LMFDB - Embedded newform 145.2.a.d.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [145,2,Mod(1,145)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("145.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(145, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 145 = 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	145.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$1.15783082931$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.311108$ of defining polynomial
Character	$\chi$	$=$	145.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.21432 q^{2} -2.90321 q^{3} -0.525428 q^{4} -1.00000 q^{5} +3.52543 q^{6} +1.52543 q^{7} +3.06668 q^{8} +5.42864 q^{9} +1.21432 q^{10} +4.90321 q^{11} +1.52543 q^{12} -6.42864 q^{13} -1.85236 q^{14} +2.90321 q^{15} -2.67307 q^{16} +2.14764 q^{17} -6.59210 q^{18} +2.28100 q^{19} +0.525428 q^{20} -4.42864 q^{21} -5.95407 q^{22} +6.90321 q^{23} -8.90321 q^{24} +1.00000 q^{25} +7.80642 q^{26} -7.05086 q^{27} -0.801502 q^{28} +1.00000 q^{29} -3.52543 q^{30} +1.71900 q^{31} -2.88739 q^{32} -14.2351 q^{33} -2.60793 q^{34} -1.52543 q^{35} -2.85236 q^{36} +7.95407 q^{37} -2.76986 q^{38} +18.6637 q^{39} -3.06668 q^{40} -3.37778 q^{41} +5.37778 q^{42} -1.09679 q^{43} -2.57628 q^{44} -5.42864 q^{45} -8.38271 q^{46} +12.7096 q^{47} +7.76049 q^{48} -4.67307 q^{49} -1.21432 q^{50} -6.23506 q^{51} +3.37778 q^{52} +3.37778 q^{53} +8.56199 q^{54} -4.90321 q^{55} +4.67799 q^{56} -6.62222 q^{57} -1.21432 q^{58} -3.18421 q^{59} -1.52543 q^{60} -2.42864 q^{61} -2.08742 q^{62} +8.28100 q^{63} +8.85236 q^{64} +6.42864 q^{65} +17.2859 q^{66} -1.09679 q^{67} -1.12843 q^{68} -20.0415 q^{69} +1.85236 q^{70} +3.57136 q^{71} +16.6479 q^{72} +14.1891 q^{73} -9.65878 q^{74} -2.90321 q^{75} -1.19850 q^{76} +7.47949 q^{77} -22.6637 q^{78} +0.341219 q^{79} +2.67307 q^{80} +4.18421 q^{81} +4.10171 q^{82} -7.33185 q^{83} +2.32693 q^{84} -2.14764 q^{85} +1.33185 q^{86} -2.90321 q^{87} +15.0366 q^{88} +2.94914 q^{89} +6.59210 q^{90} -9.80642 q^{91} -3.62714 q^{92} -4.99063 q^{93} -15.4336 q^{94} -2.28100 q^{95} +8.38271 q^{96} -18.5763 q^{97} +5.67460 q^{98} +26.6178 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 2 q^{3} + 5 q^{4} - 3 q^{5} + 4 q^{6} - 2 q^{7} + 9 q^{8} + 3 q^{9} - 3 q^{10} + 8 q^{11} - 2 q^{12} - 6 q^{13} - 12 q^{14} + 2 q^{15} + 5 q^{16} - 13 q^{18} - 5 q^{20} + 2 q^{22} + 14 q^{23}+ \cdots + 20 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 - 2 * q^3 + 5 * q^4 - 3 * q^5 + 4 * q^6 - 2 * q^7 + 9 * q^8 + 3 * q^9 - 3 * q^10 + 8 * q^11 - 2 * q^12 - 6 * q^13 - 12 * q^14 + 2 * q^15 + 5 * q^16 - 13 * q^18 - 5 * q^20 + 2 * q^22 + 14 * q^23 - 20 * q^24 + 3 * q^25 + 10 * q^26 - 8 * q^27 - 22 * q^28 + 3 * q^29 - 4 * q^30 + 12 * q^31 + 11 * q^32 - 16 * q^33 - 14 * q^34 + 2 * q^35 - 15 * q^36 + 4 * q^37 - 2 * q^38 + 16 * q^39 - 9 * q^40 - 10 * q^41 + 16 * q^42 - 10 * q^43 + 12 * q^44 - 3 * q^45 + 8 * q^46 + 18 * q^47 - 10 * q^48 - q^49 + 3 * q^50 + 8 * q^51 + 10 * q^52 + 10 * q^53 + 12 * q^54 - 8 * q^55 - 32 * q^56 - 20 * q^57 + 3 * q^58 + 4 * q^59 + 2 * q^60 + 6 * q^61 + 14 * q^62 + 18 * q^63 + 33 * q^64 + 6 * q^65 + 12 * q^66 - 10 * q^67 - 36 * q^68 - 20 * q^69 + 12 * q^70 + 24 * q^71 - 3 * q^72 - 4 * q^73 - 22 * q^74 - 2 * q^75 + 16 * q^76 - 4 * q^77 - 28 * q^78 + 8 * q^79 - 5 * q^80 - q^81 - 14 * q^82 - 2 * q^83 + 20 * q^84 - 16 * q^86 - 2 * q^87 + 38 * q^88 + 22 * q^89 + 13 * q^90 - 16 * q^91 + 22 * q^92 + 12 * q^93 - 8 * q^96 - 36 * q^97 + 23 * q^98 + 20 * q^99

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 $

$2$	−1.21432	−0.858654	−0.429327	−	0.903149i	$-0.641249\pi$
$2$	−1.21432	−0.858654	−0.429327	+	0.903149i	$0.641249\pi$
$3$	−2.90321	−1.67617	−0.838085	−	0.545540i	$-0.816325\pi$
$3$	−2.90321	−1.67617	−0.838085	+	0.545540i	$0.816325\pi$
$4$	−0.525428	−0.262714
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.52543	1.43925
$7$	1.52543	0.576557	0.288279	−	0.957547i	$-0.406917\pi$
$7$	1.52543	0.576557	0.288279	+	0.957547i	$0.406917\pi$
$8$	3.06668	1.08423
$9$	5.42864	1.80955
$10$	1.21432	0.384002
$11$	4.90321	1.47837	0.739187	−	0.673500i	$-0.235210\pi$
$11$	4.90321	1.47837	0.739187	+	0.673500i	$0.235210\pi$
$12$	1.52543	0.440353
$13$	−6.42864	−1.78298	−0.891492	−	0.453037i	$-0.850341\pi$
$13$	−6.42864	−1.78298	−0.891492	+	0.453037i	$0.850341\pi$
$14$	−1.85236	−0.495063
$15$	2.90321	0.749606
$16$	−2.67307	−0.668268
$17$	2.14764	0.520880	0.260440	−	0.965490i	$-0.416132\pi$
$17$	2.14764	0.520880	0.260440	+	0.965490i	$0.416132\pi$
$18$	−6.59210	−1.55377
$19$	2.28100	0.523296	0.261648	−	0.965163i	$-0.415734\pi$
$19$	2.28100	0.523296	0.261648	+	0.965163i	$0.415734\pi$
$20$	0.525428	0.117489
$21$	−4.42864	−0.966408
$22$	−5.95407	−1.26941
$23$	6.90321	1.43942	0.719710	−	0.694275i	$-0.244275\pi$
$23$	6.90321	1.43942	0.719710	+	0.694275i	$0.244275\pi$
$24$	−8.90321	−1.81736
$25$	1.00000	0.200000
$26$	7.80642	1.53097
$27$	−7.05086	−1.35694
$28$	−0.801502	−0.151470
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−3.52543	−0.643652
$31$	1.71900	0.308742	0.154371	−	0.988013i	$-0.450665\pi$
$31$	1.71900	0.308742	0.154371	+	0.988013i	$0.450665\pi$
$32$	−2.88739	−0.510423
$33$	−14.2351	−2.47801
$34$	−2.60793	−0.447256
$35$	−1.52543	−0.257844
$36$	−2.85236	−0.475393
$37$	7.95407	1.30764	0.653820	−	0.756650i	$-0.273165\pi$
$37$	7.95407	1.30764	0.653820	+	0.756650i	$0.273165\pi$
$38$	−2.76986	−0.449330
$39$	18.6637	2.98858
$40$	−3.06668	−0.484884
$41$	−3.37778	−0.527521	−0.263761	−	0.964588i	$-0.584963\pi$
$41$	−3.37778	−0.527521	−0.263761	+	0.964588i	$0.584963\pi$
$42$	5.37778	0.829810
$43$	−1.09679	−0.167259	−0.0836293	−	0.996497i	$-0.526651\pi$
$43$	−1.09679	−0.167259	−0.0836293	+	0.996497i	$0.526651\pi$
$44$	−2.57628	−0.388389
$45$	−5.42864	−0.809254
$46$	−8.38271	−1.23596
$47$	12.7096	1.85389	0.926945	−	0.375196i	$-0.122425\pi$
$47$	12.7096	1.85389	0.926945	+	0.375196i	$0.122425\pi$
$48$	7.76049	1.12013
