LMFDB - Embedded newform 8018.2.a.i.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.a (trivial)

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:	yes
Analytic conductor:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$43$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.54429 q^{3} +1.00000 q^{4} -4.40933 q^{5} +2.54429 q^{6} -2.39004 q^{7} -1.00000 q^{8} +3.47339 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.54429 q^{3} +1.00000 q^{4} -4.40933 q^{5} +2.54429 q^{6} -2.39004 q^{7} -1.00000 q^{8} +3.47339 q^{9} +4.40933 q^{10} -3.64734 q^{11} -2.54429 q^{12} +5.13023 q^{13} +2.39004 q^{14} +11.2186 q^{15} +1.00000 q^{16} +2.22335 q^{17} -3.47339 q^{18} +1.00000 q^{19} -4.40933 q^{20} +6.08094 q^{21} +3.64734 q^{22} +3.94690 q^{23} +2.54429 q^{24} +14.4422 q^{25} -5.13023 q^{26} -1.20444 q^{27} -2.39004 q^{28} +4.94263 q^{29} -11.2186 q^{30} +9.26564 q^{31} -1.00000 q^{32} +9.27987 q^{33} -2.22335 q^{34} +10.5385 q^{35} +3.47339 q^{36} -3.48491 q^{37} -1.00000 q^{38} -13.0528 q^{39} +4.40933 q^{40} +10.8838 q^{41} -6.08094 q^{42} -9.31376 q^{43} -3.64734 q^{44} -15.3153 q^{45} -3.94690 q^{46} +7.12371 q^{47} -2.54429 q^{48} -1.28772 q^{49} -14.4422 q^{50} -5.65685 q^{51} +5.13023 q^{52} -8.00437 q^{53} +1.20444 q^{54} +16.0823 q^{55} +2.39004 q^{56} -2.54429 q^{57} -4.94263 q^{58} -2.21452 q^{59} +11.2186 q^{60} -7.43983 q^{61} -9.26564 q^{62} -8.30154 q^{63} +1.00000 q^{64} -22.6209 q^{65} -9.27987 q^{66} +12.2511 q^{67} +2.22335 q^{68} -10.0420 q^{69} -10.5385 q^{70} -6.23150 q^{71} -3.47339 q^{72} +4.65644 q^{73} +3.48491 q^{74} -36.7451 q^{75} +1.00000 q^{76} +8.71727 q^{77} +13.0528 q^{78} +12.3974 q^{79} -4.40933 q^{80} -7.35572 q^{81} -10.8838 q^{82} +9.55833 q^{83} +6.08094 q^{84} -9.80351 q^{85} +9.31376 q^{86} -12.5755 q^{87} +3.64734 q^{88} -10.8191 q^{89} +15.3153 q^{90} -12.2614 q^{91} +3.94690 q^{92} -23.5744 q^{93} -7.12371 q^{94} -4.40933 q^{95} +2.54429 q^{96} +2.60273 q^{97} +1.28772 q^{98} -12.6686 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9}+O(q^{10}) $ 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9	$ 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9} + 14 q^{11} + 3 q^{13} - 19 q^{14} + q^{15} + 43 q^{16} + 8 q^{17} - 53 q^{18} + 43 q^{19} - 14 q^{22} + 43 q^{23} + 97 q^{25} - 3 q^{26} + 15 q^{27} + 19 q^{28} - 25 q^{29} - q^{30} + 22 q^{31} - 43 q^{32} + 22 q^{33} - 8 q^{34} - 6 q^{35} + 53 q^{36} + 42 q^{37} - 43 q^{38} + 9 q^{39} - 40 q^{41} + 72 q^{43} + 14 q^{44} - q^{45} - 43 q^{46} + 27 q^{47} + 86 q^{49} - 97 q^{50} - 3 q^{51} + 3 q^{52} - 5 q^{53} - 15 q^{54} + 86 q^{55} - 19 q^{56} + 25 q^{58} - 43 q^{59} + q^{60} + 31 q^{61} - 22 q^{62} + 38 q^{63} + 43 q^{64} - 32 q^{65} - 22 q^{66} + 15 q^{67} + 8 q^{68} - 7 q^{69} + 6 q^{70} + 14 q^{71} - 53 q^{72} + 93 q^{73} - 42 q^{74} - 13 q^{75} + 43 q^{76} + 38 q^{77} - 9 q^{78} + 15 q^{79} + 43 q^{81} + 40 q^{82} + 34 q^{83} + 16 q^{85} - 72 q^{86} + 60 q^{87} - 14 q^{88} - 37 q^{89} + q^{90} - 3 q^{91} + 43 q^{92} + 19 q^{93} - 27 q^{94} + 27 q^{97} - 86 q^{98} - 24 q^{99}+O(q^{100}) $ 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9 + 14 * q^11 + 3 * q^13 - 19 * q^14 + q^15 + 43 * q^16 + 8 * q^17 - 53 * q^18 + 43 * q^19 - 14 * q^22 + 43 * q^23 + 97 * q^25 - 3 * q^26 + 15 * q^27 + 19 * q^28 - 25 * q^29 - q^30 + 22 * q^31 - 43 * q^32 + 22 * q^33 - 8 * q^34 - 6 * q^35 + 53 * q^36 + 42 * q^37 - 43 * q^38 + 9 * q^39 - 40 * q^41 + 72 * q^43 + 14 * q^44 - q^45 - 43 * q^46 + 27 * q^47 + 86 * q^49 - 97 * q^50 - 3 * q^51 + 3 * q^52 - 5 * q^53 - 15 * q^54 + 86 * q^55 - 19 * q^56 + 25 * q^58 - 43 * q^59 + q^60 + 31 * q^61 - 22 * q^62 + 38 * q^63 + 43 * q^64 - 32 * q^65 - 22 * q^66 + 15 * q^67 + 8 * q^68 - 7 * q^69 + 6 * q^70 + 14 * q^71 - 53 * q^72 + 93 * q^73 - 42 * q^74 - 13 * q^75 + 43 * q^76 + 38 * q^77 - 9 * q^78 + 15 * q^79 + 43 * q^81 + 40 * q^82 + 34 * q^83 + 16 * q^85 - 72 * q^86 + 60 * q^87 - 14 * q^88 - 37 * q^89 + q^90 - 3 * q^91 + 43 * q^92 + 19 * q^93 - 27 * q^94 + 27 * q^97 - 86 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.54429	−1.46894	−0.734472	−	0.678639i	$-0.762570\pi$
$3$	−2.54429	−1.46894	−0.734472	+	0.678639i	$0.762570\pi$
$4$	1.00000	0.500000
$5$	−4.40933	−1.97191	−0.985957	−	0.167000i	$-0.946592\pi$
$5$	−4.40933	−1.97191	−0.985957	+	0.167000i	$0.946592\pi$
$6$	2.54429	1.03870
$7$	−2.39004	−0.903350	−0.451675	−	0.892183i	$-0.649173\pi$
$7$	−2.39004	−0.903350	−0.451675	+	0.892183i	$0.649173\pi$
$8$	−1.00000	−0.353553
$9$	3.47339	1.15780
$10$	4.40933	1.39435
$11$	−3.64734	−1.09971	−0.549857	−	0.835259i	$-0.685318\pi$
$11$	−3.64734	−1.09971	−0.549857	+	0.835259i	$0.685318\pi$
$12$	−2.54429	−0.734472
$13$	5.13023	1.42287	0.711434	−	0.702753i	$-0.248046\pi$
$13$	5.13023	1.42287	0.711434	+	0.702753i	$0.248046\pi$
$14$	2.39004	0.638765
$15$	11.2186	2.89663
$16$	1.00000	0.250000
$17$	2.22335	0.539243	0.269621	−	0.962966i	$-0.413101\pi$
$17$	2.22335	0.539243	0.269621	+	0.962966i	$0.413101\pi$
$18$	−3.47339	−0.818686
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−4.40933	−0.985957
$21$	6.08094	1.32697
$22$	3.64734	0.777615
$23$	3.94690	0.822986	0.411493	−	0.911413i	$-0.365007\pi$
$23$	3.94690	0.822986	0.411493	+	0.911413i	$0.365007\pi$
$24$	2.54429	0.519350
$25$	14.4422	2.88844
$26$	−5.13023	−1.00612
$27$	−1.20444	−0.231795
$28$	−2.39004	−0.451675
$29$	4.94263	0.917823	0.458911	−	0.888482i	$-0.348240\pi$
$29$	4.94263	0.917823	0.458911	+	0.888482i	$0.348240\pi$
$30$	−11.2186	−2.04823
$31$	9.26564	1.66416	0.832079	−	0.554657i	$-0.187151\pi$
$31$	9.26564	1.66416	0.832079	+	0.554657i	$0.187151\pi$
$32$	−1.00000	−0.176777
$33$	9.27987	1.61542
$34$	−2.22335	−0.381302
$35$	10.5385	1.78133
$36$	3.47339	0.578899
$37$	−3.48491	−0.572915	−0.286457	−	0.958093i	$-0.592478\pi$
$37$	−3.48491	−0.572915	−0.286457	+	0.958093i	$0.592478\pi$
$38$	−1.00000	−0.162221
$39$	−13.0528	−2.09011
$40$	4.40933	0.697177
$41$	10.8838	1.69976	0.849878	−	0.526979i	$-0.176675\pi$
