LMFDB - Embedded newform 147.4.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,4,Mod(1,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("147.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	147.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:	$8.67328077084$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
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			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	147.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.414214 q^{2} +3.00000 q^{3} -7.82843 q^{4} -0.100505 q^{5} -1.24264 q^{6} +6.55635 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-0.414214 q^{2} +3.00000 q^{3} -7.82843 q^{4} -0.100505 q^{5} -1.24264 q^{6} +6.55635 q^{8} +9.00000 q^{9} +0.0416306 q^{10} -43.9411 q^{11} -23.4853 q^{12} -16.6447 q^{13} -0.301515 q^{15} +59.9117 q^{16} -121.640 q^{17} -3.72792 q^{18} -127.113 q^{19} +0.786797 q^{20} +18.2010 q^{22} +53.5980 q^{23} +19.6690 q^{24} -124.990 q^{25} +6.89444 q^{26} +27.0000 q^{27} +235.681 q^{29} +0.124892 q^{30} -18.7107 q^{31} -77.2670 q^{32} -131.823 q^{33} +50.3848 q^{34} -70.4558 q^{36} -191.882 q^{37} +52.6518 q^{38} -49.9340 q^{39} -0.658946 q^{40} -319.713 q^{41} -218.579 q^{43} +343.990 q^{44} -0.904546 q^{45} -22.2010 q^{46} +401.553 q^{47} +179.735 q^{48} +51.7725 q^{50} -364.919 q^{51} +130.302 q^{52} +643.117 q^{53} -11.1838 q^{54} +4.41631 q^{55} -381.338 q^{57} -97.6224 q^{58} -11.6123 q^{59} +2.36039 q^{60} -12.2426 q^{61} +7.75022 q^{62} -447.288 q^{64} +1.67287 q^{65} +54.6030 q^{66} +669.048 q^{67} +952.247 q^{68} +160.794 q^{69} +822.098 q^{71} +59.0071 q^{72} +515.100 q^{73} +79.4802 q^{74} -374.970 q^{75} +995.092 q^{76} +20.6833 q^{78} -805.754 q^{79} -6.02143 q^{80} +81.0000 q^{81} +132.429 q^{82} -394.863 q^{83} +12.2254 q^{85} +90.5382 q^{86} +707.044 q^{87} -288.093 q^{88} +673.418 q^{89} +0.374675 q^{90} -419.588 q^{92} -56.1320 q^{93} -166.329 q^{94} +12.7755 q^{95} -231.801 q^{96} -1091.11 q^{97} -395.470 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 6 q^{3} - 10 q^{4} - 20 q^{5} + 6 q^{6} - 18 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 6 * q^3 - 10 * q^4 - 20 * q^5 + 6 * q^6 - 18 * q^8 + 18 * q^9	\( 2 q + 2 q^{2} + 6 q^{3} - 10 q^{4} - 20 q^{5} + 6 q^{6} - 18 q^{8} + 18 q^{9} - 48 q^{10} - 20 q^{11} - 30 q^{12} - 104 q^{13} - 60 q^{15} + 18 q^{16} - 116 q^{17} + 18 q^{18} - 192 q^{19} + 44 q^{20} + 76 q^{22} + 28 q^{23} - 54 q^{24} + 146 q^{25} - 204 q^{26} + 54 q^{27} + 296 q^{29} - 144 q^{30} + 104 q^{31} + 18 q^{32} - 60 q^{33} + 64 q^{34} - 90 q^{36} - 248 q^{37} - 104 q^{38} - 312 q^{39} + 488 q^{40} - 20 q^{41} - 720 q^{43} + 292 q^{44} - 180 q^{45} - 84 q^{46} + 96 q^{47} + 54 q^{48} + 706 q^{50} - 348 q^{51} + 320 q^{52} + 268 q^{53} + 54 q^{54} - 472 q^{55} - 576 q^{57} + 48 q^{58} + 616 q^{59} + 132 q^{60} - 16 q^{61} + 304 q^{62} + 118 q^{64} + 1740 q^{65} + 228 q^{66} - 144 q^{67} + 940 q^{68} + 84 q^{69} + 988 q^{71} - 162 q^{72} - 104 q^{73} - 56 q^{74} + 438 q^{75} + 1136 q^{76} - 612 q^{78} - 944 q^{79} + 828 q^{80} + 162 q^{81} + 856 q^{82} - 1016 q^{83} - 100 q^{85} - 1120 q^{86} + 888 q^{87} - 876 q^{88} + 388 q^{89} - 432 q^{90} - 364 q^{92} + 312 q^{93} - 904 q^{94} + 1304 q^{95} + 54 q^{96} - 488 q^{97} - 180 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 6 * q^3 - 10 * q^4 - 20 * q^5 + 6 * q^6 - 18 * q^8 + 18 * q^9 - 48 * q^10 - 20 * q^11 - 30 * q^12 - 104 * q^13 - 60 * q^15 + 18 * q^16 - 116 * q^17 + 18 * q^18 - 192 * q^19 + 44 * q^20 + 76 * q^22 + 28 * q^23 - 54 * q^24 + 146 * q^25 - 204 * q^26 + 54 * q^27 + 296 * q^29 - 144 * q^30 + 104 * q^31 + 18 * q^32 - 60 * q^33 + 64 * q^34 - 90 * q^36 - 248 * q^37 - 104 * q^38 - 312 * q^39 + 488 * q^40 - 20 * q^41 - 720 * q^43 + 292 * q^44 - 180 * q^45 - 84 * q^46 + 96 * q^47 + 54 * q^48 + 706 * q^50 - 348 * q^51 + 320 * q^52 + 268 * q^53 + 54 * q^54 - 472 * q^55 - 576 * q^57 + 48 * q^58 + 616 * q^59 + 132 * q^60 - 16 * q^61 + 304 * q^62 + 118 * q^64 + 1740 * q^65 + 228 * q^66 - 144 * q^67 + 940 * q^68 + 84 * q^69 + 988 * q^71 - 162 * q^72 - 104 * q^73 - 56 * q^74 + 438 * q^75 + 1136 * q^76 - 612 * q^78 - 944 * q^79 + 828 * q^80 + 162 * q^81 + 856 * q^82 - 1016 * q^83 - 100 * q^85 - 1120 * q^86 + 888 * q^87 - 876 * q^88 + 388 * q^89 - 432 * q^90 - 364 * q^92 + 312 * q^93 - 904 * q^94 + 1304 * q^95 + 54 * q^96 - 488 * q^97 - 180 * 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 $

$2$	−0.414214	−0.146447	−0.0732233	−	0.997316i	$-0.523329\pi$
$2$	−0.414214	−0.146447	−0.0732233	+	0.997316i	$0.523329\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−7.82843	−0.978553
$5$	−0.100505	−0.00898945	−0.00449472	−	0.999990i	$-0.501431\pi$
$5$	−0.100505	−0.00898945	−0.00449472	+	0.999990i	$0.501431\pi$
$6$	−1.24264	−0.0845510
$7$	0	0
$7$	0	0
$8$	6.55635	0.289752
$9$	9.00000	0.333333
$10$	0.0416306	0.00131647
$11$	−43.9411	−1.20443	−0.602216	−	0.798333i	$-0.705715\pi$
$11$	−43.9411	−1.20443	−0.602216	+	0.798333i	$0.705715\pi$
$12$	−23.4853	−0.564968
$13$	−16.6447	−0.355108	−0.177554	−	0.984111i	$-0.556818\pi$
$13$	−16.6447	−0.355108	−0.177554	+	0.984111i	$0.556818\pi$
$14$	0	0
$15$	−0.301515	−0.00519006
$16$	59.9117	0.936120
$17$	−121.640	−1.73541	−0.867704	−	0.497081i	$-0.834405\pi$
$17$	−121.640	−1.73541	−0.867704	+	0.497081i	$0.834405\pi$
$18$	−3.72792	−0.0488155
$19$	−127.113	−1.53482	−0.767412	−	0.641154i	$-0.778456\pi$
$19$	−127.113	−1.53482	−0.767412	+	0.641154i	$0.778456\pi$
$20$	0.786797	0.00879665
$21$	0	0
$22$	18.2010	0.176385
$23$	53.5980	0.485911	0.242955	−	0.970037i	$-0.421883\pi$
$23$	53.5980	0.485911	0.242955	+	0.970037i	$0.421883\pi$
$24$	19.6690	0.167289
$25$	−124.990	−0.999919
$26$	6.89444	0.0520043
$27$	27.0000	0.192450
$28$	0	0
$29$	235.681	1.50913	0.754567	−	0.656223i	$-0.227847\pi$
$29$	235.681	1.50913	0.754567	+	0.656223i	$0.227847\pi$
$30$	0.124892	0.000760067 0
$31$	−18.7107	−0.108404	−0.0542022	−	0.998530i	$-0.517262\pi$
$31$	−18.7107	−0.108404	−0.0542022	+	0.998530i	$0.517262\pi$
