LMFDB - Embedded newform 1911.4.a.h.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1911,4,Mod(1,1911)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1911, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1911.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1911 = 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1911.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:	$112.752650021$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{14}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 14 $ x^2 - 14
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.74166$ of defining polynomial
Character	$\chi$	$=$	1911.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.74166 q^{2} +3.00000 q^{3} +14.4833 q^{4} -4.51669 q^{5} +14.2250 q^{6} +30.7417 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+4.74166 q^{2} +3.00000 q^{3} +14.4833 q^{4} -4.51669 q^{5} +14.2250 q^{6} +30.7417 q^{8} +9.00000 q^{9} -21.4166 q^{10} -66.8999 q^{11} +43.4499 q^{12} +13.0000 q^{13} -13.5501 q^{15} +29.8999 q^{16} -96.9666 q^{17} +42.6749 q^{18} -31.4833 q^{19} -65.4166 q^{20} -317.216 q^{22} +183.600 q^{23} +92.2250 q^{24} -104.600 q^{25} +61.6415 q^{26} +27.0000 q^{27} +112.200 q^{29} -64.2497 q^{30} +77.2831 q^{31} -104.158 q^{32} -200.700 q^{33} -459.783 q^{34} +130.350 q^{36} +54.7664 q^{37} -149.283 q^{38} +39.0000 q^{39} -138.850 q^{40} -451.716 q^{41} -113.434 q^{43} -968.932 q^{44} -40.6502 q^{45} +870.566 q^{46} +42.2670 q^{47} +89.6997 q^{48} -495.975 q^{50} -290.900 q^{51} +188.283 q^{52} -530.999 q^{53} +128.025 q^{54} +302.166 q^{55} -94.4499 q^{57} +532.015 q^{58} -219.666 q^{59} -196.250 q^{60} -822.865 q^{61} +366.450 q^{62} -733.082 q^{64} -58.7169 q^{65} -951.649 q^{66} -872.082 q^{67} -1404.40 q^{68} +550.799 q^{69} -100.299 q^{71} +276.675 q^{72} +165.634 q^{73} +259.684 q^{74} -313.799 q^{75} -455.983 q^{76} +184.925 q^{78} -545.266 q^{79} -135.048 q^{80} +81.0000 q^{81} -2141.88 q^{82} +454.534 q^{83} +437.968 q^{85} -537.864 q^{86} +336.601 q^{87} -2056.61 q^{88} +230.915 q^{89} -192.749 q^{90} +2659.13 q^{92} +231.849 q^{93} +200.415 q^{94} +142.200 q^{95} -312.475 q^{96} +1089.16 q^{97} -602.099 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 6 q^{3} + 14 q^{4} - 24 q^{5} + 6 q^{6} + 54 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 6 * q^3 + 14 * q^4 - 24 * q^5 + 6 * q^6 + 54 * q^8 + 18 * q^9	\( 2 q + 2 q^{2} + 6 q^{3} + 14 q^{4} - 24 q^{5} + 6 q^{6} + 54 q^{8} + 18 q^{9} + 32 q^{10} - 44 q^{11} + 42 q^{12} + 26 q^{13} - 72 q^{15} - 30 q^{16} - 164 q^{17} + 18 q^{18} - 48 q^{19} - 56 q^{20} - 380 q^{22} + 8 q^{23} + 162 q^{24} + 150 q^{25} + 26 q^{26} + 54 q^{27} + 404 q^{29} + 96 q^{30} - 40 q^{31} - 126 q^{32} - 132 q^{33} - 276 q^{34} + 126 q^{36} - 100 q^{37} - 104 q^{38} + 78 q^{39} - 592 q^{40} - 200 q^{41} - 616 q^{43} - 980 q^{44} - 216 q^{45} + 1352 q^{46} + 324 q^{47} - 90 q^{48} - 1194 q^{50} - 492 q^{51} + 182 q^{52} - 164 q^{53} + 54 q^{54} - 144 q^{55} - 144 q^{57} - 268 q^{58} - 140 q^{59} - 168 q^{60} - 628 q^{61} + 688 q^{62} - 194 q^{64} - 312 q^{65} - 1140 q^{66} - 472 q^{67} - 1372 q^{68} + 24 q^{69} + 428 q^{71} + 486 q^{72} + 900 q^{73} + 684 q^{74} + 450 q^{75} - 448 q^{76} + 78 q^{78} - 432 q^{79} + 1032 q^{80} + 162 q^{81} - 2832 q^{82} + 1388 q^{83} + 1744 q^{85} + 840 q^{86} + 1212 q^{87} - 1524 q^{88} - 960 q^{89} + 288 q^{90} + 2744 q^{92} - 120 q^{93} - 572 q^{94} + 464 q^{95} - 378 q^{96} + 532 q^{97} - 396 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 6 * q^3 + 14 * q^4 - 24 * q^5 + 6 * q^6 + 54 * q^8 + 18 * q^9 + 32 * q^10 - 44 * q^11 + 42 * q^12 + 26 * q^13 - 72 * q^15 - 30 * q^16 - 164 * q^17 + 18 * q^18 - 48 * q^19 - 56 * q^20 - 380 * q^22 + 8 * q^23 + 162 * q^24 + 150 * q^25 + 26 * q^26 + 54 * q^27 + 404 * q^29 + 96 * q^30 - 40 * q^31 - 126 * q^32 - 132 * q^33 - 276 * q^34 + 126 * q^36 - 100 * q^37 - 104 * q^38 + 78 * q^39 - 592 * q^40 - 200 * q^41 - 616 * q^43 - 980 * q^44 - 216 * q^45 + 1352 * q^46 + 324 * q^47 - 90 * q^48 - 1194 * q^50 - 492 * q^51 + 182 * q^52 - 164 * q^53 + 54 * q^54 - 144 * q^55 - 144 * q^57 - 268 * q^58 - 140 * q^59 - 168 * q^60 - 628 * q^61 + 688 * q^62 - 194 * q^64 - 312 * q^65 - 1140 * q^66 - 472 * q^67 - 1372 * q^68 + 24 * q^69 + 428 * q^71 + 486 * q^72 + 900 * q^73 + 684 * q^74 + 450 * q^75 - 448 * q^76 + 78 * q^78 - 432 * q^79 + 1032 * q^80 + 162 * q^81 - 2832 * q^82 + 1388 * q^83 + 1744 * q^85 + 840 * q^86 + 1212 * q^87 - 1524 * q^88 - 960 * q^89 + 288 * q^90 + 2744 * q^92 - 120 * q^93 - 572 * q^94 + 464 * q^95 - 378 * q^96 + 532 * q^97 - 396 * 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 $

$2$	4.74166	1.67643	0.838215	−	0.545341i	$-0.183600\pi$
$2$	4.74166	1.67643	0.838215	+	0.545341i	$0.183600\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	14.4833	1.81041
$5$	−4.51669	−0.403985	−0.201992	−	0.979387i	$-0.564742\pi$
$5$	−4.51669	−0.403985	−0.201992	+	0.979387i	$0.564742\pi$
$6$	14.2250	0.967887
$7$	0	0
$7$	0	0
$8$	30.7417	1.35860
$9$	9.00000	0.333333
$10$	−21.4166	−0.677252
$11$	−66.8999	−1.83373	−0.916867	−	0.399193i	$-0.869290\pi$
$11$	−66.8999	−1.83373	−0.916867	+	0.399193i	$0.869290\pi$
$12$	43.4499	1.04524
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	0	0
$15$	−13.5501	−0.233241
$16$	29.8999	0.467186
$17$	−96.9666	−1.38340	−0.691702	−	0.722183i	$-0.743139\pi$
$17$	−96.9666	−1.38340	−0.691702	+	0.722183i	$0.743139\pi$
$18$	42.6749	0.558810
$19$	−31.4833	−0.380146	−0.190073	−	0.981770i	$-0.560872\pi$
$19$	−31.4833	−0.380146	−0.190073	+	0.981770i	$0.560872\pi$
$20$	−65.4166	−0.731380
$21$	0	0
$22$	−317.216	−3.07413
$23$	183.600	1.66448	0.832242	−	0.554412i	$-0.187057\pi$
$23$	183.600	1.66448	0.832242	+	0.554412i	$0.187057\pi$
$24$	92.2250	0.784389
$25$	−104.600	−0.836796
$26$	61.6415	0.464958
$27$	27.0000	0.192450
$28$	0	0
$29$	112.200	0.718450	0.359225	−	0.933251i	$-0.383041\pi$
$29$	112.200	0.718450	0.359225	+	0.933251i	$0.383041\pi$
