LMFDB - Embedded newform 1445.2.a.o.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1445,2,Mod(1,1445)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1445, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1445.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1445 = 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1445.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:	$11.5383830921$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.7718912.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 7x^{4} + 4x^{3} + 9x^{2} - 2x - 1 $ x^6 - 2x^5 - 7x^4 + 4x^3 + 9x^2 - 2*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 85)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$3.48265$ of defining polynomial
Character	$\chi$	$=$	1445.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.12708 q^{2} -2.48265 q^{3} -0.729699 q^{4} +1.00000 q^{5} -2.79814 q^{6} +2.44256 q^{7} -3.07658 q^{8} +3.16356 q^{9} +1.12708 q^{10} +3.63808 q^{11} +1.81159 q^{12} -3.64168 q^{13} +2.75295 q^{14} -2.48265 q^{15} -2.00814 q^{16} +3.56558 q^{18} -2.61358 q^{19} -0.729699 q^{20} -6.06403 q^{21} +4.10039 q^{22} +1.40552 q^{23} +7.63808 q^{24} +1.00000 q^{25} -4.10445 q^{26} -0.406074 q^{27} -1.78234 q^{28} -0.850775 q^{29} -2.79814 q^{30} -9.44332 q^{31} +3.88983 q^{32} -9.03208 q^{33} +2.44256 q^{35} -2.30845 q^{36} +11.0054 q^{37} -2.94570 q^{38} +9.04103 q^{39} -3.07658 q^{40} +9.53958 q^{41} -6.83463 q^{42} +7.47280 q^{43} -2.65470 q^{44} +3.16356 q^{45} +1.58412 q^{46} +5.42683 q^{47} +4.98551 q^{48} -1.03389 q^{49} +1.12708 q^{50} +2.65733 q^{52} +12.9453 q^{53} -0.457676 q^{54} +3.63808 q^{55} -7.51473 q^{56} +6.48861 q^{57} -0.958888 q^{58} +1.40270 q^{59} +1.81159 q^{60} -1.13771 q^{61} -10.6433 q^{62} +7.72720 q^{63} +8.40042 q^{64} -3.64168 q^{65} -10.1798 q^{66} -2.07908 q^{67} -3.48941 q^{69} +2.75295 q^{70} +12.2919 q^{71} -9.73296 q^{72} -1.47586 q^{73} +12.4039 q^{74} -2.48265 q^{75} +1.90713 q^{76} +8.88623 q^{77} +10.1899 q^{78} +8.97276 q^{79} -2.00814 q^{80} -8.48255 q^{81} +10.7518 q^{82} -2.52680 q^{83} +4.42492 q^{84} +8.42242 q^{86} +2.11218 q^{87} -11.1928 q^{88} +1.66373 q^{89} +3.56558 q^{90} -8.89503 q^{91} -1.02560 q^{92} +23.4445 q^{93} +6.11645 q^{94} -2.61358 q^{95} -9.65710 q^{96} +12.2673 q^{97} -1.16527 q^{98} +11.5093 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 4 q^{3} + 6 q^{4} + 6 q^{5} + 4 q^{6} + 8 q^{7} + 6 q^{8} + 2 q^{9} + 2 q^{10} + 8 q^{12} + 8 q^{14} + 4 q^{15} + 2 q^{16} + 14 q^{18} - 12 q^{19} + 6 q^{20} + 8 q^{21} + 16 q^{22} + 24 q^{24}+ \cdots + 20 q^{99}+O(q^{100}) $ 6 * q + 2 * q^2 + 4 * q^3 + 6 * q^4 + 6 * q^5 + 4 * q^6 + 8 * q^7 + 6 * q^8 + 2 * q^9 + 2 * q^10 + 8 * q^12 + 8 * q^14 + 4 * q^15 + 2 * q^16 + 14 * q^18 - 12 * q^19 + 6 * q^20 + 8 * q^21 + 16 * q^22 + 24 * q^24 + 6 * q^25 - 12 * q^26 - 8 * q^27 - 8 * q^28 + 8 * q^29 + 4 * q^30 + 4 * q^31 - 6 * q^32 - 8 * q^33 + 8 * q^35 - 10 * q^36 + 16 * q^37 - 12 * q^38 + 28 * q^39 + 6 * q^40 + 12 * q^41 - 8 * q^42 + 8 * q^43 - 4 * q^44 + 2 * q^45 + 20 * q^46 + 24 * q^47 + 8 * q^48 - 10 * q^49 + 2 * q^50 - 28 * q^52 - 12 * q^54 + 20 * q^56 - 16 * q^57 + 48 * q^58 - 16 * q^59 + 8 * q^60 - 4 * q^61 - 40 * q^62 + 20 * q^63 - 14 * q^64 - 16 * q^66 - 4 * q^67 + 8 * q^70 + 32 * q^71 - 10 * q^72 - 8 * q^73 - 8 * q^74 + 4 * q^75 - 36 * q^76 + 24 * q^77 + 4 * q^78 + 36 * q^79 + 2 * q^80 - 14 * q^81 - 28 * q^82 + 20 * q^83 - 48 * q^86 + 24 * q^87 + 12 * q^88 - 12 * q^89 + 14 * q^90 + 12 * q^91 + 28 * q^92 + 36 * q^93 + 20 * q^94 - 12 * q^95 - 44 * q^96 + 16 * q^97 - 22 * q^98 + 20 * q^99

Coefficient data

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

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

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

$2$	1.12708	0.796963	0.398482	−	0.917176i	$-0.369537\pi$
$2$	1.12708	0.796963	0.398482	+	0.917176i	$0.369537\pi$
$3$	−2.48265	−1.43336	−0.716680	−	0.697402i	$-0.754339\pi$
$3$	−2.48265	−1.43336	−0.716680	+	0.697402i	$0.754339\pi$
$4$	−0.729699	−0.364850
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.79814	−1.14234
$7$	2.44256	0.923202	0.461601	−	0.887088i	$-0.347275\pi$
$7$	2.44256	0.923202	0.461601	+	0.887088i	$0.347275\pi$
$8$	−3.07658	−1.08773
$9$	3.16356	1.05452
$10$	1.12708	0.356413
$11$	3.63808	1.09692	0.548461	−	0.836176i	$-0.315214\pi$
$11$	3.63808	1.09692	0.548461	+	0.836176i	$0.315214\pi$
$12$	1.81159	0.522961
$13$	−3.64168	−1.01002	−0.505010	−	0.863113i	$-0.668511\pi$
$13$	−3.64168	−1.01002	−0.505010	+	0.863113i	$0.668511\pi$
$14$	2.75295	0.735758
$15$	−2.48265	−0.641018
$16$	−2.00814	−0.502035
$17$	0	0
$17$	0	0
$18$	3.56558	0.840415
$19$	−2.61358	−0.599596	−0.299798	−	0.954003i	$-0.596919\pi$
$19$	−2.61358	−0.599596	−0.299798	+	0.954003i	$0.596919\pi$
$20$	−0.729699	−0.163166
$21$	−6.06403	−1.32328
$22$	4.10039	0.874206
$23$	1.40552	0.293070	0.146535	−	0.989205i	$-0.453188\pi$
$23$	1.40552	0.293070	0.146535	+	0.989205i	$0.453188\pi$
$24$	7.63808	1.55912
$25$	1.00000	0.200000
$26$	−4.10445	−0.804949
$27$	−0.406074	−0.0781489
$28$	−1.78234	−0.336830
$29$	−0.850775	−0.157985	−0.0789925	−	0.996875i	$-0.525170\pi$
$29$	−0.850775	−0.157985	−0.0789925	+	0.996875i	$0.525170\pi$
$30$	−2.79814	−0.510868
$31$	−9.44332	−1.69607	−0.848035	−	0.529940i	$-0.822215\pi$
$31$	−9.44332	−1.69607	−0.848035	+	0.529940i	$0.822215\pi$
$32$	3.88983	0.687632
$33$	−9.03208	−1.57228
$34$	0	0
$35$	2.44256	0.412868
$36$	−2.30845	−0.384742
$37$	11.0054	1.80928	0.904638	−	0.426181i	$-0.140141\pi$
$37$	11.0054	1.80928	0.904638	+	0.426181i	$0.140141\pi$
$38$	−2.94570	−0.477856
$39$	9.04103	1.44772
$40$	−3.07658	−0.486450
$41$	9.53958	1.48983	0.744916	−	0.667158i	$-0.232489\pi$
$41$	9.53958	1.48983	0.744916	+	0.667158i	$0.232489\pi$
$42$	−6.83463	−1.05461
$43$	7.47280	1.13959	0.569796	−	0.821786i	$-0.307022\pi$
$43$	7.47280	1.13959	0.569796	+	0.821786i	$0.307022\pi$
$44$	−2.65470	−0.400212