$32$	−77.2670	−0.426844
$33$	−131.823	−0.695379
$34$	50.3848	0.254145
$35$	0	0
$36$	−70.4558	−0.326184
$37$	−191.882	−0.852574	−0.426287	−	0.904588i	$-0.640179\pi$
$37$	−191.882	−0.852574	−0.426287	+	0.904588i	$0.640179\pi$
$38$	52.6518	0.224770
$39$	−49.9340	−0.205021
$40$	−0.658946	−0.00260471
$41$	−319.713	−1.21782	−0.608912	−	0.793238i	$-0.708394\pi$
$41$	−319.713	−1.21782	−0.608912	+	0.793238i	$0.708394\pi$
$42$	0	0
$43$	−218.579	−0.775184	−0.387592	−	0.921831i	$-0.626693\pi$
$43$	−218.579	−0.775184	−0.387592	+	0.921831i	$0.626693\pi$
$44$	343.990	1.17860
$45$	−0.904546	−0.00299648
$46$	−22.2010	−0.0711600
$47$	401.553	1.24623	0.623113	−	0.782132i	$-0.285868\pi$
$47$	401.553	1.24623	0.623113	+	0.782132i	$0.285868\pi$
$48$	179.735	0.540469
$49$	0	0
$50$	51.7725	0.146435
$51$	−364.919	−1.00194
$52$	130.302	0.347492
$53$	643.117	1.66677	0.833386	−	0.552692i	$-0.186399\pi$
$53$	643.117	1.66677	0.833386	+	0.552692i	$0.186399\pi$
$54$	−11.1838	−0.0281837
$55$	4.41631	0.0108272
$56$	0	0
$57$	−381.338	−0.886131
$58$	−97.6224	−0.221008
$59$	−11.6123	−0.0256235	−0.0128118	−	0.999918i	$-0.504078\pi$
$59$	−11.6123	−0.0256235	−0.0128118	+	0.999918i	$0.504078\pi$
$60$	2.36039	0.00507875
$61$	−12.2426	−0.0256969	−0.0128484	−	0.999917i	$-0.504090\pi$
$61$	−12.2426	−0.0256969	−0.0128484	+	0.999917i	$0.504090\pi$
$62$	7.75022	0.0158755
$63$	0	0
$64$	−447.288	−0.873610
$65$	1.67287	0.00319222
$66$	54.6030	0.101836
$67$	669.048	1.21996	0.609979	−	0.792417i	$-0.291178\pi$
$67$	669.048	1.21996	0.609979	+	0.792417i	$0.291178\pi$
$68$	952.247	1.69819
$69$	160.794	0.280541
$70$	0	0
$71$	822.098	1.37416	0.687078	−	0.726584i	$-0.258893\pi$
$71$	822.098	1.37416	0.687078	+	0.726584i	$0.258893\pi$
$72$	59.0071	0.0965841
$73$	515.100	0.825861	0.412930	−	0.910763i	$-0.364505\pi$
$73$	515.100	0.825861	0.412930	+	0.910763i	$0.364505\pi$
$74$	79.4802	0.124857
$75$	−374.970	−0.577304
$76$	995.092	1.50191
$77$	0	0
$78$	20.6833	0.0300247
$79$	−805.754	−1.14752	−0.573762	−	0.819022i	$-0.694517\pi$
$79$	−805.754	−1.14752	−0.573762	+	0.819022i	$0.694517\pi$
$80$	−6.02143	−0.00841520
$81$	81.0000	0.111111
$82$	132.429	0.178346
$83$	−394.863	−0.522191	−0.261095	−	0.965313i	$-0.584084\pi$
$83$	−394.863	−0.522191	−0.261095	+	0.965313i	$0.584084\pi$
$84$	0	0
$85$	12.2254	0.0156004
$86$	90.5382	0.113523
$87$	707.044	0.871299
$88$	−288.093	−0.348987
$89$	673.418	0.802047	0.401024	−	0.916068i	$-0.368655\pi$
$89$	673.418	0.802047	0.401024	+	0.916068i	$0.368655\pi$
$90$	0.374675	0.000438825 0
$91$	0	0
$92$	−419.588	−0.475490
$93$	−56.1320	−0.0625873
$94$	−166.329	−0.182505
$95$	12.7755	0.0137972
$96$	−231.801	−0.246439
$97$	−1091.11	−1.14212	−0.571061	−	0.820908i	$-0.693468\pi$
$97$	−1091.11	−1.14212	−0.571061	+	0.820908i	$0.693468\pi$
$98$	0	0
$99$	−395.470	−0.401477
$100$	978.474	0.978474
$101$	−1370.79	−1.35048	−0.675242	−	0.737597i	$-0.735961\pi$
$101$	−1370.79	−1.35048	−0.675242	+	0.737597i	$0.735961\pi$
$102$	151.154	0.146730
$103$	−1413.96	−1.35263	−0.676316	−	0.736611i	$-0.736425\pi$
$103$	−1413.96	−1.35263	−0.676316	+	0.736611i	$0.736425\pi$
$104$	−109.128	−0.102893
$105$	0	0
$106$	−266.388	−0.244093
$107$	−343.539	−0.310385	−0.155192	−	0.987884i	$-0.549600\pi$
$107$	−343.539	−0.310385	−0.155192	+	0.987884i	$0.549600\pi$
$108$	−211.368	−0.188323
$109$	−317.657	−0.279138	−0.139569	−	0.990212i	$-0.544572\pi$
$109$	−317.657	−0.279138	−0.139569	+	0.990212i	$0.544572\pi$
$110$	−1.82929	−0.00158560
$111$	−575.647	−0.492234
$112$	0	0
$113$	798.373	0.664643	0.332321	−	0.943166i	$-0.392168\pi$
$113$	798.373	0.664643	0.332321	+	0.943166i	$0.392168\pi$
$114$	157.955	0.129771
$115$	−5.38687	−0.00436807
$116$	−1845.01	−1.47677
$117$	−149.802	−0.118369
$118$	4.80996	0.00375248
$119$	0	0
$120$	−1.97684	−0.00150383
$121$	599.823	0.450656
$122$	5.07107	0.00376322
$123$	−959.138	−0.703110
$124$	146.475	0.106080
$125$	25.1253	0.0179782
$126$	0	0
$127$	1071.40	0.748593	0.374297	−	0.927309i	$-0.377884\pi$
$127$	1071.40	0.748593	0.374297	+	0.927309i	$0.377884\pi$
$128$	803.409	0.554781
$129$	−655.736	−0.447553
$130$	−0.692927	−0.000467490 0
$131$	−2515.02	−1.67739	−0.838695	−	0.544601i	$-0.816681\pi$
$131$	−2515.02	−1.67739	−0.838695	+	0.544601i	$0.816681\pi$
$132$	1031.97	0.680465
$133$	0	0
$134$	−277.129	−0.178659
$135$	−2.71364	−0.00173002
$136$	−797.512	−0.502839
$137$	251.064	0.156568	0.0782841	−	0.996931i	$-0.475056\pi$
$137$	251.064	0.156568	0.0782841	+	0.996931i	$0.475056\pi$
$138$	−66.6030	−0.0410842
$139$	886.067	0.540685	0.270343	−	0.962764i	$-0.412863\pi$
$139$	886.067	0.540685	0.270343	+	0.962764i	$0.412863\pi$
$140$	0	0
$141$	1204.66	0.719508
$142$	−340.524	−0.201240
$143$	731.385	0.427703
$144$	539.205	0.312040
$145$	−23.6872	−0.0135663
$146$	−213.361	−0.120945
$147$	0	0
$148$	1502.14	0.834289
$149$	582.626	0.320339	0.160170	−	0.987090i	$-0.448796\pi$
$149$	582.626	0.320339	0.160170	+	0.987090i	$0.448796\pi$
$150$	155.318	0.0845442
$151$	−2811.76	−1.51535	−0.757676	−	0.652631i	$-0.773665\pi$
$151$	−2811.76	−1.51535	−0.757676	+	0.652631i	$0.773665\pi$
$152$	−833.395	−0.444719
$153$	−1094.76	−0.578469
$154$	0	0
$155$	1.88052	0.000974496 0
$156$	390.905	0.200624
$157$	−1691.34	−0.859770	−0.429885	−	0.902884i	$-0.641446\pi$
$157$	−1691.34	−0.859770	−0.429885	+	0.902884i	$0.641446\pi$
$158$	333.754	0.168051
$159$	1929.35	0.962311
$160$	7.76573	0.00383709
$161$	0	0
$162$	−33.5513	−0.0162718
$163$	−40.7232	−0.0195686	−0.00978432	−	0.999952i	$-0.503114\pi$
$163$	−40.7232	−0.0195686	−0.00978432	+	0.999952i	$0.503114\pi$
$164$	2502.85	1.19170
$165$	13.2489	0.00625107
$166$	163.558	0.0764731
$167$	2900.47	1.34398	0.671990	−	0.740560i	$-0.265440\pi$
$167$	2900.47	1.34398	0.671990	+	0.740560i	$0.265440\pi$
$168$	0	0
$169$	−1919.96	−0.873899
$170$	−5.06393	−0.00228462
$171$	−1144.01	−0.511608
$172$	1711.13	0.758559
$173$	−2146.15	−0.943171	−0.471585	−	0.881820i	$-0.656318\pi$
$173$	−2146.15	−0.943171	−0.471585	+	0.881820i	$0.656318\pi$
$174$	−292.867	−0.127599
$175$	0	0
$176$	−2632.59	−1.12749
