LMFDB - Embedded newform 1850.2.d.f.1701.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1850,2,Mod(1701,1850)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1850.1701"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1850, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1850 = 2 \cdot 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1850.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,4,-6,0,0,-10,0,14,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.7723243739$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.399424.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 370)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1701.4
Root			$0.264658 - 1.38923i$ of defining polynomial
Character	$\chi$	$=$	1850.1701
Dual form			1850.2.d.f.1701.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} -2.24914 q^{3} -1.00000 q^{4} -2.24914i q^{6} -1.52932 q^{7} -1.00000i q^{8} +2.05863 q^{9} +2.71982 q^{11} +2.24914 q^{12} -0.941367i q^{13} -1.52932i q^{14} +1.00000 q^{16} +4.83709i q^{17} +2.05863i q^{18} -0.249141i q^{19} +3.43965 q^{21} +2.71982i q^{22} -0.941367i q^{23} +2.24914i q^{24} +0.941367 q^{26} +2.11727 q^{27} +1.52932 q^{28} +0.719824i q^{29} +4.02760i q^{31} +1.00000i q^{32} -6.11727 q^{33} -4.83709 q^{34} -2.05863 q^{36} +(4.71982 + 3.83709i) q^{37} +0.249141 q^{38} +2.11727i q^{39} -8.27674 q^{41} +3.43965i q^{42} -2.71982i q^{43} -2.71982 q^{44} +0.941367 q^{46} +3.30777 q^{47} -2.24914 q^{48} -4.66119 q^{49} -10.8793i q^{51} +0.941367i q^{52} -8.39400 q^{53} +2.11727i q^{54} +1.52932i q^{56} +0.560352i q^{57} -0.719824 q^{58} -7.30777i q^{59} +6.83709i q^{61} -4.02760 q^{62} -3.14830 q^{63} -1.00000 q^{64} -6.11727i q^{66} +7.68879 q^{67} -4.83709i q^{68} +2.11727i q^{69} -3.05863 q^{71} -2.05863i q^{72} -9.11383 q^{73} +(-3.83709 + 4.71982i) q^{74} +0.249141i q^{76} -4.15947 q^{77} -2.11727 q^{78} -1.75086i q^{79} -10.9379 q^{81} -8.27674i q^{82} -0.131874 q^{83} -3.43965 q^{84} +2.71982 q^{86} -1.61899i q^{87} -2.71982i q^{88} -8.99656i q^{89} +1.43965i q^{91} +0.941367i q^{92} -9.05863i q^{93} +3.30777i q^{94} -2.24914i q^{96} -16.2767i q^{97} -4.66119i q^{98} +5.59912 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 4 q^{3} - 6 q^{4} - 10 q^{7} + 14 q^{9} - 2 q^{11} - 4 q^{12} + 6 q^{16} - 16 q^{21} + 4 q^{26} + 16 q^{27} + 10 q^{28} - 40 q^{33} - 14 q^{34} - 14 q^{36} + 10 q^{37} - 16 q^{38} + 2 q^{41} + 2 q^{44}+ \cdots - 58 q^{99}+O(q^{100}) $ 6 * q + 4 * q^3 - 6 * q^4 - 10 * q^7 + 14 * q^9 - 2 * q^11 - 4 * q^12 + 6 * q^16 - 16 * q^21 + 4 * q^26 + 16 * q^27 + 10 * q^28 - 40 * q^33 - 14 * q^34 - 14 * q^36 + 10 * q^37 - 16 * q^38 + 2 * q^41 + 2 * q^44 + 4 * q^46 + 4 * q^47 + 4 * q^48 - 8 * q^49 - 2 * q^53 + 14 * q^58 + 10 * q^62 - 58 * q^63 - 6 * q^64 - 8 * q^67 - 20 * q^71 + 12 * q^73 - 8 * q^74 + 30 * q^77 - 16 * q^78 + 6 * q^81 + 20 * q^83 + 16 * q^84 - 2 * q^86 - 58 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1850\mathbb{Z}\right)^\times$.

$n$	$1001$	$1777$
$\chi(n)$	$-1$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−2.24914			−1.29854			−0.649271	−	0.760557i	$-0.724926\pi$
$3$	−2.24914			−1.29854			−0.649271	+	0.760557i	$0.724926\pi$
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$		−	2.24914i		−	0.918208i
$7$	−1.52932			−0.578027			−0.289014	−	0.957325i	$-0.593327\pi$
$7$	−1.52932			−0.578027			−0.289014	+	0.957325i	$0.593327\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.05863			0.686211
$10$		0			0
$11$	2.71982			0.820058			0.410029	−	0.912073i	$-0.365519\pi$
$11$	2.71982			0.820058			0.410029	+	0.912073i	$0.365519\pi$
$12$	2.24914			0.649271
$13$		−	0.941367i		−	0.261088i	−0.991443	−	0.130544i	$-0.958328\pi$
$13$		−	0.941367i		−	0.261088i	0.991443	−	0.130544i	$-0.0416724\pi$
$14$		−	1.52932i		−	0.408727i
$15$		0			0
$16$	1.00000			0.250000
$17$			4.83709i			1.17317i	0.809889	+	0.586583i	$0.199527\pi$
$17$			4.83709i			1.17317i	−0.809889	+	0.586583i	$0.800473\pi$
$18$			2.05863i			0.485224i
$19$		−	0.249141i		−	0.0571568i	−0.999592	−	0.0285784i	$-0.990902\pi$
$19$		−	0.249141i		−	0.0571568i	0.999592	−	0.0285784i	$-0.00909802\pi$
$20$		0			0
$21$	3.43965			0.750593
$22$			2.71982i			0.579868i
$23$		−	0.941367i		−	0.196289i	−0.995172	−	0.0981443i	$-0.968709\pi$
$23$		−	0.941367i		−	0.196289i	0.995172	−	0.0981443i	$-0.0312907\pi$
$24$			2.24914i			0.459104i
$25$		0			0
$26$	0.941367			0.184617
$27$	2.11727			0.407468
$28$	1.52932			0.289014
$29$			0.719824i			0.133668i	0.997764	+	0.0668340i	$0.0212898\pi$
$29$			0.719824i			0.133668i	−0.997764	+	0.0668340i	$0.978710\pi$
$30$		0			0
$31$			4.02760i			0.723378i	0.932299	+	0.361689i	$0.117800\pi$
$31$			4.02760i			0.723378i	−0.932299	+	0.361689i	$0.882200\pi$
$32$			1.00000i			0.176777i
$33$	−6.11727			−1.06488
$34$	−4.83709			−0.829554
$35$		0			0
$36$	−2.05863			−0.343106
$37$	4.71982	+	3.83709i	0.775934	+	0.630814i
$37$	4.71982	+	3.83709i	0.775934	+	0.630814i
$38$	0.249141			0.0404159
$39$			2.11727i			0.339034i
$40$		0			0
$41$	−8.27674			−1.29261			−0.646305	−	0.763079i	$-0.723686\pi$
$41$	−8.27674			−1.29261			−0.646305	+	0.763079i	$0.723686\pi$
$42$			3.43965i			0.530749i
$43$		−	2.71982i		−	0.414769i	−0.978259	−	0.207385i	$-0.933505\pi$
$43$		−	2.71982i		−	0.414769i	0.978259	−	0.207385i	$-0.0664952\pi$
$44$	−2.71982			−0.410029
$45$		0			0
$46$	0.941367			0.138797
$47$	3.30777			0.482488			0.241244	−	0.970464i	$-0.422445\pi$
$47$	3.30777			0.482488			0.241244	+	0.970464i	$0.422445\pi$
$48$	−2.24914			−0.324635
$49$	−4.66119			−0.665884
$50$		0			0
$51$		−	10.8793i		−	1.52341i
$52$			0.941367i			0.130544i
$53$	−8.39400			−1.15301			−0.576503	−	0.817095i	$-0.695583\pi$
$53$	−8.39400			−1.15301			−0.576503	+	0.817095i	$0.695583\pi$
$54$			2.11727i			0.288123i
$55$		0			0
$56$			1.52932i			0.204364i
$57$			0.560352i			0.0742204i
$58$	−0.719824			−0.0945175
$59$		−	7.30777i		−	0.951391i	−0.879610	−	0.475696i	$-0.842196\pi$
$59$		−	7.30777i		−	0.951391i	0.879610	−	0.475696i	$-0.157804\pi$
$60$		0			0
$61$			6.83709i			0.875400i	0.899121	+	0.437700i	$0.144207\pi$