$45$	3.16356	0.471596
$46$	1.58412	0.233566
$47$	5.42683	0.791585	0.395792	−	0.918340i	$-0.370470\pi$
$47$	5.42683	0.791585	0.395792	+	0.918340i	$0.370470\pi$
$48$	4.98551	0.719597
$49$	−1.03389	−0.147699
$50$	1.12708	0.159393
$51$	0	0
$52$	2.65733	0.368506
$53$	12.9453	1.77817	0.889087	−	0.457737i	$-0.151340\pi$
$53$	12.9453	1.77817	0.889087	+	0.457737i	$0.151340\pi$
$54$	−0.457676	−0.0622818
$55$	3.63808	0.490558
$56$	−7.51473	−1.00420
$57$	6.48861	0.859437
$58$	−0.958888	−0.125908
$59$	1.40270	0.182616	0.0913081	−	0.995823i	$-0.470895\pi$
$59$	1.40270	0.182616	0.0913081	+	0.995823i	$0.470895\pi$
$60$	1.81159	0.233875
$61$	−1.13771	−0.145669	−0.0728346	−	0.997344i	$-0.523205\pi$
$61$	−1.13771	−0.145669	−0.0728346	+	0.997344i	$0.523205\pi$
$62$	−10.6433	−1.35171
$63$	7.72720	0.973536
$64$	8.40042	1.05005
$65$	−3.64168	−0.451695
$66$	−10.1798	−1.25305
$67$	−2.07908	−0.254000	−0.127000	−	0.991903i	$-0.540535\pi$
$67$	−2.07908	−0.254000	−0.127000	+	0.991903i	$0.540535\pi$
$68$	0	0
$69$	−3.48941	−0.420076
$70$	2.75295	0.329041
$71$	12.2919	1.45878	0.729389	−	0.684099i	$-0.239804\pi$
$71$	12.2919	1.45878	0.729389	+	0.684099i	$0.239804\pi$
$72$	−9.73296	−1.14704
$73$	−1.47586	−0.172737	−0.0863684	−	0.996263i	$-0.527526\pi$
$73$	−1.47586	−0.172737	−0.0863684	+	0.996263i	$0.527526\pi$
$74$	12.4039	1.44193
$75$	−2.48265	−0.286672
$76$	1.90713	0.218762
$77$	8.88623	1.01268
$78$	10.1899	1.15378
$79$	8.97276	1.00951	0.504757	−	0.863261i	$-0.331582\pi$
$79$	8.97276	1.00951	0.504757	+	0.863261i	$0.331582\pi$
$80$	−2.00814	−0.224517
$81$	−8.48255	−0.942506
$82$	10.7518	1.18734
$83$	−2.52680	−0.277353	−0.138676	−	0.990338i	$-0.544285\pi$
$83$	−2.52680	−0.277353	−0.138676	+	0.990338i	$0.544285\pi$
$84$	4.42492	0.482799
$85$	0	0
$86$	8.42242	0.908213
$87$	2.11218	0.226449
$88$	−11.1928	−1.19316
$89$	1.66373	0.176355	0.0881775	−	0.996105i	$-0.471896\pi$
$89$	1.66373	0.176355	0.0881775	+	0.996105i	$0.471896\pi$
$90$	3.56558	0.375845
$91$	−8.89503	−0.932452
$92$	−1.02560	−0.106927
$93$	23.4445	2.43108
$94$	6.11645	0.630864
$95$	−2.61358	−0.268147
$96$	−9.65710	−0.985624
$97$	12.2673	1.24556	0.622780	−	0.782397i	$-0.286003\pi$
$97$	12.2673	1.24556	0.622780	+	0.782397i	$0.286003\pi$
$98$	−1.16527	−0.117710
$99$	11.5093	1.15673
$100$	−0.729699	−0.0729699
$101$	−4.18131	−0.416056	−0.208028	−	0.978123i	$-0.566704\pi$
$101$	−4.18131	−0.416056	−0.208028	+	0.978123i	$0.566704\pi$
$102$	0	0
$103$	8.08417	0.796557	0.398279	−	0.917265i	$-0.369608\pi$
$103$	8.08417	0.796557	0.398279	+	0.917265i	$0.369608\pi$
$104$	11.2039	1.09863
$105$	−6.06403	−0.591789
$106$	14.5903	1.41714
$107$	8.80071	0.850796	0.425398	−	0.905006i	$-0.360134\pi$
$107$	8.80071	0.850796	0.425398	+	0.905006i	$0.360134\pi$
$108$	0.296312	0.0285126
$109$	−14.3144	−1.37107	−0.685537	−	0.728038i	$-0.740433\pi$
$109$	−14.3144	−1.37107	−0.685537	+	0.728038i	$0.740433\pi$
$110$	4.10039	0.390957
$111$	−27.3226	−2.59334
$112$	−4.90501	−0.463480
$113$	−11.4598	−1.07805	−0.539026	−	0.842289i	$-0.681208\pi$
$113$	−11.4598	−1.07805	−0.539026	+	0.842289i	$0.681208\pi$
$114$	7.31315	0.684940
$115$	1.40552	0.131065
$116$	0.620810	0.0576408
$117$	−11.5207	−1.06509
$118$	1.58095	0.145538
$119$	0	0
$120$	7.63808	0.697258
$121$	2.23561	0.203237
$122$	−1.28229	−0.116093
$123$	−23.6835	−2.13547
$124$	6.89079	0.618811
$125$	1.00000	0.0894427
$126$	8.70915	0.775872
$127$	−2.51562	−0.223225	−0.111613	−	0.993752i	$-0.535602\pi$
$127$	−2.51562	−0.223225	−0.111613	+	0.993752i	$0.535602\pi$
$128$	1.68825	0.149221
$129$	−18.5524	−1.63345
$130$	−4.10445	−0.359984
$131$	2.22230	0.194163	0.0970817	−	0.995276i	$-0.469049\pi$
$131$	2.22230	0.194163	0.0970817	+	0.995276i	$0.469049\pi$
$132$	6.59071	0.573647
$133$	−6.38383	−0.553548
$134$	−2.34328	−0.202428
$135$	−0.406074	−0.0349493
$136$	0	0
$137$	−22.1633	−1.89354	−0.946771	−	0.321908i	$-0.895676\pi$
$137$	−22.1633	−1.89354	−0.946771	+	0.321908i	$0.895676\pi$
$138$	−3.93283	−0.334785
$139$	13.8857	1.17777	0.588884	−	0.808218i	$-0.299568\pi$
$139$	13.8857	1.17777	0.588884	+	0.808218i	$0.299568\pi$
$140$	−1.78234	−0.150635
$141$	−13.4729	−1.13463
$142$	13.8539	1.16259
$143$	−13.2487	−1.10791
$144$	−6.35288	−0.529407
$145$	−0.850775	−0.0706530
$146$	−1.66341	−0.137665
$147$	2.56679	0.211705
$148$	−8.03063	−0.660114
$149$	11.6461	0.954087	0.477044	−	0.878880i	$-0.341708\pi$
$149$	11.6461	0.954087	0.477044	+	0.878880i	$0.341708\pi$
$150$	−2.79814	−0.228467
$151$	2.82731	0.230083	0.115042	−	0.993361i	$-0.463300\pi$
$151$	2.82731	0.230083	0.115042	+	0.993361i	$0.463300\pi$
$152$	8.04088	0.652201
$153$	0	0
$154$	10.0155	0.807068
$155$	−9.44332	−0.758506
$156$	−6.59723	−0.528201
$157$	−1.36913	−0.109268	−0.0546342	−	0.998506i	$-0.517399\pi$
$157$	−1.36913	−0.109268	−0.0546342	+	0.998506i	$0.517399\pi$
$158$	10.1130	0.804545
$159$	−32.1387	−2.54877
$160$	3.88983	0.307518
$161$	3.43306	0.270563
$162$	−9.56048	−0.751143
$163$	12.0913	0.947063	0.473532	−	0.880777i	$-0.342979\pi$
$163$	12.0913	0.947063	0.473532	+	0.880777i	$0.342979\pi$
$164$	−6.96103	−0.543565
$165$	−9.03208	−0.703147
$166$	−2.84790	−0.221040
$167$	5.89177	0.455919	0.227959	−	0.973671i	$-0.426795\pi$
$167$	5.89177	0.455919	0.227959	+	0.973671i	$0.426795\pi$
$168$	18.6565	1.43938
$169$	0.261831	0.0201408
$170$	0	0
$171$	−8.26822	−0.632287
$172$	−5.45290	−0.415780
$173$	2.07551	0.157798	0.0788992	−	0.996883i	$-0.474859\pi$
$173$	2.07551	0.157798	0.0788992	+	0.996883i	$0.474859\pi$
$174$	2.38059	0.180472
$175$	2.44256	0.184640
$176$	−7.30577	−0.550693
$177$	−3.48242	−0.261755
$178$	1.87515	0.140548
$179$	10.5373	0.787597	0.393799	−	0.919197i	$-0.371161\pi$
$179$	10.5373	0.787597	0.393799	+	0.919197i	$0.371161\pi$
$180$	−2.30845	−0.172062
$181$	−3.39068	−0.252028	−0.126014	−	0.992028i	$-0.540218\pi$
$181$	−3.39068	−0.252028	−0.126014	+	0.992028i	$0.540218\pi$
$182$	−10.0254	−0.743130
$183$	2.82455	0.208797
$184$	−4.32418	−0.318783
$185$	11.0054	0.809133
