LMFDB - Embedded newform 2366.4.a.k.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2366,4,Mod(1,2366)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2366, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2366.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2366 = 2 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2366.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:	$139.598519074$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{1169}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 292 $ x^2 - x - 292
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-16.5953$ of defining polynomial
Character	$\chi$	$=$	2366.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} -4.00000 q^{3} +4.00000 q^{4} +14.5953 q^{5} -8.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} -11.0000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -4.00000 q^{3} +4.00000 q^{4} +14.5953 q^{5} -8.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} -11.0000 q^{9} +29.1906 q^{10} +45.1906 q^{11} -16.0000 q^{12} -14.0000 q^{14} -58.3813 q^{15} +16.0000 q^{16} -71.1906 q^{17} -22.0000 q^{18} -140.167 q^{19} +58.3813 q^{20} +28.0000 q^{21} +90.3813 q^{22} +35.4047 q^{23} -32.0000 q^{24} +88.0234 q^{25} +152.000 q^{27} -28.0000 q^{28} +153.405 q^{29} -116.763 q^{30} +113.358 q^{31} +32.0000 q^{32} -180.763 q^{33} -142.381 q^{34} -102.167 q^{35} -44.0000 q^{36} -223.191 q^{37} -280.334 q^{38} +116.763 q^{40} -404.381 q^{41} +56.0000 q^{42} -30.2140 q^{43} +180.763 q^{44} -160.549 q^{45} +70.8094 q^{46} -328.502 q^{47} -64.0000 q^{48} +49.0000 q^{49} +176.047 q^{50} +284.763 q^{51} -362.502 q^{53} +304.000 q^{54} +659.572 q^{55} -56.0000 q^{56} +560.669 q^{57} +306.809 q^{58} -236.669 q^{59} -233.525 q^{60} -493.050 q^{61} +226.716 q^{62} +77.0000 q^{63} +64.0000 q^{64} -361.525 q^{66} +293.191 q^{67} -284.763 q^{68} -141.619 q^{69} -204.334 q^{70} +1078.29 q^{71} -88.0000 q^{72} -752.977 q^{73} -446.381 q^{74} -352.094 q^{75} -560.669 q^{76} -316.334 q^{77} -1006.12 q^{79} +233.525 q^{80} -311.000 q^{81} -808.763 q^{82} -548.689 q^{83} +112.000 q^{84} -1039.05 q^{85} -60.4281 q^{86} -613.619 q^{87} +361.525 q^{88} +694.836 q^{89} -321.097 q^{90} +141.619 q^{92} -453.432 q^{93} -657.003 q^{94} -2045.79 q^{95} -128.000 q^{96} +5.98009 q^{97} +98.0000 q^{98} -497.097 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} - 8 q^{3} + 8 q^{4} - 5 q^{5} - 16 q^{6} - 14 q^{7} + 16 q^{8} - 22 q^{9}+O(q^{10}) $ 2 * q + 4 * q^2 - 8 * q^3 + 8 * q^4 - 5 * q^5 - 16 * q^6 - 14 * q^7 + 16 * q^8 - 22 * q^9	\( 2 q + 4 q^{2} - 8 q^{3} + 8 q^{4} - 5 q^{5} - 16 q^{6} - 14 q^{7} + 16 q^{8} - 22 q^{9} - 10 q^{10} + 22 q^{11} - 32 q^{12} - 28 q^{14} + 20 q^{15} + 32 q^{16} - 74 q^{17} - 44 q^{18} - 41 q^{19} - 20 q^{20} + 56 q^{21} + 44 q^{22} + 105 q^{23} - 64 q^{24} + 347 q^{25} + 304 q^{27} - 56 q^{28} + 341 q^{29} + 40 q^{30} - 81 q^{31} + 64 q^{32} - 88 q^{33} - 148 q^{34} + 35 q^{35} - 88 q^{36} - 378 q^{37} - 82 q^{38} - 40 q^{40} - 672 q^{41} + 112 q^{42} - 163 q^{43} + 88 q^{44} + 55 q^{45} + 210 q^{46} + 61 q^{47} - 128 q^{48} + 98 q^{49} + 694 q^{50} + 296 q^{51} - 7 q^{53} + 608 q^{54} + 1114 q^{55} - 112 q^{56} + 164 q^{57} + 682 q^{58} + 484 q^{59} + 80 q^{60} + 108 q^{61} - 162 q^{62} + 154 q^{63} + 128 q^{64} - 176 q^{66} + 518 q^{67} - 296 q^{68} - 420 q^{69} + 70 q^{70} + 1336 q^{71} - 176 q^{72} - 1335 q^{73} - 756 q^{74} - 1388 q^{75} - 164 q^{76} - 154 q^{77} - 1431 q^{79} - 80 q^{80} - 622 q^{81} - 1344 q^{82} - 1747 q^{83} + 224 q^{84} - 984 q^{85} - 326 q^{86} - 1364 q^{87} + 176 q^{88} + 193 q^{89} + 110 q^{90} + 420 q^{92} + 324 q^{93} + 122 q^{94} - 3989 q^{95} - 256 q^{96} - 1595 q^{97} + 196 q^{98} - 242 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 - 8 * q^3 + 8 * q^4 - 5 * q^5 - 16 * q^6 - 14 * q^7 + 16 * q^8 - 22 * q^9 - 10 * q^10 + 22 * q^11 - 32 * q^12 - 28 * q^14 + 20 * q^15 + 32 * q^16 - 74 * q^17 - 44 * q^18 - 41 * q^19 - 20 * q^20 + 56 * q^21 + 44 * q^22 + 105 * q^23 - 64 * q^24 + 347 * q^25 + 304 * q^27 - 56 * q^28 + 341 * q^29 + 40 * q^30 - 81 * q^31 + 64 * q^32 - 88 * q^33 - 148 * q^34 + 35 * q^35 - 88 * q^36 - 378 * q^37 - 82 * q^38 - 40 * q^40 - 672 * q^41 + 112 * q^42 - 163 * q^43 + 88 * q^44 + 55 * q^45 + 210 * q^46 + 61 * q^47 - 128 * q^48 + 98 * q^49 + 694 * q^50 + 296 * q^51 - 7 * q^53 + 608 * q^54 + 1114 * q^55 - 112 * q^56 + 164 * q^57 + 682 * q^58 + 484 * q^59 + 80 * q^60 + 108 * q^61 - 162 * q^62 + 154 * q^63 + 128 * q^64 - 176 * q^66 + 518 * q^67 - 296 * q^68 - 420 * q^69 + 70 * q^70 + 1336 * q^71 - 176 * q^72 - 1335 * q^73 - 756 * q^74 - 1388 * q^75 - 164 * q^76 - 154 * q^77 - 1431 * q^79 - 80 * q^80 - 622 * q^81 - 1344 * q^82 - 1747 * q^83 + 224 * q^84 - 984 * q^85 - 326 * q^86 - 1364 * q^87 + 176 * q^88 + 193 * q^89 + 110 * q^90 + 420 * q^92 + 324 * q^93 + 122 * q^94 - 3989 * q^95 - 256 * q^96 - 1595 * q^97 + 196 * q^98 - 242 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−4.00000	−0.769800	−0.384900	−	0.922958i	$-0.625764\pi$
$3$	−4.00000	−0.769800	−0.384900	+	0.922958i	$0.625764\pi$
$4$	4.00000	0.500000
$5$	14.5953	1.30545	0.652723	−	0.757597i	$-0.273627\pi$
$5$	14.5953	1.30545	0.652723	+	0.757597i	$0.273627\pi$
$6$	−8.00000	−0.544331
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	8.00000	0.353553
$9$	−11.0000	−0.407407
$10$	29.1906	0.923089
$11$	45.1906	1.23868	0.619341	−	0.785122i	$-0.287400\pi$
$11$	45.1906	1.23868	0.619341	+	0.785122i	$0.287400\pi$
$12$	−16.0000	−0.384900
$13$	0	0
$13$	0	0
$14$	−14.0000	−0.267261
$15$	−58.3813	−1.00493
$16$	16.0000	0.250000
$17$	−71.1906	−1.01566	−0.507831	−	0.861456i	$-0.669553\pi$
$17$	−71.1906	−1.01566	−0.507831	+	0.861456i	$0.669553\pi$
$18$	−22.0000	−0.288081
$19$	−140.167	−1.69245	−0.846226	−	0.532825i	$-0.821130\pi$
$19$	−140.167	−1.69245	−0.846226	+	0.532825i	$0.821130\pi$
$20$	58.3813	0.652723
$21$	28.0000	0.290957
$22$	90.3813	0.875880
$23$	35.4047	0.320973	0.160487	−	0.987038i	$-0.448694\pi$
$23$	35.4047	0.320973	0.160487	+	0.987038i	$0.448694\pi$
$24$	−32.0000	−0.272166
$25$	88.0234	0.704187