$30$	−64.2497	−0.391011
$31$	77.2831	0.447757	0.223878	−	0.974617i	$-0.428128\pi$
$31$	77.2831	0.447757	0.223878	+	0.974617i	$0.428128\pi$
$32$	−104.158	−0.575398
$33$	−200.700	−1.05871
$34$	−459.783	−2.31918
$35$	0	0
$36$	130.350	0.603471
$37$	54.7664	0.243339	0.121669	−	0.992571i	$-0.461175\pi$
$37$	54.7664	0.243339	0.121669	+	0.992571i	$0.461175\pi$
$38$	−149.283	−0.637287
$39$	39.0000	0.160128
$40$	−138.850	−0.548854
$41$	−451.716	−1.72064	−0.860319	−	0.509756i	$-0.829736\pi$
$41$	−451.716	−1.72064	−0.860319	+	0.509756i	$0.829736\pi$
$42$	0	0
$43$	−113.434	−0.402291	−0.201145	−	0.979561i	$-0.564466\pi$
$43$	−113.434	−0.402291	−0.201145	+	0.979561i	$0.564466\pi$
$44$	−968.932	−3.31982
$45$	−40.6502	−0.134662
$46$	870.566	2.79039
$47$	42.2670	0.131176	0.0655880	−	0.997847i	$-0.479108\pi$
$47$	42.2670	0.131176	0.0655880	+	0.997847i	$0.479108\pi$
$48$	89.6997	0.269730
$49$	0	0
$50$	−495.975	−1.40283
$51$	−290.900	−0.798708
$52$	188.283	0.502119
$53$	−530.999	−1.37619	−0.688097	−	0.725618i	$-0.741554\pi$
$53$	−530.999	−1.37619	−0.688097	+	0.725618i	$0.741554\pi$
$54$	128.025	0.322629
$55$	302.166	0.740800
$56$	0	0
$57$	−94.4499	−0.219477
$58$	532.015	1.20443
$59$	−219.666	−0.484714	−0.242357	−	0.970187i	$-0.577920\pi$
$59$	−219.666	−0.484714	−0.242357	+	0.970187i	$0.577920\pi$
$60$	−196.250	−0.422262
$61$	−822.865	−1.72717	−0.863583	−	0.504207i	$-0.831785\pi$
$61$	−822.865	−1.72717	−0.863583	+	0.504207i	$0.831785\pi$
$62$	366.450	0.750632
$63$	0	0
$64$	−733.082	−1.43180
$65$	−58.7169	−0.112045
$66$	−951.649	−1.77485
$67$	−872.082	−1.59018	−0.795088	−	0.606495i	$-0.792575\pi$
$67$	−872.082	−1.59018	−0.795088	+	0.606495i	$0.792575\pi$
$68$	−1404.40	−2.50453
$69$	550.799	0.960991
$70$	0	0
$71$	−100.299	−0.167653	−0.0838263	−	0.996480i	$-0.526714\pi$
$71$	−100.299	−0.167653	−0.0838263	+	0.996480i	$0.526714\pi$
$72$	276.675	0.452867
$73$	165.634	0.265562	0.132781	−	0.991145i	$-0.457609\pi$
$73$	165.634	0.265562	0.132781	+	0.991145i	$0.457609\pi$
$74$	259.684	0.407941
$75$	−313.799	−0.483125
$76$	−455.983	−0.688221
$77$	0	0
$78$	184.925	0.268443
$79$	−545.266	−0.776547	−0.388273	−	0.921544i	$-0.626928\pi$
$79$	−545.266	−0.776547	−0.388273	+	0.921544i	$0.626928\pi$
$80$	−135.048	−0.188736
$81$	81.0000	0.111111
$82$	−2141.88	−2.88453
$83$	454.534	0.601103	0.300552	−	0.953766i	$-0.402829\pi$
$83$	454.534	0.601103	0.300552	+	0.953766i	$0.402829\pi$
$84$	0	0
$85$	437.968	0.558874
$86$	−537.864	−0.674412
$87$	336.601	0.414797
$88$	−2056.61	−2.49132
$89$	230.915	0.275022	0.137511	−	0.990500i	$-0.456090\pi$
$89$	230.915	0.275022	0.137511	+	0.990500i	$0.456090\pi$
$90$	−192.749	−0.225751
$91$	0	0
$92$	2659.13	3.01341
$93$	231.849	0.258512
$94$	200.415	0.219907
$95$	142.200	0.153573
$96$	−312.475	−0.332206
$97$	1089.16	1.14008	0.570041	−	0.821616i	$-0.306927\pi$
$97$	1089.16	1.14008	0.570041	+	0.821616i	$0.306927\pi$
$98$	0	0
$99$	−602.099	−0.611245
$100$	−1514.95	−1.51495
$101$	77.2336	0.0760894	0.0380447	−	0.999276i	$-0.487887\pi$
$101$	77.2336	0.0760894	0.0380447	+	0.999276i	$0.487887\pi$
$102$	−1379.35	−1.33898
$103$	−1351.36	−1.29275	−0.646377	−	0.763018i	$-0.723717\pi$
$103$	−1351.36	−1.29275	−0.646377	+	0.763018i	$0.723717\pi$
$104$	399.642	0.376808
$105$	0	0
$106$	−2517.81	−2.30709
$107$	1133.67	1.02426	0.512129	−	0.858908i	$-0.328857\pi$
$107$	1133.67	1.02426	0.512129	+	0.858908i	$0.328857\pi$
$108$	391.049	0.348414
$109$	1017.66	0.894262	0.447131	−	0.894469i	$-0.352446\pi$
$109$	1017.66	0.894262	0.447131	+	0.894469i	$0.352446\pi$
$110$	1432.77	1.24190
$111$	164.299	0.140492
$112$	0	0
$113$	1570.06	1.30707	0.653536	−	0.756895i	$-0.273285\pi$
$113$	1570.06	1.30707	0.653536	+	0.756895i	$0.273285\pi$
$114$	−447.849	−0.367938
$115$	−829.261	−0.672426
$116$	1625.03	1.30069
$117$	117.000	0.0924500
$118$	−1041.58	−0.812588
$119$	0	0
$120$	−416.551	−0.316881
$121$	3144.60	2.36258
$122$	−3901.75	−2.89547
$123$	−1355.15	−0.993411
$124$	1119.32	0.810625
$125$	1037.03	0.742037
$126$	0	0
$127$	−1248.16	−0.872099	−0.436050	−	0.899923i	$-0.643623\pi$
$127$	−1248.16	−0.872099	−0.436050	+	0.899923i	$0.643623\pi$
$128$	−2642.76	−1.82491
$129$	−340.301	−0.232263
$130$	−278.415	−0.187836
$131$	1274.80	0.850227	0.425113	−	0.905140i	$-0.360234\pi$
$131$	1274.80	0.850227	0.425113	+	0.905140i	$0.360234\pi$
$132$	−2906.80	−1.91670
$133$	0	0
$134$	−4135.11	−2.66582
$135$	−121.951	−0.0777469
$136$	−2980.91	−1.87950
$137$	874.915	0.545613	0.272807	−	0.962069i	$-0.412048\pi$
$137$	874.915	0.545613	0.272807	+	0.962069i	$0.412048\pi$
$138$	2611.70	1.61103
$139$	−310.334	−0.189368	−0.0946840	−	0.995507i	$-0.530184\pi$
$139$	−310.334	−0.189368	−0.0946840	+	0.995507i	$0.530184\pi$
$140$	0	0
$141$	126.801	0.0757345
$142$	−475.585	−0.281058
$143$	−869.699	−0.508586
$144$	269.099	0.155729
$145$	−506.773	−0.290243
$146$	785.380	0.445195
$147$	0	0
$148$	793.199	0.440544
$149$	5.08064	0.00279344	0.00139672	−	0.999999i	$-0.499555\pi$
$149$	5.08064	0.00279344	0.00139672	+	0.999999i	$0.499555\pi$
$150$	−1487.93	−0.809924
$151$	6.54894	0.00352944	0.00176472	−	0.999998i	$-0.499438\pi$
$151$	6.54894	0.00352944	0.00176472	+	0.999998i	$0.499438\pi$
$152$	−967.849	−0.516467
$153$	−872.700	−0.461135
$154$	0	0
$155$	−349.063	−0.180887
$156$	564.849	0.289898
$157$	2297.60	1.16795	0.583975	−	0.811772i	$-0.301497\pi$
$157$	2297.60	1.16795	0.583975	+	0.811772i	$0.301497\pi$
$158$	−2585.46	−1.30183
$159$	−1593.00	−0.794546
$160$	470.450	0.232452
$161$	0	0
$162$	384.074	0.186270
$163$	−1085.49	−0.521606	−0.260803	−	0.965392i	$-0.583987\pi$
$163$	−1085.49	−0.521606	−0.260803	+	0.965392i	$0.583987\pi$
$164$	−6542.34	−3.11507
$165$	906.497	0.427701
$166$	2155.24	1.00771
$167$	109.066	0.0505374	0.0252687	−	0.999681i	$-0.491956\pi$
$167$	109.066	0.0505374	0.0252687	+	0.999681i	$0.491956\pi$
$168$	0	0
$169$	169.000	0.0769231
$170$	2076.69	0.936912
$171$	−283.350	−0.126715
$172$	−1642.90	−0.728313
$173$	1889.17	0.830236	0.415118	−	0.909768i	$-0.363740\pi$
