LMFDB - Embedded newform 1815.4.a.bg.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,4,Mod(1,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, 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("1815.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1815.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:	$107.088466660$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 69 x^{10} + 157 x^{9} + 1812 x^{8} - 2703 x^{7} - 22379 x^{6} + 16453 x^{5} + \cdots + 196416 $ x^12 - 3x^11 - 69x^10 + 157x^9 + 1812x^8 - 2703x^7 - 22379x^6 + 16453x^5 + 129167x^4 - 22672x^3 - 298084x^2 - 19392*x + 196416
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 5\cdot 11^{2} $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$2.97307$ of defining polynomial
Character	$\chi$	$=$	1815.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.97307 q^{2} +3.00000 q^{3} -4.10701 q^{4} -5.00000 q^{5} +5.91920 q^{6} +17.1107 q^{7} -23.8879 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+1.97307 q^{2} +3.00000 q^{3} -4.10701 q^{4} -5.00000 q^{5} +5.91920 q^{6} +17.1107 q^{7} -23.8879 q^{8} +9.00000 q^{9} -9.86533 q^{10} -12.3210 q^{12} +70.7140 q^{13} +33.7606 q^{14} -15.0000 q^{15} -14.2763 q^{16} -95.8300 q^{17} +17.7576 q^{18} -151.060 q^{19} +20.5351 q^{20} +51.3322 q^{21} -25.9835 q^{23} -71.6638 q^{24} +25.0000 q^{25} +139.523 q^{26} +27.0000 q^{27} -70.2740 q^{28} +284.669 q^{29} -29.5960 q^{30} +17.3656 q^{31} +162.935 q^{32} -189.079 q^{34} -85.5537 q^{35} -36.9631 q^{36} -228.799 q^{37} -298.052 q^{38} +212.142 q^{39} +119.440 q^{40} +160.561 q^{41} +101.282 q^{42} -122.859 q^{43} -45.0000 q^{45} -51.2672 q^{46} -192.327 q^{47} -42.8290 q^{48} -50.2226 q^{49} +49.3266 q^{50} -287.490 q^{51} -290.423 q^{52} -297.192 q^{53} +53.2728 q^{54} -408.740 q^{56} -453.180 q^{57} +561.670 q^{58} -626.285 q^{59} +61.6052 q^{60} +377.848 q^{61} +34.2635 q^{62} +153.997 q^{63} +435.693 q^{64} -353.570 q^{65} +474.172 q^{67} +393.575 q^{68} -77.9506 q^{69} -168.803 q^{70} +167.148 q^{71} -214.991 q^{72} -477.974 q^{73} -451.436 q^{74} +75.0000 q^{75} +620.406 q^{76} +418.570 q^{78} -241.991 q^{79} +71.3817 q^{80} +81.0000 q^{81} +316.797 q^{82} -940.488 q^{83} -210.822 q^{84} +479.150 q^{85} -242.409 q^{86} +854.007 q^{87} -586.224 q^{89} -88.7879 q^{90} +1209.97 q^{91} +106.715 q^{92} +52.0969 q^{93} -379.474 q^{94} +755.301 q^{95} +488.806 q^{96} -1089.71 q^{97} -99.0925 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 9 q^{2} + 36 q^{3} + 57 q^{4} - 60 q^{5} - 27 q^{6} - 21 q^{7} - 123 q^{8} + 108 q^{9}+O(q^{10}) $ 12 * q - 9 * q^2 + 36 * q^3 + 57 * q^4 - 60 * q^5 - 27 * q^6 - 21 * q^7 - 123 * q^8 + 108 * q^9	\( 12 q - 9 q^{2} + 36 q^{3} + 57 q^{4} - 60 q^{5} - 27 q^{6} - 21 q^{7} - 123 q^{8} + 108 q^{9} + 45 q^{10} + 171 q^{12} - 78 q^{13} + 262 q^{14} - 180 q^{15} + 225 q^{16} - 313 q^{17} - 81 q^{18} - 51 q^{19} - 285 q^{20} - 63 q^{21} - 34 q^{23} - 369 q^{24} + 300 q^{25} + 28 q^{26} + 324 q^{27} - 376 q^{28} - 31 q^{29} + 135 q^{30} + 655 q^{31} - 1578 q^{32} - 10 q^{34} + 105 q^{35} + 513 q^{36} + 84 q^{37} - 1076 q^{38} - 234 q^{39} + 615 q^{40} - 1463 q^{41} + 786 q^{42} + 111 q^{43} - 540 q^{45} + q^{46} + 278 q^{47} + 675 q^{48} - 325 q^{49} - 225 q^{50} - 939 q^{51} - 1957 q^{52} + 517 q^{53} - 243 q^{54} + 1543 q^{56} - 153 q^{57} + 442 q^{58} - 308 q^{59} - 855 q^{60} - 604 q^{61} - 1773 q^{62} - 189 q^{63} + 4323 q^{64} + 390 q^{65} - 357 q^{67} - 2192 q^{68} - 102 q^{69} - 1310 q^{70} - 620 q^{71} - 1107 q^{72} - 1892 q^{73} - 581 q^{74} + 900 q^{75} - 378 q^{76} + 84 q^{78} - 415 q^{79} - 1125 q^{80} + 972 q^{81} - 2802 q^{82} - 3158 q^{83} - 1128 q^{84} + 1565 q^{85} + 747 q^{86} - 93 q^{87} + 1563 q^{89} + 405 q^{90} + 1434 q^{91} - 3466 q^{92} + 1965 q^{93} + 3 q^{94} + 255 q^{95} - 4734 q^{96} + 714 q^{97} - 6586 q^{98}+O(q^{100}) \) 12 * q - 9 * q^2 + 36 * q^3 + 57 * q^4 - 60 * q^5 - 27 * q^6 - 21 * q^7 - 123 * q^8 + 108 * q^9 + 45 * q^10 + 171 * q^12 - 78 * q^13 + 262 * q^14 - 180 * q^15 + 225 * q^16 - 313 * q^17 - 81 * q^18 - 51 * q^19 - 285 * q^20 - 63 * q^21 - 34 * q^23 - 369 * q^24 + 300 * q^25 + 28 * q^26 + 324 * q^27 - 376 * q^28 - 31 * q^29 + 135 * q^30 + 655 * q^31 - 1578 * q^32 - 10 * q^34 + 105 * q^35 + 513 * q^36 + 84 * q^37 - 1076 * q^38 - 234 * q^39 + 615 * q^40 - 1463 * q^41 + 786 * q^42 + 111 * q^43 - 540 * q^45 + q^46 + 278 * q^47 + 675 * q^48 - 325 * q^49 - 225 * q^50 - 939 * q^51 - 1957 * q^52 + 517 * q^53 - 243 * q^54 + 1543 * q^56 - 153 * q^57 + 442 * q^58 - 308 * q^59 - 855 * q^60 - 604 * q^61 - 1773 * q^62 - 189 * q^63 + 4323 * q^64 + 390 * q^65 - 357 * q^67 - 2192 * q^68 - 102 * q^69 - 1310 * q^70 - 620 * q^71 - 1107 * q^72 - 1892 * q^73 - 581 * q^74 + 900 * q^75 - 378 * q^76 + 84 * q^78 - 415 * q^79 - 1125 * q^80 + 972 * q^81 - 2802 * q^82 - 3158 * q^83 - 1128 * q^84 + 1565 * q^85 + 747 * q^86 - 93 * q^87 + 1563 * q^89 + 405 * q^90 + 1434 * q^91 - 3466 * q^92 + 1965 * q^93 + 3 * q^94 + 255 * q^95 - 4734 * q^96 + 714 * q^97 - 6586 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.97307	0.697584	0.348792	−	0.937200i	$-0.386592\pi$
$2$	1.97307	0.697584	0.348792	+	0.937200i	$0.386592\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−4.10701	−0.513377
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	5.91920	0.402750
$7$	17.1107	0.923893	0.461947	−	0.886908i	$-0.347151\pi$
$7$	17.1107	0.923893	0.461947	+	0.886908i	$0.347151\pi$
$8$	−23.8879	−1.05571
$9$	9.00000	0.333333
$10$	−9.86533	−0.311969
$11$	0	0
$11$	0	0
$12$	−12.3210	−0.296398
$13$	70.7140	1.50866	0.754328	−	0.656498i	$-0.227963\pi$
$13$	70.7140	1.50866	0.754328	+	0.656498i	$0.227963\pi$
$14$	33.7606	0.644493
$15$	−15.0000	−0.258199
$16$	−14.2763	−0.223068
$17$	−95.8300	−1.36719	−0.683594	−	0.729863i	$-0.739584\pi$
$17$	−95.8300	−1.36719	−0.683594	+	0.729863i	$0.739584\pi$
$18$	17.7576	0.232528
$19$	−151.060	−1.82398	−0.911989	−	0.410215i	$-0.865454\pi$
$19$	−151.060	−1.82398	−0.911989	+	0.410215i	$0.865454\pi$
$20$	20.5351	0.229589
$21$	51.3322	0.533410
$22$	0	0
