LMFDB - Embedded newform 889.2.a.c.1.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [889,2,Mod(1,889)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(889, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("889.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 889 = 7 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	889.a (trivial)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$7.09870073969$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} - 20 x^{14} + 38 x^{13} + 155 x^{12} - 275 x^{11} - 593 x^{10} + 957 x^{9} + 1177 x^{8} + \cdots + 1 $ x^16 - 2x^15 - 20x^14 + 38x^13 + 155x^12 - 275x^11 - 593x^10 + 957x^9 + 1177x^8 - 1655x^7 - 1150x^6 + 1279x^5 + 474x^4 - 280x^3 - 83x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$-1.45188$ of defining polynomial
Character	$\chi$	$=$	889.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.45188 q^{2} +0.155172 q^{3} +0.107956 q^{4} +0.584615 q^{5} +0.225291 q^{6} -1.00000 q^{7} -2.74702 q^{8} -2.97592 q^{9} +0.848791 q^{10} -5.41545 q^{11} +0.0167517 q^{12} -3.18339 q^{13} -1.45188 q^{14} +0.0907156 q^{15} -4.20426 q^{16} +5.06086 q^{17} -4.32068 q^{18} -5.11413 q^{19} +0.0631129 q^{20} -0.155172 q^{21} -7.86259 q^{22} +3.75579 q^{23} -0.426260 q^{24} -4.65823 q^{25} -4.62190 q^{26} -0.927293 q^{27} -0.107956 q^{28} +8.71861 q^{29} +0.131708 q^{30} +3.51720 q^{31} -0.610037 q^{32} -0.840324 q^{33} +7.34776 q^{34} -0.584615 q^{35} -0.321269 q^{36} -2.23456 q^{37} -7.42511 q^{38} -0.493971 q^{39} -1.60595 q^{40} -6.65414 q^{41} -0.225291 q^{42} -4.51015 q^{43} -0.584632 q^{44} -1.73977 q^{45} +5.45296 q^{46} +9.14467 q^{47} -0.652381 q^{48} +1.00000 q^{49} -6.76319 q^{50} +0.785302 q^{51} -0.343667 q^{52} +2.10337 q^{53} -1.34632 q^{54} -3.16596 q^{55} +2.74702 q^{56} -0.793568 q^{57} +12.6584 q^{58} -5.83902 q^{59} +0.00979332 q^{60} +14.0585 q^{61} +5.10655 q^{62} +2.97592 q^{63} +7.52281 q^{64} -1.86106 q^{65} -1.22005 q^{66} -3.86784 q^{67} +0.546352 q^{68} +0.582792 q^{69} -0.848791 q^{70} -12.1700 q^{71} +8.17492 q^{72} -11.2754 q^{73} -3.24431 q^{74} -0.722824 q^{75} -0.552103 q^{76} +5.41545 q^{77} -0.717187 q^{78} -3.62482 q^{79} -2.45787 q^{80} +8.78388 q^{81} -9.66101 q^{82} -14.1521 q^{83} -0.0167517 q^{84} +2.95866 q^{85} -6.54820 q^{86} +1.35288 q^{87} +14.8764 q^{88} -6.96813 q^{89} -2.52594 q^{90} +3.18339 q^{91} +0.405461 q^{92} +0.545769 q^{93} +13.2770 q^{94} -2.98980 q^{95} -0.0946604 q^{96} -15.9899 q^{97} +1.45188 q^{98} +16.1160 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 4 q^{3} + 12 q^{4} - 9 q^{5} - 12 q^{6} - 16 q^{7} - 6 q^{8} + 14 q^{9} - 2 q^{10} - 22 q^{11} - 10 q^{12} - 4 q^{13} + 2 q^{14} - 14 q^{15} + 12 q^{16} - 18 q^{17} - 5 q^{18} - 15 q^{19}+ \cdots - 73 q^{99}+O(q^{100}) $ 16 * q - 2 * q^2 - 4 * q^3 + 12 * q^4 - 9 * q^5 - 12 * q^6 - 16 * q^7 - 6 * q^8 + 14 * q^9 - 2 * q^10 - 22 * q^11 - 10 * q^12 - 4 * q^13 + 2 * q^14 - 14 * q^15 + 12 * q^16 - 18 * q^17 - 5 * q^18 - 15 * q^19 - 40 * q^20 + 4 * q^21 - 11 * q^22 - 5 * q^23 - 26 * q^24 + 15 * q^25 - 24 * q^26 - 10 * q^27 - 12 * q^28 - 12 * q^29 + 3 * q^30 - 32 * q^31 - 9 * q^32 - 10 * q^33 - 14 * q^34 + 9 * q^35 + 10 * q^36 - 2 * q^37 + 3 * q^38 - 41 * q^39 - 14 * q^40 - 45 * q^41 + 12 * q^42 - 3 * q^43 - 54 * q^44 - 22 * q^45 - 49 * q^47 + 10 * q^48 + 16 * q^49 - 6 * q^50 - 12 * q^51 + 38 * q^52 + 16 * q^53 - 67 * q^54 + 7 * q^55 + 6 * q^56 + 8 * q^57 + 16 * q^58 - 35 * q^59 + 56 * q^60 - 11 * q^61 + 17 * q^62 - 14 * q^63 - 2 * q^64 + 14 * q^65 + 86 * q^66 + 17 * q^67 - 71 * q^68 - 17 * q^69 + 2 * q^70 - 81 * q^71 + 13 * q^72 - 15 * q^73 + 13 * q^74 - 48 * q^75 + 14 * q^76 + 22 * q^77 - 10 * q^78 - 34 * q^79 - 33 * q^80 + 40 * q^81 - 14 * q^82 - 39 * q^83 + 10 * q^84 - 17 * q^85 + 36 * q^86 + 7 * q^87 + 61 * q^88 - 32 * q^89 + 79 * q^90 + 4 * q^91 + 37 * q^92 + 27 * q^93 + 13 * q^94 - 33 * q^95 - 55 * q^96 - 4 * q^97 - 2 * q^98 - 73 * q^99

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 $

$2$	1.45188	1.02663	0.513317	−	0.858199i	$-0.328416\pi$
$2$	1.45188	1.02663	0.513317	+	0.858199i	$0.328416\pi$
$3$	0.155172	0.0895883	0.0447942	−	0.998996i	$-0.485737\pi$
$3$	0.155172	0.0895883	0.0447942	+	0.998996i	$0.485737\pi$
$4$	0.107956	0.0539781
$5$	0.584615	0.261448	0.130724	−	0.991419i	$-0.458270\pi$
$5$	0.584615	0.261448	0.130724	+	0.991419i	$0.458270\pi$
$6$	0.225291	0.0919745
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.74702	−0.971219
$9$	−2.97592	−0.991974
$10$	0.848791	0.268411
$11$	−5.41545	−1.63282	−0.816410	−	0.577472i	$-0.804039\pi$
$11$	−5.41545	−1.63282	−0.816410	+	0.577472i	$0.804039\pi$
$12$	0.0167517	0.00483581
$13$	−3.18339	−0.882913	−0.441457	−	0.897283i	$-0.645538\pi$
$13$	−3.18339	−0.882913	−0.441457	+	0.897283i	$0.645538\pi$
$14$	−1.45188	−0.388031
$15$	0.0907156	0.0234227
$16$	−4.20426	−1.05106
$17$	5.06086	1.22744	0.613720	−	0.789524i	$-0.289673\pi$
$17$	5.06086	1.22744	0.613720	+	0.789524i	$0.289673\pi$
$18$	−4.32068	−1.01839
$19$	−5.11413	−1.17326	−0.586631	−	0.809854i	$-0.699546\pi$
$19$	−5.11413	−1.17326	−0.586631	+	0.809854i	$0.699546\pi$
$20$	0.0631129	0.0141125
$21$	−0.155172	−0.0338612
$22$	−7.86259	−1.67631
$23$	3.75579	0.783137	0.391568	−	0.920149i	$-0.371933\pi$
$23$	3.75579	0.783137	0.391568	+	0.920149i	$0.371933\pi$
$24$	−0.426260	−0.0870099
$25$	−4.65823	−0.931645
$26$	−4.62190	−0.906429
$27$	−0.927293	−0.178458
$28$	−0.107956	−0.0204018
$29$	8.71861	1.61901	0.809503	−	0.587116i	$-0.199737\pi$
$29$	8.71861	1.61901	0.809503	+	0.587116i	$0.199737\pi$
$30$	0.131708	0.0240465
$31$	3.51720	0.631707	0.315854	−	0.948808i	$-0.397709\pi$
$31$	3.51720	0.631707	0.315854	+	0.948808i	$0.397709\pi$
$32$	−0.610037	−0.107840
$33$	−0.840324	−0.146282
$34$	7.34776	1.26013
$35$	−0.584615	−0.0988180
$36$	−0.321269	−0.0535449
$37$	−2.23456	−0.367359	−0.183680	−	0.982986i	$-0.558801\pi$
$37$	−2.23456	−0.367359	−0.183680	+	0.982986i	$0.558801\pi$
$38$	−7.42511	−1.20451
$39$	−0.493971	−0.0790987
$40$	−1.60595	−0.253923
$41$	−6.65414	−1.03920	−0.519601	−	0.854409i	$-0.673919\pi$
