LMFDB - Embedded newform 1890.2.b.d.1511.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(1511,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("1890.1511");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 34x^{10} + 413x^{8} + 2164x^{6} + 4688x^{4} + 3688x^{2} + 676 $ x^12 + 34x^10 + 413x^8 + 2164x^6 + 4688x^4 + 3688*x^2 + 676
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1511.10
Root			$-2.63707i$ of defining polynomial
Character	$\chi$	$=$	1890.1511
Dual form			1890.2.b.d.1511.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +1.00000 q^{5} +(-0.00866574 - 2.64574i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +1.00000 q^{5} +(-0.00866574 - 2.64574i) q^{7} -1.00000i q^{8} +1.00000i q^{10} -1.93681i q^{11} +2.70838i q^{13} +(2.64574 - 0.00866574i) q^{14} +1.00000 q^{16} -7.22829 q^{17} -1.98267i q^{19} -1.00000 q^{20} +1.93681 q^{22} -4.56577i q^{23} +1.00000 q^{25} -2.70838 q^{26} +(0.00866574 + 2.64574i) q^{28} +2.75784i q^{29} -5.66252i q^{31} +1.00000i q^{32} -7.22829i q^{34} +(-0.00866574 - 2.64574i) q^{35} +5.77925 q^{37} +1.98267 q^{38} -1.00000i q^{40} -6.67733 q^{41} -7.37090 q^{43} +1.93681i q^{44} +4.56577 q^{46} -2.22844 q^{47} +(-6.99985 + 0.0458545i) q^{49} +1.00000i q^{50} -2.70838i q^{52} +10.7082i q^{53} -1.93681i q^{55} +(-2.64574 + 0.00866574i) q^{56} -2.75784 q^{58} -11.7446 q^{59} -8.87348i q^{61} +5.66252 q^{62} -1.00000 q^{64} +2.70838i q^{65} -13.9997 q^{67} +7.22829 q^{68} +(2.64574 - 0.00866574i) q^{70} -11.6529i q^{71} -14.9097i q^{73} +5.77925i q^{74} +1.98267i q^{76} +(-5.12430 + 0.0167839i) q^{77} +11.6666 q^{79} +1.00000 q^{80} -6.67733i q^{82} +1.98267 q^{83} -7.22829 q^{85} -7.37090i q^{86} -1.93681 q^{88} +1.54312 q^{89} +(7.16565 - 0.0234701i) q^{91} +4.56577i q^{92} -2.22844i q^{94} -1.98267i q^{95} +1.41785i q^{97} +(-0.0458545 - 6.99985i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) $ 12 * q - 12 * q^4 + 12 * q^5 - 4 * q^7	$ 12 q - 12 q^{4} + 12 q^{5} - 4 q^{7} + 12 q^{16} - 12 q^{20} + 12 q^{25} - 8 q^{26} + 4 q^{28} - 4 q^{35} - 32 q^{37} + 16 q^{38} - 8 q^{41} - 24 q^{43} + 8 q^{46} - 28 q^{47} + 4 q^{49} + 8 q^{58} - 24 q^{59} + 28 q^{62} - 12 q^{64} + 8 q^{67} + 28 q^{77} + 32 q^{79} + 12 q^{80} + 16 q^{83} + 16 q^{89} - 8 q^{91} - 16 q^{98}+O(q^{100}) $ 12 * q - 12 * q^4 + 12 * q^5 - 4 * q^7 + 12 * q^16 - 12 * q^20 + 12 * q^25 - 8 * q^26 + 4 * q^28 - 4 * q^35 - 32 * q^37 + 16 * q^38 - 8 * q^41 - 24 * q^43 + 8 * q^46 - 28 * q^47 + 4 * q^49 + 8 * q^58 - 24 * q^59 + 28 * q^62 - 12 * q^64 + 8 * q^67 + 28 * q^77 + 32 * q^79 + 12 * q^80 + 16 * q^83 + 16 * q^89 - 8 * q^91 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$-1$	$-1$

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
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	−0.00866574	−	2.64574i	−0.00327534	−	0.999995i
$7$	−0.00866574	−	2.64574i	−0.00327534	−	0.999995i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$			1.00000i			0.316228i
$11$		−	1.93681i		−	0.583971i	−0.956423	−	0.291986i	$-0.905684\pi$
$11$		−	1.93681i		−	0.583971i	0.956423	−	0.291986i	$-0.0943160\pi$
$12$		0			0
$13$			2.70838i			0.751168i	0.926788	+	0.375584i	$0.122558\pi$
$13$			2.70838i			0.751168i	−0.926788	+	0.375584i	$0.877442\pi$
$14$	2.64574	−	0.00866574i	0.707103	−	0.00231602i
$15$		0			0
$16$	1.00000			0.250000
$17$	−7.22829			−1.75312			−0.876559	−	0.481295i	$-0.840167\pi$
$17$	−7.22829			−1.75312			−0.876559	+	0.481295i	$0.840167\pi$
$18$		0			0
$19$		−	1.98267i		−	0.454855i	−0.973795	−	0.227428i	$-0.926968\pi$
$19$		−	1.98267i		−	0.454855i	0.973795	−	0.227428i	$-0.0730315\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	1.93681			0.412930
$23$		−	4.56577i		−	0.952028i	−0.879438	−	0.476014i	$-0.842081\pi$
$23$		−	4.56577i		−	0.952028i	0.879438	−	0.476014i	$-0.157919\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−2.70838			−0.531156
$27$		0			0
$28$	0.00866574	+	2.64574i	0.00163767	+	0.499997i
$29$			2.75784i			0.512119i	0.966661	+	0.256059i	$0.0824242\pi$
$29$			2.75784i			0.512119i	−0.966661	+	0.256059i	$0.917576\pi$
$30$		0			0
$31$		−	5.66252i		−	1.01702i	−0.861056	−	0.508509i	$-0.830197\pi$
$31$		−	5.66252i		−	1.01702i	0.861056	−	0.508509i	$-0.169803\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$		−	7.22829i		−	1.23964i
$35$	−0.00866574	−	2.64574i	−0.00146478	−	0.447211i
$36$		0			0
$37$	5.77925			0.950103			0.475052	−	0.879958i	$-0.342429\pi$
$37$	5.77925			0.950103			0.475052	+	0.879958i	$0.342429\pi$
$38$	1.98267			0.321631
$39$		0			0
$40$		−	1.00000i		−	0.158114i
$41$	−6.67733			−1.04282			−0.521412	−	0.853305i	$-0.674594\pi$
$41$	−6.67733			−1.04282			−0.521412	+	0.853305i	$0.674594\pi$
$42$		0			0
$43$	−7.37090			−1.12405			−0.562026	−	0.827120i	$-0.689978\pi$
$43$	−7.37090			−1.12405			−0.562026	+	0.827120i	$0.689978\pi$
$44$			1.93681i			0.291986i
$45$		0			0
$46$	4.56577			0.673186
$47$	−2.22844			−0.325051			−0.162526	−	0.986704i	$-0.551964\pi$
$47$	−2.22844			−0.325051			−0.162526	+	0.986704i	$0.551964\pi$
$48$		0			0
$49$	−6.99985	+	0.0458545i	−0.999979	+	0.00655065i
$50$			1.00000i			0.141421i
$51$		0			0
$52$		−	2.70838i		−	0.375584i
$53$			10.7082i			1.47089i	0.677586	+	0.735444i	$0.263026\pi$
$53$			10.7082i			1.47089i	−0.677586	+	0.735444i	$0.736974\pi$
$54$		0			0
$55$		−	1.93681i		−	0.261160i
$56$	−2.64574	+	0.00866574i	−0.353551	+	0.00115801i
$57$		0			0
$58$	−2.75784			−0.362123
$59$	−11.7446			−1.52902			−0.764508	−	0.644615i	$-0.777018\pi$
$59$	−11.7446			−1.52902			−0.764508	+	0.644615i	$0.777018\pi$
$60$		0			0
$61$		−	8.87348i		−	1.13613i	−0.822983	−	0.568066i	$-0.807692\pi$
$61$		−	8.87348i		−	1.13613i	0.822983	−	0.568066i	$-0.192308\pi$
$62$	5.66252			0.719141
$63$		0			0
$64$	−1.00000			−0.125000
$65$			2.70838i			0.335933i
$66$		0			0
$67$	−13.9997			−1.71034			−0.855168	−	0.518351i	$-0.826546\pi$
$67$	−13.9997			−1.71034			−0.855168	+	0.518351i	$0.826546\pi$
$68$	7.22829			0.876559
