LMFDB - Embedded newform 735.4.a.p.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,4,Mod(1,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("735.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	735.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:	$43.3664038542$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{65}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 16 $ x^2 - x - 16
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-3.53113$ of defining polynomial
Character	$\chi$	$=$	735.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.53113 q^{2} -3.00000 q^{3} +4.46887 q^{4} -5.00000 q^{5} +10.5934 q^{6} +12.4689 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.53113 q^{2} -3.00000 q^{3} +4.46887 q^{4} -5.00000 q^{5} +10.5934 q^{6} +12.4689 q^{8} +9.00000 q^{9} +17.6556 q^{10} -2.93774 q^{11} -13.4066 q^{12} +19.0623 q^{13} +15.0000 q^{15} -79.7802 q^{16} -122.498 q^{17} -31.7802 q^{18} -107.436 q^{19} -22.3444 q^{20} +10.3735 q^{22} +210.623 q^{23} -37.4066 q^{24} +25.0000 q^{25} -67.3113 q^{26} -27.0000 q^{27} +95.4942 q^{29} -52.9669 q^{30} +94.3074 q^{31} +181.963 q^{32} +8.81323 q^{33} +432.556 q^{34} +40.2198 q^{36} +97.1206 q^{37} +379.370 q^{38} -57.1868 q^{39} -62.3444 q^{40} +491.113 q^{41} -43.0039 q^{43} -13.1284 q^{44} -45.0000 q^{45} -743.735 q^{46} -473.494 q^{47} +239.340 q^{48} -88.2782 q^{50} +367.494 q^{51} +85.1868 q^{52} -183.677 q^{53} +95.3405 q^{54} +14.6887 q^{55} +322.307 q^{57} -337.202 q^{58} +760.615 q^{59} +67.0331 q^{60} +198.747 q^{61} -333.012 q^{62} -4.29373 q^{64} -95.3113 q^{65} -31.1206 q^{66} -309.992 q^{67} -547.428 q^{68} -631.868 q^{69} +665.693 q^{71} +112.220 q^{72} -621.288 q^{73} -342.945 q^{74} -75.0000 q^{75} -480.117 q^{76} +201.934 q^{78} -24.7626 q^{79} +398.901 q^{80} +81.0000 q^{81} -1734.18 q^{82} +406.724 q^{83} +612.490 q^{85} +151.852 q^{86} -286.483 q^{87} -36.6303 q^{88} -261.751 q^{89} +158.901 q^{90} +941.245 q^{92} -282.922 q^{93} +1671.97 q^{94} +537.179 q^{95} -545.889 q^{96} +1004.77 q^{97} -26.4397 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 6 q^{3} + 17 q^{4} - 10 q^{5} - 3 q^{6} + 33 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q + q^2 - 6 * q^3 + 17 * q^4 - 10 * q^5 - 3 * q^6 + 33 * q^8 + 18 * q^9	\( 2 q + q^{2} - 6 q^{3} + 17 q^{4} - 10 q^{5} - 3 q^{6} + 33 q^{8} + 18 q^{9} - 5 q^{10} - 22 q^{11} - 51 q^{12} + 22 q^{13} + 30 q^{15} - 87 q^{16} - 116 q^{17} + 9 q^{18} - 102 q^{19} - 85 q^{20} - 76 q^{22} + 260 q^{23} - 99 q^{24} + 50 q^{25} - 54 q^{26} - 54 q^{27} - 196 q^{29} + 15 q^{30} - 150 q^{31} - 15 q^{32} + 66 q^{33} + 462 q^{34} + 153 q^{36} - 96 q^{37} + 404 q^{38} - 66 q^{39} - 165 q^{40} + 176 q^{41} - 344 q^{43} - 252 q^{44} - 90 q^{45} - 520 q^{46} - 560 q^{47} + 261 q^{48} + 25 q^{50} + 348 q^{51} + 122 q^{52} + 326 q^{53} - 27 q^{54} + 110 q^{55} + 306 q^{57} - 1658 q^{58} + 844 q^{59} + 255 q^{60} + 204 q^{61} - 1440 q^{62} - 839 q^{64} - 110 q^{65} + 228 q^{66} - 104 q^{67} - 466 q^{68} - 780 q^{69} + 1670 q^{71} + 297 q^{72} + 386 q^{73} - 1218 q^{74} - 150 q^{75} - 412 q^{76} + 162 q^{78} - 888 q^{79} + 435 q^{80} + 162 q^{81} - 3162 q^{82} - 928 q^{83} + 580 q^{85} - 1212 q^{86} + 588 q^{87} - 428 q^{88} - 588 q^{89} - 45 q^{90} + 1560 q^{92} + 450 q^{93} + 1280 q^{94} + 510 q^{95} + 45 q^{96} - 522 q^{97} - 198 q^{99}+O(q^{100}) \) 2 * q + q^2 - 6 * q^3 + 17 * q^4 - 10 * q^5 - 3 * q^6 + 33 * q^8 + 18 * q^9 - 5 * q^10 - 22 * q^11 - 51 * q^12 + 22 * q^13 + 30 * q^15 - 87 * q^16 - 116 * q^17 + 9 * q^18 - 102 * q^19 - 85 * q^20 - 76 * q^22 + 260 * q^23 - 99 * q^24 + 50 * q^25 - 54 * q^26 - 54 * q^27 - 196 * q^29 + 15 * q^30 - 150 * q^31 - 15 * q^32 + 66 * q^33 + 462 * q^34 + 153 * q^36 - 96 * q^37 + 404 * q^38 - 66 * q^39 - 165 * q^40 + 176 * q^41 - 344 * q^43 - 252 * q^44 - 90 * q^45 - 520 * q^46 - 560 * q^47 + 261 * q^48 + 25 * q^50 + 348 * q^51 + 122 * q^52 + 326 * q^53 - 27 * q^54 + 110 * q^55 + 306 * q^57 - 1658 * q^58 + 844 * q^59 + 255 * q^60 + 204 * q^61 - 1440 * q^62 - 839 * q^64 - 110 * q^65 + 228 * q^66 - 104 * q^67 - 466 * q^68 - 780 * q^69 + 1670 * q^71 + 297 * q^72 + 386 * q^73 - 1218 * q^74 - 150 * q^75 - 412 * q^76 + 162 * q^78 - 888 * q^79 + 435 * q^80 + 162 * q^81 - 3162 * q^82 - 928 * q^83 + 580 * q^85 - 1212 * q^86 + 588 * q^87 - 428 * q^88 - 588 * q^89 - 45 * q^90 + 1560 * q^92 + 450 * q^93 + 1280 * q^94 + 510 * q^95 + 45 * q^96 - 522 * q^97 - 198 * 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 $

$2$	−3.53113	−1.24844	−0.624221	−	0.781248i	$-0.714584\pi$
$2$	−3.53113	−1.24844	−0.624221	+	0.781248i	$0.714584\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.46887	0.558609
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	10.5934	0.720789
$7$	0	0
$7$	0	0
$8$	12.4689	0.551051
$9$	9.00000	0.333333
$10$	17.6556	0.558320
$11$	−2.93774	−0.0805239	−0.0402619	−	0.999189i	$-0.512819\pi$
$11$	−2.93774	−0.0805239	−0.0402619	+	0.999189i	$0.512819\pi$
$12$	−13.4066	−0.322513
$13$	19.0623	0.406686	0.203343	−	0.979108i	$-0.434819\pi$
$13$	19.0623	0.406686	0.203343	+	0.979108i	$0.434819\pi$
$14$	0	0
$15$	15.0000	0.258199
$16$	−79.7802	−1.24656
$17$	−122.498	−1.74766	−0.873828	−	0.486236i	$-0.838370\pi$
$17$	−122.498	−1.74766	−0.873828	+	0.486236i	$0.838370\pi$
$18$	−31.7802	−0.416148
$19$	−107.436	−1.29723	−0.648617	−	0.761115i	$-0.724652\pi$
$19$	−107.436	−1.29723	−0.648617	+	0.761115i	$0.724652\pi$
$20$	−22.3444	−0.249817
$21$	0	0
$22$	10.3735	0.100529
$23$	210.623	1.90947	0.954736	−	0.297455i	$-0.0961379\pi$
$23$	210.623	1.90947	0.954736	+	0.297455i	$0.0961379\pi$
$24$	−37.4066	−0.318150
$25$	25.0000	0.200000
$26$	−67.3113	−0.507724
$27$	−27.0000	−0.192450
$28$	0	0
$29$	95.4942	0.611477	0.305738	−	0.952116i	$-0.401097\pi$
$29$	95.4942	0.611477	0.305738	+	0.952116i	$0.401097\pi$
$30$	−52.9669	−0.322346
$31$	94.3074	0.546391	0.273195	−	0.961959i	$-0.411919\pi$