$177$	−34.8368	−0.0147938
$178$	−278.939	−0.117457
$179$	1203.54	0.502552	0.251276	−	0.967916i	$-0.419150\pi$
$179$	1203.54	0.502552	0.251276	+	0.967916i	$0.419150\pi$
$180$	7.08117	0.00293222
$181$	−2990.47	−1.22807	−0.614033	−	0.789280i	$-0.710454\pi$
$181$	−2990.47	−1.22807	−0.614033	+	0.789280i	$0.710454\pi$
$182$	0	0
$183$	−36.7279	−0.0148361
$184$	351.407	0.140794
$185$	19.2851	0.00766417
$186$	23.2506	0.00916570
$187$	5344.98	2.09018
$188$	−3143.53	−1.21950
$189$	0	0
$190$	−5.29177	−0.00202056
$191$	−2807.41	−1.06354	−0.531772	−	0.846887i	$-0.678474\pi$
$191$	−2807.41	−1.06354	−0.531772	+	0.846887i	$0.678474\pi$
$192$	−1341.87	−0.504379
$193$	3336.37	1.24434	0.622169	−	0.782883i	$-0.286252\pi$
$193$	3336.37	1.24434	0.622169	+	0.782883i	$0.286252\pi$
$194$	451.954	0.167260
$195$	5.01862	0.00184303
$196$	0	0
$197$	−4226.65	−1.52861	−0.764305	−	0.644855i	$-0.776918\pi$
$197$	−4226.65	−1.52861	−0.764305	+	0.644855i	$0.776918\pi$
$198$	163.809	0.0587950
$199$	4385.69	1.56228	0.781140	−	0.624356i	$-0.214639\pi$
$199$	4385.69	1.56228	0.781140	+	0.624356i	$0.214639\pi$
$200$	−819.477	−0.289729
$201$	2007.14	0.704343
$202$	567.800	0.197774
$203$	0	0
$204$	2856.74	0.980450
$205$	32.1328	0.0109476
$206$	585.680	0.198088
$207$	482.382	0.161970
$208$	−997.210	−0.332423
$209$	5585.48	1.84859
$210$	0	0
$211$	2291.56	0.747665	0.373833	−	0.927496i	$-0.378043\pi$
$211$	2291.56	0.747665	0.373833	+	0.927496i	$0.378043\pi$
$212$	−5034.59	−1.63103
$213$	2466.29	0.793369
$214$	142.299	0.0454548
$215$	21.9683	0.00696848
$216$	177.021	0.0557629
$217$	0	0
$218$	131.578	0.0408788
$219$	1545.30	0.476811
$220$	−34.5727	−0.0105950
$221$	2024.65	0.616257
$222$	238.441	0.0720860
$223$	−217.970	−0.0654544	−0.0327272	−	0.999464i	$-0.510419\pi$
$223$	−217.970	−0.0654544	−0.0327272	+	0.999464i	$0.510419\pi$
$224$	0	0
$225$	−1124.91	−0.333306
$226$	−330.697	−0.0973347
$227$	1835.36	0.536639	0.268320	−	0.963330i	$-0.413532\pi$
$227$	1835.36	0.536639	0.268320	+	0.963330i	$0.413532\pi$
$228$	2985.28	0.867126
$229$	2774.01	0.800488	0.400244	−	0.916409i	$-0.368925\pi$
$229$	2774.01	0.800488	0.400244	+	0.916409i	$0.368925\pi$
$230$	2.23131	0.000639689 0
$231$	0	0
$232$	1545.21	0.437275
$233$	−988.712	−0.277994	−0.138997	−	0.990293i	$-0.544388\pi$
$233$	−988.712	−0.277994	−0.138997	+	0.990293i	$0.544388\pi$
$234$	62.0500	0.0173348
$235$	−40.3581	−0.0112029
$236$	90.9058	0.0250740
$237$	−2417.26	−0.662524
$238$	0	0
$239$	−837.928	−0.226783	−0.113391	−	0.993550i	$-0.536171\pi$
$239$	−837.928	−0.226783	−0.113391	+	0.993550i	$0.536171\pi$
$240$	−18.0643	−0.00485852
$241$	−3454.99	−0.923466	−0.461733	−	0.887019i	$-0.652772\pi$
$241$	−3454.99	−0.923466	−0.461733	+	0.887019i	$0.652772\pi$
$242$	−248.455	−0.0659970
$243$	243.000	0.0641500
$244$	95.8406	0.0251458
$245$	0	0
$246$	397.288	0.102968
$247$	2115.75	0.545028
$248$	−122.674	−0.0314104
$249$	−1184.59	−0.301487
$250$	−10.4072	−0.00263284
$251$	5635.01	1.41705	0.708523	−	0.705688i	$-0.249362\pi$
$251$	5635.01	1.41705	0.708523	+	0.705688i	$0.249362\pi$
$252$	0	0
$253$	−2355.16	−0.585246
$254$	−443.788	−0.109629
$255$	36.6762	0.00900687
$256$	3245.52	0.792364
$257$	−2271.16	−0.551248	−0.275624	−	0.961265i	$-0.588885\pi$
$257$	−2271.16	−0.551248	−0.275624	+	0.961265i	$0.588885\pi$
$258$	271.615	0.0655426
$259$	0	0
$260$	−13.0960	−0.00312376
$261$	2121.13	0.503045
$262$	1041.75	0.245648
$263$	163.867	0.0384201	0.0192101	−	0.999815i	$-0.493885\pi$
$263$	163.867	0.0384201	0.0192101	+	0.999815i	$0.493885\pi$
$264$	−864.280	−0.201488
$265$	−64.6365	−0.0149834
$266$	0	0
$267$	2020.26	0.463062
$268$	−5237.59	−1.19379
$269$	−5167.10	−1.17116	−0.585582	−	0.810613i	$-0.699134\pi$
$269$	−5167.10	−1.17116	−0.585582	+	0.810613i	$0.699134\pi$
$270$	1.12403	0.000253356 0
$271$	−1622.27	−0.363638	−0.181819	−	0.983332i	$-0.558199\pi$
$271$	−1622.27	−0.363638	−0.181819	+	0.983332i	$0.558199\pi$
$272$	−7287.63	−1.62455
$273$	0	0
$274$	−103.994	−0.0229289
$275$	5492.20	1.20433
$276$	−1258.76	−0.274524
$277$	−4612.37	−1.00047	−0.500235	−	0.865890i	$-0.666753\pi$
$277$	−4612.37	−1.00047	−0.500235	+	0.865890i	$0.666753\pi$
$278$	−367.021	−0.0791815
$279$	−168.396	−0.0361348
$280$	0	0
$281$	−2125.22	−0.451174	−0.225587	−	0.974223i	$-0.572430\pi$
$281$	−2125.22	−0.451174	−0.225587	+	0.974223i	$0.572430\pi$
$282$	−498.987	−0.105370
$283$	2571.54	0.540149	0.270075	−	0.962839i	$-0.412952\pi$
$283$	2571.54	0.540149	0.270075	+	0.962839i	$0.412952\pi$
$284$	−6435.73	−1.34468
$285$	38.3264	0.00796583
$286$	−302.950	−0.0626356
$287$	0	0
$288$	−695.403	−0.142281
$289$	9883.19	2.01164
$290$	9.81154	0.00198674
$291$	−3273.34	−0.659404
$292$	−4032.42	−0.808149
$293$	−3324.96	−0.662957	−0.331478	−	0.943463i	$-0.607547\pi$
$293$	−3324.96	−0.662957	−0.331478	+	0.943463i	$0.607547\pi$
$294$	0	0
$295$	1.16709	0.000230341 0
$296$	−1258.05	−0.247035
$297$	−1186.41	−0.231793
$298$	−241.331	−0.0469126
$299$	−892.120	−0.172551
$300$	2935.42	0.564922
$301$	0	0
$302$	1164.67	0.221918
$303$	−4112.37	−0.779702
$304$	−7615.54	−1.43678
$305$	1.23045	0.000231001 0
$306$	453.463	0.0847149
$307$	887.096	0.164916	0.0824580	−	0.996595i	$-0.473723\pi$
$307$	887.096	0.164916	0.0824580	+	0.996595i	$0.473723\pi$
$308$	0	0
$309$	−4241.87	−0.780943
$310$	−0.778936	−0.000142712 0
$311$	4510.82	0.822460	0.411230	−	0.911532i	$-0.365099\pi$
$311$	4510.82	0.822460	0.411230	+	0.911532i	$0.365099\pi$
$312$	−327.385	−0.0594055
$313$	−3715.78	−0.671018	−0.335509	−	0.942037i	$-0.608908\pi$
$313$	−3715.78	−0.671018	−0.335509	+	0.942037i	$0.608908\pi$
$314$	700.577	0.125910
$315$	0	0
$316$	6307.79	1.12291
$317$	6954.52	1.23219	0.616096	−	0.787671i	$-0.288713\pi$
$317$	6954.52	1.23219	0.616096	+	0.787671i	$0.288713\pi$
$318$	−799.163	−0.140927
$319$	−10356.1	−1.81765
$320$	44.9548	0.00785327
$321$	−1030.62	−0.179201
$322$	0	0
$323$	15461.9	2.66355
$324$	−634.103	−0.108728
$325$	2080.41	0.355079
$326$	16.8681	0.00286576
$327$	−952.971	−0.161160
$328$	−2096.15	−0.352867
$329$	0	0
$330$	−5.48788	−0.000915448 0