$41$	−6.65414	−1.03920	−0.519601	+	0.854409i	$0.673919\pi$
$42$	−0.225291	−0.0347631
$43$	−4.51015	−0.687791	−0.343896	−	0.939008i	$-0.611747\pi$
$43$	−4.51015	−0.687791	−0.343896	+	0.939008i	$0.611747\pi$
$44$	−0.584632	−0.0881366
$45$	−1.73977	−0.259349
$46$	5.45296	0.803995
$47$	9.14467	1.33389	0.666944	−	0.745108i	$-0.267602\pi$
$47$	9.14467	1.33389	0.666944	+	0.745108i	$0.267602\pi$
$48$	−0.652381	−0.0941631
$49$	1.00000	0.142857
$50$	−6.76319	−0.956459
$51$	0.785302	0.109964
$52$	−0.343667	−0.0476580
$53$	2.10337	0.288920	0.144460	−	0.989511i	$-0.453855\pi$
$53$	2.10337	0.288920	0.144460	+	0.989511i	$0.453855\pi$
$54$	−1.34632	−0.183211
$55$	−3.16596	−0.426897
$56$	2.74702	0.367086
$57$	−0.793568	−0.105111
$58$	12.6584	1.66213
$59$	−5.83902	−0.760175	−0.380088	−	0.924950i	$-0.624106\pi$
$59$	−5.83902	−0.760175	−0.380088	+	0.924950i	$0.624106\pi$
$60$	0.00979332	0.00126431
$61$	14.0585	1.80001	0.900005	−	0.435879i	$-0.143562\pi$
$61$	14.0585	1.80001	0.900005	+	0.435879i	$0.143562\pi$
$62$	5.10655	0.648533
$63$	2.97592	0.374931
$64$	7.52281	0.940352
$65$	−1.86106	−0.230836
$66$	−1.22005	−0.150178
$67$	−3.86784	−0.472532	−0.236266	−	0.971688i	$-0.575924\pi$
$67$	−3.86784	−0.472532	−0.236266	+	0.971688i	$0.575924\pi$
$68$	0.546352	0.0662549
$69$	0.582792	0.0701599
$70$	−0.848791	−0.101450
$71$	−12.1700	−1.44431	−0.722156	−	0.691731i	$-0.756849\pi$
$71$	−12.1700	−1.44431	−0.722156	+	0.691731i	$0.756849\pi$
$72$	8.17492	0.963423
$73$	−11.2754	−1.31969	−0.659844	−	0.751402i	$-0.729378\pi$
$73$	−11.2754	−1.31969	−0.659844	+	0.751402i	$0.729378\pi$
$74$	−3.24431	−0.377143
$75$	−0.722824	−0.0834645
$76$	−0.552103	−0.0633305
$77$	5.41545	0.617148
$78$	−0.717187	−0.0812055
$79$	−3.62482	−0.407824	−0.203912	−	0.978989i	$-0.565366\pi$
$79$	−3.62482	−0.407824	−0.203912	+	0.978989i	$0.565366\pi$
$80$	−2.45787	−0.274799
$81$	8.78388	0.975986
$82$	−9.66101	−1.06688
$83$	−14.1521	−1.55339	−0.776695	−	0.629877i	$-0.783105\pi$
$83$	−14.1521	−1.55339	−0.776695	+	0.629877i	$0.783105\pi$
$84$	−0.0167517	−0.00182776
$85$	2.95866	0.320911
$86$	−6.54820	−0.706110
$87$	1.35288	0.145044
$88$	14.8764	1.58583
$89$	−6.96813	−0.738621	−0.369310	−	0.929306i	$-0.620406\pi$
$89$	−6.96813	−0.738621	−0.369310	+	0.929306i	$0.620406\pi$
$90$	−2.52594	−0.266257
$91$	3.18339	0.333710
$92$	0.405461	0.0422723
$93$	0.545769	0.0565936
$94$	13.2770	1.36941
$95$	−2.98980	−0.306747
$96$	−0.0946604	−0.00966124
$97$	−15.9899	−1.62353	−0.811764	−	0.583985i	$-0.801493\pi$
$97$	−15.9899	−1.62353	−0.811764	+	0.583985i	$0.801493\pi$
$98$	1.45188	0.146662
$99$	16.1160	1.61972
$100$	−0.502885	−0.0502885
$101$	−10.4766	−1.04246	−0.521231	−	0.853416i	$-0.674527\pi$
$101$	−10.4766	−1.04246	−0.521231	+	0.853416i	$0.674527\pi$
$102$	1.14016	0.112893
$103$	−16.7816	−1.65354	−0.826772	−	0.562537i	$-0.809826\pi$
$103$	−16.7816	−1.65354	−0.826772	+	0.562537i	$0.809826\pi$
$104$	8.74483	0.857502
$105$	−0.0907156	−0.00885294
$106$	3.05384	0.296616
$107$	5.72707	0.553657	0.276828	−	0.960919i	$-0.410717\pi$
$107$	5.72707	0.553657	0.276828	+	0.960919i	$0.410717\pi$
$108$	−0.100107	−0.00963281
$109$	17.7933	1.70429	0.852143	−	0.523309i	$-0.175303\pi$
$109$	17.7933	1.70429	0.852143	+	0.523309i	$0.175303\pi$
$110$	−4.59659	−0.438267
$111$	−0.346740	−0.0329111
$112$	4.20426	0.397265
$113$	8.78023	0.825974	0.412987	−	0.910737i	$-0.364485\pi$
$113$	8.78023	0.825974	0.412987	+	0.910737i	$0.364485\pi$
$114$	−1.15217	−0.107910
$115$	2.19569	0.204749
$116$	0.941229	0.0873909
$117$	9.47351	0.875827
$118$	−8.47755	−0.780422
$119$	−5.06086	−0.463928
$120$	−0.249198	−0.0227485
$121$	18.3271	1.66610
$122$	20.4113	1.84795
$123$	−1.03253	−0.0931003
$124$	0.379704	0.0340984
$125$	−5.64634	−0.505024
$126$	4.32068	0.384917
$127$	−1.00000	−0.0887357
$127$	−1.00000	−0.0887357
$128$	12.1423	1.07324
$129$	−0.699847	−0.0616181
$130$	−2.70203	−0.236984
$131$	1.64272	0.143525	0.0717625	−	0.997422i	$-0.477138\pi$
$131$	1.64272	0.143525	0.0717625	+	0.997422i	$0.477138\pi$
$132$	−0.0907183	−0.00789601
$133$	5.11413	0.443451
$134$	−5.61565	−0.485118
$135$	−0.542110	−0.0466574
$136$	−13.9023	−1.19211
$137$	−19.4601	−1.66259	−0.831294	−	0.555833i	$-0.812399\pi$
$137$	−19.4601	−1.66259	−0.831294	+	0.555833i	$0.812399\pi$
$138$	0.846145	0.0720286
$139$	−1.07654	−0.0913113	−0.0456556	−	0.998957i	$-0.514538\pi$
$139$	−1.07654	−0.0913113	−0.0456556	+	0.998957i	$0.514538\pi$
$140$	−0.0631129	−0.00533401
$141$	1.41899	0.119501
$142$	−17.6694	−1.48278
$143$	17.2395	1.44164
$144$	12.5115	1.04263
$145$	5.09703	0.423285
$146$	−16.3706	−1.35484
$147$	0.155172	0.0127983
$148$	−0.241235	−0.0198294
$149$	16.0590	1.31561	0.657804	−	0.753189i	$-0.271486\pi$
$149$	16.0590	1.31561	0.657804	+	0.753189i	$0.271486\pi$
$150$	−1.04945	−0.0856876
$151$	−3.56737	−0.290308	−0.145154	−	0.989409i	$-0.546368\pi$
$151$	−3.56737	−0.290308	−0.145154	+	0.989409i	$0.546368\pi$
$152$	14.0486	1.13949
$153$	−15.0607	−1.21759
$154$	7.86259	0.633585
$155$	2.05621	0.165159
$156$	−0.0533273	−0.00426960
$157$	0.684661	0.0546419	0.0273210	−	0.999627i	$-0.491302\pi$
$157$	0.684661	0.0546419	0.0273210	+	0.999627i	$0.491302\pi$
$158$	−5.26281	−0.418686
$159$	0.326383	0.0258839
$160$	−0.356637	−0.0281946
$161$	−3.75579	−0.295998
$162$	12.7531	1.00198
$163$	20.5205	1.60729	0.803644	−	0.595110i	$-0.202892\pi$
$163$	20.5205	1.60729	0.803644	+	0.595110i	$0.202892\pi$
$164$	−0.718356	−0.0560941
$165$	−0.491266	−0.0382450
$166$	−20.5471	−1.59476
$167$	−3.47768	−0.269111	−0.134555	−	0.990906i	$-0.542961\pi$
$167$	−3.47768	−0.269111	−0.134555	+	0.990906i	$0.542961\pi$
$168$	0.426260	0.0328866
$169$	−2.86604	−0.220465
$170$	4.29561	0.329459
$171$	15.2193	1.16385
$172$	−0.486899	−0.0371257
$173$	10.7751	0.819217	0.409609	−	0.912261i	$-0.365665\pi$
$173$	10.7751	0.819217	0.409609	+	0.912261i	$0.365665\pi$
$174$	1.96422	0.148907
$175$	4.65823	0.352129
$176$	22.7680	1.71620
$177$	−0.906049	−0.0681028
$178$	−10.1169	−0.758293
$179$	19.4287	1.45217	0.726085	−	0.687605i	$-0.241338\pi$
