LMFDB - Embedded newform 637.2.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(1,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, 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("637.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.4507648.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 1 $ x^6 - 2x^5 - 5x^4 + 8x^3 + 7x^2 - 6*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			1.1
Root			$-1.66745$ of defining polynomial
Character	$\chi$	$=$	637.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.44785 q^{2} -0.667452 q^{3} +3.99195 q^{4} +0.910286 q^{5} +1.63382 q^{6} -4.87599 q^{8} -2.55451 q^{9} +O(q^{10})$	\(q-2.44785 q^{2} -0.667452 q^{3} +3.99195 q^{4} +0.910286 q^{5} +1.63382 q^{6} -4.87599 q^{8} -2.55451 q^{9} -2.22824 q^{10} +3.67837 q^{11} -2.66443 q^{12} +1.00000 q^{13} -0.607572 q^{15} +3.95177 q^{16} +7.18531 q^{17} +6.25304 q^{18} -1.97802 q^{19} +3.63382 q^{20} -9.00407 q^{22} -0.596700 q^{23} +3.25449 q^{24} -4.17138 q^{25} -2.44785 q^{26} +3.70737 q^{27} -3.64900 q^{29} +1.48724 q^{30} -7.08833 q^{31} +0.0786478 q^{32} -2.45513 q^{33} -17.5885 q^{34} -10.1975 q^{36} +0.710851 q^{37} +4.84189 q^{38} -0.667452 q^{39} -4.43855 q^{40} +5.27529 q^{41} +11.0790 q^{43} +14.6839 q^{44} -2.32533 q^{45} +1.46063 q^{46} +12.1135 q^{47} -2.63762 q^{48} +10.2109 q^{50} -4.79585 q^{51} +3.99195 q^{52} -11.4484 q^{53} -9.07506 q^{54} +3.34837 q^{55} +1.32023 q^{57} +8.93219 q^{58} +9.58986 q^{59} -2.42540 q^{60} +6.98536 q^{61} +17.3511 q^{62} -8.09606 q^{64} +0.910286 q^{65} +6.00978 q^{66} +1.22839 q^{67} +28.6834 q^{68} +0.398269 q^{69} +11.3635 q^{71} +12.4558 q^{72} +6.53419 q^{73} -1.74005 q^{74} +2.78419 q^{75} -7.89616 q^{76} +1.63382 q^{78} -11.5204 q^{79} +3.59725 q^{80} +5.18904 q^{81} -12.9131 q^{82} +7.16403 q^{83} +6.54069 q^{85} -27.1198 q^{86} +2.43553 q^{87} -17.9357 q^{88} +12.8490 q^{89} +5.69206 q^{90} -2.38200 q^{92} +4.73112 q^{93} -29.6520 q^{94} -1.80056 q^{95} -0.0524936 q^{96} +9.09062 q^{97} -9.39642 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 8 q^{3} + 4 q^{4} + 6 q^{5} + 4 q^{6} + 6 q^{9}+O(q^{10}) $ 6 * q + 8 * q^3 + 4 * q^4 + 6 * q^5 + 4 * q^6 + 6 * q^9	$ 6 q + 8 q^{3} + 4 q^{4} + 6 q^{5} + 4 q^{6} + 6 q^{9} + 4 q^{10} + 4 q^{11} - 4 q^{12} + 6 q^{13} + 12 q^{15} + 16 q^{17} - 4 q^{18} + 2 q^{19} + 16 q^{20} - 12 q^{22} - 6 q^{23} + 12 q^{24} - 4 q^{25} + 20 q^{27} - 6 q^{29} + 6 q^{31} - 20 q^{32} + 4 q^{33} - 24 q^{36} + 8 q^{38} + 8 q^{39} + 4 q^{40} - 8 q^{41} + 2 q^{43} - 4 q^{44} + 14 q^{45} + 8 q^{46} + 30 q^{47} - 8 q^{48} + 8 q^{50} - 4 q^{51} + 4 q^{52} - 14 q^{53} - 48 q^{54} - 8 q^{55} + 4 q^{57} - 8 q^{58} + 24 q^{59} + 12 q^{60} + 28 q^{62} - 20 q^{64} + 6 q^{65} - 4 q^{66} + 16 q^{67} + 28 q^{68} - 20 q^{69} + 8 q^{71} + 28 q^{72} - 6 q^{73} - 12 q^{74} + 12 q^{75} - 16 q^{76} + 4 q^{78} - 22 q^{79} - 28 q^{80} + 46 q^{81} - 40 q^{82} + 50 q^{83} - 8 q^{85} - 16 q^{86} - 16 q^{87} - 44 q^{88} + 26 q^{89} - 40 q^{90} + 20 q^{92} + 16 q^{93} - 32 q^{94} - 6 q^{95} - 20 q^{96} - 14 q^{97} + 12 q^{99}+O(q^{100}) $ 6 * q + 8 * q^3 + 4 * q^4 + 6 * q^5 + 4 * q^6 + 6 * q^9 + 4 * q^10 + 4 * q^11 - 4 * q^12 + 6 * q^13 + 12 * q^15 + 16 * q^17 - 4 * q^18 + 2 * q^19 + 16 * q^20 - 12 * q^22 - 6 * q^23 + 12 * q^24 - 4 * q^25 + 20 * q^27 - 6 * q^29 + 6 * q^31 - 20 * q^32 + 4 * q^33 - 24 * q^36 + 8 * q^38 + 8 * q^39 + 4 * q^40 - 8 * q^41 + 2 * q^43 - 4 * q^44 + 14 * q^45 + 8 * q^46 + 30 * q^47 - 8 * q^48 + 8 * q^50 - 4 * q^51 + 4 * q^52 - 14 * q^53 - 48 * q^54 - 8 * q^55 + 4 * q^57 - 8 * q^58 + 24 * q^59 + 12 * q^60 + 28 * q^62 - 20 * q^64 + 6 * q^65 - 4 * q^66 + 16 * q^67 + 28 * q^68 - 20 * q^69 + 8 * q^71 + 28 * q^72 - 6 * q^73 - 12 * q^74 + 12 * q^75 - 16 * q^76 + 4 * q^78 - 22 * q^79 - 28 * q^80 + 46 * q^81 - 40 * q^82 + 50 * q^83 - 8 * q^85 - 16 * q^86 - 16 * q^87 - 44 * q^88 + 26 * q^89 - 40 * q^90 + 20 * q^92 + 16 * q^93 - 32 * q^94 - 6 * q^95 - 20 * q^96 - 14 * q^97 + 12 * 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 $

$2$	−2.44785	−1.73089	−0.865444	−	0.501005i	$-0.832964\pi$
$2$	−2.44785	−1.73089	−0.865444	+	0.501005i	$0.832964\pi$
$3$	−0.667452	−0.385353	−0.192677	−	0.981262i	$-0.561717\pi$
$3$	−0.667452	−0.385353	−0.192677	+	0.981262i	$0.561717\pi$
$4$	3.99195	1.99598
$5$	0.910286	0.407092	0.203546	−	0.979065i	$-0.434753\pi$
$5$	0.910286	0.407092	0.203546	+	0.979065i	$0.434753\pi$
$6$	1.63382	0.667004
$7$	0	0
$7$	0	0
$8$	−4.87599	−1.72392
$9$	−2.55451	−0.851503
$10$	−2.22824	−0.704632
$11$	3.67837	1.10907	0.554534	−	0.832161i	$-0.312896\pi$
$11$	3.67837	1.10907	0.554534	+	0.832161i	$0.312896\pi$
$12$	−2.66443	−0.769156
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	−0.607572	−0.156874
$16$	3.95177	0.987943
$17$	7.18531	1.74269	0.871347	−	0.490668i	$-0.163247\pi$
$17$	7.18531	1.74269	0.871347	+	0.490668i	$0.163247\pi$
$18$	6.25304	1.47386
$19$	−1.97802	−0.453789	−0.226894	−	0.973919i	$-0.572857\pi$
$19$	−1.97802	−0.453789	−0.226894	+	0.973919i	$0.572857\pi$
$20$	3.63382	0.812547
$21$	0	0
$22$	−9.00407	−1.91967
$23$	−0.596700	−0.124421	−0.0622103	−	0.998063i	$-0.519815\pi$
$23$	−0.596700	−0.124421	−0.0622103	+	0.998063i	$0.519815\pi$
$24$	3.25449	0.664320
$25$	−4.17138	−0.834276
$26$	−2.44785	−0.480062
$27$	3.70737	0.713483
$28$	0	0
$29$	−3.64900	−0.677602	−0.338801	−	0.940858i	$-0.610021\pi$
$29$	−3.64900	−0.677602	−0.338801	+	0.940858i	$0.610021\pi$
$30$	1.48724	0.271532
$31$	−7.08833	−1.27310	−0.636551	−	0.771235i	$-0.719639\pi$
$31$	−7.08833	−1.27310	−0.636551	+	0.771235i	$0.719639\pi$
$32$	0.0786478	0.0139031
$33$	−2.45513	−0.427383
$34$	−17.5885	−3.01641
$35$	0	0
$36$	−10.1975	−1.69958
$37$	0.710851	0.116863	0.0584316	−	0.998291i	$-0.481390\pi$
$37$	0.710851	0.116863	0.0584316	+	0.998291i	$0.481390\pi$
$38$	4.84189	0.785458