$31$	94.3074	0.546391	0.273195	+	0.961959i	$0.411919\pi$
$32$	181.963	1.00521
$33$	8.81323	0.0464905
$34$	432.556	2.18185
$35$	0	0
$36$	40.2198	0.186203
$37$	97.1206	0.431528	0.215764	−	0.976446i	$-0.430776\pi$
$37$	97.1206	0.431528	0.215764	+	0.976446i	$0.430776\pi$
$38$	379.370	1.61952
$39$	−57.1868	−0.234800
$40$	−62.3444	−0.246438
$41$	491.113	1.87071	0.935353	−	0.353716i	$-0.115082\pi$
$41$	491.113	1.87071	0.935353	+	0.353716i	$0.115082\pi$
$42$	0	0
$43$	−43.0039	−0.152512	−0.0762562	−	0.997088i	$-0.524297\pi$
$43$	−43.0039	−0.152512	−0.0762562	+	0.997088i	$0.524297\pi$
$44$	−13.1284	−0.0449814
$45$	−45.0000	−0.149071
$46$	−743.735	−2.38387
$47$	−473.494	−1.46949	−0.734747	−	0.678341i	$-0.762699\pi$
$47$	−473.494	−1.46949	−0.734747	+	0.678341i	$0.762699\pi$
$48$	239.340	0.719705
$49$	0	0
$50$	−88.2782	−0.249689
$51$	367.494	1.00901
$52$	85.1868	0.227178
$53$	−183.677	−0.476038	−0.238019	−	0.971261i	$-0.576498\pi$
$53$	−183.677	−0.476038	−0.238019	+	0.971261i	$0.576498\pi$
$54$	95.3405	0.240263
$55$	14.6887	0.0360114
$56$	0	0
$57$	322.307	0.748959
$58$	−337.202	−0.763394
$59$	760.615	1.67837	0.839183	−	0.543849i	$-0.183034\pi$
$59$	760.615	1.67837	0.839183	+	0.543849i	$0.183034\pi$
$60$	67.0331	0.144232
$61$	198.747	0.417163	0.208582	−	0.978005i	$-0.433115\pi$
$61$	198.747	0.417163	0.208582	+	0.978005i	$0.433115\pi$
$62$	−333.012	−0.682137
$63$	0	0
$64$	−4.29373	−0.00838618
$65$	−95.3113	−0.181876
$66$	−31.1206	−0.0580407
$67$	−309.992	−0.565247	−0.282624	−	0.959231i	$-0.591205\pi$
$67$	−309.992	−0.565247	−0.282624	+	0.959231i	$0.591205\pi$
$68$	−547.428	−0.976256
$69$	−631.868	−1.10243
$70$	0	0
$71$	665.693	1.11272	0.556360	−	0.830941i	$-0.312197\pi$
$71$	665.693	1.11272	0.556360	+	0.830941i	$0.312197\pi$
$72$	112.220	0.183684
$73$	−621.288	−0.996113	−0.498057	−	0.867145i	$-0.665953\pi$
$73$	−621.288	−0.996113	−0.498057	+	0.867145i	$0.665953\pi$
$74$	−342.945	−0.538738
$75$	−75.0000	−0.115470
$76$	−480.117	−0.724647
$77$	0	0
$78$	201.934	0.293135
$79$	−24.7626	−0.0352659	−0.0176330	−	0.999845i	$-0.505613\pi$
$79$	−24.7626	−0.0352659	−0.0176330	+	0.999845i	$0.505613\pi$
$80$	398.901	0.557481
$81$	81.0000	0.111111
$82$	−1734.18	−2.33547
$83$	406.724	0.537876	0.268938	−	0.963157i	$-0.413327\pi$
$83$	406.724	0.537876	0.268938	+	0.963157i	$0.413327\pi$
$84$	0	0
$85$	612.490	0.781575
$86$	151.852	0.190403
$87$	−286.483	−0.353036
$88$	−36.6303	−0.0443728
$89$	−261.751	−0.311748	−0.155874	−	0.987777i	$-0.549819\pi$
$89$	−261.751	−0.311748	−0.155874	+	0.987777i	$0.549819\pi$
$90$	158.901	0.186107
$91$	0	0
$92$	941.245	1.06665
$93$	−282.922	−0.315459
$94$	1671.97	1.83458
$95$	537.179	0.580141
$96$	−545.889	−0.580360
$97$	1004.77	1.05175	0.525873	−	0.850563i	$-0.323739\pi$
$97$	1004.77	1.05175	0.525873	+	0.850563i	$0.323739\pi$
$98$	0	0
$99$	−26.4397	−0.0268413
$100$	111.722	0.111722
$101$	128.872	0.126962	0.0634812	−	0.997983i	$-0.479780\pi$
$101$	128.872	0.126962	0.0634812	+	0.997983i	$0.479780\pi$
$102$	−1297.67	−1.25969
$103$	−806.008	−0.771051	−0.385526	−	0.922697i	$-0.625980\pi$
$103$	−806.008	−0.771051	−0.385526	+	0.922697i	$0.625980\pi$
$104$	237.685	0.224105
$105$	0	0
$106$	648.587	0.594305
$107$	−769.712	−0.695429	−0.347714	−	0.937600i	$-0.613042\pi$
$107$	−769.712	−0.695429	−0.347714	+	0.937600i	$0.613042\pi$
$108$	−120.660	−0.107504
$109$	−780.856	−0.686169	−0.343085	−	0.939304i	$-0.611472\pi$
$109$	−780.856	−0.686169	−0.343085	+	0.939304i	$0.611472\pi$
$110$	−51.8677	−0.0449581
$111$	−291.362	−0.249143
$112$	0	0
$113$	−1115.65	−0.928771	−0.464386	−	0.885633i	$-0.653725\pi$
$113$	−1115.65	−0.928771	−0.464386	+	0.885633i	$0.653725\pi$
$114$	−1138.11	−0.935032
$115$	−1053.11	−0.853942
$116$	426.751	0.341576
$117$	171.560	0.135562
$118$	−2685.83	−2.09534
$119$	0	0
$120$	187.033	0.142281
$121$	−1322.37	−0.993516
$122$	−701.802	−0.520804
$123$	−1473.34	−1.08005
$124$	421.448	0.305219
$125$	−125.000	−0.0894427
$126$	0	0
$127$	−1875.98	−1.31076	−0.655381	−	0.755299i	$-0.727492\pi$
$127$	−1875.98	−1.31076	−0.655381	+	0.755299i	$0.727492\pi$
$128$	−1440.54	−0.994744
$129$	129.012	0.0880530
$130$	336.556	0.227061
$131$	−364.203	−0.242905	−0.121452	−	0.992597i	$-0.538755\pi$
$131$	−364.203	−0.242905	−0.121452	+	0.992597i	$0.538755\pi$
$132$	39.3852	0.0259700
$133$	0	0
$134$	1094.62	0.705679
$135$	135.000	0.0860663
$136$	−1527.41	−0.963048
$137$	1603.13	0.999743	0.499872	−	0.866099i	$-0.333380\pi$
$137$	1603.13	0.999743	0.499872	+	0.866099i	$0.333380\pi$
$138$	2231.21	1.37633
$139$	−2431.12	−1.48349	−0.741746	−	0.670681i	$-0.766002\pi$
$139$	−2431.12	−1.48349	−0.741746	+	0.670681i	$0.766002\pi$
$140$	0	0
$141$	1420.48	0.848413
$142$	−2350.65	−1.38917
$143$	−56.0000	−0.0327479
$144$	−718.021	−0.415522
$145$	−477.471	−0.273461
$146$	2193.85	1.24359
$147$	0	0
$148$	434.020	0.241055
$149$	2341.57	1.28744	0.643722	−	0.765260i	$-0.277389\pi$
$149$	2341.57	1.28744	0.643722	+	0.765260i	$0.277389\pi$
$150$	264.835	0.144158
$151$	−2104.07	−1.13395	−0.566976	−	0.823734i	$-0.691887\pi$
$151$	−2104.07	−1.13395	−0.566976	+	0.823734i	$0.691887\pi$
$152$	−1339.60	−0.714843
$153$	−1102.48	−0.582552
$154$	0	0
$155$	−471.537	−0.244353
$156$	−255.560	−0.131162
$157$	593.467	0.301680	0.150840	−	0.988558i	$-0.451802\pi$
$157$	593.467	0.301680	0.150840	+	0.988558i	$0.451802\pi$
$158$	87.4399	0.0440275
$159$	551.031	0.274840
$160$	−909.815	−0.449545
$161$	0	0
$162$	−286.021	−0.138716
$163$	2178.71	1.04693	0.523465	−	0.852047i	$-0.324639\pi$
$163$	2178.71	1.04693	0.523465	+	0.852047i	$0.324639\pi$
$164$	2194.72	1.04499
$165$	−44.0661	−0.0207912
$166$	−1436.19	−0.671508
$167$	−799.502	−0.370463	−0.185231	−	0.982695i	$-0.559303\pi$
$167$	−799.502	−0.370463	−0.185231	+	0.982695i	$0.559303\pi$
$168$	0	0
$169$	−1833.63	−0.834606
$170$	−2162.78	−0.975752
$171$	−966.922	−0.432412
$172$	−192.179	−0.0851947
$173$	1444.36	0.634754	0.317377	−	0.948299i	$-0.397198\pi$
$173$	1444.36	0.634754	0.317377	+	0.948299i	$0.397198\pi$
