LMFDB - Embedded newform 7942.2.a.bh.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7942,2,Mod(1,7942)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7942, 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("7942.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7942 = 2 \cdot 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7942.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:	$63.4171892853$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.311108$ of defining polynomial
Character	$\chi$	$=$	7942.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.688892 q^{3} +1.00000 q^{4} +0.622216 q^{5} -0.688892 q^{6} -3.11753 q^{7} +1.00000 q^{8} -2.52543 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.688892 q^{3} +1.00000 q^{4} +0.622216 q^{5} -0.688892 q^{6} -3.11753 q^{7} +1.00000 q^{8} -2.52543 q^{9} +0.622216 q^{10} -1.00000 q^{11} -0.688892 q^{12} -4.52543 q^{13} -3.11753 q^{14} -0.428639 q^{15} +1.00000 q^{16} +7.59210 q^{17} -2.52543 q^{18} +0.622216 q^{20} +2.14764 q^{21} -1.00000 q^{22} -6.23506 q^{23} -0.688892 q^{24} -4.61285 q^{25} -4.52543 q^{26} +3.80642 q^{27} -3.11753 q^{28} +2.80642 q^{29} -0.428639 q^{30} -0.280996 q^{31} +1.00000 q^{32} +0.688892 q^{33} +7.59210 q^{34} -1.93978 q^{35} -2.52543 q^{36} -2.83654 q^{37} +3.11753 q^{39} +0.622216 q^{40} +2.21432 q^{41} +2.14764 q^{42} +2.59210 q^{43} -1.00000 q^{44} -1.57136 q^{45} -6.23506 q^{46} +1.49532 q^{47} -0.688892 q^{48} +2.71900 q^{49} -4.61285 q^{50} -5.23014 q^{51} -4.52543 q^{52} -1.37778 q^{53} +3.80642 q^{54} -0.622216 q^{55} -3.11753 q^{56} +2.80642 q^{58} +4.42864 q^{59} -0.428639 q^{60} +13.7096 q^{61} -0.280996 q^{62} +7.87310 q^{63} +1.00000 q^{64} -2.81579 q^{65} +0.688892 q^{66} +4.16839 q^{67} +7.59210 q^{68} +4.29529 q^{69} -1.93978 q^{70} -12.0716 q^{71} -2.52543 q^{72} -10.9699 q^{73} -2.83654 q^{74} +3.17775 q^{75} +3.11753 q^{77} +3.11753 q^{78} +15.6795 q^{79} +0.622216 q^{80} +4.95407 q^{81} +2.21432 q^{82} +13.4494 q^{83} +2.14764 q^{84} +4.72393 q^{85} +2.59210 q^{86} -1.93332 q^{87} -1.00000 q^{88} -16.4795 q^{89} -1.57136 q^{90} +14.1082 q^{91} -6.23506 q^{92} +0.193576 q^{93} +1.49532 q^{94} -0.688892 q^{96} -17.8988 q^{97} +2.71900 q^{98} +2.52543 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 2 q^{3} + 3 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{7} + 3 q^{8} - q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 2 * q^3 + 3 * q^4 + 2 * q^5 - 2 * q^6 + 4 * q^7 + 3 * q^8 - q^9	$ 3 q + 3 q^{2} - 2 q^{3} + 3 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{7} + 3 q^{8} - q^{9} + 2 q^{10} - 3 q^{11} - 2 q^{12} - 7 q^{13} + 4 q^{14} + 12 q^{15} + 3 q^{16} + 16 q^{17} - q^{18} + 2 q^{20} - 3 q^{22} + 8 q^{23} - 2 q^{24} + 13 q^{25} - 7 q^{26} - 2 q^{27} + 4 q^{28} - 5 q^{29} + 12 q^{30} + 6 q^{31} + 3 q^{32} + 2 q^{33} + 16 q^{34} + 8 q^{35} - q^{36} - 2 q^{37} - 4 q^{39} + 2 q^{40} + q^{43} - 3 q^{44} - 18 q^{45} + 8 q^{46} - 9 q^{47} - 2 q^{48} + 15 q^{49} + 13 q^{50} - 22 q^{51} - 7 q^{52} - 4 q^{53} - 2 q^{54} - 2 q^{55} + 4 q^{56} - 5 q^{58} + 12 q^{60} + 21 q^{61} + 6 q^{62} + 10 q^{63} + 3 q^{64} - 22 q^{65} + 2 q^{66} - 14 q^{67} + 16 q^{68} + 8 q^{70} - 3 q^{71} - q^{72} - 26 q^{73} - 2 q^{74} + 10 q^{75} - 4 q^{77} - 4 q^{78} + 20 q^{79} + 2 q^{80} - 5 q^{81} + 7 q^{83} - 12 q^{85} + q^{86} - 6 q^{87} - 3 q^{88} - 23 q^{89} - 18 q^{90} + 2 q^{91} + 8 q^{92} + 14 q^{93} - 9 q^{94} - 2 q^{96} + 13 q^{97} + 15 q^{98} + q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 - 2 * q^3 + 3 * q^4 + 2 * q^5 - 2 * q^6 + 4 * q^7 + 3 * q^8 - q^9 + 2 * q^10 - 3 * q^11 - 2 * q^12 - 7 * q^13 + 4 * q^14 + 12 * q^15 + 3 * q^16 + 16 * q^17 - q^18 + 2 * q^20 - 3 * q^22 + 8 * q^23 - 2 * q^24 + 13 * q^25 - 7 * q^26 - 2 * q^27 + 4 * q^28 - 5 * q^29 + 12 * q^30 + 6 * q^31 + 3 * q^32 + 2 * q^33 + 16 * q^34 + 8 * q^35 - q^36 - 2 * q^37 - 4 * q^39 + 2 * q^40 + q^43 - 3 * q^44 - 18 * q^45 + 8 * q^46 - 9 * q^47 - 2 * q^48 + 15 * q^49 + 13 * q^50 - 22 * q^51 - 7 * q^52 - 4 * q^53 - 2 * q^54 - 2 * q^55 + 4 * q^56 - 5 * q^58 + 12 * q^60 + 21 * q^61 + 6 * q^62 + 10 * q^63 + 3 * q^64 - 22 * q^65 + 2 * q^66 - 14 * q^67 + 16 * q^68 + 8 * q^70 - 3 * q^71 - q^72 - 26 * q^73 - 2 * q^74 + 10 * q^75 - 4 * q^77 - 4 * q^78 + 20 * q^79 + 2 * q^80 - 5 * q^81 + 7 * q^83 - 12 * q^85 + q^86 - 6 * q^87 - 3 * q^88 - 23 * q^89 - 18 * q^90 + 2 * q^91 + 8 * q^92 + 14 * q^93 - 9 * q^94 - 2 * q^96 + 13 * q^97 + 15 * q^98 + 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.688892	−0.397732	−0.198866	−	0.980027i	$-0.563726\pi$
$3$	−0.688892	−0.397732	−0.198866	+	0.980027i	$0.563726\pi$
$4$	1.00000	0.500000
$5$	0.622216	0.278263	0.139132	−	0.990274i	$-0.455569\pi$
$5$	0.622216	0.278263	0.139132	+	0.990274i	$0.455569\pi$
$6$	−0.688892	−0.281239
$7$	−3.11753	−1.17832	−0.589158	−	0.808018i	$-0.700540\pi$
$7$	−3.11753	−1.17832	−0.589158	+	0.808018i	$0.700540\pi$
$8$	1.00000	0.353553
$9$	−2.52543	−0.841809
$10$	0.622216	0.196762
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.688892	−0.198866
$13$	−4.52543	−1.25513	−0.627564	−	0.778565i	$-0.715948\pi$
$13$	−4.52543	−1.25513	−0.627564	+	0.778565i	$0.715948\pi$
$14$	−3.11753	−0.833195
$15$	−0.428639	−0.110674
$16$	1.00000	0.250000
$17$	7.59210	1.84136	0.920678	−	0.390323i	$-0.127637\pi$
$17$	7.59210	1.84136	0.920678	+	0.390323i	$0.127637\pi$
$18$	−2.52543	−0.595249
$19$	0	0
$19$	0	0
$20$	0.622216	0.139132
$21$	2.14764	0.468654
$22$	−1.00000	−0.213201
$23$	−6.23506	−1.30010	−0.650050	−	0.759891i	$-0.725252\pi$
$23$	−6.23506	−1.30010	−0.650050	+	0.759891i	$0.725252\pi$
$24$	−0.688892	−0.140620
$25$	−4.61285	−0.922570
$26$	−4.52543	−0.887509
$27$	3.80642	0.732547
$28$	−3.11753	−0.589158
$29$	2.80642	0.521140	0.260570	−	0.965455i	$-0.416090\pi$
$29$	2.80642	0.521140	0.260570	+	0.965455i	$0.416090\pi$
$30$	−0.428639	−0.0782585
$31$	−0.280996	−0.0504684	−0.0252342	−	0.999682i	$-0.508033\pi$
$31$	−0.280996	−0.0504684	−0.0252342	+	0.999682i	$0.508033\pi$
$32$	1.00000	0.176777
$33$	0.688892	0.119921
$34$	7.59210	1.30204
$35$	−1.93978	−0.327882