$23$	−25.9835	−0.235563	−0.117781	−	0.993040i	$-0.537578\pi$
$23$	−25.9835	−0.235563	−0.117781	+	0.993040i	$0.537578\pi$
$24$	−71.6638	−0.609513
$25$	25.0000	0.200000
$26$	139.523	1.05241
$27$	27.0000	0.192450
$28$	−70.2740	−0.474305
$29$	284.669	1.82282	0.911409	−	0.411503i	$-0.134996\pi$
$29$	284.669	1.82282	0.911409	+	0.411503i	$0.134996\pi$
$30$	−29.5960	−0.180115
$31$	17.3656	0.100612	0.0503058	−	0.998734i	$-0.483980\pi$
$31$	17.3656	0.100612	0.0503058	+	0.998734i	$0.483980\pi$
$32$	162.935	0.900099
$33$	0	0
$34$	−189.079	−0.953728
$35$	−85.5537	−0.413178
$36$	−36.9631	−0.171126
$37$	−228.799	−1.01660	−0.508302	−	0.861179i	$-0.669727\pi$
$37$	−228.799	−1.01660	−0.508302	+	0.861179i	$0.669727\pi$
$38$	−298.052	−1.27238
$39$	212.142	0.871023
$40$	119.440	0.472127
$41$	160.561	0.611594	0.305797	−	0.952097i	$-0.401077\pi$
$41$	160.561	0.611594	0.305797	+	0.952097i	$0.401077\pi$
$42$	101.282	0.372098
$43$	−122.859	−0.435717	−0.217858	−	0.975980i	$-0.569907\pi$
$43$	−122.859	−0.435717	−0.217858	+	0.975980i	$0.569907\pi$
$44$	0	0
$45$	−45.0000	−0.149071
$46$	−51.2672	−0.164325
$47$	−192.327	−0.596889	−0.298444	−	0.954427i	$-0.596468\pi$
$47$	−192.327	−0.596889	−0.298444	+	0.954427i	$0.596468\pi$
$48$	−42.8290	−0.128788
$49$	−50.2226	−0.146422
$50$	49.3266	0.139517
$51$	−287.490	−0.789346
$52$	−290.423	−0.774509
$53$	−297.192	−0.770234	−0.385117	−	0.922868i	$-0.625839\pi$
$53$	−297.192	−0.770234	−0.385117	+	0.922868i	$0.625839\pi$
$54$	53.2728	0.134250
$55$	0	0
$56$	−408.740	−0.975361
$57$	−453.180	−1.05307
$58$	561.670	1.27157
$59$	−626.285	−1.38195	−0.690977	−	0.722876i	$-0.742820\pi$
$59$	−626.285	−1.38195	−0.690977	+	0.722876i	$0.742820\pi$
$60$	61.6052	0.132553
$61$	377.848	0.793089	0.396545	−	0.918015i	$-0.370209\pi$
$61$	377.848	0.793089	0.396545	+	0.918015i	$0.370209\pi$
$62$	34.2635	0.0701851
$63$	153.997	0.307964
$64$	435.693	0.850962
$65$	−353.570	−0.674691
$66$	0	0
$67$	474.172	0.864617	0.432309	−	0.901726i	$-0.357699\pi$
$67$	474.172	0.864617	0.432309	+	0.901726i	$0.357699\pi$
$68$	393.575	0.701882
$69$	−77.9506	−0.136002
$70$	−168.803	−0.288226
$71$	167.148	0.279391	0.139696	−	0.990194i	$-0.455388\pi$
$71$	167.148	0.279391	0.139696	+	0.990194i	$0.455388\pi$
$72$	−214.991	−0.351902
$73$	−477.974	−0.766338	−0.383169	−	0.923678i	$-0.625167\pi$
$73$	−477.974	−0.766338	−0.383169	+	0.923678i	$0.625167\pi$
$74$	−451.436	−0.709167
$75$	75.0000	0.115470
$76$	620.406	0.936387
$77$	0	0
$78$	418.570	0.607612
$79$	−241.991	−0.344634	−0.172317	−	0.985042i	$-0.555125\pi$
$79$	−241.991	−0.344634	−0.172317	+	0.985042i	$0.555125\pi$
$80$	71.3817	0.0997590
$81$	81.0000	0.111111
$82$	316.797	0.426638
$83$	−940.488	−1.24376	−0.621879	−	0.783113i	$-0.713631\pi$
$83$	−940.488	−1.24376	−0.621879	+	0.783113i	$0.713631\pi$
$84$	−210.822	−0.273840
$85$	479.150	0.611425
$86$	−242.409	−0.303949
$87$	854.007	1.05240
$88$	0	0
$89$	−586.224	−0.698199	−0.349099	−	0.937086i	$-0.613512\pi$
$89$	−586.224	−0.698199	−0.349099	+	0.937086i	$0.613512\pi$
$90$	−88.7879	−0.103990
$91$	1209.97	1.39384
$92$	106.715	0.120932
$93$	52.0969	0.0580882
$94$	−379.474	−0.416380
$95$	755.301	0.815708
$96$	488.806	0.519672
$97$	−1089.71	−1.14066	−0.570329	−	0.821417i	$-0.693184\pi$
$97$	−1089.71	−1.14066	−0.570329	+	0.821417i	$0.693184\pi$
$98$	−99.0925	−0.102141
$99$	0	0
$100$	−102.675	−0.102675
$101$	−1761.93	−1.73583	−0.867914	−	0.496714i	$-0.834540\pi$
$101$	−1761.93	−1.73583	−0.867914	+	0.496714i	$0.834540\pi$
$102$	−567.237	−0.550635
$103$	792.200	0.757843	0.378921	−	0.925429i	$-0.376295\pi$
$103$	792.200	0.757843	0.378921	+	0.925429i	$0.376295\pi$
$104$	−1689.21	−1.59270
$105$	−256.661	−0.238548
$106$	−586.379	−0.537303
$107$	733.083	0.662335	0.331167	−	0.943572i	$-0.392558\pi$
$107$	733.083	0.662335	0.331167	+	0.943572i	$0.392558\pi$
$108$	−110.889	−0.0987994
$109$	2157.31	1.89571	0.947855	−	0.318701i	$-0.103246\pi$
$109$	2157.31	1.89571	0.947855	+	0.318701i	$0.103246\pi$
$110$	0	0
$111$	−686.398	−0.586937
$112$	−244.279	−0.206091
$113$	304.067	0.253135	0.126567	−	0.991958i	$-0.459604\pi$
$113$	304.067	0.253135	0.126567	+	0.991958i	$0.459604\pi$
$114$	−894.155	−0.734607
$115$	129.918	0.105347
$116$	−1169.14	−0.935792
$117$	636.426	0.502885
$118$	−1235.70	−0.964030
$119$	−1639.72	−1.26314
$120$	358.319	0.272582
$121$	0	0
$122$	745.519	0.553247
$123$	481.682	0.353104
$124$	−71.3209	−0.0516517
$125$	−125.000	−0.0894427
$126$	303.845	0.214831
$127$	−2446.53	−1.70940	−0.854701	−	0.519121i	$-0.826259\pi$
$127$	−2446.53	−1.70940	−0.854701	+	0.519121i	$0.826259\pi$
$128$	−443.832	−0.306481
$129$	−368.577	−0.251561
$130$	−697.616	−0.470654
$131$	−539.293	−0.359681	−0.179841	−	0.983696i	$-0.557558\pi$
$131$	−539.293	−0.359681	−0.179841	+	0.983696i	$0.557558\pi$
$132$	0	0
$133$	−2584.75	−1.68516
$134$	935.573	0.603143
$135$	−135.000	−0.0860663
$136$	2289.18	1.44335
$137$	−443.186	−0.276379	−0.138189	−	0.990406i	$-0.544128\pi$
$137$	−443.186	−0.276379	−0.138189	+	0.990406i	$0.544128\pi$
$138$	−153.802	−0.0948730
$139$	−2593.37	−1.58250	−0.791248	−	0.611495i	$-0.790568\pi$
$139$	−2593.37	−1.58250	−0.791248	+	0.611495i	$0.790568\pi$
$140$	351.370	0.212116
$141$	−576.981	−0.344614
$142$	329.793	0.194899
$143$	0	0
$144$	−128.487	−0.0743559
$145$	−1423.34	−0.815189
$146$	−943.075	−0.534585
$147$	−150.668	−0.0845366
$148$	939.681	0.521901
$149$	−2408.66	−1.32433	−0.662165	−	0.749358i	$-0.730362\pi$
$149$	−2408.66	−1.32433	−0.662165	+	0.749358i	$0.730362\pi$
$150$	147.980	0.0805501
$151$	−229.080	−0.123459	−0.0617295	−	0.998093i	$-0.519662\pi$
$151$	−229.080	−0.123459	−0.0617295	+	0.998093i	$0.519662\pi$
$152$	3608.51	1.92559
$153$	−862.470	−0.455729
$154$	0	0
$155$	−86.8282	−0.0449949
$156$	−871.269	−0.447163
$157$	−3428.12	−1.74263	−0.871317	−	0.490720i	$-0.836734\pi$
$157$	−3428.12	−1.74263	−0.871317	+	0.490720i	$0.836734\pi$
$158$	−477.464	−0.240411
$159$	−891.575	−0.444695
$160$	−814.676	−0.402536
$161$	−444.598	−0.217635
$162$	159.818	0.0775093
$163$	634.283	0.304791	0.152395	−	0.988320i	$-0.451301\pi$
$163$	634.283	0.304791	0.152395	+	0.988320i	$0.451301\pi$
$164$	−659.425	−0.313978