$174$	1011.61	0.440745
$175$	0	0
$176$	234.374	0.100378
$177$	−2281.84	−0.969005
$178$	924.276	0.389199
$179$	3343.49	1.39611	0.698056	−	0.716043i	$-0.254048\pi$
$179$	3343.49	1.39611	0.698056	+	0.716043i	$0.254048\pi$
$180$	−201.099	−0.0832725
$181$	−2251.81	−0.924729	−0.462365	−	0.886690i	$-0.652999\pi$
$181$	−2251.81	−0.924729	−0.462365	+	0.886690i	$0.652999\pi$
$182$	0	0
$183$	−596.241	−0.240849
$184$	2626.23	1.05222
$185$	−485.603	−0.192985
$186$	999.035	0.393832
$187$	359.868	0.140728
$188$	−2115.98	−0.820873
$189$	0	0
$190$	−1896.85	−0.724273
$191$	−1001.93	−0.379565	−0.189782	−	0.981826i	$-0.560778\pi$
$191$	−1001.93	−0.379565	−0.189782	+	0.981826i	$0.560778\pi$
$192$	12.8812	0.00484177
$193$	−4054.97	−1.51235	−0.756173	−	0.654372i	$-0.772933\pi$
$193$	−4054.97	−1.51235	−0.756173	+	0.654372i	$0.772933\pi$
$194$	−3547.99	−1.31304
$195$	285.934	0.105006
$196$	0	0
$197$	−5140.23	−1.85902	−0.929508	−	0.368802i	$-0.879768\pi$
$197$	−5140.23	−1.85902	−0.929508	+	0.368802i	$0.879768\pi$
$198$	93.3619	0.0335098
$199$	−585.631	−0.208614	−0.104307	−	0.994545i	$-0.533263\pi$
$199$	−585.631	−0.208614	−0.104307	+	0.994545i	$0.533263\pi$
$200$	311.722	0.110210
$201$	929.977	0.326346
$202$	−455.062	−0.158505
$203$	0	0
$204$	1642.28	0.563642
$205$	−2455.56	−0.836605
$206$	2846.12	0.962614
$207$	1895.60	0.636490
$208$	−1520.79	−0.506961
$209$	315.619	0.104458
$210$	0	0
$211$	−1055.16	−0.344266	−0.172133	−	0.985074i	$-0.555066\pi$
$211$	−1055.16	−0.344266	−0.172133	+	0.985074i	$0.555066\pi$
$212$	−820.829	−0.265919
$213$	−1997.08	−0.642430
$214$	2717.95	0.868203
$215$	215.019	0.0682056
$216$	−336.660	−0.106050
$217$	0	0
$218$	2757.30	0.856643
$219$	1863.86	0.575106
$220$	65.6420	0.0201163
$221$	−2335.09	−0.710747
$222$	1028.84	0.311040
$223$	−4675.85	−1.40412	−0.702059	−	0.712119i	$-0.747736\pi$
$223$	−4675.85	−1.40412	−0.702059	+	0.712119i	$0.747736\pi$
$224$	0	0
$225$	225.000	0.0666667
$226$	3939.49	1.15952
$227$	−5443.11	−1.59151	−0.795754	−	0.605621i	$-0.792925\pi$
$227$	−5443.11	−1.59151	−0.795754	+	0.605621i	$0.792925\pi$
$228$	1440.35	0.418375
$229$	536.303	0.154759	0.0773797	−	0.997002i	$-0.475345\pi$
$229$	536.303	0.154759	0.0773797	+	0.997002i	$0.475345\pi$
$230$	3718.68	1.06610
$231$	0	0
$232$	1190.70	0.336955
$233$	−183.490	−0.0515916	−0.0257958	−	0.999667i	$-0.508212\pi$
$233$	−183.490	−0.0515916	−0.0257958	+	0.999667i	$0.508212\pi$
$234$	−605.802	−0.169241
$235$	2367.47	0.657178
$236$	3399.09	0.937550
$237$	74.2878	0.0203608
$238$	0	0
$239$	643.218	0.174085	0.0870425	−	0.996205i	$-0.472258\pi$
$239$	643.218	0.174085	0.0870425	+	0.996205i	$0.472258\pi$
$240$	−1196.70	−0.321862
$241$	5755.61	1.53839	0.769194	−	0.639015i	$-0.220658\pi$
$241$	5755.61	1.53839	0.769194	+	0.639015i	$0.220658\pi$
$242$	4669.46	1.24035
$243$	−243.000	−0.0641500
$244$	888.175	0.233031
$245$	0	0
$246$	5202.55	1.34838
$247$	−2047.97	−0.527567
$248$	1175.91	0.301089
$249$	−1220.17	−0.310543
$250$	441.391	0.111664
$251$	5132.27	1.29062	0.645311	−	0.763920i	$-0.276728\pi$
$251$	5132.27	1.29062	0.645311	+	0.763920i	$0.276728\pi$
$252$	0	0
$253$	−618.755	−0.153758
$254$	6624.34	1.63641
$255$	−1837.47	−0.451243
$256$	5121.09	1.25027
$257$	−5041.74	−1.22372	−0.611859	−	0.790967i	$-0.709578\pi$
$257$	−5041.74	−1.22372	−0.611859	+	0.790967i	$0.709578\pi$
$258$	−455.557	−0.109929
$259$	0	0
$260$	−425.934	−0.101597
$261$	859.448	0.203826
$262$	1286.05	0.303253
$263$	7577.00	1.77649	0.888246	−	0.459367i	$-0.151924\pi$
$263$	7577.00	1.77649	0.888246	+	0.459367i	$0.151924\pi$
$264$	109.891	0.0256186
$265$	918.385	0.212890
$266$	0	0
$267$	785.253	0.179988
$268$	−1385.32	−0.315752
$269$	−1023.10	−0.231893	−0.115947	−	0.993255i	$-0.536990\pi$
$269$	−1023.10	−0.231893	−0.115947	+	0.993255i	$0.536990\pi$
$270$	−476.702	−0.107449
$271$	2251.98	0.504790	0.252395	−	0.967624i	$-0.418782\pi$
$271$	2251.98	0.504790	0.252395	+	0.967624i	$0.418782\pi$
$272$	9772.91	2.17857
$273$	0	0
$274$	−5660.87	−1.24812
$275$	−73.4436	−0.0161048
$276$	−2823.74	−0.615829
$277$	−8630.72	−1.87209	−0.936047	−	0.351875i	$-0.885544\pi$
$277$	−8630.72	−1.87209	−0.936047	+	0.351875i	$0.885544\pi$
$278$	8584.61	1.85205
$279$	848.767	0.182130
$280$	0	0
$281$	−7521.62	−1.59680	−0.798402	−	0.602124i	$-0.794321\pi$
$281$	−7521.62	−1.59680	−0.798402	+	0.602124i	$0.794321\pi$
$282$	−5015.91	−1.05919
$283$	−14.8169	−0.00311226	−0.00155613	−	0.999999i	$-0.500495\pi$
$283$	−14.8169	−0.00311226	−0.00155613	+	0.999999i	$0.500495\pi$
$284$	2974.89	0.621576
$285$	−1611.54	−0.334945
$286$	197.743	0.0408839
$287$	0	0
$288$	1637.67	0.335071
$289$	10092.8	2.05430
$290$	1686.01	0.341400
$291$	−3014.32	−0.607226
$292$	−2776.46	−0.556438
$293$	−6913.39	−1.37844	−0.689222	−	0.724550i	$-0.742048\pi$
$293$	−6913.39	−1.37844	−0.689222	+	0.724550i	$0.742048\pi$
$294$	0	0
$295$	−3803.07	−0.750588
$296$	1210.98	0.237794
$297$	79.3190	0.0154968
$298$	−8268.39	−1.60730
$299$	4014.94	0.776555
$300$	−335.165	−0.0645026
$301$	0	0
$302$	7429.74	1.41567
$303$	−386.615	−0.0733018
$304$	8571.25	1.61709
$305$	−993.735	−0.186561
$306$	3893.01	0.727283
$307$	7644.12	1.42108	0.710542	−	0.703655i	$-0.248450\pi$
$307$	7644.12	1.42108	0.710542	+	0.703655i	$0.248450\pi$
$308$	0	0
$309$	2418.02	0.445167
$310$	1665.06	0.305061
$311$	−7593.99	−1.38462	−0.692308	−	0.721602i	$-0.743406\pi$
$311$	−7593.99	−1.38462	−0.692308	+	0.721602i	$0.743406\pi$
$312$	−713.055	−0.129387
$313$	9127.84	1.64836	0.824179	−	0.566329i	$-0.191637\pi$
$313$	9127.84	1.64836	0.824179	+	0.566329i	$0.191637\pi$
$314$	−2095.61	−0.376631
$315$	0	0
$316$	−110.661	−0.0196999
$317$	−4929.81	−0.873456	−0.436728	−	0.899593i	$-0.643863\pi$
$317$	−4929.81	−0.873456	−0.436728	+	0.899593i	$0.643863\pi$
$318$	−1945.76	−0.343122
$319$	−280.537	−0.0492385
$320$	21.4686	0.00375042
$321$	2309.14	0.401506
$322$	0	0
$323$	13160.7	2.26712
$324$	361.979	0.0620677
$325$	476.556	0.0813372
