LMFDB - Embedded newform 1911.4.a.k.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:	$3$
Coefficient field:	3.3.3144.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 16x - 8 $ x^3 - x^2 - 16*x - 8
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 39)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.526440$ 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)

$f(q)$	$=$	$q+1.52644 q^{2} -3.00000 q^{3} -5.66998 q^{4} -19.3400 q^{5} -4.57932 q^{6} -20.8664 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+1.52644 q^{2} -3.00000 q^{3} -5.66998 q^{4} -19.3400 q^{5} -4.57932 q^{6} -20.8664 q^{8} +9.00000 q^{9} -29.5213 q^{10} -61.0728 q^{11} +17.0099 q^{12} -13.0000 q^{13} +58.0199 q^{15} +13.5085 q^{16} +41.7885 q^{17} +13.7380 q^{18} +107.561 q^{19} +109.657 q^{20} -93.2239 q^{22} +28.5138 q^{23} +62.5992 q^{24} +249.034 q^{25} -19.8437 q^{26} -27.0000 q^{27} -89.8886 q^{29} +88.5639 q^{30} -183.108 q^{31} +187.551 q^{32} +183.218 q^{33} +63.7876 q^{34} -51.0298 q^{36} +418.029 q^{37} +164.185 q^{38} +39.0000 q^{39} +403.555 q^{40} +142.674 q^{41} -71.0935 q^{43} +346.281 q^{44} -174.060 q^{45} +43.5246 q^{46} -323.711 q^{47} -40.5256 q^{48} +380.136 q^{50} -125.365 q^{51} +73.7098 q^{52} -25.1047 q^{53} -41.2139 q^{54} +1181.15 q^{55} -322.683 q^{57} -137.210 q^{58} +684.508 q^{59} -328.972 q^{60} -308.125 q^{61} -279.503 q^{62} +178.217 q^{64} +251.420 q^{65} +279.672 q^{66} +672.808 q^{67} -236.940 q^{68} -85.5413 q^{69} -326.837 q^{71} -187.798 q^{72} -24.3058 q^{73} +638.095 q^{74} -747.103 q^{75} -609.869 q^{76} +59.5311 q^{78} +166.810 q^{79} -261.255 q^{80} +81.0000 q^{81} +217.783 q^{82} +201.093 q^{83} -808.188 q^{85} -108.520 q^{86} +269.666 q^{87} +1274.37 q^{88} -108.834 q^{89} -265.692 q^{90} -161.673 q^{92} +549.323 q^{93} -494.126 q^{94} -2080.23 q^{95} -562.654 q^{96} -1157.95 q^{97} -549.655 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} - 9 q^{3} + 10 q^{4} - 4 q^{5} - 6 q^{6} - 6 q^{8} + 27 q^{9}+O(q^{10}) $ 3 * q + 2 * q^2 - 9 * q^3 + 10 * q^4 - 4 * q^5 - 6 * q^6 - 6 * q^8 + 27 * q^9	\( 3 q + 2 q^{2} - 9 q^{3} + 10 q^{4} - 4 q^{5} - 6 q^{6} - 6 q^{8} + 27 q^{9} + 4 q^{10} - 16 q^{11} - 30 q^{12} - 39 q^{13} + 12 q^{15} - 110 q^{16} + 146 q^{17} + 18 q^{18} - 94 q^{19} + 244 q^{20} - 56 q^{22} - 48 q^{23} + 18 q^{24} + 145 q^{25} - 26 q^{26} - 81 q^{27} - 2 q^{29} - 12 q^{30} - 302 q^{31} + 154 q^{32} + 48 q^{33} - 164 q^{34} + 90 q^{36} + 374 q^{37} - 312 q^{38} + 117 q^{39} + 516 q^{40} - 480 q^{41} - 260 q^{43} + 712 q^{44} - 36 q^{45} - 1104 q^{46} + 24 q^{47} + 330 q^{48} + 814 q^{50} - 438 q^{51} - 130 q^{52} - 678 q^{53} - 54 q^{54} + 1552 q^{55} + 282 q^{57} - 628 q^{58} + 1788 q^{59} - 732 q^{60} - 230 q^{61} - 1952 q^{62} - 750 q^{64} + 52 q^{65} + 168 q^{66} + 74 q^{67} + 460 q^{68} + 144 q^{69} - 948 q^{71} - 54 q^{72} + 222 q^{73} + 1724 q^{74} - 435 q^{75} - 2392 q^{76} + 78 q^{78} - 24 q^{79} - 1100 q^{80} + 243 q^{81} - 564 q^{82} + 796 q^{83} - 248 q^{85} + 1800 q^{86} + 6 q^{87} + 1608 q^{88} - 1436 q^{89} + 36 q^{90} - 1296 q^{92} + 906 q^{93} + 1920 q^{94} - 4032 q^{95} - 462 q^{96} - 3242 q^{97} - 144 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 - 9 * q^3 + 10 * q^4 - 4 * q^5 - 6 * q^6 - 6 * q^8 + 27 * q^9 + 4 * q^10 - 16 * q^11 - 30 * q^12 - 39 * q^13 + 12 * q^15 - 110 * q^16 + 146 * q^17 + 18 * q^18 - 94 * q^19 + 244 * q^20 - 56 * q^22 - 48 * q^23 + 18 * q^24 + 145 * q^25 - 26 * q^26 - 81 * q^27 - 2 * q^29 - 12 * q^30 - 302 * q^31 + 154 * q^32 + 48 * q^33 - 164 * q^34 + 90 * q^36 + 374 * q^37 - 312 * q^38 + 117 * q^39 + 516 * q^40 - 480 * q^41 - 260 * q^43 + 712 * q^44 - 36 * q^45 - 1104 * q^46 + 24 * q^47 + 330 * q^48 + 814 * q^50 - 438 * q^51 - 130 * q^52 - 678 * q^53 - 54 * q^54 + 1552 * q^55 + 282 * q^57 - 628 * q^58 + 1788 * q^59 - 732 * q^60 - 230 * q^61 - 1952 * q^62 - 750 * q^64 + 52 * q^65 + 168 * q^66 + 74 * q^67 + 460 * q^68 + 144 * q^69 - 948 * q^71 - 54 * q^72 + 222 * q^73 + 1724 * q^74 - 435 * q^75 - 2392 * q^76 + 78 * q^78 - 24 * q^79 - 1100 * q^80 + 243 * q^81 - 564 * q^82 + 796 * q^83 - 248 * q^85 + 1800 * q^86 + 6 * q^87 + 1608 * q^88 - 1436 * q^89 + 36 * q^90 - 1296 * q^92 + 906 * q^93 + 1920 * q^94 - 4032 * q^95 - 462 * q^96 - 3242 * q^97 - 144 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.52644	0.539678	0.269839	−	0.962905i	$-0.413030\pi$
$2$	1.52644	0.539678	0.269839	+	0.962905i	$0.413030\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−5.66998	−0.708748
$5$	−19.3400	−1.72982	−0.864909	−	0.501928i	$-0.832624\pi$
$5$	−19.3400	−1.72982	−0.864909	+	0.501928i	$0.832624\pi$
$6$	−4.57932	−0.311583
$7$	0	0
$7$	0	0
$8$	−20.8664	−0.922173
$9$	9.00000	0.333333
$10$	−29.5213	−0.933545
$11$	−61.0728	−1.67401	−0.837006	−	0.547194i	$-0.815696\pi$
$11$	−61.0728	−1.67401	−0.837006	+	0.547194i	$0.815696\pi$
$12$	17.0099	0.409196
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	0	0
$15$	58.0199	0.998711
$16$	13.5085	0.211071
$17$	41.7885	0.596188	0.298094	−	0.954537i	$-0.403649\pi$
$17$	41.7885	0.596188	0.298094	+	0.954537i	$0.403649\pi$
$18$	13.7380	0.179893
$19$	107.561	1.29875	0.649374	−	0.760469i	$-0.275031\pi$
$19$	107.561	1.29875	0.649374	+	0.760469i	$0.275031\pi$
$20$	109.657	1.22601
$21$	0	0
$22$	−93.2239	−0.903427
$23$	28.5138	0.258502	0.129251	−	0.991612i	$-0.458743\pi$
$23$	28.5138	0.258502	0.129251	+	0.991612i	$0.458743\pi$
$24$	62.5992	0.532417
$25$	249.034	1.99227
$26$	−19.8437	−0.149680
$27$	−27.0000	−0.192450
$28$	0	0
$29$	−89.8886	−0.575583	−0.287791	−	0.957693i	$-0.592921\pi$
$29$	−89.8886	−0.575583	−0.287791	+	0.957693i	$0.592921\pi$
$30$	88.5639	0.538983
$31$	−183.108	−1.06087	−0.530437	−	0.847724i	$-0.677972\pi$
$31$	−183.108	−1.06087	−0.530437	+	0.847724i	$0.677972\pi$
$32$	187.551	1.03608
$33$	183.218	0.966491
$34$	63.7876	0.321750
$35$	0	0
$36$	−51.0298	−0.236249
$37$	418.029	1.85739	0.928696	−	0.370843i	$-0.120931\pi$