$165$	0	0
$166$	−1855.64	−0.867626
$167$	−810.666	−0.375636	−0.187818	−	0.982204i	$-0.560142\pi$
$167$	−810.666	−0.375636	−0.187818	+	0.982204i	$0.560142\pi$
$168$	−1226.22	−0.563125
$169$	2803.46	1.27604
$170$	945.394	0.426520
$171$	−1359.54	−0.607992
$172$	504.584	0.223687
$173$	−3001.09	−1.31889	−0.659446	−	0.751752i	$-0.729209\pi$
$173$	−3001.09	−1.31889	−0.659446	+	0.751752i	$0.729209\pi$
$174$	1685.01	0.734140
$175$	427.768	0.184779
$176$	0	0
$177$	−1878.85	−0.797872
$178$	−1156.66	−0.487052
$179$	3527.70	1.47303	0.736516	−	0.676420i	$-0.236470\pi$
$179$	3527.70	1.47303	0.736516	+	0.676420i	$0.236470\pi$
$180$	184.816	0.0765297
$181$	−3234.52	−1.32829	−0.664144	−	0.747605i	$-0.731204\pi$
$181$	−3234.52	−1.32829	−0.664144	+	0.747605i	$0.731204\pi$
$182$	2387.35	0.972318
$183$	1133.54	0.457890
$184$	620.693	0.248685
$185$	1144.00	0.454639
$186$	102.791	0.0405214
$187$	0	0
$188$	789.889	0.306429
$189$	461.990	0.177803
$190$	1490.26	0.569024
$191$	−2990.91	−1.13306	−0.566530	−	0.824041i	$-0.691714\pi$
$191$	−2990.91	−1.13306	−0.566530	+	0.824041i	$0.691714\pi$
$192$	1307.08	0.491303
$193$	1317.47	0.491365	0.245683	−	0.969350i	$-0.420988\pi$
$193$	1317.47	0.491365	0.245683	+	0.969350i	$0.420988\pi$
$194$	−2150.08	−0.795704
$195$	−1060.71	−0.389533
$196$	206.265	0.0751694
$197$	−1990.34	−0.719826	−0.359913	−	0.932986i	$-0.617194\pi$
$197$	−1990.34	−0.719826	−0.359913	+	0.932986i	$0.617194\pi$
$198$	0	0
$199$	3408.48	1.21418	0.607088	−	0.794635i	$-0.292338\pi$
$199$	3408.48	1.21418	0.607088	+	0.794635i	$0.292338\pi$
$200$	−597.198	−0.211141
$201$	1422.52	0.499187
$202$	−3476.40	−1.21089
$203$	4870.90	1.68409
$204$	1180.73	0.405232
$205$	−802.804	−0.273513
$206$	1563.06	0.528659
$207$	−233.852	−0.0785209
$208$	−1009.54	−0.336533
$209$	0	0
$210$	−506.409	−0.166407
$211$	4087.94	1.33377	0.666886	−	0.745160i	$-0.267627\pi$
$211$	4087.94	1.33377	0.666886	+	0.745160i	$0.267627\pi$
$212$	1220.57	0.395420
$213$	501.443	0.161307
$214$	1446.42	0.462034
$215$	614.295	0.194858
$216$	−644.974	−0.203171
$217$	297.139	0.0929544
$218$	4256.51	1.32242
$219$	−1433.92	−0.442445
$220$	0	0
$221$	−6776.52	−2.06262
$222$	−1354.31	−0.409438
$223$	3817.75	1.14644	0.573218	−	0.819403i	$-0.305695\pi$
$223$	3817.75	1.14644	0.573218	+	0.819403i	$0.305695\pi$
$224$	2787.94	0.831595
$225$	225.000	0.0666667
$226$	599.944	0.176583
$227$	−4434.31	−1.29654	−0.648272	−	0.761409i	$-0.724508\pi$
$227$	−4434.31	−1.29654	−0.648272	+	0.761409i	$0.724508\pi$
$228$	1861.22	0.540624
$229$	−1373.66	−0.396394	−0.198197	−	0.980162i	$-0.563509\pi$
$229$	−1373.66	−0.396394	−0.198197	+	0.980162i	$0.563509\pi$
$230$	256.336	0.0734883
$231$	0	0
$232$	−6800.15	−1.92436
$233$	−3664.65	−1.03038	−0.515191	−	0.857075i	$-0.672279\pi$
$233$	−3664.65	−1.03038	−0.515191	+	0.857075i	$0.672279\pi$
$234$	1255.71	0.350805
$235$	961.635	0.266937
$236$	2572.16	0.709463
$237$	−725.973	−0.198975
$238$	−3235.28	−0.881143
$239$	−3872.18	−1.04799	−0.523997	−	0.851720i	$-0.675560\pi$
$239$	−3872.18	−1.04799	−0.523997	+	0.851720i	$0.675560\pi$
$240$	214.145	0.0575959
$241$	−666.479	−0.178140	−0.0890698	−	0.996025i	$-0.528389\pi$
$241$	−666.479	−0.178140	−0.0890698	+	0.996025i	$0.528389\pi$
$242$	0	0
$243$	243.000	0.0641500
$244$	−1551.83	−0.407154
$245$	251.113	0.0654817
$246$	950.390	0.246320
$247$	−10682.1	−2.75175
$248$	−414.829	−0.106216
$249$	−2821.46	−0.718084
$250$	−246.633	−0.0623938
$251$	1285.33	0.323224	0.161612	−	0.986854i	$-0.448331\pi$
$251$	1285.33	0.323224	0.161612	+	0.986854i	$0.448331\pi$
$252$	−632.466	−0.158102
$253$	0	0
$254$	−4827.15	−1.19245
$255$	1437.45	0.353006
$256$	−4361.25	−1.06476
$257$	−4242.52	−1.02973	−0.514866	−	0.857271i	$-0.672158\pi$
$257$	−4242.52	−1.02973	−0.514866	+	0.857271i	$0.672158\pi$
$258$	−727.227	−0.175485
$259$	−3914.92	−0.939234
$260$	1452.12	0.346371
$261$	2562.02	0.607606
$262$	−1064.06	−0.250908
$263$	4192.29	0.982920	0.491460	−	0.870900i	$-0.336463\pi$
$263$	4192.29	0.982920	0.491460	+	0.870900i	$0.336463\pi$
$264$	0	0
$265$	1485.96	0.344459
$266$	−5099.88	−1.17554
$267$	−1758.67	−0.403105
$268$	−1947.43	−0.443874
$269$	538.610	0.122080	0.0610402	−	0.998135i	$-0.480558\pi$
$269$	538.610	0.122080	0.0610402	+	0.998135i	$0.480558\pi$
$270$	−266.364	−0.0600385
$271$	−6481.51	−1.45286	−0.726428	−	0.687243i	$-0.758821\pi$
$271$	−6481.51	−1.45286	−0.726428	+	0.687243i	$0.758821\pi$
$272$	1368.10	0.304976
$273$	3629.90	0.804732
$274$	−874.434	−0.192797
$275$	0	0
$276$	320.144	0.0698204
$277$	−4670.75	−1.01313	−0.506567	−	0.862201i	$-0.669086\pi$
$277$	−4670.75	−1.01313	−0.506567	+	0.862201i	$0.669086\pi$
$278$	−5116.89	−1.10392
$279$	156.291	0.0335372
$280$	2043.70	0.436195
$281$	3841.80	0.815597	0.407798	−	0.913072i	$-0.366297\pi$
$281$	3841.80	0.815597	0.407798	+	0.913072i	$0.366297\pi$
$282$	−1138.42	−0.240397
$283$	8612.20	1.80898	0.904491	−	0.426492i	$-0.140251\pi$
$283$	8612.20	1.80898	0.904491	+	0.426492i	$0.140251\pi$
$284$	−686.477	−0.143433
$285$	2265.90	0.470949
$286$	0	0
$287$	2747.31	0.565048
$288$	1466.42	0.300033
$289$	4270.39	0.869202
$290$	−2808.35	−0.568662
$291$	−3269.14	−0.658559
$292$	1963.05	0.393420
$293$	3176.68	0.633391	0.316695	−	0.948527i	$-0.397427\pi$
$293$	3176.68	0.633391	0.316695	+	0.948527i	$0.397427\pi$
$294$	−297.277	−0.0589713
$295$	3131.42	0.618029
$296$	5465.54	1.07324
$297$	0	0
$298$	−4752.45	−0.923832
$299$	−1837.40	−0.355383
$300$	−308.026	−0.0592796
$301$	−2102.21	−0.402556
$302$	−451.991	−0.0861230
$303$	−5285.79	−1.00218
$304$	2156.59	0.406871
$305$	−1889.24	−0.354680
$306$	−1701.71	−0.317909
$307$	1989.59	0.369875	0.184938	−	0.982750i	$-0.440792\pi$
$307$	1989.59	0.369875	0.184938	+	0.982750i	$0.440792\pi$
$308$	0	0
$309$	2376.60	0.437541
$310$	−171.318	−0.0313877
$311$	−6920.60	−1.26184	−0.630918	−	0.775849i	$-0.717322\pi$
$311$	−6920.60	−1.26184	−0.630918	+	0.775849i	$0.717322\pi$
$312$	−5067.63	−0.919545
$313$	2028.06	0.366239	0.183120	−	0.983091i	$-0.441380\pi$
$313$	2028.06	0.366239	0.183120	+	0.983091i	$0.441380\pi$
$314$	−6763.90	−1.21563
$315$	−769.983	−0.137726
$316$	993.860	0.176927
