LMFDB - Embedded newform 1815.4.a.q.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,4,Mod(1,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, 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("1815.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1815.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:	$107.088466660$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.1957.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 9x + 10 $ x^3 - x^2 - 9*x + 10
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.12946$ of defining polynomial
Character	$\chi$	$=$	1815.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.59486 q^{2} -3.00000 q^{3} +13.1127 q^{4} +5.00000 q^{5} +13.7846 q^{6} -20.6383 q^{7} -23.4921 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.59486 q^{2} -3.00000 q^{3} +13.1127 q^{4} +5.00000 q^{5} +13.7846 q^{6} -20.6383 q^{7} -23.4921 q^{8} +9.00000 q^{9} -22.9743 q^{10} -39.3381 q^{12} +15.6584 q^{13} +94.8302 q^{14} -15.0000 q^{15} +3.04132 q^{16} -72.9507 q^{17} -41.3537 q^{18} -61.0513 q^{19} +65.5635 q^{20} +61.9150 q^{21} -13.6605 q^{23} +70.4764 q^{24} +25.0000 q^{25} -71.9483 q^{26} -27.0000 q^{27} -270.624 q^{28} +31.4663 q^{29} +68.9228 q^{30} -243.008 q^{31} +173.963 q^{32} +335.198 q^{34} -103.192 q^{35} +118.014 q^{36} -65.4018 q^{37} +280.522 q^{38} -46.9753 q^{39} -117.461 q^{40} +109.087 q^{41} -284.491 q^{42} +121.750 q^{43} +45.0000 q^{45} +62.7678 q^{46} -519.530 q^{47} -9.12396 q^{48} +82.9413 q^{49} -114.871 q^{50} +218.852 q^{51} +205.324 q^{52} -542.673 q^{53} +124.061 q^{54} +484.839 q^{56} +183.154 q^{57} -144.583 q^{58} +109.478 q^{59} -196.691 q^{60} +89.6156 q^{61} +1116.59 q^{62} -185.745 q^{63} -823.664 q^{64} +78.2922 q^{65} +488.446 q^{67} -956.581 q^{68} +40.9814 q^{69} +474.151 q^{70} +837.423 q^{71} -211.429 q^{72} -351.216 q^{73} +300.512 q^{74} -75.0000 q^{75} -800.547 q^{76} +215.845 q^{78} +831.205 q^{79} +15.2066 q^{80} +81.0000 q^{81} -501.238 q^{82} -1389.13 q^{83} +811.873 q^{84} -364.754 q^{85} -559.423 q^{86} -94.3988 q^{87} +1523.70 q^{89} -206.769 q^{90} -323.164 q^{91} -179.125 q^{92} +729.025 q^{93} +2387.17 q^{94} -305.256 q^{95} -521.888 q^{96} -426.612 q^{97} -381.103 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} - 9 q^{3} + 17 q^{4} + 15 q^{5} + 3 q^{6} - 6 q^{7} + 3 q^{8} + 27 q^{9}+O(q^{10}) $ 3 * q - q^2 - 9 * q^3 + 17 * q^4 + 15 * q^5 + 3 * q^6 - 6 * q^7 + 3 * q^8 + 27 * q^9	\( 3 q - q^{2} - 9 q^{3} + 17 q^{4} + 15 q^{5} + 3 q^{6} - 6 q^{7} + 3 q^{8} + 27 q^{9} - 5 q^{10} - 51 q^{12} + 20 q^{13} + 144 q^{14} - 45 q^{15} + 25 q^{16} - 32 q^{17} - 9 q^{18} - 116 q^{19} + 85 q^{20} + 18 q^{21} + 240 q^{23} - 9 q^{24} + 75 q^{25} + 302 q^{26} - 81 q^{27} - 160 q^{28} - 238 q^{29} + 15 q^{30} + 92 q^{31} - 197 q^{32} + 354 q^{34} - 30 q^{35} + 153 q^{36} - 90 q^{37} + 324 q^{38} - 60 q^{39} + 15 q^{40} + 46 q^{41} - 432 q^{42} + 134 q^{43} + 135 q^{45} + 240 q^{46} - 220 q^{47} - 75 q^{48} - 457 q^{49} - 25 q^{50} + 96 q^{51} + 1530 q^{52} - 798 q^{53} + 27 q^{54} + 688 q^{56} + 348 q^{57} - 978 q^{58} + 1236 q^{59} - 255 q^{60} - 342 q^{61} + 1792 q^{62} - 54 q^{63} - 1919 q^{64} + 100 q^{65} + 764 q^{67} - 1074 q^{68} - 720 q^{69} + 720 q^{70} + 1816 q^{71} + 27 q^{72} - 100 q^{73} + 1874 q^{74} - 225 q^{75} - 396 q^{76} - 906 q^{78} + 96 q^{79} + 125 q^{80} + 243 q^{81} - 910 q^{82} - 858 q^{83} + 480 q^{84} - 160 q^{85} + 188 q^{86} + 714 q^{87} + 838 q^{89} - 45 q^{90} + 332 q^{91} - 688 q^{92} - 276 q^{93} + 3112 q^{94} - 580 q^{95} + 591 q^{96} - 1322 q^{97} - 1017 q^{98}+O(q^{100}) \) 3 * q - q^2 - 9 * q^3 + 17 * q^4 + 15 * q^5 + 3 * q^6 - 6 * q^7 + 3 * q^8 + 27 * q^9 - 5 * q^10 - 51 * q^12 + 20 * q^13 + 144 * q^14 - 45 * q^15 + 25 * q^16 - 32 * q^17 - 9 * q^18 - 116 * q^19 + 85 * q^20 + 18 * q^21 + 240 * q^23 - 9 * q^24 + 75 * q^25 + 302 * q^26 - 81 * q^27 - 160 * q^28 - 238 * q^29 + 15 * q^30 + 92 * q^31 - 197 * q^32 + 354 * q^34 - 30 * q^35 + 153 * q^36 - 90 * q^37 + 324 * q^38 - 60 * q^39 + 15 * q^40 + 46 * q^41 - 432 * q^42 + 134 * q^43 + 135 * q^45 + 240 * q^46 - 220 * q^47 - 75 * q^48 - 457 * q^49 - 25 * q^50 + 96 * q^51 + 1530 * q^52 - 798 * q^53 + 27 * q^54 + 688 * q^56 + 348 * q^57 - 978 * q^58 + 1236 * q^59 - 255 * q^60 - 342 * q^61 + 1792 * q^62 - 54 * q^63 - 1919 * q^64 + 100 * q^65 + 764 * q^67 - 1074 * q^68 - 720 * q^69 + 720 * q^70 + 1816 * q^71 + 27 * q^72 - 100 * q^73 + 1874 * q^74 - 225 * q^75 - 396 * q^76 - 906 * q^78 + 96 * q^79 + 125 * q^80 + 243 * q^81 - 910 * q^82 - 858 * q^83 + 480 * q^84 - 160 * q^85 + 188 * q^86 + 714 * q^87 + 838 * q^89 - 45 * q^90 + 332 * q^91 - 688 * q^92 - 276 * q^93 + 3112 * q^94 - 580 * q^95 + 591 * q^96 - 1322 * q^97 - 1017 * q^98

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 $

$2$	−4.59486	−1.62453	−0.812263	−	0.583291i	$-0.801765\pi$
$2$	−4.59486	−1.62453	−0.812263	+	0.583291i	$0.801765\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	13.1127	1.63909
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	13.7846	0.937921
$7$	−20.6383	−1.11437	−0.557183	−	0.830390i	$-0.688118\pi$
$7$	−20.6383	−1.11437	−0.557183	+	0.830390i	$0.688118\pi$
$8$	−23.4921	−1.03822
$9$	9.00000	0.333333
$10$	−22.9743	−0.726511
$11$	0	0
$11$	0	0
$12$	−39.3381	−0.946328
$13$	15.6584	0.334067	0.167033	−	0.985951i	$-0.446581\pi$
$13$	15.6584	0.334067	0.167033	+	0.985951i	$0.446581\pi$
$14$	94.8302	1.81032
$15$	−15.0000	−0.258199
$16$	3.04132	0.0475206
$17$	−72.9507	−1.04077	−0.520387	−	0.853931i	$-0.674212\pi$
$17$	−72.9507	−1.04077	−0.520387	+	0.853931i	$0.674212\pi$
$18$	−41.3537	−0.541509
$19$	−61.0513	−0.737165	−0.368582	−	0.929595i	$-0.620157\pi$
$19$	−61.0513	−0.737165	−0.368582	+	0.929595i	$0.620157\pi$
$20$	65.5635	0.733022
$21$	61.9150	0.643379
$22$	0	0
$23$	−13.6605	−0.123844	−0.0619218	−	0.998081i	$-0.519723\pi$
$23$	−13.6605	−0.123844	−0.0619218	+	0.998081i	$0.519723\pi$
$24$	70.4764	0.599414
$25$	25.0000	0.200000
$26$	−71.9483	−0.542701
$27$	−27.0000	−0.192450
$28$	−270.624	−1.82654