$39$	−0.667452	−0.106878
$40$	−4.43855	−0.701796
$41$	5.27529	0.823863	0.411931	−	0.911215i	$-0.364854\pi$
$41$	5.27529	0.823863	0.411931	+	0.911215i	$0.364854\pi$
$42$	0	0
$43$	11.0790	1.68954	0.844768	−	0.535132i	$-0.179738\pi$
$43$	11.0790	1.68954	0.844768	+	0.535132i	$0.179738\pi$
$44$	14.6839	2.21367
$45$	−2.32533	−0.346640
$46$	1.46063	0.215358
$47$	12.1135	1.76693	0.883467	−	0.468494i	$-0.155203\pi$
$47$	12.1135	1.76693	0.883467	+	0.468494i	$0.155203\pi$
$48$	−2.63762	−0.380707
$49$	0	0
$50$	10.2109	1.44404
$51$	−4.79585	−0.671553
$52$	3.99195	0.553584
$53$	−11.4484	−1.57256	−0.786282	−	0.617868i	$-0.787997\pi$
$53$	−11.4484	−1.57256	−0.786282	+	0.617868i	$0.787997\pi$
$54$	−9.07506	−1.23496
$55$	3.34837	0.451494
$56$	0	0
$57$	1.32023	0.174869
$58$	8.93219	1.17285
$59$	9.58986	1.24849	0.624247	−	0.781227i	$-0.285406\pi$
$59$	9.58986	1.24849	0.624247	+	0.781227i	$0.285406\pi$
$60$	−2.42540	−0.313118
$61$	6.98536	0.894384	0.447192	−	0.894438i	$-0.352424\pi$
$61$	6.98536	0.894384	0.447192	+	0.894438i	$0.352424\pi$
$62$	17.3511	2.20360
$63$	0	0
$64$	−8.09606	−1.01201
$65$	0.910286	0.112907
$66$	6.00978	0.739753
$67$	1.22839	0.150072	0.0750360	−	0.997181i	$-0.476093\pi$
$67$	1.22839	0.150072	0.0750360	+	0.997181i	$0.476093\pi$
$68$	28.6834	3.47837
$69$	0.398269	0.0479459
$70$	0	0
$71$	11.3635	1.34859	0.674297	−	0.738460i	$-0.264447\pi$
$71$	11.3635	1.34859	0.674297	+	0.738460i	$0.264447\pi$
$72$	12.4558	1.46793
$73$	6.53419	0.764769	0.382384	−	0.924003i	$-0.375103\pi$
$73$	6.53419	0.764769	0.382384	+	0.924003i	$0.375103\pi$
$74$	−1.74005	−0.202277
$75$	2.78419	0.321491
$76$	−7.89616	−0.905752
$77$	0	0
$78$	1.63382	0.184994
$79$	−11.5204	−1.29615	−0.648074	−	0.761577i	$-0.724425\pi$
$79$	−11.5204	−1.29615	−0.648074	+	0.761577i	$0.724425\pi$
$80$	3.59725	0.402184
$81$	5.18904	0.576560
$82$	−12.9131	−1.42601
$83$	7.16403	0.786355	0.393177	−	0.919463i	$-0.371376\pi$
$83$	7.16403	0.786355	0.393177	+	0.919463i	$0.371376\pi$
$84$	0	0
$85$	6.54069	0.709437
$86$	−27.1198	−2.92440
$87$	2.43553	0.261116
$88$	−17.9357	−1.91195
$89$	12.8490	1.36199	0.680997	−	0.732286i	$-0.261547\pi$
$89$	12.8490	1.36199	0.680997	+	0.732286i	$0.261547\pi$
$90$	5.69206	0.599996
$91$	0	0
$92$	−2.38200	−0.248341
$93$	4.73112	0.490594
$94$	−29.6520	−3.05837
$95$	−1.80056	−0.184734
$96$	−0.0524936	−0.00535761
$97$	9.09062	0.923012	0.461506	−	0.887137i	$-0.347309\pi$
$97$	9.09062	0.923012	0.461506	+	0.887137i	$0.347309\pi$
$98$	0	0
$99$	−9.39642	−0.944375
$100$	−16.6519	−1.66519
$101$	−5.80645	−0.577763	−0.288882	−	0.957365i	$-0.593283\pi$
$101$	−5.80645	−0.577763	−0.288882	+	0.957365i	$0.593283\pi$
$102$	11.7395	1.16238
$103$	12.8682	1.26794	0.633971	−	0.773357i	$-0.281424\pi$
$103$	12.8682	1.26794	0.633971	+	0.773357i	$0.281424\pi$
$104$	−4.87599	−0.478130
$105$	0	0
$106$	28.0240	2.72193
$107$	4.45747	0.430920	0.215460	−	0.976513i	$-0.430875\pi$
$107$	4.45747	0.430920	0.215460	+	0.976513i	$0.430875\pi$
$108$	14.7996	1.42409
$109$	0.878896	0.0841830	0.0420915	−	0.999114i	$-0.486598\pi$
$109$	0.878896	0.0841830	0.0420915	+	0.999114i	$0.486598\pi$
$110$	−8.19628	−0.781485
$111$	−0.474459	−0.0450336
$112$	0	0
$113$	−5.36723	−0.504906	−0.252453	−	0.967609i	$-0.581237\pi$
$113$	−5.36723	−0.504906	−0.252453	+	0.967609i	$0.581237\pi$
$114$	−3.23173	−0.302679
$115$	−0.543168	−0.0506507
$116$	−14.5666	−1.35248
$117$	−2.55451	−0.236164
$118$	−23.4745	−2.16100
$119$	0	0
$120$	2.96252	0.270439
$121$	2.53037	0.230034
$122$	−17.0991	−1.54808
$123$	−3.52100	−0.317478
$124$	−28.2963	−2.54108
$125$	−8.34858	−0.746720
$126$	0	0
$127$	6.61029	0.586568	0.293284	−	0.956025i	$-0.405252\pi$
$127$	6.61029	0.586568	0.293284	+	0.956025i	$0.405252\pi$
$128$	19.6606	1.73777
$129$	−7.39472	−0.651068
$130$	−2.22824	−0.195430
$131$	−19.9665	−1.74448	−0.872240	−	0.489079i	$-0.837333\pi$
$131$	−19.9665	−1.74448	−0.872240	+	0.489079i	$0.837333\pi$
$132$	−9.80076	−0.853047
$133$	0	0
$134$	−3.00692	−0.259758
$135$	3.37476	0.290453
$136$	−35.0355	−3.00427
$137$	5.75451	0.491641	0.245821	−	0.969315i	$-0.420943\pi$
$137$	5.75451	0.491641	0.245821	+	0.969315i	$0.420943\pi$
$138$	−0.974900	−0.0829890
$139$	−1.55138	−0.131586	−0.0657931	−	0.997833i	$-0.520958\pi$
$139$	−1.55138	−0.131586	−0.0657931	+	0.997833i	$0.520958\pi$
$140$	0	0
$141$	−8.08517	−0.680894
$142$	−27.8160	−2.33427
$143$	3.67837	0.307600
$144$	−10.0948	−0.841237
$145$	−3.32163	−0.275847
$146$	−15.9947	−1.32373
$147$	0	0
$148$	2.83768	0.233256
$149$	14.9337	1.22341	0.611707	−	0.791084i	$-0.290483\pi$
$149$	14.9337	1.22341	0.611707	+	0.791084i	$0.290483\pi$
$150$	−6.81528	−0.556465
$151$	−7.90102	−0.642976	−0.321488	−	0.946914i	$-0.604183\pi$
$151$	−7.90102	−0.642976	−0.321488	+	0.946914i	$0.604183\pi$
$152$	9.64481	0.782297
$153$	−18.3549	−1.48391
$154$	0	0
$155$	−6.45241	−0.518270
$156$	−2.66443	−0.213325
$157$	12.4948	0.997194	0.498597	−	0.866834i	$-0.333849\pi$
$157$	12.4948	0.997194	0.498597	+	0.866834i	$0.333849\pi$
$158$	28.2002	2.24349
$159$	7.64127	0.605993
$160$	0.0715920	0.00565985
$161$	0	0
$162$	−12.7020	−0.997961
$163$	7.01427	0.549400	0.274700	−	0.961530i	$-0.411421\pi$
$163$	7.01427	0.549400	0.274700	+	0.961530i	$0.411421\pi$
$164$	21.0587	1.64441
$165$	−2.23487	−0.173985
$166$	−17.5365	−1.36109
$167$	4.82764	0.373574	0.186787	−	0.982400i	$-0.440193\pi$
$167$	4.82764	0.373574	0.186787	+	0.982400i	$0.440193\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−16.0106	−1.22796
$171$	5.05287	0.386403
$172$	44.2270	3.37227
$173$	−22.2124	−1.68878	−0.844388	−	0.535732i	$-0.820036\pi$
$173$	−22.2124	−1.68878	−0.844388	+	0.535732i	$0.820036\pi$
$174$	−5.96180	−0.451963
$175$	0	0
$176$	14.5361	1.09570
$177$	−6.40077	−0.481111
$178$	−31.4524	−2.35746
$179$	4.57505	0.341956	0.170978	−	0.985275i	$-0.445307\pi$