$49$	−4.67307	−0.667582
$50$	−1.21432	−0.171731
$51$	−6.23506	−0.873084
$52$	3.37778	0.468414
$53$	3.37778	0.463974	0.231987	−	0.972719i	$-0.425477\pi$
$53$	3.37778	0.463974	0.231987	+	0.972719i	$0.425477\pi$
$54$	8.56199	1.16514
$55$	−4.90321	−0.661149
$56$	4.67799	0.625123
$57$	−6.62222	−0.877134
$58$	−1.21432	−0.159448
$59$	−3.18421	−0.414549	−0.207274	−	0.978283i	$-0.566459\pi$
$59$	−3.18421	−0.414549	−0.207274	+	0.978283i	$0.566459\pi$
$60$	−1.52543	−0.196932
$61$	−2.42864	−0.310955	−0.155478	−	0.987839i	$-0.549692\pi$
$61$	−2.42864	−0.310955	−0.155478	+	0.987839i	$0.549692\pi$
$62$	−2.08742	−0.265103
$63$	8.28100	1.04331
$64$	8.85236	1.10654
$65$	6.42864	0.797375
$66$	17.2859	2.12775
$67$	−1.09679	−0.133994	−0.0669970	−	0.997753i	$-0.521342\pi$
$67$	−1.09679	−0.133994	−0.0669970	+	0.997753i	$0.521342\pi$
$68$	−1.12843	−0.136842
$69$	−20.0415	−2.41271
$70$	1.85236	0.221399
$71$	3.57136	0.423843	0.211921	−	0.977287i	$-0.432028\pi$
$71$	3.57136	0.423843	0.211921	+	0.977287i	$0.432028\pi$
$72$	16.6479	1.96197
$73$	14.1891	1.66071	0.830356	−	0.557233i	$-0.188137\pi$
$73$	14.1891	1.66071	0.830356	+	0.557233i	$0.188137\pi$
$74$	−9.65878	−1.12281
$75$	−2.90321	−0.335234
$76$	−1.19850	−0.137477
$77$	7.47949	0.852368
$78$	−22.6637	−2.56616
$79$	0.341219	0.0383902	0.0191951	−	0.999816i	$-0.493890\pi$
$79$	0.341219	0.0383902	0.0191951	+	0.999816i	$0.493890\pi$
$80$	2.67307	0.298858
$81$	4.18421	0.464912
$82$	4.10171	0.452958
$83$	−7.33185	−0.804775	−0.402388	−	0.915469i	$-0.631820\pi$
$83$	−7.33185	−0.804775	−0.402388	+	0.915469i	$0.631820\pi$
$84$	2.32693	0.253889
$85$	−2.14764	−0.232945
$86$	1.33185	0.143617
$87$	−2.90321	−0.311257
$88$	15.0366	1.60290
$89$	2.94914	0.312609	0.156304	−	0.987709i	$-0.450042\pi$
$89$	2.94914	0.312609	0.156304	+	0.987709i	$0.450042\pi$
$90$	6.59210	0.694869
$91$	−9.80642	−1.02799
$92$	−3.62714	−0.378155
$93$	−4.99063	−0.517504
$94$	−15.4336	−1.59185
$95$	−2.28100	−0.234025
$96$	8.38271	0.855556
$97$	−18.5763	−1.88614	−0.943068	−	0.332600i	$-0.892074\pi$
$97$	−18.5763	−1.88614	−0.943068	+	0.332600i	$0.892074\pi$
$98$	5.67460	0.573221
$99$	26.6178	2.67519
$100$	−0.525428	−0.0525428
$101$	15.4193	1.53427	0.767137	−	0.641483i	$-0.221680\pi$
$101$	15.4193	1.53427	0.767137	+	0.641483i	$0.221680\pi$
$102$	7.57136	0.749676
$103$	7.76049	0.764664	0.382332	−	0.924025i	$-0.375121\pi$
$103$	7.76049	0.764664	0.382332	+	0.924025i	$0.375121\pi$
$104$	−19.7146	−1.93317
$105$	4.42864	0.432191
$106$	−4.10171	−0.398393
$107$	−3.03657	−0.293556	−0.146778	−	0.989169i	$-0.546890\pi$
$107$	−3.03657	−0.293556	−0.146778	+	0.989169i	$0.546890\pi$
$108$	3.70471	0.356486
$109$	−7.93978	−0.760493	−0.380246	−	0.924885i	$-0.624161\pi$
$109$	−7.93978	−0.760493	−0.380246	+	0.924885i	$0.624161\pi$
$110$	5.95407	0.567698
$111$	−23.0923	−2.19183
$112$	−4.07758	−0.385295
$113$	7.82071	0.735711	0.367855	−	0.929883i	$-0.380092\pi$
$113$	7.82071	0.735711	0.367855	+	0.929883i	$0.380092\pi$
$114$	8.04149	0.753154
$115$	−6.90321	−0.643728
$116$	−0.525428	−0.0487847
$117$	−34.8988	−3.22639
$118$	3.86665	0.355954
$119$	3.27607	0.300317
$120$	8.90321	0.812748
$121$	13.0415	1.18559
$122$	2.94914	0.267003
$123$	9.80642	0.884215
$124$	−0.903212	−0.0811108
$125$	−1.00000	−0.0894427
$126$	−10.0558	−0.895840
$127$	−12.4429	−1.10413	−0.552066	−	0.833801i	$-0.686160\pi$
$127$	−12.4429	−1.10413	−0.552066	+	0.833801i	$0.686160\pi$
$128$	−4.97481	−0.439715
$129$	3.18421	0.280354
$130$	−7.80642	−0.684669
$131$	4.08742	0.357120	0.178560	−	0.983929i	$-0.442856\pi$
$131$	4.08742	0.357120	0.178560	+	0.983929i	$0.442856\pi$
$132$	7.47949	0.651006
$133$	3.47949	0.301710
$134$	1.33185	0.115054
$135$	7.05086	0.606841
$136$	6.58613	0.564756
$137$	−19.9541	−1.70479	−0.852395	−	0.522898i	$-0.824851\pi$
$137$	−19.9541	−1.70479	−0.852395	+	0.522898i	$0.824851\pi$
$138$	24.3368	2.07168
$139$	7.90813	0.670759	0.335380	−	0.942083i	$-0.391135\pi$
$139$	7.90813	0.670759	0.335380	+	0.942083i	$0.391135\pi$
$140$	0.801502	0.0677393
$141$	−36.8988	−3.10744
$142$	−4.33677	−0.363934
$143$	−31.5210	−2.63592
$144$	−14.5111	−1.20926
$145$	−1.00000	−0.0830455
$146$	−17.2301	−1.42598
$147$	13.5669	1.11898
$148$	−4.17929	−0.343535
$149$	−16.1017	−1.31910	−0.659552	−	0.751659i	$-0.729254\pi$
$149$	−16.1017	−1.31910	−0.659552	+	0.751659i	$0.729254\pi$
$150$	3.52543	0.287850
$151$	5.67307	0.461668	0.230834	−	0.972993i	$-0.425855\pi$
$151$	5.67307	0.461668	0.230834	+	0.972993i	$0.425855\pi$
$152$	6.99508	0.567376
$153$	11.6588	0.942557
$154$	−9.08250	−0.731889
$155$	−1.71900	−0.138074
$156$	−9.80642	−0.785142
$157$	1.89384	0.151145	0.0755726	−	0.997140i	$-0.475922\pi$
$157$	1.89384	0.151145	0.0755726	+	0.997140i	$0.475922\pi$
$158$	−0.414349	−0.0329639
$159$	−9.80642	−0.777700
$160$	2.88739	0.228268
$161$	10.5303	0.829908
$162$	−5.08097	−0.399198
$163$	−5.95407	−0.466359	−0.233179	−	0.972434i	$-0.574913\pi$
$163$	−5.95407	−0.466359	−0.233179	+	0.972434i	$0.574913\pi$
$164$	1.77478	0.138587
$165$	14.2351	1.10820
$166$	8.90321	0.691023
$167$	4.23951	0.328063	0.164032	−	0.986455i	$-0.447550\pi$
$167$	4.23951	0.328063	0.164032	+	0.986455i	$0.447550\pi$
$168$	−13.5812	−1.04781
$169$	28.3274	2.17903
$170$	2.60793	0.200019
$171$	12.3827	0.946929
$172$	0.576283	0.0439411
$173$	24.4099	1.85585	0.927925	−	0.372766i	$-0.121591\pi$
$173$	24.4099	1.85585	0.927925	+	0.372766i	$0.121591\pi$
$174$	3.52543	0.267262
$175$	1.52543	0.115311
$176$	−13.1066	−0.987950
$177$	9.24443	0.694854
$178$	−3.58120	−0.268423
$179$	−3.61285	−0.270037	−0.135018	−	0.990843i	$-0.543109\pi$
$179$	−3.61285	−0.270037	−0.135018	+	0.990843i	$0.543109\pi$
$180$	2.85236	0.212602
$181$	18.0415	1.34101	0.670507	−	0.741904i	$-0.266077\pi$
$181$	18.0415	1.34101	0.670507	+	0.741904i	$0.266077\pi$
$182$	11.9081	0.882690
$183$	7.05086	0.521214
$184$	21.1699	1.56067
$185$	−7.95407	−0.584795
$186$	6.06022	0.444357
$187$	10.5303	0.770055
$188$	−6.67799	−0.487043
$189$	−10.7556	−0.782353