$186$	26.4237	1.93748
$187$	0	0
$188$	−3.95995	−0.288809
$189$	−0.991860	−0.0721472
$190$	−2.94570	−0.213704
$191$	12.3426	0.893077	0.446538	−	0.894764i	$-0.352657\pi$
$191$	12.3426	0.893077	0.446538	+	0.894764i	$0.352657\pi$
$192$	−20.8553	−1.50510
$193$	11.9557	0.860590	0.430295	−	0.902688i	$-0.358409\pi$
$193$	11.9557	0.860590	0.430295	+	0.902688i	$0.358409\pi$
$194$	13.8262	0.992665
$195$	9.04103	0.647441
$196$	0.754430	0.0538878
$197$	−1.22210	−0.0870711	−0.0435356	−	0.999052i	$-0.513862\pi$
$197$	−1.22210	−0.0870711	−0.0435356	+	0.999052i	$0.513862\pi$
$198$	12.9718	0.921869
$199$	−21.7349	−1.54075	−0.770374	−	0.637592i	$-0.779930\pi$
$199$	−21.7349	−1.54075	−0.770374	+	0.637592i	$0.779930\pi$
$200$	−3.07658	−0.217547
$201$	5.16162	0.364073
$202$	−4.71265	−0.331581
$203$	−2.07807	−0.145852
$204$	0	0
$205$	9.53958	0.666273
$206$	9.11148	0.634827
$207$	4.44644	0.309049
$208$	7.31300	0.507065
$209$	−9.50840	−0.657710
$210$	−6.83463	−0.471634
$211$	16.8853	1.16243	0.581217	−	0.813749i	$-0.302577\pi$
$211$	16.8853	1.16243	0.581217	+	0.813749i	$0.302577\pi$
$212$	−9.44618	−0.648767
$213$	−30.5165	−2.09096
$214$	9.91907	0.678053
$215$	7.47280	0.509641
$216$	1.24932	0.0850053
$217$	−23.0659	−1.56582
$218$	−16.1335	−1.09270
$219$	3.66406	0.247594
$220$	−2.65470	−0.178980
$221$	0	0
$222$	−30.7946	−2.06680
$223$	9.61320	0.643748	0.321874	−	0.946783i	$-0.395687\pi$
$223$	9.61320	0.643748	0.321874	+	0.946783i	$0.395687\pi$
$224$	9.50115	0.634823
$225$	3.16356	0.210904
$226$	−12.9161	−0.859168
$227$	1.77929	0.118096	0.0590479	−	0.998255i	$-0.481194\pi$
$227$	1.77929	0.118096	0.0590479	+	0.998255i	$0.481194\pi$
$228$	−4.73473	−0.313565
$229$	−16.7429	−1.10640	−0.553201	−	0.833048i	$-0.686594\pi$
$229$	−16.7429	−1.10640	−0.553201	+	0.833048i	$0.686594\pi$
$230$	1.58412	0.104454
$231$	−22.0614	−1.45153
$232$	2.61748	0.171846
$233$	−13.0860	−0.857295	−0.428648	−	0.903472i	$-0.641010\pi$
$233$	−13.0860	−0.857295	−0.428648	+	0.903472i	$0.641010\pi$
$234$	−12.9847	−0.848836
$235$	5.42683	0.354007
$236$	−1.02355	−0.0666275
$237$	−22.2762	−1.44700
$238$	0	0
$239$	−23.9469	−1.54900	−0.774498	−	0.632577i	$-0.781997\pi$
$239$	−23.9469	−1.54900	−0.774498	+	0.632577i	$0.781997\pi$
$240$	4.98551	0.321814
$241$	−17.2911	−1.11382	−0.556908	−	0.830574i	$-0.688012\pi$
$241$	−17.2911	−1.11382	−0.556908	+	0.830574i	$0.688012\pi$
$242$	2.51970	0.161972
$243$	22.2775	1.42910
$244$	0.830189	0.0531474
$245$	−1.03389	−0.0660529
$246$	−26.6931	−1.70189
$247$	9.51781	0.605604
$248$	29.0531	1.84488
$249$	6.27318	0.397546
$250$	1.12708	0.0712826
$251$	−18.2106	−1.14944	−0.574722	−	0.818349i	$-0.694890\pi$
$251$	−18.2106	−1.14944	−0.574722	+	0.818349i	$0.694890\pi$
$252$	−5.63854	−0.355194
$253$	5.11338	0.321475
$254$	−2.83529	−0.177902
$255$	0	0
$256$	−14.8981	−0.931128
$257$	2.58018	0.160947	0.0804735	−	0.996757i	$-0.474357\pi$
$257$	2.58018	0.160947	0.0804735	+	0.996757i	$0.474357\pi$
$258$	−20.9099	−1.30180
$259$	26.8814	1.67033
$260$	2.65733	0.164801
$261$	−2.69148	−0.166599
$262$	2.50470	0.154741
$263$	9.58787	0.591213	0.295607	−	0.955310i	$-0.404478\pi$
$263$	9.58787	0.591213	0.295607	+	0.955310i	$0.404478\pi$
$264$	27.7879	1.71023
$265$	12.9453	0.795224
$266$	−7.19506	−0.441157
$267$	−4.13046	−0.252780
$268$	1.51710	0.0926717
$269$	−7.08590	−0.432035	−0.216018	−	0.976389i	$-0.569307\pi$
$269$	−7.08590	−0.432035	−0.216018	+	0.976389i	$0.569307\pi$
$270$	−0.457676	−0.0278533
$271$	−13.7773	−0.836909	−0.418454	−	0.908238i	$-0.637428\pi$
$271$	−13.7773	−0.836909	−0.418454	+	0.908238i	$0.637428\pi$
$272$	0	0
$273$	22.0833	1.33654
$274$	−24.9798	−1.50908
$275$	3.63808	0.219384
$276$	2.54622	0.153264
$277$	−4.51506	−0.271284	−0.135642	−	0.990758i	$-0.543310\pi$
$277$	−4.51506	−0.271284	−0.135642	+	0.990758i	$0.543310\pi$
$278$	15.6502	0.938637
$279$	−29.8746	−1.78854
$280$	−7.51473	−0.449091
$281$	−3.44172	−0.205316	−0.102658	−	0.994717i	$-0.532735\pi$
$281$	−3.44172	−0.205316	−0.102658	+	0.994717i	$0.532735\pi$
$282$	−15.1850	−0.904255
$283$	23.5408	1.39935	0.699677	−	0.714459i	$-0.253327\pi$
$283$	23.5408	1.39935	0.699677	+	0.714459i	$0.253327\pi$
$284$	−8.96938	−0.532235
$285$	6.48861	0.384352
$286$	−14.9323	−0.882966
$287$	23.3010	1.37542
$288$	12.3057	0.725122
$289$	0	0
$290$	−0.958888	−0.0563079
$291$	−30.4555	−1.78534
$292$	1.07694	0.0630230
$293$	−15.5924	−0.910918	−0.455459	−	0.890257i	$-0.650525\pi$
$293$	−15.5924	−0.910918	−0.455459	+	0.890257i	$0.650525\pi$
$294$	2.89297	0.168721
$295$	1.40270	0.0816685
$296$	−33.8590	−1.96801
$297$	−1.47733	−0.0857232
$298$	13.1261	0.760372
$299$	−5.11844	−0.296007
$300$	1.81159	0.104592
$301$	18.2528	1.05207
$302$	3.18660	0.183368
$303$	10.3807	0.596358
$304$	5.24843	0.301018
$305$	−1.13771	−0.0651453
$306$	0	0
$307$	21.6549	1.23591	0.617955	−	0.786214i	$-0.287962\pi$
$307$	21.6549	1.23591	0.617955	+	0.786214i	$0.287962\pi$
$308$	−6.48428	−0.369476
$309$	−20.0702	−1.14175
$310$	−10.6433	−0.604501
$311$	8.86449	0.502659	0.251330	−	0.967902i	$-0.419132\pi$
$311$	8.86449	0.502659	0.251330	+	0.967902i	$0.419132\pi$
$312$	−27.8154	−1.57474
$313$	17.1141	0.967345	0.483672	−	0.875249i	$-0.339303\pi$
$313$	17.1141	0.967345	0.483672	+	0.875249i	$0.339303\pi$
$314$	−1.54311	−0.0870828
$315$	7.72720	0.435379
$316$	−6.54742	−0.368321
$317$	10.3241	0.579862	0.289931	−	0.957048i	$-0.406368\pi$
$317$	10.3241	0.579862	0.289931	+	0.957048i	$0.406368\pi$
$318$	−36.2228	−2.03127
$319$	−3.09519	−0.173297
$320$	8.40042	0.469598
$321$	−21.8491	−1.21950
$322$	3.86932	0.215629
$323$	0	0
$324$	6.18971	0.343873
$325$	−3.64168	−0.202004
$326$	13.6278	0.754775
$327$	35.5378	1.96524
$328$	−29.3493	−1.62054
$329$	13.2554	0.730792
$330$	−10.1798	−0.560382
$331$	−6.56727	−0.360970	−0.180485	−	0.983578i	$-0.557767\pi$
$331$	−6.56727	−0.360970	−0.180485	+	0.983578i	$0.557767\pi$
$332$	1.84381	0.101192
$333$	34.8163	1.90792
$334$	6.64048	0.363351
$335$	−2.07908	−0.113592