$37$	418.029	1.85739	0.928696	+	0.370843i	$0.120931\pi$
$38$	164.185	0.700905
$39$	39.0000	0.160128
$40$	403.555	1.59519
$41$	142.674	0.543460	0.271730	−	0.962373i	$-0.412404\pi$
$41$	142.674	0.543460	0.271730	+	0.962373i	$0.412404\pi$
$42$	0	0
$43$	−71.0935	−0.252132	−0.126066	−	0.992022i	$-0.540235\pi$
$43$	−71.0935	−0.252132	−0.126066	+	0.992022i	$0.540235\pi$
$44$	346.281	1.18645
$45$	−174.060	−0.576606
$46$	43.5246	0.139508
$47$	−323.711	−1.00464	−0.502321	−	0.864681i	$-0.667520\pi$
$47$	−323.711	−1.00464	−0.502321	+	0.864681i	$0.667520\pi$
$48$	−40.5256	−0.121862
$49$	0	0
$50$	380.136	1.07519
$51$	−125.365	−0.344209
$52$	73.7098	0.196571
$53$	−25.1047	−0.0650641	−0.0325321	−	0.999471i	$-0.510357\pi$
$53$	−25.1047	−0.0650641	−0.0325321	+	0.999471i	$0.510357\pi$
$54$	−41.2139	−0.103861
$55$	1181.15	2.89574
$56$	0	0
$57$	−322.683	−0.749832
$58$	−137.210	−0.310629
$59$	684.508	1.51043	0.755215	−	0.655477i	$-0.227533\pi$
$59$	684.508	1.51043	0.755215	+	0.655477i	$0.227533\pi$
$60$	−328.972	−0.707834
$61$	−308.125	−0.646744	−0.323372	−	0.946272i	$-0.604816\pi$
$61$	−308.125	−0.646744	−0.323372	+	0.946272i	$0.604816\pi$
$62$	−279.503	−0.572531
$63$	0	0
$64$	178.217	0.348081
$65$	251.420	0.479765
$66$	279.672	0.521594
$67$	672.808	1.22681	0.613407	−	0.789767i	$-0.289798\pi$
$67$	672.808	1.22681	0.613407	+	0.789767i	$0.289798\pi$
$68$	−236.940	−0.422547
$69$	−85.5413	−0.149246
$70$	0	0
$71$	−326.837	−0.546315	−0.273158	−	0.961969i	$-0.588068\pi$
$71$	−326.837	−0.546315	−0.273158	+	0.961969i	$0.588068\pi$
$72$	−187.798	−0.307391
$73$	−24.3058	−0.0389695	−0.0194847	−	0.999810i	$-0.506203\pi$
$73$	−24.3058	−0.0389695	−0.0194847	+	0.999810i	$0.506203\pi$
$74$	638.095	1.00239
$75$	−747.103	−1.15024
$76$	−609.869	−0.920484
$77$	0	0
$78$	59.5311	0.0864176
$79$	166.810	0.237565	0.118783	−	0.992920i	$-0.462101\pi$
$79$	166.810	0.237565	0.118783	+	0.992920i	$0.462101\pi$
$80$	−261.255	−0.365115
$81$	81.0000	0.111111
$82$	217.783	0.293294
$83$	201.093	0.265938	0.132969	−	0.991120i	$-0.457549\pi$
$83$	201.093	0.265938	0.132969	+	0.991120i	$0.457549\pi$
$84$	0	0
$85$	−808.188	−1.03130
$86$	−108.520	−0.136070
$87$	269.666	0.332313
$88$	1274.37	1.54373
$89$	−108.834	−0.129622	−0.0648109	−	0.997898i	$-0.520644\pi$
$89$	−108.834	−0.129622	−0.0648109	+	0.997898i	$0.520644\pi$
$90$	−265.692	−0.311182
$91$	0	0
$92$	−161.673	−0.183212
$93$	549.323	0.612496
$94$	−494.126	−0.542183
$95$	−2080.23	−2.24660
$96$	−562.654	−0.598183
$97$	−1157.95	−1.21208	−0.606041	−	0.795434i	$-0.707243\pi$
$97$	−1157.95	−1.21208	−0.606041	+	0.795434i	$0.707243\pi$
$98$	0	0
$99$	−549.655	−0.558004
$100$	−1412.02	−1.41202
$101$	−1702.75	−1.67752	−0.838761	−	0.544500i	$-0.816719\pi$
$101$	−1702.75	−1.67752	−0.838761	+	0.544500i	$0.816719\pi$
$102$	−191.363	−0.185762
$103$	1455.14	1.39203	0.696015	−	0.718027i	$-0.254955\pi$
$103$	1455.14	1.39203	0.696015	+	0.718027i	$0.254955\pi$
$104$	271.263	0.255765
$105$	0	0
$106$	−38.3209	−0.0351137
$107$	−822.762	−0.743359	−0.371679	−	0.928361i	$-0.621218\pi$
$107$	−822.762	−0.743359	−0.371679	+	0.928361i	$0.621218\pi$
$108$	153.090	0.136399
$109$	457.264	0.401816	0.200908	−	0.979610i	$-0.435611\pi$
$109$	457.264	0.401816	0.200908	+	0.979610i	$0.435611\pi$
$110$	1802.95	1.56277
$111$	−1254.09	−1.07237
$112$	0	0
$113$	−381.693	−0.317758	−0.158879	−	0.987298i	$-0.550788\pi$
$113$	−381.693	−0.317758	−0.158879	+	0.987298i	$0.550788\pi$
$114$	−492.556	−0.404668
$115$	−551.456	−0.447161
$116$	509.667	0.407943
$117$	−117.000	−0.0924500
$118$	1044.86	0.815146
$119$	0	0
$120$	−1210.67	−0.920985
$121$	2398.88	1.80232
$122$	−470.334	−0.349033
$123$	−428.021	−0.313767
$124$	1038.22	0.751892
$125$	−2398.82	−1.71645
$126$	0	0
$127$	−1129.09	−0.788905	−0.394452	−	0.918916i	$-0.629066\pi$
$127$	−1129.09	−0.788905	−0.394452	+	0.918916i	$0.629066\pi$
$128$	−1228.37	−0.848232
$129$	213.281	0.145568
$130$	383.777	0.258919
$131$	852.761	0.568749	0.284374	−	0.958713i	$-0.408214\pi$
$131$	852.761	0.568749	0.284374	+	0.958713i	$0.408214\pi$
$132$	−1038.84	−0.684999
$133$	0	0
$134$	1027.00	0.662085
$135$	522.179	0.332904
$136$	−871.975	−0.549789
$137$	−488.903	−0.304889	−0.152445	−	0.988312i	$-0.548715\pi$
$137$	−488.903	−0.304889	−0.152445	+	0.988312i	$0.548715\pi$
$138$	−130.574	−0.0805447
$139$	−407.123	−0.248430	−0.124215	−	0.992255i	$-0.539641\pi$
$139$	−407.123	−0.248430	−0.124215	+	0.992255i	$0.539641\pi$
$140$	0	0
$141$	971.134	0.580030
$142$	−498.897	−0.294834
$143$	793.946	0.464287
$144$	121.577	0.0703570
$145$	1738.44	0.995654
$146$	−37.1013	−0.0210310
$147$	0	0
$148$	−2370.21	−1.31642
$149$	1717.63	0.944388	0.472194	−	0.881495i	$-0.343462\pi$
$149$	1717.63	0.944388	0.472194	+	0.881495i	$0.343462\pi$
$150$	−1140.41	−0.620759
$151$	1341.79	0.723133	0.361567	−	0.932346i	$-0.382242\pi$
$151$	1341.79	0.723133	0.361567	+	0.932346i	$0.382242\pi$
$152$	−2244.41	−1.19767
$153$	376.096	0.198729
$154$	0	0
$155$	3541.30	1.83512
$156$	−221.129	−0.113490
$157$	760.546	0.386612	0.193306	−	0.981138i	$-0.438079\pi$
$157$	760.546	0.386612	0.193306	+	0.981138i	$0.438079\pi$
$158$	254.626	0.128209
$159$	75.3142	0.0375648
$160$	−3627.23	−1.79224
$161$	0	0
$162$	123.642	0.0599642
$163$	2712.09	1.30323	0.651616	−	0.758549i	$-0.274091\pi$
$163$	2712.09	1.30323	0.651616	+	0.758549i	$0.274091\pi$
$164$	−808.957	−0.385176
$165$	−3543.44	−1.67185
$166$	306.957	0.143521
$167$	−1551.69	−0.719004	−0.359502	−	0.933144i	$-0.617053\pi$
$167$	−1551.69	−0.719004	−0.359502	+	0.933144i	$0.617053\pi$
$168$	0	0
$169$	169.000	0.0769231
$170$	−1233.65	−0.556568
$171$	968.050	0.432916
$172$	403.099	0.178698
$173$	3970.26	1.74482	0.872409	−	0.488777i	$-0.162557\pi$
$173$	3970.26	1.74482	0.872409	+	0.488777i	$0.162557\pi$
$174$	411.629	0.179342
$175$	0	0
$176$	−825.004	−0.353335
$177$	−2053.52	−0.872047
$178$	−166.128	−0.0699540
$179$	−2690.95	−1.12364	−0.561818	−	0.827261i	$-0.689898\pi$