$190$	2.76986	0.200947
$191$	9.85236	0.712892	0.356446	−	0.934316i	$-0.383988\pi$
$191$	9.85236	0.712892	0.356446	+	0.934316i	$0.383988\pi$
$192$	−25.7003	−1.85476
$193$	2.23951	0.161203	0.0806017	−	0.996746i	$-0.474316\pi$
$193$	2.23951	0.161203	0.0806017	+	0.996746i	$0.474316\pi$
$194$	22.5575	1.61954
$195$	−18.6637	−1.33654
$196$	2.45536	0.175383
$197$	−10.5620	−0.752511	−0.376255	−	0.926516i	$-0.622788\pi$
$197$	−10.5620	−0.752511	−0.376255	+	0.926516i	$0.622788\pi$
$198$	−32.3225	−2.29706
$199$	3.18421	0.225723	0.112861	−	0.993611i	$-0.463998\pi$
$199$	3.18421	0.225723	0.112861	+	0.993611i	$0.463998\pi$
$200$	3.06668	0.216847
$201$	3.18421	0.224597
$202$	−18.7239	−1.31741
$203$	1.52543	0.107064
$204$	3.27607	0.229371
$205$	3.37778	0.235915
$206$	−9.42372	−0.656581
$207$	37.4750	2.60470
$208$	17.1842	1.19151
$209$	11.1842	0.773628
$210$	−5.37778	−0.371102
$211$	−5.76049	−0.396569	−0.198284	−	0.980145i	$-0.563537\pi$
$211$	−5.76049	−0.396569	−0.198284	+	0.980145i	$0.563537\pi$
$212$	−1.77478	−0.121892
$213$	−10.3684	−0.710432
$214$	3.68736	0.252063
$215$	1.09679	0.0748003
$216$	−21.6227	−1.47124
$217$	2.62222	0.178008
$218$	9.64143	0.653000
$219$	−41.1941	−2.78364
$220$	2.57628	0.173693
$221$	−13.8064	−0.928721
$222$	28.0415	1.88202
$223$	8.14764	0.545607	0.272803	−	0.962070i	$-0.412049\pi$
$223$	8.14764	0.545607	0.272803	+	0.962070i	$0.412049\pi$
$224$	−4.40451	−0.294288
$225$	5.42864	0.361909
$226$	−9.49685	−0.631721
$227$	10.5161	0.697975	0.348988	−	0.937127i	$-0.386525\pi$
$227$	10.5161	0.697975	0.348988	+	0.937127i	$0.386525\pi$
$228$	3.47949	0.230435
$229$	8.48886	0.560960	0.280480	−	0.959860i	$-0.409506\pi$
$229$	8.48886	0.560960	0.280480	+	0.959860i	$0.409506\pi$
$230$	8.38271	0.552739
$231$	−21.7146	−1.42871
$232$	3.06668	0.201337
$233$	−20.5718	−1.34771	−0.673853	−	0.738866i	$-0.735362\pi$
$233$	−20.5718	−1.34771	−0.673853	+	0.738866i	$0.735362\pi$
$234$	42.3783	2.77035
$235$	−12.7096	−0.829085
$236$	1.67307	0.108908
$237$	−0.990632	−0.0643485
$238$	−3.97820	−0.257869
$239$	0.815792	0.0527692	0.0263846	−	0.999652i	$-0.491601\pi$
$239$	0.815792	0.0527692	0.0263846	+	0.999652i	$0.491601\pi$
$240$	−7.76049	−0.500938
$241$	−7.24443	−0.466655	−0.233327	−	0.972398i	$-0.574961\pi$
$241$	−7.24443	−0.466655	−0.233327	+	0.972398i	$0.574961\pi$
$242$	−15.8365	−1.01801
$243$	9.00492	0.577666
$244$	1.27607	0.0816923
$245$	4.67307	0.298552
$246$	−11.9081	−0.759235
$247$	−14.6637	−0.933029
$248$	5.27163	0.334749
$249$	21.2859	1.34894
$250$	1.21432	0.0768003
$251$	−20.4242	−1.28916	−0.644582	−	0.764535i	$-0.722969\pi$
$251$	−20.4242	−1.28916	−0.644582	+	0.764535i	$0.722969\pi$
$252$	−4.35106	−0.274091
$253$	33.8479	2.12800
$254$	15.1097	0.948067
$255$	6.23506	0.390455
$256$	−11.6637	−0.728981
$257$	3.08250	0.192281	0.0961405	−	0.995368i	$-0.469350\pi$
$257$	3.08250	0.192281	0.0961405	+	0.995368i	$0.469350\pi$
$258$	−3.86665	−0.240727
$259$	12.1334	0.753930
$260$	−3.37778	−0.209481
$261$	5.42864	0.336024
$262$	−4.96343	−0.306642
$263$	20.0558	1.23669	0.618346	−	0.785906i	$-0.287803\pi$
$263$	20.0558	1.23669	0.618346	+	0.785906i	$0.287803\pi$
$264$	−43.6543	−2.68674
$265$	−3.37778	−0.207496
$266$	−4.22522	−0.259065
$267$	−8.56199	−0.523985
$268$	0.576283	0.0352021
$269$	−23.4608	−1.43043	−0.715214	−	0.698906i	$-0.753671\pi$
$269$	−23.4608	−1.43043	−0.715214	+	0.698906i	$0.753671\pi$
$270$	−8.56199	−0.521066
$271$	−21.9353	−1.33248	−0.666238	−	0.745739i	$-0.732097\pi$
$271$	−21.9353	−1.33248	−0.666238	+	0.745739i	$0.732097\pi$
$272$	−5.74080	−0.348087
$273$	28.4701	1.72309
$274$	24.2306	1.46383
$275$	4.90321	0.295675
$276$	10.5303	0.633853
$277$	18.3368	1.10175	0.550875	−	0.834588i	$-0.314294\pi$
$277$	18.3368	1.10175	0.550875	+	0.834588i	$0.314294\pi$
$278$	−9.60300	−0.575950
$279$	9.33185	0.558683
$280$	−4.67799	−0.279564
$281$	6.89877	0.411546	0.205773	−	0.978600i	$-0.434029\pi$
$281$	6.89877	0.411546	0.205773	+	0.978600i	$0.434029\pi$
$282$	44.8069	2.66821
$283$	−29.0049	−1.72416	−0.862082	−	0.506769i	$-0.830840\pi$
$283$	−29.0049	−1.72416	−0.862082	+	0.506769i	$0.830840\pi$
$284$	−1.87649	−0.111349
$285$	6.62222	0.392266
$286$	38.2766	2.26334
$287$	−5.15257	−0.304146
$288$	−15.6746	−0.923635
$289$	−12.3876	−0.728684
$290$	1.21432	0.0713073
$291$	53.9309	3.16148
$292$	−7.45536	−0.436292
$293$	7.79213	0.455221	0.227611	−	0.973752i	$-0.426909\pi$
$293$	7.79213	0.455221	0.227611	+	0.973752i	$0.426909\pi$
$294$	−16.4746	−0.960817
$295$	3.18421	0.185392
$296$	24.3926	1.41779
$297$	−34.5718	−2.00606
$298$	19.5526	1.13265
$299$	−44.3783	−2.56646
$300$	1.52543	0.0880706
$301$	−1.67307	−0.0964342
$302$	−6.88892	−0.396413
$303$	−44.7654	−2.57171
$304$	−6.09726	−0.349702
$305$	2.42864	0.139063
$306$	−14.1575	−0.809330
$307$	5.92549	0.338185	0.169093	−	0.985600i	$-0.445916\pi$
$307$	5.92549	0.338185	0.169093	+	0.985600i	$0.445916\pi$
$308$	−3.92993	−0.223929
$309$	−22.5303	−1.28171
$310$	2.08742	0.118557
$311$	8.94470	0.507207	0.253604	−	0.967308i	$-0.418384\pi$
$311$	8.94470	0.507207	0.253604	+	0.967308i	$0.418384\pi$
$312$	57.2355	3.24032
$313$	−30.5116	−1.72462	−0.862309	−	0.506382i	$-0.830983\pi$
$313$	−30.5116	−1.72462	−0.862309	+	0.506382i	$0.830983\pi$
$314$	−2.29973	−0.129781
$315$	−8.28100	−0.466581
$316$	−0.179286	−0.0100856
$317$	−22.2306	−1.24860	−0.624298	−	0.781186i	$-0.714615\pi$
$317$	−22.2306	−1.24860	−0.624298	+	0.781186i	$0.714615\pi$
$318$	11.9081	0.667775
$319$	4.90321	0.274527
$320$	−8.85236	−0.494862
$321$	8.81579	0.492050
$322$	−12.7872	−0.712603
$323$	4.89877	0.272575
$324$	−2.19850	−0.122139
$325$	−6.42864	−0.356597
$326$	7.23014	0.400440
$327$	23.0509	1.27472
$328$	−10.3586	−0.571956
$329$	19.3876	1.06887
$330$	−17.2859	−0.951558
$331$	−6.54770	−0.359894	−0.179947	−	0.983676i	$-0.557593\pi$
$331$	−6.54770	−0.359894	−0.179947	+	0.983676i	$0.557593\pi$
$332$	3.85236	0.211426
$333$	43.1798	2.36624
$334$	−5.14812	−0.281693
$335$	1.09679	0.0599239