$336$	12.1774	0.664333
$337$	−30.1761	−1.64380	−0.821899	−	0.569633i	$-0.807085\pi$
$337$	−30.1761	−1.64380	−0.821899	+	0.569633i	$0.807085\pi$
$338$	0.295103	0.0160515
$339$	28.4508	1.54524
$340$	0	0
$341$	−34.3555	−1.86046
$342$	−9.31892	−0.503909
$343$	−19.6233	−1.05956
$344$	−22.9907	−1.23957
$345$	−3.48941	−0.187863
$346$	2.33926	0.125759
$347$	−7.04017	−0.377936	−0.188968	−	0.981983i	$-0.560514\pi$
$347$	−7.04017	−0.377936	−0.188968	+	0.981983i	$0.560514\pi$
$348$	−1.54126	−0.0826200
$349$	−35.4396	−1.89704	−0.948518	−	0.316723i	$-0.897417\pi$
$349$	−35.4396	−1.89704	−0.948518	+	0.316723i	$0.897417\pi$
$350$	2.75295	0.147152
$351$	1.47879	0.0789320
$352$	14.1515	0.754278
$353$	8.54669	0.454895	0.227447	−	0.973790i	$-0.426962\pi$
$353$	8.54669	0.454895	0.227447	+	0.973790i	$0.426962\pi$
$354$	−3.92495	−0.208609
$355$	12.2919	0.652386
$356$	−1.21402	−0.0643430
$357$	0	0
$358$	11.8764	0.627686
$359$	−20.2839	−1.07054	−0.535271	−	0.844681i	$-0.679790\pi$
$359$	−20.2839	−1.07054	−0.535271	+	0.844681i	$0.679790\pi$
$360$	−9.73296	−0.512972
$361$	−12.1692	−0.640485
$362$	−3.82156	−0.200857
$363$	−5.55023	−0.291312
$364$	6.49070	0.340205
$365$	−1.47586	−0.0772503
$366$	3.18348	0.166403
$367$	12.7223	0.664097	0.332048	−	0.943262i	$-0.392260\pi$
$367$	12.7223	0.664097	0.332048	+	0.943262i	$0.392260\pi$
$368$	−2.82247	−0.147132
$369$	30.1791	1.57106
$370$	12.4039	0.644849
$371$	31.6197	1.64161
$372$	−17.1074	−0.886979
$373$	−11.1454	−0.577086	−0.288543	−	0.957467i	$-0.593171\pi$
$373$	−11.1454	−0.577086	−0.288543	+	0.957467i	$0.593171\pi$
$374$	0	0
$375$	−2.48265	−0.128204
$376$	−16.6961	−0.861034
$377$	3.09825	0.159568
$378$	−1.11790	−0.0574987
$379$	−12.6811	−0.651386	−0.325693	−	0.945476i	$-0.605598\pi$
$379$	−12.6811	−0.651386	−0.325693	+	0.945476i	$0.605598\pi$
$380$	1.90713	0.0978335
$381$	6.24541	0.319962
$382$	13.9110	0.711749
$383$	17.3523	0.886661	0.443331	−	0.896358i	$-0.353797\pi$
$383$	17.3523	0.886661	0.443331	+	0.896358i	$0.353797\pi$
$384$	−4.19133	−0.213888
$385$	8.88623	0.452884
$386$	13.4750	0.685859
$387$	23.6407	1.20172
$388$	−8.95147	−0.454442
$389$	19.4510	0.986205	0.493103	−	0.869971i	$-0.335863\pi$
$389$	19.4510	0.986205	0.493103	+	0.869971i	$0.335863\pi$
$390$	10.1899	0.515987
$391$	0	0
$392$	3.18085	0.160657
$393$	−5.51720	−0.278306
$394$	−1.37740	−0.0693925
$395$	8.97276	0.451468
$396$	−8.39832	−0.422032
$397$	−4.75987	−0.238891	−0.119446	−	0.992841i	$-0.538112\pi$
$397$	−4.75987	−0.238891	−0.119446	+	0.992841i	$0.538112\pi$
$398$	−24.4969	−1.22792
$399$	15.8488	0.793434
$400$	−2.00814	−0.100407
$401$	−24.2040	−1.20869	−0.604345	−	0.796723i	$-0.706565\pi$
$401$	−24.2040	−1.20869	−0.604345	+	0.796723i	$0.706565\pi$
$402$	5.81754	0.290153
$403$	34.3896	1.71307
$404$	3.05110	0.151798
$405$	−8.48255	−0.421501
$406$	−2.34214	−0.116239
$407$	40.0385	1.98463
$408$	0	0
$409$	18.2463	0.902221	0.451111	−	0.892468i	$-0.351028\pi$
$409$	18.2463	0.902221	0.451111	+	0.892468i	$0.351028\pi$
$410$	10.7518	0.530995
$411$	55.0239	2.71413
$412$	−5.89901	−0.290624
$413$	3.42619	0.168592
$414$	5.01148	0.246301
$415$	−2.52680	−0.124036
$416$	−14.1655	−0.694522
$417$	−34.4733	−1.68816
$418$	−10.7167	−0.524170
$419$	1.74273	0.0851377	0.0425689	−	0.999094i	$-0.486446\pi$
$419$	1.74273	0.0851377	0.0425689	+	0.999094i	$0.486446\pi$
$420$	4.42492	0.215914
$421$	37.0251	1.80449	0.902247	−	0.431220i	$-0.141917\pi$
$421$	37.0251	1.80449	0.902247	+	0.431220i	$0.141917\pi$
$422$	19.0310	0.926417
$423$	17.1681	0.834743
$424$	−39.8273	−1.93418
$425$	0	0
$426$	−34.3944	−1.66641
$427$	−2.77894	−0.134482
$428$	−6.42187	−0.310413
$429$	32.8920	1.58804
$430$	8.42242	0.406165
$431$	30.3883	1.46375	0.731876	−	0.681438i	$-0.238645\pi$
$431$	30.3883	1.46375	0.731876	+	0.681438i	$0.238645\pi$
$432$	0.815453	0.0392335
$433$	15.8246	0.760483	0.380242	−	0.924887i	$-0.375841\pi$
$433$	15.8246	0.760483	0.380242	+	0.924887i	$0.375841\pi$
$434$	−25.9970	−1.24790
$435$	2.11218	0.101271
$436$	10.4452	0.500236
$437$	−3.67343	−0.175724
$438$	4.12967	0.197323
$439$	−4.16714	−0.198887	−0.0994434	−	0.995043i	$-0.531706\pi$
$439$	−4.16714	−0.198887	−0.0994434	+	0.995043i	$0.531706\pi$
$440$	−11.1928	−0.533597
$441$	−3.27078	−0.155751
$442$	0	0
$443$	15.7201	0.746884	0.373442	−	0.927654i	$-0.378177\pi$
$443$	15.7201	0.746884	0.373442	+	0.927654i	$0.378177\pi$
$444$	19.9373	0.946181
$445$	1.66373	0.0788683
$446$	10.8348	0.513043
$447$	−28.9133	−1.36755
$448$	20.5185	0.969410
$449$	16.5469	0.780895	0.390447	−	0.920625i	$-0.372320\pi$
$449$	16.5469	0.780895	0.390447	+	0.920625i	$0.372320\pi$
$450$	3.56558	0.168083
$451$	34.7057	1.63423
$452$	8.36224	0.393327
$453$	−7.01924	−0.329792
$454$	2.00540	0.0941181
$455$	−8.89503	−0.417005
$456$	−19.9627	−0.934839
$457$	−1.42830	−0.0668131	−0.0334066	−	0.999442i	$-0.510636\pi$
$457$	−1.42830	−0.0668131	−0.0334066	+	0.999442i	$0.510636\pi$
$458$	−18.8705	−0.881761
$459$	0	0
$460$	−1.02560	−0.0478191
$461$	11.1662	0.520062	0.260031	−	0.965600i	$-0.416267\pi$
$461$	11.1662	0.520062	0.260031	+	0.965600i	$0.416267\pi$
$462$	−24.8649	−1.15682
$463$	29.2204	1.35799	0.678994	−	0.734144i	$-0.262416\pi$
$463$	29.2204	1.35799	0.678994	+	0.734144i	$0.262416\pi$
$464$	1.70848	0.0793140
$465$	23.4445	1.08721
$466$	−14.7490	−0.683233
$467$	−10.9388	−0.506187	−0.253093	−	0.967442i	$-0.581448\pi$
$467$	−10.9388	−0.506187	−0.253093	+	0.967442i	$0.581448\pi$
$468$	8.40664	0.388597
$469$	−5.07827	−0.234493
$470$	6.11645	0.282131
$471$	3.39907	0.156621
$472$	−4.31552	−0.198638
$473$	27.1866	1.25004
$474$	−25.1070	−1.15320
$475$	−2.61358	−0.119919
$476$	0	0
$477$	40.9533	1.87512
$478$	−26.9900	−1.23449
$479$	−17.1996	−0.785871	−0.392935	−	0.919566i	$-0.628540\pi$
$479$	−17.1996	−0.785871	−0.392935	+	0.919566i	$0.628540\pi$
$480$	−9.65710	−0.440784
$481$	−40.0781	−1.82741
$482$	−19.4884	−0.887670
$483$	−8.52310	−0.387814
$484$	−1.63132	−0.0741509
$485$	12.2673	0.557031