$69$		0			0
$70$	2.64574	−	0.00866574i	0.316226	−	0.00103575i
$71$		−	11.6529i		−	1.38294i	−0.722404	−	0.691471i	$-0.756963\pi$
$71$		−	11.6529i		−	1.38294i	0.722404	−	0.691471i	$-0.243037\pi$
$72$		0			0
$73$		−	14.9097i		−	1.74505i	−0.488572	−	0.872524i	$-0.662482\pi$
$73$		−	14.9097i		−	1.74505i	0.488572	−	0.872524i	$-0.337518\pi$
$74$			5.77925i			0.671824i
$75$		0			0
$76$			1.98267i			0.227428i
$77$	−5.12430	+	0.0167839i	−0.583968	+	0.00191271i
$78$		0			0
$79$	11.6666			1.31259			0.656297	−	0.754502i	$-0.272122\pi$
$79$	11.6666			1.31259			0.656297	+	0.754502i	$0.272122\pi$
$80$	1.00000			0.111803
$81$		0			0
$82$		−	6.67733i		−	0.737387i
$83$	1.98267			0.217626			0.108813	−	0.994062i	$-0.465295\pi$
$83$	1.98267			0.217626			0.108813	+	0.994062i	$0.465295\pi$
$84$		0			0
$85$	−7.22829			−0.784018
$86$		−	7.37090i		−	0.794824i
$87$		0			0
$88$	−1.93681			−0.206465
$89$	1.54312			0.163571			0.0817854	−	0.996650i	$-0.473938\pi$
$89$	1.54312			0.163571			0.0817854	+	0.996650i	$0.473938\pi$
$90$		0			0
$91$	7.16565	−	0.0234701i	0.751164	−	0.00246033i
$92$			4.56577i			0.476014i
$93$		0			0
$94$		−	2.22844i		−	0.229846i
$95$		−	1.98267i		−	0.203417i
$96$		0			0
$97$			1.41785i			0.143960i	0.997406	+	0.0719802i	$0.0229319\pi$
$97$			1.41785i			0.143960i	−0.997406	+	0.0719802i	$0.977068\pi$
$98$	−0.0458545	−	6.99985i	−0.00463201	−	0.707092i
$99$		0			0
$100$	−1.00000			−0.100000
$101$	−2.74194			−0.272834			−0.136417	−	0.990652i	$-0.543559\pi$
$101$	−2.74194			−0.272834			−0.136417	+	0.990652i	$0.543559\pi$
$102$		0			0
$103$		−	11.1998i		−	1.10355i	−0.833994	−	0.551773i	$-0.813952\pi$
$103$		−	11.1998i		−	1.10355i	0.833994	−	0.551773i	$-0.186048\pi$
$104$	2.70838			0.265578
$105$		0			0
$106$	−10.7082			−1.04007
$107$			10.7309i			1.03739i	0.854959	+	0.518696i	$0.173582\pi$
$107$			10.7309i			1.03739i	−0.854959	+	0.518696i	$0.826418\pi$
$108$		0			0
$109$	1.84006			0.176246			0.0881229	−	0.996110i	$-0.471913\pi$
$109$	1.84006			0.176246			0.0881229	+	0.996110i	$0.471913\pi$
$110$	1.93681			0.184668
$111$		0			0
$112$	−0.00866574	−	2.64574i	−0.000818835	−	0.249999i
$113$		−	12.6838i		−	1.19319i	−0.802543	−	0.596595i	$-0.796520\pi$
$113$		−	12.6838i		−	1.19319i	0.802543	−	0.596595i	$-0.203480\pi$
$114$		0			0
$115$		−	4.56577i		−	0.425760i
$116$		−	2.75784i		−	0.256059i
$117$		0			0
$118$		−	11.7446i		−	1.08118i
$119$	0.0626385	+	19.1242i	0.00574206	+	1.75311i
$120$		0			0
$121$	7.24875			0.658977
$122$	8.87348			0.803367
$123$		0			0
$124$			5.66252i			0.508509i
$125$	1.00000			0.0894427
$126$		0			0
$127$	13.9352			1.23655			0.618276	−	0.785961i	$-0.287831\pi$
$127$	13.9352			1.23655			0.618276	+	0.785961i	$0.287831\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	−2.70838			−0.237540
$131$	4.36156			0.381071			0.190535	−	0.981680i	$-0.438978\pi$
$131$	4.36156			0.381071			0.190535	+	0.981680i	$0.438978\pi$
$132$		0			0
$133$	−5.24562	+	0.0171813i	−0.454853	+	0.00148981i
$134$		−	13.9997i		−	1.20939i
$135$		0			0
$136$			7.22829i			0.619821i
$137$			6.89081i			0.588722i	0.955694	+	0.294361i	$0.0951067\pi$
$137$			6.89081i			0.588722i	−0.955694	+	0.294361i	$0.904893\pi$
$138$		0			0
$139$		−	12.0344i		−	1.02074i	−0.859955	−	0.510371i	$-0.829508\pi$
$139$		−	12.0344i		−	1.02074i	0.859955	−	0.510371i	$-0.170492\pi$
$140$	0.00866574	+	2.64574i	0.000732389	+	0.223606i
$141$		0			0
$142$	11.6529			0.977888
$143$	5.24562			0.438661
$144$		0			0
$145$			2.75784i			0.229026i
$146$	14.9097			1.23393
$147$		0			0
$148$	−5.77925			−0.475052
$149$			9.33623i			0.764854i	0.923986	+	0.382427i	$0.124912\pi$
$149$			9.33623i			0.764854i	−0.923986	+	0.382427i	$0.875088\pi$
$150$		0			0
$151$	17.0559			1.38799			0.693995	−	0.719980i	$-0.255849\pi$
$151$	17.0559			1.38799			0.693995	+	0.719980i	$0.255849\pi$
$152$	−1.98267			−0.160816
$153$		0			0
$154$	−0.0167839	−	5.12430i	−0.00135249	−	0.412928i
$155$		−	5.66252i		−	0.454825i
$156$		0			0
$157$		−	9.90924i		−	0.790843i	−0.918500	−	0.395422i	$-0.870599\pi$
$157$		−	9.90924i		−	0.790843i	0.918500	−	0.395422i	$-0.129401\pi$
$158$			11.6666i			0.928145i
$159$		0			0
$160$			1.00000i			0.0790569i
$161$	−12.0798	+	0.0395657i	−0.952023	+	0.00311822i
$162$		0			0
$163$	8.47282			0.663643			0.331821	−	0.943342i	$-0.392337\pi$
$163$	8.47282			0.663643			0.331821	+	0.943342i	$0.392337\pi$
$164$	6.67733			0.521412
$165$		0			0
$166$			1.98267i			0.153885i
$167$	3.01718			0.233476			0.116738	−	0.993163i	$-0.462756\pi$
$167$	3.01718			0.233476			0.116738	+	0.993163i	$0.462756\pi$
$168$		0			0
$169$	5.66470			0.435746
$170$		−	7.22829i		−	0.554384i
$171$		0			0
$172$	7.37090			0.562026
$173$	−23.4738			−1.78468			−0.892338	−	0.451367i	$-0.850937\pi$
$173$	−23.4738			−1.78468			−0.892338	+	0.451367i	$0.850937\pi$
$174$		0			0
$175$	−0.00866574	−	2.64574i	−0.000655068	−	0.199999i
$176$		−	1.93681i		−	0.145993i
$177$		0			0
$178$			1.54312i			0.115662i
$179$			0.491540i			0.0367394i	0.999831	+	0.0183697i	$0.00584759\pi$
$179$			0.491540i			0.0367394i	−0.999831	+	0.0183697i	$0.994152\pi$
$180$		0			0
$181$		−	8.00696i		−	0.595153i	−0.954698	−	0.297576i	$-0.903822\pi$
$181$		−	8.00696i		−	0.595153i	0.954698	−	0.297576i	$-0.0961783\pi$
$182$	0.0234701	+	7.16565i	0.00173972	+	0.531153i
$183$		0			0
$184$	−4.56577			−0.336593
$185$	5.77925			0.424899
$186$		0			0
$187$			13.9998i			1.02377i
$188$	2.22844			0.162526
$189$		0			0
$190$	1.98267			0.143838
$191$		−	19.7296i		−	1.42759i	−0.700357	−	0.713793i	$-0.746976\pi$
$191$		−	19.7296i		−	1.42759i	0.700357	−	0.713793i	$-0.253024\pi$
$192$		0			0
$193$	−14.4739			−1.04185			−0.520927	−	0.853601i	$-0.674414\pi$
$193$	−14.4739			−1.04185			−0.520927	+	0.853601i	$0.674414\pi$
$194$	−1.41785			−0.101795
$195$		0			0
$196$	6.99985	−	0.0458545i	0.499989	−	0.00327532i
$197$			4.18955i			0.298493i	0.988800	+	0.149246i	$0.0476848\pi$
$197$			4.18955i			0.298493i	−0.988800	+	0.149246i	$0.952315\pi$