$179$	−2690.95	−1.12364	−0.561818	+	0.827261i	$0.689898\pi$
$180$	986.915	0.408668
$181$	4371.10	1.79503	0.897517	−	0.440980i	$-0.145369\pi$
$181$	4371.10	1.79503	0.897517	+	0.440980i	$0.145369\pi$
$182$	0	0
$183$	924.375	0.373398
$184$	−594.980	−0.238383
$185$	−8084.66	−3.21295
$186$	838.508	0.330551
$187$	−2552.14	−0.998026
$188$	1835.44	0.712038
$189$	0	0
$190$	−3175.34	−1.21244
$191$	1408.47	0.533578	0.266789	−	0.963755i	$-0.414037\pi$
$191$	1408.47	0.533578	0.266789	+	0.963755i	$0.414037\pi$
$192$	−534.652	−0.200964
$193$	−4131.69	−1.54096	−0.770481	−	0.637463i	$-0.779984\pi$
$193$	−4131.69	−1.54096	−0.770481	+	0.637463i	$0.779984\pi$
$194$	−1767.54	−0.654134
$195$	−754.259	−0.276993
$196$	0	0
$197$	−3401.23	−1.23009	−0.615045	−	0.788492i	$-0.710862\pi$
$197$	−3401.23	−1.23009	−0.615045	+	0.788492i	$0.710862\pi$
$198$	−839.015	−0.301142
$199$	3520.74	1.25416	0.627081	−	0.778954i	$-0.284249\pi$
$199$	3520.74	1.25416	0.627081	+	0.778954i	$0.284249\pi$
$200$	−5196.45	−1.83722
$201$	−2018.42	−0.708302
$202$	−2599.14	−0.905321
$203$	0	0
$204$	710.820	0.243958
$205$	−2759.30	−0.940088
$206$	2221.18	0.751248
$207$	256.624	0.0861672
$208$	−175.611	−0.0585406
$209$	−6569.05	−2.17412
$210$	0	0
$211$	−2245.22	−0.732545	−0.366272	−	0.930508i	$-0.619366\pi$
$211$	−2245.22	−0.732545	−0.366272	+	0.930508i	$0.619366\pi$
$212$	142.343	0.0461141
$213$	980.510	0.315415
$214$	−1255.90	−0.401174
$215$	1374.95	0.436142
$216$	563.393	0.177472
$217$	0	0
$218$	697.986	0.216851
$219$	72.9173	0.0224990
$220$	−6697.07	−2.05235
$221$	−543.250	−0.165353
$222$	−1914.29	−0.578732
$223$	−3431.26	−1.03038	−0.515188	−	0.857077i	$-0.672278\pi$
$223$	−3431.26	−1.03038	−0.515188	+	0.857077i	$0.672278\pi$
$224$	0	0
$225$	2241.31	0.664091
$226$	−582.631	−0.171487
$227$	4757.91	1.39116	0.695581	−	0.718448i	$-0.255147\pi$
$227$	4757.91	1.39116	0.695581	+	0.718448i	$0.255147\pi$
$228$	1829.61	0.531442
$229$	4368.93	1.26073	0.630364	−	0.776300i	$-0.282906\pi$
$229$	4368.93	1.26073	0.630364	+	0.776300i	$0.282906\pi$
$230$	−841.764	−0.241323
$231$	0	0
$232$	1875.65	0.530787
$233$	−3642.00	−1.02401	−0.512007	−	0.858981i	$-0.671098\pi$
$233$	−3642.00	−1.02401	−0.512007	+	0.858981i	$0.671098\pi$
$234$	−178.593	−0.0498932
$235$	6260.57	1.73785
$236$	−3881.15	−1.07051
$237$	−500.431	−0.137158
$238$	0	0
$239$	2236.17	0.605213	0.302606	−	0.953116i	$-0.402143\pi$
$239$	2236.17	0.605213	0.302606	+	0.953116i	$0.402143\pi$
$240$	783.764	0.210799
$241$	−6538.78	−1.74772	−0.873858	−	0.486181i	$-0.838390\pi$
$241$	−6538.78	−1.74772	−0.873858	+	0.486181i	$0.838390\pi$
$242$	3661.75	0.972670
$243$	−243.000	−0.0641500
$244$	1747.06	0.458378
$245$	0	0
$246$	−653.348	−0.169333
$247$	−1398.29	−0.360208
$248$	3820.80	0.978310
$249$	−603.280	−0.153539
$250$	−3661.65	−0.926332
$251$	−2507.12	−0.630470	−0.315235	−	0.949014i	$-0.602083\pi$
$251$	−2507.12	−0.630470	−0.315235	+	0.949014i	$0.602083\pi$
$252$	0	0
$253$	−1741.42	−0.432735
$254$	−1723.49	−0.425755
$255$	2424.56	0.595420
$256$	−3300.77	−0.805853
$257$	808.131	0.196147	0.0980735	−	0.995179i	$-0.468732\pi$
$257$	808.131	0.196147	0.0980735	+	0.995179i	$0.468732\pi$
$258$	325.560	0.0785600
$259$	0	0
$260$	−1425.54	−0.340033
$261$	−808.998	−0.191861
$262$	1301.69	0.306941
$263$	2940.70	0.689472	0.344736	−	0.938700i	$-0.387968\pi$
$263$	2940.70	0.689472	0.344736	+	0.938700i	$0.387968\pi$
$264$	−3823.11	−0.891273
$265$	485.525	0.112549
$266$	0	0
$267$	326.501	0.0748371
$268$	−3814.81	−0.869502
$269$	−7111.50	−1.61188	−0.805940	−	0.591997i	$-0.798340\pi$
$269$	−7111.50	−1.61188	−0.805940	+	0.591997i	$0.798340\pi$
$270$	797.075	0.179661
$271$	−2034.96	−0.456145	−0.228072	−	0.973644i	$-0.573242\pi$
$271$	−2034.96	−0.456145	−0.228072	+	0.973644i	$0.573242\pi$
$272$	564.502	0.125838
$273$	0	0
$274$	−746.281	−0.164542
$275$	−15209.2	−3.33509
$276$	485.018	0.105778
$277$	2723.20	0.590689	0.295345	−	0.955391i	$-0.404566\pi$
$277$	2723.20	0.590689	0.295345	+	0.955391i	$0.404566\pi$
$278$	−621.449	−0.134072
$279$	−1647.97	−0.353625
$280$	0	0
$281$	3265.56	0.693263	0.346632	−	0.938001i	$-0.387325\pi$
$281$	3265.56	0.693263	0.346632	+	0.938001i	$0.387325\pi$
$282$	1482.38	0.313030
$283$	−1144.02	−0.240299	−0.120150	−	0.992756i	$-0.538337\pi$
$283$	−1144.02	−0.240299	−0.120150	+	0.992756i	$0.538337\pi$
$284$	1853.16	0.387200
$285$	6240.68	1.29707
$286$	1211.91	0.250566
$287$	0	0
$288$	1687.96	0.345361
$289$	−3166.72	−0.644560
$290$	2653.63	0.537333
$291$	3473.85	0.699796
$292$	137.813	0.0276195
$293$	1677.35	0.334444	0.167222	−	0.985919i	$-0.446520\pi$
$293$	1677.35	0.334444	0.167222	+	0.985919i	$0.446520\pi$
$294$	0	0
$295$	−13238.4	−2.61277
$296$	−8722.75	−1.71284
$297$	1648.96	0.322164
$298$	2621.86	0.509666
$299$	−370.679	−0.0716954
$300$	4236.06	0.815230
$301$	0	0
$302$	2048.16	0.390259
$303$	5108.24	0.968518
$304$	1452.99	0.274128
$305$	5959.13	1.11875
$306$	574.088	0.107250
$307$	−7207.70	−1.33995	−0.669975	−	0.742383i	$-0.733695\pi$
$307$	−7207.70	−1.33995	−0.669975	+	0.742383i	$0.733695\pi$
$308$	0	0
$309$	−4365.42	−0.803689
$310$	5405.57	0.990374
$311$	−412.963	−0.0752958	−0.0376479	−	0.999291i	$-0.511987\pi$
$311$	−412.963	−0.0752958	−0.0376479	+	0.999291i	$0.511987\pi$
$312$	−813.790	−0.147666
$313$	−2936.39	−0.530270	−0.265135	−	0.964211i	$-0.585417\pi$
$313$	−2936.39	−0.530270	−0.265135	+	0.964211i	$0.585417\pi$
$314$	1160.93	0.208646
$315$	0	0
$316$	−945.812	−0.168374
$317$	377.956	0.0669657	0.0334828	−	0.999439i	$-0.489340\pi$
$317$	377.956	0.0669657	0.0334828	+	0.999439i	$0.489340\pi$
$318$	114.963	0.0202729
$319$	5489.75	0.963533
$320$	−3446.71	−0.602116
$321$	2468.28	0.429178
$322$	0	0
$323$	4494.81	0.774298
$324$	−459.269	−0.0787497
$325$	−3237.44	−0.552557
$326$	4139.83	0.703326
$327$	−1371.79	−0.231989
$328$	−2977.09	−0.501165
$329$	0	0
$330$	−5408.84	−0.902263
$331$	−4428.17	−0.735330	−0.367665	−	0.929958i	$-0.619843\pi$
$331$	−4428.17	−0.735330	−0.367665	+	0.929958i	$0.619843\pi$
