LMFDB - Embedded newform 579.2.a.g.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [579,2,Mod(1,579)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(579, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("579.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 579 = 3 \cdot 193 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	579.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:	$4.62333827703$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 2 x^{12} - 20 x^{11} + 39 x^{10} + 148 x^{9} - 275 x^{8} - 508 x^{7} + 865 x^{6} + 823 x^{5} + \cdots - 48 $ x^13 - 2x^12 - 20x^11 + 39x^10 + 148x^9 - 275x^8 - 508x^7 + 865x^6 + 823x^5 - 1187x^4 - 556x^3 + 576x^2 + 64x - 48
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$1.68916$ of defining polynomial
Character	$\chi$	$=$	579.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.68916 q^{2} +1.00000 q^{3} +0.853276 q^{4} -1.44492 q^{5} +1.68916 q^{6} +2.45560 q^{7} -1.93701 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.68916 q^{2} +1.00000 q^{3} +0.853276 q^{4} -1.44492 q^{5} +1.68916 q^{6} +2.45560 q^{7} -1.93701 q^{8} +1.00000 q^{9} -2.44072 q^{10} +5.26332 q^{11} +0.853276 q^{12} +3.78153 q^{13} +4.14792 q^{14} -1.44492 q^{15} -4.97847 q^{16} -0.858046 q^{17} +1.68916 q^{18} +4.03245 q^{19} -1.23292 q^{20} +2.45560 q^{21} +8.89061 q^{22} -2.21760 q^{23} -1.93701 q^{24} -2.91219 q^{25} +6.38762 q^{26} +1.00000 q^{27} +2.09531 q^{28} -7.87396 q^{29} -2.44072 q^{30} +7.07051 q^{31} -4.53544 q^{32} +5.26332 q^{33} -1.44938 q^{34} -3.54816 q^{35} +0.853276 q^{36} -7.45792 q^{37} +6.81147 q^{38} +3.78153 q^{39} +2.79883 q^{40} -5.27074 q^{41} +4.14792 q^{42} -3.38817 q^{43} +4.49106 q^{44} -1.44492 q^{45} -3.74590 q^{46} -5.84151 q^{47} -4.97847 q^{48} -0.970011 q^{49} -4.91917 q^{50} -0.858046 q^{51} +3.22668 q^{52} +5.20251 q^{53} +1.68916 q^{54} -7.60510 q^{55} -4.75652 q^{56} +4.03245 q^{57} -13.3004 q^{58} -3.43605 q^{59} -1.23292 q^{60} -2.93414 q^{61} +11.9433 q^{62} +2.45560 q^{63} +2.29583 q^{64} -5.46402 q^{65} +8.89061 q^{66} -6.89075 q^{67} -0.732150 q^{68} -2.21760 q^{69} -5.99343 q^{70} +12.5393 q^{71} -1.93701 q^{72} -1.19175 q^{73} -12.5976 q^{74} -2.91219 q^{75} +3.44079 q^{76} +12.9246 q^{77} +6.38762 q^{78} +10.0506 q^{79} +7.19352 q^{80} +1.00000 q^{81} -8.90315 q^{82} -6.10832 q^{83} +2.09531 q^{84} +1.23981 q^{85} -5.72318 q^{86} -7.87396 q^{87} -10.1951 q^{88} -11.8076 q^{89} -2.44072 q^{90} +9.28593 q^{91} -1.89223 q^{92} +7.07051 q^{93} -9.86726 q^{94} -5.82659 q^{95} -4.53544 q^{96} -9.60171 q^{97} -1.63851 q^{98} +5.26332 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 2 q^{2} + 13 q^{3} + 18 q^{4} + 6 q^{5} + 2 q^{6} + 15 q^{7} + 3 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 2 * q^2 + 13 * q^3 + 18 * q^4 + 6 * q^5 + 2 * q^6 + 15 * q^7 + 3 * q^8 + 13 * q^9	\( 13 q + 2 q^{2} + 13 q^{3} + 18 q^{4} + 6 q^{5} + 2 q^{6} + 15 q^{7} + 3 q^{8} + 13 q^{9} - q^{10} + 3 q^{11} + 18 q^{12} + 11 q^{13} - 4 q^{14} + 6 q^{15} + 20 q^{16} - 2 q^{17} + 2 q^{18} + 9 q^{19} - 9 q^{20} + 15 q^{21} - 8 q^{22} - 8 q^{23} + 3 q^{24} + 21 q^{25} - 15 q^{26} + 13 q^{27} + 16 q^{28} + 5 q^{29} - q^{30} + 25 q^{31} - 17 q^{32} + 3 q^{33} - 10 q^{34} - 10 q^{35} + 18 q^{36} + 29 q^{37} - 40 q^{38} + 11 q^{39} - 21 q^{40} - 11 q^{41} - 4 q^{42} + 8 q^{43} - 18 q^{44} + 6 q^{45} - 6 q^{46} - 12 q^{47} + 20 q^{48} + 20 q^{49} - 4 q^{50} - 2 q^{51} + 2 q^{52} + 14 q^{53} + 2 q^{54} + 12 q^{55} - 7 q^{56} + 9 q^{57} + 9 q^{58} + 10 q^{59} - 9 q^{60} + 6 q^{61} - 14 q^{62} + 15 q^{63} + 23 q^{64} - 15 q^{65} - 8 q^{66} + 25 q^{67} - 33 q^{68} - 8 q^{69} - 21 q^{70} + 3 q^{72} + 8 q^{73} - 2 q^{74} + 21 q^{75} + 20 q^{76} - 25 q^{77} - 15 q^{78} + 7 q^{79} - 40 q^{80} + 13 q^{81} - 19 q^{82} - 28 q^{83} + 16 q^{84} - 3 q^{85} + 2 q^{86} + 5 q^{87} - 21 q^{88} + 7 q^{89} - q^{90} + 7 q^{91} + 9 q^{92} + 25 q^{93} - 35 q^{94} - 26 q^{95} - 17 q^{96} + 26 q^{97} - 14 q^{98} + 3 q^{99}+O(q^{100}) \) 13 * q + 2 * q^2 + 13 * q^3 + 18 * q^4 + 6 * q^5 + 2 * q^6 + 15 * q^7 + 3 * q^8 + 13 * q^9 - q^10 + 3 * q^11 + 18 * q^12 + 11 * q^13 - 4 * q^14 + 6 * q^15 + 20 * q^16 - 2 * q^17 + 2 * q^18 + 9 * q^19 - 9 * q^20 + 15 * q^21 - 8 * q^22 - 8 * q^23 + 3 * q^24 + 21 * q^25 - 15 * q^26 + 13 * q^27 + 16 * q^28 + 5 * q^29 - q^30 + 25 * q^31 - 17 * q^32 + 3 * q^33 - 10 * q^34 - 10 * q^35 + 18 * q^36 + 29 * q^37 - 40 * q^38 + 11 * q^39 - 21 * q^40 - 11 * q^41 - 4 * q^42 + 8 * q^43 - 18 * q^44 + 6 * q^45 - 6 * q^46 - 12 * q^47 + 20 * q^48 + 20 * q^49 - 4 * q^50 - 2 * q^51 + 2 * q^52 + 14 * q^53 + 2 * q^54 + 12 * q^55 - 7 * q^56 + 9 * q^57 + 9 * q^58 + 10 * q^59 - 9 * q^60 + 6 * q^61 - 14 * q^62 + 15 * q^63 + 23 * q^64 - 15 * q^65 - 8 * q^66 + 25 * q^67 - 33 * q^68 - 8 * q^69 - 21 * q^70 + 3 * q^72 + 8 * q^73 - 2 * q^74 + 21 * q^75 + 20 * q^76 - 25 * q^77 - 15 * q^78 + 7 * q^79 - 40 * q^80 + 13 * q^81 - 19 * q^82 - 28 * q^83 + 16 * q^84 - 3 * q^85 + 2 * q^86 + 5 * q^87 - 21 * q^88 + 7 * q^89 - q^90 + 7 * q^91 + 9 * q^92 + 25 * q^93 - 35 * q^94 - 26 * q^95 - 17 * q^96 + 26 * q^97 - 14 * q^98 + 3 * 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 $

$2$	1.68916	1.19442	0.597210	−	0.802085i	$-0.296276\pi$
$2$	1.68916	1.19442	0.597210	+	0.802085i	$0.296276\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.853276	0.426638
$5$	−1.44492	−0.646190	−0.323095	−	0.946367i	$-0.604723\pi$
$5$	−1.44492	−0.646190	−0.323095	+	0.946367i	$0.604723\pi$
$6$	1.68916	0.689598
$7$	2.45560	0.928131	0.464065	−	0.885801i	$-0.346390\pi$
$7$	2.45560	0.928131	0.464065	+	0.885801i	$0.346390\pi$
$8$	−1.93701	−0.684835
$9$	1.00000	0.333333
$10$	−2.44072	−0.771822
$11$	5.26332	1.58695	0.793475	−	0.608602i	$-0.208270\pi$
$11$	5.26332	1.58695	0.793475	+	0.608602i	$0.208270\pi$
$12$	0.853276	0.246319
$13$	3.78153	1.04881	0.524403	−	0.851470i	$-0.324288\pi$
$13$	3.78153	1.04881	0.524403	+	0.851470i	$0.324288\pi$
$14$	4.14792	1.10858
$15$	−1.44492	−0.373078
$16$	−4.97847	−1.24462
$17$	−0.858046	−0.208107	−0.104053	−	0.994572i	$-0.533181\pi$
$17$	−0.858046	−0.208107	−0.104053	+	0.994572i	$0.533181\pi$
$18$	1.68916	0.398140
$19$	4.03245	0.925108	0.462554	−	0.886591i	$-0.346933\pi$
$19$	4.03245	0.925108	0.462554	+	0.886591i	$0.346933\pi$