$198$		0			0
$199$			24.9132i			1.76605i	0.469329	+	0.883024i	$0.344496\pi$
$199$			24.9132i			1.76605i	−0.469329	+	0.883024i	$0.655504\pi$
$200$		−	1.00000i		−	0.0707107i
$201$		0			0
$202$		−	2.74194i		−	0.192922i
$203$	7.29653	−	0.0238987i	0.512116	−	0.00167736i
$204$		0			0
$205$	−6.67733			−0.466365
$206$	11.1998			0.780325
$207$		0			0
$208$			2.70838i			0.187792i
$209$	−3.84006			−0.265623
$210$		0			0
$211$	−26.5757			−1.82955			−0.914773	−	0.403969i	$-0.867630\pi$
$211$	−26.5757			−1.82955			−0.914773	+	0.403969i	$0.867630\pi$
$212$		−	10.7082i		−	0.735444i
$213$		0			0
$214$	−10.7309			−0.733547
$215$	−7.37090			−0.502691
$216$		0			0
$217$	−14.9815	+	0.0490699i	−1.01701	+	0.00333108i
$218$			1.84006i			0.124625i
$219$		0			0
$220$			1.93681i			0.130580i
$221$		−	19.5769i		−	1.31689i
$222$		0			0
$223$			5.90829i			0.395648i	0.980238	+	0.197824i	$0.0633875\pi$
$223$			5.90829i			0.395648i	−0.980238	+	0.197824i	$0.936612\pi$
$224$	2.64574	−	0.00866574i	0.176776	−	0.000579004i
$225$		0			0
$226$	12.6838			0.843712
$227$	16.7418			1.11119			0.555596	−	0.831452i	$-0.312490\pi$
$227$	16.7418			1.11119			0.555596	+	0.831452i	$0.312490\pi$
$228$		0			0
$229$			1.83897i			0.121522i	0.998152	+	0.0607611i	$0.0193528\pi$
$229$			1.83897i			0.121522i	−0.998152	+	0.0607611i	$0.980647\pi$
$230$	4.56577			0.301058
$231$		0			0
$232$	2.75784			0.181061
$233$			1.17822i			0.0771875i	0.999255	+	0.0385938i	$0.0122878\pi$
$233$			1.17822i			0.0771875i	−0.999255	+	0.0385938i	$0.987712\pi$
$234$		0			0
$235$	−2.22844			−0.145367
$236$	11.7446			0.764508
$237$		0			0
$238$	−19.1242	+	0.0626385i	−1.23963	+	0.00406025i
$239$		−	2.75676i		−	0.178320i	−0.996017	−	0.0891599i	$-0.971582\pi$
$239$		−	2.75676i		−	0.178320i	0.996017	−	0.0891599i	$-0.0284182\pi$
$240$		0			0
$241$			3.79421i			0.244406i	0.992505	+	0.122203i	$0.0389959\pi$
$241$			3.79421i			0.244406i	−0.992505	+	0.122203i	$0.961004\pi$
$242$			7.24875i			0.465967i
$243$		0			0
$244$			8.87348i			0.568066i
$245$	−6.99985	+	0.0458545i	−0.447204	+	0.00292954i
$246$		0			0
$247$	5.36981			0.341673
$248$	−5.66252			−0.359570
$249$		0			0
$250$			1.00000i			0.0632456i
$251$	16.1061			1.01661			0.508305	−	0.861177i	$-0.330272\pi$
$251$	16.1061			1.01661			0.508305	+	0.861177i	$0.330272\pi$
$252$		0			0
$253$	−8.84304			−0.555957
$254$			13.9352i			0.874374i
$255$		0			0
$256$	1.00000			0.0625000
$257$	9.70415			0.605328			0.302664	−	0.953097i	$-0.402124\pi$
$257$	9.70415			0.605328			0.302664	+	0.953097i	$0.402124\pi$
$258$		0			0
$259$	−0.0500815	−	15.2904i	−0.00311191	−	0.950098i
$260$		−	2.70838i		−	0.167966i
$261$		0			0
$262$			4.36156i			0.269458i
$263$		−	8.65227i		−	0.533522i	−0.963763	−	0.266761i	$-0.914047\pi$
$263$		−	8.65227i		−	0.533522i	0.963763	−	0.266761i	$-0.0859534\pi$
$264$		0			0
$265$			10.7082i			0.657801i
$266$	−0.0171813	−	5.24562i	−0.00105345	−	0.321630i
$267$		0			0
$268$	13.9997			0.855168
$269$	1.66459			0.101492			0.0507460	−	0.998712i	$-0.483840\pi$
$269$	1.66459			0.101492			0.0507460	+	0.998712i	$0.483840\pi$
$270$		0			0
$271$		−	15.5359i		−	0.943736i	−0.881669	−	0.471868i	$-0.843580\pi$
$271$		−	15.5359i		−	0.943736i	0.881669	−	0.471868i	$-0.156420\pi$
$272$	−7.22829			−0.438279
$273$		0			0
$274$	−6.89081			−0.416289
$275$		−	1.93681i		−	0.116794i
$276$		0			0
$277$	2.80103			0.168298			0.0841488	−	0.996453i	$-0.473183\pi$
$277$	2.80103			0.168298			0.0841488	+	0.996453i	$0.473183\pi$
$278$	12.0344			0.721773
$279$		0			0
$280$	−2.64574	+	0.00866574i	−0.158113	+	0.000517877i
$281$		−	25.3801i		−	1.51405i	−0.653385	−	0.757026i	$-0.726652\pi$
$281$		−	25.3801i		−	1.51405i	0.653385	−	0.757026i	$-0.273348\pi$
$282$		0			0
$283$			29.6822i			1.76442i	0.470853	+	0.882211i	$0.343946\pi$
$283$			29.6822i			1.76442i	−0.470853	+	0.882211i	$0.656054\pi$
$284$			11.6529i			0.691471i
$285$		0			0
$286$			5.24562i			0.310180i
$287$	0.0578640	+	17.6664i	0.00341560	+	1.04282i
$288$		0			0
$289$	35.2482			2.07342
$290$	−2.75784			−0.161946
$291$		0			0
$292$			14.9097i			0.872524i
$293$	−17.1968			−1.00465			−0.502323	−	0.864680i	$-0.667521\pi$
$293$	−17.1968			−1.00465			−0.502323	+	0.864680i	$0.667521\pi$
$294$		0			0
$295$	−11.7446			−0.683796
$296$		−	5.77925i		−	0.335912i
$297$		0			0
$298$	−9.33623			−0.540833
$299$	12.3658			0.715133
$300$		0			0
$301$	0.0638743	+	19.5015i	0.00368165	+	1.12405i
$302$			17.0559i			0.981457i
$303$		0			0
$304$		−	1.98267i		−	0.113714i
$305$		−	8.87348i		−	0.508094i
$306$		0			0
$307$			3.64191i			0.207855i	0.994585	+	0.103927i	$0.0331409\pi$
$307$			3.64191i			0.207855i	−0.994585	+	0.103927i	$0.966859\pi$
$308$	5.12430	−	0.0167839i	0.291984	−	0.000956353i
$309$		0			0
$310$	5.66252			0.321610
$311$	−20.1943			−1.14511			−0.572557	−	0.819865i	$-0.694048\pi$
$311$	−20.1943			−1.14511			−0.572557	+	0.819865i	$0.694048\pi$
$312$		0			0
$313$			27.9080i			1.57745i	0.614744	+	0.788726i	$0.289259\pi$
$313$			27.9080i			1.57745i	−0.614744	+	0.788726i	$0.710741\pi$
$314$	9.90924			0.559211
$315$		0			0
$316$	−11.6666			−0.656297
$317$			25.7816i			1.44804i	0.689779	+	0.724020i	$0.257708\pi$
$317$			25.7816i			1.44804i	−0.689779	+	0.724020i	$0.742292\pi$
$318$		0			0
$319$	5.34143			0.299063
$320$	−1.00000			−0.0559017
$321$		0			0
$322$	−0.0395657	−	12.0798i	−0.00220491	−	0.673182i
$323$			14.3313i			0.797415i
$324$		0			0
$325$			2.70838i			0.150234i
$326$			8.47282i			0.469266i
$327$		0			0
$328$			6.67733i			0.368694i
$329$	0.0193111	+	5.89586i	0.00106465	+	0.325049i
$330$		0			0
$331$	24.1188			1.32569			0.662845	−	0.748757i	$-0.269349\pi$
$331$	24.1188			1.32569			0.662845	+	0.748757i	$0.269349\pi$
$332$	−1.98267			−0.108813
$333$		0			0
$334$			3.01718i			0.165093i
$335$	−13.9997			−0.764885
$336$		0			0
$337$	−27.5238			−1.49932			−0.749660	−	0.661824i	$-0.769783\pi$
$337$	−27.5238			−1.49932			−0.749660	+	0.661824i	$0.769783\pi$
$338$			5.66470i			0.308119i
$339$		0			0