$26$	0	0
$27$	152.000	1.08342
$28$	−28.0000	−0.188982
$29$	153.405	0.982294	0.491147	−	0.871077i	$-0.336578\pi$
$29$	153.405	0.982294	0.491147	+	0.871077i	$0.336578\pi$
$30$	−116.763	−0.710594
$31$	113.358	0.656764	0.328382	−	0.944545i	$-0.393497\pi$
$31$	113.358	0.656764	0.328382	+	0.944545i	$0.393497\pi$
$32$	32.0000	0.176777
$33$	−180.763	−0.953537
$34$	−142.381	−0.718182
$35$	−102.167	−0.493412
$36$	−44.0000	−0.203704
$37$	−223.191	−0.991684	−0.495842	−	0.868413i	$-0.665141\pi$
$37$	−223.191	−0.991684	−0.495842	+	0.868413i	$0.665141\pi$
$38$	−280.334	−1.19674
$39$	0	0
$40$	116.763	0.461545
$41$	−404.381	−1.54034	−0.770168	−	0.637842i	$-0.779827\pi$
$41$	−404.381	−1.54034	−0.770168	+	0.637842i	$0.779827\pi$
$42$	56.0000	0.205738
$43$	−30.2140	−0.107153	−0.0535767	−	0.998564i	$-0.517062\pi$
$43$	−30.2140	−0.107153	−0.0535767	+	0.998564i	$0.517062\pi$
$44$	180.763	0.619341
$45$	−160.549	−0.531848
$46$	70.8094	0.226962
$47$	−328.502	−1.01951	−0.509754	−	0.860320i	$-0.670264\pi$
$47$	−328.502	−1.01951	−0.509754	+	0.860320i	$0.670264\pi$
$48$	−64.0000	−0.192450
$49$	49.0000	0.142857
$50$	176.047	0.497936
$51$	284.763	0.781858
$52$	0	0
$53$	−362.502	−0.939499	−0.469749	−	0.882800i	$-0.655656\pi$
$53$	−362.502	−0.939499	−0.469749	+	0.882800i	$0.655656\pi$
$54$	304.000	0.766096
$55$	659.572	1.61703
$56$	−56.0000	−0.133631
$57$	560.669	1.30285
$58$	306.809	0.694587
$59$	−236.669	−0.522232	−0.261116	−	0.965307i	$-0.584090\pi$
$59$	−236.669	−0.522232	−0.261116	+	0.965307i	$0.584090\pi$
$60$	−233.525	−0.502466
$61$	−493.050	−1.03490	−0.517448	−	0.855715i	$-0.673118\pi$
$61$	−493.050	−1.03490	−0.517448	+	0.855715i	$0.673118\pi$
$62$	226.716	0.464402
$63$	77.0000	0.153986
$64$	64.0000	0.125000
$65$	0	0
$66$	−361.525	−0.674253
$67$	293.191	0.534611	0.267306	−	0.963612i	$-0.413867\pi$
$67$	293.191	0.534611	0.267306	+	0.963612i	$0.413867\pi$
$68$	−284.763	−0.507831
$69$	−141.619	−0.247085
$70$	−204.334	−0.348895
$71$	1078.29	1.80238	0.901192	−	0.433421i	$-0.142694\pi$
$71$	1078.29	1.80238	0.901192	+	0.433421i	$0.142694\pi$
$72$	−88.0000	−0.144040
$73$	−752.977	−1.20725	−0.603625	−	0.797268i	$-0.706278\pi$
$73$	−752.977	−1.20725	−0.603625	+	0.797268i	$0.706278\pi$
$74$	−446.381	−0.701227
$75$	−352.094	−0.542084
$76$	−560.669	−0.846226
$77$	−316.334	−0.468177
$78$	0	0
$79$	−1006.12	−1.43288	−0.716439	−	0.697650i	$-0.754229\pi$
$79$	−1006.12	−1.43288	−0.716439	+	0.697650i	$0.754229\pi$
$80$	233.525	0.326361
$81$	−311.000	−0.426612
$82$	−808.763	−1.08918
$83$	−548.689	−0.725620	−0.362810	−	0.931863i	$-0.618183\pi$
$83$	−548.689	−0.725620	−0.362810	+	0.931863i	$0.618183\pi$
$84$	112.000	0.145479
$85$	−1039.05	−1.32589
$86$	−60.4281	−0.0757689
$87$	−613.619	−0.756170
$88$	361.525	0.437940
$89$	694.836	0.827556	0.413778	−	0.910378i	$-0.364209\pi$
$89$	694.836	0.827556	0.413778	+	0.910378i	$0.364209\pi$
$90$	−321.097	−0.376073
$91$	0	0
$92$	141.619	0.160487
$93$	−453.432	−0.505577
$94$	−657.003	−0.720901
$95$	−2045.79	−2.20940
$96$	−128.000	−0.136083
$97$	5.98009	0.00625965	0.00312982	−	0.999995i	$-0.499004\pi$
$97$	5.98009	0.00625965	0.00312982	+	0.999995i	$0.499004\pi$
$98$	98.0000	0.101015
$99$	−497.097	−0.504648
$100$	352.094	0.352094
$101$	1284.77	1.26574	0.632868	−	0.774260i	$-0.281878\pi$
$101$	1284.77	1.26574	0.632868	+	0.774260i	$0.281878\pi$
$102$	569.525	0.552857
$103$	462.475	0.442417	0.221209	−	0.975226i	$-0.429000\pi$
$103$	462.475	0.442417	0.221209	+	0.975226i	$0.429000\pi$
$104$	0	0
$105$	408.669	0.379829
$106$	−725.003	−0.664326
$107$	1261.34	1.13961	0.569804	−	0.821780i	$-0.307019\pi$
$107$	1261.34	1.13961	0.569804	+	0.821780i	$0.307019\pi$
$108$	608.000	0.541711
$109$	−1019.24	−0.895651	−0.447825	−	0.894121i	$-0.647801\pi$
$109$	−1019.24	−0.895651	−0.447825	+	0.894121i	$0.647801\pi$
$110$	1319.14	1.14341
$111$	892.763	0.763399
$112$	−112.000	−0.0944911
$113$	1757.55	1.46316	0.731578	−	0.681758i	$-0.238784\pi$
$113$	1757.55	1.46316	0.731578	+	0.681758i	$0.238784\pi$
$114$	1121.34	0.921254
$115$	516.743	0.419013
$116$	613.619	0.491147
$117$	0	0
$118$	−473.338	−0.369274
$119$	498.334	0.383884
$120$	−467.050	−0.355297
$121$	711.194	0.534331
$122$	−986.101	−0.731782
$123$	1617.53	1.18575
$124$	453.432	0.328382
$125$	−539.685	−0.386167
$126$	154.000	0.108884
$127$	−1837.06	−1.28356	−0.641781	−	0.766888i	$-0.721804\pi$
$127$	−1837.06	−1.28356	−0.641781	+	0.766888i	$0.721804\pi$
$128$	128.000	0.0883883
$129$	120.856	0.0824867
$130$	0	0
$131$	−1552.95	−1.03574	−0.517870	−	0.855460i	$-0.673275\pi$
$131$	−1552.95	−1.03574	−0.517870	+	0.855460i	$0.673275\pi$
$132$	−723.050	−0.476769
$133$	981.171	0.639686
$134$	586.381	0.378027
$135$	2218.49	1.41435
$136$	−569.525	−0.359091
$137$	872.047	0.543825	0.271912	−	0.962322i	$-0.412344\pi$
$137$	872.047	0.543825	0.271912	+	0.962322i	$0.412344\pi$
$138$	−283.237	−0.174716
$139$	150.047	0.0915597	0.0457799	−	0.998952i	$-0.485423\pi$
$139$	150.047	0.0915597	0.0457799	+	0.998952i	$0.485423\pi$
$140$	−408.669	−0.246706
$141$	1314.01	0.784818
$142$	2156.58	1.27448
$143$	0	0
$144$	−176.000	−0.101852
$145$	2238.99	1.28233
$146$	−1505.95	−0.853655
$147$	−196.000	−0.109971
$148$	−892.763	−0.495842
$149$	−1766.96	−0.971512	−0.485756	−	0.874094i	$-0.661456\pi$
$149$	−1766.96	−0.971512	−0.485756	+	0.874094i	$0.661456\pi$
$150$	−704.187	−0.383311
$151$	−1358.10	−0.731925	−0.365962	−	0.930630i	$-0.619260\pi$
$151$	−1358.10	−0.731925	−0.365962	+	0.930630i	$0.619260\pi$
$152$	−1121.34	−0.598372
$153$	783.097	0.413789
$154$	−632.669	−0.331051
$155$	1654.49	0.857369
$156$	0	0
$157$	2977.87	1.51376	0.756878	−	0.653556i	$-0.226724\pi$
$157$	2977.87	1.51376	0.756878	+	0.653556i	$0.226724\pi$
$158$	−2012.24	−1.01320
$159$	1450.01	0.723227
$160$	467.050	0.230772
$161$	−247.833	−0.121317
$162$	−622.000	−0.301660
$163$	−2374.38	−1.14096	−0.570478	−	0.821313i	$-0.693242\pi$
$163$	−2374.38	−1.14096	−0.570478	+	0.821313i	$0.693242\pi$
$164$	−1617.53	−0.770168
$165$	−2638.29	−1.24479
$166$	−1097.38	−0.513091
$167$	−3604.18	−1.67006	−0.835030	−	0.550205i	$-0.814550\pi$
$167$	−3604.18	−1.67006	−0.835030	+	0.550205i	$0.814550\pi$