$61$			6.83709i			0.875400i	−0.899121	+	0.437700i	$0.855793\pi$
$62$	−4.02760			−0.511505
$63$	−3.14830			−0.396649
$64$	−1.00000			−0.125000
$65$		0			0
$66$		−	6.11727i		−	0.752983i
$67$	7.68879			0.939335			0.469668	−	0.882843i	$-0.344374\pi$
$67$	7.68879			0.939335			0.469668	+	0.882843i	$0.344374\pi$
$68$		−	4.83709i		−	0.586583i
$69$			2.11727i			0.254889i
$70$		0			0
$71$	−3.05863			−0.362993			−0.181496	−	0.983392i	$-0.558094\pi$
$71$	−3.05863			−0.362993			−0.181496	+	0.983392i	$0.558094\pi$
$72$		−	2.05863i		−	0.242612i
$73$	−9.11383			−1.06669			−0.533346	−	0.845897i	$-0.679066\pi$
$73$	−9.11383			−1.06669			−0.533346	+	0.845897i	$0.679066\pi$
$74$	−3.83709	+	4.71982i	−0.446053	+	0.548668i
$75$		0			0
$76$			0.249141i			0.0285784i
$77$	−4.15947			−0.474016
$78$	−2.11727			−0.239733
$79$		−	1.75086i		−	0.196987i	−0.995138	−	0.0984935i	$-0.968598\pi$
$79$		−	1.75086i		−	0.196987i	0.995138	−	0.0984935i	$-0.0314024\pi$
$80$		0			0
$81$	−10.9379			−1.21533
$82$		−	8.27674i		−	0.914013i
$83$	−0.131874			−0.0144751			−0.00723754	−	0.999974i	$-0.502304\pi$
$83$	−0.131874			−0.0144751			−0.00723754	+	0.999974i	$0.502304\pi$
$84$	−3.43965			−0.375296
$85$		0			0
$86$	2.71982			0.293286
$87$		−	1.61899i		−	0.173573i
$88$		−	2.71982i		−	0.289934i
$89$		−	8.99656i		−	0.953634i	−0.879003	−	0.476817i	$-0.841790\pi$
$89$		−	8.99656i		−	0.953634i	0.879003	−	0.476817i	$-0.158210\pi$
$90$		0			0
$91$			1.43965i			0.150916i
$92$			0.941367i			0.0981443i
$93$		−	9.05863i		−	0.939337i
$94$			3.30777i			0.341171i
$95$		0			0
$96$		−	2.24914i		−	0.229552i
$97$		−	16.2767i		−	1.65265i	−0.563192	−	0.826326i	$-0.690427\pi$
$97$		−	16.2767i		−	1.65265i	0.563192	−	0.826326i	$-0.309573\pi$
$98$		−	4.66119i		−	0.470851i
$99$	5.59912			0.562733
$100$		0			0
$101$	−11.1138			−1.10587			−0.552934	−	0.833225i	$-0.686492\pi$
$101$	−11.1138			−1.10587			−0.552934	+	0.833225i	$0.686492\pi$
$102$	10.8793			1.07721
$103$		−	14.1725i		−	1.39645i	−0.715876	−	0.698227i	$-0.753973\pi$
$103$		−	14.1725i		−	1.39645i	0.715876	−	0.698227i	$-0.246027\pi$
$104$	−0.941367			−0.0923086
$105$		0			0
$106$		−	8.39400i		−	0.815298i
$107$	−10.6922			−1.03366			−0.516828	−	0.856089i	$-0.672887\pi$
$107$	−10.6922			−1.03366			−0.516828	+	0.856089i	$0.672887\pi$
$108$	−2.11727			−0.203734
$109$			12.2767i			1.17590i	0.808898	+	0.587949i	$0.200064\pi$
$109$			12.2767i			1.17590i	−0.808898	+	0.587949i	$0.799936\pi$
$110$		0			0
$111$	−10.6155	−	8.63016i	−1.00758	−	0.819138i
$112$	−1.52932			−0.144507
$113$			2.95436i			0.277922i	0.990298	+	0.138961i	$0.0443763\pi$
$113$			2.95436i			0.277922i	−0.990298	+	0.138961i	$0.955624\pi$
$114$	−0.560352			−0.0524818
$115$		0			0
$116$		−	0.719824i		−	0.0668340i
$117$		−	1.93793i		−	0.179162i
$118$	7.30777			0.672735
$119$		−	7.39744i		−	0.678122i
$120$		0			0
$121$	−3.60256			−0.327505
$122$	−6.83709			−0.619001
$123$	18.6155			1.67851
$124$		−	4.02760i		−	0.361689i
$125$		0			0
$126$		−	3.14830i		−	0.280473i
$127$	−8.30434			−0.736891			−0.368445	−	0.929649i	$-0.620110\pi$
$127$	−8.30434			−0.736891			−0.368445	+	0.929649i	$0.620110\pi$
$128$		−	1.00000i		−	0.0883883i
$129$			6.11727i			0.538595i
$130$		0			0
$131$		−	11.0732i		−	0.967474i	−0.875214	−	0.483737i	$-0.839279\pi$
$131$		−	11.0732i		−	0.967474i	0.875214	−	0.483737i	$-0.160721\pi$
$132$	6.11727			0.532440
$133$			0.381015i			0.0330382i
$134$			7.68879i			0.664210i
$135$		0			0
$136$	4.83709			0.414777
$137$	−0.325819			−0.0278366			−0.0139183	−	0.999903i	$-0.504430\pi$
$137$	−0.325819			−0.0278366			−0.0139183	+	0.999903i	$0.504430\pi$
$138$	−2.11727			−0.180234
$139$	−13.3906			−1.13577			−0.567887	−	0.823107i	$-0.692239\pi$
$139$	−13.3906			−1.13577			−0.567887	+	0.823107i	$0.692239\pi$
$140$		0			0
$141$	−7.43965			−0.626531
$142$		−	3.05863i		−	0.256675i
$143$		−	2.56035i		−	0.214107i
$144$	2.05863			0.171553
$145$		0			0
$146$		−	9.11383i		−	0.754266i
$147$	10.4837			0.864679
$148$	−4.71982	−	3.83709i	−0.387967	−	0.315407i
$149$	8.44309			0.691685			0.345842	−	0.938293i	$-0.387593\pi$
$149$	8.44309			0.691685			0.345842	+	0.938293i	$0.387593\pi$
$150$		0			0
$151$	−4.94137			−0.402123			−0.201061	−	0.979579i	$-0.564439\pi$
$151$	−4.94137			−0.402123			−0.201061	+	0.979579i	$0.564439\pi$
$152$	−0.249141			−0.0202080
$153$			9.95779i			0.805040i
$154$		−	4.15947i		−	0.335180i
$155$		0			0
$156$		−	2.11727i		−	0.169517i
$157$	−19.2733			−1.53818			−0.769088	−	0.639142i	$-0.779289\pi$
$157$	−19.2733			−1.53818			−0.769088	+	0.639142i	$0.779289\pi$
$158$	1.75086			0.139291
$159$	18.8793			1.49723
$160$		0			0
$161$			1.43965i			0.113460i
$162$		−	10.9379i		−	0.859365i
$163$			17.3354i			1.35781i	0.734226	+	0.678906i	$0.237545\pi$
$163$			17.3354i			1.35781i	−0.734226	+	0.678906i	$0.762455\pi$
$164$	8.27674			0.646305
$165$		0			0
$166$		−	0.131874i		−	0.0102354i
$167$			17.0518i			1.31950i	0.751483	+	0.659752i	$0.229339\pi$
$167$			17.0518i			1.31950i	−0.751483	+	0.659752i	$0.770661\pi$
$168$		−	3.43965i		−	0.265375i
$169$	12.1138			0.931833
$170$		0			0
$171$		−	0.512889i		−	0.0392216i
$172$			2.71982i			0.207385i
$173$	−10.7198			−0.815013			−0.407507	−	0.913202i	$-0.633602\pi$
$173$	−10.7198			−0.815013			−0.407507	+	0.913202i	$0.633602\pi$
$174$	1.61899			0.122735
$175$		0			0
$176$	2.71982			0.205014
$177$			16.4362i			1.23542i
$178$	8.99656			0.674321
$179$		−	9.48024i		−	0.708586i	−0.935134	−	0.354293i	$-0.884722\pi$
$179$		−	9.48024i		−	0.708586i	0.935134	−	0.354293i	$-0.115278\pi$
$180$		0			0
$181$	20.9966			1.56066			0.780331	−	0.625367i	$-0.215051\pi$
$181$	20.9966			1.56066			0.780331	+	0.625367i	$0.215051\pi$
$182$	−1.43965			−0.106714
$183$		−	15.3776i		−	1.13674i
$184$	−0.941367			−0.0693985
$185$		0			0
$186$	9.05863			0.664211
$187$			13.1560i			0.962064i
$188$	−3.30777			−0.241244
$189$	−3.23797			−0.235528
$190$		0			0
$191$		−	11.0862i		−	0.802172i	−0.916041	−	0.401086i	$-0.868633\pi$
$191$		−	11.0862i		−	0.802172i	0.916041	−	0.401086i	$-0.131367\pi$
$192$	2.24914			0.162318
$193$		−	2.23453i		−	0.160845i	−0.996761	−	0.0804226i	$-0.974373\pi$
$193$		−	2.23453i		−	0.160845i	0.996761	−	0.0804226i	$-0.0256270\pi$