$326$	−7693.30	−1.30703
$327$	2342.57	0.396160
$328$	6123.62	1.03086
$329$	0	0
$330$	155.603	0.0259566
$331$	1221.67	0.202867	0.101433	−	0.994842i	$-0.467657\pi$
$331$	1221.67	0.202867	0.101433	+	0.994842i	$0.467657\pi$
$332$	1817.60	0.300463
$333$	874.086	0.143843
$334$	2823.14	0.462502
$335$	1549.96	0.252786
$336$	0	0
$337$	−8744.83	−1.41354	−0.706768	−	0.707446i	$-0.749847\pi$
$337$	−8744.83	−1.41354	−0.706768	+	0.707446i	$0.749847\pi$
$338$	6474.79	1.04196
$339$	3346.94	0.536226
$340$	2737.14	0.436595
$341$	−277.051	−0.0439975
$342$	3414.33	0.539841
$343$	0	0
$344$	−536.210	−0.0840421
$345$	3159.34	0.493023
$346$	−5100.21	−0.792454
$347$	4589.56	0.710031	0.355015	−	0.934860i	$-0.384476\pi$
$347$	4589.56	0.710031	0.355015	+	0.934860i	$0.384476\pi$
$348$	−1280.25	−0.197209
$349$	3989.89	0.611960	0.305980	−	0.952038i	$-0.401016\pi$
$349$	3989.89	0.611960	0.305980	+	0.952038i	$0.401016\pi$
$350$	0	0
$351$	−514.681	−0.0782668
$352$	−534.561	−0.0809437
$353$	−2416.35	−0.364333	−0.182166	−	0.983268i	$-0.558311\pi$
$353$	−2416.35	−0.364333	−0.182166	+	0.983268i	$0.558311\pi$
$354$	8057.49	1.20975
$355$	−3328.46	−0.497624
$356$	−1169.73	−0.174145
$357$	0	0
$358$	−11806.3	−1.74297
$359$	−2756.24	−0.405206	−0.202603	−	0.979261i	$-0.564940\pi$
$359$	−2756.24	−0.405206	−0.202603	+	0.979261i	$0.564940\pi$
$360$	−561.099	−0.0821459
$361$	4683.45	0.682818
$362$	7951.44	1.15447
$363$	3967.11	0.573607
$364$	0	0
$365$	3106.44	0.445475
$366$	2105.40	0.300687
$367$	−11112.8	−1.58061	−0.790307	−	0.612711i	$-0.790079\pi$
$367$	−11112.8	−1.58061	−0.790307	+	0.612711i	$0.790079\pi$
$368$	−16803.5	−2.38028
$369$	4420.02	0.623569
$370$	1714.73	0.240931
$371$	0	0
$372$	−1264.34	−0.176218
$373$	6091.09	0.845535	0.422768	−	0.906238i	$-0.361059\pi$
$373$	6091.09	0.845535	0.422768	+	0.906238i	$0.361059\pi$
$374$	−1270.74	−0.175691
$375$	375.000	0.0516398
$376$	−5903.94	−0.809767
$377$	1820.33	0.248679
$378$	0	0
$379$	3984.29	0.539998	0.269999	−	0.962861i	$-0.412977\pi$
$379$	3984.29	0.539998	0.269999	+	0.962861i	$0.412977\pi$
$380$	2400.58	0.324072
$381$	5627.95	0.756768
$382$	3537.93	0.473865
$383$	−318.475	−0.0424890	−0.0212445	−	0.999774i	$-0.506763\pi$
$383$	−318.475	−0.0424890	−0.0212445	+	0.999774i	$0.506763\pi$
$384$	4321.63	0.574316
$385$	0	0
$386$	14318.6	1.88808
$387$	−387.035	−0.0508374
$388$	4490.21	0.587515
$389$	3885.46	0.506429	0.253214	−	0.967410i	$-0.418512\pi$
$389$	3885.46	0.506429	0.253214	+	0.967410i	$0.418512\pi$
$390$	−1009.67	−0.131094
$391$	−25800.9	−3.33710
$392$	0	0
$393$	1092.61	0.140241
$394$	18150.8	2.32088
$395$	123.813	0.0157714
$396$	−118.156	−0.0149938
$397$	−4806.04	−0.607578	−0.303789	−	0.952739i	$-0.598252\pi$
$397$	−4806.04	−0.607578	−0.303789	+	0.952739i	$0.598252\pi$
$398$	2067.94	0.260443
$399$	0	0
$400$	−1994.50	−0.249313
$401$	3618.59	0.450633	0.225316	−	0.974286i	$-0.427658\pi$
$401$	3618.59	0.450633	0.225316	+	0.974286i	$0.427658\pi$
$402$	−3283.87	−0.407424
$403$	1797.71	0.222209
$404$	575.911	0.0709223
$405$	−405.000	−0.0496904
$406$	0	0
$407$	−285.315	−0.0347483
$408$	4582.24	0.556016
$409$	2109.05	0.254978	0.127489	−	0.991840i	$-0.459308\pi$
$409$	2109.05	0.254978	0.127489	+	0.991840i	$0.459308\pi$
$410$	8670.91	1.04445
$411$	−4809.40	−0.577202
$412$	−3601.94	−0.430716
$413$	0	0
$414$	−6693.62	−0.794622
$415$	−2033.62	−0.240546
$416$	3468.63	0.408806
$417$	7293.37	0.856494
$418$	−1114.49	−0.130410
$419$	6905.91	0.805193	0.402597	−	0.915377i	$-0.368108\pi$
$419$	6905.91	0.805193	0.402597	+	0.915377i	$0.368108\pi$
$420$	0	0
$421$	−9647.54	−1.11685	−0.558423	−	0.829556i	$-0.688593\pi$
$421$	−9647.54	−1.11685	−0.558423	+	0.829556i	$0.688593\pi$
$422$	3725.91	0.429797
$423$	−4261.45	−0.489831
$424$	−2290.25	−0.262321
$425$	−3062.45	−0.349531
$426$	7051.94	0.802037
$427$	0	0
$428$	−3439.74	−0.388473
$429$	168.000	0.0189070
$430$	−759.261	−0.0851508
$431$	−13002.7	−1.45318	−0.726589	−	0.687073i	$-0.758895\pi$
$431$	−13002.7	−1.45318	−0.726589	+	0.687073i	$0.758895\pi$
$432$	2154.06	0.239902
$433$	−7356.07	−0.816420	−0.408210	−	0.912888i	$-0.633847\pi$
$433$	−7356.07	−0.816420	−0.408210	+	0.912888i	$0.633847\pi$
$434$	0	0
$435$	1432.41	0.157883
$436$	−3489.55	−0.383300
$437$	−22628.4	−2.47703
$438$	−6581.54	−0.717987
$439$	−6909.21	−0.751159	−0.375579	−	0.926790i	$-0.622556\pi$
$439$	−6909.21	−0.751159	−0.375579	+	0.926790i	$0.622556\pi$
$440$	183.152	0.0198441
$441$	0	0
$442$	8245.50	0.887327
$443$	−14812.6	−1.58864	−0.794318	−	0.607502i	$-0.792172\pi$
$443$	−14812.6	−1.58864	−0.794318	+	0.607502i	$0.792172\pi$
$444$	−1302.06	−0.139173
$445$	1308.75	0.139418
$446$	16511.0	1.75296
$447$	−7024.72	−0.743306
$448$	0	0
$449$	−10654.5	−1.11986	−0.559932	−	0.828538i	$-0.689173\pi$
$449$	−10654.5	−1.11986	−0.559932	+	0.828538i	$0.689173\pi$
$450$	−794.504	−0.0832295
$451$	−1442.76	−0.150636
$452$	−4985.68	−0.518820
$453$	6312.21	0.654688
$454$	19220.3	1.98691
$455$	0	0
$456$	4018.81	0.412715
$457$	−5855.16	−0.599328	−0.299664	−	0.954045i	$-0.596875\pi$
$457$	−5855.16	−0.599328	−0.299664	+	0.954045i	$0.596875\pi$
$458$	−1893.76	−0.193208
$459$	3307.45	0.336336
$460$	−4706.23	−0.477019
$461$	−3204.74	−0.323774	−0.161887	−	0.986809i	$-0.551758\pi$
$461$	−3204.74	−0.323774	−0.161887	+	0.986809i	$0.551758\pi$
$462$	0	0
$463$	371.658	0.0373054	0.0186527	−	0.999826i	$-0.494062\pi$
$463$	371.658	0.0373054	0.0186527	+	0.999826i	$0.494062\pi$
$464$	−7618.54	−0.762245
$465$	1414.61	0.141077
$466$	647.927	0.0644091
$467$	19752.3	1.95723	0.978614	−	0.205703i	$-0.0659482\pi$
$467$	19752.3	1.95723	0.978614	+	0.205703i	$0.0659482\pi$
$468$	766.681	0.0757262
$469$	0	0
$470$	−8359.84	−0.820449
$471$	−1780.40	−0.174175
$472$	9484.01	0.924866
$473$	126.334	0.0122809
$474$	−262.320	−0.0254193
$475$	−2685.90	−0.259447
$476$	0	0
$477$	−1653.09	−0.158679
$478$	−2271.28	−0.217335
$479$	20762.0	1.98046	0.990232	−	0.139433i	$-0.0445279\pi$