$173$	1889.17	0.830236	0.415118	+	0.909768i	$0.363740\pi$
$174$	1596.05	0.695379
$175$	0	0
$176$	−2000.30	−0.856694
$177$	−658.999	−0.279850
$178$	1094.92	0.461054
$179$	3427.86	1.43134	0.715672	−	0.698437i	$-0.246121\pi$
$179$	3427.86	1.43134	0.715672	+	0.698437i	$0.246121\pi$
$180$	−588.749	−0.243793
$181$	−208.403	−0.0855826	−0.0427913	−	0.999084i	$-0.513625\pi$
$181$	−208.403	−0.0855826	−0.0427913	+	0.999084i	$0.513625\pi$
$182$	0	0
$183$	−2468.60	−0.997180
$184$	5644.15	2.26137
$185$	−247.363	−0.0983052
$186$	1099.35	0.433378
$187$	6487.06	2.53679
$188$	612.166	0.237483
$189$	0	0
$190$	674.265	0.257454
$191$	957.735	0.362824	0.181412	−	0.983407i	$-0.441933\pi$
$191$	957.735	0.362824	0.181412	+	0.983407i	$0.441933\pi$
$192$	−2199.25	−0.826650
$193$	−512.730	−0.191228	−0.0956142	−	0.995418i	$-0.530482\pi$
$193$	−512.730	−0.191228	−0.0956142	+	0.995418i	$0.530482\pi$
$194$	5164.45	1.91127
$195$	−176.151	−0.0646893
$196$	0	0
$197$	−3870.35	−1.39975	−0.699876	−	0.714265i	$-0.746761\pi$
$197$	−3870.35	−1.39975	−0.699876	+	0.714265i	$0.746761\pi$
$198$	−2854.95	−1.02471
$199$	−2305.83	−0.821388	−0.410694	−	0.911773i	$-0.634714\pi$
$199$	−2305.83	−0.821388	−0.410694	+	0.911773i	$0.634714\pi$
$200$	−3215.56	−1.13687
$201$	−2616.25	−0.918088
$202$	366.215	0.127558
$203$	0	0
$204$	−4213.19	−1.44599
$205$	2040.26	0.695111
$206$	−6407.70	−2.16721
$207$	1652.40	0.554828
$208$	388.699	0.129574
$209$	2106.23	0.697086
$210$	0	0
$211$	−3672.40	−1.19819	−0.599096	−	0.800677i	$-0.704473\pi$
$211$	−3672.40	−1.19819	−0.599096	+	0.800677i	$0.704473\pi$
$212$	−7690.62	−2.49148
$213$	−300.898	−0.0967942
$214$	5375.46	1.71710
$215$	512.345	0.162519
$216$	830.025	0.261463
$217$	0	0
$218$	4825.41	1.49917
$219$	496.902	0.153322
$220$	4376.36	1.34116
$221$	−1260.57	−0.383687
$222$	779.051	0.235525
$223$	−5087.05	−1.52760	−0.763798	−	0.645455i	$-0.776668\pi$
$223$	−5087.05	−1.52760	−0.763798	+	0.645455i	$0.776668\pi$
$224$	0	0
$225$	−941.396	−0.278932
$226$	7444.71	2.19122
$227$	2625.83	0.767763	0.383882	−	0.923382i	$-0.374587\pi$
$227$	2625.83	0.767763	0.383882	+	0.923382i	$0.374587\pi$
$228$	−1367.95	−0.397345
$229$	−1678.73	−0.484425	−0.242213	−	0.970223i	$-0.577873\pi$
$229$	−1678.73	−0.484425	−0.242213	+	0.970223i	$0.577873\pi$
$230$	−3932.07	−1.12727
$231$	0	0
$232$	3449.22	0.976088
$233$	648.506	0.182339	0.0911696	−	0.995835i	$-0.470939\pi$
$233$	648.506	0.182339	0.0911696	+	0.995835i	$0.470939\pi$
$234$	554.774	0.154986
$235$	−190.907	−0.0529931
$236$	−3181.50	−0.877533
$237$	−1635.80	−0.448340
$238$	0	0
$239$	5219.69	1.41269	0.706347	−	0.707866i	$-0.250342\pi$
$239$	5219.69	1.41269	0.706347	+	0.707866i	$0.250342\pi$
$240$	−405.145	−0.108967
$241$	−6103.56	−1.63139	−0.815695	−	0.578483i	$-0.803645\pi$
$241$	−6103.56	−1.63139	−0.815695	+	0.578483i	$0.803645\pi$
$242$	14910.6	3.96070
$243$	243.000	0.0641500
$244$	−11917.8	−3.12689
$245$	0	0
$246$	−6425.64	−1.66538
$247$	−409.283	−0.105433
$248$	2375.81	0.608323
$249$	1363.60	0.347047
$250$	4917.24	1.24397
$251$	−6423.40	−1.61530	−0.807652	−	0.589660i	$-0.799262\pi$
$251$	−6423.40	−1.61530	−0.807652	+	0.589660i	$0.799262\pi$
$252$	0	0
$253$	−12282.8	−3.05222
$254$	−5918.36	−1.46201
$255$	1313.90	0.322666
$256$	−6666.39	−1.62754
$257$	1230.23	0.298597	0.149299	−	0.988792i	$-0.452298\pi$
$257$	1230.23	0.298597	0.149299	+	0.988792i	$0.452298\pi$
$258$	−1613.59	−0.389372
$259$	0	0
$260$	−850.415	−0.202848
$261$	1009.80	0.239483
$262$	6044.66	1.42534
$263$	−514.992	−0.120744	−0.0603722	−	0.998176i	$-0.519229\pi$
$263$	−514.992	−0.120744	−0.0603722	+	0.998176i	$0.519229\pi$
$264$	−6169.84	−1.43836
$265$	2398.35	0.555961
$266$	0	0
$267$	692.745	0.158784
$268$	−12630.6	−2.87888
$269$	5132.60	1.16335	0.581673	−	0.813423i	$-0.302398\pi$
$269$	5132.60	1.16335	0.581673	+	0.813423i	$0.302398\pi$
$270$	−578.247	−0.130337
$271$	4300.00	0.963862	0.481931	−	0.876209i	$-0.339936\pi$
$271$	4300.00	0.963862	0.481931	+	0.876209i	$0.339936\pi$
$272$	−2899.29	−0.646306
$273$	0	0
$274$	4148.55	0.914682
$275$	6997.70	1.53446
$276$	7977.39	1.73979
$277$	−1812.80	−0.393215	−0.196607	−	0.980482i	$-0.562992\pi$
$277$	−1812.80	−0.393215	−0.196607	+	0.980482i	$0.562992\pi$
$278$	−1471.50	−0.317462
$279$	695.548	0.149252
$280$	0	0
$281$	−4073.08	−0.864696	−0.432348	−	0.901707i	$-0.642315\pi$
$281$	−4073.08	−0.864696	−0.432348	+	0.901707i	$0.642315\pi$
$282$	601.246	0.126963
$283$	−6346.29	−1.33303	−0.666516	−	0.745491i	$-0.732215\pi$
$283$	−6346.29	−1.33303	−0.666516	+	0.745491i	$0.732215\pi$
$284$	−1452.67	−0.303520
$285$	426.601	0.0886654
$286$	−4123.81	−0.852609
$287$	0	0
$288$	−937.424	−0.191799
$289$	4489.53	0.913806
$290$	−2402.94	−0.486572
$291$	3267.49	0.658226
$292$	2398.93	0.480777
$293$	8390.97	1.67306	0.836529	−	0.547923i	$-0.184581\pi$
$293$	8390.97	1.67306	0.836529	+	0.547923i	$0.184581\pi$
$294$	0	0
$295$	992.164	0.195817
$296$	1683.61	0.330601
$297$	−1806.30	−0.352902
$298$	24.0907	0.00468300
$299$	2386.79	0.461645
$300$	−4544.84	−0.874656
$301$	0	0
$302$	31.0528	0.00591685
$303$	231.701	0.0439302
$304$	−941.348	−0.177599
$305$	3716.62	0.697748
$306$	−4138.04	−0.773059
$307$	−4005.27	−0.744603	−0.372301	−	0.928112i	$-0.621431\pi$
$307$	−4005.27	−0.744603	−0.372301	+	0.928112i	$0.621431\pi$
$308$	0	0
$309$	−4054.09	−0.746372
$310$	−1655.14	−0.303244
$311$	−5836.53	−1.06418	−0.532088	−	0.846689i	$-0.678593\pi$
$311$	−5836.53	−1.06418	−0.532088	+	0.846689i	$0.678593\pi$
$312$	1198.92	0.217550
$313$	−1763.19	−0.318407	−0.159204	−	0.987246i	$-0.550893\pi$
$313$	−1763.19	−0.318407	−0.159204	+	0.987246i	$0.550893\pi$
$314$	10894.4	1.95798
$315$	0	0
$316$	−7897.26	−1.40587
$317$	−6106.35	−1.08191	−0.540957	−	0.841050i	$-0.681938\pi$
$317$	−6106.35	−1.08191	−0.540957	+	0.841050i	$0.681938\pi$
$318$	−7553.44	−1.33200
$319$	−7506.18	−1.31745
$320$	3311.10	0.578425
$321$	3401.00	0.591356
$322$	0	0
$323$	3052.83	0.525895
$324$	1173.15	0.201157
$325$	−1359.79	−0.232086