$29$	31.4663	0.201487	0.100744	−	0.994912i	$-0.467878\pi$
$29$	31.4663	0.201487	0.100744	+	0.994912i	$0.467878\pi$
$30$	68.9228	0.419451
$31$	−243.008	−1.40792	−0.703961	−	0.710239i	$-0.748587\pi$
$31$	−243.008	−1.40792	−0.703961	+	0.710239i	$0.748587\pi$
$32$	173.963	0.961016
$33$	0	0
$34$	335.198	1.69076
$35$	−103.192	−0.498360
$36$	118.014	0.546363
$37$	−65.4018	−0.290594	−0.145297	−	0.989388i	$-0.546414\pi$
$37$	−65.4018	−0.290594	−0.145297	+	0.989388i	$0.546414\pi$
$38$	280.522	1.19754
$39$	−46.9753	−0.192874
$40$	−117.461	−0.464304
$41$	109.087	0.415524	0.207762	−	0.978179i	$-0.433382\pi$
$41$	109.087	0.415524	0.207762	+	0.978179i	$0.433382\pi$
$42$	−284.491	−1.04519
$43$	121.750	0.431783	0.215891	−	0.976417i	$-0.430734\pi$
$43$	121.750	0.431783	0.215891	+	0.976417i	$0.430734\pi$
$44$	0	0
$45$	45.0000	0.149071
$46$	62.7678	0.201187
$47$	−519.530	−1.61237	−0.806184	−	0.591665i	$-0.798471\pi$
$47$	−519.530	−1.61237	−0.806184	+	0.591665i	$0.798471\pi$
$48$	−9.12396	−0.0274361
$49$	82.9413	0.241811
$50$	−114.871	−0.324905
$51$	218.852	0.600891
$52$	205.324	0.547565
$53$	−542.673	−1.40645	−0.703226	−	0.710967i	$-0.748258\pi$
$53$	−542.673	−1.40645	−0.703226	+	0.710967i	$0.748258\pi$
$54$	124.061	0.312640
$55$	0	0
$56$	484.839	1.15695
$57$	183.154	0.425602
$58$	−144.583	−0.327322
$59$	109.478	0.241574	0.120787	−	0.992678i	$-0.461458\pi$
$59$	109.478	0.241574	0.120787	+	0.992678i	$0.461458\pi$
$60$	−196.691	−0.423211
$61$	89.6156	0.188100	0.0940501	−	0.995567i	$-0.470019\pi$
$61$	89.6156	0.188100	0.0940501	+	0.995567i	$0.470019\pi$
$62$	1116.59	2.28721
$63$	−185.745	−0.371455
$64$	−823.664	−1.60872
$65$	78.2922	0.149399
$66$	0	0
$67$	488.446	0.890644	0.445322	−	0.895371i	$-0.353089\pi$
$67$	488.446	0.890644	0.445322	+	0.895371i	$0.353089\pi$
$68$	−956.581	−1.70592
$69$	40.9814	0.0715011
$70$	474.151	0.809599
$71$	837.423	1.39977	0.699887	−	0.714254i	$-0.253234\pi$
$71$	837.423	1.39977	0.699887	+	0.714254i	$0.253234\pi$
$72$	−211.429	−0.346072
$73$	−351.216	−0.563105	−0.281553	−	0.959546i	$-0.590849\pi$
$73$	−351.216	−0.563105	−0.281553	+	0.959546i	$0.590849\pi$
$74$	300.512	0.472078
$75$	−75.0000	−0.115470
$76$	−800.547	−1.20828
$77$	0	0
$78$	215.845	0.313328
$79$	831.205	1.18377	0.591885	−	0.806022i	$-0.298384\pi$
$79$	831.205	1.18377	0.591885	+	0.806022i	$0.298384\pi$
$80$	15.2066	0.0212519
$81$	81.0000	0.111111
$82$	−501.238	−0.675031
$83$	−1389.13	−1.83707	−0.918537	−	0.395335i	$-0.870629\pi$
$83$	−1389.13	−1.83707	−0.918537	+	0.395335i	$0.870629\pi$
$84$	811.873	1.05456
$85$	−364.754	−0.465448
$86$	−559.423	−0.701443
$87$	−94.3988	−0.116329
$88$	0	0
$89$	1523.70	1.81474	0.907369	−	0.420335i	$-0.138088\pi$
$89$	1523.70	1.81474	0.907369	+	0.420335i	$0.138088\pi$
$90$	−206.769	−0.242170
$91$	−323.164	−0.372273
$92$	−179.125	−0.202990
$93$	729.025	0.812864
$94$	2387.17	2.61933
$95$	−305.256	−0.329670
$96$	−521.888	−0.554843
$97$	−426.612	−0.446555	−0.223278	−	0.974755i	$-0.571676\pi$
$97$	−426.612	−0.446555	−0.223278	+	0.974755i	$0.571676\pi$
$98$	−381.103	−0.392829
$99$	0	0
$100$	327.818	0.327818
$101$	−74.1387	−0.0730403	−0.0365202	−	0.999333i	$-0.511627\pi$
$101$	−74.1387	−0.0730403	−0.0365202	+	0.999333i	$0.511627\pi$
$102$	−1005.59	−0.976163
$103$	−69.3916	−0.0663821	−0.0331911	−	0.999449i	$-0.510567\pi$
$103$	−69.3916	−0.0663821	−0.0331911	+	0.999449i	$0.510567\pi$
$104$	−367.850	−0.346833
$105$	309.575	0.287728
$106$	2493.51	2.28482
$107$	−1141.71	−1.03152	−0.515761	−	0.856733i	$-0.672491\pi$
$107$	−1141.71	−1.03152	−0.515761	+	0.856733i	$0.672491\pi$
$108$	−354.043	−0.315443
$109$	2226.85	1.95682	0.978409	−	0.206680i	$-0.0662659\pi$
$109$	2226.85	1.95682	0.978409	+	0.206680i	$0.0662659\pi$
$110$	0	0
$111$	196.205	0.167775
$112$	−62.7678	−0.0529554
$113$	−1719.76	−1.43169	−0.715847	−	0.698257i	$-0.753959\pi$
$113$	−1719.76	−1.43169	−0.715847	+	0.698257i	$0.753959\pi$
$114$	−841.566	−0.691402
$115$	−68.3023	−0.0553845
$116$	412.608	0.330256
$117$	140.926	0.111356
$118$	−503.038	−0.392444
$119$	1505.58	1.15980
$120$	352.382	0.268066
$121$	0	0
$122$	−411.771	−0.305574
$123$	−327.260	−0.239903
$124$	−3186.49	−2.30771
$125$	125.000	0.0894427
$126$	853.472	0.603439
$127$	1601.63	1.11907	0.559534	−	0.828807i	$-0.310980\pi$
$127$	1601.63	1.11907	0.559534	+	0.828807i	$0.310980\pi$
$128$	2392.91	1.65239
$129$	−365.249	−0.249290
$130$	−359.741	−0.242703
$131$	−2004.13	−1.33665	−0.668327	−	0.743868i	$-0.732989\pi$
$131$	−2004.13	−1.33665	−0.668327	+	0.743868i	$0.732989\pi$
$132$	0	0
$133$	1260.00	0.821471
$134$	−2244.34	−1.44687
$135$	−135.000	−0.0860663
$136$	1713.77	1.08055
$137$	−1672.85	−1.04322	−0.521610	−	0.853184i	$-0.674669\pi$
$137$	−1672.85	−1.04322	−0.521610	+	0.853184i	$0.674669\pi$
$138$	−188.303	−0.116155
$139$	−2540.38	−1.55016	−0.775080	−	0.631863i	$-0.782291\pi$
$139$	−2540.38	−1.55016	−0.775080	+	0.631863i	$0.782291\pi$
$140$	−1353.12	−0.816855
$141$	1558.59	0.930901
$142$	−3847.84	−2.27397
$143$	0	0
$144$	27.3719	0.0158402
$145$	157.331	0.0901079
$146$	1613.79	0.914780
$147$	−248.824	−0.139610
$148$	−857.594	−0.476310
$149$	−3090.68	−1.69932	−0.849658	−	0.527334i	$-0.823192\pi$
$149$	−3090.68	−1.69932	−0.849658	+	0.527334i	$0.823192\pi$
$150$	344.614	0.187584
$151$	−1358.74	−0.732267	−0.366134	−	0.930562i	$-0.619319\pi$
$151$	−1358.74	−0.732267	−0.366134	+	0.930562i	$0.619319\pi$
$152$	1434.22	0.765335
$153$	−656.557	−0.346925
$154$	0	0
$155$	−1215.04	−0.629642
$156$	−615.973	−0.316137
$157$	−1011.95	−0.514411	−0.257205	−	0.966357i	$-0.582802\pi$
$157$	−1011.95	−0.514411	−0.257205	+	0.966357i	$0.582802\pi$
$158$	−3819.27	−1.92307
$159$	1628.02	0.812015
$160$	869.813	0.429780
$161$	281.929	0.138007
$162$	−372.183	−0.180503
$163$	−2816.37	−1.35334	−0.676672	−	0.736285i	$-0.736578\pi$
$163$	−2816.37	−1.35334	−0.676672	+	0.736285i	$0.736578\pi$
$164$	1430.42	0.681081
$165$	0	0
$166$	6382.87	2.98438
$167$	−3448.89	−1.59810	−0.799052	−	0.601262i	$-0.794665\pi$
$167$	−3448.89	−1.59810	−0.799052	+	0.601262i	$0.794665\pi$
$168$	−1454.52	−0.667966
$169$	−1951.81	−0.888399
$170$	1675.99	0.756133