$20$	−1.23292	−0.275689
$21$	2.45560	0.535857
$22$	8.89061	1.89548
$23$	−2.21760	−0.462403	−0.231201	−	0.972906i	$-0.574266\pi$
$23$	−2.21760	−0.462403	−0.231201	+	0.972906i	$0.574266\pi$
$24$	−1.93701	−0.395390
$25$	−2.91219	−0.582438
$26$	6.38762	1.25272
$27$	1.00000	0.192450
$28$	2.09531	0.395976
$29$	−7.87396	−1.46216	−0.731079	−	0.682293i	$-0.760983\pi$
$29$	−7.87396	−1.46216	−0.731079	+	0.682293i	$0.760983\pi$
$30$	−2.44072	−0.445612
$31$	7.07051	1.26990	0.634951	−	0.772553i	$-0.281020\pi$
$31$	7.07051	1.26990	0.634951	+	0.772553i	$0.281020\pi$
$32$	−4.53544	−0.801761
$33$	5.26332	0.916226
$34$	−1.44938	−0.248567
$35$	−3.54816	−0.599749
$36$	0.853276	0.142213
$37$	−7.45792	−1.22607	−0.613037	−	0.790054i	$-0.710052\pi$
$37$	−7.45792	−1.22607	−0.613037	+	0.790054i	$0.710052\pi$
$38$	6.81147	1.10497
$39$	3.78153	0.605529
$40$	2.79883	0.442534
$41$	−5.27074	−0.823152	−0.411576	−	0.911375i	$-0.635022\pi$
$41$	−5.27074	−0.823152	−0.411576	+	0.911375i	$0.635022\pi$
$42$	4.14792	0.640038
$43$	−3.38817	−0.516691	−0.258346	−	0.966053i	$-0.583177\pi$
$43$	−3.38817	−0.516691	−0.258346	+	0.966053i	$0.583177\pi$
$44$	4.49106	0.677053
$45$	−1.44492	−0.215397
$46$	−3.74590	−0.552303
$47$	−5.84151	−0.852071	−0.426036	−	0.904706i	$-0.640090\pi$
$47$	−5.84151	−0.852071	−0.426036	+	0.904706i	$0.640090\pi$
$48$	−4.97847	−0.718581
$49$	−0.970011	−0.138573
$50$	−4.91917	−0.695676
$51$	−0.858046	−0.120151
$52$	3.22668	0.447461
$53$	5.20251	0.714620	0.357310	−	0.933986i	$-0.383694\pi$
$53$	5.20251	0.714620	0.357310	+	0.933986i	$0.383694\pi$
$54$	1.68916	0.229866
$55$	−7.60510	−1.02547
$56$	−4.75652	−0.635617
$57$	4.03245	0.534111
$58$	−13.3004	−1.74643
$59$	−3.43605	−0.447336	−0.223668	−	0.974665i	$-0.571803\pi$
$59$	−3.43605	−0.447336	−0.223668	+	0.974665i	$0.571803\pi$
$60$	−1.23292	−0.159169
$61$	−2.93414	−0.375678	−0.187839	−	0.982200i	$-0.560148\pi$
$61$	−2.93414	−0.375678	−0.187839	+	0.982200i	$0.560148\pi$
$62$	11.9433	1.51679
$63$	2.45560	0.309377
$64$	2.29583	0.286979
$65$	−5.46402	−0.677728
$66$	8.89061	1.09436
$67$	−6.89075	−0.841840	−0.420920	−	0.907098i	$-0.638293\pi$
$67$	−6.89075	−0.841840	−0.420920	+	0.907098i	$0.638293\pi$
$68$	−0.732150	−0.0887862
$69$	−2.21760	−0.266968
$70$	−5.99343	−0.716352
$71$	12.5393	1.48814	0.744068	−	0.668104i	$-0.232894\pi$
$71$	12.5393	1.48814	0.744068	+	0.668104i	$0.232894\pi$
$72$	−1.93701	−0.228278
$73$	−1.19175	−0.139484	−0.0697421	−	0.997565i	$-0.522218\pi$
$73$	−1.19175	−0.139484	−0.0697421	+	0.997565i	$0.522218\pi$
$74$	−12.5976	−1.46445
$75$	−2.91219	−0.336271
$76$	3.44079	0.394686
$77$	12.9246	1.47290
$78$	6.38762	0.723255
$79$	10.0506	1.13078	0.565392	−	0.824823i	$-0.308725\pi$
$79$	10.0506	1.13078	0.565392	+	0.824823i	$0.308725\pi$
$80$	7.19352	0.804260
$81$	1.00000	0.111111
$82$	−8.90315	−0.983189
$83$	−6.10832	−0.670475	−0.335237	−	0.942134i	$-0.608817\pi$
$83$	−6.10832	−0.670475	−0.335237	+	0.942134i	$0.608817\pi$
$84$	2.09531	0.228617
$85$	1.23981	0.134477
$86$	−5.72318	−0.617146
$87$	−7.87396	−0.844177
$88$	−10.1951	−1.08680
$89$	−11.8076	−1.25160	−0.625801	−	0.779983i	$-0.715228\pi$
$89$	−11.8076	−1.25160	−0.625801	+	0.779983i	$0.715228\pi$
$90$	−2.44072	−0.257274
$91$	9.28593	0.973430
$92$	−1.89223	−0.197278
$93$	7.07051	0.733178
$94$	−9.86726	−1.01773
$95$	−5.82659	−0.597795
$96$	−4.53544	−0.462897
$97$	−9.60171	−0.974906	−0.487453	−	0.873149i	$-0.662074\pi$
$97$	−9.60171	−0.974906	−0.487453	+	0.873149i	$0.662074\pi$
$98$	−1.63851	−0.165514
$99$	5.26332	0.528984
$100$	−2.48490	−0.248490
$101$	7.94106	0.790165	0.395082	−	0.918646i	$-0.370716\pi$
$101$	7.94106	0.790165	0.395082	+	0.918646i	$0.370716\pi$
$102$	−1.44938	−0.143510
$103$	15.0437	1.48230	0.741151	−	0.671339i	$-0.234280\pi$
$103$	15.0437	1.48230	0.741151	+	0.671339i	$0.234280\pi$
$104$	−7.32484	−0.718259
$105$	−3.54816	−0.346265
$106$	8.78790	0.853556
$107$	−7.44849	−0.720073	−0.360036	−	0.932938i	$-0.617236\pi$
$107$	−7.44849	−0.720073	−0.360036	+	0.932938i	$0.617236\pi$
$108$	0.853276	0.0821065
$109$	7.38126	0.706996	0.353498	−	0.935435i	$-0.384992\pi$
$109$	7.38126	0.706996	0.353498	+	0.935435i	$0.384992\pi$
$110$	−12.8463	−1.22484
$111$	−7.45792	−0.707874
$112$	−12.2252	−1.15517
$113$	−9.44816	−0.888808	−0.444404	−	0.895826i	$-0.646585\pi$
$113$	−9.44816	−0.888808	−0.444404	+	0.895826i	$0.646585\pi$
$114$	6.81147	0.637953
$115$	3.20427	0.298800
$116$	−6.71865	−0.623811
$117$	3.78153	0.349602
$118$	−5.80406	−0.534307
$119$	−2.10702	−0.193150
$120$	2.79883	0.255497
$121$	16.7025	1.51841
$122$	−4.95625	−0.448718
$123$	−5.27074	−0.475247
$124$	6.03309	0.541788
$125$	11.4325	1.02256
$126$	4.14792	0.369526
$127$	19.9462	1.76994	0.884971	−	0.465646i	$-0.154178\pi$
$127$	19.9462	1.76994	0.884971	+	0.465646i	$0.154178\pi$
$128$	12.9489	1.14453
$129$	−3.38817	−0.298312
$130$	−9.22963	−0.809492
$131$	2.21285	0.193338	0.0966688	−	0.995317i	$-0.469181\pi$
$131$	2.21285	0.193338	0.0966688	+	0.995317i	$0.469181\pi$
$132$	4.49106	0.390897
$133$	9.90210	0.858621
$134$	−11.6396	−1.00551
$135$	−1.44492	−0.124359
$136$	1.66204	0.142519
$137$	8.48164	0.724636	0.362318	−	0.932055i	$-0.381986\pi$
$137$	8.48164	0.724636	0.362318	+	0.932055i	$0.381986\pi$
$138$	−3.74590	−0.318872
$139$	−7.71002	−0.653956	−0.326978	−	0.945032i	$-0.606030\pi$
$139$	−7.71002	−0.653956	−0.326978	+	0.945032i	$0.606030\pi$
$140$	−3.02756	−0.255876
$141$	−5.84151	−0.491944
$142$	21.1809	1.77746
$143$	19.9034	1.66440
$144$	−4.97847	−0.414873
$145$	11.3773	0.944831
$146$	−2.01307	−0.166603
$147$	−0.970011	−0.0800051
$148$	−6.36366	−0.523090
$149$	−15.2068	−1.24579	−0.622894	−	0.782306i	$-0.714043\pi$
$149$	−15.2068	−1.24579	−0.622894	+	0.782306i	$0.714043\pi$
$150$	−4.91917	−0.401649
$151$	13.2142	1.07536	0.537679	−	0.843150i	$-0.319301\pi$
$151$	13.2142	1.07536	0.537679	+	0.843150i	$0.319301\pi$
$152$	−7.81088	−0.633546
$153$	−0.858046	−0.0693689
$154$	21.8318	1.75926
$155$	−10.2164	−0.820597
$156$	3.22668	0.258341
$157$	−17.7105	−1.41345	−0.706727	−	0.707487i	$-0.749829\pi$
$157$	−17.7105	−1.41345	−0.706727	+	0.707487i	$0.749829\pi$
$158$	16.9771	1.35063
$159$	5.20251	0.412586
$160$	6.55338	0.518090
$161$	−5.44556	−0.429170
$162$	1.68916	0.132713
$163$	16.2387	1.27191	0.635955	−	0.771726i	$-0.280606\pi$