$36$	−2.52543	−0.420905
$37$	−2.83654	−0.466324	−0.233162	−	0.972438i	$-0.574907\pi$
$37$	−2.83654	−0.466324	−0.233162	+	0.972438i	$0.574907\pi$
$38$	0	0
$39$	3.11753	0.499205
$40$	0.622216	0.0983809
$41$	2.21432	0.345819	0.172909	−	0.984938i	$-0.444683\pi$
$41$	2.21432	0.345819	0.172909	+	0.984938i	$0.444683\pi$
$42$	2.14764	0.331389
$43$	2.59210	0.395292	0.197646	−	0.980273i	$-0.436670\pi$
$43$	2.59210	0.395292	0.197646	+	0.980273i	$0.436670\pi$
$44$	−1.00000	−0.150756
$45$	−1.57136	−0.234245
$46$	−6.23506	−0.919310
$47$	1.49532	0.218114	0.109057	−	0.994035i	$-0.465217\pi$
$47$	1.49532	0.218114	0.109057	+	0.994035i	$0.465217\pi$
$48$	−0.688892	−0.0994330
$49$	2.71900	0.388429
$50$	−4.61285	−0.652355
$51$	−5.23014	−0.732366
$52$	−4.52543	−0.627564
$53$	−1.37778	−0.189253	−0.0946266	−	0.995513i	$-0.530166\pi$
$53$	−1.37778	−0.189253	−0.0946266	+	0.995513i	$0.530166\pi$
$54$	3.80642	0.517989
$55$	−0.622216	−0.0838995
$56$	−3.11753	−0.416598
$57$	0	0
$58$	2.80642	0.368502
$59$	4.42864	0.576560	0.288280	−	0.957546i	$-0.406917\pi$
$59$	4.42864	0.576560	0.288280	+	0.957546i	$0.406917\pi$
$60$	−0.428639	−0.0553371
$61$	13.7096	1.75534	0.877669	−	0.479266i	$-0.159097\pi$
$61$	13.7096	1.75534	0.877669	+	0.479266i	$0.159097\pi$
$62$	−0.280996	−0.0356866
$63$	7.87310	0.991917
$64$	1.00000	0.125000
$65$	−2.81579	−0.349256
$66$	0.688892	0.0847968
$67$	4.16839	0.509249	0.254625	−	0.967040i	$-0.418048\pi$
$67$	4.16839	0.509249	0.254625	+	0.967040i	$0.418048\pi$
$68$	7.59210	0.920678
$69$	4.29529	0.517092
$70$	−1.93978	−0.231848
$71$	−12.0716	−1.43264	−0.716318	−	0.697774i	$-0.754174\pi$
$71$	−12.0716	−1.43264	−0.716318	+	0.697774i	$0.754174\pi$
$72$	−2.52543	−0.297624
$73$	−10.9699	−1.28393	−0.641964	−	0.766735i	$-0.721880\pi$
$73$	−10.9699	−1.28393	−0.641964	+	0.766735i	$0.721880\pi$
$74$	−2.83654	−0.329741
$75$	3.17775	0.366936
$76$	0	0
$77$	3.11753	0.355276
$78$	3.11753	0.352991
$79$	15.6795	1.76408	0.882042	−	0.471171i	$-0.156168\pi$
$79$	15.6795	1.76408	0.882042	+	0.471171i	$0.156168\pi$
$80$	0.622216	0.0695658
$81$	4.95407	0.550452
$82$	2.21432	0.244531
$83$	13.4494	1.47626	0.738131	−	0.674658i	$-0.235709\pi$
$83$	13.4494	1.47626	0.738131	+	0.674658i	$0.235709\pi$
$84$	2.14764	0.234327
$85$	4.72393	0.512382
$86$	2.59210	0.279514
$87$	−1.93332	−0.207274
$88$	−1.00000	−0.106600
$89$	−16.4795	−1.74682	−0.873411	−	0.486983i	$-0.838097\pi$
$89$	−16.4795	−1.74682	−0.873411	+	0.486983i	$0.838097\pi$
$90$	−1.57136	−0.165636
$91$	14.1082	1.47894
$92$	−6.23506	−0.650050
$93$	0.193576	0.0200729
$94$	1.49532	0.154230
$95$	0	0
$96$	−0.688892	−0.0703098
$97$	−17.8988	−1.81734	−0.908672	−	0.417510i	$-0.862903\pi$
$97$	−17.8988	−1.81734	−0.908672	+	0.417510i	$0.862903\pi$
$98$	2.71900	0.274661
$99$	2.52543	0.253815
$100$	−4.61285	−0.461285
$101$	−3.38271	−0.336592	−0.168296	−	0.985737i	$-0.553826\pi$
$101$	−3.38271	−0.336592	−0.168296	+	0.985737i	$0.553826\pi$
$102$	−5.23014	−0.517861
$103$	0.638037	0.0628677	0.0314338	−	0.999506i	$-0.489993\pi$
$103$	0.638037	0.0628677	0.0314338	+	0.999506i	$0.489993\pi$
$104$	−4.52543	−0.443755
$105$	1.33630	0.130409
$106$	−1.37778	−0.133822
$107$	14.4128	1.39334	0.696670	−	0.717392i	$-0.254664\pi$
$107$	14.4128	1.39334	0.696670	+	0.717392i	$0.254664\pi$
$108$	3.80642	0.366273
$109$	1.57628	0.150980	0.0754902	−	0.997147i	$-0.475948\pi$
$109$	1.57628	0.150980	0.0754902	+	0.997147i	$0.475948\pi$
$110$	−0.622216	−0.0593259
$111$	1.95407	0.185472
$112$	−3.11753	−0.294579
$113$	15.5303	1.46097	0.730486	−	0.682927i	$-0.239294\pi$
$113$	15.5303	1.46097	0.730486	+	0.682927i	$0.239294\pi$
$114$	0	0
$115$	−3.87955	−0.361770
$116$	2.80642	0.260570
$117$	11.4286	1.05658
$118$	4.42864	0.407689
$119$	−23.6686	−2.16970
$120$	−0.428639	−0.0391293
$121$	1.00000	0.0909091
$122$	13.7096	1.24121
$123$	−1.52543	−0.137543
$124$	−0.280996	−0.0252342
$125$	−5.98126	−0.534981
$126$	7.87310	0.701392
$127$	7.09234	0.629344	0.314672	−	0.949201i	$-0.398106\pi$
$127$	7.09234	0.629344	0.314672	+	0.949201i	$0.398106\pi$
$128$	1.00000	0.0883883
$129$	−1.78568	−0.157220
$130$	−2.81579	−0.246961
$131$	12.6795	1.10782	0.553908	−	0.832578i	$-0.313136\pi$
$131$	12.6795	1.10782	0.553908	+	0.832578i	$0.313136\pi$
$132$	0.688892	0.0599604
$133$	0	0
$134$	4.16839	0.360094
$135$	2.36842	0.203841
$136$	7.59210	0.651018
$137$	7.47457	0.638596	0.319298	−	0.947654i	$-0.396553\pi$
$137$	7.47457	0.638596	0.319298	+	0.947654i	$0.396553\pi$
$138$	4.29529	0.365639
$139$	5.28592	0.448346	0.224173	−	0.974549i	$-0.428032\pi$
$139$	5.28592	0.448346	0.224173	+	0.974549i	$0.428032\pi$
$140$	−1.93978	−0.163941
$141$	−1.03011	−0.0867510
$142$	−12.0716	−1.01303
$143$	4.52543	0.378435
$144$	−2.52543	−0.210452
$145$	1.74620	0.145014
$146$	−10.9699	−0.907874
$147$	−1.87310	−0.154491
$148$	−2.83654	−0.233162
$149$	5.09679	0.417545	0.208773	−	0.977964i	$-0.433053\pi$
$149$	5.09679	0.417545	0.208773	+	0.977964i	$0.433053\pi$
$150$	3.17775	0.259463
$151$	−11.4128	−0.928762	−0.464381	−	0.885636i	$-0.653723\pi$
$151$	−11.4128	−0.928762	−0.464381	+	0.885636i	$0.653723\pi$
$152$	0	0
$153$	−19.1733	−1.55007
$154$	3.11753	0.251218
$155$	−0.174840	−0.0140435
$156$	3.11753	0.249602
$157$	11.7462	0.937449	0.468724	−	0.883344i	$-0.344714\pi$
$157$	11.7462	0.937449	0.468724	+	0.883344i	$0.344714\pi$
$158$	15.6795	1.24740
$159$	0.949145	0.0752721
$160$	0.622216	0.0491905
$161$	19.4380	1.53193
$162$	4.95407	0.389228
$163$	18.3368	1.43625	0.718123	−	0.695916i	$-0.245001\pi$
$163$	18.3368	1.43625	0.718123	+	0.695916i	$0.245001\pi$
$164$	2.21432	0.172909
$165$	0.428639	0.0333695
$166$	13.4494	1.04387
$167$	0.822245	0.0636272	0.0318136	−	0.999494i	$-0.489872\pi$
$167$	0.822245	0.0636272	0.0318136	+	0.999494i	$0.489872\pi$
$168$	2.14764	0.165694
$169$	7.47949	0.575346
$170$	4.72393	0.362309
$171$	0	0
$172$	2.59210	0.197646
$173$	−2.90321	−0.220727	−0.110364	−	0.993891i	$-0.535202\pi$
$173$	−2.90321	−0.220727	−0.110364	+	0.993891i	$0.535202\pi$
$174$	−1.93332	−0.146565
$175$	14.3807	1.08708
$176$	−1.00000	−0.0753778
$177$	−3.05086	−0.229316