$479$	20762.0	1.98046	0.990232	+	0.139433i	$0.0445279\pi$
$480$	2729.45	0.259545
$481$	1851.34	0.175496
$482$	−20323.8	−1.92059
$483$	0	0
$484$	−5909.50	−0.554987
$485$	−5023.87	−0.470355
$486$	858.064	0.0800876
$487$	17647.6	1.64207	0.821035	−	0.570878i	$-0.193397\pi$
$487$	17647.6	1.64207	0.821035	+	0.570878i	$0.193397\pi$
$488$	2478.15	0.229878
$489$	−6536.12	−0.604445
$490$	0	0
$491$	−5637.46	−0.518157	−0.259078	−	0.965856i	$-0.583419\pi$
$491$	−5637.46	−0.518157	−0.259078	+	0.965856i	$0.583419\pi$
$492$	−6584.16	−0.603327
$493$	−11697.9	−1.06865
$494$	7231.64	0.658638
$495$	132.198	0.0120038
$496$	−7523.86	−0.681112
$497$	0	0
$498$	4308.58	0.387695
$499$	−17474.1	−1.56764	−0.783818	−	0.620991i	$-0.786730\pi$
$499$	−17474.1	−1.56764	−0.783818	+	0.620991i	$0.786730\pi$
$500$	−558.609	−0.0499635
$501$	2398.51	0.213887
$502$	−18122.7	−1.61127
$503$	−7444.81	−0.659936	−0.329968	−	0.943992i	$-0.607038\pi$
$503$	−7444.81	−0.659936	−0.329968	+	0.943992i	$0.607038\pi$
$504$	0	0
$505$	−644.358	−0.0567793
$506$	2184.90	0.191958
$507$	5500.89	0.481860
$508$	−8383.53	−0.732203
$509$	3384.48	0.294724	0.147362	−	0.989083i	$-0.452922\pi$
$509$	3384.48	0.294724	0.147362	+	0.989083i	$0.452922\pi$
$510$	6488.35	0.563351
$511$	0	0
$512$	−6558.89	−0.566142
$513$	2900.77	0.249653
$514$	17803.0	1.52774
$515$	4030.04	0.344825
$516$	576.536	0.0491872
$517$	1391.00	0.118329
$518$	0	0
$519$	−4333.07	−0.366476
$520$	−1188.42	−0.100223
$521$	−2973.12	−0.250009	−0.125005	−	0.992156i	$-0.539895\pi$
$521$	−2973.12	−0.250009	−0.125005	+	0.992156i	$0.539895\pi$
$522$	−3034.82	−0.254465
$523$	−2689.02	−0.224823	−0.112412	−	0.993662i	$-0.535858\pi$
$523$	−2689.02	−0.224823	−0.112412	+	0.993662i	$0.535858\pi$
$524$	−1627.57	−0.135689
$525$	0	0
$526$	−26755.3	−2.21785
$527$	−11552.5	−0.954903
$528$	−703.121	−0.0579534
$529$	32194.9	2.64608
$530$	−3242.94	−0.265781
$531$	6845.53	0.559455
$532$	0	0
$533$	9361.72	0.760790
$534$	−2772.83	−0.224704
$535$	3848.56	0.311005
$536$	−3865.25	−0.311480
$537$	−10030.5	−0.806046
$538$	3612.69	0.289506
$539$	0	0
$540$	603.298	0.0480774
$541$	−14429.5	−1.14671	−0.573356	−	0.819306i	$-0.694359\pi$
$541$	−14429.5	−1.14671	−0.573356	+	0.819306i	$0.694359\pi$
$542$	−7952.03	−0.630201
$543$	6755.44	0.533893
$544$	−22290.1	−1.75677
$545$	3904.28	0.306864
$546$	0	0
$547$	13811.2	1.07957	0.539784	−	0.841804i	$-0.318506\pi$
$547$	13811.2	1.07957	0.539784	+	0.841804i	$0.318506\pi$
$548$	7164.19	0.558466
$549$	1788.72	0.139054
$550$	259.339	0.0201059
$551$	−10259.5	−0.793229
$552$	−7878.68	−0.607498
$553$	0	0
$554$	30476.2	2.33720
$555$	1456.81	0.111420
$556$	−10864.4	−0.828692
$557$	−6033.26	−0.458954	−0.229477	−	0.973314i	$-0.573702\pi$
$557$	−6033.26	−0.458954	−0.229477	+	0.973314i	$0.573702\pi$
$558$	−2997.10	−0.227379
$559$	−819.751	−0.0620246
$560$	0	0
$561$	−1079.60	−0.0812493
$562$	26559.8	1.99352
$563$	6958.47	0.520896	0.260448	−	0.965488i	$-0.416130\pi$
$563$	6958.47	0.520896	0.260448	+	0.965488i	$0.416130\pi$
$564$	6347.95	0.473931
$565$	5578.23	0.415359
$566$	52.3202	0.00388548
$567$	0	0
$568$	8300.44	0.613166
$569$	−13396.4	−0.987009	−0.493505	−	0.869743i	$-0.664284\pi$
$569$	−13396.4	−0.987009	−0.493505	+	0.869743i	$0.664284\pi$
$570$	5690.55	0.418159
$571$	−8055.84	−0.590414	−0.295207	−	0.955433i	$-0.595389\pi$
$571$	−8055.84	−0.590414	−0.295207	+	0.955433i	$0.595389\pi$
$572$	−250.257	−0.0182933
$573$	3005.78	0.219142
$574$	0	0
$575$	5265.56	0.381894
$576$	−38.6435	−0.00279539
$577$	21456.9	1.54812	0.774059	−	0.633114i	$-0.218223\pi$
$577$	21456.9	1.54812	0.774059	+	0.633114i	$0.218223\pi$
$578$	−35638.9	−2.56468
$579$	12164.9	0.873153
$580$	−2133.76	−0.152758
$581$	0	0
$582$	10644.0	0.758087
$583$	539.596	0.0383324
$584$	−7746.76	−0.548910
$585$	−857.802	−0.0606252
$586$	24412.1	1.72091
$587$	−20156.3	−1.41728	−0.708638	−	0.705572i	$-0.750690\pi$
$587$	−20156.3	−1.41728	−0.708638	+	0.705572i	$0.750690\pi$
$588$	0	0
$589$	−10132.0	−0.708797
$590$	13429.1	0.937066
$591$	15420.7	1.07330
$592$	−7748.30	−0.537928
$593$	−599.307	−0.0415018	−0.0207509	−	0.999785i	$-0.506606\pi$
$593$	−599.307	−0.0415018	−0.0207509	+	0.999785i	$0.506606\pi$
$594$	−280.086	−0.0193469
$595$	0	0
$596$	10464.2	0.719177
$597$	1756.89	0.120444
$598$	−14177.3	−0.969485
$599$	−5493.05	−0.374691	−0.187346	−	0.982294i	$-0.559988\pi$
$599$	−5493.05	−0.374691	−0.187346	+	0.982294i	$0.559988\pi$
$600$	−935.165	−0.0636299
$601$	−24292.8	−1.64879	−0.824396	−	0.566014i	$-0.808485\pi$
$601$	−24292.8	−1.64879	−0.824396	+	0.566014i	$0.808485\pi$
$602$	0	0
$603$	−2789.93	−0.188416
$604$	−9402.82	−0.633436
$605$	6611.85	0.444314
$606$	1365.19	0.0915131
$607$	−3029.50	−0.202576	−0.101288	−	0.994857i	$-0.532296\pi$
$607$	−3029.50	−0.202576	−0.101288	+	0.994857i	$0.532296\pi$
$608$	−19549.3	−1.30400
$609$	0	0
$610$	3509.01	0.232911
$611$	−9025.87	−0.597623
$612$	−4926.85	−0.325419
$613$	−19339.6	−1.27426	−0.637129	−	0.770757i	$-0.719878\pi$
$613$	−19339.6	−1.27426	−0.637129	+	0.770757i	$0.719878\pi$
$614$	−26992.4	−1.77414
$615$	7366.69	0.483014
$616$	0	0
$617$	−5743.91	−0.374783	−0.187391	−	0.982285i	$-0.560003\pi$
$617$	−5743.91	−0.374783	−0.187391	+	0.982285i	$0.560003\pi$
$618$	−8538.35	−0.555765
$619$	8243.35	0.535264	0.267632	−	0.963521i	$-0.413759\pi$
$619$	8243.35	0.535264	0.267632	+	0.963521i	$0.413759\pi$
$620$	−2107.24	−0.136498
$621$	−5686.81	−0.367478
$622$	26815.4	1.72861
$623$	0	0
$624$	4562.37	0.292694
$625$	625.000	0.0400000
$626$	−32231.6	−2.05788
$627$	−946.856	−0.0603091
$628$	2652.13	0.168521
$629$	−11897.1	−0.754162
$630$	0	0
$631$	−4376.56	−0.276114	−0.138057	−	0.990424i	$-0.544086\pi$
$631$	−4376.56	−0.276114	−0.138057	+	0.990424i	$0.544086\pi$
$632$	−308.762	−0.0194334
$633$	3165.48	0.198762
$634$	17407.8	1.09046
$635$	9379.92	0.586190
$636$	2462.49	0.153528
$637$	0	0
$638$	990.613	0.0614714
$639$	5991.23	0.370907
$640$	7202.71	0.444863
$641$	11836.6	0.729357	0.364678	−	0.931133i	$-0.381179\pi$