$317$	4652.77	0.824370	0.412185	−	0.911100i	$-0.364766\pi$
$317$	4652.77	0.824370	0.412185	+	0.911100i	$0.364766\pi$
$318$	−1759.14	−0.310212
$319$	0	0
$320$	−2178.46	−0.380562
$321$	2199.25	0.382399
$322$	−877.220	−0.151819
$323$	14476.1	2.49372
$324$	−332.668	−0.0570418
$325$	1767.85	0.301731
$326$	1251.48	0.212617
$327$	6471.92	1.09449
$328$	−3835.46	−0.645665
$329$	−3290.86	−0.551461
$330$	0	0
$331$	4063.67	0.674802	0.337401	−	0.941361i	$-0.390452\pi$
$331$	4063.67	0.674802	0.337401	+	0.941361i	$0.390452\pi$
$332$	3862.60	0.638517
$333$	−2059.19	−0.338868
$334$	−1599.50	−0.262038
$335$	−2370.86	−0.386669
$336$	−732.836	−0.118987
$337$	4963.14	0.802254	0.401127	−	0.916023i	$-0.368619\pi$
$337$	4963.14	0.802254	0.401127	+	0.916023i	$0.368619\pi$
$338$	5531.42	0.890147
$339$	912.200	0.146147
$340$	−1967.88	−0.313891
$341$	0	0
$342$	−2682.46	−0.424126
$343$	−6728.33	−1.05917
$344$	2934.85	0.459989
$345$	389.753	0.0608220
$346$	−5921.34	−0.920038
$347$	−462.942	−0.0716197	−0.0358099	−	0.999359i	$-0.511401\pi$
$347$	−462.942	−0.0716197	−0.0358099	+	0.999359i	$0.511401\pi$
$348$	−3507.42	−0.540280
$349$	−2791.95	−0.428223	−0.214112	−	0.976809i	$-0.568686\pi$
$349$	−2791.95	−0.428223	−0.214112	+	0.976809i	$0.568686\pi$
$350$	844.015	0.128899
$351$	1909.28	0.290341
$352$	0	0
$353$	2988.45	0.450592	0.225296	−	0.974290i	$-0.427665\pi$
$353$	2988.45	0.450592	0.225296	+	0.974290i	$0.427665\pi$
$354$	−3707.10	−0.556583
$355$	−835.738	−0.124948
$356$	2407.63	0.358439
$357$	−4919.17	−0.729271
$358$	6960.38	1.02756
$359$	−8218.36	−1.20821	−0.604106	−	0.796904i	$-0.706470\pi$
$359$	−8218.36	−1.20821	−0.604106	+	0.796904i	$0.706470\pi$
$360$	1074.96	0.157376
$361$	15960.2	2.32689
$362$	−6381.92	−0.926592
$363$	0	0
$364$	−4969.35	−0.715563
$365$	2389.87	0.342717
$366$	2236.56	0.319417
$367$	5218.56	0.742253	0.371126	−	0.928582i	$-0.378972\pi$
$367$	5218.56	0.742253	0.371126	+	0.928582i	$0.378972\pi$
$368$	370.950	0.0525465
$369$	1445.05	0.203865
$370$	2257.18	0.317149
$371$	−5085.17	−0.711614
$372$	−213.963	−0.0298211
$373$	−1411.21	−0.195898	−0.0979489	−	0.995191i	$-0.531228\pi$
$373$	−1411.21	−0.195898	−0.0979489	+	0.995191i	$0.531228\pi$
$374$	0	0
$375$	−375.000	−0.0516398
$376$	4594.29	0.630140
$377$	20130.1	2.75000
$378$	911.536	0.124033
$379$	2433.82	0.329860	0.164930	−	0.986305i	$-0.447260\pi$
$379$	2433.82	0.329860	0.164930	+	0.986305i	$0.447260\pi$
$380$	−3102.03	−0.418765
$381$	−7339.58	−0.986923
$382$	−5901.26	−0.790405
$383$	8813.26	1.17581	0.587907	−	0.808929i	$-0.299952\pi$
$383$	8813.26	1.17581	0.587907	+	0.808929i	$0.299952\pi$
$384$	−1331.50	−0.176947
$385$	0	0
$386$	2599.45	0.342768
$387$	−1105.73	−0.145239
$388$	4475.47	0.585587
$389$	−4944.47	−0.644459	−0.322230	−	0.946662i	$-0.604432\pi$
$389$	−4944.47	−0.644459	−0.322230	+	0.946662i	$0.604432\pi$
$390$	−2092.85	−0.271732
$391$	2490.00	0.322058
$392$	1199.71	0.154578
$393$	−1617.88	−0.207662
$394$	−3927.07	−0.502139
$395$	1209.96	0.154125
$396$	0	0
$397$	556.393	0.0703390	0.0351695	−	0.999381i	$-0.488803\pi$
$397$	556.393	0.0703390	0.0351695	+	0.999381i	$0.488803\pi$
$398$	6725.16	0.846990
$399$	−7754.25	−0.972928
$400$	−356.909	−0.0446136
$401$	4607.95	0.573840	0.286920	−	0.957955i	$-0.407369\pi$
$401$	4607.95	0.573840	0.286920	+	0.957955i	$0.407369\pi$
$402$	2806.72	0.348225
$403$	1227.99	0.151788
$404$	7236.27	0.891134
$405$	−405.000	−0.0496904
$406$	9610.60	1.17479
$407$	0	0
$408$	6867.54	0.833318
$409$	−12903.5	−1.55999	−0.779996	−	0.625785i	$-0.784779\pi$
$409$	−12903.5	−1.55999	−0.779996	+	0.625785i	$0.784779\pi$
$410$	−1583.98	−0.190799
$411$	−1329.56	−0.159567
$412$	−3253.58	−0.389059
$413$	−10716.2	−1.27678
$414$	−461.405	−0.0547749
$415$	4702.44	0.556226
$416$	11521.8	1.35794
$417$	−7780.12	−0.913655
$418$	0	0
$419$	4111.63	0.479394	0.239697	−	0.970848i	$-0.422952\pi$
$419$	4111.63	0.479394	0.239697	+	0.970848i	$0.422952\pi$
$420$	1054.11	0.122465
$421$	15370.0	1.77931	0.889654	−	0.456636i	$-0.150946\pi$
$421$	15370.0	1.77931	0.889654	+	0.456636i	$0.150946\pi$
$422$	8065.78	0.930417
$423$	−1730.94	−0.198963
$424$	7099.29	0.813142
$425$	−2395.75	−0.273438
$426$	989.379	0.112525
$427$	6465.26	0.732730
$428$	−3010.78	−0.340027
$429$	0	0
$430$	1212.04	0.135930
$431$	5542.58	0.619436	0.309718	−	0.950829i	$-0.399765\pi$
$431$	5542.58	0.619436	0.309718	+	0.950829i	$0.399765\pi$
$432$	−385.461	−0.0429294
$433$	6282.40	0.697259	0.348629	−	0.937261i	$-0.386647\pi$
$433$	6282.40	0.697259	0.348629	+	0.937261i	$0.386647\pi$
$434$	586.275	0.0648435
$435$	−4270.03	−0.470649
$436$	−8860.09	−0.973214
$437$	3925.08	0.429661
$438$	−2829.22	−0.308643
$439$	2570.99	0.279514	0.139757	−	0.990186i	$-0.455368\pi$
$439$	2570.99	0.279514	0.139757	+	0.990186i	$0.455368\pi$
$440$	0	0
$441$	−452.003	−0.0488072
$442$	−13370.5	−1.43885
$443$	14527.9	1.55810	0.779052	−	0.626959i	$-0.215701\pi$
$443$	14527.9	1.55810	0.779052	+	0.626959i	$0.215701\pi$
$444$	2819.04	0.301320
$445$	2931.12	0.312244
$446$	7532.67	0.799736
$447$	−7225.99	−0.764603
$448$	7455.02	0.786198
$449$	5399.07	0.567478	0.283739	−	0.958902i	$-0.408425\pi$
$449$	5399.07	0.567478	0.283739	+	0.958902i	$0.408425\pi$
$450$	443.940	0.0465056
$451$	0	0
$452$	−1248.81	−0.129953
$453$	−687.241	−0.0712791
$454$	−8749.18	−0.904448
$455$	−6049.84	−0.623343
$456$	10825.5	1.11174
$457$	6254.12	0.640165	0.320083	−	0.947390i	$-0.396289\pi$
$457$	6254.12	0.640165	0.320083	+	0.947390i	$0.396289\pi$
$458$	−2710.32	−0.276518
$459$	−2587.41	−0.263115
$460$	−533.574	−0.0540826
$461$	−8098.00	−0.818137	−0.409069	−	0.912504i	$-0.634146\pi$
$461$	−8098.00	−0.818137	−0.409069	+	0.912504i	$0.634146\pi$
$462$	0	0
$463$	13462.7	1.35133	0.675666	−	0.737208i	$-0.263856\pi$
$463$	13462.7	1.35133	0.675666	+	0.737208i	$0.263856\pi$
$464$	−4064.03	−0.406612
$465$	−260.485	−0.0259778
$466$	−7230.59	−0.718778
$467$	559.264	0.0554168	0.0277084	−	0.999616i	$-0.491179\pi$
$467$	559.264	0.0554168	0.0277084	+	0.999616i	$0.491179\pi$
$468$	−2613.81	−0.258170
$469$	8113.44	0.798814
$470$	1897.37	0.186211
$471$	−10284.4	−1.00611