$332$	−1140.20	−0.188483
$333$	3762.26	0.619130
$334$	−2368.57	−0.388031
$335$	−13012.1	−2.12217
$336$	0	0
$337$	−1768.76	−0.285907	−0.142953	−	0.989729i	$-0.545660\pi$
$337$	−1768.76	−0.285907	−0.142953	+	0.989729i	$0.545660\pi$
$338$	257.968	0.0415137
$339$	1145.08	0.183458
$340$	4582.41	0.730930
$341$	11182.9	1.77592
$342$	1477.67	0.233635
$343$	0	0
$344$	1483.47	0.232509
$345$	1654.37	0.258168
$346$	6060.36	0.941639
$347$	2412.97	0.373300	0.186650	−	0.982426i	$-0.440237\pi$
$347$	2412.97	0.373300	0.186650	+	0.982426i	$0.440237\pi$
$348$	−1529.00	−0.235526
$349$	9967.45	1.52878	0.764392	−	0.644752i	$-0.223039\pi$
$349$	9967.45	1.52878	0.764392	+	0.644752i	$0.223039\pi$
$350$	0	0
$351$	351.000	0.0533761
$352$	−11454.3	−1.73442
$353$	−4516.30	−0.680959	−0.340479	−	0.940252i	$-0.610589\pi$
$353$	−4516.30	−0.680959	−0.340479	+	0.940252i	$0.610589\pi$
$354$	−3134.58	−0.470625
$355$	6321.01	0.945027
$356$	617.084	0.0918691
$357$	0	0
$358$	−4107.57	−0.606401
$359$	12159.8	1.78767	0.893833	−	0.448400i	$-0.148006\pi$
$359$	12159.8	1.78767	0.893833	+	0.448400i	$0.148006\pi$
$360$	3632.00	0.531731
$361$	4710.38	0.686745
$362$	6672.22	0.968740
$363$	−7196.65	−1.04057
$364$	0	0
$365$	470.072	0.0674102
$366$	1411.00	0.201514
$367$	2674.25	0.380367	0.190183	−	0.981749i	$-0.439092\pi$
$367$	2674.25	0.380367	0.190183	+	0.981749i	$0.439092\pi$
$368$	385.180	0.0545622
$369$	1284.06	0.181153
$370$	−12340.7	−1.73396
$371$	0	0
$372$	−3114.65	−0.434105
$373$	9601.74	1.33287	0.666433	−	0.745564i	$-0.267820\pi$
$373$	9601.74	1.33287	0.666433	+	0.745564i	$0.267820\pi$
$374$	−3895.69	−0.538613
$375$	7196.45	0.990995
$376$	6754.69	0.926454
$377$	1168.55	0.159638
$378$	0	0
$379$	9019.65	1.22245	0.611225	−	0.791457i	$-0.290677\pi$
$379$	9019.65	1.22245	0.611225	+	0.791457i	$0.290677\pi$
$380$	11794.9	1.59227
$381$	3387.28	0.455474
$382$	2149.95	0.287960
$383$	4015.34	0.535703	0.267852	−	0.963460i	$-0.413686\pi$
$383$	4015.34	0.535703	0.267852	+	0.963460i	$0.413686\pi$
$384$	3685.12	0.489727
$385$	0	0
$386$	−6306.78	−0.831623
$387$	−639.842	−0.0840439
$388$	6565.55	0.859060
$389$	−2725.35	−0.355221	−0.177610	−	0.984101i	$-0.556837\pi$
$389$	−2725.35	−0.355221	−0.177610	+	0.984101i	$0.556837\pi$
$390$	−1151.33	−0.149487
$391$	1191.55	0.154115
$392$	0	0
$393$	−2558.28	−0.328367
$394$	−5191.78	−0.663853
$395$	−3226.11	−0.410945
$396$	3116.53	0.395484
$397$	4391.59	0.555182	0.277591	−	0.960699i	$-0.410464\pi$
$397$	4391.59	0.555182	0.277591	+	0.960699i	$0.410464\pi$
$398$	5374.19	0.676844
$399$	0	0
$400$	3364.09	0.420511
$401$	3762.48	0.468552	0.234276	−	0.972170i	$-0.424728\pi$
$401$	3762.48	0.468552	0.234276	+	0.972170i	$0.424728\pi$
$402$	−3081.00	−0.382255
$403$	2380.40	0.294234
$404$	9654.55	1.18894
$405$	−1566.54	−0.192202
$406$	0	0
$407$	−25530.2	−3.10930
$408$	2615.93	0.317421
$409$	6797.81	0.821833	0.410917	−	0.911673i	$-0.365209\pi$
$409$	6797.81	0.821833	0.410917	+	0.911673i	$0.365209\pi$
$410$	−4211.91	−0.507345
$411$	1466.71	0.176028
$412$	−8250.61	−0.986599
$413$	0	0
$414$	391.721	0.0465025
$415$	−3889.14	−0.460025
$416$	−2438.17	−0.287358
$417$	1221.37	0.143431
$418$	−10027.3	−1.17332
$419$	12594.2	1.46841	0.734207	−	0.678925i	$-0.237554\pi$
$419$	12594.2	1.46841	0.734207	+	0.678925i	$0.237554\pi$
$420$	0	0
$421$	6888.04	0.797393	0.398697	−	0.917083i	$-0.369463\pi$
$421$	6888.04	0.797393	0.398697	+	0.917083i	$0.369463\pi$
$422$	−3427.19	−0.395338
$423$	−2913.40	−0.334881
$424$	523.845	0.0600004
$425$	10406.8	1.18777
$426$	1496.69	0.170223
$427$	0	0
$428$	4665.04	0.526854
$429$	−2381.84	−0.268056
$430$	2098.77	0.235376
$431$	−7384.53	−0.825291	−0.412645	−	0.910892i	$-0.635395\pi$
$431$	−7384.53	−0.825291	−0.412645	+	0.910892i	$0.635395\pi$
$432$	−364.731	−0.0406206
$433$	−9068.33	−1.00646	−0.503229	−	0.864153i	$-0.667855\pi$
$433$	−9068.33	−1.00646	−0.503229	+	0.864153i	$0.667855\pi$
$434$	0	0
$435$	−5215.33	−0.574841
$436$	−2592.68	−0.284786
$437$	3066.97	0.335728
$438$	111.304	0.0121422
$439$	−16875.4	−1.83466	−0.917331	−	0.398125i	$-0.869661\pi$
$439$	−16875.4	−1.83466	−0.917331	+	0.398125i	$0.869661\pi$
$440$	−24646.3	−2.67037
$441$	0	0
$442$	−829.239	−0.0892373
$443$	−6766.18	−0.725668	−0.362834	−	0.931854i	$-0.618191\pi$
$443$	−6766.18	−0.725668	−0.362834	+	0.931854i	$0.618191\pi$
$444$	7110.64	0.760037
$445$	2104.84	0.224222
$446$	−5237.61	−0.556072
$447$	−5152.90	−0.545243
$448$	0	0
$449$	140.944	0.0148141	0.00740706	−	0.999973i	$-0.497642\pi$
$449$	140.944	0.0148141	0.00740706	+	0.999973i	$0.497642\pi$
$450$	3421.22	0.358395
$451$	−8713.47	−0.909759
$452$	2164.19	0.225210
$453$	−4025.36	−0.417501
$454$	7262.67	0.750779
$455$	0	0
$456$	6733.24	0.691475
$457$	−17733.1	−1.81514	−0.907571	−	0.419898i	$-0.862066\pi$
$457$	−17733.1	−1.81514	−0.907571	+	0.419898i	$0.862066\pi$
$458$	6668.90	0.680387
$459$	−1128.29	−0.114736
$460$	3126.74	0.316924
$461$	−2293.37	−0.231699	−0.115849	−	0.993267i	$-0.536959\pi$
$461$	−2293.37	−0.231699	−0.115849	+	0.993267i	$0.536959\pi$
$462$	0	0
$463$	13770.9	1.38226	0.691129	−	0.722731i	$-0.257113\pi$
$463$	13770.9	1.38226	0.691129	+	0.722731i	$0.257113\pi$
$464$	−1214.27	−0.121489
$465$	−10623.9	−1.05951
$466$	−5559.29	−0.552638
$467$	3477.37	0.344568	0.172284	−	0.985047i	$-0.444885\pi$
$467$	3477.37	0.344568	0.172284	+	0.985047i	$0.444885\pi$
$468$	663.388	0.0655237
$469$	0	0
$470$	9556.38	0.937879
$471$	−2281.64	−0.223211
$472$	−14283.2	−1.39288
$473$	4341.88	0.422072
$474$	−763.878	−0.0740213
$475$	26786.4	2.58746
$476$	0	0
$477$	−225.943	−0.0216880
$478$	3413.38	0.326620
$479$	3137.39	0.299271	0.149636	−	0.988741i	$-0.452190\pi$
$479$	3137.39	0.299271	0.149636	+	0.988741i	$0.452190\pi$
$480$	10881.7	1.03475
$481$	−5434.37	−0.515148
$482$	−9981.05	−0.943204
$483$	0	0
$484$	−13601.6	−1.27739
$485$	22394.7	2.09668
$486$	−370.925	−0.0346204
$487$	5996.52	0.557964	0.278982	−	0.960296i	$-0.410003\pi$