$641$	11836.6	0.729357	0.364678	+	0.931133i	$0.381179\pi$
$642$	−8153.86	−0.501257
$643$	−1448.21	−0.0888209	−0.0444104	−	0.999013i	$-0.514141\pi$
$643$	−1448.21	−0.0888209	−0.0444104	+	0.999013i	$0.514141\pi$
$644$	0	0
$645$	−645.058	−0.0393785
$646$	−46472.0	−2.83037
$647$	8732.95	0.530646	0.265323	−	0.964160i	$-0.414521\pi$
$647$	8732.95	0.530646	0.265323	+	0.964160i	$0.414521\pi$
$648$	1009.98	0.0612279
$649$	−2234.49	−0.135149
$650$	−1682.78	−0.101545
$651$	0	0
$652$	9736.37	0.584824
$653$	−21978.4	−1.31712	−0.658562	−	0.752527i	$-0.728835\pi$
$653$	−21978.4	−1.31712	−0.658562	+	0.752527i	$0.728835\pi$
$654$	−8271.91	−0.494583
$655$	1821.01	0.108630
$656$	−39181.1	−2.33196
$657$	−5591.59	−0.332038
$658$	0	0
$659$	−27761.7	−1.64103	−0.820516	−	0.571623i	$-0.806314\pi$
$659$	−27761.7	−1.64103	−0.820516	+	0.571623i	$0.806314\pi$
$660$	−196.926	−0.0116141
$661$	8573.72	0.504507	0.252254	−	0.967661i	$-0.418828\pi$
$661$	8573.72	0.504507	0.252254	+	0.967661i	$0.418828\pi$
$662$	−4313.86	−0.253267
$663$	7005.27	0.410350
$664$	5071.39	0.296398
$665$	0	0
$666$	−3086.51	−0.179579
$667$	20113.2	1.16760
$668$	−3572.87	−0.206944
$669$	14027.6	0.810668
$670$	−5473.11	−0.315589
$671$	−583.868	−0.0335916
$672$	0	0
$673$	27159.2	1.55559	0.777795	−	0.628518i	$-0.216338\pi$
$673$	27159.2	1.55559	0.777795	+	0.628518i	$0.216338\pi$
$674$	30879.1	1.76472
$675$	−675.000	−0.0384900
$676$	−8194.26	−0.466219
$677$	1392.30	0.0790404	0.0395202	−	0.999219i	$-0.487417\pi$
$677$	1392.30	0.0790404	0.0395202	+	0.999219i	$0.487417\pi$
$678$	−11818.5	−0.669448
$679$	0	0
$680$	7637.06	0.430688
$681$	16329.3	0.918857
$682$	978.302	0.0549283
$683$	−8675.09	−0.486007	−0.243004	−	0.970025i	$-0.578133\pi$
$683$	−8675.09	−0.486007	−0.243004	+	0.970025i	$0.578133\pi$
$684$	−4321.05	−0.241549
$685$	−8015.66	−0.447099
$686$	0	0
$687$	−1608.91	−0.0893504
$688$	3430.86	0.190117
$689$	−3501.30	−0.193598
$690$	−11156.0	−0.615511
$691$	21426.0	1.17957	0.589785	−	0.807561i	$-0.299213\pi$
$691$	21426.0	1.17957	0.589785	+	0.807561i	$0.299213\pi$
$692$	6454.65	0.354579
$693$	0	0
$694$	−16206.3	−0.886433
$695$	12155.6	0.663438
$696$	−3572.11	−0.194541
$697$	−60160.4	−3.26935
$698$	−14088.8	−0.763997
$699$	550.470	0.0297864
$700$	0	0
$701$	24840.5	1.33839	0.669197	−	0.743085i	$-0.266638\pi$
$701$	24840.5	1.33839	0.669197	+	0.743085i	$0.266638\pi$
$702$	1817.40	0.0977116
$703$	−10434.2	−0.559793
$704$	12.6139	0.000675288 0
$705$	−7102.41	−0.379422
$706$	8532.45	0.454848
$707$	0	0
$708$	−10197.3	−0.541295
$709$	12525.0	0.663450	0.331725	−	0.943376i	$-0.392369\pi$
$709$	12525.0	0.663450	0.331725	+	0.943376i	$0.392369\pi$
$710$	11753.2	0.621255
$711$	−222.863	−0.0117553
$712$	−3263.74	−0.171789
$713$	19863.3	1.04332
$714$	0	0
$715$	280.000	0.0146453
$716$	14941.6	0.779881
$717$	−1929.65	−0.100508
$718$	9732.66	0.505877
$719$	−28085.0	−1.45674	−0.728369	−	0.685185i	$-0.759721\pi$
$719$	−28085.0	−1.45674	−0.728369	+	0.685185i	$0.759721\pi$
$720$	3590.11	0.185827
$721$	0	0
$722$	−16537.9	−0.852460
$723$	−17266.8	−0.888189
$724$	−10063.1	−0.516562
$725$	2387.35	0.122295
$726$	−14008.4	−0.716115
$727$	14326.2	0.730851	0.365426	−	0.930841i	$-0.380923\pi$
$727$	14326.2	0.730851	0.365426	+	0.930841i	$0.380923\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−10969.2	−0.556150
$731$	5267.89	0.266539
$732$	−2664.53	−0.134541
$733$	−6727.85	−0.339016	−0.169508	−	0.985529i	$-0.554218\pi$
$733$	−6727.85	−0.339016	−0.169508	+	0.985529i	$0.554218\pi$
$734$	39240.8	1.97331
$735$	0	0
$736$	38325.5	1.91943
$737$	910.677	0.0455159
$738$	−15607.6	−0.778490
$739$	−3418.51	−0.170165	−0.0850826	−	0.996374i	$-0.527115\pi$
$739$	−3418.51	−0.170165	−0.0850826	+	0.996374i	$0.527115\pi$
$740$	−2170.10	−0.107803
$741$	6143.91	0.304591
$742$	0	0
$743$	8095.50	0.399724	0.199862	−	0.979824i	$-0.435951\pi$
$743$	8095.50	0.399724	0.199862	+	0.979824i	$0.435951\pi$
$744$	−3527.72	−0.173834
$745$	−11707.9	−0.575762
$746$	−21508.4	−1.05560
$747$	3660.51	0.179292
$748$	1608.20	0.0786119
$749$	0	0
$750$	−1324.17	−0.0644693
$751$	13446.8	0.653371	0.326686	−	0.945133i	$-0.394068\pi$
$751$	13446.8	0.653371	0.326686	+	0.945133i	$0.394068\pi$
$752$	37775.4	1.83182
$753$	−15396.8	−0.745141
$754$	−6427.84	−0.310462
$755$	10520.4	0.507119
$756$	0	0
$757$	−2593.24	−0.124508	−0.0622541	−	0.998060i	$-0.519829\pi$
$757$	−2593.24	−0.124508	−0.0622541	+	0.998060i	$0.519829\pi$
$758$	−14069.0	−0.674156
$759$	1856.26	0.0887722
$760$	6698.02	0.319688
$761$	−27079.4	−1.28992	−0.644959	−	0.764217i	$-0.723125\pi$
$761$	−27079.4	−1.28992	−0.644959	+	0.764217i	$0.723125\pi$
$762$	−19873.0	−0.944782
$763$	0	0
$764$	−4477.48	−0.212028
$765$	5512.41	0.260525
$766$	1124.58	0.0530451
$767$	14499.0	0.682568
$768$	−15363.3	−0.721842
$769$	−2138.72	−0.100292	−0.0501458	−	0.998742i	$-0.515969\pi$
$769$	−2138.72	−0.100292	−0.0501458	+	0.998742i	$0.515969\pi$
$770$	0	0
$771$	15125.2	0.706513
$772$	−18121.1	−0.844810
$773$	−25864.0	−1.20345	−0.601724	−	0.798704i	$-0.705519\pi$
$773$	−25864.0	−1.20345	−0.601724	+	0.798704i	$0.705519\pi$
$774$	1366.67	0.0634676
$775$	2357.69	0.109278
$776$	12528.4	0.579566
$777$	0	0
$778$	−13720.1	−0.632247
$779$	−52763.1	−2.42675
$780$	1277.80	0.0586572
$781$	−1955.63	−0.0896006
$782$	91106.2	4.16618
$783$	−2578.34	−0.117679
$784$	0	0
$785$	−2967.33	−0.134916
$786$	−3858.14	−0.175083
$787$	32371.3	1.46621	0.733107	−	0.680113i	$-0.238069\pi$
$787$	32371.3	1.46621	0.733107	+	0.680113i	$0.238069\pi$
$788$	−22971.0	−1.03846
$789$	−22731.0	−1.02566
$790$	−437.200	−0.0196897
$791$	0	0
$792$	−329.673	−0.0147909
$793$	3788.57	0.169654
$794$	16970.8	0.758526
$795$	−2755.16	−0.122912
$796$	−2617.11	−0.116534
$797$	−2024.33	−0.0899691	−0.0449845	−	0.998988i	$-0.514324\pi$
$797$	−2024.33	−0.0899691	−0.0449845	+	0.998988i	$0.514324\pi$
$798$	0	0
$799$	58002.1	2.56817
$800$	4549.08	0.201043
$801$	−2355.76	−0.103916
$802$	−12777.7	−0.562589