$336$	11.8381	0.645819
$337$	2.66815	0.145343	0.0726717	−	0.997356i	$-0.476847\pi$
$337$	2.66815	0.145343	0.0726717	+	0.997356i	$0.476847\pi$
$338$	−34.3985	−1.87103
$339$	−22.7052	−1.23318
$340$	1.12843	0.0611978
$341$	8.42864	0.456436
$342$	−15.0366	−0.813084
$343$	−17.8064	−0.961457
$344$	−3.36349	−0.181347
$345$	20.0415	1.07900
$346$	−29.6414	−1.59353
$347$	14.6780	0.787956	0.393978	−	0.919120i	$-0.371099\pi$
$347$	14.6780	0.787956	0.393978	+	0.919120i	$0.371099\pi$
$348$	1.52543	0.0817715
$349$	−11.1240	−0.595453	−0.297727	−	0.954651i	$-0.596228\pi$
$349$	−11.1240	−0.595453	−0.297727	+	0.954651i	$0.596228\pi$
$350$	−1.85236	−0.0990126
$351$	45.3274	2.41940
$352$	−14.1575	−0.754597
$353$	−13.4795	−0.717441	−0.358721	−	0.933445i	$-0.616787\pi$
$353$	−13.4795	−0.717441	−0.358721	+	0.933445i	$0.616787\pi$
$354$	−11.2257	−0.596639
$355$	−3.57136	−0.189548
$356$	−1.54956	−0.0821266
$357$	−9.51114	−0.503383
$358$	4.38715	0.231868
$359$	26.1891	1.38221	0.691105	−	0.722755i	$-0.257124\pi$
$359$	26.1891	1.38221	0.691105	+	0.722755i	$0.257124\pi$
$360$	−16.6479	−0.877420
$361$	−13.7971	−0.726161
$362$	−21.9081	−1.15147
$363$	−37.8622	−1.98725
$364$	5.15257	0.270068
$365$	−14.1891	−0.742693
$366$	−8.56199	−0.447543
$367$	−22.9862	−1.19987	−0.599935	−	0.800049i	$-0.704807\pi$
$367$	−22.9862	−1.19987	−0.599935	+	0.800049i	$0.704807\pi$
$368$	−18.4528	−0.961917
$369$	−18.3368	−0.954574
$370$	9.65878	0.502136
$371$	5.15257	0.267508
$372$	2.62222	0.135956
$373$	−24.2766	−1.25699	−0.628496	−	0.777813i	$-0.716329\pi$
$373$	−24.2766	−1.25699	−0.628496	+	0.777813i	$0.716329\pi$
$374$	−12.7872	−0.661211
$375$	2.90321	0.149921
$376$	38.9763	2.01005
$377$	−6.42864	−0.331092
$378$	13.0607	0.671770
$379$	29.7605	1.52869	0.764347	−	0.644805i	$-0.223062\pi$
$379$	29.7605	1.52869	0.764347	+	0.644805i	$0.223062\pi$
$380$	1.19850	0.0614817
$381$	36.1245	1.85071
$382$	−11.9639	−0.612127
$383$	23.8020	1.21622	0.608112	−	0.793851i	$-0.291927\pi$
$383$	23.8020	1.21622	0.608112	+	0.793851i	$0.291927\pi$
$384$	14.4429	0.737038
$385$	−7.47949	−0.381190
$386$	−2.71948	−0.138418
$387$	−5.95407	−0.302662
$388$	9.76049	0.495514
$389$	−6.52051	−0.330603	−0.165301	−	0.986243i	$-0.552860\pi$
$389$	−6.52051	−0.330603	−0.165301	+	0.986243i	$0.552860\pi$
$390$	22.6637	1.14762
$391$	14.8256	0.749765
$392$	−14.3308	−0.723815
$393$	−11.8666	−0.598593
$394$	12.8256	0.646146
$395$	−0.341219	−0.0171686
$396$	−13.9857	−0.702808
$397$	−14.7654	−0.741055	−0.370527	−	0.928822i	$-0.620823\pi$
$397$	−14.7654	−0.741055	−0.370527	+	0.928822i	$0.620823\pi$
$398$	−3.86665	−0.193817
$399$	−10.1017	−0.505718
$400$	−2.67307	−0.133654
$401$	6.81579	0.340364	0.170182	−	0.985413i	$-0.445564\pi$
$401$	6.81579	0.340364	0.170182	+	0.985413i	$0.445564\pi$
$402$	−3.86665	−0.192851
$403$	−11.0509	−0.550482
$404$	−8.10171	−0.403075
$405$	−4.18421	−0.207915
$406$	−1.85236	−0.0919309
$407$	39.0005	1.93318
$408$	−19.1209	−0.946627
$409$	−11.0825	−0.547994	−0.273997	−	0.961731i	$-0.588346\pi$
$409$	−11.0825	−0.547994	−0.273997	+	0.961731i	$0.588346\pi$
$410$	−4.10171	−0.202569
$411$	57.9309	2.85752
$412$	−4.07758	−0.200888
$413$	−4.85728	−0.239011
$414$	−45.5067	−2.23653
$415$	7.33185	0.359906
$416$	18.5620	0.910077
$417$	−22.9590	−1.12431
$418$	−13.5812	−0.664278
$419$	30.9719	1.51308	0.756538	−	0.653950i	$-0.226889\pi$
$419$	30.9719	1.51308	0.756538	+	0.653950i	$0.226889\pi$
$420$	−2.32693	−0.113543
$421$	22.8988	1.11602	0.558009	−	0.829835i	$-0.311566\pi$
$421$	22.8988	1.11602	0.558009	+	0.829835i	$0.311566\pi$
$422$	6.99508	0.340515
$423$	68.9960	3.35470
$424$	10.3586	0.503057
$425$	2.14764	0.104176
$426$	12.5906	0.610015
$427$	−3.70471	−0.179284
$428$	1.59549	0.0771212
$429$	91.5121	4.41825
$430$	−1.33185	−0.0642276
$431$	−28.0830	−1.35271	−0.676355	−	0.736576i	$-0.736441\pi$
$431$	−28.0830	−1.35271	−0.676355	+	0.736576i	$0.736441\pi$
$432$	18.8474	0.906798
$433$	23.0049	1.10555	0.552773	−	0.833332i	$-0.313570\pi$
$433$	23.0049	1.10555	0.552773	+	0.833332i	$0.313570\pi$
$434$	−3.18421	−0.152847
$435$	2.90321	0.139198
$436$	4.17178	0.199792
$437$	15.7462	0.753243
$438$	50.0228	2.39018
$439$	11.7462	0.560616	0.280308	−	0.959910i	$-0.409563\pi$
$439$	11.7462	0.560616	0.280308	+	0.959910i	$0.409563\pi$
$440$	−15.0366	−0.716840
$441$	−25.3684	−1.20802
$442$	16.7654	0.797449
$443$	17.6874	0.840352	0.420176	−	0.907443i	$-0.361968\pi$
$443$	17.6874	0.840352	0.420176	+	0.907443i	$0.361968\pi$
$444$	12.1334	0.575823
$445$	−2.94914	−0.139803
$446$	−9.89384	−0.468487
$447$	46.7467	2.21104
$448$	13.5036	0.637987
$449$	1.57136	0.0741571	0.0370785	−	0.999312i	$-0.488195\pi$
$449$	1.57136	0.0741571	0.0370785	+	0.999312i	$0.488195\pi$
$450$	−6.59210	−0.310755
$451$	−16.5620	−0.779874
$452$	−4.10922	−0.193281
$453$	−16.4701	−0.773834
$454$	−12.7699	−0.599319
$455$	9.80642	0.459732
$456$	−20.3082	−0.951018
$457$	1.47949	0.0692078	0.0346039	−	0.999401i	$-0.488983\pi$
$457$	1.47949	0.0692078	0.0346039	+	0.999401i	$0.488983\pi$
$458$	−10.3082	−0.481670
$459$	−15.1427	−0.706802
$460$	3.62714	0.169116
$461$	−41.2543	−1.92140	−0.960702	−	0.277583i	$-0.910467\pi$
$461$	−41.2543	−1.92140	−0.960702	+	0.277583i	$0.910467\pi$
$462$	26.3684	1.22677
$463$	−34.4242	−1.59983	−0.799914	−	0.600115i	$-0.795122\pi$
$463$	−34.4242	−1.59983	−0.799914	+	0.600115i	$0.795122\pi$
$464$	−2.67307	−0.124094
$465$	4.99063	0.231435
$466$	24.9808	1.15721
$467$	15.1699	0.701980	0.350990	−	0.936379i	$-0.385845\pi$
$467$	15.1699	0.701980	0.350990	+	0.936379i	$0.385845\pi$
$468$	18.3368	0.847618
$469$	−1.67307	−0.0772552
$470$	15.4336	0.711897
$471$	−5.49823	−0.253345
$472$	−9.76494	−0.449468
$473$	−5.37778	−0.247271
$474$	1.20294	0.0552531
$475$	2.28100	0.104659
$476$	−1.72134	−0.0788975
$477$	18.3368	0.839583
$478$	−0.990632	−0.0453105
$479$	−18.9763	−0.867051	−0.433526	−	0.901141i	$-0.642731\pi$
$479$	−18.9763	−0.867051	−0.433526	+	0.901141i	$0.642731\pi$
$480$	−8.38271	−0.382616