$340$	7.22829			0.392009
$341$	−10.9673			−0.593910
$342$		0			0
$343$	0.181978	+	18.5194i	0.00982588	+	0.999952i
$344$			7.37090i			0.397412i
$345$		0			0
$346$		−	23.4738i		−	1.26196i
$347$			26.6045i			1.42820i	0.700042	+	0.714102i	$0.253165\pi$
$347$			26.6045i			1.42820i	−0.700042	+	0.714102i	$0.746835\pi$
$348$		0			0
$349$			3.16431i			0.169381i	0.996407	+	0.0846907i	$0.0269902\pi$
$349$			3.16431i			0.169381i	−0.996407	+	0.0846907i	$0.973010\pi$
$350$	2.64574	−	0.00866574i	0.141421	−	0.000463203i
$351$		0			0
$352$	1.93681			0.103233
$353$	−24.9081			−1.32572			−0.662862	−	0.748741i	$-0.730659\pi$
$353$	−24.9081			−1.32572			−0.662862	+	0.748741i	$0.730659\pi$
$354$		0			0
$355$		−	11.6529i		−	0.618471i
$356$	−1.54312			−0.0817854
$357$		0			0
$358$	−0.491540			−0.0259787
$359$		−	4.01733i		−	0.212027i	−0.994365	−	0.106013i	$-0.966191\pi$
$359$		−	4.01733i		−	0.212027i	0.994365	−	0.106013i	$-0.0338086\pi$
$360$		0			0
$361$	15.0690			0.793107
$362$	8.00696			0.420837
$363$		0			0
$364$	−7.16565	+	0.0234701i	−0.375582	+	0.00123017i
$365$		−	14.9097i		−	0.780409i
$366$		0			0
$367$			5.23333i			0.273178i	0.990628	+	0.136589i	$0.0436139\pi$
$367$			5.23333i			0.273178i	−0.990628	+	0.136589i	$0.956386\pi$
$368$		−	4.56577i		−	0.238007i
$369$		0			0
$370$			5.77925i			0.300449i
$371$	28.3311	−	0.0927947i	1.47088	−	0.00481766i
$372$		0			0
$373$	−3.51440			−0.181969			−0.0909845	−	0.995852i	$-0.529001\pi$
$373$	−3.51440			−0.181969			−0.0909845	+	0.995852i	$0.529001\pi$
$374$	−13.9998			−0.723915
$375$		0			0
$376$			2.22844i			0.114923i
$377$	−7.46927			−0.384687
$378$		0			0
$379$	−11.9938			−0.616082			−0.308041	−	0.951373i	$-0.599673\pi$
$379$	−11.9938			−0.616082			−0.308041	+	0.951373i	$0.599673\pi$
$380$			1.98267i			0.101709i
$381$		0			0
$382$	19.7296			1.00946
$383$	17.2456			0.881210			0.440605	−	0.897701i	$-0.354764\pi$
$383$	17.2456			0.881210			0.440605	+	0.897701i	$0.354764\pi$
$384$		0			0
$385$	−5.12430	+	0.0167839i	−0.261159	+	0.000855388i
$386$		−	14.4739i		−	0.736703i
$387$		0			0
$388$		−	1.41785i		−	0.0719802i
$389$		−	23.7904i		−	1.20622i	−0.797657	−	0.603112i	$-0.793927\pi$
$389$		−	23.7904i		−	1.20622i	0.797657	−	0.603112i	$-0.206073\pi$
$390$		0			0
$391$			33.0027i			1.66902i
$392$	0.0458545	+	6.99985i	0.00231600	+	0.353546i
$393$		0			0
$394$	−4.18955			−0.211066
$395$	11.6666			0.587010
$396$		0			0
$397$			3.13534i			0.157358i	0.996900	+	0.0786792i	$0.0250703\pi$
$397$			3.13534i			0.157358i	−0.996900	+	0.0786792i	$0.974930\pi$
$398$	−24.9132			−1.24878
$399$		0			0
$400$	1.00000			0.0500000
$401$		−	28.9308i		−	1.44473i	−0.691510	−	0.722367i	$-0.743054\pi$
$401$		−	28.9308i		−	1.44473i	0.691510	−	0.722367i	$-0.256946\pi$
$402$		0			0
$403$	15.3362			0.763952
$404$	2.74194			0.136417
$405$		0			0
$406$	0.0238987	+	7.29653i	0.00118607	+	0.362121i
$407$		−	11.1933i		−	0.554833i
$408$		0			0
$409$		−	2.39644i		−	0.118496i	−0.998243	−	0.0592481i	$-0.981130\pi$
$409$		−	2.39644i		−	0.118496i	0.998243	−	0.0592481i	$-0.0188703\pi$
$410$		−	6.67733i		−	0.329770i
$411$		0			0
$412$			11.1998i			0.551773i
$413$	0.101776	+	31.0731i	0.00500805	+	1.52901i
$414$		0			0
$415$	1.98267			0.0973254
$416$	−2.70838			−0.132789
$417$		0			0
$418$		−	3.84006i		−	0.187823i
$419$	0.733427			0.0358302			0.0179151	−	0.999840i	$-0.494297\pi$
$419$	0.733427			0.0358302			0.0179151	+	0.999840i	$0.494297\pi$
$420$		0			0
$421$	26.8631			1.30923			0.654614	−	0.755963i	$-0.272831\pi$
$421$	26.8631			1.30923			0.654614	+	0.755963i	$0.272831\pi$
$422$		−	26.5757i		−	1.29368i
$423$		0			0
$424$	10.7082			0.520037
$425$	−7.22829			−0.350623
$426$		0			0
$427$	−23.4769	+	0.0768952i	−1.13613	+	0.00372122i
$428$		−	10.7309i		−	0.518696i
$429$		0			0
$430$		−	7.37090i		−	0.355456i
$431$			5.49569i			0.264718i	0.991202	+	0.132359i	$0.0422552\pi$
$431$			5.49569i			0.264718i	−0.991202	+	0.132359i	$0.957745\pi$
$432$		0			0
$433$		−	22.0046i		−	1.05747i	−0.848786	−	0.528736i	$-0.822666\pi$
$433$		−	22.0046i		−	1.05747i	0.848786	−	0.528736i	$-0.177334\pi$
$434$	−0.0490699	−	14.9815i	−0.00235543	−	0.719137i
$435$		0			0
$436$	−1.84006			−0.0881229
$437$	−9.05240			−0.433035
$438$		0			0
$439$		−	9.41645i		−	0.449423i	−0.974425	−	0.224711i	$-0.927856\pi$
$439$		−	9.41645i		−	0.449423i	0.974425	−	0.224711i	$-0.0721439\pi$
$440$	−1.93681			−0.0923340
$441$		0			0
$442$	19.5769			0.931179
$443$			5.82695i			0.276847i	0.990373	+	0.138423i	$0.0442034\pi$
$443$			5.82695i			0.276847i	−0.990373	+	0.138423i	$0.955797\pi$
$444$		0			0
$445$	1.54312			0.0731511
$446$	−5.90829			−0.279766
$447$		0			0
$448$	0.00866574	+	2.64574i	0.000409418	+	0.124999i
$449$			20.2077i			0.953659i	0.878996	+	0.476830i	$0.158214\pi$
$449$			20.2077i			0.953659i	−0.878996	+	0.476830i	$0.841786\pi$
$450$		0			0
$451$			12.9327i			0.608979i
$452$			12.6838i			0.596595i
$453$		0			0
$454$			16.7418i			0.785731i
$455$	7.16565	−	0.0234701i	0.335931	−	0.00110029i
$456$		0			0
$457$	10.5338			0.492751			0.246376	−	0.969174i	$-0.420760\pi$
$457$	10.5338			0.492751			0.246376	+	0.969174i	$0.420760\pi$
$458$	−1.83897			−0.0859292
$459$		0			0
$460$			4.56577i			0.212880i
$461$	14.3945			0.670418			0.335209	−	0.942144i	$-0.391193\pi$
$461$	14.3945			0.670418			0.335209	+	0.942144i	$0.391193\pi$
$462$		0			0
$463$	−7.13173			−0.331440			−0.165720	−	0.986173i	$-0.552995\pi$
$463$	−7.13173			−0.331440			−0.165720	+	0.986173i	$0.552995\pi$
$464$			2.75784i			0.128030i
$465$		0			0
$466$	−1.17822			−0.0545798
$467$	−36.8760			−1.70642			−0.853209	−	0.521569i	$-0.825347\pi$
$467$	−36.8760			−1.70642			−0.853209	+	0.521569i	$0.825347\pi$
$468$		0			0
$469$	0.121318	+	37.0395i	0.00560193	+	1.71033i
$470$		−	2.22844i		−	0.102790i
$471$		0			0
$472$			11.7446i			0.540588i
$473$			14.2761i			0.656414i
$474$		0			0
$475$		−	1.98267i		−	0.0909711i
$476$	−0.0626385	−	19.1242i	−0.00287103	−	0.876554i
$477$		0			0
$478$	2.75676			0.126091