$179$	19.4287	1.45217	0.726085	+	0.687605i	$0.241338\pi$
$180$	−0.187819	−0.0139992
$181$	18.3686	1.36533	0.682664	−	0.730732i	$-0.260821\pi$
$181$	18.3686	1.36533	0.682664	+	0.730732i	$0.260821\pi$
$182$	4.62190	0.342598
$183$	2.18148	0.161260
$184$	−10.3172	−0.760597
$185$	−1.30636	−0.0960452
$186$	0.792391	0.0581010
$187$	−27.4069	−2.00419
$188$	0.987225	0.0720008
$189$	0.927293	0.0674507
$190$	−4.34083	−0.314917
$191$	3.24268	0.234632	0.117316	−	0.993095i	$-0.462571\pi$
$191$	3.24268	0.234632	0.117316	+	0.993095i	$0.462571\pi$
$192$	1.16733	0.0842446
$193$	−19.0343	−1.37012	−0.685059	−	0.728487i	$-0.740224\pi$
$193$	−19.0343	−1.37012	−0.685059	+	0.728487i	$0.740224\pi$
$194$	−23.2154	−1.66677
$195$	−0.288783	−0.0206802
$196$	0.107956	0.00771116
$197$	−9.92678	−0.707254	−0.353627	−	0.935387i	$-0.615052\pi$
$197$	−9.92678	−0.707254	−0.353627	+	0.935387i	$0.615052\pi$
$198$	23.3984	1.66286
$199$	8.65223	0.613340	0.306670	−	0.951816i	$-0.400785\pi$
$199$	8.65223	0.613340	0.306670	+	0.951816i	$0.400785\pi$
$200$	12.7962	0.904831
$201$	−0.600179	−0.0423334
$202$	−15.2108	−1.07023
$203$	−8.71861	−0.611927
$204$	0.0847782	0.00593566
$205$	−3.89011	−0.271697
$206$	−24.3649	−1.69759
$207$	−11.1769	−0.776851
$208$	13.3838	0.927999
$209$	27.6953	1.91573
$210$	−0.131708	−0.00908873
$211$	−28.4387	−1.95780	−0.978901	−	0.204336i	$-0.934496\pi$
$211$	−28.4387	−1.95780	−0.978901	+	0.204336i	$0.934496\pi$
$212$	0.227072	0.0155954
$213$	−1.88844	−0.129393
$214$	8.31502	0.568403
$215$	−2.63670	−0.179822
$216$	2.54729	0.173321
$217$	−3.51720	−0.238763
$218$	25.8337	1.74968
$219$	−1.74963	−0.118229
$220$	−0.341785	−0.0230431
$221$	−16.1107	−1.08372
$222$	−0.503425	−0.0337877
$223$	1.32183	0.0885163	0.0442581	−	0.999020i	$-0.485908\pi$
$223$	1.32183	0.0885163	0.0442581	+	0.999020i	$0.485908\pi$
$224$	0.610037	0.0407598
$225$	13.8625	0.924168
$226$	12.7478	0.847974
$227$	3.52975	0.234277	0.117139	−	0.993116i	$-0.462628\pi$
$227$	3.52975	0.234277	0.117139	+	0.993116i	$0.462628\pi$
$228$	−0.0856706	−0.00567368
$229$	−13.5473	−0.895230	−0.447615	−	0.894226i	$-0.647726\pi$
$229$	−13.5473	−0.895230	−0.447615	+	0.894226i	$0.647726\pi$
$230$	3.18788	0.210203
$231$	0.840324	0.0552893
$232$	−23.9502	−1.57241
$233$	−9.26564	−0.607012	−0.303506	−	0.952829i	$-0.598157\pi$
$233$	−9.26564	−0.607012	−0.303506	+	0.952829i	$0.598157\pi$
$234$	13.7544	0.899154
$235$	5.34611	0.348742
$236$	−0.630358	−0.0410328
$237$	−0.562469	−0.0365363
$238$	−7.34776	−0.476285
$239$	5.54274	0.358530	0.179265	−	0.983801i	$-0.442628\pi$
$239$	5.54274	0.358530	0.179265	+	0.983801i	$0.442628\pi$
$240$	−0.381392	−0.0246187
$241$	18.1165	1.16699	0.583494	−	0.812117i	$-0.301685\pi$
$241$	18.1165	1.16699	0.583494	+	0.812117i	$0.301685\pi$
$242$	26.6088	1.71048
$243$	4.14489	0.265895
$244$	1.51771	0.0971612
$245$	0.584615	0.0373497
$246$	−1.49911	−0.0955800
$247$	16.2803	1.03589
$248$	−9.66182	−0.613526
$249$	−2.19600	−0.139166
$250$	−8.19782	−0.518475
$251$	−16.8288	−1.06223	−0.531113	−	0.847301i	$-0.678226\pi$
$251$	−16.8288	−1.06223	−0.531113	+	0.847301i	$0.678226\pi$
$252$	0.321269	0.0202381
$253$	−20.3393	−1.27872
$254$	−1.45188	−0.0910991
$255$	0.459099	0.0287499
$256$	2.58354	0.161471
$257$	−0.164440	−0.0102575	−0.00512876	−	0.999987i	$-0.501633\pi$
$257$	−0.164440	−0.0102575	−0.00512876	+	0.999987i	$0.501633\pi$
$258$	−1.01609	−0.0632592
$259$	2.23456	0.138849
$260$	−0.200913	−0.0124601
$261$	−25.9459	−1.60601
$262$	2.38503	0.147348
$263$	−12.6341	−0.779053	−0.389527	−	0.921015i	$-0.627361\pi$
$263$	−12.6341	−0.779053	−0.389527	+	0.921015i	$0.627361\pi$
$264$	2.30839	0.142071
$265$	1.22966	0.0755376
$266$	7.42511	0.455263
$267$	−1.08126	−0.0661718
$268$	−0.417558	−0.0255064
$269$	−5.50729	−0.335785	−0.167893	−	0.985805i	$-0.553696\pi$
$269$	−5.50729	−0.335785	−0.167893	+	0.985805i	$0.553696\pi$
$270$	−0.787078	−0.0479001
$271$	−28.0965	−1.70674	−0.853370	−	0.521305i	$-0.825445\pi$
$271$	−28.0965	−1.70674	−0.853370	+	0.521305i	$0.825445\pi$
$272$	−21.2772	−1.29012
$273$	0.493971	0.0298965
$274$	−28.2537	−1.70687
$275$	25.2264	1.52121
$276$	0.0629161	0.00378710
$277$	19.2463	1.15640	0.578198	−	0.815897i	$-0.303756\pi$
$277$	19.2463	1.15640	0.578198	+	0.815897i	$0.303756\pi$
$278$	−1.56301	−0.0937433
$279$	−10.4669	−0.626637
$280$	1.60595	0.0959739
$281$	−10.0850	−0.601623	−0.300812	−	0.953684i	$-0.597258\pi$
$281$	−10.0850	−0.601623	−0.300812	+	0.953684i	$0.597258\pi$
$282$	2.06021	0.122684
$283$	28.0175	1.66546	0.832732	−	0.553676i	$-0.186775\pi$
$283$	28.0175	1.66546	0.832732	+	0.553676i	$0.186775\pi$
$284$	−1.31383	−0.0779612
$285$	−0.463932	−0.0274809
$286$	25.0297	1.48004
$287$	6.65414	0.392781
$288$	1.81542	0.106975
$289$	8.61231	0.506607
$290$	7.40028	0.434559
$291$	−2.48118	−0.145449
$292$	−1.21725	−0.0712343
$293$	−24.0283	−1.40375	−0.701875	−	0.712300i	$-0.747654\pi$
$293$	−24.0283	−1.40375	−0.701875	+	0.712300i	$0.747654\pi$
$294$	0.225291	0.0131392
$295$	−3.41358	−0.198746
$296$	6.13838	0.356786
$297$	5.02171	0.291389
$298$	23.3158	1.35065
$299$	−11.9561	−0.691442
$300$	−0.0780334	−0.00450526
$301$	4.51015	0.259961
$302$	−5.17939	−0.298041
$303$	−1.62567	−0.0933924
$304$	21.5011	1.23317
$305$	8.21883	0.470609
$306$	−21.8664	−1.25002
$307$	−16.4884	−0.941045	−0.470523	−	0.882388i	$-0.655935\pi$
$307$	−16.4884	−0.941045	−0.470523	+	0.882388i	$0.655935\pi$
$308$	0.584632	0.0333125
$309$	−2.60403	−0.148138
$310$	2.98537	0.169557
$311$	−30.3835	−1.72289	−0.861446	−	0.507849i	$-0.830441\pi$
$311$	−30.3835	−1.72289	−0.861446	+	0.507849i	$0.830441\pi$
$312$	1.35695	0.0768221
$313$	19.7235	1.11484	0.557420	−	0.830230i	$-0.311791\pi$
$313$	19.7235	1.11484	0.557420	+	0.830230i	$0.311791\pi$
$314$	0.994046	0.0560973
$315$	1.73977	0.0980249
$316$	−0.391322	−0.0220136
$317$	22.1712	1.24526	0.622630	−	0.782516i	$-0.286064\pi$
$317$	22.1712	1.24526	0.622630	+	0.782516i	$0.286064\pi$
$318$	0.473870	0.0265733
$319$	−47.2152	−2.64355
$320$	4.39795	0.245853
$321$	0.888679	0.0496012
$322$	−5.45296	−0.303882
$323$	−25.8819	−1.44011