$326$	−5147.00	−0.874436
$327$	3052.99	0.516302
$328$	−13886.5	−2.33766
$329$	0	0
$330$	4298.30	0.717011
$331$	7490.38	1.24383	0.621916	−	0.783084i	$-0.286354\pi$
$331$	7490.38	1.24383	0.621916	+	0.783084i	$0.286354\pi$
$332$	6583.16	1.08825
$333$	492.898	0.0811130
$334$	517.152	0.0847224
$335$	3938.92	0.642406
$336$	0	0
$337$	9462.46	1.52953	0.764767	−	0.644307i	$-0.222854\pi$
$337$	9462.46	1.52953	0.764767	+	0.644307i	$0.222854\pi$
$338$	801.340	0.128956
$339$	4710.19	0.754639
$340$	6343.22	1.01179
$341$	−5170.23	−0.821066
$342$	−1343.55	−0.212429
$343$	0	0
$344$	−3487.14	−0.546553
$345$	−2487.78	−0.388226
$346$	8957.79	1.39183
$347$	11460.3	1.77297	0.886487	−	0.462753i	$-0.153138\pi$
$347$	11460.3	1.77297	0.886487	+	0.462753i	$0.153138\pi$
$348$	4875.09	0.750955
$349$	3673.96	0.563503	0.281751	−	0.959487i	$-0.409085\pi$
$349$	3673.96	0.563503	0.281751	+	0.959487i	$0.409085\pi$
$350$	0	0
$351$	351.000	0.0533761
$352$	6968.17	1.05513
$353$	−3388.65	−0.510935	−0.255467	−	0.966818i	$-0.582229\pi$
$353$	−3388.65	−0.510935	−0.255467	+	0.966818i	$0.582229\pi$
$354$	−3124.75	−0.469148
$355$	453.020	0.0677290
$356$	3344.41	0.497903
$357$	0	0
$358$	16253.7	2.39955
$359$	−9673.98	−1.42221	−0.711105	−	0.703086i	$-0.751805\pi$
$359$	−9673.98	−1.42221	−0.711105	+	0.703086i	$0.751805\pi$
$360$	−1249.65	−0.182951
$361$	−5867.80	−0.855489
$362$	−988.174	−0.143473
$363$	9433.79	1.36404
$364$	0	0
$365$	−748.117	−0.107283
$366$	−11705.2	−1.67170
$367$	8715.98	1.23970	0.619851	−	0.784720i	$-0.287193\pi$
$367$	8715.98	1.23970	0.619851	+	0.784720i	$0.287193\pi$
$368$	5489.61	0.777624
$369$	−4065.44	−0.573546
$370$	−1172.91	−0.164802
$371$	0	0
$372$	3357.95	0.468014
$373$	4667.99	0.647987	0.323994	−	0.946059i	$-0.394974\pi$
$373$	4667.99	0.647987	0.323994	+	0.946059i	$0.394974\pi$
$374$	30759.4	4.25276
$375$	3111.09	0.428416
$376$	1299.36	0.178216
$377$	1458.60	0.199262
$378$	0	0
$379$	10862.7	1.47225	0.736123	−	0.676848i	$-0.236655\pi$
$379$	10862.7	1.47225	0.736123	+	0.676848i	$0.236655\pi$
$380$	2059.53	0.278031
$381$	−3744.49	−0.503507
$382$	4541.25	0.608248
$383$	−10054.2	−1.34137	−0.670686	−	0.741742i	$-0.734000\pi$
$383$	−10054.2	−1.34137	−0.670686	+	0.741742i	$0.734000\pi$
$384$	−7928.27	−1.05361
$385$	0	0
$386$	−2431.19	−0.320581
$387$	−1020.90	−0.134097
$388$	15774.7	2.06402
$389$	6418.50	0.836584	0.418292	−	0.908313i	$-0.362629\pi$
$389$	6418.50	0.836584	0.418292	+	0.908313i	$0.362629\pi$
$390$	−835.246	−0.108447
$391$	−17803.0	−2.30265
$392$	0	0
$393$	3824.40	0.490879
$394$	−18351.9	−2.34658
$395$	2462.79	0.313713
$396$	−8720.39	−1.10661
$397$	12019.9	1.51955	0.759775	−	0.650186i	$-0.225309\pi$
$397$	12019.9	1.51955	0.759775	+	0.650186i	$0.225309\pi$
$398$	−10933.5	−1.37700
$399$	0	0
$400$	−3127.52	−0.390939
$401$	3599.80	0.448293	0.224147	−	0.974555i	$-0.428041\pi$
$401$	3599.80	0.448293	0.224147	+	0.974555i	$0.428041\pi$
$402$	−12405.3	−1.53911
$403$	1004.68	0.124185
$404$	1118.60	0.137753
$405$	−365.852	−0.0448872
$406$	0	0
$407$	−3663.87	−0.446219
$408$	−8942.74	−1.08513
$409$	48.0968	0.00581475	0.00290737	−	0.999996i	$-0.499075\pi$
$409$	48.0968	0.00581475	0.00290737	+	0.999996i	$0.499075\pi$
$410$	9674.20	1.16530
$411$	2624.74	0.315010
$412$	−19572.2	−2.34042
$413$	0	0
$414$	7835.10	0.930130
$415$	−2052.99	−0.242837
$416$	−1354.06	−0.159587
$417$	−931.001	−0.109332
$418$	9987.02	1.16862
$419$	−723.462	−0.0843518	−0.0421759	−	0.999110i	$-0.513429\pi$
$419$	−723.462	−0.0843518	−0.0421759	+	0.999110i	$0.513429\pi$
$420$	0	0
$421$	−14845.5	−1.71859	−0.859295	−	0.511481i	$-0.829097\pi$
$421$	−14845.5	−1.71859	−0.859295	+	0.511481i	$0.829097\pi$
$422$	−17413.3	−2.00868
$423$	380.403	0.0437253
$424$	−16323.8	−1.86970
$425$	10142.7	1.15763
$426$	−1426.75	−0.162269
$427$	0	0
$428$	16419.2	1.85433
$429$	−2609.10	−0.293632
$430$	2429.36	0.272452
$431$	1103.11	0.123283	0.0616417	−	0.998098i	$-0.480366\pi$
$431$	1103.11	0.123283	0.0616417	+	0.998098i	$0.480366\pi$
$432$	807.297	0.0899099
$433$	−8893.53	−0.987057	−0.493528	−	0.869730i	$-0.664293\pi$
$433$	−8893.53	−0.987057	−0.493528	+	0.869730i	$0.664293\pi$
$434$	0	0
$435$	−1520.32	−0.167572
$436$	14739.1	1.61898
$437$	−5780.32	−0.632747
$438$	2356.14	0.257034
$439$	10901.7	1.18521	0.592607	−	0.805492i	$-0.298099\pi$
$439$	10901.7	1.18521	0.592607	+	0.805492i	$0.298099\pi$
$440$	9289.08	1.00645
$441$	0	0
$442$	−5977.17	−0.643224
$443$	−3781.37	−0.405550	−0.202775	−	0.979225i	$-0.564996\pi$
$443$	−3781.37	−0.405550	−0.202775	+	0.979225i	$0.564996\pi$
$444$	2379.60	0.254348
$445$	−1042.97	−0.111105
$446$	−24121.0	−2.56091
$447$	15.2419	0.00161279
$448$	0	0
$449$	106.834	0.0112289	0.00561447	−	0.999984i	$-0.498213\pi$
$449$	106.834	0.0112289	0.00561447	+	0.999984i	$0.498213\pi$
$450$	−4463.78	−0.467610
$451$	30219.7	3.15519
$452$	22739.7	2.36634
$453$	19.6468	0.00203772
$454$	12450.8	1.28710
$455$	0	0
$456$	−2903.55	−0.298182
$457$	−1237.64	−0.126684	−0.0633419	−	0.997992i	$-0.520176\pi$
$457$	−1237.64	−0.126684	−0.0633419	+	0.997992i	$0.520176\pi$
$458$	−7959.95	−0.812105
$459$	−2618.10	−0.266236
$460$	−12010.5	−1.21737
$461$	−8790.90	−0.888141	−0.444071	−	0.895992i	$-0.646466\pi$
$461$	−8790.90	−0.888141	−0.444071	+	0.895992i	$0.646466\pi$
$462$	0	0
$463$	−3861.55	−0.387606	−0.193803	−	0.981040i	$-0.562082\pi$
$463$	−3861.55	−0.387606	−0.193803	+	0.981040i	$0.562082\pi$
$464$	3354.77	0.335650
$465$	−1047.19	−0.104435
$466$	3074.99	0.305679
$467$	8991.38	0.890945	0.445473	−	0.895296i	$-0.353036\pi$
$467$	8991.38	0.890945	0.445473	+	0.895296i	$0.353036\pi$
$468$	1694.55	0.167373
$469$	0	0
$470$	−905.214	−0.0888391
$471$	6892.79	0.674316
$472$	−6752.91	−0.658533
$473$	7588.71	0.737694
$474$	−7756.39	−0.751609
$475$	3293.14	0.318105
$476$	0	0
$477$	−4778.99	−0.458731
$478$	24750.0	2.36828
$479$	−4179.82	−0.398707	−0.199354	−	0.979928i	$-0.563884\pi$
$479$	−4179.82	−0.398707	−0.199354	+	0.979928i	$0.563884\pi$
$480$	1411.35	0.134206