$179$	4.57505	0.341956	0.170978	+	0.985275i	$0.445307\pi$
$180$	−9.28262	−0.691886
$181$	−7.23332	−0.537649	−0.268824	−	0.963189i	$-0.586635\pi$
$181$	−7.23332	−0.537649	−0.268824	+	0.963189i	$0.586635\pi$
$182$	0	0
$183$	−4.66239	−0.344654
$184$	2.90951	0.214492
$185$	0.647078	0.0475741
$186$	−11.5810	−0.849163
$187$	26.4302	1.93277
$188$	48.3565	3.52676
$189$	0	0
$190$	4.40751	0.319754
$191$	1.97242	0.142719	0.0713596	−	0.997451i	$-0.477266\pi$
$191$	1.97242	0.142719	0.0713596	+	0.997451i	$0.477266\pi$
$192$	5.40373	0.389981
$193$	−25.2073	−1.81446	−0.907230	−	0.420635i	$-0.861807\pi$
$193$	−25.2073	−1.81446	−0.907230	+	0.420635i	$0.861807\pi$
$194$	−22.2524	−1.59763
$195$	−0.607572	−0.0435091
$196$	0	0
$197$	−3.04497	−0.216945	−0.108473	−	0.994099i	$-0.534596\pi$
$197$	−3.04497	−0.216945	−0.108473	+	0.994099i	$0.534596\pi$
$198$	23.0010	1.63461
$199$	4.05691	0.287587	0.143794	−	0.989608i	$-0.454070\pi$
$199$	4.05691	0.287587	0.143794	+	0.989608i	$0.454070\pi$
$200$	20.3396	1.43823
$201$	−0.819893	−0.0578308
$202$	14.2133	1.00004
$203$	0	0
$204$	−19.1448	−1.34040
$205$	4.80203	0.335388
$206$	−31.4994	−2.19467
$207$	1.52428	0.105944
$208$	3.95177	0.274006
$209$	−7.27588	−0.503283
$210$	0	0
$211$	16.4116	1.12982	0.564910	−	0.825152i	$-0.308911\pi$
$211$	16.4116	1.12982	0.564910	+	0.825152i	$0.308911\pi$
$212$	−45.7016	−3.13880
$213$	−7.58456	−0.519685
$214$	−10.9112	−0.745875
$215$	10.0851	0.687797
$216$	−18.0771	−1.22999
$217$	0	0
$218$	−2.15140	−0.145711
$219$	−4.36125	−0.294706
$220$	13.3665	0.901170
$221$	7.18531	0.483336
$222$	1.16140	0.0779482
$223$	−16.1205	−1.07951	−0.539755	−	0.841822i	$-0.681483\pi$
$223$	−16.1205	−1.07951	−0.539755	+	0.841822i	$0.681483\pi$
$224$	0	0
$225$	10.6558	0.710388
$226$	13.1381	0.873936
$227$	−8.67804	−0.575982	−0.287991	−	0.957633i	$-0.592987\pi$
$227$	−8.67804	−0.575982	−0.287991	+	0.957633i	$0.592987\pi$
$228$	5.27031	0.349034
$229$	−20.7592	−1.37180	−0.685902	−	0.727694i	$-0.740592\pi$
$229$	−20.7592	−1.37180	−0.685902	+	0.727694i	$0.740592\pi$
$230$	1.32959	0.0876707
$231$	0	0
$232$	17.7925	1.16813
$233$	−9.84468	−0.644946	−0.322473	−	0.946579i	$-0.604514\pi$
$233$	−9.84468	−0.644946	−0.322473	+	0.946579i	$0.604514\pi$
$234$	6.25304	0.408774
$235$	11.0267	0.719305
$236$	38.2823	2.49196
$237$	7.68932	0.499475
$238$	0	0
$239$	1.13539	0.0734424	0.0367212	−	0.999326i	$-0.488309\pi$
$239$	1.13539	0.0734424	0.0367212	+	0.999326i	$0.488309\pi$
$240$	−2.40099	−0.154983
$241$	−21.8208	−1.40560	−0.702802	−	0.711386i	$-0.748068\pi$
$241$	−21.8208	−1.40560	−0.702802	+	0.711386i	$0.748068\pi$
$242$	−6.19396	−0.398163
$243$	−14.5855	−0.935662
$244$	27.8852	1.78517
$245$	0	0
$246$	8.61888	0.549519
$247$	−1.97802	−0.125858
$248$	34.5626	2.19473
$249$	−4.78165	−0.303025
$250$	20.4360	1.29249
$251$	9.44377	0.596086	0.298043	−	0.954552i	$-0.403666\pi$
$251$	9.44377	0.596086	0.298043	+	0.954552i	$0.403666\pi$
$252$	0	0
$253$	−2.19488	−0.137991
$254$	−16.1810	−1.01528
$255$	−4.36559	−0.273384
$256$	−31.9341	−1.99588
$257$	−3.62752	−0.226279	−0.113139	−	0.993579i	$-0.536091\pi$
$257$	−3.62752	−0.226279	−0.113139	+	0.993579i	$0.536091\pi$
$258$	18.1011	1.12693
$259$	0	0
$260$	3.63382	0.225360
$261$	9.32140	0.576980
$262$	48.8749	3.01950
$263$	6.59584	0.406717	0.203359	−	0.979104i	$-0.434814\pi$
$263$	6.59584	0.406717	0.203359	+	0.979104i	$0.434814\pi$
$264$	11.9712	0.736776
$265$	−10.4214	−0.640179
$266$	0	0
$267$	−8.57610	−0.524849
$268$	4.90369	0.299540
$269$	23.5313	1.43473	0.717365	−	0.696698i	$-0.245348\pi$
$269$	23.5313	1.43473	0.717365	+	0.696698i	$0.245348\pi$
$270$	−8.26090	−0.502743
$271$	2.69767	0.163872	0.0819358	−	0.996638i	$-0.473890\pi$
$271$	2.69767	0.163872	0.0819358	+	0.996638i	$0.473890\pi$
$272$	28.3947	1.72168
$273$	0	0
$274$	−14.0862	−0.850976
$275$	−15.3439	−0.925269
$276$	1.58987	0.0956988
$277$	−24.7549	−1.48738	−0.743690	−	0.668525i	$-0.766926\pi$
$277$	−24.7549	−1.48738	−0.743690	+	0.668525i	$0.766926\pi$
$278$	3.79754	0.227761
$279$	18.1072	1.08405
$280$	0	0
$281$	−4.05377	−0.241828	−0.120914	−	0.992663i	$-0.538582\pi$
$281$	−4.05377	−0.241828	−0.120914	+	0.992663i	$0.538582\pi$
$282$	19.7912	1.17855
$283$	12.9237	0.768235	0.384118	−	0.923284i	$-0.374506\pi$
$283$	12.9237	0.768235	0.384118	+	0.923284i	$0.374506\pi$
$284$	45.3624	2.69176
$285$	1.20179	0.0711879
$286$	−9.00407	−0.532422
$287$	0	0
$288$	−0.200906	−0.0118385
$289$	34.6287	2.03698
$290$	8.13085	0.477460
$291$	−6.06755	−0.355686
$292$	26.0842	1.52646
$293$	−23.5553	−1.37611	−0.688057	−	0.725656i	$-0.741536\pi$
$293$	−23.5553	−1.37611	−0.688057	+	0.725656i	$0.741536\pi$
$294$	0	0
$295$	8.72952	0.508252
$296$	−3.46610	−0.201463
$297$	13.6370	0.791302
$298$	−36.5553	−2.11759
$299$	−0.596700	−0.0345081
$300$	11.1144	0.641688
$301$	0	0
$302$	19.3405	1.11292
$303$	3.87552	0.222643
$304$	−7.81669	−0.448318
$305$	6.35868	0.364097
$306$	44.9301	2.56848
$307$	19.9551	1.13890	0.569450	−	0.822026i	$-0.307156\pi$
$307$	19.9551	1.13890	0.569450	+	0.822026i	$0.307156\pi$
$308$	0	0
$309$	−8.58891	−0.488606
$310$	15.7945	0.897068
$311$	6.48069	0.367486	0.183743	−	0.982974i	$-0.441179\pi$
$311$	6.48069	0.367486	0.183743	+	0.982974i	$0.441179\pi$
$312$	3.25449	0.184249
$313$	16.1154	0.910897	0.455449	−	0.890262i	$-0.349479\pi$
$313$	16.1154	0.910897	0.455449	+	0.890262i	$0.349479\pi$
$314$	−30.5854	−1.72603
$315$	0	0
$316$	−45.9889	−2.58708
$317$	14.5303	0.816106	0.408053	−	0.912958i	$-0.366208\pi$
$317$	14.5303	0.816106	0.408053	+	0.912958i	$0.366208\pi$
$318$	−18.7047	−1.04891
$319$	−13.4224	−0.751508
$320$	−7.36974	−0.411981
$321$	−2.97515	−0.166057
$322$	0	0
$323$	−14.2127	−0.790815
$324$	20.7144	1.15080
$325$	−4.17138	−0.231386
$326$	−17.1699	−0.950951
$327$	−0.586621	−0.0324402
$328$	−25.7223	−1.42028
$329$	0	0
$330$	5.47062	0.301148