$168$	224.000	0.102869
$169$	0	0
$170$	−2078.10	−0.937547
$171$	1541.84	0.689517
$172$	−120.856	−0.0535767
$173$	1406.15	0.617962	0.308981	−	0.951068i	$-0.400012\pi$
$173$	1406.15	0.617962	0.308981	+	0.951068i	$0.400012\pi$
$174$	−1227.24	−0.534693
$175$	−616.164	−0.266158
$176$	723.050	0.309670
$177$	946.676	0.402014
$178$	1389.67	0.585171
$179$	−4611.75	−1.92569	−0.962845	−	0.270054i	$-0.912959\pi$
$179$	−4611.75	−1.92569	−0.962845	+	0.270054i	$0.912959\pi$
$180$	−642.194	−0.265924
$181$	4259.06	1.74902	0.874512	−	0.485004i	$-0.161182\pi$
$181$	4259.06	1.74902	0.874512	+	0.485004i	$0.161182\pi$
$182$	0	0
$183$	1972.20	0.796663
$184$	283.237	0.113481
$185$	−3257.54	−1.29459
$186$	−906.863	−0.357497
$187$	−3217.15	−1.25808
$188$	−1314.01	−0.509754
$189$	−1064.00	−0.409495
$190$	−4091.57	−1.56228
$191$	−1226.09	−0.464484	−0.232242	−	0.972658i	$-0.574606\pi$
$191$	−1226.09	−0.464484	−0.232242	+	0.972658i	$0.574606\pi$
$192$	−256.000	−0.0962250
$193$	1133.33	0.422689	0.211344	−	0.977412i	$-0.432216\pi$
$193$	1133.33	0.422689	0.211344	+	0.977412i	$0.432216\pi$
$194$	11.9602	0.00442624
$195$	0	0
$196$	196.000	0.0714286
$197$	−1577.34	−0.570463	−0.285231	−	0.958459i	$-0.592070\pi$
$197$	−1577.34	−0.570463	−0.285231	+	0.958459i	$0.592070\pi$
$198$	−994.194	−0.356840
$199$	−4491.72	−1.60005	−0.800024	−	0.599968i	$-0.795180\pi$
$199$	−4491.72	−1.60005	−0.800024	+	0.599968i	$0.795180\pi$
$200$	704.187	0.248968
$201$	−1172.76	−0.411544
$202$	2569.54	0.895011
$203$	−1073.83	−0.371272
$204$	1139.05	0.390929
$205$	−5902.07	−2.01082
$206$	924.950	0.312836
$207$	−389.451	−0.130767
$208$	0	0
$209$	−6334.25	−2.09641
$210$	817.338	0.268579
$211$	552.743	0.180343	0.0901715	−	0.995926i	$-0.471258\pi$
$211$	552.743	0.180343	0.0901715	+	0.995926i	$0.471258\pi$
$212$	−1450.01	−0.469749
$213$	−4313.15	−1.38748
$214$	2522.68	0.805825
$215$	−440.984	−0.139883
$216$	1216.00	0.383048
$217$	−793.505	−0.248233
$218$	−2038.49	−0.633321
$219$	3011.91	0.929341
$220$	2638.29	0.808515
$221$	0	0
$222$	1785.53	0.539805
$223$	1391.69	0.417911	0.208955	−	0.977925i	$-0.432994\pi$
$223$	1391.69	0.417911	0.208955	+	0.977925i	$0.432994\pi$
$224$	−224.000	−0.0668153
$225$	−968.257	−0.286891
$226$	3515.10	1.03461
$227$	−2047.24	−0.598590	−0.299295	−	0.954161i	$-0.596751\pi$
$227$	−2047.24	−0.598590	−0.299295	+	0.954161i	$0.596751\pi$
$228$	2242.68	0.651425
$229$	1824.58	0.526514	0.263257	−	0.964726i	$-0.415203\pi$
$229$	1824.58	0.526514	0.263257	+	0.964726i	$0.415203\pi$
$230$	1033.49	0.296287
$231$	1265.34	0.360403
$232$	1227.24	0.347293
$233$	4400.38	1.23725	0.618623	−	0.785688i	$-0.287691\pi$
$233$	4400.38	1.23725	0.618623	+	0.785688i	$0.287691\pi$
$234$	0	0
$235$	−4794.59	−1.33091
$236$	−946.676	−0.261116
$237$	4024.48	1.10303
$238$	996.669	0.271447
$239$	−1596.87	−0.432188	−0.216094	−	0.976373i	$-0.569332\pi$
$239$	−1596.87	−0.432188	−0.216094	+	0.976373i	$0.569332\pi$
$240$	−934.101	−0.251233
$241$	−991.157	−0.264921	−0.132461	−	0.991188i	$-0.542288\pi$
$241$	−991.157	−0.264921	−0.132461	+	0.991188i	$0.542288\pi$
$242$	1422.39	0.377829
$243$	−2860.00	−0.755017
$244$	−1972.20	−0.517448
$245$	715.171	0.186492
$246$	3235.05	0.838452
$247$	0	0
$248$	906.863	0.232201
$249$	2194.76	0.558582
$250$	−1079.37	−0.273062
$251$	−6914.65	−1.73884	−0.869420	−	0.494074i	$-0.835507\pi$
$251$	−6914.65	−1.73884	−0.869420	+	0.494074i	$0.835507\pi$
$252$	308.000	0.0769928
$253$	1599.96	0.397584
$254$	−3674.11	−0.907616
$255$	4156.20	1.02067
$256$	256.000	0.0625000
$257$	−2463.71	−0.597985	−0.298993	−	0.954255i	$-0.596651\pi$
$257$	−2463.71	−0.597985	−0.298993	+	0.954255i	$0.596651\pi$
$258$	241.712	0.0583269
$259$	1562.33	0.374821
$260$	0	0
$261$	−1687.45	−0.400194
$262$	−3105.90	−0.732378
$263$	−3481.43	−0.816251	−0.408125	−	0.912926i	$-0.633817\pi$
$263$	−3481.43	−0.816251	−0.408125	+	0.912926i	$0.633817\pi$
$264$	−1446.10	−0.337126
$265$	−5290.83	−1.22646
$266$	1962.34	0.452327
$267$	−2779.34	−0.637053
$268$	1172.76	0.267306
$269$	−4863.77	−1.10241	−0.551206	−	0.834369i	$-0.685832\pi$
$269$	−4863.77	−1.10241	−0.551206	+	0.834369i	$0.685832\pi$
$270$	4436.98	1.00010
$271$	−1754.86	−0.393359	−0.196680	−	0.980468i	$-0.563016\pi$
$271$	−1754.86	−0.393359	−0.196680	+	0.980468i	$0.563016\pi$
$272$	−1139.05	−0.253916
$273$	0	0
$274$	1744.09	0.384542
$275$	3977.83	0.872263
$276$	−566.475	−0.123543
$277$	8400.91	1.82224	0.911122	−	0.412136i	$-0.135217\pi$
$277$	8400.91	1.82224	0.911122	+	0.412136i	$0.135217\pi$
$278$	300.094	0.0647425
$279$	−1246.94	−0.267570
$280$	−817.338	−0.174447
$281$	3116.10	0.661534	0.330767	−	0.943713i	$-0.392693\pi$
$281$	3116.10	0.661534	0.330767	+	0.943713i	$0.392693\pi$
$282$	2628.01	0.554950
$283$	8619.44	1.81050	0.905252	−	0.424876i	$-0.139682\pi$
$283$	8619.44	1.81050	0.905252	+	0.424876i	$0.139682\pi$
$284$	4313.15	0.901192
$285$	8183.14	1.70080
$286$	0	0
$287$	2830.67	0.582192
$288$	−352.000	−0.0720201
$289$	155.108	0.0315708
$290$	4477.98	0.906745
$291$	−23.9203	−0.00481868
$292$	−3011.91	−0.603625
$293$	−5767.88	−1.15004	−0.575022	−	0.818138i	$-0.695007\pi$
$293$	−5767.88	−1.15004	−0.575022	+	0.818138i	$0.695007\pi$
$294$	−392.000	−0.0777616
$295$	−3454.26	−0.681745
$296$	−1785.53	−0.350613
$297$	6868.98	1.34202
$298$	−3533.93	−0.686963
$299$	0	0
$300$	−1408.37	−0.271042
$301$	211.498	0.0405002
$302$	−2716.20	−0.517549
$303$	−5139.08	−0.974364
$304$	−2242.68	−0.423113
$305$	−7196.23	−1.35100
$306$	1566.19	0.292593
$307$	−6678.62	−1.24159	−0.620796	−	0.783972i	$-0.713190\pi$
$307$	−6678.62	−1.24159	−0.620796	+	0.783972i	$0.713190\pi$
$308$	−1265.34	−0.234089
$309$	−1849.90	−0.340573
$310$	3308.99	0.606252
$311$	6058.34	1.10462	0.552310	−	0.833639i	$-0.313746\pi$
$311$	6058.34	1.10462	0.552310	+	0.833639i	$0.313746\pi$
$312$	0	0
$313$	−1803.43	−0.325674	−0.162837	−	0.986653i	$-0.552064\pi$
$313$	−1803.43	−0.325674	−0.162837	+	0.986653i	$0.552064\pi$
$314$	5955.73	1.07039
$315$	1123.84	0.201020
$316$	−4024.48	−0.716439
$317$	2991.79	0.530082	0.265041	−	0.964237i	$-0.414615\pi$
$317$	2991.79	0.530082	0.265041	+	0.964237i	$0.414615\pi$