$331$	−9863.18	−1.63785	−0.818926	−	0.573899i	$-0.805430\pi$
$331$	−9863.18	−1.63785	−0.818926	+	0.573899i	$0.805430\pi$
$332$	3091.16	0.510992
$333$	−1726.94	−0.284191
$334$	−1201.41	−0.196821
$335$	−67.2427	−0.0109668
$336$	0	0
$337$	−5945.06	−0.960974	−0.480487	−	0.877002i	$-0.659540\pi$
$337$	−5945.06	−0.960974	−0.480487	+	0.877002i	$0.659540\pi$
$338$	795.272	0.127979
$339$	2395.12	0.383732
$340$	−95.7056	−0.0152658
$341$	822.168	0.130566
$342$	473.866	0.0749232
$343$	0	0
$344$	−1433.08	−0.224612
$345$	−16.1606	−0.00252191
$346$	888.963	0.138124
$347$	1169.57	0.180939	0.0904697	−	0.995899i	$-0.471163\pi$
$347$	1169.57	0.180939	0.0904697	+	0.995899i	$0.471163\pi$
$348$	−5535.04	−0.852613
$349$	9176.66	1.40749	0.703747	−	0.710451i	$-0.251509\pi$
$349$	9176.66	1.40749	0.703747	+	0.710451i	$0.251509\pi$
$350$	0	0
$351$	−449.406	−0.0683405
$352$	3395.20	0.514104
$353$	−10587.2	−1.59632	−0.798158	−	0.602448i	$-0.794192\pi$
$353$	−10587.2	−1.59632	−0.798158	+	0.602448i	$0.794192\pi$
$354$	14.4299	0.00216649
$355$	−82.6250	−0.0123529
$356$	−5271.81	−0.784846
$357$	0	0
$358$	−498.522	−0.0735970
$359$	8615.21	1.26656	0.633278	−	0.773924i	$-0.281709\pi$
$359$	8615.21	1.26656	0.633278	+	0.773924i	$0.281709\pi$
$360$	−5.93052	−0.000868238 0
$361$	9298.64	1.35568
$362$	1238.69	0.179846
$363$	1799.47	0.260186
$364$	0	0
$365$	−51.7701	−0.00742403
$366$	15.2132	0.00217270
$367$	−8297.79	−1.18022	−0.590110	−	0.807323i	$-0.700916\pi$
$367$	−8297.79	−1.18022	−0.590110	+	0.807323i	$0.700916\pi$
$368$	3211.15	0.454871
$369$	−2877.41	−0.405941
$370$	−7.98817	−0.00112239
$371$	0	0
$372$	439.426	0.0612450
$373$	−5123.86	−0.711269	−0.355634	−	0.934625i	$-0.615735\pi$
$373$	−5123.86	−0.711269	−0.355634	+	0.934625i	$0.615735\pi$
$374$	−2213.96	−0.306100
$375$	75.3758	0.0103797
$376$	2632.72	0.361097
$377$	−3922.83	−0.535905
$378$	0	0
$379$	−1502.49	−0.203635	−0.101817	−	0.994803i	$-0.532466\pi$
$379$	−1502.49	−0.203635	−0.101817	+	0.994803i	$0.532466\pi$
$380$	−100.012	−0.0135013
$381$	3214.20	0.432200
$382$	1162.87	0.155753
$383$	10872.9	1.45060	0.725301	−	0.688431i	$-0.241700\pi$
$383$	10872.9	1.45060	0.725301	+	0.688431i	$0.241700\pi$
$384$	2410.23	0.320303
$385$	0	0
$386$	−1381.97	−0.182229
$387$	−1967.21	−0.258395
$388$	8541.71	1.11763
$389$	4618.99	0.602036	0.301018	−	0.953618i	$-0.402674\pi$
$389$	4618.99	0.602036	0.301018	+	0.953618i	$0.402674\pi$
$390$	−2.07878	−0.000269905 0
$391$	−6519.64	−0.843254
$392$	0	0
$393$	−7545.05	−0.968442
$394$	1750.73	0.223860
$395$	80.9824	0.0103156
$396$	3095.91	0.392867
$397$	−9606.95	−1.21451	−0.607253	−	0.794508i	$-0.707729\pi$
$397$	−9606.95	−1.21451	−0.607253	+	0.794508i	$0.707729\pi$
$398$	−1816.61	−0.228791
$399$	0	0
$400$	−7488.36	−0.936044
$401$	−10501.0	−1.30772	−0.653862	−	0.756614i	$-0.726852\pi$
$401$	−10501.0	−1.30772	−0.653862	+	0.756614i	$0.726852\pi$
$402$	−831.386	−0.103149
$403$	311.433	0.0384952
$404$	10731.1	1.32152
$405$	−8.14091	−0.000998827 0
$406$	0	0
$407$	8431.52	1.02687
$408$	−2392.54	−0.290314
$409$	12066.9	1.45885	0.729427	−	0.684059i	$-0.239787\pi$
$409$	12066.9	1.45885	0.729427	+	0.684059i	$0.239787\pi$
$410$	−13.3098	−0.00160323
$411$	753.192	0.0903947
$412$	11069.0	1.32362
$413$	0	0
$414$	−199.809	−0.0237200
$415$	39.6857	0.00469421
$416$	1286.08	0.151576
$417$	2658.20	0.312165
$418$	−2313.58	−0.270720
$419$	6366.31	0.742278	0.371139	−	0.928577i	$-0.378967\pi$
$419$	6366.31	0.742278	0.371139	+	0.928577i	$0.378967\pi$
$420$	0	0
$421$	−4731.84	−0.547781	−0.273890	−	0.961761i	$-0.588311\pi$
$421$	−4731.84	−0.547781	−0.273890	+	0.961761i	$0.588311\pi$
$422$	−949.194	−0.109493
$423$	3613.98	0.415408
$424$	4216.50	0.482951
$425$	15203.7	1.73527
$426$	−1021.57	−0.116186
$427$	0	0
$428$	2689.37	0.303728
$429$	2194.16	0.246934
$430$	−9.09955	−0.00102051
$431$	3752.78	0.419409	0.209704	−	0.977765i	$-0.432750\pi$
$431$	3752.78	0.419409	0.209704	+	0.977765i	$0.432750\pi$
$432$	1617.62	0.180156
$433$	−11709.2	−1.29956	−0.649780	−	0.760122i	$-0.725139\pi$
$433$	−11709.2	−1.29956	−0.649780	+	0.760122i	$0.725139\pi$
$434$	0	0
$435$	−71.0615	−0.00783250
$436$	2486.75	0.273151
$437$	−6812.98	−0.745788
$438$	−640.084	−0.0698274
$439$	14924.7	1.62259	0.811296	−	0.584635i	$-0.198762\pi$
$439$	14924.7	1.62259	0.811296	+	0.584635i	$0.198762\pi$
$440$	28.9548	0.00313720
$441$	0	0
$442$	−838.638	−0.0902487
$443$	−8517.66	−0.913513	−0.456756	−	0.889592i	$-0.650989\pi$
$443$	−8517.66	−0.913513	−0.456756	+	0.889592i	$0.650989\pi$
$444$	4506.41	0.481677
$445$	−67.6820	−0.00720996
$446$	90.2860	0.00958557
$447$	1747.88	0.184948
$448$	0	0
$449$	−5965.73	−0.627038	−0.313519	−	0.949582i	$-0.601508\pi$
$449$	−5965.73	−0.627038	−0.313519	+	0.949582i	$0.601508\pi$
$450$	465.953	0.0488116
$451$	14048.5	1.46678
$452$	−6250.01	−0.650389
$453$	−8435.29	−0.874889
$454$	−760.231	−0.0785890
$455$	0	0
$456$	−2500.19	−0.256759
$457$	−13860.6	−1.41875	−0.709376	−	0.704830i	$-0.751023\pi$
$457$	−13860.6	−1.41875	−0.709376	+	0.704830i	$0.751023\pi$
$458$	−1149.03	−0.117229
$459$	−3284.27	−0.333979
$460$	42.1707	0.00427439
$461$	149.312	0.0150850	0.00754249	−	0.999972i	$-0.497599\pi$
$461$	149.312	0.0150850	0.00754249	+	0.999972i	$0.497599\pi$
$462$	0	0
$463$	5403.95	0.542425	0.271213	−	0.962519i	$-0.412575\pi$
$463$	5403.95	0.542425	0.271213	+	0.962519i	$0.412575\pi$
$464$	14120.1	1.41273
$465$	5.64155	0.000562625 0
$466$	409.538	0.0407113
$467$	−3704.66	−0.367090	−0.183545	−	0.983011i	$-0.558757\pi$
$467$	−3704.66	−0.367090	−0.183545	+	0.983011i	$0.558757\pi$
$468$	1172.71	0.115831
$469$	0	0
$470$	16.7169	0.00164062
$471$	−5074.03	−0.496389
$472$	−76.1341	−0.00742448
$473$	9604.59	0.933657
$474$	1001.26	0.0970244
$475$	15887.8	1.53470
$476$	0	0
$477$	5788.05	0.555591
$478$	347.081	0.0332115
$479$	10671.8	1.01796	0.508982	−	0.860777i	$-0.330022\pi$
$479$	10671.8	1.01796	0.508982	+	0.860777i	$0.330022\pi$
$480$	23.2972	0.00221535
$481$	3193.82	0.302756
$482$	1431.10	0.135238
$483$	0	0
$484$	−4695.67	−0.440990
$485$	109.662	0.0102670