$324$	0.948274	0.0526819
$325$	14.8289	0.822562
$326$	29.7933	1.65010
$327$	2.76101	0.152684
$328$	18.2790	1.00929
$329$	−9.14467	−0.504162
$330$	−0.713260	−0.0392637
$331$	−5.62100	−0.308958	−0.154479	−	0.987996i	$-0.549370\pi$
$331$	−5.62100	−0.308958	−0.154479	+	0.987996i	$0.549370\pi$
$332$	−1.52780	−0.0838491
$333$	6.64987	0.364411
$334$	−5.04917	−0.276278
$335$	−2.26120	−0.123543
$336$	0.652381	0.0355903
$337$	8.56317	0.466465	0.233233	−	0.972421i	$-0.425070\pi$
$337$	8.56317	0.466465	0.233233	+	0.972421i	$0.425070\pi$
$338$	−4.16115	−0.226337
$339$	1.36244	0.0739977
$340$	0.319405	0.0173222
$341$	−19.0472	−1.03146
$342$	22.0965	1.19484
$343$	−1.00000	−0.0539949
$344$	12.3895	0.667996
$345$	0.340709	0.0183432
$346$	15.6442	0.841037
$347$	−0.292076	−0.0156795	−0.00783973	−	0.999969i	$-0.502495\pi$
$347$	−0.292076	−0.0156795	−0.00783973	+	0.999969i	$0.502495\pi$
$348$	0.146052	0.00782920
$349$	1.71700	0.0919090	0.0459545	−	0.998944i	$-0.485367\pi$
$349$	1.71700	0.0919090	0.0459545	+	0.998944i	$0.485367\pi$
$350$	6.76319	0.361507
$351$	2.95193	0.157563
$352$	3.30363	0.176084
$353$	2.50642	0.133403	0.0667016	−	0.997773i	$-0.478752\pi$
$353$	2.50642	0.133403	0.0667016	+	0.997773i	$0.478752\pi$
$354$	−1.31548	−0.0699167
$355$	−7.11476	−0.377612
$356$	−0.752254	−0.0398694
$357$	−0.785302	−0.0415626
$358$	28.2081	1.49085
$359$	−30.7410	−1.62245	−0.811224	−	0.584736i	$-0.801198\pi$
$359$	−30.7410	−1.62245	−0.811224	+	0.584736i	$0.801198\pi$
$360$	4.77918	0.251885
$361$	7.15435	0.376545
$362$	26.6690	1.40169
$363$	2.84385	0.149263
$364$	0.343667	0.0180130
$365$	−6.59178	−0.345030
$366$	3.16725	0.165555
$367$	0.365574	0.0190828	0.00954140	−	0.999954i	$-0.496963\pi$
$367$	0.365574	0.0190828	0.00954140	+	0.999954i	$0.496963\pi$
$368$	−15.7903	−0.823127
$369$	19.8022	1.03086
$370$	−1.89667	−0.0986033
$371$	−2.10337	−0.109202
$372$	0.0589192	0.00305482
$373$	28.3498	1.46790	0.733950	−	0.679204i	$-0.237675\pi$
$373$	28.3498	1.46790	0.733950	+	0.679204i	$0.237675\pi$
$374$	−39.7915	−2.05757
$375$	−0.876152	−0.0452443
$376$	−25.1206	−1.29550
$377$	−27.7547	−1.42944
$378$	1.34632	0.0692472
$379$	25.0643	1.28747	0.643734	−	0.765250i	$-0.277384\pi$
$379$	25.0643	1.28747	0.643734	+	0.765250i	$0.277384\pi$
$380$	−0.322767	−0.0165576
$381$	−0.155172	−0.00794968
$382$	4.70799	0.240882
$383$	−11.0735	−0.565828	−0.282914	−	0.959145i	$-0.591301\pi$
$383$	−11.0735	−0.565828	−0.282914	+	0.959145i	$0.591301\pi$
$384$	1.88414	0.0961496
$385$	3.16596	0.161352
$386$	−27.6355	−1.40661
$387$	13.4219	0.682271
$388$	−1.72621	−0.0876350
$389$	−6.67744	−0.338560	−0.169280	−	0.985568i	$-0.554144\pi$
$389$	−6.67744	−0.338560	−0.169280	+	0.985568i	$0.554144\pi$
$390$	−0.419278	−0.0212310
$391$	19.0075	0.961253
$392$	−2.74702	−0.138746
$393$	0.254903	0.0128582
$394$	−14.4125	−0.726091
$395$	−2.11913	−0.106625
$396$	1.73982	0.0874292
$397$	23.2489	1.16683	0.583414	−	0.812175i	$-0.301717\pi$
$397$	23.2489	1.16683	0.583414	+	0.812175i	$0.301717\pi$
$398$	12.5620	0.629676
$399$	0.793568	0.0397281
$400$	19.5844	0.979219
$401$	−12.7702	−0.637712	−0.318856	−	0.947803i	$-0.603299\pi$
$401$	−12.7702	−0.637712	−0.318856	+	0.947803i	$0.603299\pi$
$402$	−0.871389	−0.0434609
$403$	−11.1966	−0.557743
$404$	−1.13102	−0.0562701
$405$	5.13519	0.255169
$406$	−12.6584	−0.628225
$407$	12.1011	0.599831
$408$	−2.15724	−0.106799
$409$	2.99975	0.148328	0.0741641	−	0.997246i	$-0.476371\pi$
$409$	2.99975	0.148328	0.0741641	+	0.997246i	$0.476371\pi$
$410$	−5.64797	−0.278933
$411$	−3.01965	−0.148949
$412$	−1.81168	−0.0892553
$413$	5.83902	0.287319
$414$	−16.2276	−0.797542
$415$	−8.27351	−0.406131
$416$	1.94199	0.0952137
$417$	−0.167049	−0.00818043
$418$	40.2103	1.96675
$419$	−16.0099	−0.782134	−0.391067	−	0.920362i	$-0.627894\pi$
$419$	−16.0099	−0.782134	−0.391067	+	0.920362i	$0.627894\pi$
$420$	−0.00979332	−0.000477865 0
$421$	−17.0046	−0.828751	−0.414376	−	0.910106i	$-0.636000\pi$
$421$	−17.0046	−0.828751	−0.414376	+	0.910106i	$0.636000\pi$
$422$	−41.2896	−2.00995
$423$	−27.2138	−1.32318
$424$	−5.77801	−0.280605
$425$	−23.5746	−1.14354
$426$	−2.74178	−0.132840
$427$	−14.0585	−0.680340
$428$	0.618273	0.0298854
$429$	2.67508	0.129154
$430$	−3.82817	−0.184611
$431$	36.2193	1.74462	0.872311	−	0.488951i	$-0.162620\pi$
$431$	36.2193	1.74462	0.872311	+	0.488951i	$0.162620\pi$
$432$	3.89858	0.187570
$433$	−23.3247	−1.12091	−0.560457	−	0.828184i	$-0.689374\pi$
$433$	−23.3247	−1.12091	−0.560457	+	0.828184i	$0.689374\pi$
$434$	−5.10655	−0.245122
$435$	0.790914	0.0379214
$436$	1.92089	0.0919942
$437$	−19.2076	−0.918825
$438$	−2.54025	−0.121378
$439$	31.0060	1.47984	0.739919	−	0.672696i	$-0.234864\pi$
$439$	31.0060	1.47984	0.739919	+	0.672696i	$0.234864\pi$
$440$	8.69695	0.414611
$441$	−2.97592	−0.141711
$442$	−23.3908	−1.11259
$443$	−1.04527	−0.0496622	−0.0248311	−	0.999692i	$-0.507905\pi$
$443$	−1.04527	−0.0496622	−0.0248311	+	0.999692i	$0.507905\pi$
$444$	−0.0374327	−0.00177648
$445$	−4.07368	−0.193111
$446$	1.91914	0.0908739
$447$	2.49191	0.117863
$448$	−7.52281	−0.355420
$449$	30.8628	1.45651	0.728253	−	0.685309i	$-0.240333\pi$
$449$	30.8628	1.45651	0.728253	+	0.685309i	$0.240333\pi$
$450$	20.1267	0.948782
$451$	36.0352	1.69683
$452$	0.947880	0.0445845
$453$	−0.553554	−0.0260083
$454$	5.12477	0.240517
$455$	1.86106	0.0872477
$456$	2.17995	0.102085
$457$	−3.39633	−0.158874	−0.0794369	−	0.996840i	$-0.525312\pi$
$457$	−3.39633	−0.158874	−0.0794369	+	0.996840i	$0.525312\pi$
$458$	−19.6690	−0.919074
$459$	−4.69290	−0.219046
$460$	0.237039	0.0110520
$461$	−10.3660	−0.482792	−0.241396	−	0.970427i	$-0.577605\pi$
$461$	−10.3660	−0.482792	−0.241396	+	0.970427i	$0.577605\pi$
$462$	1.22005	0.0567619
$463$	−23.6359	−1.09846	−0.549228	−	0.835673i	$-0.685078\pi$
$463$	−23.6359	−1.09846	−0.549228	+	0.835673i	$0.685078\pi$
$464$	−36.6553	−1.70168
$465$	0.319065	0.0147963
$466$	−13.4526	−0.623180
$467$	−19.0928	−0.883510	−0.441755	−	0.897136i	$-0.645644\pi$
$467$	−19.0928	−0.883510	−0.441755	+	0.897136i	$0.645644\pi$
$468$	1.02273	0.0472755