$331$	21.0945	1.15946	0.579730	−	0.814809i	$-0.303158\pi$
$331$	21.0945	1.15946	0.579730	+	0.814809i	$0.303158\pi$
$332$	28.5985	1.56955
$333$	−1.81588	−0.0995094
$334$	−11.8173	−0.646615
$335$	1.11819	0.0610932
$336$	0	0
$337$	−32.8693	−1.79050	−0.895251	−	0.445562i	$-0.853004\pi$
$337$	−32.8693	−1.79050	−0.895251	+	0.445562i	$0.853004\pi$
$338$	−2.44785	−0.133145
$339$	3.58236	0.194567
$340$	26.1101	1.41602
$341$	−26.0735	−1.41196
$342$	−12.3686	−0.668820
$343$	0	0
$344$	−54.0213	−2.91263
$345$	0.362538	0.0195184
$346$	54.3725	2.92308
$347$	15.9160	0.854418	0.427209	−	0.904153i	$-0.359497\pi$
$347$	15.9160	0.854418	0.427209	+	0.904153i	$0.359497\pi$
$348$	9.72252	0.521182
$349$	−29.6245	−1.58576	−0.792882	−	0.609375i	$-0.791420\pi$
$349$	−29.6245	−1.58576	−0.792882	+	0.609375i	$0.791420\pi$
$350$	0	0
$351$	3.70737	0.197885
$352$	0.289295	0.0154195
$353$	−28.7078	−1.52796	−0.763980	−	0.645240i	$-0.776757\pi$
$353$	−28.7078	−1.52796	−0.763980	+	0.645240i	$0.776757\pi$
$354$	15.6681	0.832750
$355$	10.3440	0.549002
$356$	51.2927	2.71851
$357$	0	0
$358$	−11.1990	−0.591887
$359$	27.2931	1.44048	0.720238	−	0.693727i	$-0.244032\pi$
$359$	27.2931	1.44048	0.720238	+	0.693727i	$0.244032\pi$
$360$	11.3383	0.597581
$361$	−15.0874	−0.794076
$362$	17.7061	0.930610
$363$	−1.68890	−0.0886443
$364$	0	0
$365$	5.94798	0.311332
$366$	11.4128	0.596558
$367$	−9.98326	−0.521122	−0.260561	−	0.965457i	$-0.583907\pi$
$367$	−9.98326	−0.521122	−0.260561	+	0.965457i	$0.583907\pi$
$368$	−2.35802	−0.122921
$369$	−13.4758	−0.701521
$370$	−1.58395	−0.0823455
$371$	0	0
$372$	18.8864	0.979214
$373$	4.68608	0.242636	0.121318	−	0.992614i	$-0.461288\pi$
$373$	4.68608	0.242636	0.121318	+	0.992614i	$0.461288\pi$
$374$	−64.6971	−3.34541
$375$	5.57227	0.287751
$376$	−59.0653	−3.04606
$377$	−3.64900	−0.187933
$378$	0	0
$379$	−2.45019	−0.125858	−0.0629288	−	0.998018i	$-0.520044\pi$
$379$	−2.45019	−0.125858	−0.0629288	+	0.998018i	$0.520044\pi$
$380$	−7.18777	−0.368725
$381$	−4.41205	−0.226036
$382$	−4.82818	−0.247031
$383$	−10.7671	−0.550175	−0.275087	−	0.961419i	$-0.588707\pi$
$383$	−10.7671	−0.550175	−0.275087	+	0.961419i	$0.588707\pi$
$384$	−13.1225	−0.669656
$385$	0	0
$386$	61.7035	3.14063
$387$	−28.3015	−1.43864
$388$	36.2893	1.84231
$389$	14.0372	0.711714	0.355857	−	0.934540i	$-0.384189\pi$
$389$	14.0372	0.711714	0.355857	+	0.934540i	$0.384189\pi$
$390$	1.48724	0.0753095
$391$	−4.28748	−0.216827
$392$	0	0
$393$	13.3267	0.672241
$394$	7.45363	0.375508
$395$	−10.4869	−0.527652
$396$	−37.5100	−1.88495
$397$	26.4605	1.32801	0.664007	−	0.747726i	$-0.268854\pi$
$397$	26.4605	1.32801	0.664007	+	0.747726i	$0.268854\pi$
$398$	−9.93070	−0.497781
$399$	0	0
$400$	−16.4843	−0.824217
$401$	−19.0156	−0.949593	−0.474796	−	0.880096i	$-0.657478\pi$
$401$	−19.0156	−0.949593	−0.474796	+	0.880096i	$0.657478\pi$
$402$	2.00697	0.100099
$403$	−7.08833	−0.353095
$404$	−23.1791	−1.15320
$405$	4.72351	0.234713
$406$	0	0
$407$	2.61477	0.129609
$408$	23.3845	1.15771
$409$	12.7759	0.631728	0.315864	−	0.948804i	$-0.397706\pi$
$409$	12.7759	0.631728	0.315864	+	0.948804i	$0.397706\pi$
$410$	−11.7546	−0.580520
$411$	−3.84086	−0.189456
$412$	51.3693	2.53078
$413$	0	0
$414$	−3.73119	−0.183378
$415$	6.52132	0.320119
$416$	0.0786478	0.00385603
$417$	1.03547	0.0507072
$418$	17.8102	0.871127
$419$	12.9811	0.634170	0.317085	−	0.948397i	$-0.397296\pi$
$419$	12.9811	0.634170	0.317085	+	0.948397i	$0.397296\pi$
$420$	0	0
$421$	−11.6737	−0.568943	−0.284472	−	0.958684i	$-0.591818\pi$
$421$	−11.6737	−0.568943	−0.284472	+	0.958684i	$0.591818\pi$
$422$	−40.1731	−1.95559
$423$	−30.9440	−1.50455
$424$	55.8225	2.71098
$425$	−29.9726	−1.45389
$426$	18.5658	0.899517
$427$	0	0
$428$	17.7940	0.860107
$429$	−2.45513	−0.118535
$430$	−24.6868	−1.19050
$431$	−0.467684	−0.0225275	−0.0112638	−	0.999937i	$-0.503585\pi$
$431$	−0.467684	−0.0225275	−0.0112638	+	0.999937i	$0.503585\pi$
$432$	14.6507	0.704881
$433$	−9.27593	−0.445773	−0.222886	−	0.974844i	$-0.571548\pi$
$433$	−9.27593	−0.445773	−0.222886	+	0.974844i	$0.571548\pi$
$434$	0	0
$435$	2.21703	0.106298
$436$	3.50851	0.168027
$437$	1.18029	0.0564607
$438$	10.6757	0.510104
$439$	−35.7077	−1.70424	−0.852119	−	0.523348i	$-0.824683\pi$
$439$	−35.7077	−1.70424	−0.852119	+	0.523348i	$0.824683\pi$
$440$	−16.3266	−0.778340
$441$	0	0
$442$	−17.5885	−0.836601
$443$	−36.3458	−1.72684	−0.863421	−	0.504484i	$-0.831683\pi$
$443$	−36.3458	−1.72684	−0.863421	+	0.504484i	$0.831683\pi$
$444$	−1.89402	−0.0898860
$445$	11.6963	0.554457
$446$	39.4605	1.86851
$447$	−9.96750	−0.471447
$448$	0	0
$449$	−40.4910	−1.91089	−0.955444	−	0.295171i	$-0.904623\pi$
$449$	−40.4910	−1.91089	−0.955444	+	0.295171i	$0.904623\pi$
$450$	−26.0838	−1.22960
$451$	19.4045	0.913720
$452$	−21.4257	−1.00778
$453$	5.27355	0.247773
$454$	21.2425	0.996960
$455$	0	0
$456$	−6.43744	−0.301461
$457$	5.01988	0.234820	0.117410	−	0.993084i	$-0.462541\pi$
$457$	5.01988	0.234820	0.117410	+	0.993084i	$0.462541\pi$
$458$	50.8153	2.37444
$459$	26.6386	1.24338
$460$	−2.16830	−0.101098
$461$	−17.3627	−0.808661	−0.404331	−	0.914613i	$-0.632495\pi$
$461$	−17.3627	−0.808661	−0.404331	+	0.914613i	$0.632495\pi$
$462$	0	0
$463$	35.4306	1.64660	0.823301	−	0.567606i	$-0.192130\pi$
$463$	35.4306	1.64660	0.823301	+	0.567606i	$0.192130\pi$
$464$	−14.4200	−0.669433
$465$	4.30667	0.199717
$466$	24.0983	1.11633
$467$	35.4958	1.64255	0.821275	−	0.570533i	$-0.193263\pi$
$467$	35.4958	1.64255	0.821275	+	0.570533i	$0.193263\pi$
$468$	−10.1975	−0.471378
$469$	0	0
$470$	−26.9918	−1.24504
$471$	−8.33967	−0.384272
$472$	−46.7601	−2.15231
$473$	40.7527	1.87381
$474$	−18.8223	−0.864536
$475$	8.25107	0.378585
$476$	0	0
$477$	29.2451	1.33904
$478$	−2.77926	−0.127121
$479$	−24.0270	−1.09782	−0.548911	−	0.835881i	$-0.684958\pi$
$479$	−24.0270	−1.09782	−0.548911	+	0.835881i	$0.684958\pi$