$479$	−6.23127			−0.284714			−0.142357	−	0.989815i	$-0.545468\pi$
$479$	−6.23127			−0.284714			−0.142357	+	0.989815i	$0.545468\pi$
$480$		0			0
$481$			15.6524i			0.713687i
$482$	−3.79421			−0.172821
$483$		0			0
$484$	−7.24875			−0.329489
$485$			1.41785i			0.0643811i
$486$		0			0
$487$	−21.9179			−0.993195			−0.496597	−	0.867981i	$-0.665417\pi$
$487$	−21.9179			−0.993195			−0.496597	+	0.867981i	$0.665417\pi$
$488$	−8.87348			−0.401683
$489$		0			0
$490$	−0.0458545	−	6.99985i	−0.00207150	−	0.316221i
$491$		−	9.81628i		−	0.443003i	−0.975160	−	0.221501i	$-0.928904\pi$
$491$		−	9.81628i		−	0.443003i	0.975160	−	0.221501i	$-0.0710957\pi$
$492$		0			0
$493$		−	19.9345i		−	0.897804i
$494$			5.36981i			0.241599i
$495$		0			0
$496$		−	5.66252i		−	0.254255i
$497$	−30.8305	+	0.100981i	−1.38293	+	0.00452961i
$498$		0			0
$499$	11.1925			0.501045			0.250523	−	0.968111i	$-0.419398\pi$
$499$	11.1925			0.501045			0.250523	+	0.968111i	$0.419398\pi$
$500$	−1.00000			−0.0447214
$501$		0			0
$502$			16.1061i			0.718852i
$503$	−0.898995			−0.0400842			−0.0200421	−	0.999799i	$-0.506380\pi$
$503$	−0.898995			−0.0400842			−0.0200421	+	0.999799i	$0.506380\pi$
$504$		0			0
$505$	−2.74194			−0.122015
$506$		−	8.84304i		−	0.393121i
$507$		0			0
$508$	−13.9352			−0.618276
$509$	−1.81138			−0.0802879			−0.0401439	−	0.999194i	$-0.512782\pi$
$509$	−1.81138			−0.0802879			−0.0401439	+	0.999194i	$0.512782\pi$
$510$		0			0
$511$	−39.4471	+	0.129203i	−1.74504	+	0.00571562i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$			9.70415i			0.428032i
$515$		−	11.1998i		−	0.493521i
$516$		0			0
$517$			4.31607i			0.189821i
$518$	15.2904	−	0.0500815i	0.671821	−	0.00220045i
$519$		0			0
$520$	2.70838			0.118770
$521$	−15.9088			−0.696977			−0.348488	−	0.937313i	$-0.613305\pi$
$521$	−15.9088			−0.696977			−0.348488	+	0.937313i	$0.613305\pi$
$522$		0			0
$523$		−	3.79096i		−	0.165767i	−0.996559	−	0.0828836i	$-0.973587\pi$
$523$		−	3.79096i		−	0.165767i	0.996559	−	0.0828836i	$-0.0264130\pi$
$524$	−4.36156			−0.190535
$525$		0			0
$526$	8.65227			0.377257
$527$			40.9303i			1.78295i
$528$		0			0
$529$	2.15377			0.0936422
$530$	−10.7082			−0.465136
$531$		0			0
$532$	5.24562	−	0.0171813i	0.227426	−	0.000744903i
$533$		−	18.0847i		−	0.783336i
$534$		0			0
$535$			10.7309i			0.463936i
$536$			13.9997i			0.604695i
$537$		0			0
$538$			1.66459i			0.0717656i
$539$	0.0888117	+	13.5574i	0.00382539	+	0.583959i
$540$		0			0
$541$	16.8827			0.725846			0.362923	−	0.931819i	$-0.381779\pi$
$541$	16.8827			0.725846			0.362923	+	0.931819i	$0.381779\pi$
$542$	15.5359			0.667322
$543$		0			0
$544$		−	7.22829i		−	0.309910i
$545$	1.84006			0.0788195
$546$		0			0
$547$	−29.8082			−1.27451			−0.637253	−	0.770655i	$-0.719929\pi$
$547$	−29.8082			−1.27451			−0.637253	+	0.770655i	$0.719929\pi$
$548$		−	6.89081i		−	0.294361i
$549$		0			0
$550$	1.93681			0.0825860
$551$	5.46789			0.232940
$552$		0			0
$553$	−0.101100	−	30.8668i	−0.00429920	−	1.31259i
$554$			2.80103i			0.119004i
$555$		0			0
$556$			12.0344i			0.510371i
$557$			28.6123i			1.21234i	0.795335	+	0.606170i	$0.207295\pi$
$557$			28.6123i			1.21234i	−0.795335	+	0.606170i	$0.792705\pi$
$558$		0			0
$559$		−	19.9632i		−	0.844352i
$560$	−0.00866574	−	2.64574i	−0.000366194	−	0.111803i
$561$		0			0
$562$	25.3801			1.07060
$563$	32.8609			1.38492			0.692460	−	0.721456i	$-0.256527\pi$
$563$	32.8609			1.38492			0.692460	+	0.721456i	$0.256527\pi$
$564$		0			0
$565$		−	12.6838i		−	0.533611i
$566$	−29.6822			−1.24764
$567$		0			0
$568$	−11.6529			−0.488944
$569$		−	9.88780i		−	0.414518i	−0.978286	−	0.207259i	$-0.933546\pi$
$569$		−	9.88780i		−	0.414518i	0.978286	−	0.207259i	$-0.0664543\pi$
$570$		0			0
$571$	−13.4455			−0.562678			−0.281339	−	0.959608i	$-0.590778\pi$
$571$	−13.4455			−0.562678			−0.281339	+	0.959608i	$0.590778\pi$
$572$	−5.24562			−0.219330
$573$		0			0
$574$	−17.6664	+	0.0578640i	−0.737383	+	0.00241519i
$575$		−	4.56577i		−	0.190406i
$576$		0			0
$577$			16.8384i			0.700990i	0.936565	+	0.350495i	$0.113987\pi$
$577$			16.8384i			0.700990i	−0.936565	+	0.350495i	$0.886013\pi$
$578$			35.2482i			1.46613i
$579$		0			0
$580$		−	2.75784i		−	0.114513i
$581$	−0.0171813	−	5.24562i	−0.000712800	−	0.217625i
$582$		0			0
$583$	20.7398			0.858956
$584$	−14.9097			−0.616967
$585$		0			0
$586$		−	17.1968i		−	0.710391i
$587$	40.9995			1.69223			0.846115	−	0.533000i	$-0.178935\pi$
$587$	40.9995			1.69223			0.846115	+	0.533000i	$0.178935\pi$
$588$		0			0
$589$	−11.2269			−0.462596
$590$		−	11.7446i		−	0.483517i
$591$		0			0
$592$	5.77925			0.237526
$593$	17.8661			0.733672			0.366836	−	0.930286i	$-0.380441\pi$
$593$	17.8661			0.733672			0.366836	+	0.930286i	$0.380441\pi$
$594$		0			0
$595$	0.0626385	+	19.1242i	0.00256793	+	0.784014i
$596$		−	9.33623i		−	0.382427i
$597$		0			0
$598$			12.3658i			0.505676i
$599$		−	2.52134i		−	0.103019i	−0.998672	−	0.0515097i	$-0.983597\pi$
$599$		−	2.52134i		−	0.103019i	0.998672	−	0.0515097i	$-0.0164033\pi$
$600$		0			0
$601$			40.5442i			1.65383i	0.562327	+	0.826915i	$0.309906\pi$
$601$			40.5442i			1.65383i	−0.562327	+	0.826915i	$0.690094\pi$
$602$	−19.5015	+	0.0638743i	−0.794820	+	0.00260332i
$603$		0			0
$604$	−17.0559			−0.693995
$605$	7.24875			0.294704
$606$		0			0
$607$			5.84372i			0.237189i	0.992943	+	0.118595i	$0.0378389\pi$
$607$			5.84372i			0.237189i	−0.992943	+	0.118595i	$0.962161\pi$
$608$	1.98267			0.0804078
$609$		0			0
$610$	8.87348			0.359277
$611$		−	6.03545i		−	0.244168i
$612$		0			0
$613$	36.9464			1.49225			0.746126	−	0.665805i	$-0.231912\pi$
$613$	36.9464			1.49225			0.746126	+	0.665805i	$0.231912\pi$
$614$	−3.64191			−0.146975
$615$		0			0
$616$	0.0167839	+	5.12430i	0.000676244	+	0.206464i
$617$		−	25.5176i		−	1.02730i	−0.858000	−	0.513650i	$-0.828293\pi$
$617$		−	25.5176i		−	1.02730i	0.858000	−	0.513650i	$-0.171707\pi$
$618$		0			0
$619$			2.25871i			0.0907851i	0.998969	+	0.0453926i	$0.0144539\pi$