$178$	−16.4795	−1.23519
$179$	18.5620	1.38739	0.693694	−	0.720270i	$-0.255982\pi$
$179$	18.5620	1.38739	0.693694	+	0.720270i	$0.255982\pi$
$180$	−1.57136	−0.117122
$181$	5.88739	0.437606	0.218803	−	0.975769i	$-0.429785\pi$
$181$	5.88739	0.437606	0.218803	+	0.975769i	$0.429785\pi$
$182$	14.1082	1.04577
$183$	−9.44446	−0.698155
$184$	−6.23506	−0.459655
$185$	−1.76494	−0.129761
$186$	0.193576	0.0141937
$187$	−7.59210	−0.555190
$188$	1.49532	0.109057
$189$	−11.8666	−0.863172
$190$	0	0
$191$	−3.55554	−0.257270	−0.128635	−	0.991692i	$-0.541060\pi$
$191$	−3.55554	−0.257270	−0.128635	+	0.991692i	$0.541060\pi$
$192$	−0.688892	−0.0497165
$193$	26.6113	1.91552	0.957762	−	0.287561i	$-0.0928445\pi$
$193$	26.6113	1.91552	0.957762	+	0.287561i	$0.0928445\pi$
$194$	−17.8988	−1.28506
$195$	1.93978	0.138910
$196$	2.71900	0.194215
$197$	−13.5303	−0.963998	−0.481999	−	0.876172i	$-0.660089\pi$
$197$	−13.5303	−0.963998	−0.481999	+	0.876172i	$0.660089\pi$
$198$	2.52543	0.179474
$199$	17.3477	1.22974	0.614872	−	0.788627i	$-0.289208\pi$
$199$	17.3477	1.22974	0.614872	+	0.788627i	$0.289208\pi$
$200$	−4.61285	−0.326178
$201$	−2.87157	−0.202545
$202$	−3.38271	−0.238006
$203$	−8.74912	−0.614068
$204$	−5.23014	−0.366183
$205$	1.37778	0.0962286
$206$	0.638037	0.0444541
$207$	15.7462	1.09444
$208$	−4.52543	−0.313782
$209$	0	0
$210$	1.33630	0.0922133
$211$	−0.428639	−0.0295088	−0.0147544	−	0.999891i	$-0.504697\pi$
$211$	−0.428639	−0.0295088	−0.0147544	+	0.999891i	$0.504697\pi$
$212$	−1.37778	−0.0946266
$213$	8.31603	0.569805
$214$	14.4128	0.985240
$215$	1.61285	0.109995
$216$	3.80642	0.258994
$217$	0.876015	0.0594678
$218$	1.57628	0.106759
$219$	7.55707	0.510659
$220$	−0.622216	−0.0419498
$221$	−34.3575	−2.31114
$222$	1.95407	0.131148
$223$	23.7447	1.59006	0.795030	−	0.606570i	$-0.207455\pi$
$223$	23.7447	1.59006	0.795030	+	0.606570i	$0.207455\pi$
$224$	−3.11753	−0.208299
$225$	11.6494	0.776628
$226$	15.5303	1.03306
$227$	−5.23014	−0.347137	−0.173568	−	0.984822i	$-0.555530\pi$
$227$	−5.23014	−0.347137	−0.173568	+	0.984822i	$0.555530\pi$
$228$	0	0
$229$	5.55062	0.366795	0.183398	−	0.983039i	$-0.441290\pi$
$229$	5.55062	0.366795	0.183398	+	0.983039i	$0.441290\pi$
$230$	−3.87955	−0.255810
$231$	−2.14764	−0.141305
$232$	2.80642	0.184251
$233$	5.82717	0.381750	0.190875	−	0.981614i	$-0.438867\pi$
$233$	5.82717	0.381750	0.190875	+	0.981614i	$0.438867\pi$
$234$	11.4286	0.747114
$235$	0.930409	0.0606932
$236$	4.42864	0.288280
$237$	−10.8015	−0.701633
$238$	−23.6686	−1.53421
$239$	14.1017	0.912164	0.456082	−	0.889938i	$-0.349252\pi$
$239$	14.1017	0.912164	0.456082	+	0.889938i	$0.349252\pi$
$240$	−0.428639	−0.0276686
$241$	−28.0415	−1.80631	−0.903155	−	0.429314i	$-0.858756\pi$
$241$	−28.0415	−1.80631	−0.903155	+	0.429314i	$0.858756\pi$
$242$	1.00000	0.0642824
$243$	−14.8321	−0.951479
$244$	13.7096	0.877669
$245$	1.69181	0.108086
$246$	−1.52543	−0.0972577
$247$	0	0
$248$	−0.280996	−0.0178433
$249$	−9.26517	−0.587157
$250$	−5.98126	−0.378288
$251$	15.3526	0.969047	0.484524	−	0.874778i	$-0.338993\pi$
$251$	15.3526	0.969047	0.484524	+	0.874778i	$0.338993\pi$
$252$	7.87310	0.495959
$253$	6.23506	0.391995
$254$	7.09234	0.445013
$255$	−3.25428	−0.203791
$256$	1.00000	0.0625000
$257$	−21.7748	−1.35827	−0.679137	−	0.734012i	$-0.737646\pi$
$257$	−21.7748	−1.35827	−0.679137	+	0.734012i	$0.737646\pi$
$258$	−1.78568	−0.111172
$259$	8.84299	0.549477
$260$	−2.81579	−0.174628
$261$	−7.08742	−0.438700
$262$	12.6795	0.783344
$263$	28.3684	1.74927	0.874636	−	0.484781i	$-0.161101\pi$
$263$	28.3684	1.74927	0.874636	+	0.484781i	$0.161101\pi$
$264$	0.688892	0.0423984
$265$	−0.857279	−0.0526622
$266$	0	0
$267$	11.3526	0.694768
$268$	4.16839	0.254625
$269$	−16.3763	−0.998478	−0.499239	−	0.866464i	$-0.666387\pi$
$269$	−16.3763	−0.998478	−0.499239	+	0.866464i	$0.666387\pi$
$270$	2.36842	0.144137
$271$	−17.6731	−1.07356	−0.536781	−	0.843721i	$-0.680360\pi$
$271$	−17.6731	−1.07356	−0.536781	+	0.843721i	$0.680360\pi$
$272$	7.59210	0.460339
$273$	−9.71900	−0.588221
$274$	7.47457	0.451555
$275$	4.61285	0.278165
$276$	4.29529	0.258546
$277$	30.8435	1.85320	0.926602	−	0.376043i	$-0.122716\pi$
$277$	30.8435	1.85320	0.926602	+	0.376043i	$0.122716\pi$
$278$	5.28592	0.317028
$279$	0.709636	0.0424848
$280$	−1.93978	−0.115924
$281$	−19.5734	−1.16765	−0.583825	−	0.811880i	$-0.698444\pi$
$281$	−19.5734	−1.16765	−0.583825	+	0.811880i	$0.698444\pi$
$282$	−1.03011	−0.0613422
$283$	−16.3368	−0.971120	−0.485560	−	0.874203i	$-0.661384\pi$
$283$	−16.3368	−0.971120	−0.485560	+	0.874203i	$0.661384\pi$
$284$	−12.0716	−0.716318
$285$	0	0
$286$	4.52543	0.267594
$287$	−6.90321	−0.407484
$288$	−2.52543	−0.148812
$289$	40.6400	2.39059
$290$	1.74620	0.102540
$291$	12.3303	0.722816
$292$	−10.9699	−0.641964
$293$	2.05086	0.119812	0.0599061	−	0.998204i	$-0.480920\pi$
$293$	2.05086	0.119812	0.0599061	+	0.998204i	$0.480920\pi$
$294$	−1.87310	−0.109241
$295$	2.75557	0.160435
$296$	−2.83654	−0.164870
$297$	−3.80642	−0.220871
$298$	5.09679	0.295249
$299$	28.2163	1.63179
$300$	3.17775	0.183468
$301$	−8.08097	−0.465779
$302$	−11.4128	−0.656734
$303$	2.33032	0.133873
$304$	0	0
$305$	8.53035	0.488446
$306$	−19.1733	−1.09607
$307$	−6.11753	−0.349146	−0.174573	−	0.984644i	$-0.555854\pi$
$307$	−6.11753	−0.349146	−0.174573	+	0.984644i	$0.555854\pi$
$308$	3.11753	0.177638
$309$	−0.439539	−0.0250045
$310$	−0.174840	−0.00993026
$311$	−29.5052	−1.67308	−0.836542	−	0.547903i	$-0.815426\pi$
$311$	−29.5052	−1.67308	−0.836542	+	0.547903i	$0.815426\pi$
$312$	3.11753	0.176495
$313$	11.4143	0.645177	0.322589	−	0.946539i	$-0.395447\pi$
$313$	11.4143	0.645177	0.322589	+	0.946539i	$0.395447\pi$
$314$	11.7462	0.662876
$315$	4.89877	0.276014
$316$	15.6795	0.882042
$317$	−18.3160	−1.02873	−0.514365	−	0.857571i	$-0.671972\pi$
$317$	−18.3160	−1.02873	−0.514365	+	0.857571i	$0.671972\pi$
$318$	0.949145	0.0532254
$319$	−2.80642	−0.157130
$320$	0.622216	0.0347829
$321$	−9.92888	−0.554176
$322$	19.4380	1.08324
$323$	0	0
$324$	4.95407	0.275226
$325$	20.8751	1.15794
$326$	18.3368	1.01558
$327$	−1.08589	−0.0600498
$328$	2.21432	0.122265