$163$	16.2387	1.27191	0.635955	+	0.771726i	$0.280606\pi$
$164$	−4.49740	−0.351188
$165$	−7.60510	−0.592056
$166$	−10.3179	−0.800828
$167$	−20.6283	−1.59626	−0.798132	−	0.602482i	$-0.794178\pi$
$167$	−20.6283	−1.59626	−0.798132	+	0.602482i	$0.794178\pi$
$168$	−4.75652	−0.366973
$169$	1.29994	0.0999954
$170$	2.09425	0.160621
$171$	4.03245	0.308369
$172$	−2.89104	−0.220440
$173$	−19.8341	−1.50796	−0.753980	−	0.656898i	$-0.771868\pi$
$173$	−19.8341	−1.50796	−0.753980	+	0.656898i	$0.771868\pi$
$174$	−13.3004	−1.00830
$175$	−7.15119	−0.540579
$176$	−26.2033	−1.97515
$177$	−3.43605	−0.258269
$178$	−19.9450	−1.49494
$179$	5.15575	0.385359	0.192680	−	0.981262i	$-0.438282\pi$
$179$	5.15575	0.385359	0.192680	+	0.981262i	$0.438282\pi$
$180$	−1.23292	−0.0918964
$181$	−7.70169	−0.572462	−0.286231	−	0.958161i	$-0.592402\pi$
$181$	−7.70169	−0.572462	−0.286231	+	0.958161i	$0.592402\pi$
$182$	15.6855	1.16268
$183$	−2.93414	−0.216898
$184$	4.29551	0.316669
$185$	10.7761	0.792277
$186$	11.9433	0.875722
$187$	−4.51617	−0.330255
$188$	−4.98441	−0.363526
$189$	2.45560	0.178619
$190$	−9.84206	−0.714018
$191$	−2.46329	−0.178237	−0.0891185	−	0.996021i	$-0.528405\pi$
$191$	−2.46329	−0.178237	−0.0891185	+	0.996021i	$0.528405\pi$
$192$	2.29583	0.165688
$193$	−1.00000	−0.0719816
$193$	−1.00000	−0.0719816
$194$	−16.2189	−1.16445
$195$	−5.46402	−0.391287
$196$	−0.827686	−0.0591205
$197$	9.40645	0.670181	0.335091	−	0.942186i	$-0.391233\pi$
$197$	9.40645	0.670181	0.335091	+	0.942186i	$0.391233\pi$
$198$	8.89061	0.631828
$199$	5.84728	0.414503	0.207251	−	0.978288i	$-0.433548\pi$
$199$	5.84728	0.414503	0.207251	+	0.978288i	$0.433548\pi$
$200$	5.64093	0.398874
$201$	−6.89075	−0.486036
$202$	13.4137	0.943788
$203$	−19.3353	−1.35707
$204$	−0.732150	−0.0512607
$205$	7.61583	0.531913
$206$	25.4113	1.77049
$207$	−2.21760	−0.154134
$208$	−18.8262	−1.30536
$209$	21.2241	1.46810
$210$	−5.99343	−0.413586
$211$	13.3109	0.916358	0.458179	−	0.888860i	$-0.348502\pi$
$211$	13.3109	0.916358	0.458179	+	0.888860i	$0.348502\pi$
$212$	4.43918	0.304884
$213$	12.5393	0.859176
$214$	−12.5817	−0.860069
$215$	4.89565	0.333881
$216$	−1.93701	−0.131797
$217$	17.3624	1.17863
$218$	12.4682	0.844450
$219$	−1.19175	−0.0805312
$220$	−6.48925	−0.437505
$221$	−3.24472	−0.218264
$222$	−12.5976	−0.845499
$223$	−28.8013	−1.92868	−0.964340	−	0.264666i	$-0.914738\pi$
$223$	−28.8013	−1.92868	−0.964340	+	0.264666i	$0.914738\pi$
$224$	−11.1373	−0.744139
$225$	−2.91219	−0.194146
$226$	−15.9595	−1.06161
$227$	−19.1850	−1.27335	−0.636675	−	0.771132i	$-0.719691\pi$
$227$	−19.1850	−1.27335	−0.636675	+	0.771132i	$0.719691\pi$
$228$	3.44079	0.227872
$229$	5.06674	0.334820	0.167410	−	0.985887i	$-0.446460\pi$
$229$	5.06674	0.334820	0.167410	+	0.985887i	$0.446460\pi$
$230$	5.41254	0.356892
$231$	12.9246	0.850378
$232$	15.2519	1.00134
$233$	22.8573	1.49743	0.748716	−	0.662891i	$-0.230671\pi$
$233$	22.8573	1.49743	0.748716	+	0.662891i	$0.230671\pi$
$234$	6.38762	0.417572
$235$	8.44054	0.550600
$236$	−2.93190	−0.190850
$237$	10.0506	0.652858
$238$	−3.55911	−0.230703
$239$	−1.26308	−0.0817022	−0.0408511	−	0.999165i	$-0.513007\pi$
$239$	−1.26308	−0.0817022	−0.0408511	+	0.999165i	$0.513007\pi$
$240$	7.19352	0.464340
$241$	16.4700	1.06093	0.530463	−	0.847708i	$-0.322018\pi$
$241$	16.4700	1.06093	0.530463	+	0.847708i	$0.322018\pi$
$242$	28.2133	1.81362
$243$	1.00000	0.0641500
$244$	−2.50363	−0.160279
$245$	1.40159	0.0895445
$246$	−8.90315	−0.567644
$247$	15.2488	0.970259
$248$	−13.6956	−0.869673
$249$	−6.10832	−0.387099
$250$	19.3114	1.22136
$251$	−11.9847	−0.756466	−0.378233	−	0.925710i	$-0.623468\pi$
$251$	−11.9847	−0.756466	−0.378233	+	0.925710i	$0.623468\pi$
$252$	2.09531	0.131992
$253$	−11.6720	−0.733810
$254$	33.6925	2.11405
$255$	1.23981	0.0776401
$256$	17.2812	1.08007
$257$	−1.41069	−0.0879967	−0.0439984	−	0.999032i	$-0.514010\pi$
$257$	−1.41069	−0.0879967	−0.0439984	+	0.999032i	$0.514010\pi$
$258$	−5.72318	−0.356309
$259$	−18.3137	−1.13796
$260$	−4.66232	−0.289145
$261$	−7.87396	−0.487386
$262$	3.73787	0.230926
$263$	−16.8917	−1.04159	−0.520795	−	0.853682i	$-0.674364\pi$
$263$	−16.8917	−1.04159	−0.520795	+	0.853682i	$0.674364\pi$
$264$	−10.1951	−0.627464
$265$	−7.51724	−0.461780
$266$	16.7263	1.02555
$267$	−11.8076	−0.722613
$268$	−5.87971	−0.359161
$269$	−2.25119	−0.137258	−0.0686288	−	0.997642i	$-0.521862\pi$
$269$	−2.25119	−0.137258	−0.0686288	+	0.997642i	$0.521862\pi$
$270$	−2.44072	−0.148537
$271$	−22.3890	−1.36003	−0.680017	−	0.733197i	$-0.738027\pi$
$271$	−22.3890	−1.36003	−0.680017	+	0.733197i	$0.738027\pi$
$272$	4.27176	0.259013
$273$	9.28593	0.562010
$274$	14.3269	0.865519
$275$	−15.3278	−0.924301
$276$	−1.89223	−0.113899
$277$	21.7579	1.30730	0.653651	−	0.756796i	$-0.273236\pi$
$277$	21.7579	1.30730	0.653651	+	0.756796i	$0.273236\pi$
$278$	−13.0235	−0.781097
$279$	7.07051	0.423300
$280$	6.87281	0.410729
$281$	−18.4006	−1.09769	−0.548843	−	0.835925i	$-0.684932\pi$
$281$	−18.4006	−1.09769	−0.548843	+	0.835925i	$0.684932\pi$
$282$	−9.86726	−0.587587
$283$	11.9137	0.708199	0.354099	−	0.935208i	$-0.384787\pi$
$283$	11.9137	0.708199	0.354099	+	0.935208i	$0.384787\pi$
$284$	10.6994	0.634895
$285$	−5.82659	−0.345137
$286$	33.6201	1.98800
$287$	−12.9429	−0.763993
$288$	−4.53544	−0.267254
$289$	−16.2638	−0.956692
$290$	19.2181	1.12852
$291$	−9.60171	−0.562862
$292$	−1.01689	−0.0595092
$293$	32.1770	1.87980	0.939899	−	0.341451i	$-0.110918\pi$
$293$	32.1770	1.87980	0.939899	+	0.341451i	$0.110918\pi$
$294$	−1.63851	−0.0955597
$295$	4.96484	0.289064
$296$	14.4460	0.839658
$297$	5.26332	0.305409
$298$	−25.6868	−1.48799
$299$	−8.38593	−0.484971
$300$	−2.48490	−0.143466
$301$	−8.32001	−0.479557
$302$	22.3210	1.28443
$303$	7.94106	0.456202
$304$	−20.0754	−1.15141
$305$	4.23962	0.242760
$306$	−1.44938	−0.0828556
$307$	27.3311	1.55987	0.779935	−	0.625860i	$-0.215252\pi$
$307$	27.3311	1.55987	0.779935	+	0.625860i	$0.215252\pi$
$308$	11.0283	0.628394
$309$	15.0437	0.855807
$310$	−17.2571	−0.980138
$311$	20.2842	1.15021	0.575104	−	0.818080i	$-0.304961\pi$
$311$	20.2842	1.15021	0.575104	+	0.818080i	$0.304961\pi$
$312$	−7.32484	−0.414687
$313$	3.96033	0.223851	0.111926	−	0.993717i	$-0.464298\pi$
$313$	3.96033	0.223851	0.111926	+	0.993717i	$0.464298\pi$
$314$	−29.9160	−1.68826