$487$	5996.52	0.557964	0.278982	+	0.960296i	$0.410003\pi$
$488$	6429.46	0.596410
$489$	−8136.26	−0.752422
$490$	0	0
$491$	−9401.49	−0.864121	−0.432060	−	0.901845i	$-0.642213\pi$
$491$	−9401.49	−0.864121	−0.432060	+	0.901845i	$0.642213\pi$
$492$	2426.87	0.222382
$493$	−3756.31	−0.343156
$494$	−2134.41	−0.194396
$495$	10630.3	0.965246
$496$	−2473.52	−0.223920
$497$	0	0
$498$	−920.871	−0.0828619
$499$	−5052.33	−0.453253	−0.226626	−	0.973982i	$-0.572770\pi$
$499$	−5052.33	−0.453253	−0.226626	+	0.973982i	$0.572770\pi$
$500$	13601.2	1.21653
$501$	4655.08	0.415117
$502$	−3826.96	−0.340251
$503$	−8184.02	−0.725462	−0.362731	−	0.931894i	$-0.618156\pi$
$503$	−8184.02	−0.725462	−0.362731	+	0.931894i	$0.618156\pi$
$504$	0	0
$505$	32931.1	2.90181
$506$	−2658.17	−0.233537
$507$	−507.000	−0.0444116
$508$	6401.94	0.559134
$509$	−6039.12	−0.525892	−0.262946	−	0.964811i	$-0.584694\pi$
$509$	−6039.12	−0.525892	−0.262946	+	0.964811i	$0.584694\pi$
$510$	3700.95	0.321335
$511$	0	0
$512$	4788.54	0.413331
$513$	−2904.15	−0.249944
$514$	1233.56	0.105856
$515$	−28142.3	−2.40796
$516$	−1209.30	−0.103171
$517$	19770.0	1.68178
$518$	0	0
$519$	−11910.8	−1.00737
$520$	−5246.22	−0.442427
$521$	14602.5	1.22792	0.613960	−	0.789337i	$-0.289576\pi$
$521$	14602.5	1.22792	0.613960	+	0.789337i	$0.289576\pi$
$522$	−1234.89	−0.103543
$523$	−8910.70	−0.745005	−0.372502	−	0.928031i	$-0.621500\pi$
$523$	−8910.70	−0.745005	−0.372502	+	0.928031i	$0.621500\pi$
$524$	−4835.14	−0.403099
$525$	0	0
$526$	4488.80	0.372093
$527$	−7651.79	−0.632481
$528$	2475.01	0.203998
$529$	−11354.0	−0.933177
$530$	741.124	0.0607403
$531$	6160.57	0.503477
$532$	0	0
$533$	−1854.76	−0.150729
$534$	498.384	0.0403879
$535$	15912.2	1.28588
$536$	−14039.1	−1.13134
$537$	8072.84	0.648731
$538$	−10855.3	−0.869897
$539$	0	0
$540$	−2960.75	−0.235945
$541$	−13313.6	−1.05803	−0.529017	−	0.848611i	$-0.677439\pi$
$541$	−13313.6	−1.05803	−0.529017	+	0.848611i	$0.677439\pi$
$542$	−3106.25	−0.246171
$543$	−13113.3	−1.03636
$544$	7837.48	0.617701
$545$	−8843.47	−0.695069
$546$	0	0
$547$	−4116.94	−0.321806	−0.160903	−	0.986970i	$-0.551441\pi$
$547$	−4116.94	−0.321806	−0.160903	+	0.986970i	$0.551441\pi$
$548$	2772.07	0.216090
$549$	−2773.12	−0.215581
$550$	−23215.9	−1.79987
$551$	−9668.52	−0.747537
$552$	1784.94	0.137631
$553$	0	0
$554$	4156.79	0.318782
$555$	24254.0	1.85500
$556$	2308.38	0.176074
$557$	−6888.37	−0.524003	−0.262002	−	0.965067i	$-0.584383\pi$
$557$	−6888.37	−0.524003	−0.262002	+	0.965067i	$0.584383\pi$
$558$	−2515.53	−0.190844
$559$	924.216	0.0699288
$560$	0	0
$561$	7656.42	0.576211
$562$	4984.68	0.374139
$563$	−10537.1	−0.788782	−0.394391	−	0.918943i	$-0.629045\pi$
$563$	−10537.1	−0.788782	−0.394391	+	0.918943i	$0.629045\pi$
$564$	−5506.31	−0.411095
$565$	7381.92	0.549664
$566$	−1746.27	−0.129684
$567$	0	0
$568$	6819.91	0.503798
$569$	26930.1	1.98413	0.992065	−	0.125722i	$-0.0401248\pi$
$569$	26930.1	1.98413	0.992065	+	0.125722i	$0.0401248\pi$
$570$	9526.02	0.700002
$571$	−3125.60	−0.229076	−0.114538	−	0.993419i	$-0.536539\pi$
$571$	−3125.60	−0.229076	−0.114538	+	0.993419i	$0.536539\pi$
$572$	−4501.66	−0.329063
$573$	−4225.42	−0.308062
$574$	0	0
$575$	7100.91	0.515006
$576$	1603.96	0.116027
$577$	−4787.13	−0.345391	−0.172696	−	0.984975i	$-0.555248\pi$
$577$	−4787.13	−0.345391	−0.172696	+	0.984975i	$0.555248\pi$
$578$	−4833.81	−0.347855
$579$	12395.1	0.889675
$580$	−9856.94	−0.705668
$581$	0	0
$582$	5302.62	0.377664
$583$	1533.22	0.108918
$584$	507.174	0.0359366
$585$	2262.78	0.159922
$586$	2560.38	0.180492
$587$	−18380.8	−1.29243	−0.646214	−	0.763156i	$-0.723649\pi$
$587$	−18380.8	−1.29243	−0.646214	+	0.763156i	$0.723649\pi$
$588$	0	0
$589$	−19695.3	−1.37781
$590$	−20207.6	−1.41005
$591$	10203.7	0.710193
$592$	5646.96	0.392042
$593$	13831.7	0.957843	0.478922	−	0.877858i	$-0.341028\pi$
$593$	13831.7	0.957843	0.478922	+	0.877858i	$0.341028\pi$
$594$	2517.05	0.173865
$595$	0	0
$596$	−9738.94	−0.669333
$597$	−10562.2	−0.724091
$598$	−565.819	−0.0386924
$599$	12248.6	0.835502	0.417751	−	0.908562i	$-0.362818\pi$
$599$	12248.6	0.835502	0.417751	+	0.908562i	$0.362818\pi$
$600$	15589.3	1.06072
$601$	−9719.56	−0.659682	−0.329841	−	0.944036i	$-0.606995\pi$
$601$	−9719.56	−0.659682	−0.329841	+	0.944036i	$0.606995\pi$
$602$	0	0
$603$	6055.27	0.408938
$604$	−7607.91	−0.512519
$605$	−46394.3	−3.11768
$606$	7797.42	0.522688
$607$	−1607.83	−0.107512	−0.0537560	−	0.998554i	$-0.517119\pi$
$607$	−1607.83	−0.107512	−0.0537560	+	0.998554i	$0.517119\pi$
$608$	20173.2	1.34561
$609$	0	0
$610$	9096.25	0.603764
$611$	4208.25	0.278638
$612$	−2132.46	−0.140849
$613$	14731.1	0.970610	0.485305	−	0.874345i	$-0.338709\pi$
$613$	14731.1	0.970610	0.485305	+	0.874345i	$0.338709\pi$
$614$	−11002.1	−0.723142
$615$	8277.91	0.542760
$616$	0	0
$617$	27951.8	1.82382	0.911909	−	0.410392i	$-0.134608\pi$
$617$	27951.8	1.82382	0.911909	+	0.410392i	$0.134608\pi$
$618$	−6663.55	−0.433733
$619$	−16200.2	−1.05192	−0.525961	−	0.850509i	$-0.676294\pi$
$619$	−16200.2	−1.05192	−0.525961	+	0.850509i	$0.676294\pi$
$620$	−20079.1	−1.30064
$621$	−769.872	−0.0497486
$622$	−630.364	−0.0406355
$623$	0	0
$624$	526.833	0.0337984
$625$	15263.8	0.976880
$626$	−4482.22	−0.286175
$627$	19707.2	1.25523
$628$	−4312.28	−0.274011
$629$	17468.8	1.10735
$630$	0	0
$631$	12731.8	0.803239	0.401619	−	0.915807i	$-0.368447\pi$
$631$	12731.8	0.803239	0.401619	+	0.915807i	$0.368447\pi$
$632$	−3480.73	−0.219076
$633$	6735.65	0.422935
$634$	576.927	0.0361399
$635$	21836.6	1.36466
$636$	−427.030	−0.0266240
$637$	0	0
$638$	8379.77	0.519997
$639$	−2941.53	−0.182105
$640$	23756.7	1.46729
$641$	−11556.9	−0.712119	−0.356059	−	0.934463i	$-0.615880\pi$
$641$	−11556.9	−0.712119	−0.356059	+	0.934463i	$0.615880\pi$
$642$	3767.69	0.231618
$643$	9181.25	0.563100	0.281550	−	0.959547i	$-0.409152\pi$
$643$	9181.25	0.563100	0.281550	+	0.959547i	$0.409152\pi$
$644$	0	0
$645$	−4124.84	−0.251807
$646$	6861.06	0.417871