$329$	−4.66170	−0.257008
$330$	0.428639	0.0235958
$331$	2.85083	0.156696	0.0783478	−	0.996926i	$-0.475036\pi$
$331$	2.85083	0.156696	0.0783478	+	0.996926i	$0.475036\pi$
$332$	13.4494	0.738131
$333$	7.16346	0.392555
$334$	0.822245	0.0449913
$335$	2.59364	0.141705
$336$	2.14764	0.117164
$337$	−3.15257	−0.171731	−0.0858656	−	0.996307i	$-0.527366\pi$
$337$	−3.15257	−0.171731	−0.0858656	+	0.996307i	$0.527366\pi$
$338$	7.47949	0.406831
$339$	−10.6987	−0.581076
$340$	4.72393	0.256191
$341$	0.280996	0.0152168
$342$	0	0
$343$	13.3461	0.720624
$344$	2.59210	0.139757
$345$	2.67259	0.143888
$346$	−2.90321	−0.156078
$347$	−1.20003	−0.0644210	−0.0322105	−	0.999481i	$-0.510255\pi$
$347$	−1.20003	−0.0644210	−0.0322105	+	0.999481i	$0.510255\pi$
$348$	−1.93332	−0.103637
$349$	28.9496	1.54964	0.774819	−	0.632183i	$-0.217841\pi$
$349$	28.9496	1.54964	0.774819	+	0.632183i	$0.217841\pi$
$350$	14.3807	0.768681
$351$	−17.2257	−0.919440
$352$	−1.00000	−0.0533002
$353$	1.19358	0.0635276	0.0317638	−	0.999495i	$-0.489888\pi$
$353$	1.19358	0.0635276	0.0317638	+	0.999495i	$0.489888\pi$
$354$	−3.05086	−0.162151
$355$	−7.51114	−0.398650
$356$	−16.4795	−0.873411
$357$	16.3051	0.862959
$358$	18.5620	0.981032
$359$	−13.7748	−0.727005	−0.363503	−	0.931593i	$-0.618419\pi$
$359$	−13.7748	−0.727005	−0.363503	+	0.931593i	$0.618419\pi$
$360$	−1.57136	−0.0828180
$361$	0	0
$362$	5.88739	0.309434
$363$	−0.688892	−0.0361575
$364$	14.1082	0.739469
$365$	−6.82564	−0.357270
$366$	−9.44446	−0.493670
$367$	−2.73530	−0.142782	−0.0713908	−	0.997448i	$-0.522744\pi$
$367$	−2.73530	−0.142782	−0.0713908	+	0.997448i	$0.522744\pi$
$368$	−6.23506	−0.325025
$369$	−5.59210	−0.291113
$370$	−1.76494	−0.0917547
$371$	4.29529	0.223000
$372$	0.193576	0.0100365
$373$	21.1383	1.09450	0.547249	−	0.836970i	$-0.315675\pi$
$373$	21.1383	1.09450	0.547249	+	0.836970i	$0.315675\pi$
$374$	−7.59210	−0.392578
$375$	4.12045	0.212779
$376$	1.49532	0.0771150
$377$	−12.7003	−0.654097
$378$	−11.8666	−0.610354
$379$	−17.4859	−0.898193	−0.449096	−	0.893483i	$-0.648254\pi$
$379$	−17.4859	−0.898193	−0.449096	+	0.893483i	$0.648254\pi$
$380$	0	0
$381$	−4.88586	−0.250310
$382$	−3.55554	−0.181917
$383$	−2.23506	−0.114206	−0.0571032	−	0.998368i	$-0.518186\pi$
$383$	−2.23506	−0.114206	−0.0571032	+	0.998368i	$0.518186\pi$
$384$	−0.688892	−0.0351549
$385$	1.93978	0.0988602
$386$	26.6113	1.35448
$387$	−6.54617	−0.332761
$388$	−17.8988	−0.908672
$389$	17.6652	0.895663	0.447831	−	0.894118i	$-0.352196\pi$
$389$	17.6652	0.895663	0.447831	+	0.894118i	$0.352196\pi$
$390$	1.93978	0.0982244
$391$	−47.3372	−2.39395
$392$	2.71900	0.137330
$393$	−8.73483	−0.440614
$394$	−13.5303	−0.681649
$395$	9.75605	0.490880
$396$	2.52543	0.126908
$397$	7.88739	0.395857	0.197928	−	0.980216i	$-0.436579\pi$
$397$	7.88739	0.395857	0.197928	+	0.980216i	$0.436579\pi$
$398$	17.3477	0.869560
$399$	0	0
$400$	−4.61285	−0.230642
$401$	−10.8617	−0.542409	−0.271204	−	0.962522i	$-0.587422\pi$
$401$	−10.8617	−0.542409	−0.271204	+	0.962522i	$0.587422\pi$
$402$	−2.87157	−0.143221
$403$	1.27163	0.0633443
$404$	−3.38271	−0.168296
$405$	3.08250	0.153171
$406$	−8.74912	−0.434211
$407$	2.83654	0.140602
$408$	−5.23014	−0.258931
$409$	14.8494	0.734258	0.367129	−	0.930170i	$-0.380341\pi$
$409$	14.8494	0.734258	0.367129	+	0.930170i	$0.380341\pi$
$410$	1.37778	0.0680439
$411$	−5.14917	−0.253990
$412$	0.638037	0.0314338
$413$	−13.8064	−0.679370
$414$	15.7462	0.773884
$415$	8.36842	0.410789
$416$	−4.52543	−0.221877
$417$	−3.64143	−0.178321
$418$	0	0
$419$	14.6889	0.717599	0.358800	−	0.933415i	$-0.383186\pi$
$419$	14.6889	0.717599	0.358800	+	0.933415i	$0.383186\pi$
$420$	1.33630	0.0652046
$421$	−14.3763	−0.700656	−0.350328	−	0.936627i	$-0.613930\pi$
$421$	−14.3763	−0.700656	−0.350328	+	0.936627i	$0.613930\pi$
$422$	−0.428639	−0.0208658
$423$	−3.77631	−0.183611
$424$	−1.37778	−0.0669111
$425$	−35.0212	−1.69878
$426$	8.31603	0.402913
$427$	−42.7402	−2.06834
$428$	14.4128	0.696670
$429$	−3.11753	−0.150516
$430$	1.61285	0.0777784
$431$	−14.4035	−0.693790	−0.346895	−	0.937904i	$-0.612764\pi$
$431$	−14.4035	−0.693790	−0.346895	+	0.937904i	$0.612764\pi$
$432$	3.80642	0.183137
$433$	−22.3733	−1.07519	−0.537597	−	0.843202i	$-0.680668\pi$
$433$	−22.3733	−1.07519	−0.537597	+	0.843202i	$0.680668\pi$
$434$	0.876015	0.0420501
$435$	−1.20294	−0.0576768
$436$	1.57628	0.0754902
$437$	0	0
$438$	7.55707	0.361091
$439$	−14.0731	−0.671674	−0.335837	−	0.941920i	$-0.609019\pi$
$439$	−14.0731	−0.671674	−0.335837	+	0.941920i	$0.609019\pi$
$440$	−0.622216	−0.0296630
$441$	−6.86665	−0.326983
$442$	−34.3575	−1.63422
$443$	−16.6572	−0.791410	−0.395705	−	0.918378i	$-0.629500\pi$
$443$	−16.6572	−0.791410	−0.395705	+	0.918378i	$0.629500\pi$
$444$	1.95407	0.0927359
$445$	−10.2538	−0.486077
$446$	23.7447	1.12434
$447$	−3.51114	−0.166071
$448$	−3.11753	−0.147290
$449$	12.4143	0.585869	0.292935	−	0.956132i	$-0.405368\pi$
$449$	12.4143	0.585869	0.292935	+	0.956132i	$0.405368\pi$
$450$	11.6494	0.549159
$451$	−2.21432	−0.104268
$452$	15.5303	0.730486
$453$	7.86220	0.369398
$454$	−5.23014	−0.245463
$455$	8.77832	0.411534
$456$	0	0
$457$	11.5002	0.537958	0.268979	−	0.963146i	$-0.413314\pi$
$457$	11.5002	0.537958	0.268979	+	0.963146i	$0.413314\pi$
$458$	5.55062	0.259363
$459$	28.8988	1.34888
$460$	−3.87955	−0.180885
$461$	−25.6178	−1.19314	−0.596569	−	0.802562i	$-0.703470\pi$
$461$	−25.6178	−1.19314	−0.596569	+	0.802562i	$0.703470\pi$
$462$	−2.14764	−0.0999174
$463$	2.60639	0.121129	0.0605647	−	0.998164i	$-0.480710\pi$
$463$	2.60639	0.121129	0.0605647	+	0.998164i	$0.480710\pi$
$464$	2.80642	0.130285
$465$	0.120446	0.00558555
$466$	5.82717	0.269938
$467$	−16.4953	−0.763312	−0.381656	−	0.924304i	$-0.624646\pi$
$467$	−16.4953	−0.763312	−0.381656	+	0.924304i	$0.624646\pi$
$468$	11.4286	0.528289
$469$	−12.9951	−0.600057
$470$	0.930409	0.0429166
$471$	−8.09187	−0.372853
$472$	4.42864	0.203845
$473$	−2.59210	−0.119185
$474$	−10.8015	−0.496129
$475$	0	0
$476$	−23.6686	−1.08485
$477$	3.47949	0.159315
$478$	14.1017	0.644997
$479$	−11.2509	−0.514066	−0.257033	−	0.966403i	$-0.582745\pi$