$486$	−100.654	−0.00939455
$487$	5853.92	0.544695	0.272348	−	0.962199i	$-0.412200\pi$
$487$	5853.92	0.544695	0.272348	+	0.962199i	$0.412200\pi$
$488$	−80.2670	−0.00744573
$489$	−122.170	−0.0112980
$490$	0	0
$491$	4065.31	0.373656	0.186828	−	0.982393i	$-0.440179\pi$
$491$	4065.31	0.373656	0.186828	+	0.982393i	$0.440179\pi$
$492$	7508.54	0.688031
$493$	−28668.2	−2.61896
$494$	−876.371	−0.0798174
$495$	39.7468	0.00360906
$496$	−1120.99	−0.101480
$497$	0	0
$498$	490.673	0.0441517
$499$	4811.19	0.431620	0.215810	−	0.976435i	$-0.430761\pi$
$499$	4811.19	0.431620	0.215810	+	0.976435i	$0.430761\pi$
$500$	−196.691	−0.0175926
$501$	8701.40	0.775947
$502$	−2334.10	−0.207522
$503$	−17001.2	−1.50705	−0.753526	−	0.657418i	$-0.771649\pi$
$503$	−17001.2	−1.50705	−0.753526	+	0.657418i	$0.771649\pi$
$504$	0	0
$505$	137.771	0.0121401
$506$	975.537	0.0857074
$507$	−5759.87	−0.504546
$508$	−8387.37	−0.732538
$509$	−13797.2	−1.20148	−0.600738	−	0.799446i	$-0.705126\pi$
$509$	−13797.2	−1.20148	−0.600738	+	0.799446i	$0.705126\pi$
$510$	−15.1918	−0.00131903
$511$	0	0
$512$	−7771.61	−0.670820
$513$	−3432.04	−0.295377
$514$	940.744	0.0807284
$515$	142.110	0.0121594
$516$	5133.38	0.437954
$517$	−17644.7	−1.50099
$518$	0	0
$519$	−6438.44	−0.544540
$520$	10.9679	0.000924954 0
$521$	−3936.61	−0.331029	−0.165515	−	0.986207i	$-0.552928\pi$
$521$	−3936.61	−0.331029	−0.165515	+	0.986207i	$0.552928\pi$
$522$	−878.601	−0.0736692
$523$	−17459.3	−1.45973	−0.729866	−	0.683590i	$-0.760418\pi$
$523$	−17459.3	−1.45973	−0.729866	+	0.683590i	$0.760418\pi$
$524$	19688.6	1.64142
$525$	0	0
$526$	−67.8760	−0.00562649
$527$	2275.96	0.188126
$528$	−7897.76	−0.650958
$529$	−9294.26	−0.763891
$530$	26.7733	0.00219426
$531$	−104.510	−0.00854118
$532$	0	0
$533$	5321.51	0.432458
$534$	−836.817	−0.0678139
$535$	34.5274	0.00279019
$536$	4386.51	0.353486
$537$	3610.62	0.290148
$538$	2140.28	0.171513
$539$	0	0
$540$	21.2435	0.00169292
$541$	19101.3	1.51798	0.758992	−	0.651100i	$-0.225692\pi$
$541$	19101.3	1.51798	0.758992	+	0.651100i	$0.225692\pi$
$542$	671.967	0.0532536
$543$	−8971.41	−0.709024
$544$	9398.73	0.740749
$545$	31.9261	0.00250929
$546$	0	0
$547$	15413.5	1.20481	0.602407	−	0.798189i	$-0.294208\pi$
$547$	15413.5	1.20481	0.602407	+	0.798189i	$0.294208\pi$
$548$	−1965.44	−0.153210
$549$	−110.184	−0.00856563
$550$	−2274.94	−0.176371
$551$	−29958.1	−2.31626
$552$	1054.22	0.0812874
$553$	0	0
$554$	1910.51	0.146516
$555$	57.8554	0.00442491
$556$	−6936.51	−0.529089
$557$	−20492.9	−1.55891	−0.779453	−	0.626460i	$-0.784503\pi$
$557$	−20492.9	−1.55891	−0.779453	+	0.626460i	$0.784503\pi$
$558$	69.7519	0.00529182
$559$	3638.17	0.275274
$560$	0	0
$561$	16034.9	1.20677
$562$	880.294	0.0660729
$563$	7142.49	0.534671	0.267336	−	0.963603i	$-0.413857\pi$
$563$	7142.49	0.534671	0.267336	+	0.963603i	$0.413857\pi$
$564$	−9430.59	−0.704077
$565$	−80.2406	−0.00597477
$566$	−1065.17	−0.0791030
$567$	0	0
$568$	5389.96	0.398165
$569$	4097.91	0.301922	0.150961	−	0.988540i	$-0.451763\pi$
$569$	4097.91	0.301922	0.150961	+	0.988540i	$0.451763\pi$
$570$	−15.8753	−0.00116657
$571$	−2838.48	−0.208033	−0.104016	−	0.994576i	$-0.533169\pi$
$571$	−2838.48	−0.208033	−0.104016	+	0.994576i	$0.533169\pi$
$572$	−5725.60	−0.418530
$573$	−8422.23	−0.614038
$574$	0	0
$575$	−6699.21	−0.485872
$576$	−4025.60	−0.291203
$577$	15464.5	1.11576	0.557881	−	0.829921i	$-0.311615\pi$
$577$	15464.5	1.11576	0.557881	+	0.829921i	$0.311615\pi$
$578$	−4093.75	−0.294598
$579$	10009.1	0.718418
$580$	185.433	0.0132753
$581$	0	0
$582$	1355.86	0.0965675
$583$	−28259.3	−2.00751
$584$	3377.17	0.239295
$585$	15.0559	0.00106407
$586$	1377.24	0.0970878
$587$	−14003.6	−0.984652	−0.492326	−	0.870411i	$-0.663853\pi$
$587$	−14003.6	−0.984652	−0.492326	+	0.870411i	$0.663853\pi$
$588$	0	0
$589$	2378.36	0.166382
$590$	−0.483425	−3.37327e−5 0
$591$	−12679.9	−0.882543
$592$	−11496.0	−0.798112
$593$	−6504.50	−0.450435	−0.225217	−	0.974309i	$-0.572309\pi$
$593$	−6504.50	−0.450435	−0.225217	+	0.974309i	$0.572309\pi$
$594$	491.427	0.0339453
$595$	0	0
$596$	−4561.04	−0.313469
$597$	13157.1	0.901982
$598$	369.528	0.0252695
$599$	−12616.1	−0.860567	−0.430284	−	0.902694i	$-0.641586\pi$
$599$	−12616.1	−0.860567	−0.430284	+	0.902694i	$0.641586\pi$
$600$	−2458.43	−0.167275
$601$	−8270.87	−0.561358	−0.280679	−	0.959802i	$-0.590560\pi$
$601$	−8270.87	−0.561358	−0.280679	+	0.959802i	$0.590560\pi$
$602$	0	0
$603$	6021.43	0.406653
$604$	22011.7	1.48285
$605$	−60.2852	−0.00405114
$606$	1703.40	0.114185
$607$	−3811.84	−0.254889	−0.127445	−	0.991846i	$-0.540677\pi$
$607$	−3811.84	−0.254889	−0.127445	+	0.991846i	$0.540677\pi$
$608$	9821.62	0.655130
$609$	0	0
$610$	−0.509668	−3.38293e−5 0
$611$	−6683.72	−0.442544
$612$	8570.22	0.566063
$613$	11359.3	0.748445	0.374222	−	0.927339i	$-0.377910\pi$
$613$	11359.3	0.748445	0.374222	+	0.927339i	$0.377910\pi$
$614$	−367.447	−0.0241514
$615$	96.3983	0.00632057
$616$	0	0
$617$	−18272.2	−1.19224	−0.596118	−	0.802896i	$-0.703291\pi$
$617$	−18272.2	−1.19224	−0.596118	+	0.802896i	$0.703291\pi$
$618$	1757.04	0.114366
$619$	−29600.2	−1.92203	−0.961013	−	0.276503i	$-0.910824\pi$
$619$	−29600.2	−1.92203	−0.961013	+	0.276503i	$0.910824\pi$
$620$	−14.7215	−0.000953596 0
$621$	1447.15	0.0935136
$622$	−1868.44	−0.120447
$623$	0	0
$624$	−2991.63	−0.191925
$625$	15621.2	0.999758
$626$	1539.13	0.0982682
$627$	16756.4	1.06728
$628$	13240.6	0.841331
$629$	23340.5	1.47956
$630$	0	0
$631$	7185.41	0.453322	0.226661	−	0.973974i	$-0.427219\pi$
$631$	7185.41	0.453322	0.226661	+	0.973974i	$0.427219\pi$
$632$	−5282.81	−0.332498
$633$	6874.67	0.431665
$634$	−2880.66	−0.180450
$635$	−107.681	−0.00672944
$636$	−15103.8	−0.941673
$637$	0	0
$638$	4289.64	0.266189
$639$	7398.88	0.458052
$640$	−80.7467	−0.00498718
$641$	−232.982	−0.0143561	−0.00717803	−	0.999974i	$-0.502285\pi$
$641$	−232.982	−0.0143561	−0.00717803	+	0.999974i	$0.502285\pi$
$642$	426.896	0.0262433
$643$	1837.96	0.112725	0.0563624	−	0.998410i	$-0.482050\pi$
$643$	1837.96	0.112725	0.0563624	+	0.998410i	$0.482050\pi$