$318$	2900.01	0.511398
$319$	6932.46	1.21675
$320$	934.101	0.163181
$321$	−5045.35	−0.877271
$322$	−495.666	−0.0857837
$323$	9978.60	1.71896
$324$	−1244.00	−0.213306
$325$	0	0
$326$	−4748.76	−0.806778
$327$	4076.98	0.689472
$328$	−3235.05	−0.544591
$329$	2299.51	0.385338
$330$	−5276.58	−0.880200
$331$	−7014.45	−1.16480	−0.582400	−	0.812902i	$-0.697886\pi$
$331$	−7014.45	−1.16480	−0.582400	+	0.812902i	$0.697886\pi$
$332$	−2194.76	−0.362810
$333$	2455.10	0.404019
$334$	−7208.36	−1.18091
$335$	4279.21	0.697905
$336$	448.000	0.0727393
$337$	−8929.62	−1.44340	−0.721702	−	0.692204i	$-0.756640\pi$
$337$	−8929.62	−1.44340	−0.721702	+	0.692204i	$0.756640\pi$
$338$	0	0
$339$	−7030.21	−1.12634
$340$	−4156.20	−0.662946
$341$	5122.72	0.813521
$342$	3083.68	0.487562
$343$	−343.000	−0.0539949
$344$	−241.712	−0.0378845
$345$	−2066.97	−0.322556
$346$	2812.29	0.436965
$347$	−756.295	−0.117003	−0.0585015	−	0.998287i	$-0.518632\pi$
$347$	−756.295	−0.117003	−0.0585015	+	0.998287i	$0.518632\pi$
$348$	−2454.47	−0.378085
$349$	−5261.38	−0.806978	−0.403489	−	0.914985i	$-0.632203\pi$
$349$	−5261.38	−0.806978	−0.403489	+	0.914985i	$0.632203\pi$
$350$	−1232.33	−0.188202
$351$	0	0
$352$	1446.10	0.218970
$353$	−11077.7	−1.67027	−0.835134	−	0.550046i	$-0.814610\pi$
$353$	−11077.7	−1.67027	−0.835134	+	0.550046i	$0.814610\pi$
$354$	1893.35	0.284267
$355$	15738.0	2.35291
$356$	2779.34	0.413778
$357$	−1993.34	−0.295514
$358$	−9223.51	−1.36167
$359$	−9411.37	−1.38360	−0.691801	−	0.722088i	$-0.743183\pi$
$359$	−9411.37	−1.38360	−0.691801	+	0.722088i	$0.743183\pi$
$360$	−1284.39	−0.188037
$361$	12787.9	1.86439
$362$	8518.11	1.23675
$363$	−2844.78	−0.411328
$364$	0	0
$365$	−10989.9	−1.57600
$366$	3944.40	0.563326
$367$	2360.07	0.335680	0.167840	−	0.985814i	$-0.446321\pi$
$367$	2360.07	0.335680	0.167840	+	0.985814i	$0.446321\pi$
$368$	566.475	0.0802433
$369$	4448.19	0.627544
$370$	−6515.08	−0.915413
$371$	2537.51	0.355097
$372$	−1813.73	−0.252789
$373$	−4014.36	−0.557254	−0.278627	−	0.960399i	$-0.589879\pi$
$373$	−4014.36	−0.557254	−0.278627	+	0.960399i	$0.589879\pi$
$374$	−6434.30	−0.889598
$375$	2158.74	0.297272
$376$	−2628.01	−0.360451
$377$	0	0
$378$	−2128.00	−0.289557
$379$	−1283.48	−0.173952	−0.0869761	−	0.996210i	$-0.527720\pi$
$379$	−1283.48	−0.173952	−0.0869761	+	0.996210i	$0.527720\pi$
$380$	−8183.14	−1.10470
$381$	7348.23	0.988087
$382$	−2452.17	−0.328440
$383$	8156.71	1.08822	0.544110	−	0.839014i	$-0.316867\pi$
$383$	8156.71	1.08822	0.544110	+	0.839014i	$0.316867\pi$
$384$	−512.000	−0.0680414
$385$	−4617.00	−0.611180
$386$	2266.66	0.298886
$387$	332.354	0.0436551
$388$	23.9203	0.00312982
$389$	12631.7	1.64641	0.823206	−	0.567742i	$-0.192183\pi$
$389$	12631.7	1.64641	0.823206	+	0.567742i	$0.192183\pi$
$390$	0	0
$391$	−2520.48	−0.326001
$392$	392.000	0.0505076
$393$	6211.80	0.797312
$394$	−3154.69	−0.403378
$395$	−14684.7	−1.87054
$396$	−1988.39	−0.252324
$397$	9436.79	1.19299	0.596497	−	0.802615i	$-0.296559\pi$
$397$	9436.79	1.19299	0.596497	+	0.802615i	$0.296559\pi$
$398$	−8983.44	−1.13140
$399$	−3924.68	−0.492431
$400$	1408.37	0.176047
$401$	−14114.7	−1.75774	−0.878870	−	0.477061i	$-0.841702\pi$
$401$	−14114.7	−1.75774	−0.878870	+	0.477061i	$0.841702\pi$
$402$	−2345.53	−0.291005
$403$	0	0
$404$	5139.08	0.632868
$405$	−4539.14	−0.556918
$406$	−2147.67	−0.262529
$407$	−10086.1	−1.22838
$408$	2278.10	0.276428
$409$	4057.73	0.490566	0.245283	−	0.969451i	$-0.421119\pi$
$409$	4057.73	0.490566	0.245283	+	0.969451i	$0.421119\pi$
$410$	−11804.1	−1.42187
$411$	−3488.19	−0.418636
$412$	1849.90	0.221209
$413$	1656.68	0.197385
$414$	−778.903	−0.0924662
$415$	−8008.29	−0.947257
$416$	0	0
$417$	−600.187	−0.0704827
$418$	−12668.5	−1.48238
$419$	−6602.20	−0.769781	−0.384891	−	0.922962i	$-0.625761\pi$
$419$	−6602.20	−0.769781	−0.384891	+	0.922962i	$0.625761\pi$
$420$	1634.68	0.189914
$421$	11217.2	1.29856	0.649281	−	0.760548i	$-0.275070\pi$
$421$	11217.2	1.29856	0.649281	+	0.760548i	$0.275070\pi$
$422$	1105.49	0.127522
$423$	3613.52	0.415355
$424$	−2900.01	−0.332163
$425$	−6266.44	−0.715217
$426$	−8626.30	−0.981093
$427$	3451.35	0.391154
$428$	5045.35	0.569804
$429$	0	0
$430$	−881.967	−0.0989122
$431$	−9337.27	−1.04353	−0.521764	−	0.853090i	$-0.674726\pi$
$431$	−9337.27	−1.04353	−0.521764	+	0.853090i	$0.674726\pi$
$432$	2432.00	0.270856
$433$	−6352.77	−0.705069	−0.352534	−	0.935799i	$-0.614680\pi$
$433$	−6352.77	−0.705069	−0.352534	+	0.935799i	$0.614680\pi$
$434$	−1587.01	−0.175528
$435$	−8955.96	−0.987139
$436$	−4076.98	−0.447825
$437$	−4962.58	−0.543232
$438$	6023.81	0.657144
$439$	3015.43	0.327832	0.163916	−	0.986474i	$-0.447587\pi$
$439$	3015.43	0.327832	0.163916	+	0.986474i	$0.447587\pi$
$440$	5276.58	0.571707
$441$	−539.000	−0.0582011
$442$	0	0
$443$	4907.23	0.526297	0.263149	−	0.964755i	$-0.415239\pi$
$443$	4907.23	0.526297	0.263149	+	0.964755i	$0.415239\pi$
$444$	3571.05	0.381699
$445$	10141.4	1.08033
$446$	2783.37	0.295508
$447$	7067.85	0.747870
$448$	−448.000	−0.0472456
$449$	5172.97	0.543714	0.271857	−	0.962338i	$-0.412362\pi$
$449$	5172.97	0.543714	0.271857	+	0.962338i	$0.412362\pi$
$450$	−1936.51	−0.202863
$451$	−18274.2	−1.90798
$452$	7030.21	0.731578
$453$	5432.40	0.563436
$454$	−4094.47	−0.423267
$455$	0	0
$456$	4485.35	0.460627
$457$	−6236.10	−0.638321	−0.319160	−	0.947701i	$-0.603401\pi$
$457$	−6236.10	−0.638321	−0.319160	+	0.947701i	$0.603401\pi$
$458$	3649.16	0.372302
$459$	−10821.0	−1.10039
$460$	2066.97	0.209507
$461$	−14436.3	−1.45849	−0.729246	−	0.684251i	$-0.760129\pi$
$461$	−14436.3	−1.45849	−0.729246	+	0.684251i	$0.760129\pi$
$462$	2530.68	0.254844
$463$	−7279.88	−0.730723	−0.365361	−	0.930866i	$-0.619055\pi$
$463$	−7279.88	−0.730723	−0.365361	+	0.930866i	$0.619055\pi$
$464$	2454.47	0.245574
$465$	−6617.98	−0.660003
$466$	8800.75	0.874865
$467$	6041.12	0.598608	0.299304	−	0.954158i	$-0.403246\pi$
$467$	6041.12	0.598608	0.299304	+	0.954158i	$0.403246\pi$
$468$	0	0
$469$	−2052.33	−0.202064
$470$	−9589.18	−0.941097
$471$	−11911.5	−1.16529
$472$	−1893.35	−0.184637
$473$	−1365.39	−0.132729
$474$	8048.96	0.779960
$475$	−12338.0	−1.19180