$41$	10.8838	1.69976	0.849878	+	0.526979i	$0.176675\pi$
$42$	−6.08094	−0.938310
$43$	−9.31376	−1.42034	−0.710168	−	0.704032i	$-0.751381\pi$
$43$	−9.31376	−1.42034	−0.710168	+	0.704032i	$0.751381\pi$
$44$	−3.64734	−0.549857
$45$	−15.3153	−2.28308
$46$	−3.94690	−0.581939
$47$	7.12371	1.03910	0.519550	−	0.854440i	$-0.326100\pi$
$47$	7.12371	1.03910	0.519550	+	0.854440i	$0.326100\pi$
$48$	−2.54429	−0.367236
$49$	−1.28772	−0.183959
$50$	−14.4422	−2.04244
$51$	−5.65685	−0.792117
$52$	5.13023	0.711434
$53$	−8.00437	−1.09948	−0.549742	−	0.835334i	$-0.685274\pi$
$53$	−8.00437	−1.09948	−0.549742	+	0.835334i	$0.685274\pi$
$54$	1.20444	0.163904
$55$	16.0823	2.16854
$56$	2.39004	0.319382
$57$	−2.54429	−0.336999
$58$	−4.94263	−0.648999
$59$	−2.21452	−0.288306	−0.144153	−	0.989555i	$-0.546046\pi$
$59$	−2.21452	−0.288306	−0.144153	+	0.989555i	$0.546046\pi$
$60$	11.2186	1.44832
$61$	−7.43983	−0.952573	−0.476286	−	0.879290i	$-0.658017\pi$
$61$	−7.43983	−0.952573	−0.476286	+	0.879290i	$0.658017\pi$
$62$	−9.26564	−1.17674
$63$	−8.30154	−1.04590
$64$	1.00000	0.125000
$65$	−22.6209	−2.80577
$66$	−9.27987	−1.14227
$67$	12.2511	1.49672	0.748358	−	0.663295i	$-0.230843\pi$
$67$	12.2511	1.49672	0.748358	+	0.663295i	$0.230843\pi$
$68$	2.22335	0.269621
$69$	−10.0420	−1.20892
$70$	−10.5385	−1.25959
$71$	−6.23150	−0.739543	−0.369772	−	0.929123i	$-0.620564\pi$
$71$	−6.23150	−0.739543	−0.369772	+	0.929123i	$0.620564\pi$
$72$	−3.47339	−0.409343
$73$	4.65644	0.544995	0.272498	−	0.962156i	$-0.412150\pi$
$73$	4.65644	0.544995	0.272498	+	0.962156i	$0.412150\pi$
$74$	3.48491	0.405112
$75$	−36.7451	−4.24296
$76$	1.00000	0.114708
$77$	8.71727	0.993425
$78$	13.0528	1.47793
$79$	12.3974	1.39482	0.697410	−	0.716672i	$-0.254336\pi$
$79$	12.3974	1.39482	0.697410	+	0.716672i	$0.254336\pi$
$80$	−4.40933	−0.492978
$81$	−7.35572	−0.817303
$82$	−10.8838	−1.20191
$83$	9.55833	1.04916	0.524581	−	0.851360i	$-0.324222\pi$
$83$	9.55833	1.04916	0.524581	+	0.851360i	$0.324222\pi$
$84$	6.08094	0.663485
$85$	−9.80351	−1.06334
$86$	9.31376	1.00433
$87$	−12.5755	−1.34823
$88$	3.64734	0.388807
$89$	−10.8191	−1.14682	−0.573410	−	0.819269i	$-0.694380\pi$
$89$	−10.8191	−1.14682	−0.573410	+	0.819269i	$0.694380\pi$
$90$	15.3153	1.61438
$91$	−12.2614	−1.28535
$92$	3.94690	0.411493
$93$	−23.5744	−2.44455
$94$	−7.12371	−0.734754
$95$	−4.40933	−0.452388
$96$	2.54429	0.259675
$97$	2.60273	0.264268	0.132134	−	0.991232i	$-0.457817\pi$
$97$	2.60273	0.264268	0.132134	+	0.991232i	$0.457817\pi$
$98$	1.28772	0.130079
$99$	−12.6686	−1.27324
$100$	14.4422	1.44422
$101$	−17.3905	−1.73042	−0.865212	−	0.501407i	$-0.832816\pi$
$101$	−17.3905	−1.73042	−0.865212	+	0.501407i	$0.832816\pi$
$102$	5.65685	0.560111
$103$	12.5311	1.23472	0.617361	−	0.786680i	$-0.288202\pi$
$103$	12.5311	1.23472	0.617361	+	0.786680i	$0.288202\pi$
$104$	−5.13023	−0.503060
$105$	−26.8129	−2.61667
$106$	8.00437	0.777453
$107$	11.3669	1.09888	0.549441	−	0.835533i	$-0.314841\pi$
$107$	11.3669	1.09888	0.549441	+	0.835533i	$0.314841\pi$
$108$	−1.20444	−0.115898
$109$	2.08737	0.199934	0.0999671	−	0.994991i	$-0.468126\pi$
$109$	2.08737	0.199934	0.0999671	+	0.994991i	$0.468126\pi$
$110$	−16.0823	−1.53339
$111$	8.86660	0.841580
$112$	−2.39004	−0.225837
$113$	2.50919	0.236045	0.118022	−	0.993011i	$-0.462345\pi$
$113$	2.50919	0.236045	0.118022	+	0.993011i	$0.462345\pi$
$114$	2.54429	0.238294
$115$	−17.4032	−1.62286
$116$	4.94263	0.458911
$117$	17.8193	1.64739
$118$	2.21452	0.203863
$119$	−5.31390	−0.487125
$120$	−11.2186	−1.02411
$121$	2.30306	0.209369
$122$	7.43983	0.673571
$123$	−27.6914	−2.49685
$124$	9.26564	0.832079
$125$	−41.6339	−3.72385
$126$	8.30154	0.739560
$127$	11.1864	0.992634	0.496317	−	0.868141i	$-0.334685\pi$
$127$	11.1864	0.992634	0.496317	+	0.868141i	$0.334685\pi$
$128$	−1.00000	−0.0883883
$129$	23.6969	2.08639
$130$	22.6209	1.98398
$131$	19.2343	1.68051	0.840256	−	0.542190i	$-0.182405\pi$
$131$	19.2343	1.68051	0.840256	+	0.542190i	$0.182405\pi$
$132$	9.27987	0.807709
$133$	−2.39004	−0.207243
$134$	−12.2511	−1.05834
$135$	5.31080	0.457081
$136$	−2.22335	−0.190651
$137$	−4.03585	−0.344806	−0.172403	−	0.985027i	$-0.555153\pi$
$137$	−4.03585	−0.344806	−0.172403	+	0.985027i	$0.555153\pi$
$138$	10.0420	0.854836
$139$	−1.78377	−0.151298	−0.0756488	−	0.997135i	$-0.524103\pi$
$139$	−1.78377	−0.151298	−0.0756488	+	0.997135i	$0.524103\pi$
$140$	10.5385	0.890664
$141$	−18.1248	−1.52638
$142$	6.23150	0.522936
$143$	−18.7117	−1.56475
$144$	3.47339	0.289449
$145$	−21.7937	−1.80987
$146$	−4.65644	−0.385370
$147$	3.27632	0.270226
$148$	−3.48491	−0.286457
$149$	3.01827	0.247266	0.123633	−	0.992328i	$-0.460545\pi$
$149$	3.01827	0.247266	0.123633	+	0.992328i	$0.460545\pi$
$150$	36.7451	3.00023
$151$	22.0762	1.79654	0.898269	−	0.439445i	$-0.144825\pi$
$151$	22.0762	1.79654	0.898269	+	0.439445i	$0.144825\pi$
$152$	−1.00000	−0.0811107
$153$	7.72258	0.624334
$154$	−8.71727	−0.702458
$155$	−40.8553	−3.28158
$156$	−13.0528	−1.04506
$157$	−4.90713	−0.391632	−0.195816	−	0.980641i	$-0.562735\pi$
$157$	−4.90713	−0.391632	−0.195816	+	0.980641i	$0.562735\pi$
$158$	−12.3974	−0.986287
$159$	20.3654	1.61508
$160$	4.40933	0.348588
$161$	−9.43325	−0.743444
$162$	7.35572	0.577920
$163$	−2.05868	−0.161248	−0.0806241	−	0.996745i	$-0.525691\pi$
$163$	−2.05868	−0.161248	−0.0806241	+	0.996745i	$0.525691\pi$
$164$	10.8838	0.849878
$165$	−40.9180	−3.18546
$166$	−9.55833	−0.741870
$167$	14.9187	1.15444	0.577220	−	0.816589i	$-0.304137\pi$
$167$	14.9187	1.15444	0.577220	+	0.816589i	$0.304137\pi$
$168$	−6.08094	−0.469155
$169$	13.3192	1.02455
$170$	9.80351	0.751895
$171$	3.47339	0.265617
$172$	−9.31376	−0.710168
$173$	0.202697	0.0154108	0.00770540	−	0.999970i	$-0.497547\pi$
$173$	0.202697	0.0154108	0.00770540	+	0.999970i	$0.497547\pi$
$174$	12.5755	0.953343
$175$	−34.5175	−2.60928
$176$	−3.64734	−0.274928
$177$	5.63437	0.423505
$178$	10.8191	0.810924
$179$	13.7338	1.02651	0.513256	−	0.858236i	$-0.328439\pi$
$179$	13.7338	1.02651	0.513256	+	0.858236i	$0.328439\pi$