$481$	−51.1338	−2.33150
$482$	8.79706	0.400695
$483$	−30.5718	−1.39107
$484$	−6.85236	−0.311471
$485$	18.5763	0.843506
$486$	−10.9349	−0.496015
$487$	−32.3926	−1.46785	−0.733923	−	0.679232i	$-0.762313\pi$
$487$	−32.3926	−1.46785	−0.733923	+	0.679232i	$0.762313\pi$
$488$	−7.44785	−0.337148
$489$	17.2859	0.781696
$490$	−5.67460	−0.256352
$491$	2.69673	0.121702	0.0608508	−	0.998147i	$-0.480619\pi$
$491$	2.69673	0.121702	0.0608508	+	0.998147i	$0.480619\pi$
$492$	−5.15257	−0.232296
$493$	2.14764	0.0967250
$494$	17.8064	0.801149
$495$	−26.6178	−1.19638
$496$	−4.59502	−0.206322
$497$	5.44785	0.244370
$498$	−25.8479	−1.15827
$499$	14.5718	0.652325	0.326163	−	0.945314i	$-0.394244\pi$
$499$	14.5718	0.652325	0.326163	+	0.945314i	$0.394244\pi$
$500$	0.525428	0.0234978
$501$	−12.3082	−0.549890
$502$	24.8015	1.10695
$503$	−22.2494	−0.992050	−0.496025	−	0.868308i	$-0.665208\pi$
$503$	−22.2494	−0.992050	−0.496025	+	0.868308i	$0.665208\pi$
$504$	25.3951	1.13119
$505$	−15.4193	−0.686149
$506$	−41.1022	−1.82722
$507$	−82.2405	−3.65243
$508$	6.53786	0.290071
$509$	−9.18421	−0.407083	−0.203541	−	0.979066i	$-0.565245\pi$
$509$	−9.18421	−0.407083	−0.203541	+	0.979066i	$0.565245\pi$
$510$	−7.57136	−0.335265
$511$	21.6445	0.957496
$512$	24.1131	1.06566
$513$	−16.0830	−0.710081
$514$	−3.74314	−0.165103
$515$	−7.76049	−0.341968
$516$	−1.67307	−0.0736528
$517$	62.3180	2.74074
$518$	−14.7338	−0.647365
$519$	−70.8671	−3.11072
$520$	19.7146	0.864541
$521$	7.01921	0.307517	0.153759	−	0.988108i	$-0.450862\pi$
$521$	7.01921	0.307517	0.153759	+	0.988108i	$0.450862\pi$
$522$	−6.59210	−0.288529
$523$	−7.29036	−0.318785	−0.159393	−	0.987215i	$-0.550954\pi$
$523$	−7.29036	−0.318785	−0.159393	+	0.987215i	$0.550954\pi$
$524$	−2.14764	−0.0938202
$525$	−4.42864	−0.193282
$526$	−24.3541	−1.06189
$527$	3.69181	0.160818
$528$	38.0513	1.65597
$529$	24.6543	1.07193
$530$	4.10171	0.178167
$531$	−17.2859	−0.750145
$532$	−1.82822	−0.0792635
$533$	21.7146	0.940562
$534$	10.3970	0.449922
$535$	3.03657	0.131282
$536$	−3.36349	−0.145281
$537$	10.4889	0.452628
$538$	28.4889	1.22824
$539$	−22.9131	−0.986935
$540$	−3.70471	−0.159425
$541$	30.9491	1.33061	0.665304	−	0.746573i	$-0.268302\pi$
$541$	30.9491	1.33061	0.665304	+	0.746573i	$0.268302\pi$
$542$	26.6365	1.14414
$543$	−52.3783	−2.24777
$544$	−6.20108	−0.265869
$545$	7.93978	0.340103
$546$	−34.5718	−1.47954
$547$	−19.4237	−0.830498	−0.415249	−	0.909708i	$-0.636306\pi$
$547$	−19.4237	−0.830498	−0.415249	+	0.909708i	$0.636306\pi$
$548$	10.4844	0.447872
$549$	−13.1842	−0.562688
$550$	−5.95407	−0.253882
$551$	2.28100	0.0971737
$552$	−61.4608	−2.61594
$553$	0.520505	0.0221341
$554$	−22.2667	−0.946022
$555$	23.0923	0.980215
$556$	−4.15515	−0.176218
$557$	30.3497	1.28596	0.642979	−	0.765884i	$-0.277698\pi$
$557$	30.3497	1.28596	0.642979	+	0.765884i	$0.277698\pi$
$558$	−11.3319	−0.479716
$559$	7.05086	0.298219
$560$	4.07758	0.172309
$561$	−30.5718	−1.29074
$562$	−8.37731	−0.353375
$563$	−33.1798	−1.39836	−0.699180	−	0.714946i	$-0.746451\pi$
$563$	−33.1798	−1.39836	−0.699180	+	0.714946i	$0.746451\pi$
$564$	19.3876	0.816366
$565$	−7.82071	−0.329020
$566$	35.2212	1.48046
$567$	6.38271	0.268048
$568$	10.9522	0.459544
$569$	−4.06022	−0.170213	−0.0851067	−	0.996372i	$-0.527123\pi$
$569$	−4.06022	−0.170213	−0.0851067	+	0.996372i	$0.527123\pi$
$570$	−8.04149	−0.336821
$571$	−31.5496	−1.32031	−0.660154	−	0.751130i	$-0.729509\pi$
$571$	−31.5496	−1.32031	−0.660154	+	0.751130i	$0.729509\pi$
$572$	16.5620	0.692492
$573$	−28.6035	−1.19493
$574$	6.25686	0.261156
$575$	6.90321	0.287884
$576$	48.0563	2.00234
$577$	33.7891	1.40666	0.703329	−	0.710865i	$-0.251696\pi$
$577$	33.7891	1.40666	0.703329	+	0.710865i	$0.251696\pi$
$578$	15.0425	0.625687
$579$	−6.50177	−0.270204
$580$	0.525428	0.0218172
$581$	−11.1842	−0.463999
$582$	−65.4893	−2.71462
$583$	16.5620	0.685928
$584$	43.5135	1.80060
$585$	34.8988	1.44289
$586$	−9.46214	−0.390877
$587$	−25.5669	−1.05526	−0.527630	−	0.849474i	$-0.676919\pi$
$587$	−25.5669	−1.05526	−0.527630	+	0.849474i	$0.676919\pi$
$588$	−7.12843	−0.293972
$589$	3.92104	0.161564
$590$	−3.86665	−0.159187
$591$	30.6637	1.26134
$592$	−21.2618	−0.873854
$593$	7.96836	0.327221	0.163611	−	0.986525i	$-0.447686\pi$
$593$	7.96836	0.327221	0.163611	+	0.986525i	$0.447686\pi$
$594$	41.9813	1.72251
$595$	−3.27607	−0.134306
$596$	8.46028	0.346547
$597$	−9.24443	−0.378349
$598$	53.8894	2.20370
$599$	37.2815	1.52328	0.761640	−	0.648001i	$-0.224395\pi$
$599$	37.2815	1.52328	0.761640	+	0.648001i	$0.224395\pi$
$600$	−8.90321	−0.363472
$601$	−29.9496	−1.22167	−0.610835	−	0.791758i	$-0.709166\pi$
$601$	−29.9496	−1.22167	−0.610835	+	0.791758i	$0.709166\pi$
$602$	2.03164	0.0828036
$603$	−5.95407	−0.242468
$604$	−2.98079	−0.121287
$605$	−13.0415	−0.530212
$606$	54.3595	2.20820
$607$	−31.8435	−1.29249	−0.646243	−	0.763132i	$-0.723661\pi$
$607$	−31.8435	−1.29249	−0.646243	+	0.763132i	$0.723661\pi$
$608$	−6.58613	−0.267103
$609$	−4.42864	−0.179458
$610$	−2.94914	−0.119407
$611$	−81.7057	−3.30546
$612$	−6.12584	−0.247623
$613$	−2.65386	−0.107188	−0.0535942	−	0.998563i	$-0.517068\pi$
$613$	−2.65386	−0.107188	−0.0535942	+	0.998563i	$0.517068\pi$
$614$	−7.19544	−0.290384
$615$	−9.80642	−0.395433
$616$	22.9372	0.924166
$617$	−18.3096	−0.737116	−0.368558	−	0.929605i	$-0.620148\pi$
$617$	−18.3096	−0.737116	−0.368558	+	0.929605i	$0.620148\pi$
$618$	27.3590	1.10054
$619$	12.8113	0.514931	0.257466	−	0.966287i	$-0.417113\pi$
$619$	12.8113	0.514931	0.257466	+	0.966287i	$0.417113\pi$
$620$	0.903212	0.0362739
$621$	−48.6735	−1.95320
$622$	−10.8617	−0.435515
$623$	4.49871	0.180237
$624$	−49.8894	−1.99717
$625$	1.00000	0.0400000
$626$	37.0509	1.48085
$627$	−32.4701	−1.29673
$628$	−0.995078	−0.0397079
$629$	17.0825	0.681124
$630$	10.0558	0.400632
$631$	30.2766	1.20529	0.602645	−	0.798009i	$-0.294113\pi$
$631$	30.2766	1.20529	0.602645	+	0.798009i	$0.294113\pi$
$632$	1.04641	0.0416239
$633$	16.7239	0.664716
$634$	26.9951	1.07211