$803$	1825.18	0.0802109
$804$	4155.95	0.182300
$805$	0	0
$806$	−6347.95	−0.277416
$807$	3069.29	0.133884
$808$	1606.88	0.0699628
$809$	12391.7	0.538526	0.269263	−	0.963067i	$-0.413220\pi$
$809$	12391.7	0.538526	0.269263	+	0.963067i	$0.413220\pi$
$810$	1430.11	0.0620356
$811$	−14654.5	−0.634511	−0.317256	−	0.948340i	$-0.602761\pi$
$811$	−14654.5	−0.634511	−0.317256	+	0.948340i	$0.602761\pi$
$812$	0	0
$813$	−6755.94	−0.291441
$814$	1007.49	0.0433813
$815$	−10893.5	−0.468201
$816$	−29318.7	−1.25780
$817$	4620.16	0.197844
$818$	−7447.33	−0.318325
$819$	0	0
$820$	−10973.6	−0.467335
$821$	23887.9	1.01546	0.507731	−	0.861516i	$-0.330485\pi$
$821$	23887.9	1.01546	0.507731	+	0.861516i	$0.330485\pi$
$822$	16982.6	0.720604
$823$	−4008.41	−0.169774	−0.0848871	−	0.996391i	$-0.527053\pi$
$823$	−4008.41	−0.169774	−0.0848871	+	0.996391i	$0.527053\pi$
$824$	−10050.0	−0.424889
$825$	220.331	0.00929810
$826$	0	0
$827$	−45110.4	−1.89679	−0.948394	−	0.317096i	$-0.897292\pi$
$827$	−45110.4	−1.89679	−0.948394	+	0.317096i	$0.897292\pi$
$828$	8471.21	0.355549
$829$	−16165.4	−0.677260	−0.338630	−	0.940920i	$-0.609964\pi$
$829$	−16165.4	−0.677260	−0.338630	+	0.940920i	$0.609964\pi$
$830$	7180.97	0.300307
$831$	25892.2	1.08085
$832$	−81.8481	−0.00341054
$833$	0	0
$834$	−25753.8	−1.06928
$835$	3997.51	0.165676
$836$	1410.46	0.0583514
$837$	−2546.30	−0.105153
$838$	−24385.7	−1.00524
$839$	25244.4	1.03878	0.519388	−	0.854538i	$-0.326160\pi$
$839$	25244.4	1.03878	0.519388	+	0.854538i	$0.326160\pi$
$840$	0	0
$841$	−15269.9	−0.626096
$842$	34066.7	1.39432
$843$	22564.9	0.921916
$844$	−4715.37	−0.192310
$845$	9168.15	0.373247
$846$	15047.7	0.611526
$847$	0	0
$848$	14653.8	0.593412
$849$	44.4506	0.00179687
$850$	10813.9	0.436370
$851$	20455.8	0.823990
$852$	−8924.68	−0.358867
$853$	30168.1	1.21094	0.605472	−	0.795867i	$-0.292984\pi$
$853$	30168.1	1.21094	0.605472	+	0.795867i	$0.292984\pi$
$854$	0	0
$855$	4834.61	0.193380
$856$	−9597.44	−0.383217
$857$	13393.6	0.533857	0.266929	−	0.963716i	$-0.413991\pi$
$857$	13393.6	0.533857	0.266929	+	0.963716i	$0.413991\pi$
$858$	−593.230	−0.0236043
$859$	−19060.4	−0.757081	−0.378541	−	0.925585i	$-0.623574\pi$
$859$	−19060.4	−0.757081	−0.378541	+	0.925585i	$0.623574\pi$
$860$	960.894	0.0381002
$861$	0	0
$862$	45914.3	1.81421
$863$	−9466.86	−0.373413	−0.186707	−	0.982416i	$-0.559781\pi$
$863$	−9466.86	−0.373413	−0.186707	+	0.982416i	$0.559781\pi$
$864$	−4913.00	−0.193453
$865$	−7221.79	−0.283871
$866$	25975.2	1.01925
$867$	−30278.3	−1.18605
$868$	0	0
$869$	72.7461	0.00283975
$870$	−5058.03	−0.197107
$871$	−5909.15	−0.229878
$872$	−9736.39	−0.378115
$873$	9042.97	0.350582
$874$	79903.8	3.09243
$875$	0	0
$876$	8329.37	0.321259
$877$	37740.6	1.45315	0.726573	−	0.687090i	$-0.241112\pi$
$877$	37740.6	1.45315	0.726573	+	0.687090i	$0.241112\pi$
$878$	24397.3	0.937778
$879$	20740.2	0.795845
$880$	−1171.87	−0.0448905
$881$	−25991.5	−0.993957	−0.496979	−	0.867763i	$-0.665557\pi$
$881$	−25991.5	−0.993957	−0.496979	+	0.867763i	$0.665557\pi$
$882$	0	0
$883$	39420.3	1.50238	0.751189	−	0.660087i	$-0.229481\pi$
$883$	39420.3	1.50238	0.751189	+	0.660087i	$0.229481\pi$
$884$	−10435.2	−0.397030
$885$	11409.2	0.433352
$886$	52305.0	1.98332
$887$	−46005.2	−1.74149	−0.870745	−	0.491735i	$-0.836363\pi$
$887$	−46005.2	−1.74149	−0.870745	+	0.491735i	$0.836363\pi$
$888$	−3632.95	−0.137290
$889$	0	0
$890$	−4621.38	−0.174055
$891$	−237.957	−0.00894710
$892$	−20895.8	−0.784353
$893$	50870.2	1.90628
$894$	24805.2	0.927975
$895$	−16717.5	−0.624361
$896$	0	0
$897$	−12044.8	−0.448345
$898$	37622.6	1.39809
$899$	9005.81	0.334105
$900$	1005.50	0.0372406
$901$	22500.1	0.831950
$902$	5094.58	0.188061
$903$	0	0
$904$	−13910.8	−0.511801
$905$	11259.1	0.413551
$906$	−22289.2	−0.817340
$907$	−2838.97	−0.103932	−0.0519661	−	0.998649i	$-0.516549\pi$
$907$	−2838.97	−0.103932	−0.0519661	+	0.998649i	$0.516549\pi$
$908$	−24324.6	−0.889030
$909$	1159.84	0.0423208
$910$	0	0
$911$	39890.9	1.45076	0.725382	−	0.688347i	$-0.241663\pi$
$911$	39890.9	1.45076	0.725382	+	0.688347i	$0.241663\pi$
$912$	−25713.7	−0.933626
$913$	−1194.85	−0.0433119
$914$	20675.3	0.748226
$915$	2981.21	0.107711
$916$	2396.67	0.0864500
$917$	0	0
$918$	−11679.0	−0.419897
$919$	−646.475	−0.0232048	−0.0116024	−	0.999933i	$-0.503693\pi$
$919$	−646.475	−0.0232048	−0.0116024	+	0.999933i	$0.503693\pi$
$920$	−13131.1	−0.470566
$921$	−22932.4	−0.820463
$922$	11316.3	0.404213
$923$	12689.6	0.452528
$924$	0	0
$925$	2428.02	0.0863056
$926$	−1312.37	−0.0465737
$927$	−7254.07	−0.257017
$928$	17376.4	0.614665
$929$	−51188.2	−1.80778	−0.903892	−	0.427760i	$-0.859303\pi$
$929$	−51188.2	−1.80778	−0.903892	+	0.427760i	$0.859303\pi$
$930$	−4995.17	−0.176127
$931$	0	0
$932$	−819.993	−0.0288195
$933$	22782.0	0.799409
$934$	−69747.8	−2.44349
$935$	−1799.34	−0.0629355
$936$	2139.16	0.0747017
$937$	−29786.1	−1.03849	−0.519247	−	0.854624i	$-0.673788\pi$
$937$	−29786.1	−1.03849	−0.519247	+	0.854624i	$0.673788\pi$
$938$	0	0
$939$	−27383.5	−0.951680
$940$	10579.9	0.367105
$941$	44817.4	1.55261	0.776304	−	0.630358i	$-0.217092\pi$
$941$	44817.4	1.55261	0.776304	+	0.630358i	$0.217092\pi$
$942$	6286.82	0.217448
$943$	103439.	3.57206
$944$	−60682.0	−2.09219
$945$	0	0
$946$	−446.103	−0.0153320
$947$	54697.1	1.87689	0.938446	−	0.345425i	$-0.112265\pi$
$947$	54697.1	1.87689	0.938446	+	0.345425i	$0.112265\pi$
$948$	331.983	0.0113737
$949$	−11843.2	−0.405105
$950$	9484.24	0.323905
$951$	14789.4	0.504290
$952$	0	0
$953$	−7577.51	−0.257565	−0.128783	−	0.991673i	$-0.541107\pi$
$953$	−7577.51	−0.257565	−0.128783	+	0.991673i	$0.541107\pi$
$954$	5837.29	0.198102
$955$	5009.63	0.169746
$956$	2874.46	0.0972454
$957$	841.612	0.0284278
$958$	−73313.4	−2.47249
$959$	0	0
$960$	−64.4059	−0.00216530
$961$	−20897.1	−0.701457
$962$	−6537.32	−0.219097
$963$	−6927.41	−0.231810
$964$	25721.1	0.859357
$965$	20274.8	0.676342
$966$	0	0
$967$	50779.0	1.68867	0.844334	−	0.535817i	$-0.179996\pi$