$479$	−11.2509	−0.514066	−0.257033	+	0.966403i	$0.582745\pi$
$480$	−0.428639	−0.0195646
$481$	12.8365	0.585296
$482$	−28.0415	−1.27725
$483$	−13.3907	−0.609298
$484$	1.00000	0.0454545
$485$	−11.1369	−0.505700
$486$	−14.8321	−0.672797
$487$	−11.9382	−0.540974	−0.270487	−	0.962724i	$-0.587185\pi$
$487$	−11.9382	−0.540974	−0.270487	+	0.962724i	$0.587185\pi$
$488$	13.7096	0.620606
$489$	−12.6321	−0.571241
$490$	1.69181	0.0764280
$491$	−5.20294	−0.234806	−0.117403	−	0.993084i	$-0.537457\pi$
$491$	−5.20294	−0.234806	−0.117403	+	0.993084i	$0.537457\pi$
$492$	−1.52543	−0.0687716
$493$	21.3067	0.959604
$494$	0	0
$495$	1.57136	0.0706274
$496$	−0.280996	−0.0126171
$497$	37.6336	1.68810
$498$	−9.26517	−0.415182
$499$	2.50177	0.111995	0.0559973	−	0.998431i	$-0.482166\pi$
$499$	2.50177	0.111995	0.0559973	+	0.998431i	$0.482166\pi$
$500$	−5.98126	−0.267490
$501$	−0.566438	−0.0253066
$502$	15.3526	0.685220
$503$	41.5812	1.85401	0.927007	−	0.375044i	$-0.122372\pi$
$503$	41.5812	1.85401	0.927007	+	0.375044i	$0.122372\pi$
$504$	7.87310	0.350696
$505$	−2.10477	−0.0936612
$506$	6.23506	0.277182
$507$	−5.15257	−0.228833
$508$	7.09234	0.314672
$509$	−24.4415	−1.08335	−0.541676	−	0.840587i	$-0.682210\pi$
$509$	−24.4415	−1.08335	−0.541676	+	0.840587i	$0.682210\pi$
$510$	−3.25428	−0.144102
$511$	34.1990	1.51287
$512$	1.00000	0.0441942
$513$	0	0
$514$	−21.7748	−0.960444
$515$	0.396997	0.0174938
$516$	−1.78568	−0.0786102
$517$	−1.49532	−0.0657639
$518$	8.84299	0.388539
$519$	2.00000	0.0877903
$520$	−2.81579	−0.123481
$521$	24.5353	1.07491	0.537455	−	0.843293i	$-0.319386\pi$
$521$	24.5353	1.07491	0.537455	+	0.843293i	$0.319386\pi$
$522$	−7.08742	−0.310208
$523$	43.8321	1.91664	0.958322	−	0.285691i	$-0.0922232\pi$
$523$	43.8321	1.91664	0.958322	+	0.285691i	$0.0922232\pi$
$524$	12.6795	0.553908
$525$	−9.90675	−0.432366
$526$	28.3684	1.23692
$527$	−2.13335	−0.0929303
$528$	0.688892	0.0299802
$529$	15.8760	0.690262
$530$	−0.857279	−0.0372378
$531$	−11.1842	−0.485353
$532$	0	0
$533$	−10.0207	−0.434047
$534$	11.3526	0.491275
$535$	8.96788	0.387715
$536$	4.16839	0.180047
$537$	−12.7872	−0.551809
$538$	−16.3763	−0.706030
$539$	−2.71900	−0.117116
$540$	2.36842	0.101920
$541$	−30.8528	−1.32647	−0.663233	−	0.748413i	$-0.730816\pi$
$541$	−30.8528	−1.32647	−0.663233	+	0.748413i	$0.730816\pi$
$542$	−17.6731	−0.759123
$543$	−4.05578	−0.174050
$544$	7.59210	0.325509
$545$	0.980788	0.0420123
$546$	−9.71900	−0.415935
$547$	−37.2242	−1.59159	−0.795795	−	0.605566i	$-0.792947\pi$
$547$	−37.2242	−1.59159	−0.795795	+	0.605566i	$0.792947\pi$
$548$	7.47457	0.319298
$549$	−34.6227	−1.47766
$550$	4.61285	0.196692
$551$	0	0
$552$	4.29529	0.182820
$553$	−48.8814	−2.07865
$554$	30.8435	1.31041
$555$	1.21585	0.0516100
$556$	5.28592	0.224173
$557$	−26.6084	−1.12743	−0.563717	−	0.825968i	$-0.690629\pi$
$557$	−26.6084	−1.12743	−0.563717	+	0.825968i	$0.690629\pi$
$558$	0.709636	0.0300413
$559$	−11.7304	−0.496142
$560$	−1.93978	−0.0819705
$561$	5.23014	0.220817
$562$	−19.5734	−0.825653
$563$	−16.7239	−0.704829	−0.352415	−	0.935844i	$-0.614639\pi$
$563$	−16.7239	−0.704829	−0.352415	+	0.935844i	$0.614639\pi$
$564$	−1.03011	−0.0433755
$565$	9.66323	0.406535
$566$	−16.3368	−0.686686
$567$	−15.4445	−0.648606
$568$	−12.0716	−0.506513
$569$	−33.5210	−1.40527	−0.702636	−	0.711549i	$-0.747994\pi$
$569$	−33.5210	−1.40527	−0.702636	+	0.711549i	$0.747994\pi$
$570$	0	0
$571$	31.7116	1.32709	0.663545	−	0.748136i	$-0.269051\pi$
$571$	31.7116	1.32709	0.663545	+	0.748136i	$0.269051\pi$
$572$	4.52543	0.189218
$573$	2.44938	0.102324
$574$	−6.90321	−0.288134
$575$	28.7614	1.19943
$576$	−2.52543	−0.105226
$577$	9.86220	0.410569	0.205284	−	0.978702i	$-0.434188\pi$
$577$	9.86220	0.410569	0.205284	+	0.978702i	$0.434188\pi$
$578$	40.6400	1.69040
$579$	−18.3323	−0.761866
$580$	1.74620	0.0725070
$581$	−41.9289	−1.73950
$582$	12.3303	0.511108
$583$	1.37778	0.0570620
$584$	−10.9699	−0.453937
$585$	7.11108	0.294007
$586$	2.05086	0.0847200
$587$	46.9467	1.93770	0.968849	−	0.247652i	$-0.0796591\pi$
$587$	46.9467	1.93770	0.968849	+	0.247652i	$0.0796591\pi$
$588$	−1.87310	−0.0772454
$589$	0	0
$590$	2.75557	0.113445
$591$	9.32095	0.383413
$592$	−2.83654	−0.116581
$593$	12.0286	0.493955	0.246977	−	0.969021i	$-0.420563\pi$
$593$	12.0286	0.493955	0.246977	+	0.969021i	$0.420563\pi$
$594$	−3.80642	−0.156179
$595$	−14.7270	−0.603748
$596$	5.09679	0.208773
$597$	−11.9507	−0.489109
$598$	28.2163	1.15385
$599$	−17.0939	−0.698437	−0.349218	−	0.937041i	$-0.613553\pi$
$599$	−17.0939	−0.698437	−0.349218	+	0.937041i	$0.613553\pi$
$600$	3.17775	0.129731
$601$	40.2351	1.64122	0.820611	−	0.571487i	$-0.193633\pi$
$601$	40.2351	1.64122	0.820611	+	0.571487i	$0.193633\pi$
$602$	−8.08097	−0.329356
$603$	−10.5270	−0.428691
$604$	−11.4128	−0.464381
$605$	0.622216	0.0252967
$606$	2.33032	0.0946628
$607$	−27.7309	−1.12556	−0.562780	−	0.826606i	$-0.690268\pi$
$607$	−27.7309	−1.12556	−0.562780	+	0.826606i	$0.690268\pi$
$608$	0	0
$609$	6.02720	0.244234
$610$	8.53035	0.345384
$611$	−6.76694	−0.273761
$612$	−19.1733	−0.775035
$613$	−22.3319	−0.901975	−0.450987	−	0.892530i	$-0.648928\pi$
$613$	−22.3319	−0.901975	−0.450987	+	0.892530i	$0.648928\pi$
$614$	−6.11753	−0.246883
$615$	−0.949145	−0.0382732
$616$	3.11753	0.125609
$617$	36.3131	1.46191	0.730955	−	0.682425i	$-0.239075\pi$
$617$	36.3131	1.46191	0.730955	+	0.682425i	$0.239075\pi$
$618$	−0.439539	−0.0176808
$619$	0.714082	0.0287014	0.0143507	−	0.999897i	$-0.495432\pi$
$619$	0.714082	0.0287014	0.0143507	+	0.999897i	$0.495432\pi$
$620$	−0.174840	−0.00702175
$621$	−23.7333	−0.952384
$622$	−29.5052	−1.18305
$623$	51.3753	2.05831
$624$	3.11753	0.124801
$625$	19.3426	0.773704
$626$	11.4143	0.456209
$627$	0	0
$628$	11.7462	0.468724
$629$	−21.5353	−0.858668
$630$	4.89877	0.195172
$631$	28.6622	1.14102	0.570512	−	0.821290i	$-0.306745\pi$
$631$	28.6622	1.14102	0.570512	+	0.821290i	$0.306745\pi$
$632$	15.6795	0.623698
$633$	0.295286	0.0117366
$634$	−18.3160	−0.727422
$635$	4.41297	0.175123
$636$	0.949145	0.0376360
$637$	−12.3047	−0.487528
$638$	−2.80642	−0.111107