$480$	−0.0477842	−0.00218104
$481$	0.710851	0.0324120
$482$	53.4140	2.43294
$483$	0	0
$484$	10.1011	0.459142
$485$	8.27506	0.375751
$486$	35.7031	1.61953
$487$	20.8076	0.942880	0.471440	−	0.881898i	$-0.343734\pi$
$487$	20.8076	0.942880	0.471440	+	0.881898i	$0.343734\pi$
$488$	−34.0606	−1.54185
$489$	−4.68169	−0.211713
$490$	0	0
$491$	−36.2195	−1.63456	−0.817281	−	0.576240i	$-0.804519\pi$
$491$	−36.2195	−1.63456	−0.817281	+	0.576240i	$0.804519\pi$
$492$	−14.0557	−0.633679
$493$	−26.2192	−1.18085
$494$	4.84189	0.217847
$495$	−8.55343	−0.384448
$496$	−28.0115	−1.25775
$497$	0	0
$498$	11.7047	0.524502
$499$	−40.1828	−1.79883	−0.899416	−	0.437094i	$-0.856008\pi$
$499$	−40.1828	−1.79883	−0.899416	+	0.437094i	$0.856008\pi$
$500$	−33.3271	−1.49043
$501$	−3.22222	−0.143958
$502$	−23.1169	−1.03176
$503$	38.5636	1.71946	0.859732	−	0.510745i	$-0.170630\pi$
$503$	38.5636	1.71946	0.859732	+	0.510745i	$0.170630\pi$
$504$	0	0
$505$	−5.28553	−0.235203
$506$	5.37273	0.238847
$507$	−0.667452	−0.0296426
$508$	26.3879	1.17078
$509$	4.33977	0.192357	0.0961785	−	0.995364i	$-0.469338\pi$
$509$	4.33977	0.192357	0.0961785	+	0.995364i	$0.469338\pi$
$510$	10.6863	0.473197
$511$	0	0
$512$	38.8484	1.71687
$513$	−7.33324	−0.323771
$514$	8.87962	0.391663
$515$	11.7138	0.516170
$516$	−29.5193	−1.29952
$517$	44.5578	1.95965
$518$	0	0
$519$	14.8257	0.650776
$520$	−4.43855	−0.194643
$521$	13.7844	0.603905	0.301952	−	0.953323i	$-0.402362\pi$
$521$	13.7844	0.603905	0.301952	+	0.953323i	$0.402362\pi$
$522$	−22.8174	−0.998689
$523$	−29.4834	−1.28922	−0.644609	−	0.764512i	$-0.722980\pi$
$523$	−29.4834	−1.28922	−0.644609	+	0.764512i	$0.722980\pi$
$524$	−79.7052	−3.48194
$525$	0	0
$526$	−16.1456	−0.703982
$527$	−50.9318	−2.21863
$528$	−9.70212	−0.422231
$529$	−22.6439	−0.984520
$530$	25.5099	1.10808
$531$	−24.4974	−1.06310
$532$	0	0
$533$	5.27529	0.228498
$534$	20.9930	0.908455
$535$	4.05758	0.175424
$536$	−5.98963	−0.258713
$537$	−3.05363	−0.131774
$538$	−57.6011	−2.48336
$539$	0	0
$540$	13.4719	0.579738
$541$	23.2519	0.999679	0.499840	−	0.866118i	$-0.333392\pi$
$541$	23.2519	0.999679	0.499840	+	0.866118i	$0.333392\pi$
$542$	−6.60348	−0.283644
$543$	4.82789	0.207185
$544$	0.565109	0.0242288
$545$	0.800047	0.0342703
$546$	0	0
$547$	1.18365	0.0506093	0.0253046	−	0.999680i	$-0.491944\pi$
$547$	1.18365	0.0506093	0.0253046	+	0.999680i	$0.491944\pi$
$548$	22.9717	0.981304
$549$	−17.8442	−0.761571
$550$	37.5594	1.60154
$551$	7.21780	0.307488
$552$	−1.94195	−0.0826550
$553$	0	0
$554$	60.5962	2.57449
$555$	−0.431893	−0.0183328
$556$	−6.19303	−0.262643
$557$	−6.42824	−0.272373	−0.136187	−	0.990683i	$-0.543485\pi$
$557$	−6.42824	−0.272373	−0.136187	+	0.990683i	$0.543485\pi$
$558$	−44.3236	−1.87637
$559$	11.0790	0.468593
$560$	0	0
$561$	−17.6409	−0.744798
$562$	9.92300	0.418577
$563$	11.4563	0.482824	0.241412	−	0.970423i	$-0.422390\pi$
$563$	11.4563	0.482824	0.241412	+	0.970423i	$0.422390\pi$
$564$	−32.2756	−1.35905
$565$	−4.88571	−0.205543
$566$	−31.6353	−1.32973
$567$	0	0
$568$	−55.4081	−2.32487
$569$	38.3335	1.60702	0.803512	−	0.595288i	$-0.202962\pi$
$569$	38.3335	1.60702	0.803512	+	0.595288i	$0.202962\pi$
$570$	−2.94180	−0.123218
$571$	6.25857	0.261913	0.130956	−	0.991388i	$-0.458195\pi$
$571$	6.25857	0.261913	0.130956	+	0.991388i	$0.458195\pi$
$572$	14.6839	0.613963
$573$	−1.31649	−0.0549973
$574$	0	0
$575$	2.48906	0.103801
$576$	20.6815	0.861728
$577$	0.0451932	0.00188142	0.000940708	−	1.00000i	$-0.499701\pi$
$577$	0.0451932	0.00188142	0.000940708		1.00000i	$0.499701\pi$
$578$	−84.7657	−3.52579
$579$	16.8246	0.699208
$580$	−13.2598	−0.550583
$581$	0	0
$582$	14.8524	0.615653
$583$	−42.1115	−1.74408
$584$	−31.8606	−1.31840
$585$	−2.32533	−0.0961407
$586$	57.6597	2.38190
$587$	2.71409	0.112023	0.0560113	−	0.998430i	$-0.482162\pi$
$587$	2.71409	0.112023	0.0560113	+	0.998430i	$0.482162\pi$
$588$	0	0
$589$	14.0209	0.577719
$590$	−21.3685	−0.879728
$591$	2.03237	0.0836006
$592$	2.80912	0.115454
$593$	6.78615	0.278674	0.139337	−	0.990245i	$-0.455503\pi$
$593$	6.78615	0.278674	0.139337	+	0.990245i	$0.455503\pi$
$594$	−33.3814	−1.36965
$595$	0	0
$596$	59.6145	2.44190
$597$	−2.70779	−0.110823
$598$	1.46063	0.0597296
$599$	−26.8337	−1.09640	−0.548198	−	0.836348i	$-0.684686\pi$
$599$	−26.8337	−1.09640	−0.548198	+	0.836348i	$0.684686\pi$
$600$	−13.5757	−0.554226
$601$	12.3356	0.503178	0.251589	−	0.967834i	$-0.419047\pi$
$601$	12.3356	0.503178	0.251589	+	0.967834i	$0.419047\pi$
$602$	0	0
$603$	−3.13794	−0.127787
$604$	−31.5405	−1.28336
$605$	2.30336	0.0936450
$606$	−9.48668	−0.385370
$607$	−17.4596	−0.708665	−0.354332	−	0.935120i	$-0.615292\pi$
$607$	−17.4596	−0.708665	−0.354332	+	0.935120i	$0.615292\pi$
$608$	−0.155567	−0.00630907
$609$	0	0
$610$	−15.5651	−0.630211
$611$	12.1135	0.490059
$612$	−73.2720	−2.96185
$613$	1.05026	0.0424198	0.0212099	−	0.999775i	$-0.493248\pi$
$613$	1.05026	0.0424198	0.0212099	+	0.999775i	$0.493248\pi$
$614$	−48.8471	−1.97131
$615$	−3.20512	−0.129243
$616$	0	0
$617$	10.5872	0.426223	0.213111	−	0.977028i	$-0.431640\pi$
$617$	10.5872	0.426223	0.213111	+	0.977028i	$0.431640\pi$
$618$	21.0243	0.845723
$619$	1.23805	0.0497616	0.0248808	−	0.999690i	$-0.492079\pi$
$619$	1.23805	0.0497616	0.0248808	+	0.999690i	$0.492079\pi$
$620$	−25.7577	−1.03445
$621$	−2.21219	−0.0887720
$622$	−15.8637	−0.636078
$623$	0	0
$624$	−2.63762	−0.105589
$625$	13.2573	0.530292
$626$	−39.4481	−1.57666
$627$	4.85630	0.193942
$628$	49.8786	1.99037
$629$	5.10769	0.203657
$630$	0	0
$631$	−21.2658	−0.846577	−0.423289	−	0.905995i	$-0.639124\pi$
$631$	−21.2658	−0.846577	−0.423289	+	0.905995i	$0.639124\pi$
$632$	56.1735	2.23446
$633$	−10.9539	−0.435380
$634$	−35.5681	−1.41259
$635$	6.01725	0.238787
$636$	30.5036	1.20955
$637$	0	0
$638$	32.8559	1.30078
$639$	−29.0280	−1.14833
$640$	17.8968	0.707433