$315$	−3.54816	−0.199916
$316$	8.57595	0.482435
$317$	26.2360	1.47356	0.736781	−	0.676132i	$-0.236345\pi$
$317$	26.2360	1.47356	0.736781	+	0.676132i	$0.236345\pi$
$318$	8.78790	0.492801
$319$	−41.4432	−2.32037
$320$	−3.31731	−0.185443
$321$	−7.44849	−0.415734
$322$	−9.19844	−0.512609
$323$	−3.46003	−0.192521
$324$	0.853276	0.0474042
$325$	−11.0125	−0.610865
$326$	27.4298	1.51919
$327$	7.38126	0.408184
$328$	10.2095	0.563723
$329$	−14.3444	−0.790834
$330$	−12.8463	−0.707164
$331$	22.3835	1.23031	0.615154	−	0.788407i	$-0.289094\pi$
$331$	22.3835	1.23031	0.615154	+	0.788407i	$0.289094\pi$
$332$	−5.21208	−0.286050
$333$	−7.45792	−0.408691
$334$	−34.8446	−1.90661
$335$	9.95662	0.543988
$336$	−12.2252	−0.666937
$337$	32.4389	1.76706	0.883529	−	0.468376i	$-0.155161\pi$
$337$	32.4389	1.76706	0.883529	+	0.468376i	$0.155161\pi$
$338$	2.19581	0.119436
$339$	−9.44816	−0.513154
$340$	1.05790	0.0573728
$341$	37.2144	2.01527
$342$	6.81147	0.368322
$343$	−19.5712	−1.05674
$344$	6.56291	0.353848
$345$	3.20427	0.172512
$346$	−33.5031	−1.80114
$347$	−1.22305	−0.0656569	−0.0328285	−	0.999461i	$-0.510451\pi$
$347$	−1.22305	−0.0656569	−0.0328285	+	0.999461i	$0.510451\pi$
$348$	−6.71865	−0.360158
$349$	20.6268	1.10412	0.552062	−	0.833803i	$-0.313841\pi$
$349$	20.6268	1.10412	0.552062	+	0.833803i	$0.313841\pi$
$350$	−12.0795	−0.645678
$351$	3.78153	0.201843
$352$	−23.8715	−1.27235
$353$	3.21291	0.171006	0.0855029	−	0.996338i	$-0.472750\pi$
$353$	3.21291	0.171006	0.0855029	+	0.996338i	$0.472750\pi$
$354$	−5.80406	−0.308482
$355$	−18.1183	−0.961619
$356$	−10.0751	−0.533981
$357$	−2.10702	−0.111515
$358$	8.70891	0.460280
$359$	−7.58991	−0.400580	−0.200290	−	0.979737i	$-0.564188\pi$
$359$	−7.58991	−0.400580	−0.200290	+	0.979737i	$0.564188\pi$
$360$	2.79883	0.147511
$361$	−2.73934	−0.144176
$362$	−13.0094	−0.683760
$363$	16.7025	0.876656
$364$	7.92346	0.415302
$365$	1.72199	0.0901332
$366$	−4.95625	−0.259067
$367$	−11.2532	−0.587414	−0.293707	−	0.955896i	$-0.594889\pi$
$367$	−11.2532	−0.587414	−0.293707	+	0.955896i	$0.594889\pi$
$368$	11.0403	0.575515
$369$	−5.27074	−0.274384
$370$	18.2027	0.946311
$371$	12.7753	0.663261
$372$	6.03309	0.312801
$373$	17.1534	0.888169	0.444084	−	0.895985i	$-0.353529\pi$
$373$	17.1534	0.888169	0.444084	+	0.895985i	$0.353529\pi$
$374$	−7.62856	−0.394463
$375$	11.4325	0.590373
$376$	11.3150	0.583528
$377$	−29.7756	−1.53352
$378$	4.14792	0.213346
$379$	−17.9398	−0.921507	−0.460754	−	0.887528i	$-0.652421\pi$
$379$	−17.9398	−0.921507	−0.460754	+	0.887528i	$0.652421\pi$
$380$	−4.97169	−0.255042
$381$	19.9462	1.02188
$382$	−4.16089	−0.212890
$383$	11.4267	0.583878	0.291939	−	0.956437i	$-0.405700\pi$
$383$	11.4267	0.583878	0.291939	+	0.956437i	$0.405700\pi$
$384$	12.9489	0.660797
$385$	−18.6751	−0.951772
$386$	−1.68916	−0.0859762
$387$	−3.38817	−0.172230
$388$	−8.19291	−0.415932
$389$	28.3638	1.43810	0.719050	−	0.694959i	$-0.244577\pi$
$389$	28.3638	1.43810	0.719050	+	0.694959i	$0.244577\pi$
$390$	−9.22963	−0.467360
$391$	1.90281	0.0962291
$392$	1.87892	0.0948996
$393$	2.21285	0.111623
$394$	15.8890	0.800478
$395$	−14.5224	−0.730701
$396$	4.49106	0.225684
$397$	−3.94999	−0.198244	−0.0991221	−	0.995075i	$-0.531603\pi$
$397$	−3.94999	−0.198244	−0.0991221	+	0.995075i	$0.531603\pi$
$398$	9.87702	0.495090
$399$	9.90210	0.495725
$400$	14.4983	0.724913
$401$	−9.73822	−0.486304	−0.243152	−	0.969988i	$-0.578181\pi$
$401$	−9.73822	−0.486304	−0.243152	+	0.969988i	$0.578181\pi$
$402$	−11.6396	−0.580531
$403$	26.7373	1.33188
$404$	6.77591	0.337114
$405$	−1.44492	−0.0717989
$406$	−32.6605	−1.62091
$407$	−39.2534	−1.94572
$408$	1.66204	0.0822833
$409$	−0.410667	−0.0203062	−0.0101531	−	0.999948i	$-0.503232\pi$
$409$	−0.410667	−0.0203062	−0.0101531	+	0.999948i	$0.503232\pi$
$410$	12.8644	0.635327
$411$	8.48164	0.418369
$412$	12.8364	0.632406
$413$	−8.43758	−0.415186
$414$	−3.74590	−0.184101
$415$	8.82606	0.433254
$416$	−17.1509	−0.840892
$417$	−7.71002	−0.377561
$418$	35.8510	1.75353
$419$	40.4009	1.97371	0.986857	−	0.161598i	$-0.0516649\pi$
$419$	40.4009	1.97371	0.986857	+	0.161598i	$0.0516649\pi$
$420$	−3.02756	−0.147730
$421$	−18.8200	−0.917231	−0.458616	−	0.888635i	$-0.651655\pi$
$421$	−18.8200	−0.917231	−0.458616	+	0.888635i	$0.651655\pi$
$422$	22.4842	1.09452
$423$	−5.84151	−0.284024
$424$	−10.0773	−0.489397
$425$	2.49880	0.121209
$426$	21.1809	1.02622
$427$	−7.20509	−0.348679
$428$	−6.35561	−0.307210
$429$	19.9034	0.960944
$430$	8.26956	0.398794
$431$	31.8176	1.53260	0.766299	−	0.642484i	$-0.222096\pi$
$431$	31.8176	1.53260	0.766299	+	0.642484i	$0.222096\pi$
$432$	−4.97847	−0.239527
$433$	16.6983	0.802468	0.401234	−	0.915976i	$-0.368581\pi$
$433$	16.6983	0.802468	0.401234	+	0.915976i	$0.368581\pi$
$434$	29.3279	1.40778
$435$	11.3773	0.545499
$436$	6.29825	0.301631
$437$	−8.94238	−0.427772
$438$	−2.01307	−0.0961880
$439$	−13.2585	−0.632792	−0.316396	−	0.948627i	$-0.602473\pi$
$439$	−13.2585	−0.632792	−0.316396	+	0.948627i	$0.602473\pi$
$440$	14.7311	0.702279
$441$	−0.970011	−0.0461910
$442$	−5.48087	−0.260699
$443$	−7.62687	−0.362363	−0.181182	−	0.983450i	$-0.557992\pi$
$443$	−7.62687	−0.362363	−0.181182	+	0.983450i	$0.557992\pi$
$444$	−6.36366	−0.302006
$445$	17.0611	0.808773
$446$	−48.6502	−2.30365
$447$	−15.2068	−0.719256
$448$	5.63766	0.266354
$449$	−24.2798	−1.14583	−0.572917	−	0.819613i	$-0.694188\pi$
$449$	−24.2798	−1.14583	−0.572917	+	0.819613i	$0.694188\pi$
$450$	−4.91917	−0.231892
$451$	−27.7416	−1.30630
$452$	−8.06189	−0.379199
$453$	13.2142	0.620858
$454$	−32.4065	−1.52091
$455$	−13.4175	−0.629021
$456$	−7.81088	−0.365778
$457$	−5.15367	−0.241079	−0.120539	−	0.992709i	$-0.538462\pi$
$457$	−5.15367	−0.241079	−0.120539	+	0.992709i	$0.538462\pi$
$458$	8.55856	0.399915
$459$	−0.858046	−0.0400502
$460$	2.73413	0.127479
$461$	13.8519	0.645148	0.322574	−	0.946544i	$-0.395452\pi$
$461$	13.8519	0.645148	0.322574	+	0.946544i	$0.395452\pi$
$462$	21.8318	1.01571
$463$	−15.7013	−0.729700	−0.364850	−	0.931066i	$-0.618880\pi$
$463$	−15.7013	−0.729700	−0.364850	+	0.931066i	$0.618880\pi$
$464$	39.2003	1.81983
$465$	−10.2164	−0.473772
$466$	38.6098	1.78856
$467$	32.4824	1.50311	0.751553	−	0.659673i	$-0.229305\pi$
$467$	32.4824	1.50311	0.751553	+	0.659673i	$0.229305\pi$
$468$	3.22668	0.149154
$469$	−16.9210	−0.781337