$476$	1993.34	0.191942
$477$	3987.52	0.382759
$478$	−3193.74	−0.305603
$479$	1148.38	0.109542	0.0547712	−	0.998499i	$-0.482557\pi$
$479$	1148.38	0.109542	0.0547712	+	0.998499i	$0.482557\pi$
$480$	−1868.20	−0.177649
$481$	0	0
$482$	−1982.31	−0.187328
$483$	991.331	0.0933895
$484$	2844.78	0.267165
$485$	87.2813	0.00817163
$486$	−5720.00	−0.533878
$487$	−5186.15	−0.482561	−0.241280	−	0.970455i	$-0.577567\pi$
$487$	−5186.15	−0.482561	−0.241280	+	0.970455i	$0.577567\pi$
$488$	−3944.40	−0.365891
$489$	9497.53	0.878309
$490$	1430.34	0.131870
$491$	11669.4	1.07257	0.536284	−	0.844037i	$-0.319828\pi$
$491$	11669.4	1.07257	0.536284	+	0.844037i	$0.319828\pi$
$492$	6470.10	0.592875
$493$	−10921.0	−0.997680
$494$	0	0
$495$	−7255.29	−0.658790
$496$	1813.73	0.164191
$497$	−7548.01	−0.681237
$498$	4389.51	0.394977
$499$	15641.0	1.40318	0.701591	−	0.712580i	$-0.252474\pi$
$499$	15641.0	1.40318	0.701591	+	0.712580i	$0.252474\pi$
$500$	−2158.74	−0.193084
$501$	14416.7	1.28561
$502$	−13829.3	−1.22955
$503$	−5233.06	−0.463878	−0.231939	−	0.972730i	$-0.574507\pi$
$503$	−5233.06	−0.463878	−0.231939	+	0.972730i	$0.574507\pi$
$504$	616.000	0.0544421
$505$	18751.6	1.65235
$506$	3199.92	0.281134
$507$	0	0
$508$	−7348.23	−0.641781
$509$	−4060.88	−0.353626	−0.176813	−	0.984244i	$-0.556579\pi$
$509$	−4060.88	−0.353626	−0.176813	+	0.984244i	$0.556579\pi$
$510$	8312.40	0.721724
$511$	5270.84	0.456298
$512$	512.000	0.0441942
$513$	−21305.4	−1.83364
$514$	−4927.42	−0.422839
$515$	6749.97	0.577552
$516$	483.425	0.0412434
$517$	−14845.2	−1.26285
$518$	3124.67	0.265039
$519$	−5624.59	−0.475707
$520$	0	0
$521$	−10601.1	−0.891444	−0.445722	−	0.895171i	$-0.647053\pi$
$521$	−10601.1	−0.891444	−0.445722	+	0.895171i	$0.647053\pi$
$522$	−3374.90	−0.282980
$523$	−5860.52	−0.489986	−0.244993	−	0.969525i	$-0.578786\pi$
$523$	−5860.52	−0.489986	−0.244993	+	0.969525i	$0.578786\pi$
$524$	−6211.80	−0.517870
$525$	2464.66	0.204888
$526$	−6962.85	−0.577176
$527$	−8070.02	−0.667051
$528$	−2892.20	−0.238384
$529$	−10913.5	−0.896976
$530$	−10581.7	−0.867241
$531$	2603.36	0.212761
$532$	3924.68	0.319843
$533$	0	0
$534$	−5558.69	−0.450464
$535$	18409.6	1.48770
$536$	2345.53	0.189014
$537$	18447.0	1.48240
$538$	−9727.53	−0.779524
$539$	2214.34	0.176954
$540$	8873.96	0.707174
$541$	−7541.64	−0.599335	−0.299668	−	0.954044i	$-0.596876\pi$
$541$	−7541.64	−0.599335	−0.299668	+	0.954044i	$0.596876\pi$
$542$	−3509.73	−0.278147
$543$	−17036.2	−1.34640
$544$	−2278.10	−0.179546
$545$	−14876.2	−1.16922
$546$	0	0
$547$	2986.04	0.233407	0.116704	−	0.993167i	$-0.462767\pi$
$547$	2986.04	0.233407	0.116704	+	0.993167i	$0.462767\pi$
$548$	3488.19	0.271912
$549$	5423.55	0.421624
$550$	7955.67	0.616783
$551$	−21502.3	−1.66249
$552$	−1132.95	−0.0873579
$553$	7042.84	0.541577
$554$	16801.8	1.28852
$555$	13030.2	0.996575
$556$	600.187	0.0457799
$557$	−2255.08	−0.171546	−0.0857728	−	0.996315i	$-0.527336\pi$
$557$	−2255.08	−0.171546	−0.0857728	+	0.996315i	$0.527336\pi$
$558$	−2493.87	−0.189201
$559$	0	0
$560$	−1634.68	−0.123353
$561$	12868.6	0.968472
$562$	6232.20	0.467775
$563$	−13066.1	−0.978100	−0.489050	−	0.872256i	$-0.662657\pi$
$563$	−13066.1	−0.978100	−0.489050	+	0.872256i	$0.662657\pi$
$564$	5256.03	0.392409
$565$	25652.0	1.91007
$566$	17238.9	1.28022
$567$	2177.00	0.161244
$568$	8626.30	0.637239
$569$	−17119.7	−1.26133	−0.630665	−	0.776055i	$-0.717218\pi$
$569$	−17119.7	−1.26133	−0.630665	+	0.776055i	$0.717218\pi$
$570$	16366.3	1.20265
$571$	13365.4	0.979555	0.489777	−	0.871848i	$-0.337078\pi$
$571$	13365.4	0.979555	0.489777	+	0.871848i	$0.337078\pi$
$572$	0	0
$573$	4904.35	0.357560
$574$	5661.34	0.411672
$575$	3116.44	0.226025
$576$	−704.000	−0.0509259
$577$	21590.5	1.55776	0.778878	−	0.627176i	$-0.215789\pi$
$577$	21590.5	1.55776	0.778878	+	0.627176i	$0.215789\pi$
$578$	310.215	0.0223240
$579$	−4533.32	−0.325386
$580$	8955.96	0.641166
$581$	3840.82	0.274258
$582$	−47.8407	−0.00340732
$583$	−16381.7	−1.16374
$584$	−6023.81	−0.426827
$585$	0	0
$586$	−11535.8	−0.813204
$587$	28308.0	1.99045	0.995225	−	0.0976053i	$-0.0311183\pi$
$587$	28308.0	1.99045	0.995225	+	0.0976053i	$0.0311183\pi$
$588$	−784.000	−0.0549857
$589$	−15889.1	−1.11154
$590$	−6908.52	−0.482067
$591$	6309.38	0.439142
$592$	−3571.05	−0.247921
$593$	−26787.9	−1.85505	−0.927526	−	0.373758i	$-0.878069\pi$
$593$	−26787.9	−1.85505	−0.927526	+	0.373758i	$0.878069\pi$
$594$	13738.0	0.948948
$595$	7273.35	0.501140
$596$	−7067.85	−0.485756
$597$	17966.9	1.23172
$598$	0	0
$599$	13976.8	0.953384	0.476692	−	0.879070i	$-0.341836\pi$
$599$	13976.8	0.953384	0.476692	+	0.879070i	$0.341836\pi$
$600$	−2816.75	−0.191655
$601$	12370.2	0.839589	0.419794	−	0.907619i	$-0.362102\pi$
$601$	12370.2	0.839589	0.419794	+	0.907619i	$0.362102\pi$
$602$	422.997	0.0286380
$603$	−3225.10	−0.217804
$604$	−5432.40	−0.365962
$605$	10380.1	0.697539
$606$	−10278.2	−0.688979
$607$	9119.67	0.609812	0.304906	−	0.952382i	$-0.401375\pi$
$607$	9119.67	0.609812	0.304906	+	0.952382i	$0.401375\pi$
$608$	−4485.35	−0.299186
$609$	4295.33	0.285806
$610$	−14392.5	−0.955301
$611$	0	0
$612$	3132.39	0.206894
$613$	19688.3	1.29723	0.648616	−	0.761116i	$-0.275348\pi$
$613$	19688.3	1.29723	0.648616	+	0.761116i	$0.275348\pi$
$614$	−13357.2	−0.877938
$615$	23608.3	1.54793
$616$	−2530.68	−0.165526
$617$	10008.8	0.653059	0.326529	−	0.945187i	$-0.394121\pi$
$617$	10008.8	0.653059	0.326529	+	0.945187i	$0.394121\pi$
$618$	−3699.80	−0.240822
$619$	−557.553	−0.0362035	−0.0181017	−	0.999836i	$-0.505762\pi$
$619$	−557.553	−0.0362035	−0.0181017	+	0.999836i	$0.505762\pi$
$620$	6617.98	0.428685
$621$	5381.51	0.347750
$622$	12116.7	0.781085
$623$	−4863.85	−0.312787
$624$	0	0
$625$	−18879.8	−1.20831
$626$	−3606.86	−0.230286
$627$	25337.0	1.61381
$628$	11911.5	0.756878
$629$	15889.1	1.00722
$630$	2247.68	0.142142
$631$	8719.45	0.550105	0.275052	−	0.961429i	$-0.411305\pi$
$631$	8719.45	0.550105	0.275052	+	0.961429i	$0.411305\pi$
$632$	−8048.96	−0.506599
$633$	−2210.97	−0.138828
$634$	5983.59	0.374824
$635$	−26812.4	−1.67562
$636$	5800.03	0.361613
$637$	0	0
$638$	13864.9	0.860372
$639$	−11861.2	−0.734304