$641$	11.0506	0.436474	0.218237	−	0.975896i	$-0.429969\pi$
$641$	11.0506	0.436474	0.218237	+	0.975896i	$0.429969\pi$
$642$	7.28271	0.287425
$643$	6.50321	0.256461	0.128231	−	0.991744i	$-0.459070\pi$
$643$	6.50321	0.256461	0.128231	+	0.991744i	$0.459070\pi$
$644$	0	0
$645$	−6.73131	−0.265045
$646$	34.7905	1.36881
$647$	−0.893941	−0.0351444	−0.0175722	−	0.999846i	$-0.505594\pi$
$647$	−0.893941	−0.0351444	−0.0175722	+	0.999846i	$0.505594\pi$
$648$	−25.3017	−0.993945
$649$	35.2750	1.38467
$650$	10.2109	0.400504
$651$	0	0
$652$	28.0006	1.09659
$653$	−38.5477	−1.50849	−0.754244	−	0.656594i	$-0.771997\pi$
$653$	−38.5477	−1.50849	−0.754244	+	0.656594i	$0.771997\pi$
$654$	1.43596	0.0561504
$655$	−18.1752	−0.710164
$656$	20.8468	0.813930
$657$	−16.6916	−0.651203
$658$	0	0
$659$	−10.8013	−0.420759	−0.210380	−	0.977620i	$-0.567470\pi$
$659$	−10.8013	−0.420759	−0.210380	+	0.977620i	$0.567470\pi$
$660$	−8.92150	−0.347269
$661$	40.6339	1.58047	0.790237	−	0.612801i	$-0.209957\pi$
$661$	40.6339	1.58047	0.790237	+	0.612801i	$0.209957\pi$
$662$	−51.6361	−2.00690
$663$	−4.79585	−0.186255
$664$	−34.9318	−1.35562
$665$	0	0
$666$	4.44498	0.172240
$667$	2.17736	0.0843077
$668$	19.2717	0.745645
$669$	10.7597	0.415992
$670$	−2.73716	−0.105746
$671$	25.6947	0.991934
$672$	0	0
$673$	32.3136	1.24560	0.622799	−	0.782382i	$-0.285995\pi$
$673$	32.3136	1.24560	0.622799	+	0.782382i	$0.285995\pi$
$674$	80.4589	3.09916
$675$	−15.4648	−0.595241
$676$	3.99195	0.153537
$677$	−25.2158	−0.969123	−0.484562	−	0.874757i	$-0.661021\pi$
$677$	−25.2158	−0.969123	−0.484562	+	0.874757i	$0.661021\pi$
$678$	−8.76908	−0.336774
$679$	0	0
$680$	−31.8923	−1.22302
$681$	5.79217	0.221956
$682$	63.8238	2.44394
$683$	−6.28731	−0.240577	−0.120289	−	0.992739i	$-0.538382\pi$
$683$	−6.28731	−0.240577	−0.120289	+	0.992739i	$0.538382\pi$
$684$	20.1708	0.771250
$685$	5.23826	0.200143
$686$	0	0
$687$	13.8557	0.528629
$688$	43.7818	1.66917
$689$	−11.4484	−0.436151
$690$	−0.887438	−0.0337842
$691$	17.1531	0.652533	0.326267	−	0.945278i	$-0.394209\pi$
$691$	17.1531	0.652533	0.326267	+	0.945278i	$0.394209\pi$
$692$	−88.6707	−3.37076
$693$	0	0
$694$	−38.9600	−1.47890
$695$	−1.41220	−0.0535678
$696$	−11.8756	−0.450144
$697$	37.9046	1.43574
$698$	72.5162	2.74478
$699$	6.57085	0.248532
$700$	0	0
$701$	−23.6620	−0.893702	−0.446851	−	0.894609i	$-0.647455\pi$
$701$	−23.6620	−0.893702	−0.446851	+	0.894609i	$0.647455\pi$
$702$	−9.07506	−0.342516
$703$	−1.40608	−0.0530312
$704$	−29.7803	−1.12239
$705$	−7.35982	−0.277187
$706$	70.2722	2.64473
$707$	0	0
$708$	−25.5516	−0.960286
$709$	−21.5030	−0.807563	−0.403782	−	0.914855i	$-0.632304\pi$
$709$	−21.5030	−0.807563	−0.403782	+	0.914855i	$0.632304\pi$
$710$	−25.3205	−0.950262
$711$	29.4290	1.10367
$712$	−62.6517	−2.34797
$713$	4.22961	0.158400
$714$	0	0
$715$	3.34837	0.125222
$716$	18.2634	0.682535
$717$	−0.757819	−0.0283013
$718$	−66.8094	−2.49330
$719$	−12.8693	−0.479943	−0.239971	−	0.970780i	$-0.577138\pi$
$719$	−12.8693	−0.479943	−0.239971	+	0.970780i	$0.577138\pi$
$720$	−9.18919	−0.342461
$721$	0	0
$722$	36.9317	1.37446
$723$	14.5643	0.541654
$724$	−28.8751	−1.07313
$725$	15.2214	0.565307
$726$	4.13417	0.153433
$727$	−16.4329	−0.609463	−0.304732	−	0.952438i	$-0.598567\pi$
$727$	−16.4329	−0.609463	−0.304732	+	0.952438i	$0.598567\pi$
$728$	0	0
$729$	−5.83198	−0.215999
$730$	−14.5597	−0.538880
$731$	79.6063	2.94434
$732$	−18.6120	−0.687921
$733$	21.7222	0.802328	0.401164	−	0.916006i	$-0.368606\pi$
$733$	21.7222	0.802328	0.401164	+	0.916006i	$0.368606\pi$
$734$	24.4375	0.902004
$735$	0	0
$736$	−0.0469292	−0.00172983
$737$	4.51848	0.166440
$738$	32.9866	1.21426
$739$	1.58001	0.0581218	0.0290609	−	0.999578i	$-0.490748\pi$
$739$	1.58001	0.0581218	0.0290609	+	0.999578i	$0.490748\pi$
$740$	2.58310	0.0949568
$741$	1.32023	0.0485000
$742$	0	0
$743$	45.9718	1.68654	0.843271	−	0.537489i	$-0.180627\pi$
$743$	45.9718	1.68654	0.843271	+	0.537489i	$0.180627\pi$
$744$	−23.0689	−0.845746
$745$	13.5939	0.498043
$746$	−11.4708	−0.419976
$747$	−18.3006	−0.669583
$748$	105.508	3.85776
$749$	0	0
$750$	−13.6401	−0.498065
$751$	−6.42286	−0.234373	−0.117187	−	0.993110i	$-0.537388\pi$
$751$	−6.42286	−0.234373	−0.117187	+	0.993110i	$0.537388\pi$
$752$	47.8698	1.74563
$753$	−6.30326	−0.229704
$754$	8.93219	0.325291
$755$	−7.19219	−0.261750
$756$	0	0
$757$	−6.10016	−0.221714	−0.110857	−	0.993836i	$-0.535360\pi$
$757$	−6.10016	−0.221714	−0.110857	+	0.993836i	$0.535360\pi$
$758$	5.99768	0.217846
$759$	1.46498	0.0531753
$760$	8.77954	0.318467
$761$	18.3948	0.666812	0.333406	−	0.942783i	$-0.391802\pi$
$761$	18.3948	0.666812	0.333406	+	0.942783i	$0.391802\pi$
$762$	10.8000	0.391243
$763$	0	0
$764$	7.87380	0.284864
$765$	−16.7082	−0.604088
$766$	26.3563	0.952291
$767$	9.58986	0.346270
$768$	21.3144	0.769119
$769$	−24.1850	−0.872133	−0.436066	−	0.899914i	$-0.643629\pi$
$769$	−24.1850	−0.872133	−0.436066	+	0.899914i	$0.643629\pi$
$770$	0	0
$771$	2.42120	0.0871973
$772$	−100.626	−3.62162
$773$	−10.7601	−0.387014	−0.193507	−	0.981099i	$-0.561986\pi$
$773$	−10.7601	−0.387014	−0.193507	+	0.981099i	$0.561986\pi$
$774$	69.2777	2.49013
$775$	29.5681	1.06212
$776$	−44.3258	−1.59120
$777$	0	0
$778$	−34.3609	−1.23190
$779$	−10.4346	−0.373860
$780$	−2.42540	−0.0868432
$781$	41.7989	1.49568
$782$	10.4951	0.375303
$783$	−13.5282	−0.483458
$784$	0	0
$785$	11.3738	0.405950
$786$	−32.6216	−1.16357
$787$	−14.7348	−0.525238	−0.262619	−	0.964900i	$-0.584586\pi$
$787$	−14.7348	−0.525238	−0.262619	+	0.964900i	$0.584586\pi$
$788$	−12.1554	−0.433018
$789$	−4.40240	−0.156730
$790$	25.6703	0.913307
$791$	0	0
$792$	45.8168	1.62803
$793$	6.98536	0.248058
$794$	−64.7713	−2.29865
$795$	6.95575	0.246695
$796$	16.1950	0.574017
$797$	32.5732	1.15380	0.576901	−	0.816814i	$-0.304262\pi$
$797$	32.5732	1.15380	0.576901	+	0.816814i	$0.304262\pi$