$194$	16.2767			1.16860
$195$		0			0
$196$	4.66119			0.332942
$197$	−13.4396			−0.957535			−0.478768	−	0.877942i	$-0.658916\pi$
$197$	−13.4396			−0.957535			−0.478768	+	0.877942i	$0.658916\pi$
$198$			5.59912i			0.397912i
$199$		−	23.4802i		−	1.66447i	−0.554423	−	0.832235i	$-0.687061\pi$
$199$		−	23.4802i		−	1.66447i	0.554423	−	0.832235i	$-0.312939\pi$
$200$		0			0
$201$	−17.2932			−1.21977
$202$		−	11.1138i		−	0.781966i
$203$		−	1.10084i		−	0.0772637i
$204$			10.8793i			0.761703i
$205$		0			0
$206$	14.1725			0.987442
$207$		−	1.93793i		−	0.134695i
$208$		−	0.941367i		−	0.0652720i
$209$		−	0.677618i		−	0.0468718i
$210$		0			0
$211$	−19.7716			−1.36113			−0.680566	−	0.732687i	$-0.738266\pi$
$211$	−19.7716			−1.36113			−0.680566	+	0.732687i	$0.738266\pi$
$212$	8.39400			0.576503
$213$	6.87930			0.471362
$214$		−	10.6922i		−	0.730906i
$215$		0			0
$216$		−	2.11727i		−	0.144062i
$217$		−	6.15947i		−	0.418132i
$218$	−12.2767			−0.831486
$219$	20.4983			1.38515
$220$		0			0
$221$	4.55348			0.306300
$222$	8.63016	−	10.6155i	0.579218	−	0.712469i
$223$	9.14143			0.612155			0.306078	−	0.952007i	$-0.400983\pi$
$223$	9.14143			0.612155			0.306078	+	0.952007i	$0.400983\pi$
$224$		−	1.52932i		−	0.102182i
$225$		0			0
$226$	−2.95436			−0.196521
$227$			18.7198i			1.24248i	0.783621	+	0.621239i	$0.213370\pi$
$227$			18.7198i			1.24248i	−0.783621	+	0.621239i	$0.786630\pi$
$228$		−	0.560352i		−	0.0371102i
$229$	−25.1138			−1.65957			−0.829784	−	0.558084i	$-0.811537\pi$
$229$	−25.1138			−1.65957			−0.829784	+	0.558084i	$0.811537\pi$
$230$		0			0
$231$	9.35524			0.615529
$232$	0.719824			0.0472588
$233$	−20.4362			−1.33882			−0.669410	−	0.742893i	$-0.733453\pi$
$233$	−20.4362			−1.33882			−0.669410	+	0.742893i	$0.733453\pi$
$234$	1.93793			0.126686
$235$		0			0
$236$			7.30777i			0.475696i
$237$			3.93793i			0.255796i
$238$	7.39744			0.479505
$239$			8.91377i			0.576584i	0.957543	+	0.288292i	$0.0930873\pi$
$239$			8.91377i			0.576584i	−0.957543	+	0.288292i	$0.906913\pi$
$240$		0			0
$241$			13.8827i			0.894265i	0.894468	+	0.447133i	$0.147555\pi$
$241$			13.8827i			0.894265i	−0.894468	+	0.447133i	$0.852445\pi$
$242$		−	3.60256i		−	0.231581i
$243$	18.2491			1.17068
$244$		−	6.83709i		−	0.437700i
$245$		0			0
$246$			18.6155i			1.18688i
$247$	−0.234533			−0.0149230
$248$	4.02760			0.255753
$249$	0.296604			0.0187965
$250$		0			0
$251$			3.80605i			0.240236i	0.992760	+	0.120118i	$0.0383273\pi$
$251$			3.80605i			0.240236i	−0.992760	+	0.120118i	$0.961673\pi$
$252$	3.14830			0.198324
$253$		−	2.56035i		−	0.160968i
$254$		−	8.30434i		−	0.521060i
$255$		0			0
$256$	1.00000			0.0625000
$257$			8.78801i			0.548181i	0.961704	+	0.274090i	$0.0883768\pi$
$257$			8.78801i			0.548181i	−0.961704	+	0.274090i	$0.911623\pi$
$258$	−6.11727			−0.380844
$259$	−7.21811	−	5.86813i	−0.448511	−	0.364628i
$260$		0			0
$261$			1.48185i			0.0917244i
$262$	11.0732			0.684107
$263$	10.4707			0.645650			0.322825	−	0.946459i	$-0.395367\pi$
$263$	10.4707			0.645650			0.322825	+	0.946459i	$0.395367\pi$
$264$			6.11727i			0.376492i
$265$		0			0
$266$	−0.381015			−0.0233615
$267$			20.2345i			1.23833i
$268$	−7.68879			−0.469668
$269$	−5.88273			−0.358677			−0.179338	−	0.983787i	$-0.557396\pi$
$269$	−5.88273			−0.358677			−0.179338	+	0.983787i	$0.557396\pi$
$270$		0			0
$271$	7.61211			0.462403			0.231201	−	0.972906i	$-0.425734\pi$
$271$	7.61211			0.462403			0.231201	+	0.972906i	$0.425734\pi$
$272$			4.83709i			0.293292i
$273$		−	3.23797i		−	0.195971i
$274$		−	0.325819i		−	0.0196835i
$275$		0			0
$276$		−	2.11727i		−	0.127444i
$277$		−	26.4914i		−	1.59171i	−0.605484	−	0.795857i	$-0.707021\pi$
$277$		−	26.4914i		−	1.59171i	0.605484	−	0.795857i	$-0.292979\pi$
$278$		−	13.3906i		−	0.803113i
$279$			8.29135i			0.496390i
$280$		0			0
$281$			26.6707i			1.59104i	0.605925	+	0.795522i	$0.292803\pi$
$281$			26.6707i			1.59104i	−0.605925	+	0.795522i	$0.707197\pi$
$282$		−	7.43965i		−	0.443025i
$283$		−	8.73281i		−	0.519112i	−0.965728	−	0.259556i	$-0.916424\pi$
$283$		−	8.73281i		−	0.519112i	0.965728	−	0.259556i	$-0.0835762\pi$
$284$	3.05863			0.181496
$285$		0			0
$286$	2.56035			0.151397
$287$	12.6578			0.747164
$288$			2.05863i			0.121306i
$289$	−6.39744			−0.376320
$290$		0			0
$291$			36.6087i			2.14604i
$292$	9.11383			0.533346
$293$	−23.4819			−1.37182			−0.685912	−	0.727684i	$-0.740597\pi$
$293$	−23.4819			−1.37182			−0.685912	+	0.727684i	$0.740597\pi$
$294$			10.4837i			0.611420i
$295$		0			0
$296$	3.83709	−	4.71982i	0.223026	−	0.274334i
$297$	5.75859			0.334147
$298$			8.44309i			0.489095i
$299$	−0.886172			−0.0512486
$300$		0			0
$301$			4.15947i			0.239748i
$302$		−	4.94137i		−	0.284344i
$303$	24.9966			1.43601
$304$		−	0.249141i		−	0.0142892i
$305$		0			0
$306$	−9.95779			−0.569249
$307$	−27.2457			−1.55499			−0.777497	−	0.628886i	$-0.783511\pi$
$307$	−27.2457			−1.55499			−0.777497	+	0.628886i	$0.783511\pi$
$308$	4.15947			0.237008
$309$			31.8759i			1.81335i
$310$		0			0
$311$			17.7018i			1.00378i	0.864933	+	0.501888i	$0.167361\pi$
$311$			17.7018i			1.00378i	−0.864933	+	0.501888i	$0.832639\pi$
$312$	2.11727			0.119867
$313$			23.9931i			1.35617i	0.734983	+	0.678086i	$0.237190\pi$
$313$			23.9931i			1.35617i	−0.734983	+	0.678086i	$0.762810\pi$
$314$		−	19.2733i		−	1.08766i
$315$		0			0
$316$			1.75086i			0.0984935i
$317$	3.16291			0.177647			0.0888234	−	0.996047i	$-0.471689\pi$
$317$	3.16291			0.177647			0.0888234	+	0.996047i	$0.471689\pi$
$318$			18.8793i			1.05870i
$319$			1.95779i			0.109615i
$320$		0			0
$321$	24.0483			1.34225
$322$	−1.43965			−0.0802284
$323$	1.20512			0.0670544
$324$	10.9379			0.607663
$325$		0			0
$326$	−17.3354			−0.960117
$327$		−	27.6121i		−	1.52695i
$328$			8.27674i			0.457006i
$329$	−5.05863			−0.278891
$330$		0			0
$331$			4.48367i			0.246445i	0.992379	+	0.123222i	$0.0393229\pi$
$331$			4.48367i			0.246445i	−0.992379	+	0.123222i	$0.960677\pi$
$332$	0.131874			0.00723754
$333$	9.71639	+	7.89916i	0.532455	+	0.432871i
$334$	−17.0518			−0.933031
$335$		0			0
$336$	3.43965			0.187648
$337$	11.2051			0.610382			0.305191	−	0.952291i	$-0.401280\pi$