$469$	3.86784	0.178600
$470$	7.76192	0.358031
$471$	0.106240	0.00489528
$472$	16.0399	0.738296
$473$	24.4245	1.12304
$474$	−0.816638	−0.0375094
$475$	23.8228	1.09306
$476$	−0.546352	−0.0250420
$477$	−6.25947	−0.286601
$478$	8.04739	0.368079
$479$	−13.9575	−0.637733	−0.318867	−	0.947800i	$-0.603302\pi$
$479$	−13.9575	−0.637733	−0.318867	+	0.947800i	$0.603302\pi$
$480$	−0.0553399	−0.00252591
$481$	7.11347	0.324346
$482$	26.3030	1.19807
$483$	−0.582792	−0.0265180
$484$	1.97853	0.0899331
$485$	−9.34794	−0.424468
$486$	6.01788	0.272977
$487$	17.8690	0.809722	0.404861	−	0.914378i	$-0.367320\pi$
$487$	17.8690	0.809722	0.404861	+	0.914378i	$0.367320\pi$
$488$	−38.6191	−1.74820
$489$	3.18420	0.143994
$490$	0.848791	0.0383445
$491$	1.53715	0.0693706	0.0346853	−	0.999398i	$-0.488957\pi$
$491$	1.53715	0.0693706	0.0346853	+	0.999398i	$0.488957\pi$
$492$	−0.111468	−0.00502538
$493$	44.1237	1.98723
$494$	23.6370	1.06348
$495$	9.42164	0.423471
$496$	−14.7872	−0.663965
$497$	12.1700	0.545898
$498$	−3.18833	−0.142872
$499$	−35.1272	−1.57251	−0.786255	−	0.617902i	$-0.787983\pi$
$499$	−35.1272	−1.57251	−0.786255	+	0.617902i	$0.787983\pi$
$500$	−0.609558	−0.0272603
$501$	−0.539637	−0.0241092
$502$	−24.4334	−1.09052
$503$	23.3017	1.03897	0.519486	−	0.854479i	$-0.326123\pi$
$503$	23.3017	1.03897	0.519486	+	0.854479i	$0.326123\pi$
$504$	−8.17492	−0.364140
$505$	−6.12479	−0.272549
$506$	−29.5303	−1.31278
$507$	−0.444728	−0.0197511
$508$	−0.107956	−0.00478978
$509$	40.7781	1.80746	0.903730	−	0.428104i	$-0.140818\pi$
$509$	40.7781	1.80746	0.903730	+	0.428104i	$0.140818\pi$
$510$	0.666557	0.0295156
$511$	11.2754	0.498796
$512$	−20.5336	−0.907466
$513$	4.74230	0.209378
$514$	−0.238748	−0.0105307
$515$	−9.81080	−0.432316
$516$	−0.0755529	−0.00332603
$517$	−49.5225	−2.17800
$518$	3.24431	0.142547
$519$	1.67199	0.0733923
$520$	5.11236	0.224192
$521$	6.66265	0.291896	0.145948	−	0.989292i	$-0.453377\pi$
$521$	6.66265	0.291896	0.145948	+	0.989292i	$0.453377\pi$
$522$	−37.6703	−1.64879
$523$	−24.2779	−1.06160	−0.530799	−	0.847497i	$-0.678108\pi$
$523$	−24.2779	−1.06160	−0.530799	+	0.847497i	$0.678108\pi$
$524$	0.177342	0.00774721
$525$	0.722824	0.0315466
$526$	−18.3432	−0.799803
$527$	17.8001	0.775382
$528$	3.53294	0.153751
$529$	−8.89402	−0.386696
$530$	1.78532	0.0775495
$531$	17.3765	0.754074
$532$	0.552103	0.0239367
$533$	21.1827	0.917524
$534$	−1.56985	−0.0679342
$535$	3.34813	0.144752
$536$	10.6250	0.458932
$537$	3.01478	0.130097
$538$	−7.99592	−0.344729
$539$	−5.41545	−0.233260
$540$	−0.0585241	−0.00251848
$541$	28.1614	1.21075	0.605377	−	0.795939i	$-0.293023\pi$
$541$	28.1614	1.21075	0.605377	+	0.795939i	$0.293023\pi$
$542$	−40.7927	−1.75220
$543$	2.85029	0.122317
$544$	−3.08731	−0.132367
$545$	10.4022	0.445582
$546$	0.717187	0.0306928
$547$	−31.8313	−1.36101	−0.680503	−	0.732745i	$-0.738239\pi$
$547$	−31.8313	−1.36101	−0.680503	+	0.732745i	$0.738239\pi$
$548$	−2.10084	−0.0897434
$549$	−41.8371	−1.78556
$550$	36.6257	1.56173
$551$	−44.5881	−1.89952
$552$	−1.60094	−0.0681406
$553$	3.62482	0.154143
$554$	27.9433	1.18720
$555$	−0.202709	−0.00860453
$556$	−0.116220	−0.00492881
$557$	−23.7141	−1.00480	−0.502399	−	0.864636i	$-0.667549\pi$
$557$	−23.7141	−1.00480	−0.502399	+	0.864636i	$0.667549\pi$
$558$	−15.1967	−0.643327
$559$	14.3576	0.607260
$560$	2.45787	0.103864
$561$	−4.25276	−0.179552
$562$	−14.6423	−0.617647
$563$	6.95606	0.293163	0.146582	−	0.989199i	$-0.453173\pi$
$563$	6.95606	0.293163	0.146582	+	0.989199i	$0.453173\pi$
$564$	0.153189	0.00645043
$565$	5.13305	0.215949
$566$	40.6780	1.70982
$567$	−8.78388	−0.368888
$568$	33.4312	1.40274
$569$	−14.2834	−0.598790	−0.299395	−	0.954129i	$-0.596785\pi$
$569$	−14.2834	−0.598790	−0.299395	+	0.954129i	$0.596785\pi$
$570$	−0.673573	−0.0282129
$571$	−4.94964	−0.207136	−0.103568	−	0.994622i	$-0.533026\pi$
$571$	−4.94964	−0.207136	−0.103568	+	0.994622i	$0.533026\pi$
$572$	1.86111	0.0778169
$573$	0.503172	0.0210203
$574$	9.66101	0.403243
$575$	−17.4953	−0.729606
$576$	−22.3873	−0.932805
$577$	4.53775	0.188909	0.0944546	−	0.995529i	$-0.469889\pi$
$577$	4.53775	0.188909	0.0944546	+	0.995529i	$0.469889\pi$
$578$	12.5040	0.520100
$579$	−2.95358	−0.122747
$580$	0.550256	0.0228482
$581$	14.1521	0.587126
$582$	−3.60237	−0.149323
$583$	−11.3907	−0.471755
$584$	30.9738	1.28171
$585$	5.53836	0.228983
$586$	−34.8863	−1.44114
$587$	0.284682	0.0117501	0.00587505	−	0.999983i	$-0.498130\pi$
$587$	0.284682	0.0117501	0.00587505	+	0.999983i	$0.498130\pi$
$588$	0.0167517	0.000690830 0
$589$	−17.9874	−0.741159
$590$	−4.95611	−0.204040
$591$	−1.54035	−0.0633617
$592$	9.39466	0.386118
$593$	−11.4352	−0.469589	−0.234795	−	0.972045i	$-0.575442\pi$
$593$	−11.4352	−0.469589	−0.234795	+	0.972045i	$0.575442\pi$
$594$	7.29092	0.299150
$595$	−2.95866	−0.121293
$596$	1.73367	0.0710140
$597$	1.34258	0.0549482
$598$	−17.3589	−0.709858
$599$	11.9250	0.487241	0.243620	−	0.969871i	$-0.421665\pi$
$599$	11.9250	0.487241	0.243620	+	0.969871i	$0.421665\pi$
$600$	1.98561	0.0810623
$601$	29.4693	1.20208	0.601039	−	0.799220i	$-0.294754\pi$
$601$	29.4693	1.20208	0.601039	+	0.799220i	$0.294754\pi$
$602$	6.54820	0.266885
$603$	11.5104	0.468740
$604$	−0.385120	−0.0156703
$605$	10.7143	0.435599
$606$	−2.36028	−0.0958799
$607$	−7.54814	−0.306369	−0.153185	−	0.988198i	$-0.548953\pi$
$607$	−7.54814	−0.306369	−0.153185	+	0.988198i	$0.548953\pi$
$608$	3.11981	0.126525
$609$	−1.35288	−0.0548215
$610$	11.9328	0.483143
$611$	−29.1110	−1.17771
$612$	−1.62590	−0.0657231
$613$	42.7869	1.72815	0.864074	−	0.503365i	$-0.167905\pi$
$613$	42.7869	1.72815	0.864074	+	0.503365i	$0.167905\pi$
$614$	−23.9393	−0.966110
$615$	−0.603634	−0.0243409
$616$	−14.8764	−0.599386
$617$	22.1822	0.893020	0.446510	−	0.894779i	$-0.352667\pi$
$617$	22.1822	0.893020	0.446510	+	0.894779i	$0.352667\pi$
$618$	−3.78075	−0.152084
$619$	8.41815	0.338354	0.169177	−	0.985586i	$-0.445889\pi$
$619$	8.41815	0.338354	0.169177	+	0.985586i	$0.445889\pi$
$620$	0.221980	0.00891495
$621$	−3.48272	−0.139757
$622$	−44.1133	−1.76878
$623$	6.96813	0.279172