$967$	50779.0	1.68867	0.844334	+	0.535817i	$0.179996\pi$
$968$	−16488.5	−0.547478
$969$	−39482.0	−1.30892
$970$	17739.9	0.587212
$971$	15313.2	0.506102	0.253051	−	0.967453i	$-0.418566\pi$
$971$	15313.2	0.506102	0.253051	+	0.967453i	$0.418566\pi$
$972$	−1085.94	−0.0358348
$973$	0	0
$974$	−62315.9	−2.05003
$975$	−1429.67	−0.0469601
$976$	−15856.1	−0.520021
$977$	46620.4	1.52663	0.763316	−	0.646025i	$-0.223570\pi$
$977$	46620.4	1.52663	0.763316	+	0.646025i	$0.223570\pi$
$978$	23079.9	0.754615
$979$	768.957	0.0251031
$980$	0	0
$981$	−7027.70	−0.228723
$982$	19906.6	0.646889
$983$	2824.37	0.0916414	0.0458207	−	0.998950i	$-0.485410\pi$
$983$	2824.37	0.0916414	0.0458207	+	0.998950i	$0.485410\pi$
$984$	−18370.9	−0.595165
$985$	25701.1	0.831377
$986$	41306.6	1.33415
$987$	0	0
$988$	−9152.11	−0.294704
$989$	−9057.59	−0.291218
$990$	−466.810	−0.0149860
$991$	16951.4	0.543370	0.271685	−	0.962386i	$-0.412419\pi$
$991$	16951.4	0.543370	0.271685	+	0.962386i	$0.412419\pi$
$992$	17160.5	0.549239
$993$	−3665.00	−0.117125
$994$	0	0
$995$	2928.15	0.0932952
$996$	−5452.79	−0.173472
$997$	−23847.8	−0.757540	−0.378770	−	0.925491i	$-0.623653\pi$
$997$	−23847.8	−0.757540	−0.378770	+	0.925491i	$0.623653\pi$
$998$	61703.4	1.95710
$999$	−2622.26	−0.0830476

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.4.a.p.1.1		2
3.2	odd	2		2205.4.a.z.1.2		2
7.6	odd	2		105.4.a.f.1.1	✓	2
21.20	even	2		315.4.a.i.1.2		2
28.27	even	2		1680.4.a.bg.1.1		2
35.13	even	4		525.4.d.h.274.3		4
35.27	even	4		525.4.d.h.274.2		4
35.34	odd	2		525.4.a.k.1.2		2
105.104	even	2		1575.4.a.w.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.a.f.1.1	✓	2	7.6	odd	2
315.4.a.i.1.2		2	21.20	even	2
525.4.a.k.1.2		2	35.34	odd	2
525.4.d.h.274.2		4	35.27	even	4
525.4.d.h.274.3		4	35.13	even	4
735.4.a.p.1.1		2	1.1	even	1	trivial
1575.4.a.w.1.1		2	105.104	even	2
1680.4.a.bg.1.1		2	28.27	even	2
2205.4.a.z.1.2		2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	735.a (trivial)

\(f(q)\)	\(=\)	\(q-3.53113 q^{2} -3.00000 q^{3} +4.46887 q^{4} -5.00000 q^{5} +10.5934 q^{6} +12.4689 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.53113 q^{2} -3.00000 q^{3} +4.46887 q^{4} -5.00000 q^{5} +10.5934 q^{6} +12.4689 q^{8} +9.00000 q^{9} +17.6556 q^{10} -2.93774 q^{11} -13.4066 q^{12} +19.0623 q^{13} +15.0000 q^{15} -79.7802 q^{16} -122.498 q^{17} -31.7802 q^{18} -107.436 q^{19} -22.3444 q^{20} +10.3735 q^{22} +210.623 q^{23} -37.4066 q^{24} +25.0000 q^{25} -67.3113 q^{26} -27.0000 q^{27} +95.4942 q^{29} -52.9669 q^{30} +94.3074 q^{31} +181.963 q^{32} +8.81323 q^{33} +432.556 q^{34} +40.2198 q^{36} +97.1206 q^{37} +379.370 q^{38} -57.1868 q^{39} -62.3444 q^{40} +491.113 q^{41} -43.0039 q^{43} -13.1284 q^{44} -45.0000 q^{45} -743.735 q^{46} -473.494 q^{47} +239.340 q^{48} -88.2782 q^{50} +367.494 q^{51} +85.1868 q^{52} -183.677 q^{53} +95.3405 q^{54} +14.6887 q^{55} +322.307 q^{57} -337.202 q^{58} +760.615 q^{59} +67.0331 q^{60} +198.747 q^{61} -333.012 q^{62} -4.29373 q^{64} -95.3113 q^{65} -31.1206 q^{66} -309.992 q^{67} -547.428 q^{68} -631.868 q^{69} +665.693 q^{71} +112.220 q^{72} -621.288 q^{73} -342.945 q^{74} -75.0000 q^{75} -480.117 q^{76} +201.934 q^{78} -24.7626 q^{79} +398.901 q^{80} +81.0000 q^{81} -1734.18 q^{82} +406.724 q^{83} +612.490 q^{85} +151.852 q^{86} -286.483 q^{87} -36.6303 q^{88} -261.751 q^{89} +158.901 q^{90} +941.245 q^{92} -282.922 q^{93} +1671.97 q^{94} +537.179 q^{95} -545.889 q^{96} +1004.77 q^{97} -26.4397 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 6 q^{3} + 17 q^{4} - 10 q^{5} - 3 q^{6} + 33 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q + q^2 - 6 * q^3 + 17 * q^4 - 10 * q^5 - 3 * q^6 + 33 * q^8 + 18 * q^9	\( 2 q + q^{2} - 6 q^{3} + 17 q^{4} - 10 q^{5} - 3 q^{6} + 33 q^{8} + 18 q^{9} - 5 q^{10} - 22 q^{11} - 51 q^{12} + 22 q^{13} + 30 q^{15} - 87 q^{16} - 116 q^{17} + 9 q^{18} - 102 q^{19} - 85 q^{20} - 76 q^{22} + 260 q^{23} - 99 q^{24} + 50 q^{25} - 54 q^{26} - 54 q^{27} - 196 q^{29} + 15 q^{30} - 150 q^{31} - 15 q^{32} + 66 q^{33} + 462 q^{34} + 153 q^{36} - 96 q^{37} + 404 q^{38} - 66 q^{39} - 165 q^{40} + 176 q^{41} - 344 q^{43} - 252 q^{44} - 90 q^{45} - 520 q^{46} - 560 q^{47} + 261 q^{48} + 25 q^{50} + 348 q^{51} + 122 q^{52} + 326 q^{53} - 27 q^{54} + 110 q^{55} + 306 q^{57} - 1658 q^{58} + 844 q^{59} + 255 q^{60} + 204 q^{61} - 1440 q^{62} - 839 q^{64} - 110 q^{65} + 228 q^{66} - 104 q^{67} - 466 q^{68} - 780 q^{69} + 1670 q^{71} + 297 q^{72} + 386 q^{73} - 1218 q^{74} - 150 q^{75} - 412 q^{76} + 162 q^{78} - 888 q^{79} + 435 q^{80} + 162 q^{81} - 3162 q^{82} - 928 q^{83} + 580 q^{85} - 1212 q^{86} + 588 q^{87} - 428 q^{88} - 588 q^{89} - 45 q^{90} + 1560 q^{92} + 450 q^{93} + 1280 q^{94} + 510 q^{95} + 45 q^{96} - 522 q^{97} - 198 q^{99}+O(q^{100}) \) 2 * q + q^2 - 6 * q^3 + 17 * q^4 - 10 * q^5 - 3 * q^6 + 33 * q^8 + 18 * q^9 - 5 * q^10 - 22 * q^11 - 51 * q^12 + 22 * q^13 + 30 * q^15 - 87 * q^16 - 116 * q^17 + 9 * q^18 - 102 * q^19 - 85 * q^20 - 76 * q^22 + 260 * q^23 - 99 * q^24 + 50 * q^25 - 54 * q^26 - 54 * q^27 - 196 * q^29 + 15 * q^30 - 150 * q^31 - 15 * q^32 + 66 * q^33 + 462 * q^34 + 153 * q^36 - 96 * q^37 + 404 * q^38 - 66 * q^39 - 165 * q^40 + 176 * q^41 - 344 * q^43 - 252 * q^44 - 90 * q^45 - 520 * q^46 - 560 * q^47 + 261 * q^48 + 25 * q^50 + 348 * q^51 + 122 * q^52 + 326 * q^53 - 27 * q^54 + 110 * q^55 + 306 * q^57 - 1658 * q^58 + 844 * q^59 + 255 * q^60 + 204 * q^61 - 1440 * q^62 - 839 * q^64 - 110 * q^65 + 228 * q^66 - 104 * q^67 - 466 * q^68 - 780 * q^69 + 1670 * q^71 + 297 * q^72 + 386 * q^73 - 1218 * q^74 - 150 * q^75 - 412 * q^76 + 162 * q^78 - 888 * q^79 + 435 * q^80 + 162 * q^81 - 3162 * q^82 - 928 * q^83 + 580 * q^85 - 1212 * q^86 + 588 * q^87 - 428 * q^88 - 588 * q^89 - 45 * q^90 + 1560 * q^92 + 450 * q^93 + 1280 * q^94 + 510 * q^95 + 45 * q^96 - 522 * q^97 - 198 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more