$481$	711.963	0.0674901
$482$	−28941.0	−2.73491
$483$	0	0
$484$	45544.2	4.27725
$485$	−4919.41	−0.460575
$486$	1152.22	0.107543
$487$	−18443.8	−1.71616	−0.858078	−	0.513519i	$-0.828342\pi$
$487$	−18443.8	−1.71616	−0.858078	+	0.513519i	$0.828342\pi$
$488$	−25296.2	−2.34653
$489$	−3256.46	−0.301149
$490$	0	0
$491$	8093.26	0.743877	0.371939	−	0.928257i	$-0.378693\pi$
$491$	8093.26	0.743877	0.371939	+	0.928257i	$0.378693\pi$
$492$	−19627.0	−1.79849
$493$	−10879.7	−0.993907
$494$	−1940.68	−0.176752
$495$	2719.49	0.246933
$496$	2310.76	0.209185
$497$	0	0
$498$	6465.73	0.581800
$499$	−10941.6	−0.981591	−0.490796	−	0.871275i	$-0.663294\pi$
$499$	−10941.6	−0.981591	−0.490796	+	0.871275i	$0.663294\pi$
$500$	15019.6	1.34340
$501$	327.197	0.0291778
$502$	−30457.5	−2.70794
$503$	9260.11	0.820851	0.410425	−	0.911894i	$-0.365380\pi$
$503$	9260.11	0.820851	0.410425	+	0.911894i	$0.365380\pi$
$504$	0	0
$505$	−348.840	−0.0307389
$506$	−58240.8	−5.11684
$507$	507.000	0.0444116
$508$	−18077.5	−1.57886
$509$	9996.40	0.870497	0.435248	−	0.900310i	$-0.356661\pi$
$509$	9996.40	0.870497	0.435248	+	0.900310i	$0.356661\pi$
$510$	6230.08	0.540927
$511$	0	0
$512$	−10467.7	−0.903538
$513$	−850.049	−0.0731591
$514$	5833.32	0.500577
$515$	6103.68	0.522253
$516$	−4928.69	−0.420491
$517$	−2827.66	−0.240542
$518$	0	0
$519$	5667.51	0.479337
$520$	−1805.06	−0.152225
$521$	−11427.9	−0.960973	−0.480486	−	0.877002i	$-0.659540\pi$
$521$	−11427.9	−0.960973	−0.480486	+	0.877002i	$0.659540\pi$
$522$	4788.14	0.401477
$523$	4810.47	0.402193	0.201097	−	0.979571i	$-0.435549\pi$
$523$	4810.47	0.402193	0.201097	+	0.979571i	$0.435549\pi$
$524$	18463.3	1.53926
$525$	0	0
$526$	−2441.92	−0.202419
$527$	−7493.88	−0.619428
$528$	−6000.90	−0.494613
$529$	21541.8	1.77051
$530$	11372.2	0.932030
$531$	−1977.00	−0.161571
$532$	0	0
$533$	−5872.31	−0.477219
$534$	3284.76	0.266190
$535$	−5120.41	−0.413785
$536$	−26809.2	−2.16042
$537$	10283.6	0.826386
$538$	24337.0	1.95027
$539$	0	0
$540$	−1766.25	−0.140754
$541$	2411.99	0.191681	0.0958406	−	0.995397i	$-0.469446\pi$
$541$	2411.99	0.191681	0.0958406	+	0.995397i	$0.469446\pi$
$542$	20389.1	1.61585
$543$	−625.208	−0.0494111
$544$	10099.9	0.796008
$545$	−4596.47	−0.361268
$546$	0	0
$547$	−4396.34	−0.343646	−0.171823	−	0.985128i	$-0.554966\pi$
$547$	−4396.34	−0.343646	−0.171823	+	0.985128i	$0.554966\pi$
$548$	12671.7	0.987786
$549$	−7405.79	−0.575722
$550$	33180.7	2.57242
$551$	−3532.43	−0.273116
$552$	16932.5	1.30560
$553$	0	0
$554$	−8595.67	−0.659197
$555$	−742.088	−0.0567565
$556$	−4494.66	−0.342835
$557$	−17488.0	−1.33032	−0.665160	−	0.746701i	$-0.731637\pi$
$557$	−17488.0	−1.33032	−0.665160	+	0.746701i	$0.731637\pi$
$558$	3298.05	0.250211
$559$	−1474.64	−0.111575
$560$	0	0
$561$	19461.2	1.46462
$562$	−19313.2	−1.44960
$563$	6881.77	0.515154	0.257577	−	0.966258i	$-0.417076\pi$
$563$	6881.77	0.515154	0.257577	+	0.966258i	$0.417076\pi$
$564$	1836.50	0.137111
$565$	−7091.49	−0.528037
$566$	−30092.0	−2.23473
$567$	0	0
$568$	−3083.36	−0.227773
$569$	14733.5	1.08552	0.542758	−	0.839889i	$-0.317380\pi$
$569$	14733.5	1.08552	0.542758	+	0.839889i	$0.317380\pi$
$570$	2022.79	0.148641
$571$	4488.51	0.328964	0.164482	−	0.986380i	$-0.447405\pi$
$571$	4488.51	0.328964	0.164482	+	0.986380i	$0.447405\pi$
$572$	−12596.1	−0.920752
$573$	2873.21	0.209476
$574$	0	0
$575$	−19204.4	−1.39284
$576$	−6597.74	−0.477267
$577$	10552.2	0.761338	0.380669	−	0.924711i	$-0.375694\pi$
$577$	10552.2	0.761338	0.380669	+	0.924711i	$0.375694\pi$
$578$	21287.8	1.53193
$579$	−1538.19	−0.110406
$580$	−7339.75	−0.525460
$581$	0	0
$582$	15493.3	1.10347
$583$	35523.8	2.52357
$584$	5091.86	0.360793
$585$	−528.452	−0.0373484
$586$	39787.1	2.80476
$587$	1637.20	0.115118	0.0575591	−	0.998342i	$-0.481668\pi$
$587$	1637.20	0.115118	0.0575591	+	0.998342i	$0.481668\pi$
$588$	0	0
$589$	−2433.13	−0.170213
$590$	4704.50	0.328273
$591$	−11611.1	−0.808147
$592$	1637.51	0.113685
$593$	−14024.0	−0.971155	−0.485577	−	0.874194i	$-0.661391\pi$
$593$	−14024.0	−0.971155	−0.485577	+	0.874194i	$0.661391\pi$
$594$	−8564.84	−0.591616
$595$	0	0
$596$	73.5845	0.00505728
$597$	−6917.50	−0.474229
$598$	11317.4	0.773915
$599$	365.860	0.0249560	0.0124780	−	0.999922i	$-0.496028\pi$
$599$	365.860	0.0249560	0.0124780	+	0.999922i	$0.496028\pi$
$600$	−9646.69	−0.656374
$601$	10128.9	0.687465	0.343733	−	0.939068i	$-0.388309\pi$
$601$	10128.9	0.687465	0.343733	+	0.939068i	$0.388309\pi$
$602$	0	0
$603$	−7848.74	−0.530058
$604$	94.8504	0.00638975
$605$	−14203.1	−0.954446
$606$	1098.65	0.0736459
$607$	−2324.97	−0.155465	−0.0777327	−	0.996974i	$-0.524768\pi$
$607$	−2324.97	−0.155465	−0.0777327	+	0.996974i	$0.524768\pi$
$608$	3279.25	0.218735
$609$	0	0
$610$	17623.0	1.16973
$611$	549.471	0.0363817
$612$	−12639.6	−0.834845
$613$	633.133	0.0417162	0.0208581	−	0.999782i	$-0.493360\pi$
$613$	633.133	0.0417162	0.0208581	+	0.999782i	$0.493360\pi$
$614$	−18991.6	−1.24827
$615$	6120.77	0.401323
$616$	0	0
$617$	−2981.85	−0.194562	−0.0972810	−	0.995257i	$-0.531015\pi$
$617$	−2981.85	−0.194562	−0.0972810	+	0.995257i	$0.531015\pi$
$618$	−19223.1	−1.25124
$619$	−15158.6	−0.984292	−0.492146	−	0.870513i	$-0.663787\pi$
$619$	−15158.6	−0.984292	−0.492146	+	0.870513i	$0.663787\pi$
$620$	−5055.60	−0.327480
$621$	4957.19	0.320330
$622$	−27674.8	−1.78402
$623$	0	0
$624$	1166.10	0.0748096
$625$	8391.01	0.537025
$626$	−8360.45	−0.533787
$627$	6318.69	0.402463
$628$	33276.8	2.11447
$629$	−5310.51	−0.336636
$630$	0	0
$631$	5562.30	0.350922	0.175461	−	0.984486i	$-0.443858\pi$
$631$	5562.30	0.350922	0.175461	+	0.984486i	$0.443858\pi$
$632$	−16762.4	−1.05502
$633$	−11017.2	−0.691776
$634$	−28954.2	−1.81375
$635$	5637.56	0.352315
$636$	−23071.9	−1.43846
$637$	0	0
$638$	−35591.7	−2.20861
$639$	−902.693	−0.0558842
$640$	11936.5	0.737237
$641$	−24140.7	−1.48752	−0.743761	−	0.668446i	$-0.766960\pi$
$641$	−24140.7	−1.48752	−0.743761	+	0.668446i	$0.766960\pi$
$642$	16126.4	0.991366
$643$	1749.69	0.107311	0.0536555	−	0.998560i	$-0.482913\pi$