$337$	11.2051			0.610382			0.305191	+	0.952291i	$0.401280\pi$
$338$			12.1138i			0.658905i
$339$		−	6.64476i		−	0.360894i
$340$		0			0
$341$			10.9544i			0.593212i
$342$	0.512889			0.0277339
$343$	17.8337			0.962927
$344$	−2.71982			−0.146643
$345$		0			0
$346$		−	10.7198i		−	0.576301i
$347$		−	13.9931i		−	0.751190i	−0.926784	−	0.375595i	$-0.877438\pi$
$347$		−	13.9931i		−	0.751190i	0.926784	−	0.375595i	$-0.122562\pi$
$348$			1.61899i			0.0867867i
$349$	−6.56035			−0.351168			−0.175584	−	0.984464i	$-0.556181\pi$
$349$	−6.56035			−0.351168			−0.175584	+	0.984464i	$0.556181\pi$
$350$		0			0
$351$		−	1.99312i		−	0.106385i
$352$			2.71982i			0.144967i
$353$			36.5957i			1.94779i	0.226995	+	0.973896i	$0.427110\pi$
$353$			36.5957i			1.94779i	−0.226995	+	0.973896i	$0.572890\pi$
$354$	−16.4362			−0.873575
$355$		0			0
$356$			8.99656i			0.476817i
$357$			16.6379i			0.880570i
$358$	9.48024			0.501046
$359$	21.2311			1.12053			0.560267	−	0.828312i	$-0.310698\pi$
$359$	21.2311			1.12053			0.560267	+	0.828312i	$0.310698\pi$
$360$		0			0
$361$	18.9379			0.996733
$362$			20.9966i			1.10355i
$363$	8.10266			0.425279
$364$		−	1.43965i		−	0.0754581i
$365$		0			0
$366$	15.3776			0.803799
$367$	−23.4932			−1.22634			−0.613168	−	0.789952i	$-0.710105\pi$
$367$	−23.4932			−1.22634			−0.613168	+	0.789952i	$0.710105\pi$
$368$		−	0.941367i		−	0.0490721i
$369$	−17.0388			−0.887003
$370$		0			0
$371$	12.8371			0.666469
$372$			9.05863i			0.469668i
$373$	7.55691			0.391282			0.195641	−	0.980676i	$-0.437321\pi$
$373$	7.55691			0.391282			0.195641	+	0.980676i	$0.437321\pi$
$374$	−13.1560			−0.680282
$375$		0			0
$376$		−	3.30777i		−	0.170585i
$377$	0.677618			0.0348991
$378$		−	3.23797i		−	0.166543i
$379$	12.2637			0.629946			0.314973	−	0.949101i	$-0.398004\pi$
$379$	12.2637			0.629946			0.314973	+	0.949101i	$0.398004\pi$
$380$		0			0
$381$	18.6776			0.956883
$382$	11.0862			0.567221
$383$		−	33.5208i		−	1.71283i	−0.516285	−	0.856417i	$-0.672685\pi$
$383$		−	33.5208i		−	1.71283i	0.516285	−	0.856417i	$-0.327315\pi$
$384$			2.24914i			0.114776i
$385$		0			0
$386$	2.23453			0.113735
$387$		−	5.59912i		−	0.284619i
$388$			16.2767i			0.826326i
$389$			9.95092i			0.504532i	0.967658	+	0.252266i	$0.0811757\pi$
$389$			9.95092i			0.504532i	−0.967658	+	0.252266i	$0.918824\pi$
$390$		0			0
$391$	4.55348			0.230279
$392$			4.66119i			0.235426i
$393$			24.9053i			1.25630i
$394$		−	13.4396i		−	0.677080i
$395$		0			0
$396$	−5.59912			−0.281366
$397$	−8.67762			−0.435517			−0.217759	−	0.976003i	$-0.569875\pi$
$397$	−8.67762			−0.435517			−0.217759	+	0.976003i	$0.569875\pi$
$398$	23.4802			1.17696
$399$		−	0.856956i		−	0.0429014i
$400$		0			0
$401$		−	11.5569i		−	0.577125i	−0.957461	−	0.288562i	$-0.906823\pi$
$401$		−	11.5569i		−	0.577125i	0.957461	−	0.288562i	$-0.0931773\pi$
$402$		−	17.2932i		−	0.862505i
$403$	3.79145			0.188865
$404$	11.1138			0.552934
$405$		0			0
$406$	1.10084			0.0546337
$407$	12.8371	+	10.4362i	0.636311	+	0.517304i
$408$	−10.8793			−0.538605
$409$			3.34836i			0.165566i	0.996568	+	0.0827829i	$0.0263808\pi$
$409$			3.34836i			0.165566i	−0.996568	+	0.0827829i	$0.973619\pi$
$410$		0			0
$411$	0.732814			0.0361470
$412$			14.1725i			0.698227i
$413$			11.1759i			0.549930i
$414$	1.93793			0.0952440
$415$		0			0
$416$	0.941367			0.0461543
$417$	30.1173			1.47485
$418$	0.677618			0.0331434
$419$	−11.3776			−0.555831			−0.277916	−	0.960606i	$-0.589644\pi$
$419$	−11.3776			−0.555831			−0.277916	+	0.960606i	$0.589644\pi$
$420$		0			0
$421$		−	3.23109i		−	0.157474i	−0.996895	−	0.0787370i	$-0.974911\pi$
$421$		−	3.23109i		−	0.157474i	0.996895	−	0.0787370i	$-0.0250887\pi$
$422$		−	19.7716i		−	0.962466i
$423$	6.80949			0.331089
$424$			8.39400i			0.407649i
$425$		0			0
$426$			6.87930i			0.333303i
$427$		−	10.4561i		−	0.506005i
$428$	10.6922			0.516828
$429$			5.75859i			0.278027i
$430$		0			0
$431$			29.2327i			1.40809i	0.710155	+	0.704045i	$0.248625\pi$
$431$			29.2327i			1.40809i	−0.710155	+	0.704045i	$0.751375\pi$
$432$	2.11727			0.101867
$433$	−17.7655			−0.853754			−0.426877	−	0.904310i	$-0.640386\pi$
$433$	−17.7655			−0.853754			−0.426877	+	0.904310i	$0.640386\pi$
$434$	6.15947			0.295664
$435$		0			0
$436$		−	12.2767i		−	0.587949i
$437$	−0.234533			−0.0112192
$438$			20.4983i			0.979446i
$439$		−	32.7604i		−	1.56357i	−0.623549	−	0.781785i	$-0.714310\pi$
$439$		−	32.7604i		−	1.56357i	0.623549	−	0.781785i	$-0.285690\pi$
$440$		0			0
$441$	−9.59568			−0.456937
$442$			4.55348i			0.216587i
$443$	0.600939			0.0285515			0.0142757	−	0.999898i	$-0.495456\pi$
$443$	0.600939			0.0285515			0.0142757	+	0.999898i	$0.495456\pi$
$444$	10.6155	+	8.63016i	0.503792	+	0.409569i
$445$		0			0
$446$			9.14143i			0.432859i
$447$	−18.9897			−0.898181
$448$	1.52932			0.0722534
$449$			34.0191i			1.60546i	0.596342	+	0.802730i	$0.296620\pi$
$449$			34.0191i			1.60546i	−0.596342	+	0.802730i	$0.703380\pi$
$450$		0			0
$451$	−22.5113			−1.06001
$452$		−	2.95436i		−	0.138961i
$453$	11.1138			0.522173
$454$	−18.7198			−0.878565
$455$		0			0
$456$	0.560352			0.0262409
$457$		−	30.9215i		−	1.44645i	−0.690614	−	0.723223i	$-0.742660\pi$
$457$		−	30.9215i		−	1.44645i	0.690614	−	0.723223i	$-0.257340\pi$
$458$		−	25.1138i		−	1.17349i
$459$			10.2414i			0.478028i
$460$		0			0
$461$		−	1.27330i		−	0.0593035i	−0.999560	−	0.0296518i	$-0.990560\pi$
$461$		−	1.27330i		−	0.0593035i	0.999560	−	0.0296518i	$-0.00943983\pi$
$462$			9.35524i			0.435245i
$463$			2.61555i			0.121555i	0.998151	+	0.0607774i	$0.0193580\pi$
$463$			2.61555i			0.121555i	−0.998151	+	0.0607774i	$0.980642\pi$
$464$			0.719824i			0.0334170i
$465$		0			0
$466$		−	20.4362i		−	0.946689i
$467$			19.0096i			0.879657i	0.898082	+	0.439829i	$0.144961\pi$
$467$			19.0096i			0.879657i	−0.898082	+	0.439829i	$0.855039\pi$
$468$			1.93793i			0.0895808i
$469$	−11.7586			−0.542961
$470$		0			0
$471$	43.3484			1.99739
$472$	−7.30777			−0.336368
$473$		−	7.39744i		−	0.340135i
$474$	−3.93793			−0.180875
$475$		0			0
$476$			7.39744i			0.339061i
$477$	−17.2802			−0.791205
$478$	−8.91377			−0.407706
$479$			38.8578i			1.77546i	0.460366	+	0.887729i	$0.347718\pi$