$639$	30.4859	1.20601
$640$	0.622216	0.0245952
$641$	30.2988	1.19673	0.598366	−	0.801223i	$-0.295817\pi$
$641$	30.2988	1.19673	0.598366	+	0.801223i	$0.295817\pi$
$642$	−9.92888	−0.391862
$643$	14.0252	0.553099	0.276550	−	0.961000i	$-0.410809\pi$
$643$	14.0252	0.553099	0.276550	+	0.961000i	$0.410809\pi$
$644$	19.4380	0.765965
$645$	−1.11108	−0.0437487
$646$	0	0
$647$	26.6336	1.04707	0.523537	−	0.852003i	$-0.324612\pi$
$647$	26.6336	1.04707	0.523537	+	0.852003i	$0.324612\pi$
$648$	4.95407	0.194614
$649$	−4.42864	−0.173839
$650$	20.8751	0.818789
$651$	−0.603480	−0.0236522
$652$	18.3368	0.718123
$653$	39.1131	1.53061	0.765307	−	0.643666i	$-0.222587\pi$
$653$	39.1131	1.53061	0.765307	+	0.643666i	$0.222587\pi$
$654$	−1.08589	−0.0424616
$655$	7.88940	0.308264
$656$	2.21432	0.0864547
$657$	27.7037	1.08082
$658$	−4.66170	−0.181732
$659$	14.4030	0.561060	0.280530	−	0.959845i	$-0.409490\pi$
$659$	14.4030	0.561060	0.280530	+	0.959845i	$0.409490\pi$
$660$	0.428639	0.0166848
$661$	6.28745	0.244553	0.122277	−	0.992496i	$-0.460980\pi$
$661$	6.28745	0.244553	0.122277	+	0.992496i	$0.460980\pi$
$662$	2.85083	0.110800
$663$	23.6686	0.919213
$664$	13.4494	0.521937
$665$	0	0
$666$	7.16346	0.277579
$667$	−17.4982	−0.677534
$668$	0.822245	0.0318136
$669$	−16.3575	−0.632418
$670$	2.59364	0.100201
$671$	−13.7096	−0.529255
$672$	2.14764	0.0828471
$673$	28.1037	1.08332	0.541659	−	0.840598i	$-0.317796\pi$
$673$	28.1037	1.08332	0.541659	+	0.840598i	$0.317796\pi$
$674$	−3.15257	−0.121432
$675$	−17.5585	−0.675825
$676$	7.47949	0.287673
$677$	−36.0049	−1.38378	−0.691891	−	0.722002i	$-0.743222\pi$
$677$	−36.0049	−1.38378	−0.691891	+	0.722002i	$0.743222\pi$
$678$	−10.6987	−0.410883
$679$	55.8000	2.14141
$680$	4.72393	0.181154
$681$	3.60300	0.138067
$682$	0.280996	0.0107599
$683$	4.32048	0.165318	0.0826592	−	0.996578i	$-0.473659\pi$
$683$	4.32048	0.165318	0.0826592	+	0.996578i	$0.473659\pi$
$684$	0	0
$685$	4.65080	0.177698
$686$	13.3461	0.509558
$687$	−3.82378	−0.145886
$688$	2.59210	0.0988230
$689$	6.23506	0.237537
$690$	2.67259	0.101744
$691$	3.99355	0.151922	0.0759608	−	0.997111i	$-0.475798\pi$
$691$	3.99355	0.151922	0.0759608	+	0.997111i	$0.475798\pi$
$692$	−2.90321	−0.110364
$693$	−7.87310	−0.299074
$694$	−1.20003	−0.0455525
$695$	3.28898	0.124758
$696$	−1.93332	−0.0732824
$697$	16.8113	0.636775
$698$	28.9496	1.09576
$699$	−4.01429	−0.151834
$700$	14.3807	0.543539
$701$	20.1111	0.759585	0.379792	−	0.925072i	$-0.375995\pi$
$701$	20.1111	0.759585	0.379792	+	0.925072i	$0.375995\pi$
$702$	−17.2257	−0.650142
$703$	0	0
$704$	−1.00000	−0.0376889
$705$	−0.640951	−0.0241396
$706$	1.19358	0.0449208
$707$	10.5457	0.396612
$708$	−3.05086	−0.114658
$709$	12.9590	0.486685	0.243343	−	0.969940i	$-0.421756\pi$
$709$	12.9590	0.486685	0.243343	+	0.969940i	$0.421756\pi$
$710$	−7.51114	−0.281888
$711$	−39.5975	−1.48502
$712$	−16.4795	−0.617595
$713$	1.75203	0.0656140
$714$	16.3051	0.610204
$715$	2.81579	0.105305
$716$	18.5620	0.693694
$717$	−9.71456	−0.362797
$718$	−13.7748	−0.514070
$719$	9.93825	0.370634	0.185317	−	0.982679i	$-0.440669\pi$
$719$	9.93825	0.370634	0.185317	+	0.982679i	$0.440669\pi$
$720$	−1.57136	−0.0585611
$721$	−1.98910	−0.0740780
$722$	0	0
$723$	19.3176	0.718428
$724$	5.88739	0.218803
$725$	−12.9456	−0.480788
$726$	−0.688892	−0.0255672
$727$	15.5225	0.575698	0.287849	−	0.957676i	$-0.407060\pi$
$727$	15.5225	0.575698	0.287849	+	0.957676i	$0.407060\pi$
$728$	14.1082	0.522883
$729$	−4.64449	−0.172018
$730$	−6.82564	−0.252628
$731$	19.6795	0.727873
$732$	−9.44446	−0.349077
$733$	−44.3225	−1.63709	−0.818544	−	0.574444i	$-0.805218\pi$
$733$	−44.3225	−1.63709	−0.818544	+	0.574444i	$0.805218\pi$
$734$	−2.73530	−0.100962
$735$	−1.16547	−0.0429891
$736$	−6.23506	−0.229827
$737$	−4.16839	−0.153545
$738$	−5.59210	−0.205848
$739$	−23.0765	−0.848884	−0.424442	−	0.905455i	$-0.639530\pi$
$739$	−23.0765	−0.848884	−0.424442	+	0.905455i	$0.639530\pi$
$740$	−1.76494	−0.0648804
$741$	0	0
$742$	4.29529	0.157685
$743$	−1.96190	−0.0719753	−0.0359876	−	0.999352i	$-0.511458\pi$
$743$	−1.96190	−0.0719753	−0.0359876	+	0.999352i	$0.511458\pi$
$744$	0.193576	0.00709685
$745$	3.17130	0.116187
$746$	21.1383	0.773927
$747$	−33.9654	−1.24273
$748$	−7.59210	−0.277595
$749$	−44.9324	−1.64179
$750$	4.12045	0.150457
$751$	16.7540	0.611364	0.305682	−	0.952134i	$-0.401116\pi$
$751$	16.7540	0.611364	0.305682	+	0.952134i	$0.401116\pi$
$752$	1.49532	0.0545286
$753$	−10.5763	−0.385421
$754$	−12.7003	−0.462516
$755$	−7.10123	−0.258440
$756$	−11.8666	−0.431586
$757$	16.2766	0.591581	0.295791	−	0.955253i	$-0.404417\pi$
$757$	16.2766	0.591581	0.295791	+	0.955253i	$0.404417\pi$
$758$	−17.4859	−0.635118
$759$	−4.29529	−0.155909
$760$	0	0
$761$	−4.53035	−0.164225	−0.0821125	−	0.996623i	$-0.526167\pi$
$761$	−4.53035	−0.164225	−0.0821125	+	0.996623i	$0.526167\pi$
$762$	−4.88586	−0.176996
$763$	−4.91411	−0.177903
$764$	−3.55554	−0.128635
$765$	−11.9299	−0.431328
$766$	−2.23506	−0.0807561
$767$	−20.0415	−0.723656
$768$	−0.688892	−0.0248583
$769$	21.1655	0.763246	0.381623	−	0.924318i	$-0.375365\pi$
$769$	21.1655	0.763246	0.381623	+	0.924318i	$0.375365\pi$
$770$	1.93978	0.0699047
$771$	15.0005	0.540229
$772$	26.6113	0.957762
$773$	27.8972	1.00339	0.501697	−	0.865043i	$-0.332709\pi$
$773$	27.8972	1.00339	0.501697	+	0.865043i	$0.332709\pi$
$774$	−6.54617	−0.235297
$775$	1.29619	0.0465606
$776$	−17.8988	−0.642528
$777$	−6.09187	−0.218544
$778$	17.6652	0.633329
$779$	0	0
$780$	1.93978	0.0694552
$781$	12.0716	0.431956
$782$	−47.3372	−1.69278
$783$	10.6824	0.381759
$784$	2.71900	0.0971073
$785$	7.30867	0.260858
$786$	−8.73483	−0.311561
$787$	26.7067	0.951992	0.475996	−	0.879447i	$-0.342088\pi$
$787$	26.7067	0.951992	0.475996	+	0.879447i	$0.342088\pi$
$788$	−13.5303	−0.481999
$789$	−19.5428	−0.695741
$790$	9.75605	0.347105
$791$	−48.4164	−1.72149
$792$	2.52543	0.0897372
$793$	−62.0420	−2.20317
$794$	7.88739	0.279913
$795$	0.590573	0.0209455
$796$	17.3477	0.614872
$797$	−4.21432	−0.149279	−0.0746394	−	0.997211i	$-0.523781\pi$
$797$	−4.21432	−0.149279	−0.0746394	+	0.997211i	$0.523781\pi$