$643$	1749.69	0.107311	0.0536555	+	0.998560i	$0.482913\pi$
$644$	0	0
$645$	1537.03	0.0938305
$646$	14475.5	0.881626
$647$	−1489.51	−0.0905083	−0.0452542	−	0.998976i	$-0.514410\pi$
$647$	−1489.51	−0.0905083	−0.0452542	+	0.998976i	$0.514410\pi$
$648$	2490.07	0.150956
$649$	14695.7	0.888836
$650$	−6447.68	−0.389075
$651$	0	0
$652$	−15721.4	−0.944323
$653$	10668.2	0.639327	0.319663	−	0.947531i	$-0.396430\pi$
$653$	10668.2	0.639327	0.319663	+	0.947531i	$0.396430\pi$
$654$	14476.2	0.865544
$655$	−5757.86	−0.343478
$656$	−13506.3	−0.803858
$657$	1490.71	0.0885205
$658$	0	0
$659$	−13933.1	−0.823608	−0.411804	−	0.911272i	$-0.635101\pi$
$659$	−13933.1	−0.823608	−0.411804	+	0.911272i	$0.635101\pi$
$660$	13129.1	0.774317
$661$	2349.69	0.138264	0.0691320	−	0.997608i	$-0.477977\pi$
$661$	2349.69	0.138264	0.0691320	+	0.997608i	$0.477977\pi$
$662$	35516.8	2.08520
$663$	−3781.70	−0.221522
$664$	13973.1	0.816660
$665$	0	0
$666$	2337.15	0.135980
$667$	20599.9	1.19585
$668$	1579.63	0.0914937
$669$	−15261.1	−0.881958
$670$	18677.0	1.07695
$671$	55049.6	3.16716
$672$	0	0
$673$	−32421.0	−1.85697	−0.928483	−	0.371374i	$-0.878887\pi$
$673$	−32421.0	−1.85697	−0.928483	+	0.371374i	$0.878887\pi$
$674$	44867.7	2.56415
$675$	−2824.19	−0.161042
$676$	2447.68	0.139263
$677$	1071.74	0.0608421	0.0304211	−	0.999537i	$-0.490315\pi$
$677$	1071.74	0.0608421	0.0304211	+	0.999537i	$0.490315\pi$
$678$	22334.1	1.26510
$679$	0	0
$680$	13463.9	0.759287
$681$	7877.48	0.443268
$682$	−24515.5	−1.37646
$683$	−305.487	−0.0171144	−0.00855721	−	0.999963i	$-0.502724\pi$
$683$	−305.487	−0.0171144	−0.00855721	+	0.999963i	$0.502724\pi$
$684$	−4103.84	−0.229407
$685$	−3951.72	−0.220419
$686$	0	0
$687$	−5036.18	−0.279683
$688$	−3391.66	−0.187944
$689$	−6902.99	−0.381688
$690$	−11796.2	−0.650833
$691$	−2180.81	−0.120061	−0.0600303	−	0.998197i	$-0.519120\pi$
$691$	−2180.81	−0.120061	−0.0600303	+	0.998197i	$0.519120\pi$
$692$	27361.4	1.50307
$693$	0	0
$694$	54340.9	2.97227
$695$	1401.68	0.0765018
$696$	10347.7	0.563545
$697$	43801.4	2.38034
$698$	17420.6	0.944672
$699$	1945.52	0.105274
$700$	0	0
$701$	−15168.3	−0.817259	−0.408629	−	0.912700i	$-0.633993\pi$
$701$	−15168.3	−0.817259	−0.408629	+	0.912700i	$0.633993\pi$
$702$	1664.32	0.0894812
$703$	−1724.23	−0.0925043
$704$	49043.1	2.62554
$705$	−572.720	−0.0305956
$706$	−16067.8	−0.856545
$707$	0	0
$708$	−9544.49	−0.506644
$709$	−8988.17	−0.476104	−0.238052	−	0.971252i	$-0.576509\pi$
$709$	−8988.17	−0.476104	−0.238052	+	0.971252i	$0.576509\pi$
$710$	2148.07	0.113543
$711$	−4907.39	−0.258849
$712$	7098.71	0.373645
$713$	14189.1	0.745284
$714$	0	0
$715$	3928.15	0.205461
$716$	49646.8	2.59132
$717$	15659.1	0.815619
$718$	−45870.7	−2.38423
$719$	−8448.18	−0.438198	−0.219099	−	0.975703i	$-0.570312\pi$
$719$	−8448.18	−0.438198	−0.219099	+	0.975703i	$0.570312\pi$
$720$	−1215.44	−0.0629120
$721$	0	0
$722$	−27823.1	−1.43417
$723$	−18310.7	−0.941883
$724$	−3018.36	−0.154940
$725$	−11736.1	−0.601197
$726$	44731.8	2.28671
$727$	8624.18	0.439963	0.219982	−	0.975504i	$-0.429400\pi$
$727$	8624.18	0.439963	0.219982	+	0.975504i	$0.429400\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−3547.31	−0.179852
$731$	10999.3	0.556530
$732$	−35753.5	−1.80531
$733$	−31124.2	−1.56835	−0.784174	−	0.620541i	$-0.786913\pi$
$733$	−31124.2	−1.56835	−0.784174	+	0.620541i	$0.786913\pi$
$734$	41328.2	2.07827
$735$	0	0
$736$	−19123.4	−0.957742
$737$	58342.2	2.91596
$738$	−19276.9	−0.961509
$739$	−17671.1	−0.879626	−0.439813	−	0.898089i	$-0.644955\pi$
$739$	−17671.1	−0.879626	−0.439813	+	0.898089i	$0.644955\pi$
$740$	−3582.63	−0.177973
$741$	−1227.85	−0.0608720
$742$	0	0
$743$	−21331.1	−1.05325	−0.526623	−	0.850099i	$-0.676542\pi$
$743$	−21331.1	−1.05325	−0.526623	+	0.850099i	$0.676542\pi$
$744$	7127.43	0.351215
$745$	−22.9477	−0.00112851
$746$	22134.0	1.08630
$747$	4090.81	0.200368
$748$	93954.1	4.59265
$749$	0	0
$750$	14751.7	0.718208
$751$	11712.9	0.569122	0.284561	−	0.958658i	$-0.408152\pi$
$751$	11712.9	0.569122	0.284561	+	0.958658i	$0.408152\pi$
$752$	1263.78	0.0612835
$753$	−19270.2	−0.932596
$754$	6916.20	0.334049
$755$	−29.5795	−0.00142584
$756$	0	0
$757$	−16610.9	−0.797537	−0.398768	−	0.917052i	$-0.630562\pi$
$757$	−16610.9	−0.797537	−0.398768	+	0.917052i	$0.630562\pi$
$758$	51507.4	2.46812
$759$	−36848.4	−1.76220
$760$	4371.47	0.208645
$761$	29365.5	1.39882	0.699408	−	0.714723i	$-0.253447\pi$
$761$	29365.5	1.39882	0.699408	+	0.714723i	$0.253447\pi$
$762$	−17755.1	−0.844093
$763$	0	0
$764$	13871.2	0.656861
$765$	3941.71	0.186291
$766$	−47673.5	−2.24871
$767$	−2855.66	−0.134435
$768$	−19999.2	−0.939659
$769$	28599.9	1.34114	0.670572	−	0.741844i	$-0.266049\pi$
$769$	28599.9	1.34114	0.670572	+	0.741844i	$0.266049\pi$
$770$	0	0
$771$	3690.68	0.172395
$772$	−7426.03	−0.346203
$773$	−13491.8	−0.627772	−0.313886	−	0.949461i	$-0.601631\pi$
$773$	−13491.8	−0.627772	−0.313886	+	0.949461i	$0.601631\pi$
$774$	−4840.78	−0.224804
$775$	−8083.78	−0.374681
$776$	33482.7	1.54892
$777$	0	0
$778$	30434.3	1.40247
$779$	14221.5	0.654093
$780$	−2551.25	−0.117114
$781$	6710.01	0.307430
$782$	−84415.9	−3.86024
$783$	3029.41	0.138266
$784$	0	0
$785$	−10377.5	−0.471834
$786$	18134.0	0.822923
$787$	−25876.7	−1.17205	−0.586025	−	0.810293i	$-0.699308\pi$
$787$	−25876.7	−1.17205	−0.586025	+	0.810293i	$0.699308\pi$
$788$	−56055.5	−2.53413
$789$	−1544.98	−0.0697118
$790$	11677.7	0.525918
$791$	0	0
$792$	−18509.5	−0.830438
$793$	−10697.3	−0.479030
$794$	56994.2	2.54742
$795$	7195.06	0.320984
$796$	−33396.1	−1.48705
$797$	−21936.4	−0.974938	−0.487469	−	0.873140i	$-0.662080\pi$
$797$	−21936.4	−0.974938	−0.487469	+	0.873140i	$0.662080\pi$
$798$	0	0
$799$	−4098.49	−0.181469
$800$	10894.9	0.481491
$801$	2078.23	0.0916739
$802$	17069.0	0.751531
$803$	−11080.9	−0.486969
$804$	−37891.9	−1.66212
$805$	0	0
$806$	4763.85	0.208188
$807$	15397.8	0.671658
$808$	2374.29	0.103375
$809$	5583.23	0.242640	0.121320	−	0.992613i	$-0.461287\pi$