$479$			38.8578i			1.77546i	−0.460366	+	0.887729i	$0.652282\pi$
$480$		0			0
$481$	3.61211	−	4.44309i	0.164698	−	0.202587i
$482$	−13.8827			−0.632341
$483$		−	3.23797i		−	0.147333i
$484$	3.60256			0.163753
$485$		0			0
$486$			18.2491i			0.827798i
$487$		−	38.4914i		−	1.74421i	−0.489317	−	0.872106i	$-0.662754\pi$
$487$		−	38.4914i		−	1.74421i	0.489317	−	0.872106i	$-0.337246\pi$
$488$	6.83709			0.309501
$489$		−	38.9897i		−	1.76317i
$490$		0			0
$491$	−11.2672			−0.508481			−0.254240	−	0.967141i	$-0.581825\pi$
$491$	−11.2672			−0.508481			−0.254240	+	0.967141i	$0.581825\pi$
$492$	−18.6155			−0.839254
$493$	−3.48185			−0.156815
$494$		−	0.234533i		−	0.0105521i
$495$		0			0
$496$			4.02760i			0.180844i
$497$	4.67762			0.209820
$498$			0.296604i			0.0132911i
$499$		−	20.8578i		−	0.933724i	−0.884330	−	0.466862i	$-0.845384\pi$
$499$		−	20.8578i		−	0.933724i	0.884330	−	0.466862i	$-0.154616\pi$
$500$		0			0
$501$		−	38.3518i		−	1.71343i
$502$	−3.80605			−0.169873
$503$		−	6.64476i		−	0.296275i	−0.988967	−	0.148138i	$-0.952672\pi$
$503$		−	6.64476i		−	0.296275i	0.988967	−	0.148138i	$-0.0473279\pi$
$504$			3.14830i			0.140237i
$505$		0			0
$506$	2.56035			0.113822
$507$	−27.2457			−1.21002
$508$	8.30434			0.368445
$509$	−18.5535			−0.822368			−0.411184	−	0.911552i	$-0.634885\pi$
$509$	−18.5535			−0.822368			−0.411184	+	0.911552i	$0.634885\pi$
$510$		0			0
$511$	13.9379			0.616578
$512$			1.00000i			0.0441942i
$513$		−	0.527497i		−	0.0232896i
$514$	−8.78801			−0.387622
$515$		0			0
$516$		−	6.11727i		−	0.269298i
$517$	8.99656			0.395668
$518$	5.86813	−	7.21811i	0.257831	−	0.317145i
$519$	24.1104			1.05833
$520$		0			0
$521$	−42.6509			−1.86857			−0.934284	−	0.356529i	$-0.883960\pi$
$521$	−42.6509			−1.86857			−0.934284	+	0.356529i	$0.883960\pi$
$522$	−1.48185			−0.0648590
$523$			12.3879i			0.541685i	0.962624	+	0.270842i	$0.0873022\pi$
$523$			12.3879i			0.541685i	−0.962624	+	0.270842i	$0.912698\pi$
$524$			11.0732i			0.483737i
$525$		0			0
$526$			10.4707i			0.456543i
$527$	−19.4819			−0.848643
$528$	−6.11727			−0.266220
$529$	22.1138			0.961471
$530$		0			0
$531$		−	15.0440i		−	0.652855i
$532$		−	0.381015i		−	0.0165191i
$533$			7.79145i			0.337485i
$534$	−20.2345			−0.875634
$535$		0			0
$536$		−	7.68879i		−	0.332105i
$537$			21.3224i			0.920129i
$538$		−	5.88273i		−	0.253623i
$539$	−12.6776			−0.546064
$540$		0			0
$541$			7.64820i			0.328822i	0.986392	+	0.164411i	$0.0525723\pi$
$541$			7.64820i			0.328822i	−0.986392	+	0.164411i	$0.947428\pi$
$542$			7.61211i			0.326968i
$543$	−47.2242			−2.02659
$544$	−4.83709			−0.207389
$545$		0			0
$546$	3.23797			0.138572
$547$			12.6837i			0.542317i	0.962535	+	0.271159i	$0.0874068\pi$
$547$			12.6837i			0.542317i	−0.962535	+	0.271159i	$0.912593\pi$
$548$	0.325819			0.0139183
$549$			14.0751i			0.600709i
$550$		0			0
$551$	0.179337			0.00764003
$552$	2.11727			0.0901168
$553$			2.67762i			0.113864i
$554$	26.4914			1.12551
$555$		0			0
$556$	13.3906			0.567887
$557$			2.61555i			0.110824i	0.998464	+	0.0554121i	$0.0176473\pi$
$557$			2.61555i			0.110824i	−0.998464	+	0.0554121i	$0.982353\pi$
$558$	−8.29135			−0.351001
$559$	−2.56035			−0.108291
$560$		0			0
$561$		−	29.5898i		−	1.24928i
$562$	−26.6707			−1.12504
$563$			35.3285i			1.48892i	0.667668	+	0.744459i	$0.267293\pi$
$563$			35.3285i			1.48892i	−0.667668	+	0.744459i	$0.732707\pi$
$564$	7.43965			0.313266
$565$		0			0
$566$	8.73281			0.367068
$567$	16.7276			0.702491
$568$			3.05863i			0.128337i
$569$		−	28.8724i		−	1.21039i	−0.796075	−	0.605197i	$-0.793094\pi$
$569$		−	28.8724i		−	1.21039i	0.796075	−	0.605197i	$-0.206906\pi$
$570$		0			0
$571$	−8.15947			−0.341463			−0.170732	−	0.985318i	$-0.554613\pi$
$571$	−8.15947			−0.341463			−0.170732	+	0.985318i	$0.554613\pi$
$572$			2.56035i			0.107054i
$573$			24.9345i			1.04165i
$574$			12.6578i			0.528324i
$575$		0			0
$576$	−2.05863			−0.0857764
$577$		−	37.5500i		−	1.56323i	−0.623762	−	0.781614i	$-0.714397\pi$
$577$		−	37.5500i		−	1.56323i	0.623762	−	0.781614i	$-0.285603\pi$
$578$		−	6.39744i		−	0.266099i
$579$			5.02578i			0.208864i
$580$		0			0
$581$	0.201677			0.00836699
$582$	−36.6087			−1.51748
$583$	−22.8302			−0.945531
$584$			9.11383i			0.377133i
$585$		0			0
$586$		−	23.4819i		−	0.970026i
$587$		−	19.5078i		−	0.805174i	−0.915382	−	0.402587i	$-0.868111\pi$
$587$		−	19.5078i		−	0.805174i	0.915382	−	0.402587i	$-0.131889\pi$
$588$	−10.4837			−0.432339
$589$	1.00344			0.0413459
$590$		0			0
$591$	30.2277			1.24340
$592$	4.71982	+	3.83709i	0.193984	+	0.157703i
$593$	−41.5569			−1.70654			−0.853269	−	0.521471i	$-0.825383\pi$
$593$	−41.5569			−1.70654			−0.853269	+	0.521471i	$0.825383\pi$
$594$			5.75859i			0.236278i
$595$		0			0
$596$	−8.44309			−0.345842
$597$			52.8103i			2.16138i
$598$		−	0.886172i		−	0.0362382i
$599$	27.6381			1.12926			0.564631	−	0.825344i	$-0.309019\pi$
$599$	27.6381			1.12926			0.564631	+	0.825344i	$0.309019\pi$
$600$		0			0
$601$	14.4301			0.588616			0.294308	−	0.955711i	$-0.404911\pi$
$601$	14.4301			0.588616			0.294308	+	0.955711i	$0.404911\pi$
$602$	−4.15947			−0.169527
$603$	15.8284			0.644582
$604$	4.94137			0.201061
$605$		0			0
$606$			24.9966i			1.01542i
$607$		−	47.4880i		−	1.92748i	−0.266848	−	0.963739i	$-0.585982\pi$
$607$		−	47.4880i		−	1.92748i	0.266848	−	0.963739i	$-0.414018\pi$
$608$	0.249141			0.0101040
$609$			2.47594i			0.100330i
$610$		0			0
$611$		−	3.11383i		−	0.125972i
$612$		−	9.95779i		−	0.402520i
$613$	18.7198			0.756087			0.378043	−	0.925788i	$-0.376597\pi$
$613$	18.7198			0.756087			0.378043	+	0.925788i	$0.376597\pi$
$614$		−	27.2457i		−	1.09955i
$615$		0			0
$616$			4.15947i			0.167590i
$617$	15.0225			0.604785			0.302392	−	0.953184i	$-0.402215\pi$
$617$	15.0225			0.604785			0.302392	+	0.953184i	$0.402215\pi$
$618$	−31.8759			−1.28224
$619$	16.6318			0.668487			0.334244	−	0.942487i	$-0.391519\pi$
$619$	16.6318			0.668487			0.334244	+	0.942487i	$0.391519\pi$
$620$		0			0
$621$		−	1.99312i		−	0.0799813i
$622$	−17.7018			−0.709777
$623$			13.7586i			0.551226i
$624$			2.11727i			0.0847585i
$625$		0			0
$626$	−23.9931			−0.958958
$627$			1.52406i			0.0608651i