$180$	−15.3153	−1.14154
$181$	19.9206	1.48069	0.740344	−	0.672228i	$-0.234663\pi$
$181$	19.9206	1.48069	0.740344	+	0.672228i	$0.234663\pi$
$182$	12.2614	0.908878
$183$	18.9291	1.39928
$184$	−3.94690	−0.290969
$185$	15.3661	1.12974
$186$	23.5744	1.72856
$187$	−8.10932	−0.593012
$188$	7.12371	0.519550
$189$	2.87867	0.209392
$190$	4.40933	0.319887
$191$	−17.0501	−1.23370	−0.616850	−	0.787081i	$-0.711592\pi$
$191$	−17.0501	−1.23370	−0.616850	+	0.787081i	$0.711592\pi$
$192$	−2.54429	−0.183618
$193$	9.36697	0.674249	0.337124	−	0.941460i	$-0.390546\pi$
$193$	9.36697	0.674249	0.337124	+	0.941460i	$0.390546\pi$
$194$	−2.60273	−0.186865
$195$	57.5540	4.12153
$196$	−1.28772	−0.0919797
$197$	−5.52992	−0.393991	−0.196995	−	0.980404i	$-0.563118\pi$
$197$	−5.52992	−0.393991	−0.196995	+	0.980404i	$0.563118\pi$
$198$	12.6686	0.900320
$199$	−14.3525	−1.01742	−0.508711	−	0.860938i	$-0.669878\pi$
$199$	−14.3525	−1.01742	−0.508711	+	0.860938i	$0.669878\pi$
$200$	−14.4422	−1.02122
$201$	−31.1704	−2.19859
$202$	17.3905	1.22359
$203$	−11.8131	−0.829115
$204$	−5.65685	−0.396059
$205$	−47.9901	−3.35177
$206$	−12.5311	−0.873080
$207$	13.7091	0.952851
$208$	5.13023	0.355717
$209$	−3.64734	−0.252291
$210$	26.8129	1.85027
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−8.00437	−0.549742
$213$	15.8547	1.08635
$214$	−11.3669	−0.777026
$215$	41.0675	2.80078
$216$	1.20444	0.0819520
$217$	−22.1452	−1.50332
$218$	−2.08737	−0.141375
$219$	−11.8473	−0.800567
$220$	16.0823	1.08427
$221$	11.4063	0.767271
$222$	−8.86660	−0.595087
$223$	12.6094	0.844390	0.422195	−	0.906505i	$-0.361260\pi$
$223$	12.6094	0.844390	0.422195	+	0.906505i	$0.361260\pi$
$224$	2.39004	0.159691
$225$	50.1635	3.34423
$226$	−2.50919	−0.166909
$227$	−11.2737	−0.748265	−0.374132	−	0.927375i	$-0.622059\pi$
$227$	−11.2737	−0.748265	−0.374132	+	0.927375i	$0.622059\pi$
$228$	−2.54429	−0.168499
$229$	−19.3605	−1.27938	−0.639689	−	0.768634i	$-0.720937\pi$
$229$	−19.3605	−1.27938	−0.639689	+	0.768634i	$0.720937\pi$
$230$	17.4032	1.14753
$231$	−22.1792	−1.45929
$232$	−4.94263	−0.324499
$233$	5.24098	0.343348	0.171674	−	0.985154i	$-0.445082\pi$
$233$	5.24098	0.343348	0.171674	+	0.985154i	$0.445082\pi$
$234$	−17.8193	−1.16488
$235$	−31.4108	−2.04901
$236$	−2.21452	−0.144153
$237$	−31.5426	−2.04891
$238$	5.31390	0.344449
$239$	3.83161	0.247846	0.123923	−	0.992292i	$-0.460452\pi$
$239$	3.83161	0.247846	0.123923	+	0.992292i	$0.460452\pi$
$240$	11.2186	0.724158
$241$	19.3982	1.24955	0.624773	−	0.780807i	$-0.285192\pi$
$241$	19.3982	1.24955	0.624773	+	0.780807i	$0.285192\pi$
$242$	−2.30306	−0.148046
$243$	22.3284	1.43237
$244$	−7.43983	−0.476286
$245$	5.67797	0.362752
$246$	27.6914	1.76554
$247$	5.13023	0.326428
$248$	−9.26564	−0.588369
$249$	−24.3191	−1.54116
$250$	41.6339	2.63316
$251$	−9.18112	−0.579507	−0.289754	−	0.957101i	$-0.593573\pi$
$251$	−9.18112	−0.579507	−0.289754	+	0.957101i	$0.593573\pi$
$252$	−8.30154	−0.522948
$253$	−14.3957	−0.905048
$254$	−11.1864	−0.701899
$255$	24.9429	1.56199
$256$	1.00000	0.0625000
$257$	−22.6068	−1.41018	−0.705088	−	0.709120i	$-0.749093\pi$
$257$	−22.6068	−1.41018	−0.705088	+	0.709120i	$0.749093\pi$
$258$	−23.6969	−1.47530
$259$	8.32906	0.517543
$260$	−22.6209	−1.40289
$261$	17.1677	1.06265
$262$	−19.2343	−1.18830
$263$	−3.62823	−0.223726	−0.111863	−	0.993724i	$-0.535682\pi$
$263$	−3.62823	−0.223726	−0.111863	+	0.993724i	$0.535682\pi$
$264$	−9.27987	−0.571136
$265$	35.2939	2.16809
$266$	2.39004	0.146543
$267$	27.5268	1.68461
$268$	12.2511	0.748358
$269$	1.16357	0.0709443	0.0354722	−	0.999371i	$-0.488706\pi$
$269$	1.16357	0.0709443	0.0354722	+	0.999371i	$0.488706\pi$
$270$	−5.31080	−0.323205
$271$	−13.2733	−0.806294	−0.403147	−	0.915135i	$-0.632084\pi$
$271$	−13.2733	−0.806294	−0.403147	+	0.915135i	$0.632084\pi$
$272$	2.22335	0.134811
$273$	31.1966	1.88810
$274$	4.03585	0.243815
$275$	−52.6756	−3.17646
$276$	−10.0420	−0.604460
$277$	13.3413	0.801599	0.400799	−	0.916166i	$-0.368732\pi$
$277$	13.3413	0.801599	0.400799	+	0.916166i	$0.368732\pi$
$278$	1.78377	0.106984
$279$	32.1832	1.92676
$280$	−10.5385	−0.629794
$281$	−18.3206	−1.09292	−0.546458	−	0.837487i	$-0.684024\pi$
$281$	−18.3206	−1.09292	−0.546458	+	0.837487i	$0.684024\pi$
$282$	18.1248	1.07931
$283$	23.0148	1.36809	0.684045	−	0.729440i	$-0.260219\pi$
$283$	23.0148	1.36809	0.684045	+	0.729440i	$0.260219\pi$
$284$	−6.23150	−0.369772
$285$	11.2186	0.664533
$286$	18.7117	1.10644
$287$	−26.0126	−1.53547
$288$	−3.47339	−0.204672
$289$	−12.0567	−0.709217
$290$	21.7937	1.27977
$291$	−6.62210	−0.388194
$292$	4.65644	0.272498
$293$	−12.6328	−0.738015	−0.369008	−	0.929426i	$-0.620302\pi$
$293$	−12.6328	−0.738015	−0.369008	+	0.929426i	$0.620302\pi$
$294$	−3.27632	−0.191079
$295$	9.76455	0.568514
$296$	3.48491	0.202556
$297$	4.39301	0.254908
$298$	−3.01827	−0.174844
$299$	20.2485	1.17100
$300$	−36.7451	−2.12148
$301$	22.2603	1.28306
$302$	−22.0762	−1.27034
$303$	44.2465	2.54190
$304$	1.00000	0.0573539
$305$	32.8047	1.87839
$306$	−7.72258	−0.441470
$307$	−1.45263	−0.0829059	−0.0414530	−	0.999140i	$-0.513199\pi$
$307$	−1.45263	−0.0829059	−0.0414530	+	0.999140i	$0.513199\pi$
$308$	8.71727	0.496713
$309$	−31.8826	−1.81374
$310$	40.8553	2.32042
$311$	−3.96295	−0.224718	−0.112359	−	0.993668i	$-0.535841\pi$
$311$	−3.96295	−0.224718	−0.112359	+	0.993668i	$0.535841\pi$
$312$	13.0528	0.738967
$313$	−3.67199	−0.207553	−0.103777	−	0.994601i	$-0.533093\pi$
$313$	−3.67199	−0.207553	−0.103777	+	0.994601i	$0.533093\pi$
$314$	4.90713	0.276925
$315$	36.6043	2.06242
$316$	12.3974	0.697410
$317$	5.50832	0.309378	0.154689	−	0.987963i	$-0.450562\pi$
$317$	5.50832	0.309378	0.154689	+	0.987963i	$0.450562\pi$
$318$	−20.3654	−1.14204
$319$	−18.0274	−1.00934
$320$	−4.40933	−0.246489
$321$	−28.9207	−1.61420
$322$	9.43325	0.525694
$323$	2.22335	0.123711
$324$	−7.35572	−0.408651
$325$	74.0918	4.10988
$326$	2.05868	0.114020
$327$	−5.31088	−0.293692
$328$	−10.8838	−0.600955
$329$	−17.0259	−0.938670
$330$	40.9180	2.25246