$472$	14960.6	1.45894
$473$	0	0
$474$	−1432.39	−0.138802
$475$	−3776.50	−0.364795
$476$	6734.36	0.648464
$477$	−2674.73	−0.256745
$478$	−7640.07	−0.731064
$479$	7950.36	0.758374	0.379187	−	0.925320i	$-0.376204\pi$
$479$	7950.36	0.758374	0.379187	+	0.925320i	$0.376204\pi$
$480$	−2444.03	−0.232404
$481$	−16179.3	−1.53371
$482$	−1315.01	−0.124267
$483$	−1333.79	−0.125652
$484$	0	0
$485$	5448.57	0.510118
$486$	479.455	0.0447500
$487$	7057.00	0.656639	0.328320	−	0.944567i	$-0.393518\pi$
$487$	7057.00	0.656639	0.328320	+	0.944567i	$0.393518\pi$
$488$	−9026.00	−0.837270
$489$	1902.85	0.175971
$490$	495.462	0.0456790
$491$	4969.44	0.456757	0.228378	−	0.973572i	$-0.426658\pi$
$491$	4969.44	0.456757	0.228378	+	0.973572i	$0.426658\pi$
$492$	−1978.27	−0.181275
$493$	−27279.8	−2.49213
$494$	−21076.4	−1.91958
$495$	0	0
$496$	−247.918	−0.0224432
$497$	2860.02	0.258128
$498$	−5566.93	−0.500924
$499$	−10288.0	−0.922957	−0.461479	−	0.887151i	$-0.652681\pi$
$499$	−10288.0	−0.922957	−0.461479	+	0.887151i	$0.652681\pi$
$500$	513.377	0.0459178
$501$	−2432.00	−0.216874
$502$	2536.04	0.225476
$503$	−8600.96	−0.762421	−0.381211	−	0.924488i	$-0.624493\pi$
$503$	−8600.96	−0.762421	−0.381211	+	0.924488i	$0.624493\pi$
$504$	−3678.66	−0.325120
$505$	8809.65	0.776286
$506$	0	0
$507$	8410.39	0.736723
$508$	10047.9	0.877567
$509$	−1734.44	−0.151037	−0.0755183	−	0.997144i	$-0.524061\pi$
$509$	−1734.44	−0.151037	−0.0755183	+	0.997144i	$0.524061\pi$
$510$	2836.18	0.246252
$511$	−8178.50	−0.708014
$512$	−5054.38	−0.436277
$513$	−4078.62	−0.351025
$514$	−8370.76	−0.718324
$515$	−3961.00	−0.338918
$516$	1513.75	0.129146
$517$	0	0
$518$	−7724.40	−0.655194
$519$	−9003.26	−0.761463
$520$	8446.05	0.712277
$521$	−9104.52	−0.765597	−0.382799	−	0.923832i	$-0.625040\pi$
$521$	−9104.52	−0.765597	−0.382799	+	0.923832i	$0.625040\pi$
$522$	5055.03	0.423856
$523$	439.205	0.0367210	0.0183605	−	0.999831i	$-0.494155\pi$
$523$	439.205	0.0367210	0.0183605	+	0.999831i	$0.494155\pi$
$524$	2214.88	0.184652
$525$	1283.31	0.106682
$526$	8271.67	0.685669
$527$	−1664.15	−0.137555
$528$	0	0
$529$	−11491.9	−0.944510
$530$	2931.89	0.240289
$531$	−5636.56	−0.460652
$532$	10615.6	0.865122
$533$	11353.9	0.922685
$534$	−3469.98	−0.281200
$535$	−3665.42	−0.296205
$536$	−11327.0	−0.912783
$537$	10583.1	0.850455
$538$	1062.71	0.0851613
$539$	0	0
$540$	554.447	0.0441844
$541$	14399.6	1.14434	0.572171	−	0.820134i	$-0.306101\pi$
$541$	14399.6	1.14434	0.572171	+	0.820134i	$0.306101\pi$
$542$	−12788.5	−1.01349
$543$	−9703.57	−0.766887
$544$	−15614.1	−1.23060
$545$	−10786.5	−0.847788
$546$	7162.04	0.561368
$547$	−962.703	−0.0752509	−0.0376254	−	0.999292i	$-0.511979\pi$
$547$	−962.703	−0.0752509	−0.0376254	+	0.999292i	$0.511979\pi$
$548$	1820.17	0.141886
$549$	3400.63	0.264363
$550$	0	0
$551$	−43002.1	−3.32478
$552$	1862.08	0.143579
$553$	−4140.65	−0.318405
$554$	−9215.69	−0.706746
$555$	3431.99	0.262486
$556$	10651.0	0.812417
$557$	7460.63	0.567535	0.283768	−	0.958893i	$-0.408416\pi$
$557$	7460.63	0.567535	0.283768	+	0.958893i	$0.408416\pi$
$558$	308.372	0.0233950
$559$	−8687.85	−0.657347
$560$	1221.39	0.0921666
$561$	0	0
$562$	7580.13	0.568947
$563$	−18197.1	−1.36220	−0.681099	−	0.732191i	$-0.738498\pi$
$563$	−18197.1	−1.36220	−0.681099	+	0.732191i	$0.738498\pi$
$564$	2369.67	0.176917
$565$	−1520.33	−0.113205
$566$	16992.4	1.26192
$567$	1385.97	0.102655
$568$	−3992.81	−0.294955
$569$	−22405.0	−1.65073	−0.825365	−	0.564600i	$-0.809031\pi$
$569$	−22405.0	−1.65073	−0.825365	+	0.564600i	$0.809031\pi$
$570$	4470.77	0.328526
$571$	3948.38	0.289377	0.144689	−	0.989477i	$-0.453782\pi$
$571$	3948.38	0.289377	0.144689	+	0.989477i	$0.453782\pi$
$572$	0	0
$573$	−8972.72	−0.654173
$574$	5420.63	0.394168
$575$	−649.589	−0.0471126
$576$	3921.23	0.283654
$577$	−9431.11	−0.680454	−0.340227	−	0.940343i	$-0.610504\pi$
$577$	−9431.11	−0.680454	−0.340227	+	0.940343i	$0.610504\pi$
$578$	8425.76	0.606341
$579$	3952.41	0.283690
$580$	5845.70	0.418499
$581$	−16092.4	−1.14910
$582$	−6450.24	−0.459400
$583$	0	0
$584$	11417.8	0.809029
$585$	−3182.13	−0.224897
$586$	6267.79	0.441843
$587$	−1312.29	−0.0922726	−0.0461363	−	0.998935i	$-0.514691\pi$
$587$	−1312.29	−0.0922726	−0.0461363	+	0.998935i	$0.514691\pi$
$588$	618.795	0.0433991
$589$	−2623.26	−0.183513
$590$	6178.50	0.431127
$591$	−5971.01	−0.415592
$592$	3266.42	0.226772
$593$	−12334.9	−0.854188	−0.427094	−	0.904207i	$-0.640463\pi$
$593$	−12334.9	−0.854188	−0.427094	+	0.904207i	$0.640463\pi$
$594$	0	0
$595$	8198.61	0.564891
$596$	9892.41	0.679880
$597$	10225.5	0.701005
$598$	−3625.31	−0.247910
$599$	669.273	0.0456523	0.0228262	−	0.999739i	$-0.492734\pi$
$599$	669.273	0.0456523	0.0228262	+	0.999739i	$0.492734\pi$
$600$	−1791.59	−0.121903
$601$	14104.3	0.957282	0.478641	−	0.878011i	$-0.341129\pi$
$601$	14104.3	0.957282	0.478641	+	0.878011i	$0.341129\pi$
$602$	−4147.79	−0.280816
$603$	4267.55	0.288206
$604$	940.836	0.0633809
$605$	0	0
$606$	−10429.2	−0.699105
$607$	9848.13	0.658522	0.329261	−	0.944239i	$-0.393200\pi$
$607$	9848.13	0.658522	0.329261	+	0.944239i	$0.393200\pi$
$608$	−24613.0	−1.64176
$609$	14612.7	0.972309
$610$	−3727.59	−0.247419
$611$	−13600.2	−0.900500
$612$	3542.18	0.233961
$613$	12699.5	0.836747	0.418374	−	0.908275i	$-0.362600\pi$
$613$	12699.5	0.836747	0.418374	+	0.908275i	$0.362600\pi$
$614$	3925.59	0.258019
$615$	−2408.41	−0.157913
$616$	0	0
$617$	20943.8	1.36656	0.683279	−	0.730157i	$-0.260553\pi$
$617$	20943.8	1.36656	0.683279	+	0.730157i	$0.260553\pi$
$618$	4689.19	0.305221
$619$	−2213.89	−0.143754	−0.0718771	−	0.997413i	$-0.522899\pi$
$619$	−2213.89	−0.143754	−0.0718771	+	0.997413i	$0.522899\pi$
$620$	356.605	0.0230993
$621$	−701.556	−0.0453341
$622$	−13654.8	−0.880237
$623$	−10030.7	−0.645061
$624$	−3028.61	−0.194297
$625$	625.000	0.0400000
$626$	4001.50	0.255483
$627$	0	0
$628$	14079.3	0.894628
$629$	21925.8	1.38989
$630$	−1519.23	−0.0960753
$631$	4281.58	0.270122	0.135061	−	0.990837i	$-0.456877\pi$
$631$	4281.58	0.270122	0.135061	+	0.990837i	$0.456877\pi$
$632$	5780.67	0.363833
$633$	12263.8	0.770053
$634$	9180.21	0.575067
$635$	12232.6	0.764468