$798$	0	0
$799$	87.0392	3.07922
$800$	−0.328070	−0.0115990
$801$	−32.8229	−1.15974
$802$	46.5472	1.64364
$803$	24.0351	0.848181
$804$	−3.27297	−0.115429
$805$	0	0
$806$	17.3511	0.611168
$807$	−15.7060	−0.552878
$808$	28.3122	0.996019
$809$	−23.6926	−0.832987	−0.416493	−	0.909139i	$-0.636741\pi$
$809$	−23.6926	−0.832987	−0.416493	+	0.909139i	$0.636741\pi$
$810$	−11.5624	−0.406262
$811$	45.8568	1.61025	0.805125	−	0.593105i	$-0.202098\pi$
$811$	45.8568	1.61025	0.805125	+	0.593105i	$0.202098\pi$
$812$	0	0
$813$	−1.80056	−0.0631485
$814$	−6.40056	−0.224339
$815$	6.38500	0.223657
$816$	−18.9521	−0.663456
$817$	−21.9145	−0.766693
$818$	−31.2735	−1.09345
$819$	0	0
$820$	19.1695	0.669427
$821$	13.2923	0.463905	0.231953	−	0.972727i	$-0.425489\pi$
$821$	13.2923	0.463905	0.231953	+	0.972727i	$0.425489\pi$
$822$	9.40183	0.327927
$823$	−4.13033	−0.143974	−0.0719871	−	0.997406i	$-0.522934\pi$
$823$	−4.13033	−0.143974	−0.0719871	+	0.997406i	$0.522934\pi$
$824$	−62.7453	−2.18584
$825$	10.2413	0.356556
$826$	0	0
$827$	−4.67317	−0.162502	−0.0812510	−	0.996694i	$-0.525892\pi$
$827$	−4.67317	−0.162502	−0.0812510	+	0.996694i	$0.525892\pi$
$828$	6.08484	0.211463
$829$	1.74971	0.0607700	0.0303850	−	0.999538i	$-0.490327\pi$
$829$	1.74971	0.0607700	0.0303850	+	0.999538i	$0.490327\pi$
$830$	−15.9632	−0.554091
$831$	16.5227	0.573167
$832$	−8.09606	−0.280681
$833$	0	0
$834$	−2.53467	−0.0877685
$835$	4.39454	0.152079
$836$	−29.0450	−1.00454
$837$	−26.2790	−0.908336
$838$	−31.7758	−1.09768
$839$	−15.4495	−0.533374	−0.266687	−	0.963783i	$-0.585929\pi$
$839$	−15.4495	−0.533374	−0.266687	+	0.963783i	$0.585929\pi$
$840$	0	0
$841$	−15.6848	−0.540855
$842$	28.5755	0.984777
$843$	2.70569	0.0931891
$844$	65.5143	2.25510
$845$	0.910286	0.0313148
$846$	75.7462	2.60421
$847$	0	0
$848$	−45.2416	−1.55360
$849$	−8.62595	−0.296042
$850$	73.3684	2.51652
$851$	−0.424165	−0.0145402
$852$	−30.2772	−1.03728
$853$	−0.602575	−0.0206318	−0.0103159	−	0.999947i	$-0.503284\pi$
$853$	−0.602575	−0.0206318	−0.0103159	+	0.999947i	$0.503284\pi$
$854$	0	0
$855$	4.59956	0.157302
$856$	−21.7346	−0.742874
$857$	−43.1639	−1.47445	−0.737226	−	0.675647i	$-0.763865\pi$
$857$	−43.1639	−1.47445	−0.737226	+	0.675647i	$0.763865\pi$
$858$	6.00978	0.205171
$859$	37.9408	1.29452	0.647261	−	0.762269i	$-0.275914\pi$
$859$	37.9408	1.29452	0.647261	+	0.762269i	$0.275914\pi$
$860$	40.2592	1.37283
$861$	0	0
$862$	1.14482	0.0389927
$863$	33.9067	1.15420	0.577098	−	0.816675i	$-0.304185\pi$
$863$	33.9067	1.15420	0.577098	+	0.816675i	$0.304185\pi$
$864$	0.291576	0.00991962
$865$	−20.2196	−0.687488
$866$	22.7061	0.771583
$867$	−23.1130	−0.784957
$868$	0	0
$869$	−42.3763	−1.43752
$870$	−5.42695	−0.183991
$871$	1.22839	0.0416225
$872$	−4.28549	−0.145125
$873$	−23.2221	−0.785948
$874$	−2.88916	−0.0977272
$875$	0	0
$876$	−17.4099	−0.588226
$877$	6.51036	0.219839	0.109920	−	0.993940i	$-0.464941\pi$
$877$	6.51036	0.219839	0.109920	+	0.993940i	$0.464941\pi$
$878$	87.4071	2.94985
$879$	15.7220	0.530290
$880$	13.2320	0.446050
$881$	−24.5160	−0.825966	−0.412983	−	0.910739i	$-0.635513\pi$
$881$	−24.5160	−0.825966	−0.412983	+	0.910739i	$0.635513\pi$
$882$	0	0
$883$	−28.7175	−0.966419	−0.483210	−	0.875505i	$-0.660529\pi$
$883$	−28.7175	−0.966419	−0.483210	+	0.875505i	$0.660529\pi$
$884$	28.6834	0.964727
$885$	−5.82653	−0.195857
$886$	88.9690	2.98897
$887$	6.94442	0.233171	0.116585	−	0.993181i	$-0.462805\pi$
$887$	6.94442	0.233171	0.116585	+	0.993181i	$0.462805\pi$
$888$	2.31346	0.0776345
$889$	0	0
$890$	−28.6307	−0.959704
$891$	19.0872	0.639445
$892$	−64.3523	−2.15467
$893$	−23.9607	−0.801815
$894$	24.3989	0.816022
$895$	4.16461	0.139208
$896$	0	0
$897$	0.398269	0.0132978
$898$	99.1158	3.30754
$899$	25.8653	0.862656
$900$	42.5375	1.41792
$901$	−82.2605	−2.74050
$902$	−47.4991	−1.58155
$903$	0	0
$904$	26.1705	0.870419
$905$	−6.58439	−0.218873
$906$	−12.9088	−0.428867
$907$	0.229549	0.00762204	0.00381102	−	0.999993i	$-0.498787\pi$
$907$	0.229549	0.00762204	0.00381102	+	0.999993i	$0.498787\pi$
$908$	−34.6423	−1.14965
$909$	14.8326	0.491967
$910$	0	0
$911$	−26.6727	−0.883706	−0.441853	−	0.897087i	$-0.645679\pi$
$911$	−26.6727	−0.883706	−0.441853	+	0.897087i	$0.645679\pi$
$912$	5.21726	0.172761
$913$	26.3519	0.872122
$914$	−12.2879	−0.406447
$915$	−4.24411	−0.140306
$916$	−82.8696	−2.73809
$917$	0	0
$918$	−65.2071	−2.15216
$919$	−43.2331	−1.42613	−0.713064	−	0.701099i	$-0.752693\pi$
$919$	−43.2331	−1.42613	−0.713064	+	0.701099i	$0.752693\pi$
$920$	2.64848	0.0873179
$921$	−13.3191	−0.438879
$922$	42.5012	1.39970
$923$	11.3635	0.374033
$924$	0	0
$925$	−2.96523	−0.0974961
$926$	−86.7287	−2.85008
$927$	−32.8720	−1.07966
$928$	−0.286986	−0.00942077
$929$	−23.8491	−0.782465	−0.391233	−	0.920292i	$-0.627951\pi$
$929$	−23.8491	−0.782465	−0.391233	+	0.920292i	$0.627951\pi$
$930$	−10.5421	−0.345688
$931$	0	0
$932$	−39.2995	−1.28730
$933$	−4.32555	−0.141612
$934$	−86.8883	−2.84307
$935$	24.0590	0.786815
$936$	12.4558	0.407129
$937$	−27.2033	−0.888694	−0.444347	−	0.895855i	$-0.646564\pi$
$937$	−27.2033	−0.888694	−0.444347	+	0.895855i	$0.646564\pi$
$938$	0	0
$939$	−10.7563	−0.351017
$940$	44.0182	1.43572
$941$	13.4515	0.438505	0.219253	−	0.975668i	$-0.429638\pi$
$941$	13.4515	0.438505	0.219253	+	0.975668i	$0.429638\pi$
$942$	20.4142	0.665132
$943$	−3.14777	−0.102505
$944$	37.8970	1.23344
$945$	0	0
$946$	−99.7564	−3.24336
$947$	15.0341	0.488543	0.244271	−	0.969707i	$-0.421451\pi$
$947$	15.0341	0.488543	0.244271	+	0.969707i	$0.421451\pi$
$948$	30.6954	0.996940
$949$	6.53419	0.212109
$950$	−20.1974	−0.655289
$951$	−9.69830	−0.314489
$952$	0	0
$953$	28.3775	0.919237	0.459618	−	0.888116i	$-0.347986\pi$
$953$	28.3775	0.919237	0.459618	+	0.888116i	$0.347986\pi$
$954$	−71.5876	−2.31773
$955$	1.79546	0.0580999
$956$	4.53243	0.146589