$809$	5583.23	0.242640	0.121320	+	0.992613i	$0.461287\pi$
$810$	−1734.74	−0.0752502
$811$	−12925.4	−0.559647	−0.279823	−	0.960052i	$-0.590276\pi$
$811$	−12925.4	−0.559647	−0.279823	+	0.960052i	$0.590276\pi$
$812$	0	0
$813$	12900.0	0.556486
$814$	−17372.8	−0.748054
$815$	4902.80	0.210721
$816$	−8697.87	−0.373145
$817$	3571.27	0.152929
$818$	228.058	0.00974801
$819$	0	0
$820$	29549.7	1.25844
$821$	−10153.2	−0.431608	−0.215804	−	0.976437i	$-0.569237\pi$
$821$	−10153.2	−0.431608	−0.215804	+	0.976437i	$0.569237\pi$
$822$	12445.6	0.528092
$823$	3282.93	0.139047	0.0695235	−	0.997580i	$-0.477852\pi$
$823$	3282.93	0.139047	0.0695235	+	0.997580i	$0.477852\pi$
$824$	−41543.1	−1.75634
$825$	20993.1	0.885922
$826$	0	0
$827$	−17689.3	−0.743795	−0.371897	−	0.928274i	$-0.621293\pi$
$827$	−17689.3	−0.743795	−0.371897	+	0.928274i	$0.621293\pi$
$828$	23932.2	1.00447
$829$	−38181.5	−1.59964	−0.799818	−	0.600243i	$-0.795070\pi$
$829$	−38181.5	−1.59964	−0.799818	+	0.600243i	$0.795070\pi$
$830$	−9734.56	−0.407098
$831$	−5438.40	−0.227023
$832$	−9530.06	−0.397110
$833$	0	0
$834$	−4414.49	−0.183287
$835$	−492.615	−0.0204163
$836$	30505.2	1.26201
$837$	2086.64	0.0861708
$838$	−3430.41	−0.141410
$839$	−43895.2	−1.80623	−0.903117	−	0.429395i	$-0.858727\pi$
$839$	−43895.2	−1.80623	−0.903117	+	0.429395i	$0.858727\pi$
$840$	0	0
$841$	−11800.1	−0.483829
$842$	−70392.4	−2.88109
$843$	−12219.2	−0.499233
$844$	−53188.5	−2.16922
$845$	−763.320	−0.0310757
$846$	1803.74	0.0733024
$847$	0	0
$848$	−15876.8	−0.642938
$849$	−19038.9	−0.769626
$850$	48093.0	1.94068
$851$	10055.1	0.405034
$852$	−4358.00	−0.175238
$853$	19955.2	0.800998	0.400499	−	0.916297i	$-0.368837\pi$
$853$	19955.2	0.800998	0.400499	+	0.916297i	$0.368837\pi$
$854$	0	0
$855$	1279.80	0.0511910
$856$	34850.8	1.39156
$857$	−26030.4	−1.03755	−0.518776	−	0.854910i	$-0.673612\pi$
$857$	−26030.4	−1.03755	−0.518776	+	0.854910i	$0.673612\pi$
$858$	−12371.4	−0.492254
$859$	45617.4	1.81193	0.905964	−	0.423354i	$-0.139147\pi$
$859$	45617.4	1.81193	0.905964	+	0.423354i	$0.139147\pi$
$860$	7420.45	0.294227
$861$	0	0
$862$	5230.59	0.206676
$863$	−2010.93	−0.0793195	−0.0396597	−	0.999213i	$-0.512627\pi$
$863$	−2010.93	−0.0793195	−0.0396597	+	0.999213i	$0.512627\pi$
$864$	−2812.27	−0.110735
$865$	−8532.78	−0.335403
$866$	−42170.1	−1.65473
$867$	13468.6	0.527586
$868$	0	0
$869$	36478.2	1.42398
$870$	−7208.83	−0.280922
$871$	−11337.1	−0.441035
$872$	31284.7	1.21495
$873$	9802.48	0.380027
$874$	−27408.3	−1.06076
$875$	0	0
$876$	7196.79	0.277576
$877$	−36767.3	−1.41567	−0.707836	−	0.706376i	$-0.750329\pi$
$877$	−36767.3	−1.41567	−0.707836	+	0.706376i	$0.750329\pi$
$878$	51692.0	1.98693
$879$	25172.9	0.965940
$880$	9034.72	0.346091
$881$	−35401.2	−1.35380	−0.676899	−	0.736076i	$-0.736677\pi$
$881$	−35401.2	−1.35380	−0.676899	+	0.736076i	$0.736677\pi$
$882$	0	0
$883$	−11928.0	−0.454596	−0.227298	−	0.973825i	$-0.572989\pi$
$883$	−11928.0	−0.454596	−0.227298	+	0.973825i	$0.572989\pi$
$884$	−18257.2	−0.694633
$885$	2976.49	0.113055
$886$	−17930.0	−0.679875
$887$	32939.3	1.24689	0.623447	−	0.781866i	$-0.285732\pi$
$887$	32939.3	1.24689	0.623447	+	0.781866i	$0.285732\pi$
$888$	5050.83	0.190872
$889$	0	0
$890$	−4945.41	−0.186259
$891$	−5418.89	−0.203748
$892$	−73677.3	−2.76558
$893$	−1330.70	−0.0498660
$894$	72.2720	0.00270373
$895$	−15482.6	−0.578241
$896$	0	0
$897$	7160.38	0.266531
$898$	506.569	0.0188245
$899$	8671.18	0.321691
$900$	−13634.5	−0.504983
$901$	51489.2	1.90383
$902$	143292.	5.28946
$903$	0	0
$904$	48266.4	1.77579
$905$	941.289	0.0345740
$906$	93.1585	0.00341610
$907$	1500.89	0.0549461	0.0274731	−	0.999623i	$-0.491254\pi$
$907$	1500.89	0.0549461	0.0274731	+	0.999623i	$0.491254\pi$
$908$	38030.7	1.38997
$909$	695.102	0.0253631
$910$	0	0
$911$	19728.2	0.717481	0.358740	−	0.933437i	$-0.383206\pi$
$911$	19728.2	0.717481	0.358740	+	0.933437i	$0.383206\pi$
$912$	−2824.04	−0.102537
$913$	−30408.3	−1.10226
$914$	−5868.48	−0.212376
$915$	11149.9	0.402845
$916$	−24313.5	−0.877011
$917$	0	0
$918$	−12414.1	−0.446326
$919$	19992.0	0.717602	0.358801	−	0.933414i	$-0.383186\pi$
$919$	19992.0	0.717602	0.358801	+	0.933414i	$0.383186\pi$
$920$	−25492.9	−0.913560
$921$	−12015.8	−0.429897
$922$	−41683.4	−1.48891
$923$	−1303.89	−0.0464984
$924$	0	0
$925$	−5728.54	−0.203625
$926$	−18310.2	−0.649794
$927$	−12162.3	−0.430918
$928$	−11686.6	−0.413395
$929$	1923.62	0.0679354	0.0339677	−	0.999423i	$-0.489186\pi$
$929$	1923.62	0.0679354	0.0339677	+	0.999423i	$0.489186\pi$
$930$	−4965.42	−0.175078
$931$	0	0
$932$	9392.52	0.330110
$933$	−17509.6	−0.614403
$934$	42634.0	1.49361
$935$	−29300.0	−1.02483
$936$	3596.77	0.125603
$937$	10252.9	0.357468	0.178734	−	0.983897i	$-0.442800\pi$
$937$	10252.9	0.357468	0.178734	+	0.983897i	$0.442800\pi$
$938$	0	0
$939$	−5289.58	−0.183833
$940$	−2764.96	−0.0959394
$941$	−11043.0	−0.382563	−0.191282	−	0.981535i	$-0.561264\pi$
$941$	−11043.0	−0.382563	−0.191282	+	0.981535i	$0.561264\pi$
$942$	32683.2	1.13044
$943$	−82934.8	−2.86398
$944$	−6568.00	−0.226451
$945$	0	0
$946$	35983.1	1.23669
$947$	32105.2	1.10167	0.550833	−	0.834615i	$-0.314310\pi$
$947$	32105.2	1.10167	0.550833	+	0.834615i	$0.314310\pi$
$948$	−23691.8	−0.811680
$949$	2153.24	0.0736535
$950$	15614.9	0.533280
$951$	−18319.0	−0.624643
$952$	0	0
$953$	−9473.37	−0.322007	−0.161003	−	0.986954i	$-0.551473\pi$
$953$	−9473.37	−0.322007	−0.161003	+	0.986954i	$0.551473\pi$
$954$	−22660.3	−0.769031
$955$	−4325.79	−0.146575
$956$	75598.4	2.55756
$957$	−22518.5	−0.760628
$958$	−19819.3	−0.668404
$959$	0	0
$960$	9933.30	0.333954
$961$	−23818.3	−0.799514
$962$	3375.89	0.113142
$963$	10203.0	0.341419
$964$	−88399.8	−2.95349
$965$	2315.84	0.0772534
$966$	0	0
$967$	−5310.75	−0.176610	−0.0883052	−	0.996093i	$-0.528145\pi$
$967$	−5310.75	−0.176610	−0.0883052	+	0.996093i	$0.528145\pi$
$968$	96670.1	3.20981
$969$	9158.49	0.303626
$970$	−23326.2	−0.772122
$971$	−24271.2	−0.802164	−0.401082	−	0.916042i	$-0.631366\pi$