$331$	−1.07397	−0.0590306	−0.0295153	−	0.999564i	$-0.509396\pi$
$331$	−1.07397	−0.0590306	−0.0295153	+	0.999564i	$0.509396\pi$
$332$	9.55833	0.524581
$333$	−12.1044	−0.663319
$334$	−14.9187	−0.816312
$335$	−54.0194	−2.95139
$336$	6.08094	0.331743
$337$	27.2925	1.48672	0.743359	−	0.668893i	$-0.233232\pi$
$337$	27.2925	1.48672	0.743359	+	0.668893i	$0.233232\pi$
$338$	−13.3192	−0.724470
$339$	−6.38410	−0.346737
$340$	−9.80351	−0.531670
$341$	−33.7949	−1.83010
$342$	−3.47339	−0.187820
$343$	19.8080	1.06953
$344$	9.31376	0.502164
$345$	44.2787	2.38389
$346$	−0.202697	−0.0108971
$347$	16.1349	0.866168	0.433084	−	0.901354i	$-0.357425\pi$
$347$	16.1349	0.866168	0.433084	+	0.901354i	$0.357425\pi$
$348$	−12.5755	−0.674115
$349$	2.01986	0.108121	0.0540603	−	0.998538i	$-0.482784\pi$
$349$	2.01986	0.108121	0.0540603	+	0.998538i	$0.482784\pi$
$350$	34.5175	1.84504
$351$	−6.17907	−0.329814
$352$	3.64734	0.194404
$353$	−24.3716	−1.29717	−0.648585	−	0.761142i	$-0.724639\pi$
$353$	−24.3716	−1.29717	−0.648585	+	0.761142i	$0.724639\pi$
$354$	−5.63437	−0.299463
$355$	27.4768	1.45832
$356$	−10.8191	−0.573410
$357$	13.5201	0.715559
$358$	−13.7338	−0.725853
$359$	21.2156	1.11972	0.559859	−	0.828588i	$-0.310855\pi$
$359$	21.2156	1.11972	0.559859	+	0.828588i	$0.310855\pi$
$360$	15.3153	0.807189
$361$	1.00000	0.0526316
$362$	−19.9206	−1.04700
$363$	−5.85964	−0.307551
$364$	−12.2614	−0.642674
$365$	−20.5318	−1.07468
$366$	−18.9291	−0.989438
$367$	2.16080	0.112793	0.0563963	−	0.998408i	$-0.482039\pi$
$367$	2.16080	0.112793	0.0563963	+	0.998408i	$0.482039\pi$
$368$	3.94690	0.205746
$369$	37.8035	1.96797
$370$	−15.3661	−0.798846
$371$	19.1307	0.993219
$372$	−23.5744	−1.22228
$373$	16.5405	0.856437	0.428218	−	0.903675i	$-0.359141\pi$
$373$	16.5405	0.856437	0.428218	+	0.903675i	$0.359141\pi$
$374$	8.10932	0.419323
$375$	105.929	5.47013
$376$	−7.12371	−0.367377
$377$	25.3568	1.30594
$378$	−2.87867	−0.148063
$379$	24.9911	1.28371	0.641853	−	0.766828i	$-0.278166\pi$
$379$	24.9911	1.28371	0.641853	+	0.766828i	$0.278166\pi$
$380$	−4.40933	−0.226194
$381$	−28.4615	−1.45812
$382$	17.0501	0.872358
$383$	−33.6778	−1.72086	−0.860428	−	0.509571i	$-0.829804\pi$
$383$	−33.6778	−1.72086	−0.860428	+	0.509571i	$0.829804\pi$
$384$	2.54429	0.129838
$385$	−38.4374	−1.95895
$386$	−9.36697	−0.476766
$387$	−32.3503	−1.64446
$388$	2.60273	0.132134
$389$	7.31001	0.370632	0.185316	−	0.982679i	$-0.440669\pi$
$389$	7.31001	0.370632	0.185316	+	0.982679i	$0.440669\pi$
$390$	−57.5540	−2.91436
$391$	8.77536	0.443789
$392$	1.28772	0.0650395
$393$	−48.9377	−2.46858
$394$	5.52992	0.278594
$395$	−54.6644	−2.75047
$396$	−12.6686	−0.636622
$397$	25.2383	1.26667	0.633336	−	0.773877i	$-0.281685\pi$
$397$	25.2383	1.26667	0.633336	+	0.773877i	$0.281685\pi$
$398$	14.3525	0.719426
$399$	6.08094	0.304428
$400$	14.4422	0.722111
$401$	−31.5643	−1.57625	−0.788123	−	0.615518i	$-0.788947\pi$
$401$	−31.5643	−1.57625	−0.788123	+	0.615518i	$0.788947\pi$
$402$	31.1704	1.55464
$403$	47.5348	2.36788
$404$	−17.3905	−0.865212
$405$	32.4338	1.61165
$406$	11.8131	0.586273
$407$	12.7106	0.630042
$408$	5.65685	0.280056
$409$	0.697980	0.0345129	0.0172564	−	0.999851i	$-0.494507\pi$
$409$	0.697980	0.0345129	0.0172564	+	0.999851i	$0.494507\pi$
$410$	47.9901	2.37006
$411$	10.2684	0.506501
$412$	12.5311	0.617361
$413$	5.29278	0.260441
$414$	−13.7091	−0.673767
$415$	−42.1459	−2.06886
$416$	−5.13023	−0.251530
$417$	4.53843	0.222248
$418$	3.64734	0.178397
$419$	22.4417	1.09635	0.548173	−	0.836365i	$-0.315323\pi$
$419$	22.4417	1.09635	0.548173	+	0.836365i	$0.315323\pi$
$420$	−26.8129	−1.30834
$421$	36.6806	1.78771	0.893853	−	0.448361i	$-0.147992\pi$
$421$	36.6806	1.78771	0.893853	+	0.448361i	$0.147992\pi$
$422$	1.00000	0.0486792
$423$	24.7434	1.20307
$424$	8.00437	0.388727
$425$	32.1102	1.55757
$426$	−15.8547	−0.768164
$427$	17.7815	0.860506
$428$	11.3669	0.549441
$429$	47.6078	2.29853
$430$	−41.0675	−1.98045
$431$	−35.1875	−1.69492	−0.847461	−	0.530857i	$-0.821870\pi$
$431$	−35.1875	−1.69492	−0.847461	+	0.530857i	$0.821870\pi$
$432$	−1.20444	−0.0579488
$433$	−2.99565	−0.143962	−0.0719809	−	0.997406i	$-0.522932\pi$
$433$	−2.99565	−0.143962	−0.0719809	+	0.997406i	$0.522932\pi$
$434$	22.1452	1.06301
$435$	55.4494	2.65859
$436$	2.08737	0.0999671
$437$	3.94690	0.188806
$438$	11.8473	0.566087
$439$	17.0132	0.811994	0.405997	−	0.913874i	$-0.366924\pi$
$439$	17.0132	0.811994	0.405997	+	0.913874i	$0.366924\pi$
$440$	−16.0823	−0.766694
$441$	−4.47274	−0.212988
$442$	−11.4063	−0.542543
$443$	2.01077	0.0955344	0.0477672	−	0.998858i	$-0.484789\pi$
$443$	2.01077	0.0955344	0.0477672	+	0.998858i	$0.484789\pi$
$444$	8.86660	0.420790
$445$	47.7049	2.26143
$446$	−12.6094	−0.597074
$447$	−7.67934	−0.363220
$448$	−2.39004	−0.112919
$449$	−11.7629	−0.555125	−0.277562	−	0.960708i	$-0.589527\pi$
$449$	−11.7629	−0.555125	−0.277562	+	0.960708i	$0.589527\pi$
$450$	−50.1635	−2.36473
$451$	−39.6967	−1.86924
$452$	2.50919	0.118022
$453$	−56.1683	−2.63902
$454$	11.2737	0.529103
$455$	54.0648	2.53459
$456$	2.54429	0.119147
$457$	−14.8551	−0.694891	−0.347446	−	0.937700i	$-0.612951\pi$
$457$	−14.8551	−0.694891	−0.347446	+	0.937700i	$0.612951\pi$
$458$	19.3605	0.904657
$459$	−2.67791	−0.124994
$460$	−17.4032	−0.811429
$461$	10.2012	0.475119	0.237559	−	0.971373i	$-0.423653\pi$
$461$	10.2012	0.475119	0.237559	+	0.971373i	$0.423653\pi$
$462$	22.1792	1.03187
$463$	3.57951	0.166354	0.0831770	−	0.996535i	$-0.473493\pi$
$463$	3.57951	0.166354	0.0831770	+	0.996535i	$0.473493\pi$
$464$	4.94263	0.229456
$465$	103.948	4.82045
$466$	−5.24098	−0.242784
$467$	−32.4056	−1.49955	−0.749777	−	0.661691i	$-0.769839\pi$
$467$	−32.4056	−1.49955	−0.749777	+	0.661691i	$0.769839\pi$
$468$	17.8193	0.823697
$469$	−29.2807	−1.35206
$470$	31.4108	1.44887
$471$	12.4851	0.575285
$472$	2.21452	0.101931
$473$	33.9704	1.56196
$474$	31.5426	1.44880
$475$	14.4422	0.662655
$476$	−5.31390	−0.243562
$477$	−27.8023	−1.27298
$478$	−3.83161	−0.175254
$479$	−1.53913	−0.0703248	−0.0351624	−	0.999382i	$-0.511195\pi$