$619$			2.25871i			0.0907851i	−0.998969	+	0.0453926i	$0.985546\pi$
$620$			5.66252i			0.227412i
$621$		0			0
$622$		−	20.1943i		−	0.809718i
$623$	−0.0133723	−	4.08270i	−0.000535750	−	0.163570i
$624$		0			0
$625$	1.00000			0.0400000
$626$	−27.9080			−1.11543
$627$		0			0
$628$			9.90924i			0.395422i
$629$	−41.7741			−1.66564
$630$		0			0
$631$	−5.74003			−0.228507			−0.114254	−	0.993452i	$-0.536448\pi$
$631$	−5.74003			−0.228507			−0.114254	+	0.993452i	$0.536448\pi$
$632$		−	11.6666i		−	0.464072i
$633$		0			0
$634$	−25.7816			−1.02392
$635$	13.9352			0.553003
$636$		0			0
$637$	−0.124191	−	18.9582i	−0.00492064	−	0.751152i
$638$			5.34143i			0.211469i
$639$		0			0
$640$		−	1.00000i		−	0.0395285i
$641$		−	38.6182i		−	1.52533i	−0.646795	−	0.762664i	$-0.723891\pi$
$641$		−	38.6182i		−	1.52533i	0.646795	−	0.762664i	$-0.276109\pi$
$642$		0			0
$643$			19.4595i			0.767409i	0.923456	+	0.383704i	$0.125352\pi$
$643$			19.4595i			0.767409i	−0.923456	+	0.383704i	$0.874648\pi$
$644$	12.0798	−	0.0395657i	0.476012	−	0.00155911i
$645$		0			0
$646$	−14.3313			−0.563857
$647$	46.7723			1.83881			0.919404	−	0.393314i	$-0.128671\pi$
$647$	46.7723			1.83881			0.919404	+	0.393314i	$0.128671\pi$
$648$		0			0
$649$			22.7471i			0.892901i
$650$	−2.70838			−0.106231
$651$		0			0
$652$	−8.47282			−0.331821
$653$			5.40173i			0.211386i	0.994399	+	0.105693i	$0.0337061\pi$
$653$			5.40173i			0.211386i	−0.994399	+	0.105693i	$0.966294\pi$
$654$		0			0
$655$	4.36156			0.170420
$656$	−6.67733			−0.260706
$657$		0			0
$658$	−5.89586	+	0.0193111i	−0.229845	+	0.000752824i
$659$		−	11.8006i		−	0.459686i	−0.973228	−	0.229843i	$-0.926179\pi$
$659$		−	11.8006i		−	0.459686i	0.973228	−	0.229843i	$-0.0738213\pi$
$660$		0			0
$661$		−	36.3800i		−	1.41502i	−0.706705	−	0.707509i	$-0.749819\pi$
$661$		−	36.3800i		−	1.41502i	0.706705	−	0.707509i	$-0.250181\pi$
$662$			24.1188i			0.937404i
$663$		0			0
$664$		−	1.98267i		−	0.0769425i
$665$	−5.24562	+	0.0171813i	−0.203416	+	0.000666262i
$666$		0			0
$667$	12.5917			0.487551
$668$	−3.01718			−0.116738
$669$		0			0
$670$		−	13.9997i		−	0.540856i
$671$	−17.1863			−0.663469
$672$		0			0
$673$	−35.1190			−1.35374			−0.676868	−	0.736104i	$-0.736663\pi$
$673$	−35.1190			−1.35374			−0.676868	+	0.736104i	$0.736663\pi$
$674$		−	27.5238i		−	1.06018i
$675$		0			0
$676$	−5.66470			−0.217873
$677$	−11.5742			−0.444833			−0.222417	−	0.974952i	$-0.571395\pi$
$677$	−11.5742			−0.444833			−0.222417	+	0.974952i	$0.571395\pi$
$678$		0			0
$679$	3.75125	−	0.0122867i	0.143960	−	0.000471520i
$680$			7.22829i			0.277192i
$681$		0			0
$682$		−	10.9673i		−	0.419958i
$683$		−	48.9808i		−	1.87420i	−0.349062	−	0.937100i	$-0.613500\pi$
$683$		−	48.9808i		−	1.87420i	0.349062	−	0.937100i	$-0.386500\pi$
$684$		0			0
$685$			6.89081i			0.263284i
$686$	−18.5194	+	0.181978i	−0.707073	+	0.00694795i
$687$		0			0
$688$	−7.37090			−0.281013
$689$	−29.0019			−1.10488
$690$		0			0
$691$			12.5401i			0.477049i	0.971136	+	0.238525i	$0.0766637\pi$
$691$			12.5401i			0.477049i	−0.971136	+	0.238525i	$0.923336\pi$
$692$	23.4738			0.892338
$693$		0			0
$694$	−26.6045			−1.00989
$695$		−	12.0344i		−	0.456489i
$696$		0			0
$697$	48.2656			1.82819
$698$	−3.16431			−0.119771
$699$		0			0
$700$	0.00866574	+	2.64574i	0.000327534	+	0.0999995i
$701$			1.27366i			0.0481053i	0.999711	+	0.0240527i	$0.00765694\pi$
$701$			1.27366i			0.0481053i	−0.999711	+	0.0240527i	$0.992343\pi$
$702$		0			0
$703$		−	11.4583i		−	0.432159i
$704$			1.93681i			0.0729964i
$705$		0			0
$706$		−	24.9081i		−	0.937429i
$707$	0.0237610	+	7.25446i	0.000893623	+	0.272832i
$708$		0			0
$709$	21.0427			0.790275			0.395137	−	0.918622i	$-0.370697\pi$
$709$	21.0427			0.790275			0.395137	+	0.918622i	$0.370697\pi$
$710$	11.6529			0.437325
$711$		0			0
$712$		−	1.54312i		−	0.0578310i
$713$	−25.8538			−0.968231
$714$		0			0
$715$	5.24562			0.196175
$716$		−	0.491540i		−	0.0183697i
$717$		0			0
$718$	4.01733			0.149925
$719$	48.6565			1.81458			0.907291	−	0.420502i	$-0.138146\pi$
$719$	48.6565			1.81458			0.907291	+	0.420502i	$0.138146\pi$
$720$		0			0
$721$	−29.6316	+	0.0970542i	−1.10354	+	0.00361449i
$722$			15.0690i			0.560811i
$723$		0			0
$724$			8.00696i			0.297576i
$725$			2.75784i			0.102424i
$726$		0			0
$727$		−	14.5676i		−	0.540283i	−0.962821	−	0.270142i	$-0.912929\pi$
$727$		−	14.5676i		−	0.540283i	0.962821	−	0.270142i	$-0.0870705\pi$
$728$	−0.0234701	−	7.16565i	−0.000869859	−	0.265577i
$729$		0			0
$730$	14.9097			0.551832
$731$	53.2790			1.97059
$732$		0			0
$733$			2.42727i			0.0896532i	0.998995	+	0.0448266i	$0.0142735\pi$
$733$			2.42727i			0.0896532i	−0.998995	+	0.0448266i	$0.985726\pi$
$734$	−5.23333			−0.193166
$735$		0			0
$736$	4.56577			0.168296
$737$			27.1148i			0.998787i
$738$		0			0
$739$	43.4758			1.59928			0.799641	−	0.600479i	$-0.205023\pi$
$739$	43.4758			1.59928			0.799641	+	0.600479i	$0.205023\pi$
$740$	−5.77925			−0.212449
$741$		0			0
$742$	0.0927947	+	28.3311i	0.00340660	+	1.04007i
$743$			53.9749i			1.98015i	0.140549	+	0.990074i	$0.455113\pi$
$743$			53.9749i			1.98015i	−0.140549	+	0.990074i	$0.544887\pi$
$744$		0			0
$745$			9.33623i			0.342053i
$746$		−	3.51440i		−	0.128671i
$747$		0			0
$748$		−	13.9998i		−	0.511885i
$749$	28.3911	−	0.0929909i	1.03739	−	0.00339781i
$750$		0			0
$751$	3.59727			0.131266			0.0656332	−	0.997844i	$-0.479093\pi$
$751$	3.59727			0.131266			0.0656332	+	0.997844i	$0.479093\pi$
$752$	−2.22844			−0.0812628
$753$		0			0
$754$		−	7.46927i		−	0.272015i
$755$	17.0559			0.620728
$756$		0			0
$757$	−53.1823			−1.93294			−0.966471	−	0.256776i	$-0.917340\pi$
$757$	−53.1823			−1.93294			−0.966471	+	0.256776i	$0.917340\pi$
$758$		−	11.9938i		−	0.435636i
$759$		0			0
$760$	−1.98267			−0.0719189
$761$	1.32298			0.0479578			0.0239789	−	0.999712i	$-0.492367\pi$
$761$	1.32298			0.0479578			0.0239789	+	0.999712i	$0.492367\pi$
$762$		0			0
$763$	−0.0159455	−	4.86832i	−0.000577265	−	0.176245i
$764$			19.7296i			0.713793i
$765$		0			0