$628$	19.2733			0.769088
$629$	−18.5604	+	22.8302i	−0.740050	+	0.910300i
$630$		0			0
$631$		−	35.9294i		−	1.43033i	−0.698957	−	0.715164i	$-0.746352\pi$
$631$		−	35.9294i		−	1.43033i	0.698957	−	0.715164i	$-0.253648\pi$
$632$	−1.75086			−0.0696454
$633$	44.4691			1.76749
$634$			3.16291i			0.125615i
$635$		0			0
$636$	−18.8793			−0.748613
$637$			4.38789i			0.173855i
$638$	−1.95779			−0.0775098
$639$	−6.29660			−0.249090
$640$		0			0
$641$	29.3354			1.15868			0.579339	−	0.815087i	$-0.303311\pi$
$641$	29.3354			1.15868			0.579339	+	0.815087i	$0.303311\pi$
$642$			24.0483i			0.949111i
$643$			0.368025i			0.0145135i	0.999974	+	0.00725674i	$0.00230991\pi$
$643$			0.368025i			0.0145135i	−0.999974	+	0.00725674i	$0.997690\pi$
$644$		−	1.43965i		−	0.0567301i
$645$		0			0
$646$			1.20512i			0.0474146i
$647$		−	26.7811i		−	1.05287i	−0.850214	−	0.526437i	$-0.823527\pi$
$647$		−	26.7811i		−	1.05287i	0.850214	−	0.526437i	$-0.176473\pi$
$648$			10.9379i			0.429682i
$649$		−	19.8759i		−	0.780196i
$650$		0			0
$651$			13.8535i			0.542962i
$652$		−	17.3354i		−	0.678906i
$653$		−	2.00000i		−	0.0782660i	−0.999234	−	0.0391330i	$-0.987540\pi$
$653$		−	2.00000i		−	0.0782660i	0.999234	−	0.0391330i	$-0.0124596\pi$
$654$	27.6121			1.07972
$655$		0			0
$656$	−8.27674			−0.323152
$657$	−18.7620			−0.731976
$658$		−	5.05863i		−	0.197206i
$659$	−12.9966			−0.506274			−0.253137	−	0.967430i	$-0.581462\pi$
$659$	−12.9966			−0.506274			−0.253137	+	0.967430i	$0.581462\pi$
$660$		0			0
$661$		−	18.6026i		−	0.723556i	−0.932264	−	0.361778i	$-0.882170\pi$
$661$		−	18.6026i		−	0.723556i	0.932264	−	0.361778i	$-0.117830\pi$
$662$	−4.48367			−0.174263
$663$	−10.2414			−0.397743
$664$			0.131874i			0.00511771i
$665$		0			0
$666$	−7.89916	+	9.71639i	−0.306086	+	0.376502i
$667$	0.677618			0.0262375
$668$		−	17.0518i		−	0.659752i
$669$	−20.5604			−0.794909
$670$		0			0
$671$			18.5957i			0.717878i
$672$			3.43965i			0.132687i
$673$	−20.4622			−0.788759			−0.394380	−	0.918948i	$-0.629041\pi$
$673$	−20.4622			−0.788759			−0.394380	+	0.918948i	$0.629041\pi$
$674$			11.2051i			0.431605i
$675$		0			0
$676$	−12.1138			−0.465916
$677$	39.9018			1.53355			0.766776	−	0.641915i	$-0.221860\pi$
$677$	39.9018			1.53355			0.766776	+	0.641915i	$0.221860\pi$
$678$	6.64476			0.255191
$679$			24.8923i			0.955278i
$680$		0			0
$681$		−	42.1035i		−	1.61341i
$682$	−10.9544			−0.419464
$683$		−	12.3940i		−	0.474243i	−0.971480	−	0.237122i	$-0.923796\pi$
$683$		−	12.3940i		−	0.474243i	0.971480	−	0.237122i	$-0.0762040\pi$
$684$			0.512889i			0.0196108i
$685$		0			0
$686$			17.8337i			0.680892i
$687$	56.4845			2.15502
$688$		−	2.71982i		−	0.103692i
$689$			7.90184i			0.301036i
$690$		0			0
$691$	−51.5630			−1.96155			−0.980775	−	0.195142i	$-0.937483\pi$
$691$	−51.5630			−1.96155			−0.980775	+	0.195142i	$0.937483\pi$
$692$	10.7198			0.407507
$693$	−8.56283			−0.325275
$694$	13.9931			0.531172
$695$		0			0
$696$	−1.61899			−0.0613675
$697$		−	40.0353i		−	1.51645i
$698$		−	6.56035i		−	0.248313i
$699$	45.9639			1.73851
$700$		0			0
$701$		−	9.76547i		−	0.368837i	−0.982848	−	0.184418i	$-0.940960\pi$
$701$		−	9.76547i		−	0.368837i	0.982848	−	0.184418i	$-0.0590401\pi$
$702$	1.99312			0.0752256
$703$	0.955975	−	1.17590i	0.0360553	−	0.0443499i
$704$	−2.71982			−0.102507
$705$		0			0
$706$	−36.5957			−1.37730
$707$	16.9966			0.639222
$708$		−	16.4362i		−	0.617711i
$709$		−	49.8268i		−	1.87128i	−0.352951	−	0.935642i	$-0.614822\pi$
$709$		−	49.8268i		−	1.87128i	0.352951	−	0.935642i	$-0.385178\pi$
$710$		0			0
$711$		−	3.60438i		−	0.135175i
$712$	−8.99656			−0.337160
$713$	3.79145			0.141991
$714$	−16.6379			−0.622657
$715$		0			0
$716$			9.48024i			0.354293i
$717$		−	20.0483i		−	0.748718i
$718$			21.2311i			0.792337i
$719$	−4.26375			−0.159011			−0.0795055	−	0.996834i	$-0.525334\pi$
$719$	−4.26375			−0.159011			−0.0795055	+	0.996834i	$0.525334\pi$
$720$		0			0
$721$			21.6742i			0.807189i
$722$			18.9379i			0.704797i
$723$		−	31.2242i		−	1.16124i
$724$	−20.9966			−0.780331
$725$		0			0
$726$			8.10266i			0.300718i
$727$			13.1759i			0.488667i	0.969691	+	0.244334i	$0.0785692\pi$
$727$			13.1759i			0.488667i	−0.969691	+	0.244334i	$0.921431\pi$
$728$	1.43965			0.0533569
$729$	−8.23109			−0.304855
$730$		0			0
$731$	13.1560			0.486593
$732$			15.3776i			0.568372i
$733$	−9.39057			−0.346848			−0.173424	−	0.984847i	$-0.555483\pi$
$733$	−9.39057			−0.346848			−0.173424	+	0.984847i	$0.555483\pi$
$734$		−	23.4932i		−	0.867151i
$735$		0			0
$736$	0.941367			0.0346992
$737$	20.9122			0.770309
$738$		−	17.0388i		−	0.627206i
$739$	−9.62510			−0.354065			−0.177033	−	0.984205i	$-0.556650\pi$
$739$	−9.62510			−0.354065			−0.177033	+	0.984205i	$0.556650\pi$
$740$		0			0
$741$	0.527497			0.0193781
$742$			12.8371i			0.471264i
$743$	25.6137			0.939677			0.469838	−	0.882753i	$-0.344312\pi$
$743$	25.6137			0.939677			0.469838	+	0.882753i	$0.344312\pi$
$744$	−9.05863			−0.332106
$745$		0			0
$746$			7.55691i			0.276678i
$747$	−0.271481			−0.00993296
$748$		−	13.1560i		−	0.481032i
$749$	16.3518			0.597482
$750$		0			0
$751$	11.9740			0.436938			0.218469	−	0.975844i	$-0.429894\pi$
$751$	11.9740			0.436938			0.218469	+	0.975844i	$0.429894\pi$
$752$	3.30777			0.120622
$753$		−	8.56035i		−	0.311957i
$754$			0.677618i			0.0246774i
$755$		0			0
$756$	3.23797			0.117764
$757$			19.2051i			0.698022i	0.937119	+	0.349011i	$0.113482\pi$
$757$			19.2051i			0.698022i	−0.937119	+	0.349011i	$0.886518\pi$
$758$			12.2637i			0.445439i
$759$			5.75859i			0.209024i
$760$		0			0
$761$	−31.8596			−1.15491			−0.577455	−	0.816422i	$-0.695954\pi$
$761$	−31.8596			−1.15491			−0.577455	+	0.816422i	$0.695954\pi$
$762$			18.6776i			0.676619i
$763$		−	18.7750i		−	0.679701i
$764$			11.0862i			0.401086i
$765$		0			0
$766$	33.5208			1.21116
$767$	−6.87930			−0.248397
$768$	−2.24914			−0.0811589
$769$			35.2242i			1.27022i	0.772423	+	0.635109i	$0.219045\pi$
$769$			35.2242i			1.27022i	−0.772423	+	0.635109i	$0.780955\pi$
$770$		0			0
$771$		−	19.7655i		−	0.711836i
$772$			2.23453i			0.0804226i
$773$	50.2630			1.80783			0.903917	−	0.427708i	$-0.140679\pi$