$636$	3661.71	0.228296
$637$	−3551.44	−0.220900
$638$	0	0
$639$	1504.33	0.0931304
$640$	2219.16	0.137063
$641$	3510.70	0.216325	0.108162	−	0.994133i	$-0.465503\pi$
$641$	3510.70	0.216325	0.108162	+	0.994133i	$0.465503\pi$
$642$	4339.26	0.266756
$643$	−6948.79	−0.426180	−0.213090	−	0.977033i	$-0.568353\pi$
$643$	−6948.79	−0.426180	−0.213090	+	0.977033i	$0.568353\pi$
$644$	1825.97	0.111729
$645$	1842.89	0.112502
$646$	28562.3	1.73958
$647$	−5925.70	−0.360067	−0.180034	−	0.983660i	$-0.557621\pi$
$647$	−5925.70	−0.360067	−0.180034	+	0.983660i	$0.557621\pi$
$648$	−1934.92	−0.117301
$649$	0	0
$650$	3488.08	0.210483
$651$	891.417	0.0536673
$652$	−2605.01	−0.156473
$653$	18164.5	1.08856	0.544282	−	0.838902i	$-0.316802\pi$
$653$	18164.5	1.08856	0.544282	+	0.838902i	$0.316802\pi$
$654$	12769.5	0.763498
$655$	2696.46	0.160854
$656$	−2292.22	−0.136427
$657$	−4301.77	−0.255446
$658$	−6493.08	−0.384691
$659$	−4165.64	−0.246237	−0.123119	−	0.992392i	$-0.539290\pi$
$659$	−4165.64	−0.246237	−0.123119	+	0.992392i	$0.539290\pi$
$660$	0	0
$661$	−362.103	−0.0213074	−0.0106537	−	0.999943i	$-0.503391\pi$
$661$	−362.103	−0.0213074	−0.0106537	+	0.999943i	$0.503391\pi$
$662$	8017.88	0.470731
$663$	−20329.6	−1.19085
$664$	22466.3	1.31304
$665$	12923.8	0.753627
$666$	−4062.92	−0.236389
$667$	−7396.71	−0.429388
$668$	3329.41	0.192843
$669$	11453.2	0.661896
$670$	−4677.86	−0.269734
$671$	0	0
$672$	8363.83	0.480122
$673$	−21519.7	−1.23257	−0.616287	−	0.787521i	$-0.711364\pi$
$673$	−21519.7	−1.23257	−0.616287	+	0.787521i	$0.711364\pi$
$674$	9792.60	0.559639
$675$	675.000	0.0384900
$676$	−11513.9	−0.655090
$677$	−297.437	−0.0168855	−0.00844273	−	0.999964i	$-0.502687\pi$
$677$	−297.437	−0.0168855	−0.00844273	+	0.999964i	$0.502687\pi$
$678$	1799.83	0.101950
$679$	−18645.8	−1.05385
$680$	−11445.9	−0.645486
$681$	−13302.9	−0.748560
$682$	0	0
$683$	17814.8	0.998042	0.499021	−	0.866590i	$-0.333693\pi$
$683$	17814.8	0.998042	0.499021	+	0.866590i	$0.333693\pi$
$684$	5583.65	0.312129
$685$	2215.93	0.123600
$686$	−13275.4	−0.738861
$687$	−4120.99	−0.228858
$688$	1753.98	0.0971944
$689$	−21015.6	−1.16202
$690$	769.008	0.0424285
$691$	−28123.9	−1.54831	−0.774155	−	0.632996i	$-0.781825\pi$
$691$	−28123.9	−1.54831	−0.774155	+	0.632996i	$0.781825\pi$
$692$	12325.5	0.677089
$693$	0	0
$694$	−913.416	−0.0499608
$695$	12966.9	0.707714
$696$	−20400.5	−1.11103
$697$	−15386.5	−0.836164
$698$	−5508.71	−0.298722
$699$	−10993.9	−0.594892
$700$	−1756.85	−0.0948610
$701$	19884.4	1.07136	0.535680	−	0.844421i	$-0.320055\pi$
$701$	19884.4	1.07136	0.535680	+	0.844421i	$0.320055\pi$
$702$	3767.13	0.202537
$703$	34562.4	1.85426
$704$	0	0
$705$	2884.91	0.154116
$706$	5896.40	0.314326
$707$	−30147.9	−1.60372
$708$	7716.48	0.409609
$709$	−22984.0	−1.21746	−0.608731	−	0.793376i	$-0.708321\pi$
$709$	−22984.0	−1.21746	−0.608731	+	0.793376i	$0.708321\pi$
$710$	−1648.97	−0.0871614
$711$	−2177.92	−0.114878
$712$	14003.7	0.737093
$713$	−451.221	−0.0237004
$714$	−9705.84	−0.508728
$715$	0	0
$716$	−14488.3	−0.756220
$717$	−11616.5	−0.605060
$718$	−16215.4	−0.842830
$719$	−25442.4	−1.31967	−0.659833	−	0.751412i	$-0.729373\pi$
$719$	−25442.4	−1.31967	−0.659833	+	0.751412i	$0.729373\pi$
$720$	642.435	0.0332530
$721$	13555.1	0.700166
$722$	31490.4	1.62320
$723$	−1999.44	−0.102849
$724$	13284.2	0.681912
$725$	7116.72	0.364563
$726$	0	0
$727$	27179.0	1.38654	0.693269	−	0.720679i	$-0.256170\pi$
$727$	27179.0	1.38654	0.693269	+	0.720679i	$0.256170\pi$
$728$	−28903.6	−1.47148
$729$	729.000	0.0370370
$730$	4715.37	0.239074
$731$	11773.6	0.595707
$732$	−4655.48	−0.235070
$733$	36330.3	1.83068	0.915340	−	0.402681i	$-0.131922\pi$
$733$	36330.3	1.83068	0.915340	+	0.402681i	$0.131922\pi$
$734$	10296.6	0.517784
$735$	753.339	0.0378059
$736$	−4233.64	−0.212030
$737$	0	0
$738$	2851.17	0.142213
$739$	−3656.83	−0.182028	−0.0910140	−	0.995850i	$-0.529011\pi$
$739$	−3656.83	−0.182028	−0.0910140	+	0.995850i	$0.529011\pi$
$740$	−4698.41	−0.233401
$741$	−32046.2	−1.58873
$742$	−10033.4	−0.496411
$743$	−22372.8	−1.10468	−0.552342	−	0.833618i	$-0.686266\pi$
$743$	−22372.8	−1.10468	−0.552342	+	0.833618i	$0.686266\pi$
$744$	−1244.49	−0.0613241
$745$	12043.3	0.592259
$746$	−2784.42	−0.136655
$747$	−8464.39	−0.414586
$748$	0	0
$749$	12543.6	0.611926
$750$	−739.900	−0.0360231
$751$	30796.1	1.49636	0.748179	−	0.663497i	$-0.230928\pi$
$751$	30796.1	1.49636	0.748179	+	0.663497i	$0.230928\pi$
$752$	2745.73	0.133147
$753$	3855.99	0.186613
$754$	39717.9	1.91836
$755$	1145.40	0.0552125
$756$	−1897.40	−0.0912801
$757$	−14603.4	−0.701151	−0.350576	−	0.936534i	$-0.614014\pi$
$757$	−14603.4	−0.701151	−0.350576	+	0.936534i	$0.614014\pi$
$758$	4802.09	0.230105
$759$	0	0
$760$	−18042.6	−0.861148
$761$	37860.2	1.80346	0.901730	−	0.432300i	$-0.142298\pi$
$761$	37860.2	1.80346	0.901730	+	0.432300i	$0.142298\pi$
$762$	−14481.5	−0.688462
$763$	36913.1	1.75143
$764$	12283.7	0.581687
$765$	4312.35	0.203808
$766$	17389.1	0.820228
$767$	−44287.1	−2.08489
$768$	−13083.8	−0.614739
$769$	39116.6	1.83431	0.917154	−	0.398534i	$-0.130481\pi$
$769$	39116.6	1.83431	0.917154	+	0.398534i	$0.130481\pi$
$770$	0	0
$771$	−12727.6	−0.594516
$772$	−5410.86	−0.252255
$773$	−14843.3	−0.690654	−0.345327	−	0.938482i	$-0.612232\pi$
$773$	−14843.3	−0.690654	−0.345327	+	0.938482i	$0.612232\pi$
$774$	−2181.68	−0.101316
$775$	434.141	0.0201223
$776$	26031.0	1.20420
$777$	−11744.8	−0.542267
$778$	−9755.76	−0.449564
$779$	−24254.3	−1.11553
$780$	4356.35	0.199977
$781$	0	0
$782$	4912.94	0.224663
$783$	7686.06	0.350801
$784$	716.995	0.0326620
$785$	17140.6	0.779330
$786$	−3192.18	−0.144862
$787$	−806.801	−0.0365430	−0.0182715	−	0.999833i	$-0.505816\pi$
$787$	−806.801	−0.0365430	−0.0182715	+	0.999833i	$0.505816\pi$
$788$	8174.34	0.369542
$789$	12576.9	0.567489
$790$	2387.32	0.107515
$791$	5202.81	0.233869
$792$	0	0
$793$	26719.1	1.19650
$794$	1097.80	0.0490674
$795$	4457.88	0.198874
$796$	−13998.7	−0.623330
$797$	−4071.96	−0.180974	−0.0904869	−	0.995898i	$-0.528842\pi$
$797$	−4071.96	−0.180974	−0.0904869	+	0.995898i	$0.528842\pi$
$798$	−15299.6	−0.678699