$479$	−1.53913	−0.0703248	−0.0351624	+	0.999382i	$0.511195\pi$
$480$	−11.2186	−0.512057
$481$	−17.8784	−0.815183
$482$	−19.3982	−0.883562
$483$	24.0009	1.09208
$484$	2.30306	0.104684
$485$	−11.4763	−0.521113
$486$	−22.3284	−1.01284
$487$	−40.3178	−1.82697	−0.913487	−	0.406869i	$-0.866621\pi$
$487$	−40.3178	−1.82697	−0.913487	+	0.406869i	$0.866621\pi$
$488$	7.43983	0.336785
$489$	5.23787	0.236865
$490$	−5.67797	−0.256505
$491$	−15.0575	−0.679536	−0.339768	−	0.940509i	$-0.610349\pi$
$491$	−15.0575	−0.679536	−0.339768	+	0.940509i	$0.610349\pi$
$492$	−27.6914	−1.24842
$493$	10.9892	0.494929
$494$	−5.13023	−0.230820
$495$	55.8602	2.51073
$496$	9.26564	0.416039
$497$	14.8935	0.668066
$498$	24.3191	1.08977
$499$	−36.8699	−1.65052	−0.825261	−	0.564751i	$-0.808972\pi$
$499$	−36.8699	−1.65052	−0.825261	+	0.564751i	$0.808972\pi$
$500$	−41.6339	−1.86192
$501$	−37.9573	−1.69581
$502$	9.18112	0.409773
$503$	16.6670	0.743146	0.371573	−	0.928404i	$-0.378819\pi$
$503$	16.6670	0.743146	0.371573	+	0.928404i	$0.378819\pi$
$504$	8.30154	0.369780
$505$	76.6807	3.41225
$506$	14.3957	0.639966
$507$	−33.8879	−1.50501
$508$	11.1864	0.496317
$509$	−10.7964	−0.478542	−0.239271	−	0.970953i	$-0.576908\pi$
$509$	−10.7964	−0.478542	−0.239271	+	0.970953i	$0.576908\pi$
$510$	−24.9429	−1.10449
$511$	−11.1291	−0.492321
$512$	−1.00000	−0.0441942
$513$	−1.20444	−0.0531775
$514$	22.6068	0.997145
$515$	−55.2536	−2.43476
$516$	23.6969	1.04320
$517$	−25.9826	−1.14271
$518$	−8.32906	−0.365958
$519$	−0.515720	−0.0226376
$520$	22.6209	0.991991
$521$	0.235363	0.0103115	0.00515573	−	0.999987i	$-0.498359\pi$
$521$	0.235363	0.0103115	0.00515573	+	0.999987i	$0.498359\pi$
$522$	−17.1677	−0.751409
$523$	−20.4361	−0.893608	−0.446804	−	0.894632i	$-0.647438\pi$
$523$	−20.4361	−0.893608	−0.446804	+	0.894632i	$0.647438\pi$
$524$	19.2343	0.840256
$525$	87.8223	3.83288
$526$	3.62823	0.158199
$527$	20.6008	0.897385
$528$	9.27987	0.403854
$529$	−7.42197	−0.322694
$530$	−35.2939	−1.53307
$531$	−7.69189	−0.333799
$532$	−2.39004	−0.103621
$533$	55.8361	2.41853
$534$	−27.5268	−1.19120
$535$	−50.1205	−2.16690
$536$	−12.2511	−0.529169
$537$	−34.9427	−1.50789
$538$	−1.16357	−0.0501652
$539$	4.69673	0.202303
$540$	5.31080	0.228540
$541$	8.38541	0.360517	0.180259	−	0.983619i	$-0.442307\pi$
$541$	8.38541	0.360517	0.180259	+	0.983619i	$0.442307\pi$
$542$	13.2733	0.570136
$543$	−50.6837	−2.17505
$544$	−2.22335	−0.0953255
$545$	−9.20393	−0.394253
$546$	−31.1966	−1.33509
$547$	7.53940	0.322362	0.161181	−	0.986925i	$-0.448470\pi$
$547$	7.53940	0.322362	0.161181	+	0.986925i	$0.448470\pi$
$548$	−4.03585	−0.172403
$549$	−25.8415	−1.10289
$550$	52.6756	2.24610
$551$	4.94263	0.210563
$552$	10.0420	0.427418
$553$	−29.6304	−1.26001
$554$	−13.3413	−0.566816
$555$	−39.0958	−1.65952
$556$	−1.78377	−0.0756488
$557$	−7.66821	−0.324913	−0.162456	−	0.986716i	$-0.551942\pi$
$557$	−7.66821	−0.324913	−0.162456	+	0.986716i	$0.551942\pi$
$558$	−32.1832	−1.36242
$559$	−47.7817	−2.02095
$560$	10.5385	0.445332
$561$	20.6324	0.871102
$562$	18.3206	0.772808
$563$	35.2321	1.48486	0.742428	−	0.669926i	$-0.233674\pi$
$563$	35.2321	1.48486	0.742428	+	0.669926i	$0.233674\pi$
$564$	−18.1248	−0.763190
$565$	−11.0639	−0.465460
$566$	−23.0148	−0.967386
$567$	17.5805	0.738310
$568$	6.23150	0.261468
$569$	−31.8435	−1.33495	−0.667475	−	0.744632i	$-0.732625\pi$
$569$	−31.8435	−1.33495	−0.667475	+	0.744632i	$0.732625\pi$
$570$	−11.2186	−0.469896
$571$	−5.05416	−0.211510	−0.105755	−	0.994392i	$-0.533726\pi$
$571$	−5.05416	−0.211510	−0.105755	+	0.994392i	$0.533726\pi$
$572$	−18.7117	−0.782374
$573$	43.3803	1.81224
$574$	26.0126	1.08574
$575$	57.0020	2.37715
$576$	3.47339	0.144725
$577$	−45.4411	−1.89174	−0.945870	−	0.324546i	$-0.894788\pi$
$577$	−45.4411	−1.89174	−0.945870	+	0.324546i	$0.894788\pi$
$578$	12.0567	0.501492
$579$	−23.8322	−0.990434
$580$	−21.7937	−0.904934
$581$	−22.8448	−0.947761
$582$	6.62210	0.274495
$583$	29.1946	1.20912
$584$	−4.65644	−0.192685
$585$	−78.5712	−3.24852
$586$	12.6328	0.521855
$587$	−29.7555	−1.22814	−0.614071	−	0.789251i	$-0.710469\pi$
$587$	−29.7555	−1.22814	−0.614071	+	0.789251i	$0.710469\pi$
$588$	3.27632	0.135113
$589$	9.26564	0.381784
$590$	−9.76455	−0.402000
$591$	14.0697	0.578751
$592$	−3.48491	−0.143229
$593$	24.1030	0.989793	0.494896	−	0.868952i	$-0.335206\pi$
$593$	24.1030	0.989793	0.494896	+	0.868952i	$0.335206\pi$
$594$	−4.39301	−0.180247
$595$	23.4308	0.960568
$596$	3.01827	0.123633
$597$	36.5169	1.49454
$598$	−20.2485	−0.828023
$599$	14.7876	0.604204	0.302102	−	0.953276i	$-0.402312\pi$
$599$	14.7876	0.604204	0.302102	+	0.953276i	$0.402312\pi$
$600$	36.7451	1.50011
$601$	1.32943	0.0542285	0.0271142	−	0.999632i	$-0.491368\pi$
$601$	1.32943	0.0542285	0.0271142	+	0.999632i	$0.491368\pi$
$602$	−22.2603	−0.907260
$603$	42.5530	1.73289
$604$	22.0762	0.898269
$605$	−10.1549	−0.412857
$606$	−44.2465	−1.79739
$607$	42.7309	1.73439	0.867197	−	0.497964i	$-0.165919\pi$
$607$	42.7309	1.73439	0.867197	+	0.497964i	$0.165919\pi$
$608$	−1.00000	−0.0405554
$609$	30.0558	1.21792
$610$	−32.8047	−1.32822
$611$	36.5462	1.47850
$612$	7.72258	0.312167
$613$	−10.3072	−0.416304	−0.208152	−	0.978096i	$-0.566745\pi$
$613$	−10.3072	−0.416304	−0.208152	+	0.978096i	$0.566745\pi$
$614$	1.45263	0.0586233
$615$	122.101	4.92357
$616$	−8.71727	−0.351229
$617$	8.18132	0.329367	0.164684	−	0.986346i	$-0.447340\pi$
$617$	8.18132	0.329367	0.164684	+	0.986346i	$0.447340\pi$
$618$	31.8826	1.28251
$619$	−31.6019	−1.27019	−0.635093	−	0.772436i	$-0.719038\pi$
$619$	−31.6019	−1.27019	−0.635093	+	0.772436i	$0.719038\pi$
$620$	−40.8553	−1.64079
$621$	−4.75382	−0.190764
$622$	3.96295	0.158900
$623$	25.8580	1.03598
$624$	−13.0528	−0.522529
$625$	111.367	4.45467
$626$	3.67199	0.146762
$627$	9.27987	0.370602
$628$	−4.90713	−0.195816
$629$	−7.74818	−0.308940
$630$	−36.6043	−1.45835
$631$	−30.7032	−1.22227	−0.611137	−	0.791525i	$-0.709288\pi$
$631$	−30.7032	−1.22227	−0.611137	+	0.791525i	$0.709288\pi$
$632$	−12.3974	−0.493144