$486$	25.1084	1.13894
$487$	−25.8446	−1.17113	−0.585564	−	0.810626i	$-0.699127\pi$
$487$	−25.8446	−1.17113	−0.585564	+	0.810626i	$0.699127\pi$
$488$	3.50026	0.158450
$489$	−30.0185	−1.35748
$490$	−1.16527	−0.0526417
$491$	12.2373	0.552261	0.276131	−	0.961120i	$-0.410948\pi$
$491$	12.2373	0.552261	0.276131	+	0.961120i	$0.410948\pi$
$492$	17.2818	0.779124
$493$	0	0
$494$	10.7273	0.482644
$495$	11.5093	0.517304
$496$	18.9635	0.851487
$497$	30.0237	1.34675
$498$	7.07035	0.316830
$499$	6.41606	0.287222	0.143611	−	0.989634i	$-0.454129\pi$
$499$	6.41606	0.287222	0.143611	+	0.989634i	$0.454129\pi$
$500$	−0.729699	−0.0326332
$501$	−14.6272	−0.653496
$502$	−20.5248	−0.916065
$503$	−21.3299	−0.951054	−0.475527	−	0.879701i	$-0.657743\pi$
$503$	−21.3299	−0.951054	−0.475527	+	0.879701i	$0.657743\pi$
$504$	−23.7733	−1.05895
$505$	−4.18131	−0.186066
$506$	5.76317	0.256204
$507$	−0.650034	−0.0288690
$508$	1.83565	0.0814436
$509$	14.2265	0.630577	0.315289	−	0.948996i	$-0.397899\pi$
$509$	14.2265	0.630577	0.315289	+	0.948996i	$0.397899\pi$
$510$	0	0
$511$	−3.60489	−0.159471
$512$	−20.1677	−0.891296
$513$	1.06131	0.0468578
$514$	2.90805	0.128269
$515$	8.08417	0.356231
$516$	13.5377	0.595962
$517$	19.7432	0.868306
$518$	30.2973	1.33119
$519$	−5.15278	−0.226182
$520$	11.2039	0.491324
$521$	−24.5559	−1.07581	−0.537906	−	0.843005i	$-0.680784\pi$
$521$	−24.5559	−1.07581	−0.537906	+	0.843005i	$0.680784\pi$
$522$	−3.03351	−0.132773
$523$	−39.8642	−1.74314	−0.871570	−	0.490271i	$-0.836898\pi$
$523$	−39.8642	−1.74314	−0.871570	+	0.490271i	$0.836898\pi$
$524$	−1.62161	−0.0708404
$525$	−6.06403	−0.264656
$526$	10.8063	0.471175
$527$	0	0
$528$	18.1377	0.789341
$529$	−21.0245	−0.914110
$530$	14.5903	0.633764
$531$	4.43754	0.192573
$532$	4.65827	0.201962
$533$	−34.7401	−1.50476
$534$	−4.65534	−0.201456
$535$	8.80071	0.380488
$536$	6.39644	0.276284
$537$	−26.1605	−1.12891
$538$	−7.98635	−0.344316
$539$	−3.76138	−0.162014
$540$	0.296312	0.0127512
$541$	22.8827	0.983803	0.491901	−	0.870651i	$-0.336302\pi$
$541$	22.8827	0.983803	0.491901	+	0.870651i	$0.336302\pi$
$542$	−15.5280	−0.666985
$543$	8.41789	0.361246
$544$	0	0
$545$	−14.3144	−0.613163
$546$	24.8895	1.06517
$547$	15.5350	0.664231	0.332115	−	0.943239i	$-0.392238\pi$
$547$	15.5350	0.664231	0.332115	+	0.943239i	$0.392238\pi$
$548$	16.1726	0.690858
$549$	−3.59923	−0.153611
$550$	4.10039	0.174841
$551$	2.22357	0.0947271
$552$	10.7354	0.456931
$553$	21.9165	0.931985
$554$	−5.08882	−0.216203
$555$	−27.3226	−1.15978
$556$	−10.1324	−0.429708
$557$	0.980081	0.0415274	0.0207637	−	0.999784i	$-0.493390\pi$
$557$	0.980081	0.0415274	0.0207637	+	0.999784i	$0.493390\pi$
$558$	−33.6709	−1.42540
$559$	−27.2136	−1.15101
$560$	−4.90501	−0.207274
$561$	0	0
$562$	−3.87908	−0.163629
$563$	28.8837	1.21730	0.608652	−	0.793437i	$-0.291711\pi$
$563$	28.8837	1.21730	0.608652	+	0.793437i	$0.291711\pi$
$564$	9.83119	0.413968
$565$	−11.4598	−0.482119
$566$	26.5322	1.11523
$567$	−20.7192	−0.870123
$568$	−37.8170	−1.58676
$569$	18.2893	0.766729	0.383365	−	0.923597i	$-0.374765\pi$
$569$	18.2893	0.766729	0.383365	+	0.923597i	$0.374765\pi$
$570$	7.31315	0.306314
$571$	10.4044	0.435410	0.217705	−	0.976015i	$-0.430143\pi$
$571$	10.4044	0.435410	0.217705	+	0.976015i	$0.430143\pi$
$572$	9.66758	0.404222
$573$	−30.6423	−1.28010
$574$	26.2620	1.09616
$575$	1.40552	0.0586141
$576$	26.5753	1.10730
$577$	−28.3066	−1.17842	−0.589209	−	0.807980i	$-0.700561\pi$
$577$	−28.3066	−1.17842	−0.589209	+	0.807980i	$0.700561\pi$
$578$	0	0
$579$	−29.6819	−1.23354
$580$	0.620810	0.0257777
$581$	−6.17187	−0.256052
$582$	−34.3257	−1.42285
$583$	47.0960	1.95052
$584$	4.54061	0.187892
$585$	−11.5207	−0.476322
$586$	−17.5738	−0.725968
$587$	2.68137	0.110672	0.0553360	−	0.998468i	$-0.482377\pi$
$587$	2.68137	0.110672	0.0553360	+	0.998468i	$0.482377\pi$
$588$	−1.87299	−0.0772407
$589$	24.6809	1.01696
$590$	1.58095	0.0650868
$591$	3.03405	0.124804
$592$	−22.1004	−0.908320
$593$	−15.3155	−0.628934	−0.314467	−	0.949268i	$-0.601826\pi$
$593$	−15.3155	−0.628934	−0.314467	+	0.949268i	$0.601826\pi$
$594$	−1.66506	−0.0683183
$595$	0	0
$596$	−8.49817	−0.348098
$597$	53.9603	2.20845
$598$	−5.76887	−0.235907
$599$	−43.5243	−1.77836	−0.889178	−	0.457561i	$-0.848723\pi$
$599$	−43.5243	−1.77836	−0.889178	+	0.457561i	$0.848723\pi$
$600$	7.63808	0.311823
$601$	30.7307	1.25353	0.626766	−	0.779208i	$-0.284378\pi$
$601$	30.7307	1.25353	0.626766	+	0.779208i	$0.284378\pi$
$602$	20.5723	0.838463
$603$	−6.57729	−0.267848
$604$	−2.06309	−0.0839459
$605$	2.23561	0.0908903
$606$	11.6999	0.475275
$607$	14.7075	0.596957	0.298479	−	0.954416i	$-0.403521\pi$
$607$	14.7075	0.596957	0.298479	+	0.954416i	$0.403521\pi$
$608$	−10.1664	−0.412301
$609$	5.15913	0.209058
$610$	−1.28229	−0.0519184
$611$	−19.7628	−0.799516
$612$	0	0
$613$	23.6535	0.955354	0.477677	−	0.878535i	$-0.341479\pi$
$613$	23.6535	0.955354	0.477677	+	0.878535i	$0.341479\pi$
$614$	24.4067	0.984974
$615$	−23.6835	−0.955009
$616$	−27.3392	−1.10153
$617$	−10.0479	−0.404512	−0.202256	−	0.979333i	$-0.564827\pi$
$617$	−10.0479	−0.404512	−0.202256	+	0.979333i	$0.564827\pi$
$618$	−22.6206	−0.909935
$619$	34.3858	1.38208	0.691042	−	0.722815i	$-0.257152\pi$
$619$	34.3858	1.38208	0.691042	+	0.722815i	$0.257152\pi$
$620$	6.89079	0.276741
$621$	−0.570743	−0.0229031
$622$	9.99096	0.400601
$623$	4.06376	0.162811
$624$	−18.1556	−0.726807
$625$	1.00000	0.0400000
$626$	19.2889	0.770938
$627$	23.6060	0.942735
$628$	0.999052	0.0398665
$629$	0	0
$630$	8.70915	0.346981
$631$	8.25061	0.328451	0.164226	−	0.986423i	$-0.447487\pi$
$631$	8.25061	0.328451	0.164226	+	0.986423i	$0.447487\pi$
$632$	−27.6054	−1.09808
$633$	−41.9204	−1.66619
$634$	11.6361	0.462128
$635$	−2.51562	−0.0998293
$636$	23.4516	0.929916
$637$	3.76510	0.149179
$638$	−3.48851	−0.138111
$639$	38.8862	1.53831
$640$	1.68825	0.0667337
$641$	−17.2231	−0.680271	−0.340136	−	0.940376i	$-0.610473\pi$
$641$	−17.2231	−0.680271	−0.340136	+	0.940376i	$0.610473\pi$