$171$	−549.462	−0.245722
$172$	1596.47	0.707730
$173$	2287.85	1.00545	0.502723	−	0.864448i	$-0.332332\pi$
$173$	2287.85	1.00545	0.502723	+	0.864448i	$0.332332\pi$
$174$	433.749	0.188979
$175$	−515.959	−0.222873
$176$	0	0
$177$	−328.435	−0.139473
$178$	−7001.17	−2.94809
$179$	3249.06	1.35668	0.678340	−	0.734748i	$-0.262700\pi$
$179$	3249.06	1.35668	0.678340	+	0.734748i	$0.262700\pi$
$180$	590.072	0.244341
$181$	1170.45	0.480655	0.240328	−	0.970692i	$-0.422745\pi$
$181$	1170.45	0.480655	0.240328	+	0.970692i	$0.422745\pi$
$182$	1484.89	0.604767
$183$	−268.847	−0.108600
$184$	320.913	0.128576
$185$	−327.009	−0.129958
$186$	−3349.76	−1.32052
$187$	0	0
$188$	−6812.44	−2.64281
$189$	557.235	0.214460
$190$	1402.61	0.535558
$191$	−2760.35	−1.04572	−0.522859	−	0.852419i	$-0.675134\pi$
$191$	−2760.35	−1.04572	−0.522859	+	0.852419i	$0.675134\pi$
$192$	2470.99	0.928794
$193$	1250.61	0.466430	0.233215	−	0.972425i	$-0.425075\pi$
$193$	1250.61	0.466430	0.233215	+	0.972425i	$0.425075\pi$
$194$	1960.22	0.725441
$195$	−234.877	−0.0862557
$196$	1087.58	0.396350
$197$	143.991	0.0520756	0.0260378	−	0.999661i	$-0.491711\pi$
$197$	143.991	0.0520756	0.0260378	+	0.999661i	$0.491711\pi$
$198$	0	0
$199$	761.249	0.271174	0.135587	−	0.990765i	$-0.456708\pi$
$199$	761.249	0.271174	0.135587	+	0.990765i	$0.456708\pi$
$200$	−587.303	−0.207643
$201$	−1465.34	−0.514213
$202$	340.657	0.118656
$203$	−649.411	−0.224531
$204$	2869.74	0.984913
$205$	545.434	0.185828
$206$	318.844	0.107840
$207$	−122.944	−0.0412812
$208$	47.6223	0.0158751
$209$	0	0
$210$	−1422.45	−0.467422
$211$	−3976.58	−1.29743	−0.648717	−	0.761029i	$-0.724694\pi$
$211$	−3976.58	−1.29743	−0.648717	+	0.761029i	$0.724694\pi$
$212$	−7115.91	−2.30530
$213$	−2512.27	−0.808159
$214$	5245.97	1.67573
$215$	608.749	0.193099
$216$	634.287	0.199805
$217$	5015.29	1.56894
$218$	−10232.0	−3.17890
$219$	1053.65	0.325109
$220$	0	0
$221$	−1142.29	−0.347688
$222$	−901.535	−0.272555
$223$	908.084	0.272690	0.136345	−	0.990661i	$-0.456464\pi$
$223$	908.084	0.272690	0.136345	+	0.990661i	$0.456464\pi$
$224$	−3590.30	−1.07092
$225$	225.000	0.0666667
$226$	7902.05	2.32583
$227$	2062.15	0.602951	0.301475	−	0.953474i	$-0.402521\pi$
$227$	2062.15	0.602951	0.301475	+	0.953474i	$0.402521\pi$
$228$	2401.64	0.697599
$229$	4077.47	1.17662	0.588312	−	0.808634i	$-0.299793\pi$
$229$	4077.47	1.17662	0.588312	+	0.808634i	$0.299793\pi$
$230$	313.839	0.0899737
$231$	0	0
$232$	−739.209	−0.209187
$233$	−1682.76	−0.473138	−0.236569	−	0.971615i	$-0.576023\pi$
$233$	−1682.76	−0.473138	−0.236569	+	0.971615i	$0.576023\pi$
$234$	−647.534	−0.180900
$235$	−2597.65	−0.721073
$236$	1435.56	0.395961
$237$	−2493.62	−0.683450
$238$	−6917.93	−1.88413
$239$	−4024.96	−1.08934	−0.544672	−	0.838649i	$-0.683346\pi$
$239$	−4024.96	−1.08934	−0.544672	+	0.838649i	$0.683346\pi$
$240$	−45.6198	−0.0122698
$241$	2784.27	0.744194	0.372097	−	0.928194i	$-0.378639\pi$
$241$	2784.27	0.744194	0.372097	+	0.928194i	$0.378639\pi$
$242$	0	0
$243$	−243.000	−0.0641500
$244$	1175.10	0.308313
$245$	414.707	0.108141
$246$	1503.71	0.389729
$247$	−955.968	−0.246262
$248$	5708.78	1.46173
$249$	4167.40	1.06064
$250$	−574.357	−0.145302
$251$	−1827.60	−0.459591	−0.229796	−	0.973239i	$-0.573806\pi$
$251$	−1827.60	−0.459591	−0.229796	+	0.973239i	$0.573806\pi$
$252$	−2435.62	−0.608848
$253$	0	0
$254$	−7359.26	−1.81796
$255$	1094.26	0.268727
$256$	−4405.79	−1.07563
$257$	585.171	0.142031	0.0710155	−	0.997475i	$-0.477376\pi$
$257$	585.171	0.142031	0.0710155	+	0.997475i	$0.477376\pi$
$258$	1678.27	0.404978
$259$	1349.78	0.323828
$260$	1026.62	0.244878
$261$	283.196	0.0671625
$262$	9208.69	2.17143
$263$	238.098	0.0558241	0.0279120	−	0.999610i	$-0.491114\pi$
$263$	238.098	0.0558241	0.0279120	+	0.999610i	$0.491114\pi$
$264$	0	0
$265$	−2713.37	−0.628984
$266$	−5789.51	−1.33450
$267$	−4571.09	−1.04774
$268$	6404.84	1.45984
$269$	4618.46	1.04681	0.523406	−	0.852083i	$-0.324661\pi$
$269$	4618.46	1.04681	0.523406	+	0.852083i	$0.324661\pi$
$270$	620.306	0.139817
$271$	143.439	0.0321525	0.0160762	−	0.999871i	$-0.494883\pi$
$271$	143.439	0.0321525	0.0160762	+	0.999871i	$0.494883\pi$
$272$	−221.867	−0.0494582
$273$	969.493	0.214932
$274$	7686.51	1.69474
$275$	0	0
$276$	537.376	0.117197
$277$	8602.51	1.86597	0.932987	−	0.359911i	$-0.117193\pi$
$277$	8602.51	1.86597	0.932987	+	0.359911i	$0.117193\pi$
$278$	11672.7	2.51828
$279$	−2187.07	−0.469307
$280$	2424.19	0.517404
$281$	2992.81	0.635360	0.317680	−	0.948198i	$-0.397096\pi$
$281$	2992.81	0.635360	0.317680	+	0.948198i	$0.397096\pi$
$282$	−7161.50	−1.51227
$283$	6858.89	1.44070	0.720351	−	0.693610i	$-0.243981\pi$
$283$	6858.89	1.44070	0.720351	+	0.693610i	$0.243981\pi$
$284$	10980.9	2.29435
$285$	915.769	0.190335
$286$	0	0
$287$	−2251.37	−0.463046
$288$	1565.66	0.320339
$289$	408.809	0.0832096
$290$	−722.915	−0.146383
$291$	1279.84	0.257819
$292$	−4605.39	−0.922979
$293$	−4049.70	−0.807461	−0.403731	−	0.914878i	$-0.632287\pi$
$293$	−4049.70	−0.807461	−0.403731	+	0.914878i	$0.632287\pi$
$294$	1143.31	0.226800
$295$	547.392	0.108035
$296$	1536.43	0.301699
$297$	0	0
$298$	14201.2	2.76059
$299$	−213.901	−0.0413720
$300$	−983.453	−0.189266
$301$	−2512.71	−0.481164
$302$	6243.20	1.18959
$303$	222.416	0.0421699
$304$	−185.677	−0.0350305
$305$	448.078	0.0841209
$306$	3016.78	0.563588
$307$	9572.69	1.77962	0.889808	−	0.456335i	$-0.150838\pi$
$307$	9572.69	1.77962	0.889808	+	0.456335i	$0.150838\pi$
$308$	0	0
$309$	208.175	0.0383257
$310$	5582.94	1.02287
$311$	5396.42	0.983932	0.491966	−	0.870614i	$-0.336278\pi$
$311$	5396.42	0.983932	0.491966	+	0.870614i	$0.336278\pi$
$312$	1103.55	0.200244
$313$	9755.04	1.76162	0.880811	−	0.473469i	$-0.156998\pi$
$313$	9755.04	1.76162	0.880811	+	0.473469i	$0.156998\pi$
$314$	4649.77	0.835674
$315$	−928.726	−0.166120
$316$	10899.3	1.94030
$317$	−4353.75	−0.771391	−0.385695	−	0.922626i	$-0.626038\pi$
$317$	−4353.75	−0.771391	−0.385695	+	0.922626i	$0.626038\pi$
$318$	−7480.52	−1.31914
$319$	0	0
$320$	−4118.32	−0.719440
$321$	3425.12	0.595549
$322$	−1295.42	−0.224196