$640$	1868.20	0.115386
$641$	25748.3	1.58658	0.793290	−	0.608844i	$-0.208367\pi$
$641$	25748.3	1.58658	0.793290	+	0.608844i	$0.208367\pi$
$642$	−10090.7	−0.620324
$643$	−8232.31	−0.504900	−0.252450	−	0.967610i	$-0.581236\pi$
$643$	−8232.31	−0.504900	−0.252450	+	0.967610i	$0.581236\pi$
$644$	−991.331	−0.0606583
$645$	1763.93	0.107682
$646$	19957.2	1.21549
$647$	18148.2	1.10275	0.551374	−	0.834258i	$-0.314104\pi$
$647$	18148.2	1.10275	0.551374	+	0.834258i	$0.314104\pi$
$648$	−2488.00	−0.150830
$649$	−10695.2	−0.646879
$650$	0	0
$651$	3174.02	0.191090
$652$	−9497.53	−0.570478
$653$	2181.33	0.130723	0.0653615	−	0.997862i	$-0.479180\pi$
$653$	2181.33	0.130723	0.0653615	+	0.997862i	$0.479180\pi$
$654$	8153.96	0.487530
$655$	−22665.8	−1.35210
$656$	−6470.10	−0.385084
$657$	8282.74	0.491843
$658$	4599.02	0.272475
$659$	−21918.6	−1.29564	−0.647821	−	0.761792i	$-0.724320\pi$
$659$	−21918.6	−1.29564	−0.647821	+	0.761792i	$0.724320\pi$
$660$	−10553.2	−0.622395
$661$	−442.755	−0.0260532	−0.0130266	−	0.999915i	$-0.504147\pi$
$661$	−442.755	−0.0260532	−0.0130266	+	0.999915i	$0.504147\pi$
$662$	−14028.9	−0.823638
$663$	0	0
$664$	−4389.51	−0.256545
$665$	14320.5	0.835076
$666$	4910.19	0.285685
$667$	5431.24	0.315290
$668$	−14416.7	−0.835030
$669$	−5566.74	−0.321708
$670$	8558.42	0.493494
$671$	−22281.3	−1.28191
$672$	896.000	0.0514344
$673$	6938.42	0.397409	0.198705	−	0.980059i	$-0.436327\pi$
$673$	6938.42	0.397409	0.198705	+	0.980059i	$0.436327\pi$
$674$	−17859.2	−1.02064
$675$	13379.6	0.762932
$676$	0	0
$677$	−4240.88	−0.240754	−0.120377	−	0.992728i	$-0.538410\pi$
$677$	−4240.88	−0.240754	−0.120377	+	0.992728i	$0.538410\pi$
$678$	−14060.4	−0.796441
$679$	−41.8606	−0.00236592
$680$	−8312.40	−0.468774
$681$	8188.95	0.460795
$682$	10245.4	0.575246
$683$	−5071.56	−0.284126	−0.142063	−	0.989858i	$-0.545374\pi$
$683$	−5071.56	−0.284126	−0.142063	+	0.989858i	$0.545374\pi$
$684$	6167.36	0.344759
$685$	12727.8	0.709933
$686$	−686.000	−0.0381802
$687$	−7298.33	−0.405311
$688$	−483.425	−0.0267884
$689$	0	0
$690$	−4133.94	−0.228082
$691$	3457.17	0.190329	0.0951643	−	0.995462i	$-0.469662\pi$
$691$	3457.17	0.190329	0.0951643	+	0.995462i	$0.469662\pi$
$692$	5624.59	0.308981
$693$	3479.68	0.190739
$694$	−1512.59	−0.0827336
$695$	2189.98	0.119526
$696$	−4908.95	−0.267347
$697$	28788.2	1.56446
$698$	−10522.8	−0.570619
$699$	−17601.5	−0.952432
$700$	−2464.66	−0.133079
$701$	32549.3	1.75374	0.876869	−	0.480730i	$-0.159628\pi$
$701$	32549.3	1.75374	0.876869	+	0.480730i	$0.159628\pi$
$702$	0	0
$703$	31284.0	1.67838
$704$	2892.20	0.154835
$705$	19178.4	1.02454
$706$	−22155.3	−1.18106
$707$	−8993.39	−0.478403
$708$	3786.70	0.201007
$709$	31821.1	1.68557	0.842783	−	0.538253i	$-0.180916\pi$
$709$	31821.1	1.68557	0.842783	+	0.538253i	$0.180916\pi$
$710$	31475.9	1.66376
$711$	11067.3	0.583765
$712$	5558.69	0.292585
$713$	4013.40	0.210804
$714$	−3986.68	−0.208960
$715$	0	0
$716$	−18447.0	−0.962845
$717$	6387.48	0.332698
$718$	−18822.7	−0.978355
$719$	−24974.7	−1.29541	−0.647705	−	0.761891i	$-0.724271\pi$
$719$	−24974.7	−1.29541	−0.647705	+	0.761891i	$0.724271\pi$
$720$	−2568.78	−0.132962
$721$	−3237.32	−0.167218
$722$	25575.7	1.31832
$723$	3964.63	0.203936
$724$	17036.2	0.874512
$725$	13503.2	0.691719
$726$	−5689.55	−0.290853
$727$	−19276.0	−0.983364	−0.491682	−	0.870775i	$-0.663618\pi$
$727$	−19276.0	−0.983364	−0.491682	+	0.870775i	$0.663618\pi$
$728$	0	0
$729$	19837.0	1.00782
$730$	−21979.9	−1.11440
$731$	2150.96	0.108832
$732$	7888.80	0.398331
$733$	−17945.0	−0.904250	−0.452125	−	0.891955i	$-0.649334\pi$
$733$	−17945.0	−0.904250	−0.452125	+	0.891955i	$0.649334\pi$
$734$	4720.14	0.237362
$735$	−2860.68	−0.143562
$736$	1132.95	0.0567406
$737$	13249.5	0.662213
$738$	8896.39	0.443741
$739$	35780.6	1.78107	0.890534	−	0.454917i	$-0.150331\pi$
$739$	35780.6	1.78107	0.890534	+	0.454917i	$0.150331\pi$
$740$	−13030.2	−0.647295
$741$	0	0
$742$	5075.02	0.251092
$743$	−15436.8	−0.762207	−0.381104	−	0.924532i	$-0.624456\pi$
$743$	−15436.8	−0.762207	−0.381104	+	0.924532i	$0.624456\pi$
$744$	−3627.45	−0.178748
$745$	−25789.4	−1.26826
$746$	−8028.72	−0.394038
$747$	6035.58	0.295623
$748$	−12868.6	−0.629041
$749$	−8829.37	−0.430732
$750$	4317.48	0.210203
$751$	21774.5	1.05801	0.529004	−	0.848619i	$-0.322566\pi$
$751$	21774.5	1.05801	0.529004	+	0.848619i	$0.322566\pi$
$752$	−5256.03	−0.254877
$753$	27658.6	1.33856
$754$	0	0
$755$	−19821.9	−0.955488
$756$	−4256.00	−0.204748
$757$	12456.0	0.598048	0.299024	−	0.954246i	$-0.403339\pi$
$757$	12456.0	0.598048	0.299024	+	0.954246i	$0.403339\pi$
$758$	−2566.96	−0.123003
$759$	−6399.84	−0.306060
$760$	−16366.3	−0.781142
$761$	8480.56	0.403969	0.201984	−	0.979389i	$-0.435261\pi$
$761$	8480.56	0.403969	0.201984	+	0.979389i	$0.435261\pi$
$762$	14696.5	0.698683
$763$	7134.71	0.338524
$764$	−4904.35	−0.232242
$765$	11429.6	0.540178
$766$	16313.4	0.769488
$767$	0	0
$768$	−1024.00	−0.0481125
$769$	−3990.61	−0.187133	−0.0935664	−	0.995613i	$-0.529827\pi$
$769$	−3990.61	−0.187133	−0.0935664	+	0.995613i	$0.529827\pi$
$770$	−9234.01	−0.432169
$771$	9854.85	0.460329
$772$	4533.32	0.211344
$773$	38183.5	1.77667	0.888334	−	0.459198i	$-0.151863\pi$
$773$	38183.5	1.77667	0.888334	+	0.459198i	$0.151863\pi$
$774$	664.709	0.0308688
$775$	9978.15	0.462485
$776$	47.8407	0.00221312
$777$	−6249.34	−0.288538
$778$	25263.5	1.16419
$779$	56681.0	2.60694
$780$	0	0
$781$	48728.5	2.23258
$782$	−5040.96	−0.230517
$783$	23317.5	1.06424
$784$	784.000	0.0357143
$785$	43462.9	1.97612
$786$	12423.6	0.563785
$787$	−13726.8	−0.621740	−0.310870	−	0.950452i	$-0.600620\pi$
$787$	−13726.8	−0.621740	−0.310870	+	0.950452i	$0.600620\pi$
$788$	−6309.38	−0.285231
$789$	13925.7	0.628350
$790$	−29369.3	−1.32267
$791$	−12302.9	−0.553021
$792$	−3976.78	−0.178420
$793$	0	0
$794$	18873.6	0.843575
$795$	21163.3	0.944133
$796$	−17966.9	−0.800024
$797$	10705.2	0.475780	0.237890	−	0.971292i	$-0.423544\pi$
$797$	10705.2	0.475780	0.237890	+	0.971292i	$0.423544\pi$
$798$	−7849.37	−0.348201
$799$	23386.2	1.03548
$800$	2816.75	0.124484
$801$	−7643.20	−0.337152
$802$	−28229.4	−1.24291
