{40} +27.0829i q^{41} +(4.95445 + 16.4150i) q^{42} -30.6690 q^{43} -10.0161 q^{44} -6.70820i q^{45} +57.9383 q^{46} +58.1430i q^{47} +6.92820i q^{48} +(40.8178 - 27.1092i) q^{49} +7.07107 q^{50} -34.1924 q^{51} -18.1386i q^{52} +65.6199 q^{53} +7.34847i q^{54} -11.1984i q^{55} +(18.9545 - 5.72091i) q^{56} +44.4900 q^{57} +31.5469 q^{58} -32.5746i q^{59} -7.74597 q^{60} +83.5349i q^{61} +22.4881i q^{62} +(20.1042 - 6.06794i) q^{63} +8.00000 q^{64} +20.2796 q^{65} +12.2672i q^{66} +72.0585 q^{67} +39.4819i q^{68} -70.9597i q^{69} +(6.39617 + 21.1917i) q^{70} -24.8675 q^{71} +8.48528 q^{72} +67.8725i q^{73} +63.2870 q^{74} -8.66025i q^{75} -51.3726i q^{76} +(33.5610 - 10.1295i) q^{77} -22.2151 q^{78} +30.4452 q^{79} +8.94427i q^{80} +9.00000 q^{81} -38.3009i q^{82} +72.4623i q^{83} +(-7.00665 - 23.2144i) q^{84} -44.1421 q^{85} +43.3725 q^{86} -38.6370i q^{87} +14.1649 q^{88} -113.756i q^{89} +9.48683i q^{90} +(18.3440 + 60.7770i) q^{91} -81.9372 q^{92} +27.5422 q^{93} -82.2267i q^{94} +57.4363 q^{95} -9.79796i q^{96} +103.804i q^{97} +(-57.7251 + 38.3381i) q^{98} +15.0242 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) 8 * q + 16 * q^4 - 24 * q^9	\( 8 q + 16 q^{4} - 24 q^{9} - 16 q^{11} + 32 q^{14} + 32 q^{16} + 96 q^{22} - 40 q^{25} - 144 q^{29} - 80 q^{35} - 48 q^{36} - 48 q^{37} - 48 q^{39} - 48 q^{42} - 64 q^{43} - 32 q^{44} + 128 q^{46} - 24 q^{49} + 128 q^{53} + 64 q^{56} + 144 q^{57} + 224 q^{58} + 64 q^{64} + 80 q^{65} - 192 q^{67} + 176 q^{71} - 160 q^{74} + 192 q^{77} - 96 q^{78} - 288 q^{79} + 72 q^{81} - 240 q^{85} - 64 q^{86} + 192 q^{88} + 64 q^{91} + 336 q^{93} + 80 q^{95} + 48 q^{99}+O(q^{100}) \) 8 * q + 16 * q^4 - 24 * q^9 - 16 * q^11 + 32 * q^14 + 32 * q^16 + 96 * q^22 - 40 * q^25 - 144 * q^29 - 80 * q^35 - 48 * q^36 - 48 * q^37 - 48 * q^39 - 48 * q^42 - 64 * q^43 - 32 * q^44 + 128 * q^46 - 24 * q^49 + 128 * q^53 + 64 * q^56 + 144 * q^57 + 224 * q^58 + 64 * q^64 + 80 * q^65 - 192 * q^67 + 176 * q^71 - 160 * q^74 + 192 * q^77 - 96 * q^78 - 288 * q^79 + 72 * q^81 - 240 * q^85 - 64 * q^86 + 192 * q^88 + 64 * q^91 + 336 * q^93 + 80 * q^95 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more