$323$	4453.74	0.767221
$324$	1062.13	0.182121
$325$	391.461	0.0668134
$326$	12940.8	2.19854
$327$	−6680.54	−1.12977
$328$	−2562.68	−0.431404
$329$	10722.2	1.79677
$330$	0	0
$331$	5387.64	0.894656	0.447328	−	0.894370i	$-0.352376\pi$
$331$	5387.64	0.894656	0.447328	+	0.894370i	$0.352376\pi$
$332$	−18215.3	−3.01113
$333$	−588.616	−0.0968648
$334$	15847.2	2.59616
$335$	2442.23	0.398308
$336$	188.303	0.0305738
$337$	4500.27	0.727434	0.363717	−	0.931509i	$-0.381508\pi$
$337$	4500.27	0.727434	0.363717	+	0.931509i	$0.381508\pi$
$338$	8968.30	1.44323
$339$	5159.28	0.826589
$340$	−4782.91	−0.762910
$341$	0	0
$342$	2524.70	0.399181
$343$	5367.18	0.844899
$344$	−2860.16	−0.448283
$345$	204.907	0.0319763
$346$	−10512.4	−1.63337
$347$	−5906.32	−0.913740	−0.456870	−	0.889533i	$-0.651030\pi$
$347$	−5906.32	−0.913740	−0.456870	+	0.889533i	$0.651030\pi$
$348$	−1237.82	−0.190673
$349$	−3636.26	−0.557721	−0.278860	−	0.960332i	$-0.589957\pi$
$349$	−3636.26	−0.557721	−0.278860	+	0.960332i	$0.589957\pi$
$350$	2370.76	0.362063
$351$	−422.778	−0.0642912
$352$	0	0
$353$	210.408	0.0317248	0.0158624	−	0.999874i	$-0.494951\pi$
$353$	210.408	0.0317248	0.0158624	+	0.999874i	$0.494951\pi$
$354$	1509.11	0.226577
$355$	4187.12	0.625998
$356$	19979.8	2.97451
$357$	−4516.75	−0.669612
$358$	−14928.9	−2.20396
$359$	−2499.68	−0.367488	−0.183744	−	0.982974i	$-0.558822\pi$
$359$	−2499.68	−0.367488	−0.183744	+	0.982974i	$0.558822\pi$
$360$	−1057.15	−0.154768
$361$	−3131.74	−0.456588
$362$	−5378.03	−0.780837
$363$	0	0
$364$	−4237.56	−0.610188
$365$	−1756.08	−0.251828
$366$	1235.31	0.176423
$367$	5748.70	0.817656	0.408828	−	0.912612i	$-0.365938\pi$
$367$	5748.70	0.817656	0.408828	+	0.912612i	$0.365938\pi$
$368$	−41.5458	−0.00588512
$369$	981.781	0.138508
$370$	1502.56	0.211120
$371$	11199.9	1.56730
$372$	9559.48	1.33236
$373$	−4467.78	−0.620196	−0.310098	−	0.950705i	$-0.600362\pi$
$373$	−4467.78	−0.620196	−0.310098	+	0.950705i	$0.600362\pi$
$374$	0	0
$375$	−375.000	−0.0516398
$376$	12204.9	1.67398
$377$	492.712	0.0673103
$378$	−2560.42	−0.348396
$379$	7804.08	1.05770	0.528851	−	0.848715i	$-0.322623\pi$
$379$	7804.08	1.05770	0.528851	+	0.848715i	$0.322623\pi$
$380$	−4002.74	−0.540358
$381$	−4804.89	−0.646094
$382$	12683.4	1.69880
$383$	−11161.1	−1.48904	−0.744522	−	0.667597i	$-0.767323\pi$
$383$	−11161.1	−1.48904	−0.744522	+	0.667597i	$0.767323\pi$
$384$	−7178.74	−0.954007
$385$	0	0
$386$	−5746.38	−0.757728
$387$	1095.75	0.143928
$388$	−5594.04	−0.731944
$389$	8490.24	1.10661	0.553306	−	0.832978i	$-0.313366\pi$
$389$	8490.24	1.10661	0.553306	+	0.832978i	$0.313366\pi$
$390$	1079.22	0.140125
$391$	996.540	0.128893
$392$	−1948.47	−0.251052
$393$	6012.39	0.771717
$394$	−661.616	−0.0845983
$395$	4156.03	0.529398
$396$	0	0
$397$	6019.74	0.761013	0.380507	−	0.924778i	$-0.375750\pi$
$397$	6019.74	0.761013	0.380507	+	0.924778i	$0.375750\pi$
$398$	−3497.83	−0.440529
$399$	−3779.99	−0.474277
$400$	76.0330	0.00950413
$401$	−10398.8	−1.29499	−0.647495	−	0.762069i	$-0.724184\pi$
$401$	−10398.8	−1.29499	−0.647495	+	0.762069i	$0.724184\pi$
$402$	6733.01	0.835354
$403$	−3805.13	−0.470340
$404$	−972.158	−0.119720
$405$	405.000	0.0496904
$406$	2983.95	0.364756
$407$	0	0
$408$	−5141.30	−0.623854
$409$	4733.68	0.572287	0.286144	−	0.958187i	$-0.407627\pi$
$409$	4733.68	0.572287	0.286144	+	0.958187i	$0.407627\pi$
$410$	−2506.19	−0.301883
$411$	5018.55	0.602304
$412$	−909.911	−0.108806
$413$	−2259.45	−0.269202
$414$	564.910	0.0670624
$415$	−6945.67	−0.821565
$416$	2723.98	0.321044
$417$	7621.14	0.894985
$418$	0	0
$419$	−8117.57	−0.946466	−0.473233	−	0.880937i	$-0.656913\pi$
$419$	−8117.57	−0.946466	−0.473233	+	0.880937i	$0.656913\pi$
$420$	4059.37	0.471611
$421$	−9484.27	−1.09795	−0.548973	−	0.835840i	$-0.684981\pi$
$421$	−9484.27	−1.09795	−0.548973	+	0.835840i	$0.684981\pi$
$422$	18271.8	2.10772
$423$	−4675.77	−0.537456
$424$	12748.5	1.46020
$425$	−1823.77	−0.208155
$426$	11543.5	1.31288
$427$	−1849.52	−0.209612
$428$	−14970.8	−1.69075
$429$	0	0
$430$	−2797.11	−0.313695
$431$	−9335.16	−1.04329	−0.521646	−	0.853162i	$-0.674682\pi$
$431$	−9335.16	−1.04329	−0.521646	+	0.853162i	$0.674682\pi$
$432$	−82.1157	−0.00914535
$433$	−2983.02	−0.331074	−0.165537	−	0.986204i	$-0.552936\pi$
$433$	−2983.02	−0.331074	−0.165537	+	0.986204i	$0.552936\pi$
$434$	−23044.5	−2.54878
$435$	−471.994	−0.0520238
$436$	29200.0	3.20739
$437$	833.988	0.0912931
$438$	−4841.36	−0.528148
$439$	5232.32	0.568850	0.284425	−	0.958698i	$-0.408197\pi$
$439$	5232.32	0.568850	0.284425	+	0.958698i	$0.408197\pi$
$440$	0	0
$441$	746.472	0.0806038
$442$	5248.68	0.564828
$443$	7517.71	0.806269	0.403135	−	0.915141i	$-0.367921\pi$
$443$	7517.71	0.806269	0.403135	+	0.915141i	$0.367921\pi$
$444$	2572.78	0.274997
$445$	7618.49	0.811575
$446$	−4172.52	−0.442992
$447$	9272.03	0.981101
$448$	16999.1	1.79270
$449$	16070.9	1.68916	0.844581	−	0.535428i	$-0.179850\pi$
$449$	16070.9	1.68916	0.844581	+	0.535428i	$0.179850\pi$
$450$	−1033.84	−0.108302
$451$	0	0
$452$	−22550.7	−2.34667
$453$	4076.21	0.422775
$454$	−9475.29	−0.979510
$455$	−1615.82	−0.166485
$456$	−4302.67	−0.441867
$457$	−9718.51	−0.994776	−0.497388	−	0.867528i	$-0.665707\pi$
$457$	−9718.51	−0.994776	−0.497388	+	0.867528i	$0.665707\pi$
$458$	−18735.4	−1.91146
$459$	1969.67	0.200297
$460$	−895.627	−0.0907801
$461$	14538.0	1.46877	0.734385	−	0.678733i	$-0.237471\pi$
$461$	14538.0	1.46877	0.734385	+	0.678733i	$0.237471\pi$
$462$	0	0
$463$	−9978.17	−1.00157	−0.500783	−	0.865573i	$-0.666955\pi$
$463$	−9978.17	−1.00157	−0.500783	+	0.865573i	$0.666955\pi$
$464$	95.6990	0.00957481
$465$	3645.12	0.363524
$466$	7732.03	0.768625
$467$	15188.2	1.50498	0.752489	−	0.658605i	$-0.228853\pi$
$467$	15188.2	1.50498	0.752489	+	0.658605i	$0.228853\pi$
$468$	1847.92	0.182522
$469$	−10080.7	−0.992503
$470$	11935.8	1.17140
$471$	3035.85	0.296995
$472$	−2571.88	−0.250806
$473$	0	0
$474$	11457.8	1.11028
$475$	−1526.28	−0.147433
$476$	19742.3	1.90102
$477$	−4884.06	−0.468817
$478$	18494.1	1.76967
$479$	−11330.8	−1.08083	−0.540415	−	0.841399i	$-0.681733\pi$