$803$	−34027.5	−1.49540
$804$	−4691.05	−0.205772
$805$	−3617.20	−0.158372
$806$	0	0
$807$	19455.1	0.848638
$808$	10278.2	0.447505
$809$	15455.6	0.671683	0.335841	−	0.941919i	$-0.390979\pi$
$809$	15455.6	0.671683	0.335841	+	0.941919i	$0.390979\pi$
$810$	−9078.29	−0.393801
$811$	11348.1	0.491352	0.245676	−	0.969352i	$-0.420990\pi$
$811$	11348.1	0.491352	0.245676	+	0.969352i	$0.420990\pi$
$812$	−4295.33	−0.185636
$813$	7019.45	0.302808
$814$	−20172.3	−0.868596
$815$	−34654.9	−1.48946
$816$	4556.20	0.195464
$817$	4235.02	0.181352
$818$	8115.45	0.346883
$819$	0	0
$820$	−23608.3	−1.00541
$821$	23152.6	0.984205	0.492103	−	0.870537i	$-0.336228\pi$
$821$	23152.6	0.984205	0.492103	+	0.870537i	$0.336228\pi$
$822$	−6976.37	−0.296021
$823$	−10049.3	−0.425633	−0.212816	−	0.977092i	$-0.568264\pi$
$823$	−10049.3	−0.425633	−0.212816	+	0.977092i	$0.568264\pi$
$824$	3699.80	0.156418
$825$	−15911.3	−0.671469
$826$	3313.37	0.139572
$827$	−11736.0	−0.493470	−0.246735	−	0.969083i	$-0.579358\pi$
$827$	−11736.0	−0.493470	−0.246735	+	0.969083i	$0.579358\pi$
$828$	−1557.81	−0.0653834
$829$	32907.0	1.37866	0.689328	−	0.724449i	$-0.257906\pi$
$829$	32907.0	1.37866	0.689328	+	0.724449i	$0.257906\pi$
$830$	−16016.6	−0.669812
$831$	−33603.6	−1.40276
$832$	0	0
$833$	−3488.34	−0.145095
$834$	−1200.37	−0.0498388
$835$	−52604.2	−2.18017
$836$	−25337.0	−1.04820
$837$	17230.4	0.711553
$838$	−13204.4	−0.544318
$839$	−16844.3	−0.693122	−0.346561	−	0.938027i	$-0.612651\pi$
$839$	−16844.3	−0.693122	−0.346561	+	0.938027i	$0.612651\pi$
$840$	3269.35	0.134290
$841$	−856.004	−0.0350980
$842$	22434.5	0.918222
$843$	−12464.4	−0.509249
$844$	2210.97	0.0901715
$845$	0	0
$846$	7227.04	0.293701
$847$	−4978.36	−0.201958
$848$	−5800.03	−0.234875
$849$	−34477.8	−1.39373
$850$	−12532.9	−0.505735
$851$	−7901.99	−0.318304
$852$	−17252.6	−0.693738
$853$	24234.7	0.972780	0.486390	−	0.873742i	$-0.338313\pi$
$853$	24234.7	0.972780	0.486390	+	0.873742i	$0.338313\pi$
$854$	6902.70	0.276587
$855$	22503.6	0.900127
$856$	10090.7	0.402913
$857$	12928.3	0.515313	0.257657	−	0.966237i	$-0.417050\pi$
$857$	12928.3	0.515313	0.257657	+	0.966237i	$0.417050\pi$
$858$	0	0
$859$	25031.3	0.994245	0.497122	−	0.867680i	$-0.334390\pi$
$859$	25031.3	0.994245	0.497122	+	0.867680i	$0.334390\pi$
$860$	−1763.93	−0.0699415
$861$	−11322.7	−0.448172
$862$	−18674.5	−0.737886
$863$	43433.2	1.71319	0.856595	−	0.515990i	$-0.172576\pi$
$863$	43433.2	1.71319	0.856595	+	0.515990i	$0.172576\pi$
$864$	4864.00	0.191524
$865$	20523.2	0.806715
$866$	−12705.5	−0.498559
$867$	−620.430	−0.0243032
$868$	−3174.02	−0.124117
$869$	−45467.2	−1.77488
$870$	−17911.9	−0.698013
$871$	0	0
$872$	−8153.96	−0.316660
$873$	−65.7810	−0.00255023
$874$	−9925.15	−0.384123
$875$	3777.80	0.145958
$876$	12047.6	0.464671
$877$	−38457.0	−1.48073	−0.740366	−	0.672205i	$-0.765348\pi$
$877$	−38457.0	−1.48073	−0.740366	+	0.672205i	$0.765348\pi$
$878$	6030.85	0.231813
$879$	23071.5	0.885305
$880$	10553.2	0.404258
$881$	6886.60	0.263355	0.131677	−	0.991293i	$-0.457964\pi$
$881$	6886.60	0.263355	0.131677	+	0.991293i	$0.457964\pi$
$882$	−1078.00	−0.0411544
$883$	−19659.5	−0.749257	−0.374628	−	0.927175i	$-0.622230\pi$
$883$	−19659.5	−0.749257	−0.374628	+	0.927175i	$0.622230\pi$
$884$	0	0
$885$	13817.0	0.524808
$886$	9814.46	0.372148
$887$	9763.21	0.369579	0.184790	−	0.982778i	$-0.440840\pi$
$887$	9763.21	0.369579	0.184790	+	0.982778i	$0.440840\pi$
$888$	7142.10	0.269902
$889$	12859.4	0.485141
$890$	20282.7	0.763908
$891$	−14054.3	−0.528436
$892$	5566.74	0.208955
$893$	46045.2	1.72547
$894$	14135.7	0.528824
$895$	−67310.0	−2.51388
$896$	−896.000	−0.0334077
$897$	0	0
$898$	10345.9	0.384464
$899$	17389.6	0.645135
$900$	−3873.03	−0.143446
$901$	25806.7	0.954214
$902$	−36548.5	−1.34915
$903$	−845.993	−0.0311771
$904$	14060.4	0.517304
$905$	62162.3	2.28325
$906$	10864.8	0.398409
$907$	17437.9	0.638387	0.319193	−	0.947690i	$-0.396588\pi$
$907$	17437.9	0.638387	0.319193	+	0.947690i	$0.396588\pi$
$908$	−8188.95	−0.299295
$909$	−14132.5	−0.515670
$910$	0	0
$911$	407.455	0.0148184	0.00740920	−	0.999973i	$-0.497642\pi$
$911$	407.455	0.0148184	0.00740920	+	0.999973i	$0.497642\pi$
$912$	8970.70	0.325712
$913$	−24795.6	−0.898811
$914$	−12472.2	−0.451361
$915$	28784.9	1.04000
$916$	7298.33	0.263257
$917$	10870.6	0.391473
$918$	−21642.0	−0.778095
$919$	−33299.6	−1.19527	−0.597634	−	0.801769i	$-0.703893\pi$
$919$	−33299.6	−1.19527	−0.597634	+	0.801769i	$0.703893\pi$
$920$	4133.94	0.148143
$921$	26714.5	0.955778
$922$	−28872.6	−1.03131
$923$	0	0
$924$	5061.35	0.180202
$925$	−19646.0	−0.698331
$926$	−14559.8	−0.516699
$927$	−5087.22	−0.180244
$928$	4908.95	0.173647
$929$	12796.3	0.451919	0.225959	−	0.974137i	$-0.427448\pi$
$929$	12796.3	0.451919	0.225959	+	0.974137i	$0.427448\pi$
$930$	−13236.0	−0.466693
$931$	−6868.20	−0.241779
$932$	17601.5	0.618623
$933$	−24233.4	−0.850337
$934$	12082.2	0.423280
$935$	−46955.3	−1.64236
$936$	0	0
$937$	−11598.2	−0.404373	−0.202187	−	0.979347i	$-0.564805\pi$
$937$	−11598.2	−0.404373	−0.202187	+	0.979347i	$0.564805\pi$
$938$	−4104.67	−0.142881
$939$	7213.73	0.250704
$940$	−19178.4	−0.665456
$941$	1581.89	0.0548014	0.0274007	−	0.999625i	$-0.491277\pi$
$941$	1581.89	0.0548014	0.0274007	+	0.999625i	$0.491277\pi$
$942$	−23822.9	−0.823984
$943$	−14317.0	−0.494406
$944$	−3786.70	−0.130558
$945$	−15529.4	−0.534574
$946$	−2730.78	−0.0938535
$947$	2122.54	0.0728335	0.0364168	−	0.999337i	$-0.488406\pi$
$947$	2122.54	0.0728335	0.0364168	+	0.999337i	$0.488406\pi$
$948$	16097.9	0.551515
$949$	0	0
$950$	−24676.0	−0.842732
$951$	−11967.2	−0.408057
$952$	3986.68	0.135724
$953$	44038.0	1.49688	0.748441	−	0.663201i	$-0.230802\pi$
$953$	44038.0	1.49688	0.748441	+	0.663201i	$0.230802\pi$
$954$	7975.04	0.270651
$955$	−17895.1	−0.606359
$956$	−6387.48	−0.216094
$957$	−27729.8	−0.936654
$958$	2296.76	0.0774582
$959$	−6104.33	−0.205546
$960$	−3736.40	−0.125617
$961$	−16941.0	−0.568661
$962$	0	0
$963$	−13874.7	−0.464285
$964$	−3964.63	−0.132461
$965$	16541.3	0.551797
$966$	1982.66	0.0660363
$967$	36277.8	1.20643	0.603214	−	0.797579i	$-0.293886\pi$