$799$	18430.7	0.816059
$800$	4073.38	0.180020
$801$	−5276.02	−0.232733
$802$	9091.78	0.400302
$803$	0	0
$804$	−5842.30	−0.256271
$805$	2222.99	0.0973292
$806$	2422.91	0.105885
$807$	1615.83	0.0704831
$808$	42088.9	1.83253
$809$	−14634.0	−0.635973	−0.317987	−	0.948095i	$-0.603007\pi$
$809$	−14634.0	−0.635973	−0.317987	+	0.948095i	$0.603007\pi$
$810$	−799.091	−0.0346632
$811$	−1244.70	−0.0538930	−0.0269465	−	0.999637i	$-0.508578\pi$
$811$	−1244.70	−0.0538930	−0.0269465	+	0.999637i	$0.508578\pi$
$812$	−20004.8	−0.864571
$813$	−19444.5	−0.838807
$814$	0	0
$815$	−3171.42	−0.136307
$816$	4104.31	0.176078
$817$	18559.1	0.794738
$818$	−25459.4	−1.08822
$819$	10889.7	0.464612
$820$	3297.12	0.140415
$821$	1273.32	0.0541283	0.0270641	−	0.999634i	$-0.491384\pi$
$821$	1273.32	0.0541283	0.0270641	+	0.999634i	$0.491384\pi$
$822$	−2623.30	−0.111312
$823$	−2179.61	−0.0923165	−0.0461583	−	0.998934i	$-0.514698\pi$
$823$	−2179.61	−0.0923165	−0.0461583	+	0.998934i	$0.514698\pi$
$824$	−18924.0	−0.800060
$825$	0	0
$826$	−21143.8	−0.890660
$827$	−42985.4	−1.80744	−0.903718	−	0.428128i	$-0.859173\pi$
$827$	−42985.4	−1.80744	−0.903718	+	0.428128i	$0.859173\pi$
$828$	960.433	0.0403108
$829$	25888.8	1.08463	0.542313	−	0.840177i	$-0.317549\pi$
$829$	25888.8	1.08463	0.542313	+	0.840177i	$0.317549\pi$
$830$	9278.22	0.388014
$831$	−14012.2	−0.584933
$832$	30809.6	1.28381
$833$	4812.83	0.200186
$834$	−15350.7	−0.637351
$835$	4053.33	0.167989
$836$	0	0
$837$	468.872	0.0193627
$838$	8112.51	0.334418
$839$	−20841.3	−0.857593	−0.428796	−	0.903401i	$-0.641062\pi$
$839$	−20841.3	−0.857593	−0.428796	+	0.903401i	$0.641062\pi$
$840$	6131.10	0.251837
$841$	56647.4	2.32266
$842$	30326.0	1.24122
$843$	11525.4	0.470885
$844$	−16789.2	−0.684727
$845$	−14017.3	−0.570663
$846$	−3415.26	−0.138793
$847$	0	0
$848$	4242.81	0.171814
$849$	25836.6	1.04442
$850$	−4726.97	−0.190746
$851$	5945.01	0.239474
$852$	−2059.43	−0.0828110
$853$	−38475.0	−1.54438	−0.772191	−	0.635390i	$-0.780839\pi$
$853$	−38475.0	−1.54438	−0.772191	+	0.635390i	$0.780839\pi$
$854$	12756.4	0.511141
$855$	6797.71	0.271903
$856$	−17511.8	−0.699232
$857$	−41292.2	−1.64587	−0.822937	−	0.568133i	$-0.807666\pi$
$857$	−41292.2	−1.64587	−0.822937	+	0.568133i	$0.807666\pi$
$858$	0	0
$859$	7507.08	0.298182	0.149091	−	0.988823i	$-0.452365\pi$
$859$	7507.08	0.298182	0.149091	+	0.988823i	$0.452365\pi$
$860$	−2522.92	−0.100036
$861$	8241.94	0.326231
$862$	10935.9	0.432108
$863$	27312.0	1.07730	0.538651	−	0.842529i	$-0.318934\pi$
$863$	27312.0	1.07730	0.538651	+	0.842529i	$0.318934\pi$
$864$	4399.25	0.173224
$865$	15005.4	0.589827
$866$	12395.6	0.486396
$867$	12811.2	0.501834
$868$	−1220.35	−0.0477206
$869$	0	0
$870$	−8425.06	−0.328317
$871$	33530.6	1.30441
$872$	−51533.6	−2.00132
$873$	−9807.43	−0.380219
$874$	7744.44	0.299725
$875$	−2138.84	−0.0826355
$876$	5889.14	0.227141
$877$	−36310.3	−1.39807	−0.699037	−	0.715086i	$-0.746388\pi$
$877$	−36310.3	−1.39807	−0.699037	+	0.715086i	$0.746388\pi$
$878$	5072.74	0.194985
$879$	9530.03	0.365688
$880$	0	0
$881$	34743.3	1.32864	0.664320	−	0.747448i	$-0.268721\pi$
$881$	34743.3	1.32864	0.664320	+	0.747448i	$0.268721\pi$
$882$	−891.832	−0.0340471
$883$	51715.7	1.97098	0.985488	−	0.169744i	$-0.0542941\pi$
$883$	51715.7	1.97098	0.985488	+	0.169744i	$0.0542941\pi$
$884$	27831.3	1.05890
$885$	9394.27	0.356819
$886$	28664.5	1.08691
$887$	8560.08	0.324035	0.162018	−	0.986788i	$-0.448200\pi$
$887$	8560.08	0.324035	0.162018	+	0.986788i	$0.448200\pi$
$888$	16396.6	0.619633
$889$	−41861.9	−1.57930
$890$	5783.30	0.217816
$891$	0	0
$892$	−15679.5	−0.588554
$893$	29052.9	1.08871
$894$	−14257.3	−0.533375
$895$	−17638.5	−0.658760
$896$	−7594.29	−0.283156
$897$	−5512.20	−0.205181
$898$	10652.7	0.395864
$899$	4943.46	0.183397
$900$	−924.078	−0.0342251
$901$	28479.9	1.05305
$902$	0	0
$903$	−6306.63	−0.232416
$904$	−7263.53	−0.267236
$905$	16172.6	0.594028
$906$	−1355.97	−0.0497231
$907$	−32709.4	−1.19746	−0.598730	−	0.800951i	$-0.704328\pi$
$907$	−32709.4	−1.19746	−0.598730	+	0.800951i	$0.704328\pi$
$908$	18211.8	0.665615
$909$	−15857.4	−0.578609
$910$	−11936.7	−0.434834
$911$	14108.8	0.513112	0.256556	−	0.966529i	$-0.417412\pi$
$911$	14108.8	0.513112	0.256556	+	0.966529i	$0.417412\pi$
$912$	6469.76	0.234907
$913$	0	0
$914$	12339.8	0.446569
$915$	−5667.72	−0.204775
$916$	5641.65	0.203499
$917$	−9227.70	−0.332307
$918$	−5105.13	−0.183545
$919$	22852.4	0.820272	0.410136	−	0.912024i	$-0.365481\pi$
$919$	22852.4	0.820272	0.410136	+	0.912024i	$0.365481\pi$
$920$	−3103.47	−0.111215
$921$	5968.76	0.213548
$922$	−15977.9	−0.570719
$923$	11819.7	0.421505
$924$	0	0
$925$	−5719.98	−0.203321
$926$	26562.9	0.942668
$927$	7129.80	0.252614
$928$	46382.6	1.64072
$929$	−38975.2	−1.37646	−0.688232	−	0.725491i	$-0.741613\pi$
$929$	−38975.2	−1.37646	−0.688232	+	0.725491i	$0.741613\pi$
$930$	−513.953	−0.0181217
$931$	7586.63	0.267070
$932$	15050.8	0.528974
$933$	−20761.8	−0.728521
$934$	1103.46	0.0386579
$935$	0	0
$936$	−15202.9	−0.530900
$937$	34763.4	1.21203	0.606015	−	0.795453i	$-0.292767\pi$
$937$	34763.4	1.21203	0.606015	+	0.795453i	$0.292767\pi$
$938$	16008.3	0.557240
$939$	6084.19	0.211448
$940$	−3949.45	−0.137039
$941$	−28931.8	−1.00228	−0.501142	−	0.865365i	$-0.667087\pi$
$941$	−28931.8	−1.00228	−0.501142	+	0.865365i	$0.667087\pi$
$942$	−20291.7	−0.701847
$943$	−4171.94	−0.144069
$944$	8941.06	0.308270
$945$	−2309.95	−0.0795161
$946$	0	0
$947$	−39885.8	−1.36865	−0.684326	−	0.729176i	$-0.739903\pi$
$947$	−39885.8	−1.36865	−0.684326	+	0.729176i	$0.739903\pi$
$948$	2981.58	0.102149
$949$	−33799.5	−1.15614
$950$	−7451.29	−0.254475
$951$	13958.3	0.475950
$952$	39169.6	1.33350
$953$	37148.3	1.26270	0.631349	−	0.775499i	$-0.282502\pi$
$953$	37148.3	1.26270	0.631349	+	0.775499i	$0.282502\pi$
$954$	−5277.41	−0.179101
$955$	14954.5	0.506720
$956$	15903.1	0.538016
$957$	0	0
$958$	15686.6	0.529030
$959$	−7583.23	−0.255345
$960$	−6535.39	−0.219718
$961$	−29489.4	−0.989877
$962$	−31922.8	−1.06989
$963$	6597.75	0.220778
$964$	2737.24	0.0914527
$965$	−6587.34	−0.219745
$966$	−2631.66	−0.0876525