$479$	−11330.8	−1.08083	−0.540415	+	0.841399i	$0.681733\pi$
$480$	−2609.44	−0.248133
$481$	−1024.09	−0.0970779
$482$	−12793.3	−1.20896
$483$	−845.788	−0.0796784
$484$	0	0
$485$	−2133.06	−0.199706
$486$	1116.55	0.104213
$487$	19086.9	1.77599	0.887997	−	0.459850i	$-0.152097\pi$
$487$	19086.9	1.77599	0.887997	+	0.459850i	$0.152097\pi$
$488$	−2105.26	−0.195288
$489$	8449.11	0.781353
$490$	−1905.52	−0.175679
$491$	8112.85	0.745677	0.372839	−	0.927896i	$-0.378384\pi$
$491$	8112.85	0.745677	0.372839	+	0.927896i	$0.378384\pi$
$492$	−4291.27	−0.393222
$493$	−2295.49	−0.209703
$494$	4392.53	0.400060
$495$	0	0
$496$	−739.066	−0.0669053
$497$	−17283.0	−1.55986
$498$	−19148.6	−1.72303
$499$	18329.1	1.64433	0.822167	−	0.569246i	$-0.192765\pi$
$499$	18329.1	1.64433	0.822167	+	0.569246i	$0.192765\pi$
$500$	1639.09	0.146604
$501$	10346.7	0.922666
$502$	8397.58	0.746618
$503$	−7739.57	−0.686064	−0.343032	−	0.939324i	$-0.611454\pi$
$503$	−7739.57	−0.686064	−0.343032	+	0.939324i	$0.611454\pi$
$504$	4363.55	0.385651
$505$	−370.693	−0.0326646
$506$	0	0
$507$	5855.44	0.512918
$508$	21001.7	1.83425
$509$	15914.9	1.38589	0.692943	−	0.720993i	$-0.256314\pi$
$509$	15914.9	1.38589	0.692943	+	0.720993i	$0.256314\pi$
$510$	−5027.97	−0.436554
$511$	7248.51	0.627505
$512$	1100.65	0.0950048
$513$	1648.38	0.141867
$514$	−2688.78	−0.230733
$515$	−346.958	−0.0296870
$516$	−4789.40	−0.408608
$517$	0	0
$518$	−6202.07	−0.526068
$519$	−6863.56	−0.580495
$520$	−1839.25	−0.155109
$521$	2274.50	0.191262	0.0956312	−	0.995417i	$-0.469513\pi$
$521$	2274.50	0.191262	0.0956312	+	0.995417i	$0.469513\pi$
$522$	−1301.25	−0.109107
$523$	−10971.1	−0.917274	−0.458637	−	0.888624i	$-0.651662\pi$
$523$	−10971.1	−0.917274	−0.458637	+	0.888624i	$0.651662\pi$
$524$	−26279.6	−2.19089
$525$	1547.88	0.128676
$526$	−1094.02	−0.0906877
$527$	17727.6	1.46533
$528$	0	0
$529$	−11980.4	−0.984663
$530$	12467.5	1.02180
$531$	985.306	0.0805247
$532$	16522.0	1.34646
$533$	1708.13	0.138813
$534$	21003.5	1.70208
$535$	−5708.53	−0.461310
$536$	−11474.6	−0.924680
$537$	−9747.17	−0.783280
$538$	−21221.2	−1.70058
$539$	0	0
$540$	−1770.21	−0.141070
$541$	−5313.05	−0.422229	−0.211115	−	0.977461i	$-0.567709\pi$
$541$	−5313.05	−0.422229	−0.211115	+	0.977461i	$0.567709\pi$
$542$	−659.084	−0.0522326
$543$	−3511.34	−0.277506
$544$	−12690.7	−1.00020
$545$	11134.2	0.875115
$546$	−4454.68	−0.349162
$547$	−20685.1	−1.61688	−0.808439	−	0.588581i	$-0.799687\pi$
$547$	−20685.1	−1.61688	−0.808439	+	0.588581i	$0.799687\pi$
$548$	−21935.6	−1.70993
$549$	806.541	0.0627000
$550$	0	0
$551$	−1921.06	−0.148529
$552$	−962.739	−0.0742335
$553$	−17154.7	−1.31915
$554$	−39527.3	−3.03132
$555$	981.027	0.0750311
$556$	−33311.2	−2.54085
$557$	10853.8	0.825659	0.412830	−	0.910808i	$-0.364540\pi$
$557$	10853.8	0.825659	0.412830	+	0.910808i	$0.364540\pi$
$558$	10049.3	0.762402
$559$	1906.41	0.144244
$560$	−313.839	−0.0236824
$561$	0	0
$562$	−13751.5	−1.03216
$563$	15381.2	1.15141	0.575704	−	0.817658i	$-0.304728\pi$
$563$	15381.2	1.15141	0.575704	+	0.817658i	$0.304728\pi$
$564$	20437.3	1.52583
$565$	−8598.80	−0.640273
$566$	−31515.6	−2.34046
$567$	−1671.71	−0.123818
$568$	−19672.9	−1.45327
$569$	1348.88	0.0993814	0.0496907	−	0.998765i	$-0.484176\pi$
$569$	1348.88	0.0993814	0.0496907	+	0.998765i	$0.484176\pi$
$570$	−4207.83	−0.309204
$571$	−3463.51	−0.253841	−0.126920	−	0.991913i	$-0.540509\pi$
$571$	−3463.51	−0.253841	−0.126920	+	0.991913i	$0.540509\pi$
$572$	0	0
$573$	8281.05	0.603745
$574$	10344.7	0.752231
$575$	−341.511	−0.0247687
$576$	−7412.97	−0.536239
$577$	12052.6	0.869598	0.434799	−	0.900528i	$-0.356819\pi$
$577$	12052.6	0.869598	0.434799	+	0.900528i	$0.356819\pi$
$578$	−1878.42	−0.135176
$579$	−3751.83	−0.269293
$580$	2063.04	0.147695
$581$	28669.4	2.04717
$582$	−5880.66	−0.418834
$583$	0	0
$584$	8250.80	0.584624
$585$	704.630	0.0497997
$586$	18607.8	1.31174
$587$	−11133.1	−0.782813	−0.391407	−	0.920218i	$-0.628011\pi$
$587$	−11133.1	−0.782813	−0.391407	+	0.920218i	$0.628011\pi$
$588$	−3262.75	−0.228833
$589$	14836.0	1.03787
$590$	−2515.19	−0.175506
$591$	−431.972	−0.0300659
$592$	−198.908	−0.0138092
$593$	7939.69	0.549821	0.274911	−	0.961470i	$-0.411352\pi$
$593$	7939.69	0.549821	0.274911	+	0.961470i	$0.411352\pi$
$594$	0	0
$595$	7527.91	0.518680
$596$	−40527.1	−2.78533
$597$	−2283.75	−0.156562
$598$	982.846	0.0672100
$599$	−19474.7	−1.32840	−0.664202	−	0.747553i	$-0.731229\pi$
$599$	−19474.7	−1.32840	−0.664202	+	0.747553i	$0.731229\pi$
$600$	1761.91	0.119883
$601$	19946.1	1.35377	0.676887	−	0.736087i	$-0.263329\pi$
$601$	19946.1	1.35377	0.676887	+	0.736087i	$0.263329\pi$
$602$	11545.6	0.781664
$603$	4396.01	0.296881
$604$	−17816.7	−1.20025
$605$	0	0
$606$	−1021.97	−0.0685061
$607$	−1427.44	−0.0954496	−0.0477248	−	0.998861i	$-0.515197\pi$
$607$	−1427.44	−0.0954496	−0.0477248	+	0.998861i	$0.515197\pi$
$608$	−10620.6	−0.708427
$609$	1948.23	0.129633
$610$	−2058.85	−0.136657
$611$	−8135.03	−0.538638
$612$	−8609.23	−0.568640
$613$	8029.40	0.529045	0.264522	−	0.964380i	$-0.414786\pi$
$613$	8029.40	0.529045	0.264522	+	0.964380i	$0.414786\pi$
$614$	−43985.1	−2.89103
$615$	−1636.30	−0.107288
$616$	0	0
$617$	20795.5	1.35688	0.678440	−	0.734655i	$-0.262656\pi$
$617$	20795.5	1.35688	0.678440	+	0.734655i	$0.262656\pi$
$618$	−956.533	−0.0622612
$619$	1677.43	0.108920	0.0544602	−	0.998516i	$-0.482656\pi$
$619$	1677.43	0.108920	0.0544602	+	0.998516i	$0.482656\pi$
$620$	−15932.5	−1.03204
$621$	368.832	0.0238337
$622$	−24795.8	−1.59842
$623$	−31446.6	−2.02228
$624$	−142.867	−0.00916547
$625$	625.000	0.0400000
$626$	−44823.0	−2.86180
$627$	0	0
$628$	−13269.4	−0.843165
$629$	4771.11	0.302443
$630$	4267.36	0.269866
$631$	−25225.2	−1.59144	−0.795719	−	0.605666i	$-0.792907\pi$
$631$	−25225.2	−1.59144	−0.795719	+	0.605666i	$0.792907\pi$
$632$	−19526.8	−1.22901
$633$	11929.7	0.749074
$634$	20004.8	1.25315
$635$	8008.15	0.500462
$636$	21347.7	1.33096
$637$	1298.73	0.0807812
$638$	0	0
$639$	7536.81	0.466591
$640$	11964.6	0.738971
$641$	15165.3	0.934468	0.467234	−	0.884134i	$-0.345251\pi$