$644$	0	0
$645$	65.9048	0.00402325
$646$	−6404.54	−0.390067
$647$	18594.7	1.12988	0.564941	−	0.825131i	$-0.308899\pi$
$647$	18594.7	1.12988	0.564941	+	0.825131i	$0.308899\pi$
$648$	531.064	0.0321947
$649$	510.256	0.0308618
$650$	−861.736	−0.0520001
$651$	0	0
$652$	318.799	0.0191490
$653$	−28864.7	−1.72980	−0.864902	−	0.501940i	$-0.832620\pi$
$653$	−28864.7	−1.72980	−0.864902	+	0.501940i	$0.832620\pi$
$654$	394.733	0.0236014
$655$	252.772	0.0150788
$656$	−19154.5	−1.14003
$657$	4635.90	0.275287
$658$	0	0
$659$	−29066.3	−1.71815	−0.859076	−	0.511847i	$-0.828961\pi$
$659$	−29066.3	−1.71815	−0.859076	+	0.511847i	$0.828961\pi$
$660$	−103.718	−0.00611701
$661$	3979.51	0.234168	0.117084	−	0.993122i	$-0.462645\pi$
$661$	3979.51	0.234168	0.117084	+	0.993122i	$0.462645\pi$
$662$	4085.46	0.239858
$663$	6073.95	0.355796
$664$	−2588.86	−0.151306
$665$	0	0
$666$	715.322	0.0416189
$667$	12632.0	0.733305
$668$	−22706.1	−1.31516
$669$	−653.909	−0.0377901
$670$	27.8528	0.00160604
$671$	537.955	0.0309501
$672$	0	0
$673$	−184.229	−0.0105520	−0.00527601	−	0.999986i	$-0.501679\pi$
$673$	−184.229	−0.0105520	−0.00527601	+	0.999986i	$0.501679\pi$
$674$	2462.52	0.140731
$675$	−3374.73	−0.192435
$676$	15030.2	0.855156
$677$	16683.5	0.947116	0.473558	−	0.880763i	$-0.342969\pi$
$677$	16683.5	0.947116	0.473558	+	0.880763i	$0.342969\pi$
$678$	−992.091	−0.0561962
$679$	0	0
$680$	80.1540	0.00452024
$681$	5506.08	0.309829
$682$	−340.553	−0.0191209
$683$	17808.2	0.997676	0.498838	−	0.866695i	$-0.333760\pi$
$683$	17808.2	0.997676	0.498838	+	0.866695i	$0.333760\pi$
$684$	8955.83	0.500636
$685$	−25.2332	−0.00140746
$686$	0	0
$687$	8322.03	0.462162
$688$	−13095.4	−0.725666
$689$	−10704.5	−0.591883
$690$	6.69394	0.000369325 0
$691$	20145.7	1.10908	0.554542	−	0.832156i	$-0.312894\pi$
$691$	20145.7	1.10908	0.554542	+	0.832156i	$0.312894\pi$
$692$	16801.0	0.922943
$693$	0	0
$694$	−484.453	−0.0264980
$695$	−89.0542	−0.00486046
$696$	4635.63	0.252461
$697$	38889.7	2.11342
$698$	−3801.10	−0.206123
$699$	−2966.14	−0.160500
$700$	0	0
$701$	−2719.67	−0.146534	−0.0732672	−	0.997312i	$-0.523343\pi$
$701$	−2719.67	−0.146534	−0.0732672	+	0.997312i	$0.523343\pi$
$702$	186.150	0.0100082
$703$	24390.7	1.30855
$704$	19654.4	1.05220
$705$	−121.074	−0.00646798
$706$	4385.36	0.233775
$707$	0	0
$708$	272.717	0.0144765
$709$	−625.708	−0.0331438	−0.0165719	−	0.999863i	$-0.505275\pi$
$709$	−625.708	−0.0331438	−0.0165719	+	0.999863i	$0.505275\pi$
$710$	34.2244	0.00180904
$711$	−7251.79	−0.382508
$712$	4415.17	0.232395
$713$	−1002.85	−0.0526749
$714$	0	0
$715$	−73.5079	−0.00384481
$716$	−9421.82	−0.491774
$717$	−2513.78	−0.130933
$718$	−3568.54	−0.185483
$719$	9577.54	0.496776	0.248388	−	0.968661i	$-0.420099\pi$
$719$	9577.54	0.496776	0.248388	+	0.968661i	$0.420099\pi$
$720$	−54.1929	−0.00280507
$721$	0	0
$722$	−3851.62	−0.198535
$723$	−10365.0	−0.533163
$724$	23410.7	1.20173
$725$	−29457.8	−1.50901
$726$	−745.364	−0.0381034
$727$	16741.2	0.854053	0.427027	−	0.904239i	$-0.359561\pi$
$727$	16741.2	0.854053	0.427027	+	0.904239i	$0.359561\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	21.4439	0.00108722
$731$	26587.8	1.34526
$732$	287.522	0.0145179
$733$	6496.04	0.327335	0.163668	−	0.986516i	$-0.447668\pi$
$733$	6496.04	0.327335	0.163668	+	0.986516i	$0.447668\pi$
$734$	3437.06	0.172839
$735$	0	0
$736$	−4141.36	−0.207408
$737$	−29398.7	−1.46936
$738$	1191.86	0.0594487
$739$	499.280	0.0248529	0.0124265	−	0.999923i	$-0.496044\pi$
$739$	499.280	0.0248529	0.0124265	+	0.999923i	$0.496044\pi$
$740$	−150.972	−0.00749980
$741$	6347.24	0.314672
$742$	0	0
$743$	−6367.30	−0.314393	−0.157196	−	0.987567i	$-0.550246\pi$
$743$	−6367.30	−0.314393	−0.157196	+	0.987567i	$0.550246\pi$
$744$	−368.021	−0.0181348
$745$	−58.5568	−0.00287967
$746$	2122.37	0.104163
$747$	−3553.77	−0.174064
$748$	−41842.8	−2.04535
$749$	0	0
$750$	−31.2217	−0.00152007
$751$	496.098	0.0241050	0.0120525	−	0.999927i	$-0.496163\pi$
$751$	496.098	0.0241050	0.0120525	+	0.999927i	$0.496163\pi$
$752$	24057.7	1.16662
$753$	16905.0	0.818132
$754$	1624.89	0.0784815
$755$	282.597	0.0136222
$756$	0	0
$757$	13025.9	0.625408	0.312704	−	0.949851i	$-0.398765\pi$
$757$	13025.9	0.625408	0.312704	+	0.949851i	$0.398765\pi$
$758$	622.350	0.0298216
$759$	−7065.47	−0.337892
$760$	83.7604	0.00399778
$761$	25474.6	1.21347	0.606736	−	0.794904i	$-0.292479\pi$
$761$	25474.6	1.21347	0.606736	+	0.794904i	$0.292479\pi$
$762$	−1331.36	−0.0632943
$763$	0	0
$764$	21977.6	1.04074
$765$	110.029	0.00520012
$766$	−4503.72	−0.212436
$767$	193.282	0.00909911
$768$	9736.57	0.457472
$769$	29054.0	1.36244	0.681218	−	0.732080i	$-0.261450\pi$
$769$	29054.0	1.36244	0.681218	+	0.732080i	$0.261450\pi$
$770$	0	0
$771$	−6813.47	−0.318263
$772$	−26118.5	−1.21765
$773$	−1897.35	−0.0882834	−0.0441417	−	0.999025i	$-0.514055\pi$
$773$	−1897.35	−0.0882834	−0.0441417	+	0.999025i	$0.514055\pi$
$774$	814.844	0.0378410
$775$	2338.65	0.108396
$776$	−7153.72	−0.330933
$777$	0	0
$778$	−1913.25	−0.0881662
$779$	40639.6	1.86914
$780$	−39.2879	−0.00180350
$781$	−36123.9	−1.65508
$782$	2700.52	0.123492
$783$	6363.39	0.290433
$784$	0	0
$785$	169.989	0.00772886
$786$	3125.26	0.141825
$787$	−42650.3	−1.93179	−0.965895	−	0.258936i	$-0.916628\pi$
$787$	−42650.3	−1.93179	−0.965895	+	0.258936i	$0.916628\pi$
$788$	33088.0	1.49583
$789$	491.602	0.0221819
$790$	−33.5440	−0.00151069
$791$	0	0
$792$	−2592.84	−0.116329
$793$	203.775	0.00912516
$794$	3979.33	0.177860
$795$	−193.910	−0.00865064
$796$	−34333.1	−1.52877
$797$	−36822.8	−1.63655	−0.818275	−	0.574828i	$-0.805069\pi$
$797$	−36822.8	−1.63655	−0.818275	+	0.574828i	$0.805069\pi$
$798$	0	0
$799$	−48844.8	−2.16271
$800$	9657.60	0.426810
$801$	6060.77	0.267349
$802$	4349.68	0.191512
$803$	−22634.1	−0.994693
$804$	−15712.8	−0.689238
$805$	0	0
$806$	−129.000	−0.00563750
$807$	−15501.3	−0.676172
$808$	−8987.38	−0.391306
$809$	5081.94	0.220855	0.110427	−	0.993884i	$-0.464778\pi$
$809$	5081.94	0.220855	0.110427	+	0.993884i	$0.464778\pi$
$810$	3.37208	0.000146275 0