$647$	−5244.11	−0.318651	−0.159326	−	0.987226i	$-0.550932\pi$
$647$	−5244.11	−0.318651	−0.159326	+	0.987226i	$0.550932\pi$
$648$	−1690.18	−0.102464
$649$	−41804.8	−2.52848
$650$	−4941.76	−0.298203
$651$	0	0
$652$	−15377.5	−0.923663
$653$	−16421.4	−0.984106	−0.492053	−	0.870565i	$-0.663753\pi$
$653$	−16421.4	−0.984106	−0.492053	+	0.870565i	$0.663753\pi$
$654$	−2093.96	−0.125199
$655$	−16492.4	−0.983832
$656$	1927.31	0.114709
$657$	−218.752	−0.0129898
$658$	0	0
$659$	1838.11	0.108653	0.0543266	−	0.998523i	$-0.482699\pi$
$659$	1838.11	0.108653	0.0543266	+	0.998523i	$0.482699\pi$
$660$	20091.2	1.18492
$661$	5500.93	0.323694	0.161847	−	0.986816i	$-0.448255\pi$
$661$	5500.93	0.323694	0.161847	+	0.986816i	$0.448255\pi$
$662$	−6759.34	−0.396841
$663$	1629.75	0.0954665
$664$	−4196.10	−0.245241
$665$	0	0
$666$	5742.86	0.334131
$667$	−2563.07	−0.148789
$668$	8798.08	0.509593
$669$	10293.8	0.594888
$670$	−19862.2	−1.14529
$671$	18818.0	1.08266
$672$	0	0
$673$	−25986.7	−1.48843	−0.744216	−	0.667939i	$-0.767177\pi$
$673$	−25986.7	−1.48843	−0.744216	+	0.667939i	$0.767177\pi$
$674$	−2699.91	−0.154298
$675$	−6723.92	−0.383413
$676$	−958.227	−0.0545191
$677$	11691.3	0.663714	0.331857	−	0.943330i	$-0.392325\pi$
$677$	11691.3	0.663714	0.331857	+	0.943330i	$0.392325\pi$
$678$	1747.89	0.0990080
$679$	0	0
$680$	16864.0	0.951035
$681$	−14273.7	−0.803188
$682$	17070.0	0.958423
$683$	−11111.5	−0.622501	−0.311251	−	0.950328i	$-0.600748\pi$
$683$	−11111.5	−0.622501	−0.311251	+	0.950328i	$0.600748\pi$
$684$	−5488.82	−0.306828
$685$	9455.37	0.527403
$686$	0	0
$687$	−13106.8	−0.727882
$688$	−960.370	−0.0532177
$689$	326.361	0.0180455
$690$	2525.29	0.139328
$691$	7542.55	0.415242	0.207621	−	0.978209i	$-0.433428\pi$
$691$	7542.55	0.415242	0.207621	+	0.978209i	$0.433428\pi$
$692$	−22511.3	−1.23664
$693$	0	0
$694$	3683.26	0.201462
$695$	7873.75	0.429738
$696$	−5626.96	−0.306450
$697$	5962.11	0.324005
$698$	15214.7	0.825051
$699$	10926.0	0.591215
$700$	0	0
$701$	−8231.17	−0.443491	−0.221745	−	0.975105i	$-0.571175\pi$
$701$	−8231.17	−0.443491	−0.221745	+	0.975105i	$0.571175\pi$
$702$	535.780	0.0288059
$703$	44963.6	2.41228
$704$	−10884.2	−0.582691
$705$	−18781.7	−1.00335
$706$	−6893.86	−0.367498
$707$	0	0
$708$	11643.4	0.618061
$709$	28044.6	1.48553	0.742764	−	0.669554i	$-0.233515\pi$
$709$	28044.6	1.48553	0.742764	+	0.669554i	$0.233515\pi$
$710$	9648.64	0.510010
$711$	1501.29	0.0791884
$712$	2270.96	0.119534
$713$	−5221.09	−0.274238
$714$	0	0
$715$	−15354.9	−0.803133
$716$	15257.6	0.796374
$717$	−6708.51	−0.349420
$718$	18561.3	0.964764
$719$	−29686.4	−1.53980	−0.769901	−	0.638163i	$-0.779694\pi$
$719$	−29686.4	−1.53980	−0.769901	+	0.638163i	$0.779694\pi$
$720$	−2351.29	−0.121705
$721$	0	0
$722$	7190.12	0.370621
$723$	19616.3	1.00904
$724$	−24784.0	−1.27223
$725$	−22385.3	−1.14672
$726$	−10985.3	−0.561572
$727$	27654.5	1.41080	0.705398	−	0.708812i	$-0.250768\pi$
$727$	27654.5	1.41080	0.705398	+	0.708812i	$0.250768\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	717.537	0.0363798
$731$	−2970.89	−0.150318
$732$	−5241.19	−0.264645
$733$	13077.5	0.658975	0.329488	−	0.944160i	$-0.393124\pi$
$733$	13077.5	0.658975	0.329488	+	0.944160i	$0.393124\pi$
$734$	4082.08	0.205276
$735$	0	0
$736$	5347.79	0.267829
$737$	−41090.3	−2.05370
$738$	1960.04	0.0977645
$739$	−4218.33	−0.209978	−0.104989	−	0.994473i	$-0.533481\pi$
$739$	−4218.33	−0.209978	−0.104989	+	0.994473i	$0.533481\pi$
$740$	45839.9	2.27717
$741$	4194.88	0.207966
$742$	0	0
$743$	7725.54	0.381457	0.190728	−	0.981643i	$-0.438915\pi$
$743$	7725.54	0.381457	0.190728	+	0.981643i	$0.438915\pi$
$744$	−11462.4	−0.564828
$745$	−33218.9	−1.63362
$746$	14656.5	0.719319
$747$	1809.84	0.0886460
$748$	14470.6	0.707349
$749$	0	0
$750$	10984.9	0.534818
$751$	7506.12	0.364717	0.182358	−	0.983232i	$-0.441627\pi$
$751$	7506.12	0.364717	0.182358	+	0.983232i	$0.441627\pi$
$752$	−4372.87	−0.212051
$753$	7521.35	0.364002
$754$	1783.72	0.0861531
$755$	−25950.1	−1.25089
$756$	0	0
$757$	−2741.62	−0.131632	−0.0658162	−	0.997832i	$-0.520965\pi$
$757$	−2741.62	−0.131632	−0.0658162	+	0.997832i	$0.520965\pi$
$758$	13768.0	0.659729
$759$	5224.25	0.249839
$760$	43406.9	2.07175
$761$	−29740.0	−1.41666	−0.708328	−	0.705883i	$-0.750550\pi$
$761$	−29740.0	−1.41666	−0.708328	+	0.705883i	$0.750550\pi$
$762$	5170.48	0.245809
$763$	0	0
$764$	−7986.01	−0.378172
$765$	−7273.69	−0.343766
$766$	6129.18	0.289107
$767$	−8898.60	−0.418918
$768$	9902.32	0.465259
$769$	19896.3	0.933004	0.466502	−	0.884520i	$-0.345514\pi$
$769$	19896.3	0.933004	0.466502	+	0.884520i	$0.345514\pi$
$770$	0	0
$771$	−2424.39	−0.113246
$772$	23426.6	1.09215
$773$	13601.3	0.632866	0.316433	−	0.948615i	$-0.397515\pi$
$773$	13601.3	0.632866	0.316433	+	0.948615i	$0.397515\pi$
$774$	−976.680	−0.0453566
$775$	−45600.1	−2.11355
$776$	24162.2	1.11775
$777$	0	0
$778$	−4160.09	−0.191705
$779$	15346.1	0.705818
$780$	4276.63	0.196318
$781$	19960.8	0.914539
$782$	1818.83	0.0831727
$783$	2426.99	0.110771
$784$	0	0
$785$	−14708.9	−0.668770
$786$	−3905.06	−0.177212
$787$	1498.29	0.0678631	0.0339315	−	0.999424i	$-0.489197\pi$
$787$	1498.29	0.0678631	0.0339315	+	0.999424i	$0.489197\pi$
$788$	19284.9	0.871824
$789$	−8822.09	−0.398067
$790$	−4924.46	−0.221778
$791$	0	0
$792$	11469.3	0.514577
$793$	4005.62	0.179374
$794$	6703.49	0.299620
$795$	−1456.57	−0.0649803
$796$	−19962.5	−0.888885
$797$	3713.30	0.165034	0.0825168	−	0.996590i	$-0.473704\pi$
$797$	3713.30	0.165034	0.0825168	+	0.996590i	$0.473704\pi$
$798$	0	0
$799$	−13527.4	−0.598955
$800$	46706.7	2.06416
$801$	−979.502	−0.0432072
$802$	5743.20	0.252867
$803$	1484.42	0.0652354
$804$	11444.4	0.502007
$805$	0	0
$806$	3633.54	0.158791
$807$	21334.5	0.930620
$808$	35530.2	1.54697
$809$	−34527.6	−1.50053	−0.750263	−	0.661139i	$-0.770073\pi$
$809$	−34527.6	−1.50053	−0.750263	+	0.661139i	$0.770073\pi$
$810$	−2391.22	−0.103727
$811$	37279.2	1.61412	0.807059	−	0.590471i	$-0.201058\pi$