$641$	15165.3	0.934468	0.467234	+	0.884134i	$0.345251\pi$
$642$	−15737.9	−0.967486
$643$	27156.1	1.66553	0.832763	−	0.553630i	$-0.186758\pi$
$643$	27156.1	1.66553	0.832763	+	0.553630i	$0.186758\pi$
$644$	3696.85	0.226206
$645$	−1826.25	−0.111486
$646$	−20464.3	−1.24637
$647$	29154.9	1.77156	0.885778	−	0.464110i	$-0.153626\pi$
$647$	29154.9	1.77156	0.885778	+	0.464110i	$0.153626\pi$
$648$	−1902.86	−0.115357
$649$	0	0
$650$	−1798.71	−0.108540
$651$	−15045.9	−0.905828
$652$	−36930.2	−2.21825
$653$	−19141.7	−1.14713	−0.573564	−	0.819161i	$-0.694440\pi$
$653$	−19141.7	−1.14713	−0.573564	+	0.819161i	$0.694440\pi$
$654$	30696.1	1.83534
$655$	−10020.7	−0.597770
$656$	331.768	0.0197460
$657$	−3160.94	−0.187702
$658$	−49267.2	−2.91890
$659$	24939.6	1.47422	0.737110	−	0.675773i	$-0.236190\pi$
$659$	24939.6	1.47422	0.737110	+	0.675773i	$0.236190\pi$
$660$	0	0
$661$	22617.7	1.33090	0.665452	−	0.746440i	$-0.268239\pi$
$661$	22617.7	1.33090	0.665452	+	0.746440i	$0.268239\pi$
$662$	−24755.4	−1.45339
$663$	3426.88	0.200738
$664$	32633.7	1.90728
$665$	6299.99	0.367373
$666$	2704.61	0.157359
$667$	−429.843	−0.0249529
$668$	−45224.3	−2.61943
$669$	−2724.25	−0.157438
$670$	−11221.7	−0.647062
$671$	0	0
$672$	10770.9	0.618298
$673$	13855.8	0.793615	0.396807	−	0.917902i	$-0.370118\pi$
$673$	13855.8	0.793615	0.396807	+	0.917902i	$0.370118\pi$
$674$	−20678.1	−1.18174
$675$	−675.000	−0.0384900
$676$	−25593.5	−1.45616
$677$	24992.8	1.41884	0.709419	−	0.704787i	$-0.248957\pi$
$677$	24992.8	1.41884	0.709419	+	0.704787i	$0.248957\pi$
$678$	−23706.1	−1.34282
$679$	8804.57	0.497626
$680$	8568.84	0.483235
$681$	−6186.46	−0.348114
$682$	0	0
$683$	−14420.5	−0.807887	−0.403943	−	0.914784i	$-0.632361\pi$
$683$	−14420.5	−0.807887	−0.403943	+	0.914784i	$0.632361\pi$
$684$	−7204.93	−0.402759
$685$	−8364.25	−0.466543
$686$	−24661.4	−1.37256
$687$	−12232.4	−0.679324
$688$	370.280	0.0205186
$689$	−8497.42	−0.469849
$690$	−941.517	−0.0519463
$691$	30552.4	1.68201	0.841005	−	0.541027i	$-0.181964\pi$
$691$	30552.4	1.68201	0.841005	+	0.541027i	$0.181964\pi$
$692$	29999.9	1.64801
$693$	0	0
$694$	27138.7	1.48440
$695$	−12701.9	−0.693253
$696$	2217.63	0.120774
$697$	−7957.96	−0.432467
$698$	16708.1	0.906032
$699$	5048.27	0.273166
$700$	−6765.61	−0.365309
$701$	9151.47	0.493076	0.246538	−	0.969133i	$-0.420707\pi$
$701$	9151.47	0.493076	0.246538	+	0.969133i	$0.420707\pi$
$702$	1942.60	0.104443
$703$	3992.86	0.214216
$704$	0	0
$705$	7792.95	0.416311
$706$	−966.793	−0.0515378
$707$	1530.10	0.0813937
$708$	−4306.67	−0.228608
$709$	−6261.96	−0.331697	−0.165848	−	0.986151i	$-0.553036\pi$
$709$	−6261.96	−0.331697	−0.165848	+	0.986151i	$0.553036\pi$
$710$	−19239.2	−1.01695
$711$	7480.85	0.394590
$712$	−35794.9	−1.88409
$713$	3319.60	0.174362
$714$	20753.8	1.08780
$715$	0	0
$716$	42603.9	2.22372
$717$	12074.9	0.628933
$718$	11485.7	0.596995
$719$	−18228.7	−0.945500	−0.472750	−	0.881197i	$-0.656739\pi$
$719$	−18228.7	−0.945500	−0.472750	+	0.881197i	$0.656739\pi$
$720$	136.859	0.00708396
$721$	1432.13	0.0739740
$722$	14389.9	0.741740
$723$	−8352.81	−0.429660
$724$	15347.7	0.787836
$725$	786.656	0.0402975
$726$	0	0
$727$	−7233.66	−0.369026	−0.184513	−	0.982830i	$-0.559071\pi$
$727$	−7233.66	−0.369026	−0.184513	+	0.982830i	$0.559071\pi$
$728$	7591.81	0.386499
$729$	729.000	0.0370370
$730$	8068.93	0.409102
$731$	−8881.73	−0.449388
$732$	−3525.31	−0.178004
$733$	13444.8	0.677485	0.338743	−	0.940879i	$-0.389998\pi$
$733$	13444.8	0.677485	0.338743	+	0.940879i	$0.389998\pi$
$734$	−26414.4	−1.32830
$735$	−1244.12	−0.0624355
$736$	−2376.41	−0.119016
$737$	0	0
$738$	−4511.14	−0.225010
$739$	−18490.9	−0.920432	−0.460216	−	0.887807i	$-0.652228\pi$
$739$	−18490.9	−0.920432	−0.460216	+	0.887807i	$0.652228\pi$
$740$	−4287.97	−0.213012
$741$	2867.90	0.142180
$742$	−51461.8	−2.54612
$743$	25160.9	1.24235	0.621173	−	0.783674i	$-0.286657\pi$
$743$	25160.9	1.24235	0.621173	+	0.783674i	$0.286657\pi$
$744$	−17126.3	−0.843927
$745$	−15453.4	−0.759957
$746$	20528.8	1.00752
$747$	−12502.2	−0.612358
$748$	0	0
$749$	23562.9	1.14949
$750$	1723.07	0.0838902
$751$	−13419.5	−0.652045	−0.326023	−	0.945362i	$-0.605709\pi$
$751$	−13419.5	−0.652045	−0.326023	+	0.945362i	$0.605709\pi$
$752$	−1580.06	−0.0766207
$753$	5482.81	0.265345
$754$	−2263.94	−0.109347
$755$	−6793.68	−0.327480
$756$	7306.86	0.351518
$757$	−7014.90	−0.336804	−0.168402	−	0.985718i	$-0.553861\pi$
$757$	−7014.90	−0.336804	−0.168402	+	0.985718i	$0.553861\pi$
$758$	−35858.6	−1.71826
$759$	0	0
$760$	7171.12	0.342268
$761$	30156.9	1.43651	0.718256	−	0.695779i	$-0.244941\pi$
$761$	30156.9	1.43651	0.718256	+	0.695779i	$0.244941\pi$
$762$	22077.8	1.04960
$763$	−45958.4	−2.18061
$764$	−36195.7	−1.71402
$765$	−3282.78	−0.155149
$766$	51283.5	2.41899
$767$	1714.26	0.0807019
$768$	13217.4	0.621017
$769$	−11292.2	−0.529530	−0.264765	−	0.964313i	$-0.585294\pi$
$769$	−11292.2	−0.529530	−0.264765	+	0.964313i	$0.585294\pi$
$770$	0	0
$771$	−1755.51	−0.0820016
$772$	16398.9	0.764519
$773$	8524.10	0.396624	0.198312	−	0.980139i	$-0.436454\pi$
$773$	8524.10	0.396624	0.198312	+	0.980139i	$0.436454\pi$
$774$	−5034.80	−0.233814
$775$	−6075.21	−0.281584
$776$	10022.0	0.463621
$777$	−4049.35	−0.186962
$778$	−39011.4	−1.79772
$779$	−6659.89	−0.306310
$780$	−3079.87	−0.141381
$781$	0	0
$782$	−4578.96	−0.209390
$783$	−849.589	−0.0387763
$784$	252.251	0.0114910
$785$	−5059.76	−0.230052
$786$	−27626.1	−1.25368
$787$	14983.9	0.678676	0.339338	−	0.940665i	$-0.389797\pi$
$787$	14983.9	0.678676	0.339338	+	0.940665i	$0.389797\pi$
$788$	1888.10	0.0853565
$789$	−714.293	−0.0322300
$790$	−19096.3	−0.860022
$791$	35493.0	1.59543
$792$	0	0
$793$	1403.24	0.0628380
$794$	−27659.9	−1.23629
$795$	8140.10	0.363144
$796$	9982.04	0.444477
$797$	37172.3	1.65208	0.826041	−	0.563610i	$-0.190588\pi$
$797$	37172.3	1.65208	0.826041	+	0.563610i	$0.190588\pi$
$798$	17368.5	0.770475
$799$	37900.1	1.67811
$800$	4349.06	0.192203
$801$	13713.3	0.604913
$802$	47781.0	2.10375
$803$	0	0
$804$	−19214.5	−0.842841
$805$	1409.65	0.0617186
$806$	17484.0	0.764080