$624$	2.07678	0.0831379
$625$	19.9902	0.799608
$626$	28.6362	1.14453
$627$	4.29753	0.171627
$628$	0.0739135	0.00294947
$629$	−11.3088	−0.450911
$630$	2.52594	0.100636
$631$	−42.9906	−1.71143	−0.855715	−	0.517448i	$-0.826882\pi$
$631$	−42.9906	−1.71143	−0.855715	+	0.517448i	$0.826882\pi$
$632$	9.95746	0.396087
$633$	−4.41288	−0.175396
$634$	32.1900	1.27843
$635$	−0.584615	−0.0231997
$636$	0.0352351	0.00139716
$637$	−3.18339	−0.126130
$638$	−68.5509	−2.71395
$639$	36.2169	1.43272
$640$	7.09857	0.280596
$641$	−21.6825	−0.856407	−0.428203	−	0.903682i	$-0.640853\pi$
$641$	−21.6825	−0.856407	−0.428203	+	0.903682i	$0.640853\pi$
$642$	1.29025	0.0509223
$643$	7.73727	0.305128	0.152564	−	0.988294i	$-0.451247\pi$
$643$	7.73727	0.305128	0.152564	+	0.988294i	$0.451247\pi$
$644$	−0.405461	−0.0159774
$645$	−0.409141	−0.0161099
$646$	−37.5774	−1.47846
$647$	−20.9296	−0.822827	−0.411414	−	0.911449i	$-0.634965\pi$
$647$	−20.9296	−0.822827	−0.411414	+	0.911449i	$0.634965\pi$
$648$	−24.1295	−0.947896
$649$	31.6209	1.24123
$650$	21.5298	0.844470
$651$	−0.545769	−0.0213904
$652$	2.21531	0.0867584
$653$	4.52343	0.177015	0.0885077	−	0.996075i	$-0.471790\pi$
$653$	4.52343	0.177015	0.0885077	+	0.996075i	$0.471790\pi$
$654$	4.00865	0.156751
$655$	0.960358	0.0375243
$656$	27.9757	1.09227
$657$	33.5548	1.30910
$658$	−13.2770	−0.517590
$659$	−11.5665	−0.450567	−0.225283	−	0.974293i	$-0.572331\pi$
$659$	−11.5665	−0.450567	−0.225283	+	0.974293i	$0.572331\pi$
$660$	−0.0530353	−0.00206439
$661$	−0.556631	−0.0216504	−0.0108252	−	0.999941i	$-0.503446\pi$
$661$	−0.556631	−0.0216504	−0.0108252	+	0.999941i	$0.503446\pi$
$662$	−8.16101	−0.317187
$663$	−2.49992	−0.0970889
$664$	38.8760	1.50868
$665$	2.98980	0.115939
$666$	9.65482	0.374117
$667$	32.7453	1.26790
$668$	−0.375437	−0.0145261
$669$	0.205110	0.00793003
$670$	−3.28299	−0.126833
$671$	−76.1333	−2.93909
$672$	0.0946604	0.00365161
$673$	−23.9745	−0.924150	−0.462075	−	0.886841i	$-0.652895\pi$
$673$	−23.9745	−0.924150	−0.462075	+	0.886841i	$0.652895\pi$
$674$	12.4327	0.478889
$675$	4.31954	0.166259
$676$	−0.309407	−0.0119003
$677$	−51.7020	−1.98707	−0.993535	−	0.113524i	$-0.963786\pi$
$677$	−51.7020	−1.98707	−0.993535	+	0.113524i	$0.963786\pi$
$678$	1.97810	0.0759685
$679$	15.9899	0.613636
$680$	−8.12749	−0.311675
$681$	0.547716	0.0209885
$682$	−27.6543	−1.05894
$683$	29.9749	1.14696	0.573479	−	0.819220i	$-0.305594\pi$
$683$	29.9749	1.14696	0.573479	+	0.819220i	$0.305594\pi$
$684$	1.64301	0.0628222
$685$	−11.3767	−0.434680
$686$	−1.45188	−0.0554330
$687$	−2.10215	−0.0802021
$688$	18.9618	0.722913
$689$	−6.69585	−0.255091
$690$	0.494669	0.0188317
$691$	−39.1395	−1.48894	−0.744468	−	0.667658i	$-0.767297\pi$
$691$	−39.1395	−1.48894	−0.744468	+	0.667658i	$0.767297\pi$
$692$	1.16324	0.0442198
$693$	−16.1160	−0.612195
$694$	−0.424059	−0.0160971
$695$	−0.629364	−0.0238731
$696$	−3.71639	−0.140869
$697$	−33.6757	−1.27556
$698$	2.49288	0.0943570
$699$	−1.43776	−0.0543812
$700$	0.502885	0.0190073
$701$	29.4425	1.11203	0.556013	−	0.831173i	$-0.312330\pi$
$701$	29.4425	1.11203	0.556013	+	0.831173i	$0.312330\pi$
$702$	4.28585	0.161759
$703$	11.4278	0.431009
$704$	−40.7394	−1.53543
$705$	0.829565	0.0312432
$706$	3.63902	0.136956
$707$	10.4766	0.394014
$708$	−0.0978137	−0.00367606
$709$	19.0173	0.714210	0.357105	−	0.934064i	$-0.383764\pi$
$709$	19.0173	0.714210	0.357105	+	0.934064i	$0.383764\pi$
$710$	−10.3298	−0.387669
$711$	10.7872	0.404551
$712$	19.1416	0.717362
$713$	13.2099	0.494713
$714$	−1.14016	−0.0426696
$715$	10.0785	0.376913
$716$	2.09745	0.0783854
$717$	0.860076	0.0321201
$718$	−44.6322	−1.66566
$719$	0.197837	0.00737807	0.00368903	−	0.999993i	$-0.498826\pi$
$719$	0.197837	0.00737807	0.00368903	+	0.999993i	$0.498826\pi$
$720$	7.31444	0.272593
$721$	16.7816	0.624981
$722$	10.3873	0.386574
$723$	2.81117	0.104549
$724$	1.98301	0.0736978
$725$	−40.6133	−1.50834
$726$	4.12893	0.153239
$727$	34.0943	1.26449	0.632244	−	0.774769i	$-0.282134\pi$
$727$	34.0943	1.26449	0.632244	+	0.774769i	$0.282134\pi$
$728$	−8.74483	−0.324105
$729$	−25.7085	−0.952165
$730$	−9.57048	−0.354219
$731$	−22.8252	−0.844222
$732$	0.235505	0.00870451
$733$	−2.86047	−0.105654	−0.0528270	−	0.998604i	$-0.516823\pi$
$733$	−2.86047	−0.105654	−0.0528270	+	0.998604i	$0.516823\pi$
$734$	0.530769	0.0195911
$735$	0.0907156	0.00334610
$736$	−2.29117	−0.0844538
$737$	20.9461	0.771560
$738$	28.7504	1.05832
$739$	20.3860	0.749912	0.374956	−	0.927043i	$-0.377658\pi$
$739$	20.3860	0.749912	0.374956	+	0.927043i	$0.377658\pi$
$740$	−0.141029	−0.00518434
$741$	2.52623	0.0928035
$742$	−3.05384	−0.112110
$743$	−20.0394	−0.735174	−0.367587	−	0.929989i	$-0.619816\pi$
$743$	−20.0394	−0.735174	−0.367587	+	0.929989i	$0.619816\pi$
$744$	−1.49924	−0.0549648
$745$	9.38835	0.343963
$746$	41.1606	1.50700
$747$	42.1154	1.54092
$748$	−2.95874	−0.108182
$749$	−5.72707	−0.209263
$750$	−1.27207	−0.0464494
$751$	−1.06573	−0.0388890	−0.0194445	−	0.999811i	$-0.506190\pi$
$751$	−1.06573	−0.0388890	−0.0194445	+	0.999811i	$0.506190\pi$
$752$	−38.4466	−1.40200
$753$	−2.61135	−0.0951630
$754$	−40.2965	−1.46751
$755$	−2.08554	−0.0759005
$756$	0.100107	0.00364086
$757$	37.0228	1.34562	0.672808	−	0.739817i	$-0.265088\pi$
$757$	37.0228	1.34562	0.672808	+	0.739817i	$0.265088\pi$
$758$	36.3904	1.32176
$759$	−3.15608	−0.114559
$760$	8.21304	0.297918
$761$	3.94528	0.143016	0.0715081	−	0.997440i	$-0.477219\pi$
$761$	3.94528	0.143016	0.0715081	+	0.997440i	$0.477219\pi$
$762$	−0.225291	−0.00816141
$763$	−17.7933	−0.644159
$764$	0.350068	0.0126650
$765$	−8.80473	−0.318336
$766$	−16.0773	−0.580898
$767$	18.5879	0.671169
$768$	0.400891	0.0144659
$769$	−22.9790	−0.828644	−0.414322	−	0.910130i	$-0.635981\pi$
$769$	−22.9790	−0.828644	−0.414322	+	0.910130i	$0.635981\pi$
$770$	4.59659	0.165650
$771$	−0.0255165	−0.000918953 0
$772$	−2.05487	−0.0739565
$773$	−15.6983	−0.564627	−0.282314	−	0.959322i	$-0.591102\pi$
$773$	−15.6983	−0.564627	−0.282314	+	0.959322i	$0.591102\pi$
$774$	19.4869	0.700443
$775$	−16.3839	−0.588527
$776$	43.9246	1.57680