$633$	2.54429	0.101126
$634$	−5.50832	−0.218763
$635$	−49.3247	−1.95739
$636$	20.3654	0.807541
$637$	−6.60627	−0.261750
$638$	18.0274	0.713712
$639$	−21.6444	−0.856241
$640$	4.40933	0.174294
$641$	25.1822	0.994639	0.497319	−	0.867567i	$-0.334318\pi$
$641$	25.1822	0.994639	0.497319	+	0.867567i	$0.334318\pi$
$642$	28.9207	1.14141
$643$	−10.1007	−0.398332	−0.199166	−	0.979966i	$-0.563823\pi$
$643$	−10.1007	−0.398332	−0.199166	+	0.979966i	$0.563823\pi$
$644$	−9.43325	−0.371722
$645$	−104.487	−4.11419
$646$	−2.22335	−0.0874767
$647$	15.0701	0.592466	0.296233	−	0.955116i	$-0.404269\pi$
$647$	15.0701	0.592466	0.296233	+	0.955116i	$0.404269\pi$
$648$	7.35572	0.288960
$649$	8.07709	0.317053
$650$	−74.0918	−2.90612
$651$	56.3438	2.20829
$652$	−2.05868	−0.0806241
$653$	−25.1127	−0.982736	−0.491368	−	0.870952i	$-0.663503\pi$
$653$	−25.1127	−0.982736	−0.491368	+	0.870952i	$0.663503\pi$
$654$	5.31088	0.207672
$655$	−84.8106	−3.31383
$656$	10.8838	0.424939
$657$	16.1736	0.630994
$658$	17.0259	0.663740
$659$	49.9533	1.94590	0.972952	−	0.231005i	$-0.0742015\pi$
$659$	49.9533	1.94590	0.972952	+	0.231005i	$0.0742015\pi$
$660$	−40.9180	−1.59273
$661$	4.23596	0.164760	0.0823799	−	0.996601i	$-0.473748\pi$
$661$	4.23596	0.164760	0.0823799	+	0.996601i	$0.473748\pi$
$662$	1.07397	0.0417409
$663$	−29.0209	−1.12708
$664$	−9.55833	−0.370935
$665$	10.5385	0.408665
$666$	12.1044	0.469038
$667$	19.5081	0.755355
$668$	14.9187	0.577220
$669$	−32.0820	−1.24036
$670$	54.0194	2.08695
$671$	27.1356	1.04756
$672$	−6.08094	−0.234577
$673$	36.4880	1.40651	0.703254	−	0.710939i	$-0.251730\pi$
$673$	36.4880	1.40651	0.703254	+	0.710939i	$0.251730\pi$
$674$	−27.2925	−1.05127
$675$	−17.3948	−0.669528
$676$	13.3192	0.512277
$677$	−19.1974	−0.737817	−0.368908	−	0.929466i	$-0.620268\pi$
$677$	−19.1974	−0.737817	−0.368908	+	0.929466i	$0.620268\pi$
$678$	6.38410	0.245180
$679$	−6.22063	−0.238726
$680$	9.80351	0.375947
$681$	28.6836	1.09916
$682$	33.7949	1.29407
$683$	15.3064	0.585683	0.292842	−	0.956161i	$-0.405399\pi$
$683$	15.3064	0.585683	0.292842	+	0.956161i	$0.405399\pi$
$684$	3.47339	0.132808
$685$	17.7954	0.679927
$686$	−19.8080	−0.756271
$687$	49.2587	1.87934
$688$	−9.31376	−0.355084
$689$	−41.0642	−1.56442
$690$	−44.2787	−1.68566
$691$	−35.8566	−1.36405	−0.682026	−	0.731328i	$-0.738901\pi$
$691$	−35.8566	−1.36405	−0.682026	+	0.731328i	$0.738901\pi$
$692$	0.202697	0.00770540
$693$	30.2785	1.15019
$694$	−16.1349	−0.612473
$695$	7.86524	0.298346
$696$	12.5755	0.476671
$697$	24.1984	0.916581
$698$	−2.01986	−0.0764528
$699$	−13.3346	−0.504359
$700$	−34.5175	−1.30464
$701$	−3.16369	−0.119491	−0.0597455	−	0.998214i	$-0.519029\pi$
$701$	−3.16369	−0.119491	−0.0597455	+	0.998214i	$0.519029\pi$
$702$	6.17907	0.233214
$703$	−3.48491	−0.131436
$704$	−3.64734	−0.137464
$705$	79.9181	3.00989
$706$	24.3716	0.917237
$707$	41.5641	1.56318
$708$	5.63437	0.211752
$709$	−4.22699	−0.158748	−0.0793740	−	0.996845i	$-0.525292\pi$
$709$	−4.22699	−0.158748	−0.0793740	+	0.996845i	$0.525292\pi$
$710$	−27.4768	−1.03118
$711$	43.0612	1.61492
$712$	10.8191	0.405462
$713$	36.5706	1.36958
$714$	−13.5201	−0.505977
$715$	82.5059	3.08555
$716$	13.7338	0.513256
$717$	−9.74872	−0.364072
$718$	−21.2156	−0.791761
$719$	−28.9614	−1.08008	−0.540040	−	0.841639i	$-0.681591\pi$
$719$	−28.9614	−1.08008	−0.540040	+	0.841639i	$0.681591\pi$
$720$	−15.3153	−0.570769
$721$	−29.9497	−1.11538
$722$	−1.00000	−0.0372161
$723$	−49.3545	−1.83551
$724$	19.9206	0.740344
$725$	71.3825	2.65108
$726$	5.85964	0.217471
$727$	27.7238	1.02822	0.514109	−	0.857725i	$-0.328123\pi$
$727$	27.7238	1.02822	0.514109	+	0.857725i	$0.328123\pi$
$728$	12.2614	0.454439
$729$	−34.7427	−1.28677
$730$	20.5318	0.759916
$731$	−20.7078	−0.765905
$732$	18.9291	0.699638
$733$	10.7732	0.397918	0.198959	−	0.980008i	$-0.436244\pi$
$733$	10.7732	0.397918	0.198959	+	0.980008i	$0.436244\pi$
$734$	−2.16080	−0.0797564
$735$	−14.4464	−0.532863
$736$	−3.94690	−0.145485
$737$	−44.6840	−1.64596
$738$	−37.8035	−1.39157
$739$	21.8775	0.804778	0.402389	−	0.915469i	$-0.368180\pi$
$739$	21.8775	0.804778	0.402389	+	0.915469i	$0.368180\pi$
$740$	15.3661	0.564869
$741$	−13.0528	−0.479505
$742$	−19.1307	−0.702312
$743$	8.37169	0.307128	0.153564	−	0.988139i	$-0.450925\pi$
$743$	8.37169	0.307128	0.153564	+	0.988139i	$0.450925\pi$
$744$	23.5744	0.864281
$745$	−13.3086	−0.487588
$746$	−16.5405	−0.605592
$747$	33.1998	1.21472
$748$	−8.10932	−0.296506
$749$	−27.1674	−0.992674
$750$	−105.929	−3.86796
$751$	30.8088	1.12423	0.562115	−	0.827059i	$-0.309988\pi$
$751$	30.8088	1.12423	0.562115	+	0.827059i	$0.309988\pi$
$752$	7.12371	0.259775
$753$	23.3594	0.851264
$754$	−25.3568	−0.923440
$755$	−97.3415	−3.54262
$756$	2.87867	0.104696
$757$	43.0562	1.56490	0.782451	−	0.622712i	$-0.213969\pi$
$757$	43.0562	1.56490	0.782451	+	0.622712i	$0.213969\pi$
$758$	−24.9911	−0.907718
$759$	36.6267	1.32947
$760$	4.40933	0.159943
$761$	34.7615	1.26010	0.630051	−	0.776553i	$-0.283034\pi$
$761$	34.7615	1.26010	0.630051	+	0.776553i	$0.283034\pi$
$762$	28.4615	1.03105
$763$	−4.98891	−0.180611
$764$	−17.0501	−0.616850
$765$	−34.0514	−1.23113
$766$	33.6778	1.21683
$767$	−11.3610	−0.410221
$768$	−2.54429	−0.0918090
$769$	−10.1551	−0.366201	−0.183100	−	0.983094i	$-0.558613\pi$
$769$	−10.1551	−0.366201	−0.183100	+	0.983094i	$0.558613\pi$
$770$	38.4374	1.38519
$771$	57.5183	2.07147
$772$	9.36697	0.337124
$773$	50.9674	1.83317	0.916586	−	0.399838i	$-0.130934\pi$
$773$	50.9674	1.83317	0.916586	+	0.399838i	$0.130934\pi$
$774$	32.3503	1.16281
$775$	133.816	4.80683
$776$	−2.60273	−0.0934327
$777$	−21.1915	−0.760241
$778$	−7.31001	−0.262077
$779$	10.8838	0.389951
$780$	57.5540	2.06076
$781$	22.7284	0.813285
$782$	−8.77536	−0.313806
$783$	−5.95312	−0.212747
$784$	−1.28772	−0.0459899
$785$	21.6372	0.772264
$786$	48.9377	1.74555
$787$	−45.7030	−1.62914	−0.814568	−	0.580069i	$-0.803026\pi$
$787$	−45.7030	−1.62914	−0.814568	+	0.580069i	$0.803026\pi$
$788$	−5.52992	−0.196995
$789$	9.23127	0.328642