$470$	14.2575	0.657647
$471$	−17.7105	−0.816057
$472$	6.65565	0.306351
$473$	−17.8330	−0.819964
$474$	16.9771	0.779786
$475$	−11.7433	−0.538818
$476$	−1.79787	−0.0824052
$477$	5.20251	0.238207
$478$	−2.13356	−0.0975866
$479$	1.32294	0.0604466	0.0302233	−	0.999543i	$-0.490378\pi$
$479$	1.32294	0.0604466	0.0302233	+	0.999543i	$0.490378\pi$
$480$	6.55338	0.299119
$481$	−28.2023	−1.28591
$482$	27.8205	1.26719
$483$	−5.44556	−0.247781
$484$	14.2519	0.647812
$485$	13.8738	0.629975
$486$	1.68916	0.0766220
$487$	−37.1267	−1.68237	−0.841185	−	0.540747i	$-0.818141\pi$
$487$	−37.1267	−1.68237	−0.841185	+	0.540747i	$0.818141\pi$
$488$	5.68345	0.257278
$489$	16.2387	0.734338
$490$	2.36752	0.106954
$491$	18.7450	0.845952	0.422976	−	0.906141i	$-0.360985\pi$
$491$	18.7450	0.845952	0.422976	+	0.906141i	$0.360985\pi$
$492$	−4.49740	−0.202758
$493$	6.75622	0.304285
$494$	25.7578	1.15890
$495$	−7.60510	−0.341824
$496$	−35.2003	−1.58054
$497$	30.7915	1.38119
$498$	−10.3179	−0.462358
$499$	−21.9520	−0.982704	−0.491352	−	0.870961i	$-0.663497\pi$
$499$	−21.9520	−0.982704	−0.491352	+	0.870961i	$0.663497\pi$
$500$	9.75509	0.436261
$501$	−20.6283	−0.921604
$502$	−20.2441	−0.903538
$503$	31.8471	1.41999	0.709996	−	0.704206i	$-0.248697\pi$
$503$	31.8471	1.41999	0.709996	+	0.704206i	$0.248697\pi$
$504$	−4.75652	−0.211872
$505$	−11.4742	−0.510596
$506$	−19.7159	−0.876477
$507$	1.29994	0.0577324
$508$	17.0196	0.755124
$509$	21.1302	0.936579	0.468290	−	0.883575i	$-0.344870\pi$
$509$	21.1302	0.936579	0.468290	+	0.883575i	$0.344870\pi$
$510$	2.09425	0.0927348
$511$	−2.92647	−0.129460
$512$	3.29293	0.145528
$513$	4.03245	0.178037
$514$	−2.38289	−0.105105
$515$	−21.7370	−0.957848
$516$	−2.89104	−0.127271
$517$	−30.7457	−1.35219
$518$	−30.9348	−1.35920
$519$	−19.8341	−0.870621
$520$	10.5838	0.464132
$521$	−11.8767	−0.520330	−0.260165	−	0.965564i	$-0.583777\pi$
$521$	−11.8767	−0.520330	−0.260165	+	0.965564i	$0.583777\pi$
$522$	−13.3004	−0.582143
$523$	−21.4741	−0.938996	−0.469498	−	0.882933i	$-0.655565\pi$
$523$	−21.4741	−0.938996	−0.469498	+	0.882933i	$0.655565\pi$
$524$	1.88817	0.0824851
$525$	−7.15119	−0.312104
$526$	−28.5329	−1.24409
$527$	−6.06682	−0.264275
$528$	−26.2033	−1.14035
$529$	−18.0822	−0.786184
$530$	−12.6979	−0.551560
$531$	−3.43605	−0.149112
$532$	8.44922	0.366320
$533$	−19.9315	−0.863327
$534$	−19.9450	−0.863103
$535$	10.7625	0.465304
$536$	13.3474	0.576521
$537$	5.15575	0.222487
$538$	−3.80263	−0.163943
$539$	−5.10548	−0.219908
$540$	−1.23292	−0.0530564
$541$	6.99342	0.300671	0.150335	−	0.988635i	$-0.451965\pi$
$541$	6.99342	0.300671	0.150335	+	0.988635i	$0.451965\pi$
$542$	−37.8186	−1.62445
$543$	−7.70169	−0.330511
$544$	3.89162	0.166852
$545$	−10.6654	−0.456854
$546$	15.6855	0.671276
$547$	−15.0870	−0.645074	−0.322537	−	0.946557i	$-0.604536\pi$
$547$	−15.0870	−0.645074	−0.322537	+	0.946557i	$0.604536\pi$
$548$	7.23718	0.309157
$549$	−2.93414	−0.125226
$550$	−25.8912	−1.10400
$551$	−31.7513	−1.35265
$552$	4.29551	0.182829
$553$	24.6803	1.04951
$554$	36.7526	1.56147
$555$	10.7761	0.457421
$556$	−6.57877	−0.279002
$557$	38.5179	1.63206	0.816029	−	0.578011i	$-0.196171\pi$
$557$	38.5179	1.63206	0.816029	+	0.578011i	$0.196171\pi$
$558$	11.9433	0.505598
$559$	−12.8125	−0.541909
$560$	17.6644	0.746458
$561$	−4.51617	−0.190673
$562$	−31.0816	−1.31110
$563$	−34.0670	−1.43575	−0.717876	−	0.696171i	$-0.754886\pi$
$563$	−34.0670	−1.43575	−0.717876	+	0.696171i	$0.754886\pi$
$564$	−4.98441	−0.209882
$565$	13.6519	0.574339
$566$	20.1243	0.845886
$567$	2.45560	0.103126
$568$	−24.2886	−1.01913
$569$	3.22359	0.135140	0.0675699	−	0.997715i	$-0.478475\pi$
$569$	3.22359	0.135140	0.0675699	+	0.997715i	$0.478475\pi$
$570$	−9.84206	−0.412239
$571$	34.0417	1.42460	0.712301	−	0.701874i	$-0.247653\pi$
$571$	34.0417	1.42460	0.712301	+	0.701874i	$0.247653\pi$
$572$	16.9831	0.710098
$573$	−2.46329	−0.102905
$574$	−21.8626	−0.912528
$575$	6.45809	0.269321
$576$	2.29583	0.0956597
$577$	5.45841	0.227237	0.113618	−	0.993524i	$-0.463756\pi$
$577$	5.45841	0.227237	0.113618	+	0.993524i	$0.463756\pi$
$578$	−27.4722	−1.14269
$579$	−1.00000	−0.0415586
$580$	9.70795	0.403101
$581$	−14.9996	−0.622288
$582$	−16.2189	−0.672294
$583$	27.3825	1.13407
$584$	2.30843	0.0955236
$585$	−5.46402	−0.225909
$586$	54.3522	2.24527
$587$	−36.8175	−1.51962	−0.759811	−	0.650144i	$-0.774709\pi$
$587$	−36.8175	−1.51962	−0.759811	+	0.650144i	$0.774709\pi$
$588$	−0.827686	−0.0341332
$589$	28.5115	1.17480
$590$	8.38642	0.345264
$591$	9.40645	0.386929
$592$	37.1290	1.52599
$593$	4.42551	0.181734	0.0908670	−	0.995863i	$-0.471036\pi$
$593$	4.42551	0.181734	0.0908670	+	0.995863i	$0.471036\pi$
$594$	8.89061	0.364786
$595$	3.04449	0.124812
$596$	−12.9756	−0.531500
$597$	5.84728	0.239313
$598$	−14.1652	−0.579259
$599$	−35.7470	−1.46058	−0.730291	−	0.683136i	$-0.760615\pi$
$599$	−35.7470	−1.46058	−0.730291	+	0.683136i	$0.760615\pi$
$600$	5.64093	0.230290
$601$	−25.8654	−1.05507	−0.527535	−	0.849533i	$-0.676884\pi$
$601$	−25.8654	−1.05507	−0.527535	+	0.849533i	$0.676884\pi$
$602$	−14.0539	−0.572792
$603$	−6.89075	−0.280613
$604$	11.2754	0.458788
$605$	−24.1339	−0.981183
$606$	13.4137	0.544896
$607$	19.4234	0.788371	0.394186	−	0.919031i	$-0.371027\pi$
$607$	19.4234	0.788371	0.394186	+	0.919031i	$0.371027\pi$
$608$	−18.2890	−0.741715
$609$	−19.3353	−0.783507
$610$	7.16141	0.289957
$611$	−22.0898	−0.893658
$612$	−0.732150	−0.0295954
$613$	0.530563	0.0214292	0.0107146	−	0.999943i	$-0.496589\pi$
$613$	0.530563	0.0214292	0.0107146	+	0.999943i	$0.496589\pi$
$614$	46.1668	1.86314
$615$	7.61583	0.307100
$616$	−25.0351	−1.00869
$617$	−43.9644	−1.76994	−0.884970	−	0.465649i	$-0.845821\pi$
$617$	−43.9644	−1.76994	−0.884970	+	0.465649i	$0.845821\pi$
$618$	25.4113	1.02219
$619$	−36.6443	−1.47286	−0.736430	−	0.676513i	$-0.763490\pi$
$619$	−36.6443	−1.47286	−0.736430	+	0.676513i	$0.763490\pi$
$620$	−8.71737	−0.350098
$621$	−2.21760	−0.0889894
$622$	34.2633	1.37383
$623$	−28.9948	−1.16165
$624$	−18.8262	−0.753652
$625$	−1.95818	−0.0783270
$626$	6.68965	0.267372
$627$	21.2241	0.847608
$628$	−15.1119	−0.603032
$629$	6.39924	0.255154
$630$	−5.99343	−0.238784
$631$	−0.938392	−0.0373568	−0.0186784	−	0.999826i	$-0.505946\pi$
$631$	−0.938392	−0.0373568	−0.0186784	+	0.999826i	$0.505946\pi$