$811$	−11873.4	−0.514097	−0.257048	−	0.966399i	$-0.582750\pi$
$811$	−11873.4	−0.514097	−0.257048	+	0.966399i	$0.582750\pi$
$812$	0	0
$813$	−4866.82	−0.209947
$814$	−3492.45	−0.150381
$815$	4.09289	0.000175911 0
$816$	−21862.9	−0.937935
$817$	27784.1	1.18977
$818$	−4998.29	−0.213644
$819$	0	0
$820$	−251.549	−0.0107128
$821$	16969.4	0.721361	0.360681	−	0.932689i	$-0.382544\pi$
$821$	16969.4	0.721361	0.360681	+	0.932689i	$0.382544\pi$
$822$	−311.982	−0.0132380
$823$	3995.94	0.169246	0.0846231	−	0.996413i	$-0.473031\pi$
$823$	3995.94	0.169246	0.0846231	+	0.996413i	$0.473031\pi$
$824$	−9270.39	−0.391929
$825$	16476.6	0.695323
$826$	0	0
$827$	−13589.7	−0.571417	−0.285708	−	0.958317i	$-0.592229\pi$
$827$	−13589.7	−0.571417	−0.285708	+	0.958317i	$0.592229\pi$
$828$	−3776.29	−0.158497
$829$	30646.0	1.28393	0.641966	−	0.766733i	$-0.278119\pi$
$829$	30646.0	1.28393	0.641966	+	0.766733i	$0.278119\pi$
$830$	−16.4384	−0.000687451 0
$831$	−13837.1	−0.577622
$832$	7444.96	0.310226
$833$	0	0
$834$	−1101.06	−0.0457155
$835$	−291.511	−0.0120816
$836$	−43725.5	−1.80894
$837$	−505.188	−0.0208624
$838$	−2637.01	−0.108704
$839$	7497.57	0.308516	0.154258	−	0.988031i	$-0.450701\pi$
$839$	7497.57	0.308516	0.154258	+	0.988031i	$0.450701\pi$
$840$	0	0
$841$	31156.6	1.27749
$842$	1959.99	0.0802207
$843$	−6375.65	−0.260485
$844$	−17939.3	−0.731630
$845$	192.965	0.00785586
$846$	−1496.96	−0.0608351
$847$	0	0
$848$	38530.2	1.56030
$849$	7714.62	0.311855
$850$	−6297.59	−0.254124
$851$	−10284.5	−0.414275
$852$	−19307.2	−0.776354
$853$	10347.6	0.415352	0.207676	−	0.978198i	$-0.433410\pi$
$853$	10347.6	0.415352	0.207676	+	0.978198i	$0.433410\pi$
$854$	0	0
$855$	114.979	0.00459907
$856$	−2252.36	−0.0899348
$857$	−1550.00	−0.0617817	−0.0308909	−	0.999523i	$-0.509834\pi$
$857$	−1550.00	−0.0617817	−0.0308909	+	0.999523i	$0.509834\pi$
$858$	−908.849	−0.0361627
$859$	−15187.5	−0.603250	−0.301625	−	0.953427i	$-0.597529\pi$
$859$	−15187.5	−0.603250	−0.301625	+	0.953427i	$0.597529\pi$
$860$	−171.977	−0.00681903
$861$	0	0
$862$	−1554.45	−0.0614210
$863$	41550.2	1.63892	0.819459	−	0.573138i	$-0.194274\pi$
$863$	41550.2	1.63892	0.819459	+	0.573138i	$0.194274\pi$
$864$	−2086.21	−0.0821462
$865$	215.699	0.00847858
$866$	4850.12	0.190316
$867$	29649.6	1.16142
$868$	0	0
$869$	35405.8	1.38212
$870$	29.4346	0.00114704
$871$	−11136.1	−0.433216
$872$	−2082.67	−0.0808808
$873$	−9820.03	−0.380707
$874$	2822.03	0.109218
$875$	0	0
$876$	−12097.3	−0.466585
$877$	27837.4	1.07184	0.535919	−	0.844269i	$-0.319965\pi$
$877$	27837.4	1.07184	0.535919	+	0.844269i	$0.319965\pi$
$878$	−6182.02	−0.237623
$879$	−9974.89	−0.382758
$880$	264.588	0.0101355
$881$	2587.85	0.0989635	0.0494817	−	0.998775i	$-0.484243\pi$
$881$	2587.85	0.0989635	0.0494817	+	0.998775i	$0.484243\pi$
$882$	0	0
$883$	−16382.0	−0.624346	−0.312173	−	0.950025i	$-0.601057\pi$
$883$	−16382.0	−0.624346	−0.312173	+	0.950025i	$0.601057\pi$
$884$	−15849.8	−0.603040
$885$	3.50127	0.000132988 0
$886$	3528.13	0.133781
$887$	22980.2	0.869896	0.434948	−	0.900456i	$-0.356767\pi$
$887$	22980.2	0.869896	0.434948	+	0.900456i	$0.356767\pi$
$888$	−3774.14	−0.142626
$889$	0	0
$890$	28.0348	0.00105587
$891$	−3559.23	−0.133826
$892$	1706.36	0.0640506
$893$	−51042.5	−1.91274
$894$	−723.994	−0.0270850
$895$	−120.962	−0.00451766
$896$	0	0
$897$	−2676.36	−0.0996222
$898$	2471.09	0.0918276
$899$	−4409.76	−0.163597
$900$	8806.27	0.326158
$901$	−78228.5	−2.89253
$902$	−5819.10	−0.214806
$903$	0	0
$904$	5234.42	0.192582
$905$	300.557	0.0110396
$906$	3494.01	0.128125
$907$	−22715.4	−0.831590	−0.415795	−	0.909458i	$-0.636497\pi$
$907$	−22715.4	−0.831590	−0.415795	+	0.909458i	$0.636497\pi$
$908$	−14368.0	−0.525130
$909$	−12337.1	−0.450161
$910$	0	0
$911$	34922.3	1.27006	0.635031	−	0.772487i	$-0.280987\pi$
$911$	34922.3	1.27006	0.635031	+	0.772487i	$0.280987\pi$
$912$	−22846.6	−0.829525
$913$	17350.7	0.628943
$914$	5741.24	0.207772
$915$	3.69134	0.000133368 0
$916$	−21716.1	−0.783320
$917$	0	0
$918$	1360.39	0.0489102
$919$	11702.6	0.420059	0.210030	−	0.977695i	$-0.432644\pi$
$919$	11702.6	0.420059	0.210030	+	0.977695i	$0.432644\pi$
$920$	−35.3182	−0.00126566
$921$	2661.29	0.0952144
$922$	−61.8473	−0.00220914
$923$	−13683.5	−0.487973
$924$	0	0
$925$	23983.3	0.852505
$926$	−2238.39	−0.0794364
$927$	−12725.6	−0.450878
$928$	−18210.4	−0.644165
$929$	53096.5	1.87518	0.937588	−	0.347747i	$-0.113053\pi$
$929$	53096.5	1.87518	0.937588	+	0.347747i	$0.113053\pi$
$930$	−2.33681	−8.23946e−5 0
$931$	0	0
$932$	7740.06	0.272032
$933$	13532.5	0.474848
$934$	1534.52	0.0537591
$935$	−537.198	−0.0187896
$936$	−982.154	−0.0342978
$937$	39020.6	1.36046	0.680229	−	0.733000i	$-0.261880\pi$
$937$	39020.6	1.36046	0.680229	+	0.733000i	$0.261880\pi$
$938$	0	0
$939$	−11147.4	−0.387412
$940$	315.941	0.0109626
$941$	−30743.8	−1.06506	−0.532528	−	0.846412i	$-0.678758\pi$
$941$	−30743.8	−1.06506	−0.532528	+	0.846412i	$0.678758\pi$
$942$	2101.73	0.0726944
$943$	−17136.0	−0.591754
$944$	−695.710	−0.0239867
$945$	0	0
$946$	−3978.35	−0.136731
$947$	16300.3	0.559332	0.279666	−	0.960097i	$-0.409776\pi$
$947$	16300.3	0.559332	0.279666	+	0.960097i	$0.409776\pi$
$948$	18923.4	0.648315
$949$	−8573.66	−0.293269
$950$	−6580.94	−0.224752
$951$	20863.6	0.711406
$952$	0	0
$953$	−11512.7	−0.391325	−0.195663	−	0.980671i	$-0.562686\pi$
$953$	−11512.7	−0.391325	−0.195663	+	0.980671i	$0.562686\pi$
$954$	−2397.49	−0.0813644
$955$	282.159	0.00956068
$956$	6559.65	0.221919
$957$	−31068.3	−1.04942
$958$	−4420.39	−0.149078
$959$	0	0
$960$	134.864	0.00453409
$961$	−29440.9	−0.988248
$962$	−1322.92	−0.0443375
$963$	−3091.85	−0.103462
$964$	27047.1	0.903661
$965$	−335.322	−0.0111859
$966$	0	0
$967$	−18178.4	−0.604528	−0.302264	−	0.953224i	$-0.597742\pi$
$967$	−18178.4	−0.604528	−0.302264	+	0.953224i	$0.597742\pi$
$968$	3932.65	0.130579
$969$	46385.8	1.53780
$970$	−45.4237	−0.00150357
$971$	28276.7	0.934543	0.467271	−	0.884114i	$-0.345237\pi$
$971$	28276.7	0.934543	0.467271	+	0.884114i	$0.345237\pi$
$972$	−1902.31	−0.0627742