$777$	0.346740	0.0124392
$778$	−9.69485	−0.347577
$779$	34.0301	1.21926
$780$	−0.0311759	−0.00111628
$781$	65.9060	2.35830
$782$	27.5967	0.986855
$783$	−8.08471	−0.288924
$784$	−4.20426	−0.150152
$785$	0.400263	0.0142860
$786$	0.370089	0.0132006
$787$	−19.5950	−0.698485	−0.349242	−	0.937032i	$-0.613561\pi$
$787$	−19.5950	−0.698485	−0.349242	+	0.937032i	$0.613561\pi$
$788$	−1.07166	−0.0381762
$789$	−1.96046	−0.0697941
$790$	−3.07672	−0.109465
$791$	−8.78023	−0.312189
$792$	−44.2709	−1.57310
$793$	−44.7538	−1.58925
$794$	33.7546	1.19791
$795$	0.190809	0.00676729
$796$	0.934063	0.0331070
$797$	32.2337	1.14178	0.570888	−	0.821028i	$-0.306599\pi$
$797$	32.2337	1.14178	0.570888	+	0.821028i	$0.306599\pi$
$798$	1.15217	0.0407862
$799$	46.2799	1.63727
$800$	2.84169	0.100469
$801$	20.7366	0.732692
$802$	−18.5407	−0.654697
$803$	61.0615	2.15482
$804$	−0.0647931	−0.00228508
$805$	−2.19569	−0.0773880
$806$	−16.2561	−0.572598
$807$	−0.854575	−0.0300825
$808$	28.7795	1.01246
$809$	50.1803	1.76424	0.882122	−	0.471021i	$-0.156114\pi$
$809$	50.1803	1.76424	0.882122	+	0.471021i	$0.156114\pi$
$810$	7.45568	0.261966
$811$	−32.2851	−1.13368	−0.566841	−	0.823827i	$-0.691835\pi$
$811$	−32.2851	−1.13368	−0.566841	+	0.823827i	$0.691835\pi$
$812$	−0.941229	−0.0330306
$813$	−4.35978	−0.152904
$814$	17.5694	0.615808
$815$	11.9966	0.420222
$816$	−3.30161	−0.115579
$817$	23.0655	0.806960
$818$	4.35528	0.152279
$819$	−9.47351	−0.331031
$820$	−0.419961	−0.0146657
$821$	−2.84821	−0.0994032	−0.0497016	−	0.998764i	$-0.515827\pi$
$821$	−2.84821	−0.0994032	−0.0497016	+	0.998764i	$0.515827\pi$
$822$	−4.38418	−0.152916
$823$	−20.4935	−0.714358	−0.357179	−	0.934036i	$-0.616261\pi$
$823$	−20.4935	−0.714358	−0.357179	+	0.934036i	$0.616261\pi$
$824$	46.0995	1.60595
$825$	3.91442	0.136283
$826$	8.47755	0.294972
$827$	12.8868	0.448117	0.224059	−	0.974576i	$-0.428069\pi$
$827$	12.8868	0.448117	0.224059	+	0.974576i	$0.428069\pi$
$828$	−1.20662	−0.0419330
$829$	9.04317	0.314082	0.157041	−	0.987592i	$-0.449804\pi$
$829$	9.04317	0.314082	0.157041	+	0.987592i	$0.449804\pi$
$830$	−12.0121	−0.416948
$831$	2.98647	0.103600
$832$	−23.9480	−0.830249
$833$	5.06086	0.175348
$834$	−0.242535	−0.00839831
$835$	−2.03310	−0.0703584
$836$	2.98989	0.103407
$837$	−3.26147	−0.112733
$838$	−23.2444	−0.802965
$839$	14.0717	0.485807	0.242904	−	0.970050i	$-0.421900\pi$
$839$	14.0717	0.485807	0.242904	+	0.970050i	$0.421900\pi$
$840$	0.249198	0.00859814
$841$	47.0142	1.62118
$842$	−24.6886	−0.850825
$843$	−1.56491	−0.0538984
$844$	−3.07014	−0.105678
$845$	−1.67553	−0.0576400
$846$	−39.5112	−1.35842
$847$	−18.3271	−0.629728
$848$	−8.84312	−0.303674
$849$	4.34751	0.149206
$850$	−34.2275	−1.17399
$851$	−8.39254	−0.287693
$852$	−0.203868	−0.00698442
$853$	−36.9212	−1.26416	−0.632080	−	0.774903i	$-0.717799\pi$
$853$	−36.9212	−1.26416	−0.632080	+	0.774903i	$0.717799\pi$
$854$	−20.4113	−0.698461
$855$	8.89741	0.304285
$856$	−15.7324	−0.537722
$857$	−26.3947	−0.901626	−0.450813	−	0.892619i	$-0.648866\pi$
$857$	−26.3947	−0.901626	−0.450813	+	0.892619i	$0.648866\pi$
$858$	3.88389	0.132594
$859$	53.7029	1.83232	0.916160	−	0.400813i	$-0.131272\pi$
$859$	53.7029	1.83232	0.916160	+	0.400813i	$0.131272\pi$
$860$	−0.284648	−0.00970643
$861$	1.03253	0.0351886
$862$	52.5861	1.79109
$863$	4.39848	0.149726	0.0748630	−	0.997194i	$-0.476148\pi$
$863$	4.39848	0.149726	0.0748630	+	0.997194i	$0.476148\pi$
$864$	0.565683	0.0192449
$865$	6.29930	0.214183
$866$	−33.8647	−1.15077
$867$	1.33639	0.0453860
$868$	−0.379704	−0.0128880
$869$	19.6301	0.665904
$870$	1.14831	0.0389315
$871$	12.3128	0.417205
$872$	−48.8785	−1.65523
$873$	47.5847	1.61050
$874$	−27.8872	−0.943297
$875$	5.64634	0.190881
$876$	−0.188883	−0.00638177
$877$	27.9653	0.944321	0.472161	−	0.881513i	$-0.343474\pi$
$877$	27.9653	0.944321	0.472161	+	0.881513i	$0.343474\pi$
$878$	45.0171	1.51925
$879$	−3.72852	−0.125760
$880$	13.3105	0.448697
$881$	−31.8646	−1.07355	−0.536773	−	0.843727i	$-0.680357\pi$
$881$	−31.8646	−1.07355	−0.536773	+	0.843727i	$0.680357\pi$
$882$	−4.32068	−0.145485
$883$	22.9214	0.771367	0.385684	−	0.922631i	$-0.373966\pi$
$883$	22.9214	0.771367	0.385684	+	0.922631i	$0.373966\pi$
$884$	−1.73925	−0.0584973
$885$	−0.529690	−0.0178053
$886$	−1.51760	−0.0509849
$887$	52.3948	1.75924	0.879622	−	0.475673i	$-0.157796\pi$
$887$	52.3948	1.75924	0.879622	+	0.475673i	$0.157796\pi$
$888$	0.952502	0.0319639
$889$	1.00000	0.0335389
$890$	−5.91449	−0.198254
$891$	−47.5687	−1.59361
$892$	0.142700	0.00477794
$893$	−46.7671	−1.56500
$894$	3.61795	0.121002
$895$	11.3583	0.379666
$896$	−12.1423	−0.405646
$897$	−1.85525	−0.0619451
$898$	44.8091	1.49530
$899$	30.6651	1.02274
$900$	1.49655	0.0498848
$901$	10.6449	0.354632
$902$	52.3187	1.74202
$903$	0.699847	0.0232894
$904$	−24.1195	−0.802201
$905$	10.7386	0.356962
$906$	−0.803695	−0.0267010
$907$	8.25274	0.274028	0.137014	−	0.990569i	$-0.456250\pi$
$907$	8.25274	0.274028	0.137014	+	0.990569i	$0.456250\pi$
$908$	0.381058	0.0126459
$909$	31.1776	1.03409
$910$	2.70203	0.0895715
$911$	−41.0478	−1.35998	−0.679988	−	0.733223i	$-0.738015\pi$
$911$	−41.0478	−1.35998	−0.679988	+	0.733223i	$0.738015\pi$
$912$	3.33636	0.110478
$913$	76.6398	2.53641
$914$	−4.93107	−0.163105
$915$	1.27533	0.0421611
$916$	−1.46251	−0.0483228
$917$	−1.64272	−0.0542473
$918$	−6.81353	−0.224880
$919$	18.6013	0.613601	0.306801	−	0.951774i	$-0.400741\pi$
$919$	18.6013	0.613601	0.306801	+	0.951774i	$0.400741\pi$
$920$	−6.03162	−0.198856
$921$	−2.55854	−0.0843067
$922$	−15.0502	−0.495651
$923$	38.7418	1.27520
$924$	0.0907183	0.00298441
$925$	10.4091	0.342248
$926$	−34.3166	−1.12771
$927$	49.9409	1.64027
$928$	−5.31868	−0.174594
$929$	24.4625	0.802588	0.401294	−	0.915949i	$-0.368561\pi$
$929$	24.4625	0.802588	0.401294	+	0.915949i	$0.368561\pi$
$930$	0.463244	0.0151904
$931$	−5.11413	−0.167609
$932$	−1.00028	−0.0327654
$933$	−4.71466	−0.154351
$934$	−27.7205	−0.907042
$935$	−16.0225	−0.523990
$936$	−26.0239	−0.850619
$937$	52.8188	1.72552	0.862758	−	0.505617i	$-0.168735\pi$