$807$	−13855.4	−0.604378
$808$	1741.68	0.0758316
$809$	−23797.1	−1.03419	−0.517096	−	0.855928i	$-0.672987\pi$
$809$	−23797.1	−1.03419	−0.517096	+	0.855928i	$0.672987\pi$
$810$	−1860.92	−0.0807234
$811$	−8988.35	−0.389178	−0.194589	−	0.980885i	$-0.562337\pi$
$811$	−8988.35	−0.389178	−0.194589	+	0.980885i	$0.562337\pi$
$812$	−8515.54	−0.368026
$813$	−430.318	−0.0185633
$814$	0	0
$815$	−14081.8	−0.605234
$816$	665.600	0.0285547
$817$	−7432.98	−0.318295
$818$	−21750.6	−0.929696
$819$	−2908.48	−0.124091
$820$	7152.11	0.304589
$821$	25156.8	1.06940	0.534702	−	0.845041i	$-0.320424\pi$
$821$	25156.8	1.06940	0.534702	+	0.845041i	$0.320424\pi$
$822$	−23059.5	−0.978459
$823$	1318.51	0.0558447	0.0279224	−	0.999610i	$-0.491111\pi$
$823$	1318.51	0.0558447	0.0279224	+	0.999610i	$0.491111\pi$
$824$	1630.16	0.0689189
$825$	0	0
$826$	10381.9	0.437326
$827$	−124.982	−0.00525519	−0.00262760	−	0.999997i	$-0.500836\pi$
$827$	−124.982	−0.00525519	−0.00262760	+	0.999997i	$0.500836\pi$
$828$	−1612.13	−0.0676635
$829$	−8886.80	−0.372318	−0.186159	−	0.982520i	$-0.559604\pi$
$829$	−8886.80	−0.372318	−0.186159	+	0.982520i	$0.559604\pi$
$830$	31914.3	1.33465
$831$	−25807.5	−1.07732
$832$	−12897.3	−0.537419
$833$	−6050.63	−0.251671
$834$	−35018.0	−1.45393
$835$	−17244.5	−0.714694
$836$	0	0
$837$	6561.22	0.270955
$838$	37299.1	1.53756
$839$	2995.21	0.123249	0.0616247	−	0.998099i	$-0.480372\pi$
$839$	2995.21	0.123249	0.0616247	+	0.998099i	$0.480372\pi$
$840$	−7272.58	−0.298724
$841$	−23398.9	−0.959403
$842$	43578.8	1.78364
$843$	−8978.43	−0.366825
$844$	−52143.6	−2.12661
$845$	−9759.07	−0.397304
$846$	21484.5	0.873111
$847$	0	0
$848$	−1650.44	−0.0668355
$849$	−20576.7	−0.831789
$850$	8379.95	0.338153
$851$	893.418	0.0359882
$852$	−32942.7	−1.32464
$853$	−18130.5	−0.727757	−0.363878	−	0.931446i	$-0.618548\pi$
$853$	−18130.5	−0.727757	−0.363878	+	0.931446i	$0.618548\pi$
$854$	8498.27	0.340521
$855$	−2747.31	−0.109890
$856$	26821.1	1.07094
$857$	−26394.1	−1.05205	−0.526024	−	0.850470i	$-0.676318\pi$
$857$	−26394.1	−1.05205	−0.526024	+	0.850470i	$0.676318\pi$
$858$	0	0
$859$	−29456.2	−1.17000	−0.585002	−	0.811032i	$-0.698906\pi$
$859$	−29456.2	−1.17000	−0.585002	+	0.811032i	$0.698906\pi$
$860$	7982.34	0.316506
$861$	6754.12	0.267340
$862$	42893.7	1.69486
$863$	−762.616	−0.0300808	−0.0150404	−	0.999887i	$-0.504788\pi$
$863$	−762.616	−0.0300808	−0.0150404	+	0.999887i	$0.504788\pi$
$864$	−4696.99	−0.184948
$865$	11439.3	0.449649
$866$	13706.6	0.537838
$867$	−1226.43	−0.0480411
$868$	65764.0	2.57163
$869$	0	0
$870$	2168.74	0.0845141
$871$	7648.29	0.297535
$872$	−52313.3	−2.03160
$873$	−3839.51	−0.148852
$874$	−3832.06	−0.148308
$875$	−2579.79	−0.0996719
$876$	13816.2	0.532882
$877$	−44767.2	−1.72369	−0.861847	−	0.507168i	$-0.830692\pi$
$877$	−44767.2	−1.72369	−0.861847	+	0.507168i	$0.830692\pi$
$878$	−24041.8	−0.924112
$879$	12149.1	0.466188
$880$	0	0
$881$	−32057.9	−1.22595	−0.612973	−	0.790104i	$-0.710027\pi$
$881$	−32057.9	−1.22595	−0.612973	+	0.790104i	$0.710027\pi$
$882$	−3429.93	−0.130943
$883$	7078.95	0.269791	0.134896	−	0.990860i	$-0.456930\pi$
$883$	7078.95	0.269791	0.134896	+	0.990860i	$0.456930\pi$
$884$	−14978.6	−0.569891
$885$	−1642.18	−0.0623742
$886$	−34542.8	−1.30981
$887$	25148.1	0.951964	0.475982	−	0.879455i	$-0.342093\pi$
$887$	25148.1	0.951964	0.475982	+	0.879455i	$0.342093\pi$
$888$	−4609.28	−0.174186
$889$	−33055.0	−1.24705
$890$	−35005.9	−1.31843
$891$	0	0
$892$	11907.4	0.446963
$893$	31718.0	1.18858
$894$	−42603.6	−1.59382
$895$	16245.3	0.606726
$896$	−49385.8	−1.84137
$897$	641.704	0.0238862
$898$	−73843.6	−2.74409
$899$	−7646.56	−0.283679
$900$	2950.36	0.109273
$901$	39588.4	1.46380
$902$	0	0
$903$	7538.14	0.277800
$904$	40400.8	1.48641
$905$	5852.23	0.214955
$906$	−18729.6	−0.686809
$907$	1269.76	0.0464848	0.0232424	−	0.999730i	$-0.492601\pi$
$907$	1269.76	0.0464848	0.0232424	+	0.999730i	$0.492601\pi$
$908$	27040.4	0.988289
$909$	−667.248	−0.0243468
$910$	7424.47	0.270460
$911$	−33783.1	−1.22863	−0.614316	−	0.789060i	$-0.710568\pi$
$911$	−33783.1	−1.22863	−0.614316	+	0.789060i	$0.710568\pi$
$912$	557.030	0.0202249
$913$	0	0
$914$	44655.1	1.61604
$915$	−1344.23	−0.0485672
$916$	53466.6	1.92859
$917$	41361.9	1.48952
$918$	−9050.35	−0.325388
$919$	−39262.5	−1.40930	−0.704652	−	0.709553i	$-0.748897\pi$
$919$	−39262.5	−1.40930	−0.704652	+	0.709553i	$0.748897\pi$
$920$	1604.57	0.0575010
$921$	−28718.1	−1.02746
$922$	−66800.1	−2.38606
$923$	13112.7	0.467618
$924$	0	0
$925$	−1635.04	−0.0581189
$926$	45848.3	1.62707
$927$	−624.525	−0.0221274
$928$	5473.95	0.193633
$929$	−21175.0	−0.747825	−0.373913	−	0.927464i	$-0.621984\pi$
$929$	−21175.0	−0.747825	−0.373913	+	0.927464i	$0.621984\pi$
$930$	−16748.8	−0.590554
$931$	−5063.68	−0.178255
$932$	−22065.5	−0.775515
$933$	−16189.3	−0.568073
$934$	−69787.5	−2.44488
$935$	0	0
$936$	−3310.65	−0.115611
$937$	5135.11	0.179036	0.0895180	−	0.995985i	$-0.471467\pi$
$937$	5135.11	0.179036	0.0895180	+	0.995985i	$0.471467\pi$
$938$	46319.4	1.61235
$939$	−29265.1	−1.01707
$940$	−34062.2	−1.18190
$941$	9702.77	0.336133	0.168067	−	0.985776i	$-0.446248\pi$
$941$	9702.77	0.336133	0.168067	+	0.985776i	$0.446248\pi$
$942$	−13949.3	−0.482477
$943$	−1490.18	−0.0514600
$944$	332.959	0.0114798
$945$	2786.18	0.0959094
$946$	0	0
$947$	−699.579	−0.0240055	−0.0120028	−	0.999928i	$-0.503821\pi$
$947$	−699.579	−0.0240055	−0.0120028	+	0.999928i	$0.503821\pi$
$948$	−32698.0	−1.12024
$949$	−5499.49	−0.188115
$950$	7013.05	0.239509
$951$	13061.2	0.445363
$952$	−35369.3	−1.20412
$953$	−42039.3	−1.42895	−0.714473	−	0.699663i	$-0.753333\pi$
$953$	−42039.3	−1.42895	−0.714473	+	0.699663i	$0.753333\pi$
$954$	22441.6	0.761606
$955$	−13801.8	−0.467659
$956$	−52778.1	−1.78553
$957$	0	0
$958$	52063.4	1.75584
$959$	34524.9	1.16253
$960$	12355.0	0.415369
$961$	29262.0	0.982243
$962$	4705.55	0.157706
$963$	−10275.3	−0.343841
$964$	36509.3	1.21980
$965$	6253.05	0.208594
$966$	3886.27	0.129440
$967$	32794.8	1.09060	0.545299	−	0.838242i	$-0.316416\pi$
$967$	32794.8	1.09060	0.545299	+	0.838242i	$0.316416\pi$