$642$	−24.6256	−0.971895
$643$	−12.5592	−0.495287	−0.247644	−	0.968851i	$-0.579656\pi$
$643$	−12.5592	−0.495287	−0.247644	+	0.968851i	$0.579656\pi$
$644$	−2.50510	−0.0987149
$645$	−18.5524	−0.730499
$646$	0	0
$647$	−3.62337	−0.142449	−0.0712247	−	0.997460i	$-0.522691\pi$
$647$	−3.62337	−0.142449	−0.0712247	+	0.997460i	$0.522691\pi$
$648$	26.0972	1.02520
$649$	5.10314	0.200316
$650$	−4.10445	−0.160990
$651$	57.2646	2.24438
$652$	−8.82301	−0.345536
$653$	−9.74594	−0.381388	−0.190694	−	0.981650i	$-0.561074\pi$
$653$	−9.74594	−0.381388	−0.190694	+	0.981650i	$0.561074\pi$
$654$	40.0538	1.56623
$655$	2.22230	0.0868325
$656$	−19.1568	−0.747948
$657$	−4.66899	−0.182155
$658$	14.9398	0.582414
$659$	7.19930	0.280445	0.140222	−	0.990120i	$-0.455218\pi$
$659$	7.19930	0.280445	0.140222	+	0.990120i	$0.455218\pi$
$660$	6.59071	0.256543
$661$	−11.0362	−0.429258	−0.214629	−	0.976696i	$-0.568854\pi$
$661$	−11.0362	−0.429258	−0.214629	+	0.976696i	$0.568854\pi$
$662$	−7.40181	−0.287680
$663$	0	0
$664$	7.77391	0.301686
$665$	−6.38383	−0.247554
$666$	39.2406	1.52054
$667$	−1.19578	−0.0463007
$668$	−4.29922	−0.166342
$669$	−23.8662	−0.922722
$670$	−2.34328	−0.0905287
$671$	−4.13909	−0.159788
$672$	−23.5881	−0.909929
$673$	−29.5111	−1.13757	−0.568784	−	0.822487i	$-0.692586\pi$
$673$	−29.5111	−1.13757	−0.568784	+	0.822487i	$0.692586\pi$
$674$	−34.0108	−1.31005
$675$	−0.406074	−0.0156298
$676$	−0.191058	−0.00734837
$677$	0.557951	0.0214438	0.0107219	−	0.999943i	$-0.496587\pi$
$677$	0.557951	0.0214438	0.0107219	+	0.999943i	$0.496587\pi$
$678$	32.0662	1.23150
$679$	29.9637	1.14990
$680$	0	0
$681$	−4.41737	−0.169274
$682$	−38.7213	−1.48272
$683$	−36.1564	−1.38348	−0.691742	−	0.722144i	$-0.743157\pi$
$683$	−36.1564	−1.38348	−0.691742	+	0.722144i	$0.743157\pi$
$684$	6.03332	0.230690
$685$	−22.1633	−0.846818
$686$	−22.1169	−0.844428
$687$	41.5668	1.58587
$688$	−15.0064	−0.572115
$689$	−47.1427	−1.79599
$690$	−3.93283	−0.149720
$691$	39.8226	1.51492	0.757461	−	0.652880i	$-0.226439\pi$
$691$	39.8226	1.51492	0.757461	+	0.652880i	$0.226439\pi$
$692$	−1.51450	−0.0575727
$693$	28.1122	1.06789
$694$	−7.93480	−0.301201
$695$	13.8857	0.526714
$696$	−6.49829	−0.246317
$697$	0	0
$698$	−39.9431	−1.51187
$699$	32.4881	1.22881
$700$	−1.78234	−0.0673660
$701$	−20.0299	−0.756520	−0.378260	−	0.925699i	$-0.623478\pi$
$701$	−20.0299	−0.756520	−0.378260	+	0.925699i	$0.623478\pi$
$702$	1.66671	0.0629059
$703$	−28.7635	−1.08483
$704$	30.5614	1.15182
$705$	−13.4729	−0.507420
$706$	9.63277	0.362534
$707$	−10.2131	−0.384103
$708$	2.54112	0.0955012
$709$	9.70848	0.364610	0.182305	−	0.983242i	$-0.441644\pi$
$709$	9.70848	0.364610	0.182305	+	0.983242i	$0.441644\pi$
$710$	13.8539	0.519927
$711$	28.3859	1.06455
$712$	−5.11859	−0.191827
$713$	−13.2727	−0.497068
$714$	0	0
$715$	−13.2487	−0.495474
$716$	−7.68909	−0.287355
$717$	59.4518	2.22027
$718$	−22.8615	−0.853182
$719$	−20.8091	−0.776050	−0.388025	−	0.921649i	$-0.626843\pi$
$719$	−20.8091	−0.776050	−0.388025	+	0.921649i	$0.626843\pi$
$720$	−6.35288	−0.236758
$721$	19.7461	0.735383
$722$	−13.7156	−0.510443
$723$	42.9277	1.59650
$724$	2.47418	0.0919522
$725$	−0.850775	−0.0315970
$726$	−6.25554	−0.232165
$727$	−39.1557	−1.45220	−0.726102	−	0.687587i	$-0.758670\pi$
$727$	−39.1557	−1.45220	−0.726102	+	0.687587i	$0.758670\pi$
$728$	27.3663	1.01426
$729$	−29.8595	−1.10591
$730$	−1.66341	−0.0615656
$731$	0	0
$732$	−2.06107	−0.0761793
$733$	12.9215	0.477265	0.238633	−	0.971110i	$-0.423301\pi$
$733$	12.9215	0.477265	0.238633	+	0.971110i	$0.423301\pi$
$734$	14.3390	0.529261
$735$	2.56679	0.0946776
$736$	5.46722	0.201525
$737$	−7.56384	−0.278618
$738$	34.0141	1.25208
$739$	−37.9866	−1.39736	−0.698680	−	0.715434i	$-0.746229\pi$
$739$	−37.9866	−1.39736	−0.698680	+	0.715434i	$0.746229\pi$
$740$	−8.03063	−0.295212
$741$	−23.6294	−0.868049
$742$	35.6378	1.30831
$743$	−12.2402	−0.449050	−0.224525	−	0.974468i	$-0.572083\pi$
$743$	−12.2402	−0.449050	−0.224525	+	0.974468i	$0.572083\pi$
$744$	−72.1288	−2.64437
$745$	11.6461	0.426681
$746$	−12.5617	−0.459916
$747$	−7.99371	−0.292474
$748$	0	0
$749$	21.4963	0.785457
$750$	−2.79814	−0.102174
$751$	−14.1068	−0.514766	−0.257383	−	0.966309i	$-0.582860\pi$
$751$	−14.1068	−0.514766	−0.257383	+	0.966309i	$0.582860\pi$
$752$	−10.8978	−0.397403
$753$	45.2107	1.64757
$754$	3.49196	0.127170
$755$	2.82731	0.102896
$756$	0.723760	0.0263229
$757$	−0.782070	−0.0284248	−0.0142124	−	0.999899i	$-0.504524\pi$
$757$	−0.782070	−0.0284248	−0.0142124	+	0.999899i	$0.504524\pi$
$758$	−14.2926	−0.519130
$759$	−12.6947	−0.460790
$760$	8.04088	0.291673
$761$	−2.86350	−0.103802	−0.0519009	−	0.998652i	$-0.516528\pi$
$761$	−2.86350	−0.103802	−0.0519009	+	0.998652i	$0.516528\pi$
$762$	7.03905	0.254998
$763$	−34.9639	−1.26578
$764$	−9.00636	−0.325839
$765$	0	0
$766$	19.5574	0.706636
$767$	−5.10819	−0.184446
$768$	36.9867	1.33464
$769$	−38.6633	−1.39423	−0.697117	−	0.716957i	$-0.745534\pi$
$769$	−38.6633	−1.39423	−0.697117	+	0.716957i	$0.745534\pi$
$770$	10.0155	0.360932
$771$	−6.40568	−0.230695
$772$	−8.72407	−0.313986
$773$	−37.9989	−1.36672	−0.683362	−	0.730080i	$-0.739483\pi$
$773$	−37.9989	−1.36672	−0.683362	+	0.730080i	$0.739483\pi$
$774$	26.6449	0.957730
$775$	−9.44332	−0.339214
$776$	−37.7414	−1.35484
$777$	−66.7371	−2.39418
$778$	21.9228	0.785969
$779$	−24.9324	−0.893297
$780$	−6.59723	−0.236219
$781$	44.7188	1.60017
$782$	0	0
$783$	0.345477	0.0123464
$784$	2.07620	0.0741499
$785$	−1.36913	−0.0488663
$786$	−6.21831	−0.221800
$787$	35.3733	1.26092	0.630461	−	0.776221i	$-0.282866\pi$
$787$	35.3733	1.26092	0.630461	+	0.776221i	$0.282866\pi$
$788$	0.891767	0.0317679
$789$	−23.8033	−0.847421
$790$	10.1130	0.359804
$791$	−27.9914	−0.995259
$792$	−35.4092	−1.25821
$793$	4.14319	0.147129
$794$	−5.36474	−0.190387
$795$	−32.1387	−1.13984
$796$	15.8600	0.562141
$797$	−26.7826	−0.948688	−0.474344	−	0.880340i	$-0.657315\pi$