$937$	52.8188	1.72552	0.862758	+	0.505617i	$0.168735\pi$
$938$	5.61565	0.183357
$939$	3.06053	0.0998767
$940$	0.577146	0.0188244
$941$	−7.92118	−0.258223	−0.129111	−	0.991630i	$-0.541213\pi$
$941$	−7.92118	−0.258223	−0.129111	+	0.991630i	$0.541213\pi$
$942$	0.154248	0.00502566
$943$	−24.9916	−0.813837
$944$	24.5487	0.798993
$945$	0.542110	0.0176348
$946$	35.4614	1.15295
$947$	−56.1375	−1.82422	−0.912111	−	0.409943i	$-0.865549\pi$
$947$	−56.1375	−1.82422	−0.912111	+	0.409943i	$0.865549\pi$
$948$	−0.0607221	−0.00197216
$949$	35.8941	1.16517
$950$	34.5878	1.12218
$951$	3.44034	0.111561
$952$	13.9023	0.450576
$953$	−1.73578	−0.0562273	−0.0281137	−	0.999605i	$-0.508950\pi$
$953$	−1.73578	−0.0562273	−0.0281137	+	0.999605i	$0.508950\pi$
$954$	−9.08800	−0.294235
$955$	1.89572	0.0613441
$956$	0.598373	0.0193528
$957$	−7.32646	−0.236831
$958$	−20.2646	−0.654719
$959$	19.4601	0.628399
$960$	0.682437	0.0220256
$961$	−18.6293	−0.600946
$962$	10.3279	0.332985
$963$	−17.0433	−0.549213
$964$	1.95579	0.0629918
$965$	−11.1277	−0.358215
$966$	−0.846145	−0.0272243
$967$	−26.7443	−0.860038	−0.430019	−	0.902820i	$-0.641493\pi$
$967$	−26.7443	−0.860038	−0.430019	+	0.902820i	$0.641493\pi$
$968$	−50.3450	−1.61815
$969$	−4.01614	−0.129017
$970$	−13.5721	−0.435773
$971$	−33.1012	−1.06227	−0.531134	−	0.847288i	$-0.678234\pi$
$971$	−33.1012	−1.06227	−0.531134	+	0.847288i	$0.678234\pi$
$972$	0.447467	0.0143525
$973$	1.07654	0.0345124
$974$	25.9437	0.831288
$975$	2.30103	0.0736919
$976$	−59.1057	−1.89193
$977$	7.19435	0.230168	0.115084	−	0.993356i	$-0.463286\pi$
$977$	7.19435	0.230168	0.115084	+	0.993356i	$0.463286\pi$
$978$	4.62307	0.147829
$979$	37.7356	1.20603
$980$	0.0631129	0.00201607
$981$	−52.9514	−1.69061
$982$	2.23176	0.0712182
$983$	−22.7413	−0.725334	−0.362667	−	0.931919i	$-0.618134\pi$
$983$	−22.7413	−0.725334	−0.362667	+	0.931919i	$0.618134\pi$
$984$	2.83639	0.0904208
$985$	−5.80335	−0.184910
$986$	64.0623	2.04016
$987$	−1.41899	−0.0451671
$988$	1.75756	0.0559153
$989$	−16.9392	−0.538635
$990$	13.6791	0.434750
$991$	50.6822	1.60997	0.804987	−	0.593292i	$-0.202172\pi$
$991$	50.6822	1.60997	0.804987	+	0.593292i	$0.202172\pi$
$992$	−2.14562	−0.0681236
$993$	−0.872219	−0.0276790
$994$	17.6694	0.560438
$995$	5.05823	0.160357
$996$	−0.237072	−0.00751190
$997$	−14.1678	−0.448700	−0.224350	−	0.974509i	$-0.572026\pi$
$997$	−14.1678	−0.448700	−0.224350	+	0.974509i	$0.572026\pi$
$998$	−51.0005	−1.61439
$999$	2.07209	0.0655580

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	889.2.a.c.1.12	✓	16
3.2	odd	2		8001.2.a.t.1.5		16
7.6	odd	2		6223.2.a.k.1.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
889.2.a.c.1.12	✓	16	1.1	even	1	trivial
6223.2.a.k.1.12		16	7.6	odd	2
8001.2.a.t.1.5		16	3.2	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 889 = 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	889.a (trivial)

\(f(q)\)	\(=\)	\(q+1.45188 q^{2} +0.155172 q^{3} +0.107956 q^{4} +0.584615 q^{5} +0.225291 q^{6} -1.00000 q^{7} -2.74702 q^{8} -2.97592 q^{9} +0.848791 q^{10} -5.41545 q^{11} +0.0167517 q^{12} -3.18339 q^{13} -1.45188 q^{14} +0.0907156 q^{15} -4.20426 q^{16} +5.06086 q^{17} -4.32068 q^{18} -5.11413 q^{19} +0.0631129 q^{20} -0.155172 q^{21} -7.86259 q^{22} +3.75579 q^{23} -0.426260 q^{24} -4.65823 q^{25} -4.62190 q^{26} -0.927293 q^{27} -0.107956 q^{28} +8.71861 q^{29} +0.131708 q^{30} +3.51720 q^{31} -0.610037 q^{32} -0.840324 q^{33} +7.34776 q^{34} -0.584615 q^{35} -0.321269 q^{36} -2.23456 q^{37} -7.42511 q^{38} -0.493971 q^{39} -1.60595 q^{40} -6.65414 q^{41} -0.225291 q^{42} -4.51015 q^{43} -0.584632 q^{44} -1.73977 q^{45} +5.45296 q^{46} +9.14467 q^{47} -0.652381 q^{48} +1.00000 q^{49} -6.76319 q^{50} +0.785302 q^{51} -0.343667 q^{52} +2.10337 q^{53} -1.34632 q^{54} -3.16596 q^{55} +2.74702 q^{56} -0.793568 q^{57} +12.6584 q^{58} -5.83902 q^{59} +0.00979332 q^{60} +14.0585 q^{61} +5.10655 q^{62} +2.97592 q^{63} +7.52281 q^{64} -1.86106 q^{65} -1.22005 q^{66} -3.86784 q^{67} +0.546352 q^{68} +0.582792 q^{69} -0.848791 q^{70} -12.1700 q^{71} +8.17492 q^{72} -11.2754 q^{73} -3.24431 q^{74} -0.722824 q^{75} -0.552103 q^{76} +5.41545 q^{77} -0.717187 q^{78} -3.62482 q^{79} -2.45787 q^{80} +8.78388 q^{81} -9.66101 q^{82} -14.1521 q^{83} -0.0167517 q^{84} +2.95866 q^{85} -6.54820 q^{86} +1.35288 q^{87} +14.8764 q^{88} -6.96813 q^{89} -2.52594 q^{90} +3.18339 q^{91} +0.405461 q^{92} +0.545769 q^{93} +13.2770 q^{94} -2.98980 q^{95} -0.0946604 q^{96} -15.9899 q^{97} +1.45188 q^{98} +16.1160 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 4 q^{3} + 12 q^{4} - 9 q^{5} - 12 q^{6} - 16 q^{7} - 6 q^{8} + 14 q^{9} - 2 q^{10} - 22 q^{11} - 10 q^{12} - 4 q^{13} + 2 q^{14} - 14 q^{15} + 12 q^{16} - 18 q^{17} - 5 q^{18} - 15 q^{19}+ \cdots - 73 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 - 4 * q^3 + 12 * q^4 - 9 * q^5 - 12 * q^6 - 16 * q^7 - 6 * q^8 + 14 * q^9 - 2 * q^10 - 22 * q^11 - 10 * q^12 - 4 * q^13 + 2 * q^14 - 14 * q^15 + 12 * q^16 - 18 * q^17 - 5 * q^18 - 15 * q^19 - 40 * q^20 + 4 * q^21 - 11 * q^22 - 5 * q^23 - 26 * q^24 + 15 * q^25 - 24 * q^26 - 10 * q^27 - 12 * q^28 - 12 * q^29 + 3 * q^30 - 32 * q^31 - 9 * q^32 - 10 * q^33 - 14 * q^34 + 9 * q^35 + 10 * q^36 - 2 * q^37 + 3 * q^38 - 41 * q^39 - 14 * q^40 - 45 * q^41 + 12 * q^42 - 3 * q^43 - 54 * q^44 - 22 * q^45 - 49 * q^47 + 10 * q^48 + 16 * q^49 - 6 * q^50 - 12 * q^51 + 38 * q^52 + 16 * q^53 - 67 * q^54 + 7 * q^55 + 6 * q^56 + 8 * q^57 + 16 * q^58 - 35 * q^59 + 56 * q^60 - 11 * q^61 + 17 * q^62 - 14 * q^63 - 2 * q^64 + 14 * q^65 + 86 * q^66 + 17 * q^67 - 71 * q^68 - 17 * q^69 + 2 * q^70 - 81 * q^71 + 13 * q^72 - 15 * q^73 + 13 * q^74 - 48 * q^75 + 14 * q^76 + 22 * q^77 - 10 * q^78 - 34 * q^79 - 33 * q^80 + 40 * q^81 - 14 * q^82 - 39 * q^83 + 10 * q^84 - 17 * q^85 + 36 * q^86 + 7 * q^87 + 61 * q^88 - 32 * q^89 + 79 * q^90 + 4 * q^91 + 37 * q^92 + 27 * q^93 + 13 * q^94 - 33 * q^95 - 55 * q^96 - 4 * q^97 - 2 * q^98 - 73 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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