$973$	0	0
$974$	−2424.77	−0.0797688
$975$	6241.24	0.205005
$976$	−733.477	−0.0240554
$977$	−13947.1	−0.456710	−0.228355	−	0.973578i	$-0.573335\pi$
$977$	−13947.1	−0.456710	−0.228355	+	0.973578i	$0.573335\pi$
$978$	50.6043	0.00165455
$979$	−29590.8	−0.966011
$980$	0	0
$981$	−2858.91	−0.0930459
$982$	−1683.91	−0.0547206
$983$	−26576.8	−0.862327	−0.431164	−	0.902274i	$-0.641897\pi$
$983$	−26576.8	−0.862327	−0.431164	+	0.902274i	$0.641897\pi$
$984$	−6288.45	−0.203728
$985$	424.799	0.0137414
$986$	11874.7	0.383539
$987$	0	0
$988$	−16563.0	−0.533339
$989$	−11715.4	−0.376671
$990$	−16.4636	−0.000528534 0
$991$	16249.9	0.520884	0.260442	−	0.965490i	$-0.416132\pi$
$991$	16249.9	0.520884	0.260442	+	0.965490i	$0.416132\pi$
$992$	1445.72	0.0462718
$993$	−29589.5	−0.945615
$994$	0	0
$995$	−440.784	−0.0140440
$996$	9273.47	0.295021
$997$	18814.1	0.597642	0.298821	−	0.954309i	$-0.403407\pi$
$997$	18814.1	0.597642	0.298821	+	0.954309i	$0.403407\pi$
$998$	−1992.86	−0.0632092
$999$	−5180.82	−0.164078

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.a.k.1.1	yes	2
3.2	odd	2		441.4.a.o.1.2		2
4.3	odd	2		2352.4.a.bl.1.2		2
7.2	even	3		147.4.e.j.67.2		4
7.3	odd	6		147.4.e.k.79.2		4
7.4	even	3		147.4.e.j.79.2		4
7.5	odd	6		147.4.e.k.67.2		4
7.6	odd	2		147.4.a.j.1.1	✓	2
21.2	odd	6		441.4.e.u.361.1		4
21.5	even	6		441.4.e.v.361.1		4
21.11	odd	6		441.4.e.u.226.1		4
21.17	even	6		441.4.e.v.226.1		4
21.20	even	2		441.4.a.n.1.2		2
28.27	even	2		2352.4.a.cf.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.4.a.j.1.1	✓	2	7.6	odd	2
147.4.a.k.1.1	yes	2	1.1	even	1	trivial
147.4.e.j.67.2		4	7.2	even	3
147.4.e.j.79.2		4	7.4	even	3
147.4.e.k.67.2		4	7.5	odd	6
147.4.e.k.79.2		4	7.3	odd	6
441.4.a.n.1.2		2	21.20	even	2
441.4.a.o.1.2		2	3.2	odd	2
441.4.e.u.226.1		4	21.11	odd	6
441.4.e.u.361.1		4	21.2	odd	6
441.4.e.v.226.1		4	21.17	even	6
441.4.e.v.361.1		4	21.5	even	6
2352.4.a.bl.1.2		2	4.3	odd	2
2352.4.a.cf.1.1		2	28.27	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.a (trivial)

\(f(q)\)	\(=\)	\(q-0.414214 q^{2} +3.00000 q^{3} -7.82843 q^{4} -0.100505 q^{5} -1.24264 q^{6} +6.55635 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-0.414214 q^{2} +3.00000 q^{3} -7.82843 q^{4} -0.100505 q^{5} -1.24264 q^{6} +6.55635 q^{8} +9.00000 q^{9} +0.0416306 q^{10} -43.9411 q^{11} -23.4853 q^{12} -16.6447 q^{13} -0.301515 q^{15} +59.9117 q^{16} -121.640 q^{17} -3.72792 q^{18} -127.113 q^{19} +0.786797 q^{20} +18.2010 q^{22} +53.5980 q^{23} +19.6690 q^{24} -124.990 q^{25} +6.89444 q^{26} +27.0000 q^{27} +235.681 q^{29} +0.124892 q^{30} -18.7107 q^{31} -77.2670 q^{32} -131.823 q^{33} +50.3848 q^{34} -70.4558 q^{36} -191.882 q^{37} +52.6518 q^{38} -49.9340 q^{39} -0.658946 q^{40} -319.713 q^{41} -218.579 q^{43} +343.990 q^{44} -0.904546 q^{45} -22.2010 q^{46} +401.553 q^{47} +179.735 q^{48} +51.7725 q^{50} -364.919 q^{51} +130.302 q^{52} +643.117 q^{53} -11.1838 q^{54} +4.41631 q^{55} -381.338 q^{57} -97.6224 q^{58} -11.6123 q^{59} +2.36039 q^{60} -12.2426 q^{61} +7.75022 q^{62} -447.288 q^{64} +1.67287 q^{65} +54.6030 q^{66} +669.048 q^{67} +952.247 q^{68} +160.794 q^{69} +822.098 q^{71} +59.0071 q^{72} +515.100 q^{73} +79.4802 q^{74} -374.970 q^{75} +995.092 q^{76} +20.6833 q^{78} -805.754 q^{79} -6.02143 q^{80} +81.0000 q^{81} +132.429 q^{82} -394.863 q^{83} +12.2254 q^{85} +90.5382 q^{86} +707.044 q^{87} -288.093 q^{88} +673.418 q^{89} +0.374675 q^{90} -419.588 q^{92} -56.1320 q^{93} -166.329 q^{94} +12.7755 q^{95} -231.801 q^{96} -1091.11 q^{97} -395.470 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 6 q^{3} - 10 q^{4} - 20 q^{5} + 6 q^{6} - 18 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 6 * q^3 - 10 * q^4 - 20 * q^5 + 6 * q^6 - 18 * q^8 + 18 * q^9	\( 2 q + 2 q^{2} + 6 q^{3} - 10 q^{4} - 20 q^{5} + 6 q^{6} - 18 q^{8} + 18 q^{9} - 48 q^{10} - 20 q^{11} - 30 q^{12} - 104 q^{13} - 60 q^{15} + 18 q^{16} - 116 q^{17} + 18 q^{18} - 192 q^{19} + 44 q^{20} + 76 q^{22} + 28 q^{23} - 54 q^{24} + 146 q^{25} - 204 q^{26} + 54 q^{27} + 296 q^{29} - 144 q^{30} + 104 q^{31} + 18 q^{32} - 60 q^{33} + 64 q^{34} - 90 q^{36} - 248 q^{37} - 104 q^{38} - 312 q^{39} + 488 q^{40} - 20 q^{41} - 720 q^{43} + 292 q^{44} - 180 q^{45} - 84 q^{46} + 96 q^{47} + 54 q^{48} + 706 q^{50} - 348 q^{51} + 320 q^{52} + 268 q^{53} + 54 q^{54} - 472 q^{55} - 576 q^{57} + 48 q^{58} + 616 q^{59} + 132 q^{60} - 16 q^{61} + 304 q^{62} + 118 q^{64} + 1740 q^{65} + 228 q^{66} - 144 q^{67} + 940 q^{68} + 84 q^{69} + 988 q^{71} - 162 q^{72} - 104 q^{73} - 56 q^{74} + 438 q^{75} + 1136 q^{76} - 612 q^{78} - 944 q^{79} + 828 q^{80} + 162 q^{81} + 856 q^{82} - 1016 q^{83} - 100 q^{85} - 1120 q^{86} + 888 q^{87} - 876 q^{88} + 388 q^{89} - 432 q^{90} - 364 q^{92} + 312 q^{93} - 904 q^{94} + 1304 q^{95} + 54 q^{96} - 488 q^{97} - 180 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 6 * q^3 - 10 * q^4 - 20 * q^5 + 6 * q^6 - 18 * q^8 + 18 * q^9 - 48 * q^10 - 20 * q^11 - 30 * q^12 - 104 * q^13 - 60 * q^15 + 18 * q^16 - 116 * q^17 + 18 * q^18 - 192 * q^19 + 44 * q^20 + 76 * q^22 + 28 * q^23 - 54 * q^24 + 146 * q^25 - 204 * q^26 + 54 * q^27 + 296 * q^29 - 144 * q^30 + 104 * q^31 + 18 * q^32 - 60 * q^33 + 64 * q^34 - 90 * q^36 - 248 * q^37 - 104 * q^38 - 312 * q^39 + 488 * q^40 - 20 * q^41 - 720 * q^43 + 292 * q^44 - 180 * q^45 - 84 * q^46 + 96 * q^47 + 54 * q^48 + 706 * q^50 - 348 * q^51 + 320 * q^52 + 268 * q^53 + 54 * q^54 - 472 * q^55 - 576 * q^57 + 48 * q^58 + 616 * q^59 + 132 * q^60 - 16 * q^61 + 304 * q^62 + 118 * q^64 + 1740 * q^65 + 228 * q^66 - 144 * q^67 + 940 * q^68 + 84 * q^69 + 988 * q^71 - 162 * q^72 - 104 * q^73 - 56 * q^74 + 438 * q^75 + 1136 * q^76 - 612 * q^78 - 944 * q^79 + 828 * q^80 + 162 * q^81 + 856 * q^82 - 1016 * q^83 - 100 * q^85 - 1120 * q^86 + 888 * q^87 - 876 * q^88 + 388 * q^89 - 432 * q^90 - 364 * q^92 + 312 * q^93 - 904 * q^94 + 1304 * q^95 + 54 * q^96 - 488 * q^97 - 180 * q^99

Introduction

L-functions

Modular forms

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