$797$	−26.7826	−0.948688	−0.474344	+	0.880340i	$0.657315\pi$
$798$	17.8628	0.632337
$799$	0	0
$800$	3.88983	0.137526
$801$	5.26331	0.185970
$802$	−27.2797	−0.963281
$803$	−5.36931	−0.189479
$804$	−3.76643	−0.132832
$805$	3.43306	0.121000
$806$	38.7596	1.36525
$807$	17.5918	0.619262
$808$	12.8641	0.452558
$809$	54.0086	1.89884	0.949420	−	0.314009i	$-0.101672\pi$
$809$	54.0086	1.89884	0.949420	+	0.314009i	$0.101672\pi$
$810$	−9.56048	−0.335921
$811$	52.7965	1.85394	0.926968	−	0.375141i	$-0.122406\pi$
$811$	52.7965	1.85394	0.926968	+	0.375141i	$0.122406\pi$
$812$	1.51637	0.0532141
$813$	34.2041	1.19959
$814$	45.1264	1.58168
$815$	12.0913	0.423540
$816$	0	0
$817$	−19.5308	−0.683295
$818$	20.5650	0.719037
$819$	−28.1400	−0.983291
$820$	−6.96103	−0.243090
$821$	11.9083	0.415601	0.207801	−	0.978171i	$-0.433369\pi$
$821$	11.9083	0.415601	0.207801	+	0.978171i	$0.433369\pi$
$822$	62.0161	2.16306
$823$	39.5415	1.37833	0.689165	−	0.724604i	$-0.257977\pi$
$823$	39.5415	1.37833	0.689165	+	0.724604i	$0.257977\pi$
$824$	−24.8716	−0.866443
$825$	−9.03208	−0.314457
$826$	3.86157	0.134361
$827$	−18.3299	−0.637392	−0.318696	−	0.947857i	$-0.603245\pi$
$827$	−18.3299	−0.637392	−0.318696	+	0.947857i	$0.603245\pi$
$828$	−3.24457	−0.112756
$829$	39.4065	1.36864	0.684322	−	0.729180i	$-0.260098\pi$
$829$	39.4065	1.36864	0.684322	+	0.729180i	$0.260098\pi$
$830$	−2.84790	−0.0988521
$831$	11.2093	0.388847
$832$	−30.5916	−1.06057
$833$	0	0
$834$	−38.8540	−1.34541
$835$	5.89177	0.203893
$836$	6.93827	0.239965
$837$	3.83468	0.132546
$838$	1.96418	0.0678516
$839$	−20.6064	−0.711410	−0.355705	−	0.934598i	$-0.615759\pi$
$839$	−20.6064	−0.711410	−0.355705	+	0.934598i	$0.615759\pi$
$840$	18.6565	0.643710
$841$	−28.2762	−0.975041
$842$	41.7301	1.43812
$843$	8.54459	0.294291
$844$	−12.3212	−0.424114
$845$	0.261831	0.00900725
$846$	19.3498	0.665259
$847$	5.46061	0.187629
$848$	−25.9960	−0.892706
$849$	−58.4436	−2.00578
$850$	0	0
$851$	15.4683	0.530245
$852$	22.2679	0.762884
$853$	8.24316	0.282241	0.141120	−	0.989992i	$-0.454930\pi$
$853$	8.24316	0.282241	0.141120	+	0.989992i	$0.454930\pi$
$854$	−3.13207	−0.107177
$855$	−8.26822	−0.282767
$856$	−27.0761	−0.925441
$857$	−27.7260	−0.947104	−0.473552	−	0.880766i	$-0.657028\pi$
$857$	−27.7260	−0.947104	−0.473552	+	0.880766i	$0.657028\pi$
$858$	37.0717	1.26561
$859$	−7.00671	−0.239066	−0.119533	−	0.992830i	$-0.538140\pi$
$859$	−7.00671	−0.239066	−0.119533	+	0.992830i	$0.538140\pi$
$860$	−5.45290	−0.185942
$861$	−57.8483	−1.97147
$862$	34.2499	1.16656
$863$	−29.4176	−1.00139	−0.500693	−	0.865625i	$-0.666921\pi$
$863$	−29.4176	−1.00139	−0.500693	+	0.865625i	$0.666921\pi$
$864$	−1.57956	−0.0537377
$865$	2.07551	0.0705696
$866$	17.8356	0.606077
$867$	0	0
$868$	16.8312	0.571287
$869$	32.6436	1.10736
$870$	2.38059	0.0807095
$871$	7.57133	0.256545
$872$	44.0395	1.49137
$873$	38.8085	1.31347
$874$	−4.14023	−0.140045
$875$	2.44256	0.0825737
$876$	−2.67366	−0.0903347
$877$	51.5386	1.74034	0.870168	−	0.492755i	$-0.164010\pi$
$877$	51.5386	1.74034	0.870168	+	0.492755i	$0.164010\pi$
$878$	−4.69668	−0.158505
$879$	38.7105	1.30567
$880$	−7.30577	−0.246277
$881$	−46.6768	−1.57258	−0.786291	−	0.617856i	$-0.788002\pi$
$881$	−46.6768	−1.57258	−0.786291	+	0.617856i	$0.788002\pi$
$882$	−3.68642	−0.124128
$883$	9.95880	0.335140	0.167570	−	0.985860i	$-0.446408\pi$
$883$	9.95880	0.335140	0.167570	+	0.985860i	$0.446408\pi$
$884$	0	0
$885$	−3.48242	−0.117060
$886$	17.7177	0.595239
$887$	18.8375	0.632502	0.316251	−	0.948676i	$-0.397576\pi$
$887$	18.8375	0.632502	0.316251	+	0.948676i	$0.397576\pi$
$888$	84.0601	2.82087
$889$	−6.14455	−0.206082
$890$	1.87515	0.0628551
$891$	−30.8602	−1.03386
$892$	−7.01475	−0.234871
$893$	−14.1834	−0.474631
$894$	−32.5875	−1.08989
$895$	10.5373	0.352224
$896$	4.12364	0.137761
$897$	12.7073	0.424285
$898$	18.6496	0.622344
$899$	8.03414	0.267954
$900$	−2.30845	−0.0769484
$901$	0	0
$902$	39.1160	1.30242
$903$	−45.3153	−1.50800
$904$	35.2571	1.17263
$905$	−3.39068	−0.112710
$906$	−7.91121	−0.262832
$907$	26.7419	0.887950	0.443975	−	0.896039i	$-0.353568\pi$
$907$	26.7419	0.887950	0.443975	+	0.896039i	$0.353568\pi$
$908$	−1.29835	−0.0430872
$909$	−13.2278	−0.438740
$910$	−10.0254	−0.332338
$911$	−10.3831	−0.344008	−0.172004	−	0.985096i	$-0.555024\pi$
$911$	−10.3831	−0.344008	−0.172004	+	0.985096i	$0.555024\pi$
$912$	−13.0300	−0.431467
$913$	−9.19271	−0.304234
$914$	−1.60980	−0.0532476
$915$	2.82455	0.0933766
$916$	12.2173	0.403670
$917$	5.42811	0.179252
$918$	0	0
$919$	20.4602	0.674919	0.337460	−	0.941340i	$-0.390432\pi$
$919$	20.4602	0.674919	0.337460	+	0.941340i	$0.390432\pi$
$920$	−4.32418	−0.142564
$921$	−53.7615	−1.77150
$922$	12.5852	0.414470
$923$	−44.7631	−1.47340
$924$	16.0982	0.529592
$925$	11.0054	0.361855
$926$	32.9337	1.08227
$927$	25.5748	0.839986
$928$	−3.30937	−0.108635
$929$	4.56763	0.149859	0.0749296	−	0.997189i	$-0.476127\pi$
$929$	4.56763	0.149859	0.0749296	+	0.997189i	$0.476127\pi$
$930$	26.4237	0.866468
$931$	2.70215	0.0885595
$932$	9.54888	0.312784
$933$	−22.0075	−0.720492
$934$	−12.3288	−0.403412
$935$	0	0
$936$	35.4443	1.15853
$937$	2.90874	0.0950243	0.0475122	−	0.998871i	$-0.484871\pi$
$937$	2.90874	0.0950243	0.0475122	+	0.998871i	$0.484871\pi$
$938$	−5.72360	−0.186882
$939$	−42.4883	−1.38655
$940$	−3.95995	−0.129159
$941$	−15.3951	−0.501865	−0.250933	−	0.968005i	$-0.580737\pi$
$941$	−15.3951	−0.501865	−0.250933	+	0.968005i	$0.580737\pi$
$942$	3.83101	0.124821
$943$	13.4080	0.436626
$944$	−2.81682	−0.0916797
$945$	−0.991860	−0.0322652
$946$	30.6414	0.996238
$947$	−23.9883	−0.779514	−0.389757	−	0.920918i	$-0.627441\pi$
$947$	−23.9883	−0.779514	−0.389757	+	0.920918i	$0.627441\pi$
$948$	16.2550	0.527937
$949$	5.37463	0.174468
$950$	−2.94570	−0.0955712
$951$	−25.6313	−0.831151
$952$	0	0
$953$	−9.31030	−0.301590	−0.150795	−	0.988565i	$-0.548183\pi$
$953$	−9.31030	−0.301590	−0.150795	+	0.988565i	$0.548183\pi$
$954$	46.1575	1.49440
$955$	12.3426	0.399396