$798$	0	0
$799$	11.3526	0.401626
$800$	−4.61285	−0.163089
$801$	41.6178	1.47049
$802$	−10.8617	−0.383541
$803$	10.9699	0.387119
$804$	−2.87157	−0.101272
$805$	12.0946	0.426280
$806$	1.27163	0.0447912
$807$	11.2815	0.397127
$808$	−3.38271	−0.119003
$809$	−26.8780	−0.944981	−0.472490	−	0.881336i	$-0.656645\pi$
$809$	−26.8780	−0.944981	−0.472490	+	0.881336i	$0.656645\pi$
$810$	3.08250	0.108308
$811$	36.4686	1.28059	0.640293	−	0.768131i	$-0.278813\pi$
$811$	36.4686	1.28059	0.640293	+	0.768131i	$0.278813\pi$
$812$	−8.74912	−0.307034
$813$	12.1748	0.426990
$814$	2.83654	0.0994205
$815$	11.4094	0.399655
$816$	−5.23014	−0.183092
$817$	0	0
$818$	14.8494	0.519199
$819$	−35.6291	−1.24498
$820$	1.37778	0.0481143
$821$	6.54464	0.228410	0.114205	−	0.993457i	$-0.463568\pi$
$821$	6.54464	0.228410	0.114205	+	0.993457i	$0.463568\pi$
$822$	−5.14917	−0.179598
$823$	−24.7210	−0.861720	−0.430860	−	0.902419i	$-0.641790\pi$
$823$	−24.7210	−0.861720	−0.430860	+	0.902419i	$0.641790\pi$
$824$	0.638037	0.0222271
$825$	−3.17775	−0.110635
$826$	−13.8064	−0.480387
$827$	−9.47796	−0.329581	−0.164791	−	0.986329i	$-0.552695\pi$
$827$	−9.47796	−0.329581	−0.164791	+	0.986329i	$0.552695\pi$
$828$	15.7462	0.547218
$829$	8.11261	0.281763	0.140881	−	0.990026i	$-0.455006\pi$
$829$	8.11261	0.281763	0.140881	+	0.990026i	$0.455006\pi$
$830$	8.36842	0.290472
$831$	−21.2478	−0.737079
$832$	−4.52543	−0.156891
$833$	20.6430	0.715236
$834$	−3.64143	−0.126092
$835$	0.511614	0.0177051
$836$	0	0
$837$	−1.06959	−0.0369705
$838$	14.6889	0.507419
$839$	−33.0622	−1.14143	−0.570717	−	0.821146i	$-0.693335\pi$
$839$	−33.0622	−1.14143	−0.570717	+	0.821146i	$0.693335\pi$
$840$	1.33630	0.0461066
$841$	−21.1240	−0.728413
$842$	−14.3763	−0.495438
$843$	13.4839	0.464412
$844$	−0.428639	−0.0147544
$845$	4.65386	0.160098
$846$	−3.77631	−0.129832
$847$	−3.11753	−0.107120
$848$	−1.37778	−0.0473133
$849$	11.2543	0.386246
$850$	−35.0212	−1.20122
$851$	17.6860	0.606268
$852$	8.31603	0.284902
$853$	−30.5575	−1.04627	−0.523135	−	0.852250i	$-0.675238\pi$
$853$	−30.5575	−1.04627	−0.523135	+	0.852250i	$0.675238\pi$
$854$	−42.7402	−1.46254
$855$	0	0
$856$	14.4128	0.492620
$857$	−43.0944	−1.47207	−0.736037	−	0.676941i	$-0.763305\pi$
$857$	−43.0944	−1.47207	−0.736037	+	0.676941i	$0.763305\pi$
$858$	−3.11753	−0.106431
$859$	28.6222	0.976577	0.488289	−	0.872682i	$-0.337621\pi$
$859$	28.6222	0.976577	0.488289	+	0.872682i	$0.337621\pi$
$860$	1.61285	0.0549977
$861$	4.75557	0.162069
$862$	−14.4035	−0.490583
$863$	−30.0069	−1.02145	−0.510724	−	0.859745i	$-0.670623\pi$
$863$	−30.0069	−1.02145	−0.510724	+	0.859745i	$0.670623\pi$
$864$	3.80642	0.129497
$865$	−1.80642	−0.0614203
$866$	−22.3733	−0.760277
$867$	−27.9966	−0.950815
$868$	0.876015	0.0297339
$869$	−15.6795	−0.531891
$870$	−1.20294	−0.0407836
$871$	−18.8637	−0.639173
$872$	1.57628	0.0533797
$873$	45.2020	1.52986
$874$	0	0
$875$	18.6468	0.630376
$876$	7.55707	0.255330
$877$	−31.7146	−1.07092	−0.535462	−	0.844559i	$-0.679863\pi$
$877$	−31.7146	−1.07092	−0.535462	+	0.844559i	$0.679863\pi$
$878$	−14.0731	−0.474945
$879$	−1.41282	−0.0476532
$880$	−0.622216	−0.0209749
$881$	47.5986	1.60364	0.801818	−	0.597568i	$-0.203866\pi$
$881$	47.5986	1.60364	0.801818	+	0.597568i	$0.203866\pi$
$882$	−6.86665	−0.231212
$883$	−35.5274	−1.19559	−0.597797	−	0.801648i	$-0.703957\pi$
$883$	−35.5274	−1.19559	−0.597797	+	0.801648i	$0.703957\pi$
$884$	−34.3575	−1.15557
$885$	−1.89829	−0.0638103
$886$	−16.6572	−0.559611
$887$	12.2286	0.410597	0.205298	−	0.978699i	$-0.434184\pi$
$887$	12.2286	0.410597	0.205298	+	0.978699i	$0.434184\pi$
$888$	1.95407	0.0655742
$889$	−22.1106	−0.741566
$890$	−10.2538	−0.343708
$891$	−4.95407	−0.165967
$892$	23.7447	0.795030
$893$	0	0
$894$	−3.51114	−0.117430
$895$	11.5496	0.386059
$896$	−3.11753	−0.104149
$897$	−19.4380	−0.649016
$898$	12.4143	0.414272
$899$	−0.788595	−0.0263011
$900$	11.6494	0.388314
$901$	−10.4603	−0.348483
$902$	−2.21432	−0.0737288
$903$	5.56691	0.185255
$904$	15.5303	0.516532
$905$	3.66323	0.121770
$906$	7.86220	0.261204
$907$	57.5910	1.91228	0.956140	−	0.292911i	$-0.0946240\pi$
$907$	57.5910	1.91228	0.956140	+	0.292911i	$0.0946240\pi$
$908$	−5.23014	−0.173568
$909$	8.54278	0.283346
$910$	8.77832	0.290998
$911$	−50.3970	−1.66973	−0.834863	−	0.550457i	$-0.814453\pi$
$911$	−50.3970	−1.66973	−0.834863	+	0.550457i	$0.814453\pi$
$912$	0	0
$913$	−13.4494	−0.445110
$914$	11.5002	0.380394
$915$	−5.87649	−0.194271
$916$	5.55062	0.183398
$917$	−39.5288	−1.30536
$918$	28.8988	0.953801
$919$	−0.965443	−0.0318470	−0.0159235	−	0.999873i	$-0.505069\pi$
$919$	−0.965443	−0.0318470	−0.0159235	+	0.999873i	$0.505069\pi$
$920$	−3.87955	−0.127905
$921$	4.21432	0.138867
$922$	−25.6178	−0.843676
$923$	54.6291	1.79814
$924$	−2.14764	−0.0706523
$925$	13.0845	0.430216
$926$	2.60639	0.0856514
$927$	−1.61132	−0.0529226
$928$	2.80642	0.0921254
$929$	−31.5433	−1.03490	−0.517450	−	0.855713i	$-0.673119\pi$
$929$	−31.5433	−1.03490	−0.517450	+	0.855713i	$0.673119\pi$
$930$	0.120446	0.00394958
$931$	0	0
$932$	5.82717	0.190875
$933$	20.3259	0.665439
$934$	−16.4953	−0.539743
$935$	−4.72393	−0.154489
$936$	11.4286	0.373557
$937$	24.8256	0.811018	0.405509	−	0.914091i	$-0.367094\pi$
$937$	24.8256	0.811018	0.405509	+	0.914091i	$0.367094\pi$
$938$	−12.9951	−0.424304
$939$	−7.86326	−0.256608
$940$	0.930409	0.0303466
$941$	−4.26809	−0.139136	−0.0695679	−	0.997577i	$-0.522162\pi$
$941$	−4.26809	−0.139136	−0.0695679	+	0.997577i	$0.522162\pi$
$942$	−8.09187	−0.263647
$943$	−13.8064	−0.449599
$944$	4.42864	0.144140
$945$	−7.38361	−0.240189
$946$	−2.59210	−0.0842766
$947$	−7.75605	−0.252038	−0.126019	−	0.992028i	$-0.540220\pi$
$947$	−7.75605	−0.252038	−0.126019	+	0.992028i	$0.540220\pi$
$948$	−10.8015	−0.350816
$949$	49.6434	1.61149
$950$	0	0
$951$	12.6178	0.409159
$952$	−23.6686	−0.767105
$953$	32.9719	1.06806	0.534032	−	0.845464i	$-0.320676\pi$
$953$	32.9719	1.06806	0.534032	+	0.845464i	$0.320676\pi$
$954$	3.47949	0.112653
$955$	−2.21231	−0.0715887
$956$	14.1017	0.456082
$957$	1.93332	0.0624955
$958$	−11.2509	−0.363500