$635$	12.4429	0.493783
$636$	5.15257	0.204313
$637$	30.0415	1.19029
$638$	−5.95407	−0.235724
$639$	19.3876	0.766963
$640$	4.97481	0.196647
$641$	−4.50177	−0.177809	−0.0889046	−	0.996040i	$-0.528337\pi$
$641$	−4.50177	−0.177809	−0.0889046	+	0.996040i	$0.528337\pi$
$642$	−10.7052	−0.422500
$643$	−40.0272	−1.57852	−0.789259	−	0.614060i	$-0.789535\pi$
$643$	−40.0272	−1.57852	−0.789259	+	0.614060i	$0.789535\pi$
$644$	−5.53294	−0.218028
$645$	−3.18421	−0.125378
$646$	−5.94867	−0.234047
$647$	27.3604	1.07565	0.537825	−	0.843057i	$-0.319246\pi$
$647$	27.3604	1.07565	0.537825	+	0.843057i	$0.319246\pi$
$648$	12.8316	0.504073
$649$	−15.6128	−0.612858
$650$	7.80642	0.306193
$651$	−7.61285	−0.298371
$652$	3.12843	0.122519
$653$	22.8430	0.893915	0.446958	−	0.894555i	$-0.352507\pi$
$653$	22.8430	0.893915	0.446958	+	0.894555i	$0.352507\pi$
$654$	−27.9911	−1.09454
$655$	−4.08742	−0.159709
$656$	9.02906	0.352525
$657$	77.0277	3.00514
$658$	−23.5428	−0.917793
$659$	15.0178	0.585012	0.292506	−	0.956264i	$-0.405511\pi$
$659$	15.0178	0.585012	0.292506	+	0.956264i	$0.405511\pi$
$660$	−7.47949	−0.291139
$661$	−4.65080	−0.180895	−0.0904475	−	0.995901i	$-0.528830\pi$
$661$	−4.65080	−0.180895	−0.0904475	+	0.995901i	$0.528830\pi$
$662$	7.95100	0.309025
$663$	40.0830	1.55669
$664$	−22.4844	−0.872565
$665$	−3.47949	−0.134929
$666$	−52.4340	−2.03178
$667$	6.90321	0.267293
$668$	−2.22755	−0.0861867
$669$	−23.6543	−0.914529
$670$	−1.33185	−0.0514539
$671$	−11.9081	−0.459708
$672$	12.7872	0.493277
$673$	−44.8671	−1.72950	−0.864750	−	0.502202i	$-0.832523\pi$
$673$	−44.8671	−1.72950	−0.864750	+	0.502202i	$0.832523\pi$
$674$	−3.23999	−0.124800
$675$	−7.05086	−0.271388
$676$	−14.8840	−0.572462
$677$	27.2212	1.04620	0.523099	−	0.852272i	$-0.324776\pi$
$677$	27.2212	1.04620	0.523099	+	0.852272i	$0.324776\pi$
$678$	27.5714	1.05887
$679$	−28.3368	−1.08747
$680$	−6.58613	−0.252566
$681$	−30.5303	−1.16993
$682$	−10.2351	−0.391921
$683$	12.0558	0.461301	0.230651	−	0.973037i	$-0.425915\pi$
$683$	12.0558	0.461301	0.230651	+	0.973037i	$0.425915\pi$
$684$	−6.50622	−0.248771
$685$	19.9541	0.762406
$686$	21.6227	0.825558
$687$	−24.6450	−0.940264
$688$	2.93179	0.111774
$689$	−21.7146	−0.827259
$690$	−24.3368	−0.926485
$691$	37.5812	1.42966	0.714828	−	0.699300i	$-0.246505\pi$
$691$	37.5812	1.42966	0.714828	+	0.699300i	$0.246505\pi$
$692$	−12.8256	−0.487558
$693$	40.6035	1.54240
$694$	−17.8238	−0.676581
$695$	−7.90813	−0.299973
$696$	−8.90321	−0.337475
$697$	−7.25428	−0.274775
$698$	13.5081	0.511288
$699$	59.7244	2.25898
$700$	−0.801502	−0.0302939
$701$	2.04149	0.0771059	0.0385530	−	0.999257i	$-0.487725\pi$
$701$	2.04149	0.0771059	0.0385530	+	0.999257i	$0.487725\pi$
$702$	−55.0420	−2.07743
$703$	18.1432	0.684284
$704$	43.4050	1.63589
$705$	36.8988	1.38969
$706$	16.3684	0.616033
$707$	23.5210	0.884598
$708$	−4.85728	−0.182548
$709$	−32.1432	−1.20716	−0.603582	−	0.797301i	$-0.706260\pi$
$709$	−32.1432	−1.20716	−0.603582	+	0.797301i	$0.706260\pi$
$710$	4.33677	0.162756
$711$	1.85236	0.0694688
$712$	9.04407	0.338941
$713$	11.8666	0.444409
$714$	11.5496	0.432231
$715$	31.5210	1.17882
$716$	1.89829	0.0709424
$717$	−2.36842	−0.0884501
$718$	−31.8020	−1.18684
$719$	1.01921	0.0380102	0.0190051	−	0.999819i	$-0.493950\pi$
$719$	1.01921	0.0380102	0.0190051	+	0.999819i	$0.493950\pi$
$720$	14.5111	0.540798
$721$	11.8381	0.440873
$722$	16.7540	0.623521
$723$	21.0321	0.782193
$724$	−9.47949	−0.352303
$725$	1.00000	0.0371391
$726$	45.9768	1.70636
$727$	−24.1476	−0.895587	−0.447793	−	0.894137i	$-0.647790\pi$
$727$	−24.1476	−0.895587	−0.447793	+	0.894137i	$0.647790\pi$
$728$	−30.0731	−1.11458
$729$	−38.6958	−1.43318
$730$	17.2301	0.637716
$731$	−2.35551	−0.0871217
$732$	−3.70471	−0.136930
$733$	18.8845	0.697514	0.348757	−	0.937213i	$-0.386604\pi$
$733$	18.8845	0.697514	0.348757	+	0.937213i	$0.386604\pi$
$734$	27.9126	1.03027
$735$	−13.5669	−0.500423
$736$	−19.9323	−0.734713
$737$	−5.37778	−0.198093
$738$	22.2667	0.819649
$739$	−3.31312	−0.121875	−0.0609375	−	0.998142i	$-0.519409\pi$
$739$	−3.31312	−0.121875	−0.0609375	+	0.998142i	$0.519409\pi$
$740$	4.17929	0.153634
$741$	42.5718	1.56392
$742$	−6.25686	−0.229697
$743$	2.99508	0.109879	0.0549394	−	0.998490i	$-0.482503\pi$
$743$	2.99508	0.109879	0.0549394	+	0.998490i	$0.482503\pi$
$744$	−15.3047	−0.561096
$745$	16.1017	0.589921
$746$	29.4795	1.07932
$747$	−39.8020	−1.45628
$748$	−5.53294	−0.202304
$749$	−4.63206	−0.169252
$750$	−3.52543	−0.128730
$751$	11.9956	0.437724	0.218862	−	0.975756i	$-0.429766\pi$
$751$	11.9956	0.437724	0.218862	+	0.975756i	$0.429766\pi$
$752$	−33.9738	−1.23890
$753$	59.2958	2.16086
$754$	7.80642	0.284293
$755$	−5.67307	−0.206464
$756$	5.65127	0.205535
$757$	18.5763	0.675166	0.337583	−	0.941296i	$-0.390391\pi$
$757$	18.5763	0.675166	0.337583	+	0.941296i	$0.390391\pi$
$758$	−36.1388	−1.31262
$759$	−98.2677	−3.56689
$760$	−6.99508	−0.253738
$761$	2.59057	0.0939082	0.0469541	−	0.998897i	$-0.485049\pi$
$761$	2.59057	0.0939082	0.0469541	+	0.998897i	$0.485049\pi$
$762$	−43.8666	−1.58912
$763$	−12.1116	−0.438468
$764$	−5.17670	−0.187286
$765$	−11.6588	−0.421524
$766$	−28.9032	−1.04432
$767$	20.4701	0.739133
$768$	33.8622	1.22190
$769$	32.7467	1.18088	0.590438	−	0.807083i	$-0.298955\pi$
$769$	32.7467	1.18088	0.590438	+	0.807083i	$0.298955\pi$
$770$	9.08250	0.327311
$771$	−8.94914	−0.322296
$772$	−1.17670	−0.0423504
$773$	28.2208	1.01503	0.507515	−	0.861643i	$-0.330564\pi$
$773$	28.2208	1.01503	0.507515	+	0.861643i	$0.330564\pi$
$774$	7.23014	0.259882
$775$	1.71900	0.0617484
$776$	−56.9675	−2.04501
$777$	−35.2257	−1.26371
$778$	7.91798	0.283873
$779$	−7.70471	−0.276050
$780$	9.80642	0.351126
$781$	17.5111	0.626598
$782$	−18.0031	−0.643788
$783$	−7.05086	−0.251977
$784$	12.4914	0.446123
$785$	−1.89384	−0.0675942
$786$	14.4099	0.513984
$787$	11.9857	0.427244	0.213622	−	0.976916i	$-0.431474\pi$
$787$	11.9857	0.427244	0.213622	+	0.976916i	$0.431474\pi$
$788$	5.54956	0.197695