$956$	17.4740	0.565151
$957$	7.68427	0.248397
$958$	−19.3853	−0.626310
$959$	−54.1353	−1.74812
$960$	−20.8553	−0.673102
$961$	58.1763	1.87666
$962$	−45.1711	−1.45637
$963$	27.8416	0.897183
$964$	12.6173	0.406375
$965$	11.9557	0.384868
$966$	−9.60618	−0.309074
$967$	−1.29315	−0.0415848	−0.0207924	−	0.999784i	$-0.506619\pi$
$967$	−1.29315	−0.0415848	−0.0207924	+	0.999784i	$0.506619\pi$
$968$	−6.87802	−0.221068
$969$	0	0
$970$	13.8262	0.443933
$971$	−39.3251	−1.26200	−0.631002	−	0.775781i	$-0.717356\pi$
$971$	−39.3251	−1.26200	−0.631002	+	0.775781i	$0.717356\pi$
$972$	−16.2558	−0.521407
$973$	33.9166	1.08732
$974$	−29.1288	−0.933346
$975$	9.04103	0.289545
$976$	2.28469	0.0731311
$977$	53.3750	1.70762	0.853809	−	0.520586i	$-0.174286\pi$
$977$	53.3750	1.70762	0.853809	+	0.520586i	$0.174286\pi$
$978$	−33.8331	−1.08186
$979$	6.05277	0.193448
$980$	0.754430	0.0240994
$981$	−45.2846	−1.44583
$982$	13.7924	0.440132
$983$	−51.0753	−1.62905	−0.814524	−	0.580129i	$-0.803002\pi$
$983$	−51.0753	−1.62905	−0.814524	+	0.580129i	$0.803002\pi$
$984$	72.8641	2.32282
$985$	−1.22210	−0.0389394
$986$	0	0
$987$	−32.9085	−1.04749
$988$	−6.94514	−0.220954
$989$	10.5031	0.333981
$990$	12.9718	0.412272
$991$	−10.5889	−0.336369	−0.168185	−	0.985756i	$-0.553790\pi$
$991$	−10.5889	−0.336369	−0.168185	+	0.985756i	$0.553790\pi$
$992$	−36.7329	−1.16627
$993$	16.3042	0.517400
$994$	33.8390	1.07331
$995$	−21.7349	−0.689043
$996$	−4.57753	−0.145045
$997$	−3.44530	−0.109114	−0.0545568	−	0.998511i	$-0.517375\pi$
$997$	−3.44530	−0.109114	−0.0545568	+	0.998511i	$0.517375\pi$
$998$	7.23139	0.228906
$999$	−4.46900	−0.141393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1445.2.a.o.1.4		6
5.4	even	2		7225.2.a.z.1.3		6
17.2	even	8		85.2.e.a.21.4	✓	12
17.4	even	4		1445.2.d.g.866.6		12
17.9	even	8		85.2.e.a.81.3	yes	12
17.13	even	4		1445.2.d.g.866.5		12
17.16	even	2		1445.2.a.n.1.4		6
51.2	odd	8		765.2.k.b.361.3		12
51.26	odd	8		765.2.k.b.676.4		12
68.19	odd	8		1360.2.bt.d.1041.6		12
68.43	odd	8		1360.2.bt.d.81.6		12
85.2	odd	8		425.2.j.b.174.3		12
85.9	even	8		425.2.e.f.251.4		12
85.19	even	8		425.2.e.f.276.3		12
85.43	odd	8		425.2.j.b.149.3		12
85.53	odd	8		425.2.j.c.174.4		12
85.77	odd	8		425.2.j.c.149.4		12
85.84	even	2		7225.2.a.bb.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.e.a.21.4	✓	12	17.2	even	8
85.2.e.a.81.3	yes	12	17.9	even	8
425.2.e.f.251.4		12	85.9	even	8
425.2.e.f.276.3		12	85.19	even	8
425.2.j.b.149.3		12	85.43	odd	8
425.2.j.b.174.3		12	85.2	odd	8
425.2.j.c.149.4		12	85.77	odd	8
425.2.j.c.174.4		12	85.53	odd	8
765.2.k.b.361.3		12	51.2	odd	8
765.2.k.b.676.4		12	51.26	odd	8
1360.2.bt.d.81.6		12	68.43	odd	8
1360.2.bt.d.1041.6		12	68.19	odd	8
1445.2.a.n.1.4		6	17.16	even	2
1445.2.a.o.1.4		6	1.1	even	1	trivial
1445.2.d.g.866.5		12	17.13	even	4
1445.2.d.g.866.6		12	17.4	even	4
7225.2.a.z.1.3		6	5.4	even	2
7225.2.a.bb.1.3		6	85.84	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:	\( N \)	\(=\)	\( 1445 = 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1445.a (trivial)

\(f(q)\)	\(=\)	\(q+1.12708 q^{2} -2.48265 q^{3} -0.729699 q^{4} +1.00000 q^{5} -2.79814 q^{6} +2.44256 q^{7} -3.07658 q^{8} +3.16356 q^{9} +1.12708 q^{10} +3.63808 q^{11} +1.81159 q^{12} -3.64168 q^{13} +2.75295 q^{14} -2.48265 q^{15} -2.00814 q^{16} +3.56558 q^{18} -2.61358 q^{19} -0.729699 q^{20} -6.06403 q^{21} +4.10039 q^{22} +1.40552 q^{23} +7.63808 q^{24} +1.00000 q^{25} -4.10445 q^{26} -0.406074 q^{27} -1.78234 q^{28} -0.850775 q^{29} -2.79814 q^{30} -9.44332 q^{31} +3.88983 q^{32} -9.03208 q^{33} +2.44256 q^{35} -2.30845 q^{36} +11.0054 q^{37} -2.94570 q^{38} +9.04103 q^{39} -3.07658 q^{40} +9.53958 q^{41} -6.83463 q^{42} +7.47280 q^{43} -2.65470 q^{44} +3.16356 q^{45} +1.58412 q^{46} +5.42683 q^{47} +4.98551 q^{48} -1.03389 q^{49} +1.12708 q^{50} +2.65733 q^{52} +12.9453 q^{53} -0.457676 q^{54} +3.63808 q^{55} -7.51473 q^{56} +6.48861 q^{57} -0.958888 q^{58} +1.40270 q^{59} +1.81159 q^{60} -1.13771 q^{61} -10.6433 q^{62} +7.72720 q^{63} +8.40042 q^{64} -3.64168 q^{65} -10.1798 q^{66} -2.07908 q^{67} -3.48941 q^{69} +2.75295 q^{70} +12.2919 q^{71} -9.73296 q^{72} -1.47586 q^{73} +12.4039 q^{74} -2.48265 q^{75} +1.90713 q^{76} +8.88623 q^{77} +10.1899 q^{78} +8.97276 q^{79} -2.00814 q^{80} -8.48255 q^{81} +10.7518 q^{82} -2.52680 q^{83} +4.42492 q^{84} +8.42242 q^{86} +2.11218 q^{87} -11.1928 q^{88} +1.66373 q^{89} +3.56558 q^{90} -8.89503 q^{91} -1.02560 q^{92} +23.4445 q^{93} +6.11645 q^{94} -2.61358 q^{95} -9.65710 q^{96} +12.2673 q^{97} -1.16527 q^{98} +11.5093 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 4 q^{3} + 6 q^{4} + 6 q^{5} + 4 q^{6} + 8 q^{7} + 6 q^{8} + 2 q^{9} + 2 q^{10} + 8 q^{12} + 8 q^{14} + 4 q^{15} + 2 q^{16} + 14 q^{18} - 12 q^{19} + 6 q^{20} + 8 q^{21} + 16 q^{22} + 24 q^{24}+ \cdots + 20 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 + 4 * q^3 + 6 * q^4 + 6 * q^5 + 4 * q^6 + 8 * q^7 + 6 * q^8 + 2 * q^9 + 2 * q^10 + 8 * q^12 + 8 * q^14 + 4 * q^15 + 2 * q^16 + 14 * q^18 - 12 * q^19 + 6 * q^20 + 8 * q^21 + 16 * q^22 + 24 * q^24 + 6 * q^25 - 12 * q^26 - 8 * q^27 - 8 * q^28 + 8 * q^29 + 4 * q^30 + 4 * q^31 - 6 * q^32 - 8 * q^33 + 8 * q^35 - 10 * q^36 + 16 * q^37 - 12 * q^38 + 28 * q^39 + 6 * q^40 + 12 * q^41 - 8 * q^42 + 8 * q^43 - 4 * q^44 + 2 * q^45 + 20 * q^46 + 24 * q^47 + 8 * q^48 - 10 * q^49 + 2 * q^50 - 28 * q^52 - 12 * q^54 + 20 * q^56 - 16 * q^57 + 48 * q^58 - 16 * q^59 + 8 * q^60 - 4 * q^61 - 40 * q^62 + 20 * q^63 - 14 * q^64 - 16 * q^66 - 4 * q^67 + 8 * q^70 + 32 * q^71 - 10 * q^72 - 8 * q^73 - 8 * q^74 + 4 * q^75 - 36 * q^76 + 24 * q^77 + 4 * q^78 + 36 * q^79 + 2 * q^80 - 14 * q^81 - 28 * q^82 + 20 * q^83 - 48 * q^86 + 24 * q^87 + 12 * q^88 - 12 * q^89 + 14 * q^90 + 12 * q^91 + 28 * q^92 + 36 * q^93 + 20 * q^94 - 12 * q^95 - 44 * q^96 + 16 * q^97 - 22 * q^98 + 20 * q^99

Introduction

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