$773$	50.2630			1.80783			0.903917	+	0.427708i	$0.140679\pi$
$774$	5.59912			0.201256
$775$		0			0
$776$	−16.2767			−0.584301
$777$	16.2345	+	13.1982i	0.582411	+	0.473484i
$778$	−9.95092			−0.356758
$779$			2.06207i			0.0738814i
$780$		0			0
$781$	−8.31894			−0.297675
$782$			4.55348i			0.162832i
$783$			1.52406i			0.0544654i
$784$	−4.66119			−0.166471
$785$		0			0
$786$	−24.9053			−0.888342
$787$	51.9525			1.85191			0.925954	−	0.377636i	$-0.123263\pi$
$787$	51.9525			1.85191			0.925954	+	0.377636i	$0.123263\pi$
$788$	13.4396			0.478768
$789$	−23.5500			−0.838404
$790$		0			0
$791$		−	4.51815i		−	0.160647i
$792$		−	5.59912i		−	0.198956i
$793$	6.43621			0.228557
$794$		−	8.67762i		−	0.307957i
$795$		0			0
$796$			23.4802i			0.832235i
$797$			35.4880i			1.25705i	0.777790	+	0.628524i	$0.216341\pi$
$797$			35.4880i			1.25705i	−0.777790	+	0.628524i	$0.783659\pi$
$798$	0.856956			0.0303359
$799$			16.0000i			0.566039i
$800$		0			0
$801$		−	18.5206i		−	0.654394i
$802$	11.5569			0.408089
$803$	−24.7880			−0.874750
$804$	17.2932			0.609883
$805$		0			0
$806$			3.79145i			0.133548i
$807$	13.2311			0.465757
$808$			11.1138i			0.390983i
$809$		−	13.2051i		−	0.464267i	−0.972684	−	0.232134i	$-0.925429\pi$
$809$		−	13.2051i		−	0.464267i	0.972684	−	0.232134i	$-0.0745706\pi$
$810$		0			0
$811$	−10.1173			−0.355265			−0.177633	−	0.984097i	$-0.556844\pi$
$811$	−10.1173			−0.355265			−0.177633	+	0.984097i	$0.556844\pi$
$812$			1.10084i			0.0386319i
$813$	−17.1207			−0.600449
$814$	−10.4362	+	12.8371i	−0.365789	+	0.449940i
$815$		0			0
$816$		−	10.8793i		−	0.380852i
$817$	−0.677618			−0.0237069
$818$	−3.34836			−0.117073
$819$			2.96371i			0.103560i
$820$		0			0
$821$	5.68106			0.198270			0.0991351	−	0.995074i	$-0.468392\pi$
$821$	5.68106			0.198270			0.0991351	+	0.995074i	$0.468392\pi$
$822$			0.732814i			0.0255598i
$823$	22.3404			0.778738			0.389369	−	0.921082i	$-0.372693\pi$
$823$	22.3404			0.778738			0.389369	+	0.921082i	$0.372693\pi$
$824$	−14.1725			−0.493721
$825$		0			0
$826$	−11.1759			−0.388859
$827$			3.71639i			0.129231i	0.997910	+	0.0646157i	$0.0205822\pi$
$827$			3.71639i			0.129231i	−0.997910	+	0.0646157i	$0.979418\pi$
$828$			1.93793i			0.0673477i
$829$		−	15.8596i		−	0.550828i	−0.961326	−	0.275414i	$-0.911185\pi$
$829$		−	15.8596i		−	0.550828i	0.961326	−	0.275414i	$-0.0888149\pi$
$830$		0			0
$831$			59.5829i			2.06691i
$832$			0.941367i			0.0326360i
$833$		−	22.5466i		−	0.781193i
$834$			30.1173i			1.04288i
$835$		0			0
$836$			0.677618i			0.0234359i
$837$			8.52750i			0.294753i
$838$		−	11.3776i		−	0.393032i
$839$	−33.8950			−1.17018			−0.585092	−	0.810967i	$-0.698942\pi$
$839$	−33.8950			−1.17018			−0.585092	+	0.810967i	$0.698942\pi$
$840$		0			0
$841$	28.4819			0.982133
$842$	3.23109			0.111351
$843$		−	59.9862i		−	2.06604i
$844$	19.7716			0.680566
$845$		0			0
$846$			6.80949i			0.234115i
$847$	5.50945			0.189307
$848$	−8.39400			−0.288251
$849$			19.6413i			0.674089i
$850$		0			0
$851$	3.61211	−	4.44309i	0.123822	−	0.152307i
$852$	−6.87930			−0.235681
$853$		−	35.7586i		−	1.22435i	−0.790722	−	0.612175i	$-0.790295\pi$
$853$		−	35.7586i		−	1.22435i	0.790722	−	0.612175i	$-0.209705\pi$
$854$	10.4561			0.357800
$855$		0			0
$856$			10.6922i			0.365453i
$857$		−	17.3837i		−	0.593816i	−0.954906	−	0.296908i	$-0.904045\pi$
$857$		−	17.3837i		−	0.593816i	0.954906	−	0.296908i	$-0.0959554\pi$
$858$	−5.75859			−0.196595
$859$		−	43.3922i		−	1.48052i	−0.672319	−	0.740261i	$-0.734702\pi$
$859$		−	43.3922i		−	1.48052i	0.672319	−	0.740261i	$-0.265298\pi$
$860$		0			0
$861$	−28.4691			−0.970223
$862$	−29.2327			−0.995670
$863$	−34.8708			−1.18702			−0.593508	−	0.804828i	$-0.702257\pi$
$863$	−34.8708			−1.18702			−0.593508	+	0.804828i	$0.702257\pi$
$864$			2.11727i			0.0720309i
$865$		0			0
$866$		−	17.7655i		−	0.603695i
$867$	14.3887			0.488667
$868$			6.15947i			0.209066i
$869$		−	4.76203i		−	0.161541i
$870$		0			0
$871$		−	7.23797i		−	0.245249i
$872$	12.2767			0.415743
$873$		−	33.5078i		−	1.13407i
$874$		−	0.234533i		−	0.00793318i
$875$		0			0
$876$	−20.4983			−0.692573
$877$	−47.0907			−1.59014			−0.795070	−	0.606517i	$-0.792566\pi$
$877$	−47.0907			−1.59014			−0.795070	+	0.606517i	$0.792566\pi$
$878$	32.7604			1.10561
$879$	52.8140			1.78137
$880$		0			0
$881$	29.0027			0.977125			0.488562	−	0.872529i	$-0.337521\pi$
$881$	29.0027			0.977125			0.488562	+	0.872529i	$0.337521\pi$
$882$		−	9.59568i		−	0.323103i
$883$			11.0388i			0.371484i	0.982599	+	0.185742i	$0.0594689\pi$
$883$			11.0388i			0.371484i	−0.982599	+	0.185742i	$0.940531\pi$
$884$	−4.55348			−0.153150
$885$		0			0
$886$			0.600939i			0.0201890i
$887$	5.76709			0.193640			0.0968199	−	0.995302i	$-0.469133\pi$
$887$	5.76709			0.193640			0.0968199	+	0.995302i	$0.469133\pi$
$888$	−8.63016	+	10.6155i	−0.289609	+	0.356234i
$889$	12.7000			0.425943
$890$		0			0
$891$	−29.7492			−0.996637
$892$	−9.14143			−0.306078
$893$		−	0.824101i		−	0.0275775i
$894$		−	18.9897i		−	0.635110i
$895$		0			0
$896$			1.52932i			0.0510909i
$897$	1.99312			0.0665485
$898$	−34.0191			−1.13523
$899$	−2.89916			−0.0966924
$900$		0			0
$901$		−	40.6026i		−	1.35267i
$902$		−	22.5113i		−	0.749543i
$903$		−	9.35524i		−	0.311323i
$904$	2.95436			0.0982604
$905$		0			0
$906$			11.1138i			0.369232i
$907$			54.2139i			1.80014i	0.435742	+	0.900072i	$0.356486\pi$
$907$			54.2139i			1.80014i	−0.435742	+	0.900072i	$0.643514\pi$
$908$		−	18.7198i		−	0.621239i
$909$	−22.8793			−0.758858
$910$		0			0
$911$		−	37.1284i		−	1.23012i	−0.788480	−	0.615060i	$-0.789132\pi$
$911$		−	37.1284i		−	1.23012i	0.788480	−	0.615060i	$-0.210868\pi$
$912$			0.560352i			0.0185551i
$913$	−0.358675			−0.0118704
$914$	30.9215			1.02279
$915$		0			0
$916$	25.1138			0.829784
$917$			16.9345i			0.559226i
$918$	−10.2414			−0.338017
$919$		−	20.0889i		−	0.662672i	−0.943513	−	0.331336i	$-0.892501\pi$
$919$		−	20.0889i		−	0.662672i	0.943513	−	0.331336i	$-0.107499\pi$
$920$		0			0
$921$	61.2794			2.01923
$922$	1.27330			0.0419339
$923$			2.87930i			0.0947732i
$924$	−9.35524			−0.307765
$925$		0			0
$926$	−2.61555			−0.0859522
$927$		−	29.1759i		−	0.958262i
$928$	−0.719824			−0.0236294