$632$	−19.4681	−0.774400
$633$	13.3109	0.529059
$634$	44.3169	1.76005
$635$	−28.8208	−1.14372
$636$	4.43918	0.176025
$637$	−3.66812	−0.145336
$638$	−70.0043	−2.77150
$639$	12.5393	0.496046
$640$	−18.7102	−0.739587
$641$	−2.10376	−0.0830936	−0.0415468	−	0.999137i	$-0.513229\pi$
$641$	−2.10376	−0.0830936	−0.0415468	+	0.999137i	$0.513229\pi$
$642$	−12.5817	−0.496561
$643$	0.157043	0.00619317	0.00309658	−	0.999995i	$-0.499014\pi$
$643$	0.157043	0.00619317	0.00309658	+	0.999995i	$0.499014\pi$
$644$	−4.64656	−0.183100
$645$	4.89565	0.192766
$646$	−5.84456	−0.229951
$647$	−23.1168	−0.908815	−0.454407	−	0.890794i	$-0.650149\pi$
$647$	−23.1168	−0.908815	−0.454407	+	0.890794i	$0.650149\pi$
$648$	−1.93701	−0.0760928
$649$	−18.0850	−0.709900
$650$	−18.6020	−0.729629
$651$	17.3624	0.680485
$652$	13.8561	0.542645
$653$	−35.5847	−1.39254	−0.696269	−	0.717781i	$-0.745158\pi$
$653$	−35.5847	−1.39254	−0.696269	+	0.717781i	$0.745158\pi$
$654$	12.4682	0.487543
$655$	−3.19740	−0.124933
$656$	26.2403	1.02451
$657$	−1.19175	−0.0464947
$658$	−24.2301	−0.944587
$659$	−4.02769	−0.156896	−0.0784482	−	0.996918i	$-0.524997\pi$
$659$	−4.02769	−0.156896	−0.0784482	+	0.996918i	$0.524997\pi$
$660$	−6.48925	−0.252594
$661$	−21.8047	−0.848103	−0.424052	−	0.905638i	$-0.639393\pi$
$661$	−21.8047	−0.848103	−0.424052	+	0.905638i	$0.639393\pi$
$662$	37.8094	1.46950
$663$	−3.24472	−0.126015
$664$	11.8318	0.459165
$665$	−14.3078	−0.554832
$666$	−12.5976	−0.488149
$667$	17.4613	0.676105
$668$	−17.6016	−0.681027
$669$	−28.8013	−1.11352
$670$	16.8184	0.649750
$671$	−15.4433	−0.596183
$672$	−11.1373	−0.429629
$673$	−32.8310	−1.26554	−0.632772	−	0.774338i	$-0.718083\pi$
$673$	−32.8310	−1.26554	−0.632772	+	0.774338i	$0.718083\pi$
$674$	54.7946	2.11061
$675$	−2.91219	−0.112090
$676$	1.10921	0.0426618
$677$	26.0138	0.999790	0.499895	−	0.866086i	$-0.333372\pi$
$677$	26.0138	0.999790	0.499895	+	0.866086i	$0.333372\pi$
$678$	−15.9595	−0.612921
$679$	−23.5780	−0.904841
$680$	−2.40152	−0.0920942
$681$	−19.1850	−0.735169
$682$	62.8612	2.40708
$683$	23.3530	0.893578	0.446789	−	0.894639i	$-0.352567\pi$
$683$	23.3530	0.893578	0.446789	+	0.894639i	$0.352567\pi$
$684$	3.44079	0.131562
$685$	−12.2553	−0.468252
$686$	−33.0589	−1.26220
$687$	5.06674	0.193308
$688$	16.8679	0.643083
$689$	19.6734	0.749498
$690$	5.41254	0.206052
$691$	37.7486	1.43602	0.718012	−	0.696031i	$-0.245052\pi$
$691$	37.7486	1.43602	0.718012	+	0.696031i	$0.245052\pi$
$692$	−16.9240	−0.643352
$693$	12.9246	0.490966
$694$	−2.06594	−0.0784219
$695$	11.1404	0.422580
$696$	15.2519	0.578122
$697$	4.52254	0.171303
$698$	34.8420	1.31879
$699$	22.8573	0.864543
$700$	−6.10194	−0.230631
$701$	29.3166	1.10727	0.553635	−	0.832759i	$-0.313240\pi$
$701$	29.3166	1.10727	0.553635	+	0.832759i	$0.313240\pi$
$702$	6.38762	0.241085
$703$	−30.0737	−1.13425
$704$	12.0837	0.455422
$705$	8.44054	0.317889
$706$	5.42713	0.204253
$707$	19.5001	0.733376
$708$	−2.93190	−0.110188
$709$	47.3213	1.77719	0.888594	−	0.458694i	$-0.151683\pi$
$709$	47.3213	1.77719	0.888594	+	0.458694i	$0.151683\pi$
$710$	−30.6048	−1.14858
$711$	10.0506	0.376928
$712$	22.8714	0.857141
$713$	−15.6796	−0.587206
$714$	−3.55911	−0.133196
$715$	−28.7589	−1.07552
$716$	4.39928	0.164409
$717$	−1.26308	−0.0471708
$718$	−12.8206	−0.478461
$719$	14.3255	0.534252	0.267126	−	0.963662i	$-0.413926\pi$
$719$	14.3255	0.534252	0.267126	+	0.963662i	$0.413926\pi$
$720$	7.19352	0.268087
$721$	36.9414	1.37577
$722$	−4.62720	−0.172206
$723$	16.4700	0.612526
$724$	−6.57166	−0.244234
$725$	22.9305	0.851616
$726$	28.2133	1.04709
$727$	45.2485	1.67818	0.839088	−	0.543996i	$-0.183089\pi$
$727$	45.2485	1.67818	0.839088	+	0.543996i	$0.183089\pi$
$728$	−17.9869	−0.666639
$729$	1.00000	0.0370370
$730$	2.90873	0.107657
$731$	2.90721	0.107527
$732$	−2.50363	−0.0925369
$733$	−21.5786	−0.797022	−0.398511	−	0.917164i	$-0.630473\pi$
$733$	−21.5786	−0.797022	−0.398511	+	0.917164i	$0.630473\pi$
$734$	−19.0086	−0.701618
$735$	1.40159	0.0516985
$736$	10.0578	0.370736
$737$	−36.2682	−1.33596
$738$	−8.90315	−0.327730
$739$	3.15424	0.116031	0.0580154	−	0.998316i	$-0.481523\pi$
$739$	3.15424	0.116031	0.0580154	+	0.998316i	$0.481523\pi$
$740$	9.19501	0.338015
$741$	15.2488	0.560179
$742$	21.5796	0.792212
$743$	−28.4790	−1.04479	−0.522397	−	0.852703i	$-0.674962\pi$
$743$	−28.4790	−1.04479	−0.522397	+	0.852703i	$0.674962\pi$
$744$	−13.6956	−0.502106
$745$	21.9727	0.805016
$746$	28.9749	1.06085
$747$	−6.10832	−0.223492
$748$	−3.85354	−0.140899
$749$	−18.2905	−0.668322
$750$	19.3114	0.705153
$751$	−11.3748	−0.415071	−0.207536	−	0.978227i	$-0.566544\pi$
$751$	−11.3748	−0.415071	−0.207536	+	0.978227i	$0.566544\pi$
$752$	29.0818	1.06050
$753$	−11.9847	−0.436746
$754$	−50.2958	−1.83167
$755$	−19.0935	−0.694885
$756$	2.09531	0.0762056
$757$	39.3892	1.43163	0.715813	−	0.698293i	$-0.246057\pi$
$757$	39.3892	1.43163	0.715813	+	0.698293i	$0.246057\pi$
$758$	−30.3033	−1.10067
$759$	−11.6720	−0.423665
$760$	11.2861	0.409391
$761$	−28.6305	−1.03785	−0.518927	−	0.854819i	$-0.673668\pi$
$761$	−28.6305	−1.03785	−0.518927	+	0.854819i	$0.673668\pi$
$762$	33.6925	1.22055
$763$	18.1254	0.656185
$764$	−2.10186	−0.0760427
$765$	1.23981	0.0448255
$766$	19.3016	0.697395
$767$	−12.9935	−0.469169
$768$	17.2812	0.623582
$769$	−44.0196	−1.58739	−0.793694	−	0.608317i	$-0.791845\pi$
$769$	−44.0196	−1.58739	−0.793694	+	0.608317i	$0.791845\pi$
$770$	−31.5453	−1.13681
$771$	−1.41069	−0.0508049
$772$	−0.853276	−0.0307101
$773$	10.3466	0.372143	0.186071	−	0.982536i	$-0.440424\pi$
$773$	10.3466	0.372143	0.186071	+	0.982536i	$0.440424\pi$
$774$	−5.72318	−0.205715
$775$	−20.5907	−0.739639
$776$	18.5986	0.667650
$777$	−18.3137	−0.657000
$778$	47.9110	1.71769
$779$	−21.2540	−0.761504
$780$	−4.66232	−0.166938
$781$	65.9981	2.36160
$782$	3.21415	0.114938
$783$	−7.87396	−0.281392
$784$	4.82917	0.172470
$785$	25.5904	0.913359
$786$	3.73787	0.133325
$787$	16.1088	0.574218	0.287109	−	0.957898i	$-0.407306\pi$
$787$	16.1088	0.574218	0.287109	+	0.957898i	$0.407306\pi$
$788$	8.02629	0.285925
$789$	−16.8917	−0.601362
$790$	−24.5307	−0.872763
$791$	−23.2009	−0.824931
$792$	−10.1951	−0.362266
$793$	−11.0955	−0.394014
$794$	−6.67217	−0.236787
$795$	−7.51724	−0.266609
$796$	4.98934	0.176843