$790$	54.6644	1.94487
$791$	−5.99707	−0.213231
$792$	12.6686	0.450160
$793$	−38.1680	−1.35539
$794$	−25.2383	−0.895673
$795$	−89.7979	−3.18480
$796$	−14.3525	−0.508711
$797$	39.0809	1.38432	0.692159	−	0.721745i	$-0.256660\pi$
$797$	39.0809	1.38432	0.692159	+	0.721745i	$0.256660\pi$
$798$	−6.08094	−0.215263
$799$	15.8385	0.560327
$800$	−14.4422	−0.510610
$801$	−37.5789	−1.32779
$802$	31.5643	1.11457
$803$	−16.9836	−0.599338
$804$	−31.1704	−1.09930
$805$	41.5943	1.46601
$806$	−47.5348	−1.67434
$807$	−2.96046	−0.104213
$808$	17.3905	0.611797
$809$	9.23461	0.324672	0.162336	−	0.986736i	$-0.448097\pi$
$809$	9.23461	0.324672	0.162336	+	0.986736i	$0.448097\pi$
$810$	−32.4338	−1.13961
$811$	−45.3004	−1.59071	−0.795356	−	0.606142i	$-0.792716\pi$
$811$	−45.3004	−1.59071	−0.795356	+	0.606142i	$0.792716\pi$
$812$	−11.8131	−0.414557
$813$	33.7710	1.18440
$814$	−12.7106	−0.445507
$815$	9.07741	0.317968
$816$	−5.65685	−0.198029
$817$	−9.31376	−0.325847
$818$	−0.697980	−0.0244043
$819$	−42.5888	−1.48817
$820$	−47.9901	−1.67589
$821$	−14.5545	−0.507957	−0.253978	−	0.967210i	$-0.581739\pi$
$821$	−14.5545	−0.507957	−0.253978	+	0.967210i	$0.581739\pi$
$822$	−10.2684	−0.358150
$823$	10.4904	0.365674	0.182837	−	0.983143i	$-0.441472\pi$
$823$	10.4904	0.365674	0.182837	+	0.983143i	$0.441472\pi$
$824$	−12.5311	−0.436540
$825$	134.022	4.66604
$826$	−5.29278	−0.184159
$827$	32.4712	1.12913	0.564566	−	0.825388i	$-0.309043\pi$
$827$	32.4712	1.12913	0.564566	+	0.825388i	$0.309043\pi$
$828$	13.7091	0.476425
$829$	−4.82959	−0.167738	−0.0838692	−	0.996477i	$-0.526728\pi$
$829$	−4.82959	−0.167738	−0.0838692	+	0.996477i	$0.526728\pi$
$830$	42.1459	1.46290
$831$	−33.9440	−1.17750
$832$	5.13023	0.177859
$833$	−2.86305	−0.0991988
$834$	−4.53843	−0.157153
$835$	−65.7813	−2.27646
$836$	−3.64734	−0.126146
$837$	−11.1599	−0.385744
$838$	−22.4417	−0.775234
$839$	−55.9904	−1.93300	−0.966501	−	0.256663i	$-0.917377\pi$
$839$	−55.9904	−1.93300	−0.966501	+	0.256663i	$0.917377\pi$
$840$	26.8129	0.925133
$841$	−4.57044	−0.157601
$842$	−36.6806	−1.26410
$843$	46.6128	1.60543
$844$	−1.00000	−0.0344214
$845$	−58.7288	−2.02033
$846$	−24.7434	−0.850697
$847$	−5.50439	−0.189133
$848$	−8.00437	−0.274871
$849$	−58.5564	−2.00965
$850$	−32.1102	−1.10137
$851$	−13.7546	−0.471501
$852$	15.8547	0.543174
$853$	−46.4121	−1.58912	−0.794560	−	0.607185i	$-0.792299\pi$
$853$	−46.4121	−1.58912	−0.794560	+	0.607185i	$0.792299\pi$
$854$	−17.7815	−0.608470
$855$	−15.3153	−0.523774
$856$	−11.3669	−0.388513
$857$	41.4427	1.41566	0.707828	−	0.706385i	$-0.249675\pi$
$857$	41.4427	1.41566	0.707828	+	0.706385i	$0.249675\pi$
$858$	−47.6078	−1.62530
$859$	46.7482	1.59503	0.797513	−	0.603301i	$-0.206148\pi$
$859$	46.7482	1.59503	0.797513	+	0.603301i	$0.206148\pi$
$860$	41.0675	1.40039
$861$	66.1835	2.25553
$862$	35.1875	1.19849
$863$	10.4312	0.355081	0.177541	−	0.984113i	$-0.443186\pi$
$863$	10.4312	0.355081	0.177541	+	0.984113i	$0.443186\pi$
$864$	1.20444	0.0409760
$865$	−0.893760	−0.0303888
$866$	2.99565	0.101796
$867$	30.6757	1.04180
$868$	−22.1452	−0.751658
$869$	−45.2176	−1.53390
$870$	−55.4494	−1.87991
$871$	62.8511	2.12963
$872$	−2.08737	−0.0706874
$873$	9.04031	0.305968
$874$	−3.94690	−0.133506
$875$	99.5066	3.36394
$876$	−11.8473	−0.400284
$877$	−32.3928	−1.09383	−0.546913	−	0.837190i	$-0.684197\pi$
$877$	−32.3928	−1.09383	−0.546913	+	0.837190i	$0.684197\pi$
$878$	−17.0132	−0.574166
$879$	32.1414	1.08410
$880$	16.0823	0.542135
$881$	36.7785	1.23910	0.619550	−	0.784957i	$-0.287315\pi$
$881$	36.7785	1.23910	0.619550	+	0.784957i	$0.287315\pi$
$882$	4.47274	0.150605
$883$	38.8804	1.30843	0.654216	−	0.756308i	$-0.272999\pi$
$883$	38.8804	1.30843	0.654216	+	0.756308i	$0.272999\pi$
$884$	11.4063	0.383636
$885$	−24.8438	−0.835115
$886$	−2.01077	−0.0675530
$887$	−24.3680	−0.818196	−0.409098	−	0.912490i	$-0.634157\pi$
$887$	−24.3680	−0.818196	−0.409098	+	0.912490i	$0.634157\pi$
$888$	−8.86660	−0.297544
$889$	−26.7360	−0.896696
$890$	−47.7049	−1.59907
$891$	26.8288	0.898799
$892$	12.6094	0.422195
$893$	7.12371	0.238386
$894$	7.67934	0.256835
$895$	−60.5569	−2.02419
$896$	2.39004	0.0798456
$897$	−51.5180	−1.72013
$898$	11.7629	0.392532
$899$	45.7966	1.52740
$900$	50.1635	1.67212
$901$	−17.7965	−0.592889
$902$	39.6967	1.32176
$903$	−56.6365	−1.88474
$904$	−2.50919	−0.0834545
$905$	−87.8366	−2.91979
$906$	56.1683	1.86607
$907$	−29.4578	−0.978131	−0.489066	−	0.872247i	$-0.662662\pi$
$907$	−29.4578	−0.978131	−0.489066	+	0.872247i	$0.662662\pi$
$908$	−11.2737	−0.374132
$909$	−60.4042	−2.00348
$910$	−54.0648	−1.79223
$911$	−11.5768	−0.383556	−0.191778	−	0.981438i	$-0.561425\pi$
$911$	−11.5768	−0.383556	−0.191778	+	0.981438i	$0.561425\pi$
$912$	−2.54429	−0.0842497
$913$	−34.8624	−1.15378
$914$	14.8551	0.491362
$915$	−83.4645	−2.75925
$916$	−19.3605	−0.639689
$917$	−45.9708	−1.51809
$918$	2.67791	0.0883841
$919$	−48.2716	−1.59233	−0.796166	−	0.605078i	$-0.793142\pi$
$919$	−48.2716	−1.59233	−0.796166	+	0.605078i	$0.793142\pi$
$920$	17.4032	0.573767
$921$	3.69590	0.121784
$922$	−10.2012	−0.335960
$923$	−31.9690	−1.05227
$924$	−22.1792	−0.729643
$925$	−50.3298	−1.65483
$926$	−3.57951	−0.117630
$927$	43.5252	1.42956
$928$	−4.94263	−0.162250
$929$	16.7729	0.550299	0.275150	−	0.961401i	$-0.411273\pi$
$929$	16.7729	0.550299	0.275150	+	0.961401i	$0.411273\pi$
$930$	−103.948	−3.40857
$931$	−1.28772	−0.0422032
$932$	5.24098	0.171674
$933$	10.0829	0.330098
$934$	32.4056	1.06034
$935$	35.7567	1.16937
$936$	−17.8193	−0.582441
$937$	57.1482	1.86695	0.933475	−	0.358642i	$-0.116760\pi$
$937$	57.1482	1.86695	0.933475	+	0.358642i	$0.116760\pi$
$938$	29.2807	0.956049
$939$	9.34260	0.304884
$940$	−31.4108	−1.02451
$941$	34.8699	1.13673	0.568363	−	0.822778i	$-0.307577\pi$
$941$	34.8699	1.13673	0.568363	+	0.822778i	$0.307577\pi$
$942$	−12.4851	−0.406788
$943$	42.9571	1.39888
$944$	−2.21452	−0.0720764
$945$	−12.6930	−0.412904
$946$	−33.9704	−1.10447
$947$	−10.1221	−0.328925	−0.164463	−	0.986383i	$-0.552589\pi$