$929$	12.9803			0.425871			0.212936	−	0.977066i	$-0.431698\pi$
$929$	12.9803			0.425871			0.212936	+	0.977066i	$0.431698\pi$
$930$		0			0
$931$			1.16129i			0.0380598i
$932$	20.4362			0.669410
$933$		−	39.8138i		−	1.30344i
$934$	−19.0096			−0.622012
$935$		0			0
$936$	−1.93793			−0.0633432
$937$	9.32238			0.304549			0.152274	−	0.988338i	$-0.451340\pi$
$937$	9.32238			0.304549			0.152274	+	0.988338i	$0.451340\pi$
$938$		−	11.7586i		−	0.383932i
$939$		−	53.9639i		−	1.76105i
$940$		0			0
$941$	−17.7586			−0.578914			−0.289457	−	0.957191i	$-0.593475\pi$
$941$	−17.7586			−0.578914			−0.289457	+	0.957191i	$0.593475\pi$
$942$			43.3484i			1.41237i
$943$			7.79145i			0.253724i
$944$		−	7.30777i		−	0.237848i
$945$		0			0
$946$	7.39744			0.240512
$947$			17.3354i			0.563324i	0.959514	+	0.281662i	$0.0908857\pi$
$947$			17.3354i			0.563324i	−0.959514	+	0.281662i	$0.909114\pi$
$948$		−	3.93793i		−	0.127898i
$949$			8.57946i			0.278501i
$950$		0			0
$951$	−7.11383			−0.230682
$952$	−7.39744			−0.239752
$953$	5.88961			0.190783			0.0953916	−	0.995440i	$-0.469590\pi$
$953$	5.88961			0.190783			0.0953916	+	0.995440i	$0.469590\pi$
$954$		−	17.2802i		−	0.559466i
$955$		0			0
$956$		−	8.91377i		−	0.288292i
$957$		−	4.40335i		−	0.142340i
$958$	−38.8578			−1.25544
$959$	0.498281			0.0160903
$960$		0			0
$961$	14.7785			0.476724
$962$	4.44309	+	3.61211i	0.143251	+	0.116459i
$963$	−22.0114			−0.709307
$964$		−	13.8827i		−	0.447133i
$965$		0			0
$966$	3.23797			0.104180
$967$			32.3189i			1.03931i	0.854377	+	0.519654i	$0.173939\pi$
$967$			32.3189i			1.03931i	−0.854377	+	0.519654i	$0.826061\pi$
$968$			3.60256i			0.115791i
$969$	−2.71047			−0.0870730
$970$		0			0
$971$	6.11115			0.196116			0.0980581	−	0.995181i	$-0.468737\pi$
$971$	6.11115			0.196116			0.0980581	+	0.995181i	$0.468737\pi$
$972$	−18.2491			−0.585341
$973$	20.4784			0.656508
$974$	38.4914			1.23334
$975$		0			0
$976$			6.83709i			0.218850i
$977$		−	47.3906i		−	1.51616i	−0.652162	−	0.758079i	$-0.726138\pi$
$977$		−	47.3906i		−	1.51616i	0.652162	−	0.758079i	$-0.273862\pi$
$978$	38.9897			1.24675
$979$		−	24.4691i		−	0.782035i
$980$		0			0
$981$			25.2733i			0.806914i
$982$		−	11.2672i		−	0.359550i
$983$	55.7862			1.77930			0.889652	−	0.456640i	$-0.150947\pi$
$983$	55.7862			1.77930			0.889652	+	0.456640i	$0.150947\pi$
$984$		−	18.6155i		−	0.593442i
$985$		0			0
$986$		−	3.48185i		−	0.110885i
$987$	11.3776			0.362152
$988$	0.234533			0.00746148
$989$	−2.56035			−0.0814145
$990$		0			0
$991$			29.9655i			0.951886i	0.879476	+	0.475943i	$0.157893\pi$
$991$			29.9655i			0.951886i	−0.879476	+	0.475943i	$0.842107\pi$
$992$	−4.02760			−0.127876
$993$		−	10.0844i		−	0.320019i
$994$			4.67762i			0.148365i
$995$		0			0
$996$	−0.296604			−0.00939825
$997$			20.7811i			0.658145i	0.944305	+	0.329073i	$0.106736\pi$
$997$			20.7811i			0.658145i	−0.944305	+	0.329073i	$0.893264\pi$
$998$	20.8578			0.660243
$999$	9.99312	+	8.12414i	0.316168	+	0.257036i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1850.2.d.f.1701.4		6
5.2	odd	4		1850.2.c.i.1849.5		6
5.3	odd	4		1850.2.c.j.1849.2		6
5.4	even	2		370.2.d.c.221.3	✓	6
15.14	odd	2		3330.2.h.n.2071.5		6
20.19	odd	2		2960.2.p.g.961.2		6
37.36	even	2	inner	1850.2.d.f.1701.1		6
185.73	odd	4		1850.2.c.i.1849.2		6
185.147	odd	4		1850.2.c.j.1849.5		6
185.184	even	2		370.2.d.c.221.6	yes	6
555.554	odd	2		3330.2.h.n.2071.2		6
740.739	odd	2		2960.2.p.g.961.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.d.c.221.3	✓	6	5.4	even	2
370.2.d.c.221.6	yes	6	185.184	even	2
1850.2.c.i.1849.2		6	185.73	odd	4
1850.2.c.i.1849.5		6	5.2	odd	4
1850.2.c.j.1849.2		6	5.3	odd	4
1850.2.c.j.1849.5		6	185.147	odd	4
1850.2.d.f.1701.1		6	37.36	even	2	inner
1850.2.d.f.1701.4		6	1.1	even	1	trivial
2960.2.p.g.961.1		6	740.739	odd	2
2960.2.p.g.961.2		6	20.19	odd	2
3330.2.h.n.2071.2		6	555.554	odd	2
3330.2.h.n.2071.5		6	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1850.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -2.24914 q^{3} -1.00000 q^{4} -2.24914i q^{6} -1.52932 q^{7} -1.00000i q^{8} +2.05863 q^{9} +2.71982 q^{11} +2.24914 q^{12} -0.941367i q^{13} -1.52932i q^{14} +1.00000 q^{16} +4.83709i q^{17} +2.05863i q^{18} -0.249141i q^{19} +3.43965 q^{21} +2.71982i q^{22} -0.941367i q^{23} +2.24914i q^{24} +0.941367 q^{26} +2.11727 q^{27} +1.52932 q^{28} +0.719824i q^{29} +4.02760i q^{31} +1.00000i q^{32} -6.11727 q^{33} -4.83709 q^{34} -2.05863 q^{36} +(4.71982 + 3.83709i) q^{37} +0.249141 q^{38} +2.11727i q^{39} -8.27674 q^{41} +3.43965i q^{42} -2.71982i q^{43} -2.71982 q^{44} +0.941367 q^{46} +3.30777 q^{47} -2.24914 q^{48} -4.66119 q^{49} -10.8793i q^{51} +0.941367i q^{52} -8.39400 q^{53} +2.11727i q^{54} +1.52932i q^{56} +0.560352i q^{57} -0.719824 q^{58} -7.30777i q^{59} +6.83709i q^{61} -4.02760 q^{62} -3.14830 q^{63} -1.00000 q^{64} -6.11727i q^{66} +7.68879 q^{67} -4.83709i q^{68} +2.11727i q^{69} -3.05863 q^{71} -2.05863i q^{72} -9.11383 q^{73} +(-3.83709 + 4.71982i) q^{74} +0.249141i q^{76} -4.15947 q^{77} -2.11727 q^{78} -1.75086i q^{79} -10.9379 q^{81} -8.27674i q^{82} -0.131874 q^{83} -3.43965 q^{84} +2.71982 q^{86} -1.61899i q^{87} -2.71982i q^{88} -8.99656i q^{89} +1.43965i q^{91} +0.941367i q^{92} -9.05863i q^{93} +3.30777i q^{94} -2.24914i q^{96} -16.2767i q^{97} -4.66119i q^{98} +5.59912 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 4 q^{3} - 6 q^{4} - 10 q^{7} + 14 q^{9} - 2 q^{11} - 4 q^{12} + 6 q^{16} - 16 q^{21} + 4 q^{26} + 16 q^{27} + 10 q^{28} - 40 q^{33} - 14 q^{34} - 14 q^{36} + 10 q^{37} - 16 q^{38} + 2 q^{41} + 2 q^{44}+ \cdots - 58 q^{99}+O(q^{100}) \) 6 * q + 4 * q^3 - 6 * q^4 - 10 * q^7 + 14 * q^9 - 2 * q^11 - 4 * q^12 + 6 * q^16 - 16 * q^21 + 4 * q^26 + 16 * q^27 + 10 * q^28 - 40 * q^33 - 14 * q^34 - 14 * q^36 + 10 * q^37 - 16 * q^38 + 2 * q^41 + 2 * q^44 + 4 * q^46 + 4 * q^47 + 4 * q^48 - 8 * q^49 - 2 * q^53 + 14 * q^58 + 10 * q^62 - 58 * q^63 - 6 * q^64 - 8 * q^67 - 20 * q^71 + 12 * q^73 - 8 * q^74 + 30 * q^77 - 16 * q^78 + 6 * q^81 + 20 * q^83 + 16 * q^84 - 2 * q^86 - 58 * q^99

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