$959$	−23.3022	−0.752468
$960$	−0.428639	−0.0138343
$961$	−30.9210	−0.997453
$962$	12.8365	0.413867
$963$	−36.3985	−1.17293
$964$	−28.0415	−0.903155
$965$	16.5580	0.533020
$966$	−13.3907	−0.430838
$967$	−44.3051	−1.42476	−0.712378	−	0.701795i	$-0.752382\pi$
$967$	−44.3051	−1.42476	−0.712378	+	0.701795i	$0.752382\pi$
$968$	1.00000	0.0321412
$969$	0	0
$970$	−11.1369	−0.357584
$971$	20.4449	0.656109	0.328055	−	0.944659i	$-0.393607\pi$
$971$	20.4449	0.656109	0.328055	+	0.944659i	$0.393607\pi$
$972$	−14.8321	−0.475739
$973$	−16.4790	−0.528293
$974$	−11.9382	−0.382526
$975$	−14.3807	−0.460551
$976$	13.7096	0.438835
$977$	−29.2538	−0.935912	−0.467956	−	0.883752i	$-0.655009\pi$
$977$	−29.2538	−0.935912	−0.467956	+	0.883752i	$0.655009\pi$
$978$	−12.6321	−0.403929
$979$	16.4795	0.526687
$980$	1.69181	0.0540428
$981$	−3.98079	−0.127097
$982$	−5.20294	−0.166033
$983$	12.7571	0.406888	0.203444	−	0.979087i	$-0.434786\pi$
$983$	12.7571	0.406888	0.203444	+	0.979087i	$0.434786\pi$
$984$	−1.52543	−0.0486289
$985$	−8.41880	−0.268245
$986$	21.3067	0.678542
$987$	3.21141	0.102220
$988$	0	0
$989$	−16.1619	−0.513920
$990$	1.57136	0.0499411
$991$	26.5560	0.843580	0.421790	−	0.906694i	$-0.361402\pi$
$991$	26.5560	0.843580	0.421790	+	0.906694i	$0.361402\pi$
$992$	−0.280996	−0.00892164
$993$	−1.96391	−0.0623228
$994$	37.6336	1.19367
$995$	10.7940	0.342193
$996$	−9.26517	−0.293578
$997$	−12.2222	−0.387080	−0.193540	−	0.981092i	$-0.561997\pi$
$997$	−12.2222	−0.387080	−0.193540	+	0.981092i	$0.561997\pi$
$998$	2.50177	0.0791921
$999$	−10.7971	−0.341604

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7942.2.a.bh.1.2		3
19.7	even	3		418.2.e.h.353.2	yes	6
19.11	even	3		418.2.e.h.45.2	✓	6
19.18	odd	2		7942.2.a.be.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.e.h.45.2	✓	6	19.11	even	3
418.2.e.h.353.2	yes	6	19.7	even	3
7942.2.a.be.1.2		3	19.18	odd	2
7942.2.a.bh.1.2		3	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:	\( N \)	\(=\)	\( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7942.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.688892 q^{3} +1.00000 q^{4} +0.622216 q^{5} -0.688892 q^{6} -3.11753 q^{7} +1.00000 q^{8} -2.52543 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.688892 q^{3} +1.00000 q^{4} +0.622216 q^{5} -0.688892 q^{6} -3.11753 q^{7} +1.00000 q^{8} -2.52543 q^{9} +0.622216 q^{10} -1.00000 q^{11} -0.688892 q^{12} -4.52543 q^{13} -3.11753 q^{14} -0.428639 q^{15} +1.00000 q^{16} +7.59210 q^{17} -2.52543 q^{18} +0.622216 q^{20} +2.14764 q^{21} -1.00000 q^{22} -6.23506 q^{23} -0.688892 q^{24} -4.61285 q^{25} -4.52543 q^{26} +3.80642 q^{27} -3.11753 q^{28} +2.80642 q^{29} -0.428639 q^{30} -0.280996 q^{31} +1.00000 q^{32} +0.688892 q^{33} +7.59210 q^{34} -1.93978 q^{35} -2.52543 q^{36} -2.83654 q^{37} +3.11753 q^{39} +0.622216 q^{40} +2.21432 q^{41} +2.14764 q^{42} +2.59210 q^{43} -1.00000 q^{44} -1.57136 q^{45} -6.23506 q^{46} +1.49532 q^{47} -0.688892 q^{48} +2.71900 q^{49} -4.61285 q^{50} -5.23014 q^{51} -4.52543 q^{52} -1.37778 q^{53} +3.80642 q^{54} -0.622216 q^{55} -3.11753 q^{56} +2.80642 q^{58} +4.42864 q^{59} -0.428639 q^{60} +13.7096 q^{61} -0.280996 q^{62} +7.87310 q^{63} +1.00000 q^{64} -2.81579 q^{65} +0.688892 q^{66} +4.16839 q^{67} +7.59210 q^{68} +4.29529 q^{69} -1.93978 q^{70} -12.0716 q^{71} -2.52543 q^{72} -10.9699 q^{73} -2.83654 q^{74} +3.17775 q^{75} +3.11753 q^{77} +3.11753 q^{78} +15.6795 q^{79} +0.622216 q^{80} +4.95407 q^{81} +2.21432 q^{82} +13.4494 q^{83} +2.14764 q^{84} +4.72393 q^{85} +2.59210 q^{86} -1.93332 q^{87} -1.00000 q^{88} -16.4795 q^{89} -1.57136 q^{90} +14.1082 q^{91} -6.23506 q^{92} +0.193576 q^{93} +1.49532 q^{94} -0.688892 q^{96} -17.8988 q^{97} +2.71900 q^{98} +2.52543 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 2 q^{3} + 3 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{7} + 3 q^{8} - q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 2 * q^3 + 3 * q^4 + 2 * q^5 - 2 * q^6 + 4 * q^7 + 3 * q^8 - q^9	\( 3 q + 3 q^{2} - 2 q^{3} + 3 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{7} + 3 q^{8} - q^{9} + 2 q^{10} - 3 q^{11} - 2 q^{12} - 7 q^{13} + 4 q^{14} + 12 q^{15} + 3 q^{16} + 16 q^{17} - q^{18} + 2 q^{20} - 3 q^{22} + 8 q^{23} - 2 q^{24} + 13 q^{25} - 7 q^{26} - 2 q^{27} + 4 q^{28} - 5 q^{29} + 12 q^{30} + 6 q^{31} + 3 q^{32} + 2 q^{33} + 16 q^{34} + 8 q^{35} - q^{36} - 2 q^{37} - 4 q^{39} + 2 q^{40} + q^{43} - 3 q^{44} - 18 q^{45} + 8 q^{46} - 9 q^{47} - 2 q^{48} + 15 q^{49} + 13 q^{50} - 22 q^{51} - 7 q^{52} - 4 q^{53} - 2 q^{54} - 2 q^{55} + 4 q^{56} - 5 q^{58} + 12 q^{60} + 21 q^{61} + 6 q^{62} + 10 q^{63} + 3 q^{64} - 22 q^{65} + 2 q^{66} - 14 q^{67} + 16 q^{68} + 8 q^{70} - 3 q^{71} - q^{72} - 26 q^{73} - 2 q^{74} + 10 q^{75} - 4 q^{77} - 4 q^{78} + 20 q^{79} + 2 q^{80} - 5 q^{81} + 7 q^{83} - 12 q^{85} + q^{86} - 6 q^{87} - 3 q^{88} - 23 q^{89} - 18 q^{90} + 2 q^{91} + 8 q^{92} + 14 q^{93} - 9 q^{94} - 2 q^{96} + 13 q^{97} + 15 q^{98} + q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 2 * q^3 + 3 * q^4 + 2 * q^5 - 2 * q^6 + 4 * q^7 + 3 * q^8 - q^9 + 2 * q^10 - 3 * q^11 - 2 * q^12 - 7 * q^13 + 4 * q^14 + 12 * q^15 + 3 * q^16 + 16 * q^17 - q^18 + 2 * q^20 - 3 * q^22 + 8 * q^23 - 2 * q^24 + 13 * q^25 - 7 * q^26 - 2 * q^27 + 4 * q^28 - 5 * q^29 + 12 * q^30 + 6 * q^31 + 3 * q^32 + 2 * q^33 + 16 * q^34 + 8 * q^35 - q^36 - 2 * q^37 - 4 * q^39 + 2 * q^40 + q^43 - 3 * q^44 - 18 * q^45 + 8 * q^46 - 9 * q^47 - 2 * q^48 + 15 * q^49 + 13 * q^50 - 22 * q^51 - 7 * q^52 - 4 * q^53 - 2 * q^54 - 2 * q^55 + 4 * q^56 - 5 * q^58 + 12 * q^60 + 21 * q^61 + 6 * q^62 + 10 * q^63 + 3 * q^64 - 22 * q^65 + 2 * q^66 - 14 * q^67 + 16 * q^68 + 8 * q^70 - 3 * q^71 - q^72 - 26 * q^73 - 2 * q^74 + 10 * q^75 - 4 * q^77 - 4 * q^78 + 20 * q^79 + 2 * q^80 - 5 * q^81 + 7 * q^83 - 12 * q^85 + q^86 - 6 * q^87 - 3 * q^88 - 23 * q^89 - 18 * q^90 + 2 * q^91 + 8 * q^92 + 14 * q^93 - 9 * q^94 - 2 * q^96 + 13 * q^97 + 15 * q^98 + q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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