$766$			17.2456i			0.623110i
$767$		−	31.8088i		−	1.14855i
$768$		0			0
$769$		−	7.85382i		−	0.283216i	−0.989923	−	0.141608i	$-0.954773\pi$
$769$		−	7.85382i		−	0.283216i	0.989923	−	0.141608i	$-0.0452272\pi$
$770$	−0.0167839	−	5.12430i	−0.000604851	−	0.184667i
$771$		0			0
$772$	14.4739			0.520927
$773$	44.9476			1.61665			0.808326	−	0.588736i	$-0.200374\pi$
$773$	44.9476			1.61665			0.808326	+	0.588736i	$0.200374\pi$
$774$		0			0
$775$		−	5.66252i		−	0.203404i
$776$	1.41785			0.0508977
$777$		0			0
$778$	23.7904			0.852929
$779$			13.2389i			0.474334i
$780$		0			0
$781$	−22.5695			−0.807599
$782$	−33.0027			−1.18017
$783$		0			0
$784$	−6.99985	+	0.0458545i	−0.249995	+	0.00163766i
$785$		−	9.90924i		−	0.353676i
$786$		0			0
$787$		−	35.1718i		−	1.25374i	−0.779124	−	0.626870i	$-0.784336\pi$
$787$		−	35.1718i		−	1.25374i	0.779124	−	0.626870i	$-0.215664\pi$
$788$		−	4.18955i		−	0.149246i
$789$		0			0
$790$			11.6666i			0.415079i
$791$	−33.5579	+	0.109914i	−1.19318	+	0.00390810i
$792$		0			0
$793$	24.0327			0.853427
$794$	−3.13534			−0.111269
$795$		0			0
$796$		−	24.9132i		−	0.883024i
$797$	−10.6990			−0.378976			−0.189488	−	0.981883i	$-0.560683\pi$
$797$	−10.6990			−0.378976			−0.189488	+	0.981883i	$0.560683\pi$
$798$		0			0
$799$	16.1078			0.569853
$800$			1.00000i			0.0353553i
$801$		0			0
$802$	28.9308			1.02158
$803$	−28.8773			−1.01906
$804$		0			0
$805$	−12.0798	+	0.0395657i	−0.425758	+	0.00139451i
$806$			15.3362i			0.540196i
$807$		0			0
$808$			2.74194i			0.0964612i
$809$			50.6693i			1.78144i	0.454555	+	0.890719i	$0.349798\pi$
$809$			50.6693i			1.78144i	−0.454555	+	0.890719i	$0.650202\pi$
$810$		0			0
$811$		−	32.3154i		−	1.13475i	−0.823461	−	0.567373i	$-0.807960\pi$
$811$		−	32.3154i		−	1.13475i	0.823461	−	0.567373i	$-0.192040\pi$
$812$	−7.29653	+	0.0238987i	−0.256058	+	0.000838681i
$813$		0			0
$814$	11.1933			0.392326
$815$	8.47282			0.296790
$816$		0			0
$817$			14.6140i			0.511281i
$818$	2.39644			0.0837895
$819$		0			0
$820$	6.67733			0.233182
$821$			46.2704i			1.61485i	0.589972	+	0.807424i	$0.299139\pi$
$821$			46.2704i			1.61485i	−0.589972	+	0.807424i	$0.700861\pi$
$822$		0			0
$823$	55.3629			1.92983			0.964915	−	0.262562i	$-0.0845676\pi$
$823$	55.3629			1.92983			0.964915	+	0.262562i	$0.0845676\pi$
$824$	−11.1998			−0.390162
$825$		0			0
$826$	−31.0731	+	0.101776i	−1.08117	+	0.00354122i
$827$			23.9044i			0.831238i	0.909539	+	0.415619i	$0.136435\pi$
$827$			23.9044i			0.831238i	−0.909539	+	0.415619i	$0.863565\pi$
$828$		0			0
$829$			23.1662i			0.804595i	0.915509	+	0.402298i	$0.131788\pi$
$829$			23.1662i			0.804595i	−0.915509	+	0.402298i	$0.868212\pi$
$830$			1.98267i			0.0688194i
$831$		0			0
$832$		−	2.70838i		−	0.0938960i
$833$	50.5969	−	0.331450i	1.75308	−	0.0114841i
$834$		0			0
$835$	3.01718			0.104414
$836$	3.84006			0.132811
$837$		0			0
$838$			0.733427i			0.0253358i
$839$	34.8072			1.20168			0.600838	−	0.799371i	$-0.294834\pi$
$839$	34.8072			1.20168			0.600838	+	0.799371i	$0.294834\pi$
$840$		0			0
$841$	21.3943			0.737735
$842$			26.8631i			0.925764i
$843$		0			0
$844$	26.5757			0.914773
$845$	5.66470			0.194872
$846$		0			0
$847$	−0.0628158	−	19.1783i	−0.00215838	−	0.658974i
$848$			10.7082i			0.367722i
$849$		0			0
$850$		−	7.22829i		−	0.247928i
$851$		−	26.3867i		−	0.904525i
$852$		0			0
$853$			18.5543i			0.635287i	0.948210	+	0.317643i	$0.102891\pi$
$853$			18.5543i			0.635287i	−0.948210	+	0.317643i	$0.897109\pi$
$854$	−0.0768952	−	23.4769i	−0.00263130	−	0.803363i
$855$		0			0
$856$	10.7309			0.366774
$857$	48.6598			1.66219			0.831094	−	0.556132i	$-0.187715\pi$
$857$	48.6598			1.66219			0.831094	+	0.556132i	$0.187715\pi$
$858$		0			0
$859$		−	27.8112i		−	0.948907i	−0.880281	−	0.474453i	$-0.842646\pi$
$859$		−	27.8112i		−	0.948907i	0.880281	−	0.474453i	$-0.157354\pi$
$860$	7.37090			0.251345
$861$		0			0
$862$	−5.49569			−0.187184
$863$			11.1490i			0.379517i	0.981831	+	0.189758i	$0.0607705\pi$
$863$			11.1490i			0.379517i	−0.981831	+	0.189758i	$0.939230\pi$
$864$		0			0
$865$	−23.4738			−0.798132
$866$	22.0046			0.747745
$867$		0			0
$868$	14.9815	−	0.0490699i	0.508507	−	0.00166554i
$869$		−	22.5960i		−	0.766518i
$870$		0			0
$871$		−	37.9164i		−	1.28475i
$872$		−	1.84006i		−	0.0623123i
$873$		0			0
$874$		−	9.05240i		−	0.306202i
$875$	−0.00866574	−	2.64574i	−0.000292955	−	0.0894422i
$876$		0			0
$877$	−23.1602			−0.782066			−0.391033	−	0.920377i	$-0.627882\pi$
$877$	−23.1602			−0.782066			−0.391033	+	0.920377i	$0.627882\pi$
$878$	9.41645			0.317790
$879$		0			0
$880$		−	1.93681i		−	0.0652900i
$881$	26.0063			0.876173			0.438087	−	0.898933i	$-0.355656\pi$
$881$	26.0063			0.876173			0.438087	+	0.898933i	$0.355656\pi$
$882$		0			0
$883$	19.8272			0.667239			0.333619	−	0.942708i	$-0.391730\pi$
$883$	19.8272			0.667239			0.333619	+	0.942708i	$0.391730\pi$
$884$			19.5769i			0.658443i
$885$		0			0
$886$	−5.82695			−0.195760
$887$	−6.12220			−0.205563			−0.102782	−	0.994704i	$-0.532774\pi$
$887$	−6.12220			−0.205563			−0.102782	+	0.994704i	$0.532774\pi$
$888$		0			0
$889$	−0.120759	−	36.8690i	−0.00405013	−	1.23655i
$890$			1.54312i			0.0517256i
$891$		0			0
$892$		−	5.90829i		−	0.197824i
$893$			4.41825i			0.147851i
$894$		0			0
$895$			0.491540i			0.0164304i
$896$	−2.64574	+	0.00866574i	−0.0883879	+	0.000289502i
$897$		0			0
$898$	−20.2077			−0.674339
$899$	15.6163			0.520834
$900$		0			0
$901$		−	77.4021i		−	2.57864i
$902$	−12.9327			−0.430613
$903$		0			0
$904$	−12.6838			−0.421856
$905$		−	8.00696i		−	0.266161i
$906$		0			0
$907$	−46.3115			−1.53775			−0.768874	−	0.639401i	$-0.779182\pi$
$907$	−46.3115			−1.53775			−0.768874	+	0.639401i	$0.779182\pi$
$908$	−16.7418			−0.555596
$909$		0			0
$910$	0.0234701	+	7.16565i	0.000778025	+	0.237539i
$911$		−	21.7585i		−	0.720892i	−0.932780	−	0.360446i	$-0.882625\pi$
$911$		−	21.7585i		−	0.720892i	0.932780	−	0.360446i	$-0.117375\pi$
$912$		0			0
$913$		−	3.84006i		−	0.127087i
$914$			10.5338i			0.348428i