$971$	−24271.2	−0.802164	−0.401082	+	0.916042i	$0.631366\pi$
$972$	3519.45	0.116138
$973$	0	0
$974$	−87454.2	−2.87702
$975$	−4079.38	−0.133995
$976$	−24603.6	−0.806907
$977$	−49602.5	−1.62428	−0.812142	−	0.583460i	$-0.801699\pi$
$977$	−49602.5	−1.62428	−0.812142	+	0.583460i	$0.801699\pi$
$978$	−15441.0	−0.504856
$979$	−15448.2	−0.504317
$980$	0	0
$981$	9158.98	0.298087
$982$	38375.5	1.24706
$983$	−47385.7	−1.53751	−0.768753	−	0.639545i	$-0.779123\pi$
$983$	−47385.7	−1.53751	−0.768753	+	0.639545i	$0.779123\pi$
$984$	−41659.5	−1.34965
$985$	17481.2	0.565478
$986$	−51587.7	−1.66621
$987$	0	0
$988$	−5927.78	−0.190878
$989$	−20826.4	−0.669607
$990$	12894.9	0.413966
$991$	−8947.33	−0.286802	−0.143401	−	0.989665i	$-0.545804\pi$
$991$	−8947.33	−0.286802	−0.143401	+	0.989665i	$0.545804\pi$
$992$	−8049.67	−0.257638
$993$	22471.1	0.718127
$994$	0	0
$995$	10414.7	0.331828
$996$	19749.5	0.628299
$997$	14908.6	0.473582	0.236791	−	0.971561i	$-0.423904\pi$
$997$	14908.6	0.473582	0.236791	+	0.971561i	$0.423904\pi$
$998$	−51881.4	−1.64557
$999$	1478.69	0.0468306

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1911.4.a.h.1.2		2
7.6	odd	2		39.4.a.b.1.2	✓	2
21.20	even	2		117.4.a.c.1.1		2
28.27	even	2		624.4.a.r.1.1		2
35.34	odd	2		975.4.a.j.1.1		2
56.13	odd	2		2496.4.a.bc.1.2		2
56.27	even	2		2496.4.a.s.1.2		2
84.83	odd	2		1872.4.a.t.1.2		2
91.34	even	4		507.4.b.f.337.4		4
91.83	even	4		507.4.b.f.337.1		4
91.90	odd	2		507.4.a.f.1.1		2
273.272	even	2		1521.4.a.s.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.a.b.1.2	✓	2	7.6	odd	2
117.4.a.c.1.1		2	21.20	even	2
507.4.a.f.1.1		2	91.90	odd	2
507.4.b.f.337.1		4	91.83	even	4
507.4.b.f.337.4		4	91.34	even	4
624.4.a.r.1.1		2	28.27	even	2
975.4.a.j.1.1		2	35.34	odd	2
1521.4.a.s.1.2		2	273.272	even	2
1872.4.a.t.1.2		2	84.83	odd	2
1911.4.a.h.1.2		2	1.1	even	1	trivial
2496.4.a.s.1.2		2	56.27	even	2
2496.4.a.bc.1.2		2	56.13	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1911.a (trivial)

\(f(q)\)	\(=\)	\(q+4.74166 q^{2} +3.00000 q^{3} +14.4833 q^{4} -4.51669 q^{5} +14.2250 q^{6} +30.7417 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+4.74166 q^{2} +3.00000 q^{3} +14.4833 q^{4} -4.51669 q^{5} +14.2250 q^{6} +30.7417 q^{8} +9.00000 q^{9} -21.4166 q^{10} -66.8999 q^{11} +43.4499 q^{12} +13.0000 q^{13} -13.5501 q^{15} +29.8999 q^{16} -96.9666 q^{17} +42.6749 q^{18} -31.4833 q^{19} -65.4166 q^{20} -317.216 q^{22} +183.600 q^{23} +92.2250 q^{24} -104.600 q^{25} +61.6415 q^{26} +27.0000 q^{27} +112.200 q^{29} -64.2497 q^{30} +77.2831 q^{31} -104.158 q^{32} -200.700 q^{33} -459.783 q^{34} +130.350 q^{36} +54.7664 q^{37} -149.283 q^{38} +39.0000 q^{39} -138.850 q^{40} -451.716 q^{41} -113.434 q^{43} -968.932 q^{44} -40.6502 q^{45} +870.566 q^{46} +42.2670 q^{47} +89.6997 q^{48} -495.975 q^{50} -290.900 q^{51} +188.283 q^{52} -530.999 q^{53} +128.025 q^{54} +302.166 q^{55} -94.4499 q^{57} +532.015 q^{58} -219.666 q^{59} -196.250 q^{60} -822.865 q^{61} +366.450 q^{62} -733.082 q^{64} -58.7169 q^{65} -951.649 q^{66} -872.082 q^{67} -1404.40 q^{68} +550.799 q^{69} -100.299 q^{71} +276.675 q^{72} +165.634 q^{73} +259.684 q^{74} -313.799 q^{75} -455.983 q^{76} +184.925 q^{78} -545.266 q^{79} -135.048 q^{80} +81.0000 q^{81} -2141.88 q^{82} +454.534 q^{83} +437.968 q^{85} -537.864 q^{86} +336.601 q^{87} -2056.61 q^{88} +230.915 q^{89} -192.749 q^{90} +2659.13 q^{92} +231.849 q^{93} +200.415 q^{94} +142.200 q^{95} -312.475 q^{96} +1089.16 q^{97} -602.099 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 6 q^{3} + 14 q^{4} - 24 q^{5} + 6 q^{6} + 54 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 6 * q^3 + 14 * q^4 - 24 * q^5 + 6 * q^6 + 54 * q^8 + 18 * q^9	\( 2 q + 2 q^{2} + 6 q^{3} + 14 q^{4} - 24 q^{5} + 6 q^{6} + 54 q^{8} + 18 q^{9} + 32 q^{10} - 44 q^{11} + 42 q^{12} + 26 q^{13} - 72 q^{15} - 30 q^{16} - 164 q^{17} + 18 q^{18} - 48 q^{19} - 56 q^{20} - 380 q^{22} + 8 q^{23} + 162 q^{24} + 150 q^{25} + 26 q^{26} + 54 q^{27} + 404 q^{29} + 96 q^{30} - 40 q^{31} - 126 q^{32} - 132 q^{33} - 276 q^{34} + 126 q^{36} - 100 q^{37} - 104 q^{38} + 78 q^{39} - 592 q^{40} - 200 q^{41} - 616 q^{43} - 980 q^{44} - 216 q^{45} + 1352 q^{46} + 324 q^{47} - 90 q^{48} - 1194 q^{50} - 492 q^{51} + 182 q^{52} - 164 q^{53} + 54 q^{54} - 144 q^{55} - 144 q^{57} - 268 q^{58} - 140 q^{59} - 168 q^{60} - 628 q^{61} + 688 q^{62} - 194 q^{64} - 312 q^{65} - 1140 q^{66} - 472 q^{67} - 1372 q^{68} + 24 q^{69} + 428 q^{71} + 486 q^{72} + 900 q^{73} + 684 q^{74} + 450 q^{75} - 448 q^{76} + 78 q^{78} - 432 q^{79} + 1032 q^{80} + 162 q^{81} - 2832 q^{82} + 1388 q^{83} + 1744 q^{85} + 840 q^{86} + 1212 q^{87} - 1524 q^{88} - 960 q^{89} + 288 q^{90} + 2744 q^{92} - 120 q^{93} - 572 q^{94} + 464 q^{95} - 378 q^{96} + 532 q^{97} - 396 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 6 * q^3 + 14 * q^4 - 24 * q^5 + 6 * q^6 + 54 * q^8 + 18 * q^9 + 32 * q^10 - 44 * q^11 + 42 * q^12 + 26 * q^13 - 72 * q^15 - 30 * q^16 - 164 * q^17 + 18 * q^18 - 48 * q^19 - 56 * q^20 - 380 * q^22 + 8 * q^23 + 162 * q^24 + 150 * q^25 + 26 * q^26 + 54 * q^27 + 404 * q^29 + 96 * q^30 - 40 * q^31 - 126 * q^32 - 132 * q^33 - 276 * q^34 + 126 * q^36 - 100 * q^37 - 104 * q^38 + 78 * q^39 - 592 * q^40 - 200 * q^41 - 616 * q^43 - 980 * q^44 - 216 * q^45 + 1352 * q^46 + 324 * q^47 - 90 * q^48 - 1194 * q^50 - 492 * q^51 + 182 * q^52 - 164 * q^53 + 54 * q^54 - 144 * q^55 - 144 * q^57 - 268 * q^58 - 140 * q^59 - 168 * q^60 - 628 * q^61 + 688 * q^62 - 194 * q^64 - 312 * q^65 - 1140 * q^66 - 472 * q^67 - 1372 * q^68 + 24 * q^69 + 428 * q^71 + 486 * q^72 + 900 * q^73 + 684 * q^74 + 450 * q^75 - 448 * q^76 + 78 * q^78 - 432 * q^79 + 1032 * q^80 + 162 * q^81 - 2832 * q^82 + 1388 * q^83 + 1744 * q^85 + 840 * q^86 + 1212 * q^87 - 1524 * q^88 - 960 * q^89 + 288 * q^90 + 2744 * q^92 - 120 * q^93 - 572 * q^94 + 464 * q^95 - 378 * q^96 + 532 * q^97 - 396 * q^99

Introduction

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