$967$	36277.8	1.20643	0.603214	+	0.797579i	$0.293886\pi$
$968$	5689.55	0.188914
$969$	−39914.4	−1.32326
$970$	174.563	0.00577821
$971$	−38873.1	−1.28475	−0.642377	−	0.766389i	$-0.722052\pi$
$971$	−38873.1	−1.28475	−0.642377	+	0.766389i	$0.722052\pi$
$972$	−11440.0	−0.377508
$973$	−1050.33	−0.0346063
$974$	−10372.3	−0.341222
$975$	0	0
$976$	−7888.80	−0.258724
$977$	−20503.7	−0.671414	−0.335707	−	0.941966i	$-0.608975\pi$
$977$	−20503.7	−0.671414	−0.335707	+	0.941966i	$0.608975\pi$
$978$	18995.1	0.621058
$979$	31400.1	1.02508
$980$	2860.68	0.0932461
$981$	11211.7	0.364895
$982$	23338.7	0.758420
$983$	−16430.4	−0.533112	−0.266556	−	0.963819i	$-0.585886\pi$
$983$	−16430.4	−0.533112	−0.266556	+	0.963819i	$0.585886\pi$
$984$	12940.2	0.419226
$985$	−23021.9	−0.744708
$986$	−21842.0	−0.705466
$987$	−9198.05	−0.296633
$988$	0	0
$989$	−1069.72	−0.0343934
$990$	−14510.6	−0.465835
$991$	−33349.7	−1.06901	−0.534504	−	0.845166i	$-0.679502\pi$
$991$	−33349.7	−1.06901	−0.534504	+	0.845166i	$0.679502\pi$
$992$	3627.45	0.116101
$993$	28057.8	0.896664
$994$	−15096.0	−0.481707
$995$	−65558.1	−2.08877
$996$	8779.02	0.279291
$997$	47080.5	1.49554	0.747770	−	0.663958i	$-0.231125\pi$
$997$	47080.5	1.49554	0.747770	+	0.663958i	$0.231125\pi$
$998$	31282.0	0.992199
$999$	−33925.0	−1.07441

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.4.a.k.1.2		2
13.12	even	2		182.4.a.f.1.1	✓	2
39.38	odd	2		1638.4.a.p.1.2		2
52.51	odd	2		1456.4.a.l.1.1		2
91.90	odd	2		1274.4.a.k.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.4.a.f.1.1	✓	2	13.12	even	2
1274.4.a.k.1.2		2	91.90	odd	2
1456.4.a.l.1.1		2	52.51	odd	2
1638.4.a.p.1.2		2	39.38	odd	2
2366.4.a.k.1.2		2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2366.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -4.00000 q^{3} +4.00000 q^{4} +14.5953 q^{5} -8.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} -11.0000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -4.00000 q^{3} +4.00000 q^{4} +14.5953 q^{5} -8.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} -11.0000 q^{9} +29.1906 q^{10} +45.1906 q^{11} -16.0000 q^{12} -14.0000 q^{14} -58.3813 q^{15} +16.0000 q^{16} -71.1906 q^{17} -22.0000 q^{18} -140.167 q^{19} +58.3813 q^{20} +28.0000 q^{21} +90.3813 q^{22} +35.4047 q^{23} -32.0000 q^{24} +88.0234 q^{25} +152.000 q^{27} -28.0000 q^{28} +153.405 q^{29} -116.763 q^{30} +113.358 q^{31} +32.0000 q^{32} -180.763 q^{33} -142.381 q^{34} -102.167 q^{35} -44.0000 q^{36} -223.191 q^{37} -280.334 q^{38} +116.763 q^{40} -404.381 q^{41} +56.0000 q^{42} -30.2140 q^{43} +180.763 q^{44} -160.549 q^{45} +70.8094 q^{46} -328.502 q^{47} -64.0000 q^{48} +49.0000 q^{49} +176.047 q^{50} +284.763 q^{51} -362.502 q^{53} +304.000 q^{54} +659.572 q^{55} -56.0000 q^{56} +560.669 q^{57} +306.809 q^{58} -236.669 q^{59} -233.525 q^{60} -493.050 q^{61} +226.716 q^{62} +77.0000 q^{63} +64.0000 q^{64} -361.525 q^{66} +293.191 q^{67} -284.763 q^{68} -141.619 q^{69} -204.334 q^{70} +1078.29 q^{71} -88.0000 q^{72} -752.977 q^{73} -446.381 q^{74} -352.094 q^{75} -560.669 q^{76} -316.334 q^{77} -1006.12 q^{79} +233.525 q^{80} -311.000 q^{81} -808.763 q^{82} -548.689 q^{83} +112.000 q^{84} -1039.05 q^{85} -60.4281 q^{86} -613.619 q^{87} +361.525 q^{88} +694.836 q^{89} -321.097 q^{90} +141.619 q^{92} -453.432 q^{93} -657.003 q^{94} -2045.79 q^{95} -128.000 q^{96} +5.98009 q^{97} +98.0000 q^{98} -497.097 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} - 8 q^{3} + 8 q^{4} - 5 q^{5} - 16 q^{6} - 14 q^{7} + 16 q^{8} - 22 q^{9}+O(q^{10}) \) 2 * q + 4 * q^2 - 8 * q^3 + 8 * q^4 - 5 * q^5 - 16 * q^6 - 14 * q^7 + 16 * q^8 - 22 * q^9	\( 2 q + 4 q^{2} - 8 q^{3} + 8 q^{4} - 5 q^{5} - 16 q^{6} - 14 q^{7} + 16 q^{8} - 22 q^{9} - 10 q^{10} + 22 q^{11} - 32 q^{12} - 28 q^{14} + 20 q^{15} + 32 q^{16} - 74 q^{17} - 44 q^{18} - 41 q^{19} - 20 q^{20} + 56 q^{21} + 44 q^{22} + 105 q^{23} - 64 q^{24} + 347 q^{25} + 304 q^{27} - 56 q^{28} + 341 q^{29} + 40 q^{30} - 81 q^{31} + 64 q^{32} - 88 q^{33} - 148 q^{34} + 35 q^{35} - 88 q^{36} - 378 q^{37} - 82 q^{38} - 40 q^{40} - 672 q^{41} + 112 q^{42} - 163 q^{43} + 88 q^{44} + 55 q^{45} + 210 q^{46} + 61 q^{47} - 128 q^{48} + 98 q^{49} + 694 q^{50} + 296 q^{51} - 7 q^{53} + 608 q^{54} + 1114 q^{55} - 112 q^{56} + 164 q^{57} + 682 q^{58} + 484 q^{59} + 80 q^{60} + 108 q^{61} - 162 q^{62} + 154 q^{63} + 128 q^{64} - 176 q^{66} + 518 q^{67} - 296 q^{68} - 420 q^{69} + 70 q^{70} + 1336 q^{71} - 176 q^{72} - 1335 q^{73} - 756 q^{74} - 1388 q^{75} - 164 q^{76} - 154 q^{77} - 1431 q^{79} - 80 q^{80} - 622 q^{81} - 1344 q^{82} - 1747 q^{83} + 224 q^{84} - 984 q^{85} - 326 q^{86} - 1364 q^{87} + 176 q^{88} + 193 q^{89} + 110 q^{90} + 420 q^{92} + 324 q^{93} + 122 q^{94} - 3989 q^{95} - 256 q^{96} - 1595 q^{97} + 196 q^{98} - 242 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 - 8 * q^3 + 8 * q^4 - 5 * q^5 - 16 * q^6 - 14 * q^7 + 16 * q^8 - 22 * q^9 - 10 * q^10 + 22 * q^11 - 32 * q^12 - 28 * q^14 + 20 * q^15 + 32 * q^16 - 74 * q^17 - 44 * q^18 - 41 * q^19 - 20 * q^20 + 56 * q^21 + 44 * q^22 + 105 * q^23 - 64 * q^24 + 347 * q^25 + 304 * q^27 - 56 * q^28 + 341 * q^29 + 40 * q^30 - 81 * q^31 + 64 * q^32 - 88 * q^33 - 148 * q^34 + 35 * q^35 - 88 * q^36 - 378 * q^37 - 82 * q^38 - 40 * q^40 - 672 * q^41 + 112 * q^42 - 163 * q^43 + 88 * q^44 + 55 * q^45 + 210 * q^46 + 61 * q^47 - 128 * q^48 + 98 * q^49 + 694 * q^50 + 296 * q^51 - 7 * q^53 + 608 * q^54 + 1114 * q^55 - 112 * q^56 + 164 * q^57 + 682 * q^58 + 484 * q^59 + 80 * q^60 + 108 * q^61 - 162 * q^62 + 154 * q^63 + 128 * q^64 - 176 * q^66 + 518 * q^67 - 296 * q^68 - 420 * q^69 + 70 * q^70 + 1336 * q^71 - 176 * q^72 - 1335 * q^73 - 756 * q^74 - 1388 * q^75 - 164 * q^76 - 154 * q^77 - 1431 * q^79 - 80 * q^80 - 622 * q^81 - 1344 * q^82 - 1747 * q^83 + 224 * q^84 - 984 * q^85 - 326 * q^86 - 1364 * q^87 + 176 * q^88 + 193 * q^89 + 110 * q^90 + 420 * q^92 + 324 * q^93 + 122 * q^94 - 3989 * q^95 - 256 * q^96 - 1595 * q^97 + 196 * q^98 - 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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