$915$		0			0
$916$		−	1.83897i		−	0.0607611i
$917$	−0.0377961	−	11.5395i	−0.00124814	−	0.381069i
$918$		0			0
$919$	−30.3672			−1.00172			−0.500860	−	0.865528i	$-0.666983\pi$
$919$	−30.3672			−1.00172			−0.500860	+	0.865528i	$0.666983\pi$
$920$	−4.56577			−0.150529
$921$		0			0
$922$			14.3945i			0.474057i
$923$	31.5604			1.03882
$924$		0			0
$925$	5.77925			0.190021
$926$		−	7.13173i		−	0.234363i
$927$		0			0
$928$	−2.75784			−0.0905306
$929$	−5.70553			−0.187193			−0.0935963	−	0.995610i	$-0.529836\pi$
$929$	−5.70553			−0.187193			−0.0935963	+	0.995610i	$0.529836\pi$
$930$		0			0
$931$	0.0909143	+	13.8784i	0.00297960	+	0.454846i
$932$		−	1.17822i		−	0.0385938i
$933$		0			0
$934$		−	36.8760i		−	1.20662i
$935$			13.9998i			0.457844i
$936$		0			0
$937$		−	56.1676i		−	1.83492i	−0.397833	−	0.917458i	$-0.630238\pi$
$937$		−	56.1676i		−	1.83492i	0.397833	−	0.917458i	$-0.369762\pi$
$938$	−37.0395	+	0.121318i	−1.20938	+	0.00396116i
$939$		0			0
$940$	2.22844			0.0726836
$941$	−52.7466			−1.71949			−0.859746	−	0.510723i	$-0.829378\pi$
$941$	−52.7466			−1.71949			−0.859746	+	0.510723i	$0.829378\pi$
$942$		0			0
$943$			30.4871i			0.992797i
$944$	−11.7446			−0.382254
$945$		0			0
$946$	−14.2761			−0.464155
$947$		−	36.4124i		−	1.18324i	−0.806216	−	0.591621i	$-0.798488\pi$
$947$		−	36.4124i		−	1.18324i	0.806216	−	0.591621i	$-0.201512\pi$
$948$		0			0
$949$	40.3810			1.31082
$950$	1.98267			0.0643263
$951$		0			0
$952$	19.1242	−	0.0626385i	0.619817	−	0.00203012i
$953$		−	36.6368i		−	1.18678i	−0.804914	−	0.593391i	$-0.797789\pi$
$953$		−	36.6368i		−	1.18678i	0.804914	−	0.593391i	$-0.202211\pi$
$954$		0			0
$955$		−	19.7296i		−	0.638436i
$956$			2.75676i			0.0891599i
$957$		0			0
$958$		−	6.23127i		−	0.201323i
$959$	18.2313	−	0.0597139i	0.588718	−	0.00192826i
$960$		0			0
$961$	−1.06414			−0.0343272
$962$	−15.6524			−0.504653
$963$		0			0
$964$		−	3.79421i		−	0.122203i
$965$	−14.4739			−0.465932
$966$		0			0
$967$	−45.8410			−1.47415			−0.737074	−	0.675812i	$-0.763793\pi$
$967$	−45.8410			−1.47415			−0.737074	+	0.675812i	$0.763793\pi$
$968$		−	7.24875i		−	0.232984i
$969$		0			0
$970$	−1.41785			−0.0455243
$971$	30.8802			0.990993			0.495497	−	0.868610i	$-0.334986\pi$
$971$	30.8802			0.990993			0.495497	+	0.868610i	$0.334986\pi$
$972$		0			0
$973$	−31.8398	+	0.104287i	−1.02074	+	0.00334328i
$974$		−	21.9179i		−	0.702295i
$975$		0			0
$976$		−	8.87348i		−	0.284033i
$977$		−	50.1594i		−	1.60474i	−0.596825	−	0.802371i	$-0.703572\pi$
$977$		−	50.1594i		−	1.60474i	0.596825	−	0.802371i	$-0.296428\pi$
$978$		0			0
$979$		−	2.98874i		−	0.0955206i
$980$	6.99985	−	0.0458545i	0.223602	−	0.00146477i
$981$		0			0
$982$	9.81628			0.313250
$983$	−36.3659			−1.15989			−0.579946	−	0.814655i	$-0.696927\pi$
$983$	−36.3659			−1.15989			−0.579946	+	0.814655i	$0.696927\pi$
$984$		0			0
$985$			4.18955i			0.133490i
$986$	19.9345			0.634843
$987$		0			0
$988$	−5.36981			−0.170836
$989$			33.6538i			1.07013i
$990$		0			0
$991$	−38.4103			−1.22014			−0.610071	−	0.792347i	$-0.708859\pi$
$991$	−38.4103			−1.22014			−0.610071	+	0.792347i	$0.708859\pi$
$992$	5.66252			0.179785
$993$		0			0
$994$	−0.100981	−	30.8305i	−0.00320292	−	0.977883i
$995$			24.9132i			0.789800i
$996$		0			0
$997$			7.08214i			0.224294i	0.993692	+	0.112147i	$0.0357727\pi$
$997$			7.08214i			0.224294i	−0.993692	+	0.112147i	$0.964227\pi$
$998$			11.1925i			0.354292i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.b.d.1511.10	yes	12
3.2	odd	2		1890.2.b.c.1511.4	✓	12
7.6	odd	2		1890.2.b.c.1511.10	yes	12
21.20	even	2	inner	1890.2.b.d.1511.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1890.2.b.c.1511.4	✓	12	3.2	odd	2
1890.2.b.c.1511.10	yes	12	7.6	odd	2
1890.2.b.d.1511.4	yes	12	21.20	even	2	inner
1890.2.b.d.1511.10	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +1.00000 q^{5} +(-0.00866574 - 2.64574i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +1.00000 q^{5} +(-0.00866574 - 2.64574i) q^{7} -1.00000i q^{8} +1.00000i q^{10} -1.93681i q^{11} +2.70838i q^{13} +(2.64574 - 0.00866574i) q^{14} +1.00000 q^{16} -7.22829 q^{17} -1.98267i q^{19} -1.00000 q^{20} +1.93681 q^{22} -4.56577i q^{23} +1.00000 q^{25} -2.70838 q^{26} +(0.00866574 + 2.64574i) q^{28} +2.75784i q^{29} -5.66252i q^{31} +1.00000i q^{32} -7.22829i q^{34} +(-0.00866574 - 2.64574i) q^{35} +5.77925 q^{37} +1.98267 q^{38} -1.00000i q^{40} -6.67733 q^{41} -7.37090 q^{43} +1.93681i q^{44} +4.56577 q^{46} -2.22844 q^{47} +(-6.99985 + 0.0458545i) q^{49} +1.00000i q^{50} -2.70838i q^{52} +10.7082i q^{53} -1.93681i q^{55} +(-2.64574 + 0.00866574i) q^{56} -2.75784 q^{58} -11.7446 q^{59} -8.87348i q^{61} +5.66252 q^{62} -1.00000 q^{64} +2.70838i q^{65} -13.9997 q^{67} +7.22829 q^{68} +(2.64574 - 0.00866574i) q^{70} -11.6529i q^{71} -14.9097i q^{73} +5.77925i q^{74} +1.98267i q^{76} +(-5.12430 + 0.0167839i) q^{77} +11.6666 q^{79} +1.00000 q^{80} -6.67733i q^{82} +1.98267 q^{83} -7.22829 q^{85} -7.37090i q^{86} -1.93681 q^{88} +1.54312 q^{89} +(7.16565 - 0.0234701i) q^{91} +4.56577i q^{92} -2.22844i q^{94} -1.98267i q^{95} +1.41785i q^{97} +(-0.0458545 - 6.99985i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) \) 12 * q - 12 * q^4 + 12 * q^5 - 4 * q^7	\( 12 q - 12 q^{4} + 12 q^{5} - 4 q^{7} + 12 q^{16} - 12 q^{20} + 12 q^{25} - 8 q^{26} + 4 q^{28} - 4 q^{35} - 32 q^{37} + 16 q^{38} - 8 q^{41} - 24 q^{43} + 8 q^{46} - 28 q^{47} + 4 q^{49} + 8 q^{58} - 24 q^{59} + 28 q^{62} - 12 q^{64} + 8 q^{67} + 28 q^{77} + 32 q^{79} + 12 q^{80} + 16 q^{83} + 16 q^{89} - 8 q^{91} - 16 q^{98}+O(q^{100}) \) 12 * q - 12 * q^4 + 12 * q^5 - 4 * q^7 + 12 * q^16 - 12 * q^20 + 12 * q^25 - 8 * q^26 + 4 * q^28 - 4 * q^35 - 32 * q^37 + 16 * q^38 - 8 * q^41 - 24 * q^43 + 8 * q^46 - 28 * q^47 + 4 * q^49 + 8 * q^58 - 24 * q^59 + 28 * q^62 - 12 * q^64 + 8 * q^67 + 28 * q^77 + 32 * q^79 + 12 * q^80 + 16 * q^83 + 16 * q^89 - 8 * q^91 - 16 * q^98

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