$789$	−58.2262	−2.07291
$790$	0.414349	0.0147419
$791$	11.9299	0.424180
$792$	81.6281	2.90053
$793$	15.6128	0.554428
$794$	17.9299	0.636309
$795$	9.80642	0.347798
$796$	−1.67307	−0.0593004
$797$	−33.0366	−1.17022	−0.585108	−	0.810956i	$-0.698948\pi$
$797$	−33.0366	−1.17022	−0.585108	+	0.810956i	$0.698948\pi$
$798$	12.2667	0.434237
$799$	27.2958	0.965655
$800$	−2.88739	−0.102085
$801$	16.0098	0.565680
$802$	−8.27655	−0.292255
$803$	69.5723	2.45515
$804$	−1.67307	−0.0590047
$805$	−10.5303	−0.371146
$806$	13.4193	0.472674
$807$	68.1116	2.39764
$808$	47.2859	1.66351
$809$	−32.1303	−1.12964	−0.564820	−	0.825214i	$-0.691055\pi$
$809$	−32.1303	−1.12964	−0.564820	+	0.825214i	$0.691055\pi$
$810$	5.08097	0.178527
$811$	15.3176	0.537872	0.268936	−	0.963158i	$-0.413328\pi$
$811$	15.3176	0.537872	0.268936	+	0.963158i	$0.413328\pi$
$812$	−0.801502	−0.0281272
$813$	63.6829	2.23346
$814$	−47.3590	−1.65993
$815$	5.95407	0.208562
$816$	16.6668	0.583453
$817$	−2.50177	−0.0875258
$818$	13.4577	0.470537
$819$	−53.2355	−1.86020
$820$	−1.77478	−0.0619780
$821$	−17.1427	−0.598285	−0.299143	−	0.954208i	$-0.596701\pi$
$821$	−17.1427	−0.598285	−0.299143	+	0.954208i	$0.596701\pi$
$822$	−70.3466	−2.45362
$823$	−35.6400	−1.24233	−0.621167	−	0.783678i	$-0.713341\pi$
$823$	−35.6400	−1.24233	−0.621167	+	0.783678i	$0.713341\pi$
$824$	23.7989	0.829075
$825$	−14.2351	−0.495601
$826$	5.89829	0.205228
$827$	4.70964	0.163770	0.0818850	−	0.996642i	$-0.473906\pi$
$827$	4.70964	0.163770	0.0818850	+	0.996642i	$0.473906\pi$
$828$	−19.6904	−0.684290
$829$	2.25380	0.0782777	0.0391388	−	0.999234i	$-0.487539\pi$
$829$	2.25380	0.0782777	0.0391388	+	0.999234i	$0.487539\pi$
$830$	−8.90321	−0.309035
$831$	−53.2355	−1.84672
$832$	−56.9086	−1.97295
$833$	−10.0361	−0.347730
$834$	27.8796	0.965390
$835$	−4.23951	−0.146714
$836$	−5.87649	−0.203243
$837$	−12.1204	−0.418944
$838$	−37.6098	−1.29921
$839$	−8.42419	−0.290835	−0.145418	−	0.989370i	$-0.546453\pi$
$839$	−8.42419	−0.290835	−0.145418	+	0.989370i	$0.546453\pi$
$840$	13.5812	0.468596
$841$	1.00000	0.0344828
$842$	−27.8064	−0.958273
$843$	−20.0286	−0.689821
$844$	3.02672	0.104184
$845$	−28.3274	−0.974492
$846$	−83.7832	−2.88053
$847$	19.8938	0.683561
$848$	−9.02906	−0.310059
$849$	84.2074	2.88999
$850$	−2.60793	−0.0894511
$851$	54.9086	1.88224
$852$	5.44785	0.186640
$853$	51.8247	1.77444	0.887222	−	0.461342i	$-0.152632\pi$
$853$	51.8247	1.77444	0.887222	+	0.461342i	$0.152632\pi$
$854$	4.49871	0.153943
$855$	−12.3827	−0.423480
$856$	−9.31216	−0.318283
$857$	−30.0415	−1.02620	−0.513099	−	0.858330i	$-0.671503\pi$
$857$	−30.0415	−1.02620	−0.513099	+	0.858330i	$0.671503\pi$
$858$	−111.125	−3.79374
$859$	19.6874	0.671724	0.335862	−	0.941911i	$-0.390972\pi$
$859$	19.6874	0.671724	0.335862	+	0.941911i	$0.390972\pi$
$860$	−0.576283	−0.0196511
$861$	14.9590	0.509801
$862$	34.1017	1.16151
$863$	19.5986	0.667143	0.333571	−	0.942725i	$-0.391746\pi$
$863$	19.5986	0.667143	0.333571	+	0.942725i	$0.391746\pi$
$864$	20.3586	0.692613
$865$	−24.4099	−0.829962
$866$	−27.9353	−0.949281
$867$	35.9639	1.22140
$868$	−1.37778	−0.0467650
$869$	1.67307	0.0567550
$870$	−3.52543	−0.119523
$871$	7.05086	0.238909
$872$	−24.3487	−0.824552
$873$	−100.844	−3.41305
$874$	−19.1209	−0.646775
$875$	−1.52543	−0.0515689
$876$	21.6445	0.731300
$877$	−16.2351	−0.548219	−0.274110	−	0.961698i	$-0.588383\pi$
$877$	−16.2351	−0.548219	−0.274110	+	0.961698i	$0.588383\pi$
$878$	−14.2636	−0.481375
$879$	−22.6222	−0.763028
$880$	13.1066	0.441824
$881$	−20.7052	−0.697576	−0.348788	−	0.937202i	$-0.613407\pi$
$881$	−20.7052	−0.697576	−0.348788	+	0.937202i	$0.613407\pi$
$882$	30.8054	1.03727
$883$	8.75112	0.294499	0.147249	−	0.989099i	$-0.452958\pi$
$883$	8.75112	0.294499	0.147249	+	0.989099i	$0.452958\pi$
$884$	7.25428	0.243988
$885$	−9.24443	−0.310748
$886$	−21.4781	−0.721571
$887$	0.414349	0.0139125	0.00695625	−	0.999976i	$-0.497786\pi$
$887$	0.414349	0.0139125	0.00695625	+	0.999976i	$0.497786\pi$
$888$	−70.8167	−2.37645
$889$	−18.9808	−0.636595
$890$	3.58120	0.120042
$891$	20.5161	0.687314
$892$	−4.28100	−0.143338
$893$	28.9906	0.970135
$894$	−56.7654	−1.89852
$895$	3.61285	0.120764
$896$	−7.58871	−0.253521
$897$	128.839	4.30183
$898$	−1.90813	−0.0636753
$899$	1.71900	0.0573320
$900$	−2.85236	−0.0950786
$901$	7.25428	0.241675
$902$	20.1116	0.669642
$903$	4.85728	0.161640
$904$	23.9836	0.797683
$905$	−18.0415	−0.599719
$906$	20.0000	0.664455
$907$	−46.9862	−1.56015	−0.780075	−	0.625686i	$-0.784819\pi$
$907$	−46.9862	−1.56015	−0.780075	+	0.625686i	$0.784819\pi$
$908$	−5.52543	−0.183368
$909$	83.7057	2.77634
$910$	−11.9081	−0.394751
$911$	−12.1704	−0.403223	−0.201612	−	0.979466i	$-0.564618\pi$
$911$	−12.1704	−0.403223	−0.201612	+	0.979466i	$0.564618\pi$
$912$	17.7017	0.586160
$913$	−35.9496	−1.18976
$914$	−1.79658	−0.0594256
$915$	−7.05086	−0.233094
$916$	−4.46028	−0.147372
$917$	6.23506	0.205900
$918$	18.3881	0.606898
$919$	−23.2672	−0.767514	−0.383757	−	0.923434i	$-0.625370\pi$
$919$	−23.2672	−0.767514	−0.383757	+	0.923434i	$0.625370\pi$
$920$	−21.1699	−0.697952
$921$	−17.2029	−0.566856
$922$	50.0959	1.64982
$923$	−22.9590	−0.755704
$924$	11.4094	0.375343
$925$	7.95407	0.261528
$926$	41.8020	1.37370
$927$	42.1289	1.38369
$928$	−2.88739	−0.0947832
$929$	44.7556	1.46838	0.734191	−	0.678943i	$-0.237562\pi$
$929$	44.7556	1.46838	0.734191	+	0.678943i	$0.237562\pi$
$930$	−6.06022	−0.198723
$931$	−10.6593	−0.349343
$932$	10.8090	0.354061
$933$	−25.9684	−0.850166
$934$	−18.4211	−0.602758
$935$	−10.5303	−0.344379
$936$	−107.023	−3.49816
$937$	−22.7239	−0.742358	−0.371179	−	0.928561i	$-0.621046\pi$
$937$	−22.7239	−0.742358	−0.371179	+	0.928561i	$0.621046\pi$
$938$	2.03164	0.0663355
$939$	88.5817	2.89075
$940$	6.67799	0.217812
$941$	4.10171	0.133712	0.0668560	−	0.997763i	$-0.478703\pi$
$941$	4.10171	0.133712	0.0668560	+	0.997763i	$0.478703\pi$
$942$	6.67661	0.217536
$943$	−23.3176	−0.759324
$944$	8.51161	0.277029
$945$	10.7556	0.349879