$947$	−10.1221	−0.328925	−0.164463	+	0.986383i	$0.552589\pi$
$948$	−31.5426	−1.02446
$949$	23.8886	0.775456
$950$	−14.4422	−0.468568
$951$	−14.0148	−0.454459
$952$	5.31390	0.172225
$953$	−29.8415	−0.966661	−0.483331	−	0.875438i	$-0.660573\pi$
$953$	−29.8415	−0.966661	−0.483331	+	0.875438i	$0.660573\pi$
$954$	27.8023	0.900133
$955$	75.1795	2.43275
$956$	3.83161	0.123923
$957$	45.8669	1.48267
$958$	1.53913	0.0497271
$959$	9.64583	0.311480
$960$	11.2186	0.362079
$961$	54.8520	1.76942
$962$	17.8784	0.576421
$963$	39.4818	1.27228
$964$	19.3982	0.624773
$965$	−41.3021	−1.32956
$966$	−24.0009	−0.772216
$967$	19.8754	0.639150	0.319575	−	0.947561i	$-0.396460\pi$
$967$	19.8754	0.639150	0.319575	+	0.947561i	$0.396460\pi$
$968$	−2.30306	−0.0740230
$969$	−5.65685	−0.181724
$970$	11.4763	0.368482
$971$	26.4503	0.848830	0.424415	−	0.905468i	$-0.360480\pi$
$971$	26.4503	0.848830	0.424415	+	0.905468i	$0.360480\pi$
$972$	22.3284	0.716184
$973$	4.26328	0.136675
$974$	40.3178	1.29187
$975$	−188.511	−6.03718
$976$	−7.43983	−0.238143
$977$	−22.0857	−0.706585	−0.353292	−	0.935513i	$-0.614938\pi$
$977$	−22.0857	−0.706585	−0.353292	+	0.935513i	$0.614938\pi$
$978$	−5.23787	−0.167489
$979$	39.4608	1.26117
$980$	5.67797	0.181376
$981$	7.25027	0.231483
$982$	15.0575	0.480504
$983$	7.62077	0.243065	0.121532	−	0.992587i	$-0.461219\pi$
$983$	7.62077	0.243065	0.121532	+	0.992587i	$0.461219\pi$
$984$	27.6914	0.882769
$985$	24.3833	0.776916
$986$	−10.9892	−0.349968
$987$	43.3189	1.37885
$988$	5.13023	0.163214
$989$	−36.7605	−1.16892
$990$	−55.8602	−1.77535
$991$	53.8557	1.71078	0.855392	−	0.517982i	$-0.173317\pi$
$991$	53.8557	1.71078	0.855392	+	0.517982i	$0.173317\pi$
$992$	−9.26564	−0.294184
$993$	2.73248	0.0867127
$994$	−14.8935	−0.472394
$995$	63.2849	2.00627
$996$	−24.3191	−0.770581
$997$	−4.01603	−0.127189	−0.0635944	−	0.997976i	$-0.520256\pi$
$997$	−4.01603	−0.127189	−0.0635944	+	0.997976i	$0.520256\pi$
$998$	36.8699	1.16710
$999$	4.19737	0.132799

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.i.1.6	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.i.1.6	✓	43	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.54429 q^{3} +1.00000 q^{4} -4.40933 q^{5} +2.54429 q^{6} -2.39004 q^{7} -1.00000 q^{8} +3.47339 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.54429 q^{3} +1.00000 q^{4} -4.40933 q^{5} +2.54429 q^{6} -2.39004 q^{7} -1.00000 q^{8} +3.47339 q^{9} +4.40933 q^{10} -3.64734 q^{11} -2.54429 q^{12} +5.13023 q^{13} +2.39004 q^{14} +11.2186 q^{15} +1.00000 q^{16} +2.22335 q^{17} -3.47339 q^{18} +1.00000 q^{19} -4.40933 q^{20} +6.08094 q^{21} +3.64734 q^{22} +3.94690 q^{23} +2.54429 q^{24} +14.4422 q^{25} -5.13023 q^{26} -1.20444 q^{27} -2.39004 q^{28} +4.94263 q^{29} -11.2186 q^{30} +9.26564 q^{31} -1.00000 q^{32} +9.27987 q^{33} -2.22335 q^{34} +10.5385 q^{35} +3.47339 q^{36} -3.48491 q^{37} -1.00000 q^{38} -13.0528 q^{39} +4.40933 q^{40} +10.8838 q^{41} -6.08094 q^{42} -9.31376 q^{43} -3.64734 q^{44} -15.3153 q^{45} -3.94690 q^{46} +7.12371 q^{47} -2.54429 q^{48} -1.28772 q^{49} -14.4422 q^{50} -5.65685 q^{51} +5.13023 q^{52} -8.00437 q^{53} +1.20444 q^{54} +16.0823 q^{55} +2.39004 q^{56} -2.54429 q^{57} -4.94263 q^{58} -2.21452 q^{59} +11.2186 q^{60} -7.43983 q^{61} -9.26564 q^{62} -8.30154 q^{63} +1.00000 q^{64} -22.6209 q^{65} -9.27987 q^{66} +12.2511 q^{67} +2.22335 q^{68} -10.0420 q^{69} -10.5385 q^{70} -6.23150 q^{71} -3.47339 q^{72} +4.65644 q^{73} +3.48491 q^{74} -36.7451 q^{75} +1.00000 q^{76} +8.71727 q^{77} +13.0528 q^{78} +12.3974 q^{79} -4.40933 q^{80} -7.35572 q^{81} -10.8838 q^{82} +9.55833 q^{83} +6.08094 q^{84} -9.80351 q^{85} +9.31376 q^{86} -12.5755 q^{87} +3.64734 q^{88} -10.8191 q^{89} +15.3153 q^{90} -12.2614 q^{91} +3.94690 q^{92} -23.5744 q^{93} -7.12371 q^{94} -4.40933 q^{95} +2.54429 q^{96} +2.60273 q^{97} +1.28772 q^{98} -12.6686 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9}+O(q^{10}) \) 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9	\( 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9} + 14 q^{11} + 3 q^{13} - 19 q^{14} + q^{15} + 43 q^{16} + 8 q^{17} - 53 q^{18} + 43 q^{19} - 14 q^{22} + 43 q^{23} + 97 q^{25} - 3 q^{26} + 15 q^{27} + 19 q^{28} - 25 q^{29} - q^{30} + 22 q^{31} - 43 q^{32} + 22 q^{33} - 8 q^{34} - 6 q^{35} + 53 q^{36} + 42 q^{37} - 43 q^{38} + 9 q^{39} - 40 q^{41} + 72 q^{43} + 14 q^{44} - q^{45} - 43 q^{46} + 27 q^{47} + 86 q^{49} - 97 q^{50} - 3 q^{51} + 3 q^{52} - 5 q^{53} - 15 q^{54} + 86 q^{55} - 19 q^{56} + 25 q^{58} - 43 q^{59} + q^{60} + 31 q^{61} - 22 q^{62} + 38 q^{63} + 43 q^{64} - 32 q^{65} - 22 q^{66} + 15 q^{67} + 8 q^{68} - 7 q^{69} + 6 q^{70} + 14 q^{71} - 53 q^{72} + 93 q^{73} - 42 q^{74} - 13 q^{75} + 43 q^{76} + 38 q^{77} - 9 q^{78} + 15 q^{79} + 43 q^{81} + 40 q^{82} + 34 q^{83} + 16 q^{85} - 72 q^{86} + 60 q^{87} - 14 q^{88} - 37 q^{89} + q^{90} - 3 q^{91} + 43 q^{92} + 19 q^{93} - 27 q^{94} + 27 q^{97} - 86 q^{98} - 24 q^{99}+O(q^{100}) \) 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9 + 14 * q^11 + 3 * q^13 - 19 * q^14 + q^15 + 43 * q^16 + 8 * q^17 - 53 * q^18 + 43 * q^19 - 14 * q^22 + 43 * q^23 + 97 * q^25 - 3 * q^26 + 15 * q^27 + 19 * q^28 - 25 * q^29 - q^30 + 22 * q^31 - 43 * q^32 + 22 * q^33 - 8 * q^34 - 6 * q^35 + 53 * q^36 + 42 * q^37 - 43 * q^38 + 9 * q^39 - 40 * q^41 + 72 * q^43 + 14 * q^44 - q^45 - 43 * q^46 + 27 * q^47 + 86 * q^49 - 97 * q^50 - 3 * q^51 + 3 * q^52 - 5 * q^53 - 15 * q^54 + 86 * q^55 - 19 * q^56 + 25 * q^58 - 43 * q^59 + q^60 + 31 * q^61 - 22 * q^62 + 38 * q^63 + 43 * q^64 - 32 * q^65 - 22 * q^66 + 15 * q^67 + 8 * q^68 - 7 * q^69 + 6 * q^70 + 14 * q^71 - 53 * q^72 + 93 * q^73 - 42 * q^74 - 13 * q^75 + 43 * q^76 + 38 * q^77 - 9 * q^78 + 15 * q^79 + 43 * q^81 + 40 * q^82 + 34 * q^83 + 16 * q^85 - 72 * q^86 + 60 * q^87 - 14 * q^88 - 37 * q^89 + q^90 - 3 * q^91 + 43 * q^92 + 19 * q^93 - 27 * q^94 + 27 * q^97 - 86 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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