$967$	3603.64	0.119840	0.0599199	−	0.998203i	$-0.480915\pi$
$967$	3603.64	0.119840	0.0599199	+	0.998203i	$0.480915\pi$
$968$	0	0
$969$	43428.3	1.43975
$970$	10750.4	0.355850
$971$	−4910.73	−0.162300	−0.0811498	−	0.996702i	$-0.525859\pi$
$971$	−4910.73	−0.162300	−0.0811498	+	0.996702i	$0.525859\pi$
$972$	−998.004	−0.0329331
$973$	−44374.5	−1.46206
$974$	13923.9	0.458061
$975$	5303.55	0.174205
$976$	−5394.28	−0.176913
$977$	24108.2	0.789446	0.394723	−	0.918800i	$-0.370841\pi$
$977$	24108.2	0.789446	0.394723	+	0.918800i	$0.370841\pi$
$978$	3754.45	0.122755
$979$	0	0
$980$	−1031.32	−0.0336168
$981$	19415.8	0.631904
$982$	9805.03	0.318626
$983$	14587.4	0.473311	0.236655	−	0.971594i	$-0.423949\pi$
$983$	14587.4	0.473311	0.236655	+	0.971594i	$0.423949\pi$
$984$	−11506.4	−0.372775
$985$	9951.69	0.321916
$986$	−53824.9	−1.73847
$987$	−9872.57	−0.318386
$988$	43871.4	1.41269
$989$	3192.31	0.102639
$990$	0	0
$991$	−21233.0	−0.680615	−0.340308	−	0.940314i	$-0.610531\pi$
$991$	−21233.0	−0.680615	−0.340308	+	0.940314i	$0.610531\pi$
$992$	2829.48	0.0905604
$993$	12191.0	0.389597
$994$	5643.00	0.180066
$995$	−17042.4	−0.542996
$996$	11587.8	0.368648
$997$	20653.8	0.656081	0.328041	−	0.944664i	$-0.393612\pi$
$997$	20653.8	0.656081	0.328041	+	0.944664i	$0.393612\pi$
$998$	−20299.0	−0.643840
$999$	−6177.58	−0.195646

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.4.a.bg.1.9		12
11.3	even	5		165.4.m.d.31.5	yes	24
11.4	even	5		165.4.m.d.16.5	✓	24
11.10	odd	2		1815.4.a.bo.1.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.m.d.16.5	✓	24	11.4	even	5
165.4.m.d.31.5	yes	24	11.3	even	5
1815.4.a.bg.1.9		12	1.1	even	1	trivial
1815.4.a.bo.1.4		12	11.10	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:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1815.a (trivial)

\(f(q)\)	\(=\)	\(q+1.97307 q^{2} +3.00000 q^{3} -4.10701 q^{4} -5.00000 q^{5} +5.91920 q^{6} +17.1107 q^{7} -23.8879 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+1.97307 q^{2} +3.00000 q^{3} -4.10701 q^{4} -5.00000 q^{5} +5.91920 q^{6} +17.1107 q^{7} -23.8879 q^{8} +9.00000 q^{9} -9.86533 q^{10} -12.3210 q^{12} +70.7140 q^{13} +33.7606 q^{14} -15.0000 q^{15} -14.2763 q^{16} -95.8300 q^{17} +17.7576 q^{18} -151.060 q^{19} +20.5351 q^{20} +51.3322 q^{21} -25.9835 q^{23} -71.6638 q^{24} +25.0000 q^{25} +139.523 q^{26} +27.0000 q^{27} -70.2740 q^{28} +284.669 q^{29} -29.5960 q^{30} +17.3656 q^{31} +162.935 q^{32} -189.079 q^{34} -85.5537 q^{35} -36.9631 q^{36} -228.799 q^{37} -298.052 q^{38} +212.142 q^{39} +119.440 q^{40} +160.561 q^{41} +101.282 q^{42} -122.859 q^{43} -45.0000 q^{45} -51.2672 q^{46} -192.327 q^{47} -42.8290 q^{48} -50.2226 q^{49} +49.3266 q^{50} -287.490 q^{51} -290.423 q^{52} -297.192 q^{53} +53.2728 q^{54} -408.740 q^{56} -453.180 q^{57} +561.670 q^{58} -626.285 q^{59} +61.6052 q^{60} +377.848 q^{61} +34.2635 q^{62} +153.997 q^{63} +435.693 q^{64} -353.570 q^{65} +474.172 q^{67} +393.575 q^{68} -77.9506 q^{69} -168.803 q^{70} +167.148 q^{71} -214.991 q^{72} -477.974 q^{73} -451.436 q^{74} +75.0000 q^{75} +620.406 q^{76} +418.570 q^{78} -241.991 q^{79} +71.3817 q^{80} +81.0000 q^{81} +316.797 q^{82} -940.488 q^{83} -210.822 q^{84} +479.150 q^{85} -242.409 q^{86} +854.007 q^{87} -586.224 q^{89} -88.7879 q^{90} +1209.97 q^{91} +106.715 q^{92} +52.0969 q^{93} -379.474 q^{94} +755.301 q^{95} +488.806 q^{96} -1089.71 q^{97} -99.0925 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 9 q^{2} + 36 q^{3} + 57 q^{4} - 60 q^{5} - 27 q^{6} - 21 q^{7} - 123 q^{8} + 108 q^{9}+O(q^{10}) \) 12 * q - 9 * q^2 + 36 * q^3 + 57 * q^4 - 60 * q^5 - 27 * q^6 - 21 * q^7 - 123 * q^8 + 108 * q^9	\( 12 q - 9 q^{2} + 36 q^{3} + 57 q^{4} - 60 q^{5} - 27 q^{6} - 21 q^{7} - 123 q^{8} + 108 q^{9} + 45 q^{10} + 171 q^{12} - 78 q^{13} + 262 q^{14} - 180 q^{15} + 225 q^{16} - 313 q^{17} - 81 q^{18} - 51 q^{19} - 285 q^{20} - 63 q^{21} - 34 q^{23} - 369 q^{24} + 300 q^{25} + 28 q^{26} + 324 q^{27} - 376 q^{28} - 31 q^{29} + 135 q^{30} + 655 q^{31} - 1578 q^{32} - 10 q^{34} + 105 q^{35} + 513 q^{36} + 84 q^{37} - 1076 q^{38} - 234 q^{39} + 615 q^{40} - 1463 q^{41} + 786 q^{42} + 111 q^{43} - 540 q^{45} + q^{46} + 278 q^{47} + 675 q^{48} - 325 q^{49} - 225 q^{50} - 939 q^{51} - 1957 q^{52} + 517 q^{53} - 243 q^{54} + 1543 q^{56} - 153 q^{57} + 442 q^{58} - 308 q^{59} - 855 q^{60} - 604 q^{61} - 1773 q^{62} - 189 q^{63} + 4323 q^{64} + 390 q^{65} - 357 q^{67} - 2192 q^{68} - 102 q^{69} - 1310 q^{70} - 620 q^{71} - 1107 q^{72} - 1892 q^{73} - 581 q^{74} + 900 q^{75} - 378 q^{76} + 84 q^{78} - 415 q^{79} - 1125 q^{80} + 972 q^{81} - 2802 q^{82} - 3158 q^{83} - 1128 q^{84} + 1565 q^{85} + 747 q^{86} - 93 q^{87} + 1563 q^{89} + 405 q^{90} + 1434 q^{91} - 3466 q^{92} + 1965 q^{93} + 3 q^{94} + 255 q^{95} - 4734 q^{96} + 714 q^{97} - 6586 q^{98}+O(q^{100}) \) 12 * q - 9 * q^2 + 36 * q^3 + 57 * q^4 - 60 * q^5 - 27 * q^6 - 21 * q^7 - 123 * q^8 + 108 * q^9 + 45 * q^10 + 171 * q^12 - 78 * q^13 + 262 * q^14 - 180 * q^15 + 225 * q^16 - 313 * q^17 - 81 * q^18 - 51 * q^19 - 285 * q^20 - 63 * q^21 - 34 * q^23 - 369 * q^24 + 300 * q^25 + 28 * q^26 + 324 * q^27 - 376 * q^28 - 31 * q^29 + 135 * q^30 + 655 * q^31 - 1578 * q^32 - 10 * q^34 + 105 * q^35 + 513 * q^36 + 84 * q^37 - 1076 * q^38 - 234 * q^39 + 615 * q^40 - 1463 * q^41 + 786 * q^42 + 111 * q^43 - 540 * q^45 + q^46 + 278 * q^47 + 675 * q^48 - 325 * q^49 - 225 * q^50 - 939 * q^51 - 1957 * q^52 + 517 * q^53 - 243 * q^54 + 1543 * q^56 - 153 * q^57 + 442 * q^58 - 308 * q^59 - 855 * q^60 - 604 * q^61 - 1773 * q^62 - 189 * q^63 + 4323 * q^64 + 390 * q^65 - 357 * q^67 - 2192 * q^68 - 102 * q^69 - 1310 * q^70 - 620 * q^71 - 1107 * q^72 - 1892 * q^73 - 581 * q^74 + 900 * q^75 - 378 * q^76 + 84 * q^78 - 415 * q^79 - 1125 * q^80 + 972 * q^81 - 2802 * q^82 - 3158 * q^83 - 1128 * q^84 + 1565 * q^85 + 747 * q^86 - 93 * q^87 + 1563 * q^89 + 405 * q^90 + 1434 * q^91 - 3466 * q^92 + 1965 * q^93 + 3 * q^94 + 255 * q^95 - 4734 * q^96 + 714 * q^97 - 6586 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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