$811$	37279.2	1.61412	0.807059	+	0.590471i	$0.201058\pi$
$812$	0	0
$813$	6104.89	0.263355
$814$	−38970.3	−1.67802
$815$	−52451.6	−2.25436
$816$	−1693.51	−0.0726526
$817$	−7646.90	−0.327455
$818$	10376.4	0.443525
$819$	0	0
$820$	15645.2	0.666285
$821$	13877.9	0.589943	0.294972	−	0.955506i	$-0.404690\pi$
$821$	13877.9	0.589943	0.294972	+	0.955506i	$0.404690\pi$
$822$	2238.84	0.0949983
$823$	18945.1	0.802410	0.401205	−	0.915988i	$-0.368592\pi$
$823$	18945.1	0.802410	0.401205	+	0.915988i	$0.368592\pi$
$824$	−30363.5	−1.28369
$825$	45627.6	1.92552
$826$	0	0
$827$	−7804.75	−0.328171	−0.164086	−	0.986446i	$-0.552467\pi$
$827$	−7804.75	−0.328171	−0.164086	+	0.986446i	$0.552467\pi$
$828$	−1455.05	−0.0610708
$829$	−5784.85	−0.242360	−0.121180	−	0.992631i	$-0.538668\pi$
$829$	−5784.85	−0.242360	−0.121180	+	0.992631i	$0.538668\pi$
$830$	−5936.54	−0.248265
$831$	−8169.59	−0.341035
$832$	−2316.82	−0.0965402
$833$	0	0
$834$	1864.35	0.0774065
$835$	30009.7	1.24375
$836$	37246.4	1.54090
$837$	4943.91	0.204165
$838$	19224.3	0.792471
$839$	5011.42	0.206214	0.103107	−	0.994670i	$-0.467122\pi$
$839$	5011.42	0.206214	0.103107	+	0.994670i	$0.467122\pi$
$840$	0	0
$841$	−16309.0	−0.668704
$842$	10514.2	0.430336
$843$	−9796.68	−0.400256
$844$	12730.3	0.519190
$845$	−3268.45	−0.133063
$846$	−4447.13	−0.180728
$847$	0	0
$848$	−339.128	−0.0137332
$849$	3432.05	0.138737
$850$	15885.3	0.641013
$851$	11919.6	0.480138
$852$	−5559.48	−0.223550
$853$	22059.0	0.885446	0.442723	−	0.896659i	$-0.354013\pi$
$853$	22059.0	0.885446	0.442723	+	0.896659i	$0.354013\pi$
$854$	0	0
$855$	−18722.0	−0.748866
$856$	17168.1	0.685506
$857$	−13956.2	−0.556283	−0.278141	−	0.960540i	$-0.589718\pi$
$857$	−13956.2	−0.556283	−0.278141	+	0.960540i	$0.589718\pi$
$858$	−3635.73	−0.144664
$859$	−12498.5	−0.496442	−0.248221	−	0.968703i	$-0.579846\pi$
$859$	−12498.5	−0.496442	−0.248221	+	0.968703i	$0.579846\pi$
$860$	−7795.92	−0.309115
$861$	0	0
$862$	−11272.0	−0.445391
$863$	−38631.2	−1.52378	−0.761890	−	0.647707i	$-0.775728\pi$
$863$	−38631.2	−1.52378	−0.761890	+	0.647707i	$0.775728\pi$
$864$	−5063.88	−0.199394
$865$	−76784.7	−3.01822
$866$	−13842.3	−0.543163
$867$	9500.17	0.372137
$868$	0	0
$869$	−10187.6	−0.397687
$870$	−7960.89	−0.310229
$871$	−8746.51	−0.340257
$872$	−9541.46	−0.370544
$873$	−10421.5	−0.404027
$874$	4681.55	0.181185
$875$	0	0
$876$	−413.440	−0.0159462
$877$	−856.756	−0.0329881	−0.0164941	−	0.999864i	$-0.505250\pi$
$877$	−856.756	−0.0329881	−0.0164941	+	0.999864i	$0.505250\pi$
$878$	−25759.2	−0.990127
$879$	−5032.06	−0.193091
$880$	15955.6	0.611206
$881$	−33638.6	−1.28640	−0.643198	−	0.765700i	$-0.722393\pi$
$881$	−33638.6	−1.28640	−0.643198	+	0.765700i	$0.722393\pi$
$882$	0	0
$883$	−31109.1	−1.18562	−0.592811	−	0.805342i	$-0.701982\pi$
$883$	−31109.1	−1.18562	−0.592811	+	0.805342i	$0.701982\pi$
$884$	3080.22	0.117193
$885$	39715.1	1.50848
$886$	−10328.2	−0.391627
$887$	−26080.3	−0.987248	−0.493624	−	0.869675i	$-0.664328\pi$
$887$	−26080.3	−0.987248	−0.493624	+	0.869675i	$0.664328\pi$
$888$	26168.3	0.988907
$889$	0	0
$890$	3212.91	0.121008
$891$	−4946.89	−0.186001
$892$	19455.2	0.730277
$893$	−34818.8	−1.30478
$894$	−7865.58	−0.294256
$895$	52042.8	1.94369
$896$	0	0
$897$	1112.04	0.0413934
$898$	215.142	0.00799486
$899$	16459.3	0.610621
$900$	−12708.2	−0.470673
$901$	−1049.09	−0.0387905
$902$	−13300.6	−0.490977
$903$	0	0
$904$	7964.56	0.293028
$905$	−84536.9	−3.10508
$906$	−6144.47	−0.225316
$907$	20169.0	0.738369	0.369184	−	0.929356i	$-0.379637\pi$
$907$	20169.0	0.738369	0.369184	+	0.929356i	$0.379637\pi$
$908$	−26977.3	−0.985983
$909$	−15324.7	−0.559174
$910$	0	0
$911$	19982.2	0.726716	0.363358	−	0.931650i	$-0.381630\pi$
$911$	19982.2	0.726716	0.363358	+	0.931650i	$0.381630\pi$
$912$	−4358.98	−0.158268
$913$	−12281.3	−0.445184
$914$	−27068.5	−0.979593
$915$	−17877.4	−0.645910
$916$	−24771.7	−0.893538
$917$	0	0
$918$	−1722.27	−0.0619207
$919$	38513.1	1.38241	0.691203	−	0.722661i	$-0.257081\pi$
$919$	38513.1	1.38241	0.691203	+	0.722661i	$0.257081\pi$
$920$	11506.9	0.412360
$921$	21623.1	0.773621
$922$	−3500.70	−0.125043
$923$	4248.88	0.151521
$924$	0	0
$925$	104103.	3.70043
$926$	21020.4	0.745975
$927$	13096.3	0.464010
$928$	−16858.7	−0.596352
$929$	−23218.9	−0.820009	−0.410005	−	0.912083i	$-0.634473\pi$
$929$	−23218.9	−0.820009	−0.410005	+	0.912083i	$0.634473\pi$
$930$	−16216.7	−0.571793
$931$	0	0
$932$	20650.1	0.725768
$933$	1238.89	0.0434721
$934$	5307.99	0.185956
$935$	49358.3	1.72640
$936$	2441.37	0.0852550
$937$	11112.9	0.387452	0.193726	−	0.981056i	$-0.437943\pi$
$937$	11112.9	0.387452	0.193726	+	0.981056i	$0.437943\pi$
$938$	0	0
$939$	8809.17	0.306152
$940$	−35497.3	−1.23170
$941$	−45570.4	−1.57869	−0.789347	−	0.613947i	$-0.789581\pi$
$941$	−45570.4	−1.57869	−0.789347	+	0.613947i	$0.789581\pi$
$942$	−3482.78	−0.120462
$943$	4068.16	0.140485
$944$	9246.71	0.318808
$945$	0	0
$946$	6627.62	0.227783
$947$	34903.9	1.19770	0.598852	−	0.800860i	$-0.295624\pi$
$947$	34903.9	1.19770	0.598852	+	0.800860i	$0.295624\pi$
$948$	2837.44	0.0972106
$949$	315.975	0.0108082
$950$	40887.8	1.39640
$951$	−1133.87	−0.0386626
$952$	0	0
$953$	−2886.52	−0.0981151	−0.0490575	−	0.998796i	$-0.515622\pi$
$953$	−2886.52	−0.0981151	−0.0490575	+	0.998796i	$0.515622\pi$
$954$	−344.888	−0.0117046
$955$	−27239.8	−0.922994
$956$	−12679.0	−0.428943
$957$	−16469.2	−0.556296
$958$	4789.03	0.161510
$959$	0	0
$960$	10340.1	0.347632
$961$	3737.42	0.125455
$962$	−8295.24	−0.278014
$963$	−7404.85	−0.247786
$964$	37074.8	1.23869
$965$	79906.8	2.66559
$966$	0	0
$967$	11593.8	0.385556	0.192778	−	0.981242i	$-0.438250\pi$
$967$	11593.8	0.385556	0.192778	+	0.981242i	$0.438250\pi$
$968$	−50056.1	−1.66205
$969$	−13484.4	−0.447041
$970$	34184.1	1.13153
$971$	4952.12	0.163667	0.0818337	−	0.996646i	$-0.473922\pi$
$971$	4952.12	0.163667	0.0818337	+	0.996646i	$0.473922\pi$
$972$	1377.81	0.0454662
$973$	0	0
$974$	9153.33	0.301121