$946$	6.53035	0.212320
$947$	16.6178	0.540005	0.270002	−	0.962860i	$-0.412975\pi$
$947$	16.6178	0.540005	0.270002	+	0.962860i	$0.412975\pi$
$948$	0.520505	0.0169052
$949$	−91.2168	−2.96102
$950$	−2.76986	−0.0898661
$951$	64.5402	2.09286
$952$	10.0467	0.325614
$953$	2.85728	0.0925563	0.0462782	−	0.998929i	$-0.485264\pi$
$953$	2.85728	0.0925563	0.0462782	+	0.998929i	$0.485264\pi$
$954$	−22.2667	−0.720911
$955$	−9.85236	−0.318815
$956$	−0.428639	−0.0138632
$957$	−14.2351	−0.460154
$958$	23.0433	0.744497
$959$	−30.4385	−0.982910
$960$	25.7003	0.829473
$961$	−28.0450	−0.904678
$962$	62.0928	2.00195
$963$	−16.4844	−0.531203
$964$	3.80642	0.122597
$965$	−2.23951	−0.0720923
$966$	37.1240	1.19444
$967$	16.8015	0.540300	0.270150	−	0.962818i	$-0.412927\pi$
$967$	16.8015	0.540300	0.270150	+	0.962818i	$0.412927\pi$
$968$	39.9940	1.28546
$969$	−14.2222	−0.456881
$970$	−22.5575	−0.724279
$971$	38.3640	1.23116	0.615579	−	0.788075i	$-0.288922\pi$
$971$	38.3640	1.23116	0.615579	+	0.788075i	$0.288922\pi$
$972$	−4.73143	−0.151761
$973$	12.0633	0.386731
$974$	39.3349	1.26037
$975$	18.6637	0.597717
$976$	6.49193	0.207801
$977$	31.6356	1.01211	0.506056	−	0.862500i	$-0.331103\pi$
$977$	31.6356	1.01211	0.506056	+	0.862500i	$0.331103\pi$
$978$	−20.9906	−0.671206
$979$	14.4603	0.462153
$980$	−2.45536	−0.0784336
$981$	−43.1022	−1.37615
$982$	−3.27469	−0.104500
$983$	−35.3733	−1.12823	−0.564117	−	0.825695i	$-0.690783\pi$
$983$	−35.3733	−1.12823	−0.564117	+	0.825695i	$0.690783\pi$
$984$	30.0731	0.958696
$985$	10.5620	0.336533
$986$	−2.60793	−0.0830533
$987$	−56.2864	−1.79162
$988$	7.70471	0.245120
$989$	−7.57136	−0.240755
$990$	32.3225	1.02728
$991$	24.6953	0.784474	0.392237	−	0.919864i	$-0.371701\pi$
$991$	24.6953	0.784474	0.392237	+	0.919864i	$0.371701\pi$
$992$	−4.96343	−0.157589
$993$	19.0094	0.603244
$994$	−6.61543	−0.209829
$995$	−3.18421	−0.100946
$996$	−11.1842	−0.354385
$997$	−11.4050	−0.361199	−0.180600	−	0.983557i	$-0.557804\pi$
$997$	−11.4050	−0.361199	−0.180600	+	0.983557i	$0.557804\pi$
$998$	−17.6949	−0.560121
$999$	−56.0830	−1.77439

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	145.2.a.d.1.1	✓	3
3.2	odd	2		1305.2.a.o.1.3		3
4.3	odd	2		2320.2.a.s.1.3		3
5.2	odd	4		725.2.b.d.349.3		6
5.3	odd	4		725.2.b.d.349.4		6
5.4	even	2		725.2.a.d.1.3		3
7.6	odd	2		7105.2.a.p.1.1		3
8.3	odd	2		9280.2.a.bm.1.1		3
8.5	even	2		9280.2.a.bu.1.3		3
15.14	odd	2		6525.2.a.bh.1.1		3
29.28	even	2		4205.2.a.e.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.a.d.1.1	✓	3	1.1	even	1	trivial
725.2.a.d.1.3		3	5.4	even	2
725.2.b.d.349.3		6	5.2	odd	4
725.2.b.d.349.4		6	5.3	odd	4
1305.2.a.o.1.3		3	3.2	odd	2
2320.2.a.s.1.3		3	4.3	odd	2
4205.2.a.e.1.3		3	29.28	even	2
6525.2.a.bh.1.1		3	15.14	odd	2
7105.2.a.p.1.1		3	7.6	odd	2
9280.2.a.bm.1.1		3	8.3	odd	2
9280.2.a.bu.1.3		3	8.5	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	145.a (trivial)

\(f(q)\)	\(=\)	\(q-1.21432 q^{2} -2.90321 q^{3} -0.525428 q^{4} -1.00000 q^{5} +3.52543 q^{6} +1.52543 q^{7} +3.06668 q^{8} +5.42864 q^{9} +1.21432 q^{10} +4.90321 q^{11} +1.52543 q^{12} -6.42864 q^{13} -1.85236 q^{14} +2.90321 q^{15} -2.67307 q^{16} +2.14764 q^{17} -6.59210 q^{18} +2.28100 q^{19} +0.525428 q^{20} -4.42864 q^{21} -5.95407 q^{22} +6.90321 q^{23} -8.90321 q^{24} +1.00000 q^{25} +7.80642 q^{26} -7.05086 q^{27} -0.801502 q^{28} +1.00000 q^{29} -3.52543 q^{30} +1.71900 q^{31} -2.88739 q^{32} -14.2351 q^{33} -2.60793 q^{34} -1.52543 q^{35} -2.85236 q^{36} +7.95407 q^{37} -2.76986 q^{38} +18.6637 q^{39} -3.06668 q^{40} -3.37778 q^{41} +5.37778 q^{42} -1.09679 q^{43} -2.57628 q^{44} -5.42864 q^{45} -8.38271 q^{46} +12.7096 q^{47} +7.76049 q^{48} -4.67307 q^{49} -1.21432 q^{50} -6.23506 q^{51} +3.37778 q^{52} +3.37778 q^{53} +8.56199 q^{54} -4.90321 q^{55} +4.67799 q^{56} -6.62222 q^{57} -1.21432 q^{58} -3.18421 q^{59} -1.52543 q^{60} -2.42864 q^{61} -2.08742 q^{62} +8.28100 q^{63} +8.85236 q^{64} +6.42864 q^{65} +17.2859 q^{66} -1.09679 q^{67} -1.12843 q^{68} -20.0415 q^{69} +1.85236 q^{70} +3.57136 q^{71} +16.6479 q^{72} +14.1891 q^{73} -9.65878 q^{74} -2.90321 q^{75} -1.19850 q^{76} +7.47949 q^{77} -22.6637 q^{78} +0.341219 q^{79} +2.67307 q^{80} +4.18421 q^{81} +4.10171 q^{82} -7.33185 q^{83} +2.32693 q^{84} -2.14764 q^{85} +1.33185 q^{86} -2.90321 q^{87} +15.0366 q^{88} +2.94914 q^{89} +6.59210 q^{90} -9.80642 q^{91} -3.62714 q^{92} -4.99063 q^{93} -15.4336 q^{94} -2.28100 q^{95} +8.38271 q^{96} -18.5763 q^{97} +5.67460 q^{98} +26.6178 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 2 q^{3} + 5 q^{4} - 3 q^{5} + 4 q^{6} - 2 q^{7} + 9 q^{8} + 3 q^{9} - 3 q^{10} + 8 q^{11} - 2 q^{12} - 6 q^{13} - 12 q^{14} + 2 q^{15} + 5 q^{16} - 13 q^{18} - 5 q^{20} + 2 q^{22} + 14 q^{23}+ \cdots + 20 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 2 * q^3 + 5 * q^4 - 3 * q^5 + 4 * q^6 - 2 * q^7 + 9 * q^8 + 3 * q^9 - 3 * q^10 + 8 * q^11 - 2 * q^12 - 6 * q^13 - 12 * q^14 + 2 * q^15 + 5 * q^16 - 13 * q^18 - 5 * q^20 + 2 * q^22 + 14 * q^23 - 20 * q^24 + 3 * q^25 + 10 * q^26 - 8 * q^27 - 22 * q^28 + 3 * q^29 - 4 * q^30 + 12 * q^31 + 11 * q^32 - 16 * q^33 - 14 * q^34 + 2 * q^35 - 15 * q^36 + 4 * q^37 - 2 * q^38 + 16 * q^39 - 9 * q^40 - 10 * q^41 + 16 * q^42 - 10 * q^43 + 12 * q^44 - 3 * q^45 + 8 * q^46 + 18 * q^47 - 10 * q^48 - q^49 + 3 * q^50 + 8 * q^51 + 10 * q^52 + 10 * q^53 + 12 * q^54 - 8 * q^55 - 32 * q^56 - 20 * q^57 + 3 * q^58 + 4 * q^59 + 2 * q^60 + 6 * q^61 + 14 * q^62 + 18 * q^63 + 33 * q^64 + 6 * q^65 + 12 * q^66 - 10 * q^67 - 36 * q^68 - 20 * q^69 + 12 * q^70 + 24 * q^71 - 3 * q^72 - 4 * q^73 - 22 * q^74 - 2 * q^75 + 16 * q^76 - 4 * q^77 - 28 * q^78 + 8 * q^79 - 5 * q^80 - q^81 - 14 * q^82 - 2 * q^83 + 20 * q^84 - 16 * q^86 - 2 * q^87 + 38 * q^88 + 22 * q^89 + 13 * q^90 - 16 * q^91 + 22 * q^92 + 12 * q^93 - 8 * q^96 - 36 * q^97 + 23 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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