$797$	−10.9570	−0.388118	−0.194059	−	0.980990i	$-0.562165\pi$
$797$	−10.9570	−0.388118	−0.194059	+	0.980990i	$0.562165\pi$
$798$	16.7263	0.592104
$799$	5.01228	0.177322
$800$	13.2081	0.466976
$801$	−11.8076	−0.417201
$802$	−16.4495	−0.580851
$803$	−6.27258	−0.221354
$804$	−5.87971	−0.207361
$805$	7.86842	0.277325
$806$	45.1637	1.59082
$807$	−2.25119	−0.0792457
$808$	−15.3819	−0.541132
$809$	16.9641	0.596427	0.298213	−	0.954499i	$-0.403609\pi$
$809$	16.9641	0.596427	0.298213	+	0.954499i	$0.403609\pi$
$810$	−2.44072	−0.0857580
$811$	−5.88415	−0.206621	−0.103310	−	0.994649i	$-0.532943\pi$
$811$	−5.88415	−0.206621	−0.103310	+	0.994649i	$0.532943\pi$
$812$	−16.4984	−0.578979
$813$	−22.3890	−0.785216
$814$	−66.3054	−2.32400
$815$	−23.4637	−0.821896
$816$	4.27176	0.149541
$817$	−13.6626	−0.477995
$818$	−0.693683	−0.0242541
$819$	9.28593	0.324477
$820$	6.49840	0.226934
$821$	54.4044	1.89873	0.949363	−	0.314182i	$-0.101730\pi$
$821$	54.4044	1.89873	0.949363	+	0.314182i	$0.101730\pi$
$822$	14.3269	0.499708
$823$	−20.4999	−0.714580	−0.357290	−	0.933993i	$-0.616299\pi$
$823$	−20.4999	−0.714580	−0.357290	+	0.933993i	$0.616299\pi$
$824$	−29.1398	−1.01513
$825$	−15.3278	−0.533645
$826$	−14.2525	−0.495906
$827$	17.6988	0.615449	0.307724	−	0.951476i	$-0.400432\pi$
$827$	17.6988	0.615449	0.307724	+	0.951476i	$0.400432\pi$
$828$	−1.89223	−0.0657595
$829$	−55.0939	−1.91349	−0.956744	−	0.290930i	$-0.906035\pi$
$829$	−55.0939	−1.91349	−0.956744	+	0.290930i	$0.906035\pi$
$830$	14.9087	0.517487
$831$	21.7579	0.754772
$832$	8.68175	0.300986
$833$	0.832314	0.0288380
$834$	−13.0235	−0.450967
$835$	29.8063	1.03149
$836$	18.1100	0.626347
$837$	7.07051	0.244393
$838$	68.2438	2.35744
$839$	2.52000	0.0869999	0.0435000	−	0.999053i	$-0.486149\pi$
$839$	2.52000	0.0869999	0.0435000	+	0.999053i	$0.486149\pi$
$840$	6.87281	0.237135
$841$	32.9992	1.13790
$842$	−31.7901	−1.09556
$843$	−18.4006	−0.633749
$844$	11.3578	0.390953
$845$	−1.87832	−0.0646160
$846$	−9.86726	−0.339243
$847$	41.0148	1.40929
$848$	−25.9006	−0.889429
$849$	11.9137	0.408879
$850$	4.22088	0.144775
$851$	16.5387	0.566940
$852$	10.6994	0.366557
$853$	−26.7427	−0.915653	−0.457826	−	0.889042i	$-0.651372\pi$
$853$	−26.7427	−0.915653	−0.457826	+	0.889042i	$0.651372\pi$
$854$	−12.1706	−0.416469
$855$	−5.82659	−0.199265
$856$	14.4278	0.493131
$857$	16.1901	0.553043	0.276521	−	0.961008i	$-0.410818\pi$
$857$	16.1901	0.553043	0.276521	+	0.961008i	$0.410818\pi$
$858$	33.6201	1.14777
$859$	−28.1540	−0.960603	−0.480302	−	0.877103i	$-0.659473\pi$
$859$	−28.1540	−0.960603	−0.480302	+	0.877103i	$0.659473\pi$
$860$	4.17734	0.142446
$861$	−12.9429	−0.441091
$862$	53.7451	1.83057
$863$	32.6647	1.11192	0.555959	−	0.831210i	$-0.312351\pi$
$863$	32.6647	1.11192	0.555959	+	0.831210i	$0.312351\pi$
$864$	−4.53544	−0.154299
$865$	28.6588	0.974428
$866$	28.2061	0.958483
$867$	−16.2638	−0.552346
$868$	14.8149	0.502850
$869$	52.8996	1.79450
$870$	19.2181	0.651554
$871$	−26.0576	−0.882927
$872$	−14.2975	−0.484176
$873$	−9.60171	−0.324969
$874$	−15.1052	−0.510939
$875$	28.0737	0.949066
$876$	−1.01689	−0.0343576
$877$	25.7920	0.870934	0.435467	−	0.900205i	$-0.356583\pi$
$877$	25.7920	0.870934	0.435467	+	0.900205i	$0.356583\pi$
$878$	−22.3957	−0.755819
$879$	32.1770	1.08530
$880$	37.8618	1.27632
$881$	52.5016	1.76882	0.884412	−	0.466708i	$-0.154560\pi$
$881$	52.5016	1.76882	0.884412	+	0.466708i	$0.154560\pi$
$882$	−1.63851	−0.0551714
$883$	44.5711	1.49994	0.749969	−	0.661473i	$-0.230068\pi$
$883$	44.5711	1.49994	0.749969	+	0.661473i	$0.230068\pi$
$884$	−2.76864	−0.0931196
$885$	4.96484	0.166891
$886$	−12.8830	−0.432814
$887$	−22.8894	−0.768550	−0.384275	−	0.923219i	$-0.625548\pi$
$887$	−22.8894	−0.768550	−0.384275	+	0.923219i	$0.625548\pi$
$888$	14.4460	0.484777
$889$	48.9800	1.64274
$890$	28.8190	0.966014
$891$	5.26332	0.176328
$892$	−24.5755	−0.822848
$893$	−23.5556	−0.788258
$894$	−25.6868	−0.859094
$895$	−7.44968	−0.249015
$896$	31.7974	1.06228
$897$	−8.38593	−0.279998
$898$	−41.0126	−1.36861
$899$	−55.6729	−1.85679
$900$	−2.48490	−0.0828301
$901$	−4.46400	−0.148717
$902$	−46.8601	−1.56027
$903$	−8.32001	−0.276872
$904$	18.3011	0.608687
$905$	11.1284	0.369919
$906$	22.3210	0.741565
$907$	−53.7367	−1.78430	−0.892149	−	0.451742i	$-0.850803\pi$
$907$	−53.7367	−1.78430	−0.892149	+	0.451742i	$0.850803\pi$
$908$	−16.3701	−0.543259
$909$	7.94106	0.263388
$910$	−22.6643	−0.751315
$911$	39.0107	1.29248	0.646241	−	0.763134i	$-0.276340\pi$
$911$	39.0107	1.29248	0.646241	+	0.763134i	$0.276340\pi$
$912$	−20.0754	−0.664764
$913$	−32.1500	−1.06401
$914$	−8.70540	−0.287949
$915$	4.23962	0.140157
$916$	4.32333	0.142847
$917$	5.43388	0.179443
$918$	−1.44938	−0.0478367
$919$	41.6686	1.37452	0.687260	−	0.726411i	$-0.258813\pi$
$919$	41.6686	1.37452	0.687260	+	0.726411i	$0.258813\pi$
$920$	−6.20669	−0.204629
$921$	27.3311	0.900592
$922$	23.3982	0.770578
$923$	47.4175	1.56077
$924$	11.0283	0.362803
$925$	21.7189	0.714113
$926$	−26.5220	−0.871568
$927$	15.0437	0.494100
$928$	35.7119	1.17230
$929$	40.9634	1.34396	0.671982	−	0.740567i	$-0.265443\pi$
$929$	40.9634	1.34396	0.671982	+	0.740567i	$0.265443\pi$
$930$	−17.2571	−0.565883
$931$	−3.91152	−0.128195
$932$	19.5036	0.638861
$933$	20.2842	0.664073
$934$	54.8681	1.79534
$935$	6.52553	0.213408
$936$	−7.32484	−0.239420
$937$	−21.9291	−0.716392	−0.358196	−	0.933647i	$-0.616608\pi$
$937$	−21.9291	−0.716392	−0.358196	+	0.933647i	$0.616608\pi$
$938$	−28.5823	−0.933245
$939$	3.96033	0.129241
$940$	7.20210	0.234907
$941$	7.65724	0.249619	0.124809	−	0.992181i	$-0.460168\pi$
$941$	7.65724	0.249619	0.124809	+	0.992181i	$0.460168\pi$
$942$	−29.9160	−0.974715
$943$	11.6884	0.380628
$944$	17.1063	0.556762
$945$	−3.54816	−0.115422
$946$	−30.1229	−0.979380
$947$	55.9980	1.81969	0.909846	−	0.414946i	$-0.136200\pi$
$947$	55.9980	1.81969	0.909846	+	0.414946i	$0.136200\pi$
$948$	8.57595	0.278534
$949$	−4.50664	−0.146292
$950$	−19.8363	−0.643575
$951$	26.2360	0.850761
$952$	4.08131	0.132276
$953$	−27.3337	−0.885424	−0.442712	−	0.896664i	$-0.645984\pi$
$953$	−27.3337	−0.885424	−0.442712	+	0.896664i	$0.645984\pi$
$954$	8.78790	0.284519
$955$	3.55926	0.115175
$956$	−1.07776	−0.0348572
$957$	−41.4432	−1.33967
$958$	2.23466	0.0721985
$959$	20.8276	0.672557
$960$	−3.31731	−0.107066