$975$	9712.33	0.319019
$976$	−4162.32	−0.136509
$977$	−19650.1	−0.643462	−0.321731	−	0.946831i	$-0.604265\pi$
$977$	−19650.1	−0.643462	−0.321731	+	0.946831i	$0.604265\pi$
$978$	−12419.5	−0.406065
$979$	6646.77	0.216988
$980$	0	0
$981$	4115.38	0.133939
$982$	−14350.8	−0.466347
$983$	−56818.4	−1.84357	−0.921783	−	0.387707i	$-0.873267\pi$
$983$	−56818.4	−1.84357	−0.921783	+	0.387707i	$0.873267\pi$
$984$	8931.26	0.289348
$985$	65779.7	2.12783
$986$	−5733.78	−0.185193
$987$	0	0
$988$	7928.30	0.255296
$989$	−2027.15	−0.0651764
$990$	16226.5	0.520922
$991$	−19120.4	−0.612897	−0.306448	−	0.951887i	$-0.599141\pi$
$991$	−19120.4	−0.612897	−0.306448	+	0.951887i	$0.599141\pi$
$992$	−34342.1	−1.09915
$993$	13284.5	0.424543
$994$	0	0
$995$	−68090.9	−2.16947
$996$	3420.59	0.108821
$997$	−38887.9	−1.23530	−0.617650	−	0.786453i	$-0.711915\pi$
$997$	−38887.9	−1.23530	−0.617650	+	0.786453i	$0.711915\pi$
$998$	−7712.07	−0.244611
$999$	−11286.8	−0.357455

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1911.4.a.k.1.2		3
7.6	odd	2		39.4.a.c.1.2	✓	3
21.20	even	2		117.4.a.f.1.2		3
28.27	even	2		624.4.a.t.1.3		3
35.34	odd	2		975.4.a.l.1.2		3
56.13	odd	2		2496.4.a.bl.1.1		3
56.27	even	2		2496.4.a.bp.1.1		3
84.83	odd	2		1872.4.a.bk.1.1		3
91.34	even	4		507.4.b.g.337.4		6
91.83	even	4		507.4.b.g.337.3		6
91.90	odd	2		507.4.a.h.1.2		3
273.272	even	2		1521.4.a.u.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.a.c.1.2	✓	3	7.6	odd	2
117.4.a.f.1.2		3	21.20	even	2
507.4.a.h.1.2		3	91.90	odd	2
507.4.b.g.337.3		6	91.83	even	4
507.4.b.g.337.4		6	91.34	even	4
624.4.a.t.1.3		3	28.27	even	2
975.4.a.l.1.2		3	35.34	odd	2
1521.4.a.u.1.2		3	273.272	even	2
1872.4.a.bk.1.1		3	84.83	odd	2
1911.4.a.k.1.2		3	1.1	even	1	trivial
2496.4.a.bl.1.1		3	56.13	odd	2
2496.4.a.bp.1.1		3	56.27	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:	\( N \)	\(=\)	\( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1911.a (trivial)

\(f(q)\)	\(=\)	\(q+1.52644 q^{2} -3.00000 q^{3} -5.66998 q^{4} -19.3400 q^{5} -4.57932 q^{6} -20.8664 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+1.52644 q^{2} -3.00000 q^{3} -5.66998 q^{4} -19.3400 q^{5} -4.57932 q^{6} -20.8664 q^{8} +9.00000 q^{9} -29.5213 q^{10} -61.0728 q^{11} +17.0099 q^{12} -13.0000 q^{13} +58.0199 q^{15} +13.5085 q^{16} +41.7885 q^{17} +13.7380 q^{18} +107.561 q^{19} +109.657 q^{20} -93.2239 q^{22} +28.5138 q^{23} +62.5992 q^{24} +249.034 q^{25} -19.8437 q^{26} -27.0000 q^{27} -89.8886 q^{29} +88.5639 q^{30} -183.108 q^{31} +187.551 q^{32} +183.218 q^{33} +63.7876 q^{34} -51.0298 q^{36} +418.029 q^{37} +164.185 q^{38} +39.0000 q^{39} +403.555 q^{40} +142.674 q^{41} -71.0935 q^{43} +346.281 q^{44} -174.060 q^{45} +43.5246 q^{46} -323.711 q^{47} -40.5256 q^{48} +380.136 q^{50} -125.365 q^{51} +73.7098 q^{52} -25.1047 q^{53} -41.2139 q^{54} +1181.15 q^{55} -322.683 q^{57} -137.210 q^{58} +684.508 q^{59} -328.972 q^{60} -308.125 q^{61} -279.503 q^{62} +178.217 q^{64} +251.420 q^{65} +279.672 q^{66} +672.808 q^{67} -236.940 q^{68} -85.5413 q^{69} -326.837 q^{71} -187.798 q^{72} -24.3058 q^{73} +638.095 q^{74} -747.103 q^{75} -609.869 q^{76} +59.5311 q^{78} +166.810 q^{79} -261.255 q^{80} +81.0000 q^{81} +217.783 q^{82} +201.093 q^{83} -808.188 q^{85} -108.520 q^{86} +269.666 q^{87} +1274.37 q^{88} -108.834 q^{89} -265.692 q^{90} -161.673 q^{92} +549.323 q^{93} -494.126 q^{94} -2080.23 q^{95} -562.654 q^{96} -1157.95 q^{97} -549.655 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} - 9 q^{3} + 10 q^{4} - 4 q^{5} - 6 q^{6} - 6 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q + 2 * q^2 - 9 * q^3 + 10 * q^4 - 4 * q^5 - 6 * q^6 - 6 * q^8 + 27 * q^9	\( 3 q + 2 q^{2} - 9 q^{3} + 10 q^{4} - 4 q^{5} - 6 q^{6} - 6 q^{8} + 27 q^{9} + 4 q^{10} - 16 q^{11} - 30 q^{12} - 39 q^{13} + 12 q^{15} - 110 q^{16} + 146 q^{17} + 18 q^{18} - 94 q^{19} + 244 q^{20} - 56 q^{22} - 48 q^{23} + 18 q^{24} + 145 q^{25} - 26 q^{26} - 81 q^{27} - 2 q^{29} - 12 q^{30} - 302 q^{31} + 154 q^{32} + 48 q^{33} - 164 q^{34} + 90 q^{36} + 374 q^{37} - 312 q^{38} + 117 q^{39} + 516 q^{40} - 480 q^{41} - 260 q^{43} + 712 q^{44} - 36 q^{45} - 1104 q^{46} + 24 q^{47} + 330 q^{48} + 814 q^{50} - 438 q^{51} - 130 q^{52} - 678 q^{53} - 54 q^{54} + 1552 q^{55} + 282 q^{57} - 628 q^{58} + 1788 q^{59} - 732 q^{60} - 230 q^{61} - 1952 q^{62} - 750 q^{64} + 52 q^{65} + 168 q^{66} + 74 q^{67} + 460 q^{68} + 144 q^{69} - 948 q^{71} - 54 q^{72} + 222 q^{73} + 1724 q^{74} - 435 q^{75} - 2392 q^{76} + 78 q^{78} - 24 q^{79} - 1100 q^{80} + 243 q^{81} - 564 q^{82} + 796 q^{83} - 248 q^{85} + 1800 q^{86} + 6 q^{87} + 1608 q^{88} - 1436 q^{89} + 36 q^{90} - 1296 q^{92} + 906 q^{93} + 1920 q^{94} - 4032 q^{95} - 462 q^{96} - 3242 q^{97} - 144 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 - 9 * q^3 + 10 * q^4 - 4 * q^5 - 6 * q^6 - 6 * q^8 + 27 * q^9 + 4 * q^10 - 16 * q^11 - 30 * q^12 - 39 * q^13 + 12 * q^15 - 110 * q^16 + 146 * q^17 + 18 * q^18 - 94 * q^19 + 244 * q^20 - 56 * q^22 - 48 * q^23 + 18 * q^24 + 145 * q^25 - 26 * q^26 - 81 * q^27 - 2 * q^29 - 12 * q^30 - 302 * q^31 + 154 * q^32 + 48 * q^33 - 164 * q^34 + 90 * q^36 + 374 * q^37 - 312 * q^38 + 117 * q^39 + 516 * q^40 - 480 * q^41 - 260 * q^43 + 712 * q^44 - 36 * q^45 - 1104 * q^46 + 24 * q^47 + 330 * q^48 + 814 * q^50 - 438 * q^51 - 130 * q^52 - 678 * q^53 - 54 * q^54 + 1552 * q^55 + 282 * q^57 - 628 * q^58 + 1788 * q^59 - 732 * q^60 - 230 * q^61 - 1952 * q^62 - 750 * q^64 + 52 * q^65 + 168 * q^66 + 74 * q^67 + 460 * q^68 + 144 * q^69 - 948 * q^71 - 54 * q^72 + 222 * q^73 + 1724 * q^74 - 435 * q^75 - 2392 * q^76 + 78 * q^78 - 24 * q^79 - 1100 * q^80 + 243 * q^81 - 564 * q^82 + 796 * q^83 - 248 * q^85 + 1800 * q^86 + 6 * q^87 + 1608 * q^88 - 1436 * q^89 + 36 * q^90 - 1296 * q^92 + 906 * q^93 + 1920 * q^94 - 4032 * q^95 - 462 * q^96 - 3242 * q^97 - 144 * q^99

Introduction

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