$957$	8.95877	0.289596
$958$	58.8144	1.90021
$959$	0	0
$960$	4.91894	0.158758
$961$	19.2444	0.620787
$962$	−1.74005	−0.0561016
$963$	−11.3867	−0.366930
$964$	−87.1077	−2.80555
$965$	−22.9458	−0.738653
$966$	0	0
$967$	−52.0994	−1.67540	−0.837701	−	0.546129i	$-0.816101\pi$
$967$	−52.0994	−1.67540	−0.837701	+	0.546129i	$0.816101\pi$
$968$	−12.3381	−0.396561
$969$	9.48628	0.304743
$970$	−20.2561	−0.650384
$971$	−20.8418	−0.668845	−0.334423	−	0.942423i	$-0.608541\pi$
$971$	−20.8418	−0.668845	−0.334423	+	0.942423i	$0.608541\pi$
$972$	−58.2247	−1.86756
$973$	0	0
$974$	−50.9337	−1.63202
$975$	2.78419	0.0891655
$976$	27.6046	0.883601
$977$	34.6302	1.10792	0.553960	−	0.832544i	$-0.313116\pi$
$977$	34.6302	1.10792	0.553960	+	0.832544i	$0.313116\pi$
$978$	11.4600	0.366452
$979$	47.2634	1.51054
$980$	0	0
$981$	−2.24515	−0.0716820
$982$	88.6597	2.82924
$983$	−58.8628	−1.87743	−0.938717	−	0.344690i	$-0.887984\pi$
$983$	−58.8628	−1.87743	−0.938717	+	0.344690i	$0.887984\pi$
$984$	17.1684	0.547308
$985$	−2.77180	−0.0883168
$986$	64.1806	2.04393
$987$	0	0
$988$	−7.89616	−0.251210
$989$	−6.61086	−0.210213
$990$	20.9375	0.665437
$991$	−29.3747	−0.933118	−0.466559	−	0.884490i	$-0.654507\pi$
$991$	−29.3747	−0.933118	−0.466559	+	0.884490i	$0.654507\pi$
$992$	−0.557482	−0.0177001
$993$	−14.0796	−0.446802
$994$	0	0
$995$	3.69295	0.117075
$996$	−19.0881	−0.604830
$997$	−7.50606	−0.237719	−0.118860	−	0.992911i	$-0.537924\pi$
$997$	−7.50606	−0.237719	−0.118860	+	0.992911i	$0.537924\pi$
$998$	98.3614	3.11358
$999$	2.63539	0.0833799

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.a.n.1.1	yes	6
3.2	odd	2		5733.2.a.br.1.6		6
7.2	even	3		637.2.e.n.508.6		12
7.3	odd	6		637.2.e.o.79.6		12
7.4	even	3		637.2.e.n.79.6		12
7.5	odd	6		637.2.e.o.508.6		12
7.6	odd	2		637.2.a.m.1.1	✓	6
13.12	even	2		8281.2.a.cd.1.6		6
21.20	even	2		5733.2.a.bu.1.6		6
91.90	odd	2		8281.2.a.cc.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.a.m.1.1	✓	6	7.6	odd	2
637.2.a.n.1.1	yes	6	1.1	even	1	trivial
637.2.e.n.79.6		12	7.4	even	3
637.2.e.n.508.6		12	7.2	even	3
637.2.e.o.79.6		12	7.3	odd	6
637.2.e.o.508.6		12	7.5	odd	6
5733.2.a.br.1.6		6	3.2	odd	2
5733.2.a.bu.1.6		6	21.20	even	2
8281.2.a.cc.1.6		6	91.90	odd	2
8281.2.a.cd.1.6		6	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.a (trivial)

\(f(q)\)	\(=\)	\(q-2.44785 q^{2} -0.667452 q^{3} +3.99195 q^{4} +0.910286 q^{5} +1.63382 q^{6} -4.87599 q^{8} -2.55451 q^{9} +O(q^{10})\)	\(q-2.44785 q^{2} -0.667452 q^{3} +3.99195 q^{4} +0.910286 q^{5} +1.63382 q^{6} -4.87599 q^{8} -2.55451 q^{9} -2.22824 q^{10} +3.67837 q^{11} -2.66443 q^{12} +1.00000 q^{13} -0.607572 q^{15} +3.95177 q^{16} +7.18531 q^{17} +6.25304 q^{18} -1.97802 q^{19} +3.63382 q^{20} -9.00407 q^{22} -0.596700 q^{23} +3.25449 q^{24} -4.17138 q^{25} -2.44785 q^{26} +3.70737 q^{27} -3.64900 q^{29} +1.48724 q^{30} -7.08833 q^{31} +0.0786478 q^{32} -2.45513 q^{33} -17.5885 q^{34} -10.1975 q^{36} +0.710851 q^{37} +4.84189 q^{38} -0.667452 q^{39} -4.43855 q^{40} +5.27529 q^{41} +11.0790 q^{43} +14.6839 q^{44} -2.32533 q^{45} +1.46063 q^{46} +12.1135 q^{47} -2.63762 q^{48} +10.2109 q^{50} -4.79585 q^{51} +3.99195 q^{52} -11.4484 q^{53} -9.07506 q^{54} +3.34837 q^{55} +1.32023 q^{57} +8.93219 q^{58} +9.58986 q^{59} -2.42540 q^{60} +6.98536 q^{61} +17.3511 q^{62} -8.09606 q^{64} +0.910286 q^{65} +6.00978 q^{66} +1.22839 q^{67} +28.6834 q^{68} +0.398269 q^{69} +11.3635 q^{71} +12.4558 q^{72} +6.53419 q^{73} -1.74005 q^{74} +2.78419 q^{75} -7.89616 q^{76} +1.63382 q^{78} -11.5204 q^{79} +3.59725 q^{80} +5.18904 q^{81} -12.9131 q^{82} +7.16403 q^{83} +6.54069 q^{85} -27.1198 q^{86} +2.43553 q^{87} -17.9357 q^{88} +12.8490 q^{89} +5.69206 q^{90} -2.38200 q^{92} +4.73112 q^{93} -29.6520 q^{94} -1.80056 q^{95} -0.0524936 q^{96} +9.09062 q^{97} -9.39642 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 8 q^{3} + 4 q^{4} + 6 q^{5} + 4 q^{6} + 6 q^{9}+O(q^{10}) \) 6 * q + 8 * q^3 + 4 * q^4 + 6 * q^5 + 4 * q^6 + 6 * q^9	\( 6 q + 8 q^{3} + 4 q^{4} + 6 q^{5} + 4 q^{6} + 6 q^{9} + 4 q^{10} + 4 q^{11} - 4 q^{12} + 6 q^{13} + 12 q^{15} + 16 q^{17} - 4 q^{18} + 2 q^{19} + 16 q^{20} - 12 q^{22} - 6 q^{23} + 12 q^{24} - 4 q^{25} + 20 q^{27} - 6 q^{29} + 6 q^{31} - 20 q^{32} + 4 q^{33} - 24 q^{36} + 8 q^{38} + 8 q^{39} + 4 q^{40} - 8 q^{41} + 2 q^{43} - 4 q^{44} + 14 q^{45} + 8 q^{46} + 30 q^{47} - 8 q^{48} + 8 q^{50} - 4 q^{51} + 4 q^{52} - 14 q^{53} - 48 q^{54} - 8 q^{55} + 4 q^{57} - 8 q^{58} + 24 q^{59} + 12 q^{60} + 28 q^{62} - 20 q^{64} + 6 q^{65} - 4 q^{66} + 16 q^{67} + 28 q^{68} - 20 q^{69} + 8 q^{71} + 28 q^{72} - 6 q^{73} - 12 q^{74} + 12 q^{75} - 16 q^{76} + 4 q^{78} - 22 q^{79} - 28 q^{80} + 46 q^{81} - 40 q^{82} + 50 q^{83} - 8 q^{85} - 16 q^{86} - 16 q^{87} - 44 q^{88} + 26 q^{89} - 40 q^{90} + 20 q^{92} + 16 q^{93} - 32 q^{94} - 6 q^{95} - 20 q^{96} - 14 q^{97} + 12 q^{99}+O(q^{100}) \) 6 * q + 8 * q^3 + 4 * q^4 + 6 * q^5 + 4 * q^6 + 6 * q^9 + 4 * q^10 + 4 * q^11 - 4 * q^12 + 6 * q^13 + 12 * q^15 + 16 * q^17 - 4 * q^18 + 2 * q^19 + 16 * q^20 - 12 * q^22 - 6 * q^23 + 12 * q^24 - 4 * q^25 + 20 * q^27 - 6 * q^29 + 6 * q^31 - 20 * q^32 + 4 * q^33 - 24 * q^36 + 8 * q^38 + 8 * q^39 + 4 * q^40 - 8 * q^41 + 2 * q^43 - 4 * q^44 + 14 * q^45 + 8 * q^46 + 30 * q^47 - 8 * q^48 + 8 * q^50 - 4 * q^51 + 4 * q^52 - 14 * q^53 - 48 * q^54 - 8 * q^55 + 4 * q^57 - 8 * q^58 + 24 * q^59 + 12 * q^60 + 28 * q^62 - 20 * q^64 + 6 * q^65 - 4 * q^66 + 16 * q^67 + 28 * q^68 - 20 * q^69 + 8 * q^71 + 28 * q^72 - 6 * q^73 - 12 * q^74 + 12 * q^75 - 16 * q^76 + 4 * q^78 - 22 * q^79 - 28 * q^80 + 46 * q^81 - 40 * q^82 + 50 * q^83 - 8 * q^85 - 16 * q^86 - 16 * q^87 - 44 * q^88 + 26 * q^89 - 40 * q^90 + 20 * q^92 + 16 * q^93 - 32 * q^94 - 6 * q^95 - 20 * q^96 - 14 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more