$968$	0	0
$969$	−13361.2	−0.442955
$970$	9801.10	0.324427
$971$	−3322.53	−0.109810	−0.0549048	−	0.998492i	$-0.517486\pi$
$971$	−3322.53	−0.109810	−0.0549048	+	0.998492i	$0.517486\pi$
$972$	−3186.39	−0.105148
$973$	52429.3	1.72745
$974$	−87701.4	−2.88515
$975$	−1174.38	−0.0385747
$976$	272.550	0.00893864
$977$	22192.5	0.726716	0.363358	−	0.931650i	$-0.381630\pi$
$977$	22192.5	0.726716	0.363358	+	0.931650i	$0.381630\pi$
$978$	−38822.4	−1.26933
$979$	0	0
$980$	5437.92	0.177253
$981$	20041.6	0.652272
$982$	−37277.4	−1.21137
$983$	7383.09	0.239556	0.119778	−	0.992801i	$-0.461782\pi$
$983$	7383.09	0.239556	0.119778	+	0.992801i	$0.461782\pi$
$984$	7688.04	0.249071
$985$	719.953	0.0232889
$986$	10547.4	0.340668
$987$	−32166.7	−1.03736
$988$	−12535.3	−0.403645
$989$	−1663.16	−0.0534735
$990$	0	0
$991$	46260.8	1.48287	0.741434	−	0.671026i	$-0.234146\pi$
$991$	46260.8	1.48287	0.741434	+	0.671026i	$0.234146\pi$
$992$	−42274.3	−1.35304
$993$	−16162.9	−0.516530
$994$	79413.1	2.53403
$995$	3806.25	0.121273
$996$	54645.9	1.73847
$997$	−41196.8	−1.30864	−0.654320	−	0.756217i	$-0.727045\pi$
$997$	−41196.8	−1.30864	−0.654320	+	0.756217i	$0.727045\pi$
$998$	−84219.5	−2.67127
$999$	1765.85	0.0559249

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.4.a.q.1.1		3
11.10	odd	2		165.4.a.g.1.3	✓	3
33.32	even	2		495.4.a.i.1.1		3
55.32	even	4		825.4.c.m.199.6		6
55.43	even	4		825.4.c.m.199.1		6
55.54	odd	2		825.4.a.p.1.1		3
165.164	even	2		2475.4.a.z.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.a.g.1.3	✓	3	11.10	odd	2
495.4.a.i.1.1		3	33.32	even	2
825.4.a.p.1.1		3	55.54	odd	2
825.4.c.m.199.1		6	55.43	even	4
825.4.c.m.199.6		6	55.32	even	4
1815.4.a.q.1.1		3	1.1	even	1	trivial
2475.4.a.z.1.3		3	165.164	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:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1815.a (trivial)

\(f(q)\)	\(=\)	\(q-4.59486 q^{2} -3.00000 q^{3} +13.1127 q^{4} +5.00000 q^{5} +13.7846 q^{6} -20.6383 q^{7} -23.4921 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.59486 q^{2} -3.00000 q^{3} +13.1127 q^{4} +5.00000 q^{5} +13.7846 q^{6} -20.6383 q^{7} -23.4921 q^{8} +9.00000 q^{9} -22.9743 q^{10} -39.3381 q^{12} +15.6584 q^{13} +94.8302 q^{14} -15.0000 q^{15} +3.04132 q^{16} -72.9507 q^{17} -41.3537 q^{18} -61.0513 q^{19} +65.5635 q^{20} +61.9150 q^{21} -13.6605 q^{23} +70.4764 q^{24} +25.0000 q^{25} -71.9483 q^{26} -27.0000 q^{27} -270.624 q^{28} +31.4663 q^{29} +68.9228 q^{30} -243.008 q^{31} +173.963 q^{32} +335.198 q^{34} -103.192 q^{35} +118.014 q^{36} -65.4018 q^{37} +280.522 q^{38} -46.9753 q^{39} -117.461 q^{40} +109.087 q^{41} -284.491 q^{42} +121.750 q^{43} +45.0000 q^{45} +62.7678 q^{46} -519.530 q^{47} -9.12396 q^{48} +82.9413 q^{49} -114.871 q^{50} +218.852 q^{51} +205.324 q^{52} -542.673 q^{53} +124.061 q^{54} +484.839 q^{56} +183.154 q^{57} -144.583 q^{58} +109.478 q^{59} -196.691 q^{60} +89.6156 q^{61} +1116.59 q^{62} -185.745 q^{63} -823.664 q^{64} +78.2922 q^{65} +488.446 q^{67} -956.581 q^{68} +40.9814 q^{69} +474.151 q^{70} +837.423 q^{71} -211.429 q^{72} -351.216 q^{73} +300.512 q^{74} -75.0000 q^{75} -800.547 q^{76} +215.845 q^{78} +831.205 q^{79} +15.2066 q^{80} +81.0000 q^{81} -501.238 q^{82} -1389.13 q^{83} +811.873 q^{84} -364.754 q^{85} -559.423 q^{86} -94.3988 q^{87} +1523.70 q^{89} -206.769 q^{90} -323.164 q^{91} -179.125 q^{92} +729.025 q^{93} +2387.17 q^{94} -305.256 q^{95} -521.888 q^{96} -426.612 q^{97} -381.103 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} - 9 q^{3} + 17 q^{4} + 15 q^{5} + 3 q^{6} - 6 q^{7} + 3 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q - q^2 - 9 * q^3 + 17 * q^4 + 15 * q^5 + 3 * q^6 - 6 * q^7 + 3 * q^8 + 27 * q^9	\( 3 q - q^{2} - 9 q^{3} + 17 q^{4} + 15 q^{5} + 3 q^{6} - 6 q^{7} + 3 q^{8} + 27 q^{9} - 5 q^{10} - 51 q^{12} + 20 q^{13} + 144 q^{14} - 45 q^{15} + 25 q^{16} - 32 q^{17} - 9 q^{18} - 116 q^{19} + 85 q^{20} + 18 q^{21} + 240 q^{23} - 9 q^{24} + 75 q^{25} + 302 q^{26} - 81 q^{27} - 160 q^{28} - 238 q^{29} + 15 q^{30} + 92 q^{31} - 197 q^{32} + 354 q^{34} - 30 q^{35} + 153 q^{36} - 90 q^{37} + 324 q^{38} - 60 q^{39} + 15 q^{40} + 46 q^{41} - 432 q^{42} + 134 q^{43} + 135 q^{45} + 240 q^{46} - 220 q^{47} - 75 q^{48} - 457 q^{49} - 25 q^{50} + 96 q^{51} + 1530 q^{52} - 798 q^{53} + 27 q^{54} + 688 q^{56} + 348 q^{57} - 978 q^{58} + 1236 q^{59} - 255 q^{60} - 342 q^{61} + 1792 q^{62} - 54 q^{63} - 1919 q^{64} + 100 q^{65} + 764 q^{67} - 1074 q^{68} - 720 q^{69} + 720 q^{70} + 1816 q^{71} + 27 q^{72} - 100 q^{73} + 1874 q^{74} - 225 q^{75} - 396 q^{76} - 906 q^{78} + 96 q^{79} + 125 q^{80} + 243 q^{81} - 910 q^{82} - 858 q^{83} + 480 q^{84} - 160 q^{85} + 188 q^{86} + 714 q^{87} + 838 q^{89} - 45 q^{90} + 332 q^{91} - 688 q^{92} - 276 q^{93} + 3112 q^{94} - 580 q^{95} + 591 q^{96} - 1322 q^{97} - 1017 q^{98}+O(q^{100}) \) 3 * q - q^2 - 9 * q^3 + 17 * q^4 + 15 * q^5 + 3 * q^6 - 6 * q^7 + 3 * q^8 + 27 * q^9 - 5 * q^10 - 51 * q^12 + 20 * q^13 + 144 * q^14 - 45 * q^15 + 25 * q^16 - 32 * q^17 - 9 * q^18 - 116 * q^19 + 85 * q^20 + 18 * q^21 + 240 * q^23 - 9 * q^24 + 75 * q^25 + 302 * q^26 - 81 * q^27 - 160 * q^28 - 238 * q^29 + 15 * q^30 + 92 * q^31 - 197 * q^32 + 354 * q^34 - 30 * q^35 + 153 * q^36 - 90 * q^37 + 324 * q^38 - 60 * q^39 + 15 * q^40 + 46 * q^41 - 432 * q^42 + 134 * q^43 + 135 * q^45 + 240 * q^46 - 220 * q^47 - 75 * q^48 - 457 * q^49 - 25 * q^50 + 96 * q^51 + 1530 * q^52 - 798 * q^53 + 27 * q^54 + 688 * q^56 + 348 * q^57 - 978 * q^58 + 1236 * q^59 - 255 * q^60 - 342 * q^61 + 1792 * q^62 - 54 * q^63 - 1919 * q^64 + 100 * q^65 + 764 * q^67 - 1074 * q^68 - 720 * q^69 + 720 * q^70 + 1816 * q^71 + 27 * q^72 - 100 * q^73 + 1874 * q^74 - 225 * q^75 - 396 * q^76 - 906 * q^78 + 96 * q^79 + 125 * q^80 + 243 * q^81 - 910 * q^82 - 858 * q^83 + 480 * q^84 - 160 * q^85 + 188 * q^86 + 714 * q^87 + 838 * q^89 - 45 * q^90 + 332 * q^91 - 688 * q^92 - 276 * q^93 + 3112 * q^94 - 580 * q^95 + 591 * q^96 - 1322 * q^97 - 1017 * q^98

Introduction

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