$961$	18.9921	0.612649
$962$	−47.6383	−1.53592
$963$	−7.44849	−0.240024
$964$	14.0534	0.452631
$965$	1.44492	0.0465138
$966$	−9.19844	−0.295955
$967$	−1.24090	−0.0399046	−0.0199523	−	0.999801i	$-0.506351\pi$
$967$	−1.24090	−0.0399046	−0.0199523	+	0.999801i	$0.506351\pi$
$968$	−32.3529	−1.03986
$969$	−3.46003	−0.111152
$970$	23.4350	0.752454
$971$	−25.9199	−0.831810	−0.415905	−	0.909408i	$-0.636535\pi$
$971$	−25.9199	−0.831810	−0.415905	+	0.909408i	$0.636535\pi$
$972$	0.853276	0.0273688
$973$	−18.9328	−0.606956
$974$	−62.7130	−2.00946
$975$	−11.0125	−0.352683
$976$	14.6075	0.467576
$977$	17.6037	0.563191	0.281596	−	0.959533i	$-0.409136\pi$
$977$	17.6037	0.563191	0.281596	+	0.959533i	$0.409136\pi$
$978$	27.4298	0.877108
$979$	−62.1471	−1.98623
$980$	1.19594	0.0382031
$981$	7.38126	0.235665
$982$	31.6635	1.01042
$983$	4.01123	0.127938	0.0639692	−	0.997952i	$-0.479624\pi$
$983$	4.01123	0.127938	0.0639692	+	0.997952i	$0.479624\pi$
$984$	10.2095	0.325466
$985$	−13.5916	−0.433065
$986$	11.4124	0.363444
$987$	−14.3444	−0.456588
$988$	13.0114	0.413949
$989$	7.51363	0.238919
$990$	−12.8463	−0.408281
$991$	58.0671	1.84456	0.922281	−	0.386519i	$-0.126323\pi$
$991$	58.0671	1.84456	0.922281	+	0.386519i	$0.126323\pi$
$992$	−32.0679	−1.01816
$993$	22.3835	0.710319
$994$	52.0118	1.64971
$995$	−8.44889	−0.267848
$996$	−5.21208	−0.165151
$997$	21.8914	0.693307	0.346653	−	0.937993i	$-0.387318\pi$
$997$	21.8914	0.693307	0.346653	+	0.937993i	$0.387318\pi$
$998$	−37.0804	−1.17376
$999$	−7.45792	−0.235958

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	579.2.a.g.1.9	✓	13
3.2	odd	2		1737.2.a.j.1.5		13
4.3	odd	2		9264.2.a.bp.1.4		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
579.2.a.g.1.9	✓	13	1.1	even	1	trivial
1737.2.a.j.1.5		13	3.2	odd	2
9264.2.a.bp.1.4		13	4.3	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:	\( N \)	\(=\)	\( 579 = 3 \cdot 193 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	579.a (trivial)

\(f(q)\)	\(=\)	\(q+1.68916 q^{2} +1.00000 q^{3} +0.853276 q^{4} -1.44492 q^{5} +1.68916 q^{6} +2.45560 q^{7} -1.93701 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.68916 q^{2} +1.00000 q^{3} +0.853276 q^{4} -1.44492 q^{5} +1.68916 q^{6} +2.45560 q^{7} -1.93701 q^{8} +1.00000 q^{9} -2.44072 q^{10} +5.26332 q^{11} +0.853276 q^{12} +3.78153 q^{13} +4.14792 q^{14} -1.44492 q^{15} -4.97847 q^{16} -0.858046 q^{17} +1.68916 q^{18} +4.03245 q^{19} -1.23292 q^{20} +2.45560 q^{21} +8.89061 q^{22} -2.21760 q^{23} -1.93701 q^{24} -2.91219 q^{25} +6.38762 q^{26} +1.00000 q^{27} +2.09531 q^{28} -7.87396 q^{29} -2.44072 q^{30} +7.07051 q^{31} -4.53544 q^{32} +5.26332 q^{33} -1.44938 q^{34} -3.54816 q^{35} +0.853276 q^{36} -7.45792 q^{37} +6.81147 q^{38} +3.78153 q^{39} +2.79883 q^{40} -5.27074 q^{41} +4.14792 q^{42} -3.38817 q^{43} +4.49106 q^{44} -1.44492 q^{45} -3.74590 q^{46} -5.84151 q^{47} -4.97847 q^{48} -0.970011 q^{49} -4.91917 q^{50} -0.858046 q^{51} +3.22668 q^{52} +5.20251 q^{53} +1.68916 q^{54} -7.60510 q^{55} -4.75652 q^{56} +4.03245 q^{57} -13.3004 q^{58} -3.43605 q^{59} -1.23292 q^{60} -2.93414 q^{61} +11.9433 q^{62} +2.45560 q^{63} +2.29583 q^{64} -5.46402 q^{65} +8.89061 q^{66} -6.89075 q^{67} -0.732150 q^{68} -2.21760 q^{69} -5.99343 q^{70} +12.5393 q^{71} -1.93701 q^{72} -1.19175 q^{73} -12.5976 q^{74} -2.91219 q^{75} +3.44079 q^{76} +12.9246 q^{77} +6.38762 q^{78} +10.0506 q^{79} +7.19352 q^{80} +1.00000 q^{81} -8.90315 q^{82} -6.10832 q^{83} +2.09531 q^{84} +1.23981 q^{85} -5.72318 q^{86} -7.87396 q^{87} -10.1951 q^{88} -11.8076 q^{89} -2.44072 q^{90} +9.28593 q^{91} -1.89223 q^{92} +7.07051 q^{93} -9.86726 q^{94} -5.82659 q^{95} -4.53544 q^{96} -9.60171 q^{97} -1.63851 q^{98} +5.26332 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 2 q^{2} + 13 q^{3} + 18 q^{4} + 6 q^{5} + 2 q^{6} + 15 q^{7} + 3 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 2 * q^2 + 13 * q^3 + 18 * q^4 + 6 * q^5 + 2 * q^6 + 15 * q^7 + 3 * q^8 + 13 * q^9	\( 13 q + 2 q^{2} + 13 q^{3} + 18 q^{4} + 6 q^{5} + 2 q^{6} + 15 q^{7} + 3 q^{8} + 13 q^{9} - q^{10} + 3 q^{11} + 18 q^{12} + 11 q^{13} - 4 q^{14} + 6 q^{15} + 20 q^{16} - 2 q^{17} + 2 q^{18} + 9 q^{19} - 9 q^{20} + 15 q^{21} - 8 q^{22} - 8 q^{23} + 3 q^{24} + 21 q^{25} - 15 q^{26} + 13 q^{27} + 16 q^{28} + 5 q^{29} - q^{30} + 25 q^{31} - 17 q^{32} + 3 q^{33} - 10 q^{34} - 10 q^{35} + 18 q^{36} + 29 q^{37} - 40 q^{38} + 11 q^{39} - 21 q^{40} - 11 q^{41} - 4 q^{42} + 8 q^{43} - 18 q^{44} + 6 q^{45} - 6 q^{46} - 12 q^{47} + 20 q^{48} + 20 q^{49} - 4 q^{50} - 2 q^{51} + 2 q^{52} + 14 q^{53} + 2 q^{54} + 12 q^{55} - 7 q^{56} + 9 q^{57} + 9 q^{58} + 10 q^{59} - 9 q^{60} + 6 q^{61} - 14 q^{62} + 15 q^{63} + 23 q^{64} - 15 q^{65} - 8 q^{66} + 25 q^{67} - 33 q^{68} - 8 q^{69} - 21 q^{70} + 3 q^{72} + 8 q^{73} - 2 q^{74} + 21 q^{75} + 20 q^{76} - 25 q^{77} - 15 q^{78} + 7 q^{79} - 40 q^{80} + 13 q^{81} - 19 q^{82} - 28 q^{83} + 16 q^{84} - 3 q^{85} + 2 q^{86} + 5 q^{87} - 21 q^{88} + 7 q^{89} - q^{90} + 7 q^{91} + 9 q^{92} + 25 q^{93} - 35 q^{94} - 26 q^{95} - 17 q^{96} + 26 q^{97} - 14 q^{98} + 3 q^{99}+O(q^{100}) \) 13 * q + 2 * q^2 + 13 * q^3 + 18 * q^4 + 6 * q^5 + 2 * q^6 + 15 * q^7 + 3 * q^8 + 13 * q^9 - q^10 + 3 * q^11 + 18 * q^12 + 11 * q^13 - 4 * q^14 + 6 * q^15 + 20 * q^16 - 2 * q^17 + 2 * q^18 + 9 * q^19 - 9 * q^20 + 15 * q^21 - 8 * q^22 - 8 * q^23 + 3 * q^24 + 21 * q^25 - 15 * q^26 + 13 * q^27 + 16 * q^28 + 5 * q^29 - q^30 + 25 * q^31 - 17 * q^32 + 3 * q^33 - 10 * q^34 - 10 * q^35 + 18 * q^36 + 29 * q^37 - 40 * q^38 + 11 * q^39 - 21 * q^40 - 11 * q^41 - 4 * q^42 + 8 * q^43 - 18 * q^44 + 6 * q^45 - 6 * q^46 - 12 * q^47 + 20 * q^48 + 20 * q^49 - 4 * q^50 - 2 * q^51 + 2 * q^52 + 14 * q^53 + 2 * q^54 + 12 * q^55 - 7 * q^56 + 9 * q^57 + 9 * q^58 + 10 * q^59 - 9 * q^60 + 6 * q^61 - 14 * q^62 + 15 * q^63 + 23 * q^64 - 15 * q^65 - 8 * q^66 + 25 * q^67 - 33 * q^68 - 8 * q^69 - 21 * q^70 + 3 * q^72 + 8 * q^73 - 2 * q^74 + 21 * q^75 + 20 * q^76 - 25 * q^77 - 15 * q^78 + 7 * q^79 - 40 * q^80 + 13 * q^81 - 19 * q^82 - 28 * q^83 + 16 * q^84 - 3 * q^85 + 2 * q^86 + 5 * q^87 - 21 * q^88 + 7 * q^89 - q^90 + 7 * q^91 + 9 * q^92 + 25 * q^93 - 35 * q^94 - 26 * q^95 - 17 * q^96 + 26 * q^97 - 14 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more